LMFDB - Embedded newform 680.2.br.a.189.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(189,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 4, 4, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.br (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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$104$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			189.16
Character	$\chi$	$=$	680.189
Dual form			680.2.br.a.349.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.25660 - 0.648820i) q^{2} +(-1.86646 + 0.773113i) q^{3} +(1.15807 + 1.63061i) q^{4} +(-0.689354 - 2.12716i) q^{5} +(2.84700 + 0.239505i) q^{6} +(0.739929 + 0.306488i) q^{7} +(-0.397251 - 2.80039i) q^{8} +(0.764647 - 0.764647i) q^{9} +(-0.513900 + 3.12024i) q^{10} +(1.31559 - 3.17611i) q^{11} +(-3.42213 - 2.14815i) q^{12} +2.51816i q^{13} +(-0.730936 - 0.865212i) q^{14} +(2.93118 + 3.43730i) q^{15} +(-1.31776 + 3.77670i) q^{16} +(0.897680 + 4.02420i) q^{17} +(-1.45697 + 0.464734i) q^{18} +(0.658797 - 0.658797i) q^{19} +(2.67024 - 3.58745i) q^{20} -1.61800 q^{21} +(-3.71389 + 3.13751i) q^{22} +(1.90342 - 4.59527i) q^{23} +(2.90647 + 4.91970i) q^{24} +(-4.04958 + 2.93273i) q^{25} +(1.63383 - 3.16431i) q^{26} +(1.48331 - 3.58104i) q^{27} +(0.357124 + 1.56147i) q^{28} +(-9.10861 + 3.77291i) q^{29} +(-1.45312 - 6.22111i) q^{30} +(3.43384 - 1.42234i) q^{31} +(4.10630 - 3.89080i) q^{32} +6.94518i q^{33} +(1.48296 - 5.63922i) q^{34} +(0.141876 - 1.78522i) q^{35} +(2.13235 + 0.361327i) q^{36} +(-1.11757 + 0.462911i) q^{37} +(-1.25528 + 0.400401i) q^{38} +(-1.94682 - 4.70005i) q^{39} +(-5.68302 + 2.77548i) q^{40} +(4.76899 - 11.5134i) q^{41} +(2.03317 + 1.04979i) q^{42} +(2.63427 - 2.63427i) q^{43} +(6.70253 - 1.53294i) q^{44} +(-2.15364 - 1.09941i) q^{45} +(-5.37333 + 4.53942i) q^{46} -10.2098 q^{47} +(-0.460265 - 8.06785i) q^{48} +(-4.49619 - 4.49619i) q^{49} +(6.99150 - 1.05781i) q^{50} +(-4.78664 - 6.81699i) q^{51} +(-4.10614 + 2.91620i) q^{52} +(-3.65503 - 3.65503i) q^{53} +(-4.18737 + 3.53751i) q^{54} +(-7.66299 - 0.608996i) q^{55} +(0.564350 - 2.19384i) q^{56} +(-0.720293 + 1.73894i) q^{57} +(13.8938 + 1.16882i) q^{58} +(-5.24423 - 5.24423i) q^{59} +(-2.21039 + 8.76023i) q^{60} +(-8.77111 - 3.63311i) q^{61} +(-5.23779 - 0.440632i) q^{62} +(0.800139 - 0.331429i) q^{63} +(-7.68438 + 2.22492i) q^{64} +(5.35652 - 1.73591i) q^{65} +(4.50617 - 8.72729i) q^{66} -5.11009 q^{67} +(-5.52232 + 6.12405i) q^{68} +10.0484i q^{69} +(-1.33657 + 2.15125i) q^{70} +(7.58430 - 3.14152i) q^{71} +(-2.44507 - 1.83755i) q^{72} +(-5.76929 + 2.38972i) q^{73} +(1.70468 + 0.143407i) q^{74} +(5.29105 - 8.60460i) q^{75} +(1.83717 + 0.311309i) q^{76} +(1.94688 - 1.94688i) q^{77} +(-0.603112 + 7.16920i) q^{78} +(-11.6727 - 4.83500i) q^{79} +(8.94204 + 0.199603i) q^{80} +11.0748i q^{81} +(-13.4628 + 11.3734i) q^{82} +(4.85020 + 4.85020i) q^{83} +(-1.87375 - 2.63832i) q^{84} +(7.94128 - 4.68360i) q^{85} +(-5.01938 + 1.60105i) q^{86} +(14.0840 - 14.0840i) q^{87} +(-9.41698 - 2.42245i) q^{88} -1.79163i q^{89} +(1.99293 + 2.77883i) q^{90} +(-0.771788 + 1.86326i) q^{91} +(9.69737 - 2.21789i) q^{92} +(-5.30949 + 5.30949i) q^{93} +(12.8296 + 6.62430i) q^{94} +(-1.85551 - 0.947219i) q^{95} +(-4.65621 + 10.4367i) q^{96} +(5.86683 - 2.43012i) q^{97} +(2.73268 + 8.56711i) q^{98} +(-1.42264 - 3.43457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 16 q^{6} - 16 q^{9} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 16 q^{16} - 20 q^{20} + 24 q^{26} - 16 q^{31} - 40 q^{34} - 8 q^{36} + 32 q^{39} + 56 q^{40} - 32 q^{41} - 24 q^{44} + 32 q^{46} - 16 q^{49}+ \cdots - 160 q^{96}+O(q^{100}) $ 416 * q - 16 * q^6 - 16 * q^9 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 16 * q^16 - 20 * q^20 + 24 * q^26 - 16 * q^31 - 40 * q^34 - 8 * q^36 + 32 * q^39 + 56 * q^40 - 32 * q^41 - 24 * q^44 + 32 * q^46 - 16 * q^49 - 48 * q^50 - 64 * q^54 - 8 * q^56 - 40 * q^60 + 72 * q^65 - 112 * q^66 - 24 * q^70 + 48 * q^71 - 8 * q^74 - 40 * q^76 - 16 * q^79 - 56 * q^80 - 32 * q^84 + 96 * q^86 - 148 * q^90 + 40 * q^94 - 8 * q^95 - 160 * q^96

Character values

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

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$	$-1$	$1$

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 $

$2$	−1.25660	−	0.648820i	−0.888547	−	0.458785i
$2$	−1.25660	−	0.648820i	−0.888547	−	0.458785i
$3$	−1.86646	+	0.773113i	−1.07760	+	0.446357i	−0.849667	−	0.527320i	$-0.823197\pi$
$3$	−1.86646	+	0.773113i	−1.07760	+	0.446357i	−0.227934	+	0.973677i	$0.573197\pi$
$4$	1.15807	+	1.63061i	0.579033	+	0.815304i
$5$	−0.689354	−	2.12716i	−0.308289	−	0.951293i
$5$	−0.689354	−	2.12716i	−0.308289	−	0.951293i
$6$	2.84700	+	0.239505i	1.16228	+	0.0977775i
$7$	0.739929	+	0.306488i	0.279667	+	0.115842i	0.518108	−	0.855315i	$-0.326636\pi$
$7$	0.739929	+	0.306488i	0.279667	+	0.115842i	−0.238441	+	0.971157i	$0.576636\pi$
$8$	−0.397251	−	2.80039i	−0.140450	−	0.990088i
$9$	0.764647	−	0.764647i	0.254882	−	0.254882i
$10$	−0.513900	+	3.12024i	−0.162510	+	0.986707i
$11$	1.31559	−	3.17611i	0.396665	−	0.957634i	−0.591786	−	0.806095i	$-0.701577\pi$
$11$	1.31559	−	3.17611i	0.396665	−	0.957634i	0.988451	−	0.151539i	$-0.0484230\pi$
$12$	−3.42213	−	2.14815i	−0.987883	−	0.620117i
$13$			2.51816i			0.698413i	0.937046	+	0.349206i	$0.113549\pi$
$13$			2.51816i			0.698413i	−0.937046	+	0.349206i	$0.886451\pi$
$14$	−0.730936	−	0.865212i	−0.195351	−	0.231238i
$15$	2.93118	+	3.43730i	0.756828	+	0.887507i
$16$	−1.31776	+	3.77670i	−0.329441	+	0.944176i
$17$	0.897680	+	4.02420i	0.217719	+	0.976011i
$17$	0.897680	+	4.02420i	0.217719	+	0.976011i
$18$	−1.45697	+	0.464734i	−0.343411	+	0.109539i
$19$	0.658797	−	0.658797i	0.151138	−	0.151138i	−0.627488	−	0.778626i	$-0.715917\pi$
$19$	0.658797	−	0.658797i	0.151138	−	0.151138i	0.778626	+	0.627488i	$0.215917\pi$
$20$	2.67024	−	3.58745i	0.597084	−	0.802179i
$21$	−1.61800			−0.353076
$22$	−3.71389	+	3.13751i	−0.791804	+	0.668919i
$23$	1.90342	−	4.59527i	0.396891	−	0.958179i	−0.591508	−	0.806299i	$-0.701467\pi$
$23$	1.90342	−	4.59527i	0.396891	−	0.958179i	0.988399	−	0.151880i	$-0.0485328\pi$
$24$	2.90647	+	4.91970i	0.593281	+	1.00423i
$25$	−4.04958	+	2.93273i	−0.809916	+	0.586545i
$26$	1.63383	−	3.16431i	0.320421	−	0.620573i
$27$	1.48331	−	3.58104i	0.285464	−	0.689171i
$28$	0.357124	+	1.56147i	0.0674901	+	0.295090i
$29$	−9.10861	+	3.77291i	−1.69143	+	0.700611i	−0.999766	−	0.0216126i	$-0.993120\pi$
$29$	−9.10861	+	3.77291i	−1.69143	+	0.700611i	−0.691659	+	0.722224i	$0.743120\pi$
$30$	−1.45312	−	6.22111i	−0.265303	−	1.13581i
$31$	3.43384	−	1.42234i	0.616736	−	0.255460i	−0.0523696	−	0.998628i	$-0.516677\pi$
$31$	3.43384	−	1.42234i	0.616736	−	0.255460i	0.669106	+	0.743167i	$0.266677\pi$
$32$	4.10630	−	3.89080i	0.725898	−	0.687803i
$33$			6.94518i			1.20900i
$34$	1.48296	−	5.63922i	0.254325	−	0.967119i
$35$	0.141876	−	1.78522i	0.0239814	−	0.301758i
$36$	2.13235	+	0.361327i	0.355392	+	0.0602212i
$37$	−1.11757	+	0.462911i	−0.183727	+	0.0761022i	−0.472650	−	0.881250i	$-0.656703\pi$
$37$	−1.11757	+	0.462911i	−0.183727	+	0.0761022i	0.288924	+	0.957352i	$0.406703\pi$
$38$	−1.25528	+	0.400401i	−0.203634	+	0.0649536i
$39$	−1.94682	−	4.70005i	−0.311741	−	0.752610i
$40$	−5.68302	+	2.77548i	−0.898565	+	0.438841i
$41$	4.76899	−	11.5134i	0.744791	−	1.79808i	0.159612	−	0.987180i	$-0.448976\pi$
$41$	4.76899	−	11.5134i	0.744791	−	1.79808i	0.585179	−	0.810904i	$-0.301024\pi$
$42$	2.03317	+	1.04979i	0.313725	+	0.161986i
$43$	2.63427	−	2.63427i	0.401722	−	0.401722i	−0.477117	−	0.878840i	$-0.658318\pi$
$43$	2.63427	−	2.63427i	0.401722	−	0.401722i	0.878840	+	0.477117i	$0.158318\pi$
$44$	6.70253	−	1.53294i	1.01045	−	0.231099i
$45$	−2.15364	−	1.09941i	−0.321045	−	0.163890i
$46$	−5.37333	+	4.53942i	−0.792254	+	0.669300i
$47$	−10.2098			−1.48925			−0.744625	−	0.667483i	$-0.767372\pi$
$47$	−10.2098			−1.48925			−0.744625	+	0.667483i	$0.767372\pi$
$48$	−0.460265	−	8.06785i	−0.0664335	−	1.16449i
$49$	−4.49619	−	4.49619i	−0.642313	−	0.642313i
$50$	6.99150	−	1.05781i	0.988747	−	0.149596i
$51$	−4.78664	−	6.81699i	−0.670264	−	0.954570i
$52$	−4.10614	+	2.91620i	−0.569419	+	0.404404i
$53$	−3.65503	−	3.65503i	−0.502057	−	0.502057i	0.410020	−	0.912077i	$-0.365522\pi$
$53$	−3.65503	−	3.65503i	−0.502057	−	0.502057i	−0.912077	+	0.410020i	$0.865522\pi$
$54$	−4.18737	+	3.53751i	−0.569829	+	0.481395i
$55$	−7.66299	−	0.608996i	−1.03328	−	0.0821170i
$56$	0.564350	−	2.19384i	0.0754145	−	0.293165i
$57$	−0.720293	+	1.73894i	−0.0954052	+	0.230328i
$58$	13.8938	+	1.16882i	1.82434	+	0.153474i
$59$	−5.24423	−	5.24423i	−0.682741	−	0.682741i	0.277876	−	0.960617i	$-0.410369\pi$
$59$	−5.24423	−	5.24423i	−0.682741	−	0.682741i	−0.960617	+	0.277876i	$0.910369\pi$
$60$	−2.21039	+	8.76023i	−0.285360	+	1.13094i
$61$	−8.77111	−	3.63311i	−1.12303	−	0.465173i	−0.257621	−	0.966246i	$-0.582939\pi$
$61$	−8.77111	−	3.63311i	−1.12303	−	0.465173i	−0.865405	+	0.501074i	$0.832939\pi$
$62$	−5.23779	−	0.440632i	−0.665200	−	0.0559603i
$63$	0.800139	−	0.331429i	0.100808	−	0.0417561i
$64$	−7.68438	+	2.22492i	−0.960548	+	0.278115i
$65$	5.35652	−	1.73591i	0.664395	−	0.215313i
$66$	4.50617	−	8.72729i	0.554671	−	1.07426i
$67$	−5.11009			−0.624297			−0.312149	−	0.950033i	$-0.601049\pi$
