LMFDB - Embedded newform 384.2.v.a.37.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			37.28
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25252 + 0.656645i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(1.13764 + 1.64493i) q^{4} +(2.18182 - 1.79058i) q^{5} +(-0.0113273 - 1.41417i) q^{6} +(-0.557832 + 0.372732i) q^{7} +(0.344785 + 2.80733i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(1.25252 + 0.656645i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(1.13764 + 1.64493i) q^{4} +(2.18182 - 1.79058i) q^{5} +(-0.0113273 - 1.41417i) q^{6} +(-0.557832 + 0.372732i) q^{7} +(0.344785 + 2.80733i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(3.90856 - 0.810059i) q^{10} +(0.180988 + 0.596639i) q^{11} +(0.914418 - 1.77872i) q^{12} +(2.83020 - 3.44861i) q^{13} +(-0.943451 + 0.100558i) q^{14} +(-2.60765 - 1.08013i) q^{15} +(-1.41157 + 3.74266i) q^{16} +(0.583182 - 0.241562i) q^{17} +(-1.24185 + 0.676624i) q^{18} +(2.17473 - 0.214192i) q^{19} +(5.42749 + 1.55192i) q^{20} +(0.591680 + 0.316260i) q^{21} +(-0.165087 + 0.866150i) q^{22} +(-4.71146 + 0.937168i) q^{23} +(2.31332 - 1.62744i) q^{24} +(0.578741 - 2.90953i) q^{25} +(5.80941 - 2.46103i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-1.24773 - 0.493561i) q^{28} +(-2.59588 - 0.787452i) q^{29} +(-2.55689 - 3.06519i) q^{30} +(-0.199841 - 0.199841i) q^{31} +(-4.22562 + 3.76087i) q^{32} +(0.440871 - 0.440871i) q^{33} +(0.889071 + 0.0803811i) q^{34} +(-0.549688 + 1.81208i) q^{35} +(-1.99974 + 0.0320373i) q^{36} +(-0.317241 + 3.22100i) q^{37} +(2.86455 + 1.15974i) q^{38} +(-4.37555 - 0.870351i) q^{39} +(5.77901 + 5.50775i) q^{40} +(-1.48329 - 7.45701i) q^{41} +(0.533424 + 0.784647i) q^{42} +(-5.98534 + 11.1978i) q^{43} +(-0.775528 + 0.976470i) q^{44} +(0.276654 + 2.80891i) q^{45} +(-6.51661 - 1.91993i) q^{46} +(1.14068 + 2.75384i) q^{47} +(3.96614 - 0.519383i) q^{48} +(-2.50654 + 6.05131i) q^{49} +(2.63541 - 3.26423i) q^{50} +(-0.487949 - 0.400449i) q^{51} +(8.89245 + 0.732211i) q^{52} +(7.31262 - 2.21826i) q^{53} +(1.18213 + 0.776251i) q^{54} +(1.46321 + 0.977688i) q^{55} +(-1.23871 - 1.43751i) q^{56} +(-1.21406 - 1.81697i) q^{57} +(-2.73433 - 2.69088i) q^{58} +(-8.19591 - 9.98675i) q^{59} +(-1.18983 - 5.51819i) q^{60} +(-6.84776 + 3.66020i) q^{61} +(-0.119081 - 0.381529i) q^{62} -0.670899i q^{63} +(-7.76225 + 1.93585i) q^{64} -12.5920i q^{65} +(0.841697 - 0.262706i) q^{66} +(-3.47804 + 1.85905i) q^{67} +(1.06080 + 0.684483i) q^{68} +(3.04748 + 3.71336i) q^{69} +(-1.87839 + 1.90872i) q^{70} +(-3.19190 - 4.77701i) q^{71} +(-2.52577 - 1.27299i) q^{72} +(-12.0764 - 8.06917i) q^{73} +(-2.51240 + 3.82607i) q^{74} +(-2.83879 + 0.861138i) q^{75} +(2.82638 + 3.33359i) q^{76} +(-0.323347 - 0.265364i) q^{77} +(-4.90897 - 3.96332i) q^{78} +(0.835822 - 2.01785i) q^{79} +(3.62172 + 10.6933i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(3.03875 - 10.3141i) q^{82} +(-0.0389887 - 0.395859i) q^{83} +(0.152893 + 1.33306i) q^{84} +(0.839866 - 1.57128i) q^{85} +(-14.8497 + 10.0953i) q^{86} +(0.529220 + 2.66057i) q^{87} +(-1.61256 + 0.713807i) q^{88} +(-7.46918 - 1.48571i) q^{89} +(-1.49794 + 3.69990i) q^{90} +(-0.293372 + 2.97865i) q^{91} +(-6.90150 - 6.68385i) q^{92} +(-0.0820394 + 0.270448i) q^{93} +(-0.379567 + 4.19828i) q^{94} +(4.36134 - 4.36134i) q^{95} +(5.30873 + 1.95380i) q^{96} +(12.9669 + 12.9669i) q^{97} +(-7.11306 + 5.93352i) q^{98} +(-0.596639 - 0.180988i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

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 $

$2$	1.25252	+	0.656645i	0.885669	+	0.464318i
$2$	1.25252	+	0.656645i	0.885669	+	0.464318i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$4$	1.13764	+	1.64493i	0.568818	+	0.822463i
$5$	2.18182	−	1.79058i	0.975742	−	0.800771i	−0.00421290	−	0.999991i	$-0.501341\pi$
$5$	2.18182	−	1.79058i	0.975742	−	0.800771i	0.979955	+	0.199221i	$0.0638410\pi$
$6$	−0.0113273	−	1.41417i	−0.00462434	−	0.577332i
$7$	−0.557832	+	0.372732i	−0.210841	+	0.140879i	−0.656507	−	0.754320i	$-0.727967\pi$
$7$	−0.557832	+	0.372732i	−0.210841	+	0.140879i	0.445666	+	0.895199i	$0.352967\pi$
$8$	0.344785	+	2.80733i	0.121900	+	0.992542i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	3.90856	−	0.810059i	1.23600	−	0.256163i
$11$	0.180988	+	0.596639i	0.0545701	+	0.179893i	0.979989	−	0.199053i	$-0.0637865\pi$
$11$	0.180988	+	0.596639i	0.0545701	+	0.179893i	−0.925419	+	0.378946i	$0.876287\pi$
$12$	0.914418	−	1.77872i	0.263970	−	0.513472i
$13$	2.83020	−	3.44861i	0.784957	−	0.956472i	−0.214840	−	0.976649i	$-0.568923\pi$
$13$	2.83020	−	3.44861i	0.784957	−	0.956472i	0.999796	+	0.0201769i	$0.00642296\pi$
$14$	−0.943451	+	0.100558i	−0.252148	+	0.0268753i
$15$	−2.60765	−	1.08013i	−0.673293	−	0.278887i
$16$	−1.41157	+	3.74266i	−0.352892	+	0.935664i
$17$	0.583182	−	0.241562i	0.141442	−	0.0585874i	−0.310839	−	0.950462i	$-0.600610\pi$
$17$	0.583182	−	0.241562i	0.141442	−	0.0585874i	0.452282	+	0.891875i	$0.350610\pi$
$18$	−1.24185	+	0.676624i	−0.292706	+	0.159482i
$19$	2.17473	−	0.214192i	0.498916	−	0.0491390i	0.154570	−	0.987982i	$-0.450601\pi$
$19$	2.17473	−	0.214192i	0.498916	−	0.0491390i	0.344346	+	0.938843i	$0.388101\pi$
$20$	5.42749	+	1.55192i	1.21362	+	0.347019i
$21$	0.591680	+	0.316260i	0.129115	+	0.0690135i
$22$	−0.165087	+	0.866150i	−0.0351967	+	0.184664i
$23$	−4.71146	+	0.937168i	−0.982408	+	0.195413i	−0.660064	−	0.751210i	$-0.729471\pi$
$23$	−4.71146	+	0.937168i	−0.982408	+	0.195413i	−0.322344	+	0.946623i	$0.604471\pi$
$24$	2.31332	−	1.62744i	0.472204	−	0.332200i
$25$	0.578741	−	2.90953i	0.115748	−	0.581905i
$26$	5.80941	−	2.46103i	1.13932	−	0.482648i
$27$	0.995185	+	0.0980171i	0.191523	+	0.0188634i
$28$	−1.24773	−	0.493561i	−0.235798	−	0.0932742i
$29$	−2.59588	−	0.787452i	−0.482043	−	0.146226i	0.0399048	−	0.999203i	$-0.487295\pi$
$29$	−2.59588	−	0.787452i	−0.482043	−	0.146226i	−0.521948	+	0.852977i	$0.674795\pi$
$30$	−2.55689	−	3.06519i	−0.466822	−	0.559624i
$31$	−0.199841	−	0.199841i	−0.0358924	−	0.0358924i	0.688933	−	0.724825i	$-0.258080\pi$
$31$	−0.199841	−	0.199841i	−0.0358924	−	0.0358924i	−0.724825	+	0.688933i	$0.758080\pi$
$32$	−4.22562	+	3.76087i	−0.746991	+	0.664834i
$33$	0.440871	−	0.440871i	0.0767458	−	0.0767458i
$34$	0.889071	+	0.0803811i	0.152474	+	0.0137852i
$35$	−0.549688	+	1.81208i	−0.0929142	+	0.306297i
$36$	−1.99974	+	0.0320373i	−0.333291	+	0.00533956i
$37$	−0.317241	+	3.22100i	−0.0521540	+	0.529529i	0.933242	+	0.359249i	$0.116967\pi$
$37$	−0.317241	+	3.22100i	−0.0521540	+	0.529529i	−0.985396	+	0.170280i	$0.945533\pi$
$38$	2.86455	+	1.15974i	0.464691	+	0.188135i
$39$	−4.37555	−	0.870351i	−0.700649	−	0.139368i
$40$	5.77901	+	5.50775i	0.913742	+	0.870851i
$41$	−1.48329	−	7.45701i	−0.231651	−	1.16459i	−0.905048	−	0.425308i	$-0.860166\pi$
$41$	−1.48329	−	7.45701i	−0.231651	−	1.16459i	0.673397	−	0.739281i	$-0.264834\pi$
$42$	0.533424	+	0.784647i	0.0823091	+	0.121074i
$43$	−5.98534	+	11.1978i	−0.912755	+	1.70765i	−0.235534	+	0.971866i	$0.575684\pi$
$43$	−5.98534	+	11.1978i	−0.912755	+	1.70765i	−0.677221	+	0.735779i	$0.736816\pi$
$44$	−0.775528	+	0.976470i	−0.116915	+	0.147208i
$45$	0.276654	+	2.80891i	0.0412411	+	0.418728i
$46$	−6.51661	−	1.91993i	−0.960822	−	0.283078i
$47$	1.14068	+	2.75384i	0.166385	+	0.401689i	0.984977	−	0.172687i	$-0.0552448\pi$
$47$	1.14068	+	2.75384i	0.166385	+	0.401689i	−0.818592	+	0.574376i	$0.805245\pi$
$48$	3.96614	−	0.519383i	0.572463	−	0.0749665i
$49$	−2.50654	+	6.05131i	−0.358077	+	0.864473i
$50$	2.63541	−	3.26423i	0.372704	−	0.461631i
$51$	−0.487949	−	0.400449i	−0.0683265	−	0.0560741i
$52$	8.89245	+	0.732211i	1.23316	+	0.101539i
$53$	7.31262	−	2.21826i	1.00447	−	0.304701i	0.255141	−	0.966904i	$-0.417878\pi$
$53$	7.31262	−	2.21826i	1.00447	−	0.304701i	0.749325	+	0.662203i	$0.230378\pi$
$54$	1.18213	+	0.776251i	0.160868	+	0.105634i
$55$	1.46321	+	0.977688i	0.197300	+	0.131831i
$56$	−1.23871	−	1.43751i	−0.165530	−	0.192095i
$57$	−1.21406	−	1.81697i	−0.160806	−	0.240663i
$58$	−2.73433	−	2.69088i	−0.359035	−	0.353329i
$59$	−8.19591	−	9.98675i	−1.06702	−	1.30016i	−0.951765	−	0.306827i	$-0.900733\pi$
$59$	−8.19591	−	9.98675i	−1.06702	−	1.30016i	−0.115251	−	0.993336i	$-0.536767\pi$
$60$	−1.18983	−	5.51819i	−0.153607	−	0.712395i
$61$	−6.84776	+	3.66020i	−0.876765	+	0.468641i	−0.847417	−	0.530928i	$-0.821843\pi$
$61$	−6.84776	+	3.66020i	−0.876765	+	0.468641i	−0.0293487	+	0.999569i	$0.509343\pi$
$62$	−0.119081	−	0.381529i	−0.0151233	−	0.0484543i
$63$		−	0.670899i		−	0.0845254i
$64$	−7.76225	+	1.93585i	−0.970281	+	0.241982i
$65$		−	12.5920i		−	1.56184i
$66$	0.841697	−	0.262706i	0.103606	−	0.0323369i
$67$	−3.47804	+	1.85905i	−0.424910	+	0.227119i	−0.669969	−	0.742389i	$-0.733693\pi$
$67$	−3.47804	+	1.85905i	−0.424910	+	0.227119i	0.245059	+	0.969508i	$0.421193\pi$
$68$	1.06080	+	0.684483i	0.128641	+	0.0830057i
$69$	3.04748	+	3.71336i	0.366873	+	0.447036i
$70$	−1.87839	+	1.90872i	−0.224510	+	0.228136i
$71$	−3.19190	−	4.77701i	−0.378809	−	0.566927i	0.592254	−	0.805751i	$-0.298238\pi$
$71$	−3.19190	−	4.77701i	−0.378809	−	0.566927i	−0.971063	+	0.238824i	$0.923238\pi$
$72$	−2.52577	−	1.27299i	−0.297664	−	0.150024i
$73$	−12.0764	−	8.06917i	−1.41343	−	0.944425i	−0.999417	−	0.0341554i	$-0.989126\pi$
$73$	−12.0764	−	8.06917i	−1.41343	−	0.944425i	−0.414016	−	0.910270i	$-0.635874\pi$
$74$	−2.51240	+	3.82607i	−0.292061	+	0.444771i
