LMFDB - Embedded newform 840.2.u.e.629.154

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(629,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.629"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.u (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [160,0,0,-24,0,0,0,0,-32,0,0,0,0,0,-48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$160$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			629.154
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.157

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37073 - 0.347977i) q^{2} +(-0.973146 + 1.43282i) q^{3} +(1.75782 - 0.953969i) q^{4} +(1.31834 + 1.80610i) q^{5} +(-0.835334 + 2.30265i) q^{6} +(2.61441 + 0.406058i) q^{7} +(2.07755 - 1.91932i) q^{8} +(-1.10597 - 2.78870i) q^{9} +(2.43557 + 2.01693i) q^{10} +2.00814 q^{11} +(-0.343750 + 3.44700i) q^{12} +1.33017i q^{13} +(3.72495 - 0.353156i) q^{14} +(-3.87076 + 0.131346i) q^{15} +(2.17989 - 3.35382i) q^{16} -4.12882i q^{17} +(-2.48640 - 3.43771i) q^{18} -2.33202 q^{19} +(4.04036 + 1.91715i) q^{20} +(-3.12601 + 3.35083i) q^{21} +(2.75262 - 0.698786i) q^{22} +0.0975649 q^{23} +(0.728290 + 4.84454i) q^{24} +(-1.52398 + 4.76209i) q^{25} +(0.462871 + 1.82332i) q^{26} +(5.07198 + 1.12915i) q^{27} +(4.98303 - 1.78028i) q^{28} -7.56166 q^{29} +(-5.26007 + 1.52698i) q^{30} +9.48706i q^{31} +(1.82099 - 5.35574i) q^{32} +(-1.95421 + 2.87731i) q^{33} +(-1.43674 - 5.65952i) q^{34} +(2.71328 + 5.25719i) q^{35} +(-4.60443 - 3.84697i) q^{36} +6.19728 q^{37} +(-3.19658 + 0.811490i) q^{38} +(-1.90591 - 1.29445i) q^{39} +(6.20539 + 1.22195i) q^{40} -5.88262 q^{41} +(-3.11891 + 5.68088i) q^{42} +3.65928 q^{43} +(3.52995 - 1.91570i) q^{44} +(3.57862 - 5.67393i) q^{45} +(0.133736 - 0.0339504i) q^{46} -7.79115i q^{47} +(2.68408 + 6.38715i) q^{48} +(6.67023 + 2.12320i) q^{49} +(-0.431874 + 7.05787i) q^{50} +(5.91588 + 4.01795i) q^{51} +(1.26895 + 2.33821i) q^{52} -2.49399i q^{53} +(7.34526 - 0.217177i) q^{54} +(2.64740 + 3.62689i) q^{55} +(6.21091 - 4.17428i) q^{56} +(2.26939 - 3.34137i) q^{57} +(-10.3650 + 2.63129i) q^{58} -1.86318i q^{59} +(-6.67880 + 3.92346i) q^{60} -11.3191 q^{61} +(3.30128 + 13.0042i) q^{62} +(-1.75909 - 7.73987i) q^{63} +(0.632417 - 7.97496i) q^{64} +(-2.40243 + 1.75362i) q^{65} +(-1.67747 + 4.62404i) q^{66} -7.33230 q^{67} +(-3.93877 - 7.25774i) q^{68} +(-0.0949450 + 0.139793i) q^{69} +(5.54857 + 6.26205i) q^{70} +8.88677i q^{71} +(-7.65011 - 3.67094i) q^{72} -6.85080 q^{73} +(8.49482 - 2.15651i) q^{74} +(-5.34018 - 6.81781i) q^{75} +(-4.09928 + 2.22467i) q^{76} +(5.25008 + 0.815421i) q^{77} +(-3.06293 - 1.11114i) q^{78} +10.9789 q^{79} +(8.93115 - 0.484370i) q^{80} +(-6.55365 + 6.16844i) q^{81} +(-8.06351 + 2.04702i) q^{82} +10.1647 q^{83} +(-2.29839 + 8.87228i) q^{84} +(7.45706 - 5.44318i) q^{85} +(5.01590 - 1.27335i) q^{86} +(7.35861 - 10.8345i) q^{87} +(4.17200 - 3.85426i) q^{88} -13.4335 q^{89} +(2.93093 - 9.02273i) q^{90} +(-0.540128 + 3.47762i) q^{91} +(0.171502 - 0.0930739i) q^{92} +(-13.5933 - 9.23230i) q^{93} +(-2.71114 - 10.6796i) q^{94} +(-3.07438 - 4.21185i) q^{95} +(5.90175 + 7.82108i) q^{96} -9.65918 q^{97} +(9.88194 + 0.589255i) q^{98} +(-2.22094 - 5.60008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) $ 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.37073	−	0.347977i	0.969255	−	0.246057i
$2$	1.37073	−	0.347977i	0.969255	−	0.246057i
$3$	−0.973146	+	1.43282i	−0.561846	+	0.827242i
$3$	−0.973146	+	1.43282i	−0.561846	+	0.827242i
$4$	1.75782	−	0.953969i	0.878912	−	0.476984i
$5$	1.31834	+	1.80610i	0.589578	+	0.807712i
$5$	1.31834	+	1.80610i	0.589578	+	0.807712i
$6$	−0.835334	+	2.30265i	−0.341024	+	0.940055i
$7$	2.61441	+	0.406058i	0.988152	+	0.153476i
$7$	2.61441	+	0.406058i	0.988152	+	0.153476i
$8$	2.07755	−	1.91932i	0.734524	−	0.678582i
$9$	−1.10597	−	2.78870i	−0.368657	−	0.929565i
$10$	2.43557	+	2.01693i	0.770195	+	0.637809i
$11$	2.00814			0.605476			0.302738	−	0.953074i	$-0.402099\pi$
$11$	2.00814			0.605476			0.302738	+	0.953074i	$0.402099\pi$
$12$	−0.343750	+	3.44700i	−0.0992319	+	0.995064i
$13$			1.33017i			0.368924i	0.982840	+	0.184462i	$0.0590543\pi$
$13$			1.33017i			0.368924i	−0.982840	+	0.184462i	$0.940946\pi$
$14$	3.72495	−	0.353156i	0.995536	−	0.0943849i
$15$	−3.87076	+	0.131346i	−0.999425	+	0.0339133i
$16$	2.17989	−	3.35382i	0.544972	−	0.838455i
$17$		−	4.12882i		−	1.00139i	−0.865625	−	0.500693i	$-0.833078\pi$
$17$		−	4.12882i		−	1.00139i	0.865625	−	0.500693i	$-0.166922\pi$
$18$	−2.48640	−	3.43771i	−0.586049	−	0.810275i
$19$	−2.33202			−0.535002			−0.267501	−	0.963558i	$-0.586198\pi$
$19$	−2.33202			−0.535002			−0.267501	+	0.963558i	$0.586198\pi$
$20$	4.04036	+	1.91715i	0.903453	+	0.428688i
$21$	−3.12601	+	3.35083i	−0.682151	+	0.731211i
$22$	2.75262	−	0.698786i	0.586861	−	0.148982i
$23$	0.0975649			0.0203437			0.0101718	−	0.999948i	$-0.496762\pi$
$23$	0.0975649			0.0203437			0.0101718	+	0.999948i	$0.496762\pi$
$24$	0.728290	+	4.84454i	0.148662	+	0.988888i
$25$	−1.52398	+	4.76209i	−0.304796	+	0.952418i
$26$	0.462871	+	1.82332i	0.0907764	+	0.357582i
$27$	5.07198	+	1.12915i	0.976104	+	0.217304i
$28$	4.98303	−	1.78028i	0.941704	−	0.336442i
$29$	−7.56166			−1.40417			−0.702083	−	0.712095i	$-0.747746\pi$
$29$	−7.56166			−1.40417			−0.702083	+	0.712095i	$0.747746\pi$
$30$	−5.26007	+	1.52698i	−0.960353	+	0.278786i
$31$			9.48706i			1.70393i	0.523602	+	0.851963i	$0.324588\pi$
$31$			9.48706i			1.70393i	−0.523602	+	0.851963i	$0.675412\pi$
$32$	1.82099	−	5.35574i	0.321909	−	0.946771i
$33$	−1.95421	+	2.87731i	−0.340184	+	0.500875i
$34$	−1.43674	−	5.65952i	−0.246398	−	0.970600i
$35$	2.71328	+	5.25719i	0.458629	+	0.888628i
$36$	−4.60443	−	3.84697i	−0.767405	−	0.641162i
$37$	6.19728			1.01883			0.509413	−	0.860522i	$-0.329863\pi$
$37$	6.19728			1.01883			0.509413	+	0.860522i	$0.329863\pi$
$38$	−3.19658	+	0.811490i	−0.518553	+	0.131641i
$39$	−1.90591	−	1.29445i	−0.305189	−	0.207279i
$40$	6.20539	+	1.22195i	0.981158	+	0.193207i
$41$	−5.88262			−0.918711			−0.459355	−	0.888253i	$-0.651920\pi$
$41$	−5.88262			−0.918711			−0.459355	+	0.888253i	$0.651920\pi$
$42$	−3.11891	+	5.68088i	−0.481259	+	0.876578i
$43$	3.65928			0.558035			0.279017	−	0.960286i	$-0.409991\pi$
$43$	3.65928			0.558035			0.279017	+	0.960286i	$0.409991\pi$
$44$	3.52995	−	1.91570i	0.532160	−	0.288803i
$45$	3.57862	−	5.67393i	0.533469	−	0.845820i
$46$	0.133736	−	0.0339504i	0.0197182	−	0.00500571i
$47$		−	7.79115i		−	1.13646i	−0.822871	−	0.568228i	$-0.807629\pi$
$47$		−	7.79115i		−	1.13646i	0.822871	−	0.568228i	$-0.192371\pi$
$48$	2.68408	+	6.38715i	0.387414	+	0.921906i
$49$	6.67023	+	2.12320i	0.952890	+	0.303315i
$50$	−0.431874	+	7.05787i	−0.0610762	+	0.998133i
$51$	5.91588	+	4.01795i	0.828389	+	0.562626i
$52$	1.26895	+	2.33821i	0.175971	+	0.324252i
$53$		−	2.49399i		−	0.342576i	−0.985221	−	0.171288i	$-0.945207\pi$
$53$		−	2.49399i		−	0.342576i	0.985221	−	0.171288i	$-0.0547928\pi$
$54$	7.34526	−	0.217177i	0.999563	−	0.0295541i
$55$	2.64740	+	3.62689i	0.356975	+	0.489050i
$56$	6.21091	−	4.17428i	0.829968	−	0.557811i
$57$	2.26939	−	3.34137i	0.300589	−	0.442576i
$58$	−10.3650	+	2.63129i	−1.36100	+	0.345505i
$59$		−	1.86318i		−	0.242565i	−0.992618	−	0.121282i	$-0.961299\pi$
$59$		−	1.86318i		−	0.242565i	0.992618	−	0.121282i	$-0.0387007\pi$
$60$	−6.67880	+	3.92346i	−0.862230	+	0.506517i
$61$	−11.3191			−1.44926			−0.724632	−	0.689136i	$-0.757990\pi$
$61$	−11.3191			−1.44926			−0.724632	+	0.689136i	$0.757990\pi$
$62$	3.30128	+	13.0042i	0.419263	+	1.65154i
$63$	−1.75909	−	7.73987i	−0.221624	−	0.975132i
$64$	0.632417	−	7.97496i	0.0790521	−	0.996870i
$65$	−2.40243	+	1.75362i	−0.297984	+	0.217509i
$66$	−1.67747	+	4.62404i	−0.206482	+	0.569180i
$67$	−7.33230			−0.895783			−0.447892	−	0.894088i	$-0.647825\pi$
$67$	−7.33230			−0.895783			−0.447892	+	0.894088i	$0.647825\pi$
$68$	−3.93877	−	7.25774i	−0.477646	−	0.880131i
$69$	−0.0949450	+	0.139793i	−0.0114300	+	0.0168291i
$70$	5.54857	+	6.26205i	0.663182	+	0.748459i
$71$			8.88677i			1.05467i	0.849659	+	0.527333i	$0.176808\pi$
$71$			8.88677i			1.05467i	−0.849659	+	0.527333i	$0.823192\pi$
$72$	−7.65011	−	3.67094i	−0.901574	−	0.432624i
$73$	−6.85080			−0.801825			−0.400913	−	0.916116i	$-0.631307\pi$
$73$	−6.85080			−0.801825			−0.400913	+	0.916116i	$0.631307\pi$
$74$	8.49482	−	2.15651i	0.987503	−	0.250690i
$75$	−5.34018	−	6.81781i	−0.616631	−	0.787253i
$76$	−4.09928	+	2.22467i	−0.470219	+	0.255187i
$77$	5.25008	+	0.815421i	0.598303	+	0.0929258i
$78$	−3.06293	−	1.11114i	−0.346809	−	0.125812i
$79$	10.9789			1.23522			0.617612	−	0.786483i	$-0.288100\pi$
