LMFDB - Embedded newform 416.2.bg.a.77.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(77,416)] 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("416.77"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.10
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17991 - 0.779620i) q^{2} +(-0.174001 + 0.420075i) q^{3} +(0.784386 + 1.83977i) q^{4} +(0.828671 + 2.00059i) q^{5} +(0.532805 - 0.359998i) q^{6} +(-1.24243 - 1.24243i) q^{7} +(0.508812 - 2.78229i) q^{8} +(1.97513 + 1.97513i) q^{9} +(0.581940 - 3.00657i) q^{10} +(-0.631621 + 0.261626i) q^{11} +(-0.909324 + 0.00938021i) q^{12} +(1.89800 - 3.06555i) q^{13} +(0.497333 + 2.43457i) q^{14} -0.984588 q^{15} +(-2.76948 + 2.88617i) q^{16} +3.22356i q^{17} +(-0.790631 - 3.87034i) q^{18} +(-3.19102 + 7.70380i) q^{19} +(-3.03062 + 3.09380i) q^{20} +(0.738096 - 0.305729i) q^{21} +(0.949227 + 0.183729i) q^{22} +(1.08411 + 1.08411i) q^{23} +(1.08024 + 0.697859i) q^{24} +(0.219872 - 0.219872i) q^{25} +(-4.62944 + 2.13736i) q^{26} +(-2.43361 + 1.00803i) q^{27} +(1.31123 - 3.26031i) q^{28} +(-1.71969 + 4.15169i) q^{29} +(1.16173 + 0.767604i) q^{30} +1.42007i q^{31} +(5.51786 - 1.24629i) q^{32} -0.310852i q^{33} +(2.51315 - 3.80352i) q^{34} +(1.45602 - 3.51515i) q^{35} +(-2.08452 + 5.18305i) q^{36} +(3.03939 + 7.33774i) q^{37} +(9.77115 - 6.60202i) q^{38} +(0.957508 + 1.33071i) q^{39} +(5.98785 - 1.28768i) q^{40} +(-2.85091 + 2.85091i) q^{41} +(-1.10924 - 0.214700i) q^{42} +(-3.34568 - 8.07717i) q^{43} +(-0.976766 - 0.956820i) q^{44} +(-2.31469 + 5.58817i) q^{45} +(-0.433961 - 2.12435i) q^{46} +10.2647 q^{47} +(-0.730519 - 1.66559i) q^{48} -3.91276i q^{49} +(-0.430846 + 0.0880131i) q^{50} +(-1.35414 - 0.560903i) q^{51} +(7.12866 + 1.08730i) q^{52} +(4.71873 + 11.3920i) q^{53} +(3.65732 + 0.707898i) q^{54} +(-1.04681 - 1.04681i) q^{55} +(-4.08894 + 2.82462i) q^{56} +(-2.68094 - 2.68094i) q^{57} +(5.26582 - 3.55793i) q^{58} +(3.95651 + 9.55186i) q^{59} +(-0.772297 - 1.81141i) q^{60} +(3.81992 - 9.22211i) q^{61} +(1.10711 - 1.67555i) q^{62} -4.90791i q^{63} +(-7.48222 - 2.83132i) q^{64} +(7.70572 + 1.25679i) q^{65} +(-0.242346 + 0.366778i) q^{66} +(-7.79130 - 3.22726i) q^{67} +(-5.93060 + 2.52852i) q^{68} +(-0.644044 + 0.266772i) q^{69} +(-4.45845 + 3.01242i) q^{70} +(-2.79193 - 2.79193i) q^{71} +(6.50035 - 4.49041i) q^{72} +(-1.15383 + 1.15383i) q^{73} +(2.13443 - 11.0275i) q^{74} +(0.0541049 + 0.130621i) q^{75} +(-16.6762 + 0.172024i) q^{76} +(1.10979 + 0.459691i) q^{77} +(-0.0923263 - 2.31662i) q^{78} -12.8221i q^{79} +(-8.06903 - 3.14890i) q^{80} +7.18208i q^{81} +(5.58645 - 1.14120i) q^{82} +(-0.901406 + 2.17619i) q^{83} +(1.14142 + 1.11811i) q^{84} +(-6.44903 + 2.67127i) q^{85} +(-2.34952 + 12.1387i) q^{86} +(-1.44480 - 1.44480i) q^{87} +(0.406542 + 1.89047i) q^{88} +(-6.20172 - 6.20172i) q^{89} +(7.08778 - 4.78896i) q^{90} +(-6.16684 + 1.45059i) q^{91} +(-1.14415 + 2.84487i) q^{92} +(-0.596535 - 0.247093i) q^{93} +(-12.1114 - 8.00253i) q^{94} -18.0564 q^{95} +(-0.436576 + 2.53477i) q^{96} -5.70249i q^{97} +(-3.05046 + 4.61671i) q^{98} +(-1.76428 - 0.730790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.17991	−	0.779620i	−0.834324	−	0.551274i
$2$	−1.17991	−	0.779620i	−0.834324	−	0.551274i
$3$	−0.174001	+	0.420075i	−0.100459	+	0.242531i	−0.966116	−	0.258107i	$-0.916901\pi$
$3$	−0.174001	+	0.420075i	−0.100459	+	0.242531i	0.865657	+	0.500638i	$0.166901\pi$
$4$	0.784386	+	1.83977i	0.392193	+	0.919883i
$5$	0.828671	+	2.00059i	0.370593	+	0.894691i	0.993650	+	0.112514i	$0.0358904\pi$
$5$	0.828671	+	2.00059i	0.370593	+	0.894691i	−0.623057	+	0.782176i	$0.714110\pi$
$6$	0.532805	−	0.359998i	0.217517	−	0.146968i
$7$	−1.24243	−	1.24243i	−0.469593	−	0.469593i	0.432190	−	0.901783i	$-0.357741\pi$
$7$	−1.24243	−	1.24243i	−0.469593	−	0.469593i	−0.901783	+	0.432190i	$0.857741\pi$
$8$	0.508812	−	2.78229i	0.179892	−	0.983686i
$9$	1.97513	+	1.97513i	0.658378	+	0.658378i
$10$	0.581940	−	3.00657i	0.184026	−	0.950760i
$11$	−0.631621	+	0.261626i	−0.190441	+	0.0788832i	−0.475866	−	0.879518i	$-0.657865\pi$
$11$	−0.631621	+	0.261626i	−0.190441	+	0.0788832i	0.285425	+	0.958401i	$0.407865\pi$
$12$	−0.909324	+	0.00938021i	−0.262499	+	0.00270783i
$13$	1.89800	−	3.06555i	0.526411	−	0.850230i
$13$	1.89800	−	3.06555i	0.526411	−	0.850230i
$14$	0.497333	+	2.43457i	0.132918	+	0.650667i
$15$	−0.984588			−0.254220
$16$	−2.76948	+	2.88617i	−0.692369	+	0.721543i
$17$			3.22356i			0.781829i	0.920427	+	0.390915i	$0.127841\pi$
$17$			3.22356i			0.781829i	−0.920427	+	0.390915i	$0.872159\pi$
$18$	−0.790631	−	3.87034i	−0.186353	−	0.912247i
$19$	−3.19102	+	7.70380i	−0.732070	+	1.76737i	−0.0964942	+	0.995334i	$0.530763\pi$
$19$	−3.19102	+	7.70380i	−0.732070	+	1.76737i	−0.635575	+	0.772039i	$0.719237\pi$
$20$	−3.03062	+	3.09380i	−0.677667	+	0.691794i
$21$	0.738096	−	0.305729i	0.161066	−	0.0667156i
$22$	0.949227	+	0.183729i	0.202376	+	0.0391711i
$23$	1.08411	+	1.08411i	0.226052	+	0.226052i	0.811041	−	0.584989i	$-0.198901\pi$
$23$	1.08411	+	1.08411i	0.226052	+	0.226052i	−0.584989	+	0.811041i	$0.698901\pi$
$24$	1.08024	+	0.697859i	0.220502	+	0.142450i
$25$	0.219872	−	0.219872i	0.0439744	−	0.0439744i
$26$	−4.62944	+	2.13736i	−0.907907	+	0.419171i
$27$	−2.43361	+	1.00803i	−0.468348	+	0.193996i
$28$	1.31123	−	3.26031i	0.247799	−	0.616141i
$29$	−1.71969	+	4.15169i	−0.319338	+	0.770950i	0.679951	+	0.733257i	$0.262001\pi$
$29$	−1.71969	+	4.15169i	−0.319338	+	0.770950i	−0.999289	+	0.0376928i	$0.987999\pi$
$30$	1.16173	+	0.767604i	0.212101	+	0.140145i
$31$			1.42007i			0.255051i	0.991835	+	0.127526i	$0.0407035\pi$
$31$			1.42007i			0.255051i	−0.991835	+	0.127526i	$0.959296\pi$
$32$	5.51786	−	1.24629i	0.975429	−	0.220315i
$33$		−	0.310852i		−	0.0541123i
$34$	2.51315	−	3.80352i	0.431002	−	0.652299i
$35$	1.45602	−	3.51515i	0.246112	−	0.594168i
$36$	−2.08452	+	5.18305i	−0.347419	+	0.863842i
$37$	3.03939	+	7.33774i	0.499673	+	1.20632i	0.949660	+	0.313282i	$0.101429\pi$
$37$	3.03939	+	7.33774i	0.499673	+	1.20632i	−0.449987	+	0.893035i	$0.648571\pi$
$38$	9.77115	−	6.60202i	1.58509	−	1.07099i
$39$	0.957508	+	1.33071i	0.153324	+	0.213084i
$40$	5.98785	−	1.28768i	0.946762	−	0.203600i
$41$	−2.85091	+	2.85091i	−0.445237	+	0.445237i	−0.893768	−	0.448530i	$-0.851948\pi$
$41$	−2.85091	+	2.85091i	−0.445237	+	0.445237i	0.448530	+	0.893768i	$0.351948\pi$
$42$	−1.10924	−	0.214700i	−0.171160	−	0.0331290i
$43$	−3.34568	−	8.07717i	−0.510211	−	1.23176i	−0.943761	−	0.330628i	$-0.892739\pi$
$43$	−3.34568	−	8.07717i	−0.510211	−	1.23176i	0.433550	−	0.901129i	$-0.357261\pi$
$44$	−0.976766	−	0.956820i	−0.147253	−	0.144246i
$45$	−2.31469	+	5.58817i	−0.345054	+	0.833035i
$46$	−0.433961	−	2.12435i	−0.0639840	−	0.313218i
$47$	10.2647			1.49725			0.748627	−	0.662992i	$-0.230714\pi$
$47$	10.2647			1.49725			0.748627	+	0.662992i	$0.230714\pi$
$48$	−0.730519	−	1.66559i	−0.105441	−	0.240407i
$49$		−	3.91276i		−	0.558966i
$50$	−0.430846	+	0.0880131i	−0.0609309	+	0.0124469i
$51$	−1.35414	−	0.560903i	−0.189618	−	0.0785422i
$52$	7.12866	+	1.08730i	0.988567	+	0.150782i
$53$	4.71873	+	11.3920i	0.648167	+	1.56481i	0.815401	+	0.578897i	$0.196517\pi$
$53$	4.71873	+	11.3920i	0.648167	+	1.56481i	−0.167233	+	0.985917i	$0.553483\pi$
$54$	3.65732	+	0.707898i	0.497699	+	0.0963327i
$55$	−1.04681	−	1.04681i	−0.141152	−	0.141152i
$56$	−4.08894	+	2.82462i	−0.546408	+	0.377456i
$57$	−2.68094	−	2.68094i	−0.355099	−	0.355099i
$58$	5.26582	−	3.55793i	0.691436	−	0.467179i
$59$	3.95651	+	9.55186i	0.515094	+	1.24355i	0.940885	+	0.338725i	$0.109996\pi$
$59$	3.95651	+	9.55186i	0.515094	+	1.24355i	−0.425792	+	0.904821i	$0.640004\pi$
$60$	−0.772297	−	1.81141i	−0.0997031	−	0.233852i
$61$	3.81992	−	9.22211i	0.489091	−	1.18077i	−0.466087	−	0.884739i	$-0.654337\pi$
$61$	3.81992	−	9.22211i	0.489091	−	1.18077i	0.955178	−	0.296032i	$-0.0956634\pi$
$62$	1.10711	−	1.67555i	0.140603	−	0.212795i
$63$		−	4.90791i		−	0.618339i
$64$	−7.48222	−	2.83132i	−0.935278	−	0.353915i
$65$	7.70572	+	1.25679i	0.955777	+	0.155885i
$66$	−0.242346	+	0.366778i	−0.0298308	+	0.0451472i
$67$	−7.79130	−	3.22726i	−0.951859	−	0.394273i	−0.147930	−	0.988998i	$-0.547261\pi$
$67$	−7.79130	−	3.22726i	−0.951859	−	0.394273i	−0.803929	+	0.594725i	$0.797261\pi$
$68$	−5.93060	+	2.52852i	−0.719191	+	0.306628i
$69$	−0.644044	+	0.266772i	−0.0775337	+	0.0321155i
$70$	−4.45845	+	3.01242i	−0.532887	+	0.360053i
$71$	−2.79193	−	2.79193i	−0.331341	−	0.331341i	0.521755	−	0.853095i	$-0.325278\pi$
$71$	−2.79193	−	2.79193i	−0.331341	−	0.331341i	−0.853095	+	0.521755i	$0.825278\pi$
$72$	6.50035	−	4.49041i	0.766074	−	0.529200i
$73$	−1.15383	+	1.15383i	−0.135045	+	0.135045i	−0.771398	−	0.636353i	$-0.780442\pi$
$73$	−1.15383	+	1.15383i	−0.135045	+	0.135045i	0.636353	+	0.771398i	$0.280442\pi$
$74$	2.13443	−	11.0275i	0.248123	−	1.28192i
$75$	0.0541049	+	0.130621i	0.00624750	+	0.0150828i
$76$	−16.6762	+	0.172024i	−1.91289	+	0.0197326i
$77$	1.10979	+	0.459691i	0.126473	+	0.0523867i
$78$	−0.0923263	−	2.31662i	−0.0104539	−	0.262305i
