LMFDB - Embedded newform 680.2.br.a.349.89

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			349.89
Character	$\chi$	$=$	680.349
Dual form			680.2.br.a.189.89

$q$-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} +(1.01668 - 1.99157i) 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} +(-0.0146169 - 3.16224i) q^{10} +(1.31559 + 3.17611i) q^{11} +(3.42213 - 2.14815i) q^{12} +2.51816i q^{13} +(-0.730936 + 0.865212i) q^{14} +(3.43730 - 2.93118i) 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} +(-2.07009 - 3.96418i) q^{20} -1.61800 q^{21} +(3.71389 + 3.13751i) q^{22} +(-1.90342 - 4.59527i) q^{23} +(2.90647 - 4.91970i) q^{24} +(-2.93273 - 4.04958i) 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} +(2.41749 - 5.91350i) 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} +(-5.17331 - 3.63825i) 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} +(2.30025 - 0.745450i) q^{45} +(-5.37333 - 4.53942i) q^{46} +10.2098 q^{47} +(0.460265 - 8.06785i) q^{48} +(-4.49619 + 4.49619i) q^{49} +(-6.31270 - 3.18588i) 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} +(-0.798987 - 8.99939i) 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} +(5.01510 + 2.56016i) q^{65} +(4.50617 + 8.72729i) q^{66} +5.11009 q^{67} +(5.52232 + 6.12405i) q^{68} -10.0484i q^{69} +(0.980007 + 2.33535i) 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} +(-2.34303 - 9.82571i) 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} +(-8.86133 - 1.21527i) q^{80} -11.0748i q^{81} +(13.4628 + 11.3734i) q^{82} +(-4.85020 + 4.85020i) q^{83} +(-1.87375 + 2.63832i) q^{84} +(7.10183 + 5.87911i) q^{85} +(-5.01938 - 1.60105i) q^{86} +(-14.0840 - 14.0840i) q^{87} +(9.41698 - 2.42245i) q^{88} +1.79163i q^{89} +(2.40682 - 2.42918i) 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} +(1.98183 - 0.642257i) 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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

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

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	$-0.176803\pi$
$3$	1.86646	+	0.773113i	1.07760	+	0.446357i	0.227934	+	0.973677i	$0.426803\pi$
$4$	1.15807	−	1.63061i	0.579033	−	0.815304i
$5$	1.01668	−	1.99157i	0.454673	−	0.890659i
$5$	1.01668	−	1.99157i	0.454673	−	0.890659i
$6$	2.84700	−	0.239505i	1.16228	−	0.0977775i
$7$	−0.739929	+	0.306488i	−0.279667	+	0.115842i	−0.518108	−	0.855315i	$-0.673364\pi$
$7$	−0.739929	+	0.306488i	−0.279667	+	0.115842i	0.238441	+	0.971157i	$0.423364\pi$
$8$	0.397251	−	2.80039i	0.140450	−	0.990088i
$9$	0.764647	+	0.764647i	0.254882	+	0.254882i
$10$	−0.0146169	−	3.16224i	−0.00462226	−	0.999989i
$11$	1.31559	+	3.17611i	0.396665	+	0.957634i	0.988451	+	0.151539i	$0.0484230\pi$
$11$	1.31559	+	3.17611i	0.396665	+	0.957634i	−0.591786	+	0.806095i	$0.701577\pi$
$12$	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
$15$	3.43730	−	2.93118i	0.887507	−	0.756828i
$16$	−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	0.778626	−	0.627488i	$-0.215917\pi$
$19$	0.658797	+	0.658797i	0.151138	+	0.151138i	−0.627488	+	0.778626i	$0.715917\pi$
$20$	−2.07009	−	3.96418i	−0.462887	−	0.886417i
$21$	−1.61800			−0.353076
$22$	3.71389	+	3.13751i	0.791804	+	0.668919i
$23$	−1.90342	−	4.59527i	−0.396891	−	0.958179i	−0.988399	−	0.151880i	$-0.951467\pi$
$23$	−1.90342	−	4.59527i	−0.396891	−	0.958179i	0.591508	−	0.806299i	$-0.298533\pi$
$24$	2.90647	−	4.91970i	0.593281	−	1.00423i
$25$	−2.93273	−	4.04958i	−0.586545	−	0.809916i
$26$	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	−0.691659	−	0.722224i	$-0.743120\pi$
$29$	−9.10861	−	3.77291i	−1.69143	−	0.700611i	−0.999766	+	0.0216126i	$0.993120\pi$
$30$	2.41749	−	5.91350i	0.441371	−	1.07965i
$31$	3.43384	+	1.42234i	0.616736	+	0.255460i	0.669106	−	0.743167i	$-0.266677\pi$
$31$	3.43384	+	1.42234i	0.616736	+	0.255460i	−0.0523696	+	0.998628i	$0.516677\pi$
$32$	−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	$-0.343297\pi$
$37$	1.11757	+	0.462911i	0.183727	+	0.0761022i	−0.288924	+	0.957352i	$0.593297\pi$
$38$	1.25528	+	0.400401i	0.203634	+	0.0649536i
$39$	−1.94682	+	4.70005i	−0.311741	+	0.752610i
$40$	−5.17331	−	3.63825i	−0.817972	−	0.575258i
$41$	4.76899	+	11.5134i	0.744791	+	1.79808i	0.585179	+	0.810904i	$0.301024\pi$
$41$	4.76899	+	11.5134i	0.744791	+	1.79808i	0.159612	+	0.987180i	$0.448976\pi$
$42$	−2.03317	+	1.04979i	−0.313725	+	0.161986i
$43$	−2.63427	−	2.63427i	−0.401722	−	0.401722i	0.477117	−	0.878840i	$-0.341682\pi$
$43$	−2.63427	−	2.63427i	−0.401722	−	0.401722i	−0.878840	+	0.477117i	$0.841682\pi$
$44$	6.70253	+	1.53294i	1.01045	+	0.231099i
$45$	2.30025	−	0.745450i	0.342901	−	0.111125i
$46$	−5.37333	−	4.53942i	−0.792254	−	0.669300i
$47$	10.2098			1.48925			0.744625	−	0.667483i	$-0.232628\pi$
$47$	10.2098			1.48925			0.744625	+	0.667483i	$0.232628\pi$
$48$	0.460265	−	8.06785i	0.0664335	−	1.16449i
$49$	−4.49619	+	4.49619i	−0.642313	+	0.642313i
$50$	−6.31270	−	3.18588i	−0.892751	−	0.450551i
$51$	−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	$-0.634478\pi$
$53$	3.65503	−	3.65503i	0.502057	−	0.502057i	0.912077	+	0.410020i	$0.134478\pi$
$54$	−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	−0.960617	−	0.277876i	$-0.910369\pi$
$59$	−5.24423	+	5.24423i	−0.682741	+	0.682741i	0.277876	+	0.960617i	$0.410369\pi$
$60$	−0.798987	−	8.99939i	−0.103149	−	1.16182i
$61$	−8.77111	+	3.63311i	−1.12303	+	0.465173i	−0.865405	−	0.501074i	$-0.832939\pi$
$61$	−8.77111	+	3.63311i	−1.12303	+	0.465173i	−0.257621	+	0.966246i	$0.582939\pi$
$62$	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
$65$	5.01510	+	2.56016i	0.622047	+	0.317549i
$66$	4.50617	+	8.72729i	0.554671	+	1.07426i
$67$	5.11009			0.624297			0.312149	−	0.950033i	$-0.398951\pi$
$67$	5.11009			0.624297			0.312149	+	0.950033i	$0.398951\pi$
$68$	5.52232	+	6.12405i	0.669679	+	0.742650i
$69$		−	10.0484i		−	1.20969i
$70$	0.980007	+	2.33535i	0.117133	+	0.279128i
$71$	7.58430	+	3.14152i	0.900091	+	0.372830i	0.784255	−	0.620439i	$-0.213045\pi$
$71$	7.58430	+	3.14152i	0.900091	+	0.372830i	0.115836	+	0.993268i	$0.463045\pi$
$72$	2.44507	−	1.83755i	0.288154	−	0.216558i
