LMFDB - Embedded newform 680.2.cf.a.37.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(37,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 8, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cf (of order $16$, degree $8$, 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.17
Character	$\chi$	$=$	680.37
Dual form			680.2.cf.a.533.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25304 - 0.655652i) q^{2} +(0.577178 + 0.863808i) q^{3} +(1.14024 + 1.64312i) q^{4} +(-1.97239 + 1.05341i) q^{5} +(-0.156872 - 1.46082i) q^{6} +(-3.87241 + 0.770271i) q^{7} +(-0.351454 - 2.80651i) q^{8} +(0.735021 - 1.77450i) q^{9} +(3.16216 - 0.0267698i) q^{10} +(0.874343 - 0.173918i) q^{11} +(-0.761221 + 1.93332i) q^{12} -2.28012i q^{13} +(5.35733 + 1.57377i) q^{14} +(-2.04837 - 1.09576i) q^{15} +(-1.39971 + 3.74711i) q^{16} +(-4.08814 + 0.535855i) q^{17} +(-2.08447 + 1.74161i) q^{18} +(5.94539 - 2.46266i) q^{19} +(-3.97988 - 2.03974i) q^{20} +(-2.90044 - 2.90044i) q^{21} +(-1.20962 - 0.355339i) q^{22} +(1.61159 - 2.41192i) q^{23} +(2.22143 - 1.92344i) q^{24} +(2.78065 - 4.15548i) q^{25} +(-1.49497 + 2.85709i) q^{26} +(5.01385 - 0.997318i) q^{27} +(-5.68113 - 5.48456i) q^{28} +(-1.30777 + 0.873827i) q^{29} +(1.84826 + 2.71605i) q^{30} +(0.405395 - 2.03806i) q^{31} +(4.21069 - 3.77757i) q^{32} +(0.654883 + 0.654883i) q^{33} +(5.47395 + 2.00895i) q^{34} +(6.82649 - 5.59852i) q^{35} +(3.75382 - 0.815623i) q^{36} +(6.98072 - 4.66437i) q^{37} +(-9.06448 - 0.812285i) q^{38} +(1.96959 - 1.31603i) q^{39} +(3.64961 + 5.16530i) q^{40} +(-0.653766 + 0.978430i) q^{41} +(1.73270 + 5.53605i) q^{42} +(2.12275 + 5.12477i) q^{43} +(1.28273 + 1.23835i) q^{44} +(0.419529 + 4.27428i) q^{45} +(-3.60077 + 1.96559i) q^{46} +2.65486i q^{47} +(-4.04466 + 0.953672i) q^{48} +(7.93510 - 3.28683i) q^{49} +(-6.20882 + 3.38386i) q^{50} +(-2.82246 - 3.22208i) q^{51} +(3.74652 - 2.59988i) q^{52} +(-2.44306 - 1.01195i) q^{53} +(-6.93648 - 2.03766i) q^{54} +(-1.54134 + 1.26408i) q^{55} +(3.52274 + 10.5972i) q^{56} +(5.55881 + 3.71428i) q^{57} +(2.21163 - 0.237498i) q^{58} +(3.82876 - 9.24344i) q^{59} +(-0.535160 - 4.61515i) q^{60} +(4.80516 - 7.19144i) q^{61} +(-1.84423 + 2.28798i) q^{62} +(-1.47946 + 7.43775i) q^{63} +(-7.75296 + 1.97271i) q^{64} +(2.40191 + 4.49729i) q^{65} +(-0.391222 - 1.24997i) q^{66} +(-0.596874 - 0.596874i) q^{67} +(-5.54193 - 6.10631i) q^{68} +3.01361 q^{69} +(-12.2246 + 2.53939i) q^{70} +(-8.85604 - 1.76158i) q^{71} +(-5.23846 - 1.43919i) q^{72} +(-14.8560 - 2.95504i) q^{73} +(-11.8053 + 1.26773i) q^{74} +(5.19446 + 0.00349235i) q^{75} +(10.8256 + 6.96098i) q^{76} +(-3.25185 + 1.34696i) q^{77} +(-3.33084 + 0.357687i) q^{78} +(7.25794 - 1.44369i) q^{79} +(-1.18648 - 8.86523i) q^{80} +(-0.319046 - 0.319046i) q^{81} +(1.46071 - 0.797373i) q^{82} +(6.88930 - 16.6322i) q^{83} +(1.45858 - 8.07297i) q^{84} +(7.49892 - 5.36341i) q^{85} +(0.700169 - 7.81335i) q^{86} +(-1.50964 - 0.625312i) q^{87} +(-0.795392 - 2.39273i) q^{88} +(-7.27719 - 7.27719i) q^{89} +(2.27675 - 5.63093i) q^{90} +(1.75631 + 8.82956i) q^{91} +(5.80068 - 0.102121i) q^{92} +(1.99447 - 0.826139i) q^{93} +(1.74066 - 3.32666i) q^{94} +(-9.13243 + 11.1203i) q^{95} +(5.69342 + 1.45690i) q^{96} +(-0.158428 - 0.0315133i) q^{97} +(-12.0980 - 1.08413i) q^{98} +(0.334044 - 1.67935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) $ 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$1$

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 $

$2$	−1.25304	−	0.655652i	−0.886036	−	0.463616i
$2$	−1.25304	−	0.655652i	−0.886036	−	0.463616i
$3$	0.577178	+	0.863808i	0.333234	+	0.498720i	0.959814	−	0.280637i	$-0.0905458\pi$
$3$	0.577178	+	0.863808i	0.333234	+	0.498720i	−0.626580	+	0.779357i	$0.715546\pi$
$4$	1.14024	+	1.64312i	0.570120	+	0.821561i
$5$	−1.97239	+	1.05341i	−0.882080	+	0.471100i
$5$	−1.97239	+	1.05341i	−0.882080	+	0.471100i
$6$	−0.156872	−	1.46082i	−0.0640427	−	0.596376i
$7$	−3.87241	+	0.770271i	−1.46363	+	0.291135i	−0.861703	−	0.507413i	$-0.830602\pi$
$7$	−3.87241	+	0.770271i	−1.46363	+	0.291135i	−0.601931	+	0.798548i	$0.705602\pi$
$8$	−0.351454	−	2.80651i	−0.124258	−	0.992250i
$9$	0.735021	−	1.77450i	0.245007	−	0.591499i
$10$	3.16216	−	0.0267698i	0.999964	−	0.00846536i
$11$	0.874343	−	0.173918i	0.263624	−	0.0524381i	−0.0615083	−	0.998107i	$-0.519591\pi$
$11$	0.874343	−	0.173918i	0.263624	−	0.0524381i	0.325133	+	0.945668i	$0.394591\pi$
$12$	−0.761221	+	1.93332i	−0.219746	+	0.558102i
$13$		−	2.28012i		−	0.632391i	−0.948694	−	0.316196i	$-0.897594\pi$
$13$		−	2.28012i		−	0.632391i	0.948694	−	0.316196i	$-0.102406\pi$
$14$	5.35733	+	1.57377i	1.43181	+	0.420608i
$15$	−2.04837	−	1.09576i	−0.528886	−	0.282924i
$16$	−1.39971	+	3.74711i	−0.349926	+	0.936777i
$17$	−4.08814	+	0.535855i	−0.991519	+	0.129964i
$17$	−4.08814	+	0.535855i	−0.991519	+	0.129964i
$18$	−2.08447	+	1.74161i	−0.491313	+	0.410500i
$19$	5.94539	−	2.46266i	1.36397	−	0.564973i	0.423820	−	0.905746i	$-0.360689\pi$
$19$	5.94539	−	2.46266i	1.36397	−	0.564973i	0.940145	+	0.340773i	$0.110689\pi$
$20$	−3.97988	−	2.03974i	−0.889929	−	0.456099i
$21$	−2.90044	−	2.90044i	−0.632927	−	0.632927i
$22$	−1.20962	−	0.355339i	−0.257892	−	0.0757584i
$23$	1.61159	−	2.41192i	0.336040	−	0.502919i	−0.624514	−	0.781014i	$-0.714703\pi$
$23$	1.61159	−	2.41192i	0.336040	−	0.502919i	0.960554	+	0.278094i	$0.0897028\pi$
$24$	2.22143	−	1.92344i	0.453448	−	0.392621i
$25$	2.78065	−	4.15548i	0.556129	−	0.831096i
$26$	−1.49497	+	2.85709i	−0.293187	+	0.560322i
$27$	5.01385	−	0.997318i	0.964917	−	0.191934i
$28$	−5.68113	−	5.48456i	−1.07363	−	1.03648i
$29$	−1.30777	+	0.873827i	−0.242848	+	0.162266i	−0.671038	−	0.741423i	$-0.734151\pi$
$29$	−1.30777	+	0.873827i	−0.242848	+	0.162266i	0.428190	+	0.903689i	$0.359151\pi$
$30$	1.84826	+	2.71605i	0.337444	+	0.495881i
$31$	0.405395	−	2.03806i	0.0728111	−	0.366046i	−0.927152	−	0.374686i	$-0.877750\pi$
$31$	0.405395	−	2.03806i	0.0728111	−	0.366046i	0.999963	+	0.00864049i	$0.00275039\pi$
$32$	4.21069	−	3.77757i	0.744353	−	0.667787i
$33$	0.654883	+	0.654883i	0.114000	+	0.114000i
$34$	5.47395	+	2.00895i	0.938775	+	0.344532i
$35$	6.82649	−	5.59852i	1.15389	−	0.946323i
$36$	3.75382	−	0.815623i	0.625636	−	0.135937i
$37$	6.98072	−	4.66437i	1.14762	−	0.766817i	0.171746	−	0.985141i	$-0.445059\pi$
$37$	6.98072	−	4.66437i	1.14762	−	0.766817i	0.975876	+	0.218324i	$0.0700590\pi$
$38$	−9.06448	−	0.812285i	−1.47045	−	0.131770i
$39$	1.96959	−	1.31603i	0.315386	−	0.210734i
$40$	3.64961	+	5.16530i	0.577054	+	0.816706i
$41$	−0.653766	+	0.978430i	−0.102101	+	0.152805i	−0.879002	−	0.476817i	$-0.841790\pi$
$41$	−0.653766	+	0.978430i	−0.102101	+	0.152805i	0.776901	+	0.629622i	$0.216790\pi$
$42$	1.73270	+	5.53605i	0.267361	+	0.854232i
$43$	2.12275	+	5.12477i	0.323716	+	0.781520i	0.999032	+	0.0439913i	$0.0140074\pi$
$43$	2.12275	+	5.12477i	0.323716	+	0.781520i	−0.675316	+	0.737529i	$0.735993\pi$
$44$	1.28273	+	1.23835i	0.193379	+	0.186688i
$45$	0.419529	+	4.27428i	0.0625397	+	0.637172i
$46$	−3.60077	+	1.96559i	−0.530905	+	0.289811i
$47$			2.65486i			0.387251i	0.981076	+	0.193625i	$0.0620247\pi$
$47$			2.65486i			0.387251i	−0.981076	+	0.193625i	$0.937975\pi$
$48$	−4.04466	+	0.953672i	−0.583797	+	0.137651i
$49$	7.93510	−	3.28683i	1.13359	−	0.469547i
$50$	−6.20882	+	3.38386i	−0.878060	+	0.478550i
$51$	−2.82246	−	3.22208i	−0.395223	−	0.451182i
$52$	3.74652	−	2.59988i	0.519548	−	0.360539i
$53$	−2.44306	−	1.01195i	−0.335580	−	0.139002i	0.208530	−	0.978016i	$-0.433132\pi$
$53$	−2.44306	−	1.01195i	−0.335580	−	0.139002i	−0.544109	+	0.839014i	$0.683132\pi$
$54$	−6.93648	−	2.03766i	−0.943935	−	0.277291i
$55$	−1.54134	+	1.26408i	−0.207834	+	0.170448i
$56$	3.52274	+	10.5972i	0.470746	+	1.41612i
$57$	5.55881	+	3.71428i	0.736283	+	0.491968i
$58$	2.21163	−	0.237498i	0.290401	−	0.0311851i
$59$	3.82876	−	9.24344i	0.498462	−	1.20339i	−0.451850	−	0.892094i	$-0.649236\pi$
$59$	3.82876	−	9.24344i	0.498462	−	1.20339i	0.950312	−	0.311300i	$-0.100764\pi$
$60$	−0.535160	−	4.61515i	−0.0690889	−	0.595813i
$61$	4.80516	−	7.19144i	0.615238	−	0.920769i	−0.384759	−	0.923017i	$-0.625715\pi$
$61$	4.80516	−	7.19144i	0.615238	−	0.920769i	0.999997	+	0.00224780i	$0.000715497\pi$
$62$	−1.84423	+	2.28798i	−0.234218	+	0.290573i
$63$	−1.47946	+	7.43775i	−0.186394	+	0.937068i
$64$	−7.75296	+	1.97271i	−0.969120	+	0.246589i
$65$	2.40191	+	4.49729i	0.297920	+	0.557820i
$66$	−0.391222	−	1.24997i	−0.0481561	−	0.153861i
$67$	−0.596874	−	0.596874i	−0.0729197	−	0.0729197i	0.669706	−	0.742626i	$-0.266420\pi$
$67$	−0.596874	−	0.596874i	−0.0729197	−	0.0729197i	−0.742626	+	0.669706i	$0.766420\pi$
$68$	−5.54193	−	6.10631i	−0.672058	−	0.740499i
$69$	3.01361			0.362796
$70$	−12.2246	+	2.53939i	−1.46112	+	0.303515i
$71$	−8.85604	−	1.76158i	−1.05102	−	0.209061i	−0.360786	−	0.932648i	$-0.617492\pi$
$71$	−8.85604	−	1.76158i	−1.05102	−	0.209061i	−0.690232	+	0.723588i	$0.742492\pi$
$72$	−5.23846	−	1.43919i	−0.617359	−	0.169610i
$73$	−14.8560	−	2.95504i	−1.73876	−	0.345861i	−0.779075	−	0.626931i	$-0.784311\pi$
$73$	−14.8560	−	2.95504i	−1.73876	−	0.345861i	−0.959687	+	0.281070i	$0.909311\pi$
$74$	−11.8053	+	1.26773i	−1.37234	+	0.147371i
$75$	5.19446	+	0.00349235i	0.599805	+	0.000403262i
$76$	10.8256	+	6.96098i	1.24178	+	0.798479i
