LMFDB - Embedded newform 384.2.v.a.229.10

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			229.10
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.699590 + 1.22905i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.02115 - 1.71967i) q^{4} +(-0.339008 - 0.413082i) q^{5} +(-0.0376117 + 1.41371i) q^{6} +(-4.31689 + 2.88445i) q^{7} +(2.82795 - 0.0519807i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(-0.699590 + 1.22905i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.02115 - 1.71967i) q^{4} +(-0.339008 - 0.413082i) q^{5} +(-0.0376117 + 1.41371i) q^{6} +(-4.31689 + 2.88445i) q^{7} +(2.82795 - 0.0519807i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.744867 - 0.127671i) q^{10} +(-3.29644 + 0.999964i) q^{11} +(-1.71122 - 1.03525i) q^{12} +(2.77532 + 2.27765i) q^{13} +(-0.525094 - 7.32363i) q^{14} +(-0.493704 - 0.204499i) q^{15} +(-1.91452 + 3.51207i) q^{16} +(-4.63305 + 1.91907i) q^{17} +(0.633249 + 1.26451i) q^{18} +(0.220186 + 2.23558i) q^{19} +(-0.364188 + 1.00480i) q^{20} +(-2.44744 + 4.57883i) q^{21} +(1.07715 - 4.75107i) q^{22} +(-5.50727 + 1.09546i) q^{23} +(2.46953 - 1.37893i) q^{24} +(0.919741 - 4.62385i) q^{25} +(-4.74094 + 1.81760i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(9.36848 + 4.47817i) q^{28} +(-1.91561 + 6.31491i) q^{29} +(0.596731 - 0.463723i) q^{30} +(6.96985 + 6.96985i) q^{31} +(-2.97714 - 4.81006i) q^{32} +(-2.43582 + 2.43582i) q^{33} +(0.882594 - 7.03683i) q^{34} +(2.65498 + 0.805379i) q^{35} +(-1.99717 - 0.106344i) q^{36} +(-2.66498 - 0.262477i) q^{37} +(-2.90169 - 1.29337i) q^{38} +(3.52129 + 0.700428i) q^{39} +(-0.980170 - 1.15055i) q^{40} +(-0.485925 - 2.44291i) q^{41} +(-3.91543 - 6.21133i) q^{42} +(-5.65361 - 3.02192i) q^{43} +(5.08576 + 4.64767i) q^{44} +(-0.531808 + 0.0523785i) q^{45} +(2.50645 - 7.53511i) q^{46} +(-2.20092 - 5.31349i) q^{47} +(-0.0328781 + 3.99986i) q^{48} +(7.63668 - 18.4366i) q^{49} +(5.03952 + 4.36521i) q^{50} +(-3.18134 + 3.87647i) q^{51} +(1.08279 - 7.09844i) q^{52} +(-2.24662 - 7.40613i) q^{53} +(1.15456 + 0.816690i) q^{54} +(1.53059 + 1.02271i) q^{55} +(-12.0580 + 8.38148i) q^{56} +(1.24803 + 1.86781i) q^{57} +(-6.42123 - 6.77224i) q^{58} +(7.81729 - 6.41548i) q^{59} +(0.152474 + 1.05783i) q^{60} +(5.37122 + 10.0489i) q^{61} +(-13.4424 + 3.69028i) q^{62} +5.19188i q^{63} +(7.99460 - 0.293997i) q^{64} -1.91858i q^{65} +(-1.28968 - 4.69783i) q^{66} +(2.12238 + 3.97069i) q^{67} +(8.03119 + 6.00765i) q^{68} +(-4.34058 + 3.56222i) q^{69} +(-2.84725 + 2.69968i) q^{70} +(1.78359 + 2.66934i) q^{71} +(1.52790 - 2.38023i) q^{72} +(0.963861 + 0.644031i) q^{73} +(2.18699 - 3.09178i) q^{74} +(-1.36853 - 4.51143i) q^{75} +(3.61962 - 2.66150i) q^{76} +(11.3460 - 13.8252i) q^{77} +(-3.32432 + 3.83784i) q^{78} +(-3.81143 + 9.20161i) q^{79} +(2.09981 - 0.399765i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(3.34242 + 1.11181i) q^{82} +(-10.4553 + 1.02975i) q^{83} +(10.3733 - 0.466879i) q^{84} +(2.36338 + 1.26325i) q^{85} +(7.66931 - 4.83449i) q^{86} +(1.28741 + 6.47227i) q^{87} +(-9.27019 + 2.99920i) q^{88} +(14.4051 + 2.86536i) q^{89} +(0.307672 - 0.690265i) q^{90} +(-18.5505 - 1.82707i) q^{91} +(7.50756 + 8.35205i) q^{92} +(9.43243 + 2.86129i) q^{93} +(8.07031 + 1.01222i) q^{94} +(0.848835 - 0.848835i) q^{95} +(-4.89305 - 2.83868i) q^{96} +(9.74616 + 9.74616i) q^{97} +(17.3170 + 22.2840i) q^{98} +(-0.999964 + 3.29644i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.699590	+	1.22905i	−0.494685	+	0.869072i
$2$	−0.699590	+	1.22905i	−0.494685	+	0.869072i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	−1.02115	−	1.71967i	−0.510573	−	0.859834i
$5$	−0.339008	−	0.413082i	−0.151609	−	0.184736i	0.691668	−	0.722216i	$-0.256876\pi$
$5$	−0.339008	−	0.413082i	−0.151609	−	0.184736i	−0.843277	+	0.537480i	$0.819376\pi$
$6$	−0.0376117	+	1.41371i	−0.0153549	+	0.577146i
$7$	−4.31689	+	2.88445i	−1.63163	+	1.09022i	−0.708518	+	0.705693i	$0.750636\pi$
$7$	−4.31689	+	2.88445i	−1.63163	+	1.09022i	−0.923113	+	0.384528i	$0.874364\pi$
$8$	2.82795	−	0.0519807i	0.999831	−	0.0183779i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	0.744867	−	0.127671i	0.235548	−	0.0403730i
$11$	−3.29644	+	0.999964i	−0.993914	+	0.301501i	−0.745029	−	0.667032i	$-0.767564\pi$
$11$	−3.29644	+	0.999964i	−0.993914	+	0.301501i	−0.248885	+	0.968533i	$0.580064\pi$
$12$	−1.71122	−	1.03525i	−0.493986	−	0.298850i
$13$	2.77532	+	2.27765i	0.769735	+	0.631705i	0.935042	−	0.354537i	$-0.115361\pi$
$13$	2.77532	+	2.27765i	0.769735	+	0.631705i	−0.165307	+	0.986242i	$0.552861\pi$
$14$	−0.525094	−	7.32363i	−0.140337	−	1.95732i
$15$	−0.493704	−	0.204499i	−0.127474	−	0.0528014i
$16$	−1.91452	+	3.51207i	−0.478630	+	0.878017i
$17$	−4.63305	+	1.91907i	−1.12368	+	0.465443i	−0.865628	−	0.500688i	$-0.833080\pi$
$17$	−4.63305	+	1.91907i	−1.12368	+	0.465443i	−0.258051	+	0.966131i	$0.583080\pi$
$18$	0.633249	+	1.26451i	0.149258	+	0.298049i
$19$	0.220186	+	2.23558i	0.0505140	+	0.512878i	0.986835	+	0.161732i	$0.0517079\pi$
$19$	0.220186	+	2.23558i	0.0505140	+	0.512878i	−0.936321	+	0.351146i	$0.885792\pi$
$20$	−0.364188	+	1.00480i	−0.0814349	+	0.224680i
$21$	−2.44744	+	4.57883i	−0.534074	+	0.999182i
$22$	1.07715	−	4.75107i	0.229649	−	1.01293i
$23$	−5.50727	+	1.09546i	−1.14835	+	0.228420i	−0.732338	−	0.680941i	$-0.761571\pi$
$23$	−5.50727	+	1.09546i	−1.14835	+	0.228420i	−0.416007	+	0.909361i	$0.636571\pi$
$24$	2.46953	−	1.37893i	0.504090	−	0.281473i
$25$	0.919741	−	4.62385i	0.183948	−	0.924770i
$26$	−4.74094	+	1.81760i	−0.929774	+	0.356460i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	9.36848	+	4.47817i	1.77048	+	0.846295i
$29$	−1.91561	+	6.31491i	−0.355719	+	1.17265i	0.578419	+	0.815740i	$0.303670\pi$
$29$	−1.91561	+	6.31491i	−0.355719	+	1.17265i	−0.934139	+	0.356910i	$0.883830\pi$
$30$	0.596731	−	0.463723i	0.108948	−	0.0846639i
$31$	6.96985	+	6.96985i	1.25182	+	1.25182i	0.954902	+	0.296920i	$0.0959594\pi$
$31$	6.96985	+	6.96985i	1.25182	+	1.25182i	0.296920	+	0.954902i	$0.404041\pi$
$32$	−2.97714	−	4.81006i	−0.526289	−	0.850306i
$33$	−2.43582	+	2.43582i	−0.424022	+	0.424022i
$34$	0.882594	−	7.03683i	0.151364	−	1.20681i
$35$	2.65498	+	0.805379i	0.448773	+	0.136134i
$36$	−1.99717	−	0.106344i	−0.332862	−	0.0177240i
$37$	−2.66498	−	0.262477i	−0.438120	−	0.0431510i	−0.123447	−	0.992351i	$-0.539395\pi$
$37$	−2.66498	−	0.262477i	−0.438120	−	0.0431510i	−0.314673	+	0.949200i	$0.601895\pi$
$38$	−2.90169	−	1.29337i	−0.470716	−	0.209813i
$39$	3.52129	+	0.700428i	0.563857	+	0.112158i
$40$	−0.980170	−	1.15055i	−0.154978	−	0.181919i
$41$	−0.485925	−	2.44291i	−0.0758888	−	0.381519i	0.924111	−	0.382124i	$-0.124807\pi$
$41$	−0.485925	−	2.44291i	−0.0758888	−	0.381519i	−1.00000		0.000605315i	$0.999807\pi$
$42$	−3.91543	−	6.21133i	−0.604163	−	0.958430i
$43$	−5.65361	−	3.02192i	−0.862168	−	0.460838i	−0.0198394	−	0.999803i	$-0.506315\pi$
$43$	−5.65361	−	3.02192i	−0.862168	−	0.460838i	−0.842328	+	0.538965i	$0.818815\pi$
$44$	5.08576	+	4.64767i	0.766706	+	0.700663i
$45$	−0.531808	+	0.0523785i	−0.0792773	+	0.00780813i
$46$	2.50645	−	7.53511i	0.369556	−	1.11099i
$47$	−2.20092	−	5.31349i	−0.321037	−	0.775053i	−0.999194	−	0.0401355i	$-0.987221\pi$
$47$	−2.20092	−	5.31349i	−0.321037	−	0.775053i	0.678157	−	0.734917i	$-0.262779\pi$
$48$	−0.0328781	+	3.99986i	−0.00474555	+	0.577331i
$49$	7.63668	−	18.4366i	1.09095	−	2.63380i
$50$	5.03952	+	4.36521i	0.712696	+	0.617334i
$51$	−3.18134	+	3.87647i	−0.445477	+	0.542815i
$52$	1.08279	−	7.09844i	0.150156	−	0.984376i
$53$	−2.24662	−	7.40613i	−0.308598	−	1.01731i	−0.964857	−	0.262775i	$-0.915362\pi$
$53$	−2.24662	−	7.40613i	−0.308598	−	1.01731i	0.656260	−	0.754535i	$-0.272138\pi$
$54$	1.15456	+	0.816690i	0.157116	+	0.111137i
$55$	1.53059	+	1.02271i	0.206384	+	0.137902i
$56$	−12.0580	+	8.38148i	−1.61132	+	1.12002i
$57$	1.24803	+	1.86781i	0.165306	+	0.247398i
$58$	−6.42123	−	6.77224i	−0.843148	−	0.889238i
$59$	7.81729	−	6.41548i	1.01772	−	0.835224i	0.0313110	−	0.999510i	$-0.490032\pi$
$59$	7.81729	−	6.41548i	1.01772	−	0.835224i	0.986413	+	0.164285i	$0.0525318\pi$
$60$	0.152474	+	1.05783i	0.0196843	+	0.136565i
$61$	5.37122	+	10.0489i	0.687715	+	1.28662i	0.947128	+	0.320857i	$0.103971\pi$
$61$	5.37122	+	10.0489i	0.687715	+	1.28662i	−0.259413	+	0.965766i	$0.583529\pi$
$62$	−13.4424	+	3.69028i	−1.70718	+	0.468666i
$63$			5.19188i			0.654115i
$64$	7.99460	−	0.293997i	0.999325	−	0.0367497i
$65$		−	1.91858i		−	0.237970i
$66$	−1.28968	−	4.69783i	−0.158748	−	0.578263i
$67$	2.12238	+	3.97069i	0.259290	+	0.485097i	0.977557	−	0.210670i	$-0.0675645\pi$
$67$	2.12238	+	3.97069i	0.259290	+	0.485097i	−0.718267	+	0.695767i	$0.755064\pi$
$68$	8.03119	+	6.00765i	0.973925	+	0.728535i
$69$	−4.34058	+	3.56222i	−0.522544	+	0.428841i
$70$	−2.84725	+	2.69968i	−0.340312	+	0.322673i
$71$	1.78359	+	2.66934i	0.211674	+	0.316792i	0.922080	−	0.387000i	$-0.126489\pi$
$71$	1.78359	+	2.66934i	0.211674	+	0.316792i	−0.710406	+	0.703792i	$0.751489\pi$
$72$	1.52790	−	2.38023i	0.180065	−	0.280513i
$73$	0.963861	+	0.644031i	0.112811	+	0.0753782i	0.610696	−	0.791865i	$-0.290890\pi$
$73$	0.963861	+	0.644031i	0.112811	+	0.0753782i	−0.497885	+	0.867243i	$0.665890\pi$
$74$	2.18699	−	3.09178i	0.254233	−	0.359412i
