LMFDB - Embedded newform 980.2.s.f.619.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(19,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,12,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			619.15
Character	$\chi$	$=$	980.619
Dual form			980.2.s.f.19.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35625 - 0.400736i) q^{2} +(-1.84964 - 1.06789i) q^{3} +(1.67882 - 1.08700i) q^{4} +(-0.0159590 - 2.23601i) q^{5} +(-2.93651 - 0.707107i) q^{6} +(1.84130 - 2.14700i) q^{8} +(0.780776 + 1.35234i) q^{9} +(-0.917695 - 3.02619i) q^{10} +(2.01961 + 1.16602i) q^{11} +(-4.26600 + 0.217754i) q^{12} +1.09190 q^{13} +(-2.35829 + 4.15286i) q^{15} +(1.63688 - 3.64974i) q^{16} +(2.49037 - 4.31345i) q^{17} +(1.60086 + 1.52123i) q^{18} +(-1.28751 - 2.23003i) q^{19} +(-2.45733 - 3.73652i) q^{20} +(3.20636 + 0.772087i) q^{22} +(-3.02045 - 5.23157i) q^{23} +(-5.69850 + 2.00487i) q^{24} +(-4.99949 + 0.0713692i) q^{25} +(1.48088 - 0.437562i) q^{26} +3.07221i q^{27} +0.561553 q^{29} +(-1.53423 + 6.57736i) q^{30} +(-3.29801 + 5.71233i) q^{31} +(0.757434 - 5.60592i) q^{32} +(-2.49037 - 4.31345i) q^{33} +(1.64901 - 6.84809i) q^{34} +(2.78078 + 1.42164i) q^{36} +(-4.76284 + 2.74983i) q^{37} +(-2.63983 - 2.50852i) q^{38} +(-2.01961 - 1.16602i) q^{39} +(-4.83010 - 4.08290i) q^{40} +8.48528i q^{41} -1.32431 q^{43} +(4.65803 - 0.237764i) q^{44} +(3.01140 - 1.76741i) q^{45} +(-6.19296 - 5.88491i) q^{46} +(-8.43723 + 4.87123i) q^{47} +(-6.92516 + 5.00270i) q^{48} +(-6.75195 + 2.10027i) q^{50} +(-9.21257 + 5.31888i) q^{51} +(1.83310 - 1.18689i) q^{52} +(7.43743 + 4.29400i) q^{53} +(1.23114 + 4.16667i) q^{54} +(2.57501 - 4.53448i) q^{55} +5.49966i q^{57} +(0.761605 - 0.225034i) q^{58} +(7.16053 - 12.4024i) q^{59} +(0.554981 + 9.53536i) q^{60} +(0.536986 - 0.310029i) q^{61} +(-2.18379 + 9.06897i) q^{62} +(-1.21922 - 7.90655i) q^{64} +(-0.0174256 - 2.44149i) q^{65} +(-5.10611 - 4.85213i) q^{66} +(-2.35829 + 4.08469i) q^{67} +(-0.507812 - 9.94853i) q^{68} +12.9020i q^{69} -11.9473i q^{71} +(4.34113 + 0.813745i) q^{72} +(4.98074 - 8.62689i) q^{73} +(-5.35764 + 5.63809i) q^{74} +(9.32347 + 5.20690i) q^{75} +(-4.58552 - 2.34430i) q^{76} +(-3.20636 - 0.772087i) q^{78} +(9.21257 - 5.31888i) q^{79} +(-8.18699 - 3.60184i) q^{80} +(5.62311 - 9.73950i) q^{81} +(3.40036 + 11.5082i) q^{82} -3.86098i q^{83} +(-9.68466 - 5.49966i) q^{85} +(-1.79609 + 0.530698i) q^{86} +(-1.03867 - 0.599676i) q^{87} +(6.22217 - 2.18911i) q^{88} +(-2.44949 + 1.41421i) q^{89} +(3.37594 - 3.60382i) q^{90} +(-10.7575 - 5.49966i) q^{92} +(12.2003 - 7.04383i) q^{93} +(-9.49090 + 9.98771i) q^{94} +(-4.96581 + 2.91447i) q^{95} +(-7.38748 + 9.56006i) q^{96} +14.9422 q^{97} +3.64162i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 8 q^{9} + 12 q^{16} - 8 q^{25} - 48 q^{29} + 4 q^{30} + 56 q^{36} - 32 q^{44} + 32 q^{46} - 24 q^{50} - 44 q^{60} - 72 q^{64} + 32 q^{65} - 88 q^{74} + 48 q^{81} - 112 q^{85} - 40 q^{86}+O(q^{100}) $ 32 * q + 12 * q^4 - 8 * q^9 + 12 * q^16 - 8 * q^25 - 48 * q^29 + 4 * q^30 + 56 * q^36 - 32 * q^44 + 32 * q^46 - 24 * q^50 - 44 * q^60 - 72 * q^64 + 32 * q^65 - 88 * q^74 + 48 * q^81 - 112 * q^85 - 40 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.35625	−	0.400736i	0.959013	−	0.283363i
$2$	1.35625	−	0.400736i	0.959013	−	0.283363i
$3$	−1.84964	−	1.06789i	−1.06789	−	0.616546i	−0.140285	−	0.990111i	$-0.544802\pi$
$3$	−1.84964	−	1.06789i	−1.06789	−	0.616546i	−0.927604	+	0.373565i	$0.878135\pi$
$4$	1.67882	−	1.08700i	0.839411	−	0.543498i
$5$	−0.0159590	−	2.23601i	−0.00713710	−	0.999975i
$5$	−0.0159590	−	2.23601i	−0.00713710	−	0.999975i
$6$	−2.93651	−	0.707107i	−1.19883	−	0.288675i
$7$		0			0
$7$		0			0
$8$	1.84130	−	2.14700i	0.650998	−	0.759079i
$9$	0.780776	+	1.35234i	0.260259	+	0.450781i
$10$	−0.917695	−	3.02619i	−0.290201	−	0.956966i
$11$	2.01961	+	1.16602i	0.608936	+	0.351569i	0.772549	−	0.634955i	$-0.218981\pi$
$11$	2.01961	+	1.16602i	0.608936	+	0.351569i	−0.163613	+	0.986525i	$0.552315\pi$
$12$	−4.26600	+	0.217754i	−1.23149	+	0.0628601i
$13$	1.09190			0.302837			0.151419	−	0.988470i	$-0.451616\pi$
$13$	1.09190			0.302837			0.151419	+	0.988470i	$0.451616\pi$
$14$		0			0
$15$	−2.35829	+	4.15286i	−0.608909	+	1.07226i
$16$	1.63688	−	3.64974i	0.409220	−	0.912436i
$17$	2.49037	−	4.31345i	0.604003	−	1.04616i	−0.388205	−	0.921573i	$-0.626905\pi$
$17$	2.49037	−	4.31345i	0.604003	−	1.04616i	0.992208	−	0.124591i	$-0.0397620\pi$
$18$	1.60086	+	1.52123i	0.377326	+	0.358557i
$19$	−1.28751	−	2.23003i	−0.295374	−	0.511603i	0.679698	−	0.733492i	$-0.262111\pi$
$19$	−1.28751	−	2.23003i	−0.295374	−	0.511603i	−0.975072	+	0.221889i	$0.928778\pi$
$20$	−2.45733	−	3.73652i	−0.549475	−	0.835510i
$21$		0			0
$22$	3.20636	+	0.772087i	0.683599	+	0.164609i
$23$	−3.02045	−	5.23157i	−0.629807	−	1.09086i	−0.987590	−	0.157053i	$-0.949801\pi$
$23$	−3.02045	−	5.23157i	−0.629807	−	1.09086i	0.357783	−	0.933805i	$-0.383533\pi$
$24$	−5.69850	+	2.00487i	−1.16320	+	0.409242i
$25$	−4.99949	+	0.0713692i	−0.999898	+	0.0142738i
$26$	1.48088	−	0.437562i	0.290425	−	0.0858130i
$27$			3.07221i			0.591246i
$28$		0			0
$29$	0.561553			0.104278			0.0521389	−	0.998640i	$-0.483396\pi$
$29$	0.561553			0.104278			0.0521389	+	0.998640i	$0.483396\pi$
$30$	−1.53423	+	6.57736i	−0.280112	+	1.20086i
$31$	−3.29801	+	5.71233i	−0.592341	+	1.02596i	0.401576	+	0.915826i	$0.368463\pi$
$31$	−3.29801	+	5.71233i	−0.592341	+	1.02596i	−0.993916	+	0.110138i	$0.964871\pi$
$32$	0.757434	−	5.60592i	0.133897	−	0.990995i
$33$	−2.49037	−	4.31345i	−0.433518	−	0.750875i
$34$	1.64901	−	6.84809i	0.282802	−	1.17444i
$35$		0			0
$36$	2.78078	+	1.42164i	0.463463	+	0.236941i
$37$	−4.76284	+	2.74983i	−0.783006	+	0.452069i	−0.837495	−	0.546446i	$-0.815981\pi$
$37$	−4.76284	+	2.74983i	−0.783006	+	0.452069i	0.0544884	+	0.998514i	$0.482647\pi$
$38$	−2.63983	−	2.50852i	−0.428237	−	0.406935i
$39$	−2.01961	−	1.16602i	−0.323397	−	0.186713i
$40$	−4.83010	−	4.08290i	−0.763706	−	0.645564i
$41$			8.48528i			1.32518i	0.748983	+	0.662589i	$0.230542\pi$
$41$			8.48528i			1.32518i	−0.748983	+	0.662589i	$0.769458\pi$
$42$		0			0
$43$	−1.32431			−0.201955			−0.100977	−	0.994889i	$-0.532197\pi$
$43$	−1.32431			−0.201955			−0.100977	+	0.994889i	$0.532197\pi$
$44$	4.65803	−	0.237764i	0.702225	−	0.0358443i
$45$	3.01140	−	1.76741i	0.448912	−	0.263469i
$46$	−6.19296	−	5.88491i	−0.913102	−	0.867682i
$47$	−8.43723	+	4.87123i	−1.23070	+	0.710543i	−0.967175	−	0.254111i	$-0.918217\pi$
$47$	−8.43723	+	4.87123i	−1.23070	+	0.710543i	−0.263521	+	0.964654i	$0.584884\pi$
$48$	−6.92516	+	5.00270i	−0.999561	+	0.722077i
$49$		0			0
$50$	−6.75195	+	2.10027i	−0.954870	+	0.297023i
$51$	−9.21257	+	5.31888i	−1.29002	+	0.744792i
$52$	1.83310	−	1.18689i	0.254205	−	0.164591i
$53$	7.43743	+	4.29400i	1.02161	+	0.589826i	0.914570	−	0.404428i	$-0.132529\pi$
$53$	7.43743	+	4.29400i	1.02161	+	0.589826i	0.107040	+	0.994255i	$0.465863\pi$
$54$	1.23114	+	4.16667i	0.167537	+	0.567013i
$55$	2.57501	−	4.53448i	0.347214	−	0.611430i
$56$		0			0
$57$			5.49966i			0.728447i
$58$	0.761605	−	0.225034i	0.100004	−	0.0295485i
$59$	7.16053	−	12.4024i	0.932222	−	1.61466i	0.152707	−	0.988272i	$-0.451201\pi$
$59$	7.16053	−	12.4024i	0.932222	−	1.61466i	0.779515	−	0.626384i	$-0.215466\pi$
$60$	0.554981	+	9.53536i	0.0716478	+	1.23101i
$61$	0.536986	−	0.310029i	0.0687540	−	0.0396951i	−0.465229	−	0.885190i	$-0.654028\pi$
$61$	0.536986	−	0.310029i	0.0687540	−	0.0396951i	0.533983	+	0.845495i	$0.320695\pi$
$62$	−2.18379	+	9.06897i	−0.277342	+	1.15176i
$63$		0			0
$64$	−1.21922	−	7.90655i	−0.152403	−	0.988318i
$65$	−0.0174256	−	2.44149i	−0.00216138	−	0.302830i
$66$	−5.10611	−	4.85213i	−0.628519	−	0.597255i
$67$	−2.35829	+	4.08469i	−0.288112	+	0.499024i	−0.973359	−	0.229287i	$-0.926361\pi$
$67$	−2.35829	+	4.08469i	−0.288112	+	0.499024i	0.685247	+	0.728310i	$0.259694\pi$
$68$	−0.507812	−	9.94853i	−0.0615813	−	1.20644i
$69$			12.9020i			1.55322i
$70$		0			0
$71$		−	11.9473i		−	1.41789i	−0.705265	−	0.708943i	$-0.749172\pi$
$71$		−	11.9473i		−	1.41789i	0.705265	−	0.708943i	$-0.250828\pi$
$72$	4.34113	+	0.813745i	0.511607	+	0.0959008i
$73$	4.98074	−	8.62689i	0.582951	−	1.00970i	−0.412176	−	0.911104i	$-0.635231\pi$
$73$	4.98074	−	8.62689i	0.582951	−	1.00970i	0.995127	−	0.0985973i	$-0.0314356\pi$
$74$	−5.35764	+	5.63809i	−0.622813	+	0.655415i
$75$	9.32347	+	5.20690i	1.07658	+	0.601241i
$76$	−4.58552	−	2.34430i	−0.525995	−	0.268910i
$77$		0			0
$78$	−3.20636	−	0.772087i	−0.363049	−	0.0874216i
$79$	9.21257	−	5.31888i	1.03650	−	0.598421i	0.117657	−	0.993054i	$-0.462462\pi$
$79$	9.21257	−	5.31888i	1.03650	−	0.598421i	0.918839	+	0.394634i	$0.129128\pi$