$77$	−3.25185	+	1.34696i	−0.370583	+	0.153500i
$78$	−3.33084	+	0.357687i	−0.377143	+	0.0405000i
$79$	7.25794	−	1.44369i	0.816582	−	0.162428i	0.230908	−	0.972975i	$-0.425830\pi$
$79$	7.25794	−	1.44369i	0.816582	−	0.162428i	0.585673	+	0.810547i	$0.300830\pi$
$80$	−1.18648	−	8.86523i	−0.132653	−	0.991163i
$81$	−0.319046	−	0.319046i	−0.0354495	−	0.0354495i
$82$	1.46071	−	0.797373i	0.161308	−	0.0880551i
$83$	6.88930	−	16.6322i	0.756199	−	1.82563i	0.235531	−	0.971867i	$-0.424317\pi$
$83$	6.88930	−	16.6322i	0.756199	−	1.82563i	0.520668	−	0.853759i	$-0.325683\pi$
$84$	1.45858	−	8.07297i	0.159144	−	0.880833i
$85$	7.49892	−	5.36341i	0.813373	−	0.581743i
$86$	0.700169	−	7.81335i	0.0755012	−	0.842535i
$87$	−1.50964	−	0.625312i	−0.161850	−	0.0670405i
$88$	−0.795392	−	2.39273i	−0.0847891	−	0.255065i
$89$	−7.27719	−	7.27719i	−0.771380	−	0.771380i	0.206968	−	0.978348i	$-0.433641\pi$
$89$	−7.27719	−	7.27719i	−0.771380	−	0.771380i	−0.978348	+	0.206968i	$0.933641\pi$
$90$	2.27675	−	5.63093i	0.239991	−	0.593552i
$91$	1.75631	+	8.82956i	0.184111	+	0.925590i
$92$	5.80068	−	0.102121i	0.604762	−	0.0106469i
$93$	1.99447	−	0.826139i	0.206817	−	0.0856666i
$94$	1.74066	−	3.32666i	0.179536	−	0.343118i
$95$	−9.13243	+	11.1203i	−0.936967	+	1.14092i
$96$	5.69342	+	1.45690i	0.581082	+	0.148694i
$97$	−0.158428	−	0.0315133i	−0.0160860	−	0.00319970i	0.187041	−	0.982352i	$-0.440110\pi$
$97$	−0.158428	−	0.0315133i	−0.0160860	−	0.00319970i	−0.203127	+	0.979152i	$0.565110\pi$
$98$	−12.0980	−	1.08413i	−1.22209	−	0.109514i
$99$	0.334044	−	1.67935i	0.0335727	−	0.168781i
$100$	9.99857	−	0.169301i	0.999857	−	0.0169301i
$101$	−5.94421			−0.591471			−0.295736	−	0.955270i	$-0.595565\pi$
$101$	−5.94421			−0.591471			−0.295736	+	0.955270i	$0.595565\pi$
$102$	1.42410	+	5.88796i	0.141007	+	0.582995i
$103$	9.94803	−	9.94803i	0.980209	−	0.980209i	−0.0195991	−	0.999808i	$-0.506239\pi$
$103$	9.94803	−	9.94803i	0.980209	−	0.980209i	0.999808	+	0.0195991i	$0.00623897\pi$
$104$	−6.39917	+	0.801356i	−0.627490	+	0.0785795i
$105$	8.77615	+	2.66544i	0.856464	+	0.260120i
$106$	2.39777	+	2.86981i	0.232892	+	0.278741i
$107$	−19.7693	−	3.93235i	−1.91117	−	0.380155i	−0.911642	−	0.410986i	$-0.865184\pi$
$107$	−19.7693	−	3.93235i	−1.91117	−	0.380155i	−0.999525	+	0.0308317i	$0.990184\pi$
$108$	7.35571	+	7.10120i	0.707804	+	0.683313i
$109$	−6.69807	+	10.0244i	−0.641559	+	0.960160i	0.358091	+	0.933687i	$0.383428\pi$
$109$	−6.69807	+	10.0244i	−0.641559	+	0.960160i	−0.999650	+	0.0264735i	$0.991572\pi$
$110$	2.76016	−	0.573362i	0.263171	−	0.0546679i
$111$	8.05823	+	3.33783i	0.764853	+	0.316813i
$112$	2.53395	−	15.5885i	0.239436	−	1.47297i
$113$	−4.49773	−	3.00529i	−0.423111	−	0.282714i	0.325731	−	0.945463i	$-0.394390\pi$
$113$	−4.49773	−	3.00529i	−0.423111	−	0.282714i	−0.748842	+	0.662749i	$0.769390\pi$
$114$	−4.53016	−	8.29881i	−0.424289	−	0.777254i
$115$	−0.637944	+	6.45491i	−0.0594886	+	0.601923i
$116$	−2.92698	−	1.15246i	−0.271763	−	0.107003i
$117$	−4.04606	−	1.67593i	−0.374059	−	0.154940i
$118$	−10.8581	+	9.07211i	−0.999568	+	0.835155i
$119$	15.4182	−	5.22402i	1.41338	−	0.478885i
$120$	−2.35535	+	6.13386i	−0.215013	+	0.559942i
$121$	−9.42845	+	3.90539i	−0.857132	+	0.355035i
$122$	−10.7362	+	5.86067i	−0.972007	+	0.530600i
$123$	−1.22252			−0.110230
$124$	3.81103	−	1.65776i	0.342240	−	0.148871i
$125$	−1.10709	+	11.1254i	−0.0990207	+	0.995085i
$126$	6.73041	−	8.34982i	0.599592	−	0.743861i
$127$	−1.32092	+	0.547142i	−0.117213	+	0.0485510i	−0.440519	−	0.897743i	$-0.645206\pi$
$127$	−1.32092	+	0.547142i	−0.117213	+	0.0485510i	0.323306	+	0.946294i	$0.395206\pi$
$128$	11.0082	+	2.61135i	0.972998	+	0.230813i
$129$	−3.20161	+	4.79155i	−0.281886	+	0.421873i
$130$	−0.0610384	−	7.21011i	−0.00535342	−	0.632369i
$131$	6.01872	+	9.00765i	0.525858	+	0.787002i	0.995390	−	0.0959136i	$-0.0305773\pi$
$131$	6.01872	+	9.00765i	0.525858	+	0.787002i	−0.469532	+	0.882916i	$0.655577\pi$
$132$	−0.329329	+	1.82278i	−0.0286645	+	0.158652i
$133$	−21.1261	+	14.1160i	−1.83186	+	1.22401i
$134$	0.356568	+	1.13925i	0.0308027	+	0.0984163i
$135$	−8.83869	+	7.24876i	−0.760713	+	0.623874i
$136$	2.94067	+	11.2851i	0.252160	+	0.967685i
$137$	−2.31293	−	2.31293i	−0.197607	−	0.197607i	0.601366	−	0.798974i	$-0.294623\pi$
$137$	−2.31293	−	2.31293i	−0.197607	−	0.197607i	−0.798974	+	0.601366i	$0.794623\pi$
$138$	−3.77618	−	1.97588i	−0.321450	−	0.168198i
$139$	17.5793	+	3.49674i	1.49106	+	0.296590i	0.872292	−	0.488985i	$-0.162633\pi$
$139$	17.5793	+	3.49674i	1.49106	+	0.296590i	0.618766	+	0.785575i	$0.287633\pi$
$140$	16.9829	+	4.83311i	1.43532	+	0.408473i
$141$	−2.29329	+	1.53233i	−0.193130	+	0.129045i
$142$	9.94203	+	8.01382i	0.834317	+	0.672505i
$143$	−0.396553	−	1.99361i	−0.0331614	−	0.166714i
$144$	5.62042	+	5.23798i	0.468368	+	0.436498i
$145$	1.65894	−	3.10115i	0.137768	−	0.257537i
$146$	16.6777	+	13.4432i	1.38026	+	1.11256i
$147$	7.41915	+	4.95732i	0.611921	+	0.408873i
$148$	15.6238	+	6.15168i	1.28427	+	0.505665i
$149$	−15.2950	−	15.2950i	−1.25301	−	1.25301i	−0.954362	−	0.298653i	$-0.903463\pi$
$149$	−15.2950	−	15.2950i	−1.25301	−	1.25301i	−0.298653	−	0.954362i	$-0.596537\pi$
$150$	−6.50660	−	3.41014i	−0.531262	−	0.278437i
$151$	−3.68358	−	8.89295i	−0.299766	−	0.723698i	−0.999953	−	0.00973869i	$-0.996900\pi$
$151$	−3.68358	−	8.89295i	−0.299766	−	0.723698i	0.700187	−	0.713960i	$-0.253100\pi$
$152$	−9.00100	−	15.8203i	−0.730078	−	1.28319i
$153$	−2.05399	+	7.64825i	−0.166055	+	0.618324i
$154$	4.95785	+	0.444283i	0.399515	+	0.0358013i
$155$	1.34732	+	4.44689i	0.108219	+	0.357183i
$156$	4.40821	+	1.73568i	0.352939	+	0.138965i
$157$			6.89136i			0.549990i	0.961446	+	0.274995i	$0.0886763\pi$
$157$			6.89136i			0.549990i	−0.961446	+	0.274995i	$0.911324\pi$
$158$	−10.0411	−	2.94967i	−0.798825	−	0.234663i
$159$	−0.535950	−	2.69440i	−0.0425036	−	0.213680i
$160$	−4.32579	+	11.8864i	−0.341984	+	0.939706i
$161$	−4.38292	+	10.5813i	−0.345422	+	0.833923i
$162$	0.190595	+	0.608962i	0.0149746	+	0.0478445i
$163$	3.64780	+	18.3387i	0.285718	+	1.43640i	0.810787	+	0.585341i	$0.199039\pi$
$163$	3.64780	+	18.3387i	0.285718	+	1.43640i	−0.525070	+	0.851059i	$0.675961\pi$
$164$	−2.35313	+	0.0414270i	−0.183749	+	0.00323491i
$165$	−1.98155	−	0.601823i	−0.154263	−	0.0468519i
$166$	−19.5376	+	16.3240i	−1.51641	+	1.26698i
$167$	11.2483	−	7.51585i	0.870417	−	0.581594i	−0.0381784	−	0.999271i	$-0.512156\pi$
$167$	11.2483	−	7.51585i	0.870417	−	0.581594i	0.908596	+	0.417677i	$0.137156\pi$
$168$	−7.12073	+	9.15946i	−0.549376	+	0.706668i
$169$	7.80105			0.600081
$170$	−12.9130	+	1.80390i	−0.990383	+	0.138353i
$171$		−	12.3602i		−	0.945206i
$172$	−6.00018	+	9.33141i	−0.457510	+	0.711513i
$173$	4.62233	+	6.91780i	0.351429	+	0.525951i	0.964502	−	0.264076i	$-0.0850668\pi$
$173$	4.62233	+	6.91780i	0.351429	+	0.525951i	−0.613073	+	0.790026i	$0.710067\pi$
$174$	1.48165	+	1.77334i	0.112324	+	0.134437i
$175$	−7.56696	+	18.2336i	−0.572009	+	1.37833i
$176$	−0.572135	+	3.51969i	−0.0431263	+	0.265307i
$177$	10.1944	−	2.02780i	0.766261	−	0.152419i
$178$	4.34733	+	13.8899i	0.325846	+	1.04110i
$179$	10.6251	+	4.40106i	0.794158	+	0.328951i	0.742614	−	0.669720i	$-0.233586\pi$
$179$	10.6251	+	4.40106i	0.794158	+	0.328951i	0.0515440	+	0.998671i	$0.483586\pi$
$180$	−6.54480	+	5.56304i	−0.487821	+	0.414645i
$181$	11.2333	−	2.23443i	0.834961	−	0.166084i	0.240946	−	0.970538i	$-0.422542\pi$
$181$	11.2333	−	2.23443i	0.834961	−	0.166084i	0.594014	+	0.804454i	$0.297542\pi$
$182$	3.58839	−	12.2154i	0.265989	−	0.905463i
$183$	8.98546			0.664224
$184$	−7.33546	−	3.67526i	−0.540777	−	0.270944i
$185$	−8.85520	+	16.5535i	−0.651047	+	1.21704i
$186$	−3.04083	−	0.272494i	−0.222964	−	0.0199802i
$187$	−3.48124	+	1.17952i	−0.254573	+	0.0862550i
$188$	−4.36226	+	3.02718i	−0.318150	+	0.220779i
$189$	−18.6475	+	7.72405i	−1.35641	+	0.561842i
$190$	18.7344	−	7.94649i	1.35913	−	0.576499i
$191$	5.11132	−	5.11132i	0.369842	−	0.369842i	−0.497578	−	0.867419i	$-0.665777\pi$
$191$	5.11132	−	5.11132i	0.369842	−	0.369842i	0.867419	+	0.497578i	$0.165777\pi$
$192$	−6.17888	−	5.55846i	−0.445923	−	0.401147i
$193$	9.80938	−	14.6808i	0.706094	−	1.05674i	−0.288953	−	0.957343i	$-0.593307\pi$
$193$	9.80938	−	14.6808i	0.706094	−	1.05674i	0.995047	−	0.0994016i	$-0.0316928\pi$
$194$	0.177856	+	0.143361i	0.0127693	+	0.0102928i
$195$	−2.49846	+	4.67052i	−0.178919	+	0.334463i
$196$	14.4486	+	9.29057i	1.03204	+	0.663612i
$197$	−10.3842	+	2.06555i	−0.739844	+	0.147164i	−0.550604	−	0.834767i	$-0.685602\pi$
$197$	−10.3842	+	2.06555i	−0.739844	+	0.147164i	−0.189240	+	0.981931i	$0.560602\pi$
$198$	−1.51964	+	1.88529i	−0.107996	+	0.133981i
$199$	−0.727150	−	1.08826i	−0.0515463	−	0.0771445i	0.804801	−	0.593544i	$-0.202272\pi$
$199$	−0.727150	−	1.08826i	−0.0515463	−	0.0771445i	−0.856348	+	0.516400i	$0.827272\pi$
$200$	−12.6396	−	6.34344i	−0.893758	−	0.448549i
$201$	0.171082	−	0.860087i	0.0120672	−	0.0606658i
$202$	7.44836	+	3.89734i	0.524065	+	0.274216i
$203$	4.39116	−	4.39116i	0.308199	−	0.308199i
$204$	2.07600	−	8.31159i	0.145349	−	0.581928i
$205$	0.258792	−	2.61853i	0.0180748	−	0.182886i
$206$	−18.9878	+	5.94287i	−1.32294	+	0.414060i
$207$	−3.09539	−	4.63257i	−0.215144	−	0.321986i
$208$	8.54386	+	3.19150i	0.592410	+	0.221290i
$209$	4.77001	−	3.18722i	0.329948	−	0.220464i
$210$	−9.24930	−	9.09401i	−0.638262	−	0.627547i
