LMFDB - Embedded newform 640.2.bm.a.101.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.18
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.914044 - 1.07913i) q^{2} +(-0.140766 + 0.0752410i) q^{3} +(-0.329046 + 1.97275i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(0.209861 + 0.0831313i) q^{6} +(0.912540 - 0.609740i) q^{7} +(2.42961 - 1.44809i) q^{8} +(-1.65256 + 2.47323i) q^{9} +(-0.254316 + 1.39116i) q^{10} +(-0.229366 + 0.0695775i) q^{11} +(-0.102113 - 0.302453i) q^{12} +(1.96164 + 1.60987i) q^{13} +(-1.49209 - 0.427421i) q^{14} +(0.147463 + 0.0610812i) q^{15} +(-3.78346 - 1.29825i) q^{16} +(-1.52200 + 0.630431i) q^{17} +(4.17944 - 0.477313i) q^{18} +(0.387253 + 3.93185i) q^{19} +(1.73370 - 0.997141i) q^{20} +(-0.0825772 + 0.154491i) q^{21} +(0.284734 + 0.183919i) q^{22} +(-0.471000 + 0.0936877i) q^{23} +(-0.233051 + 0.386649i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.0557585 - 3.58836i) q^{26} +(0.0934702 - 0.949019i) q^{27} +(0.902594 + 2.00084i) q^{28} +(-0.314685 + 1.03738i) q^{29} +(-0.0688732 - 0.214963i) q^{30} +(4.53630 + 4.53630i) q^{31} +(2.05727 + 5.26950i) q^{32} +(0.0270519 - 0.0270519i) q^{33} +(2.07149 + 1.06619i) q^{34} +(-1.05024 - 0.318588i) q^{35} +(-4.33528 - 4.07388i) q^{36} +(6.31233 + 0.621710i) q^{37} +(3.88901 - 4.01178i) q^{38} +(-0.397260 - 0.0790200i) q^{39} +(-2.66072 - 0.959457i) q^{40} +(-0.669203 - 3.36431i) q^{41} +(0.242195 - 0.0521001i) q^{42} +(7.57950 + 4.05133i) q^{43} +(-0.0617866 - 0.475376i) q^{44} +(2.96020 - 0.291554i) q^{45} +(0.531616 + 0.422636i) q^{46} +(4.85538 + 11.7219i) q^{47} +(0.630264 - 0.101922i) q^{48} +(-2.21784 + 5.35433i) q^{49} +(1.23672 - 0.685953i) q^{50} +(0.166811 - 0.203260i) q^{51} +(-3.82134 + 3.34009i) q^{52} +(0.673861 + 2.22142i) q^{53} +(-1.10955 + 0.766579i) q^{54} +(0.199293 + 0.133163i) q^{55} +(1.33416 - 2.80287i) q^{56} +(-0.350348 - 0.524333i) q^{57} +(1.40710 - 0.608623i) q^{58} +(4.98010 - 4.08706i) q^{59} +(-0.169020 + 0.270809i) q^{60} +(-3.46974 - 6.49143i) q^{61} +(0.748883 - 9.04164i) q^{62} +3.26455i q^{63} +(3.80605 - 7.03662i) q^{64} -2.53766i q^{65} +(-0.0539192 - 0.00446590i) q^{66} +(1.98752 + 3.71840i) q^{67} +(-0.742874 - 3.20995i) q^{68} +(0.0592516 - 0.0486266i) q^{69} +(0.616171 + 1.42455i) q^{70} +(-1.31504 - 1.96810i) q^{71} +(-0.433613 + 8.40204i) q^{72} +(2.82999 + 1.89094i) q^{73} +(-5.09884 - 7.38010i) q^{74} +(-0.0463332 - 0.152740i) q^{75} +(-7.88396 - 0.529808i) q^{76} +(-0.166882 + 0.203346i) q^{77} +(0.277841 + 0.500924i) q^{78} +(-1.84901 + 4.46390i) q^{79} +(1.39664 + 3.74825i) q^{80} +(-3.35666 - 8.10368i) q^{81} +(-3.01885 + 3.79729i) q^{82} +(9.11127 - 0.897381i) q^{83} +(-0.277600 - 0.213739i) q^{84} +(1.45287 + 0.776577i) q^{85} +(-2.55609 - 11.8824i) q^{86} +(-0.0337564 - 0.169705i) q^{87} +(-0.456517 + 0.501190i) q^{88} +(-4.58286 - 0.911587i) q^{89} +(-3.02038 - 2.92795i) q^{90} +(2.77168 + 0.272986i) q^{91} +(-0.0298413 - 0.959991i) q^{92} +(-0.979873 - 0.297241i) q^{93} +(8.21147 - 15.9540i) q^{94} +(2.79369 - 2.79369i) q^{95} +(-0.686076 - 0.586976i) q^{96} +(-10.1720 - 10.1720i) q^{97} +(7.80523 - 2.50076i) q^{98} +(0.206960 - 0.682255i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.914044	−	1.07913i	−0.646327	−	0.763061i
$2$	−0.914044	−	1.07913i	−0.646327	−	0.763061i
$3$	−0.140766	+	0.0752410i	−0.0812713	+	0.0434404i	−0.511532	−	0.859264i	$-0.670922\pi$
$3$	−0.140766	+	0.0752410i	−0.0812713	+	0.0434404i	0.430260	+	0.902705i	$0.358422\pi$
$4$	−0.329046	+	1.97275i	−0.164523	+	0.986373i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$5$	−0.634393	−	0.773010i	−0.283709	−	0.345701i
$6$	0.209861	+	0.0831313i	0.0856755	+	0.0339382i
$7$	0.912540	−	0.609740i	0.344908	−	0.230460i	−0.371035	−	0.928619i	$-0.620997\pi$
$7$	0.912540	−	0.609740i	0.344908	−	0.230460i	0.715943	+	0.698159i	$0.245997\pi$
$8$	2.42961	−	1.44809i	0.858998	−	0.511978i
$9$	−1.65256	+	2.47323i	−0.550852	+	0.824409i
$10$	−0.254316	+	1.39116i	−0.0804217	+	0.439923i
$11$	−0.229366	+	0.0695775i	−0.0691565	+	0.0209784i	−0.324673	−	0.945826i	$-0.605254\pi$
$11$	−0.229366	+	0.0695775i	−0.0691565	+	0.0209784i	0.255517	+	0.966805i	$0.417754\pi$
$12$	−0.102113	−	0.302453i	−0.0294775	−	0.0873108i
$13$	1.96164	+	1.60987i	0.544060	+	0.446499i	0.865844	−	0.500315i	$-0.166782\pi$
$13$	1.96164	+	1.60987i	0.544060	+	0.446499i	−0.321784	+	0.946813i	$0.604282\pi$
$14$	−1.49209	−	0.427421i	−0.398778	−	0.114233i
$15$	0.147463	+	0.0610812i	0.0380748	+	0.0157711i
$16$	−3.78346	−	1.29825i	−0.945864	−	0.324563i
$17$	−1.52200	+	0.630431i	−0.369138	+	0.152902i	−0.559538	−	0.828805i	$-0.689021\pi$
$17$	−1.52200	+	0.630431i	−0.369138	+	0.152902i	0.190400	+	0.981707i	$0.439021\pi$
$18$	4.17944	−	0.477313i	0.985104	−	0.112504i
$19$	0.387253	+	3.93185i	0.0888420	+	0.902028i	0.931539	+	0.363640i	$0.118466\pi$
$19$	0.387253	+	3.93185i	0.0888420	+	0.902028i	−0.842697	+	0.538387i	$0.819034\pi$
$20$	1.73370	−	0.997141i	0.387667	−	0.222967i
$21$	−0.0825772	+	0.154491i	−0.0180198	+	0.0337127i
$22$	0.284734	+	0.183919i	0.0607055	+	0.0392117i
$23$	−0.471000	+	0.0936877i	−0.0982103	+	0.0195352i	−0.243951	−	0.969788i	$-0.578444\pi$
$23$	−0.471000	+	0.0936877i	−0.0982103	+	0.0195352i	0.145741	+	0.989323i	$0.453444\pi$
$24$	−0.233051	+	0.386649i	−0.0475714	+	0.0789244i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−0.0557585	−	3.58836i	−0.0109351	−	0.703735i
$27$	0.0934702	−	0.949019i	0.0179884	−	0.182639i
$28$	0.902594	+	2.00084i	0.170574	+	0.378124i
$29$	−0.314685	+	1.03738i	−0.0584356	+	0.192636i	−0.981298	−	0.192492i	$-0.938343\pi$
$29$	−0.314685	+	1.03738i	−0.0584356	+	0.192636i	0.922863	+	0.385129i	$0.125843\pi$
$30$	−0.0688732	−	0.214963i	−0.0125745	−	0.0392467i
$31$	4.53630	+	4.53630i	0.814744	+	0.814744i	0.985341	−	0.170597i	$-0.0545696\pi$
$31$	4.53630	+	4.53630i	0.814744	+	0.814744i	−0.170597	+	0.985341i	$0.554570\pi$
$32$	2.05727	+	5.26950i	0.363677	+	0.931525i
$33$	0.0270519	−	0.0270519i	0.00470913	−	0.00470913i
$34$	2.07149	+	1.06619i	0.355257	+	0.182850i
$35$	−1.05024	−	0.318588i	−0.177524	−	0.0538512i
$36$	−4.33528	−	4.07388i	−0.722547	−	0.678980i
$37$	6.31233	+	0.621710i	1.03774	+	0.102209i	0.602511	−	0.798111i	$-0.294167\pi$
$37$	6.31233	+	0.621710i	1.03774	+	0.102209i	0.435230	+	0.900319i	$0.356667\pi$
$38$	3.88901	−	4.01178i	0.630881	−	0.650797i
$39$	−0.397260	−	0.0790200i	−0.0636126	−	0.0126533i
$40$	−2.66072	−	0.959457i	−0.420697	−	0.151703i
$41$	−0.669203	−	3.36431i	−0.104512	−	0.525417i	−0.997203	−	0.0747470i	$-0.976185\pi$
$41$	−0.669203	−	3.36431i	−0.104512	−	0.525417i	0.892691	−	0.450670i	$-0.148815\pi$
$42$	0.242195	−	0.0521001i	0.0373715	−	0.00803921i
$43$	7.57950	+	4.05133i	1.15586	+	0.617822i	0.934006	−	0.357258i	$-0.116288\pi$
$43$	7.57950	+	4.05133i	1.15586	+	0.617822i	0.221857	+	0.975079i	$0.428788\pi$
$44$	−0.0617866	−	0.475376i	−0.00931468	−	0.0716656i
$45$	2.96020	−	0.291554i	0.441281	−	0.0434624i
$46$	0.531616	+	0.422636i	0.0783825	+	0.0623142i
$47$	4.85538	+	11.7219i	0.708231	+	1.70982i	0.704376	+	0.709827i	$0.251227\pi$
$47$	4.85538	+	11.7219i	0.708231	+	1.70982i	0.00385510	+	0.999993i	$0.498773\pi$
$48$	0.630264	−	0.101922i	0.0909708	−	0.0147111i
$49$	−2.21784	+	5.35433i	−0.316834	+	0.764905i
$50$	1.23672	−	0.685953i	0.174898	−	0.0970084i
$51$	0.166811	−	0.203260i	0.0233582	−	0.0284621i
$52$	−3.82134	+	3.34009i	−0.529925	+	0.463187i
$53$	0.673861	+	2.22142i	0.0925619	+	0.305136i	0.990981	−	0.134004i	$-0.0427834\pi$
$53$	0.673861	+	2.22142i	0.0925619	+	0.305136i	−0.898419	+	0.439139i	$0.855283\pi$
$54$	−1.10955	+	0.766579i	−0.150991	+	0.104318i
$55$	0.199293	+	0.133163i	0.0268726	+	0.0179557i
$56$	1.33416	−	2.80287i	0.178285	−	0.374550i
$57$	−0.350348	−	0.524333i	−0.0464048	−	0.0694496i
$58$	1.40710	−	0.608623i	0.184762	−	0.0799161i
$59$	4.98010	−	4.08706i	0.648354	−	0.532090i	−0.251735	−	0.967796i	$-0.581001\pi$
$59$	4.98010	−	4.08706i	0.648354	−	0.532090i	0.900089	+	0.435706i	$0.143501\pi$
$60$	−0.169020	+	0.270809i	−0.0218204	+	0.0349613i
$61$	−3.46974	−	6.49143i	−0.444255	−	0.831142i	0.555745	−	0.831353i	$-0.312433\pi$
$61$	−3.46974	−	6.49143i	−0.444255	−	0.831142i	−1.00000		0.000210569i	$0.999933\pi$
$62$	0.748883	−	9.04164i	0.0951082	−	1.14829i
$63$			3.26455i			0.411294i
$64$	3.80605	−	7.03662i	0.475756	−	0.879577i
$65$		−	2.53766i		−	0.314758i
$66$	−0.0539192	−	0.00446590i	−0.00663699	−	0.000549715i
$67$	1.98752	+	3.71840i	0.242815	+	0.454274i	0.973577	−	0.228357i	$-0.0733354\pi$
$67$	1.98752	+	3.71840i	0.242815	+	0.454274i	−0.730763	+	0.682632i	$0.760835\pi$
$68$	−0.742874	−	3.20995i	−0.0900867	−	0.389264i
$69$	0.0592516	−	0.0486266i	0.00713306	−	0.00585395i
$70$	0.616171	+	1.42455i	0.0736466	+	0.170267i
$71$	−1.31504	−	1.96810i	−0.156067	−	0.233570i	0.745194	−	0.666848i	$-0.232357\pi$
$71$	−1.31504	−	1.96810i	−0.156067	−	0.233570i	−0.901261	+	0.433278i	$0.857357\pi$
$72$	−0.433613	+	8.40204i	−0.0511018	+	0.990190i
$73$	2.82999	+	1.89094i	0.331225	+	0.221318i	0.710051	−	0.704151i	$-0.248672\pi$
$73$	2.82999	+	1.89094i	0.331225	+	0.221318i	−0.378826	+	0.925468i	$0.623672\pi$
$74$	−5.09884	−	7.38010i	−0.592728	−	0.857919i
$75$	−0.0463332	−	0.152740i	−0.00535010	−	0.0176369i
$76$	−7.88396	−	0.529808i	−0.904353	−	0.0607731i
$77$	−0.166882	+	0.203346i	−0.0190179	+	0.0231734i
$78$	0.277841	+	0.500924i	0.0314593	+	0.0567184i
$79$	−1.84901	+	4.46390i	−0.208030	+	0.502228i	−0.993113	−	0.117162i	$-0.962620\pi$