$73$	5.76929	+	2.38972i	0.675245	+	0.279696i	0.693837	−	0.720132i	$-0.255919\pi$
$73$	5.76929	+	2.38972i	0.675245	+	0.279696i	−0.0185928	+	0.999827i	$0.505919\pi$
$74$	1.70468	−	0.143407i	0.198165	−	0.0166707i
$75$	−2.34303	−	9.82571i	−0.270550	−	1.13458i
$76$	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	−0.925841	−	0.377914i	$-0.876642\pi$
$79$	−11.6727	+	4.83500i	−1.31328	+	0.543980i	−0.387443	+	0.921894i	$0.626642\pi$
$80$	−8.86133	−	1.21527i	−0.990726	−	0.135872i
$81$		−	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	$-0.872855\pi$
$83$	−4.85020	+	4.85020i	−0.532378	+	0.532378i	0.388901	+	0.921279i	$0.372855\pi$
$84$	−1.87375	+	2.63832i	−0.204443	+	0.287864i
$85$	7.10183	+	5.87911i	0.770302	+	0.637679i
$86$	−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	$0.0302712\pi$
$89$			1.79163i			0.189913i	−0.995481	+	0.0949564i	$0.969729\pi$
$90$	2.40682	−	2.42918i	0.253701	−	0.256058i
$91$	−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
$95$	1.98183	−	0.642257i	0.203331	−	0.0658942i
$96$	−4.65621	−	10.4367i	−0.475222	−	1.06519i
$97$	−5.86683	−	2.43012i	−0.595686	−	0.246741i	0.0644085	−	0.997924i	$-0.479484\pi$
$97$	−5.86683	−	2.43012i	−0.595686	−	0.246741i	−0.660095	+	0.751182i	$0.729484\pi$
$98$	−2.73268	+	8.56711i	−0.276042	+	0.865408i
$99$	−1.42264	+	3.43457i	−0.142981	+	0.345187i
$100$	−9.99957	+	0.0924442i	−0.999957	+	0.00924442i
$101$			5.75052i			0.572198i	0.958200	+	0.286099i	$0.0923586\pi$
$101$			5.75052i			0.572198i	−0.958200	+	0.286099i	$0.907641\pi$
$102$	−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
$105$	−1.64498	+	3.22236i	−0.160534	+	0.314470i
$106$	2.22144	−	6.96435i	0.215765	−	0.676438i
$107$	−0.898334	+	2.16877i	−0.0868452	+	0.209663i	−0.961335	−	0.275380i	$-0.911196\pi$
$107$	−0.898334	+	2.16877i	−0.0868452	+	0.209663i	0.874490	+	0.485043i	$0.161196\pi$
$108$	−7.55705	−	1.72838i	−0.727177	−	0.166313i
$109$	7.28774	−	3.01868i	0.698039	−	0.289137i	−0.00530589	−	0.999986i	$-0.501689\pi$
$109$	7.28774	−	3.01868i	0.698039	−	0.289137i	0.703345	+	0.710849i	$0.251689\pi$
$110$	10.0244	−	4.20664i	0.955790	−	0.401087i
$111$	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	$-0.0253035\pi$
$113$	2.50677	+	6.05188i	0.235817	+	0.569313i	−0.761025	+	0.648723i	$0.775303\pi$
$114$	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
$120$	−6.84299	−	10.7902i	−0.624676	−	0.985006i
$121$	−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
$125$	−11.0467	+	1.72362i	−0.988045	+	0.154165i
$126$	−1.22049	+	0.102674i	−0.108730	+	0.00914695i
$127$	11.6008	−	11.6008i	1.02940	−	1.02940i	0.0298492	−	0.999554i	$-0.490497\pi$
$127$	11.6008	−	11.6008i	1.02940	−	1.02940i	0.999554	−	0.0298492i	$-0.00950269\pi$
$128$	−11.0997	+	2.18996i	−0.981087	+	0.193567i
$129$	−2.88017	−	6.95334i	−0.253585	−	0.612208i
$130$	7.96304	−	0.0368077i	0.698405	−	0.00322825i
$131$	−7.95995	−	3.29712i	−0.695464	−	0.288071i	0.00681066	−	0.999977i	$-0.497832\pi$
$131$	−7.95995	−	3.29712i	−0.695464	−	0.288071i	−0.702275	+	0.711906i	$0.747832\pi$
$132$	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	−0.509192	−	0.860653i	$-0.670056\pi$
$139$	5.41665	−	13.0770i	0.459435	−	1.10917i	0.968627	−	0.248520i	$-0.0799443\pi$
$140$	2.74670	+	2.29875i	0.232138	+	0.194280i
$141$	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
$145$	−16.7746	+	14.3046i	−1.39305	+	1.18793i
$146$	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	$0.820977\pi$
$150$	−9.31936	−	10.8267i	−0.760922	−	0.884000i
$151$	0.775751	−	0.775751i	0.0631297	−	0.0631297i	−0.674837	−	0.737967i	$-0.735786\pi$
$151$	0.775751	−	0.775751i	0.0631297	−	0.0631297i	0.737967	+	0.674837i	$0.235786\pi$
$152$	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
$155$	6.32381	−	5.39268i	0.507941	−	0.433150i
$156$	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
$160$	−11.9236	+	4.22230i	−0.942643	+	0.333802i
$161$	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	−0.942489	−	0.334236i	$-0.891522\pi$
$163$	−6.54175	−	15.7932i	−0.512389	−	1.23702i	0.430100	−	0.902781i	$-0.358478\pi$
$164$	24.2966	+	5.55688i	1.89724	+	0.433920i
$165$	13.8318	+	7.06102i	1.07681	+	0.549700i
$166$	−2.94783	+	9.24164i	−0.228796	+	0.717290i
$167$	4.29888	−	10.3784i	0.332657	−	0.803105i	−0.665722	−	0.746199i	$-0.731877\pi$
$167$	4.29888	−	10.3784i	0.332657	−	0.803105i	0.998380	−	0.0569058i	$-0.0181235\pi$
$168$	−0.642751	+	4.53102i	−0.0495893	+	0.349576i
$169$	6.65886			0.512220
$170$	12.7386	+	2.77986i	0.977007	+	0.213206i
$171$			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	$-0.443402\pi$
$173$	−5.18252	−	2.14667i	−0.394020	−	0.163208i	−0.570891	+	0.821026i	$0.693402\pi$
$174$	−26.8358	−	8.55990i	−2.03442	−	0.648924i
$175$	3.41116	+	2.09755i	0.257859	+	0.158560i
$176$	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	−0.0828317	−	0.996564i	$-0.526396\pi$
$179$	12.2249	−	12.2249i	0.913732	−	0.913732i	0.996564	+	0.0828317i	$0.0263964\pi$
$180$	1.44831	−	4.61409i	0.107950	−	0.343914i
$181$	4.22381	+	10.1972i	0.313953	+	0.757950i	0.999551	+	0.0299693i	$0.00954096\pi$
$181$	4.22381	+	10.1972i	0.313953	+	0.757950i	−0.685598	+	0.727981i	$0.740459\pi$
$182$	−2.17875	−	1.84061i	−0.161499	−	0.136435i
$183$	−19.1797			−1.41781
$184$	−13.6247	+	3.50485i	−1.00442	+	0.258381i
$185$	2.05813	−	1.75508i	0.151317	−	0.129036i
$186$	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
$190$	2.07365	−	2.09291i	0.150438	−	0.151835i
$191$			5.37161i			0.388676i	0.980935	+	0.194338i	$0.0622558\pi$
$191$			5.37161i			0.388676i	−0.980935	+	0.194338i	$0.937744\pi$
$192$	−12.6225	−	10.0936i	−0.910949	−	0.728444i
$193$	7.18708	+	17.3511i	0.517337	+	1.24896i	0.939533	+	0.342458i	$0.111259\pi$
$193$	7.18708	+	17.3511i	0.517337	+	1.24896i	−0.422196	+	0.906505i	$0.638741\pi$
$194$	−8.94895	+	0.752835i	−0.642497	+	0.0540504i
$195$	7.38119	+	8.65568i	0.528578	+	0.619846i
$196$	2.12464	+	12.5384i	0.151760	+	0.895600i
$197$	4.77474	+	11.5272i	0.340186	+	0.821282i	0.997696	+	0.0678366i	$0.0216097\pi$
$197$	4.77474	+	11.5272i	0.340186	+	0.821282i	−0.657510	+	0.753446i	$0.728390\pi$
$198$	0.440725	+	5.23890i	0.0313210	+	0.372312i