$75$	−2.83879	+	0.861138i	−0.327795	+	0.0994356i
$76$	2.82638	+	3.33359i	0.324208	+	0.382389i
$77$	−0.323347	−	0.265364i	−0.0368489	−	0.0302411i
$78$	−4.90897	−	3.96332i	−0.555832	−	0.448757i
$79$	0.835822	−	2.01785i	0.0940373	−	0.227026i	−0.869861	−	0.493297i	$-0.835792\pi$
$79$	0.835822	−	2.01785i	0.0940373	−	0.227026i	0.963898	+	0.266271i	$0.0857916\pi$
$80$	3.62172	+	10.6933i	0.404921	+	1.19555i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	3.03875	−	10.3141i	0.335573	−	1.13900i
$83$	−0.0389887	−	0.395859i	−0.00427957	−	0.0434512i	0.992808	−	0.119719i	$-0.0381995\pi$
$83$	−0.0389887	−	0.395859i	−0.00427957	−	0.0434512i	−0.997087	+	0.0762682i	$0.975699\pi$
$84$	0.152893	+	1.33306i	0.0166820	+	0.145449i
$85$	0.839866	−	1.57128i	0.0910963	−	0.170429i
$86$	−14.8497	+	10.0953i	−1.60129	+	1.08860i
$87$	0.529220	+	2.66057i	0.0567383	+	0.285243i
$88$	−1.61256	+	0.713807i	−0.171900	+	0.0760921i
$89$	−7.46918	−	1.48571i	−0.791732	−	0.157485i	−0.217373	−	0.976089i	$-0.569749\pi$
$89$	−7.46918	−	1.48571i	−0.791732	−	0.157485i	−0.574359	+	0.818604i	$0.694749\pi$
$90$	−1.49794	+	3.69990i	−0.157897	+	0.390003i
$91$	−0.293372	+	2.97865i	−0.0307537	+	0.312248i
$92$	−6.90150	−	6.68385i	−0.719531	−	0.696840i
$93$	−0.0820394	+	0.270448i	−0.00850709	+	0.0280441i
$94$	−0.379567	+	4.19828i	−0.0391494	+	0.433019i
$95$	4.36134	−	4.36134i	0.447464	−	0.447464i
$96$	5.30873	+	1.95380i	0.541820	+	0.199409i
$97$	12.9669	+	12.9669i	1.31658	+	1.31658i	0.916462	+	0.400123i	$0.131033\pi$
$97$	12.9669	+	12.9669i	1.31658	+	1.31658i	0.400123	+	0.916462i	$0.368967\pi$
$98$	−7.11306	+	5.93352i	−0.718528	+	0.599376i
$99$	−0.596639	−	0.180988i	−0.0599645	−	0.0181900i
$100$	5.44436	−	2.35800i	0.544436	−	0.235800i
$101$	13.7543	+	1.35468i	1.36861	+	0.134796i	0.755472	−	0.655181i	$-0.227408\pi$
$101$	13.7543	+	1.35468i	1.36861	+	0.134796i	0.613136	+	0.789977i	$0.289908\pi$
$102$	−0.348215	−	0.821982i	−0.0344784	−	0.0813883i
$103$	0.932479	−	4.68789i	0.0918799	−	0.461911i	−0.907265	−	0.420560i	$-0.861834\pi$
$103$	0.932479	−	4.68789i	0.0918799	−	0.461911i	0.999145	−	0.0413515i	$-0.0131663\pi$
$104$	10.6572	+	6.75629i	1.04503	+	0.662509i
$105$	1.85723	−	0.369426i	0.181247	−	0.0360523i
$106$	10.6158	+	2.02337i	1.03110	+	0.196527i
$107$	3.40664	+	1.82089i	0.329333	+	0.176032i	0.627773	−	0.778396i	$-0.283967\pi$
$107$	3.40664	+	1.82089i	0.329333	+	0.176032i	−0.298441	+	0.954428i	$0.596467\pi$
$108$	0.970927	+	1.74851i	0.0934275	+	0.168251i
$109$	−3.61225	+	0.355776i	−0.345991	+	0.0340771i	−0.269520	−	0.962995i	$-0.586865\pi$
$109$	−3.61225	+	0.355776i	−0.345991	+	0.0340771i	−0.0764706	+	0.997072i	$0.524365\pi$
$110$	1.19072	+	2.18539i	0.113530	+	0.208369i
$111$	2.99021	−	1.23859i	0.283818	−	0.117561i
$112$	−0.607588	−	2.61391i	−0.0574116	−	0.246991i
$113$	−7.83864	−	3.24687i	−0.737397	−	0.305440i	−0.0178095	−	0.999841i	$-0.505669\pi$
$113$	−7.83864	−	3.24687i	−0.737397	−	0.305440i	−0.719588	+	0.694401i	$0.755669\pi$
$114$	−0.327537	−	3.07300i	−0.0306766	−	0.287813i
$115$	−8.60151	+	10.4810i	−0.802095	+	0.977356i
$116$	−1.65787	−	5.16587i	−0.153929	−	0.479639i
$117$	1.29504	+	4.26917i	0.119726	+	0.394685i
$118$	−3.70784	−	17.8904i	−0.341334	−	1.64695i
$119$	−0.235280	+	0.352122i	−0.0215681	+	0.0322789i
$120$	2.13319	−	7.69296i	0.194733	−	0.702268i
$121$	8.82294	−	5.89530i	0.802086	−	0.535937i
$122$	−10.9804	+	0.0879516i	−0.994122	+	0.00796276i
$123$	−5.87728	+	4.82336i	−0.529936	+	0.434907i
$124$	0.101377	−	0.556069i	0.00910395	−	0.0499365i
$125$	2.70557	+	5.06177i	0.241994	+	0.452739i
$126$	0.440542	−	0.840318i	0.0392466	−	0.0748615i
$127$	16.1528			1.43333			0.716666	−	0.697416i	$-0.245667\pi$
$127$	16.1528			1.43333			0.716666	+	0.697416i	$0.245667\pi$
$128$	−10.9936	−	2.67233i	−0.971704	−	0.236203i
$129$	12.6970			1.11791
$130$	8.26844	−	15.7717i	0.725190	−	1.38327i
$131$	−4.85634	−	9.08557i	−0.424300	−	0.793810i	0.575410	−	0.817865i	$-0.304842\pi$
$131$	−4.85634	−	9.08557i	−0.424300	−	0.793810i	−0.999711	+	0.0240549i	$0.992342\pi$
$132$	1.22675	+	0.223650i	0.106775	+	0.0194662i
$133$	−1.13330	+	0.930072i	−0.0982693	+	0.0806475i
$134$	−5.57706	+	0.0446714i	−0.481785	+	0.00385902i
$135$	2.34683	−	1.56810i	0.201983	−	0.134960i
$136$	0.879218	+	1.55390i	0.0753923	+	0.133246i
$137$	2.77164	−	4.14805i	0.236797	−	0.354392i	−0.693970	−	0.720004i	$-0.744140\pi$
$137$	2.77164	−	4.14805i	0.236797	−	0.354392i	0.930768	+	0.365612i	$0.119140\pi$
$138$	1.37868	+	6.65218i	0.117361	+	0.566272i
$139$	3.50085	+	11.5408i	0.296939	+	0.978876i	0.970774	+	0.239994i	$0.0771456\pi$
$139$	3.50085	+	11.5408i	0.296939	+	0.978876i	−0.673836	+	0.738881i	$0.735354\pi$
$140$	−3.60608	+	1.15729i	−0.304769	+	0.0978087i
$141$	1.89096	−	2.30414i	0.159248	−	0.194044i
$142$	−0.861132	−	8.07927i	−0.0722646	−	0.677997i
$143$	2.56981	+	1.06445i	0.214898	+	0.0890137i
$144$	−2.32768	−	3.25298i	−0.193973	−	0.271082i
$145$	−7.07376	+	2.93005i	−0.587443	+	0.243327i
$146$	−9.82737	−	18.0367i	−0.813319	−	1.49273i
$147$	6.51835	−	0.642002i	0.537625	−	0.0529514i
$148$	−5.65921	+	3.14249i	−0.465184	+	0.258311i
$149$	16.2895	+	8.70694i	1.33449	+	0.713300i	0.975491	−	0.220038i	$-0.0706180\pi$
$149$	16.2895	+	8.70694i	1.33449	+	0.713300i	0.358999	+	0.933338i	$0.383118\pi$
$150$	−4.12112	−	0.785480i	−0.336488	−	0.0641342i
$151$	12.7026	−	2.52671i	1.03373	−	0.205621i	0.351061	−	0.936352i	$-0.385821\pi$
$151$	12.7026	−	2.52671i	1.03373	−	0.205621i	0.682665	+	0.730732i	$0.260821\pi$
$152$	1.35112	+	6.03133i	0.109590	+	0.489206i
$153$	−0.123147	+	0.619103i	−0.00995586	+	0.0500515i
$154$	−0.230751	−	0.544700i	−0.0185944	−	0.0438931i
$155$	−0.793847	−	0.0781871i	−0.0637633	−	0.00628014i
$156$	−3.54612	−	8.18760i	−0.283917	−	0.655533i
$157$	14.6180	+	4.43432i	1.16664	+	0.353897i	0.813440	−	0.581649i	$-0.197592\pi$
$157$	14.6180	+	4.43432i	1.16664	+	0.353897i	0.353203	+	0.935547i	$0.385092\pi$
$158$	2.37190	−	1.97857i	0.188698	−	0.157407i
$159$	−5.40348	−	5.40348i	−0.428523	−	0.428523i
$160$	−2.48543	+	15.7719i	−0.196491	+	1.24687i
$161$	2.27889	−	2.27889i	0.179602	−	0.179602i
$162$	0.127340	−	1.40847i	0.0100048	−	0.110660i
$163$	−2.84855	+	9.39040i	−0.223115	+	0.735513i	0.771896	+	0.635749i	$0.219309\pi$
$163$	−2.84855	+	9.39040i	−0.223115	+	0.735513i	−0.995011	+	0.0997638i	$0.968191\pi$
$164$	10.5788	−	10.9233i	0.826065	−	0.852964i
$165$	0.172490	−	1.75132i	0.0134283	−	0.136340i
$166$	0.211104	−	0.521425i	0.0163849	−	0.0404704i
$167$	−21.3460	−	4.24598i	−1.65180	−	0.328564i	−0.720679	−	0.693269i	$-0.756170\pi$
$167$	−21.3460	−	4.24598i	−1.65180	−	0.328564i	−0.931123	+	0.364705i	$0.881170\pi$
$168$	−0.683844	+	1.77009i	−0.0527597	+	0.136565i
$169$	−1.34670	−	6.77031i	−0.103592	−	0.520793i
$170$	2.08372	−	1.41657i	0.159814	−	0.108646i
$171$	−1.03012	+	1.92722i	−0.0787752	+	0.147378i
$172$	−25.2287	+	2.89355i	−1.92367	+	0.220631i
$173$	1.55630	+	15.8014i	0.118323	+	1.20136i	0.852621	+	0.522530i	$0.175012\pi$
$173$	1.55630	+	15.8014i	0.118323	+	1.20136i	−0.734297	+	0.678828i	$0.762488\pi$
$174$	−1.08419	+	3.67993i	−0.0821919	+	0.278975i
$175$	0.761632	+	1.83874i	0.0575740	+	0.138996i
$176$	−2.48849	−	0.164819i	−0.187577	−	0.0124237i
$177$	−4.94400	+	11.9359i	−0.371614	+	0.897155i
$178$	−8.37975	−	6.76549i	−0.628089	−	0.507095i
$179$	−7.01643	−	5.75823i	−0.524433	−	0.430391i	0.334563	−	0.942373i	$-0.391411\pi$
$179$	−7.01643	−	5.75823i	−0.524433	−	0.430391i	−0.858996	+	0.511983i	$0.828911\pi$
$180$	−4.30572	+	3.65060i	−0.320930	+	0.272099i
$181$	7.20670	−	2.18613i	0.535670	−	0.162494i	−0.0108479	−	0.999941i	$-0.503453\pi$
$181$	7.20670	−	2.18613i	0.535670	−	0.162494i	0.546518	+	0.837447i	$0.315953\pi$
$182$	−2.32337	+	3.53819i	−0.172220	+	0.262268i
$183$	6.45602	+	4.31378i	0.477243	+	0.318883i
$184$	−4.25538	−	12.9035i	−0.313711	−	0.951261i
$185$	5.07528	+	7.59570i	0.373142	+	0.558447i
$186$	−0.280344	+	0.284872i	−0.0205559	+	0.0208878i
$187$	0.249674	+	0.304229i	0.0182580	+	0.0222474i
$188$	−3.23219	+	5.00921i	−0.235732	+	0.365334i
$189$	−0.591680	+	0.316260i	−0.0430384	+	0.0230045i
$190$	8.32654	−	2.59884i	0.604071	−	0.188540i
$191$		−	20.4303i		−	1.47829i	−0.673548	−	0.739144i	$-0.735230\pi$
$191$		−	20.4303i		−	1.47829i	0.673548	−	0.739144i	$-0.264770\pi$
$192$	5.36637	+	5.93314i	0.387284	+	0.428187i
$193$		−	5.57472i		−	0.401277i	−0.979665	−	0.200639i	$-0.935698\pi$
$193$		−	5.57472i		−	0.401277i	0.979665	−	0.200639i	$-0.0643017\pi$
$194$	7.72669	+	24.7559i	0.554744	+	1.77737i
$195$	−11.1051	+	5.93581i	−0.795254	+	0.425072i
$196$	−12.8055	+	2.76112i	−0.914678	+	0.197223i
$197$	5.57471	+	6.79280i	0.397182	+	0.483967i	0.932750	−	0.360525i	$-0.117402\pi$
$197$	5.57471	+	6.79280i	0.397182	+	0.483967i	−0.535568	+	0.844492i	$0.679902\pi$
$198$	−0.628460	−	0.618472i	−0.0446627	−	0.0439529i
$199$	11.0815	+	16.5846i	0.785544	+	1.17565i	0.980823	+	0.194902i	$0.0624388\pi$
$199$	11.0815	+	16.5846i	0.785544	+	1.17565i	−0.195279	+	0.980748i	$0.562561\pi$
$200$	8.36755	+	0.621558i	0.591675	+	0.0439508i
$201$	3.27907	+	2.19101i	0.231288	+	0.154542i
$202$	16.3381	+	10.7285i	1.14954	+	0.754853i
$203$	1.74158	−	0.528301i	0.122235	−	0.0370795i
$204$	0.103602	−	1.25821i	0.00725356	−	0.0880920i
$205$	−16.5886	−	13.6139i	−1.15860	−	0.950839i
$206$	4.24623	−	5.25939i	0.295849	−	0.366439i
$207$	1.83832	−	4.43810i	0.127772	−	0.308469i
$208$	8.91194	+	15.4604i	0.617932	+	1.07199i
$209$	0.521395	+	1.25876i	0.0360657	+	0.0870702i
