LMFDB - Embedded newform 180.2.n.d.59.5

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			59.5
Character	$\chi$	$=$	180.59
Dual form			180.2.n.d.119.5

$q$-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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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	0.964150	−	0.265357i	$-0.0854898\pi$
$7$	0.667441	+	1.15604i	0.252269	+	0.436943i	−0.711881	+	0.702300i	$0.752157\pi$
$8$	−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	0.980692	+	0.195558i	$0.0626519\pi$
$11$	2.18799	+	3.78971i	0.659705	+	1.14264i	−0.320987	+	0.947083i	$0.604015\pi$
$12$	−2.61611	−	2.27068i	−0.755206	−	0.655488i
$13$	3.56180	+	2.05641i	0.987867	+	0.570345i	0.904636	−	0.426185i	$-0.140143\pi$
$13$	3.56180	+	2.05641i	0.987867	+	0.570345i	0.0832309	+	0.996530i	$0.473476\pi$
$14$	−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	$-0.766240\pi$
$19$		−	5.84202i		−	1.34025i	0.742248	−	0.670125i	$-0.233760\pi$
$20$	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	0.509097	−	0.860709i	$-0.329980\pi$
$23$	0.0875178	+	0.0505284i	0.0182487	+	0.0105359i	−0.490848	+	0.871245i	$0.663313\pi$
$24$	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	−0.857814	−	0.513960i	$-0.828178\pi$
$29$	−4.53226	+	2.61670i	−0.841620	+	0.485909i	0.0161948	+	0.999869i	$0.494845\pi$
$30$	−3.25285	−	4.40670i	−0.593886	−	0.804549i
$31$	4.18262	+	2.41484i	0.751222	+	0.433718i	0.826135	−	0.563472i	$-0.190535\pi$
$31$	4.18262	+	2.41484i	0.751222	+	0.433718i	−0.0749136	+	0.997190i	$0.523868\pi$
$32$	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	$0.0859013\pi$
$37$			3.24337i			0.533206i	−0.963806	+	0.266603i	$0.914099\pi$
$38$	−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	0.748079	−	0.663609i	$-0.230976\pi$
$41$	3.50518	+	2.02372i	0.547417	+	0.316051i	−0.200663	+	0.979660i	$0.564310\pi$
$42$	0.969443	+	3.12276i	0.149588	+	0.481853i
$43$	−1.92364	−	3.33185i	−0.293353	−	0.508102i	0.681248	−	0.732053i	$-0.261438\pi$
$43$	−1.92364	−	3.33185i	−0.293353	−	0.508102i	−0.974600	+	0.223951i	$0.928104\pi$
$44$	−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	−0.703053	−	0.711138i	$-0.748180\pi$
$47$	−3.00768	+	1.73649i	−0.438715	+	0.253292i	0.264337	+	0.964430i	$0.414847\pi$
$48$	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	−0.941460	−	0.337124i	$-0.890546\pi$
$59$	−1.37318	+	2.37841i	−0.178772	+	0.309642i	0.762688	+	0.646766i	$0.223879\pi$
$60$	1.10881	+	7.66619i	0.143147	+	0.989701i
$61$	1.04419	+	1.80858i	0.133694	+	0.231566i	0.925098	−	0.379729i	$-0.123983\pi$
$61$	1.04419	+	1.80858i	0.133694	+	0.231566i	−0.791404	+	0.611294i	$0.790649\pi$
$62$	−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	−0.878935	−	0.476941i	$-0.841746\pi$
$67$	−0.216298	+	0.374638i	−0.0264250	+	0.0457694i	0.852511	+	0.522710i	$0.175079\pi$
$68$	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	$-0.859878\pi$
$73$		−	7.28163i		−	0.852250i	0.904664	−	0.426125i	$-0.140122\pi$
$74$	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	−0.347327	−	0.937744i	$-0.612911\pi$
$79$	2.58753	−	1.49391i	0.291120	−	0.168078i	0.638447	+	0.769666i	$0.279577\pi$
$80$	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	0.298524	−	0.954402i	$-0.403506\pi$
$83$	11.6096	−	6.70282i	1.27432	−	0.735730i	0.975798	+	0.218672i	$0.0701724\pi$
$84$	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	$0.120508\pi$
