LMFDB - Embedded newform 840.2.u.e.629.3

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			629.3
Character	$\chi$	$=$	840.629
Dual form			840.2.u.e.629.8

$q$-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} +(-1.83252 + 1.62539i) 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} +(3.07749 - 1.59030i) q^{12} -1.33017i q^{13} +(-3.72495 - 0.353156i) q^{14} +(1.30489 + 3.64654i) q^{15} +(2.17989 + 3.35382i) q^{16} -4.12882i q^{17} +(0.545590 + 4.20741i) 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} +(-4.77181 + 1.10898i) 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} +(-0.519740 - 5.45251i) 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} +(0.716226 - 5.95710i) 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} +(-4.13094 + 4.99353i) q^{42} +3.65928 q^{43} +(-3.52995 - 1.91570i) q^{44} +(6.49470 + 1.67894i) q^{45} +(0.133736 + 0.0339504i) q^{46} -7.79115i q^{47} +(6.92678 + 0.140362i) 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} +(6.55942 + 3.31270i) 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} +(-1.18493 + 7.65480i) 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} +(3.67994 - 3.26400i) 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} +(-3.05469 + 7.91637i) q^{72} -6.85080 q^{73} +(-8.49482 - 2.15651i) q^{74} +(-8.30629 - 2.45061i) q^{75} +(-4.09928 - 2.22467i) q^{76} +(-5.25008 + 0.815421i) q^{77} +(2.16205 + 2.43757i) 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} +(7.40005 - 5.40733i) 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} +(-8.31827 - 4.56140i) 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} +(-9.44593 - 2.60276i) 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
$6$	−1.83252	+	1.62539i	−0.748121	+	0.663562i
$7$	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	$-0.597901\pi$
$11$	−2.00814			−0.605476			−0.302738	+	0.953074i	$0.597901\pi$
$12$	3.07749	−	1.59030i	0.888395	−	0.459080i
$13$		−	1.33017i		−	0.368924i	−0.982840	−	0.184462i	$-0.940946\pi$
$13$		−	1.33017i		−	0.368924i	0.982840	−	0.184462i	$-0.0590543\pi$
$14$	−3.72495	−	0.353156i	−0.995536	−	0.0943849i
$15$	1.30489	+	3.64654i	0.336921	+	0.941533i
$16$	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	$-0.166922\pi$
$18$	0.545590	+	4.20741i	0.128597	+	0.991697i
$19$	−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
$21$	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	$-0.503238\pi$
$23$	−0.0975649			−0.0203437			−0.0101718	+	0.999948i	$0.503238\pi$
$24$	−4.77181	+	1.10898i	−0.974041	+	0.226370i
$25$	−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	$-0.252254\pi$
$29$	7.56166			1.40417			0.702083	+	0.712095i	$0.252254\pi$
$30$	−0.519740	−	5.45251i	−0.0948911	−	0.995488i
$31$		−	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
$35$	−2.71328	+	5.25719i	−0.458629	+	0.888628i
$36$	0.716226	−	5.95710i	0.119371	−	0.992850i
$37$	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	$0.348080\pi$
$42$	−4.13094	+	4.99353i	−0.637417	+	0.770519i
$43$	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
$45$	6.49470	+	1.67894i	0.968173	+	0.250282i
$46$	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	$-0.192371\pi$
$48$	6.92678	+	0.140362i	0.999795	+	0.0202595i
$49$	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	$-0.0547928\pi$
$54$	6.55942	+	3.31270i	0.892625	+	0.450801i
$55$	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	$-0.0387007\pi$
$60$	−1.18493	+	7.65480i	−0.152973	+	0.988230i
$61$	−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
$63$	−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
$66$	3.67994	−	3.26400i	0.452969	−	0.401771i
$67$	−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	$0.823192\pi$
$72$	−3.05469	+	7.91637i	−0.359999	+	0.932953i
$73$	−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
$75$	−8.30629	−	2.45061i	−0.959128	−	0.282972i
$76$	−4.09928	−	2.22467i	−0.470219	−	0.255187i
$77$	−5.25008	+	0.815421i	−0.598303	+	0.0929258i
$78$	2.16205	+	2.43757i	0.244804	+	0.276000i
$79$	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	$0.688377\pi$
$84$	7.40005	−	5.40733i	0.807412	−	0.589988i
$85$	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	$0.247802\pi$