$79$	−1.84901	+	4.46390i	−0.208030	+	0.502228i	0.785083	+	0.619390i	$0.212620\pi$
$80$	1.39664	+	3.74825i	0.156149	+	0.419067i
$81$	−3.35666	−	8.10368i	−0.372962	−	0.900409i
$82$	−3.01885	+	3.79729i	−0.333376	+	0.419340i
$83$	9.11127	−	0.897381i	1.00009	−	0.0985004i	0.415300	−	0.909684i	$-0.363677\pi$
$83$	9.11127	−	0.897381i	1.00009	−	0.0985004i	0.584791	+	0.811184i	$0.301177\pi$
$84$	−0.277600	−	0.213739i	−0.0302886	−	0.0233208i
$85$	1.45287	+	0.776577i	0.157586	+	0.0842316i
$86$	−2.55609	−	11.8824i	−0.275630	−	1.28131i
$87$	−0.0337564	−	0.169705i	−0.00361907	−	0.0181943i
$88$	−0.456517	+	0.501190i	−0.0486649	+	0.0534271i
$89$	−4.58286	−	0.911587i	−0.485782	−	0.0966280i	−0.0538777	−	0.998548i	$-0.517158\pi$
$89$	−4.58286	−	0.911587i	−0.485782	−	0.0966280i	−0.431904	+	0.901920i	$0.642158\pi$
$90$	−3.02038	−	2.92795i	−0.318376	−	0.308633i
$91$	2.77168	+	0.272986i	0.290551	+	0.0286167i
$92$	−0.0298413	−	0.959991i	−0.00311117	−	0.100086i
$93$	−0.979873	−	0.297241i	−0.101608	−	0.0308225i
$94$	8.21147	−	15.9540i	0.846948	−	1.64553i
$95$	2.79369	−	2.79369i	0.286626	−	0.286626i
$96$	−0.686076	−	0.586976i	−0.0700223	−	0.0599080i
$97$	−10.1720	−	10.1720i	−1.03281	−	1.03281i	−0.999443	−	0.0333703i	$-0.989376\pi$
$97$	−10.1720	−	10.1720i	−1.03281	−	1.03281i	−0.0333703	−	0.999443i	$-0.510624\pi$
$98$	7.80523	−	2.50076i	0.788447	−	0.252615i
$99$	0.206960	−	0.682255i	0.0208003	−	0.0685692i
$100$	−1.87065	−	0.707588i	−0.187065	−	0.0707588i
$101$	0.654666	−	6.64694i	0.0651417	−	0.661395i	−0.906062	−	0.423145i	$-0.860926\pi$
$101$	0.654666	−	6.64694i	0.0651417	−	0.661395i	0.971204	−	0.238250i	$-0.0765738\pi$
$102$	−0.371817	+	0.00577755i	−0.0368153	+	0.000572063i
$103$	−2.41390	+	12.1355i	−0.237849	+	1.19575i	0.658564	+	0.752525i	$0.271164\pi$
$103$	−2.41390	+	12.1355i	−0.237849	+	1.19575i	−0.896412	+	0.443221i	$0.853836\pi$
$104$	7.09727	+	1.07074i	0.695944	+	0.104995i
$105$	0.171810	−	0.0341751i	0.0167669	−	0.00333514i
$106$	1.78127	−	2.75766i	0.173012	−	0.267848i
$107$	5.89580	−	11.0303i	0.569969	−	1.06634i	−0.417523	−	0.908666i	$-0.637102\pi$
$107$	5.89580	−	11.0303i	0.569969	−	1.06634i	0.987492	−	0.157670i	$-0.0503982\pi$
$108$	1.84142	+	0.496664i	0.177191	+	0.0477916i
$109$	1.60955	+	16.3421i	0.154167	+	1.56529i	0.691788	+	0.722101i	$0.256823\pi$
$109$	1.60955	+	16.3421i	0.154167	+	1.56529i	−0.537621	+	0.843187i	$0.680677\pi$
$110$	−0.0384619	−	0.336780i	−0.00366720	−	0.0321107i
$111$	−0.935339	+	0.387430i	−0.0887785	+	0.0367733i
$112$	−4.24415	+	1.12222i	−0.401034	+	0.106040i
$113$	−11.9715	−	4.95876i	−1.12618	−	0.466481i	−0.259702	−	0.965689i	$-0.583624\pi$
$113$	−11.9715	−	4.95876i	−1.12618	−	0.466481i	−0.866482	+	0.499208i	$0.833624\pi$
$114$	−0.245590	+	0.857335i	−0.0230016	+	0.0802968i
$115$	0.371221	+	0.304653i	0.0346165	+	0.0284090i
$116$	−1.94294	−	0.962140i	−0.180397	−	0.0893325i
$117$	−7.22330	+	2.19116i	−0.667794	+	0.202573i
$118$	−8.96251	−	1.63842i	−0.825066	−	0.150829i
$119$	−1.00448	+	1.50331i	−0.0920808	+	0.137809i
$120$	0.446730	−	0.0651365i	0.0407807	−	0.00594613i
$121$	−9.09840	+	6.07936i	−0.827127	+	0.552669i
$122$	−3.83360	+	9.67775i	−0.347078	+	0.876183i
$123$	0.347335	+	0.423229i	0.0313182	+	0.0381613i
$124$	−10.4416	+	7.45632i	−0.937686	+	0.669597i
$125$	0.881921	−	0.471397i	0.0788814	−	0.0421630i
$126$	3.52287	−	2.98394i	0.313842	−	0.265830i
$127$	4.71015			0.417958			0.208979	−	0.977920i	$-0.432986\pi$
$127$	4.71015			0.417958			0.208979	+	0.977920i	$0.432986\pi$
$128$	−11.0723	+	2.32455i	−0.978665	+	0.205463i
$129$	−1.37176			−0.120777
$130$	−2.73847	+	2.31953i	−0.240179	+	0.203436i
$131$	−5.19613	+	2.77739i	−0.453988	+	0.242662i	−0.682509	−	0.730877i	$-0.739111\pi$
$131$	−5.19613	+	2.77739i	−0.453988	+	0.242662i	0.228521	+	0.973539i	$0.426611\pi$
$132$	0.0444652	+	0.0622679i	0.00387020	+	0.00541972i
$133$	2.75079	+	3.35184i	0.238524	+	0.290642i
$134$	2.19595	−	5.54358i	0.189701	−	0.478892i
$135$	−0.792899	+	0.529798i	−0.0682419	+	0.0455978i
$136$	−2.78494	+	3.73570i	−0.238807	+	0.320333i
$137$	−3.49272	+	5.22722i	−0.298403	+	0.446592i	−0.950126	−	0.311865i	$-0.899046\pi$
$137$	−3.49272	+	5.22722i	−0.298403	+	0.446592i	0.651723	+	0.758457i	$0.274046\pi$
$138$	−0.106633	−	0.0194934i	−0.00907721	−	0.00165939i
$139$	4.60368	−	1.39651i	0.390479	−	0.118450i	−0.0889393	−	0.996037i	$-0.528348\pi$
$139$	4.60368	−	1.39651i	0.390479	−	0.118450i	0.479418	+	0.877587i	$0.340848\pi$
$140$	0.974073	−	1.96704i	0.0823242	−	0.166245i
$141$	−1.56544	−	1.28473i	−0.131834	−	0.108193i
$142$	−0.921830	+	3.21803i	−0.0773583	+	0.270051i
$143$	−0.561944	−	0.232765i	−0.0469921	−	0.0194648i
$144$	9.46324	−	7.21191i	0.788604	−	0.600993i
$145$	1.00154	−	0.414851i	0.0831733	−	0.0344515i
$146$	−0.546165	−	4.78233i	−0.0452010	−	0.395788i
$147$	−0.0906693	−	0.920581i	−0.00747828	−	0.0759282i
$148$	−3.30353	+	12.2481i	−0.271548	+	1.00678i
$149$	−7.71882	+	14.4409i	−0.632350	+	1.18304i	0.337955	+	0.941162i	$0.390265\pi$
$149$	−7.71882	+	14.4409i	−0.632350	+	1.18304i	−0.970306	+	0.241882i	$0.922235\pi$
$150$	−0.122476	+	0.189611i	−0.0100001	+	0.0154817i
$151$	−16.5719	+	3.29635i	−1.34860	+	0.268253i	−0.815969	−	0.578096i	$-0.803796\pi$
$151$	−16.5719	+	3.29635i	−1.34860	+	0.268253i	−0.532629	+	0.846349i	$0.678796\pi$
$152$	6.63456	+	8.99209i	0.538134	+	0.729355i
$153$	0.955985	−	4.80606i	0.0772868	−	0.388547i
$154$	0.371974	−	0.00578000i	0.0299745	−	0.000465766i
$155$	0.628809	−	6.38441i	0.0505072	−	0.512808i
$156$	0.286603	−	0.757693i	0.0229466	−	0.0606640i
$157$	−0.549199	+	1.81047i	−0.0438309	+	0.144491i	−0.976125	−	0.217211i	$-0.930304\pi$
$157$	−0.549199	+	1.81047i	−0.0438309	+	0.144491i	0.932294	+	0.361702i	$0.117804\pi$
$158$	6.50721	−	2.08488i	0.517685	−	0.165864i
$159$	−0.261999	−	0.261999i	−0.0207778	−	0.0207778i
$160$	2.76827	−	4.93322i	0.218851	−	0.390006i
$161$	−0.372681	+	0.372681i	−0.0293714	+	0.0293714i
$162$	−5.67680	+	11.0294i	−0.446012	+	0.866551i
$163$	3.03888	+	0.921835i	0.238024	+	0.0722037i	0.407043	−	0.913409i	$-0.366560\pi$
$163$	3.03888	+	0.921835i	0.238024	+	0.0722037i	−0.169019	+	0.985613i	$0.554060\pi$
$164$	6.85713	−	0.213154i	0.535452	−	0.0166445i
$165$	−0.0380729	−	0.00374986i	−0.00296397	−	0.000291926i
$166$	−9.29649	−	9.01200i	−0.721548	−	0.699467i
$167$	2.85980	+	0.568849i	0.221298	+	0.0440189i	0.304494	−	0.952514i	$-0.401513\pi$
$167$	2.85980	+	0.568849i	0.221298	+	0.0440189i	−0.0831959	+	0.996533i	$0.526513\pi$
$168$	0.0230867	+	0.494933i	0.00178118	+	0.0381849i
$169$	−1.27985	−	6.43423i	−0.0984499	−	0.494941i
$170$	−0.489962	−	2.27767i	−0.0375784	−	0.174689i
$171$	−10.3643	−	5.53984i	−0.792578	−	0.423642i
$172$	−10.4862	+	13.6194i	−0.799569	+	1.03847i
$173$	−15.7960	+	1.55577i	−1.20095	+	0.118283i	−0.678639	−	0.734472i	$-0.737430\pi$
$173$	−15.7960	+	1.55577i	−1.20095	+	0.118283i	−0.522311	+	0.852755i	$0.674930\pi$
$174$	−0.152279	+	0.191545i	−0.0115442	+	0.0145210i
$175$	0.419996	+	1.01396i	0.0317487	+	0.0766482i
$176$	0.958126	+	0.0345313i	0.0722215	+	0.00260290i
$177$	−0.393514	+	0.950028i	−0.0295783	+	0.0714084i
$178$	3.20521	+	5.77873i	0.240241	+	0.433134i
$179$	−6.66631	+	8.12292i	−0.498263	+	0.607135i	−0.960041	−	0.279860i	$-0.909712\pi$
$179$	−6.66631	+	8.12292i	−0.498263	+	0.607135i	0.461778	+	0.886996i	$0.347212\pi$
$180$	−0.398881	+	5.93566i	−0.0297308	+	0.442418i
$181$	−0.868013	−	2.86145i	−0.0645189	−	0.212690i	0.918753	−	0.394832i	$-0.129197\pi$
$181$	−0.868013	−	2.86145i	−0.0645189	−	0.212690i	−0.983272	+	0.182142i	$0.941697\pi$
$182$	−2.23885	−	3.24052i	−0.165954	−	0.240203i
$183$	0.976843	+	0.652706i	0.0722103	+	0.0482494i
$184$	−1.00868	+	0.909677i	−0.0743608	+	0.0670623i
$185$	−3.52391	−	5.27390i	−0.259083	−	0.387745i
$186$	0.574885	+	1.32910i	0.0421526	+	0.0974546i
$187$	0.305231	−	0.250496i	0.0223207	−	0.0183181i
$188$	−24.7221	+	5.72138i	−1.80304	+	0.417275i
$189$	−0.493359	−	0.923010i	−0.0358866	−	0.0671391i
$190$	−5.56831	−	0.461200i	−0.403968	−	0.0334590i
$191$		−	12.0983i		−	0.875400i	−0.899121	−	0.437700i	$-0.855793\pi$
$191$		−	12.0983i		−	0.875400i	0.899121	−	0.437700i	$-0.144207\pi$
$192$	−0.00632057	+	1.27689i	−0.000456148	+	0.0921514i
$193$		−	19.1244i		−	1.37660i	−0.725424	−	0.688302i	$-0.758356\pi$
$193$		−	19.1244i		−	1.37660i	0.725424	−	0.688302i	$-0.241644\pi$
$194$	−1.67927	+	20.2746i	−0.120564	+	1.45563i
$195$	0.190936	+	0.357216i	0.0136732	+	0.0255808i
$196$	−9.83297	−	6.13706i	−0.702355	−	0.438361i
$197$	19.5890	−	16.0762i	1.39566	−	1.14539i	0.424921	−	0.905230i	$-0.360302\pi$
$197$	19.5890	−	16.0762i	1.39566	−	1.14539i	0.970735	−	0.240155i	$-0.0771982\pi$
$198$	−0.925413	+	0.400275i	−0.0657663	+	0.0284463i
$199$	−3.71727	−	5.56329i	−0.263510	−	0.394371i	0.675994	−	0.736907i	$-0.263714\pi$
$199$	−3.71727	−	5.56329i	−0.263510	−	0.394371i	−0.939505	+	0.342535i	$0.888714\pi$
$200$	0.946274	+	2.66544i	0.0669117	+	0.188475i
$201$	−0.559552	−	0.373881i	−0.0394677	−	0.0263715i
$202$	−7.77131	+	5.36912i	−0.546787	+	0.377770i
$203$	0.345368	+	1.13853i	0.0242401	+	0.0799088i
$204$	0.346091	+	0.395958i	0.0242313	+	0.0277226i
$205$	−2.17611	+	2.65160i	−0.151986	+	0.185196i
$206$	15.3022	−	8.48747i	1.06615	−	0.591350i
$207$	0.546643	−	1.31971i	0.0379943	−	0.0917264i
$208$	−5.33175	−	8.63758i	−0.369690	−	0.598909i
$209$	−0.362391	−	0.874889i	−0.0250671	−	0.0605173i
$210$	−0.193921	−	0.154168i	−0.0133818	−	0.0106386i
