LMFDB - Embedded newform 640.2.bm.a.221.41

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			221.41
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.41

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.555972 + 1.30034i) q^{2} +(-2.36224 - 0.232661i) q^{3} +(-1.38179 + 1.44591i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01080 - 3.20108i) q^{6} +(-0.593396 - 2.98320i) q^{7} +(-2.64842 - 0.992915i) q^{8} +(2.58370 + 0.513930i) q^{9} +O(q^{10})$	\(q+(0.555972 + 1.30034i) q^{2} +(-2.36224 - 0.232661i) q^{3} +(-1.38179 + 1.44591i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01080 - 3.20108i) q^{6} +(-0.593396 - 2.98320i) q^{7} +(-2.64842 - 0.992915i) q^{8} +(2.58370 + 0.513930i) q^{9} +(-0.884718 + 1.10330i) q^{10} +(-0.829813 - 0.681010i) q^{11} +(3.60053 - 3.09410i) q^{12} +(3.26520 + 1.74528i) q^{13} +(3.54928 - 2.43020i) q^{14} +(-0.908365 - 2.19299i) q^{15} +(-0.181316 - 3.99589i) q^{16} +(1.93607 - 4.67409i) q^{17} +(0.768181 + 3.64543i) q^{18} +(-0.398280 + 0.120817i) q^{19} +(-1.92655 - 0.537032i) q^{20} +(0.707672 + 7.18511i) q^{21} +(0.424194 - 1.45766i) q^{22} +(1.62694 - 1.08709i) q^{23} +(6.02519 + 2.96169i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-0.454110 + 5.21621i) q^{26} +(0.830627 + 0.251968i) q^{27} +(5.13340 + 3.26416i) q^{28} +(3.98951 + 4.86124i) q^{29} +(2.34661 - 2.40043i) q^{30} +(-0.375400 + 0.375400i) q^{31} +(5.09522 - 2.45738i) q^{32} +(1.80177 + 1.80177i) q^{33} +(7.15433 - 0.0811058i) q^{34} +(2.35123 - 1.92960i) q^{35} +(-4.31323 + 3.02566i) q^{36} +(1.40416 - 4.62888i) q^{37} +(-0.378536 - 0.450730i) q^{38} +(-7.30712 - 4.88246i) q^{39} +(-0.372783 - 2.80375i) q^{40} +(0.672363 + 1.00626i) q^{41} +(-8.94967 + 4.91494i) q^{42} +(10.3043 - 1.01488i) q^{43} +(2.13131 - 0.258823i) q^{44} +(0.764703 + 2.52089i) q^{45} +(2.31813 + 1.51120i) q^{46} +(-4.91567 - 2.03614i) q^{47} +(-0.501374 + 9.48144i) q^{48} +(-2.08024 + 0.861662i) q^{49} +(-1.39008 - 0.260158i) q^{50} +(-5.66095 + 10.5909i) q^{51} +(-7.03534 + 2.30957i) q^{52} +(0.753431 - 0.918059i) q^{53} +(0.134161 + 1.22019i) q^{54} +(0.209426 - 1.05286i) q^{55} +(-1.39051 + 8.48997i) q^{56} +(0.968943 - 0.192735i) q^{57} +(-4.10322 + 7.89045i) q^{58} +(1.99713 - 1.06749i) q^{59} +(4.42603 + 1.71683i) q^{60} +(0.648129 - 6.58056i) q^{61} +(-0.696861 - 0.279437i) q^{62} -8.01268i q^{63} +(6.02824 + 5.25931i) q^{64} +3.70237i q^{65} +(-1.34119 + 3.34466i) q^{66} +(1.15425 - 11.7193i) q^{67} +(4.08307 + 9.25799i) q^{68} +(-4.09616 + 2.18944i) q^{69} +(3.81636 + 1.98460i) q^{70} +(2.98638 - 0.594027i) q^{71} +(-6.33244 - 3.92650i) q^{72} +(-1.10943 + 5.57749i) q^{73} +(6.79981 - 0.747645i) q^{74} +(1.50584 - 1.83487i) q^{75} +(0.375648 - 0.742821i) q^{76} +(-1.53918 + 2.87961i) q^{77} +(2.28632 - 12.2163i) q^{78} +(-2.41671 + 1.00104i) q^{79} +(3.43859 - 2.04356i) q^{80} +(-9.20490 - 3.81280i) q^{81} +(-0.934672 + 1.43376i) q^{82} +(-1.13297 - 3.73491i) q^{83} +(-11.3669 - 8.90508i) q^{84} +(5.03484 - 0.495888i) q^{85} +(7.04860 + 12.8349i) q^{86} +(-8.29318 - 12.4116i) q^{87} +(1.52151 + 2.62753i) q^{88} +(-12.3967 - 8.28323i) q^{89} +(-2.85287 + 2.39592i) q^{90} +(3.26898 - 10.7764i) q^{91} +(-0.676260 + 3.85454i) q^{92} +(0.974126 - 0.799445i) q^{93} +(-0.0852978 - 7.52410i) q^{94} +(-0.294299 - 0.294299i) q^{95} +(-12.6079 + 4.61946i) q^{96} +(11.9118 - 11.9118i) q^{97} +(-2.27701 - 2.22596i) q^{98} +(-1.79400 - 2.18599i) 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	0.555972	+	1.30034i	0.393132	+	0.919482i
$2$	0.555972	+	1.30034i	0.393132	+	0.919482i
$3$	−2.36224	−	0.232661i	−1.36384	−	0.134327i	−0.610531	−	0.791992i	$-0.709044\pi$
$3$	−2.36224	−	0.232661i	−1.36384	−	0.134327i	−0.753310	+	0.657666i	$0.771544\pi$
$4$	−1.38179	+	1.44591i	−0.690895	+	0.722955i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$6$	−1.01080	−	3.20108i	−0.412659	−	1.30684i
$7$	−0.593396	−	2.98320i	−0.224283	−	1.12755i	−0.914700	−	0.404134i	$-0.867573\pi$
$7$	−0.593396	−	2.98320i	−0.224283	−	1.12755i	0.690417	−	0.723412i	$-0.257427\pi$
$8$	−2.64842	−	0.992915i	−0.936357	−	0.351049i
$9$	2.58370	+	0.513930i	0.861234	+	0.171310i
$10$	−0.884718	+	1.10330i	−0.279772	+	0.348895i
$11$	−0.829813	−	0.681010i	−0.250198	−	0.205332i	0.500932	−	0.865487i	$-0.332991\pi$
$11$	−0.829813	−	0.681010i	−0.250198	−	0.205332i	−0.751130	+	0.660155i	$0.770491\pi$
$12$	3.60053	−	3.09410i	1.03938	−	0.893191i
$13$	3.26520	+	1.74528i	0.905602	+	0.484054i	0.857323	−	0.514779i	$-0.172126\pi$
$13$	3.26520	+	1.74528i	0.905602	+	0.484054i	0.0482795	+	0.998834i	$0.484626\pi$
$14$	3.54928	−	2.43020i	0.948585	−	0.649498i
$15$	−0.908365	−	2.19299i	−0.234539	−	0.566227i
$16$	−0.181316	−	3.99589i	−0.0453290	−	0.998972i
$17$	1.93607	−	4.67409i	0.469566	−	1.13363i	−0.494787	−	0.869014i	$-0.664754\pi$
$17$	1.93607	−	4.67409i	0.469566	−	1.13363i	0.964353	−	0.264619i	$-0.0852462\pi$
$18$	0.768181	+	3.64543i	0.181062	+	0.859237i
$19$	−0.398280	+	0.120817i	−0.0913717	+	0.0277173i	−0.335640	−	0.941991i	$-0.608952\pi$
$19$	−0.398280	+	0.120817i	−0.0913717	+	0.0277173i	0.244268	+	0.969708i	$0.421452\pi$
$20$	−1.92655	−	0.537032i	−0.430790	−	0.120084i
$21$	0.707672	+	7.18511i	0.154427	+	1.56792i
$22$	0.424194	−	1.45766i	0.0904384	−	0.310775i
$23$	1.62694	−	1.08709i	0.339241	−	0.226674i	−0.374266	−	0.927321i	$-0.622105\pi$
$23$	1.62694	−	1.08709i	0.339241	−	0.226674i	0.713508	+	0.700648i	$0.247105\pi$
$24$	6.02519	+	2.96169i	1.22989	+	0.604552i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	−0.454110	+	5.21621i	−0.0890584	+	1.02298i
$27$	0.830627	+	0.251968i	0.159854	+	0.0484912i
$28$	5.13340	+	3.26416i	0.970121	+	0.616869i
$29$	3.98951	+	4.86124i	0.740834	+	0.902709i	0.997971	−	0.0636662i	$-0.0202793\pi$
$29$	3.98951	+	4.86124i	0.740834	+	0.902709i	−0.257137	+	0.966375i	$0.582779\pi$
$30$	2.34661	−	2.40043i	0.428431	−	0.438256i
$31$	−0.375400	+	0.375400i	−0.0674238	+	0.0674238i	−0.740015	−	0.672591i	$-0.765181\pi$
$31$	−0.375400	+	0.375400i	−0.0674238	+	0.0674238i	0.672591	+	0.740015i	$0.265181\pi$
$32$	5.09522	−	2.45738i	0.900717	−	0.434407i
$33$	1.80177	+	1.80177i	0.313649	+	0.313649i
$34$	7.15433	−	0.0811058i	1.22696	−	0.0139095i
$35$	2.35123	−	1.92960i	0.397430	−	0.326162i
$36$	−4.31323	+	3.02566i	−0.718872	+	0.504277i
$37$	1.40416	−	4.62888i	0.230842	−	0.760984i	−0.762623	−	0.646843i	$-0.776089\pi$
$37$	1.40416	−	4.62888i	0.230842	−	0.760984i	0.993465	−	0.114140i	$-0.0364113\pi$
$38$	−0.378536	−	0.450730i	−0.0614067	−	0.0731181i
$39$	−7.30712	−	4.88246i	−1.17008	−	0.781820i
$40$	−0.372783	−	2.80375i	−0.0589421	−	0.443312i
$41$	0.672363	+	1.00626i	0.105005	+	0.157152i	0.880251	−	0.474508i	$-0.157374\pi$
$41$	0.672363	+	1.00626i	0.105005	+	0.157152i	−0.775246	+	0.631660i	$0.782374\pi$
$42$	−8.94967	+	4.91494i	−1.38096	+	0.758392i
$43$	10.3043	−	1.01488i	1.57139	−	0.154768i	0.725537	−	0.688183i	$-0.241591\pi$
$43$	10.3043	−	1.01488i	1.57139	−	0.154768i	0.845854	+	0.533415i	$0.179091\pi$
$44$	2.13131	−	0.258823i	0.321306	−	0.0390190i
$45$	0.764703	+	2.52089i	0.113995	+	0.375792i
$46$	2.31813	+	1.51120i	0.341789	+	0.222814i
$47$	−4.91567	−	2.03614i	−0.717025	−	0.297001i	−0.00581669	−	0.999983i	$-0.501852\pi$
$47$	−4.91567	−	2.03614i	−0.717025	−	0.297001i	−0.711208	+	0.702982i	$0.751852\pi$
$48$	−0.501374	+	9.48144i	−0.0723671	+	1.36853i
$49$	−2.08024	+	0.861662i	−0.297176	+	0.123095i
$50$	−1.39008	−	0.260158i	−0.196587	−	0.0367919i
$51$	−5.66095	+	10.5909i	−0.792691	+	1.48302i
$52$	−7.03534	+	2.30957i	−0.975626	+	0.320279i
$53$	0.753431	−	0.918059i	0.103492	−	0.126105i	−0.718689	−	0.695332i	$-0.755257\pi$
$53$	0.753431	−	0.918059i	0.103492	−	0.126105i	0.822181	+	0.569227i	$0.192757\pi$
$54$	0.134161	+	1.22019i	0.0182569	+	0.166047i
$55$	0.209426	−	1.05286i	0.0282390	−	0.141967i
$56$	−1.39051	+	8.48997i	−0.185814	+	1.13452i
$57$	0.968943	−	0.192735i	0.128340	−	0.0255283i
$58$	−4.10322	+	7.89045i	−0.538779	+	1.03607i
$59$	1.99713	−	1.06749i	0.260004	−	0.138975i	−0.336245	−	0.941775i	$-0.609157\pi$
$59$	1.99713	−	1.06749i	0.260004	−	0.138975i	0.596249	+	0.802799i	$0.296657\pi$
$60$	4.42603	+	1.71683i	0.571398	+	0.221642i
$61$	0.648129	−	6.58056i	0.0829844	−	0.842555i	−0.860127	−	0.510079i	$-0.829616\pi$
$61$	0.648129	−	6.58056i	0.0829844	−	0.842555i	0.943112	−	0.332476i	$-0.107884\pi$
$62$	−0.696861	−	0.279437i	−0.0885014	−	0.0354885i
$63$		−	8.01268i		−	1.00950i
$64$	6.02824	+	5.25931i	0.753530	+	0.657414i
$65$			3.70237i			0.459222i
$66$	−1.34119	+	3.34466i	−0.165089	+	0.411700i
$67$	1.15425	−	11.7193i	0.141014	−	1.43173i	−0.620816	−	0.783957i	$-0.713198\pi$
$67$	1.15425	−	11.7193i	0.141014	−	1.43173i	0.761829	−	0.647778i	$-0.224302\pi$
$68$	4.08307	+	9.25799i	0.495145	+	1.12270i
$69$	−4.09616	+	2.18944i	−0.493120	+	0.263578i
$70$	3.81636	+	1.98460i	0.456143	+	0.237205i
$71$	2.98638	−	0.594027i	0.354418	−	0.0704981i	−0.0146706	−	0.999892i	$-0.504670\pi$
$71$	2.98638	−	0.594027i	0.354418	−	0.0704981i	0.369088	+	0.929394i	$0.379670\pi$
$72$	−6.33244	−	3.92650i	−0.746285	−	0.462743i
$73$	−1.10943	+	5.57749i	−0.129849	+	0.652795i	0.859956	+	0.510368i	$0.170491\pi$
$73$	−1.10943	+	5.57749i	−0.129849	+	0.652795i	−0.989805	+	0.142427i	$0.954509\pi$
$74$	6.79981	−	0.747645i	0.790462	−	0.0869119i
$75$	1.50584	−	1.83487i	0.173880	−	0.211873i