$67$	−5.11009			−0.624297			−0.312149	+	0.950033i	$0.601049\pi$
$68$	−5.52232	+	6.12405i	−0.669679	+	0.742650i
$69$			10.0484i			1.20969i
$70$	−1.33657	+	2.15125i	−0.159750	+	0.257124i
$71$	7.58430	−	3.14152i	0.900091	−	0.372830i	0.115836	−	0.993268i	$-0.463045\pi$
$71$	7.58430	−	3.14152i	0.900091	−	0.372830i	0.784255	+	0.620439i	$0.213045\pi$
$72$	−2.44507	−	1.83755i	−0.288154	−	0.216558i
$73$	−5.76929	+	2.38972i	−0.675245	+	0.279696i	−0.693837	−	0.720132i	$-0.744081\pi$
$73$	−5.76929	+	2.38972i	−0.675245	+	0.279696i	0.0185928	+	0.999827i	$0.494081\pi$
$74$	1.70468	+	0.143407i	0.198165	+	0.0166707i
$75$	5.29105	−	8.60460i	0.610958	−	0.993574i
$76$	1.83717	+	0.311309i	0.210738	+	0.0357096i
$77$	1.94688	−	1.94688i	0.221868	−	0.221868i
$78$	−0.603112	+	7.16920i	−0.0682890	+	0.811752i
$79$	−11.6727	−	4.83500i	−1.31328	−	0.543980i	−0.387443	−	0.921894i	$-0.626642\pi$
$79$	−11.6727	−	4.83500i	−1.31328	−	0.543980i	−0.925841	+	0.377914i	$0.876642\pi$
$80$	8.94204	+	0.199603i	0.999751	+	0.0223162i
$81$			11.0748i			1.23053i
$82$	−13.4628	+	11.3734i	−1.48672	+	1.25598i
$83$	4.85020	+	4.85020i	0.532378	+	0.532378i	0.921279	−	0.388901i	$-0.127145\pi$
$83$	4.85020	+	4.85020i	0.532378	+	0.532378i	−0.388901	+	0.921279i	$0.627145\pi$
$84$	−1.87375	−	2.63832i	−0.204443	−	0.287864i
$85$	7.94128	−	4.68360i	0.861352	−	0.508008i
$86$	−5.01938	+	1.60105i	−0.541253	+	0.172645i
$87$	14.0840	−	14.0840i	1.50996	−	1.50996i
$88$	−9.41698	−	2.42245i	−1.00385	−	0.258234i
$89$		−	1.79163i		−	0.189913i	−0.995481	−	0.0949564i	$-0.969729\pi$
$89$		−	1.79163i		−	0.189913i	0.995481	−	0.0949564i	$-0.0302712\pi$
$90$	1.99293	+	2.77883i	0.210073	+	0.292915i
$91$	−0.771788	+	1.86326i	−0.0809053	+	0.195323i
$92$	9.69737	−	2.21789i	1.01102	−	0.231231i
$93$	−5.30949	+	5.30949i	−0.550569	+	0.550569i
$94$	12.8296	+	6.62430i	1.32327	+	0.683245i
$95$	−1.85551	−	0.947219i	−0.190371	−	0.0971826i
$96$	−4.65621	+	10.4367i	−0.475222	+	1.06519i
$97$	5.86683	−	2.43012i	0.595686	−	0.246741i	−0.0644085	−	0.997924i	$-0.520516\pi$
$97$	5.86683	−	2.43012i	0.595686	−	0.246741i	0.660095	+	0.751182i	$0.270516\pi$
$98$	2.73268	+	8.56711i	0.276042	+	0.865408i
$99$	−1.42264	−	3.43457i	−0.142981	−	0.345187i
$100$	−9.47181	−	3.20699i	−0.947181	−	0.320699i
$101$		−	5.75052i		−	0.572198i	−0.958200	−	0.286099i	$-0.907641\pi$
$101$		−	5.75052i		−	0.572198i	0.958200	−	0.286099i	$-0.0923586\pi$
$102$	1.59187	+	11.6719i	0.157619	+	1.15569i
$103$		−	12.9489i		−	1.27589i	−0.770082	−	0.637945i	$-0.779785\pi$
$103$		−	12.9489i		−	1.27589i	0.770082	−	0.637945i	$-0.220215\pi$
$104$	7.05184	−	1.00034i	0.691490	−	0.0980917i
$105$	1.11537	+	3.44173i	0.108849	+	0.335879i
$106$	2.22144	+	6.96435i	0.215765	+	0.676438i
$107$	0.898334	+	2.16877i	0.0868452	+	0.209663i	0.961335	−	0.275380i	$-0.0888038\pi$
$107$	0.898334	+	2.16877i	0.0868452	+	0.209663i	−0.874490	+	0.485043i	$0.838804\pi$
$108$	7.55705	−	1.72838i	0.727177	−	0.166313i
$109$	7.28774	+	3.01868i	0.698039	+	0.289137i	0.703345	−	0.710849i	$-0.251689\pi$
$109$	7.28774	+	3.01868i	0.698039	+	0.289137i	−0.00530589	+	0.999986i	$0.501689\pi$
$110$	9.23416	+	5.73716i	0.880442	+	0.547017i
$111$	1.72801	−	1.72801i	0.164016	−	0.164016i
$112$	−2.13257	+	2.39061i	−0.201509	+	0.225892i
$113$	−2.50677	+	6.05188i	−0.235817	+	0.569313i	−0.996842	−	0.0794095i	$-0.974697\pi$
$113$	−2.50677	+	6.05188i	−0.235817	+	0.569313i	0.761025	+	0.648723i	$0.224697\pi$
$114$	2.03338	−	1.71781i	0.190443	−	0.160887i
$115$	−11.0870	−	0.881108i	−1.03387	−	0.0821637i
$116$	−16.7005	−	10.4833i	−1.55060	−	0.973349i
$117$	1.92550	+	1.92550i	0.178013	+	0.178013i
$118$	3.18732	+	9.99244i	0.293416	+	0.919878i
$119$	−0.569152	+	3.25275i	−0.0521740	+	0.298179i
$120$	8.46137	−	9.57393i	0.772414	−	0.873976i
$121$	−0.578744	−	0.578744i	−0.0526131	−	0.0526131i
$122$	8.66451	+	10.2562i	0.784448	+	0.928555i
$123$			25.1762i			2.27006i
$124$	6.29590	+	3.95208i	0.565388	+	0.354907i
$125$	9.02996	+	6.59240i	0.807664	+	0.589642i
$126$	−1.22049	−	0.102674i	−0.108730	−	0.00914695i
$127$	−11.6008	−	11.6008i	−1.02940	−	1.02940i	−0.999554	−	0.0298492i	$-0.990497\pi$
$127$	−11.6008	−	11.6008i	−1.02940	−	1.02940i	−0.0298492	−	0.999554i	$-0.509503\pi$
$128$	11.0997	+	2.18996i	0.981087	+	0.193567i
$129$	−2.88017	+	6.95334i	−0.253585	+	0.612208i
$130$	−7.85727	−	1.29408i	−0.689129	−	0.113499i
$131$	−7.95995	+	3.29712i	−0.695464	+	0.288071i	−0.702275	−	0.711906i	$-0.747832\pi$
$131$	−7.95995	+	3.29712i	−0.695464	+	0.288071i	0.00681066	+	0.999977i	$0.497832\pi$
$132$	−11.3249	+	8.04298i	−0.985704	+	0.700052i
$133$	0.689376	−	0.285549i	0.0597765	−	0.0247602i
$134$	6.42132	+	3.31553i	0.554718	+	0.286418i
$135$	−8.63995	−	0.686637i	−0.743609	−	0.0590963i
$136$	10.9127	−	4.11247i	0.935758	−	0.352642i
$137$		−	11.1253i		−	0.950503i	−0.879850	−	0.475251i	$-0.842357\pi$
$137$		−	11.1253i		−	0.950503i	0.879850	−	0.475251i	$-0.157643\pi$
$138$	6.51962	−	12.6268i	0.554987	−	1.07487i
$139$	5.41665	+	13.0770i	0.459435	+	1.10917i	0.968627	+	0.248520i	$0.0799443\pi$
$139$	5.41665	+	13.0770i	0.459435	+	1.10917i	−0.509192	+	0.860653i	$0.670056\pi$
$140$	3.07530	−	1.83606i	0.259910	−	0.155176i
$141$	19.0561	−	7.89331i	1.60482	−	0.664737i
$142$	−11.5687	−	0.973221i	−0.970822	−	0.0816709i
$143$	7.99797	+	3.31287i	0.668824	+	0.277036i
$144$	1.88022	+	3.89547i	0.156685	+	0.324622i
$145$	14.3046	+	16.7746i	1.18793	+	1.39305i
$146$	8.80017	+	0.740319i	0.728307	+	0.0612692i
$147$	11.8680	+	4.91589i	0.978857	+	0.405456i
$148$	−2.04904	−	1.28623i	−0.168430	−	0.105728i
$149$	−20.6527			−1.69194			−0.845969	−	0.533232i	$-0.820977\pi$
$149$	−20.6527			−1.69194			−0.845969	+	0.533232i	$0.820977\pi$
$150$	−12.2315	+	7.37957i	−0.998701	+	0.602539i
$151$	0.775751	+	0.775751i	0.0631297	+	0.0631297i	0.737967	−	0.674837i	$-0.235786\pi$
$151$	0.775751	+	0.775751i	0.0631297	+	0.0631297i	−0.674837	+	0.737967i	$0.735786\pi$
$152$	−2.10660	−	1.58318i	−0.170868	−	0.128413i
$153$	3.76350	+	2.39068i	0.304261	+	0.193275i
$154$	−3.70962	+	1.18327i	−0.298930	+	0.0953506i
$155$	−5.39268	−	6.32381i	−0.433150	−	0.507941i
$156$	5.40938	−	8.61747i	0.433097	−	0.689950i
$157$		−	4.01079i		−	0.320096i	−0.987109	−	0.160048i	$-0.948835\pi$
$157$		−	4.01079i		−	0.320096i	0.987109	−	0.160048i	$-0.0511649\pi$
$158$	11.5309	+	13.6491i	0.917345	+	1.08587i
$159$	9.64772	+	3.99621i	0.765114	+	0.316920i
$160$	−11.1070	−	6.05259i	−0.878088	−	0.478499i
$161$	2.81679	−	2.81679i	0.221994	−	0.221994i
$162$	7.18552	−	13.9165i	0.564547	−	1.09338i
$163$	6.54175	−	15.7932i	0.512389	−	1.23702i	−0.430100	−	0.902781i	$-0.641522\pi$
$163$	6.54175	−	15.7932i	0.512389	−	1.23702i	0.942489	−	0.334236i	$-0.108478\pi$
$164$	24.2966	−	5.55688i	1.89724	−	0.433920i
$165$	14.7735	−	4.78769i	1.15011	−	0.372721i
$166$	−2.94783	−	9.24164i	−0.228796	−	0.717290i
$167$	−4.29888	−	10.3784i	−0.332657	−	0.803105i	−0.998380	−	0.0569058i	$-0.981877\pi$
$167$	−4.29888	−	10.3784i	−0.332657	−	0.803105i	0.665722	−	0.746199i	$-0.268123\pi$
$168$	0.642751	+	4.53102i	0.0495893	+	0.349576i
$169$	6.65886			0.512220
$170$	−13.0178	+	0.732940i	−0.998419	+	0.0562139i
$171$		−	1.00749i		−	0.0770450i
$172$	7.34612	+	1.24480i	0.560136	+	0.0949152i
$173$	5.18252	−	2.14667i	0.394020	−	0.163208i	−0.176871	−	0.984234i	$-0.556598\pi$
$173$	5.18252	−	2.14667i	0.394020	−	0.163208i	0.570891	+	0.821026i	$0.306598\pi$
$174$	−26.8358	+	8.55990i	−2.03442	+	0.648924i
$175$	−3.89525	+	0.928859i	−0.294453	+	0.0702151i
$176$	10.2616	+	9.15396i	0.773497	+	0.690006i
$177$	13.8425	+	5.73376i	1.04047	+	0.430976i
$178$	−1.16245	+	2.25136i	−0.0871291	+	0.168747i
$179$	12.2249	+	12.2249i	0.913732	+	0.913732i	0.996564	−	0.0828317i	$-0.0263964\pi$
$179$	12.2249	+	12.2249i	0.913732	+	0.913732i	−0.0828317	+	0.996564i	$0.526396\pi$
$180$	−0.701346	−	4.78492i	−0.0522752	−	0.356647i
$181$	4.22381	−	10.1972i	0.313953	−	0.757950i	−0.685598	−	0.727981i	$-0.740459\pi$
$181$	4.22381	−	10.1972i	0.313953	−	0.757950i	0.999551	−	0.0299693i	$-0.00954096\pi$
$182$	2.17875	−	1.84061i	0.161499	−	0.136435i
$183$	19.1797			1.41781
$184$	−13.6247	−	3.50485i	−1.00442	−	0.258381i
$185$	1.75508	+	2.05813i	0.129036	+	0.151317i
$186$	10.1168	−	3.22698i	0.741799	−	0.236614i
$187$	13.9623	+	2.44306i	1.02102	+	0.178654i
$188$	−11.8236	−	16.6481i	−0.862325	−	1.21419i
$189$	2.19509	−	2.19509i	0.159670	−	0.159670i
$190$	1.71705	+	2.39416i	0.124568	+	0.173691i
$191$		−	5.37161i		−	0.388676i	−0.980935	−	0.194338i	$-0.937744\pi$
$191$		−	5.37161i		−	0.388676i	0.980935	−	0.194338i	$-0.0622558\pi$
$192$	12.6225	−	10.0936i	0.910949	−	0.728444i
$193$	−7.18708	+	17.3511i	−0.517337	+	1.24896i	0.422196	+	0.906505i	$0.361259\pi$
$193$	−7.18708	+	17.3511i	−0.517337	+	1.24896i	−0.939533	+	0.342458i	$0.888741\pi$
$194$	−8.94895	−	0.752835i	−0.642497	−	0.0540504i
$195$	−8.65568	+	7.38119i	−0.619846	+	0.528578i
$196$	2.12464	−	12.5384i	0.151760	−	0.895600i
$197$	−4.77474	+	11.5272i	−0.340186	+	0.821282i	0.657510	+	0.753446i	$0.271610\pi$
$197$	−4.77474	+	11.5272i	−0.340186	+	0.821282i	−0.997696	+	0.0678366i	$0.978390\pi$
$198$	−0.440725	+	5.23890i	−0.0313210	+	0.372312i
$199$	6.72373	+	16.2325i	0.476632	+	1.15069i	0.961179	+	0.275927i	$0.0889848\pi$
$199$	6.72373	+	16.2325i	0.476632	+	1.15069i	−0.484546	+	0.874766i	$0.661015\pi$
$200$	9.82149	+	10.1754i	0.694484	+	0.719508i
