LMFDB - Embedded newform 980.2.o.f.411.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(31,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.31"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [32,2,0,-2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == 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			411.4
Character	$\chi$	$=$	980.411
Dual form			980.2.o.f.31.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.950668 - 1.04701i) q^{2} +(-1.36859 - 2.37047i) q^{3} +(-0.192463 + 1.99072i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.18083 + 3.68646i) q^{6} +(2.26727 - 1.69100i) q^{8} +(-2.24609 + 3.89033i) q^{9} +(-0.299797 - 1.38207i) q^{10} +(0.0868131 - 0.0501216i) q^{11} +(4.98234 - 2.26825i) q^{12} -4.11735i q^{13} -2.73718i q^{15} +(-3.92592 - 0.766277i) q^{16} +(-4.67424 + 2.69867i) q^{17} +(6.20850 - 1.34674i) q^{18} +(-3.72967 + 6.45997i) q^{19} +(-1.16204 + 1.62778i) q^{20} +(-0.135008 - 0.0432453i) q^{22} +(1.30623 + 0.754151i) q^{23} +(-7.11143 - 3.06021i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-4.31091 + 3.91424i) q^{26} +4.08434 q^{27} -2.37688 q^{29} +(-2.86586 + 2.60215i) q^{30} +(2.72129 + 4.71341i) q^{31} +(2.92994 + 4.83895i) q^{32} +(-0.237623 - 0.137192i) q^{33} +(7.26919 + 2.32844i) q^{34} +(-7.31227 - 5.22007i) q^{36} +(-0.519260 + 0.899386i) q^{37} +(10.3093 - 2.23629i) q^{38} +(-9.76007 + 5.63498i) q^{39} +(2.80901 - 0.330814i) q^{40} +7.99125i q^{41} +7.04778i q^{43} +(0.0830696 + 0.182467i) q^{44} +(-3.89033 + 2.24609i) q^{45} +(-0.452184 - 2.08458i) q^{46} +(-2.22188 + 3.84841i) q^{47} +(3.55654 + 10.3550i) q^{48} +(0.431404 - 1.34681i) q^{50} +(12.7943 + 7.38677i) q^{51} +(8.19649 + 0.792437i) q^{52} +(-3.07131 - 5.31966i) q^{53} +(-3.88285 - 4.27635i) q^{54} +0.100243 q^{55} +20.4176 q^{57} +(2.25962 + 2.48862i) q^{58} +(-4.26148 - 7.38111i) q^{59} +(5.44896 + 0.526805i) q^{60} +(-6.84408 - 3.95143i) q^{61} +(2.34795 - 7.33010i) q^{62} +(2.28103 - 7.66791i) q^{64} +(2.05868 - 3.56573i) q^{65} +(0.0822594 + 0.379218i) q^{66} +(-0.0950895 + 0.0549000i) q^{67} +(-4.47268 - 9.82449i) q^{68} -4.12850i q^{69} -6.73221i q^{71} +(1.48607 + 12.6186i) q^{72} +(5.32344 - 3.07349i) q^{73} +(1.43531 - 0.311345i) q^{74} +(1.36859 - 2.37047i) q^{75} +(-12.1422 - 8.66802i) q^{76} +(15.1785 + 4.86190i) q^{78} +(3.70178 + 2.13723i) q^{79} +(-3.01680 - 2.62657i) q^{80} +(1.14846 + 1.98919i) q^{81} +(8.36692 - 7.59702i) q^{82} +6.50159 q^{83} -5.39735 q^{85} +(7.37910 - 6.70009i) q^{86} +(3.25298 + 5.63433i) q^{87} +(0.112073 - 0.260440i) q^{88} +(2.76417 + 1.59589i) q^{89} +(6.05009 + 1.93794i) q^{90} +(-1.75270 + 2.45519i) q^{92} +(7.44866 - 12.9015i) q^{93} +(6.14160 - 1.33223i) q^{94} +(-6.45997 + 3.72967i) q^{95} +(7.46070 - 13.5679i) q^{96} +11.0691i q^{97} +0.450309i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 16 q^{9} + 30 q^{12} - 14 q^{16} - 8 q^{22} - 36 q^{24} + 16 q^{25} - 30 q^{26} - 40 q^{29} + 2 q^{32} + 60 q^{36} + 8 q^{37} + 60 q^{38} - 18 q^{44} - 12 q^{45} + 2 q^{46}+ \cdots + 60 q^{96}+O(q^{100})$ 32 * q + 2 * q^2 - 2 * q^4 - 4 * q^8 - 16 * q^9 + 30 * q^12 - 14 * q^16 - 8 * q^22 - 36 * q^24 + 16 * q^25 - 30 * q^26 - 40 * q^29 + 2 * q^32 + 60 * q^36 + 8 * q^37 + 60 * q^38 - 18 * q^44 - 12 * q^45 + 2 * q^46 + 4 * q^50 + 36 * q^52 - 8 * q^53 - 12 * q^54 + 48 * q^57 + 2 * q^58 + 14 * q^60 - 24 * q^61 + 4 * q^64 + 4 * q^65 - 24 * q^66 - 60 * q^68 + 4 * q^72 + 72 * q^73 + 38 * q^74 + 120 * q^78 - 36 * q^81 - 42 * q^82 + 28 * q^86 + 4 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^93 - 18 * q^94 + 60 * q^96

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

)

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

$2$	−0.950668	−	1.04701i	−0.672223	−	0.740348i
$2$	−0.950668	−	1.04701i	−0.672223	−	0.740348i
$3$	−1.36859	−	2.37047i	−0.790157	−	1.36859i	−0.925870	−	0.377843i	$-0.876666\pi$
$3$	−1.36859	−	2.37047i	−0.790157	−	1.36859i	0.135713	−	0.990748i	$-0.456668\pi$
$4$	−0.192463	+	1.99072i	−0.0962313	+	0.995359i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.18083	+	3.68646i	−0.482073	+	1.50499i
$7$		0			0
$7$		0			0
$8$	2.26727	−	1.69100i	0.801601	−	0.597859i
$9$	−2.24609	+	3.89033i	−0.748695	+	1.29678i
$10$	−0.299797	−	1.38207i	−0.0948041	−	0.437049i
$11$	0.0868131	−	0.0501216i	0.0261751	−	0.0151122i	−0.486855	−	0.873483i	$-0.661856\pi$
$11$	0.0868131	−	0.0501216i	0.0261751	−	0.0151122i	0.513030	+	0.858370i	$0.328523\pi$
$12$	4.98234	−	2.26825i	1.43828	−	0.654788i
$13$		−	4.11735i		−	1.14195i	−0.820968	−	0.570974i	$-0.806566\pi$
$13$		−	4.11735i		−	1.14195i	0.820968	−	0.570974i	$-0.193434\pi$
$14$		0			0
$15$		−	2.73718i		−	0.706738i
$16$	−3.92592	−	0.766277i	−0.981479	−	0.191569i
$17$	−4.67424	+	2.69867i	−1.13367	+	0.654525i	−0.944855	−	0.327488i	$-0.893798\pi$
$17$	−4.67424	+	2.69867i	−1.13367	+	0.654525i	−0.188815	+	0.982013i	$0.560465\pi$
$18$	6.20850	−	1.34674i	1.46336	−	0.317429i
$19$	−3.72967	+	6.45997i	−0.855645	+	1.48202i	0.0204012	+	0.999792i	$0.493506\pi$
$19$	−3.72967	+	6.45997i	−0.855645	+	1.48202i	−0.876046	+	0.482228i	$0.839828\pi$
$20$	−1.16204	+	1.62778i	−0.259839	+	0.363983i
$21$		0			0
$22$	−0.135008	−	0.0432453i	−0.0287838	−	0.00921993i
$23$	1.30623	+	0.754151i	0.272367	+	0.157251i	0.629963	−	0.776625i	$-0.283070\pi$
$23$	1.30623	+	0.754151i	0.272367	+	0.157251i	−0.357596	+	0.933877i	$0.616403\pi$
$24$	−7.11143	−	3.06021i	−1.45162	−	0.624662i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−4.31091	+	3.91424i	−0.845440	+	0.767645i
$27$	4.08434			0.786032
$28$		0			0
$29$	−2.37688			−0.441376			−0.220688	−	0.975344i	$-0.570830\pi$
$29$	−2.37688			−0.441376			−0.220688	+	0.975344i	$0.570830\pi$
$30$	−2.86586	+	2.60215i	−0.523232	+	0.475086i
$31$	2.72129	+	4.71341i	0.488758	+	0.846553i	0.999916	−	0.0129330i	$-0.00411682\pi$
$31$	2.72129	+	4.71341i	0.488758	+	0.846553i	−0.511159	+	0.859486i	$0.670783\pi$
$32$	2.92994	+	4.83895i	0.517945	+	0.855414i
$33$	−0.237623	−	0.137192i	−0.0413649	−	0.0238820i
$34$	7.26919	+	2.32844i	1.24666	+	0.399324i
$35$		0			0
$36$	−7.31227	−	5.22007i	−1.21871	−	0.870011i
$37$	−0.519260	+	0.899386i	−0.0853659	+	0.147858i	−0.905547	−	0.424246i	$-0.860539\pi$
$37$	−0.519260	+	0.899386i	−0.0853659	+	0.147858i	0.820181	+	0.572104i	$0.193873\pi$
$38$	10.3093	−	2.23629i	1.67240	−	0.362773i
$39$	−9.76007	+	5.63498i	−1.56286	+	0.902318i
$40$	2.80901	−	0.330814i	0.444144	−	0.0523063i
$41$			7.99125i			1.24802i	0.781415	+	0.624012i	$0.214498\pi$
$41$			7.99125i			1.24802i	−0.781415	+	0.624012i	$0.785502\pi$
$42$		0			0
$43$			7.04778i			1.07478i	0.843335	+	0.537388i	$0.180589\pi$
$43$			7.04778i			1.07478i	−0.843335	+	0.537388i	$0.819411\pi$
$44$	0.0830696	+	0.182467i	0.0125232	+	0.0275079i
$45$	−3.89033	+	2.24609i	−0.579937	+	0.334827i
$46$	−0.452184	−	2.08458i	−0.0666710	−	0.307355i
$47$	−2.22188	+	3.84841i	−0.324095	+	0.561348i	−0.981329	−	0.192338i	$-0.938393\pi$
$47$	−2.22188	+	3.84841i	−0.324095	+	0.561348i	0.657234	+	0.753686i	$0.271726\pi$
$48$	3.55654	+	10.3550i	0.513342	+	1.49461i
$49$		0			0
$50$	0.431404	−	1.34681i	0.0610097	−	0.190467i
$51$	12.7943	+	7.38677i	1.79155	+	1.03435i
$52$	8.19649	+	0.792437i	1.13665	+	0.109891i
$53$	−3.07131	−	5.31966i	−0.421876	−	0.730711i	0.574247	−	0.818682i	$-0.305295\pi$
$53$	−3.07131	−	5.31966i	−0.421876	−	0.730711i	−0.996123	+	0.0879710i	$0.971962\pi$
$54$	−3.88285	−	4.27635i	−0.528389	−	0.581938i
$55$	0.100243			0.0135168
$56$		0			0
$57$	20.4176			2.70437
$58$	2.25962	+	2.48862i	0.296703	+	0.326772i
$59$	−4.26148	−	7.38111i	−0.554798	−	0.960938i	−0.997919	−	0.0644767i	$-0.979462\pi$
$59$	−4.26148	−	7.38111i	−0.554798	−	0.960938i	0.443121	−	0.896462i	$-0.353871\pi$
$60$	5.44896	+	0.526805i	0.703458	+	0.0680103i
$61$	−6.84408	−	3.95143i	−0.876295	−	0.505929i	−0.00685975	−	0.999976i	$-0.502184\pi$
$61$	−6.84408	−	3.95143i	−0.876295	−	0.505929i	−0.869435	+	0.494048i	$0.835517\pi$
$62$	2.34795	−	7.33010i	0.298190	−	0.930924i
$63$		0			0
$64$	2.28103	−	7.66791i	0.285129	−	0.958489i
$65$	2.05868	−	3.56573i	0.255348	−	0.442275i
$66$	0.0822594	+	0.379218i	0.0101254	+	0.0466785i