$76$	0.375648	−	0.742821i	0.0430898	−	0.0852074i
$77$	−1.53918	+	2.87961i	−0.175406	+	0.328162i
$78$	2.28632	−	12.2163i	0.258875	−	1.38322i
$79$	−2.41671	+	1.00104i	−0.271902	+	0.112625i	−0.514468	−	0.857509i	$-0.672011\pi$
$79$	−2.41671	+	1.00104i	−0.271902	+	0.112625i	0.242567	+	0.970135i	$0.422011\pi$
$80$	3.43859	−	2.04356i	0.384446	−	0.228476i
$81$	−9.20490	−	3.81280i	−1.02277	−	0.423644i
$82$	−0.934672	+	1.43376i	−0.103217	+	0.158332i
$83$	−1.13297	−	3.73491i	−0.124360	−	0.409959i	0.872549	−	0.488526i	$-0.162465\pi$
$83$	−1.13297	−	3.73491i	−0.124360	−	0.409959i	−0.996909	+	0.0785673i	$0.974965\pi$
$84$	−11.3669	−	8.90508i	−1.24023	−	0.971624i
$85$	5.03484	−	0.495888i	0.546105	−	0.0537866i
$86$	7.04860	+	12.8349i	0.760071	+	1.38402i
$87$	−8.29318	−	12.4116i	−0.889122	−	1.33067i
$88$	1.52151	+	2.62753i	0.162193	+	0.280096i
$89$	−12.3967	−	8.28323i	−1.31405	−	0.878020i	−0.316543	−	0.948578i	$-0.602522\pi$
$89$	−12.3967	−	8.28323i	−1.31405	−	0.878020i	−0.997508	+	0.0705580i	$0.977522\pi$
$90$	−2.85287	+	2.39592i	−0.300719	+	0.252552i
$91$	3.26898	−	10.7764i	0.342682	−	1.12967i
$92$	−0.676260	+	3.85454i	−0.0705050	+	0.401864i
$93$	0.974126	−	0.799445i	0.101012	−	0.0828985i
$94$	−0.0852978	−	7.52410i	−0.00879780	−	0.776052i
$95$	−0.294299	−	0.294299i	−0.0301944	−	0.0301944i
$96$	−12.6079	+	4.61946i	−1.28679	+	0.471472i
$97$	11.9118	−	11.9118i	1.20946	−	1.20946i	0.238265	−	0.971200i	$-0.423421\pi$
$97$	11.9118	−	11.9118i	1.20946	−	1.20946i	0.971200	−	0.238265i	$-0.0765786\pi$
$98$	−2.27701	−	2.22596i	−0.230013	−	0.224856i
$99$	−1.79400	−	2.18599i	−0.180304	−	0.219701i
$100$	−0.434550	−	1.95222i	−0.0434550	−	0.195222i
$101$	11.7722	+	3.57105i	1.17138	+	0.355333i	0.815252	−	0.579106i	$-0.196598\pi$
$101$	11.7722	+	3.57105i	1.17138	+	0.355333i	0.356124	+	0.934439i	$0.384098\pi$
$102$	−16.9191	−	1.47294i	−1.67524	−	0.145843i
$103$	8.29252	−	12.4106i	0.817086	−	1.22286i	−0.154926	−	0.987926i	$-0.549514\pi$
$103$	8.29252	−	12.4106i	0.817086	−	1.22286i	0.972012	−	0.234930i	$-0.0754861\pi$
$104$	−6.91468	−	7.86430i	−0.678041	−	0.771158i
$105$	−6.00311	+	4.01115i	−0.585844	+	0.391448i
$106$	1.61268	+	0.469305i	0.156637	+	0.0455829i
$107$	−0.255879	−	2.59798i	−0.0247368	−	0.251157i	−0.999598	−	0.0283446i	$-0.990976\pi$
$107$	−0.255879	−	2.59798i	−0.0247368	−	0.251157i	0.974861	−	0.222812i	$-0.0715236\pi$
$108$	−1.51207	+	0.852846i	−0.145499	+	0.0820651i
$109$	−12.4374	+	3.77283i	−1.19128	+	0.361372i	−0.822837	−	0.568277i	$-0.807610\pi$
$109$	−12.4374	+	3.77283i	−1.19128	+	0.361372i	−0.368446	+	0.929649i	$0.620110\pi$
$110$	1.48551	−	0.313033i	0.141638	−	0.0298465i
$111$	−4.39392	+	10.6079i	−0.417052	+	1.00685i
$112$	−11.8130	+	2.91205i	−1.11622	+	0.275163i
$113$	0.676120	+	1.63230i	0.0636040	+	0.153554i	0.952486	−	0.304583i	$-0.0985171\pi$
$113$	0.676120	+	1.63230i	0.0636040	+	0.153554i	−0.888882	+	0.458137i	$0.848517\pi$
$114$	0.789327	+	1.15280i	0.0739272	+	0.107970i
$115$	1.72566	+	0.922386i	0.160919	+	0.0860129i
$116$	−12.5416	−	0.948724i	−1.16446	−	0.0880868i
$117$	7.53934	+	6.18738i	0.697012	+	0.572023i
$118$	2.49845	+	2.00346i	0.230001	+	0.184434i
$119$	−15.0926	−	3.00211i	−1.38354	−	0.275203i
$120$	0.228280	+	6.70988i	0.0208390	+	0.612525i
$121$	−1.92118	−	9.65842i	−0.174653	−	0.878038i
$122$	8.91734	−	2.81582i	0.807338	−	0.254932i
$123$	−1.35417	−	2.53347i	−0.122101	−	0.228435i
$124$	−0.0240711	−	1.06152i	−0.00216165	−	0.0953271i
$125$	−0.995185	−	0.0980171i	−0.0890120	−	0.00876692i
$126$	10.4192	−	4.45483i	0.928220	−	0.396868i
$127$	−6.21864			−0.551815			−0.275907	−	0.961184i	$-0.588978\pi$
$127$	−6.21864			−0.551815			−0.275907	+	0.961184i	$0.588978\pi$
$128$	−3.48738	+	10.7628i	−0.308244	+	0.951307i
$129$	−24.5774			−2.16392
$130$	−4.81435	+	2.05841i	−0.422246	+	0.180535i
$131$	−20.1834	−	1.98790i	−1.76344	−	0.173683i	−0.836266	−	0.548324i	$-0.815266\pi$
$131$	−20.1834	−	1.98790i	−1.76344	−	0.173683i	−0.927170	+	0.374641i	$0.877766\pi$
$132$	−5.09488	+	0.115532i	−0.443452	+	0.0100558i
$133$	0.596759	+	1.11646i	0.0517456	+	0.0968092i
$134$	15.8808	−	5.01466i	1.37189	−	0.433201i
$135$	0.169339	+	0.851324i	0.0145744	+	0.0732703i
$136$	−9.76850	+	10.4566i	−0.837642	+	0.896645i
$137$	7.41851	+	1.47563i	0.633806	+	0.126072i	0.501529	−	0.865141i	$-0.332771\pi$
$137$	7.41851	+	1.47563i	0.633806	+	0.126072i	0.132277	+	0.991213i	$0.457771\pi$
$138$	−5.12438	−	4.10915i	−0.436216	−	0.349794i
$139$	17.8906	+	14.6824i	1.51746	+	1.24534i	0.880112	+	0.474766i	$0.157467\pi$
$139$	17.8906	+	14.6824i	1.51746	+	1.24534i	0.637345	+	0.770579i	$0.280033\pi$
$140$	−0.458868	+	6.06597i	−0.0387814	+	0.512668i
$141$	11.1383	+	5.95354i	0.938013	+	0.501378i
$142$	2.43278	+	3.55306i	0.204155	+	0.298166i
$143$	−1.52095	−	3.67189i	−0.127188	−	0.307059i
$144$	1.58514	−	10.4174i	0.132095	−	0.868114i
$145$	−2.40658	+	5.81001i	−0.199856	+	0.482495i
$146$	−7.86946	+	1.65829i	−0.651281	+	0.137241i
$147$	5.11450	−	1.55147i	0.421836	−	0.127963i
$148$	4.75270	+	8.42642i	0.390670	+	0.692648i
$149$	2.03448	+	20.6564i	0.166671	+	1.69224i	0.607241	+	0.794518i	$0.292276\pi$
$149$	2.03448	+	20.6564i	0.166671	+	1.69224i	−0.440570	+	0.897718i	$0.645224\pi$
$150$	3.22317	+	0.937973i	0.263171	+	0.0765852i
$151$	11.1909	−	7.47752i	0.910703	−	0.608512i	−0.00949979	−	0.999955i	$-0.503024\pi$
$151$	11.1909	−	7.47752i	0.910703	−	0.608512i	0.920202	+	0.391443i	$0.128024\pi$
$152$	1.17477	+	0.0754845i	0.0952866	+	0.00612260i
$153$	7.40439	−	11.0815i	0.598609	−	0.895882i
$154$	−4.60023	−	0.400485i	−0.370697	−	0.0322720i
$155$	−0.508035	−	0.154111i	−0.0408064	−	0.0123785i
$156$	17.1565	−	3.81891i	1.37362	−	0.305758i
$157$	−11.7842	−	14.3591i	−0.940482	−	1.14598i	−0.989112	−	0.147163i	$-0.952986\pi$
$157$	−11.7842	−	14.3591i	−0.940482	−	1.14598i	0.0486306	−	0.998817i	$-0.484514\pi$
$158$	−2.64532	−	2.58601i	−0.210450	−	0.205732i
$159$	−1.99338	+	1.99338i	−0.158086	+	0.158086i
$160$	4.56908	+	3.33519i	0.361218	+	0.263670i
$161$	−4.20843	−	4.20843i	−0.331671	−	0.331671i
$162$	−0.159726	−	14.0894i	−0.0125492	−	1.10696i
$163$	−18.0189	+	14.7878i	−1.41135	+	1.15827i	−0.446718	+	0.894675i	$0.647407\pi$
$163$	−18.0189	+	14.7878i	−1.41135	+	1.15827i	−0.964634	+	0.263592i	$0.915093\pi$
$164$	−2.38403	−	0.418266i	−0.186161	−	0.0326611i
$165$	−0.739673	+	2.43837i	−0.0575834	+	0.189827i
$166$	4.22676	−	3.54976i	0.328060	−	0.275515i
$167$	2.58553	+	1.72760i	0.200074	+	0.133685i	0.651572	−	0.758587i	$-0.274110\pi$
$167$	2.58553	+	1.72760i	0.200074	+	0.133685i	−0.451497	+	0.892272i	$0.649110\pi$
$168$	5.26000	−	19.7318i	0.405818	−	1.52234i
$169$	0.393073	+	0.588276i	0.0302364	+	0.0452520i
$170$	3.44406	+	6.27132i	0.264147	+	0.480988i
$171$	−1.09113	+	0.107467i	−0.0834407	+	0.00821819i
$172$	−12.7709	+	16.3015i	−0.973775	+	1.24297i
$173$	−1.17525	−	3.87427i	−0.0893524	−	0.294556i	0.900863	−	0.434104i	$-0.142935\pi$
$173$	−1.17525	−	3.87427i	−0.0893524	−	0.294556i	−0.990215	+	0.139548i	$0.955435\pi$
$174$	11.5286	−	17.6845i	0.873981	−	1.34066i
$175$	2.81012	+	1.16399i	0.212425	+	0.0879893i
$176$	−2.57078	+	3.43932i	−0.193780	+	0.259248i
$177$	−4.96606	+	2.05701i	−0.373272	+	0.154614i
$178$	3.87881	−	20.7253i	0.290729	−	1.55342i
$179$	−8.35971	+	15.6399i	−0.624834	+	1.16898i	0.348004	+	0.937493i	$0.386860\pi$
$179$	−8.35971	+	15.6399i	−0.624834	+	1.16898i	−0.972838	+	0.231489i	$0.925640\pi$
$180$	−4.70164	−	2.37764i	−0.350439	−	0.177219i
$181$	11.1689	−	13.6093i	0.830175	−	1.01157i	−0.169486	−	0.985533i	$-0.554211\pi$
$181$	11.1689	−	13.6093i	0.830175	−	1.01157i	0.999661	−	0.0260384i	$-0.00828920\pi$
$182$	15.8305	−	1.74057i	1.17343	−	0.129020i
$183$	−3.06208	+	15.3941i	−0.226355	+	1.13796i
$184$	−5.38821	+	1.26365i	−0.397224	+	0.0931575i
$185$	4.74422	−	0.943685i	0.348802	−	0.0693811i
$186$	1.58114	+	0.822230i	0.115935	+	0.0602888i
$187$	−4.78968	+	2.56014i	−0.350256	+	0.187216i
$188$	9.73650	−	4.29411i	0.710107	−	0.313180i
$189$	0.258781	−	2.62745i	0.0188235	−	0.191119i
$190$	0.219068	−	0.546312i	0.0158928	−	0.0396336i
$191$			4.01701i			0.290661i	0.989383	+	0.145330i	$0.0464245\pi$
$191$			4.01701i			0.290661i	−0.989383	+	0.145330i	$0.953576\pi$
$192$	−13.0165	−	13.8263i	−0.939387	−	0.997827i
$193$			2.47695i			0.178294i	0.996018	+	0.0891472i	$0.0284142\pi$
$193$			2.47695i			0.178294i	−0.996018	+	0.0891472i	$0.971586\pi$
$194$	22.1122	+	8.86684i	1.58756	+	0.636602i
$195$	0.861395	−	8.74589i	0.0616857	−	0.626306i
$196$	1.62856	−	4.19847i	0.116326	−	0.299891i
$197$	14.0310	−	7.49972i	0.999666	−	0.534333i	0.111456	−	0.993769i	$-0.464449\pi$
$197$	14.0310	−	7.49972i	0.999666	−	0.534333i	0.888211	+	0.459437i	$0.151949\pi$
$198$	1.84513	−	3.54817i	0.131128	−	0.252157i
$199$	3.44898	−	0.686045i	0.244492	−	0.0486325i	−0.0713230	−	0.997453i	$-0.522722\pi$
$199$	3.44898	−	0.686045i	0.244492	−	0.0486325i	0.315815	+	0.948821i	$0.397722\pi$
$200$	2.29696	−	1.65045i	0.162420	−	0.116704i
$201$	−5.45322	+	27.4152i	−0.384640	+	1.93372i
$202$	1.90141	+	17.2933i	0.133783	+	1.21675i
$203$	12.1347	−	14.7862i	0.851689	−	1.03779i
$204$	−7.49124	−	22.8196i	−0.524492	−	1.59769i
$205$	−0.570494	+	1.06732i	−0.0398451	+	0.0745449i
$206$	20.7485	+	3.88316i	1.44562	+	0.270553i
$207$	4.76223	−	1.97258i	0.330998	−	0.137104i
$208$	6.38193	−	13.3638i	0.442507	−	0.926613i
$209$	0.412775	+	0.170977i	0.0285522	+	0.0118267i