$79$		−	12.8221i		−	1.44260i	−0.692623	−	0.721300i	$-0.743545\pi$
$79$		−	12.8221i		−	1.44260i	0.692623	−	0.721300i	$-0.256455\pi$
$80$	−8.06903	−	3.14890i	−0.902145	−	0.352058i
$81$			7.18208i			0.798009i
$82$	5.58645	−	1.14120i	0.616920	−	0.126024i
$83$	−0.901406	+	2.17619i	−0.0989422	+	0.238868i	−0.965598	−	0.260039i	$-0.916265\pi$
$83$	−0.901406	+	2.17619i	−0.0989422	+	0.238868i	0.866656	+	0.498906i	$0.166265\pi$
$84$	1.14142	+	1.11811i	0.124539	+	0.121996i
$85$	−6.44903	+	2.67127i	−0.699495	+	0.289740i
$86$	−2.34952	+	12.1387i	−0.253355	+	1.30895i
$87$	−1.44480	−	1.44480i	−0.154898	−	0.154898i
$88$	0.406542	+	1.89047i	0.0433375	+	0.201525i
$89$	−6.20172	−	6.20172i	−0.657381	−	0.657381i	0.297379	−	0.954760i	$-0.403888\pi$
$89$	−6.20172	−	6.20172i	−0.657381	−	0.657381i	−0.954760	+	0.297379i	$0.903888\pi$
$90$	7.08778	−	4.78896i	0.747118	−	0.504801i
$91$	−6.16684	+	1.45059i	−0.646461	+	0.152063i
$92$	−1.14415	+	2.84487i	−0.119286	+	0.296598i
$93$	−0.596535	−	0.247093i	−0.0618578	−	0.0256223i
$94$	−12.1114	−	8.00253i	−1.24919	−	0.825398i
$95$	−18.0564			−1.85255
$96$	−0.436576	+	2.53477i	−0.0445579	+	0.258704i
$97$		−	5.70249i		−	0.579001i	−0.957178	−	0.289500i	$-0.906511\pi$
$97$		−	5.70249i		−	0.579001i	0.957178	−	0.289500i	$-0.0934891\pi$
$98$	−3.05046	+	4.61671i	−0.308143	+	0.466358i
$99$	−1.76428	−	0.730790i	−0.177317	−	0.0734471i
$100$	0.576978	+	0.232049i	0.0576978	+	0.0232049i
$101$	−2.20771	+	0.914465i	−0.219676	+	0.0909927i	−0.489807	−	0.871831i	$-0.662933\pi$
$101$	−2.20771	+	0.914465i	−0.219676	+	0.0909927i	0.270131	+	0.962823i	$0.412933\pi$
$102$	1.16048	+	1.71753i	0.114904	+	0.170061i
$103$	3.86184	−	3.86184i	0.380518	−	0.380518i	−0.490771	−	0.871289i	$-0.663285\pi$
$103$	3.86184	−	3.86184i	0.380518	−	0.380518i	0.871289	+	0.490771i	$0.163285\pi$
$104$	−7.56351	−	6.84057i	−0.741663	−	0.670773i
$105$	1.22328	+	1.22328i	0.119380	+	0.119380i
$106$	3.31376	−	17.1204i	0.321861	−	1.66288i
$107$	1.96613	+	4.74665i	0.190073	+	0.458876i	0.989973	−	0.141257i	$-0.0451143\pi$
$107$	1.96613	+	4.74665i	0.190073	+	0.458876i	−0.799900	+	0.600133i	$0.795114\pi$
$108$	−3.76343	−	3.68658i	−0.362136	−	0.354741i
$109$	3.12582	−	7.54639i	0.299399	−	0.722813i	−0.700559	−	0.713595i	$-0.747066\pi$
$109$	3.12582	−	7.54639i	0.299399	−	0.722813i	0.999958	−	0.00921806i	$-0.00293424\pi$
$110$	0.419031	+	2.05126i	0.0399531	+	0.195580i
$111$	−3.61126			−0.342766
$112$	7.02672	−	0.144985i	0.663963	−	0.0136998i
$113$		−	7.89937i		−	0.743111i	−0.928411	−	0.371555i	$-0.878825\pi$
$113$		−	7.89937i		−	0.743111i	0.928411	−	0.371555i	$-0.121175\pi$
$114$	1.07316	+	5.25338i	0.100510	+	0.492024i
$115$	−1.27049	+	3.06723i	−0.118474	+	0.286020i
$116$	−8.98704	+	0.0927066i	−0.834426	+	0.00860759i
$117$	9.80367	−	2.30607i	0.906350	−	0.213196i
$118$	2.77848	−	14.3549i	0.255780	−	1.32148i
$119$	4.00504	−	4.00504i	0.367141	−	0.367141i
$120$	−0.500970	+	2.73940i	−0.0457321	+	0.250072i
$121$	−7.44768	+	7.44768i	−0.677062	+	0.677062i
$122$	−11.6969	+	7.90320i	−1.05899	+	0.715522i
$123$	−0.701536	−	1.69366i	−0.0632554	−	0.152712i
$124$	−2.61259	+	1.11388i	−0.234617	+	0.100029i
$125$	10.6250	+	4.40103i	0.950331	+	0.393640i
$126$	−3.82630	+	5.79090i	−0.340874	+	0.515895i
$127$	−7.93901			−0.704473			−0.352236	−	0.935911i	$-0.614579\pi$
$127$	−7.93901			−0.704473			−0.352236	+	0.935911i	$0.614579\pi$
$128$	6.62101	+	9.17399i	0.585220	+	0.810874i
$129$	3.97517			0.349994
$130$	−8.11226	−	7.49043i	−0.711493	−	0.656954i
$131$	7.06489	−	17.0561i	0.617262	−	1.49020i	−0.237609	−	0.971361i	$-0.576364\pi$
$131$	7.06489	−	17.0561i	0.617262	−	1.49020i	0.854871	−	0.518841i	$-0.173636\pi$
$132$	0.571895	−	0.243828i	0.0497770	−	0.0212225i
$133$	13.5360	−	5.60679i	1.17372	−	0.486171i
$134$	6.67702	+	9.88214i	0.576806	+	0.853687i
$135$	−4.03332	−	4.03332i	−0.347133	−	0.347133i
$136$	8.96887	+	1.64019i	0.769075	+	0.140645i
$137$	4.54096	−	4.54096i	0.387960	−	0.387960i	−0.485999	−	0.873959i	$-0.661544\pi$
$137$	4.54096	−	4.54096i	0.387960	−	0.387960i	0.873959	+	0.485999i	$0.161544\pi$
$138$	0.967895	+	0.187342i	0.0823927	+	0.0159476i
$139$	6.18907	+	14.9417i	0.524950	+	1.26734i	0.934795	+	0.355187i	$0.115583\pi$
$139$	6.18907	+	14.9417i	0.524950	+	1.26734i	−0.409845	+	0.912155i	$0.634417\pi$
$140$	7.60913	−	0.0784926i	0.643089	−	0.00663383i
$141$	−1.78606	+	4.31193i	−0.150413	+	0.363130i
$142$	1.11759	+	5.47087i	0.0937858	+	0.459105i
$143$	−0.396790	+	2.43283i	−0.0331812	+	0.203444i
$144$	−11.1707	+	0.230488i	−0.930889	+	0.0192074i
$145$	−9.73089			−0.808106
$146$	2.26096	−	0.461868i	0.187118	−	0.0382244i
$147$	1.64365	+	0.680824i	0.135566	+	0.0561534i
$148$	−11.1157	+	11.3474i	−0.913702	+	0.932750i
$149$	12.4174	−	5.14345i	1.01727	−	0.421368i	0.189169	−	0.981944i	$-0.439420\pi$
$149$	12.4174	−	5.14345i	1.01727	−	0.421368i	0.828103	+	0.560577i	$0.189420\pi$
$150$	0.0379955	−	0.196302i	0.00310232	−	0.0160280i
$151$	12.9564	−	12.9564i	1.05438	−	1.05438i	0.0559418	−	0.998434i	$-0.482184\pi$
$151$	12.9564	−	12.9564i	1.05438	−	1.05438i	0.998434	−	0.0559418i	$-0.0178161\pi$
$152$	19.8105	+	12.7981i	1.60685	+	1.03806i
$153$	−6.36697	+	6.36697i	−0.514739	+	0.514739i
$154$	−0.951074	−	1.40761i	−0.0766397	−	0.113429i
$155$	−2.84097	+	1.17677i	−0.228192	+	0.0945203i
$156$	−1.69714	+	2.80538i	−0.135880	+	0.224610i
$157$	6.97926	−	16.8494i	0.557006	−	1.34473i	−0.355121	−	0.934821i	$-0.615560\pi$
$157$	6.97926	−	16.8494i	0.557006	−	1.34473i	0.912126	−	0.409910i	$-0.134440\pi$
$158$	−9.99636	+	15.1290i	−0.795268	+	1.20360i
$159$	−5.60657			−0.444630
$160$	7.06581	+	10.0062i	0.558601	+	0.791060i
$161$		−	2.69385i		−	0.212305i
$162$	5.59930	−	8.47423i	0.439922	−	0.665798i
$163$	3.58008	+	1.48292i	0.280413	+	0.116151i	0.518458	−	0.855103i	$-0.326506\pi$
$163$	3.58008	+	1.48292i	0.280413	+	0.116151i	−0.238044	+	0.971254i	$0.576506\pi$
$164$	−7.48122	−	3.00879i	−0.584185	−	0.234947i
$165$	0.621887	−	0.257594i	0.0484138	−	0.0200537i
$166$	2.76018	−	1.86496i	0.214231	−	0.144749i
$167$	0.118888	+	0.118888i	0.00919981	+	0.00919981i	0.711692	−	0.702492i	$-0.247929\pi$
$167$	0.118888	+	0.118888i	0.00919981	+	0.00919981i	−0.702492	+	0.711692i	$0.747929\pi$
$168$	−0.475074	−	2.20915i	−0.0366528	−	0.170440i
$169$	−5.79519	−	11.6368i	−0.445784	−	0.895141i
$170$	9.69187	+	1.87592i	0.743332	+	0.143876i
$171$	−21.5187	+	8.91334i	−1.64558	+	0.681620i
$172$	12.2358	−	12.4909i	0.932972	−	0.952421i
$173$	−13.4366	−	5.56564i	−1.02157	−	0.423148i	−0.191907	−	0.981413i	$-0.561467\pi$
$173$	−13.4366	−	5.56564i	−1.02157	−	0.423148i	−0.829662	+	0.558266i	$0.811467\pi$
$174$	0.578341	+	2.83113i	0.0438439	+	0.214627i
$175$	−0.546349			−0.0413001
$176$	0.994163	−	2.54754i	0.0749378	−	0.192028i
$177$	−4.70094			−0.353344
$178$	2.48250	+	12.1525i	0.186071	+	0.910866i
$179$	−4.85794	−	2.01223i	−0.363100	−	0.150401i	0.193672	−	0.981066i	$-0.437960\pi$
$179$	−4.85794	−	2.01223i	−0.363100	−	0.150401i	−0.556772	+	0.830666i	$0.687960\pi$
$180$	−12.0965	+	0.124783i	−0.901622	+	0.00930076i
$181$	8.81093	+	21.2715i	0.654912	+	1.58110i	0.805564	+	0.592509i	$0.201863\pi$
$181$	8.81093	+	21.2715i	0.654912	+	1.58110i	−0.150652	+	0.988587i	$0.548137\pi$
$182$	8.40724	+	3.09622i	0.623186	+	0.229507i
$183$	3.20931	+	3.20931i	0.237239	+	0.237239i
$184$	3.56791	−	2.46469i	0.263030	−	0.181700i
$185$	−12.1611	+	12.1611i	−0.894105	+	0.894105i
$186$	0.511220	+	0.756618i	0.0374845	+	0.0554779i
$187$	−0.843368	−	2.03607i	−0.0616732	−	0.148892i
$188$	8.05145	+	18.8846i	0.587212	+	1.37730i
$189$	4.27598	+	1.77117i	0.311032	+	0.128834i
$190$	21.3050	+	14.0772i	1.54563	+	1.02126i
$191$	−3.36201			−0.243267			−0.121633	−	0.992575i	$-0.538813\pi$
$191$	−3.36201			−0.243267			−0.121633	+	0.992575i	$0.538813\pi$
$192$	2.49128	−	2.65045i	0.179793	−	0.191279i
$193$		−	17.0821i		−	1.22960i	−0.788685	−	0.614798i	$-0.789238\pi$
$193$		−	17.0821i		−	1.22960i	0.788685	−	0.614798i	$-0.210762\pi$
$194$	−4.44578	+	6.72844i	−0.319188	+	0.483074i
$195$	−1.86875	+	3.01830i	−0.133824	+	0.216145i
$196$	7.19856	−	3.06911i	0.514183	−	0.219222i
$197$	−0.911191	−	2.19981i	−0.0649196	−	0.156730i	0.888090	−	0.459669i	$-0.152032\pi$
$197$	−0.911191	−	2.19981i	−0.0649196	−	0.156730i	−0.953010	+	0.302939i	$0.902032\pi$
$198$	1.51196	+	2.23774i	0.107450	+	0.159029i
$199$	10.2786	−	10.2786i	0.728634	−	0.728634i	−0.241714	−	0.970348i	$-0.577710\pi$
$199$	10.2786	−	10.2786i	0.728634	−	0.728634i	0.970348	+	0.241714i	$0.0777096\pi$
$200$	−0.499873	−	0.723620i	−0.0353464	−	0.0511677i
$201$	2.71139	−	2.71139i	0.191247	−	0.191247i
$202$	3.31784	+	0.642189i	0.233443	+	0.0451843i
$203$	7.29475	−	3.02158i	0.511991	−	0.212074i
$204$	−0.0302377	−	2.93127i	−0.00211706	−	0.205230i
$205$	−8.06596	−	3.34103i	−0.563351	−	0.233348i
$206$	−7.56739	+	1.54586i	−0.527245	+	0.107705i
$207$			4.28252i			0.297656i
$208$	3.59124	+	13.9679i	0.249007	+	0.968502i
$209$		−	5.70074i		−	0.394328i
$210$	−0.489669	−	2.39705i	−0.0337903	−	0.165412i
$211$	15.0726	+	6.24330i	1.03764	+	0.429806i	0.835466	−	0.549543i	$-0.185198\pi$