$75$	−1.36853	−	4.51143i	−0.158024	−	0.520936i
$76$	3.61962	−	2.66150i	0.415199	−	0.305295i
$77$	11.3460	−	13.8252i	1.29300	−	1.57552i
$78$	−3.32432	+	3.83784i	−0.376405	+	0.434550i
$79$	−3.81143	+	9.20161i	−0.428819	+	1.03526i	0.550843	+	0.834609i	$0.314306\pi$
$79$	−3.81143	+	9.20161i	−0.428819	+	1.03526i	−0.979662	+	0.200653i	$0.935694\pi$
$80$	2.09981	−	0.399765i	0.234766	−	0.0446951i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	3.34242	+	1.11181i	0.369108	+	0.122779i
$83$	−10.4553	+	1.02975i	−1.14761	+	0.113030i	−0.653890	−	0.756589i	$-0.726864\pi$
$83$	−10.4553	+	1.02975i	−1.14761	+	0.113030i	−0.493723	+	0.869619i	$0.664364\pi$
$84$	10.3733	−	0.466879i	1.13182	−	0.0509407i
$85$	2.36338	+	1.26325i	0.256344	+	0.137019i
$86$	7.66931	−	4.83449i	0.827003	−	0.521316i
$87$	1.28741	+	6.47227i	0.138025	+	0.693900i
$88$	−9.27019	+	2.99920i	−0.988205	+	0.319716i
$89$	14.4051	+	2.86536i	1.52694	+	0.303728i	0.885936	−	0.463808i	$-0.153517\pi$
$89$	14.4051	+	2.86536i	1.52694	+	0.303728i	0.641007	+	0.767535i	$0.278517\pi$
$90$	0.307672	−	0.690265i	0.0324315	−	0.0727603i
$91$	−18.5505	−	1.82707i	−1.94462	−	0.191529i
$92$	7.50756	+	8.35205i	0.782718	+	0.870761i
$93$	9.43243	+	2.86129i	0.978097	+	0.296702i
$94$	8.07031	+	1.01222i	0.832389	+	0.104402i
$95$	0.848835	−	0.848835i	0.0870886	−	0.0870886i
$96$	−4.89305	−	2.83868i	−0.499395	−	0.289721i
$97$	9.74616	+	9.74616i	0.989572	+	0.989572i	0.999946	−	0.0103737i	$-0.00330212\pi$
$97$	9.74616	+	9.74616i	0.989572	+	0.989572i	−0.0103737	+	0.999946i	$0.503302\pi$
$98$	17.3170	+	22.2840i	1.74928	+	2.25102i
$99$	−0.999964	+	3.29644i	−0.100500	+	0.331305i
$100$	−8.89068	+	3.13998i	−0.889068	+	0.313998i
$101$	−0.120717	+	1.22566i	−0.0120118	+	0.121958i	−0.999321	−	0.0368539i	$-0.988266\pi$
$101$	−0.120717	+	1.22566i	−0.0120118	+	0.121958i	0.987309	+	0.158812i	$0.0507664\pi$
$102$	−2.53876	−	6.62198i	−0.251375	−	0.655674i
$103$	−0.0864331	+	0.434529i	−0.00851651	+	0.0428154i	−0.984810	−	0.173636i	$-0.944448\pi$
$103$	−0.0864331	+	0.434529i	−0.00851651	+	0.0428154i	0.976293	+	0.216452i	$0.0694483\pi$
$104$	7.96686	+	6.29680i	0.781214	+	0.617452i
$105$	2.72113	−	0.541267i	0.265556	−	0.0528223i
$106$	10.6742	+	2.42003i	1.03677	+	0.235054i
$107$	−5.70433	+	10.6721i	−0.551459	+	1.03171i	0.439589	+	0.898199i	$0.355124\pi$
$107$	−5.70433	+	10.6721i	−0.551459	+	1.03171i	−0.991048	+	0.133508i	$0.957376\pi$
$108$	−1.81148	+	0.847673i	−0.174310	+	0.0815673i
$109$	−1.01846	−	10.3406i	−0.0975512	−	0.990454i	−0.911992	−	0.410208i	$-0.865456\pi$
$109$	−1.01846	−	10.3406i	−0.0975512	−	0.990454i	0.814441	−	0.580246i	$-0.197044\pi$
$110$	−2.32774	+	1.16570i	−0.221942	+	0.111145i
$111$	−2.47403	+	1.02478i	−0.234825	+	0.0972676i
$112$	−1.86563	−	20.6836i	−0.176285	−	1.95441i
$113$	0.255573	+	0.105862i	0.0240422	+	0.00995862i	0.394672	−	0.918822i	$-0.370858\pi$
$113$	0.255573	+	0.105862i	0.0240422	+	0.00995862i	−0.370630	+	0.928781i	$0.620858\pi$
$114$	−3.16875	+	0.227195i	−0.296781	+	0.0212788i
$115$	2.31953	+	1.90359i	0.216297	+	0.177510i
$116$	12.8157	−	3.15424i	1.18991	−	0.292864i
$117$	3.43568	−	1.04220i	0.317629	−	0.0963516i
$118$	2.41607	+	14.0961i	0.222418	+	1.29765i
$119$	14.4649	−	21.6482i	1.32599	−	1.98449i
$120$	−1.40680	−	0.552650i	−0.128423	−	0.0504498i
$121$	0.720423	−	0.481371i	0.0654930	−	0.0437610i
$122$	−16.1082	−	0.428558i	−1.45837	−	0.0387998i
$123$	−1.58013	−	1.92539i	−0.142475	−	0.173607i
$124$	4.86859	−	19.1031i	0.437213	−	1.71551i
$125$	−4.57824	+	2.44712i	−0.409491	+	0.218877i
$126$	−6.38110	−	3.63219i	−0.568474	−	0.323581i
$127$	5.14857			0.456862			0.228431	−	0.973560i	$-0.426640\pi$
$127$	5.14857			0.456862			0.228431	+	0.973560i	$0.426640\pi$
$128$	−5.23160	+	10.0315i	−0.462413	+	0.886665i
$129$	−6.41056			−0.564419
$130$	2.35803	+	1.34222i	0.206813	+	0.117720i
$131$	0.127636	−	0.0682228i	0.0111516	−	0.00596065i	−0.465812	−	0.884884i	$-0.654238\pi$
$131$	0.127636	−	0.0682228i	0.0111516	−	0.00596065i	0.476963	+	0.878923i	$0.341738\pi$
$132$	6.67613	+	1.70147i	0.581083	+	0.148094i
$133$	−7.39895	−	9.01565i	−0.641570	−	0.781756i
$134$	−6.36499	−	0.169340i	−0.549852	−	0.0146287i
$135$	−0.444322	+	0.296886i	−0.0382411	+	0.0255519i
$136$	−13.0023	+	5.66787i	−1.11494	+	0.486015i
$137$	0.435981	−	0.652491i	0.0372484	−	0.0557461i	−0.812378	−	0.583131i	$-0.801827\pi$
$137$	0.435981	−	0.652491i	0.0372484	−	0.0557461i	0.849626	+	0.527385i	$0.176827\pi$
$138$	−1.34153	−	7.82690i	−0.114199	−	0.666270i
$139$	−5.26946	+	1.59847i	−0.446950	+	0.135581i	−0.505733	−	0.862690i	$-0.668778\pi$
$139$	−5.26946	+	1.59847i	−0.446950	+	0.135581i	0.0587833	+	0.998271i	$0.481278\pi$
$140$	−1.32614	−	5.38809i	−0.112079	−	0.455377i
$141$	−4.44580	−	3.64858i	−0.374404	−	0.307266i
$142$	−4.52855	+	0.324691i	−0.380027	+	0.0272474i
$143$	−11.4262	−	4.73290i	−0.955510	−	0.395785i
$144$	1.85653	+	3.54306i	0.154711	+	0.295255i
$145$	3.25799	−	1.34950i	0.270561	−	0.112070i
$146$	−1.46586	+	0.734079i	−0.121315	+	0.0607528i
$147$	−1.95599	−	19.8595i	−0.161328	−	1.63799i
$148$	2.26996	+	4.85091i	0.186590	+	0.398742i
$149$	−8.34001	+	15.6031i	−0.683240	+	1.27825i	0.266083	+	0.963950i	$0.414271\pi$
$149$	−8.34001	+	15.6031i	−0.683240	+	1.27825i	−0.949323	+	0.314302i	$0.898229\pi$
$150$	6.50221	+	1.47416i	0.530903	+	0.120365i
$151$	6.15257	−	1.22382i	0.500689	−	0.0995932i	0.0617163	−	0.998094i	$-0.480343\pi$
$151$	6.15257	−	1.22382i	0.500689	−	0.0995932i	0.438972	+	0.898501i	$0.355343\pi$
$152$	0.738881	+	6.31067i	0.0599311	+	0.511863i
$153$	−0.978334	+	4.91842i	−0.0790936	+	0.397630i
$154$	9.05431	+	23.6168i	0.729617	+	1.90310i
$155$	0.516288	−	5.24196i	0.0414692	−	0.421044i
$156$	−2.39125	−	6.77069i	−0.191453	−	0.542089i
$157$	0.916763	−	3.02216i	0.0731657	−	0.241195i	−0.912728	−	0.408568i	$-0.866028\pi$
$157$	0.916763	−	3.02216i	0.0731657	−	0.241195i	0.985894	+	0.167373i	$0.0535284\pi$
$158$	−8.64283	−	11.1218i	−0.687587	−	0.884804i
$159$	−5.47257	−	5.47257i	−0.434003	−	0.434003i
$160$	−0.977675	+	2.86045i	−0.0772920	+	0.226139i
$161$	20.6145	−	20.6145i	1.62465	−	1.62465i
$162$	1.40322	+	0.175999i	0.110247	+	0.0138278i
$163$	5.01597	+	1.52158i	0.392881	+	0.119179i	0.480543	−	0.876971i	$-0.340440\pi$
$163$	5.01597	+	1.52158i	0.392881	+	0.119179i	−0.0876619	+	0.996150i	$0.527940\pi$
$164$	−3.70480	+	3.33020i	−0.289296	+	0.260045i
$165$	1.83196	+	0.180432i	0.142618	+	0.0140466i
$166$	6.04877	−	13.5705i	0.469476	−	1.05327i
$167$	8.40668	+	1.67219i	0.650529	+	0.129398i	0.509314	−	0.860581i	$-0.329899\pi$
$167$	8.40668	+	1.67219i	0.650529	+	0.129398i	0.141215	+	0.989979i	$0.454899\pi$
$168$	−6.68321	+	13.0759i	−0.515621	+	1.00883i
$169$	−0.0214470	−	0.107821i	−0.00164977	−	0.00829396i
$170$	−3.20600	+	2.02096i	−0.245889	+	0.155000i
$171$	1.98115	+	1.05895i	0.151502	+	0.0809796i
$172$	0.576469	+	12.8082i	0.0439553	+	0.976613i
$173$	−11.8558	+	1.16769i	−0.901380	+	0.0887781i	−0.538080	−	0.842894i	$-0.680850\pi$
$173$	−11.8558	+	1.16769i	−0.901380	+	0.0887781i	−0.363300	+	0.931672i	$0.618350\pi$
$174$	−8.85543	−	2.94563i	−0.671328	−	0.223308i
$175$	9.36686	+	22.6136i	0.708068	+	1.70943i
$176$	2.79916	−	13.4918i	0.210994	−	1.01698i
$177$	3.86999	−	9.34299i	0.290887	−	0.702262i
$178$	−13.5994	+	15.7001i	−1.01932	+	1.17677i
$179$	−9.42567	+	11.4852i	−0.704508	+	0.858445i	−0.995148	−	0.0983872i	$-0.968632\pi$
$179$	−9.42567	+	11.4852i	−0.704508	+	0.858445i	0.290641	+	0.956832i	$0.406132\pi$
$180$	0.633128	+	0.861048i	0.0471906	+	0.0641787i
$181$	−3.64165	−	12.0049i	−0.270681	−	0.892317i	−0.981909	−	0.189355i	$-0.939360\pi$
$181$	−3.64165	−	12.0049i	−0.270681	−	0.892317i	0.711227	−	0.702962i	$-0.248140\pi$
$182$	15.2233	−	21.5214i	1.12843	−	1.59527i
$183$	9.47399	+	6.33032i	0.700338	+	0.467951i
$184$	−15.5173	+	3.38419i	−1.14395	+	0.249486i
$185$	0.795024	+	1.18984i	0.0584513	+	0.0874786i
$186$	−10.1155	+	9.59122i	−0.741706	+	0.703263i
$187$	13.3536	−	10.9590i	0.976509	−	0.801400i
$188$	−6.88998	+	9.21071i	−0.502504	+	0.671760i
$189$	2.44744	+	4.57883i	0.178025	+	0.333061i
$190$	0.449427	+	1.63710i	0.0326049	+	0.118768i
$191$			9.27629i			0.671209i	0.942003	+	0.335604i	$0.108941\pi$
$191$			9.27629i			0.671209i	−0.942003	+	0.335604i	$0.891059\pi$
$192$	6.91201	−	4.02791i	0.498832	−	0.290689i
$193$		−	4.64540i		−	0.334383i	−0.985924	−	0.167192i	$-0.946530\pi$
$193$		−	4.64540i		−	0.334383i	0.985924	−	0.167192i	$-0.0534698\pi$
$194$	−18.7969	+	5.16023i	−1.34954	+	0.370483i
$195$	−0.904410	−	1.69203i	−0.0647662	−	0.121169i
$196$	−39.5030	+	5.69389i	−2.82164	+	0.406707i
$197$	−8.13297	+	6.67455i	−0.579450	+	0.475542i	−0.877874	−	0.478891i	$-0.841039\pi$
$197$	−8.13297	+	6.67455i	−0.579450	+	0.475542i	0.298424	+	0.954433i	$0.403539\pi$
$198$	−3.35194	−	3.53517i	−0.238212	−	0.251233i
$199$	−12.7702	−	19.1120i	−0.905257	−	1.35481i	−0.934772	−	0.355249i	$-0.884396\pi$
$199$	−12.7702	−	19.1120i	−0.905257	−	1.35481i	0.0295149	−	0.999564i	$-0.490604\pi$
$200$	2.36063	−	13.1238i	0.166922	−	0.927994i
$201$	3.74354	+	2.50136i	0.264049	+	0.176432i
$202$	−1.42195	−	1.00583i	−0.100048	−	0.0707700i
$203$	−9.94561	−	32.7863i	−0.698045	−	2.30114i
$204$	9.91486	+	1.51240i	0.694179	+	0.105889i
$205$	−0.844392	+	1.02889i	−0.0589749	+	0.0718611i
