LMFDB - Embedded newform 384.2.v.a.13.7

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			13.7
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06403 - 0.931580i) q^{2} +(0.290285 + 0.956940i) q^{3} +(0.264317 + 1.98246i) q^{4} +(-0.231940 - 2.35493i) q^{5} +(0.582595 - 1.28864i) q^{6} +(0.430118 - 0.643717i) q^{7} +(1.56558 - 2.35563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.06403 - 0.931580i) q^{2} +(0.290285 + 0.956940i) q^{3} +(0.264317 + 1.98246i) q^{4} +(-0.231940 - 2.35493i) q^{5} +(0.582595 - 1.28864i) q^{6} +(0.430118 - 0.643717i) q^{7} +(1.56558 - 2.35563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-1.94701 + 2.72179i) q^{10} +(2.50304 - 1.33790i) q^{11} +(-1.82037 + 0.828413i) q^{12} +(-2.62518 - 0.258558i) q^{13} +(-1.05733 + 0.284245i) q^{14} +(2.18620 - 0.905553i) q^{15} +(-3.86027 + 1.04800i) q^{16} +(0.809188 + 0.335177i) q^{17} +(1.40227 + 0.183437i) q^{18} +(0.782804 - 0.642431i) q^{19} +(4.60724 - 1.08226i) q^{20} +(0.740856 + 0.224736i) q^{21} +(-3.90966 - 0.908213i) q^{22} +(1.67434 - 8.41747i) q^{23} +(2.70866 + 0.814361i) q^{24} +(-0.587974 + 0.116955i) q^{25} +(2.55240 + 2.72068i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(1.38983 + 0.682545i) q^{28} +(2.09512 - 3.91970i) q^{29} +(-3.16978 - 1.07308i) q^{30} +(5.38932 - 5.38932i) q^{31} +(5.08374 + 2.48106i) q^{32} +(2.00688 + 2.00688i) q^{33} +(-0.548756 - 1.11046i) q^{34} +(-1.61567 - 0.863594i) q^{35} +(-1.32117 - 1.50151i) q^{36} +(-1.98847 + 2.42296i) q^{37} +(-1.43140 - 0.0456795i) q^{38} +(-0.514625 - 2.58720i) q^{39} +(-5.91045 - 3.14046i) q^{40} +(0.0909338 + 0.0180878i) q^{41} +(-0.578932 - 0.929292i) q^{42} +(1.94008 - 6.39559i) q^{43} +(3.31393 + 4.60853i) q^{44} +(1.50118 + 1.82919i) q^{45} +(-9.62309 + 7.39665i) q^{46} +(-3.55765 + 8.58892i) q^{47} +(-2.12345 - 3.38983i) q^{48} +(2.44941 + 5.91341i) q^{49} +(0.734575 + 0.423301i) q^{50} +(-0.0858492 + 0.871641i) q^{51} +(-0.181301 - 5.27265i) q^{52} +(-3.74120 - 6.99929i) q^{53} +(0.231518 + 1.39513i) q^{54} +(-3.73122 - 5.58416i) q^{55} +(-0.842974 - 2.02099i) q^{56} +(0.842004 + 0.562609i) q^{57} +(-5.88079 + 2.21890i) q^{58} +(1.53129 - 0.150819i) q^{59} +(2.37307 + 4.09469i) q^{60} +(-4.76028 + 1.44402i) q^{61} +(-10.7550 + 0.713812i) q^{62} +0.774192i q^{63} +(-3.09794 - 7.37582i) q^{64} +6.24208i q^{65} +(-0.265811 - 4.00496i) q^{66} +(-5.86212 + 1.77825i) q^{67} +(-0.450591 + 1.69277i) q^{68} +(8.54105 - 0.841220i) q^{69} +(0.914614 + 2.42402i) q^{70} +(-3.79243 - 2.53402i) q^{71} +(0.00698639 + 2.82842i) q^{72} +(6.25875 + 9.36688i) q^{73} +(4.37297 - 0.725680i) q^{74} +(-0.282599 - 0.528706i) q^{75} +(1.48050 + 1.38207i) q^{76} +(0.215371 - 2.18670i) q^{77} +(-1.86260 + 3.23227i) q^{78} +(4.49830 + 10.8599i) q^{79} +(3.36331 + 8.84760i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.0799059 - 0.103958i) q^{82} +(0.226883 + 0.276458i) q^{83} +(-0.249709 + 1.52812i) q^{84} +(0.601634 - 1.98332i) q^{85} +(-8.02231 + 4.99776i) q^{86} +(4.35910 + 0.867080i) q^{87} +(0.767101 - 7.99080i) q^{88} +(1.91512 + 9.62797i) q^{89} +(0.106740 - 3.34479i) q^{90} +(-1.29558 + 1.57866i) q^{91} +(17.1298 + 1.09442i) q^{92} +(6.72169 + 3.59282i) q^{93} +(11.7867 - 5.82463i) q^{94} +(-1.69444 - 1.69444i) q^{95} +(-0.898491 + 5.58504i) q^{96} +(-7.99181 + 7.99181i) q^{97} +(2.90256 - 8.57387i) q^{98} +(-1.33790 + 2.50304i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−1.06403	−	0.931580i	−0.752382	−	0.658727i
$2$	−1.06403	−	0.931580i	−0.752382	−	0.658727i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	0.264317	+	1.98246i	0.132159	+	0.991229i
$5$	−0.231940	−	2.35493i	−0.103727	−	1.05316i	−0.896321	−	0.443407i	$-0.853770\pi$
$5$	−0.231940	−	2.35493i	−0.103727	−	1.05316i	0.792594	−	0.609750i	$-0.208730\pi$
$6$	0.582595	−	1.28864i	0.237843	−	0.526083i
$7$	0.430118	−	0.643717i	0.162569	−	0.243302i	−0.741238	−	0.671243i	$-0.765761\pi$
$7$	0.430118	−	0.643717i	0.162569	−	0.243302i	0.903807	+	0.427941i	$0.140761\pi$
$8$	1.56558	−	2.35563i	0.553515	−	0.832839i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−1.94701	+	2.72179i	−0.615700	+	0.860704i
$11$	2.50304	−	1.33790i	0.754694	−	0.403392i	−0.0487208	−	0.998812i	$-0.515514\pi$
$11$	2.50304	−	1.33790i	0.754694	−	0.403392i	0.803414	+	0.595420i	$0.203014\pi$
$12$	−1.82037	+	0.828413i	−0.525494	+	0.239142i
$13$	−2.62518	−	0.258558i	−0.728094	−	0.0717110i	−0.272823	−	0.962064i	$-0.587957\pi$
$13$	−2.62518	−	0.258558i	−0.728094	−	0.0717110i	−0.455270	+	0.890353i	$0.650457\pi$
$14$	−1.05733	+	0.284245i	−0.282584	+	0.0759676i
$15$	2.18620	−	0.905553i	0.564474	−	0.233813i
$16$	−3.86027	+	1.04800i	−0.965068	+	0.261999i
$17$	0.809188	+	0.335177i	0.196257	+	0.0812923i	0.478647	−	0.878007i	$-0.341127\pi$
$17$	0.809188	+	0.335177i	0.196257	+	0.0812923i	−0.282390	+	0.959300i	$0.591127\pi$
$18$	1.40227	+	0.183437i	0.330517	+	0.0432366i
$19$	0.782804	−	0.642431i	0.179588	−	0.147384i	−0.540305	−	0.841469i	$-0.681691\pi$
$19$	0.782804	−	0.642431i	0.179588	−	0.147384i	0.719892	+	0.694086i	$0.244191\pi$
$20$	4.60724	−	1.08226i	1.03021	−	0.242001i
$21$	0.740856	+	0.224736i	0.161668	+	0.0490414i
$22$	−3.90966	−	0.908213i	−0.833543	−	0.193632i
$23$	1.67434	−	8.41747i	0.349124	−	1.75516i	−0.263377	−	0.964693i	$-0.584836\pi$
$23$	1.67434	−	8.41747i	0.349124	−	1.75516i	0.612501	−	0.790470i	$-0.290164\pi$
$24$	2.70866	+	0.814361i	0.552902	+	0.166231i
$25$	−0.587974	+	0.116955i	−0.117595	+	0.0233911i
$26$	2.55240	+	2.72068i	0.500567	+	0.533569i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	1.38983	+	0.682545i	0.262653	+	0.128989i
$29$	2.09512	−	3.91970i	0.389055	−	0.727870i	−0.608801	−	0.793323i	$-0.708349\pi$
$29$	2.09512	−	3.91970i	0.389055	−	0.727870i	0.997856	+	0.0654527i	$0.0208491\pi$
$30$	−3.16978	−	1.07308i	−0.578719	−	0.195917i
$31$	5.38932	−	5.38932i	0.967950	−	0.967950i	−0.0315517	−	0.999502i	$-0.510045\pi$
$31$	5.38932	−	5.38932i	0.967950	−	0.967950i	0.999502	+	0.0315517i	$0.0100449\pi$
$32$	5.08374	+	2.48106i	0.898686	+	0.438593i
$33$	2.00688	+	2.00688i	0.349354	+	0.349354i
$34$	−0.548756	−	1.11046i	−0.0941109	−	0.190442i
$35$	−1.61567	−	0.863594i	−0.273098	−	0.145974i
$36$	−1.32117	−	1.50151i	−0.220194	−	0.250251i
$37$	−1.98847	+	2.42296i	−0.326903	+	0.398332i	−0.910364	−	0.413809i	$-0.864198\pi$
$37$	−1.98847	+	2.42296i	−0.326903	+	0.398332i	0.583461	+	0.812141i	$0.301698\pi$
$38$	−1.43140	−	0.0456795i	−0.232204	−	0.00741019i
$39$	−0.514625	−	2.58720i	−0.0824060	−	0.414283i
$40$	−5.91045	−	3.14046i	−0.934525	−	0.496550i
$41$	0.0909338	+	0.0180878i	0.0142015	+	0.00282485i	0.202186	−	0.979347i	$-0.435195\pi$
$41$	0.0909338	+	0.0180878i	0.0142015	+	0.00282485i	−0.187984	+	0.982172i	$0.560195\pi$
$42$	−0.578932	−	0.929292i	−0.0893312	−	0.143393i
$43$	1.94008	−	6.39559i	0.295860	−	0.975319i	−0.675431	−	0.737423i	$-0.736042\pi$
$43$	1.94008	−	6.39559i	0.295860	−	0.975319i	0.971291	−	0.237896i	$-0.0764576\pi$
$44$	3.31393	+	4.60853i	0.499593	+	0.694762i
$45$	1.50118	+	1.82919i	0.223783	+	0.272680i
$46$	−9.62309	+	7.39665i	−1.41885	+	1.09058i
$47$	−3.55765	+	8.58892i	−0.518936	+	1.25282i	0.419621	+	0.907699i	$0.362163\pi$
$47$	−3.55765	+	8.58892i	−0.518936	+	1.25282i	−0.938557	+	0.345123i	$0.887837\pi$
$48$	−2.12345	−	3.38983i	−0.306493	−	0.489280i
$49$	2.44941	+	5.91341i	0.349916	+	0.844773i
$50$	0.734575	+	0.423301i	0.103885	+	0.0598638i
$51$	−0.0858492	+	0.871641i	−0.0120213	+	0.122054i
$52$	−0.181301	−	5.27265i	−0.0251419	−	0.731185i
$53$	−3.74120	−	6.99929i	−0.513893	−	0.961427i	−0.996338	−	0.0855003i	$-0.972751\pi$
$53$	−3.74120	−	6.99929i	−0.513893	−	0.961427i	0.482445	−	0.875926i	$-0.339749\pi$
$54$	0.231518	+	1.39513i	0.0315056	+	0.189854i
$55$	−3.73122	−	5.58416i	−0.503117	−	0.752968i
$56$	−0.842974	−	2.02099i	−0.112647	−	0.270066i
$57$	0.842004	+	0.562609i	0.111526	+	0.0745194i
$58$	−5.88079	+	2.21890i	−0.772186	+	0.291356i
$59$	1.53129	−	0.150819i	0.199357	−	0.0196350i	0.00215431	−	0.999998i	$-0.499314\pi$
$59$	1.53129	−	0.150819i	0.199357	−	0.0196350i	0.197203	+	0.980363i	$0.436814\pi$
$60$	2.37307	+	4.09469i	0.306362	+	0.528623i
$61$	−4.76028	+	1.44402i	−0.609492	+	0.184887i	−0.579917	−	0.814675i	$-0.696915\pi$
$61$	−4.76028	+	1.44402i	−0.609492	+	0.184887i	−0.0295743	+	0.999563i	$0.509415\pi$
$62$	−10.7550	+	0.713812i	−1.36588	+	0.0906542i
$63$			0.774192i			0.0975390i
$64$	−3.09794	−	7.37582i	−0.387243	−	0.921978i
$65$			6.24208i			0.774235i
$66$	−0.265811	−	4.00496i	−0.0327190	−	0.492976i
$67$	−5.86212	+	1.77825i	−0.716172	+	0.217248i	−0.627281	−	0.778793i	$-0.715832\pi$
$67$	−5.86212	+	1.77825i	−0.716172	+	0.217248i	−0.0888909	+	0.996041i	$0.528332\pi$
$68$	−0.450591	+	1.69277i	−0.0546422	+	0.205279i
$69$	8.54105	−	0.841220i	1.02822	−	0.101271i
$70$	0.914614	+	2.42402i	0.109317	+	0.289725i
$71$	−3.79243	−	2.53402i	−0.450079	−	0.300733i	0.309795	−	0.950803i	$-0.399739\pi$
$71$	−3.79243	−	2.53402i	−0.450079	−	0.300733i	−0.759874	+	0.650070i	$0.774739\pi$
$72$	0.00698639	+	2.82842i	0.000823354	+	0.333332i
$73$	6.25875	+	9.36688i	0.732531	+	1.09631i	0.991460	+	0.130414i	$0.0416306\pi$
$73$	6.25875	+	9.36688i	0.732531	+	1.09631i	−0.258929	+	0.965896i	$0.583369\pi$
$74$	4.37297	−	0.725680i	0.508348	−	0.0843586i
$75$	−0.282599	−	0.528706i	−0.0326317	−	0.0610497i
$76$	1.48050	+	1.38207i	0.169825	+	0.158534i