$210$	2.56881	+	0.756825i	0.177265	+	0.0522259i
$211$	−0.884971	−	8.98527i	−0.0609239	−	0.618571i	−0.976366	−	0.216122i	$-0.930659\pi$
$211$	−0.884971	−	8.98527i	−0.0609239	−	0.618571i	0.915442	−	0.402449i	$-0.131841\pi$
$212$	11.9680	+	9.50515i	0.821964	+	0.652817i
$213$	−2.70830	+	5.06687i	−0.185570	+	0.347176i
$214$	3.07123	+	4.51766i	0.209945	+	0.308821i
$215$	6.99153	+	35.1488i	0.476819	+	2.39713i
$216$	0.0679578	+	2.82761i	0.00462394	+	0.192395i
$217$	0.185964	+	0.0369906i	0.0126241	+	0.00251109i
$218$	−4.75805	−	1.92635i	−0.322256	−	0.130469i
$219$	−1.42361	+	14.4542i	−0.0961989	+	0.976724i
$220$	0.0563790	+	3.51913i	0.00380107	+	0.237260i
$221$	0.817470	−	2.69484i	0.0549890	−	0.181274i
$222$	4.55863	+	0.412146i	0.305955	+	0.0276615i
$223$	13.9997	−	13.9997i	0.937488	−	0.937488i	−0.0606696	−	0.998158i	$-0.519324\pi$
$223$	13.9997	−	13.9997i	0.937488	−	0.937488i	0.998158	+	0.0606696i	$0.0193236\pi$
$224$	0.955392	−	3.67296i	0.0638348	−	0.245410i
$225$	2.09765	+	2.09765i	0.139843	+	0.139843i
$226$	−7.68605	−	9.21399i	−0.511268	−	0.612905i
$227$	−4.37869	−	1.32826i	−0.290624	−	0.0881597i	0.141607	−	0.989923i	$-0.454773\pi$
$227$	−4.37869	−	1.32826i	−0.290624	−	0.0881597i	−0.432230	+	0.901763i	$0.642273\pi$
$228$	1.60762	−	4.06409i	0.106467	−	0.269151i
$229$	−16.4632	−	1.62149i	−1.08792	−	0.107151i	−0.461881	−	0.886942i	$-0.652825\pi$
$229$	−16.4632	−	1.62149i	−1.08792	−	0.107151i	−0.626040	+	0.779791i	$0.715325\pi$
$230$	−17.6559	+	7.47954i	−1.16419	+	0.493186i
$231$	−0.0816055	+	0.410259i	−0.00536925	+	0.0269930i
$232$	1.31562	−	7.55901i	0.0863747	−	0.496273i
$233$	−3.87634	+	0.771051i	−0.253947	+	0.0505132i	−0.320422	−	0.947275i	$-0.603825\pi$
$233$	−3.87634	+	0.771051i	−0.253947	+	0.0505132i	0.0664749	+	0.997788i	$0.478825\pi$
$234$	−1.18126	+	6.19762i	−0.0772214	+	0.405151i
$235$	7.41974	+	3.96593i	0.484010	+	0.258709i
$236$	7.10350	−	24.8430i	0.462399	−	1.61714i
$237$	−2.17359	+	0.214080i	−0.141190	+	0.0139060i
$238$	−0.525913	+	0.286546i	−0.0340899	+	0.0185740i
$239$	25.1780	−	10.4291i	1.62863	−	0.674599i	0.633550	−	0.773702i	$-0.281597\pi$
$239$	25.1780	−	10.4291i	1.62863	−	0.674599i	0.995077	+	0.0991023i	$0.0315971\pi$
$240$	7.72342	−	8.23488i	0.498545	−	0.531559i
$241$	−22.4044	−	9.28023i	−1.44320	−	0.597792i	−0.482626	−	0.875826i	$-0.660317\pi$
$241$	−22.4044	−	9.28023i	−1.44320	−	0.597792i	−0.960571	+	0.278035i	$0.910317\pi$
$242$	14.9221	−	1.59047i	0.959227	−	0.102240i
$243$	−0.634393	+	0.773010i	−0.0406963	+	0.0495886i
$244$	−13.8110	−	7.10008i	−0.884160	−	0.454536i
$245$	5.36652	+	17.6911i	0.342855	+	1.13024i
$246$	−10.5287	+	2.18209i	−0.671283	+	0.139125i
$247$	5.41625	−	8.10599i	0.344628	−	0.515772i
$248$	0.492117	−	0.629921i	0.0312495	−	0.0400000i
$249$	−0.330737	+	0.220992i	−0.0209596	+	0.0140048i
$250$	0.0650127	+	8.11659i	0.00411176	+	0.513339i
$251$	23.2310	−	19.0652i	1.46633	−	1.20339i	0.532118	−	0.846670i	$-0.321396\pi$
$251$	23.2310	−	19.0652i	1.46633	−	1.20339i	0.934213	−	0.356716i	$-0.116104\pi$
$252$	1.10358	−	0.763239i	0.0695190	−	0.0480795i
$253$	−1.41187	−	2.64142i	−0.0887636	−	0.166065i
$254$	20.2318	+	10.6067i	1.26946	+	0.665522i
$255$	−1.78165			−0.111572
$256$	−12.0149	−	10.5660i	−0.750934	−	0.660377i
$257$	−19.6336			−1.22471			−0.612355	−	0.790583i	$-0.709778\pi$
$257$	−19.6336			−1.22471			−0.612355	+	0.790583i	$0.709778\pi$
$258$	15.9033	+	8.33743i	0.990099	+	0.519066i
$259$	−1.02360	−	1.91502i	−0.0636035	−	0.118994i
$260$	20.7128	−	14.3251i	1.28456	−	0.888403i
$261$	2.09694	−	1.72091i	0.129797	−	0.106522i
$262$	−0.116694	−	14.5688i	−0.00720936	−	0.900063i
$263$	0.0188371	−	0.0125865i	0.00116154	−	0.000776119i	−0.554989	−	0.831857i	$-0.687278\pi$
$263$	0.0188371	−	0.0125865i	0.00116154	−	0.000776119i	0.556151	+	0.831081i	$0.312278\pi$
$264$	1.38968	+	1.08567i	0.0855288	+	0.0668182i
$265$	11.9829	−	17.9337i	0.736103	−	1.10166i
$266$	−2.03021	+	0.420766i	−0.124480	+	0.0257988i
$267$	2.21067	+	7.28759i	0.135291	+	0.445993i
$268$	−7.01474	−	3.60620i	−0.428494	−	0.220284i
$269$	10.9035	−	13.2859i	0.664796	−	0.810056i	−0.326007	−	0.945367i	$-0.605703\pi$
$269$	10.9035	−	13.2859i	0.664796	−	0.810056i	0.990803	+	0.135311i	$0.0432034\pi$
$270$	3.96914	−	0.423052i	0.241554	−	0.0257461i
$271$	8.14244	+	3.37271i	0.494618	+	0.204878i	0.616027	−	0.787725i	$-0.288741\pi$
$271$	8.14244	+	3.37271i	0.494618	+	0.204878i	−0.121409	+	0.992603i	$0.538741\pi$
$272$	0.0808816	+	2.52363i	0.00490417	+	0.153018i
$273$	2.76523	−	1.14540i	0.167359	−	0.0693225i
$274$	6.19534	−	3.37556i	0.374274	−	0.203925i
$275$	1.84068	−	0.181291i	0.110997	−	0.0109323i
$276$	−2.64129	+	9.23733i	−0.158987	+	0.556022i
$277$	−17.6353	−	9.42624i	−1.05960	−	0.566368i	−0.152942	−	0.988235i	$-0.548875\pi$
$277$	−17.6353	−	9.42624i	−1.05960	−	0.566368i	−0.906658	+	0.421867i	$0.861375\pi$
$278$	−3.19328	+	16.7539i	−0.191520	+	1.00483i
$279$	0.277187	−	0.0551359i	0.0165947	−	0.00330090i
$280$	−5.27663	−	0.918380i	−0.315339	−	0.0548837i
$281$	−2.54553	+	12.7972i	−0.151853	+	0.763419i	0.827532	+	0.561419i	$0.189744\pi$
$281$	−2.54553	+	12.7972i	−0.151853	+	0.763419i	−0.979385	+	0.202000i	$0.935256\pi$
$282$	3.88148	−	1.64431i	0.231139	−	0.0979170i
$283$	29.0589	+	2.86205i	1.72737	+	0.170131i	0.912381	−	0.409343i	$-0.134242\pi$
$283$	29.0589	+	2.86205i	1.72737	+	0.170131i	0.814991	+	0.579474i	$0.196742\pi$
$284$	4.22662	−	10.6849i	0.250804	−	0.634035i
$285$	−5.90229	−	1.79044i	−0.349621	−	0.106056i
$286$	2.51978	+	3.02070i	0.148998	+	0.178618i
$287$	3.60689	+	3.60689i	0.212908	+	0.212908i
$288$	−0.779421	−	5.60290i	−0.0459278	−	0.330154i
$289$	−11.7391	+	11.7391i	−0.690533	+	0.690533i
$290$	−10.7841	−	0.974989i	−0.633261	−	0.0572533i
$291$	5.32321	−	17.5483i	0.312052	−	1.02870i
$292$	−0.465314	−	29.0445i	−0.0272305	−	1.69970i
$293$	1.72268	−	17.4907i	0.100640	−	1.02182i	−0.803709	−	0.595022i	$-0.797143\pi$
$293$	1.72268	−	17.4907i	0.100640	−	1.02182i	0.904349	−	0.426793i	$-0.140357\pi$
$294$	8.58597	+	3.47612i	0.500744	+	0.202731i
$295$	−35.7641	−	7.11392i	−2.08227	−	0.414188i
$296$	−9.15180	+	0.219951i	−0.531937	+	0.0127844i
$297$	0.121636	+	0.611506i	0.00705804	+	0.0354832i
$298$	14.6857	+	21.6021i	0.850719	+	1.25138i
$299$	−10.1025	+	18.9004i	−0.584240	+	1.09304i
$300$	−4.64602	−	3.68994i	−0.268238	−	0.213039i
$301$	−0.834952	−	8.47741i	−0.0481258	−	0.488630i
$302$	17.5695	+	5.17635i	1.01101	+	0.297865i
$303$	−5.28902	−	12.7688i	−0.303846	−	0.733550i
$304$	−2.26813	+	8.44160i	−0.130086	+	0.484159i
$305$	−8.38673	+	20.2474i	−0.480223	+	1.15936i
$306$	−0.560776	+	0.694578i	−0.0320574	+	0.0397064i
$307$	−4.68760	−	3.84701i	−0.267536	−	0.219561i	0.491055	−	0.871129i	$-0.336612\pi$
$307$	−4.68760	−	3.84701i	−0.267536	−	0.219561i	−0.758590	+	0.651568i	$0.774112\pi$
$308$	0.0686533	−	0.833771i	0.00391189	−	0.0475085i
$309$	−4.57392	+	1.38748i	−0.260201	+	0.0789311i
$310$	−0.942972	−	0.619207i	−0.0535572	−	0.0351686i
$311$	3.87693	+	2.59048i	0.219841	+	0.146893i	0.660614	−	0.750725i	$-0.270296\pi$
$311$	3.87693	+	2.59048i	0.219841	+	0.146893i	−0.440774	+	0.897618i	$0.645296\pi$
$312$	0.934742	−	12.5837i	0.0529194	−	0.712413i
$313$	−5.44624	−	8.15088i	−0.307840	−	0.460715i	0.645003	−	0.764180i	$-0.276856\pi$
$313$	−5.44624	−	8.15088i	−0.307840	−	0.460715i	−0.952842	+	0.303465i	$0.901856\pi$
$314$	15.3976	+	15.1529i	0.868938	+	0.855129i
$315$	−1.20130	−	1.46378i	−0.0676854	−	0.0824749i
$316$	4.27008	−	0.920715i	0.240211	−	0.0517943i
$317$	0.660351	−	0.352965i	0.0370890	−	0.0198245i	−0.452748	−	0.891639i	$-0.649556\pi$
$317$	0.660351	−	0.352965i	0.0370890	−	0.0198245i	0.489837	+	0.871814i	$0.337056\pi$
$318$	−3.21982	−	10.3161i	−0.180559	−	0.578501i
$319$		−	1.69132i		−	0.0946960i
$320$	−13.4696	+	18.1226i	−0.752972	+	1.01308i
$321$		−	3.86275i		−	0.215598i
$322$	4.35079	−	1.35795i	0.242460	−	0.0756755i
$323$	1.21652	−	0.650244i	0.0676890	−	0.0361805i
$324$	1.08436	−	1.68052i	0.0602422	−	0.0933625i
$325$	−8.39587	−	10.2304i	−0.465719	−	0.567480i
$326$	−9.73403	+	9.89123i	−0.539118	+	0.547824i
$327$	2.01657	+	3.01801i	0.111517	+	0.166896i
$328$	20.4229	−	6.73516i	1.12767	−	0.371887i
$329$	−1.66275	−	1.11102i	−0.0916705	−	0.0612523i
$330$	1.36604	−	2.08030i	0.0751981	−	0.114517i
$331$	10.2571	−	3.11147i	0.563784	−	0.171022i	0.00448774	−	0.999990i	$-0.498572\pi$
$331$	10.2571	−	3.11147i	0.563784	−	0.171022i	0.559296	+	0.828968i	$0.311072\pi$
$332$	0.606804	−	0.514477i	0.0333027	−	0.0282356i
$333$	−2.50191	−	2.05327i	−0.137104	−	0.112518i
$334$	−23.9483	−	19.3349i	−1.31039	−	1.05796i
$335$	−4.25970	+	10.2838i	−0.232732	+	0.561865i
$336$	−2.01885	+	1.76803i	−0.110137	+	0.0964541i
$337$	1.06989	+	2.58295i	0.0582809	+	0.140702i	0.950338	−	0.311221i	$-0.100738\pi$
$337$	1.06989	+	2.58295i	0.0582809	+	0.140702i	−0.892057	+	0.451924i	$0.850738\pi$
$338$	2.75891	−	9.36428i	0.150065	−	0.509350i
$339$	0.831625	+	8.44363i	0.0451677	+	0.458595i
$340$	3.54010	−	0.406025i	0.191989	−	0.0220198i
$341$	0.0830638	−	0.155401i	0.00449816	−	0.00841546i
$342$	−2.55575	+	1.73746i	−0.138199	+	0.0939513i
$343$	−1.77349	−	8.91594i	−0.0957595	−	0.481416i
$344$	−33.4996	−	12.9420i	−1.80618	−	0.697787i
$345$	13.2981	+	2.64516i	0.715947	+	0.142411i
$346$	−8.42659	+	20.8136i	−0.453016	+	1.11894i
$347$	−0.980033	+	9.95044i	−0.0526109	+	0.534168i	0.932370	+	0.361505i	$0.117737\pi$
