LMFDB - Embedded newform 640.2.bm.a.341.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			341.28
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.299966 - 1.38203i) q^{2} +(1.24334 - 1.51502i) q^{3} +(-1.82004 + 0.829128i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-2.46677 - 1.26389i) q^{6} +(-3.15235 - 0.627042i) q^{7} +(1.69183 + 2.26665i) q^{8} +(-0.164108 - 0.825025i) q^{9} +O(q^{10})$	\(q+(-0.299966 - 1.38203i) q^{2} +(1.24334 - 1.51502i) q^{3} +(-1.82004 + 0.829128i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-2.46677 - 1.26389i) q^{6} +(-3.15235 - 0.627042i) q^{7} +(1.69183 + 2.26665i) q^{8} +(-0.164108 - 0.825025i) q^{9} +(0.688233 + 1.23545i) q^{10} +(-1.65165 - 0.162673i) q^{11} +(-1.00679 + 3.78829i) q^{12} +(-0.324442 + 1.06954i) q^{13} +(0.0790057 + 4.54475i) q^{14} +(-0.750019 + 1.81071i) q^{15} +(2.62509 - 3.01809i) q^{16} +(-3.01647 - 7.28240i) q^{17} +(-1.09099 + 0.474282i) q^{18} +(-5.54337 + 2.96299i) q^{19} +(1.50099 - 1.32176i) q^{20} +(-4.86944 + 3.99625i) q^{21} +(0.270618 + 2.33143i) q^{22} +(-4.69814 + 7.03127i) q^{23} +(5.53755 + 0.255064i) q^{24} +(0.831470 - 0.555570i) q^{25} +(1.57546 + 0.127564i) q^{26} +(3.73145 + 1.99450i) q^{27} +(6.25731 - 1.47246i) q^{28} +(0.474107 + 4.81369i) q^{29} +(2.72744 + 0.493402i) q^{30} +(4.56452 + 4.56452i) q^{31} +(-4.95855 - 2.72265i) q^{32} +(-2.30002 + 2.30002i) q^{33} +(-9.15969 + 6.35333i) q^{34} +(3.19863 - 0.315038i) q^{35} +(0.982733 + 1.36551i) q^{36} +(2.53133 - 4.73578i) q^{37} +(5.75778 + 6.77233i) q^{38} +(1.21698 + 1.82134i) q^{39} +(-2.27696 - 1.67793i) q^{40} +(-8.89347 - 5.94243i) q^{41} +(6.98362 + 5.53100i) q^{42} +(-3.35466 - 4.08766i) q^{43} +(3.14094 - 1.07335i) q^{44} +(0.396533 + 0.741861i) q^{45} +(11.1267 + 4.38386i) q^{46} +(3.29444 - 1.36460i) q^{47} +(-1.30857 - 7.72960i) q^{48} +(3.07699 + 1.27453i) q^{49} +(-1.01723 - 0.982468i) q^{50} +(-14.7835 - 4.48452i) q^{51} +(-0.296289 - 2.21561i) q^{52} +(0.820378 - 8.32944i) q^{53} +(1.63716 - 5.75527i) q^{54} +(1.62775 - 0.323779i) q^{55} +(-3.91197 - 8.20613i) q^{56} +(-2.40332 + 12.0823i) q^{57} +(6.51047 - 2.09918i) q^{58} +(0.273393 + 0.901255i) q^{59} +(-0.136241 - 3.91742i) q^{60} +(-10.4416 - 8.56924i) q^{61} +(4.93912 - 7.67753i) q^{62} +2.70367i q^{63} +(-2.27540 + 7.66959i) q^{64} -1.11767i q^{65} +(3.86863 + 2.48878i) q^{66} +(0.658052 + 0.540050i) q^{67} +(11.5281 + 10.7532i) q^{68} +(4.81110 + 15.8601i) q^{69} +(-1.39488 - 4.32612i) q^{70} +(-1.43269 + 7.20264i) q^{71} +(1.59240 - 1.76778i) q^{72} +(8.68694 - 1.72794i) q^{73} +(-7.30433 - 2.07781i) q^{74} +(0.192103 - 1.95046i) q^{75} +(7.63246 - 9.98893i) q^{76} +(5.10457 + 1.54845i) q^{77} +(2.15211 - 2.22825i) q^{78} +(0.257484 + 0.106653i) q^{79} +(-1.63595 + 3.65016i) q^{80} +(9.99265 - 4.13909i) q^{81} +(-5.54490 + 14.0736i) q^{82} +(-3.97218 - 7.43142i) q^{83} +(5.54918 - 11.3107i) q^{84} +(5.00055 + 6.09318i) q^{85} +(-4.64301 + 5.86241i) q^{86} +(7.88230 + 5.26679i) q^{87} +(-2.42559 - 4.01892i) q^{88} +(-7.19185 - 10.7634i) q^{89} +(0.906332 - 0.770556i) q^{90} +(1.69340 - 3.16813i) q^{91} +(2.72099 - 16.6926i) q^{92} +(12.5906 - 1.24007i) q^{93} +(-2.87415 - 4.14370i) q^{94} +(4.44456 - 4.44456i) q^{95} +(-10.2900 + 4.12711i) q^{96} +(6.13377 + 6.13377i) q^{97} +(0.838454 - 4.63483i) q^{98} +(0.136838 + 1.38934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

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 $

$2$	−0.299966	−	1.38203i	−0.212108	−	0.977246i
$2$	−0.299966	−	1.38203i	−0.212108	−	0.977246i
$3$	1.24334	−	1.51502i	0.717845	−	0.874697i	−0.278472	−	0.960444i	$-0.589828\pi$
$3$	1.24334	−	1.51502i	0.717845	−	0.874697i	0.996317	+	0.0857477i	$0.0273279\pi$
$4$	−1.82004	+	0.829128i	−0.910020	+	0.414564i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$6$	−2.46677	−	1.26389i	−1.00705	−	0.515981i
$7$	−3.15235	−	0.627042i	−1.19148	−	0.237000i	−0.440761	−	0.897624i	$-0.645291\pi$
$7$	−3.15235	−	0.627042i	−1.19148	−	0.237000i	−0.750716	+	0.660625i	$0.770291\pi$
$8$	1.69183	+	2.26665i	0.598154	+	0.801381i
$9$	−0.164108	−	0.825025i	−0.0547025	−	0.275008i
$10$	0.688233	+	1.23545i	0.217638	+	0.390683i
$11$	−1.65165	−	0.162673i	−0.497990	−	0.0490477i	−0.154095	−	0.988056i	$-0.549246\pi$
$11$	−1.65165	−	0.162673i	−0.497990	−	0.0490477i	−0.343895	+	0.939008i	$0.611746\pi$
$12$	−1.00679	+	3.78829i	−0.290636	+	1.09358i
$13$	−0.324442	+	1.06954i	−0.0899839	+	0.296637i	−0.990368	−	0.138458i	$-0.955785\pi$
$13$	−0.324442	+	1.06954i	−0.0899839	+	0.296637i	0.900384	+	0.435095i	$0.143285\pi$
$14$	0.0790057	+	4.54475i	0.0211152	+	1.21464i
$15$	−0.750019	+	1.81071i	−0.193654	+	0.467522i
$16$	2.62509	−	3.01809i	0.656274	−	0.754523i
$17$	−3.01647	−	7.28240i	−0.731601	−	1.76624i	−0.637190	−	0.770707i	$-0.719903\pi$
$17$	−3.01647	−	7.28240i	−0.731601	−	1.76624i	−0.0944109	−	0.995533i	$-0.530097\pi$
$18$	−1.09099	+	0.474282i	−0.257148	+	0.111789i
$19$	−5.54337	+	2.96299i	−1.27174	+	0.679757i	−0.962514	−	0.271233i	$-0.912569\pi$
$19$	−5.54337	+	2.96299i	−1.27174	+	0.679757i	−0.309222	+	0.950990i	$0.600069\pi$
$20$	1.50099	−	1.32176i	0.335631	−	0.295554i
$21$	−4.86944	+	3.99625i	−1.06260	+	0.872053i
$22$	0.270618	+	2.33143i	0.0576960	+	0.497062i
$23$	−4.69814	+	7.03127i	−0.979631	+	1.46612i	−0.0974331	+	0.995242i	$0.531063\pi$
$23$	−4.69814	+	7.03127i	−0.979631	+	1.46612i	−0.882198	+	0.470879i	$0.843937\pi$
$24$	5.53755	+	0.255064i	1.13035	+	0.0520647i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	1.57546	+	0.127564i	0.308974	+	0.0250173i
$27$	3.73145	+	1.99450i	0.718118	+	0.383842i
$28$	6.25731	−	1.47246i	1.18252	−	0.278269i
$29$	0.474107	+	4.81369i	0.0880394	+	0.893879i	0.933198	+	0.359363i	$0.117006\pi$
$29$	0.474107	+	4.81369i	0.0880394	+	0.893879i	−0.845158	+	0.534516i	$0.820494\pi$
$30$	2.72744	+	0.493402i	0.497960	+	0.0900824i
$31$	4.56452	+	4.56452i	0.819812	+	0.819812i	0.986081	−	0.166268i	$-0.0531718\pi$
$31$	4.56452	+	4.56452i	0.819812	+	0.819812i	−0.166268	+	0.986081i	$0.553172\pi$
$32$	−4.95855	−	2.72265i	−0.876556	−	0.481300i
$33$	−2.30002	+	2.30002i	−0.400382	+	0.400382i
$34$	−9.15969	+	6.35333i	−1.57087	+	1.08959i
$35$	3.19863	−	0.315038i	0.540668	−	0.0532511i
$36$	0.982733	+	1.36551i	0.163789	+	0.227585i
$37$	2.53133	−	4.73578i	0.416148	−	0.778558i	−0.583284	−	0.812268i	$-0.698232\pi$
$37$	2.53133	−	4.73578i	0.416148	−	0.778558i	0.999432	+	0.0337106i	$0.0107325\pi$
$38$	5.75778	+	6.77233i	0.934036	+	1.09862i
$39$	1.21698	+	1.82134i	0.194873	+	0.291648i
$40$	−2.27696	−	1.67793i	−0.360019	−	0.265305i
$41$	−8.89347	−	5.94243i	−1.38893	−	0.928051i	−0.999977	−	0.00679192i	$-0.997838\pi$
$41$	−8.89347	−	5.94243i	−1.38893	−	0.928051i	−0.388950	−	0.921259i	$-0.627162\pi$
$42$	6.98362	+	5.53100i	1.07760	+	0.853451i
$43$	−3.35466	−	4.08766i	−0.511580	−	0.623362i	0.451599	−	0.892221i	$-0.350854\pi$
$43$	−3.35466	−	4.08766i	−0.511580	−	0.623362i	−0.963180	+	0.268858i	$0.913354\pi$
$44$	3.14094	−	1.07335i	0.473514	−	0.161814i
$45$	0.396533	+	0.741861i	0.0591117	+	0.110590i
$46$	11.1267	+	4.38386i	1.64055	+	0.646364i
$47$	3.29444	−	1.36460i	0.480543	−	0.199048i	−0.129244	−	0.991613i	$-0.541255\pi$
$47$	3.29444	−	1.36460i	0.480543	−	0.199048i	0.609787	+	0.792565i	$0.291255\pi$
$48$	−1.30857	−	7.72960i	−0.188876	−	1.11567i
$49$	3.07699	+	1.27453i	0.439570	+	0.182076i
$50$	−1.01723	−	0.982468i	−0.143858	−	0.138942i
$51$	−14.7835	−	4.48452i	−2.07010	−	0.627958i
$52$	−0.296289	−	2.21561i	−0.0410879	−	0.307250i
$53$	0.820378	−	8.32944i	0.112688	−	1.14414i	−0.757985	−	0.652272i	$-0.773816\pi$
$53$	0.820378	−	8.32944i	0.112688	−	1.14414i	0.870672	−	0.491864i	$-0.163684\pi$
$54$	1.63716	−	5.75527i	0.222789	−	0.783194i
$55$	1.62775	−	0.323779i	0.219485	−	0.0436584i
$56$	−3.91197	−	8.20613i	−0.522760	−	1.09659i
$57$	−2.40332	+	12.0823i	−0.318328	+	1.60034i
$58$	6.51047	−	2.09918i	0.854866	−	0.275635i
$59$	0.273393	+	0.901255i	0.0355927	+	0.117333i	0.972937	−	0.231072i	$-0.0742233\pi$
$59$	0.273393	+	0.901255i	0.0355927	+	0.117333i	−0.937344	+	0.348405i	$0.886723\pi$
$60$	−0.136241	−	3.91742i	−0.0175887	−	0.505737i
$61$	−10.4416	−	8.56924i	−1.33692	−	1.09718i	−0.987056	−	0.160377i	$-0.948729\pi$
$61$	−10.4416	−	8.56924i	−1.33692	−	1.09718i	−0.349860	−	0.936802i	$-0.613771\pi$
$62$	4.93912	−	7.67753i	0.627269	−	0.975047i
$63$			2.70367i			0.340631i
$64$	−2.27540	+	7.66959i	−0.284424	+	0.958698i
$65$		−	1.11767i		−	0.138630i
$66$	3.86863	+	2.48878i	0.476196	+	0.306347i
$67$	0.658052	+	0.540050i	0.0803939	+	0.0659776i	0.673732	−	0.738976i	$-0.264690\pi$
$67$	0.658052	+	0.540050i	0.0803939	+	0.0659776i	−0.593338	+	0.804953i	$0.702190\pi$
$68$	11.5281	+	10.7532i	1.39799	+	1.30402i
$69$	4.81110	+	15.8601i	0.579188	+	1.90933i
$70$	−1.39488	−	4.32612i	−0.166720	−	0.517071i
$71$	−1.43269	+	7.20264i	−0.170029	+	0.854796i	0.797749	+	0.602990i	$0.206024\pi$
$71$	−1.43269	+	7.20264i	−0.170029	+	0.854796i	−0.967778	+	0.251805i	$0.918976\pi$
$72$	1.59240	−	1.76778i	0.187666	−	0.208335i
$73$	8.68694	−	1.72794i	1.01673	−	0.202240i	0.341526	−	0.939872i	$-0.389056\pi$
$73$	8.68694	−	1.72794i	1.01673	−	0.202240i	0.675203	+	0.737632i	$0.264056\pi$
$74$	−7.30433	−	2.07781i	−0.849111	−	0.241540i
$75$	0.192103	−	1.95046i	0.0221822	−	0.225219i
$76$	7.63246	−	9.98893i	0.875503	−	1.14581i
$77$	5.10457	+	1.54845i	0.581720	+	0.176463i
