LMFDB - Embedded newform 980.2.s.f.19.1

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			19.1
Character	$\chi$	$=$	980.19
Dual form			980.2.s.f.619.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35625 - 0.400736i) q^{2} +(-1.84964 + 1.06789i) q^{3} +(1.67882 + 1.08700i) q^{4} +(-1.92846 + 1.13183i) q^{5} +(2.93651 - 0.707107i) q^{6} +(-1.84130 - 2.14700i) q^{8} +(0.780776 - 1.35234i) q^{9} +(3.06904 - 0.762234i) 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} +(-4.46783 - 0.196096i) q^{20} +(-3.20636 + 0.772087i) q^{22} +(3.02045 - 5.23157i) q^{23} +(5.69850 + 2.00487i) q^{24} +(2.43794 - 4.36537i) q^{25} +(-1.48088 - 0.437562i) q^{26} -3.07221i q^{27} +0.561553 q^{29} +(-4.86263 + 4.68725i) 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} +(5.98091 + 2.05638i) q^{40} +8.48528i q^{41} +1.32431 q^{43} +(4.65803 + 0.237764i) q^{44} +(0.0249209 + 3.49165i) q^{45} +(-6.19296 + 5.88491i) q^{46} +(-8.43723 - 4.87123i) q^{47} +(-6.92516 - 5.00270i) q^{48} +(-5.05581 + 4.94356i) 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} +(8.47329 - 4.40845i) q^{60} +(-0.536986 - 0.310029i) q^{61} +(-2.18379 - 9.06897i) q^{62} +(-1.21922 + 7.90655i) q^{64} +(-2.10568 + 1.23584i) 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} +(0.152429 + 10.6778i) q^{75} +(4.58552 - 2.34430i) q^{76} +(3.20636 - 0.772087i) q^{78} +(9.21257 + 5.31888i) q^{79} +(-7.28754 - 5.18573i) 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} +(1.36543 - 4.74553i) q^{90} +(10.7575 - 5.49966i) q^{92} +(-12.2003 - 7.04383i) q^{93} +(9.49090 + 9.98771i) q^{94} +(0.0410947 + 5.75775i) 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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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	−0.927604	−	0.373565i	$-0.878135\pi$
$3$	−1.84964	+	1.06789i	−1.06789	+	0.616546i	−0.140285	+	0.990111i	$0.544802\pi$
$4$	1.67882	+	1.08700i	0.839411	+	0.543498i
$5$	−1.92846	+	1.13183i	−0.862435	+	0.506168i
$5$	−1.92846	+	1.13183i	−0.862435	+	0.506168i
$6$	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
$10$	3.06904	−	0.762234i	0.970515	−	0.241039i
$11$	2.01961	−	1.16602i	0.608936	−	0.351569i	−0.163613	−	0.986525i	$-0.552315\pi$
$11$	2.01961	−	1.16602i	0.608936	−	0.351569i	0.772549	+	0.634955i	$0.218981\pi$
$12$	−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	0.992208	+	0.124591i	$0.0397620\pi$
$17$	2.49037	+	4.31345i	0.604003	+	1.04616i	−0.388205	+	0.921573i	$0.626905\pi$
$18$	−1.60086	+	1.52123i	−0.377326	+	0.358557i
$19$	1.28751	−	2.23003i	0.295374	−	0.511603i	−0.679698	−	0.733492i	$-0.737889\pi$
$19$	1.28751	−	2.23003i	0.295374	−	0.511603i	0.975072	+	0.221889i	$0.0712224\pi$
$20$	−4.46783	−	0.196096i	−0.999038	−	0.0438485i
$21$		0			0
$22$	−3.20636	+	0.772087i	−0.683599	+	0.164609i
$23$	3.02045	−	5.23157i	0.629807	−	1.09086i	−0.357783	−	0.933805i	$-0.616467\pi$
$23$	3.02045	−	5.23157i	0.629807	−	1.09086i	0.987590	−	0.157053i	$-0.0501993\pi$
$24$	5.69850	+	2.00487i	1.16320	+	0.409242i
$25$	2.43794	−	4.36537i	0.487588	−	0.873074i
$26$	−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	$0.483396\pi$
$30$	−4.86263	+	4.68725i	−0.887791	+	0.855771i
$31$	3.29801	+	5.71233i	0.592341	+	1.02596i	0.993916	+	0.110138i	$0.0351294\pi$
$31$	3.29801	+	5.71233i	0.592341	+	1.02596i	−0.401576	+	0.915826i	$0.631537\pi$
$32$	−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	$-0.184019\pi$
$37$	4.76284	+	2.74983i	0.783006	+	0.452069i	−0.0544884	+	0.998514i	$0.517353\pi$
$38$	−2.63983	+	2.50852i	−0.428237	+	0.406935i
$39$	−2.01961	+	1.16602i	−0.323397	+	0.186713i
$40$	5.98091	+	2.05638i	0.945665	+	0.325142i
$41$			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	$-0.467803\pi$
$43$	1.32431			0.201955			0.100977	+	0.994889i	$0.467803\pi$
$44$	4.65803	+	0.237764i	0.702225	+	0.0358443i
$45$	0.0249209	+	3.49165i	0.00371498	+	0.520504i
$46$	−6.19296	+	5.88491i	−0.913102	+	0.867682i
$47$	−8.43723	−	4.87123i	−1.23070	−	0.710543i	−0.263521	−	0.964654i	$-0.584884\pi$
$47$	−8.43723	−	4.87123i	−1.23070	−	0.710543i	−0.967175	+	0.254111i	$0.918217\pi$
$48$	−6.92516	−	5.00270i	−0.999561	−	0.722077i
$49$		0			0
$50$	−5.05581	+	4.94356i	−0.715000	+	0.699125i
$51$	−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	$-0.867471\pi$
$53$	−7.43743	+	4.29400i	−1.02161	+	0.589826i	−0.107040	+	0.994255i	$0.534137\pi$
$54$	−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	−0.779515	−	0.626384i	$-0.784534\pi$
$59$	−7.16053	−	12.4024i	−0.932222	−	1.61466i	−0.152707	−	0.988272i	$-0.548799\pi$
$60$	8.47329	−	4.40845i	1.09390	−	0.569128i
$61$	−0.536986	−	0.310029i	−0.0687540	−	0.0396951i	0.465229	−	0.885190i	$-0.345972\pi$
$61$	−0.536986	−	0.310029i	−0.0687540	−	0.0396951i	−0.533983	+	0.845495i	$0.679305\pi$
$62$	−2.18379	−	9.06897i	−0.277342	−	1.15176i
$63$		0			0
$64$	−1.21922	+	7.90655i	−0.152403	+	0.988318i
$65$	−2.10568	+	1.23584i	−0.261177	+	0.153287i
$66$	5.10611	−	4.85213i	0.628519	−	0.597255i
$67$	2.35829	+	4.08469i	0.288112	+	0.499024i	0.973359	−	0.229287i	$-0.0736393\pi$
$67$	2.35829	+	4.08469i	0.288112	+	0.499024i	−0.685247	+	0.728310i	$0.740306\pi$
$68$	−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	$0.250828\pi$
$71$			11.9473i			1.41789i	−0.705265	+	0.708943i	$0.749172\pi$
$72$	−4.34113	+	0.813745i	−0.511607	+	0.0959008i
$73$	4.98074	+	8.62689i	0.582951	+	1.00970i	0.995127	+	0.0985973i	$0.0314356\pi$
$73$	4.98074	+	8.62689i	0.582951	+	1.00970i	−0.412176	+	0.911104i	$0.635231\pi$
$74$	−5.35764	−	5.63809i	−0.622813	−	0.655415i
$75$	0.152429	+	10.6778i	0.0176010	+	1.23297i
$76$	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	0.918839	−	0.394634i	$-0.129128\pi$
