LMFDB - Embedded newform 378.2.z.a.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(41,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([17, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.984808 + 0.173648i) q^{2} +(-1.71625 + 0.233448i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.0848896 - 0.0712308i) q^{5} +(1.64964 - 0.527925i) q^{6} +(-1.74235 - 1.99104i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.89100 - 0.801309i) q^{9} +(0.0959690 + 0.0554077i) q^{10} +(3.36170 + 4.00632i) q^{11} +(-1.53290 + 0.806360i) q^{12} +(-3.05494 - 0.538668i) q^{13} +(2.06162 + 1.65823i) q^{14} +(0.162320 + 0.102432i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.286983 - 0.497069i) q^{17} +(-2.70794 + 1.29115i) q^{18} +(-7.21933 + 4.16808i) q^{19} +(-0.104133 - 0.0379011i) q^{20} +(3.45510 + 3.01036i) q^{21} +(-4.00632 - 3.36170i) q^{22} +(1.79468 + 4.93085i) q^{23} +(1.36959 - 1.06030i) q^{24} +(-0.866108 - 4.91195i) q^{25} +3.10207 q^{26} +(-4.77461 + 2.05014i) q^{27} +(-2.31825 - 1.27504i) q^{28} +(-8.47148 + 1.49375i) q^{29} +(-0.177641 - 0.0726896i) q^{30} +(2.29466 + 6.30454i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-6.70477 - 6.09105i) q^{33} +(-0.196308 + 0.539351i) q^{34} +(0.00608391 + 0.293127i) q^{35} +(2.44259 - 1.74177i) q^{36} +(-0.699352 + 1.21131i) q^{37} +(6.38587 - 5.35839i) q^{38} +(5.36878 + 0.211318i) q^{39} +(0.109132 + 0.0192429i) q^{40} +(-0.875429 + 4.96481i) q^{41} +(-3.92535 - 2.36466i) q^{42} +(-5.33369 + 4.47550i) q^{43} +(4.52921 + 2.61494i) q^{44} +(-0.302494 - 0.137906i) q^{45} +(-2.62365 - 4.54429i) q^{46} +(-7.79301 - 2.83642i) q^{47} +(-1.16466 + 1.28201i) q^{48} +(-0.928455 + 6.93815i) q^{49} +(1.70590 + 4.68692i) q^{50} +(-0.376493 + 0.920088i) q^{51} +(-3.05494 + 0.538668i) q^{52} +6.95222i q^{53} +(4.34607 - 2.84810i) q^{54} -0.579551i q^{55} +(2.50444 + 0.853115i) q^{56} +(11.4171 - 8.83880i) q^{57} +(8.08339 - 2.94211i) q^{58} +(10.2351 + 8.58825i) q^{59} +(0.187565 + 0.0407382i) q^{60} +(4.38186 - 12.0391i) q^{61} +(-3.35458 - 5.81030i) q^{62} +(-6.63257 - 4.35994i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.220963 + 0.263333i) q^{65} +(7.66061 + 4.83424i) q^{66} +(-0.0706818 + 0.400857i) q^{67} +(0.0996681 - 0.565246i) q^{68} +(-4.23121 - 8.04359i) q^{69} +(-0.0568925 - 0.287617i) q^{70} +(-6.50408 - 3.75513i) q^{71} +(-2.10303 + 2.13946i) q^{72} +(12.2644 - 7.08086i) q^{73} +(0.478385 - 1.31435i) q^{74} +(2.63314 + 8.22792i) q^{75} +(-5.35839 + 6.38587i) q^{76} +(2.11948 - 13.6737i) q^{77} +(-5.32391 + 0.724171i) q^{78} +(-1.16950 - 6.63255i) q^{79} -0.110815 q^{80} +(7.71581 - 4.63317i) q^{81} -5.04140i q^{82} +(-1.04808 - 5.94396i) q^{83} +(4.27634 + 1.64710i) q^{84} +(-0.0597685 + 0.0217539i) q^{85} +(4.47550 - 5.33369i) q^{86} +(14.1904 - 4.54129i) q^{87} +(-4.91448 - 1.78872i) q^{88} +(3.86050 + 6.68658i) q^{89} +(0.321846 + 0.0832832i) q^{90} +(4.25026 + 7.02104i) q^{91} +(3.37290 + 4.01966i) q^{92} +(-5.40999 - 10.2845i) q^{93} +(8.16716 + 1.44009i) q^{94} +(0.909742 + 0.160412i) q^{95} +(0.924350 - 1.46478i) q^{96} +(5.16157 + 6.15132i) q^{97} +(-0.290448 - 6.99397i) q^{98} +(12.9290 + 8.88852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	−1.71625	+	0.233448i	−0.990875	+	0.134781i
$3$	−1.71625	+	0.233448i	−0.990875	+	0.134781i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−0.0848896	−	0.0712308i	−0.0379638	−	0.0318554i	0.623608	−	0.781737i	$-0.285666\pi$
$5$	−0.0848896	−	0.0712308i	−0.0379638	−	0.0318554i	−0.661572	+	0.749882i	$0.730110\pi$
$6$	1.64964	−	0.527925i	0.673461	−	0.215524i
$7$	−1.74235	−	1.99104i	−0.658545	−	0.752541i
$7$	−1.74235	−	1.99104i	−0.658545	−	0.752541i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	2.89100	−	0.801309i	0.963668	−	0.267103i
$10$	0.0959690	+	0.0554077i	0.0303481	+	0.0175215i
$11$	3.36170	+	4.00632i	1.01359	+	1.20795i	0.978005	+	0.208584i	$0.0668854\pi$
$11$	3.36170	+	4.00632i	1.01359	+	1.20795i	0.0355861	+	0.999367i	$0.488670\pi$
$12$	−1.53290	+	0.806360i	−0.442510	+	0.232776i
$13$	−3.05494	−	0.538668i	−0.847288	−	0.149400i	−0.266884	−	0.963729i	$-0.585994\pi$
$13$	−3.05494	−	0.538668i	−0.847288	−	0.149400i	−0.580404	+	0.814329i	$0.697105\pi$
$14$	2.06162	+	1.65823i	0.550990	+	0.443181i
$15$	0.162320	+	0.102432i	0.0419109	+	0.0264479i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.286983	−	0.497069i	0.0696036	−	0.120557i	−0.829123	−	0.559066i	$-0.811160\pi$
$17$	0.286983	−	0.497069i	0.0696036	−	0.120557i	0.898727	+	0.438509i	$0.144493\pi$
$18$	−2.70794	+	1.29115i	−0.638267	+	0.304328i
$19$	−7.21933	+	4.16808i	−1.65623	+	0.956224i	−0.681796	+	0.731542i	$0.738801\pi$
$19$	−7.21933	+	4.16808i	−1.65623	+	0.956224i	−0.974432	+	0.224682i	$0.927866\pi$
$20$	−0.104133	−	0.0379011i	−0.0232847	−	0.00847495i
$21$	3.45510	+	3.01036i	0.753965	+	0.656915i
$22$	−4.00632	−	3.36170i	−0.854150	−	0.716717i
$23$	1.79468	+	4.93085i	0.374217	+	1.02815i	0.973714	+	0.227776i	$0.0731453\pi$
$23$	1.79468	+	4.93085i	0.374217	+	1.02815i	−0.599497	+	0.800377i	$0.704632\pi$
$24$	1.36959	−	1.06030i	0.279566	−	0.216432i
$25$	−0.866108	−	4.91195i	−0.173222	−	0.982389i
$26$	3.10207			0.608365
$27$	−4.77461	+	2.05014i	−0.918874	+	0.394550i
$28$	−2.31825	−	1.27504i	−0.438107	−	0.240961i
$29$	−8.47148	+	1.49375i	−1.57311	+	0.277383i	−0.891048	−	0.453908i	$-0.850029\pi$
$29$	−8.47148	+	1.49375i	−1.57311	+	0.277383i	−0.682066	+	0.731291i	$0.738918\pi$
$30$	−0.177641	−	0.0726896i	−0.0324327	−	0.0132712i
$31$	2.29466	+	6.30454i	0.412134	+	1.13233i	0.956054	+	0.293192i	$0.0947174\pi$
$31$	2.29466	+	6.30454i	0.412134	+	1.13233i	−0.543920	+	0.839137i	$0.683060\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−6.70477	−	6.09105i	−1.16715	−	1.06032i
$34$	−0.196308	+	0.539351i	−0.0336665	+	0.0924980i
$35$	0.00608391	+	0.293127i	0.00102837	+	0.0495475i
$36$	2.44259	−	1.74177i	0.407099	−	0.290294i
$37$	−0.699352	+	1.21131i	−0.114973	+	0.199139i	−0.917769	−	0.397115i	$-0.870011\pi$
$37$	−0.699352	+	1.21131i	−0.114973	+	0.199139i	0.802796	+	0.596254i	$0.203345\pi$
$38$	6.38587	−	5.35839i	1.03593	−	0.869245i
$39$	5.36878	+	0.211318i	0.859693	+	0.0338379i
$40$	0.109132	+	0.0192429i	0.0172553	+	0.00304257i
$41$	−0.875429	+	4.96481i	−0.136719	+	0.775373i	0.836928	+	0.547313i	$0.184349\pi$
$41$	−0.875429	+	4.96481i	−0.136719	+	0.775373i	−0.973647	+	0.228060i	$0.926762\pi$
$42$	−3.92535	−	2.36466i	−0.605695	−	0.364874i
$43$	−5.33369	+	4.47550i	−0.813381	+	0.682507i	−0.951412	−	0.307921i	$-0.900367\pi$
$43$	−5.33369	+	4.47550i	−0.813381	+	0.682507i	0.138032	+	0.990428i	$0.455922\pi$
$44$	4.52921	+	2.61494i	0.682804	+	0.394217i
$45$	−0.302494	−	0.137906i	−0.0450931	−	0.0205578i
$46$	−2.62365	−	4.54429i	−0.386836	−	0.670020i
$47$	−7.79301	−	2.83642i	−1.13673	−	0.413735i	−0.295997	−	0.955189i	$-0.595652\pi$
$47$	−7.79301	−	2.83642i	−1.13673	−	0.413735i	−0.840731	+	0.541454i	$0.817874\pi$
$48$	−1.16466	+	1.28201i	−0.168105	+	0.185043i
$49$	−0.928455	+	6.93815i	−0.132636	+	0.991165i
$50$	1.70590	+	4.68692i	0.241251	+	0.662831i
$51$	−0.376493	+	0.920088i	−0.0527196	+	0.128838i
$52$	−3.05494	+	0.538668i	−0.423644	+	0.0746998i
$53$			6.95222i			0.954961i	0.878642	+	0.477480i	$0.158450\pi$
$53$			6.95222i			0.954961i	−0.878642	+	0.477480i	$0.841550\pi$
$54$	4.34607	−	2.84810i	0.591425	−	0.387577i
$55$		−	0.579551i		−	0.0781467i
$56$	2.50444	+	0.853115i	0.334669	+	0.114002i
$57$	11.4171	−	8.83880i	1.51223	−	1.17073i
$58$	8.08339	−	2.94211i	1.06140	−	0.386319i
$59$	10.2351	+	8.58825i	1.33249	+	1.11809i	0.983488	+	0.180974i	$0.0579248\pi$
$59$	10.2351	+	8.58825i	1.33249	+	1.11809i	0.349005	+	0.937121i	$0.386520\pi$
$60$	0.187565	+	0.0407382i	0.0242145	+	0.00525927i
$61$	4.38186	−	12.0391i	0.561040	−	1.54145i	−0.257075	−	0.966391i	$-0.582759\pi$
$61$	4.38186	−	12.0391i	0.561040	−	1.54145i	0.818115	−	0.575054i	$-0.195019\pi$
$62$	−3.35458	−	5.81030i	−0.426032	−	0.737908i
$63$	−6.63257	−	4.35994i	−0.835625	−	0.549301i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	0.220963	+	0.263333i	0.0274071	+	0.0326625i
$66$	7.66061	+	4.83424i	0.942956	+	0.595054i
$67$	−0.0706818	+	0.400857i	−0.00863516	+	0.0489724i	−0.988821	−	0.149108i	$-0.952360\pi$
$67$	−0.0706818	+	0.400857i	−0.00863516	+	0.0489724i	0.980186	+	0.198081i	$0.0634708\pi$
$68$	0.0996681	−	0.565246i	0.0120865	−	0.0685461i
$69$	−4.23121	−	8.04359i	−0.509378	−	0.968334i
$70$	−0.0568925	−	0.287617i	−0.00679995	−	0.0343769i
$71$	−6.50408	−	3.75513i	−0.771893	−	0.445653i	0.0616566	−	0.998097i	$-0.480362\pi$
$71$	−6.50408	−	3.75513i	−0.771893	−	0.445653i	−0.833549	+	0.552445i	$0.813695\pi$
$72$	−2.10303	+	2.13946i	−0.247844	+	0.252137i
$73$	12.2644	−	7.08086i	1.43544	−	0.828752i	0.437912	−	0.899018i	$-0.355718\pi$
$73$	12.2644	−	7.08086i	1.43544	−	0.828752i	0.997528	+	0.0702659i	$0.0223848\pi$
$74$	0.478385	−	1.31435i	0.0556111	−	0.152790i
$75$	2.63314	+	8.22792i	0.304049	+	0.950078i
$76$	−5.35839	+	6.38587i	−0.614649	+	0.732510i
$77$	2.11948	−	13.6737i	0.241537	−	1.55826i
$78$	−5.32391	+	0.724171i	−0.602814	+	0.0819963i
$79$	−1.16950	−	6.63255i	−0.131579	−	0.746220i	−0.977181	−	0.212407i	$-0.931870\pi$
$79$	−1.16950	−	6.63255i	−0.131579	−	0.746220i	0.845602	−	0.533813i	$-0.179241\pi$