$206$	−0.473591	−	0.410223i	−0.0329967	−	0.0285816i
$207$	−2.14883	+	5.18773i	−0.149354	+	0.360572i
$208$	−13.3126	+	5.38651i	−0.923066	+	0.373487i
$209$	−2.96133	−	7.14928i	−0.204840	−	0.494526i
$210$	−1.23843	+	3.72309i	−0.0854600	+	0.256917i
$211$	−5.20379	+	0.512529i	−0.358244	+	0.0352839i	−0.275538	−	0.961290i	$-0.588856\pi$
$211$	−5.20379	+	0.512529i	−0.358244	+	0.0352839i	−0.0827055	+	0.996574i	$0.526356\pi$
$212$	−10.4419	+	11.4262i	−0.717156	+	0.784754i
$213$	2.83131	+	1.51337i	0.193998	+	0.103694i
$214$	−9.12584	−	14.4770i	−0.623829	−	0.989628i
$215$	0.668318	+	3.35986i	0.0455789	+	0.229141i
$216$	0.225457	−	2.81943i	0.0153404	−	0.191838i
$217$	−50.1923	−	9.98387i	−3.40728	−	0.677749i
$218$	13.4217	+	5.98247i	0.909033	+	0.405184i
$219$	1.15364	+	0.113624i	0.0779560	+	0.00767800i
$220$	0.195761	−	3.67644i	0.0131982	−	0.247865i
$221$	−17.2292	−	5.22641i	−1.15896	−	0.351566i
$222$	0.471302	−	3.75764i	0.0316317	−	0.252196i
$223$	−10.2301	+	10.2301i	−0.685060	+	0.685060i	−0.961136	−	0.276076i	$-0.910966\pi$
$223$	−10.2301	+	10.2301i	−0.685060	+	0.685060i	0.276076	+	0.961136i	$0.410966\pi$
$224$	26.7264	+	12.1771i	1.78573	+	0.813614i
$225$	−3.33361	−	3.33361i	−0.222241	−	0.222241i
$226$	−0.308906	+	0.240053i	−0.0205481	+	0.0159681i
$227$	4.48007	−	14.7688i	0.297353	−	0.980240i	−0.673222	−	0.739440i	$-0.735090\pi$
$227$	4.48007	−	14.7688i	0.297353	−	0.980240i	0.970575	−	0.240800i	$-0.0774098\pi$
$228$	1.93759	−	4.05351i	0.128320	−	0.268450i
$229$	−2.56408	+	26.0335i	−0.169439	+	1.72034i	0.415778	+	0.909466i	$0.363509\pi$
$229$	−2.56408	+	26.0335i	−0.169439	+	1.72034i	−0.585217	+	0.810877i	$0.698991\pi$
$230$	−3.96233	+	1.51909i	−0.261268	+	0.100166i
$231$	3.48916	−	17.5412i	0.229570	−	1.15413i
$232$	−5.08899	+	17.9578i	−0.334108	+	1.17899i
$233$	9.11155	−	1.81240i	0.596918	−	0.118734i	0.112621	−	0.993638i	$-0.464075\pi$
$233$	9.11155	−	1.81240i	0.596918	−	0.118734i	0.484297	+	0.874904i	$0.339075\pi$
$234$	−1.12265	+	4.95175i	−0.0733896	+	0.323706i
$235$	−1.44878	+	2.71048i	−0.0945081	+	0.176812i
$236$	−19.0151	−	6.89199i	−1.23778	−	0.448631i
$237$	0.976226	+	9.91179i	0.0634127	+	0.643840i
$238$	16.4873	+	32.9230i	1.06872	+	2.13408i
$239$	15.3473	−	6.35707i	0.992735	−	0.411204i	0.173607	−	0.984815i	$-0.444458\pi$
$239$	15.3473	−	6.35707i	0.992735	−	0.411204i	0.819128	+	0.573611i	$0.194458\pi$
$240$	1.66342	−	1.34240i	0.107373	−	0.0866519i
$241$	2.51660	+	1.04241i	0.162108	+	0.0671474i	0.462262	−	0.886743i	$-0.347038\pi$
$241$	2.51660	+	1.04241i	0.162108	+	0.0671474i	−0.300154	+	0.953891i	$0.597038\pi$
$242$	0.0876301	+	1.22220i	0.00563308	+	0.0785660i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	11.7959	−	19.4981i	0.755154	−	1.24824i
$245$	−10.2047	+	3.09557i	−0.651956	+	0.197769i
$246$	3.47185	−	0.595077i	0.221357	−	0.0379407i
$247$	−4.48078	+	6.70596i	−0.285105	+	0.426690i
$248$	20.0727	+	19.3481i	1.27462	+	1.22860i
$249$	−8.73529	+	5.83673i	−0.553576	+	0.369888i
$250$	0.195250	−	7.33889i	0.0123487	−	0.464152i
$251$	14.6799	+	17.8875i	0.926588	+	1.12905i	0.991363	+	0.131150i	$0.0418670\pi$
$251$	14.6799	+	17.8875i	0.926588	+	1.12905i	−0.0647750	+	0.997900i	$0.520633\pi$
$252$	8.92831	−	5.30167i	0.562431	−	0.333974i
$253$	17.0590	−	9.11820i	1.07249	−	0.573257i
$254$	−3.60189	+	6.32788i	−0.226003	+	0.397046i
$255$	2.67980			0.167816
$256$	−8.66923	−	13.4478i	−0.541827	−	0.840490i
$257$	−1.33845			−0.0834901			−0.0417451	−	0.999128i	$-0.513292\pi$
$257$	−1.33845			−0.0834901			−0.0417451	+	0.999128i	$0.513292\pi$
$258$	4.48477	−	7.87893i	0.279209	−	0.490520i
$259$	12.2615	−	6.55392i	0.761894	−	0.407241i
$260$	−3.29931	+	1.95915i	−0.204615	+	0.121501i
$261$	4.18640	+	5.10115i	0.259132	+	0.315753i
$262$	−0.00544334	+	0.204599i	−0.000336290	+	0.0126402i
$263$	22.4082	−	14.9727i	1.38175	−	0.923253i	0.381747	−	0.924267i	$-0.375323\pi$
$263$	22.4082	−	14.9727i	1.38175	−	0.923253i	0.999999	+	0.00101382i	$0.000322709\pi$
$264$	−6.76176	+	7.01499i	−0.416158	+	0.431743i
$265$	−2.29772	+	3.43878i	−0.141148	+	0.211242i
$266$	16.2570	−	2.78645i	0.996778	−	0.170848i
$267$	14.0549	−	4.26352i	0.860148	−	0.260923i
$268$	4.66102	−	7.70445i	0.284717	−	0.470624i
$269$	10.0918	+	8.28215i	0.615309	+	0.504971i	0.889639	−	0.456664i	$-0.150956\pi$
$269$	10.0918	+	8.28215i	0.615309	+	0.504971i	−0.274330	+	0.961636i	$0.588456\pi$
$270$	−0.0540461	−	0.753795i	−0.00328914	−	0.0458745i
$271$	−7.75338	−	3.21156i	−0.470984	−	0.195088i	0.134551	−	0.990907i	$-0.457041\pi$
$271$	−7.75338	−	3.21156i	−0.470984	−	0.195088i	−0.605535	+	0.795819i	$0.707041\pi$
$272$	2.13015	−	19.9457i	0.129159	−	1.20938i
$273$	−17.2214	+	7.13332i	−1.04228	+	0.431728i
$274$	0.496939	+	0.992321i	0.0300212	+	0.0599483i
$275$	1.59181	+	16.1620i	0.0959900	+	0.974602i
$276$	10.5582	+	3.82681i	0.635529	+	0.230347i
$277$	−9.58154	+	17.9258i	−0.575699	+	1.07706i	0.410557	+	0.911835i	$0.365334\pi$
$277$	−9.58154	+	17.9258i	−0.575699	+	1.07706i	−0.986256	+	0.165222i	$0.947166\pi$
$278$	1.72185	−	7.59473i	0.103270	−	0.455501i
$279$	9.66746	−	1.92298i	0.578776	−	0.115126i
$280$	7.55001	+	2.13956i	0.451199	+	0.127863i
$281$	−0.466355	+	2.34453i	−0.0278204	+	0.139863i	−0.992199	−	0.124662i	$-0.960215\pi$
$281$	−0.466355	+	2.34453i	−0.0278204	+	0.139863i	0.964379	+	0.264525i	$0.0852152\pi$
$282$	7.59454	−	2.91162i	0.452248	−	0.173385i
$283$	−1.43408	+	14.5604i	−0.0852471	+	0.865528i	0.853539	+	0.521029i	$0.174451\pi$
$283$	−1.43408	+	14.5604i	−0.0852471	+	0.865528i	−0.938786	+	0.344500i	$0.888049\pi$
$284$	2.76907	−	5.79298i	0.164314	−	0.343750i
$285$	0.348468	−	1.14874i	0.0206414	−	0.0680457i
$286$	13.8107	−	10.7324i	0.816642	−	0.634618i
$287$	9.14416	+	9.14416i	0.539762	+	0.539762i
$288$	−5.65343	−	0.196922i	−0.333131	−	0.0116037i
$289$	5.76148	−	5.76148i	0.338911	−	0.338911i
$290$	−0.620645	+	4.94834i	−0.0364455	+	0.290576i
$291$	13.1897	+	4.00104i	0.773191	+	0.234545i
$292$	0.123277	−	2.31517i	0.00721424	−	0.135485i
$293$	−16.4903	−	1.62415i	−0.963373	−	0.0948840i	−0.395916	−	0.918287i	$-0.629573\pi$
$293$	−16.4903	−	1.62415i	−0.963373	−	0.0948840i	−0.567457	+	0.823403i	$0.692073\pi$
$294$	25.7768	+	11.4895i	1.50333	+	0.670082i
$295$	−5.30025	−	1.05428i	−0.308592	−	0.0613828i
$296$	−7.55007	−	0.603746i	−0.438839	−	0.0350920i
$297$	0.672041	+	3.37858i	0.0389958	+	0.196045i
$298$	−13.3424	−	21.1661i	−0.772905	−	1.22612i
$299$	−17.7795	−	9.50335i	−1.02822	−	0.549593i
$300$	−6.36070	+	6.96025i	−0.367235	+	0.401850i
$301$	33.1226	−	3.26229i	1.90916	−	0.188035i
$302$	−2.80013	+	8.41801i	−0.161130	+	0.484402i
$303$	0.471311	+	1.13784i	0.0270761	+	0.0653674i
$304$	−8.27306	−	3.50676i	−0.474493	−	0.201126i
$305$	2.33012	−	5.62540i	0.133422	−	0.322109i
$306$	−5.36057	−	4.64330i	−0.306443	−	0.265440i
$307$	0.0516129	−	0.0628905i	0.00294570	−	0.00358935i	−0.771536	−	0.636186i	$-0.780511\pi$
$307$	0.0516129	−	0.0628905i	0.00294570	−	0.00358935i	0.774481	+	0.632597i	$0.218011\pi$
$308$	−35.3606	−	5.39387i	−2.01486	−	0.307344i
$309$	0.128608	+	0.423964i	0.00731626	+	0.0241185i
$310$	6.08146	+	4.30177i	0.345404	+	0.244324i
$311$	−6.83253	−	4.56535i	−0.387437	−	0.258877i	0.346563	−	0.938027i	$-0.387349\pi$
$311$	−6.83253	−	4.56535i	−0.387437	−	0.258877i	−0.734000	+	0.679149i	$0.762349\pi$
$312$	9.99443	+	1.79774i	0.565823	+	0.101777i
$313$	12.2876	+	18.3897i	0.694535	+	1.03945i	0.996290	+	0.0860601i	$0.0274277\pi$
$313$	12.2876	+	18.3897i	0.694535	+	1.03945i	−0.301755	+	0.953386i	$0.597572\pi$
$314$	3.07304	+	3.24103i	0.173422	+	0.182902i
$315$	2.14467	−	1.76009i	0.120839	−	0.0991698i
$316$	19.7157	−	2.84179i	1.10910	−	0.159863i
$317$	4.79556	+	8.97186i	0.269345	+	0.503910i	0.979838	−	0.199795i	$-0.0640277\pi$
$317$	4.79556	+	8.97186i	0.269345	+	0.503910i	−0.710492	+	0.703705i	$0.751528\pi$
$318$	10.5546	−	2.89753i	0.591875	−	0.162485i
$319$		−	22.7323i		−	1.27276i
$320$	−2.83168	−	3.20276i	−0.158296	−	0.179040i
$321$			12.1009i			0.675408i
$322$	10.9146	+	39.7580i	0.608247	+	2.21562i
$323$	−5.31037	−	9.93501i	−0.295477	−	0.552799i
$324$	−1.19799	+	1.60151i	−0.0665550	+	0.0889725i
$325$	13.0841	−	10.7378i	0.725773	−	0.595627i
$326$	−5.37923	+	5.10042i	−0.297928	+	0.282486i
$327$	−5.77275	−	8.63953i	−0.319234	−	0.477767i
$328$	−1.50116	−	6.88317i	−0.0828875	−	0.380060i
$329$	24.8277	+	16.5893i	1.36879	+	0.914598i
$330$	−1.50338	+	2.12535i	−0.0827584	+	0.116996i
$331$	2.61642	+	8.62519i	0.143812	+	0.474083i	0.999023	−	0.0441962i	$-0.0140727\pi$
$331$	2.61642	+	8.62519i	0.143812	+	0.474083i	−0.855211	+	0.518280i	$0.826573\pi$
$332$	12.4472	+	16.9280i	0.683128	+	0.929047i
$333$	−1.69882	+	2.07002i	−0.0930950	+	0.113437i
$334$	−7.93645	+	9.16242i	−0.434263	+	0.501345i
$335$	0.920720	−	2.22282i	0.0503043	−	0.121445i
$336$	−11.3955	−	17.3618i	−0.621675	−	0.947165i
$337$	−6.99118	−	16.8782i	−0.380834	−	0.919415i	−0.991805	−	0.127762i	$-0.959221\pi$
$337$	−6.99118	−	16.8782i	−0.380834	−	0.919415i	0.610971	−	0.791653i	$-0.290779\pi$
$338$	0.147523	+	0.0490713i	0.00802417	+	0.00266913i
$339$	0.275298	−	0.0271145i	0.0149521	−	0.00147266i
$340$	−0.240981	−	5.35419i	−0.0130690	−	0.290371i
$341$	−29.9453	−	16.0061i	−1.62163	−	0.866779i
$342$	−2.68749	+	1.69411i	−0.145323	+	0.0916069i