$211$	15.0726	+	6.24330i	1.03764	+	0.429806i	0.202178	+	0.979349i	$0.435198\pi$
$212$	−17.2573	+	17.6171i	−1.18524	+	1.20995i
$213$	1.65862	−	0.687022i	0.113647	−	0.0470740i
$214$	1.38073	−	7.13346i	0.0943845	−	0.487634i
$215$	13.3866	−	13.3866i	0.912962	−	0.912962i
$216$	1.56639	+	7.28389i	0.106579	+	0.495606i
$217$	1.76433	−	1.76433i	0.119770	−	0.119770i
$218$	−9.57150	+	6.46713i	−0.648264	+	0.438009i
$219$	−0.283927	−	0.685460i	−0.0191860	−	0.0463191i
$220$	1.10479	−	2.74700i	0.0744846	−	0.185202i
$221$	9.88199	+	6.11833i	0.664735	+	0.411563i
$222$	4.26097	+	2.81541i	0.285978	+	0.188958i
$223$		−	10.4356i		−	0.698820i	−0.936970	−	0.349410i	$-0.886382\pi$
$223$		−	10.4356i		−	0.698820i	0.936970	−	0.349410i	$-0.113618\pi$
$224$	−8.40395	−	5.30710i	−0.561513	−	0.354596i
$225$	0.868553			0.0579035
$226$	−6.15851	+	9.32057i	−0.409658	+	0.619995i
$227$	13.9479	+	5.77742i	0.925756	+	0.383461i	0.794067	−	0.607830i	$-0.207960\pi$
$227$	13.9479	+	5.77742i	0.925756	+	0.383461i	0.131689	+	0.991291i	$0.457960\pi$
$228$	2.82941	−	7.03518i	0.187382	−	0.465916i
$229$	3.90762	+	9.43382i	0.258223	+	0.623404i	0.998821	−	0.0485433i	$-0.0154579\pi$
$229$	3.90762	+	9.43382i	0.258223	+	0.623404i	−0.740598	+	0.671948i	$0.765458\pi$
$230$	3.89033	−	2.62856i	0.256521	−	0.173322i
$231$	−0.386210	+	0.386210i	−0.0254108	+	0.0254108i
$232$	10.6762	+	6.89709i	0.700927	+	0.452816i
$233$	11.9643	+	11.9643i	0.783805	+	0.783805i	0.980471	−	0.196666i	$-0.0630115\pi$
$233$	11.9643	+	11.9643i	0.783805	+	0.783805i	−0.196666	+	0.980471i	$0.563011\pi$
$234$	−13.3653	−	4.92218i	−0.873719	−	0.321773i
$235$	8.50602	+	20.5354i	0.554872	+	1.33958i
$236$	−14.4698	+	14.7714i	−0.941901	+	0.961536i
$237$	5.38625	+	2.23106i	0.349875	+	0.144923i
$238$	−7.84800	+	1.60319i	−0.508710	+	0.103919i
$239$	−5.33984			−0.345406			−0.172703	−	0.984974i	$-0.555250\pi$
$239$	−5.33984			−0.345406			−0.172703	+	0.984974i	$0.555250\pi$
$240$	2.72679	−	2.84169i	0.176014	−	0.183430i
$241$	−16.8816			−1.08744			−0.543720	−	0.839267i	$-0.682984\pi$
$241$	−16.8816			−1.08744			−0.543720	+	0.839267i	$0.682984\pi$
$242$	14.5940	−	2.98125i	0.938135	−	0.191642i
$243$	−10.3178	−	4.27379i	−0.661890	−	0.274164i
$244$	19.9628	−	0.205928i	1.27799	−	0.0131832i
$245$	7.82782	−	3.24239i	0.500101	−	0.207149i
$246$	−0.492658	+	2.54530i	−0.0314107	+	0.162282i
$247$	17.5598	+	24.4040i	1.11730	+	1.55279i
$248$	3.95103	+	0.722546i	0.250891	+	0.0458817i
$249$	−0.757317	−	0.757317i	−0.0479930	−	0.0479930i
$250$	−9.10547	−	13.4763i	−0.575880	−	0.852316i
$251$	−7.47098	+	3.09458i	−0.471564	+	0.195328i	−0.605793	−	0.795622i	$-0.707144\pi$
$251$	−7.47098	+	3.09458i	−0.471564	+	0.195328i	0.134229	+	0.990950i	$0.457144\pi$
$252$	9.02941	−	3.84970i	0.568799	−	0.242508i
$253$	−0.968378	−	0.401115i	−0.0608814	−	0.0252179i
$254$	9.36733	+	6.18941i	0.587759	+	0.388358i
$255$		−	3.17388i		−	0.198756i
$256$	−0.659987	−	15.9864i	−0.0412492	−	0.999149i
$257$	15.2689			0.952449			0.476225	−	0.879324i	$-0.342005\pi$
$257$	15.2689			0.952449			0.476225	+	0.879324i	$0.342005\pi$
$258$	−4.69036	−	3.09912i	−0.292009	−	0.192943i
$259$	5.34038	−	12.8928i	0.331835	−	0.801120i
$260$	3.73207	+	15.1625i	0.231453	+	0.940341i
$261$	−11.5968	+	4.80353i	−0.717821	+	0.297331i
$262$	−21.6333	+	14.6168i	−1.33651	+	0.903031i
$263$	10.8884	−	10.8884i	0.671409	−	0.671409i	−0.286632	−	0.958041i	$-0.592536\pi$
$263$	10.8884	−	10.8884i	0.671409	−	0.671409i	0.958041	+	0.286632i	$0.0925356\pi$
$264$	−0.864878	−	0.158165i	−0.0532296	−	0.00973438i
$265$	−18.8805	+	18.8805i	−1.15982	+	1.15982i
$266$	−20.3425	−	3.93741i	−1.24728	−	0.241418i
$267$	3.68430	−	1.52609i	0.225475	−	0.0933949i
$268$	−0.173978	−	16.8656i	−0.0106274	−	1.03023i
$269$	−16.3947	−	6.79091i	−0.999603	−	0.414049i	−0.177951	−	0.984039i	$-0.556947\pi$
$269$	−16.3947	−	6.79091i	−0.999603	−	0.414049i	−0.821651	+	0.569990i	$0.806947\pi$
$270$	1.61451	+	7.90342i	0.0982558	+	0.480987i
$271$	11.3843			0.691546			0.345773	−	0.938318i	$-0.387617\pi$
$271$	11.3843			0.691546			0.345773	+	0.938318i	$0.387617\pi$
$272$	−9.30376	−	8.92759i	−0.564123	−	0.541315i
$273$	0.463678	−	2.84294i	0.0280630	−	0.172063i
$274$	−8.89815	+	1.81771i	−0.537557	+	0.109812i
$275$	−0.0813516	+	0.196400i	−0.00490569	+	0.0118434i
$276$	−0.995976	−	0.975638i	−0.0599507	−	0.0587265i
$277$	−1.64050	−	3.96053i	−0.0985684	−	0.237965i	0.866902	−	0.498479i	$-0.166108\pi$
$277$	−1.64050	−	3.96053i	−0.0985684	−	0.237965i	−0.965470	+	0.260514i	$0.916108\pi$
$278$	4.34632	−	22.4551i	0.260675	−	1.34677i
$279$	−2.80482	+	2.80482i	−0.167920	+	0.167920i
$280$	−9.03930	−	5.83961i	−0.540201	−	0.348984i
$281$	−9.42804	−	9.42804i	−0.562430	−	0.562430i	0.367567	−	0.929997i	$-0.380191\pi$
$281$	−9.42804	−	9.42804i	−0.562430	−	0.562430i	−0.929997	+	0.367567i	$0.880191\pi$
$282$	5.46906	−	3.69525i	0.325678	−	0.220049i
$283$	−25.8596	+	10.7114i	−1.53719	+	0.636726i	−0.980944	−	0.194291i	$-0.937759\pi$
$283$	−25.8596	+	10.7114i	−1.53719	+	0.636726i	−0.556248	+	0.831016i	$0.687759\pi$
$284$	2.94654	−	7.32644i	0.174845	−	0.434744i
$285$	3.14184	−	7.58507i	0.186106	−	0.449301i
$286$	2.36486	−	2.56118i	0.139837	−	0.151446i
$287$	7.08408			0.418160
$288$	13.3601	+	8.43691i	0.787251	+	0.497150i
$289$	6.60864			0.388743
$290$	11.4816	+	7.58639i	0.674222	+	0.445488i
$291$	2.39548	+	0.992239i	0.140425	+	0.0581661i
$292$	−3.02781	−	1.21772i	−0.177189	−	0.0712619i
$293$	−8.37974	−	20.2305i	−0.489550	−	1.18188i	−0.954947	−	0.296776i	$-0.904089\pi$
$293$	−8.37974	−	20.2305i	−0.489550	−	1.18188i	0.465398	−	0.885102i	$-0.345911\pi$
$294$	−1.40858	−	2.08474i	−0.0821503	−	0.121584i
$295$	−15.8307	+	15.8307i	−0.921699	+	0.921699i
$296$	21.9622	−	4.72293i	1.27652	−	0.274515i
$297$	1.27339	−	1.27339i	0.0738896	−	0.0738896i
$298$	−18.6614	−	3.61202i	−1.08102	−	0.209239i
$299$	5.38103	−	1.26575i	0.311193	−	0.0732003i
$300$	−0.197873	+	0.201997i	−0.0114242	+	0.0116623i
$301$	−5.87853	+	14.1920i	−0.338833	+	0.818015i
$302$	−25.3885	+	5.18634i	−1.46094	+	0.298441i
$303$		−	1.08652i		−	0.0624192i
$304$	−13.3970	−	30.5453i	−0.768373	−	1.75189i
$305$	21.6151			1.23768
$306$	12.4763	−	2.54865i	0.713221	−	0.145697i
$307$	−0.496395	+	1.19840i	−0.0283308	+	0.0683966i	−0.937412	−	0.348223i	$-0.886785\pi$
$307$	−0.496395	+	1.19840i	−0.0283308	+	0.0683966i	0.909081	+	0.416619i	$0.136785\pi$
$308$	0.0247815	+	2.40234i	0.00141206	+	0.136886i
$309$	0.950300	+	2.29423i	0.0540607	+	0.130514i
$310$	4.26953	+	0.826393i	0.242493	+	0.0469360i
$311$	15.3023	+	15.3023i	0.867716	+	0.867716i	0.992219	−	0.124503i	$-0.0397337\pi$
$311$	15.3023	+	15.3023i	0.867716	+	0.867716i	−0.124503	+	0.992219i	$0.539734\pi$
$312$	4.18961	−	1.98698i	0.237190	−	0.112491i
$313$	−3.69280	+	3.69280i	−0.208730	+	0.208730i	−0.803727	−	0.594998i	$-0.797153\pi$
$313$	−3.69280	+	3.69280i	−0.208730	+	0.208730i	0.594998	+	0.803727i	$0.297153\pi$
$314$	−21.3711	+	14.4397i	−1.20604	+	0.814878i
$315$	9.81872	−	4.06705i	0.553222	−	0.229152i
$316$	23.5897	−	10.0575i	1.32702	−	0.565777i
$317$	−22.3560	−	9.26016i	−1.25564	−	0.520102i	−0.347070	−	0.937839i	$-0.612823\pi$
$317$	−22.3560	−	9.26016i	−1.25564	−	0.520102i	−0.908568	+	0.417737i	$0.862823\pi$
$318$	6.61526	+	4.37099i	0.370965	+	0.245113i
$319$		−	3.07221i		−	0.172011i
$320$	−0.535998	−	17.3151i	−0.0299632	−	0.967943i
$321$	−2.33606			−0.130386
$322$	−2.10018	+	3.17851i	−0.117038	+	0.177131i
$323$	−24.8337	−	10.2864i	−1.38178	−	0.572353i
$324$	−13.2134	+	5.63352i	−0.734075	+	0.312974i
$325$	−0.256711	−	1.09135i	−0.0142398	−	0.0605370i
$326$	−3.06807	−	4.54081i	−0.169924	−	0.251492i
$327$	2.62616	+	2.62616i	0.145227	+	0.145227i
$328$	6.48146	+	9.38262i	0.357879	+	0.518068i
$329$	−12.7531	−	12.7531i	−0.703099	−	0.703099i
$330$	−0.934597	−	0.180897i	−0.0514479	−	0.00995805i
$331$	−18.6026	+	7.70544i	−1.02249	+	0.423529i	−0.829996	−	0.557769i	$-0.811657\pi$
$331$	−18.6026	+	7.70544i	−1.02249	+	0.423529i	−0.192494	+	0.981298i	$0.561657\pi$
$332$	−4.71072	+	0.0485939i	−0.258535	+	0.00266694i
$333$	−8.48981	+	20.4962i	−0.465239	+	1.12319i
$334$	−0.0475898	−	0.232964i	−0.00260400	−	0.0127472i
$335$		−	18.2615i		−	0.997734i
$336$	−1.16175	+	2.97698i	−0.0633788	+	0.162408i
$337$		−	6.47362i		−	0.352641i	−0.984333	−	0.176320i	$-0.943581\pi$
$337$		−	6.47362i		−	0.352641i	0.984333	−	0.176320i	$-0.0564195\pi$
$338$	−2.23449	+	18.2485i	−0.121540	+	0.992587i
$339$	3.31833	+	1.37450i	0.180227	+	0.0746525i
$340$	−9.97305	−	9.76939i	−0.540864	−	0.529820i
$341$	−0.371526	−	0.896944i	−0.0201193	−	0.0485722i
$342$	32.3392	+	6.25945i	1.74870	+	0.338472i
$343$	−13.5583	+	13.5583i	−0.732079	+	0.732079i
$344$	−24.1753	+	5.19886i	−1.30345	+	0.280304i
$345$	−1.06740	−	1.06740i	−0.0574669	−	0.0574669i
$346$	11.5150	+	17.0424i	0.619049	+	0.916207i
$347$	15.7116	−	6.50798i	0.843445	−	0.349367i	0.0812343	−	0.996695i	$-0.474114\pi$
$347$	15.7116	−	6.50798i	0.843445	−	0.349367i	0.762211	+	0.647328i	$0.224114\pi$
$348$	1.52481	−	3.79137i	0.0817384	−	0.203239i
