LMFDB - Embedded newform 378.2.z.a.41.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			41.12
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.71625 - 0.233448i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.0848896 + 0.0712308i) q^{5} +(-1.64964 + 0.527925i) q^{6} +(-2.61453 + 0.405264i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.89100 - 0.801309i) q^{9} +O(q^{10})$	\(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} +(-2.61453 + 0.405264i) 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} +(2.50444 - 0.853115i) 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} +(-4.39257 + 1.30589i) 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} +(-0.250814 - 0.151832i) 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} +(4.09907 - 2.04881i) 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} +(6.67152 - 2.11915i) 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} +(2.06162 - 1.65823i) 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} +(-7.23387 + 3.26666i) 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} +(0.273369 + 0.105972i) 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} +(-10.4129 - 9.11226i) 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} +(-3.68102 + 2.72948i) 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} +(-8.20553 - 0.170307i) 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} +(-6.20218 + 3.24545i) q^{98} +(12.9290 + 8.88852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	0.661572	−	0.749882i	$-0.269890\pi$
$5$	0.0848896	+	0.0712308i	0.0379638	+	0.0318554i	−0.623608	+	0.781737i	$0.714334\pi$
$6$	−1.64964	+	0.527925i	−0.673461	+	0.215524i
$7$	−2.61453	+	0.405264i	−0.988199	+	0.153175i
$7$	−2.61453	+	0.405264i	−0.988199	+	0.153175i
$8$	−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	0.580404	−	0.814329i	$-0.302895\pi$
$13$	3.05494	+	0.538668i	0.847288	+	0.149400i	0.266884	+	0.963729i	$0.414006\pi$
$14$	2.50444	−	0.853115i	0.669338	−	0.228005i
$15$	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	−0.898727	−	0.438509i	$-0.855507\pi$
$17$	−0.286983	+	0.497069i	−0.0696036	+	0.120557i	0.829123	+	0.559066i	$0.188840\pi$
$18$	−2.70794	+	1.29115i	−0.638267	+	0.304328i
$19$	7.21933	−	4.16808i	1.65623	−	0.956224i	0.681796	−	0.731542i	$-0.261199\pi$
$19$	7.21933	−	4.16808i	1.65623	−	0.956224i	0.974432	−	0.224682i	$-0.0721343\pi$
$20$	0.104133	+	0.0379011i	0.0232847	+	0.00847495i
$21$	−4.39257	+	1.30589i	−0.958537	+	0.284968i
$22$	−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	$-0.905283\pi$
$31$	−2.29466	−	6.30454i	−0.412134	−	1.13233i	0.543920	−	0.839137i	$-0.316940\pi$
$32$	−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
$35$	−0.250814	−	0.151832i	−0.0423952	−	0.0256644i
$36$	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	$-0.815651\pi$
$41$	0.875429	−	4.96481i	0.136719	−	0.775373i	0.973647	−	0.228060i	$-0.0732381\pi$
$42$	4.09907	−	2.04881i	0.632500	−	0.316138i
$43$	−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	0.840731	−	0.541454i	$-0.182126\pi$
$47$	7.79301	+	2.83642i	1.13673	+	0.413735i	0.295997	+	0.955189i	$0.404348\pi$
$48$	1.16466	−	1.28201i	0.168105	−	0.185043i
$49$	6.67152	−	2.11915i	0.953075	−	0.302735i
$50$	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
$56$	2.06162	−	1.65823i	0.275495	−	0.221591i
$57$	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	$-0.942075\pi$
$59$	−10.2351	−	8.58825i	−1.33249	−	1.11809i	−0.349005	−	0.937121i	$-0.613480\pi$
$60$	0.187565	+	0.0407382i	0.0242145	+	0.00525927i
$61$	−4.38186	+	12.0391i	−0.561040	+	1.54145i	0.257075	+	0.966391i	$0.417241\pi$
$61$	−4.38186	+	12.0391i	−0.561040	+	1.54145i	−0.818115	+	0.575054i	$0.804981\pi$
$62$	3.35458	+	5.81030i	0.426032	+	0.737908i
$63$	−7.23387	+	3.26666i	−0.911382	+	0.411561i
$64$	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
$70$	0.273369	+	0.105972i	0.0326738	+	0.0126661i