$78$	2.15211	−	2.22825i	0.243678	−	0.252300i
$79$	0.257484	+	0.106653i	0.0289692	+	0.0119995i	0.397121	−	0.917766i	$-0.370009\pi$
$79$	0.257484	+	0.106653i	0.0289692	+	0.0119995i	−0.368152	+	0.929766i	$0.620009\pi$
$80$	−1.63595	+	3.65016i	−0.182905	+	0.408100i
$81$	9.99265	−	4.13909i	1.11029	−	0.459899i
$82$	−5.54490	+	14.0736i	−0.612332	+	1.55417i
$83$	−3.97218	−	7.43142i	−0.436003	−	0.815704i	0.563946	−	0.825812i	$-0.309283\pi$
$83$	−3.97218	−	7.43142i	−0.436003	−	0.815704i	−0.999949	+	0.0101077i	$0.996783\pi$
$84$	5.54918	−	11.3107i	0.605465	−	1.23410i
$85$	5.00055	+	6.09318i	0.542385	+	0.660899i
$86$	−4.64301	+	5.86241i	−0.500668	+	0.632160i
$87$	7.88230	+	5.26679i	0.845072	+	0.564659i
$88$	−2.42559	−	4.01892i	−0.258569	−	0.428418i
$89$	−7.19185	−	10.7634i	−0.762335	−	1.14091i	−0.986081	−	0.166267i	$-0.946829\pi$
$89$	−7.19185	−	10.7634i	−0.762335	−	1.14091i	0.223746	−	0.974648i	$-0.428171\pi$
$90$	0.906332	−	0.770556i	0.0955358	−	0.0812237i
$91$	1.69340	−	3.16813i	0.177517	−	0.332111i
$92$	2.72099	−	16.6926i	0.283683	−	1.74032i
$93$	12.5906	−	1.24007i	1.30559	−	0.128589i
$94$	−2.87415	−	4.14370i	−0.296446	−	0.427390i
$95$	4.44456	−	4.44456i	0.456002	−	0.456002i
$96$	−10.2900	+	4.12711i	−1.05022	+	0.421221i
$97$	6.13377	+	6.13377i	0.622790	+	0.622790i	0.946244	−	0.323454i	$-0.104844\pi$
$97$	6.13377	+	6.13377i	0.622790	+	0.622790i	−0.323454	+	0.946244i	$0.604844\pi$
$98$	0.838454	−	4.63483i	0.0846966	−	0.468188i
$99$	0.136838	+	1.38934i	0.0137528	+	0.139634i
$100$	−1.05267	+	1.70055i	−0.105267	+	0.170055i
$101$	−0.318613	−	0.170302i	−0.0317031	−	0.0169457i	0.455469	−	0.890252i	$-0.349472\pi$
$101$	−0.318613	−	0.170302i	−0.0317031	−	0.0169457i	−0.487172	+	0.873306i	$0.661972\pi$
$102$	−1.76322	+	21.7765i	−0.174584	+	2.15619i
$103$	−15.2472	+	10.1879i	−1.50235	+	1.00384i	−0.512984	+	0.858398i	$0.671460\pi$
$103$	−15.2472	+	10.1879i	−1.50235	+	1.00384i	−0.989367	+	0.145441i	$0.953540\pi$
$104$	−2.97318	+	1.07409i	−0.291544	+	0.105323i
$105$	3.49972	−	5.23769i	0.341537	−	0.511147i
$106$	−11.7577	+	1.36476i	−1.14200	+	0.132557i
$107$	7.82340	−	6.42050i	0.756317	−	0.620693i	−0.175141	−	0.984543i	$-0.556038\pi$
$107$	7.82340	−	6.42050i	0.756317	−	0.620693i	0.931457	+	0.363850i	$0.118538\pi$
$108$	−8.44508	−	0.536225i	−0.812628	−	0.0515983i
$109$	−13.8446	+	7.40010i	−1.32607	+	0.708801i	−0.973867	−	0.227121i	$-0.927069\pi$
$109$	−13.8446	+	7.40010i	−1.32607	+	0.708801i	−0.352207	+	0.935922i	$0.614569\pi$
$110$	−0.935744	−	2.15248i	−0.0892197	−	0.205231i
$111$	−4.02749	−	9.72322i	−0.382272	−	0.922887i
$112$	−10.1677	+	7.86805i	−0.960757	+	0.743461i
$113$	0.175041	−	0.422585i	0.0164664	−	0.0397535i	−0.915432	−	0.402472i	$-0.868151\pi$
$113$	0.175041	−	0.422585i	0.0164664	−	0.0397535i	0.931899	+	0.362718i	$0.118151\pi$
$114$	17.4191	−	0.302813i	1.63145	−	0.0283610i
$115$	2.45477	−	8.09231i	0.228909	−	0.754611i
$116$	−4.85405	−	8.36801i	−0.450688	−	0.776950i
$117$	0.935641	+	0.0921526i	0.0865000	+	0.00851951i
$118$	1.16356	−	0.648185i	0.107114	−	0.0596702i
$119$	4.94260	+	24.8481i	0.453088	+	2.27782i
$120$	−5.37314	+	1.36338i	−0.490499	+	0.124459i
$121$	−8.08717	−	1.60864i	−0.735197	−	0.146240i
$122$	−8.71084	+	17.0012i	−0.788643	+	1.53922i
$123$	−20.0605	+	6.08530i	−1.80880	+	0.548693i
$124$	−12.0922	−	4.52304i	−1.08591	−	0.406181i
$125$	−0.634393	+	0.773010i	−0.0567419	+	0.0691402i
$126$	3.73657	−	0.811010i	0.332880	−	0.0722505i
$127$	−10.1472			−0.900421			−0.450211	−	0.892922i	$-0.648651\pi$
$127$	−10.1472			−0.900421			−0.450211	+	0.892922i	$0.648651\pi$
$128$	11.2822	+	0.844059i	0.997213	+	0.0746049i
$129$	−10.3639			−0.912488
$130$	−1.54466	+	0.335262i	−0.135475	+	0.0294045i
$131$	4.77932	−	5.82362i	0.417571	−	0.508812i	−0.521161	−	0.853458i	$-0.674501\pi$
$131$	4.77932	−	5.82362i	0.417571	−	0.508812i	0.938733	+	0.344646i	$0.112001\pi$
$132$	2.27912	−	6.09313i	0.198372	−	0.530339i
$133$	19.3326	−	5.86447i	1.67635	−	0.508514i
$134$	0.548974	−	1.07145i	0.0474241	−	0.0925590i
$135$	−4.14975	−	0.825436i	−0.357153	−	0.0710422i
$136$	11.4033	−	19.1579i	0.977823	−	1.64277i
$137$	1.32284	+	6.65036i	0.113018	+	0.568178i	0.995249	+	0.0973622i	$0.0310405\pi$
$137$	1.32284	+	6.65036i	0.113018	+	0.568178i	−0.882231	+	0.470816i	$0.843959\pi$
$138$	20.4760	−	11.4066i	1.74303	−	0.970994i
$139$	−0.0192277	−	0.00189377i	−0.00163088	−	0.000160627i	0.0972017	−	0.995265i	$-0.469011\pi$
$139$	−0.0192277	−	0.00189377i	−0.00163088	−	0.000160627i	−0.0988325	+	0.995104i	$0.531511\pi$
$140$	−5.56044	+	3.22546i	−0.469943	+	0.272601i
$141$	2.02872	−	6.68781i	0.170849	−	0.563215i
$142$	10.3841	−	0.180516i	0.871410	−	0.0151485i
$143$	0.709848	−	1.71372i	0.0593605	−	0.143309i
$144$	−2.92080	−	1.67048i	−0.243400	−	0.139206i
$145$	−1.85103	−	4.46878i	−0.153720	−	0.371112i
$146$	−4.99386	−	11.4873i	−0.413295	−	0.950698i
$147$	5.75670	−	3.07702i	0.474805	−	0.253788i
$148$	−0.680552	+	10.7181i	−0.0559410	+	0.881023i
$149$	17.5728	−	14.4216i	1.43962	−	1.18146i	0.488530	−	0.872547i	$-0.337533\pi$
$149$	17.5728	−	14.4216i	1.43962	−	1.18146i	0.951089	−	0.308917i	$-0.0999667\pi$
$150$	−2.75322	+	0.319578i	−0.224800	+	0.0260934i
$151$	−12.0179	+	17.9861i	−0.978005	+	1.46369i	−0.0943562	+	0.995538i	$0.530079\pi$
$151$	−12.0179	+	17.9861i	−0.978005	+	1.46369i	−0.883649	+	0.468150i	$0.844921\pi$
$152$	−16.0945	−	7.55198i	−1.30544	−	0.612547i
$153$	−5.51313	+	3.68376i	−0.445710	+	0.297814i
$154$	0.608819	−	7.51918i	0.0490600	−	0.605912i
$155$	−5.69298	−	3.04296i	−0.457272	−	0.244417i
$156$	−3.72508	−	2.30588i	−0.298245	−	0.184618i
$157$	0.475683	+	4.82970i	0.0379637	+	0.385452i	0.995327	+	0.0965643i	$0.0307853\pi$
$157$	0.475683	+	4.82970i	0.0379637	+	0.385452i	−0.957363	+	0.288887i	$0.906715\pi$
$158$	0.0701622	−	0.387845i	0.00558181	−	0.0308553i
$159$	−11.5992	−	11.5992i	−0.919880	−	0.919880i
$160$	5.53538	+	1.16602i	0.437610	+	0.0921820i
$161$	19.2191	−	19.2191i	1.51468	−	1.51468i
$162$	−8.71783	−	12.5686i	−0.684937	−	0.987483i
$163$	−6.75609	+	0.665416i	−0.529178	+	0.0521194i	−0.359078	−	0.933307i	$-0.616909\pi$
$163$	−6.75609	+	0.665416i	−0.529178	+	0.0521194i	−0.170099	+	0.985427i	$0.554409\pi$
$164$	21.1135	+	3.44164i	1.64869	+	0.268747i
$165$	1.53332	−	2.86864i	0.119369	−	0.223323i
$166$	−9.07896	+	7.71886i	−0.704664	+	0.599100i
$167$	−9.79725	−	14.6626i	−0.758134	−	1.13463i	−0.986929	−	0.161153i	$-0.948479\pi$
$167$	−9.79725	−	14.6626i	−0.758134	−	1.13463i	0.228796	−	0.973474i	$-0.426521\pi$
$168$	−17.2964	−	4.27633i	−1.33444	−	0.329926i
$169$	9.77045	+	6.52841i	0.751573	+	0.502185i
$170$	6.92100	−	8.73868i	0.530816	−	0.670226i
$171$	3.35425	+	4.08717i	0.256506	+	0.312553i
$172$	9.49480	+	4.65827i	0.723972	+	0.355190i
$173$	−4.92863	−	9.22083i	−0.374717	−	0.701046i	0.621912	−	0.783087i	$-0.286356\pi$
$173$	−4.92863	−	9.22083i	−0.374717	−	0.701046i	−0.996629	+	0.0820409i	$0.973856\pi$
$174$	4.91446	−	12.4735i	0.372564	−	0.945612i
$175$	−2.96945	+	1.22999i	−0.224469	+	0.0929783i
$176$	−4.82669	+	4.55779i	−0.363825	+	0.343556i
$177$	1.70534	+	0.706375i	0.128181	+	0.0530944i
$178$	−12.7180	+	13.1680i	−0.953257	+	0.986986i
$179$	4.44692	+	1.34896i	0.332378	+	0.100826i	0.452063	−	0.891986i	$-0.350688\pi$
$179$	4.44692	+	1.34896i	0.332378	+	0.100826i	−0.119685	+	0.992812i	$0.538188\pi$
$180$	−1.33680	−	1.02144i	−0.0996395	−	0.0761337i
$181$	−0.459680	+	4.66721i	−0.0341677	+	0.346911i	0.962868	+	0.269972i	$0.0870145\pi$
$181$	−0.459680	+	4.66721i	−0.0341677	+	0.346911i	−0.997036	+	0.0769386i	$0.975485\pi$
$182$	−4.88643	−	1.39001i	−0.362206	−	0.103034i
$183$	−25.9651	+	5.16478i	−1.91940	+	0.381792i
$184$	−23.8859	+	1.24670i	−1.76089	+	0.0919077i
$185$	−1.04761	+	5.26667i	−0.0770215	+	0.387213i
$186$	−5.49057	−	17.0287i	−0.402588	−	1.24860i
$187$	3.79749	+	12.5186i	0.277700	+	0.915453i
$188$	−4.86459	+	5.21514i	−0.354786	+	0.380353i
$189$	−10.5122	−	8.62715i	−0.764651	−	0.627533i
$190$	−7.47576	−	4.80932i	−0.542349	−	0.348905i
$191$		−	10.3465i		−	0.748646i	−0.927298	−	0.374323i	$-0.877875\pi$
$191$		−	10.3465i		−	0.748646i	0.927298	−	0.374323i	$-0.122125\pi$
$192$	8.79047	+	12.9832i	0.634398	+	0.936982i
$193$			19.5571i			1.40775i	0.710322	+	0.703876i	$0.248549\pi$
$193$			19.5571i			1.40775i	−0.710322	+	0.703876i	$0.751451\pi$
$194$	6.63716	−	10.3170i	0.476520	−	0.740718i
$195$	−1.69329	−	1.38965i	−0.121259	−	0.0995146i
$196$	−6.65700	+	0.231520i	−0.475500	+	0.0165371i
$197$	0.0628244	+	0.207104i	0.00447605	+	0.0147556i	0.959150	−	0.282898i	$-0.0912959\pi$
$197$	0.0628244	+	0.207104i	0.00447605	+	0.0147556i	−0.954674	+	0.297654i	$0.903796\pi$
$198$	1.87908	−	0.605872i	0.133540	−	0.0430574i
$199$	4.61190	−	23.1856i	0.326929	−	1.64358i	−0.371884	−	0.928279i	$-0.621288\pi$
$199$	4.61190	−	23.1856i	0.326929	−	1.64358i	0.698813	−	0.715304i	$-0.253712\pi$
$200$	2.66599	+	0.944717i	0.188514	+	0.0668016i
$201$	1.63637	−	0.325494i	0.115421	−	0.0229586i
$202$	−0.139790	+	0.491418i	−0.00983561	+	0.0345761i
$203$	1.52383	−	15.4717i	0.106952	−	1.08590i
$204$	30.6248	−	4.09538i	2.14416	−	0.286734i
$205$	10.2355	+	3.10491i	0.714879	+	0.216856i
$206$	18.6536	+	18.0162i	1.29966	+	1.25524i
$207$	6.57197	+	2.72220i	0.456784	+	0.189206i
$208$	2.37628	+	3.78684i	0.164766	+	0.262570i
$209$	9.63768	−	3.99206i	0.666652	−	0.276136i
$210$	−8.28847	−	3.26560i	−0.571959	−	0.225348i