$343$	13.1226	+	65.9716i	0.708552	+	3.56213i
$344$	−16.1452	−	8.25195i	−0.870491	−	0.444915i
$345$	2.94298	+	0.585396i	0.158445	+	0.0315166i
$346$	6.85904	−	15.3883i	0.368744	−	0.827281i
$347$	−5.78519	−	0.569792i	−0.310565	−	0.0305880i	−0.0584661	−	0.998289i	$-0.518621\pi$
$347$	−5.78519	−	0.569792i	−0.310565	−	0.0305880i	−0.252099	+	0.967701i	$0.581121\pi$
$348$	9.81551	−	8.82306i	0.526167	−	0.472966i
$349$	−9.61343	−	2.91620i	−0.514595	−	0.156101i	0.0222975	−	0.999751i	$-0.492902\pi$
$349$	−9.61343	−	2.91620i	−0.514595	−	0.156101i	−0.536892	+	0.843651i	$0.680402\pi$
$350$	−34.3463	−	4.30788i	−1.83589	−	0.230266i
$351$	2.53871	−	2.53871i	0.135506	−	0.135506i
$352$	14.6238	+	12.8790i	0.779454	+	0.686454i
$353$	7.33143	+	7.33143i	0.390213	+	0.390213i	0.874763	−	0.484551i	$-0.161017\pi$
$353$	7.33143	+	7.33143i	0.390213	+	0.390213i	−0.484551	+	0.874763i	$0.661017\pi$
$354$	8.77563	+	11.2927i	0.466419	+	0.600200i
$355$	0.498004	−	1.64170i	0.0264313	−	0.0871323i
$356$	−9.78229	−	27.6980i	−0.518461	−	1.46799i
$357$	2.55199	−	25.9107i	0.135065	−	1.37134i
$358$	−7.52184	−	19.6196i	−0.397541	−	1.03693i
$359$	5.59337	−	28.1198i	0.295207	−	1.48411i	−0.493721	−	0.869620i	$-0.664364\pi$
$359$	5.59337	−	28.1198i	0.295207	−	1.48411i	0.788928	−	0.614485i	$-0.210636\pi$
$360$	−1.50120	+	0.175768i	−0.0791204	+	0.00926377i
$361$	13.6856	−	2.72223i	0.720293	−	0.143275i
$362$	17.3023	+	3.92273i	0.909390	+	0.206174i
$363$	0.408439	−	0.764136i	0.0214375	−	0.0401067i
$364$	15.8008	+	33.7664i	0.828189	+	1.76984i
$365$	−0.0607186	−	0.616486i	−0.00317815	−	0.0322683i
$366$	−14.4082	+	7.21542i	−0.753130	+	0.377156i
$367$	−12.4662	+	5.16369i	−0.650733	+	0.269542i	−0.683533	−	0.729920i	$-0.739558\pi$
$367$	−12.4662	+	5.16369i	−0.650733	+	0.269542i	0.0328002	+	0.999462i	$0.489558\pi$
$368$	6.69643	−	21.4392i	0.349076	−	1.11759i
$369$	−2.30117	−	0.953177i	−0.119794	−	0.0496204i
$370$	−2.01857	+	0.144728i	−0.104940	+	0.00752407i
$371$	31.0611	+	25.4912i	1.61261	+	1.32343i
$372$	−4.71141	−	19.1424i	−0.244275	−	0.992490i
$373$	−11.9542	+	3.62626i	−0.618963	+	0.187760i	−0.584166	−	0.811634i	$-0.698578\pi$
$373$	−11.9542	+	3.62626i	−0.618963	+	0.187760i	−0.0347968	+	0.999394i	$0.511078\pi$
$374$	4.12716	+	24.0790i	0.213410	+	1.24510i
$375$	−2.88408	+	4.31634i	−0.148933	+	0.222895i
$376$	−6.50029	−	14.9119i	−0.335227	−	0.769022i
$377$	−19.6996	+	13.1628i	−1.01458	+	0.677920i
$378$	−7.33983	−	0.195275i	−0.377520	−	0.0100439i
$379$	−19.9061	−	24.2556i	−1.02251	−	1.24593i	−0.968923	−	0.247363i	$-0.920436\pi$
$379$	−19.9061	−	24.2556i	−1.02251	−	1.24593i	−0.0535829	−	0.998563i	$-0.517064\pi$
$380$	−2.32650	−	0.592930i	−0.119347	−	0.0304167i
$381$	4.54064	−	2.42702i	0.232624	−	0.124340i
$382$	−11.4011	−	6.48960i	−0.583329	−	0.332037i
$383$	−15.6012			−0.797185			−0.398592	−	0.917128i	$-0.630501\pi$
$383$	−15.6012			−0.797185			−0.398592	+	0.917128i	$0.630501\pi$
$384$	0.114938	+	11.3131i	0.00586540	+	0.577320i
$385$	−9.55733			−0.487086
$386$	5.70944	+	3.24988i	0.290603	+	0.165414i
$387$	−5.65361	+	3.02192i	−0.287389	+	0.153613i
$388$	6.80790	−	26.7124i	0.345619	−	1.35612i
$389$	10.8779	+	13.2548i	0.551532	+	0.672043i	0.971923	−	0.235300i	$-0.0756072\pi$
$389$	10.8779	+	13.2548i	0.551532	+	0.672043i	−0.420391	+	0.907343i	$0.638107\pi$
$390$	2.71232	+	0.0721608i	0.137343	+	0.00365401i
$391$	23.4132	−	15.6442i	1.18405	−	0.791160i
$392$	20.6378	−	52.5347i	1.04237	−	2.65340i
$393$	0.0804047	−	0.120334i	0.00405588	−	0.00607006i
$394$	−2.51364	−	14.6653i	−0.126635	−	0.738828i
$395$	5.09313	−	1.54498i	0.256263	−	0.0777366i
$396$	6.68989	−	1.64654i	0.336180	−	0.0827418i
$397$	−11.5638	−	9.49015i	−0.580370	−	0.476297i	0.297812	−	0.954625i	$-0.403743\pi$
$397$	−11.5638	−	9.49015i	−0.580370	−	0.476297i	−0.878182	+	0.478327i	$0.841243\pi$
$398$	32.4236	−	2.32473i	1.62525	−	0.116528i
$399$	−10.7752	−	4.46325i	−0.539437	−	0.223442i
$400$	14.4784	+	12.0826i	0.723920	+	0.604132i
$401$	−23.8700	+	9.88726i	−1.19201	+	0.493746i	−0.888409	−	0.459053i	$-0.848189\pi$
$401$	−23.8700	+	9.88726i	−1.19201	+	0.493746i	−0.303600	+	0.952799i	$0.598189\pi$
$402$	−5.69325	+	2.85109i	−0.283953	+	0.142200i
$403$	3.46871	+	35.2184i	0.172789	+	1.75435i
$404$	2.23100	−	1.04399i	0.110997	−	0.0519404i
$405$	−0.251906	+	0.471282i	−0.0125173	+	0.0234182i
$406$	47.2539	+	10.7133i	2.34517	+	0.531691i
$407$	9.04741	−	1.79964i	0.448463	−	0.0892049i
$408$	−8.79517	+	11.1278i	−0.435426	+	0.550910i
$409$	−1.39241	+	7.00012i	−0.0688502	+	0.346134i	−0.999820	−	0.0189622i	$-0.993964\pi$
$409$	−1.39241	+	7.00012i	−0.0688502	+	0.346134i	0.930970	+	0.365096i	$0.118964\pi$
$410$	−0.673838	−	1.75761i	−0.0332785	−	0.0868020i
$411$	0.0769184	−	0.780966i	0.00379411	−	0.0385222i
$412$	0.835506	−	0.295081i	0.0411624	−	0.0145376i
$413$	−15.2412	+	50.2435i	−0.749971	+	2.47232i
$414$	−4.87270	−	6.27032i	−0.239480	−	0.308169i
$415$	3.96979	+	3.96979i	0.194869	+	0.194869i
$416$	2.69309	−	20.1303i	0.132039	−	0.986970i
$417$	−3.89373	+	3.89373i	−0.190677	+	0.190677i
$418$	10.8586	+	1.36194i	0.531110	+	0.0666145i
$419$	3.43685	+	1.04256i	0.167901	+	0.0509322i	0.373116	−	0.927785i	$-0.378289\pi$
$419$	3.43685	+	1.04256i	0.167901	+	0.0509322i	−0.205215	+	0.978717i	$0.565789\pi$
$420$	−3.70948	−	4.12674i	−0.181004	−	0.201364i
$421$	23.1964	+	2.28464i	1.13052	+	0.111347i	0.645932	−	0.763395i	$-0.276469\pi$
$421$	23.1964	+	2.28464i	1.13052	+	0.111347i	0.484589	+	0.874742i	$0.338969\pi$
$422$	3.01060	−	6.75430i	0.146554	−	0.328794i
$423$	−5.64077	−	1.12202i	−0.274264	−	0.0545545i
$424$	−6.73831	−	20.8274i	−0.327241	−	1.01147i
$425$	4.61229	+	23.1876i	0.223729	+	1.12476i
$426$	−3.84076	+	2.42109i	−0.186086	+	0.117302i
$427$	−52.1724	−	27.8867i	−2.52480	−	1.34953i
$428$	24.1774	−	1.08817i	1.16866	−	0.0525988i
$429$	−12.3081	+	1.21224i	−0.594241	+	0.0585277i
$430$	−4.59700	−	1.52913i	−0.221687	−	0.0737411i
$431$	8.25506	+	19.9295i	0.397632	+	0.959969i	0.988226	+	0.153000i	$0.0488934\pi$
$431$	8.25506	+	19.9295i	0.397632	+	0.959969i	−0.590594	+	0.806969i	$0.701107\pi$
$432$	3.30750	+	2.24954i	0.159132	+	0.108231i
$433$	−10.5317	+	25.4257i	−0.506121	+	1.22188i	0.439979	+	0.898008i	$0.354986\pi$
$433$	−10.5317	+	25.4257i	−0.506121	+	1.22188i	−0.946100	+	0.323875i	$0.895014\pi$
$434$	47.3848	−	54.7044i	2.27454	−	2.62590i
$435$	2.23714	−	2.72596i	0.107262	−	0.130700i
$436$	−16.7425	+	12.3107i	−0.801819	+	0.589577i
$437$	−3.66162	−	12.0707i	−0.175159	−	0.577422i
$438$	−0.946728	+	1.33840i	−0.0452364	+	0.0639512i
$439$	−16.8457	−	11.2559i	−0.803999	−	0.537215i	0.0843215	−	0.996439i	$-0.473128\pi$
$439$	−16.8457	−	11.2559i	−0.803999	−	0.537215i	−0.888321	+	0.459223i	$0.848128\pi$
$440$	4.38158	+	2.81260i	0.208884	+	0.134085i
$441$	−11.0867	−	16.5925i	−0.527940	−	0.790119i
$442$	18.4769	−	17.5192i	0.878856	−	0.833304i
$443$	−17.8026	+	14.6102i	−0.845827	+	0.694152i	−0.953944	−	0.299986i	$-0.903018\pi$
$443$	−17.8026	+	14.6102i	−0.845827	+	0.694152i	0.108117	+	0.994138i	$0.465518\pi$
$444$	4.28863	+	3.20807i	0.203529	+	0.152248i
$445$	−3.69983	−	6.92189i	−0.175389	−	0.328129i
$446$	−5.41648	−	19.7303i	−0.256478	−	0.934256i
$447$			17.6921i			0.836809i
$448$	−33.6638	+	24.3292i	−1.59046	+	1.14945i
$449$			11.0430i			0.521152i	0.965453	+	0.260576i	$0.0839125\pi$
$449$			11.0430i			0.521152i	−0.965453	+	0.260576i	$0.916087\pi$
$450$	6.42935	−	1.76502i	0.303082	−	0.0832041i
$451$	4.04465	+	7.56701i	0.190455	+	0.356316i
$452$	−0.0789302	−	0.547600i	−0.00371256	−	0.0257570i
$453$	4.84917	−	3.97961i	0.227834	−	0.186979i
$454$	15.0174	+	15.8384i	0.704804	+	0.743331i
$455$	5.53404	+	8.28228i	0.259440	+	0.388279i
$456$	3.62646	+	5.21721i	0.169825	+	0.244318i
$457$	11.7728	+	7.86634i	0.550709	+	0.367972i	0.799575	−	0.600566i	$-0.205058\pi$
$457$	11.7728	+	7.86634i	0.550709	+	0.367972i	−0.248867	+	0.968538i	$0.580058\pi$
$458$	−30.2028	−	21.3642i	−1.41128	−	0.998283i
$459$	1.45571	+	4.79884i	0.0679468	+	0.223991i
$460$	0.904960	−	5.93265i	0.0421940	−	0.276611i
$461$	4.70369	−	5.73147i	0.219073	−	0.266941i	−0.651864	−	0.758336i	$-0.726013\pi$
$461$	4.70369	−	5.73147i	0.219073	−	0.266941i	0.870937	+	0.491395i	$0.163513\pi$
$462$	19.1181	+	16.5600i	0.889453	+	0.770441i
$463$	12.2279	−	29.5208i	0.568279	−	1.37195i	−0.334726	−	0.942315i	$-0.608644\pi$
$463$	12.2279	−	29.5208i	0.568279	−	1.37195i	0.903005	−	0.429631i	$-0.141356\pi$
$464$	−18.5109	−	18.8178i	−0.859348	−	0.873593i
$465$	−2.01572	−	4.86637i	−0.0934766	−	0.225673i
$466$	−4.14682	+	12.4665i	−0.192098	+	0.577501i
$467$	19.4693	−	1.91755i	0.900930	−	0.0887339i	0.363064	−	0.931764i	$-0.381731\pi$
$467$	19.4693	−	1.91755i	0.900930	−	0.0887339i	0.537866	+	0.843030i	$0.319231\pi$
$468$	−5.30057	−	4.84399i	−0.245019	−	0.223913i
$469$	−20.6154	−	11.0191i	−0.951929	−	0.508817i
$470$	−2.31777	−	3.67686i	−0.106911	−	0.169601i
$471$	−0.616125	−	3.09747i	−0.0283895	−	0.142724i
$472$	21.7734	−	18.5490i	1.00220	−	0.853787i
$473$	21.6586	+	4.30816i	0.995863	+	0.198090i
$474$	−12.8651	−	5.73436i	−0.590913	−	0.263388i
$475$	10.5395	+	1.03805i	0.483586	+	0.0476290i
$476$	−51.9986	−	2.76879i	−2.38335	−	0.126907i
$477$	−7.40613	−	2.24662i	−0.339103	−	0.102866i
$478$	−2.92366	+	23.3100i	−0.133725	+	1.06618i