$349$	13.5627	+	5.61784i	0.725993	+	0.300716i	0.714904	−	0.699222i	$-0.246470\pi$
$349$	13.5627	+	5.61784i	0.725993	+	0.300716i	0.0110887	+	0.999939i	$0.496470\pi$
$350$	0.644644	+	0.425945i	0.0344577	+	0.0227677i
$351$	−1.52881	+	9.37359i	−0.0816019	+	0.500325i
$352$	−3.15913	+	2.23080i	−0.168382	+	0.118902i
$353$		−	3.10476i		−	0.165250i	−0.996581	−	0.0826249i	$-0.973670\pi$
$353$		−	3.10476i		−	0.165250i	0.996581	−	0.0826249i	$-0.0263303\pi$
$354$	5.54669	+	3.66494i	0.294803	+	0.194790i
$355$	3.27191	−	7.89909i	0.173655	−	0.419240i
$356$	6.54517	−	16.2743i	0.346893	−	0.862534i
$357$	0.985538	+	2.37930i	0.0521602	+	0.125926i
$358$	4.16317	+	6.16160i	0.220031	+	0.325651i
$359$	8.90891	+	8.90891i	0.470194	+	0.470194i	0.901977	−	0.431783i	$-0.142115\pi$
$359$	8.90891	+	8.90891i	0.470194	+	0.470194i	−0.431783	+	0.901977i	$0.642115\pi$
$360$	14.3701	+	9.28346i	0.757372	+	0.489282i
$361$	−35.7309	−	35.7309i	−1.88057	−	1.88057i
$362$	6.18754	−	31.9677i	0.325210	−	1.68018i
$363$	−1.83268	−	4.42449i	−0.0961909	−	0.232225i
$364$	−7.50593	−	10.2077i	−0.393418	−	0.535030i
$365$	−3.26447	−	1.35219i	−0.170870	−	0.0707768i
$366$	−1.28466	−	6.28875i	−0.0671504	−	0.328718i
$367$			8.81129i			0.459945i	0.973197	+	0.229973i	$0.0738637\pi$
$367$			8.81129i			0.459945i	−0.973197	+	0.229973i	$0.926136\pi$
$368$	−6.13134	+	0.126510i	−0.319618	+	0.00659480i
$369$	−11.2618			−0.586268
$370$	23.8302	−	4.86802i	1.23887	−	0.253076i
$371$	8.29107	−	20.0164i	0.430451	−	1.03920i
$372$	−0.0133205	−	1.29130i	−0.000690637	−	0.0669508i
$373$	−6.61867	−	15.9789i	−0.342702	−	0.827355i	−0.997441	−	0.0714997i	$-0.977222\pi$
$373$	−6.61867	−	15.9789i	−0.342702	−	0.827355i	0.654739	−	0.755855i	$-0.272778\pi$
$374$	−0.592261	+	3.05989i	−0.0306251	+	0.158223i
$375$	−3.69753	+	3.69753i	−0.190940	+	0.190940i
$376$	5.22277	−	28.5592i	0.269344	−	1.47283i
$377$	9.46325	+	13.1517i	0.487382	+	0.677347i
$378$	−3.66444	−	5.42346i	−0.188479	−	0.278953i
$379$	7.52074	+	18.1567i	0.386315	+	0.932646i	0.990714	+	0.135964i	$0.0434132\pi$
$379$	7.52074	+	18.1567i	0.386315	+	0.932646i	−0.604399	+	0.796682i	$0.706587\pi$
$380$	−14.1632	−	33.2196i	−0.726558	−	1.70413i
$381$	1.38139	−	3.33498i	0.0707710	−	0.170856i
$382$	3.96688	+	2.62109i	0.202963	+	0.134107i
$383$		−	17.2273i		−	0.880276i	−0.897930	−	0.440138i	$-0.854930\pi$
$383$		−	17.2273i		−	0.880276i	0.897930	−	0.440138i	$-0.145070\pi$
$384$	−5.00583	+	1.18504i	−0.255453	+	0.0604739i
$385$			2.60117i			0.132568i
$386$	−13.3175	+	20.1554i	−0.677845	+	1.02588i
$387$	9.34534	−	22.5617i	0.475050	−	1.14687i
$388$	10.4913	−	4.47296i	0.532613	−	0.227080i
$389$	−26.9640	+	11.1689i	−1.36713	+	0.566284i	−0.941009	−	0.338383i	$-0.890120\pi$
$389$	−26.9640	+	11.1689i	−1.36713	+	0.566284i	−0.426121	+	0.904666i	$0.640120\pi$
$390$	4.55809	−	2.10442i	0.230808	−	0.106561i
$391$	−3.49469	+	3.49469i	−0.176734	+	0.176734i
$392$	−10.8864	−	1.99086i	−0.549847	−	0.100553i
$393$	5.93557	+	5.93557i	0.299410	+	0.299410i
$394$	−0.639890	+	3.30596i	−0.0322372	+	0.166552i
$395$	25.6518	−	10.6253i	1.29068	−	0.534617i
$396$	−0.0393961	−	3.81909i	−0.00197973	−	0.191916i
$397$	−4.00117	+	9.65968i	−0.200813	+	0.484805i	−0.991919	−	0.126874i	$-0.959506\pi$
$397$	−4.00117	+	9.65968i	−0.200813	+	0.484805i	0.791106	+	0.611679i	$0.209506\pi$
$398$	−20.1413	+	4.11446i	−1.00959	+	0.206239i
$399$			6.66173i			0.333503i
$400$	0.0256580	+	1.24352i	0.00128290	+	0.0621760i
$401$	−10.4665			−0.522674			−0.261337	−	0.965248i	$-0.584163\pi$
$401$	−10.4665			−0.522674			−0.261337	+	0.965248i	$0.584163\pi$
$402$	−5.31305	+	1.08535i	−0.264991	+	0.0541322i
$403$	4.35328	+	2.69529i	0.216852	+	0.134262i
$404$	−3.41410	−	3.34438i	−0.169858	−	0.166389i
$405$	−14.3684	+	5.95159i	−0.713972	+	0.295737i
$406$	−10.9629	−	2.12193i	−0.544077	−	0.105310i
$407$	−3.83949	−	3.83949i	−0.190316	−	0.190316i
$408$	−2.24959	+	3.48221i	−0.111372	+	0.172395i
$409$	22.0820	+	22.0820i	1.09189	+	1.09189i	0.995327	+	0.0965587i	$0.0307835\pi$
$409$	22.0820	+	22.0820i	1.09189	+	1.09189i	0.0965587	+	0.995327i	$0.469216\pi$
$410$	6.91239	+	10.2305i	0.341379	+	0.505249i
$411$	1.11741	+	2.69768i	0.0551180	+	0.133067i
$412$	10.1340	+	4.07571i	0.499269	+	0.200796i
$413$	6.95180	−	16.7831i	0.342076	−	0.825844i
$414$	3.33874	−	5.05300i	0.164090	−	0.248341i
$415$	−5.10063			−0.250380
$416$	6.65233	−	19.2807i	0.326157	−	0.945316i
$417$	−7.35357			−0.360106
$418$	−4.44441	+	6.72637i	−0.217383	+	0.328997i
$419$	−5.19959	+	12.5529i	−0.254016	+	0.613250i	−0.998521	−	0.0543676i	$-0.982686\pi$
$419$	−5.19959	+	12.5529i	−0.254016	+	0.613250i	0.744505	+	0.667617i	$0.232686\pi$
$420$	−1.29102	+	3.21006i	−0.0629954	+	0.156635i
$421$	4.21285	+	10.1707i	0.205322	+	0.495690i	0.992676	−	0.120811i	$-0.0385496\pi$
$421$	4.21285	+	10.1707i	0.205322	+	0.495690i	−0.787354	+	0.616501i	$0.788550\pi$
$422$	−12.9170	−	19.1175i	−0.628790	−	0.930624i
$423$	20.2741	+	20.2741i	0.985758	+	0.985758i
$424$	34.0968	−	7.33246i	1.65589	−	0.356096i
$425$	0.708772	+	0.708772i	0.0343805	+	0.0343805i
$426$	−2.49264	−	0.482465i	−0.120769	−	0.0233755i
$427$	−16.2038	+	6.71182i	−0.784155	+	0.324808i
$428$	−7.19053	+	7.34042i	−0.347567	+	0.354813i
$429$	−0.952932	−	0.589997i	−0.0460080	−	0.0284853i
$430$	−26.2316	+	5.35857i	−1.26500	+	0.258413i
$431$	−22.3780			−1.07791			−0.538956	−	0.842334i	$-0.681181\pi$
$431$	−22.3780			−1.07791			−0.538956	+	0.842334i	$0.681181\pi$
$432$	3.83046	−	9.81553i	0.184293	−	0.472250i
$433$		−	14.4868i		−	0.696192i	−0.937459	−	0.348096i	$-0.886828\pi$
$433$		−	14.4868i		−	0.696192i	0.937459	−	0.348096i	$-0.113172\pi$
$434$	−3.45725	+	0.706246i	−0.165953	+	0.0339009i
$435$	1.69318	−	4.08771i	0.0811819	−	0.195991i
$436$	16.3354	−	0.168510i	0.782325	−	0.00807014i
$437$	−11.8112	+	4.89235i	−0.565005	+	0.234033i
$438$	−0.199390	+	1.03014i	−0.00952720	+	0.0492219i
$439$	16.2539	+	16.2539i	0.775758	+	0.775758i	0.979106	−	0.203348i	$-0.0651824\pi$
$439$	16.2539	+	16.2539i	0.775758	+	0.775758i	−0.203348	+	0.979106i	$0.565182\pi$
$440$	−3.44516	+	2.37990i	−0.164242	+	0.113457i
$441$	7.72822	−	7.72822i	0.368010	−	0.368010i
$442$	−6.88992	−	14.9233i	−0.327720	−	0.709828i
$443$	−6.94725	+	2.87765i	−0.330074	+	0.136721i	−0.541565	−	0.840659i	$-0.682168\pi$
$443$	−6.94725	+	2.87765i	−0.330074	+	0.136721i	0.211491	+	0.977380i	$0.432168\pi$
$444$	−2.83262	−	6.64388i	−0.134430	−	0.315304i
$445$	7.26791	−	17.5463i	0.344532	−	0.831774i
$446$	−8.13580	+	12.3131i	−0.385241	+	0.583042i
$447$			6.11120i			0.289050i
$448$	5.77840	+	12.8138i	0.273004	+	0.605395i
$449$			40.5466i			1.91351i	0.290888	+	0.956757i	$0.406049\pi$
$449$			40.5466i			1.91351i	−0.290888	+	0.956757i	$0.593951\pi$
$450$	−1.02482	−	0.677141i	−0.0483103	−	0.0319207i
$451$	1.05482	−	2.54657i	0.0496696	−	0.119913i
$452$	14.5330	−	6.19616i	0.683575	−	0.291443i
$453$	3.18824	+	7.69708i	0.149796	+	0.361641i
$454$	−11.9531	−	17.6909i	−0.560988	−	0.830276i
$455$	−8.01232	−	11.1353i	−0.375624	−	0.522029i
$456$	−8.82322	+	6.09504i	−0.413185	+	0.285426i
$457$	24.7168	−	24.7168i	1.15620	−	1.15620i	0.170916	−	0.985286i	$-0.445327\pi$
$457$	24.7168	−	24.7168i	1.15620	−	1.15620i	0.985286	−	0.170916i	$-0.0546728\pi$
$458$	2.74415	−	14.1775i	0.128226	−	0.662473i
$459$	−3.24946	−	7.84489i	−0.151672	−	0.366168i
$460$	−6.63953	+	0.0684907i	−0.309570	+	0.00319339i
$461$	11.4592	−	27.6651i	0.533710	−	1.28849i	−0.395339	−	0.918535i	$-0.629373\pi$
$461$	11.4592	−	27.6651i	0.533710	−	1.28849i	0.929050	−	0.369955i	$-0.120627\pi$
$462$	0.756791	−	0.154597i	0.0352091	−	0.00719250i
$463$	9.91349			0.460719			0.230360	−	0.973106i	$-0.426010\pi$
$463$	9.91349			0.460719			0.230360	+	0.973106i	$0.426010\pi$
$464$	−7.21987	−	16.4613i	−0.335174	−	0.764198i
$465$		−	1.39818i		−	0.0648390i
$466$	−4.78920	−	23.4443i	−0.221855	−	1.08604i
$467$	24.6502	+	10.2104i	1.14067	+	0.472483i	0.871396	−	0.490580i	$-0.163215\pi$
$467$	24.6502	+	10.2104i	1.14067	+	0.472483i	0.269278	+	0.963063i	$0.413215\pi$
$468$	11.9325	+	16.2276i	0.551579	+	0.750122i
$469$	5.67048	+	13.6897i	0.261838	+	0.632134i
$470$	5.97341	−	30.8614i	0.275533	−	1.42353i
$471$	5.86363	+	5.86363i	0.270182	+	0.270182i
$472$	28.5891	−	6.14804i	1.31592	−	0.282987i
$473$	4.22640	+	4.22640i	0.194330	+	0.194330i
$474$	−4.61593	−	6.83168i	−0.212016	−	0.313789i
$475$	0.992234	+	2.39547i	0.0455268	+	0.109911i
$476$	10.5098	+	4.22684i	0.481717	+	0.193737i
$477$	−13.1806	+	31.8209i	−0.603500	+	1.45698i
$478$	6.30054	+	4.16305i	0.288180	+	0.190413i
$479$			41.4247i			1.89274i	0.323081	+	0.946371i	$0.395281\pi$
$479$			41.4247i			1.89274i	−0.323081	+	0.946371i	$0.604719\pi$
$480$	−5.43282	+	1.22708i	−0.247973	+	0.0560084i
$481$	28.2630	+	4.60963i	1.28868	+	0.210181i
$482$	19.9188	+	13.1612i	0.907277	+	0.599477i
$483$	1.13162	+	0.468732i	0.0514905	+	0.0213281i
$484$	−19.5438	−	7.86013i	−0.888356	−	0.357279i
$485$	11.4083	−	4.72549i	0.518026	−	0.214574i
$486$	8.84221	+	13.0867i	0.401091	+	0.593624i
$487$	7.64611	+	7.64611i	0.346478	+	0.346478i	0.858796	−	0.512318i	$-0.171213\pi$