$71$	−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	−0.997528	−	0.0702659i	$-0.977615\pi$
$73$	−12.2644	+	7.08086i	−1.43544	+	0.828752i	−0.437912	+	0.899018i	$0.644282\pi$
$74$	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
$77$	−10.4129	−	9.11226i	−1.18666	−	1.03844i
$78$	−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	$0.0519146\pi$
$83$	1.04808	+	5.94396i	0.115042	+	0.652434i	−0.871688	+	0.490061i	$0.836974\pi$
$84$	−3.68102	+	2.72948i	−0.401633	+	0.297811i
$85$	−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	0.585590	−	0.810608i	$-0.300863\pi$
$89$	−3.86050	−	6.68658i	−0.409212	−	0.708776i	−0.994802	+	0.101832i	$0.967530\pi$
$90$	−0.321846	−	0.0832832i	−0.0339255	−	0.00877882i
$91$	−8.20553	−	0.170307i	−0.860173	−	0.0178531i
$92$	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	0.437462	−	0.899237i	$-0.355877\pi$
$97$	−5.16157	−	6.15132i	−0.524078	−	0.624571i	−0.961540	+	0.274665i	$0.911433\pi$
$98$	−6.20218	+	3.24545i	−0.626515	+	0.327840i
$99$	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	0.211839	−	0.977305i	$-0.432055\pi$
$101$	−2.55350	−	0.929399i	−0.254083	−	0.0924787i	−0.465922	+	0.884826i	$0.654277\pi$
$102$	0.211002	−	0.971487i	0.0208923	−	0.0961916i
$103$	8.01929	−	9.55702i	0.790164	−	0.941681i	−0.209181	−	0.977877i	$-0.567080\pi$
$103$	8.01929	−	9.55702i	0.790164	−	0.941681i	0.999345	+	0.0361962i	$0.0115241\pi$
$104$	−2.91499	+	1.06097i	−0.285838	+	0.104037i
$105$	−0.465903	−	0.202030i	−0.0454675	−	0.0197161i
$106$	−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
$112$	−1.74235	+	1.99104i	−0.164636	+	0.188135i
$113$	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
$119$	0.548881	−	1.41590i	0.0503158	−	0.129796i
$120$	−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
$126$	6.55672	−	4.47318i	0.584119	−	0.398503i
$127$	−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	0.135278	−	0.990808i	$-0.456807\pi$
$131$	10.0238	−	3.64838i	0.875787	−	0.318760i	0.740508	+	0.672047i	$0.234585\pi$
$132$	8.38369	+	3.43054i	0.729706	+	0.298591i
$133$	−17.1860	+	13.8233i	−1.49021	+	1.19863i
$134$		−	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	$0.0394577\pi$
$139$	3.67414	+	10.0946i	0.311636	+	0.856214i	−0.680690	+	0.732571i	$0.738320\pi$
$140$	−0.287617	−	0.0568925i	−0.0243081	−	0.00480829i
$141$	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
$147$	10.9553	−	5.19443i	0.903575	−	0.428430i
$148$	−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
$154$	11.8370	+	7.16565i	0.953853	+	0.577424i
$155$	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	−0.422045	−	0.906575i	$-0.638688\pi$
$157$	6.81686	−	8.12401i	0.544044	−	0.648367i	0.966089	+	0.258208i	$0.0831320\pi$
$158$	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	0.144735	−	0.989470i	$-0.453767\pi$
$167$	−10.3973	−	8.72440i	−0.804570	−	0.675115i	−0.949305	+	0.314356i	$0.898212\pi$
$168$	3.15113	−	3.32722i	0.243115	−	0.256700i
$169$	−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	−0.731324	−	0.682030i	$-0.761097\pi$
$173$	−2.45499	+	2.05998i	−0.186650	+	0.156618i	0.544675	+	0.838647i	$0.316653\pi$
$174$	13.1863	−	6.93645i	0.999648	−	0.525851i
$175$	4.25510	+	12.4914i	0.321655	+	0.944263i
$176$	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	−0.312573	−	0.949894i	$-0.601191\pi$
$181$	4.75951	−	2.74791i	0.353772	−	0.204250i	0.666345	+	0.745643i	$0.267858\pi$
$182$	8.11044	−	1.25716i	0.601186	−	0.0931865i
$183$	−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
$189$	−11.6525	+	7.29513i	−0.847595	+	0.530643i
$190$	−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
$196$	5.54439	−	4.27314i	0.396028	−	0.305224i
$197$	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	0.871644	−	0.490139i	$-0.163054\pi$
$199$	12.4562	+	7.19157i	0.882994	+	0.509797i	0.0113494	+	0.999936i	$0.496387\pi$
$200$	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