$77$	0.215371	−	2.18670i	0.0245438	−	0.249198i
$78$	−1.86260	+	3.23227i	−0.210898	+	0.365982i
$79$	4.49830	+	10.8599i	0.506098	+	1.22183i	0.946112	+	0.323839i	$0.104974\pi$
$79$	4.49830	+	10.8599i	0.506098	+	1.22183i	−0.440014	+	0.897991i	$0.645026\pi$
$80$	3.36331	+	8.84760i	0.376029	+	0.989192i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−0.0799059	−	0.103958i	−0.00882413	−	0.0114802i
$83$	0.226883	+	0.276458i	0.0249037	+	0.0303452i	0.785313	−	0.619098i	$-0.212502\pi$
$83$	0.226883	+	0.276458i	0.0249037	+	0.0303452i	−0.760410	+	0.649444i	$0.775002\pi$
$84$	−0.249709	+	1.52812i	−0.0272455	+	0.166731i
$85$	0.601634	−	1.98332i	0.0652564	−	0.215121i
$86$	−8.02231	+	4.99776i	−0.865068	+	0.538922i
$87$	4.35910	+	0.867080i	0.467345	+	0.0929607i
$88$	0.767101	−	7.99080i	0.0817732	−	0.851822i
$89$	1.91512	+	9.62797i	0.203003	+	1.02056i	0.939089	+	0.343675i	$0.111672\pi$
$89$	1.91512	+	9.62797i	0.203003	+	1.02056i	−0.736086	+	0.676888i	$0.763328\pi$
$90$	0.106740	−	3.34479i	0.0112514	−	0.352571i
$91$	−1.29558	+	1.57866i	−0.135813	+	0.165489i
$92$	17.1298	+	1.09442i	1.78591	+	0.114101i
$93$	6.72169	+	3.59282i	0.697007	+	0.372558i
$94$	11.7867	−	5.82463i	1.21571	−	0.600765i
$95$	−1.69444	−	1.69444i	−0.173846	−	0.173846i
$96$	−0.898491	+	5.58504i	−0.0917019	+	0.570021i
$97$	−7.99181	+	7.99181i	−0.811446	+	0.811446i	−0.984851	−	0.173405i	$-0.944523\pi$
$97$	−7.99181	+	7.99181i	−0.811446	+	0.811446i	0.173405	+	0.984851i	$0.444523\pi$
$98$	2.90256	−	8.57387i	0.293203	−	0.866091i
$99$	−1.33790	+	2.50304i	−0.134464	+	0.251565i
$100$	−0.387270	−	1.13472i	−0.0387270	−	0.113472i
$101$	13.9233	+	11.4265i	1.38542	+	1.13698i	0.974262	+	0.225417i	$0.0723745\pi$
$101$	13.9233	+	11.4265i	1.38542	+	1.13698i	0.411155	+	0.911565i	$0.365126\pi$
$102$	0.903349	−	0.847476i	0.0894449	−	0.0839127i
$103$	13.8738	−	2.75966i	1.36702	−	0.271918i	0.543599	−	0.839345i	$-0.317061\pi$
$103$	13.8738	−	2.75966i	1.36702	−	0.271918i	0.823424	+	0.567427i	$0.192061\pi$
$104$	−4.71898	+	5.77915i	−0.462734	+	0.566692i
$105$	0.357403	−	1.79679i	0.0348790	−	0.175349i
$106$	−2.53965	+	10.9327i	−0.246673	+	1.06188i
$107$	−11.8066	−	3.58148i	−1.14138	−	0.346235i	−0.337678	−	0.941262i	$-0.609641\pi$
$107$	−11.8066	−	3.58148i	−1.14138	−	0.346235i	−0.803706	+	0.595027i	$0.797141\pi$
$108$	1.05334	−	1.70014i	0.101357	−	0.163596i
$109$	−5.28727	+	4.33915i	−0.506428	+	0.415615i	−0.852606	−	0.522554i	$-0.824979\pi$
$109$	−5.28727	+	4.33915i	−0.506428	+	0.415615i	0.346178	+	0.938169i	$0.387479\pi$
$110$	−1.23197	+	9.41764i	−0.117464	+	0.897937i
$111$	−2.89585	−	1.19950i	−0.274862	−	0.113852i
$112$	−0.985760	+	2.93569i	−0.0931456	+	0.277396i
$113$	−1.03978	+	0.430691i	−0.0978142	+	0.0405160i	−0.431054	−	0.902326i	$-0.641858\pi$
$113$	−1.03978	+	0.430691i	−0.0978142	+	0.0405160i	0.333240	+	0.942842i	$0.391858\pi$
$114$	−0.371802	−	1.38303i	−0.0348224	−	0.129532i
$115$	−20.2109	−	1.99060i	−1.88468	−	0.185624i
$116$	8.32442	+	3.11745i	0.772903	+	0.289448i
$117$	2.32640	−	1.24349i	0.215076	−	0.114961i
$118$	−1.76984	−	1.26604i	−0.162927	−	0.116549i
$119$	0.563805	−	0.376723i	0.0516839	−	0.0345341i
$120$	1.28952	−	6.56758i	0.117716	−	0.599535i
$121$	−1.63606	+	2.44854i	−0.148733	+	0.222595i
$122$	6.41030	+	2.89811i	0.580361	+	0.262382i
$123$	0.00908768	+	0.0922688i	0.000819409	+	0.00831960i
$124$	12.1086	+	9.25961i	1.08738	+	0.831537i
$125$	−3.02274	−	9.96465i	−0.270362	−	0.891265i
$126$	0.721222	−	0.823763i	0.0642515	−	0.0733866i
$127$	12.2766			1.08937			0.544685	−	0.838640i	$-0.316649\pi$
$127$	12.2766			1.08937			0.544685	+	0.838640i	$0.316649\pi$
$128$	−3.57487	+	10.7341i	−0.315977	+	0.948767i
$129$	6.68338			0.588439
$130$	5.81500	−	6.64176i	0.510009	−	0.582521i
$131$	−1.44963	−	4.77879i	−0.126655	−	0.417525i	0.870564	−	0.492055i	$-0.163754\pi$
$131$	−1.44963	−	4.77879i	−0.126655	−	0.417525i	−0.997219	+	0.0745306i	$0.976254\pi$
$132$	−3.44811	+	4.50901i	−0.300119	+	0.392459i
$133$	−0.0768455	−	0.780226i	−0.00666335	−	0.0676541i
$134$	7.89405	+	3.56892i	0.681942	+	0.308308i
$135$	−1.31466	+	1.96753i	−0.113148	+	0.169338i
$136$	2.05640	−	1.38140i	0.176334	−	0.118454i
$137$	−13.8188	+	9.23343i	−1.18062	+	0.788865i	−0.981566	−	0.191124i	$-0.938787\pi$
$137$	−13.8188	+	9.23343i	−1.18062	+	0.788865i	−0.199054	+	0.979989i	$0.563787\pi$
$138$	−9.87159	−	7.06159i	−0.840326	−	0.601122i
$139$	13.5623	−	7.24919i	1.15034	−	0.614868i	0.217819	−	0.975989i	$-0.430106\pi$
$139$	13.5623	−	7.24919i	1.15034	−	0.614868i	0.932519	+	0.361121i	$0.117606\pi$
$140$	1.28499	−	3.43126i	0.108601	−	0.289994i
$141$	−9.25181	−	0.911224i	−0.779143	−	0.0767389i
$142$	1.67462	+	6.22923i	0.140531	+	0.522745i
$143$	−6.91684	+	2.86505i	−0.578415	+	0.239587i
$144$	2.62746	−	3.01603i	0.218955	−	0.251336i
$145$	−9.71657	−	4.02473i	−0.806917	−	0.334236i
$146$	2.06650	−	15.7972i	0.171025	−	1.30738i
$147$	−4.94775	+	4.06051i	−0.408084	+	0.334906i
$148$	−5.32900	−	3.30163i	−0.438041	−	0.271392i
$149$	−11.8690	−	3.60042i	−0.972345	−	0.294958i	−0.236142	−	0.971718i	$-0.575883\pi$
$149$	−11.8690	−	3.60042i	−0.972345	−	0.294958i	−0.736203	+	0.676761i	$0.763383\pi$
$150$	−0.191838	+	0.825822i	−0.0156635	+	0.0674281i
$151$	−1.13738	+	5.71801i	−0.0925589	+	0.465325i	0.906510	+	0.422184i	$0.138736\pi$
$151$	−1.13738	+	5.71801i	−0.0925589	+	0.465325i	−0.999069	+	0.0431408i	$0.986264\pi$
$152$	−0.287787	−	2.84977i	−0.0233426	−	0.231147i
$153$	−0.859029	+	0.170872i	−0.0694484	+	0.0138141i
$154$	−2.26625	+	2.12608i	−0.182620	+	0.171324i
$155$	−13.9415	−	11.4415i	−1.11981	−	0.919001i
$156$	4.99298	−	1.70406i	0.399758	−	0.136434i
$157$	−1.17072	+	2.19026i	−0.0934334	+	0.174802i	−0.924296	−	0.381675i	$-0.875347\pi$
$157$	−1.17072	+	2.19026i	−0.0934334	+	0.174802i	0.830863	+	0.556477i	$0.187847\pi$
$158$	5.33050	−	15.7457i	0.424072	−	1.25266i
$159$	5.61189	−	5.61189i	0.445052	−	0.445052i
$160$	4.66359	−	12.5473i	0.368689	−	0.991951i
$161$	−4.69830	−	4.69830i	−0.370278	−	0.370278i
$162$	−1.26785	+	0.626535i	−0.0996120	+	0.0492252i
$163$	5.01315	+	2.67959i	0.392660	+	0.209881i	0.655898	−	0.754850i	$-0.272290\pi$
$163$	5.01315	+	2.67959i	0.392660	+	0.209881i	−0.263237	+	0.964731i	$0.584790\pi$
$164$	−0.0118230	+	0.185053i	−0.000923223	+	0.0144502i
$165$	4.26059	−	5.19155i	0.331687	−	0.404161i
$166$	0.0161324	−	0.505520i	0.00125211	−	0.0392360i
$167$	−2.93003	−	14.7302i	−0.226732	−	1.13986i	−0.911564	−	0.411159i	$-0.865124\pi$
$167$	−2.93003	−	14.7302i	−0.226732	−	1.13986i	0.684831	−	0.728702i	$-0.259876\pi$
$168$	1.68926	−	1.39334i	0.130329	−	0.107498i
$169$	−5.92549	−	1.17865i	−0.455807	−	0.0906657i
$170$	−2.48778	+	1.54984i	−0.190804	+	0.118867i
$171$	−0.293962	+	0.969064i	−0.0224799	+	0.0741062i
$172$	13.1918	+	2.15566i	1.00586	+	0.164368i
$173$	−8.31267	−	10.1290i	−0.632001	−	0.770095i	0.354286	−	0.935137i	$-0.384724\pi$
$173$	−8.31267	−	10.1290i	−0.632001	−	0.770095i	−0.986287	+	0.165042i	$0.947224\pi$
$174$	−3.83046	−	4.98345i	−0.290386	−	0.377795i
$175$	−0.177612	+	0.428793i	−0.0134262	+	0.0324137i
$176$	−8.26029	+	7.78783i	−0.622643	+	0.587030i
$177$	0.588835	+	1.42157i	0.0442596	+	0.106852i
$178$	6.93148	−	12.0285i	0.519536	−	0.901576i
$179$	−1.78349	+	18.1081i	−0.133304	+	1.35346i	0.663025	+	0.748597i	$0.269272\pi$
$179$	−1.78349	+	18.1081i	−0.133304	+	1.35346i	−0.796329	+	0.604864i	$0.793228\pi$
$180$	−3.22951	+	3.45951i	−0.240713	+	0.257857i
$181$	0.835013	+	1.56220i	0.0620661	+	0.116117i	0.911041	−	0.412315i	$-0.135280\pi$
$181$	0.835013	+	1.56220i	0.0620661	+	0.116117i	−0.848975	+	0.528433i	$0.822780\pi$
$182$	2.84918	−	0.472812i	0.211195	−	0.0350471i
$183$	−2.76367	−	4.13613i	−0.204297	−	0.305752i
$184$	−17.2071	−	17.1223i	−1.26852	−	1.26227i
$185$	6.16711	+	4.12073i	0.453415	+	0.302962i
$186$	−3.80508	−	10.0847i	−0.279002	−	0.739443i
$187$	2.47386	−	0.243654i	0.180906	−	0.0178177i
$188$	−17.9675	−	4.78268i	−1.31042	−	0.348813i
$189$	−0.740856	+	0.224736i	−0.0538893	+	0.0163471i
$190$	0.224428	+	3.38145i	0.0162817	+	0.245316i
$191$			8.65026i			0.625911i	0.949768	+	0.312955i	$0.101319\pi$
$191$			8.65026i			0.625911i	−0.949768	+	0.312955i	$0.898681\pi$
$192$	6.15894	−	5.10563i	0.444483	−	0.368467i
$193$		−	13.9983i		−	1.00762i	−0.863814	−	0.503811i	$-0.831931\pi$
$193$		−	13.9983i		−	1.00762i	0.863814	−	0.503811i	$-0.168069\pi$
$194$	15.9485	−	1.05851i	1.14504	−	0.0759967i
$195$	−5.97330	+	1.81198i	−0.427757	+	0.129759i
$196$	−11.0757	+	6.41887i	−0.791118	+	0.458491i
$197$	3.80115	−	0.374380i	0.270821	−	0.0266735i	0.0383047	−	0.999266i	$-0.487804\pi$
$197$	3.80115	−	0.374380i	0.270821	−	0.0266735i	0.232516	+	0.972593i	$0.425304\pi$
$198$	3.75534	−	1.41694i	0.266881	−	0.100698i
$199$	17.5486	+	11.7256i	1.24399	+	0.831207i	0.990684	−	0.136180i	$-0.0434825\pi$
$199$	17.5486	+	11.7256i	1.24399	+	0.831207i	0.253305	+	0.967387i	$0.418483\pi$
$200$	−0.645015	+	1.56815i	−0.0456094	+	0.110885i
$201$	−3.40337	−	5.09350i	−0.240055	−	0.359268i
$202$	−4.17004	−	25.1288i	−0.293403	−	1.76806i
$203$	−1.62203	−	3.03460i	−0.113844	−	0.212987i
$204$	−1.75068	+	0.0601975i	−0.122572	+	0.00421467i
$205$	0.0215044	−	0.218338i	0.00150193	−	0.0152494i
$206$	−17.3329	−	9.98816i	−1.20764	−	0.695908i
$207$	3.28433	+	7.92908i	0.228277	+	0.551109i
$208$	10.4049	−	1.75307i	0.721448	−	0.121554i
$209$	1.09988	−	2.65534i	0.0760802	−	0.183674i
$210$	−2.05414	+	1.57889i	−0.141749	+	0.108953i