$211$	11.8854	+	7.94154i	0.818222	+	0.546718i	0.892777	−	0.450498i	$-0.148754\pi$
$211$	11.8854	+	7.94154i	0.818222	+	0.546718i	−0.0745553	+	0.997217i	$0.523754\pi$
$212$	−1.12292	−	5.16810i	−0.0771222	−	0.354947i
$213$	−3.58985	−	8.66666i	−0.245972	−	0.593830i
$214$	22.1935	+	17.8892i	1.51712	+	1.22288i
$215$	−9.58539	−	7.87192i	−0.653718	−	0.536860i
$216$	−4.56112	−	13.7209i	−0.310345	−	0.933589i
$217$			8.20446i			0.556955i
$218$	14.9655	−	8.16937i	1.01359	−	0.553300i
$219$	−6.02196	−	14.5383i	−0.406927	−	0.982408i
$220$	−3.83453	−	1.09126i	−0.258524	−	0.0735726i
$221$	1.22181	+	9.32144i	0.0821880	+	0.627028i
$222$	−7.90887	−	9.46585i	−0.530808	−	0.635306i
$223$	1.63852	−	3.95573i	0.109723	−	0.264895i	−0.859475	−	0.511178i	$-0.829209\pi$
$223$	1.63852	−	3.95573i	0.109723	−	0.264895i	0.969198	+	0.246283i	$0.0792093\pi$
$224$	−13.3958	+	17.8717i	−0.895044	+	1.19410i
$225$	−5.33005	−	7.98861i	−0.355337	−	0.532574i
$226$	3.66543	+	6.71471i	0.243821	+	0.446656i
$227$	−2.11208	+	3.16095i	−0.140184	+	0.209800i	−0.894918	−	0.446231i	$-0.852766\pi$
$227$	−2.11208	+	3.16095i	−0.140184	+	0.209800i	0.754734	+	0.656031i	$0.227766\pi$
$228$	0.235362	+	13.3690i	0.0155872	+	0.885382i
$229$	3.17302	−	7.66034i	0.209679	−	0.506210i	−0.783694	−	0.621147i	$-0.786667\pi$
$229$	3.17302	−	7.66034i	0.209679	−	0.506210i	0.993373	+	0.114938i	$0.0366668\pi$
$230$	5.03155	−	7.67002i	0.331771	−	0.505746i
$231$	−3.04041	−	2.03154i	−0.200045	−	0.133665i
$232$	2.91202	+	3.36317i	0.191184	+	0.220803i
$233$	−2.54747	+	12.8070i	−0.166890	+	0.839013i	0.803095	+	0.595851i	$0.203185\pi$
$233$	−2.54747	+	12.8070i	−0.166890	+	0.839013i	−0.969985	+	0.243163i	$0.921815\pi$
$234$	3.97107	+	4.75283i	0.259597	+	0.310702i
$235$	−2.79666	−	5.23642i	−0.182434	−	0.341586i
$236$	19.5538	−	4.24862i	1.27285	−	0.276562i
$237$	5.43619	+	5.43619i	0.353119	+	0.353119i
$238$	−22.7448	−	3.56305i	−1.47433	−	0.230958i
$239$			5.81216i			0.375957i	0.982173	+	0.187979i	$0.0601936\pi$
$239$			5.81216i			0.375957i	−0.982173	+	0.187979i	$0.939806\pi$
$240$	6.97304	−	6.14171i	0.450108	−	0.396446i
$241$	−12.3194	−	2.45048i	−0.793561	−	0.157849i	−0.218368	−	0.975867i	$-0.570073\pi$
$241$	−12.3194	−	2.45048i	−0.793561	−	0.157849i	−0.575193	+	0.818018i	$0.695073\pi$
$242$	14.3748	+	1.28816i	0.924050	+	0.0828058i
$243$	3.08340	−	15.5013i	0.197800	−	0.994409i
$244$	17.2955	−	0.304488i	1.10723	−	0.0194928i
$245$	−12.1887	+	14.8418i	−0.778709	+	0.948210i
$246$	1.53187	+	0.801545i	0.0976682	+	0.0511046i
$247$	−5.61516	−	13.5562i	−0.357284	−	0.862560i
$248$	−5.86230	−	0.421461i	−0.372256	−	0.0267628i
$249$	18.3434	−	3.64873i	1.16247	−	0.231229i
$250$	8.68162	−	13.2147i	0.549074	−	0.835774i
$251$	−9.23711	+	9.23711i	−0.583041	+	0.583041i	−0.935738	−	0.352697i	$-0.885265\pi$
$251$	−9.23711	+	9.23711i	−0.583041	+	0.583041i	0.352697	+	0.935738i	$0.385265\pi$
$252$	−13.9081	+	6.04988i	−0.876126	+	0.381107i
$253$	0.989609	−	2.38913i	0.0622162	−	0.150203i
$254$	2.01390	+	0.180470i	0.126364	+	0.0113237i
$255$	8.96117	+	3.38199i	0.561170	+	0.211788i
$256$	−12.0816	−	10.4897i	−0.755103	−	0.655606i
$257$	27.8225	+	11.5245i	1.73552	+	0.718877i	0.999103	+	0.0423523i	$0.0134852\pi$
$257$	27.8225	+	11.5245i	1.73552	+	0.718877i	0.736420	+	0.676525i	$0.236515\pi$
$258$	7.15336	−	3.90488i	0.445348	−	0.243107i
$259$	−23.4394	+	23.4394i	−1.45645	+	1.45645i
$260$	−4.65084	+	9.07461i	−0.288433	+	0.562783i
$261$	0.589362	+	2.96292i	0.0364806	+	0.183400i
$262$	−1.63583	−	15.2332i	−0.101062	−	0.941108i
$263$	−5.56305	−	13.4304i	−0.343032	−	0.828154i	−0.997406	−	0.0719821i	$-0.977068\pi$
$263$	−5.56305	−	13.4304i	−0.343032	−	0.828154i	0.654373	−	0.756172i	$-0.272932\pi$
$264$	1.60777	−	2.06809i	0.0989515	−	0.127282i
$265$	5.88466	−	0.577591i	0.361492	−	0.0354811i
$266$	35.7271	−	3.83660i	2.19057	−	0.235237i
$267$	2.08586	−	10.4863i	0.127653	−	0.641753i
$268$	0.300158	−	1.66132i	0.0183350	−	0.101481i
$269$	−1.19490	+	6.00716i	−0.0728542	+	0.366263i	−0.999964	−	0.00852785i	$-0.997285\pi$
$269$	−1.19490	+	6.00716i	−0.0728542	+	0.366263i	0.927109	+	0.374791i	$0.122285\pi$
$270$	15.8279	−	3.28790i	0.963257	−	0.200095i
$271$		−	5.05018i		−	0.306777i	−0.988166	−	0.153388i	$-0.950981\pi$
$271$		−	5.05018i		−	0.306777i	0.988166	−	0.153388i	$-0.0490185\pi$
$272$	3.71428	−	16.0687i	0.225211	−	0.974310i
$273$	−6.61334	+	6.61334i	−0.400258	+	0.400258i
$274$	1.38173	+	4.41469i	0.0834733	+	0.266701i
$275$	1.70853	−	4.11692i	0.103028	−	0.248259i
$276$	3.43624	+	4.95173i	0.206837	+	0.298059i
$277$	−13.6623	−	2.71759i	−0.820886	−	0.163284i	−0.233257	−	0.972415i	$-0.574938\pi$
$277$	−13.6623	−	2.71759i	−0.820886	−	0.163284i	−0.587629	+	0.809131i	$0.699938\pi$
$278$	−19.7350	−	15.9075i	−1.18363	−	0.954068i
$279$	−3.31855	−	2.21739i	−0.198677	−	0.132751i
$280$	−18.1115	−	17.1910i	−1.08237	−	1.02736i
$281$	−23.3760	−	9.68267i	−1.39450	−	0.577619i	−0.446179	−	0.894944i	$-0.647216\pi$
$281$	−23.3760	−	9.68267i	−1.39450	−	0.577619i	−0.948317	+	0.317324i	$0.897216\pi$
$282$	3.87826	−	0.416473i	0.230947	−	0.0248006i
$283$	0.868117	−	1.29923i	0.0516042	−	0.0772311i	−0.804770	−	0.593586i	$-0.797712\pi$
$283$	0.868117	−	1.29923i	0.0516042	−	0.0772311i	0.856375	+	0.516355i	$0.172712\pi$
$284$	−7.20353	−	16.5602i	−0.427451	−	0.982666i
$285$	−14.8768	−	1.47029i	−0.881226	−	0.0870923i
$286$	−0.810214	+	2.75808i	−0.0479090	+	0.163089i
$287$	1.77800	−	4.29246i	0.104952	−	0.253376i
$288$	−3.60834	−	10.2485i	−0.212624	−	0.603896i
$289$	16.4257	−	4.38129i	0.966219	−	0.257723i
$290$	−4.11200	+	2.79819i	−0.241465	+	0.164316i
$291$	−0.0642198	−	0.155040i	−0.00376463	−	0.00908863i
$292$	−12.0839	−	27.7797i	−0.707157	−	1.62568i
$293$	2.86120			0.167153			0.0835765	−	0.996501i	$-0.473366\pi$
$293$	2.86120			0.167153			0.0835765	+	0.996501i	$0.473366\pi$
$294$	−6.04625	−	11.0761i	−0.352624	−	0.645973i
$295$	2.18535	+	22.2649i	0.127236	+	1.29631i
$296$	−15.5440	−	17.9521i	−0.903475	−	1.04345i
$297$	4.21038	−	1.74400i	0.244311	−	0.101197i
$298$	9.13711	+	29.1935i	0.529298	+	1.69113i
$299$	−5.49946	−	3.67462i	−0.318042	−	0.212509i
$300$	5.91720	+	8.53912i	0.341629	+	0.493007i
$301$	−12.1676	−	18.2101i	−0.701330	−	1.04961i
$302$	−1.21499	+	13.5584i	−0.0699151	+	0.780199i
$303$	−3.43087	−	5.13466i	−0.197098	−	0.294978i
$304$	0.906062	+	25.7250i	0.0519662	+	1.47543i
$305$	−1.90211	+	19.2461i	−0.108915	+	1.10203i
$306$	7.58834	−	8.23689i	0.433796	−	0.470872i
$307$	−5.63745	+	5.63745i	−0.321746	+	0.321746i	−0.849437	−	0.527690i	$-0.823058\pi$
$307$	−5.63745	+	5.63745i	−0.321746	+	0.321746i	0.527690	+	0.849437i	$0.323058\pi$
$308$	−5.92111	−	3.80733i	−0.337387	−	0.216943i
$309$	14.3350	+	2.85140i	0.815488	+	0.162211i
$310$	1.22737	−	6.45552i	0.0697097	−	0.366649i
$311$	15.3185	+	22.9258i	0.868633	+	1.30000i	0.952815	+	0.303550i	$0.0981720\pi$
$311$	15.3185	+	22.9258i	0.868633	+	1.30000i	−0.0841828	+	0.996450i	$0.526828\pi$
$312$	−4.38568	−	5.06513i	−0.248290	−	0.286756i
$313$	−2.03911	−	10.2513i	−0.115257	−	0.579438i	−0.994647	−	0.103334i	$-0.967049\pi$
$313$	−2.03911	−	10.2513i	−0.115257	−	0.579438i	0.879389	−	0.476103i	$-0.157951\pi$
$314$	4.51834	−	8.63518i	0.254985	−	0.487311i
$315$	−4.91694	−	16.2286i	−0.277038	−	0.914379i
$316$	10.6480	+	10.2795i	0.598994	+	0.578268i
$317$	14.7309	+	9.84290i	0.827372	+	0.552832i	0.895612	−	0.444837i	$-0.146738\pi$
$317$	14.7309	+	9.84290i	0.827372	+	0.552832i	−0.0682397	+	0.997669i	$0.521738\pi$
$318$	−1.09502	+	3.72761i	−0.0614058	+	0.209034i
$319$	−0.991469	+	0.991469i	−0.0555116	+	0.0555116i
$320$	13.2138	−	12.0580i	0.738673	−	0.674064i
$321$	−8.01358	−	19.3465i	−0.447275	−	1.07982i
$322$	12.4296	−	10.3852i	0.692677	−	0.578742i
$323$	−22.9859	+	13.2536i	−1.27897	+	0.737448i
$324$	0.160443	−	0.888020i	0.00891348	−	0.0493345i
$325$	−9.47499	−	6.34020i	−0.525578	−	0.351691i
$326$	7.45297	−	25.3709i	0.412782	−	1.40517i
$327$	−12.5251			−0.692640
$328$	2.97574	+	1.49093i	0.164308	+	0.0823226i
$329$	−2.04496	−	10.2807i	−0.112742	−	0.566794i
$330$	2.08838	+	2.05332i	0.114961	+	0.113031i
$331$	−18.2151	−	7.54496i	−1.00120	−	0.414709i	−0.178960	−	0.983856i	$-0.557273\pi$
$331$	−18.2151	−	7.54496i	−1.00120	−	0.414709i	−0.822235	+	0.569148i	$0.807273\pi$
$332$	35.1843	−	7.64478i	1.93099	−	0.419562i
$333$	−3.14593	−	15.8157i	−0.172396	−	0.866693i
$334$	−19.0224	+	2.04274i	−1.04086	+	0.111774i
$335$	1.80602	+	0.548514i	0.0986735	+	0.0299685i
$336$	14.9280	−	6.80849i	0.814390	−	0.371434i
$337$	−24.2225	+	16.1850i	−1.31948	+	0.881651i	−0.997871	−	0.0652205i	$-0.979225\pi$
$337$	−24.2225	+	16.1850i	−1.31948	+	0.881651i	−0.321613	+	0.946871i	$0.604225\pi$
$338$	−9.77507	−	5.11478i	−0.531694	−	0.278207i
$339$		−	5.61977i		−	0.305224i
$340$	17.3633	+	6.20608i	0.941658	+	0.336572i
$341$		−	1.85247i		−	0.100317i
$342$	−8.10398	+	15.4878i	−0.438213	+	0.837487i
$343$	−5.21612	+	3.48530i	−0.281644	+	0.188189i
$344$	13.6367	−	7.75863i	0.735239	−	0.418317i
$345$	−5.94401	+	3.17457i	−0.320015	+	0.170913i
$346$	−1.25631	−	11.6990i	−0.0675395	−	0.628940i
$347$	−0.0550933	−	0.276973i	−0.00295756	−	0.0148687i	0.979278	−	0.202519i	$-0.0649128\pi$
$347$	−0.0550933	−	0.276973i	−0.00295756	−	0.0148687i	−0.982236	+	0.187650i	$0.939913\pi$
$348$	−0.693884	−	3.19352i	−0.0371961	−	0.171191i