$199$	6.72373	−	16.2325i	0.476632	−	1.15069i	−0.484546	−	0.874766i	$-0.661015\pi$
$199$	6.72373	−	16.2325i	0.476632	−	1.15069i	0.961179	−	0.275927i	$-0.0889848\pi$
$200$	−12.5054	+	6.60408i	−0.884268	+	0.466979i
$201$	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
$210$	0.0236501	+	5.11650i	0.00163201	+	0.353072i
$211$	−1.37308	+	0.568750i	−0.0945269	+	0.0391543i	−0.429446	−	0.903093i	$-0.641291\pi$
$211$	−1.37308	+	0.568750i	−0.0945269	+	0.0391543i	0.334919	+	0.942247i	$0.391291\pi$
$212$	−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
$215$	−7.92455	+	2.56813i	−0.540450	+	0.175145i
$216$	−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
$220$	9.86729	−	11.7901i	0.665252	−	0.794887i
$221$	−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	$-0.194278\pi$
$223$	3.67807	+	3.67807i	0.246302	+	0.246302i	−0.573149	+	0.819451i	$0.694278\pi$
$224$	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	$-0.717580\pi$
$227$	−7.98332	+	3.30680i	−0.529872	+	0.219480i	0.101675	+	0.994818i	$0.467580\pi$
$228$	3.66968	+	0.839294i	0.243030	+	0.0555836i
$229$	−0.402482	+	0.402482i	−0.0265968	+	0.0265968i	−0.720280	−	0.693683i	$-0.755987\pi$
$229$	−0.402482	+	0.402482i	−0.0265968	+	0.0265968i	0.693683	+	0.720280i	$0.255987\pi$
$230$	−14.5035	+	6.08625i	−0.956335	+	0.401316i
$231$	−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	$-0.165312\pi$
$233$	17.2651	+	7.15144i	1.13107	+	0.468506i	0.262928	+	0.964815i	$0.415312\pi$
$234$	−1.17028	+	3.66889i	−0.0765034	+	0.239843i
$235$	10.3801	−	20.3335i	0.677121	−	1.32641i
$236$	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	$0.518907\pi$
$240$	−15.5998	−	9.11906i	−1.00696	−	0.588633i
$241$	23.2271	+	9.62098i	1.49619	+	0.619742i	0.972653	−	0.232262i	$-0.0746126\pi$
$241$	23.2271	+	9.62098i	1.49619	+	0.619742i	0.523536	+	0.852004i	$0.324613\pi$
$242$	−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
$245$	4.38331	+	13.5257i	0.280039	+	0.864123i
$246$	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
$250$	−12.7629	+	9.33319i	−0.807196	+	0.590283i
$251$	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
$255$	8.71007	+	16.4636i	0.545445	+	1.03099i
$256$	−12.5270	+	9.95361i	−0.782937	+	0.622101i
$257$	−11.2755	−	11.2755i	−0.703349	−	0.703349i	0.261779	−	0.965128i	$-0.415691\pi$
$257$	−11.2755	−	11.2755i	−0.703349	−	0.703349i	−0.965128	+	0.261779i	$0.915691\pi$
$258$	−8.13067	−	6.86883i	−0.506194	−	0.427635i
$259$	−0.968797			−0.0601981
$260$	9.98245	−	5.21283i	0.619085	−	0.323286i
$261$	−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	$-0.886979\pi$
$263$	−9.56770	+	9.56770i	−0.589969	+	0.589969i	0.347654	+	0.937623i	$0.386979\pi$
$264$	19.4492	+	2.75898i	1.19702	+	0.169804i
$265$	−3.56327	−	10.9953i	−0.218890	−	0.675433i
$266$	−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	−0.988179	−	0.153303i	$-0.951009\pi$
$269$	−2.96911	+	7.16806i	−0.181030	+	0.437044i	0.807150	+	0.590347i	$0.201009\pi$
$270$	−11.3024	+	4.74295i	−0.687844	+	0.288646i
$271$	−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
$275$	9.00366	−	14.6423i	0.542941	−	0.882961i
$276$	−16.3851	−	11.6368i	−0.986265	−	0.700451i
$277$	1.31819	−	3.18240i	0.0792025	−	0.191212i	−0.879318	−	0.476235i	$-0.842001\pi$
$277$	1.31819	−	3.18240i	0.0792025	−	0.191212i	0.958521	+	0.285023i	$0.0920012\pi$
$278$	−1.67804	−	19.9469i	−0.100642	−	1.19633i
$279$	1.53808	+	3.71326i	0.0920827	+	0.222307i
$280$	4.94296	+	1.10649i	0.295398	+	0.0661254i
$281$	−15.8250	−	15.8250i	−0.944041	−	0.944041i	0.0544739	−	0.998515i	$-0.482652\pi$
$281$	−15.8250	−	15.8250i	−0.944041	−	0.944041i	−0.998515	+	0.0544739i	$0.982652\pi$
$282$	29.0672	−	2.44529i	1.73093	−	0.145615i
$283$	24.8341	−	10.2866i	1.47624	−	0.611477i	0.507964	−	0.861378i	$-0.330398\pi$
$283$	24.8341	−	10.2866i	1.47624	−	0.611477i	0.968271	+	0.249901i	$0.0803982\pi$
$284$	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
$290$	−11.7977	+	28.8588i	−0.692786	+	1.69465i
$291$	−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
$295$	5.11257	+	15.7760i	0.297665	+	0.918512i
$296$	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
$300$	−18.7353	−	7.55825i	−1.08168	−	0.436376i
$301$	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	$-0.531413\pi$
$307$	−3.45261			−0.197051			−0.0985255	+	0.995135i	$0.531413\pi$
$308$	−5.42923	+	0.919984i	−0.309359	+	0.0524209i
$309$	10.0109	−	24.1685i	0.569502	−	1.37490i
$310$	4.44760	−	10.8794i	0.252607	−	0.617910i
$311$	−5.20738	+	12.5717i	−0.295283	+	0.712877i	0.704711	+	0.709495i	$0.251077\pi$
$311$	−5.20738	+	12.5717i	−0.295283	+	0.712877i	−0.999994	+	0.00338247i	$0.998923\pi$
$312$	12.3886	+	7.31897i	0.701366	+	0.414355i
$313$	21.7726	−	9.01851i	1.23066	−	0.509756i	0.329877	−	0.944024i	$-0.392993\pi$
$313$	21.7726	−	9.01851i	1.23066	−	0.509756i	0.900784	+	0.434267i	$0.142993\pi$
$314$	−2.60228	−	5.03994i	−0.146855	−	0.284420i
$315$	−1.47355	+	1.25658i	−0.0830251	+	0.0708002i
$316$	−5.63380	+	24.6329i	−0.316926	+	1.38571i
$317$	−4.81232	+	1.99333i	−0.270287	+	0.111956i	−0.513710	−	0.857964i	$-0.671729\pi$
$317$	−4.81232	+	1.99333i	−0.270287	+	0.111956i	0.243424	+	0.969920i	$0.421729\pi$
$318$	9.53046	−	11.2813i	0.534441	−	0.632621i
$319$		−	33.8936i		−	1.89767i
$320$	−12.2436	+	13.0420i	−0.684440	+	0.729069i
$321$	−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
$325$	10.1975	−	7.38508i	0.565656	−	0.409651i
$326$	−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
$330$	21.9624	−	0.101517i	1.20899	−	0.00558832i
$331$	12.5846	−	12.5846i	0.691713	−	0.691713i	−0.270895	−	0.962609i	$-0.587320\pi$
$331$	12.5846	−	12.5846i	0.691713	−	0.691713i	0.962609	+	0.270895i	$0.0873197\pi$
$332$	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
$335$	5.19532	−	10.1771i	0.283851	−	0.556036i
$336$	2.13214	+	6.11070i	0.116318	+	0.333366i
$337$	−6.40806	+	15.4704i	−0.349069	+	0.842727i	0.647661	+	0.761928i	$0.275747\pi$
$337$	−6.40806	+	15.4704i	−0.349069	+	0.842727i	−0.996730	+	0.0807991i	$0.974253\pi$
$338$	8.36749	−	4.32040i	0.455132	−	0.234999i
$339$			13.2336i			0.718751i
$340$	17.8109	−	4.77190i	0.965933	−	0.258793i