$479$	23.6608	−	23.6608i	1.08109	−	1.08109i	0.0846799	−	0.996408i	$-0.473013\pi$
$479$	23.6608	−	23.6608i	1.08109	−	1.08109i	0.996408	−	0.0846799i	$-0.0269868\pi$
$480$	0.486175	+	2.98357i	0.0221908	+	0.136181i
$481$	−6.79833	−	6.79833i	−0.309977	−	0.309977i
$482$	−3.04176	+	2.36377i	−0.138548	+	0.107667i
$483$	8.46274	−	27.8979i	0.385068	−	1.26940i
$484$	−1.56346	−	0.747338i	−0.0710662	−	0.0339699i
$485$	0.721941	−	7.32999i	0.0327817	−	0.332838i
$486$	1.32049	−	0.506256i	0.0598988	−	0.0229642i
$487$	−0.734123	+	3.69069i	−0.0332663	+	0.167241i	−0.993847	−	0.110759i	$-0.964672\pi$
$487$	−0.734123	+	3.69069i	−0.0332663	+	0.167241i	0.960581	+	0.278000i	$0.0896717\pi$
$488$	15.7119	+	28.1384i	0.711244	+	1.27377i
$489$	5.14096	−	1.02260i	0.232482	−	0.0462436i
$490$	3.33451	−	14.7078i	0.150638	−	0.664430i
$491$	−2.41253	+	4.51353i	−0.108876	+	0.203693i	−0.930459	−	0.366396i	$-0.880591\pi$
$491$	−2.41253	+	4.51353i	−0.108876	+	0.203693i	0.821583	+	0.570089i	$0.193091\pi$
$492$	−1.69749	+	4.68341i	−0.0765289	+	0.211144i
$493$	−3.24366	−	32.9335i	−0.146087	−	1.48325i
$494$	−5.10727	−	10.1985i	−0.229787	−	0.458854i
$495$	1.70070	−	0.704452i	0.0764407	−	0.0316628i
$496$	−37.8225	+	11.1347i	−1.69828	+	0.499962i
$497$	−15.3992	−	6.37854i	−0.690747	−	0.286117i
$498$	−1.06254	−	14.8195i	−0.0476133	−	0.664076i
$499$	−2.34581	−	1.92516i	−0.105013	−	0.0861819i	0.580422	−	0.814316i	$-0.302888\pi$
$499$	−2.34581	−	1.92516i	−0.105013	−	0.0861819i	−0.685435	+	0.728134i	$0.740388\pi$
$500$	8.88330	+	5.37419i	0.397273	+	0.240341i
$501$	8.20230	−	2.48814i	0.366452	−	0.111162i
$502$	−32.2546	+	5.52846i	−1.43960	+	0.246747i
$503$	−2.49809	+	3.73866i	−0.111385	+	0.166699i	−0.882974	−	0.469422i	$-0.844462\pi$
$503$	−2.49809	+	3.73866i	−0.111385	+	0.166699i	0.771589	+	0.636121i	$0.219462\pi$
$504$	0.269877	+	14.6824i	0.0120213	+	0.654005i
$505$	0.547224	−	0.365644i	0.0243512	−	0.0162709i
$506$	−0.727520	+	27.3454i	−0.0323422	+	1.21565i
$507$	−0.0697413	−	0.0849800i	−0.00309732	−	0.00377409i
$508$	−5.25745	−	8.85384i	−0.233262	−	0.392826i
$509$	−21.5313	+	11.5087i	−0.954357	+	0.510114i	−0.873613	−	0.486621i	$-0.838229\pi$
$509$	−21.5313	+	11.5087i	−0.954357	+	0.510114i	−0.0807432	+	0.996735i	$0.525729\pi$
$510$	−1.87476	+	3.29362i	−0.0830160	+	0.145844i
$511$	−6.01856			−0.266245
$512$	22.5930	−	1.24697i	0.998480	−	0.0551090i
$513$	2.24640			0.0991809
$514$	0.936366	−	1.64503i	0.0413013	−	0.0725590i
$515$	0.208798	−	0.111605i	0.00920073	−	0.00491789i
$516$	6.54612	+	11.0240i	0.288177	+	0.485306i
$517$	12.5685	+	15.3148i	0.552762	+	0.673543i
$518$	−0.522922	+	19.6551i	−0.0229759	+	0.863597i
$519$	−9.90543	+	6.61860i	−0.434800	+	0.290524i
$520$	−0.0997289	−	5.42564i	−0.00437340	−	0.237930i
$521$	−16.1743	+	24.2066i	−0.708611	+	1.06051i	0.286140	+	0.958188i	$0.407628\pi$
$521$	−16.1743	+	24.2066i	−0.708611	+	1.06051i	−0.994751	+	0.102323i	$0.967372\pi$
$522$	−9.19835	+	1.57660i	−0.402601	+	0.0690060i
$523$	38.6897	−	11.7364i	1.69178	−	0.513197i	0.710163	−	0.704037i	$-0.248621\pi$
$523$	38.6897	−	11.7364i	1.69178	−	0.513197i	0.981621	+	0.190840i	$0.0611211\pi$
$524$	−0.247655	−	0.149826i	−0.0108189	−	0.00654517i
$525$	18.9208	+	15.5279i	0.825772	+	0.677694i
$526$	2.72566	+	38.0156i	0.118845	+	1.65756i
$527$	−45.6673	−	18.9160i	−1.98930	−	0.823995i
$528$	−3.89134	−	13.2182i	−0.169349	−	0.575248i
$529$	7.88074	−	3.26431i	0.342641	−	0.141927i
$530$	−2.61898	−	5.22975i	−0.113761	−	0.227166i
$531$	−0.991226	−	10.0641i	−0.0430155	−	0.436744i
$532$	−7.94851	+	21.9300i	−0.344612	+	0.950788i
$533$	4.21549	−	7.88663i	0.182593	−	0.341608i
$534$	−4.59260	+	20.2570i	−0.198741	+	0.876605i
$535$	6.34226	−	1.26155i	0.274200	−	0.0545417i
$536$	6.20838	+	11.1186i	0.268161	+	0.480250i
$537$	−2.89861	+	14.5723i	−0.125084	+	0.628840i
$538$	−17.2393	+	6.60929i	−0.743241	+	0.284947i
$539$	−6.73795	+	68.4115i	−0.290224	+	2.94669i
$540$	0.964264	+	0.460922i	0.0414953	+	0.0198349i
$541$	−0.462326	+	1.52409i	−0.0198770	+	0.0655256i	−0.966318	−	0.257352i	$-0.917150\pi$
$541$	−0.462326	+	1.52409i	−0.0198770	+	0.0655256i	0.946441	+	0.322877i	$0.104650\pi$
$542$	9.37137	−	7.28255i	0.402535	−	0.312812i
$543$	−8.87072	−	8.87072i	−0.380679	−	0.380679i
$544$	23.0241	+	16.5719i	0.987149	+	0.710513i
$545$	−3.92627	+	3.92627i	−0.168183	+	0.168183i
$546$	3.28066	−	26.1564i	0.140399	−	1.11939i
$547$	36.3399	+	11.0236i	1.55378	+	0.471335i	0.946379	−	0.323058i	$-0.104711\pi$
$547$	36.3399	+	11.0236i	1.55378	+	0.471335i	0.607404	+	0.794393i	$0.292211\pi$
$548$	−1.56727	−	0.0834531i	−0.0669504	−	0.00356494i
$549$	11.3394	+	1.11683i	0.483954	+	0.0476653i
$550$	−20.9775	−	9.35032i	−0.894485	−	0.398699i
$551$	−14.5393	−	2.89205i	−0.619395	−	0.123205i
$552$	−12.0898	+	10.2994i	−0.514575	+	0.438372i
$553$	−10.0881	−	50.7162i	−0.428989	−	2.15667i
$554$	−15.3286	−	24.3170i	−0.651251	−	1.03313i
$555$	1.26203	+	0.674571i	0.0535704	+	0.0286340i
$556$	8.12974	+	7.42945i	0.344778	+	0.315079i
$557$	35.2905	−	3.47581i	1.49531	−	0.147275i	0.682962	−	0.730454i	$-0.260692\pi$
$557$	35.2905	−	3.47581i	1.49531	−	0.147275i	0.812343	+	0.583179i	$0.198192\pi$
$558$	−4.39982	+	13.2271i	−0.186259	+	0.559949i
$559$	−8.80772	−	21.2637i	−0.372527	−	0.899359i
$560$	−7.91155	+	7.78255i	−0.334324	+	0.328873i
$561$	6.61076	−	15.9598i	0.279107	−	0.673823i
$562$	−2.55529	−	2.21338i	−0.107788	−	0.0933660i
$563$	−6.62427	+	8.07170i	−0.279180	+	0.340182i	−0.893655	−	0.448754i	$-0.851868\pi$
$563$	−6.62427	+	8.07170i	−0.279180	+	0.340182i	0.614475	+	0.788936i	$0.289368\pi$
$564$	−1.73452	+	11.3710i	−0.0730367	+	0.478807i
$565$	−0.0429116	−	0.141461i	−0.00180530	−	0.00595129i
$566$	−16.8923	−	11.9489i	−0.710036	−	0.502250i
$567$	4.31689	+	2.88445i	0.181292	+	0.121136i
$568$	5.18267	+	7.45604i	0.217460	+	0.312849i
$569$	7.65948	+	11.4632i	0.321102	+	0.480563i	0.956545	−	0.291585i	$-0.0941825\pi$
$569$	7.65948	+	11.4632i	0.321102	+	0.480563i	−0.635443	+	0.772148i	$0.719182\pi$
$570$	1.16808	+	1.23194i	0.0489256	+	0.0516001i
$571$	20.4555	−	16.7874i	0.856035	−	0.702529i	−0.100252	−	0.994962i	$-0.531965\pi$
$571$	20.4555	−	16.7874i	0.856035	−	0.702529i	0.956286	+	0.292433i	$0.0944648\pi$
$572$	3.52884	+	24.4823i	0.147548	+	1.02366i
$573$	4.37281	+	8.18096i	0.182677	+	0.341764i
$574$	−17.6358	+	4.84150i	−0.736105	+	0.202080i
$575$			26.4723i			1.10397i
$576$	4.19711	−	6.81060i	0.174880	−	0.283775i
$577$			3.89244i			0.162044i	0.996712	+	0.0810222i	$0.0258185\pi$
$577$			3.89244i			0.162044i	−0.996712	+	0.0810222i	$0.974182\pi$
$578$	3.05049	+	11.1119i	0.126884	+	0.462192i
$579$	−2.18983	−	4.09688i	−0.0910060	−	0.170260i
$580$	−5.64758	−	4.22462i	−0.234503	−	0.175418i
$581$	42.1639	−	34.6030i	1.74925	−	1.43558i
$582$	−14.1448	+	13.4117i	−0.586323	+	0.555933i
$583$	14.8117	+	22.1673i	0.613439	+	0.918076i
$584$	2.75923	+	1.77119i	0.114178	+	0.0732922i
$585$	−1.59524	−	1.06590i	−0.0659550	−	0.0440697i
$586$	13.5326	−	19.1312i	0.559028	−	0.790304i
$587$	10.5336	+	34.7247i	0.434769	+	1.43324i	0.851568	+	0.524243i	$0.175652\pi$
$587$	10.5336	+	34.7247i	0.434769	+	1.43324i	−0.416799	+	0.908999i	$0.636848\pi$
$588$	−32.1544	+	23.6431i	−1.32603	+	0.975027i
$589$	−14.0470	+	17.1163i	−0.578797	+	0.705266i
$590$	5.00377	−	5.77672i	0.206002	−	0.237824i
$591$	−4.02627	+	9.72029i	−0.165619	+	0.399839i
$592$	6.02399	−	8.85706i	0.247584	−	0.364023i
$593$	−3.90213	−	9.42058i	−0.160241	−	0.386857i	0.823283	−	0.567631i	$-0.192140\pi$
$593$	−3.90213	−	9.42058i	−0.160241	−	0.386857i	−0.983525	+	0.180774i	$0.942140\pi$
$594$	−4.62261	−	1.53765i	−0.189668	−	0.0630904i
$595$	−13.8462	+	1.36373i	−0.567640	+	0.0559076i
$596$	35.3485	−	1.59096i	1.44793	−	0.0651683i
$597$	−20.2717	−	10.8354i	−0.829664	−	0.443465i
$598$	24.1185	−	15.2035i	0.986279	−	0.621718i
$599$	−4.34707	−	21.8542i	−0.177616	−	0.892938i	−0.962081	−	0.272764i	$-0.912062\pi$
$599$	−4.34707	−	21.8542i	−0.177616	−	0.892938i	0.784464	−	0.620174i	$-0.212938\pi$
$600$	−4.10464	−	12.6870i	−0.167571	−	0.517943i
$601$	−22.7111	−	4.51752i	−0.926405	−	0.184273i	−0.291240	−	0.956650i	$-0.594068\pi$
$601$	−22.7111	−	4.51752i	−0.926405	−	0.184273i	−0.635165	+	0.772377i	$0.719068\pi$
$602$	−19.1627	+	42.9917i	−0.781014	+	1.75221i
$603$	4.48064	+	0.441305i	0.182466	+	0.0179713i
$604$	−8.38724	−	9.33067i	−0.341272	−	0.379660i
$605$	−0.443075	−	0.134405i	−0.0180136	−	0.00546435i
$606$	−1.72820	−	0.216759i	−0.0702032	−	0.00880523i
$607$	11.0345	−	11.0345i	0.447876	−	0.447876i	−0.446772	−	0.894648i	$-0.647426\pi$
$607$	11.0345	−	11.0345i	0.447876	−	0.447876i	0.894648	+	0.446772i	$0.147426\pi$
$608$	10.0978	−	7.71475i	0.409518	−	0.312874i
$609$	−24.2266	−	24.2266i	−0.981711	−	0.981711i
$610$	5.28379	+	6.79931i	0.213934	+	0.275296i
$611$	5.99400	−	19.7596i	0.242491	−	0.799386i
$612$	9.45707	−	3.34002i	0.382279	−	0.135012i
$613$	−3.22927	+	32.7873i	−0.130429	+	1.32427i	0.677734	+	0.735307i	$0.262962\pi$
$613$	−3.22927	+	32.7873i	−0.130429	+	1.32427i	−0.808163	+	0.588959i	$0.799538\pi$
$614$	0.0411879	+	0.107433i	0.00166221	+	0.00433563i
$615$	−0.259670	+	1.30545i	−0.0104709	+	0.0526407i
$616$	31.3673	−	39.6866i	1.26383	−	1.59902i
$617$	23.7640	−	4.72695i	0.956702	−	0.190300i	0.308037	−	0.951374i	$-0.400328\pi$
