LMFDB - Embedded newform 702.2.bs.a.5.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(5,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 27])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$702 = 2 \cdot 3^{3} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	702.bs (of order $36$ , degree $12$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$504$
Relative dimension:	$42$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			5.20
Character	$\chi$	$=$	702.5
Dual form			702.2.bs.a.281.20

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(1.58718 + 0.693439i) q^{3} +(0.984808 + 0.173648i) q^{4} +(1.27501 + 0.594545i) q^{5} +(-1.52070 - 0.829132i) q^{6} +(0.673612 - 0.962018i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.03829 + 2.20123i) q^{9} +(-1.21834 - 0.703407i) q^{10} +(-2.31982 + 1.08175i) q^{11} +(1.44265 + 0.958515i) q^{12} +(0.291962 + 3.59371i) q^{13} +(-0.754894 + 0.899648i) q^{14} +(1.61138 + 1.82779i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.191833 + 0.332265i) q^{17} +(-1.83868 - 2.37050i) q^{18} +(5.54341 + 1.48535i) q^{19} +(1.15239 + 0.806915i) q^{20} +(1.73624 - 1.05979i) q^{21} +(2.40527 - 0.875448i) q^{22} +(-0.221287 + 1.25498i) q^{23} +(-1.35362 - 1.08060i) q^{24} +(-1.94178 - 2.31412i) q^{25} +(0.0223619 - 3.60548i) q^{26} +(1.70871 + 4.90717i) q^{27} +(0.830431 - 0.830431i) q^{28} +(2.37380 + 2.82898i) q^{29} +(-1.44595 - 1.96128i) q^{30} +(-2.79198 - 3.98736i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-4.43210 + 0.108279i) q^{33} +(0.220062 - 0.314282i) q^{34} +(1.43082 - 0.826086i) q^{35} +(1.62508 + 2.52173i) q^{36} +(9.36622 - 2.50967i) q^{37} +(-5.39286 - 1.96284i) q^{38} +(-2.02862 + 5.90633i) q^{39} +(-1.07768 - 0.904282i) q^{40} +(-0.451844 - 5.16460i) q^{41} +(-1.82200 + 0.904431i) q^{42} +(-0.854796 + 2.34853i) q^{43} +(-2.47242 + 0.662484i) q^{44} +(1.29010 + 4.01843i) q^{45} +(0.329823 - 1.23092i) q^{46} +(-9.76996 - 6.84100i) q^{47} +(1.25429 + 1.19447i) q^{48} +(1.92242 + 5.28179i) q^{49} +(1.73270 + 2.47456i) q^{50} +(-0.534880 + 0.394340i) q^{51} +(-0.336515 + 3.58981i) q^{52} +11.0757i q^{53} +(-1.27452 - 5.03742i) q^{54} -3.60094 q^{55} +(-0.899648 + 0.754894i) q^{56} +(7.76839 + 6.20154i) q^{57} +(-2.11820 - 3.02511i) q^{58} +(0.117880 - 0.252794i) q^{59} +(1.26951 + 2.07984i) q^{60} +(-1.21719 - 6.90300i) q^{61} +(2.43383 + 4.21552i) q^{62} +(3.49063 - 0.478095i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.76437 + 4.75559i) q^{65} +(4.42468 + 0.278416i) q^{66} +(6.22493 - 0.544611i) q^{67} +(-0.246616 + 0.293906i) q^{68} +(-1.22147 + 1.83843i) q^{69} +(-1.49738 + 0.698238i) q^{70} +(-9.06561 + 2.42912i) q^{71} +(-1.39911 - 2.65377i) q^{72} +(3.17700 - 11.8567i) q^{73} +(-9.54931 + 1.68380i) q^{74} +(-1.47725 - 5.01944i) q^{75} +(5.20127 + 2.42539i) q^{76} +(-0.521997 + 2.96039i) q^{77} +(2.53567 - 5.70704i) q^{78} +(11.6652 - 9.78829i) q^{79} +(0.994768 + 0.994768i) q^{80} +(-0.690787 + 8.97345i) q^{81} +5.18433i q^{82} +(2.08063 + 0.182032i) q^{83} +(1.89390 - 0.742191i) q^{84} +(-0.442136 + 0.309587i) q^{85} +(1.05623 - 2.26510i) q^{86} +(1.80592 + 6.13619i) q^{87} +(2.52075 - 0.444477i) q^{88} +(2.86754 + 0.768355i) q^{89} +(-0.934960 - 4.11558i) q^{90} +(3.65388 + 2.13989i) q^{91} +(-0.435849 + 1.19749i) q^{92} +(-1.66638 - 8.26472i) q^{93} +(9.13655 + 7.66647i) q^{94} +(6.18477 + 5.18964i) q^{95} +(-1.14541 - 1.29924i) q^{96} +(-8.16690 + 3.80829i) q^{97} +(-1.45476 - 5.42925i) q^{98} +(-7.10964 - 2.90153i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$504 q - 24 q^{11} + 24 q^{15} + 24 q^{21} - 144 q^{27} + 24 q^{39} + 48 q^{41} + 12 q^{45} + 132 q^{47} + 24 q^{50} + 72 q^{54} - 72 q^{57} + 12 q^{63} - 156 q^{65} + 96 q^{66} - 48 q^{72} + 36 q^{73} - 96 q^{74}+ \cdots - 144 q^{99}+O(q^{100})$ 504 * q - 24 * q^11 + 24 * q^15 + 24 * q^21 - 144 * q^27 + 24 * q^39 + 48 * q^41 + 12 * q^45 + 132 * q^47 + 24 * q^50 + 72 * q^54 - 72 * q^57 + 12 * q^63 - 156 * q^65 + 96 * q^66 - 48 * q^72 + 36 * q^73 - 96 * q^74 - 24 * q^78 + 288 * q^79 + 24 * q^83 + 24 * q^84 - 144 * q^85 - 96 * q^86 - 192 * q^87 + 96 * q^92 - 60 * q^93 - 72 * q^98 - 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$ .

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	1.58718	+	0.693439i	0.916359	+	0.400357i
$3$	1.58718	+	0.693439i	0.916359	+	0.400357i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	1.27501	+	0.594545i	0.570200	+	0.265889i	0.686263	−	0.727353i	$-0.259250\pi$
$5$	1.27501	+	0.594545i	0.570200	+	0.265889i	−0.116063	+	0.993242i	$0.537028\pi$
$6$	−1.52070	−	0.829132i	−0.620825	−	0.338492i
$7$	0.673612	−	0.962018i	0.254601	−	0.363609i	−0.671422	−	0.741076i	$-0.734316\pi$
$7$	0.673612	−	0.962018i	0.254601	−	0.363609i	0.926023	+	0.377467i	$0.123205\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	2.03829	+	2.20123i	0.679428	+	0.733742i
$10$	−1.21834	−	0.703407i	−0.385272	−	0.222437i
$11$	−2.31982	+	1.08175i	−0.699453	+	0.326160i	−0.739612	−	0.673033i	$-0.764991\pi$
$11$	−2.31982	+	1.08175i	−0.699453	+	0.326160i	0.0401597	+	0.999193i	$0.487213\pi$
$12$	1.44265	+	0.958515i	0.416458	+	0.276699i
$13$	0.291962	+	3.59371i	0.0809756	+	0.996716i
$13$	0.291962	+	3.59371i	0.0809756	+	0.996716i
$14$	−0.754894	+	0.899648i	−0.201754	+	0.240441i
$15$	1.61138	+	1.82779i	0.416058	+	0.471933i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.191833	+	0.332265i	−0.0465264	+	0.0805862i	−0.888351	−	0.459165i	$-0.848149\pi$
$17$	−0.191833	+	0.332265i	−0.0465264	+	0.0805862i	0.841824	+	0.539752i	$0.181482\pi$
$18$	−1.83868	−	2.37050i	−0.433381	−	0.558732i
$19$	5.54341	+	1.48535i	1.27175	+	0.340763i	0.830699	−	0.556721i	$-0.187941\pi$
$19$	5.54341	+	1.48535i	1.27175	+	0.340763i	0.441046	+	0.897484i	$0.354607\pi$
$20$	1.15239	+	0.806915i	0.257683	+	0.180432i
$21$	1.73624	−	1.05979i	0.378880	−	0.231265i
$22$	2.40527	−	0.875448i	0.512806	−	0.186646i
$23$	−0.221287	+	1.25498i	−0.0461414	+	0.261681i	−0.999148	−	0.0412682i	$-0.986860\pi$
$23$	−0.221287	+	1.25498i	−0.0461414	+	0.261681i	0.953007	+	0.302949i	$0.0979713\pi$
$24$	−1.35362	−	1.08060i	−0.276307	−	0.220577i
$25$	−1.94178	−	2.31412i	−0.388356	−	0.462825i
$26$	0.0223619	−	3.60548i	0.00438552	−	0.707093i
$27$	1.70871	+	4.90717i	0.328842	+	0.944385i
$28$	0.830431	−	0.830431i	0.156937	−	0.156937i
$29$	2.37380	+	2.82898i	0.440803	+	0.525329i	0.940007	−	0.341156i	$-0.110818\pi$
$29$	2.37380	+	2.82898i	0.440803	+	0.525329i	−0.499204	+	0.866485i	$0.666374\pi$
$30$	−1.44595	−	1.96128i	−0.263993	−	0.358078i
$31$	−2.79198	−	3.98736i	−0.501454	−	0.716151i	0.486017	−	0.873949i	$-0.338449\pi$
$31$	−2.79198	−	3.98736i	−0.501454	−	0.716151i	−0.987471	+	0.157799i	$0.949560\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	−4.43210	+	0.108279i	−0.771530	+	0.0188490i
$34$	0.220062	−	0.314282i	0.0377404	−	0.0538988i
$35$	1.43082	−	0.826086i	0.241853	−	0.139634i
$36$	1.62508	+	2.52173i	0.270847	+	0.420288i
$37$	9.36622	−	2.50967i	1.53980	−	0.412587i	0.613597	−	0.789620i	$-0.289722\pi$
$37$	9.36622	−	2.50967i	1.53980	−	0.412587i	0.926200	+	0.377032i	$0.123055\pi$
$38$	−5.39286	−	1.96284i	−0.874837	−	0.318415i
$39$	−2.02862	+	5.90633i	−0.324840	+	0.945769i
$40$	−1.07768	−	0.904282i	−0.170396	−	0.142980i
$41$	−0.451844	−	5.16460i	−0.0705662	−	0.806575i	−0.946196	−	0.323593i	$-0.895109\pi$
$41$	−0.451844	−	5.16460i	−0.0705662	−	0.806575i	0.875630	−	0.482982i	$-0.160446\pi$
$42$	−1.82200	+	0.904431i	−0.281141	+	0.139557i
$43$	−0.854796	+	2.34853i	−0.130355	+	0.358148i	−0.987650	−	0.156678i	$-0.949921\pi$
$43$	−0.854796	+	2.34853i	−0.130355	+	0.358148i	0.857294	+	0.514826i	$0.172144\pi$
$44$	−2.47242	+	0.662484i	−0.372732	+	0.0998732i
$45$	1.29010	+	4.01843i	0.192317	+	0.599032i
$46$	0.329823	−	1.23092i	0.0486298	−	0.181489i
$47$	−9.76996	−	6.84100i	−1.42509	−	0.997862i	−0.995492	−	0.0948437i	$-0.969765\pi$
$47$	−9.76996	−	6.84100i	−1.42509	−	0.997862i	−0.429602	−	0.903018i	$-0.641346\pi$
$48$	1.25429	+	1.19447i	0.181041	+	0.172406i
$49$	1.92242	+	5.28179i	0.274631	+	0.754542i
$50$	1.73270	+	2.47456i	0.245041	+	0.349955i
$51$	−0.534880	+	0.394340i	−0.0748982	+	0.0552187i
$52$	−0.336515	+	3.58981i	−0.0466663	+	0.497817i
$53$			11.0757i			1.52137i	0.649122	+	0.760684i	$0.275136\pi$
$53$			11.0757i			1.52137i	−0.649122	+	0.760684i	$0.724864\pi$
$54$	−1.27452	−	5.03742i	−0.173440	−	0.685506i
$55$	−3.60094			−0.485550
$56$	−0.899648	+	0.754894i	−0.120220	+	0.100877i
$57$	7.76839	+	6.20154i	1.02895	+	0.821414i
$58$	−2.11820	−	3.02511i	−0.278134	−	0.397216i
$59$	0.117880	−	0.252794i	0.0153466	−	0.0329110i	−0.898485	−	0.439004i	$-0.855331\pi$
$59$	0.117880	−	0.252794i	0.0153466	−	0.0329110i	0.913832	+	0.406093i	$0.133109\pi$
$60$	1.26951	+	2.07984i	0.163893	+	0.268506i
$61$	−1.21719	−	6.90300i	−0.155845	−	0.883839i	−0.958010	−	0.286736i	$-0.907430\pi$
$61$	−1.21719	−	6.90300i	−0.155845	−	0.883839i	0.802165	−	0.597103i	$-0.203681\pi$
$62$	2.43383	+	4.21552i	0.309097	+	0.535372i
$63$	3.49063	−	0.478095i	0.439778	−	0.0602342i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−1.76437	+	4.75559i	−0.218843	+	0.589858i