$201$	9.53778	−	3.95068i	0.672743	−	0.278659i
$202$	−3.73105	+	7.22608i	−0.262516	+	0.508425i
$203$	−7.89607			−0.554196
$204$	5.57260	−	15.6997i	0.390160	−	1.09920i
$205$	−27.7782	−	2.20760i	−1.94012	−	0.154185i
$206$	−8.40148	+	16.2715i	−0.585359	+	1.13369i
$207$	−2.05831	−	4.96920i	−0.143062	−	0.345383i
$208$	−9.51036	−	3.31834i	−0.659425	−	0.230086i
$209$	−1.22571	−	2.95912i	−0.0847839	−	0.204686i
$210$	0.831489	−	5.04854i	0.0573782	−	0.348382i
$211$	−1.37308	−	0.568750i	−0.0945269	−	0.0391543i	0.334919	−	0.942247i	$-0.391291\pi$
$211$	−1.37308	−	0.568750i	−0.0945269	−	0.0391543i	−0.429446	+	0.903093i	$0.641291\pi$
$212$	1.72715	−	10.1927i	0.118621	−	0.700037i
$213$	−11.7270	+	11.7270i	−0.803524	+	0.803524i
$214$	0.278298	−	3.30812i	0.0190240	−	0.226139i
$215$	−7.41945	−	3.78756i	−0.506002	−	0.258309i
$216$	−10.6176	−	2.73129i	−0.722433	−	0.185841i
$217$	2.97673			0.202073
$218$	−7.19917	−	8.52169i	−0.487589	−	0.577162i
$219$	8.92063	−	8.92063i	0.602800	−	0.602800i
$220$	−7.88122	−	13.2006i	−0.531352	−	0.889984i
$221$	−10.1336	+	2.26050i	−0.681659	+	0.152058i
$222$	−3.29258	+	1.05024i	−0.220983	+	0.0704878i
$223$	−3.67807	+	3.67807i	−0.246302	+	0.246302i	−0.819451	−	0.573149i	$-0.805722\pi$
$223$	−3.67807	+	3.67807i	−0.246302	+	0.246302i	0.573149	+	0.819451i	$0.305722\pi$
$224$	4.23085	−	1.62038i	0.282686	−	0.108266i
$225$	−0.853999	+	5.33900i	−0.0569333	+	0.355933i
$226$	7.07658	−	5.97833i	0.470727	−	0.397673i
$227$	7.98332	+	3.30680i	0.529872	+	0.219480i	0.631547	−	0.775338i	$-0.282420\pi$
$227$	7.98332	+	3.30680i	0.529872	+	0.219480i	−0.101675	+	0.994818i	$0.532420\pi$
$228$	−3.66968	+	0.839294i	−0.243030	+	0.0555836i
$229$	−0.402482	−	0.402482i	−0.0265968	−	0.0265968i	0.693683	−	0.720280i	$-0.255987\pi$
$229$	−0.402482	−	0.402482i	−0.0265968	−	0.0265968i	−0.720280	+	0.693683i	$0.755987\pi$
$230$	13.3602	+	8.30064i	0.880944	+	0.547328i
$231$	−2.12862	+	5.13894i	−0.140053	+	0.338117i
$232$	14.1840	+	24.0089i	0.931227	+	1.57626i
$233$	−17.2651	+	7.15144i	−1.13107	+	0.468506i	−0.868146	−	0.496309i	$-0.834688\pi$
$233$	−17.2651	+	7.15144i	−1.13107	+	0.468506i	−0.262928	+	0.964815i	$0.584688\pi$
$234$	−1.17028	−	3.66889i	−0.0765034	−	0.239843i
$235$	7.03815	+	21.7178i	0.459119	+	1.41671i
$236$	2.47812	−	14.6244i	0.161312	−	0.951971i
$237$	25.5247			1.65800
$238$	2.82564	−	3.71811i	0.183159	−	0.241009i
$239$	−1.83542			−0.118723			−0.0593617	−	0.998237i	$-0.518907\pi$
$239$	−1.83542			−0.118723			−0.0593617	+	0.998237i	$0.518907\pi$
$240$	−16.8443	+	6.54066i	−1.08729	+	0.422198i
$241$	23.2271	−	9.62098i	1.49619	−	0.619742i	0.523536	−	0.852004i	$-0.324613\pi$
$241$	23.2271	−	9.62098i	1.49619	−	0.619742i	0.972653	+	0.232262i	$0.0746126\pi$
$242$	0.351747	+	1.10275i	0.0226111	+	0.0708873i
$243$	−4.11209	−	9.92746i	−0.263791	−	0.636847i
$244$	−4.23335	−	18.5096i	−0.271012	−	1.18496i
$245$	−6.46463	+	12.6636i	−0.413010	+	0.809045i
$246$	16.3348	−	31.6363i	1.04147	−	2.01706i
$247$	1.65896	+	1.65896i	0.105557	+	0.105557i
$248$	−5.34721	−	9.05107i	−0.339548	−	0.574743i
$249$	−12.8024	−	5.30295i	−0.811322	−	0.336061i
$250$	−7.06974	−	14.1428i	−0.447129	−	0.894469i
$251$	3.79764			0.239705			0.119852	−	0.992792i	$-0.461758\pi$
$251$	3.79764			0.239705			0.119852	+	0.992792i	$0.461758\pi$
$252$	1.46704	+	0.920897i	0.0924151	+	0.0580111i
$253$	−12.0910	−	12.0910i	−0.760152	−	0.760152i
$254$	7.05069	+	22.1043i	0.442399	+	1.38695i
$255$	−11.2011	+	14.8813i	−0.701441	+	0.931900i
$256$	−12.5270	−	9.95361i	−0.782937	−	0.622101i
$257$	11.2755	−	11.2755i	0.703349	−	0.703349i	−0.261779	−	0.965128i	$-0.584309\pi$
$257$	11.2755	−	11.2755i	0.703349	−	0.703349i	0.965128	+	0.261779i	$0.0843090\pi$
$258$	8.13067	−	6.86883i	0.506194	−	0.427635i
$259$	−0.968797			−0.0601981
$260$	9.03379	+	6.72410i	0.560252	+	0.417011i
$261$	−4.07992	+	9.84981i	−0.252541	+	0.609688i
$262$	12.1417	+	1.02142i	0.750115	+	0.0631038i
$263$	9.56770	+	9.56770i	0.589969	+	0.589969i	0.937623	−	0.347654i	$-0.113021\pi$
$263$	9.56770	+	9.56770i	0.589969	+	0.589969i	−0.347654	+	0.937623i	$0.613021\pi$
$264$	19.4492	−	2.75898i	1.19702	−	0.169804i
$265$	−5.25521	+	10.2944i	−0.322825	+	0.632382i
$266$	−1.05154	−	0.0884611i	−0.0644739	−	0.00542390i
$267$	1.38514	+	3.34401i	0.0847689	+	0.204650i
$268$	−5.91783	−	8.33256i	−0.361489	−	0.508992i
$269$	−2.96911	−	7.16806i	−0.181030	−	0.437044i	0.807150	−	0.590347i	$-0.201009\pi$
$269$	−2.96911	−	7.16806i	−0.181030	−	0.437044i	−0.988179	+	0.153303i	$0.951009\pi$
$270$	10.4114	+	6.46860i	0.633619	+	0.393666i
$271$	−21.9604			−1.33400			−0.666999	−	0.745059i	$-0.732421\pi$
$271$	−21.9604			−1.33400			−0.666999	+	0.745059i	$0.732421\pi$
$272$	−16.3811	−	1.91267i	−0.993252	−	0.115973i
$273$		−	4.07438i		−	0.246593i
$274$	−7.21834	+	13.9801i	−0.436076	+	0.844567i
$275$	3.98709	+	16.7202i	0.240430	+	1.00827i
$276$	−16.3851	+	11.6368i	−0.986265	+	0.700451i
$277$	−1.31819	−	3.18240i	−0.0792025	−	0.191212i	0.879318	−	0.476235i	$-0.157999\pi$
$277$	−1.31819	−	3.18240i	−0.0792025	−	0.191212i	−0.958521	+	0.285023i	$0.907999\pi$
$278$	1.67804	−	19.9469i	0.100642	−	1.19633i
$279$	1.53808	−	3.71326i	0.0920827	−	0.222307i
$280$	−5.05568	+	0.311874i	−0.302135	+	0.0186380i
$281$	−15.8250	+	15.8250i	−0.944041	+	0.944041i	−0.998515	−	0.0544739i	$-0.982652\pi$
$281$	−15.8250	+	15.8250i	−0.944041	+	0.944041i	0.0544739	+	0.998515i	$0.482652\pi$
$282$	−29.0672	−	2.44529i	−1.73093	−	0.145615i
$283$	−24.8341	−	10.2866i	−1.47624	−	0.611477i	−0.507964	−	0.861378i	$-0.669602\pi$
$283$	−24.8341	−	10.2866i	−1.47624	−	0.611477i	−0.968271	+	0.249901i	$0.919602\pi$
$284$	13.9057	+	8.72893i	0.825152	+	0.517967i
$285$	4.19554	+	0.333429i	0.248522	+	0.0197506i
$286$	−7.90076	−	9.35217i	−0.467182	−	0.553006i
$287$	7.05742	−	7.05742i	0.416586	−	0.416586i
$288$	0.164779	−	6.11495i	0.00970970	−	0.360327i
$289$	−15.3883	+	7.22488i	−0.905197	+	0.424993i
$290$	−7.09147	−	30.3599i	−0.416425	−	1.78280i
$291$	−9.07144	+	9.07144i	−0.531777	+	0.531777i
$292$	−10.5779	−	6.64000i	−0.619026	−	0.388577i
$293$		−	27.1764i		−	1.58766i	−0.608140	−	0.793830i	$-0.708084\pi$
$293$		−	27.1764i		−	1.58766i	0.608140	−	0.793830i	$-0.291916\pi$
$294$	−11.7238	−	13.8775i	−0.683744	−	0.809352i
$295$	−7.54016	+	14.7704i	−0.439005	+	0.859967i
$296$	1.74029	+	2.94573i	0.101152	+	0.171217i
$297$	−9.42235	−	9.42235i	−0.546740	−	0.546740i
$298$	25.9521	+	13.3999i	1.50337	+	0.776235i
$299$	11.5716	+	4.79313i	0.669205	+	0.277194i
$300$	20.1581	−	1.33707i	1.16383	−	0.0771957i
$301$	2.75654	−	1.14180i	0.158885	−	0.0658122i
$302$	−0.471483	−	1.47813i	−0.0271308	−	0.0850567i
$303$	4.44580	+	10.7331i	0.255404	+	0.616601i
$304$	1.61994	+	3.35622i	0.0929100	+	0.192492i
$305$	−1.68179	+	21.1620i	−0.0962993	+	1.21173i
$306$	−3.17807	−	5.44595i	−0.181678	−	0.311324i
$307$	3.45261			0.197051			0.0985255	−	0.995135i	$-0.468587\pi$
$307$	3.45261			0.197051			0.0985255	+	0.995135i	$0.468587\pi$
$308$	5.42923	+	0.919984i	0.309359	+	0.0524209i
$309$	10.0109	+	24.1685i	0.569502	+	1.37490i
$310$	2.67340	+	11.4454i	0.151839	+	0.650052i
$311$	−5.20738	−	12.5717i	−0.295283	−	0.712877i	−0.999994	−	0.00338247i	$-0.998923\pi$
$311$	−5.20738	−	12.5717i	−0.295283	−	0.712877i	0.704711	−	0.709495i	$-0.251077\pi$
$312$	−12.3886	+	7.31897i	−0.701366	+	0.414355i
$313$	−21.7726	−	9.01851i	−1.23066	−	0.509756i	−0.329877	−	0.944024i	$-0.607007\pi$
$313$	−21.7726	−	9.01851i	−1.23066	−	0.509756i	−0.900784	+	0.434267i	$0.857007\pi$
$314$	−2.60228	+	5.03994i	−0.146855	+	0.284420i
$315$	−1.25658	−	1.47355i	−0.0708002	−	0.0830251i
$316$	−5.63380	−	24.6329i	−0.316926	−	1.38571i
$317$	4.81232	+	1.99333i	0.270287	+	0.111956i	0.513710	−	0.857964i	$-0.328271\pi$
$317$	4.81232	+	1.99333i	0.270287	+	0.111956i	−0.243424	+	0.969920i	$0.578271\pi$
$318$	−9.53046	−	11.2813i	−0.534441	−	0.632621i
$319$			33.8936i			1.89767i
$320$	10.0300	+	14.8121i	0.560694	+	0.828023i
$321$	−3.35341	−	3.35341i	−0.187169	−	0.187169i
$322$	−5.36716	+	1.71198i	−0.299100	+	0.0954049i
$323$	3.24252	+	2.05974i	0.180418	+	0.114607i
$324$	−18.0586	+	12.8253i	−1.00325	+	0.712517i
$325$	−7.38508	−	10.1975i	−0.409651	−	0.565656i
$326$	−18.4673	+	15.6012i	−1.02281	+	0.864072i
$327$	−15.9361			−0.881266
$328$	−34.1364	−	8.78134i	−1.88487	−	0.484868i
$329$	−7.55451	−	3.12918i	−0.416494	−	0.172517i
$330$	−21.6707	−	3.56913i	−1.19293	−	0.196474i
$331$	12.5846	+	12.5846i	0.691713	+	0.691713i	0.962609	−	0.270895i	$-0.0873197\pi$
$331$	12.5846	+	12.5846i	0.691713	+	0.691713i	−0.270895	+	0.962609i	$0.587320\pi$
$332$	−2.29192	+	13.5256i	−0.125785	+	0.742315i
$333$	−0.500580	+	1.20851i	−0.0274316	+	0.0662258i
$334$	−1.33176	+	15.8307i	−0.0728708	+	0.866215i
$335$	3.52266	+	10.8700i	0.192464	+	0.593889i
$336$	2.13214	−	6.11070i	0.116318	−	0.333366i
$337$	6.40806	+	15.4704i	0.349069	+	0.842727i	0.996730	+	0.0807991i	$0.0257472\pi$
$337$	6.40806	+	15.4704i	0.349069	+	0.842727i	−0.647661	+	0.761928i	$0.724253\pi$
$338$	−8.36749	−	4.32040i	−0.455132	−	0.234999i
$339$		−	13.2336i		−	0.718751i
$340$	16.8336	+	7.52519i	0.912933	+	0.408111i
$341$		−	12.7775i		−	0.691939i
$342$	−0.653681	+	1.26601i	−0.0353470	+	0.0684581i
$343$	−4.09425	−	9.88439i	−0.221069	−	0.533707i
$344$	−8.42345	−	6.33052i	−0.454162	−	0.341319i
$345$	21.3746	−	6.92693i	1.15077	−	0.372934i