$210$	−8.55344	−	5.57602i	−0.590243	−	0.384782i
$211$	6.80780	+	22.4423i	0.468668	+	1.54499i	0.799122	+	0.601169i	$0.205298\pi$
$211$	6.80780	+	22.4423i	0.468668	+	1.54499i	−0.330454	+	0.943822i	$0.607202\pi$
$212$	0.286348	+	2.35796i	0.0196664	+	0.161945i
$213$	−7.19275	+	0.708424i	−0.492839	+	0.0485404i
$214$	3.23601	−	1.77714i	0.221209	−	0.121483i
$215$	5.75246	+	8.60917i	0.392315	+	0.587140i
$216$	−1.94966	−	1.49206i	−0.132658	−	0.101522i
$217$	1.34266	+	0.897134i	0.0911454	+	0.0609014i
$218$	−11.8208	−	14.0753i	−0.800606	−	0.953297i
$219$	3.91841	−	12.9173i	0.264781	−	0.872867i
$220$	1.23295	+	1.75764i	0.0831256	+	0.118500i
$221$	14.4793	−	11.8828i	0.973981	−	0.799325i
$222$	−16.2368	+	0.184070i	−1.08974	+	0.0123540i
$223$	−6.63422	−	6.63422i	−0.444260	−	0.444260i	0.449181	−	0.893441i	$-0.351716\pi$
$223$	−6.63422	−	6.63422i	−0.444260	−	0.444260i	−0.893441	+	0.449181i	$0.851716\pi$
$224$	−10.3543	−	13.7419i	−0.691829	−	0.918169i
$225$	−1.86275	+	1.86275i	−0.124183	+	0.124183i
$226$	−1.74665	+	1.78670i	−0.116185	+	0.118850i
$227$	10.0745	+	12.2758i	0.668667	+	0.814773i	0.991282	−	0.131758i	$-0.0420620\pi$
$227$	10.0745	+	12.2758i	0.668667	+	0.814773i	−0.322615	+	0.946530i	$0.604562\pi$
$228$	−1.06020	+	1.66732i	−0.0702133	+	0.110421i
$229$	18.6073	+	5.64447i	1.22961	+	0.372997i	0.837252	−	0.546817i	$-0.184160\pi$
$229$	18.6073	+	5.64447i	1.22961	+	0.372997i	0.392355	+	0.919814i	$0.371660\pi$
$230$	−0.239998	+	2.75678i	−0.0158250	+	0.181776i
$231$	4.30590	−	6.44423i	0.283307	−	0.423999i
$232$	−5.73910	−	16.8358i	−0.376791	−	1.10533i
$233$	−20.4379	+	13.6562i	−1.33893	+	0.894647i	−0.998951	−	0.0457851i	$-0.985421\pi$
$233$	−20.4379	+	13.6562i	−1.33893	+	0.894647i	−0.339982	+	0.940432i	$0.610421\pi$
$234$	−3.85405	+	13.2437i	−0.251947	+	0.865771i
$235$	−0.521518	−	5.29507i	−0.0340201	−	0.345412i
$236$	−1.21612	+	4.36271i	−0.0791626	+	0.283988i
$237$	5.94177	−	1.80242i	0.385959	−	0.117079i
$238$	−4.48731	−	21.2947i	−0.290869	−	1.38033i
$239$	6.40902	−	15.4727i	0.414565	−	1.00085i	−0.569331	−	0.822108i	$-0.692798\pi$
$239$	6.40902	−	15.4727i	0.414565	−	1.00085i	0.983896	−	0.178740i	$-0.0572021\pi$
$240$	−8.59823	+	4.02735i	−0.555013	+	0.259964i
$241$	−2.87337	−	6.93693i	−0.185090	−	0.446847i	0.803912	−	0.594748i	$-0.202748\pi$
$241$	−2.87337	−	6.93693i	−0.185090	−	0.446847i	−0.989002	+	0.147901i	$0.952748\pi$
$242$	11.4911	−	7.86801i	0.738679	−	0.505775i
$243$	18.5606	+	9.92085i	1.19066	+	0.636423i
$244$	8.61933	+	10.0301i	0.551796	+	0.642111i
$245$	−1.74053	−	1.42842i	−0.111199	−	0.0912584i
$246$	2.54150	−	3.16942i	0.162040	−	0.202075i
$247$	−1.51132	−	0.300620i	−0.0961631	−	0.0191280i
$248$	1.36696	−	0.621475i	0.0868018	−	0.0394637i
$249$	1.80739	+	9.08635i	0.114539	+	0.575824i
$250$	−0.425839	−	1.34858i	−0.0269324	−	0.0852915i
$251$	6.20687	+	11.6122i	0.391774	+	0.732958i	0.998058	−	0.0622904i	$-0.0198405\pi$
$251$	6.20687	+	11.6122i	0.391774	+	0.732958i	−0.606284	+	0.795248i	$0.707340\pi$
$252$	11.5856	+	11.0718i	0.729825	+	0.697460i
$253$	−2.09038	−	0.205884i	−0.131421	−	0.0129438i
$254$	−3.45739	−	8.08637i	−0.216936	−	0.507384i
$255$	−12.0089			−0.752025
$256$	−15.9342	+	1.44904i	−0.995891	+	0.0905648i
$257$	20.9281			1.30546			0.652730	−	0.757590i	$-0.273623\pi$
$257$	20.9281			1.30546			0.652730	+	0.757590i	$0.273623\pi$
$258$	−13.6643	−	31.9590i	−0.850705	−	1.98968i
$259$	−14.6421	−	1.44212i	−0.909817	−	0.0896092i
$260$	−5.35329	−	5.11589i	−0.331997	−	0.317274i
$261$	7.80938	+	14.6103i	0.483388	+	0.904356i
$262$	−8.63649	−	27.3506i	−0.533564	−	1.68973i
$263$	5.73859	+	28.8498i	0.353856	+	1.77896i	0.590169	+	0.807280i	$0.299061\pi$
$263$	5.73859	+	28.8498i	0.353856	+	1.77896i	−0.236313	+	0.971677i	$0.575939\pi$
$264$	−2.98284	−	6.56086i	−0.183581	−	0.403793i
$265$	1.16482	+	0.231697i	0.0715543	+	0.0142330i
$266$	−1.12000	+	1.39671i	−0.0686715	+	0.0856379i
$267$	27.3569	+	22.4512i	1.67421	+	1.37399i
$268$	15.3501	+	17.8625i	0.937655	+	1.09112i
$269$	−11.1401	−	5.95451i	−0.679224	−	0.363053i	0.0954320	−	0.995436i	$-0.469577\pi$
$269$	−11.1401	−	5.95451i	−0.679224	−	0.363053i	−0.774656	+	0.632383i	$0.782077\pi$
$270$	−1.01287	+	0.693512i	−0.0616411	+	0.0422058i
$271$	0.438098	+	1.05766i	0.0266125	+	0.0642484i	0.936627	−	0.350328i	$-0.113930\pi$
$271$	0.438098	+	1.05766i	0.0266125	+	0.0642484i	−0.910015	+	0.414576i	$0.863930\pi$
$272$	−19.0282	−	6.88884i	−1.15375	−	0.417697i
$273$	−10.2294	+	24.6959i	−0.619110	+	1.49466i
$274$	2.20565	+	10.4670i	0.133248	+	0.632336i
$275$	1.02726	−	0.311615i	0.0619460	−	0.0187911i
$276$	2.49429	−	8.94803i	0.150139	−	0.538608i
$277$	1.98306	+	20.1344i	0.119151	+	1.20976i	0.849838	+	0.527045i	$0.176700\pi$
$277$	1.98306	+	20.1344i	0.119151	+	1.20976i	−0.730687	+	0.682713i	$0.760800\pi$
$278$	−9.14551	+	31.4269i	−0.548512	+	1.88486i
$279$	−1.16285	+	0.776992i	−0.0696181	+	0.0465173i
$280$	−8.14296	+	2.77582i	−0.486635	+	0.165887i
$281$	−1.93169	+	2.89098i	−0.115235	+	0.172461i	−0.884604	−	0.466344i	$-0.845571\pi$
$281$	−1.93169	+	2.89098i	−0.115235	+	0.172461i	0.769369	+	0.638805i	$0.220571\pi$
$282$	−1.54907	+	17.7936i	−0.0922456	+	1.05959i
$283$	−22.9288	−	6.95538i	−1.36298	−	0.413454i	−0.477701	−	0.878522i	$-0.658530\pi$
$283$	−22.9288	−	6.95538i	−1.36298	−	0.413454i	−0.885275	+	0.465068i	$0.846030\pi$
$284$	−3.26763	+	5.13886i	−0.193898	+	0.304935i
$285$	0.626733	+	0.763677i	0.0371245	+	0.0452363i
$286$	3.92911	−	4.01922i	0.232333	−	0.237661i
$287$	2.60291	−	2.60291i	0.153645	−	0.153645i
$288$	14.4275	−	3.73054i	0.850146	−	0.219824i
$289$	−6.07793	−	6.07793i	−0.357525	−	0.357525i
$290$	−8.89300	+	0.100817i	−0.522215	+	0.00592015i
$291$	−30.9101	+	25.3673i	−1.81198	+	1.48705i
$292$	−6.53155	−	9.31105i	−0.382230	−	0.544888i
$293$	3.30510	−	10.8955i	0.193086	−	0.636520i	−0.805923	−	0.592020i	$-0.798331\pi$
$293$	3.30510	−	10.8955i	0.193086	−	0.636520i	0.999009	−	0.0444998i	$-0.0141694\pi$
$294$	4.86096	+	5.78803i	0.283497	+	0.337565i
$295$	1.88288	+	1.25810i	0.109625	+	0.0732494i
$296$	−8.31488	+	10.8650i	−0.483293	+	0.631516i
$297$	−0.517672	−	0.774751i	−0.0300384	−	0.0449556i
$298$	−25.7293	+	14.1299i	−1.49046	+	0.818523i
$299$	7.20957	−	0.710080i	0.416940	−	0.0410650i
$300$	0.572307	+	4.71272i	0.0330422	+	0.272089i
$301$	−9.14214	−	30.1376i	−0.526944	−	1.73710i
$302$	15.9452	+	10.3947i	0.917542	+	0.598149i
$303$	−26.9779	−	11.1746i	−1.54984	−	0.641965i
$304$	0.554985	+	1.56958i	0.0318306	+	0.0900213i
$305$	6.10907	−	2.53046i	0.349804	−	0.144894i
$306$	18.5263	+	3.46727i	1.05908	+	0.198211i
$307$	−8.12415	+	15.1992i	−0.463670	+	0.867465i	0.536059	+	0.844180i	$0.319912\pi$
$307$	−8.12415	+	15.1992i	−0.463670	+	0.867465i	−0.999729	+	0.0232846i	$0.992588\pi$
$308$	−2.03683	−	6.20454i	−0.116059	−	0.353536i
$309$	−22.4764	+	27.3876i	−1.27864	+	1.55803i
$310$	−0.0820565	−	0.746302i	−0.00466050	−	0.0423871i
$311$	−4.16950	+	20.9615i	−0.236431	+	1.18862i	0.662000	+	0.749504i	$0.269708\pi$
$311$	−4.16950	+	20.9615i	−0.236431	+	1.18862i	−0.898431	+	0.439115i	$0.855292\pi$
$312$	14.5044	+	20.1862i	0.821153	+	1.14282i
$313$	6.77764	−	1.34816i	0.383095	−	0.0762023i	0.000213881	−	1.00000i	$-0.499932\pi$
$313$	6.77764	−	1.34816i	0.383095	−	0.0762023i	0.382881	+	0.923798i	$0.374932\pi$
$314$	12.1201	−	23.3068i	0.683975	−	1.31528i
$315$	7.06655	−	3.77715i	0.398155	−	0.212818i
$316$	1.89198	−	4.87758i	0.106432	−	0.274385i
$317$	−0.717506	+	7.28496i	−0.0402992	+	0.409164i	0.953780	+	0.300506i	$0.0971555\pi$
$317$	−0.717506	+	7.28496i	−0.0402992	+	0.409164i	−0.994079	+	0.108658i	$0.965345\pi$
$318$	−3.70035	−	1.48382i	−0.207505	−	0.0832084i
$319$		−	6.75081i		−	0.377973i
$320$	−1.79661	+	7.79565i	−0.100433	+	0.435790i
$321$			6.19660i			0.345861i
$322$	3.13264	−	7.81218i	0.174575	−	0.435356i
$323$	−0.206389	+	2.09551i	−0.0114838	+	0.116597i
$324$	18.2322	−	8.04099i	1.01290	−	0.446722i
$325$	−3.26520	+	1.74528i	−0.181120	+	0.0968109i
$326$	−29.2472	−	15.2092i	−1.61985	−	0.842362i
$327$	30.2579	−	6.01866i	1.67326	−	0.332833i
$328$	−0.781565	−	3.33260i	−0.0431547	−	0.184012i
$329$	−3.15728	+	15.8727i	−0.174066	+	0.875090i
$330$	−3.58196	+	0.393840i	−0.197181	+	0.0216802i
$331$	−5.13829	+	6.26102i	−0.282426	+	0.344137i	−0.894829	−	0.446409i	$-0.852703\pi$
$331$	−5.13829	+	6.26102i	−0.282426	+	0.344137i	0.612403	+	0.790545i	$0.290203\pi$
$332$	6.96587	+	3.52268i	0.382302	+	0.193332i
$333$	6.00685	−	11.2380i	0.329173	−	0.615840i
$334$	−0.808986	+	4.32258i	−0.0442658	+	0.236521i
$335$	10.8796	−	4.50646i	0.594414	−	0.246214i
$336$	28.5826	−	4.13055i	1.55931	−	0.225340i
$337$	−12.7157	−	5.26704i	−0.692671	−	0.286914i	0.00844153	−	0.999964i	$-0.497313\pi$
$337$	−12.7157	−	5.26704i	−0.692671	−	0.286914i	−0.701113	+	0.713051i	$0.747313\pi$
$338$	−0.546423	+	0.838196i	−0.0297215	+	0.0455918i
$339$	−1.21739	−	4.01319i	−0.0661195	−	0.217967i
$340$	−6.24007	+	7.96514i	−0.338416	+	0.431970i
$341$	0.567162	−	0.0558606i	0.0307136	−	0.00302502i
$342$	−0.746381	−	1.35909i	−0.0403597	−	0.0734914i
$343$	−8.02403	−	12.0088i	−0.433257	−	0.648415i
$344$	−28.2978	−	7.54346i	−1.52571	−	0.406716i
$345$	−3.86183	−	2.58039i	−0.207914	−	0.138924i
$346$	4.38448	−	3.68222i	0.235711	−	0.197957i
$347$	−5.05828	+	16.6749i	−0.271543	+	0.895157i	0.710047	+	0.704155i	$0.248674\pi$
$347$	−5.05828	+	16.6749i	−0.271543	+	0.895157i	−0.981590	+	0.191002i	$0.938826\pi$