$66$	4.42468	+	0.278416i	0.544640	+	0.0342706i
$67$	6.22493	−	0.544611i	0.760496	−	0.0665348i	0.299691	−	0.954036i	$-0.403116\pi$
$67$	6.22493	−	0.544611i	0.760496	−	0.0665348i	0.460805	+	0.887502i	$0.347561\pi$
$68$	−0.246616	+	0.293906i	−0.0299066	+	0.0356413i
$69$	−1.22147	+	1.83843i	−0.147048	+	0.221321i
$70$	−1.49738	+	0.698238i	−0.178971	+	0.0834554i
$71$	−9.06561	+	2.42912i	−1.07589	+	0.288284i	−0.752911	−	0.658122i	$-0.771351\pi$
$71$	−9.06561	+	2.42912i	−1.07589	+	0.288284i	−0.322979	+	0.946406i	$0.604684\pi$
$72$	−1.39911	−	2.65377i	−0.164887	−	0.312750i
$73$	3.17700	−	11.8567i	0.371840	−	1.38772i	−0.486068	−	0.873921i	$-0.661569\pi$
$73$	3.17700	−	11.8567i	0.371840	−	1.38772i	0.857908	−	0.513803i	$-0.171764\pi$
$74$	−9.54931	+	1.68380i	−1.11008	+	0.195738i
$75$	−1.47725	−	5.01944i	−0.170579	−	0.579595i
$76$	5.20127	+	2.42539i	0.596626	+	0.278211i
$77$	−0.521997	+	2.96039i	−0.0594870	+	0.337368i
$78$	2.53567	−	5.70704i	0.287108	−	0.646196i
$79$	11.6652	−	9.78829i	1.31244	−	1.10127i	0.324592	−	0.945854i	$-0.394773\pi$
$79$	11.6652	−	9.78829i	1.31244	−	1.10127i	0.987849	−	0.155415i	$-0.0496715\pi$
$80$	0.994768	+	0.994768i	0.111218	+	0.111218i
$81$	−0.690787	+	8.97345i	−0.0767541	+	0.997050i
$82$			5.18433i			0.572513i
$83$	2.08063	+	0.182032i	0.228379	+	0.0199806i	0.200771	−	0.979638i	$-0.435655\pi$
$83$	2.08063	+	0.182032i	0.228379	+	0.0199806i	0.0276082	+	0.999619i	$0.491211\pi$
$84$	1.89390	−	0.742191i	0.206641	−	0.0809797i
$85$	−0.442136	+	0.309587i	−0.0479563	+	0.0335794i
$86$	1.05623	−	2.26510i	0.113896	−	0.244252i
$87$	1.80592	+	6.13619i	0.193615	+	0.657869i
$88$	2.52075	−	0.444477i	0.268713	−	0.0473814i
$89$	2.86754	+	0.768355i	0.303959	+	0.0814455i	0.407575	−	0.913172i	$-0.366375\pi$
$89$	2.86754	+	0.768355i	0.303959	+	0.0814455i	−0.103616	+	0.994617i	$0.533041\pi$
$90$	−0.934960	−	4.11558i	−0.0985534	−	0.433820i
$91$	3.65388	+	2.13989i	0.383031	+	0.224322i
$92$	−0.435849	+	1.19749i	−0.0454405	+	0.124847i
$93$	−1.66638	−	8.26472i	−0.172796	−	0.857012i
$94$	9.13655	+	7.66647i	0.942363	+	0.790736i
$95$	6.18477	+	5.18964i	0.634544	+	0.532446i
$96$	−1.14541	−	1.29924i	−0.116903	−	0.132603i
$97$	−8.16690	+	3.80829i	−0.829223	+	0.386673i	−0.790414	−	0.612574i	$-0.790134\pi$
$97$	−8.16690	+	3.80829i	−0.829223	+	0.386673i	−0.0388094	+	0.999247i	$0.512357\pi$
$98$	−1.45476	−	5.42925i	−0.146953	−	0.548437i
$99$	−7.10964	−	2.90153i	−0.714545	−	0.291615i
$100$	−1.51044	−	2.61615i	−0.151044	−	0.261615i
$101$	0.0911896	+	0.517162i	0.00907370	+	0.0514595i	0.989008	−	0.147859i	$-0.0472382\pi$
$101$	0.0911896	+	0.517162i	0.00907370	+	0.0514595i	−0.979935	+	0.199319i	$0.936127\pi$
$102$	0.567214	−	0.346222i	0.0561625	−	0.0342811i
$103$	3.52200	+	9.67661i	0.347033	+	0.953465i	0.983299	+	0.181995i	$0.0582556\pi$
$103$	3.52200	+	9.67661i	0.347033	+	0.953465i	−0.636267	+	0.771469i	$0.719522\pi$
$104$	0.648108	−	3.54682i	0.0635522	−	0.347795i
$105$	2.84381	−	0.318960i	0.277528	−	0.0311273i
$106$	0.965314	−	11.0336i	0.0937595	−	1.07168i
$107$		−	6.03754i		−	0.583671i	−0.956468	−	0.291836i	$-0.905734\pi$
$107$		−	6.03754i		−	0.583671i	0.956468	−	0.291836i	$-0.0942660\pi$
$108$	0.830632	+	5.12933i	0.0799276	+	0.493570i
$109$	−6.55861	+	6.55861i	−0.628201	+	0.628201i	−0.947615	−	0.319414i	$-0.896514\pi$
$109$	−6.55861	+	6.55861i	−0.628201	+	0.628201i	0.319414	+	0.947615i	$0.396514\pi$
$110$	3.58723	+	0.313842i	0.342029	+	0.0299237i
$111$	16.6062	+	2.51160i	1.57619	+	0.238390i
$112$	0.962018	−	0.673612i	0.0909021	−	0.0636504i
$113$	−0.435121	−	1.19548i	−0.0409327	−	0.112462i	0.917542	−	0.397638i	$-0.130170\pi$
$113$	−0.435121	−	1.19548i	−0.0409327	−	0.112462i	−0.958475	+	0.285176i	$0.907948\pi$
$114$	−7.19833	−	6.85500i	−0.674186	−	0.642030i
$115$	−1.02828	+	1.46854i	−0.0958879	+	0.136942i
$116$	1.84649	+	3.19821i	0.171442	+	0.296946i
$117$	−7.31547	+	7.96768i	−0.676315	+	0.736612i
$118$	−0.139464	+	0.241558i	−0.0128387	+	0.0222372i
$119$	0.190424	+	0.408365i	0.0174561	+	0.0374348i
$120$	−1.08341	−	2.18257i	−0.0989015	−	0.199240i
$121$	−2.85928	+	3.40755i	−0.259934	+	0.309777i
$122$	0.610918	+	6.98282i	0.0553099	+	0.632195i
$123$	2.86418	−	8.51048i	0.258254	−	0.767364i
$124$	−2.05716	−	4.41160i	−0.184739	−	0.396174i
$125$	−2.92048	−	10.8994i	−0.261216	−	0.974871i
$126$	−3.51902	+	0.172047i	−0.313499	+	0.0153271i
$127$	−4.19409	+	2.42146i	−0.372166	+	0.214870i	−0.674404	−	0.738362i	$-0.735599\pi$
$127$	−4.19409	+	2.42146i	−0.372166	+	0.214870i	0.302239	+	0.953232i	$0.402266\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	−2.98528	+	3.13480i	−0.262839	+	0.276004i
$130$	2.17213	−	4.58372i	0.190509	−	0.402019i
$131$	0.149204	+	0.0263087i	0.0130360	+	0.00229860i	0.180162	−	0.983637i	$-0.442338\pi$
$131$	0.149204	+	0.0263087i	0.0130360	+	0.00229860i	−0.167126	+	0.985935i	$0.553449\pi$
$132$	−4.38357	−	0.662992i	−0.381541	−	0.0577061i
$133$	5.16304	−	4.33231i	0.447693	−	0.375659i
$134$	−6.24871			−0.539806
$135$	−0.738915	+	7.27258i	−0.0635957	+	0.625924i
$136$	0.271293	−	0.271293i	0.0232632	−	0.0232632i
$137$	0.120244	−	1.37440i	0.0102731	−	0.117423i	−0.989327	−	0.145716i	$-0.953452\pi$
$137$	0.120244	−	1.37440i	0.0102731	−	0.117423i	0.999600	+	0.0282929i	$0.00900712\pi$
$138$	1.37705	−	1.72497i	0.117223	−	0.146840i
$139$	0.685885	−	3.88984i	0.0581760	−	0.329932i	−0.941805	−	0.336161i	$-0.890871\pi$
$139$	0.685885	−	3.88984i	0.0581760	−	0.329932i	0.999981	+	0.00622840i	$0.00198257\pi$
$140$	1.55253	−	0.565076i	0.131213	−	0.0477576i
$141$	−10.7629	−	17.6328i	−0.906397	−	1.48495i
$142$	9.24283	−	1.62976i	0.775641	−	0.136766i
$143$	−4.56480	−	8.02094i	−0.381728	−	0.670745i
$144$	1.16250	+	2.76561i	0.0968748	+	0.230467i
$145$	1.34465	+	5.01830i	0.111667	+	0.416747i
$146$	−4.19829	+	11.5347i	−0.347453	+	0.954619i
$147$	−0.611380	+	9.71624i	−0.0504258	+	0.801382i
$148$	9.65972	−	0.845116i	0.794024	−	0.0694681i
$149$	−1.08728	−	12.4277i	−0.0890734	−	1.01811i	−0.900846	−	0.434139i	$-0.857053\pi$
$149$	−1.08728	−	12.4277i	−0.0890734	−	1.01811i	0.811772	−	0.583974i	$-0.198503\pi$
$150$	1.03416	+	5.12909i	0.0844387	+	0.418789i
$151$	−7.52811	−	16.1441i	−0.612629	−	1.31379i	−0.930722	−	0.365728i	$-0.880820\pi$
$151$	−7.52811	−	16.1441i	−0.612629	−	1.31379i	0.318092	−	0.948060i	$-0.396958\pi$
$152$	−4.97009	−	2.86948i	−0.403127	−	0.232746i
$153$	−1.12240	+	0.254983i	−0.0907408	+	0.0206141i
$154$	0.778025	−	2.90363i	0.0626951	−	0.233981i
$155$	−1.18912	−	6.74386i	−0.0955128	−	0.541680i
$156$	−3.02343	+	5.46433i	−0.242068	+	0.437496i
$157$	7.72040	−	2.80999i	0.616155	−	0.224262i	−0.0150394	−	0.999887i	$-0.504787\pi$
$157$	7.72040	−	2.80999i	0.616155	−	0.224262i	0.631194	+	0.775625i	$0.282565\pi$
$158$	−12.4740	+	8.73435i	−0.992374	+	0.694868i
$159$	−7.68034	+	17.5792i	−0.609091	+	1.39412i
$160$	−0.904282	−	1.07768i	−0.0714898	−	0.0851982i
$161$	1.05825	+	1.05825i	0.0834018	+	0.0834018i
$162$	1.47025	−	8.87910i	0.115513	−	0.697608i
$163$	−16.7174	−	16.7174i	−1.30941	−	1.30941i	−0.921842	−	0.387565i	$-0.873316\pi$
$163$	−16.7174	−	16.7174i	−1.30941	−	1.30941i	−0.387565	−	0.921842i	$-0.626684\pi$
$164$	0.451844	−	5.16460i	0.0352831	−	0.403288i
$165$	−5.71534	−	2.49703i	−0.444938	−	0.194393i
$166$	−2.05685	−	0.362678i	−0.159642	−	0.0281493i
$167$	6.81851	−	14.6223i	0.527632	−	1.13151i	−0.444220	−	0.895918i	$-0.646519\pi$
$167$	6.81851	−	14.6223i	0.527632	−	1.13151i	0.971852	−	0.235593i	$-0.0757031\pi$
$168$	−1.95138	+	0.574303i	−0.150552	+	0.0443084i
$169$	−12.8295	+	2.09845i	−0.986886	+	0.161419i
$170$	0.467435	−	0.269874i	0.0358507	−	0.0206984i
$171$	8.02946	+	15.2299i	0.614028	+	1.16466i
$172$	−1.24963	+	2.16442i	−0.0952833	+	0.165035i
$173$	−17.4896	−	6.36568i	−1.32971	−	0.483973i	−0.423150	−	0.906060i	$-0.639076\pi$
$173$	−17.4896	−	6.36568i	−1.32971	−	0.483973i	−0.906556	+	0.422086i	$0.861298\pi$
$174$	−1.26424	−	6.27024i	−0.0958421	−	0.475345i
$175$	−3.53424	+	0.309206i	−0.267163	+	0.0233737i
$176$	−2.54990	+	0.223087i	−0.192206	+	0.0168158i
$177$	0.362394	−	0.319487i	0.0272392	−	0.0240141i
$178$	−2.78966	−	1.01535i	−0.209094	−	0.0761040i
$179$	7.72899	−	13.3870i	0.577692	−	1.00059i	−0.418052	−	0.908423i	$-0.637287\pi$
$179$	7.72899	−	13.3870i	0.577692	−	1.00059i	0.995743	−	0.0921681i	$-0.0293797\pi$
$180$	0.572706	+	4.18140i	0.0426870	+	0.311663i
$181$	−2.47183	+	1.42711i	−0.183730	+	0.106076i	−0.589044	−	0.808101i	$-0.700496\pi$
$181$	−2.47183	+	1.42711i	−0.183730	+	0.106076i	0.405314	+	0.914178i	$0.367162\pi$
$182$	−3.45347	−	2.45021i	−0.255989	−	0.181622i
$183$	2.85492	−	11.8004i	0.211041	−	0.872307i
$184$	0.538559	−	1.15494i	0.0397031	−	0.0851435i
$185$	13.4341	+	2.36879i	0.987694	+	0.174157i
$186$	0.939726	+	8.37851i	0.0689040	+	0.614342i
$187$	0.0855912	−	0.978312i	0.00625905	−	0.0715413i
$188$	−8.43360	−	8.43360i	−0.615084	−	0.615084i
$189$	5.87179	+	1.66172i	0.427110	+	0.120872i
$190$	−5.70893	−	5.70893i	−0.414169	−	0.414169i
$191$	−12.3430	−	14.7098i	−0.893105	−	1.06436i	−0.997559	−	0.0698308i	$-0.977754\pi$
$191$	−12.3430	−	14.7098i	−0.893105	−	1.06436i	0.104454	−	0.994530i	$-0.466690\pi$