$341$			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
$345$	−20.0122	−	10.2160i	−1.07742	−	0.550013i
$346$	−7.90514	+	0.665024i	−0.424983	+	0.0357519i
$347$	−13.5431	−	32.6959i	−0.727030	−	1.75521i	−0.652248	−	0.758005i	$-0.726174\pi$
$347$	−13.5431	−	32.6959i	−0.727030	−	1.75521i	−0.0747814	−	0.997200i	$-0.523826\pi$
$348$	−39.2756	+	6.65526i	−2.10539	+	0.356759i
$349$	0.124066	−	0.124066i	0.00664112	−	0.00664112i	−0.703778	−	0.710420i	$-0.748505\pi$
$349$	0.124066	−	0.124066i	0.00664112	−	0.00664112i	0.710420	+	0.703778i	$0.248505\pi$
$350$	5.64738	+	0.422551i	0.301865	+	0.0225863i
$351$	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	$-0.418702\pi$
$353$	9.49323			0.505274			0.252637	+	0.967561i	$0.418702\pi$
$354$	−13.6743	+	16.1863i	−0.726780	+	0.860293i
$355$	13.9674	−	11.9108i	0.741311	−	0.632158i
$356$	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	−0.907260	−	0.420570i	$-0.861830\pi$
$359$	−9.22146	+	9.22146i	−0.486690	+	0.486690i	0.420570	+	0.907260i	$0.361830\pi$
$360$	−1.17377	−	6.73773i	−0.0618633	−	0.355110i
$361$		−	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
$365$	10.6248	−	9.06039i	0.556129	−	0.474243i
$366$	−24.1012	+	12.4442i	−1.25979	+	0.650468i
$367$	4.74433	−	1.96516i	0.247652	−	0.102581i	−0.255405	−	0.966834i	$-0.582209\pi$
$367$	4.74433	−	1.96516i	0.247652	−	0.102581i	0.503057	+	0.864253i	$0.332209\pi$
$368$	−14.8467	+	13.2441i	−0.773938	+	0.690399i
$369$	−5.15706	+	12.4502i	−0.268466	+	0.648134i
$370$	1.44750	−	3.54079i	0.0752521	−	0.184077i
$371$	−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	$-0.778705\pi$
$373$	−29.6618			−1.53583			−0.767914	+	0.640553i	$0.778705\pi$
$374$	−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	0.999182	+	0.0404378i	$0.0128753\pi$
$379$	33.7633	+	13.9852i	1.73430	+	0.718372i	0.735122	+	0.677935i	$0.237125\pi$
$380$	1.24782	−	3.97536i	0.0640117	−	0.203932i
$381$	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	$-0.651831\pi$
$383$	8.40105	−	8.40105i	0.429274	−	0.429274i	0.888381	+	0.459107i	$0.151831\pi$
$384$	−22.4103	−	4.49388i	−1.14362	−	0.229328i
$385$	−5.85672	+	1.89801i	−0.298486	+	0.0967313i
$386$	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	−0.999925	−	0.0122458i	$-0.996102\pi$
$389$	−19.9631	−	19.9631i	−1.01217	−	1.01217i	−0.0122458	−	0.999925i	$-0.503898\pi$
$390$	14.8912	+	6.08763i	0.754043	+	0.308259i
$391$	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	$-0.858985\pi$
$397$	−24.6909	+	10.2273i	−1.23920	+	0.513293i	−0.335735	+	0.941956i	$0.608985\pi$
$398$	−2.08296	−	24.7602i	−0.104410	−	1.24112i
$399$	−1.06593	−	1.06593i	−0.0533633	−	0.0533633i
$400$	−11.4294	+	16.4124i	−0.571471	+	0.820622i
$401$	−1.51850	−	3.66598i	−0.0758303	−	0.183070i	0.881419	−	0.472336i	$-0.156589\pi$
$401$	−1.51850	−	3.66598i	−0.0758303	−	0.183070i	−0.957249	+	0.289265i	$0.906589\pi$
$402$	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
$405$	−22.0562	−	11.2595i	−1.09598	−	0.559487i
$406$	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	$0.359838\pi$
$410$	36.3383	−	15.2490i	1.79462	−	0.753094i
$411$	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
$415$	4.72843	+	14.5906i	0.232109	+	0.716225i
$416$	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	0.832986	+	0.553294i	$0.186629\pi$
$419$	13.0025	+	31.3908i	0.635214	+	1.53354i	−0.197772	+	0.980248i	$0.563371\pi$
$420$	3.34940	+	6.41403i	0.163434	+	0.312973i
$421$	−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
$425$	18.9290	−	8.16665i	0.918190	−	0.396141i
$426$	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
$430$	−8.29170	+	8.36871i	−0.399861	+	0.403575i
$431$	−4.69595	+	1.94513i	−0.226196	+	0.0936935i	−0.492903	−	0.870084i	$-0.664064\pi$
$431$	−4.69595	+	1.94513i	−0.226196	+	0.0936935i	0.266707	+	0.963778i	$0.414064\pi$
$432$	−11.5699	+	10.3210i	−0.556655	+	0.496570i
$433$	−13.2027	+	13.2027i	−0.634479	+	0.634479i	−0.949188	−	0.314709i	$-0.898093\pi$
$433$	−13.2027	+	13.2027i	−0.634479	+	0.634479i	0.314709	+	0.949188i	$0.398093\pi$
$434$	−3.74054	+	1.93136i	−0.179552	+	0.0927082i
$435$	−42.3681	+	13.7304i	−2.03139	+	0.658321i
$436$	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	0.641038	−	0.767509i	$-0.278504\pi$
$439$	11.5575	+	4.78728i	0.551610	+	0.228484i	−0.0894281	+	0.995993i	$0.528504\pi$
$440$	4.74956	−	21.2175i	0.226426	−	1.01150i
$441$	−6.87599			−0.327428
$442$	−14.2005	+	3.73433i	−0.675448	+	0.177624i
$443$	−25.9778			−1.23424			−0.617122	−	0.786867i	$-0.711702\pi$
$443$	−25.9778			−1.23424			−0.617122	+	0.786867i	$0.711702\pi$
$444$	4.81886	−	0.816557i	0.228693	−	0.0387521i
$445$	3.56817	+	1.82152i	0.169148	+	0.0863482i
$446$	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	1.00000		0.000653907i	$0.000208145\pi$
$449$	6.21609	+	15.0070i	0.293356	+	0.708223i	−0.706644	+	0.707569i	$0.749792\pi$
$450$	−2.39092	−	7.26306i	−0.112709	−	0.342384i
$451$	−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	$-0.407741\pi$
$457$	−14.3762	−	14.3762i	−0.672489	−	0.672489i	−0.958289	+	0.285800i	$0.907741\pi$
$458$	−0.244619	+	0.766896i	−0.0114303	+	0.0358347i
$459$	15.7423	−	2.75453i	0.734790	−	0.128570i
$460$	−14.2762	+	17.0581i	−0.665631	+	0.795340i
$461$	−7.47698	−	7.47698i	−0.348238	−	0.348238i	0.511215	−	0.859453i	$-0.329196\pi$
$461$	−7.47698	−	7.47698i	−0.348238	−	0.348238i	−0.859453	+	0.511215i	$0.829196\pi$
$462$	−6.00906	−	5.07648i	−0.279567	−	0.236179i
$463$	25.7018			1.19446			0.597232	−	0.802068i	$-0.296267\pi$
$463$	25.7018			1.19446			0.597232	+	0.802068i	$0.296267\pi$
$464$	−2.24616	+	39.3723i	−0.104275	+	1.82781i
$465$	15.9723	−	5.17619i	0.740697	−	0.240040i
$466$	26.3352	−	2.21547i	1.21996	−	0.102629i
$467$	15.1664	+	15.1664i	0.701818	+	0.701818i	0.964801	−	0.262982i	$-0.0847061\pi$
$467$	15.1664	+	15.1664i	0.701818	+	0.701818i	−0.262982	+	0.964801i	$0.584706\pi$
$468$	0.909881	+	5.36961i	0.0420593	+	0.248210i
$469$	−3.78110	+	1.56618i	−0.174595	+	0.0723197i
$470$	−0.149235	−	32.2858i	−0.00688370	−	1.48923i
$471$	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	0.985482	−	0.169780i	$-0.0543058\pi$