$348$	29.4055	+	5.15905i	1.57630	+	0.276554i
$349$	26.4723	−	21.7252i	1.41703	−	1.16293i	0.454830	−	0.890578i	$-0.349700\pi$
$349$	26.4723	−	21.7252i	1.41703	−	1.16293i	0.962199	−	0.272347i	$-0.0878000\pi$
$350$	0.0487618	+	4.30127i	0.00260643	+	0.229912i
$351$	2.27240	+	2.27240i	0.121292	+	0.121292i
$352$	−5.90158	−	1.43073i	−0.314555	−	0.0762584i
$353$	−3.33454	+	3.33454i	−0.177480	+	0.177480i	−0.790256	−	0.612777i	$-0.790053\pi$
$353$	−3.33454	+	3.33454i	−0.177480	+	0.177480i	0.612777	+	0.790256i	$0.290053\pi$
$354$	−5.43582	−	5.31395i	−0.288910	−	0.282433i
$355$	1.93165	+	2.35373i	0.102522	+	0.124923i
$356$	29.1065	−	6.47888i	1.54264	−	0.343380i
$357$	34.9540	+	10.6032i	1.84996	+	0.561179i
$358$	−24.9850	−	2.17514i	−1.32050	−	0.114960i
$359$	18.3218	−	27.4206i	0.966989	−	1.44720i	0.0739297	−	0.997263i	$-0.476446\pi$
$359$	18.3218	−	27.4206i	0.966989	−	1.44720i	0.893060	−	0.449938i	$-0.148554\pi$
$360$	0.477775	−	7.43565i	0.0251809	−	0.391893i
$361$	−15.6539	+	10.4596i	−0.823889	+	0.550505i
$362$	23.9063	+	6.95697i	1.25649	+	0.365650i
$363$	2.29116	+	23.2625i	0.120255	+	1.22096i
$364$	11.0647	+	19.6174i	0.579945	+	1.02823i
$365$	−5.44189	+	1.65078i	−0.284841	+	0.0864057i
$366$	−21.7200	+	4.57694i	−1.13533	+	0.239240i
$367$	5.68094	−	13.7150i	0.296543	−	0.715917i	−0.703444	−	0.710751i	$-0.748355\pi$
$367$	5.68094	−	13.7150i	0.296543	−	0.715917i	0.999987	−	0.00516669i	$-0.00164462\pi$
$368$	−4.63888	−	6.30398i	−0.241818	−	0.328618i
$369$	1.22004	+	2.94543i	0.0635126	+	0.153333i
$370$	3.86477	+	5.64446i	0.200920	+	0.293442i
$371$	−3.18584	−	1.70287i	−0.165401	−	0.0884085i
$372$	−0.190112	+	2.51316i	−0.00985682	+	0.130301i
$373$	−21.5924	−	17.7204i	−1.11801	−	0.917529i	−0.120840	−	0.992672i	$-0.538559\pi$
$373$	−21.5924	−	17.7204i	−1.11801	−	0.917529i	−0.997173	+	0.0751430i	$0.976059\pi$
$374$	−5.99198	−	4.80486i	−0.309838	−	0.248454i
$375$	2.32806	+	0.463081i	0.120221	+	0.0239134i
$376$	10.9970	+	10.2734i	0.567129	+	0.529810i
$377$	4.54231	+	22.8357i	0.233941	+	1.17610i
$378$	3.56046	−	1.12428i	0.183130	−	0.0578269i
$379$	−9.79326	−	18.3219i	−0.503046	−	0.941133i	−0.997413	−	0.0718798i	$-0.977100\pi$
$379$	−9.79326	−	18.3219i	−0.503046	−	0.941133i	0.494367	−	0.869253i	$-0.335400\pi$
$380$	0.832189	−	0.0188708i	0.0426904	−	0.000968053i
$381$	14.6899	+	1.44683i	0.752588	+	0.0741234i
$382$	−5.22349	+	2.23335i	−0.267257	+	0.114268i
$383$	16.7844			0.857645			0.428823	−	0.903389i	$-0.358929\pi$
$383$	16.7844			0.857645			0.428823	+	0.903389i	$0.358929\pi$
$384$	10.7421	−	24.6130i	0.548181	−	1.25603i
$385$	−3.26515			−0.166408
$386$	−3.22088	+	1.37711i	−0.163939	+	0.0700932i
$387$	27.1448	+	2.67353i	1.37985	+	0.135903i
$388$	0.763804	+	33.6831i	0.0387762	+	1.71000i
$389$	12.0763	+	22.5933i	0.612295	+	1.14552i	0.976766	+	0.214309i	$0.0687499\pi$
$389$	12.0763	+	22.5933i	0.612295	+	1.14552i	−0.364471	+	0.931215i	$0.618750\pi$
$390$	11.8516	−	3.74236i	0.600128	−	0.189502i
$391$	−1.93127	−	9.70916i	−0.0976687	−	0.491013i
$392$	6.36489	−	0.216543i	0.321476	−	0.0109371i
$393$	47.2157	+	9.39178i	2.38172	+	0.473753i
$394$	17.5531	+	14.0755i	0.884310	+	0.709112i
$395$	−2.02207	−	1.65947i	−0.101741	−	0.0834969i
$396$	5.63968	+	0.426621i	0.283404	+	0.0214385i
$397$	−33.8577	−	18.0973i	−1.69927	−	0.908280i	−0.976016	−	0.217699i	$-0.930145\pi$
$397$	−33.8577	−	18.0973i	−1.69927	−	0.908280i	−0.723256	−	0.690580i	$-0.757355\pi$
$398$	2.80963	+	4.10344i	0.140834	+	0.205687i
$399$	−1.14993	−	2.77619i	−0.0575687	−	0.138983i
$400$	3.42319	+	2.06924i	0.171160	+	0.103462i
$401$	0.493609	−	1.19168i	0.0246496	−	0.0595095i	−0.911075	−	0.412240i	$-0.864747\pi$
$401$	0.493609	−	1.19168i	0.0246496	−	0.0595095i	0.935725	+	0.352730i	$0.114747\pi$
$402$	−38.6810	+	8.15102i	−1.92923	+	0.406536i
$403$	−1.88093	+	0.570575i	−0.0936959	+	0.0284223i
$404$	−21.4301	+	12.0871i	−1.06619	+	0.601355i
$405$	−0.976576	−	9.91534i	−0.0485264	−	0.492697i
$406$	25.9737	+	7.55858i	1.28905	+	0.375126i
$407$	−4.31750	+	2.88486i	−0.214010	+	0.142997i
$408$	25.5084	−	22.4283i	1.26285	−	1.11036i
$409$	12.9914	−	19.4431i	0.642386	−	0.961398i	−0.357239	−	0.934013i	$-0.616282\pi$
$409$	12.9914	−	19.4431i	0.642386	−	0.961398i	0.999625	−	0.0273852i	$-0.00871807\pi$
$410$	−1.70506	−	0.148439i	−0.0842070	−	0.00733086i
$411$	−17.1810	−	5.21180i	−0.847476	−	0.257079i
$412$	6.48615	+	29.1391i	0.319550	+	1.43558i
$413$	−4.36962	−	5.32440i	−0.215015	−	0.261997i
$414$	5.21270	+	5.09583i	0.256190	+	0.250447i
$415$	2.75981	−	2.75981i	0.135474	−	0.135474i
$416$	20.9257	+	0.868793i	1.02597	+	0.0425961i
$417$	−38.8458	−	38.8458i	−1.90229	−	1.90229i
$418$	0.00716256	+	0.631808i	0.000350332	+	0.0309027i
$419$	0.998753	−	0.819656i	0.0487923	−	0.0400428i	−0.609681	−	0.792647i	$-0.708702\pi$
$419$	0.998753	−	0.819656i	0.0487923	−	0.0400428i	0.658473	+	0.752604i	$0.271202\pi$
$420$	2.49527	−	14.2225i	0.121757	−	0.693988i
$421$	8.69900	−	28.6767i	0.423963	−	1.39762i	−0.441777	−	0.897125i	$-0.645652\pi$
$421$	8.69900	−	28.6767i	0.423963	−	1.39762i	0.865740	−	0.500494i	$-0.166848\pi$
$422$	−25.3978	+	21.3298i	−1.23634	+	1.03832i
$423$	−11.6542	−	7.78709i	−0.566647	−	0.378621i
$424$	−2.90696	+	1.68331i	−0.141174	+	0.0817487i
$425$	2.81074	+	4.20657i	0.136341	+	0.204049i
$426$	−4.92017	−	8.95919i	−0.238383	−	0.434074i
$427$	−20.0158	+	1.97138i	−0.968631	+	0.0954018i
$428$	4.11002	+	3.21989i	0.198666	+	0.155639i
$429$	2.73854	+	9.02775i	0.132218	+	0.435864i
$430$	−7.99667	+	12.2666i	−0.385634	+	0.591550i
$431$	16.0770	+	6.65933i	0.774404	+	0.320769i	0.734655	−	0.678441i	$-0.237344\pi$
$431$	16.0770	+	6.65933i	0.774404	+	0.320769i	0.0397493	+	0.999210i	$0.487344\pi$
$432$	0.856230	−	3.36478i	0.0411954	−	0.161888i
$433$	−18.8221	+	7.79637i	−0.904533	+	0.374670i	−0.785961	−	0.618276i	$-0.787832\pi$
$433$	−18.8221	+	7.79637i	−0.904533	+	0.374670i	−0.118572	+	0.992945i	$0.537832\pi$
$434$	−0.420103	+	2.24470i	−0.0201656	+	0.107749i
$435$	7.03669	−	13.1647i	0.337384	−	0.631200i
$436$	11.7306	−	23.1966i	0.561796	−	1.11091i
$437$	−0.516640	+	0.629528i	−0.0247143	+	0.0301144i
$438$	18.9754	−	2.08636i	0.906680	−	0.0996901i
$439$	1.36938	−	6.88433i	0.0653569	−	0.328571i	−0.934250	−	0.356620i	$-0.883929\pi$
$439$	1.36938	−	6.88433i	0.0653569	−	0.328571i	0.999607	+	0.0280484i	$0.00892926\pi$
$440$	−1.60004	+	2.58046i	−0.0762791	+	0.123019i
$441$	−5.81754	+	1.15718i	−0.277026	+	0.0551039i
$442$	23.5018	+	12.2215i	1.11787	+	0.581317i
$443$	−21.1993	+	11.3313i	−1.00721	+	0.538365i	−0.890588	−	0.454811i	$-0.849707\pi$
$443$	−21.1993	+	11.3313i	−1.00721	+	0.538365i	−0.116622	+	0.993176i	$0.537207\pi$
$444$	−9.26654	−	21.0110i	−0.439770	−	0.997139i
$445$	1.46138	−	14.8376i	0.0692760	−	0.703371i
$446$	4.93833	−	12.3152i	0.233837	−	0.583142i
$447$		−	49.2687i		−	2.33033i
$448$	12.1125	−	21.1043i	0.572260	−	0.997086i
$449$			40.0389i			1.88955i	0.327716	+	0.944776i	$0.393721\pi$
$449$			40.0389i			1.88955i	−0.327716	+	0.944776i	$0.606279\pi$
$450$	−3.45785	−	1.38658i	−0.163004	−	0.0653638i
$451$	0.127339	−	1.29289i	0.00599616	−	0.0608800i
$452$	−3.29441	−	1.27788i	−0.154956	−	0.0601066i
$453$	−28.1753	+	15.0600i	−1.32379	+	0.707582i
$454$	−10.3616	+	19.9253i	−0.486295	+	0.935140i
$455$	11.0449	−	2.19697i	0.517794	−	0.102996i
$456$	−2.75754	−	0.451636i	−0.129133	−	0.0211498i
$457$	2.85963	−	14.3763i	0.133768	−	0.672496i	−0.854461	−	0.519515i	$-0.826113\pi$
$457$	2.85963	−	14.3763i	0.133768	−	0.672496i	0.988229	−	0.152981i	$-0.0488873\pi$
$458$	3.00541	+	27.3341i	0.140433	+	1.27724i
$459$	2.78587	−	3.39460i	0.130033	−	0.158446i
$460$	−3.71819	+	1.22061i	−0.173362	+	0.0569113i
$461$	−2.20342	+	4.12231i	−0.102624	+	0.191995i	−0.927993	−	0.372598i	$-0.878467\pi$
$461$	−2.20342	+	4.12231i	−0.102624	+	0.191995i	0.825369	+	0.564593i	$0.190967\pi$
$462$	10.7737	+	2.01633i	0.501237	+	0.0938083i
$463$	−17.4699	+	7.23628i	−0.811897	+	0.336299i	−0.749711	−	0.661766i	$-0.769807\pi$
$463$	−17.4699	+	7.23628i	−0.811897	+	0.336299i	−0.0621863	+	0.998065i	$0.519807\pi$
$464$	18.7016	−	16.8231i	0.868200	−	0.780991i
$465$	1.16425	+	0.482247i	0.0539907	+	0.0223637i
$466$	−29.1207	−	18.9839i	−1.34899	−	0.879411i
$467$	−0.683019	−	2.25161i	−0.0316063	−	0.104192i	0.939718	−	0.341950i	$-0.111087\pi$
$467$	−0.683019	−	2.25161i	−0.0316063	−	0.104192i	−0.971324	+	0.237758i	$0.923587\pi$
$468$	−19.3642	+	2.35156i	−0.895109	+	0.108701i
$469$	−35.6459	+	3.51081i	−1.64597	+	0.162114i
$470$	6.59546	−	3.62206i	0.304226	−	0.167073i
$471$	24.4963	+	36.6614i	1.12873	+	1.68927i
$472$	−6.34916	+	0.844174i	−0.292244	+	0.0388562i
$473$	−9.24178	−	6.17516i	−0.424938	−	0.283934i
$474$	5.64722	+	6.72425i	0.259385	+	0.308855i
$475$	0.120817	−	0.398280i	0.00554346	−	0.0182743i
$476$	25.1956	−	17.6743i	1.15484	−	0.810100i
$477$	2.41846	−	1.98478i	0.110734	−	0.0908768i
$478$	23.6831	−	0.268486i	1.08324	−	0.0122803i
$479$	−6.65742	−	6.65742i	−0.304185	−	0.304185i	0.538464	−	0.842649i	$-0.319005\pi$
$479$	−6.65742	−	6.65742i	−0.304185	−	0.304185i	−0.842649	+	0.538464i	$0.819005\pi$
$480$	−10.0173	−	8.94157i	−0.457226	−	0.408125i
$481$	12.6636	−	12.6636i	0.577408	−	0.577408i
$482$	7.42288	−	7.59311i	0.338103	−	0.345857i
$483$	8.96220	+	10.9205i	0.407794	+	0.496899i
$484$	16.6199	+	10.5680i	0.755449	+	0.480366i
$485$	16.1205	+	4.89011i	0.731995	+	0.222048i
