LMFDB - Embedded newform 980.2.s.f.619.2

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			619.2
Character	$\chi$	$=$	980.619
Dual form			980.2.s.f.19.2

$q$-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 $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

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

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	0.927604	−	0.373565i	$-0.121865\pi$
$3$	1.84964	+	1.06789i	1.06789	+	0.616546i	0.140285	+	0.990111i	$0.455198\pi$
$4$	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	0.772549	−	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	$-0.548384\pi$
$13$	−1.09190			−0.302837			−0.151419	+	0.988470i	$0.548384\pi$
$14$		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	$0.373095\pi$
$17$	−2.49037	+	4.31345i	−0.604003	+	1.04616i	−0.992208	+	0.124591i	$0.960238\pi$
$18$	−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	$0.928778\pi$
$20$	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	0.987590	+	0.157053i	$0.0501993\pi$
$23$	3.02045	+	5.23157i	0.629807	+	1.09086i	−0.357783	+	0.933805i	$0.616467\pi$
$24$	−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	0.401576	+	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	−0.0544884	−	0.998514i	$-0.517353\pi$
$37$	4.76284	−	2.74983i	0.783006	−	0.452069i	0.837495	+	0.546446i	$0.184019\pi$
$38$	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	$-0.415116\pi$
$47$	8.43723	−	4.87123i	1.23070	−	0.710543i	0.967175	+	0.254111i	$0.0817829\pi$
$48$	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	−0.107040	−	0.994255i	$-0.534137\pi$
$53$	−7.43743	−	4.29400i	−1.02161	−	0.589826i	−0.914570	+	0.404428i	$0.867471\pi$
$54$	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	$-0.215466\pi$
$60$	8.47329	+	4.40845i	1.09390	+	0.569128i
$61$	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
$65$	−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	−0.685247	−	0.728310i	$-0.740306\pi$
$67$	2.35829	−	4.08469i	0.288112	−	0.499024i	0.973359	+	0.229287i	$0.0736393\pi$
$68$	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	$0.364769\pi$
$73$	−4.98074	+	8.62689i	−0.582951	+	1.00970i	−0.995127	+	0.0985973i	$0.968564\pi$
$74$	−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	0.117657	−	0.993054i	$-0.462462\pi$
$79$	9.21257	−	5.31888i	1.03650	−	0.598421i	0.918839	+	0.394634i	$0.129128\pi$
$80$	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	$-0.714564\pi$
$89$	−2.44949	+	1.41421i	−0.259645	+	0.149906i	0.364527	+	0.931193i	$0.381231\pi$
$90$	−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	$-0.774105\pi$
$97$	−14.9422			−1.51715			−0.758576	+	0.651584i	$0.774105\pi$
$98$		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	$-0.0625337\pi$
$101$	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	−0.714918	−	0.699209i	$-0.753536\pi$
$103$	−4.73795	+	2.73546i	−0.466844	+	0.269532i	0.248074	+	0.968741i	$0.420202\pi$
$104$	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	0.515796	−	0.856712i	$-0.327496\pi$
$107$	−5.00691	−	8.67222i	−0.484036	−	0.838375i	−0.999832	+	0.0183365i	$0.994163\pi$
$108$	−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	$0.236770\pi$
$110$	−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	$0.0832882\pi$
$113$			5.49966i			0.517364i	−0.965963	+	0.258682i	$0.916712\pi$
$114$	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	$-0.130784\pi$
$131$	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
$135$	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	0.609882	−	0.792492i	$-0.291217\pi$
$137$	2.67459	+	1.54417i	0.228505	+	0.131928i	−0.381377	+	0.924420i	$0.624550\pi$
$138$	−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
$145$	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	0.904076	−	0.427372i	$-0.140560\pi$
$149$	1.00000	+	1.73205i	0.0819232	+	0.141895i	−0.822153	+	0.569267i	$0.807227\pi$
$150$	−4.07225	−	14.5428i	−0.332498	−	1.18742i
$151$	−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	−0.777943	−	0.628334i	$-0.783737\pi$
$157$	1.94442	−	3.36784i	0.155182	−	0.268783i	0.933125	+	0.359552i	$0.117070\pi$