$79$	10.9789			1.23522			0.617612	+	0.786483i	$0.288100\pi$
$80$	8.93115	−	0.484370i	0.998533	−	0.0541542i
$81$	−6.55365	+	6.16844i	−0.728184	+	0.685382i
$82$	−8.06351	+	2.04702i	−0.890465	+	0.226055i
$83$	10.1647			1.11572			0.557858	−	0.829936i	$-0.311623\pi$
$83$	10.1647			1.11572			0.557858	+	0.829936i	$0.311623\pi$
$84$	−2.29839	+	8.87228i	−0.250774	+	0.968046i
$85$	7.45706	−	5.44318i	0.808832	−	0.590395i
$86$	5.01590	−	1.27335i	0.540878	−	0.137308i
$87$	7.35861	−	10.8345i	0.788925	−	1.16158i
$88$	4.17200	−	3.85426i	0.444737	−	0.410865i
$89$	−13.4335			−1.42395			−0.711974	−	0.702206i	$-0.752198\pi$
$89$	−13.4335			−1.42395			−0.711974	+	0.702206i	$0.752198\pi$
$90$	2.93093	−	9.02273i	0.308947	−	0.951079i
$91$	−0.540128	+	3.47762i	−0.0566209	+	0.364553i
$92$	0.171502	−	0.0930739i	0.0178803	−	0.00970363i
$93$	−13.5933	−	9.23230i	−1.40956	−	0.957345i
$94$	−2.71114	−	10.6796i	−0.279633	−	1.10152i
$95$	−3.07438	−	4.21185i	−0.315425	−	0.432127i
$96$	5.90175	+	7.82108i	0.602345	+	0.798236i
$97$	−9.65918			−0.980742			−0.490371	−	0.871514i	$-0.663139\pi$
$97$	−9.65918			−0.980742			−0.490371	+	0.871514i	$0.663139\pi$
$98$	9.88194	+	0.589255i	0.998227	+	0.0595238i
$99$	−2.22094	−	5.60008i	−0.223213	−	0.562829i
$100$	1.86399	+	9.82474i	0.186399	+	0.982474i
$101$		−	15.6655i		−	1.55878i	−0.626539	−	0.779390i	$-0.715529\pi$
$101$		−	15.6655i		−	1.55878i	0.626539	−	0.779390i	$-0.284471\pi$
$102$	9.50725	+	3.44895i	0.941358	+	0.341497i
$103$	8.59402			0.846794			0.423397	−	0.905944i	$-0.360838\pi$
$103$	8.59402			0.846794			0.423397	+	0.905944i	$0.360838\pi$
$104$	2.55303	+	2.76350i	0.250345	+	0.270984i
$105$	−10.1731	−	1.22836i	−0.992789	−	0.119876i
$106$	−0.867851	−	3.41859i	−0.0842932	−	0.332043i
$107$		−	2.50519i		−	0.242186i	−0.992641	−	0.121093i	$-0.961360\pi$
$107$		−	2.50519i		−	0.242186i	0.992641	−	0.121093i	$-0.0386399\pi$
$108$	9.99282	−	2.85368i	0.961560	−	0.274595i
$109$		−	14.4916i		−	1.38804i	−0.719954	−	0.694022i	$-0.755837\pi$
$109$		−	14.4916i		−	1.38804i	0.719954	−	0.694022i	$-0.244163\pi$
$110$	4.89096	+	4.05027i	0.466334	+	0.386178i
$111$	−6.03086	+	8.87961i	−0.572424	+	0.842815i
$112$	7.06095	−	7.88308i	0.667197	−	0.744881i
$113$	14.2102			1.33678			0.668390	−	0.743811i	$-0.266984\pi$
$113$	14.2102			1.33678			0.668390	+	0.743811i	$0.266984\pi$
$114$	1.94801	−	5.36983i	0.182448	−	0.502931i
$115$	0.128623	+	0.176212i	0.0119942	+	0.0164318i
$116$	−13.2921	+	7.21359i	−1.23414	+	0.669765i
$117$	3.70945	−	1.47114i	0.342939	−	0.136007i
$118$	−0.648343	−	2.55392i	−0.0596848	−	0.235107i
$119$	1.67654	−	10.7944i	0.153689	−	0.989523i
$120$	−7.78959	+	7.70210i	−0.711089	+	0.703102i
$121$	−6.96739			−0.633399
$122$	−15.5155	+	3.93880i	−1.40471	+	0.356602i
$123$	5.72465	−	8.42876i	0.516174	−	0.759996i
$124$	9.05036	+	16.6766i	0.812747	+	1.49760i
$125$	−10.6099	+	3.52557i	−0.948980	+	0.315337i
$126$	−5.10454	−	9.99718i	−0.454749	−	0.890620i
$127$		−	1.45342i		−	0.128970i	−0.997919	−	0.0644849i	$-0.979460\pi$
$127$		−	1.45342i		−	0.128970i	0.997919	−	0.0644849i	$-0.0205404\pi$
$128$	−1.90823	−	11.1516i	−0.168665	−	0.985673i
$129$	−3.56101	+	5.24310i	−0.313530	+	0.461629i
$130$	−2.68287	+	3.23973i	−0.235303	+	0.284143i
$131$		−	1.87492i		−	0.163813i	−0.996640	−	0.0819064i	$-0.973899\pi$
$131$		−	1.87492i		−	0.163813i	0.996640	−	0.0819064i	$-0.0261009\pi$
$132$	−0.690296	+	6.92205i	−0.0600826	+	0.602488i
$133$	−6.09684	−	0.946935i	−0.528663	−	0.0821097i
$134$	−10.0506	+	2.55148i	−0.868243	+	0.220414i
$135$	4.64723	+	10.6491i	0.399970	+	0.916528i
$136$	−7.92454	−	8.57783i	−0.679523	−	0.735543i
$137$	−18.4986			−1.58044			−0.790222	−	0.612821i	$-0.790035\pi$
$137$	−18.4986			−1.58044			−0.790222	+	0.612821i	$0.790035\pi$
$138$	−0.0814993	+	0.224658i	−0.00693768	+	0.0191242i
$139$	−0.685361			−0.0581315			−0.0290658	−	0.999578i	$-0.509253\pi$
$139$	−0.685361			−0.0581315			−0.0290658	+	0.999578i	$0.509253\pi$
$140$	9.78467	+	6.65283i	0.826956	+	0.562267i
$141$	11.1633	+	7.58193i	0.940124	+	0.638514i
$142$	3.09240	+	12.1814i	0.259508	+	1.02224i
$143$			2.67117i			0.223375i
$144$	−11.7637	−	2.36981i	−0.980306	−	0.197484i
$145$	−9.96881	−	13.6571i	−0.827865	−	1.13416i
$146$	−9.39062	+	2.38392i	−0.777174	+	0.197295i
$147$	−9.53329	+	7.49109i	−0.786293	+	0.617854i
$148$	10.8937	−	5.91201i	0.895458	−	0.485964i
$149$	2.34916			0.192450			0.0962252	−	0.995360i	$-0.469323\pi$
$149$	2.34916			0.192450			0.0962252	+	0.995360i	$0.469323\pi$
$150$	−9.69241	−	7.48714i	−0.791382	−	0.611322i
$151$	−8.32682			−0.677627			−0.338814	−	0.940853i	$-0.610026\pi$
$151$	−8.32682			−0.677627			−0.338814	+	0.940853i	$0.610026\pi$
$152$	−4.84488	+	4.47589i	−0.392972	+	0.363043i
$153$	−11.5140	+	4.56636i	−0.930855	+	0.369169i
$154$	7.48022	−	0.709186i	0.602773	−	0.0571478i
$155$	−17.1346	+	12.5071i	−1.37628	+	1.00460i
$156$	−4.58512	−	0.457247i	−0.367103	−	0.0366090i
$157$		−	14.0657i		−	1.12256i	−0.827625	−	0.561281i	$-0.810309\pi$
$157$		−	14.0657i		−	1.12256i	0.827625	−	0.561281i	$-0.189691\pi$
$158$	15.0492	−	3.82041i	1.19725	−	0.303936i
$159$	3.57345	+	2.42702i	0.283393	+	0.192475i
$160$	12.0737	−	3.77178i	0.954508	−	0.298185i
$161$	0.255074	+	0.0396171i	0.0201027	+	0.00312226i
$162$	−6.83684	+	10.7358i	−0.537153	+	0.843485i
$163$	−10.6143			−0.831372			−0.415686	−	0.909508i	$-0.636459\pi$
$163$	−10.6143			−0.831372			−0.415686	+	0.909508i	$0.636459\pi$
$164$	−10.3406	+	5.61184i	−0.807466	+	0.438211i
$165$	−7.77301	+	0.263760i	−0.605128	+	0.0205337i
$166$	13.9330	−	3.53707i	1.08141	−	0.274530i
$167$		−	0.462349i		−	0.0357776i	−0.999840	−	0.0178888i	$-0.994306\pi$
$167$		−	0.462349i		−	0.0357776i	0.999840	−	0.0178888i	$-0.00569449\pi$
$168$	−0.0631207	+	12.9613i	−0.00486986	+	0.999988i
$169$	11.2306			0.863895
$170$	8.32755	−	10.0560i	0.638694	−	0.771263i
$171$	2.57915	+	6.50329i	0.197232	+	0.497319i
$172$	6.43236	−	3.49084i	0.490463	−	0.266174i
$173$	3.85404			0.293017			0.146508	−	0.989209i	$-0.453196\pi$
$173$	3.85404			0.293017			0.146508	+	0.989209i	$0.453196\pi$
$174$	6.31652	−	17.4119i	0.478854	−	1.31999i
$175$	−5.91799	+	11.8312i	−0.447358	+	0.894355i
$176$	4.37751	−	6.73492i	0.329967	−	0.507664i
$177$	2.66960	+	1.81314i	0.200660	+	0.136284i
$178$	−18.4137	+	4.67455i	−1.38017	+	0.350372i
$179$	−13.7858			−1.03040			−0.515199	−	0.857070i	$-0.672282\pi$
$179$	−13.7858			−1.03040			−0.515199	+	0.857070i	$0.672282\pi$
$180$	0.877821	−	13.3877i	0.0654289	−	0.997857i
$181$	23.4970			1.74652			0.873260	−	0.487254i	$-0.162001\pi$
$181$	23.4970			1.74652			0.873260	+	0.487254i	$0.162001\pi$
$182$	0.469759	+	4.95484i	0.0348209	+	0.367277i
$183$	11.0152	−	16.2183i	0.814264	−	1.19889i
$184$	0.202696	−	0.187258i	0.0149429	−	0.0138049i
$185$	8.17009	+	11.1929i	0.600677	+	0.822918i
$186$	−21.8454	−	7.92487i	−1.60178	−	0.581080i
$187$		−	8.29124i		−	0.606316i
$188$	−7.43251	−	13.6955i	−0.542072	−	0.998844i
$189$	12.8017	+	5.01157i	0.931189	+	0.364538i
$190$	−5.67979	−	4.70351i	−0.412055	−	0.341229i
$191$		−	13.7417i		−	0.994314i	−0.867661	−	0.497157i	$-0.834377\pi$
$191$		−	13.7417i		−	0.994314i	0.867661	−	0.497157i	$-0.165623\pi$
$192$	10.8113	+	8.66695i	0.780238	+	0.625483i
$193$		−	12.8635i		−	0.925933i	−0.886376	−	0.462967i	$-0.846785\pi$
$193$		−	12.8635i		−	0.925933i	0.886376	−	0.462967i	$-0.153215\pi$
$194$	−13.2402	+	3.36118i	−0.950589	+	0.241319i
$195$	−0.174713	−	5.14878i	−0.0125114	−	0.368712i
$196$	13.7506	−	2.63098i	0.982183	−	0.187927i
$197$			25.5732i			1.82201i	0.412392	+	0.911006i	$0.364693\pi$
$197$			25.5732i			1.82201i	−0.412392	+	0.911006i	$0.635307\pi$
$198$	−4.99302	−	6.90339i	−0.354839	−	0.490602i
$199$		−	17.1175i		−	1.21342i	−0.794921	−	0.606712i	$-0.792488\pi$
$199$		−	17.1175i		−	1.21342i	0.794921	−	0.606712i	$-0.207512\pi$
$200$	5.97383	+	12.8185i	0.422413	+	0.906403i
$201$	7.13540	−	10.5059i	0.503293	−	0.741029i
$202$	−5.45126	−	21.4733i	−0.383549	−	1.51086i
$203$	−19.7693	−	3.07048i	−1.38753	−	0.215505i
$204$	14.2321	+	1.41928i	0.996444	+	0.0993696i
$205$	−7.75527	−	10.6246i	−0.541651	−	0.742053i
$206$	11.7801	−	2.99053i	0.820760	−	0.208360i
$207$	−0.107904	−	0.272079i	−0.00749985	−	0.0189108i
$208$	4.46116	+	2.89963i	0.309326	+	0.201053i
$209$	−4.68301			−0.323931
$210$	−14.3720	+	1.85624i	−0.991762	+	0.128093i
$211$			17.3613i			1.19520i	0.801795	+	0.597599i	$0.203879\pi$
$211$			17.3613i			1.19520i	−0.801795	+	0.597599i	$0.796121\pi$
$212$	−2.37919	−	4.38399i	−0.163403	−	0.301094i
$213$	−12.7332	−	8.64813i	−0.872463	−	0.592560i
$214$	−0.871749	−	3.43395i	−0.0595915	−	0.234740i
