LMFDB - Embedded newform 180.2.n.d.119.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(59,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.5
Character	$\chi$	$=$	180.119
Dual form			180.2.n.d.59.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.24631 + 0.668359i) q^{2} +(-1.66946 - 0.461412i) q^{3} +(1.10659 - 1.66597i) q^{4} +(-1.69235 + 1.46149i) q^{5} +(2.38906 - 0.540736i) q^{6} +(0.667441 - 1.15604i) q^{7} +(-0.265693 + 2.81592i) q^{8} +(2.57420 + 1.54062i) q^{9} +(1.13240 - 2.95257i) q^{10} +(2.18799 - 3.78971i) q^{11} +(-2.61611 + 2.27068i) q^{12} +(3.56180 - 2.05641i) q^{13} +(-0.0591892 + 1.88688i) q^{14} +(3.49966 - 1.65903i) q^{15} +(-1.55091 - 3.68710i) q^{16} +6.45392 q^{17} +(-4.23794 - 0.199603i) q^{18} +5.84202i q^{19} +(0.562053 + 4.43668i) q^{20} +(-1.64768 + 1.62200i) q^{21} +(-0.194033 + 6.18554i) q^{22} +(0.0875178 - 0.0505284i) q^{23} +(1.74286 - 4.57847i) q^{24} +(0.728104 - 4.94670i) q^{25} +(-3.06470 + 4.94349i) q^{26} +(-3.58666 - 3.75977i) q^{27} +(-1.18735 - 2.39120i) q^{28} +(-4.53226 - 2.61670i) q^{29} +(-3.25285 + 4.40670i) q^{30} +(4.18262 - 2.41484i) q^{31} +(4.39722 + 3.55871i) q^{32} +(-5.40139 + 5.31721i) q^{33} +(-8.04361 + 4.31354i) q^{34} +(0.559997 + 2.93189i) q^{35} +(5.41521 - 2.58370i) q^{36} -3.24337i q^{37} +(-3.90457 - 7.28098i) q^{38} +(-6.89514 + 1.78964i) q^{39} +(-3.66579 - 5.15383i) q^{40} +(3.50518 - 2.02372i) q^{41} +(0.969443 - 3.12276i) q^{42} +(-1.92364 + 3.33185i) q^{43} +(-3.89233 - 7.83880i) q^{44} +(-6.60804 + 1.15489i) q^{45} +(-0.0753035 + 0.121468i) q^{46} +(-3.00768 - 1.73649i) q^{47} +(0.887912 + 6.87107i) q^{48} +(2.60904 + 4.51900i) q^{49} +(2.39873 + 6.65177i) q^{50} +(-10.7746 - 2.97792i) q^{51} +(0.515549 - 8.20946i) q^{52} -2.77476 q^{53} +(6.98298 + 2.28867i) q^{54} +(1.83577 + 9.61125i) q^{55} +(3.07799 + 2.18661i) q^{56} +(2.69558 - 9.75302i) q^{57} +(7.39751 + 0.232051i) q^{58} +(-1.37318 - 2.37841i) q^{59} +(1.10881 - 7.66619i) q^{60} +(1.04419 - 1.80858i) q^{61} +(-3.59888 + 5.80514i) q^{62} +(3.49915 - 1.94761i) q^{63} +(-7.85881 - 1.49634i) q^{64} +(-3.02241 + 8.68570i) q^{65} +(3.17801 - 10.2370i) q^{66} +(-0.216298 - 0.374638i) q^{67} +(7.14186 - 10.7520i) q^{68} +(-0.169422 + 0.0439735i) q^{69} +(-2.65749 - 3.27977i) q^{70} +8.41810 q^{71} +(-5.02220 + 6.83941i) q^{72} +7.28163i q^{73} +(2.16773 + 4.04225i) q^{74} +(-3.49801 + 7.92237i) q^{75} +(9.73262 + 6.46473i) q^{76} +(-2.92071 - 5.05882i) q^{77} +(7.39739 - 6.83888i) q^{78} +(2.58753 + 1.49391i) q^{79} +(8.01333 + 3.97323i) q^{80} +(4.25299 + 7.93171i) q^{81} +(-3.01598 + 4.86490i) q^{82} +(11.6096 + 6.70282i) q^{83} +(0.878898 + 4.53988i) q^{84} +(-10.9223 + 9.43234i) q^{85} +(0.170590 - 5.43821i) q^{86} +(6.35905 + 6.45972i) q^{87} +(10.0902 + 7.16812i) q^{88} -6.97377i q^{89} +(7.46380 - 5.85591i) q^{90} -5.49013i q^{91} +(0.0126677 - 0.201716i) q^{92} +(-8.09696 + 2.10157i) q^{93} +(4.90911 + 0.153993i) q^{94} +(-8.53804 - 9.88674i) q^{95} +(-5.69896 - 7.97006i) q^{96} +(2.08608 + 1.20440i) q^{97} +(-6.27200 - 3.88831i) q^{98} +(11.4708 - 6.38462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.24631	+	0.668359i	−0.881276	+	0.472601i
$2$	−1.24631	+	0.668359i	−0.881276	+	0.472601i
$3$	−1.66946	−	0.461412i	−0.963864	−	0.266396i
$3$	−1.66946	−	0.461412i	−0.963864	−	0.266396i
$4$	1.10659	−	1.66597i	0.553296	−	0.832985i
$5$	−1.69235	+	1.46149i	−0.756842	+	0.653597i
$5$	−1.69235	+	1.46149i	−0.756842	+	0.653597i
$6$	2.38906	−	0.540736i	0.975329	−	0.220755i
$7$	0.667441	−	1.15604i	0.252269	−	0.436943i	−0.711881	−	0.702300i	$-0.752157\pi$
$7$	0.667441	−	1.15604i	0.252269	−	0.436943i	0.964150	+	0.265357i	$0.0854898\pi$
$8$	−0.265693	+	2.81592i	−0.0939368	+	0.995578i
$9$	2.57420	+	1.54062i	0.858066	+	0.513539i
$10$	1.13240	−	2.95257i	0.358096	−	0.933685i
$11$	2.18799	−	3.78971i	0.659705	−	1.14264i	−0.320987	−	0.947083i	$-0.604015\pi$
$11$	2.18799	−	3.78971i	0.659705	−	1.14264i	0.980692	−	0.195558i	$-0.0626519\pi$
$12$	−2.61611	+	2.27068i	−0.755206	+	0.655488i
$13$	3.56180	−	2.05641i	0.987867	−	0.570345i	0.0832309	−	0.996530i	$-0.473476\pi$
$13$	3.56180	−	2.05641i	0.987867	−	0.570345i	0.904636	+	0.426185i	$0.140143\pi$
$14$	−0.0591892	+	1.88688i	−0.0158190	+	0.504290i
$15$	3.49966	−	1.65903i	0.903609	−	0.428359i
$16$	−1.55091	−	3.68710i	−0.387727	−	0.921774i
$17$	6.45392			1.56531			0.782653	−	0.622458i	$-0.213866\pi$
$17$	6.45392			1.56531			0.782653	+	0.622458i	$0.213866\pi$
$18$	−4.23794	−	0.199603i	−0.998893	−	0.0470468i
$19$			5.84202i			1.34025i	0.742248	+	0.670125i	$0.233760\pi$
$19$			5.84202i			1.34025i	−0.742248	+	0.670125i	$0.766240\pi$
$20$	0.562053	+	4.43668i	0.125679	+	0.992071i
$21$	−1.64768	+	1.62200i	−0.359553	+	0.353950i
$22$	−0.194033	+	6.18554i	−0.0413679	+	1.31876i
$23$	0.0875178	−	0.0505284i	0.0182487	−	0.0105359i	−0.490848	−	0.871245i	$-0.663313\pi$
$23$	0.0875178	−	0.0505284i	0.0182487	−	0.0105359i	0.509097	+	0.860709i	$0.329980\pi$
$24$	1.74286	−	4.57847i	0.355761	−	0.934577i
$25$	0.728104	−	4.94670i	0.145621	−	0.989340i
$26$	−3.06470	+	4.94349i	−0.601038	+	0.969499i
$27$	−3.58666	−	3.75977i	−0.690254	−	0.723567i
$28$	−1.18735	−	2.39120i	−0.224387	−	0.451895i
$29$	−4.53226	−	2.61670i	−0.841620	−	0.485909i	0.0161948	−	0.999869i	$-0.494845\pi$
$29$	−4.53226	−	2.61670i	−0.841620	−	0.485909i	−0.857814	+	0.513960i	$0.828178\pi$
$30$	−3.25285	+	4.40670i	−0.593886	+	0.804549i
$31$	4.18262	−	2.41484i	0.751222	−	0.433718i	−0.0749136	−	0.997190i	$-0.523868\pi$
$31$	4.18262	−	2.41484i	0.751222	−	0.433718i	0.826135	+	0.563472i	$0.190535\pi$
$32$	4.39722	+	3.55871i	0.777327	+	0.629097i
$33$	−5.40139	+	5.31721i	−0.940261	+	0.925608i
$34$	−8.04361	+	4.31354i	−1.37947	+	0.739766i
$35$	0.559997	+	2.93189i	0.0946568	+	0.495579i
$36$	5.41521	−	2.58370i	0.902535	−	0.430617i
$37$		−	3.24337i		−	0.533206i	−0.963806	−	0.266603i	$-0.914099\pi$
$37$		−	3.24337i		−	0.533206i	0.963806	−	0.266603i	$-0.0859013\pi$
$38$	−3.90457	−	7.28098i	−0.633404	−	1.18113i
$39$	−6.89514	+	1.78964i	−1.10411	+	0.286571i
$40$	−3.66579	−	5.15383i	−0.579612	−	0.814893i
$41$	3.50518	−	2.02372i	0.547417	−	0.316051i	−0.200663	−	0.979660i	$-0.564310\pi$
$41$	3.50518	−	2.02372i	0.547417	−	0.316051i	0.748079	+	0.663609i	$0.230976\pi$
$42$	0.969443	−	3.12276i	0.149588	−	0.481853i
$43$	−1.92364	+	3.33185i	−0.293353	+	0.508102i	−0.974600	−	0.223951i	$-0.928104\pi$
$43$	−1.92364	+	3.33185i	−0.293353	+	0.508102i	0.681248	+	0.732053i	$0.261438\pi$
$44$	−3.89233	−	7.83880i	−0.586792	−	1.18174i
$45$	−6.60804	+	1.15489i	−0.985069	+	0.172162i
$46$	−0.0753035	+	0.121468i	−0.0111029	+	0.0179094i
$47$	−3.00768	−	1.73649i	−0.438715	−	0.253292i	0.264337	−	0.964430i	$-0.414847\pi$
$47$	−3.00768	−	1.73649i	−0.438715	−	0.253292i	−0.703053	+	0.711138i	$0.748180\pi$
$48$	0.887912	+	6.87107i	0.128159	+	0.991754i
$49$	2.60904	+	4.51900i	0.372721	+	0.645571i
$50$	2.39873	+	6.65177i	0.339232	+	0.940703i
$51$	−10.7746	−	2.97792i	−1.50874	−	0.416992i
$52$	0.515549	−	8.20946i	0.0714938	−	1.13845i
$53$	−2.77476			−0.381143			−0.190571	−	0.981673i	$-0.561034\pi$
$53$	−2.77476			−0.381143			−0.190571	+	0.981673i	$0.561034\pi$
$54$	6.98298	+	2.28867i	0.950263	+	0.311448i
$55$	1.83577	+	9.61125i	0.247535	+	1.29598i
$56$	3.07799	+	2.18661i	0.411313	+	0.292199i
$57$	2.69558	−	9.75302i	0.357038	−	1.29182i
$58$	7.39751	+	0.232051i	0.971341	+	0.0304698i
$59$	−1.37318	−	2.37841i	−0.178772	−	0.309642i	0.762688	−	0.646766i	$-0.223879\pi$
$59$	−1.37318	−	2.37841i	−0.178772	−	0.309642i	−0.941460	+	0.337124i	$0.890546\pi$
$60$	1.10881	−	7.66619i	0.143147	−	0.989701i
$61$	1.04419	−	1.80858i	0.133694	−	0.231566i	−0.791404	−	0.611294i	$-0.790649\pi$
$61$	1.04419	−	1.80858i	0.133694	−	0.231566i	0.925098	+	0.379729i	$0.123983\pi$
$62$	−3.59888	+	5.80514i	−0.457058	+	0.737254i
$63$	3.49915	−	1.94761i	0.440851	−	0.245376i
$64$	−7.85881	−	1.49634i	−0.982352	−	0.187043i
$65$	−3.02241	+	8.68570i	−0.374883	+	1.07733i
$66$	3.17801	−	10.2370i	0.391186	−	1.26009i
$67$	−0.216298	−	0.374638i	−0.0264250	−	0.0457694i	0.852511	−	0.522710i	$-0.175079\pi$
$67$	−0.216298	−	0.374638i	−0.0264250	−	0.0457694i	−0.878935	+	0.476941i	$0.841746\pi$
$68$	7.14186	−	10.7520i	0.866078	−	1.30388i
$69$	−0.169422	+	0.0439735i	−0.0203960	+	0.00529379i
$70$	−2.65749	−	3.27977i	−0.317630	−	0.392007i
$71$	8.41810			0.999044			0.499522	−	0.866301i	$-0.333509\pi$
$71$	8.41810			0.999044			0.499522	+	0.866301i	$0.333509\pi$
$72$	−5.02220	+	6.83941i	−0.591872	+	0.806032i
$73$			7.28163i			0.852250i	0.904664	+	0.426125i	$0.140122\pi$
$73$			7.28163i			0.852250i	−0.904664	+	0.426125i	$0.859878\pi$
$74$	2.16773	+	4.04225i	0.251994	+	0.469902i
$75$	−3.49801	+	7.92237i	−0.403915	+	0.914796i
$76$	9.73262	+	6.46473i	1.11641	+	0.741555i
$77$	−2.92071	−	5.05882i	−0.332846	−	0.576507i
$78$	7.39739	−	6.83888i	0.837589	−	0.774351i
$79$	2.58753	+	1.49391i	0.291120	+	0.168078i	0.638447	−	0.769666i	$-0.279577\pi$
$79$	2.58753	+	1.49391i	0.291120	+	0.168078i	−0.347327	+	0.937744i	$0.612911\pi$
$80$	8.01333	+	3.97323i	0.895918	+	0.444220i
$81$	4.25299	+	7.93171i	0.472555	+	0.881301i
$82$	−3.01598	+	4.86490i	−0.333059	+	0.537238i