$486$	−2.58133	+	29.6509i	−0.117092	+	1.34499i
$487$	12.8782	−	19.2736i	0.583566	−	0.873368i	−0.415782	−	0.909464i	$-0.636492\pi$
$487$	12.8782	−	19.2736i	0.583566	−	0.873368i	0.999348	+	0.0360958i	$0.0114922\pi$
$488$	−8.25046	+	16.7845i	−0.373481	+	0.759801i
$489$	46.0056	−	30.7400i	2.08045	−	1.39011i
$490$	0.889748	−	3.05745i	0.0401947	−	0.138122i
$491$	−4.02520	−	40.8685i	−0.181655	−	1.84437i	−0.464948	−	0.885338i	$-0.653927\pi$
$491$	−4.02520	−	40.8685i	−0.181655	−	1.84437i	0.283294	−	0.959033i	$-0.408573\pi$
$492$	5.53434	+	1.54271i	0.249507	+	0.0695510i
$493$	30.4458	−	9.23564i	1.37121	−	0.415952i
$494$	−0.449343	−	2.13237i	−0.0202169	−	0.0959400i
$495$	1.08219	−	2.61263i	0.0486408	−	0.117429i
$496$	1.56812	+	1.43199i	0.0704107	+	0.0642982i
$497$	−3.54421	−	8.55648i	−0.158980	−	0.383811i
$498$	−10.8105	+	7.40199i	−0.484431	+	0.331691i
$499$	5.61542	+	3.00151i	0.251381	+	0.134366i	0.592275	−	0.805736i	$-0.298230\pi$
$499$	5.61542	+	3.00151i	0.251381	+	0.134366i	−0.340894	+	0.940102i	$0.610730\pi$
$500$	1.51686	−	1.30351i	0.0678360	−	0.0582947i
$501$	−5.70571	−	4.68255i	−0.254912	−	0.209201i
$502$	−11.6491	+	14.5271i	−0.519923	+	0.648378i
$503$	−6.83691	−	1.35995i	−0.304843	−	0.0606370i	0.0402987	−	0.999188i	$-0.487169\pi$
$503$	−6.83691	−	1.35995i	−0.304843	−	0.0606370i	−0.345141	+	0.938551i	$0.612169\pi$
$504$	−7.95591	+	21.2209i	−0.354384	+	0.945255i
$505$	2.39998	+	12.0655i	0.106798	+	0.536909i
$506$	−0.894471	−	2.83267i	−0.0397641	−	0.125928i
$507$	−0.791666	−	1.48110i	−0.0351591	−	0.0657781i
$508$	8.59285	−	8.99159i	0.381246	−	0.398937i
$509$	−22.7663	−	2.24228i	−1.00910	−	0.0993874i	−0.420062	−	0.907495i	$-0.637992\pi$
$509$	−22.7663	−	2.24228i	−1.00910	−	0.0993874i	−0.589034	+	0.808108i	$0.700492\pi$
$510$	−6.67661	−	15.6157i	−0.295645	−	0.691474i
$511$	17.2971			0.765179
$512$	−10.7432	−	19.9144i	−0.474789	−	0.880100i
$513$	−0.361264			−0.0159502
$514$	11.6355	+	27.2138i	0.513218	+	1.20035i
$515$	14.8543	+	1.46302i	0.654557	+	0.0644683i
$516$	33.9608	−	35.5367i	1.49504	−	1.56442i
$517$	2.69246	+	5.03723i	0.118414	+	0.221537i
$518$	−6.26536	−	19.8416i	−0.275284	−	0.871789i
$519$	1.87483	+	9.42541i	0.0822959	+	0.413729i
$520$	3.67614	−	9.80541i	0.161209	−	0.429996i
$521$	−5.28729	−	1.05171i	−0.231640	−	0.0460761i	0.0779052	−	0.996961i	$-0.475177\pi$
$521$	−5.28729	−	1.05171i	−0.231640	−	0.0460761i	−0.309545	+	0.950885i	$0.600177\pi$
$522$	−14.6566	+	18.2778i	−0.641504	+	0.799998i
$523$	4.90517	+	4.02557i	0.214488	+	0.176026i	0.735502	−	0.677522i	$-0.236946\pi$
$523$	4.90517	+	4.02557i	0.214488	+	0.176026i	−0.521014	+	0.853548i	$0.674446\pi$
$524$	30.7636	−	26.4366i	1.34391	−	1.15489i
$525$	−6.36736	−	3.40343i	−0.277895	−	0.148538i
$526$	−34.3242	+	23.5018i	−1.49661	+	1.02473i
$527$	1.02785	+	2.48145i	0.0447739	+	0.108094i
$528$	6.87300	−	7.52638i	0.299109	−	0.327544i
$529$	−7.33654	+	17.7120i	−0.318980	+	0.770085i
$530$	0.346322	+	1.64348i	0.0150433	+	0.0713884i
$531$	5.70860	−	1.73169i	0.247732	−	0.0751487i
$532$	−2.43889	−	0.679849i	−0.105739	−	0.0294752i
$533$	0.439184	+	4.45911i	0.0190232	+	0.193145i
$534$	−13.9846	+	48.0556i	−0.605174	+	2.07957i
$535$	2.17060	−	1.45035i	0.0938431	−	0.0627039i
$536$	−14.6932	+	29.8914i	−0.634648	+	1.29111i
$537$	23.3864	−	35.0003i	1.00920	−	1.51037i
$538$	1.54932	−	17.7965i	0.0667959	−	0.767261i
$539$	2.31301	+	0.701643i	0.0996282	+	0.0302219i
$540$	−1.46493	−	0.931502i	−0.0630405	−	0.0400855i
$541$	24.6510	+	30.0373i	1.05983	+	1.29141i	0.954901	+	0.296925i	$0.0959612\pi$
$541$	24.6510	+	30.0373i	1.05983	+	1.29141i	0.104928	+	0.994480i	$0.466539\pi$
$542$	−1.13175	+	1.15771i	−0.0486130	+	0.0497278i
$543$	−29.5499	+	29.5499i	−1.26811	+	1.26811i
$544$	−1.62128	−	28.5732i	−0.0695119	−	1.22507i
$545$	−9.19028	−	9.19028i	−0.393668	−	0.393668i
$546$	−37.8004	+	0.428528i	−1.61771	+	0.0183393i
$547$	−19.5678	+	16.0589i	−0.836660	+	0.686629i	−0.951800	−	0.306720i	$-0.900769\pi$
$547$	−19.5678	+	16.0589i	−0.836660	+	0.686629i	0.115139	+	0.993349i	$0.463269\pi$
$548$	−12.3844	+	8.68748i	−0.529037	+	0.371111i
$549$	5.05653	−	16.6691i	0.215807	−	0.711421i
$550$	0.976334	+	1.16254i	0.0416310	+	0.0495708i
$551$	−2.17626	−	1.45413i	−0.0927119	−	0.0619481i
$552$	13.0223	−	1.73142i	0.554265	−	0.0736942i
$553$	4.42037	+	6.61554i	0.187973	+	0.281322i
$554$	−25.0791	+	13.7728i	−1.06551	+	0.585151i
$555$	−11.4266	+	1.12542i	−0.485031	+	0.0477714i
$556$	−45.9504	+	5.58016i	−1.94873	+	0.236652i
$557$	−7.17719	−	23.6600i	−0.304107	−	1.00251i	−0.967210	−	0.253979i	$-0.918261\pi$
$557$	−7.17719	−	23.6600i	−0.304107	−	1.00251i	0.663103	−	0.748529i	$-0.269239\pi$
$558$	−1.65687	−	1.08012i	−0.0701409	−	0.0457251i
$559$	35.4168	+	14.6701i	1.49797	+	0.620480i
$560$	−8.13679	−	9.04537i	−0.343842	−	0.382237i
$561$	11.9100	−	4.93329i	0.502841	−	0.208284i
$562$	−4.83324	−	0.904558i	−0.203878	−	0.0381565i
$563$	7.02271	−	13.1386i	0.295972	−	0.553725i	−0.689350	−	0.724428i	$-0.742104\pi$
$563$	7.02271	−	13.1386i	0.295972	−	0.553725i	0.985322	+	0.170703i	$0.0546039\pi$
$564$	−23.9990	+	7.87843i	−1.01054	+	0.331742i
$565$	−1.12084	+	1.36575i	−0.0471540	+	0.0574573i
$566$	−3.70340	−	33.6823i	−0.155666	−	1.41577i
$567$	−5.91220	+	29.7226i	−0.248289	+	1.24823i
$568$	−8.49899	−	1.39199i	−0.356610	−	0.0584065i
$569$	0.444788	−	0.0884738i	0.0186465	−	0.00370902i	−0.185758	−	0.982595i	$-0.559474\pi$
$569$	0.444788	−	0.0884738i	0.0186465	−	0.00370902i	0.204405	+	0.978886i	$0.434474\pi$
$570$	−0.644596	+	1.23955i	−0.0269992	+	0.0519191i
$571$	−18.1725	+	9.71338i	−0.760494	+	0.406492i	−0.805577	−	0.592491i	$-0.798145\pi$
$571$	−18.1725	+	9.71338i	−0.760494	+	0.406492i	0.0450833	+	0.998983i	$0.485645\pi$
$572$	7.41085	+	2.87462i	0.309863	+	0.120194i
$573$	0.934600	−	9.48915i	0.0390435	−	0.396415i
$574$	4.83182	+	1.93753i	0.201676	+	0.0808710i
$575$			1.95671i			0.0816004i
$576$	12.8723	+	16.6866i	0.536344	+	0.695275i
$577$		−	22.9665i		−	0.956109i	−0.878330	−	0.478054i	$-0.841342\pi$
$577$		−	22.9665i		−	0.956109i	0.878330	−	0.478054i	$-0.158658\pi$
$578$	4.52424	−	11.2826i	0.188183	−	0.469292i
$579$	0.576288	−	5.85115i	0.0239497	−	0.243165i
$580$	−5.07536	−	11.5079i	−0.210743	−	0.477840i
$581$	−10.4697	+	5.59616i	−0.434356	+	0.232168i
$582$	−50.1713	−	26.0903i	−2.07967	−	1.08148i
$583$	−1.25041	+	0.248723i	−0.0517868	+	0.0103010i
$584$	8.47621	−	13.6699i	0.350748	−	0.565666i
$585$	−1.90276	+	9.56581i	−0.0786694	+	0.395498i
$586$	16.0054	−	1.75981i	0.661177	−	0.0726969i
$587$	−17.9607	+	21.8851i	−0.741316	+	0.903296i	−0.998001	−	0.0631994i	$-0.979870\pi$
$587$	−17.9607	+	21.8851i	−0.741316	+	0.903296i	0.256685	+	0.966495i	$0.417370\pi$
$588$	−4.82388	+	9.53890i	−0.198933	+	0.393378i
$589$	0.104160	−	0.194869i	0.00429182	−	0.00802943i
$590$	−0.589134	+	3.14786i	−0.0242543	+	0.129595i
$591$	−34.8895	+	14.4517i	−1.43516	+	0.594463i
$592$	−18.7511	−	4.77156i	−0.770665	−	0.196110i
$593$	41.5595	+	17.2145i	1.70665	+	0.706916i	1.00000		0.000651938i	$-0.000207518\pi$
$593$	41.5595	+	17.2145i	1.70665	+	0.706916i	0.706646	+	0.707568i	$0.250208\pi$
$594$	0.719632	−	1.10389i	0.0295268	−	0.0452932i
$595$	−4.46699	−	14.7257i	−0.183129	−	0.603694i
$596$	−32.6785	−	25.6011i	−1.33856	−	1.04866i
$597$	−8.30695	+	0.818163i	−0.339981	+	0.0334852i
$598$	4.93167	+	8.98013i	0.201671	+	0.367225i
$599$	7.14843	+	10.6984i	0.292077	+	0.437124i	0.948268	−	0.317471i	$-0.102833\pi$
$599$	7.14843	+	10.6984i	0.292077	+	0.437124i	−0.656191	+	0.754595i	$0.727833\pi$
$600$	−5.80997	+	3.36434i	−0.237191	+	0.137349i
$601$	−13.1852	−	8.81006i	−0.537835	−	0.359370i	0.256793	−	0.966466i	$-0.417334\pi$
$601$	−13.1852	−	8.81006i	−0.537835	−	0.359370i	−0.794628	+	0.607097i	$0.792334\pi$
$602$	34.1065	−	28.6436i	1.39008	−	1.16743i
$603$	9.00511	−	29.6859i	0.366716	−	1.20890i
$604$	−4.65164	+	26.5134i	−0.189273	+	1.07882i
$605$	7.61233	−	6.24727i	0.309485	−	0.253988i
$606$	−0.468127	−	41.2934i	−0.0190163	−	1.67743i
$607$	6.44858	+	6.44858i	0.261740	+	0.261740i	0.825761	−	0.564021i	$-0.190746\pi$
$607$	6.44858	+	6.44858i	0.261740	+	0.261740i	−0.564021	+	0.825761i	$0.690746\pi$
$608$	−1.73243	+	1.59431i	−0.0702594	+	0.0646579i
$609$	−32.1053	+	32.1053i	−1.30097	+	1.30097i
$610$	6.68694	+	6.53702i	0.270746	+	0.264676i
$611$	−12.4970	−	15.2276i	−0.505574	−	0.616044i
$612$	5.79148	+	26.0183i	0.234107	+	1.05173i
$613$	−5.09500	−	1.54555i	−0.205785	−	0.0624242i	0.185709	−	0.982605i	$-0.440542\pi$
$613$	−5.09500	−	1.54555i	−0.205785	−	0.0624242i	−0.391494	+	0.920181i	$0.628042\pi$
$614$	−24.2810	−	2.11385i	−0.979902	−	0.0853079i
$615$	1.59597	−	2.38854i	0.0643557	−	0.0963151i
$616$	6.93561	−	6.09813i	0.279444	−	0.245701i
$617$	1.59659	−	1.06681i	0.0642764	−	0.0429481i	−0.523017	−	0.852322i	$-0.675194\pi$
$617$	1.59659	−	1.06681i	0.0642764	−	0.0429481i	0.587293	+	0.809374i	$0.300194\pi$
$618$	−48.1096	−	14.0003i	−1.93525	−	0.563176i
$619$	2.68414	+	27.2525i	0.107885	+	1.09537i	0.884866	+	0.465846i	$0.154250\pi$
$619$	2.68414	+	27.2525i	0.107885	+	1.09537i	−0.776981	+	0.629524i	$0.783250\pi$
$620$	0.924828	−	0.521625i	0.0371420	−	0.0209490i
$621$	1.62529	−	0.493028i	0.0652208	−	0.0197845i
$622$	−29.5753	+	6.23223i	−1.18586	+	0.249890i
$623$	−17.3544	+	41.8972i	−0.695289	+	1.67858i
$624$	−18.1849	+	30.0837i	−0.727978	+	1.20431i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	5.52125	+	8.06373i	0.220673	+	0.322291i