$487$	7.64611	+	7.64611i	0.346478	+	0.346478i	−0.512318	+	0.858796i	$0.671213\pi$
$488$	−23.7149	−	15.3204i	−1.07352	−	0.693524i
$489$	−1.24587	+	1.24587i	−0.0563404	+	0.0563404i
$490$	−11.7640	−	2.27699i	−0.531442	−	0.102864i
$491$	6.60247	+	15.9398i	0.297965	+	0.719351i	0.999974	+	0.00718339i	$0.00228656\pi$
$491$	6.60247	+	15.9398i	0.297965	+	0.719351i	−0.702009	+	0.712168i	$0.747713\pi$
$492$	2.56566	−	2.61914i	0.115669	−	0.118080i
$493$	−13.3832	−	5.54352i	−0.602751	−	0.249668i
$494$	−1.69318	−	42.4846i	−0.0761798	−	1.91147i
$495$		−	4.13519i		−	0.185863i
$496$	−4.09856	−	3.93284i	−0.184031	−	0.176590i
$497$			6.93752i			0.311190i
$498$	0.303148	+	1.48399i	0.0135844	+	0.0664991i
$499$	0.620608	−	1.49828i	0.0277823	−	0.0670723i	−0.909380	−	0.415967i	$-0.863443\pi$
$499$	0.620608	−	1.49828i	0.0277823	−	0.0670723i	0.937162	+	0.348895i	$0.113443\pi$
$500$	0.237255	+	22.9997i	0.0106104	+	1.02858i
$501$	−0.0706284	+	0.0292552i	−0.00315544	+	0.00130703i
$502$	11.2277	+	2.17319i	0.501116	+	0.0969942i
$503$	−6.70523	−	6.70523i	−0.298971	−	0.298971i	0.541640	−	0.840611i	$-0.317804\pi$
$503$	−6.70523	−	6.70523i	−0.298971	−	0.298971i	−0.840611	+	0.541640i	$0.817804\pi$
$504$	−13.6552	−	2.49720i	−0.608251	−	0.111234i
$505$	−3.65894	−	3.65894i	−0.162821	−	0.162821i
$506$	0.829883	+	1.22825i	0.0368928	+	0.0546022i
$507$	5.89671	−	0.409597i	0.261882	−	0.0181909i
$508$	−6.22724	−	14.6059i	−0.276289	−	0.648033i
$509$	10.8701	+	4.50253i	0.481807	+	0.199571i	0.610348	−	0.792133i	$-0.291029\pi$
$509$	10.8701	+	4.50253i	0.481807	+	0.199571i	−0.128541	+	0.991704i	$0.541029\pi$
$510$	−2.47442	+	3.74490i	−0.109569	+	0.165827i
$511$	2.86708			0.126832
$512$	−11.6846	+	19.3771i	−0.516390	+	0.856353i
$513$		−	21.9647i		−	0.969763i
$514$	−18.0160	−	11.9040i	−0.794651	−	0.525061i
$515$	10.9261	+	4.52576i	0.481463	+	0.199429i
$516$	3.11807	+	7.31339i	0.137265	+	0.321954i
$517$	−6.48337	+	2.68550i	−0.285138	+	0.118108i
$518$	−16.3527	+	11.0489i	−0.718495	+	0.485462i
$519$	4.67598	−	4.67598i	0.205253	−	0.205253i
$520$	7.41750	−	20.8001i	0.325279	−	0.912143i
$521$	−4.70225	−	4.70225i	−0.206009	−	0.206009i	0.596560	−	0.802569i	$-0.296534\pi$
$521$	−4.70225	−	4.70225i	−0.206009	−	0.206009i	−0.802569	+	0.596560i	$0.796534\pi$
$522$	17.4281	+	3.37331i	0.762807	+	0.147646i
$523$	15.9562	+	38.5217i	0.697717	+	1.68444i	0.728623	+	0.684915i	$0.240160\pi$
$523$	15.9562	+	38.5217i	0.697717	+	1.68444i	−0.0309068	+	0.999522i	$0.509840\pi$
$524$	36.9209	−	0.380861i	1.61290	−	0.0166380i
$525$	0.0950653	−	0.229508i	0.00414899	−	0.0100165i
$526$	−21.3362	+	4.35855i	−0.930303	+	0.190042i
$527$	−4.57767			−0.199407
$528$	0.897172	+	0.860897i	0.0390444	+	0.0374657i
$529$		−	20.6494i		−	0.897801i
$530$	36.9969	−	7.55771i	1.60704	−	0.328286i
$531$	−11.0516	+	26.6808i	−0.479597	+	1.15785i
$532$	20.9326	+	20.5052i	0.907545	+	0.889012i
$533$	3.32858	+	14.1506i	0.144177	+	0.612932i
$534$	−5.53691	−	1.07170i	−0.239606	−	0.0463771i
$535$	−7.86683	+	7.86683i	−0.340113	+	0.340113i
$536$	−12.9435	+	20.0356i	−0.559073	+	0.865404i
$537$	1.69057	−	1.69057i	0.0729536	−	0.0729536i
$538$	14.0500	+	20.7943i	0.605738	+	0.896506i
$539$	1.02368	+	2.47138i	0.0440930	+	0.106450i
$540$	4.25669	−	10.5840i	0.183179	−	0.455465i
$541$	−35.1528	−	14.5608i	−1.51134	−	0.626016i	−0.535504	−	0.844533i	$-0.679878\pi$
$541$	−35.1528	−	14.5608i	−1.51134	−	0.626016i	−0.975833	+	0.218516i	$0.929878\pi$
$542$	−13.4325	−	8.87541i	−0.576973	−	0.381232i
$543$	−10.4687			−0.449256
$544$	4.01750	+	17.7872i	0.172249	+	0.762619i
$545$	17.6875			0.757649
$546$	−2.76351	+	2.99293i	−0.118267	+	0.128086i
$547$	−10.9195	+	26.3621i	−0.466885	+	1.12716i	0.498630	+	0.866815i	$0.333837\pi$
$547$	−10.9195	+	26.3621i	−0.466885	+	1.12716i	−0.965515	+	0.260346i	$0.916163\pi$
$548$	11.9162	+	4.79244i	0.509033	+	0.204723i
$549$	25.7598	−	10.6700i	1.09940	−	0.455386i
$550$	0.249105	−	0.168312i	0.0106219	−	0.00717683i
$551$	−26.4962	−	26.4962i	−1.12878	−	1.12878i
$552$	0.414538	+	1.92765i	0.0176439	+	0.0820462i
$553$	−15.9305	+	15.9305i	−0.677434	+	0.677434i
$554$	−1.15206	+	5.95205i	−0.0489461	+	0.252878i
$555$	−2.99255	−	7.22465i	−0.127027	−	0.306669i
$556$	−22.6347	+	23.1065i	−0.959925	+	0.979936i
$557$	9.95797	−	24.0407i	0.421933	−	1.01864i	−0.559844	−	0.828598i	$-0.689139\pi$
$557$	9.95797	−	24.0407i	0.421933	−	1.01864i	0.981777	−	0.190037i	$-0.0608609\pi$
$558$	5.49613	−	1.12275i	0.232670	−	0.0475297i
$559$	−31.1111	−	5.07415i	−1.31586	−	0.214614i
$560$	6.11290	+	13.9374i	0.258317	+	0.588964i
$561$	1.00205			0.0423066
$562$	3.77397	+	18.4745i	0.159195	+	0.779302i
$563$	−31.8752	−	13.2032i	−1.34338	−	0.556447i	−0.408939	−	0.912562i	$-0.634101\pi$
$563$	−31.8752	−	13.2032i	−1.34338	−	0.556447i	−0.934442	+	0.356115i	$0.884101\pi$
$564$	−9.33390	+	0.0962846i	−0.393028	+	0.00405431i
$565$	15.8034	−	6.54598i	0.664854	−	0.275392i
$566$	38.8628	+	7.52214i	1.63353	+	0.316179i
$567$	8.92320	−	8.92320i	0.374739	−	0.374739i
$568$	−9.18850	+	6.34737i	−0.385541	+	0.266330i
$569$	−19.2168	+	19.2168i	−0.805608	+	0.805608i	−0.983966	−	0.178357i	$-0.942922\pi$
$569$	−19.2168	+	19.2168i	−0.805608	+	0.805608i	0.178357	+	0.983966i	$0.442922\pi$
$570$	−9.62056	+	6.50027i	−0.402961	+	0.272267i
$571$	−12.9031	+	5.34463i	−0.539977	+	0.223666i	−0.635967	−	0.771716i	$-0.719398\pi$
$571$	−12.9031	+	5.34463i	−0.539977	+	0.223666i	0.0959895	+	0.995382i	$0.469398\pi$
$572$	−4.78708	+	1.17828i	−0.200158	+	0.0492663i
$573$	0.584993	−	1.41230i	0.0244384	−	0.0589996i
$574$	−8.35859	−	5.52289i	−0.348881	−	0.230521i
$575$	0.476731			0.0198810
$576$	−9.18616	−	20.3706i	−0.382756	−	0.848776i
$577$			14.8820i			0.619545i	0.950811	+	0.309772i	$0.100253\pi$
$577$			14.8820i			0.619545i	−0.950811	+	0.309772i	$0.899747\pi$
$578$	−7.79761	−	5.15222i	−0.324338	−	0.214304i
$579$	7.17577	+	2.97230i	0.298215	+	0.123525i
$580$	−7.63277	−	17.9026i	−0.316934	−	0.743363i
$581$	3.82368	−	1.58382i	0.158633	−	0.0657079i
$582$	−2.05288	−	3.03832i	−0.0850948	−	0.125942i
$583$	−5.96090	−	5.96090i	−0.246875	−	0.246875i
$584$	2.62319	+	3.79735i	0.108548	+	0.157135i
$585$	12.7375	+	17.7022i	0.526631	+	0.731894i
$586$	−5.88473	+	30.4032i	−0.243096	+	1.25594i
$587$	19.1796	−	7.94445i	0.791627	−	0.327903i	0.0500294	−	0.998748i	$-0.484068\pi$
$587$	19.1796	−	7.94445i	0.791627	−	0.327903i	0.741597	+	0.670845i	$0.234068\pi$
$588$	0.0367025	+	3.55797i	0.00151359	+	0.146728i
$589$	−10.9399	−	4.53146i	−0.450771	−	0.186715i
$590$	31.0208	−	6.33691i	1.27710	−	0.260886i
$591$	1.08263			0.0445336
$592$	−29.5955	−	11.5495i	−1.21637	−	0.474681i
$593$	16.5993			0.681652			0.340826	−	0.940126i	$-0.389293\pi$
$593$	16.5993			0.681652			0.340826	+	0.940126i	$0.389293\pi$
$594$	−2.49525	+	0.509728i	−0.102381	+	0.0209144i
$595$	11.3313	+	4.69358i	0.464538	+	0.192418i
$596$	19.2028	+	18.8106i	0.786576	+	0.770514i
$597$	2.52931	+	6.10630i	0.103518	+	0.249914i
$598$	−7.33595	−	2.70168i	−0.299989	−	0.110480i
$599$	−12.5536	−	12.5536i	−0.512927	−	0.512927i	0.402495	−	0.915422i	$-0.368143\pi$
$599$	−12.5536	−	12.5536i	−0.512927	−	0.512927i	−0.915422	+	0.402495i	$0.868143\pi$
$600$	0.390953	−	0.0840739i	0.0159606	−	0.00343230i
$601$	−5.61813	+	5.61813i	−0.229168	+	0.229168i	−0.812345	−	0.583177i	$-0.801809\pi$
$601$	−5.61813	+	5.61813i	−0.229168	+	0.229168i	0.583177	+	0.812345i	$0.301809\pi$
$602$	18.0005	−	12.1623i	0.733648	−	0.495700i
$603$	−9.01459	−	21.7631i	−0.367102	−	0.886264i
$604$	33.9995	+	13.6739i	1.38342	+	0.556384i
$605$	−21.0714	−	8.72807i	−0.856675	−	0.354846i
$606$	−0.847076	+	1.28200i	−0.0344101	+	0.0520778i
$607$	17.5376			0.711830			0.355915	−	0.934518i	$-0.384169\pi$
$607$	17.5376			0.711830			0.355915	+	0.934518i	$0.384169\pi$
$608$	−8.00641	+	46.4854i	−0.324703	+	1.88523i
$609$			3.59010i			0.145478i
$610$	−25.5039	−	16.8516i	−1.03262	−	0.682300i
$611$	19.4823	−	31.4668i	0.788170	−	1.27301i
$612$	−16.7079	−	6.71957i	−0.675376	−	0.271623i
$613$	−6.21641	−	15.0077i	−0.251079	−	0.606157i	0.747213	−	0.664585i	$-0.231391\pi$
$613$	−6.21641	−	15.0077i	−0.251079	−	0.606157i	−0.998292	+	0.0584272i	$0.981391\pi$
$614$	1.52000	−	1.02701i	0.0613423	−	0.0414469i
$615$	2.80697	−	2.80697i	0.113188	−	0.113188i
$616$	1.84367	−	2.85386i	0.0742835	−	0.114985i
$617$	9.76163	−	9.76163i	0.392988	−	0.392988i	−0.482763	−	0.875751i	$-0.660367\pi$
$617$	9.76163	−	9.76163i	0.392988	−	0.392988i	0.875751	+	0.482763i	$0.160367\pi$
$618$	0.667354	−	3.44786i	0.0268449	−	0.138693i
$619$	23.0683	−	9.55522i	0.927195	−	0.384057i	0.132581	−	0.991172i	$-0.457673\pi$
$619$	23.0683	−	9.55522i	0.927195	−	0.384057i	0.794614	+	0.607115i	$0.207673\pi$
$620$	−4.39339	−	4.30368i	−0.176443	−	0.172840i
$621$	−3.73111	−	1.54548i	−0.149724	−	0.0620179i
$622$	−6.12541	−	29.9854i	−0.245607	−	1.20231i
$623$			15.4103i			0.617403i
$624$	−6.49246	−	0.921843i	−0.259906	−	0.0369032i
$625$			23.3486i			0.933943i
$626$	7.23617	−	1.47820i	0.289215	−	0.0590808i
$627$	2.39474	+	0.991933i	0.0956367	+	0.0396140i