$79$	9.21257	+	5.31888i	1.03650	+	0.598421i	0.117657	+	0.993054i	$0.462462\pi$
$80$	−7.28754	−	5.18573i	−0.814772	−	0.579782i
$81$	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	$0.0679648\pi$
$83$			3.86098i			0.423798i	−0.977292	+	0.211899i	$0.932035\pi$
$84$		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	$-0.285436\pi$
$89$	2.44949	+	1.41421i	0.259645	+	0.149906i	−0.364527	+	0.931193i	$0.618769\pi$
$90$	1.36543	−	4.74553i	0.143929	−	0.500223i
$91$		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
$95$	0.0410947	+	5.75775i	0.00421623	+	0.590733i
$96$	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
$100$	8.83800	−	4.67865i	0.883800	−	0.467865i
$101$	−13.0860	+	7.55519i	−1.30210	+	0.751770i	−0.980765	−	0.195194i	$-0.937466\pi$
$101$	−13.0860	+	7.55519i	−1.30210	+	0.751770i	−0.321339	+	0.946964i	$0.604133\pi$
$102$	10.3631	+	10.9055i	1.02610	+	1.07981i
$103$	4.73795	+	2.73546i	0.466844	+	0.269532i	0.714918	−	0.699209i	$-0.246464\pi$
$103$	4.73795	+	2.73546i	0.466844	+	0.269532i	−0.248074	+	0.968741i	$0.579798\pi$
$104$	−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	$-0.994163\pi$
$107$	−5.00691	+	8.67222i	−0.484036	+	0.838375i	0.515796	+	0.856712i	$0.327496\pi$
$108$	3.33947	−	5.15768i	0.321341	−	0.496298i
$109$	−2.28078	−	3.95042i	−0.218459	−	0.378382i	0.735878	−	0.677114i	$-0.236770\pi$
$109$	−2.28078	−	3.95042i	−0.218459	−	0.378382i	−0.954337	+	0.298732i	$0.903436\pi$
$110$	5.30949	−	5.11799i	0.506240	−	0.487981i
$111$	−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
$115$	0.0964069	+	13.5075i	0.00898999	+	1.25958i
$116$	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
$120$	−13.2585	+	2.58340i	−1.21033	+	0.235831i
$121$	−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	$-0.575518\pi$
$127$	−5.29723			−0.470053			−0.235026	+	0.971989i	$0.575518\pi$
$128$	4.82201	−	10.2347i	0.426209	−	0.904625i
$129$	−2.44949	+	1.41421i	−0.215666	+	0.124515i
$130$	3.35107	−	0.832279i	0.293908	−	0.0729957i
$131$	−1.28751	+	2.23003i	−0.112490	+	0.194838i	−0.916774	−	0.399407i	$-0.869216\pi$
$131$	−1.28751	+	2.23003i	−0.112490	+	0.194838i	0.804284	+	0.594246i	$0.202549\pi$
$132$	−8.86958	+	4.53448i	−0.771998	+	0.394676i
$133$		0			0
$134$	−1.56155	−	6.48490i	−0.134898	−	0.560210i
$135$	3.47720	+	5.92463i	0.299270	+	0.509911i
$136$	4.67545	−	13.2892i	0.400917	−	1.13954i
$137$	2.67459	−	1.54417i	0.228505	−	0.131928i	−0.381377	−	0.924420i	$-0.624550\pi$
$137$	2.67459	−	1.54417i	0.228505	−	0.131928i	0.609882	+	0.792492i	$0.291217\pi$
$138$	5.17030	−	17.4983i	0.440126	−	1.48956i
$139$	4.02102			0.341058			0.170529	−	0.985353i	$-0.445452\pi$
$139$	4.02102			0.341058			0.170529	+	0.985353i	$0.445452\pi$
$140$		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
$145$	−1.08293	+	0.635580i	−0.0899328	+	0.0527821i
$146$	−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	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$	4.07225	−	14.5428i	0.332498	−	1.18742i
$151$	−4.28785	+	2.47559i	−0.348940	+	0.201461i	−0.664218	−	0.747539i	$-0.731236\pi$
$151$	−4.28785	+	2.47559i	−0.348940	+	0.201461i	0.315278	+	0.948999i	$0.397902\pi$
$152$	−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	0.777943	−	0.628334i	$-0.216263\pi$
$157$	−1.94442	−	3.36784i	−0.155182	−	0.268783i	−0.933125	+	0.359552i	$0.882930\pi$
$158$	−10.3631	−	10.9055i	−0.824442	−	0.867598i
$159$	9.17104	−	15.8847i	0.727311	−	1.25974i
$160$	7.80561	+	9.95352i	0.617087	+	0.786895i
$161$		0			0
$162$	−3.72336	−	15.4626i	−0.292535	−	1.21485i
$163$	−5.75058	+	9.96029i	−0.450420	+	0.780150i	−0.998412	−	0.0563333i	$-0.982059\pi$
$163$	−5.75058	+	9.96029i	−0.450420	+	0.780150i	0.547992	+	0.836484i	$0.315392\pi$
$164$	−9.22346	+	14.2453i	−0.720232	+	1.11237i
$165$	−0.0794878	−	11.1370i	−0.00618812	−	0.867013i
$166$	1.54724	−	5.23646i	0.120089	−	0.406428i
$167$		−	0.673500i		−	0.0521170i	−0.999660	−	0.0260585i	$-0.991704\pi$
$167$		−	0.673500i		−	0.0521170i	0.999660	−	0.0260585i	$-0.00829562\pi$
$168$		0			0
$169$	−11.8078			−0.908290
$170$	10.9309	+	11.3399i	0.838361	+	0.869730i
$171$	−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	−0.575771	−	0.817611i	$-0.695298\pi$
$173$	5.52669	−	9.57250i	0.420186	−	0.727784i	0.995957	+	0.0898270i	$0.0286314\pi$
$174$	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	−0.206490	−	0.978449i	$-0.566204\pi$
$179$	7.19296	−	4.15286i	0.537627	−	0.310399i	0.744117	+	0.668050i	$0.232871\pi$
$180$	−3.75357	+	5.88894i	−0.279775	+	0.438936i
$181$		−	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
$185$	−12.2973	+	0.0877692i	−0.904115	+	0.00645292i
$186$	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
$190$	2.25161	−	7.82541i	0.163349	−	0.567715i
$191$	17.2910	+	9.98298i	1.25113	+	0.722343i	0.971335	−	0.237716i	$-0.0763987\pi$
$191$	17.2910	+	9.98298i	1.25113	+	0.722343i	0.279800	+	0.960058i	$0.409732\pi$
$192$	−6.18820	−	15.9263i	−0.446595	−	1.14938i
$193$	4.76284	−	2.74983i	0.342837	−	0.197937i	−0.318689	−	0.947859i	$-0.603243\pi$
$193$	4.76284	−	2.74983i	0.342837	−	0.197937i	0.661526	+	0.749922i	$0.269909\pi$
$194$	−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	−0.983094	−	0.183102i	$-0.941386\pi$
$199$	−9.17104	−	15.8847i	−0.650118	−	1.12604i	0.332976	−	0.942935i	$-0.391947\pi$
$200$	−13.8614	+	2.80371i	−0.980151	+	0.198252i
$201$	−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
$205$	−9.60387	−	16.3635i	−0.670763	−	1.14288i
$206$	−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	$0.00314558\pi$
$211$			0.287088i			0.0197640i	−0.999951	+	0.00988198i	$0.996854\pi$
$212$	−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
$215$	−2.55388	+	1.49889i	−0.174173	+	0.102223i