$203$	21.5436	−	7.33864i	1.51206	−	0.515071i
$204$	−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
$210$	0.493907	+	0.118057i	0.0340828	+	0.00814673i
$211$	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	−0.973087	−	0.230440i	$-0.925984\pi$
$223$	−1.18771	+	3.26322i	−0.0795352	+	0.218521i	0.893551	+	0.448961i	$0.148206\pi$
$224$	1.37014	−	2.26334i	0.0915461	−	0.151226i
$225$	−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	−0.169965	−	0.985450i	$-0.554365\pi$
$227$	11.6163	−	9.74722i	0.771000	−	0.646946i	0.940965	+	0.338504i	$0.109921\pi$
$228$	7.70554	−	12.2106i	0.510312	−	0.808669i
$229$	−7.85437	−	1.38494i	−0.519031	−	0.0915192i	−0.0920052	−	0.995759i	$-0.529328\pi$
$229$	−7.85437	−	1.38494i	−0.519031	−	0.0915192i	−0.427026	+	0.904239i	$0.640439\pi$
$230$	0.100973	−	0.572648i	0.00665798	−	0.0377593i
$231$	−19.9983	−	13.2080i	−1.31579	−	0.869024i
$232$	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
$238$	−0.294673	+	1.48971i	−0.0191008	+	0.0965633i
$239$	−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	−0.523018	−	0.852322i	$-0.675194\pi$
$241$	−11.2237	+	1.97904i	−0.722982	+	0.127481i	−0.199964	+	0.979803i	$0.564083\pi$
$242$		−	16.3516i		−	1.05112i
$243$	12.1606	−	9.75291i	0.780104	−	0.625649i
$244$			12.8117i			0.820186i
$245$	0.717291	+	0.295324i	0.0458261	+	0.0188676i
$246$	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	0.749447	−	0.662064i	$-0.230319\pi$
$251$	−3.14706	−	5.45087i	−0.198641	−	0.344056i	−0.948088	+	0.318008i	$0.896986\pi$
$252$	−5.68035	+	5.54379i	−0.357828	+	0.349226i
$253$	−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	$0.113518\pi$
$257$	−1.00824	+	5.71799i	−0.0628921	+	0.356679i	−0.999971	+	0.00756212i	$0.997593\pi$
$258$	6.43592	−	10.1987i	0.400683	−	0.634945i
$259$	1.33757	−	3.45044i	0.0831128	−	0.214400i
$260$	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
$266$	14.5245	−	16.5976i	0.890554	−	1.01767i
$267$	−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	$-0.546664\pi$
$269$	−4.79165			−0.292152			−0.146076	+	0.989273i	$0.546664\pi$
$270$	−0.571809	−	0.0678003i	−0.0347992	−	0.00412619i
$271$			0.902646i			0.0548318i	0.999624	+	0.0274159i	$0.00872785\pi$
$271$			0.902646i			0.0548318i	−0.999624	+	0.0274159i	$0.991272\pi$
$272$	0.0996681	+	0.565246i	0.00604326	+	0.0342731i
$273$	−14.1225	+	1.62328i	−0.854731	+	0.0982451i
$274$	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
$280$	0.293127	+	0.00608391i	0.0175177	+	0.000363583i
$281$	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	−0.0488499	−	0.998806i	$-0.515556\pi$
$283$	−7.34081	−	1.29438i	−0.436366	−	0.0769430i	−0.387516	+	0.921863i	$0.626667\pi$
$284$	−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
$287$	−0.276779	+	13.3354i	−0.0163378	+	0.787164i
$288$	−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	−0.835483	−	0.549517i	$-0.814812\pi$
$293$	−19.2103	+	6.99198i	−1.12228	+	0.408476i	−0.286795	+	0.957992i	$0.592590\pi$
$294$	−9.88683	+	7.01788i	−0.576611	+	0.409291i
$295$	−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
$301$	12.1313	−	13.8629i	0.699239	−	0.799043i
$302$	−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	0.486041	−	0.873936i	$-0.338441\pi$
$307$	−0.486924	−	0.281126i	−0.0277902	−	0.0160447i	−0.513831	+	0.857892i	$0.671774\pi$
$308$	−12.9015	−	5.00131i	−0.735130	−	0.284976i
$309$	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	$0.149553\pi$
$311$	−1.78245	+	10.1088i	−0.101073	+	0.573215i	−0.992716	+	0.120476i	$0.961558\pi$
$312$	−4.75516	+	2.50138i	−0.269208	+	0.141613i
$313$	12.1355	+	14.4625i	0.685936	+	0.817467i	0.990858	−	0.134910i	$-0.0430747\pi$
$313$	12.1355	+	14.4625i	0.685936	+	0.817467i	−0.304921	+	0.952377i	$0.598630\pi$
$314$	−5.30257	+	9.18432i	−0.299241	+	0.518301i
$315$	−0.846768	−	0.237969i	−0.0477100	−	0.0134080i
$316$	−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