$211$	−2.91192	−	5.44783i	−0.200465	−	0.375044i	0.761522	−	0.648139i	$-0.224453\pi$
$211$	−2.91192	−	5.44783i	−0.200465	−	0.375044i	−0.961987	+	0.273095i	$0.911953\pi$
$212$	5.41304	+	15.8401i	0.371769	+	1.08790i
$213$	9.13080	+	11.1259i	0.625632	+	0.762335i
$214$	−11.2201	−	8.88628i	−0.766991	−	0.607454i
$215$	4.39679	+	2.93784i	0.299859	+	0.200359i
$216$	1.79216	+	11.8322i	0.121941	+	0.805083i
$217$	−11.5268	−	17.2511i	−0.782493	−	1.17108i
$218$	14.3801	+	16.9140i	0.973944	+	1.14556i
$219$	8.18299	−	15.3093i	0.552955	−	1.03451i
$220$	−2.69411	+	1.93890i	−0.181637	+	0.130721i
$221$	8.76749	−	0.863522i	0.589765	−	0.0580868i
$222$	−12.2297	+	8.48277i	−0.820805	+	0.569326i
$223$	−3.68291	+	3.68291i	−0.246626	+	0.246626i	−0.819584	−	0.572959i	$-0.805796\pi$
$223$	−3.68291	+	3.68291i	−0.246626	+	0.246626i	0.572959	+	0.819584i	$0.305796\pi$
$224$	13.9239	+	11.6920i	0.930328	+	0.781202i
$225$	−0.594810	−	0.594810i	−0.0396540	−	0.0396540i
$226$	−0.636534	−	0.115151i	−0.0423416	−	0.00765972i
$227$	−0.166686	−	1.69240i	−0.0110634	−	0.112328i	0.988067	−	0.154025i	$-0.0492236\pi$
$227$	−0.166686	−	1.69240i	−0.0110634	−	0.112328i	−0.999130	+	0.0416968i	$0.986724\pi$
$228$	−5.64364	−	23.9830i	−0.373760	−	1.58831i
$229$	8.53417	+	4.56161i	0.563954	+	0.301440i	0.728629	−	0.684908i	$-0.240158\pi$
$229$	8.53417	+	4.56161i	0.563954	+	0.301440i	−0.164675	+	0.986348i	$0.552658\pi$
$230$	−11.9202	−	0.965165i	−0.785995	−	0.0636411i
$231$	8.69267	−	5.80826i	0.571936	−	0.382155i
$232$	−10.1088	+	9.21859i	−0.663677	+	0.605230i
$233$	7.71611	−	11.5480i	0.505499	−	0.756533i	−0.487694	−	0.873015i	$-0.662162\pi$
$233$	7.71611	−	11.5480i	0.505499	−	0.756533i	0.993193	+	0.116482i	$0.0371617\pi$
$234$	−0.153303	−	1.32073i	−0.0100217	−	0.0863389i
$235$	−2.75646	+	2.26217i	−0.179812	+	0.147568i
$236$	−1.24484	−	1.41364i	−0.0810323	−	0.0920204i
$237$	0.481724	−	0.257487i	0.0312913	−	0.0167256i
$238$	32.8584	−	14.2844i	2.12989	−	0.925923i
$239$	8.68966	+	20.9787i	0.562087	+	1.35700i	0.908094	+	0.418767i	$0.137538\pi$
$239$	8.68966	+	20.9787i	0.562087	+	1.35700i	−0.346006	+	0.938232i	$0.612462\pi$
$240$	3.49601	+	7.01690i	0.225666	+	0.452939i
$241$	−5.89640	+	14.2352i	−0.379820	+	0.916967i	0.612178	+	0.790720i	$0.290293\pi$
$241$	−5.89640	+	14.2352i	−0.379820	+	0.916967i	−0.991999	+	0.126248i	$0.959707\pi$
$242$	0.202684	+	11.6593i	0.0130290	+	0.749487i
$243$	2.46888	−	8.13880i	0.158379	−	0.522104i
$244$	26.1092	+	6.93890i	1.67147	+	0.444218i
$245$	−3.31448	−	0.326447i	−0.211754	−	0.0208560i
$246$	14.4276	+	25.8990i	0.919868	+	1.65126i
$247$	−1.37054	−	6.89018i	−0.0872055	−	0.438412i
$248$	−2.62376	+	18.0686i	−0.166609	+	1.14736i
$249$	−16.1975	−	3.22189i	−1.02648	−	0.204179i
$250$	1.25862	+	0.644877i	0.0796024	+	0.0407856i
$251$	2.66023	−	0.806973i	0.167912	−	0.0509357i	−0.205209	−	0.978718i	$-0.565787\pi$
$251$	2.66023	−	0.806973i	0.167912	−	0.0509357i	0.373122	+	0.927782i	$0.378287\pi$
$252$	−2.24169	−	4.92079i	−0.141213	−	0.309981i
$253$	8.90347	−	10.8489i	0.559756	−	0.682065i
$254$	3.04383	+	14.0238i	0.190987	+	0.879933i
$255$	15.4487			0.967434
$256$	−2.21775	−	15.8456i	−0.138610	−	0.990347i
$257$	14.3557			0.895485			0.447742	−	0.894163i	$-0.352228\pi$
$257$	14.3557			0.895485			0.447742	+	0.894163i	$0.352228\pi$
$258$	3.10881	+	14.3232i	0.193546	+	0.891726i
$259$	−10.9492	+	13.3416i	−0.680349	+	0.829007i
$260$	0.926689	+	2.03420i	0.0574708	+	0.126156i
$261$	3.89361	−	1.18111i	0.241008	−	0.0731090i
$262$	−9.48208	−	4.85830i	−0.585805	−	0.300147i
$263$	1.49879	+	0.298128i	0.0924193	+	0.0183833i	0.241083	−	0.970504i	$-0.422497\pi$
$263$	1.49879	+	0.298128i	0.0924193	+	0.0183833i	−0.148664	+	0.988888i	$0.547497\pi$
$264$	−9.10458	−	1.32208i	−0.560348	−	0.0813687i
$265$	1.63285	+	8.20892i	0.100305	+	0.504270i
$266$	−13.9040	−	24.9592i	−0.852511	−	1.53034i
$267$	−25.2487	−	2.48678i	−1.54519	−	0.152188i
$268$	−1.64545	−	0.437303i	−0.100512	−	0.0267125i
$269$	5.89820	−	19.4437i	0.359619	−	1.18551i	−0.571442	−	0.820643i	$-0.693616\pi$
$269$	5.89820	−	19.4437i	0.359619	−	1.18551i	0.931061	−	0.364863i	$-0.118884\pi$
$270$	0.104003	+	5.98270i	0.00632941	+	0.364095i
$271$	1.19857	−	2.89361i	0.0728082	−	0.175774i	−0.883286	−	0.468835i	$-0.844674\pi$
$271$	1.19857	−	2.89361i	0.0728082	−	0.175774i	0.956094	+	0.293061i	$0.0946738\pi$
$272$	−29.8974	−	10.0130i	−1.81280	−	0.607128i
$273$	−2.69430	−	6.50462i	−0.163066	−	0.393677i
$274$	8.79422	−	3.82309i	0.531278	−	0.230961i
$275$	−1.46367	+	0.782348i	−0.0882626	+	0.0471773i
$276$	−21.9064	−	24.8769i	−1.31861	−	1.49742i
$277$	11.7052	−	9.60622i	0.703298	−	0.577182i	−0.213302	−	0.976986i	$-0.568422\pi$
$277$	11.7052	−	9.60622i	0.703298	−	0.577182i	0.916601	+	0.399804i	$0.130922\pi$
$278$	0.00315042	+	0.0271415i	0.000188950	+	0.00162784i
$279$	3.01677	−	4.51491i	0.180609	−	0.270301i
$280$	6.12564	+	6.71719i	0.366077	+	0.401429i
$281$	−8.58477	+	5.73616i	−0.512125	+	0.342191i	−0.784631	−	0.619963i	$-0.787147\pi$
$281$	−8.58477	+	5.73616i	−0.512125	+	0.342191i	0.272506	+	0.962154i	$0.412147\pi$
$282$	−9.85133	−	0.797651i	−0.586638	−	0.0474994i
$283$	12.5731	+	6.72046i	0.747393	+	0.399490i	0.800682	−	0.599089i	$-0.204470\pi$
$283$	12.5731	+	6.72046i	0.747393	+	0.399490i	−0.0532890	+	0.998579i	$0.516970\pi$
$284$	−3.36434	−	14.2970i	−0.199637	−	0.848369i
$285$	−1.20748	−	12.2597i	−0.0715247	−	0.726203i
$286$	−2.58136	−	0.466975i	−0.152639	−	0.0276128i
$287$	24.3092	+	24.3092i	1.43493	+	1.43493i
$288$	−1.43252	+	4.53773i	−0.0844118	+	0.267388i
$289$	−31.9134	+	31.9134i	−1.87726	+	1.87726i
$290$	−5.62077	+	3.89867i	−0.330063	+	0.228938i
$291$	16.9192	−	1.66639i	0.991819	−	0.0976856i
$292$	−14.3779	+	10.3475i	−0.841403	+	0.605541i
$293$	−5.93817	+	11.1095i	−0.346912	+	0.649026i	−0.993502	−	0.113811i	$-0.963694\pi$
$293$	−5.93817	+	11.1095i	−0.346912	+	0.649026i	0.646591	+	0.762837i	$0.276194\pi$
$294$	−5.97937	−	7.03296i	−0.348724	−	0.410171i
$295$	−0.523241	−	0.783086i	−0.0304643	−	0.0455930i
$296$	15.0169	−	2.27452i	0.872842	−	0.132204i
$297$	−5.83858	−	3.90121i	−0.338789	−	0.226371i
$298$	−25.2024	−	19.9602i	−1.45994	−	1.15626i
$299$	−5.99596	−	7.30609i	−0.346755	−	0.422522i
$300$	1.26754	+	3.70919i	0.0731816	+	0.214150i
$301$	8.01193	+	14.9893i	0.461800	+	0.863967i
$302$	28.4624	+	11.2140i	1.63783	+	0.645292i
$303$	−0.654156	+	0.270960i	−0.0375803	+	0.0155663i
$304$	−5.60929	+	24.5085i	−0.321715	+	1.40566i
$305$	12.4796	+	5.16920i	0.714577	+	0.295988i
$306$	6.74483	+	6.51434i	0.385576	+	0.372400i
$307$	25.2158	+	7.64912i	1.43914	+	0.436558i	0.910932	−	0.412556i	$-0.135364\pi$
$307$	25.2158	+	7.64912i	1.43914	+	0.436558i	0.528208	+	0.849115i	$0.322864\pi$
$308$	−10.5744	+	1.41409i	−0.602532	+	0.0805753i
$309$	−3.52272	+	35.7668i	−0.200401	+	2.03470i
$310$	−2.49778	+	8.78069i	−0.141864	+	0.498710i
$311$	−2.79565	+	0.556089i	−0.158527	+	0.0315329i	−0.273715	−	0.961811i	$-0.588253\pi$
$311$	−2.79565	+	0.556089i	−0.158527	+	0.0315329i	0.115189	+	0.993344i	$0.463253\pi$
$312$	−2.06941	+	5.83988i	−0.117157	+	0.330618i
$313$	−3.11570	+	15.6637i	−0.176110	+	0.885362i	0.787144	+	0.616769i	$0.211559\pi$
$313$	−3.11570	+	15.6637i	−0.176110	+	0.885362i	−0.963254	+	0.268593i	$0.913441\pi$
$314$	6.53212	−	2.10616i	0.368629	−	0.118857i
$315$	−0.784834	−	2.58725i	−0.0442204	−	0.145775i
$316$	−0.557061	+	0.0193737i	−0.0313371	+	0.00108985i
$317$	3.83730	+	3.14919i	0.215524	+	0.176876i	0.735961	−	0.677024i	$-0.236731\pi$
$317$	3.83730	+	3.14919i	0.215524	+	0.176876i	−0.520437	+	0.853900i	$0.674231\pi$
$318$	−12.5512	+	19.5099i	−0.703835	+	1.09406i
$319$		−	8.02763i		−	0.449461i
$320$	−0.0489459	−	7.99985i	−0.00273616	−	0.447205i
$321$		−	19.8355i		−	1.10711i
$322$	−32.3266	−	20.7964i	−1.80149	−	1.15894i
$323$	38.2991	+	31.4312i	2.13102	+	1.74888i
$324$	−14.7552	+	15.8185i	−0.819733	+	0.878805i
$325$	0.324442	+	1.06954i	0.0179968	+	0.0593275i
$326$	2.94623	+	9.13754i	0.163176	+	0.506082i
$327$	−6.00233	+	30.1757i	−0.331929	+	1.66872i
$328$	−1.57688	−	30.2120i	−0.0870686	−	1.66818i
$329$	−11.2409	+	2.23595i	−0.619731	+	0.123272i
$330$	−4.42450	−	1.25861i	−0.243561	−	0.0692840i
$331$	2.35787	−	23.9399i	0.129600	−	1.31585i	−0.681875	−	0.731468i	$-0.738835\pi$
$331$	2.35787	−	23.9399i	0.129600	−	1.31585i	0.811476	−	0.584386i	$-0.198665\pi$
$332$	13.3911	+	10.2320i	0.734933	+	0.561556i
$333$	−4.32255	−	1.31123i	−0.236874	−	0.0718550i
$334$	−17.3254	+	17.9384i	−0.948004	+	0.981547i
$335$	−0.786485	−	0.325773i	−0.0429703	−	0.0177989i
$336$	−0.721704	+	25.1869i	−0.0393722	+	1.37406i
$337$	9.52895	−	3.94702i	0.519075	−	0.215008i	−0.107736	−	0.994180i	$-0.534360\pi$
$337$	9.52895	−	3.94702i	0.519075	−	0.215008i	0.626811	+	0.779172i	$0.284360\pi$
$338$	6.09168	−	15.4614i	0.331344	−	0.840989i
$339$	−0.422589	−	0.790608i	−0.0229519	−	0.0429400i
$340$	−14.1532	−	6.94375i	−0.767566	−	0.376578i
$341$	−6.79645	−	8.28150i	−0.368048	−	0.448468i
$342$	4.64244	−	5.86170i	0.251035	−	0.316965i
$343$	9.80647	+	6.55247i	0.529500	+	0.353800i
$344$	3.58977	−	14.5195i	0.193547	−	0.782837i
$345$	−9.20787	−	13.7805i	−0.495735	−	0.741920i
$346$	−11.2651	+	9.57748i	−0.605614	+	0.514889i
$347$	5.49349	−	10.2776i	0.294906	−	0.551730i	−0.690212	−	0.723607i	$-0.742483\pi$
$347$	5.49349	−	10.2776i	0.294906	−	0.551730i	0.985119	+	0.171876i	$0.0549829\pi$