$90$	−8.31827	−	4.56140i	−0.876823	−	0.480813i
$91$	−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
$96$	−9.44593	−	2.60276i	−0.964071	−	0.265643i
$97$	−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	$-0.284471\pi$
$102$	6.71094	+	7.56613i	0.664482	+	0.749159i
$103$	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
$105$	4.89221	+	9.00368i	0.477431	+	0.878669i
$106$	−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	$-0.0386399\pi$
$108$	−7.83848	−	6.82336i	−0.754258	−	0.656578i
$109$			14.4916i			1.38804i	0.719954	+	0.694022i	$0.244163\pi$
$109$			14.4916i			1.38804i	−0.719954	+	0.694022i	$0.755837\pi$
$110$	−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	$-0.733016\pi$
$113$	−14.2102			−1.33678			−0.668390	+	0.743811i	$0.733016\pi$
$114$	4.27346	−	3.79043i	0.400246	−	0.355007i
$115$	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
$120$	4.28792	−	10.0804i	0.391431	−	0.920207i
$121$	−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
$126$	3.13485	+	10.7783i	0.279275	+	0.960211i
$127$			1.45342i			0.128970i	0.997919	+	0.0644849i	$0.0205404\pi$
$127$			1.45342i			0.128970i	−0.997919	+	0.0644849i	$0.979460\pi$
$128$	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	$-0.0261009\pi$
$132$	−6.18002	+	3.19354i	−0.537902	+	0.277962i
$133$	−6.09684	+	0.946935i	−0.528663	+	0.0821097i
$134$	10.0506	+	2.55148i	0.868243	+	0.220414i
$135$	8.72593	−	7.67191i	0.751008	−	0.660293i
$136$	−7.92454	+	8.57783i	−0.679523	+	0.735543i
$137$	18.4986			1.58044			0.790222	−	0.612821i	$-0.209965\pi$
$137$	18.4986			1.58044			0.790222	+	0.612821i	$0.209965\pi$
$138$	0.178789	−	0.158581i	0.0152196	−	0.0134993i
$139$	−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
$144$	6.94189	−	9.78827i	0.578491	−	0.815689i
$145$	−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	$-0.530677\pi$
$149$	−2.34916			−0.192450			−0.0962252	+	0.995360i	$0.530677\pi$
$150$	10.5330	+	6.24954i	0.860013	+	0.510273i
$151$	−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
$156$	−2.11538	−	4.09360i	−0.169366	−	0.327750i
$157$			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
$162$	11.1298	−	6.17477i	0.874439	−	0.485135i
$163$	−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
$165$	−2.62039	−	7.32275i	−0.203997	−	0.570076i
$166$	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	$-0.00569449\pi$
$168$	−12.0251	+	4.83696i	−0.927759	+	0.373180i
$169$	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	$0.546804\pi$
$174$	−13.8569	+	12.2906i	−1.05049	+	0.931751i
$175$	−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	$-0.327718\pi$
$179$	13.7858			1.03040			0.515199	+	0.857070i	$0.327718\pi$
$180$	9.81488	+	9.14703i	0.731558	+	0.681779i
$181$	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
$186$	15.4202	+	17.3852i	1.13066	+	1.27474i
$187$			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	$-0.165623\pi$
$192$	12.0422	+	6.85467i	0.869068	+	0.494693i
$193$			12.8635i			0.925933i	0.886376	+	0.462967i	$0.153215\pi$
$193$			12.8635i			0.925933i	−0.886376	+	0.462967i	$0.846785\pi$
$194$	13.2402	+	3.36118i	0.950589	+	0.241319i
$195$	4.85054	−	1.73573i	0.347354	−	0.124298i
$196$	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	$0.635307\pi$
$198$	−1.09562	−	8.44906i	−0.0778623	−	0.600449i
$199$			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
$204$	−6.56607	−	12.7064i	−0.459717	−	0.889627i
$205$	−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
$210$	−3.57285	−	14.0440i	−0.246550	−	0.969130i
$211$		−	17.3613i		−	1.19520i	−0.801795	−	0.597599i	$-0.796121\pi$
$211$		−	17.3613i		−	1.19520i	0.801795	−	0.597599i	$-0.203879\pi$
$212$	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
$216$	8.37010	+	12.0806i	0.569513	+	0.821982i
$217$	−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
$222$	−11.3566	+	10.0730i	−0.762206	+	0.676054i
$223$	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
$225$	−11.5945	+	9.51666i	−0.772969	+	0.634444i
$226$	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	$0.635685\pi$
$228$	−7.17676	+	3.70861i	−0.475293	+	0.245609i
$229$	−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