$479$	34.1920	+	14.1628i	1.56227	+	0.647114i	0.576788	+	0.816894i	$0.304306\pi$
$480$	−25.5192	−	1.33754i	−1.16479	−	0.0610502i
$481$	−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
$485$	−10.8044	+	9.21357i	−0.490605	+	0.418367i
$486$	−1.27390	−	15.1428i	−0.0577851	−	0.686892i
$487$	8.38068	+	20.2327i	0.379765	+	0.916833i	0.992009	+	0.126165i	$0.0402668\pi$
$487$	8.38068	+	20.2327i	0.379765	+	0.916833i	−0.612245	+	0.790668i	$0.709733\pi$
$488$	6.68980	+	26.0058i	0.302833	+	1.17723i
$489$		−	34.5348i		−	1.56172i
$490$	14.2838	+	14.1523i	0.645275	+	0.639337i
$491$	−10.3358	−	10.3358i	−0.466448	−	0.466448i	0.434314	−	0.900762i	$-0.356991\pi$
$491$	−10.3358	−	10.3358i	−0.466448	−	0.466448i	−0.900762	+	0.434314i	$0.856991\pi$
$492$	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
$495$	5.39382	+	6.32515i	0.242434	+	0.284294i
$496$	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	0.874967	+	0.484182i	$0.160883\pi$
$499$	13.3726	+	32.2843i	0.598640	+	1.44525i	−0.276327	+	0.961064i	$0.589117\pi$
$500$	−9.98225	+	20.0089i	−0.446420	+	0.894824i
$501$	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	$-0.909898\pi$
$503$	−32.3335	+	13.3930i	−1.44168	+	0.597163i	−0.481474	+	0.876460i	$0.659898\pi$
$504$	−1.24599	+	2.10904i	−0.0555006	+	0.0939442i
$505$	11.4526	+	5.84643i	0.509633	+	0.260163i
$506$	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	$0.0331331\pi$
$509$			4.68831i			0.207806i	−0.994587	+	0.103903i	$0.966867\pi$
$510$	21.6270	+	15.0369i	0.957658	+	0.665844i
$511$	−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
$515$	−25.7886	−	13.1648i	−1.13638	−	0.580112i
$516$	−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
$520$	9.16171	−	13.0272i	0.401768	−	0.571282i
$521$	−31.4790	+	13.0390i	−1.37912	+	0.571250i	−0.944246	−	0.329241i	$-0.893207\pi$
$521$	−31.4790	+	13.0390i	−1.37912	+	0.571250i	−0.434874	+	0.900491i	$0.643207\pi$
$522$	−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
$525$	4.74514	+	6.55221i	0.207095	+	0.285962i
$526$	−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
$530$	−11.6115	−	11.5047i	−0.504372	−	0.499731i
$531$	−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
$535$	3.40595	+	3.99404i	0.147252	+	0.172677i
$536$	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
$540$	−11.1253	+	13.2932i	−0.478756	+	0.572048i
$541$	8.31450	−	20.0730i	0.357468	−	0.863005i	−0.638186	−	0.769882i	$-0.720315\pi$
$541$	8.31450	−	20.0730i	0.357468	−	0.863005i	0.995655	−	0.0931229i	$-0.0296850\pi$
$542$	−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	$-0.321942\pi$
$547$	7.17008	+	2.96995i	0.306571	+	0.126986i	−0.224094	+	0.974567i	$0.571942\pi$
$548$	−18.1411	−	12.8839i	−0.774949	−	0.550373i
$549$	−9.48485	−	3.92875i	−0.404804	−	0.167675i
$550$	1.81378	−	24.2412i	0.0773400	−	1.03365i
$551$	−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
$555$	5.19829	−	1.68463i	0.220655	−	0.0715085i
$556$	−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
$560$	6.92922	−	1.81668i	0.292813	−	0.0767687i
$561$	−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	$-0.654196\pi$
$563$	9.94781	−	9.94781i	0.419250	−	0.419250i	0.884945	+	0.465695i	$0.154196\pi$
$564$	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	0.996678	+	0.0814486i	$0.0259547\pi$
$569$	25.7173	+	25.7173i	1.07813	+	1.07813i	0.0814486	+	0.996678i	$0.474045\pi$
$570$	5.48843	−	2.30316i	0.229885	−	0.0964688i
$571$	16.0004	−	6.62758i	0.669596	−	0.277356i	−0.0218742	−	0.999761i	$-0.506963\pi$
$571$	16.0004	−	6.62758i	0.669596	−	0.277356i	0.691470	+	0.722405i	$0.256963\pi$
$572$	−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
$575$	−13.0267	+	21.1847i	−0.543250	+	0.883464i
$576$	−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
$580$	3.89918	+	43.9184i	0.161905	+	1.82361i
$581$	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
$585$	1.87716	+	5.79240i	0.0776111	+	0.239486i
$586$	−17.6326	−	34.1497i	−0.728394	−	1.41071i
$587$	6.62698	+	6.62698i	0.273525	+	0.273525i	0.830517	−	0.556993i	$-0.188045\pi$
$587$	6.62698	+	6.62698i	0.273525	+	0.273525i	−0.556993	+	0.830517i	$0.688045\pi$
$588$	−5.72805	+	25.0450i	−0.236221	+	1.03284i
$589$	1.32517	+	3.19924i	0.0546026	+	0.131822i
$590$	16.6602	+	16.5069i	0.685889	+	0.679577i
$591$			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	$-0.373352\pi$
$593$	−13.0141	−	13.0141i	−0.534426	−	0.534426i	−0.921886	+	0.387460i	$0.873352\pi$
$594$	5.72668	−	17.9535i	0.234969	−	0.736641i
$595$	−7.05673	−	2.17349i	−0.289298	−	0.0891046i
$596$	−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	$-0.961658\pi$
$599$		−	5.88190i		−	0.240328i	0.992754	−	0.120164i	$-0.0383420\pi$
$600$	−28.4466	+	2.65814i	−1.16133	+	0.108518i
$601$	32.1759	−	13.3277i	1.31248	−	0.543648i	0.386874	−	0.922132i	$-0.373555\pi$
$601$	32.1759	−	13.3277i	1.31248	−	0.543648i	0.925608	+	0.378485i	$0.123555\pi$
$602$	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
$605$	0.564214	+	1.74101i	0.0229386	+	0.0707820i
$606$	1.37728	+	16.3717i	0.0559481	+	0.665055i
$607$	−12.7745	−	5.29138i	−0.518502	−	0.214771i	0.108057	−	0.994145i	$-0.465537\pi$
$607$	−12.7745	−	5.29138i	−0.518502	−	0.214771i	−0.626559	+	0.779374i	$0.715537\pi$
$608$	−0.141969	−	5.26846i	−0.00575759	−	0.213664i
$609$	14.7377	+	6.10455i	0.597202	+	0.247369i
$610$	11.6170	+	27.6833i	0.470358	+	1.12086i
$611$			25.7099i			1.04011i
$612$	−0.460115	+	8.90536i	−0.0185990	+	0.359978i
$613$	9.54282			0.385431			0.192715	−	0.981255i	$-0.438271\pi$
$613$	9.54282			0.385431			0.192715	+	0.981255i	$0.438271\pi$
$614$	−4.33854	+	2.24012i	−0.175089	+	0.0904040i
$615$	50.1402	+	25.5961i	2.02185	+	1.03213i
$616$	−6.22544	+	4.67864i	−0.250830	+	0.188508i
$617$	−4.68910	−	1.94229i	−0.188776	−	0.0781935i	0.286293	−	0.958142i	$-0.407577\pi$
$617$	−4.68910	−	1.94229i	−0.188776	−	0.0781935i	−0.475069	+	0.879949i	$0.657577\pi$
$618$	−3.10132	−	36.8654i	−0.124753	−	1.48294i
$619$	12.3060	−	5.09733i	0.494621	−	0.204879i	−0.121407	−	0.992603i	$-0.538741\pi$
$619$	12.3060	−	5.09733i	0.494621	−	0.204879i	0.616028	+	0.787724i	$0.288741\pi$
$620$	−1.46995	−	16.5567i	−0.0590345	−	0.664935i