$347$	−0.980033	+	9.95044i	−0.0526109	+	0.534168i	−0.984981	+	0.172663i	$0.944763\pi$
$348$	−3.77438	+	3.89728i	−0.202328	+	0.208916i
$349$	−2.44876	+	8.07249i	−0.131079	+	0.432111i	−0.997771	−	0.0667339i	$-0.978742\pi$
$349$	−2.44876	+	8.07249i	−0.131079	+	0.432111i	0.866691	+	0.498845i	$0.166242\pi$
$350$	−0.253437	+	2.80319i	−0.0135468	+	0.149837i
$351$	3.15460	−	3.15460i	0.168380	−	0.168380i
$352$	−3.00867	−	1.84049i	−0.160363	−	0.0980987i
$353$	12.0299	+	12.0299i	0.640288	+	0.640288i	0.950626	−	0.310338i	$-0.100442\pi$
$353$	12.0299	+	12.0299i	0.640288	+	0.640288i	−0.310338	+	0.950626i	$0.600442\pi$
$354$	−14.0301	+	11.7035i	−0.745691	+	0.622035i
$355$	−15.5178	−	4.70727i	−0.823598	−	0.249836i
$356$	−6.05332	−	13.9765i	−0.320825	−	0.740751i
$357$	0.421454	+	0.0415096i	0.0223057	+	0.00219692i
$358$	−5.00714	−	11.8196i	−0.264635	−	0.624687i
$359$	−1.05339	+	5.29576i	−0.0555959	+	0.279500i	−0.998576	−	0.0533499i	$-0.983010\pi$
$359$	−1.05339	+	5.29576i	−0.0555959	+	0.279500i	0.942980	+	0.332850i	$0.108010\pi$
$360$	−7.79017	+	1.74513i	−0.410578	+	0.0919764i
$361$	−13.9514	+	2.77510i	−0.734282	+	0.146058i
$362$	10.4621	+	1.99406i	0.549875	+	0.104806i
$363$	−9.35830	−	5.00212i	−0.491183	−	0.262543i
$364$	−5.23341	+	2.90605i	−0.274305	+	0.152318i
$365$	−40.7970	+	4.01815i	−2.13541	+	0.210320i
$366$	5.25371	+	9.64242i	0.274616	+	0.504017i
$367$	−8.23215	+	3.40987i	−0.429715	+	0.177994i	−0.587048	−	0.809552i	$-0.699710\pi$
$367$	−8.23215	+	3.40987i	−0.429715	+	0.177994i	0.157334	+	0.987545i	$0.449710\pi$
$368$	3.14306	−	18.9563i	0.163843	−	0.988163i
$369$	7.02435	+	2.90958i	0.365673	+	0.151467i
$370$	1.36924	+	12.8465i	0.0711836	+	0.667855i
$371$	−3.25240	+	3.96306i	−0.168856	+	0.205752i
$372$	−0.538198	+	0.172722i	−0.0279043	+	0.00895523i
$373$	10.1668	+	33.5154i	0.526416	+	1.73536i	0.666775	+	0.745259i	$0.267674\pi$
$373$	10.1668	+	33.5154i	0.526416	+	1.73536i	−0.140359	+	0.990101i	$0.544826\pi$
$374$	0.112953	+	0.545002i	0.00584066	+	0.0281814i
$375$	3.18869	−	4.77221i	0.164663	−	0.246436i
$376$	−7.33767	+	4.15175i	−0.378412	+	0.214110i
$377$	−10.0625	+	6.72354i	−0.518244	+	0.346280i
$378$	−0.948764	+	0.00759946i	−0.0487992	+	0.000390874i
$379$	26.1897	−	21.4933i	1.34527	−	1.10404i	0.360017	−	0.932946i	$-0.382771\pi$
$379$	26.1897	−	21.4933i	1.34527	−	1.10404i	0.985255	−	0.171091i	$-0.0547291\pi$
$380$	12.1357	+	2.21247i	0.622549	+	0.113497i
$381$	−7.61439	−	14.2455i	−0.390097	−	0.729820i
$382$	13.4155	−	25.5895i	0.686395	−	1.30927i
$383$	−24.3530			−1.24438			−0.622190	−	0.782866i	$-0.713757\pi$
$383$	−24.3530			−1.24438			−0.622190	+	0.782866i	$0.713757\pi$
$384$	2.82555	+	10.9552i	0.144191	+	0.559055i
$385$	−1.18064			−0.0601711
$386$	3.66061	−	6.98248i	0.186320	−	0.355399i
$387$	−5.98534	−	11.1978i	−0.304252	−	0.569215i
$388$	−6.57797	+	36.0811i	−0.333946	+	1.83174i
$389$	5.72373	−	4.69734i	0.290205	−	0.238165i	−0.478014	−	0.878352i	$-0.658643\pi$
$389$	5.72373	−	4.69734i	0.290205	−	0.238165i	0.768219	+	0.640187i	$0.221143\pi$
$390$	−17.8071	+	0.142633i	−0.901700	+	0.00722248i
$391$	−2.52126	+	1.68465i	−0.127505	+	0.0851964i
$392$	−17.8523	−	4.95028i	−0.901676	−	0.250027i
$393$	−5.72349	+	8.56582i	−0.288712	+	0.432088i
$394$	2.52200	+	12.1688i	0.127057	+	0.613053i
$395$	−1.78950	−	5.89920i	−0.0900397	−	0.296821i
$396$	−0.381045	−	1.18733i	−0.0191482	−	0.0596654i
$397$	−8.60463	+	10.4848i	−0.431854	+	0.526216i	−0.942783	−	0.333407i	$-0.891802\pi$
$397$	−8.60463	+	10.4848i	−0.431854	+	0.526216i	0.510929	+	0.859623i	$0.329302\pi$
$398$	2.98963	+	28.0492i	0.149857	+	1.40598i
$399$	1.35448	+	0.561045i	0.0678090	+	0.0280874i
$400$	10.0724	+	6.27303i	0.503621	+	0.313651i
$401$	−17.6219	+	7.29925i	−0.879998	+	0.364507i	−0.776496	−	0.630122i	$-0.783005\pi$
$401$	−17.6219	+	7.29925i	−0.879998	+	0.364507i	−0.103502	+	0.994629i	$0.533005\pi$
$402$	2.66841	+	4.89747i	0.133088	+	0.244264i
$403$	−1.25476	+	0.123583i	−0.0625041	+	0.00615612i
$404$	13.4191	+	24.1660i	0.667624	+	1.20230i
$405$	−2.48923	−	1.33052i	−0.123691	−	0.0661140i
$406$	2.52827	+	0.481886i	0.125476	+	0.0239156i
$407$	−1.97919	+	0.393685i	−0.0981048	+	0.0195143i
$408$	0.955958	−	1.50790i	0.0473269	−	0.0746524i
$409$	−0.310484	+	1.56091i	−0.0153524	+	0.0771819i	−0.987702	−	0.156348i	$-0.950028\pi$
$409$	−0.310484	+	1.56091i	−0.0153524	+	0.0771819i	0.972350	+	0.233530i	$0.0750278\pi$
$410$	−11.8382	−	27.9446i	−0.584645	−	1.38009i
$411$	−4.96480	−	0.488990i	−0.244895	−	0.0241201i
$412$	8.77206	−	3.79925i	0.432168	−	0.187176i
$413$	8.29432	+	2.51605i	0.408137	+	0.123807i
$414$	5.21680	−	4.35171i	0.256392	−	0.213875i
$415$	−0.793883	−	0.793883i	−0.0389702	−	0.0389702i
$416$	1.01042	+	25.2165i	0.0495400	+	1.23634i
$417$	8.52776	−	8.52776i	0.417606	−	0.417606i
$418$	−0.173497	+	1.91900i	−0.00848602	+	0.0938613i
$419$	8.05724	−	26.5612i	0.393622	−	1.29760i	−0.506605	−	0.862178i	$-0.669100\pi$
$419$	8.05724	−	26.5612i	0.393622	−	1.29760i	0.900227	−	0.435420i	$-0.143400\pi$
$420$	2.72053	+	2.63474i	0.132748	+	0.128562i
$421$	2.65420	−	26.9485i	0.129358	−	1.31339i	−0.683081	−	0.730343i	$-0.739360\pi$
$421$	2.65420	−	26.9485i	0.129358	−	1.31339i	0.812438	−	0.583047i	$-0.198140\pi$
$422$	4.79168	−	11.8354i	0.233255	−	0.576137i
$423$	−2.92347	−	0.581513i	−0.142144	−	0.0282742i
$424$	8.74868	+	19.7641i	0.424873	+	0.959832i
$425$	−0.365320	−	1.83659i	−0.0177206	−	0.0890875i
$426$	−6.71934	+	4.56799i	−0.325553	+	0.221320i
$427$	2.45563	−	4.59416i	0.118836	−	0.222327i
$428$	0.880291	+	7.67519i	0.0425505	+	0.370994i
$429$	−0.272639	−	2.76815i	−0.0131631	−	0.133647i
$430$	−14.3232	+	48.6157i	−0.690726	+	2.34446i
$431$	2.72576	+	6.58056i	0.131295	+	0.316974i	0.975832	−	0.218523i	$-0.0701240\pi$
$431$	2.72576	+	6.58056i	0.131295	+	0.316974i	−0.844537	+	0.535498i	$0.820124\pi$
$432$	−1.77162	+	3.58628i	−0.0852369	+	0.172545i
$433$	−4.46980	+	10.7911i	−0.214805	+	0.518585i	−0.994150	−	0.108010i	$-0.965552\pi$
$433$	−4.46980	+	10.7911i	−0.214805	+	0.518585i	0.779345	+	0.626595i	$0.215552\pi$
$434$	0.208635	+	0.168444i	0.0100148	+	0.00808558i
$435$	5.91862	+	4.85728i	0.283776	+	0.232889i
$436$	−4.69465	−	5.53715i	−0.224833	−	0.265181i
$437$	−10.0454	+	3.04724i	−0.480537	+	0.145769i
$438$	−11.2744	+	17.1694i	−0.538710	+	0.820387i
$439$	−31.0024	−	20.7152i	−1.47967	−	0.988681i	−0.993379	−	0.114881i	$-0.963351\pi$
$439$	−31.0024	−	20.7152i	−1.47967	−	0.988681i	−0.486286	−	0.873800i	$-0.661649\pi$
$440$	−2.24020	+	4.44482i	−0.106797	+	0.211898i
$441$	−3.63893	−	5.44604i	−0.173282	−	0.259335i
$442$	2.79345	−	2.83856i	0.132871	−	0.135017i
$443$	9.35165	+	11.3950i	0.444310	+	0.541394i	0.946219	−	0.323527i	$-0.104869\pi$
$443$	9.35165	+	11.3950i	0.444310	+	0.541394i	−0.501909	+	0.864921i	$0.667369\pi$
$444$	5.43916	+	3.50962i	0.258131	+	0.166559i
$445$	−18.9567	+	10.1326i	−0.898635	+	0.480330i
$446$	26.7278	−	8.34213i	1.26560	−	0.395012i
$447$		−	18.4705i		−	0.873625i
$448$	3.60848	−	3.97312i	0.170485	−	0.187712i
$449$		−	17.1954i		−	0.811501i	−0.913984	−	0.405750i	$-0.867010\pi$
$449$		−	17.1954i		−	0.811501i	0.913984	−	0.405750i	$-0.132990\pi$
$450$	1.24995	+	4.00477i	0.0589232	+	0.188787i
$451$	4.18068	−	2.23462i	0.196861	−	0.105224i
$452$	−3.57665	−	16.5877i	−0.168232	−	0.780222i
$453$	−8.21634	−	10.0116i	−0.386038	−	0.470388i
$454$	−4.61222	−	4.53892i	−0.216462	−	0.213022i
$455$	4.69342	+	7.02420i	0.220031	+	0.329300i
$456$	4.68225	−	4.03473i	0.219266	−	0.188944i
$457$	−11.4268	−	7.63514i	−0.534523	−	0.357157i	0.258826	−	0.965924i	$-0.416664\pi$
$457$	−11.4268	−	7.63514i	−0.534523	−	0.357157i	−0.793349	+	0.608767i	$0.791664\pi$
$458$	−19.5559	−	12.8414i	−0.913786	−	0.600041i
$459$	0.604051	−	0.183237i	0.0281947	−	0.00855277i
$460$	−27.0258	−	2.22533i	−1.26009	−	0.103756i
$461$	−29.7391	−	24.4062i	−1.38509	−	1.13671i	−0.974370	−	0.224950i	$-0.927778\pi$
$461$	−29.7391	−	24.4062i	−1.38509	−	1.13671i	−0.410718	−	0.911763i	$-0.634722\pi$
$462$	−0.371607	+	0.460273i	−0.0172887	+	0.0214139i
$463$	−2.08535	+	5.03448i	−0.0969144	+	0.233972i	−0.964900	−	0.262617i	$-0.915414\pi$
$463$	−2.08535	+	5.03448i	−0.0969144	+	0.233972i	0.867986	+	0.496589i	$0.165414\pi$
$464$	6.61143	−	8.60395i	0.306928	−	0.399428i
$465$	0.305262	+	0.736968i	0.0141562	+	0.0341761i
$466$	−5.36151	−	1.57961i	−0.248367	−	0.0731742i
$467$	−3.23391	−	32.8344i	−0.149647	−	1.51939i	−0.717671	−	0.696382i	$-0.754792\pi$
$467$	−3.23391	−	32.8344i	−0.149647	−	1.51939i	0.568024	−	0.823012i	$-0.307708\pi$
$468$	−5.54919	+	6.98701i	−0.256511	+	0.322975i
$469$	1.24724	−	2.33341i	0.0575920	−	0.107747i
$470$	6.68919	+	9.83955i	0.308550	+	0.453865i
$471$	−2.98015	−	14.9822i	−0.137318	−	0.690345i
$472$	25.2103	−	26.4519i	1.16040	−	1.21755i
$473$	−7.76431	−	1.54442i	−0.357003	−	0.0710123i
$474$	−2.86305	−	1.15914i	−0.131504	−	0.0532409i
$475$	0.635406	−	6.45138i	0.0291544	−	0.296010i
$476$	−0.846878	+	0.0135676i	−0.0388166	+	0.000621869i
$477$	−2.21826	+	7.31262i	−0.101567	+	0.334822i
$478$	38.3842	+	3.47032i	1.75565	+	0.158729i
$479$	−18.8929	+	18.8929i	−0.863239	+	0.863239i	−0.991713	−	0.128473i	$-0.958992\pi$
$479$	−18.8929	+	18.8929i	−0.863239	+	0.863239i	0.128473	+	0.991713i	$0.458992\pi$
$480$	15.0812	−	5.24285i	0.688358	−	0.239302i
$481$	10.2101	+	10.2101i	0.465541	+	0.465541i
$482$	−21.9683	−	26.3355i	−1.00063	−	1.19955i
$483$	−3.08407	−	0.935542i	−0.140330	−	0.0425686i
$484$	19.7346	+	7.80639i	0.897029	+	0.354836i