$346$	−7.90514	−	0.665024i	−0.424983	−	0.0357519i
$347$	13.5431	−	32.6959i	0.727030	−	1.75521i	0.0747814	−	0.997200i	$-0.476174\pi$
$347$	13.5431	−	32.6959i	0.727030	−	1.75521i	0.652248	−	0.758005i	$-0.273826\pi$
$348$	39.2756	+	6.65526i	2.10539	+	0.356759i
$349$	0.124066	+	0.124066i	0.00664112	+	0.00664112i	0.710420	−	0.703778i	$-0.248505\pi$
$349$	0.124066	+	0.124066i	0.00664112	+	0.00664112i	−0.703778	+	0.710420i	$0.748505\pi$
$350$	5.49741	+	1.36011i	0.293849	+	0.0727011i
$351$	9.01764	+	3.73523i	0.481326	+	0.199372i
$352$	−6.95542	−	18.1608i	−0.370725	−	0.967972i
$353$	−9.49323			−0.505274			−0.252637	−	0.967561i	$-0.581298\pi$
$353$	−9.49323			−0.505274			−0.252637	+	0.967561i	$0.581298\pi$
$354$	−13.6743	−	16.1863i	−0.726780	−	0.860293i
$355$	−11.9108	−	13.9674i	−0.632158	−	0.741311i
$356$	2.92145	−	2.07483i	0.154837	−	0.109966i
$357$	−1.45244	−	6.51114i	−0.0768714	−	0.344606i
$358$	−7.43000	−	23.2935i	−0.392688	−	1.23110i
$359$	−9.22146	−	9.22146i	−0.486690	−	0.486690i	0.420570	−	0.907260i	$-0.361830\pi$
$359$	−9.22146	−	9.22146i	−0.486690	−	0.486690i	−0.907260	+	0.420570i	$0.861830\pi$
$360$	−2.22324	+	6.46776i	−0.117175	+	0.340881i
$361$			18.1320i			0.954314i
$362$	−11.9237	+	10.0732i	−0.626698	+	0.529438i
$363$	1.52764	+	0.632768i	0.0801801	+	0.0332117i
$364$	−3.93203	+	0.899296i	−0.206094	+	0.0471359i
$365$	9.06039	+	10.6248i	0.474243	+	0.556129i
$366$	−24.1012	−	12.4442i	−1.25979	−	0.650468i
$367$	−4.74433	−	1.96516i	−0.247652	−	0.102581i	0.255405	−	0.966834i	$-0.417791\pi$
$367$	−4.74433	−	1.96516i	−0.247652	−	0.102581i	−0.503057	+	0.864253i	$0.667791\pi$
$368$	14.8467	+	13.2441i	0.773938	+	0.690399i
$369$	−5.15706	−	12.4502i	−0.268466	−	0.648134i
$370$	−0.870077	−	3.72497i	−0.0452332	−	0.193652i
$371$	−1.58424	−	3.82469i	−0.0822495	−	0.198568i
$372$	−14.8064	−	2.50896i	−0.767678	−	0.130083i
$373$	29.6618			1.53583			0.767914	−	0.640553i	$-0.221295\pi$
$373$	29.6618			1.53583			0.767914	+	0.640553i	$0.221295\pi$
$374$	−15.9598	−	12.1289i	−0.825264	−	0.627173i
$375$	−21.9507	−	5.32327i	−1.13353	−	0.274892i
$376$	4.05585	+	28.5914i	0.209164	+	1.47449i
$377$	−9.50080	−	22.9369i	−0.489316	−	1.18131i
$378$	−4.18257	+	1.33413i	−0.215128	+	0.0686200i
$379$	33.7633	−	13.9852i	1.73430	−	0.718372i	0.735122	−	0.677935i	$-0.237125\pi$
$379$	33.7633	−	13.9852i	1.73430	−	0.718372i	0.999182	−	0.0404378i	$-0.0128753\pi$
$380$	−0.604258	−	4.12255i	−0.0309978	−	0.211482i
$381$	30.6211	+	12.6837i	1.56877	+	0.649805i
$382$	−3.48520	+	6.74994i	−0.178318	+	0.345357i
$383$	−8.40105	−	8.40105i	−0.429274	−	0.429274i	0.459107	−	0.888381i	$-0.348169\pi$
$383$	−8.40105	−	8.40105i	−0.429274	−	0.429274i	−0.888381	+	0.459107i	$0.848169\pi$
$384$	−22.4103	+	4.49388i	−1.14362	+	0.229328i
$385$	−5.48342	−	2.79923i	−0.279461	−	0.142662i
$386$	20.2890	−	17.1403i	1.03268	−	0.872416i
$387$		−	4.02857i		−	0.204784i
$388$	10.7568	+	6.75226i	0.546091	+	0.342794i
$389$	−19.9631	+	19.9631i	−1.01217	+	1.01217i	−0.0122458	+	0.999925i	$0.503898\pi$
$389$	−19.9631	+	19.9631i	−1.01217	+	1.01217i	−0.999925	+	0.0122458i	$0.996102\pi$
$390$	15.6658	−	3.65920i	0.793266	−	0.185291i
$391$	20.2009	+	3.53467i	1.02160	+	0.178756i
$392$	−10.8050	+	14.3772i	−0.545733	+	0.726158i
$393$	12.3079	−	12.3079i	0.620850	−	0.620850i
$394$	13.4790	−	11.3871i	0.679063	−	0.573676i
$395$	−2.23816	+	28.1627i	−0.112614	+	1.41702i
$396$	3.95291	−	6.29723i	0.198641	−	0.316448i
$397$	24.6909	+	10.2273i	1.23920	+	0.513293i	0.903464	−	0.428663i	$-0.141015\pi$
$397$	24.6909	+	10.2273i	1.23920	+	0.513293i	0.335735	+	0.941956i	$0.391015\pi$
$398$	2.08296	−	24.7602i	0.104410	−	1.24112i
$399$	−1.06593	+	1.06593i	−0.0533633	+	0.0533633i
$400$	−5.73965	−	19.1587i	−0.286983	−	0.957936i
$401$	−1.51850	+	3.66598i	−0.0758303	+	0.183070i	−0.957249	−	0.289265i	$-0.906589\pi$
$401$	−1.51850	+	3.66598i	−0.0758303	+	0.183070i	0.881419	+	0.472336i	$0.156589\pi$
$402$	−14.5484	−	1.22389i	−0.725609	−	0.0610422i
$403$	3.58169	+	8.64697i	0.178417	+	0.430736i
$404$	9.37684	−	6.65948i	0.466515	−	0.331322i
$405$	23.5577	−	7.63443i	1.17059	−	0.379358i
$406$	9.92217	+	5.12313i	0.492429	+	0.254256i
$407$			4.15852i			0.206130i
$408$	−17.1888	+	16.1125i	−0.850970	+	0.797689i
$409$	17.2403			0.852478			0.426239	−	0.904611i	$-0.359838\pi$
$409$	17.2403			0.852478			0.426239	+	0.904611i	$0.359838\pi$
$410$	33.4737	+	20.7971i	1.65315	+	1.02710i
$411$	8.60115	+	20.7650i	0.424263	+	1.02426i
$412$	21.1145	−	14.9957i	1.04024	−	0.738783i
$413$	−2.27306	−	5.48765i	−0.111850	−	0.270030i
$414$	−0.637650	+	7.57975i	−0.0313388	+	0.372524i
$415$	6.97362	−	13.6606i	0.342321	−	0.670574i
$416$	9.79767	+	10.3403i	0.480370	+	0.506976i
$417$	−20.2199	−	20.2199i	−0.990174	−	0.990174i
$418$	−0.379715	+	4.51368i	−0.0185725	+	0.220771i
$419$	13.0025	−	31.3908i	0.635214	−	1.53354i	−0.197772	−	0.980248i	$-0.563371\pi$
$419$	13.0025	−	31.3908i	0.635214	−	1.53354i	0.832986	−	0.553294i	$-0.186629\pi$
$420$	−4.32044	+	5.80449i	−0.210816	+	0.283230i
$421$	−2.90390			−0.141527			−0.0707637	−	0.997493i	$-0.522544\pi$
$421$	−2.90390			−0.141527			−0.0707637	+	0.997493i	$0.522544\pi$
$422$	1.35639	+	1.60557i	0.0660283	+	0.0781580i
$423$	−7.80687	+	7.80687i	−0.379583	+	0.379583i
$424$	−8.78355	+	11.6875i	−0.426567	+	0.567594i
$425$	−15.4371	−	13.6637i	−0.748809	−	0.662785i
$426$	22.3449	−	7.12742i	1.08261	−	0.345324i
$427$	−5.37649	−	5.37649i	−0.260187	−	0.260187i
$428$	−2.49608	+	3.97641i	−0.120653	+	0.192207i
$429$	−17.4891			−0.844382
$430$	6.86580	+	9.57331i	0.331098	+	0.461666i
$431$	−4.69595	−	1.94513i	−0.226196	−	0.0936935i	0.266707	−	0.963778i	$-0.414064\pi$
$431$	−4.69595	−	1.94513i	−0.226196	−	0.0936935i	−0.492903	+	0.870084i	$0.664064\pi$
$432$	11.5699	+	10.3210i	0.556655	+	0.496570i
$433$	13.2027	+	13.2027i	0.634479	+	0.634479i	0.949188	−	0.314709i	$-0.101907\pi$
$433$	13.2027	+	13.2027i	0.634479	+	0.634479i	−0.314709	+	0.949188i	$0.601907\pi$
$434$	−3.74054	−	1.93136i	−0.179552	−	0.0927082i
$435$	−39.6676	−	20.2499i	−1.90192	−	0.970910i
$436$	3.51740	+	15.3793i	0.168453	+	0.736534i
$437$	−1.77338	−	4.28131i	−0.0848322	−	0.204803i
$438$	−16.9975	+	5.42175i	−0.812172	+	0.259061i
$439$	11.5575	−	4.78728i	0.551610	−	0.228484i	−0.0894281	−	0.995993i	$-0.528504\pi$
$439$	11.5575	−	4.78728i	0.551610	−	0.228484i	0.641038	+	0.767509i	$0.278504\pi$
$440$	1.33871	+	21.7013i	0.0638204	+	1.03457i
$441$	−6.87599			−0.327428
$442$	14.2005	+	3.73433i	0.675448	+	0.177624i
$443$	25.9778			1.23424			0.617122	−	0.786867i	$-0.288298\pi$
$443$	25.9778			1.23424			0.617122	+	0.786867i	$0.288298\pi$
$444$	4.81886	+	0.816557i	0.228693	+	0.0387521i
$445$	−3.81108	+	1.23507i	−0.180663	+	0.0585480i
$446$	7.00826	−	2.23545i	0.331851	−	0.105851i
$447$	38.5475	−	15.9669i	1.82323	−	0.755208i
$448$	−6.36781	−	0.708895i	−0.300851	−	0.0334921i
$449$	6.21609	−	15.0070i	0.293356	−	0.708223i	−0.706644	−	0.707569i	$-0.749792\pi$
$449$	6.21609	−	15.0070i	0.293356	−	0.708223i	1.00000		0.000653907i	$-0.000208145\pi$
$450$	4.53718	−	6.15487i	0.213885	−	0.290144i
$451$	−30.2937	−	30.2937i	−1.42647	−	1.42647i
$452$	−12.7713	+	2.92092i	−0.600709	+	0.137389i
$453$	−2.04765	−	0.848164i	−0.0962070	−	0.0398502i
$454$	−7.88629	−	9.33505i	−0.370122	−	0.438115i
$455$	4.49548	+	0.357266i	0.210751	+	0.0167489i
$456$	5.15585	+	1.32631i	0.241445	+	0.0621100i
$457$	14.3762	−	14.3762i	0.672489	−	0.672489i	−0.285800	−	0.958289i	$-0.592259\pi$
$457$	14.3762	−	14.3762i	0.672489	−	0.672489i	0.958289	+	0.285800i	$0.0922594\pi$
$458$	0.244619	+	0.766896i	0.0114303	+	0.0358347i
$459$	15.7423	+	2.75453i	0.734790	+	0.128570i
$460$	−11.4027	−	19.0989i	−0.531654	−	0.890491i
$461$	−7.47698	+	7.47698i	−0.348238	+	0.348238i	−0.859453	−	0.511215i	$-0.829196\pi$
$461$	−7.47698	+	7.47698i	−0.348238	+	0.348238i	0.511215	+	0.859453i	$0.329196\pi$
$462$	6.00906	−	5.07648i	0.279567	−	0.236179i
$463$	−25.7018			−1.19446			−0.597232	−	0.802068i	$-0.703733\pi$
$463$	−25.7018			−1.19446			−0.597232	+	0.802068i	$0.703733\pi$
$464$	−2.24616	−	39.3723i	−0.104275	−	1.82781i
$465$	14.9542	+	7.63399i	0.693486	+	0.354018i
$466$	26.3352	+	2.21547i	1.21996	+	0.102629i
$467$	−15.1664	+	15.1664i	−0.701818	+	0.701818i	−0.964801	−	0.262982i	$-0.915294\pi$
$467$	−15.1664	+	15.1664i	−0.701818	+	0.701818i	0.262982	+	0.964801i	$0.415294\pi$
$468$	−0.909881	+	5.36961i	−0.0420593	+	0.248210i
$469$	−3.78110	−	1.56618i	−0.174595	−	0.0723197i
$470$	5.24681	−	31.8570i	0.242017	−	1.46945i
$471$	3.10079	+	7.48598i	0.142877	+	0.344936i
$472$	−12.6026	+	16.7692i	−0.580083	+	0.771864i
$473$	−4.90112	−	11.8324i	−0.225354	−	0.544052i
$474$	−32.0742	−	16.5609i	−1.47322	−	0.760667i
$475$	−0.735780	+	4.59992i	−0.0337599	+	0.211059i
$476$	−5.96307	+	2.83884i	−0.273317	+	0.130118i
$477$	−5.58961			−0.255931
$478$	2.30638	+	1.19086i	0.105491	+	0.0544685i
$479$	34.1920	−	14.1628i	1.56227	−	0.647114i	0.576788	−	0.816894i	$-0.304306\pi$
$479$	34.1920	−	14.1628i	1.56227	−	0.647114i	0.985482	+	0.169780i	$0.0543058\pi$
$480$	25.4102	+	2.70993i	1.15981	+	0.123691i
$481$	−1.16569	−	2.81422i	−0.0531507	−	0.128317i
$482$	−35.4294	−	2.98051i	−1.61376	−	0.135759i
$483$	−3.07973	+	7.43513i	−0.140133	+	0.338310i
$484$	0.273480	−	1.61393i	0.0124309	−	0.0733604i
$485$	−9.21357	−	10.8044i	−0.418367	−	0.490605i