$215$	4.82416	+	6.60901i	0.329005	+	0.450731i
$216$	12.7045	−	7.38891i	0.864431	−	0.502752i
$217$	−3.85230	+	24.8030i	−0.261511	+	1.68374i
$218$	−5.04275	−	19.8641i	−0.341538	−	1.34537i
$219$	6.66683	−	9.81599i	0.450503	−	0.663303i
$220$	8.11360	+	3.84990i	0.547019	+	0.259560i
$221$	5.49206			0.369436
$222$	−5.17680	+	14.2702i	−0.347444	+	0.957752i
$223$	6.52959			0.437253			0.218627	−	0.975809i	$-0.429842\pi$
$223$	6.52959			0.437253			0.218627	+	0.975809i	$0.429842\pi$
$224$	6.93555	−	13.2627i	0.463401	−	0.886149i
$225$	14.9655	−	1.01681i	0.997700	−	0.0677876i
$226$	19.4784	−	4.94482i	1.29568	−	0.328924i
$227$	12.4592			0.826949			0.413474	−	0.910516i	$-0.364315\pi$
$227$	12.4592			0.826949			0.413474	+	0.910516i	$0.364315\pi$
$228$	0.801630	−	8.03847i	0.0530892	−	0.532361i
$229$	−3.65759			−0.241701			−0.120850	−	0.992671i	$-0.538562\pi$
$229$	−3.65759			−0.241701			−0.120850	+	0.992671i	$0.538562\pi$
$230$	0.237626	+	0.196782i	0.0156686	+	0.0129754i
$231$	−6.27745	+	6.72892i	−0.413026	+	0.442731i
$232$	−15.7097	+	14.5133i	−1.03139	+	0.952842i
$233$	1.23863			0.0811454			0.0405727	−	0.999177i	$-0.487082\pi$
$233$	1.23863			0.0811454			0.0405727	+	0.999177i	$0.487082\pi$
$234$	4.57275	−	3.30734i	0.298930	−	0.216208i
$235$	14.0716	−	10.2714i	0.917929	−	0.670029i
$236$	−1.77741	−	3.27513i	−0.115700	−	0.213193i
$237$	−10.6841	+	15.7309i	−0.694006	+	1.02183i
$238$	−1.45812	−	15.3797i	−0.0945159	−	0.996917i
$239$			19.6091i			1.26841i	0.773165	+	0.634205i	$0.218672\pi$
$239$			19.6091i			1.26841i	−0.773165	+	0.634205i	$0.781328\pi$
$240$	−7.99730	+	13.2681i	−0.516223	+	0.856454i
$241$		−	24.2251i		−	1.56048i	−0.625482	−	0.780239i	$-0.715098\pi$
$241$		−	24.2251i		−	1.56048i	0.625482	−	0.780239i	$-0.284902\pi$
$242$	−9.55043	+	2.42449i	−0.613925	+	0.155852i
$243$	−2.46063	−	15.3930i	−0.157849	−	0.987463i
$244$	−19.8970	+	10.7981i	−1.27378	+	0.691277i
$245$	4.95890	+	14.8462i	0.316812	+	0.948488i
$246$	4.91395	−	13.5456i	0.313302	−	0.863638i
$247$		−	3.10199i		−	0.197375i
$248$	18.2087	+	19.7098i	1.15625	+	1.25158i
$249$	−9.89171	+	14.5642i	−0.626861	+	0.922967i
$250$	−13.3166	+	8.52463i	−0.842213	+	0.539145i
$251$			14.6425i			0.924229i	0.886820	+	0.462115i	$0.152909\pi$
$251$			14.6425i			0.924229i	−0.886820	+	0.462115i	$0.847091\pi$
$252$	−10.4758	−	11.9272i	−0.659911	−	0.751344i
$253$	0.195924			0.0123176
$254$	−0.505756	−	1.99225i	−0.0317339	−	0.125005i
$255$	0.542304	+	15.9817i	0.0339604	+	1.00081i
$256$	−6.49619	−	14.6219i	−0.406012	−	0.913868i
$257$			15.8068i			0.986002i	0.870029	+	0.493001i	$0.164100\pi$
$257$			15.8068i			0.986002i	−0.870029	+	0.493001i	$0.835900\pi$
$258$	−3.05672	+	8.42605i	−0.190303	+	0.524583i
$259$	16.2022	+	2.51646i	1.00676	+	0.156365i
$260$	−2.55014	+	5.37439i	−0.158153	+	0.333305i
$261$	8.36299	+	21.0872i	0.517656	+	1.30526i
$262$	−0.652431	−	2.57002i	−0.0403073	−	0.158777i
$263$	−14.2549			−0.878997			−0.439499	−	0.898243i	$-0.644844\pi$
$263$	−14.2549			−0.878997			−0.439499	+	0.898243i	$0.644844\pi$
$264$	1.46251	+	9.72850i	0.0900111	+	0.598748i
$265$	4.50439	−	3.28791i	0.276702	−	0.201975i
$266$	−8.68666	+	0.823566i	−0.532613	+	0.0504961i
$267$	13.0728	−	19.2478i	0.800040	−	1.17795i
$268$	−12.8889	+	6.99479i	−0.787314	+	0.427275i
$269$		−	9.33525i		−	0.569180i	−0.958649	−	0.284590i	$-0.908142\pi$
$269$		−	9.33525i		−	0.569180i	0.958649	−	0.284590i	$-0.0918575\pi$
$270$	10.0758	+	12.9799i	0.613191	+	0.789934i
$271$		−	0.207201i		−	0.0125865i	−0.999980	−	0.00629327i	$-0.997997\pi$
$271$		−	0.207201i		−	0.0125865i	0.999980	−	0.00629327i	$-0.00200322\pi$
$272$	−13.8473	−	9.00037i	−0.839617	−	0.545727i
$273$	−4.45719	−	4.15814i	−0.269761	−	0.251662i
$274$	−25.3567	+	6.43710i	−1.53185	+	0.388880i
$275$	−3.06036	+	9.56292i	−0.184547	+	0.576666i
$276$	−0.0335379	+	0.336307i	−0.00201874	+	0.0202433i
$277$	28.6571			1.72184			0.860918	−	0.508744i	$-0.169890\pi$
$277$	28.6571			1.72184			0.860918	+	0.508744i	$0.169890\pi$
$278$	−0.939447	+	0.238490i	−0.0563443	+	0.0143037i
$279$	26.4565	−	10.4924i	1.58391	−	0.628165i
$280$	15.7272	+	5.71442i	0.939881	+	0.341502i
$281$		−	3.11015i		−	0.185536i	−0.995688	−	0.0927681i	$-0.970428\pi$
$281$		−	3.11015i		−	0.185536i	0.995688	−	0.0927681i	$-0.0295715\pi$
$282$	17.9403	+	6.50821i	1.06833	+	0.387559i
$283$			20.5801i			1.22336i	0.791106	+	0.611679i	$0.209505\pi$
$283$			20.5801i			1.22336i	−0.791106	+	0.611679i	$0.790495\pi$
$284$	8.47770	+	15.6214i	0.503059	+	0.926958i
$285$	9.02667	−	0.306301i	0.534694	−	0.0181437i
$286$	0.929508	+	3.66147i	0.0549629	+	0.216507i
$287$	−15.3796	−	2.38869i	−0.907826	−	0.141000i
$288$	−16.9495	+	0.845110i	−0.998759	+	0.0497986i
$289$	−0.0471902			−0.00277589
$290$	−18.4170	−	15.2513i	−1.08148	−	0.895589i
$291$	9.39980	−	13.8399i	0.551026	−	0.811310i
$292$	−12.0425	+	6.53545i	−0.704734	+	0.382458i
$293$	−11.9389			−0.697476			−0.348738	−	0.937220i	$-0.613390\pi$
$293$	−11.9389			−0.697476			−0.348738	+	0.937220i	$0.613390\pi$
$294$	−10.4609	+	13.5857i	−0.610091	+	0.792332i
$295$	3.36508	−	2.45629i	0.195922	−	0.143011i
$296$	12.8751	−	11.8946i	0.748353	−	0.691357i
$297$	10.1852	+	2.26748i	0.591007	+	0.131573i
$298$	3.22007	−	0.817453i	0.186534	−	0.0473538i
$299$			0.129778i			0.00750528i
$300$	−15.8911	−	6.89014i	−0.917471	−	0.397802i
$301$	9.56684	+	1.48588i	0.551423	+	0.0856447i
$302$	−11.4139	+	2.89755i	−0.656794	+	0.166735i
$303$	22.4460	+	15.2449i	1.28949	+	0.875795i
$304$	−5.08353	+	7.82116i	−0.291561	+	0.448574i
$305$	−14.9224	−	20.4434i	−0.854454	−	1.17059i
$306$	−14.1937	+	10.2659i	−0.811399	+	0.586862i
$307$			7.70581i			0.439794i	0.975523	+	0.219897i	$0.0705721\pi$
$307$			7.70581i			0.439794i	−0.975523	+	0.219897i	$0.929428\pi$
$308$	10.0066	−	3.57505i	0.570179	−	0.203707i
$309$	−8.36324	+	12.3137i	−0.475768	+	0.700503i
$310$	−19.1347	+	23.1064i	−1.08678	+	1.31236i
$311$	26.8427			1.52211			0.761054	−	0.648688i	$-0.224682\pi$
$311$	26.8427			1.52211			0.761054	+	0.648688i	$0.224682\pi$
$312$	−6.44409	+	0.968753i	−0.364825	+	0.0548449i
$313$	8.20422			0.463730			0.231865	−	0.972748i	$-0.425517\pi$
$313$	8.20422			0.463730			0.231865	+	0.972748i	$0.425517\pi$
$314$	−4.89454	−	19.2803i	−0.276215	−	1.08805i
$315$	11.6599	−	13.3808i	0.656961	−	0.753924i
$316$	19.2990	−	10.4735i	1.08565	−	0.589183i
$317$			30.7315i			1.72605i	0.505159	+	0.863026i	$0.331434\pi$
$317$			30.7315i			1.72605i	−0.505159	+	0.863026i	$0.668566\pi$
$318$	5.74279	+	2.08331i	0.322040	+	0.116826i
$319$	−15.1849			−0.850189
$320$	15.2373	−	9.37147i	0.851791	−	0.523881i
$321$	3.58949	+	2.43791i	0.200346	+	0.136071i
$322$	0.363425	−	0.0344556i	0.0202529	−	0.00192014i
$323$			9.62849i			0.535744i
$324$	−5.63566	+	17.0950i	−0.313092	+	0.949723i
$325$	−6.33441	−	2.02716i	−0.351370	−	0.112447i
$326$	−14.5493	+	3.69352i	−0.805812	+	0.204565i
$327$	20.7639	+	14.1025i	1.14825	+	0.779867i
$328$	−12.2214	+	11.2906i	−0.674815	+	0.623421i
$329$	3.16366	−	20.3692i	0.174418	−	1.12299i
$330$	−10.5629	+	3.06638i	−0.581471	+	0.168798i
$331$			20.3258i			1.11721i	0.829434	+	0.558604i	$0.188663\pi$
$331$			20.3258i			1.11721i	−0.829434	+	0.558604i	$0.811337\pi$
$332$	17.8677	−	9.69677i	0.980617	−	0.532180i
$333$	−6.85402	−	17.2823i	−0.375598	−	0.947066i
$334$	−0.160887	−	0.633758i	−0.00880335	−	0.0346777i
$335$	−9.66644	−	13.2429i	−0.528134	−	0.723535i
$336$	4.42373	+	17.7885i	0.241334	+	0.970442i
$337$			8.04781i			0.438392i	0.975681	+	0.219196i	$0.0703434\pi$
$337$			8.04781i			0.438392i	−0.975681	+	0.219196i	$0.929657\pi$
$338$	15.3942	−	3.90801i	0.837335	−	0.212568i
$339$	−13.8286	+	20.3607i	−0.751065	+	1.10584i
$340$	7.91558	−	16.6819i	0.429282	−	0.904706i
$341$			19.0513i			1.03169i
$342$	5.79832	+	8.01679i	0.313537	+	0.433499i
$343$	16.5766	+	8.25942i	0.895050	+	0.445967i
$344$	7.60233	−	7.02333i	0.409890	−	0.378672i
$345$	−0.377650	+	0.0128147i	−0.0203320	+	0.000689922i
$346$	5.28286	−	1.34112i	0.284008	−	0.0720989i
$347$		−	20.1082i		−	1.07946i	−0.841837	−	0.539732i	$-0.818525\pi$
$347$		−	20.1082i		−	1.07946i	0.841837	−	0.539732i	$-0.181475\pi$
$348$	2.59932	−	26.0651i	0.139338	−	1.39724i
$349$	−2.29568			−0.122885			−0.0614423	−	0.998111i	$-0.519570\pi$
$349$	−2.29568			−0.122885			−0.0614423	+	0.998111i	$0.519570\pi$
$350$	−3.99500	+	18.2768i	−0.213542	+	0.976934i
$351$	−1.50196	+	6.74662i	−0.0801688	+	0.360108i
$352$	3.65680	−	10.7551i	0.194908	−	0.573247i
$353$			15.2039i			0.809221i	0.914489	+	0.404610i	$0.132593\pi$
$353$			15.2039i			0.809221i	−0.914489	+	0.404610i	$0.867407\pi$
$354$	4.29025	+	1.55638i	0.228024	+	0.0827204i