$211$	7.63516	−	0.751998i	0.525626	−	0.0517696i	0.168276	−	0.985740i	$-0.446180\pi$
$211$	7.63516	−	0.751998i	0.525626	−	0.0517696i	0.357350	+	0.933970i	$0.383680\pi$
$212$	−4.60403	+	0.598406i	−0.316206	+	0.0410987i
$213$	0.333195	+	0.178096i	0.0228302	+	0.0122030i
$214$	−17.2921	+	3.71981i	−1.18207	+	0.254281i
$215$	−1.67667	−	8.42917i	−0.114348	−	0.574864i
$216$	−1.14717	−	2.44110i	−0.0780552	−	0.166096i
$217$	6.90552	+	1.37359i	0.468777	+	0.0932456i
$218$	16.1640	−	16.6743i	1.09477	−	1.12933i
$219$	−0.540642	−	0.0532486i	−0.0365332	−	0.00359821i
$220$	−0.328273	+	0.349337i	−0.0221322	+	0.0235523i
$221$	−4.00052	−	1.21354i	−0.269104	−	0.0816318i
$222$	1.27303	+	0.655225i	0.0854401	+	0.0439758i
$223$	−15.4413	+	15.4413i	−1.03403	+	1.03403i	−0.0346268	+	0.999400i	$0.511024\pi$
$223$	−15.4413	+	15.4413i	−1.03403	+	1.03403i	−0.999400	+	0.0346268i	$0.988976\pi$
$224$	5.09036	+	3.55423i	0.340114	+	0.237477i
$225$	−2.10331	−	2.10331i	−0.140220	−	0.140220i
$226$	5.59133	+	17.4513i	0.371930	+	1.16085i
$227$	4.88127	−	16.0914i	0.323982	−	1.06802i	−0.632091	−	0.774894i	$-0.717803\pi$
$227$	4.88127	−	16.0914i	0.323982	−	1.06802i	0.956073	−	0.293130i	$-0.0946969\pi$
$228$	1.14966	−	0.518618i	0.0761379	−	0.0343463i
$229$	0.257388	−	2.61331i	0.0170087	−	0.172692i	−0.982927	−	0.183994i	$-0.941097\pi$
$229$	0.257388	−	2.61331i	0.0170087	−	0.172692i	0.999936	+	0.0113014i	$0.00359743\pi$
$230$	−0.0105518	−	0.679062i	−0.000695762	−	0.0447760i
$231$	0.00819132	−	0.0411805i	0.000538949	−	0.00270948i
$232$	0.737657	+	2.97612i	0.0484295	+	0.195392i
$233$	0.915882	−	0.182180i	0.0600014	−	0.0119350i	−0.164998	−	0.986294i	$-0.552762\pi$
$233$	0.915882	−	0.182180i	0.0600014	−	0.0119350i	0.225000	+	0.974359i	$0.427762\pi$
$234$	8.96697	+	5.79206i	0.586189	+	0.378639i
$235$	5.98096	−	11.1896i	0.390155	−	0.729928i
$236$	6.42406	+	11.1693i	0.418170	+	0.727060i
$237$	−0.0755908	−	0.767487i	−0.00491015	−	0.0498536i
$238$	2.54041	−	0.290128i	0.164671	−	0.0188062i
$239$	7.97742	−	3.30435i	0.516016	−	0.213741i	−0.109450	−	0.993992i	$-0.534909\pi$
$239$	7.97742	−	3.30435i	0.516016	−	0.213741i	0.625466	+	0.780251i	$0.284909\pi$
$240$	−0.478622	−	0.422542i	−0.0308949	−	0.0272750i
$241$	−3.49320	−	1.44693i	−0.225017	−	0.0932050i	0.267327	−	0.963606i	$-0.413860\pi$
$241$	−3.49320	−	1.44693i	−0.225017	−	0.0932050i	−0.492344	+	0.870401i	$0.663860\pi$
$242$	14.8768	+	4.26156i	0.956314	+	0.273944i
$243$	3.29369	+	2.70306i	0.211290	+	0.173401i
$244$	13.9476	−	4.70894i	0.892906	−	0.301459i
$245$	5.54594	−	1.68234i	0.354317	−	0.107481i
$246$	0.139240	−	0.761670i	0.00887761	−	0.0485623i
$247$	−5.57013	+	8.33629i	−0.354419	+	0.530425i
$248$	17.5905	+	4.45248i	1.11699	+	0.282732i
$249$	−1.21504	+	0.811862i	−0.0769998	+	0.0514496i
$250$	−1.31481	−	0.520831i	−0.0831561	−	0.0329402i
$251$	0.557347	+	0.679129i	0.0351794	+	0.0428662i	0.790303	−	0.612716i	$-0.209923\pi$
$251$	0.557347	+	0.679129i	0.0351794	+	0.0428662i	−0.755124	+	0.655583i	$0.772423\pi$
$252$	−6.44012	−	1.07419i	−0.405690	−	0.0676674i
$253$	0.101513	−	0.0542598i	0.00638206	−	0.00341128i
$254$	−4.30528	−	5.08286i	−0.270137	−	0.318927i
$255$	−0.262946			−0.0164663
$256$	12.6291	+	9.82375i	0.789318	+	0.613984i
$257$	14.1578			0.883136			0.441568	−	0.897228i	$-0.354422\pi$
$257$	14.1578			0.883136			0.441568	+	0.897228i	$0.354422\pi$
$258$	1.25385	+	1.48031i	0.0780614	+	0.0921601i
$259$	6.13933	−	3.28154i	0.381480	−	0.203905i
$260$	5.00616	+	0.835007i	0.310469	+	0.0517850i
$261$	−2.04564	−	2.49261i	−0.126622	−	0.154289i
$262$	7.74666	+	3.06865i	0.478590	+	0.189582i
$263$	0.883844	−	0.590565i	0.0545001	−	0.0364158i	−0.528022	−	0.849231i	$-0.677066\pi$
$263$	0.883844	−	0.590565i	0.0545001	−	0.0364158i	0.582522	+	0.812815i	$0.302066\pi$
$264$	0.0265520	−	0.104899i	0.00163416	−	0.00645611i
$265$	1.28969	−	1.93016i	0.0792250	−	0.118569i
$266$	1.10274	−	6.03219i	0.0676131	−	0.369857i
$267$	0.713699	−	0.216498i	0.0436777	−	0.0132495i
$268$	−7.98944	+	2.69736i	−0.488033	+	0.164767i
$269$	9.67228	+	7.93783i	0.589729	+	0.483978i	0.881291	−	0.472574i	$-0.156675\pi$
$269$	9.67228	+	7.93783i	0.589729	+	0.483978i	−0.291562	+	0.956552i	$0.594175\pi$
$270$	1.29647	+	0.371383i	0.0789004	+	0.0226016i
$271$	21.5009	+	8.90598i	1.30609	+	0.541000i	0.923741	−	0.383019i	$-0.125115\pi$
$271$	21.5009	+	8.90598i	1.30609	+	0.541000i	0.382348	+	0.924018i	$0.375115\pi$
$272$	6.57686	−	0.409278i	0.398781	−	0.0248161i
$273$	−0.410697	+	0.170116i	−0.0248565	+	0.0102959i
$274$	8.83336	−	1.00881i	0.533643	−	0.0609446i
$275$	−0.0234934	−	0.238533i	−0.00141671	−	0.0143841i
$276$	0.0764313	+	0.132889i	0.00460063	+	0.00799897i
$277$	12.0511	−	22.5460i	0.724079	−	1.35466i	−0.202772	−	0.979226i	$-0.564995\pi$
$277$	12.0511	−	22.5460i	0.724079	−	1.35466i	0.926851	−	0.375430i	$-0.122505\pi$
$278$	−5.71498	−	3.69150i	−0.342762	−	0.221401i
$279$	−18.7158	+	3.72280i	−1.12049	+	0.222878i
$280$	−3.01303	+	0.746805i	−0.180063	+	0.0446302i
$281$	0.808882	−	4.06652i	0.0482538	−	0.242588i	−0.949129	−	0.314887i	$-0.898033\pi$
$281$	0.808882	−	4.06652i	0.0482538	−	0.242588i	0.997383	+	0.0722985i	$0.0230334\pi$
$282$	0.0444969	+	2.86361i	0.00264975	+	0.170526i
$283$	0.0627300	−	0.636908i	0.00372891	−	0.0378603i	−0.993140	−	0.116930i	$-0.962695\pi$
$283$	0.0627300	−	0.636908i	0.00372891	−	0.0378603i	0.996869	+	0.0790693i	$0.0251948\pi$
$284$	4.31527	−	1.94665i	0.256064	−	0.115512i
$285$	−0.183057	+	0.603456i	−0.0108433	+	0.0357457i
$286$	0.262458	+	0.819169i	0.0155195	+	0.0484385i
$287$	−2.66203	−	2.66203i	−0.157135	−	0.157135i
$288$	−16.4324	−	3.62007i	−0.968290	−	0.213315i
$289$	−10.1018	+	10.1018i	−0.594223	+	0.594223i
$290$	−1.36313	−	0.701599i	−0.0800457	−	0.0411993i
$291$	2.19723	+	0.666523i	0.128804	+	0.0390722i
$292$	−4.66154	+	4.96064i	−0.272796	+	0.290300i
$293$	5.92857	+	0.583913i	0.346351	+	0.0341126i	0.269697	−	0.962945i	$-0.413076\pi$
$293$	5.92857	+	0.583913i	0.346351	+	0.0341126i	0.0766537	+	0.997058i	$0.475576\pi$
$294$	−0.910551	+	0.939295i	−0.0531044	+	0.0547808i
$295$	−6.31869	−	1.25686i	−0.367888	−	0.0731775i
$296$	16.2368	−	7.63032i	0.943746	−	0.443504i
$297$	0.0445915	+	0.224176i	0.00258746	+	0.0130080i
$298$	22.6390	−	4.87000i	1.31144	−	0.282112i
$299$	−1.07476	−	0.574469i	−0.0621547	−	0.0332224i
$300$	0.316563	−	0.0411451i	0.0182768	−	0.00237551i
$301$	9.38685	−	0.924524i	0.541049	−	0.0532887i
$302$	18.7046	+	14.8702i	1.07633	+	0.855683i
$303$	0.407967	+	0.984921i	0.0234371	+	0.0565822i
$304$	3.63937	−	15.3787i	0.208732	−	0.882031i
$305$	−2.81676	+	6.80026i	−0.161287	+	0.389382i
$306$	−6.06018	+	3.36132i	−0.346438	+	0.192154i
$307$	1.28422	−	1.56483i	0.0732945	−	0.0893097i	−0.735072	−	0.677989i	$-0.762852\pi$
$307$	1.28422	−	1.56483i	0.0732945	−	0.0893097i	0.808367	+	0.588679i	$0.200352\pi$
$308$	−0.346238	−	0.396125i	−0.0197287	−	0.0225713i
$309$	−0.573292	−	1.88989i	−0.0326134	−	0.107512i
$310$	−7.46437	+	5.15706i	−0.423948	+	0.292902i
$311$	16.2518	+	10.8591i	0.921552	+	0.615762i	0.923234	−	0.384237i	$-0.125535\pi$
$311$	16.2518	+	10.8591i	0.921552	+	0.615762i	−0.00168222	+	0.999999i	$0.500535\pi$
$312$	−1.07962	+	0.383282i	−0.0611213	+	0.0216991i
$313$	−3.96974	−	5.94114i	−0.224383	−	0.335813i	0.702148	−	0.712031i	$-0.252224\pi$
$313$	−3.96974	−	5.94114i	−0.224383	−	0.335813i	−0.926531	+	0.376218i	$0.877224\pi$
$314$	2.45572	−	1.06219i	0.138584	−	0.0599428i
$315$	2.52353	−	2.07101i	0.142185	−	0.116688i
$316$	−8.19773	−	5.11645i	−0.461158	−	0.287823i
$317$	−1.08252	−	2.02526i	−0.0608006	−	0.113750i	0.849685	−	0.527290i	$-0.176792\pi$
$317$	−1.08252	−	2.02526i	−0.0608006	−	0.113750i	−0.910486	+	0.413540i	$0.864292\pi$
$318$	−0.0432525	+	0.522209i	−0.00242548	+	0.0292840i
$319$		−	0.259835i		−	0.0145479i
$320$	−7.85391	+	1.52186i	−0.439047	+	0.0850748i
$321$			1.99629i			0.111422i
$322$	0.742819	+	0.0615246i	0.0413957	+	0.00342863i
$323$	−3.06816	−	5.74012i	−0.170717	−	0.319389i
$324$	17.0910	−	3.95534i	0.949500	−	0.219741i
$325$	−1.96164	+	1.60987i	−0.108812	+	0.0892997i
$326$	−1.78289	−	4.12195i	−0.0987453	−	0.228294i
$327$	−1.45617	−	2.17931i	−0.0805261	−	0.120516i
$328$	−6.49774	−	7.20491i	−0.358778	−	0.397825i
$329$	11.5781	+	7.73621i	0.638319	+	0.426511i
$330$	0.0307538	+	0.0445132i	0.00169294	+	0.00245037i
$331$	−3.73652	−	12.3177i	−0.205378	−	0.677040i	−0.997753	−	0.0670055i	$-0.978655\pi$
$331$	−3.73652	−	12.3177i	−0.205378	−	0.677040i	0.792375	−	0.610035i	$-0.208845\pi$
$332$	−1.22772	+	18.2695i	−0.0673801	+	1.00267i
$333$	−11.9691	+	14.5844i	−0.655903	+	0.799220i
$334$	−2.00012	−	3.60605i	−0.109442	−	0.197314i
$335$	1.61349	−	3.89530i	0.0881542	−	0.212823i
$336$	0.512995	−	0.477304i	0.0279862	−	0.0260391i
$337$	−8.03442	−	19.3968i	−0.437663	−	1.05661i	−0.976754	−	0.214364i	$-0.931232\pi$
$337$	−8.03442	−	19.3968i	−0.437663	−	1.05661i	0.539091	−	0.842247i	$-0.318768\pi$
$338$	−5.77354	+	7.26230i	−0.314039	+	0.395017i
$339$	2.05828	−	0.202723i	0.111791	−	0.0110104i
$340$	−2.01005	+	2.61062i	−0.109010	+	0.141581i
$341$	−1.35610	−	0.724850i	−0.0734369	−	0.0392528i
$342$	3.49523	+	16.2481i	0.189000	+	0.878597i
$343$	2.73967	+	13.7732i	0.147928	+	0.743685i
$344$	24.2820	−	1.13266i	1.30920	−	0.0610690i
$345$	−0.0751777	−	0.0149538i	−0.00404743	−	0.000805084i
$346$	16.1171	+	15.6239i	0.866463	+	0.839948i
$347$	11.8470	+	1.16683i	0.635979	+	0.0626385i	0.410868	−	0.911695i	$-0.365226\pi$
$347$	11.8470	+	1.16683i	0.635979	+	0.0626385i	0.225111	+	0.974333i	$0.427726\pi$