$211$	−4.30331	−	5.24360i	−0.296252	−	0.360985i	0.603517	−	0.797350i	$-0.293765\pi$
$211$	−4.30331	−	5.24360i	−0.296252	−	0.360985i	−0.899770	+	0.436365i	$0.856265\pi$
$212$	12.8869	−	9.26680i	0.885078	−	0.636447i
$213$	1.32402	−	4.36472i	0.0907206	−	0.299066i
$214$	9.22609	+	14.8096i	0.630683	+	1.01236i
$215$	−15.5112	−	3.08536i	−1.05785	−	0.210420i
$216$	−2.70460	+	0.827732i	−0.184025	+	0.0563200i
$217$	−1.15115	−	5.78724i	−0.0781454	−	0.392864i
$218$	9.66807	+	0.308531i	0.654804	+	0.0208964i
$219$	−7.14673	+	8.70831i	−0.482931	+	0.588453i
$220$	10.0841	−	8.87297i	0.679872	−	0.598215i
$221$	−2.03760	−	1.08912i	−0.137064	−	0.0732622i
$222$	1.96384	+	3.97402i	0.131804	+	0.266719i
$223$	−2.57334	−	2.57334i	−0.172324	−	0.172324i	0.615676	−	0.788000i	$-0.288883\pi$
$223$	−2.57334	−	2.57334i	−0.172324	−	0.172324i	−0.788000	+	0.615676i	$0.788883\pi$
$224$	3.78370	−	2.20534i	0.252809	−	0.147351i
$225$	0.423906	−	0.423906i	0.0282604	−	0.0282604i
$226$	1.50758	+	0.510370i	0.100283	+	0.0339493i
$227$	6.38326	−	11.9422i	0.423672	−	0.792635i	−0.576020	−	0.817435i	$-0.695395\pi$
$227$	6.38326	−	11.9422i	0.423672	−	0.792635i	0.999692	+	0.0248006i	$0.00789508\pi$
$228$	−0.892792	+	1.81794i	−0.0591266	+	0.120396i
$229$	16.7475	+	13.7443i	1.10670	+	0.908249i	0.996326	−	0.0856409i	$-0.0272938\pi$
$229$	16.7475	+	13.7443i	1.10670	+	0.908249i	0.110378	+	0.993890i	$0.464794\pi$
$230$	19.6506	+	20.9461i	1.29572	+	1.38115i
$231$	2.15506	−	0.428669i	0.141793	−	0.0282043i
$232$	−5.95327	−	11.0719i	−0.390852	−	0.726907i
$233$	−3.58230	+	18.0095i	−0.234685	+	1.17984i	0.666198	+	0.745775i	$0.267921\pi$
$233$	−3.58230	+	18.0095i	−0.234685	+	1.17984i	−0.900882	+	0.434064i	$0.857079\pi$
$234$	−3.63377	−	0.844123i	−0.237547	−	0.0551820i
$235$	21.0515	+	6.38589i	1.37325	+	0.416570i
$236$	0.703739	+	2.99585i	0.0458095	+	0.195014i
$237$	−9.08645	+	7.45706i	−0.590228	+	0.484388i
$238$	−0.950853	−	0.124386i	−0.0616346	−	0.00806273i
$239$	18.2635	+	7.56497i	1.18137	+	0.489337i	0.884934	−	0.465717i	$-0.154203\pi$
$239$	18.2635	+	7.56497i	1.18137	+	0.489337i	0.296431	+	0.955054i	$0.404203\pi$
$240$	−7.49031	+	5.78681i	−0.483497	+	0.373537i
$241$	9.45432	−	3.91611i	0.609007	−	0.252259i	−0.0567971	−	0.998386i	$-0.518089\pi$
$241$	9.45432	−	3.91611i	0.609007	−	0.252259i	0.665804	+	0.746127i	$0.268089\pi$
$242$	4.02183	−	1.08120i	0.258533	−	0.0695020i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	−4.12092	−	9.05538i	−0.263815	−	0.579711i
$245$	13.3575	−	7.13976i	0.853382	−	0.456142i
$246$	0.0762862	−	0.106643i	0.00486383	−	0.00679929i
$247$	−2.22111	+	1.48410i	−0.141326	+	0.0944308i
$248$	−4.25783	−	21.1326i	−0.270372	−	1.34192i
$249$	−0.198693	+	0.297366i	−0.0125917	+	0.0188448i
$250$	−6.06658	+	13.4186i	−0.383684	+	0.848667i
$251$	1.29551	+	13.1536i	0.0817721	+	0.830246i	0.945356	+	0.326041i	$0.105715\pi$
$251$	1.29551	+	13.1536i	0.0817721	+	0.830246i	−0.863584	+	0.504206i	$0.831785\pi$
$252$	−1.53480	+	0.204632i	−0.0966835	+	0.0128906i
$253$	−7.07080	−	23.3093i	−0.444538	−	1.46544i
$254$	−13.0626	−	11.4366i	−0.819623	−	0.717597i
$255$	2.07257			0.129789
$256$	13.8034	−	8.09110i	0.862713	−	0.505693i
$257$	26.1424			1.63072			0.815359	−	0.578956i	$-0.196540\pi$
$257$	26.1424			1.63072			0.815359	+	0.578956i	$0.196540\pi$
$258$	−7.11131	−	6.22610i	−0.442731	−	0.387620i
$259$	0.704423	+	2.32217i	0.0437707	+	0.144293i
$260$	−12.3747	+	1.64989i	−0.767444	+	0.102322i
$261$	0.435638	+	4.42310i	0.0269653	+	0.273783i
$262$	−2.90937	+	6.43522i	−0.179742	+	0.397569i
$263$	−11.6024	+	17.3642i	−0.715434	+	1.07072i	0.278467	+	0.960446i	$0.410174\pi$
$263$	−11.6024	+	17.3642i	−0.715434	+	1.07072i	−0.993901	+	0.110277i	$0.964826\pi$
$264$	7.86940	−	1.58554i	0.484328	−	0.0975831i
$265$	−15.6151	+	10.4337i	−0.959228	+	0.640936i
$266$	−0.645077	+	0.901771i	−0.0395522	+	0.0552911i
$267$	−8.65746	+	4.62751i	−0.529828	+	0.283199i
$268$	−5.07477	−	11.1514i	−0.309991	−	0.681179i
$269$	−25.2084	−	2.48281i	−1.53698	−	0.151380i	−0.706216	−	0.707997i	$-0.749599\pi$
$269$	−25.2084	−	2.48281i	−1.53698	−	0.151380i	−0.830769	+	0.556617i	$0.812099\pi$
$270$	3.23175	−	0.868796i	0.196678	−	0.0528732i
$271$	24.1437	−	10.0007i	1.46663	−	0.607497i	0.500539	−	0.865714i	$-0.333135\pi$
$271$	24.1437	−	10.0007i	1.46663	−	0.607497i	0.966087	+	0.258217i	$0.0831350\pi$
$272$	−3.47495	−	0.445848i	−0.210700	−	0.0270335i
$273$	−1.88677	−	0.781526i	−0.114193	−	0.0473001i
$274$	23.3053	+	3.04868i	1.40792	+	0.184177i
$275$	−1.31524	+	1.07939i	−0.0793122	+	0.0650899i
$276$	3.92523	+	16.7099i	0.236271	+	1.00582i
$277$	−10.9544	−	3.32297i	−0.658184	−	0.199658i	−0.0565130	−	0.998402i	$-0.517998\pi$
$277$	−10.9544	−	3.32297i	−0.658184	−	0.199658i	−0.601671	+	0.798744i	$0.705498\pi$
$278$	−21.1839	−	4.92100i	−1.27052	−	0.295142i
$279$	−1.48691	+	7.47520i	−0.0890190	+	0.447529i
$280$	−4.56376	+	2.45389i	−0.272737	+	0.146648i
$281$	25.5356	−	5.07935i	1.52333	−	0.303009i	0.638755	−	0.769410i	$-0.279450\pi$
$281$	25.5356	−	5.07935i	1.52333	−	0.303009i	0.884573	+	0.466402i	$0.154450\pi$
$282$	8.99532	+	9.58837i	0.535664	+	0.570979i
$283$	−15.0461	−	12.3480i	−0.894400	−	0.734015i	0.0702557	−	0.997529i	$-0.477618\pi$
$283$	−15.0461	−	12.3480i	−0.894400	−	0.734015i	−0.964656	+	0.263514i	$0.915118\pi$
$284$	4.02119	−	8.18812i	0.238613	−	0.485876i
$285$	1.12961	−	2.11335i	0.0669124	−	0.125184i
$286$	10.0287	+	3.39509i	0.593012	+	0.200756i
$287$	0.0507557	−	0.0507557i	0.00299601	−	0.00299601i
$288$	−5.60537	+	0.761450i	−0.330300	+	0.0448689i
$289$	−11.4784	−	11.4784i	−0.675198	−	0.675198i
$290$	6.58935	+	13.3342i	0.386940	+	0.783011i
$291$	−9.96759	−	5.32779i	−0.584310	−	0.312320i
$292$	−16.9151	+	14.8835i	−0.989884	+	0.870993i
$293$	−0.953331	+	1.16164i	−0.0556942	+	0.0678635i	−0.800112	−	0.599850i	$-0.795227\pi$
$293$	−0.953331	+	1.16164i	−0.0556942	+	0.0678635i	0.744418	+	0.667714i	$0.232727\pi$
$294$	9.04725	+	0.288719i	0.527646	+	0.0168385i
$295$	−0.710336	−	3.57110i	−0.0413574	−	0.207918i
$296$	2.59448	+	8.47742i	0.150801	+	0.492740i
$297$	−2.78363	−	0.553698i	−0.161522	−	0.0321288i
$298$	9.27488	+	14.8879i	0.537279	+	0.862431i
$299$	−6.57184	+	21.6644i	−0.380059	+	1.25289i
$300$	0.973440	−	0.699986i	0.0562016	−	0.0404137i
$301$	−3.28249	−	3.99972i	−0.189199	−	0.230540i
$302$	6.53699	−	5.02457i	0.376162	−	0.289131i
$303$	−6.89280	+	16.6407i	−0.395981	+	0.955983i
$304$	−2.34857	+	3.30033i	−0.134700	+	0.189287i
$305$	4.50466	+	10.8752i	0.257936	+	0.622713i
$306$	1.07321	+	0.618442i	0.0613515	+	0.0353540i
$307$	−1.25347	+	12.7267i	−0.0715391	+	0.726348i	0.890782	+	0.454431i	$0.150158\pi$
$307$	−1.25347	+	12.7267i	−0.0715391	+	0.726348i	−0.962321	+	0.271917i	$0.912342\pi$
$308$	4.39197	−	0.151019i	0.250256	−	0.00860508i
$309$	6.66817	+	12.4753i	0.379339	+	0.709694i
$310$	4.17549	+	25.1617i	0.237152	+	1.42909i
$311$	−8.01776	−	11.9994i	−0.454646	−	0.680425i	0.531358	−	0.847147i	$-0.321682\pi$
$311$	−8.01776	−	11.9994i	−0.454646	−	0.680425i	−0.986004	+	0.166722i	$0.946682\pi$
$312$	−6.90015	−	2.83819i	−0.390644	−	0.160681i
$313$	12.4740	+	8.33487i	0.705073	+	0.471115i	0.855698	−	0.517476i	$-0.173128\pi$
$313$	12.4740	+	8.33487i	0.705073	+	0.471115i	−0.150625	+	0.988591i	$0.548128\pi$
$314$	3.28608	−	1.23988i	0.185444	−	0.0699706i
$315$	1.82317	−	0.179566i	0.102724	−	0.0101174i
$316$	−20.3402	+	11.7881i	−1.14423	+	0.663135i
$317$	−13.0343	+	3.95391i	−0.732078	+	0.222074i	−0.634248	−	0.773130i	$-0.718690\pi$
$317$	−13.0343	+	3.95391i	−0.732078	+	0.222074i	−0.0978303	+	0.995203i	$0.531190\pi$
$318$	−11.1991	+	0.743292i	−0.628017	+	0.0416817i
$319$		−	12.6142i		−	0.706261i
$320$	−16.6510	+	9.00619i	−0.930820	+	0.503461i
$321$		−	12.3378i		−	0.688630i
$322$	0.622288	+	9.37598i	0.0346787	+	0.522503i
$323$	0.848763	−	0.257470i	0.0472265	−	0.0143260i
$324$	1.93270	+	0.514456i	0.107372	+	0.0285809i
$325$	1.57378	−	0.155003i	0.0872974	−	0.00859804i
$326$	−2.83789	−	7.52131i	−0.157176	−	0.416567i
$327$	−5.68712	−	3.80001i	−0.314498	−	0.210141i
$328$	0.184972	−	0.185888i	0.0102134	−	0.0102639i
$329$	3.99863	+	5.98437i	0.220451	+	0.329929i
$330$	−9.36974	+	1.55488i	−0.515787	+	0.0855931i
$331$	12.1189	+	22.6728i	0.666114	+	1.24621i	0.957176	+	0.289508i	$0.0934916\pi$
$331$	12.1189	+	22.6728i	0.666114	+	1.24621i	−0.291061	+	0.956704i	$0.594008\pi$
$332$	−0.488098	+	0.522859i	−0.0267878	+	0.0286956i
$333$	0.307229	−	3.11935i	0.0168361	−	0.170939i
$334$	−10.6048	+	18.4030i	−0.580267	+	1.00697i
$335$	5.54733	+	13.3924i	0.303083	+	0.731707i
$336$	−3.09543	−	0.0911294i	−0.168869	−	0.00497152i
$337$	12.3955	−	29.9255i	0.675228	−	1.63015i	−0.0973685	−	0.995248i	$-0.531043\pi$
$337$	12.3955	−	29.9255i	0.675228	−	1.63015i	0.772597	−	0.634897i	$-0.218957\pi$
$338$	5.20689	+	6.77419i	0.283217	+	0.368468i
$339$	−0.713977	−	0.869984i	−0.0387779	−	0.0472510i
$340$	4.09087	+	0.668488i	0.221859	+	0.0362538i
$341$	6.27929	−	20.7000i	0.340042	−	1.12097i
$342$	1.21555	−	0.757264i	0.0657292	−	0.0409481i
$343$	10.1753	+	2.02400i	0.549415	+	0.109285i
$344$	−12.0283	−	14.5829i	−0.648521	−	0.786257i
$345$	−3.96203	−	19.9185i	−0.213308	−	1.07237i
$346$	−0.591065	+	18.5215i	−0.0317759	+	0.995721i
$347$	20.5130	−	24.9952i	1.10120	−	1.34181i	0.166632	−	0.986019i	$-0.446711\pi$
$347$	20.5130	−	24.9952i	1.10120	−	1.34181i	0.934565	−	0.355793i	$-0.115789\pi$