$67$	−0.0950895	+	0.0549000i	−0.0116170	+	0.00670710i	−0.505797	−	0.862652i	$-0.668802\pi$
$67$	−0.0950895	+	0.0549000i	−0.0116170	+	0.00670710i	0.494180	+	0.869359i	$0.335468\pi$
$68$	−4.47268	−	9.82449i	−0.542393	−	1.19139i
$69$		−	4.12850i		−	0.497013i
$70$		0			0
$71$		−	6.73221i		−	0.798967i	−0.916740	−	0.399483i	$-0.869190\pi$
$71$		−	6.73221i		−	0.798967i	0.916740	−	0.399483i	$-0.130810\pi$
$72$	1.48607	+	12.6186i	0.175135	+	1.48711i
$73$	5.32344	−	3.07349i	0.623062	−	0.359725i	−0.154998	−	0.987915i	$-0.549537\pi$
$73$	5.32344	−	3.07349i	0.623062	−	0.359725i	0.778060	+	0.628190i	$0.216204\pi$
$74$	1.43531	−	0.311345i	0.166851	−	0.0361932i
$75$	1.36859	−	2.37047i	0.158031	−	0.273718i
$76$	−12.1422	−	8.66802i	−1.39280	−	0.994290i
$77$		0			0
$78$	15.1785	+	4.86190i	1.71862	+	0.550502i
$79$	3.70178	+	2.13723i	0.416483	+	0.240457i	0.693572	−	0.720388i	$-0.256036\pi$
$79$	3.70178	+	2.13723i	0.416483	+	0.240457i	−0.277088	+	0.960844i	$0.589369\pi$
$80$	−3.01680	−	2.62657i	−0.337289	−	0.293660i
$81$	1.14846	+	1.98919i	0.127607	+	0.221021i
$82$	8.36692	−	7.59702i	0.923972	−	0.838951i
$83$	6.50159			0.713642			0.356821	−	0.934173i	$-0.383861\pi$
$83$	6.50159			0.713642			0.356821	+	0.934173i	$0.383861\pi$
$84$		0			0
$85$	−5.39735			−0.585425
$86$	7.37910	−	6.70009i	0.795709	−	0.722490i
$87$	3.25298	+	5.63433i	0.348756	+	0.604063i
$88$	0.112073	−	0.260440i	0.0119470	−	0.0277630i
$89$	2.76417	+	1.59589i	0.293001	+	0.169164i	0.639294	−	0.768962i	$-0.279226\pi$
$89$	2.76417	+	1.59589i	0.293001	+	0.169164i	−0.346293	+	0.938126i	$0.612560\pi$
$90$	6.05009	+	1.93794i	0.637735	+	0.204277i
$91$		0			0
$92$	−1.75270	+	2.45519i	−0.182732	+	0.255971i
$93$	7.44866	−	12.9015i	0.772391	−	1.33782i
$94$	6.14160	−	1.33223i	0.633457	−	0.137409i
$95$	−6.45997	+	3.72967i	−0.662779	+	0.382656i
$96$	7.46070	−	13.5679i	0.761454	−	1.38477i
$97$			11.0691i			1.12390i	0.827173	+	0.561948i	$0.189948\pi$
$97$			11.0691i			1.12390i	−0.827173	+	0.561948i	$0.810052\pi$
$98$		0			0
$99$			0.450309i			0.0452578i
$100$	−1.82024	+	0.828682i	−0.182024	+	0.0828682i
$101$	6.20412	−	3.58195i	0.617333	−	0.356418i	−0.158497	−	0.987359i	$-0.550665\pi$
$101$	6.20412	−	3.58195i	0.617333	−	0.356418i	0.775830	+	0.630942i	$0.217331\pi$
$102$	−4.42906	−	20.4181i	−0.438542	−	2.02169i
$103$	−2.44304	+	4.23147i	−0.240720	+	0.416939i	−0.960920	−	0.276828i	$-0.910717\pi$
$103$	−2.44304	+	4.23147i	−0.240720	+	0.416939i	0.720200	+	0.693767i	$0.244050\pi$
$104$	−6.96245	−	9.33516i	−0.682724	−	0.915388i
$105$		0			0
$106$	−2.64995	+	8.27292i	−0.257386	+	0.803537i
$107$	6.55470	+	3.78436i	0.633667	+	0.365848i	0.782171	−	0.623064i	$-0.214112\pi$
$107$	6.55470	+	3.78436i	0.633667	+	0.365848i	−0.148504	+	0.988912i	$0.547446\pi$
$108$	−0.786083	+	8.13077i	−0.0756409	+	0.782384i
$109$	9.02662	+	15.6346i	0.864593	+	1.49752i	0.867451	+	0.497523i	$0.165757\pi$
$109$	9.02662	+	15.6346i	0.864593	+	1.49752i	−0.00285729	+	0.999996i	$0.500910\pi$
$110$	−0.0952979	−	0.104956i	−0.00908630	−	0.0100071i
$111$	2.84262			0.269810
$112$		0			0
$113$	−18.1432			−1.70677			−0.853384	−	0.521283i	$-0.825453\pi$
$113$	−18.1432			−1.70677			−0.853384	+	0.521283i	$0.825453\pi$
$114$	−19.4103	−	21.3774i	−1.81794	−	2.00218i
$115$	0.754151	+	1.30623i	0.0703250	+	0.121806i
$116$	0.457461	−	4.73170i	0.0424742	−	0.439328i
$117$	16.0179	+	9.24793i	1.48085	+	0.854971i
$118$	−3.67684	+	11.4788i	−0.338481	+	1.05671i
$119$		0			0
$120$	−4.62858	−	6.20593i	−0.422529	−	0.566522i
$121$	−5.49498	+	9.51758i	−0.499543	+	0.865234i
$122$	2.36925	+	10.9223i	0.214502	+	0.988861i
$123$	18.9430	−	10.9368i	1.70803	−	0.986134i
$124$	−9.90682	+	4.51016i	−0.889658	+	0.405025i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			4.37573i			0.388283i	0.980974	+	0.194141i	$0.0621921\pi$
$127$			4.37573i			0.388283i	−0.980974	+	0.194141i	$0.937808\pi$
$128$	−10.1969	+	4.90137i	−0.901286	+	0.433224i
$129$	16.7065	−	9.64553i	1.47093	−	0.849241i
$130$	−5.69048	+	1.23437i	−0.499088	+	0.108261i
$131$	1.49073	−	2.58201i	0.130245	−	0.225592i	−0.793526	−	0.608537i	$-0.791757\pi$
$131$	1.49073	−	2.58201i	0.130245	−	0.225592i	0.923771	+	0.382945i	$0.125090\pi$
$132$	0.318844	−	0.446637i	0.0277518	−	0.0388747i
$133$		0			0
$134$	0.147879	+	0.0473681i	0.0127748	+	0.00409198i
$135$	3.53714	+	2.04217i	0.304429	+	0.175762i
$136$	−6.03431	+	14.0228i	−0.517438	+	1.20244i
$137$	0.762377	+	1.32048i	0.0651342	+	0.112816i	0.896754	−	0.442530i	$-0.145919\pi$
$137$	0.762377	+	1.32048i	0.0651342	+	0.112816i	−0.831619	+	0.555346i	$0.812586\pi$
$138$	−4.32258	+	3.92483i	−0.367963	+	0.334104i
$139$	−7.16082			−0.607373			−0.303686	−	0.952772i	$-0.598217\pi$
$139$	−7.16082			−0.607373			−0.303686	+	0.952772i	$0.598217\pi$
$140$		0			0
$141$	12.1634			1.02434
$142$	−7.04870	+	6.40010i	−0.591514	+	0.537084i
$143$	−0.206368	−	0.357440i	−0.0172574	−	0.0298907i
$144$	11.7990	−	13.5520i	0.983251	−	1.12933i
$145$	−2.05844	−	1.18844i	−0.170944	−	0.0986947i
$146$	−8.27880	−	2.65183i	−0.685158	−	0.219467i
$147$		0			0
$148$	−1.69048	−	1.20680i	−0.138957	−	0.0991983i
$149$	10.5236	−	18.2275i	0.862129	−	1.49325i	−0.00774027	−	0.999970i	$-0.502464\pi$
$149$	10.5236	−	18.2275i	0.862129	−	1.49325i	0.869870	−	0.493282i	$-0.164203\pi$
$150$	−3.78298	+	0.820599i	−0.308879	+	0.0670016i
$151$	−3.31081	+	1.91150i	−0.269430	+	0.155555i	−0.628628	−	0.777706i	$-0.716383\pi$
$151$	−3.31081	+	1.91150i	−0.269430	+	0.155555i	0.359199	+	0.933261i	$0.383050\pi$
$152$	2.46765	+	20.9534i	0.200153	+	1.69954i
$153$		−	24.2458i		−	1.96016i
$154$		0			0
$155$			5.44258i			0.437158i
$156$	−9.33920	−	20.5141i	−0.747735	−	1.64244i
$157$	1.11209	−	0.642065i	0.0887543	−	0.0512423i	−0.454966	−	0.890509i	$-0.650349\pi$
$157$	1.11209	−	0.642065i	0.0887543	−	0.0512423i	0.543720	+	0.839266i	$0.317015\pi$
$158$	−1.28147	−	5.90760i	−0.101948	−	0.469983i
$159$	−8.40673	+	14.5609i	−0.666697	+	1.15475i
$160$	0.117927	+	5.65562i	0.00932296	+	0.447116i
$161$		0			0
$162$	0.990900	−	3.09351i	0.0778525	−	0.243049i
$163$	−7.44875	−	4.30054i	−0.583431	−	0.336844i	0.179064	−	0.983837i	$-0.442693\pi$
$163$	−7.44875	−	4.30054i	−0.583431	−	0.336844i	−0.762496	+	0.646993i	$0.776026\pi$
$164$	−15.9083	−	1.53802i	−1.24223	−	0.120099i
$165$	−0.137192	−	0.237623i	−0.0106804	−	0.0184989i
$166$	−6.18085	−	6.80723i	−0.479727	−	0.528343i
$167$	8.10448			0.627144			0.313572	−	0.949565i	$-0.398474\pi$
$167$	8.10448			0.627144			0.313572	+	0.949565i	$0.398474\pi$
$168$		0			0
$169$	−3.95261			−0.304047
$170$	5.13109	+	5.65108i	0.393536	+	0.433418i
$171$	−16.7543	−	29.0193i	−1.28123	−	2.21916i
$172$	−14.0301	−	1.35643i	−1.06979	−	0.103427i
$173$	6.95744	+	4.01688i	0.528964	+	0.305398i	0.740595	−	0.671952i	$-0.234544\pi$
$173$	6.95744	+	4.01688i	0.528964	+	0.305398i	−0.211630	+	0.977350i	$0.567877\pi$
$174$	2.80670	−	8.76228i	0.212775	−	0.664267i
$175$		0			0
$176$	−0.379228	+	0.130250i	−0.0285854	+	0.00981797i
$177$	−11.6645	+	20.2034i	−0.876755	+	1.51858i
$178$	−0.956887	−	4.41128i	−0.0717217	−	0.330639i
$179$	−7.66309	+	4.42429i	−0.572766	+	0.330687i	−0.758253	−	0.651960i	$-0.773947\pi$
$179$	−7.66309	+	4.42429i	−0.572766	+	0.330687i	0.185487	+	0.982647i	$0.440614\pi$
$180$	−3.72258	−	8.17684i	−0.277465	−	0.609466i
$181$			21.3610i			1.58775i	0.608082	+	0.793874i	$0.291939\pi$
$181$			21.3610i			1.58775i	−0.608082	+	0.793874i	$0.708061\pi$
$182$		0			0
$183$			21.6316i			1.59905i
$184$	4.23684	−	0.498968i	0.312344	−	0.0367844i
$185$	−0.899386	+	0.519260i	−0.0661241	+	0.0381768i
$186$	−20.5892	+	4.46617i	−1.50967	+	0.327476i
$187$	−0.270524	+	0.468561i	−0.0197826	+	0.0342645i
$188$	−7.23347	−	5.16381i	−0.527555	−	0.376610i
$189$		0			0
$190$	10.0463	+	3.21799i	0.728835	+	0.233457i
$191$	−21.6710	−	12.5117i	−1.56806	−	0.905317i	−0.996396	−	0.0848269i	$-0.972966\pi$
$191$	−21.6710	−	12.5117i	−1.56806	−	0.905317i	−0.571660	−	0.820491i	$-0.693700\pi$
$192$	−21.2984	+	5.08712i	−1.53708	+	0.367131i
$193$	−4.08078	−	7.06813i	−0.293741	−	0.508775i	0.680950	−	0.732330i	$-0.261567\pi$
$193$	−4.08078	−	7.06813i	−0.293741	−	0.508775i	−0.974691	+	0.223555i	$0.928234\pi$
$194$	11.5894	−	10.5230i	0.832074	−	0.755509i