$89$			6.97377i			0.739218i	−0.929187	+	0.369609i	$0.879492\pi$
$90$	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	−0.390343	−	0.920670i	$-0.627644\pi$
$97$	2.08608	−	1.20440i	0.211809	−	0.122288i	0.602152	+	0.798382i	$0.294310\pi$
$98$	−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	−0.682493	−	0.730892i	$-0.739104\pi$
$101$	−3.92717	+	2.26735i	−0.390768	+	0.225610i	0.291725	+	0.956502i	$0.405771\pi$
$102$	15.4188	+	3.48987i	1.52669	+	0.345549i
$103$	1.95140	−	3.37992i	0.192277	−	0.333034i	−0.753727	−	0.657187i	$-0.771746\pi$
$103$	1.95140	−	3.37992i	0.192277	−	0.333034i	0.946005	+	0.324153i	$0.105079\pi$
$104$	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	$0.0775142\pi$
$107$			4.98830i			0.482237i	−0.970496	+	0.241118i	$0.922486\pi$
$108$	−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	−0.237767	+	0.971322i	$0.576416\pi$
$113$	−10.2057	+	17.6768i	−0.960073	+	1.66290i	−0.722306	+	0.691574i	$0.756918\pi$
$114$	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	−0.219488	−	0.975615i	$-0.570439\pi$
$131$	8.41433	−	14.5740i	0.735163	−	1.27334i	0.954652	−	0.297725i	$-0.0962279\pi$
$132$	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	0.709102	−	0.705106i	$-0.249101\pi$
$137$	−2.99744	−	5.19172i	−0.256089	−	0.443559i	−0.965191	+	0.261547i	$0.915767\pi$
$138$	0.181763	+	0.168040i	0.0154727	+	0.0143045i
$139$	−0.206175	−	0.119035i	−0.0174875	−	0.0100964i	0.491231	−	0.871029i	$-0.336547\pi$
$139$	−0.206175	−	0.119035i	−0.0174875	−	0.0100964i	−0.508718	+	0.860933i	$0.669881\pi$
$140$	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	0.0916368	−	0.995792i	$-0.470790\pi$
$149$	−8.84885	−	5.10889i	−0.724926	−	0.418536i	−0.816563	+	0.577256i	$0.804123\pi$
$150$	−0.935377	+	12.2117i	−0.0763732	+	0.997079i
$151$	−13.0489	+	7.53379i	−1.06190	+	0.613091i	−0.925958	−	0.377625i	$-0.876741\pi$
$151$	−13.0489	+	7.53379i	−1.06190	+	0.613091i	−0.135946	+	0.990716i	$0.543407\pi$
$152$	−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	0.606611	−	0.794999i	$-0.292529\pi$
$157$	2.77448	+	1.60184i	0.221427	+	0.127841i	−0.385184	+	0.922840i	$0.625862\pi$
$158$	−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	0.0143236	−	0.999897i	$-0.495440\pi$
$167$	−10.9127	−	6.30046i	−0.844451	−	0.487544i	−0.858775	+	0.512353i	$0.828774\pi$
$168$	−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	0.831558	−	0.555439i	$-0.187450\pi$
$173$	−0.858165	−	1.48639i	−0.0652451	−	0.113008i	−0.896803	+	0.442431i	$0.854116\pi$
$174$	−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	−0.930115	−	0.367268i	$-0.880293\pi$
$191$	−10.8229	−	18.7459i	−0.783121	−	1.35641i	0.146994	−	0.989137i	$-0.453040\pi$
$192$	12.4296	−	6.12424i	0.897026	−	0.441979i
$193$	9.00614	+	5.19970i	0.648276	+	0.374282i	0.787795	−	0.615937i	$-0.211222\pi$
$193$	9.00614	+	5.19970i	0.648276	+	0.374282i	−0.139519	+	0.990219i	$0.544556\pi$
$194$	−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	$0.105512\pi$
$199$			9.18172i			0.650875i	−0.945564	+	0.325438i	$0.894488\pi$
$200$	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	0.773239	−	0.634115i	$-0.218635\pi$
$211$	8.87092	+	5.12163i	0.610699	+	0.352587i	−0.162540	+	0.986702i	$0.551969\pi$
$212$	−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	−0.932843	−	0.360283i	$-0.882680\pi$
$223$	−11.6245	−	20.1343i	−0.778436	−	1.34829i	0.154407	−	0.988007i	$-0.450653\pi$