$348$	0.345892	−	0.0107520i	0.0185418	−	0.000576370i
$349$	9.40992	+	2.85447i	0.503701	+	0.152796i	0.531902	−	0.846806i	$-0.321478\pi$
$349$	9.40992	+	2.85447i	0.503701	+	0.152796i	−0.0282003	+	0.999602i	$0.508978\pi$
$350$	0.710300	−	1.38003i	0.0379672	−	0.0737660i
$351$	1.71116	−	1.71116i	0.0913347	−	0.0913347i
$352$	−0.838506	−	1.06551i	−0.0446925	−	0.0567917i
$353$	−22.3716	−	22.3716i	−1.19072	−	1.19072i	−0.976865	−	0.213855i	$-0.931398\pi$
$353$	−22.3716	−	22.3716i	−1.19072	−	1.19072i	−0.213855	−	0.976865i	$-0.568602\pi$
$354$	1.38489	−	0.443714i	0.0736063	−	0.0235831i
$355$	−0.687108	+	2.26509i	−0.0364679	+	0.120219i
$356$	3.30630	−	8.74086i	0.175234	−	0.463265i
$357$	0.0282861	−	0.287194i	0.00149706	−	0.0151999i
$358$	14.8590	−	0.230890i	0.785322	−	0.0122029i
$359$	2.11313	−	10.6234i	0.111527	−	0.560682i	−0.884103	−	0.467292i	$-0.845230\pi$
$359$	2.11313	−	10.6234i	0.111527	−	0.560682i	0.995630	−	0.0933898i	$-0.0297703\pi$
$360$	6.76995	−	4.99501i	0.356808	−	0.263260i
$361$	3.32546	−	0.661475i	0.175024	−	0.0348145i
$362$	−2.29448	+	3.55219i	−0.120595	+	0.186699i
$363$	0.823329	−	1.54034i	0.0432135	−	0.0808468i
$364$	−1.45054	+	5.37799i	−0.0760291	+	0.281883i
$365$	−0.333611	−	3.38721i	−0.0174620	−	0.177295i
$366$	−0.188523	−	1.65074i	−0.00985425	−	0.0862857i
$367$	14.9699	−	6.20075i	0.781424	−	0.323676i	0.0439340	−	0.999034i	$-0.486011\pi$
$367$	14.9699	−	6.20075i	0.781424	−	0.323676i	0.737490	+	0.675358i	$0.236011\pi$
$368$	1.90364	+	0.257012i	0.0992340	+	0.0133977i
$369$	9.42660	+	3.90462i	0.490729	+	0.203267i
$370$	−2.47022	+	8.62334i	−0.128421	+	0.448306i
$371$	1.96941	+	1.61626i	0.102247	+	0.0839118i
$372$	0.908805	−	1.83524i	0.0471194	−	0.0951525i
$373$	15.3234	−	4.64830i	0.793416	−	0.240680i	0.132542	−	0.991177i	$-0.457686\pi$
$373$	15.3234	−	4.64830i	0.793416	−	0.240680i	0.660873	+	0.750497i	$0.270186\pi$
$374$	−0.549313	−	0.100419i	−0.0284043	−	0.00519255i
$375$	−0.0886762	+	0.132713i	−0.00457922	+	0.00685329i
$376$	28.7712	+	21.4487i	1.48376	+	1.10613i
$377$	−2.28735	+	1.52836i	−0.117804	+	0.0787143i
$378$	−0.545097	+	1.37607i	−0.0280367	+	0.0707775i
$379$	−15.9735	−	19.4638i	−0.820505	−	0.999788i	−0.999872	−	0.0160056i	$-0.994905\pi$
$379$	−15.9735	−	19.4638i	−0.820505	−	0.999788i	0.179367	−	0.983782i	$-0.442595\pi$
$380$	4.59199	+	6.43049i	0.235564	+	0.329877i
$381$	−0.663028	+	0.354396i	−0.0339680	+	0.0181563i
$382$	−13.0556	+	11.0584i	−0.667984	+	0.565795i
$383$	−10.4880			−0.535913			−0.267957	−	0.963431i	$-0.586348\pi$
$383$	−10.4880			−0.535913			−0.267957	+	0.963431i	$0.586348\pi$
$384$	1.38371	−	1.16031i	0.0706120	−	0.0592119i
$385$	0.263057			0.0134066
$386$	−20.6377	+	17.4805i	−1.05043	+	0.889736i
$387$	−22.5454	+	12.0508i	−1.14605	+	0.612575i
$388$	23.4139	−	16.7198i	1.18866	−	0.848818i
$389$	10.0048	+	12.1909i	0.507266	+	0.618105i	0.962175	−	0.272433i	$-0.0878283\pi$
$389$	10.0048	+	12.1909i	0.507266	+	0.618105i	−0.454909	+	0.890538i	$0.650328\pi$
$390$	0.210959	−	0.532556i	0.0106823	−	0.0269670i
$391$	0.657796	−	0.439525i	0.0332662	−	0.0222278i
$392$	2.36508	+	16.2206i	0.119455	+	0.819264i
$393$	0.522465	−	0.781924i	0.0263549	−	0.0394429i
$394$	−35.2535	−	6.44465i	−1.77605	−	0.324677i
$395$	4.62364	−	1.40257i	0.232641	−	0.0705707i
$396$	1.27782	+	0.632773i	0.0642127	+	0.0317980i
$397$	9.68191	+	7.94573i	0.485921	+	0.398785i	0.845204	−	0.534444i	$-0.179479\pi$
$397$	9.68191	+	7.94573i	0.485921	+	0.398785i	−0.359283	+	0.933229i	$0.616979\pi$
$398$	−2.60577	+	9.09652i	−0.130615	+	0.455967i
$399$	−0.639414	−	0.264854i	−0.0320107	−	0.0132593i
$400$	2.01142	−	3.45748i	0.100571	−	0.172874i
$401$	0.433349	−	0.179499i	0.0216404	−	0.00896376i	−0.371837	−	0.928298i	$-0.621272\pi$
$401$	0.433349	−	0.179499i	0.0216404	−	0.00896376i	0.393477	+	0.919334i	$0.371272\pi$
$402$	0.107989	+	0.945573i	0.00538600	+	0.0471609i
$403$	1.59570	+	16.2015i	0.0794877	+	0.807052i
$404$	12.8973	+	3.47864i	0.641665	+	0.173069i
$405$	−4.13479	+	7.73565i	−0.205459	+	0.384388i
$406$	0.912936	−	1.41336i	0.0453083	−	0.0701438i
$407$	−1.49109	+	0.296597i	−0.0739107	+	0.0147017i
$408$	0.110947	−	0.735401i	0.00549271	−	0.0364078i
$409$	−4.99190	+	25.0960i	−0.246833	+	1.24092i	0.636170	+	0.771549i	$0.280518\pi$
$409$	−4.99190	+	25.0960i	−0.246833	+	1.24092i	−0.883003	+	0.469366i	$0.844482\pi$
$410$	4.85048	−	0.0753703i	0.239548	−	0.00372227i
$411$	0.0983546	−	0.998611i	0.00485147	−	0.0492578i
$412$	−23.1460	−	8.75515i	−1.14032	−	0.431335i
$413$	2.05250	−	6.76617i	0.100997	−	0.332942i
$414$	−1.92380	+	0.616377i	−0.0945496	+	0.0302933i
$415$	−6.47381	−	6.47381i	−0.317787	−	0.317787i
$416$	−4.44763	+	13.6488i	−0.218063	+	0.669187i
$417$	−0.542967	+	0.542967i	−0.0265892	+	0.0265892i
$418$	−0.612878	+	1.19075i	−0.0299769	+	0.0582417i
$419$	−26.4377	−	8.01979i	−1.29157	−	0.391793i	−0.431564	−	0.902082i	$-0.642038\pi$
$419$	−26.4377	−	8.01979i	−1.29157	−	0.391793i	−0.860003	+	0.510290i	$0.829538\pi$
$420$	0.0108854	+	0.350182i	0.000531153	+	0.0170871i
$421$	34.6117	+	3.40895i	1.68687	+	0.166142i	0.895459	−	0.445144i	$-0.146847\pi$
$421$	34.6117	+	3.40895i	1.68687	+	0.166142i	0.791410	+	0.611286i	$0.209347\pi$
$422$	−7.79038	−	7.55198i	−0.379230	−	0.367624i
$423$	−37.0148	−	7.36270i	−1.79972	−	0.357987i
$424$	4.85405	+	4.42138i	0.235733	+	0.214721i
$425$	−0.321391	−	1.61574i	−0.0155898	−	0.0783750i
$426$	−0.112366	−	0.522349i	−0.00544413	−	0.0253079i
$427$	−7.12436	−	3.80805i	−0.344772	−	0.184284i
$428$	19.8199	+	15.2604i	0.958032	+	0.737639i
$429$	0.0966161	−	0.00951586i	0.00466467	−	0.000459430i
$430$	−7.56363	+	9.51397i	−0.364750	+	0.458805i
$431$	7.00225	+	16.9049i	0.337286	+	0.814281i	0.997974	+	0.0636206i	$0.0202647\pi$
$431$	7.00225	+	16.9049i	0.337286	+	0.814281i	−0.660688	+	0.750661i	$0.729735\pi$
$432$	−1.58571	+	3.46923i	−0.0762923	+	0.166913i
$433$	2.89905	−	6.99893i	0.139320	−	0.336347i	−0.838784	−	0.544464i	$-0.816733\pi$
$433$	2.89905	−	6.99893i	0.139320	−	0.336347i	0.978104	+	0.208116i	$0.0667332\pi$
$434$	−4.82966	−	8.70748i	−0.231831	−	0.417973i
$435$	−0.109769	+	0.133754i	−0.00526301	+	0.00641300i
$436$	−32.7684	−	2.20206i	−1.56932	−	0.105460i
$437$	−0.550762	−	1.81562i	−0.0263465	−	0.0868528i
$438$	0.436709	+	0.632095i	0.0208668	+	0.0302027i
$439$	−5.67096	−	3.78922i	−0.270660	−	0.180849i	0.412832	−	0.910807i	$-0.364540\pi$
$439$	−5.67096	−	3.78922i	−0.270660	−	0.180849i	−0.683492	+	0.729958i	$0.739540\pi$
$440$	0.677036	+	0.0349406i	0.0322764	+	0.00166573i
$441$	−9.57737	−	14.3336i	−0.456065	−	0.682550i
$442$	2.34708	+	5.42631i	0.111639	+	0.258103i
$443$	0.0932141	−	0.0764988i	0.00442873	−	0.00363457i	−0.632176	−	0.774825i	$-0.717838\pi$
$443$	0.0932141	−	0.0764988i	0.00442873	−	0.00363457i	0.636605	+	0.771190i	$0.280338\pi$
$444$	−0.456532	−	1.97267i	−0.0216660	−	0.0936188i
$445$	2.20267	+	4.12090i	0.104416	+	0.195349i
$446$	30.7772	+	2.54915i	1.45734	+	0.120706i
$447$		−	2.61356i		−	0.123617i
$448$	−0.817331	−	8.74189i	−0.0386152	−	0.413016i
$449$		−	2.67521i		−	0.126251i	−0.998006	−	0.0631255i	$-0.979893\pi$
$449$		−	2.67521i		−	0.126251i	0.998006	−	0.0631255i	$-0.0201068\pi$
$450$	−0.347228	+	4.19226i	−0.0163685	+	0.197625i
$451$	0.387573	+	0.725098i	0.0182501	+	0.0341435i
$452$	13.7216	−	21.9851i	0.645408	−	1.03409i
$453$	2.08473	−	1.71090i	0.0979493	−	0.0803850i
$454$	−21.8264	+	9.44072i	−1.02437	+	0.443075i
$455$	−1.54731	−	2.31571i	−0.0725391	−	0.108562i
$456$	−1.61049	−	0.766591i	−0.0754183	−	0.0358989i
$457$	29.8613	+	19.9527i	1.39685	+	0.933347i	0.999880	+	0.0155165i	$0.00493927\pi$
$457$	29.8613	+	19.9527i	1.39685	+	0.933347i	0.396973	+	0.917830i	$0.370061\pi$
$458$	−3.05536	+	2.11092i	−0.142768	+	0.0986369i
$459$	0.456030	+	1.50333i	0.0212857	+	0.0701694i
$460$	−0.723152	+	0.632079i	−0.0337171	+	0.0294709i
$461$	−8.69217	+	10.5914i	−0.404835	+	0.493293i	−0.935023	−	0.354587i	$-0.884621\pi$
$461$	−8.69217	+	10.5914i	−0.404835	+	0.493293i	0.530188	+	0.847880i	$0.322121\pi$
$462$	−0.0519264	+	0.0288013i	−0.00241584	+	0.00133996i
$463$	4.50734	−	10.8817i	0.209474	−	0.505715i	−0.783867	−	0.620929i	$-0.786755\pi$
$463$	4.50734	−	10.8817i	0.209474	−	0.505715i	0.993341	+	0.115214i	$0.0367555\pi$
$464$	2.53738	−	3.51634i	0.117795	−	0.163242i
$465$	0.391854	+	0.946020i	0.0181718	+	0.0438706i
$466$	−1.03375	−	0.821836i	−0.0478877	−	0.0380708i
$467$	24.4800	−	2.41107i	1.13280	−	0.111571i	0.485805	−	0.874067i	$-0.338527\pi$
$467$	24.4800	−	2.41107i	1.13280	−	0.111571i	0.646992	+	0.762496i	$0.276027\pi$
$468$	−1.94581	−	14.9707i	−0.0899451	−	0.692022i
$469$	4.08095	+	2.18131i	0.188441	+	0.100724i
$470$	−17.5419	+	3.77354i	−0.809147	+	0.174060i
$471$	−0.0589128	−	0.296175i	−0.00271456	−	0.0136470i
$472$	6.18128	−	17.1416i	0.284516	−	0.789008i
$473$	−2.02036	−	0.401875i	−0.0928964	−	0.0184782i
$474$	−0.759125	+	0.783089i	−0.0348678	+	0.0359685i
$475$	−3.93185	−	0.387253i	−0.180406	−	0.0177684i
$476$	−2.63514	−	2.47625i	−0.120781	−	0.113499i
$477$	−6.60767	−	2.00441i	−0.302544	−	0.0917759i
$478$	−10.8575	−	5.58835i	−0.496612	−	0.255605i
$479$	−8.03951	+	8.03951i	−0.367334	+	0.367334i	−0.866504	−	0.499170i	$-0.833638\pi$
$479$	−8.03951	+	8.03951i	−0.367334	+	0.367334i	0.499170	+	0.866504i	$0.333638\pi$
$480$	−0.0184969	+	0.902718i	−0.000844266	+	0.0412032i
$481$	11.3816	+	11.3816i	0.518957	+	0.518957i
$482$	1.63151	+	5.09218i	0.0743133	+	0.231942i
$483$	0.0244199	−	0.0805017i	0.00111115	−	0.00366296i