$195$	−11.2700			−0.807058
$196$		0			0
$197$	−12.4517			−0.887149			−0.443574	−	0.896238i	$-0.646290\pi$
$197$	−12.4517			−0.887149			−0.443574	+	0.896238i	$0.646290\pi$
$198$	0.471478	−	0.428094i	0.0335065	−	0.0304233i
$199$	11.5867	+	20.0687i	0.821358	+	1.42263i	0.904671	+	0.426110i	$0.140116\pi$
$199$	11.5867	+	20.0687i	0.821358	+	1.42263i	−0.0833132	+	0.996523i	$0.526550\pi$
$200$	2.59808	+	1.11801i	0.183712	+	0.0790555i
$201$	0.260277	+	0.150271i	0.0183586	+	0.0105993i
$202$	−9.64840	−	3.09054i	−0.678859	−	0.217449i
$203$		0			0
$204$	−17.1674	+	24.0481i	−1.20196	+	1.68370i
$205$	−3.99562	+	6.92062i	−0.279067	+	0.483357i
$206$	6.75291	−	1.46483i	0.470498	−	0.102060i
$207$	−5.86780	+	3.38778i	−0.407840	+	0.235467i
$208$	−3.15504	+	16.1644i	−0.218762	+	1.12080i
$209$			0.747747i			0.0517228i
$210$		0			0
$211$			10.9759i			0.755613i	0.925885	+	0.377807i	$0.123322\pi$
$211$			10.9759i			0.755613i	−0.925885	+	0.377807i	$0.876678\pi$
$212$	11.1811	−	5.09027i	0.767918	−	0.349601i
$213$	−15.9585	+	9.21365i	−1.09346	+	0.631309i
$214$	−2.26908	−	10.4605i	−0.155111	−	0.715066i
$215$	−3.52389	+	6.10355i	−0.240327	+	0.416259i
$216$	9.26031	−	6.90663i	0.630084	−	0.469936i
$217$		0			0
$218$	7.78824	−	24.3142i	0.527486	−	1.64677i
$219$	−14.5712	−	8.41270i	−0.984633	−	0.568478i
$220$	−0.0192930	+	0.199556i	−0.00130074	+	0.0134540i
$221$	11.1114	+	19.2455i	0.747434	+	1.29459i
$222$	−2.70239	−	2.97626i	−0.181372	−	0.199753i
$223$	−14.9798			−1.00312			−0.501559	−	0.865123i	$-0.667240\pi$
$223$	−14.9798			−1.00312			−0.501559	+	0.865123i	$0.667240\pi$
$224$		0			0
$225$	−4.49217			−0.299478
$226$	17.2481	+	18.9961i	1.14733	+	1.26360i
$227$	0.753708	+	1.30546i	0.0500254	+	0.0866465i	0.889954	−	0.456051i	$-0.150736\pi$
$227$	0.753708	+	1.30546i	0.0500254	+	0.0866465i	−0.839928	+	0.542697i	$0.817403\pi$
$228$	−3.92962	+	40.6456i	−0.260245	+	2.69182i
$229$	−7.38329	−	4.26274i	−0.487901	−	0.281690i	0.235802	−	0.971801i	$-0.424228\pi$
$229$	−7.38329	−	4.26274i	−0.487901	−	0.281690i	−0.723703	+	0.690111i	$0.757562\pi$
$230$	0.650688	−	2.03139i	0.0429051	−	0.133946i
$231$		0			0
$232$	−5.38904	+	4.01931i	−0.353808	+	0.263881i
$233$	10.6117	−	18.3799i	0.695193	−	1.20411i	−0.274922	−	0.961467i	$-0.588652\pi$
$233$	10.6117	−	18.3799i	0.695193	−	1.20411i	0.970115	−	0.242644i	$-0.0780146\pi$
$234$	−5.54500	−	25.5626i	−0.362488	−	1.67108i
$235$	−3.84841	+	2.22188i	−0.251043	+	0.144940i
$236$	15.5139	−	7.06283i	1.00987	−	0.459751i
$237$		−	11.7000i		−	0.759994i
$238$		0			0
$239$		−	10.1532i		−	0.656754i	−0.944547	−	0.328377i	$-0.893498\pi$
$239$		−	10.1532i		−	0.656754i	0.944547	−	0.328377i	$-0.106502\pi$
$240$	−2.09744	+	10.7460i	−0.135389	+	0.693648i
$241$	−16.4985	+	9.52539i	−1.06276	+	0.613584i	−0.926194	−	0.377047i	$-0.876940\pi$
$241$	−16.4985	+	9.52539i	−1.06276	+	0.613584i	−0.136565	+	0.990631i	$0.543606\pi$
$242$	15.1889	−	3.29475i	0.976379	−	0.211795i
$243$	9.27006	−	16.0562i	0.594674	−	1.03001i
$244$	9.18342	−	12.8641i	0.587908	−	0.823542i
$245$		0			0
$246$	−29.4594	−	9.43632i	−1.87826	−	0.601638i
$247$	26.5980	+	15.3564i	1.69239	+	0.977102i
$248$	14.1403	+	6.08488i	0.897909	+	0.386390i
$249$	−8.89801	−	15.4118i	−0.563889	−	0.976684i
$250$	1.04701	−	0.950668i	0.0662188	−	0.0601255i
$251$	9.46184			0.597226			0.298613	−	0.954374i	$-0.403476\pi$
$251$	9.46184			0.597226			0.298613	+	0.954374i	$0.403476\pi$
$252$		0			0
$253$	0.151197			0.00950567
$254$	4.58143	−	4.15986i	0.287465	−	0.261013i
$255$	7.38677	+	12.7943i	0.462577	+	0.801207i
$256$	14.8256	+	6.01668i	0.926602	+	0.376043i
$257$	−2.37760	−	1.37271i	−0.148310	−	0.0856270i	0.424008	−	0.905658i	$-0.360623\pi$
$257$	−2.37760	−	1.37271i	−0.148310	−	0.0856270i	−0.572319	+	0.820031i	$0.693956\pi$
$258$	−25.9813	−	8.32224i	−1.61753	−	0.518120i
$259$		0			0
$260$	6.70215	+	4.78452i	0.415650	+	0.296723i
$261$	5.33868	−	9.24686i	0.330456	−	0.572367i
$262$	−4.12058	+	0.893830i	−0.254570	+	0.0552210i
$263$	−22.2367	+	12.8384i	−1.37117	+	0.791648i	−0.991076	−	0.133298i	$-0.957443\pi$
$263$	−22.2367	+	12.8384i	−1.37117	+	0.791648i	−0.380098	+	0.924946i	$0.624110\pi$
$264$	−0.770748	+	0.0907700i	−0.0474363	+	0.00558651i
$265$		−	6.14261i		−	0.377338i
$266$		0			0
$267$		−	8.73650i		−	0.534665i
$268$	−0.0909892	−	0.199863i	−0.00555805	−	0.0122086i
$269$	−7.10140	+	4.10000i	−0.432980	+	0.249981i	−0.700615	−	0.713539i	$-0.747091\pi$
$269$	−7.10140	+	4.10000i	−0.432980	+	0.249981i	0.267635	+	0.963520i	$0.413758\pi$
$270$	−1.22447	−	5.64485i	−0.0745191	−	0.343535i
$271$	−3.20364	+	5.54886i	−0.194607	+	0.337069i	−0.946772	−	0.321906i	$-0.895676\pi$
$271$	−3.20364	+	5.54886i	−0.194607	+	0.337069i	0.752165	+	0.658975i	$0.229010\pi$
$272$	20.4186	−	7.01301i	1.23806	−	0.425226i
$273$		0			0
$274$	0.657785	−	2.05355i	0.0397382	−	0.124059i
$275$	0.0868131	+	0.0501216i	0.00523503	+	0.00302244i
$276$	8.21868	+	0.794582i	0.494706	+	0.0478282i
$277$	−7.98456	−	13.8297i	−0.479746	−	0.830944i	0.519984	−	0.854176i	$-0.325938\pi$
$277$	−7.98456	−	13.8297i	−0.479746	−	0.830944i	−0.999730	+	0.0232316i	$0.992604\pi$
$278$	6.80756	+	7.49745i	0.408290	+	0.449667i
$279$	−24.4490			−1.46372
$280$		0			0
$281$	−9.68409			−0.577704			−0.288852	−	0.957374i	$-0.593274\pi$
$281$	−9.68409			−0.577704			−0.288852	+	0.957374i	$0.593274\pi$
$282$	−11.5633	−	12.7352i	−0.688587	−	0.758370i
$283$	−13.0633	−	22.6264i	−0.776535	−	1.34500i	−0.933928	−	0.357462i	$-0.883642\pi$
$283$	−13.0633	−	22.6264i	−0.776535	−	1.34500i	0.157393	−	0.987536i	$-0.449691\pi$
$284$	13.4019	+	1.29570i	0.795259	+	0.0768856i
$285$	17.6821	+	10.2088i	1.04740	+	0.604716i
$286$	−0.178056	+	0.555877i	−0.0105287	+	0.0328697i
$287$		0			0
$288$	−25.4060	+	0.529749i	−1.49706	+	0.0312158i
$289$	6.06569	−	10.5061i	0.356805	−	0.618005i
$290$	0.712582	+	3.28502i	0.0418443	+	0.192903i
$291$	26.2389	−	15.1491i	1.53815	−	0.888053i
$292$	5.09389	+	11.1890i	0.298097	+	0.654787i
$293$		−	16.2389i		−	0.948684i	−0.880341	−	0.474342i	$-0.842686\pi$
$293$		−	16.2389i		−	0.948684i	0.880341	−	0.474342i	$-0.157314\pi$
$294$		0			0
$295$		−	8.52297i		−	0.496226i
$296$	0.343557	+	2.91722i	0.0199689	+	0.169560i
$297$	0.354574	−	0.204714i	0.0205745	−	0.0118787i
$298$	−29.0888	+	6.30990i	−1.68507	+	0.365523i
$299$	3.10511	−	5.37821i	0.179573	−	0.311030i
$300$	4.45553	+	3.18071i	0.257240	+	0.183638i
$301$		0			0
$302$	5.14883	+	1.64925i	0.296282	+	0.0949039i
$303$	−16.9818	−	9.80446i	−0.975580	−	0.563251i
$304$	19.5925	−	22.5034i	1.12371	−	1.29066i
$305$	−3.95143	−	6.84408i	−0.226258	−	0.391891i
$306$	−25.3856	+	23.0497i	−1.45120	+	1.31766i
$307$	23.5437			1.34371			0.671854	−	0.740684i	$-0.265498\pi$
$307$	23.5437			1.34371			0.671854	+	0.740684i	$0.265498\pi$
$308$		0			0
$309$	13.3741			0.760825
$310$	5.69844	−	5.17408i	0.323649	−	0.293868i
$311$	2.69773	+	4.67261i	0.152974	+	0.264959i	0.932320	−	0.361635i	$-0.117781\pi$
$311$	2.69773	+	4.67261i	0.152974	+	0.264959i	−0.779345	+	0.626595i	$0.784448\pi$
$312$	−12.6000	+	29.2803i	−0.713333	+	1.65767i
$313$	−28.1990	−	16.2807i	−1.59390	−	0.920240i	−0.992629	−	0.121197i	$-0.961327\pi$
$313$	−28.1990	−	16.2807i	−1.59390	−	0.920240i	−0.601274	−	0.799043i	$-0.705340\pi$
$314$	−1.72948	−	0.553979i	−0.0975999	−	0.0312628i
$315$		0			0
$316$	−4.96707	+	6.95787i	−0.279420	+	0.391411i
$317$	−6.85587	+	11.8747i	−0.385064	+	0.666951i	−0.991778	−	0.127970i	$-0.959154\pi$
$317$	−6.85587	+	11.8747i	−0.385064	+	0.666951i	0.606714	+	0.794920i	$0.292487\pi$
$318$	23.2374	−	5.04062i	1.30309	−	0.282664i
$319$	−0.206344	+	0.119133i	−0.0115531	+	0.00667017i
$320$	5.80939	−	5.50009i	0.324755	−	0.307464i
$321$		−	20.7170i		−	1.15631i
$322$		0			0
$323$		−	40.2606i		−	2.24016i
$324$	−4.18095	+	1.90341i	−0.232275	+	0.105745i
$325$	3.56573	−	2.05868i	0.197791	−	0.114195i
$326$	2.57858	+	11.8873i	0.142814	+	0.658377i
$327$	24.7075	−	42.7947i	1.36633	−	2.36655i
$328$	13.5132	+	18.1183i	0.746142	+	1.00042i
$329$		0			0
$330$	−0.118370	+	0.369542i	−0.00651607	+	0.0203426i
$331$	−4.92495	−	2.84342i	−0.270700	−	0.156289i	0.358506	−	0.933527i	$-0.383286\pi$
$331$	−4.92495	−	2.84342i	−0.270700	−	0.156289i	−0.629206	+	0.777239i	$0.716620\pi$