$224$	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	0.0763513	−	0.997081i	$-0.475673\pi$
$227$	14.7354	−	8.50750i	0.978024	−	0.564663i	0.901673	+	0.432418i	$0.142340\pi$
$228$	−13.2653	+	15.2834i	−0.878518	+	1.01217i
$229$	−0.750685	+	1.30022i	−0.0496066	+	0.0859212i	−0.889762	−	0.456424i	$-0.849130\pi$
$229$	−0.750685	+	1.30022i	−0.0496066	+	0.0859212i	0.840156	+	0.542345i	$0.182463\pi$
$230$	−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	−0.525846	−	0.850580i	$-0.676251\pi$
$239$	7.32324	−	12.6842i	0.473701	−	0.820474i	0.999547	+	0.0301057i	$0.00958440\pi$
$240$	−11.5446	+	10.3306i	−0.745204	+	0.666837i
$241$	−12.2259	−	21.1758i	−0.787537	−	1.36405i	−0.927472	−	0.373894i	$-0.878022\pi$
$241$	−12.2259	−	21.1758i	−0.787537	−	1.36405i	0.139934	−	0.990161i	$-0.455311\pi$
$242$	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	−0.736617	−	0.676310i	$-0.763578\pi$
$257$	3.48508	−	6.03633i	0.217393	−	0.376536i	0.954010	+	0.299774i	$0.0969113\pi$
$258$	−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	−0.864716	−	0.502262i	$-0.832501\pi$
$263$	−13.9809	+	8.07190i	−0.862102	+	0.497735i	0.00261352	+	0.999997i	$0.499168\pi$
$264$	−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	$-0.769084\pi$
$269$		−	21.7634i		−	1.32694i	0.748204	−	0.663468i	$-0.230916\pi$
$270$	−15.1625	−	6.33232i	−0.922761	−	0.385373i
$271$			30.1548i			1.83177i	0.401436	+	0.915887i	$0.368511\pi$
$271$			30.1548i			1.83177i	−0.401436	+	0.915887i	$0.631489\pi$
$272$	−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	−0.798585	−	0.601882i	$-0.794418\pi$
$277$	−11.2614	+	6.50177i	−0.676632	+	0.390654i	0.121953	+	0.992536i	$0.461084\pi$
$278$	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	−0.527679	−	0.849444i	$-0.676938\pi$
$281$	−0.936692	+	0.540799i	−0.0558784	+	0.0322614i	0.471801	+	0.881705i	$0.343604\pi$
$282$	−8.12451	+	2.52221i	−0.483808	+	0.150195i
$283$	−14.6158	+	25.3154i	−0.868821	+	1.50484i	−0.00561859	+	0.999984i	$0.501788\pi$
$283$	−14.6158	+	25.3154i	−0.868821	+	1.50484i	−0.863202	+	0.504858i	$0.831545\pi$
$284$	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	−0.771988	−	0.635637i	$-0.780737\pi$
$293$	2.81552	−	4.87662i	0.164484	−	0.284895i	0.936472	+	0.350742i	$0.114071\pi$
$294$	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	−0.809326	−	0.587360i	$-0.800167\pi$
$311$	1.83417	−	3.17688i	0.104006	−	0.180144i	0.913332	+	0.407216i	$0.133500\pi$
$312$	−3.20748	+	19.8917i	−0.181588	+	1.12614i
$313$	−21.3301	+	12.3149i	−1.20565	+	0.696081i	−0.961805	−	0.273734i	$-0.911741\pi$
$313$	−21.3301	+	12.3149i	−1.20565	+	0.696081i	−0.243842	+	0.969815i	$0.578408\pi$
$314$	−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	0.676859	−	0.736113i	$-0.263341\pi$
$317$	−5.32466	−	9.22258i	−0.299063	−	0.517992i	−0.975922	+	0.218121i	$0.930007\pi$
$318$	−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	−0.413952	−	0.910299i	$-0.635852\pi$
$331$	3.04582	−	1.75851i	0.167414	−	0.0966563i	0.581366	+	0.813642i	$0.302519\pi$
$332$	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	−0.171147	−	0.985245i	$-0.554747\pi$
$337$	−20.3763	−	11.7643i	−1.10997	−	0.640841i	−0.938821	+	0.344405i	$0.888081\pi$
$338$	−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	0.594297	−	0.804246i	$-0.297431\pi$
$347$	3.63147	+	2.09663i	0.194947	+	0.112553i	−0.399349	+	0.916799i	$0.630764\pi$