$83$	11.6096	+	6.70282i	1.27432	+	0.735730i	0.975798	−	0.218672i	$-0.0701724\pi$
$83$	11.6096	+	6.70282i	1.27432	+	0.735730i	0.298524	+	0.954402i	$0.403506\pi$
$84$	0.878898	+	4.53988i	0.0958957	+	0.495341i
$85$	−10.9223	+	9.43234i	−1.18469	+	1.02308i
$86$	0.170590	−	5.43821i	0.0183952	−	0.586417i
$87$	6.35905	+	6.45972i	0.681762	+	0.692555i
$88$	10.0902	+	7.16812i	1.07562	+	0.764124i
$89$		−	6.97377i		−	0.739218i	−0.929187	−	0.369609i	$-0.879492\pi$
$89$		−	6.97377i		−	0.739218i	0.929187	−	0.369609i	$-0.120508\pi$
$90$	7.46380	−	5.85591i	0.786754	−	0.617267i
$91$		−	5.49013i		−	0.575522i
$92$	0.0126677	−	0.201716i	0.00132070	−	0.0210304i
$93$	−8.09696	+	2.10157i	−0.839616	+	0.217922i
$94$	4.90911	+	0.153993i	0.506336	+	0.0158831i
$95$	−8.53804	−	9.88674i	−0.875984	−	1.01436i
$96$	−5.69896	−	7.97006i	−0.581648	−	0.813441i
$97$	2.08608	+	1.20440i	0.211809	+	0.122288i	0.602152	−	0.798382i	$-0.294310\pi$
$97$	2.08608	+	1.20440i	0.211809	+	0.122288i	−0.390343	+	0.920670i	$0.627644\pi$
$98$	−6.27200	−	3.88831i	−0.633568	−	0.392778i
$99$	11.4708	−	6.38462i	1.15286	−	0.641678i
$100$	−7.43534	−	6.68698i	−0.743534	−	0.668698i
$101$	−3.92717	−	2.26735i	−0.390768	−	0.225610i	0.291725	−	0.956502i	$-0.405771\pi$
$101$	−3.92717	−	2.26735i	−0.390768	−	0.225610i	−0.682493	+	0.730892i	$0.739104\pi$
$102$	15.4188	−	3.48987i	1.52669	−	0.345549i
$103$	1.95140	+	3.37992i	0.192277	+	0.333034i	0.946005	−	0.324153i	$-0.105079\pi$
$103$	1.95140	+	3.37992i	0.192277	+	0.333034i	−0.753727	+	0.657187i	$0.771746\pi$
$104$	4.84434	+	10.5761i	0.475026	+	1.03708i
$105$	0.417914	−	5.15306i	0.0407842	−	0.502887i
$106$	3.45822	−	1.85454i	0.335892	−	0.180129i
$107$		−	4.98830i		−	0.482237i	−0.970496	−	0.241118i	$-0.922486\pi$
$107$		−	4.98830i		−	0.482237i	0.970496	−	0.241118i	$-0.0775142\pi$
$108$	−10.2326	+	1.81475i	−0.984635	+	0.174624i
$109$	−4.98669			−0.477638			−0.238819	−	0.971064i	$-0.576760\pi$
$109$	−4.98669			−0.477638			−0.238819	+	0.971064i	$0.576760\pi$
$110$	−8.71172	−	10.7517i	−0.830630	−	1.02513i
$111$	−1.49653	+	5.41467i	−0.142044	+	0.513938i
$112$	−5.29758	−	0.668004i	−0.500574	−	0.0631204i
$113$	−10.2057	−	17.6768i	−0.960073	−	1.66290i	−0.722306	−	0.691574i	$-0.756918\pi$
$113$	−10.2057	−	17.6768i	−0.960073	−	1.66290i	−0.237767	−	0.971322i	$-0.576416\pi$
$114$	3.15899	+	13.9569i	0.295866	+	1.30719i
$115$	−0.0742642	+	0.213418i	−0.00692517	+	0.0199013i
$116$	−9.37471	+	4.65499i	−0.870420	+	0.432205i
$117$	12.3369	+	0.193775i	1.14055	+	0.0179145i
$118$	3.30104	+	2.04647i	0.303885	+	0.188393i
$119$	4.30762	−	7.46101i	0.394879	−	0.683950i
$120$	3.74185	+	10.2956i	0.341583	+	0.939852i
$121$	−4.07462	−	7.05746i	−0.370420	−	0.641587i
$122$	−0.0925992	+	2.95195i	−0.00838354	+	0.267257i
$123$	−6.78552	+	1.76118i	−0.611830	+	0.158800i
$124$	0.605409	−	9.64037i	0.0543673	−	0.865730i
$125$	5.99734	+	9.43567i	0.536418	+	0.843952i
$126$	−3.05933	+	4.76602i	−0.272547	+	0.424591i
$127$	−19.1833			−1.70224			−0.851122	−	0.524968i	$-0.824077\pi$
$127$	−19.1833			−1.70224			−0.851122	+	0.524968i	$0.824077\pi$
$128$	10.7946	−	3.38760i	0.954120	−	0.299424i
$129$	4.74880	−	4.67479i	0.418108	−	0.411593i
$130$	−2.03831	−	12.8452i	−0.178771	−	1.12659i
$131$	8.41433	+	14.5740i	0.735163	+	1.27334i	0.954652	+	0.297725i	$0.0962279\pi$
$131$	8.41433	+	14.5740i	0.735163	+	1.27334i	−0.219488	+	0.975615i	$0.570439\pi$
$132$	2.88119	+	14.8825i	0.250775	+	1.29536i
$133$	6.75362	+	3.89920i	0.585613	+	0.338104i
$134$	0.519967	+	0.322352i	0.0449183	+	0.0278470i
$135$	11.5647	+	1.12098i	0.995335	+	0.0964784i
$136$	−1.71477	+	18.1737i	−0.147040	+	1.55839i
$137$	−2.99744	+	5.19172i	−0.256089	+	0.443559i	−0.965191	−	0.261547i	$-0.915767\pi$
$137$	−2.99744	+	5.19172i	−0.256089	+	0.443559i	0.709102	+	0.705106i	$0.249101\pi$
$138$	0.181763	−	0.168040i	0.0154727	−	0.0143045i
$139$	−0.206175	+	0.119035i	−0.0174875	+	0.0100964i	−0.508718	−	0.860933i	$-0.669881\pi$
$139$	−0.206175	+	0.119035i	−0.0174875	+	0.0100964i	0.491231	+	0.871029i	$0.336547\pi$
$140$	5.50412	+	2.31146i	0.465183	+	0.195354i
$141$	4.21997	+	4.28677i	0.355386	+	0.361012i
$142$	−10.4916	+	5.62631i	−0.880434	+	0.472150i
$143$		−	17.9976i		−	1.50504i
$144$	1.68806	−	11.8807i	0.140672	−	0.990056i
$145$	11.4945	−	2.19547i	0.954563	−	0.182324i
$146$	−4.86674	−	9.07519i	−0.402775	−	0.751068i
$147$	−2.27058	−	8.74813i	−0.187274	−	0.721534i
$148$	−5.40335	−	3.58908i	−0.444153	−	0.295021i
$149$	−8.84885	+	5.10889i	−0.724926	+	0.418536i	−0.816563	−	0.577256i	$-0.804123\pi$
$149$	−8.84885	+	5.10889i	−0.724926	+	0.418536i	0.0916368	+	0.995792i	$0.470790\pi$
$150$	−0.935377	−	12.2117i	−0.0763732	−	0.997079i
$151$	−13.0489	−	7.53379i	−1.06190	−	0.613091i	−0.135946	−	0.990716i	$-0.543407\pi$
$151$	−13.0489	−	7.53379i	−1.06190	−	0.613091i	−0.925958	+	0.377625i	$0.876741\pi$
$152$	−16.4507	−	1.55219i	−1.33432	−	0.125899i
$153$	16.6137	+	9.94303i	1.34314	+	0.803846i
$154$	7.02124	+	4.35279i	0.565787	+	0.350758i
$155$	−3.54921	+	10.1996i	−0.285079	+	0.819253i
$156$	−4.64863	+	13.4675i	−0.372188	+	1.07826i
$157$	2.77448	−	1.60184i	0.221427	−	0.127841i	−0.385184	−	0.922840i	$-0.625862\pi$
$157$	2.77448	−	1.60184i	0.221427	−	0.127841i	0.606611	+	0.794999i	$0.292529\pi$
$158$	−4.22334	−	0.132481i	−0.335991	−	0.0105396i
$159$	4.63235	+	1.28031i	0.367370	+	0.101535i
$160$	−12.6427	+	0.403902i	−0.999490	+	0.0319313i
$161$		−	0.134899i		−	0.0106315i
$162$	−10.6018	−	7.04287i	−0.832956	−	0.553340i
$163$	10.6182			0.831684			0.415842	−	0.909437i	$-0.363487\pi$
$163$	10.6182			0.831684			0.415842	+	0.909437i	$0.363487\pi$
$164$	0.507353	−	8.07895i	0.0396176	−	0.630860i
$165$	1.37000	−	16.8927i	0.106654	−	1.31509i
$166$	−18.9491	−	0.594411i	−1.47074	−	0.0461352i
$167$	−10.9127	+	6.30046i	−0.844451	+	0.487544i	−0.858775	−	0.512353i	$-0.828774\pi$
$167$	−10.9127	+	6.30046i	−0.844451	+	0.487544i	0.0143236	+	0.999897i	$0.495440\pi$
$168$	−4.12965	−	5.07069i	−0.318609	−	0.391212i
$169$	1.95764	−	3.39073i	0.150587	−	0.260825i
$170$	7.30842	−	19.0557i	0.560530	−	1.46150i
$171$	−9.00032	+	15.0385i	−0.688271	+	1.15002i
$172$	3.42207	+	6.89172i	0.260930	+	0.525489i
$173$	−0.858165	+	1.48639i	−0.0652451	+	0.113008i	−0.896803	−	0.442431i	$-0.854116\pi$
$173$	−0.858165	+	1.48639i	−0.0652451	+	0.113008i	0.831558	+	0.555439i	$0.187450\pi$
$174$	−12.2428	−	3.80070i	−0.928123	−	0.288130i
$175$	−5.23263	−	4.14335i	−0.395550	−	0.313208i
$176$	−17.3664	−	2.18984i	−1.30904	−	0.165065i
$177$	1.19504	+	4.60426i	0.0898244	+	0.346077i
$178$	4.66099	+	8.69150i	0.349356	+	0.651456i
$179$	−18.6630			−1.39494			−0.697468	−	0.716616i	$-0.745690\pi$
$179$	−18.6630			−1.39494			−0.697468	+	0.716616i	$0.745690\pi$
$180$	−5.38839	+	12.2868i	−0.401627	+	0.915804i
$181$	−19.9281			−1.48125			−0.740623	−	0.671920i	$-0.765470\pi$
$181$	−19.9281			−1.48125			−0.740623	+	0.671920i	$0.765470\pi$
$182$	3.66938	+	6.84242i	0.271992	+	0.507194i
$183$	−2.57773	+	2.53756i	−0.190551	+	0.187582i
$184$	0.119031	+	0.259868i	0.00877509	+	0.0191577i
$185$	4.74014	+	5.48891i	0.348502	+	0.403553i
$186$	8.68675	−	8.03089i	0.636943	−	0.588853i
$187$	14.1211	−	24.4585i	1.03264	−	1.78859i
$188$	−6.22121	+	3.08912i	−0.453728	+	0.225298i
$189$	−6.74034	+	1.63691i	−0.490287	+	0.119068i
$190$	17.2490	+	6.61550i	1.25137	+	0.479939i
$191$	−10.8229	+	18.7459i	−0.783121	+	1.35641i	0.146994	+	0.989137i	$0.453040\pi$
$191$	−10.8229	+	18.7459i	−0.783121	+	1.35641i	−0.930115	+	0.367268i	$0.880293\pi$
$192$	12.4296	+	6.12424i	0.897026	+	0.441979i
$193$	9.00614	−	5.19970i	0.648276	−	0.374282i	−0.139519	−	0.990219i	$-0.544556\pi$
$193$	9.00614	−	5.19970i	0.648276	−	0.374282i	0.787795	+	0.615937i	$0.211222\pi$
$194$	−3.40487	−	0.106807i	−0.244456	−	0.00766827i
$195$	9.05347	−	13.1059i	0.648333	−	0.938530i
$196$	10.4157	+	0.654097i	0.743976	+	0.0467212i
$197$	8.15715			0.581173			0.290586	−	0.956849i	$-0.406150\pi$
$197$	8.15715			0.581173			0.290586	+	0.956849i	$0.406150\pi$
$198$	−10.0290	+	15.6239i	−0.712732	+	1.11034i
$199$		−	9.18172i		−	0.650875i	−0.945564	−	0.325438i	$-0.894488\pi$
$199$		−	9.18172i		−	0.650875i	0.945564	−	0.325438i	$-0.105512\pi$
$200$	13.7361	+	3.36459i	0.971287	+	0.237912i
$201$	0.188238	+	0.725246i	0.0132773	+	0.0511549i
$202$	6.40988	+	0.201070i	0.450998	+	0.0141473i
$203$	−6.05004	+	3.49299i	−0.424629	+	0.245160i
$204$	−16.8842	+	14.6548i	−1.18213	+	1.02604i
$205$	−2.97435	+	8.54761i	−0.207738	+	0.596991i
$206$	−4.69106	−	2.90821i	−0.326842	−	0.202624i
$207$	0.303133	+	0.00476130i	0.0210692	+	0.000330933i
$208$	−13.1062	−	9.94341i	−0.908752	−	0.689452i
$209$	22.1396	+	12.7823i	1.53143	+	0.884170i
$210$	2.92324	+	6.70164i	0.201723	+	0.462457i
$211$	8.87092	−	5.12163i	0.610699	−	0.352587i	−0.162540	−	0.986702i	$-0.551969\pi$
$211$	8.87092	−	5.12163i	0.610699	−	0.352587i	0.773239	+	0.634115i	$0.218635\pi$
$212$	−3.07053	+	4.62267i	−0.210885	+	0.317486i
$213$	−14.0537	−	3.88421i	−0.962942	−	0.266142i
$214$	3.33397	+	6.21698i	0.227906	+	0.424984i
$215$	−1.61398	−	8.45003i	−0.110072	−	0.576287i
$216$	11.5402	−	9.10081i	0.785208	−	0.619232i
$217$		−	6.44705i		−	0.437655i
$218$	6.21497	−	3.33290i	0.420931	−	0.225732i