$332$	−1.25131	+	12.9428i	−0.0686747	+	0.710330i
$333$	−2.33261	−	4.04019i	−0.127826	−	0.221401i
$334$	−7.70467	−	8.48548i	−0.421581	−	0.464305i
$335$	−0.109800			−0.00599901
$336$		0			0
$337$	−14.7219			−0.801955			−0.400978	−	0.916088i	$-0.631330\pi$
$337$	−14.7219			−0.801955			−0.400978	+	0.916088i	$0.631330\pi$
$338$	3.75762	+	4.13843i	0.204388	+	0.225101i
$339$	24.8306	+	43.0079i	1.34861	+	2.33587i
$340$	1.03879	−	10.7446i	0.0563362	−	0.582708i
$341$	0.472487	+	0.272790i	0.0255866	+	0.0147724i
$342$	−14.4557	+	45.1296i	−0.781677	+	2.44033i
$343$		0			0
$344$	11.9178	+	15.9792i	0.642564	+	0.861542i
$345$	2.06425	−	3.57539i	0.111135	−	0.192492i
$346$	−2.40850	−	11.1032i	−0.129482	−	0.596913i
$347$	13.3966	−	7.73454i	0.719168	−	0.415212i	−0.0952784	−	0.995451i	$-0.530374\pi$
$347$	13.3966	−	7.73454i	0.719168	−	0.415212i	0.814446	+	0.580239i	$0.197041\pi$
$348$	−11.8424	+	5.39137i	−0.634821	+	0.289008i
$349$			11.5290i			0.617132i	0.951203	+	0.308566i	$0.0998491\pi$
$349$			11.5290i			0.617132i	−0.951203	+	0.308566i	$0.900151\pi$
$350$		0			0
$351$		−	16.8167i		−	0.897608i
$352$	0.496893	+	0.273231i	0.0264845	+	0.0145633i
$353$	−17.6983	+	10.2181i	−0.941985	+	0.543855i	−0.890582	−	0.454823i	$-0.849703\pi$
$353$	−17.6983	+	10.2181i	−0.941985	+	0.543855i	−0.0514030	+	0.998678i	$0.516369\pi$
$354$	32.2422	−	6.99394i	1.71366	−	0.371724i
$355$	3.36611	−	5.83027i	0.178654	−	0.309438i
$356$	−3.70897	+	5.19553i	−0.196575	+	0.275362i
$357$		0			0
$358$	11.9173	+	3.81731i	0.629850	+	0.201751i
$359$	18.3761	+	10.6095i	0.969856	+	0.559946i	0.899192	−	0.437554i	$-0.144155\pi$
$359$	18.3761	+	10.6095i	0.969856	+	0.559946i	0.0706634	+	0.997500i	$0.477488\pi$
$360$	−5.02231	+	11.6710i	−0.264699	+	0.615118i
$361$	−18.3208	−	31.7326i	−0.964255	−	1.67014i
$362$	22.3652	−	20.3072i	1.17549	−	1.06732i
$363$	30.0815			1.57887
$364$		0			0
$365$	6.14698			0.321748
$366$	22.6485	−	20.5644i	1.18386	−	1.07492i
$367$	−3.82574	−	6.62637i	−0.199702	−	0.345894i	0.748730	−	0.662875i	$-0.230664\pi$
$367$	−3.82574	−	6.62637i	−0.199702	−	0.345894i	−0.948432	+	0.316982i	$0.897331\pi$
$368$	−4.55025	−	3.96167i	−0.237198	−	0.206516i
$369$	−31.0886	−	17.9490i	−1.61841	−	0.934389i
$370$	1.39869	+	0.448022i	0.0727143	+	0.0232916i
$371$		0			0
$372$	24.2496	+	17.3112i	1.25728	+	0.897546i
$373$	−12.8172	+	22.2000i	−0.663647	+	1.14947i	0.316003	+	0.948758i	$0.397659\pi$
$373$	−12.8172	+	22.2000i	−0.663647	+	1.14947i	−0.979650	+	0.200713i	$0.935674\pi$
$374$	0.747766	−	0.162204i	0.0386661	−	0.00838738i
$375$	2.37047	−	1.36859i	0.122411	−	0.0706738i
$376$	1.47006	+	12.4826i	0.0758125	+	0.643740i
$377$			9.78647i			0.504029i
$378$		0			0
$379$			29.1039i			1.49497i	0.664279	+	0.747485i	$0.268739\pi$
$379$			29.1039i			1.49497i	−0.664279	+	0.747485i	$0.731261\pi$
$380$	−6.18141	−	13.5778i	−0.317100	−	0.696527i
$381$	10.3725	−	5.98858i	0.531401	−	0.306804i
$382$	7.50196	+	34.5842i	0.383834	+	1.76948i
$383$	−4.32161	+	7.48525i	−0.220824	+	0.382478i	−0.955058	−	0.296418i	$-0.904208\pi$
$383$	−4.32161	+	7.48525i	−0.220824	+	0.382478i	0.734234	+	0.678896i	$0.237541\pi$
$384$	25.5739	+	17.4635i	1.30506	+	0.891178i
$385$		0			0
$386$	−3.52093	+	10.9921i	−0.179211	+	0.559481i
$387$	−27.4182	−	15.8299i	−1.39375	−	0.804679i
$388$	−22.0354	−	2.13038i	−1.11868	−	0.108154i
$389$	7.08846	+	12.2776i	0.359399	+	0.622498i	0.987861	−	0.155343i	$-0.0496483\pi$
$389$	7.08846	+	12.2776i	0.359399	+	0.622498i	−0.628461	+	0.777841i	$0.716315\pi$
$390$	10.7140	+	11.7998i	0.542523	+	0.597504i
$391$	−8.14084			−0.411700
$392$		0			0
$393$	−8.16078			−0.411657
$394$	11.8375	+	13.0371i	0.596362	+	0.656799i
$395$	2.13723	+	3.70178i	0.107536	+	0.186257i
$396$	−0.896438	−	0.0866677i	−0.0450477	−	0.00435521i
$397$	−0.151559	−	0.0875029i	−0.00760655	−	0.00439164i	0.496192	−	0.868213i	$-0.334731\pi$
$397$	−0.151559	−	0.0875029i	−0.00760655	−	0.00439164i	−0.503798	+	0.863821i	$0.668065\pi$
$398$	9.99708	−	31.2101i	0.501108	−	1.56442i
$399$		0			0
$400$	−1.29934	−	3.78308i	−0.0649671	−	0.189154i
$401$	−12.0285	+	20.8339i	−0.600674	+	1.04040i	0.392046	+	0.919946i	$0.371768\pi$
$401$	−12.0285	+	20.8339i	−0.600674	+	1.04040i	−0.992719	+	0.120452i	$0.961566\pi$
$402$	−0.0901017	−	0.415371i	−0.00449386	−	0.0207168i
$403$	19.4068	−	11.2045i	0.966721	−	0.558136i
$404$	5.93659	+	13.0401i	0.295357	+	0.648767i
$405$			2.29692i			0.114135i
$406$		0			0
$407$			0.104105i			0.00516027i
$408$	41.4991	−	4.88729i	2.05451	−	0.241957i
$409$	10.3372	−	5.96818i	0.511141	−	0.295108i	−0.222161	−	0.975010i	$-0.571311\pi$
$409$	10.3372	−	5.96818i	0.511141	−	0.295108i	0.733303	+	0.679902i	$0.237978\pi$
$410$	11.0445	−	2.39575i	0.545448	−	0.118318i
$411$	2.08676	−	3.61438i	0.102932	−	0.178284i
$412$	−7.95347	−	5.67780i	−0.391839	−	0.279725i
$413$		0			0
$414$	9.12536	+	2.92300i	0.448487	+	0.143658i
$415$	5.63054	+	3.25079i	0.276392	+	0.159575i
$416$	19.9237	−	12.0636i	0.976839	−	0.591467i
$417$	9.80023	+	16.9745i	0.479919	+	0.831245i
$418$	0.782899	−	0.710859i	0.0382929	−	0.0347692i
$419$	−30.1003			−1.47050			−0.735249	−	0.677798i	$-0.762935\pi$
$419$	−30.1003			−1.47050			−0.735249	+	0.677798i	$0.762935\pi$
$420$		0			0
$421$	6.78256			0.330562			0.165281	−	0.986247i	$-0.447147\pi$
$421$	6.78256			0.330562			0.165281	+	0.986247i	$0.447147\pi$
$422$	11.4919	−	10.4344i	0.559417	−	0.507941i
$423$	−9.98107	−	17.2877i	−0.485296	−	0.840557i
$424$	−15.9590	−	6.86753i	−0.775039	−	0.333517i
$425$	−4.67424	−	2.69867i	−0.226734	−	0.130905i
$426$	24.8180	+	7.94961i	1.20244	+	0.385160i
$427$		0			0
$428$	−8.79513	+	12.3202i	−0.425128	+	0.595520i
$429$	−0.564868	+	0.978379i	−0.0272721	+	0.0472366i
$430$	9.74053	−	2.11290i	0.469730	−	0.101893i
$431$	13.8010	−	7.96802i	0.664772	−	0.383806i	−0.129321	−	0.991603i	$-0.541280\pi$
$431$	13.8010	−	7.96802i	0.664772	−	0.383806i	0.794093	+	0.607797i	$0.207946\pi$
$432$	−16.0348	−	3.12974i	−0.771474	−	0.150580i
$433$			15.1291i			0.727057i	0.931583	+	0.363529i	$0.118428\pi$
$433$			15.1291i			0.727057i	−0.931583	+	0.363529i	$0.881572\pi$
$434$		0			0
$435$			6.50596i			0.311937i
$436$	−32.8613	+	14.9604i	−1.57377	+	0.716472i
$437$	−9.74360	+	5.62547i	−0.466099	+	0.269103i
$438$	5.04421	+	23.2539i	0.241021	+	1.11112i
$439$	2.18337	−	3.78171i	0.104207	−	0.180491i	−0.809207	−	0.587523i	$-0.800103\pi$
$439$	2.18337	−	3.78171i	0.104207	−	0.180491i	0.913414	+	0.407032i	$0.133436\pi$
$440$	0.227278	−	0.169511i	0.0108351	−	0.00808113i
$441$		0			0
$442$	9.58701	−	29.9298i	0.456007	−	1.42362i
$443$	−12.2094	−	7.04909i	−0.580086	−	0.334913i	0.181082	−	0.983468i	$-0.442040\pi$
$443$	−12.2094	−	7.04909i	−0.580086	−	0.334913i	−0.761167	+	0.648555i	$0.775373\pi$
$444$	−0.547098	+	5.65886i	−0.0259641	+	0.268558i
$445$	1.59589	+	2.76417i	0.0756526	+	0.131034i
$446$	14.2408	+	15.6840i	0.674320	+	0.742657i
$447$	−57.6102			−2.72487
$448$		0			0
$449$	17.0120			0.802848			0.401424	−	0.915892i	$-0.368515\pi$
$449$	17.0120			0.802848			0.401424	+	0.915892i	$0.368515\pi$
$450$	4.27056	+	4.70335i	0.201316	+	0.221718i
$451$	0.400534	+	0.693745i	0.0188604	+	0.0326672i
$452$	3.49188	−	36.1180i	0.164244	−	1.69885i
$453$	9.06228	+	5.23211i	0.425783	+	0.245826i
$454$	0.650306	−	2.03020i	0.0305204	−	0.0952820i
$455$		0			0
$456$	46.2922	−	34.5261i	2.16783	−	1.61683i
$457$	−5.83234	+	10.1019i	−0.272825	+	0.472548i	−0.969584	−	0.244758i	$-0.921291\pi$
$457$	−5.83234	+	10.1019i	−0.272825	+	0.472548i	0.696759	+	0.717306i	$0.254625\pi$
$458$	2.55591	+	11.7828i	0.119430	+	0.550575i
$459$	−19.0912	+	11.0223i	−0.891101	+	0.514477i
$460$	−2.74548	+	1.24990i	−0.128009	+	0.0582770i
$461$		−	26.4488i		−	1.23184i	−0.787808	−	0.615921i	$-0.788784\pi$
$461$		−	26.4488i		−	1.23184i	0.787808	−	0.615921i	$-0.211216\pi$
$462$		0			0
$463$			3.13685i			0.145782i	0.997340	+	0.0728909i	$0.0232225\pi$
$463$			3.13685i			0.145782i	−0.997340	+	0.0728909i	$0.976778\pi$
$464$	9.33144	+	1.82135i	0.433201	+	0.0845541i
$465$	12.9015	−	7.44866i	0.598291	−	0.345424i
$466$	−29.3322	+	6.36269i	−1.35879	+	0.294746i
$467$	4.07057	−	7.05043i	0.188363	−	0.326255i	−0.756341	−	0.654177i	$-0.773015\pi$