$80$	−8.18699	−	3.60184i	−0.915333	−	0.402698i
$81$	5.62311	−	9.73950i	0.624790	−	1.08217i
$82$	3.40036	+	11.5082i	0.375507	+	1.27086i
$83$		−	3.86098i		−	0.423798i	−0.977292	−	0.211899i	$-0.932035\pi$
$83$		−	3.86098i		−	0.423798i	0.977292	−	0.211899i	$-0.0679648\pi$
$84$		0			0
$85$	−9.68466	−	5.49966i	−1.05045	−	0.596521i
$86$	−1.79609	+	0.530698i	−0.193677	+	0.0572266i
$87$	−1.03867	−	0.599676i	−0.111357	−	0.0642921i
$88$	6.22217	−	2.18911i	0.663285	−	0.233360i
$89$	−2.44949	+	1.41421i	−0.259645	+	0.149906i	−0.624173	−	0.781286i	$-0.714564\pi$
$89$	−2.44949	+	1.41421i	−0.259645	+	0.149906i	0.364527	+	0.931193i	$0.381231\pi$
$90$	3.37594	−	3.60382i	0.355855	−	0.379876i
$91$		0			0
$92$	−10.7575	−	5.49966i	−1.12155	−	0.573379i
$93$	12.2003	−	7.04383i	1.26511	−	0.730411i
$94$	−9.49090	+	9.98771i	−0.978911	+	1.03015i
$95$	−4.96581	+	2.91447i	−0.509482	+	0.299018i
$96$	−7.38748	+	9.56006i	−0.753981	+	0.975720i
$97$	14.9422			1.51715			0.758576	−	0.651584i	$-0.225895\pi$
$97$	14.9422			1.51715			0.758576	+	0.651584i	$0.225895\pi$
$98$		0			0
$99$			3.64162i			0.365996i
$100$	−8.31567	+	5.55424i	−0.831567	+	0.555424i
$101$	13.0860	+	7.55519i	1.30210	+	0.751770i	0.980765	−	0.195194i	$-0.0625337\pi$
$101$	13.0860	+	7.55519i	1.30210	+	0.751770i	0.321339	+	0.946964i	$0.395867\pi$
$102$	−10.3631	+	10.9055i	−1.02610	+	1.07981i
$103$	4.73795	−	2.73546i	0.466844	−	0.269532i	−0.248074	−	0.968741i	$-0.579798\pi$
$103$	4.73795	−	2.73546i	0.466844	−	0.269532i	0.714918	+	0.699209i	$0.246464\pi$
$104$	2.01051	−	2.34430i	0.197147	−	0.229878i
$105$		0			0
$106$	11.8078	+	2.84329i	1.14687	+	0.276165i
$107$	5.00691	+	8.67222i	0.484036	+	0.838375i	0.999832	−	0.0183365i	$-0.00583701\pi$
$107$	5.00691	+	8.67222i	0.484036	+	0.838375i	−0.515796	+	0.856712i	$0.672504\pi$
$108$	3.33947	+	5.15768i	0.321341	+	0.496298i
$109$	−2.28078	+	3.95042i	−0.218459	+	0.378382i	−0.954337	−	0.298732i	$-0.903436\pi$
$109$	−2.28078	+	3.95042i	−0.218459	+	0.378382i	0.735878	+	0.677114i	$0.236770\pi$
$110$	1.67522	−	7.18179i	0.159726	−	0.684757i
$111$	11.7460			1.11489
$112$		0			0
$113$		−	5.49966i		−	0.517364i	−0.965963	−	0.258682i	$-0.916712\pi$
$113$		−	5.49966i		−	0.517364i	0.965963	−	0.258682i	$-0.0832882\pi$
$114$	2.20391	+	7.45890i	0.206415	+	0.698590i
$115$	−11.6496	+	6.83725i	−1.08633	+	0.637576i
$116$	0.942747	−	0.610405i	0.0875318	−	0.0566747i
$117$	0.852526	+	1.47662i	0.0788161	+	0.136513i
$118$	4.74137	−	19.6902i	0.436478	−	1.81263i
$119$		0			0
$120$	4.57385	+	12.7099i	0.417534	+	1.16025i
$121$	−2.78078	−	4.81645i	−0.252798	−	0.437859i
$122$	0.604047	−	0.635666i	0.0546878	−	0.0575505i
$123$	9.06134	−	15.6947i	0.817034	−	1.41514i
$124$	0.672500	+	13.1749i	0.0603922	+	1.18314i
$125$	0.239369	+	11.1778i	0.0214098	+	0.999771i
$126$		0			0
$127$	5.29723			0.470053			0.235026	−	0.971989i	$-0.424482\pi$
$127$	5.29723			0.470053			0.235026	+	0.971989i	$0.424482\pi$
$128$	−4.82201	−	10.2347i	−0.426209	−	0.904625i
$129$	2.44949	+	1.41421i	0.215666	+	0.124515i
$130$	−1.00203	−	3.30429i	−0.0878836	−	0.289805i
$131$	1.28751	+	2.23003i	0.112490	+	0.194838i	0.916774	−	0.399407i	$-0.130784\pi$
$131$	1.28751	+	2.23003i	0.112490	+	0.194838i	−0.804284	+	0.594246i	$0.797451\pi$
$132$	−8.86958	−	4.53448i	−0.771998	−	0.394676i
$133$		0			0
$134$	−1.56155	+	6.48490i	−0.134898	+	0.560210i
$135$	6.86949	−	0.0490294i	0.591231	−	0.00421978i
$136$	−4.67545	−	13.2892i	−0.400917	−	1.13954i
$137$	−2.67459	−	1.54417i	−0.228505	−	0.131928i	0.381377	−	0.924420i	$-0.375450\pi$
$137$	−2.67459	−	1.54417i	−0.228505	−	0.131928i	−0.609882	+	0.792492i	$0.708783\pi$
$138$	5.17030	+	17.4983i	0.440126	+	1.48956i
$139$	−4.02102			−0.341058			−0.170529	−	0.985353i	$-0.554548\pi$
$139$	−4.02102			−0.341058			−0.170529	+	0.985353i	$0.554548\pi$
$140$		0			0
$141$	20.8078			1.75233
$142$	−4.78773	−	16.2035i	−0.401777	−	1.35977i
$143$	2.20521	+	1.27318i	0.184409	+	0.106468i
$144$	6.21375	−	0.636006i	0.517812	−	0.0530005i
$145$	−0.00896184	−	1.25564i	−0.000744240	−	0.104275i
$146$	3.29801	−	13.6962i	0.272946	−	1.13350i
$147$		0			0
$148$	−5.00691	+	9.79366i	−0.411565	+	0.805034i
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$	14.7315	+	3.32560i	1.20282	+	0.271534i
$151$	−4.28785	−	2.47559i	−0.348940	−	0.201461i	0.315278	−	0.948999i	$-0.397902\pi$
$151$	−4.28785	−	2.47559i	−0.348940	−	0.201461i	−0.664218	+	0.747539i	$0.731236\pi$
$152$	−7.15855	−	1.34187i	−0.580635	−	0.108840i
$153$	7.77769			0.628789
$154$		0			0
$155$	12.8255	+	7.28323i	1.03017	+	0.585003i
$156$	−4.65803	+	0.237764i	−0.372941	+	0.0190364i
$157$	−1.94442	+	3.36784i	−0.155182	+	0.268783i	−0.933125	−	0.359552i	$-0.882930\pi$
$157$	−1.94442	+	3.36784i	−0.155182	+	0.268783i	0.777943	+	0.628334i	$0.216263\pi$
$158$	10.3631	−	10.9055i	0.824442	−	0.867598i
$159$	−9.17104	−	15.8847i	−0.727311	−	1.25974i
$160$	−12.5470	−	1.60417i	−0.991926	−	0.126820i
$161$		0			0
$162$	3.72336	−	15.4626i	0.292535	−	1.21485i
$163$	5.75058	+	9.96029i	0.450420	+	0.780150i	0.998412	−	0.0563333i	$-0.0179410\pi$
$163$	5.75058	+	9.96029i	0.450420	+	0.780150i	−0.547992	+	0.836484i	$0.684608\pi$
$164$	9.22346	+	14.2453i	0.720232	+	1.11237i
$165$	−9.60517	+	5.63733i	−0.747762	+	0.438866i
$166$	−1.54724	−	5.23646i	−0.120089	−	0.406428i
$167$			0.673500i			0.0521170i	0.999660	+	0.0260585i	$0.00829562\pi$
$167$			0.673500i			0.0521170i	−0.999660	+	0.0260585i	$0.991704\pi$
$168$		0			0
$169$	−11.8078			−0.908290
$170$	−15.3387	−	3.57791i	−1.17643	−	0.274413i
$171$	2.01051	−	3.48230i	0.153747	−	0.266298i
$172$	−2.22327	+	1.43952i	−0.169523	+	0.109762i
$173$	5.52669	+	9.57250i	0.420186	+	0.727784i	0.995957	−	0.0898270i	$-0.0286314\pi$
$173$	5.52669	+	9.57250i	0.420186	+	0.727784i	−0.575771	+	0.817611i	$0.695298\pi$
$174$	−1.64901	−	0.397078i	−0.125011	−	0.0301024i
$175$		0			0
$176$	7.56155	−	5.46242i	0.569973	−	0.411746i
$177$	−26.4888	+	15.2933i	−1.99102	+	1.14952i
$178$	−2.75539	+	2.89962i	−0.206525	+	0.217336i
$179$	7.19296	+	4.15286i	0.537627	+	0.310399i	0.744117	−	0.668050i	$-0.232871\pi$
$179$	7.19296	+	4.15286i	0.537627	+	0.310399i	−0.206490	+	0.978449i	$0.566204\pi$
$180$	3.13443	−	6.24053i	0.233627	−	0.465142i
$181$		−	3.44849i		−	0.256324i	−0.991753	−	0.128162i	$-0.959092\pi$
$181$		−	3.44849i		−	0.256324i	0.991753	−	0.128162i	$-0.0409077\pi$
$182$		0			0
$183$	−1.32431			−0.0978956
$184$	−16.7937	−	3.14799i	−1.23805	−	0.232073i
$185$	6.22466	+	10.6059i	0.457646	+	0.779760i
$186$	13.7239	−	14.4423i	1.00628	−	1.05896i
$187$	10.0592	−	5.80766i	0.735599	−	0.424698i
$188$	−8.86958	+	17.3492i	−0.646881	+	1.26532i
$189$		0			0
$190$	−5.56695	+	5.94272i	−0.403869	+	0.431130i
$191$	17.2910	−	9.98298i	1.25113	−	0.722343i	0.279800	−	0.960058i	$-0.409732\pi$
$191$	17.2910	−	9.98298i	1.25113	−	0.722343i	0.971335	+	0.237716i	$0.0763987\pi$
$192$	−6.18820	+	15.9263i	−0.446595	+	1.14938i
$193$	−4.76284	−	2.74983i	−0.342837	−	0.197937i	0.318689	−	0.947859i	$-0.396757\pi$
$193$	−4.76284	−	2.74983i	−0.342837	−	0.197937i	−0.661526	+	0.749922i	$0.730091\pi$
$194$	20.2654	−	5.98789i	1.45497	−	0.429905i
$195$	−2.57501	+	4.53448i	−0.184400	+	0.324721i
$196$		0			0
$197$			16.4990i			1.17550i	0.809042	+	0.587751i	$0.199987\pi$
$197$			16.4990i			1.17550i	−0.809042	+	0.587751i	$0.800013\pi$
$198$	1.45933	+	4.93894i	0.103710	+	0.350995i
$199$	9.17104	−	15.8847i	0.650118	−	1.12604i	−0.332976	−	0.942935i	$-0.608053\pi$
$199$	9.17104	−	15.8847i	0.650118	−	1.12604i	0.983094	−	0.183102i	$-0.0586138\pi$
$200$	−9.05234	+	10.8653i	−0.640097	+	0.768294i
$201$	8.72399	−	5.03680i	0.615343	−	0.355268i
$202$	20.7755	+	5.00270i	1.46176	+	0.351989i
$203$		0			0
$204$	−9.68466	+	18.9435i	−0.678062	+	1.32631i
$205$	18.9732	−	0.135417i	1.32514	−	0.00945793i
$206$	5.32964	−	5.60862i	0.371334	−	0.390771i
$207$	4.71659	−	8.16937i	0.327826	−	0.567811i
$208$	1.78730	−	3.98514i	0.123927	−	0.276320i
$209$		−	6.00505i		−	0.415378i
$210$		0			0
$211$		−	0.287088i		−	0.0197640i	−0.999951	−	0.00988198i	$-0.996854\pi$
$211$		−	0.287088i		−	0.0197640i	0.999951	−	0.00988198i	$-0.00314558\pi$
$212$	17.1537	−	0.875592i	1.17812	−	0.0601359i
$213$	−12.7584	+	22.0982i	−0.874193	+	1.51415i
$214$	10.2659	+	9.75524i	0.701761	+	0.666854i
$215$	0.0211347	+	2.96116i	0.00144137	+	0.201950i
$216$	6.59603	+	5.65685i	0.448803	+	0.384900i
$217$		0			0
$218$	−1.51022	+	6.27174i	−0.102285	+	0.424776i
$219$	−18.4251	+	10.6378i	−1.24506	+	0.718833i
$220$	−0.605982	−	10.4116i	−0.0408553	−	0.701951i
$221$	2.71922	−	4.70983i	0.182915	−	0.316818i
$222$	15.9306	−	4.70707i	1.06919	−	0.315918i