$628$	36.4734	−	0.376245i	1.45545	−	0.0150138i
$629$	−23.6537	+	9.79767i	−0.943134	+	0.390659i
$630$	−14.7560	−	2.85611i	−0.587892	−	0.113790i
$631$	0.978585	−	0.978585i	0.0389568	−	0.0389568i	−0.687360	−	0.726317i	$-0.741231\pi$
$631$	0.978585	−	0.978585i	0.0389568	−	0.0389568i	0.726317	+	0.687360i	$0.241231\pi$
$632$	−35.6747	−	6.52403i	−1.41907	−	0.259512i
$633$	−5.24531	+	5.24531i	−0.208482	+	0.208482i
$634$	19.1587	+	28.3553i	0.760890	+	1.12613i
$635$	−6.57883	−	15.8827i	−0.261073	−	0.630285i
$636$	−4.39772	−	10.3148i	−0.174381	−	0.409008i
$637$	−11.9948	−	7.42642i	−0.475250	−	0.294245i
$638$	−2.39516	+	3.62494i	−0.0948252	+	0.143513i
$639$		−	11.0289i		−	0.436295i
$640$	−12.8668	+	20.8482i	−0.508603	+	0.824096i
$641$	−31.5471			−1.24604			−0.623018	−	0.782207i	$-0.714094\pi$
$641$	−31.5471			−1.24604			−0.623018	+	0.782207i	$0.714094\pi$
$642$	2.75635	+	1.82124i	0.108784	+	0.0718786i
$643$	−27.9498	−	11.5772i	−1.10223	−	0.456559i	−0.243976	−	0.969781i	$-0.578452\pi$
$643$	−27.9498	−	11.5772i	−1.10223	−	0.456559i	−0.858256	+	0.513222i	$0.828452\pi$
$644$	4.95605	−	2.11302i	0.195296	−	0.0832645i
$645$	3.29411	+	7.95269i	0.129706	+	0.313137i
$646$	21.2820	+	31.4979i	0.837331	+	1.23927i
$647$	−9.78790	+	9.78790i	−0.384802	+	0.384802i	−0.872829	−	0.488027i	$-0.837717\pi$
$647$	−9.78790	+	9.78790i	−0.384802	+	0.384802i	0.488027	+	0.872829i	$0.337717\pi$
$648$	19.9826	+	3.65433i	0.784991	+	0.143556i
$649$	−4.99803	−	4.99803i	−0.196190	−	0.196190i
$650$	−0.547938	+	1.48783i	−0.0214919	+	0.0583575i
$651$	0.434156	+	1.04814i	0.0170159	+	0.0410800i
$652$	0.0799425	+	7.74968i	0.00313079	+	0.303501i
$653$	18.3231	+	7.58966i	0.717037	+	0.297006i	0.711213	−	0.702977i	$-0.248146\pi$
$653$	18.3231	+	7.58966i	0.717037	+	0.297006i	0.00582405	+	0.999983i	$0.498146\pi$
$654$	−1.05123	−	5.14604i	−0.0411064	−	0.201226i
$655$	39.9768			1.56202
$656$	−0.332687	−	16.1237i	−0.0129892	−	0.629526i
$657$	−4.55792			−0.177821
$658$	5.10495	+	24.9900i	0.199012	+	0.974213i
$659$	−41.5018	−	17.1906i	−1.61668	−	0.669651i	−0.623034	−	0.782195i	$-0.714100\pi$
$659$	−41.5018	−	17.1906i	−1.61668	−	0.669651i	−0.993647	+	0.112544i	$0.964100\pi$
$660$	0.961712	+	0.942073i	0.0374346	+	0.0366701i
$661$	−6.49628	+	2.69085i	−0.252676	+	0.104662i	−0.505427	−	0.862870i	$-0.668665\pi$
$661$	−6.49628	+	2.69085i	−0.252676	+	0.104662i	0.252750	+	0.967532i	$0.418665\pi$
$662$	27.9567	+	5.41119i	1.08657	+	0.210312i
$663$	−4.28963	+	3.08659i	−0.166596	+	0.119873i
$664$	5.59613	+	3.61524i	0.217172	+	0.140298i
$665$	22.4338	+	22.4338i	0.869945	+	0.869945i
$666$	25.9965	−	17.5649i	1.00734	−	0.680627i
$667$	−6.36522	+	2.63656i	−0.246462	+	0.102088i
$668$	−0.125472	+	0.311979i	−0.00485465	+	0.0120708i
$669$	4.38374	+	1.81580i	0.169485	+	0.0702031i
$670$	−14.2371	+	21.5470i	−0.550026	+	0.832434i
$671$			6.82427i			0.263448i
$672$	3.69168	−	2.60685i	0.142410	−	0.100562i
$673$	9.97848			0.384642			0.192321	−	0.981332i	$-0.438399\pi$
$673$	9.97848			0.384642			0.192321	+	0.981332i	$0.438399\pi$
$674$	−5.04697	+	7.63831i	−0.194402	+	0.294217i
$675$	−0.313444	+	0.756720i	−0.0120645	+	0.0291262i
$676$	16.8634	−	19.7896i	0.648591	−	0.761137i
$677$	22.2181	−	9.20304i	0.853911	−	0.353701i	0.0875878	−	0.996157i	$-0.472084\pi$
$677$	22.2181	−	9.20304i	0.853911	−	0.353701i	0.766323	+	0.642455i	$0.222084\pi$
$678$	−2.84376	−	4.20883i	−0.109214	−	0.161639i
$679$	−7.08492	+	7.08492i	−0.271894	+	0.271894i
$680$	4.15091	+	19.3022i	0.159180	+	0.740206i
$681$	−4.85390	+	4.85390i	−0.186002	+	0.186002i
$682$	−0.260907	+	1.34796i	−0.00999064	+	0.0516162i
$683$	30.7897	−	12.7535i	1.17813	−	0.487999i	0.294261	−	0.955725i	$-0.404927\pi$
$683$	30.7897	−	12.7535i	1.17813	−	0.487999i	0.883874	+	0.467726i	$0.154927\pi$
$684$	−33.2774	−	32.5979i	−1.27239	−	1.24641i
$685$	12.8476	+	5.32163i	0.490880	+	0.203329i
$686$	26.5679	−	5.42728i	1.01437	−	0.207215i
$687$	−4.64285			−0.177136
$688$	32.5779	+	12.7134i	1.24202	+	0.484692i
$689$	43.8790	+	7.15656i	1.67165	+	0.272643i
$690$	0.427272	+	2.09161i	0.0162660	+	0.0796261i
$691$	10.5495	−	25.4688i	0.401322	−	0.968878i	−0.586023	−	0.810294i	$-0.699307\pi$
$691$	10.5495	−	25.4688i	0.401322	−	0.968878i	0.987346	−	0.158583i	$-0.0506927\pi$
$692$	−0.300038	−	29.0859i	−0.0114057	−	1.10568i
$693$	1.28404	+	3.09994i	0.0487766	+	0.117757i
$694$	−23.6121	−	4.57027i	−0.896304	−	0.173485i
$695$	−24.7636	+	24.7636i	−0.939337	+	0.939337i
$696$	−4.75497	+	3.28471i	−0.180237	+	0.124507i
$697$	−9.19008	−	9.19008i	−0.348099	−	0.348099i
$698$	−11.6230	−	17.2023i	−0.439936	−	0.651116i
$699$	−7.10768	+	2.94410i	−0.268837	+	0.111356i
$700$	−0.428549	−	1.00515i	−0.0161976	−	0.0379913i
$701$	−5.92461	+	14.3033i	−0.223770	+	0.540227i	−0.995396	−	0.0958486i	$-0.969444\pi$
$701$	−5.92461	+	14.3033i	−0.223770	+	0.540227i	0.771626	+	0.636076i	$0.219444\pi$
$702$	9.11170	−	9.86812i	0.343899	−	0.372448i
$703$	−66.2272			−2.49781
$704$	5.46668	−	0.169224i	0.206033	−	0.00637787i
$705$	−10.1065			−0.380631
$706$	−2.42053	+	3.66335i	−0.0910980	+	0.137872i
$707$	3.87907	+	1.60677i	0.145888	+	0.0604286i
$708$	−3.68735	−	8.64862i	−0.138579	−	0.325035i
$709$	−6.99692	−	16.8921i	−0.262775	−	0.634395i	0.736333	−	0.676619i	$-0.236556\pi$
$709$	−6.99692	−	16.8921i	−0.262775	−	0.634395i	−0.999108	+	0.0422242i	$0.986556\pi$
$710$	−10.0188	+	6.76938i	−0.376001	+	0.254050i
$711$	25.3254	−	25.3254i	0.949775	−	0.949775i
$712$	−20.4105	+	14.0994i	−0.764914	+	0.528399i
$713$	−1.53951	+	1.53951i	−0.0576550	+	0.0576550i
$714$	0.692100	−	3.57571i	0.0259012	−	0.133817i
$715$	−5.19591	+	1.22221i	−0.194316	+	0.0457079i
$716$	−0.108477	−	10.5158i	−0.00405398	−	0.392995i
$717$	0.929137	−	2.24314i	0.0346993	−	0.0837714i
$718$	−3.56617	−	17.4573i	−0.133088	−	0.651500i
$719$			4.33751i			0.161762i	0.996724	+	0.0808808i	$0.0257733\pi$
$719$			4.33751i			0.161762i	−0.996724	+	0.0808808i	$0.974227\pi$
$720$	−9.71792	−	22.1569i	−0.362166	−	0.825739i
$721$	−9.59609			−0.357377
$722$	14.3028	+	70.0158i	0.532295	+	2.60572i
$723$	2.93741	−	7.09154i	0.109244	−	0.263737i
$724$	−32.2234	+	32.8951i	−1.19757	+	1.22254i
$725$	0.534730	+	1.29095i	0.0198594	+	0.0479448i
$726$	−1.28701	+	6.64931i	−0.0477656	+	0.246779i
$727$	23.7173	+	23.7173i	0.879627	+	0.879627i	0.993496	−	0.113869i	$-0.0363243\pi$
$727$	23.7173	+	23.7173i	0.879627	+	0.879627i	−0.113869	+	0.993496i	$0.536324\pi$
$728$	0.898203	+	17.8960i	0.0332896	+	0.663269i
$729$	−11.6449	+	11.6449i	−0.431292	+	0.431292i
$730$	2.79760	+	4.14051i	0.103544	+	0.153247i
$731$	26.0373	−	10.7850i	0.963024	−	0.398898i
$732$	−3.38704	+	8.42172i	−0.125189	+	0.311276i
$733$	−6.60993	−	2.73792i	−0.244143	−	0.101128i	0.257257	−	0.966343i	$-0.417181\pi$
$733$	−6.60993	−	2.73792i	−0.244143	−	0.101128i	−0.501400	+	0.865216i	$0.667181\pi$
$734$	6.86945	−	10.3965i	0.253556	−	0.383744i
$735$			3.85246i			0.142100i
$736$	7.33308	+	4.63084i	0.270301	+	0.170695i
$737$	5.76549			0.212375
$738$	13.2880	+	8.77996i	0.489138	+	0.323195i
$739$	−0.121215	−	0.0502091i	−0.00445898	−	0.00184697i	0.380453	−	0.924800i	$-0.375768\pi$
$739$	−0.121215	−	0.0502091i	−0.00445898	−	0.00184697i	−0.384912	+	0.922953i	$0.625768\pi$
$740$	−31.9127	−	12.8346i	−1.17313	−	0.471811i
$741$	−13.3070	+	3.13012i	−0.488843	+	0.114988i
$742$	−25.3879	+	17.1537i	−0.932020	+	0.629733i
$743$	−5.87765	−	5.87765i	−0.215630	−	0.215630i	0.591024	−	0.806654i	$-0.298724\pi$
$743$	−5.87765	−	5.87765i	−0.215630	−	0.215630i	−0.806654	+	0.591024i	$0.798724\pi$
$744$	−0.991007	+	1.53401i	−0.0363321	+	0.0562394i
$745$	20.5799	+	20.5799i	0.753988	+	0.753988i
$746$	−4.64800	+	24.0137i	−0.170175	+	0.879204i
$747$	−6.07866	+	2.51786i	−0.222406	+	0.0921238i
$748$	3.08437	−	3.14867i	0.112776	−	0.115127i
$749$	3.45459	−	8.34013i	0.126228	−	0.304742i
$750$	7.24542	−	1.48009i	0.264565	−	0.0540453i
$751$		−	41.9497i		−	1.53077i	−0.643575	−	0.765383i	$-0.722550\pi$
$751$		−	41.9497i		−	1.53077i	0.643575	−	0.765383i	$-0.277450\pi$
$752$	−28.4277	+	29.6256i	−1.03665	+	1.08033i
$753$		−	3.67683i		−	0.133991i
$754$	−0.912480	−	22.8956i	−0.0332306	−	0.833808i
$755$	36.6570	+	15.1838i	1.33408	+	0.552596i
$756$	0.0954819	+	9.25608i	0.00347264	+	0.336640i
$757$	−1.46723	−	3.54221i	−0.0533274	−	0.128744i	0.894971	−	0.446125i	$-0.147196\pi$
$757$	−1.46723	−	3.54221i	−0.0533274	−	0.128744i	−0.948298	+	0.317382i	$0.897196\pi$
$758$	5.28149	−	27.2866i	0.191832	−	0.991094i
$759$	0.336997	−	0.336997i	0.0122322	−	0.0122322i
$760$	−9.18733	+	50.2382i	−0.333259	+	1.82233i
$761$	8.63169	+	8.63169i	0.312898	+	0.312898i	0.846031	−	0.533133i	$-0.178985\pi$
$761$	8.63169	+	8.63169i	0.312898	+	0.312898i	−0.533133	+	0.846031i	$0.678985\pi$
$762$	−4.22994	+	2.85802i	−0.153235	+	0.103535i
$763$	−13.2594	+	5.49223i	−0.480023	+	0.198832i
$764$	−2.63711	−	6.18531i	−0.0954074	−	0.223777i
$765$	−18.0138	−	7.46157i	−0.651291	−	0.269773i
$766$	−13.4308	+	20.3267i	−0.485273	+	0.734435i
$767$	36.7912	+	6.00056i	1.32845	+	0.216667i
$768$	6.83032	+	2.50440i	0.246468	+	0.0903698i