$485$	51.5096	+	5.07325i	2.33893	+	0.230364i
$486$	−1.30219	+	0.551644i	−0.0590684	+	0.0250231i
$487$	−0.662913	+	3.33269i	−0.0300395	+	0.151019i	−0.992894	−	0.119002i	$-0.962031\pi$
$487$	−0.662913	+	3.33269i	−0.0300395	+	0.151019i	0.962855	+	0.270021i	$0.0870305\pi$
$488$	−12.6364	−	17.9620i	−0.572024	−	0.813100i
$489$	9.62439	−	1.91441i	0.435230	−	0.0865726i
$490$	−4.89503	+	25.6824i	−0.221135	+	1.16021i
$491$	−10.1876	−	5.44537i	−0.459759	−	0.245746i	0.225222	−	0.974307i	$-0.427689\pi$
$491$	−10.1876	−	5.44537i	−0.459759	−	0.245746i	−0.684980	+	0.728561i	$0.740189\pi$
$492$	−14.6203	−	4.18047i	−0.659133	−	0.188470i
$493$	−1.70409	+	0.167838i	−0.0767484	+	0.00755906i
$494$	12.1067	−	6.59640i	0.544708	−	0.296786i
$495$	−1.62584	+	0.673443i	−0.0730759	+	0.0302690i
$496$	1.03002	−	0.465846i	0.0462494	−	0.0209171i
$497$	3.56109	+	1.47505i	0.159737	+	0.0661651i
$498$	−0.559370	+	0.0596206i	−0.0250660	+	0.00267166i
$499$	−15.2516	+	18.5841i	−0.682756	+	0.831941i	−0.992925	−	0.118741i	$-0.962114\pi$
$499$	−15.2516	+	18.5841i	−0.682756	+	0.831941i	0.310169	+	0.950681i	$0.399614\pi$
$500$	−5.24829	+	10.2089i	−0.234711	+	0.456557i
$501$	6.31781	+	20.8270i	0.282259	+	0.930483i
$502$	41.6165	−	8.62513i	1.85744	−	0.384958i
$503$	6.75033	−	10.1026i	0.300982	−	0.450452i	−0.649893	−	0.760026i	$-0.725186\pi$
$503$	6.75033	−	10.1026i	0.300982	−	0.450452i	0.950875	+	0.309574i	$0.100186\pi$
$504$	1.88344	−	0.231316i	0.0838950	−	0.0103036i
$505$	32.4352	−	21.6725i	1.44335	−	0.964414i
$506$	−0.0339261	−	4.23555i	−0.00150820	−	0.188293i
$507$	−5.33605	+	4.37919i	−0.236982	+	0.194486i
$508$	18.3760	+	26.5702i	0.815305	+	1.17886i
$509$	13.0499	+	24.4146i	0.578425	+	1.08216i	0.985646	+	0.168828i	$0.0539981\pi$
$509$	13.0499	+	24.4146i	0.578425	+	1.08216i	−0.407220	+	0.913330i	$0.633502\pi$
$510$	−2.23157	−	1.16991i	−0.0988154	−	0.0518047i
$511$	9.74423			0.431059
$512$	−8.11089	−	21.1238i	−0.358454	−	0.933547i
$513$	2.18525			0.0964811
$514$	−24.5916	−	12.8923i	−1.08469	−	0.568655i
$515$	−6.35952	−	11.8978i	−0.280234	−	0.524281i
$516$	14.4446	+	20.8857i	0.635888	+	0.919441i
$517$	−1.43660	+	1.17899i	−0.0631816	+	0.0518518i
$518$	−0.0245963	−	3.07076i	−0.00108070	−	0.134921i
$519$	13.2020	−	8.82126i	0.579501	−	0.387210i
$520$	35.3498	−	4.34152i	1.55019	−	0.190388i
$521$	22.4481	−	33.5959i	0.983468	−	1.47186i	0.104764	−	0.994497i	$-0.466591\pi$
$521$	22.4481	−	33.5959i	0.983468	−	1.47186i	0.878704	−	0.477367i	$-0.158409\pi$
$522$	3.75649	−	0.778543i	0.164417	−	0.0340759i
$523$	9.75302	+	32.1514i	0.426470	+	1.40588i	0.862549	+	0.505974i	$0.168867\pi$
$523$	9.75302	+	32.1514i	0.426470	+	1.40588i	−0.436079	+	0.899909i	$0.643633\pi$
$524$	9.42035	−	18.3244i	0.411530	−	0.800505i
$525$	1.26260	−	1.53848i	0.0551042	−	0.0671447i
$526$	0.0318588	−	0.00339568i	0.00138911	−	0.000148059i
$527$	−0.164817	−	0.0682696i	−0.00717956	−	0.00297387i
$528$	1.02771	+	2.27235i	0.0447253	+	0.0988913i
$529$	0.0703637	−	0.0291456i	0.00305929	−	0.00126720i
$530$	26.7849	−	14.5939i	1.16346	−	0.633917i
$531$	12.8571	−	1.26631i	0.557950	−	0.0549533i
$532$	−2.81918	−	0.806106i	−0.122227	−	0.0349491i
$533$	−29.9143	−	15.9895i	−1.29573	−	0.692584i
$534$	−2.01644	+	10.5795i	−0.0872600	+	0.457820i
$535$	10.6931	−	2.12700i	0.462305	−	0.0919581i
$536$	−6.41815	−	9.12304i	−0.277222	−	0.394055i
$537$	−1.77079	+	8.90235i	−0.0764151	+	0.384165i
$538$	22.3810	−	9.48123i	0.964912	−	0.408765i
$539$	−4.06410	−	0.400279i	−0.175053	−	0.0172412i
$540$	5.24924	+	2.07643i	0.225891	+	0.0893554i
$541$	41.7366	+	12.6607i	1.79440	+	0.544324i	0.998159	−	0.0606582i	$-0.0193200\pi$
$541$	41.7366	+	12.6607i	1.79440	+	0.544324i	0.796239	+	0.604983i	$0.206820\pi$
$542$	7.98394	+	9.57110i	0.342940	+	0.411114i
$543$	−5.32521	−	5.32521i	−0.228527	−	0.228527i
$544$	−1.55582	+	3.21402i	−0.0667054	+	0.137800i
$545$	−7.24426	+	7.24426i	−0.310310	+	0.310310i
$546$	4.21564	+	0.381137i	0.180413	+	0.0163111i
$547$	8.76469	−	28.8933i	0.374751	−	1.23539i	−0.543506	−	0.839405i	$-0.682904\pi$
$547$	8.76469	−	28.8933i	0.374751	−	1.23539i	0.918258	−	0.395984i	$-0.129596\pi$
$548$	9.97636	−	0.159829i	0.426169	−	0.00682754i
$549$	0.761063	−	7.72720i	0.0324814	−	0.329789i
$550$	2.42454	+	0.981602i	0.103383	+	0.0418556i
$551$	−5.81400	−	1.15648i	−0.247685	−	0.0492675i
$552$	−9.37392	+	9.83559i	−0.398981	+	0.418631i
$553$	0.285869	+	1.43716i	0.0121564	+	0.0611143i
$554$	−15.8989	−	23.3867i	−0.675480	−	0.993605i
$555$	4.30634	−	8.05659i	0.182794	−	0.341983i
$556$	−15.0010	+	18.8878i	−0.636185	+	0.801023i
$557$	3.56068	+	36.1521i	0.150871	+	1.53182i	0.710871	+	0.703323i	$0.248301\pi$
$557$	3.56068	+	36.1521i	0.150871	+	1.53182i	−0.560000	+	0.828493i	$0.689199\pi$
$558$	0.383388	+	0.112954i	0.0162301	+	0.00478173i
$559$	21.6771	+	52.3331i	0.916842	+	2.21345i
$560$	−6.00606	−	4.61516i	−0.253802	−	0.195026i
$561$	0.150611	−	0.363606i	0.00635878	−	0.0153515i
$562$	−11.5916	+	14.3573i	−0.488961	+	0.605628i
$563$	35.6547	+	29.2611i	1.50267	+	1.23321i	0.900515	+	0.434824i	$0.143190\pi$
$563$	35.6547	+	29.2611i	1.50267	+	1.23321i	0.602151	+	0.798382i	$0.294310\pi$
$564$	5.94137	+	0.489217i	0.250177	+	0.0205998i
$565$	−22.9163	+	6.95159i	−0.964097	+	0.292456i
$566$	34.5176	+	22.6661i	1.45088	+	0.952729i
$567$	0.557832	+	0.372732i	0.0234268	+	0.0156533i
$568$	12.3102	−	10.6078i	0.516522	−	0.445092i
$569$	−5.76636	−	8.62997i	−0.241738	−	0.361787i	0.690684	−	0.723156i	$-0.257309\pi$
$569$	−5.76636	−	8.62997i	−0.241738	−	0.361787i	−0.932423	+	0.361369i	$0.882309\pi$
$570$	−6.21708	−	6.11827i	−0.260405	−	0.256266i
$571$	−1.12016	−	1.36491i	−0.0468771	−	0.0571199i	0.749044	−	0.662520i	$-0.230513\pi$
$571$	−1.12016	−	1.36491i	−0.0468771	−	0.0571199i	−0.795921	+	0.605400i	$0.793013\pi$
$572$	1.17256	+	5.43810i	0.0490274	+	0.227378i
$573$	−18.0180	+	9.63080i	−0.752711	+	0.402332i
$574$	2.14928	+	6.88617i	0.0897090	+	0.287423i
$575$			14.2505i			0.594287i
$576$	2.70287	−	7.52957i	0.112620	−	0.313732i
$577$			7.77143i			0.323529i	0.986829	+	0.161764i	$0.0517185\pi$
$577$			7.77143i			0.323529i	−0.986829	+	0.161764i	$0.948282\pi$
$578$	−22.4119	+	6.99508i	−0.932211	+	0.290957i
$579$	−4.91646	+	2.62791i	−0.204321	+	0.109212i
$580$	−12.8671	−	8.30249i	−0.534276	−	0.344742i
$581$	0.169298	+	0.206291i	0.00702368	+	0.00855838i
$582$	18.1904	−	18.4842i	0.754018	−	0.766194i
$583$	2.64700	+	3.96151i	0.109627	+	0.164069i
$584$	18.4891	−	36.6845i	0.765085	−	1.51802i
$585$	10.4698	+	6.99572i	0.432874	+	0.289237i
$586$	13.6428	−	20.7763i	0.563581	−	0.858261i
$587$	−14.8812	+	4.51415i	−0.614211	+	0.186319i	−0.582036	−	0.813163i	$-0.697744\pi$
$587$	−14.8812	+	4.51415i	−0.614211	+	0.186319i	−0.0321756	+	0.999482i	$0.510244\pi$
$588$	8.47156	+	9.99185i	0.349361	+	0.412057i
$589$	−0.477403	−	0.391794i	−0.0196710	−	0.0161436i
$590$	−40.1241	−	32.3946i	−1.65188	−	1.33367i
$591$	3.36282	−	8.11856i	0.138328	−	0.333953i
$592$	−11.6073	−	5.73398i	−0.477056	−	0.235665i
$593$	8.42429	+	20.3380i	0.345944	+	0.835183i	0.997090	+	0.0762306i	$0.0242885\pi$
$593$	8.42429	+	20.3380i	0.345944	+	0.835183i	−0.651146	+	0.758952i	$0.725711\pi$
$594$	−0.249190	+	0.845798i	−0.0102244	+	0.0347035i
$595$	0.117161	+	1.18956i	0.00480313	+	0.0487670i
$596$	4.20929	+	36.7004i	0.172419	+	1.50331i
$597$	9.40253	−	17.5909i	0.384820	−	0.719947i
$598$	−25.0644	+	17.0395i	−1.02496	+	0.696795i
$599$	6.88081	+	34.5922i	0.281142	+	1.41340i	0.820657	+	0.571421i	$0.193608\pi$
$599$	6.88081	+	34.5922i	0.281142	+	1.41340i	−0.539515	+	0.841976i	$0.681392\pi$
$600$	−3.39627	−	7.67252i	−0.138652	−	0.313229i
$601$	35.6578	+	7.09278i	1.45451	+	0.289321i	0.858152	−	0.513396i	$-0.171613\pi$
$601$	35.6578	+	7.09278i	1.45451	+	0.289321i	0.596361	+	0.802716i	$0.296613\pi$
$602$	4.52085	−	11.1664i	0.184256	−	0.455110i
$603$	0.386551	−	3.92472i	0.0157416	−	0.159827i
$604$	18.6072	+	18.0204i	0.757118	+	0.733241i
$605$	8.69412	−	28.6607i	0.353466	−	1.16522i
$606$	1.75995	−	19.4663i	0.0714931	−	0.790764i
$607$	2.00073	−	2.00073i	0.0812071	−	0.0812071i	−0.665336	−	0.746544i	$-0.731712\pi$
$607$	2.00073	−	2.00073i	0.0812071	−	0.0812071i	0.746544	+	0.665336i	$0.231712\pi$
$608$	−8.38402	+	9.08395i	−0.340017	+	0.368403i
$609$	−1.28689	−	1.28689i	−0.0521475	−	0.0521475i
$610$	−23.7999	+	19.8532i	−0.963630	+	0.803833i
$611$	12.7253	+	3.86017i	0.514810	+	0.156166i
$612$	−1.15848	+	0.501746i	−0.0468286	+	0.0202819i
$613$	−1.11227	−	0.109549i	−0.0449241	−	0.00442463i	0.0755301	−	0.997144i	$-0.475935\pi$
$613$	−1.11227	−	0.109549i	−0.0449241	−	0.00442463i	−0.120454	+	0.992719i	$0.538435\pi$
$614$	−3.34521	−	7.89657i	−0.135002	−	0.318680i
$615$	−4.18660	+	21.0474i	−0.168820	+	0.848715i
$616$	0.633481	−	0.999238i	0.0255237	−	0.0402604i
$617$	−41.6216	+	8.27904i	−1.67562	+	0.333302i	−0.939239	−	0.343264i	$-0.888467\pi$
$617$	−41.6216	+	8.27904i	−1.67562	+	0.333302i	−0.736382	+	0.676566i	$0.763467\pi$
$618$	−6.64003	−	1.26558i	−0.267101	−	0.0509091i
$619$	−33.4343	−	17.8710i	−1.34384	−	0.718296i	−0.366587	−	0.930384i	$-0.619474\pi$
$619$	−33.4343	−	17.8710i	−1.34384	−	0.718296i	−0.977251	+	0.212087i	$0.931974\pi$
$620$	−0.774497	−	1.39477i	−0.0311045	−	0.0560153i
$621$	−4.78063	+	0.470851i	−0.191840	+	0.0188946i
$622$	3.15493	+	5.79041i	0.126501	+	0.232174i
$623$	4.72032	−	1.95522i	0.189116	−	0.0783343i
$624$	9.43381	−	15.1476i	0.377655	−	0.606390i
$625$	28.6702	+	11.8756i	1.14681	+	0.475023i