$348$	17.7986	+	3.44572i	0.954104	+	0.184710i
$349$	2.78198	+	4.81854i	0.148916	+	0.257930i	0.930827	−	0.365460i	$-0.119088\pi$
$349$	2.78198	+	4.81854i	0.148916	+	0.257930i	−0.781911	+	0.623390i	$0.785755\pi$
$350$	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	0.681268	−	0.732034i	$-0.261429\pi$
$353$	−5.51109	−	9.54549i	−0.293326	−	0.508055i	−0.974594	+	0.223979i	$0.928095\pi$
$354$	−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	−0.904306	−	0.426885i	$-0.859611\pi$
$367$	−15.7443	−	27.2699i	−0.821846	−	1.42348i	0.0824597	−	0.996594i	$-0.473722\pi$
$368$	−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	0.922937	−	0.384950i	$-0.125781\pi$
$373$	20.2988	+	11.7195i	1.05103	+	0.606812i	0.128092	+	0.991762i	$0.459115\pi$
$374$	−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	$-0.904108\pi$
$379$		−	11.5529i		−	0.593434i	0.954965	−	0.296717i	$-0.0958918\pi$
$380$	−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	0.951304	−	0.308256i	$-0.0997452\pi$
$383$	22.7016	+	13.1068i	1.16000	+	0.669725i	0.208695	+	0.977981i	$0.433079\pi$
$384$	−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	−0.534711	−	0.845035i	$-0.679580\pi$
$389$	−1.38545	+	0.799888i	−0.0702449	+	0.0405559i	0.464466	+	0.885591i	$0.346246\pi$
$390$	−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	$-0.774401\pi$
$397$		−	25.9373i		−	1.30176i	0.759182	−	0.650879i	$-0.225599\pi$
$398$	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	−0.145872	−	0.989304i	$-0.546599\pi$
$401$	−21.5383	−	12.4351i	−1.07557	−	0.620980i	−0.929698	+	0.368323i	$0.879932\pi$
$402$	−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	0.471018	+	0.882124i	$0.343887\pi$
$409$	−10.6869	+	18.5102i	−0.528433	+	0.915272i	−0.999450	+	0.0331484i	$0.989447\pi$
$410$	−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	−0.779440	−	0.626476i	$-0.784496\pi$
$419$	3.12824	−	5.41826i	0.152824	−	0.264700i	0.932265	+	0.361777i	$0.117830\pi$
$420$	−8.12238	+	6.39857i	−0.396332	+	0.312218i
$421$	15.3599	+	26.6041i	0.748596	+	1.29661i	0.948496	+	0.316790i	$0.102605\pi$
$421$	15.3599	+	26.6041i	0.748596	+	1.29661i	−0.199900	+	0.979816i	$0.564062\pi$
$422$	−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	$-0.799601\pi$
$433$		−	24.5043i		−	1.17760i	0.808279	−	0.588800i	$-0.200399\pi$
$434$	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	−0.0860332	−	0.996292i	$-0.527419\pi$
$439$	15.3741	−	8.87623i	0.733765	−	0.423639i	0.819798	+	0.572653i	$0.194086\pi$
$440$	−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	−0.637585	−	0.770380i	$-0.720067\pi$
$443$	−6.08715	+	3.51442i	−0.289209	+	0.166975i	0.348376	+	0.937355i	$0.386733\pi$
$444$	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	$0.128731\pi$
$449$			16.6756i			0.786971i	−0.919331	+	0.393485i	$0.871269\pi$
$450$	−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	0.241854	−	0.970313i	$-0.422244\pi$
$457$	25.7193	−	14.8490i	1.20310	−	0.694608i	0.961242	+	0.275704i	$0.0889111\pi$
$458$	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	−0.186415	−	0.982471i	$-0.559687\pi$
$461$	12.2647	−	7.08100i	0.571222	−	0.329795i	0.757637	+	0.652676i	$0.226354\pi$
$462$	−9.71325	+	10.5065i	−0.451901	+	0.488806i
$463$	2.85520	−	4.94535i	0.132692	−	0.229830i	−0.792021	−	0.610494i	$-0.790971\pi$
$463$	2.85520	−	4.94535i	0.132692	−	0.229830i	0.924714	+	0.380664i	$0.124304\pi$