$348$	−18.7130	−	3.05033i	−1.00312	−	0.163515i
$349$	2.09656	−	0.206493i	0.112226	−	0.0110533i	−0.0417480	−	0.999128i	$-0.513293\pi$
$349$	2.09656	−	0.206493i	0.112226	−	0.0110533i	0.153974	+	0.988075i	$0.450793\pi$
$350$	2.59062	+	3.73493i	0.138474	+	0.199640i
$351$	−3.34384	+	3.34384i	−0.178481	+	0.178481i
$352$	7.74686	+	5.30347i	0.412909	+	0.282676i
$353$	−17.2801	−	17.2801i	−0.919728	−	0.919728i	0.0772817	−	0.997009i	$-0.475376\pi$
$353$	−17.2801	−	17.2801i	−0.919728	−	0.919728i	−0.997009	+	0.0772817i	$0.975376\pi$
$354$	0.464691	−	2.56873i	0.0246980	−	0.136526i
$355$	−0.719813	−	7.30838i	−0.0382037	−	0.387889i
$356$	22.0137	+	13.6268i	1.16672	+	0.722219i
$357$	43.7908	+	23.4066i	2.31765	+	1.23881i
$358$	0.530381	−	6.55044i	0.0280315	−	0.346201i
$359$	−2.85463	+	1.90740i	−0.150662	+	0.100669i	−0.628616	−	0.777716i	$-0.716378\pi$
$359$	−2.85463	+	1.90740i	−0.150662	+	0.100669i	0.477955	+	0.878385i	$0.341378\pi$
$360$	−1.01067	+	2.15391i	−0.0532670	+	0.113521i
$361$	11.3938	−	17.0520i	0.599673	−	0.897474i
$362$	6.58813	−	0.764711i	0.346265	−	0.0401923i
$363$	−12.4922	+	10.2521i	−0.655673	+	0.538097i
$364$	−0.455274	+	7.17018i	−0.0238629	+	0.375819i
$365$	−7.81128	+	4.17522i	−0.408861	+	0.218541i
$366$	14.9266	+	34.3354i	0.780224	+	1.79474i
$367$	−4.13465	−	9.98194i	−0.215827	−	0.521053i	0.778472	−	0.627679i	$-0.215995\pi$
$367$	−4.13465	−	9.98194i	−0.215827	−	0.521053i	−0.994299	+	0.106627i	$0.965995\pi$
$368$	8.88794	+	32.6372i	0.463316	+	1.70133i
$369$	−3.44316	+	8.31253i	−0.179244	+	0.432733i
$370$	7.59296	−	0.131996i	0.394739	−	0.00686212i
$371$	−7.80903	+	25.7429i	−0.405424	+	1.33651i
$372$	−21.8872	+	12.6962i	−1.13480	+	0.658267i
$373$	9.89056	+	0.974136i	0.512114	+	0.0504388i	0.350774	−	0.936460i	$-0.385918\pi$
$373$	9.89056	+	0.974136i	0.512114	+	0.0504388i	0.161340	+	0.986899i	$0.448418\pi$
$374$	16.1621	−	9.00343i	0.835721	−	0.465556i
$375$	0.382357	+	1.92224i	0.0197448	+	0.0992638i
$376$	8.66672	+	5.15866i	0.446952	+	0.266038i
$377$	−5.30225	−	1.05468i	−0.273080	−	0.0543190i
$378$	−8.76971	+	17.1161i	−0.451065	+	0.880357i
$379$	−1.66801	+	0.505986i	−0.0856801	+	0.0259908i	−0.332834	−	0.942986i	$-0.608005\pi$
$379$	−1.66801	+	0.505986i	−0.0856801	+	0.0259908i	0.247154	+	0.968976i	$0.420505\pi$
$380$	−4.40417	+	11.7744i	−0.225929	+	0.604014i
$381$	−12.6165	+	15.3733i	−0.646363	+	0.787596i
$382$	−14.2992	+	3.10360i	−0.731611	+	0.158794i
$383$	−21.9401			−1.12109			−0.560544	−	0.828125i	$-0.689408\pi$
$383$	−21.9401			−1.12109			−0.560544	+	0.828125i	$0.689408\pi$
$384$	15.3064	−	16.0433i	0.781101	−	0.818704i
$385$	−5.33426			−0.271859
$386$	27.0286	−	5.86648i	1.37572	−	0.298596i
$387$	−2.82190	+	3.43849i	−0.143445	+	0.174788i
$388$	−16.2494	−	6.07803i	−0.824938	−	0.308565i
$389$	−21.9245	+	6.65071i	−1.11161	+	0.337204i	−0.792109	−	0.610380i	$-0.791017\pi$
$389$	−21.9245	+	6.65071i	−1.11161	+	0.337204i	−0.319505	+	0.947584i	$0.603517\pi$
$390$	−1.41261	+	2.75703i	−0.0715302	+	0.139608i
$391$	65.3763	+	13.0042i	3.30622	+	0.657648i
$392$	2.31684	+	9.13076i	0.117018	+	0.461173i
$393$	−2.88055	−	14.4815i	−0.145305	−	0.730496i
$394$	0.267380	−	0.148950i	0.0134704	−	0.00750398i
$395$	−0.277357	−	0.0273173i	−0.0139553	−	0.00137448i
$396$	−1.40100	−	2.41521i	−0.0704027	−	0.121369i
$397$	2.64162	−	8.70826i	0.132579	−	0.437055i	−0.865365	−	0.501142i	$-0.832913\pi$
$397$	2.64162	−	8.70826i	0.132579	−	0.437055i	0.997944	+	0.0640867i	$0.0204134\pi$
$398$	−33.4267	+	0.581088i	−1.67553	+	0.0291273i
$399$	15.1523	−	36.5808i	0.758562	−	1.83133i
$400$	0.505925	−	3.96788i	0.0252962	−	0.198394i
$401$	9.28000	+	22.4039i	0.463421	+	1.11880i	0.966984	+	0.254838i	$0.0820223\pi$
$401$	9.28000	+	22.4039i	0.463421	+	1.11880i	−0.503563	+	0.863959i	$0.667978\pi$
$402$	−0.940701	−	2.16388i	−0.0469179	−	0.107925i
$403$	−6.36286	+	3.40102i	−0.316957	+	0.169417i
$404$	0.721090	+	0.0457860i	0.0358756	+	0.00227794i
$405$	−8.36086	+	6.86158i	−0.415454	+	0.340954i
$406$	−21.8396	+	2.53501i	−1.08388	+	0.125810i
$407$	−4.95124	+	7.41006i	−0.245424	+	0.367303i
$408$	−14.8464	−	41.0960i	−0.735004	−	2.03456i
$409$	−30.1632	+	20.1544i	−1.49147	+	0.996571i	−0.500034	+	0.866006i	$0.666679\pi$
$409$	−30.1632	+	20.1544i	−1.49147	+	0.996571i	−0.991440	+	0.130565i	$0.958321\pi$
$410$	1.22078	−	15.0772i	0.0602902	−	0.744610i
$411$	11.7202	+	6.26456i	0.578113	+	0.309008i
$412$	19.3035	−	31.1842i	0.951015	−	1.53633i
$413$	−0.296706	−	3.01250i	−0.0145999	−	0.148236i
$414$	1.79081	−	9.89926i	0.0880133	−	0.486522i
$415$	5.95836	+	5.95836i	0.292484	+	0.292484i
$416$	4.52074	−	4.42003i	0.221648	−	0.216710i
$417$	−0.0267758	+	0.0267758i	−0.00131122	+	0.00131122i
$418$	−8.40814	−	12.1221i	−0.411256	−	0.592913i
$419$	26.6297	−	2.62280i	1.30095	−	0.128132i	0.576291	−	0.817244i	$-0.304499\pi$
$419$	26.6297	−	2.62280i	1.30095	−	0.128132i	0.724655	+	0.689112i	$0.241999\pi$
$420$	−2.02691	+	12.4345i	−0.0989029	+	0.606743i
$421$	−2.42335	+	4.53377i	−0.118107	+	0.220962i	−0.934027	−	0.357202i	$-0.883731\pi$
$421$	−2.42335	+	4.53377i	−0.118107	+	0.220962i	0.815920	+	0.578164i	$0.196231\pi$
$422$	−6.65561	+	5.65854i	−0.323990	+	0.275454i
$423$	−1.66647	−	2.49405i	−0.0810267	−	0.121265i
$424$	20.2679	−	12.2325i	0.984294	−	0.594063i
$425$	−6.55398	−	4.37923i	−0.317915	−	0.212424i
$426$	12.6375	−	15.9565i	0.612287	−	0.773094i
$427$	27.5425	+	33.5606i	1.33287	+	1.62411i
$428$	−8.91549	+	18.1722i	−0.430947	+	0.878385i
$429$	−1.71374	−	3.20618i	−0.0827402	−	0.154796i
$430$	2.74131	−	6.95777i	0.132198	−	0.335534i
$431$	−13.5080	+	5.59522i	−0.650660	+	0.269512i	−0.683502	−	0.729948i	$-0.739544\pi$
$431$	−13.5080	+	5.59522i	−0.650660	+	0.269512i	0.0328424	+	0.999461i	$0.489544\pi$
$432$	15.8150	−	6.02610i	0.760899	−	0.289931i
$433$	−1.15048	−	0.476545i	−0.0552886	−	0.0229013i	0.354868	−	0.934916i	$-0.384526\pi$
$433$	−1.15048	−	0.476545i	−0.0552886	−	0.0229013i	−0.410156	+	0.912015i	$0.634526\pi$
$434$	−20.3840	+	21.1052i	−0.978463	+	1.01308i
$435$	−9.07176	−	2.75189i	−0.434958	−	0.131943i
$436$	19.0621	−	24.9474i	0.912911	−	1.19477i
$437$	5.20995	−	52.8975i	0.249226	−	2.53043i
$438$	−23.6126	−	6.71690i	−1.12825	−	0.320946i
$439$	3.25486	−	0.647432i	0.155346	−	0.0309002i	−0.116805	−	0.993155i	$-0.537265\pi$
$439$	3.25486	−	0.647432i	0.155346	−	0.0309002i	0.272151	+	0.962255i	$0.412265\pi$
$440$	3.48777	+	3.14175i	0.166273	+	0.149777i
$441$	0.546563	−	2.74776i	0.0260268	−	0.130846i
$442$	−3.82337	−	11.8579i	−0.181859	−	0.564025i
$443$	−6.40990	−	21.1306i	−0.304544	−	1.00395i	−0.966985	−	0.254832i	$-0.917980\pi$
$443$	−6.40990	−	21.1306i	−0.304544	−	1.00395i	0.662442	−	0.749113i	$-0.269520\pi$
$444$	15.3920	+	14.3573i	0.730471	+	0.681370i
$445$	10.0066	+	8.21222i	0.474359	+	0.389296i
$446$	6.19466	+	3.98516i	0.293326	+	0.188703i
$447$		−	44.5541i		−	2.10734i
$448$	11.9820	−	22.7505i	0.566097	−	1.07486i
$449$			21.5803i			1.01844i	0.860637	+	0.509219i	$0.170066\pi$
$449$			21.5803i			1.01844i	−0.860637	+	0.509219i	$0.829934\pi$
$450$	−0.643625	+	1.00047i	−0.0303408	+	0.0471626i
$451$	13.7222	+	11.2615i	0.646153	+	0.530284i
$452$	0.0317962	+	0.914253i	0.00149557	+	0.0430028i
$453$	12.3069	+	40.5703i	0.578227	+	1.90616i
$454$	−2.28895	+	0.738028i	−0.107426	+	0.0346374i
$455$	−0.700824	+	3.52328i	−0.0328552	+	0.165174i
$456$	−31.4524	+	14.9938i	−1.47289	+	0.702149i
$457$	−13.3218	+	2.64988i	−0.623169	+	0.123956i	−0.496568	−	0.867998i	$-0.665407\pi$
$457$	−13.3218	+	2.64988i	−0.623169	+	0.123956i	−0.126601	+	0.991954i	$0.540407\pi$
$458$	3.74434	−	13.1629i	0.174962	−	0.615060i
$459$	3.26895	−	33.1902i	0.152582	−	1.54919i
$460$	2.24177	+	16.7636i	0.104523	+	0.781609i
$461$	−8.93358	−	2.70997i	−0.416078	−	0.126216i	0.0753026	−	0.997161i	$-0.476008\pi$
$461$	−8.93358	−	2.70997i	−0.416078	−	0.126216i	−0.491381	+	0.870945i	$0.663508\pi$
$462$	−10.6347	−	10.2713i	−0.494772	−	0.477864i
$463$	−4.27046	−	1.76888i	−0.198465	−	0.0822069i	0.281237	−	0.959638i	$-0.409255\pi$
$463$	−4.27046	−	1.76888i	−0.198465	−	0.0822069i	−0.479702	+	0.877431i	$0.659255\pi$
$464$	15.7727	+	11.2055i	0.732230	+	0.520202i
$465$	−11.6885	+	4.84153i	−0.542041	+	0.224521i
$466$	−18.2743	−	7.19993i	−0.846540	−	0.333530i
$467$	6.98906	+	13.0756i	0.323415	+	0.605067i	0.990115	−	0.140259i	$-0.0447937\pi$
$467$	6.98906	+	13.0756i	0.323415	+	0.605067i	−0.666700	+	0.745326i	$0.732294\pi$
$468$	−1.77931	+	0.608044i	−0.0822487	+	0.0281069i
$469$	−1.73578	−	2.11505i	−0.0801509	−	0.0976641i
$470$	3.95324	+	3.13095i	0.182349	+	0.144420i
$471$	7.90852	+	5.28430i	0.364405	+	0.243488i
$472$	−1.58029	+	2.14446i	−0.0727389	+	0.0987068i
$473$	4.87575	+	7.29708i	0.224187	+	0.335520i
$474$	−0.500356	−	0.588522i	−0.0229821	−	0.0270317i
$475$	−2.96299	+	5.54337i	−0.135951	+	0.254347i
$476$	−29.5980	−	41.1266i	−1.35662	−	1.88503i
$477$	−7.00662	+	0.690092i	−0.320811	+	0.0315971i
$478$	26.3867	−	18.3023i	1.20690	−	0.837128i
$479$	−4.57716	+	4.57716i	−0.209136	+	0.209136i	−0.803900	−	0.594764i	$-0.797245\pi$
$479$	−4.57716	+	4.57716i	−0.209136	+	0.209136i	0.594764	+	0.803900i	$0.297245\pi$
$480$	8.64892	−	6.93644i	0.394767	−	0.316604i
$481$	4.24384	+	4.24384i	0.193503	+	0.193503i
$482$	21.4422	+	3.87896i	0.976666	+	0.176682i
$483$	−5.22135	−	53.0133i	−0.237580	−	2.41219i
$484$	16.0527	−	3.77751i	0.729670	−	0.171705i
$485$	−7.65019	−	4.08911i	−0.347377	−	0.185677i