$231$	−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	$-0.512918\pi$
$233$	−1.23863			−0.0811454			−0.0405727	+	0.999177i	$0.512918\pi$
$234$	5.59659	−	0.725730i	0.365861	−	0.0474424i
$235$	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	$0.781328\pi$
$240$	−9.38533	+	12.3254i	−0.605821	+	0.795601i
$241$			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
$245$	−4.95890	+	14.8462i	−0.316812	+	0.948488i
$246$	−10.7800	+	9.56154i	−0.687307	+	0.609621i
$247$			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	$0.847091\pi$
$252$	−0.546424	−	15.8651i	−0.0344215	−	0.999407i
$253$	0.195924			0.0123176
$254$	0.505756	−	1.99225i	0.0317339	−	0.125005i
$255$	15.0559	−	5.38765i	0.942839	−	0.337388i
$256$	−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	$0.835900\pi$
$258$	−6.70568	+	5.94775i	−0.417478	+	0.370291i
$259$	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	$-0.355156\pi$
$263$	14.2549			0.878997			0.439499	+	0.898243i	$0.355156\pi$
$264$	9.58244	−	2.22699i	0.589759	−	0.137062i
$265$	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	$-0.0918575\pi$
$270$	−14.6306	+	7.47972i	−0.890389	+	0.455201i
$271$			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
$276$	−0.300255	+	0.155158i	−0.0180732	+	0.00933939i
$277$	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	$-0.0295715\pi$
$282$	12.6636	+	14.2774i	0.754109	+	0.850207i
$283$		−	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
$285$	−3.04302	−	8.50380i	−0.180253	−	0.503722i
$286$	0.929508	−	3.66147i	0.0549629	−	0.216507i
$287$	15.3796	−	2.38869i	0.907826	−	0.141000i
$288$	−12.9216	+	11.0015i	−0.761411	+	0.648269i
$289$	−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	$0.386610\pi$
$294$	−8.77228	+	14.7325i	−0.511610	+	0.859218i
$295$	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
$300$	−12.2632	−	12.2317i	−0.708016	−	0.706197i
$301$	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
$306$	17.3717	−	2.25265i	0.993072	−	0.128775i
$307$		−	7.70581i		−	0.439794i	−0.975523	−	0.219897i	$-0.929428\pi$
$307$		−	7.70581i		−	0.439794i	0.975523	−	0.219897i	$-0.0705721\pi$
$308$	−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	$-0.775318\pi$
$311$	−26.8427			−1.52211			−0.761054	+	0.648688i	$0.775318\pi$
$312$	1.47514	+	6.34734i	0.0835134	+	0.359347i
$313$	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
$315$	17.6615	+	1.75221i	0.995115	+	0.0987260i
$316$	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	$0.668566\pi$
$318$	4.05370	+	4.57027i	0.227320	+	0.256288i
$319$	−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
$324$	−17.4047	+	4.59105i	−0.966926	+	0.255058i
$325$	−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
$330$	1.04371	+	10.9494i	0.0574543	+	0.602744i
$331$		−	20.3258i		−	1.11721i	−0.829434	−	0.558604i	$-0.811337\pi$
$331$		−	20.3258i		−	1.11721i	0.829434	−	0.558604i	$-0.188663\pi$
$332$	−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
$336$	18.1664	−	2.44572i	0.991059	−	0.133425i
$337$		−	8.04781i		−	0.438392i	−0.975681	−	0.219196i	$-0.929657\pi$
$337$		−	8.04781i		−	0.438392i	0.975681	−	0.219196i	$-0.0703434\pi$
$338$	−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
$342$	−1.27233	−	9.81176i	−0.0687995	−	0.530559i
$343$	16.5766	−	8.25942i	0.895050	−	0.445967i
$344$	−7.60233	−	7.02333i	−0.409890	−	0.378672i
$345$	−0.127311	−	0.355775i	−0.00685421	−	0.0191543i
$346$	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	$-0.181475\pi$
$348$	23.2709	−	12.0253i	1.24745	−	0.644625i
$349$	−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	$0.867407\pi$
$354$	3.02838	+	3.41430i	0.160957	+	0.181468i
$355$	−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	$-0.278095\pi$
$360$	−10.2706	−	15.9535i	−0.541310	−	0.840823i
$361$	−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
$366$	20.7425	−	18.3980i	1.08423	−	0.961677i
$367$	−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
$372$	−15.0873	−	29.1963i	−0.782239	−	1.51376i
$373$	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
$375$	15.3765	−	11.7713i	0.794041	−	0.607865i
$376$	−14.9537	+	16.1865i	−0.771179	+	0.834755i
$377$		−	10.0583i		−	0.518030i
$378$	18.4941	+	5.99722i	0.951236	+	0.308464i