$355$	−16.0504	+	11.7157i	−0.851866	+	0.621807i
$356$	−23.6137	+	12.8151i	−1.25152	+	0.679201i
$357$	13.8350	+	12.9067i	0.732225	+	0.683097i
$358$	−18.8967	+	4.79715i	−0.998719	+	0.253537i
$359$		−	29.0532i		−	1.53337i	−0.642023	−	0.766685i	$-0.721905\pi$
$359$		−	29.0532i		−	1.53337i	0.642023	−	0.766685i	$-0.278095\pi$
$360$	−3.45534	−	18.6564i	−0.182113	−	0.983278i
$361$	−13.5617			−0.713773
$362$	32.2082	−	8.17644i	1.69282	−	0.429744i
$363$	6.78029	−	9.98304i	0.355873	−	0.523974i
$364$	2.36809	+	6.62830i	0.124121	+	0.347417i
$365$	−9.03165	−	12.3732i	−0.472738	−	0.647644i
$366$	9.45525	−	26.0640i	0.494234	−	1.36239i
$367$	−7.34446			−0.383378			−0.191689	−	0.981456i	$-0.561396\pi$
$367$	−7.34446			−0.383378			−0.191689	+	0.981456i	$0.561396\pi$
$368$	0.212680	−	0.327215i	0.0110867	−	0.0170573i
$369$	6.50601	+	16.4048i	0.338689	+	0.854002i
$370$	15.0939	+	12.4995i	0.784694	+	0.649817i
$371$	1.01270	−	6.52030i	0.0525770	−	0.338517i
$372$	−32.7019	−	3.26117i	−1.69552	−	0.169084i
$373$	19.5085			1.01011			0.505056	−	0.863086i	$-0.331472\pi$
$373$	19.5085			1.01011			0.505056	+	0.863086i	$0.331472\pi$
$374$	−2.88517	−	11.3651i	−0.149188	−	0.587675i
$375$	5.27348	−	18.6330i	0.272321	−	0.962206i
$376$	−14.9537	−	16.1865i	−0.771179	−	0.834755i
$377$		−	10.0583i		−	0.518030i
$378$	19.2917	+	2.41481i	0.992257	+	0.124205i
$379$		−	3.57410i		−	0.183589i	−0.995778	−	0.0917945i	$-0.970740\pi$
$379$		−	3.57410i		−	0.183589i	0.995778	−	0.0917945i	$-0.0292603\pi$
$380$	−9.42220	−	4.47083i	−0.483349	−	0.229349i
$381$	2.08249	+	1.41439i	0.106689	+	0.0724612i
$382$	−4.78180	−	18.8362i	−0.244658	−	0.963744i
$383$		−	14.6339i		−	0.747757i	−0.927478	−	0.373878i	$-0.878028\pi$
$383$		−	14.6339i		−	0.747757i	0.927478	−	0.373878i	$-0.121972\pi$
$384$	17.8353	+	8.11800i	0.910154	+	0.414270i
$385$	5.44864	+	10.5572i	0.277689	+	0.538043i
$386$	−4.47620	−	17.6324i	−0.227833	−	0.897466i
$387$	−4.04706	−	10.2046i	−0.205724	−	0.518730i
$388$	−16.9791	+	9.21456i	−0.861985	+	0.467798i
$389$	−13.4414			−0.681507			−0.340754	−	0.940153i	$-0.610682\pi$
$389$	−13.4414			−0.681507			−0.340754	+	0.940153i	$0.610682\pi$
$390$	−2.03114	−	6.99681i	−0.102851	−	0.354297i
$391$		−	0.402828i		−	0.0203719i
$392$	17.9328	−	8.39126i	0.905745	−	0.423823i
$393$	2.68644	+	1.82458i	0.135513	+	0.0920377i
$394$	8.89888	+	35.0540i	0.448319	+	1.76600i
$395$	14.4739	+	19.8290i	0.728260	+	0.997705i
$396$	−9.24633	−	7.72525i	−0.464646	−	0.388208i
$397$		−	7.47449i		−	0.375134i	−0.982252	−	0.187567i	$-0.939940\pi$
$397$		−	7.47449i		−	0.375134i	0.982252	−	0.187567i	$-0.0600601\pi$
$398$	−5.95649	−	23.4635i	−0.298572	−	1.17612i
$399$	7.28991	−	7.81419i	0.364952	−	0.391199i
$400$	12.6491	+	15.4920i	0.632454	+	0.774598i
$401$			30.4076i			1.51848i	0.650808	+	0.759242i	$0.274430\pi$
$401$			30.4076i			1.51848i	−0.650808	+	0.759242i	$0.725570\pi$
$402$	6.12492	−	16.8838i	0.305483	−	0.842085i
$403$	−12.6194			−0.628619
$404$	−14.9444	−	27.5373i	−0.743514	−	1.37003i
$405$	−19.7807	−	3.70447i	−0.982912	−	0.184076i
$406$	−28.1668	+	2.67045i	−1.39790	+	0.132532i
$407$	12.4450			0.616875
$408$	20.0023	−	3.00698i	0.990260	−	0.148868i
$409$			24.7533i			1.22397i	0.790868	+	0.611986i	$0.209629\pi$
$409$			24.7533i			1.22397i	−0.790868	+	0.611986i	$0.790371\pi$
$410$	−14.3275	−	11.8648i	−0.707586	−	0.585962i
$411$	18.0019	−	26.5053i	0.887967	−	1.30741i
$412$	15.1068	−	8.19843i	0.744257	−	0.403908i
$413$	0.756558	−	4.87110i	0.0372278	−	0.239691i
$414$	−0.242585	−	0.335400i	−0.0119224	−	0.0164840i
$415$	13.4004	+	18.3584i	0.657802	+	0.901177i
$416$	7.12407	+	2.42224i	0.349286	+	0.118760i
$417$	0.666956	−	0.982002i	0.0326610	−	0.0480888i
$418$	−6.41916	+	1.62958i	−0.313971	+	0.0797055i
$419$		−	11.5934i		−	0.566374i	−0.959065	−	0.283187i	$-0.908608\pi$
$419$		−	11.5934i		−	0.566374i	0.959065	−	0.283187i	$-0.0913918\pi$
$420$	−19.0543	+	7.54554i	−0.929753	+	0.368185i
$421$			12.7176i			0.619816i	0.950767	+	0.309908i	$0.100298\pi$
$421$			12.7176i			0.619816i	−0.950767	+	0.309908i	$0.899702\pi$
$422$	6.04133	+	23.7977i	0.294087	+	1.15845i
$423$	−21.7271	+	8.61679i	−1.05641	+	0.418963i
$424$	−4.78676	−	5.18138i	−0.232466	−	0.251630i
$425$	19.6618	+	6.29225i	0.953739	+	0.305219i
$426$	−20.4632	−	7.42343i	−0.991443	−	0.359666i
$427$	−29.5928	−	4.59622i	−1.43209	−	0.222427i
$428$	−2.38987	−	4.40368i	−0.115519	−	0.212860i
$429$	−3.82732	−	2.59944i	−0.184785	−	0.125502i
$430$	8.91242	+	7.38050i	0.429795	+	0.355919i
$431$			2.50836i			0.120823i	0.998174	+	0.0604117i	$0.0192414\pi$
$431$			2.50836i			0.120823i	−0.998174	+	0.0604117i	$0.980759\pi$
$432$	14.8433	−	14.5491i	0.714149	−	0.699994i
$433$	24.6527			1.18473			0.592366	−	0.805669i	$-0.298194\pi$
$433$	24.6527			1.18473			0.592366	+	0.805669i	$0.298194\pi$
$434$	3.35041	+	35.3389i	0.160825	+	1.69632i
$435$	29.2694	−	0.993192i	1.40336	−	0.0476199i
$436$	−13.8245	−	25.4737i	−0.662075	−	1.21997i
$437$	−0.227523			−0.0108839
$438$	5.72271	−	15.7750i	0.273442	−	0.753760i
$439$		−	5.50924i		−	0.262942i	−0.991320	−	0.131471i	$-0.958030\pi$
$439$		−	5.50924i		−	0.262942i	0.991320	−	0.131471i	$-0.0419700\pi$
$440$	12.4613	+	2.45384i	0.594068	+	0.116982i
$441$	−1.45612	−	20.9495i	−0.0693392	−	0.997593i
$442$	7.52815	−	1.91111i	0.358078	−	0.0909023i
$443$			13.1356i			0.624093i	0.950067	+	0.312047i	$0.101014\pi$
$443$			13.1356i			0.624093i	−0.950067	+	0.312047i	$0.898986\pi$
$444$	−2.13031	+	21.3620i	−0.101100	+	1.01380i
$445$	−17.7099	−	24.2622i	−0.839527	−	1.15014i
$446$	8.95033	−	2.27215i	0.423810	−	0.107589i
$447$	−2.28607	+	3.36593i	−0.108128	+	0.159203i
$448$	4.89170	−	20.5930i	0.231111	−	0.972927i
$449$			10.4000i			0.490806i	0.969421	+	0.245403i	$0.0789203\pi$
$449$			10.4000i			0.490806i	−0.969421	+	0.245403i	$0.921080\pi$
$450$	20.1599	−	6.60144i	0.950346	−	0.311195i
$451$	−11.8131			−0.556257
$452$	24.9790	−	13.5561i	1.17491	−	0.637624i
$453$	8.10322	−	11.9309i	0.380722	−	0.560562i
$454$	17.0783	−	4.33553i	0.801524	−	0.203477i
$455$	−6.99299	+	3.60914i	−0.327836	+	0.169199i
$456$	−1.69839	−	11.2976i	−0.0795342	−	0.529057i
$457$		−	40.4322i		−	1.89134i	−0.325129	−	0.945670i	$-0.605408\pi$
$457$		−	40.4322i		−	1.89134i	0.325129	−	0.945670i	$-0.394592\pi$
$458$	−5.01359	+	1.27276i	−0.234270	+	0.0594722i
$459$	4.66205	−	20.9413i	0.217606	−	0.977458i
$460$	0.394198	+	0.187047i	0.0183796	+	0.00872109i
$461$			18.2567i			0.850301i	0.905123	+	0.425151i	$0.139779\pi$
$461$			18.2567i			0.850301i	−0.905123	+	0.425151i	$0.860221\pi$
$462$	−6.26321	+	11.4080i	−0.291391	+	0.530747i
$463$		−	42.1208i		−	1.95752i	−0.205016	−	0.978759i	$-0.565725\pi$
$463$		−	42.1208i		−	1.95752i	0.205016	−	0.978759i	$-0.434275\pi$
$464$	−16.4836	+	25.3604i	−0.765230	+	1.17733i
$465$	−1.24609	−	36.7221i	−0.0577858	−	1.70295i
$466$	1.69783	−	0.431015i	0.0786506	−	0.0199664i
$467$	−32.5243			−1.50504			−0.752521	−	0.658568i	$-0.771163\pi$
$467$	−32.5243			−1.50504			−0.752521	+	0.658568i	$0.771163\pi$
$468$	5.11714	−	6.12470i	0.236540	−	0.283114i
$469$	−19.1696	−	2.97734i	−0.885170	−	0.137481i
$470$	15.7142	−	18.9759i	0.724842	−	0.875292i
$471$	20.1536	+	13.6880i	0.928631	+	0.630708i
$472$	−3.57603	−	3.87084i	−0.164600	−	0.178170i
$473$	7.34833			0.337877
$474$	−9.17106	+	25.2806i	−0.421241	+	1.16118i
$475$	3.55395	−	11.1053i	0.163066	−	0.509545i
$476$	−7.35048	−	20.5741i	−0.336908	−	0.943010i
$477$	−6.95497	+	2.75828i	−0.318446	+	0.126293i
$478$	6.82354	+	26.8789i	0.312101	+	1.22941i
$479$	−15.9517			−0.728852			−0.364426	−	0.931232i	$-0.618735\pi$
$479$	−15.9517			−0.728852			−0.364426	+	0.931232i	$0.618735\pi$
$480$	−6.34516	+	20.9700i	−0.289616	+	0.957143i
$481$			8.24346i			0.375869i
$482$	−8.42980	−	33.2062i	−0.383967	−	1.51250i
$483$	−0.304989	+	0.326923i	−0.0138775	+	0.0148755i
$484$	−12.2474	+	6.64667i	−0.556702	+	0.302121i
$485$	−12.7340	−	17.4454i	−0.578223	−	0.792156i
$486$	−8.72929	−	20.2435i	−0.395969	−	0.918264i
$487$		−	8.42432i		−	0.381742i	−0.981615	−	0.190871i	$-0.938869\pi$
$487$		−	8.42432i		−	0.381742i	0.981615	−	0.190871i	$-0.0611313\pi$
$488$	−23.5160	+	21.7250i	−1.06452	+	0.983445i
$489$	10.3292	−	15.2084i	0.467104	−	0.687746i
$490$	11.9635	+	18.6246i	0.540454	+	0.841373i
$491$	16.9685			0.765777			0.382888	−	0.923795i	$-0.374929\pi$
$491$	16.9685			0.765777			0.382888	+	0.923795i	$0.374929\pi$
$492$	2.02215	−	20.2774i	0.0911655	−	0.914176i
$493$			31.2208i			1.40611i
$494$	−1.07942	−	4.25200i	−0.0485655	−	0.191307i
$495$	7.18635	−	11.3940i	0.323002	−	0.512124i
$496$	31.8179	+	20.6807i	1.42866	+	0.928592i
$497$	−3.60855	+	23.2336i	−0.161865	+	1.04217i