$348$	−0.566762	+	8.87092i	−0.0303816	+	0.475531i
$349$	9.14259	+	4.88682i	0.489392	+	0.261585i	0.697585	−	0.716502i	$-0.254258\pi$
$349$	9.14259	+	4.88682i	0.489392	+	0.261585i	−0.208193	+	0.978088i	$0.566758\pi$
$350$	0.588440	−	0.290789i	0.0314534	−	0.0155433i
$351$	1.86526	+	1.86526i	0.0995604	+	0.0995604i
$352$	16.0442	−	0.591362i	0.855157	−	0.0315197i
$353$	18.9124	−	18.9124i	1.00660	−	1.00660i	0.00662587	−	0.999978i	$-0.497891\pi$
$353$	18.9124	−	18.9124i	1.00660	−	1.00660i	0.999978	−	0.00662587i	$-0.00210909\pi$
$354$	0.697772	−	2.06114i	0.0370861	−	0.109549i
$355$	−5.08783	+	9.51866i	−0.270034	+	0.505198i
$356$	−18.5808	+	6.34149i	−0.984782	+	0.336098i
$357$	0.524165	+	0.430171i	0.0277418	+	0.0227671i
$358$	18.7668	−	17.6061i	0.991857	−	0.930509i
$359$	15.1705	−	3.01761i	0.800671	−	0.159263i	0.222237	−	0.974993i	$-0.428664\pi$
$359$	15.1705	−	3.01761i	0.800671	−	0.159263i	0.578434	+	0.815729i	$0.303664\pi$
$360$	6.65911	−	0.672477i	0.350966	−	0.0354426i
$361$	−3.50665	+	17.6291i	−0.184561	+	0.927849i
$362$	0.566836	−	2.44011i	0.0297922	−	0.128249i
$363$	−2.81803	−	0.854841i	−0.147908	−	0.0448675i
$364$	−3.47207	−	2.15115i	−0.181986	−	0.112751i
$365$	20.6067	−	16.9115i	1.07860	−	0.885187i
$366$	−0.912506	+	6.97555i	−0.0476975	+	0.364618i
$367$	−4.83399	−	2.00230i	−0.252332	−	0.104519i	0.252932	−	0.967484i	$-0.418605\pi$
$367$	−4.83399	−	2.00230i	−0.252332	−	0.104519i	−0.505264	+	0.862965i	$0.668605\pi$
$368$	2.35806	+	34.2484i	0.122923	+	1.78532i
$369$	−0.0856577	+	0.0354806i	−0.00445916	+	0.00184705i
$370$	−2.72319	−	10.1297i	−0.141572	−	0.526620i
$371$	−6.11472	−	0.602247i	−0.317461	−	0.0312671i
$372$	−5.34595	+	14.2751i	−0.277175	+	0.740130i
$373$	5.53240	−	2.95713i	0.286457	−	0.153114i	−0.321910	−	0.946770i	$-0.604325\pi$
$373$	5.53240	−	2.95713i	0.286457	−	0.153114i	0.608367	+	0.793656i	$0.291825\pi$
$374$	−2.85924	−	2.04534i	−0.147848	−	0.105762i
$375$	8.65812	−	5.78517i	0.447103	−	0.298745i
$376$	14.6625	+	21.8271i	0.756161	+	1.12565i
$377$	−6.51355	+	9.74821i	−0.335465	+	0.502058i
$378$	0.997652	+	0.451040i	0.0513137	+	0.0231990i
$379$	0.497588	+	5.05210i	0.0255594	+	0.259509i	0.999469	+	0.0325740i	$0.0103704\pi$
$379$	0.497588	+	5.05210i	0.0255594	+	0.259509i	−0.973910	+	0.226935i	$0.927130\pi$
$380$	2.91129	−	3.80703i	0.149346	−	0.195297i
$381$	3.56370	+	11.7480i	0.182574	+	0.601866i
$382$	8.05841	−	9.20413i	0.412304	−	0.470924i
$383$	−23.1125			−1.18099			−0.590497	−	0.807040i	$-0.701068\pi$
$383$	−23.1125			−1.18099			−0.590497	+	0.807040i	$0.701068\pi$
$384$	−11.3096	−	0.304997i	−0.577140	−	0.0155643i
$385$	−5.19948			−0.264990
$386$	−13.0406	+	14.8947i	−0.663748	+	0.758118i
$387$	1.94008	+	6.39559i	0.0986199	+	0.325106i
$388$	−17.9558	−	13.7311i	−0.911568	−	0.697089i
$389$	−2.54738	−	25.8639i	−0.129157	−	1.31135i	−0.813231	−	0.581941i	$-0.802293\pi$
$389$	−2.54738	−	25.8639i	−0.129157	−	1.31135i	0.684074	−	0.729413i	$-0.260207\pi$
$390$	8.04378	+	3.63661i	0.407312	+	0.184147i
$391$	4.17619	−	6.25011i	0.211199	−	0.316082i
$392$	17.7645	+	3.48799i	0.897244	+	0.176170i
$393$	4.15221	−	2.77442i	0.209451	−	0.139951i
$394$	−4.39330	−	3.14272i	−0.221331	−	0.158328i
$395$	24.5309	−	13.1120i	1.23428	−	0.659738i
$396$	−5.31579	−	1.99073i	−0.267129	−	0.100038i
$397$	−3.57234	−	0.351845i	−0.179291	−	0.0176586i	0.00797340	−	0.999968i	$-0.497462\pi$
$397$	−3.57234	−	0.351845i	−0.179291	−	0.0176586i	−0.187264	+	0.982310i	$0.559962\pi$
$398$	−7.74890	−	28.8243i	−0.388417	−	1.44483i
$399$	0.724322	−	0.300024i	0.0362615	−	0.0150200i
$400$	2.14717	−	1.06767i	0.107359	−	0.0533837i
$401$	−27.2918	−	11.3046i	−1.36289	−	0.564526i	−0.423036	−	0.906113i	$-0.639036\pi$
$401$	−27.2918	−	11.3046i	−1.36289	−	0.564526i	−0.939850	+	0.341587i	$0.889036\pi$
$402$	−1.12372	+	8.59014i	−0.0560460	+	0.428437i
$403$	−15.5414	+	12.7545i	−0.774171	+	0.635346i
$404$	−18.9725	+	30.6225i	−0.943915	+	1.52353i
$405$	−2.26443	−	0.686908i	−0.112521	−	0.0341327i
$406$	−1.10109	+	4.73996i	−0.0546461	+	0.235240i
$407$	−1.73554	+	8.72513i	−0.0860273	+	0.432489i
$408$	1.91886	+	1.56685i	0.0949976	+	0.0775706i
$409$	−30.4705	+	6.06097i	−1.50667	+	0.299696i	−0.878259	−	0.478185i	$-0.841295\pi$
$409$	−30.4705	+	6.06097i	−1.50667	+	0.299696i	−0.628412	+	0.777881i	$0.716295\pi$
$410$	−0.226281	+	0.212285i	−0.0111752	+	0.0104840i
$411$	−12.8472	−	10.5434i	−0.633707	−	0.520070i
$412$	9.13799	+	26.7747i	0.450196	+	1.31910i
$413$	0.561551	−	1.05059i	0.0276321	−	0.0516961i
$414$	3.89195	−	11.4964i	0.191279	−	0.565017i
$415$	0.598417	−	0.598417i	0.0293751	−	0.0293751i
$416$	−12.7042	−	7.82765i	−0.622876	−	0.383782i
$417$	10.8740	+	10.8740i	0.532500	+	0.532500i
$418$	−3.64397	+	1.80074i	−0.178232	+	0.0880769i
$419$	31.1295	+	16.6391i	1.52078	+	0.812872i	0.999187	−	0.0403241i	$-0.0128390\pi$
$419$	31.1295	+	16.6391i	1.52078	+	0.812872i	0.521590	+	0.853196i	$0.325339\pi$
$420$	3.65652	+	0.233615i	0.178420	+	0.0113992i
$421$	−18.9749	+	23.1210i	−0.924782	+	1.12685i	0.0668516	+	0.997763i	$0.478705\pi$
$421$	−18.9749	+	23.1210i	−0.924782	+	1.12685i	−0.991633	+	0.129087i	$0.958795\pi$
$422$	−0.305983	+	9.58823i	−0.0148950	+	0.466748i
$423$	−1.81367	−	9.11795i	−0.0881838	−	0.443330i
$424$	−22.3448	−	2.14506i	−1.08516	−	0.104173i
$425$	−0.514982	−	0.102436i	−0.0249803	−	0.00496889i
$426$	−5.47489	+	3.41076i	−0.265259	+	0.165252i
$427$	−1.11795	+	3.68537i	−0.0541012	+	0.178348i
$428$	3.97946	−	24.3527i	0.192354	−	1.17713i
$429$	−4.74953	−	5.78732i	−0.229310	−	0.279415i
$430$	13.6301	+	17.7328i	0.657300	+	0.855152i
$431$	−12.3007	+	29.6965i	−0.592503	+	1.43043i	0.288575	+	0.957457i	$0.406819\pi$
$431$	−12.3007	+	29.6965i	−0.592503	+	1.43043i	−0.881078	+	0.472971i	$0.843181\pi$
$432$	3.64887	+	1.63882i	0.175556	+	0.0788478i
$433$	−6.76264	−	16.3265i	−0.324992	−	0.784600i	−0.998949	−	0.0458297i	$-0.985407\pi$
$433$	−6.76264	−	16.3265i	−0.324992	−	0.784600i	0.673957	−	0.738770i	$-0.264593\pi$
$434$	−4.16642	+	7.23019i	−0.199994	+	0.347060i
$435$	1.03086	−	10.4665i	0.0494259	−	0.501830i
$436$	−9.99969	−	9.33487i	−0.478898	−	0.447059i
$437$	−4.09696	−	7.66488i	−0.195984	−	0.366661i
$438$	15.7168	−	2.60815i	0.750978	−	0.124622i
$439$	−12.5469	−	18.7778i	−0.598832	−	0.896215i	0.400971	−	0.916091i	$-0.368673\pi$
$439$	−12.5469	−	18.7778i	−0.598832	−	0.896215i	−0.999802	+	0.0198761i	$0.993673\pi$
$440$	−18.9957	+	0.0469207i	−0.905584	+	0.00223686i
$441$	−5.32193	−	3.55600i	−0.253425	−	0.169333i
$442$	1.15346	+	3.05704i	0.0548647	+	0.145409i
$443$	9.82817	−	0.967990i	0.466950	−	0.0459906i	0.138194	−	0.990405i	$-0.455870\pi$
$443$	9.82817	−	0.967990i	0.466950	−	0.0459906i	0.328757	+	0.944415i	$0.393370\pi$
$444$	1.61254	−	6.05795i	0.0765275	−	0.287498i
$445$	22.2290	−	6.74309i	1.05376	−	0.319653i
$446$	0.340838	+	5.13539i	0.0161391	+	0.243168i
$447$		−	12.4031i		−	0.586645i
$448$	−6.08042	−	1.17828i	−0.287273	−	0.0556683i
$449$		−	1.59790i		−	0.0754095i	−0.999289	−	0.0377048i	$-0.987995\pi$
$449$		−	1.59790i		−	0.0754095i	0.999289	−	0.0377048i	$-0.0120046\pi$
$450$	−0.845950	+	0.0561460i	−0.0398785	+	0.00264675i
$451$	0.251810	−	0.0763858i	0.0118573	−	0.00359687i
$452$	−1.12866	−	1.94748i	−0.0530876	−	0.0916017i
$453$	−5.80196	+	0.571443i	−0.272600	+	0.0268487i
$454$	−17.9171	+	6.76038i	−0.840893	+	0.317280i
$455$	4.01814	+	2.68483i	0.188373	+	0.125867i
$456$	2.64352	−	1.10264i	0.123794	−	0.0516358i
$457$	17.1124	+	25.6105i	0.800484	+	1.19801i	0.976901	+	0.213694i	$0.0685494\pi$
$457$	17.1124	+	25.6105i	0.800484	+	1.19801i	−0.176417	+	0.984316i	$0.556451\pi$
$458$	−5.01589	−	30.2259i	−0.234377	−	1.41237i
$459$	−0.412877	−	0.772438i	−0.0192714	−	0.0360543i
$460$	−1.39581	−	40.5934i	−0.0650800	−	1.89268i
$461$	−1.28841	+	13.0814i	−0.0600072	+	0.609263i	0.917410	+	0.397944i	$0.130276\pi$
$461$	−1.28841	+	13.0814i	−0.0600072	+	0.609263i	−0.977417	+	0.211319i	$0.932224\pi$
$462$	−2.69239	−	1.55150i	−0.125261	−	0.0721822i
$463$	−10.0686	−	24.3077i	−0.467927	−	1.12968i	−0.965067	−	0.262005i	$-0.915616\pi$
$463$	−10.0686	−	24.3077i	−0.467927	−	1.12968i	0.497140	−	0.867670i	$-0.334384\pi$
$464$	−3.97992	+	17.3268i	−0.184763	+	0.804377i
$465$	6.90181	−	16.6624i	0.320064	−	0.772702i
$466$	20.5889	−	15.8254i	0.953764	−	0.733097i
$467$	15.7402	+	19.1795i	0.728369	+	0.887520i	0.997132	−	0.0756866i	$-0.0241148\pi$
$467$	15.7402	+	19.1795i	0.728369	+	0.887520i	−0.268763	+	0.963206i	$0.586615\pi$
$468$	3.08007	+	4.28332i	0.142376	+	0.197997i
$469$	−1.37671	+	4.53841i	−0.0635706	+	0.209564i
$470$	−16.4504	−	26.4059i	−0.758801	−	1.21801i
$471$	−2.43579	−	0.484508i	−0.112235	−	0.0223250i
$472$	2.04208	−	3.84327i	0.0939943	−	0.176901i
$473$	−3.70057	−	18.6040i	−0.170152	−	0.855414i
$474$	16.6151	+	0.530228i	0.763157	+	0.0243542i
$475$	−0.385133	+	0.469286i	−0.0176711	+	0.0215323i
$476$	0.895860	+	1.01815i	0.0410617	+	0.0466666i
$477$	6.99929	+	3.74120i	0.320476	+	0.171298i
$478$	−12.3855	−	25.0632i	−0.566499	−	1.14637i
$479$	6.49046	+	6.49046i	0.296557	+	0.296557i	0.839664	−	0.543107i	$-0.182752\pi$
$479$	6.49046	+	6.49046i	0.296557	+	0.296557i	−0.543107	+	0.839664i	$0.682752\pi$
$480$	13.3608	+	0.820487i	0.609834	+	0.0374499i
$481$	5.84657	−	5.84657i	0.266581	−	0.266581i
$482$	−13.7078	−	4.64060i	−0.624375	−	0.211374i
$483$	3.13215	−	5.85984i	0.142518	−	0.266632i
$484$	−5.28657	−	2.59623i	−0.240299	−	0.118011i
