LMFDB - Embedded newform 840.2.u.e.629.155

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			629.155
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.160

$q$-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} +(-3.44236 + 1.46635i) 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} +(-1.96239 + 4.14114i) 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} +(-4.20830 + 3.20784i) 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} +(4.18005 + 4.18655i) 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} +(-1.24889 + 6.35927i) 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} +(-4.65220 + 5.86149i) 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} +(4.02383 + 6.84169i) 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} +(7.18656 + 4.28409i) 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} +(0.500984 + 9.15145i) 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} +(8.40429 - 5.23144i) 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	$-0.940946\pi$
$13$		−	1.33017i		−	0.368924i	0.982840	−	0.184462i	$-0.0590543\pi$
$14$	−3.44236	+	1.46635i	−0.920008	+	0.391899i
$15$	−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	$0.166922\pi$
$17$			4.12882i			1.00139i	−0.865625	+	0.500693i	$0.833078\pi$
$18$	−2.48640	−	3.43771i	−0.586049	−	0.810275i
$19$	2.33202			0.535002			0.267501	−	0.963558i	$-0.413802\pi$
$19$	2.33202			0.535002			0.267501	+	0.963558i	$0.413802\pi$
$20$	−4.04036	−	1.91715i	−0.903453	−	0.428688i
$21$	−1.96239	+	4.14114i	−0.428228	+	0.903671i
$22$	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
$28$	−4.20830	+	3.20784i	−0.795293	+	0.606225i
$29$	−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	$-0.675412\pi$
$31$		−	9.48706i		−	1.70393i	0.523602	−	0.851963i	$-0.324588\pi$
$32$	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
$35$	4.18005	+	4.18655i	0.706557	+	0.707656i
$36$	−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	$-0.348080\pi$
$41$	5.88262			0.918711			0.459355	+	0.888253i	$0.348080\pi$
$42$	−1.24889	+	6.35927i	−0.192708	+	0.981256i
$43$	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	$0.192371\pi$
$47$			7.79115i			1.13646i	−0.822871	+	0.568228i	$0.807629\pi$
$48$	−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
$56$	−4.65220	+	5.86149i	−0.621676	+	0.783274i
$57$	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	$0.0387007\pi$
$59$			1.86318i			0.242565i	−0.992618	+	0.121282i	$0.961299\pi$
$60$	−6.67880	+	3.92346i	−0.862230	+	0.506517i
$61$	11.3191			1.44926			0.724632	−	0.689136i	$-0.242010\pi$
$61$	11.3191			1.44926			0.724632	+	0.689136i	$0.242010\pi$
$62$	−3.30128	−	13.0042i	−0.419263	−	1.65154i
$63$	4.02383	+	6.84169i	0.506955	+	0.861972i
$64$	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
$70$	7.18656	+	4.28409i	0.858958	+	0.512046i
$71$			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	$-0.368693\pi$
$73$	6.85080			0.801825			0.400913	+	0.916116i	$0.368693\pi$
$74$	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	$-0.688377\pi$
$83$	−10.1647			−1.11572			−0.557858	+	0.829936i	$0.688377\pi$
$84$	0.500984	+	9.15145i	0.0546618	+	0.998505i
$85$	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	$-0.247802\pi$
$89$	13.4335			1.42395			0.711974	+	0.702206i	$0.247802\pi$
$90$	−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	$-0.336861\pi$
$97$	9.65918			0.980742			0.490371	+	0.871514i	$0.336861\pi$
$98$	8.40429	−	5.23144i	0.848961	−	0.528455i
$99$	−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	$0.284471\pi$
$101$			15.6655i			1.55878i	−0.626539	+	0.779390i	$0.715529\pi$