$349$	−4.41812	−	1.83005i	−0.236497	−	0.0979602i	0.261288	−	0.965261i	$-0.415853\pi$
$349$	−4.41812	−	1.83005i	−0.236497	−	0.0979602i	−0.497784	+	0.867301i	$0.665853\pi$
$350$	21.4366	−	17.8862i	1.14584	−	0.956057i
$351$	−2.27400	−	11.4322i	−0.121377	−	0.610205i
$352$	3.02460	−	4.03521i	0.161212	−	0.215077i
$353$	27.7209			1.47543			0.737717	−	0.675110i	$-0.235904\pi$
$353$	27.7209			1.47543			0.737717	+	0.675110i	$0.235904\pi$
$354$	−14.1036	−	4.14308i	−0.749598	−	0.220202i
$355$	19.3232	−	5.85455i	1.02557	−	0.310727i
$356$	3.65957	−	20.2550i	0.193957	−	1.07352i
$357$	13.4116	+	10.3032i	0.709817	+	0.545302i
$358$	−10.4282	−	12.4811i	−0.551146	−	0.659647i
$359$	3.49004	+	8.42569i	0.184197	+	0.444691i	0.988824	−	0.149090i	$-0.0476345\pi$
$359$	3.49004	+	8.42569i	0.184197	+	0.444691i	−0.804627	+	0.593781i	$0.797634\pi$
$360$	11.8483	−	2.67962i	0.624463	−	0.141229i
$361$	15.8479	−	15.8479i	0.834101	−	0.834101i
$362$	−15.5408	−	4.56526i	−0.816805	−	0.239945i
$363$	−8.81540	−	5.89026i	−0.462688	−	0.309159i
$364$	−12.5054	+	12.9537i	−0.655463	+	0.678956i
$365$	32.4147	−	9.82099i	1.69666	−	0.514054i
$366$	−11.2592	−	5.89134i	−0.588526	−	0.307945i
$367$	−1.84961	−	9.29863i	−0.0965489	−	0.485384i	−0.998559	−	0.0536689i	$-0.982908\pi$
$367$	−1.84961	−	9.29863i	−0.0965489	−	0.485384i	0.902010	−	0.431715i	$-0.142092\pi$
$368$	6.78196	+	9.41478i	0.353534	+	0.490779i
$369$	1.25569	+	1.87927i	0.0653686	+	0.0978310i
$370$	21.9493	−	14.9364i	1.14109	−	0.776505i
$371$	10.2400	+	2.03686i	0.531634	+	0.105749i
$372$	3.63163	+	2.33517i	0.188291	+	0.121073i
$373$	21.2294	−	21.2294i	1.09922	−	1.09922i	0.104714	−	0.994502i	$-0.466607\pi$
$373$	21.2294	−	21.2294i	1.09922	−	1.09922i	0.994502	−	0.104714i	$-0.0333928\pi$
$374$	5.13550	+	0.804492i	0.265550	+	0.0415993i
$375$	−10.2492	+	5.46502i	−0.529266	+	0.282213i
$376$	7.45088	−	0.933060i	0.384250	−	0.0481189i
$377$	1.99243	+	2.98188i	0.102615	+	0.153575i
$378$	28.4304	+	2.54771i	1.46230	+	0.131040i
$379$	−12.1218	−	18.1416i	−0.622656	−	0.931871i	−0.999983	−	0.00579091i	$-0.998157\pi$
$379$	−12.1218	−	18.1416i	−0.622656	−	0.931871i	0.377327	−	0.926080i	$-0.376843\pi$
$380$	−28.6851	−	2.32593i	−1.47152	−	0.119317i
$381$	−1.23503	−	0.825221i	−0.0632725	−	0.0422773i
$382$	−9.75595	+	3.05346i	−0.499158	+	0.156229i
$383$	9.75871	−	4.04219i	0.498647	−	0.206546i	−0.119162	−	0.992875i	$-0.538021\pi$
$383$	9.75871	−	4.04219i	0.498647	−	0.206546i	0.617809	+	0.786329i	$0.288021\pi$
$384$	4.09800	+	11.0162i	0.209125	+	0.562168i
$385$	4.99502	−	6.08227i	0.254570	−	0.309981i
$386$	−21.9171	+	11.9641i	−1.11555	+	0.608957i
$387$	10.6542			0.541581
$388$	−0.128866	−	0.296250i	−0.00654218	−	0.0150398i
$389$	8.99050	+	21.7050i	0.455837	+	1.10049i	0.970068	+	0.242835i	$0.0780774\pi$
$389$	8.99050	+	21.7050i	0.455837	+	1.10049i	−0.514231	+	0.857652i	$0.671923\pi$
$390$	6.19292	−	4.21424i	0.313591	−	0.213397i
$391$	−5.29597	+	10.7238i	−0.267829	+	0.542327i
$392$	−12.0133	−	21.1147i	−0.606764	−	1.06646i
$393$	−4.30701	+	10.3980i	−0.217260	+	0.524511i
$394$	14.3661	+	4.22021i	0.723756	+	0.212611i
$395$	−12.7947	+	10.4931i	−0.643770	+	0.527966i
$396$	3.14027	−	1.36599i	0.157805	−	0.0686435i
$397$	22.0984	−	33.0727i	1.10909	−	1.65987i	0.504044	−	0.863678i	$-0.331845\pi$
$397$	22.0984	−	33.0727i	1.10909	−	1.65987i	0.605045	−	0.796191i	$-0.293155\pi$
$398$	0.197633	+	1.84039i	0.00990645	+	0.0922505i
$399$	−24.3870	−	10.1014i	−1.22088	−	0.505704i
$400$	11.6789	+	16.2358i	0.583947	+	0.811792i
$401$	−28.1385	−	18.8015i	−1.40517	−	0.938903i	−0.999693	−	0.0247967i	$-0.992106\pi$
$401$	−28.1385	−	18.8015i	−1.40517	−	0.938903i	−0.405475	−	0.914106i	$-0.632894\pi$
$402$	−0.778291	+	0.965557i	−0.0388176	+	0.0481576i
$403$	−4.64701	−	0.924349i	−0.231484	−	0.0460451i
$404$	−6.77783	−	9.76707i	−0.337209	−	0.485930i
$405$	0.965369	+	0.293196i	0.0479696	+	0.0145690i
$406$	−8.38139	+	2.62324i	−0.415961	+	0.130189i
$407$	5.29232	−	5.29232i	0.262331	−	0.262331i
$408$	−8.05083	+	9.05366i	−0.398575	+	0.448223i
$409$		−	27.5497i		−	1.36224i	−0.732170	−	0.681122i	$-0.761492\pi$
$409$		−	27.5497i		−	1.36224i	0.732170	−	0.681122i	$-0.238508\pi$
$410$	−2.04112	+	3.11146i	−0.100804	+	0.153664i
$411$	0.662956	−	3.33291i	0.0327012	−	0.164400i
$412$	27.6890	+	5.00270i	1.36414	+	0.246465i
$413$	−7.70658	+	38.7436i	−0.379216	+	1.90645i
$414$	0.841298	+	7.83431i	0.0413476	+	0.385036i
$415$	3.93222	+	40.0626i	0.193025	+	1.96659i
$416$	−8.61332	−	9.60089i	−0.422303	−	0.470722i
$417$	7.12588	+	17.2034i	0.348956	+	0.842454i
$418$	−8.06674	+	0.866257i	−0.394557	+	0.0423700i
$419$	7.40631	+	37.2340i	0.361822	+	1.81900i	0.547993	+	0.836483i	$0.315392\pi$
$419$	7.40631	+	37.2340i	0.361822	+	1.81900i	−0.186171	+	0.982517i	$0.559608\pi$
$420$	5.62727	+	17.4595i	0.274583	+	0.851938i
$421$	−5.27775	+	5.27775i	−0.257222	+	0.257222i	−0.823923	−	0.566702i	$-0.808219\pi$
$421$	−5.27775	+	5.27775i	−0.257222	+	0.257222i	0.566702	+	0.823923i	$0.308219\pi$
$422$	−9.68599	−	17.7438i	−0.471507	−	0.863753i
$423$	4.71104	+	1.95138i	0.229058	+	0.0948791i
$424$	−1.98141	+	7.21211i	−0.0962260	+	0.350251i
$425$	−9.14093	+	18.4782i	−0.443400	+	0.896324i
$426$	−1.18408	+	13.2134i	−0.0573688	+	0.640191i
$427$	−13.0682	+	31.5495i	−0.632416	+	1.52679i
$428$	−16.0804	−	36.9671i	−0.777274	−	1.78687i
$429$	1.49321	−	1.49321i	0.0720929	−	0.0720929i
$430$	6.84967	+	16.1485i	0.330320	+	0.778752i
$431$	−11.9350	+	2.37401i	−0.574887	+	0.114352i	−0.473967	−	0.880543i	$-0.657178\pi$
$431$	−11.9350	+	2.37401i	−0.574887	+	0.114352i	−0.100919	+	0.994895i	$0.532178\pi$
$432$	−3.28086	+	20.1834i	−0.157851	+	0.971075i
$433$	5.95234	+	14.3702i	0.286051	+	0.690588i	0.999953	−	0.00965703i	$-0.00307398\pi$
$433$	5.95234	+	14.3702i	0.286051	+	0.690588i	−0.713902	+	0.700245i	$0.753074\pi$
$434$	5.37927	−	10.2806i	0.258213	−	0.493482i
$435$	3.63630	−	0.356911i	0.174347	−	0.0171125i
$436$	−24.1087	+	0.424435i	−1.15460	+	0.0203267i
$437$	3.64180	−	18.3086i	0.174211	−	0.875818i
$438$	−1.98629	+	22.1655i	−0.0949085	+	1.05911i
$439$	−22.3059	−	4.43693i	−1.06460	−	0.211763i	−0.368445	−	0.929650i	$-0.620110\pi$
$439$	−22.3059	−	4.43693i	−1.06460	−	0.211763i	−0.696160	+	0.717887i	$0.745110\pi$
$440$	4.08935	+	3.88151i	0.194952	+	0.185044i
$441$		−	16.4967i		−	0.785557i
$442$	4.58064	−	12.4813i	0.217879	−	0.593673i
$443$	5.08940	+	5.08940i	0.241805	+	0.241805i	0.817596	−	0.575792i	$-0.195306\pi$
$443$	5.08940	+	5.08940i	0.241805	+	0.241805i	−0.575792	+	0.817596i	$0.695306\pi$
$444$	3.70385	+	17.0466i	0.175777	+	0.808995i
$445$	22.0193	+	6.68757i	1.04382	+	0.317021i
$446$	−4.64671	+	3.88240i	−0.220028	+	0.183837i
$447$	4.38400	−	22.0399i	0.207356	−	1.04245i
$448$	28.5031	−	13.6110i	1.34665	−	0.643061i
$449$	−15.3855	−	10.2803i	−0.726087	−	0.485156i	0.136770	−	0.990603i	$-0.456328\pi$
$449$	−15.3855	−	10.2803i	−0.726087	−	0.485156i	−0.862858	+	0.505447i	$0.831328\pi$
$450$	1.44104	+	13.5047i	0.0679313	+	0.636620i
$451$	−0.401450	+	0.969185i	−0.0189035	+	0.0456371i
$452$	−0.190435	−	10.8171i	−0.00895733	−	0.508793i
$453$	5.55572	−	8.31472i	0.261031	−	0.390660i
$454$	4.71901	−	2.57602i	0.221474	−	0.120899i
$455$	−12.7653	−	15.5652i	−0.598446	−	0.729709i
$456$	8.47049	−	16.9062i	0.396667	−	0.791707i
$457$	−13.4978	+	32.5865i	−0.631399	+	1.52433i	0.206466	+	0.978454i	$0.433804\pi$
$457$	−13.4978	+	32.5865i	−0.631399	+	1.52433i	−0.837865	+	0.545878i	$0.816196\pi$
$458$	−8.99845	+	7.51835i	−0.420470	+	0.351310i
$459$	−19.9629	+	6.76387i	−0.931789	+	0.315710i
$460$	−11.3336	+	6.31193i	−0.528433	+	0.294295i
$461$	6.13885	+	14.8205i	0.285915	+	0.690260i	0.999952	−	0.00984867i	$-0.00313498\pi$
$461$	6.13885	+	14.8205i	0.285915	+	0.690260i	−0.714037	+	0.700108i	$0.753135\pi$
$462$	2.47779	+	4.53906i	0.115277	+	0.211176i
$463$			29.9900i			1.39376i	0.717190	+	0.696878i	$0.245428\pi$
$463$			29.9900i			1.39376i	−0.717190	+	0.696878i	$0.754572\pi$
$464$	−1.44382	−	6.12347i	−0.0670279	−	0.284275i
$465$	−3.06362	+	3.73047i	−0.142072	+	0.172996i
$466$	11.5890	−	14.3775i	0.536851	−	0.666023i
$467$	−3.88104	−	9.36967i	−0.179593	−	0.433576i	0.808288	−	0.588787i	$-0.200394\pi$
$467$	−3.88104	−	9.36967i	−0.179593	−	0.433576i	−0.987881	+	0.155211i	$0.950394\pi$
$468$	−1.85972	−	8.55915i	−0.0859655	−	0.395647i
$469$	2.77110	+	1.85159i	0.127957	+	0.0854983i
$470$	0.0710701	+	8.39510i	0.00327822	+	0.387237i
$471$	−5.95281	+	3.97754i	−0.274291	+	0.183275i
$472$	−27.2874	−	7.49680i	−1.25601	−	0.345068i
$473$	2.74730	+	4.11162i	0.126321	+	0.189053i
$474$	−3.24754	−	10.3760i	−0.149164	−	0.476588i
$475$	6.29848	−	31.5537i	0.288994	−	1.44778i
$476$	26.1642	+	19.3774i	1.19923	+	0.888159i
$477$	−3.59139	+	3.59139i	−0.164439	+	0.164439i
$478$	3.81075	−	7.28289i	0.174300	−	0.333112i
$479$	−3.28719	+	16.5258i	−0.150195	+	0.755084i	0.830111	+	0.557599i	$0.188277\pi$
$479$	−3.28719	+	16.5258i	−0.150195	+	0.755084i	−0.980306	+	0.197485i	$0.936723\pi$
$480$	−12.7644	+	3.12394i	−0.582610	+	0.142588i
$481$	−10.6353	−	15.9169i	−0.484928	−	0.725747i
$482$	13.8301	+	11.1478i	0.629942	+	0.507768i
$483$	−11.6699	+	2.32129i	−0.531000	+	0.105622i
$484$	−17.1677	−	11.0390i	−0.780351	−	0.501773i
$485$	0.345679	−	0.104734i	0.0156965	−	0.00475571i
$486$	−14.0271	+	17.4022i	−0.636282	+	0.789379i