$216$	−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
$220$	−9.25195	+	4.81356i	−0.623766	+	0.324530i
$221$	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	$0.00157360\pi$
$223$			0.147647i			0.00988718i	−0.999988	+	0.00494359i	$0.998426\pi$
$224$		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	−0.178964	−	0.983856i	$-0.557275\pi$
$227$	8.79279	−	5.07652i	0.583598	−	0.336941i	0.762562	+	0.646915i	$0.223941\pi$
$228$	−5.97810	+	9.23294i	−0.395909	+	0.611466i
$229$	−8.18700	−	4.72677i	−0.541012	−	0.312354i	0.204477	−	0.978871i	$-0.434451\pi$
$229$	−8.18700	−	4.72677i	−0.541012	−	0.312354i	−0.745489	+	0.666518i	$0.767784\pi$
$230$	5.28219	−	18.3582i	0.348298	−	1.21050i
$231$		0			0
$232$	−1.03399	−	1.20565i	−0.0678846	−	0.0791551i
$233$	−9.52568	−	5.49966i	−0.624048	−	0.360294i	0.154395	−	0.988009i	$-0.450657\pi$
$233$	−9.52568	−	5.49966i	−0.624048	−	0.360294i	−0.778443	+	0.627715i	$0.783990\pi$
$234$	−1.74797	+	1.66102i	−0.114269	+	0.108585i
$235$	21.7843	−	0.155480i	1.42105	−	0.0101424i
$236$	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	$0.0240310\pi$
$239$			2.33205i			0.150848i	−0.997152	+	0.0754238i	$0.975969\pi$
$240$	19.0171	+	1.80944i	1.22755	+	0.116799i
$241$	13.9245	−	8.03932i	0.896957	−	0.517858i	0.0207451	−	0.999785i	$-0.493396\pi$
$241$	13.9245	−	8.03932i	0.896957	−	0.517858i	0.876212	+	0.481927i	$0.160063\pi$
$242$	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
$250$	4.15469	−	15.2558i	0.262766	−	0.964860i
$251$	9.17104			0.578871			0.289435	−	0.957198i	$-0.406532\pi$
$251$	9.17104			0.578871			0.289435	+	0.957198i	$0.406532\pi$
$252$		0			0
$253$		−	14.0877i		−	0.885683i
$254$	7.18436	+	2.12279i	0.450787	+	0.133196i
$255$	23.7861	−	0.169768i	1.48955	−	0.0106313i
$256$	−10.6412	+	11.9484i	−0.665078	+	0.746774i
$257$	3.27569	−	5.67366i	0.204332	−	0.353913i	−0.745588	−	0.666407i	$-0.767831\pi$
$257$	3.27569	−	5.67366i	0.204332	−	0.353913i	0.949920	+	0.312494i	$0.101165\pi$
$258$	3.88884	−	0.936426i	0.242109	−	0.0582994i
$259$		0			0
$260$	−4.87841	−	0.214117i	−0.302546	−	0.0132790i
$261$	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	0.958107	+	0.286412i	$0.0924626\pi$
$263$	11.7915	+	20.4234i	0.727093	+	1.25936i	−0.231013	+	0.972951i	$0.574204\pi$
$264$	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	$-0.676064\pi$
$269$	−0.838532	+	0.484127i	−0.0511262	+	0.0295177i	0.474219	+	0.880407i	$0.342730\pi$
$270$	−2.34174	−	9.42872i	−0.142514	−	0.573814i
$271$	−3.29801	+	5.71233i	−0.200340	+	0.346999i	−0.948638	−	0.316364i	$-0.897538\pi$
$271$	−3.29801	+	5.71233i	−0.200340	+	0.346999i	0.748298	+	0.663363i	$0.230871\pi$
$272$	−11.6665	+	16.1498i	−0.707387	+	0.979226i
$273$		0			0
$274$	−4.24621	+	1.02248i	−0.256523	+	0.0617703i
$275$	−0.166436	−	11.6591i	−0.0100365	−	0.703067i
$276$	−14.0244	+	21.6602i	−0.844172	+	1.30379i
$277$	−16.9631	+	9.79366i	−1.01921	+	0.588444i	−0.913876	−	0.405993i	$-0.866926\pi$
$277$	−16.9631	+	9.79366i	−1.01921	+	0.588444i	−0.105338	+	0.994436i	$0.533593\pi$
$278$	−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	−0.295563	−	0.955323i	$-0.595507\pi$
$283$	6.45972	−	3.72952i	0.383991	−	0.221697i	0.679553	+	0.733626i	$0.262174\pi$
$284$	−12.9867	+	20.0574i	−0.770618	+	1.19019i
$285$	−6.22466	−	10.6059i	−0.368717	−	0.628238i
$286$	−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
$290$	1.72343	−	0.428034i	0.101203	−	0.0251350i
$291$	−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
$300$	−11.3508	+	18.0918i	−0.655340	+	1.04453i
$301$		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
$305$	1.38646	−	0.00989553i	0.0793883	−	0.000566616i
$306$	−10.5485	−	3.11680i	−0.603016	−	0.178176i
$307$			13.8987i			0.793243i	0.917982	+	0.396622i	$0.129818\pi$
$307$			13.8987i			0.793243i	−0.917982	+	0.396622i	$0.870182\pi$
$308$		0			0
$309$	−11.6847			−0.664717
$310$	14.4759	+	15.0175i	0.822174	+	0.852937i
$311$	−0.723002	−	1.25228i	−0.0409977	−	0.0710101i	0.844798	−	0.535085i	$-0.179720\pi$
$311$	−0.723002	−	1.25228i	−0.0409977	−	0.0710101i	−0.885796	+	0.464075i	$0.846387\pi$
$312$	6.22217	+	2.18911i	0.352261	+	0.123934i
$313$	−3.58227	+	6.20467i	−0.202482	+	0.350708i	−0.949327	−	0.314289i	$-0.898234\pi$
$313$	−3.58227	+	6.20467i	−0.202482	+	0.350708i	0.746846	+	0.664997i	$0.231567\pi$
$314$	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	$-0.0929174\pi$
$317$	21.1396	+	12.2050i	1.18732	+	0.685499i	0.229623	+	0.973280i	$0.426251\pi$
$318$	−18.8038	+	17.8684i	−1.05446	+	1.00201i
$319$	1.13412	−	0.654784i	0.0634985	−	0.0366609i
$320$	−6.59761	−	16.6274i	−0.368818	−	0.929502i
$321$		−	21.3873i		−	1.19372i
$322$		0			0
$323$	12.8255			0.713628
$324$	−1.14661	+	22.4632i	−0.0637006	+	1.24795i
$325$	2.66197	−	4.76653i	0.147660	−	0.264399i
$326$	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
$330$	−4.35519	+	15.1364i	−0.239745	+	0.833230i
$331$	−7.19296	−	4.15286i	−0.395361	−	0.228262i	0.289120	−	0.957293i	$-0.406637\pi$
$331$	−7.19296	−	4.15286i	−0.395361	−	0.228262i	−0.684480	+	0.729031i	$0.739971\pi$
$332$	−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
$340$	−10.2807	−	19.7601i	−0.557550	−	1.07164i
$341$	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
$345$	−14.6028	−	24.8811i	−0.786191	−	1.33955i
$346$	−11.3316	+	10.7680i	−0.609191	+	0.578889i
$347$	−0.662153	−	1.14688i	−0.0355463	−	0.0615679i	0.847705	−	0.530468i	$-0.177984\pi$
$347$	−0.662153	−	1.14688i	−0.0355463	−	0.0615679i	−0.883251	+	0.468900i	$0.844650\pi$
$348$	−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	0.996897	−	0.0787120i	$-0.0250808\pi$
$353$	8.08427	+	14.0024i	0.430282	+	0.745270i	−0.566615	+	0.823982i	$0.691747\pi$
$354$	−29.7968	−	31.3566i	−1.58368	−	1.66658i