$498$	−8.49089	+	23.4057i	−0.380486	+	1.04883i
$499$			34.6615i			1.55166i	0.630940	+	0.775831i	$0.282669\pi$
$499$			34.6615i			1.55166i	−0.630940	+	0.775831i	$0.717331\pi$
$500$	−15.2871	+	16.3189i	−0.683659	+	0.729802i
$501$	0.662465	+	0.449933i	0.0295968	+	0.0201015i
$502$	5.09528	+	20.0710i	0.227413	+	0.895814i
$503$			20.2162i			0.901396i	0.892676	+	0.450698i	$0.148825\pi$
$503$			20.2162i			0.901396i	−0.892676	+	0.450698i	$0.851175\pi$
$504$	−18.5099	−	12.7037i	−0.824496	−	0.565868i
$505$	28.2935	−	20.6524i	1.25904	−	0.919022i
$506$	0.268559	−	0.0681770i	0.0119389	−	0.00303084i
$507$	−10.9291	+	16.0915i	−0.485376	+	0.714650i
$508$	−1.38651	−	2.55485i	−0.0615166	−	0.113353i
$509$			2.33728i			0.103598i	0.998658	+	0.0517992i	$0.0164956\pi$
$509$			2.33728i			0.103598i	−0.998658	+	0.0517992i	$0.983504\pi$
$510$	6.30461	+	21.7179i	0.279173	+	0.961685i
$511$	−17.9108	−	2.78182i	−0.792326	−	0.123061i
$512$	−13.9926	−	17.7822i	−0.618393	−	0.785869i
$513$	−11.8280	−	2.63319i	−0.522217	−	0.116258i
$514$	5.50041	+	21.6669i	0.242613	+	0.955687i
$515$	11.3298	+	15.5216i	0.499251	+	0.683966i
$516$	−1.25788	+	12.6135i	−0.0553749	+	0.555280i
$517$		−	15.6457i		−	0.688097i
$518$	23.0846	−	2.18861i	1.01428	−	0.0961619i
$519$	−3.75054	+	5.52216i	−0.164631	+	0.242396i
$520$	−1.62540	+	8.25425i	−0.0712787	+	0.361973i
$521$	18.0595			0.791203			0.395601	−	0.918422i	$-0.370536\pi$
$521$	18.0595			0.791203			0.395601	+	0.918422i	$0.370536\pi$
$522$	18.8013	+	25.9948i	0.822910	+	1.13776i
$523$			15.6316i			0.683522i	0.939787	+	0.341761i	$0.111023\pi$
$523$			15.6316i			0.683522i	−0.939787	+	0.341761i	$0.888977\pi$
$524$	−1.78862	−	3.29579i	−0.0781362	−	0.143977i
$525$	−11.1930	−	19.9929i	−0.488501	−	0.872563i
$526$	−19.5397	+	4.96040i	−0.851973	+	0.216284i
$527$	39.1704			1.70629
$528$	5.39001	+	12.8263i	0.234570	+	0.558192i
$529$	−22.9905			−0.999586
$530$	5.03020	−	6.07428i	0.218498	−	0.263850i
$531$	−5.19583	+	2.06062i	−0.225480	+	0.0894233i
$532$	−11.6205	+	4.15165i	−0.503813	+	0.179997i
$533$		−	7.82491i		−	0.338934i
$534$	11.2215	−	30.9327i	0.485600	−	1.33859i
$535$	4.52462	−	3.30268i	0.195616	−	0.142787i
$536$	−15.2332	+	14.0730i	−0.657975	+	0.607863i
$537$	13.4156	−	19.7526i	0.578926	−	0.852389i
$538$	−3.24846	−	12.7961i	−0.140051	−	0.551681i
$539$	13.3947	+	4.26368i	0.576952	+	0.183650i
$540$	18.3279	+	14.2859i	0.788708	+	0.614768i
$541$		−	14.7905i		−	0.635895i	−0.948108	−	0.317948i	$-0.897006\pi$
$541$		−	14.7905i		−	0.635895i	0.948108	−	0.317948i	$-0.102994\pi$
$542$	−0.0721011	−	0.284017i	−0.00309701	−	0.0121996i
$543$	−22.8661	+	33.6671i	−0.981276	+	1.44479i
$544$	−22.1129	−	7.51855i	−0.948084	−	0.322355i
$545$	26.1733	−	19.1048i	1.12114	−	0.818360i
$546$	−7.55656	−	4.14870i	−0.323391	−	0.177548i
$547$	−35.5600			−1.52043			−0.760217	−	0.649669i	$-0.774908\pi$
$547$	−35.5600			−1.52043			−0.760217	+	0.649669i	$0.774908\pi$
$548$	−32.5173	+	17.6471i	−1.38907	+	0.753847i
$549$	12.5186	+	31.5656i	0.534282	+	1.34719i
$550$	−0.867262	+	14.1732i	−0.0369802	+	0.604346i
$551$	17.6339			0.751231
$552$	0.0710556	+	0.472657i	0.00302433	+	0.0201176i
$553$	28.7033	+	4.45808i	1.22059	+	0.189577i
$554$	39.2812	−	9.97201i	1.66890	−	0.423670i
$555$	−23.9881	+	0.813986i	−1.01824	+	0.0345518i
$556$	−1.20474	+	0.653813i	−0.0510925	+	0.0277278i
$557$		−	1.35270i		−	0.0573158i	−0.999589	−	0.0286579i	$-0.990877\pi$
$557$		−	1.35270i		−	0.0573158i	0.999589	−	0.0286579i	$-0.00912334\pi$
$558$	32.6137	−	23.5886i	1.38065	−	0.998585i
$559$			4.86748i			0.205872i
$560$	23.5463	+	2.36023i	0.995014	+	0.0997378i
$561$	11.8799	+	8.06859i	0.501570	+	0.340656i
$562$	−1.08226	−	4.26319i	−0.0456525	−	0.179832i
$563$	30.5252			1.28649			0.643243	−	0.765662i	$-0.277589\pi$
$563$	30.5252			1.28649			0.643243	+	0.765662i	$0.277589\pi$
$564$	26.8561	+	2.67820i	1.13085	+	0.112773i
$565$	18.7338	+	25.6650i	0.788136	+	1.07973i
$566$	7.16140	+	28.2098i	0.301016	+	1.18575i
$567$	−19.6387	+	13.4656i	−0.824746	+	0.565504i
$568$	17.0566	+	18.4627i	0.715677	+	0.774678i
$569$			15.3875i			0.645079i	0.946556	+	0.322539i	$0.104536\pi$
$569$			15.3875i			0.645079i	−0.946556	+	0.322539i	$0.895464\pi$
$570$	12.2666	−	3.56093i	0.513790	−	0.149151i
$571$			42.4541i			1.77665i	0.459217	+	0.888324i	$0.348130\pi$
$571$			42.4541i			1.77665i	−0.459217	+	0.888324i	$0.651870\pi$
$572$	2.54822	+	4.69545i	0.106546	+	0.196327i
$573$	19.6894	+	13.3727i	0.822538	+	0.558652i
$574$	−21.9125	+	2.07748i	−0.914609	+	0.0867125i
$575$	−0.148687	+	0.464613i	−0.00620068	+	0.0193757i
$576$	−22.9392	+	7.05647i	−0.955799	+	0.294019i
$577$	−0.806615			−0.0335798			−0.0167899	−	0.999859i	$-0.505345\pi$
$577$	−0.806615			−0.0335798			−0.0167899	+	0.999859i	$0.505345\pi$
$578$	−0.0646852	+	0.0164211i	−0.00269055	+	0.000683028i
$579$	18.4311	+	12.5180i	0.765971	+	0.520232i
$580$	−30.5519	−	14.4968i	−1.26860	−	0.601949i
$581$	26.5746	+	4.12745i	1.10250	+	0.171235i
$582$	8.06865	−	22.2418i	0.334456	−	0.921951i
$583$		−	5.00827i		−	0.207421i
$584$	−14.2329	+	13.1489i	−0.588960	+	0.544105i
$585$	7.54732	+	4.76018i	0.312043	+	0.196809i
$586$	−16.3650	+	4.15446i	−0.676033	+	0.171619i
$587$	−2.83907			−0.117181			−0.0585905	−	0.998282i	$-0.518661\pi$
$587$	−2.83907			−0.117181			−0.0585905	+	0.998282i	$0.518661\pi$
$588$	−9.61158	+	22.2625i	−0.396375	+	0.918089i
$589$		−	22.1240i		−	0.911603i
$590$	3.75789	−	4.53789i	0.154710	−	0.186822i
$591$	−36.6419	−	24.8864i	−1.50724	−	1.02369i
$592$	13.5094	−	20.7845i	0.555231	−	0.854239i
$593$		−	32.6365i		−	1.34022i	−0.742262	−	0.670110i	$-0.766247\pi$
$593$		−	32.6365i		−	1.34022i	0.742262	−	0.670110i	$-0.233753\pi$
$594$	14.7503	−	0.436121i	0.605211	−	0.0178943i
$595$	21.7060	−	11.2027i	0.889861	−	0.459265i
$596$	4.12940	−	2.24102i	0.169147	−	0.0917958i
$597$	24.5263	+	16.6578i	1.00380	+	0.681758i
$598$	0.0451599	+	0.177892i	0.00184673	+	0.00727453i
$599$			38.2058i			1.56105i	0.625128	+	0.780523i	$0.285047\pi$
$599$			38.2058i			1.56105i	−0.625128	+	0.780523i	$0.714953\pi$
$600$	−24.1800	−	3.91481i	−0.987146	−	0.159821i
$601$			36.9925i			1.50896i	0.656325	+	0.754479i	$0.272110\pi$
$601$			36.9925i			1.50896i	−0.656325	+	0.754479i	$0.727890\pi$
$602$	13.6306	−	1.29230i	0.555543	−	0.0526701i
$603$	8.10932	+	20.4476i	0.330237	+	0.832689i
$604$	−14.6371	+	7.94353i	−0.595575	+	0.323218i
$605$	−9.18536	−	12.5838i	−0.373438	−	0.511604i
$606$	36.0723	+	13.0860i	1.46534	+	0.531581i
$607$	−29.2308			−1.18644			−0.593220	−	0.805041i	$-0.702143\pi$
$607$	−29.2308			−1.18644			−0.593220	+	0.805041i	$0.702143\pi$
$608$	−4.24658	+	12.4897i	−0.172222	+	0.506524i
$609$	23.6378	−	25.3378i	0.957853	−	1.02674i
$610$	−27.5685	−	22.8299i	−1.11622	−	0.924354i
$611$	10.3636			0.419266
$612$	−15.8835	+	19.0109i	−0.642051	+	0.768470i
$613$	−1.66640			−0.0673052			−0.0336526	−	0.999434i	$-0.510714\pi$
$613$	−1.66640			−0.0673052			−0.0336526	+	0.999434i	$0.510714\pi$
$614$	2.68145	+	10.5626i	0.108214	+	0.426273i
$615$	22.7702	−	0.772657i	0.918182	−	0.0311565i
$616$	12.4724	−	8.38252i	0.502526	−	0.337741i
$617$	21.0418			0.847111			0.423556	−	0.905870i	$-0.360782\pi$
$617$	21.0418			0.847111			0.423556	+	0.905870i	$0.360782\pi$
$618$	−7.17888	+	19.7891i	−0.288777	+	0.796033i
$619$	8.07998			0.324762			0.162381	−	0.986728i	$-0.448083\pi$
$619$	8.07998			0.324762			0.162381	+	0.986728i	$0.448083\pi$
$620$	−18.1881	+	38.3312i	−0.730453	+	1.53942i
$621$	0.494848	+	0.110165i	0.0198576	+	0.00442077i
$622$	36.7942	−	9.34065i	1.47531	−	0.374526i
$623$	−35.1206	−	5.45478i	−1.40708	−	0.218541i
$624$	−8.49602	+	3.57030i	−0.340113	+	0.142926i
$625$	−20.3550	−	14.5147i	−0.814198	−	0.580587i
$626$	11.2458	−	2.85488i	0.449473	−	0.114104i
$627$	4.55725	−	6.70993i	0.181999	−	0.267969i
$628$	−13.4182	−	24.7250i	−0.535445	−	0.986634i
$629$		−	25.5875i		−	1.02024i
$630$	11.3264	−	22.3989i	0.451254	−	0.892395i
$631$	−27.5940			−1.09850			−0.549250	−	0.835658i	$-0.685087\pi$
$631$	−27.5940			−1.09850			−0.549250	+	0.835658i	$0.685087\pi$
$632$	22.8092	−	21.0720i	0.907302	−	0.838201i
$633$	−24.8756	−	16.8951i	−0.988718	−	0.671518i
$634$	10.6939	+	42.1247i	0.424708	+	1.67299i
$635$	2.62501	−	1.91609i	0.104170	−	0.0760377i
$636$	8.59679	+	0.857307i	0.340885	+	0.0339944i
$637$	−2.82423	+	8.87257i	−0.111900	+	0.351544i
$638$	−20.8144	+	5.28399i	−0.824050	+	0.209195i
$639$	24.7825	−	9.82852i	0.980381	−	0.388810i
$640$	17.6252	−	18.1480i	0.696698	−	0.717364i
$641$		−	26.2441i		−	1.03658i	−0.855205	−	0.518290i	$-0.826569\pi$
$641$		−	26.2441i		−	1.03658i	0.855205	−	0.518290i	$-0.173431\pi$