$379$			3.57410i			0.183589i	0.995778	+	0.0917945i	$0.0292603\pi$
$379$			3.57410i			0.183589i	−0.995778	+	0.0917945i	$0.970740\pi$
$380$	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	$-0.121972\pi$
$384$	−14.1213	−	13.5863i	−0.720626	−	0.693324i
$385$	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	$-0.389318\pi$
$389$	13.4414			0.681507			0.340754	+	0.940153i	$0.389318\pi$
$390$	−7.25279	+	0.691345i	−0.367259	+	0.0350076i
$391$			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
$396$	−1.43828	+	11.9627i	−0.0722763	+	0.601147i
$397$			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	$0.725570\pi$
$402$	13.4366	−	11.9178i	0.670155	−	0.594408i
$403$	−12.6194			−0.628619
$404$	14.9444	−	27.5373i	0.743514	−	1.37003i
$405$	−2.50089	−	19.9686i	−0.124270	−	0.992248i
$406$	−28.1668	−	2.67045i	−1.39790	−	0.132532i
$407$	−12.4450			−0.616875
$408$	4.57879	+	19.7020i	0.226684	+	0.975392i
$409$		−	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
$414$	−0.0532304	−	0.410496i	−0.00261613	−	0.0201748i
$415$	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	$-0.0913918\pi$
$420$	0.0104195	+	20.4939i	0.000508419	+	1.00000i
$421$		−	12.7176i		−	0.619816i	−0.950767	−	0.309908i	$-0.899702\pi$
$421$		−	12.7176i		−	0.619816i	0.950767	−	0.309908i	$-0.100298\pi$
$422$	−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
$426$	−14.4445	−	16.2851i	−0.699836	−	0.789018i
$427$	−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	$0.980759\pi$
$432$	−7.26940	−	19.4719i	−0.349749	−	0.936843i
$433$	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
$435$	9.86712	+	27.5739i	0.473092	+	1.32207i
$436$	−13.8245	+	25.4737i	−0.662075	+	1.21997i
$437$	0.227523			0.0108839
$438$	12.5542	−	11.1352i	0.599863	−	0.532061i
$439$			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	$0.898986\pi$
$444$	19.0721	−	9.85554i	0.905120	−	0.467723i
$445$	−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	$0.921080\pi$
$450$	19.2046	−	9.01017i	0.905314	−	0.424743i
$451$	−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
$456$	11.1279	−	2.58617i	0.521114	−	0.121108i
$457$			40.4322i			1.89134i	0.325129	+	0.945670i	$0.394592\pi$
$457$			40.4322i			1.89134i	−0.325129	+	0.945670i	$0.605408\pi$
$458$	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	$0.860221\pi$
$462$	8.29548	−	10.0277i	0.385941	−	0.466531i
$463$			42.1208i			1.95752i	0.205016	+	0.978759i	$0.434275\pi$
$463$			42.1208i			1.95752i	−0.205016	+	0.978759i	$0.565725\pi$
$464$	16.4836	+	25.3604i	0.765230	+	1.17733i
$465$	34.5950	−	12.3796i	1.60430	−	0.574088i
$466$	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	$0.228837\pi$
$468$	−7.92398	−	0.952706i	−0.366286	−	0.0440388i
$469$	−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
$474$	−20.1190	+	17.8450i	−0.924097	+	0.819648i
$475$	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	$-0.381265\pi$
$479$	15.9517			0.728852			0.364426	+	0.931232i	$0.381265\pi$
$480$	17.1538	−	13.6290i	0.782958	−	0.622074i
$481$		−	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
$486$	1.98356	−	21.9560i	0.0899762	−	0.995944i
$487$			8.42432i			0.381742i	0.981615	+	0.190871i	$0.0611313\pi$
$487$			8.42432i			0.381742i	−0.981615	+	0.190871i	$0.938869\pi$
$488$	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	$-0.625071\pi$
$491$	−16.9685			−0.765777			−0.382888	+	0.923795i	$0.625071\pi$
$492$	18.1037	−	9.35513i	0.816178	−	0.421762i
$493$		−	31.2208i		−	1.40611i
$494$	1.07942	−	4.25200i	0.0485655	−	0.191307i
$495$	−13.0422	−	3.37155i	−0.586205	−	0.151540i
$496$	31.8179	−	20.6807i	1.42866	−	0.928592i
$497$	3.60855	+	23.2336i	0.161865	+	1.04217i
$498$	18.6269	−	16.5215i	0.834692	−	0.740347i
$499$		−	34.6615i		−	1.55166i	−0.630940	−	0.775831i	$-0.717331\pi$
$499$		−	34.6615i		−	1.55166i	0.630940	−	0.775831i	$-0.282669\pi$
$500$	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	$0.851175\pi$
$504$	−4.77170	+	21.9370i	−0.212548	+	0.977151i
$505$	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	$0.983504\pi$
$510$	−22.5125	+	2.14591i	−0.996868	+	0.0950227i
$511$	−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
$516$	11.2614	−	5.81935i	0.495755	−	0.256183i