$484$	−8.99923	−	19.9492i	−0.409056	−	0.906783i
$485$	−1.41002	+	14.3162i	−0.0640256	+	0.650063i
$486$	−0.0936213	−	6.02503i	−0.00424675	−	0.273301i
$487$	5.03849	−	25.3302i	0.228316	−	1.14782i	−0.681182	−	0.732114i	$-0.738534\pi$
$487$	5.03849	−	25.3302i	0.228316	−	1.14782i	0.909498	−	0.415708i	$-0.136466\pi$
$488$	−17.8303	−	10.7472i	−0.807141	−	0.486501i
$489$	−0.497131	+	0.0988856i	−0.0224811	+	0.00447176i
$490$	−6.88470	−	4.44706i	−0.311019	−	0.200898i
$491$	15.5317	−	29.0577i	0.700935	−	1.31136i	−0.239338	−	0.970936i	$-0.576930\pi$
$491$	15.5317	−	29.0577i	0.700935	−	1.31136i	0.940273	−	0.340421i	$-0.110570\pi$
$492$	−0.949213	+	0.545942i	−0.0427938	+	0.0246130i
$493$	−0.175046	−	1.77727i	−0.00788368	−	0.0800443i
$494$	14.0873	−	1.60884i	0.633817	−	0.0723850i
$495$	−0.658684	+	0.272836i	−0.0296057	+	0.0122631i
$496$	−11.2736	−	23.0522i	−0.506202	−	1.03507i
$497$	−2.40006	−	0.994136i	−0.107657	−	0.0445931i
$498$	1.98670	+	0.569106i	0.0890263	+	0.0255023i
$499$	−11.8235	−	9.70327i	−0.529291	−	0.434378i	0.331411	−	0.943486i	$-0.392475\pi$
$499$	−11.8235	−	9.70327i	−0.529291	−	0.434378i	−0.860702	+	0.509108i	$0.829975\pi$
$500$	0.639753	+	1.89492i	0.0286106	+	0.0847433i
$501$	−0.445363	+	0.135099i	−0.0198974	+	0.00603580i
$502$	0.223429	−	1.22220i	0.00997214	−	0.0545496i
$503$	−16.5052	+	24.7018i	−0.735930	+	1.10140i	0.254989	+	0.966944i	$0.417928\pi$
$503$	−16.5052	+	24.7018i	−0.735930	+	1.10140i	−0.990920	+	0.134454i	$0.957072\pi$
$504$	4.72737	+	7.93159i	0.210574	+	0.353301i
$505$	−5.55347	+	3.71071i	−0.247126	+	0.165124i
$506$	−0.151341	−	0.0599499i	−0.00672792	−	0.00266510i
$507$	0.664277	+	0.809424i	0.0295016	+	0.0359478i
$508$	−1.54986	+	9.29192i	−0.0687638	+	0.412262i
$509$	−27.6371	+	14.7724i	−1.22499	+	0.654773i	−0.951662	−	0.307146i	$-0.900626\pi$
$509$	−27.6371	+	14.7724i	−1.22499	+	0.654773i	−0.273332	+	0.961920i	$0.588126\pi$
$510$	0.240344	+	0.283753i	0.0106426	+	0.0125648i
$511$	3.73546			0.165247
$512$	−0.942441	−	22.6078i	−0.0416504	−	0.999132i
$513$	3.76760			0.166343
$514$	−12.9408	−	15.2781i	−0.570795	−	0.673887i
$515$	10.9122	−	5.83271i	0.480850	−	0.257020i
$516$	0.451373	−	2.70614i	0.0198706	−	0.119131i
$517$	−1.92924	−	2.35079i	−0.0848481	−	0.103388i
$518$	−9.15283	−	3.62567i	−0.402152	−	0.159303i
$519$	2.10649	−	1.40751i	0.0924645	−	0.0617828i
$520$	−3.67477	−	6.16553i	−0.161149	−	0.270376i
$521$	−23.0088	+	34.4351i	−1.00803	+	1.50863i	−0.154227	+	0.988035i	$0.549289\pi$
$521$	−23.0088	+	34.4351i	−1.00803	+	1.50863i	−0.853805	+	0.520592i	$0.825711\pi$
$522$	−0.820055	+	4.48587i	−0.0358929	+	0.196341i
$523$	40.1500	−	12.1794i	1.75564	−	0.532566i	0.762238	−	0.647296i	$-0.224100\pi$
$523$	40.1500	−	12.1794i	1.75564	−	0.532566i	0.993397	+	0.114730i	$0.0366004\pi$
$524$	−3.76932	−	11.1645i	−0.164663	−	0.487725i
$525$	−0.135413	−	0.111130i	−0.00590989	−	0.00485012i
$526$	−1.44517	−	0.413980i	−0.0630124	−	0.0180504i
$527$	−9.76406	−	4.04441i	−0.425329	−	0.176177i
$528$	−0.137470	+	0.0672296i	−0.00598261	+	0.00292579i
$529$	−21.0362	+	8.71347i	−0.914616	+	0.378846i
$530$	−3.26172	+	0.372505i	−0.141680	+	0.0161806i
$531$	1.87833	+	19.0710i	0.0815126	+	0.827612i
$532$	−7.51747	+	4.32369i	−0.325924	+	0.187456i
$533$	4.10338	−	7.67689i	0.177737	−	0.332523i
$534$	−0.885982	−	0.572286i	−0.0383402	−	0.0247652i
$535$	−12.2668	+	2.44001i	−0.530339	+	0.105491i
$536$	10.2135	+	6.15615i	0.441156	+	0.265905i
$537$	0.327213	−	1.64501i	0.0141203	−	0.0709874i
$538$	−0.274929	−	17.6932i	−0.0118531	−	0.762807i
$539$	0.136156	−	1.38241i	0.00586465	−	0.0595448i
$540$	−0.784257	−	1.73852i	−0.0337490	−	0.0748138i
$541$	5.18385	−	17.0889i	0.222871	−	0.734708i	−0.772185	−	0.635397i	$-0.780836\pi$
$541$	5.18385	−	17.0889i	0.222871	−	0.734708i	0.995057	−	0.0993104i	$-0.0316637\pi$
$542$	−10.0421	−	31.3428i	−0.431345	−	1.34629i
$543$	0.337485	+	0.337485i	0.0144829	+	0.0144829i
$544$	−6.45321	−	6.72320i	−0.276679	−	0.288255i
$545$	11.6115	−	11.6115i	0.497382	−	0.497382i
$546$	0.558974	+	0.287702i	0.0239219	+	0.0123125i
$547$	−24.3695	−	7.39241i	−1.04197	−	0.316077i	−0.277489	−	0.960729i	$-0.589502\pi$
$547$	−24.3695	−	7.39241i	−1.04197	−	0.316077i	−0.764476	+	0.644652i	$0.777002\pi$
$548$	−9.16272	−	8.61025i	−0.391412	−	0.367811i
$549$	21.7887	+	2.14600i	0.929919	+	0.0915891i
$550$	−0.235934	+	0.243382i	−0.0100603	+	0.0103778i
$551$	−4.20068	−	0.835567i	−0.178955	−	0.0355963i
$552$	0.0735428	−	0.203946i	0.00313019	−	0.00868050i
$553$	1.03452	+	5.20090i	0.0439924	+	0.221165i
$554$	−35.3453	+	7.60333i	−1.50168	+	0.323034i
$555$	0.892861	+	0.477244i	0.0378998	+	0.0202579i
$556$	1.24014	+	9.54141i	0.0525935	+	0.404646i
$557$	−20.5756	+	2.02652i	−0.871816	+	0.0858663i	−0.524022	−	0.851705i	$-0.675569\pi$
$557$	−20.5756	+	2.02652i	−0.871816	+	0.0858663i	−0.347794	+	0.937571i	$0.613069\pi$
$558$	21.1245	+	16.7940i	0.894270	+	0.710946i
$559$	8.34610	+	20.1493i	0.353002	+	0.852223i
$560$	3.55995	+	2.56884i	0.150435	+	0.108553i
$561$	−0.0241185	+	0.0582272i	−0.00101828	+	0.00245836i
$562$	−5.12766	+	2.84409i	−0.216297	+	0.119971i
$563$	−15.1751	+	18.4910i	−0.639556	+	0.779301i	−0.987399	−	0.158252i	$-0.949414\pi$
$563$	−15.1751	+	18.4910i	−0.639556	+	0.779301i	0.347843	+	0.937553i	$0.386914\pi$
$564$	3.04954	−	2.66549i	0.128409	−	0.112237i
$565$	3.76147	+	12.3999i	0.158246	+	0.521668i
$566$	−0.744645	+	0.514468i	−0.0312998	+	0.0216247i
$567$	−8.00422	−	5.34825i	−0.336146	−	0.224605i
$568$	−6.04504	−	2.87742i	−0.253644	−	0.120734i
$569$	9.79143	+	14.6539i	0.410478	+	0.614324i	0.977892	−	0.209109i	$-0.0670562\pi$
$569$	9.79143	+	14.6539i	0.410478	+	0.614324i	−0.567414	+	0.823432i	$0.692056\pi$
$570$	0.818530	−	0.354044i	0.0342845	−	0.0148293i
$571$	−34.2968	+	28.1466i	−1.43527	+	1.17790i	−0.481855	+	0.876251i	$0.660037\pi$
$571$	−34.2968	+	28.1466i	−1.43527	+	1.17790i	−0.953419	+	0.301648i	$0.902463\pi$
$572$	0.644092	−	1.03198i	0.0269308	−	0.0431494i
$573$	0.910286	+	1.70303i	0.0380278	+	0.0711449i
$574$	−0.439465	+	5.30589i	−0.0183429	+	0.221463i
$575$		−	0.480227i		−	0.0200269i
$576$	11.1134	+	21.0416i	0.463059	+	0.876735i
$577$		−	26.1501i		−	1.08864i	−0.838876	−	0.544322i	$-0.816787\pi$
$577$		−	26.1501i		−	1.08864i	0.838876	−	0.544322i	$-0.183213\pi$
$578$	20.1346	+	1.66767i	0.837490	+	0.0693659i
$579$	1.43894	+	2.69206i	0.0598002	+	0.111878i
$580$	0.488843	+	2.11229i	0.0202981	+	0.0877079i
$581$	7.76722	−	6.37440i	0.322239	−	0.264454i
$582$	−1.28910	−	2.98033i	−0.0534349	−	0.123539i
$583$	−0.309122	−	0.462634i	−0.0128025	−	0.0191603i
$584$	9.61404	+	0.496162i	0.397832	+	0.0205313i
$585$	6.27620	+	4.19363i	0.259489	+	0.173385i
$586$	−4.78886	−	6.93143i	−0.197826	−	0.286335i
$587$	−3.48150	−	11.4770i	−0.143697	−	0.473705i	0.855317	−	0.518105i	$-0.173362\pi$
$587$	−3.48150	−	11.4770i	−0.143697	−	0.473705i	−0.999014	+	0.0444003i	$0.985862\pi$
$588$	1.84591	+	0.124046i	0.0761239	+	0.00511558i
$589$	−16.0794	+	19.5927i	−0.662538	+	0.807305i
$590$	4.41924	+	7.96752i	0.181937	+	0.328018i
$591$	−1.54787	+	3.73688i	−0.0636708	+	0.153715i
$592$	−23.0753	−	10.5472i	−0.948388	−	0.433487i
$593$	−4.12219	−	9.95185i	−0.169278	−	0.408673i	0.816360	−	0.577543i	$-0.195988\pi$
$593$	−4.12219	−	9.95185i	−0.169278	−	0.408673i	−0.985638	+	0.168869i	$0.945988\pi$
$594$	0.201157	−	0.253027i	0.00825358	−	0.0103818i
$595$	1.79931	−	0.177217i	0.0737647	−	0.00726519i
$596$	−25.9484	−	19.9790i	−1.06289	−	0.818372i
$597$	0.941853	+	0.503431i	0.0385475	+	0.0206041i
$598$	0.362447	+	1.68489i	0.0148216	+	0.0689004i
$599$	−0.592379	−	2.97809i	−0.0242039	−	0.121681i	0.966794	−	0.255555i	$-0.0822583\pi$
$599$	−0.592379	−	2.97809i	−0.0242039	−	0.121681i	−0.990998	+	0.133874i	$0.957258\pi$
$600$	−0.333754	−	0.304005i	−0.0136254	−	0.0124109i
$601$	28.8961	+	5.74780i	1.17870	+	0.234457i	0.745290	−	0.666741i	$-0.232311\pi$
$601$	28.8961	+	5.74780i	1.17870	+	0.234457i	0.433407	+	0.901198i	$0.357311\pi$
$602$	−9.57768	−	9.28458i	−0.390357	−	0.378411i
$603$	−12.4809	−	1.22926i	−0.508263	−	0.0500595i
$604$	−1.04995	−	33.7767i	−0.0427218	−	1.37436i
$605$	10.4714	+	3.17645i	0.425722	+	0.129141i
$606$	0.689958	−	1.34051i	0.0280276	−	0.0544545i
$607$	−18.9930	+	18.9930i	−0.770901	+	0.770901i	−0.978264	−	0.207363i	$-0.933512\pi$
$607$	−18.9930	+	18.9930i	−0.770901	+	0.770901i	0.207363	+	0.978264i	$0.433512\pi$
$608$	−19.9222	+	10.1295i	−0.807952	+	0.410805i
$609$	−0.134280	−	0.134280i	−0.00544129	−	0.00544129i
$610$	9.91302	−	3.17609i	0.401366	−	0.128596i
$611$	−9.34633	+	30.8107i	−0.378112	+	1.24647i
$612$	9.16658	+	3.46733i	0.370537	+	0.140159i
$613$	−2.05231	+	20.8374i	−0.0828920	+	0.841616i	0.860393	+	0.509631i	$0.170218\pi$
$613$	−2.05231	+	20.8374i	−0.0828920	+	0.841616i	−0.943285	+	0.331985i	$0.892282\pi$
$614$	−2.86250	+	0.0444795i	−0.115521	+	0.00179505i
$615$	0.106813	−	0.536988i	0.00430713	−	0.0216534i
$616$	−0.110994	+	0.735712i	−0.00447209	+	0.0296427i
$617$	18.1953	−	3.61927i	0.732514	−	0.145706i	0.185280	−	0.982686i	$-0.440681\pi$
$617$	18.1953	−	3.61927i	0.732514	−	0.145706i	0.547234	+	0.836980i	$0.315681\pi$
$618$	−1.51542	+	2.34610i	−0.0609593	+	0.0943740i
$619$	10.1782	−	19.0422i	0.409098	−	0.765369i	−0.590019	−	0.807390i	$-0.700880\pi$
$619$	10.1782	−	19.0422i	0.409098	−	0.765369i	0.999117	+	0.0420208i	$0.0133796\pi$
$620$	12.3879	+	3.34125i	0.497511	+	0.134188i
$621$	0.0448870	+	0.455745i	0.00180125	+	0.0182884i