$487$	−4.85803	+	7.27055i	−0.220138	+	0.329460i	−0.925057	−	0.379828i	$-0.875983\pi$
$487$	−4.85803	+	7.27055i	−0.220138	+	0.329460i	0.704919	+	0.709288i	$0.250983\pi$
$488$	−21.8716	−	10.9583i	−0.990081	−	0.496058i
$489$	−13.7357	+	13.7357i	−0.621150	+	0.621150i
$490$	25.0041	−	10.6059i	1.12957	−	0.479126i
$491$	−3.91165	+	1.62026i	−0.176530	+	0.0731213i	−0.469198	−	0.883093i	$-0.655457\pi$
$491$	−3.91165	+	1.62026i	−0.176530	+	0.0731213i	0.292668	+	0.956214i	$0.405457\pi$
$492$	−1.39396	−	2.00874i	−0.0628446	−	0.0905611i
$493$	4.87812	−	4.27310i	0.219699	−	0.192451i
$494$	−1.85211	+	20.6681i	−0.0833303	+	0.929902i
$495$	1.11018	+	3.66422i	0.0498991	+	0.164695i
$496$	7.06939	+	4.37174i	0.317425	+	0.196297i
$497$	35.6511			1.59917
$498$	−25.3774	−	7.45488i	−1.13719	−	0.334061i
$499$	7.61266	−	1.51425i	0.340789	−	0.0677872i	−0.0217289	−	0.999764i	$-0.506917\pi$
$499$	7.61266	−	1.51425i	0.340789	−	0.0677872i	0.362518	+	0.931977i	$0.381917\pi$
$500$	−19.5427	+	10.8665i	−0.873977	+	0.485966i
$501$	12.9845	+	5.37836i	0.580105	+	0.240287i
$502$	17.6308	−	5.51817i	0.786903	−	0.246288i
$503$	39.5570	−	7.86838i	1.76376	−	0.350834i	0.796504	−	0.604633i	$-0.206680\pi$
$503$	39.5570	−	7.86838i	1.76376	−	0.350834i	0.967257	+	0.253800i	$0.0816804\pi$
$504$	21.3940	+	1.53809i	0.952967	+	0.0685120i
$505$	11.7243	−	6.26170i	0.521725	−	0.278642i
$506$	−2.80646	+	2.34484i	−0.124762	+	0.104241i
$507$	4.50260	+	6.73861i	0.199967	+	0.299272i
$508$	−2.40518	−	1.54656i	−0.106713	−	0.0686174i
$509$		−	43.3283i		−	1.92049i	−0.279152	−	0.960247i	$-0.590053\pi$
$509$		−	43.3283i		−	1.92049i	0.279152	−	0.960247i	$-0.409947\pi$
$510$	−9.01133	−	10.1132i	−0.399028	−	0.447820i
$511$	59.8047			2.64560
$512$	8.26124	+	21.0654i	0.365099	+	0.930969i
$513$	27.3533	−	18.2769i	1.20768	−	0.806943i
$514$	−27.3068	−	32.6826i	−1.20445	−	1.44157i
$515$	−9.14202	+	30.1008i	−0.402846	+	1.32640i
$516$	−11.5237	+	0.202876i	−0.507303	+	0.00893111i
$517$	0.461727	+	2.32126i	0.0203067	+	0.102089i
$518$	44.7387	−	14.0025i	1.96570	−	0.615234i
$519$	−3.30775	+	7.98561i	−0.145194	+	0.350529i
$520$	11.7775	−	8.32155i	0.516478	−	0.364924i
$521$	−4.28477	−	21.5410i	−0.187719	−	0.943729i	−0.953676	−	0.300836i	$-0.902734\pi$
$521$	−4.28477	−	21.5410i	−0.187719	−	0.943729i	0.765956	−	0.642892i	$-0.222266\pi$
$522$	1.20415	−	4.09909i	0.0527042	−	0.179412i
$523$		−	16.7021i		−	0.730331i	−0.930943	−	0.365166i	$-0.881012\pi$
$523$		−	16.7021i		−	0.730331i	0.930943	−	0.365166i	$-0.118988\pi$
$524$	−7.93789	+	20.1604i	−0.346768	+	0.880710i
$525$	−20.1178	+	3.98762i	−0.878012	+	0.174034i
$526$	−1.83492	+	20.4763i	−0.0800063	+	0.892809i
$527$	−0.565207	+	8.54909i	−0.0246208	+	0.372404i
$528$	−3.37056	+	1.53727i	−0.146685	+	0.0669013i
$529$	5.58160	+	13.4752i	0.242678	+	0.585878i
$530$	−7.75243	−	3.13454i	−0.336744	−	0.136156i
$531$	−13.5882	−	13.5882i	−0.589680	−	0.589680i
$532$	−47.2831	−	18.6171i	−2.04998	−	0.807155i
$533$	2.23094	+	1.49067i	0.0966327	+	0.0645679i
$534$	−9.48906	+	11.7722i	−0.410632	+	0.509434i
$535$	43.1351	−	13.0690i	1.86489	−	0.565024i
$536$	−1.46536	+	1.88490i	−0.0632938	+	0.0814154i
$537$	2.33091	+	11.7183i	0.100586	+	0.505680i
$538$	5.43587	−	6.74380i	0.234357	−	0.290746i
$539$	6.36636	−	4.25387i	0.274219	−	0.183227i
$540$	−21.9888	−	6.25774i	−0.946248	−	0.269290i
$541$	−23.3800	−	4.65057i	−1.00518	−	0.199944i	−0.335063	−	0.942196i	$-0.608758\pi$
$541$	−23.3800	−	4.65057i	−1.00518	−	0.199944i	−0.670121	+	0.742252i	$0.733758\pi$
$542$	−3.31116	+	6.32810i	−0.142227	+	0.271815i
$543$	8.41370	+	8.41370i	0.361067	+	0.361067i
$544$	−15.1897	+	17.6996i	−0.651251	+	0.758862i
$545$	2.65141	−	26.8278i	0.113574	−	1.14918i
$546$	12.6229	−	3.95076i	0.540209	−	0.169077i
$547$	1.76337	−	1.17825i	0.0753964	−	0.0503782i	−0.517301	−	0.855804i	$-0.673063\pi$
$547$	1.76337	−	1.17825i	0.0753964	−	0.0503782i	0.592697	+	0.805425i	$0.298063\pi$
$548$	1.16314	−	6.43774i	0.0496867	−	0.275006i
$549$	−9.22929	−	13.8126i	−0.393896	−	0.589508i
$550$	−4.84013	+	4.03848i	−0.206384	+	0.172201i
$551$	−5.62329	+	8.41584i	−0.239560	+	0.358527i
$552$	−1.05914	−	8.45771i	−0.0450801	−	0.359984i
$553$	−26.9937	+	11.1811i	−1.14789	+	0.475471i
$554$	15.3376	+	12.3630i	0.651634	+	0.525252i
$555$	−19.4101	+	1.90514i	−0.823912	+	0.0808686i
$556$	14.2991	+	32.8721i	0.606415	+	1.39409i
$557$	−15.7521			−0.667436			−0.333718	−	0.942673i	$-0.608303\pi$
$557$	−15.7521			−0.667436			−0.333718	+	0.942673i	$0.608303\pi$
$558$	2.70446	+	4.95430i	0.114489	+	0.209732i
$559$	11.6851	−	4.84012i	0.494227	−	0.204715i
$560$	11.4232	+	33.4159i	0.482717	+	1.41208i
$561$	−3.02817	−	2.32633i	−0.127850	−	0.0982177i
$562$	22.9427	+	27.4594i	0.967781	+	1.15830i
$563$	12.4032	+	5.13757i	0.522732	+	0.216523i	0.628416	−	0.777877i	$-0.283703\pi$
$563$	12.4032	+	5.13757i	0.522732	+	0.216523i	−0.105685	+	0.994400i	$0.533703\pi$
$564$	−5.13270	−	2.02093i	−0.216126	−	0.0850967i
$565$	12.0371	+	1.18964i	0.506404	+	0.0500484i
$566$	−1.93963	+	1.05881i	−0.0815288	+	0.0445050i
$567$	1.48123	+	0.989725i	0.0622057	+	0.0415645i
$568$	−1.83139	+	25.4737i	−0.0768433	+	1.06885i
$569$	−26.3755	−	10.9251i	−1.10572	−	0.458004i	−0.246258	−	0.969204i	$-0.579201\pi$
$569$	−26.3755	−	10.9251i	−1.10572	−	0.458004i	−0.859462	+	0.511200i	$0.829201\pi$
$570$	17.6773	+	11.5964i	0.740421	+	0.485718i
$571$	−0.324508	+	0.485661i	−0.0135802	+	0.0203243i	−0.838198	−	0.545367i	$-0.816390\pi$
$571$	−0.324508	+	0.485661i	−0.0135802	+	0.0203243i	0.824617	+	0.565691i	$0.191390\pi$
$572$	2.82357	−	2.92477i	0.118060	−	0.122291i
$573$	7.36534	+	1.46506i	0.307691	+	0.0612036i
$574$	−5.04227	+	4.21290i	−0.210460	+	0.175843i
$575$	−5.54141	−	13.4036i	−0.231093	−	0.558970i
$576$	−2.19801	+	15.2076i	−0.0915838	+	0.633650i
$577$	−21.8681	+	21.8681i	−0.910379	+	0.910379i	−0.996302	−	0.0859228i	$-0.972616\pi$
$577$	−21.8681	+	21.8681i	−0.910379	+	0.910379i	0.0859228	+	0.996302i	$0.472616\pi$
$578$	−23.4548	−	5.27961i	−0.975589	−	0.219603i
$579$	18.3431			0.762314
$580$	6.98717	−	0.810214i	0.290126	−	0.0336423i
$581$	−13.8669	+	69.7135i	−0.575295	+	2.89220i
$582$	−0.0211823	+	0.236378i	−0.000878035	+	0.00979820i
$583$	−2.31206	−	0.459898i	−0.0957559	−	0.0190470i
$584$	−3.07215	+	42.7320i	−0.127126	+	1.76826i
$585$	9.74587	−	0.956576i	0.402942	−	0.0395496i
$586$	−3.58521	−	1.87595i	−0.148104	−	0.0774949i
$587$	20.6047	−	8.53473i	0.850445	−	0.352266i	0.0854819	−	0.996340i	$-0.472757\pi$
$587$	20.6047	−	8.53473i	0.850445	−	0.352266i	0.764963	+	0.644074i	$0.222757\pi$
$588$	0.314129	+	17.8431i	0.0129545	+	0.735837i
$589$	−2.60881	−	13.1154i	−0.107494	−	0.540410i
$590$	11.8597	−	29.3318i	0.488257	−	1.20757i
$591$	−7.77777	−	7.77777i	−0.319935	−	0.319935i
$592$	7.70694	+	32.6862i	0.316753	+	1.34340i
$593$	21.2635	+	8.80765i	0.873189	+	0.361687i	0.773851	−	0.633367i	$-0.218328\pi$
$593$	21.2635	+	8.80765i	0.873189	+	0.361687i	0.0993374	+	0.995054i	$0.468328\pi$
$594$	−6.41924	−	0.575240i	−0.263385	−	0.0236024i
$595$	−24.9076	+	26.5455i	−1.02111	+	1.08826i
$596$	7.69159	−	42.5715i	0.315060	−	1.74380i
$597$	0.520350	−	1.25624i	0.0212965	−	0.0514143i
$598$	4.48179	+	8.21019i	0.183274	+	0.335740i
$599$	6.29900	+	6.29900i	0.257370	+	0.257370i	0.823984	−	0.566613i	$-0.191747\pi$
$599$	6.29900	+	6.29900i	0.257370	+	0.257370i	−0.566613	+	0.823984i	$0.691747\pi$
$600$	−1.81581	−	14.5795i	−0.0741302	−	0.595207i
$601$	−16.0052	+	3.18363i	−0.652866	+	0.129863i	−0.510401	−	0.859937i	$-0.670503\pi$
$601$	−16.0052	+	3.18363i	−0.652866	+	0.129863i	−0.142465	+	0.989800i	$0.545503\pi$
$602$	3.30705	+	30.7958i	0.134785	+	1.25514i
$603$	−1.49787	+	0.620436i	−0.0609978	+	0.0252661i
$604$	10.4120	−	16.1927i	0.423660	−	0.658871i
$605$	14.4826	−	17.6350i	0.588801	−	0.716964i
$606$	0.932479	+	8.68341i	0.0378794	+	0.352739i
$607$	−26.3633	−	5.24399i	−1.07005	−	0.212847i	−0.371521	−	0.928424i	$-0.621164\pi$
$607$	−26.3633	−	5.24399i	−1.07005	−	0.212847i	−0.698533	+	0.715577i	$0.746164\pi$
$608$	15.7313	−	32.8286i	0.637990	−	1.33138i
$609$	6.32760	+	1.25864i	0.256407	+	0.0510025i
$610$	15.0022	−	22.8691i	0.607422	−	0.925944i
$611$	6.05339			0.244894
$612$	−14.9091	+	5.34588i	−0.602663	+	0.216094i
$613$	27.1466	+	27.1466i	1.09644	+	1.09644i	0.994824	+	0.101616i	$0.0324014\pi$
$613$	27.1466	+	27.1466i	1.09644	+	1.09644i	0.101616	+	0.994824i	$0.467599\pi$
$614$	10.7602	−	3.36777i	0.434246	−	0.135912i
$615$	2.41128	−	1.28781i	0.0972321	−	0.0519296i
$616$	4.92313	+	8.65295i	0.198359	+	0.348637i
$617$	5.37167	−	27.0052i	0.216255	−	1.08719i	−0.708233	−	0.705979i	$-0.750507\pi$
$617$	5.37167	−	27.0052i	0.216255	−	1.08719i	0.924488	−	0.381210i	$-0.124493\pi$
$618$	−16.0928	−	12.9717i	−0.647349	−	0.521798i
$619$	7.12919	−	10.6696i	0.286546	−	0.428847i	−0.660073	−	0.751202i	$-0.729474\pi$
$619$	7.12919	−	10.6696i	0.286546	−	0.428847i	0.946619	+	0.322355i	$0.104474\pi$
$620$	−5.77052	+	7.28433i	−0.231750	+	0.292546i
$621$	5.67484	−	13.7003i	0.227723	−	0.549773i
$622$	−4.16343	−	38.7706i	−0.166938	−	1.55456i
$623$	33.7857	+	22.5749i	1.35359	+	0.904443i
$624$	2.17449	+	9.22231i	0.0870491	+	0.369188i
$625$	−9.53602	−	23.1098i	−0.381441	−	0.924393i
$626$	−4.16619	+	14.1823i	−0.166515	+	0.566838i
$627$	5.50629	+	2.28078i	0.219900	+	0.0910855i
$628$	−11.3234	+	7.85780i	−0.451851	+	0.313561i