$80$	−0.110815			−0.0123895
$81$	7.71581	−	4.63317i	0.857312	−	0.514797i
$82$		−	5.04140i		−	0.556729i
$83$	−1.04808	−	5.94396i	−0.115042	−	0.652434i	−0.986730	−	0.162372i	$-0.948085\pi$
$83$	−1.04808	−	5.94396i	−0.115042	−	0.652434i	0.871688	−	0.490061i	$-0.163026\pi$
$84$	4.27634	+	1.64710i	0.466587	+	0.179714i
$85$	−0.0597685	+	0.0217539i	−0.00648280	+	0.00235955i
$86$	4.47550	−	5.33369i	0.482606	−	0.575147i
$87$	14.1904	−	4.54129i	1.52137	−	0.486878i
$88$	−4.91448	−	1.78872i	−0.523885	−	0.190679i
$89$	3.86050	+	6.68658i	0.409212	+	0.708776i	0.994802	−	0.101832i	$-0.0324703\pi$
$89$	3.86050	+	6.68658i	0.409212	+	0.708776i	−0.585590	+	0.810608i	$0.699137\pi$
$90$	0.321846	+	0.0832832i	0.0339255	+	0.00877882i
$91$	4.25026	+	7.02104i	0.445548	+	0.736005i
$92$	3.37290	+	4.01966i	0.351649	+	0.419079i
$93$	−5.40999	−	10.2845i	−0.560990	−	1.06645i
$94$	8.16716	+	1.44009i	0.842378	+	0.148534i
$95$	0.909742	+	0.160412i	0.0933376	+	0.0164579i
$96$	0.924350	−	1.46478i	0.0943411	−	0.149498i
$97$	5.16157	+	6.15132i	0.524078	+	0.624571i	0.961540	−	0.274665i	$-0.0885671\pi$
$97$	5.16157	+	6.15132i	0.524078	+	0.624571i	−0.437462	+	0.899237i	$0.644123\pi$
$98$	−0.290448	−	6.99397i	−0.0293397	−	0.706498i
$99$	12.9290	+	8.88852i	1.29941	+	0.893330i
$100$	−2.49386	−	4.31949i	−0.249386	−	0.431949i
$101$	2.55350	+	0.929399i	0.254083	+	0.0924787i	0.465922	−	0.884826i	$-0.345723\pi$
$101$	2.55350	+	0.929399i	0.254083	+	0.0924787i	−0.211839	+	0.977305i	$0.567945\pi$
$102$	0.211002	−	0.971487i	0.0208923	−	0.0961916i
$103$	−8.01929	+	9.55702i	−0.790164	+	0.941681i	−0.999345	−	0.0361962i	$-0.988476\pi$
$103$	−8.01929	+	9.55702i	−0.790164	+	0.941681i	0.209181	+	0.977877i	$0.432920\pi$
$104$	2.91499	−	1.06097i	0.285838	−	0.104037i
$105$	−0.0788714	−	0.501658i	−0.00769707	−	0.0489568i
$106$	−1.20724	−	6.84660i	−0.117258	−	0.665001i
$107$		−	1.58705i		−	0.153426i	−0.997053	−	0.0767131i	$-0.975557\pi$
$107$		−	1.58705i		−	0.153426i	0.997053	−	0.0767131i	$-0.0244426\pi$
$108$	−3.78548	+	3.55952i	−0.364258	+	0.342515i
$109$	−7.69237			−0.736796			−0.368398	−	0.929668i	$-0.620094\pi$
$109$	−7.69237			−0.736796			−0.368398	+	0.929668i	$0.620094\pi$
$110$	0.100638	+	0.570747i	0.00959546	+	0.0544186i
$111$	0.917482	−	2.24217i	0.0870835	−	0.212818i
$112$	−2.61453	−	0.405264i	−0.247050	−	0.0382938i
$113$	2.64963	−	3.15771i	0.249256	−	0.297052i	−0.626880	−	0.779116i	$-0.715668\pi$
$113$	2.64963	−	3.15771i	0.249256	−	0.297052i	0.876136	+	0.482064i	$0.160113\pi$
$114$	−9.70883	+	10.6871i	−0.909315	+	1.00094i
$115$	0.198879	−	0.546414i	0.0185455	−	0.0509534i
$116$	−7.44969	+	4.30108i	−0.691687	+	0.399346i
$117$	−9.26348	+	0.890658i	−0.856409	+	0.0823413i
$118$	−11.5709	−	6.68047i	−1.06519	−	0.614987i
$119$	−1.48971	+	0.294673i	−0.136561	+	0.0270126i
$120$	−0.191790	−	0.00754893i	−0.0175079	−	0.000689120i
$121$	−2.83943	+	16.1032i	−0.258130	+	1.46393i
$122$	−2.22473	+	12.6171i	−0.201418	+	1.14230i
$123$	0.343428	−	8.72520i	0.0309659	−	0.786725i
$124$	4.31256	+	5.13951i	0.387279	+	0.461541i
$125$	−0.553397	+	0.958512i	−0.0494973	+	0.0857319i
$126$	7.28890	+	3.14197i	0.649347	+	0.279909i
$127$	−3.05268	−	5.28739i	−0.270881	−	0.469180i	0.698207	−	0.715896i	$-0.253982\pi$
$127$	−3.05268	−	5.28739i	−0.270881	−	0.469180i	−0.969088	+	0.246716i	$0.920648\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	8.10913	−	8.92620i	0.713969	−	0.785908i
$130$	−0.263333	−	0.220963i	−0.0230958	−	0.0193797i
$131$	−10.0238	+	3.64838i	−0.875787	+	0.318760i	−0.740508	−	0.672047i	$-0.765415\pi$
$131$	−10.0238	+	3.64838i	−0.875787	+	0.318760i	−0.135278	+	0.990808i	$0.543193\pi$
$132$	−8.38369	−	3.43054i	−0.729706	−	0.298591i
$133$	20.8774	+	7.11171i	1.81030	+	0.616663i
$134$		−	0.407040i		−	0.0351629i
$135$	0.551348	+	0.166064i	0.0474525	+	0.0142925i
$136$			0.573966i			0.0492171i
$137$	−15.9503	+	2.81246i	−1.36272	+	0.240285i	−0.806739	−	0.590908i	$-0.798770\pi$
$137$	−15.9503	+	2.81246i	−1.36272	+	0.240285i	−0.555984	+	0.831193i	$0.687658\pi$
$138$	5.56369	+	7.18664i	0.473612	+	0.611768i
$139$	−3.67414	−	10.0946i	−0.311636	−	0.856214i	−0.992327	−	0.123643i	$-0.960542\pi$
$139$	−3.67414	−	10.0946i	−0.311636	−	0.856214i	0.680690	−	0.732571i	$-0.261680\pi$
$140$	0.105972	+	0.273369i	0.00895630	+	0.0231039i
$141$	14.0369	+	3.04874i	1.18212	+	0.256750i
$142$	7.05734	+	2.56866i	0.592239	+	0.215557i
$143$	−8.11171	−	14.0499i	−0.678336	−	1.17491i
$144$	1.69957	−	2.47214i	0.141631	−	0.206012i
$145$	0.825542	+	0.476627i	0.0685575	+	0.0395817i
$146$	−10.8485	+	9.10298i	−0.897829	+	0.753368i
$147$	−0.0262404	−	12.1243i	−0.00216427	−	0.999998i
$148$	−0.242882	+	1.37745i	−0.0199648	+	0.113226i
$149$	−5.73431	−	1.01111i	−0.469773	−	0.0828337i	−0.0662499	−	0.997803i	$-0.521103\pi$
$149$	−5.73431	−	1.01111i	−0.469773	−	0.0828337i	−0.403523	+	0.914969i	$0.632215\pi$
$150$	−4.02190	−	7.64568i	−0.328387	−	0.624267i
$151$	6.45781	−	5.41874i	0.525529	−	0.440971i	−0.341025	−	0.940054i	$-0.610774\pi$
$151$	6.45781	−	5.41874i	0.525529	−	0.440971i	0.866554	+	0.499083i	$0.166330\pi$
$152$	4.16808	−	7.21933i	0.338076	−	0.585565i
$153$	0.431363	−	1.66699i	0.0348736	−	0.134768i
$154$	0.287127	+	13.8340i	0.0231374	+	1.11477i
$155$	0.254284	−	0.698641i	0.0204246	−	0.0561162i
$156$	5.11728	−	1.63766i	0.409710	−	0.131117i
$157$	−6.81686	+	8.12401i	−0.544044	+	0.648367i	−0.966089	−	0.258208i	$-0.916868\pi$
$157$	−6.81686	+	8.12401i	−0.544044	+	0.648367i	0.422045	+	0.906575i	$0.361312\pi$
$158$	2.30346	+	6.32871i	0.183254	+	0.503485i
$159$	−1.62298	−	11.9317i	−0.128711	−	0.946247i
$160$	0.109132	−	0.0192429i	0.00862764	−	0.00152129i
$161$	6.69054	−	12.1645i	0.527289	−	0.958699i
$162$	−6.79405	+	5.90262i	−0.533791	+	0.463754i
$163$	8.63779			0.676564			0.338282	−	0.941045i	$-0.390154\pi$
$163$	8.63779			0.676564			0.338282	+	0.941045i	$0.390154\pi$
$164$	0.875429	+	4.96481i	0.0683596	+	0.387686i
$165$	0.135295	+	0.994653i	0.0105327	+	0.0774336i
$166$	2.06431	+	5.67166i	0.160222	+	0.440206i
$167$	10.3973	+	8.72440i	0.804570	+	0.675115i	0.949305	−	0.314356i	$-0.101788\pi$
$167$	10.3973	+	8.72440i	0.804570	+	0.675115i	−0.144735	+	0.989470i	$0.546233\pi$
$168$	−4.49739	−	0.879500i	−0.346981	−	0.0678549i
$169$	−3.17351	−	1.15506i	−0.244116	−	0.0888511i
$170$	0.0550829	−	0.0318021i	0.00422467	−	0.00243911i
$171$	−17.5312	+	17.8349i	−1.34064	+	1.36387i
$172$	−3.48132	+	6.02982i	−0.265448	+	0.459770i
$173$	2.45499	−	2.05998i	0.186650	−	0.156618i	−0.544675	−	0.838647i	$-0.683347\pi$
$173$	2.45499	−	2.05998i	0.186650	−	0.156618i	0.731324	+	0.682030i	$0.238903\pi$
$174$	−13.1863	+	6.93645i	−0.999648	+	0.525851i
$175$	−8.27080	+	10.2828i	−0.625214	+	0.777304i
$176$	5.15042	+	0.908159i	0.388228	+	0.0684550i
$177$	−19.5708	−	12.3502i	−1.47103	−	0.928297i
$178$	−4.96296	−	5.91463i	−0.371990	−	0.443320i
$179$	−0.703065	−	0.405915i	−0.0525495	−	0.0303395i	0.473495	−	0.880796i	$-0.342992\pi$
$179$	−0.703065	−	0.405915i	−0.0525495	−	0.0303395i	−0.526045	+	0.850457i	$0.676326\pi$
$180$	−0.331418	−	0.0261300i	−0.0247024	−	0.00194762i
$181$	−4.75951	+	2.74791i	−0.353772	+	0.204250i	−0.666345	−	0.745643i	$-0.732142\pi$
$181$	−4.75951	+	2.74791i	−0.353772	+	0.204250i	0.312573	+	0.949894i	$0.398809\pi$
$182$	−5.40488	−	6.17633i	−0.400636	−	0.457820i
$183$	−4.70986	+	21.6850i	−0.348163	+	1.60300i
$184$	−4.01966	−	3.37290i	−0.296334	−	0.248653i
$185$	0.145651	−	0.0530125i	0.0107084	−	0.00389755i
$186$	7.11368	+	9.18878i	0.521600	+	0.673754i
$187$	2.95617	−	0.521252i	0.216176	−	0.0381177i
$188$	−8.29315			−0.604840
$189$	12.4009	+	5.93437i	0.902036	+	0.431662i
$190$	−0.923776			−0.0670178
$191$	6.95169	−	1.22577i	0.503007	−	0.0886936i	0.0836133	−	0.996498i	$-0.473354\pi$
$191$	6.95169	−	1.22577i	0.503007	−	0.0886936i	0.419393	+	0.907805i	$0.362243\pi$
$192$	−0.655951	+	1.60304i	−0.0473392	+	0.115689i
$193$	11.5296	−	4.19645i	0.829922	−	0.302067i	0.108095	−	0.994141i	$-0.465525\pi$
$193$	11.5296	−	4.19645i	0.829922	−	0.302067i	0.721827	+	0.692074i	$0.243303\pi$
$194$	−6.15132	−	5.16157i	−0.441639	−	0.370579i
$195$	−0.440701	−	0.400361i	−0.0315593	−	0.0286705i
$196$	1.50053	+	6.83728i	0.107180	+	0.488377i
$197$	2.77971	−	1.60486i	0.198046	−	0.114342i	−0.397698	−	0.917516i	$-0.630191\pi$
$197$	2.77971	−	1.60486i	0.198046	−	0.114342i	0.595744	+	0.803175i	$0.296857\pi$
$198$	−14.2760	−	6.50839i	−1.01455	−	0.462531i
$199$	−12.4562	−	7.19157i	−0.882994	−	0.509797i	−0.0113494	−	0.999936i	$-0.503613\pi$
$199$	−12.4562	−	7.19157i	−0.882994	−	0.509797i	−0.871644	+	0.490139i	$0.836946\pi$
$200$	3.20604	+	3.82082i	0.226702	+	0.270172i
$201$	0.0277283	−	0.704469i	0.00195580	−	0.0496894i
$202$	−2.67610	−	0.471868i	−0.188290	−	0.0332005i
$203$	17.7344	+	14.2644i	1.24471	+	1.00116i
$204$	−0.0390995	+	0.993368i	−0.00273751	+	0.0695497i
$205$	0.427962	−	0.359103i	0.0298902	−	0.0250808i
$206$	6.23790	−	10.8044i	0.434615	−	0.752775i
$207$	9.13957	+	12.8170i	0.635244	+	0.890844i
$208$	−2.68647	+	1.55103i	−0.186273	+	0.107545i
$209$	−40.9679	−	14.9111i	−2.83381	−	1.03142i
$210$	0.164785	+	0.480341i	0.0113713	+	0.0331467i
$211$	6.08994	+	5.11007i	0.419249	+	0.351792i	0.827877	−	0.560909i	$-0.189548\pi$
$211$	6.08994	+	5.11007i	0.419249	+	0.351792i	−0.408628	+	0.912701i	$0.633993\pi$