$617$	23.7640	−	4.72695i	0.956702	−	0.190300i	0.648665	+	0.761074i	$0.275328\pi$
$618$	−0.611048	−	0.138535i	−0.0245800	−	0.00557270i
$619$	22.8405	−	42.7315i	0.918036	−	1.71753i	0.258240	−	0.966081i	$-0.416858\pi$
$619$	22.8405	−	42.7315i	0.918036	−	1.71753i	0.659797	−	0.751444i	$-0.270642\pi$
$620$	−9.54164	+	4.46496i	−0.383201	+	0.179317i
$621$	0.550382	+	5.58812i	0.0220861	+	0.224244i
$622$	10.3910	−	5.20367i	0.416643	−	0.208648i
$623$	−70.4504	+	29.1815i	−2.82254	+	1.16913i
$624$	−9.20152	+	11.0260i	−0.368356	+	0.441394i
$625$	−19.2149	−	7.95909i	−0.768597	−	0.318363i
$626$	−31.1982	+	2.23687i	−1.24693	+	0.0894032i
$627$	−5.98181	−	4.90914i	−0.238890	−	0.196052i
$628$	−6.13327	+	1.50954i	−0.244744	+	0.0602373i
$629$	12.8507	−	3.89821i	0.512390	−	0.155432i
$630$	0.662850	+	3.86726i	0.0264086	+	0.154075i
$631$	−17.0750	+	25.5545i	−0.679744	+	1.01731i	0.317861	+	0.948137i	$0.397035\pi$
$631$	−17.0750	+	25.5545i	−0.679744	+	1.01731i	−0.997605	+	0.0691713i	$0.977965\pi$
$632$	−10.3002	+	26.2198i	−0.409721	+	1.04297i
$633$	−4.34773	+	2.90506i	−0.172807	+	0.115466i
$634$	−14.3818	−	0.382627i	−0.571175	−	0.0151960i
$635$	−1.74541	−	2.12679i	−0.0692644	−	0.0843989i
$636$	−3.82271	+	14.9993i	−0.151580	+	0.594761i
$637$	63.1862	−	33.7738i	2.50353	−	1.33816i
$638$	27.9392	+	15.9033i	1.10612	+	0.629617i
$639$	3.21039			0.127001
$640$	5.91738	−	1.23966i	0.233905	−	0.0490020i
$641$	47.7760			1.88704			0.943520	−	0.331315i	$-0.107492\pi$
$641$	47.7760			1.88704			0.943520	+	0.331315i	$0.107492\pi$
$642$	−14.8727	−	8.46569i	−0.586978	−	0.334114i
$643$	−10.2200	+	5.46271i	−0.403038	+	0.215428i	−0.660444	−	0.750875i	$-0.729632\pi$
$643$	−10.2200	+	5.46271i	−0.403038	+	0.215428i	0.257406	+	0.966303i	$0.417132\pi$
$644$	−56.5004	−	14.3997i	−2.22643	−	0.567426i
$645$	2.17323	+	2.64809i	0.0855709	+	0.104268i
$646$	15.9257	+	0.423702i	0.626590	+	0.0166703i
$647$	−33.1209	+	22.1307i	−1.30212	+	0.870047i	−0.996620	−	0.0821464i	$-0.973823\pi$
$647$	−33.1209	+	22.1307i	−1.30212	+	0.870047i	−0.305497	+	0.952193i	$0.598823\pi$
$648$	−1.13023	−	2.59279i	−0.0443998	−	0.101855i
$649$	−19.3540	+	28.9653i	−0.759709	+	1.13699i
$650$	4.04387	+	23.5931i	0.158613	+	0.925397i
$651$	−48.9720	+	14.8555i	−1.91936	+	0.582233i
$652$	−2.50543	−	10.1796i	−0.0981203	−	0.398662i
$653$	14.9173	+	12.2424i	0.583761	+	0.479080i	0.879312	−	0.476247i	$-0.158003\pi$
$653$	14.9173	+	12.2424i	0.583761	+	0.479080i	−0.295551	+	0.955327i	$0.595503\pi$
$654$	14.6570	−	1.05089i	0.573134	−	0.0410930i
$655$	−0.0714512	−	0.0295961i	−0.00279183	−	0.00115641i
$656$	9.50999	+	2.97040i	0.371303	+	0.115975i
$657$	1.07098	−	0.443616i	0.0417831	−	0.0173071i
$658$	−37.7584	+	18.9088i	−1.47197	+	0.737142i
$659$	0.735491	+	7.46756i	0.0286507	+	0.290895i	0.998824	+	0.0484829i	$0.0154386\pi$
$659$	0.735491	+	7.46756i	0.0286507	+	0.290895i	−0.970173	+	0.242412i	$0.922061\pi$
$660$	−1.56041	−	3.33461i	−0.0607390	−	0.129799i
$661$	−7.86661	+	14.7174i	−0.305976	+	0.572440i	−0.987172	−	0.159661i	$-0.948960\pi$
$661$	−7.86661	+	14.7174i	−0.305976	+	0.572440i	0.681196	+	0.732101i	$0.261460\pi$
$662$	−12.4312	−	2.81838i	−0.483154	−	0.109539i
$663$	−17.6585	+	3.51249i	−0.685798	+	0.136414i
$664$	−29.5134	+	3.45556i	−1.14534	+	0.134102i
$665$	−1.21590	+	6.11275i	−0.0471507	+	0.237042i
$666$	−1.35569	−	3.53612i	−0.0525319	−	0.137022i
$667$	3.63201	−	36.8764i	0.140632	−	1.42786i
$668$	−5.70884	−	16.1643i	−0.220882	−	0.625414i
$669$	−4.19972	+	13.8446i	−0.162371	+	0.535264i
$670$	2.08783	+	2.68667i	0.0806600	+	0.103795i
$671$	−27.7544	−	27.7544i	−1.07145	−	1.07145i
$672$	29.3108	−	1.85952i	1.13069	−	0.0717325i
$673$	−5.57698	+	5.57698i	−0.214977	+	0.214977i	−0.806378	−	0.591401i	$-0.798575\pi$
$673$	−5.57698	+	5.57698i	−0.214977	+	0.214977i	0.591401	+	0.806378i	$0.298575\pi$
$674$	25.6352	+	3.21529i	0.987431	+	0.123848i
$675$	−4.51143	−	1.36853i	−0.173645	−	0.0526747i
$676$	−0.163517	+	0.146983i	−0.00628910	+	0.00565321i
$677$	−30.4282	−	2.99691i	−1.16945	−	0.115181i	−0.505411	−	0.862879i	$-0.668659\pi$
$677$	−30.4282	−	2.99691i	−1.16945	−	0.115181i	−0.664039	+	0.747698i	$0.731159\pi$
$678$	−0.159271	+	0.357325i	−0.00611675	+	0.0137230i
$679$	−70.1854	−	13.9608i	−2.69347	−	0.535765i
$680$	6.74917	+	3.44956i	0.258819	+	0.132285i
$681$	−3.01090	−	15.1368i	−0.115378	−	0.580044i
$682$	40.6218	−	25.6067i	1.55549	−	0.980530i
$683$	40.0665	+	21.4160i	1.53310	+	0.819461i	0.999652	−	0.0263699i	$-0.00839476\pi$
$683$	40.0665	+	21.4160i	1.53310	+	0.819461i	0.533451	+	0.845831i	$0.320895\pi$
$684$	−0.202007	−	4.48825i	−0.00772393	−	0.171613i
$685$	−0.417334	+	0.0411038i	−0.0159455	+	0.00157050i
$686$	−90.2630	−	30.0247i	−3.44626	−	1.14635i
$687$	10.0108	+	24.1682i	0.381936	+	0.922075i
$688$	21.4371	−	14.0703i	0.817283	−	0.536427i
$689$	10.6334	−	25.6714i	0.405102	−	0.978002i
$690$	−2.77837	+	3.20755i	−0.105771	+	0.122109i
$691$	11.9969	−	14.6183i	0.456385	−	0.556107i	−0.493078	−	0.869985i	$-0.664128\pi$
$691$	11.9969	−	14.6183i	0.456385	−	0.556107i	0.949463	+	0.313878i	$0.101628\pi$
$692$	14.1146	+	19.1957i	0.536555	+	0.729709i
$693$	−5.19169	−	17.1147i	−0.197216	−	0.650134i
$694$	4.74757	−	6.71169i	0.180215	−	0.254772i
$695$	2.44669	+	1.63483i	0.0928083	+	0.0620125i
$696$	3.97717	+	18.2363i	0.150754	+	0.691246i
$697$	6.93944	+	10.3856i	0.262850	+	0.393383i
$698$	10.3096	−	9.77527i	0.390225	−	0.370000i
$699$	7.18131	−	5.89355i	0.271622	−	0.222915i
$700$	29.3230	−	39.1997i	1.10830	−	1.48161i
$701$	−16.0769	−	30.0778i	−0.607216	−	1.13602i	−0.978255	−	0.207405i	$-0.933498\pi$
$701$	−16.0769	−	30.0778i	−0.607216	−	1.13602i	0.371039	−	0.928617i	$-0.379002\pi$
$702$	1.34415	+	4.89626i	0.0507318	+	0.184798i
$703$		−	6.01557i		−	0.226882i
$704$	−26.0597	+	8.96345i	−0.982163	+	0.337823i
$705$			3.07338i			0.115750i
$706$	−14.1397	+	3.88173i	−0.532156	+	0.146091i
$707$	−3.01425	−	5.63926i	−0.113362	−	0.212086i
$708$	−20.0187	+	2.88546i	−0.752348	+	0.108442i
$709$	16.1292	−	13.2369i	0.605746	−	0.497123i	−0.280798	−	0.959767i	$-0.590599\pi$
$709$	16.1292	−	13.2369i	0.605746	−	0.497123i	0.886544	+	0.462644i	$0.153099\pi$
$710$	1.66934	+	1.76059i	0.0626491	+	0.0660738i
$711$	5.53334	+	8.28123i	0.207516	+	0.310570i
$712$	40.8860	+	7.35431i	1.53227	+	0.275614i
$713$	−46.0201	−	30.7496i	−1.72347	−	1.15158i
$714$	30.0603	+	21.2634i	1.12498	+	0.795764i
$715$	1.91851	+	6.32447i	0.0717481	+	0.236522i
$716$	29.3757	+	4.48094i	1.09782	+	0.167461i
$717$	10.5384	−	12.8411i	0.393565	−	0.479560i
$718$	30.6477	+	26.5469i	1.14376	+	0.990721i
$719$	3.15492	−	7.61665i	0.117659	−	0.284053i	−0.854068	−	0.520161i	$-0.825872\pi$
$719$	3.15492	−	7.61665i	0.117659	−	0.284053i	0.971727	+	0.236108i	$0.0758719\pi$
$720$	0.834200	−	1.96803i	0.0310888	−	0.0733440i
$721$	−0.880256	−	2.12513i	−0.0327824	−	0.0791438i
$722$	−6.22853	+	18.7248i	−0.231802	+	0.696863i
$723$	2.71083	−	0.266993i	0.100817	−	0.00992958i
$724$	−16.9258	+	18.5212i	−0.629042	+	0.688335i
$725$	27.4373	+	14.6656i	1.01900	+	0.544665i
$726$	0.653424	+	1.03658i	0.0242508	+	0.0384709i
$727$	−6.39658	−	32.1578i	−0.237236	−	1.19267i	−0.897288	−	0.441446i	$-0.854466\pi$
$727$	−6.39658	−	32.1578i	−0.237236	−	1.19267i	0.660052	−	0.751220i	$-0.270534\pi$
$728$	−52.5549	−	4.20258i	−1.94781	−	0.155758i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	0.800172	+	0.356661i	0.0296157	+	0.0132006i
$731$	31.9927	+	3.15101i	1.18329	+	0.116544i
$732$	1.21172	−	22.7563i	0.0447863	−	0.841097i
$733$	10.1917	+	3.09161i	0.376438	+	0.114191i	0.472833	−	0.881152i	$-0.343231\pi$
$733$	10.1917	+	3.09161i	0.376438	+	0.114191i	−0.0963953	+	0.995343i	$0.530731\pi$
$734$	2.37482	−	18.9342i	0.0876560	−	0.698873i
$735$	−7.54053	+	7.54053i	−0.278136	+	0.278136i
$736$	21.6652	+	23.2289i	0.798588	+	0.856229i
$737$	−10.9669	−	10.9669i	−0.403969	−	0.403969i
$738$	2.78138	−	2.16143i	0.102384	−	0.0795634i
$739$	−2.95849	+	9.75283i	−0.108830	+	0.358764i	−0.994392	−	0.105757i	$-0.966273\pi$
$739$	−2.95849	+	9.75283i	−0.108830	+	0.358764i	0.885562	+	0.464521i	$0.153773\pi$
$740$	1.23429	−	2.58218i	0.0453734	−	0.0949227i
$741$	−0.790527	+	8.02635i	−0.0290407	+	0.294855i
$742$	−53.0600	+	20.3423i	−1.94789	+	0.746791i
$743$	7.87406	−	39.5856i	0.288871	−	1.45225i	−0.514866	−	0.857270i	$-0.672158\pi$
$743$	7.87406	−	39.5856i	0.288871	−	1.45225i	0.803738	−	0.594984i	$-0.202842\pi$
$744$	26.8232	+	7.60129i	0.983385	+	0.278677i
$745$	9.27268	−	1.84445i	0.339725	−	0.0675755i
$746$	3.90615	−	17.2292i	0.143014	−	0.630806i
$747$	−4.95242	+	9.26532i	−0.181200	+	0.339000i
$748$	−32.4818	−	11.7730i	−1.18765	−	0.430462i
$749$	−6.15808	−	62.5240i	−0.225011	−	2.28458i
$750$	−3.28733	−	6.56436i	−0.120036	−	0.239697i
$751$	12.5412	−	5.19472i	0.457634	−	0.189558i	−0.141944	−	0.989875i	$-0.545335\pi$
$751$	12.5412	−	5.19472i	0.457634	−	0.189558i	0.599578	+	0.800317i	$0.295335\pi$
$752$	22.8751	+	2.44300i	0.834167	+	0.0890871i
$753$	21.3786	+	8.85532i	0.779081	+	0.322706i
$754$	−2.39620	−	33.4204i	−0.0872644	−	1.21710i
$755$	−2.59131	−	2.12663i	−0.0943074	−	0.0773961i
$756$	5.37488	−	8.88443i	0.195482	−	0.323124i
$757$	6.33281	−	1.92104i	0.230170	−	0.0698213i	−0.173093	−	0.984906i	$-0.555376\pi$