$219$	3.35983	−	12.1564i	0.227036	−	0.821453i
$220$	18.0435	+	7.57739i	1.21649	+	0.510868i
$221$	22.9876	−	13.2719i	1.54631	−	0.892765i
$222$	−1.75381	−	7.74859i	−0.117708	−	0.520052i
$223$	−11.6245	+	20.1343i	−0.778436	+	1.34829i	0.154407	+	0.988007i	$0.450653\pi$
$223$	−11.6245	+	20.1343i	−0.778436	+	1.34829i	−0.932843	+	0.360283i	$0.882680\pi$
$224$	7.04891	−	2.70815i	0.470975	−	0.180946i
$225$	9.49526	−	11.6121i	0.633017	−	0.774138i
$226$	24.5340	+	15.2098i	1.63198	+	1.01174i
$227$	14.7354	+	8.50750i	0.978024	+	0.564663i	0.901673	−	0.432418i	$-0.142340\pi$
$227$	14.7354	+	8.50750i	0.978024	+	0.564663i	0.0763513	+	0.997081i	$0.475673\pi$
$228$	−13.2653	−	15.2834i	−0.878518	−	1.01217i
$229$	−0.750685	−	1.30022i	−0.0496066	−	0.0859212i	0.840156	−	0.542345i	$-0.182463\pi$
$229$	−0.750685	−	1.30022i	−0.0496066	−	0.0859212i	−0.889762	+	0.456424i	$0.849130\pi$
$230$	−0.0500836	−	0.315621i	−0.00330242	−	0.0208114i
$231$	2.54182	+	9.79316i	0.167239	+	0.644343i
$232$	8.57262	−	12.0672i	0.562820	−	0.792253i
$233$	13.5483			0.887579			0.443789	−	0.896131i	$-0.353634\pi$
$233$	13.5483			0.887579			0.443789	+	0.896131i	$0.353634\pi$
$234$	−15.5052	+	8.00400i	−1.01361	+	0.523238i
$235$	7.62791	−	1.45695i	0.497590	−	0.0950408i
$236$	−5.48190	−	0.344260i	−0.356841	−	0.0224094i
$237$	−3.63047	−	3.68794i	−0.235824	−	0.239557i
$238$	−0.382002	+	12.1778i	−0.0247615	+	0.789369i
$239$	7.32324	+	12.6842i	0.473701	+	0.820474i	0.999547	−	0.0301057i	$-0.00958440\pi$
$239$	7.32324	+	12.6842i	0.473701	+	0.820474i	−0.525846	+	0.850580i	$0.676251\pi$
$240$	−11.5446	−	10.3306i	−0.745204	−	0.666837i
$241$	−12.2259	+	21.1758i	−0.787537	+	1.36405i	0.139934	+	0.990161i	$0.455311\pi$
$241$	−12.2259	+	21.1758i	−0.787537	+	1.36405i	−0.927472	+	0.373894i	$0.878022\pi$
$242$	9.79517	+	6.07249i	0.629658	+	0.390354i
$243$	−3.44042	−	15.2041i	−0.220703	−	0.975341i
$244$	−1.85756	−	3.74095i	−0.118918	−	0.239490i
$245$	−11.0199	−	3.83464i	−0.704034	−	0.244986i
$246$	7.27978	−	6.73015i	0.464142	−	0.429099i
$247$	12.0136	+	20.8081i	0.764406	+	1.32399i
$248$	5.68870	+	12.4195i	0.361233	+	0.788642i
$249$	−16.2891	−	16.5469i	−1.03228	−	1.04862i
$250$	−13.7810	−	7.75142i	−0.871586	−	0.490243i
$251$	13.1808			0.831965			0.415982	−	0.909373i	$-0.363438\pi$
$251$	13.1808			0.831965			0.415982	+	0.909373i	$0.363438\pi$
$252$	0.627467	−	7.98468i	0.0395267	−	0.502988i
$253$		−	0.442223i		−	0.0278024i
$254$	23.9084	−	12.8214i	1.50015	−	0.804483i
$255$	22.5866	−	10.7072i	1.41442	−	0.670513i
$256$	−11.1894	+	11.4367i	−0.699335	+	0.714794i
$257$	3.48508	+	6.03633i	0.217393	+	0.376536i	0.954010	−	0.299774i	$-0.0969113\pi$
$257$	3.48508	+	6.03633i	0.217393	+	0.376536i	−0.736617	+	0.676310i	$0.763578\pi$
$258$	−2.79405	+	9.00016i	−0.173950	+	0.560325i
$259$	−3.74947	−	2.16476i	−0.232981	−	0.134511i
$260$	11.1255	+	14.6468i	0.689977	+	0.908354i
$261$	−7.63560	−	13.7184i	−0.472632	−	0.849147i
$262$	−20.2276	−	12.5400i	−1.24966	−	0.774725i
$263$	−13.9809	−	8.07190i	−0.862102	−	0.497735i	0.00261352	−	0.999997i	$-0.499168\pi$
$263$	−13.9809	−	8.07190i	−0.862102	−	0.497735i	−0.864716	+	0.502262i	$0.832501\pi$
$264$	−13.5377	−	16.6226i	−0.833190	−	1.02305i
$265$	4.69587	−	4.05528i	0.288465	−	0.249114i
$266$	−11.0232	−	0.345784i	−0.675875	−	0.0212014i
$267$	−3.21778	+	11.6424i	−0.196925	+	0.712506i
$268$	−0.863489	−	0.0542266i	−0.0527460	−	0.00331242i
$269$			21.7634i			1.32694i	0.748204	+	0.663468i	$0.230916\pi$
$269$			21.7634i			1.32694i	−0.748204	+	0.663468i	$0.769084\pi$
$270$	−15.1625	+	6.33232i	−0.922761	+	0.385373i
$271$		−	30.1548i		−	1.83177i	−0.401436	−	0.915887i	$-0.631489\pi$
$271$		−	30.1548i		−	1.83177i	0.401436	−	0.915887i	$-0.368511\pi$
$272$	−10.0095	−	23.7962i	−0.606912	−	1.44286i
$273$	−2.53321	+	9.16556i	−0.153317	+	0.554725i
$274$	0.265815	−	8.47388i	0.0160585	−	0.511926i
$275$	−17.1535	−	13.5827i	−1.03440	−	0.819065i
$276$	−0.114223	+	0.330913i	−0.00687539	+	0.0199186i
$277$	−11.2614	−	6.50177i	−0.676632	−	0.390654i	0.121953	−	0.992536i	$-0.461084\pi$
$277$	−11.2614	−	6.50177i	−0.676632	−	0.390654i	−0.798585	+	0.601882i	$0.794418\pi$
$278$	0.177400	−	0.286153i	0.0106397	−	0.0171623i
$279$	14.4872	+	0.227550i	0.867329	+	0.0136231i
$280$	−8.40475	+	0.797925i	−0.502280	+	0.0476851i
$281$	−0.936692	−	0.540799i	−0.0558784	−	0.0322614i	0.471801	−	0.881705i	$-0.343604\pi$
$281$	−0.936692	−	0.540799i	−0.0558784	−	0.0322614i	−0.527679	+	0.849444i	$0.676938\pi$
$282$	−8.12451	−	2.52221i	−0.483808	−	0.150195i
$283$	−14.6158	−	25.3154i	−0.868821	−	1.50484i	−0.863202	−	0.504858i	$-0.831545\pi$
$283$	−14.6158	−	25.3154i	−0.868821	−	1.50484i	−0.00561859	−	0.999984i	$-0.501788\pi$
$284$	9.31540	−	14.0243i	0.552767	−	0.832189i
$285$	9.69206	+	20.4451i	0.574108	+	1.21106i
$286$	12.0289	+	22.4307i	0.711283	+	1.32635i
$287$		−	5.40284i		−	0.318920i
$288$	5.83671	+	15.9353i	0.343931	+	0.938995i
$289$	24.6531			1.45019
$290$	−12.8583	+	10.4187i	−0.755067	+	0.611805i
$291$	−2.92690	−	2.97323i	−0.171578	−	0.174294i
$292$	12.1310	+	8.05779i	0.709911	+	0.471547i
$293$	2.81552	+	4.87662i	0.164484	+	0.284895i	0.936472	−	0.350742i	$-0.114071\pi$
$293$	2.81552	+	4.87662i	0.164484	+	0.284895i	−0.771988	+	0.635637i	$0.780737\pi$
$294$	8.67675	+	9.38535i	0.506038	+	0.547365i
$295$	5.79991	+	2.01822i	0.337684	+	0.117506i
$296$	9.13306	+	0.861741i	0.530848	+	0.0500877i
$297$	−22.0960	+	5.36609i	−1.28214	+	0.311372i
$298$	7.61387	−	12.2815i	0.441060	−	0.711447i
$299$	0.207814	−	0.359945i	0.0120182	−	0.0208162i
$300$	9.32756	+	14.5944i	0.538527	+	0.842608i
$301$	2.56784	+	4.44762i	0.148008	+	0.256357i
$302$	21.2983	+	0.668101i	1.22558	+	0.0384449i
$303$	5.51007	+	5.59729i	0.316545	+	0.321556i
$304$	21.5401	−	9.06044i	1.23541	−	0.519652i
$305$	0.876095	+	4.58683i	0.0501650	+	0.262641i
$306$	−27.3514	−	1.28822i	−1.56357	−	0.0736426i
$307$	15.2931			0.872826			0.436413	−	0.899747i	$-0.356249\pi$
$307$	15.2931			0.872826			0.436413	+	0.899747i	$0.356249\pi$
$308$	−11.6599	−	0.732233i	−0.664384	−	0.0417229i
$309$	−1.69825	−	6.54305i	−0.0966100	−	0.372221i
$310$	−2.39358	−	15.0841i	−0.135946	−	0.856717i
$311$	1.83417	+	3.17688i	0.104006	+	0.180144i	0.913332	−	0.407216i	$-0.133500\pi$
$311$	1.83417	+	3.17688i	0.104006	+	0.180144i	−0.809326	+	0.587360i	$0.800167\pi$
$312$	−3.20748	−	19.8917i	−0.181588	−	1.12614i
$313$	−21.3301	−	12.3149i	−1.20565	−	0.696081i	−0.243842	−	0.969815i	$-0.578408\pi$
$313$	−21.3301	−	12.3149i	−1.20565	−	0.696081i	−0.961805	+	0.273734i	$0.911741\pi$
$314$	−2.38726	+	3.85075i	−0.134721	+	0.217310i
$315$	−3.07537	+	8.41000i	−0.173278	+	0.473850i
$316$	5.35215	−	2.65759i	0.301082	−	0.149501i
$317$	−5.32466	+	9.22258i	−0.299063	+	0.517992i	−0.975922	−	0.218121i	$-0.930007\pi$
$317$	−5.32466	+	9.22258i	−0.299063	+	0.517992i	0.676859	+	0.736113i	$0.263341\pi$
$318$	−6.62907	+	1.50041i	−0.371740	+	0.0841390i
$319$	−19.8331	+	11.4506i	−1.11044	+	0.641113i
$320$	15.4868	−	8.95323i	0.865736	−	0.500501i
$321$	−2.30166	+	8.32777i	−0.128466	+	0.464811i
$322$	0.0901611	+	0.168126i	0.00502448	+	0.00936932i
$323$			37.7039i			2.09790i
$324$	17.9203	+	1.69181i	0.995573	+	0.0939894i
$325$	−7.57908	−	19.1165i	−0.420412	−	1.06039i
$326$	−13.2336	+	7.09679i	−0.732943	+	0.393055i
$327$	8.32508	+	2.30092i	0.460378	+	0.127241i
$328$	4.76732	+	10.4080i	0.263231	+	0.574685i
$329$	−4.01490	+	2.31800i	−0.221349	+	0.127796i
$330$	9.58292	+	21.9692i	0.527522	+	1.20936i
$331$	3.04582	+	1.75851i	0.167414	+	0.0966563i	0.581366	−	0.813642i	$-0.302519\pi$
$331$	3.04582	+	1.75851i	0.167414	+	0.0966563i	−0.413952	+	0.910299i	$0.635852\pi$
$332$	24.0138	−	11.9240i	1.31793	−	0.654415i
$333$	4.99679	−	8.34907i	0.273822	−	0.457526i
$334$	9.38969	−	15.1460i	0.513781	−	0.828750i
$335$	0.913581	+	0.317903i	0.0499143	+	0.0173689i
$336$	8.53588	+	3.55957i	0.465670	+	0.194191i
$337$	−20.3763	+	11.7643i	−1.10997	+	0.640841i	−0.938821	−	0.344405i	$-0.888081\pi$
$337$	−20.3763	+	11.7643i	−1.10997	+	0.640841i	−0.171147	+	0.985245i	$0.554747\pi$
$338$	−0.173605	+	5.53431i	−0.00944284	+	0.301027i
$339$	8.88175	+	34.2198i	0.482391	+	1.85856i
$340$	3.62745	+	28.6340i	0.196726	+	1.55290i
$341$		−	21.1346i		−	1.14450i
$342$	1.16608	−	24.7581i	0.0630545	−	1.33877i
$343$	16.3097			0.880642
$344$	−8.87111	−	6.30207i	−0.478298	−	0.339785i
$345$	0.222455	−	0.322027i	0.0119766	−	0.0173373i
$346$	0.0761027	−	2.42607i	0.00409131	−	0.130426i
$347$	3.63147	−	2.09663i	0.194947	−	0.112553i	−0.399349	−	0.916799i	$-0.630764\pi$
$347$	3.63147	−	2.09663i	0.194947	−	0.112553i	0.594297	+	0.804246i	$0.297431\pi$
$348$	17.7986	−	3.44572i	0.954104	−	0.184710i
$349$	2.78198	−	4.81854i	0.148916	−	0.257930i	−0.781911	−	0.623390i	$-0.785755\pi$
$349$	2.78198	−	4.81854i	0.148916	−	0.257930i	0.930827	+	0.365460i	$0.119088\pi$
$350$	9.29074	+	1.66664i	0.496611	+	0.0890855i
$351$	−20.5066	−	6.01591i	−1.09456	−	0.321105i
$352$	23.1076	−	8.87779i	1.23164	−	0.473188i
$353$	−5.51109	+	9.54549i	−0.293326	+	0.508055i	−0.974594	−	0.223979i	$-0.928095\pi$
$353$	−5.51109	+	9.54549i	−0.293326	+	0.508055i	0.681268	+	0.732034i	$0.261429\pi$
$354$	−4.56669	−	4.93964i	−0.242717	−	0.262539i
$355$	−14.2464	+	12.3029i	−0.756119	+	0.652973i