$223$		−	0.147647i		−	0.00988718i	−0.999988	−	0.00494359i	$-0.998426\pi$
$223$		−	0.147647i		−	0.00988718i	0.999988	−	0.00494359i	$-0.00157360\pi$
$224$		0			0
$225$	−4.00000	−	6.70531i	−0.266667	−	0.447021i
$226$	−2.20391	−	7.45890i	−0.146602	−	0.496159i
$227$	8.79279	+	5.07652i	0.583598	+	0.336941i	0.762562	−	0.646915i	$-0.223941\pi$
$227$	8.79279	+	5.07652i	0.583598	+	0.336941i	−0.178964	+	0.983856i	$0.557275\pi$
$228$	5.97810	+	9.23294i	0.395909	+	0.611466i
$229$	8.18700	−	4.72677i	0.541012	−	0.312354i	−0.204477	−	0.978871i	$-0.565549\pi$
$229$	8.18700	−	4.72677i	0.541012	−	0.312354i	0.745489	+	0.666518i	$0.232216\pi$
$230$	−13.0599	+	13.9414i	−0.861143	+	0.919271i
$231$		0			0
$232$	1.03399	−	1.20565i	0.0678846	−	0.0791551i
$233$	9.52568	−	5.49966i	0.624048	−	0.360294i	−0.154395	−	0.988009i	$-0.549343\pi$
$233$	9.52568	−	5.49966i	0.624048	−	0.360294i	0.778443	+	0.627715i	$0.216010\pi$
$234$	1.74797	+	1.66102i	0.114269	+	0.108585i
$235$	11.0268	+	18.7880i	0.719308	+	1.22559i
$236$	−1.46011	−	28.6049i	−0.0950449	−	1.86202i
$237$	−22.7199			−1.47582
$238$		0			0
$239$		−	2.33205i		−	0.150848i	−0.997152	−	0.0754238i	$-0.975969\pi$
$239$		−	2.33205i		−	0.150848i	0.997152	−	0.0754238i	$-0.0240310\pi$
$240$	11.2966	+	15.4049i	0.729193	+	0.994382i
$241$	−13.9245	−	8.03932i	−0.896957	−	0.517858i	−0.0207451	−	0.999785i	$-0.506604\pi$
$241$	−13.9245	−	8.03932i	−0.896957	−	0.517858i	−0.876212	+	0.481927i	$0.839937\pi$
$242$	−5.70155	−	5.41794i	−0.366509	−	0.348278i
$243$	−12.8196	+	7.40140i	−0.822378	+	0.474800i
$244$	0.564503	−	1.10418i	0.0361386	−	0.0706882i
$245$		0			0
$246$	6.00000	−	24.9171i	0.382546	−	1.58866i
$247$	−1.40582	−	2.43495i	−0.0894503	−	0.154932i
$248$	6.19174	+	17.5989i	0.393176	+	1.11753i
$249$	−4.12311	+	7.14143i	−0.261291	+	0.452570i
$250$	4.80398	+	15.0639i	0.303831	+	0.952726i
$251$	−9.17104			−0.578871			−0.289435	−	0.957198i	$-0.593468\pi$
$251$	−9.17104			−0.578871			−0.289435	+	0.957198i	$0.593468\pi$
$252$		0			0
$253$		−	14.0877i		−	0.885683i
$254$	7.18436	−	2.12279i	0.450787	−	0.133196i
$255$	12.0401	+	20.5145i	0.753980	+	1.28467i
$256$	−10.6412	−	11.9484i	−0.665078	−	0.746774i
$257$	3.27569	+	5.67366i	0.204332	+	0.353913i	0.949920	−	0.312494i	$-0.101165\pi$
$257$	3.27569	+	5.67366i	0.204332	+	0.353913i	−0.745588	+	0.666407i	$0.767831\pi$
$258$	3.88884	+	0.936426i	0.242109	+	0.0582994i
$259$		0			0
$260$	−2.68314	−	4.07988i	−0.166402	−	0.253024i
$261$	0.438447	+	0.759413i	0.0271392	+	0.0470065i
$262$	2.63983	+	2.50852i	0.163089	+	0.154977i
$263$	−11.7915	+	20.4234i	−0.727093	+	1.25936i	0.231013	+	0.972951i	$0.425796\pi$
$263$	−11.7915	+	20.4234i	−0.727093	+	1.25936i	−0.958107	+	0.286412i	$0.907537\pi$
$264$	−13.8465	−	2.59553i	−0.852193	−	0.159744i
$265$	9.48274	−	16.6987i	0.582520	−	1.02579i
$266$		0			0
$267$	6.04090			0.369697
$268$	0.480881	+	9.42091i	0.0293745	+	0.575474i
$269$	0.838532	+	0.484127i	0.0511262	+	0.0295177i	0.525345	−	0.850889i	$-0.323936\pi$
$269$	0.838532	+	0.484127i	0.0511262	+	0.0295177i	−0.474219	+	0.880407i	$0.657270\pi$
$270$	9.29708	−	2.81935i	0.565802	−	0.171580i
$271$	3.29801	+	5.71233i	0.200340	+	0.346999i	0.948638	−	0.316364i	$-0.102462\pi$
$271$	3.29801	+	5.71233i	0.200340	+	0.346999i	−0.748298	+	0.663363i	$0.769129\pi$
$272$	−11.6665	−	16.1498i	−0.707387	−	0.979226i
$273$		0			0
$274$	−4.24621	−	1.02248i	−0.256523	−	0.0617703i
$275$	−10.1803	−	5.68539i	−0.613892	−	0.342842i
$276$	14.0244	+	21.6602i	0.844172	+	1.30379i
$277$	16.9631	+	9.79366i	1.01921	+	0.588444i	0.913876	−	0.405993i	$-0.133074\pi$
$277$	16.9631	+	9.79366i	1.01921	+	0.588444i	0.105338	+	0.994436i	$0.466407\pi$
$278$	−5.45350	+	1.61137i	−0.327079	+	0.0966433i
$279$	−10.3000			−0.616648
$280$		0			0
$281$	17.0540			1.01735			0.508677	−	0.860957i	$-0.330135\pi$
$281$	17.0540			1.01735			0.508677	+	0.860957i	$0.330135\pi$
$282$	28.2205	−	8.33842i	1.68051	−	0.496546i
$283$	6.45972	+	3.72952i	0.383991	+	0.221697i	0.679553	−	0.733626i	$-0.262174\pi$
$283$	6.45972	+	3.72952i	0.383991	+	0.221697i	−0.295563	+	0.955323i	$0.595507\pi$
$284$	−12.9867	−	20.0574i	−0.770618	−	1.19019i
$285$	12.2973	−	0.0877692i	0.728429	−	0.00519900i
$286$	3.50102	+	0.843038i	0.207019	+	0.0498499i
$287$		0			0
$288$	8.17252	−	3.35265i	0.481570	−	0.197557i
$289$	−3.90388	−	6.76172i	−0.229640	−	0.397748i
$290$	−0.515334	−	1.69937i	−0.0302615	−	0.0997902i
$291$	−27.6377	−	15.9566i	−1.62015	−	0.935395i
$292$	−1.01562	−	19.8971i	−0.0594350	−	1.16439i
$293$	−14.4635			−0.844965			−0.422483	−	0.906371i	$-0.638841\pi$
$293$	−14.4635			−0.844965			−0.422483	+	0.906371i	$0.638841\pi$
$294$		0			0
$295$	−27.8462	−	15.8131i	−1.62127	−	0.920674i
$296$	−2.86594	+	15.2891i	−0.166579	+	0.888660i
$297$	−3.58227	+	6.20467i	−0.207864	+	0.360031i
$298$	2.05034	+	1.94836i	0.118773	+	0.112865i
$299$	−3.29801	−	5.71233i	−0.190729	−	0.330352i
$300$	21.3123	−	1.39312i	1.23047	−	0.0804318i
$301$		0			0
$302$	−6.80745	−	1.63922i	−0.391725	−	0.0943266i
$303$	−16.1362	−	27.9488i	−0.927002	−	1.60561i
$304$	−10.2465	+	1.04878i	−0.587678	+	0.0601516i
$305$	−0.701798	−	1.19576i	−0.0401848	−	0.0684689i
$306$	10.5485	−	3.11680i	0.603016	−	0.178176i
$307$		−	13.8987i		−	0.793243i	−0.917982	−	0.396622i	$-0.870182\pi$
$307$		−	13.8987i		−	0.793243i	0.917982	−	0.396622i	$-0.129818\pi$
$308$		0			0
$309$	−11.6847			−0.664717
$310$	20.3132	+	4.73825i	1.15371	+	0.269114i
$311$	0.723002	−	1.25228i	0.0409977	−	0.0710101i	−0.844798	−	0.535085i	$-0.820280\pi$
$311$	0.723002	−	1.25228i	0.0409977	−	0.0710101i	0.885796	+	0.464075i	$0.153613\pi$
$312$	−6.22217	+	2.18911i	−0.352261	+	0.123934i
$313$	−3.58227	−	6.20467i	−0.202482	−	0.350708i	0.746846	−	0.664997i	$-0.231567\pi$
$313$	−3.58227	−	6.20467i	−0.202482	−	0.350708i	−0.949327	+	0.314289i	$0.898234\pi$
$314$	−1.28751	+	5.34683i	−0.0726581	+	0.301739i
$315$		0			0
$316$	9.68466	−	18.9435i	0.544805	−	1.06565i
$317$	−21.1396	+	12.2050i	−1.18732	+	0.685499i	−0.957696	−	0.287781i	$-0.907083\pi$
$317$	−21.1396	+	12.2050i	−1.18732	+	0.685499i	−0.229623	+	0.973280i	$0.573749\pi$
$318$	−18.8038	−	17.8684i	−1.05446	−	1.00201i
$319$	1.13412	+	0.654784i	0.0634985	+	0.0366609i
$320$	−17.6597	+	2.85238i	−0.987206	+	0.159453i
$321$		−	21.3873i		−	1.19372i
$322$		0			0
$323$	−12.8255			−0.713628
$324$	−1.14661	−	22.4632i	−0.0637006	−	1.24795i
$325$	−5.45892	+	0.0779277i	−0.302806	+	0.00432265i
$326$	11.7907	+	11.2042i	0.653024	+	0.620541i
$327$	8.43723	−	4.87123i	0.466580	−	0.269380i
$328$	18.2179	+	15.6240i	1.00592	+	0.862689i
$329$		0			0
$330$	−10.7679	+	11.4948i	−0.592754	+	0.632766i
$331$	−7.19296	+	4.15286i	−0.395361	+	0.228262i	−0.684480	−	0.729031i	$-0.739971\pi$
$331$	−7.19296	+	4.15286i	−0.395361	+	0.228262i	0.289120	+	0.957293i	$0.406637\pi$
$332$	−4.19687	−	6.48190i	−0.230333	−	0.355741i
$333$	−7.43743	−	4.29400i	−0.407569	−	0.235310i
$334$	0.269896	+	0.913433i	0.0147680	+	0.0499809i
$335$	9.17104	+	5.20798i	0.501067	+	0.284543i
$336$		0			0
$337$			30.5866i			1.66616i	0.553153	+	0.833080i	$0.313425\pi$
$337$			30.5866i			1.66616i	−0.553153	+	0.833080i	$0.686575\pi$
$338$	−16.0143	+	4.73180i	−0.871061	+	0.257376i
$339$	−5.87302	+	10.1724i	−0.318979	+	0.552488i
$340$	−22.2369	+	1.29424i	−1.20597	+	0.0701902i
$341$	−13.3214	+	7.69113i	−0.721395	+	0.416498i
$342$	1.33126	−	5.52855i	0.0719866	−	0.298950i
$343$		0			0
$344$	−2.43845	+	2.84329i	−0.131472	+	0.153300i
$345$	28.8491	−	0.205904i	1.55318	−	0.0110855i
$346$	11.3316	+	10.7680i	0.609191	+	0.578889i
$347$	0.662153	−	1.14688i	0.0355463	−	0.0615679i	−0.847705	−	0.530468i	$-0.822016\pi$
$347$	0.662153	−	1.14688i	0.0355463	−	0.0615679i	0.883251	+	0.468900i	$0.155350\pi$
$348$	−2.39559	+	0.122280i	−0.128417	+	0.00655491i
$349$		−	18.8307i		−	1.00799i	−0.863708	−	0.503993i	$-0.831864\pi$
$349$		−	18.8307i		−	1.00799i	0.863708	−	0.503993i	$-0.168136\pi$
$350$		0			0
$351$			3.35453i			0.179051i
$352$	8.06636	−	10.4386i	0.429938	−	0.556379i
$353$	8.08427	−	14.0024i	0.430282	−	0.745270i	−0.566615	−	0.823982i	$-0.691747\pi$
$353$	8.08427	−	14.0024i	0.430282	−	0.745270i	0.996897	+	0.0787120i	$0.0250808\pi$
$354$	−29.7968	+	31.3566i	−1.58368	+	1.66658i
$355$	−26.7144	+	0.190668i	−1.41785	+	0.0101196i
$356$	−2.57501	+	5.03680i	−0.136475	+	0.266950i
$357$		0			0
$358$	11.4196	+	2.74983i	0.603547	+	0.145333i
$359$	−8.96394	+	5.17534i	−0.473099	+	0.273144i	−0.717536	−	0.696521i	$-0.754730\pi$
$359$	−8.96394	+	5.17534i	−0.473099	+	0.273144i	0.244437	+	0.969665i	$0.421397\pi$
$360$	1.75026	−	9.71980i	0.0922470	−	0.512278i
$361$	6.18466	−	10.7121i	0.325508	−	0.563797i
$362$	−1.38193	−	4.67700i	−0.0726328	−	0.245818i