$629$	−26.0387	+	22.8092i	−1.03823	+	0.909463i
$630$	−4.47919	+	23.5590i	−0.178455	+	0.938612i
$631$	−2.80461	+	1.16171i	−0.111650	+	0.0462468i	−0.437809	−	0.899068i	$-0.644245\pi$
$631$	−2.80461	+	1.16171i	−0.111650	+	0.0462468i	0.326159	+	0.945315i	$0.394245\pi$
$632$	−6.60256	−	19.8621i	−0.262636	−	0.790070i
$633$			14.8504i			0.590249i
$634$	−12.0050	−	21.9920i	−0.476779	−	0.873413i
$635$	2.02900	−	2.47065i	0.0805184	−	0.0980447i
$636$	3.81613	−	3.95290i	0.151319	−	0.156743i
$637$	−7.49436	−	18.0930i	−0.296937	−	0.716870i
$638$	1.89241	−	0.592296i	0.0749214	−	0.0234492i
$639$	−9.63528	+	14.4202i	−0.381166	+	0.570455i
$640$	−24.4633	+	6.44559i	−0.966998	+	0.254784i
$641$	30.3051	−	20.2492i	1.19698	−	0.799796i	0.212822	−	0.977091i	$-0.431735\pi$
$641$	30.3051	−	20.2492i	1.19698	−	0.799796i	0.984158	+	0.177295i	$0.0567346\pi$
$642$	−2.64321	+	29.4962i	−0.104319	+	1.16412i
$643$	−29.0345	+	19.4002i	−1.14501	+	0.765069i	−0.975400	−	0.220443i	$-0.929250\pi$
$643$	−29.0345	+	19.4002i	−1.14501	+	0.765069i	−0.169607	+	0.985512i	$0.554250\pi$
$644$	−22.3839	+	4.86355i	−0.882051	+	0.191651i
$645$	1.26735	−	12.8234i	0.0499019	−	0.504922i
$646$	37.4921	−	1.53651i	1.47511	−	0.0604533i
$647$	−26.8220	−	26.8220i	−1.05448	−	1.05448i	−0.998428	−	0.0560525i	$-0.982149\pi$
$647$	−26.8220	−	26.8220i	−1.05448	−	1.05448i	−0.0560525	−	0.998428i	$-0.517851\pi$
$648$	−0.783274	+	1.00753i	−0.0307699	+	0.0395797i
$649$	1.74005	−	8.74783i	0.0683030	−	0.343382i
$650$	7.71561	+	14.1569i	0.302631	+	0.555278i
$651$	−7.08708	+	4.73543i	−0.277764	+	0.185596i
$652$	−25.9734	+	26.9043i	−1.01720	+	1.05365i
$653$	23.9087	−	4.75573i	0.935618	−	0.186106i	0.296341	−	0.955082i	$-0.404234\pi$
$653$	23.9087	−	4.75573i	0.935618	−	0.186106i	0.639277	+	0.768976i	$0.279234\pi$
$654$	15.6945	+	8.21211i	0.613704	+	0.321119i
$655$	−21.3600	−	11.4264i	−0.834605	−	0.446467i
$656$	−2.75120	−	3.81925i	−0.107416	−	0.149117i
$657$	−16.1632	+	24.1899i	−0.630585	+	0.943737i
$658$	−4.17814	+	14.2230i	−0.162881	+	0.554469i
$659$	−14.9828	−	14.9828i	−0.583648	−	0.583648i	0.352256	−	0.935904i	$-0.385415\pi$
$659$	−14.9828	−	14.9828i	−0.583648	−	0.583648i	−0.935904	+	0.352256i	$0.885415\pi$
$660$	−1.27057	−	3.94215i	−0.0494568	−	0.153448i
$661$	10.8667	−	4.50113i	0.422665	−	0.175074i	−0.161204	−	0.986921i	$-0.551538\pi$
$661$	10.8667	−	4.50113i	0.422665	−	0.175074i	0.583870	+	0.811847i	$0.301538\pi$
$662$	17.8775	+	21.3970i	0.694829	+	0.831617i
$663$	−7.34673	+	6.43554i	−0.285323	+	0.249936i
$664$	−49.0998	−	13.4894i	−1.90544	−	0.523491i
$665$	26.7989	−	50.0967i	1.03922	−	1.94267i
$666$	−6.42759	+	21.8804i	−0.249064	+	0.847847i
$667$			4.56249i			0.176660i
$668$	25.1752	+	9.91241i	0.974058	+	0.383523i
$669$	4.36270	−	0.867796i	0.168672	−	0.0335509i
$670$	−1.90339	−	1.87143i	−0.0735344	−	0.0722998i
$671$	2.95064	−	7.12349i	0.113908	−	0.274999i
$672$	−23.1695	−	1.25624i	−0.893781	−	0.0484606i
$673$	4.68093	−	0.931095i	0.180437	−	0.0358911i	−0.104045	−	0.994573i	$-0.533179\pi$
$673$	4.68093	−	0.931095i	0.180437	−	0.0358911i	0.284481	+	0.958682i	$0.408179\pi$
$674$	40.9636	−	4.39893i	1.57786	−	0.169440i
$675$	9.79742	−	23.6082i	0.377103	−	0.908678i
$676$	8.89507	+	12.8181i	0.342118	+	0.493004i
$677$	20.3758	+	30.4945i	0.783105	+	1.17200i	0.981422	+	0.191861i	$0.0614524\pi$
$677$	20.3758	+	30.4945i	0.783105	+	1.17200i	−0.198317	+	0.980138i	$0.563548\pi$
$678$	−3.68461	+	7.04181i	−0.141507	+	0.270439i
$679$	0.637773			0.0244755
$680$	−17.6880	−	19.1608i	−0.678302	−	0.734783i
$681$	−3.94950			−0.151345
$682$	−1.21457	+	2.32122i	−0.0465084	+	0.0888842i
$683$	1.47218	+	2.20328i	0.0563315	+	0.0843060i	0.858566	−	0.512703i	$-0.171356\pi$
$683$	1.47218	+	2.20328i	0.0563315	+	0.0843060i	−0.802235	+	0.597009i	$0.796356\pi$
$684$	20.3093	−	14.0936i	0.776545	−	0.538881i
$685$	6.99848	+	2.12554i	0.267398	+	0.0812125i
$686$	8.82118	−	0.947274i	0.336794	−	0.0361671i
$687$	8.44846	−	1.68050i	0.322329	−	0.0641152i
$688$	−22.1743	+	0.781002i	−0.845387	+	0.0297754i
$689$	−2.30736	+	5.57046i	−0.0879034	+	0.212218i
$690$	9.52952	−	0.0806737i	0.362783	−	0.00307120i
$691$	−16.6351	+	3.30892i	−0.632828	+	0.125877i	−0.501073	−	0.865405i	$-0.667061\pi$
$691$	−16.6351	+	3.30892i	−0.632828	+	0.125877i	−0.131755	+	0.991282i	$0.542061\pi$
$692$	−6.09624	+	15.4830i	−0.231744	+	0.588576i
$693$			6.76045i			0.256808i
$694$	−0.112563	+	0.383181i	−0.00427285	+	0.0145453i
$695$	−38.3568	+	11.6213i	−1.45496	+	0.440822i
$696$	−1.22438	+	4.45657i	−0.0464098	+	0.168926i
$697$	2.14839	−	4.35028i	0.0813760	−	0.164779i
$698$	4.33623	+	5.18988i	0.164129	+	0.196440i
$699$	−12.5331	+	5.19139i	−0.474046	+	0.196356i
$700$	−38.5882	+	8.35721i	−1.45850	+	0.315873i
$701$	−7.11271	−	7.11271i	−0.268643	−	0.268643i	0.559910	−	0.828553i	$-0.310836\pi$
$701$	−7.11271	−	7.11271i	−0.268643	−	0.268643i	−0.828553	+	0.559910i	$0.810836\pi$
$702$	−4.64611	+	15.8160i	−0.175356	+	0.596936i
$703$	30.0163	−	44.9226i	1.13209	−	1.69429i
$704$	−6.43566	+	3.07321i	−0.242553	+	0.115826i
$705$	2.90909	−	5.43812i	0.109563	−	0.204812i
$706$	−34.7355	−	18.1753i	−1.30729	−	0.684035i
$707$	23.0184	−	4.57865i	0.865697	−	0.172198i
$708$	14.9560	+	14.4385i	0.562082	+	0.542633i
$709$	29.4216	−	19.6589i	1.10495	−	0.738305i	0.137284	−	0.990532i	$-0.456163\pi$
$709$	29.4216	−	19.6589i	1.10495	−	0.738305i	0.967668	+	0.252226i	$0.0811628\pi$
$710$	−28.0514	−	5.33332i	−1.05275	−	0.200156i
$711$	2.77290	−	13.9403i	0.103992	−	0.522803i
$712$	−17.8659	+	22.9811i	−0.669552	+	0.861252i
$713$	−4.26229	−	4.26229i	−0.159624	−	0.159624i
$714$	−10.0500	−	21.7037i	−0.376113	−	0.812239i
$715$	2.88225	+	3.51444i	0.107790	+	0.131432i
$716$	4.88368	+	22.4766i	0.182512	+	0.839991i
$717$	−5.02059	+	3.35465i	−0.187497	+	0.125282i
$718$	1.15116	−	12.8460i	0.0429608	−	0.479409i
$719$	−1.24932	+	0.834767i	−0.0465916	+	0.0311315i	−0.578648	−	0.815577i	$-0.696419\pi$
$719$	−1.24932	+	0.834767i	−0.0465916	+	0.0311315i	0.532056	+	0.846709i	$0.321419\pi$
$720$	−16.6034	−	4.41071i	−0.618772	−	0.164378i
$721$	−30.8602	+	46.1856i	−1.14929	+	1.72004i
$722$	−30.2489	+	9.46741i	−1.12575	+	0.352341i
$723$	−4.99373	−	12.0559i	−0.185719	−	0.448365i
$724$	16.4800	+	15.9098i	0.612476	+	0.591284i
$725$	−0.00528730	+	7.86423i	−0.000196365	+	0.292070i
$726$	7.18412	+	13.1606i	0.266628	+	0.488436i
$727$			41.8750i			1.55306i	0.630082	+	0.776528i	$0.283021\pi$
$727$			41.8750i			1.55306i	−0.630082	+	0.776528i	$0.716979\pi$
$728$	24.1630	−	8.03228i	0.895539	−	0.297696i
$729$	13.9193	−	5.76555i	0.515528	−	0.213539i
$730$	−47.0562	−	8.94663i	−1.74163	−	0.331130i
$731$	−11.4242	−	19.8133i	−0.422540	−	0.732820i
$732$	10.2456	+	14.7642i	0.378687	+	0.545701i
$733$	−26.7543	−	11.0820i	−0.988193	−	0.409323i	−0.170739	−	0.985316i	$-0.554615\pi$
$733$	−26.7543	−	11.0820i	−0.988193	−	0.409323i	−0.817454	+	0.575993i	$0.804615\pi$
$734$	−3.77902	+	12.8643i	−0.139486	+	0.474830i
$735$	−19.8556	−	1.96234i	−0.732383	−	0.0723821i
$736$	−2.32527	−	16.2437i	−0.0857107	−	0.598752i
$737$	−0.625679	−	0.418066i	−0.0230472	−	0.0153996i
$738$	−0.341285	−	3.17811i	−0.0125629	−	0.116988i
$739$	−14.9807	+	36.1666i	−0.551074	+	1.33041i	0.365599	+	0.930772i	$0.380864\pi$
$739$	−14.9807	+	36.1666i	−0.551074	+	1.33041i	−0.916673	+	0.399638i	$0.869136\pi$
$740$	−37.2965	+	4.32481i	−1.37105	+	0.158983i
$741$	8.46900	−	12.6748i	0.311117	−	0.465619i
$742$	−11.4957	−	9.26615i	−0.422020	−	0.340171i
$743$	5.26721	−	26.4800i	0.193235	−	0.971459i	−0.755443	−	0.655215i	$-0.772578\pi$
$743$	5.26721	−	26.4800i	0.193235	−	0.971459i	0.948678	−	0.316244i	$-0.102422\pi$
$744$	−3.01953	−	5.30716i	−0.110701	−	0.194570i
$745$	46.2796	+	14.0558i	1.69555	+	0.514963i
$746$	−40.5205	+	12.6823i	−1.48356	+	0.464331i
$747$	−24.4501	−	24.4501i	−0.894582	−	0.894582i
$748$	−5.90754	−	4.37517i	−0.216001	−	0.159972i
$749$	79.5837			2.90792
$750$	16.4258	−	0.128011i	0.599787	−	0.00467432i
$751$	−25.9093	−	5.15368i	−0.945445	−	0.188061i	−0.301788	−	0.953375i	$-0.597583\pi$
$751$	−25.9093	−	5.15368i	−0.945445	−	0.188061i	−0.643657	+	0.765314i	$0.722583\pi$
$752$	−9.94804	−	3.71602i	−0.362768	−	0.135509i
$753$	−13.3105	−	2.64763i	−0.485063	−	0.0964851i
$754$	−0.541525	−	5.04277i	−0.0197212	−	0.183647i
$755$	16.6334	+	13.6600i	0.605352	+	0.497140i
$756$	−33.9542	−	21.8329i	−1.23490	−	0.794054i
$757$	25.9287	−	10.7400i	0.942396	−	0.390353i	0.142028	−	0.989863i	$-0.454638\pi$
$757$	25.9287	−	10.7400i	0.942396	−	0.390353i	0.800368	+	0.599510i	$0.204638\pi$
$758$	3.29460	+	30.6799i	0.119665	+	1.11434i
$759$	2.63493	−	0.524119i	0.0956418	−	0.0190243i
$760$	34.4187	+	21.7220i	1.24850	+	0.787938i
$761$	22.5397	+	22.5397i	0.817062	+	0.817062i	0.985681	−	0.168619i	$-0.0539309\pi$
$761$	22.5397	+	22.5397i	0.817062	+	0.817062i	−0.168619	+	0.985681i	$0.553931\pi$
$762$	1.00649	+	1.84379i	0.0364613	+	0.0667934i
$763$	18.2162	−	43.9778i	0.659471	−	1.59210i
$764$	14.2267	+	2.57039i	0.514702	+	0.0929936i
$765$	−4.00548	−	17.2490i	−0.144819	−	0.623640i
$766$	−14.8784	−	1.33328i	−0.537577	−	0.0481733i
$767$	−21.0762	−	8.73003i	−0.761016	−	0.315223i
$768$	2.08782	−	16.4906i	0.0753379	−	0.595055i
$769$	6.93098	+	6.93098i	0.249937	+	0.249937i	0.820945	−	0.571007i	$-0.193447\pi$
$769$	6.93098	+	6.93098i	0.249937	+	0.249937i	−0.571007	+	0.820945i	$0.693447\pi$