$212$	2.37780	+	6.53295i	0.163308	+	0.448685i
$213$	12.0392	+	4.92637i	0.824915	+	0.337549i
$214$	0.275589	+	1.56294i	0.0188389	+	0.106841i
$215$	0.771569			0.0526205
$216$	3.10986	−	4.16278i	0.211599	−	0.283241i
$217$	8.55447	−	15.5535i	0.580715	−	1.05584i
$218$	7.57551	−	1.33577i	0.513078	−	0.0904695i
$219$	−19.3957	+	15.0156i	−1.31064	+	1.01466i
$220$	−0.198218	−	0.544600i	−0.0133639	−	0.0367169i
$221$	−1.14447	+	1.36393i	−0.0769854	+	0.0917476i
$222$	−0.514194	+	2.36743i	−0.0345104	+	0.158891i
$223$	1.18771	−	3.26322i	0.0795352	−	0.218521i	−0.893551	−	0.448961i	$-0.851794\pi$
$223$	1.18771	−	3.26322i	0.0795352	−	0.218521i	0.973087	+	0.230440i	$0.0740165\pi$
$224$	2.64518	−	0.0549013i	0.176739	−	0.00366825i
$225$	−6.43991	−	13.5064i	−0.429327	−	0.900429i
$226$	−2.06105	+	3.56984i	−0.137099	+	0.237462i
$227$	−11.6163	+	9.74722i	−0.771000	+	0.646946i	−0.940965	−	0.338504i	$-0.890079\pi$
$227$	−11.6163	+	9.74722i	−0.771000	+	0.646946i	0.169965	+	0.985450i	$0.445635\pi$
$228$	7.70554	−	12.2106i	0.510312	−	0.808669i
$229$	7.85437	+	1.38494i	0.519031	+	0.0915192i	0.427026	−	0.904239i	$-0.359561\pi$
$229$	7.85437	+	1.38494i	0.519031	+	0.0915192i	0.0920052	+	0.995759i	$0.470672\pi$
$230$	−0.100973	+	0.572648i	−0.00665798	+	0.0377593i
$231$	−0.445459	+	23.9622i	−0.0293091	+	1.57659i
$232$	6.58964	−	5.52937i	0.432631	−	0.363021i
$233$	−10.5142	−	6.07035i	−0.688805	−	0.397682i	0.114359	−	0.993439i	$-0.463519\pi$
$233$	−10.5142	−	6.07035i	−0.688805	−	0.397682i	−0.803164	+	0.595758i	$0.796852\pi$
$234$	8.96809	−	2.48571i	0.586262	−	0.162496i
$235$	0.459505	+	0.795886i	0.0299748	+	0.0519179i
$236$	12.5552	+	4.56971i	0.817272	+	0.297463i
$237$	3.55550	+	11.1101i	0.230955	+	0.721677i
$238$	1.41590	−	0.548881i	0.0917794	−	0.0355787i
$239$	−8.71213	−	23.9364i	−0.563541	−	1.54832i	−0.814407	−	0.580294i	$-0.802938\pi$
$239$	−8.71213	−	23.9364i	−0.563541	−	1.54832i	0.250866	−	0.968022i	$-0.419285\pi$
$240$	0.190187	−	0.0258697i	0.0122765	−	0.00166988i
$241$	11.2237	−	1.97904i	0.722982	−	0.127481i	0.199964	−	0.979803i	$-0.435917\pi$
$241$	11.2237	−	1.97904i	0.722982	−	0.127481i	0.523018	+	0.852322i	$0.324806\pi$
$242$		−	16.3516i		−	1.05112i
$243$	−12.1606	+	9.75291i	−0.780104	+	0.625649i
$244$		−	12.8117i		−	0.820186i
$245$	0.573027	−	0.522842i	0.0366093	−	0.0334032i
$246$	1.17690	+	8.65228i	0.0750367	+	0.551649i
$247$	24.2998	−	8.84442i	1.54616	−	0.562757i
$248$	−5.13951	−	4.31256i	−0.326359	−	0.273848i
$249$	3.18637	+	9.95662i	0.201928	+	0.630975i
$250$	0.378546	−	1.04005i	0.0239413	−	0.0657783i
$251$	3.14706	+	5.45087i	0.198641	+	0.344056i	0.948088	−	0.318008i	$-0.103014\pi$
$251$	3.14706	+	5.45087i	0.198641	+	0.344056i	−0.749447	+	0.662064i	$0.769681\pi$
$252$	−7.72376	−	1.82853i	−0.486551	−	0.115187i
$253$	−13.7214	+	23.7661i	−0.862655	+	1.49416i
$254$	3.92444	+	4.67697i	0.246242	+	0.293459i
$255$	0.0974990	−	0.0512880i	0.00610563	−	0.00321178i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.00824	−	5.71799i	0.0628921	−	0.356679i	−0.937079	−	0.349116i	$-0.886482\pi$
$257$	1.00824	−	5.71799i	0.0628921	−	0.356679i	0.999971	−	0.00756212i	$-0.00240712\pi$
$258$	−6.43592	+	10.1987i	−0.400683	+	0.634945i
$259$	3.63028	−	0.718092i	0.225575	−	0.0446201i
$260$	0.297702	+	0.171879i	0.0184627	+	0.0106595i
$261$	−23.2941	+	11.1067i	−1.44187	+	0.687488i
$262$	9.23802	−	5.33357i	0.570727	−	0.329509i
$263$	−4.44200	+	12.2043i	−0.273906	+	0.752549i	0.724116	+	0.689678i	$0.242248\pi$
$263$	−4.44200	+	12.2043i	−0.273906	+	0.752549i	−0.998022	+	0.0628712i	$0.979974\pi$
$264$	8.85203	+	1.92261i	0.544805	+	0.118329i
$265$	0.495212	−	0.590171i	0.0304207	−	0.0362539i
$266$	−21.7952	−	3.37835i	−1.33635	−	0.207140i
$267$	−8.18654	−	10.5746i	−0.501008	−	0.647155i
$268$	0.0706818	+	0.400857i	0.00431758	+	0.0244862i
$269$	4.79165			0.292152			0.146076	−	0.989273i	$-0.453336\pi$
$269$	4.79165			0.292152			0.146076	+	0.989273i	$0.453336\pi$
$270$	−0.571809	−	0.0678003i	−0.0347992	−	0.00412619i
$271$		−	0.902646i		−	0.0548318i	−0.999624	−	0.0274159i	$-0.991272\pi$
$271$		−	0.902646i		−	0.0548318i	0.999624	−	0.0274159i	$-0.00872785\pi$
$272$	−0.0996681	−	0.565246i	−0.00604326	−	0.0342731i
$273$	−8.93353	−	11.0576i	−0.540682	−	0.669238i
$274$	15.2196	−	5.53947i	0.919447	−	0.334651i
$275$	16.7672	−	19.9824i	1.01110	−	1.20498i
$276$	−6.72711	−	6.11134i	−0.404924	−	0.367859i
$277$	−15.6495	−	5.69594i	−0.940285	−	0.342236i	−0.174007	−	0.984744i	$-0.555671\pi$
$277$	−15.6495	−	5.69594i	−0.940285	−	0.342236i	−0.766278	+	0.642509i	$0.777894\pi$
$278$	5.37123	+	9.30324i	0.322145	+	0.557972i
$279$	11.6858	+	16.3877i	0.699609	+	0.981107i
$280$	−0.151832	−	0.250814i	−0.00907372	−	0.0149890i
$281$	0.926358	+	1.10399i	0.0552619	+	0.0658585i	0.792967	−	0.609264i	$-0.208535\pi$
$281$	0.926358	+	1.10399i	0.0552619	+	0.0658585i	−0.737705	+	0.675123i	$0.764091\pi$
$282$	−14.3530	−	0.564943i	−0.854711	−	0.0336419i
$283$	7.34081	+	1.29438i	0.436366	+	0.0769430i	0.387516	−	0.921863i	$-0.373333\pi$
$283$	7.34081	+	1.29438i	0.436366	+	0.0769430i	0.0488499	+	0.998806i	$0.484444\pi$
$284$	−7.39617	−	1.30414i	−0.438882	−	0.0773867i
$285$	−1.59879	−	0.0629292i	−0.0947041	−	0.00372760i
$286$	10.4282	+	12.4279i	0.616633	+	0.734875i
$287$	11.4104	−	6.90740i	0.673535	−	0.407731i
$288$	−1.24446	+	2.72971i	−0.0733307	+	0.160850i
$289$	8.33528	+	14.4371i	0.490311	+	0.849243i
$290$	−0.895765	−	0.326032i	−0.0526011	−	0.0191452i
$291$	−10.2945	−	9.35222i	−0.603476	−	0.548237i
$292$	9.10298	−	10.8485i	0.532711	−	0.634861i
$293$	19.2103	−	6.99198i	1.12228	−	0.408476i	0.286795	−	0.957992i	$-0.407410\pi$
$293$	19.2103	−	6.99198i	1.12228	−	0.408476i	0.835483	+	0.549517i	$0.185188\pi$
$294$	2.13121	+	11.9356i	0.124295	+	0.696097i
$295$	−0.257103	−	1.45811i	−0.0149691	−	0.0848942i
$296$		−	1.39870i		−	0.0812980i
$297$	−24.2643	−	12.2366i	−1.40796	−	0.710042i
$298$	5.82277			0.337304
$299$	−2.82655	−	16.0302i	−0.163464	−	0.927049i
$300$	5.28846	+	6.83113i	0.305329	+	0.394395i
$301$	18.2040	+	2.82171i	1.04926	+	0.162640i
$302$	−5.41874	+	6.45781i	−0.311814	+	0.371605i
$303$	−4.59941	−	0.998968i	−0.264229	−	0.0573892i
$304$	−2.85114	+	7.83343i	−0.163524	+	0.449278i
$305$	−1.22953	+	0.709868i	−0.0704026	+	0.0406469i
$306$	−0.135340	+	1.71657i	−0.00773686	+	0.0981298i
$307$	0.486924	+	0.281126i	0.0277902	+	0.0160447i	0.513831	−	0.857892i	$-0.328226\pi$
$307$	0.486924	+	0.281126i	0.0277902	+	0.0160447i	−0.486041	+	0.873936i	$0.661559\pi$
$308$	−2.68501	−	13.5739i	−0.152993	−	0.773447i
$309$	11.5320	−	18.2743i	0.656033	−	1.03959i
$310$	−0.129104	+	0.732183i	−0.00733259	+	0.0415852i
$311$	1.78245	−	10.1088i	0.101073	−	0.573215i	−0.891643	−	0.452739i	$-0.850447\pi$
$311$	1.78245	−	10.1088i	0.101073	−	0.573215i	0.992716	−	0.120476i	$-0.0384421\pi$
$312$	−4.75516	+	2.50138i	−0.269208	+	0.141613i
$313$	−12.1355	−	14.4625i	−0.685936	−	0.817467i	0.304921	−	0.952377i	$-0.401370\pi$
$313$	−12.1355	−	14.4625i	−0.685936	−	0.817467i	−0.990858	+	0.134910i	$0.956925\pi$
$314$	5.30257	−	9.18432i	0.299241	−	0.518301i
$315$	0.252474	+	0.842557i	0.0142253	+	0.0474727i
$316$	−3.36744	−	5.83257i	−0.189433	−	0.328108i
$317$	1.91149	−	5.25178i	0.107360	−	0.294969i	−0.874367	−	0.485266i	$-0.838723\pi$
$317$	1.91149	−	5.25178i	0.107360	−	0.294969i	0.981727	+	0.190297i	$0.0609450\pi$
$318$	3.67025	+	11.4686i	0.205817	+	0.643129i
$319$	−34.4630	−	28.9179i	−1.92956	−	1.61909i
$320$	−0.104133	+	0.0379011i	−0.00582118	+	0.00211874i
$321$	0.370494	+	2.72377i	0.0206790	+	0.152026i
$322$	−4.47655	+	13.1415i	−0.249468	+	0.732348i
$323$			4.78467i			0.266226i
$324$	5.66585	−	6.99272i	0.314769	−	0.388485i
$325$			15.4722i			0.858245i
$326$	−8.50656	+	1.49994i	−0.471135	+	0.0830738i
$327$	13.2020	−	1.79577i	0.730073	−	0.0993063i
$328$	−1.72426	−	4.73736i	−0.0952063	−	0.261577i
$329$	7.93070	+	20.4582i	0.437234	+	1.12790i
$330$	−0.305959	−	0.956048i	−0.0168425	−	0.0526287i
$331$	17.4775	+	6.36129i	0.960650	+	0.349648i	0.774288	−	0.632833i	$-0.218108\pi$
$331$	17.4775	+	6.36129i	0.960650	+	0.349648i	0.186362	+	0.982481i	$0.440330\pi$
$332$	−3.01783	−	5.22703i	−0.165625	−	0.286870i
$333$	−1.05119	+	4.06231i	−0.0576051	+	0.222613i
$334$	−11.7544	−	6.78638i	−0.643170	−	0.371334i
$335$	0.0345535	−	0.0289938i	0.00188786	−	0.00158410i
$336$	4.58178	+	0.0851758i	0.249957	+	0.00464672i
$337$	−4.92361	+	27.9232i	−0.268206	+	1.52107i	0.491541	+	0.870855i	$0.336434\pi$
$337$	−4.92361	+	27.9232i	−0.268206	+	1.52107i	−0.759747	+	0.650219i	$0.774677\pi$
$338$	3.32588	+	0.586442i	0.180904	+	0.0318982i
$339$	−3.81026	+	6.03795i	−0.206945	+	0.327937i
$340$	−0.0487237	+	0.0408840i	−0.00264241	+	0.00221725i
$341$	−17.5440	+	30.3871i	−0.950062	+	1.64556i
$342$	14.1679	−	20.6082i	0.766111	−	1.11436i
$343$	15.4318	−	10.2401i	0.833239	−	0.552912i
$344$	2.38136	−	6.54274i	0.128395	−	0.352761i
$345$	−0.213765	+	0.984210i	−0.0115087	+	0.0529881i
$346$	−2.05998	+	2.45499i	−0.110745	+	0.131981i
$347$	10.6589	+	29.2850i	0.572199	+	1.57210i	0.801022	+	0.598635i	$0.204290\pi$
$347$	10.6589	+	29.2850i	0.572199	+	1.57210i	−0.228823	+	0.973468i	$0.573488\pi$
$348$	11.7814	−	9.12084i	0.631551	−	0.488928i
$349$	8.70853	−	1.53555i	0.466157	−	0.0821961i	0.0643639	−	0.997926i	$-0.479498\pi$