$102$	9.50725	+	3.44895i	0.941358	+	0.341497i
$103$	−8.59402			−0.846794			−0.423397	−	0.905944i	$-0.639162\pi$
$103$	−8.59402			−0.846794			−0.423397	+	0.905944i	$0.639162\pi$
$104$	−2.55303	−	2.76350i	−0.250345	−	0.270984i
$105$	10.0664	−	1.91514i	0.982379	−	0.186899i
$106$	−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
$112$	−4.33726	+	9.65340i	−0.409833	+	0.912161i
$113$	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
$126$	7.89636	+	7.97794i	0.703464	+	0.710731i
$127$		−	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	$0.0261009\pi$
$131$			1.87492i			0.163813i	−0.996640	+	0.0819064i	$0.973899\pi$
$132$	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	$-0.490747\pi$
$139$	0.685361			0.0581315			0.0290658	+	0.999578i	$0.490747\pi$
$140$	11.3416	+	3.37158i	0.958542	+	0.284951i
$141$	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
$147$	3.44894	−	11.6235i	0.284464	−	0.958687i
$148$	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
$154$	−6.91272	+	2.94464i	−0.557043	+	0.237285i
$155$	−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	$0.189691\pi$
$157$			14.0657i			1.12256i	−0.827625	+	0.561281i	$0.810309\pi$
$158$	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	$0.00569449\pi$
$167$			0.462349i			0.0357776i	−0.999840	+	0.0178888i	$0.994306\pi$
$168$	3.87121	+	12.3699i	0.298671	+	0.954356i
$169$	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	$-0.546804\pi$
$173$	−3.85404			−0.293017			−0.146508	+	0.989209i	$0.546804\pi$
$174$	−6.31652	+	17.4119i	−0.478854	+	1.31999i
$175$	2.05062	−	13.0689i	0.155012	−	0.987913i
$176$	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	$-0.837999\pi$
$181$	−23.4970			−1.74652			−0.873260	+	0.487254i	$0.837999\pi$
$182$	1.95050	+	4.57893i	0.144581	+	0.339413i
$183$	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
$189$	13.7187	+	0.892524i	0.997890	+	0.0649216i
$190$	−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
$196$	9.69962	−	10.0954i	0.692830	−	0.721101i
$197$			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	$0.207512\pi$
$199$			17.1175i			1.21342i	−0.794921	+	0.606712i	$0.792488\pi$
$200$	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
$210$	13.1319	−	6.12803i	0.906188	−	0.422874i
$211$			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	$-0.570158\pi$
$223$	−6.52959			−0.437253			−0.218627	+	0.975809i	$0.570158\pi$
$224$	−2.58607	+	14.7415i	−0.172789	+	0.984959i
$225$	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	$-0.635685\pi$
$227$	−12.4592			−0.826949			−0.413474	+	0.910516i	$0.635685\pi$
$228$	0.801630	−	8.03847i	0.0530892	−	0.532361i
$229$	3.65759			0.241701			0.120850	−	0.992671i	$-0.461438\pi$
$229$	3.65759			0.241701			0.120850	+	0.992671i	$0.461438\pi$
$230$	−0.237626	−	0.196782i	−0.0156686	−	0.0129754i
$231$	−3.94075	+	8.31597i	−0.259282	+	0.547151i
$232$	−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
$238$	−6.05431	−	14.2129i	−0.392443	−	0.921284i
$239$			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	$0.284902\pi$
$241$			24.2251i			1.56048i	−0.625482	+	0.780239i	$0.715098\pi$
$242$	−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
$245$	−12.6283	−	9.24800i	−0.806794	−	0.590833i
$246$	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	$-0.847091\pi$
$251$		−	14.6425i		−	0.924229i	0.886820	−	0.462115i	$-0.152909\pi$
$252$	13.6000	+	8.18788i	0.856716	+	0.515788i
$253$	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	$-0.835900\pi$
$257$		−	15.8068i		−	0.986002i	0.870029	−	0.493001i	$-0.164100\pi$