$467$	4.07057	−	7.05043i	0.188363	−	0.326255i	0.944705	+	0.327922i	$0.106348\pi$
$468$	−21.4929	+	30.1072i	−0.993508	+	1.39171i
$469$		0			0
$470$	5.98489	+	1.91706i	0.276062	+	0.0884272i
$471$	−3.04399	−	1.75745i	−0.140260	−	0.0809789i
$472$	−22.1434	−	9.52880i	−1.01923	−	0.438599i
$473$	0.353246	+	0.611839i	0.0162422	+	0.0281324i
$474$	−12.2500	+	11.1228i	−0.562660	+	0.510886i
$475$	−7.45934			−0.342258
$476$		0			0
$477$	27.5937			1.26343
$478$	−10.6305	+	9.65229i	−0.486227	+	0.441485i
$479$	−12.3904	−	21.4608i	−0.566131	−	0.980567i	−0.996944	−	0.0781258i	$-0.975106\pi$
$479$	−12.3904	−	21.4608i	−0.566131	−	0.980567i	0.430813	−	0.902441i	$-0.358227\pi$
$480$	13.2451	−	8.01978i	0.604553	−	0.366051i
$481$	3.70309	+	2.13798i	0.168846	+	0.0974835i
$482$	25.6577	+	8.21858i	1.16868	+	0.374346i
$483$		0			0
$484$	−17.8892	−	12.7707i	−0.813147	−	0.580487i
$485$	−5.53454	+	9.58611i	−0.251311	+	0.435283i
$486$	−25.6238	+	5.55827i	−1.16232	+	0.252128i
$487$	10.9938	−	6.34726i	0.498175	−	0.287622i	−0.229784	−	0.973242i	$-0.573802\pi$
$487$	10.9938	−	6.34726i	0.498175	−	0.287622i	0.727960	+	0.685620i	$0.240469\pi$
$488$	−22.1993	+	2.61438i	−1.00491	+	0.118347i
$489$			23.5427i			1.06464i
$490$		0			0
$491$			9.51192i			0.429267i	0.976695	+	0.214633i	$0.0688557\pi$
$491$			9.51192i			0.429267i	−0.976695	+	0.214633i	$0.931144\pi$
$492$	18.1262	+	39.8151i	0.817191	+	1.79500i
$493$	11.1101	−	6.41443i	0.500375	−	0.288892i
$494$	−9.20758	−	42.4472i	−0.414269	−	1.90979i
$495$	−0.225155	+	0.389979i	−0.0101199	+	0.0175283i
$496$	−7.07177	−	20.5897i	−0.317532	−	0.924506i
$497$		0			0
$498$	−7.67728	+	23.9678i	−0.344027	+	1.07402i
$499$	−7.35497	−	4.24639i	−0.329254	−	0.190095i	0.326256	−	0.945281i	$-0.394213\pi$
$499$	−7.35497	−	4.24639i	−0.329254	−	0.190095i	−0.655510	+	0.755187i	$0.727546\pi$
$500$	−1.99072	−	0.192463i	−0.0890276	−	0.00860719i
$501$	−11.0917	−	19.2114i	−0.495542	−	0.858303i
$502$	−8.99507	−	9.90665i	−0.401469	−	0.442155i
$503$	10.4796			0.467261			0.233630	−	0.972325i	$-0.424939\pi$
$503$	10.4796			0.467261			0.233630	+	0.972325i	$0.424939\pi$
$504$		0			0
$505$	7.16390			0.318790
$506$	−0.143738	−	0.158305i	−0.00638993	−	0.00703751i
$507$	5.40951	+	9.36955i	0.240245	+	0.416116i
$508$	−8.71084	−	0.842164i	−0.386481	−	0.0373650i
$509$	19.7483	+	11.4017i	0.875329	+	0.505371i	0.869115	−	0.494609i	$-0.164689\pi$
$509$	19.7483	+	11.4017i	0.875329	+	0.505371i	0.00621337	+	0.999981i	$0.498022\pi$
$510$	6.37336	−	19.8971i	0.282217	−	0.881059i
$511$		0			0
$512$	−7.79472	−	21.2425i	−0.344481	−	0.938793i
$513$	−15.2332	+	26.3847i	−0.672564	+	1.16492i
$514$	0.823066	+	3.79435i	0.0363039	+	0.167362i
$515$	−4.23147	+	2.44304i	−0.186461	+	0.107653i
$516$	15.9861	+	35.1144i	0.703751	+	1.54583i
$517$			0.445456i			0.0195912i
$518$		0			0
$519$		−	21.9899i		−	0.965248i
$520$	−1.36208	−	11.5657i	−0.0597311	−	0.507190i
$521$	7.88048	−	4.54980i	0.345250	−	0.199330i	−0.317341	−	0.948311i	$-0.602790\pi$
$521$	7.88048	−	4.54980i	0.345250	−	0.199330i	0.662591	+	0.748981i	$0.269457\pi$
$522$	−14.7569	+	3.20104i	−0.645891	+	0.140106i
$523$	−2.38048	+	4.12311i	−0.104091	+	0.180291i	−0.913366	−	0.407138i	$-0.866527\pi$
$523$	−2.38048	+	4.12311i	−0.104091	+	0.180291i	0.809275	+	0.587429i	$0.199860\pi$
$524$	4.85315	+	3.46456i	0.212011	+	0.151350i
$525$		0			0
$526$	34.5816	+	11.0771i	1.50783	+	0.482982i
$527$	−25.4399	−	14.6877i	−1.10818	−	0.639808i
$528$	0.827762	+	0.720689i	0.0360237	+	0.0313640i
$529$	−10.3625	−	17.9484i	−0.450544	−	0.780365i
$530$	−6.43138	+	5.83958i	−0.279361	+	0.253655i
$531$	38.2866			1.66150
$532$		0			0
$533$	32.9028			1.42518
$534$	−9.14721	+	8.30551i	−0.395838	+	0.359414i
$535$	3.78436	+	6.55470i	0.163612	+	0.283384i
$536$	−0.122758	+	0.285270i	−0.00530233	+	0.0123218i
$537$	20.9753	+	12.1101i	0.905150	+	0.522588i
$538$	11.0438	+	3.53751i	0.476133	+	0.152513i
$539$		0			0
$540$	−4.74615	+	6.64842i	−0.204242	+	0.286102i
$541$	11.2312	−	19.4530i	0.482867	−	0.836350i	−0.516939	−	0.856022i	$-0.672929\pi$
$541$	11.2312	−	19.4530i	0.482867	−	0.836350i	0.999806	+	0.0196717i	$0.00626211\pi$
$542$	8.85531	−	1.92088i	0.380368	−	0.0825089i
$543$	50.6355	−	29.2344i	2.17298	−	1.25457i
$544$	−26.7540	−	14.7115i	−1.14707	−	0.630749i
$545$			18.0532i			0.773316i
$546$		0			0
$547$		−	24.4644i		−	1.04602i	−0.852326	−	0.523012i	$-0.824808\pi$
$547$		−	24.4644i		−	1.04602i	0.852326	−	0.523012i	$-0.175192\pi$
$548$	−2.77542	+	1.26353i	−0.118560	+	0.0539755i
$549$	30.7448	−	17.7505i	1.31215	−	0.757573i
$550$	−0.0300526	−	0.138543i	−0.00128145	−	0.00590750i
$551$	8.86498	−	15.3546i	0.377661	−	0.654128i
$552$	−6.98130	−	9.36043i	−0.297144	−	0.398406i
$553$		0			0
$554$	−6.88915	+	21.5073i	−0.292692	+	0.913759i
$555$	2.46178	+	1.42131i	0.104497	+	0.0603313i
$556$	1.37819	−	14.2552i	0.0584483	−	0.604554i
$557$	4.21627	+	7.30280i	0.178649	+	0.309430i	0.941418	−	0.337242i	$-0.109494\pi$
$557$	4.21627	+	7.30280i	0.178649	+	0.309430i	−0.762769	+	0.646671i	$0.776161\pi$
$558$	23.2429	+	25.5983i	0.983948	+	1.08366i
$559$	29.0182			1.22734
$560$		0			0
$561$	1.48095			0.0625255
$562$	9.20635	+	10.1393i	0.388346	+	0.427702i
$563$	−13.5833	−	23.5269i	−0.572467	−	0.991541i	−0.996312	−	0.0858067i	$-0.972653\pi$
$563$	−13.5833	−	23.5269i	−0.572467	−	0.991541i	0.423845	−	0.905735i	$-0.360680\pi$
$564$	−2.34100	+	24.2139i	−0.0985738	+	1.01959i
$565$	−15.7125	−	9.07159i	−0.661028	−	0.381645i
$566$	−11.2712	+	35.1876i	−0.473762	+	1.47905i
$567$		0			0
$568$	−11.3842	−	15.2638i	−0.477669	−	0.640453i
$569$	−7.11643	+	12.3260i	−0.298336	+	0.516733i	−0.975755	−	0.218864i	$-0.929765\pi$
$569$	−7.11643	+	12.3260i	−0.298336	+	0.516733i	0.677419	+	0.735597i	$0.263098\pi$
$570$	−6.12112	−	28.2185i	−0.256386	−	1.18194i
$571$	−14.5870	+	8.42181i	−0.610447	+	0.352442i	−0.773140	−	0.634235i	$-0.781315\pi$
$571$	−14.5870	+	8.42181i	−0.610447	+	0.352442i	0.162693	+	0.986677i	$0.447982\pi$
$572$	0.751281	−	0.342027i	0.0314126	−	0.0143009i
$573$			68.4938i			2.86137i
$574$		0			0
$575$			1.50830i			0.0629006i
$576$	24.7073	+	26.0968i	1.02947	+	1.08737i
$577$	−1.86487	+	1.07668i	−0.0776356	+	0.0448230i	−0.538315	−	0.842744i	$-0.680939\pi$
$577$	−1.86487	+	1.07668i	−0.0776356	+	0.0448230i	0.460680	+	0.887566i	$0.347606\pi$
$578$	−16.7664	+	3.63695i	−0.697392	+	0.151277i
$579$	−11.1699	+	19.3468i	−0.464203	+	0.804024i
$580$	2.76202	−	3.86904i	0.114687	−	0.160653i
$581$		0			0
$582$	−40.8057	−	13.0707i	−1.69145	−	0.541799i
$583$	−0.533259	−	0.307877i	−0.0220853	−	0.0127510i
$584$	6.87241	−	15.9704i	0.284382	−	0.660859i
$585$	9.24793	+	16.0179i	0.382355	+	0.662258i
$586$	−17.0023	+	15.4378i	−0.702357	+	0.637728i
$587$	11.3061			0.466652			0.233326	−	0.972399i	$-0.425039\pi$
$587$	11.3061			0.466652			0.233326	+	0.972399i	$0.425039\pi$
$588$		0			0
$589$	−40.5980			−1.67281
$590$	−8.92364	+	8.10251i	−0.367380	+	0.333575i
$591$	17.0413	+	29.5164i	0.700986	+	1.21414i
$592$	2.72775	−	3.13301i	0.112110	−	0.128766i
$593$	−14.7570	−	8.51993i	−0.605996	−	0.349872i	0.165401	−	0.986226i	$-0.447108\pi$
$593$	−14.7570	−	8.51993i	−0.605996	−	0.349872i	−0.771397	+	0.636355i	$0.780442\pi$
$594$	−0.551420	−	0.176629i	−0.0226250	−	0.00724716i
$595$		0			0
$596$	34.2603	+	24.4577i	1.40336	+	1.00183i
$597$	31.7149	−	54.9318i	1.29800	−	2.24821i
$598$	−8.58296	+	1.86180i	−0.350984	+	0.0761348i
$599$	3.39864	−	1.96221i	0.138865	−	0.0801736i	−0.428958	−	0.903324i	$-0.641119\pi$
$599$	3.39864	−	1.96221i	0.138865	−	0.0801736i	0.567823	+	0.823151i	$0.307786\pi$
$600$	−0.905498	−	7.68879i	−0.0369668	−	0.313893i
$601$			8.98026i			0.366312i	0.983084	+	0.183156i	$0.0586314\pi$
$601$			8.98026i			0.366312i	−0.983084	+	0.183156i	$0.941369\pi$
$602$		0			0
$603$		−	0.493240i		−	0.0200863i
$604$	−3.16804	−	6.95877i	−0.128906	−	0.283149i
$605$	−9.51758	+	5.49498i	−0.386945	+	0.223403i
$606$	5.87869	+	27.1009i	0.238806	+	1.10090i
$607$	−18.7895	+	32.5444i	−0.762644	+	1.32094i	0.178840	+	0.983878i	$0.442766\pi$
$607$	−18.7895	+	32.5444i	−0.762644	+	1.32094i	−0.941483	+	0.337059i	$0.890568\pi$
$608$	−42.1872	+	0.879659i	−1.71092	+	0.0356749i
$609$		0			0