$486$	−1.27390	+	15.1428i	−0.0577851	+	0.686892i
$487$	−8.38068	+	20.2327i	−0.379765	+	0.916833i	0.612245	+	0.790668i	$0.290267\pi$
$487$	−8.38068	+	20.2327i	−0.379765	+	0.916833i	−0.992009	+	0.126165i	$0.959733\pi$
$488$	−6.68980	+	26.0058i	−0.302833	+	1.17723i
$489$			34.5348i			1.56172i
$490$	16.3398	−	11.7186i	0.738156	−	0.529392i
$491$	−10.3358	+	10.3358i	−0.466448	+	0.466448i	−0.900762	−	0.434314i	$-0.856991\pi$
$491$	−10.3358	+	10.3358i	−0.466448	+	0.466448i	0.434314	+	0.900762i	$0.356991\pi$
$492$	−41.0525	+	29.1557i	−1.85079	+	1.31444i
$493$	−23.3595	−	33.2680i	−1.05206	−	1.49831i
$494$	−1.00827	−	3.16100i	−0.0453644	−	0.142220i
$495$	−6.32515	+	5.39382i	−0.284294	+	0.242434i
$496$	0.846778	+	14.8429i	0.0380214	+	0.666466i
$497$	6.57468			0.294915
$498$	12.6468	+	14.9701i	0.566719	+	0.670828i
$499$	13.3726	−	32.2843i	0.598640	−	1.44525i	−0.276327	−	0.961064i	$-0.589117\pi$
$499$	13.3726	−	32.2843i	0.598640	−	1.44525i	0.874967	−	0.484182i	$-0.160883\pi$
$500$	−0.292325	+	22.3588i	−0.0130732	+	0.999915i
$501$	16.0474	+	16.0474i	0.716943	+	0.716943i
$502$	−4.77209	−	2.46398i	−0.212989	−	0.109973i
$503$	32.3335	+	13.3930i	1.44168	+	0.597163i	0.960205	−	0.279298i	$-0.0901016\pi$
$503$	32.3335	+	13.3930i	1.44168	+	0.597163i	0.481474	+	0.876460i	$0.340102\pi$
$504$	−1.24599	−	2.10904i	−0.0555006	−	0.0939442i
$505$	−12.2322	+	3.96414i	−0.544328	+	0.176402i
$506$	7.34860	+	23.0383i	0.326685	+	1.02418i
$507$	−12.4285	+	5.14805i	−0.551968	+	0.228633i
$508$	5.48185	−	32.3508i	0.243218	−	1.43534i
$509$		−	4.68831i		−	0.207806i	−0.994587	−	0.103903i	$-0.966867\pi$
$509$		−	4.68831i		−	0.207806i	0.994587	−	0.103903i	$-0.0331331\pi$
$510$	23.7305	−	11.4322i	1.05081	−	0.506227i
$511$	−5.00129			−0.221244
$512$	9.28327	+	20.6354i	0.410266	+	0.911966i
$513$	−1.38197	−	3.33638i	−0.0610156	−	0.147305i
$514$	−21.4846	+	6.85301i	−0.947645	+	0.302273i
$515$	−27.5443	+	8.92636i	−1.21375	+	0.393342i
$516$	−14.6736	+	3.35601i	−0.645969	+	0.147740i
$517$	−13.4319	+	32.4274i	−0.590733	+	1.42616i
$518$	1.21739	+	0.628574i	0.0534889	+	0.0276180i
$519$	−8.01335	+	8.01335i	−0.351747	+	0.351747i
$520$	−6.98910	−	14.3108i	−0.306492	−	0.627569i
$521$	−31.4790	−	13.0390i	−1.37912	−	0.571250i	−0.434874	−	0.900491i	$-0.643207\pi$
$521$	−31.4790	−	13.0390i	−1.37912	−	0.571250i	−0.944246	+	0.329241i	$0.893207\pi$
$522$	11.5176	−	9.73009i	0.504110	−	0.425875i
$523$		−	20.8969i		−	0.913758i	−0.889529	−	0.456879i	$-0.848967\pi$
$523$		−	20.8969i		−	0.913758i	0.889529	−	0.456879i	$-0.151033\pi$
$524$	−14.5945	−	9.16127i	−0.637562	−	0.400212i
$525$	6.55221	−	4.74514i	0.285962	−	0.207095i
$526$	−5.81502	−	18.2304i	−0.253547	−	0.794885i
$527$	8.80628	+	12.5416i	0.383608	+	0.546323i
$528$	−26.2299	−	9.15212i	−1.14151	−	0.398295i
$529$	−1.23000	−	1.23000i	−0.0534784	−	0.0534784i
$530$	13.2829	−	9.52625i	0.576972	−	0.413794i
$531$	−8.01997			−0.348037
$532$	1.26396	+	0.793418i	0.0547997	+	0.0343990i
$533$	28.9925	+	12.0091i	1.25580	+	0.520171i
$534$	0.429105	−	5.10077i	0.0185692	−	0.220732i
$535$	3.99404	−	3.40595i	0.172677	−	0.147252i
$536$	2.02999	+	14.3103i	0.0876822	+	0.618109i
$537$	−32.2685	−	13.3661i	−1.39249	−	0.576788i
$538$	−0.919809	+	10.9338i	−0.0396558	+	0.471388i
$539$	−20.1955	+	8.36527i	−0.869883	+	0.360317i
$540$	−8.88600	−	14.8835i	−0.382393	−	0.640486i
$541$	8.31450	+	20.0730i	0.357468	+	0.863005i	0.995655	+	0.0931229i	$0.0296850\pi$
$541$	8.31450	+	20.0730i	0.357468	+	0.863005i	−0.638186	+	0.769882i	$0.720315\pi$
$542$	27.5953	+	14.2483i	1.18532	+	0.612018i
$543$			22.2981i			0.956903i
$544$	19.3435	+	13.0319i	0.829345	+	0.558736i
$545$	1.39737	−	17.5831i	0.0598567	−	0.753177i
$546$	−2.64354	+	5.11985i	−0.113133	+	0.219109i
$547$	−7.17008	+	2.96995i	−0.306571	+	0.126986i	−0.530665	−	0.847582i	$-0.678058\pi$
$547$	−7.17008	+	2.96995i	−0.306571	+	0.126986i	0.224094	+	0.974567i	$0.428058\pi$
$548$	18.1411	−	12.8839i	0.774949	−	0.550373i
$549$	−9.48485	+	3.92875i	−0.404804	+	0.167675i
$550$	5.83823	−	23.5974i	0.248943	−	1.00620i
$551$	−3.51514	+	8.48630i	−0.149750	+	0.361528i
$552$	28.1396	−	3.99175i	1.19770	−	0.169900i
$553$	−7.15511	−	7.15511i	−0.304266	−	0.304266i
$554$	−0.408367	+	4.85426i	−0.0173499	+	0.206238i
$555$	−4.86696	−	2.48454i	−0.206591	−	0.105463i
$556$	−15.0506	+	23.9764i	−0.638286	+	1.01683i
$557$			21.4735i			0.909863i	0.890526	+	0.454932i	$0.150336\pi$
$557$			21.4735i			0.909863i	−0.890526	+	0.454932i	$0.849664\pi$
$558$	−4.34199	+	3.66813i	−0.183811	+	0.155284i
$559$	6.63352	+	6.63352i	0.280568	+	0.280568i
$560$	6.55530	+	2.88833i	0.277012	+	0.122054i
$561$	−27.9488	+	6.23455i	−1.18000	+	0.263223i
$562$	30.1532	−	9.61807i	1.27194	−	0.405714i
$563$	−9.94781	−	9.94781i	−0.419250	−	0.419250i	0.465695	−	0.884945i	$-0.345804\pi$
$563$	−9.94781	−	9.94781i	−0.419250	−	0.419250i	−0.884945	+	0.465695i	$0.845804\pi$
$564$	34.9392	+	21.9321i	1.47120	+	0.923509i
$565$	14.6014	+	1.16040i	0.614284	+	0.0488185i
$566$	24.5323	+	29.0390i	1.03117	+	1.22060i
$567$	−3.39428	+	8.19453i	−0.142547	+	0.344138i
$568$	−11.8104	−	19.9910i	−0.495552	−	0.838805i
$569$	25.7173	−	25.7173i	1.07813	−	1.07813i	0.0814486	−	0.996678i	$-0.474045\pi$
$569$	25.7173	−	25.7173i	1.07813	−	1.07813i	0.996678	−	0.0814486i	$-0.0259547\pi$
$570$	−5.05576	−	3.14113i	−0.211762	−	0.131567i
$571$	16.0004	+	6.62758i	0.669596	+	0.277356i	0.691470	−	0.722405i	$-0.256963\pi$
$571$	16.0004	+	6.62758i	0.669596	+	0.277356i	−0.0218742	+	0.999761i	$0.506963\pi$
$572$	3.86019	+	16.8781i	0.161403	+	0.705708i
$573$	4.15286	+	10.0259i	0.173488	+	0.418837i
$574$	−13.4473	+	4.28933i	−0.561280	+	0.179033i
$575$	5.76860	+	24.1911i	0.240567	+	1.00884i
$576$	−4.17456	+	7.57711i	−0.173940	+	0.315713i
$577$		−	13.3350i		−	0.555145i	−0.960705	−	0.277573i	$-0.910470\pi$
$577$		−	13.3350i		−	0.555145i	0.960705	−	0.277573i	$-0.0895299\pi$
$578$	24.0246	+	0.905502i	0.999290	+	0.0376639i
$579$		−	37.9416i		−	1.57680i
$580$	−10.7870	+	42.7513i	−0.447907	+	1.77515i
$581$	2.10227	+	5.07533i	0.0872168	+	0.210560i
$582$	17.2849	−	5.51341i	0.716481	−	0.228538i
$583$	−16.4173	+	6.80027i	−0.679935	+	0.281638i
$584$	8.98401	+	15.2070i	0.371761	+	0.629268i
$585$	2.76849	−	5.42320i	0.114463	−	0.224222i
$586$	−17.6326	+	34.1497i	−0.728394	+	1.41071i
$587$	−6.62698	+	6.62698i	−0.273525	+	0.273525i	−0.830517	−	0.556993i	$-0.811955\pi$
$587$	−6.62698	+	6.62698i	−0.273525	+	0.273525i	0.556993	+	0.830517i	$0.311955\pi$
$588$	5.72805	+	25.0450i	0.236221	+	1.03284i
$589$	1.32517	−	3.19924i	0.0546026	−	0.131822i
$590$	19.0583	−	13.6683i	0.784617	−	0.562713i
$591$		−	25.2065i		−	1.03686i
$592$	−0.275590	−	4.83073i	−0.0113267	−	0.198542i
$593$	13.0141	−	13.0141i	0.534426	−	0.534426i	−0.387460	−	0.921886i	$-0.626648\pi$
$593$	13.0141	−	13.0141i	0.534426	−	0.534426i	0.921886	+	0.387460i	$0.126648\pi$
$594$	5.72668	+	17.9535i	0.234969	+	0.736641i
$595$	7.31145	−	1.03162i	0.299740	−	0.0422924i
$596$	−23.9172	−	33.6765i	−0.979689	−	1.37944i
$597$	−25.0991	−	25.0991i	−1.02724	−	1.02724i
$598$	−11.4310	−	13.5309i	−0.467448	−	0.553320i
$599$			5.88190i			0.240328i	0.992754	+	0.120164i	$0.0383420\pi$
$599$			5.88190i			0.240328i	−0.992754	+	0.120164i	$0.961658\pi$
$600$	−26.1981	−	11.3988i	−1.06953	−	0.465355i
$601$	32.1759	+	13.3277i	1.31248	+	0.543648i	0.925608	−	0.378485i	$-0.123555\pi$
$601$	32.1759	+	13.3277i	1.31248	+	0.543648i	0.386874	+	0.922132i	$0.373555\pi$
$602$	−4.20468	−	0.353721i	−0.171370	−	0.0144166i
$603$	−3.90741	+	3.90741i	−0.159122	+	0.159122i
$604$	−0.366574	+	2.16332i	−0.0149157	+	0.0880241i
$605$	−0.832119	+	1.63004i	−0.0338304	+	0.0662704i
$606$	1.37728	−	16.3717i	0.0559481	−	0.665055i
$607$	12.7745	−	5.29138i	0.518502	−	0.214771i	−0.108057	−	0.994145i	$-0.534463\pi$
$607$	12.7745	−	5.29138i	0.518502	−	0.214771i	0.626559	+	0.779374i	$0.284463\pi$
$608$	0.141969	−	5.26846i	0.00575759	−	0.213664i
$609$	14.7377	−	6.10455i	0.597202	−	0.247369i
$610$	15.8437	−	25.5009i	0.641491	−	1.03250i
$611$		−	25.7099i		−	1.04011i
$612$	0.460115	+	8.90536i	0.0185990	+	0.359978i
$613$	−9.54282			−0.385431			−0.192715	−	0.981255i	$-0.561729\pi$
$613$	−9.54282			−0.385431			−0.192715	+	0.981255i	$0.561729\pi$
$614$	−4.33854	−	2.24012i	−0.175089	−	0.0904040i
$615$	53.5536	−	17.3553i	2.15949	−	0.699833i
$616$	−6.22544	−	4.67864i	−0.250830	−	0.188508i
$617$	4.68910	−	1.94229i	0.188776	−	0.0781935i	−0.286293	−	0.958142i	$-0.592423\pi$
$617$	4.68910	−	1.94229i	0.188776	−	0.0781935i	0.475069	+	0.879949i	$0.342423\pi$
$618$	3.10132	−	36.8654i	0.124753	−	1.48294i
$619$	12.3060	+	5.09733i	0.494621	+	0.204879i	0.616028	−	0.787724i	$-0.288741\pi$
$619$	12.3060	+	5.09733i	0.494621	+	0.204879i	−0.121407	+	0.992603i	$0.538741\pi$
$620$	4.06658	−	16.1167i	0.163318	−	0.647264i
$621$	−13.6325	−	13.6325i	−0.547051	−	0.547051i
$622$	−1.61321	+	19.1762i	−0.0646838	+	0.768896i
$623$	0.549115	−	1.32568i	0.0219998	−	0.0531123i
$624$	20.3161	−	1.15902i	0.813297	−	0.0463980i
$625$	7.79822	−	23.7526i	0.311929	−	0.950105i
$626$	21.5080	+	25.4591i	0.859632	+	1.01755i
$627$	4.57546	+	4.57546i	0.182726	+	0.182726i
$628$	6.54003	−	4.64476i	0.260976	−	0.185346i
$629$	−2.86606	−	4.08177i	−0.114277	−	0.162751i
$630$	0.622945	+	2.66695i	0.0248187	+	0.106254i
$631$	−5.41599	−	5.41599i	−0.215607	−	0.215607i	0.591037	−	0.806644i	$-0.298719\pi$