$517$			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	$-0.629464\pi$
$521$	−18.0595			−0.791203			−0.395601	+	0.918422i	$0.629464\pi$
$522$	4.12557	+	31.8150i	0.180571	+	1.39251i
$523$		−	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
$525$	−22.7111	−	3.03405i	−0.991194	−	0.132417i
$526$	−19.5397	−	4.96040i	−0.851973	−	0.216284i
$527$	−39.1704			−1.70629
$528$	−13.9099	−	0.281865i	−0.605352	−	0.0122666i
$529$	−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
$534$	−24.6171	+	21.8346i	−1.06529	+	0.944877i
$535$	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
$540$	22.6574	−	5.16160i	0.975019	−	0.222120i
$541$			14.7905i			0.635895i	0.948108	+	0.317948i	$0.102994\pi$
$541$			14.7905i			0.635895i	−0.948108	+	0.317948i	$0.897006\pi$
$542$	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
$546$	6.64227	+	5.49487i	0.284263	+	0.235159i
$547$	−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
$552$	0.465561	−	0.108198i	0.0198156	−	0.00460520i
$553$	28.7033	−	4.45808i	1.22059	−	0.189577i
$554$	−39.2812	−	9.97201i	−1.66890	−	0.423670i
$555$	8.08675	+	22.5986i	0.343264	+	0.959259i
$556$	−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	$-0.00912334\pi$
$558$	39.9160	−	5.17605i	1.68978	−	0.219119i
$559$		−	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	$-0.722411\pi$
$563$	−30.5252			−1.28649			−0.643243	+	0.765662i	$0.722411\pi$
$564$	−12.3903	−	23.9772i	−0.521725	−	1.00962i
$565$	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	$0.895464\pi$
$570$	1.21204	+	12.7154i	0.0507669	+	0.532587i
$571$		−	42.4541i		−	1.77665i	−0.459217	−	0.888324i	$-0.651870\pi$
$571$		−	42.4541i		−	1.77665i	0.459217	−	0.888324i	$-0.348130\pi$
$572$	−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
$576$	21.5403	−	10.5837i	0.897513	−	0.440988i
$577$	−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
$582$	17.7006	−	15.6999i	0.733714	−	0.650783i
$583$			5.00827i			0.207421i
$584$	14.2329	+	13.1489i	0.588960	+	0.544105i
$585$	2.23329	−	8.63909i	0.0923351	−	0.357182i
$586$	−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	$0.481339\pi$
$588$	17.1510	−	17.1418i	0.707297	−	0.706916i
$589$			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	$-0.233753\pi$
$594$	−13.1722	−	6.65234i	−0.540463	−	0.272949i
$595$	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	$0.714953\pi$
$600$	12.5532	+	21.0337i	0.512483	+	0.858697i
$601$		−	36.9925i		−	1.50896i	−0.656325	−	0.754479i	$-0.727890\pi$
$601$		−	36.9925i		−	1.50896i	0.656325	−	0.754479i	$-0.272110\pi$
$602$	−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
$606$	25.4626	+	28.7074i	1.03435	+	1.16616i
$607$	−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
$609$	14.8389	−	31.3139i	0.601304	−	1.26890i
$610$	−27.5685	+	22.8299i	−1.11622	+	0.924354i
$611$	−10.3636			−0.419266
$612$	−24.5958	−	2.95717i	−0.994227	−	0.119537i
$613$	−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
$615$	7.67616	+	21.4512i	0.309533	+	0.864997i
$616$	12.4724	+	8.38252i	0.502526	+	0.337741i
$617$	−21.0418			−0.847111			−0.423556	−	0.905870i	$-0.639218\pi$
$617$	−21.0418			−0.847111			−0.423556	+	0.905870i	$0.639218\pi$
$618$	−15.7487	+	13.9686i	−0.633505	+	0.561900i
$619$	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
$624$	0.186706	−	9.21383i	0.00747420	−	0.368848i
$625$	−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
$630$	−23.5995	−	8.54763i	−0.940228	−	0.340546i
$631$	−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
$636$	−3.96619	−	7.67522i	−0.157270	−	0.304342i
$637$	−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	$-0.173431\pi$
$642$	4.07190	+	4.59080i	0.160705	+	0.181184i
$643$		−	10.0020i		−	0.394440i	−0.980359	−	0.197220i	$-0.936809\pi$
$643$		−	10.0020i		−	0.394440i	0.980359	−	0.197220i	$-0.0631913\pi$
$644$	−0.486169	−	0.173693i	−0.0191577	−	0.00684447i
$645$	4.77495	+	13.3437i	0.188013	+	0.525408i
$646$	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	$0.719470\pi$
$648$	25.4547	−	0.236673i	0.999957	−	0.00929738i
$649$			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	$-0.0910592\pi$
$654$	−23.5545	−	26.5561i	−0.921053	−	1.03843i