$355$	−13.5223	−	23.0400i	−0.717689	−	1.22284i
$356$	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	0.244437	−	0.969665i	$-0.421397\pi$
$359$	−8.96394	−	5.17534i	−0.473099	−	0.273144i	−0.717536	+	0.696521i	$0.754730\pi$
$360$	7.45069	−	6.48268i	0.392686	−	0.341667i
$361$	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	−0.924557	−	0.381043i	$-0.875565\pi$
$367$	−20.2462	+	11.6891i	−1.05684	+	0.610168i	−0.132286	+	0.991212i	$0.542232\pi$
$368$	24.0380	+	2.46040i	1.25307	+	0.128257i
$369$	11.4750	+	6.62511i	0.597366	+	0.344889i
$370$	16.7134	+	4.80893i	0.868886	+	0.250004i
$371$		0			0
$372$	−12.8255	−	25.0870i	−0.664969	−	1.30070i
$373$	10.1120	+	5.83817i	0.523580	+	0.302289i	0.738398	−	0.674365i	$-0.235582\pi$
$373$	10.1120	+	5.83817i	0.523580	+	0.302289i	−0.214818	+	0.976654i	$0.568916\pi$
$374$	−11.3154	−	11.9077i	−0.585105	−	0.615733i
$375$	−12.3794	−	20.4192i	−0.639268	−	1.05444i
$376$	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	$-0.778954\pi$
$379$		−	24.9171i		−	1.27991i	0.768414	−	0.639954i	$-0.221046\pi$
$380$	−6.18966	+	9.71091i	−0.317523	+	0.498159i
$381$	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	0.852449	−	0.522810i	$-0.175116\pi$
$383$	16.1633	+	9.33190i	0.825907	+	0.476838i	−0.0265422	+	0.999648i	$0.508450\pi$
$384$	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	0.976692	−	0.214643i	$-0.0688589\pi$
$389$	5.96543	+	10.3324i	0.302460	+	0.523875i	−0.674233	+	0.738519i	$0.735526\pi$
$390$	−5.30949	+	5.11799i	−0.268856	+	0.259159i
$391$	30.0881			1.52162
$392$		0			0
$393$		−	5.49966i		−	0.277421i
$394$	6.61173	−	22.3767i	0.333094	−	1.12732i
$395$	−23.7861	+	0.169768i	−1.19681	+	0.00854197i
$396$	3.95842	−	6.11362i	0.198918	−	0.307221i
$397$	−10.5074	+	18.1994i	−0.527353	+	0.913402i	0.472139	+	0.881524i	$0.343482\pi$
$397$	−10.5074	+	18.1994i	−0.527353	+	0.913402i	−0.999492	+	0.0318775i	$0.989851\pi$
$398$	6.07263	+	25.2188i	0.304394	+	1.26410i
$399$		0			0
$400$	19.9231	+	1.75225i	0.996155	+	0.0876127i
$401$	−6.71922	+	11.6380i	−0.335542	+	0.581176i	−0.983589	−	0.180425i	$-0.942253\pi$
$401$	−6.71922	+	11.6380i	−0.335542	+	0.581176i	0.648047	+	0.761601i	$0.275586\pi$
$402$	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	$-0.398083\pi$
$409$	26.1720	−	15.1104i	1.29412	−	0.747161i	0.979382	+	0.202018i	$0.0647499\pi$
$410$	6.46777	+	26.0417i	0.319420	+	1.28611i
$411$	−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
$415$	−4.36996	−	7.44577i	−0.214513	−	0.365498i
$416$	−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	$-0.683947\pi$
$419$	−22.3631			−1.09251			−0.546254	+	0.837619i	$0.683947\pi$
$420$		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
$425$	24.9012	−	0.355471i	1.20788	−	0.0172429i
$426$	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
$430$	4.06435	−	1.00943i	0.196000	−	0.0486791i
$431$	10.0981	−	5.83012i	0.486407	−	0.280827i	−0.236676	−	0.971589i	$-0.576058\pi$
$431$	10.0981	−	5.83012i	0.486407	−	0.280827i	0.723083	+	0.690762i	$0.242725\pi$
$432$	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	0.194076	+	0.980986i	$0.437829\pi$
$439$	−15.7671	+	27.3094i	−0.752521	+	1.30340i	−0.946597	+	0.322418i	$0.895504\pi$
$440$	14.4769	−	2.82080i	0.690160	−	0.134476i
$441$		0			0
$442$	−1.80054	−	7.47740i	−0.0856431	−	0.355663i
$443$	−8.77102	+	15.1919i	−0.416724	+	0.721787i	−0.995608	−	0.0936230i	$-0.970155\pi$
$443$	−8.77102	+	15.1919i	−0.416724	+	0.721787i	0.578884	+	0.815410i	$0.303488\pi$
$444$	−19.7195	−	12.7679i	−0.935847	−	0.605938i
$445$	−6.32439	+	0.0451390i	−0.299805	+	0.00213979i
$446$	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	$0.452388\pi$
$450$	2.73794	+	10.6970i	0.129068	+	0.504262i
$451$	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	$-0.255718\pi$
$457$	8.93935	+	5.16114i	0.418165	+	0.241428i	−0.276127	+	0.961121i	$0.589051\pi$
$458$	9.20942	+	9.69150i	0.430328	+	0.452854i
$459$	13.2518	−	7.65093i	0.618541	−	0.357115i
$460$	−14.5208	+	22.7815i	−0.677034	+	1.06219i
$461$			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	$-0.691231\pi$
$463$	−24.3266			−1.13055			−0.565277	+	0.824901i	$0.691231\pi$
$464$	0.919195	+	2.04952i	0.0426726	+	0.0951467i
$465$	31.5002	−	0.224825i	1.46078	−	0.0104260i
$466$	10.7153	+	11.2762i	0.496376	+	0.522359i
$467$	20.0903	+	11.5991i	0.929668	+	0.536744i	0.886707	−	0.462333i	$-0.152987\pi$
$467$	20.0903	+	11.5991i	0.929668	+	0.536744i	0.0429615	+	0.999077i	$0.486321\pi$
$468$	3.03632	−	1.55229i	0.140354	−	0.0717545i
$469$		0			0
$470$	−29.6072	−	8.51887i	−1.36568	−	0.392946i
$471$	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	0.972682	+	0.232141i	$0.0745730\pi$
$479$	15.0441	+	26.0571i	0.687381	+	1.19058i	−0.285301	+	0.958438i	$0.592094\pi$
$480$	−25.0668	−	10.0749i	−1.14414	−	0.459853i
$481$	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
$485$	−28.8155	+	16.9120i	−1.30844	+	0.767934i
$486$	14.4206	+	15.1754i	0.654130	+	0.688371i
$487$	−0.580639	−	1.00570i	−0.0263112	−	0.0455724i	0.852570	−	0.522613i	$-0.175043\pi$
$487$	−0.580639	−	1.00570i	−0.0263112	−	0.0455724i	−0.878881	+	0.477041i	$0.841709\pi$
$488$	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	$-0.895574\pi$
$491$		−	14.2794i		−	0.644419i	0.946668	−	0.322210i	$-0.104426\pi$
$492$	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
$495$	4.12168	+	7.02272i	0.185256	+	0.315648i
$496$	−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	0.906620	−	0.421948i	$-0.138653\pi$
$499$	22.2157	+	12.8263i	0.994513	+	0.574182i	0.0878928	+	0.996130i	$0.471987\pi$
$500$	−11.7483	+	19.0257i	−0.525402	+	0.850854i
$501$	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	$-0.862247\pi$
$503$		−	18.8114i		−	0.838761i	0.907811	−	0.419380i	$-0.137753\pi$