$363$			11.8782i			0.623446i
$364$		0			0
$365$	−19.3693	−	10.9993i	−1.01384	−	0.575730i
$366$	−1.79609	+	0.530698i	−0.0938831	+	0.0277400i
$367$	−20.2462	−	11.6891i	−1.05684	−	0.610168i	−0.132286	−	0.991212i	$-0.542232\pi$
$367$	−20.2462	−	11.6891i	−1.05684	−	0.610168i	−0.924557	+	0.381043i	$0.875565\pi$
$368$	−24.0380	+	2.46040i	−1.25307	+	0.128257i
$369$	−11.4750	+	6.62511i	−0.597366	+	0.344889i
$370$	12.6923	+	11.8898i	0.659843	+	0.618120i
$371$		0			0
$372$	12.8255	−	25.0870i	0.664969	−	1.30070i
$373$	−10.1120	+	5.83817i	−0.523580	+	0.302289i	−0.738398	−	0.674365i	$-0.764418\pi$
$373$	−10.1120	+	5.83817i	−0.523580	+	0.302289i	0.214818	+	0.976654i	$0.431084\pi$
$374$	11.3154	−	11.9077i	0.585105	−	0.615733i
$375$	11.4939	−	20.9305i	0.593542	−	1.08084i
$376$	−5.07693	+	27.0841i	−0.261822	+	1.39676i
$377$	0.613157			0.0315792
$378$		0			0
$379$			24.9171i			1.27991i	0.768414	+	0.639954i	$0.221046\pi$
$379$			24.9171i			1.27991i	−0.768414	+	0.639954i	$0.778954\pi$
$380$	−5.16870	+	10.2907i	−0.265149	+	0.527901i
$381$	−9.79796	−	5.65685i	−0.501965	−	0.289809i
$382$	19.4504	−	20.4685i	0.995168	−	1.04726i
$383$	16.1633	−	9.33190i	0.825907	−	0.476838i	−0.0265422	−	0.999648i	$-0.508450\pi$
$383$	16.1633	−	9.33190i	0.825907	−	0.476838i	0.852449	+	0.522810i	$0.175116\pi$
$384$	−2.01051	+	24.0798i	−0.102598	+	1.22882i
$385$		0			0
$386$	−7.56155	−	1.82081i	−0.384873	−	0.0926767i
$387$	−1.03399	−	1.79092i	−0.0525605	−	0.0910375i
$388$	25.0853	−	16.2421i	1.27351	−	0.824569i
$389$	5.96543	−	10.3324i	0.302460	−	0.523875i	−0.674233	−	0.738519i	$-0.735526\pi$
$389$	5.96543	−	10.3324i	0.302460	−	0.523875i	0.976692	+	0.214643i	$0.0688589\pi$
$390$	−1.67522	+	7.18179i	−0.0848283	+	0.363664i
$391$	−30.0881			−1.52162
$392$		0			0
$393$		−	5.49966i		−	0.277421i
$394$	6.61173	+	22.3767i	0.333094	+	1.12732i
$395$	−12.0401	−	20.5145i	−0.605803	−	1.03220i
$396$	3.95842	+	6.11362i	0.198918	+	0.307221i
$397$	−10.5074	−	18.1994i	−0.527353	−	0.913402i	−0.999492	−	0.0318775i	$-0.989851\pi$
$397$	−10.5074	−	18.1994i	−0.527353	−	0.913402i	0.472139	−	0.881524i	$-0.343482\pi$
$398$	6.07263	−	25.2188i	0.304394	−	1.26410i
$399$		0			0
$400$	−7.92309	+	18.3637i	−0.396155	+	0.918184i
$401$	−6.71922	−	11.6380i	−0.335542	−	0.581176i	0.648047	−	0.761601i	$-0.275586\pi$
$401$	−6.71922	−	11.6380i	−0.335542	−	0.581176i	−0.983589	+	0.180425i	$0.942253\pi$
$402$	9.81347	−	10.3272i	0.489451	−	0.515072i
$403$	−3.60109	+	6.23726i	−0.179383	+	0.310700i
$404$	30.1815	−	1.54058i	1.50158	−	0.0766469i
$405$	−21.8674	−	12.4179i	−1.08660	−	0.617050i
$406$		0			0
$407$	−12.8255			−0.635734
$408$	−5.54347	+	29.5731i	−0.274443	+	1.46408i
$409$	−26.1720	−	15.1104i	−1.29412	−	0.747161i	−0.314738	−	0.949178i	$-0.601917\pi$
$409$	−26.1720	−	15.1104i	−1.29412	−	0.747161i	−0.979382	+	0.202018i	$0.935250\pi$
$410$	25.6781	−	7.78690i	1.26815	−	0.384567i
$411$	3.29801	+	5.71233i	0.162679	+	0.281768i
$412$	4.98074	−	9.74247i	0.245383	−	0.479977i
$413$		0			0
$414$	3.12311	−	12.9698i	0.153492	−	0.637431i
$415$	−8.63320	+	0.0616176i	−0.423787	+	0.00302469i
$416$	0.827039	−	6.12107i	0.0405489	−	0.300110i
$417$	7.43743	+	4.29400i	0.364212	+	0.210278i
$418$	−2.40644	−	8.14434i	−0.117703	−	0.398353i
$419$	22.3631			1.09251			0.546254	−	0.837619i	$-0.316053\pi$
$419$	22.3631			1.09251			0.546254	+	0.837619i	$0.316053\pi$
$420$		0			0
$421$	12.5616			0.612213			0.306106	−	0.951997i	$-0.400974\pi$
$421$	12.5616			0.612213			0.306106	+	0.951997i	$0.400974\pi$
$422$	−0.115047	−	0.389363i	−0.00560038	−	0.0189539i
$423$	−13.1752	−	7.60669i	−0.640599	−	0.369850i
$424$	22.9138	−	8.06162i	1.11279	−	0.391507i
$425$	−12.1427	+	21.7428i	−0.589009	+	1.05468i
$426$	−8.44804	+	35.0835i	−0.409309	+	1.69980i
$427$		0			0
$428$	17.8324	+	9.11662i	0.861960	+	0.440668i
$429$	−2.71922	−	4.70983i	−0.131285	−	0.227393i
$430$	1.21531	+	4.00761i	0.0586074	+	0.193264i
$431$	10.0981	+	5.83012i	0.486407	+	0.280827i	0.723083	−	0.690762i	$-0.242725\pi$
$431$	10.0981	+	5.83012i	0.486407	+	0.280827i	−0.236676	+	0.971589i	$0.576058\pi$
$432$	11.2128	+	5.02884i	0.539474	+	0.241950i
$433$	9.00400			0.432705			0.216352	−	0.976315i	$-0.430584\pi$
$433$	9.00400			0.432705			0.216352	+	0.976315i	$0.430584\pi$
$434$		0			0
$435$	−1.32431	+	2.33205i	−0.0634957	+	0.111813i
$436$	0.465074	+	9.11124i	0.0222730	+	0.436349i
$437$	−7.77769	+	13.4713i	−0.372057	+	0.644422i
$438$	−20.7261	+	21.8111i	−0.990333	+	1.04217i
$439$	15.7671	+	27.3094i	0.752521	+	1.30340i	0.946597	+	0.322418i	$0.104496\pi$
$439$	15.7671	+	27.3094i	0.752521	+	1.30340i	−0.194076	+	0.980986i	$0.562171\pi$
$440$	−4.99417	−	13.8779i	−0.238088	−	0.661603i
$441$		0			0
$442$	1.80054	−	7.47740i	0.0856431	−	0.355663i
$443$	8.77102	+	15.1919i	0.416724	+	0.721787i	0.995608	−	0.0936230i	$-0.0298448\pi$
$443$	8.77102	+	15.1919i	0.416724	+	0.721787i	−0.578884	+	0.815410i	$0.696512\pi$
$444$	19.7195	−	12.7679i	0.935847	−	0.605938i
$445$	3.20129	+	5.45452i	0.151756	+	0.258569i
$446$	−0.0591675	−	0.200246i	−0.00280166	−	0.00948193i
$447$		−	4.27156i		−	0.202038i
$448$		0			0
$449$	6.31534			0.298039			0.149020	−	0.988834i	$-0.452388\pi$
$449$	6.31534			0.298039			0.149020	+	0.988834i	$0.452388\pi$
$450$	−8.11205	−	7.49112i	−0.382406	−	0.353135i
$451$	−9.89404	+	17.1370i	−0.465892	+	0.806949i
$452$	−5.97810	−	9.23294i	−0.281186	−	0.434281i
$453$	5.28732	+	9.15790i	0.248420	+	0.430276i
$454$	13.9596	+	3.36144i	0.655155	+	0.157760i
$455$		0			0
$456$	11.8078	+	10.1265i	0.552949	+	0.474218i
$457$	−8.93935	+	5.16114i	−0.418165	+	0.241428i	−0.694292	−	0.719693i	$-0.744282\pi$
$457$	−8.93935	+	5.16114i	−0.418165	+	0.241428i	0.276127	+	0.961121i	$0.410949\pi$
$458$	9.20942	−	9.69150i	0.430328	−	0.452854i
$459$	13.2518	+	7.65093i	0.618541	+	0.357115i
$460$	−12.1256	+	24.1416i	−0.565360	+	1.12561i
$461$			21.1154i			0.983444i	0.870752	+	0.491722i	$0.163632\pi$
$461$			21.1154i			0.983444i	−0.870752	+	0.491722i	$0.836368\pi$
$462$		0			0
$463$	24.3266			1.13055			0.565277	−	0.824901i	$-0.308769\pi$
$463$	24.3266			1.13055			0.565277	+	0.824901i	$0.308769\pi$
$464$	0.919195	−	2.04952i	0.0426726	−	0.0951467i
$465$	−15.9448	−	27.1675i	−0.739422	−	1.25986i
$466$	10.7153	−	11.2762i	0.496376	−	0.522359i
$467$	20.0903	−	11.5991i	0.929668	−	0.536744i	0.0429615	−	0.999077i	$-0.486321\pi$
$467$	20.0903	−	11.5991i	0.929668	−	0.536744i	0.886707	+	0.462333i	$0.152987\pi$
$468$	3.03632	+	1.55229i	0.140354	+	0.0717545i
$469$		0			0
$470$	22.4841	+	21.0624i	1.03711	+	0.971534i
$471$	7.19296	−	4.15286i	0.331434	−	0.191353i
$472$	−13.4433	−	38.2102i	−0.618777	−	1.75877i
$473$	−2.67459	−	1.54417i	−0.122978	−	0.0710012i
$474$	−30.8138	+	9.10469i	−1.41533	+	0.418192i
$475$	6.59603	+	11.0571i	0.302646	+	0.507335i
$476$		0			0
$477$			13.4106i			0.614030i
$478$	−0.934536	−	3.16284i	−0.0427447	−	0.144665i
$479$	−15.0441	+	26.0571i	−0.687381	+	1.19058i	0.285301	+	0.958438i	$0.407906\pi$
$479$	−15.0441	+	26.0571i	−0.687381	+	1.19058i	−0.972682	+	0.232141i	$0.925427\pi$
$480$	21.4943	+	16.3659i	0.981076	+	0.746998i
$481$	−5.20053	+	3.00252i	−0.237124	+	0.136903i
$482$	−22.1067	−	5.32326i	−1.00693	−	0.242468i
$483$		0			0
$484$	−9.90388	−	5.06326i	−0.450176	−	0.230148i
$485$	−0.238463	−	33.4110i	−0.0108281	−	1.51711i
$486$	−14.4206	+	15.1754i	−0.654130	+	0.688371i
$487$	0.580639	−	1.00570i	0.0263112	−	0.0455724i	−0.852570	−	0.522613i	$-0.824957\pi$
$487$	0.580639	−	1.00570i	0.0263112	−	0.0455724i	0.878881	+	0.477041i	$0.158291\pi$
$488$	0.323120	−	1.72377i	0.0146270	−	0.0780312i
$489$		−	24.5639i		−	1.11082i
$490$		0			0
$491$			14.2794i			0.644419i	0.946668	+	0.322210i	$0.104426\pi$
$491$			14.2794i			0.644419i	−0.946668	+	0.322210i	$0.895574\pi$
$492$	−1.84770	−	36.1982i	−0.0833009	−	1.63194i
$493$	1.39847	−	2.42223i	0.0629841	−	0.109092i
$494$	−2.88242	−	2.73904i	−0.129686	−	0.123235i
$495$	8.14269	−	0.0581167i	0.365987	−	0.00261215i
$496$	15.4501	+	21.3873i	0.693729	+	0.960318i
$497$		0			0
$498$	−2.73013	+	11.3378i	−0.122340	+	0.508060i
$499$	22.2157	−	12.8263i	0.994513	−	0.574182i	0.0878928	−	0.996130i	$-0.471987\pi$
$499$	22.2157	−	12.8263i	0.994513	−	0.574182i	0.906620	+	0.421948i	$0.138653\pi$
$500$	12.5521	+	18.5053i	0.561345	+	0.827582i
$501$	0.719224	−	1.24573i	0.0321325	−	0.0556552i
$502$	−12.4382	+	3.67517i	−0.555144	+	0.164031i
$503$			18.8114i			0.838761i	0.907811	+	0.419380i	$0.137753\pi$
$503$			18.8114i			0.838761i	−0.907811	+	0.419380i	$0.862247\pi$
$504$		0			0
$505$	16.6847	−	29.3810i	0.742458	−	1.30744i
$506$	−5.64543	−	19.1064i	−0.250970	−	0.849382i