$464$	−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	$-0.856781\pi$
$467$		−	18.7968i		−	0.869813i	0.900476	−	0.434907i	$-0.143219\pi$
$468$	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	0.970254	+	0.242090i	$0.0778329\pi$
$479$	15.2061	+	26.3377i	0.694783	+	1.20340i	−0.275471	+	0.961309i	$0.588834\pi$
$480$	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	−0.994747	−	0.102364i	$-0.967359\pi$
$491$	−9.05671	+	15.6867i	−0.408724	+	0.707930i	0.586023	+	0.810294i	$0.300693\pi$
$492$	−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	0.874933	−	0.484244i	$-0.160905\pi$
$499$	19.9488	+	11.5175i	0.893032	+	0.515592i	0.0180991	+	0.999836i	$0.494239\pi$
$500$	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	$0.244124\pi$
$503$			31.1266i			1.38787i	−0.720039	+	0.693934i	$0.755876\pi$
$504$	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	0.489108	−	0.872223i	$-0.337322\pi$
$509$	−0.489681	−	0.282717i	−0.0217047	−	0.0125312i	−0.510813	+	0.859692i	$0.670656\pi$
$510$	−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	$-0.966422\pi$
$521$		−	4.80678i		−	0.210589i	0.994441	−	0.105294i	$-0.0335785\pi$
$522$	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	0.895206	−	0.445653i	$-0.147029\pi$
$547$	1.44201	+	2.49763i	0.0616557	+	0.106791i	−0.833550	+	0.552444i	$0.813695\pi$
$548$	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	0.0406715	−	0.999173i	$-0.487050\pi$
$563$	−19.0842	−	11.0182i	−0.804302	−	0.464364i	−0.844973	+	0.534809i	$0.820384\pi$
$564$	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	−0.912073	−	0.410029i	$-0.865519\pi$
$569$	−24.1641	+	13.9512i	−1.01301	+	0.584864i	−0.100941	+	0.994892i	$0.532185\pi$
$570$	−25.7440	+	19.0032i	−1.07830	+	0.795956i
$571$	−11.2510	−	6.49576i	−0.470839	−	0.271839i	0.245752	−	0.969333i	$-0.420965\pi$
$571$	−11.2510	−	6.49576i	−0.470839	−	0.271839i	−0.716591	+	0.697494i	$0.754298\pi$
$572$	−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	$0.256193\pi$
$577$			34.6251i			1.44146i	−0.693216	+	0.720730i	$0.743807\pi$
$578$	−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	−0.293022	−	0.956106i	$-0.594661\pi$
$587$	9.41209	−	5.43407i	0.388479	−	0.224288i	0.681501	+	0.731817i	$0.261328\pi$
$588$	−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	−0.927889	−	0.372856i	$-0.878379\pi$
$599$	−3.45192	+	5.97890i	−0.141042	+	0.244291i	0.786847	+	0.617148i	$0.211712\pi$
$600$	−21.3794	+	11.9550i	−0.872809	+	0.488062i
$601$	−15.7058	−	27.2032i	−0.640653	−	1.10964i	−0.985287	−	0.170906i	$-0.945331\pi$
$601$	−15.7058	−	27.2032i	−0.640653	−	1.10964i	0.344635	−	0.938737i	$-0.388003\pi$
$602$	−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	−0.993519	−	0.113665i	$-0.963741\pi$
$607$	−9.81362	+	16.9977i	−0.398322	+	0.689915i	0.595197	+	0.803580i	$0.297074\pi$
$608$	−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	$-0.802353\pi$
$613$		−	28.8088i		−	1.16358i	0.813340	−	0.581788i	$-0.197647\pi$
$614$	−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	−0.981102	−	0.193493i	$-0.938018\pi$
$617$	−8.02269	+	13.8957i	−0.322981	+	0.559420i	0.658120	+	0.752913i	$0.271352\pi$
$618$	6.48966	−	7.01965i	0.261052	−	0.282372i
$619$	−2.13387	+	1.23199i	−0.0857674	+	0.0495178i	−0.542270	−	0.840204i	$-0.682435\pi$
$619$	−2.13387	+	1.23199i	−0.0857674	+	0.0495178i	0.456503	+	0.889722i	$0.349102\pi$
$620$	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	$-0.653997\pi$