$621$	−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
$630$	−1.03636	+	2.53508i	−0.0412897	+	0.101000i
$631$	−5.41599	+	5.41599i	−0.215607	+	0.215607i	−0.806644	−	0.591037i	$-0.798719\pi$
$631$	−5.41599	+	5.41599i	−0.215607	+	0.215607i	0.591037	+	0.806644i	$0.298719\pi$
$632$	8.90289	+	34.6089i	0.354138	+	1.37667i
$633$	−3.00251			−0.119339
$634$	−4.75383	+	5.62713i	−0.188799	+	0.223482i
$635$	−11.3095	−	34.8981i	−0.448805	−	1.38489i
$636$	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
$640$	−6.92341	+	24.3324i	−0.273672	+	0.961823i
$641$	1.32058	−	3.18817i	0.0521599	−	0.125925i	−0.895652	−	0.444756i	$-0.853290\pi$
$641$	1.32058	−	3.18817i	0.0521599	−	0.125925i	0.947812	+	0.318831i	$0.103290\pi$
$642$	−2.03812	+	6.38964i	−0.0804383	+	0.252179i
$643$	2.28217	+	0.945307i	0.0900001	+	0.0372793i	0.427229	−	0.904143i	$-0.359490\pi$
$643$	2.28217	+	0.945307i	0.0900001	+	0.0372793i	−0.337229	+	0.941423i	$0.609490\pi$
$644$	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
$650$	8.02255	−	15.8964i	0.314670	−	0.623508i
$651$	−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	0.860858	+	0.508845i	$0.169927\pi$
$653$	15.6376	+	37.7525i	0.611947	+	1.47737i	−0.248911	+	0.968526i	$0.580073\pi$
$654$	20.0252	−	10.3396i	0.783047	−	0.404311i
$655$	−14.6592	+	12.5007i	−0.572781	+	0.488443i
$656$	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	$0.718594\pi$
$660$	27.5320	−	14.3772i	1.07168	−	0.559631i
$661$	31.6703	+	31.6703i	1.23183	+	1.23183i	0.963260	+	0.268572i	$0.0865516\pi$
$661$	31.6703	+	31.6703i	1.23183	+	1.23183i	0.268572	+	0.963260i	$0.413448\pi$
$662$	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
$665$	−1.26957	+	1.08263i	−0.0492317	+	0.0419826i
$666$	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
$670$	−0.0746936	−	16.1594i	−0.00288566	−	0.624290i
$671$	−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	$-0.868118\pi$
$673$	−33.1545	+	13.7330i	−1.27801	+	0.529369i	−0.362620	+	0.931937i	$0.618118\pi$
$674$	1.98517	+	23.5977i	0.0764660	+	0.908951i
$675$	−10.1515	+	16.5090i	−0.390733	+	0.635432i
$676$	7.71140	−	10.8580i	0.296592	−	0.417615i
$677$	−41.3616	−	17.1325i	−1.58965	−	0.658456i	−0.599749	−	0.800188i	$-0.704733\pi$
$677$	−41.3616	−	17.1325i	−1.58965	−	0.658456i	−0.989905	+	0.141732i	$0.954733\pi$
$678$	8.58623	+	16.6293i	0.329752	+	0.638645i
$679$	5.08584			0.195177
$680$	19.2850	−	17.5524i	0.739547	−	0.673105i
$681$	−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	$-0.393662\pi$
$683$	−2.82950	−	1.17202i	−0.108268	−	0.0448459i	−0.436160	+	0.899869i	$0.643662\pi$
$684$	1.64283	+	1.16674i	0.0628151	+	0.0446116i
$685$	−22.1569	−	11.3109i	−0.846573	−	0.432168i
$686$	−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
$690$	−31.7756	+	0.146877i	−1.20968	+	0.00559150i
$691$	−15.3642	−	37.0925i	−0.584483	−	1.41107i	−0.888711	−	0.458467i	$-0.848399\pi$
$691$	−15.3642	−	37.0925i	−0.584483	−	1.41107i	0.304229	−	0.952599i	$-0.401601\pi$
$692$	−9.50209	+	5.96468i	−0.361215	+	0.226743i
$693$		−	2.97736i		−	0.113100i
$694$	−38.2319	−	32.2985i	−1.45126	−	1.22603i
$695$	−20.5367	−	24.0827i	−0.779002	−	0.913510i
$696$	−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
$700$	7.37064	−	3.13316i	0.278584	−	0.118422i
$701$	−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
$705$	35.0941	−	29.9267i	1.32172	−	1.12711i
$706$	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	−0.255033	−	0.966932i	$-0.582086\pi$
$709$	−29.7981	−	12.3428i	−1.11909	−	0.463543i	−0.864060	+	0.503389i	$0.832086\pi$
$710$	9.82339	−	24.0293i	0.368665	−	0.901805i
$711$	−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	−0.998494	−	0.0548683i	$-0.982526\pi$
$719$	−6.80153	+	16.4203i	−0.253654	+	0.612376i	0.744839	+	0.667244i	$0.232526\pi$
$720$	−5.84653	−	7.70504i	−0.217887	−	0.287150i
$721$	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
$725$	11.4344	+	47.9510i	0.424661	+	1.78085i
$726$	−1.50907	+	1.78629i	−0.0560068	+	0.0662956i
$727$	10.0605			0.373123			0.186562	−	0.982443i	$-0.440266\pi$
$727$	10.0605			0.373123			0.186562	+	0.982443i	$0.440266\pi$
$728$	−5.52445	+	1.42113i	−0.204750	+	0.0526704i
$729$	−8.14300	+	8.14300i	−0.301593	+	0.301593i
$730$	7.47255	−	18.2788i	0.276571	−	0.676530i
$731$	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	$-0.986296\pi$
$733$	−25.8836	+	25.8836i	−0.956033	+	0.956033i	0.0430403	+	0.999073i	$0.486296\pi$
$734$	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	−0.461002	−	0.887399i	$-0.652510\pi$
$739$	11.5914	−	11.5914i	0.426398	−	0.426398i	0.887399	+	0.461002i	$0.152510\pi$
$740$	−0.478404	−	5.38851i	−0.0175865	−	0.198085i
$741$	−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	$-0.0794984\pi$
$743$	40.3247	+	16.7031i	1.47937	+	0.612776i	0.510397	+	0.859939i	$0.329498\pi$
$744$	16.9779	−	12.7595i	0.622438	−	0.467784i
$745$	−20.9972	+	41.1314i	−0.769278	+	1.50694i
$746$	−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
$750$	−31.0370	+	7.55286i	−1.13331	+	0.275792i
$751$	−13.9326	−	5.77108i	−0.508409	−	0.210590i	0.113708	−	0.993514i	$-0.463727\pi$
$751$	−13.9326	−	5.77108i	−0.508409	−	0.210590i	−0.622117	+	0.782924i	$0.713727\pi$
$752$	−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
$755$	−0.756275	−	2.33365i	−0.0275237	−	0.0849303i
$756$	6.12140	−	1.03727i	0.222633	−	0.0377252i
$757$	21.4211	+	21.4211i	0.778562	+	0.778562i	0.979586	−	0.201025i	$-0.0644271\pi$
$757$	21.4211	+	21.4211i	0.778562	+	0.778562i	−0.201025	+	0.979586i	$0.564427\pi$
$758$	51.5007	−	4.33252i	1.87059	−	0.157364i
$759$	31.9150	−	13.2196i	1.15844	−	0.479842i
$760$	−1.01129	−	5.80503i	−0.0366833	−	0.210570i
$761$			0.147141i			0.00533387i	0.999996	+	0.00266694i	$0.000848913\pi$
$761$			0.147141i			0.00533387i	−0.999996	+	0.00266694i	$0.999151\pi$
$762$	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
$765$	0.934949	+	9.92584i	0.0338032	+	0.358869i
$766$	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	$-0.844691\pi$
$769$		−	25.9998i		−	0.937576i	0.883311	−	0.468788i	$-0.155309\pi$
$770$	−6.12806	+	6.18498i	−0.220840	+	0.222891i