$507$	21.8401	+	12.6094i	0.969953	+	0.560003i
$508$	8.89310	−	5.75806i	0.394567	−	0.255473i
$509$	−24.2595	+	14.0062i	−1.07528	+	0.620814i	−0.929620	−	0.368520i	$-0.879864\pi$
$509$	−24.2595	+	14.0062i	−1.07528	+	0.620814i	−0.145662	+	0.989334i	$0.546531\pi$
$510$	24.5503	+	22.9979i	1.08710	+	1.01836i
$511$		0			0
$512$	−19.2203	−	11.9407i	−0.849426	−	0.527707i
$513$	6.85110	−	3.95548i	0.302483	−	0.174639i
$514$	6.71628	+	6.38220i	0.296243	+	0.281507i
$515$	−6.19212	−	10.5504i	−0.272857	−	0.464908i
$516$	5.64950	−	0.288373i	0.248705	−	0.0126949i
$517$	−22.7199			−0.999220
$518$		0			0
$519$		−	23.6076i		−	1.03626i
$520$	−5.27397	−	4.45811i	−0.231279	−	0.195501i
$521$	−2.44949	−	1.41421i	−0.107314	−	0.0619578i	0.445382	−	0.895340i	$-0.353068\pi$
$521$	−2.44949	−	1.41421i	−0.107314	−	0.0619578i	−0.552696	+	0.833383i	$0.686401\pi$
$522$	0.898968	+	0.854251i	0.0393467	+	0.0373896i
$523$	−18.1408	+	10.4736i	−0.793243	+	0.457979i	−0.841103	−	0.540875i	$-0.818093\pi$
$523$	−18.1408	+	10.4736i	−0.793243	+	0.457979i	0.0478601	+	0.998854i	$0.484760\pi$
$524$	4.58552	+	2.34430i	0.200319	+	0.102411i
$525$		0			0
$526$	−7.80776	+	32.4245i	−0.340435	+	1.41378i
$527$	16.4265	+	28.4516i	0.715552	+	1.23937i
$528$	−19.8194	+	2.02861i	−0.862529	+	0.0882839i
$529$	−6.74621	+	11.6848i	−0.293314	+	0.508034i
$530$	6.16918	−	26.4477i	0.267972	−	1.14881i
$531$	22.3631			0.970476
$532$		0			0
$533$			9.26504i			0.401313i
$534$	8.19296	−	2.42080i	0.354544	−	0.104758i
$535$	19.3113	−	11.3339i	0.834899	−	0.490007i
$536$	4.42749	+	12.5844i	0.191239	+	0.543563i
$537$	−8.86958	−	15.3626i	−0.382751	−	0.662944i
$538$	1.33126	+	0.320566i	0.0573949	+	0.0138206i
$539$		0			0
$540$	11.4793	−	7.54941i	0.493992	−	0.324875i
$541$	9.71922	+	16.8342i	0.417862	+	0.723758i	0.995724	−	0.0923761i	$-0.0294462\pi$
$541$	9.71922	+	16.8342i	0.417862	+	0.723758i	−0.577862	+	0.816134i	$0.696113\pi$
$542$	6.76206	+	6.42570i	0.290455	+	0.276008i
$543$	−3.68260	+	6.37845i	−0.158036	+	0.273726i
$544$	−22.2945	−	17.2280i	−0.955870	−	0.738642i
$545$	8.86958	+	5.03680i	0.379931	+	0.215753i
$546$		0			0
$547$	33.4337			1.42952			0.714762	−	0.699368i	$-0.246535\pi$
$547$	33.4337			1.42952			0.714762	+	0.699368i	$0.246535\pi$
$548$	−6.16866	+	0.314873i	−0.263512	+	0.0134507i
$549$	0.838532	+	0.484127i	0.0357877	+	0.0206620i
$550$	−16.0853	−	3.63120i	−0.685879	−	0.154835i
$551$	−0.723002	−	1.25228i	−0.0308009	−	0.0533488i
$552$	27.7006	+	23.7565i	1.17902	+	1.01114i
$553$		0			0
$554$	26.9309	+	6.48490i	1.14418	+	0.275517i
$555$	−0.187456	−	26.2643i	−0.00795705	−	1.11486i
$556$	−6.75057	+	4.37083i	−0.286288	+	0.185364i
$557$	−7.43743	−	4.29400i	−0.315134	−	0.181943i	0.334088	−	0.942542i	$-0.391572\pi$
$557$	−7.43743	−	4.29400i	−0.315134	−	0.181943i	−0.649222	+	0.760599i	$0.724905\pi$
$558$	−13.9694	+	4.12760i	−0.591373	+	0.174735i
$559$	−1.44600			−0.0611595
$560$		0			0
$561$	−24.8078			−1.04738
$562$	23.1294	−	6.83414i	0.975656	−	0.288281i
$563$	5.87645	+	3.39277i	0.247663	+	0.142988i	0.618694	−	0.785632i	$-0.287662\pi$
$563$	5.87645	+	3.39277i	0.247663	+	0.142988i	−0.371031	+	0.928621i	$0.620996\pi$
$564$	34.9325	−	22.6179i	1.47092	−	0.952387i
$565$	−12.2973	+	0.0877692i	−0.517351	+	0.00369248i
$566$	10.2555	+	2.46952i	0.431073	+	0.103801i
$567$		0			0
$568$	−25.6509	−	21.9986i	−1.07629	−	0.923042i
$569$	21.9309	+	37.9854i	0.919390	+	1.59243i	0.800344	+	0.599541i	$0.204650\pi$
$569$	21.9309	+	37.9854i	0.919390	+	1.59243i	0.119046	+	0.992889i	$0.462016\pi$
$570$	16.6430	−	5.04700i	0.697099	−	0.211396i
$571$	13.5004	+	7.79447i	0.564975	+	0.326188i	0.755140	−	0.655564i	$-0.227569\pi$
$571$	13.5004	+	7.79447i	0.564975	+	0.326188i	−0.190165	+	0.981752i	$0.560902\pi$
$572$	5.08608	−	0.259614i	0.212660	−	0.0108550i
$573$	−42.6429			−1.78143
$574$		0			0
$575$	15.4741	+	25.9396i	0.645313	+	1.08176i
$576$	9.74043	−	7.82206i	0.405851	−	0.325919i
$577$	18.0457	−	31.2561i	0.751254	−	1.30121i	−0.195961	−	0.980612i	$-0.562783\pi$
$577$	18.0457	−	31.2561i	0.751254	−	1.30121i	0.947215	−	0.320599i	$-0.103884\pi$
$578$	−8.00430	−	7.60615i	−0.332935	−	0.316374i
$579$	5.87302	+	10.1724i	0.244075	+	0.422750i
$580$	−1.37992	−	2.09825i	−0.0572980	−	0.0871251i
$581$		0			0
$582$	−43.8780	−	10.5657i	−1.81880	−	0.437964i
$583$	10.0138	+	17.3444i	0.414730	+	0.718333i
$584$	−9.35091	−	26.5784i	−0.386943	−	1.09982i
$585$	3.28813	−	1.92982i	0.135947	−	0.0797884i
$586$	−19.6161	+	5.79604i	−0.810333	+	0.239432i
$587$			2.80928i			0.115951i	0.998318	+	0.0579757i	$0.0184646\pi$
$587$			2.80928i			0.115951i	−0.998318	+	0.0579757i	$0.981535\pi$
$588$		0			0
$589$	16.9848			0.699848
$590$	−44.1032	−	10.2875i	−1.81570	−	0.423530i
$591$	17.6191	−	30.5171i	0.724752	−	1.25531i
$592$	2.23996	+	21.8843i	0.0920617	+	0.899439i
$593$	−3.10353	−	5.37547i	−0.127447	−	0.220744i	0.795240	−	0.606295i	$-0.207345\pi$
$593$	−3.10353	−	5.37547i	−0.127447	−	0.220744i	−0.922687	+	0.385551i	$0.874011\pi$
$594$	−2.37201	+	9.85061i	−0.0973247	+	0.404176i
$595$		0			0
$596$	3.56155	+	1.82081i	0.145887	+	0.0745832i
$597$	−33.9262	+	19.5873i	−1.38851	+	0.801655i
$598$	−6.76206	−	6.42570i	−0.276521	−	0.262767i
$599$	−15.5200	−	8.96050i	−0.634131	−	0.366116i	0.148219	−	0.988955i	$-0.452646\pi$
$599$	−15.5200	−	8.96050i	−0.634131	−	0.366116i	−0.782350	+	0.622839i	$0.785979\pi$
$600$	28.3465	−	10.4300i	1.15724	−	0.425804i
$601$		−	42.2309i		−	1.72263i	−0.508068	−	0.861317i	$-0.669640\pi$
$601$		−	42.2309i		−	1.72263i	0.508068	−	0.861317i	$-0.330360\pi$
$602$		0			0
$603$	−7.36520			−0.299934
$604$	−9.88949	+	0.504799i	−0.402398	+	0.0205400i
$605$	−10.7252	+	6.29471i	−0.436043	+	0.255916i
$606$	−33.0848	−	31.4391i	−1.34398	−	1.27713i
$607$	−38.9423	+	22.4833i	−1.58062	+	0.912570i	−0.585848	+	0.810421i	$0.699239\pi$
$607$	−38.9423	+	22.4833i	−1.58062	+	0.912570i	−0.994769	+	0.102149i	$0.967428\pi$
$608$	−13.4765	+	5.52855i	−0.546546	+	0.224212i
$609$		0			0
$610$	−1.43100	−	1.34051i	−0.0579393	−	0.0542757i
$611$	−9.21257	+	5.31888i	−0.372701	+	0.215179i
$612$	13.0573	−	8.45431i	0.527812	−	0.341745i
$613$	−41.3637	−	23.8813i	−1.67066	−	0.964557i	−0.967268	−	0.253757i	$-0.918334\pi$
$613$	−41.3637	−	23.8813i	−1.67066	−	0.964557i	−0.703394	−	0.710800i	$-0.748333\pi$
$614$	−5.56973	−	18.8502i	−0.224776	−	0.760731i
$615$	−35.2381	−	20.0108i	−1.42094	−	0.806913i
$616$		0			0
$617$		−	14.7647i		−	0.594404i	−0.954815	−	0.297202i	$-0.903946\pi$
$617$		−	14.7647i		−	0.594404i	0.954815	−	0.297202i	$-0.0960535\pi$
$618$	−15.8473	+	4.68246i	−0.637472	+	0.188356i
$619$	−13.0336	+	22.5748i	−0.523863	+	0.907357i	0.475751	+	0.879580i	$0.342176\pi$
$619$	−13.0336	+	22.5748i	−0.523863	+	0.907357i	−0.999614	+	0.0277772i	$0.991157\pi$
$620$	29.4485	−	1.71398i	1.18268	−	0.0688349i
$621$	16.0725	−	9.27944i	0.644965	−	0.372371i
$622$	0.478739	−	1.98813i	0.0191957	−	0.0797168i
$623$		0			0
$624$	−7.56155	+	5.46242i	−0.302704	+	0.218672i
$625$	24.9898	−	0.713619i	0.999593	−	0.0285448i
$626$	−7.34488	−	6.97953i	−0.293560	−	0.278958i
$627$	−6.41273	+	11.1072i	−0.256100	+	0.443578i
$628$	0.396488	+	7.76757i	0.0158216	+	0.309960i
$629$			27.3924i			1.09220i
$630$		0			0
$631$		−	33.9582i		−	1.35186i	−0.736968	−	0.675928i	$-0.763743\pi$
$631$		−	33.9582i		−	1.35186i	0.736968	−	0.675928i	$-0.236257\pi$
$632$	5.54347	−	29.5731i	0.220508	−	1.17635i
$633$	−0.306579	+	0.531010i	−0.0121854	+	0.0211057i
$634$	−23.7796	+	25.0244i	−0.944409	+	0.993845i
$635$	−0.0845386	−	11.8447i	−0.00335481	−	0.470041i
$636$	−32.6631	−	16.6987i	−1.29518	−	0.662147i
$637$		0			0
$638$	1.80054	+	0.433567i	0.0712842	+	0.0171651i
$639$	16.1569	−	9.32819i	0.639157	−	0.369018i
$640$	−22.8079	+	10.9454i	−0.901560	+	0.432655i
$641$	−19.9309	+	34.5213i	−0.787222	+	1.36351i	0.140441	+	0.990089i	$0.455148\pi$
$641$	−19.9309	+	34.5213i	−0.787222	+	1.36351i	−0.927663	+	0.373419i	$0.878185\pi$
$642$	−8.57066	−	29.0065i	−0.338257	−	1.14480i
$643$		−	36.8341i		−	1.45260i	−0.687380	−	0.726298i	$-0.741239\pi$
$643$		−	36.8341i		−	1.45260i	0.687380	−	0.726298i	$-0.258761\pi$
$644$		0			0
$645$	3.12311	−	5.49966i	0.122972	−	0.216549i
$646$	−17.3945	+	5.13962i	−0.684378	+	0.202216i
$647$	−31.6716	−	18.2856i	−1.24514	−	0.718881i	−0.275002	−	0.961444i	$-0.588679\pi$
$647$	−31.6716	−	18.2856i	−1.24514	−	0.718881i	−0.970136	+	0.242563i	$0.922012\pi$
$648$	−10.5569	−	30.0062i	−0.414714	−	1.17875i
$649$	28.9230	−	16.6987i	1.13533	−	0.655481i
$650$	−7.37243	+	2.29328i	−0.289170	+	0.0899497i
$651$		0			0
$652$	20.4810	+	10.4707i	0.802097	+	0.410064i
$653$	14.2885	−	8.24948i	0.559153	−	0.322827i	−0.193652	−	0.981070i	$-0.562033\pi$