$622$	−3.13646	−	27.4634i	−0.125761	−	1.10118i
$623$	−4.73787	+	1.96249i	−0.189819	+	0.0786255i
$624$	1.40043	+	0.814712i	0.0560621	+	0.0326146i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−2.78274	+	9.71433i	−0.111221	+	0.388263i
$627$	0.116840	+	0.0958880i	0.00466613	+	0.00382940i
$628$	−3.39088	−	1.67916i	−0.135311	−	0.0670057i
$629$	−9.99928	+	3.03325i	−0.398697	+	0.120944i
$630$	−4.54150	−	0.830226i	−0.180938	−	0.0330770i
$631$	−12.4836	+	18.6830i	−0.496963	+	0.743757i	−0.992153	−	0.125027i	$-0.960098\pi$
$631$	−12.4836	+	18.6830i	−0.496963	+	0.743757i	0.495191	+	0.868784i	$0.335098\pi$
$632$	1.97177	+	13.5231i	0.0784327	+	0.537920i
$633$	−1.01819	+	0.680333i	−0.0404694	+	0.0270408i
$634$	−1.19605	+	3.01936i	−0.0475010	+	0.119914i
$635$	−2.98808	−	3.64099i	−0.118579	−	0.144488i
$636$	0.603067	−	0.430647i	0.0239132	−	0.0170763i
$637$	−12.9704	+	6.93282i	−0.513906	+	0.274688i
$638$	−0.280396	+	0.237500i	−0.0111010	+	0.00940273i
$639$	7.04074			0.278527
$640$	8.82111	+	7.08435i	0.348685	+	0.280033i
$641$	15.4033			0.608395			0.304198	−	0.952609i	$-0.401612\pi$
$641$	15.4033			0.608395			0.304198	+	0.952609i	$0.401612\pi$
$642$	2.15426	−	1.82470i	0.0850219	−	0.0720152i
$643$	5.63839	−	3.01378i	0.222356	−	0.118852i	−0.356458	−	0.934311i	$-0.616016\pi$
$643$	5.63839	−	3.01378i	0.222356	−	0.118852i	0.578814	+	0.815460i	$0.303516\pi$
$644$	−0.612576	−	0.857835i	−0.0241389	−	0.0338034i
$645$	0.870237	+	1.06039i	0.0342655	+	0.0417527i
$646$	−3.38991	+	8.55767i	−0.133374	+	0.336697i
$647$	39.3927	−	26.3214i	1.54869	−	1.03480i	0.571969	−	0.820275i	$-0.306180\pi$
$647$	39.3927	−	26.3214i	1.54869	−	1.03480i	0.976719	−	0.214525i	$-0.0688203\pi$
$648$	−19.8903	−	14.8281i	−0.781363	−	0.582502i
$649$	−0.857900	+	1.28394i	−0.0336755	+	0.0503989i
$650$	3.53029	+	0.645367i	0.138469	+	0.0253134i
$651$	−1.07541	+	0.326223i	−0.0421488	+	0.0127857i
$652$	−2.81848	+	5.69162i	−0.110380	+	0.222901i
$653$	20.1732	+	16.5557i	0.789437	+	0.647874i	0.940172	−	0.340700i	$-0.110664\pi$
$653$	20.1732	+	16.5557i	0.789437	+	0.647874i	−0.150735	+	0.988574i	$0.548164\pi$
$654$	−1.02076	+	3.56337i	−0.0399147	+	0.139339i
$655$	5.44334	+	2.25471i	0.212689	+	0.0880986i
$656$	−1.83582	+	13.5975i	−0.0716766	+	0.530894i
$657$	−9.35343	+	3.87432i	−0.364912	+	0.151152i
$658$	−2.23447	−	19.5655i	−0.0871089	−	0.762742i
$659$	−0.211536	−	2.14776i	−0.00824028	−	0.0836649i	0.990185	−	0.139763i	$-0.0446341\pi$
$659$	−0.211536	−	2.14776i	−0.00824028	−	0.0836649i	−0.998425	+	0.0560980i	$0.982134\pi$
$660$	0.0199253	−	0.0738744i	0.000775590	−	0.00287556i
$661$	−0.877608	+	1.64189i	−0.0341350	+	0.0638621i	−0.898411	−	0.439157i	$-0.855277\pi$
$661$	−0.877608	+	1.64189i	−0.0341350	+	0.0638621i	0.864276	+	0.503019i	$0.167777\pi$
$662$	−9.87703	+	15.2911i	−0.383882	+	0.594305i
$663$	0.654445	−	0.130177i	0.0254165	−	0.00505567i
$664$	20.8374	−	15.3743i	0.808647	−	0.596637i
$665$	0.845929	−	4.25277i	0.0328037	−	0.164916i
$666$	26.6788	−	0.414554i	1.03378	−	0.0160636i
$667$	0.0510271	−	0.518087i	0.00197578	−	0.0200604i
$668$	−2.06320	+	5.45448i	−0.0798277	+	0.211040i
$669$	1.01179	−	3.33543i	0.0391182	−	0.128955i
$670$	−5.67834	+	1.81931i	−0.219373	+	0.0702863i
$671$	1.24750	+	1.24750i	0.0481591	+	0.0481591i
$672$	−0.983974	−	0.117312i	−0.0379576	−	0.00452540i
$673$	18.7489	−	18.7489i	0.722717	−	0.722717i	−0.246441	−	0.969158i	$-0.579261\pi$
$673$	18.7489	−	18.7489i	0.722717	−	0.722717i	0.969158	+	0.246441i	$0.0792611\pi$
$674$	−13.5879	+	26.3997i	−0.523385	+	1.01688i
$675$	0.912549	+	0.276819i	0.0351240	+	0.0106548i
$676$	13.1142	−	0.407656i	0.504394	−	0.0156791i
$677$	−22.7780	−	2.24343i	−0.875428	−	0.0862221i	−0.349687	−	0.936867i	$-0.613712\pi$
$677$	−22.7780	−	2.24343i	−0.875428	−	0.0862221i	−0.525741	+	0.850644i	$0.676212\pi$
$678$	−2.10013	−	2.03586i	−0.0806549	−	0.0781867i
$679$	−15.4847	−	3.08009i	−0.594247	−	0.118203i
$680$	4.65448	−	0.217114i	0.178491	−	0.00832593i
$681$	0.523616	+	2.63240i	0.0200650	+	0.100874i
$682$	0.457327	+	2.12595i	0.0175119	+	0.0814070i
$683$	6.28676	+	3.36034i	0.240556	+	0.128580i	0.587270	−	0.809391i	$-0.300203\pi$
$683$	6.28676	+	3.36034i	0.240556	+	0.128580i	−0.346714	+	0.937971i	$0.612703\pi$
$684$	14.3390	−	18.6233i	0.548267	−	0.712079i
$685$	6.25645	−	0.616207i	0.239047	−	0.0235441i
$686$	12.3590	−	15.5458i	0.471867	−	0.593542i
$687$	0.160396	+	0.387231i	0.00611950	+	0.0147738i
$688$	−23.4171	−	25.1681i	−0.892768	−	0.959525i
$689$	−2.25434	+	5.44245i	−0.0858834	+	0.207341i
$690$	0.0525786	+	0.0947949i	0.00200163	+	0.00360878i
$691$	−27.3716	+	33.3523i	−1.04126	+	1.26878i	−0.0789388	+	0.996879i	$0.525153\pi$
$691$	−27.3716	+	33.3523i	−1.04126	+	1.26878i	−0.962325	+	0.271904i	$0.912347\pi$
$692$	2.12848	−	31.6735i	0.0809127	−	1.20404i
$693$	−0.227139	−	0.748777i	−0.00862830	−	0.0284437i
$694$	−9.56951	−	13.8510i	−0.363254	−	0.525776i
$695$	−4.00006	−	2.67275i	−0.151731	−	0.101383i
$696$	−0.327764	−	0.363435i	−0.0124238	−	0.0137760i
$697$	3.13949	+	4.69858i	0.118917	+	0.177971i
$698$	−5.52074	−	12.7636i	−0.208963	−	0.483111i
$699$	−0.115218	+	0.0945567i	−0.00435793	+	0.00357646i
$700$	−2.13848	+	0.494906i	−0.0808271	+	0.0187057i
$701$	−20.0393	−	37.4910i	−0.756875	−	1.41601i	−0.904281	−	0.426938i	$-0.859592\pi$
$701$	−20.0393	−	37.4910i	−0.756875	−	1.41601i	0.147405	−	0.989076i	$-0.452908\pi$
$702$	−3.41063	−	0.282489i	−0.128726	−	0.0106619i
$703$			25.0599i			0.945151i
$704$	−0.383390	+	1.87878i	−0.0144495	+	0.0708091i
$705$			2.02513i			0.0762707i
$706$	−3.69325	+	44.5905i	−0.138997	+	1.67819i
$707$	−3.45549	−	6.46477i	−0.129957	−	0.243133i
$708$	−1.74468	−	1.08891i	−0.0655691	−	0.0409236i
$709$	36.2453	−	29.7457i	1.36122	−	1.11712i	0.379839	−	0.925053i	$-0.375980\pi$
$709$	36.2453	−	29.7457i	1.36122	−	1.11712i	0.981381	−	0.192071i	$-0.0615205\pi$
$710$	3.07238	−	1.32891i	0.115304	−	0.0498733i
$711$	−7.98464	−	11.9499i	−0.299447	−	0.448155i
$712$	−12.4546	+	4.42160i	−0.466757	+	0.165706i
$713$	−2.56159	−	1.71160i	−0.0959324	−	0.0641000i
$714$	−0.335775	+	0.231984i	−0.0125660	+	0.00868176i
$715$	0.176564	+	0.582053i	0.00660312	+	0.0217676i
$716$	−13.8309	−	15.8237i	−0.516886	−	0.591361i
$717$	−0.874326	+	1.06537i	−0.0326523	+	0.0397870i
$718$	−13.3955	+	7.42992i	−0.499917	+	0.277282i
$719$	16.8091	−	40.5806i	0.626872	−	1.51340i	−0.216618	−	0.976257i	$-0.569502\pi$
$719$	16.8091	−	40.5806i	0.626872	−	1.51340i	0.843489	−	0.537146i	$-0.180498\pi$
$720$	−11.5783	−	2.74000i	−0.431498	−	0.102114i
$721$	5.19671	+	12.5460i	0.193536	+	0.467236i
$722$	−3.75343	−	2.98399i	−0.139688	−	0.111053i
$723$	0.600592	−	0.0591532i	0.0223363	−	0.00219993i
$724$	5.93054	−	0.770818i	0.220407	−	0.0286472i
$725$	−0.956053	−	0.511021i	−0.0355069	−	0.0189789i
$726$	−2.41479	+	0.519459i	−0.0896211	+	0.0192789i
$727$	−1.67291	−	8.41030i	−0.0620449	−	0.311921i	0.937283	−	0.348568i	$-0.113332\pi$
$727$	−1.67291	−	8.41030i	−0.0620449	−	0.311921i	−0.999328	+	0.0366475i	$0.988332\pi$
$728$	7.12941	−	3.35039i	0.264234	−	0.124174i
$729$	25.1414	+	5.00095i	0.931165	+	0.185220i
$730$	−3.35031	+	3.45607i	−0.124000	+	0.127915i
$731$	−14.0900	−	1.38775i	−0.521139	−	0.0513277i
$732$	−1.60905	+	1.71229i	−0.0594722	+	0.0632882i
$733$	20.1823	+	6.12222i	0.745449	+	0.226129i	0.640085	−	0.768304i	$-0.278899\pi$
$733$	20.1823	+	6.12222i	0.745449	+	0.226129i	0.105364	+	0.994434i	$0.466399\pi$
$734$	−20.3746	−	10.4868i	−0.752040	−	0.387073i
$735$	−0.654098	+	0.654098i	−0.0241268	+	0.0241268i
$736$	−1.46266	−	2.28919i	−0.0539143	−	0.0843808i
$737$	−0.714588	−	0.714588i	−0.0263222	−	0.0263222i
$738$	−4.40273	−	13.7415i	−0.162067	−	0.505833i
$739$	12.8599	−	42.3936i	0.473061	−	1.55947i	−0.318218	−	0.948017i	$-0.603085\pi$
$739$	12.8599	−	42.3936i	0.473061	−	1.55947i	0.791279	−	0.611455i	$-0.209415\pi$
$740$	11.5636	−	5.21642i	0.425087	−	0.191759i
$741$	0.156854	−	1.59257i	0.00576219	−	0.0585044i
$742$	−0.0559795	−	3.60258i	−0.00205507	−	0.132255i
$743$	0.874137	−	4.39458i	0.0320690	−	0.161222i	−0.961432	−	0.275041i	$-0.911309\pi$
$743$	0.874137	−	4.39458i	0.0320690	−	0.161222i	0.993501	+	0.113819i	$0.0363086\pi$
$744$	−2.81115	+	0.696766i	−0.103062	+	0.0255447i
$745$	16.0597	−	3.19448i	0.588383	−	0.117037i
$746$	−19.0224	−	12.2872i	−0.696459	−	0.449866i
$747$	−12.8375	+	24.0172i	−0.469698	+	0.878743i
$748$	0.393731	+	0.684567i	0.0143962	+	0.0250303i
$749$	−1.34544	−	13.6605i	−0.0491612	−	0.499142i
$750$	0.224269	−	0.0256126i	0.00818914	−	0.000935240i
$751$	34.3490	−	14.2278i	1.25341	−	0.519181i	0.345531	−	0.938407i	$-0.387699\pi$
$751$	34.3490	−	14.2278i	1.25341	−	0.519181i	0.907882	+	0.419227i	$0.137699\pi$
$752$	−3.15213	−	50.6529i	−0.114947	−	1.84712i
$753$	−0.129554	−	0.0536629i	−0.00472120	−	0.00195559i
$754$	3.74003	+	1.07136i	0.136204	+	0.0390167i
$755$	13.0612	+	10.7190i	0.475345	+	0.390106i
$756$	1.98320	−	0.669560i	0.0721284	−	0.0243516i
$757$	16.6069	−	5.03765i	0.603588	−	0.183096i	0.0263232	−	0.999653i	$-0.491620\pi$
$757$	16.6069	−	5.03765i	0.603588	−	0.183096i	0.577265	+	0.816557i	$0.304120\pi$
$758$	−6.40347	+	35.0283i	−0.232585	+	1.27228i
$759$	−0.0102070	+	0.0152759i	−0.000370491	+	0.000554479i
$760$	2.74206	−	10.8331i	0.0994651	−	0.392958i
$761$	−40.2815	+	26.9153i	−1.46020	+	0.975677i	−0.464261	+	0.885699i	$0.653680\pi$
$761$	−40.2815	+	26.9153i	−1.46020	+	0.975677i	−0.995944	+	0.0899789i	$0.971320\pi$
$762$	0.988477	+	0.391561i	0.0358087	+	0.0141847i