$322$	8.70125	+	10.8179i	0.484902	+	0.602859i
$323$			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
$329$	−21.5246	−	4.25769i	−1.18669	−	0.234734i
$330$	−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
$336$	−2.52549	+	3.82386i	−0.137777	+	0.208609i
$337$	−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
$343$	−16.5841	+	8.24430i	−0.895456	+	0.445150i
$344$	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	−0.401793	−	0.915730i	$-0.631613\pi$
$349$	−8.70853	+	1.53555i	−0.466157	+	0.0821961i	−0.0643639	+	0.997926i	$0.520502\pi$
$350$	−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	$-0.980548\pi$
$353$	−1.52341	−	8.63967i	−0.0810827	−	0.459843i	0.917051	−	0.398771i	$-0.130563\pi$
$354$	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
$357$	0.611475	−	2.55818i	0.0323627	−	0.135393i
$358$	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
$364$	−7.76892	+	2.64642i	−0.407202	+	0.138710i
$365$	−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	0.967817	−	0.251657i	$-0.0809754\pi$
$367$	10.5733	+	12.6008i	0.551923	+	0.657757i	−0.415893	+	0.909413i	$0.636531\pi$
$368$	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
$371$	−2.81748	−	18.1768i	−0.146276	−	0.943692i
$372$	−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
$378$	10.2087	−	9.20774i	0.525079	−	0.473595i
$379$	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	0.896669	−	0.442701i	$-0.145980\pi$
$383$	12.0632	+	10.1222i	0.616399	+	0.517221i	−0.280270	+	0.959921i	$0.590424\pi$
$384$	−0.367621	+	1.69259i	−0.0187601	+	0.0863745i
$385$	−0.234871	−	1.51525i	−0.0119701	−	0.0772245i
$386$	−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
$392$	−4.71813	+	5.17100i	−0.238302	+	0.261175i
$393$	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	0.320579	−	0.947222i	$-0.396123\pi$
$397$	25.9260	−	14.9684i	1.30119	−	0.751240i	0.980608	+	0.195981i	$0.0627892\pi$
$398$	−13.5157	−	4.91932i	−0.677482	−	0.246583i
$399$	−26.2684	+	27.7362i	−1.31506	+	1.38855i
$400$	−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	$0.232506\pi$
$409$	12.1976	+	33.5128i	0.603135	+	1.65710i	−0.141747	+	0.989903i	$0.545272\pi$
$410$	−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
$413$	30.2404	+	18.3063i	1.48803	+	0.900795i
$414$	−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	$0.260518\pi$
$419$	−4.26770	+	24.2033i	−0.208491	+	1.18241i	−0.891851	+	0.452329i	$0.850593\pi$
$420$	−0.506904	−	0.0304978i	−0.0247344	−	0.00148814i
$421$	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
$427$	6.57751	−	33.2523i	0.318308	−	1.60919i
$428$	−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	$-0.890398\pi$
$433$		−	14.0484i		−	0.675123i	0.941303	−	0.337562i	$-0.109602\pi$
$434$	−11.1253	−	13.8317i	−0.534033	−	0.663943i
$435$	−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	−0.948320	−	0.317315i	$-0.897219\pi$
$439$	−0.375011	+	1.03033i	−0.0178983	+	0.0491752i	0.930422	+	0.366491i	$0.119441\pi$
$440$	−0.289776	−	0.501906i	−0.0138145	−	0.0239274i
$441$	17.5893	−	11.4724i	0.837586	−	0.546305i
$442$	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
$448$	−0.956296	+	2.46688i	−0.0451807	+	0.116549i
$449$	−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
$455$	−0.684433	−	0.598944i	−0.0320867	−	0.0280789i
$456$	−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	$-0.718809\pi$
$461$	−6.49736	−	36.8483i	−0.302612	−	1.71620i	0.331925	−	0.943306i	$-0.392302\pi$
$462$	21.9880	+	9.53469i	1.02298	+	0.443594i
$463$	−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	0.569088	−	0.822276i	$-0.307296\pi$
$467$	−9.23983	−	16.0038i	−0.427568	−	0.740570i	−0.996656	+	0.0817066i	$0.973963\pi$
$468$	8.40020	−	4.00524i	0.388299	−	0.185142i
$469$	0.0223470	−	1.07670i	0.00103189	−	0.0497172i
$470$	−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
$476$	0.0315115	−	1.51824i	0.00144433	−	0.0695886i