$504$		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	$-0.120136\pi$
$509$	24.2595	+	14.0062i	1.07528	+	0.620814i	0.145662	+	0.989334i	$0.453469\pi$
$510$	−32.3280	−	9.30172i	−1.43151	−	0.411887i
$511$		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
$515$	−12.2330	+	0.0873105i	−0.539051	+	0.00384736i
$516$	−5.64950	−	0.288373i	−0.248705	−	0.0126949i
$517$	−22.7199			−0.999220
$518$		0			0
$519$			23.6076i			1.03626i
$520$	6.53053	+	2.24535i	0.286383	+	0.0984651i
$521$	2.44949	−	1.41421i	0.107314	−	0.0619578i	−0.445382	−	0.895340i	$-0.646932\pi$
$521$	2.44949	−	1.41421i	0.107314	−	0.0619578i	0.552696	+	0.833383i	$0.313599\pi$
$522$	−0.898968	+	0.854251i	−0.0393467	+	0.0373896i
$523$	−18.1408	−	10.4736i	−0.793243	−	0.457979i	0.0478601	−	0.998854i	$-0.484760\pi$
$523$	−18.1408	−	10.4736i	−0.793243	−	0.457979i	−0.841103	+	0.540875i	$0.818093\pi$
$524$	−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
$530$	−19.5527	+	18.8475i	−0.849316	+	0.818684i
$531$	−22.3631			−0.970476
$532$		0			0
$533$			9.26504i			0.401313i
$534$	8.19296	+	2.42080i	0.354544	+	0.104758i
$535$	−0.159811	−	22.3910i	−0.00690923	−	0.968048i
$536$	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
$540$	−0.602449	+	13.7261i	−0.0259253	+	0.590678i
$541$	9.71922	−	16.8342i	0.417862	−	0.723758i	−0.577862	−	0.816134i	$-0.696113\pi$
$541$	9.71922	−	16.8342i	0.417862	−	0.723758i	0.995724	+	0.0923761i	$0.0294462\pi$
$542$	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	$-0.753465\pi$
$547$	−33.4337			−1.42952			−0.714762	+	0.699368i	$0.753465\pi$
$548$	6.16866	+	0.314873i	0.263512	+	0.0134507i
$549$	−0.838532	+	0.484127i	−0.0357877	+	0.0206620i
$550$	−4.44647	+	15.8793i	−0.189598	+	0.677094i
$551$	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
$555$	22.6518	−	13.2945i	0.961516	−	0.564320i
$556$	6.75057	+	4.37083i	0.286288	+	0.185364i
$557$	7.43743	−	4.29400i	0.315134	−	0.181943i	−0.334088	−	0.942542i	$-0.608428\pi$
$557$	7.43743	−	4.29400i	0.315134	−	0.181943i	0.649222	+	0.760599i	$0.275095\pi$
$558$	−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	−0.371031	−	0.928621i	$-0.620996\pi$
$563$	5.87645	−	3.39277i	0.247663	−	0.142988i	0.618694	+	0.785632i	$0.287662\pi$
$564$	34.9325	+	22.6179i	1.47092	+	0.952387i
$565$	6.22466	+	10.6059i	0.261873	+	0.446193i
$566$	−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	0.119046	−	0.992889i	$-0.462016\pi$
$569$	21.9309	−	37.9854i	0.919390	−	1.59243i	0.800344	−	0.599541i	$-0.204650\pi$
$570$	4.19202	+	16.8787i	0.175584	+	0.706969i
$571$	13.5004	−	7.79447i	0.564975	−	0.326188i	−0.190165	−	0.981752i	$-0.560902\pi$
$571$	13.5004	−	7.79447i	0.564975	−	0.326188i	0.755140	+	0.655564i	$0.227569\pi$
$572$	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	0.947215	+	0.320599i	$0.103884\pi$
$577$	18.0457	+	31.2561i	0.751254	+	1.30121i	−0.195961	+	0.980612i	$0.562783\pi$
$578$	8.00430	−	7.60615i	0.332935	−	0.316374i
$579$	−5.87302	+	10.1724i	−0.244075	+	0.422750i
$580$	−2.50893	−	0.110119i	−0.104177	−	0.00457242i
$581$		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
$585$	0.0272110	+	3.81252i	0.00112504	+	0.157628i
$586$	19.6161	+	5.79604i	0.810333	+	0.239432i
$587$		−	2.80928i		−	0.115951i	−0.998318	−	0.0579757i	$-0.981535\pi$
$587$		−	2.80928i		−	0.115951i	0.998318	−	0.0579757i	$-0.0184646\pi$
$588$		0			0
$589$	16.9848			0.699848
$590$	−31.4295	−	32.6055i	−1.29393	−	1.34235i
$591$	−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	−0.922687	−	0.385551i	$-0.874011\pi$
$593$	−3.10353	+	5.37547i	−0.127447	+	0.220744i	0.795240	+	0.606295i	$0.207345\pi$
$594$	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	−0.782350	−	0.622839i	$-0.785979\pi$
$599$	−15.5200	+	8.96050i	−0.634131	+	0.366116i	0.148219	+	0.988955i	$0.452646\pi$
$600$	22.6446	−	19.9883i	0.924462	−	0.816020i
$601$		−	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
$605$	−0.0887570	−	12.4357i	−0.00360849	−	0.505583i
$606$	−33.0848	+	31.4391i	−1.34398	+	1.27713i
$607$	−38.9423	−	22.4833i	−1.58062	−	0.912570i	−0.994769	−	0.102149i	$-0.967428\pi$
$607$	−38.9423	−	22.4833i	−1.58062	−	0.912570i	−0.585848	−	0.810421i	$-0.699239\pi$
$608$	−13.4765	−	5.52855i	−0.546546	−	0.224212i
$609$		0			0
$610$	−1.88435	−	0.542182i	−0.0762949	−	0.0219523i
$611$	−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	0.703394	−	0.710800i	$-0.251667\pi$
$613$	41.3637	−	23.8813i	1.67066	−	0.964557i	0.967268	−	0.253757i	$-0.0816664\pi$
$614$	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	0.999614	+	0.0277772i	$0.00884289\pi$
$619$	13.0336	+	22.5748i	0.523863	+	0.907357i	−0.475751	+	0.879580i	$0.657824\pi$
$620$	−13.6148	−	26.1685i	−0.546784	−	1.05095i
$621$	−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
$625$	−13.1129	−	21.2850i	−0.524517	−	0.851400i
$626$	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	$0.236257\pi$
$631$			33.9582i			1.35186i	−0.736968	+	0.675928i	$0.763743\pi$
$632$	−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
$635$	10.2155	−	5.99554i	0.405390	−	0.237926i
$636$	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
$640$	2.28479	+	25.1948i	0.0903143	+	0.995913i
$641$	−19.9309	−	34.5213i	−0.787222	−	1.36351i	−0.927663	−	0.373419i	$-0.878185\pi$
$641$	−19.9309	−	34.5213i	−0.787222	−	1.36351i	0.140441	−	0.990089i	$-0.455148\pi$
$642$	−8.57066	+	29.0065i	−0.338257	+	1.14480i
$643$			36.8341i			1.45260i	0.687380	+	0.726298i	$0.258761\pi$
$643$			36.8341i			1.45260i	−0.687380	+	0.726298i	$0.741239\pi$
$644$		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	−0.970136	−	0.242563i	$-0.922012\pi$
$647$	−31.6716	+	18.2856i	−1.24514	+	0.718881i	−0.275002	+	0.961444i	$0.588679\pi$