$769$			0.0117627i			0.000424175i	1.00000		0.000212088i	$6.75096e-5\pi$
$769$			0.0117627i			0.000424175i	−1.00000		0.000212088i	$0.999932\pi$
$770$	2.02793	−	3.06916i	0.0730814	−	0.110605i
$771$	−2.65681	+	6.41410i	−0.0956825	+	0.230998i
$772$	31.4271	−	13.3990i	1.13108	−	0.482239i
$773$	−12.8782	−	31.0907i	−0.463196	−	1.11825i	−0.967078	−	0.254482i	$-0.918095\pi$
$773$	−12.8782	−	31.0907i	−0.463196	−	1.11825i	0.503881	−	0.863773i	$-0.331905\pi$
$774$	−28.6162	+	19.3350i	−1.02859	+	0.694981i
$775$	0.312233	+	0.312233i	0.0112157	+	0.0112157i
$776$	−15.8660	−	2.90149i	−0.569555	−	0.104158i
$777$	4.48672	+	4.48672i	0.160960	+	0.160960i
$778$	40.5226	+	7.84340i	1.45281	+	0.281200i
$779$	−12.8655	−	31.0601i	−0.460955	−	1.11284i
$780$	−7.01879	−	1.07055i	−0.251313	−	0.0383317i
$781$	2.49388	+	1.03300i	0.0892381	+	0.0369636i
$782$	6.84797	−	1.39890i	0.244883	−	0.0500246i
$783$		−	11.8371i		−	0.423023i
$784$	11.2929	+	10.8363i	0.403318	+	0.387011i
$785$	39.4923			1.40954
$786$	−2.37596	−	11.6309i	−0.0847478	−	0.414862i
$787$	11.5867	−	27.9729i	0.413023	−	0.997126i	−0.571299	−	0.820742i	$-0.693560\pi$
$787$	11.5867	−	27.9729i	0.413023	−	0.997126i	0.984322	−	0.176383i	$-0.0564398\pi$
$788$	3.33241	−	3.40188i	0.118712	−	0.121187i
$789$	2.67936	+	6.46856i	0.0953879	+	0.230287i
$790$	−38.5505	−	7.46169i	−1.37157	−	0.265475i
$791$	−9.81438	+	9.81438i	−0.348959	+	0.348959i
$792$	−2.93095	+	4.53690i	−0.104147	+	0.161212i
$793$	−21.0206	−	29.2137i	−0.746464	−	1.03741i
$794$	12.2519	−	8.27818i	0.434804	−	0.293782i
$795$	−4.64600	−	11.2164i	−0.164777	−	0.397806i
$796$	26.9727	+	10.8479i	0.956023	+	0.384493i
$797$	5.29111	−	12.7739i	0.187421	−	0.452474i	−0.802041	−	0.597269i	$-0.796252\pi$
$797$	5.29111	−	12.7739i	0.187421	−	0.452474i	0.989462	+	0.144795i	$0.0462524\pi$
$798$	5.19361	−	7.86025i	0.183852	−	0.278250i
$799$			33.0888i			1.17060i
$800$	0.939198	−	1.48725i	0.0332057	−	0.0525821i
$801$		−	24.4985i		−	0.865610i
$802$	12.3496	+	8.15991i	0.436079	+	0.288137i
$803$	0.426910	−	1.03065i	0.0150653	−	0.0363709i
$804$	7.11509	+	2.86155i	0.250930	+	0.100919i
$805$	5.38929	−	2.23232i	0.189947	−	0.0786788i
$806$	−3.03519	−	6.57411i	−0.106910	−	0.231563i
$807$	5.70539	−	5.70539i	0.200839	−	0.200839i
$808$	1.42099	+	6.60778i	0.0499903	+	0.232461i
$809$	22.9403	+	22.9403i	0.806538	+	0.806538i	0.984108	−	0.177570i	$-0.0568237\pi$
$809$	22.9403	+	22.9403i	0.806538	+	0.806538i	−0.177570	+	0.984108i	$0.556824\pi$
$810$	21.5934	+	4.17954i	0.758716	+	0.146854i
$811$	28.1959	−	11.6791i	0.990092	−	0.410110i	0.171937	−	0.985108i	$-0.444997\pi$
$811$	28.1959	−	11.6791i	0.990092	−	0.410110i	0.818155	+	0.574998i	$0.194997\pi$
$812$	11.2809	+	11.0505i	0.395882	+	0.387798i
$813$	−1.98088	+	4.78226i	−0.0694724	+	0.167721i
$814$	1.53692	+	7.52360i	0.0538690	+	0.263702i
$815$			8.39112i			0.293928i
$816$	5.36912	−	2.35487i	0.187957	−	0.0824371i
$817$	72.9010			2.55048
$818$	−8.83927	−	43.2704i	−0.309058	−	1.51292i
$819$	−15.0454	−	9.31522i	−0.525730	−	0.325500i
$820$	−0.180112	−	17.4601i	−0.00628977	−	0.609735i
$821$	24.8742	−	10.3032i	0.868117	−	0.359586i	0.0962403	−	0.995358i	$-0.469318\pi$
$821$	24.8742	−	10.3032i	0.868117	−	0.359586i	0.771877	+	0.635772i	$0.219318\pi$
$822$	0.784711	−	4.05418i	0.0273699	−	0.141406i
$823$	−6.25050	−	6.25050i	−0.217879	−	0.217879i	0.589725	−	0.807604i	$-0.299236\pi$
$823$	−6.25050	−	6.25050i	−0.217879	−	0.217879i	−0.807604	+	0.589725i	$0.799236\pi$
$824$	−8.77979	−	12.7097i	−0.305858	−	0.442763i
$825$	−0.0683476	−	0.0683476i	−0.00237956	−	0.00237956i
$826$	−21.2870	+	14.3829i	−0.740669	+	0.500444i
$827$	−13.6578	−	32.9729i	−0.474929	−	1.14658i	−0.961959	−	0.273195i	$-0.911920\pi$
$827$	−13.6578	−	32.9729i	−0.474929	−	1.14658i	0.487029	−	0.873386i	$-0.338080\pi$
$828$	−7.87883	+	3.35915i	−0.273808	+	0.116738i
$829$	9.93946	−	23.9960i	0.345212	−	0.833415i	−0.651960	−	0.758254i	$-0.726053\pi$
$829$	9.93946	−	23.9960i	0.345212	−	0.833415i	0.997171	−	0.0751613i	$-0.0239472\pi$
$830$	6.01829	+	3.97655i	0.208898	+	0.138028i
$831$	1.94917			0.0676160
$832$	−22.8808	+	17.5633i	−0.793249	+	0.608897i
$833$	12.6130			0.437015
$834$	8.67656	+	5.73299i	0.300445	+	0.198517i
$835$	−0.139327	+	0.336364i	−0.00482160	+	0.0116404i
$836$	10.4880	−	4.47158i	0.362736	−	0.154653i
$837$	−1.43147	−	3.45588i	−0.0494789	−	0.119453i
$838$	15.9216	−	10.7576i	0.550001	−	0.371616i
$839$	1.44317	+	1.44317i	0.0498236	+	0.0498236i	0.731580	−	0.681756i	$-0.238783\pi$
$839$	1.44317	+	1.44317i	0.0498236	+	0.0498236i	−0.681756	+	0.731580i	$0.738783\pi$
$840$	4.02592	−	2.78109i	0.138908	−	0.0959567i
$841$	6.22687	+	6.22687i	0.214720	+	0.214720i
$842$	2.95850	−	15.2850i	0.101957	−	0.526755i
$843$	5.60097	−	2.32000i	0.192908	−	0.0799050i
$844$	0.336570	+	32.6273i	0.0115852	+	1.12308i
$845$	18.4782	−	21.2369i	0.635670	−	0.730572i
$846$	−8.11555	−	39.7277i	−0.279018	−	1.36587i
$847$	18.5064			0.635886
$848$	−45.9478	−	17.9309i	−1.57785	−	0.615749i
$849$		−	12.7268i		−	0.436781i
$850$	−0.283716	−	1.38886i	−0.00973137	−	0.0476375i
$851$	−4.65988	+	11.2499i	−0.159739	+	0.385643i
$852$	2.56496	+	2.51258i	0.0878739	+	0.0860795i
$853$	−16.1458	+	6.68779i	−0.552820	+	0.228986i	−0.641565	−	0.767069i	$-0.721714\pi$
$853$	−16.1458	+	6.68779i	−0.552820	+	0.228986i	0.0887447	+	0.996054i	$0.471714\pi$
$854$	24.3517	+	4.71342i	0.833297	+	0.161290i
$855$	−35.6639	−	35.6639i	−1.21968	−	1.21968i
$856$	14.2069	−	3.05518i	0.485583	−	0.104424i
$857$	13.5432	−	13.5432i	0.462626	−	0.462626i	−0.436889	−	0.899515i	$-0.643920\pi$
$857$	13.5432	−	13.5432i	0.462626	−	0.462626i	0.899515	+	0.436889i	$0.143920\pi$
$858$	0.664402	+	1.43907i	0.0226823	+	0.0491290i
$859$	−6.76608	+	2.80260i	−0.230856	+	0.0956236i	−0.495113	−	0.868829i	$-0.664873\pi$
$859$	−6.76608	+	2.80260i	−0.230856	+	0.0956236i	0.264257	+	0.964452i	$0.414873\pi$
$860$	35.1286	+	14.1280i	1.19787	+	0.481761i
$861$	−1.23264	+	2.97585i	−0.0420082	+	0.101417i
$862$	26.4041	+	17.4464i	0.899328	+	0.594226i
$863$			7.26538i			0.247316i	0.992325	+	0.123658i	$0.0394626\pi$
$863$			7.26538i			0.247316i	−0.992325	+	0.123658i	$0.960537\pi$
$864$	−12.1720	+	8.59516i	−0.414100	+	0.292413i
$865$		−	31.4933i		−	1.07080i
$866$	−11.2942	+	17.0932i	−0.383793	+	0.580849i
$867$	−1.14991	+	2.77613i	−0.0390530	+	0.0942822i
$868$	4.62986	+	1.86203i	0.157148	+	0.0632016i
$869$	3.35460	+	8.09871i	0.113797	+	0.274730i
$870$	−5.18467	+	3.50310i	−0.175777	+	0.118766i
$871$	−24.6812	+	17.7593i	−0.836292	+	0.601750i
$872$	−19.4058	−	12.5366i	−0.657162	−	0.424543i
$873$	11.2632	−	11.2632i	0.381201	−	0.381201i
$874$	17.7503	+	3.43568i	0.600413	+	0.116214i
$875$	−7.73285	−	18.6687i	−0.261418	−	0.631119i
$876$	1.03838	−	1.06002i	0.0350836	−	0.0358149i
$877$	−19.6517	+	47.4435i	−0.663592	+	1.60205i	0.128541	+	0.991704i	$0.458971\pi$
$877$	−19.6517	+	47.4435i	−0.663592	+	1.60205i	−0.792133	+	0.610348i	$0.791029\pi$
$878$	−6.50633	−	31.8501i	−0.219578	−	1.07489i
$879$	9.95641			0.335821
$880$	5.92041	−	0.122158i	0.199577	−	0.00411794i
$881$			10.6269i			0.358030i	0.983846	+	0.179015i	$0.0572911\pi$
$881$			10.6269i			0.358030i	−0.983846	+	0.179015i	$0.942709\pi$
$882$	−15.1437	+	3.09355i	−0.509915	+	0.104165i
$883$	−34.8518	−	14.4361i	−1.17286	−	0.485814i	−0.290721	−	0.956808i	$-0.593895\pi$
$883$	−34.8518	−	14.4361i	−1.17286	−	0.485814i	−0.882136	+	0.470994i	$0.843895\pi$
$884$	−3.50499	+	22.9797i	−0.117886	+	0.772890i
$885$	−3.89553	−	9.40465i	−0.130947	−	0.316134i
$886$	10.4406	+	2.02085i	0.350759	+	0.0678916i
$887$	−34.3092	−	34.3092i	−1.15199	−	1.15199i	−0.986153	−	0.165838i	$-0.946967\pi$
$887$	−34.3092	−	34.3092i	−1.15199	−	1.15199i	−0.165838	−	0.986153i	$-0.553033\pi$
$888$	−1.83745	+	10.0476i	−0.0616608	+	0.337174i
$889$	9.86362	+	9.86362i	0.330815	+	0.330815i
$890$	−22.2549	+	15.0369i	−0.745987	+	0.504037i
$891$	−1.87902	−	4.53636i	−0.0629496	−	0.151974i
$892$	19.1991	−	8.18554i	0.642832	−	0.274072i
$893$	−32.7547	+	79.0768i	−1.09609	+	2.64620i
$894$	4.76442	−	7.21069i	0.159346	−	0.241161i
$895$		−	11.3862i		−	0.380599i
$896$	3.17189	−	19.6241i	0.105965	−	0.655596i
$897$	−0.404593	+	2.48068i	−0.0135090	+	0.0828275i
$898$	31.6110	−	47.8415i	1.05487	−	1.59649i
$899$	−5.89568	−	2.44207i	−0.196632	−	0.0814476i
$900$	0.681281	+	1.59793i	0.0227094	+	0.0532645i
$901$	−36.7229	+	15.2111i	−1.22342	+	0.506756i
$902$	−3.22995	+	2.18236i	−0.107546	+	0.0726648i
$903$	−4.93886	−	4.93886i	−0.164355	−	0.164355i
$904$	−21.9783	−	4.01929i	−0.730988	−	0.133680i
$905$	−35.2541	+	35.2541i	−1.17189	+	1.17189i
$906$	2.23896	−	11.5675i	0.0743845	−	0.384304i
$907$	−11.4092	−	27.5444i	−0.378838	−	0.914596i	−0.992184	−	0.124782i	$-0.960177\pi$
$907$	−11.4092	−	27.5444i	−0.378838	−	0.914596i	0.613346	−	0.789814i	$-0.289823\pi$
$908$	0.311455	+	30.1926i	0.0103360	+	1.00198i
$909$	−6.16672	−	2.55434i	−0.204537	−	0.0847221i
$910$	0.772577	+	19.3852i	0.0256107	+	0.642613i
$911$		−	8.70745i		−	0.288491i	−0.989542	−	0.144245i	$-0.953925\pi$