$770$	−10.2468	+	4.34636i	−0.369270	+	0.156632i
$771$	6.10363	+	30.6850i	0.219817	+	1.10509i
$772$	35.3073	−	0.621588i	1.27074	−	0.0223714i
$773$	46.1690	−	19.1238i	1.66058	−	0.687836i	0.662460	−	0.749097i	$-0.269512\pi$
$773$	46.1690	−	19.1238i	1.66058	−	0.687836i	0.998122	+	0.0612613i	$0.0195123\pi$
$774$	−13.3501	−	6.98542i	−0.479860	−	0.251086i
$775$	−7.34185	−	7.35172i	−0.263727	−	0.264082i
$776$	−0.0327622	+	0.455705i	−0.00117609	+	0.0163589i
$777$	−33.7758	−	6.71843i	−1.21170	−	0.241022i
$778$	2.96543	−	33.0920i	0.106316	−	1.18640i
$779$	−1.47735	+	7.42715i	−0.0529316	+	0.266105i
$780$	−10.5231	+	1.22023i	−0.376787	+	0.0436912i
$781$	−8.04959			−0.288037
$782$	13.6672	−	9.96511i	0.488737	−	0.356352i
$783$	−5.68551	+	5.68551i	−0.203183	+	0.203183i
$784$	1.20929	+	34.3343i	0.0431889	+	1.22622i
$785$	−7.25944	−	13.5925i	−0.259101	−	0.485135i
$786$	12.2144	−	10.2053i	0.435672	−	0.364011i
$787$	41.0165	+	8.15868i	1.46208	+	0.290826i	0.861098	−	0.508438i	$-0.169777\pi$
$787$	41.0165	+	8.15868i	1.46208	+	0.290826i	0.600980	+	0.799264i	$0.294777\pi$
$788$	−15.2344	−	14.7073i	−0.542704	−	0.523926i
$789$	8.39041	−	12.5571i	0.298707	−	0.447046i
$790$	22.9121	−	4.75949i	0.815177	−	0.169335i
$791$	19.7320	+	8.17325i	0.701588	+	0.290607i
$792$	−4.83051	−	0.347282i	−0.171645	−	0.0123401i
$793$	−16.3973	−	10.9564i	−0.582287	−	0.389071i
$794$	−49.3745	+	26.9526i	−1.75224	+	0.956512i
$795$	3.89542	+	4.74984i	0.138156	+	0.168459i
$796$	0.959015	−	2.43567i	0.0339914	−	0.0863301i
$797$	−22.5504	−	9.34070i	−0.798777	−	0.330864i	−0.0543108	−	0.998524i	$-0.517296\pi$
$797$	−22.5504	−	9.34070i	−0.798777	−	0.330864i	−0.744467	+	0.667660i	$0.767296\pi$
$798$	23.9350	+	28.6469i	0.847289	+	1.01409i
$799$	−1.42262	−	10.8534i	−0.0503286	−	0.383967i
$800$	−3.98918	−	28.0015i	−0.141039	−	0.990004i
$801$	−18.2622	+	7.56446i	−0.645264	+	0.267277i
$802$	22.9315	+	42.0082i	0.809738	+	1.48336i
$803$	−13.5032			−0.476516
$804$	1.60830	−	0.699597i	0.0567205	−	0.0246729i
$805$	−2.50164	−	25.4875i	−0.0881714	−	0.898315i
$806$	5.21686	+	4.20508i	0.183756	+	0.148117i
$807$	−5.87870	+	2.43504i	−0.206940	+	0.0857174i
$808$	2.08911	+	16.6825i	0.0734948	+	0.586887i
$809$	6.42823	−	9.62053i	0.226005	−	0.338240i	−0.701086	−	0.713076i	$-0.747301\pi$
$809$	6.42823	−	9.62053i	0.226005	−	0.338240i	0.927091	+	0.374837i	$0.122301\pi$
$810$	−1.01742	−	1.00033i	−0.0357484	−	0.0351482i
$811$	4.99087	+	7.46936i	0.175253	+	0.262285i	0.908689	−	0.417474i	$-0.137085\pi$
$811$	4.99087	+	7.46936i	0.175253	+	0.262285i	−0.733436	+	0.679759i	$0.762085\pi$
$812$	12.2222	+	2.20824i	0.428915	+	0.0774940i
$813$	4.36239	−	2.91485i	0.152996	−	0.102228i
$814$	−10.1014	+	3.16159i	−0.354055	+	0.110814i
$815$	−26.5131	−	32.3285i	−0.928714	−	1.13242i
$816$	16.0241	−	6.06609i	0.560956	−	0.212356i
$817$	25.2411	+	25.2411i	0.883076	+	0.883076i
$818$	−18.0630	+	34.5210i	−0.631558	+	1.20700i
$819$	16.9590	+	3.37335i	0.592594	+	0.117874i
$820$	4.59765	−	2.56053i	0.160557	−	0.0894175i
$821$	21.7785	−	14.5519i	0.760075	−	0.507866i	−0.114104	−	0.993469i	$-0.536400\pi$
$821$	21.7785	−	14.5519i	0.760075	−	0.507866i	0.874180	+	0.485603i	$0.161400\pi$
$822$	−3.01594	+	3.74161i	−0.105193	+	0.130504i
$823$	−6.91833	−	34.7808i	−0.241158	−	1.21238i	−0.891599	−	0.452825i	$-0.850416\pi$
$823$	−6.91833	−	34.7808i	−0.241158	−	1.21238i	0.650441	−	0.759556i	$-0.274584\pi$
$824$	−31.4155	−	24.4230i	−1.09441	−	0.850814i
$825$	4.54235	−	0.900355i	0.158144	−	0.0313463i
$826$	35.0590	−	43.4946i	1.21986	−	1.51337i
$827$	−39.2787	−	26.2452i	−1.36585	−	0.912635i	−0.366016	−	0.930608i	$-0.619279\pi$
$827$	−39.2787	−	26.2452i	−1.36585	−	0.912635i	−0.999838	+	0.0179735i	$0.994279\pi$
$828$	4.08240	−	10.3683i	0.141873	−	0.360325i
$829$	11.5594	+	11.5594i	0.401476	+	0.401476i	0.878753	−	0.477277i	$-0.158376\pi$
$829$	11.5594	+	11.5594i	0.401476	+	0.401476i	−0.477277	+	0.878753i	$0.658376\pi$
$830$	21.3399	−	52.7783i	0.740717	−	1.83196i
$831$	−5.53808	−	13.3701i	−0.192114	−	0.463804i
$832$	4.49802	+	17.6777i	0.155941	+	0.612863i
$833$	−30.6785	+	17.6891i	−1.06295	+	0.612889i
$834$	2.35040	−	26.2287i	0.0813879	−	0.908226i
$835$	−14.2687	+	26.6733i	−0.493788	+	0.923066i
$836$	10.6759	+	4.20352i	0.369235	+	0.145382i
$837$		−	10.6228i		−	0.367179i
$838$	15.1321	−	51.5118i	0.522731	−	1.77945i
$839$	7.31573	+	36.7787i	0.252567	+	1.26974i	0.873866	+	0.486167i	$0.161605\pi$
$839$	7.31573	+	36.7787i	0.252567	+	1.26974i	−0.621299	+	0.783574i	$0.713395\pi$
$840$	4.39616	−	25.5671i	0.151682	−	0.882149i
$841$	−10.1511	+	24.5070i	−0.350039	+	0.845068i
$842$	10.0736	−	3.15288i	0.347160	−	0.108656i
$843$	−5.12816	−	25.7810i	−0.176623	−	0.887945i
$844$	0.503230	+	28.5844i	0.0173219	+	0.983915i
$845$	−15.3867	+	8.21773i	−0.529319	+	0.282698i
$846$	−4.62371	−	5.53396i	−0.158967	−	0.190262i
$847$	33.5026	−	22.3857i	1.15116	−	0.769183i
$848$	7.21143	−	7.73797i	0.247642	−	0.265723i
$849$	1.62334			0.0557129
$850$	23.5693	−	17.1607i	0.808419	−	0.588608i
$851$		−	24.3540i		−	0.834843i
$852$	10.1471	−	15.7806i	0.347634	−	0.540636i
$853$	6.47928	+	9.69693i	0.221846	+	0.332017i	0.925652	−	0.378376i	$-0.123517\pi$
$853$	6.47928	+	9.69693i	0.221846	+	0.332017i	−0.703806	+	0.710393i	$0.748517\pi$
$854$	37.0606	−	30.9647i	1.26819	−	1.05959i
$855$	13.0204	+	24.3791i	0.445287	+	0.833747i
$856$	−4.08819	+	56.8646i	−0.139731	+	1.94359i
$857$	34.6497	−	6.89226i	1.18361	−	0.235435i	0.436234	−	0.899833i	$-0.356312\pi$
$857$	34.6497	−	6.89226i	1.18361	−	0.235435i	0.747379	+	0.664398i	$0.231312\pi$
$858$	−2.85009	+	0.892032i	−0.0973004	+	0.0304535i
$859$	−30.0127	−	12.4317i	−1.02402	−	0.424163i	−0.193470	−	0.981106i	$-0.561974\pi$
$859$	−30.0127	−	12.4317i	−1.02402	−	0.424163i	−0.830551	+	0.556943i	$0.811974\pi$
$860$	2.00489	−	24.7258i	0.0683661	−	0.843144i
$861$	4.73408	−	0.941668i	0.161337	−	0.0320919i
$862$	16.5116	+	4.85044i	0.562386	+	0.165207i
$863$	−19.9564			−0.679325			−0.339663	−	0.940547i	$-0.610313\pi$
$863$	−19.9564			−0.679325			−0.339663	+	0.940547i	$0.610313\pi$
$864$	17.3444	−	23.1396i	0.590067	−	0.787225i
$865$	−16.4043	−	8.77539i	−0.557764	−	0.298372i
$866$	1.96332	−	21.9092i	0.0667164	−	0.744504i
$867$	13.2652	+	11.6599i	0.450508	+	0.395990i
$868$	−13.4809	+	9.35505i	−0.457573	+	0.317531i
$869$	6.09484	−	2.52457i	0.206753	−	0.0856400i
$870$	−4.79046	−	1.93693i	−0.162412	−	0.0656680i
$871$	−1.36094	+	1.36094i	−0.0461138	+	0.0461138i
$872$	30.4875	+	15.2751i	1.03244	+	0.517279i
$873$	−0.172368	+	0.257968i	−0.00583379	+	0.00873088i
$874$	−16.5674	+	20.5537i	−0.560401	+	0.695239i
$875$	−4.28247	−	43.9349i	−0.144774	−	1.48527i
$876$	17.0217	−	26.4720i	0.575111	−	0.894405i
$877$	33.3906	−	6.64180i	1.12752	−	0.224277i	0.404119	−	0.914706i	$-0.367578\pi$
$877$	33.3906	−	6.64180i	1.12752	−	0.224277i	0.723400	+	0.690429i	$0.242578\pi$
$878$	25.0413	+	20.1846i	0.845101	+	0.681198i
$879$	1.65142	+	2.47153i	0.0557011	+	0.0833625i
$880$	−2.57921	−	7.54490i	−0.0869453	−	0.254338i
$881$	−8.88494	+	44.6676i	−0.299341	+	1.50489i	0.479430	+	0.877580i	$0.340844\pi$
$881$	−8.88494	+	44.6676i	−0.299341	+	1.50489i	−0.778771	+	0.627309i	$0.784156\pi$
$882$	−10.8161	+	20.6711i	−0.364197	+	0.696032i
$883$	13.6254	−	13.6254i	0.458530	−	0.458530i	−0.439642	−	0.898173i	$-0.644895\pi$
$883$	13.6254	−	13.6254i	0.458530	−	0.458530i	0.898173	+	0.439642i	$0.144895\pi$
$884$	−13.9231	+	12.6363i	−0.468285	+	0.425004i
$885$	−17.9713	+	14.7386i	−0.604098	+	0.495431i
$886$	−3.04037	−	9.71412i	−0.102143	−	0.326352i
$887$	18.9676	+	28.3870i	0.636869	+	0.953141i	0.999773	+	0.0213148i	$0.00678522\pi$
$887$	18.9676	+	28.3870i	0.636869	+	0.953141i	−0.362904	+	0.931826i	$0.618215\pi$
$888$	6.53554	−	23.7886i	0.219318	−	0.798292i
$889$	4.69369	−	3.13622i	0.157421	−	0.105186i
$890$	−23.2065	−	22.8168i	−0.777883	−	0.764823i
$891$	−0.334443	−	0.223468i	−0.0112043	−	0.00748645i
$892$	8.36805	−	1.81819i	0.280183	−	0.0608777i
$893$	6.53801	+	15.7842i	0.218786	+	0.528197i
$894$	−19.9438	+	24.7426i	−0.667022	+	0.827515i
$895$	−25.5930	+	2.51200i	−0.855480	+	0.0839670i
$896$	−44.6398	−	1.63291i	−1.49131	−	0.0545517i
$897$		−	6.87139i		−	0.229429i
$898$	12.5384	+	22.9692i	0.418413	+	0.766492i
$899$	1.25074	+	3.01956i	0.0417147	+	0.100708i
$900$	7.04873	−	17.8669i	0.234958	−	0.595562i
$901$	10.5298	+	2.82785i	0.350799	+	0.0942095i
$902$	1.13848	−	0.951220i	0.0379073	−	0.0316722i
$903$	8.70717	−	21.0210i	0.289757	−	0.699534i
$904$	−6.85362	+	13.6791i	−0.227948	+	0.454961i
$905$	−19.8026	+	16.2404i	−0.658260	+	0.539850i
$906$	−12.4131	+	6.77610i	−0.412399	+	0.225121i
$907$	0.479020	−	0.716904i	0.0159056	−	0.0238044i	−0.823432	−	0.567416i	$-0.807943\pi$
$907$	0.479020	−	0.716904i	0.0159056	−	0.0238044i	0.839337	+	0.543611i	$0.182943\pi$
$908$	−7.60210	+	0.133835i	−0.252285	+	0.00444149i
$909$	−4.36912	+	10.5480i	−0.144914	+	0.349855i
$910$	5.79010	+	27.8735i	0.191940	+	0.923998i
$911$	11.7222	+	7.83250i	0.388373	+	0.259502i	0.734393	−	0.678725i	$-0.237467\pi$
$911$	11.7222	+	7.83250i	0.388373	+	0.259502i	−0.346020	+	0.938227i	$0.612467\pi$
$912$	−21.6985	+	15.6306i	−0.718510	+	0.517580i
$913$	3.13097	−	15.7405i	0.103620	−	0.520933i
$914$	38.2787	−	31.9825i	1.26615	−	1.05789i
$915$	−17.7228	+	9.46539i	−0.585898	+	0.312916i