$631$	−5.41599	−	5.41599i	−0.215607	−	0.215607i	−0.806644	+	0.591037i	$0.798719\pi$
$632$	−8.90289	+	34.6089i	−0.354138	+	1.37667i
$633$	3.00251			0.119339
$634$	−4.75383	−	5.62713i	−0.188799	−	0.223482i
$635$	−16.6796	+	32.6737i	−0.661911	+	1.29662i
$636$	4.65644	+	20.3595i	0.184640	+	0.807308i
$637$	11.3221	−	11.3221i	0.448599	−	0.448599i
$638$	21.9908	−	42.5905i	0.870624	−	1.68617i
$639$	3.39716	−	8.20146i	0.134389	−	0.324445i
$640$	−2.99327	−	25.1205i	−0.118319	−	0.992976i
$641$	1.32058	+	3.18817i	0.0521599	+	0.125925i	0.947812	−	0.318831i	$-0.103290\pi$
$641$	1.32058	+	3.18817i	0.0521599	+	0.125925i	−0.895652	+	0.444756i	$0.853290\pi$
$642$	2.03812	+	6.38964i	0.0804383	+	0.252179i
$643$	−2.28217	+	0.945307i	−0.0900001	+	0.0372793i	−0.427229	−	0.904143i	$-0.640510\pi$
$643$	−2.28217	+	0.945307i	−0.0900001	+	0.0372793i	0.337229	+	0.941423i	$0.390510\pi$
$644$	7.85512	+	1.33105i	0.309535	+	0.0524508i
$645$	16.7763	+	1.33325i	0.660566	+	0.0524967i
$646$	−2.73813	−	4.69207i	−0.107730	−	0.184607i
$647$			38.4771i			1.51269i	0.654172	+	0.756346i	$0.273017\pi$
$647$			38.4771i			1.51269i	−0.654172	+	0.756346i	$0.726983\pi$
$648$	31.0136	−	4.39946i	1.21833	−	0.172827i
$649$	−23.5555	+	9.75701i	−0.924635	+	0.382996i
$650$	2.66373	+	17.6057i	0.104480	+	0.690553i
$651$	−5.55594	+	2.30135i	−0.217755	+	0.0901969i
$652$	33.3283	−	7.62252i	1.30524	−	0.298521i
$653$	−15.6376	+	37.7525i	−0.611947	+	1.47737i	0.248911	+	0.968526i	$0.419927\pi$
$653$	−15.6376	+	37.7525i	−0.611947	+	1.47737i	−0.860858	+	0.508845i	$0.830073\pi$
$654$	20.0252	+	10.3396i	0.783047	+	0.404311i
$655$	12.5007	+	14.6592i	0.488443	+	0.572781i
$656$	37.1981	+	33.1830i	1.45234	+	1.29558i
$657$	−2.58418	+	6.23876i	−0.100818	+	0.243397i
$658$	7.46269	+	8.83363i	0.290926	+	0.344371i
$659$	−32.5515			−1.26803			−0.634014	−	0.773322i	$-0.718594\pi$
$659$	−32.5515			−1.26803			−0.634014	+	0.773322i	$0.718594\pi$
$660$	24.9155	+	18.5453i	0.969836	+	0.721875i
$661$	31.6703	−	31.6703i	1.23183	−	1.23183i	0.268572	−	0.963260i	$-0.413448\pi$
$661$	31.6703	−	31.6703i	1.23183	−	1.23183i	0.963260	−	0.268572i	$-0.0865516\pi$
$662$	−7.64864	−	23.9789i	−0.297273	−	0.931968i
$663$	17.1663	−	12.0535i	0.666684	−	0.468121i
$664$	11.6557	−	15.5092i	0.452329	−	0.601873i
$665$	−1.08263	−	1.26957i	−0.0419826	−	0.0492317i
$666$	1.41313	−	1.19382i	0.0547577	−	0.0462596i
$667$			49.0379i			1.89876i
$668$	11.9447	−	19.0287i	0.462155	−	0.736241i
$669$	4.02141	−	9.70854i	0.155477	−	0.375354i
$670$	2.62608	−	15.9447i	0.101454	−	0.615998i
$671$	−23.0784	+	23.0784i	−0.890930	+	0.890930i
$672$	−6.64398	+	6.29530i	−0.256297	+	0.242847i
$673$	33.1545	+	13.7330i	1.27801	+	0.529369i	0.915390	−	0.402568i	$-0.131882\pi$
$673$	33.1545	+	13.7330i	1.27801	+	0.529369i	0.362620	+	0.931937i	$0.381882\pi$
$674$	1.98517	−	23.5977i	0.0764660	−	0.908951i
$675$	4.49541	+	18.8519i	0.173028	+	0.725608i
$676$	7.71140	+	10.8580i	0.296592	+	0.417615i
$677$	41.3616	−	17.1325i	1.58965	−	0.658456i	0.599749	−	0.800188i	$-0.295267\pi$
$677$	41.3616	−	17.1325i	1.58965	−	0.658456i	0.989905	+	0.141732i	$0.0452670\pi$
$678$	−8.58623	+	16.6293i	−0.329752	+	0.638645i
$679$	5.08584			0.195177
$680$	−16.2706	−	20.3781i	−0.623949	−	0.781465i
$681$	−17.4571			−0.668957
$682$	−8.29028	+	16.0561i	−0.317451	+	0.614821i
$683$	2.82950	−	1.17202i	0.108268	−	0.0448459i	−0.327892	−	0.944715i	$-0.606338\pi$
$683$	2.82950	−	1.17202i	0.108268	−	0.0448459i	0.436160	+	0.899869i	$0.356338\pi$
$684$	1.64283	−	1.16674i	0.0628151	−	0.0446116i
$685$	−23.6653	+	7.66931i	−0.904206	+	0.293029i
$686$	−1.26837	+	15.0771i	−0.0484266	+	0.575647i
$687$	1.06238	+	0.440053i	0.0405324	+	0.0167891i
$688$	6.47751	+	13.4202i	0.246953	+	0.511640i
$689$	9.20396	−	9.20396i	0.350643	−	0.350643i
$690$	−31.3536	−	5.16390i	−1.19361	−	0.196586i
$691$	−15.3642	+	37.0925i	−0.584483	+	1.41107i	0.304229	+	0.952599i	$0.401601\pi$
$691$	−15.3642	+	37.0925i	−0.584483	+	1.41107i	−0.888711	+	0.458467i	$0.848399\pi$
$692$	9.50209	+	5.96468i	0.361215	+	0.226743i
$693$		−	2.97736i		−	0.113100i
$694$	−38.2319	+	32.2985i	−1.45126	+	1.22603i
$695$	24.0827	−	20.5367i	0.913510	−	0.779002i
$696$	−45.0355	−	33.8457i	−1.70706	−	1.28292i
$697$	50.6131	+	8.85605i	1.91711	+	0.335447i
$698$	−0.0754046	−	0.236398i	−0.00285411	−	0.00894780i
$699$	26.6957	−	26.6957i	1.00973	−	1.00973i
$700$	−6.02556	−	5.27594i	−0.227745	−	0.199412i
$701$	−44.5817			−1.68383			−0.841914	−	0.539611i	$-0.818571\pi$
$701$	−44.5817			−1.68383			−0.841914	+	0.539611i	$0.818571\pi$
$702$	−8.90804	−	10.5445i	−0.336212	−	0.397976i
$703$	−0.431285	+	1.04121i	−0.0162662	+	0.0392701i
$704$	−3.04290	+	27.3335i	−0.114684	+	1.03017i
$705$	−29.9267	−	35.0941i	−1.12711	−	1.32172i
$706$	11.9292	+	6.15939i	0.448959	+	0.231812i
$707$	1.76247	−	4.25497i	0.0662844	−	0.160025i
$708$	6.68104	+	29.2118i	0.251089	+	1.09785i
$709$	−29.7981	+	12.3428i	−1.11909	+	0.463543i	−0.864060	−	0.503389i	$-0.832086\pi$
$709$	−29.7981	+	12.3428i	−1.11909	+	0.463543i	−0.255033	+	0.966932i	$0.582086\pi$
$710$	5.90473	+	25.2793i	0.221600	+	0.948714i
$711$	−12.6226	+	5.22844i	−0.473383	+	0.196082i
$712$	−5.01728	+	0.711729i	−0.188030	+	0.0266732i
$713$		−	18.4867i		−	0.692333i
$714$	−2.39942	+	9.12425i	−0.0897961	+	0.341466i
$715$	1.53355	−	19.2967i	0.0573515	−	0.721654i
$716$	−5.77677	+	34.0913i	−0.215888	+	1.27405i
$717$	3.42573	−	1.41899i	0.127936	−	0.0529930i
$718$	5.60459	+	17.5707i	0.209161	+	0.655733i
$719$	−6.80153	−	16.4203i	−0.253654	−	0.612376i	0.744839	−	0.667244i	$-0.232526\pi$
$719$	−6.80153	−	16.4203i	−0.253654	−	0.612376i	−0.998494	+	0.0548683i	$0.982526\pi$
$720$	6.99013	−	6.68488i	0.260507	−	0.249131i
$721$	3.96868	−	9.58124i	0.147801	−	0.356824i
$722$	11.7644	−	22.7846i	0.437825	−	0.847954i
$723$	−35.9143	+	35.9143i	−1.33567	+	1.33567i
$724$	21.5190	−	4.92163i	0.799749	−	0.182911i
$725$	25.8211	−	41.9918i	0.958973	−	1.55953i
$726$	−1.50907	−	1.78629i	−0.0560068	−	0.0662956i
$727$	−10.0605			−0.373123			−0.186562	−	0.982443i	$-0.559734\pi$
$727$	−10.0605			−0.373123			−0.186562	+	0.982443i	$0.559734\pi$
$728$	5.52445	+	1.42113i	0.204750	+	0.0526704i
$729$	−8.14300	−	8.14300i	−0.301593	−	0.301593i
$730$	−4.49166	−	19.2297i	−0.166244	−	0.711722i
$731$	12.9656	+	8.23609i	0.479548	+	0.304623i
$732$	22.2114	+	31.2746i	0.820957	+	1.15594i
$733$	25.8836	+	25.8836i	0.956033	+	0.956033i	0.999073	−	0.0430403i	$-0.0137044\pi$
$733$	25.8836	+	25.8836i	0.956033	+	0.956033i	−0.0430403	+	0.999073i	$0.513704\pi$
$734$	4.68666	+	5.54763i	0.172988	+	0.204767i
$735$	2.27560	−	28.6339i	0.0839368	−	1.05618i
$736$	−10.0632	−	26.2754i	−0.370936	−	0.968523i
$737$	−6.72278	+	16.2302i	−0.247637	+	0.597848i
$738$	−1.59762	+	18.9909i	−0.0588092	+	0.699066i
$739$	11.5914	+	11.5914i	0.426398	+	0.426398i	0.887399	−	0.461002i	$-0.152510\pi$
$739$	11.5914	+	11.5914i	0.426398	+	0.426398i	−0.461002	+	0.887399i	$0.652510\pi$
$740$	−1.32350	+	5.24531i	−0.0486527	+	0.192821i
$741$	−4.37894	−	1.81382i	−0.160864	−	0.0666322i
$742$	−0.490786	+	5.83397i	−0.0180173	+	0.214172i
$743$	−40.3247	+	16.7031i	−1.47937	+	0.612776i	−0.968974	−	0.247163i	$-0.920502\pi$
$743$	−40.3247	+	16.7031i	−1.47937	+	0.612776i	−0.510397	+	0.859939i	$0.670502\pi$
$744$	16.9779	+	12.7595i	0.622438	+	0.467784i
$745$	14.2371	+	43.9316i	0.521605	+	1.60953i
$746$	−37.2728	−	19.2451i	−1.36466	−	0.704614i
$747$	7.41737			0.271388
$748$	12.1856	+	25.5962i	0.445549	+	0.935891i
$749$			1.88006i			0.0686961i
$750$	24.1294	+	20.9313i	0.881079	+	0.764302i
$751$	−13.9326	+	5.77108i	−0.508409	+	0.210590i	−0.622117	−	0.782924i	$-0.713727\pi$
$751$	−13.9326	+	5.77108i	−0.508409	+	0.210590i	0.113708	+	0.993514i	$0.463727\pi$
$752$	13.4541	−	38.5593i	0.490620	−	1.40611i
$753$	−7.08813	+	2.93600i	−0.258306	+	0.106994i
$754$	−2.94328	+	34.9868i	−0.107188	+	1.27414i
$755$	1.11538	−	2.18491i	0.0405927	−	0.0795170i
$756$	6.12140	+	1.03727i	0.222633	+	0.0377252i
$757$	−21.4211	+	21.4211i	−0.778562	+	0.778562i	−0.979586	−	0.201025i	$-0.935573\pi$
$757$	−21.4211	+	21.4211i	−0.778562	+	0.778562i	0.201025	+	0.979586i	$0.435573\pi$
$758$	−51.5007	−	4.33252i	−1.87059	−	0.157364i
$759$	31.9150	+	13.2196i	1.15844	+	0.479842i
$760$	−1.91548	+	5.57243i	−0.0694818	+	0.202133i
$761$		−	0.147141i		−	0.00533387i	−0.999996	−	0.00266694i	$-0.999151\pi$
$761$		−	0.147141i		−	0.00533387i	0.999996	−	0.00266694i	$-0.000848913\pi$
$762$	−30.2490	−	35.8058i	−1.09580	−	1.29711i
$763$	4.46722	+	4.46722i	0.161724	+	0.161724i
$764$	8.75898	−	6.22068i	0.316889	−	0.225056i
$765$	2.49097	−	9.65357i	0.0900612	−	0.349026i
$766$	5.10596	+	16.0075i	0.184486	+	0.578374i
$767$	13.2058	−	13.2058i	0.476835	−	0.476835i
$768$	31.0764	+	8.89324i	1.12137	+	0.320907i
$769$			25.9998i			0.937576i	0.883311	+	0.468788i	$0.155309\pi$
$769$			25.9998i			0.937576i	−0.883311	+	0.468788i	$0.844691\pi$
$770$	5.07424	+	7.07525i	0.182863	+	0.254974i
$771$	−12.3281	+	29.7626i	−0.443985	+	1.07187i
$772$	−36.6160	+	8.37447i	−1.31784	+	0.301404i
$773$	−17.5516	+	17.5516i	−0.631289	+	0.631289i	−0.948391	−	0.317103i	$-0.897290\pi$
$773$	−17.5516	+	17.5516i	−0.631289	+	0.631289i	0.317103	+	0.948391i	$0.397290\pi$
$774$	−2.61382	+	5.06229i	−0.0939517	+	0.181960i
$775$	−9.73427	+	15.8304i	−0.349665	+	0.568645i