$192$	1.02782	+	1.39413i	0.0741765	+	0.100612i
$193$	−2.56817	+	1.79825i	−0.184861	+	0.129441i	−0.662344	−	0.749200i	$-0.730438\pi$
$193$	−2.56817	+	1.79825i	−0.184861	+	0.129441i	0.477483	+	0.878641i	$0.341549\pi$
$194$	8.46773	−	3.08200i	0.607948	−	0.221275i
$195$	−6.09808	+	6.32449i	−0.436693	+	0.452906i
$196$	0.976036	+	5.53538i	0.0697169	+	0.395384i
$197$	−2.19345	+	8.18607i	−0.156277	+	0.583233i	0.842716	+	0.538359i	$0.180955\pi$
$197$	−2.19345	+	8.18607i	−0.156277	+	0.583233i	−0.998993	+	0.0448744i	$0.985711\pi$
$198$	6.82970	+	3.51014i	0.485365	+	0.249455i
$199$	−16.7404	−	9.66505i	−1.18669	−	0.685137i	−0.229139	−	0.973394i	$-0.573591\pi$
$199$	−16.7404	−	9.66505i	−1.18669	−	0.685137i	−0.957553	+	0.288257i	$0.906924\pi$
$200$	1.27668	+	2.73784i	0.0902747	+	0.193595i
$201$	10.2577	+	3.45221i	0.723525	+	0.243500i
$202$	−0.0457690	−	0.523142i	−0.00322029	−	0.0368081i
$203$	4.32055	−	0.377999i	0.303243	−	0.0265303i
$204$	−0.595230	+	0.295468i	−0.0416745	+	0.0206869i
$205$	2.49448	−	6.85354i	0.174222	−	0.478672i
$206$	−2.66522	−	9.94675i	−0.185695	−	0.693023i
$207$	−3.21354	+	2.07090i	−0.223356	+	0.143938i
$208$	−0.954767	+	3.47684i	−0.0662012	+	0.241076i
$209$	−14.4665	+	2.55084i	−1.00067	+	0.176445i
$210$	−2.86079	+	0.0698911i	−0.197413	+	0.00482294i
$211$	−2.89440	+	1.05348i	−0.199259	+	0.0725243i	−0.439722	−	0.898134i	$-0.644923\pi$
$211$	−2.89440	+	1.05348i	−0.199259	+	0.0725243i	0.240463	+	0.970658i	$0.422701\pi$
$212$	−1.92328	+	10.9075i	−0.132091	+	0.749128i
$213$	−16.0732	−	2.43099i	−1.10132	−	0.166569i
$214$	−0.526207	+	6.01457i	−0.0359707	+	0.411147i
$215$	−2.48618	+	2.48618i	−0.169556	+	0.169556i
$216$	−0.380420	−	5.18221i	−0.0258843	−	0.352605i
$217$	−5.71662			−0.388069
$218$	7.10527	−	5.96203i	0.481230	−	0.403800i
$219$	13.2644	−	16.6157i	0.896324	−	1.12279i
$220$	−3.54623	−	0.625296i	−0.239087	−	0.0421575i
$221$	−1.25007	−	0.592385i	−0.0840890	−	0.0398481i
$222$	−16.3241	−	3.94936i	−1.09560	−	0.265064i
$223$	−15.5775	−	10.9075i	−1.04315	−	0.730421i	−0.0792955	−	0.996851i	$-0.525267\pi$
$223$	−15.5775	−	10.9075i	−1.04315	−	0.730421i	−0.963854	+	0.266430i	$0.914156\pi$
$224$	−1.01707	+	0.587203i	−0.0679556	+	0.0392342i
$225$	1.13601	−	8.99114i	0.0757337	−	0.599410i
$226$	0.329272	+	1.22886i	0.0219028	+	0.0817425i
$227$	4.80537	+	10.3052i	0.318944	+	0.683977i	0.998780	−	0.0493871i	$-0.0157268\pi$
$227$	4.80537	+	10.3052i	0.318944	+	0.683977i	−0.679836	+	0.733364i	$0.737949\pi$
$228$	6.57349	+	7.45629i	0.435340	+	0.493805i
$229$	1.03066	+	11.7805i	0.0681082	+	0.778480i	0.951058	+	0.309013i	$0.0999985\pi$
$229$	1.03066	+	11.7805i	0.0681082	+	0.778480i	−0.882950	+	0.469467i	$0.844446\pi$
$230$	1.15236	−	1.37333i	0.0759845	−	0.0905548i
$231$	−2.88135	+	4.33670i	−0.189579	+	0.285334i
$232$	−1.56072	−	3.34697i	−0.102466	−	0.219739i
$233$	−0.638143	+	1.10530i	−0.0418061	+	0.0724103i	−0.886171	−	0.463358i	$-0.846645\pi$
$233$	−0.638143	+	1.10530i	−0.0418061	+	0.0724103i	0.844365	+	0.535768i	$0.179978\pi$
$234$	7.98206	−	7.29978i	0.521803	−	0.477201i
$235$	−8.38947	−	14.5310i	−0.547269	−	0.947897i
$236$	0.159986	−	0.228484i	0.0104142	−	0.0148730i
$237$	25.3024	−	7.44666i	1.64357	−	0.483713i
$238$	−0.154108	−	0.423408i	−0.00998932	−	0.0274454i
$239$	25.1677	−	17.6226i	1.62796	−	1.13991i	0.749638	−	0.661848i	$-0.230228\pi$
$239$	25.1677	−	17.6226i	1.62796	−	1.13991i	0.878325	−	0.478064i	$-0.158661\pi$
$240$	0.889065	+	2.26869i	0.0573889	+	0.146443i
$241$	18.6128	+	1.62841i	1.19896	+	0.104895i	0.669086	−	0.743185i	$-0.266686\pi$
$241$	18.6128	+	1.62841i	1.19896	+	0.104895i	0.529869	+	0.848080i	$0.322241\pi$
$242$	3.14538	−	3.14538i	0.202193	−	0.202193i
$243$	−7.31894	+	13.7635i	−0.469510	+	0.882927i
$244$		−	7.00949i		−	0.448737i
$245$	−0.689173	+	7.87728i	−0.0440297	+	0.503261i
$246$	−3.59502	+	8.22847i	−0.229210	+	0.524628i
$247$	−3.71946	+	20.3551i	−0.236664	+	1.29516i
$248$	1.66484	+	4.57411i	0.105717	+	0.290456i
$249$	3.17611	+	1.73171i	0.201278	+	0.109742i
$250$	1.95942	+	11.1124i	0.123925	+	0.702813i
$251$	4.60588	+	7.97762i	0.290721	+	0.503543i	0.973980	−	0.226633i	$-0.0727717\pi$
$251$	4.60588	+	7.97762i	0.290721	+	0.503543i	−0.683260	+	0.730175i	$0.739438\pi$
$252$	3.52062	+	0.135311i	0.221778	+	0.00852377i
$253$	−0.844228	−	3.15070i	−0.0530762	−	0.198083i
$254$	4.38918	−	2.04671i	0.275401	−	0.128422i
$255$	−0.916429	+	0.184776i	−0.0573890	+	0.0115711i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	19.8499	+	16.6560i	1.23820	+	1.03897i	0.997662	+	0.0683355i	$0.0217688\pi$
$257$	19.8499	+	16.6560i	1.23820	+	1.03897i	0.240540	+	0.970639i	$0.422676\pi$
$258$	3.24714	−	2.86268i	0.202158	−	0.178223i
$259$	3.89485	−	10.7010i	0.242014	−	0.664928i
$260$	−2.56337	+	4.37696i	−0.158973	+	0.271448i
$261$	−1.38875	+	10.9915i	−0.0859615	+	0.680359i
$262$	−0.146343	−	0.0392126i	−0.00904113	−	0.00242256i
$263$	3.89942	−	0.687572i	0.240448	−	0.0423975i	−0.0521252	−	0.998641i	$-0.516599\pi$
$263$	3.89942	−	0.687572i	0.240448	−	0.0423975i	0.292574	+	0.956243i	$0.405488\pi$
$264$	4.30911	+	1.04252i	0.265207	+	0.0641629i
$265$	−6.58502	+	14.1216i	−0.404515	+	0.867485i
$266$	−5.52098	+	3.86583i	−0.338513	+	0.237029i
$267$	4.01850	+	3.20798i	0.245928	+	0.196325i
$268$	6.22493	+	0.544611i	0.380248	+	0.0332674i
$269$		−	22.4084i		−	1.36626i	−0.730296	−	0.683131i	$-0.760618\pi$
$269$		−	22.4084i		−	1.36626i	0.730296	−	0.683131i	$-0.239382\pi$
$270$	1.36995	−	7.18050i	0.0833725	−	0.436991i
$271$	−2.07196	−	2.07196i	−0.125863	−	0.125863i	0.641370	−	0.767232i	$-0.278367\pi$
$271$	−2.07196	−	2.07196i	−0.125863	−	0.125863i	−0.767232	+	0.641370i	$0.778367\pi$
$272$	−0.293906	+	0.246616i	−0.0178207	+	0.0149533i
$273$	4.31549	+	5.93014i	0.261185	+	0.358909i
$274$	−0.239573	+	1.35869i	−0.0144731	+	0.0820813i
$275$	7.00789	+	3.26783i	0.422592	+	0.197058i
$276$	−1.52216	+	1.59839i	−0.0916230	+	0.0962119i
$277$	−2.69039	+	0.474388i	−0.161650	+	0.0285032i	−0.253887	−	0.967234i	$-0.581709\pi$
$277$	−2.69039	+	0.474388i	−0.161650	+	0.0285032i	0.0922374	+	0.995737i	$0.470598\pi$
$278$	−1.02230	+	3.81526i	−0.0613133	+	0.228824i
$279$	3.08623	−	14.2731i	0.184767	−	0.854511i
$280$	−1.59588	+	0.427613i	−0.0953718	+	0.0255548i
$281$	6.80735	−	3.17432i	0.406093	−	0.189364i	−0.208829	−	0.977952i	$-0.566965\pi$
$281$	6.80735	−	3.17432i	0.406093	−	0.189364i	0.614922	+	0.788588i	$0.289188\pi$
$282$	9.18512	+	18.5037i	0.546966	+	1.10188i
$283$	2.36593	−	2.81961i	0.140640	−	0.167608i	−0.691127	−	0.722734i	$-0.742885\pi$
$283$	2.36593	−	2.81961i	0.140640	−	0.167608i	0.831767	+	0.555125i	$0.187330\pi$
$284$	−9.34970	+	0.817992i	−0.554802	+	0.0485389i
$285$	6.21766	+	12.5257i	0.368302	+	0.741956i
$286$	3.84836	+	8.38826i	0.227558	+	0.496009i
$287$	−5.27281	−	3.04426i	−0.311244	−	0.179697i
$288$	−0.917036	−	2.85640i	−0.0540368	−	0.168315i
$289$	8.42640	+	14.5950i	0.495671	+	0.858527i
$290$	−0.902159	−	5.11640i	−0.0529766	−	0.300445i
$291$	−15.6032	+	0.381196i	−0.914673	+	0.0223461i
$292$	5.18763	−	11.1249i	0.303583	−	0.651036i
$293$	11.8636	+	16.9430i	0.693079	+	0.989819i	0.999283	+	0.0378534i	$0.0120520\pi$
$293$	11.8636	+	16.9430i	0.693079	+	0.989819i	−0.306204	+	0.951966i	$0.599059\pi$
$294$	1.45588	−	9.62598i	0.0849086	−	0.561399i
$295$	0.300595	−	0.252229i	0.0175013	−	0.0146853i
$296$	−9.69662			−0.563605
$297$	−9.27224	−	9.53536i	−0.538030	−	0.553297i
$298$			12.4751i			0.722665i
$299$	−4.57464	−	0.428834i	−0.264558	−	0.0248001i
$300$	−0.583194	−	5.19971i	−0.0336707	−	0.300205i
$301$	1.68353	+	2.40433i	0.0970370	+	0.138583i
$302$	6.09242	+	16.7388i	0.350579	+	0.963208i
$303$	−0.213886	+	0.884064i	−0.0122874	+	0.0507881i
$304$	4.70108	+	3.29173i	0.269626	+	0.188794i
$305$	2.55223	−	9.52504i	0.146140	−	0.545402i
$306$	1.14035	−	0.156189i	0.0651897	−	0.00892871i
$307$	−29.7384	+	7.96838i	−1.69726	+	0.454779i	−0.972247	−	0.233957i	$-0.924833\pi$
$307$	−29.7384	+	7.96838i	−1.69726	+	0.454779i	−0.725012	+	0.688736i	$0.758166\pi$
$308$	−1.02813	+	2.82477i	−0.0585833	+	0.160956i
$309$	−1.12009	+	17.8008i	−0.0637197	+	1.01265i
$310$	0.596834	+	6.82184i	0.0338979	+	0.387454i
$311$	−23.1547	−	19.4291i	−1.31298	−	1.10172i	−0.987743	−	0.156089i	$-0.950111\pi$
$311$	−23.1547	−	19.4291i	−1.31298	−	1.10172i	−0.325238	−	0.945632i	$-0.605444\pi$
$312$	3.48817	−	5.18003i	0.197479	−	0.293261i
$313$	−9.56491	−	3.48134i	−0.540641	−	0.196777i	0.0572426	−	0.998360i	$-0.481769\pi$
$313$	−9.56491	−	3.48134i	−0.540641	−	0.196777i	−0.597883	+	0.801583i	$0.703991\pi$
$314$	−7.93593	+	2.12642i	−0.447850	+	0.120001i
$315$	4.73483	+	1.46576i	0.266777	+	0.0825865i
$316$	13.1877	−	7.61394i	0.741868	−	0.428318i
$317$	−4.54406	+	6.48959i	−0.255220	+	0.364492i	−0.926232	−	0.376955i	$-0.876971\pi$
$317$	−4.54406	+	6.48959i	−0.255220	+	0.364492i	0.671012	+	0.741447i	$0.265860\pi$
$318$	9.18324	−	16.8429i	0.514971	−	0.944503i
$319$	−8.56704	−	3.99488i	−0.479662	−	0.223670i
$320$	0.806915	+	1.15239i	0.0451079	+	0.0644208i
$321$	4.18667	−	9.58267i	0.233677	−	0.534853i
$322$	−0.961991	−	1.14646i	−0.0536096	−	0.0638895i
$323$	−1.55694	+	1.55694i	−0.0866306	+	0.0866306i