$757$	6.33281	−	1.92104i	0.230170	−	0.0698213i	0.403263	+	0.915084i	$0.367876\pi$
$758$	43.7375	−	7.49663i	1.58862	−	0.272290i
$759$	10.7464	−	16.0831i	0.390068	−	0.583779i
$760$	2.35634	−	2.44459i	0.0854734	−	0.0886744i
$761$	40.1714	−	26.8417i	1.45621	−	0.973009i	0.459831	−	0.888007i	$-0.347910\pi$
$761$	40.1714	−	26.8417i	1.45621	−	0.973009i	0.996381	−	0.0850026i	$-0.0270899\pi$
$762$	−0.193646	+	7.27861i	−0.00701507	+	0.263676i
$763$	34.2237	+	41.7017i	1.23898	+	1.50970i
$764$	15.9521	−	9.47245i	0.577128	−	0.342701i
$765$	2.36338	−	1.26325i	0.0854480	−	0.0456729i
$766$	10.9145	−	19.1747i	0.394355	−	0.692811i
$767$	36.3077			1.31099
$768$	−13.9848	−	7.77329i	−0.504635	−	0.280494i
$769$	29.9330			1.07941			0.539705	−	0.841854i	$-0.318536\pi$
$769$	29.9330			1.07941			0.539705	+	0.841854i	$0.318536\pi$
$770$	6.68621	−	11.7465i	0.240954	−	0.423313i
$771$	−1.18041	+	0.630940i	−0.0425113	+	0.0227228i
$772$	−7.98854	+	4.74363i	−0.287514	+	0.170727i
$773$	−12.9858	−	15.8233i	−0.467068	−	0.569125i	0.485193	−	0.874407i	$-0.338749\pi$
$773$	−12.9858	−	15.8233i	−0.467068	−	0.569125i	−0.952262	+	0.305282i	$0.901249\pi$
$774$	0.241112	−	9.06270i	0.00866659	−	0.325752i
$775$	38.6380	−	25.8171i	1.38792	−	0.927377i
$776$	28.0683	+	27.0550i	1.00759	+	0.971219i
$777$	7.72420	−	11.5601i	0.277104	−	0.414716i
$778$	−23.9009	+	4.09662i	−0.856889	+	0.146871i
$779$	5.35434	−	1.62422i	0.191839	−	0.0581937i
$780$	−1.98620	+	3.28310i	−0.0711174	+	0.117554i
$781$	−8.54876	−	7.01578i	−0.305899	−	0.251044i
$782$	2.84791	+	39.7206i	0.101841	+	1.42040i
$783$	6.09674	+	2.52535i	0.217880	+	0.0902488i
$784$	50.1300	+	62.1177i	1.79036	+	2.21849i
$785$	−1.55919	+	0.645839i	−0.0556500	+	0.0230510i
$786$	0.0916468	+	0.183006i	0.00326893	+	0.00652762i
$787$	0.564001	+	5.72640i	0.0201045	+	0.204124i	0.999990	+	0.00456168i	$0.00145203\pi$
$787$	0.564001	+	5.72640i	0.0201045	+	0.204124i	−0.979885	+	0.199562i	$0.936048\pi$
$788$	19.7830	+	7.17031i	0.704739	+	0.255432i
$789$	12.7042	−	23.7678i	0.452280	−	0.846157i
$790$	−1.66424	+	7.34058i	−0.0592108	+	0.261166i
$791$	−1.40863	+	0.280194i	−0.0500852	+	0.00996256i
$792$	−2.65650	+	9.37414i	−0.0943945	+	0.333096i
$793$	−7.98086	+	40.1225i	−0.283409	+	1.42479i
$794$	19.7538	−	7.57329i	0.701037	−	0.268766i
$795$	−0.405378	+	4.11587i	−0.0143773	+	0.145975i
$796$	−19.8260	+	41.4767i	−0.702714	+	1.47010i
$797$	−3.41182	+	11.2472i	−0.120853	+	0.398398i	−0.996404	−	0.0847268i	$-0.972998\pi$
$797$	−3.41182	+	11.2472i	−0.120853	+	0.398398i	0.875552	+	0.483125i	$0.160498\pi$
$798$	13.0238	−	10.1209i	0.461038	−	0.358276i
$799$	20.3939	+	20.3939i	0.721486	+	0.721486i
$800$	−24.9792	+	9.34185i	−0.883147	+	0.330284i
$801$	10.3855	−	10.3855i	0.366955	−	0.366955i
$802$	4.54722	−	36.2545i	0.160568	−	1.28019i
$803$	−3.82132	−	1.15918i	−0.134851	−	0.0409067i
$804$	0.478796	−	8.99191i	0.0168858	−	0.317120i
$805$	−15.5039	−	1.52701i	−0.546442	−	0.0538199i
$806$	−45.7120	−	20.3752i	−1.61014	−	0.717687i
$807$	12.8044	+	2.54695i	0.450735	+	0.0896568i
$808$	−0.277672	+	3.47239i	−0.00976845	+	0.122158i
$809$	−0.819765	−	4.12124i	−0.0288214	−	0.144895i	0.963695	−	0.267005i	$-0.0860340\pi$
$809$	−0.819765	−	4.12124i	−0.0288214	−	0.144895i	−0.992517	+	0.122110i	$0.961034\pi$
$810$	−0.403001	−	0.639310i	−0.0141600	−	0.0224631i
$811$	−44.5920	−	23.8349i	−1.56584	−	0.836958i	−0.999922	−	0.0124951i	$-0.996023\pi$
$811$	−44.5920	−	23.8349i	−1.56584	−	0.836958i	−0.565916	−	0.824463i	$-0.691477\pi$
$812$	−46.2256	+	50.5827i	−1.62220	+	1.77511i
$813$	−8.35179	+	0.822580i	−0.292910	+	0.0288491i
$814$	−4.11762	+	12.3788i	−0.144323	+	0.433875i
$815$	−1.07192	−	2.58784i	−0.0375476	−	0.0906480i
$816$	−7.52370	−	18.5947i	−0.263382	−	0.650943i
$817$	5.51090	−	13.3045i	0.192802	−	0.465465i
$818$	−7.62940	−	6.60856i	−0.266756	−	0.231063i
$819$	−11.8253	+	14.4091i	−0.413208	+	0.503496i
$820$	2.63160	+	0.401422i	0.0918996	+	0.0140183i
$821$	0.419497	+	1.38290i	0.0146406	+	0.0482634i	0.963956	−	0.266061i	$-0.0857221\pi$
$821$	0.419497	+	1.38290i	0.0146406	+	0.0482634i	−0.949316	+	0.314324i	$0.898222\pi$
$822$	0.906038	+	0.640893i	0.0316017	+	0.0223537i
$823$	−11.2983	−	7.54930i	−0.393835	−	0.263152i	0.342847	−	0.939391i	$-0.388609\pi$
$823$	−11.2983	−	7.54930i	−0.393835	−	0.263152i	−0.736682	+	0.676239i	$0.763609\pi$
$824$	−0.221841	+	1.23332i	−0.00772821	+	0.0429647i
$825$	9.02255	+	13.5032i	0.314125	+	0.470121i
$826$	−51.0894	−	53.8822i	−1.77763	−	1.87480i
$827$	−21.0352	+	17.2632i	−0.731467	+	0.600299i	−0.924630	−	0.380868i	$-0.875625\pi$
$827$	−21.0352	+	17.2632i	−0.731467	+	0.600299i	0.193163	+	0.981167i	$0.438125\pi$
$828$	11.1155	−	1.60216i	0.386289	−	0.0556790i
$829$	−9.03501	−	16.9033i	−0.313799	−	0.587076i	0.674738	−	0.738057i	$-0.264257\pi$
$829$	−9.03501	−	16.9033i	−0.313799	−	0.587076i	−0.988537	+	0.150981i	$0.951757\pi$
$830$	−7.65631	+	2.10186i	−0.265754	+	0.0729565i
$831$			20.3259i			0.705096i
$832$	22.8572	+	17.3929i	0.792430	+	0.602991i
$833$			100.073i			3.46732i
$834$	−2.06159	−	7.50963i	−0.0713870	−	0.260037i
$835$	−2.15918	−	4.03954i	−0.0747215	−	0.139794i
$836$	−9.27045	+	12.3930i	−0.320625	+	0.428620i
$837$	7.61945	−	6.25312i	0.263367	−	0.216140i
$838$	−3.68574	+	3.49471i	−0.127322	+	0.120723i
$839$	3.14997	+	4.71427i	0.108749	+	0.162755i	0.881852	−	0.471526i	$-0.156297\pi$
$839$	3.14997	+	4.71427i	0.108749	+	0.162755i	−0.773103	+	0.634280i	$0.781297\pi$
$840$	7.66710	−	1.67212i	0.264540	−	0.0576937i
$841$	−12.0959	−	8.08225i	−0.417102	−	0.278698i
$842$	−19.0359	+	26.9112i	−0.656020	+	0.927423i
$843$	0.693913	+	2.28753i	0.0238996	+	0.0787866i
$844$	6.19521	+	8.42543i	0.213248	+	0.290015i
$845$	−0.0372685	+	0.0454117i	−0.00128207	+	0.00156221i
$846$	5.32525	−	6.14786i	0.183086	−	0.211368i
$847$	−1.72149	+	4.15605i	−0.0591512	+	0.142804i
$848$	30.3120	+	6.28888i	1.04092	+	0.215961i
$849$	5.59900	+	13.5172i	0.192157	+	0.463909i
$850$	−31.7255	−	10.5530i	−1.08818	−	0.361966i
$851$	14.9643	−	1.47385i	0.512969	−	0.0505231i
$852$	−0.288693	−	6.41428i	−0.00989047	−	0.219750i
$853$	16.0421	+	8.57466i	0.549270	+	0.293591i	0.722592	−	0.691274i	$-0.242950\pi$
$853$	16.0421	+	8.57466i	0.549270	+	0.293591i	−0.173323	+	0.984865i	$0.555450\pi$
$854$	70.7736	−	44.6134i	2.42182	−	1.52664i
$855$	−0.234193	−	1.17737i	−0.00800923	−	0.0402651i
$856$	−15.5768	+	30.4766i	−0.532405	+	1.04167i
$857$	−56.1951	−	11.1779i	−1.91959	−	0.381830i	−0.919647	−	0.392745i	$-0.871525\pi$
$857$	−56.1951	−	11.1779i	−1.91959	−	0.381830i	−0.999940	+	0.0109153i	$0.996525\pi$
$858$	7.12073	−	15.9754i	0.243098	−	0.545392i
$859$	1.38949	+	0.136853i	0.0474088	+	0.00466936i	0.121694	−	0.992568i	$-0.461167\pi$
$859$	1.38949	+	0.136853i	0.0474088	+	0.00466936i	−0.0742849	+	0.997237i	$0.523667\pi$
$860$	5.09540	−	4.58020i	0.173752	−	0.156183i
$861$	12.3749	+	3.75390i	0.421737	+	0.127933i
$862$	−30.2695	−	3.79656i	−1.03098	−	0.129311i
$863$	29.6678	−	29.6678i	1.00990	−	1.00990i	0.00995189	−	0.999950i	$-0.496832\pi$
$863$	29.6678	−	29.6678i	1.00990	−	1.00990i	0.999950	−	0.00995189i	$-0.00316784\pi$
$864$	−5.07870	+	2.49134i	−0.172781	+	0.0847570i
$865$	4.50156	+	4.50156i	0.153058	+	0.153058i
$866$	−23.8817	−	30.7316i	−0.811535	−	1.04430i
$867$	2.36523	−	7.79712i	0.0803274	−	0.264804i
$868$	34.0848	+	96.5091i	1.15691	+	3.27573i
$869$	3.36287	−	34.1438i	0.114078	−	1.15825i
$870$	1.78527	+	4.65662i	0.0605263	+	0.157874i
$871$	−3.15355	+	15.8540i	−0.106854	+	0.537191i
$872$	−3.41768	−	29.1899i	−0.115737	−	0.988494i
$873$	13.5183	−	2.68896i	0.457525	−	0.0910075i
$874$	17.3972	+	3.94425i	0.588470	+	0.133416i
$875$	12.7052	−	23.7697i	0.429513	−	0.803562i
$876$	−0.982644	−	2.09991i	−0.0332005	−	0.0709494i
$877$	−2.94329	−	29.8837i	−0.0993877	−	1.00910i	−0.907494	−	0.420064i	$-0.862008\pi$
$877$	−2.94329	−	29.8837i	−0.0993877	−	1.00910i	0.808107	−	0.589036i	$-0.200492\pi$
$878$	25.6192	−	12.8297i	0.864605	−	0.432981i
$879$	−15.3088	+	6.34110i	−0.516352	+	0.213880i
$880$	−6.52215	+	3.41754i	−0.219862	+	0.115205i
$881$	20.7975	+	8.61462i	0.700687	+	0.290234i	0.704445	−	0.709759i	$-0.251196\pi$
$881$	20.7975	+	8.61462i	0.700687	+	0.290234i	−0.00375777	+	0.999993i	$0.501196\pi$
$882$	28.1492	−	2.01826i	0.947834	−	0.0679584i
$883$	−3.92386	−	3.22023i	−0.132049	−	0.108369i	0.566051	−	0.824370i	$-0.308471\pi$
$883$	−3.92386	−	3.22023i	−0.132049	−	0.108369i	−0.698099	+	0.716001i	$0.745971\pi$
$884$	8.60580	+	34.9654i	0.289445	+	1.17601i
$885$	−5.17139	+	1.56872i	−0.173834	+	0.0527320i
$886$	−5.50221	−	32.1015i	−0.184850	−	1.07847i
$887$	19.2153	−	28.7578i	0.645188	−	0.965592i	−0.354347	−	0.935114i	$-0.615297\pi$
$887$	19.2153	−	28.7578i	0.645188	−	0.965592i	0.999535	−	0.0304784i	$-0.00970307\pi$
$888$	−6.94317	+	3.02662i	−0.232997	+	0.101567i
$889$	−22.2258	+	14.8508i	−0.745431	+	0.498081i
$890$	11.0957	+	0.295201i	0.371930	+	0.00989516i
$891$	2.18534	+	2.66284i	0.0732116	+	0.0892086i
$892$	28.0389	+	7.14597i	0.938811	+	0.239265i
$893$	11.3941	−	6.09029i	0.381290	−	0.203804i
$894$	−21.7446	−	12.3772i	−0.727247	−	0.413957i
$895$	7.93972			0.265396
$896$	−6.35104	−	58.3951i	−0.212173	−	1.95084i
$897$	−20.1600			−0.673122
$898$	−13.5725	−	7.72559i	−0.452919	−	0.257806i
$899$	−57.3655	+	30.6625i	−1.91325	+	1.02265i