$776$	−9.13589	−	15.4641i	−0.327960	−	0.555127i
$777$	1.80822	−	0.748989i	0.0648695	−	0.0268698i
$778$	38.0381	−	12.1331i	1.36373	−	0.434993i
$779$	−4.44317	−	10.7268i	−0.159193	−	0.384326i
$780$	−22.0597	−	5.56611i	−0.789864	−	0.199299i
$781$		−	28.2215i		−	1.00985i
$782$	−23.0910	−	17.5484i	−0.825734	−	0.627530i
$783$			38.2147i			1.36568i
$784$	22.9057	−	11.0559i	0.818060	−	0.394852i
$785$	−8.53158	+	2.76486i	−0.304505	+	0.0986819i
$786$	−23.4516	+	7.48043i	−0.836491	+	0.266818i
$787$	−5.58683	−	13.4878i	−0.199149	−	0.480788i	0.792482	−	0.609896i	$-0.208789\pi$
$787$	−5.58683	−	13.4878i	−0.199149	−	0.480788i	−0.991631	+	0.129108i	$0.958789\pi$
$788$	−24.3259	+	5.56358i	−0.866574	+	0.198194i
$789$	−25.2546	−	10.4608i	−0.899088	−	0.372415i
$790$	21.0850	−	33.9370i	0.750170	−	1.20742i
$791$	−3.70967	+	3.70967i	−0.131901	+	0.131901i
$792$	−9.05298	+	5.34834i	−0.321684	+	0.190045i
$793$	9.14877	−	22.0871i	0.324882	−	0.784335i
$794$	−24.3908	−	28.8715i	−0.865597	−	1.02461i
$795$	1.84988	−	23.2770i	0.0656084	−	0.825550i
$796$	−18.6823	+	29.7621i	−0.662178	+	1.05489i
$797$	−14.6037	−	14.6037i	−0.517291	−	0.517291i	0.399460	−	0.916751i	$-0.369198\pi$
$797$	−14.6037	−	14.6037i	−0.517291	−	0.517291i	−0.916751	+	0.399460i	$0.869198\pi$
$798$	2.03104	−	0.647848i	0.0718981	−	0.0229336i
$799$	−9.16511	−	41.0862i	−0.324238	−	1.45352i
$800$	−5.21813	+	27.7988i	−0.184489	+	0.982835i
$801$	−1.36997	−	1.36997i	−0.0484054	−	0.0484054i
$802$	4.28670	−	3.62143i	0.151369	−	0.127877i
$803$			21.4678i			0.757583i
$804$	17.4874	+	10.9772i	0.616733	+	0.387137i
$805$	−7.93352	−	4.04999i	−0.279620	−	0.142743i
$806$	1.10958	−	13.1896i	0.0390834	−	0.464584i
$807$	11.0834	+	11.0834i	0.390156	+	0.390156i
$808$	−16.1037	+	2.28440i	−0.566526	+	0.0803649i
$809$	2.45549	−	5.92808i	0.0863305	−	0.208420i	−0.874818	−	0.484451i	$-0.839019\pi$
$809$	2.45549	−	5.92808i	0.0863305	−	0.208420i	0.961149	+	0.276031i	$0.0890193\pi$
$810$	−34.5559	−	5.69132i	−1.21417	−	0.199973i
$811$	11.3665	−	4.70816i	0.399132	−	0.165326i	−0.174083	−	0.984731i	$-0.555696\pi$
$811$	11.3665	−	4.70816i	0.399132	−	0.165326i	0.573215	+	0.819405i	$0.305696\pi$
$812$	−9.14417	−	12.8754i	−0.320898	−	0.451838i
$813$	40.9881	−	16.9778i	1.43752	−	0.595439i
$814$	2.69813	−	5.22558i	0.0945694	−	0.183156i
$815$	−38.1041	−	3.02822i	−1.33473	−	0.106074i
$816$	32.0534	−	9.09454i	1.12209	−	0.318372i
$817$		−	3.47090i		−	0.121431i
$818$	−21.6641	−	11.1858i	−0.757467	−	0.391104i
$819$	0.834591	+	2.01488i	0.0291630	+	0.0704056i
$820$	−28.5693	−	47.8519i	−0.997683	−	1.67106i
$821$	−0.756234	+	0.313242i	−0.0263927	+	0.0109322i	−0.395841	−	0.918319i	$-0.629547\pi$
$821$	−0.756234	+	0.313242i	−0.0263927	+	0.0109322i	0.369448	+	0.929251i	$0.379547\pi$
$822$	2.66458	−	31.6738i	0.0929378	−	1.10475i
$823$	−0.0289680	−	0.0119989i	−0.00100976	−	0.000418256i	0.382178	−	0.924089i	$-0.375174\pi$
$823$	−0.0289680	−	0.0119989i	−0.00100976	−	0.000418256i	−0.383188	+	0.923670i	$0.625174\pi$
$824$	−36.2619	+	5.14395i	−1.26324	+	0.179198i
$825$	−20.3683	−	28.1251i	−0.709134	−	0.979190i
$826$	−0.704178	+	8.37057i	−0.0245015	+	0.291249i
$827$	−43.4870	−	18.0129i	−1.51219	−	0.626370i	−0.536183	−	0.844102i	$-0.680134\pi$
$827$	−43.4870	−	18.0129i	−1.51219	−	0.626370i	−0.976009	+	0.217731i	$0.930134\pi$
$828$	5.71916	−	9.11096i	0.198754	−	0.316628i
$829$	−23.2567			−0.807738			−0.403869	−	0.914817i	$-0.632335\pi$
$829$	−23.2567			−0.807738			−0.403869	+	0.914817i	$0.632335\pi$
$830$	−17.6263	+	12.6413i	−0.611818	+	0.438785i
$831$	4.92071	+	4.92071i	0.170697	+	0.170697i
$832$	−5.60270	−	19.3505i	−0.194239	−	0.670859i
$833$	14.0574	−	22.1297i	0.487061	−	0.766748i
$834$	12.2892	+	38.5274i	0.425540	+	1.33409i
$835$	−19.1130	+	16.2988i	−0.661434	+	0.564042i
$836$	3.40571	−	5.42550i	0.117789	−	0.187645i
$837$		−	14.4065i		−	0.497961i
$838$	−36.7059	+	31.0093i	−1.26798	+	1.07120i
$839$	−31.8256	−	13.1826i	−1.09874	−	0.455114i	−0.241696	−	0.970352i	$-0.577704\pi$
$839$	−31.8256	−	13.1826i	−1.09874	−	0.455114i	−0.857047	+	0.515238i	$0.827704\pi$
$840$	9.19511	−	4.49071i	0.317261	−	0.154944i
$841$	48.2258	−	48.2258i	1.66296	−	1.66296i
$842$	3.64903	+	1.88411i	0.125754	+	0.0649306i
$843$	17.3022	−	41.7713i	0.595920	−	1.43868i
$844$	−0.662714	−	2.89761i	−0.0228115	−	0.0997399i
$845$	−4.59031	−	14.1644i	−0.157912	−	0.487271i
$846$	14.8753	−	4.74483i	0.511425	−	0.163131i
$847$	−0.250851	−	0.605607i	−0.00861934	−	0.0208089i
$848$	18.6204	−	8.98750i	0.639428	−	0.308632i
$849$	54.3046			1.86373
$850$	10.5329	+	27.1856i	0.361277	+	0.932459i
$851$			6.01663i			0.206248i
$852$	−32.7029	−	5.54151i	−1.12038	−	0.189849i
$853$	−27.8292	+	11.5273i	−0.952855	+	0.394686i	−0.804303	−	0.594219i	$-0.797461\pi$
$853$	−27.8292	+	11.5273i	−0.952855	+	0.394686i	−0.148552	+	0.988905i	$0.547461\pi$
$854$	3.26770	+	10.2444i	0.111818	+	0.350558i
$855$	−2.14310	+	0.694520i	−0.0732923	+	0.0237521i
$856$	5.71654	−	3.37723i	0.195387	−	0.115431i
$857$	−32.7884	−	13.5814i	−1.12003	−	0.463932i	−0.255650	−	0.966769i	$-0.582290\pi$
$857$	−32.7884	−	13.5814i	−1.12003	−	0.463932i	−0.864381	+	0.502837i	$0.832290\pi$
$858$	21.9767	+	11.3473i	0.750273	+	0.387389i
$859$	3.84458	+	3.84458i	0.131175	+	0.131175i	0.769646	−	0.638471i	$-0.220433\pi$
$859$	3.84458	+	3.84458i	0.131175	+	0.131175i	−0.638471	+	0.769646i	$0.720433\pi$
$860$	−2.41619	−	16.4844i	−0.0823915	−	0.562115i
$861$	−7.71621	+	18.6286i	−0.262968	+	0.634860i
$862$	4.63888	+	5.49106i	0.158001	+	0.187026i
$863$	35.1148			1.19532			0.597661	−	0.801749i	$-0.296097\pi$
$863$	35.1148			1.19532			0.597661	+	0.801749i	$0.296097\pi$
$864$	−7.84217	−	20.4761i	−0.266796	−	0.696611i
$865$	−8.13890	−	9.54422i	−0.276731	−	0.324513i
$866$	−8.02427	−	25.1566i	−0.272676	−	0.854855i
$867$	23.1361	−	25.3819i	0.785742	−	0.862014i
$868$	3.44725	+	4.85388i	0.117007	+	0.164751i
$869$	−30.7130	+	30.7130i	−1.04187	+	1.04187i
$870$	36.7076	+	51.1831i	1.24450	+	1.73527i
$871$		−	12.8680i		−	0.436017i
$872$	5.55843	−	21.6077i	0.188232	−	0.731729i
$873$	2.62787	−	6.34424i	0.0889399	−	0.214720i
$874$	−0.549380	+	6.53048i	−0.0185831	+	0.220897i
$875$	4.66103	+	7.64549i	0.157572	+	0.258465i
$876$	24.8767	+	4.21537i	0.840507	+	0.142424i
$877$	−5.50861	+	13.2990i	−0.186013	+	0.449074i	−0.989185	−	0.146672i	$-0.953144\pi$
$877$	−5.50861	+	13.2990i	−0.186013	+	0.449074i	0.803173	+	0.595746i	$0.203144\pi$
$878$	−17.6292	−	1.48307i	−0.594957	−	0.0500511i
$879$	21.0104	+	50.7236i	0.708663	+	1.71086i
$880$	12.3980	−	28.1383i	0.417937	−	0.948543i
$881$	−10.2912	+	4.26275i	−0.346719	+	0.143616i	−0.549245	−	0.835661i	$-0.685085\pi$
$881$	−10.2912	+	4.26275i	−0.346719	+	0.143616i	0.202527	+	0.979277i	$0.435085\pi$
$882$	8.64034	+	4.46128i	0.290935	+	0.150219i
$883$	−21.7804			−0.732968			−0.366484	−	0.930424i	$-0.619439\pi$
$883$	−21.7804			−0.732968			−0.366484	+	0.930424i	$0.619439\pi$
$884$	−15.4214	−	13.9061i	−0.518676	−	0.467712i
$885$	2.65420	−	33.3978i	0.0892199	−	1.12265i
$886$	−32.6436	−	16.8549i	−1.09668	−	0.566252i
$887$	−0.445547	−	1.07565i	−0.0149600	−	0.0361167i	0.916223	−	0.400669i	$-0.131222\pi$
$887$	−0.445547	−	1.07565i	−0.0149600	−	0.0361167i	−0.931183	+	0.364552i	$0.881222\pi$
$888$	−5.52556	−	4.15265i	−0.185426	−	0.139354i
$889$	−5.02825	−	12.1393i	−0.168642	−	0.407138i
$890$	5.59033	+	0.920721i	0.187388	+	0.0308627i
$891$	35.1747	+	14.5698i	1.17840	+	0.488107i
$892$	−10.2570	−	1.73804i	−0.343428	−	0.0581940i
$893$	−6.72617	+	6.72617i	−0.225083	+	0.225083i
$894$	−58.7983	−	4.94643i	−1.96651	−	0.165433i
$895$	17.5770	−	34.4315i	0.587533	−	1.15092i
$896$	7.54181	+	5.02235i	0.251954	+	0.167785i
$897$	−25.3036			−0.844863
$898$	−17.5479	+	14.8246i	−0.585582	+	0.494703i
$899$	−25.9111	+	25.9111i	−0.864184	+	0.864184i
$900$	−9.69480	+	4.79038i	−0.323160	+	0.159679i
$901$	11.4275	−	17.9896i	0.380706	−	0.599321i
$902$	18.4118	+	57.7221i	0.613045	+	1.92193i
$903$	−4.26224	+	4.26224i	−0.141838	+	0.141838i
$904$	17.9435	+	4.61583i	0.596791	+	0.153520i
$905$	−24.6027	−	1.95523i	−0.817821	−	0.0649941i
$906$	2.02276	+	2.39435i	0.0672018	+	0.0795471i
$907$	30.4750	+	12.6232i	1.01191	+	0.419146i	0.826150	−	0.563450i	$-0.190526\pi$
$907$	30.4750	+	12.6232i	1.01191	+	0.419146i	0.185757	+	0.982596i	$0.440526\pi$
$908$	3.85312	+	16.8472i	0.127870	+	0.559093i
$909$	−4.39711	−	4.39711i	−0.145843	−	0.145843i
$910$	−5.41720	−	3.36569i	−0.179578	−	0.111572i
$911$	19.8214	−	47.8532i	0.656714	−	1.58545i	−0.146135	−	0.989265i	$-0.546683\pi$
$911$	19.8214	−	47.8532i	0.656714	−	1.58545i	0.802849	−	0.596183i	$-0.203317\pi$
$912$	−5.61829	−	5.01185i	−0.186040	−	0.165959i
$913$	21.7856	−	9.02391i	0.720999	−	0.298648i
$914$	−27.3926	+	8.73750i	−0.906066	+	0.289011i
$915$	−13.2216	−	40.7983i	−0.437094	−	1.34875i
$916$	0.190190	−	1.12239i	0.00628404	−	0.0370849i
$917$	−6.90032			−0.227869
$918$	−17.9946	−	13.6753i	−0.593910	−	0.451351i
$919$	−9.92489			−0.327392			−0.163696	−	0.986511i	$-0.552342\pi$
$919$	−9.92489			−0.327392			−0.163696	+	0.986511i	$0.552342\pi$
$920$	1.93687	+	31.3979i	0.0638567	+	1.03516i
$921$	−6.44416	+	2.66926i	−0.212342	+	0.0879551i
$922$	14.2467	−	4.54433i	0.469192	−	0.149660i
$923$	7.91086	+	19.0985i	0.260389	+	0.628635i
$924$	−10.8447	+	2.48029i	−0.356764	+	0.0815956i
$925$	3.16809	−	5.15212i	0.104166	−	0.169401i