$771$	−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	$-0.102710\pi$
$773$	17.5516	+	17.5516i	0.631289	+	0.631289i	−0.317103	+	0.948391i	$0.602710\pi$
$774$	−2.61382	−	5.06229i	−0.0939517	−	0.181960i
$775$	−4.31062	−	18.0770i	−0.154842	−	0.649344i
$776$	−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
$780$	22.6619	−	2.01198i	0.811428	−	0.0720404i
$781$			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
$785$	−7.98778	−	4.07769i	−0.285096	−	0.145539i
$786$	−23.4516	−	7.48043i	−0.836491	−	0.266818i
$787$	5.58683	−	13.4878i	0.199149	−	0.480788i	−0.792482	−	0.609896i	$-0.791211\pi$
$787$	5.58683	−	13.4878i	0.199149	−	0.480788i	0.991631	+	0.129108i	$0.0412113\pi$
$788$	24.3259	+	5.56358i	0.866574	+	0.198194i
$789$	−25.2546	+	10.4608i	−0.899088	+	0.372415i
$790$	15.4601	+	36.8413i	0.550044	+	1.31076i
$791$	−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	$-0.630802\pi$
$797$	14.6037	−	14.6037i	0.517291	−	0.517291i	0.916751	+	0.399460i	$0.130802\pi$
$798$	−2.03104	−	0.647848i	−0.0718981	−	0.0229336i
$799$	−9.16511	+	41.0862i	−0.324238	+	1.45352i
$800$	−3.71346	+	28.0394i	−0.131291	+	0.991344i
$801$	−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
$805$	8.47362	−	2.74607i	0.298656	−	0.0967864i
$806$	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	0.961149	−	0.276031i	$-0.0890193\pi$
$809$	2.45549	+	5.92808i	0.0863305	+	0.208420i	−0.874818	+	0.484451i	$0.839019\pi$
$810$	−35.0211	+	0.161878i	−1.23051	+	0.00568782i
$811$	11.3665	+	4.70816i	0.399132	+	0.165326i	0.573215	−	0.819405i	$-0.305696\pi$
$811$	11.3665	+	4.70816i	0.399132	+	0.165326i	−0.174083	+	0.984731i	$0.555696\pi$
$812$	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
$820$	35.7688	−	42.7388i	1.24910	−	1.49251i
$821$	−0.756234	−	0.313242i	−0.0263927	−	0.0109322i	0.369448	−	0.929251i	$-0.379547\pi$
$821$	−0.756234	−	0.313242i	−0.0263927	−	0.0109322i	−0.395841	+	0.918319i	$0.629547\pi$
$822$	−2.66458	−	31.6738i	−0.0929378	−	1.10475i
$823$	0.0289680	−	0.0119989i	0.00100976	−	0.000418256i	−0.382178	−	0.924089i	$-0.624826\pi$
$823$	0.0289680	−	0.0119989i	0.00100976	−	0.000418256i	0.383188	+	0.923670i	$0.374826\pi$
$824$	−36.2619	−	5.14395i	−1.26324	−	0.179198i
$825$	28.1251	−	20.3683i	0.979190	−	0.709134i
$826$	−0.704178	−	8.37057i	−0.0245015	−	0.291249i
$827$	43.4870	−	18.0129i	1.51219	−	0.626370i	0.536183	−	0.844102i	$-0.319866\pi$
$827$	43.4870	−	18.0129i	1.51219	−	0.626370i	0.976009	+	0.217731i	$0.0698657\pi$
$828$	−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	$0.632335\pi$
$830$	15.4084	+	15.2666i	0.534833	+	0.529912i
$831$	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
$835$	−16.2988	−	19.1130i	−0.564042	−	0.661434i
$836$	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	−0.857047	−	0.515238i	$-0.827704\pi$
$839$	−31.8256	+	13.1826i	−1.09874	+	0.455114i	−0.241696	+	0.970352i	$0.577704\pi$
$840$	8.37039	+	5.88668i	0.288806	+	0.203110i
$841$	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
$845$	6.76992	−	13.2616i	0.232892	−	0.456213i
$846$	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
$850$	18.4874	−	22.5437i	0.634112	−	0.773241i
$851$		−	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	$-0.202539\pi$
$853$	27.8292	+	11.5273i	0.952855	+	0.394686i	0.148552	+	0.988905i	$0.452539\pi$
$854$	3.26770	−	10.2444i	0.111818	−	0.350558i
$855$	2.00650	+	1.02430i	0.0686207	+	0.0350302i
$856$	5.71654	+	3.37723i	0.195387	+	0.115431i
$857$	32.7884	−	13.5814i	1.12003	−	0.463932i	0.255650	−	0.966769i	$-0.417710\pi$
$857$	32.7884	−	13.5814i	1.12003	−	0.463932i	0.864381	+	0.502837i	$0.167710\pi$
$858$	−21.9767	+	11.3473i	−0.750273	+	0.387389i
$859$	3.84458	−	3.84458i	0.131175	−	0.131175i	−0.638471	−	0.769646i	$-0.720433\pi$
$859$	3.84458	−	3.84458i	0.131175	−	0.131175i	0.769646	+	0.638471i	$0.220433\pi$
$860$	−4.98953	+	15.8959i	−0.170142	+	0.542046i
$861$	−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	$-0.703903\pi$
$863$	−35.1148			−1.19532			−0.597661	+	0.801749i	$0.703903\pi$
$864$	−7.84217	+	20.4761i	−0.266796	+	0.696611i
$865$	−9.54422	+	8.13890i	−0.324513	+	0.276731i
$866$	−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
$870$	−44.3310	+	44.7428i	−1.50296	+	1.51692i
$871$			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
$875$	7.64549	−	4.66103i	0.258465	−	0.157572i
$876$	24.8767	−	4.21537i	0.840507	−	0.142424i
$877$	5.50861	+	13.2990i	0.186013	+	0.449074i	0.989185	−	0.146672i	$-0.0468563\pi$
$877$	5.50861	+	13.2990i	0.186013	+	0.449074i	−0.803173	+	0.595746i	$0.796856\pi$
$878$	17.6292	−	1.48307i	0.594957	−	0.0500511i
$879$	21.0104	−	50.7236i	0.708663	−	1.71086i
$880$	−7.79802	−	29.7434i	−0.262871	−	1.00265i
$881$	−10.2912	−	4.26275i	−0.346719	−	0.143616i	0.202527	−	0.979277i	$-0.435085\pi$
$881$	−10.2912	−	4.26275i	−0.346719	−	0.143616i	−0.549245	+	0.835661i	$0.685085\pi$
$882$	−8.64034	+	4.46128i	−0.290935	+	0.150219i
$883$	21.7804			0.732968			0.366484	−	0.930424i	$-0.380561\pi$
$883$	21.7804			0.732968			0.366484	+	0.930424i	$0.380561\pi$
$884$	−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	$-0.868778\pi$
$887$	0.445547	−	1.07565i	0.0149600	−	0.0361167i	0.931183	+	0.364552i	$0.118778\pi$
$888$	5.52556	−	4.15265i	0.185426	−	0.139354i
$889$	−5.02825	+	12.1393i	−0.168642	+	0.407138i
$890$	5.66558	−	0.0261881i	0.189911	−	0.000877827i
$891$	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
$895$	−11.9180	−	36.7756i	−0.398374	−	1.22927i
$896$	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
$900$	−7.71683	−	7.57545i	−0.257228	−	0.252515i
$901$	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	$-0.809474\pi$
$907$	−30.4750	+	12.6232i	−1.01191	+	0.419146i	−0.185757	+	0.982596i	$0.559474\pi$
$908$	−3.85312	+	16.8472i	−0.127870	+	0.559093i
$909$	−4.39711	+	4.39711i	−0.145843	+	0.145843i
$910$	−5.88080	+	2.46782i	−0.194947	+	0.0818073i
$911$	19.8214	+	47.8532i	0.656714	+	1.58545i	0.802849	+	0.596183i	$0.203317\pi$
$911$	19.8214	+	47.8532i	0.656714	+	1.58545i	−0.146135	+	0.989265i	$0.546683\pi$
$912$	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
$915$	−19.4996	+	38.1978i	−0.644638	+	1.26278i