$763$	11.4332	+	13.9314i	0.413909	+	0.504350i
$764$	23.8668	+	3.98089i	0.863471	+	0.144024i
$765$	−4.32161	+	2.30995i	−0.156248	+	0.0835163i
$766$	9.58652	+	11.3180i	0.346375	+	0.408934i
$767$	16.3488			0.590321
$768$	−2.51690	−	0.432624i	−0.0908207	−	0.0156110i
$769$	12.8880			0.464755			0.232377	−	0.972626i	$-0.425350\pi$
$769$	12.8880			0.464755			0.232377	+	0.972626i	$0.425350\pi$
$770$	−0.240446	−	0.283873i	−0.00866507	−	0.0102301i
$771$	−1.99293	+	1.06524i	−0.0717736	+	0.0383638i
$772$	37.7276	+	6.29281i	1.35784	+	0.226483i
$773$	7.06408	+	8.60761i	0.254077	+	0.309594i	0.884391	−	0.466746i	$-0.154574\pi$
$773$	7.06408	+	8.60761i	0.254077	+	0.309594i	−0.630314	+	0.776340i	$0.717074\pi$
$774$	33.6118	+	13.3145i	1.20815	+	0.478580i
$775$	−5.33413	+	3.56415i	−0.191608	+	0.128028i
$776$	−39.4442	−	9.98406i	−1.41596	−	0.358407i
$777$	−0.617303	+	0.923859i	−0.0221456	+	0.0331433i
$778$	4.01074	−	21.9396i	0.143792	−	0.786572i
$779$	12.9688	−	3.93404i	0.464656	−	0.140952i
$780$	−0.767524	+	0.259128i	−0.0274818	+	0.00927826i
$781$	0.438562	+	0.359918i	0.0156930	+	0.0128789i
$782$	−1.07556	−	0.308102i	−0.0384619	−	0.0110177i
$783$	0.955078	+	0.395606i	0.0341317	+	0.0141378i
$784$	15.3424	−	17.3786i	0.547941	−	0.620664i
$785$	1.74792	−	0.724012i	0.0623859	−	0.0258411i
$786$	−1.32135	+	0.150905i	−0.0471312	+	0.00538261i
$787$	0.138878	+	1.41005i	0.00495046	+	0.0502629i	0.997343	−	0.0728544i	$-0.0232109\pi$
$787$	0.138878	+	1.41005i	0.00495046	+	0.0502629i	−0.992392	+	0.123117i	$0.960711\pi$
$788$	25.2687	+	43.9339i	0.900159	+	1.56508i
$789$	−0.0799804	+	0.149633i	−0.00284738	+	0.00532707i
$790$	−5.73976	−	3.70750i	−0.204212	−	0.131907i
$791$	−13.9480	+	2.77443i	−0.495935	+	0.0986475i
$792$	−0.485137	−	1.95731i	−0.0172386	−	0.0695501i
$793$	3.64401	−	18.3197i	0.129403	−	0.650550i
$794$	−0.275203	−	17.7108i	−0.00976659	−	0.628533i
$795$	−0.0363175	+	0.368738i	−0.00128805	+	0.0130778i
$796$	12.1981	−	5.50265i	0.432351	−	0.195036i
$797$	−2.07996	+	6.85670i	−0.0736759	+	0.242877i	−0.986042	−	0.166499i	$-0.946754\pi$
$797$	−2.07996	+	6.85670i	−0.0736759	+	0.242877i	0.912366	+	0.409376i	$0.134254\pi$
$798$	0.298640	+	0.932099i	0.0105718	+	0.0329959i
$799$	−14.7797	−	14.7797i	−0.522870	−	0.522870i
$800$	−5.56960	+	0.989706i	−0.196915	+	0.0349914i
$801$	9.82799	−	9.82799i	0.347255	−	0.347255i
$802$	−0.589803	−	0.303570i	−0.0208267	−	0.0107194i
$803$	−0.780671	−	0.236814i	−0.0275493	−	0.00835698i
$804$	0.921690	−	0.980830i	0.0325055	−	0.0345912i
$805$	0.524513	+	0.0516600i	0.0184866	+	0.00182078i
$806$	16.0249	−	16.5308i	0.564454	−	0.582273i
$807$	−1.95878	−	0.389625i	−0.0689523	−	0.0137155i
$808$	−8.03480	−	17.0975i	−0.282663	−	0.601488i
$809$	10.3105	+	51.8344i	0.362498	+	1.82240i	0.544091	+	0.839026i	$0.316875\pi$
$809$	10.3105	+	51.8344i	0.362498	+	1.82240i	−0.181593	+	0.983374i	$0.558125\pi$
$810$	12.1272	−	2.60875i	0.426105	−	0.0916620i
$811$	−30.4539	−	16.2780i	−1.06938	−	0.571597i	−0.159813	−	0.987147i	$-0.551089\pi$
$811$	−30.4539	−	16.2780i	−1.06938	−	0.571597i	−0.909570	+	0.415550i	$0.863589\pi$
$812$	−2.35966	+	0.306696i	−0.0828080	+	0.0107629i
$813$	−3.69670	+	0.364093i	−0.129649	+	0.0127693i
$814$	1.68299	+	1.33798i	0.0589888	+	0.0468962i
$815$	−1.21526	−	2.93390i	−0.0425687	−	0.102770i
$816$	−0.895004	+	0.552462i	−0.0313314	+	0.0193400i
$817$	−12.9940	+	31.3703i	−0.454603	+	1.09751i
$818$	31.6446	−	17.5519i	1.10643	−	0.613688i
$819$	−5.25551	+	6.40385i	−0.183642	+	0.223769i
$820$	−4.51489	−	5.16541i	−0.157667	−	0.180384i
$821$	3.13916	+	10.3484i	0.109557	+	0.361162i	0.994526	−	0.104488i	$-0.0333204\pi$
$821$	3.13916	+	10.3484i	0.109557	+	0.361162i	−0.884969	+	0.465650i	$0.845820\pi$
$822$	−1.16753	+	0.806637i	−0.0407224	+	0.0281347i
$823$	26.6444	+	17.8032i	0.928764	+	0.620580i	0.925227	−	0.379414i	$-0.123874\pi$
$823$	26.6444	+	17.8032i	0.928764	+	0.620580i	0.00353662	+	0.999994i	$0.498874\pi$
$824$	11.7085	+	32.9801i	0.407884	+	1.14892i
$825$	0.0212545	+	0.0318097i	0.000739988	+	0.00110747i
$826$	−9.17766	+	3.96967i	−0.319332	+	0.138122i
$827$	−26.3575	+	21.6311i	−0.916542	+	0.752186i	−0.969161	−	0.246428i	$-0.920743\pi$
$827$	−26.3575	+	21.6311i	−0.916542	+	0.752186i	0.0526193	+	0.998615i	$0.483243\pi$
$828$	2.42359	+	1.51264i	0.0842255	+	0.0525677i
$829$	−13.1982	−	24.6922i	−0.458394	−	0.857594i	−0.999858	−	0.0168704i	$-0.994630\pi$
$829$	−13.1982	−	24.6922i	−0.458394	−	0.857594i	0.541464	−	0.840724i	$-0.317870\pi$
$830$	−1.06874	+	12.9034i	−0.0370965	+	0.447885i
$831$			4.08044i			0.141549i
$832$	18.7942	−	7.67602i	0.651570	−	0.266118i
$833$		−	9.54747i		−	0.330800i
$834$	1.08223	+	0.0896365i	0.0374745	+	0.00310386i
$835$	−1.37451	−	2.57153i	−0.0475669	−	0.0889914i
$836$	1.84518	−	0.427026i	0.0638168	−	0.0147690i
$837$	4.72905	−	3.88103i	0.163460	−	0.134148i
$838$	15.5108	+	35.8602i	0.535813	+	1.23877i
$839$	−20.4396	−	30.5900i	−0.705652	−	1.05608i	−0.995099	−	0.0988886i	$-0.968471\pi$
$839$	−20.4396	−	30.5900i	−0.705652	−	1.05608i	0.289447	−	0.957194i	$-0.406529\pi$
$840$	0.367942	−	0.331829i	0.0126952	−	0.0114492i
$841$	23.1355	+	15.4586i	0.797776	+	0.533057i
$842$	−27.9579	−	40.4664i	−0.963492	−	1.39457i
$843$	0.192106	+	0.633289i	0.00661649	+	0.0218116i
$844$	−1.02882	+	15.3097i	−0.0354135	+	0.526981i
$845$	−4.16180	+	5.07117i	−0.143170	+	0.174454i
$846$	25.8878	+	46.6736i	0.890042	+	1.60467i
$847$	−4.59583	+	11.0953i	−0.157914	+	0.381239i
$848$	0.334437	−	9.27949i	0.0114846	−	0.318659i
$849$	0.0390914	+	0.0943749i	0.00134161	+	0.00323894i
$850$	−1.44983	+	1.82368i	−0.0497288	+	0.0625518i
$851$	−3.03135	+	0.298562i	−0.103913	+	0.0102346i
$852$	−0.460976	+	0.598707i	−0.0157928	+	0.0205114i
$853$	−16.9829	−	9.07755i	−0.581484	−	0.310809i	0.154302	−	0.988024i	$-0.450687\pi$
$853$	−16.9829	−	9.07755i	−0.581484	−	0.310809i	−0.735786	+	0.677214i	$0.763187\pi$
$854$	2.40259	+	11.1688i	0.0822151	+	0.382190i
$855$	2.29269	+	11.5262i	0.0784085	+	0.394186i
$856$	−1.64834	−	35.3370i	−0.0563389	−	1.20779i
$857$	−30.5577	−	6.07830i	−1.04383	−	0.207631i	−0.356740	−	0.934204i	$-0.616112\pi$
$857$	−30.5577	−	6.07830i	−1.04383	−	0.207631i	−0.687089	+	0.726573i	$0.741112\pi$
$858$	−0.0985803	−	0.0955635i	−0.00336547	−	0.00326248i
$859$	−26.0937	−	2.57001i	−0.890306	−	0.0876875i	−0.357488	−	0.933918i	$-0.616367\pi$
$859$	−26.0937	−	2.57001i	−0.890306	−	0.0876875i	−0.532818	+	0.846230i	$0.678867\pi$
$860$	17.1803	−	0.534049i	0.585844	−	0.0182109i
$861$	0.575017	+	0.174429i	0.0195965	+	0.00594454i
$862$	11.8423	−	23.0082i	0.403349	−	0.783662i
$863$	−2.44711	+	2.44711i	−0.0833005	+	0.0833005i	−0.747529	−	0.664229i	$-0.768760\pi$
$863$	−2.44711	+	2.44711i	−0.0833005	+	0.0833005i	0.664229	+	0.747529i	$0.268760\pi$
$864$	5.19315	−	1.45984i	0.176675	−	0.0496649i
$865$	11.2235	+	11.2235i	0.381611	+	0.381611i
$866$	−10.2026	+	3.26888i	−0.346699	+	0.111081i
$867$	0.661920	−	2.18206i	0.0224800	−	0.0741066i
$868$	−4.98199	+	13.1709i	−0.169100	+	0.447048i
$869$	0.113513	−	1.15252i	0.00385067	−	0.0390965i
$870$	0.244671	−	0.00380188i	0.00829513	−	0.000128896i
$871$	−2.08735	+	10.4938i	−0.0707271	+	0.355569i
$872$	27.5755	+	37.3742i	0.933823	+	1.26565i
$873$	41.9676	−	8.34787i	1.42039	−	0.282533i
$874$	−1.45587	+	2.25390i	−0.0492455	+	0.0762393i
$875$	0.517359	−	0.967911i	0.0174899	−	0.0327214i
$876$	0.282942	−	1.04903i	0.00955974	−	0.0354434i
$877$	−1.03090	−	10.4669i	−0.0348111	−	0.353443i	−0.996774	−	0.0802622i	$-0.974424\pi$
$877$	−1.03090	−	10.4669i	−0.0348111	−	0.353443i	0.961963	−	0.273181i	$-0.0880758\pi$
$878$	1.09445	+	9.58322i	0.0369359	+	0.323418i
$879$	−0.878476	+	0.363877i	−0.0296303	+	0.0122733i
$880$	−0.581136	−	0.762548i	−0.0195901	−	0.0257055i
$881$	13.8705	+	5.74533i	0.467308	+	0.193565i	0.603897	−	0.797063i	$-0.293614\pi$
$881$	13.8705	+	5.74533i	0.467308	+	0.193565i	−0.136589	+	0.990628i	$0.543614\pi$
$882$	−6.71364	+	23.4367i	−0.226060	+	0.789156i
$883$	34.1580	+	28.0328i	1.14951	+	0.943377i	0.998977	−	0.0452280i	$-0.0144014\pi$
$883$	34.1580	+	28.0328i	1.14951	+	0.943377i	0.150532	+	0.988605i	$0.451901\pi$
$884$	3.71037	−	7.49269i	0.124793	−	0.252007i
$885$	0.984024	−	0.298500i	0.0330776	−	0.0100340i
$886$	−0.167754	−	0.0306669i	−0.00563581	−	0.00103027i
$887$	3.33434	−	4.99019i	0.111956	−	0.167554i	−0.771260	−	0.636520i	$-0.780373\pi$
$887$	3.33434	−	4.99019i	0.111956	−	0.167554i	0.883216	+	0.468966i	$0.155373\pi$
$888$	−1.71148	+	2.29577i	−0.0574335	+	0.0770408i
$889$	4.29820	−	2.87196i	0.144157	−	0.0963225i
$890$	2.43365	−	6.14365i	0.0815763	−	0.205936i
$891$	1.33374	+	1.62516i	0.0446819	+	0.0544450i
$892$	−25.3809	−	35.5427i	−0.849815	−	1.19006i
$893$	−44.2086	+	23.6300i	−1.47938	+	0.790748i
$894$	−2.82037	+	2.38891i	−0.0943274	+	0.0798971i
$895$	10.5082			0.351249
$896$	−8.68657	+	8.87248i	−0.290198	+	0.296409i
$897$	0.194513			0.00649459
$898$	−2.88690	+	2.44526i	−0.0963372	+	0.0815994i
$899$	−6.13337	+	3.27835i	−0.204559	+	0.109339i
$900$	4.84137	−	3.45720i	0.161379	−	0.115240i
$901$	−2.42607	−	2.95617i	−0.0808240	−	0.0984843i
$902$	0.428217	−	1.08101i	0.0142581	−	0.0359938i
$903$	−1.25179	+	0.836418i	−0.0416569	+	0.0278342i
$904$	−36.2669	+	5.28798i	−1.20622	+	0.175876i
$905$	−1.66127	+	2.48627i	−0.0552226	+	0.0826464i
$906$	−3.75182	−	0.685865i	−0.124646	−	0.0227863i
$907$	14.6442	−	4.44228i	0.486254	−	0.147503i	−0.0376327	−	0.999292i	$-0.511982\pi$
$907$	14.6442	−	4.44228i	0.486254	−	0.147503i	0.523886	+	0.851788i	$0.324482\pi$