$648$	10.5569	−	30.0062i	0.414714	−	1.17875i
$649$	−28.9230	−	16.6987i	−1.13533	−	0.655481i
$650$	−5.52042	+	5.39785i	−0.216529	+	0.211721i
$651$		0			0
$652$	−20.4810	+	10.4707i	−0.802097	+	0.410064i
$653$	−14.2885	−	8.24948i	−0.559153	−	0.322827i	0.193652	−	0.981070i	$-0.437967\pi$
$653$	−14.2885	−	8.24948i	−0.559153	−	0.322827i	−0.752806	+	0.658243i	$0.771300\pi$
$654$	−9.49090	−	9.98771i	−0.371123	−	0.390550i
$655$	−0.0410947	−	5.75775i	−0.00160570	−	0.224974i
$656$	−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	$0.314167\pi$
$659$			42.8381i			1.66874i	−0.551207	+	0.834368i	$0.685833\pi$
$660$	11.9724	−	18.7834i	0.466025	−	0.731143i
$661$	1.30941	−	0.755989i	0.0509302	−	0.0294046i	−0.474319	−	0.880353i	$-0.657306\pi$
$661$	1.30941	−	0.755989i	0.0509302	−	0.0294046i	0.525249	+	0.850949i	$0.323972\pi$
$662$	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
$670$	10.3512	+	10.7385i	0.399901	+	0.414864i
$671$	−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
$675$	−13.4113	−	7.48985i	−0.516202	−	0.288284i
$676$	−19.8231	−	12.8350i	−0.762428	−	0.493653i
$677$	23.2659	−	40.2976i	0.894179	−	1.54876i	0.0593624	−	0.998236i	$-0.481093\pi$
$677$	23.2659	−	40.2976i	0.894179	−	1.54876i	0.834817	−	0.550528i	$-0.185573\pi$
$678$	−3.88884	−	16.1498i	−0.149350	−	0.620230i
$679$		0			0
$680$	6.02460	+	30.9195i	0.231033	+	1.18571i
$681$	−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	$-0.292909\pi$
$683$	−10.0953	−	17.4856i	−0.386287	−	0.669069i	−0.991947	+	0.126655i	$0.959576\pi$
$684$	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
$690$	9.83435	+	39.5968i	0.374387	+	1.50742i
$691$	18.9066	−	32.7472i	0.719240	−	1.24576i	−0.242061	−	0.970261i	$-0.577823\pi$
$691$	18.9066	−	32.7472i	0.719240	−	1.24576i	0.961301	−	0.275500i	$-0.0888433\pi$
$692$	19.6836	−	10.0630i	0.748258	−	0.382539i
$693$		0			0
$694$	0.438447	+	1.82081i	0.0166432	+	0.0691169i
$695$	−7.75438	+	4.55109i	−0.294140	+	0.172633i
$696$	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
$705$	−40.1270	+	23.5508i	−1.51127	+	0.886974i
$706$	−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	0.417146	+	0.908839i	$0.363030\pi$
$709$	−15.4039	+	26.6803i	−0.578505	+	1.00200i	−0.995651	+	0.0931605i	$0.970303\pi$
$710$	9.10665	+	36.6668i	0.341767	+	1.37608i
$711$	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	0.492844	+	0.870118i	$0.335957\pi$
$719$	−13.5981	+	23.5525i	−0.507122	+	0.878361i	−0.999966	+	0.00824342i	$0.997376\pi$
$720$	−12.7028	+	5.80637i	−0.473406	+	0.216391i
$721$		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
$725$	1.36903	−	2.45139i	0.0508445	−	0.0910422i
$726$	−4.76004	+	16.1099i	−0.176662	+	0.597893i
$727$		−	32.8255i		−	1.21743i	−0.793389	−	0.608715i	$-0.791685\pi$
$727$		−	32.8255i		−	1.21743i	0.793389	−	0.608715i	$-0.208315\pi$
$728$		0			0
$729$	−2.12311			−0.0786335
$730$	21.8618	+	22.6798i	0.809141	+	0.839417i
$731$	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	−0.998453	−	0.0555970i	$-0.982294\pi$
$733$	−12.2125	+	21.1526i	−0.451078	+	0.781290i	0.547375	+	0.836887i	$0.315627\pi$
$734$	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	−0.583360	+	0.812214i	$0.698262\pi$
$739$	−42.9091	+	24.7736i	−1.57844	+	0.911311i	−0.995078	+	0.0990973i	$0.968404\pi$
$740$	−20.7404	−	13.2198i	−0.762431	−	0.485968i
$741$			6.00505i			0.220601i
$742$		0			0
$743$	−9.43318			−0.346070			−0.173035	−	0.984916i	$-0.555357\pi$
$743$	−9.43318			−0.346070			−0.173035	+	0.984916i	$0.555357\pi$
$744$	7.34126	+	39.1638i	0.269144	+	1.43581i
$745$	0.0319181	+	4.47202i	0.00116939	+	0.163842i
$746$	−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
$750$	8.60679	+	32.6544i	0.314276	+	1.19237i
$751$	−32.5624	−	18.7999i	−1.18822	−	0.686019i	−0.230318	−	0.973115i	$-0.573977\pi$
$751$	−32.5624	−	18.7999i	−1.18822	−	0.686019i	−0.957902	+	0.287096i	$0.907310\pi$
$752$	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
$760$	12.2862	−	10.6900i	0.445669	−	0.387767i
$761$	37.3454	+	21.5614i	1.35377	+	0.781600i	0.988775	−	0.149409i	$-0.0477372\pi$
$761$	37.3454	+	21.5614i	1.35377	+	0.781600i	0.364996	+	0.931009i	$0.381070\pi$
$762$	−15.5554	+	3.74571i	−0.563512	+	0.135693i
$763$		0			0
$764$	18.1771	+	35.5549i	0.657624	+	1.28633i
$765$	−14.9990	+	8.80299i	−0.542289	+	0.318273i
$766$	−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	0.689756	−	0.724042i	$-0.257718\pi$
$773$	−7.84490	−	13.5878i	−0.282161	−	0.488718i	−0.971917	+	0.235325i	$0.924385\pi$
$774$	−2.12003	+	2.01458i	−0.0762029	+	0.0724124i
$775$	32.9768	−	0.470753i	1.18456	−	0.0169099i
$776$	−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
$780$	9.25195	−	4.81356i	0.331273	−	0.172353i
$781$	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	0.101878	−	0.994797i	$-0.467515\pi$
$787$	28.4557	−	16.4289i	1.01434	−	0.585628i	0.912459	+	0.409169i	$0.134181\pi$
$788$	−17.9343	+	27.6988i	−0.638883	+	0.986729i
$789$	−43.6199	−	25.1840i	−1.55291	−	0.896573i
$790$	32.3280	+	9.30172i	1.15018	+	0.330940i
$791$		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
$795$	0.292722	+	41.0131i	0.0103818	+	1.45458i
$796$	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
$800$	−26.3185	−	10.3604i	−0.930499	−	0.366295i
$801$	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	0.999609	−	0.0279678i	$-0.00890360\pi$
$809$	13.5270	+	23.4294i	0.475584	+	0.823735i	−0.524025	+	0.851703i	$0.675570\pi$
$810$	24.6813	+	25.6048i	0.867213	+	0.899661i
$811$	−9.17104			−0.322039			−0.161019	−	0.986951i	$-0.551478\pi$
$811$	−9.17104			−0.322039			−0.161019	+	0.986951i	$0.551478\pi$
$812$		0			0
$813$		−	14.0877i		−	0.494076i
$814$	−17.3945	−	5.13962i	−0.609677	−	0.180144i