$631$		−	44.4737i		−	1.77047i	0.465144	−	0.885235i	$-0.346003\pi$
$632$	−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	−0.753391	−	0.657573i	$-0.771583\pi$
$641$	−14.1935	+	8.19465i	−0.560611	+	0.323669i	0.192779	+	0.981242i	$0.438250\pi$
$642$	−2.69735	+	11.9173i	−0.106456	+	0.470340i
$643$	−17.5507	+	30.3987i	−0.692133	+	1.19881i	0.279005	+	0.960290i	$0.409995\pi$
$643$	−17.5507	+	30.3987i	−0.692133	+	1.19881i	−0.971138	+	0.238520i	$0.923338\pi$
$644$	−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	$-0.877773\pi$
$647$		−	19.0579i		−	0.749243i	0.927178	−	0.374621i	$-0.122227\pi$
$648$	−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	−0.0776903	−	0.996978i	$-0.524755\pi$
$653$	21.0708	−	36.4956i	0.824563	−	1.42818i	0.902253	−	0.431207i	$-0.141912\pi$
$654$	−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	0.992747	−	0.120225i	$-0.0383616\pi$
$659$	10.0696	+	17.4410i	0.392256	+	0.679407i	−0.600491	+	0.799631i	$0.705028\pi$
$660$	−26.6266	+	20.9756i	−1.03644	+	0.816476i
$661$	3.54725	−	6.14402i	0.137972	−	0.238975i	−0.788757	−	0.614705i	$-0.789275\pi$
$661$	3.54725	−	6.14402i	0.137972	−	0.238975i	0.926729	+	0.375731i	$0.122608\pi$
$662$	−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	−0.831018	−	0.556245i	$-0.812242\pi$
$673$	−19.8408	+	11.4551i	−0.764806	+	0.441561i	0.0662129	+	0.997806i	$0.478908\pi$
$674$	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	0.998169	−	0.0604934i	$-0.0192674\pi$
$677$	11.6227	+	20.1311i	0.446696	+	0.773699i	−0.551473	+	0.834193i	$0.685934\pi$
$678$	−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	$-0.802738\pi$
$683$		−	30.3578i		−	1.16161i	0.814043	−	0.580804i	$-0.197262\pi$
$684$	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	−0.284607	−	0.958644i	$-0.591863\pi$
$691$	10.6015	−	6.12077i	0.403299	−	0.232845i	0.687907	+	0.725799i	$0.258530\pi$
$692$	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	$0.000219688\pi$
$701$			0.0365464i			0.00138034i	−1.00000		0.000690169i	$0.999780\pi$
$702$	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	0.999901	+	0.0140387i	$0.00446880\pi$
$709$	13.6359	+	23.6181i	0.512109	+	0.886998i	−0.487793	+	0.872959i	$0.662198\pi$
$710$	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	0.977475	−	0.211053i	$-0.0676894\pi$
$727$	8.24957	+	14.2887i	0.305960	+	0.529938i	−0.671515	+	0.740991i	$0.734356\pi$
$728$	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	−0.380641	−	0.924723i	$-0.624297\pi$
$733$	−37.1399	−	21.4427i	−1.37179	−	0.792006i	−0.991154	+	0.132717i	$0.957630\pi$
$734$	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	$-0.982166\pi$
$739$		−	3.04457i		−	0.111996i	0.998431	−	0.0559981i	$-0.0178341\pi$
$740$	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	−0.307078	−	0.951684i	$-0.599351\pi$
$743$	−35.0211	−	20.2194i	−1.28480	−	0.741779i	−0.977722	+	0.209905i	$0.932684\pi$
$744$	−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	0.704034	−	0.710166i	$-0.251380\pi$
$751$	12.0862	+	6.97795i	0.441030	+	0.254629i	−0.263004	+	0.964795i	$0.584713\pi$
$752$	−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	$0.196026\pi$
$757$			31.7859i			1.15528i	−0.816293	+	0.577639i	$0.803974\pi$
$758$	−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	0.0523332	−	0.998630i	$-0.483334\pi$
$761$	−21.6921	−	12.5240i	−0.786339	−	0.453993i	−0.838672	+	0.544637i	$0.816668\pi$