$349$	8.70853	−	1.53555i	0.466157	−	0.0821961i	0.401793	+	0.915730i	$0.368387\pi$
$350$	6.35957	−	11.5628i	0.339933	−	0.618055i
$351$	15.6905	−	3.69113i	0.837497	−	0.197018i
$352$	−5.22988			−0.278753
$353$	1.52341	+	8.63967i	0.0810827	+	0.459843i	0.998133	+	0.0610722i	$0.0194520\pi$
$353$	1.52341	+	8.63967i	0.0810827	+	0.459843i	−0.917051	+	0.398771i	$0.869437\pi$
$354$	21.4181	+	8.76413i	1.13836	+	0.465808i
$355$	0.284648	+	0.782063i	0.0151075	+	0.0415076i
$356$	5.91463	+	4.96296i	0.313475	+	0.263036i
$357$	2.48791	−	0.853500i	0.131674	−	0.0451720i
$358$	0.762870	+	0.277662i	0.0403189	+	0.0146749i
$359$	22.6039	−	13.0503i	1.19299	−	0.688771i	0.234003	−	0.972236i	$-0.424817\pi$
$359$	22.6039	−	13.0503i	1.19299	−	0.688771i	0.958983	+	0.283465i	$0.0914841\pi$
$360$	0.330920	−	0.0318171i	0.0174410	−	0.00167691i
$361$	25.2458	−	43.7271i	1.32873	−	2.30143i
$362$	4.21004	−	3.53264i	0.221275	−	0.185671i
$363$	1.11390	−	28.2999i	0.0584645	−	1.48536i
$364$	6.39527	+	5.14395i	0.335203	+	0.269616i
$365$	−1.54550	−	0.272513i	−0.0808950	−	0.0142640i
$366$	0.872755	−	22.1734i	0.0456196	−	1.15902i
$367$	−10.5733	−	12.6008i	−0.551923	−	0.657757i	0.415893	−	0.909413i	$-0.363469\pi$
$367$	−10.5733	−	12.6008i	−0.551923	−	0.657757i	−0.967817	+	0.251657i	$0.919025\pi$
$368$	4.54429	+	2.62365i	0.236888	+	0.136767i
$369$	1.44747	+	15.0548i	0.0753525	+	0.783720i
$370$	−0.134232	+	0.0774990i	−0.00697840	+	0.00402898i
$371$	13.8421	−	12.1132i	0.718647	−	0.628885i
$372$	−8.60122	−	7.81390i	−0.445953	−	0.405132i
$373$	1.42297	+	1.19401i	0.0736784	+	0.0618235i	0.678883	−	0.734246i	$-0.262464\pi$
$373$	1.42297	+	1.19401i	0.0736784	+	0.0618235i	−0.605205	+	0.796070i	$0.706909\pi$
$374$	−2.82074	+	1.02667i	−0.145857	+	0.0530876i
$375$	0.726003	−	1.77423i	0.0374906	−	0.0916209i
$376$	8.16716	−	1.44009i	0.421189	−	0.0742670i
$377$	26.6845			1.37432
$378$	−13.2430	−	3.69081i	−0.681148	−	0.189835i
$379$	2.24840			0.115492			0.0577462	−	0.998331i	$-0.481609\pi$
$379$	2.24840			0.115492			0.0577462	+	0.998331i	$0.481609\pi$
$380$	0.909742	−	0.160412i	0.0466688	−	0.00822897i
$381$	6.47348	+	8.36182i	0.331646	+	0.428389i
$382$	−6.63323	+	2.41430i	−0.339385	+	0.123526i
$383$	−12.0632	−	10.1222i	−0.616399	−	0.517221i	0.280270	−	0.959921i	$-0.409576\pi$
$383$	−12.0632	−	10.1222i	−0.616399	−	0.517221i	−0.896669	+	0.442701i	$0.854020\pi$
$384$	0.367621	−	1.69259i	0.0187601	−	0.0863745i
$385$	−1.15391	+	1.00978i	−0.0588086	+	0.0514631i
$386$	−10.6258	+	6.13479i	−0.540838	+	0.312253i
$387$	−11.8335	+	17.2126i	−0.601529	+	0.874967i
$388$	6.95416	+	4.01499i	0.353044	+	0.203830i
$389$	16.4621	+	19.6187i	0.834661	+	0.994710i	0.999964	+	0.00846700i	$0.00269516\pi$
$389$	16.4621	+	19.6187i	0.834661	+	0.994710i	−0.165304	+	0.986243i	$0.552860\pi$
$390$	0.503528	+	0.317752i	0.0254971	+	0.0160900i
$391$	2.96601	+	0.522988i	0.149998	+	0.0264487i
$392$	−2.66501	−	6.47284i	−0.134603	−	0.326928i
$393$	16.3517	−	8.60156i	0.824833	−	0.433891i
$394$	−2.45880	+	2.06317i	−0.123872	+	0.103941i
$395$	−0.373164	+	0.646339i	−0.0187759	+	0.0325208i
$396$	15.1893	+	3.93050i	0.763292	+	0.197515i
$397$	−25.9260	+	14.9684i	−1.30119	+	0.751240i	−0.980608	−	0.195981i	$-0.937211\pi$
$397$	−25.9260	+	14.9684i	−1.30119	+	0.751240i	−0.320579	+	0.947222i	$0.603877\pi$
$398$	13.5157	+	4.91932i	0.677482	+	0.246583i
$399$	−37.4910	−	7.33166i	−1.87690	−	0.367042i
$400$	−3.82082	−	3.20604i	−0.191041	−	0.160302i
$401$	−2.24812	−	6.17665i	−0.112266	−	0.308447i	0.870818	−	0.491606i	$-0.163590\pi$
$401$	−2.24812	−	6.17665i	−0.112266	−	0.308447i	−0.983083	+	0.183159i	$0.941368\pi$
$402$	0.0950228	+	0.698582i	0.00473931	+	0.0348421i
$403$	−3.61401	−	20.4960i	−0.180026	−	1.02098i
$404$	2.71738			0.135195
$405$	−0.985017	−	0.156295i	−0.0489459	−	0.00776637i
$406$	−19.9419	−	10.9681i	−0.989701	−	0.544340i
$407$	−7.20392	+	1.27025i	−0.357085	+	0.0629637i
$408$	−0.133991	−	0.985066i	−0.00663355	−	0.0487681i
$409$	−12.1976	−	33.5128i	−0.603135	−	1.65710i	−0.744882	−	0.667197i	$-0.767494\pi$
$409$	−12.1976	−	33.5128i	−0.603135	−	1.65710i	0.141747	−	0.989903i	$-0.454728\pi$
$410$	−0.359103	+	0.427962i	−0.0177348	+	0.0211355i
$411$	26.7180	−	8.55043i	1.31790	−	0.421762i
$412$	−4.26697	+	11.7234i	−0.210219	+	0.577571i
$413$	−0.733533	−	35.3421i	−0.0360948	−	1.73907i
$414$	−11.2264	−	11.0352i	−0.551746	−	0.542352i
$415$	−0.334422	+	0.579236i	−0.0164161	+	0.0284336i
$416$	2.37632	−	1.99397i	0.116509	−	0.0977624i
$417$	8.66229	+	16.4671i	0.424194	+	0.806398i
$418$	42.9348	+	7.57056i	2.10001	+	0.370288i
$419$	4.26770	−	24.2033i	0.208491	−	1.18241i	−0.683361	−	0.730081i	$-0.739482\pi$
$419$	4.26770	−	24.2033i	0.208491	−	1.18241i	0.891851	−	0.452329i	$-0.149407\pi$
$420$	−0.245692	−	0.444429i	−0.0119885	−	0.0216859i
$421$	9.69790	−	8.13750i	0.472647	−	0.396598i	−0.375112	−	0.926979i	$-0.622396\pi$
$421$	9.69790	−	8.13750i	0.472647	−	0.396598i	0.847759	+	0.530382i	$0.177951\pi$
$422$	−6.88478	−	3.97493i	−0.335146	−	0.193496i
$423$	−24.8025	−	1.95551i	−1.20594	−	0.0950799i
$424$	−3.47611	−	6.02080i	−0.168815	−	0.292396i
$425$	−2.69013	−	0.979128i	−0.130491	−	0.0474947i
$426$	−12.7118	−	2.76094i	−0.615888	−	0.133768i
$427$	−31.6050	+	12.2518i	−1.52947	+	0.592906i
$428$	−0.542804	−	1.49134i	−0.0262374	−	0.0720867i
$429$	17.2016	+	22.2194i	0.830502	+	1.07276i
$430$	−0.759847	+	0.133981i	−0.0366431	+	0.00646116i
$431$			32.4385i			1.56251i	0.624215	+	0.781253i	$0.285419\pi$
$431$			32.4385i			1.56251i	−0.624215	+	0.781253i	$0.714581\pi$
$432$	−2.33976	+	4.63956i	−0.112572	+	0.223221i
$433$			14.0484i			0.675123i	0.941303	+	0.337562i	$0.109602\pi$
$433$			14.0484i			0.675123i	−0.941303	+	0.337562i	$0.890398\pi$
$434$	−5.72368	+	16.8026i	−0.274745	+	0.806552i
$435$	−1.52810	−	0.625288i	−0.0732668	−	0.0299803i
$436$	−7.22847	+	2.63095i	−0.346181	+	0.126000i
$437$	−33.5086	−	28.1171i	−1.60293	−	1.34502i
$438$	16.4936	−	18.1555i	0.788096	−	0.867504i
$439$	0.375011	−	1.03033i	0.0178983	−	0.0491752i	−0.930422	−	0.366491i	$-0.880559\pi$
$439$	0.375011	−	1.03033i	0.0178983	−	0.0491752i	0.948320	+	0.317315i	$0.102781\pi$
$440$	0.289776	+	0.501906i	0.0138145	+	0.0239274i
$441$	2.87544	+	20.8022i	0.136925	+	0.990581i
$442$	0.890240	−	1.54194i	0.0423444	−	0.0733426i
$443$	5.14345	+	6.12973i	0.244373	+	0.291232i	0.874264	−	0.485452i	$-0.161345\pi$
$443$	5.14345	+	6.12973i	0.244373	+	0.291232i	−0.629891	+	0.776684i	$0.716900\pi$
$444$	0.0952820	−	2.42075i	0.00452188	−	0.114884i
$445$	0.148574	−	0.842608i	0.00704310	−	0.0399434i
$446$	−0.603018	+	3.41989i	−0.0285537	+	0.161936i
$447$	10.0775	+	0.396657i	0.476651	+	0.0187612i
$448$	−2.59546	+	0.513398i	−0.122624	+	0.0242558i
$449$	−11.2056	−	6.46953i	−0.528823	−	0.305316i	0.211714	−	0.977332i	$-0.432095\pi$
$449$	−11.2056	−	6.46953i	−0.528823	−	0.305316i	−0.740537	+	0.672016i	$0.765429\pi$
$450$	8.68744	+	12.1830i	0.409530	+	0.574310i
$451$	−22.8335	+	13.1829i	−1.07519	+	0.620761i
$452$	1.40984	−	3.87350i	0.0663132	−	0.182194i
$453$	−9.81819	+	10.8075i	−0.461299	+	0.507779i
$454$	9.74722	−	11.6163i	0.457460	−	0.545179i
$455$	0.139312	−	0.898763i	0.00653106	−	0.0421346i
$456$	−5.46812	+	13.3632i	−0.256068	+	0.625788i
$457$	2.85895	+	16.2139i	0.133736	+	0.758456i	0.975731	+	0.218971i	$0.0702699\pi$
$457$	2.85895	+	16.2139i	0.133736	+	0.758456i	−0.841995	+	0.539485i	$0.818619\pi$
$458$	−7.97554			−0.372672
$459$	−0.351169	+	2.96167i	−0.0163912	+	0.138239i
$460$		−	0.581482i		−	0.0271117i
$461$	6.49736	+	36.8483i	0.302612	+	1.71620i	0.634537	+	0.772892i	$0.281191\pi$
$461$	6.49736	+	36.8483i	0.302612	+	1.71620i	−0.331925	+	0.943306i	$0.607698\pi$
$462$	−3.72229	−	23.6755i	−0.173177	−	1.10148i
$463$	−8.17143	+	2.97416i	−0.379759	+	0.138221i	−0.524844	−	0.851198i	$-0.675876\pi$
$463$	−8.17143	+	2.97416i	−0.379759	+	0.138221i	0.145086	+	0.989419i	$0.453654\pi$
$464$	−5.52937	+	6.58964i	−0.256694	+	0.305916i
$465$	−0.273318	+	1.25840i	−0.0126748	+	0.0583570i
$466$	11.4085	+	4.15236i	0.528490	+	0.192355i
$467$	9.23983	+	16.0038i	0.427568	+	0.740570i	0.996656	−	0.0817066i	$-0.0260371\pi$
$467$	9.23983	+	16.0038i	0.427568	+	0.740570i	−0.569088	+	0.822276i	$0.692704\pi$
$468$	−8.40020	+	4.00524i	−0.388299	+	0.185142i
$469$	0.921272	−	0.557701i	0.0425404	−	0.0257522i
$470$	−0.590728	−	0.704002i	−0.0272482	−	0.0324732i
$471$	9.80287	−	15.5342i	0.451692	−	0.715778i
$472$	−13.1580	−	2.32010i	−0.605644	−	0.106791i
$473$	−35.8605	−	6.32318i	−1.64887	−	0.290740i
$474$	−5.43073	−	10.3239i	−0.249442	−	0.474192i
$475$	26.7261	+	31.8510i	1.22628	+	1.46142i
$476$	−1.29908	+	0.786411i	−0.0595433	+	0.0360451i
$477$	5.57088	+	20.0989i	0.255073	+	0.920265i
$478$	12.7363	+	22.0599i	0.582544	+	1.00900i
$479$	1.63729	+	0.595925i	0.0748097	+	0.0272285i	0.379154	−	0.925334i	$-0.376215\pi$
$479$	1.63729	+	0.595925i	0.0748097	+	0.0272285i	−0.304344	+	0.952562i	$0.598437\pi$
$480$	−0.182805	+	0.0585022i	−0.00834387	+	0.00267025i
$481$	2.78897	−	3.32377i	0.127166	−	0.151551i
$482$	−10.7095	+	3.89795i	−0.487806	+	0.177547i
$483$	−8.64284	+	22.4392i	−0.393263	+	1.02102i
$484$	2.83943	+	16.1032i	0.129065	+	0.731963i
$485$		−	0.889845i		−	0.0404058i
$486$	10.2823	−	11.7164i	0.466415	−	0.531467i