$610$	−3.40933	+	10.6436i	−0.138040	+	0.430948i
$611$	15.8453	+	9.14827i	0.641031	+	0.370099i
$612$	48.2666	+	4.66641i	1.95106	+	0.188629i
$613$	23.1299	+	40.0621i	0.934207	+	1.61809i	0.776042	+	0.630681i	$0.217224\pi$
$613$	23.1299	+	40.0621i	0.934207	+	1.61809i	0.158165	+	0.987413i	$0.449442\pi$
$614$	−22.3822	−	24.6505i	−0.903272	−	0.994812i
$615$	21.8735			0.882025
$616$		0			0
$617$	−42.8844			−1.72646			−0.863231	−	0.504809i	$-0.831563\pi$
$617$	−42.8844			−1.72646			−0.863231	+	0.504809i	$0.831563\pi$
$618$	−12.7143	−	14.0028i	−0.511445	−	0.563276i
$619$	14.7503	+	25.5483i	0.592865	+	1.02687i	0.993844	+	0.110785i	$0.0353364\pi$
$619$	14.7503	+	25.5483i	0.592865	+	1.02687i	−0.400980	+	0.916087i	$0.631330\pi$
$620$	−10.8346	−	1.04749i	−0.435129	−	0.0420683i
$621$	5.33508	+	3.08021i	0.214090	+	0.123605i
$622$	2.32762	−	7.26665i	0.0933293	−	0.291366i
$623$		0			0
$624$	42.6352	−	14.6435i	1.70677	−	0.586210i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.76181	+	45.0022i	0.390160	+	1.79865i
$627$	1.77251	−	1.02336i	0.0707873	−	0.0408691i
$628$	1.06413	+	2.33743i	0.0424636	+	0.0932735i
$629$		−	5.60526i		−	0.223496i
$630$		0			0
$631$			20.5872i			0.819563i	0.912184	+	0.409781i	$0.134395\pi$
$631$			20.5872i			0.819563i	−0.912184	+	0.409781i	$0.865605\pi$
$632$	12.0070	−	1.41405i	0.477613	−	0.0562478i
$633$	26.0181	−	15.0215i	1.03413	−	0.597053i
$634$	18.9506	−	4.11074i	0.752625	−	0.163258i
$635$	−2.18786	+	3.78949i	−0.0868227	+	0.150381i
$636$	−27.3686	−	19.5378i	−1.08524	−	0.774726i
$637$		0			0
$638$	0.320899	+	0.102789i	0.0127045	+	0.00406945i
$639$	26.1906	+	15.1211i	1.03608	+	0.598182i
$640$	−11.2815	−	0.853736i	−0.445939	−	0.0337469i
$641$	18.4263	+	31.9153i	0.727795	+	1.26058i	0.957813	+	0.287392i	$0.0927883\pi$
$641$	18.4263	+	31.9153i	0.727795	+	1.26058i	−0.230018	+	0.973186i	$0.573878\pi$
$642$	−21.6909	+	19.6949i	−0.856071	+	0.777297i
$643$	48.4719			1.91154			0.955772	−	0.294108i	$-0.0950227\pi$
$643$	48.4719			1.91154			0.955772	+	0.294108i	$0.0950227\pi$
$644$		0			0
$645$	19.2911			0.759585
$646$	−42.1533	+	38.2745i	−1.65850	+	1.50589i
$647$	−19.5933	−	33.9366i	−0.770292	−	1.33418i	−0.937403	−	0.348247i	$-0.886777\pi$
$647$	−19.5933	−	33.9366i	−0.770292	−	1.33418i	0.167111	−	0.985938i	$-0.446556\pi$
$648$	5.96759	+	2.56799i	0.234429	+	0.100880i
$649$	−0.739905	−	0.427185i	−0.0290438	−	0.0167685i
$650$	−5.54528	−	1.77624i	−0.217504	−	0.0696700i
$651$		0			0
$652$	9.99477	−	14.0007i	0.391425	−	0.548309i
$653$	−3.44161	+	5.96105i	−0.134681	+	0.233274i	−0.925475	−	0.378808i	$-0.876334\pi$
$653$	−3.44161	+	5.96105i	−0.134681	+	0.233274i	0.790795	+	0.612082i	$0.209668\pi$
$654$	−68.2951	+	14.8145i	−2.67055	+	0.579291i
$655$	2.58201	−	1.49073i	0.100888	−	0.0582475i
$656$	6.12351	−	31.3730i	0.239083	−	1.22491i
$657$			27.6133i			1.07730i
$658$		0			0
$659$		−	40.9792i		−	1.59632i	−0.602444	−	0.798161i	$-0.705806\pi$
$659$		−	40.9792i		−	1.59632i	0.602444	−	0.798161i	$-0.294194\pi$
$660$	0.499445	−	0.227377i	0.0194409	−	0.00885063i
$661$	−10.4696	+	6.04460i	−0.407219	+	0.235108i	−0.689594	−	0.724196i	$-0.742211\pi$
$661$	−10.4696	+	6.04460i	−0.407219	+	0.235108i	0.282375	+	0.959304i	$0.408878\pi$
$662$	1.70490	+	7.85962i	0.0662627	+	0.305473i
$663$	30.4139	−	52.6785i	1.18118	−	2.04586i
$664$	14.7409	−	10.9942i	0.572056	−	0.426657i
$665$		0			0
$666$	−2.01259	+	6.28314i	−0.0779863	+	0.243467i
$667$	−3.10475	−	1.79253i	−0.120216	−	0.0694070i
$668$	−1.55981	+	16.1337i	−0.0603508	+	0.624233i
$669$	20.5012	+	35.5091i	0.792621	+	1.37286i
$670$	0.104383	+	0.114962i	0.00403268	+	0.00444136i
$671$	−0.792208			−0.0305828
$672$		0			0
$673$	29.0006			1.11789			0.558945	−	0.829205i	$-0.311206\pi$
$673$	29.0006			1.11789			0.558945	+	0.829205i	$0.311206\pi$
$674$	13.9957	+	15.4140i	0.539093	+	0.593726i
$675$	2.04217	+	3.53714i	0.0786032	+	0.136145i
$676$	0.760730	−	7.86853i	0.0292588	−	0.302636i
$677$	−41.8361	−	24.1541i	−1.60789	−	0.928317i	−0.989841	−	0.142178i	$-0.954589\pi$
$677$	−41.8361	−	24.1541i	−1.60789	−	0.928317i	−0.618051	−	0.786138i	$-0.712077\pi$
$678$	21.4240	−	66.8841i	0.822786	−	2.56867i
$679$		0			0
$680$	−12.2373	+	9.12692i	−0.469277	+	0.350001i
$681$	2.06304	−	3.57329i	0.0790558	−	0.136929i
$682$	−0.163563	−	0.754032i	−0.00626317	−	0.0288734i
$683$	11.4528	−	6.61231i	0.438231	−	0.253013i	−0.264616	−	0.964354i	$-0.585245\pi$
$683$	11.4528	−	6.61231i	0.438231	−	0.253013i	0.702847	+	0.711341i	$0.251912\pi$
$684$	60.9938	−	27.7680i	2.33216	−	1.06173i
$685$			1.52475i			0.0582578i
$686$		0			0
$687$			23.3358i			0.890317i
$688$	5.40055	−	27.6690i	0.205894	−	1.05487i
$689$	−21.9029	+	12.6457i	−0.834435	+	0.481761i
$690$	−5.70588	+	1.23771i	−0.217219	+	0.0471189i
$691$	19.9447	−	34.5453i	0.758733	−	1.31416i	−0.184763	−	0.982783i	$-0.559152\pi$
$691$	19.9447	−	34.5453i	0.758733	−	1.31416i	0.943497	−	0.331382i	$-0.107515\pi$
$692$	−9.33552	+	13.0772i	−0.354883	+	0.497121i
$693$		0			0
$694$	−20.8339	−	6.67342i	−0.790843	−	0.253320i
$695$	−6.20145	−	3.58041i	−0.235234	−	0.135813i
$696$	16.9030	+	7.27376i	0.640708	+	0.275711i
$697$	−21.5658	−	37.3530i	−0.816862	−	1.41485i
$698$	12.0710	−	10.9602i	0.456893	−	0.414851i
$699$	−58.0921			−2.19725
$700$		0			0
$701$	−5.82647			−0.220063			−0.110031	−	0.993928i	$-0.535095\pi$
$701$	−5.82647			−0.220063			−0.110031	+	0.993928i	$0.535095\pi$
$702$	−17.6072	+	15.9871i	−0.664543	+	0.603393i
$703$	−3.87334	−	6.70882i	−0.146086	−	0.253028i
$704$	−0.186304	−	0.780004i	−0.00702160	−	0.0293975i
$705$	10.5338	+	6.08169i	0.396726	+	0.229050i
$706$	27.5237	+	8.81627i	1.03587	+	0.331805i
$707$		0			0
$708$	−37.9744	−	27.1091i	−1.42716	−	1.01882i
$709$	8.29615	−	14.3694i	0.311569	−	0.539653i	−0.667134	−	0.744938i	$-0.732479\pi$
$709$	8.29615	−	14.3694i	0.311569	−	0.539653i	0.978702	+	0.205286i	$0.0658123\pi$
$710$	−9.30440	+	2.01830i	−0.349188	+	0.0757453i
$711$	−16.6290	+	9.60078i	−0.623638	+	0.360058i
$712$	8.96577	−	1.05589i	0.336006	−	0.0395710i
$713$			8.20905i			0.307431i
$714$		0			0
$715$		−	0.412736i		−	0.0154355i
$716$	−7.33265	−	16.1066i	−0.274034	−	0.601930i
$717$	−24.0678	+	13.8955i	−0.898828	+	0.518938i
$718$	−6.36137	−	29.3261i	−0.237404	−	1.09444i
$719$	−1.69923	+	2.94314i	−0.0633704	+	0.109761i	−0.895970	−	0.444115i	$-0.853518\pi$
$719$	−1.69923	+	2.94314i	−0.0633704	+	0.109761i	0.832600	+	0.553875i	$0.186852\pi$
$720$	16.9942	−	5.83687i	0.633338	−	0.217527i
$721$		0			0
$722$	−15.8074	+	49.3493i	−0.588290	+	1.83659i
$723$	45.1593	+	26.0727i	1.67949	+	0.969655i
$724$	−42.5237	−	4.11119i	−1.58038	−	0.152791i
$725$	−1.18844	−	2.05844i	−0.0441376	−	0.0764486i
$726$	−28.5975	−	31.4957i	−1.06135	−	1.16891i
$727$	14.3045			0.530526			0.265263	−	0.964176i	$-0.414541\pi$
$727$	14.3045			0.530526			0.265263	+	0.964176i	$0.414541\pi$
$728$		0			0
$729$	−43.8569			−1.62433
$730$	−5.84373	−	6.43595i	−0.216286	−	0.238205i
$731$	−19.0197	−	32.9430i	−0.703468	−	1.21844i
$732$	−43.0624	−	4.16327i	−1.59163	−	0.153879i
$733$	42.8607	+	24.7457i	1.58310	+	0.914001i	0.994404	+	0.105645i	$0.0336907\pi$
$733$	42.8607	+	24.7457i	1.58310	+	0.914001i	0.588693	+	0.808357i	$0.299643\pi$
$734$	−3.30088	+	10.3051i	−0.121838	+	0.380367i
$735$		0			0
$736$	0.177870	+	8.53039i	0.00655637	+	0.314434i
$737$	−0.00550334	+	0.00953207i	−0.000202718	+	0.000351118i
$738$	10.7621	+	49.6137i	0.396159	+	1.82630i
$739$	−23.2184	+	13.4052i	−0.854104	+	0.493117i	−0.862033	−	0.506852i	$-0.830809\pi$
$739$	−23.2184	+	13.4052i	−0.854104	+	0.493117i	0.00792968	+	0.999969i	$0.497476\pi$
$740$	−0.860603	−	1.89036i	−0.0316364	−	0.0694911i
$741$		−	84.0664i		−	3.08826i
$742$		0			0
$743$			22.2896i			0.817727i	0.912596	+	0.408863i	$0.134075\pi$
$743$			22.2896i			0.817727i	−0.912596	+	0.408863i	$0.865925\pi$
$744$	−4.92824	−	41.8468i	−0.180678	−	1.53418i
$745$	18.2275	−	10.5236i	0.667803	−	0.385556i
$746$	35.4285	−	7.68509i	1.29713	−	0.281371i
$747$	−14.6031	+	25.2933i	−0.534300	+	0.925435i
$748$	−0.880706	−	0.628717i	−0.0322018	−	0.0229882i
$749$		0			0
$750$	−3.68646	−	1.18083i	−0.134610	−	0.0431179i
$751$	−11.1427	−	6.43324i	−0.406603	−	0.234752i	0.282726	−	0.959201i	$-0.408761\pi$