$655$	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	$-0.311540\pi$
$659$	28.6527			1.11615			0.558075	+	0.829790i	$0.311540\pi$
$660$	2.37949	−	15.3719i	0.0926216	−	0.598350i
$661$	−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
$666$	3.38117	+	26.0745i	0.131018	+	1.01037i
$667$	−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
$672$	−25.7524	−	2.96908i	−0.993419	−	0.114535i
$673$		−	35.2784i		−	1.35988i	−0.733267	−	0.679940i	$-0.762006\pi$
$673$		−	35.2784i		−	1.35988i	0.733267	−	0.679940i	$-0.237994\pi$
$674$	−2.80046	+	11.0314i	−0.107870	+	0.424914i
$675$	2.35252	+	25.8740i	0.0905484	+	0.995892i
$676$	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	$0.379948\pi$
$678$	26.0404	−	23.0970i	1.00007	−	0.887037i
$679$	−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	$0.918612\pi$
$684$	−1.67025	+	13.8921i	−0.0638637	+	0.531176i
$685$	−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
$690$	0.0507084	+	0.531974i	0.00193043	+	0.0202519i
$691$	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
$693$	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
$696$	−36.0828	+	8.38575i	−1.36772	+	0.317861i
$697$		−	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	$-0.529300\pi$
$701$	−4.86743			−0.183840			−0.0919201	+	0.995766i	$0.529300\pi$
$702$	4.40646	−	8.72518i	0.166311	−	0.329311i
$703$	−14.4522			−0.545074
$704$	−1.26998	−	16.0148i	−0.0478642	−	0.603581i
$705$	28.4108	−	10.1666i	1.07001	−	0.382895i
$706$	5.29061	−	20.8405i	0.199115	−	0.784342i
$707$	−6.36113	−	40.9561i	−0.239235	−	1.54031i
$708$	−2.96301	−	5.73391i	−0.111357	−	0.215493i
$709$			0.768670i			0.0288680i	0.999896	+	0.0144340i	$0.00459465\pi$
$709$			0.768670i			0.0288680i	−0.999896	+	0.0144340i	$0.995405\pi$
$710$	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
$714$	20.6174	+	17.0559i	0.771587	+	0.638301i
$715$	−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	$0.179554\pi$
$720$	8.52684	+	25.4420i	0.317776	+	0.948166i
$721$	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
$726$	12.7678	−	11.3247i	0.473859	−	0.420299i
$727$	−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
$732$	−34.8345	+	18.0008i	−1.28752	+	0.665329i
$733$		−	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
$735$	16.4463	+	21.5527i	0.606629	+	0.794985i
$736$	0.177665	+	0.522533i	0.00654881	+	0.0192608i
$737$	14.7243			0.542375
$738$	3.20950	+	24.7506i	0.118143	+	0.911083i
$739$			12.9023i			0.474619i	0.971434	+	0.237310i	$0.0762656\pi$
$739$			12.9023i			0.474619i	−0.971434	+	0.237310i	$0.923734\pi$
$740$	−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	$-0.620647\pi$
$743$	−20.1716			−0.740025			−0.370012	+	0.929027i	$0.620647\pi$
$744$	10.5210	+	45.2704i	0.385718	+	1.65969i
$745$	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
$750$	−25.1733	+	10.7846i	−0.919197	+	0.393797i
$751$	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
$756$	−23.2637	−	14.6561i	−0.846091	−	0.533039i
$757$	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	$0.226262\pi$
$762$	−2.36236	−	2.66341i	−0.0855795	−	0.0964851i
$763$	5.88444	+	37.8869i	0.213031	+	1.37160i
$764$	13.1091	−	24.1555i	0.474272	−	0.873914i
$765$	6.93207	−	26.8155i	0.250629	−	0.969516i
$766$	−5.09226	+	20.0592i	−0.183991	+	0.724767i
$767$	−2.47835			−0.0894880
$768$	14.6288	+	23.5371i	0.527873	+	0.849323i
$769$			9.12224i			0.328956i	0.986381	+	0.164478i	$0.0525940\pi$
$769$			9.12224i			0.328956i	−0.986381	+	0.164478i	$0.947406\pi$
$770$	−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	$-0.604394\pi$
$773$	−17.9114			−0.644228			−0.322114	+	0.946701i	$0.604394\pi$
$774$	1.99647	+	15.3961i	0.0717615	+	0.553401i
$775$	−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
$780$	10.1822	+	1.57616i	0.364582	+	0.0564355i
$781$		−	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
$786$	3.04748	+	3.43583i	0.108700	+	0.122552i
$787$			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
$792$	6.13424	−	15.8971i	0.217971	−	0.564880i
$793$			15.0564i			0.534668i
$794$	2.60095	−	10.2455i	0.0923044	−	0.363600i
$795$	9.09443	−	3.25437i	0.322546	−	0.115421i
$796$	−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	$0.676833\pi$