$916$	16.2049	−	3.52097i	0.535425	−	0.116336i
$917$	−30.2453	−	30.2453i	−0.998787	−	0.998787i
$918$	29.4492	+	4.61330i	0.971967	+	0.152262i
$919$			47.4915i			1.56660i	0.621644	+	0.783300i	$0.286465\pi$
$919$			47.4915i			1.56660i	−0.621644	+	0.783300i	$0.713535\pi$
$920$	18.3400	−	0.478207i	0.604650	−	0.0157660i
$921$	−8.12349	−	1.61586i	−0.267678	−	0.0532445i
$922$	2.02484	−	22.5957i	0.0666847	−	0.744150i
$923$	−4.01660	+	20.1928i	−0.132208	+	0.664655i
$924$	−0.128732	−	7.31222i	−0.00423497	−	0.240554i
$925$	0.0282229	−	41.9782i	0.000927962	−	1.38023i
$926$	19.6630	−	37.5788i	0.646168	−	1.23492i
$927$	−10.3407	−	24.9648i	−0.339635	−	0.819950i
$928$	−2.20569	+	8.61963i	−0.0724054	+	0.282953i
$929$	0.833125	−	0.165719i	0.0273339	−	0.00543706i	−0.181404	−	0.983409i	$-0.558064\pi$
$929$	0.833125	−	0.165719i	0.0273339	−	0.00543706i	0.208738	+	0.977972i	$0.433064\pi$
$930$	6.28474	−	2.66578i	0.206085	−	0.0874143i
$931$	39.0829	−	39.0829i	1.28089	−	1.28089i
$932$	−23.9482	+	10.4172i	−0.784448	+	0.341228i
$933$	−10.9619	+	26.4645i	−0.358878	+	0.866408i
$934$	−1.28013	+	14.2852i	−0.0418870	+	0.467427i
$935$	5.62384	−	5.99365i	0.183919	−	0.196013i
$936$	−3.28152	+	11.9443i	−0.107260	+	0.390412i
$937$	9.08644	+	3.76373i	0.296841	+	0.122956i	0.526134	−	0.850402i	$-0.323641\pi$
$937$	9.08644	+	3.76373i	0.296841	+	0.122956i	−0.229292	+	0.973358i	$0.573641\pi$
$938$	−2.25831	−	4.13700i	−0.0737364	−	0.135078i
$939$	7.67822	−	7.67822i	0.250569	−	0.250569i
$940$	5.41521	−	10.5660i	0.176625	−	0.344626i
$941$	−4.61268	−	23.1895i	−0.150369	−	0.755956i	−0.980211	−	0.197957i	$-0.936569\pi$
$941$	−4.61268	−	23.1895i	−0.150369	−	0.755956i	0.829842	−	0.557999i	$-0.188431\pi$
$942$	10.0670	−	1.08106i	0.328001	−	0.0352229i
$943$	1.30629	+	3.15366i	0.0425386	+	0.102697i
$944$	29.2770	+	27.2849i	0.952887	+	0.888047i
$945$	28.6435	−	34.8783i	0.931775	−	1.13459i
$946$	−0.746692	−	6.95332i	−0.0242770	−	0.226072i
$947$	−3.91498	+	19.6819i	−0.127220	+	0.639576i	0.863577	+	0.504217i	$0.168219\pi$
$947$	−3.91498	+	19.6819i	−0.127220	+	0.639576i	−0.990797	+	0.135359i	$0.956781\pi$
$948$	−2.73377	+	15.1309i	−0.0887887	+	0.491429i
$949$	−6.73784	+	33.8734i	−0.218720	+	1.09958i
$950$	−28.5805	+	35.4086i	−0.927275	+	1.14881i
$951$			18.4058i			0.596849i
$952$	−20.0800	−	41.4353i	−0.650798	−	1.34292i
$953$	−37.0796	+	37.0796i	−1.20112	+	1.20112i	−0.227300	+	0.973825i	$0.572990\pi$
$953$	−37.0796	+	37.0796i	−1.20112	+	1.20112i	−0.973825	+	0.227300i	$0.927010\pi$
$954$	6.85488	−	2.14547i	0.221935	−	0.0694621i
$955$	−4.69719	+	15.4658i	−0.151997	+	0.500463i
$956$	−9.55009	+	6.62725i	−0.308872	+	0.214341i
$957$	−1.42869	−	0.284185i	−0.0461831	−	0.00918639i
$958$	14.9542	−	18.5523i	0.483148	−	0.599398i
$959$	10.7382	+	7.17505i	0.346755	+	0.231694i
$960$	18.0425	+	4.45454i	0.582320	+	0.143770i
$961$	24.6509	+	10.2108i	0.795191	+	0.329379i
$962$	2.89058	+	26.9176i	0.0931961	+	0.867858i
$963$	−21.5088	+	32.1901i	−0.693110	+	1.03731i
$964$	−10.0206	−	23.0364i	−0.322742	−	0.741952i
$965$	−3.88302	+	39.2895i	−0.124999	+	1.26477i
$966$	16.1449	+	4.74273i	0.519454	+	0.152595i
$967$	12.7309	−	30.7352i	0.409399	−	0.988377i	−0.575897	−	0.817522i	$-0.695347\pi$
$967$	12.7309	−	30.7352i	0.409399	−	0.988377i	0.985296	−	0.170855i	$-0.0546529\pi$
$968$	14.2742	+	25.0884i	0.458789	+	0.806373i
$969$	−24.7155	−	12.2058i	−0.793976	−	0.392106i
$970$	−0.501820	−	0.0954093i	−0.0161125	−	0.00306341i
$971$	8.86801	+	21.4093i	0.284588	+	0.687056i	0.999931	−	0.0117170i	$-0.00372972\pi$
$971$	8.86801	+	21.4093i	0.284588	+	0.687056i	−0.715343	+	0.698773i	$0.753730\pi$
$972$	28.9864	−	12.6088i	0.929738	−	0.404427i
$973$	−70.7678			−2.26871
$974$	10.8543	−	5.92515i	0.347794	−	0.189854i
$975$	0.00796298	−	11.8440i	0.000255020	−	0.379311i
$976$	20.2213	+	28.0714i	0.647267	+	0.898543i
$977$	15.2299	−	6.30843i	0.487247	−	0.201824i	−0.125515	−	0.992092i	$-0.540058\pi$
$977$	15.2299	−	6.30843i	0.487247	−	0.201824i	0.612762	+	0.790267i	$0.290058\pi$
$978$	26.2173	−	8.20560i	0.838337	−	0.262386i
$979$	−7.62839	−	5.09713i	−0.243804	−	0.162905i
$980$	−38.2850	−	3.10433i	−1.22297	−	0.0991642i
$981$	12.8650	+	19.2538i	0.410747	+	0.614727i
$982$	5.96380	+	0.534428i	0.190313	+	0.0170543i
$983$	23.8384	+	35.6767i	0.760326	+	1.13791i	0.986490	+	0.163820i	$0.0523815\pi$
$983$	23.8384	+	35.6767i	0.760326	+	1.13791i	−0.226164	+	0.974089i	$0.572618\pi$
$984$	0.429657	+	3.43100i	0.0136970	+	0.109376i
$985$	18.3058	−	15.0129i	0.583272	−	0.478351i
$986$	−8.91416	+	2.15604i	−0.283885	+	0.0686622i
$987$	7.70025	−	7.70025i	0.245102	−	0.245102i
$988$	15.8719	−	24.6837i	0.504951	−	0.785293i
$989$	15.7815	+	3.13914i	0.501823	+	0.0998188i
$990$	1.01135	−	5.31933i	0.0321427	−	0.169059i
$991$	13.7159	+	20.5273i	0.435700	+	0.652071i	0.982731	−	0.185041i	$-0.0592419\pi$
$991$	13.7159	+	20.5273i	0.435700	+	0.652071i	−0.547031	+	0.837113i	$0.684242\pi$
$992$	−5.99192	−	10.1130i	−0.190244	−	0.321089i
$993$	−3.99599	−	20.0892i	−0.126809	−	0.637511i
$994$	−44.6724	−	23.3747i	−1.41692	−	0.741402i
$995$	2.58061	+	1.38048i	0.0818108	+	0.0437641i
$996$	26.9112	+	25.9801i	0.852714	+	0.823210i
$997$	−11.0894	−	7.40967i	−0.351203	−	0.234667i	0.367437	−	0.930048i	$-0.380235\pi$
$997$	−11.0894	−	7.40967i	−0.351203	−	0.234667i	−0.718640	+	0.695382i	$0.755235\pi$
$998$	−10.5318	−	3.09383i	−0.333379	−	0.0979335i
$999$	30.3484	−	30.3484i	0.960182	−	0.960182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cf.a.37.17	yes	832
5.3	odd	4		680.2.ct.a.173.38	yes	832
8.5	even	2	inner	680.2.cf.a.37.11	✓	832
17.6	odd	16		680.2.ct.a.397.42	yes	832
40.13	odd	4		680.2.ct.a.173.42	yes	832
85.23	even	16	inner	680.2.cf.a.533.11	yes	832
136.125	odd	16		680.2.ct.a.397.38	yes	832
680.533	even	16	inner	680.2.cf.a.533.17	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cf.a.37.11	✓	832	8.5	even	2	inner
680.2.cf.a.37.17	yes	832	1.1	even	1	trivial
680.2.cf.a.533.11	yes	832	85.23	even	16	inner
680.2.cf.a.533.17	yes	832	680.533	even	16	inner
680.2.ct.a.173.38	yes	832	5.3	odd	4
680.2.ct.a.173.42	yes	832	40.13	odd	4
680.2.ct.a.397.38	yes	832	136.125	odd	16
680.2.ct.a.397.42	yes	832	17.6	odd	16

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25304 - 0.655652i) q^{2} +(0.577178 + 0.863808i) q^{3} +(1.14024 + 1.64312i) q^{4} +(-1.97239 + 1.05341i) q^{5} +(-0.156872 - 1.46082i) q^{6} +(-3.87241 + 0.770271i) q^{7} +(-0.351454 - 2.80651i) q^{8} +(0.735021 - 1.77450i) q^{9} +(3.16216 - 0.0267698i) q^{10} +(0.874343 - 0.173918i) q^{11} +(-0.761221 + 1.93332i) q^{12} -2.28012i q^{13} +(5.35733 + 1.57377i) q^{14} +(-2.04837 - 1.09576i) q^{15} +(-1.39971 + 3.74711i) q^{16} +(-4.08814 + 0.535855i) q^{17} +(-2.08447 + 1.74161i) q^{18} +(5.94539 - 2.46266i) q^{19} +(-3.97988 - 2.03974i) q^{20} +(-2.90044 - 2.90044i) q^{21} +(-1.20962 - 0.355339i) q^{22} +(1.61159 - 2.41192i) q^{23} +(2.22143 - 1.92344i) q^{24} +(2.78065 - 4.15548i) q^{25} +(-1.49497 + 2.85709i) q^{26} +(5.01385 - 0.997318i) q^{27} +(-5.68113 - 5.48456i) q^{28} +(-1.30777 + 0.873827i) q^{29} +(1.84826 + 2.71605i) q^{30} +(0.405395 - 2.03806i) q^{31} +(4.21069 - 3.77757i) q^{32} +(0.654883 + 0.654883i) q^{33} +(5.47395 + 2.00895i) q^{34} +(6.82649 - 5.59852i) q^{35} +(3.75382 - 0.815623i) q^{36} +(6.98072 - 4.66437i) q^{37} +(-9.06448 - 0.812285i) q^{38} +(1.96959 - 1.31603i) q^{39} +(3.64961 + 5.16530i) q^{40} +(-0.653766 + 0.978430i) q^{41} +(1.73270 + 5.53605i) q^{42} +(2.12275 + 5.12477i) q^{43} +(1.28273 + 1.23835i) q^{44} +(0.419529 + 4.27428i) q^{45} +(-3.60077 + 1.96559i) q^{46} +2.65486i q^{47} +(-4.04466 + 0.953672i) q^{48} +(7.93510 - 3.28683i) q^{49} +(-6.20882 + 3.38386i) q^{50} +(-2.82246 - 3.22208i) q^{51} +(3.74652 - 2.59988i) q^{52} +(-2.44306 - 1.01195i) q^{53} +(-6.93648 - 2.03766i) q^{54} +(-1.54134 + 1.26408i) q^{55} +(3.52274 + 10.5972i) q^{56} +(5.55881 + 3.71428i) q^{57} +(2.21163 - 0.237498i) q^{58} +(3.82876 - 9.24344i) q^{59} +(-0.535160 - 4.61515i) q^{60} +(4.80516 - 7.19144i) q^{61} +(-1.84423 + 2.28798i) q^{62} +(-1.47946 + 7.43775i) q^{63} +(-7.75296 + 1.97271i) q^{64} +(2.40191 + 4.49729i) q^{65} +(-0.391222 - 1.24997i) q^{66} +(-0.596874 - 0.596874i) q^{67} +(-5.54193 - 6.10631i) q^{68} +3.01361 q^{69} +(-12.2246 + 2.53939i) q^{70} +(-8.85604 - 1.76158i) q^{71} +(-5.23846 - 1.43919i) q^{72} +(-14.8560 - 2.95504i) q^{73} +(-11.8053 + 1.26773i) q^{74} +(5.19446 + 0.00349235i) q^{75} +(10.8256 + 6.96098i) q^{76} +(-3.25185 + 1.34696i) q^{77} +(-3.33084 + 0.357687i) q^{78} +(7.25794 - 1.44369i) q^{79} +(-1.18648 - 8.86523i) q^{80} +(-0.319046 - 0.319046i) q^{81} +(1.46071 - 0.797373i) q^{82} +(6.88930 - 16.6322i) q^{83} +(1.45858 - 8.07297i) q^{84} +(7.49892 - 5.36341i) q^{85} +(0.700169 - 7.81335i) q^{86} +(-1.50964 - 0.625312i) q^{87} +(-0.795392 - 2.39273i) q^{88} +(-7.27719 - 7.27719i) q^{89} +(2.27675 - 5.63093i) q^{90} +(1.75631 + 8.82956i) q^{91} +(5.80068 - 0.102121i) q^{92} +(1.99447 - 0.826139i) q^{93} +(1.74066 - 3.32666i) q^{94} +(-9.13243 + 11.1203i) q^{95} +(5.69342 + 1.45690i) q^{96} +(-0.158428 - 0.0315133i) q^{97} +(-12.0980 - 1.08413i) q^{98} +(0.334044 - 1.67935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) \) 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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