$751$	−11.1427	−	6.43324i	−0.406603	−	0.234752i	−0.689329	+	0.724448i	$0.742095\pi$
$752$	11.6719	−	13.4060i	0.425629	−	0.488865i
$753$	−12.9494	−	22.4290i	−0.471902	−	0.817359i
$754$	10.2465	−	9.30368i	0.373157	−	0.338820i
$755$	−3.82299			−0.139133
$756$		0			0
$757$	−3.66830			−0.133327			−0.0666633	−	0.997776i	$-0.521235\pi$
$757$	−3.66830			−0.133327			−0.0666633	+	0.997776i	$0.521235\pi$
$758$	30.4721	−	27.6682i	1.10680	−	1.00495i
$759$	−0.206927	−	0.358408i	−0.00751097	−	0.0130094i
$760$	−8.33964	+	19.3800i	−0.302511	+	0.702986i
$761$	2.56137	+	1.47880i	0.0928494	+	0.0536066i	0.545706	−	0.837977i	$-0.316262\pi$
$761$	2.56137	+	1.47880i	0.0928494	+	0.0536066i	−0.452856	+	0.891583i	$0.649595\pi$
$762$	−16.1309	−	5.16700i	−0.584362	−	0.187181i
$763$		0			0
$764$	29.0782	−	40.7327i	1.05201	−	1.47366i
$765$	12.1229	−	20.9975i	0.438305	−	0.759166i
$766$	11.9456	−	2.59121i	0.431610	−	0.0936243i
$767$	−30.3906	+	17.5460i	−1.09734	+	0.633551i
$768$	−6.02788	−	43.3781i	−0.217512	−	1.56527i
$769$		−	32.6324i		−	1.17676i	−0.808586	−	0.588378i	$-0.799767\pi$
$769$		−	32.6324i		−	1.17676i	0.808586	−	0.588378i	$-0.200233\pi$
$770$		0			0
$771$			7.51469i			0.270635i
$772$	14.8560	−	6.76334i	0.534681	−	0.243418i
$773$	4.76043	−	2.74844i	0.171221	−	0.0988544i	−0.411941	−	0.911211i	$-0.635149\pi$
$773$	4.76043	−	2.74844i	0.171221	−	0.0988544i	0.583161	+	0.812356i	$0.301816\pi$
$774$	9.49151	+	43.7561i	0.341165	+	1.57278i
$775$	−2.72129	+	4.71341i	−0.0977516	+	0.169311i
$776$	18.7178	+	25.0966i	0.671931	+	0.900916i
$777$		0			0
$778$	6.11598	−	19.0936i	0.219269	−	0.684538i
$779$	−51.6233	−	29.8047i	−1.84960	−	1.06786i
$780$	2.16904	−	22.4353i	0.0776642	−	0.803313i
$781$	−0.337429	−	0.584444i	−0.0120742	−	0.0209131i
$782$	7.73923	+	8.52354i	0.276754	+	0.304801i
$783$	−9.70800			−0.346936
$784$		0			0
$785$	1.28413			0.0458325
$786$	7.75819	+	8.54443i	0.276725	+	0.304770i
$787$	15.7430	+	27.2677i	0.561177	+	0.971987i	0.997394	+	0.0721455i	$0.0229846\pi$
$787$	15.7430	+	27.2677i	0.561177	+	0.971987i	−0.436217	+	0.899841i	$0.643682\pi$
$788$	2.39649	−	24.7879i	0.0853715	−	0.883031i
$789$	60.8659	+	35.1410i	2.16689	+	1.25105i
$790$	1.84402	−	5.75687i	0.0656072	−	0.204820i
$791$		0			0
$792$	0.761473	+	1.02097i	0.0270578	+	0.0362787i
$793$	−16.2694	+	28.1795i	−0.577745	+	1.00068i
$794$	0.0524662	+	0.241870i	0.00186195	+	0.00858366i
$795$	−14.5609	+	8.40673i	−0.516421	+	0.298156i
$796$	−42.1812	+	19.2033i	−1.49507	+	0.680644i
$797$		−	20.2691i		−	0.717968i	−0.933344	−	0.358984i	$-0.883123\pi$
$797$		−	20.2691i		−	0.717968i	0.933344	−	0.358984i	$-0.116877\pi$
$798$		0			0
$799$		−	23.9845i		−	0.848512i
$800$	−2.72568	+	4.95688i	−0.0963675	+	0.175252i
$801$	−12.4171	+	7.16902i	−0.438737	+	0.253305i
$802$	33.2484	−	7.21220i	1.17404	−	0.254672i
$803$	0.308096	−	0.533638i	0.0108725	−	0.0188317i
$804$	−0.349241	+	0.489217i	−0.0123168	+	0.0172534i
$805$		0			0
$806$	−30.1806	−	9.66734i	−1.06307	−	0.340518i
$807$	19.4378	+	11.2224i	0.684244	+	0.395049i
$808$	8.00934	−	18.6124i	0.281768	−	0.654783i
$809$	15.6376	+	27.0851i	0.549789	+	0.952262i	0.998289	+	0.0584790i	$0.0186251\pi$
$809$	15.6376	+	27.0851i	0.549789	+	0.952262i	−0.448500	+	0.893783i	$0.648042\pi$
$810$	2.40490	−	2.18361i	0.0844995	−	0.0767241i
$811$	−51.4855			−1.80790			−0.903950	−	0.427638i	$-0.859346\pi$
$811$	−51.4855			−1.80790			−0.903950	+	0.427638i	$0.859346\pi$
$812$		0			0
$813$	17.5379			0.615080
$814$	0.108999	−	0.0989688i	0.00382040	−	0.00346886i
$815$	−4.30054	−	7.44875i	−0.150641	−	0.260918i
$816$	−44.5689	−	38.8038i	−1.56022	−	1.35840i
$817$	−45.5285	−	26.2859i	−1.59284	−	0.919626i
$818$	−16.0760	−	5.14940i	−0.562084	−	0.180044i
$819$		0			0
$820$	−13.0080	−	9.28612i	−0.454259	−	0.324285i
$821$	24.0601	−	41.6733i	0.839702	−	1.45441i	−0.0504413	−	0.998727i	$-0.516063\pi$
$821$	24.0601	−	41.6733i	0.839702	−	1.45441i	0.890144	−	0.455680i	$-0.150604\pi$
$822$	−5.76812	+	1.25121i	−0.201186	+	0.0436410i
$823$	21.3892	−	12.3490i	0.745580	−	0.430461i	−0.0785148	−	0.996913i	$-0.525018\pi$
$823$	21.3892	−	12.3490i	0.745580	−	0.430461i	0.824095	+	0.566452i	$0.191684\pi$
$824$	1.61638	+	13.7251i	0.0563094	+	0.478135i
$825$		−	0.274384i		−	0.00955282i
$826$		0			0
$827$		−	19.9120i		−	0.692408i	−0.938159	−	0.346204i	$-0.887470\pi$
$827$		−	19.9120i		−	0.692408i	0.938159	−	0.346204i	$-0.112530\pi$
$828$	−5.61477	−	12.3332i	−0.195127	−	0.428607i
$829$	13.8257	−	7.98225i	0.480185	−	0.277235i	−0.240308	−	0.970697i	$-0.577249\pi$
$829$	13.8257	−	7.98225i	0.480185	−	0.277235i	0.720494	+	0.693461i	$0.243915\pi$
$830$	−1.94916	−	8.98566i	−0.0676562	−	0.311897i
$831$	−21.8552	+	37.8543i	−0.758149	+	1.31315i
$832$	−31.5715	−	9.39183i	−1.09455	−	0.325603i
$833$		0			0
$834$	8.45572	−	26.3981i	0.292798	−	0.914090i
$835$	7.01869	+	4.05224i	0.242892	+	0.140234i
$836$	−1.48855	−	0.143913i	−0.0514827	−	0.00497735i
$837$	11.1147	+	19.2512i	0.384179	+	0.665418i
$838$	28.6154	+	31.5154i	0.988503	+	1.08868i
$839$	14.5375			0.501889			0.250944	−	0.968002i	$-0.419259\pi$
$839$	14.5375			0.501889			0.250944	+	0.968002i	$0.419259\pi$
$840$		0			0
$841$	−23.3504			−0.805187
$842$	−6.44796	−	7.10141i	−0.222211	−	0.244731i
$843$	13.2536	+	22.9558i	0.456477	+	0.790641i
$844$	−21.8500	−	2.11245i	−0.752106	−	0.0727136i
$845$	−3.42306	−	1.97631i	−0.117757	−	0.0679870i
$846$	−8.61174	+	26.8851i	−0.296078	+	0.924330i
$847$		0			0
$848$	7.98136	+	23.2380i	0.274081	+	0.797996i
$849$	−35.7568	+	61.9325i	−1.22717	+	2.12552i
$850$	1.61811	+	7.45952i	0.0555007	+	0.255860i
$851$	−1.35655	+	0.783202i	−0.0465018	+	0.0268478i
$852$	−15.2704	−	33.5422i	−0.523154	−	1.14914i
$853$		−	36.2299i		−	1.24049i	−0.784408	−	0.620245i	$-0.787033\pi$
$853$		−	36.2299i		−	1.24049i	0.784408	−	0.620245i	$-0.212967\pi$
$854$		0			0
$855$		−	33.5086i		−	1.14597i
$856$	21.2606	−	2.50384i	0.726674	−	0.0855794i
$857$	32.9576	−	19.0281i	1.12581	−	0.649986i	0.182932	−	0.983126i	$-0.441441\pi$
$857$	32.9576	−	19.0281i	1.12581	−	0.649986i	0.942878	+	0.333139i	$0.108108\pi$
$858$	1.56137	−	0.338691i	0.0533045	−	0.0115627i
$859$	13.3104	−	23.0543i	0.454145	−	0.786602i	−0.544494	−	0.838765i	$-0.683278\pi$
$859$	13.3104	−	23.0543i	0.454145	−	0.786602i	0.998639	+	0.0521630i	$0.0166115\pi$
$860$	−11.4722	−	8.18977i	−0.391200	−	0.279269i
$861$		0			0
$862$	−21.4628	−	6.87487i	−0.731025	−	0.234159i
$863$	−20.1195	−	11.6160i	−0.684876	−	0.395413i	0.116814	−	0.993154i	$-0.462732\pi$
$863$	−20.1195	−	11.6160i	−0.684876	−	0.395413i	−0.801690	+	0.597741i	$0.796065\pi$
$864$	11.9669	+	19.7639i	0.407122	+	0.672383i
$865$	4.01688	+	6.95744i	0.136578	+	0.236560i
$866$	15.8403	−	14.3827i	0.538276	−	0.488745i
$867$	−33.2058			−1.12773
$868$		0			0
$869$	0.428484			0.0145353
$870$	6.81181	−	6.18501i	0.230942	−	0.209691i
$871$	0.226043	+	0.391517i	0.00765916	+	0.0132661i
$872$	46.9038	+	20.1838i	1.58836	+	0.683509i
$873$	−43.0624	−	24.8621i	−1.45744	−	0.841455i
$874$	15.1528	+	4.85370i	0.512553	+	0.164179i
$875$		0			0
$876$	19.5517	−	27.3881i	0.660592	−	0.925358i
$877$	1.28202	−	2.22052i	0.0432907	−	0.0749817i	−0.843568	−	0.537022i	$-0.819549\pi$
$877$	1.28202	−	2.22052i	0.0432907	−	0.0749817i	0.886859	+	0.462040i	$0.152882\pi$
$878$	−6.03515	+	1.30914i	−0.203676	+	0.0441812i
$879$	−38.4937	+	22.2244i	−1.29836	+	0.749609i
$880$	−0.393546	−	0.0768140i	−0.0132664	−	0.00258940i
$881$			11.4074i			0.384324i	0.981363	+	0.192162i	$0.0615498\pi$
$881$			11.4074i			0.384324i	−0.981363	+	0.192162i	$0.938450\pi$
$882$		0			0
$883$			15.8634i			0.533845i	0.963718	+	0.266922i	$0.0860068\pi$
$883$			15.8634i			0.533845i	−0.963718	+	0.266922i	$0.913993\pi$
$884$	−40.4509	+	18.4156i	−1.36051	+	0.619385i
$885$	−20.2034	+	11.6645i	−0.679131	+	0.392097i
$886$	4.22659	+	19.4847i	0.141995	+	0.654601i
$887$	−13.5260	+	23.4277i	−0.454159	+	0.786626i	−0.998639	−	0.0521471i	$-0.983394\pi$
$887$	−13.5260	+	23.4277i	−0.454159	+	0.786626i	0.544480	+	0.838774i	$0.316727\pi$
$888$	6.44499	−	4.80687i	0.216280	−	0.161308i
$889$		0			0
$890$	1.37695	−	4.29872i	0.0461554	−	0.144093i
$891$	0.199403	+	0.115125i	0.00668024	+	0.00385684i