$356$	−11.6181	−	7.71712i	−0.615758	−	0.409006i
$357$	−10.6340	+	10.4683i	−0.562811	+	0.554040i
$358$	23.2599	−	12.4736i	1.22932	−	0.659248i
$359$	−27.2920			−1.44042			−0.720209	−	0.693757i	$-0.755954\pi$
$359$	−27.2920			−1.44042			−0.720209	+	0.693757i	$0.755954\pi$
$360$	−1.49638	−	18.9146i	−0.0788661	−	0.996885i
$361$	−15.1292			−0.796272
$362$	24.8367	−	13.3192i	1.30539	−	0.700039i
$363$	3.54603	+	13.6622i	0.186118	+	0.717081i
$364$	−9.14639	−	6.07533i	−0.479401	−	0.318434i
$365$	−10.6420	−	12.3231i	−0.557029	−	0.645019i
$366$	1.51666	−	4.88545i	0.0792770	−	0.255366i
$367$	−15.7443	+	27.2699i	−0.821846	+	1.42348i	0.0824597	+	0.996594i	$0.473722\pi$
$367$	−15.7443	+	27.2699i	−0.821846	+	1.42348i	−0.904306	+	0.426885i	$0.859611\pi$
$368$	−0.322035	−	0.244322i	−0.0167873	−	0.0127361i
$369$	12.1408	+	0.190695i	0.632024	+	0.00992717i
$370$	−9.57627	−	3.67279i	−0.497846	−	0.190939i
$371$	−1.85199	+	3.20774i	−0.0961505	+	0.166538i
$372$	−5.45889	+	15.8149i	−0.283030	+	0.819963i
$373$	20.2988	−	11.7195i	1.05103	−	0.606812i	0.128092	−	0.991762i	$-0.459115\pi$
$373$	20.2988	−	11.7195i	1.05103	−	0.606812i	0.922937	+	0.384950i	$0.125781\pi$
$374$	−1.25227	+	39.9210i	−0.0647535	+	2.06426i
$375$	−5.65859	−	18.5197i	−0.292209	−	0.956355i
$376$	5.68893	−	8.00802i	0.293384	−	0.412982i
$377$	−21.5240			−1.10854
$378$	7.30652	−	6.54507i	0.375807	−	0.336642i
$379$			11.5529i			0.593434i	0.954965	+	0.296717i	$0.0958918\pi$
$379$			11.5529i			0.593434i	−0.954965	+	0.296717i	$0.904108\pi$
$380$	−25.9191	+	3.28353i	−1.32962	+	0.168441i
$381$	32.0258	+	8.85141i	1.64073	+	0.453472i
$382$	0.959787	−	30.5969i	0.0491070	−	1.56547i
$383$	22.7016	−	13.1068i	1.16000	−	0.669725i	0.208695	−	0.977981i	$-0.433079\pi$
$383$	22.7016	−	13.1068i	1.16000	−	0.669725i	0.951304	+	0.308256i	$0.0997452\pi$
$384$	−19.5843	+	0.674692i	−0.999407	+	0.0344302i
$385$	12.3363	+	4.29272i	0.628715	+	0.218777i
$386$	−7.74920	+	12.4998i	−0.394424	+	0.636222i
$387$	−10.0849	+	5.61323i	−0.512646	+	0.285337i
$388$	4.31492	−	2.14256i	0.219057	−	0.108772i
$389$	−1.38545	−	0.799888i	−0.0702449	−	0.0405559i	0.464466	−	0.885591i	$-0.346246\pi$
$389$	−1.38545	−	0.799888i	−0.0702449	−	0.0405559i	−0.534711	+	0.845035i	$0.679580\pi$
$390$	−2.52404	+	22.3850i	−0.127810	+	1.13351i
$391$	0.564834	−	0.326107i	0.0285649	−	0.0164919i
$392$	−13.4183	+	6.14619i	−0.677729	+	0.310430i
$393$	−7.32275	−	28.2133i	−0.369384	−	1.42317i
$394$	−10.1664	+	5.45190i	−0.512174	+	0.274663i
$395$	−6.56234	+	1.25342i	−0.330187	+	0.0630665i
$396$	2.05695	−	26.1752i	0.103366	−	1.31535i
$397$			25.9373i			1.30176i	0.759182	+	0.650879i	$0.225599\pi$
$397$			25.9373i			1.30176i	−0.759182	+	0.650879i	$0.774401\pi$
$398$	6.13669	+	11.4433i	0.307605	+	0.573601i
$399$	−9.47576	−	9.62577i	−0.474382	−	0.481891i
$400$	−19.3682	+	4.98730i	−0.968410	+	0.249365i
$401$	−21.5383	+	12.4351i	−1.07557	+	0.620980i	−0.929698	−	0.368323i	$-0.879932\pi$
$401$	−21.5383	+	12.4351i	−1.07557	+	0.620980i	−0.145872	+	0.989304i	$0.546599\pi$
$402$	−0.719328	−	0.778073i	−0.0358768	−	0.0388068i
$403$	9.93179	−	17.2024i	0.494738	−	0.856911i
$404$	−8.12311	+	4.03351i	−0.404140	+	0.200675i
$405$	−18.7897	−	7.20754i	−0.933666	−	0.358145i
$406$	5.20567	−	8.39696i	0.258353	−	0.416734i
$407$	−12.2914	−	7.09646i	−0.609264	−	0.351759i
$408$	11.2483	−	29.5491i	0.556874	−	1.46290i
$409$	−10.6869	−	18.5102i	−0.528433	−	0.915272i	−0.999450	−	0.0331484i	$-0.989447\pi$
$409$	−10.6869	−	18.5102i	−0.528433	−	0.915272i	0.471018	−	0.882124i	$-0.343887\pi$
$410$	−2.00590	−	12.6409i	−0.0990643	−	0.624291i
$411$	7.39963	−	7.28432i	0.364997	−	0.359309i
$412$	7.79025	+	0.489223i	0.383798	+	0.0241023i
$413$	−3.66606			−0.180395
$414$	−0.380981	+	0.196668i	−0.0187242	+	0.00966570i
$415$	−29.4437	+	5.62381i	−1.44533	+	0.276062i
$416$	22.9802	+	3.63295i	1.12670	+	0.178120i
$417$	0.399124	−	0.103593i	0.0195452	−	0.00507296i
$418$	−36.1360	−	1.13354i	−1.76747	−	0.0554434i
$419$	3.12824	+	5.41826i	0.152824	+	0.264700i	0.932265	−	0.361777i	$-0.117830\pi$
$419$	3.12824	+	5.41826i	0.152824	+	0.264700i	−0.779440	+	0.626476i	$0.784496\pi$
$420$	−8.12238	−	6.39857i	−0.396332	−	0.312218i
$421$	15.3599	−	26.6041i	0.748596	−	1.29661i	−0.199900	−	0.979816i	$-0.564062\pi$
$421$	15.3599	−	26.6041i	0.748596	−	1.29661i	0.948496	−	0.316790i	$-0.102605\pi$
$422$	−7.63286	+	12.3121i	−0.371562	+	0.599344i
$423$	−5.06711	−	9.10375i	−0.246371	−	0.442639i
$424$	0.737236	−	7.81350i	0.0358033	−	0.379457i
$425$	4.69913	−	31.9256i	0.227941	−	1.54862i
$426$	20.1113	−	4.55197i	0.974397	−	0.220544i
$427$	−1.39387	−	2.41425i	−0.0674540	−	0.116834i
$428$	−8.31035	−	5.52001i	−0.401696	−	0.266820i
$429$	−8.30432	+	30.0463i	−0.400936	+	1.45065i
$430$	7.65918	+	9.45267i	0.369358	+	0.455848i
$431$	35.1049			1.69094			0.845472	−	0.534020i	$-0.179319\pi$
$431$	35.1049			1.69094			0.845472	+	0.534020i	$0.179319\pi$
$432$	−8.30003	+	19.0554i	−0.399335	+	0.916805i
$433$			24.5043i			1.17760i	0.808279	+	0.588800i	$0.200399\pi$
$433$			24.5043i			1.17760i	−0.808279	+	0.588800i	$0.799601\pi$
$434$	4.30895	+	8.03505i	0.206836	+	0.385695i
$435$	−20.2026	−	1.63843i	−0.968638	−	0.0785567i
$436$	−5.51823	+	8.30767i	−0.264275	+	0.397865i
$437$	0.295188	+	0.511281i	0.0141208	+	0.0244579i
$438$	3.93744	+	17.3962i	0.188138	+	0.831225i
$439$	15.3741	+	8.87623i	0.733765	+	0.423639i	0.819798	−	0.572653i	$-0.194086\pi$
$439$	15.3741	+	8.87623i	0.733765	+	0.423639i	−0.0860332	+	0.996292i	$0.527419\pi$
$440$	−27.5523	+	2.61574i	−1.31350	+	0.124701i
$441$	−0.245850	+	15.6523i	−0.0117072	+	0.745349i
$442$	−19.7794	+	31.9049i	−0.940808	+	1.51756i
$443$	−6.08715	−	3.51442i	−0.289209	−	0.166975i	0.348376	−	0.937355i	$-0.386733\pi$
$443$	−6.08715	−	3.51442i	−0.289209	−	0.166975i	−0.637585	+	0.770380i	$0.720067\pi$
$444$	7.36463	+	8.48500i	0.349510	+	0.402680i
$445$	10.1921	+	11.8021i	0.483151	+	0.559472i
$446$	1.03087	−	32.8630i	0.0488132	−	1.55611i
$447$	17.1301	−	4.44612i	0.810227	−	0.210294i
$448$	−6.97513	+	8.08640i	−0.329544	+	0.382047i
$449$		−	16.6756i		−	0.786971i	−0.919331	−	0.393485i	$-0.871269\pi$
$449$		−	16.6756i		−	0.786971i	0.919331	−	0.393485i	$-0.128731\pi$
$450$	−4.07304	+	20.8185i	−0.192005	+	0.981394i
$451$		−	17.7115i		−	0.834002i
$452$	−40.7426	−	2.55861i	−1.91637	−	0.120347i
$453$	18.3085	+	18.5983i	0.860206	+	0.873823i
$454$	−24.0510	−	0.754451i	−1.12877	−	0.0354081i
$455$	8.02376	+	9.29123i	0.376160	+	0.435579i
$456$	26.7475	+	10.1818i	1.25257	+	0.476808i
$457$	25.7193	+	14.8490i	1.20310	+	0.694608i	0.961242	−	0.275704i	$-0.0889111\pi$
$457$	25.7193	+	14.8490i	1.20310	+	0.694608i	0.241854	+	0.970313i	$0.422244\pi$
$458$	1.80460	+	1.11876i	0.0843236	+	0.0522762i
$459$	−23.1481	−	24.2652i	−1.08046	−	1.13260i
$460$	0.273368	+	0.359889i	0.0127459	+	0.0167799i
$461$	12.2647	+	7.08100i	0.571222	+	0.329795i	0.757637	−	0.652676i	$-0.226354\pi$
$461$	12.2647	+	7.08100i	0.571222	+	0.329795i	−0.186415	+	0.982471i	$0.559687\pi$
$462$	−9.71325	−	10.5065i	−0.451901	−	0.488806i
$463$	2.85520	+	4.94535i	0.132692	+	0.229830i	0.924714	−	0.380664i	$-0.124304\pi$
$463$	2.85520	+	4.94535i	0.132692	+	0.229830i	−0.792021	+	0.610494i	$0.790971\pi$
$464$	−2.61891	+	20.7691i	−0.121580	+	0.964184i
$465$	10.6315	−	15.3902i	0.493023	−	0.713704i
$466$	−16.8854	+	9.05513i	−0.782202	+	0.419471i
$467$			18.7968i			0.869813i	0.900476	+	0.434907i	$0.143219\pi$
$467$			18.7968i			0.869813i	−0.900476	+	0.434907i	$0.856781\pi$
$468$	13.9748	−	20.3385i	0.645984	−	0.940149i
$469$	−0.577464			−0.0266648
$470$	−8.53299	+	6.91399i	−0.393598	+	0.318919i
$471$	−5.37099	+	1.39404i	−0.247482	+	0.0642340i
$472$	7.06225	−	3.23482i	0.325067	−	0.148895i
$473$	8.41783	+	14.5801i	0.387052	+	0.670394i
$474$	6.98957	+	2.16987i	0.321042	+	0.0996654i
$475$	28.8987	+	4.25359i	1.32596	+	0.195168i
$476$	−7.66304	−	15.4327i	−0.351235	−	0.707354i
$477$	−7.14278	−	4.27485i	−0.327046	−	0.195732i
$478$	−17.6047	−	10.9140i	−0.805219	−	0.499193i
$479$	15.2061	−	26.3377i	0.694783	−	1.20340i	−0.275471	−	0.961309i	$-0.588834\pi$
$479$	15.2061	−	26.3377i	0.694783	−	1.20340i	0.970254	−	0.242090i	$-0.0778329\pi$
$480$	21.2928	+	5.15917i	0.971878	+	0.235483i
$481$	−6.66969	−	11.5522i	−0.304112	−	0.526737i
$482$	1.08420	−	34.5630i	0.0493839	−	1.57430i
$483$	−0.0622440	+	0.225209i	−0.00283220	+	0.0102474i
$484$	−16.2665	−	1.02152i	−0.739384	−	0.0464329i
$485$	−5.29058	+	1.01051i	−0.240233	+	0.0458851i
$486$	14.4496	+	16.6496i	0.655448	+	0.755240i
$487$	−3.67889			−0.166706			−0.0833532	−	0.996520i	$-0.526563\pi$
$487$	−3.67889			−0.166706			−0.0833532	+	0.996520i	$0.526563\pi$
$488$	4.81540	+	3.42088i	0.217983	+	0.154856i
$489$	−17.7267	−	4.89938i	−0.801630	−	0.221557i
$490$	16.2971	−	2.58608i	0.736230	−	0.116827i
$491$	−9.05671	−	15.6867i	−0.408724	−	0.707930i	0.586023	−	0.810294i	$-0.300693\pi$
$491$	−9.05671	−	15.6867i	−0.408724	−	0.707930i	−0.994747	+	0.102364i	$0.967359\pi$
$492$	−4.57473	+	13.2534i	−0.206245	+	0.597509i
$493$	−29.2509	−	16.8880i	−1.31739	−	0.760597i
$494$	−28.8800	−	17.9040i	−1.29937	−	0.805541i
$495$	−10.0816	+	27.5695i	−0.453135	+	1.23916i
$496$	−15.3906	−	11.6765i	−0.691059	−	0.524292i