$642$	5.76858	+	2.09267i	0.227668	+	0.0825911i
$643$			10.0020i			0.394440i	0.980359	+	0.197220i	$0.0631913\pi$
$643$			10.0020i			0.394440i	−0.980359	+	0.197220i	$0.936809\pi$
$644$	0.486169	−	0.173693i	0.0191577	−	0.00684447i
$645$	−14.1642	+	0.480631i	−0.557714	+	0.0189248i
$646$	3.35050	+	13.1981i	0.131824	+	0.519272i
$647$			39.2518i			1.54315i	0.636140	+	0.771573i	$0.280530\pi$
$647$			39.2518i			1.54315i	−0.636140	+	0.771573i	$0.719470\pi$
$648$	−1.77632	+	25.3938i	−0.0697804	+	0.997562i
$649$		−	3.74151i		−	0.146867i
$650$	−9.38819	−	0.574468i	−0.368235	−	0.0225325i
$651$	−31.7895	−	29.6566i	−1.24593	−	1.16234i
$652$	−18.6580	+	10.1257i	−0.730703	+	0.396552i
$653$		−	14.4218i		−	0.564370i	−0.959360	−	0.282185i	$-0.908941\pi$
$653$		−	14.4218i		−	0.564370i	0.959360	−	0.282185i	$-0.0910592\pi$
$654$	33.3692	+	12.1053i	1.30484	+	0.473356i
$655$	3.38630	−	2.47178i	0.132314	−	0.0965804i
$656$	−12.8234	+	19.7292i	−0.500671	+	0.770297i
$657$	7.57679	+	19.1048i	0.295599	+	0.745349i
$658$	−2.75149	−	29.0217i	−0.107264	−	1.13138i
$659$	−28.6527			−1.11615			−0.558075	−	0.829790i	$-0.688460\pi$
$659$	−28.6527			−1.11615			−0.558075	+	0.829790i	$0.688460\pi$
$660$	−13.4120	+	7.87885i	−0.522060	+	0.306684i
$661$	−30.3370			−1.17997			−0.589987	−	0.807413i	$-0.700867\pi$
$661$	−30.3370			−1.17997			−0.589987	+	0.807413i	$0.700867\pi$
$662$	7.07293	+	27.8613i	0.274897	+	1.08286i
$663$	−5.34458	+	7.86915i	−0.207566	+	0.305613i
$664$	21.1176	−	19.5092i	0.819521	−	0.757106i
$665$	−6.32742	−	12.2599i	−0.245367	−	0.475417i
$666$	−15.4089	−	21.3044i	−0.597082	−	0.825530i
$667$	−0.737753			−0.0285659
$668$	−0.441067	−	0.812728i	−0.0170654	−	0.0314454i
$669$	−6.35424	+	9.35575i	−0.245669	+	0.361714i
$670$	−17.8583	−	14.7887i	−0.689927	−	0.571339i
$671$	−22.7303			−0.877495
$672$	12.2537	+	22.8439i	0.472699	+	0.881224i
$673$			35.2784i			1.35988i	0.733267	+	0.679940i	$0.237994\pi$
$673$			35.2784i			1.35988i	−0.733267	+	0.679940i	$0.762006\pi$
$674$	2.80046	+	11.0314i	0.107870	+	0.424914i
$675$	−13.1067	+	22.4324i	−0.504477	+	0.863425i
$676$	19.7415	−	10.7137i	0.759287	−	0.412065i
$677$	−19.1645			−0.736552			−0.368276	−	0.929717i	$-0.620052\pi$
$677$	−19.1645			−0.736552			−0.368276	+	0.929717i	$0.620052\pi$
$678$	−11.8702	+	32.7211i	−0.455874	+	1.25665i
$679$	−25.2530	−	3.92219i	−0.969122	−	0.150520i
$680$	5.04521	−	25.6210i	0.193475	−	0.982519i
$681$	−12.1247	+	17.8519i	−0.464618	+	0.684086i
$682$	6.62943	+	26.1143i	0.253854	+	0.999968i
$683$			13.2192i			0.505820i	0.967490	+	0.252910i	$0.0813877\pi$
$683$			13.2192i			0.505820i	−0.967490	+	0.252910i	$0.918612\pi$
$684$	10.7376	+	8.97121i	0.410563	+	0.343023i
$685$	−24.3874	−	33.4103i	−0.931795	−	1.27654i
$686$	25.5961	+	5.55320i	0.977265	+	0.212022i
$687$	3.55938	−	5.24069i	0.135799	−	0.199945i
$688$	7.97681	−	12.2726i	0.304113	−	0.467887i
$689$	3.31744			0.126384
$690$	−0.513198	+	0.148979i	−0.0195371	+	0.00567154i
$691$	36.7836			1.39931			0.699657	−	0.714479i	$-0.253336\pi$
$691$	36.7836			1.39931			0.699657	+	0.714479i	$0.253336\pi$
$692$	6.77472	−	3.67663i	0.257536	−	0.139765i
$693$	−3.53248	−	15.5427i	−0.134188	−	0.590419i
$694$	−6.99720	−	27.5630i	−0.265610	−	1.04628i
$695$	−0.903535	−	1.23783i	−0.0342731	−	0.0469535i
$696$	−5.50709	−	36.6328i	−0.208746	−	1.38856i
$697$			24.2883i			0.919985i
$698$	−3.14676	+	0.798843i	−0.119107	+	0.0302367i
$699$	−1.20537	+	1.77474i	−0.0455912	+	0.0671268i
$700$	0.883818	+	26.4427i	0.0334052	+	0.999442i
$701$	4.86743			0.183840			0.0919201	−	0.995766i	$-0.470700\pi$
$701$	4.86743			0.183840			0.0919201	+	0.995766i	$0.470700\pi$
$702$	0.288883	+	9.77048i	0.0109032	+	0.368763i
$703$	−14.4522			−0.545074
$704$	1.26998	−	16.0148i	0.0478642	−	0.603581i
$705$	1.02333	+	30.1576i	0.0385410	+	1.13580i
$706$	5.29061	+	20.8405i	0.199115	+	0.784342i
$707$	6.36113	−	40.9561i	0.239235	−	1.54031i
$708$	6.42238	+	0.640466i	0.241368	+	0.0240702i
$709$		−	0.768670i		−	0.0288680i	−0.999896	−	0.0144340i	$-0.995405\pi$
$709$		−	0.768670i		−	0.0288680i	0.999896	−	0.0144340i	$-0.00459465\pi$
$710$	−17.9240	+	21.6443i	−0.672675	+	0.812298i
$711$	−12.1424	−	30.6168i	−0.455374	−	1.14822i
$712$	−27.9087	+	25.7832i	−1.04592	+	0.966265i
$713$			0.925604i			0.0346642i
$714$	23.4553	+	12.8775i	0.877794	+	0.481927i
$715$	−4.82440	+	3.52150i	−0.180422	+	0.131697i
$716$	−24.2330	+	13.1512i	−0.905629	+	0.491484i
$717$	−28.0965	−	19.0826i	−1.04928	−	0.712651i
$718$	−10.1099	−	39.8242i	−0.377297	−	1.48623i
$719$	−45.3201			−1.69015			−0.845077	−	0.534644i	$-0.820446\pi$
$719$	−45.3201			−1.69015			−0.845077	+	0.534644i	$0.820446\pi$
$720$	−11.2284	−	24.3706i	−0.418456	−	0.908237i
$721$	22.4683	+	3.48968i	0.836762	+	0.129962i
$722$	−18.5895	+	4.71916i	−0.691829	+	0.175629i
$723$	34.7104	+	23.5746i	1.29089	+	0.876749i
$724$	41.3036	−	22.4154i	1.53504	−	0.833063i
$725$	11.5238	−	36.0093i	0.427984	−	1.33735i
$726$	5.82010	−	16.0435i	0.216004	−	0.595430i
$727$	−19.4319			−0.720688			−0.360344	−	0.932819i	$-0.617341\pi$
$727$	−19.4319			−0.720688			−0.360344	+	0.932819i	$0.617341\pi$
$728$	5.55252	+	8.26160i	0.205790	+	0.306195i
$729$	24.4501	+	11.4540i	0.905558	+	0.424223i
$730$	−16.6856	−	13.8176i	−0.617562	−	0.511411i
$731$		−	15.1085i		−	0.558809i
$732$	3.89094	−	39.0170i	0.143813	−	1.44211i
$733$			33.0895i			1.22219i	0.791558	+	0.611094i	$0.209270\pi$
$733$			33.0895i			1.22219i	−0.791558	+	0.611094i	$0.790730\pi$
$734$	−10.0673	+	2.55571i	−0.371591	+	0.0943329i
$735$	−26.0977	−	7.34229i	−0.962629	−	0.270824i
$736$	0.177665	−	0.522533i	0.00654881	−	0.0192608i
$737$	−14.7243			−0.542375
$738$	14.6265	+	20.2227i	0.538410	+	0.744409i
$739$		−	12.9023i		−	0.474619i	−0.971434	−	0.237310i	$-0.923734\pi$
$739$		−	12.9023i		−	0.474619i	0.971434	−	0.237310i	$-0.0762656\pi$
$740$	25.0393	+	11.8811i	0.920461	+	0.436758i
$741$	4.44461	+	3.01869i	0.163277	+	0.110894i
$742$	−0.880767	−	9.28999i	−0.0323340	−	0.341046i
$743$	20.1716			0.740025			0.370012	−	0.929027i	$-0.379353\pi$
$743$	20.1716			0.740025			0.370012	+	0.929027i	$0.379353\pi$
$744$	−45.9605	+	6.90934i	−1.68499	+	0.253309i
$745$	3.09698	+	4.24281i	0.113464	+	0.155444i
$746$	26.7410	−	6.78852i	0.979057	−	0.248545i
$747$	−11.2418	−	28.3462i	−0.411317	−	1.03713i
$748$	−7.90959	−	14.5745i	−0.289203	−	0.532898i
$749$	1.01725	−	6.54958i	0.0371696	−	0.239316i
$750$	0.744657	−	27.3760i	0.0271910	−	0.999630i
$751$	15.5652			0.567982			0.283991	−	0.958827i	$-0.408341\pi$
$751$	15.5652			0.567982			0.283991	+	0.958827i	$0.408341\pi$
$752$	−26.1301	−	16.9838i	−0.952867	−	0.619336i
$753$	−20.9802	−	14.2493i	−0.764561	−	0.519275i
$754$	−3.50007	−	13.7873i	−0.127465	−	0.502104i
$755$	−10.9776	−	15.0391i	−0.399514	−	0.547327i
$756$	27.2841	−	3.40300i	0.992311	−	0.123766i
$757$	29.6612			1.07806			0.539028	−	0.842288i	$-0.318792\pi$
$757$	29.6612			1.07806			0.539028	+	0.842288i	$0.318792\pi$
$758$	−1.24370	−	4.89914i	−0.0451734	−	0.177945i
$759$	−0.190662	+	0.280724i	−0.00692061	+	0.0101896i
$760$	−14.4711	−	2.84960i	−0.524921	−	0.103366i
$761$	−41.8111			−1.51565			−0.757825	−	0.652457i	$-0.773738\pi$
$761$	−41.8111			−1.51565			−0.757825	+	0.652457i	$0.773738\pi$
$762$	3.34671	+	1.21409i	0.121239	+	0.0439818i
$763$	5.88444	−	37.8869i	0.213031	−	1.37160i
$764$	−13.1091	−	24.1555i	−0.474272	−	0.873914i
$765$	−23.4267	−	14.7755i	−0.846993	−	0.534209i
$766$	−5.09226	−	20.0592i	−0.183991	−	0.724767i
$767$	2.47835			0.0894880
$768$	27.2723	+	4.92133i	0.984106	+	0.177583i
$769$		−	9.12224i		−	0.328956i	−0.986381	−	0.164478i	$-0.947406\pi$
$769$		−	9.12224i		−	0.328956i	0.986381	−	0.164478i	$-0.0525940\pi$
$770$	11.1423	+	12.5751i	0.401540	+	0.453174i
$771$	−22.6484	−	15.3823i	−0.815662	−	0.553982i
$772$	−12.2714	−	22.6117i	−0.441656	−	0.813814i
$773$	17.9114			0.644228			0.322114	−	0.946701i	$-0.395606\pi$
$773$	17.9114			0.644228			0.322114	+	0.946701i	$0.395606\pi$
$774$	−9.09842	−	12.5795i	−0.327036	−	0.452162i
$775$	−45.1782	−	14.4581i	−1.62285	−	0.519350i
$776$	−20.0674	+	18.5391i	−0.720379	+	0.665514i
$777$	−19.3728	+	20.7660i	−0.694994	+	0.744977i
$778$	−18.4246	+	4.67731i	−0.660555	+	0.167690i
$779$	13.7184			0.491512
$780$	−5.21889	−	8.88398i	−0.186866	−	0.318097i
$781$			17.8458i			0.638575i
$782$	−0.140175	−	0.552171i	−0.00501265	−	0.0197456i
$783$	−38.3526	−	8.53822i	−1.37061	−	0.305131i
$784$	21.6612	−	17.7424i	0.773614	−	0.633657i
$785$	25.4040	−	18.5433i	0.906707	−	0.661838i
$786$	4.31730	+	1.56619i	0.153993	+	0.0558641i
$787$		−	36.9161i		−	1.31592i	−0.753055	−	0.657958i	$-0.771421\pi$