$627$	−0.935295	−	0.499926i	−0.0373521	−	0.0199651i
$628$	37.0452	+	2.80234i	1.47827	+	0.111825i
$629$	−18.9173	−	15.5250i	−0.754281	−	0.619022i
$630$	8.84040	+	7.08896i	0.352210	+	0.282431i
$631$	36.6503	+	7.29019i	1.45902	+	0.290218i	0.859910	−	0.510446i	$-0.170520\pi$
$631$	36.6503	+	7.29019i	1.45902	+	0.290218i	0.599114	+	0.800664i	$0.295520\pi$
$632$	7.39442	−	0.251569i	0.294134	−	0.0100069i
$633$	−10.8602	−	54.5981i	−0.431655	−	2.17008i
$634$	−9.87187	+	3.11723i	−0.392062	+	0.123801i
$635$	−2.93145	−	5.48435i	−0.116331	−	0.217640i
$636$	−0.127818	−	5.63669i	−0.00506833	−	0.223509i
$637$	−8.29622	−	0.817106i	−0.328708	−	0.0323749i
$638$	8.77838	−	3.75326i	0.347539	−	0.148593i
$639$	8.02120			0.317314
$640$	−11.1359	+	1.99796i	−0.440185	+	0.0789764i
$641$	9.83581			0.388491			0.194246	−	0.980953i	$-0.437774\pi$
$641$	9.83581			0.388491			0.194246	+	0.980953i	$0.437774\pi$
$642$	−8.05771	+	3.44514i	−0.318013	+	0.135969i
$643$	−0.918855	−	0.0904993i	−0.0362361	−	0.00356894i	0.0798828	−	0.996804i	$-0.474545\pi$
$643$	−0.918855	−	0.0904993i	−0.0362361	−	0.00356894i	−0.116119	+	0.993235i	$0.537045\pi$
$644$	11.9002	−	0.269850i	0.468933	−	0.0106336i
$645$	−11.5857	−	21.6753i	−0.456186	−	0.853464i
$646$	−2.83963	+	0.896666i	−0.111724	+	0.0352789i
$647$	0.957799	+	4.81518i	0.0376550	+	0.189304i	0.995035	−	0.0995275i	$-0.0317331\pi$
$647$	0.957799	+	4.81518i	0.0376550	+	0.189304i	−0.957380	+	0.288832i	$0.906733\pi$
$648$	20.5927	+	19.2376i	0.808956	+	0.755723i
$649$	−2.38421	−	0.474249i	−0.0935885	−	0.0186159i
$650$	−4.08483	−	3.27555i	−0.160220	−	0.128478i
$651$	−2.96295	−	2.43163i	−0.116127	−	0.0953031i
$652$	3.51660	−	46.4874i	0.137721	−	1.82059i
$653$	−14.7749	−	7.89736i	−0.578187	−	0.309048i	0.156257	−	0.987716i	$-0.450057\pi$
$653$	−14.7749	−	7.89736i	−0.578187	−	0.309048i	−0.734444	+	0.678669i	$0.762557\pi$
$654$	24.6489	+	35.9994i	0.963847	+	1.40769i
$655$	−7.76124	−	18.7373i	−0.303257	−	0.732127i
$656$	3.89900	−	2.86914i	0.152230	−	0.112021i
$657$	−5.73288	+	13.8404i	−0.223661	+	0.539965i
$658$	−22.3953	+	4.71924i	−0.873061	+	0.183975i
$659$	−22.2911	+	6.76193i	−0.868338	+	0.263408i	−0.692857	−	0.721075i	$-0.743648\pi$
$659$	−22.2911	+	6.76193i	−0.868338	+	0.263408i	−0.175481	+	0.984483i	$0.556148\pi$
$660$	−2.50360	−	4.43882i	−0.0974525	−	0.172781i
$661$	−3.60028	−	36.5542i	−0.140035	−	1.42179i	−0.766449	−	0.642305i	$-0.777978\pi$
$661$	−3.60028	−	36.5542i	−0.140035	−	1.42179i	0.626415	−	0.779490i	$-0.284522\pi$
$662$	−10.9982	−	3.20059i	−0.427458	−	0.124394i
$663$	−36.9682	+	24.7014i	−1.43573	+	0.959321i
$664$	−0.707863	+	11.0165i	−0.0274704	+	0.427525i
$665$	−0.703318	+	1.05259i	−0.0272735	+	0.0408177i
$666$	17.9529	+	1.56294i	0.695662	+	0.0605626i
$667$	11.7753	+	3.57200i	0.455942	+	0.138308i
$668$	−6.07061	+	1.35127i	−0.234879	+	0.0522823i
$669$	14.1281	+	17.2152i	0.546225	+	0.665577i
$670$	11.9087	+	11.6417i	0.460073	+	0.449759i
$671$	−5.01925	+	5.01925i	−0.193766	+	0.193766i
$672$	21.2623	+	34.8707i	0.820210	+	1.34517i
$673$	−13.2970	−	13.2970i	−0.512561	−	0.512561i	0.402749	−	0.915310i	$-0.368055\pi$
$673$	−13.2970	−	13.2970i	−0.512561	−	0.512561i	−0.915310	+	0.402749i	$0.868055\pi$
$674$	−0.220646	−	19.4632i	−0.00849899	−	0.749694i
$675$	−0.670975	+	0.550655i	−0.0258258	+	0.0211947i
$676$	−1.39374	−	0.244524i	−0.0536053	−	0.00940478i
$677$	−1.27411	+	4.20018i	−0.0489680	+	0.161426i	−0.978014	−	0.208537i	$-0.933130\pi$
$677$	−1.27411	+	4.20018i	−0.0489680	+	0.161426i	0.929046	+	0.369963i	$0.120630\pi$
$678$	4.54170	−	3.81425i	0.174423	−	0.146485i
$679$	−42.6039	−	28.4670i	−1.63499	−	1.09246i
$680$	−13.8267	−	3.68585i	−0.530231	−	0.141346i
$681$	−20.9423	−	31.3423i	−0.802509	−	1.20104i
$682$	0.387965	+	0.706449i	0.0148559	+	0.0270513i
$683$	24.0278	−	2.36653i	0.919399	−	0.0905529i	0.372766	−	0.927925i	$-0.378409\pi$
$683$	24.0278	−	2.36653i	0.919399	−	0.0905529i	0.546633	+	0.837372i	$0.315909\pi$
$684$	1.35232	−	1.72617i	0.0517073	−	0.0660018i
$685$	2.19567	+	7.23815i	0.0838922	+	0.276555i
$686$	11.1544	−	17.1106i	0.425879	−	0.653285i
$687$	−42.6418	−	17.6628i	−1.62689	−	0.673878i
$688$	−5.92370	−	40.9908i	−0.225839	−	1.56276i
$689$	4.06237	−	1.68269i	0.154764	−	0.0641054i
$690$	1.20833	−	6.45634i	0.0460002	−	0.245789i
$691$	−0.0208126	+	0.0389377i	−0.000791750	+	0.00148126i	−0.882317	−	0.470656i	$-0.844017\pi$
$691$	−0.0208126	+	0.0389377i	−0.000791750	+	0.00148126i	0.881525	+	0.472137i	$0.156517\pi$
$692$	7.22580	+	3.65413i	0.274684	+	0.138909i
$693$	−5.45671	+	6.64902i	−0.207283	+	0.252575i
$694$	−24.4954	+	2.69329i	−0.929833	+	0.102236i
$695$	−4.51517	+	22.6993i	−0.171270	+	0.861033i
$696$	9.64012	+	41.1056i	0.365408	+	1.55810i
$697$	6.00510	−	1.19449i	0.227460	−	0.0452445i
$698$	42.9682	+	22.3444i	1.62637	+	0.845750i
$699$	51.4566	−	27.5041i	1.94627	−	1.04030i
$700$	−5.56601	+	2.45479i	−0.210376	+	0.0927824i
$701$	−3.38666	+	34.3853i	−0.127912	+	1.29872i	0.690184	+	0.723634i	$0.257530\pi$
$701$	−3.38666	+	34.3853i	−0.127912	+	1.29872i	−0.818096	+	0.575081i	$0.804970\pi$
$702$	−1.69151	+	4.21830i	−0.0638420	+	0.159209i
$703$			2.01324i			0.0759306i
$704$	−1.42067	−	8.46953i	−0.0535434	−	0.319207i
$705$			12.6296i			0.475657i
$706$	−6.18996	−	2.48214i	−0.232962	−	0.0934164i
$707$	3.66761	−	37.2379i	0.137935	−	1.40048i
$708$	3.88780	−	10.0228i	0.146112	−	0.376681i
$709$	−30.1933	+	16.1386i	−1.13393	+	0.606099i	−0.928042	−	0.372476i	$-0.878509\pi$
$709$	−30.1933	+	16.1386i	−1.13393	+	0.606099i	−0.205890	+	0.978575i	$0.566009\pi$
$710$	−1.98671	+	3.82042i	−0.0745599	+	0.143378i
$711$	−6.75854	+	1.34436i	−0.253465	+	0.0504173i
$712$	24.6072	+	34.2463i	0.922193	+	1.28344i
$713$	−0.202661	+	1.01885i	−0.00758973	+	0.0381561i
$714$	5.64567	+	51.3473i	0.211284	+	1.92162i
$715$	2.52135	−	3.07227i	0.0942930	−	0.114896i
$716$	−11.0626	−	33.6985i	−0.413427	−	1.25937i
$717$	−18.7396	+	35.0592i	−0.699841	+	1.30931i
$718$	45.8426	+	8.57961i	1.71083	+	0.320188i
$719$	29.9505	−	12.4059i	1.11696	−	0.462661i	0.253633	−	0.967301i	$-0.418374\pi$
$719$	29.9505	−	12.4059i	1.11696	−	0.462661i	0.863330	+	0.504639i	$0.168374\pi$
$720$	9.93453	−	3.51274i	0.370238	−	0.130912i
$721$	−41.9442	−	17.3739i	−1.56208	−	0.647037i
$722$	−22.3042	−	14.5402i	−0.830077	−	0.541130i
$723$	5.17365	+	17.0552i	0.192410	+	0.634291i
$724$	4.24481	+	34.9544i	0.157757	+	1.29907i
$725$	−6.25842	+	0.616401i	−0.232432	+	0.0228926i
$726$	−28.9754	+	15.9126i	−1.07538	+	0.590572i
$727$	29.3980	+	43.9973i	1.09031	+	1.63177i	0.705390	+	0.708819i	$0.250772\pi$
$727$	29.3980	+	43.9973i	1.09031	+	1.63177i	0.384923	+	0.922949i	$0.374228\pi$
$728$	−19.3577	+	25.2946i	−0.717443	+	0.937479i
$729$	−16.6839	−	11.1478i	−0.617921	−	0.412881i
$730$	−5.17212	−	6.15854i	−0.191429	−	0.227938i
$731$	15.2062	−	50.1281i	0.562421	−	1.85405i
$732$	−18.0273	−	25.6989i	−0.666310	−	0.949858i
$733$	14.0466	−	11.5278i	0.518824	−	0.425788i	−0.338192	−	0.941077i	$-0.609815\pi$
$733$	14.0466	−	11.5278i	0.518824	−	0.425788i	0.857016	+	0.515289i	$0.172315\pi$
$734$	20.9927	−	0.237986i	0.774854	−	0.00878422i
$735$	3.77923	+	3.77923i	0.139399	+	0.139399i
$736$	5.61825	−	9.53697i	0.207092	−	0.351538i
$737$	−8.93873	+	8.93873i	−0.329262	+	0.329262i
$738$	−3.15177	+	3.22405i	−0.116018	+	0.118679i
$739$	30.7961	+	37.5252i	1.13285	+	1.38039i	0.914534	+	0.404509i	$0.132558\pi$
$739$	30.7961	+	37.5252i	1.13285	+	1.38039i	0.218320	+	0.975877i	$0.429942\pi$
$740$	−5.19103	+	8.16370i	−0.190826	+	0.300104i
$741$	3.50016	+	1.06176i	0.128582	+	0.0390048i
$742$	0.443074	−	5.08944i	0.0162658	−	0.186839i
$743$	−5.95074	+	8.90592i	−0.218312	+	0.326726i	−0.924419	−	0.381378i	$-0.875450\pi$
$743$	−5.95074	+	8.90592i	−0.218312	+	0.326726i	0.706107	+	0.708105i	$0.250450\pi$
$744$	−3.37367	+	1.15004i	−0.123685	+	0.0421625i
$745$	−17.2583	+	11.5316i	−0.632293	+	0.422485i
$746$	11.0379	−	37.9296i	0.404125	−	1.38870i
$747$	−1.00778	−	10.2322i	−0.0368727	−	0.374375i
$748$	2.91660	−	10.4630i	0.106641	−	0.382566i
$749$	−7.59848	+	2.30497i	−0.277642	+	0.0842219i
$750$	0.692175	+	3.28474i	0.0252746	+	0.119942i
$751$	10.7702	−	26.0014i	0.393008	−	0.948806i	−0.596273	−	0.802782i	$-0.703352\pi$
$751$	10.7702	−	26.0014i	0.393008	−	0.948806i	0.989281	−	0.146024i	$-0.0466478\pi$
$752$	−7.24489	+	20.0117i	−0.264194	+	0.729750i
$753$	−11.9604	−	28.8750i	−0.435862	−	1.05226i
$754$	−27.1689	+	18.6026i	−0.989432	+	0.677466i
$755$	11.8699	+	6.34461i	0.431991	+	0.230904i
$756$	3.44147	+	4.00475i	0.125165	+	0.145651i
$757$	36.4229	+	29.8915i	1.32381	+	1.08642i	0.989588	+	0.143931i	$0.0459744\pi$
$757$	36.4229	+	29.8915i	1.32381	+	1.08642i	0.334225	+	0.942493i	$0.391526\pi$
$758$	18.3800	−	22.9211i	0.667591	−	0.832531i
$759$	4.89008	+	0.972696i	0.177498	+	0.0353066i
$760$	0.487213	+	1.07164i	0.0176731	+	0.0388725i
$761$	−5.51402	−	27.7208i	−0.199883	−	1.00488i	−0.942256	−	0.334893i	$-0.891300\pi$
$761$	−5.51402	−	27.7208i	−0.199883	−	1.00488i	0.742373	−	0.669986i	$-0.233700\pi$
$762$	6.28582	+	19.9064i	0.227711	+	0.721131i
$763$	18.6354	+	34.8644i	0.674648	+	1.26218i
$764$	−5.80824	−	5.55066i	−0.210135	−	0.200816i
$765$	13.2634	+	1.30633i	0.479538	+	0.0472304i
$766$	9.33169	+	21.8256i	0.337168	+	0.788589i
$767$	8.38408			0.302732
$768$	37.9777	+	0.284297i	1.37040	+	0.0102587i