$477$	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	0.304344	−	0.952562i	$-0.401563\pi$
$479$	−1.63729	−	0.595925i	−0.0748097	−	0.0272285i	−0.379154	+	0.925334i	$0.623785\pi$
$480$	−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
$483$	−14.3224	−	19.3154i	−0.651692	−	0.878883i
$484$	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
$490$	−0.757677	−	0.166281i	−0.0342283	−	0.00751183i
$491$	−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
$497$	18.5269	+	7.18204i	0.831047	+	0.322158i
$498$	−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	−0.813672	−	0.581324i	$-0.802535\pi$
$503$	2.16662	−	3.75270i	0.0966050	−	0.167325i	0.910277	+	0.413999i	$0.135868\pi$
$504$	4.63138	−	6.44595i	0.206298	−	0.287125i
$505$	−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	−0.346677	−	0.937985i	$-0.612690\pi$
$509$	−0.210305	+	0.0765449i	−0.00932162	+	0.00339279i	0.337355	+	0.941377i	$0.390468\pi$
$510$	0.0871117	−	0.0674393i	0.00385737	−	0.00298626i
$511$	29.1960	−	23.4834i	1.29156	−	1.03885i
$512$			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
$518$	−0.718092	+	3.63028i	−0.0315512	+	0.159505i
$519$	−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	$-0.784612\pi$
$521$	−21.2763	−	36.8517i	−0.932133	−	1.61450i	−0.152464	−	0.988309i	$-0.548721\pi$
$522$	21.0116	−	14.9830i	0.919652	−	0.655786i
$523$	4.18823	+	2.41808i	0.183139	+	0.105735i	0.588766	−	0.808303i	$-0.299614\pi$
$523$	4.18823	+	2.41808i	0.183139	+	0.105735i	−0.405628	+	0.914038i	$0.632947\pi$
$524$	8.17151	−	6.85671i	0.356974	−	0.299537i
$525$	10.2189	+	20.4450i	0.445989	+	0.892293i
$526$	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
$532$	−11.4217	+	18.8676i	−0.495193	+	0.818015i
$533$	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
$546$	13.6260	−	4.05096i	0.583141	−	0.173365i
$547$	−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
$553$	5.74562	+	16.8670i	0.244329	+	0.717260i
$554$	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
$560$	−0.289730	+	0.0449095i	−0.0122433	+	0.00189777i
$561$	−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	−0.102577	−	0.994725i	$-0.532709\pi$
$563$	10.8730	−	3.95744i	0.458241	−	0.166786i	0.560818	+	0.827939i	$0.310487\pi$
$564$	14.2331	−	1.93602i	0.599321	−	0.0815211i
$565$	0.449852	−	0.0793210i	0.0189254	−	0.00333706i
$566$	7.45405			0.313317
$567$	−18.2955	+	15.2405i	−0.768341	+	0.640041i
$568$	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
$574$	−2.04310	−	13.1809i	−0.0852772	−	0.550159i
$575$	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	−0.351698	−	0.936114i	$-0.614396\pi$
$577$	−32.1457	−	18.5594i	−1.33824	−	0.772636i	−0.986547	+	0.163478i	$0.947729\pi$
$578$	−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
$581$	−5.14910	−	15.1159i	−0.213621	−	0.627113i
$582$	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	0.182938	−	0.983125i	$-0.441439\pi$
$587$	−7.48319	−	2.72366i	−0.308864	−	0.112417i	−0.491802	+	0.870707i	$0.663662\pi$
$588$	8.51798	−	8.62809i	0.351276	−	0.355817i
$589$	−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	$-0.465586\pi$
$593$	5.25522			0.215806			0.107903	+	0.994161i	$0.465586\pi$
$594$	−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	$-0.762998\pi$
$601$	6.46075	−	17.7508i	0.263540	−	0.724069i	0.998922	−	0.0464169i	$-0.0147803\pi$
$602$	−9.53977	+	15.7589i	−0.388812	+	0.642283i
$603$	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	−0.521598	−	0.853191i	$-0.674664\pi$
$607$	−32.1160	−	5.66292i	−1.30355	−	0.229851i	−0.781951	+	0.623341i	$0.785775\pi$
$608$	−1.44756	+	8.20952i	−0.0587063	+	0.332940i
$609$	35.2609	−	17.6242i	1.42884	−	0.714169i
$610$	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
$616$	13.5739	+	2.68501i	0.546910	+	0.108182i
$617$	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	0.627903	−	0.778291i	$-0.283913\pi$