$626$	−1.46932	−	13.7854i	−0.0587260	−	0.550976i
$627$	0.864343	−	1.05320i	0.0345185	−	0.0420609i
$628$	9.33582	+	29.0902i	0.372540	+	1.16082i
$629$	0.593062	+	1.95506i	0.0236469	+	0.0779534i
$630$	−0.543468	−	2.62225i	−0.0216523	−	0.104473i
$631$	9.11950	−	13.6483i	0.363042	−	0.543330i	−0.604316	−	0.796745i	$-0.706554\pi$
$631$	9.11950	−	13.6483i	0.363042	−	0.543330i	0.967358	+	0.253414i	$0.0815536\pi$
$632$	5.95296	+	1.65071i	0.236796	+	0.0656615i
$633$	−7.50712	+	5.01610i	−0.298381	+	0.199372i
$634$	1.05888	−	0.00848145i	0.0420534	−	0.000336841i
$635$	35.2427	−	28.9229i	1.39856	−	1.14777i
$636$	2.74113	−	15.0355i	0.108693	−	0.596197i
$637$	13.7746	+	25.7705i	0.545770	+	1.02106i
$638$	1.11060	−	2.11843i	0.0439690	−	0.0838693i
$639$	5.74526			0.227279
$640$	−28.7711	+	13.8543i	−1.13728	+	0.547638i
$641$	11.3635			0.448833			0.224417	−	0.974493i	$-0.427952\pi$
$641$	11.3635			0.448833			0.224417	+	0.974493i	$0.427952\pi$
$642$	2.53645	−	4.83819i	0.100106	−	0.190948i
$643$	−8.12080	−	15.1929i	−0.320253	−	0.599151i	0.669355	−	0.742943i	$-0.266571\pi$
$643$	−8.12080	−	15.1929i	−0.320253	−	0.599151i	−0.989608	+	0.143791i	$0.954071\pi$
$644$	6.34117	+	1.15606i	0.249877	+	0.0455552i
$645$	27.7027	−	22.7350i	1.09079	−	0.895190i
$646$	1.95070	−	0.0156248i	0.0767493	−	0.000614750i
$647$	−30.7968	+	20.5777i	−1.21075	+	0.808994i	−0.986214	−	0.165472i	$-0.947085\pi$
$647$	−30.7968	+	20.5777i	−1.21075	+	0.808994i	−0.224531	+	0.974467i	$0.572085\pi$
$648$	2.46169	−	1.39286i	0.0967045	−	0.0547167i
$649$	4.47512	−	6.69748i	0.175664	−	0.262899i
$650$	−3.79830	−	18.3269i	−0.148982	−	0.718841i
$651$	−0.0550402	−	0.181443i	−0.00215720	−	0.00711132i
$652$	−18.6871	+	5.99721i	−0.731845	+	0.234869i
$653$	−4.94785	+	6.02897i	−0.193624	+	0.235932i	−0.860768	−	0.508997i	$-0.830017\pi$
$653$	−4.94785	+	6.02897i	−0.193624	+	0.235932i	0.667144	+	0.744929i	$0.267517\pi$
$654$	0.544044	+	5.10430i	0.0212738	+	0.199594i
$655$	−26.8641	−	11.1275i	−1.04967	−	0.434786i
$656$	30.0028	+	4.97463i	1.17141	+	0.194227i
$657$	13.4185	−	5.55814i	0.523507	−	0.216844i
$658$	−1.35310	−	2.48341i	−0.0527492	−	0.0968135i
$659$	−0.498731	+	0.0491207i	−0.0194278	+	0.00191347i	−0.107726	−	0.994181i	$-0.534357\pi$
$659$	−0.498731	+	0.0491207i	−0.0194278	+	0.00191347i	0.0882986	+	0.996094i	$0.471857\pi$
$660$	3.07702	−	1.70863i	0.119773	−	0.0665083i
$661$	19.2190	+	10.2728i	0.747534	+	0.399565i	0.800735	−	0.599019i	$-0.204442\pi$
$661$	19.2190	+	10.2728i	0.747534	+	0.399565i	−0.0532012	+	0.998584i	$0.516942\pi$
$662$	14.8905	+	2.83810i	0.578734	+	0.110306i
$663$	−2.76199	+	0.549393i	−0.107267	+	0.0213367i
$664$	1.09787	−	0.245941i	0.0426055	−	0.00954435i
$665$	−0.807288	+	4.05851i	−0.0313053	+	0.157382i
$666$	−1.78544	−	4.21463i	−0.0691844	−	0.163314i
$667$	12.9684	+	1.27727i	0.502138	+	0.0494562i
$668$	−17.2996	−	39.9430i	−0.669343	−	1.54544i
$669$	−18.9460	−	5.74721i	−0.732496	−	0.222200i
$670$	−12.0882	+	10.0836i	−0.467008	+	0.389565i
$671$	−3.42318	−	3.42318i	−0.132151	−	0.132151i
$672$	−3.68963	+	0.888840i	−0.142330	+	0.0342877i
$673$	−16.2221	+	16.2221i	−0.625315	+	0.625315i	−0.946886	−	0.321570i	$-0.895789\pi$
$673$	−16.2221	+	16.2221i	−0.625315	+	0.625315i	0.321570	+	0.946886i	$0.395789\pi$
$674$	−0.356013	+	3.93775i	−0.0137131	+	0.151677i
$675$	0.861138	−	2.83879i	0.0331452	−	0.109265i
$676$	9.60461	−	9.91737i	0.369408	−	0.381437i
$677$	−1.95184	+	19.8173i	−0.0750151	+	0.761641i	0.881932	+	0.471378i	$0.156243\pi$
$677$	−1.95184	+	19.8173i	−0.0750151	+	0.761641i	−0.956947	+	0.290264i	$0.906257\pi$
$678$	−4.50283	+	11.1219i	−0.172930	+	0.427135i
$679$	−12.0665	−	2.40017i	−0.463069	−	0.0921102i
$680$	4.70068	+	1.81603i	0.180263	+	0.0696416i
$681$	0.892677	+	4.48779i	0.0342075	+	0.171973i
$682$	0.206083	−	0.140101i	0.00789132	−	0.00536473i
$683$	−12.1685	+	22.7657i	−0.465616	+	0.871107i	0.534055	+	0.845450i	$0.320668\pi$
$683$	−12.1685	+	22.7657i	−0.465616	+	0.871107i	−0.999671	+	0.0256567i	$0.991832\pi$
$684$	−4.34203	+	0.498001i	−0.166022	+	0.0190415i
$685$	−1.38018	−	14.0132i	−0.0527338	−	0.535415i
$686$	3.63326	−	12.3320i	0.138719	−	0.470838i
$687$	6.33069	+	15.2836i	0.241531	+	0.583107i
$688$	−33.4607	−	38.2075i	−1.27568	−	1.45665i
$689$	13.0463	−	31.4965i	0.497024	−	1.19992i
$690$	14.9193	+	12.0453i	0.567968	+	0.458555i
$691$	33.7993	+	27.7384i	1.28579	+	1.05522i	0.995148	+	0.0983857i	$0.0313679\pi$
$691$	33.7993	+	27.7384i	1.28579	+	1.05522i	0.290639	+	0.956833i	$0.406132\pi$
$692$	−24.2216	+	20.5362i	−0.920768	+	0.780671i
$693$	0.400285	−	0.121425i	0.0152056	−	0.00461255i
$694$	−7.76142	+	11.8196i	−0.294619	+	0.448668i
$695$	28.3029	+	18.9114i	1.07359	+	0.717350i
$696$	−7.28663	+	2.40302i	−0.276199	+	0.0910862i
$697$	−2.66636	−	3.99049i	−0.100996	−	0.151151i
$698$	−8.36790	+	8.50303i	−0.316730	+	0.321844i
$699$	2.50730	+	3.05515i	0.0948347	+	0.115556i
$700$	−2.15814	+	3.34465i	−0.0815699	+	0.126416i
$701$	39.4615	−	21.0926i	1.49044	−	0.796657i	0.493130	−	0.869956i	$-0.335853\pi$
$701$	39.4615	−	21.0926i	1.49044	−	0.796657i	0.997310	+	0.0732993i	$0.0233528\pi$
$702$	6.02266	−	1.87976i	0.227311	−	0.0709470i
$703$			7.07274i			0.266753i
$704$	−2.55988	−	4.28089i	−0.0964792	−	0.161342i
$705$		−	8.41315i		−	0.316858i
$706$	7.16839	+	22.9672i	0.269786	+	0.864380i
$707$	−8.17755	+	4.37099i	−0.307548	+	0.164388i
$708$	−25.2581	+	5.44616i	−0.949258	+	0.204679i
$709$	−27.7283	−	33.7870i	−1.04136	−	1.26890i	−0.962289	−	0.272028i	$-0.912306\pi$
$709$	−27.7283	−	33.7870i	−1.04136	−	1.26890i	−0.0790681	−	0.996869i	$-0.525194\pi$
$710$	−16.3454	−	16.0856i	−0.613432	−	0.603683i
$711$	1.21342	+	1.81602i	0.0455070	+	0.0681060i
$712$	1.59563	−	21.4807i	0.0597988	−	0.805025i
$713$	1.12883	+	0.754257i	0.0422748	+	0.0282471i
$714$	0.500624	+	0.328737i	0.0187354	+	0.0123027i
$715$	7.51285	−	2.27900i	0.280965	−	0.0852297i
$716$	1.48973	−	18.0923i	0.0556739	−	0.676141i
$717$	−21.0664	−	17.2888i	−0.786740	−	0.645661i
$718$	−4.79683	+	5.94137i	−0.179016	+	0.221730i
$719$	−11.1999	+	27.0390i	−0.417686	+	1.00838i	0.565331	+	0.824864i	$0.308749\pi$
$719$	−11.1999	+	27.0390i	−0.417686	+	1.00838i	−0.983016	+	0.183518i	$0.941251\pi$
$720$	−10.9033	−	2.92955i	−0.406342	−	0.109178i
$721$	1.22716	+	2.96262i	0.0457017	+	0.110334i
$722$	−19.2967	−	5.68521i	−0.718148	−	0.211582i
$723$	2.37695	+	24.1336i	0.0883999	+	0.897539i
$724$	11.7946	+	9.36748i	0.438344	+	0.348140i
$725$	−3.79346	+	7.09706i	−0.140885	+	0.263578i
$726$	−8.43689	−	12.4104i	−0.313122	−	0.460591i
$727$	−4.42272	−	22.2345i	−0.164030	−	0.824633i	−0.971922	−	0.235303i	$-0.924392\pi$
$727$	−4.42272	−	22.2345i	−0.164030	−	0.824633i	0.807892	−	0.589330i	$-0.200608\pi$
$728$	−8.46322	+	0.203402i	−0.313668	+	0.00753858i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−53.7378	−	21.7563i	−1.98892	−	0.805236i
$731$	−0.785585	+	7.97618i	−0.0290559	+	0.295010i
$732$	0.248757	+	15.5272i	0.00919431	+	0.573901i
$733$	5.18915	−	17.1063i	0.191666	−	0.631837i	−0.807456	−	0.589928i	$-0.799156\pi$
$733$	5.18915	−	17.1063i	0.191666	−	0.631837i	0.999121	−	0.0419089i	$-0.0133439\pi$
$734$	−12.5500	−	1.13465i	−0.463230	−	0.0418808i
$735$	13.0724	−	13.0724i	0.482181	−	0.482181i
$736$	16.3843	−	21.6793i	0.603933	−	0.799110i
$737$	−1.73867	−	1.73867i	−0.0640446	−	0.0640446i
$738$	6.88761	+	8.25682i	0.253536	+	0.303938i
$739$	−7.57865	−	2.29896i	−0.278785	−	0.0845686i	0.147796	−	0.989018i	$-0.452782\pi$
$739$	−7.57865	−	2.29896i	−0.278785	−	0.0845686i	−0.426581	+	0.904449i	$0.640282\pi$
$740$	−6.72054	+	16.9896i	−0.247052	+	0.624550i
$741$	−9.70204	−	0.955568i	−0.356413	−	0.0351037i
$742$	−6.67604	+	2.82816i	−0.245085	+	0.103825i
$743$	−2.93208	+	14.7406i	−0.107568	+	0.540779i	0.888994	+	0.457919i	$0.151405\pi$
$743$	−2.93208	+	14.7406i	−0.107568	+	0.540779i	−0.996561	+	0.0828592i	$0.973595\pi$
$744$	−0.787523	−	0.137066i	−0.0288720	−	0.00502508i
$745$	51.1314	−	10.1707i	1.87331	−	0.372624i
$746$	−9.27355	+	48.6548i	−0.339529	+	1.78138i
$747$	0.350806	+	0.187510i	0.0128353	+	0.00686062i
$748$	−0.216396	+	0.756798i	−0.00791223	+	0.0276713i
$749$	−2.57904	+	0.254013i	−0.0942360	+	0.00928144i
$750$	7.12755	−	3.88347i	0.260261	−	0.141804i
$751$	−8.57012	+	3.54986i	−0.312728	+	0.129536i	−0.533527	−	0.845783i	$-0.679134\pi$
$751$	−8.57012	+	3.54986i	−0.312728	+	0.129536i	0.220799	+	0.975319i	$0.429134\pi$
$752$	−11.9168	+	0.381931i	−0.434562	+	0.0139276i
$753$	−27.7651	−	11.5007i	−1.01182	−	0.419108i
$754$	−17.0185	+	1.81392i	−0.619777	+	0.0660591i
$755$	23.1907	−	28.2579i	0.843995	−	1.02841i
$756$	−1.19334	−	0.613482i	−0.0434014	−	0.0223121i
$757$	−8.68295	−	28.6239i	−0.315587	−	1.04035i	−0.961007	−	0.276524i	$-0.910818\pi$
$757$	−8.68295	−	28.6239i	−0.315587	−	1.04035i	0.645420	−	0.763828i	$-0.276682\pi$
$758$	46.9166	−	9.72359i	1.70409	−	0.353177i
$759$	−1.66398	+	2.49032i	−0.0603985	+	0.0903928i
$760$	13.7475	+	10.7400i	0.498673	+	0.389582i
$761$	−26.7430	+	17.8691i	−0.969432	+	0.647754i	−0.936116	−	0.351691i	$-0.885607\pi$
$761$	−26.7430	+	17.8691i	−0.969432	+	0.647754i	−0.0333161	+	0.999445i	$0.510607\pi$
$762$	−0.182968	−	22.8428i	−0.00662821	−	0.827508i
$763$	1.88242	−	1.54486i	0.0681483	−	0.0559278i
$764$	33.6064	−	23.2423i	1.21584	−	0.840877i
$765$	0.839866	+	1.57128i	0.0303654	+	0.0568097i
$766$	−30.5027	−	15.9913i	−1.10211	−	0.577788i
$767$	−57.6365			−2.08113
$768$	−3.65460	+	15.5770i	−0.131874	+	0.562088i