$485$	20.6738	+	16.9665i	0.938748	+	0.770411i
$486$	−0.967595	−	1.03139i	−0.0438910	−	0.0467847i
$487$	−9.27847	+	1.84560i	−0.420447	+	0.0836322i	−0.400780	−	0.916174i	$-0.631261\pi$
$487$	−9.27847	+	1.84560i	−0.420447	+	0.0836322i	−0.0196676	+	0.999807i	$0.506261\pi$
$488$	−4.05102	+	13.4742i	−0.183381	+	0.609946i
$489$	−1.10896	+	5.57513i	−0.0501490	+	0.252116i
$490$	−20.8641	−	4.84671i	−0.942543	−	0.218952i
$491$	24.4455	+	7.41545i	1.10321	+	0.334654i	0.788810	−	0.614637i	$-0.210697\pi$
$491$	24.4455	+	7.41545i	1.10321	+	0.334654i	0.314398	+	0.949291i	$0.398197\pi$
$492$	−0.180517	+	0.0424042i	−0.00813833	+	0.00191173i
$493$	3.00914	−	2.46954i	0.135525	−	0.111222i
$494$	3.74588	+	0.490017i	0.168535	+	0.0220469i
$495$	6.20479	+	2.57011i	0.278884	+	0.115518i
$496$	−15.1563	+	26.4522i	−0.680536	+	1.18774i
$497$	−3.26239	+	1.35133i	−0.146338	+	0.0606152i
$498$	0.488435	−	0.131307i	0.0218873	−	0.00588401i
$499$	−33.9793	−	3.34666i	−1.52112	−	0.149817i	−0.697346	−	0.716735i	$-0.745636\pi$
$499$	−33.9793	−	3.34666i	−1.52112	−	0.149817i	−0.823775	+	0.566918i	$0.808136\pi$
$500$	18.9555	−	8.62629i	0.847717	−	0.385779i
$501$	13.2454	−	7.07982i	0.591762	−	0.316303i
$502$	10.8751	−	15.2027i	0.485381	−	0.678528i
$503$	−19.2516	+	12.8635i	−0.858387	+	0.573556i	−0.905026	−	0.425356i	$-0.860149\pi$
$503$	−19.2516	+	12.8635i	−0.858387	+	0.573556i	0.0466390	+	0.998912i	$0.485149\pi$
$504$	1.82371	+	1.21206i	0.0812343	+	0.0539893i
$505$	23.6793	−	35.4386i	1.05372	−	1.57700i
$506$	−14.1909	+	31.3888i	−0.630865	+	1.39540i
$507$	−0.592178	−	6.01249i	−0.0262996	−	0.267024i
$508$	3.24491	+	24.3378i	0.143970	+	1.07982i
$509$	1.86692	+	6.15441i	0.0827497	+	0.272789i	0.988545	−	0.150926i	$-0.0482256\pi$
$509$	1.86692	+	6.15441i	0.0827497	+	0.272789i	−0.905795	+	0.423716i	$0.860726\pi$
$510$	−2.20527	−	1.93076i	−0.0976510	−	0.0854955i
$511$	8.72162			0.385822
$512$	−22.2247	−	4.24982i	−0.982204	−	0.187817i
$513$	−1.01267			−0.0447105
$514$	−27.8163	−	24.3537i	−1.22692	−	1.07420i
$515$	−9.71670	−	32.0317i	−0.428169	−	1.41148i
$516$	1.76653	+	13.2495i	0.0777672	+	0.583277i
$517$	2.58620	+	26.2581i	0.113741	+	1.15483i
$518$	1.41376	−	3.12709i	0.0621171	−	0.137396i
$519$	7.27982	−	10.8950i	0.319549	−	0.478239i
$520$	14.7040	+	9.77246i	0.644814	+	0.428551i
$521$	17.5779	−	11.7452i	0.770101	−	0.514565i	−0.107356	−	0.994221i	$-0.534238\pi$
$521$	17.5779	−	11.7452i	0.770101	−	0.514565i	0.877457	+	0.479656i	$0.159238\pi$
$522$	3.65694	−	5.11214i	0.160060	−	0.223752i
$523$	33.1950	−	17.7431i	1.45152	−	0.775852i	0.457937	−	0.888985i	$-0.348588\pi$
$523$	33.1950	−	17.7431i	1.45152	−	0.775852i	0.993580	+	0.113133i	$0.0360885\pi$
$524$	9.09058	−	4.13694i	0.397124	−	0.180723i
$525$	−0.461888	−	0.0454920i	−0.0201584	−	0.00198543i
$526$	28.5214	−	7.66747i	1.24359	−	0.334317i
$527$	6.16735	−	2.55460i	0.268654	−	0.111280i
$528$	−9.85032	−	5.64391i	−0.428680	−	0.245620i
$529$	−46.8011	−	19.3857i	−2.03483	−	0.842855i
$530$	26.3347	+	3.44498i	1.14391	+	0.149640i
$531$	−1.18943	+	0.976141i	−0.0516169	+	0.0423609i
$532$	1.52645	−	0.358570i	0.0661801	−	0.0155460i
$533$	−0.234041	−	0.0709955i	−0.0101374	−	0.00307515i
$534$	13.5227	+	3.14131i	0.585184	+	0.135938i
$535$	−5.69572	+	28.6343i	−0.246248	+	1.23797i
$536$	−4.98869	+	16.5930i	−0.215479	+	0.716706i
$537$	−17.8461	+	3.54980i	−0.770115	+	0.153185i
$538$	24.5096	+	26.1255i	1.05668	+	1.12635i
$539$	14.0425	+	11.5244i	0.604854	+	0.496391i
$540$	−4.24803	−	2.08620i	−0.182806	−	0.0897760i
$541$	1.19640	−	2.23831i	0.0514374	−	0.0962327i	−0.854889	−	0.518811i	$-0.826375\pi$
$541$	1.19640	−	2.23831i	0.0514374	−	0.0962327i	0.906326	+	0.422578i	$0.138875\pi$
$542$	−35.0060	−	11.8508i	−1.50364	−	0.509036i
$543$	−1.25254	+	1.25254i	−0.0537517	+	0.0537517i
$544$	3.28211	+	3.71159i	0.140719	+	0.159133i
$545$	11.4447	+	11.4447i	0.490238	+	0.490238i
$546$	1.27953	+	2.58925i	0.0547587	+	0.110809i
$547$	3.93815	+	2.10499i	0.168383	+	0.0900027i	0.553435	−	0.832892i	$-0.313317\pi$
$547$	3.93815	+	2.10499i	0.168383	+	0.0900027i	−0.385052	+	0.922895i	$0.625817\pi$
$548$	−21.9574	−	24.9546i	−0.937974	−	1.06601i
$549$	3.15578	−	3.84533i	0.134685	−	0.164115i
$550$	2.40500	+	0.0767493i	0.102550	+	0.00327260i
$551$	−0.878065	−	4.41433i	−0.0374068	−	0.188057i
$552$	11.3901	−	21.4365i	0.484793	−	0.912398i
$553$	8.92548	+	1.77539i	0.379550	+	0.0754972i
$554$	8.56016	+	13.7406i	0.363686	+	0.583783i
$555$	−2.15308	+	7.09774i	−0.0913930	+	0.301282i
$556$	17.9560	+	24.9706i	0.761502	+	1.05899i
$557$	12.8773	+	15.6910i	0.545628	+	0.664849i	0.970696	−	0.240312i	$-0.0772498\pi$
$557$	12.8773	+	15.6910i	0.545628	+	0.664849i	−0.425068	+	0.905161i	$0.639750\pi$
$558$	8.54586	−	6.56866i	0.361775	−	0.278073i
$559$	−6.74669	+	16.2880i	−0.285355	+	0.688907i
$560$	7.14197	+	1.64049i	0.301803	+	0.0693235i
$561$	0.951285	+	2.29661i	0.0401633	+	0.0969628i
$562$	−31.9025	−	18.3839i	−1.34572	−	0.775478i
$563$	0.371259	−	3.76946i	0.0156467	−	0.158864i	−0.984186	−	0.177136i	$-0.943317\pi$
$563$	0.371259	−	3.76946i	0.0156467	−	0.158864i	0.999833	+	0.0182725i	$0.00581665\pi$
$564$	−0.638951	−	18.5822i	−0.0269047	−	0.782451i
$565$	1.25541	+	2.34871i	0.0528156	+	0.0988111i
$566$	4.50634	+	27.1554i	0.189416	+	1.14142i
$567$	−0.430118	−	0.643717i	−0.0180633	−	0.0270336i
$568$	−11.9065	+	4.96635i	−0.499588	+	0.208383i
$569$	14.6703	+	9.80241i	0.615013	+	0.410938i	0.823685	−	0.567047i	$-0.191914\pi$
$569$	14.6703	+	9.80241i	0.615013	+	0.410938i	−0.208673	+	0.977986i	$0.566914\pi$
$570$	−3.17070	+	1.19635i	−0.132806	+	0.0501095i
$571$	34.4379	−	3.39184i	1.44118	−	0.141944i	0.652986	−	0.757370i	$-0.273516\pi$
$571$	34.4379	−	3.39184i	1.44118	−	0.141944i	0.788195	+	0.615426i	$0.211016\pi$
$572$	−7.50808	−	12.9551i	−0.313929	−	0.541678i
$573$	−8.27778	+	2.51104i	−0.345809	+	0.104900i
$574$	−0.101289	+	0.00672256i	−0.00422770	+	0.000280594i
$575$			5.14507i			0.214564i
$576$	6.67363	+	4.41165i	0.278068	+	0.183819i
$577$			17.3316i			0.721524i	0.932658	+	0.360762i	$0.117483\pi$
$577$			17.3316i			0.721524i	−0.932658	+	0.360762i	$0.882517\pi$
$578$	1.52030	+	22.9064i	0.0632363	+	0.952779i
$579$	13.3956	−	4.06350i	0.556701	−	0.168873i
$580$	5.41061	−	20.3265i	0.224663	−	0.844012i
$581$	0.275548	−	0.0271391i	0.0114316	−	0.00112592i
$582$	5.64255	+	14.9545i	0.233891	+	0.619885i
$583$	−18.7287	−	12.5141i	−0.775664	−	0.518282i
$584$	31.8634	−	0.0787049i	1.31852	−	0.00325683i
$585$	−3.46792	−	5.19010i	−0.143381	−	0.214584i
$586$	2.09653	−	0.347912i	0.0866068	−	0.0143721i
$587$	−0.454744	−	0.850766i	−0.0187693	−	0.0351149i	0.872362	−	0.488861i	$-0.162587\pi$
$587$	−0.454744	−	0.850766i	−0.0187693	−	0.0351149i	−0.891131	+	0.453746i	$0.850087\pi$
$588$	−9.35757	−	8.73544i	−0.385900	−	0.360244i
$589$	0.756517	−	7.68105i	0.0311717	−	0.316492i
$590$	−2.57095	+	4.46149i	−0.105844	+	0.183677i
$591$	1.46167	+	3.52880i	0.0601253	+	0.145155i
$592$	5.13679	−	11.4372i	0.211121	−	0.470066i
$593$	−12.0858	+	29.1776i	−0.496302	+	1.19818i	0.455159	+	0.890410i	$0.349583\pi$
$593$	−12.0858	+	29.1776i	−0.496302	+	1.19818i	−0.951461	+	0.307769i	$0.900417\pi$
$594$	2.44605	+	3.18232i	0.100363	+	0.130572i
$595$	−1.01792	−	1.24034i	−0.0417308	−	0.0508492i
$596$	4.00050	−	24.4814i	0.163867	−	1.00280i
$597$	−6.12662	+	20.1967i	−0.250746	+	0.826598i
$598$	27.1748	−	16.9294i	1.11126	−	0.692295i
$599$	−17.4783	−	3.47666i	−0.714145	−	0.142052i	−0.175371	−	0.984502i	$-0.556113\pi$
$599$	−17.4783	−	3.47666i	−0.714145	−	0.142052i	−0.538774	+	0.842450i	$0.681113\pi$
$600$	−1.68786	−	0.162031i	−0.0689067	−	0.00661490i
$601$	−5.93251	−	29.8248i	−0.241992	−	1.21658i	−0.890363	−	0.455252i	$-0.849549\pi$
$601$	−5.93251	−	29.8248i	−0.241992	−	1.21658i	0.648370	−	0.761325i	$-0.275451\pi$
$602$	−0.233398	+	7.31372i	−0.00951261	+	0.298085i
$603$	3.88623	−	4.73538i	0.158259	−	0.192840i
$604$	−11.6363	−	0.743444i	−0.473476	−	0.0302503i
$605$	6.14561	+	3.28490i	0.249855	+	0.133550i
$606$	22.8363	−	11.2850i	0.927660	−	0.458421i
$607$	−27.8968	−	27.8968i	−1.13229	−	1.13229i	−0.989795	−	0.142500i	$-0.954486\pi$
$607$	−27.8968	−	27.8968i	−1.13229	−	1.13229i	−0.142500	−	0.989795i	$-0.545514\pi$
$608$	5.57348	−	1.32377i	0.226034	−	0.0536859i
$609$	2.43308	−	2.43308i	0.0985935	−	0.0985935i
$610$	5.33804	−	15.7680i	0.216131	−	0.638427i
$611$	11.5602	−	21.6276i	0.467675	−	0.874959i
$612$	−0.565802	−	1.65782i	−0.0228712	−	0.0670136i
$613$	−9.24282	−	7.58539i	−0.373314	−	0.306371i	0.428964	−	0.903322i	$-0.358879\pi$
$613$	−9.24282	−	7.58539i	−0.373314	−	0.306371i	−0.802278	+	0.596951i	$0.796379\pi$
$614$	13.1896	−	12.3738i	0.532290	−	0.499367i
$615$	0.215179	−	0.0428017i	0.00867685	−	0.00172593i
$616$	−4.81387	−	3.93078i	−0.193956	−	0.158376i
$617$	−5.91214	+	29.7223i	−0.238014	+	1.19658i	0.658162	+	0.752876i	$0.271334\pi$
$617$	−5.91214	+	29.7223i	−0.238014	+	1.19658i	−0.896176	+	0.443699i	$0.853666\pi$
$618$	4.52658	−	19.4860i	0.182086	−	0.783842i
$619$	−8.59856	−	2.60834i	−0.345605	−	0.104838i	0.112710	−	0.993628i	$-0.464047\pi$
$619$	−8.59856	−	2.60834i	−0.345605	−	0.104838i	−0.458315	+	0.888790i	$0.651547\pi$
$620$	18.9973	−	30.6626i	0.762948	−	1.23144i
$621$	−6.63427	+	5.44460i	−0.266224	+	0.218484i
$622$	−2.64729	+	20.2369i	−0.106147	+	0.811427i
$623$	7.02142	+	2.90837i	0.281307	+	0.116521i
$624$	4.69796	+	9.44796i	0.188069	+	0.378221i
$625$	−25.5342	+	10.5766i	−1.02137	+	0.423065i