$258$	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
$266$	−8.02763	+	3.41956i	−0.492206	+	0.209667i
$267$	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	$0.0918575\pi$
$269$			9.33525i			0.569180i	−0.958649	+	0.284590i	$0.908142\pi$
$270$	10.0758	+	12.9799i	0.613191	+	0.789934i
$271$			0.207201i			0.0125865i	0.999980	+	0.00629327i	$0.00200322\pi$
$271$			0.207201i			0.0125865i	−0.999980	+	0.00629327i	$0.997997\pi$
$272$	13.8473	+	9.00037i	0.839617	+	0.545727i
$273$	5.50844	+	2.61032i	0.333386	+	0.157984i
$274$	−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
$280$	16.7196	+	0.674917i	0.999186	+	0.0403340i
$281$		−	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	$-0.790495\pi$
$283$		−	20.5801i		−	1.22336i	0.791106	−	0.611679i	$-0.209505\pi$
$284$	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	$-0.386610\pi$
$293$	11.9389			0.697476			0.348738	+	0.937220i	$0.386610\pi$
$294$	0.682874	−	17.1328i	0.0398260	−	0.999207i
$295$	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	$-0.929428\pi$
$307$		−	7.70581i		−	0.439794i	0.975523	−	0.219897i	$-0.0705721\pi$
$308$	−8.45083	+	6.44178i	−0.481531	+	0.367055i
$309$	−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	$-0.775318\pi$
$311$	−26.8427			−1.52211			−0.761054	+	0.648688i	$0.775318\pi$
$312$	−6.44409	+	0.968753i	−0.364825	+	0.0548449i
$313$	−8.20422			−0.463730			−0.231865	−	0.972748i	$-0.574483\pi$
$313$	−8.20422			−0.463730			−0.231865	+	0.972748i	$0.574483\pi$
$314$	4.89454	+	19.2803i	0.276215	+	1.08805i
$315$	7.05201	−	16.2871i	0.397336	−	0.917673i
$316$	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
$322$	−0.335853	+	0.143065i	−0.0187164	+	0.00797267i
$323$			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
$336$	9.61084	+	15.6087i	0.524314	+	0.851525i
$337$			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	$-0.480430\pi$
$349$	2.29568			0.122885			0.0614423	+	0.998111i	$0.480430\pi$
$350$	−1.73681	−	18.6275i	−0.0928365	−	0.995681i
$351$	−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	$-0.867407\pi$
$353$		−	15.2039i		−	0.809221i	0.914489	−	0.404610i	$-0.132593\pi$
$354$	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
$357$	−17.0980	−	8.10236i	−0.904924	−	0.428822i
$358$	−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
$364$	4.26699	+	5.59777i	0.223651	+	0.293403i
$365$	−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	$-0.438604\pi$
$367$	7.34446			0.383378			0.191689	+	0.981456i	$0.438604\pi$
$368$	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
$378$	19.1153	−	3.55039i	0.983185	−	0.182613i
$379$		−	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	$0.121972\pi$
$383$			14.6339i			0.747757i	−0.927478	+	0.373878i	$0.878028\pi$
$384$	−17.8353	−	8.11800i	−0.910154	−	0.414270i
$385$	8.39410	+	8.40717i	0.427803	+	0.428469i
$386$	−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
$392$	9.78263	−	17.2134i	0.494097	−	0.869407i
$393$	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	$0.0600601\pi$
$397$			7.47449i			0.375134i	−0.982252	+	0.187567i	$0.939940\pi$
$398$	5.95649	+	23.4635i	0.298572	+	1.17612i
$399$	−4.57633	+	9.65721i	−0.229103	+	0.483465i
$400$	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
$406$	26.0299	−	11.0881i	1.29184	−	0.550291i
$407$	12.4450			0.616875
$408$	20.0023	−	3.00698i	0.990260	−	0.148868i
$409$		−	24.7533i		−	1.22397i	−0.790868	−	0.611986i	$-0.790371\pi$
$409$		−	24.7533i		−	1.22397i	0.790868	−	0.611986i	$-0.209629\pi$
$410$	−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	$0.0913918\pi$