$158$	−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	0.547992	−	0.836484i	$-0.315392\pi$
$163$	−5.75058	−	9.96029i	−0.450420	−	0.780150i	−0.998412	+	0.0563333i	$0.982059\pi$
$164$	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	$-0.304702\pi$
$173$	−5.52669	−	9.57250i	−0.420186	−	0.727784i	−0.995957	+	0.0898270i	$0.971369\pi$
$174$	−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	$0.566204\pi$
$180$	3.75357	+	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	0.279800	−	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	0.661526	−	0.749922i	$-0.269909\pi$
$193$	4.76284	+	2.74983i	0.342837	+	0.197937i	−0.318689	+	0.947859i	$0.603243\pi$
$194$	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	$-0.800013\pi$
$197$		−	16.4990i		−	1.17550i	0.809042	−	0.587751i	$-0.199987\pi$
$198$	−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	$-0.0586138\pi$
$200$	−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	$-0.996854\pi$
$211$		−	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
$215$	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	$-0.442725\pi$
$227$	−8.79279	−	5.07652i	−0.583598	−	0.336941i	−0.762562	+	0.646915i	$0.776059\pi$
$228$	−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	$0.232216\pi$
$230$	−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	−0.778443	−	0.627715i	$-0.783990\pi$
$233$	−9.52568	+	5.49966i	−0.624048	+	0.360294i	0.154395	+	0.988009i	$0.450657\pi$
$234$	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	$-0.975969\pi$
$239$		−	2.33205i		−	0.150848i	0.997152	−	0.0754238i	$-0.0240310\pi$
$240$	19.0171	−	1.80944i	1.22755	−	0.116799i
$241$	−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
$250$	−4.15469	−	15.2558i	−0.262766	−	0.964860i
$251$	−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
$255$	−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	$-0.232169\pi$
$257$	−3.27569	−	5.67366i	−0.204332	−	0.353913i	−0.949920	+	0.312494i	$0.898835\pi$
$258$	−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	−0.231013	−	0.972951i	$-0.574204\pi$
$263$	11.7915	−	20.4234i	0.727093	−	1.25936i	0.958107	−	0.286412i	$-0.0924626\pi$
$264$	−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	$0.657270\pi$
$270$	−2.34174	+	9.42872i	−0.142514	+	0.573814i
$271$	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
$275$	−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	−0.105338	−	0.994436i	$-0.533593\pi$
$277$	−16.9631	−	9.79366i	−1.01921	−	0.588444i	−0.913876	+	0.405993i	$0.866926\pi$
$278$	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	$-0.404493\pi$
$283$	−6.45972	−	3.72952i	−0.383991	−	0.221697i	−0.679553	+	0.733626i	$0.737826\pi$
$284$	−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	$-0.361159\pi$
$293$	14.4635			0.844965			0.422483	+	0.906371i	$0.361159\pi$
$294$		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	$-0.820280\pi$
$311$	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	0.949327	−	0.314289i	$-0.101766\pi$
$313$	3.58227	+	6.20467i	0.202482	+	0.350708i	−0.746846	+	0.664997i	$0.768433\pi$
$314$	−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	0.229623	−	0.973280i	$-0.426251\pi$
$317$	21.1396	−	12.2050i	1.18732	−	0.685499i	0.957696	+	0.287781i	$0.0929174\pi$
$318$	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	−0.684480	−	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	$-0.686575\pi$
$337$		−	30.5866i		−	1.66616i	0.553153	−	0.833080i	$-0.313425\pi$
$338$	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	−0.883251	−	0.468900i	$-0.844650\pi$
$347$	−0.662153	+	1.14688i	−0.0355463	+	0.0615679i	0.847705	+	0.530468i	$0.177984\pi$
$348$	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	$-0.974919\pi$
$353$	−8.08427	+	14.0024i	−0.430282	+	0.745270i	0.566615	+	0.823982i	$0.308253\pi$
$354$	−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	−0.717536	−	0.696521i	$-0.754730\pi$
$359$	−8.96394	+	5.17534i	−0.473099	+	0.273144i	0.244437	+	0.969665i	$0.421397\pi$
$360$	−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	$-0.124435\pi$
$367$	20.2462	+	11.6891i	1.05684	+	0.610168i	0.132286	+	0.991212i	$0.457768\pi$