$497$	5.61859	−	9.73168i	0.252028	−	0.436525i
$498$	31.3606	+	9.73570i	1.40530	+	0.436267i
$499$	19.9488	−	11.5175i	0.893032	−	0.515592i	0.0180991	−	0.999836i	$-0.494239\pi$
$499$	19.9488	−	11.5175i	0.893032	−	0.515592i	0.874933	+	0.484244i	$0.160905\pi$
$500$	22.3562	+	0.450050i	0.999797	+	0.0201268i
$501$	21.1255	−	5.48311i	0.943816	−	0.244967i
$502$	−16.4274	+	8.80951i	−0.733191	+	0.393188i
$503$		−	31.1266i		−	1.38787i	−0.720039	−	0.693934i	$-0.755876\pi$
$503$		−	31.1266i		−	1.38787i	0.720039	−	0.693934i	$-0.244124\pi$
$504$	4.55462	+	10.3708i	0.202879	+	0.461951i
$505$	9.95985	−	1.90235i	0.443208	−	0.0846537i
$506$	0.295564	+	0.551149i	0.0131394	+	0.0245016i
$507$	−4.83272	+	4.75741i	−0.214629	+	0.211284i
$508$	−21.2281	+	31.9588i	−0.941845	+	1.41794i
$509$	−0.489681	+	0.282717i	−0.0217047	+	0.0125312i	−0.510813	−	0.859692i	$-0.670656\pi$
$509$	−0.489681	+	0.282717i	−0.0217047	+	0.0125312i	0.489108	+	0.872223i	$0.337322\pi$
$510$	−20.9936	+	28.4405i	−0.929614	+	1.25937i
$511$	8.41787	+	4.86006i	0.372385	+	0.214996i
$512$	6.30162	−	21.7322i	0.278495	−	0.960438i
$513$	21.9646	−	20.9534i	0.969762	−	0.925113i
$514$	−8.37793	−	5.19387i	−0.369535	−	0.229092i
$515$	−8.24217	−	2.86807i	−0.363194	−	0.126382i
$516$	−2.53308	−	13.0844i	−0.111513	−	0.576010i
$517$	−13.1616	+	7.59884i	−0.578845	+	0.334196i
$518$	6.11985	+	0.191972i	0.268891	+	0.00843477i
$519$	2.11851	−	2.08550i	0.0929923	−	0.0915431i
$520$	−23.6552	−	10.8186i	−1.03735	−	0.474427i
$521$			4.80678i			0.210589i	0.994441	+	0.105294i	$0.0335785\pi$
$521$			4.80678i			0.210589i	−0.994441	+	0.105294i	$0.966422\pi$
$522$	18.6852	+	11.9941i	0.817827	+	0.524967i
$523$	−19.6207			−0.857954			−0.428977	−	0.903315i	$-0.641126\pi$
$523$	−19.6207			−0.857954			−0.428977	+	0.903315i	$0.641126\pi$
$524$	33.5911	+	2.10950i	1.46744	+	0.0921540i
$525$	6.82388	+	9.33156i	0.297819	+	0.407263i
$526$	22.8196	+	0.715822i	0.994980	+	0.0312113i
$527$	26.9943	−	15.5852i	1.17589	−	0.678902i
$528$	27.9821	+	11.6689i	1.21777	+	0.507824i
$529$	−11.4949	+	19.9097i	−0.499778	+	0.865641i
$530$	−3.14214	+	8.19268i	−0.136486	+	0.355867i
$531$	0.129394	−	8.23803i	0.00561523	−	0.357500i
$532$	13.9695	−	6.93650i	0.605653	−	0.300735i
$533$	8.32317	−	14.4162i	0.360517	−	0.624433i
$534$	−3.77097	−	16.6608i	−0.163186	−	0.720981i
$535$	7.29034	+	8.44195i	0.315189	+	0.364977i
$536$	1.11242	−	0.509538i	0.0480493	−	0.0220087i
$537$	31.1571	+	8.61131i	1.34453	+	0.371606i
$538$	−14.5458	−	27.1240i	−0.627112	−	1.16940i
$539$	22.8343			0.983542
$540$	14.6650	−	18.0261i	0.631080	−	0.775718i
$541$	40.3065			1.73291			0.866457	−	0.499252i	$-0.166392\pi$
$541$	40.3065			1.73291			0.866457	+	0.499252i	$0.166392\pi$
$542$	20.1542	+	37.5823i	0.865699	+	1.61430i
$543$	33.2692	+	9.19508i	1.42772	+	0.394599i
$544$	28.3793	+	22.9677i	1.21675	+	0.984730i
$545$	8.43922	−	7.28798i	0.361497	−	0.312183i
$546$	−2.96871	−	13.1162i	−0.127049	−	0.561324i
$547$	1.44201	−	2.49763i	0.0616557	−	0.106791i	−0.833550	−	0.552444i	$-0.813695\pi$
$547$	1.44201	−	2.49763i	0.0616557	−	0.106791i	0.895206	+	0.445653i	$0.147029\pi$
$548$	5.33231	+	10.7388i	0.227785	+	0.458737i
$549$	5.47428	−	3.04696i	0.233637	−	0.130041i
$550$	30.4567	+	5.46353i	1.29868	+	0.232966i
$551$	15.2868	−	26.4775i	0.651240	−	1.12798i
$552$	−0.0788115	−	0.488762i	−0.00335444	−	0.0208031i
$553$	3.45405	−	1.99419i	0.146881	−	0.0848018i
$554$	18.3807	+	0.576582i	0.780923	+	0.0244966i
$555$	−5.38083	−	11.3507i	−0.228404	−	0.481810i
$556$	−0.0298425	+	0.475204i	−0.00126560	+	0.0201531i
$557$	−17.0510			−0.722475			−0.361237	−	0.932474i	$-0.617646\pi$
$557$	−17.0510			−0.722475			−0.361237	+	0.932474i	$0.617646\pi$
$558$	−18.2077	+	9.39909i	−0.770795	+	0.397895i
$559$			15.8232i			0.669249i
$560$	9.94165	−	6.61186i	0.420111	−	0.279402i
$561$	−34.8601	+	34.3169i	−1.47180	+	1.44886i
$562$	1.52886	+	0.0479585i	0.0644910	+	0.00202301i
$563$	−19.0842	+	11.0182i	−0.804302	+	0.464364i	−0.844973	−	0.534809i	$-0.820384\pi$
$563$	−19.0842	+	11.0182i	−0.804302	+	0.464364i	0.0406715	+	0.999173i	$0.487050\pi$
$564$	11.8114	−	2.28663i	0.497351	−	0.0962847i
$565$	43.1061	+	14.9999i	1.81349	+	0.631049i
$566$	35.1357	+	21.7822i	1.47686	+	0.915576i
$567$	12.0080	+	0.377311i	0.504289	+	0.0158456i
$568$	−2.23663	+	23.7047i	−0.0938470	+	0.994627i
$569$	−24.1641	−	13.9512i	−1.01301	−	0.584864i	−0.100941	−	0.994892i	$-0.532185\pi$
$569$	−24.1641	−	13.9512i	−1.01301	−	0.584864i	−0.912073	+	0.410029i	$0.865519\pi$
$570$	−25.7440	−	19.0032i	−1.07830	−	0.795956i
$571$	−11.2510	+	6.49576i	−0.470839	+	0.271839i	−0.716591	−	0.697494i	$-0.754298\pi$
$571$	−11.2510	+	6.49576i	−0.470839	+	0.271839i	0.245752	+	0.969333i	$0.420965\pi$
$572$	−29.9835	−	19.9160i	−1.25367	−	0.832731i
$573$	26.7181	−	26.3017i	1.11616	−	1.09877i
$574$	3.61104	+	6.73364i	0.150722	+	0.281057i
$575$	−0.186227	−	0.469715i	−0.00776621	−	0.0195885i
$576$	−17.9249	−	15.9593i	−0.746869	−	0.664971i
$577$		−	34.6251i		−	1.44146i	−0.693216	−	0.720730i	$-0.743807\pi$
$577$		−	34.6251i		−	1.44146i	0.693216	−	0.720730i	$-0.256193\pi$
$578$	−30.7255	+	16.4772i	−1.27801	+	0.685359i
$579$	−17.4346	+	4.52515i	−0.724557	+	0.188059i
$580$	9.06209	−	21.5789i	0.376283	−	0.896015i
$581$	15.4975	−	8.94748i	0.642944	−	0.371204i
$582$	5.63502	+	1.74936i	0.233579	+	0.0725132i
$583$	−6.07116	+	10.5156i	−0.251442	+	0.435510i
$584$	−20.5045	−	1.93468i	−0.848482	−	0.0800577i
$585$	−21.1616	+	17.7023i	−0.874925	+	0.731902i
$586$	−6.76835	−	4.19601i	−0.279598	−	0.173336i
$587$	9.41209	+	5.43407i	0.388479	+	0.224288i	0.681501	−	0.731817i	$-0.261328\pi$
$587$	9.41209	+	5.43407i	0.388479	+	0.224288i	−0.293022	+	0.956106i	$0.594661\pi$
$588$	−17.0867	−	5.89790i	−0.704645	−	0.243225i
$589$	14.1075	+	24.4350i	0.581291	+	1.00683i
$590$	−8.57740	+	1.36109i	−0.353126	+	0.0560350i
$591$	−13.6180	−	3.76380i	−0.560171	−	0.154822i
$592$	−11.9586	+	5.03017i	−0.491496	+	0.206739i
$593$	4.49540			0.184604			0.0923019	−	0.995731i	$-0.470578\pi$
$593$	4.49540			0.184604			0.0923019	+	0.995731i	$0.470578\pi$
$594$	23.9521	−	21.4559i	0.982767	−	0.880347i
$595$	3.61418	+	18.9222i	0.148167	+	0.775734i
$596$	−1.28082	+	20.3954i	−0.0524643	+	0.835427i
$597$	−4.23656	+	15.3285i	−0.173391	+	0.627355i
$598$	−0.0184291	+	0.587499i	−0.000753623	+	0.0240246i
$599$	−3.45192	−	5.97890i	−0.141042	−	0.244291i	0.786847	−	0.617148i	$-0.211712\pi$
$599$	−3.45192	−	5.97890i	−0.141042	−	0.244291i	−0.927889	+	0.372856i	$0.878379\pi$
$600$	−21.3794	−	11.9550i	−0.872809	−	0.488062i
$601$	−15.7058	+	27.2032i	−0.640653	+	1.10964i	0.344635	+	0.938737i	$0.388003\pi$
$601$	−15.7058	+	27.2032i	−0.640653	+	1.10964i	−0.985287	+	0.170906i	$0.945331\pi$
$602$	−6.17294	−	3.82689i	−0.251590	−	0.155973i
$603$	0.0203817	−	1.29763i	0.000830008	−	0.0528434i
$604$	−26.9909	+	13.4022i	−1.09824	+	0.545330i
$605$	17.2101	+	5.98868i	0.699689	+	0.243474i
$606$	−10.6083	−	3.29327i	−0.430932	−	0.133780i
$607$	−9.81362	−	16.9977i	−0.398322	−	0.689915i	0.595197	−	0.803580i	$-0.297074\pi$
$607$	−9.81362	−	16.9977i	−0.398322	−	0.689915i	−0.993519	+	0.113665i	$0.963741\pi$
$608$	−20.7901	+	25.6887i	−0.843148	+	1.04181i
$609$	11.7120	−	3.03985i	0.474594	−	0.123181i
$610$	−4.15754	−	5.13108i	−0.168334	−	0.207751i
$611$	−14.2837			−0.577857
$612$	34.9494	−	16.6750i	1.41274	−	0.674047i
$613$			28.8088i			1.16358i	0.813340	+	0.581788i	$0.197647\pi$
$613$			28.8088i			1.16358i	−0.813340	+	0.581788i	$0.802353\pi$
$614$	−19.0600	+	10.2213i	−0.769200	+	0.412499i
$615$	8.90954	−	12.8975i	0.359267	−	0.520077i
$616$	15.0213	−	6.88040i	0.605224	−	0.277219i
$617$	−8.02269	−	13.8957i	−0.322981	−	0.559420i	0.658120	−	0.752913i	$-0.271352\pi$
$617$	−8.02269	−	13.8957i	−0.322981	−	0.559420i	−0.981102	+	0.193493i	$0.938018\pi$
$618$	6.48966	+	7.01965i	0.261052	+	0.282372i
$619$	−2.13387	−	1.23199i	−0.0857674	−	0.0495178i	0.456503	−	0.889722i	$-0.349102\pi$
$619$	−2.13387	−	1.23199i	−0.0857674	−	0.0495178i	−0.542270	+	0.840204i	$0.682435\pi$
$620$	13.0647	+	17.1997i	0.524692	+	0.690756i
$621$	−0.503872	−	0.147818i	−0.0202197	−	0.00593173i
$622$	−4.40924	−	2.73350i	−0.176795	−	0.109603i
$623$	−8.06198	−	4.65458i	−0.322996	−	0.186482i
$624$	17.2923	+	22.6475i	0.692246	+	0.906626i
$625$	−23.9397	−	7.20343i	−0.957589	−	0.288137i
$626$	34.8148	+	1.09210i	1.39148	+	0.0436490i
$627$	−31.0633	−	31.5550i	−1.24055	−	1.26019i
$628$	0.401588	−	6.39478i	0.0160251	−	0.255179i
$629$		−	20.9324i		−	0.834631i
$630$	−1.78802	−	12.5369i	−0.0712366	−	0.499484i
$631$			44.4737i			1.77047i	0.465144	+	0.885235i	$0.346003\pi$
$631$			44.4737i			1.77047i	−0.465144	+	0.885235i	$0.653997\pi$
$632$	−4.89422	+	6.88935i	−0.194682	+	0.274044i
$633$	−17.1728	+	4.45721i	−0.682559	+	0.177158i
$634$	0.472194	−	15.0530i	0.0187532	−	0.597831i
$635$	32.4649	−	28.0362i	1.28833	−	1.11258i
$636$	7.25908	−	6.30058i	0.287841	−	0.249834i
$637$	18.5858	+	10.7305i	0.736397	+	0.425159i
$638$	17.0651	−	27.5267i	0.675614	−	1.08979i
$639$	21.6698	+	12.9691i	0.857246	+	0.513048i
$640$	−13.3174	+	21.5092i	−0.526415	+	0.850227i
$641$	−14.1935	−	8.19465i	−0.560611	−	0.323669i	0.192779	−	0.981242i	$-0.438250\pi$