$419$			11.5934i			0.566374i	−0.959065	+	0.283187i	$0.908608\pi$
$420$	15.8679	−	12.9695i	0.774277	−	0.632847i
$421$			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	$-0.701806\pi$
$433$	−24.6527			−1.18473			−0.592366	+	0.805669i	$0.701806\pi$
$434$	13.9114	+	32.6578i	0.667767	+	1.56763i
$435$	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	$0.0419700\pi$
$439$			5.50924i			0.262942i	−0.991320	+	0.131471i	$0.958030\pi$
$440$	−12.4613	−	2.45384i	−0.594068	−	0.116982i
$441$	−13.2981	−	16.2531i	−0.633241	−	0.773955i
$442$	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
$448$	1.58491	+	21.1066i	0.0748798	+	0.997193i
$449$			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
$455$	5.56884	−	5.56019i	0.261071	−	0.260666i
$456$	−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	$-0.860221\pi$
$461$		−	18.2567i		−	0.850301i	0.905123	−	0.425151i	$-0.139779\pi$
$462$	−2.50794	+	12.7703i	−0.116680	+	0.594127i
$463$		−	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	$-0.228837\pi$
$467$	32.5243			1.50504			0.752521	+	0.658568i	$0.228837\pi$
$468$	−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
$476$	−13.2446	−	17.3753i	−0.607066	−	0.796396i
$477$	−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	$-0.381265\pi$
$479$	15.9517			0.728852			0.364426	+	0.931232i	$0.381265\pi$
$480$	−6.34516	+	20.9700i	−0.289616	+	0.957143i
$481$		−	8.24346i		−	0.375869i
$482$	8.42980	+	33.2062i	0.383967	+	1.51250i
$483$	−0.191460	+	0.404030i	−0.00871175	+	0.0183840i
$484$	−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
$490$	−20.5282	−	8.28218i	−0.927368	−	0.374151i
$491$	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	$-0.851175\pi$
$503$		−	20.2162i		−	0.901396i	0.892676	−	0.450698i	$-0.148825\pi$
$504$	21.4911	+	6.49093i	0.957290	+	0.289129i
$505$	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	$-0.983504\pi$
$509$		−	2.33728i		−	0.103598i	0.998658	−	0.0517992i	$-0.0164956\pi$
$510$	−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
$518$	−21.3332	+	9.08739i	−0.937329	+	0.399277i
$519$	−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	$-0.629464\pi$
$521$	−18.0595			−0.791203			−0.395601	+	0.918422i	$0.629464\pi$
$522$	18.8013	+	25.9948i	0.822910	+	1.13776i
$523$		−	15.6316i		−	0.683522i	−0.939787	−	0.341761i	$-0.888977\pi$
$523$		−	15.6316i		−	0.683522i	0.939787	−	0.341761i	$-0.111023\pi$
$524$	1.78862	+	3.29579i	0.0781362	+	0.143977i
$525$	−16.7298	−	15.6561i	−0.730149	−	0.683288i
$526$	−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
$532$	−9.81382	+	7.48074i	−0.425483	+	0.324331i
$533$		−	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
$546$	8.45893	+	1.66124i	0.362009	+	0.0710946i
$547$	−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
$560$	23.1530	−	4.89291i	0.978391	−	0.206763i
$561$	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	$-0.722411\pi$
$563$	−30.5252			−1.28649			−0.643243	+	0.765662i	$0.722411\pi$
$564$	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
$567$	14.6292	−	18.7880i	0.614367	−	0.789020i
$568$	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
$574$	−20.2501	+	8.62599i	−0.845221	+	0.360042i
$575$	−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	$-0.494655\pi$
$577$	0.806615			0.0335798			0.0167899	+	0.999859i	$0.494655\pi$
$578$	−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	$-0.481339\pi$
$587$	2.83907			0.117181			0.0585905	+	0.998282i	$0.481339\pi$
$588$	−5.02580	−	23.7222i	−0.207260	−	0.978286i
$589$		−	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	$0.233753\pi$