$653$	14.2885	−	8.24948i	0.559153	−	0.322827i	0.752806	+	0.658243i	$0.228700\pi$
$654$	9.49090	−	9.98771i	0.371123	−	0.390550i
$655$	4.96581	−	2.91447i	0.194030	−	0.113878i
$656$	30.9691	+	13.8894i	1.20914	+	0.542290i
$657$	15.5554			0.606873
$658$		0			0
$659$		−	42.8381i		−	1.66874i	−0.551207	−	0.834368i	$-0.685833\pi$
$659$		−	42.8381i		−	1.66874i	0.551207	−	0.834368i	$-0.314167\pi$
$660$	−9.99761	+	19.9049i	−0.389156	+	0.774795i
$661$	−1.30941	−	0.755989i	−0.0509302	−	0.0294046i	0.474319	−	0.880353i	$-0.342694\pi$
$661$	−1.30941	−	0.755989i	−0.0509302	−	0.0294046i	−0.525249	+	0.850949i	$0.676028\pi$
$662$	−8.09124	+	8.51478i	−0.314475	+	0.330936i
$663$	−10.0592	+	5.80766i	−0.390666	+	0.225551i
$664$	−8.28954	−	7.10923i	−0.321696	−	0.275892i
$665$		0			0
$666$	−11.8078	−	2.84329i	−0.457542	−	0.110175i
$667$	−1.69614	−	2.93780i	−0.0656748	−	0.113752i
$668$	0.732091	+	1.13069i	0.0283255	+	0.0437476i
$669$	−0.157671	+	0.273094i	−0.00609590	+	0.0105584i
$670$	14.5252	+	3.38816i	0.561159	+	0.130896i
$671$	1.44600			0.0558224
$672$		0			0
$673$			14.0877i			0.543039i	0.962433	+	0.271520i	$0.0875262\pi$
$673$			14.0877i			0.543039i	−0.962433	+	0.271520i	$0.912474\pi$
$674$	12.2572	+	41.4831i	0.472128	+	1.59787i
$675$	−0.219261	−	15.3595i	−0.00843935	−	0.591186i
$676$	−19.8231	+	12.8350i	−0.762428	+	0.493653i
$677$	23.2659	+	40.2976i	0.894179	+	1.54876i	0.834817	+	0.550528i	$0.185573\pi$
$677$	23.2659	+	40.2976i	0.894179	+	1.54876i	0.0593624	+	0.998236i	$0.481093\pi$
$678$	−3.88884	+	16.1498i	−0.149350	+	0.620230i
$679$		0			0
$680$	−29.6401	+	10.6664i	−1.13665	+	0.409040i
$681$	−10.8423	−	18.7795i	−0.415479	−	0.719631i
$682$	−14.9850	+	15.7695i	−0.573807	+	0.603844i
$683$	10.0953	−	17.4856i	0.386287	−	0.669069i	−0.605660	−	0.795724i	$-0.707091\pi$
$683$	10.0953	−	17.4856i	0.386287	−	0.669069i	0.991947	+	0.126655i	$0.0404241\pi$
$684$	−0.409964	−	8.03158i	−0.0156754	−	0.307095i
$685$	−3.41011	+	6.00505i	−0.130293	+	0.229441i
$686$		0			0
$687$	−20.1907			−0.770322
$688$	−2.16773	+	4.83338i	−0.0826440	+	0.184271i
$689$	8.12090	+	4.68860i	0.309381	+	0.178621i
$690$	39.0440	−	11.8401i	1.48638	−	0.450745i
$691$	−18.9066	−	32.7472i	−0.719240	−	1.24576i	−0.961301	−	0.275500i	$-0.911157\pi$
$691$	−18.9066	−	32.7472i	−0.719240	−	1.24576i	0.242061	−	0.970261i	$-0.422177\pi$
$692$	19.6836	+	10.0630i	0.748258	+	0.382539i
$693$		0			0
$694$	0.438447	−	1.82081i	0.0166432	−	0.0691169i
$695$	0.0641715	+	8.99104i	0.00243417	+	0.341049i
$696$	−3.20001	+	1.12584i	−0.121296	+	0.0426749i
$697$	36.6008	+	21.1315i	1.38635	+	0.800412i
$698$	−7.54616	−	25.5392i	−0.285626	−	0.966672i
$699$	−23.4921			−0.888553
$700$		0			0
$701$	−30.6695			−1.15837			−0.579186	−	0.815196i	$-0.696629\pi$
$701$	−30.6695			−1.15837			−0.579186	+	0.815196i	$0.696629\pi$
$702$	1.34428	+	4.54957i	0.0507366	+	0.171713i
$703$	12.2644	+	7.08084i	0.462559	+	0.267059i
$704$	6.75686	−	17.3898i	0.254659	−	0.655403i
$705$	−0.332072	−	46.5264i	−0.0125065	−	1.75229i
$706$	5.35302	−	22.2303i	0.201464	−	0.836650i
$707$		0			0
$708$	−27.8462	+	54.4679i	−1.04652	+	2.04703i
$709$	−15.4039	−	26.6803i	−0.578505	−	1.00200i	−0.995651	−	0.0931605i	$-0.970303\pi$
$709$	−15.4039	−	26.6803i	−0.578505	−	1.00200i	0.417146	−	0.908839i	$-0.363030\pi$
$710$	−36.1549	+	10.9640i	−1.35687	+	0.411472i
$711$	14.3859	+	8.30571i	0.539514	+	0.311489i
$712$	−1.47393	+	7.86305i	−0.0552379	+	0.294680i
$713$	39.8459			1.49224
$714$		0			0
$715$	2.81164	−	4.95118i	0.105150	−	0.185164i
$716$	16.5898	−	0.846811i	0.619991	−	0.0316468i
$717$	−2.49037	+	4.31345i	−0.0930046	+	0.161089i
$718$	−10.0834	+	10.6112i	−0.376309	+	0.396007i
$719$	13.5981	+	23.5525i	0.507122	+	0.878361i	0.999966	+	0.00824342i	$0.00262399\pi$
$719$	13.5981	+	23.5525i	0.507122	+	0.878361i	−0.492844	+	0.870118i	$0.664043\pi$
$720$	−1.52128	−	13.8839i	−0.0566948	−	0.517421i
$721$		0			0
$722$	4.09519	−	17.0067i	0.152407	−	0.632926i
$723$	17.1702	+	29.7397i	0.638567	+	1.10603i
$724$	−3.74849	−	5.78939i	−0.139311	−	0.215161i
$725$	−2.80748	+	0.0400776i	−0.104267	+	0.00148844i
$726$	4.76004	+	16.1099i	0.176662	+	0.597893i
$727$			32.8255i			1.21743i	0.793389	+	0.608715i	$0.208315\pi$
$727$			32.8255i			1.21743i	−0.793389	+	0.608715i	$0.791685\pi$
$728$		0			0
$729$	−2.12311			−0.0786335
$730$	−30.6774	−	7.15582i	−1.13542	−	0.264849i
$731$	−3.29801	+	5.71233i	−0.121981	+	0.211278i
$732$	−2.22327	+	1.43952i	−0.0821746	+	0.0532060i
$733$	−12.2125	−	21.1526i	−0.451078	−	0.781290i	0.547375	−	0.836887i	$-0.315627\pi$
$733$	−12.2125	−	21.1526i	−0.451078	−	0.781290i	−0.998453	+	0.0555970i	$0.982294\pi$
$734$	−32.1431	−	7.74001i	−1.18642	−	0.285689i
$735$		0			0
$736$	−31.6155	+	12.9698i	−1.16536	+	0.478073i
$737$	−9.52568	+	5.49966i	−0.350883	+	0.202582i
$738$	−12.9081	+	13.5837i	−0.475152	+	0.500025i
$739$	−42.9091	−	24.7736i	−1.57844	−	0.911311i	−0.995078	−	0.0990973i	$-0.968404\pi$
$739$	−42.9091	−	24.7736i	−1.57844	−	0.911311i	−0.583360	−	0.812214i	$-0.698262\pi$
$740$	21.9786	+	11.0392i	0.807951	+	0.405809i
$741$			6.00505i			0.220601i
$742$		0			0
$743$	9.43318			0.346070			0.173035	−	0.984916i	$-0.444643\pi$
$743$	9.43318			0.346070			0.173035	+	0.984916i	$0.444643\pi$
$744$	7.34126	−	39.1638i	0.269144	−	1.43581i
$745$	3.85693	−	2.26365i	0.141307	−	0.0829338i
$746$	−11.3748	+	11.9703i	−0.416463	+	0.438263i
$747$	5.22138	−	3.01457i	0.191040	−	0.110297i
$748$	10.5746	−	20.6843i	0.386647	−	0.756293i
$749$		0			0
$750$	7.20097	−	32.9929i	0.262942	−	1.20473i
$751$	−32.5624	+	18.7999i	−1.18822	+	0.686019i	−0.957902	−	0.287096i	$-0.907310\pi$
$751$	−32.5624	+	18.7999i	−1.18822	+	0.686019i	−0.230318	+	0.973115i	$0.573977\pi$
$752$	3.96802	+	38.7673i	0.144699	+	1.41370i
$753$	16.9631	+	9.79366i	0.618170	+	0.356901i
$754$	0.831593	−	0.245714i	0.0302848	−	0.00894838i
$755$	−5.46702	+	9.62719i	−0.198965	+	0.350369i
$756$		0			0
$757$			25.7640i			0.936409i	0.883620	+	0.468204i	$0.155099\pi$
$757$			25.7640i			0.936409i	−0.883620	+	0.468204i	$0.844901\pi$
$758$	9.98520	+	33.7938i	0.362679	+	1.22745i
$759$	−15.0441	+	26.0571i	−0.546065	+	0.945812i
$760$	−2.88620	+	16.0280i	−0.104693	+	0.581397i
$761$	−37.3454	+	21.5614i	−1.35377	+	0.781600i	−0.988775	−	0.149409i	$-0.952263\pi$
$761$	−37.3454	+	21.5614i	−1.35377	+	0.781600i	−0.364996	+	0.931009i	$0.618930\pi$
$762$	−15.5554	−	3.74571i	−0.563512	−	0.135693i
$763$		0			0
$764$	18.1771	−	35.5549i	0.657624	−	1.28633i
$765$	−0.124124	−	17.3910i	−0.00448773	−	0.628773i
$766$	18.1819	−	19.1336i	0.656937	−	0.691325i
$767$	7.81855	−	13.5421i	0.282312	−	0.488978i
$768$	6.92289	+	33.4639i	0.249808	+	1.20752i
$769$		−	14.4903i		−	0.522535i	−0.965266	−	0.261267i	$-0.915860\pi$
$769$		−	14.4903i		−	0.522535i	0.965266	−	0.261267i	$-0.0841404\pi$
$770$		0			0
$771$		−	13.9923i		−	0.503920i
$772$	−10.9850	+	0.560719i	−0.395359	+	0.0201807i
$773$	−7.84490	+	13.5878i	−0.282161	+	0.488718i	−0.971917	−	0.235325i	$-0.924385\pi$
$773$	−7.84490	+	13.5878i	−0.282161	+	0.488718i	0.689756	+	0.724042i	$0.257718\pi$
$774$	−2.12003	−	2.01458i	−0.0762029	−	0.0724124i
$775$	16.0807	−	28.7941i	0.577636	−	1.03431i
$776$	27.5131	−	32.0810i	0.987663	−	1.15164i
$777$		0			0
$778$	3.95003	−	16.4039i	0.141616	−	0.588109i
$779$	18.9224	−	10.9248i	0.677965	−	0.391423i
$780$	0.605982	+	10.4116i	0.0216976	+	0.372796i
$781$	13.9309	−	24.1290i	0.498486	−	0.863403i
$782$	−40.8070	+	12.0574i	−1.45925	+	0.431172i
$783$			1.72521i			0.0616538i
$784$		0			0
$785$	7.56155	+	4.29400i	0.269883	+	0.153259i
$786$	−2.20391	−	7.45890i	−0.0786109	−	0.266050i
$787$	28.4557	+	16.4289i	1.01434	+	0.585628i	0.912459	−	0.409169i	$-0.134181\pi$
$787$	28.4557	+	16.4289i	1.01434	+	0.585628i	0.101878	+	0.994797i	$0.467515\pi$
$788$	17.9343	+	27.6988i	0.638883	+	0.986729i
$789$	43.6199	−	25.1840i	1.55291	−	0.896573i
$790$	−24.5503	−	22.9979i	−0.873460	−	0.818228i
$791$		0			0
$792$	7.81855	+	6.70531i	0.277820	+	0.238263i
$793$	0.586333	−	0.338519i	0.0208213	−	0.0120212i
$794$	−21.5438	−	20.4722i	−0.764562	−	0.726531i
$795$	−35.3720	+	20.7600i	−1.25452	+	0.736283i
$796$	−1.87007	−	36.6365i	−0.0662829	−	1.29854i
$797$	2.04937			0.0725925			0.0362963	−	0.999341i	$-0.488444\pi$
$797$	2.04937			0.0725925			0.0362963	+	0.999341i	$0.488444\pi$
$798$		0			0
$799$			48.5247i			1.71668i
$800$	−3.38670	+	28.0808i	−0.119738	+	0.992806i
$801$	−3.82501	−	2.20837i	−0.135150	−	0.0780289i
$802$	−13.7767	−	13.0914i	−0.486473	−	0.462275i
$803$	20.1183	−	11.6153i	0.709960	−	0.409896i
$804$	9.17104	−	17.9388i	0.323438	−	0.632653i
$805$		0			0
$806$	−2.38447	+	9.90237i	−0.0839894	+	0.348796i