$368$	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	−0.214818	−	0.976654i	$-0.568916\pi$
$373$	10.1120	−	5.83817i	0.523580	−	0.302289i	0.738398	+	0.674365i	$0.235582\pi$
$374$	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	$0.221046\pi$
$379$			24.9171i			1.27991i	−0.768414	+	0.639954i	$0.778954\pi$
$380$	−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	$-0.824884\pi$
$383$	−16.1633	+	9.33190i	−0.825907	+	0.476838i	0.0265422	+	0.999648i	$0.491550\pi$
$384$	−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	$0.0688589\pi$
$390$	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	0.999492	+	0.0318775i	$0.0101486\pi$
$397$	10.5074	+	18.1994i	0.527353	+	0.913402i	−0.472139	+	0.881524i	$0.656518\pi$
$398$	−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	0.648047	−	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	$0.935250\pi$
$410$	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	$-0.316053\pi$
$419$	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
$425$	−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	0.723083	−	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	$-0.569416\pi$
$433$	−9.00400			−0.432705			−0.216352	+	0.976315i	$0.569416\pi$
$434$		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	$0.562171\pi$
$440$	−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	0.578884	−	0.815410i	$-0.303488\pi$
$443$	−8.77102	−	15.1919i	−0.416724	−	0.721787i	−0.995608	+	0.0936230i	$0.970155\pi$
$444$	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	−0.276127	−	0.961121i	$-0.589051\pi$
$457$	8.93935	−	5.16114i	0.418165	−	0.241428i	0.694292	+	0.719693i	$0.255718\pi$
$458$	−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	$-0.847013\pi$
$467$	−20.0903	+	11.5991i	−0.929668	+	0.536744i	−0.0429615	+	0.999077i	$0.513679\pi$
$468$	−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	0.285301	+	0.958438i	$0.407906\pi$
$479$	−15.0441	+	26.0571i	−0.687381	+	1.19058i	−0.972682	+	0.232141i	$0.925427\pi$
$480$	−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	−0.878881	−	0.477041i	$-0.841709\pi$
$487$	−0.580639	+	1.00570i	−0.0263112	+	0.0455724i	0.852570	+	0.522613i	$0.175043\pi$
$488$	−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
$495$	−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	0.0878928	−	0.996130i	$-0.471987\pi$
$499$	22.2157	−	12.8263i	0.994513	−	0.574182i	0.906620	+	0.421948i	$0.138653\pi$
$500$	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	$-0.879864\pi$
$509$	−24.2595	+	14.0062i	−1.07528	+	0.620814i	−0.145662	+	0.989334i	$0.546531\pi$
$510$	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	$-0.353068\pi$
$521$	−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	−0.0478601	−	0.998854i	$-0.515240\pi$
$523$	18.1408	−	10.4736i	0.793243	−	0.457979i	0.841103	+	0.540875i	$0.181907\pi$
$524$	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	0.995724	−	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	$-0.753465\pi$
$547$	−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	0.649222	−	0.760599i	$-0.275095\pi$
$557$	7.43743	+	4.29400i	0.315134	+	0.181943i	−0.334088	+	0.942542i	$0.608428\pi$
$558$	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	$-0.379004\pi$
$563$	−5.87645	−	3.39277i	−0.247663	−	0.142988i	−0.618694	+	0.785632i	$0.712338\pi$
$564$	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	0.800344	+	0.599541i	$0.204650\pi$
$569$	21.9309	+	37.9854i	0.919390	+	1.59243i	0.119046	+	0.992889i	$0.462016\pi$
$570$	−4.19202	+	16.8787i	−0.175584	+	0.706969i
$571$	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	$0.437217\pi$
$577$	−18.0457	+	31.2561i	−0.751254	+	1.30121i	−0.947215	+	0.320599i	$0.896116\pi$
$578$	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	$-0.125989\pi$
$593$	3.10353	+	5.37547i	0.127447	+	0.220744i	−0.795240	+	0.606295i	$0.792655\pi$
$594$	−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	$0.785979\pi$
$600$	−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	0.585848	−	0.810421i	$-0.300761\pi$
$607$	38.9423	−	22.4833i	1.58062	−	0.912570i	0.994769	−	0.102149i	$-0.0325719\pi$
$608$	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	0.967268	+	0.253757i	$0.0816664\pi$