$892$	2.88304	−	29.8205i	0.0965314	−	0.998463i
$893$	−16.5738	−	28.7066i	−0.554620	−	0.960629i
$894$	54.7681	+	60.3185i	1.83172	+	2.01735i
$895$	−8.84857			−0.295775
$896$		0			0
$897$	−16.9985			−0.567563
$898$	−16.1728	−	17.8118i	−0.539693	−	0.594387i
$899$	−6.46818	−	11.2032i	−0.215726	−	0.373648i
$900$	0.864575	−	8.94264i	0.0288192	−	0.298088i
$901$	28.7121	+	16.5769i	0.956537	+	0.552257i
$902$	0.345584	−	1.07888i	0.0115067	−	0.0359229i
$903$		0			0
$904$	−41.1355	+	30.6801i	−1.36815	+	1.02041i
$905$	−10.6805	+	18.4991i	−0.355031	+	0.614932i
$906$	−3.13714	−	14.4623i	−0.104225	−	0.480478i
$907$	−9.02842	+	5.21256i	−0.299784	+	0.173080i	−0.642346	−	0.766415i	$-0.722039\pi$
$907$	−9.02842	+	5.21256i	−0.299784	+	0.173080i	0.342562	+	0.939495i	$0.388705\pi$
$908$	−2.74387	+	1.24917i	−0.0910584	+	0.0414551i
$909$			32.1815i			1.06739i
$910$		0			0
$911$			43.7727i			1.45026i	0.688614	+	0.725128i	$0.258219\pi$
$911$			43.7727i			1.45026i	−0.688614	+	0.725128i	$0.741781\pi$
$912$	−80.1577	−	15.6455i	−2.65429	−	0.518075i
$913$	0.564423	−	0.325870i	0.0186797	−	0.0107847i
$914$	16.1214	−	3.49704i	0.533250	−	0.115672i
$915$	−10.8158	+	18.7335i	−0.357559	+	0.619310i
$916$	9.90692	−	13.8776i	0.327334	−	0.458529i
$917$		0			0
$918$	29.6899	+	9.51014i	0.979912	+	0.313881i
$919$	43.5772	+	25.1593i	1.43748	+	0.829929i	0.997674	−	0.0681637i	$-0.0217140\pi$
$919$	43.5772	+	25.1593i	1.43748	+	0.829929i	0.439806	+	0.898093i	$0.355047\pi$
$920$	3.91870	+	1.68630i	0.129196	+	0.0555958i
$921$	−32.2216	−	55.8095i	−1.06174	−	1.83899i
$922$	−27.6922	+	25.1440i	−0.911993	+	0.828073i
$923$	−27.7189			−0.912379
$924$		0			0
$925$	−1.03852			−0.0341464
$926$	3.28432	−	2.98210i	0.107929	−	0.0979980i
$927$	−10.9745	−	19.0085i	−0.360451	−	0.624320i
$928$	−6.96412	−	11.5016i	−0.228609	−	0.377559i
$929$	16.4494	+	9.49704i	0.539686	+	0.311588i	0.744952	−	0.667118i	$-0.232473\pi$
$929$	16.4494	+	9.49704i	0.539686	+	0.311588i	−0.205266	+	0.978706i	$0.565806\pi$
$930$	−20.0638	−	6.42677i	−0.657919	−	0.210742i
$931$		0			0
$932$	34.5469	+	24.6623i	1.13162	+	0.807840i
$933$	7.38419	−	12.7898i	0.241747	−	0.418719i
$934$	−11.2516	+	2.44069i	−0.368164	+	0.0798617i
$935$	−0.468561	+	0.270524i	−0.0153236	+	0.00884707i
$936$	51.9551	−	6.11869i	1.69821	−	0.199996i
$937$		−	44.7192i		−	1.46091i	−0.682959	−	0.730457i	$-0.739307\pi$
$937$		−	44.7192i		−	1.46091i	0.682959	−	0.730457i	$-0.260693\pi$
$938$		0			0
$939$			89.1265i			2.90853i
$940$	−3.68246	−	8.08873i	−0.120109	−	0.263825i
$941$	−8.88040	+	5.12710i	−0.289493	+	0.167139i	−0.637713	−	0.770274i	$-0.720119\pi$
$941$	−8.88040	+	5.12710i	−0.289493	+	0.167139i	0.348220	+	0.937413i	$0.386786\pi$
$942$	1.05376	+	4.85784i	0.0343332	+	0.158277i
$943$	−6.02661	+	10.4384i	−0.196253	+	0.339921i
$944$	11.0743	+	32.2431i	0.360436	+	1.04942i
$945$		0			0
$946$	0.304783	−	0.951508i	0.00990936	−	0.0309362i
$947$	21.6242	+	12.4847i	0.702691	+	0.405699i	0.808349	−	0.588704i	$-0.200362\pi$
$947$	21.6242	+	12.4847i	0.702691	+	0.405699i	−0.105658	+	0.994403i	$0.533695\pi$
$948$	23.2913	+	2.25180i	0.756467	+	0.0731352i
$949$	−12.6546	−	21.9185i	−0.410787	−	0.711504i
$950$	7.09135	+	7.81000i	0.230074	+	0.253390i
$951$	37.5316			1.21704
$952$		0			0
$953$	26.3831			0.854633			0.427317	−	0.904102i	$-0.359459\pi$
$953$	26.3831			0.854633			0.427317	+	0.904102i	$0.359459\pi$
$954$	−26.2324	−	28.8909i	−0.849305	−	0.935376i
$955$	−12.5117	−	21.6710i	−0.404870	−	0.701256i
$956$	20.2121	+	1.95410i	0.653706	+	0.0632003i
$957$	0.564803	+	0.326089i	0.0182575	+	0.0105410i
$958$	−10.6905	+	33.3749i	−0.345395	+	1.07829i
$959$		0			0
$960$	−20.9885	−	6.24361i	−0.677400	−	0.201512i
$961$	0.689177	−	1.19369i	0.0222315	−	0.0385061i
$962$	−1.28192	−	5.90968i	−0.0413307	−	0.190536i
$963$	−29.4448	+	17.0000i	−0.948846	+	0.547817i
$964$	−15.7870	−	34.6771i	−0.508466	−	1.11687i
$965$		−	8.16157i		−	0.262730i
$966$		0			0
$967$			47.1287i			1.51556i	0.652512	+	0.757778i	$0.273715\pi$
$967$			47.1287i			1.51556i	−0.652512	+	0.757778i	$0.726285\pi$
$968$	3.63563	+	30.8709i	0.116854	+	0.992229i
$969$	−95.4367	+	55.1004i	−3.06587	+	1.77008i
$970$	15.2983	−	3.31848i	0.491198	−	0.106550i
$971$	−27.6416	+	47.8767i	−0.887062	+	1.53644i	−0.0437306	+	0.999043i	$0.513924\pi$
$971$	−27.6416	+	47.8767i	−0.887062	+	1.53644i	−0.843332	+	0.537394i	$0.819409\pi$
$972$	30.1792	+	21.5443i	0.968000	+	0.691033i
$973$		0			0
$974$	−17.0971	−	5.47647i	−0.547826	−	0.175477i
$975$	−9.76007	−	5.63498i	−0.312572	−	0.180464i
$976$	23.8414	+	20.7575i	0.763144	+	0.664430i
$977$	−4.22669	−	7.32085i	−0.135224	−	0.234215i	0.790459	−	0.612515i	$-0.209842\pi$
$977$	−4.22669	−	7.32085i	−0.135224	−	0.234215i	−0.925683	+	0.378300i	$0.876509\pi$
$978$	24.6495	−	22.3813i	0.788204	−	0.715675i
$979$	0.319954			0.0102258
$980$		0			0
$981$	−81.0982			−2.58927
$982$	9.95908	−	9.04267i	0.317807	−	0.288563i
$983$	16.4461	+	28.4854i	0.524548	+	0.908543i	0.999591	+	0.0285811i	$0.00909888\pi$
$983$	16.4461	+	28.4854i	0.524548	+	0.908543i	−0.475044	+	0.879962i	$0.657568\pi$
$984$	24.4549	−	56.8292i	0.779593	−	1.81165i
$985$	−10.7835	−	6.22586i	−0.343591	−	0.198372i
$986$	−17.2780	−	5.53442i	−0.550244	−	0.176252i
$987$		0			0
$988$	−35.6893	+	49.9936i	−1.13543	+	1.59051i
$989$	−5.31509	+	9.20601i	−0.169010	+	0.292734i
$990$	0.622359	−	0.135001i	0.0197799	−	0.00429062i
$991$	26.5344	−	15.3196i	0.842893	−	0.486645i	−0.0153535	−	0.999882i	$-0.504887\pi$
$991$	26.5344	−	15.3196i	0.842893	−	0.486645i	0.858247	+	0.513238i	$0.171554\pi$
$992$	−14.8347	+	26.9782i	−0.471004	+	0.856559i
$993$			15.5659i			0.493970i
$994$		0			0
$995$			23.1734i			0.734645i
$996$	32.3931	−	14.7472i	1.02641	−	0.467284i
$997$	−36.7799	+	21.2349i	−1.16483	+	0.672516i	−0.952457	−	0.304673i	$-0.901453\pi$
$997$	−36.7799	+	21.2349i	−1.16483	+	0.672516i	−0.212374	+	0.977188i	$0.568120\pi$
$998$	2.54611	+	11.7376i	0.0805957	+	0.371548i
$999$	−2.12084	+	3.67340i	−0.0671003	+	0.116221i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.f.411.4		32
4.3	odd	2	inner	980.2.o.f.411.16		32
7.2	even	3		980.2.g.a.391.16		32
7.3	odd	6	inner	980.2.o.f.31.16		32
7.4	even	3		140.2.o.a.31.16	yes	32
7.5	odd	6		980.2.g.a.391.15		32
7.6	odd	2		140.2.o.a.131.4	yes	32
28.3	even	6	inner	980.2.o.f.31.4		32
28.11	odd	6		140.2.o.a.31.4	✓	32
28.19	even	6		980.2.g.a.391.14		32
28.23	odd	6		980.2.g.a.391.13		32
28.27	even	2		140.2.o.a.131.16	yes	32
35.4	even	6		700.2.p.c.451.1		32
35.13	even	4		700.2.t.c.299.5		32
35.18	odd	12		700.2.t.d.199.8		32
35.27	even	4		700.2.t.d.299.12		32
35.32	odd	12		700.2.t.c.199.9		32
35.34	odd	2		700.2.p.c.551.13		32
140.27	odd	4		700.2.t.d.299.8		32
140.39	odd	6		700.2.p.c.451.13		32
140.67	even	12		700.2.t.c.199.5		32
140.83	odd	4		700.2.t.c.299.9		32
140.123	even	12		700.2.t.d.199.12		32
140.139	even	2		700.2.p.c.551.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.4	✓	32	28.11	odd	6
140.2.o.a.31.16	yes	32	7.4	even	3
140.2.o.a.131.4	yes	32	7.6	odd	2
140.2.o.a.131.16	yes	32	28.27	even	2
700.2.p.c.451.1		32	35.4	even	6
700.2.p.c.451.13		32	140.39	odd	6
700.2.p.c.551.1		32	140.139	even	2
700.2.p.c.551.13		32	35.34	odd	2
700.2.t.c.199.5		32	140.67	even	12
700.2.t.c.199.9		32	35.32	odd	12
700.2.t.c.299.5		32	35.13	even	4
700.2.t.c.299.9		32	140.83	odd	4
700.2.t.d.199.8		32	35.18	odd	12
700.2.t.d.199.12		32	140.123	even	12
700.2.t.d.299.8		32	140.27	odd	4
700.2.t.d.299.12		32	35.27	even	4
980.2.g.a.391.13		32	28.23	odd	6
980.2.g.a.391.14		32	28.19	even	6
980.2.g.a.391.15		32	7.5	odd	6
980.2.g.a.391.16		32	7.2	even	3
980.2.o.f.31.4		32	28.3	even	6	inner
980.2.o.f.31.16		32	7.3	odd	6	inner
980.2.o.f.411.4		32	1.1	even	1	trivial
980.2.o.f.411.16		32	4.3	odd	2	inner

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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

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L-functions

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Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	980.2.o.f.411.4

Level	$980$
Weight	$2$
Character	980.411
Analytic conductor	$7.825$
Analytic rank	$0$
Dimension	$32$
Inner twists	$4$