$324$	−2.23852	+	8.71717i	−0.124362	+	0.484287i
$325$	7.74937	−	7.65384i	0.429858	−	0.424558i
$326$	15.1968	+	18.1108i	0.841671	+	1.00306i
$327$	−14.9577	+	5.86170i	−0.827162	+	0.324153i
$328$	−0.900249	+	5.10557i	−0.0497080	+	0.281908i
$329$	−13.1623	+	4.79069i	−0.725662	+	0.264119i
$330$	5.47596	+	2.98565i	0.301442	+	0.164355i
$331$	−0.510072	−	0.357156i	−0.0280361	−	0.0196311i	0.559474	−	0.828848i	$-0.311003\pi$
$331$	−0.510072	−	0.357156i	−0.0280361	−	0.0196311i	−0.587510	+	0.809217i	$0.699892\pi$
$332$	2.01741	+	0.540564i	0.110720	+	0.0296673i
$333$	24.6154	+	15.5017i	1.34891	+	0.849490i
$334$	−8.06698	+	13.9724i	−0.441406	+	0.764537i
$335$	8.26062	+	3.00662i	0.451326	+	0.164269i
$336$	1.99400	−	0.402044i	0.108782	−	0.0219333i
$337$	−7.11996	+	8.48524i	−0.387849	+	0.462221i	−0.924275	−	0.381727i	$-0.875330\pi$
$337$	−7.11996	+	8.48524i	−0.387849	+	0.462221i	0.536426	+	0.843947i	$0.319774\pi$
$338$	12.9636	−	0.972300i	0.705126	−	0.0528862i
$339$	0.138380	−	2.19918i	0.00751578	−	0.119443i
$340$	−0.489178	+	0.228107i	−0.0265294	+	0.0123709i
$341$	10.7902	+	6.22973i	0.584323	+	0.337359i
$342$	−6.67153	−	15.8717i	−0.360755	−	0.858245i
$343$	14.3169	+	3.83619i	0.773038	+	0.207135i
$344$	1.43351	−	2.04727i	0.0772899	−	0.110381i
$345$	−2.65041	+	1.61779i	−0.142694	+	0.0870988i
$346$	16.8682	+	7.86577i	0.906840	+	0.422866i
$347$	28.4256	+	5.01220i	1.52597	+	0.269069i	0.872775	−	0.488123i	$-0.162318\pi$
$347$	28.4256	+	5.01220i	1.52597	+	0.269069i	0.653192	+	0.757192i	$0.273429\pi$
$348$	0.712946	+	6.35656i	0.0382179	+	0.340747i
$349$	25.7174	+	2.24998i	1.37662	+	0.120439i	0.751316	−	0.659942i	$-0.229419\pi$
$349$	25.7174	+	2.24998i	1.37662	+	0.120439i	0.625304	+	0.780381i	$0.284975\pi$
$350$	3.54774			0.189634
$351$	−17.1361	+	7.57332i	−0.914656	+	0.404234i
$352$	2.55964			0.136429
$353$	13.4786	+	1.17923i	0.717395	+	0.0627639i	0.440007	−	0.897994i	$-0.354976\pi$
$353$	13.4786	+	1.17923i	0.717395	+	0.0627639i	0.277388	+	0.960758i	$0.410531\pi$
$354$	−0.388860	+	0.286687i	−0.0206677	+	0.0152372i
$355$	−13.0029	−	2.29277i	−0.690124	−	0.121687i
$356$	2.69055	+	1.25462i	0.142599	+	0.0664950i
$357$	0.0190607	+	0.780196i	0.00100880	+	0.0412924i
$358$	−8.86633	+	12.6624i	−0.468600	+	0.669230i
$359$	18.2821	+	4.89868i	0.964893	+	0.258542i	0.706670	−	0.707543i	$-0.250197\pi$
$359$	18.2821	+	4.89868i	0.964893	+	0.258542i	0.258223	+	0.966085i	$0.416863\pi$
$360$	−0.206093	−	4.21541i	−0.0108621	−	0.222171i
$361$	12.0686	+	6.96784i	0.635192	+	0.366728i
$362$	2.58681	−	1.20625i	0.135960	−	0.0633990i
$363$	−6.90112	+	3.42567i	−0.362215	+	0.179801i
$364$	3.22678	+	2.74187i	0.169129	+	0.143713i
$365$	11.1000	−	13.2285i	0.581003	−	0.692413i
$366$	−3.87252	+	11.5066i	−0.202420	+	0.601461i
$367$	−3.68341	−	1.34065i	−0.192272	−	0.0699815i	0.244089	−	0.969753i	$-0.421511\pi$
$367$	−3.68341	−	1.34065i	−0.192272	−	0.0699815i	−0.436362	+	0.899771i	$0.643733\pi$
$368$	−0.637169	+	1.10361i	−0.0332147	+	0.0575296i
$369$	10.4475	−	11.5215i	0.543873	−	0.599788i
$370$	−13.1765	−	3.53064i	−0.685015	−	0.183549i
$371$	10.6550	+	7.46075i	0.553183	+	0.387343i
$372$	−0.205915	−	8.42853i	−0.0106762	−	0.436999i
$373$	9.81686	−	3.57304i	0.508297	−	0.185005i	−0.0751248	−	0.997174i	$-0.523936\pi$
$373$	9.81686	−	3.57304i	0.508297	−	0.185005i	0.583422	+	0.812169i	$0.301713\pi$
$374$	−0.170531	+	0.967130i	−0.00881795	+	0.0500091i
$375$	2.92273	−	19.3245i	0.150929	−	0.997912i
$376$	7.66647	+	9.13655i	0.395368	+	0.471181i
$377$	−9.47349	+	9.35670i	−0.487909	+	0.481894i
$378$	−5.70462	−	2.16715i	−0.293414	−	0.111466i
$379$	12.4456	−	12.4456i	0.639286	−	0.639286i	−0.311093	−	0.950379i	$-0.600695\pi$
$379$	12.4456	−	12.4456i	0.639286	−	0.639286i	0.950379	+	0.311093i	$0.100695\pi$
$380$	5.18964	+	6.18477i	0.266223	+	0.317272i
$381$	−8.33592	+	0.934949i	−0.427062	+	0.0478989i
$382$	11.0139	+	15.7295i	0.563522	+	0.804793i
$383$	−13.5272	−	6.30786i	−0.691210	−	0.322317i	0.0450793	−	0.998983i	$-0.485646\pi$
$383$	−13.5272	−	6.30786i	−0.691210	−	0.322317i	−0.736289	+	0.676667i	$0.763424\pi$
$384$	−0.902402	−	1.47840i	−0.0460505	−	0.0754443i
$385$	−2.42563	+	3.46416i	−0.123622	+	0.176550i
$386$	2.71513	−	1.56758i	0.138196	−	0.0797876i
$387$	−6.91197	+	2.90538i	−0.351355	+	0.147689i
$388$	−8.70413	+	2.33226i	−0.441885	+	0.118403i
$389$	−12.4001	−	4.51327i	−0.628710	−	0.228832i	0.00795955	−	0.999968i	$-0.497466\pi$
$389$	−12.4001	−	4.51327i	−0.628710	−	0.228832i	−0.636670	+	0.771136i	$0.719689\pi$
$390$	6.62610	−	5.76895i	0.335525	−	0.292122i
$391$	−0.374536	−	0.314273i	−0.0189411	−	0.0158935i
$392$	−0.489882	−	5.59938i	−0.0247428	−	0.282811i
$393$	0.218571	+	0.145221i	0.0110254	+	0.00732541i
$394$	2.89857	−	7.96374i	0.146028	−	0.401208i
$395$	20.6928	−	5.54463i	1.04117	−	0.278980i
$396$	−6.49778	−	4.09203i	−0.326526	−	0.205632i
$397$	−6.05591	+	22.6010i	−0.303938	+	1.13431i	0.629918	+	0.776661i	$0.283088\pi$
$397$	−6.05591	+	22.6010i	−0.303938	+	1.13431i	−0.933856	+	0.357649i	$0.883578\pi$
$398$	15.8343	+	11.0873i	0.793701	+	0.555756i
$399$	11.1989	−	3.29590i	0.560645	−	0.165001i
$400$	−1.03320	−	2.83869i	−0.0516600	−	0.141935i
$401$	13.0453	+	18.6307i	0.651454	+	0.930372i	0.999976	−	0.00692821i	$-0.00220533\pi$
$401$	13.0453	+	18.6307i	0.651454	+	0.930372i	−0.348522	+	0.937300i	$0.613316\pi$
$402$	−9.91783	−	4.33310i	−0.494656	−	0.216115i
$403$	13.5143	−	11.1977i	0.673193	−	0.557798i
$404$			0.525140i			0.0261267i
$405$	−6.21588	+	11.0305i	−0.308870	+	0.548110i
$406$	−4.33705			−0.215244
$407$	−19.0131	+	15.9539i	−0.942445	+	0.790805i
$408$	0.618717	−	0.242466i	0.0306311	−	0.0120039i
$409$	0.707258	+	1.01007i	0.0349716	+	0.0499447i	0.836257	−	0.548338i	$-0.184739\pi$
$409$	0.707258	+	1.01007i	0.0349716	+	0.0499447i	−0.801285	+	0.598282i	$0.795850\pi$
$410$	−3.08232	+	6.61005i	−0.152225	+	0.326447i
$411$	1.14391	−	2.09803i	0.0564249	−	0.103488i
$412$	1.78817	+	10.1412i	0.0880966	+	0.499621i
$413$	−0.163787	−	0.283687i	−0.00805943	−	0.0139593i
$414$	3.38180	−	1.78294i	0.166206	−	0.0876269i
$415$	2.54459	+	1.46912i	0.124909	+	0.0721163i
$416$	1.25416	−	3.38040i	0.0614903	−	0.165738i
$417$	3.78599	−	5.69827i	0.185401	−	0.279045i
$418$	14.6338	−	1.28029i	0.715761	−	0.0626210i
$419$	4.40940	−	5.25491i	0.215413	−	0.256719i	−0.647507	−	0.762059i	$-0.724188\pi$
$419$	4.40940	−	5.25491i	0.215413	−	0.256719i	0.862920	+	0.505340i	$0.168633\pi$
$420$	2.85600	+	0.179709i	0.139358	+	0.00876891i
$421$	−29.0208	+	13.5326i	−1.41439	+	0.659540i	−0.971501	−	0.237037i	$-0.923824\pi$
$421$	−29.0208	+	13.5326i	−1.41439	+	0.659540i	−0.442888	+	0.896577i	$0.646046\pi$
$422$	2.97520	−	0.797203i	0.144831	−	0.0388073i
$423$	−4.85538	−	35.4498i	−0.236077	−	1.72363i
$424$	2.86661	−	10.6983i	0.139215	−	0.519557i
$425$	1.14140	−	0.201260i	0.0553661	−	0.00976254i
$426$	15.8002	+	3.82261i	0.765521	+	0.185206i
$427$	−7.46072	−	3.47899i	−0.361050	−	0.168360i
$428$	1.04841	−	5.94582i	0.0506767	−	0.287402i
$429$	−1.68313	−	15.8961i	−0.0812622	−	0.767470i
$430$	2.69340	−	2.26003i	0.129887	−	0.108989i
$431$	1.65210	+	1.65210i	0.0795787	+	0.0795787i	0.745776	−	0.666197i	$-0.232079\pi$
$431$	1.65210	+	1.65210i	0.0795787	+	0.0795787i	−0.666197	+	0.745776i	$0.732079\pi$
$432$	−0.0726866	+	5.19564i	−0.00349714	+	0.249976i
$433$			12.9513i			0.622402i	0.950344	+	0.311201i	$0.100731\pi$
$433$			12.9513i			0.622402i	−0.950344	+	0.311201i	$0.899269\pi$
$434$	5.69486	+	0.498236i	0.273362	+	0.0239161i
$435$	−1.34568	+	8.89738i	−0.0645205	+	0.426597i
$436$	−7.59786	+	5.32008i	−0.363871	+	0.254785i
$437$	−3.09077	+	6.62817i	−0.147851	+	0.317069i
$438$	−14.6621	+	15.3964i	−0.700580	+	0.735669i
$439$	30.5154	−	5.38068i	1.45642	−	0.256806i	0.611306	−	0.791394i	$-0.290644\pi$
$439$	30.5154	−	5.38068i	1.45642	−	0.256806i	0.845113	+	0.534588i	$0.179533\pi$
$440$	3.47824	+	0.931991i	0.165818	+	0.0444309i
$441$	−7.70799	+	14.9975i	−0.367047	+	0.714166i
$442$	1.19369	+	0.699082i	0.0567779	+	0.0332519i
$443$	−6.38226	+	17.5351i	−0.303230	+	0.833118i	0.690704	+	0.723138i	$0.257301\pi$
$443$	−6.38226	+	17.5351i	−0.303230	+	0.833118i	−0.993934	+	0.109980i	$0.964921\pi$
$444$	15.9178	+	5.35707i	0.755424	+	0.254235i
$445$	3.19931	+	2.68454i	0.151662	+	0.127259i
$446$	14.5676	+	12.2237i	0.689797	+	0.578808i
$447$	6.89211	−	20.4789i	0.325986	−	0.968619i
$448$	1.06437	−	0.496326i	0.0502869	−	0.0234492i
$449$	−3.58727	−	13.3879i	−0.169294	−	0.631812i	−0.997453	−	0.0713204i	$-0.977279\pi$
$449$	−3.58727	−	13.3879i	−0.169294	−	0.631812i	0.828160	−	0.560492i	$-0.189388\pi$
$450$	−1.91531	+	8.85792i	−0.0902887	+	0.417566i
$451$	6.63501	+	11.4922i	0.312430	+	0.541145i
$452$	−0.220917	−	1.25288i	−0.0103910	−	0.0589306i
$453$	−0.753537	−	30.8439i	−0.0354043	−	1.44917i
$454$	−3.88893	−	10.6848i	−0.182517	−	0.501460i
$455$	3.38646	+	4.90078i	0.158760	+	0.229752i
$456$	−5.89862	−	8.00083i	−0.276228	−	0.374673i
$457$	2.34465	−	26.7994i	0.109678	−	1.25362i	−0.719442	−	0.694553i	$-0.755602\pi$
$457$	2.34465	−	26.7994i	0.109678	−	1.25362i	0.829119	−	0.559072i	$-0.188842\pi$
$458$		−	11.8255i		−	0.552571i