$487$	−39.3666			−1.78387			−0.891935	−	0.452163i	$-0.850652\pi$
$487$	−39.3666			−1.78387			−0.891935	+	0.452163i	$0.850652\pi$
$488$	2.22473	+	12.6171i	0.100709	+	0.571148i
$489$	−14.8246	+	2.01647i	−0.670390	+	0.0911881i
$490$	−0.473530	+	0.614404i	−0.0213919	+	0.0277560i
$491$	−24.4458	+	29.1334i	−1.10323	+	1.31477i	−0.158335	+	0.987385i	$0.550613\pi$
$491$	−24.4458	+	29.1334i	−1.10323	+	1.31477i	−0.944890	+	0.327387i	$0.893832\pi$
$492$	−2.66148	−	8.31647i	−0.119989	−	0.374935i
$493$	−1.68867	+	4.63959i	−0.0760540	+	0.208957i
$494$	−22.3949	+	12.9297i	−1.00759	+	0.581733i
$495$	−0.464400	−	1.67549i	−0.0208732	−	0.0753075i
$496$	5.81030	+	3.35458i	0.260890	+	0.150625i
$497$	3.85576	+	19.4926i	0.172954	+	0.874363i
$498$	−4.86691	−	9.25205i	−0.218091	−	0.414594i
$499$	−1.35562	+	7.68811i	−0.0606859	+	0.344167i	0.939313	+	0.343060i	$0.111463\pi$
$499$	−1.35562	+	7.68811i	−0.0606859	+	0.344167i	−0.999999	+	0.00110686i	$0.999648\pi$
$500$	−0.192193	+	1.08998i	−0.00859512	+	0.0487454i
$501$	−19.8811	−	12.5460i	−0.888222	−	0.560513i
$502$	−4.04579	−	4.82158i	−0.180572	−	0.215198i
$503$	−2.16662	+	3.75270i	−0.0966050	+	0.167325i	−0.910277	−	0.413999i	$-0.864132\pi$
$503$	−2.16662	+	3.75270i	−0.0966050	+	0.167325i	0.813672	+	0.581324i	$0.197465\pi$
$504$	7.92394	+	0.459533i	0.352960	+	0.0204692i
$505$	−0.150564	−	0.260784i	−0.00670001	−	0.0116048i
$506$	9.38597	−	25.7877i	0.417257	−	1.14640i
$507$	5.71618	+	1.24152i	0.253864	+	0.0551381i
$508$	−4.67697	−	3.92444i	−0.207507	−	0.174119i
$509$	0.210305	−	0.0765449i	0.00932162	−	0.00339279i	−0.337355	−	0.941377i	$-0.609532\pi$
$509$	0.210305	−	0.0765449i	0.00932162	−	0.00339279i	0.346677	+	0.937985i	$0.387310\pi$
$510$	−0.0871117	+	0.0674393i	−0.00385737	+	0.00298626i
$511$	−35.4671	−	12.0816i	−1.56897	−	0.534457i
$512$			1.00000i			0.0441942i
$513$	25.9243	−	34.7016i	1.14459	−	1.53211i
$514$			5.80620i			0.256101i
$515$	1.36151	−	0.240071i	0.0599952	−	0.0105788i
$516$	4.56715	−	11.1614i	0.201058	−	0.491352i
$517$	−14.8342	−	40.7565i	−0.652405	−	1.79247i
$518$	−3.45044	+	1.33757i	−0.151603	+	0.0587697i
$519$	−3.73247	+	4.10855i	−0.163837	+	0.180345i
$520$	−0.323026	−	0.117572i	−0.0141656	−	0.00515587i
$521$	21.2763	+	36.8517i	0.932133	+	1.61450i	0.779668	+	0.626192i	$0.215388\pi$
$521$	21.2763	+	36.8517i	0.932133	+	1.61450i	0.152464	+	0.988309i	$0.451279\pi$
$522$	21.0116	−	14.9830i	0.919652	−	0.655786i
$523$	−4.18823	−	2.41808i	−0.183139	−	0.105735i	0.405628	−	0.914038i	$-0.367053\pi$
$523$	−4.18823	−	2.41808i	−0.183139	−	0.105735i	−0.588766	+	0.808303i	$0.700386\pi$
$524$	−8.17151	+	6.85671i	−0.356974	+	0.299537i
$525$	11.7942	−	19.5786i	0.514743	−	0.854479i
$526$	2.25526	−	12.7902i	0.0983341	−	0.557681i
$527$	3.79232	+	0.668688i	0.165196	+	0.0291285i
$528$	−9.05140	−	0.356268i	−0.393912	−	0.0155046i
$529$	−3.47336	+	2.91450i	−0.151016	+	0.126717i
$530$	−0.385207	+	0.667198i	−0.0167323	+	0.0289812i
$531$	36.4715	+	16.6272i	1.58273	+	0.721559i
$532$	22.0507	−	0.457666i	0.956018	−	0.0198424i
$533$	5.34877	−	14.6956i	0.231681	−	0.636538i
$534$	9.89842	+	8.99237i	0.428347	+	0.389138i
$535$	−0.113047	+	0.134724i	−0.00488745	+	0.00582464i
$536$	−0.139216	−	0.382493i	−0.00601322	−	0.0165212i
$537$	1.30139	+	0.532521i	0.0561592	+	0.0229800i
$538$	−4.71886	+	0.832062i	−0.203444	+	0.0358727i
$539$	−30.9176	+	19.6043i	−1.33172	+	0.844417i
$540$	0.574895	−	0.0325233i	0.0247395	−	0.00139958i
$541$	20.8332			0.895687			0.447844	−	0.894112i	$-0.352192\pi$
$541$	20.8332			0.895687			0.447844	+	0.894112i	$0.352192\pi$
$542$	0.156743	+	0.888932i	0.00673268	+	0.0381829i
$543$	7.52700	−	5.82718i	0.323015	−	0.250068i
$544$	0.196308	+	0.539351i	0.00841663	+	0.0231245i
$545$	0.653003	+	0.547934i	0.0279716	+	0.0234709i
$546$	10.7180	+	9.33835i	0.458686	+	0.399644i
$547$	−20.3530	−	7.40787i	−0.870230	−	0.316738i	−0.131970	−	0.991254i	$-0.542130\pi$
$547$	−20.3530	−	7.40787i	−0.870230	−	0.316738i	−0.738260	+	0.674516i	$0.764352\pi$
$548$	−14.0264	+	8.09816i	−0.599179	+	0.345936i
$549$	3.02097	−	38.3162i	0.128932	−	1.63530i
$550$	−13.0426	+	22.5904i	−0.556137	+	0.963258i
$551$	54.9324	−	46.0937i	2.34020	−	1.96366i
$552$	7.68613	+	4.85034i	0.327144	+	0.206444i
$553$	−11.1680	+	13.8847i	−0.474911	+	0.590438i
$554$	16.4008	+	2.89190i	0.696803	+	0.122865i
$555$	−0.237597	+	0.124984i	−0.0100854	+	0.00530529i
$556$	−6.90512	−	8.22920i	−0.292842	−	0.348996i
$557$	5.42810	+	3.13392i	0.229996	+	0.132788i	0.610570	−	0.791962i	$-0.290940\pi$
$557$	5.42810	+	3.13392i	0.229996	+	0.132788i	−0.380574	+	0.924750i	$0.624274\pi$
$558$	−14.3539	−	14.1095i	−0.607650	−	0.597304i
$559$	18.7049	−	10.7993i	0.791134	−	0.456761i
$560$	0.193079	+	0.220638i	0.00815908	+	0.00932365i
$561$	−4.95182	+	1.58471i	−0.209066	+	0.0669064i
$562$	−1.10399	−	0.926358i	−0.0465690	−	0.0390760i
$563$	−10.8730	+	3.95744i	−0.458241	+	0.166786i	−0.560818	−	0.827939i	$-0.689513\pi$
$563$	−10.8730	+	3.95744i	−0.458241	+	0.166786i	0.102577	+	0.994725i	$0.467291\pi$
$564$	14.2331	−	1.93602i	0.599321	−	0.0815211i
$565$	−0.449852	+	0.0793210i	−0.0189254	+	0.00333706i
$566$	−7.45405			−0.313317
$567$	−22.6684	−	7.28986i	−0.951985	−	0.306145i
$568$	7.51027			0.315124
$569$	−11.2109	+	1.97679i	−0.469986	+	0.0828712i	−0.403625	−	0.914924i	$-0.632250\pi$
$569$	−11.2109	+	1.97679i	−0.469986	+	0.0828712i	−0.0663609	+	0.997796i	$0.521139\pi$
$570$	1.58543	−	0.215654i	0.0664063	−	0.00903274i
$571$	24.6671	−	8.97810i	1.03229	−	0.375722i	0.230336	−	0.973111i	$-0.426018\pi$
$571$	24.6671	−	8.97810i	1.03229	−	0.375722i	0.801951	+	0.597390i	$0.203795\pi$
$572$	−12.4279	−	10.4282i	−0.519635	−	0.436026i
$573$	−11.6447	+	3.72658i	−0.486463	+	0.155680i
$574$	−10.0376	+	8.78386i	−0.418962	+	0.366631i
$575$	22.6657	−	13.0860i	0.945224	−	0.545725i
$576$	0.751548	−	2.90434i	0.0313145	−	0.121014i
$577$	32.1457	+	18.5594i	1.33824	+	0.772636i	0.986547	−	0.163478i	$-0.0522711\pi$
$577$	32.1457	+	18.5594i	1.33824	+	0.772636i	0.351698	+	0.936114i	$0.385604\pi$
$578$	−10.7156	−	12.7704i	−0.445712	−	0.531178i
$579$	−18.8081	+	9.89371i	−0.781636	+	0.411168i
$580$	0.938771	+	0.165531i	0.0389804	+	0.00687329i
$581$	−10.0085	+	12.4432i	−0.415223	+	0.516231i
$582$	11.7621	+	7.42251i	0.487556	+	0.307673i
$583$	−27.8528	+	23.3713i	−1.15355	+	0.967940i
$584$	−7.08086	+	12.2644i	−0.293008	+	0.507505i
$585$	0.849815	+	0.584238i	0.0351355	+	0.0241553i
$586$	−17.7043	+	10.2216i	−0.731358	+	0.422250i
$587$	7.48319	+	2.72366i	0.308864	+	0.112417i	0.491802	−	0.870707i	$-0.336338\pi$
$587$	7.48319	+	2.72366i	0.308864	+	0.112417i	−0.182938	+	0.983125i	$0.558561\pi$
$588$	−4.17142	−	11.3842i	−0.172027	−	0.469475i
$589$	−42.8438	−	35.9502i	−1.76535	−	1.48130i
$590$	0.506395	+	1.39131i	0.0208479	+	0.0572792i
$591$	−4.39601	+	3.40326i	−0.180828	+	0.139991i
$592$	0.242882	+	1.37745i	0.00998241	+	0.0566130i
$593$	−5.25522			−0.215806			−0.107903	−	0.994161i	$-0.534414\pi$
$593$	−5.25522			−0.215806			−0.107903	+	0.994161i	$0.534414\pi$
$594$	26.0206	+	7.83729i	1.06764	+	0.321568i
$595$	0.147450	+	0.0810983i	0.00604487	+	0.00332471i
$596$	−5.73431	+	1.01111i	−0.234887	+	0.0414169i
$597$	23.0567	+	9.43464i	0.943648	+	0.386134i
$598$	5.56722	+	15.2958i	0.227661	+	0.625493i
$599$	10.2641	−	12.2322i	0.419378	−	0.499796i	−0.514448	−	0.857521i	$-0.672003\pi$
$599$	10.2641	−	12.2322i	0.419378	−	0.499796i	0.933827	+	0.357726i	$0.116448\pi$
$600$	−6.39432	−	5.80902i	−0.261047	−	0.237152i
$601$	−6.46075	+	17.7508i	−0.263540	+	0.724069i	0.735383	+	0.677652i	$0.237002\pi$
$601$	−6.46075	+	17.7508i	−0.263540	+	0.724069i	−0.998922	+	0.0464169i	$0.985220\pi$
$602$	−18.4175	+	0.382258i	−0.750639	+	0.0155797i
$603$	0.116868	+	1.21552i	0.00475925	+	0.0494996i
$604$	4.21503	−	7.30065i	0.171507	−	0.297059i
$605$	1.38808	−	1.16474i	0.0564335	−	0.0473534i
$606$	4.70300	+	0.185112i	0.191046	+	0.00751968i
$607$	32.1160	+	5.66292i	1.30355	+	0.229851i	0.781951	−	0.623341i	$-0.214225\pi$
$607$	32.1160	+	5.66292i	1.30355	+	0.229851i	0.521598	+	0.853191i	$0.325336\pi$
$608$	1.44756	−	8.20952i	0.0587063	−	0.332940i
$609$	−33.7665	−	20.3412i	−1.36829	−	0.824266i
$610$	1.08758	−	0.912589i	0.0440349	−	0.0369497i
$611$	22.2793	+	12.8630i	0.901324	+	0.520379i
$612$	−0.164796	−	1.71399i	−0.00666147	−	0.0692840i
$613$	1.77579	+	3.07575i	0.0717233	+	0.124228i	0.899657	−	0.436598i	$-0.143817\pi$
$613$	1.77579	+	3.07575i	0.0717233	+	0.124228i	−0.827933	+	0.560826i	$0.810483\pi$
$614$	−0.528343	−	0.192301i	−0.0213222	−	0.00776065i
$615$	−0.650657	+	0.716216i	−0.0262370	+	0.0288806i
$616$	5.00131	+	12.9015i	0.201508	+	0.519815i
$617$	5.64500	+	15.5095i	0.227259	+	0.624389i	0.999946	−	0.0103984i	$-0.00330996\pi$
$617$	5.64500	+	15.5095i	0.227259	+	0.624389i	−0.772687	+	0.634787i	$0.781088\pi$
$618$	−8.18352	+	19.9992i	−0.329189	+	0.804485i
$619$	−36.9247	+	6.51083i	−1.48413	+	0.261692i	−0.856227	−	0.516599i	$-0.827198\pi$
$619$	−36.9247	+	6.51083i	−1.48413	+	0.261692i	−0.627903	+	0.778291i	$0.716087\pi$
$620$		−	0.743478i		−	0.0298588i
$621$	−18.6779	−	19.8635i	−0.749516	−	0.797096i
$622$			10.2647i			0.411577i
$623$	6.58690	−	19.3367i	0.263899	−	0.774710i
$624$	4.24856	−	3.28911i	0.170078	−	0.131670i
$625$	−23.3194	+	8.48755i	−0.932775	+	0.339502i