$593$			32.6365i			1.34022i	−0.742262	+	0.670110i	$0.766247\pi$
$594$	−14.7503	+	0.436121i	−0.605211	+	0.0178943i
$595$	−17.2855	+	17.2587i	−0.708638	+	0.707537i
$596$	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	$-0.727890\pi$
$601$		−	36.9925i		−	1.50896i	0.656325	−	0.754479i	$-0.272110\pi$
$602$	−12.5965	+	5.36579i	−0.513396	+	0.218693i
$603$	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	$-0.297857\pi$
$607$	29.2308			1.18644			0.593220	+	0.805041i	$0.297857\pi$
$608$	4.24658	−	12.4897i	0.172222	−	0.506524i
$609$	14.8389	−	31.3139i	0.601304	−	1.26890i
$610$	−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
$616$	−9.34225	+	11.7707i	−0.376410	+	0.474254i
$617$	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	$-0.551917\pi$
$619$	−8.07998			−0.324762			−0.162381	+	0.986728i	$0.551917\pi$
$620$	−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
$630$	3.99889	−	24.7792i	0.159320	−	0.987227i
$631$	−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	$-0.936809\pi$
$643$		−	10.0020i		−	0.394440i	0.980359	−	0.197220i	$-0.0631913\pi$
$644$	−0.410582	+	0.312973i	−0.0161792	+	0.0123329i
$645$	−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	$-0.719470\pi$
$647$		−	39.2518i		−	1.54315i	0.636140	−	0.771573i	$-0.280530\pi$
$648$	−1.77632	+	25.3938i	−0.0697804	+	0.997562i
$649$			3.74151i			0.146867i
$650$	9.38819	+	0.574468i	0.368235	+	0.0225325i
$651$	39.2872	+	18.6173i	1.53979	+	0.729670i
$652$	−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
$658$	−11.4246	−	26.8199i	−0.445376	−	1.04555i
$659$	−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	$-0.299133\pi$
$661$	30.3370			1.17997			0.589987	+	0.807413i	$0.299133\pi$
$662$	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
$665$	9.74794	+	9.76311i	0.378009	+	0.378597i
$666$	−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
$672$	18.6054	+	18.0510i	0.717718	+	0.696334i
$673$			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	$-0.379948\pi$
$677$	19.1645			0.736552			0.368276	+	0.929717i	$0.379948\pi$
$678$	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
$686$	−19.8480	+	17.0897i	−0.757798	+	0.652489i
$687$	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	$-0.746664\pi$
$691$	−36.7836			−1.39931			−0.699657	+	0.714479i	$0.746664\pi$
$692$	−6.77472	+	3.67663i	−0.257536	+	0.139765i
$693$	8.08041	+	13.7391i	0.306949	+	0.521904i
$694$	−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
$700$	−8.86265	−	24.9290i	−0.334977	−	0.942226i
$701$	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
$714$	−26.2563	−	5.15645i	−0.982617	−	0.192975i
$715$	−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	$-0.179554\pi$
$719$	45.3201			1.69015			0.845077	+	0.534644i	$0.179554\pi$
$720$	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	$-0.382659\pi$
$727$	19.4319			0.720688			0.360344	+	0.932819i	$0.382659\pi$
$728$	7.79680	+	6.18824i	0.288969	+	0.229351i
$729$	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	$-0.790730\pi$
$733$		−	33.0895i		−	1.22219i	0.791558	−	0.611094i	$-0.209270\pi$
$734$	10.0673	−	2.55571i	0.371591	−	0.0943329i
$735$	−25.5400	+	9.09450i	−0.942056	+	0.335456i
$736$	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
$742$	3.65706	+	8.58519i	0.134255	+	0.315172i
$743$	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
$756$	24.9665	−	11.5183i	0.908024	−	0.418918i
$757$	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	$-0.226262\pi$
$761$	41.8111			1.51565			0.757825	+	0.652457i	$0.226262\pi$
$762$	−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	$0.0525940\pi$