$619$	36.9247	−	6.51083i	1.48413	−	0.261692i	0.856227	+	0.516599i	$0.172802\pi$
$620$		−	0.743478i		−	0.0298588i
$621$	18.6779	+	19.8635i	0.749516	+	0.797096i
$622$		−	10.2647i		−	0.411577i
$623$	12.8032	+	15.9177i	0.512950	+	0.637731i
$624$	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
$630$	0.875226	+	0.0873140i	0.0348698	+	0.00347867i
$631$	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
$637$	21.5226	−	2.88013i	0.852757	−	0.114115i
$638$	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	−0.772674	−	0.634803i	$-0.781081\pi$
$643$	−0.338298	+	0.403168i	−0.0133412	+	0.0158994i	0.759333	+	0.650703i	$0.225526\pi$
$644$	−10.4476	−	9.14262i	−0.411692	−	0.360270i
$645$	−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	$-0.514245\pi$
$647$	−2.27585			−0.0894729			−0.0447365	+	0.998999i	$0.514245\pi$
$648$	−4.36550	+	7.87035i	−0.171493	+	0.309177i
$649$		−	69.8761i		−	2.74288i
$650$	2.68673	+	15.2372i	0.105382	+	0.597651i
$651$	18.3125	+	24.6965i	0.717724	+	0.967934i
$652$	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
$658$	21.9369	+	0.455305i	0.855189	+	0.0177496i
$659$	−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	0.105997	−	0.994366i	$-0.466197\pi$
$661$	−3.45779	−	0.609701i	−0.134492	−	0.0237146i	−0.240489	+	0.970652i	$0.577308\pi$
$662$	−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
$665$	−2.44356	−	0.0507165i	−0.0947571	−	0.00196670i
$666$	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
$672$	1.82312	−	4.20431i	0.0703283	−	0.162185i
$673$	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	$0.0438112\pi$
$677$	2.77529	+	15.7395i	0.106663	+	0.604917i	−0.883880	+	0.467714i	$0.845078\pi$
$678$	−2.70389	+	6.60787i	−0.103842	+	0.253774i
$679$	15.9880	+	13.9910i	0.613562	+	0.536925i
$680$	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
$686$	14.9005	−	10.9988i	0.568904	−	0.419938i
$687$	−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	$0.106317\pi$
$691$	29.0085	+	34.5709i	1.10353	+	1.31514i	0.158796	+	0.987311i	$0.449239\pi$
$692$	−1.60238	+	2.77541i	−0.0609134	+	0.105505i
$693$	−37.4054	−	17.9996i	−1.42091	−	0.683750i
$694$	−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
$700$	8.27080	+	10.2828i	0.312607	+	0.388652i
$701$			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
$707$	7.05286	+	1.39510i	0.265250	+	0.0524681i
$708$	−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
$714$	−0.157962	+	2.62549i	−0.00591159	+	0.0982566i
$715$	−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	$-0.528907\pi$
$719$	21.9102	−	37.9496i	0.817112	−	1.41528i	0.907801	−	0.419401i	$-0.137760\pi$
$720$	0.320368	−	0.0887974i	0.0119394	−	0.00330928i
$721$	−17.0935	+	28.2370i	−0.636597	+	1.05160i
$722$	−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	−0.309078	−	0.951037i	$-0.600020\pi$
$727$	−7.39436	+	1.30383i	−0.274242	+	0.0483562i	0.0348358	+	0.999393i	$0.488909\pi$
$728$	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	0.883588	−	0.468266i	$-0.155121\pi$
$733$	−2.55240	−	7.01267i	−0.0942751	−	0.259019i	−0.977863	+	0.209247i	$0.932899\pi$
$734$	−12.6008	−	10.5733i	−0.465104	−	0.390269i
$735$	1.29999	+	0.339399i	0.0479509	+	0.0125189i
$736$	−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
$742$	5.93104	+	17.4114i	0.217735	+	0.639192i
$743$	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
$749$	0.643175	+	4.14940i	0.0235011	+	0.151616i
$750$	−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
$756$	−8.45470	+	10.8406i	−0.307494	+	0.394268i
$757$	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	0.744693	−	0.667408i	$-0.232596\pi$
$761$	5.97901	+	5.01699i	0.216739	+	0.181866i	−0.527954	+	0.849273i	$0.677041\pi$
$762$	7.82714	+	7.11068i	0.283548	+	0.257593i
$763$	20.1119	−	3.11744i	0.728101	−	0.112859i
$764$	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	0.472916	−	0.881107i	$-0.343201\pi$