$908$	30.1381	+	14.9243i	1.00017	+	0.495282i
$909$	15.3575	+	12.6036i	0.509376	+	0.418034i
$910$	−1.08465	+	3.78642i	−0.0359557	+	0.125518i
$911$	40.6461	+	16.8362i	1.34666	+	0.557807i	0.935362	−	0.353692i	$-0.115074\pi$
$911$	40.6461	+	16.8362i	1.34666	+	0.557807i	0.411303	+	0.911499i	$0.365074\pi$
$912$	0.644812	+	2.43863i	0.0213519	+	0.0807512i
$913$	−2.02738	+	0.839768i	−0.0670965	+	0.0277923i
$914$	−5.76299	−	50.4619i	−0.190623	−	1.66913i
$915$	−0.115154	−	1.16918i	−0.00380689	−	0.0386520i
$916$	5.07070	+	1.36766i	0.167541	+	0.0451888i
$917$	−3.04819	+	5.70276i	−0.100660	+	0.188322i
$918$	1.20546	−	1.86623i	0.0397860	−	0.0615946i
$919$	49.7530	−	9.89649i	1.64120	−	0.326455i	0.713750	−	0.700400i	$-0.246995\pi$
$919$	49.7530	−	9.89649i	1.64120	−	0.326455i	0.927451	+	0.373945i	$0.121995\pi$
$920$	1.34309	+	0.202627i	0.0442803	+	0.00668041i
$921$	−0.0630356	+	0.316901i	−0.00207709	+	0.0104423i
$922$	19.3746	−	0.301056i	0.638068	−	0.00991476i
$923$	0.588757	−	5.97775i	0.0193792	−	0.196760i
$924$	0.0785434	+	0.0297097i	0.00258389	+	0.000977378i
$925$	−1.84124	+	6.06975i	−0.0605395	+	0.199572i
$926$	−15.8627	+	5.08233i	−0.521280	+	0.167016i
$927$	−26.0247	−	26.0247i	−0.854764	−	0.854764i
$928$	−6.11386	+	0.475927i	−0.200697	+	0.0156231i
$929$	−22.7510	+	22.7510i	−0.746438	+	0.746438i	−0.973808	−	0.227371i	$-0.926987\pi$
$929$	−22.7510	+	22.7510i	−0.746438	+	0.746438i	0.227371	+	0.973808i	$0.426987\pi$
$930$	0.662707	−	1.28757i	0.0217310	−	0.0422210i
$931$	−21.9113	−	6.64672i	−0.718113	−	0.217837i
$932$	0.0580278	+	1.86675i	0.00190076	+	0.0611474i
$933$	−3.10474	−	0.305790i	−0.101645	−	0.0100111i
$934$	−24.9776	−	24.2133i	−0.817293	−	0.792282i
$935$	−0.387272	−	0.0770333i	−0.0126652	−	0.00251926i
$936$	−14.3768	+	15.7837i	−0.469921	+	0.515906i
$937$	3.92947	+	19.7548i	0.128370	+	0.645360i	0.990369	+	0.138450i	$0.0442122\pi$
$937$	3.92947	+	19.7548i	0.128370	+	0.645360i	−0.861999	+	0.506909i	$0.830788\pi$
$938$	−1.37625	−	6.39769i	−0.0449360	−	0.208892i
$939$	1.00582	+	0.537623i	0.0328237	+	0.0175447i
$940$	20.1062	+	15.4808i	0.655792	+	0.504928i
$941$	16.8425	−	1.65884i	0.549048	−	0.0540765i	0.180310	−	0.983610i	$-0.442290\pi$
$941$	16.8425	−	1.65884i	0.549048	−	0.0540765i	0.368738	+	0.929533i	$0.379790\pi$
$942$	−0.265762	+	0.334291i	−0.00865900	+	0.0108918i
$943$	0.630389	+	1.52189i	0.0205283	+	0.0495597i
$944$	−24.1480	+	8.99781i	−0.785951	+	0.292854i
$945$	−0.400513	+	0.966924i	−0.0130287	+	0.0314540i
$946$	1.41302	+	2.54757i	0.0459414	+	0.0828285i
$947$	−7.96569	+	9.70622i	−0.258850	+	0.315410i	−0.886178	−	0.463346i	$-0.846649\pi$
$947$	−7.96569	+	9.70622i	−0.258850	+	0.315410i	0.627327	+	0.778756i	$0.284149\pi$
$948$	1.53893	+	0.103417i	0.0499821	+	0.00335883i
$949$	2.50724	+	8.26526i	0.0813884	+	0.268302i
$950$	3.17599	+	4.59694i	0.103043	+	0.149145i
$951$	0.304765	+	0.203638i	0.00988269	+	0.00660340i
$952$	−0.263566	+	5.10706i	−0.00854221	+	0.165521i
$953$	−25.7362	−	38.5170i	−0.833678	−	1.24769i	−0.966531	−	0.256551i	$-0.917414\pi$
$953$	−25.7362	−	38.5170i	−0.833678	−	1.24769i	0.132853	−	0.991136i	$-0.457586\pi$
$954$	3.87668	+	8.96266i	0.125512	+	0.290177i
$955$	−9.35209	+	7.67506i	−0.302627	+	0.248359i
$956$	3.89371	+	16.8247i	0.125932	+	0.544150i
$957$	0.0195502	+	0.0365759i	0.000631969	+	0.00118233i
$958$	16.0241	+	1.32721i	0.517717	+	0.0428803i
$959$			6.89970i			0.222803i
$960$	0.991057	−	0.805163i	0.0319862	−	0.0259865i
$961$			10.1561i			0.327615i
$962$	1.87895	−	22.6856i	0.0605799	−	0.731412i
$963$	17.5372	+	32.8098i	0.565128	+	1.05728i
$964$	4.00385	−	6.41509i	0.128955	−	0.206616i
$965$	−14.7834	+	12.1324i	−0.475893	+	0.390555i
$966$	−0.109193	+	0.0472298i	−0.00351322	+	0.00151960i
$967$	25.5686	+	38.2661i	0.822231	+	1.23056i	0.970378	+	0.241591i	$0.0776692\pi$
$967$	25.5686	+	38.2661i	0.822231	+	1.23056i	−0.148147	+	0.988965i	$0.547331\pi$
$968$	−13.3021	+	27.9458i	−0.427546	+	0.898213i
$969$	0.863785	+	0.577162i	0.0277488	+	0.0185411i
$970$	16.7378	−	11.5640i	0.537419	−	0.371298i
$971$	14.1002	+	46.4821i	0.452497	+	1.49168i	0.825794	+	0.563971i	$0.190727\pi$
$971$	14.1002	+	46.4821i	0.452497	+	1.49168i	−0.373297	+	0.927712i	$0.621773\pi$
$972$	−6.41623	+	5.60818i	−0.205801	+	0.179882i
$973$	3.34953	−	4.08142i	0.107381	−	0.130844i
$974$	−31.9400	+	17.7157i	−1.02342	+	0.567649i
$975$	0.155003	−	0.374211i	0.00496408	−	0.0119843i
$976$	4.70012	+	29.0646i	0.150447	+	0.930336i
$977$	4.13680	+	9.98712i	0.132348	+	0.319516i	0.976136	−	0.217160i	$-0.0696795\pi$
$977$	4.13680	+	9.98712i	0.132348	+	0.319516i	−0.843788	+	0.536677i	$0.819679\pi$
$978$	0.561111	+	0.446084i	0.0179423	+	0.0142642i
$979$	1.11458	−	0.109776i	0.0356221	−	0.00350847i
$980$	1.49396	+	11.4943i	0.0477229	+	0.367172i
$981$	−43.0775	−	23.0254i	−1.37536	−	0.735145i
$982$	−45.5537	+	9.79934i	−1.45368	+	0.312709i
$983$	−11.7325	−	58.9831i	−0.374208	−	1.88127i	−0.464855	−	0.885387i	$-0.653894\pi$
$983$	−11.7325	−	58.9831i	−0.374208	−	1.88127i	0.0906477	−	0.995883i	$-0.471106\pi$
$984$	1.45677	+	0.525310i	0.0464400	+	0.0167463i
$985$	−24.8542	−	4.94381i	−0.791921	−	0.157523i
$986$	−1.75791	+	1.81340i	−0.0559833	+	0.0577505i
$987$	−2.21188	−	0.217851i	−0.0704049	−	0.00693427i
$988$	−14.6125	−	13.7315i	−0.464887	−	0.436856i
$989$	−3.94950	−	1.19807i	−0.125587	−	0.0380964i
$990$	0.896493	+	0.461422i	0.0284924	+	0.0146650i
$991$	26.6641	−	26.6641i	0.847013	−	0.847013i	−0.142746	−	0.989759i	$-0.545593\pi$
$991$	26.6641	−	26.6641i	0.847013	−	0.847013i	0.989759	+	0.142746i	$0.0455933\pi$
$992$	−14.5717	+	33.2364i	−0.462651	+	1.05526i
$993$	1.45277	+	1.45277i	0.0461022	+	0.0461022i
$994$	1.12096	+	3.49866i	0.0355545	+	0.110971i
$995$	−1.94227	+	6.40280i	−0.0615741	+	0.202983i
$996$	−1.20179	−	2.66410i	−0.0380803	−	0.0844152i
$997$	3.97769	−	40.3862i	0.125975	−	1.27904i	−0.699511	−	0.714621i	$-0.746599\pi$
$997$	3.97769	−	40.3862i	0.125975	−	1.27904i	0.825486	−	0.564422i	$-0.190901\pi$
$998$	0.336076	+	21.6283i	0.0106383	+	0.684631i
$999$	1.18003	−	5.93241i	0.0373345	−	0.187693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.18	✓	1024
128.109	even	32	inner	640.2.bm.a.621.18	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.18	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.18	yes	1024	128.109	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.914044 - 1.07913i) q^{2} +(-0.140766 + 0.0752410i) q^{3} +(-0.329046 + 1.97275i) q^{4} +(-0.634393 - 0.773010i) q^{5} +(0.209861 + 0.0831313i) q^{6} +(0.912540 - 0.609740i) q^{7} +(2.42961 - 1.44809i) q^{8} +(-1.65256 + 2.47323i) q^{9} +(-0.254316 + 1.39116i) q^{10} +(-0.229366 + 0.0695775i) q^{11} +(-0.102113 - 0.302453i) q^{12} +(1.96164 + 1.60987i) q^{13} +(-1.49209 - 0.427421i) q^{14} +(0.147463 + 0.0610812i) q^{15} +(-3.78346 - 1.29825i) q^{16} +(-1.52200 + 0.630431i) q^{17} +(4.17944 - 0.477313i) q^{18} +(0.387253 + 3.93185i) q^{19} +(1.73370 - 0.997141i) q^{20} +(-0.0825772 + 0.154491i) q^{21} +(0.284734 + 0.183919i) q^{22} +(-0.471000 + 0.0936877i) q^{23} +(-0.233051 + 0.386649i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.0557585 - 3.58836i) q^{26} +(0.0934702 - 0.949019i) q^{27} +(0.902594 + 2.00084i) q^{28} +(-0.314685 + 1.03738i) q^{29} +(-0.0688732 - 0.214963i) q^{30} +(4.53630 + 4.53630i) q^{31} +(2.05727 + 5.26950i) q^{32} +(0.0270519 - 0.0270519i) q^{33} +(2.07149 + 1.06619i) q^{34} +(-1.05024 - 0.318588i) q^{35} +(-4.33528 - 4.07388i) q^{36} +(6.31233 + 0.621710i) q^{37} +(3.88901 - 4.01178i) q^{38} +(-0.397260 - 0.0790200i) q^{39} +(-2.66072 - 0.959457i) q^{40} +(-0.669203 - 3.36431i) q^{41} +(0.242195 - 0.0521001i) q^{42} +(7.57950 + 4.05133i) q^{43} +(-0.0617866 - 0.475376i) q^{44} +(2.96020 - 0.291554i) q^{45} +(0.531616 + 0.422636i) q^{46} +(4.85538 + 11.7219i) q^{47} +(0.630264 - 0.101922i) q^{48} +(-2.21784 + 5.35433i) q^{49} +(1.23672 - 0.685953i) q^{50} +(0.166811 - 0.203260i) q^{51} +(-3.82134 + 3.34009i) q^{52} +(0.673861 + 2.22142i) q^{53} +(-1.10955 + 0.766579i) q^{54} +(0.199293 + 0.133163i) q^{55} +(1.33416 - 2.80287i) q^{56} +(-0.350348 - 0.524333i) q^{57} +(1.40710 - 0.608623i) q^{58} +(4.98010 - 4.08706i) q^{59} +(-0.169020 + 0.270809i) q^{60} +(-3.46974 - 6.49143i) q^{61} +(0.748883 - 9.04164i) q^{62} +3.26455i q^{63} +(3.80605 - 7.03662i) q^{64} -2.53766i q^{65} +(-0.0539192 - 0.00446590i) q^{66} +(1.98752 + 3.71840i) q^{67} +(-0.742874 - 3.20995i) q^{68} +(0.0592516 - 0.0486266i) q^{69} +(0.616171 + 1.42455i) q^{70} +(-1.31504 - 1.96810i) q^{71} +(-0.433613 + 8.40204i) q^{72} +(2.82999 + 1.89094i) q^{73} +(-5.09884 - 7.38010i) q^{74} +(-0.0463332 - 0.152740i) q^{75} +(-7.88396 - 0.529808i) q^{76} +(-0.166882 + 0.203346i) q^{77} +(0.277841 + 0.500924i) q^{78} +(-1.84901 + 4.46390i) q^{79} +(1.39664 + 3.74825i) q^{80} +(-3.35666 - 8.10368i) q^{81} +(-3.01885 + 3.79729i) q^{82} +(9.11127 - 0.897381i) q^{83} +(-0.277600 - 0.213739i) q^{84} +(1.45287 + 0.776577i) q^{85} +(-2.55609 - 11.8824i) q^{86} +(-0.0337564 - 0.169705i) q^{87} +(-0.456517 + 0.501190i) q^{88} +(-4.58286 - 0.911587i) q^{89} +(-3.02038 - 2.92795i) q^{90} +(2.77168 + 0.272986i) q^{91} +(-0.0298413 - 0.959991i) q^{92} +(-0.979873 - 0.297241i) q^{93} +(8.21147 - 15.9540i) q^{94} +(2.79369 - 2.79369i) q^{95} +(-0.686076 - 0.586976i) q^{96} +(-10.1720 - 10.1720i) q^{97} +(7.80523 - 2.50076i) q^{98} +(0.206960 - 0.682255i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more