$769$	42.0237			1.51541			0.757707	−	0.652595i	$-0.226320\pi$
$769$	42.0237			1.51541			0.757707	+	0.652595i	$0.226320\pi$
$770$	−1.47878	−	0.775263i	−0.0532917	−	0.0279385i
$771$	9.25522	+	17.3153i	0.333318	+	0.623595i
$772$	9.17001	−	6.34200i	0.330036	−	0.228254i
$773$	−4.68902	+	3.84818i	−0.168652	+	0.138410i	−0.714934	−	0.699192i	$-0.753543\pi$
$773$	−4.68902	+	3.84818i	−0.168652	+	0.138410i	0.546281	+	0.837602i	$0.316043\pi$
$774$	−0.143823	−	17.9557i	−0.00516960	−	0.645406i
$775$	−0.697097	+	0.465786i	−0.0250405	+	0.0167315i
$776$	−31.9315	+	40.8731i	−1.14627	+	1.46726i
$777$	−1.20638	+	1.80547i	−0.0432785	+	0.0647709i
$778$	10.2536	−	2.12508i	0.367609	−	0.0761879i
$779$	−4.82298	−	15.8992i	−0.172801	−	0.569650i
$780$	−22.3975	−	11.5143i	−0.801961	−	0.412279i
$781$	2.27245	−	2.76899i	0.0813148	−	0.0990824i
$782$	−4.26415	+	0.454496i	−0.152486	+	0.0162528i
$783$	−2.50620	−	1.03810i	−0.0895642	−	0.0370987i
$784$	−19.1098	−	17.9229i	−0.682494	−	0.640105i
$785$	39.8339	−	16.4997i	1.42173	−	0.588901i
$786$	−12.7935	+	6.97059i	−0.456330	+	0.248633i
$787$	−10.8878	+	1.07235i	−0.388108	+	0.0382253i	−0.290190	−	0.956969i	$-0.593718\pi$
$787$	−10.8878	+	1.07235i	−0.388108	+	0.0382253i	−0.0979184	+	0.995194i	$0.531218\pi$
$788$	−4.83168	+	16.8977i	−0.172121	+	0.601957i
$789$	−0.0199801	−	0.0106796i	−0.000711309	−	0.000380203i
$790$	1.63228	−	8.56396i	0.0580740	−	0.304692i
$791$	5.58286	−	1.11050i	0.198504	−	0.0394848i
$792$	0.302383	−	1.73737i	0.0107447	−	0.0617346i
$793$	−6.75792	+	33.9744i	−0.239981	+	1.20646i
$794$	−17.6623	+	7.48225i	−0.626811	+	0.265535i
$795$	−21.4648	−	2.11410i	−0.761277	−	0.0749793i
$796$	−14.6737	+	37.0954i	−0.520097	+	1.31481i
$797$	−4.08883	−	1.24033i	−0.144834	−	0.0439349i	0.217035	−	0.976164i	$-0.430361\pi$
$797$	−4.08883	−	1.24033i	−0.144834	−	0.0439349i	−0.361869	+	0.932229i	$0.617861\pi$
$798$	1.32812	+	1.59214i	0.0470148	+	0.0563610i
$799$	1.33045	+	1.33045i	0.0470679	+	0.0470679i
$800$	8.49681	+	14.4711i	0.300408	+	0.511631i
$801$	5.38498	−	5.38498i	0.190269	−	0.190269i
$802$	−26.8649	−	2.42886i	−0.948634	−	0.0857662i
$803$	2.62870	−	8.66566i	0.0927648	−	0.305804i
$804$	0.126346	+	7.88640i	0.00445587	+	0.278132i
$805$	0.891612	−	9.05268i	0.0314252	−	0.319065i
$806$	−1.65277	−	0.669141i	−0.0582163	−	0.0235695i
$807$	−16.8570	−	3.35306i	−0.593394	−	0.118033i
$808$	0.939237	+	39.0801i	0.0330422	+	1.37483i
$809$	1.59333	+	8.01023i	0.0560186	+	0.281625i	0.998634	−	0.0522568i	$-0.0166414\pi$
$809$	1.59333	+	8.01023i	0.0560186	+	0.281625i	−0.942615	+	0.333882i	$0.891641\pi$
$810$	−2.24414	−	3.30104i	−0.0788510	−	0.115987i
$811$	14.1948	−	26.5567i	0.498448	−	0.932531i	−0.499363	−	0.866393i	$-0.666432\pi$
$811$	14.1948	−	26.5567i	0.498448	−	0.932531i	0.997811	−	0.0661374i	$-0.0210676\pi$
$812$	2.85030	+	2.26375i	0.100026	+	0.0794421i
$813$	−0.863856	−	8.77088i	−0.0302968	−	0.307608i
$814$	−2.73749	−	0.806523i	−0.0959491	−	0.0282686i
$815$	10.5992	+	25.5888i	0.371274	+	0.896335i
$816$	2.18752	−	1.26096i	0.0765784	−	0.0441425i
$817$	−10.6180	+	25.6341i	−0.371477	+	0.896824i
$818$	−1.41385	+	1.75120i	−0.0494341	+	0.0612292i
$819$	−2.31367	−	1.89878i	−0.0808462	−	0.0663487i
$820$	3.52211	−	42.7748i	0.122997	−	1.49376i
$821$	2.40431	−	0.729341i	0.0839111	−	0.0254542i	−0.248050	−	0.968747i	$-0.579790\pi$
$821$	2.40431	−	0.729341i	0.0839111	−	0.0254542i	0.331961	+	0.943293i	$0.392290\pi$
$822$	−5.89744	−	3.87258i	−0.205697	−	0.135072i
$823$	−12.2330	−	8.17380i	−0.426414	−	0.284921i	0.323788	−	0.946130i	$-0.395044\pi$
$823$	−12.2330	−	8.17380i	−0.426414	−	0.284921i	−0.750202	+	0.661209i	$0.770044\pi$
$824$	13.4820	+	1.00147i	0.469667	+	0.0348877i
$825$	−1.02758	−	1.53788i	−0.0357756	−	0.0535420i
$826$	8.73669	+	8.59784i	0.303988	+	0.299157i
$827$	4.36463	+	5.31831i	0.151773	+	0.184936i	0.843346	−	0.537370i	$-0.180582\pi$
$827$	4.36463	+	5.31831i	0.151773	+	0.184936i	−0.691574	+	0.722306i	$0.743082\pi$
$828$	9.39169	−	2.02504i	0.326384	−	0.0703750i
$829$	3.25455	−	1.73959i	0.113035	−	0.0604185i	−0.413910	−	0.910318i	$-0.635837\pi$
$829$	3.25455	−	1.73959i	0.113035	−	0.0604185i	0.526945	+	0.849899i	$0.323337\pi$
$830$	−0.473059	−	1.51566i	−0.0164201	−	0.0526092i
$831$			19.9964i			0.693668i
$832$	−15.2927	+	32.2478i	−0.530180	+	1.11799i
$833$			4.13450i			0.143252i
$834$	16.2809	−	5.08152i	0.563763	−	0.175959i
$835$	−54.1760	+	28.9577i	−1.87484	+	1.00212i
$836$	−1.47741	+	2.28967i	−0.0510973	+	0.0791898i
$837$	−0.179290	−	0.218466i	−0.00619718	−	0.00755129i
$838$	27.5331	−	27.9778i	0.951117	−	0.966476i
$839$	−6.51322	−	9.74772i	−0.224861	−	0.336529i	0.701835	−	0.712339i	$-0.252364\pi$
$839$	−6.51322	−	9.74772i	−0.224861	−	0.336529i	−0.926696	+	0.375811i	$0.877364\pi$
$840$	1.67745	+	5.08649i	0.0578774	+	0.175501i
$841$	−17.9941	−	12.0233i	−0.620486	−	0.414595i
$842$	21.0200	−	32.0108i	0.724398	−	1.10317i
$843$	12.4861	−	3.78762i	0.430044	−	0.130453i
$844$	13.7733	−	11.6777i	0.474098	−	0.401962i
$845$	−15.0610	−	12.3603i	−0.518115	−	0.425206i
$846$	−3.27987	−	2.64804i	−0.112764	−	0.0910414i
$847$	−2.72436	+	6.57718i	−0.0936100	+	0.225995i
$848$	−2.02009	+	30.4998i	−0.0693700	+	1.04737i
$849$	−11.1742	−	26.9768i	−0.383496	−	0.925842i
$850$	0.748412	−	2.54025i	0.0256703	−	0.0871300i
$851$	−1.52395	−	15.4729i	−0.0522403	−	0.530405i
$852$	−11.4157	+	1.30930i	−0.391095	+	0.0448559i
$853$	10.5772	−	19.7885i	0.362156	−	0.677545i	−0.633181	−	0.774003i	$-0.718251\pi$
$853$	10.5772	−	19.7885i	0.362156	−	0.677545i	0.995337	+	0.0964579i	$0.0307513\pi$
$854$	6.09246	−	4.14182i	0.208480	−	0.141730i
$855$	1.20329	+	6.04936i	0.0411517	+	0.206884i
$856$	−3.93728	+	10.1914i	−0.134574	+	0.348335i
$857$	48.5619	+	9.65956i	1.65884	+	0.329964i	0.933542	−	0.358468i	$-0.116701\pi$
$857$	48.5619	+	9.65956i	1.65884	+	0.329964i	0.725301	+	0.688432i	$0.241701\pi$
$858$	1.47620	−	3.64620i	0.0503967	−	0.124479i
$859$	−3.58480	+	36.3971i	−0.122312	+	1.24185i	0.716561	+	0.697524i	$0.245715\pi$
$859$	−3.58480	+	36.3971i	−0.122312	+	1.24185i	−0.838873	+	0.544327i	$0.816785\pi$
$860$	−49.8634	+	51.4871i	−1.70033	+	1.75570i
$861$	1.48072	−	4.88127i	0.0504627	−	0.166353i
$862$	−0.907010	+	10.0322i	−0.0308929	+	0.341697i
$863$	33.9177	−	33.9177i	1.15457	−	1.15457i	0.168948	−	0.985625i	$-0.445963\pi$
$863$	33.9177	−	33.9177i	1.15457	−	1.15457i	0.985625	−	0.168948i	$-0.0540370\pi$
$864$	−4.57390	+	3.32858i	−0.155607	+	0.113240i
$865$	31.6892	+	31.6892i	1.07747	+	1.07747i
$866$	−12.6844	+	10.5810i	−0.431034	+	0.359557i
$867$	15.8867	+	4.81917i	0.539540	+	0.163668i
$868$	0.150713	+	0.347980i	0.00511553	+	0.0118112i
$869$	1.35520	+	0.133476i	0.0459721	+	0.00452786i
$870$	4.22370	+	9.97029i	0.143197	+	0.338025i
$871$	−3.43241	+	17.2559i	−0.116303	+	0.584693i
$872$	−2.24423	−	10.0181i	−0.0759993	−	0.339257i
$873$	−17.9855	+	3.57755i	−0.608718	+	0.121082i
$874$	−14.5831	−	2.77952i	−0.493280	−	0.0940185i
$875$	−3.39594	−	1.81517i	−0.114804	−	0.0613639i
$876$	−25.3956	+	14.1019i	−0.858039	+	0.476458i
$877$	37.0399	−	3.64811i	1.25075	−	0.123188i	0.549127	−	0.835739i	$-0.314960\pi$
$877$	37.0399	−	3.64811i	1.25075	−	0.123188i	0.701621	+	0.712551i	$0.252460\pi$
$878$	−25.2288	−	46.3038i	−0.851431	−	1.56268i
$879$	−16.2374	+	6.72577i	−0.547676	+	0.226855i
$880$	−5.72457	+	4.09623i	−0.192975	+	0.138084i
$881$	−22.9340	−	9.49958i	−0.772667	−	0.320049i	−0.0387146	−	0.999250i	$-0.512326\pi$
$881$	−22.9340	−	9.49958i	−0.772667	−	0.320049i	−0.733952	+	0.679201i	$0.762326\pi$
$882$	−0.981734	−	9.21078i	−0.0330567	−	0.310143i
$883$	−12.7590	+	15.5469i	−0.429376	+	0.523196i	−0.942089	−	0.335364i	$-0.891141\pi$
$883$	−12.7590	+	15.5469i	−0.429376	+	0.523196i	0.512712	+	0.858560i	$0.328641\pi$
$884$	5.36279	−	1.72107i	0.180370	−	0.0578857i
$885$	10.5852	+	34.8946i	0.355816	+	1.17297i
$886$	4.23070	+	20.4133i	0.142133	+	0.685797i
$887$	0.532845	−	0.797459i	0.0178912	−	0.0267760i	−0.822416	−	0.568886i	$-0.807374\pi$
$887$	0.532845	−	0.797459i	0.0178912	−	0.0267760i	0.840307	+	0.542110i	$0.182374\pi$
$888$	4.50811	+	7.96748i	0.151282	+	0.267371i
$889$	−9.01057	+	6.02067i	−0.302205	+	0.201927i
$890$	−30.3973	+	0.243478i	−1.01892	+	0.00816139i
$891$	0.481961	−	0.395535i	0.0161463	−	0.0132509i
$892$	38.9550	+	7.10191i	1.30431	+	0.237790i
$893$	3.07052	+	5.74453i	0.102751	+	0.192233i
$894$	12.1286	−	23.1348i	0.405640	−	0.773742i
$895$	−25.6192			−0.856355
$896$	7.12863	−	2.60694i	0.238151	−	0.0870917i
$897$	21.4309			0.715557
$898$	11.2913	−	21.5377i	0.376794	−	0.718721i
$899$	0.361398	+	0.676128i	0.0120533	+	0.0225501i
$900$	−1.06412	+	5.83685i	−0.0354707	+	0.194562i
$901$	3.72874	−	3.06010i	0.124222	−	0.101947i
$902$	6.70376	−	0.0536961i	0.223211	−	0.00178788i
$903$	−7.08281	+	4.73258i	−0.235701	+	0.157491i
$904$	6.41241	−	23.1252i	0.213273	−	0.769131i
$905$	11.8093	−	17.6739i	0.392555	−	0.587501i
$906$	−3.71708	−	17.9350i	−0.123492	−	0.595852i
$907$	−3.25695	−	10.7367i	−0.108145	−	0.356507i	0.886119	−	0.463458i	$-0.153391\pi$
$907$	−3.25695	−	10.7367i	−0.108145	−	0.356507i	−0.994264	+	0.106950i	$0.965891\pi$
$908$	−2.79646	−	8.71369i	−0.0928038	−	0.289174i
$909$	−8.76788	+	10.6837i	−0.290812	+	0.354356i
$910$	1.26622	+	11.8799i	0.0419749	+	0.393815i
$911$	−32.6622	−	13.5291i	−1.08215	−	0.448240i	−0.230885	−	0.972981i	$-0.574162\pi$
$911$	−32.6622	−	13.5291i	−1.08215	−	0.448240i	−0.851262	+	0.524741i	$0.824162\pi$