$769$			9.12224i			0.328956i	−0.986381	+	0.164478i	$0.947406\pi$
$770$	14.4316	+	8.60303i	0.520078	+	0.310032i
$771$	−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	$-0.604394\pi$
$773$	−17.9114			−0.644228			−0.322114	+	0.946701i	$0.604394\pi$
$774$	−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
$777$	−12.1615	+	25.6638i	−0.436290	+	0.920683i
$778$	−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
$784$	7.41952	−	26.9991i	0.264983	−	0.964253i
$785$	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	$0.228579\pi$
$787$			36.9161i			1.31592i	−0.753055	+	0.657958i	$0.771421\pi$
$788$	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	$-0.676833\pi$
$797$	−29.7782			−1.05480			−0.527399	+	0.849618i	$0.676833\pi$
$798$	−2.91244	+	14.8299i	−0.103099	+	0.524974i
$799$	−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
$805$	0.407826	+	0.408461i	0.0143740	+	0.0143963i
$806$	−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	$-0.483609\pi$
$811$	2.93155			0.102941			0.0514703	+	0.998675i	$0.483609\pi$
$812$	31.8217	−	24.2566i	1.11672	−	0.851240i
$813$	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
$819$	9.10065	−	5.35240i	0.318002	−	0.187028i
$820$	−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
$826$	−2.73207	−	6.41371i	−0.0950610	−	0.223162i
$827$		−	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	$-0.648902\pi$
$829$	−25.9657			−0.901827			−0.450913	+	0.892568i	$0.648902\pi$
$830$	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	$-0.488232\pi$
$839$	2.14123			0.0739234			0.0369617	+	0.999317i	$0.488232\pi$
$840$	17.2376	−	23.2994i	0.594755	−	0.803907i
$841$	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	$0.277029\pi$
$853$			44.6580i			1.52906i	−0.644587	+	0.764531i	$0.722971\pi$
$854$	−38.9644	+	16.5978i	−1.33333	+	0.567965i
$855$	−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	$0.128794\pi$
$857$			23.0490i			0.787338i	−0.919252	+	0.393669i	$0.871206\pi$
$858$	−6.15079	−	2.23132i	−0.209984	−	0.0761761i
$859$	14.2677			0.486806			0.243403	−	0.969925i	$-0.421736\pi$
$859$	14.2677			0.486806			0.243403	+	0.969925i	$0.421736\pi$
$860$	−14.7848	−	7.01539i	−0.504158	−	0.239223i
$861$	−11.5440	+	24.3607i	−0.393418	+	0.830212i
$862$	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
$868$	30.4330	+	39.9244i	1.03296	+	1.35512i
$869$	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
$875$	−26.3070	+	13.5255i	−0.889340	+	0.457246i
$876$	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	$-0.263898\pi$
$881$	40.1040			1.35114			0.675569	+	0.737297i	$0.263898\pi$
$882$	−23.8838	−	17.6512i	−0.804209	−	0.594346i
$883$	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	$0.0741752\pi$
$887$			13.7551i			0.461850i	−0.972972	+	0.230925i	$0.925825\pi$
$888$	−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
$896$	9.51710	+	28.3800i	0.317944	+	0.948109i
$897$	−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
$903$	−7.18093	+	15.1536i	−0.238966	+	0.504279i
$904$	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
$910$	5.69858	−	9.55937i	0.188906	−	0.316890i
$911$			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
$924$	1.00604	+	18.3774i	0.0330964	+	0.604571i
$925$	−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	$-0.546688\pi$
$929$	−8.90906			−0.292297			−0.146148	+	0.989263i	$0.546688\pi$
$930$	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	$-0.662027\pi$
$937$	−29.8344			−0.974647			−0.487323	+	0.873222i	$0.662027\pi$
$938$	25.2404	−	10.7517i	0.824128	−	0.351057i
$939$	−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	$0.317085\pi$