$769$	−39.3650			−1.41954			−0.709769	−	0.704434i	$-0.751201\pi$
$769$	−39.3650			−1.41954			−0.709769	+	0.704434i	$0.751201\pi$
$770$	−1.81534	−	4.24582i	−0.0654202	−	0.153009i
$771$	−49.4373	−	4.86915i	−1.78044	−	0.175358i
$772$	−3.58144	−	3.42262i	−0.128899	−	0.123183i
$773$	−13.0038	−	24.3284i	−0.467713	−	0.875030i	−0.999602	−	0.0282157i	$-0.991017\pi$
$773$	−13.0038	−	24.3284i	−0.467713	−	0.875030i	0.531889	−	0.846814i	$-0.321483\pi$
$774$	11.6153	+	36.7840i	0.417502	+	1.32217i
$775$	−0.103573	−	0.520694i	−0.00372044	−	0.0187039i
$776$	−43.3750	+	19.7201i	−1.55707	+	0.707910i
$777$	34.2527	+	6.81329i	1.22881	+	0.244425i
$778$	−22.6649	+	28.2646i	−0.812576	+	1.01334i
$779$	−0.389362	−	0.319541i	−0.0139503	−	0.0114488i
$780$	11.4555	+	13.3305i	0.410173	+	0.477307i
$781$	−2.88267	−	1.54082i	−0.103150	−	0.0551349i
$782$	11.5515	−	7.90935i	0.413081	−	0.282838i
$783$	2.08892	+	5.04310i	0.0746520	+	0.180226i
$784$	3.82028	+	8.15616i	0.136439	+	0.291291i
$785$	7.10855	−	17.1616i	0.253715	−	0.612523i
$786$	14.0381	+	66.6182i	0.500721	+	2.37619i
$787$	0.0134404	−	0.00407709i	0.000479098	−	0.000145333i	−0.290045	−	0.957013i	$-0.593670\pi$
$787$	0.0134404	−	0.00407709i	0.000479098	−	0.000145333i	0.290524	+	0.956868i	$0.406170\pi$
$788$	−8.54395	+	30.6506i	−0.304365	+	1.09188i
$789$	−6.84372	−	69.4854i	−0.243643	−	2.47375i
$790$	1.03367	−	3.55200i	0.0367762	−	0.126374i
$791$	4.46827	−	2.98561i	0.158874	−	0.106156i
$792$	2.58075	+	7.57071i	0.0917030	+	0.269013i
$793$	13.6012	−	20.3557i	0.482993	−	0.722851i
$794$	4.70880	−	54.0883i	0.167109	−	1.91952i
$795$	−2.69768	−	0.818333i	−0.0956769	−	0.0290233i
$796$	−3.77381	+	5.93489i	−0.133759	+	0.210357i
$797$	−1.02221	−	1.24557i	−0.0362086	−	0.0441203i	0.754591	−	0.656195i	$-0.227835\pi$
$797$	−1.02221	−	1.24557i	−0.0362086	−	0.0441203i	−0.790800	+	0.612075i	$0.790335\pi$
$798$	2.97067	−	3.03879i	0.105160	−	0.107572i
$799$	−19.0342	+	19.0342i	−0.673381	+	0.673381i
$800$	−0.787520	+	5.60177i	−0.0278431	+	0.198052i
$801$	−27.7725	−	27.7725i	−0.981291	−	0.981291i
$802$	1.82402	−	0.0206782i	0.0644085	−	0.000730174i
$803$	4.71894	−	3.87273i	0.166528	−	0.136666i
$804$	−32.1047	−	45.7669i	−1.13225	−	1.61407i
$805$	1.72766	−	5.69535i	0.0608922	−	0.200735i
$806$	−1.78769	−	2.12864i	−0.0629687	−	0.0749780i
$807$	24.9302	+	16.6578i	0.877586	+	0.586384i
$808$	−27.6319	−	21.1464i	−0.972088	−	0.743929i
$809$	−17.0935	−	25.5823i	−0.600976	−	0.899425i	0.398869	−	0.917008i	$-0.369403\pi$
$809$	−17.0935	−	25.5823i	−0.600976	−	0.899425i	−0.999845	+	0.0175831i	$0.994403\pi$
$810$	12.3504	−	6.78254i	0.433949	−	0.238314i
$811$	42.0090	−	4.13753i	1.47514	−	0.145288i	0.671764	−	0.740766i	$-0.265537\pi$
$811$	42.0090	−	4.13753i	1.47514	−	0.145288i	0.803372	+	0.595477i	$0.203037\pi$
$812$	4.61189	+	37.9771i	0.161846	+	1.33273i
$813$	−0.788817	−	2.60038i	−0.0276650	−	0.0911993i
$814$	−6.15172	−	4.01033i	−0.215618	−	0.140562i
$815$	−21.5357	−	8.92038i	−0.754363	−	0.312467i
$816$	43.3464	+	20.7002i	1.51743	+	0.724652i
$817$	−3.98138	+	1.64914i	−0.139291	+	0.0576961i
$818$	32.5056	+	6.08354i	1.13653	+	0.212706i
$819$	13.9844	−	26.1630i	0.488654	−	0.914208i
$820$	−0.754946	−	2.29970i	−0.0263639	−	0.0803089i
$821$	−15.1868	+	18.5052i	−0.530024	+	0.645836i	−0.967343	−	0.253470i	$-0.918428\pi$
$821$	−15.1868	+	18.5052i	−0.530024	+	0.645836i	0.437319	+	0.899306i	$0.355928\pi$
$822$	−2.77503	−	25.2388i	−0.0967902	−	0.880305i
$823$	−5.70887	+	28.7004i	−0.198999	+	1.00043i	0.744138	+	0.668026i	$0.232861\pi$
$823$	−5.70887	+	28.7004i	−0.198999	+	1.00043i	−0.943136	+	0.332407i	$0.892139\pi$
$824$	−34.2848	+	24.6348i	−1.19437	+	0.858193i
$825$	−2.49913	+	0.497108i	−0.0870086	+	0.0173071i
$826$	4.49416	−	8.64223i	0.156372	−	0.300702i
$827$	−36.1071	+	19.2997i	−1.25557	+	0.671115i	−0.958867	−	0.283855i	$-0.908387\pi$
$827$	−36.1071	+	19.2997i	−1.25557	+	0.671115i	−0.296701	+	0.954970i	$0.595887\pi$
$828$	−3.72822	+	9.61145i	−0.129565	+	0.334021i
$829$	−1.74759	+	17.7435i	−0.0606962	+	0.616259i	0.915934	+	0.401330i	$0.131452\pi$
$829$	−1.74759	+	17.7435i	−0.0606962	+	0.616259i	−0.976630	+	0.214929i	$0.931048\pi$
$830$	5.12309	+	2.05433i	0.177825	+	0.0713067i
$831$		−	48.0237i		−	1.66592i
$832$	10.5044	+	27.6937i	0.364174	+	0.960105i
$833$			11.3914i			0.394690i
$834$	28.9157	−	72.1101i	1.00127	−	2.49697i
$835$	−0.304793	+	3.09462i	−0.0105478	+	0.107094i
$836$	−0.817586	+	0.360582i	−0.0282768	+	0.0124710i
$837$	−0.406406	+	0.217228i	−0.0140474	+	0.00750851i
$838$	1.62111	+	0.843017i	0.0560004	+	0.0291215i
$839$	14.1076	−	2.80617i	0.487048	−	0.0968799i	0.0545431	−	0.998511i	$-0.482630\pi$
$839$	14.1076	−	2.80617i	0.487048	−	0.0968799i	0.432505	+	0.901632i	$0.357630\pi$
$840$	19.8815	−	4.66262i	0.685976	−	0.160876i
$841$	−2.05778	+	10.3451i	−0.0709578	+	0.356729i
$842$	42.1260	−	4.63179i	1.45176	−	0.159622i
$843$	5.23574	−	6.37977i	0.180328	−	0.219731i
$844$	−41.8565	−	21.1671i	−1.44076	−	0.728600i
$845$	−0.333519	+	0.623971i	−0.0114734	+	0.0214653i
$846$	3.64648	−	19.4839i	0.125369	−	0.669870i
$847$	−27.6730	+	11.4625i	−0.950856	+	0.393858i
$848$	−3.80507	−	2.84417i	−0.130667	−	0.0976691i
$849$	52.5452	+	21.7649i	1.80335	+	0.746970i
$850$	−3.90729	+	5.99367i	−0.134019	+	0.205581i
$851$	−2.74752	−	9.05737i	−0.0941839	−	0.310483i
$852$	8.91455	−	11.3790i	0.305408	−	0.389837i
$853$	42.9848	−	4.23364i	1.47177	−	0.144957i	0.669899	−	0.742452i	$-0.266337\pi$
$853$	42.9848	−	4.23364i	1.47177	−	0.144957i	0.801873	+	0.597495i	$0.203837\pi$
$854$	−13.6917	−	24.9314i	−0.468520	−	0.853133i
$855$	−0.609132	−	0.911630i	−0.0208319	−	0.0311771i
$856$	−1.90190	+	7.13461i	−0.0650057	+	0.243856i
$857$	3.84590	+	2.56975i	0.131374	+	0.0877810i	0.619521	−	0.784980i	$-0.287327\pi$
$857$	3.84590	+	2.56975i	0.131374	+	0.0877810i	−0.488147	+	0.872761i	$0.662327\pi$
$858$	−10.2166	+	8.58022i	−0.348790	+	0.292924i
$859$	9.36337	−	30.8669i	0.319474	−	1.05317i	−0.639291	−	0.768965i	$-0.720772\pi$
$859$	9.36337	−	30.8669i	0.319474	−	1.05317i	0.958765	−	0.284200i	$-0.0917280\pi$
$860$	−20.3968	−	3.57851i	−0.695524	−	0.122026i
$861$	−6.75430	+	5.54311i	−0.230186	+	0.188909i
$862$	0.278973	+	24.6081i	0.00950184	+	0.838155i
$863$	20.2836	+	20.2836i	0.690462	+	0.690462i	0.962334	−	0.271872i	$-0.0876426\pi$
$863$	20.2836	+	20.2836i	0.690462	+	0.690462i	−0.271872	+	0.962334i	$0.587643\pi$
$864$	4.85141	−	0.757330i	0.165048	−	0.0257649i
$865$	2.86280	−	2.86280i	0.0973380	−	0.0973380i
$866$	−20.6025	−	20.1407i	−0.700103	−	0.684407i
$867$	12.9434	+	15.7716i	0.439582	+	0.535633i
$868$	−3.15244	+	0.701710i	−0.107001	+	0.0238176i
$869$	2.68714	+	0.815134i	0.0911548	+	0.0276515i
$870$	21.0309	+	1.83090i	0.713014	+	0.0620732i
$871$	24.2223	−	36.2512i	0.820740	−	1.22832i
$872$	36.6854	+	2.35721i	1.24233	+	0.0798252i
$873$	36.8985	−	24.6548i	1.24883	−	0.834439i
$874$	−1.10584	−	0.321810i	−0.0374056	−	0.0108854i
$875$	0.298134	+	3.02700i	0.0100788	+	0.102331i
$876$	13.2628	+	23.5146i	0.448108	+	0.794484i
$877$	21.9856	−	6.66925i	0.742400	−	0.225204i	0.103644	−	0.994614i	$-0.466950\pi$
$877$	21.9856	−	6.66925i	0.742400	−	0.225204i	0.638755	+	0.769410i	$0.279450\pi$
$878$	9.71333	−	2.04683i	0.327809	−	0.0690773i
$879$	−10.3424	+	24.9688i	−0.348841	+	0.842176i
$880$	−4.24506	−	0.645943i	−0.143101	−	0.0217747i
$881$	4.00290	+	9.66385i	0.134861	+	0.325583i	0.976855	−	0.213904i	$-0.0686180\pi$
$881$	4.00290	+	9.66385i	0.134861	+	0.325583i	−0.841994	+	0.539488i	$0.818618\pi$
$882$	−4.73913	−	6.92145i	−0.159575	−	0.233057i
$883$	15.8896	+	8.49317i	0.534728	+	0.285818i	0.716576	−	0.697509i	$-0.245708\pi$
$883$	15.8896	+	8.49317i	0.534728	+	0.285818i	−0.181849	+	0.983327i	$0.558208\pi$
$884$	−2.82579	+	37.3553i	−0.0950416	+	1.25639i
$885$	−4.15511	−	3.41001i	−0.139672	−	0.114626i
$886$	−26.5208	−	21.2665i	−0.890983	−	0.714463i
$887$	−6.39157	−	1.27136i	−0.214608	−	0.0426882i	0.0866152	−	0.996242i	$-0.472395\pi$
$887$	−6.39157	−	1.27136i	−0.214608	−	0.0426882i	−0.301223	+	0.953554i	$0.597395\pi$
$888$	22.1696	−	23.7312i	0.743964	−	0.796368i
$889$	3.69012	+	18.5515i	0.123763	+	0.622196i
$890$	20.1065	−	6.34901i	0.673971	−	0.212819i
$891$	5.04179	+	9.43253i	0.168906	+	0.316002i
$892$	18.7596	−	0.425395i	0.628118	−	0.0142433i
$893$	2.20381	+	0.217057i	0.0737478	+	0.00726352i
$894$	64.0663	−	27.3920i	2.14270	−	0.916127i
$895$	−17.7339			−0.592779
$896$	34.1771	+	4.01695i	1.14178	+	0.134197i
$897$	−17.1960			−0.574156
$898$	−52.0643	+	22.2605i	−1.73741	+	0.742843i
$899$	−3.32257	−	0.327244i	−0.110814	−	0.0109142i
$900$	−0.119442	−	5.26729i	−0.00398139	−	0.175576i
$901$	−2.83239	−	5.29903i	−0.0943606	−	0.176536i
$902$	1.75201	−	0.553229i	0.0583354	−	0.0184205i
$903$	14.5841	+	73.3193i	0.485329	+	2.43992i
$904$	−0.169915	−	4.99434i	−0.00565129	−	0.166109i
$905$	17.2673	+	3.43468i	0.573984	+	0.114173i
$906$	−35.2479	−	28.2647i	−1.17103	−	0.939031i
$907$	26.8937	+	22.0711i	0.892991	+	0.732859i	0.964361	−	0.264591i	$-0.0852370\pi$
$907$	26.8937	+	22.0711i	0.892991	+	0.732859i	−0.0713695	+	0.997450i	$0.522737\pi$
$908$	−31.6705	−	2.39576i	−1.05102	−	0.0795060i
$909$	28.5806	+	15.2766i	0.947957	+	0.506694i
$910$	8.99749	+	13.1407i	0.298264	+	0.435611i
$911$	−17.9848	−	43.4191i	−0.595863	−	1.43854i	−0.877763	−	0.479096i	$-0.840965\pi$
$911$	−17.9848	−	43.4191i	−0.595863	−	1.43854i	0.281900	−	0.959444i	$-0.409035\pi$