$769$	17.0810	+	3.01184i	0.615956	+	0.108610i	0.143039	+	0.989717i	$0.454312\pi$
$770$	0.494424	+	1.45145i	0.0178178	+	0.0523066i
$771$	−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	−0.931663	−	0.363324i	$-0.881642\pi$
$773$	−4.20333	+	7.28038i	−0.151183	+	0.261857i	0.780479	+	0.625181i	$0.214975\pi$
$774$	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
$777$	1.49011	−	6.23405i	0.0534574	−	0.223645i
$778$	−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	$-0.943743\pi$
$787$	−9.63149	−	26.4623i	−0.343326	−	0.943279i	0.641097	−	0.767460i	$-0.278480\pi$
$788$	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
$791$	−5.64783	+	9.32971i	−0.200814	+	0.331726i
$792$	−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	−0.950682	−	0.310166i	$-0.899615\pi$
$797$	1.37627	−	7.80520i	0.0487499	−	0.276474i	0.999432	+	0.0336918i	$0.0107265\pi$
$798$	21.0529	−	31.8763i	0.745266	−	1.12841i
$799$	−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
$805$	0.298532	−	1.50921i	0.0105219	−	0.0531928i
$806$	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	$0.218412\pi$
$811$			36.0858i			1.26715i	−0.773683	+	0.633573i	$0.781588\pi$
$812$	17.7344	−	14.2644i	0.622354	−	0.500582i
$813$	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
$819$	−23.8587	+	6.08280i	−0.833690	+	0.212550i
$820$	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
$826$	−32.9598	−	12.7770i	−1.14682	−	0.444569i
$827$	−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	−0.178474	−	0.983945i	$-0.557116\pi$
$829$	16.8265	−	9.71480i	0.584409	−	0.337409i	0.762884	+	0.646536i	$0.223783\pi$
$830$	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
$833$	−0.861250	+	3.92436i	−0.0298405	+	0.135971i
$834$	−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	$0.172082\pi$
$839$	6.59635	+	37.4098i	0.227731	+	1.29153i	−0.629663	+	0.776869i	$0.716807\pi$
$840$	0.504499	−	0.0579885i	0.0174069	−	0.00200079i
$841$	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
$847$	0.897725	−	43.2530i	0.0308462	−	1.48619i
$848$	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	0.339702	−	0.940533i	$-0.389674\pi$
$853$	−18.8535	−	22.4687i	−0.645530	−	0.769313i	−0.985233	+	0.171220i	$0.945229\pi$
$854$	−0.703380	+	33.8893i	−0.0240692	+	1.15967i
$855$	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	−0.512243	−	0.858840i	$-0.671185\pi$
$857$	−42.6441	−	15.5212i	−1.45670	−	0.530194i	−0.944453	+	0.328646i	$0.893408\pi$
$858$	−20.7987	−	18.8948i	−0.710054	−	0.645059i
$859$	−21.3590	+	25.4547i	−0.728760	+	0.868503i	−0.995451	−	0.0952797i	$-0.969625\pi$
$859$	−21.3590	+	25.4547i	−0.728760	+	0.868503i	0.266690	+	0.963782i	$0.414070\pi$
$860$	−0.725037	+	0.263892i	−0.0247236	+	0.00899864i
$861$	2.63810	+	22.9515i	0.0899064	+	0.782184i
$862$	−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
$868$	13.3582	+	11.6897i	0.453406	+	0.396773i
$869$	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
$875$	−1.05842	+	2.73033i	−0.0357812	+	0.0923020i
$876$	−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	−0.824104	−	0.566439i	$-0.808321\pi$
$881$	2.32996	−	4.03561i	0.0784984	−	0.135963i	0.902602	+	0.430476i	$0.141654\pi$
$882$	−15.3299	+	14.3525i	−0.516185	+	0.483273i
$883$	−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	0.146832	−	0.989161i	$-0.453092\pi$
$887$	26.6593	−	9.70320i	0.895133	−	0.325802i	0.748301	+	0.663360i	$0.230870\pi$
$888$	−0.326525	−	2.40052i	−0.0109575	−	0.0805562i
$889$	10.1241	+	12.5869i	0.339551	+	0.422151i
$890$			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
$896$	0.513398	−	2.59546i	0.0171514	−	0.0867083i
$897$	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
$903$	17.5841	−	26.6241i	0.585162	−	0.885996i
$904$	−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
$910$	0.778040	+	0.470994i	0.0257918	+	0.0156133i
$911$	−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