$762$	−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	−0.893401	−	0.449261i	$-0.851687\pi$
$769$	−1.59810	+	2.76799i	−0.0576290	+	0.0998164i	0.835772	+	0.549077i	$0.185021\pi$
$770$	−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	−0.392011	−	0.919960i	$-0.628221\pi$
$787$	16.8518	−	29.1883i	0.600703	−	1.04045i	0.992715	−	0.120488i	$-0.0384461\pi$
$788$	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	−0.487348	−	0.873208i	$-0.662036\pi$
$797$	14.4698	−	25.0624i	0.512546	−	0.887755i	0.999894	−	0.0145477i	$-0.00463085\pi$
$798$	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	$0.0849360\pi$
$809$			14.9996i			0.527358i	−0.964610	+	0.263679i	$0.915064\pi$
$810$	28.2350	+	3.57540i	0.992078	+	0.125627i
$811$		−	17.4677i		−	0.613376i	−0.951810	−	0.306688i	$-0.900779\pi$
$811$		−	17.4677i		−	0.613376i	0.951810	−	0.306688i	$-0.0992207\pi$
$812$	−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	−0.197669	−	0.980269i	$-0.563337\pi$
$821$	15.8290	−	9.13886i	0.552435	−	0.318948i	0.750103	+	0.661320i	$0.230004\pi$
$822$	−4.35372	−	14.0242i	−0.151853	−	0.489149i
$823$	14.6369	−	25.3518i	0.510210	−	0.883710i	−0.489720	−	0.871880i	$-0.662901\pi$
$823$	14.6369	−	25.3518i	0.510210	−	0.883710i	0.999930	−	0.0118300i	$-0.00376570\pi$
$824$	−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	$0.140233\pi$
$827$			24.5270i			0.852886i	−0.904514	+	0.426443i	$0.859767\pi$
$828$	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	−0.987762	−	0.155967i	$-0.950151\pi$
$839$	−18.2179	−	31.5544i	−0.628953	−	1.08938i	0.358810	−	0.933411i	$-0.383183\pi$
$840$	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	−0.886281	−	0.463148i	$-0.846720\pi$
$853$	−27.1128	+	15.6536i	−0.928324	+	0.535968i	−0.0420430	+	0.999116i	$0.513387\pi$
$854$	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	0.933854	−	0.357654i	$-0.116423\pi$
$857$	4.60165	+	7.97029i	0.157189	+	0.272260i	−0.776665	+	0.629914i	$0.783090\pi$
$858$	−9.73197	+	42.9974i	−0.332244	+	1.46791i
$859$	4.62482	+	2.67014i	0.157797	+	0.0911040i	0.576819	−	0.816872i	$-0.304294\pi$
$859$	4.62482	+	2.67014i	0.157797	+	0.0911040i	−0.419022	+	0.907976i	$0.637627\pi$
$860$	−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	$0.105026\pi$
$863$			19.0360i			0.647992i	−0.946058	+	0.323996i	$0.894974\pi$
$864$	−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	0.812135	−	0.583469i	$-0.198305\pi$
$877$	21.1121	+	12.1891i	0.712904	+	0.411595i	−0.0992316	+	0.995064i	$0.531638\pi$
$878$	−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	$-0.743243\pi$
$881$		−	42.8577i		−	1.44391i	0.691939	−	0.721956i	$-0.256757\pi$
$882$	−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	0.262717	−	0.964873i	$-0.415381\pi$
$887$	−13.1498	−	7.59206i	−0.441528	−	0.254917i	−0.704246	+	0.709956i	$0.748715\pi$
$888$	−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	0.548151	−	0.836379i	$-0.315332\pi$
$907$	−13.5599	−	23.4865i	−0.450250	−	0.779856i	−0.998401	+	0.0565230i	$0.981999\pi$
$908$	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	0.796611	−	0.604492i	$-0.206624\pi$
$911$	−3.77888	−	6.54521i	−0.125200	−	0.216852i	−0.921811	+	0.387640i	$0.873291\pi$
$912$	−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	$0.188025\pi$
$919$			33.7674i			1.11388i	−0.830552	+	0.556942i	$0.811975\pi$
$920$	−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	0.436622	−	0.899645i	$-0.356175\pi$