$613$	41.3637	+	23.8813i	1.67066	+	0.964557i	0.703394	+	0.710800i	$0.251667\pi$
$614$	−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	$0.0960535\pi$
$617$			14.7647i			0.594404i	−0.954815	+	0.297202i	$0.903946\pi$
$618$	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	$0.991157\pi$
$620$	−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	$-0.763743\pi$
$631$		−	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
$635$	−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	0.140441	+	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	$0.258761\pi$
$643$			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	$-0.0779881\pi$
$647$	31.6716	+	18.2856i	1.24514	+	0.718881i	0.275002	+	0.961444i	$0.411321\pi$
$648$	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	−0.752806	−	0.658243i	$-0.771300\pi$
$653$	−14.2885	+	8.24948i	−0.559153	+	0.322827i	0.193652	+	0.981070i	$0.437967\pi$
$654$	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	$-0.685833\pi$
$659$		−	42.8381i		−	1.66874i	0.551207	−	0.834368i	$-0.314167\pi$
$660$	11.9724	+	18.7834i	0.466025	+	0.731143i
$661$	−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
$670$	−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	$-0.912474\pi$
$673$		−	14.0877i		−	0.543039i	0.962433	−	0.271520i	$-0.0875262\pi$
$674$	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	−0.834817	−	0.550528i	$-0.814427\pi$
$677$	−23.2659	−	40.2976i	−0.894179	−	1.54876i	−0.0593624	−	0.998236i	$-0.518907\pi$
$678$	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	−0.991947	−	0.126655i	$-0.959576\pi$
$683$	−10.0953	+	17.4856i	−0.386287	+	0.669069i	0.605660	+	0.795724i	$0.292909\pi$
$684$	−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	−0.961301	−	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
$695$	−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	−0.995651	−	0.0931605i	$-0.970303\pi$
$709$	−15.4039	−	26.6803i	−0.578505	−	1.00200i	0.417146	−	0.908839i	$-0.363030\pi$
$710$	−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	0.999966	+	0.00824342i	$0.00262399\pi$
$719$	13.5981	+	23.5525i	0.507122	+	0.878361i	−0.492844	+	0.870118i	$0.664043\pi$
$720$	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	$-0.0177062\pi$
$733$	12.2125	+	21.1526i	0.451078	+	0.781290i	−0.547375	+	0.836887i	$0.684373\pi$
$734$	−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	$-0.698262\pi$
$740$	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	−0.957902	−	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	$-0.844901\pi$
$757$		−	25.7640i		−	0.936409i	0.883620	−	0.468204i	$-0.155099\pi$
$758$	−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	$-0.952263\pi$
$761$	−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
$765$	−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	$-0.742282\pi$
$773$	7.84490	−	13.5878i	0.282161	−	0.488718i	0.971917	+	0.235325i	$0.0756153\pi$
$774$	−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	$-0.532485\pi$
$787$	−28.4557	−	16.4289i	−1.01434	−	0.585628i	−0.912459	+	0.409169i	$0.865819\pi$
$788$	−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	$-0.511556\pi$
$797$	−2.04937			−0.0725925			−0.0362963	+	0.999341i	$0.511556\pi$
$798$		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	−0.524025	−	0.851703i	$-0.675570\pi$
$809$	13.5270	−	23.4294i	0.475584	−	0.823735i	0.999609	+	0.0279678i	$0.00890360\pi$
$810$	−24.6813	+	25.6048i	−0.867213	+	0.899661i
$811$	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
$815$	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	0.988151	+	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	−0.595423	−	0.803412i	$-0.703016\pi$
$823$	11.4196	−	19.7794i	0.398064	−	0.689466i	0.993487	+	0.113946i	$0.0363490\pi$
$824$	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	$-0.0616589\pi$
$829$	37.5809	+	21.6973i	1.30524	+	0.753579i	0.323940	+	0.946077i	$0.394992\pi$
$830$	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	$-0.311432\pi$
$839$	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
$845$	−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	$-0.484019\pi$