$916$	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	$0.552342\pi$
$920$	−6.87176	+	30.6979i	−0.226555	+	1.01208i
$921$	−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
$925$	−1.40292	−	5.88327i	−0.0461278	−	0.193441i
$926$	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	−0.696482	−	0.717574i	$-0.745252\pi$
$929$	−20.7738	+	8.60481i	−0.681568	+	0.282315i	0.0149143	+	0.999889i	$0.495252\pi$
$930$	16.7123	−	16.8675i	0.548018	−	0.553108i
$931$	−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
$935$	−9.32963	+	30.2907i	−0.305112	+	0.990612i
$936$	4.62726	+	6.15708i	0.151247	+	0.201250i
$937$	21.1701	+	21.1701i	0.691596	+	0.691596i	0.962583	−	0.270987i	$-0.0873501\pi$
$937$	21.1701	+	21.1701i	0.691596	+	0.691596i	−0.270987	+	0.962583i	$0.587350\pi$
$938$	−3.73515	+	4.42131i	−0.121957	+	0.144361i
$939$	47.6100			1.55369
$940$	−21.1352	−	40.4734i	−0.689354	−	1.32010i
$941$	2.94935	+	7.12035i	0.0961460	+	0.232117i	0.964634	−	0.263593i	$-0.0849077\pi$
$941$	2.94935	+	7.12035i	0.0961460	+	0.232117i	−0.868488	+	0.495710i	$0.834908\pi$
$942$	−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
$945$	6.60340	−	2.13998i	0.214808	−	0.0696137i
$946$	−1.51833	−	18.0484i	−0.0493653	−	0.586805i
$947$	−11.2256	+	27.1011i	−0.364784	+	0.880666i	0.629803	+	0.776755i	$0.283136\pi$
$947$	−11.2256	+	27.1011i	−0.364784	+	0.880666i	−0.994587	+	0.103911i	$0.966864\pi$
$948$	−29.5592	+	41.6207i	−0.960040	+	1.35178i
$949$	−6.01770	+	14.5280i	−0.195343	+	0.471599i
$950$	−2.05994	−	6.25763i	−0.0668333	−	0.203024i
$951$	−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
$955$	10.6979	+	5.46120i	0.346177	+	0.176720i
$956$	−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
$960$	−32.9352	+	14.8766i	−1.06298	+	0.480141i
$961$	−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	$-0.126293\pi$
$967$	16.6642	+	16.6642i	0.535885	+	0.535885i	−0.386433	+	0.922318i	$0.626293\pi$
$968$	1.39080	+	1.85062i	0.0447021	+	0.0594810i
$969$	−7.64444	+	1.33759i	−0.245575	+	0.0429696i
$970$	−7.59888	+	18.5879i	−0.243985	+	0.596821i
$971$	−26.5367	−	26.5367i	−0.851603	−	0.851603i	0.138728	−	0.990331i	$-0.455699\pi$
$971$	−26.5367	−	26.5367i	−0.851603	−	0.851603i	−0.990331	+	0.138728i	$0.955699\pi$
$972$	−11.4257	−	18.2019i	−0.366480	−	0.583825i
$973$			11.3362i			0.363421i
$974$	23.6585	+	19.9868i	0.758068	+	0.640420i
$975$	24.7427	−	5.90014i	0.792402	−	0.188956i
$976$	25.2795	+	28.3383i	0.809176	+	0.907087i
$977$	10.4866	−	10.4866i	0.335497	−	0.335497i	−0.519172	−	0.854670i	$-0.673760\pi$
$977$	10.4866	−	10.4866i	0.335497	−	0.335497i	0.854670	+	0.519172i	$0.173760\pi$
$978$	−22.4069	−	43.3963i	−0.716493	−	1.38766i
$979$	−5.69043	+	2.35705i	−0.181867	+	0.0753318i
$980$	27.1312	+	8.51617i	0.866675	+	0.272039i
$981$	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	$-0.804300\pi$
$983$	5.28614	−	12.7619i	0.168602	−	0.407040i	0.985485	+	0.169763i	$0.0543001\pi$
$984$	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
$990$	10.8817	+	4.44854i	0.345844	+	0.141384i
$991$	11.0247	−	26.6160i	0.350211	−	0.845484i	−0.646382	−	0.763014i	$-0.723719\pi$
$991$	11.0247	−	26.6160i	0.350211	−	0.845484i	0.996593	−	0.0824706i	$-0.0262811\pi$
$992$	−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
$995$	−25.4924	−	29.8941i	−0.808162	−	0.947705i
$996$	−6.17905	+	27.0169i	−0.195791	+	0.856064i
$997$	−19.0207	+	7.87865i	−0.602393	+	0.249519i	−0.662972	−	0.748644i	$-0.730705\pi$
$997$	−19.0207	+	7.87865i	−0.602393	+	0.249519i	0.0605792	+	0.998163i	$0.480705\pi$
$998$	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.349.89	yes	416
5.4	even	2	inner	680.2.br.a.349.16	yes	416
8.5	even	2	inner	680.2.br.a.349.37	yes	416
17.2	even	8	inner	680.2.br.a.189.68	yes	416
40.29	even	2	inner	680.2.br.a.349.68	yes	416
85.19	even	8	inner	680.2.br.a.189.37	yes	416
136.53	even	8	inner	680.2.br.a.189.16	✓	416
680.189	even	8	inner	680.2.br.a.189.89	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.br.a.189.16	✓	416	136.53	even	8	inner
680.2.br.a.189.37	yes	416	85.19	even	8	inner
680.2.br.a.189.68	yes	416	17.2	even	8	inner
680.2.br.a.189.89	yes	416	680.189	even	8	inner
680.2.br.a.349.16	yes	416	5.4	even	2	inner
680.2.br.a.349.37	yes	416	8.5	even	2	inner
680.2.br.a.349.68	yes	416	40.29	even	2	inner
680.2.br.a.349.89	yes	416	1.1	even	1	trivial

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} +(1.01668 - 1.99157i) 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} +(-0.0146169 - 3.16224i) q^{10} +(1.31559 + 3.17611i) q^{11} +(3.42213 - 2.14815i) q^{12} +2.51816i q^{13} +(-0.730936 + 0.865212i) q^{14} +(3.43730 - 2.93118i) 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} +(-2.07009 - 3.96418i) q^{20} -1.61800 q^{21} +(3.71389 + 3.13751i) q^{22} +(-1.90342 - 4.59527i) q^{23} +(2.90647 - 4.91970i) q^{24} +(-2.93273 - 4.04958i) 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} +(2.41749 - 5.91350i) 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} +(-5.17331 - 3.63825i) 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} +(2.30025 - 0.745450i) q^{45} +(-5.37333 - 4.53942i) q^{46} +10.2098 q^{47} +(0.460265 - 8.06785i) q^{48} +(-4.49619 + 4.49619i) q^{49} +(-6.31270 - 3.18588i) 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} +(-0.798987 - 8.99939i) 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} +(5.01510 + 2.56016i) q^{65} +(4.50617 + 8.72729i) q^{66} +5.11009 q^{67} +(5.52232 + 6.12405i) q^{68} -10.0484i q^{69} +(0.980007 + 2.33535i) 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} +(-2.34303 - 9.82571i) 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} +(-8.86133 - 1.21527i) q^{80} -11.0748i q^{81} +(13.4628 + 11.3734i) q^{82} +(-4.85020 + 4.85020i) q^{83} +(-1.87375 + 2.63832i) q^{84} +(7.10183 + 5.87911i) q^{85} +(-5.01938 - 1.60105i) q^{86} +(-14.0840 - 14.0840i) q^{87} +(9.41698 - 2.42245i) q^{88} +1.79163i q^{89} +(2.40682 - 2.42918i) 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} +(1.98183 - 0.642257i) 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

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