$929$	43.7091	−	25.2355i	1.43405	−	0.827949i	0.997427	+	0.0716964i	$0.0228413\pi$
$930$	−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	$-0.746561\pi$
$937$		−	43.7549i		−	1.42941i	0.699425	−	0.714706i	$-0.253439\pi$
$938$	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	0.281441	−	0.959579i	$-0.409188\pi$
$941$	−12.5420	−	7.24115i	−0.408859	−	0.236055i	−0.690299	+	0.723524i	$0.742521\pi$
$942$	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	−0.923344	−	0.383973i	$-0.874555\pi$
$947$	−32.3885	+	18.6995i	−1.05249	+	0.607653i	−0.129141	+	0.991626i	$0.541222\pi$
$948$	−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	−0.171223	+	0.985232i	$0.554772\pi$
$967$	−29.1950	+	50.5672i	−0.938848	+	1.62613i	−0.767625	+	0.640899i	$0.778562\pi$
$968$	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	−0.779185	−	0.626794i	$-0.784367\pi$
$977$	4.78940	−	8.29548i	0.153226	−	0.265396i	0.932412	+	0.361398i	$0.117700\pi$
$978$	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	−0.867229	−	0.497910i	$-0.834101\pi$
$983$	−27.2657	+	15.7419i	−0.869641	+	0.502088i	−0.00241215	+	0.999997i	$0.500768\pi$
$984$	−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	$-0.837395\pi$
$991$		−	30.7819i		−	0.977818i	0.872335	−	0.488909i	$-0.162605\pi$
$992$	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	0.0394432	−	0.999222i	$-0.487442\pi$
$997$	29.1919	−	16.8539i	0.924516	−	0.533770i	0.885073	+	0.465452i	$0.154108\pi$
$998$	−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.59.5	✓	48
3.2	odd	2		540.2.n.d.179.20		48
4.3	odd	2	inner	180.2.n.d.59.13	yes	48
5.2	odd	4		900.2.r.g.851.17		48
5.3	odd	4		900.2.r.g.851.8		48
5.4	even	2	inner	180.2.n.d.59.20	yes	48
9.2	odd	6	inner	180.2.n.d.119.12	yes	48
9.7	even	3		540.2.n.d.359.13		48
12.11	even	2		540.2.n.d.179.12		48
15.14	odd	2		540.2.n.d.179.5		48
20.3	even	4		900.2.r.g.851.1		48
20.7	even	4		900.2.r.g.851.24		48
20.19	odd	2	inner	180.2.n.d.59.12	yes	48
36.7	odd	6		540.2.n.d.359.5		48
36.11	even	6	inner	180.2.n.d.119.20	yes	48
45.2	even	12		900.2.r.g.551.24		48
45.29	odd	6	inner	180.2.n.d.119.13	yes	48
45.34	even	6		540.2.n.d.359.12		48
45.38	even	12		900.2.r.g.551.1		48
60.59	even	2		540.2.n.d.179.13		48
180.47	odd	12		900.2.r.g.551.17		48
180.79	odd	6		540.2.n.d.359.20		48
180.83	odd	12		900.2.r.g.551.8		48
180.119	even	6	inner	180.2.n.d.119.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.5	✓	48	1.1	even	1	trivial
180.2.n.d.59.12	yes	48	20.19	odd	2	inner
180.2.n.d.59.13	yes	48	4.3	odd	2	inner
180.2.n.d.59.20	yes	48	5.4	even	2	inner
180.2.n.d.119.5	yes	48	180.119	even	6	inner
180.2.n.d.119.12	yes	48	9.2	odd	6	inner
180.2.n.d.119.13	yes	48	45.29	odd	6	inner
180.2.n.d.119.20	yes	48	36.11	even	6	inner
540.2.n.d.179.5		48	15.14	odd	2
540.2.n.d.179.12		48	12.11	even	2
540.2.n.d.179.13		48	60.59	even	2
540.2.n.d.179.20		48	3.2	odd	2
540.2.n.d.359.5		48	36.7	odd	6
540.2.n.d.359.12		48	45.34	even	6
540.2.n.d.359.13		48	9.7	even	3
540.2.n.d.359.20		48	180.79	odd	6
900.2.r.g.551.1		48	45.38	even	12
900.2.r.g.551.8		48	180.83	odd	12
900.2.r.g.551.17		48	180.47	odd	12
900.2.r.g.551.24		48	45.2	even	12
900.2.r.g.851.1		48	20.3	even	4
900.2.r.g.851.8		48	5.3	odd	4
900.2.r.g.851.17		48	5.2	odd	4
900.2.r.g.851.24		48	20.7	even	4

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

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