$641$	−14.1935	−	8.19465i	−0.560611	−	0.323669i	−0.753391	+	0.657573i	$0.771583\pi$
$642$	−2.69735	−	11.9173i	−0.106456	−	0.470340i
$643$	−17.5507	−	30.3987i	−0.692133	−	1.19881i	−0.971138	−	0.238520i	$-0.923338\pi$
$643$	−17.5507	−	30.3987i	−0.692133	−	1.19881i	0.279005	−	0.960290i	$-0.409995\pi$
$644$	−0.224738	−	0.149278i	−0.00885591	−	0.00588239i
$645$	−1.20448	+	14.8517i	−0.0474262	+	0.584785i
$646$	−25.1998	−	46.9909i	−0.991472	−	1.84883i
$647$			19.0579i			0.749243i	0.927178	+	0.374621i	$0.122227\pi$
$647$			19.0579i			0.749243i	−0.927178	+	0.374621i	$0.877773\pi$
$648$	−23.4651	+	9.86869i	−0.921795	+	0.387679i
$649$	−12.0180			−0.471747
$650$	22.2226	+	18.7596i	0.871641	+	0.735810i
$651$	−2.97475	+	10.7631i	−0.116590	+	0.421839i
$652$	11.7500	−	17.6896i	0.460167	−	0.692780i
$653$	21.0708	+	36.4956i	0.824563	+	1.42818i	0.902253	+	0.431207i	$0.141912\pi$
$653$	21.0708	+	36.4956i	0.824563	+	1.42818i	−0.0776903	+	0.996978i	$0.524755\pi$
$654$	−11.9135	+	2.69648i	−0.465854	+	0.105441i
$655$	−35.5398	−	12.3670i	−1.38865	−	0.483217i
$656$	−12.8978	−	9.78533i	−0.503576	−	0.382053i
$657$	−11.2182	+	18.7444i	−0.437664	+	0.731287i
$658$	3.45456	−	5.57236i	0.134673	−	0.217233i
$659$	10.0696	−	17.4410i	0.392256	−	0.679407i	−0.600491	−	0.799631i	$-0.705028\pi$
$659$	10.0696	−	17.4410i	0.392256	−	0.679407i	0.992747	+	0.120225i	$0.0383616\pi$
$660$	−26.6266	−	20.9756i	−1.03644	−	0.816476i
$661$	3.54725	+	6.14402i	0.137972	+	0.238975i	0.926729	−	0.375731i	$-0.122608\pi$
$661$	3.54725	+	6.14402i	0.137972	+	0.238975i	−0.788757	+	0.614705i	$0.789275\pi$
$662$	−4.97136	−	0.155946i	−0.193218	−	0.00606100i
$663$	−44.5007	+	11.5502i	−1.72827	+	0.448571i
$664$	−21.9592	+	30.9109i	−0.852183	+	1.19958i
$665$	−17.1281	+	3.27151i	−0.664201	+	0.126864i
$666$	−0.647384	+	13.7452i	−0.0250856	+	0.532616i
$667$	−0.528872			−0.0204780
$668$	−1.57955	+	25.1523i	−0.0611145	+	0.973171i
$669$	28.6969	−	28.2497i	1.10949	−	1.09220i
$670$	−1.35108	+	0.214393i	−0.0521968	+	0.00828274i
$671$	−4.56935	−	7.91434i	−0.176398	−	0.305530i
$672$	−13.0174	+	1.26869i	−0.502159	+	0.0489409i
$673$	−19.8408	−	11.4551i	−0.764806	−	0.441561i	0.0662129	−	0.997806i	$-0.478908\pi$
$673$	−19.8408	−	11.4551i	−0.764806	−	0.441561i	−0.831018	+	0.556245i	$0.812242\pi$
$674$	17.5325	−	28.2807i	0.675327	−	1.08933i
$675$	−21.2099	+	15.0047i	−0.816370	+	0.577530i
$676$	−3.48254	−	7.01351i	−0.133944	−	0.269750i
$677$	11.6227	−	20.1311i	0.446696	−	0.773699i	−0.551473	−	0.834193i	$-0.685934\pi$
$677$	11.6227	−	20.1311i	0.446696	−	0.773699i	0.998169	+	0.0604934i	$0.0192674\pi$
$678$	−33.9406	−	36.7124i	−1.30348	−	1.40993i
$679$	2.78467	−	1.60773i	0.106866	−	0.0616989i
$680$	−23.6587	−	33.2625i	−0.907271	−	1.27556i
$681$	−20.6748	−	21.0020i	−0.792258	−	0.804800i
$682$	14.1255	+	26.3403i	0.540894	+	1.00862i
$683$			30.3578i			1.16161i	0.814043	+	0.580804i	$0.197262\pi$
$683$			30.3578i			1.16161i	−0.814043	+	0.580804i	$0.802738\pi$
$684$	15.0940	+	31.6357i	0.577134	+	1.20962i
$685$	−2.51492	−	13.1669i	−0.0960900	−	0.503083i
$686$	−20.3270	+	10.9007i	−0.776089	+	0.416193i
$687$	0.653300	+	2.51705i	0.0249249	+	0.0960313i
$688$	15.2682	+	1.92526i	0.582096	+	0.0734000i
$689$	−9.88316	+	5.70604i	−0.376518	+	0.217383i
$690$	−0.0620186	+	0.550026i	−0.00236101	+	0.0209391i
$691$	10.6015	+	6.12077i	0.403299	+	0.232845i	0.687907	−	0.725799i	$-0.258530\pi$
$691$	10.6015	+	6.12077i	0.403299	+	0.232845i	−0.284607	+	0.958644i	$0.591863\pi$
$692$	1.52664	+	3.07450i	0.0580340	+	0.116875i
$693$	0.275219	−	17.5221i	0.0104547	−	0.665610i
$694$	−3.12464	+	5.04018i	−0.118610	+	0.191323i
$695$	0.174952	−	0.502771i	0.00663629	−	0.0190712i
$696$	−19.8796	+	16.1903i	−0.753535	+	0.613691i
$697$	22.6222	−	13.0609i	0.856875	−	0.494717i
$698$	−0.246708	+	7.86477i	−0.00933804	+	0.297686i
$699$	−22.6184	−	6.25134i	−0.855505	−	0.236448i
$700$	−12.6931	+	4.13240i	−0.479754	+	0.156190i
$701$		−	0.0365464i		−	0.00138034i	−1.00000		0.000690169i	$-0.999780\pi$
$701$		−	0.0365464i		−	0.00138034i	1.00000		0.000690169i	$-0.000219688\pi$
$702$	29.5784	−	6.20808i	1.11637	−	0.234309i
$703$	18.9478			0.714630
$704$	−22.8657	+	26.5087i	−0.861785	+	0.999083i
$705$	−13.4067	−	1.08729i	−0.504927	−	0.0409497i
$706$	0.488727	−	15.5801i	0.0183935	−	0.586363i
$707$	−5.24231	+	3.02665i	−0.197157	+	0.113829i
$708$	8.99297	+	3.10414i	0.337977	+	0.116661i
$709$	13.6359	−	23.6181i	0.512109	−	0.886998i	−0.487793	−	0.872959i	$-0.662198\pi$
$709$	13.6359	−	23.6181i	0.512109	−	0.886998i	0.999901	−	0.0140387i	$-0.00446880\pi$
$710$	9.53265	−	24.8550i	0.357754	−	0.932792i
$711$	4.35927	+	7.83201i	0.163485	+	0.293723i
$712$	19.6376	+	1.85289i	0.735950	+	0.0694398i
$713$	0.244036	−	0.422683i	0.00913923	−	0.0158296i
$714$	6.25671	−	20.1541i	0.234152	−	0.754248i
$715$	26.3033	+	30.4583i	0.983689	+	1.13908i
$716$	−20.6523	+	31.0919i	−0.771812	+	1.16196i
$717$	−6.37321	−	24.5548i	−0.238012	−	0.917017i
$718$	34.0144	−	18.2409i	1.26941	−	0.680743i
$719$	−7.73269			−0.288381			−0.144190	−	0.989550i	$-0.546058\pi$
$719$	−7.73269			−0.288381			−0.144190	+	0.989550i	$0.546058\pi$
$720$	14.5067	+	22.5734i	0.540632	+	0.841259i
$721$	5.20978			0.194022
$722$	18.8557	−	10.1117i	0.701735	−	0.376319i
$723$	30.1814	−	29.7110i	1.12246	−	1.10497i
$724$	−22.0523	+	33.1997i	−0.819568	+	1.23386i
$725$	−16.2440	+	20.5145i	−0.603287	+	0.761890i
$726$	−13.5507	−	14.6574i	−0.502915	−	0.543987i
$727$	8.24957	−	14.2887i	0.305960	−	0.529938i	−0.671515	−	0.740991i	$-0.734356\pi$
$727$	8.24957	−	14.2887i	0.305960	−	0.529938i	0.977475	+	0.211053i	$0.0676894\pi$
$728$	15.4598	+	1.45869i	0.572977	+	0.0540627i
$729$	−1.27169	+	26.9700i	−0.0470995	+	0.998890i
$730$	21.4995	+	8.24571i	0.795733	+	0.305188i
$731$	−12.4150	+	21.5035i	−0.459187	+	0.795335i
$732$	1.37500	+	7.10247i	0.0508216	+	0.262515i
$733$	−37.1399	+	21.4427i	−1.37179	+	0.792006i	−0.991154	−	0.132717i	$-0.957630\pi$
$733$	−37.1399	+	21.4427i	−1.37179	+	0.792006i	−0.380641	+	0.924723i	$0.624297\pi$
$734$	1.39622	−	44.5097i	0.0515353	−	1.64288i
$735$	16.6279	+	11.4865i	0.613330	+	0.423685i
$736$	0.564652	+	0.0892658i	0.0208133	+	0.00329038i
$737$	−1.89303			−0.0697307
$738$	−15.2587	+	7.87675i	−0.561680	+	0.289947i
$739$			3.04457i			0.111996i	0.998431	+	0.0559981i	$0.0178341\pi$
$739$			3.04457i			0.111996i	−0.998431	+	0.0559981i	$0.982166\pi$
$740$	14.3898	−	1.82294i	0.528978	−	0.0670128i
$741$	−10.4551	−	40.2816i	−0.384077	−	1.47978i
$742$	0.164236	−	5.23564i	0.00602928	−	0.192207i
$743$	−35.0211	+	20.2194i	−1.28480	+	0.741779i	−0.977722	−	0.209905i	$-0.932684\pi$
$743$	−35.0211	+	20.2194i	−1.28480	+	0.741779i	−0.307078	+	0.951684i	$0.599351\pi$
$744$	−3.76654	−	23.3588i	−0.138088	−	0.856374i
$745$	7.50879	−	21.5785i	0.275101	−	0.790576i
$746$	−17.4658	+	28.1730i	−0.639467	+	1.03149i
$747$	19.5590	+	35.1404i	0.715626	+	1.28572i
$748$	−25.1208	−	50.5910i	−0.918509	−	1.84979i
$749$	−5.76668	−	3.32940i	−0.210710	−	0.121653i
$750$	19.4302	+	19.2994i	0.709491	+	0.704715i
$751$	12.0862	−	6.97795i	0.441030	−	0.254629i	−0.263004	−	0.964795i	$-0.584713\pi$
$751$	12.0862	−	6.97795i	0.441030	−	0.254629i	0.704034	+	0.710166i	$0.251380\pi$
$752$	−1.73795	+	13.7827i	−0.0633765	+	0.502605i
$753$	−22.0048	−	6.08178i	−0.801901	−	0.221632i
$754$	26.8257	−	14.3858i	0.976934	−	0.523900i
$755$	33.0939	−	6.32101i	1.20441	−	0.230045i
$756$	−4.73176	+	13.0406i	−0.172092	+	0.474282i
$757$		−	31.7859i		−	1.15528i	−0.816293	−	0.577639i	$-0.803974\pi$
$757$		−	31.7859i		−	1.15528i	0.816293	−	0.577639i	$-0.196026\pi$
$758$	−7.72151	−	14.3986i	−0.280458	−	0.522979i
$759$	−0.204047	+	0.738275i	−0.00740644	+	0.0267977i
$760$	30.1088	−	21.4156i	1.09216	−	0.776825i
$761$	−21.6921	+	12.5240i	−0.786339	+	0.453993i	−0.838672	−	0.544637i	$-0.816668\pi$
$761$	−21.6921	+	12.5240i	−0.786339	+	0.453993i	0.0523332	+	0.998630i	$0.483334\pi$
$762$	−45.8301	+	10.3731i	−1.66025	+	0.375778i
$763$	−3.32832	+	5.76482i	−0.120493	+	0.208700i
$764$	19.2535	+	38.7748i	0.696568	+	1.40282i
$765$	−42.6478	+	7.45360i	−1.54193	+	0.269486i
$766$	−19.5333	+	31.5080i	−0.705766	+	1.13843i
$767$	−9.78196	−	5.64762i	−0.353206	−	0.203924i
$768$	23.9572	−	13.9302i	0.864482	−	0.502664i
$769$	−1.59810	−	2.76799i	−0.0576290	−	0.0998164i	0.835772	−	0.549077i	$-0.185021\pi$
$769$	−1.59810	−	2.76799i	−0.0576290	−	0.0998164i	−0.893401	+	0.449261i	$0.851687\pi$
$770$	−18.2440	+	2.89500i	−0.657466	+	0.104329i
$771$	−3.03296	−	11.6855i	−0.109230	−	0.420842i
$772$	1.30358	−	20.7579i	0.0469170	−	0.747093i
$773$	−26.8609			−0.966121			−0.483060	−	0.875587i	$-0.660475\pi$
$773$	−26.8609			−0.966121			−0.483060	+	0.875587i	$0.660475\pi$
$774$	8.81733	−	13.7362i	0.316932	−	0.493738i
$775$	−8.90011	−	22.4485i	−0.319701	−	0.806372i
$776$	−3.94574	+	5.55422i	−0.141644	+	0.199385i
$777$	5.26075	+	5.34403i	0.188728	+	0.191716i
$778$	2.26131	+	0.0709346i	0.0810720	+	0.00254313i
$779$	11.8226	+	20.4773i	0.423588	+	0.733676i
$780$	−11.8155	−	29.5857i	−0.423062	−	1.05934i
$781$	18.4187	−	31.9022i	0.659074	−	1.14155i
$782$	−0.486003	+	0.783943i	−0.0173794	+	0.0280337i
$783$	6.41751	+	26.4255i	0.229343	+	0.944369i
$784$	12.6156	−	16.6284i	0.450557	−	0.593870i