$798$	9.63342	−	11.6450i	0.341019	−	0.412229i
$799$	−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
$804$	−22.5651	+	11.6606i	−0.795809	+	0.411236i
$805$	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	$0.954972\pi$
$810$	−3.52057	+	28.2419i	−0.123700	+	0.992320i
$811$	−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
$816$	0.579529	−	28.5995i	0.0202876	−	1.00118i
$817$	−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	$-0.332000\pi$
$821$	28.8608			1.00725			0.503624	+	0.863923i	$0.332000\pi$
$822$	−33.8990	+	30.0674i	−1.18236	+	1.04872i
$823$		−	55.7417i		−	1.94303i	−0.236970	−	0.971517i	$-0.576154\pi$
$823$		−	55.7417i		−	1.94303i	0.236970	−	0.971517i	$-0.423846\pi$
$824$	−17.8545	−	16.4947i	−0.621991	−	0.574620i
$825$	16.6802	+	4.92116i	0.580729	+	0.171333i
$826$	−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	$-0.177636\pi$
$828$	−0.0698786	+	0.581204i	−0.00242845	+	0.0201982i
$829$	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
$834$	1.25593	−	1.11398i	0.0434894	−	0.0385739i
$835$	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	$0.488232\pi$
$840$	7.11713	−	28.0953i	0.245564	−	0.969380i
$841$	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
$846$	32.7806	−	4.25077i	1.12702	−	0.146145i
$847$	−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
$852$	14.1326	+	27.3489i	0.484176	+	0.936959i
$853$			44.6580i			1.52906i	0.644587	+	0.764531i	$0.277029\pi$
$853$			44.6580i			1.52906i	−0.644587	+	0.764531i	$0.722971\pi$
$854$	42.1632	+	3.99741i	1.44279	+	0.136789i
$855$	−15.1458	−	3.91533i	−0.517974	−	0.133901i
$856$	−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	$-0.128794\pi$
$858$	−4.34169	−	4.89496i	−0.148223	−	0.167111i
$859$	−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
$861$	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	$-0.501266\pi$
$863$	−0.233651			−0.00795357			−0.00397679	+	0.999992i	$0.501266\pi$
$864$	3.18862	+	29.2204i	0.108479	+	0.994099i
$865$	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
$870$	−3.93010	−	41.2300i	−0.133243	−	1.39783i
$871$			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
$876$	−21.0833	+	10.8948i	−0.712338	+	0.368102i
$877$	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	$0.263898\pi$
$882$	12.5724	+	26.9060i	0.423335	+	0.905973i
$883$	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
$885$	6.79415	−	2.43124i	0.228383	−	0.0817251i
$886$	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	$-0.0741752\pi$
$888$	−29.5722	+	6.87267i	−0.992379	+	0.230632i
$889$	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
$894$	4.30486	−	3.81829i	0.143976	−	0.127703i
$895$	−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
$900$	−29.4597	+	5.66777i	−0.981991	+	0.188926i
$901$	−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
$906$	15.2590	−	13.5343i	0.506947	−	0.449648i
$907$	−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	$0.806870\pi$
$912$	−16.1534	−	0.327326i	−0.534892	−	0.0108388i
$913$	20.4120			0.675540
$914$	14.0695	−	55.4218i	0.465378	−	1.83319i
$915$	−14.7702	−	41.2756i	−0.488287	−	1.36453i
$916$	−6.42941	−	3.48923i	−0.212434	−	0.115287i
$917$	−0.761329	−	4.90181i	−0.0251413	−	0.161872i
$918$	13.6775	−	27.0827i	0.451426	−	0.893863i
$919$	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
$924$	−14.8603	+	10.8587i	−0.488868	+	0.357224i
$925$	−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	$0.546688\pi$
$930$	−51.7283	+	4.93080i	−1.69624	+	0.161687i
$931$	−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
$936$	10.5301	+	4.06327i	0.344189	+	0.132812i
$937$	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	$-0.317085\pi$
$942$	−22.8622	−	25.7756i	−0.744890	−	0.839813i
$943$	−0.573937			−0.0186900
$944$	6.24875	−	4.06151i	0.203380	−	0.132191i
$945$	19.6979	−	23.6007i	0.640772	−	0.767731i
$946$	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	$-0.0425193\pi$
$948$	33.7875	−	17.4598i	1.09737	−	0.567067i
$949$			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	$-0.412992\pi$
$953$	16.6673			0.539906			0.269953	+	0.962873i	$0.412992\pi$
$954$	10.4932	−	1.36069i	0.339731	−	0.0440541i
$955$	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