$807$	−1.03399	−	1.79092i	−0.0363981	−	0.0630433i
$808$	40.3162	−	14.1842i	1.41832	−	0.498999i
$809$	13.5270	−	23.4294i	0.475584	−	0.823735i	−0.524025	−	0.851703i	$-0.675570\pi$
$809$	13.5270	−	23.4294i	0.475584	−	0.823735i	0.999609	+	0.0279678i	$0.00890360\pi$
$810$	−34.6339	−	8.07870i	−1.21691	−	0.283857i
$811$	9.17104			0.322039			0.161019	−	0.986951i	$-0.448522\pi$
$811$	9.17104			0.322039			0.161019	+	0.986951i	$0.448522\pi$
$812$		0			0
$813$		−	14.0877i		−	0.494076i
$814$	−17.3945	+	5.13962i	−0.609677	+	0.180144i
$815$	22.1795	−	13.0173i	0.776916	−	0.455976i
$816$	4.33266	+	42.3299i	0.151673	+	1.48184i
$817$	1.70505	+	2.95324i	0.0596522	+	0.103321i
$818$	−41.5510	−	10.0054i	−1.45280	−	0.349830i
$819$		0			0
$820$	31.7054	−	20.8511i	1.10720	−	0.728152i
$821$	17.9654	+	31.1170i	0.626998	+	1.08599i	0.988151	+	0.153486i	$0.0490499\pi$
$821$	17.9654	+	31.1170i	0.626998	+	1.08599i	−0.361153	+	0.932507i	$0.617617\pi$
$822$	6.76206	+	6.42570i	0.235854	+	0.224122i
$823$	−11.4196	+	19.7794i	−0.398064	+	0.689466i	−0.993487	−	0.113946i	$-0.963651\pi$
$823$	−11.4196	+	19.7794i	−0.398064	+	0.689466i	0.595423	+	0.803412i	$0.296984\pi$
$824$	2.85096	−	15.2092i	0.0993180	−	0.529837i
$825$	12.7584	+	21.3873i	0.444191	+	0.744610i
$826$		0			0
$827$	4.71659			0.164012			0.0820059	−	0.996632i	$-0.473867\pi$
$827$	4.71659			0.164012			0.0820059	+	0.996632i	$0.473867\pi$
$828$	−0.961762	−	18.8418i	−0.0334235	−	0.654799i
$829$	37.5809	+	21.6973i	1.30524	+	0.753579i	0.981297	−	0.192498i	$-0.0616589\pi$
$829$	37.5809	+	21.6973i	1.30524	+	0.753579i	0.323940	+	0.946077i	$0.394992\pi$
$830$	−11.6841	+	3.54321i	−0.405560	+	0.122986i
$831$	−20.9171	−	36.2295i	−0.725606	−	1.25679i
$832$	−1.33126	−	8.63312i	−0.0461533	−	0.299300i
$833$		0			0
$834$	11.8078	+	2.84329i	0.408869	+	0.0984550i
$835$	1.50595	−	0.0107484i	0.0521157	−	0.000371964i
$836$	−6.52746	−	10.0814i	−0.225757	−	0.348673i
$837$	−17.5494	−	10.1322i	−0.606598	−	0.350219i
$838$	30.3299	−	8.96170i	1.04773	−	0.309577i
$839$	32.3461			1.11671			0.558356	−	0.829601i	$-0.311432\pi$
$839$	32.3461			1.11671			0.558356	+	0.829601i	$0.311432\pi$
$840$		0			0
$841$	−28.6847			−0.989126
$842$	17.0366	−	5.03387i	0.587120	−	0.173479i
$843$	−31.5437	−	18.2118i	−1.08642	−	0.627246i
$844$	−0.312064	−	0.481970i	−0.0107417	−	0.0165901i
$845$	0.188441	+	26.4023i	0.00648255	+	0.908266i
$846$	−20.9171	−	5.03680i	−0.719144	−	0.173169i
$847$		0			0
$848$	27.8462	−	20.1159i	0.956242	−	0.690784i
$849$	−7.96543	−	13.7965i	−0.273373	−	0.473496i
$850$	−7.75545	+	34.3546i	−0.266010	+	1.17835i
$851$	28.7718	+	16.6114i	0.986286	+	0.569432i
$852$	2.60158	+	50.9674i	0.0891286	+	1.74611i
$853$	−2.93137			−0.100368			−0.0501840	−	0.998740i	$-0.515981\pi$
$853$	−2.93137			−0.100368			−0.0501840	+	0.998740i	$0.515981\pi$
$854$		0			0
$855$	−7.81855	−	4.43994i	−0.267389	−	0.151843i
$856$	27.8385	+	5.21833i	0.951500	+	0.178359i
$857$	−2.79695	+	4.84446i	−0.0955419	+	0.165483i	−0.909835	−	0.414971i	$-0.863792\pi$
$857$	−2.79695	+	4.84446i	−0.0955419	+	0.165483i	0.814293	+	0.580454i	$0.197125\pi$
$858$	−5.57534	−	5.29801i	−0.190339	−	0.180871i
$859$	4.58552	+	7.94235i	0.156456	+	0.270990i	0.933588	−	0.358348i	$-0.116660\pi$
$859$	4.58552	+	7.94235i	0.156456	+	0.270990i	−0.777132	+	0.629337i	$0.783326\pi$
$860$	3.25425	+	4.94829i	0.110969	+	0.168735i
$861$		0			0
$862$	16.0318	+	3.86043i	0.546046	+	0.131487i
$863$	−15.3926	−	26.6607i	−0.523969	−	0.907541i	−0.999611	−	0.0279016i	$-0.991118\pi$
$863$	−15.3926	−	26.6607i	−0.523969	−	0.907541i	0.475642	−	0.879639i	$-0.342216\pi$
$864$	17.2225	+	2.32699i	0.585922	+	0.0791659i
$865$	21.3160	−	12.5105i	0.724766	−	0.425370i
$866$	12.2117	−	3.60823i	0.414969	−	0.122613i
$867$			16.6757i			0.566335i
$868$		0			0
$869$	24.8078			0.841546
$870$	−0.861554	+	3.69353i	−0.0292094	+	0.125223i
$871$	−2.57501	+	4.46005i	−0.0872509	+	0.151123i
$872$	4.28196	+	12.1707i	0.145005	+	0.412153i
$873$	11.6665	+	20.2070i	0.394852	+	0.683904i
$874$	−5.15002	+	21.3873i	−0.174202	+	0.723436i
$875$		0			0
$876$	−19.3693	+	37.8869i	−0.654429	+	1.28008i
$877$	4.76284	−	2.74983i	0.160830	−	0.0928551i	−0.417425	−	0.908711i	$-0.637067\pi$
$877$	4.76284	−	2.74983i	0.160830	−	0.0928551i	0.578255	+	0.815856i	$0.303734\pi$
$878$	32.3279	+	30.7199i	1.09101	+	1.03674i
$879$	26.7522	+	15.4454i	0.902330	+	0.520960i
$880$	−12.3347	−	16.8205i	−0.415803	−	0.567020i
$881$			30.7645i			1.03648i	0.855234	+	0.518241i	$0.173413\pi$
$881$			30.7645i			1.03648i	−0.855234	+	0.518241i	$0.826587\pi$
$882$		0			0
$883$	−48.4902			−1.63183			−0.815913	−	0.578175i	$-0.803765\pi$
$883$	−48.4902			−1.63183			−0.815913	+	0.578175i	$0.803765\pi$
$884$	−0.554478	−	10.8628i	−0.0186491	−	0.365354i
$885$	34.6188	+	58.9852i	1.16370	+	1.98276i
$886$	17.9836	+	17.0891i	0.604171	+	0.574119i
$887$	−27.5169	+	15.8869i	−0.923927	+	0.533429i	−0.884886	−	0.465808i	$-0.845764\pi$
$887$	−27.5169	+	15.8869i	−0.923927	+	0.533429i	−0.0390409	+	0.999238i	$0.512430\pi$
$888$	21.6280	−	25.2188i	0.725788	−	0.846287i
$889$		0			0
$890$	6.52757	+	6.11481i	0.218804	+	0.204969i
$891$	22.7130	−	13.1134i	0.760914	−	0.439314i
$892$	−0.160492	−	0.247873i	−0.00537366	−	0.00829940i
$893$	21.7260	+	12.5435i	0.727031	+	0.419752i
$894$	−1.71177	−	5.79330i	−0.0572501	−	0.193757i
$895$	9.17104	−	16.1498i	0.306554	−	0.539829i
$896$		0			0
$897$			14.0877i			0.470373i
$898$	8.56517	−	2.53079i	0.285824	−	0.0844534i
$899$	−1.85201	+	3.20777i	−0.0617680	+	0.106985i
$900$	−14.0039	−	6.90903i	−0.466798	−	0.230301i
$901$	37.0439	−	21.3873i	1.23411	−	0.712514i
$902$	−6.55137	+	27.2069i	−0.218137	+	0.905891i
$903$		0			0
$904$	−11.8078	−	10.1265i	−0.392720	−	0.336803i
$905$	−7.71085	+	0.0550345i	−0.256317	+	0.00182941i
$906$	10.8408	+	10.3016i	0.360162	+	0.342247i
$907$	26.8937	−	46.5813i	0.892991	−	1.54671i	0.0567196	−	0.998390i	$-0.481936\pi$
$907$	26.8937	−	46.5813i	0.892991	−	1.54671i	0.836271	−	0.548316i	$-0.184731\pi$
$908$	20.2797	−	1.03516i	0.673005	−	0.0343529i
$909$			23.5957i			0.782619i
$910$		0			0
$911$			56.0950i			1.85851i	0.369438	+	0.929255i	$0.379550\pi$
$911$			56.0950i			1.85851i	−0.369438	+	0.929255i	$0.620450\pi$
$912$	20.0723	+	9.00228i	0.664661	+	0.298095i
$913$	4.50200	−	7.79769i	0.148994	−	0.258066i
$914$	−10.0557	+	10.5821i	−0.332614	+	0.350025i
$915$	0.0211347	+	2.96116i	0.000698690	+	0.0978931i
$916$	8.60654	−	16.8346i	0.284368	−	0.556232i
$917$		0			0
$918$	21.0387	+	5.06609i	0.694382	+	0.167206i
$919$	−33.9452	+	19.5983i	−1.11975	+	0.646487i	−0.941337	−	0.337469i	$-0.890429\pi$
$919$	−33.9452	+	19.5983i	−1.11975	+	0.646487i	−0.178411	+	0.983956i	$0.557096\pi$
$920$	−6.77092	+	37.6012i	−0.223231	+	1.23968i
$921$	−14.8423	+	25.7077i	−0.489071	+	0.847096i
$922$	8.46172	+	28.6378i	0.278672	+	0.943135i
$923$		−	13.0452i		−	0.429389i
$924$		0			0
$925$	23.6155	−	14.0877i	0.776474	−	0.463199i
$926$	32.9929	−	9.74855i	1.08422	−	0.320357i
$927$	7.39856	+	4.27156i	0.243000	+	0.140296i
$928$	0.425339	−	3.14802i	0.0139624	−	0.103339i
$929$	−25.0980	+	14.4903i	−0.823438	+	0.475412i	−0.851601	−	0.524191i	$-0.824368\pi$
$929$	−25.0980	+	14.4903i	−0.823438	+	0.475412i	0.0281624	+	0.999603i	$0.491034\pi$
$930$	−32.5121	−	30.4563i	−1.06611	−	0.998700i
$931$		0			0
$932$	10.0138	−	19.5873i	0.328013	−	0.641604i
$933$	−2.67459	+	1.54417i	−0.0875620	+	0.0505540i
$934$	22.5992	−	23.7822i	0.739470	−	0.778178i
$935$	−13.1465	−	22.3997i	−0.429937	−	0.732549i
$936$	4.74006	+	0.888525i	0.154934	+	0.0290423i
$937$	49.4631			1.61589			0.807944	−	0.589259i	$-0.200580\pi$
$937$	49.4631			1.61589			0.807944	+	0.589259i	$0.200580\pi$
$938$		0			0
$939$			15.3019i			0.499357i
$940$	38.9345	+	19.5556i	1.26990	+	0.637834i
$941$	7.58391	+	4.37857i	0.247228	+	0.142737i	0.618494	−	0.785789i	$-0.287743\pi$
$941$	7.58391	+	4.37857i	0.247228	+	0.142737i	−0.371266	+	0.928527i	$0.621076\pi$
$942$	8.09124	−	8.51478i	0.263627	−	0.277427i
$943$	44.3913	−	25.6294i	1.44558	−	0.834606i
$944$	−33.5446	−	46.4354i	−1.09179	−	1.51134i
$945$		0			0
$946$	−4.24621	−	1.02248i	−0.138056	−	0.0332437i
$947$	−26.3131	−	45.5756i	−0.855060	−	1.48101i	−0.876589	−	0.481239i	$-0.840187\pi$
$947$	−26.3131	−	45.5756i	−0.855060	−	1.48101i	0.0215294	−	0.999768i	$-0.493146\pi$
$948$	−38.1427	+	24.6964i	−1.23882	+	0.802103i
$949$	5.43845	−	9.41967i	0.176539	−	0.305775i
$950$	13.3768	+	12.3529i	0.434002	+	0.400781i
$951$	52.1342			1.69057
$952$		0			0
$953$		−	31.2637i		−	1.01273i	−0.862319	−	0.506365i	$-0.830989\pi$
$953$		−	31.2637i		−	1.01273i	0.862319	−	0.506365i	$-0.169011\pi$
$954$	5.37412	+	18.1881i	0.173994	+	0.588863i