$787$		−	36.9161i		−	1.31592i	0.753055	−	0.657958i	$-0.228579\pi$
$788$	24.3960	+	44.9531i	0.869072	+	1.60139i
$789$	13.8721	−	20.4248i	0.493861	−	0.727143i
$790$	26.7399	+	22.1437i	0.951363	+	0.787837i
$791$	37.1512	+	5.77016i	1.32094	+	0.205163i
$792$	−15.3625	−	7.37174i	−0.545882	−	0.261943i
$793$		−	15.0564i		−	0.534668i
$794$	−2.60095	−	10.2455i	−0.0923044	−	0.363600i
$795$	0.327575	+	9.65362i	0.0116179	+	0.342379i
$796$	−16.3295	−	30.0895i	−0.578785	−	1.06649i
$797$	29.7782			1.05480			0.527399	−	0.849618i	$-0.323167\pi$
$797$	29.7782			1.05480			0.527399	+	0.849618i	$0.323167\pi$
$798$	7.27336	−	13.2479i	0.257474	−	0.468971i
$799$	−32.1683			−1.13803
$800$	22.7294	+	16.8338i	0.803604	+	0.595164i
$801$	14.8571	+	37.4619i	0.524948	+	1.32365i
$802$	10.5812	+	41.6808i	0.373634	+	1.47180i
$803$	−13.7573			−0.485486
$804$	2.52048	−	25.2745i	0.0888903	−	0.891362i
$805$	0.264721	+	0.512918i	0.00933020	+	0.0180780i
$806$	−17.2979	+	4.39128i	−0.609293	+	0.154676i
$807$	13.3758	+	9.08457i	0.470850	+	0.319792i
$808$	−30.0672	−	32.5459i	−1.05776	−	1.14496i
$809$			8.02026i			0.281977i	0.990011	+	0.140989i	$0.0450281\pi$
$809$			8.02026i			0.281977i	−0.990011	+	0.140989i	$0.954972\pi$
$810$	−28.4032	+	1.80541i	−0.997986	+	0.0634356i
$811$	−2.93155			−0.102941			−0.0514703	−	0.998675i	$-0.516391\pi$
$811$	−2.93155			−0.102941			−0.0514703	+	0.998675i	$0.516391\pi$
$812$	−37.6800	+	13.4619i	−1.32231	+	0.472420i
$813$	0.296882	+	0.201636i	0.0104121	+	0.00707170i
$814$	17.0588	−	4.33057i	0.597909	−	0.151786i
$815$	−13.9931	−	19.1704i	−0.490159	−	0.671509i
$816$	26.3714	−	11.0821i	0.923184	−	0.387951i
$817$	−8.53350			−0.298549
$818$	8.61360	+	33.9302i	0.301167	+	1.18634i
$819$	10.2954	−	2.33989i	0.359750	−	0.0817624i
$820$	−23.7679	−	11.2779i	−0.830012	−	0.393840i
$821$	−28.8608			−1.00725			−0.503624	−	0.863923i	$-0.668000\pi$
$821$	−28.8608			−1.00725			−0.503624	+	0.863923i	$0.668000\pi$
$822$	15.4525	−	42.5959i	0.538969	−	1.48570i
$823$			55.7417i			1.94303i	0.236970	+	0.971517i	$0.423846\pi$
$823$			55.7417i			1.94303i	−0.236970	+	0.971517i	$0.576154\pi$
$824$	17.8545	−	16.4947i	0.621991	−	0.574620i
$825$	−10.7238	−	13.6911i	−0.373355	−	0.476662i
$826$	−0.657992	−	6.94025i	−0.0228945	−	0.241482i
$827$		−	30.4567i		−	1.05908i	−0.848284	−	0.529541i	$-0.822364\pi$
$827$		−	30.4567i		−	1.05908i	0.848284	−	0.529541i	$-0.177636\pi$
$828$	−0.449231	−	0.375330i	−0.0156119	−	0.0130436i
$829$	25.9657			0.901827			0.450913	−	0.892568i	$-0.351098\pi$
$829$	25.9657			0.901827			0.450913	+	0.892568i	$0.351098\pi$
$830$	24.7567	+	20.5014i	0.859319	+	0.711614i
$831$	−27.8875	+	41.0605i	−0.967407	+	1.42437i
$832$	10.6081	+	0.841225i	0.367769	+	0.0291642i
$833$	8.76633	−	27.5402i	0.303735	−	0.954212i
$834$	0.572505	−	1.57815i	0.0198242	−	0.0546468i
$835$	0.835048	−	0.609531i	0.0288980	−	0.0210937i
$836$	−8.23190	+	4.46745i	−0.284706	+	0.154510i
$837$	−10.7123	+	48.1182i	−0.370271	+	1.66321i
$838$	−4.03424	−	15.8915i	−0.139361	−	0.548961i
$839$	−2.14123			−0.0739234			−0.0369617	−	0.999317i	$-0.511768\pi$
$839$	−2.14123			−0.0739234			−0.0369617	+	0.999317i	$0.511768\pi$
$840$	−23.4926	+	16.9734i	−0.810573	+	0.585637i
$841$	28.1788			0.971681
$842$	4.42542	+	17.4324i	0.152510	+	0.600760i
$843$	4.45631	+	3.02664i	0.153483	+	0.104243i
$844$	16.5621	+	30.5180i	0.570091	+	1.05047i
$845$	14.8057	+	20.2836i	0.509333	+	0.697778i
$846$	−26.7837	+	19.3719i	−0.920842	+	0.666019i
$847$	−18.2156	−	2.82917i	−0.625895	−	0.0972113i
$848$	−8.36438	−	5.43661i	−0.287234	−	0.186694i
$849$	−29.4876	−	20.0274i	−1.01201	−	0.687339i
$850$	29.1407	+	1.78313i	0.999518	+	0.0611609i
$851$	0.604637			0.0207267
$852$	−30.6327	−	3.05482i	−1.04946	−	0.104657i
$853$		−	44.6580i		−	1.52906i	−0.644587	−	0.764531i	$-0.722971\pi$
$853$		−	44.6580i		−	1.52906i	0.644587	−	0.764531i	$-0.277029\pi$
$854$	−42.1632	+	3.99741i	−1.44279	+	0.136789i
$855$	−8.34540	+	13.2317i	−0.285407	+	0.452515i
$856$	−4.80826	−	5.20465i	−0.164343	−	0.177891i
$857$		−	23.0490i		−	0.787338i	−0.919252	−	0.393669i	$-0.871206\pi$
$857$		−	23.0490i		−	0.787338i	0.919252	−	0.393669i	$-0.128794\pi$
$858$	−6.15079	−	2.23132i	−0.209984	−	0.0761761i
$859$	−14.2677			−0.486806			−0.243403	−	0.969925i	$-0.578264\pi$
$859$	−14.2677			−0.486806			−0.243403	+	0.969925i	$0.578264\pi$
$860$	14.7848	+	7.01539i	0.504158	+	0.239223i
$861$	18.3891	−	19.7117i	0.626700	−	0.671771i
$862$	0.872852	+	3.43829i	0.0297295	+	0.117109i
$863$	0.233651			0.00795357			0.00397679	−	0.999992i	$-0.498734\pi$
$863$	0.233651			0.00795357			0.00397679	+	0.999992i	$0.498734\pi$
$864$	15.2835	−	25.1081i	0.519954	−	0.854194i
$865$	5.08091	+	6.96077i	0.172756	+	0.236673i
$866$	33.7922	−	8.57857i	1.14831	−	0.291512i
$867$	0.0459230	−	0.0676152i	0.00155963	−	0.00229633i
$868$	16.8897	+	47.2743i	0.573272	+	1.60459i
$869$	22.0471			0.747898
$870$	39.7749	−	11.5465i	1.34849	−	0.391462i
$871$		−	9.75324i		−	0.330476i
$872$	−27.8140	−	30.1070i	−0.941902	−	1.01955i
$873$	10.6828	+	26.9365i	0.361558	+	0.911663i
$874$	−0.311874	+	0.0791729i	−0.0105493	+	0.00267806i
$875$	−29.1702	+	4.90903i	−0.986133	+	0.165955i
$876$	2.35496	−	23.6147i	0.0795667	−	0.797868i
$877$	40.6170			1.37154			0.685770	−	0.727819i	$-0.259466\pi$
$877$	40.6170			1.37154			0.685770	+	0.727819i	$0.259466\pi$
$878$	−1.91709	−	7.55170i	−0.0646987	−	0.254858i
$879$	11.6183	−	17.1063i	0.391874	−	0.576981i
$880$	17.9350	−	0.972681i	0.604587	−	0.0327891i
$881$	−40.1040			−1.35114			−0.675569	−	0.737297i	$-0.736102\pi$
$881$	−40.1040			−1.35114			−0.675569	+	0.737297i	$0.736102\pi$
$882$	−9.28590	−	28.2094i	−0.312672	−	0.949861i
$883$	57.5009			1.93506			0.967530	−	0.252757i	$-0.0813374\pi$
$883$	57.5009			1.93506			0.967530	+	0.252757i	$0.0813374\pi$
$884$	9.65407	−	5.23925i	0.324701	−	0.176215i
$885$	0.244720	+	7.21190i	0.00822618	+	0.242425i
$886$	4.57091	+	18.0055i	0.153563	+	0.604905i
$887$		−	13.7551i		−	0.461850i	−0.972972	−	0.230925i	$-0.925825\pi$
$887$		−	13.7551i		−	0.461850i	0.972972	−	0.230925i	$-0.0741752\pi$
$888$	4.51342	+	30.0230i	0.151460	+	1.00751i
$889$	0.590172	−	3.79982i	0.0197937	−	0.127442i
$890$	−32.7182	−	27.0944i	−1.09672	−	0.908206i
$891$	−13.1606	+	12.3871i	−0.440898	+	0.414982i
$892$	11.4779	−	6.22902i	0.384307	−	0.208563i
$893$			18.1691i			0.608006i
$894$	−1.96233	+	5.40929i	−0.0656302	+	0.180914i
$895$	−18.1743	−	24.8985i	−0.607500	−	0.832265i
$896$	−0.460684	−	29.9297i	−0.0153904	−	0.999882i
$897$	−0.185950	−	0.126293i	−0.00620868	−	0.00421681i
$898$	3.61896	+	14.2556i	0.120766	+	0.475716i
$899$		−	71.7380i		−	2.39260i
$900$	25.3367	−	16.0640i	0.844556	−	0.535467i
$901$	−10.2972			−0.343051
$902$	−16.1926	+	4.11069i	−0.539155	+	0.136871i
$903$	−11.4389	+	12.2616i	−0.380664	+	0.408041i
$904$	29.5223	−	27.2739i	0.981898	−	0.907116i
$905$	30.9770	+	42.4379i	1.02971	+	1.41069i
$906$	6.95568	−	19.1738i	0.231087	−	0.637007i
$907$	−53.8251			−1.78723			−0.893617	−	0.448830i	$-0.851841\pi$
$907$	−53.8251			−1.78723			−0.893617	+	0.448830i	$0.851841\pi$
$908$	21.9011	−	11.8857i	0.726815	−	0.394442i
$909$	−43.6864	+	17.3257i	−1.44899	+	0.574656i
$910$	−8.32962	+	7.38057i	−0.276124	+	0.244664i
$911$			34.4197i			1.14038i	0.821514	+	0.570188i	$0.193130\pi$
$911$			34.4197i			1.14038i	−0.821514	+	0.570188i	$0.806870\pi$
$912$	−6.25933	−	14.8949i	−0.207267	−	0.493221i
$913$	20.4120			0.675540
$914$	−14.0695	−	55.4218i	−0.465378	−	1.83319i
$915$	43.8135	−	1.48672i	1.44843	−	0.0491494i
$916$	−6.42941	+	3.48923i	−0.212434	+	0.115287i
$917$	0.761329	−	4.90181i	0.0251413	−	0.161872i
$918$	−0.896686	−	30.3273i	−0.0295951	−	1.00095i
$919$	56.8106			1.87401			0.937005	−	0.349316i	$-0.113586\pi$
$919$	56.8106			1.87401			0.937005	+	0.349316i	$0.113586\pi$
$920$	0.605428	+	0.119219i	0.0199604	+	0.00393054i
$921$	−11.0411	−	7.49888i	−0.363816	−	0.247097i
$922$	6.35293	+	25.0251i	0.209223	+	0.824159i
$923$	−11.8210			−0.389092
$924$	−4.61547	+	17.8168i	−0.151838	+	0.586128i
$925$	−9.44454	+	29.5120i	−0.310534	+	0.970348i
$926$	−14.6571	−	57.7363i	−0.481661	−	1.89733i
$927$	−9.50475	−	23.9661i	−0.312177	−	0.787151i
$928$	−13.7697	+	40.4983i	−0.452013	+	1.32942i
$929$	8.90906			0.292297			0.146148	−	0.989263i	$-0.453312\pi$
$929$	8.90906			0.292297			0.146148	+	0.989263i	$0.453312\pi$
$930$	−14.4865	−	49.9026i	−0.475031	−	1.63637i
$931$	−15.5551	−	4.95135i	−0.509798	−	0.162274i
$932$	2.17729	−	1.18161i	0.0713196	−	0.0387051i
$933$	−26.1219	+	38.4608i	−0.855191	+	1.25915i
$934$	−44.5821	+	11.3177i	−1.45877	+	0.370327i
$935$	14.9748	−	10.9306i	0.489728	−	0.357470i