$626$	−5.50812	−	20.4891i	−0.220149	−	0.818909i
$627$	2.86028	+	0.281713i	0.114229	+	0.0112505i
$628$	−4.65153	−	1.74197i	−0.185616	−	0.0695123i
$629$	−2.42117	+	1.29414i	−0.0965382	+	0.0516008i
$630$	−2.10719	−	1.50736i	−0.0839523	−	0.0600548i
$631$	−24.2903	+	16.2302i	−0.966980	+	0.646116i	−0.935477	−	0.353388i	$-0.885030\pi$
$631$	−24.2903	+	16.2302i	−0.966980	+	0.646116i	−0.0315034	+	0.999504i	$0.510030\pi$
$632$	32.6242	+	6.40563i	1.29772	+	0.254802i
$633$	3.76863	−	5.64015i	0.149790	−	0.224176i
$634$	17.5522	+	7.93541i	0.697089	+	0.315155i
$635$	−2.84744	−	28.9105i	−0.112997	−	1.14728i
$636$	12.6087	+	9.64201i	0.499966	+	0.382331i
$637$	−4.90119	−	16.1571i	−0.194192	−	0.640167i
$638$	−11.7512	+	13.4219i	−0.465233	+	0.531378i
$639$	4.56112			0.180435
$640$	26.1072	+	5.92890i	1.03198	+	0.234360i
$641$	40.9256			1.61647			0.808233	−	0.588863i	$-0.200424\pi$
$641$	40.9256			1.61647			0.808233	+	0.588863i	$0.200424\pi$
$642$	−11.4937	+	13.1278i	−0.453619	+	0.518113i
$643$	−1.45765	−	4.80523i	−0.0574842	−	0.189500i	0.923496	−	0.383608i	$-0.125319\pi$
$643$	−1.45765	−	4.80523i	−0.0574842	−	0.189500i	−0.980980	+	0.194108i	$0.937819\pi$
$644$	8.07234	−	10.5560i	0.318095	−	0.415966i
$645$	−1.55015	−	15.7389i	−0.0610369	−	0.619718i
$646$	−1.14296	−	0.516736i	−0.0449693	−	0.0203307i
$647$	−16.0843	+	24.0719i	−0.632339	+	0.946363i	0.367527	+	0.930013i	$0.380205\pi$
$647$	−16.0843	+	24.0719i	−0.632339	+	0.946363i	−0.999866	+	0.0163500i	$0.994795\pi$
$648$	−1.57719	−	2.34786i	−0.0619580	−	0.0922328i
$649$	3.63109	−	2.42622i	0.142533	−	0.0952375i
$650$	−1.81894	−	1.30117i	−0.0713448	−	0.0510361i
$651$	5.20388	−	2.78153i	0.203956	−	0.109017i
$652$	−3.98710	+	10.6466i	−0.156147	+	0.416954i
$653$	−35.6850	−	3.51467i	−1.39646	−	0.137540i	−0.628388	−	0.777900i	$-0.716285\pi$
$653$	−35.6850	−	3.51467i	−1.39646	−	0.137540i	−0.768075	+	0.640360i	$0.778785\pi$
$654$	2.51125	+	9.34133i	0.0981975	+	0.365275i
$655$	−10.9175	+	4.52217i	−0.426581	+	0.176696i
$656$	−0.369985	+	0.0254741i	−0.0144455	+	0.000994597i
$657$	−10.4079	−	4.31110i	−0.406052	−	0.168192i
$658$	1.32026	−	10.0926i	0.0514691	−	0.393450i
$659$	−25.3704	+	20.8209i	−0.988289	+	0.811068i	−0.981994	−	0.188912i	$-0.939504\pi$
$659$	−25.3704	+	20.8209i	−0.988289	+	0.811068i	−0.00629502	+	0.999980i	$0.502004\pi$
$660$	11.4182	+	7.07423i	0.444452	+	0.275364i
$661$	20.1883	+	6.12404i	0.785232	+	0.238198i	0.657344	−	0.753591i	$-0.271680\pi$
$661$	20.1883	+	6.12404i	0.785232	+	0.238198i	0.127889	+	0.991789i	$0.459180\pi$
$662$	8.22672	−	35.4143i	0.319740	−	1.37642i
$663$	0.450739	−	2.26602i	0.0175052	−	0.0880048i
$664$	1.00644	−	0.101636i	0.0390573	−	0.00394424i
$665$	−1.81955	+	0.361932i	−0.0705592	+	0.0140351i
$666$	−3.23283	+	3.03287i	−0.125270	+	0.117522i
$667$	−29.4860	−	24.1985i	−1.14170	−	0.936972i
$668$	28.4276	−	9.70211i	1.09990	−	0.375386i
$669$	1.71553	−	3.20954i	0.0663263	−	0.124088i
$670$	6.57360	−	19.4177i	0.253960	−	0.750172i
$671$	−9.98321	+	9.98321i	−0.385397	+	0.385397i
$672$	3.20873	+	2.98060i	0.123779	+	0.114979i
$673$	−11.9744	−	11.9744i	−0.461579	−	0.461579i	0.437594	−	0.899173i	$-0.355831\pi$
$673$	−11.9744	−	11.9744i	−0.461579	−	0.461579i	−0.899173	+	0.437594i	$0.855831\pi$
$674$	−41.0672	+	20.2942i	−1.58185	+	0.781702i
$675$	0.528706	+	0.282599i	0.0203499	+	0.0108772i
$676$	0.770421	−	12.0586i	0.0296316	−	0.463791i
$677$	−3.04733	+	3.71319i	−0.117119	+	0.142709i	−0.828269	−	0.560330i	$-0.810674\pi$
$677$	−3.04733	+	3.71319i	−0.117119	+	0.142709i	0.711151	+	0.703039i	$0.248174\pi$
$678$	−0.0507667	+	1.59082i	−0.00194968	+	0.0610949i
$679$	1.70704	+	8.58189i	0.0655103	+	0.329343i
$680$	−3.73006	−	4.52227i	−0.143041	−	0.173421i
$681$	13.2810	+	2.64175i	0.508928	+	0.101232i
$682$	−25.9651	+	16.1758i	−0.994254	+	0.619403i
$683$	−4.02956	+	13.2837i	−0.154187	+	0.508286i	−0.999669	−	0.0257174i	$-0.991813\pi$
$683$	−4.02956	+	13.2837i	−0.154187	+	0.508286i	0.845482	+	0.534003i	$0.179313\pi$
$684$	−1.99883	−	0.326628i	−0.0764271	−	0.0124889i
$685$	24.9492	+	30.4007i	0.953260	+	1.16155i
$686$	−8.94132	−	11.6327i	−0.341381	−	0.444139i
$687$	−8.29094	+	20.0161i	−0.316319	+	0.763662i
$688$	−0.786694	+	26.7219i	−0.0299924	+	1.01876i
$689$	8.01160	+	19.3417i	0.305218	+	0.736861i
$690$	−14.3399	+	24.8848i	−0.545912	+	0.947347i
$691$	3.49395	−	35.4746i	0.132916	−	1.34952i	−0.665042	−	0.746806i	$-0.731586\pi$
$691$	3.49395	−	35.4746i	0.132916	−	1.34952i	0.797958	−	0.602713i	$-0.205914\pi$
$692$	17.8832	−	19.1568i	0.679816	−	0.728232i
$693$	1.03579	+	1.93783i	0.0393465	+	0.0736121i
$694$	−45.1115	+	7.48610i	−1.71241	+	0.284168i
$695$	−20.2170	−	30.2568i	−0.766874	−	1.14771i
$696$	8.86702	−	8.91094i	0.336104	−	0.337768i
$697$	0.0675199	+	0.0451153i	0.00255750	+	0.00170886i
$698$	−5.17553	−	13.7168i	−0.195897	−	0.519188i
$699$	−18.2739	+	1.79982i	−0.691181	+	0.0680754i
$700$	−0.897010	−	0.238771i	−0.0339038	−	0.00902469i
$701$	23.5879	−	7.15531i	0.890903	−	0.270252i	0.188535	−	0.982066i	$-0.439626\pi$
$701$	23.5879	−	7.15531i	0.890903	−	0.270252i	0.702368	+	0.711814i	$0.252126\pi$
$702$	−0.247053	−	3.72234i	−0.00932442	−	0.140491i
$703$			3.17416i			0.119716i
$704$	−17.6224	−	14.3172i	−0.664168	−	0.539600i
$705$			21.9987i			0.828520i
$706$	−37.7417	+	2.50493i	−1.42043	+	0.0942744i
$707$	13.3441	−	4.04789i	0.501857	−	0.152237i
$708$	−2.66257	+	1.54309i	−0.100065	+	0.0579927i
$709$	−40.1676	+	3.95616i	−1.50853	+	0.148577i	−0.818205	−	0.574927i	$-0.805030\pi$
$709$	−40.1676	+	3.95616i	−1.50853	+	0.148577i	−0.690320	+	0.723504i	$0.742530\pi$
$710$	14.2810	−	5.38841i	0.535956	−	0.202223i
$711$	−9.77362	−	6.53052i	−0.366539	−	0.244914i
$712$	25.6782	+	10.5620i	0.962330	+	0.395828i
$713$	−36.3409	−	54.3880i	−1.36098	−	2.03685i
$714$	−0.156988	−	0.946016i	−0.00587514	−	0.0354038i
$715$	8.35129	+	15.6242i	0.312320	+	0.584310i
$716$	−36.3699	+	1.25059i	−1.35921	+	0.0467366i
$717$	−1.93763	+	19.6730i	−0.0723619	+	0.734703i
$718$	−18.9531	−	10.9218i	−0.707322	−	0.407596i
$719$	−14.4744	−	34.9442i	−0.539803	−	1.30320i	−0.924860	−	0.380307i	$-0.875818\pi$
$719$	−14.4744	−	34.9442i	−0.539803	−	1.30320i	0.385057	−	0.922893i	$-0.374182\pi$
$720$	−7.71195	−	5.48796i	−0.287408	−	0.204524i
$721$	4.19091	−	10.1178i	0.156078	−	0.376805i
$722$	20.1541	−	15.4912i	0.750059	−	0.576522i
$723$	6.49193	+	7.91044i	0.241437	+	0.294192i
$724$	−2.87629	+	2.06829i	−0.106896	+	0.0768676i
$725$	−0.773449	+	2.54972i	−0.0287252	+	0.0946942i
$726$	2.20212	+	3.53480i	0.0817282	+	0.131189i
$727$	−11.5031	−	2.28810i	−0.426625	−	0.0848609i	−0.0228921	−	0.999738i	$-0.507287\pi$
$727$	−11.5031	−	2.28810i	−0.426625	−	0.0848609i	−0.403733	+	0.914877i	$0.632287\pi$
$728$	1.69042	+	5.52341i	0.0626510	+	0.204711i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	−37.6805	−	1.20248i	−1.39462	−	0.0445056i
$731$	3.71354	−	4.52497i	0.137350	−	0.167362i
$732$	7.46921	−	6.57212i	0.276070	−	0.242912i
$733$	26.2366	+	14.0237i	0.969070	+	0.517979i	0.878412	−	0.477904i	$-0.158603\pi$
$733$	26.2366	+	14.0237i	0.969070	+	0.517979i	0.0906574	+	0.995882i	$0.471103\pi$
$734$	3.27820	+	6.63375i	0.121000	+	0.244856i
$735$	10.7098	+	10.7098i	0.395037	+	0.395037i
$736$	29.3961	−	38.6380i	1.08355	−	1.42422i
$737$	−12.2940	+	12.2940i	−0.452854	+	0.452854i
$738$	0.124195	+	0.0420446i	0.00457169	+	0.00154768i
$739$	−0.487818	+	0.912644i	−0.0179447	+	0.0335721i	−0.890734	−	0.454525i	$-0.849809\pi$
$739$	−0.487818	+	0.912644i	−0.0179447	+	0.0335721i	0.872789	+	0.488097i	$0.162309\pi$
$740$	−6.53910	+	13.3152i	−0.240382	+	0.489477i
$741$	−2.06494	−	1.69466i	−0.0758576	−	0.0622548i
$742$	5.94520	+	6.33716i	0.218255	+	0.232645i
$743$	31.9183	−	6.34894i	1.17097	−	0.232920i	0.428968	−	0.903320i	$-0.358877\pi$
$743$	31.9183	−	6.34894i	1.17097	−	0.232920i	0.742000	+	0.670399i	$0.233877\pi$
$744$	18.9867	−	10.2090i	0.696085	−	0.374279i
$745$	−5.72584	+	28.7857i	−0.209778	+	1.05463i
$746$	−8.64144	−	2.00740i	−0.316386	−	0.0734961i
$747$	−0.342239	−	0.103817i	−0.0125219	−	0.00379846i
$748$	1.13692	+	4.83992i	0.0415698	+	0.176965i
$749$	−7.38368	+	6.05963i	−0.269794	+	0.221414i
$750$	−14.6018	−	1.91014i	−0.533184	−	0.0697484i
$751$	3.10927	+	1.28790i	0.113459	+	0.0469962i	0.438691	−	0.898638i	$-0.355442\pi$
$751$	3.10927	+	1.28790i	0.113459	+	0.0469962i	−0.325232	+	0.945634i	$0.605442\pi$
$752$	4.73234	−	36.8840i	0.172571	−	1.34502i
$753$	−12.2111	+	5.05801i	−0.444998	+	0.184324i
$754$	16.0118	−	4.30449i	0.583117	−	0.156760i
$755$	13.7293	+	1.35222i	0.499661	+	0.0492123i
$756$	−0.641351	−	1.40931i	−0.0233257	−	0.0512562i
$757$	−2.04544	+	1.09331i	−0.0743427	+	0.0397370i	−0.508149	−	0.861269i	$-0.669670\pi$
$757$	−2.04544	+	1.09331i	−0.0743427	+	0.0397370i	0.433806	+	0.901006i	$0.357170\pi$
$758$	4.17698	−	5.83912i	0.151715	−	0.212087i
$759$	20.2531	−	13.5327i	0.735140	−	0.491205i
$760$	−6.64426	+	1.33869i	−0.241012	+	0.0485595i
$761$	−11.8233	+	17.6948i	−0.428593	+	0.641435i	−0.981422	−	0.191860i	$-0.938548\pi$
$761$	−11.8233	+	17.6948i	−0.428593	+	0.641435i	0.552829	+	0.833294i	$0.313548\pi$
$762$	7.15228	−	15.8201i	0.259100	−	0.573100i
$763$	0.519035	+	5.26985i	0.0187903	+	0.190781i
$764$	−17.1488	+	2.28641i	−0.620421	+	0.0827195i
$765$	0.601634	+	1.98332i	0.0217521	+	0.0717072i
$766$	24.5924	+	21.5312i	0.888560	+	0.777952i
$767$	−4.05891			−0.146559