$486$	−11.9887	−	0.970710i	−0.543818	−	0.0440323i
$487$	11.0818	−	7.40462i	0.502164	−	0.335535i	−0.278552	−	0.960421i	$-0.589855\pi$
$487$	11.0818	−	7.40462i	0.502164	−	0.335535i	0.780716	+	0.624886i	$0.214855\pi$
$488$	1.75792	−	38.1653i	0.0795774	−	1.72766i
$489$	−7.39202	+	11.0629i	−0.334279	+	0.500284i
$490$	0.543069	+	4.67864i	0.0245334	+	0.211360i
$491$	−29.2846	+	24.0332i	−1.32159	+	1.08460i	−0.331611	+	0.943416i	$0.607592\pi$
$491$	−29.2846	+	24.0332i	−1.32159	+	1.08460i	−0.989983	+	0.141187i	$0.954908\pi$
$492$	31.4655	−	27.7082i	1.41857	−	1.24918i
$493$	33.6250	−	17.9730i	1.51440	−	0.809461i
$494$	−9.11135	+	3.96096i	−0.409939	+	0.178212i
$495$	−0.534252	−	1.28980i	−0.0240128	−	0.0579721i
$496$	25.7584	−	1.79384i	1.15659	−	0.0805459i
$497$	9.03271	−	21.8069i	0.405172	−	0.978173i
$498$	0.405949	+	23.3520i	0.0181910	+	1.04643i
$499$	−3.93305	+	12.9655i	−0.176068	+	0.580417i	0.823840	+	0.566822i	$0.191827\pi$
$499$	−3.93305	+	12.9655i	−0.176068	+	0.580417i	−0.999908	+	0.0135946i	$0.995673\pi$
$500$	0.513697	−	1.93290i	0.0229732	−	0.0864421i
$501$	−34.3955	−	3.38766i	−1.53668	−	0.151350i
$502$	−1.91324	−	3.43447i	−0.0853923	−	0.153288i
$503$	4.92473	+	24.7583i	0.219583	+	1.10392i	0.920520	+	0.390695i	$0.127765\pi$
$503$	4.92473	+	24.7583i	0.219583	+	1.10392i	−0.700938	+	0.713223i	$0.747235\pi$
$504$	−6.12827	+	4.57416i	−0.272975	+	0.203749i
$505$	0.354329	+	0.0704805i	0.0157674	+	0.00313634i
$506$	−17.6643	−	9.05060i	−0.785274	−	0.402348i
$507$	22.0387	−	6.68536i	0.978773	−	0.296907i
$508$	18.4684	−	8.41335i	0.819402	−	0.373282i
$509$	0.914521	−	1.11435i	0.0405354	−	0.0493926i	−0.752348	−	0.658766i	$-0.771079\pi$
$509$	0.914521	−	1.11435i	0.0405354	−	0.0493926i	0.792884	+	0.609373i	$0.208579\pi$
$510$	−4.63409	−	21.3506i	−0.205201	−	0.945422i
$511$	−28.4678			−1.25934
$512$	−21.2339	+	7.81815i	−0.938413	+	0.345516i
$513$	−26.5945			−1.17418
$514$	−4.30623	−	19.8401i	−0.189940	−	0.875109i
$515$	11.6333	−	14.1752i	0.512624	−	0.624634i
$516$	18.8627	−	8.59298i	0.830383	−	0.378285i
$517$	−5.66323	+	1.71792i	−0.249069	+	0.0755542i
$518$	21.7230	+	11.1301i	0.954452	+	0.489029i
$519$	−20.0977	−	3.99768i	−0.882192	−	0.175479i
$520$	2.53336	−	1.89091i	0.111095	−	0.0829218i
$521$	−4.63195	−	23.2864i	−0.202929	−	1.02019i	−0.939164	−	0.343468i	$-0.888398\pi$
$521$	−4.63195	−	23.2864i	−0.202929	−	1.02019i	0.736235	−	0.676726i	$-0.236602\pi$
$522$	−2.80029	−	5.02680i	−0.122565	−	0.220017i
$523$	−34.9257	−	3.43988i	−1.52719	−	0.150416i	−0.700739	−	0.713418i	$-0.747146\pi$
$523$	−34.9257	−	3.43988i	−1.52719	−	0.150416i	−0.826455	+	0.563002i	$0.809646\pi$
$524$	−3.87003	+	14.5619i	−0.169063	+	0.636139i
$525$	−1.82860	+	6.02807i	−0.0798065	+	0.263087i
$526$	−0.0375633	−	2.16081i	−0.00163784	−	0.0942157i
$527$	19.4719	−	47.0094i	0.848210	−	2.04776i
$528$	0.903899	+	12.9794i	0.0393372	+	0.564857i
$529$	−18.5645	−	44.8186i	−0.807151	−	1.94864i
$530$	10.8552	−	4.71906i	0.471520	−	0.204983i
$531$	0.698692	−	0.373459i	0.0303207	−	0.0162067i
$532$	−30.3237	+	26.7028i	−1.31470	+	1.15771i
$533$	9.24108	−	7.58396i	0.400276	−	0.328498i
$534$	4.13694	+	35.6405i	0.179023	+	1.54231i
$535$	−5.62276	+	8.41505i	−0.243093	+	0.363814i
$536$	−0.110788	+	2.40525i	−0.00478530	+	0.103891i
$537$	7.57274	−	5.05995i	0.326788	−	0.218353i
$538$	−28.6412	−	2.31904i	−1.23481	−	0.0999811i
$539$	−4.87477	−	2.60562i	−0.209971	−	0.112232i
$540$	8.23710	−	1.93834i	0.354468	−	0.0834130i
$541$	−0.580817	−	5.89714i	−0.0249713	−	0.253538i	−0.999563	−	0.0295502i	$-0.990593\pi$
$541$	−0.580817	−	5.89714i	−0.0249713	−	0.253538i	0.974592	−	0.223988i	$-0.0719075\pi$
$542$	−4.35861	−	0.788484i	−0.187218	−	0.0338683i
$543$	6.49937	+	6.49937i	0.278915	+	0.278915i
$544$	−4.87009	+	44.3229i	−0.208804	+	1.90033i
$545$	11.1003	−	11.1003i	0.475486	−	0.475486i
$546$	−8.18141	+	5.67478i	−0.350132	+	0.242858i
$547$	21.0016	−	2.06847i	0.897962	−	0.0884415i	0.361506	−	0.932370i	$-0.382263\pi$
$547$	21.0016	−	2.06847i	0.897962	−	0.0884415i	0.536456	+	0.843928i	$0.319763\pi$
$548$	−7.92161	−	11.0071i	−0.338395	−	0.470201i
$549$	−5.35628	+	10.0209i	−0.228600	+	0.427681i
$550$	1.52028	+	1.78816i	0.0648251	+	0.0762476i
$551$	−16.8911	−	25.2793i	−0.719584	−	1.07693i
$552$	−27.8096	+	37.7377i	−1.18366	+	1.60622i
$553$	−0.744805	−	0.497663i	−0.0316723	−	0.0211628i
$554$	−16.7873	−	13.2955i	−0.713224	−	0.564871i
$555$	6.67657	+	8.13542i	0.283405	+	0.345329i
$556$	0.0365654	−	0.0124955i	0.00155072	−	0.000529928i
$557$	−3.89131	−	7.28014i	−0.164880	−	0.308469i	0.785890	−	0.618367i	$-0.212205\pi$
$557$	−3.89131	−	7.28014i	−0.164880	−	0.308469i	−0.950770	+	0.309897i	$0.899705\pi$
$558$	−7.14470	−	2.81496i	−0.302459	−	0.119167i
$559$	5.46031	−	2.26173i	0.230947	−	0.0956612i
$560$	7.44591	−	10.4808i	0.314647	−	0.442894i
$561$	23.6876	+	9.81171i	1.00009	+	0.414251i
$562$	10.5027	+	10.1438i	0.443030	+	0.427890i
$563$	−6.99520	−	2.12197i	−0.294812	−	0.0894304i	0.139414	−	0.990234i	$-0.455478\pi$
$563$	−6.99520	−	2.12197i	−0.294812	−	0.0894304i	−0.434226	+	0.900804i	$0.642978\pi$
$564$	1.85269	+	13.8542i	0.0780122	+	0.583365i
$565$	−0.0448333	+	0.455200i	−0.00188615	+	0.0191504i
$566$	5.51641	−	19.3924i	0.231872	−	0.815123i
$567$	−34.0957	+	6.78207i	−1.43189	+	0.284820i
$568$	−18.7497	+	8.93825i	−0.786721	+	0.375041i
$569$	−4.33817	+	21.8095i	−0.181866	+	0.914301i	0.776796	+	0.629752i	$0.216844\pi$
$569$	−4.33817	+	21.8095i	−0.181866	+	0.914301i	−0.958662	+	0.284548i	$0.908156\pi$
$570$	−16.5812	+	5.34628i	−0.694508	+	0.223931i
$571$	0.0495686	+	0.163406i	0.00207438	+	0.00683833i	0.957971	−	0.286864i	$-0.0926127\pi$
$571$	0.0495686	+	0.163406i	0.00207438	+	0.00683833i	−0.955897	+	0.293702i	$0.905113\pi$
$572$	0.128944	+	3.70760i	0.00539144	+	0.155023i
$573$	−15.6751	−	12.8643i	−0.654838	−	0.537412i
$574$	26.3042	−	40.8881i	1.09792	−	1.70664i
$575$			8.45644i			0.352658i
$576$	6.70101	+	0.618620i	0.279209	+	0.0257758i
$577$		−	14.4323i		−	0.600823i	−0.953810	−	0.300411i	$-0.902876\pi$
$577$		−	14.4323i		−	0.600823i	0.953810	−	0.300411i	$-0.0971240\pi$
$578$	53.6784	+	34.5325i	2.23273	+	1.43636i
$579$	29.6294	+	24.3162i	1.23136	+	1.01055i
$580$	7.07414	+	6.59863i	0.293738	+	0.273993i
$581$	7.86189	+	25.9172i	0.326166	+	1.07523i
$582$	−7.37819	−	22.8830i	−0.305836	−	0.948531i
$583$	−2.70995	+	13.6238i	−0.112235	+	0.564241i
$584$	18.6135	+	16.7668i	0.770231	+	0.693817i
$585$	−0.922103	+	0.183418i	−0.0381243	+	0.00758339i
$586$	17.1350	+	4.87427i	0.707841	+	0.201354i
$587$	−0.603281	+	6.12521i	−0.0249001	+	0.252814i	0.974674	+	0.223630i	$0.0717909\pi$
$587$	−0.603281	+	6.12521i	−0.0249001	+	0.252814i	−0.999574	+	0.0291840i	$0.990709\pi$
$588$	−7.92619	+	10.3733i	−0.326870	+	0.427790i
$589$	−38.8275	−	11.7782i	−1.59986	−	0.485312i
$590$	−0.925297	+	0.958037i	−0.0380939	+	0.0394418i
$591$	0.391879	+	0.162322i	0.0161197	+	0.00667702i
$592$	−7.64805	−	20.0717i	−0.314333	−	0.824940i
$593$	−6.14108	+	2.54372i	−0.252184	+	0.104458i	−0.505195	−	0.863005i	$-0.668579\pi$
$593$	−6.14108	+	2.54372i	−0.252184	+	0.104458i	0.253011	+	0.967464i	$0.418579\pi$
$594$	−3.64024	+	9.23935i	−0.149361	+	0.379095i
$595$	−11.9428	−	22.3434i	−0.489607	−	0.915991i
$596$	−20.0258	+	40.8180i	−0.820290	+	1.67197i
$597$	−29.3924	−	35.8148i	−1.20295	−	1.46580i
$598$	−8.29869	+	10.4782i	−0.339359	+	0.428486i
$599$	26.3288	+	17.5924i	1.07577	+	0.718804i	0.961544	−	0.274651i	$-0.0885623\pi$
$599$	26.3288	+	17.5924i	1.07577	+	0.718804i	0.114223	+	0.993455i	$0.463562\pi$
$600$	4.74601	−	2.86442i	0.193755	−	0.116939i
$601$	9.46390	+	14.1637i	0.386040	+	0.577750i	0.972695	−	0.232087i	$-0.0745554\pi$
$601$	9.46390	+	14.1637i	0.386040	+	0.577750i	−0.586655	+	0.809837i	$0.699555\pi$
$602$	18.3124	−	15.5690i	0.746357	−	0.634547i
$603$	0.337563	−	0.631536i	0.0137466	−	0.0257181i
$604$	6.96034	−	42.6998i	0.283212	−	1.73743i
$605$	8.20590	−	0.808210i	0.333617	−	0.0328584i
$606$	0.570701	+	0.822787i	0.0231831	+	0.0334234i
$607$	5.00284	−	5.00284i	0.203059	−	0.203059i	−0.598250	−	0.801309i	$-0.704137\pi$
$607$	5.00284	−	5.00284i	0.203059	−	0.203059i	0.801309	+	0.598250i	$0.204137\pi$
$608$	35.5542	+	0.400496i	1.44191	+	0.0162423i
$609$	−21.5453	−	21.5453i	−0.873060	−	0.873060i
$610$	3.40057	−	18.7978i	0.137685	−	0.761099i
$611$	0.390644	+	3.96627i	0.0158038	+	0.160458i
$612$	6.97982	−	11.2757i	0.282142	−	0.455792i
$613$	29.6349	+	15.8402i	1.19694	+	0.639778i	0.944716	−	0.327890i	$-0.106338\pi$
$613$	29.6349	+	15.8402i	1.19694	+	0.639778i	0.252225	+	0.967669i	$0.418838\pi$
$614$	3.00747	−	37.1436i	0.121372	−	1.49899i
$615$	17.4303	−	11.6465i	0.702856	−	0.469633i
$616$	5.12628	+	14.1900i	0.206544	+	0.571731i
$617$	−6.06873	+	9.08250i	−0.244318	+	0.365648i	−0.933280	−	0.359150i	$-0.883067\pi$
$617$	−6.06873	+	9.08250i	−0.244318	+	0.365648i	0.688962	+	0.724797i	$0.258067\pi$
$618$	50.4877	−	5.86031i	2.03091	−	0.235736i
$619$	−23.7706	+	19.5080i	−0.955421	+	0.784094i	−0.976463	−	0.215685i	$-0.930802\pi$
$619$	−23.7706	+	19.5080i	−0.955421	+	0.784094i	0.0210420	+	0.999779i	$0.493302\pi$
$620$	12.8845	+	0.818106i	0.517453	+	0.0328559i
$621$	−31.5548	+	16.8664i	−1.26625	+	0.676824i
$622$	1.60713	+	3.69687i	0.0644402	+	0.148231i
$623$	15.9222	+	38.4395i	0.637909	+	1.54005i
$624$	8.69167	+	1.10823i	0.347945	+	0.0443648i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	22.5823	−	0.392570i	0.902571	−	0.0156902i