$459$	−1.95827	−	0.373613i	−0.0914042	−	0.0174388i
$460$	−1.26767	+	1.26767i	−0.0591055	+	0.0591055i
$461$	−2.95957	−	0.258929i	−0.137841	−	0.0120595i	0.0180265	−	0.999838i	$-0.494262\pi$
$461$	−2.95957	−	0.258929i	−0.137841	−	0.0120595i	−0.155867	+	0.987778i	$0.549817\pi$
$462$	3.24836	−	4.06907i	0.151127	−	0.189310i
$463$	−11.4119	+	7.99069i	−0.530355	+	0.371359i	−0.807868	−	0.589363i	$-0.799379\pi$
$463$	−11.4119	+	7.99069i	−0.530355	+	0.371359i	0.277513	+	0.960722i	$0.410490\pi$
$464$	1.26307	+	3.47026i	0.0586366	+	0.161103i
$465$	2.78910	−	11.5283i	0.129341	−	0.534613i
$466$	0.732047	−	1.04547i	0.0339114	−	0.0484305i
$467$	15.9845	+	27.6859i	0.739673	+	1.28115i	0.952642	+	0.304093i	$0.0983534\pi$
$467$	15.9845	+	27.6859i	0.739673	+	1.28115i	−0.212969	+	0.977059i	$0.568313\pi$
$468$	−8.58790	+	6.57632i	−0.396976	+	0.303990i
$469$	3.66926	−	6.35535i	0.169431	−	0.293463i
$470$	7.09109	+	15.2069i	0.327088	+	0.701441i
$471$	14.2022	+	0.893653i	0.654404	+	0.0411774i
$472$	−0.179291	+	0.213671i	−0.00825254	+	0.00983499i
$473$	−0.557552	−	6.37285i	−0.0256363	−	0.293024i
$474$	−25.8552	+	5.21308i	−1.18757	+	0.239445i
$475$	−7.32680	−	15.7124i	−0.336177	−	0.720933i
$476$	0.116619	+	0.435228i	0.00534522	+	0.0199486i
$477$	−24.3802	+	22.5755i	−1.11629	+	1.03366i
$478$	−26.6078	+	15.3620i	−1.21701	+	0.702644i
$479$	−19.6347	−	13.7484i	−0.897131	−	0.628178i	0.0313697	−	0.999508i	$-0.490013\pi$
$479$	−19.6347	−	13.7484i	−0.897131	−	0.628178i	−0.928501	+	0.371330i	$0.878902\pi$
$480$	−0.687953	−	2.33754i	−0.0314006	−	0.106694i
$481$	11.7536	+	32.9267i	0.535918	+	1.50133i
$482$	−18.4000	−	3.24442i	−0.838099	−	0.147779i
$483$	0.945803	+	2.41347i	0.0430355	+	0.109817i
$484$	−3.40755	+	2.85928i	−0.154889	+	0.129967i
$485$	−12.6770			−0.575635
$486$	8.49066	−	13.0732i	0.385144	−	0.593013i
$487$	−25.7468	+	25.7468i	−1.16670	+	1.16670i	−0.183721	+	0.982979i	$0.558814\pi$
$487$	−25.7468	+	25.7468i	−1.16670	+	1.16670i	−0.982979	+	0.183721i	$0.941186\pi$
$488$	−0.610918	+	6.98282i	−0.0276549	+	0.316097i
$489$	−14.9410	−	38.1260i	−0.675657	−	1.72412i
$490$	1.37310	−	7.78724i	0.0620304	−	0.351792i
$491$	10.7571	−	3.91526i	0.485460	−	0.176693i	−0.0876829	−	0.996148i	$-0.527946\pi$
$491$	10.7571	−	3.91526i	0.485460	−	0.176693i	0.573143	+	0.819455i	$0.305724\pi$
$492$	4.29849	−	7.88383i	0.193791	−	0.355430i
$493$	−1.39535	+	0.246037i	−0.0628432	+	0.0110810i
$494$	5.47937	−	19.9535i	0.246529	−	0.897748i
$495$	−7.33974	−	7.92647i	−0.329897	−	0.356268i
$496$	−1.25984	−	4.70180i	−0.0565687	−	0.211117i
$497$	−3.76985	+	10.3576i	−0.169101	+	0.464600i
$498$	−3.01309	−	2.00193i	−0.135020	−	0.0897088i
$499$	−12.7031	+	1.11137i	−0.568668	+	0.0497520i	−0.367864	−	0.929880i	$-0.619911\pi$
$499$	−12.7031	+	1.11137i	−0.568668	+	0.0497520i	−0.200803	+	0.979632i	$0.564355\pi$
$500$	−0.983455	−	11.2409i	−0.0439814	−	0.502710i
$501$	20.9619	−	18.4801i	0.936508	−	0.825629i
$502$	−3.89306	−	8.34869i	−0.173756	−	0.372620i
$503$	−24.5639	−	14.1820i	−1.09525	−	0.632343i	−0.160281	−	0.987071i	$-0.551240\pi$
$503$	−24.5639	−	14.1820i	−1.09525	−	0.632343i	−0.934970	+	0.354728i	$0.884573\pi$
$504$	−3.49543	−	0.441638i	−0.155699	−	0.0196721i
$505$	−0.191209	+	0.713601i	−0.00850868	+	0.0317548i
$506$	0.566414	+	3.21229i	0.0251802	+	0.142804i
$507$	−21.8179	−	5.56586i	−0.968967	−	0.247189i
$508$	−4.55086	+	1.65638i	−0.201912	+	0.0734898i
$509$	10.1359	−	7.09726i	0.449267	−	0.314580i	−0.326955	−	0.945040i	$-0.606022\pi$
$509$	10.1359	−	7.09726i	0.449267	−	0.314580i	0.776222	+	0.630460i	$0.217134\pi$
$510$	0.929046	−	0.104201i	0.0411388	−	0.00461409i
$511$	−9.26631	−	11.0432i	−0.409917	−	0.488521i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.18322	+	29.7405i	0.0963914	+	1.31307i
$514$	−18.3227	−	18.3227i	−0.808179	−	0.808179i
$515$	−1.26261	+	14.4317i	−0.0556373	+	0.635938i
$516$	−3.48428	+	2.56878i	−0.153387	+	0.113084i
$517$	30.0648	+	5.30124i	1.32225	+	0.233148i
$518$	−4.81268	+	10.3208i	−0.211457	+	0.453471i
$519$	−23.3449	−	22.2314i	−1.02473	−	0.975851i
$520$	2.93509	−	4.13689i	0.128712	−	0.181415i
$521$	−10.9373	+	6.31466i	−0.479173	+	0.276650i	−0.720072	−	0.693900i	$-0.755891\pi$
$521$	−10.9373	+	6.31466i	−0.479173	+	0.276650i	0.240899	+	0.970550i	$0.422558\pi$
$522$	2.34144	−	10.8287i	0.102482	−	0.473958i
$523$	−21.9869	+	38.0823i	−0.961418	+	1.66522i	−0.242473	+	0.970158i	$0.577958\pi$
$523$	−21.9869	+	38.0823i	−0.961418	+	1.66522i	−0.718945	+	0.695066i	$0.755375\pi$
$524$	0.142369	+	0.0518181i	0.00621942	+	0.00226368i
$525$	−5.82389	−	1.96001i	−0.254175	−	0.0855419i
$526$	−3.94450	+	0.345099i	−0.171989	+	0.0150470i
$527$	1.86046	−	0.162769i	0.0810427	−	0.00709032i
$528$	−4.20185	−	1.41412i	−0.182862	−	0.0615417i
$529$	20.0869	+	7.31104i	0.873345	+	0.317871i
$530$	7.79075	−	13.4940i	0.338408	−	0.586140i
$531$	0.796729	−	0.255786i	0.0345751	−	0.0111002i
$532$	5.83690	−	3.36994i	0.253062	−	0.146105i
$533$	18.4282	−	3.13166i	0.798212	−	0.135647i
$534$	−3.72361	−	3.54601i	−0.161136	−	0.153451i
$535$	3.58959	−	7.69791i	0.155192	−	0.332809i
$536$	−6.15377	−	1.08508i	−0.265803	−	0.0468682i
$537$	21.5504	−	15.8880i	0.929967	−	0.685618i
$538$	−1.95302	+	22.3231i	−0.0842006	+	0.962417i
$539$	−10.1732	−	10.1732i	−0.438193	−	0.438193i
$540$	−1.99056	+	7.03378i	−0.0856600	+	0.302686i
$541$	−23.6253	−	23.6253i	−1.01573	−	1.01573i	−0.999874	−	0.0158554i	$-0.994953\pi$
$541$	−23.6253	−	23.6253i	−1.01573	−	1.01573i	−0.0158554	−	0.999874i	$-0.505047\pi$
$542$	1.88349	+	2.24466i	0.0809029	+	0.0964164i
$543$	−4.91286	+	0.551022i	−0.210831	+	0.0236466i
$544$	0.314282	−	0.220062i	0.0134747	−	0.00943509i
$545$	−12.2617	+	4.46288i	−0.525232	+	0.191169i
$546$	−3.78222	−	6.28370i	−0.161864	−	0.268917i
$547$	2.39756	+	13.5972i	0.102512	+	0.581376i	0.992185	+	0.124777i	$0.0398214\pi$
$547$	2.39756	+	13.5972i	0.102512	+	0.581376i	−0.889673	+	0.456599i	$0.849067\pi$
$548$	0.357079	−	1.33264i	0.0152537	−	0.0569274i
$549$	12.7141	−	16.7496i	0.542624	−	0.714855i
$550$	−6.69641	−	3.86618i	−0.285536	−	0.164854i
$551$	8.95690	+	19.2081i	0.381577	+	0.818294i
$552$	1.65567	−	1.45965i	0.0704701	−	0.0621266i
$553$	−1.55867	−	17.8157i	−0.0662814	−	0.757600i
$554$	2.72150	−	0.238100i	0.115625	−	0.0101159i
$555$	19.6797	+	13.0754i	0.835358	+	0.555021i
$556$	1.35093	−	3.71165i	0.0572921	−	0.157409i
$557$	1.94372	+	7.25408i	0.0823582	+	0.307365i	0.994801	−	0.101840i	$-0.0324729\pi$
$557$	1.94372	+	7.25408i	0.0823582	+	0.307365i	−0.912443	+	0.409205i	$0.865806\pi$
$558$	−4.31847	+	13.9498i	−0.182815	+	0.590544i
$559$	−8.68952	−	2.38621i	−0.367527	−	0.100926i
$560$	1.62707	−	0.286897i	0.0687563	−	0.0121236i
$561$	0.814248	−	1.49341i	0.0343776	−	0.0630516i
$562$	−7.05811	+	2.56894i	−0.297728	+	0.108364i
$563$	6.07429	−	34.4490i	0.256001	−	1.45185i	−0.537491	−	0.843270i	$-0.680628\pi$
$563$	6.07429	−	34.4490i	0.256001	−	1.45185i	0.793491	−	0.608582i	$-0.208261\pi$
$564$	−7.53746	−	19.2338i	−0.317384	−	0.809891i
$565$	0.155988	−	1.78295i	0.00656246	−	0.0750093i
$566$	−2.60267	+	2.60267i	−0.109398	+	0.109398i
$567$	8.16730	+	6.70917i	0.342994	+	0.281759i
$568$	9.38541			0.393803
$569$	−0.704529	+	0.591170i	−0.0295354	+	0.0247831i	−0.657436	−	0.753511i	$-0.728359\pi$
$569$	−0.704529	+	0.591170i	−0.0295354	+	0.0247831i	0.627900	+	0.778294i	$0.283914\pi$
$570$	−5.10231	−	13.0199i	−0.213712	−	0.545344i
$571$	−25.2076	−	4.44479i	−1.05491	−	0.186009i	−0.380811	−	0.924653i	$-0.624355\pi$
$571$	−25.2076	−	4.44479i	−1.05491	−	0.186009i	−0.674096	+	0.738644i	$0.735466\pi$
$572$	−3.10263	−	8.69175i	−0.129727	−	0.363420i
$573$	−9.39018	−	31.9061i	−0.392280	−	1.33290i
$574$	4.98742	+	3.49223i	0.208171	+	0.145763i
$575$	3.33387	−	1.92481i	0.139032	−	0.0802701i
$576$	0.664594	+	2.92546i	0.0276914	+	0.121894i
$577$	5.08749	+	18.9868i	0.211795	+	0.790430i	0.987270	+	0.159052i	$0.0508438\pi$
$577$	5.08749	+	18.9868i	0.211795	+	0.790430i	−0.775475	+	0.631378i	$0.782490\pi$
$578$	−7.12230	−	15.2738i	−0.296249	−	0.635307i
$579$	−5.32313	+	1.07328i	−0.221222	+	0.0446041i
$580$	0.452803	+	5.17556i	0.0188016	+	0.214903i
$581$	1.57666	−	1.87898i	0.0654107	−	0.0779534i
$582$	15.5770	+	0.980160i	0.645688	+	0.0406289i
$583$	−11.9812	−	25.6937i	−0.496210	−	1.06413i
$584$	−6.13749	+	10.6304i	−0.253971	+	0.439891i
$585$	−14.0644	+	5.80947i	−0.581492	+	0.240192i
$586$	−10.3418	−	17.9125i	−0.427215	−	0.739958i
$587$	−13.4676	+	19.2337i	−0.555867	+	0.793860i	−0.994492	−	0.104810i	$-0.966577\pi$
$587$	−13.4676	+	19.2337i	−0.555867	+	0.793860i	0.438625	+	0.898670i	$0.355466\pi$
$588$	−2.28930	+	9.46246i	−0.0944091	+	0.390225i
$589$	−9.55445	−	26.2506i	−0.393684	−	1.08164i
$590$	−0.321434	+	0.225071i	−0.0132332	+	0.00926601i
$591$	−9.15794	+	11.4717i	−0.376707	+	0.471884i
$592$	9.65972	+	0.845116i	0.397012	+	0.0347341i
$593$	−18.5846	+	18.5846i	−0.763178	+	0.763178i	−0.976895	−	0.213718i	$-0.931443\pi$
$593$	−18.5846	+	18.5846i	−0.763178	+	0.763178i	0.213718	+	0.976895i	$0.431443\pi$
$594$	8.40589	+	10.3072i	0.344898	+	0.422910i
$595$			0.633884i			0.0259867i
$596$	1.08728	−	12.4277i	0.0445367	−	0.509057i
$597$	−19.8678	−	26.9486i	−0.813137	−	1.10293i