$768$	11.7496	+	10.8603i	0.423978	+	0.391888i
$769$	41.2073			1.48597			0.742987	−	0.669306i	$-0.233408\pi$
$769$	41.2073			1.48597			0.742987	+	0.669306i	$0.233408\pi$
$770$	5.53240	+	4.84374i	0.199374	+	0.174556i
$771$	7.58873	+	25.0167i	0.273302	+	0.900955i
$772$	27.7511	−	3.70000i	0.998785	−	0.133166i
$773$	3.04931	+	30.9601i	0.109676	+	1.11356i	0.879695	+	0.475538i	$0.157747\pi$
$773$	3.04931	+	30.9601i	0.109676	+	1.11356i	−0.770019	+	0.638021i	$0.779753\pi$
$774$	3.89370	−	8.61244i	0.139956	−	0.309568i
$775$	−2.53847	+	3.79909i	−0.0911845	+	0.136467i
$776$	6.31393	+	31.3375i	0.226657	+	1.12495i
$777$	−2.01770	+	1.34818i	−0.0723845	+	0.0483658i
$778$	−21.3838	+	29.8931i	−0.766648	+	1.07172i
$779$	0.0828035	−	0.0442594i	0.00296674	−	0.00158576i
$780$	−5.17102	−	11.3629i	−0.185152	−	0.406856i
$781$	−12.8829	−	1.26885i	−0.460985	−	0.0454031i
$782$	−10.2661	+	2.75985i	−0.367114	+	0.0986919i
$783$	−4.10619	+	1.70084i	−0.146743	+	0.0607830i
$784$	−15.6526	−	20.2604i	−0.559022	−	0.723585i
$785$	5.42944	+	2.24895i	0.193785	+	0.0802684i
$786$	−7.00266	−	0.916053i	−0.249777	−	0.0326745i
$787$	−6.07875	+	4.98870i	−0.216684	+	0.177828i	−0.736474	−	0.676466i	$-0.763510\pi$
$787$	−6.07875	+	4.98870i	−0.216684	+	0.177828i	0.519789	+	0.854294i	$0.326010\pi$
$788$	1.74690	+	7.43666i	0.0622308	+	0.264920i
$789$	−19.9845	−	6.06223i	−0.711467	−	0.215821i
$790$	−38.3165	−	8.90089i	−1.36324	−	0.316680i
$791$	−0.169985	+	0.854572i	−0.00604397	+	0.0303851i
$792$	3.80163	+	7.07028i	0.135085	+	0.251232i
$793$	12.8700	−	2.55999i	0.457026	−	0.0909080i
$794$	3.47330	+	3.70229i	0.123263	+	0.131389i
$795$	−14.5172	−	11.9140i	−0.514873	−	0.422546i
$796$	−18.6071	+	37.8887i	−0.659512	+	1.34293i
$797$	−21.1867	+	39.6376i	−0.750472	+	1.40403i	0.158577	+	0.987347i	$0.449309\pi$
$797$	−21.1867	+	39.6376i	−0.750472	+	1.40403i	−0.909049	+	0.416688i	$0.863191\pi$
$798$	−1.05020	−	0.355530i	−0.0371766	−	0.0125856i
$799$	−5.75761	+	5.75761i	−0.203690	+	0.203690i
$800$	−3.27928	−	0.864226i	−0.115940	−	0.0305550i
$801$	−6.94138	−	6.94138i	−0.245262	−	0.245262i
$802$	18.5081	+	37.4529i	0.653544	+	1.32251i
$803$	28.1978	+	15.0720i	0.995079	+	0.531881i
$804$	9.19807	−	8.09333i	0.324391	−	0.285430i
$805$	−9.97445	+	12.1539i	−0.351553	+	0.428369i
$806$	28.4183	+	0.906896i	1.00099	+	0.0319441i
$807$	−4.94172	−	24.8437i	−0.173957	−	0.874539i
$808$	48.7146	−	14.9089i	1.71377	−	0.524493i
$809$	−43.5240	−	8.65746i	−1.53022	−	0.304380i	−0.643052	−	0.765823i	$-0.722332\pi$
$809$	−43.5240	−	8.65746i	−1.53022	−	0.304380i	−0.887170	+	0.461443i	$0.847332\pi$
$810$	1.76951	+	2.84039i	0.0621743	+	0.0998011i
$811$	1.49795	−	4.93806i	0.0526000	−	0.173399i	−0.926705	−	0.375790i	$-0.877371\pi$
$811$	1.49795	−	4.93806i	0.0526000	−	0.173399i	0.979305	+	0.202391i	$0.0648713\pi$
$812$	5.58724	−	4.01770i	0.196074	−	0.140994i
$813$	16.5786	+	20.2011i	0.581436	+	0.708482i
$814$	9.97482	−	7.66701i	0.349617	−	0.268728i
$815$	5.14748	−	12.4271i	0.180308	−	0.435303i
$816$	−0.582075	−	3.45474i	−0.0203767	−	0.120940i
$817$	−2.59002	−	6.25287i	−0.0906134	−	0.218760i
$818$	38.0678	+	21.9367i	1.33101	+	0.766999i
$819$	0.200173	−	2.03239i	0.00699462	−	0.0710176i
$820$	0.438530	−	0.0150789i	0.0153141	−	0.000526579i
$821$	−12.3948	−	23.1890i	−0.432580	−	0.809301i	0.567319	−	0.823498i	$-0.307981\pi$
$821$	−12.3948	−	23.1890i	−0.432580	−	0.809301i	−0.999899	+	0.0141976i	$0.995481\pi$
$822$	3.84776	+	23.1868i	0.134206	+	0.808731i
$823$	9.42917	+	14.1117i	0.328680	+	0.491905i	0.958600	−	0.284755i	$-0.0919124\pi$
$823$	9.42917	+	14.1117i	0.328680	+	0.491905i	−0.629920	+	0.776660i	$0.716912\pi$
$824$	15.2197	−	37.0019i	0.530203	−	1.28902i
$825$	−1.41471	−	0.945279i	−0.0492539	−	0.0329104i
$826$	−1.57621	+	0.594727i	−0.0548435	+	0.0206932i
$827$	8.39911	−	0.827240i	0.292066	−	0.0287659i	0.0490767	−	0.998795i	$-0.484372\pi$
$827$	8.39911	−	0.827240i	0.292066	−	0.0287659i	0.242989	+	0.970029i	$0.421872\pi$
$828$	−14.8510	+	8.60684i	−0.516106	+	0.299108i
$829$	33.9636	−	10.3028i	1.17961	−	0.357830i	0.361210	−	0.932484i	$-0.382364\pi$
$829$	33.9636	−	10.3028i	1.17961	−	0.357830i	0.818396	+	0.574655i	$0.194864\pi$
$830$	−1.19421	+	0.0792599i	−0.0414515	+	0.00275115i
$831$		−	11.4473i		−	0.397102i
$832$	6.22558	+	20.1639i	0.215833	+	0.699056i
$833$			5.60604i			0.194238i
$834$	−1.44025	−	21.7002i	−0.0498718	−	0.751416i
$835$	−34.0091	+	10.3165i	−1.17693	+	0.357019i
$836$	5.55482	+	1.47861i	0.192117	+	0.0511388i
$837$	−7.58495	+	0.747052i	−0.262174	+	0.0258219i
$838$	−17.6221	−	46.7041i	−0.608745	−	1.61337i
$839$	18.5462	+	12.3921i	0.640285	+	0.427825i	0.832880	−	0.553454i	$-0.186690\pi$
$839$	18.5462	+	12.3921i	0.640285	+	0.427825i	−0.192595	+	0.981278i	$0.561690\pi$
$840$	−3.67302	−	3.65492i	−0.126731	−	0.126107i
$841$	5.13702	+	7.68809i	0.177139	+	0.265107i
$842$	41.7290	−	6.92478i	1.43808	−	0.238644i
$843$	12.2732	+	22.9616i	0.422713	+	0.790840i
$844$	9.25778	−	9.91711i	0.318666	−	0.341361i
$845$	−1.40129	+	14.2275i	−0.0482057	+	0.489441i
$846$	−6.56430	+	11.3913i	−0.225685	+	0.391642i
$847$	0.872468	+	2.10632i	0.0299784	+	0.0723742i
$848$	21.7773	+	23.0984i	0.747835	+	0.793203i
$849$	7.44868	−	17.9827i	0.255638	−	0.617165i
$850$	0.452528	+	0.588742i	0.0155216	+	0.0201937i
$851$	17.0658	+	20.7947i	0.585008	+	0.712835i
$852$	9.00283	+	1.47115i	0.308432	+	0.0504007i
$853$	−15.1577	+	49.9681i	−0.518988	+	1.71088i	0.169413	+	0.985545i	$0.445813\pi$
$853$	−15.1577	+	49.9681i	−0.518988	+	1.71088i	−0.688401	+	0.725330i	$0.741687\pi$
$854$	4.62275	−	2.87989i	0.158187	−	0.0985478i
$855$	2.35026	+	0.467496i	0.0803772	+	0.0159880i
$856$	−26.9207	+	22.2048i	−0.920131	+	0.758943i
$857$	−5.49725	−	27.6365i	−0.187782	−	0.944046i	−0.953620	−	0.301012i	$-0.902676\pi$
$857$	−5.49725	−	27.6365i	−0.187782	−	0.944046i	0.765838	−	0.643034i	$-0.222324\pi$
$858$	−0.337712	+	10.5825i	−0.0115293	+	0.361279i
$859$	−8.32160	+	10.1399i	−0.283929	+	0.345969i	−0.895371	−	0.445320i	$-0.853090\pi$
$859$	−8.32160	+	10.1399i	−0.283929	+	0.345969i	0.611442	+	0.791289i	$0.290590\pi$
$860$	2.01673	−	31.5657i	0.0687699	−	1.07638i
$861$	0.0633038	+	0.0338366i	0.00215739	+	0.00115315i
$862$	40.7529	−	20.1388i	1.38805	−	0.685932i
$863$	−29.9716	−	29.9716i	−1.02025	−	1.02025i	−0.999791	−	0.0204550i	$-0.993489\pi$
$863$	−29.9716	−	29.9716i	−1.02025	−	1.02025i	−0.0204550	−	0.999791i	$-0.506511\pi$
$864$	−2.35582	−	5.14297i	−0.0801465	−	0.174967i
$865$	−21.9251	+	21.9251i	−0.745475	+	0.745475i
$866$	−8.01376	+	23.6718i	−0.272319	+	0.804400i
$867$	7.65212	−	14.3161i	0.259880	−	0.486201i
$868$	11.1687	−	3.81178i	0.379090	−	0.129380i
$869$	25.7888	+	21.1643i	0.874826	+	0.717951i
$870$	−10.8472	+	10.1763i	−0.367756	+	0.345010i
$871$	15.8489	−	3.15254i	0.537019	−	0.106820i
$872$	1.94379	+	19.2481i	0.0658249	+	0.651822i
$873$	2.20494	−	11.0850i	0.0746258	−	0.375169i
$874$	−2.78116	+	11.9723i	−0.0940741	+	0.404969i
$875$	−7.71455	−	2.34018i	−0.260799	−	0.0791126i
$876$	−19.1529	−	11.8663i	−0.647115	−	0.400926i
$877$	−31.6744	+	25.9945i	−1.06957	+	0.877773i	−0.992861	−	0.119280i	$-0.961941\pi$
$877$	−31.6744	+	25.9945i	−1.06957	+	0.877773i	−0.0767093	+	0.997054i	$0.524441\pi$
$878$	−4.14272	+	31.6686i	−0.139810	+	1.06876i
$879$	−1.38835	−	0.575075i	−0.0468280	−	0.0193968i
$880$	20.2557	+	17.6461i	0.682819	+	0.594849i
$881$	4.55860	−	1.88823i	0.153583	−	0.0636162i	−0.304568	−	0.952491i	$-0.598512\pi$
$881$	4.55860	−	1.88823i	0.153583	−	0.0636162i	0.458151	+	0.888875i	$0.348512\pi$
$882$	2.34999	+	8.74149i	0.0791283	+	0.294341i
$883$	13.5534	+	1.33489i	0.456108	+	0.0449227i	0.323463	−	0.946241i	$-0.395153\pi$
$883$	13.5534	+	1.33489i	0.456108	+	0.0449227i	0.132645	+	0.991164i	$0.457653\pi$
$884$	1.62056	−	4.32733i	0.0545054	−	0.145544i
$885$	3.21113	−	1.71639i	0.107941	−	0.0576957i
$886$	−11.3592	−	8.12575i	−0.381620	−	0.272990i
$887$	12.6879	−	8.47782i	0.426020	−	0.284657i	−0.324020	−	0.946050i	$-0.605034\pi$
$887$	12.6879	−	8.47782i	0.426020	−	0.284657i	0.750039	+	0.661393i	$0.230034\pi$
$888$	−7.35925	+	4.94363i	−0.246960	+	0.165897i
$889$	5.28038	−	7.90265i	0.177098	−	0.265046i
$890$	−29.9340	−	13.5332i	−1.00339	−	0.453635i
$891$	−0.278189	−	2.82450i	−0.00931967	−	0.0946242i
$892$	4.42136	−	5.78172i	0.148038	−	0.193586i
$893$	2.73284	+	9.00898i	0.0914512	+	0.301474i
$894$	−11.5544	+	13.1972i	−0.386438	+	0.441381i
$895$	43.0569			1.43923
$896$	5.37209	+	6.91812i	0.179469	+	0.231118i
$897$	−22.6393			−0.755904
$898$	−1.48857	+	1.70021i	−0.0496742	+	0.0567368i
$899$	−9.83323	−	32.4158i	−0.327957	−	1.08113i
$900$	0.952420	+	0.728329i	0.0317473	+	0.0242776i
$901$	−0.681334	−	6.91770i	−0.0226985	−	0.230462i
$902$	−0.339093	−	0.153305i	−0.0112906	−	0.00510448i
$903$	2.87464	−	4.30220i	0.0956621	−	0.143168i
$904$	−0.613308	+	3.12361i	−0.0203983	+	0.103890i
$905$	3.48520	−	2.32874i	0.115852	−	0.0774098i
$906$	6.70580	+	4.79695i	0.222785	+	0.159368i
$907$	−45.1411	+	24.1284i	−1.49888	+	0.801171i	−0.997930	−	0.0643032i	$-0.979518\pi$
$907$	−45.1411	+	24.1284i	−1.49888	+	0.801171i	−0.500954	+	0.865474i	$0.667018\pi$
$908$	25.3622	+	9.49801i	0.841674	+	0.315202i
$909$	−17.9250	−	1.76546i	−0.594535	−	0.0585566i
$910$	−1.77428	−	6.59996i	−0.0588168	−	0.218786i
$911$	22.0373	−	9.12816i	0.730129	−	0.302430i	0.0135242	−	0.999909i	$-0.495695\pi$
$911$	22.0373	−	9.12816i	0.730129	−	0.302430i	0.716605	+	0.697479i	$0.245695\pi$