$627$	5.93491	−	19.5648i	0.237017	−	0.781342i
$628$	−4.87020	−	8.39584i	−0.194342	−	0.335030i
$629$	−42.1235	−	4.14880i	−1.67957	−	0.165424i
$630$	−3.34025	+	1.86076i	−0.133079	+	0.0741343i
$631$	4.77387	+	23.9998i	0.190045	+	0.955419i	0.951605	+	0.307325i	$0.0994337\pi$
$631$	4.77387	+	23.9998i	0.190045	+	0.955419i	−0.761560	+	0.648094i	$0.775566\pi$
$632$	0.193875	+	0.764066i	0.00771192	+	0.0303929i
$633$	−11.8741	−	2.36190i	−0.471952	−	0.0938772i
$634$	3.20123	−	6.24793i	0.127137	−	0.248137i
$635$	9.71030	−	2.94559i	0.385341	−	0.116892i
$636$	30.7283	+	11.4938i	1.21846	+	0.455760i
$637$	−2.36147	+	2.87746i	−0.0935648	+	0.114009i
$638$	−11.0945	+	2.40802i	−0.439234	+	0.0953343i
$639$	6.17747			0.244377
$640$	−11.0414	+	2.46733i	−0.436449	+	0.0975298i
$641$	6.72929			0.265791			0.132895	−	0.991130i	$-0.457573\pi$
$641$	6.72929			0.265791			0.132895	+	0.991130i	$0.457573\pi$
$642$	−27.4133	+	5.94998i	−1.08192	+	0.234827i
$643$	−11.9662	+	14.5809i	−0.471901	+	0.575013i	−0.953506	−	0.301375i	$-0.902554\pi$
$643$	−11.9662	+	14.5809i	−0.471901	+	0.575013i	0.481604	+	0.876389i	$0.340054\pi$
$644$	−19.0445	+	50.9147i	−0.750457	+	2.00632i
$645$	9.91761	−	3.00847i	0.390506	−	0.118459i
$646$	31.9506	−	62.3590i	1.25708	−	2.45348i
$647$	−36.5191	−	7.26411i	−1.43571	−	0.285581i	−0.584925	−	0.811087i	$-0.698876\pi$
$647$	−36.5191	−	7.26411i	−1.43571	−	0.285581i	−0.850790	+	0.525506i	$0.823876\pi$
$648$	26.2878	+	15.6472i	1.03268	+	0.614679i
$649$	−0.304938	−	1.53303i	−0.0119699	−	0.0601766i
$650$	1.38082	−	0.769216i	0.0541603	−	0.0301711i
$651$	−40.4676	−	3.98571i	−1.58605	−	0.156212i
$652$	11.7446	−	6.81274i	0.459955	−	0.266808i
$653$	8.64459	−	28.4974i	0.338289	−	1.11519i	−0.608559	−	0.793508i	$-0.708252\pi$
$653$	8.64459	−	28.4974i	0.338289	−	1.11519i	0.946848	−	0.321680i	$-0.104248\pi$
$654$	43.5044	−	0.756277i	1.70116	−	0.0295728i
$655$	−2.88302	+	6.96022i	−0.112649	+	0.271958i
$656$	−41.2810	+	11.2419i	−1.61175	+	0.438921i
$657$	−2.85118	−	6.88337i	−0.111235	−	0.268546i
$658$	6.46206	+	14.8646i	0.251917	+	0.579483i
$659$	42.4353	−	22.6821i	1.65304	−	0.883570i	0.662081	−	0.749433i	$-0.269674\pi$
$659$	42.4353	−	22.6821i	1.65304	−	0.883570i	0.990963	−	0.134137i	$-0.0428264\pi$
$660$	−0.412236	+	6.49236i	−0.0160463	+	0.252715i
$661$	−4.21834	+	3.46191i	−0.164075	+	0.134653i	−0.712848	−	0.701319i	$-0.752595\pi$
$661$	−4.21834	+	3.46191i	−0.164075	+	0.134653i	0.548773	+	0.835971i	$0.315095\pi$
$662$	−33.7930	+	3.92249i	−1.31340	+	0.152452i
$663$	9.59275	−	14.3566i	0.372552	−	0.557563i
$664$	10.1242	−	21.5763i	0.392893	−	0.837321i
$665$	−16.7978	+	11.2239i	−0.651389	+	0.435244i
$666$	−0.515548	+	6.36724i	−0.0199771	+	0.246725i
$667$	−36.0737	−	19.2818i	−1.39678	−	0.746595i
$668$	29.9886	+	18.5634i	1.16029	+	0.718239i
$669$	1.00055	+	10.1588i	0.0386837	+	0.392762i
$670$	−0.214310	+	1.18467i	−0.00827953	+	0.0457678i
$671$	15.8519	+	15.8519i	0.611957	+	0.611957i
$672$	35.0257	−	6.55781i	1.35115	−	0.252973i
$673$	12.5911	−	12.5911i	0.485352	−	0.485352i	−0.421484	−	0.906836i	$-0.638491\pi$
$673$	12.5911	−	12.5911i	0.485352	−	0.485352i	0.906836	+	0.421484i	$0.138491\pi$
$674$	−8.31328	−	11.9854i	−0.320216	−	0.461659i
$675$	4.21067	−	0.414715i	0.162069	−	0.0159624i
$676$	−23.1955	−	3.78101i	−0.892134	−	0.145424i
$677$	1.06715	−	1.99649i	0.0410138	−	0.0767315i	−0.860579	−	0.509316i	$-0.829898\pi$
$677$	1.06715	−	1.99649i	0.0410138	−	0.0767315i	0.901593	+	0.432585i	$0.142398\pi$
$678$	−0.965886	+	0.821189i	−0.0370946	+	0.0315376i
$679$	−15.4897	−	23.1819i	−0.594439	−	0.889641i
$680$	−5.35101	+	21.6431i	−0.205202	+	0.829976i
$681$	−2.77126	−	1.85170i	−0.106195	−	0.0709572i
$682$	−9.40661	+	11.8771i	−0.360198	+	0.454798i
$683$	−10.9361	−	13.3256i	−0.418456	−	0.509891i	0.520531	−	0.853843i	$-0.325734\pi$
$683$	−10.9361	−	13.3256i	−0.418456	−	0.509891i	−0.938987	+	0.343952i	$0.888234\pi$
$684$	−9.49365	−	4.65771i	−0.362999	−	0.178092i
$685$	−3.19637	−	5.98000i	−0.122127	−	0.228484i
$686$	6.11414	−	15.5184i	0.233439	−	0.592495i
$687$	17.5218	−	7.25779i	0.668500	−	0.276902i
$688$	−21.1432	−	0.605836i	−0.806078	−	0.0230973i
$689$	8.64251	+	3.57984i	0.329253	+	0.136381i
$690$	−16.2831	+	16.8593i	−0.619889	+	0.641822i
$691$	−38.2486	−	11.6026i	−1.45504	−	0.441383i	−0.538947	−	0.842340i	$-0.681178\pi$
$691$	−38.2486	−	11.6026i	−1.45504	−	0.441383i	−0.916097	+	0.400957i	$0.868678\pi$
$692$	16.6156	+	12.6958i	0.631629	+	0.482622i
$693$	0.439814	−	4.46551i	0.0167072	−	0.169631i
$694$	−15.8519	−	4.50926i	−0.601729	−	0.171169i
$695$	0.0189495	−	0.00376930i	0.000718797	−	0.000142978i
$696$	1.39759	+	26.7769i	0.0529756	+	1.01498i
$697$	−16.4482	+	82.6909i	−0.623021	+	3.13214i
$698$	−0.914279	−	2.83558i	−0.0346060	−	0.107328i
$699$	−7.90162	−	26.0482i	−0.298867	−	0.985232i
$700$	4.38471	−	4.70068i	0.165726	−	0.177669i
$701$	−7.09257	−	5.82072i	−0.267883	−	0.219846i	0.490856	−	0.871241i	$-0.336684\pi$
$701$	−7.09257	−	5.82072i	−0.267883	−	0.219846i	−0.758739	+	0.651395i	$0.774184\pi$
$702$	5.62434	+	3.61826i	0.212277	+	0.136562i
$703$			33.7525i			1.27300i
$704$	5.00578	−	12.2973i	0.188663	−	0.463472i
$705$			6.98874i			0.263211i
$706$	−18.6983	+	29.0652i	−0.703719	+	1.09388i
$707$	0.897593	+	0.736635i	0.0337575	+	0.0277040i
$708$	−3.68946	+	0.128314i	−0.138659	+	0.00482232i
$709$	−4.77226	−	15.7320i	−0.179226	−	0.590829i	−0.999814	−	0.0193080i	$-0.993854\pi$
$709$	−4.77226	−	15.7320i	−0.179226	−	0.590829i	0.820588	−	0.571521i	$-0.193646\pi$
$710$	−9.88452	+	3.18707i	−0.370959	+	0.119609i
$711$	0.0457366	−	0.229934i	0.00171526	−	0.00862318i
$712$	12.2294	−	34.5112i	0.458315	−	1.29336i
$713$	−53.5392	+	10.6496i	−2.00506	+	0.398831i
$714$	19.2131	−	67.5416i	0.719030	−	2.52768i
$715$	−0.181814	+	1.84599i	−0.00679947	+	0.0690361i
$716$	−9.21203	+	1.23190i	−0.344270	+	0.0460384i
$717$	42.5874	+	12.9187i	1.59045	+	0.482459i
$718$	3.49239	+	3.37304i	0.130335	+	0.125881i
$719$	−36.6632	−	15.1864i	−1.36731	−	0.566357i	−0.426249	−	0.904606i	$-0.640165\pi$
$719$	−36.6632	−	15.1864i	−1.36731	−	0.566357i	−0.941057	+	0.338249i	$0.890165\pi$
$720$	3.27994	+	0.750683i	0.122236	+	0.0279763i
$721$	54.4528	−	22.5551i	2.02793	−	0.839995i
$722$	−26.9842	−	10.6316i	−1.00425	−	0.395666i
$723$	14.2353	+	26.6324i	0.529416	+	0.990468i
$724$	−3.03308	−	8.87564i	−0.112723	−	0.329861i
$725$	3.06855	+	3.73903i	0.113963	+	0.138864i
$726$	17.9160	+	14.1894i	0.664927	+	0.526619i
$727$	−24.1907	−	16.1637i	−0.897185	−	0.599480i	0.0191834	−	0.999816i	$-0.493893\pi$
$727$	−24.1907	−	16.1637i	−0.897185	−	0.599480i	−0.916368	+	0.400336i	$0.868893\pi$
$728$	10.0460	−	1.52161i	0.372329	−	0.0563945i
$729$	8.76631	+	13.1197i	0.324678	+	0.485915i
$730$	8.11342	+	9.54304i	0.300291	+	0.353204i
$731$	−19.6488	+	36.7602i	−0.726735	+	1.35963i
$732$	42.9753	−	30.9285i	1.58841	−	1.14315i
$733$	4.73329	−	0.466189i	0.174828	−	0.0172191i	−0.0102242	−	0.999948i	$-0.503255\pi$
$733$	4.73329	−	0.466189i	0.174828	−	0.0172191i	0.185052	+	0.982729i	$0.440755\pi$
$734$	−12.5551	+	8.70848i	−0.463418	+	0.321436i
$735$	−4.61561	+	4.61561i	−0.170249	+	0.170249i
$736$	42.4396	−	22.0735i	1.56435	−	0.813640i
$737$	−0.999018	−	0.999018i	−0.0367993	−	0.0367993i
$738$	12.5210	+	2.26509i	0.460906	+	0.0833792i
$739$	−1.92223	−	19.5167i	−0.0707102	−	0.717933i	−0.963545	−	0.267548i	$-0.913787\pi$
$739$	−1.92223	−	19.5167i	−0.0707102	−	0.717933i	0.892834	−	0.450385i	$-0.148713\pi$
$740$	−2.46006	−	10.4541i	−0.0904334	−	0.384302i
$741$	−12.1428	−	6.49047i	−0.446077	−	0.238433i
$742$	37.9200	+	3.07034i	1.39209	+	0.112716i
$743$	26.9580	−	18.0128i	0.988993	−	0.660824i	0.0478580	−	0.998854i	$-0.484761\pi$
$743$	26.9580	−	18.0128i	0.988993	−	0.660824i	0.941135	+	0.338030i	$0.109761\pi$
$744$	24.1120	+	26.4405i	0.883989	+	0.969356i
$745$	−12.6297	+	18.9017i	−0.462718	+	0.692506i
$746$	−1.62055	−	13.9613i	−0.0593324	−	0.511160i
$747$	−5.47924	+	4.49669i	−0.200475	+	0.164525i
$748$	−17.2911	−	19.6358i	−0.632226	−	0.717957i
$749$	−28.6880	+	15.3341i	−1.04824	+	0.560295i
$750$	2.54190	−	1.10504i	0.0928172	−	0.0403502i
$751$	−12.2073	−	29.4710i	−0.445451	−	1.07541i	−0.974008	−	0.226516i	$-0.927267\pi$
$751$	−12.2073	−	29.4710i	−0.445451	−	1.07541i	0.528557	−	0.848898i	$-0.322733\pi$
$752$	4.52972	−	13.5251i	0.165182	−	0.493211i
$753$	2.08501	−	5.03365i	0.0759818	−	0.183436i
$754$	0.132887	+	7.64427i	0.00483947	+	0.278388i
$755$	6.27935	−	20.7002i	0.228529	−	0.753359i
$756$	26.2856	+	6.98579i	0.956000	+	0.254071i
$757$	−42.2534	−	4.16160i	−1.53573	−	0.151256i	−0.705512	−	0.708698i	$-0.749283\pi$
$757$	−42.2534	−	4.16160i	−1.53573	−	0.151256i	−0.830216	+	0.557443i	$0.811783\pi$
$758$	1.19964	+	2.15347i	0.0435728	+	0.0782177i
$759$	−5.36623	−	26.9779i	−0.194782	−	0.979234i
$760$	17.5937	+	2.55480i	0.638191	+	0.0926724i
$761$	42.2597	+	8.40597i	1.53191	+	0.304716i	0.887805	−	0.460219i	$-0.152229\pi$
$761$	42.2597	+	8.40597i	1.53191	+	0.304716i	0.644107	+	0.764935i	$0.277229\pi$
$762$	25.0309	+	12.8250i	0.906774	+	0.464600i
$763$	48.2833	−	14.6466i	1.74797	−	0.530242i
$764$	8.57856	+	18.8310i	0.310362	+	0.681283i
$765$	4.20640	−	5.12551i	0.152083	−	0.185313i
$766$	6.58130	+	30.3220i	0.237792	+	1.09558i
$767$	−1.05263			−0.0380083
$768$	−26.7638	−	16.3415i	−0.965754	−	0.589674i