$598$	4.51985	+	0.825908i	0.184831	+	0.0337739i
$599$	−6.28544	−	17.2691i	−0.256816	−	0.705597i	−0.999359	−	0.0357981i	$-0.988603\pi$
$599$	−6.28544	−	17.2691i	−0.256816	−	0.705597i	0.742543	−	0.669799i	$-0.233620\pi$
$600$	0.127791	+	5.23075i	0.00521704	+	0.213544i
$601$	3.59949	+	20.4137i	0.146826	+	0.832692i	0.965883	+	0.258980i	$0.0833862\pi$
$601$	3.59949	+	20.4137i	0.146826	+	0.832692i	−0.819057	+	0.573713i	$0.805503\pi$
$602$	−1.46757	−	2.54191i	−0.0598138	−	0.103600i
$603$	13.8870	+	12.5924i	0.565522	+	0.512802i
$604$	−4.61035	−	17.2061i	−0.187593	−	0.700105i
$605$	−5.67154	+	2.64468i	−0.230581	+	0.107522i
$606$	0.290123	−	0.862058i	0.0117854	−	0.0350187i
$607$	5.80691	+	4.87257i	0.235695	+	0.197772i	0.752983	−	0.658040i	$-0.228614\pi$
$607$	5.80691	+	4.87257i	0.235695	+	0.197772i	−0.517288	+	0.855811i	$0.673058\pi$
$608$	−4.39630	−	3.68893i	−0.178293	−	0.149606i
$609$	7.11961	+	2.39608i	0.288501	+	0.0970942i
$610$	−3.37268	+	9.26636i	−0.136556	+	0.375184i
$611$	21.7321	−	37.1077i	0.879187	−	1.50122i
$612$	−1.14963	+	0.0562059i	−0.0464709	+	0.00227199i
$613$	13.2612	+	3.55332i	0.535614	+	0.143517i	0.516480	−	0.856299i	$-0.327242\pi$
$613$	13.2612	+	3.55332i	0.535614	+	0.143517i	0.0191347	+	0.999817i	$0.493909\pi$
$614$	30.3197	−	5.34618i	1.22360	−	0.215754i
$615$	8.71171	−	9.14804i	0.351290	−	0.368884i
$616$	1.27042	−	2.72441i	0.0511865	−	0.109770i
$617$	−13.4711	+	9.43254i	−0.542325	+	0.379740i	−0.812401	−	0.583099i	$-0.801840\pi$
$617$	−13.4711	+	9.43254i	−0.542325	+	0.379740i	0.270076	+	0.962839i	$0.412951\pi$
$618$	2.66727	−	17.6355i	0.107293	−	0.709402i
$619$	13.5098	+	1.18195i	0.543004	+	0.0475067i	0.355358	−	0.934730i	$-0.384359\pi$
$619$	13.5098	+	1.18195i	0.543004	+	0.0475067i	0.187646	+	0.982237i	$0.439914\pi$
$620$		−	6.84790i		−	0.275018i
$621$	−6.53651	+	1.05851i	−0.262301	+	0.0424764i
$622$	21.3732	+	21.3732i	0.856987	+	0.856987i
$623$	2.67078	−	2.24105i	0.107003	−	0.0897858i
$624$	−3.92636	+	4.85630i	−0.157180	+	0.194408i
$625$	0.133698	−	0.758240i	0.00534793	−	0.0303296i
$626$	9.22509	+	4.30173i	0.368709	+	0.171932i
$627$	−24.7298	−	5.98300i	−0.987613	−	0.238938i
$628$	8.09106	−	1.42667i	0.322868	−	0.0569304i
$629$	−0.962877	+	3.59351i	−0.0383924	+	0.143283i
$630$	−4.58906	−	1.87285i	−0.182832	−	0.0746163i
$631$	16.8597	−	4.51753i	0.671172	−	0.179840i	0.0928895	−	0.995676i	$-0.470390\pi$
$631$	16.8597	−	4.51753i	0.671172	−	0.179840i	0.578283	+	0.815836i	$0.303723\pi$
$632$	−13.8011	+	6.43558i	−0.548980	+	0.255994i
$633$	−5.32446	−	0.335034i	−0.211628	−	0.0133164i
$634$	5.09238	−	6.06886i	0.202244	−	0.241025i
$635$	−6.78716	+	0.593800i	−0.269340	+	0.0235642i
$636$	−10.6163	+	15.9784i	−0.420962	+	0.633586i
$637$	−18.4200	+	8.45069i	−0.729826	+	0.334829i
$638$	8.18626	+	4.72634i	0.324097	+	0.187118i
$639$	−23.8253	−	15.0042i	−0.942516	−	0.593557i
$640$	−0.703407	−	1.21834i	−0.0278046	−	0.0481590i
$641$	5.75528	+	32.6398i	0.227320	+	1.28920i	0.858200	+	0.513315i	$0.171583\pi$
$641$	5.75528	+	32.6398i	0.227320	+	1.28920i	−0.630880	+	0.775880i	$0.717306\pi$
$642$	−5.00592	+	9.18132i	−0.197568	+	0.362358i
$643$	−12.5392	+	26.8903i	−0.494496	+	1.06045i	0.487772	+	0.872971i	$0.337810\pi$
$643$	−12.5392	+	26.8903i	−0.494496	+	1.06045i	−0.982268	+	0.187480i	$0.939968\pi$
$644$	0.858410	+	1.22594i	0.0338261	+	0.0483087i
$645$	−5.67003	+	2.22200i	−0.223257	+	0.0874913i
$646$	1.68671	−	1.41532i	0.0663629	−	0.0556851i
$647$	35.8632			1.40993			0.704964	−	0.709243i	$-0.250963\pi$
$647$	35.8632			1.40993			0.704964	+	0.709243i	$0.250963\pi$
$648$	2.98975	−	8.48890i	0.117448	−	0.333475i
$649$			0.713953i			0.0280251i
$650$	−8.38696	+	6.94931i	−0.328963	+	0.272574i
$651$	−9.07331	−	3.96412i	−0.355611	−	0.155366i
$652$	−13.5605	−	19.3664i	−0.531069	−	0.758445i
$653$	5.17237	+	14.2110i	0.202410	+	0.556118i	0.998816	−	0.0486448i	$-0.0154902\pi$
$653$	5.17237	+	14.2110i	0.202410	+	0.556118i	−0.796406	+	0.604763i	$0.793268\pi$
$654$	15.4117	−	4.53575i	0.602643	−	0.177362i
$655$	0.174595	+	0.122252i	0.00682197	+	0.00477680i
$656$	1.34180	−	5.00768i	0.0523886	−	0.195517i
$657$	32.5749	−	17.1741i	1.27087	−	0.670025i
$658$	13.5298	−	3.62529i	0.527445	−	0.141329i
$659$	9.67889	−	26.5925i	0.377036	−	1.03590i	−0.595542	−	0.803324i	$-0.703063\pi$
$659$	9.67889	−	26.5925i	0.377036	−	1.03590i	0.972579	−	0.232574i	$-0.0747149\pi$
$660$	−5.19490	−	3.45155i	−0.202211	−	0.134351i
$661$	0.711441	+	8.13181i	0.0276718	+	0.316291i	0.997398	+	0.0720948i	$0.0229684\pi$
$661$	0.711441	+	8.13181i	0.0276718	+	0.316291i	−0.969726	+	0.244196i	$0.921476\pi$
$662$	0.477003	+	0.400253i	0.0185392	+	0.0155563i
$663$	−1.57331	−	1.80707i	−0.0611023	−	0.0701809i
$664$	−1.96262	−	0.714336i	−0.0761645	−	0.0277216i
$665$	9.15867	−	2.45406i	0.355158	−	0.0951642i
$666$	−23.1706	−	17.5881i	−0.897844	−	0.681526i
$667$	−4.07560	+	2.35305i	−0.157808	+	0.0911104i
$668$	9.25406	−	13.2162i	0.358050	−	0.511349i
$669$	−17.1607	−	28.1143i	−0.663471	−	1.08696i
$670$	−7.96714	−	3.71514i	−0.307797	−	0.143528i
$671$	10.2910	+	14.6970i	0.397279	+	0.567373i
$672$	−2.02146	+	0.226725i	−0.0779794	+	0.00874610i
$673$	8.87717	+	10.5794i	0.342190	+	0.407806i	0.909504	−	0.415696i	$-0.136462\pi$
$673$	8.87717	+	10.5794i	0.342190	+	0.407806i	−0.567314	+	0.823502i	$0.692017\pi$
$674$	7.83241	−	7.83241i	0.301693	−	0.301693i
$675$	8.03786	−	13.4828i	0.309377	−	0.518954i
$676$	−12.9990	−	0.161251i	−0.499962	−	0.00620195i
$677$	−16.3674	−	19.5059i	−0.629052	−	0.749674i	0.353547	−	0.935417i	$-0.384975\pi$
$677$	−16.3674	−	19.5059i	−0.629052	−	0.749674i	−0.982598	+	0.185742i	$0.940531\pi$
$678$	−0.329525	+	2.17875i	−0.0126553	+	0.0836744i
$679$	−1.83768	+	10.4220i	−0.0705237	+	0.399960i
$680$	0.507197	−	0.184605i	0.0194501	−	0.00707927i
$681$	0.481000	+	19.6884i	0.0184320	+	0.754460i
$682$	−10.2062	−	7.14646i	−0.390816	−	0.273652i
$683$	38.8747	+	10.4164i	1.48750	+	0.398574i	0.908892	−	0.417032i	$-0.136930\pi$
$683$	38.8747	+	10.4164i	1.48750	+	0.398574i	0.578607	+	0.815606i	$0.303597\pi$
$684$	5.26283	+	16.3928i	0.201229	+	0.626794i
$685$	0.970453	−	1.68087i	0.0370791	−	0.0642229i
$686$	−13.9280	−	5.06939i	−0.531775	−	0.193550i
$687$	−6.53323	+	19.4125i	−0.249258	+	0.740635i
$688$	−1.60649	+	1.91454i	−0.0612469	+	0.0729912i
$689$	−39.8030	+	3.23369i	−1.51637	+	0.123194i
$690$	2.78133	−	1.38063i	0.105883	−	0.0525598i
$691$	−23.9716	+	11.1781i	−0.911921	+	0.425236i	−0.821200	−	0.570641i	$-0.806695\pi$
$691$	−23.9716	+	11.1781i	−0.911921	+	0.425236i	−0.0907212	+	0.995876i	$0.528917\pi$
$692$	−16.1185	−	9.30600i	−0.612732	−	0.353761i
$693$	−7.58046	+	4.88509i	−0.287958	+	0.185569i
$694$	−27.8806	−	7.47059i	−1.05833	−	0.283580i
$695$	3.18720	−	4.55179i	0.120897	−	0.172659i
$696$	−0.156222	−	6.39451i	−0.00592159	−	0.242383i
$697$	1.80270	+	0.840611i	0.0682820	+	0.0318404i
$698$	−25.4234	−	4.48284i	−0.962291	−	0.169678i
$699$	−1.77930	+	1.31179i	−0.0672994	+	0.0496165i
$700$	−3.53424	−	0.309206i	−0.133582	−	0.0116869i
$701$	19.3807			0.731999			0.366000	−	0.930615i	$-0.380727\pi$
$701$	19.3807			0.731999			0.366000	+	0.930615i	$0.380727\pi$
$702$	17.7309	−	6.05100i	0.669210	−	0.228380i
$703$	55.6485			2.09882
$704$	−2.54990	−	0.223087i	−0.0961030	−	0.00840792i
$705$	−3.23925	−	28.8809i	−0.121997	−	1.08772i
$706$	−13.3246	−	2.34948i	−0.501476	−	0.0884238i
$707$	0.558945	+	0.260640i	0.0210213	+	0.00980239i
$708$	0.412366	−	0.251705i	0.0154977	−	0.00945964i
$709$	−9.11919	+	13.0236i	−0.342479	+	0.489110i	−0.953034	−	0.302864i	$-0.902057\pi$
$709$	−9.11919	+	13.0236i	−0.342479	+	0.489110i	0.610555	+	0.791974i	$0.290946\pi$
$710$	12.7536	+	3.41732i	0.478635	+	0.128250i
$711$	45.3233	+	5.72648i	1.69976	+	0.214760i
$712$	−2.57097	−	1.48435i	−0.0963510	−	0.0556283i
$713$	5.62188	−	2.62152i	0.210541	−	0.0981768i
$714$	0.0490104	−	0.778889i	0.00183417	−	0.0291492i
$715$	−1.05134	−	12.9407i	−0.0393177	−	0.483956i
$716$	9.93619	−	11.8415i	0.371333	−	0.442537i
$717$	52.1659	−	10.5180i	1.94817	−	0.392802i
$718$	−17.7856	−	6.47343i	−0.663752	−	0.241586i
$719$	−1.99716	+	3.45918i	−0.0744815	+	0.129006i	−0.900861	−	0.434108i	$-0.857063\pi$
$719$	−1.99716	+	3.45918i	−0.0744815	+	0.129006i	0.826379	+	0.563114i	$0.190397\pi$
$720$	−0.162088	+	4.21733i	−0.00604065	+	0.157171i
$721$	11.6815	+	3.13006i	0.435043	+	0.116569i
$722$	−11.4154	−	7.99317i	−0.424839	−	0.297475i
$723$	28.4127	+	15.4914i	1.05668	+	0.576132i
$724$	−2.68210	+	0.976203i	−0.0996793	+	0.0362803i
$725$	1.93722	−	10.9865i	0.0719466	−	0.408029i
$726$	7.17342	−	2.81116i	0.266231	−	0.104332i
$727$	3.51542	+	4.18952i	0.130380	+	0.155381i	0.827285	−	0.561783i	$-0.189884\pi$
$727$	3.51542	+	4.18952i	0.130380	+	0.155381i	−0.696905	+	0.717164i	$0.745440\pi$
$728$	−2.97553	−	3.01267i	−0.110281	−	0.111657i
$729$	−21.1606	+	16.7699i	−0.783726	+	0.621106i
$730$	−12.2108	+	12.2108i	−0.451940	+	0.451940i
$731$	−0.616358	−	0.734546i	−0.0227968	−	0.0271682i
$732$	4.86065	−	11.1253i	0.179655	−	0.411204i
$733$	9.19467	+	13.1313i	0.339613	+	0.485017i	0.952238	−	0.305356i	$-0.0987755\pi$
$733$	9.19467	+	13.1313i	0.339613	+	0.485017i	−0.612625	+	0.790373i	$0.709887\pi$