$626$	14.4625	+	12.1355i	0.578037	+	0.485030i
$627$	73.7920	+	16.0272i	2.94697	+	0.640066i
$628$	−3.62717	+	9.96558i	−0.144740	+	0.397670i
$629$	0.401404	+	0.695252i	0.0160050	+	0.0277215i
$630$	−0.394947	−	0.785915i	−0.0157351	−	0.0313116i
$631$	8.30649	−	14.3873i	0.330676	−	0.572748i	−0.651968	−	0.758246i	$-0.726057\pi$
$631$	8.30649	−	14.3873i	0.330676	−	0.572748i	0.982645	+	0.185498i	$0.0593899\pi$
$632$	4.32909	+	5.15921i	0.172202	+	0.205222i
$633$	−11.6448	−	7.34845i	−0.462838	−	0.292075i
$634$	−0.970490	+	5.50392i	−0.0385431	+	0.218589i
$635$	−0.117485	+	0.666289i	−0.00466224	+	0.0264409i
$636$	−5.60599	−	10.6571i	−0.222292	−	0.422580i
$637$	6.57374	−	20.6955i	0.260461	−	0.819986i
$638$	38.9610	+	22.4941i	1.54248	+	0.890551i
$639$	−21.8124	−	5.64433i	−0.862883	−	0.223286i
$640$	0.0959690	−	0.0554077i	0.00379351	−	0.00219018i
$641$	−11.6181	+	31.9203i	−0.458886	+	1.26078i	0.467430	+	0.884030i	$0.345180\pi$
$641$	−11.6181	+	31.9203i	−0.458886	+	1.26078i	−0.926316	+	0.376748i	$0.877042\pi$
$642$	−0.837844	−	2.61806i	−0.0330671	−	0.103327i
$643$	0.338298	−	0.403168i	0.0133412	−	0.0158994i	−0.759333	−	0.650703i	$-0.774474\pi$
$643$	0.338298	−	0.403168i	0.0133412	−	0.0158994i	0.772674	+	0.634803i	$0.218919\pi$
$644$	2.12654	−	13.7192i	0.0837974	−	0.540613i
$645$	−1.32420	+	0.180121i	−0.0521404	+	0.00709226i
$646$	−0.830850	−	4.71198i	−0.0326893	−	0.185390i
$647$	2.27585			0.0894729			0.0447365	−	0.998999i	$-0.485755\pi$
$647$	2.27585			0.0894729			0.0447365	+	0.998999i	$0.485755\pi$
$648$	−4.36550	+	7.87035i	−0.171493	+	0.309177i
$649$			69.8761i			2.74288i
$650$	−2.68673	−	15.2372i	−0.105382	−	0.597651i
$651$	−11.0507	+	28.6906i	−0.433109	+	1.12447i
$652$	8.11687	−	2.95430i	0.317881	−	0.115699i
$653$	−3.00807	+	3.58487i	−0.117715	+	0.140287i	−0.821684	−	0.569944i	$-0.806965\pi$
$653$	−3.00807	+	3.58487i	−0.117715	+	0.140287i	0.703969	+	0.710231i	$0.251409\pi$
$654$	−12.6896	+	4.06099i	−0.496203	+	0.158797i
$655$	1.11080	+	0.404297i	0.0434024	+	0.0157972i
$656$	2.52070	+	4.36598i	0.0984167	+	0.170463i
$657$	29.7825	−	30.2984i	1.16193	−	1.18205i
$658$	−11.3628	−	18.7703i	−0.442966	−	0.731741i
$659$	−6.65681	−	7.93328i	−0.259313	−	0.309037i	0.620642	−	0.784094i	$-0.286872\pi$
$659$	−6.65681	−	7.93328i	−0.259313	−	0.309037i	−0.879955	+	0.475057i	$0.842427\pi$
$660$	0.467327	+	0.888394i	0.0181907	+	0.0345807i
$661$	3.45779	+	0.609701i	0.134492	+	0.0237146i	0.240489	−	0.970652i	$-0.422692\pi$
$661$	3.45779	+	0.609701i	0.134492	+	0.0237146i	−0.105997	+	0.994366i	$0.533803\pi$
$662$	−18.3166	−	3.22971i	−0.711895	−	0.125526i
$663$	1.64579	−	2.60801i	0.0639171	−	0.101287i
$664$	3.87964	+	4.62358i	0.150559	+	0.179430i
$665$	−1.26570	−	2.09082i	−0.0490817	−	0.0810787i
$666$	0.329811	−	4.18313i	0.0127799	−	0.162093i
$667$	−22.5691	−	39.0908i	−0.873878	−	1.51360i
$668$	12.7542	+	4.64216i	0.493476	+	0.179611i
$669$	−1.27662	+	5.87775i	−0.0493569	+	0.227247i
$670$	−0.0289938	+	0.0345535i	−0.00112013	+	0.00133492i
$671$	62.9629	−	22.9166i	2.43065	−	0.884686i
$672$	−4.52697	+	0.711737i	−0.174632	+	0.0274558i
$673$	5.20534	+	29.5209i	0.200651	+	1.13795i	0.904138	+	0.427240i	$0.140514\pi$
$673$	5.20534	+	29.5209i	0.200651	+	1.13795i	−0.703487	+	0.710708i	$0.748375\pi$
$674$		−	28.3540i		−	1.09215i
$675$	14.2055	+	21.6770i	0.546771	+	0.834348i
$676$	−3.37718			−0.129892
$677$	−2.77529	−	15.7395i	−0.106663	−	0.604917i	−0.990543	−	0.137203i	$-0.956189\pi$
$677$	−2.77529	−	15.7395i	−0.106663	−	0.604917i	0.883880	−	0.467714i	$-0.154922\pi$
$678$	2.70389	−	6.60787i	0.103842	−	0.253774i
$679$	3.25426	−	20.9946i	0.124887	−	0.805699i
$680$	0.0408840	−	0.0487237i	0.00156783	−	0.00186847i
$681$	17.6609	−	19.4404i	0.676769	−	0.744959i
$682$	12.0008	−	32.9720i	0.459535	−	1.26256i
$683$	−2.97073	+	1.71515i	−0.113672	+	0.0656285i	−0.555758	−	0.831344i	$-0.687572\pi$
$683$	−2.97073	+	1.71515i	−0.113672	+	0.0656285i	0.442086	+	0.896973i	$0.354239\pi$
$684$	−10.3741	+	22.7553i	−0.396662	+	0.870071i
$685$	1.55435	+	0.897402i	0.0593885	+	0.0342879i
$686$	−13.4192	+	12.7642i	−0.512347	+	0.487340i
$687$	−13.8033	−	0.543306i	−0.526630	−	0.0207284i
$688$	−1.20905	+	6.85686i	−0.0460946	+	0.261415i
$689$	3.74494	−	21.2386i	0.142671	−	0.809127i
$690$	0.0396115	−	1.00638i	0.00150798	−	0.0383121i
$691$	−29.0085	−	34.5709i	−1.10353	−	1.31514i	−0.944737	−	0.327829i	$-0.893683\pi$
$691$	−29.0085	−	34.5709i	−1.10353	−	1.31514i	−0.158796	−	0.987311i	$-0.550761\pi$
$692$	1.60238	−	2.77541i	0.0609134	−	0.105505i
$693$	−4.82940	−	41.2290i	−0.183454	−	1.56616i
$694$	−15.5822	−	26.9892i	−0.591494	−	1.02450i
$695$	−0.407151	+	1.11864i	−0.0154441	+	0.0424324i
$696$	−10.0186	+	11.0281i	−0.379755	+	0.418019i
$697$	2.21662	+	1.85996i	0.0839604	+	0.0704511i
$698$	−8.30959	+	3.02444i	−0.314523	+	0.114477i
$699$	19.4620	+	7.96371i	0.736120	+	0.301215i
$700$	−4.25510	+	12.4914i	−0.160828	+	0.472131i
$701$			16.9392i			0.639785i	0.947454	+	0.319893i	$0.103647\pi$
$701$			16.9392i			0.639785i	−0.947454	+	0.319893i	$0.896353\pi$
$702$	−14.8112	+	6.35968i	−0.559011	+	0.240031i
$703$		−	11.6598i		−	0.439759i
$704$	5.15042	−	0.908159i	0.194114	−	0.0342275i
$705$	−0.974421	−	1.25867i	−0.0366988	−	0.0474041i
$706$	−3.00052	−	8.24387i	−0.112926	−	0.310262i
$707$	−2.59862	−	6.70345i	−0.0977312	−	0.252109i
$708$	−22.6146	−	4.91177i	−0.849907	−	0.184596i
$709$	−5.61321	−	2.04304i	−0.210808	−	0.0767280i	0.234458	−	0.972126i	$-0.424669\pi$
$709$	−5.61321	−	2.04304i	−0.210808	−	0.0767280i	−0.445266	+	0.895398i	$0.646891\pi$
$710$	−0.416127	−	0.720753i	−0.0156170	−	0.0270494i
$711$	−8.69575	−	18.2376i	−0.326116	−	0.683964i
$712$	−6.68658	−	3.86050i	−0.250590	−	0.144678i
$713$	−26.9685	+	22.6293i	−1.00998	+	0.847474i
$714$	−2.30191	+	1.27255i	−0.0861467	+	0.0476242i
$715$	−0.312186	+	1.77049i	−0.0116751	+	0.0662127i
$716$	−0.799496	−	0.140973i	−0.0298786	−	0.00526840i
$717$	20.5401	+	39.0469i	0.767083	+	1.45823i
$718$	−19.9943	+	16.7772i	−0.746180	+	0.626119i
$719$	−21.9102	+	37.9496i	−0.817112	+	1.41528i	0.0906891	+	0.995879i	$0.471093\pi$
$719$	−21.9102	+	37.9496i	−0.817112	+	1.41528i	−0.907801	+	0.419401i	$0.862240\pi$
$720$	−0.320368	+	0.0887974i	−0.0119394	+	0.00330928i
$721$	33.0008	−	0.684937i	1.22901	−	0.0255084i
$722$	−17.2692	+	47.4467i	−0.642692	+	1.76578i
$723$	−18.8006	+	6.01667i	−0.699203	+	0.223762i
$724$	−3.53264	+	4.21004i	−0.131290	+	0.156465i
$725$	14.6744	+	40.3177i	0.544995	+	1.49736i
$726$	3.81725	+	28.0634i	0.141671	+	1.04153i
$727$	7.39436	−	1.30383i	0.274242	−	0.0483562i	−0.0348358	−	0.999393i	$-0.511091\pi$
$727$	7.39436	−	1.30383i	0.274242	−	0.0483562i	0.309078	+	0.951037i	$0.399980\pi$
$728$	−7.19135	−	3.95527i	−0.266529	−	0.146592i
$729$	18.5938	−	19.5773i	0.688660	−	0.725084i
$730$	1.56934			0.0580838
$731$	0.693953	+	3.93560i	0.0256668	+	0.145564i
$732$	2.99087	+	21.9881i	0.110546	+	0.812702i
$733$	2.55240	+	7.01267i	0.0942751	+	0.259019i	0.977863	−	0.209247i	$-0.0671012\pi$
$733$	2.55240	+	7.01267i	0.0942751	+	0.259019i	−0.883588	+	0.468266i	$0.844879\pi$
$734$	12.6008	+	10.5733i	0.465104	+	0.390269i
$735$	−0.861398	+	1.03110i	−0.0317732	+	0.0380326i
$736$	−4.93085	−	1.79468i	−0.181754	−	0.0661529i
$737$	−1.84357	+	1.06439i	−0.0679088	+	0.0392071i
$738$	−4.03972	−	14.5747i	−0.148704	−	0.536502i
$739$	12.7404	−	22.0669i	0.468662	−	0.811746i	−0.530697	−	0.847562i	$-0.678070\pi$
$739$	12.7404	−	22.0669i	0.468662	−	0.811746i	0.999358	+	0.0358160i	$0.0114030\pi$
$740$	0.118735	−	0.0996308i	0.00436480	−	0.00366250i
$741$	−39.6398	+	20.8519i	−1.45620	+	0.766016i
$742$	−11.5284	+	14.3328i	−0.423221	+	0.526174i
$743$	16.0912	+	2.83732i	0.590329	+	0.104091i	0.460830	−	0.887488i	$-0.347552\pi$
$743$	16.0912	+	2.83732i	0.590329	+	0.104091i	0.129500	+	0.991579i	$0.458663\pi$
$744$	9.82742	+	6.20161i	0.360291	+	0.227362i
$745$	0.414761	+	0.494293i	0.0151957	+	0.0181095i
$746$	−1.60869	−	0.928775i	−0.0588982	−	0.0340049i
$747$	−7.79295	−	16.3442i	−0.285129	−	0.598002i
$748$	2.59961	−	1.50088i	0.0950511	−	0.0548778i
$749$	−3.15988	+	2.76520i	−0.115460	+	0.101038i
$750$	−0.406881	+	1.87335i	−0.0148572	+	0.0684049i
$751$	−18.7751	−	15.7542i	−0.685112	−	0.574877i	0.232383	−	0.972624i	$-0.425348\pi$
$751$	−18.7751	−	15.7542i	−0.685112	−	0.574877i	−0.917495	+	0.397747i	$0.869792\pi$
$752$	−7.79301	+	2.83642i	−0.284182	+	0.103434i
$753$	−6.67363	−	8.62037i	−0.243201	−	0.314144i
$754$	−26.2791	+	4.63371i	−0.957028	+	0.168750i
$755$	−0.934182			−0.0339984
$756$	13.6827	+	1.33511i	0.497637	+	0.0485575i
$757$	38.0265			1.38210			0.691048	−	0.722808i	$-0.257149\pi$
$757$	38.0265			1.38210			0.691048	+	0.722808i	$0.257149\pi$
$758$	−2.21424	+	0.390430i	−0.0804247	+	0.0141810i
$759$	18.0011	−	43.9917i	0.653398	−	1.59680i
$760$	−0.868066	+	0.315950i	−0.0314881	+	0.0114607i
$761$	−5.97901	−	5.01699i	−0.216739	−	0.181866i	0.527954	−	0.849273i	$-0.322959\pi$
$761$	−5.97901	−	5.01699i	−0.216739	−	0.181866i	−0.744693	+	0.667408i	$0.767404\pi$
$762$	−7.82714	−	7.11068i	−0.283548	−	0.257593i
$763$	13.4028	+	15.3158i	0.485213	+	0.554469i
$764$	6.11321	−	3.52947i	0.221168	−	0.127692i
$765$	−0.155359	+	0.110784i	−0.00561703	+	0.00400539i
$766$	13.6376	+	7.87368i	0.492747	+	0.284488i
$767$	−26.6413	−	31.7499i	−0.961962	−	1.14642i