$769$	−2.59370			−0.0935314			−0.0467657	−	0.998906i	$-0.514891\pi$
$769$	−2.59370			−0.0935314			−0.0467657	+	0.998906i	$0.514891\pi$
$770$	1.60010	+	7.37213i	0.0576635	+	0.265673i
$771$	17.8491	−	21.7492i	0.642819	−	0.783277i
$772$	−16.2154	−	35.5948i	−0.583603	−	1.28108i
$773$	−7.43908	+	2.25662i	−0.267565	+	0.0811650i	−0.421217	−	0.906960i	$-0.638397\pi$
$773$	−7.43908	+	2.25662i	−0.267565	+	0.0811650i	0.153651	+	0.988125i	$0.450897\pi$
$774$	5.59859	+	2.86853i	0.201237	+	0.103107i
$775$	6.33117	+	1.25935i	0.227422	+	0.0452371i
$776$	−3.52578	+	24.2804i	−0.126568	+	0.871616i
$777$	6.59920	+	33.1764i	0.236745	+	1.19020i
$778$	15.7681	+	28.3054i	0.565314	+	1.01480i
$779$	66.9071	+	6.58978i	2.39720	+	0.236103i
$780$	4.23404	+	1.12526i	0.151603	+	0.0402907i
$781$	3.53798	−	11.6631i	0.126599	−	0.417340i
$782$	−1.63849	−	94.2531i	−0.0585922	−	3.37048i
$783$	−7.83180	+	18.9076i	−0.279886	+	0.675703i
$784$	11.9241	−	5.94088i	0.425859	−	0.212174i
$785$	−1.85719	−	4.48365i	−0.0662859	−	0.160028i
$786$	−19.1499	+	8.32500i	−0.683054	+	0.296943i
$787$	−8.91725	+	4.76637i	−0.317865	+	0.169903i	−0.622612	−	0.782531i	$-0.713928\pi$
$787$	−8.91725	+	4.76637i	−0.317865	+	0.169903i	0.304746	+	0.952434i	$0.401428\pi$
$788$	−0.286059	−	0.324849i	−0.0101904	−	0.0115722i
$789$	2.31518	−	1.90002i	0.0824226	−	0.0676425i
$790$	0.0454443	+	0.391511i	0.00161684	+	0.0139293i
$791$	−0.816768	+	1.22238i	−0.0290409	+	0.0434628i
$792$	−2.91765	+	2.66070i	−0.103674	+	0.0945440i
$793$	12.5529	−	8.38755i	0.445765	−	0.297851i
$794$	−12.8275	−	1.03863i	−0.455232	−	0.0368596i
$795$	14.4669	+	7.73270i	0.513087	+	0.274251i
$796$	10.8300	+	46.0226i	0.383858	+	1.63123i
$797$	−1.98912	−	20.1959i	−0.0704583	−	0.715375i	−0.963912	−	0.266220i	$-0.914225\pi$
$797$	−1.98912	−	20.1959i	−0.0704583	−	0.715375i	0.893454	−	0.449155i	$-0.148275\pi$
$798$	−55.1011	−	9.96795i	−1.95056	−	0.352861i
$799$	−19.8751	−	19.8751i	−0.703132	−	0.703132i
$800$	−5.63550	+	0.491023i	−0.199245	+	0.0173603i
$801$	−7.69981	+	7.69981i	−0.272059	+	0.272059i
$802$	28.1793	−	19.5457i	0.995045	−	0.690182i
$803$	−14.6288	+	1.44081i	−0.516240	+	0.0508452i
$804$	−2.70839	+	1.94917i	−0.0955174	+	0.0687421i
$805$	−12.8125	+	23.9706i	−0.451582	+	0.844851i
$806$	6.60897	+	7.77351i	0.232791	+	0.273810i
$807$	−22.1242	−	33.1111i	−0.778807	−	1.16557i
$808$	−0.153025	−	1.01031i	−0.00538339	−	0.0355424i
$809$	0.918005	+	0.613392i	0.0322754	+	0.0215657i	0.571603	−	0.820530i	$-0.306322\pi$
$809$	0.918005	+	0.613392i	0.0322754	+	0.0215657i	−0.539328	+	0.842096i	$0.681322\pi$
$810$	11.9909	+	9.49675i	0.421318	+	0.333682i
$811$	0.623258	+	0.759442i	0.0218855	+	0.0266676i	0.783838	−	0.620965i	$-0.213259\pi$
$811$	0.623258	+	0.759442i	0.0218855	+	0.0266676i	−0.761953	+	0.647633i	$0.775759\pi$
$812$	10.0546	+	29.4226i	0.352847	+	1.03253i
$813$	−2.89364	−	5.41362i	−0.101484	−	0.189864i
$814$	11.7262	+	4.62002i	0.411002	+	0.161932i
$815$	6.27201	−	2.59795i	0.219699	−	0.0910023i
$816$	−52.3427	+	32.8456i	−1.83236	+	1.14983i
$817$	30.7078	+	12.7196i	1.07433	+	0.445002i
$818$	36.9020	+	35.6409i	1.29025	+	1.24616i
$819$	−2.89169	−	0.877184i	−0.101044	−	0.0306513i
$820$	−21.2034	+	2.83549i	−0.740455	+	0.0990195i
$821$	−2.60392	+	26.4380i	−0.0908775	+	0.922694i	0.836350	+	0.548196i	$0.184685\pi$
$821$	−2.60392	+	26.4380i	−0.0908775	+	0.922694i	−0.927228	+	0.374499i	$0.877815\pi$
$822$	5.14218	−	18.0768i	0.179354	−	0.630502i
$823$	13.5213	−	2.68956i	0.471323	−	0.0937521i	0.0462868	−	0.998928i	$-0.485261\pi$
$823$	13.5213	−	2.68956i	0.471323	−	0.0937521i	0.425037	+	0.905176i	$0.360261\pi$
$824$	−48.8880	−	17.3239i	−1.70309	−	0.603507i
$825$	−0.634573	+	3.19021i	−0.0220930	+	0.111069i
$826$	−4.07438	+	1.31371i	−0.141766	+	0.0457097i
$827$	−11.6955	−	38.5550i	−0.406693	−	1.34069i	−0.886262	−	0.463184i	$-0.846707\pi$
$827$	−11.6955	−	38.5550i	−0.406693	−	1.34069i	0.479569	−	0.877504i	$-0.340793\pi$
$828$	−14.2183	+	0.494489i	−0.494120	+	0.0171847i
$829$	6.19845	+	5.08693i	0.215281	+	0.176677i	0.735853	−	0.677141i	$-0.236781\pi$
$829$	6.19845	+	5.08693i	0.215281	+	0.176677i	−0.520572	+	0.853818i	$0.674281\pi$
$830$	6.44736	−	10.0220i	0.223791	−	0.347868i
$831$		−	29.6775i		−	1.02950i
$832$	−7.46470	−	4.92196i	−0.258792	−	0.170638i
$833$		−	26.2525i		−	0.909594i
$834$	0.0450369	+	0.0289732i	0.00155950	+	0.00100326i
$835$	13.6317	+	11.1873i	0.471745	+	0.387151i
$836$	−14.2310	+	15.2566i	−0.492191	+	0.527660i
$837$	7.92833	+	26.1362i	0.274043	+	0.903400i
$838$	−11.6128	−	36.0164i	−0.401158	−	1.24417i
$839$	−1.22780	+	6.17255i	−0.0423883	+	0.213100i	−0.996175	−	0.0873855i	$-0.972149\pi$
$839$	−1.22780	+	6.17255i	−0.0423883	+	0.213100i	0.953786	+	0.300486i	$0.0971488\pi$
$840$	17.7930	−	0.928682i	0.613915	−	0.0320426i
$841$	5.49598	−	1.09322i	0.189516	−	0.0376972i
$842$	6.99275	+	1.98918i	0.240986	+	0.0685516i
$843$	−1.98343	+	20.1381i	−0.0683130	+	0.693594i
$844$	9.81676	+	7.50091i	0.337907	+	0.258192i
$845$	−11.2448	−	3.41108i	−0.386834	−	0.117345i
$846$	−2.94698	+	3.05125i	−0.101319	+	0.104904i
$847$	24.4849	+	10.1420i	0.841312	+	0.348483i
$848$	−22.9854	−	24.3415i	−0.789323	−	0.835892i
$849$	25.8143	−	10.6926i	0.885945	−	0.366971i
$850$	−4.08628	+	10.3715i	−0.140158	+	0.355738i
$851$	21.4060	+	40.0478i	0.733789	+	1.37282i
$852$	−25.8432	−	12.6790i	−0.885374	−	0.434376i
$853$	13.4760	+	16.4206i	0.461410	+	0.562229i	0.950788	−	0.309842i	$-0.100276\pi$
$853$	13.4760	+	16.4206i	0.461410	+	0.562229i	−0.489378	+	0.872072i	$0.662776\pi$
$854$	38.1201	−	48.1317i	1.30444	−	1.64703i
$855$	−4.39626	−	2.93749i	−0.150349	−	0.100460i
$856$	27.7889	+	6.87049i	0.949806	+	0.234828i
$857$	−24.7565	−	37.0507i	−0.845665	−	1.26563i	−0.962174	−	0.272437i	$-0.912170\pi$
$857$	−24.7565	−	37.0507i	−0.845665	−	1.26563i	0.116509	−	0.993190i	$-0.462830\pi$
$858$	−3.91699	+	3.33020i	−0.133724	+	0.113691i
$859$	18.4944	−	34.6006i	0.631022	−	1.18056i	−0.339741	−	0.940519i	$-0.610340\pi$
$859$	18.4944	−	34.6006i	0.631022	−	1.18056i	0.970763	−	0.240040i	$-0.0771605\pi$
$860$	−10.4382	−	1.70149i	−0.355939	−	0.0580203i
$861$	67.0536	−	6.60421i	2.28518	−	0.225071i
$862$	11.7847	+	16.9902i	0.401390	+	0.578689i
$863$	−13.9678	+	13.9678i	−0.475470	+	0.475470i	−0.903679	−	0.428210i	$-0.859144\pi$
$863$	−13.9678	+	13.9678i	−0.475470	+	0.475470i	0.428210	+	0.903679i	$0.359144\pi$
$864$	−13.0722	−	20.0492i	−0.444727	−	0.682089i
$865$	7.39307	+	7.39307i	0.251372	+	0.251372i
$866$	−0.313496	+	1.73295i	−0.0106530	+	0.0588881i
$867$	8.67007	+	88.0287i	0.294451	+	2.98961i
$868$	35.2827	+	21.8405i	1.19757	+	0.741316i
$869$	−0.407923	−	0.218039i	−0.0138378	−	0.00739648i
$870$	−1.08198	+	13.3630i	−0.0366827	+	0.453047i
$871$	−0.791105	+	0.528599i	−0.0268056	+	0.0179109i
$872$	−40.1962	−	18.8611i	−1.36122	−	0.638719i
$873$	4.05391	−	6.06711i	0.137204	−	0.205341i
$874$	−74.6690	+	8.66713i	−2.52572	+	0.293170i
$875$	2.48454	−	2.03901i	0.0839928	−	0.0689311i
$876$	−2.20001	+	34.6483i	−0.0743315	+	1.17066i
$877$	−29.3175	+	15.6705i	−0.989981	+	0.529156i	−0.885136	−	0.465332i	$-0.845935\pi$
$877$	−29.3175	+	15.6705i	−0.989981	+	0.529156i	−0.104845	+	0.994489i	$0.533435\pi$
$878$	−1.87112	−	4.30412i	−0.0631473	−	0.145257i
$879$	9.44797	+	22.8094i	0.318672	+	0.769343i
$880$	3.29580	−	5.76264i	0.111101	−	0.194259i
$881$	−16.0921	+	38.8499i	−0.542158	+	1.30889i	0.381039	+	0.924559i	$0.375566\pi$
$881$	−16.0921	+	38.8499i	−0.542158	+	1.30889i	−0.923197	+	0.384327i	$0.874434\pi$
$882$	−3.96144	+	0.0688655i	−0.133389	+	0.00231882i
$883$	0.145718	−	0.480367i	0.00490379	−	0.0161656i	−0.954454	−	0.298357i	$-0.903561\pi$
$883$	0.145718	−	0.480367i	0.00490379	−	0.0161656i	0.959358	+	0.282192i	$0.0910614\pi$
$884$	−15.2412	+	8.84101i	−0.512617	+	0.297355i
$885$	−1.83696	−	0.180925i	−0.0617487	−	0.00608172i
$886$	−27.2805	+	15.1972i	−0.916506	+	0.510559i
$887$	−3.32136	−	16.6976i	−0.111520	−	0.560651i	−0.995631	−	0.0933736i	$-0.970235\pi$
$887$	−3.32136	−	16.6976i	−0.111520	−	0.560651i	0.884111	−	0.467278i	$-0.154765\pi$
$888$	15.2253	−	25.5790i	0.510927	−	0.858374i
$889$	31.9877	+	6.36274i	1.07283	+	0.213400i
$890$	8.34792	−	16.2929i	0.279823	−	0.546139i
$891$	−17.1776	+	5.21078i	−0.575473	+	0.174568i
$892$	3.64944	−	9.75665i	0.122192	−	0.326677i
$893$	−14.2190	+	17.3259i	−0.475820	+	0.579789i
$894$	−61.5754	+	13.3647i	−2.05939	+	0.446984i
$895$	−4.64702			−0.155333
$896$	−35.0362	−	9.73517i	−1.17048	−	0.325229i
$897$	−18.5239			−0.618495
$898$	29.8248	−	6.47337i	0.995266	−	0.216019i
$899$	−19.8081	+	24.1362i	−0.660637	+	0.804989i
$900$	1.57575	+	0.589404i	0.0525250	+	0.0196468i
$901$	−63.1329	+	19.1512i	−2.10326	+	0.638017i
$902$	11.4476	−	22.3426i	0.381164	−	0.743928i
$903$	32.6706	+	6.49859i	1.08721	+	0.216259i
$904$	1.25399	−	0.318189i	0.0417071	−	0.0105828i
$905$	−0.914933	−	4.59968i	−0.0304134	−	0.152898i
$906$	52.3779	−	29.1782i	1.74014	−	0.969382i
$907$	−59.5819	−	5.86831i	−1.97839	−	0.194854i	−0.978454	−	0.206467i	$-0.933803\pi$
$907$	−59.5819	−	5.86831i	−1.97839	−	0.194854i	−0.999933	+	0.0116132i	$0.996303\pi$
$908$	1.70659	+	2.94202i	0.0566351	+	0.0976345i
$909$	−0.0882166	+	0.290811i	−0.00292596	+	0.00964559i
$910$	5.07952	−	0.0883020i	0.168385	−	0.00292718i
$911$	7.65961	−	18.4919i	0.253774	−	0.612665i	−0.744729	−	0.667367i	$-0.767421\pi$
$911$	7.65961	−	18.4919i	0.253774	−	0.612665i	0.998503	+	0.0547027i	$0.0174211\pi$