$960$	−28.2558	+	12.7126i	−0.911952	+	0.410296i
$961$	−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
$966$	0.403034	−	0.487194i	0.0129674	−	0.0156752i
$967$			13.9782i			0.449509i	0.974415	+	0.224754i	$0.0721580\pi$
$967$			13.9782i			0.449509i	−0.974415	+	0.224754i	$0.927842\pi$
$968$	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	$0.816282\pi$
$972$	−10.3591	+	29.4056i	−0.332269	+	0.943185i
$973$	−1.79181	+	0.278296i	−0.0574428	+	0.00892177i
$974$	2.93147	−	11.5475i	0.0939305	−	0.370006i
$975$	−3.25974	+	11.0488i	−0.104395	+	0.353845i
$976$	−24.6744	−	37.9623i	−0.789808	−	1.21514i
$977$	24.4774			0.783101			0.391550	−	0.920157i	$-0.371939\pi$
$977$	24.4774			0.783101			0.391550	+	0.920157i	$0.371939\pi$
$978$	19.4508	−	17.2523i	0.621967	−	0.551667i
$979$	−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	$0.857653\pi$
$984$	−28.0707	+	6.52372i	−0.894862	+	0.207969i
$985$	−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
$990$	16.7042	+	9.15990i	0.530895	+	0.291121i
$991$	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
$996$	−31.2816	+	16.1649i	−0.991197	+	0.512204i
$997$		−	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.629.3	yes	160
3.2	odd	2	inner	840.2.u.e.629.157	yes	160
5.4	even	2	inner	840.2.u.e.629.158	yes	160
7.6	odd	2	inner	840.2.u.e.629.2	yes	160
8.5	even	2	inner	840.2.u.e.629.6	yes	160
15.14	odd	2	inner	840.2.u.e.629.4	yes	160
21.20	even	2	inner	840.2.u.e.629.160	yes	160
24.5	odd	2	inner	840.2.u.e.629.156	yes	160
35.34	odd	2	inner	840.2.u.e.629.159	yes	160
40.29	even	2	inner	840.2.u.e.629.155	yes	160
56.13	odd	2	inner	840.2.u.e.629.7	yes	160
105.104	even	2	inner	840.2.u.e.629.1	✓	160
120.29	odd	2	inner	840.2.u.e.629.5	yes	160
168.125	even	2	inner	840.2.u.e.629.153	yes	160
280.69	odd	2	inner	840.2.u.e.629.154	yes	160
840.629	even	2	inner	840.2.u.e.629.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.u.e.629.1	✓	160	105.104	even	2	inner
840.2.u.e.629.2	yes	160	7.6	odd	2	inner
840.2.u.e.629.3	yes	160	1.1	even	1	trivial
840.2.u.e.629.4	yes	160	15.14	odd	2	inner
840.2.u.e.629.5	yes	160	120.29	odd	2	inner
840.2.u.e.629.6	yes	160	8.5	even	2	inner
840.2.u.e.629.7	yes	160	56.13	odd	2	inner
840.2.u.e.629.8	yes	160	840.629	even	2	inner
840.2.u.e.629.153	yes	160	168.125	even	2	inner
840.2.u.e.629.154	yes	160	280.69	odd	2	inner
840.2.u.e.629.155	yes	160	40.29	even	2	inner
840.2.u.e.629.156	yes	160	24.5	odd	2	inner
840.2.u.e.629.157	yes	160	3.2	odd	2	inner
840.2.u.e.629.158	yes	160	5.4	even	2	inner
840.2.u.e.629.159	yes	160	35.34	odd	2	inner
840.2.u.e.629.160	yes	160	21.20	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} +(-1.83252 + 1.62539i) 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} +(3.07749 - 1.59030i) q^{12} -1.33017i q^{13} +(-3.72495 - 0.353156i) q^{14} +(1.30489 + 3.64654i) q^{15} +(2.17989 + 3.35382i) q^{16} -4.12882i q^{17} +(0.545590 + 4.20741i) 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} +(-4.77181 + 1.10898i) 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} +(-0.519740 - 5.45251i) 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} +(0.716226 - 5.95710i) 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} +(-4.13094 + 4.99353i) q^{42} +3.65928 q^{43} +(-3.52995 - 1.91570i) q^{44} +(6.49470 + 1.67894i) q^{45} +(0.133736 + 0.0339504i) q^{46} -7.79115i q^{47} +(6.92678 + 0.140362i) 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} +(6.55942 + 3.31270i) 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} +(-1.18493 + 7.65480i) 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} +(3.67994 - 3.26400i) 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} +(-3.05469 + 7.91637i) q^{72} -6.85080 q^{73} +(-8.49482 - 2.15651i) q^{74} +(-8.30629 - 2.45061i) q^{75} +(-4.09928 - 2.22467i) q^{76} +(-5.25008 + 0.815421i) q^{77} +(2.16205 + 2.43757i) 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} +(7.40005 - 5.40733i) 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} +(-8.31827 - 4.56140i) 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} +(-9.44593 - 2.60276i) 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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