$785$	−2.35431	+	6.76575i	−0.0840289	+	0.241480i
$786$	27.9830	+	30.2683i	0.998122	+	1.07964i
$787$	16.8518	+	29.1883i	0.600703	+	1.04045i	0.992715	+	0.120488i	$0.0384461\pi$
$787$	16.8518	+	29.1883i	0.600703	+	1.04045i	−0.392011	+	0.919960i	$0.628221\pi$
$788$	9.02663	−	13.5896i	0.321560	−	0.484108i
$789$	19.6162	+	19.9267i	0.698354	+	0.709409i
$790$	7.34099	−	5.94816i	0.261181	−	0.211626i
$791$	−27.2469			−0.968787
$792$	14.9308	+	33.9973i	0.530545	+	1.20804i
$793$		−	8.58910i		−	0.305008i
$794$	−17.3355	−	32.3260i	−0.615212	−	1.14721i
$795$	−9.71072	+	4.60340i	−0.344404	+	0.163266i
$796$	−15.2965	−	10.1604i	−0.542169	−	0.360127i
$797$	14.4698	+	25.0624i	0.512546	+	0.887755i	0.999894	+	0.0145477i	$0.00463085\pi$
$797$	14.4698	+	25.0624i	0.512546	+	0.887755i	−0.487348	+	0.873208i	$0.662036\pi$
$798$	18.2432	+	5.66350i	0.645804	+	0.200486i
$799$	−19.4113	−	11.2071i	−0.686724	−	0.396480i
$800$	20.8055	−	19.1606i	0.735586	−	0.677431i
$801$	10.7439	−	17.9519i	0.379618	−	0.634298i
$802$	18.5323	−	29.8934i	0.654398	−	1.05557i
$803$	27.5953	+	15.9322i	0.973817	+	0.562233i
$804$	1.41654	+	0.488953i	0.0499575	+	0.0172441i
$805$	0.197153	+	0.228297i	0.00694875	+	0.00804640i
$806$	−0.880759	+	28.0775i	−0.0310234	+	0.988989i
$807$	10.0419	−	36.3331i	0.353491	−	1.27899i
$808$	7.42810	−	10.4562i	0.261320	−	0.367847i
$809$		−	14.9996i		−	0.527358i	−0.964610	−	0.263679i	$-0.915064\pi$
$809$		−	14.9996i		−	0.527358i	0.964610	−	0.263679i	$-0.0849360\pi$
$810$	28.2350	−	3.57540i	0.992078	−	0.125627i
$811$			17.4677i			0.613376i	0.951810	+	0.306688i	$0.0992207\pi$
$811$			17.4677i			0.613376i	−0.951810	+	0.306688i	$0.900779\pi$
$812$	−0.875705	+	13.9445i	−0.0307312	+	0.489356i
$813$	−13.9138	+	50.3423i	−0.487978	+	1.76558i
$814$	20.0620	+	0.629319i	0.703171	+	0.0220576i
$815$	−17.9698	+	15.5184i	−0.629454	+	0.543587i
$816$	5.73052	+	44.3454i	0.200608	+	1.55240i
$817$	−19.4647	−	11.2379i	−0.680984	−	0.393166i
$818$	25.6907	+	15.9269i	0.898254	+	0.556870i
$819$	8.45819	−	14.1327i	0.295553	−	0.493836i
$820$	10.9487	+	14.4139i	0.382344	+	0.503355i
$821$	15.8290	+	9.13886i	0.552435	+	0.318948i	0.750103	−	0.661320i	$-0.230004\pi$
$821$	15.8290	+	9.13886i	0.552435	+	0.318948i	−0.197669	+	0.980269i	$0.563337\pi$
$822$	−4.35372	+	14.0242i	−0.151853	+	0.489149i
$823$	14.6369	+	25.3518i	0.510210	+	0.883710i	0.999930	+	0.0118300i	$0.00376570\pi$
$823$	14.6369	+	25.3518i	0.510210	+	0.883710i	−0.489720	+	0.871880i	$0.662901\pi$
$824$	−10.0361	+	4.59696i	−0.349623	+	0.160143i
$825$	22.3699	+	30.5905i	0.778820	+	1.06503i
$826$	4.56905	−	2.45024i	0.158978	−	0.0852548i
$827$		−	24.5270i		−	0.852886i	−0.904514	−	0.426443i	$-0.859767\pi$
$827$		−	24.5270i		−	0.852886i	0.904514	−	0.426443i	$-0.140233\pi$
$828$	0.343377	−	0.499742i	0.0119332	−	0.0173672i
$829$	−42.2094			−1.46599			−0.732996	−	0.680233i	$-0.761879\pi$
$829$	−42.2094			−1.46599			−0.732996	+	0.680233i	$0.761879\pi$
$830$	32.9373	−	26.6880i	1.14327	−	0.926353i
$831$	15.8005	+	16.0506i	0.548112	+	0.556789i
$832$	−31.0687	+	10.8313i	−1.07711	+	0.375506i
$833$	16.8386	+	29.1653i	0.583422	+	1.01052i
$834$	−0.428197	+	0.395868i	−0.0148272	+	0.0137078i
$835$	9.26010	−	26.6114i	0.320459	−	0.920925i
$836$	45.7944	−	22.7391i	1.58383	−	0.786448i
$837$	−24.0809	−	7.06447i	−0.832358	−	0.244184i
$838$	−7.52011	−	4.66207i	−0.259778	−	0.161048i
$839$	−18.2179	+	31.5544i	−0.628953	+	1.08938i	0.358810	+	0.933411i	$0.383183\pi$
$839$	−18.2179	+	31.5544i	−0.628953	+	1.08938i	−0.987762	+	0.155967i	$0.950151\pi$
$840$	14.3996	+	2.54595i	0.496832	+	0.0878435i
$841$	−0.805742	−	1.39559i	−0.0277842	−	0.0481237i
$842$	−1.36213	+	43.4230i	−0.0469420	+	1.49646i
$843$	1.31424	+	1.33504i	0.0452648	+	0.0459814i
$844$	1.28401	−	20.4462i	0.0441975	−	0.703788i
$845$	1.64250	+	8.59936i	0.0565036	+	0.295827i
$846$	12.3998	+	7.95947i	0.426313	+	0.273652i
$847$	−10.8783			−0.373783
$848$	4.30340	+	10.2308i	0.147779	+	0.351327i
$849$	12.7197	+	49.0069i	0.436541	+	1.68191i
$850$	15.4812	+	42.9300i	0.531001	+	1.47249i
$851$	−0.163882	−	0.283852i	−0.00561781	−	0.00973033i
$852$	−22.0227	+	19.1148i	−0.754484	+	0.654861i
$853$	−27.1128	−	15.6536i	−0.928324	−	0.535968i	−0.0420430	−	0.999116i	$-0.513387\pi$
$853$	−27.1128	−	15.6536i	−0.928324	−	0.535968i	−0.886281	+	0.463148i	$0.846720\pi$
$854$	3.35078	+	2.07731i	0.114661	+	0.0710839i
$855$	−6.74691	−	38.6043i	−0.230740	−	1.32024i
$856$	14.0466	+	1.32536i	0.480104	+	0.0452998i
$857$	4.60165	−	7.97029i	0.157189	−	0.272260i	−0.776665	−	0.629914i	$-0.783090\pi$
$857$	4.60165	−	7.97029i	0.157189	−	0.272260i	0.933854	+	0.357654i	$0.116423\pi$
$858$	−9.73197	−	42.9974i	−0.332244	−	1.46791i
$859$	4.62482	−	2.67014i	0.157797	−	0.0911040i	−0.419022	−	0.907976i	$-0.637627\pi$
$859$	4.62482	−	2.67014i	0.157797	−	0.0911040i	0.576819	+	0.816872i	$0.304294\pi$
$860$	−15.8635	−	6.66190i	−0.540941	−	0.227169i
$861$	−2.49294	+	9.01984i	−0.0849590	+	0.307395i
$862$	−43.7517	+	23.4627i	−1.49019	+	0.799142i
$863$		−	19.0360i		−	0.647992i	−0.946058	−	0.323996i	$-0.894974\pi$
$863$		−	19.0360i		−	0.647992i	0.946058	−	0.323996i	$-0.105026\pi$
$864$	−2.39144	−	29.2964i	−0.0813584	−	0.996685i
$865$	−0.720019	−	3.76969i	−0.0244814	−	0.128173i
$866$	−16.3776	−	30.5400i	−0.556535	−	1.03779i
$867$	−41.1575	−	11.3753i	−1.39778	−	0.386324i
$868$	−10.7406	−	7.13426i	−0.364560	−	0.242152i
$869$	11.3230	−	6.53733i	0.384106	−	0.221764i
$870$	26.2738	−	11.4606i	0.890764	−	0.388550i
$871$	−1.54082	−	0.889593i	−0.0522087	−	0.0301427i
$872$	1.32493	−	14.0421i	0.0448678	−	0.475526i
$873$	3.51446	+	6.31420i	0.118946	+	0.213703i
$874$	−0.709616	−	0.439924i	−0.0240031	−	0.0148807i
$875$	14.9109	−	0.635422i	0.504081	−	0.0214812i
$876$	−16.5342	−	19.0495i	−0.558640	−	0.643624i
$877$	21.1121	−	12.1891i	0.712904	−	0.411595i	−0.0992316	−	0.995064i	$-0.531638\pi$
$877$	21.1121	−	12.1891i	0.712904	−	0.411595i	0.812135	+	0.583469i	$0.198305\pi$
$878$	−25.0934	−	0.787150i	−0.846862	−	0.0265650i
$879$	−2.45026	−	9.44043i	−0.0826454	−	0.318418i
$880$	32.5905	−	21.6749i	1.09863	−	0.730659i
$881$			42.8577i			1.44391i	0.691939	+	0.721956i	$0.256757\pi$
$881$			42.8577i			1.44391i	−0.691939	+	0.721956i	$0.743243\pi$
$882$	−10.1550	−	19.6720i	−0.341936	−	0.662391i
$883$	28.8663			0.971427			0.485713	−	0.874118i	$-0.338560\pi$
$883$	28.8663			0.971427			0.485713	+	0.874118i	$0.338560\pi$
$884$	3.32732	−	52.9833i	0.111910	−	1.78202i
$885$	−8.75149	−	6.04549i	−0.294178	−	0.203217i
$886$	9.93539	+	0.311661i	0.333786	+	0.0104705i
$887$	−13.1498	+	7.59206i	−0.441528	+	0.254917i	−0.704246	−	0.709956i	$-0.748715\pi$
$887$	−13.1498	+	7.59206i	−0.441528	+	0.254917i	0.262717	+	0.964873i	$0.415381\pi$
$888$	−14.8497	−	5.65274i	−0.498322	−	0.189694i
$889$	−12.8037	+	22.1767i	−0.429424	+	0.743784i
$890$	−20.5906	−	7.89710i	−0.690197	−	0.264711i
$891$	39.3644	+	1.23689i	1.31876	+	0.0414375i
$892$	20.6795	+	41.6465i	0.692400	+	1.39443i
$893$	10.1446	−	17.5709i	0.339475	−	0.587989i
$894$	−18.3779	+	16.9903i	−0.614648	+	0.568242i
$895$	31.5843	−	27.2757i	1.05575	−	0.911726i
$896$	3.28858	−	14.7401i	0.109864	−	0.492432i
$897$	−0.513021	+	0.505026i	−0.0171293	+	0.0168623i
$898$	11.1453	+	20.7830i	0.371923	+	0.693539i
$899$	−25.2757			−0.842990
$900$	−8.83797	−	28.6686i	−0.294599	−	0.955621i
$901$	−17.9081			−0.596605
$902$	11.8376	+	22.0741i	0.394150	+	0.734986i
$903$	−2.23472	−	8.60996i	−0.0743667	−	0.286522i
$904$	52.4881	−	24.0419i	1.74573	−	0.799621i
$905$	33.7254	−	29.1247i	1.12107	−	0.968139i
$906$	−35.2484	−	10.9427i	−1.17105	−	0.363545i
$907$	−13.5599	+	23.4865i	−0.450250	+	0.779856i	−0.998401	−	0.0565230i	$-0.981999\pi$
$907$	−13.5599	+	23.4865i	−0.450250	+	0.779856i	0.548151	+	0.836379i	$0.315332\pi$
$908$	30.4793	−	15.1344i	1.01149	−	0.502254i
$909$	−6.61619	−	11.8869i	−0.219445	−	0.394263i
$910$	−16.2100	−	6.21702i	−0.537356	−	0.206092i
$911$	−3.77888	+	6.54521i	−0.125200	+	0.216852i	−0.921811	−	0.387640i	$-0.873291\pi$
$911$	−3.77888	+	6.54521i	−0.125200	+	0.216852i	0.796611	+	0.604492i	$0.206624\pi$
$912$	−40.1409	+	5.18720i	−1.32920	+	0.171765i
$913$	50.8036	−	29.3315i	1.68135	−	0.970729i
$914$	−41.9787	−	1.31682i	−1.38853	−	0.0435566i
$915$	0.653810	−	8.06177i	0.0216143	−	0.266514i
$916$	−2.99683	−	0.188199i	−0.0990182	−	0.00621828i
$917$	22.4643			0.741836
$918$	45.0676	+	14.7709i	1.48745	+	0.487512i
$919$		−	33.7674i		−	1.11388i	−0.830552	−	0.556942i	$-0.811975\pi$
$919$		−	33.7674i		−	1.11388i	0.830552	−	0.556942i	$-0.188025\pi$
$920$	−0.581237	−	0.265826i	−0.0191628	−	0.00876402i
$921$	−25.5313	−	7.05643i	−0.841285	−	0.232517i
$922$	−20.0183	−	0.627948i	−0.659266	−	0.0206804i
$923$	29.9836	−	17.3110i	0.986923	−	0.569800i
$924$	19.1279	+	6.60244i	0.629260	+	0.217204i
$925$	−16.0440	−	2.36151i	−0.527522	−	0.0776459i
$926$	−6.86375	−	4.25516i	−0.225557	−	0.139833i
$927$	−0.183880	+	11.7070i	−0.00603943	+	0.384507i
$928$	−10.6173	−	27.6352i	−0.348529	−	0.907171i
$929$	43.7091	+	25.2355i	1.43405	+	0.827949i	0.997427	−	0.0716964i	$-0.0228413\pi$
$929$	43.7091	+	25.2355i	1.43405	+	0.827949i	0.436622	+	0.899645i	$0.356175\pi$
$930$	−2.96397	+	26.2867i	−0.0971925	+	0.861974i