$911$		−	8.70745i		−	0.288491i	0.989542	−	0.144245i	$-0.0460755\pi$
$912$	15.1624	−	0.312852i	0.502078	−	0.0103596i
$913$		−	1.61036i		−	0.0532950i
$914$	−48.4333	+	9.89394i	−1.60203	+	0.327262i
$915$	−3.76105	+	9.07998i	−0.124337	+	0.300175i
$916$	−14.2909	+	14.5889i	−0.472186	+	0.482029i
$917$	−29.9686	+	12.4134i	−0.989650	+	0.409926i
$918$	−2.28195	+	11.7896i	−0.0753157	+	0.389115i
$919$	−3.34367	−	3.34367i	−0.110298	−	0.110298i	0.649804	−	0.760102i	$-0.274851\pi$
$919$	−3.34367	−	3.34367i	−0.110298	−	0.110298i	−0.760102	+	0.649804i	$0.774851\pi$
$920$	7.88746	+	5.09550i	0.260042	+	0.167994i
$921$	−0.417047	−	0.417047i	−0.0137422	−	0.0137422i
$922$	−35.0891	+	23.7085i	−1.15560	+	0.780798i
$923$	−13.8579	+	3.25971i	−0.456137	+	0.107295i
$924$	−1.01347	−	0.407598i	−0.0333408	−	0.0134090i
$925$	2.28164	+	0.945087i	0.0750199	+	0.0310743i
$926$	−11.6971	−	7.72876i	−0.384389	−	0.253983i
$927$	15.2553			0.501049
$928$	−4.31477	+	25.0517i	−0.141639	+	0.822362i
$929$			49.5962i			1.62720i	0.581427	+	0.813599i	$0.302495\pi$
$929$			49.5962i			1.62720i	−0.581427	+	0.813599i	$0.697505\pi$
$930$	−1.09005	+	1.64973i	−0.0357441	+	0.0540968i
$931$	30.1431	+	12.4857i	0.987900	+	0.409202i
$932$	−12.6268	+	31.3960i	−0.413606	+	1.02841i
$933$	−9.09076	+	3.76552i	−0.297618	+	0.123277i
$934$	−21.1248	−	31.2652i	−0.691224	−	1.02303i
$935$	3.37447	−	3.37447i	0.110357	−	0.110357i
$936$	−1.42791	−	28.4500i	−0.0466727	−	0.929916i
$937$	−28.3731	−	28.3731i	−0.926907	−	0.926907i	0.0705977	−	0.997505i	$-0.477509\pi$
$937$	−28.3731	−	28.3731i	−0.926907	−	0.926907i	−0.997505	+	0.0705977i	$0.977509\pi$
$938$	3.98213	−	20.5735i	0.130021	−	0.671749i
$939$	−0.908705	−	2.19381i	−0.0296545	−	0.0715922i
$940$	−31.1082	+	31.7567i	−1.01464	+	1.03579i
$941$	14.2181	−	34.3256i	0.463498	−	1.11898i	−0.503453	−	0.864023i	$-0.667937\pi$
$941$	14.2181	−	34.3256i	0.463498	−	1.11898i	0.966951	−	0.254961i	$-0.0820627\pi$
$942$	−2.34717	−	11.4900i	−0.0764748	−	0.374364i
$943$	−6.18139			−0.201294
$944$	−38.5258	−	15.0345i	−1.25391	−	0.489331i
$945$			10.0222i			0.326022i
$946$	−1.69180	−	8.28176i	−0.0550050	−	0.269263i
$947$	2.07636	−	5.01278i	0.0674726	−	0.162893i	−0.886546	−	0.462640i	$-0.846902\pi$
$947$	2.07636	−	5.01278i	0.0674726	−	0.162893i	0.954019	+	0.299747i	$0.0969022\pi$
$948$	0.120274	+	11.6594i	0.00390632	+	0.378681i
$949$	1.34715	+	5.72707i	0.0437303	+	0.185909i
$950$	0.696803	−	3.60000i	0.0226073	−	0.116800i
$951$	7.77993	−	7.77993i	0.252281	−	0.252281i
$952$	−9.10535	−	13.1810i	−0.295106	−	0.427198i
$953$	39.8466	−	39.8466i	1.29076	−	1.29076i	0.356438	−	0.934319i	$-0.383991\pi$
$953$	39.8466	−	39.8466i	1.29076	−	1.29076i	0.934319	−	0.356438i	$-0.116009\pi$
$954$	40.3602	−	27.2700i	1.30671	−	0.882897i
$955$	−2.78600	−	6.72600i	−0.0901529	−	0.217648i
$956$	−4.18849	−	9.82406i	−0.135466	−	0.317733i
$957$	1.29056	+	0.534568i	0.0417179	+	0.0172801i
$958$	32.2955	−	48.8775i	1.04342	−	1.57916i
$959$	−11.2836			−0.364367
$960$	7.36691	+	2.78768i	0.237766	+	0.0899720i
$961$	28.9834			0.934949
$962$	−29.7541	−	27.4733i	−0.959310	−	0.885776i
$963$	−5.49191	+	13.2586i	−0.176974	+	0.427254i
$964$	−13.2417	−	31.0582i	−0.426486	−	1.00032i
$965$	34.1743	−	14.1554i	1.10011	−	0.455680i
$966$	−0.969779	−	1.43530i	−0.0312021	−	0.0461799i
$967$	17.6376	+	17.6376i	0.567187	+	0.567187i	0.931339	−	0.364152i	$-0.118641\pi$
$967$	17.6376	+	17.6376i	0.567187	+	0.567187i	−0.364152	+	0.931339i	$0.618641\pi$
$968$	16.9321	+	24.5110i	0.544218	+	0.787814i
$969$	8.64217	−	8.64217i	0.277626	−	0.277626i
$970$	−17.1449	−	3.31851i	−0.550491	−	0.106551i
$971$	−22.7246	−	54.8619i	−0.729266	−	1.76060i	−0.645030	−	0.764157i	$-0.723155\pi$
$971$	−22.7246	−	54.8619i	−0.729266	−	1.76060i	−0.0842356	−	0.996446i	$-0.526845\pi$
$972$	−0.230396	−	22.3347i	−0.00738994	−	0.716386i
$973$	10.8745	−	26.2535i	0.348622	−	0.841647i
$974$	−3.06068	−	14.9828i	−0.0980705	−	0.480080i
$975$	0.503116	+	0.0820570i	0.0161126	+	0.00262793i
$976$	16.0374	+	36.5654i	0.513345	+	1.17043i
$977$	−36.9105			−1.18087			−0.590436	−	0.807085i	$-0.701044\pi$
$977$	−36.9105			−1.18087			−0.590436	+	0.807085i	$0.701044\pi$
$978$	2.44133	−	0.498714i	0.0780651	−	0.0159471i
$979$	5.53967	+	2.29461i	0.177049	+	0.0733359i
$980$	12.1053	+	11.8581i	0.386689	+	0.378792i
$981$	21.0790	−	8.73122i	0.673002	−	0.278766i
$982$	4.63662	−	23.9549i	0.147961	−	0.764433i
$983$	−2.70167	+	2.70167i	−0.0861698	+	0.0861698i	−0.748878	−	0.662708i	$-0.769407\pi$
$983$	−2.70167	+	2.70167i	−0.0861698	+	0.0861698i	0.662708	+	0.748878i	$0.269407\pi$
$984$	−5.06919	+	1.09012i	−0.161600	+	0.0347518i
$985$	3.64584	−	3.64584i	0.116166	−	0.116166i
$986$	11.4692	+	16.9747i	0.365254	+	0.540585i
$987$	7.57629	−	3.13820i	0.241156	−	0.0998901i
$988$	−31.1240	+	51.4481i	−0.990187	+	1.63678i
$989$	5.12946	−	12.3836i	0.163107	−	0.393776i
$990$	−3.22388	+	4.87916i	−0.102461	+	0.155070i
$991$	40.4042			1.28348			0.641740	−	0.766922i	$-0.278213\pi$
$991$	40.4042			1.28348			0.641740	+	0.766922i	$0.278213\pi$
$992$	1.76982	+	7.83572i	0.0561917	+	0.248784i
$993$		−	9.15524i		−	0.290533i
$994$	5.40863	−	8.18566i	0.171551	−	0.259633i
$995$	29.0810	+	12.0457i	0.921928	+	0.381875i
$996$	0.799257	−	1.98732i	0.0253254	−	0.0629705i
$997$	−34.3840	+	14.2423i	−1.08895	+	0.451059i	−0.853642	−	0.520861i	$-0.825611\pi$
$997$	−34.3840	+	14.2423i	−1.08895	+	0.451059i	−0.235312	+	0.971920i	$0.575611\pi$
$998$	−1.90035	+	1.28400i	−0.0601546	+	0.0406444i
$999$	−14.7934	−	14.7934i	−0.468041	−	0.468041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.10	✓	216
13.12	even	2	inner	416.2.bg.a.77.45	yes	216
32.5	even	8	inner	416.2.bg.a.389.45	yes	216
416.389	even	8	inner	416.2.bg.a.389.10	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.10	✓	216	1.1	even	1	trivial
416.2.bg.a.77.45	yes	216	13.12	even	2	inner
416.2.bg.a.389.10	yes	216	416.389	even	8	inner
416.2.bg.a.389.45	yes	216	32.5	even	8	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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bg (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17991 - 0.779620i) q^{2} +(-0.174001 + 0.420075i) q^{3} +(0.784386 + 1.83977i) q^{4} +(0.828671 + 2.00059i) q^{5} +(0.532805 - 0.359998i) q^{6} +(-1.24243 - 1.24243i) q^{7} +(0.508812 - 2.78229i) q^{8} +(1.97513 + 1.97513i) q^{9} +(0.581940 - 3.00657i) q^{10} +(-0.631621 + 0.261626i) q^{11} +(-0.909324 + 0.00938021i) q^{12} +(1.89800 - 3.06555i) q^{13} +(0.497333 + 2.43457i) q^{14} -0.984588 q^{15} +(-2.76948 + 2.88617i) q^{16} +3.22356i q^{17} +(-0.790631 - 3.87034i) q^{18} +(-3.19102 + 7.70380i) q^{19} +(-3.03062 + 3.09380i) q^{20} +(0.738096 - 0.305729i) q^{21} +(0.949227 + 0.183729i) q^{22} +(1.08411 + 1.08411i) q^{23} +(1.08024 + 0.697859i) q^{24} +(0.219872 - 0.219872i) q^{25} +(-4.62944 + 2.13736i) q^{26} +(-2.43361 + 1.00803i) q^{27} +(1.31123 - 3.26031i) q^{28} +(-1.71969 + 4.15169i) q^{29} +(1.16173 + 0.767604i) q^{30} +1.42007i q^{31} +(5.51786 - 1.24629i) q^{32} -0.310852i q^{33} +(2.51315 - 3.80352i) q^{34} +(1.45602 - 3.51515i) q^{35} +(-2.08452 + 5.18305i) q^{36} +(3.03939 + 7.33774i) q^{37} +(9.77115 - 6.60202i) q^{38} +(0.957508 + 1.33071i) q^{39} +(5.98785 - 1.28768i) q^{40} +(-2.85091 + 2.85091i) q^{41} +(-1.10924 - 0.214700i) q^{42} +(-3.34568 - 8.07717i) q^{43} +(-0.976766 - 0.956820i) q^{44} +(-2.31469 + 5.58817i) q^{45} +(-0.433961 - 2.12435i) q^{46} +10.2647 q^{47} +(-0.730519 - 1.66559i) q^{48} -3.91276i q^{49} +(-0.430846 + 0.0880131i) q^{50} +(-1.35414 - 0.560903i) q^{51} +(7.12866 + 1.08730i) q^{52} +(4.71873 + 11.3920i) q^{53} +(3.65732 + 0.707898i) q^{54} +(-1.04681 - 1.04681i) q^{55} +(-4.08894 + 2.82462i) q^{56} +(-2.68094 - 2.68094i) q^{57} +(5.26582 - 3.55793i) q^{58} +(3.95651 + 9.55186i) q^{59} +(-0.772297 - 1.81141i) q^{60} +(3.81992 - 9.22211i) q^{61} +(1.10711 - 1.67555i) q^{62} -4.90791i q^{63} +(-7.48222 - 2.83132i) q^{64} +(7.70572 + 1.25679i) q^{65} +(-0.242346 + 0.366778i) q^{66} +(-7.79130 - 3.22726i) q^{67} +(-5.93060 + 2.52852i) q^{68} +(-0.644044 + 0.266772i) q^{69} +(-4.45845 + 3.01242i) q^{70} +(-2.79193 - 2.79193i) q^{71} +(6.50035 - 4.49041i) q^{72} +(-1.15383 + 1.15383i) q^{73} +(2.13443 - 11.0275i) q^{74} +(0.0541049 + 0.130621i) q^{75} +(-16.6762 + 0.172024i) q^{76} +(1.10979 + 0.459691i) q^{77} +(-0.0923263 - 2.31662i) q^{78} -12.8221i q^{79} +(-8.06903 - 3.14890i) q^{80} +7.18208i q^{81} +(5.58645 - 1.14120i) q^{82} +(-0.901406 + 2.17619i) q^{83} +(1.14142 + 1.11811i) q^{84} +(-6.44903 + 2.67127i) q^{85} +(-2.34952 + 12.1387i) q^{86} +(-1.44480 - 1.44480i) q^{87} +(0.406542 + 1.89047i) q^{88} +(-6.20172 - 6.20172i) q^{89} +(7.08778 - 4.78896i) q^{90} +(-6.16684 + 1.45059i) q^{91} +(-1.14415 + 2.84487i) q^{92} +(-0.596535 - 0.247093i) q^{93} +(-12.1114 - 8.00253i) q^{94} -18.0564 q^{95} +(-0.436576 + 2.53477i) q^{96} -5.70249i q^{97} +(-3.05046 + 4.61671i) q^{98} +(-1.76428 - 0.730790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

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