$912$	30.1566	+	38.9707i	0.998586	+	1.29045i
$913$	5.35174	+	12.9202i	0.177117	+	0.427597i
$914$	7.65832	+	17.6164i	0.253315	+	0.582698i
$915$	23.3478	−	12.4797i	0.771855	−	0.412565i
$916$	−19.3147	−	1.22640i	−0.638176	−	0.0405213i
$917$	−18.7178	+	15.3613i	−0.618115	+	0.507274i
$918$	−46.8506	+	5.43814i	−1.54630	+	0.179485i
$919$	−25.0131	+	37.4348i	−0.825106	+	1.23486i	0.144333	+	0.989529i	$0.453896\pi$
$919$	−25.0131	+	37.4348i	−0.825106	+	1.23486i	−0.969440	+	0.245330i	$0.921104\pi$
$920$	22.4955	−	8.12673i	0.741654	−	0.267930i
$921$	42.9405	−	28.6919i	1.41494	−	0.945430i
$922$	−1.06550	+	13.1594i	−0.0350905	+	0.433383i
$923$	−7.23869	−	3.86916i	−0.238264	−	0.127355i
$924$	−11.0052	+	17.7786i	−0.362045	+	0.584873i
$925$	−0.526337	−	5.34399i	−0.0173059	−	0.175709i
$926$	−1.16366	+	6.43252i	−0.0382403	+	0.211386i
$927$	10.9074	+	10.9074i	0.358246	+	0.358246i
$928$	10.7551	−	25.1597i	0.353053	−	0.825908i
$929$	12.6095	−	12.6095i	0.413706	−	0.413706i	−0.469322	−	0.883027i	$-0.655501\pi$
$929$	12.6095	−	12.6095i	0.413706	−	0.413706i	0.883027	+	0.469322i	$0.155501\pi$
$930$	10.1973	+	14.7016i	0.334383	+	0.482084i
$931$	−20.8333	+	2.05190i	−0.682785	+	0.0672485i
$932$	−4.46889	+	27.4154i	−0.146383	+	0.898022i
$933$	−2.63347	+	4.92687i	−0.0862158	+	0.161298i
$934$	15.9745	−	13.5814i	0.522700	−	0.444396i
$935$	−7.26794	−	10.8772i	−0.237687	−	0.355724i
$936$	1.37407	+	2.27668i	0.0449129	+	0.0744155i
$937$	41.4283	+	27.6815i	1.35340	+	0.904314i	0.999520	−	0.0309758i	$-0.00986149\pi$
$937$	41.4283	+	27.6815i	1.35340	+	0.904314i	0.353882	+	0.935290i	$0.384861\pi$
$938$	−2.40240	+	3.03335i	−0.0784412	+	0.0990425i
$939$	19.8569	+	24.1957i	0.648004	+	0.789596i
$940$	3.14124	−	6.40269i	0.102456	−	0.208833i
$941$	−6.47035	−	12.1052i	−0.210927	−	0.394617i	0.754103	−	0.656756i	$-0.228072\pi$
$941$	−6.47035	−	12.1052i	−0.210927	−	0.394617i	−0.965030	+	0.262139i	$0.915572\pi$
$942$	4.93080	−	12.5150i	0.160654	−	0.407760i
$943$	83.5656	−	34.6140i	2.72127	−	1.12719i
$944$	3.43775	+	1.54076i	0.111889	+	0.0501473i
$945$	12.5639	+	5.20413i	0.408703	+	0.169290i
$946$	8.62226	−	8.92734i	0.280334	−	0.290253i
$947$	−44.3422	−	13.4511i	−1.44093	−	0.437101i	−0.529412	−	0.848365i	$-0.677588\pi$
$947$	−44.3422	−	13.4511i	−1.44093	−	0.437101i	−0.911516	+	0.411264i	$0.865088\pi$
$948$	−0.663267	+	0.868046i	−0.0215419	+	0.0281928i
$949$	−0.970303	+	9.85165i	−0.0314974	+	0.319798i
$950$	8.54993	+	2.43214i	0.277396	+	0.0789089i
$951$	9.54217	−	1.89805i	0.309426	−	0.0615487i
$952$	−47.9599	+	53.2421i	−1.55439	+	1.72559i
$953$	2.90030	−	14.5808i	0.0939499	−	0.472318i	−0.904954	−	0.425510i	$-0.860095\pi$
$953$	2.90030	−	14.5808i	0.0939499	−	0.472318i	0.998904	−	0.0468087i	$-0.0149051\pi$
$954$	3.05548	+	9.47639i	0.0989248	+	0.306809i
$955$	3.00343	+	9.90098i	0.0971887	+	0.320388i
$956$	−33.2095	−	30.9772i	−1.07407	−	1.00188i
$957$	−12.1620	−	9.98111i	−0.393142	−	0.322643i
$958$	7.69880	+	4.95281i	0.248737	+	0.160018i
$959$		−	21.7938i		−	0.703757i
$960$	−12.1808	−	9.87241i	−0.393133	−	0.318631i
$961$			10.6697i			0.344184i
$962$	4.59213	−	7.13815i	0.148056	−	0.230143i
$963$	−6.58095	−	5.40085i	−0.212068	−	0.174040i
$964$	−1.07108	−	30.7974i	−0.0344973	−	0.991919i
$965$	−5.67713	−	18.7150i	−0.182753	−	0.602457i
$966$	−71.7000	+	23.1183i	−2.30691	+	0.743819i
$967$	−0.972494	+	4.88906i	−0.0312733	+	0.157221i	−0.993266	−	0.115852i	$-0.963040\pi$
$967$	−0.972494	+	4.88906i	−0.0312733	+	0.157221i	0.961993	+	0.273073i	$0.0880402\pi$
$968$	−10.0359	−	21.0523i	−0.322567	−	0.676647i
$969$	95.2378	−	18.9440i	3.05948	−	0.608569i
$970$	−3.35650	+	11.7994i	−0.107771	+	0.378857i
$971$	−3.09929	+	31.4676i	−0.0994609	+	1.00984i	0.807851	+	0.589386i	$0.200630\pi$
$971$	−3.09929	+	31.4676i	−0.0994609	+	1.00984i	−0.907312	+	0.420457i	$0.861870\pi$
$972$	2.25465	+	16.8600i	0.0723178	+	0.540783i
$973$	0.0594252	+	0.0180264i	0.00190508	+	0.000577901i
$974$	−13.5576	−	13.0943i	−0.434414	−	0.419568i
$975$	2.02377	+	0.838272i	0.0648124	+	0.0268462i
$976$	−53.2731	+	9.01879i	−1.70523	+	0.288684i
$977$	−10.5245	+	4.35938i	−0.336708	+	0.139469i	−0.544630	−	0.838676i	$-0.683330\pi$
$977$	−10.5245	+	4.35938i	−0.336708	+	0.139469i	0.207922	+	0.978145i	$0.433330\pi$
$978$	17.5067	+	6.89752i	0.559803	+	0.220558i
$979$	10.1275	+	18.9472i	0.323676	+	0.605555i
$980$	6.30315	−	2.15398i	0.201347	−	0.0688062i
$981$	8.37727	+	10.2077i	0.267466	+	0.325908i
$982$	41.9991	+	33.2631i	1.34025	+	1.06147i
$983$	−6.98889	−	4.66983i	−0.222911	−	0.148944i	0.439101	−	0.898438i	$-0.355297\pi$
$983$	−6.98889	−	4.66983i	−0.222911	−	0.148944i	−0.662012	+	0.749493i	$0.730297\pi$
$984$	−47.7323	−	35.1749i	−1.52165	−	1.12133i
$985$	−0.120238	−	0.179949i	−0.00383111	−	0.00573366i
$986$	−34.9256	−	41.0797i	−1.11226	−	1.30824i
$987$	−10.5888	+	19.8102i	−0.337045	+	0.630567i
$988$	8.20728	+	11.4040i	0.261108	+	0.362811i
$989$	44.5021	−	4.38307i	1.41508	−	0.139374i
$990$	−1.62229	+	1.12525i	−0.0515597	+	0.0357628i
$991$	−25.9801	+	25.9801i	−0.825286	+	0.825286i	−0.986861	−	0.161574i	$-0.948343\pi$
$991$	−25.9801	+	25.9801i	−0.825286	+	0.825286i	0.161574	+	0.986861i	$0.448343\pi$
$992$	−10.2058	−	35.0610i	−0.324035	−	1.11319i
$993$	−33.3377	−	33.3377i	−1.05794	−	1.05794i
$994$	−32.8474	−	5.94219i	−1.04186	−	0.188475i
$995$	2.31711	+	23.5260i	0.0734573	+	0.745824i
$996$	32.1515	−	7.56585i	1.01876	−	0.239733i
$997$	−45.3468	−	24.2384i	−1.43615	−	0.767637i	−0.444399	−	0.895829i	$-0.646583\pi$
$997$	−45.3468	−	24.2384i	−1.43615	−	0.767637i	−0.991749	+	0.128192i	$0.959083\pi$
$998$	19.0986	+	1.54639i	0.604556	+	0.0489502i
$999$	18.8910	−	12.6226i	0.597686	−	0.399361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.28	✓	1024
128.125	even	32	inner	640.2.bm.a.381.28	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.28	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.28	yes	1024	128.125	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.299966 - 1.38203i) q^{2} +(1.24334 - 1.51502i) q^{3} +(-1.82004 + 0.829128i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-2.46677 - 1.26389i) q^{6} +(-3.15235 - 0.627042i) q^{7} +(1.69183 + 2.26665i) q^{8} +(-0.164108 - 0.825025i) q^{9} +O(q^{10})\)	\(q+(-0.299966 - 1.38203i) q^{2} +(1.24334 - 1.51502i) q^{3} +(-1.82004 + 0.829128i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-2.46677 - 1.26389i) q^{6} +(-3.15235 - 0.627042i) q^{7} +(1.69183 + 2.26665i) q^{8} +(-0.164108 - 0.825025i) q^{9} +(0.688233 + 1.23545i) q^{10} +(-1.65165 - 0.162673i) q^{11} +(-1.00679 + 3.78829i) q^{12} +(-0.324442 + 1.06954i) q^{13} +(0.0790057 + 4.54475i) q^{14} +(-0.750019 + 1.81071i) q^{15} +(2.62509 - 3.01809i) q^{16} +(-3.01647 - 7.28240i) q^{17} +(-1.09099 + 0.474282i) q^{18} +(-5.54337 + 2.96299i) q^{19} +(1.50099 - 1.32176i) q^{20} +(-4.86944 + 3.99625i) q^{21} +(0.270618 + 2.33143i) q^{22} +(-4.69814 + 7.03127i) q^{23} +(5.53755 + 0.255064i) q^{24} +(0.831470 - 0.555570i) q^{25} +(1.57546 + 0.127564i) q^{26} +(3.73145 + 1.99450i) q^{27} +(6.25731 - 1.47246i) q^{28} +(0.474107 + 4.81369i) q^{29} +(2.72744 + 0.493402i) q^{30} +(4.56452 + 4.56452i) q^{31} +(-4.95855 - 2.72265i) q^{32} +(-2.30002 + 2.30002i) q^{33} +(-9.15969 + 6.35333i) q^{34} +(3.19863 - 0.315038i) q^{35} +(0.982733 + 1.36551i) q^{36} +(2.53133 - 4.73578i) q^{37} +(5.75778 + 6.77233i) q^{38} +(1.21698 + 1.82134i) q^{39} +(-2.27696 - 1.67793i) q^{40} +(-8.89347 - 5.94243i) q^{41} +(6.98362 + 5.53100i) q^{42} +(-3.35466 - 4.08766i) q^{43} +(3.14094 - 1.07335i) q^{44} +(0.396533 + 0.741861i) q^{45} +(11.1267 + 4.38386i) q^{46} +(3.29444 - 1.36460i) q^{47} +(-1.30857 - 7.72960i) q^{48} +(3.07699 + 1.27453i) q^{49} +(-1.01723 - 0.982468i) q^{50} +(-14.7835 - 4.48452i) q^{51} +(-0.296289 - 2.21561i) q^{52} +(0.820378 - 8.32944i) q^{53} +(1.63716 - 5.75527i) q^{54} +(1.62775 - 0.323779i) q^{55} +(-3.91197 - 8.20613i) q^{56} +(-2.40332 + 12.0823i) q^{57} +(6.51047 - 2.09918i) q^{58} +(0.273393 + 0.901255i) q^{59} +(-0.136241 - 3.91742i) q^{60} +(-10.4416 - 8.56924i) q^{61} +(4.93912 - 7.67753i) q^{62} +2.70367i q^{63} +(-2.27540 + 7.66959i) q^{64} -1.11767i q^{65} +(3.86863 + 2.48878i) q^{66} +(0.658052 + 0.540050i) q^{67} +(11.5281 + 10.7532i) q^{68} +(4.81110 + 15.8601i) q^{69} +(-1.39488 - 4.32612i) q^{70} +(-1.43269 + 7.20264i) q^{71} +(1.59240 - 1.76778i) q^{72} +(8.68694 - 1.72794i) q^{73} +(-7.30433 - 2.07781i) q^{74} +(0.192103 - 1.95046i) q^{75} +(7.63246 - 9.98893i) q^{76} +(5.10457 + 1.54845i) q^{77} +(2.15211 - 2.22825i) q^{78} +(0.257484 + 0.106653i) q^{79} +(-1.63595 + 3.65016i) q^{80} +(9.99265 - 4.13909i) q^{81} +(-5.54490 + 14.0736i) q^{82} +(-3.97218 - 7.43142i) q^{83} +(5.54918 - 11.3107i) q^{84} +(5.00055 + 6.09318i) q^{85} +(-4.64301 + 5.86241i) q^{86} +(7.88230 + 5.26679i) q^{87} +(-2.42559 - 4.01892i) q^{88} +(-7.19185 - 10.7634i) q^{89} +(0.906332 - 0.770556i) q^{90} +(1.69340 - 3.16813i) q^{91} +(2.72099 - 16.6926i) q^{92} +(12.5906 - 1.24007i) q^{93} +(-2.87415 - 4.14370i) q^{94} +(4.44456 - 4.44456i) q^{95} +(-10.2900 + 4.12711i) q^{96} +(6.13377 + 6.13377i) q^{97} +(0.838454 - 4.63483i) q^{98} +(0.136838 + 1.38934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * 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

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