$931$	−26.4001	+	15.2421i	−0.865227	+	0.499539i
$932$	14.9924	−	22.5711i	0.491094	−	0.739339i
$933$	−1.59623	−	6.14998i	−0.0522581	−	0.201341i
$934$	−12.5630	−	23.4267i	−0.411075	−	0.766546i
$935$	11.8479	+	62.0303i	0.387469	+	2.02861i
$936$	−3.82350	+	34.6883i	−0.124975	+	1.13382i
$937$			43.7549i			1.42941i	0.699425	+	0.714706i	$0.253439\pi$
$937$			43.7549i			1.42941i	−0.699425	+	0.714706i	$0.746561\pi$
$938$	0.719701	−	0.385953i	0.0234991	−	0.0126018i
$939$	29.9275	+	30.4012i	0.976646	+	0.992107i
$940$	6.01375	−	14.3201i	0.196147	−	0.467070i
$941$	−12.5420	+	7.24115i	−0.408859	+	0.236055i	−0.690299	−	0.723524i	$-0.742521\pi$
$941$	−12.5420	+	7.24115i	−0.408859	+	0.236055i	0.281441	+	0.959579i	$0.409188\pi$
$942$	5.76221	−	5.32716i	0.187743	−	0.173568i
$943$	0.204510	−	0.354222i	0.00665977	−	0.0115351i
$944$	−6.63975	+	8.75173i	−0.216106	+	0.284844i
$945$	9.01469	−	12.6212i	0.293248	−	0.410566i
$946$	−20.2360	−	12.5452i	−0.657929	−	0.407881i
$947$	−32.3885	−	18.6995i	−1.05249	−	0.607653i	−0.129141	−	0.991626i	$-0.541222\pi$
$947$	−32.3885	−	18.6995i	−1.05249	−	0.607653i	−0.923344	+	0.383973i	$0.874555\pi$
$948$	−10.1614	+	1.96721i	−0.330028	+	0.0638919i
$949$	14.9740	+	25.9357i	0.486077	+	0.841910i
$950$	−38.8598	+	14.0134i	−1.26078	+	0.454655i
$951$	13.1447	−	12.9399i	0.426247	−	0.419604i
$952$	19.8651	+	14.1122i	0.643832	+	0.457381i
$953$	−22.8733			−0.740937			−0.370469	−	0.928845i	$-0.620803\pi$
$953$	−22.8733			−0.740937			−0.370469	+	0.928845i	$0.620803\pi$
$954$	11.7593	+	0.553849i	0.380721	+	0.0179315i
$955$	−9.08068	−	47.5423i	−0.293844	−	1.53843i
$956$	29.2354	+	1.83596i	0.945539	+	0.0593793i
$957$	38.3941	−	9.96518i	1.24110	−	0.322129i
$958$	−1.34848	+	42.9881i	−0.0435676	+	1.38888i
$959$	4.00123	+	6.93034i	0.129207	+	0.223792i
$960$	−29.9857	+	7.80129i	−0.967783	+	0.251785i
$961$	−3.83710	+	6.64606i	−0.123777	+	0.214389i
$962$	16.0336	+	9.93996i	0.516943	+	0.320477i
$963$	7.68506	−	12.8409i	0.247648	−	0.413791i
$964$	21.7492	+	43.8009i	0.700496	+	1.41073i
$965$	−7.64225	+	21.9621i	−0.246013	+	0.706984i
$966$	−0.0729448	−	0.322282i	−0.00234696	−	0.0103693i
$967$	−29.1950	−	50.5672i	−0.938848	−	1.62613i	−0.767625	−	0.640899i	$-0.778562\pi$
$967$	−29.1950	−	50.5672i	−0.938848	−	1.62613i	−0.171223	−	0.985232i	$-0.554772\pi$
$968$	20.9558	−	9.59870i	0.673546	−	0.308514i
$969$	17.3970	−	62.9452i	0.558874	−	2.02209i
$970$	5.91833	−	4.79543i	0.190026	−	0.153972i
$971$	−35.2792			−1.13216			−0.566082	−	0.824349i	$-0.691541\pi$
$971$	−35.2792			−1.13216			−0.566082	+	0.824349i	$0.691541\pi$
$972$	−29.1366	−	11.0931i	−0.934558	−	0.355810i
$973$			0.317795i			0.0101881i
$974$	4.58505	−	2.45882i	0.146914	−	0.0787856i
$975$	3.83241	+	35.4113i	0.122735	+	1.13407i
$976$	−8.28787	−	1.04507i	−0.265288	−	0.0334518i
$977$	4.78940	+	8.29548i	0.153226	+	0.265396i	0.932412	−	0.361398i	$-0.117700\pi$
$977$	4.78940	+	8.29548i	0.153226	+	0.265396i	−0.779185	+	0.626794i	$0.784367\pi$
$978$	25.3676	−	5.74166i	0.811166	−	0.183598i
$979$	−26.4286	−	15.2586i	−0.844662	−	0.487666i
$980$	−18.5829	+	14.1154i	−0.593609	+	0.450900i
$981$	−12.8367	−	7.68258i	−0.409845	−	0.245286i
$982$	21.7718	+	13.4974i	0.694767	+	0.430719i
$983$	−27.2657	−	15.7419i	−0.869641	−	0.502088i	−0.00241215	−	0.999997i	$-0.500768\pi$
$983$	−27.2657	−	15.7419i	−0.869641	−	0.502088i	−0.867229	+	0.497910i	$0.834101\pi$
$984$	−3.15648	−	19.5754i	−0.100625	−	0.624042i
$985$	−13.8048	+	11.9216i	−0.439856	+	0.379853i
$986$	47.7430	+	1.49764i	1.52045	+	0.0476946i
$987$	7.77228	−	2.01729i	0.247394	−	0.0642112i
$988$	47.9598	+	3.01185i	1.52581	+	0.0958196i
$989$			0.388795i			0.0123629i
$990$	−5.86147	−	41.0984i	−0.186290	−	1.30619i
$991$			30.7819i			0.977818i	0.872335	+	0.488909i	$0.162605\pi$
$991$			30.7819i			0.977818i	−0.872335	+	0.488909i	$0.837395\pi$
$992$	26.9857	+	4.26616i	0.856795	+	0.135451i
$993$	−4.27349	−	4.34114i	−0.135615	−	0.137762i
$994$	−0.498260	+	15.8839i	−0.0158039	+	0.503808i
$995$	13.4190	+	15.5387i	0.425410	+	0.492610i
$996$	−45.5920	+	8.82639i	−1.44464	+	0.279675i
$997$	29.1919	+	16.8539i	0.924516	+	0.533770i	0.885073	−	0.465452i	$-0.154108\pi$
$997$	29.1919	+	16.8539i	0.924516	+	0.533770i	0.0394432	+	0.999222i	$0.487442\pi$
$998$	−17.1647	+	27.6873i	−0.543338	+	0.876428i
$999$	−12.1943	+	11.6329i	−0.385811	+	0.368048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.d.119.5	yes	48
3.2	odd	2		540.2.n.d.359.20		48
4.3	odd	2	inner	180.2.n.d.119.13	yes	48
5.2	odd	4		900.2.r.g.551.8		48
5.3	odd	4		900.2.r.g.551.17		48
5.4	even	2	inner	180.2.n.d.119.20	yes	48
9.4	even	3		540.2.n.d.179.13		48
9.5	odd	6	inner	180.2.n.d.59.12	yes	48
12.11	even	2		540.2.n.d.359.12		48
15.14	odd	2		540.2.n.d.359.5		48
20.3	even	4		900.2.r.g.551.24		48
20.7	even	4		900.2.r.g.551.1		48
20.19	odd	2	inner	180.2.n.d.119.12	yes	48
36.23	even	6	inner	180.2.n.d.59.20	yes	48
36.31	odd	6		540.2.n.d.179.5		48
45.4	even	6		540.2.n.d.179.12		48
45.14	odd	6	inner	180.2.n.d.59.13	yes	48
45.23	even	12		900.2.r.g.851.24		48
45.32	even	12		900.2.r.g.851.1		48
60.59	even	2		540.2.n.d.359.13		48
180.23	odd	12		900.2.r.g.851.17		48
180.59	even	6	inner	180.2.n.d.59.5	✓	48
180.139	odd	6		540.2.n.d.179.20		48
180.167	odd	12		900.2.r.g.851.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.5	✓	48	180.59	even	6	inner
180.2.n.d.59.12	yes	48	9.5	odd	6	inner
180.2.n.d.59.13	yes	48	45.14	odd	6	inner
180.2.n.d.59.20	yes	48	36.23	even	6	inner
180.2.n.d.119.5	yes	48	1.1	even	1	trivial
180.2.n.d.119.12	yes	48	20.19	odd	2	inner
180.2.n.d.119.13	yes	48	4.3	odd	2	inner
180.2.n.d.119.20	yes	48	5.4	even	2	inner
540.2.n.d.179.5		48	36.31	odd	6
540.2.n.d.179.12		48	45.4	even	6
540.2.n.d.179.13		48	9.4	even	3
540.2.n.d.179.20		48	180.139	odd	6
540.2.n.d.359.5		48	15.14	odd	2
540.2.n.d.359.12		48	12.11	even	2
540.2.n.d.359.13		48	60.59	even	2
540.2.n.d.359.20		48	3.2	odd	2
900.2.r.g.551.1		48	20.7	even	4
900.2.r.g.551.8		48	5.2	odd	4
900.2.r.g.551.17		48	5.3	odd	4
900.2.r.g.551.24		48	20.3	even	4
900.2.r.g.851.1		48	45.32	even	12
900.2.r.g.851.8		48	180.167	odd	12
900.2.r.g.851.17		48	180.23	odd	12
900.2.r.g.851.24		48	45.23	even	12

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24631 + 0.668359i) q^{2} +(-1.66946 - 0.461412i) q^{3} +(1.10659 - 1.66597i) q^{4} +(-1.69235 + 1.46149i) q^{5} +(2.38906 - 0.540736i) q^{6} +(0.667441 - 1.15604i) q^{7} +(-0.265693 + 2.81592i) q^{8} +(2.57420 + 1.54062i) q^{9} +(1.13240 - 2.95257i) q^{10} +(2.18799 - 3.78971i) q^{11} +(-2.61611 + 2.27068i) q^{12} +(3.56180 - 2.05641i) q^{13} +(-0.0591892 + 1.88688i) q^{14} +(3.49966 - 1.65903i) q^{15} +(-1.55091 - 3.68710i) q^{16} +6.45392 q^{17} +(-4.23794 - 0.199603i) q^{18} +5.84202i q^{19} +(0.562053 + 4.43668i) q^{20} +(-1.64768 + 1.62200i) q^{21} +(-0.194033 + 6.18554i) q^{22} +(0.0875178 - 0.0505284i) q^{23} +(1.74286 - 4.57847i) q^{24} +(0.728104 - 4.94670i) q^{25} +(-3.06470 + 4.94349i) q^{26} +(-3.58666 - 3.75977i) q^{27} +(-1.18735 - 2.39120i) q^{28} +(-4.53226 - 2.61670i) q^{29} +(-3.25285 + 4.40670i) q^{30} +(4.18262 - 2.41484i) q^{31} +(4.39722 + 3.55871i) q^{32} +(-5.40139 + 5.31721i) q^{33} +(-8.04361 + 4.31354i) q^{34} +(0.559997 + 2.93189i) q^{35} +(5.41521 - 2.58370i) q^{36} -3.24337i q^{37} +(-3.90457 - 7.28098i) q^{38} +(-6.89514 + 1.78964i) q^{39} +(-3.66579 - 5.15383i) q^{40} +(3.50518 - 2.02372i) q^{41} +(0.969443 - 3.12276i) q^{42} +(-1.92364 + 3.33185i) q^{43} +(-3.89233 - 7.83880i) q^{44} +(-6.60804 + 1.15489i) q^{45} +(-0.0753035 + 0.121468i) q^{46} +(-3.00768 - 1.73649i) q^{47} +(0.887912 + 6.87107i) q^{48} +(2.60904 + 4.51900i) q^{49} +(2.39873 + 6.65177i) q^{50} +(-10.7746 - 2.97792i) q^{51} +(0.515549 - 8.20946i) q^{52} -2.77476 q^{53} +(6.98298 + 2.28867i) q^{54} +(1.83577 + 9.61125i) q^{55} +(3.07799 + 2.18661i) q^{56} +(2.69558 - 9.75302i) q^{57} +(7.39751 + 0.232051i) q^{58} +(-1.37318 - 2.37841i) q^{59} +(1.10881 - 7.66619i) q^{60} +(1.04419 - 1.80858i) q^{61} +(-3.59888 + 5.80514i) q^{62} +(3.49915 - 1.94761i) q^{63} +(-7.85881 - 1.49634i) q^{64} +(-3.02241 + 8.68570i) q^{65} +(3.17801 - 10.2370i) q^{66} +(-0.216298 - 0.374638i) q^{67} +(7.14186 - 10.7520i) q^{68} +(-0.169422 + 0.0439735i) q^{69} +(-2.65749 - 3.27977i) q^{70} +8.41810 q^{71} +(-5.02220 + 6.83941i) q^{72} +7.28163i q^{73} +(2.16773 + 4.04225i) q^{74} +(-3.49801 + 7.92237i) q^{75} +(9.73262 + 6.46473i) q^{76} +(-2.92071 - 5.05882i) q^{77} +(7.39739 - 6.83888i) q^{78} +(2.58753 + 1.49391i) q^{79} +(8.01333 + 3.97323i) q^{80} +(4.25299 + 7.93171i) q^{81} +(-3.01598 + 4.86490i) q^{82} +(11.6096 + 6.70282i) q^{83} +(0.878898 + 4.53988i) q^{84} +(-10.9223 + 9.43234i) q^{85} +(0.170590 - 5.43821i) q^{86} +(6.35905 + 6.45972i) q^{87} +(10.0902 + 7.16812i) q^{88} -6.97377i q^{89} +(7.46380 - 5.85591i) q^{90} -5.49013i q^{91} +(0.0126677 - 0.201716i) q^{92} +(-8.09696 + 2.10157i) q^{93} +(4.90911 + 0.153993i) q^{94} +(-8.53804 - 9.88674i) q^{95} +(-5.69896 - 7.97006i) q^{96} +(2.08608 + 1.20440i) q^{97} +(-6.27200 - 3.88831i) q^{98} +(11.4708 - 6.38462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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