$955$	−22.5980	−	38.5036i	−0.731254	−	1.24595i
$956$	−2.53493	−	3.91509i	−0.0819854	−	0.126623i
$957$	−1.39847	−	2.42223i	−0.0452062	−	0.0782995i
$958$	−9.96148	+	41.3686i	−0.321841	+	1.33656i
$959$		0			0
$960$	35.7100	+	13.5827i	1.15254	+	0.438380i
$961$	−6.25379	−	10.8319i	−0.201735	−	0.349415i
$962$	−5.84999	+	6.15621i	−0.188611	+	0.198484i
$963$	−7.81855	+	13.5421i	−0.251949	+	0.436389i
$964$	−32.1155	+	1.63930i	−1.03437	+	0.0527984i
$965$	−6.07263	+	10.6937i	−0.195485	+	0.344241i
$966$		0			0
$967$	16.2177			0.521527			0.260764	−	0.965403i	$-0.416026\pi$
$967$	16.2177			0.521527			0.260764	+	0.965403i	$0.416026\pi$
$968$	−15.4612	−	2.89820i	−0.496940	−	0.0931516i
$969$	23.7225	+	13.6962i	0.762076	+	0.439985i
$970$	−13.7124	−	45.2180i	−0.440278	−	1.45186i
$971$	18.1836	+	31.4949i	0.583539	+	1.01072i	0.995056	+	0.0993168i	$0.0316657\pi$
$971$	18.1836	+	31.4949i	0.583539	+	1.01072i	−0.411517	+	0.911402i	$0.635001\pi$
$972$	−13.4765	+	26.3605i	−0.432260	+	0.845513i
$973$		0			0
$974$	0.384472	−	1.59666i	0.0123193	−	0.0511602i
$975$	10.1803	+	5.68539i	0.326029	+	0.182078i
$976$	−0.252544	−	2.46734i	−0.00808373	−	0.0789777i
$977$	−12.2003	−	7.04383i	−0.390321	−	0.225352i	0.291978	−	0.956425i	$-0.405687\pi$
$977$	−12.2003	−	7.04383i	−0.390321	−	0.225352i	−0.682299	+	0.731073i	$0.739020\pi$
$978$	−9.84365	−	33.3148i	−0.314765	−	1.06529i
$979$	−6.59603			−0.210810
$980$		0			0
$981$	−7.12311			−0.227423
$982$	5.72226	+	19.3664i	0.182605	+	0.618006i
$983$	38.7426	+	22.3680i	1.23570	+	0.713430i	0.968212	−	0.250132i	$-0.0804741\pi$
$983$	38.7426	+	22.3680i	1.23570	+	0.713430i	0.267485	+	0.963562i	$0.413807\pi$
$984$	−17.0119	−	48.3534i	−0.542319	−	1.54145i
$985$	36.8919	−	0.263308i	1.17547	−	0.00838968i
$986$	0.926004	−	3.84556i	0.0294900	−	0.122468i
$987$		0			0
$988$	−5.00691	−	2.55973i	−0.159291	−	0.0814359i
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$	11.0202	−	3.34189i	0.350246	−	0.106212i
$991$	0.497251	+	0.287088i	0.0157957	+	0.00911966i	0.507877	−	0.861430i	$-0.330430\pi$
$991$	0.497251	+	0.287088i	0.0157957	+	0.00911966i	−0.492081	+	0.870549i	$0.663764\pi$
$992$	29.5248	+	22.8151i	0.937413	+	0.724380i
$993$	17.7392			0.562935
$994$		0			0
$995$	−35.6647	−	20.2530i	−1.13065	−	0.642065i
$996$	0.840744	+	16.4710i	0.0266400	+	0.521903i
$997$	−23.8790	+	41.3597i	−0.756256	+	1.30987i	0.188492	+	0.982075i	$0.439640\pi$
$997$	−23.8790	+	41.3597i	−0.756256	+	1.30987i	−0.944748	+	0.327799i	$0.893693\pi$
$998$	24.9901	−	26.2983i	0.791048	−	0.832457i
$999$	−8.44804	−	14.6324i	−0.267284	−	0.462950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.s.f.619.15		32
4.3	odd	2	inner	980.2.s.f.619.12		32
5.4	even	2	inner	980.2.s.f.619.2		32
7.2	even	3	inner	980.2.s.f.19.6		32
7.3	odd	6		140.2.c.b.139.7	yes	16
7.4	even	3		140.2.c.b.139.8	yes	16
7.5	odd	6	inner	980.2.s.f.19.5		32
7.6	odd	2	inner	980.2.s.f.619.16		32
20.19	odd	2	inner	980.2.s.f.619.5		32
28.3	even	6		140.2.c.b.139.12	yes	16
28.11	odd	6		140.2.c.b.139.11	yes	16
28.19	even	6	inner	980.2.s.f.19.2		32
28.23	odd	6	inner	980.2.s.f.19.1		32
28.27	even	2	inner	980.2.s.f.619.11		32
35.3	even	12		700.2.g.l.251.16		16
35.4	even	6		140.2.c.b.139.9	yes	16
35.9	even	6	inner	980.2.s.f.19.11		32
35.17	even	12		700.2.g.l.251.1		16
35.18	odd	12		700.2.g.l.251.15		16
35.19	odd	6	inner	980.2.s.f.19.12		32
35.24	odd	6		140.2.c.b.139.10	yes	16
35.32	odd	12		700.2.g.l.251.2		16
35.34	odd	2	inner	980.2.s.f.619.1		32
56.3	even	6		2240.2.e.f.2239.4		16
56.11	odd	6		2240.2.e.f.2239.13		16
56.45	odd	6		2240.2.e.f.2239.16		16
56.53	even	6		2240.2.e.f.2239.1		16
140.3	odd	12		700.2.g.l.251.13		16
140.19	even	6	inner	980.2.s.f.19.15		32
140.39	odd	6		140.2.c.b.139.6	yes	16
140.59	even	6		140.2.c.b.139.5	✓	16
140.67	even	12		700.2.g.l.251.3		16
140.79	odd	6	inner	980.2.s.f.19.16		32
140.87	odd	12		700.2.g.l.251.4		16
140.123	even	12		700.2.g.l.251.14		16
140.139	even	2	inner	980.2.s.f.619.6		32
280.59	even	6		2240.2.e.f.2239.14		16
280.109	even	6		2240.2.e.f.2239.15		16
280.179	odd	6		2240.2.e.f.2239.3		16
280.269	odd	6		2240.2.e.f.2239.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.5	✓	16	140.59	even	6
140.2.c.b.139.6	yes	16	140.39	odd	6
140.2.c.b.139.7	yes	16	7.3	odd	6
140.2.c.b.139.8	yes	16	7.4	even	3
140.2.c.b.139.9	yes	16	35.4	even	6
140.2.c.b.139.10	yes	16	35.24	odd	6
140.2.c.b.139.11	yes	16	28.11	odd	6
140.2.c.b.139.12	yes	16	28.3	even	6
700.2.g.l.251.1		16	35.17	even	12
700.2.g.l.251.2		16	35.32	odd	12
700.2.g.l.251.3		16	140.67	even	12
700.2.g.l.251.4		16	140.87	odd	12
700.2.g.l.251.13		16	140.3	odd	12
700.2.g.l.251.14		16	140.123	even	12
700.2.g.l.251.15		16	35.18	odd	12
700.2.g.l.251.16		16	35.3	even	12
980.2.s.f.19.1		32	28.23	odd	6	inner
980.2.s.f.19.2		32	28.19	even	6	inner
980.2.s.f.19.5		32	7.5	odd	6	inner
980.2.s.f.19.6		32	7.2	even	3	inner
980.2.s.f.19.11		32	35.9	even	6	inner
980.2.s.f.19.12		32	35.19	odd	6	inner
980.2.s.f.19.15		32	140.19	even	6	inner
980.2.s.f.19.16		32	140.79	odd	6	inner
980.2.s.f.619.1		32	35.34	odd	2	inner
980.2.s.f.619.2		32	5.4	even	2	inner
980.2.s.f.619.5		32	20.19	odd	2	inner
980.2.s.f.619.6		32	140.139	even	2	inner
980.2.s.f.619.11		32	28.27	even	2	inner
980.2.s.f.619.12		32	4.3	odd	2	inner
980.2.s.f.619.15		32	1.1	even	1	trivial
980.2.s.f.619.16		32	7.6	odd	2	inner
2240.2.e.f.2239.1		16	56.53	even	6
2240.2.e.f.2239.2		16	280.269	odd	6
2240.2.e.f.2239.3		16	280.179	odd	6
2240.2.e.f.2239.4		16	56.3	even	6
2240.2.e.f.2239.13		16	56.11	odd	6
2240.2.e.f.2239.14		16	280.59	even	6
2240.2.e.f.2239.15		16	280.109	even	6
2240.2.e.f.2239.16		16	56.45	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35625 - 0.400736i) q^{2} +(-1.84964 - 1.06789i) q^{3} +(1.67882 - 1.08700i) q^{4} +(-0.0159590 - 2.23601i) q^{5} +(-2.93651 - 0.707107i) q^{6} +(1.84130 - 2.14700i) q^{8} +(0.780776 + 1.35234i) q^{9} +(-0.917695 - 3.02619i) q^{10} +(2.01961 + 1.16602i) q^{11} +(-4.26600 + 0.217754i) q^{12} +1.09190 q^{13} +(-2.35829 + 4.15286i) q^{15} +(1.63688 - 3.64974i) q^{16} +(2.49037 - 4.31345i) q^{17} +(1.60086 + 1.52123i) q^{18} +(-1.28751 - 2.23003i) q^{19} +(-2.45733 - 3.73652i) q^{20} +(3.20636 + 0.772087i) q^{22} +(-3.02045 - 5.23157i) q^{23} +(-5.69850 + 2.00487i) q^{24} +(-4.99949 + 0.0713692i) q^{25} +(1.48088 - 0.437562i) q^{26} +3.07221i q^{27} +0.561553 q^{29} +(-1.53423 + 6.57736i) q^{30} +(-3.29801 + 5.71233i) q^{31} +(0.757434 - 5.60592i) q^{32} +(-2.49037 - 4.31345i) q^{33} +(1.64901 - 6.84809i) q^{34} +(2.78078 + 1.42164i) q^{36} +(-4.76284 + 2.74983i) q^{37} +(-2.63983 - 2.50852i) q^{38} +(-2.01961 - 1.16602i) q^{39} +(-4.83010 - 4.08290i) q^{40} +8.48528i q^{41} -1.32431 q^{43} +(4.65803 - 0.237764i) q^{44} +(3.01140 - 1.76741i) q^{45} +(-6.19296 - 5.88491i) q^{46} +(-8.43723 + 4.87123i) q^{47} +(-6.92516 + 5.00270i) q^{48} +(-6.75195 + 2.10027i) q^{50} +(-9.21257 + 5.31888i) q^{51} +(1.83310 - 1.18689i) q^{52} +(7.43743 + 4.29400i) q^{53} +(1.23114 + 4.16667i) q^{54} +(2.57501 - 4.53448i) q^{55} +5.49966i q^{57} +(0.761605 - 0.225034i) q^{58} +(7.16053 - 12.4024i) q^{59} +(0.554981 + 9.53536i) q^{60} +(0.536986 - 0.310029i) q^{61} +(-2.18379 + 9.06897i) q^{62} +(-1.21922 - 7.90655i) q^{64} +(-0.0174256 - 2.44149i) q^{65} +(-5.10611 - 4.85213i) q^{66} +(-2.35829 + 4.08469i) q^{67} +(-0.507812 - 9.94853i) q^{68} +12.9020i q^{69} -11.9473i q^{71} +(4.34113 + 0.813745i) q^{72} +(4.98074 - 8.62689i) q^{73} +(-5.35764 + 5.63809i) q^{74} +(9.32347 + 5.20690i) q^{75} +(-4.58552 - 2.34430i) q^{76} +(-3.20636 - 0.772087i) q^{78} +(9.21257 - 5.31888i) q^{79} +(-8.18699 - 3.60184i) q^{80} +(5.62311 - 9.73950i) q^{81} +(3.40036 + 11.5082i) q^{82} -3.86098i q^{83} +(-9.68466 - 5.49966i) q^{85} +(-1.79609 + 0.530698i) q^{86} +(-1.03867 - 0.599676i) q^{87} +(6.22217 - 2.18911i) q^{88} +(-2.44949 + 1.41421i) q^{89} +(3.37594 - 3.60382i) q^{90} +(-10.7575 - 5.49966i) q^{92} +(12.2003 - 7.04383i) q^{93} +(-9.49090 + 9.98771i) q^{94} +(-4.96581 + 2.91447i) q^{95} +(-7.38748 + 9.56006i) q^{96} +14.9422 q^{97} +3.64162i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 8 q^{9} + 12 q^{16} - 8 q^{25} - 48 q^{29} + 4 q^{30} + 56 q^{36} - 32 q^{44} + 32 q^{46} - 24 q^{50} - 44 q^{60} - 72 q^{64} + 32 q^{65} - 88 q^{74} + 48 q^{81} - 112 q^{85} - 40 q^{86}+O(q^{100}) \) 32 * q + 12 * q^4 - 8 * q^9 + 12 * q^16 - 8 * q^25 - 48 * q^29 + 4 * q^30 + 56 * q^36 - 32 * q^44 + 32 * q^46 - 24 * q^50 - 44 * q^60 - 72 * q^64 + 32 * q^65 - 88 * q^74 + 48 * q^81 - 112 * q^85 - 40 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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