$936$	4.88299	−	10.1760i	0.159605	−	0.332612i
$937$	29.8344			0.974647			0.487323	−	0.873222i	$-0.337973\pi$
$937$	29.8344			0.974647			0.487323	+	0.873222i	$0.337973\pi$
$938$	−27.3125	+	2.58945i	−0.891784	+	0.0845485i
$939$	−7.98391	+	11.7552i	−0.260545	+	0.383617i
$940$	14.9368	−	31.4791i	0.487185	−	1.02673i
$941$		−	51.4975i		−	1.67877i	−0.543537	−	0.839385i	$-0.682915\pi$
$941$		−	51.4975i		−	1.67877i	0.543537	−	0.839385i	$-0.317085\pi$
$942$	32.3884	+	11.7495i	1.05527	+	0.382821i
$943$	−0.573937			−0.0186900
$944$	−6.24875	−	4.06151i	−0.203380	−	0.132191i
$945$	7.82559	+	29.7281i	0.254566	+	0.967055i
$946$	10.0726	−	2.55705i	0.327489	−	0.0831370i
$947$		−	8.19688i		−	0.266363i	−0.991092	−	0.133181i	$-0.957481\pi$
$947$		−	8.19688i		−	0.266363i	0.991092	−	0.133181i	$-0.0425193\pi$
$948$	−3.77400	+	37.8443i	−0.122574	+	1.22913i
$949$		−	9.11276i		−	0.295813i
$950$	1.00714	−	16.4591i	0.0326759	−	0.534003i
$951$	−44.0328	−	29.9062i	−1.42786	−	0.969777i
$952$	−17.2349	−	25.6438i	−0.558585	−	0.831119i
$953$	−16.6673			−0.539906			−0.269953	−	0.962873i	$-0.587008\pi$
$953$	−16.6673			−0.539906			−0.269953	+	0.962873i	$0.587008\pi$
$954$	−8.57360	+	6.20104i	−0.277581	+	0.200766i
$955$	24.8188	−	18.1162i	0.803119	−	0.586225i
$956$	18.7065	+	34.4694i	0.605012	+	1.11482i
$957$	14.7771	−	21.7572i	0.477675	−	0.703311i
$958$	−21.8656	+	5.55084i	−0.706444	+	0.179339i
$959$	−48.3629	−	7.51152i	−1.56172	−	0.242560i
$960$	−1.40045	+	30.9522i	−0.0451994	+	0.998978i
$961$	−59.0043			−1.90337
$962$	2.86854	+	11.2996i	0.0924854	+	0.364313i
$963$	−6.98621	+	2.77067i	−0.225127	+	0.0892835i
$964$	−23.1100	−	42.5835i	−0.744324	−	1.37152i
$965$	23.2327	−	16.9584i	0.747887	−	0.545910i
$966$	−0.304297	+	0.554254i	−0.00979059	+	0.0178328i
$967$		−	13.9782i		−	0.449509i	−0.974415	−	0.224754i	$-0.927842\pi$
$967$		−	13.9782i		−	0.449509i	0.974415	−	0.224754i	$-0.0721580\pi$
$968$	−14.4751	+	13.3727i	−0.465247	+	0.429813i
$969$	−13.7959	−	9.36993i	−0.443189	−	0.301006i
$970$	−23.5256	−	19.4819i	−0.755362	−	0.625526i
$971$			34.0060i			1.09130i	0.838012	+	0.545652i	$0.183718\pi$
$971$			34.0060i			1.09130i	−0.838012	+	0.545652i	$0.816282\pi$
$972$	−19.0098	−	24.7109i	−0.609740	−	0.792601i
$973$	−1.79181	−	0.278296i	−0.0574428	−	0.00892177i
$974$	−2.93147	−	11.5475i	−0.0939305	−	0.370006i
$975$	9.06887	−	7.10337i	0.290436	−	0.227490i
$976$	−24.6744	+	37.9623i	−0.789808	+	1.21514i
$977$	−24.4774			−0.783101			−0.391550	−	0.920157i	$-0.628061\pi$
$977$	−24.4774			−0.783101			−0.391550	+	0.920157i	$0.628061\pi$
$978$	8.86645	−	24.4410i	0.283518	−	0.781535i
$979$	−26.9763			−0.862166
$980$	22.8797	+	21.3663i	0.730864	+	0.682523i
$981$	−40.4127	+	16.0273i	−1.29028	+	0.511712i
$982$	23.2593	−	5.90465i	0.742233	−	0.188425i
$983$			27.1165i			0.864881i	0.901663	+	0.432440i	$0.142347\pi$
$983$			27.1165i			0.864881i	−0.901663	+	0.432440i	$0.857653\pi$
$984$	−4.28425	−	28.4986i	−0.136577	−	0.908502i
$985$	−46.1876	+	33.7140i	−1.47166	+	1.07422i
$986$	10.8641	+	42.7954i	0.345984	+	1.36288i
$987$	26.1068	+	24.3552i	0.830989	+	0.775235i
$988$	−2.95920	−	5.45275i	−0.0941448	−	0.173475i
$989$	0.357017			0.0113525
$990$	5.88571	−	18.1189i	0.187060	−	0.575856i
$991$	37.8179			1.20133			0.600663	−	0.799502i	$-0.294903\pi$
$991$	37.8179			1.20133			0.600663	+	0.799502i	$0.294903\pi$
$992$	50.8103	+	17.2759i	1.61323	+	0.548509i
$993$	−29.1233	−	19.7800i	−0.924202	−	0.627700i
$994$	3.13842	+	33.1028i	0.0995446	+	1.04996i
$995$	30.9158	−	22.5666i	0.980097	−	0.715408i
$996$	−3.49410	+	35.0376i	−0.110715	+	1.11021i
$997$			28.4532i			0.901122i	0.892746	+	0.450561i	$0.148776\pi$
$997$			28.4532i			0.901122i	−0.892746	+	0.450561i	$0.851224\pi$
$998$	12.0614	+	47.5117i	0.381798	+	1.50396i
$999$	31.4325	+	6.99763i	0.994480	+	0.221395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.u.e.629.154	yes	160
3.2	odd	2	inner	840.2.u.e.629.8	yes	160
5.4	even	2	inner	840.2.u.e.629.7	yes	160
7.6	odd	2	inner	840.2.u.e.629.155	yes	160
8.5	even	2	inner	840.2.u.e.629.159	yes	160
15.14	odd	2	inner	840.2.u.e.629.153	yes	160
21.20	even	2	inner	840.2.u.e.629.5	yes	160
24.5	odd	2	inner	840.2.u.e.629.1	✓	160
35.34	odd	2	inner	840.2.u.e.629.6	yes	160
40.29	even	2	inner	840.2.u.e.629.2	yes	160
56.13	odd	2	inner	840.2.u.e.629.158	yes	160
105.104	even	2	inner	840.2.u.e.629.156	yes	160
120.29	odd	2	inner	840.2.u.e.629.160	yes	160
168.125	even	2	inner	840.2.u.e.629.4	yes	160
280.69	odd	2	inner	840.2.u.e.629.3	yes	160
840.629	even	2	inner	840.2.u.e.629.157	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.1	✓	160	24.5	odd	2	inner
840.2.u.e.629.2	yes	160	40.29	even	2	inner
840.2.u.e.629.3	yes	160	280.69	odd	2	inner
840.2.u.e.629.4	yes	160	168.125	even	2	inner
840.2.u.e.629.5	yes	160	21.20	even	2	inner
840.2.u.e.629.6	yes	160	35.34	odd	2	inner
840.2.u.e.629.7	yes	160	5.4	even	2	inner
840.2.u.e.629.8	yes	160	3.2	odd	2	inner
840.2.u.e.629.153	yes	160	15.14	odd	2	inner
840.2.u.e.629.154	yes	160	1.1	even	1	trivial
840.2.u.e.629.155	yes	160	7.6	odd	2	inner
840.2.u.e.629.156	yes	160	105.104	even	2	inner
840.2.u.e.629.157	yes	160	840.629	even	2	inner
840.2.u.e.629.158	yes	160	56.13	odd	2	inner
840.2.u.e.629.159	yes	160	8.5	even	2	inner
840.2.u.e.629.160	yes	160	120.29	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.u (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37073 - 0.347977i) q^{2} +(-0.973146 + 1.43282i) q^{3} +(1.75782 - 0.953969i) q^{4} +(1.31834 + 1.80610i) q^{5} +(-0.835334 + 2.30265i) q^{6} +(2.61441 + 0.406058i) q^{7} +(2.07755 - 1.91932i) q^{8} +(-1.10597 - 2.78870i) q^{9} +(2.43557 + 2.01693i) q^{10} +2.00814 q^{11} +(-0.343750 + 3.44700i) q^{12} +1.33017i q^{13} +(3.72495 - 0.353156i) q^{14} +(-3.87076 + 0.131346i) q^{15} +(2.17989 - 3.35382i) q^{16} -4.12882i q^{17} +(-2.48640 - 3.43771i) q^{18} -2.33202 q^{19} +(4.04036 + 1.91715i) q^{20} +(-3.12601 + 3.35083i) q^{21} +(2.75262 - 0.698786i) q^{22} +0.0975649 q^{23} +(0.728290 + 4.84454i) q^{24} +(-1.52398 + 4.76209i) q^{25} +(0.462871 + 1.82332i) q^{26} +(5.07198 + 1.12915i) q^{27} +(4.98303 - 1.78028i) q^{28} -7.56166 q^{29} +(-5.26007 + 1.52698i) q^{30} +9.48706i q^{31} +(1.82099 - 5.35574i) q^{32} +(-1.95421 + 2.87731i) q^{33} +(-1.43674 - 5.65952i) q^{34} +(2.71328 + 5.25719i) q^{35} +(-4.60443 - 3.84697i) q^{36} +6.19728 q^{37} +(-3.19658 + 0.811490i) q^{38} +(-1.90591 - 1.29445i) q^{39} +(6.20539 + 1.22195i) q^{40} -5.88262 q^{41} +(-3.11891 + 5.68088i) q^{42} +3.65928 q^{43} +(3.52995 - 1.91570i) q^{44} +(3.57862 - 5.67393i) q^{45} +(0.133736 - 0.0339504i) q^{46} -7.79115i q^{47} +(2.68408 + 6.38715i) q^{48} +(6.67023 + 2.12320i) q^{49} +(-0.431874 + 7.05787i) q^{50} +(5.91588 + 4.01795i) q^{51} +(1.26895 + 2.33821i) q^{52} -2.49399i q^{53} +(7.34526 - 0.217177i) q^{54} +(2.64740 + 3.62689i) q^{55} +(6.21091 - 4.17428i) q^{56} +(2.26939 - 3.34137i) q^{57} +(-10.3650 + 2.63129i) q^{58} -1.86318i q^{59} +(-6.67880 + 3.92346i) q^{60} -11.3191 q^{61} +(3.30128 + 13.0042i) q^{62} +(-1.75909 - 7.73987i) q^{63} +(0.632417 - 7.97496i) q^{64} +(-2.40243 + 1.75362i) q^{65} +(-1.67747 + 4.62404i) q^{66} -7.33230 q^{67} +(-3.93877 - 7.25774i) q^{68} +(-0.0949450 + 0.139793i) q^{69} +(5.54857 + 6.26205i) q^{70} +8.88677i q^{71} +(-7.65011 - 3.67094i) q^{72} -6.85080 q^{73} +(8.49482 - 2.15651i) q^{74} +(-5.34018 - 6.81781i) q^{75} +(-4.09928 + 2.22467i) q^{76} +(5.25008 + 0.815421i) q^{77} +(-3.06293 - 1.11114i) q^{78} +10.9789 q^{79} +(8.93115 - 0.484370i) q^{80} +(-6.55365 + 6.16844i) q^{81} +(-8.06351 + 2.04702i) q^{82} +10.1647 q^{83} +(-2.29839 + 8.87228i) q^{84} +(7.45706 - 5.44318i) q^{85} +(5.01590 - 1.27335i) q^{86} +(7.35861 - 10.8345i) q^{87} +(4.17200 - 3.85426i) q^{88} -13.4335 q^{89} +(2.93093 - 9.02273i) q^{90} +(-0.540128 + 3.47762i) q^{91} +(0.171502 - 0.0930739i) q^{92} +(-13.5933 - 9.23230i) q^{93} +(-2.71114 - 10.6796i) q^{94} +(-3.07438 - 4.21185i) q^{95} +(5.90175 + 7.82108i) q^{96} -9.65918 q^{97} +(9.88194 + 0.589255i) q^{98} +(-2.22094 - 5.60008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 24 q^{4} - 32 q^{9} - 48 q^{15} - 104 q^{16} - 16 q^{25} - 32 q^{30} + 48 q^{36} - 64 q^{39} - 64 q^{46} + 144 q^{49} + 16 q^{60} - 72 q^{64} + 8 q^{70} - 96 q^{79} + 16 q^{81} - 72 q^{84}+O(q^{100}) \) 160 * q - 24 * q^4 - 32 * q^9 - 48 * q^15 - 104 * q^16 - 16 * q^25 - 32 * q^30 + 48 * q^36 - 64 * q^39 - 64 * q^46 + 144 * q^49 + 16 * q^60 - 72 * q^64 + 8 * q^70 - 96 * q^79 + 16 * q^81 - 72 * q^84

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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