$912$	8.51401	−	1.97903i	0.281927	−	0.0655322i
$913$	0.229128	−	0.0949081i	0.00758304	−	0.00314100i
$914$	−9.29877	−	17.0666i	−0.307576	−	0.564511i
$915$	21.8101	−	2.14810i	0.721018	−	0.0710141i
$916$	−16.0619	−	28.9255i	−0.530701	−	0.955725i
$917$	6.09550	+	3.25811i	0.201291	+	0.107592i
$918$	0.876911	+	0.167138i	0.0289424	+	0.00551638i
$919$	−14.8469	+	2.95324i	−0.489756	+	0.0974184i	−0.433790	−	0.901014i	$-0.642824\pi$
$919$	−14.8469	+	2.95324i	−0.489756	+	0.0974184i	−0.0559661	+	0.998433i	$0.517824\pi$
$920$	−32.3893	−	20.5336i	−1.06784	−	0.676974i
$921$	−1.18304	+	5.94756i	−0.0389826	+	0.195979i
$922$	−21.2227	−	50.0974i	−0.698933	−	1.64987i
$923$	−25.5078	−	2.51230i	−0.839598	−	0.0826932i
$924$	−0.767683	+	0.332490i	−0.0252549	+	0.0109381i
$925$	9.18798	+	2.78714i	0.302099	+	0.0916407i
$926$	−5.91781	+	4.93647i	−0.194471	+	0.162223i
$927$	3.37978	+	3.37978i	0.111007	+	0.111007i
$928$	13.9307	−	6.43530i	0.457298	−	0.211249i
$929$	5.39321	−	5.39321i	0.176945	−	0.176945i	−0.613077	−	0.790023i	$-0.710069\pi$
$929$	5.39321	−	5.39321i	0.176945	−	0.176945i	0.790023	+	0.613077i	$0.210069\pi$
$930$	−0.101578	+	1.12352i	−0.00333086	+	0.0368416i
$931$	−4.15489	+	13.6968i	−0.136171	+	0.448895i
$932$	−5.67818	−	5.49911i	−0.185995	−	0.180129i
$933$	0.457029	−	4.64030i	0.0149625	−	0.151916i
$934$	17.5100	−	43.2494i	0.572944	−	1.41516i
$935$	1.08949	+	0.216713i	0.0356302	+	0.00708729i
$936$	−11.5385	+	5.10755i	−0.377147	+	0.166946i
$937$	7.57882	+	38.1013i	0.247589	+	1.24472i	0.881826	+	0.471576i	$0.156315\pi$
$937$	7.57882	+	38.1013i	0.247589	+	1.24472i	−0.634236	+	0.773139i	$0.718685\pi$
$938$	3.09442	−	2.10367i	0.101036	−	0.0686872i
$939$	−4.62109	+	8.64546i	−0.150804	+	0.282134i
$940$	1.91729	+	16.7167i	0.0625351	+	0.545239i
$941$	−0.00715176	−	0.0726131i	−0.000233141	−	0.00236712i	0.995067	−	0.0992006i	$-0.0316286\pi$
$941$	−0.00715176	−	0.0726131i	−0.000233141	−	0.00236712i	−0.995301	+	0.0968335i	$0.969129\pi$
$942$	6.10529	−	20.7225i	0.198921	−	0.675176i
$943$	13.9769	+	33.7433i	0.455152	+	1.09883i
$944$	48.9460	−	16.5775i	1.59306	−	0.539551i
$945$	−0.724655	+	1.74947i	−0.0235730	+	0.0569104i
$946$	−8.71085	−	7.03281i	−0.283214	−	0.228656i
$947$	0.950645	+	0.780174i	0.0308918	+	0.0253523i	0.649713	−	0.760180i	$-0.274889\pi$
$947$	0.950645	+	0.780174i	0.0308918	+	0.0253523i	−0.618821	+	0.785532i	$0.712389\pi$
$948$	−2.82490	−	3.33185i	−0.0917485	−	0.108213i
$949$	−62.0060	+	18.8093i	−2.01280	+	0.610576i
$950$	5.03213	−	7.66328i	0.163264	−	0.248630i
$951$	−0.622574	−	0.415991i	−0.0201884	−	0.0134894i
$952$	−1.06964	−	0.539104i	−0.0346674	−	0.0174725i
$953$	16.3969	+	24.5398i	0.531149	+	0.794921i	0.995894	−	0.0905238i	$-0.0288541\pi$
$953$	16.3969	+	24.5398i	0.531149	+	0.794921i	−0.464745	+	0.885444i	$0.653854\pi$
$954$	−7.58022	+	7.70263i	−0.245419	+	0.249382i
$955$	−36.5821	−	44.5754i	−1.18377	−	1.44243i
$956$	45.7984	+	29.5514i	1.48123	+	0.955762i
$957$	−1.49161	+	0.797285i	−0.0482171	+	0.0257726i
$958$	−36.0698	+	11.2579i	−1.16536	+	0.363727i
$959$			3.34700i			0.108080i
$960$	22.3322	+	3.33617i	0.720769	+	0.107674i
$961$		−	30.9201i		−	0.997423i
$962$	6.08400	+	19.4928i	0.196156	+	0.628474i
$963$	−3.40664	+	1.82089i	−0.109778	+	0.0586773i
$964$	−10.2228	−	47.4112i	−0.329255	−	1.52701i
$965$	−9.98197	−	12.1631i	−0.321331	−	0.391543i
$966$	−3.24855	−	3.19693i	−0.104520	−	0.102859i
$967$	−23.7307	−	35.5155i	−0.763129	−	1.14210i	−0.985917	−	0.167236i	$-0.946516\pi$
$967$	−23.7307	−	35.5155i	−0.763129	−	1.14210i	0.222788	−	0.974867i	$-0.428484\pi$
$968$	19.5921	+	22.7363i	0.629714	+	0.730774i
$969$	−1.14693	−	0.766353i	−0.0368446	−	0.0246188i
$970$	61.1857	+	40.1778i	1.96455	+	1.29003i
$971$	−26.2185	+	7.95328i	−0.841390	+	0.255233i	−0.681423	−	0.731889i	$-0.738639\pi$
$971$	−26.2185	+	7.95328i	−0.841390	+	0.255233i	−0.159967	+	0.987122i	$0.551139\pi$
$972$	−1.99325	−	0.164126i	−0.0639337	−	0.00526435i
$973$	−6.25450	−	5.13294i	−0.200510	−	0.164554i
$974$	−3.01871	+	3.73898i	−0.0967256	+	0.119805i
$975$	−5.06462	+	12.2271i	−0.162198	+	0.391580i
$976$	−4.03280	−	30.7954i	−0.129087	−	0.985738i
$977$	14.9705	+	36.1420i	0.478949	+	1.15629i	0.960102	+	0.279649i	$0.0902181\pi$
$977$	14.9705	+	36.1420i	0.478949	+	1.15629i	−0.481153	+	0.876636i	$0.659782\pi$
$978$	13.3119	+	3.92196i	0.425667	+	0.125410i
$979$	−0.465401	−	4.72530i	−0.0148743	−	0.151021i
$980$	−22.9953	+	28.9535i	−0.734559	+	0.924886i
$981$	1.71104	−	3.20114i	0.0546294	−	0.102204i
$982$	−9.18451	−	13.5101i	−0.293089	−	0.431124i
$983$	2.09481	+	10.5313i	0.0668141	+	0.335897i	0.999706	−	0.0242601i	$-0.00772298\pi$
$983$	2.09481	+	10.5313i	0.0668141	+	0.335897i	−0.932892	+	0.360157i	$0.882723\pi$
$984$	−15.5672	−	14.8365i	−0.496263	−	0.472969i
$985$	24.3261	+	4.83876i	0.775094	+	0.154176i
$986$	−2.24463	−	0.908761i	−0.0714835	−	0.0289408i
$987$	−0.196012	+	1.99015i	−0.00623914	+	0.0633471i
$988$	19.4955	−	0.312332i	0.620234	−	0.00993659i
$989$	17.7055	−	58.3672i	0.563002	−	1.85597i
$990$	−2.47861	−	0.224092i	−0.0787754	−	0.00712211i
$991$	15.4767	−	15.4767i	0.491634	−	0.491634i	−0.417187	−	0.908821i	$-0.636984\pi$
$991$	15.4767	−	15.4767i	0.491634	−	0.491634i	0.908821	+	0.417187i	$0.136984\pi$
$992$	1.59602	+	0.0928758i	0.0506738	+	0.00294881i
$993$	−7.57926	−	7.57926i	−0.240521	−	0.240521i
$994$	3.49177	+	4.18591i	0.110752	+	0.132769i
$995$	53.8738	+	16.3424i	1.70791	+	0.518090i
$996$	−0.739774	−	0.292631i	−0.0234406	−	0.00927236i
$997$	30.9247	+	3.04582i	0.979395	+	0.0964620i	0.575027	−	0.818134i	$-0.304991\pi$
$997$	30.9247	+	3.04582i	0.979395	+	0.0964620i	0.404368	+	0.914596i	$0.367491\pi$
$998$	−31.3062	+	13.2622i	−0.990981	+	0.419808i
$999$	−0.631426	+	3.17439i	−0.0199774	+	0.100433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.28	✓	512
128.45	even	32	inner	384.2.v.a.301.28	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.28	✓	512	1.1	even	1	trivial
384.2.v.a.301.28	yes	512	128.45	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25252 + 0.656645i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(1.13764 + 1.64493i) q^{4} +(2.18182 - 1.79058i) q^{5} +(-0.0113273 - 1.41417i) q^{6} +(-0.557832 + 0.372732i) q^{7} +(0.344785 + 2.80733i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.25252 + 0.656645i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(1.13764 + 1.64493i) q^{4} +(2.18182 - 1.79058i) q^{5} +(-0.0113273 - 1.41417i) q^{6} +(-0.557832 + 0.372732i) q^{7} +(0.344785 + 2.80733i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(3.90856 - 0.810059i) q^{10} +(0.180988 + 0.596639i) q^{11} +(0.914418 - 1.77872i) q^{12} +(2.83020 - 3.44861i) q^{13} +(-0.943451 + 0.100558i) q^{14} +(-2.60765 - 1.08013i) q^{15} +(-1.41157 + 3.74266i) q^{16} +(0.583182 - 0.241562i) q^{17} +(-1.24185 + 0.676624i) q^{18} +(2.17473 - 0.214192i) q^{19} +(5.42749 + 1.55192i) q^{20} +(0.591680 + 0.316260i) q^{21} +(-0.165087 + 0.866150i) q^{22} +(-4.71146 + 0.937168i) q^{23} +(2.31332 - 1.62744i) q^{24} +(0.578741 - 2.90953i) q^{25} +(5.80941 - 2.46103i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-1.24773 - 0.493561i) q^{28} +(-2.59588 - 0.787452i) q^{29} +(-2.55689 - 3.06519i) q^{30} +(-0.199841 - 0.199841i) q^{31} +(-4.22562 + 3.76087i) q^{32} +(0.440871 - 0.440871i) q^{33} +(0.889071 + 0.0803811i) q^{34} +(-0.549688 + 1.81208i) q^{35} +(-1.99974 + 0.0320373i) q^{36} +(-0.317241 + 3.22100i) q^{37} +(2.86455 + 1.15974i) q^{38} +(-4.37555 - 0.870351i) q^{39} +(5.77901 + 5.50775i) q^{40} +(-1.48329 - 7.45701i) q^{41} +(0.533424 + 0.784647i) q^{42} +(-5.98534 + 11.1978i) q^{43} +(-0.775528 + 0.976470i) q^{44} +(0.276654 + 2.80891i) q^{45} +(-6.51661 - 1.91993i) q^{46} +(1.14068 + 2.75384i) q^{47} +(3.96614 - 0.519383i) q^{48} +(-2.50654 + 6.05131i) q^{49} +(2.63541 - 3.26423i) q^{50} +(-0.487949 - 0.400449i) q^{51} +(8.89245 + 0.732211i) q^{52} +(7.31262 - 2.21826i) q^{53} +(1.18213 + 0.776251i) q^{54} +(1.46321 + 0.977688i) q^{55} +(-1.23871 - 1.43751i) q^{56} +(-1.21406 - 1.81697i) q^{57} +(-2.73433 - 2.69088i) q^{58} +(-8.19591 - 9.98675i) q^{59} +(-1.18983 - 5.51819i) q^{60} +(-6.84776 + 3.66020i) q^{61} +(-0.119081 - 0.381529i) q^{62} -0.670899i q^{63} +(-7.76225 + 1.93585i) q^{64} -12.5920i q^{65} +(0.841697 - 0.262706i) q^{66} +(-3.47804 + 1.85905i) q^{67} +(1.06080 + 0.684483i) q^{68} +(3.04748 + 3.71336i) q^{69} +(-1.87839 + 1.90872i) q^{70} +(-3.19190 - 4.77701i) q^{71} +(-2.52577 - 1.27299i) q^{72} +(-12.0764 - 8.06917i) q^{73} +(-2.51240 + 3.82607i) q^{74} +(-2.83879 + 0.861138i) q^{75} +(2.82638 + 3.33359i) q^{76} +(-0.323347 - 0.265364i) q^{77} +(-4.90897 - 3.96332i) q^{78} +(0.835822 - 2.01785i) q^{79} +(3.62172 + 10.6933i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(3.03875 - 10.3141i) q^{82} +(-0.0389887 - 0.395859i) q^{83} +(0.152893 + 1.33306i) q^{84} +(0.839866 - 1.57128i) q^{85} +(-14.8497 + 10.0953i) q^{86} +(0.529220 + 2.66057i) q^{87} +(-1.61256 + 0.713807i) q^{88} +(-7.46918 - 1.48571i) q^{89} +(-1.49794 + 3.69990i) q^{90} +(-0.293372 + 2.97865i) q^{91} +(-6.90150 - 6.68385i) q^{92} +(-0.0820394 + 0.270448i) q^{93} +(-0.379567 + 4.19828i) q^{94} +(4.36134 - 4.36134i) q^{95} +(5.30873 + 1.95380i) q^{96} +(12.9669 + 12.9669i) q^{97} +(-7.11306 + 5.93352i) q^{98} +(-0.596639 - 0.180988i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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