$768$	−0.0681216	+	1.73071i	−0.00245813	+	0.0624516i
$769$	−17.0810	−	3.01184i	−0.615956	−	0.108610i	−0.143039	−	0.989717i	$-0.545688\pi$
$769$	−17.0810	−	3.01184i	−0.615956	−	0.108610i	−0.472916	+	0.881107i	$0.656799\pi$
$770$	0.961031	−	1.19481i	0.0346332	−	0.0430581i
$771$	−0.395528	+	10.0489i	−0.0142446	+	0.361901i
$772$	9.39905	−	7.88674i	0.338279	−	0.283850i
$773$	4.20333	−	7.28038i	0.151183	−	0.261857i	−0.780479	−	0.625181i	$-0.785025\pi$
$773$	4.20333	−	7.28038i	0.151183	−	0.261857i	0.931663	+	0.363324i	$0.118358\pi$
$774$	8.66475	−	19.0060i	0.311448	−	0.683156i
$775$	28.9801	−	16.7317i	1.04100	−	0.601020i
$776$	−7.54571	−	2.74641i	−0.270875	−	0.0985905i
$777$	−6.06282	+	2.07991i	−0.217503	+	0.0746162i
$778$	−19.6187	−	16.4621i	−0.703366	−	0.590194i
$779$	−14.3737	−	39.4915i	−0.514992	−	1.41493i
$780$	−0.551055	−	0.225488i	−0.0197309	−	0.00807376i
$781$	−6.82052	−	38.6811i	−0.244057	−	1.38412i
$782$	−3.01177			−0.107701
$783$	37.3856	−	24.4998i	1.33605	−	0.875552i
$784$	3.74852	+	5.91173i	0.133876	+	0.211133i
$785$	1.15736	−	0.204074i	0.0413080	−	0.00728371i
$786$	−14.6096	+	11.3103i	−0.521107	+	0.403426i
$787$	9.63149	+	26.4623i	0.343326	+	0.943279i	0.984422	+	0.175819i	$0.0562575\pi$
$787$	9.63149	+	26.4623i	0.343326	+	0.943279i	−0.641097	+	0.767460i	$0.721520\pi$
$788$	2.06317	−	2.45880i	0.0734975	−	0.0875909i
$789$	4.77450	−	21.9826i	0.169977	−	0.782600i
$790$	0.255259	−	0.701319i	0.00908172	−	0.0249518i
$791$	−10.9037	+	0.226308i	−0.387690	+	0.00804659i
$792$	−15.6411	−	1.23319i	−0.555782	−	0.0438196i
$793$	−19.8714	+	34.4183i	−0.705654	+	1.22223i
$794$	22.9329	−	19.2430i	0.813857	−	0.682907i
$795$	−0.712132	+	1.12849i	−0.0252567	+	0.0400233i
$796$	−14.1646	−	2.49760i	−0.502052	−	0.0885253i
$797$	−1.37627	+	7.80520i	−0.0487499	+	0.276474i	−0.999432	−	0.0336918i	$-0.989274\pi$
$797$	−1.37627	+	7.80520i	−0.0487499	+	0.276474i	0.950682	+	0.310166i	$0.100385\pi$
$798$	38.1945	+	0.710040i	1.35207	+	0.0251351i
$799$	−3.64636	+	3.05966i	−0.128999	+	0.108243i
$800$	4.31949	+	2.49386i	0.152717	+	0.0881713i
$801$	16.5187	+	16.2375i	0.583661	+	0.573723i
$802$	3.28653	+	5.69243i	0.116051	+	0.201007i
$803$	69.5974	+	25.3314i	2.45604	+	0.893925i
$804$	−0.214887	−	0.671468i	−0.00757847	−	0.0236809i
$805$	−1.43445	+	0.556069i	−0.0505576	+	0.0195989i
$806$	7.11820	+	19.5571i	0.250728	+	0.688870i
$807$	−8.22366	+	1.11860i	−0.289486	+	0.0393767i
$808$	−2.67610	+	0.471868i	−0.0941448	+	0.0166003i
$809$			6.26392i			0.220228i	0.993919	+	0.110114i	$0.0351215\pi$
$809$			6.26392i			0.220228i	−0.993919	+	0.110114i	$0.964878\pi$
$810$	0.997192	−	0.0171257i	0.0350378	−	0.000601734i
$811$		−	36.0858i		−	1.26715i	−0.773683	−	0.633573i	$-0.781588\pi$
$811$		−	36.0858i		−	1.26715i	0.773683	−	0.633573i	$-0.218412\pi$
$812$	21.5436	+	7.33864i	0.756031	+	0.257536i
$813$	0.210721	+	1.54916i	0.00739030	+	0.0543315i
$814$	6.87390	−	2.50189i	0.240930	−	0.0876913i
$815$	−0.733258	−	0.615277i	−0.0256849	−	0.0215522i
$816$	0.303011	+	0.946834i	0.0106075	+	0.0331458i
$817$	19.8514	−	54.5414i	0.694514	−	1.90816i
$818$	17.8318	+	30.8855i	0.623473	+	1.07989i
$819$	17.9135	+	16.8921i	0.625949	+	0.590258i
$820$	0.279332	−	0.483818i	0.00975471	−	0.0168957i
$821$	−33.7656	−	40.2403i	−1.17843	−	1.40439i	−0.895388	−	0.445286i	$-0.853102\pi$
$821$	−33.7656	−	40.2403i	−1.17843	−	1.40439i	−0.283039	−	0.959108i	$-0.591343\pi$
$822$	−24.8273	+	13.0601i	−0.865953	+	0.455522i
$823$	−1.52213	+	8.63241i	−0.0530580	+	0.300907i	−0.999776	−	0.0211563i	$-0.993265\pi$
$823$	−1.52213	+	8.63241i	−0.0530580	+	0.300907i	0.946718	+	0.322063i	$0.104376\pi$
$824$	2.16640	−	12.2863i	0.0754701	−	0.428012i
$825$	−24.1118	+	38.2090i	−0.839466	+	1.33027i
$826$	6.85948	+	34.6778i	0.238672	+	1.20660i
$827$	−29.8761	−	17.2490i	−1.03889	−	0.599806i	−0.119375	−	0.992849i	$-0.538089\pi$
$827$	−29.8761	−	17.2490i	−1.03889	−	0.599806i	−0.919520	+	0.393043i	$0.871422\pi$
$828$	12.9721	+	8.91813i	0.450810	+	0.309927i
$829$	−16.8265	+	9.71480i	−0.584409	+	0.337409i	−0.762884	−	0.646536i	$-0.776217\pi$
$829$	−16.8265	+	9.71480i	−0.584409	+	0.337409i	0.178474	+	0.983945i	$0.442884\pi$
$830$	0.228758	−	0.628507i	0.00794031	−	0.0218158i
$831$	28.1880	+	6.12230i	0.977833	+	0.212380i
$832$	−1.99397	+	2.37632i	−0.0691285	+	0.0823841i
$833$	3.18229	+	2.45264i	0.110260	+	0.0849788i
$834$	−11.3902	−	14.7128i	−0.394410	−	0.509461i
$835$	−0.261179	−	1.48122i	−0.00903849	−	0.0512598i
$836$	−43.5971			−1.50784
$837$	−23.8813	−	25.3973i	−0.825460	−	0.877860i
$838$			24.5767i			0.848988i
$839$	−6.59635	−	37.4098i	−0.227731	−	1.29153i	−0.857394	−	0.514660i	$-0.827918\pi$
$839$	−6.59635	−	37.4098i	−0.227731	−	1.29153i	0.629663	−	0.776869i	$-0.283193\pi$
$840$	0.319134	+	0.395013i	0.0110112	+	0.0136292i
$841$	42.2836	−	15.3900i	1.45806	−	0.530689i
$842$	−8.13750	+	9.69790i	−0.280437	+	0.334212i
$843$	−1.84758	−	1.67846i	−0.0636341	−	0.0578093i
$844$	7.47042	+	2.71901i	0.257142	+	0.0935922i
$845$	0.187122	+	0.324105i	0.00643720	+	0.0111495i
$846$	24.7652	−	2.38111i	0.851447	−	0.0818642i
$847$	37.0093	−	22.4039i	1.27166	−	0.769809i
$848$	4.46880	+	5.32571i	0.153459	+	0.182886i
$849$	−12.9008	−	0.507782i	−0.442754	−	0.0174270i
$850$	2.81929	+	0.497116i	0.0967008	+	0.0170510i
$851$	−7.22792	−	1.27448i	−0.247770	−	0.0436885i
$852$	12.9981	+	0.511612i	0.445308	+	0.0175275i
$853$	18.8535	+	22.4687i	0.645530	+	0.769313i	0.985233	−	0.171220i	$-0.0547708\pi$
$853$	18.8535	+	22.4687i	0.645530	+	0.769313i	−0.339702	+	0.940533i	$0.610326\pi$
$854$	28.9973	−	17.5538i	0.992268	−	0.600679i
$855$	2.75861	−	0.265232i	0.0943424	−	0.00907076i
$856$	0.793527	+	1.37443i	0.0271222	+	0.0469770i
$857$	42.6441	+	15.5212i	1.45670	+	0.530194i	0.944453	−	0.328646i	$-0.106592\pi$
$857$	42.6441	+	15.5212i	1.45670	+	0.530194i	0.512243	+	0.858840i	$0.328815\pi$
$858$	−20.7987	−	18.8948i	−0.710054	−	0.645059i
$859$	21.3590	−	25.4547i	0.728760	−	0.868503i	−0.266690	−	0.963782i	$-0.585930\pi$
$859$	21.3590	−	25.4547i	0.728760	−	0.868503i	0.995451	+	0.0952797i	$0.0303745\pi$
$860$	0.725037	−	0.263892i	0.0247236	−	0.00899864i
$861$	−17.9706	+	14.5185i	−0.612435	+	0.494791i
$862$	−5.63288	−	31.9457i	−0.191857	−	1.08807i
$863$			18.4496i			0.628033i	0.949418	+	0.314017i	$0.101675\pi$
$863$			18.4496i			0.628033i	−0.949418	+	0.314017i	$0.898325\pi$
$864$	1.49856	−	4.97537i	0.0509821	−	0.169266i
$865$	−0.355137			−0.0120750
$866$	−2.43948	−	13.8350i	−0.0828969	−	0.470132i
$867$	−17.6757	−	22.8318i	−0.600299	−	0.775409i
$868$	2.71898	−	17.5413i	0.0922880	−	0.595389i
$869$	22.6406	−	26.9820i	0.768030	−	0.915303i
$870$	1.61347	+	0.350436i	0.0547016	+	0.0118809i
$871$	0.431857	−	1.18652i	0.0146329	−	0.0402036i
$872$	6.66179	−	3.84619i	0.225597	−	0.130248i
$873$	19.8512	+	13.6475i	0.671862	+	0.461897i
$874$	37.8820	+	21.8712i	1.28138	+	0.739804i
$875$	2.87264	−	0.568226i	0.0971130	−	0.0192095i
$876$	−13.0904	+	20.7438i	−0.442283	+	0.700867i
$877$	−1.84693	+	10.4745i	−0.0623663	+	0.353697i	0.937616	+	0.347674i	$0.113028\pi$
$877$	−1.84693	+	10.4745i	−0.0623663	+	0.353697i	−0.999982	+	0.00602319i	$0.998083\pi$
$878$	−0.190398	+	1.07980i	−0.00642562	+	0.0364415i
$879$	−31.3373	+	16.4846i	−1.05698	+	0.556010i
$880$	−0.372528	−	0.443962i	−0.0125579	−	0.0149660i
$881$	−2.32996	+	4.03561i	−0.0784984	+	0.135963i	−0.902602	−	0.430476i	$-0.858346\pi$
$881$	−2.32996	+	4.03561i	−0.0784984	+	0.135963i	0.824104	+	0.566439i	$0.191679\pi$
$882$	−6.44402	−	19.9869i	−0.216981	−	0.672993i
$883$	−9.67800	−	16.7628i	−0.325691	−	0.564113i	0.655961	−	0.754795i	$-0.272263\pi$
$883$	−9.67800	−	16.7628i	−0.325691	−	0.564113i	−0.981652	+	0.190682i	$0.938930\pi$
$884$	−0.608960	+	1.67310i	−0.0204815	+	0.0562726i
$885$	0.781645	+	2.44245i	0.0262747	+	0.0821020i
$886$	−6.12973	−	5.14345i	−0.205932	−	0.172798i
$887$	−26.6593	+	9.70320i	−0.895133	+	0.325802i	−0.748301	−	0.663360i	$-0.769130\pi$
$887$	−26.6593	+	9.70320i	−0.895133	+	0.325802i	−0.146832	+	0.989161i	$0.546908\pi$
$888$	0.326525	+	2.40052i	0.0109575	+	0.0805562i
$889$	−5.20857	+	15.2905i	−0.174690	+	0.512825i
$890$			0.855606i			0.0286800i
$891$	44.5002	+	15.3366i	1.49081	+	0.513797i
$892$		−	3.47264i		−	0.116273i
$893$	68.0828	−	12.0048i	2.27830	−	0.401726i
$894$	−9.99332	+	1.35932i	−0.334226	+	0.0454623i
$895$	0.0307693	+	0.0845378i	0.00102850	+	0.00282579i
$896$	2.46688	−	0.956296i	0.0824127	−	0.0319476i
$897$	8.59328	+	26.8519i	0.286921	+	0.896559i
$898$	12.1587	+	4.42542i	0.405742	+	0.147678i
$899$	−28.8566	−	49.9811i	−0.962422	−	1.66696i
$900$	−10.6710	−	10.4893i	−0.355700	−	0.349644i
$901$	3.45573	+	1.99517i	0.115127	+	0.0664687i
$902$	20.1974	−	16.9477i	0.672501	−	0.564295i
$903$	−31.9013	−	0.593049i	−1.06161	−	0.0197354i
$904$	−0.715794	+	4.05947i	−0.0238069	+	0.135016i
$905$	0.599769	+	0.105755i	0.0199370	+	0.00351543i
$906$	7.79234	−	12.3482i	0.258883	−	0.410241i
$907$	−8.48697	+	7.12141i	−0.281805	+	0.236463i	−0.772723	−	0.634743i	$-0.781106\pi$
$907$	−8.48697	+	7.12141i	−0.281805	+	0.236463i	0.490918	+	0.871206i	$0.336661\pi$
$908$	−7.58199	+	13.1324i	−0.251617	+	0.435814i
$909$	8.12692	+	0.640752i	0.269553	+	0.0212524i
$910$	0.0188727	+	0.909300i	0.000625624	+	0.0301430i