$912$	−0.945831	−	3.83684i	−0.0313196	−	0.127051i
$913$	−1.60335	+	3.87084i	−0.0530632	+	0.128106i
$914$	20.2840	−	4.27433i	0.670936	−	0.141382i
$915$	−15.0198	+	4.55622i	−0.496540	+	0.150624i
$916$	−33.8728	+	19.1051i	−1.11919	+	0.631249i
$917$	6.04648	+	61.3910i	0.199672	+	2.02731i
$918$	5.96301	+	1.73529i	0.196809	+	0.0572732i
$919$	1.02067	−	0.681987i	0.0336686	−	0.0224967i	−0.538622	−	0.842548i	$-0.681055\pi$
$919$	1.02067	−	0.681987i	0.0336686	−	0.0224967i	0.572291	+	0.820051i	$0.306055\pi$
$920$	−3.65443	−	4.15630i	−0.120483	−	0.137029i
$921$	22.7275	−	34.0141i	0.748896	−	1.12080i
$922$	−6.58546	−	0.573315i	−0.216881	−	0.0188811i
$923$	10.7879	+	3.27246i	0.355086	+	0.107714i
$924$	3.36794	+	15.1305i	0.110797	+	0.497757i
$925$	3.06867	+	3.73918i	0.100897	+	0.122944i
$926$	−19.1225	−	18.6938i	−0.628403	−	0.614315i
$927$	27.8036	−	27.8036i	0.913191	−	0.913191i
$928$	32.2733	+	14.9653i	1.05942	+	0.491261i
$929$	6.76980	+	6.76980i	0.222110	+	0.222110i	0.809386	−	0.587277i	$-0.199800\pi$
$929$	6.76980	+	6.76980i	0.222110	+	0.222110i	−0.587277	+	0.809386i	$0.699800\pi$
$930$	0.0202023	+	1.78204i	0.000662459	+	0.0584353i
$931$	0.724413	−	0.594510i	0.0237417	−	0.0194843i
$932$	8.49529	−	48.4214i	0.278272	−	1.58610i
$933$	14.7263	−	48.5461i	0.482117	−	1.58933i
$934$	2.54813	−	2.13999i	0.0833773	−	0.0700227i
$935$	−4.51568	−	3.01728i	−0.147678	−	0.0986755i
$936$	−13.8238	−	23.8727i	−0.451845	−	0.780303i
$937$	−0.828199	−	1.23949i	−0.0270561	−	0.0404923i	0.817695	−	0.575652i	$-0.195252\pi$
$937$	−0.828199	−	1.23949i	−0.0270561	−	0.0404923i	−0.844751	+	0.535159i	$0.820252\pi$
$938$	−24.3834	−	44.4000i	−0.796145	−	1.44971i
$939$	−16.3241	+	1.60778i	−0.532717	+	0.0524680i
$940$	8.37682	+	6.56260i	0.273222	+	0.214048i
$941$	0.790751	+	2.60676i	0.0257778	+	0.0849779i	0.968885	−	0.247509i	$-0.0796121\pi$
$941$	0.790751	+	2.60676i	0.0257778	+	0.0849779i	−0.943108	+	0.332487i	$0.892112\pi$
$942$	−34.0531	+	52.2364i	−1.10951	+	1.70195i
$943$	2.18779	+	0.906214i	0.0712444	+	0.0295104i
$944$	−4.62767	−	7.78675i	−0.150618	−	0.253437i
$945$	2.43919	−	1.01035i	0.0793469	−	0.0328665i
$946$	2.89166	−	15.4507i	0.0940159	−	0.502346i
$947$	20.9374	−	39.1712i	0.680375	−	1.27289i	−0.270322	−	0.962770i	$-0.587130\pi$
$947$	20.9374	−	39.1712i	0.680375	−	1.27289i	0.950697	−	0.310122i	$-0.100370\pi$
$948$	−5.60414	+	11.0818i	−0.182014	+	0.359921i
$949$	−13.3568	+	16.2753i	−0.433580	+	0.528319i
$950$	0.585072	−	0.0643291i	0.0189822	−	0.00208711i
$951$	3.38985	−	17.0419i	0.109923	−	0.552622i
$952$	36.9907	+	22.9365i	1.19888	+	0.743378i
$953$	53.3845	−	10.6188i	1.72929	−	0.343978i	0.772559	−	0.634943i	$-0.218976\pi$
$953$	53.3845	−	10.6188i	1.72929	−	0.343978i	0.956734	+	0.290965i	$0.0939764\pi$
$954$	3.92549	+	2.04135i	0.127093	+	0.0660911i
$955$	−3.54269	+	1.89361i	−0.114639	+	0.0612756i
$956$	13.5163	+	30.6469i	0.437148	+	0.991193i
$957$	−1.57065	+	15.9471i	−0.0507718	+	0.515495i
$958$	4.95560	−	12.3583i	0.160108	−	0.399278i
$959$		−	23.0066i		−	0.742921i
$960$	6.05776	−	17.9972i	0.195513	−	0.580858i
$961$			30.7182i			0.990908i
$962$	23.5076	+	9.42639i	0.757914	+	0.303919i
$963$	0.674068	−	6.84392i	0.0217215	−	0.220542i
$964$	14.0006	+	5.43074i	0.450928	+	0.174912i
$965$	−2.18447	+	1.16762i	−0.0703206	+	0.0375872i
$966$	−9.21764	+	17.7254i	−0.296573	+	0.570306i
$967$	−21.0531	+	4.18772i	−0.677022	+	0.134668i	−0.521613	−	0.853182i	$-0.674670\pi$
$967$	−21.0531	+	4.18772i	−0.677022	+	0.134668i	−0.155409	+	0.987850i	$0.549670\pi$
$968$	−4.50191	+	27.4871i	−0.144697	+	0.883469i
$969$	0.975083	−	4.90207i	0.0313242	−	0.157477i
$970$	2.60374	+	23.6810i	0.0836011	+	0.760351i
$971$	−21.1610	+	25.7848i	−0.679089	+	0.827472i	−0.992513	−	0.122141i	$-0.961024\pi$
$971$	−21.1610	+	25.7848i	−0.679089	+	0.827472i	0.313424	+	0.949613i	$0.398524\pi$
$972$	−39.9915	+	13.1284i	−1.28273	+	0.421095i
$973$	33.1844	−	62.0837i	1.06384	−	1.99031i
$974$	32.2222	+	6.03050i	1.03246	+	0.193230i
$975$	8.11924	−	3.36310i	0.260024	−	0.107705i
$976$	−26.4127	−	1.39669i	−0.845450	−	0.0447070i
$977$	15.2714	+	6.32560i	0.488574	+	0.202374i	0.613350	−	0.789811i	$-0.289821\pi$
$977$	15.2714	+	6.32560i	0.488574	+	0.202374i	−0.124776	+	0.992185i	$0.539821\pi$
$978$	65.5504	+	42.7326i	2.09607	+	1.36644i
$979$	4.64600	+	15.3158i	0.148487	+	0.489496i
$980$	4.47042	−	0.542882i	0.142802	−	0.0173417i
$981$	−34.0734	+	3.35594i	−1.08788	+	0.107147i
$982$	50.9053	−	27.9559i	1.62445	−	0.892109i
$983$	−25.6622	−	38.4062i	−0.818498	−	1.22497i	−0.971570	−	0.236753i	$-0.923917\pi$
$983$	−25.6622	−	38.4062i	−0.818498	−	1.22497i	0.153072	−	0.988215i	$-0.451083\pi$
$984$	1.07088	+	8.05426i	0.0341384	+	0.256760i
$985$	13.2283	+	8.83888i	0.421489	+	0.281630i
$986$	28.9366	+	34.4553i	0.921528	+	1.09728i
$987$	11.1512	−	36.7606i	0.354947	−	1.17010i
$988$	2.52300	−	1.76984i	0.0802673	−	0.0563062i
$989$	15.6612	−	12.8529i	0.497999	−	0.408697i
$990$	3.99899	−	0.0453350i	0.127096	−	0.00144084i
$991$	28.7969	+	28.7969i	0.914765	+	0.914765i	0.996642	−	0.0818772i	$-0.0260915\pi$
$991$	28.7969	+	28.7969i	0.914765	+	0.914765i	−0.0818772	+	0.996642i	$0.526092\pi$
$992$	−0.990247	+	2.83524i	−0.0314404	+	0.0900191i
$993$	13.5946	−	13.5946i	0.431411	−	0.431411i
$994$	9.15589	−	9.36586i	0.290407	−	0.297067i
$995$	2.23088	+	2.71833i	0.0707236	+	0.0861769i
$996$	−15.6355	−	9.94210i	−0.495429	−	0.315028i
$997$	3.64010	+	1.10421i	0.115283	+	0.0349707i	0.347399	−	0.937717i	$-0.387065\pi$
$997$	3.64010	+	1.10421i	0.115283	+	0.0349707i	−0.232116	+	0.972688i	$0.574565\pi$
$998$	−0.780971	+	8.97074i	−0.0247212	+	0.283964i
$999$	2.33266	−	3.49107i	0.0738021	−	0.110453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.41	✓	1024
128.117	even	32	inner	640.2.bm.a.501.41	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.41	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.41	yes	1024	128.117	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)

\(f(q)\)	\(=\)	\(q+(0.555972 + 1.30034i) q^{2} +(-2.36224 - 0.232661i) q^{3} +(-1.38179 + 1.44591i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01080 - 3.20108i) q^{6} +(-0.593396 - 2.98320i) q^{7} +(-2.64842 - 0.992915i) q^{8} +(2.58370 + 0.513930i) q^{9} +O(q^{10})\)	\(q+(0.555972 + 1.30034i) q^{2} +(-2.36224 - 0.232661i) q^{3} +(-1.38179 + 1.44591i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.01080 - 3.20108i) q^{6} +(-0.593396 - 2.98320i) q^{7} +(-2.64842 - 0.992915i) q^{8} +(2.58370 + 0.513930i) q^{9} +(-0.884718 + 1.10330i) q^{10} +(-0.829813 - 0.681010i) q^{11} +(3.60053 - 3.09410i) q^{12} +(3.26520 + 1.74528i) q^{13} +(3.54928 - 2.43020i) q^{14} +(-0.908365 - 2.19299i) q^{15} +(-0.181316 - 3.99589i) q^{16} +(1.93607 - 4.67409i) q^{17} +(0.768181 + 3.64543i) q^{18} +(-0.398280 + 0.120817i) q^{19} +(-1.92655 - 0.537032i) q^{20} +(0.707672 + 7.18511i) q^{21} +(0.424194 - 1.45766i) q^{22} +(1.62694 - 1.08709i) q^{23} +(6.02519 + 2.96169i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-0.454110 + 5.21621i) q^{26} +(0.830627 + 0.251968i) q^{27} +(5.13340 + 3.26416i) q^{28} +(3.98951 + 4.86124i) q^{29} +(2.34661 - 2.40043i) q^{30} +(-0.375400 + 0.375400i) q^{31} +(5.09522 - 2.45738i) q^{32} +(1.80177 + 1.80177i) q^{33} +(7.15433 - 0.0811058i) q^{34} +(2.35123 - 1.92960i) q^{35} +(-4.31323 + 3.02566i) q^{36} +(1.40416 - 4.62888i) q^{37} +(-0.378536 - 0.450730i) q^{38} +(-7.30712 - 4.88246i) q^{39} +(-0.372783 - 2.80375i) q^{40} +(0.672363 + 1.00626i) q^{41} +(-8.94967 + 4.91494i) q^{42} +(10.3043 - 1.01488i) q^{43} +(2.13131 - 0.258823i) q^{44} +(0.764703 + 2.52089i) q^{45} +(2.31813 + 1.51120i) q^{46} +(-4.91567 - 2.03614i) q^{47} +(-0.501374 + 9.48144i) q^{48} +(-2.08024 + 0.861662i) q^{49} +(-1.39008 - 0.260158i) q^{50} +(-5.66095 + 10.5909i) q^{51} +(-7.03534 + 2.30957i) q^{52} +(0.753431 - 0.918059i) q^{53} +(0.134161 + 1.22019i) q^{54} +(0.209426 - 1.05286i) q^{55} +(-1.39051 + 8.48997i) q^{56} +(0.968943 - 0.192735i) q^{57} +(-4.10322 + 7.89045i) q^{58} +(1.99713 - 1.06749i) q^{59} +(4.42603 + 1.71683i) q^{60} +(0.648129 - 6.58056i) q^{61} +(-0.696861 - 0.279437i) q^{62} -8.01268i q^{63} +(6.02824 + 5.25931i) q^{64} +3.70237i q^{65} +(-1.34119 + 3.34466i) q^{66} +(1.15425 - 11.7193i) q^{67} +(4.08307 + 9.25799i) q^{68} +(-4.09616 + 2.18944i) q^{69} +(3.81636 + 1.98460i) q^{70} +(2.98638 - 0.594027i) q^{71} +(-6.33244 - 3.92650i) q^{72} +(-1.10943 + 5.57749i) q^{73} +(6.79981 - 0.747645i) q^{74} +(1.50584 - 1.83487i) q^{75} +(0.375648 - 0.742821i) q^{76} +(-1.53918 + 2.87961i) q^{77} +(2.28632 - 12.2163i) q^{78} +(-2.41671 + 1.00104i) q^{79} +(3.43859 - 2.04356i) q^{80} +(-9.20490 - 3.81280i) q^{81} +(-0.934672 + 1.43376i) q^{82} +(-1.13297 - 3.73491i) q^{83} +(-11.3669 - 8.90508i) q^{84} +(5.03484 - 0.495888i) q^{85} +(7.04860 + 12.8349i) q^{86} +(-8.29318 - 12.4116i) q^{87} +(1.52151 + 2.62753i) q^{88} +(-12.3967 - 8.28323i) q^{89} +(-2.85287 + 2.39592i) q^{90} +(3.26898 - 10.7764i) q^{91} +(-0.676260 + 3.85454i) q^{92} +(0.974126 - 0.799445i) q^{93} +(-0.0852978 - 7.52410i) q^{94} +(-0.294299 - 0.294299i) q^{95} +(-12.6079 + 4.61946i) q^{96} +(11.9118 - 11.9118i) q^{97} +(-2.27701 - 2.22596i) q^{98} +(-1.79400 - 2.18599i) 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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