$941$			51.4975i			1.67877i	−0.543537	+	0.839385i	$0.682915\pi$
$942$	32.3884	+	11.7495i	1.05527	+	0.382821i
$943$	0.573937			0.0186900
$944$	6.24875	+	4.06151i	0.203380	+	0.132191i
$945$	−16.4739	−	25.9540i	−0.535896	−	0.844284i
$946$	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
$952$	−24.2011	−	19.2081i	−0.784361	−	0.622538i
$953$	−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
$966$	−0.121848	+	0.620441i	−0.00392039	+	0.0199624i
$967$		−	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	$-0.816282\pi$
$971$		−	34.0060i		−	1.09130i	0.838012	−	0.545652i	$-0.183718\pi$
$972$	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
$980$	−31.0207	−	4.20933i	−0.990919	−	0.134462i
$981$	−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	$-0.857653\pi$
$983$		−	27.1165i		−	0.864881i	0.901663	−	0.432440i	$-0.142347\pi$
$984$	−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
$987$	−32.2642	−	15.2893i	−1.02698	−	0.486663i
$988$	−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
$994$	−13.0311	−	30.5914i	−0.413323	−	0.970301i
$995$	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	$-0.851224\pi$
$997$		−	28.4532i		−	0.901122i	0.892746	−	0.450561i	$-0.148776\pi$
$998$	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.629.155	yes	160
3.2	odd	2	inner	840.2.u.e.629.5	yes	160
5.4	even	2	inner	840.2.u.e.629.6	yes	160
7.6	odd	2	inner	840.2.u.e.629.154	yes	160
8.5	even	2	inner	840.2.u.e.629.158	yes	160
15.14	odd	2	inner	840.2.u.e.629.156	yes	160
21.20	even	2	inner	840.2.u.e.629.8	yes	160
24.5	odd	2	inner	840.2.u.e.629.4	yes	160
35.34	odd	2	inner	840.2.u.e.629.7	yes	160
40.29	even	2	inner	840.2.u.e.629.3	yes	160
56.13	odd	2	inner	840.2.u.e.629.159	yes	160
105.104	even	2	inner	840.2.u.e.629.153	yes	160
120.29	odd	2	inner	840.2.u.e.629.157	yes	160
168.125	even	2	inner	840.2.u.e.629.1	✓	160
280.69	odd	2	inner	840.2.u.e.629.2	yes	160
840.629	even	2	inner	840.2.u.e.629.160	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.1	✓	160	168.125	even	2	inner
840.2.u.e.629.2	yes	160	280.69	odd	2	inner
840.2.u.e.629.3	yes	160	40.29	even	2	inner
840.2.u.e.629.4	yes	160	24.5	odd	2	inner
840.2.u.e.629.5	yes	160	3.2	odd	2	inner
840.2.u.e.629.6	yes	160	5.4	even	2	inner
840.2.u.e.629.7	yes	160	35.34	odd	2	inner
840.2.u.e.629.8	yes	160	21.20	even	2	inner
840.2.u.e.629.153	yes	160	105.104	even	2	inner
840.2.u.e.629.154	yes	160	7.6	odd	2	inner
840.2.u.e.629.155	yes	160	1.1	even	1	trivial
840.2.u.e.629.156	yes	160	15.14	odd	2	inner
840.2.u.e.629.157	yes	160	120.29	odd	2	inner
840.2.u.e.629.158	yes	160	8.5	even	2	inner
840.2.u.e.629.159	yes	160	56.13	odd	2	inner
840.2.u.e.629.160	yes	160	840.629	even	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} +(-3.44236 + 1.46635i) 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} +(-1.96239 + 4.14114i) 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} +(-4.20830 + 3.20784i) 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} +(4.18005 + 4.18655i) 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} +(-1.24889 + 6.35927i) 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} +(-4.65220 + 5.86149i) 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} +(4.02383 + 6.84169i) 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} +(7.18656 + 4.28409i) 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} +(0.500984 + 9.15145i) 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} +(8.40429 - 5.23144i) 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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