$911$	−0.363833	+	0.999623i	−0.0120543	+	0.0331190i	−0.945574	−	0.325408i	$-0.894499\pi$
$911$	−0.363833	+	0.999623i	−0.0120543	+	0.0331190i	0.933520	+	0.358527i	$0.116721\pi$
$912$	3.06455	−	14.1097i	0.101478	−	0.467219i
$913$	20.2900	−	24.1807i	0.671502	−	0.800266i
$914$	−5.63104	−	15.4712i	−0.186258	−	0.511740i
$915$	1.94446	−	1.50534i	0.0642817	−	0.0497650i
$916$	7.85437	−	1.38494i	0.259516	−	0.0457596i
$917$	24.7291	+	13.6011i	0.816625	+	0.449147i
$918$	−0.168453	−	2.97765i	−0.00555979	−	0.0982771i
$919$	−17.6782			−0.583150			−0.291575	−	0.956548i	$-0.594179\pi$
$919$	−17.6782			−0.583150			−0.291575	+	0.956548i	$0.594179\pi$
$920$	0.100973	+	0.572648i	0.00332899	+	0.0188796i
$921$	−0.901309	−	0.368809i	−0.0296992	−	0.0121527i
$922$	−12.7973	−	35.1603i	−0.421456	−	1.15794i
$923$	17.8468	+	14.9753i	0.587435	+	0.492916i
$924$	7.77695	+	22.6694i	0.255843	+	0.745769i
$925$	6.55562	+	2.38605i	0.215547	+	0.0784528i
$926$	7.53083	−	4.34793i	0.247478	−	0.142882i
$927$	−15.5257	+	34.0553i	−0.509930	+	1.11852i
$928$	4.30108	−	7.44969i	0.141190	−	0.244548i
$929$	−3.66691	+	3.07690i	−0.120307	+	0.100950i	−0.700957	−	0.713204i	$-0.747243\pi$
$929$	−3.66691	+	3.07690i	−0.120307	+	0.100950i	0.580649	+	0.814154i	$0.302799\pi$
$930$	0.0506469	−	1.28675i	0.00166078	−	0.0421940i
$931$	−22.2160	−	53.9587i	−0.728099	−	1.76843i
$932$	−11.9563	−	2.10821i	−0.391640	−	0.0690567i
$933$	−0.699248	+	17.7652i	−0.0228924	+	0.581608i
$934$	−11.8785	−	14.1562i	−0.388676	−	0.463206i
$935$	−0.288077	−	0.166321i	−0.00942112	−	0.00543929i
$936$	7.57708	−	5.40307i	0.247665	−	0.176605i
$937$	−2.91297	+	1.68181i	−0.0951627	+	0.0549422i	−0.546826	−	0.837246i	$-0.684164\pi$
$937$	−2.91297	+	1.68181i	−0.0951627	+	0.0549422i	0.451663	+	0.892188i	$0.350831\pi$
$938$	−0.810432	+	0.709206i	−0.0264616	+	0.0231564i
$939$	24.2037	+	21.9882i	0.789857	+	0.717557i
$940$	0.704002	+	0.590728i	0.0229620	+	0.0192674i
$941$	−21.8920	+	7.96802i	−0.713658	+	0.259750i	−0.673231	−	0.739432i	$-0.735094\pi$
$941$	−21.8920	+	7.96802i	−0.713658	+	0.259750i	−0.0404267	+	0.999183i	$0.512872\pi$
$942$	−6.95646	+	17.0004i	−0.226654	+	0.553904i
$943$	−26.0518	+	4.59364i	−0.848364	+	0.149590i
$944$	13.3609			0.434862
$945$	−0.630001	−	1.38710i	−0.0204939	−	0.0451222i
$946$	36.4138			1.18391
$947$	17.6293	−	3.10851i	0.572874	−	0.101013i	0.120296	−	0.992738i	$-0.461616\pi$
$947$	17.6293	−	3.10851i	0.572874	−	0.101013i	0.452578	+	0.891725i	$0.350505\pi$
$948$	7.14095	+	9.22401i	0.231927	+	0.299582i
$949$	−41.2813	+	15.0251i	−1.34005	+	0.487737i
$950$	−31.8510	−	26.7261i	−1.03338	−	0.867110i
$951$	−2.05457	+	9.45959i	−0.0666241	+	0.306748i
$952$	1.14279	−	1.00005i	0.0370379	−	0.0324117i
$953$	−6.51472	+	3.76127i	−0.211032	+	0.121840i	−0.601791	−	0.798654i	$-0.705546\pi$
$953$	−6.51472	+	3.76127i	−0.211032	+	0.121840i	0.390759	+	0.920493i	$0.372213\pi$
$954$	−8.97638	−	18.8262i	−0.290621	−	0.609520i
$955$	−0.677439	−	0.391119i	−0.0219214	−	0.0126563i
$956$	−16.3734	−	19.5131i	−0.529555	−	0.631099i
$957$	65.8979	+	41.5849i	2.13018	+	1.34425i
$958$	−1.71590	−	0.302559i	−0.0554381	−	0.00977524i
$959$	33.3906	+	26.8573i	1.07824	+	0.867267i
$960$	0.169869	−	0.0893572i	0.00548250	−	0.00288399i
$961$	−10.7344	+	9.00719i	−0.346270	+	0.290555i
$962$	−2.16944	+	3.75757i	−0.0699454	+	0.121149i
$963$	−1.27172	−	4.58818i	−0.0409806	−	0.147852i
$964$	9.86996	−	5.69842i	0.317890	−	0.183534i
$965$	−1.27766	−	0.465031i	−0.0411294	−	0.0149699i
$966$	4.61500	−	23.5991i	0.148485	−	0.759290i
$967$	33.9524	+	28.4894i	1.09184	+	0.916159i	0.996849	−	0.0793200i	$-0.0252749\pi$
$967$	33.9524	+	28.4894i	1.09184	+	0.916159i	0.0949861	+	0.995479i	$0.469719\pi$
$968$	−5.59258	−	15.3655i	−0.179752	−	0.493865i
$969$	−1.11697	−	8.21168i	−0.0358823	−	0.263797i
$970$	0.154520	+	0.876327i	0.00496134	+	0.0281372i
$971$	−31.2743			−1.00364			−0.501819	−	0.864972i	$-0.667336\pi$
$971$	−31.2743			−1.00364			−0.501819	+	0.864972i	$0.667336\pi$
$972$	−8.09156	+	13.3239i	−0.259537	+	0.427365i
$973$	−13.6971	+	24.9037i	−0.439110	+	0.798375i
$974$	38.7685	−	6.83594i	1.24222	−	0.219038i
$975$	−3.61196	−	26.5542i	−0.115675	−	0.850414i
$976$	−4.38186	−	12.0391i	−0.140260	−	0.385361i
$977$	7.60548	−	9.06386i	0.243321	−	0.289979i	−0.630538	−	0.776159i	$-0.717166\pi$
$977$	7.60548	−	9.06386i	0.243321	−	0.289979i	0.873859	+	0.486180i	$0.161610\pi$
$978$	14.2492	−	4.56010i	0.455639	−	0.145816i
$979$	−13.8107	+	37.9447i	−0.441393	+	1.21272i
$980$	0.359646	−	0.687298i	0.0114885	−	0.0219549i
$981$	−22.2387	+	6.16397i	−0.710027	+	0.196800i
$982$	19.0155	−	32.9358i	0.606809	−	1.05102i
$983$	11.0451	−	9.26797i	0.352285	−	0.295602i	−0.449422	−	0.893320i	$-0.648370\pi$
$983$	11.0451	−	9.26797i	0.352285	−	0.295602i	0.801707	+	0.597717i	$0.203925\pi$
$984$	4.06518	+	7.72796i	0.129593	+	0.246358i
$985$	−0.350284	−	0.0617645i	−0.0111610	−	0.00196798i
$986$	0.857361	−	4.86234i	0.0273039	−	0.154848i
$987$	−18.3870	−	33.2599i	−0.585264	−	1.05868i
$988$	19.8094	−	16.6221i	0.630221	−	0.528818i
$989$	−31.6403	−	18.2675i	−1.00610	−	0.580874i
$990$	0.748289	+	1.56939i	0.0237822	+	0.0498785i
$991$	21.6796	+	37.5502i	0.688675	+	1.19282i	0.972267	+	0.233876i	$0.0751408\pi$
$991$	21.6796	+	37.5502i	0.688675	+	1.19282i	−0.283591	+	0.958945i	$0.591526\pi$
$992$	−6.30454	−	2.29466i	−0.200169	−	0.0728557i
$993$	−31.4807	−	6.83745i	−0.999011	−	0.216980i
$994$	−7.18204	−	18.5269i	−0.227800	−	0.587639i
$995$	0.545137	+	1.49775i	0.0172820	+	0.0474819i
$996$	6.39957	+	8.26636i	0.202778	+	0.261930i
$997$	−9.47320	+	1.67038i	−0.300019	+	0.0529015i	−0.321631	−	0.946865i	$-0.604231\pi$
$997$	−9.47320	+	1.67038i	−0.300019	+	0.0529015i	0.0216122	+	0.999766i	$0.493120\pi$
$998$		−	7.80671i		−	0.247117i
$999$	0.855769	−	7.21732i	0.0270753	−	0.228346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.1	✓	144
7.6	odd	2	inner	378.2.z.a.41.12	yes	144
27.2	odd	18	inner	378.2.z.a.83.12	yes	144
189.83	even	18	inner	378.2.z.a.83.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.1	✓	144	1.1	even	1	trivial
378.2.z.a.41.12	yes	144	7.6	odd	2	inner
378.2.z.a.83.1	yes	144	189.83	even	18	inner
378.2.z.a.83.12	yes	144	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-1.71625 + 0.233448i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.0848896 - 0.0712308i) q^{5} +(1.64964 - 0.527925i) q^{6} +(-1.74235 - 1.99104i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.89100 - 0.801309i) q^{9} +(0.0959690 + 0.0554077i) q^{10} +(3.36170 + 4.00632i) q^{11} +(-1.53290 + 0.806360i) q^{12} +(-3.05494 - 0.538668i) q^{13} +(2.06162 + 1.65823i) q^{14} +(0.162320 + 0.102432i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.286983 - 0.497069i) q^{17} +(-2.70794 + 1.29115i) q^{18} +(-7.21933 + 4.16808i) q^{19} +(-0.104133 - 0.0379011i) q^{20} +(3.45510 + 3.01036i) q^{21} +(-4.00632 - 3.36170i) q^{22} +(1.79468 + 4.93085i) q^{23} +(1.36959 - 1.06030i) q^{24} +(-0.866108 - 4.91195i) q^{25} +3.10207 q^{26} +(-4.77461 + 2.05014i) q^{27} +(-2.31825 - 1.27504i) q^{28} +(-8.47148 + 1.49375i) q^{29} +(-0.177641 - 0.0726896i) q^{30} +(2.29466 + 6.30454i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-6.70477 - 6.09105i) q^{33} +(-0.196308 + 0.539351i) q^{34} +(0.00608391 + 0.293127i) q^{35} +(2.44259 - 1.74177i) q^{36} +(-0.699352 + 1.21131i) q^{37} +(6.38587 - 5.35839i) q^{38} +(5.36878 + 0.211318i) q^{39} +(0.109132 + 0.0192429i) q^{40} +(-0.875429 + 4.96481i) q^{41} +(-3.92535 - 2.36466i) q^{42} +(-5.33369 + 4.47550i) q^{43} +(4.52921 + 2.61494i) q^{44} +(-0.302494 - 0.137906i) q^{45} +(-2.62365 - 4.54429i) q^{46} +(-7.79301 - 2.83642i) q^{47} +(-1.16466 + 1.28201i) q^{48} +(-0.928455 + 6.93815i) q^{49} +(1.70590 + 4.68692i) q^{50} +(-0.376493 + 0.920088i) q^{51} +(-3.05494 + 0.538668i) q^{52} +6.95222i q^{53} +(4.34607 - 2.84810i) q^{54} -0.579551i q^{55} +(2.50444 + 0.853115i) q^{56} +(11.4171 - 8.83880i) q^{57} +(8.08339 - 2.94211i) q^{58} +(10.2351 + 8.58825i) q^{59} +(0.187565 + 0.0407382i) q^{60} +(4.38186 - 12.0391i) q^{61} +(-3.35458 - 5.81030i) q^{62} +(-6.63257 - 4.35994i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.220963 + 0.263333i) q^{65} +(7.66061 + 4.83424i) q^{66} +(-0.0706818 + 0.400857i) q^{67} +(0.0996681 - 0.565246i) q^{68} +(-4.23121 - 8.04359i) q^{69} +(-0.0568925 - 0.287617i) q^{70} +(-6.50408 - 3.75513i) q^{71} +(-2.10303 + 2.13946i) q^{72} +(12.2644 - 7.08086i) q^{73} +(0.478385 - 1.31435i) q^{74} +(2.63314 + 8.22792i) q^{75} +(-5.35839 + 6.38587i) q^{76} +(2.11948 - 13.6737i) q^{77} +(-5.32391 + 0.724171i) q^{78} +(-1.16950 - 6.63255i) q^{79} -0.110815 q^{80} +(7.71581 - 4.63317i) q^{81} -5.04140i q^{82} +(-1.04808 - 5.94396i) q^{83} +(4.27634 + 1.64710i) q^{84} +(-0.0597685 + 0.0217539i) q^{85} +(4.47550 - 5.33369i) q^{86} +(14.1904 - 4.54129i) q^{87} +(-4.91448 - 1.78872i) q^{88} +(3.86050 + 6.68658i) q^{89} +(0.321846 + 0.0832832i) q^{90} +(4.25026 + 7.02104i) q^{91} +(3.37290 + 4.01966i) q^{92} +(-5.40999 - 10.2845i) q^{93} +(8.16716 + 1.44009i) q^{94} +(0.909742 + 0.160412i) q^{95} +(0.924350 - 1.46478i) q^{96} +(5.16157 + 6.15132i) q^{97} +(-0.290448 - 6.99397i) q^{98} +(12.9290 + 8.88852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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