$853$	2.93137			0.100368			0.0501840	+	0.998740i	$0.484019\pi$
$854$		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	$-0.802875\pi$
$857$	2.79695	−	4.84446i	0.0955419	−	0.165483i	0.909835	+	0.414971i	$0.136208\pi$
$858$	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	$0.783326\pi$
$860$	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	0.999611	+	0.0279016i	$0.00888250\pi$
$863$	15.3926	+	26.6607i	0.523969	+	0.907541i	−0.475642	+	0.879639i	$0.657784\pi$
$864$	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	−0.578255	−	0.815856i	$-0.696266\pi$
$877$	−4.76284	+	2.74983i	−0.160830	+	0.0928551i	0.417425	+	0.908711i	$0.362933\pi$
$878$	−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	$-0.487570\pi$
$887$	27.5169	−	15.8869i	0.923927	−	0.533429i	0.884886	+	0.465808i	$0.154236\pi$
$888$	−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	−0.0567196	+	0.998390i	$0.518064\pi$
$907$	−26.8937	+	46.5813i	−0.892991	+	1.54671i	−0.836271	+	0.548316i	$0.815269\pi$
$908$	−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
$915$	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	−0.941337	−	0.337469i	$-0.890429\pi$
$919$	−33.9452	+	19.5983i	−1.11975	+	0.646487i	−0.178411	+	0.983956i	$0.557096\pi$
$920$	−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	$-0.824368\pi$
$929$	−25.0980	+	14.4903i	−0.823438	+	0.475412i	0.0281624	+	0.999603i	$0.491034\pi$
$930$	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	$-0.799420\pi$
$937$	−49.4631			−1.61589			−0.807944	+	0.589259i	$0.799420\pi$
$938$		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	$-0.287743\pi$
$941$	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	$0.159813\pi$
$947$	26.3131	+	45.5756i	0.855060	+	1.48101i	−0.0215294	+	0.999768i	$0.506854\pi$
$948$	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	$0.169011\pi$
$953$			31.2637i			1.01273i	−0.862319	+	0.506365i	$0.830989\pi$
$954$	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	0.995056	+	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
$975$	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	0.682299	−	0.731073i	$-0.260980\pi$
$977$	12.2003	+	7.04383i	0.390321	+	0.225352i	−0.291978	+	0.956425i	$0.594313\pi$
$978$	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	$-0.586193\pi$
$983$	−38.7426	−	22.3680i	−1.23570	−	0.713430i	−0.968212	+	0.250132i	$0.919526\pi$
$984$	−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	0.507877	−	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	$-0.560360\pi$
$997$	23.8790	−	41.3597i	0.756256	−	1.30987i	0.944748	−	0.327799i	$-0.106307\pi$
$998$	−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.619.2		32
4.3	odd	2	inner	980.2.s.f.619.5		32
5.4	even	2	inner	980.2.s.f.619.15		32
7.2	even	3	inner	980.2.s.f.19.11		32
7.3	odd	6		140.2.c.b.139.10	yes	16
7.4	even	3		140.2.c.b.139.9	yes	16
7.5	odd	6	inner	980.2.s.f.19.12		32
7.6	odd	2	inner	980.2.s.f.619.1		32
20.19	odd	2	inner	980.2.s.f.619.12		32
28.3	even	6		140.2.c.b.139.5	✓	16
28.11	odd	6		140.2.c.b.139.6	yes	16
28.19	even	6	inner	980.2.s.f.19.15		32
28.23	odd	6	inner	980.2.s.f.19.16		32
28.27	even	2	inner	980.2.s.f.619.6		32
35.3	even	12		700.2.g.l.251.1		16
35.4	even	6		140.2.c.b.139.8	yes	16
35.9	even	6	inner	980.2.s.f.19.6		32
35.17	even	12		700.2.g.l.251.16		16
35.18	odd	12		700.2.g.l.251.2		16
35.19	odd	6	inner	980.2.s.f.19.5		32
35.24	odd	6		140.2.c.b.139.7	yes	16
35.32	odd	12		700.2.g.l.251.15		16
35.34	odd	2	inner	980.2.s.f.619.16		32
56.3	even	6		2240.2.e.f.2239.14		16
56.11	odd	6		2240.2.e.f.2239.3		16
56.45	odd	6		2240.2.e.f.2239.2		16
56.53	even	6		2240.2.e.f.2239.15		16
140.3	odd	12		700.2.g.l.251.4		16
140.19	even	6	inner	980.2.s.f.19.2		32
140.39	odd	6		140.2.c.b.139.11	yes	16
140.59	even	6		140.2.c.b.139.12	yes	16
140.67	even	12		700.2.g.l.251.14		16
140.79	odd	6	inner	980.2.s.f.19.1		32
140.87	odd	12		700.2.g.l.251.13		16
140.123	even	12		700.2.g.l.251.3		16
140.139	even	2	inner	980.2.s.f.619.11		32
280.59	even	6		2240.2.e.f.2239.4		16
280.109	even	6		2240.2.e.f.2239.1		16
280.179	odd	6		2240.2.e.f.2239.13		16
280.269	odd	6		2240.2.e.f.2239.16		16

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