$734$	3.55255	+	1.65658i	0.131127	+	0.0611455i
$735$	−6.55626	+	12.0248i	−0.241831	+	0.443541i
$736$	0.730931	−	1.04388i	0.0269425	−	0.0384778i
$737$	−13.8516	+	7.99722i	−0.510230	+	0.294581i
$738$	−11.4119	+	10.5671i	−0.420077	+	0.388982i
$739$	−9.23855	+	2.47546i	−0.339846	+	0.0910614i	−0.424706	−	0.905332i	$-0.639622\pi$
$739$	−9.23855	+	2.47546i	−0.339846	+	0.0910614i	0.0848599	+	0.996393i	$0.472956\pi$
$740$	12.8187	+	4.66561i	0.471224	+	0.171511i
$741$	−20.0185	+	29.7280i	−0.735397	+	1.09208i
$742$	−9.96426	−	8.36100i	−0.365799	−	0.306942i
$743$	3.32369	+	37.9900i	0.121934	+	1.39372i	0.772861	+	0.634575i	$0.218825\pi$
$743$	3.32369	+	37.9900i	0.121934	+	1.39372i	−0.650927	+	0.759141i	$0.725619\pi$
$744$	−0.529463	+	8.41440i	−0.0194111	+	0.308487i
$745$	6.00252	−	16.4918i	0.219915	−	0.604212i
$746$	−10.0909	+	2.70385i	−0.369454	+	0.0989950i
$747$	3.84023	+	4.95097i	0.140507	+	0.181146i
$748$	0.254173	−	0.948587i	0.00929349	−	0.0346838i
$749$	−5.80822	−	4.06696i	−0.212228	−	0.148604i
$750$	−4.59584	+	18.9962i	−0.167816	+	0.693643i
$751$	−16.1321	−	44.3225i	−0.588668	−	1.61735i	−0.772943	−	0.634476i	$-0.781216\pi$
$751$	−16.1321	−	44.3225i	−0.588668	−	1.61735i	0.184275	−	0.982875i	$-0.441006\pi$
$752$	−6.84100	−	9.76996i	−0.249465	−	0.356274i
$753$	1.77837	+	15.8558i	0.0648076	+	0.577818i
$754$	10.2529	−	8.49542i	0.373390	−	0.309385i
$755$		−	25.0596i		−	0.912013i
$756$	5.49403	+	2.65610i	0.199816	+	0.0966013i
$757$	21.8257			0.793269			0.396635	−	0.917977i	$-0.370178\pi$
$757$	21.8257			0.793269			0.396635	+	0.917977i	$0.370178\pi$
$758$	−13.4829	+	11.3135i	−0.489721	+	0.410925i
$759$	0.844877	−	5.58616i	0.0306671	−	0.202765i
$760$	−4.63085	−	6.61355i	−0.167979	−	0.239899i
$761$	−22.4757	+	48.1994i	−0.814745	+	1.74723i	−0.166139	+	0.986102i	$0.553130\pi$
$761$	−22.4757	+	48.1994i	−0.814745	+	1.74723i	−0.648606	+	0.761124i	$0.724648\pi$
$762$	8.38568	−	0.204868i	0.303781	−	0.00742158i
$763$	1.89154	+	10.7275i	0.0684783	+	0.388360i
$764$	−9.60111	−	16.6296i	−0.347356	−	0.601638i
$765$	−1.58267	−	0.342214i	−0.0572215	−	0.0123728i
$766$	12.9260	+	7.46283i	0.467036	+	0.269643i
$767$	0.942885	+	0.349820i	0.0340456	+	0.0126313i
$768$	0.770117	+	1.55143i	0.0277892	+	0.0559822i
$769$	49.1651	−	4.30139i	1.77294	−	0.155112i	0.846706	−	0.532062i	$-0.178583\pi$
$769$	49.1651	−	4.30139i	1.77294	−	0.155112i	0.926234	+	0.376950i	$0.123027\pi$
$770$	2.71833	−	3.23957i	0.0979617	−	0.116746i
$771$	19.9554	+	40.2008i	0.718677	+	1.44780i
$772$	−2.84142	+	1.32497i	−0.102265	+	0.0476869i
$773$	−34.6638	+	9.28814i	−1.24677	+	0.334071i	−0.821088	−	0.570802i	$-0.806633\pi$
$773$	−34.6638	+	9.28814i	−1.24677	+	0.334071i	−0.425682	+	0.904873i	$0.639966\pi$
$774$	7.13889	−	2.29191i	0.256602	−	0.0823809i
$775$	−3.80583	+	14.2036i	−0.136710	+	0.510207i
$776$	8.87428	−	1.56477i	0.318568	−	0.0561721i
$777$	13.6023	−	14.2836i	0.487981	−	0.512421i
$778$	11.9596	+	5.57684i	0.428771	+	0.199939i
$779$	5.16650	−	29.3007i	0.185109	−	1.04980i
$780$	−7.10368	+	5.16949i	−0.254352	+	0.185097i
$781$	18.4029	−	15.4419i	0.658507	−	0.552553i
$782$	0.345720	+	0.345720i	0.0123629	+	0.0123629i
$783$	−9.82616	+	16.4825i	−0.351158	+	0.589038i
$784$			5.62077i			0.200742i
$785$	11.5142	+	1.00736i	0.410960	+	0.0359544i
$786$	−0.205082	−	0.163718i	−0.00731503	−	0.00583962i
$787$	7.56889	−	5.29980i	0.269802	−	0.188917i	−0.430844	−	0.902426i	$-0.641784\pi$
$787$	7.56889	−	5.29980i	0.269802	−	0.188917i	0.700646	+	0.713509i	$0.252895\pi$
$788$	−3.58162	+	7.68081i	−0.127590	+	0.273618i
$789$	6.66587	+	1.61271i	0.237311	+	0.0574138i
$790$	−21.0973	+	3.72003i	−0.750609	+	0.132353i
$791$	−1.44318	−	0.386699i	−0.0513136	−	0.0137494i
$792$	6.11641	+	4.64278i	0.217337	+	0.164974i
$793$	24.4520	−	6.38963i	0.868317	−	0.226902i
$794$	8.00268	−	21.9872i	0.284004	−	0.780295i
$795$	−20.2441	+	17.8473i	−0.717984	+	0.632977i
$796$	−14.8077	−	12.4251i	−0.524845	−	0.440398i
$797$	23.3335	+	19.5791i	0.826514	+	0.693527i	0.954488	−	0.298250i	$-0.0964029\pi$
$797$	23.3335	+	19.5791i	0.826514	+	0.693527i	−0.127974	+	0.991778i	$0.540847\pi$
$798$	−11.4435	+	2.30731i	−0.405096	+	0.0816780i
$799$	4.14723	−	1.93389i	0.146718	−	0.0684159i
$800$	0.781860	+	2.91794i	0.0276429	+	0.103165i
$801$	4.15354	+	7.87823i	0.146758	+	0.278363i
$802$	−11.3719	−	19.6968i	−0.401557	−	0.695517i
$803$	5.45594	+	30.9422i	0.192536	+	1.09193i
$804$	9.50243	+	5.18100i	0.335125	+	0.182720i
$805$	0.720098	+	1.97845i	0.0253801	+	0.0697313i
$806$	−14.4388	+	9.97726i	−0.508584	+	0.351434i
$807$	15.5388	−	35.5661i	0.546993	−	1.25199i
$808$	0.0457690	−	0.523142i	0.00161015	−	0.0184041i
$809$			41.4875i			1.45862i	0.684183	+	0.729311i	$0.260159\pi$
$809$			41.4875i			1.45862i	−0.684183	+	0.729311i	$0.739841\pi$
$810$	7.15360	−	10.4468i	0.251352	−	0.367062i
$811$	12.5044	−	12.5044i	0.439089	−	0.439089i	−0.452617	−	0.891705i	$-0.649509\pi$
$811$	12.5044	−	12.5044i	0.439089	−	0.439089i	0.891705	+	0.452617i	$0.149509\pi$
$812$	4.32055	+	0.377999i	0.151622	+	0.0132652i
$813$	−1.85180	−	4.72535i	−0.0649454	−	0.165725i
$814$	20.3312	−	14.2361i	0.712610	−	0.498975i
$815$	−11.3755	−	31.2540i	−0.398468	−	1.09478i
$816$	−0.637495	+	0.187619i	−0.0223168	+	0.00656798i
$817$	−8.22689	+	11.7492i	−0.287822	+	0.411053i
$818$	−0.616533	−	1.06787i	−0.0215566	−	0.0373371i
$819$	2.73726	+	12.4047i	0.0956477	+	0.433457i
$820$	3.64669	−	6.31626i	0.127348	−	0.220573i
$821$	−6.47584	−	13.8875i	−0.226008	−	0.484677i	0.760303	−	0.649568i	$-0.225050\pi$
$821$	−6.47584	−	13.8875i	−0.226008	−	0.484677i	−0.986312	+	0.164892i	$0.947273\pi$
$822$	−1.32241	+	1.99035i	−0.0461244	+	0.0694215i
$823$	12.9090	−	15.3843i	0.449979	−	0.536264i	−0.492596	−	0.870258i	$-0.663952\pi$
$823$	12.9090	−	15.3843i	0.449979	−	0.536264i	0.942575	+	0.333994i	$0.108396\pi$
$824$	−0.897498	−	10.2584i	−0.0312658	−	0.357370i
$825$	8.85675	+	10.0462i	0.308352	+	0.349763i
$826$	0.138439	+	0.296883i	0.00481690	+	0.0103299i
$827$	2.28223	+	8.51739i	0.0793608	+	0.296179i	0.994187	−	0.107670i	$-0.0343390\pi$
$827$	2.28223	+	8.51739i	0.0793608	+	0.296179i	−0.914826	+	0.403848i	$0.867672\pi$
$828$	−3.52432	+	1.48142i	−0.122479	+	0.0514828i
$829$	43.8038	−	25.2901i	1.52137	−	0.878363i	0.521687	−	0.853137i	$-0.325303\pi$
$829$	43.8038	−	25.2901i	1.52137	−	0.878363i	0.999682	−	0.0252259i	$-0.00803050\pi$
$830$	−2.40687	−	1.68531i	−0.0835435	−	0.0584978i
$831$	−4.59909	−	1.11268i	−0.159541	−	0.0385985i
$832$	−1.54401	+	3.25823i	−0.0535289	+	0.112959i
$833$	−2.12374	−	0.374473i	−0.0735833	−	0.0129747i
$834$	−4.26822	+	5.34661i	−0.147796	+	0.185138i
$835$	17.3873	−	14.5897i	0.601712	−	0.504896i
$836$	−14.6897			−0.508053
$837$	14.7959	−	20.5140i	0.511423	−	0.709066i
$838$	−4.85061	+	4.85061i	−0.167562	+	0.167562i
$839$	−1.60583	+	18.3547i	−0.0554393	+	0.633675i	0.916747	+	0.399467i	$0.130805\pi$
$839$	−1.60583	+	18.3547i	−0.0554393	+	0.633675i	−0.972187	+	0.234207i	$0.924751\pi$
$840$	−2.82947	−	0.427942i	−0.0976259	−	0.0147654i
$841$	2.66757	−	15.1286i	0.0919853	−	0.521675i
$842$	30.0898	−	10.9518i	1.03696	−	0.377424i
$843$	13.0057	−	0.317738i	0.447940	−	0.0109435i
$844$	−3.03336	+	0.534864i	−0.104413	+	0.0184108i
$845$	−17.6053	−	4.95219i	−0.605642	−	0.170360i
$846$	1.74725	+	35.7381i	0.0600718	+	1.22870i
$847$	1.35208	+	5.04604i	0.0464581	+	0.173384i
$848$	−3.78812	+	10.4078i	−0.130085	+	0.357405i
$849$	5.71038	−	2.83460i	0.195980	−	0.0972831i
$850$	−1.15460	+	0.101014i	−0.0396024	+	0.00346476i
$851$	1.07696	+	12.3098i	0.0369179	+	0.421973i
$852$	−15.4069	−	5.18514i	−0.527831	−	0.177640i
$853$	−5.90615	−	12.6658i	−0.202223	−	0.433668i	0.778876	−	0.627178i	$-0.215790\pi$
$853$	−5.90615	−	12.6658i	−0.202223	−	0.433668i	−0.981098	+	0.193511i	$0.938013\pi$
$854$	7.12912	+	4.11600i	0.243953	+	0.140847i
$855$	1.18276	+	24.1921i	0.0404496	+	0.827351i
$856$	−1.56263	+	5.83182i	−0.0534096	+	0.199327i
$857$	−5.69470	−	32.2962i	−0.194527	−	1.10322i	−0.913091	−	0.407757i	$-0.866311\pi$
$857$	−5.69470	−	32.2962i	−0.194527	−	1.10322i	0.718564	−	0.695461i	$-0.244800\pi$
$858$	0.291289	+	15.9823i	0.00994444	+	0.545626i
$859$	−38.1425	+	13.8827i	−1.30140	+	0.473672i	−0.897454	−	0.441108i	$-0.854585\pi$
$859$	−38.1425	+	13.8827i	−1.30140	+	0.473672i	−0.403950	+	0.914781i	$0.632363\pi$
$860$	−2.88013	+	2.01669i	−0.0982116	+	0.0687685i
$861$	−6.25789	−	8.48815i	−0.213268	−	0.289275i
$862$	−1.50182	−	1.78980i	−0.0511522	−	0.0609608i
$863$	32.5135	+	32.5135i	1.10677	+	1.10677i	0.993572	+	0.113200i	$0.0361101\pi$
$863$	32.5135	+	32.5135i	1.10677	+	1.10677i	0.113200	+	0.993572i	$0.463890\pi$
$864$	0.525240	−	5.16954i	0.0178690	−	0.175871i
$865$	−18.5146	−	18.5146i	−0.629515	−	0.629515i
$866$	1.12878	−	12.9021i	0.0383576	−	0.438430i
$867$	3.25351	+	29.0080i	0.110495	+	0.985164i
$868$	−5.62977	−	0.992680i	−0.191087	−	0.0336938i
$869$	−16.4728	+	35.3260i	−0.558800	+	1.19835i
$870$	2.11602	−	8.74624i	0.0717398	−	0.296525i
$871$	3.77461	+	22.2116i	0.127898	+	0.752611i
$872$	8.03262	−	4.63764i	0.272019	−	0.157050i
$873$	−25.0294	−	10.2148i	−0.847116	−	0.345719i