$912$	−3.83998	−	1.28941i	−0.127154	−	0.0426966i
$913$	0.937771	+	0.388437i	0.0310357	+	0.0128554i
$914$	5.65015	−	43.1919i	0.186890	−	1.42866i
$915$	−9.09929	+	7.46759i	−0.300813	+	0.246871i
$916$	−22.8208	+	36.8340i	−0.754022	+	1.21703i
$917$	−3.69970	−	1.12229i	−0.122175	−	0.0370613i
$918$	−0.280275	+	1.20652i	−0.00925045	+	0.0398213i
$919$	−3.48925	+	17.5416i	−0.115100	+	0.578646i	0.879591	+	0.475732i	$0.157817\pi$
$919$	−3.48925	+	17.5416i	−0.115100	+	0.578646i	−0.994690	+	0.102914i	$0.967183\pi$
$920$	−36.3308	+	44.4929i	−1.19779	+	1.46689i
$921$	−12.5425	+	2.49486i	−0.413290	+	0.0822084i
$922$	13.5573	−	12.7188i	0.446486	−	0.418871i
$923$	9.30063	+	7.63283i	0.306134	+	0.251238i
$924$	1.41944	+	4.15901i	0.0466961	+	0.136822i
$925$	0.885791	−	1.65720i	0.0291246	−	0.0544884i
$926$	−11.9313	+	35.2438i	−0.392087	+	1.15818i
$927$	−10.0024	+	10.0024i	−0.328523	+	0.328523i
$928$	20.3761	−	14.7286i	0.668877	−	0.483490i
$929$	14.5812	+	14.5812i	0.478394	+	0.478394i	0.904618	−	0.426224i	$-0.140156\pi$
$929$	14.5812	+	14.5812i	0.478394	+	0.478394i	−0.426224	+	0.904618i	$0.640156\pi$
$930$	−22.8661	+	11.2997i	−0.749810	+	0.370533i
$931$	5.71637	+	3.05546i	0.187346	+	0.100139i
$932$	−36.6498	−	2.34155i	−1.20051	−	0.0767001i
$933$	9.15531	−	11.1558i	0.299731	−	0.365224i
$934$	1.11919	−	35.0708i	0.0366211	−	1.14755i
$935$	−1.14758	−	5.76925i	−0.0375297	−	0.188675i
$936$	0.712969	−	7.42691i	0.0233041	−	0.242756i
$937$	51.0919	+	10.1628i	1.66910	+	0.332005i	0.937036	−	0.349232i	$-0.113557\pi$
$937$	51.0919	+	10.1628i	1.66910	+	0.332005i	0.732063	+	0.681237i	$0.238557\pi$
$938$	5.69275	−	3.54648i	0.185875	−	0.115797i
$939$	−4.35496	+	14.3564i	−0.142119	+	0.468503i
$940$	−7.09549	+	43.4215i	−0.231429	+	1.41625i
$941$	22.6773	+	27.6324i	0.739259	+	0.900789i	0.997873	−	0.0651915i	$-0.0207658\pi$
$941$	22.6773	+	27.6324i	0.739259	+	0.900789i	−0.258614	+	0.965981i	$0.583266\pi$
$942$	2.14039	+	2.78466i	0.0697377	+	0.0907292i
$943$	0.304508	−	0.735147i	0.00991614	−	0.0239397i
$944$	−5.75314	+	2.18699i	−0.187249	+	0.0711804i
$945$	0.701072	+	1.69254i	0.0228059	+	0.0550583i
$946$	−13.3936	+	23.2426i	−0.435464	+	0.755683i
$947$	2.78003	−	28.2261i	0.0903389	−	0.917226i	−0.838044	−	0.545602i	$-0.816301\pi$
$947$	2.78003	−	28.2261i	0.0903389	−	0.917226i	0.928383	−	0.371624i	$-0.121199\pi$
$948$	−17.1850	−	16.0425i	−0.558143	−	0.521035i
$949$	−14.0085	−	26.2080i	−0.454734	−	0.850747i
$950$	0.846970	−	0.140552i	0.0274793	−	0.00456010i
$951$	−7.56731	−	11.3253i	−0.245387	−	0.367247i
$952$	−0.00473735	−	1.91790i	−0.000153538	−	0.0621595i
$953$	−7.38076	−	4.93166i	−0.239086	−	0.159752i	0.430255	−	0.902707i	$-0.358424\pi$
$953$	−7.38076	−	4.93166i	−0.239086	−	0.159752i	−0.669341	+	0.742955i	$0.733424\pi$
$954$	−3.96223	−	10.5011i	−0.128282	−	0.339987i
$955$	20.3708	−	2.00634i	0.659182	−	0.0649238i
$956$	−10.1699	+	38.2061i	−0.328918	+	1.23567i
$957$	12.0711	−	3.66172i	0.390202	−	0.118366i
$958$	−0.859658	−	12.9524i	−0.0277743	−	0.418474i
$959$			12.8669i			0.415493i
$960$	−13.4519	−	13.3197i	−0.434159	−	0.429890i
$961$		−	27.0895i		−	0.873856i
$962$	−11.6675	+	0.774375i	−0.376174	+	0.0249668i
$963$	11.8066	−	3.58148i	0.380461	−	0.115412i
$964$	10.2625	+	17.7077i	0.330532	+	0.570327i
$965$	−32.9651	+	3.24678i	−1.06118	+	0.104518i
$966$	−8.79161	+	3.31720i	−0.282866	+	0.106729i
$967$	−10.2614	−	6.85645i	−0.329984	−	0.220489i	0.379530	−	0.925179i	$-0.376086\pi$
$967$	−10.2614	−	6.85645i	−0.329984	−	0.220489i	−0.709514	+	0.704691i	$0.751086\pi$
$968$	3.20647	+	7.68733i	0.103060	+	0.247080i
$969$	0.492766	+	0.737476i	0.0158299	+	0.0236912i
$970$	−6.19183	−	37.3122i	−0.198808	−	1.19802i
$971$	−11.1047	−	20.7755i	−0.356368	−	0.666718i	0.638306	−	0.769782i	$-0.279635\pi$
$971$	−11.1047	−	20.7755i	−0.356368	−	0.666718i	−0.994675	+	0.103064i	$0.967135\pi$
$972$	0.0687297	+	1.99882i	0.00220451	+	0.0641121i
$973$	1.16695	−	11.8483i	0.0374108	−	0.379838i
$974$	11.5919	+	6.67986i	0.371428	+	0.214036i
$975$	0.605172	+	1.46102i	0.0193810	+	0.0467899i
$976$	16.8627	−	10.5630i	0.539761	−	0.338115i
$977$	−6.81931	+	16.4633i	−0.218169	+	0.526707i	−0.994634	−	0.103453i	$-0.967011\pi$
$977$	−6.81931	+	16.4633i	−0.218169	+	0.526707i	0.776465	+	0.630160i	$0.217011\pi$
$978$	6.37365	−	4.89901i	0.203807	−	0.156653i
$979$	17.6749	+	21.5369i	0.564892	+	0.688322i
$980$	17.6849	+	24.5936i	0.564923	+	0.785614i
$981$	1.98550	−	6.54532i	0.0633921	−	0.208976i
$982$	−19.1026	−	30.6632i	−0.609588	−	0.978501i
$983$	−32.3716	−	6.43912i	−1.03249	−	0.205376i	−0.350369	−	0.936612i	$-0.613944\pi$
$983$	−32.3716	−	6.43912i	−1.03249	−	0.205376i	−0.682125	+	0.731236i	$0.738944\pi$
$984$	0.231578	+	0.123047i	0.00738244	+	0.00392258i
$985$	−1.76328	−	8.86461i	−0.0561828	−	0.282450i
$986$	−5.50239	−	0.175594i	−0.175232	−	0.00559206i
$987$	−4.56594	+	5.56362i	−0.145336	+	0.177092i
$988$	−3.52923	−	4.01098i	−0.112280	−	0.127606i
$989$	−50.5863	−	27.0390i	−1.60855	−	0.859789i
$990$	−4.20782	−	8.51493i	−0.133733	−	0.270622i
$991$	−25.5181	−	25.5181i	−0.810609	−	0.810609i	0.174116	−	0.984725i	$-0.444293\pi$
$991$	−25.5181	−	25.5181i	−0.810609	−	0.810609i	−0.984725	+	0.174116i	$0.944293\pi$
$992$	40.7691	−	14.0267i	1.29442	−	0.445347i
$993$	−18.1786	+	18.1786i	−0.576881	+	0.576881i
$994$	4.73014	+	1.60133i	0.150031	+	0.0507910i
$995$	23.5428	−	44.0454i	0.746356	−	1.39633i
$996$	−0.642033	−	0.315302i	−0.0203436	−	0.00999073i
$997$	41.4859	+	34.0466i	1.31387	+	1.07827i	0.991286	+	0.131726i	$0.0420520\pi$
$997$	41.4859	+	34.0466i	1.31387	+	1.07827i	0.322586	+	0.946540i	$0.395448\pi$
$998$	33.0372	+	35.2153i	1.04578	+	1.11472i
$999$	3.07422	−	0.611500i	0.0972640	−	0.0193470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.7	✓	512
128.69	even	32	inner	384.2.v.a.325.7	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.7	✓	512	1.1	even	1	trivial
384.2.v.a.325.7	yes	512	128.69	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)

\(f(q)\)	\(=\)	\(q+(-1.06403 - 0.931580i) q^{2} +(0.290285 + 0.956940i) q^{3} +(0.264317 + 1.98246i) q^{4} +(-0.231940 - 2.35493i) q^{5} +(0.582595 - 1.28864i) q^{6} +(0.430118 - 0.643717i) q^{7} +(1.56558 - 2.35563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.06403 - 0.931580i) q^{2} +(0.290285 + 0.956940i) q^{3} +(0.264317 + 1.98246i) q^{4} +(-0.231940 - 2.35493i) q^{5} +(0.582595 - 1.28864i) q^{6} +(0.430118 - 0.643717i) q^{7} +(1.56558 - 2.35563i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-1.94701 + 2.72179i) q^{10} +(2.50304 - 1.33790i) q^{11} +(-1.82037 + 0.828413i) q^{12} +(-2.62518 - 0.258558i) q^{13} +(-1.05733 + 0.284245i) q^{14} +(2.18620 - 0.905553i) q^{15} +(-3.86027 + 1.04800i) q^{16} +(0.809188 + 0.335177i) q^{17} +(1.40227 + 0.183437i) q^{18} +(0.782804 - 0.642431i) q^{19} +(4.60724 - 1.08226i) q^{20} +(0.740856 + 0.224736i) q^{21} +(-3.90966 - 0.908213i) q^{22} +(1.67434 - 8.41747i) q^{23} +(2.70866 + 0.814361i) q^{24} +(-0.587974 + 0.116955i) q^{25} +(2.55240 + 2.72068i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(1.38983 + 0.682545i) q^{28} +(2.09512 - 3.91970i) q^{29} +(-3.16978 - 1.07308i) q^{30} +(5.38932 - 5.38932i) q^{31} +(5.08374 + 2.48106i) q^{32} +(2.00688 + 2.00688i) q^{33} +(-0.548756 - 1.11046i) q^{34} +(-1.61567 - 0.863594i) q^{35} +(-1.32117 - 1.50151i) q^{36} +(-1.98847 + 2.42296i) q^{37} +(-1.43140 - 0.0456795i) q^{38} +(-0.514625 - 2.58720i) q^{39} +(-5.91045 - 3.14046i) q^{40} +(0.0909338 + 0.0180878i) q^{41} +(-0.578932 - 0.929292i) q^{42} +(1.94008 - 6.39559i) q^{43} +(3.31393 + 4.60853i) q^{44} +(1.50118 + 1.82919i) q^{45} +(-9.62309 + 7.39665i) q^{46} +(-3.55765 + 8.58892i) q^{47} +(-2.12345 - 3.38983i) q^{48} +(2.44941 + 5.91341i) q^{49} +(0.734575 + 0.423301i) q^{50} +(-0.0858492 + 0.871641i) q^{51} +(-0.181301 - 5.27265i) q^{52} +(-3.74120 - 6.99929i) q^{53} +(0.231518 + 1.39513i) q^{54} +(-3.73122 - 5.58416i) q^{55} +(-0.842974 - 2.02099i) q^{56} +(0.842004 + 0.562609i) q^{57} +(-5.88079 + 2.21890i) q^{58} +(1.53129 - 0.150819i) q^{59} +(2.37307 + 4.09469i) q^{60} +(-4.76028 + 1.44402i) q^{61} +(-10.7550 + 0.713812i) q^{62} +0.774192i q^{63} +(-3.09794 - 7.37582i) q^{64} +6.24208i q^{65} +(-0.265811 - 4.00496i) q^{66} +(-5.86212 + 1.77825i) q^{67} +(-0.450591 + 1.69277i) q^{68} +(8.54105 - 0.841220i) q^{69} +(0.914614 + 2.42402i) q^{70} +(-3.79243 - 2.53402i) q^{71} +(0.00698639 + 2.82842i) q^{72} +(6.25875 + 9.36688i) q^{73} +(4.37297 - 0.725680i) q^{74} +(-0.282599 - 0.528706i) q^{75} +(1.48050 + 1.38207i) q^{76} +(0.215371 - 2.18670i) q^{77} +(-1.86260 + 3.23227i) q^{78} +(4.49830 + 10.8599i) q^{79} +(3.36331 + 8.84760i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-0.0799059 - 0.103958i) q^{82} +(0.226883 + 0.276458i) q^{83} +(-0.249709 + 1.52812i) q^{84} +(0.601634 - 1.98332i) q^{85} +(-8.02231 + 4.99776i) q^{86} +(4.35910 + 0.867080i) q^{87} +(0.767101 - 7.99080i) q^{88} +(1.91512 + 9.62797i) q^{89} +(0.106740 - 3.34479i) q^{90} +(-1.29558 + 1.57866i) q^{91} +(17.1298 + 1.09442i) q^{92} +(6.72169 + 3.59282i) q^{93} +(11.7867 - 5.82463i) q^{94} +(-1.69444 - 1.69444i) q^{95} +(-0.898491 + 5.58504i) q^{96} +(-7.99181 + 7.99181i) q^{97} +(2.90256 - 8.57387i) q^{98} +(-1.33790 + 2.50304i) 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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