$815$	−0.183547	−	25.7167i	−0.00642938	−	0.900817i
$816$	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
$820$	1.66393	−	37.9108i	0.0581071	−	1.32390i
$821$	17.9654	−	31.1170i	0.626998	−	1.08599i	−0.361153	−	0.932507i	$-0.617617\pi$
$821$	17.9654	−	31.1170i	0.626998	−	1.08599i	0.988151	−	0.153486i	$-0.0490499\pi$
$822$	6.76206	−	6.42570i	0.235854	−	0.224122i
$823$	11.4196	+	19.7794i	0.398064	+	0.689466i	0.993487	−	0.113946i	$-0.0363490\pi$
$823$	11.4196	+	19.7794i	0.398064	+	0.689466i	−0.595423	+	0.803412i	$0.703016\pi$
$824$	−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	$-0.526133\pi$
$827$	−4.71659			−0.164012			−0.0820059	+	0.996632i	$0.526133\pi$
$828$	0.961762	−	18.8418i	0.0334235	−	0.654799i
$829$	−37.5809	+	21.6973i	−1.30524	+	0.753579i	−0.981297	−	0.192498i	$-0.938341\pi$
$829$	−37.5809	+	21.6973i	−1.30524	+	0.753579i	−0.323940	+	0.946077i	$0.605008\pi$
$830$	2.94297	+	11.8495i	0.102152	+	0.411303i
$831$	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
$835$	0.762285	+	1.29882i	0.0263800	+	0.0449475i
$836$	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	$-0.688568\pi$
$839$	−32.3461			−1.11671			−0.558356	+	0.829601i	$0.688568\pi$
$840$		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
$845$	22.7708	−	13.3643i	0.783341	−	0.459747i
$846$	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
$850$	−33.9146	−	9.49669i	−1.16326	−	0.325734i
$851$	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	0.814293	−	0.580454i	$-0.197125\pi$
$857$	−2.79695	−	4.84446i	−0.0955419	−	0.165483i	−0.909835	+	0.414971i	$0.863792\pi$
$858$	5.57534	−	5.29801i	0.190339	−	0.180871i
$859$	−4.58552	+	7.94235i	−0.156456	+	0.270990i	−0.933588	−	0.358348i	$-0.883340\pi$
$859$	−4.58552	+	7.94235i	−0.156456	+	0.270990i	0.777132	+	0.629337i	$0.216674\pi$
$860$	−5.91678	−	0.259692i	−0.201761	−	0.00885542i
$861$		0			0
$862$	−16.0318	+	3.86043i	−0.546046	+	0.131487i
$863$	15.3926	−	26.6607i	0.523969	−	0.907541i	−0.475642	−	0.879639i	$-0.657784\pi$
$863$	15.3926	−	26.6607i	0.523969	−	0.907541i	0.999611	−	0.0279016i	$-0.00888250\pi$
$864$	−17.2225	+	2.32699i	−0.585922	+	0.0791659i
$865$	0.176401	+	24.7155i	0.00599782	+	0.840351i
$866$	−12.2117	−	3.60823i	−0.414969	−	0.122613i
$867$		−	16.6757i		−	0.566335i
$868$		0			0
$869$	24.8078			0.841546
$870$	−2.73063	+	2.63214i	−0.0925769	+	0.0892379i
$871$	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	$-0.362933\pi$
$877$	−4.76284	−	2.74983i	−0.160830	−	0.0928551i	−0.578255	+	0.815856i	$0.696266\pi$
$878$	32.3279	−	30.7199i	1.09101	−	1.03674i
$879$	26.7522	−	15.4454i	0.902330	−	0.520960i
$880$	−20.7647	−	1.97572i	−0.699978	−	0.0666014i
$881$			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	$-0.196235\pi$
$883$	48.4902			1.63183			0.815913	+	0.578175i	$0.196235\pi$
$884$	−0.554478	+	10.8628i	−0.0186491	+	0.365354i
$885$	−68.3920	+	0.488133i	−2.29897	+	0.0164084i
$886$	17.9836	−	17.0891i	0.604171	−	0.574119i
$887$	−27.5169	−	15.8869i	−0.923927	−	0.533429i	−0.0390409	−	0.999238i	$-0.512430\pi$
$887$	−27.5169	−	15.8869i	−0.923927	−	0.533429i	−0.884886	+	0.465808i	$0.845764\pi$
$888$	21.6280	+	25.2188i	0.725788	+	0.846287i
$889$		0			0
$890$	8.59554	+	2.47319i	0.288123	+	0.0829016i
$891$	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
$900$	0.573358	−	15.6050i	0.0191119	−	0.520167i
$901$	−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
$905$	3.90309	+	6.65028i	0.129743	+	0.221063i
$906$	−10.8408	+	10.3016i	−0.360162	+	0.342247i
$907$	−26.8937	−	46.5813i	−0.892991	−	1.54671i	−0.836271	−	0.548316i	$-0.815269\pi$
$907$	−26.8937	−	46.5813i	−0.892991	−	1.54671i	−0.0567196	−	0.998390i	$-0.518064\pi$
$908$	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	$-0.620450\pi$
$911$		−	56.0950i		−	1.85851i	0.369438	−	0.929255i	$-0.379550\pi$
$912$	−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
$915$	−2.55388	+	1.49889i	−0.0844286	+	0.0495516i
$916$	−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	−0.178411	−	0.983956i	$-0.557096\pi$
$919$	−33.9452	−	19.5983i	−1.11975	−	0.646487i	−0.941337	+	0.337469i	$0.890429\pi$
$920$	28.8231	−	25.0784i	0.950270	−	0.826809i
$921$	−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	$-0.175632\pi$
$929$	25.0980	+	14.4903i	0.823438	+	0.475412i	−0.0281624	+	0.999603i	$0.508966\pi$
$930$	−42.8121	−	12.3183i	−1.40387	−	0.403934i
$931$		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
$935$	−25.9720	+	0.185369i	−0.849375	+	0.00606223i
$936$	−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
$940$	36.7409	+	23.4184i	1.19836	+	0.763823i
$941$	−7.58391	+	4.37857i	−0.247228	+	0.142737i	−0.618494	−	0.785789i	$-0.712257\pi$
$941$	−7.58391	+	4.37857i	−0.247228	+	0.142737i	0.371266	+	0.928527i	$0.378924\pi$
$942$	−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	−0.0215294	−	0.999768i	$-0.506854\pi$
$947$	26.3131	−	45.5756i	0.855060	−	1.48101i	0.876589	−	0.481239i	$-0.159813\pi$
$948$	−38.1427	−	24.6964i	−1.23882	−	0.802103i
$949$	5.43845	+	9.41967i	0.176539	+	0.305775i
$950$	4.51487	+	17.6394i	0.146482	+	0.572299i
$951$	−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
$955$	−44.6441	+	0.318637i	−1.44465	+	0.0103109i
$956$	−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
$960$	29.9595	+	23.7092i	0.966938	+	0.765212i
$961$	−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	$-0.583974\pi$
$967$	−16.2177			−0.521527			−0.260764	+	0.965403i	$0.583974\pi$
$968$	15.4612	−	2.89820i	0.496940	−	0.0931516i
$969$	−23.7225	+	13.6962i	−0.762076	+	0.439985i
$970$	45.8582	−	11.3895i	1.47242	−	0.365693i
$971$	−18.1836	+	31.4949i	−0.583539	+	1.01072i	0.411517	+	0.911402i	$0.364999\pi$