$924$	−23.3097	−	5.57165i	−0.766832	−	0.183294i
$925$	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	−0.580649	−	0.814154i	$-0.697201\pi$
$929$	3.66691	−	3.07690i	0.120307	−	0.100950i	0.700957	+	0.713204i	$0.252757\pi$
$930$	−0.0506469	+	1.28675i	−0.00166078	+	0.0421940i
$931$	39.3312	−	43.1063i	1.28903	−	1.41275i
$932$	−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	−0.451663	−	0.892188i	$-0.649169\pi$
$937$	2.91297	−	1.68181i	0.0951627	−	0.0549422i	0.546826	+	0.837246i	$0.315836\pi$
$938$	0.164959	+	1.06422i	0.00538609	+	0.0347480i
$939$	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	0.0404267	−	0.999183i	$-0.487128\pi$
$941$	21.8920	−	7.96802i	0.713658	−	0.259750i	0.673231	+	0.739432i	$0.264906\pi$
$942$	−6.95646	+	17.0004i	−0.226654	+	0.553904i
$943$	26.0518	−	4.59364i	0.848364	−	0.149590i
$944$	−13.3609			−0.434862
$945$	−1.50882	−	0.210737i	−0.0490818	−	0.00685528i
$946$	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
$952$	0.232607	+	1.50065i	0.00753885	+	0.0486363i
$953$	−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
$959$	40.5626	−	13.8173i	1.30984	−	0.446185i
$960$	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
$966$	17.4589	+	16.5349i	0.561731	+	0.532003i
$967$	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	$-0.332664\pi$
$971$	31.2743			1.00364			0.501819	+	0.864972i	$0.332664\pi$
$972$	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
$980$	0.775040	+	0.0321861i	0.0247578	+	0.00102815i
$981$	−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	−0.801707	−	0.597717i	$-0.796075\pi$
$983$	−11.0451	+	9.26797i	−0.352285	+	0.295602i	0.449422	+	0.893320i	$0.351630\pi$
$984$	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
$987$	−37.9354	−	2.28238i	−1.20750	−	0.0726489i
$988$	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
$994$	−19.4926	−	3.85576i	−0.618268	−	0.122297i
$995$	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	−0.0216122	−	0.999766i	$-0.506880\pi$
$997$	9.47320	−	1.67038i	0.300019	−	0.0529015i	0.321631	+	0.946865i	$0.395769\pi$
$998$		−	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.41.12	yes	144
7.6	odd	2	inner	378.2.z.a.41.1	✓	144
27.2	odd	18	inner	378.2.z.a.83.1	yes	144
189.83	even	18	inner	378.2.z.a.83.12	yes	144

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

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

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.71625 - 0.233448i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.0848896 + 0.0712308i) q^{5} +(-1.64964 + 0.527925i) q^{6} +(-2.61453 + 0.405264i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(2.89100 - 0.801309i) q^{9} +O(q^{10})\)	\(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} +(-2.61453 + 0.405264i) 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} +(2.50444 - 0.853115i) 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} +(-4.39257 + 1.30589i) 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} +(-0.250814 - 0.151832i) 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} +(4.09907 - 2.04881i) 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} +(6.67152 - 2.11915i) 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} +(2.06162 - 1.65823i) 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} +(-7.23387 + 3.26666i) 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} +(0.273369 + 0.105972i) 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} +(-10.4129 - 9.11226i) 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} +(-3.68102 + 2.72948i) 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} +(-8.20553 - 0.170307i) 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} +(-6.20218 + 3.24545i) q^{98} +(12.9290 + 8.88852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 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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