$874$	3.65669	−	6.33357i	0.123689	−	0.214236i
$875$	−12.4527	−	4.53240i	−0.420977	−	0.153223i
$876$	15.9482	−	14.0599i	0.538838	−	0.475041i
$877$	−33.5212	+	2.93273i	−1.13193	+	0.0990311i	−0.637689	−	0.770294i	$-0.720110\pi$
$877$	−33.5212	+	2.93273i	−1.13193	+	0.0990311i	−0.494241	+	0.869325i	$0.664554\pi$
$878$	−30.8682	+	2.70062i	−1.04175	+	0.0911414i
$879$	7.08076	+	35.1182i	0.238828	+	1.18451i
$880$	−3.38377	−	1.23159i	−0.114067	−	0.0415170i
$881$	10.7987	−	18.7039i	0.363818	−	0.630152i	−0.624767	−	0.780811i	$-0.714806\pi$
$881$	10.7987	−	18.7039i	0.363818	−	0.630152i	0.988586	+	0.150659i	$0.0481396\pi$
$882$	8.98577	−	14.2686i	0.302567	−	0.480449i
$883$	−29.6262	+	17.1047i	−0.997001	+	0.575619i	−0.907360	−	0.420355i	$-0.861905\pi$
$883$	−29.6262	+	17.1047i	−0.997001	+	0.575619i	−0.0896414	+	0.995974i	$0.528572\pi$
$884$	−1.12822	−	0.800459i	−0.0379460	−	0.0269223i
$885$	0.652004	−	0.191889i	0.0219169	−	0.00645027i
$886$	7.88626	−	16.9121i	0.264944	−	0.568174i
$887$	−46.4583	−	8.19185i	−1.55992	−	0.275055i	−0.673940	−	0.738786i	$-0.735400\pi$
$887$	−46.4583	−	8.19185i	−1.55992	−	0.275055i	−0.885976	+	0.463730i	$0.846511\pi$
$888$	−15.3903	−	6.72401i	−0.516464	−	0.225643i
$889$	−0.495703	+	5.66592i	−0.0166254	+	0.190029i
$890$	−2.95316	−	2.95316i	−0.0989902	−	0.0989902i
$891$	−8.10453	−	21.5641i	−0.271512	−	0.722423i
$892$	−13.4468	−	13.4468i	−0.450233	−	0.450233i
$893$	−43.9976	−	52.4343i	−1.47232	−	1.75465i
$894$	−8.65074	+	19.8003i	−0.289324	+	0.662221i
$895$	17.8137	−	12.4733i	0.595446	−	0.416936i
$896$	−1.10358	+	0.401671i	−0.0368681	+	0.0134189i
$897$	−6.96341	−	3.85287i	−0.232501	−	0.128644i
$898$	2.40679	+	13.6496i	0.0803156	+	0.455492i
$899$	4.65257	−	17.3636i	0.155172	−	0.579110i
$900$	2.68004	−	8.65728i	0.0893348	−	0.288576i
$901$	−3.68008	−	2.12470i	−0.122601	−	0.0707839i
$902$	−5.60815	−	12.0267i	−0.186731	−	0.400446i
$903$	1.00481	+	4.98353i	0.0334380	+	0.165841i
$904$	0.110880	+	1.26737i	0.00368782	+	0.0421520i
$905$	−4.00009	+	0.349962i	−0.132967	+	0.0116331i
$906$	−1.93755	+	30.7922i	−0.0643708	+	1.02300i
$907$	1.08403	−	2.97834i	0.0359946	−	0.0988943i	−0.920393	−	0.390993i	$-0.872132\pi$
$907$	1.08403	−	2.97834i	0.0359946	−	0.0988943i	0.956388	+	0.292099i	$0.0943537\pi$
$908$	2.94290	+	10.9830i	0.0976635	+	0.364485i
$909$	−0.952519	+	1.25485i	−0.0315931	+	0.0416208i
$910$	−2.94644	−	5.17728i	−0.0976736	−	0.171625i
$911$	−23.1583	+	4.08344i	−0.767270	+	0.135290i	−0.543566	−	0.839367i	$-0.682926\pi$
$911$	−23.1583	+	4.08344i	−0.767270	+	0.135290i	−0.223704	+	0.974657i	$0.571815\pi$
$912$	5.17885	+	8.48449i	0.171489	+	0.280949i
$913$	−5.02360	+	1.82844i	−0.166257	+	0.0605126i
$914$	−4.67145	+	26.4931i	−0.154518	+	0.876314i
$915$	10.6559	−	13.3482i	0.352273	−	0.441276i
$916$	−1.03066	+	11.7805i	−0.0340541	+	0.389240i
$917$	0.125815	−	0.125815i	0.00415478	−	0.00415478i
$918$	1.91826	+	0.542866i	0.0633119	+	0.0179173i
$919$	19.0500			0.628400			0.314200	−	0.949357i	$-0.398264\pi$
$919$	19.0500			0.628400			0.314200	+	0.949357i	$0.398264\pi$
$920$	1.37333	−	1.15236i	0.0452774	−	0.0379923i
$921$	−52.7258	−	7.97450i	−1.73737	−	0.262769i
$922$	2.92574	+	0.515887i	0.0963540	+	0.0169898i
$923$	−11.3764	−	31.8700i	−0.374458	−	1.04901i
$924$	−3.59064	+	3.77047i	−0.118123	+	0.124040i
$925$	−23.9948	−	16.8014i	−0.788945	−	0.552425i
$926$	12.0649	−	6.96567i	0.396477	−	0.228906i
$927$	−14.1216	+	27.4764i	−0.463813	+	0.902443i
$928$	−0.955812	−	3.56714i	−0.0313761	−	0.117097i
$929$	−2.19783	−	4.71327i	−0.0721086	−	0.154637i	0.866949	−	0.498396i	$-0.166077\pi$
$929$	−2.19783	−	4.71327i	−0.0721086	−	0.154637i	−0.939058	+	0.343759i	$0.888300\pi$
$930$	−3.78325	+	11.2414i	−0.124057	+	0.368619i
$931$	2.81142	+	32.1346i	0.0921404	+	1.05317i
$932$	−0.820380	+	0.977691i	−0.0268725	+	0.0320253i
$933$	−23.2778	−	46.8938i	−0.762080	−	1.53523i
$934$	−13.5107	−	28.9737i	−0.442082	−	0.948049i
$935$	0.690780	−	1.19647i	0.0225909	−	0.0391286i
$936$	9.12839	−	5.80281i	0.298371	−	0.189671i
$937$	23.5728	+	40.8293i	0.770089	+	1.33383i	0.937514	+	0.347949i	$0.113122\pi$
$937$	23.5728	+	40.8293i	0.770089	+	1.33383i	−0.167424	+	0.985885i	$0.553545\pi$
$938$	−4.20920	+	6.01137i	−0.137435	+	0.196278i
$939$	−12.7671	−	12.1582i	−0.416640	−	0.396768i
$940$	−5.73874	−	15.7671i	−0.187177	−	0.514264i
$941$	34.3199	−	24.0310i	1.11880	−	0.783390i	0.140394	−	0.990096i	$-0.455163\pi$
$941$	34.3199	−	24.0310i	1.11880	−	0.783390i	0.978403	+	0.206706i	$0.0662743\pi$
$942$	−14.0703	−	2.12806i	−0.458435	−	0.0693359i
$943$	6.58145	+	0.575802i	0.214322	+	0.0187507i
$944$	0.197231	−	0.197231i	0.00641933	−	0.00641933i
$945$	6.49861	+	5.60974i	0.211400	+	0.182485i
$946$			6.39720i			0.207991i
$947$	−2.28593	+	26.1283i	−0.0742827	+	0.849055i	0.864069	+	0.503373i	$0.167908\pi$
$947$	−2.28593	+	26.1283i	−0.0742827	+	0.849055i	−0.938352	+	0.345682i	$0.887648\pi$
$948$	26.2111	−	2.93981i	0.851297	−	0.0954807i
$949$	43.5372	+	7.95551i	1.41328	+	0.258247i
$950$	5.92950	+	16.2912i	0.192378	+	0.528555i
$951$	−11.7124	+	7.14913i	−0.379800	+	0.231826i
$952$	−0.0782426	−	0.443736i	−0.00253586	−	0.0143816i
$953$	2.54276	+	4.40418i	0.0823679	+	0.142665i	0.904267	−	0.426968i	$-0.140418\pi$
$953$	2.54276	+	4.40418i	0.0823679	+	0.142665i	−0.821899	+	0.569634i	$0.807085\pi$
$954$	26.2550	−	20.3647i	0.850037	−	0.659332i
$955$	−6.99172	−	26.0935i	−0.226247	−	0.844365i
$956$	27.8455	−	12.9846i	0.900587	−	0.419951i
$957$	−10.8272	−	12.2813i	−0.349995	−	0.396998i
$958$	18.3617	+	15.4073i	0.593240	+	0.497788i
$959$	−1.24120	−	1.04149i	−0.0400803	−	0.0336314i
$960$	0.481605	+	2.38860i	0.0155437	+	0.0770919i
$961$	2.49875	−	6.86525i	0.0806047	−	0.221460i
$962$	−8.83912	−	33.8258i	−0.284985	−	1.09059i
$963$	13.2900	−	12.3062i	0.428264	−	0.396563i
$964$	18.0473	+	4.83575i	0.581263	+	0.155749i
$965$	−4.34357	+	0.765889i	−0.139825	+	0.0246549i
$966$	−0.731856	−	2.48671i	−0.0235471	−	0.0800087i
$967$	0.531102	−	1.13895i	0.0170791	−	0.0366262i	−0.897583	−	0.440845i	$-0.854679\pi$
$967$	0.531102	−	1.13895i	0.0170791	−	0.0366262i	0.914662	+	0.404219i	$0.132457\pi$
$968$	3.64379	−	2.55141i	0.117116	−	0.0820053i
$969$	−3.55079	+	1.39150i	−0.114068	+	0.0447016i
$970$	12.6288	+	1.10488i	0.405486	+	0.0354755i
$971$			30.7620i			0.987199i	0.869689	+	0.493599i	$0.164319\pi$
$971$			30.7620i			0.987199i	−0.869689	+	0.493599i	$0.835681\pi$
$972$	−9.59775	+	12.2835i	−0.307848	+	0.393992i
$973$	−3.28008	−	3.28008i	−0.105155	−	0.105155i
$974$	27.8928	−	23.4048i	0.893743	−	0.749940i
$975$	17.6071	−	6.77431i	0.563879	−	0.216951i
$976$	1.21719	−	6.90300i	0.0389612	−	0.220960i
$977$	−51.0245	−	23.7931i	−1.63242	−	0.761209i	−0.632506	−	0.774555i	$-0.717974\pi$
$977$	−51.0245	−	23.7931i	−1.63242	−	0.761209i	−0.999911	+	0.0133469i	$0.995751\pi$
$978$	11.5613	+	39.2831i	0.369689	+	1.25614i
$979$	−7.48335	+	1.31952i	−0.239169	+	0.0421719i
$980$	−2.04658	+	7.63794i	−0.0653756	+	0.243985i
$981$	−27.8053	−	1.06866i	−0.887754	−	0.0341197i
$982$	−11.0574	+	2.96282i	−0.352855	+	0.0945472i
$983$	27.3907	−	12.7725i	0.873626	−	0.407379i	0.0665202	−	0.997785i	$-0.478810\pi$
$983$	27.3907	−	12.7725i	0.873626	−	0.407379i	0.807106	+	0.590406i	$0.201033\pi$
$984$	−4.96926	+	7.47919i	−0.158414	+	0.238428i
$985$	−7.66365	+	9.13318i	−0.244184	+	0.291007i
$986$	1.41148	−	0.123489i	0.0449507	−	0.00393268i
$987$	−24.2130	−	1.52357i	−0.770709	−	0.0484957i
$988$	−7.19758	+	19.4000i	−0.228986	+	0.617195i
$989$	−2.75820	−	1.59245i	−0.0877058	−	0.0506370i
$990$	6.62097	+	8.53601i	0.210428	+	0.271292i
$991$	3.80457	+	6.58972i	0.120856	+	0.209329i	0.920106	−	0.391670i	$-0.128103\pi$
$991$	3.80457	+	6.58972i	0.120856	+	0.209329i	−0.799249	+	0.601000i	$0.794769\pi$
$992$	0.845261	+	4.79371i	0.0268371	+	0.152201i
$993$	−0.561911	−	0.920575i	−0.0178317	−	0.0292136i
$994$	4.65822	−	9.98959i	0.147750	−	0.316850i
$995$	−15.5977	−	22.2759i	−0.494482	−	0.706193i
$996$	2.82715	+	2.25692i	0.0895816	+	0.0715134i
$997$	33.6915	−	28.2705i	1.06702	−	0.895337i	0.0722414	−	0.997387i	$-0.476985\pi$
$997$	33.6915	−	28.2705i	1.06702	−	0.895337i	0.994779	+	0.102051i	$0.0325403\pi$
$998$	12.7516			0.403645
$999$	28.3195	+	41.6733i	0.895991	+	1.31848i

Display

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p

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a_n

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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	702.2.bs.a.5.20	✓	504
13.8	odd	4	inner	702.2.bs.a.437.41	yes	504
27.11	odd	18	inner	702.2.bs.a.551.41	yes	504
351.281	even	36	inner	702.2.bs.a.281.20	yes	504

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.bs.a.5.20	✓	504	1.1	even	1	trivial
702.2.bs.a.281.20	yes	504	351.281	even	36	inner
702.2.bs.a.437.41	yes	504	13.8	odd	4	inner
702.2.bs.a.551.41	yes	504	27.11	odd	18	inner

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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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	702.2.bs.a.5.20

Level	$702$
Weight	$2$
Character	702.5
Analytic conductor	$5.605$
Analytic rank	$0$
Dimension	$504$
Inner twists	$4$