$971$	−18.1836	+	31.4949i	−0.583539	+	1.01072i	−0.995056	+	0.0993168i	$0.968334\pi$
$972$	−13.4765	−	26.3605i	−0.432260	−	0.845513i
$973$		0			0
$974$	0.384472	+	1.59666i	0.0123193	+	0.0511602i
$975$	0.166436	+	11.6591i	0.00533023	+	0.373388i
$976$	0.252544	−	2.46734i	0.00808373	−	0.0789777i
$977$	12.2003	−	7.04383i	0.390321	−	0.225352i	−0.291978	−	0.956425i	$-0.594313\pi$
$977$	12.2003	−	7.04383i	0.390321	−	0.225352i	0.682299	+	0.731073i	$0.260980\pi$
$978$	−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	0.267485	−	0.963562i	$-0.413807\pi$
$983$	38.7426	−	22.3680i	1.23570	−	0.713430i	0.968212	+	0.250132i	$0.0804741\pi$
$984$	−17.0119	+	48.3534i	−0.542319	+	1.54145i
$985$	−18.6740	−	31.8176i	−0.595002	−	1.01379i
$986$	−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
$990$	−2.77576	−	11.1763i	−0.0882195	−	0.355205i
$991$	0.497251	−	0.287088i	0.0157957	−	0.00911966i	−0.492081	−	0.870549i	$-0.663764\pi$
$991$	0.497251	−	0.287088i	0.0157957	−	0.00911966i	0.507877	+	0.861430i	$0.330430\pi$
$992$	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	−0.944748	−	0.327799i	$-0.893693\pi$
$997$	−23.8790	−	41.3597i	−0.756256	−	1.30987i	0.188492	−	0.982075i	$-0.439640\pi$
$998$	−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.19.1		32
4.3	odd	2	inner	980.2.s.f.19.6		32
5.4	even	2	inner	980.2.s.f.19.16		32
7.2	even	3		140.2.c.b.139.11	yes	16
7.3	odd	6	inner	980.2.s.f.619.11		32
7.4	even	3	inner	980.2.s.f.619.12		32
7.5	odd	6		140.2.c.b.139.12	yes	16
7.6	odd	2	inner	980.2.s.f.19.2		32
20.19	odd	2	inner	980.2.s.f.19.11		32
28.3	even	6	inner	980.2.s.f.619.16		32
28.11	odd	6	inner	980.2.s.f.619.15		32
28.19	even	6		140.2.c.b.139.7	yes	16
28.23	odd	6		140.2.c.b.139.8	yes	16
28.27	even	2	inner	980.2.s.f.19.5		32
35.2	odd	12		700.2.g.l.251.3		16
35.4	even	6	inner	980.2.s.f.619.5		32
35.9	even	6		140.2.c.b.139.6	yes	16
35.12	even	12		700.2.g.l.251.4		16
35.19	odd	6		140.2.c.b.139.5	✓	16
35.23	odd	12		700.2.g.l.251.14		16
35.24	odd	6	inner	980.2.s.f.619.6		32
35.33	even	12		700.2.g.l.251.13		16
35.34	odd	2	inner	980.2.s.f.19.15		32
56.5	odd	6		2240.2.e.f.2239.4		16
56.19	even	6		2240.2.e.f.2239.16		16
56.37	even	6		2240.2.e.f.2239.13		16
56.51	odd	6		2240.2.e.f.2239.1		16
140.19	even	6		140.2.c.b.139.10	yes	16
140.23	even	12		700.2.g.l.251.15		16
140.39	odd	6	inner	980.2.s.f.619.2		32
140.47	odd	12		700.2.g.l.251.1		16
140.59	even	6	inner	980.2.s.f.619.1		32
140.79	odd	6		140.2.c.b.139.9	yes	16
140.103	odd	12		700.2.g.l.251.16		16
140.107	even	12		700.2.g.l.251.2		16
140.139	even	2	inner	980.2.s.f.19.12		32
280.19	even	6		2240.2.e.f.2239.2		16
280.149	even	6		2240.2.e.f.2239.3		16
280.219	odd	6		2240.2.e.f.2239.15		16
280.229	odd	6		2240.2.e.f.2239.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.b.139.5	✓	16	35.19	odd	6
140.2.c.b.139.6	yes	16	35.9	even	6
140.2.c.b.139.7	yes	16	28.19	even	6
140.2.c.b.139.8	yes	16	28.23	odd	6
140.2.c.b.139.9	yes	16	140.79	odd	6
140.2.c.b.139.10	yes	16	140.19	even	6
140.2.c.b.139.11	yes	16	7.2	even	3
140.2.c.b.139.12	yes	16	7.5	odd	6
700.2.g.l.251.1		16	140.47	odd	12
700.2.g.l.251.2		16	140.107	even	12
700.2.g.l.251.3		16	35.2	odd	12
700.2.g.l.251.4		16	35.12	even	12
700.2.g.l.251.13		16	35.33	even	12
700.2.g.l.251.14		16	35.23	odd	12
700.2.g.l.251.15		16	140.23	even	12
700.2.g.l.251.16		16	140.103	odd	12
980.2.s.f.19.1		32	1.1	even	1	trivial
980.2.s.f.19.2		32	7.6	odd	2	inner
980.2.s.f.19.5		32	28.27	even	2	inner
980.2.s.f.19.6		32	4.3	odd	2	inner
980.2.s.f.19.11		32	20.19	odd	2	inner
980.2.s.f.19.12		32	140.139	even	2	inner
980.2.s.f.19.15		32	35.34	odd	2	inner
980.2.s.f.19.16		32	5.4	even	2	inner
980.2.s.f.619.1		32	140.59	even	6	inner
980.2.s.f.619.2		32	140.39	odd	6	inner
980.2.s.f.619.5		32	35.4	even	6	inner
980.2.s.f.619.6		32	35.24	odd	6	inner
980.2.s.f.619.11		32	7.3	odd	6	inner
980.2.s.f.619.12		32	7.4	even	3	inner
980.2.s.f.619.15		32	28.11	odd	6	inner
980.2.s.f.619.16		32	28.3	even	6	inner
2240.2.e.f.2239.1		16	56.51	odd	6
2240.2.e.f.2239.2		16	280.19	even	6
2240.2.e.f.2239.3		16	280.149	even	6
2240.2.e.f.2239.4		16	56.5	odd	6
2240.2.e.f.2239.13		16	56.37	even	6
2240.2.e.f.2239.14		16	280.229	odd	6
2240.2.e.f.2239.15		16	280.219	odd	6
2240.2.e.f.2239.16		16	56.19	even	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} +(-1.92846 + 1.13183i) q^{5} +(2.93651 - 0.707107i) q^{6} +(-1.84130 - 2.14700i) q^{8} +(0.780776 - 1.35234i) q^{9} +(3.06904 - 0.762234i) 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} +(-4.46783 - 0.196096i) q^{20} +(-3.20636 + 0.772087i) q^{22} +(3.02045 - 5.23157i) q^{23} +(5.69850 + 2.00487i) q^{24} +(2.43794 - 4.36537i) q^{25} +(-1.48088 - 0.437562i) q^{26} -3.07221i q^{27} +0.561553 q^{29} +(-4.86263 + 4.68725i) 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} +(5.98091 + 2.05638i) q^{40} +8.48528i q^{41} +1.32431 q^{43} +(4.65803 + 0.237764i) q^{44} +(0.0249209 + 3.49165i) q^{45} +(-6.19296 + 5.88491i) q^{46} +(-8.43723 - 4.87123i) q^{47} +(-6.92516 - 5.00270i) q^{48} +(-5.05581 + 4.94356i) 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} +(8.47329 - 4.40845i) q^{60} +(-0.536986 - 0.310029i) q^{61} +(-2.18379 - 9.06897i) q^{62} +(-1.21922 + 7.90655i) q^{64} +(-2.10568 + 1.23584i) 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} +(0.152429 + 10.6778i) q^{75} +(4.58552 - 2.34430i) q^{76} +(3.20636 - 0.772087i) q^{78} +(9.21257 + 5.31888i) q^{79} +(-7.28754 - 5.18573i) 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} +(1.36543 - 4.74553i) q^{90} +(10.7575 - 5.49966i) q^{92} +(-12.2003 - 7.04383i) q^{93} +(9.49090 + 9.98771i) q^{94} +(0.0410947 + 5.75775i) 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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