$926$	32.2968	+	16.6758i	1.06134	+	0.548002i
$927$	−9.90131	−	9.90131i	−0.325202	−	0.325202i
$928$	−22.7230	+	50.9324i	−0.745919	+	1.67194i
$929$	−20.7738	−	8.60481i	−0.681568	−	0.282315i	0.0149143	−	0.999889i	$-0.495252\pi$
$929$	−20.7738	−	8.60481i	−0.681568	−	0.282315i	−0.696482	+	0.717574i	$0.745252\pi$
$930$	−13.8383	−	19.2954i	−0.453777	−	0.632723i
$931$	−5.92415			−0.194156
$932$	−31.6553	−	19.8708i	−1.03690	−	0.650889i
$933$	19.4387	+	19.4387i	0.636395	+	0.636395i
$934$	28.8983	−	9.21779i	0.945582	−	0.301615i
$935$	−4.42819	−	31.3841i	−0.144817	−	1.02637i
$936$	4.62726	−	6.15708i	0.151247	−	0.201250i
$937$	−21.1701	+	21.1701i	−0.691596	+	0.691596i	−0.962583	−	0.270987i	$-0.912650\pi$
$937$	−21.1701	+	21.1701i	−0.691596	+	0.691596i	0.270987	+	0.962583i	$0.412650\pi$
$938$	3.73515	+	4.42131i	0.121957	+	0.144361i
$939$	47.6100			1.55369
$940$	−27.2625	+	36.6271i	−0.889206	+	1.19464i
$941$	2.94935	−	7.12035i	0.0961460	−	0.232117i	−0.868488	−	0.495710i	$-0.834908\pi$
$941$	2.94935	−	7.12035i	0.0961460	−	0.232117i	0.964634	+	0.263593i	$0.0849077\pi$
$942$	0.960604	−	11.4187i	0.0312982	−	0.372042i
$943$	−43.8295	−	43.8295i	−1.42729	−	1.42729i
$944$	26.7166	−	12.8952i	0.869550	−	0.419705i
$945$	−6.18250	−	3.15611i	−0.201117	−	0.102668i
$946$	−1.51833	+	18.0484i	−0.0493653	+	0.586805i
$947$	11.2256	+	27.1011i	0.364784	+	0.880666i	0.994587	+	0.103911i	$0.0331357\pi$
$947$	11.2256	+	27.1011i	0.364784	+	0.880666i	−0.629803	+	0.776755i	$0.716864\pi$
$948$	29.5592	+	41.6207i	0.960040	+	1.35178i
$949$	−6.01770	−	14.5280i	−0.195343	−	0.471599i
$950$	3.90910	−	5.30285i	0.126828	−	0.172047i
$951$	−10.5231			−0.341234
$952$	9.33506	+	0.301689i	0.302551	+	0.00977780i
$953$			42.6922i			1.38294i	0.722407	+	0.691468i	$0.243036\pi$
$953$			42.6922i			1.38294i	−0.722407	+	0.691468i	$0.756964\pi$
$954$	7.02389	+	3.62665i	0.227407	+	0.117417i
$955$	−11.4262	+	3.70294i	−0.369744	+	0.119824i
$956$	−2.12554	−	2.99285i	−0.0687448	−	0.0967956i
$957$	−26.2035	−	63.2609i	−0.847040	−	2.04494i
$958$	−52.1546	−	4.38753i	−1.68504	−	0.141755i
$959$	3.40979	−	8.23196i	0.110108	−	0.265824i
$960$	−30.1720	−	19.8919i	−0.973798	−	0.642008i
$961$	−12.1521	+	12.1521i	−0.392004	+	0.392004i
$962$	−0.361122	+	4.29265i	−0.0116430	+	0.138401i
$963$	2.34525	+	0.971435i	0.0755747	+	0.0313041i
$964$	42.5866	+	26.7326i	1.37162	+	0.860998i
$965$	41.8630	+	3.32695i	1.34762	+	0.107098i
$966$	8.69403	−	7.34476i	0.279726	−	0.236314i
$967$	−16.6642	+	16.6642i	−0.535885	+	0.535885i	−0.922318	−	0.386433i	$-0.873707\pi$
$967$	−16.6642	+	16.6642i	−0.535885	+	0.535885i	0.386433	+	0.922318i	$0.373707\pi$
$968$	−1.39080	+	1.85062i	−0.0447021	+	0.0594810i
$969$	−7.64444	−	1.33759i	−0.245575	−	0.0429696i
$970$	4.56760	+	19.5548i	0.146657	+	0.627866i
$971$	−26.5367	+	26.5367i	−0.851603	+	0.851603i	−0.990331	−	0.138728i	$-0.955699\pi$
$971$	−26.5367	+	26.5367i	−0.851603	+	0.851603i	0.138728	+	0.990331i	$0.455699\pi$
$972$	11.4257	−	18.2019i	0.366480	−	0.583825i
$973$			11.3362i			0.363421i
$974$	23.6585	−	19.9868i	0.758068	−	0.640420i
$975$	21.6678	+	13.3237i	0.693924	+	0.426701i
$976$	25.2795	−	28.3383i	0.809176	−	0.907087i
$977$	−10.4866	−	10.4866i	−0.335497	−	0.335497i	0.519172	−	0.854670i	$-0.326240\pi$
$977$	−10.4866	−	10.4866i	−0.335497	−	0.335497i	−0.854670	+	0.519172i	$0.826240\pi$
$978$	22.4069	−	43.3963i	0.716493	−	1.38766i
$979$	−5.69043	−	2.35705i	−0.181867	−	0.0753318i
$980$	−28.1358	+	4.12397i	−0.898764	+	0.131735i
$981$	7.88077	−	3.26432i	0.251614	−	0.104222i
$982$	19.6940	−	6.28185i	0.628460	−	0.200462i
$983$	−5.28614	−	12.7619i	−0.168602	−	0.407040i	0.816883	−	0.576803i	$-0.195700\pi$
$983$	−5.28614	−	12.7619i	−0.168602	−	0.407040i	−0.985485	+	0.169763i	$0.945700\pi$
$984$	70.5031	−	10.0013i	2.24756	−	0.318829i
$985$	27.8117	+	2.21026i	0.886155	+	0.0704248i
$986$	7.76859	+	56.9605i	0.247402	+	1.81399i
$987$	16.5194			0.525818
$988$	−0.783926	+	4.62629i	−0.0249400	+	0.147182i
$989$	−7.09104	−	17.1193i	−0.225482	−	0.544362i
$990$	11.4478	−	2.67397i	0.363834	−	0.0849842i
$991$	11.0247	+	26.6160i	0.350211	+	0.845484i	0.996593	+	0.0824706i	$0.0262811\pi$
$991$	11.0247	+	26.6160i	0.350211	+	0.845484i	−0.646382	+	0.763014i	$0.723719\pi$
$992$	8.56631	−	19.2009i	0.271981	−	0.609631i
$993$	−33.2180	−	13.7594i	−1.05414	−	0.436640i
$994$	−8.26172	−	4.26578i	−0.262046	−	0.135302i
$995$	29.8941	−	25.4924i	0.947705	−	0.808162i
$996$	−6.17905	−	27.0169i	−0.195791	−	0.856064i
$997$	19.0207	+	7.87865i	0.602393	+	0.249519i	0.662972	−	0.748644i	$-0.269295\pi$
$997$	19.0207	+	7.87865i	0.602393	+	0.249519i	−0.0605792	+	0.998163i	$0.519295\pi$
$998$	−37.7507	+	31.8920i	−1.19498	+	1.00952i
$999$			4.68869i			0.148344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.br.a.189.16	✓	416
5.4	even	2	inner	680.2.br.a.189.89	yes	416
8.5	even	2	inner	680.2.br.a.189.68	yes	416
17.9	even	8	inner	680.2.br.a.349.37	yes	416
40.29	even	2	inner	680.2.br.a.189.37	yes	416
85.9	even	8	inner	680.2.br.a.349.68	yes	416
136.77	even	8	inner	680.2.br.a.349.89	yes	416
680.349	even	8	inner	680.2.br.a.349.16	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.br.a.189.16	✓	416	1.1	even	1	trivial
680.2.br.a.189.37	yes	416	40.29	even	2	inner
680.2.br.a.189.68	yes	416	8.5	even	2	inner
680.2.br.a.189.89	yes	416	5.4	even	2	inner
680.2.br.a.349.16	yes	416	680.349	even	8	inner
680.2.br.a.349.37	yes	416	17.9	even	8	inner
680.2.br.a.349.68	yes	416	85.9	even	8	inner
680.2.br.a.349.89	yes	416	136.77	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.br (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25660 - 0.648820i) q^{2} +(-1.86646 + 0.773113i) q^{3} +(1.15807 + 1.63061i) q^{4} +(-0.689354 - 2.12716i) q^{5} +(2.84700 + 0.239505i) q^{6} +(0.739929 + 0.306488i) q^{7} +(-0.397251 - 2.80039i) q^{8} +(0.764647 - 0.764647i) q^{9} +(-0.513900 + 3.12024i) q^{10} +(1.31559 - 3.17611i) q^{11} +(-3.42213 - 2.14815i) q^{12} +2.51816i q^{13} +(-0.730936 - 0.865212i) q^{14} +(2.93118 + 3.43730i) q^{15} +(-1.31776 + 3.77670i) q^{16} +(0.897680 + 4.02420i) q^{17} +(-1.45697 + 0.464734i) q^{18} +(0.658797 - 0.658797i) q^{19} +(2.67024 - 3.58745i) q^{20} -1.61800 q^{21} +(-3.71389 + 3.13751i) q^{22} +(1.90342 - 4.59527i) q^{23} +(2.90647 + 4.91970i) q^{24} +(-4.04958 + 2.93273i) q^{25} +(1.63383 - 3.16431i) q^{26} +(1.48331 - 3.58104i) q^{27} +(0.357124 + 1.56147i) q^{28} +(-9.10861 + 3.77291i) q^{29} +(-1.45312 - 6.22111i) q^{30} +(3.43384 - 1.42234i) q^{31} +(4.10630 - 3.89080i) q^{32} +6.94518i q^{33} +(1.48296 - 5.63922i) q^{34} +(0.141876 - 1.78522i) q^{35} +(2.13235 + 0.361327i) q^{36} +(-1.11757 + 0.462911i) q^{37} +(-1.25528 + 0.400401i) q^{38} +(-1.94682 - 4.70005i) q^{39} +(-5.68302 + 2.77548i) q^{40} +(4.76899 - 11.5134i) q^{41} +(2.03317 + 1.04979i) q^{42} +(2.63427 - 2.63427i) q^{43} +(6.70253 - 1.53294i) q^{44} +(-2.15364 - 1.09941i) q^{45} +(-5.37333 + 4.53942i) q^{46} -10.2098 q^{47} +(-0.460265 - 8.06785i) q^{48} +(-4.49619 - 4.49619i) q^{49} +(6.99150 - 1.05781i) q^{50} +(-4.78664 - 6.81699i) q^{51} +(-4.10614 + 2.91620i) q^{52} +(-3.65503 - 3.65503i) q^{53} +(-4.18737 + 3.53751i) q^{54} +(-7.66299 - 0.608996i) q^{55} +(0.564350 - 2.19384i) q^{56} +(-0.720293 + 1.73894i) q^{57} +(13.8938 + 1.16882i) q^{58} +(-5.24423 - 5.24423i) q^{59} +(-2.21039 + 8.76023i) q^{60} +(-8.77111 - 3.63311i) q^{61} +(-5.23779 - 0.440632i) q^{62} +(0.800139 - 0.331429i) q^{63} +(-7.68438 + 2.22492i) q^{64} +(5.35652 - 1.73591i) q^{65} +(4.50617 - 8.72729i) q^{66} -5.11009 q^{67} +(-5.52232 + 6.12405i) q^{68} +10.0484i q^{69} +(-1.33657 + 2.15125i) q^{70} +(7.58430 - 3.14152i) q^{71} +(-2.44507 - 1.83755i) q^{72} +(-5.76929 + 2.38972i) q^{73} +(1.70468 + 0.143407i) q^{74} +(5.29105 - 8.60460i) q^{75} +(1.83717 + 0.311309i) q^{76} +(1.94688 - 1.94688i) q^{77} +(-0.603112 + 7.16920i) q^{78} +(-11.6727 - 4.83500i) q^{79} +(8.94204 + 0.199603i) q^{80} +11.0748i q^{81} +(-13.4628 + 11.3734i) q^{82} +(4.85020 + 4.85020i) q^{83} +(-1.87375 - 2.63832i) q^{84} +(7.94128 - 4.68360i) q^{85} +(-5.01938 + 1.60105i) q^{86} +(14.0840 - 14.0840i) q^{87} +(-9.41698 - 2.42245i) q^{88} -1.79163i q^{89} +(1.99293 + 2.77883i) q^{90} +(-0.771788 + 1.86326i) q^{91} +(9.69737 - 2.21789i) q^{92} +(-5.30949 + 5.30949i) q^{93} +(12.8296 + 6.62430i) q^{94} +(-1.85551 - 0.947219i) q^{95} +(-4.65621 + 10.4367i) q^{96} +(5.86683 - 2.43012i) q^{97} +(2.73268 + 8.56711i) q^{98} +(-1.42264 - 3.43457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 16 q^{6} - 16 q^{9} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 16 q^{16} - 20 q^{20} + 24 q^{26} - 16 q^{31} - 40 q^{34} - 8 q^{36} + 32 q^{39} + 56 q^{40} - 32 q^{41} - 24 q^{44} + 32 q^{46} - 16 q^{49}+ \cdots - 160 q^{96}+O(q^{100}) \) 416 * q - 16 * q^6 - 16 * q^9 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 16 * q^16 - 20 * q^20 + 24 * q^26 - 16 * q^31 - 40 * q^34 - 8 * q^36 + 32 * q^39 + 56 * q^40 - 32 * q^41 - 24 * q^44 + 32 * q^46 - 16 * q^49 - 48 * q^50 - 64 * q^54 - 8 * q^56 - 40 * q^60 + 72 * q^65 - 112 * q^66 - 24 * q^70 + 48 * q^71 - 8 * q^74 - 40 * q^76 - 16 * q^79 - 56 * q^80 - 32 * q^84 + 96 * q^86 - 148 * q^90 + 40 * q^94 - 8 * q^95 - 160 * q^96

Introduction

L-functions

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