$900$	−2.32860	+	9.13681i	−0.0776200	+	0.304560i
$901$	24.6216	+	30.0015i	0.820264	+	0.999495i
$902$	−12.1299	−	0.322713i	−0.403880	−	0.0107452i
$903$	27.6737	−	18.4910i	0.920923	−	0.615341i
$904$	0.728249	+	0.286086i	0.0242212	+	0.00951510i
$905$	−3.72447	+	5.57406i	−0.123805	+	0.185288i
$906$	1.49872	+	8.74399i	0.0497918	+	0.290500i
$907$	−1.92533	+	0.584041i	−0.0639294	+	0.0193928i	−0.322087	−	0.946710i	$-0.604384\pi$
$907$	−1.92533	+	0.584041i	−0.0639294	+	0.0193928i	0.258158	+	0.966103i	$0.416884\pi$
$908$	−29.9723	+	7.37689i	−0.994664	+	0.244811i
$909$	0.952035	+	0.781315i	0.0315770	+	0.0259146i
$910$	−14.0509	+	1.00743i	−0.465784	+	0.0333961i
$911$	−10.0485	−	4.16224i	−0.332923	−	0.137901i	0.209959	−	0.977710i	$-0.432667\pi$
$911$	−10.0485	−	4.16224i	−0.332923	−	0.137901i	−0.542882	+	0.839809i	$0.682667\pi$
$912$	−8.94927	+	0.807211i	−0.296340	+	0.0267294i
$913$	33.4354	−	13.8494i	1.10655	−	0.458348i
$914$	−17.9043	+	8.96620i	−0.592221	+	0.296575i
$915$	−0.596815	−	6.05957i	−0.0197301	−	0.200323i
$916$	47.3873	−	22.1747i	1.56572	−	0.732672i
$917$	−0.354204	+	0.662670i	−0.0116969	+	0.0218833i
$918$	−6.91644	−	1.56807i	−0.228276	−	0.0517541i
$919$	−22.9627	+	4.56757i	−0.757470	+	0.150670i	−0.558693	−	0.829375i	$-0.688697\pi$
$919$	−22.9627	+	4.56757i	−0.757470	+	0.150670i	−0.198777	+	0.980045i	$0.563697\pi$
$920$	6.65845	+	5.26267i	0.219523	+	0.173505i
$921$	0.0158721	−	0.0797946i	0.000523005	−	0.00262932i
$922$	3.75362	+	9.79077i	0.123619	+	0.322442i
$923$	−1.12976	+	11.4707i	−0.0371866	+	0.377561i
$924$	−33.7280	+	11.9119i	−1.10957	+	0.391874i
$925$	−3.66475	+	12.0810i	−0.120496	+	0.397222i
$926$	27.7281	+	35.6812i	0.911201	+	1.17256i
$927$	0.313278	+	0.313278i	0.0102894	+	0.0102894i
$928$	36.0781	−	9.58620i	1.18432	−	0.314682i
$929$	−16.2723	+	16.2723i	−0.533875	+	0.533875i	−0.921723	−	0.387848i	$-0.873219\pi$
$929$	−16.2723	+	16.2723i	−0.533875	+	0.533875i	0.387848	+	0.921723i	$0.373219\pi$
$930$	7.39121	+	0.927042i	0.242367	+	0.0303989i
$931$	42.8980	+	13.0130i	1.40592	+	0.426483i
$932$	−12.4210	−	13.8181i	−0.406862	−	0.452628i
$933$	−8.17785	−	0.805448i	−0.267731	−	0.0263692i
$934$	−11.2637	+	25.2703i	−0.368560	+	0.826869i
$935$	−9.05393	−	1.80094i	−0.296095	−	0.0588970i
$936$	9.66175	−	3.12588i	0.315804	−	0.102173i
$937$	−5.76426	−	28.9789i	−0.188310	−	0.946699i	−0.953154	−	0.302484i	$-0.902184\pi$
$937$	−5.76426	−	28.9789i	−0.188310	−	0.946699i	0.764844	−	0.644215i	$-0.222816\pi$
$938$	27.9654	−	17.6285i	0.913104	−	0.575591i
$939$	19.5055	+	10.4259i	0.636538	+	0.340237i
$940$	6.14054	−	0.276373i	0.200282	−	0.00901430i
$941$	−22.5414	+	2.22013i	−0.734829	+	0.0723743i	−0.458507	−	0.888691i	$-0.651616\pi$
$941$	−22.5414	+	2.22013i	−0.734829	+	0.0723743i	−0.276322	+	0.961065i	$0.589116\pi$
$942$	4.23799	+	1.40971i	0.138081	+	0.0459308i
$943$	5.35224	+	12.9215i	0.174293	+	0.420781i
$944$	7.56526	+	39.7374i	0.246228	+	1.29334i
$945$	1.06173	−	2.56325i	0.0345382	−	0.0833826i
$946$	−20.4471	+	23.6056i	−0.664793	+	0.767485i
$947$	−31.8489	+	38.8080i	−1.03495	+	1.26109i	−0.0703083	+	0.997525i	$0.522398\pi$
$947$	−31.8489	+	38.8080i	−1.03495	+	1.26109i	−0.964642	+	0.263565i	$0.915102\pi$
$948$	16.0481	−	11.8002i	0.521219	−	0.383252i
$949$	1.20815	+	3.98273i	0.0392181	+	0.129285i
$950$	−8.64916	+	12.2274i	−0.280616	+	0.396710i
$951$	8.45861	+	5.65186i	0.274289	+	0.183274i
$952$	39.7807	−	61.9720i	1.28930	−	2.00852i
$953$	−20.2781	−	30.3484i	−0.656873	−	0.983080i	−0.999056	−	0.0434462i	$-0.986166\pi$
$953$	−20.2781	−	30.3484i	−0.656873	−	0.983080i	0.342183	−	0.939633i	$-0.388834\pi$
$954$	7.94248	−	7.53081i	0.257147	−	0.243819i
$955$	3.83187	−	3.14474i	0.123996	−	0.101761i
$956$	−26.6039	−	19.9008i	−0.860432	−	0.643638i
$957$	−10.7159	−	20.0481i	−0.346396	−	0.648062i
$958$	12.5275	+	45.6332i	0.404746	+	1.47434i
$959$			4.07430i			0.131566i
$960$	−4.00709	−	1.48974i	−0.129328	−	0.0480811i
$961$			66.1577i			2.13412i
$962$	13.1116	−	3.59947i	0.422734	−	0.116052i
$963$	5.70433	+	10.6721i	0.183820	+	0.343902i
$964$	−0.777217	−	5.39216i	−0.0250325	−	0.173670i
$965$	−1.91893	+	1.57483i	−0.0617726	+	0.0506955i
$966$	28.3676	+	29.9183i	0.912712	+	0.962605i
$967$	10.1222	+	15.1490i	0.325508	+	0.487158i	0.957745	−	0.287617i	$-0.0928631\pi$
$967$	10.1222	+	15.1490i	0.325508	+	0.487158i	−0.632237	+	0.774775i	$0.717863\pi$
$968$	2.01230	−	1.39874i	0.0646777	−	0.0449572i
$969$	−9.36666	−	6.25860i	−0.300900	−	0.201055i
$970$	8.50389	+	6.01530i	0.273044	+	0.193140i
$971$	−2.21000	−	7.28539i	−0.0709222	−	0.233799i	0.914312	−	0.405010i	$-0.132732\pi$
$971$	−2.21000	−	7.28539i	−0.0709222	−	0.233799i	−0.985234	+	0.171211i	$0.945232\pi$
$972$	−0.301589	+	1.97713i	−0.00967348	+	0.0634165i
$973$	18.1370	−	22.0999i	0.581444	−	0.708492i
$974$	−4.02247	−	3.48425i	−0.128888	−	0.111642i
$975$	6.47734	−	15.6377i	0.207441	−	0.500807i
$976$	−45.5756	−	0.374622i	−1.45884	−	0.0119914i
$977$	−10.5407	−	25.4475i	−0.337227	−	0.814139i	−0.997980	−	0.0635347i	$-0.979763\pi$
$977$	−10.5407	−	25.4475i	−0.337227	−	0.814139i	0.660752	−	0.750604i	$-0.270237\pi$
$978$	−2.33973	+	7.03392i	−0.0748165	+	0.224920i
$979$	−50.3510	+	4.95914i	−1.60922	+	0.158495i
$980$	15.7439	+	14.3877i	0.502920	+	0.459599i
$981$	−9.16376	−	4.89813i	−0.292576	−	0.156385i
$982$	−3.85959	−	6.12276i	−0.123164	−	0.195385i
$983$	11.8976	+	59.8130i	0.379473	+	1.90774i	0.417930	+	0.908479i	$0.362756\pi$
$983$	11.8976	+	59.8130i	0.379473	+	1.90774i	−0.0384572	+	0.999260i	$0.512244\pi$
$984$	−4.56861	−	5.36278i	−0.145642	−	0.170959i
$985$	5.51428	+	1.09686i	0.175700	+	0.0349488i
$986$	42.7463	+	19.0533i	1.36132	+	0.606781i
$987$	29.7162	+	2.92679i	0.945877	+	0.0931607i
$988$	16.1076	+	0.857686i	0.512450	+	0.0272866i
$989$	34.4464	+	10.4492i	1.09533	+	0.332265i
$990$	−0.323982	+	2.58308i	−0.0102968	+	0.0820956i
$991$	43.5729	−	43.5729i	1.38414	−	1.38414i	0.547018	−	0.837121i	$-0.315763\pi$
$991$	43.5729	−	43.5729i	1.38414	−	1.38414i	0.837121	−	0.547018i	$-0.184237\pi$
$992$	12.7751	−	54.2756i	0.405611	−	1.72325i
$993$	6.37337	+	6.37337i	0.202253	+	0.202253i
$994$	18.6127	−	14.4640i	0.590358	−	0.458771i
$995$	−3.56562	+	11.7543i	−0.113038	+	0.372635i
$996$	18.9573	+	9.06164i	0.600683	+	0.287129i
$997$	−0.218071	+	2.21412i	−0.00690639	+	0.0701217i	−0.998020	−	0.0628954i	$-0.979967\pi$
$997$	−0.218071	+	2.21412i	−0.00690639	+	0.0701217i	0.991114	+	0.133017i	$0.0424665\pi$
$998$	4.00723	−	1.53631i	0.126847	−	0.0486310i
$999$	−0.522427	+	2.62642i	−0.0165289	+	0.0830962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.10	yes	512
128.109	even	32	inner	384.2.v.a.109.10	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.10	✓	512	128.109	even	32	inner
384.2.v.a.229.10	yes	512	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.699590 + 1.22905i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.02115 - 1.71967i) q^{4} +(-0.339008 - 0.413082i) q^{5} +(-0.0376117 + 1.41371i) q^{6} +(-4.31689 + 2.88445i) q^{7} +(2.82795 - 0.0519807i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(-0.699590 + 1.22905i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.02115 - 1.71967i) q^{4} +(-0.339008 - 0.413082i) q^{5} +(-0.0376117 + 1.41371i) q^{6} +(-4.31689 + 2.88445i) q^{7} +(2.82795 - 0.0519807i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.744867 - 0.127671i) q^{10} +(-3.29644 + 0.999964i) q^{11} +(-1.71122 - 1.03525i) q^{12} +(2.77532 + 2.27765i) q^{13} +(-0.525094 - 7.32363i) q^{14} +(-0.493704 - 0.204499i) q^{15} +(-1.91452 + 3.51207i) q^{16} +(-4.63305 + 1.91907i) q^{17} +(0.633249 + 1.26451i) q^{18} +(0.220186 + 2.23558i) q^{19} +(-0.364188 + 1.00480i) q^{20} +(-2.44744 + 4.57883i) q^{21} +(1.07715 - 4.75107i) q^{22} +(-5.50727 + 1.09546i) q^{23} +(2.46953 - 1.37893i) q^{24} +(0.919741 - 4.62385i) q^{25} +(-4.74094 + 1.81760i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(9.36848 + 4.47817i) q^{28} +(-1.91561 + 6.31491i) q^{29} +(0.596731 - 0.463723i) q^{30} +(6.96985 + 6.96985i) q^{31} +(-2.97714 - 4.81006i) q^{32} +(-2.43582 + 2.43582i) q^{33} +(0.882594 - 7.03683i) q^{34} +(2.65498 + 0.805379i) q^{35} +(-1.99717 - 0.106344i) q^{36} +(-2.66498 - 0.262477i) q^{37} +(-2.90169 - 1.29337i) q^{38} +(3.52129 + 0.700428i) q^{39} +(-0.980170 - 1.15055i) q^{40} +(-0.485925 - 2.44291i) q^{41} +(-3.91543 - 6.21133i) q^{42} +(-5.65361 - 3.02192i) q^{43} +(5.08576 + 4.64767i) q^{44} +(-0.531808 + 0.0523785i) q^{45} +(2.50645 - 7.53511i) q^{46} +(-2.20092 - 5.31349i) q^{47} +(-0.0328781 + 3.99986i) q^{48} +(7.63668 - 18.4366i) q^{49} +(5.03952 + 4.36521i) q^{50} +(-3.18134 + 3.87647i) q^{51} +(1.08279 - 7.09844i) q^{52} +(-2.24662 - 7.40613i) q^{53} +(1.15456 + 0.816690i) q^{54} +(1.53059 + 1.02271i) q^{55} +(-12.0580 + 8.38148i) q^{56} +(1.24803 + 1.86781i) q^{57} +(-6.42123 - 6.77224i) q^{58} +(7.81729 - 6.41548i) q^{59} +(0.152474 + 1.05783i) q^{60} +(5.37122 + 10.0489i) q^{61} +(-13.4424 + 3.69028i) q^{62} +5.19188i q^{63} +(7.99460 - 0.293997i) q^{64} -1.91858i q^{65} +(-1.28968 - 4.69783i) q^{66} +(2.12238 + 3.97069i) q^{67} +(8.03119 + 6.00765i) q^{68} +(-4.34058 + 3.56222i) q^{69} +(-2.84725 + 2.69968i) q^{70} +(1.78359 + 2.66934i) q^{71} +(1.52790 - 2.38023i) q^{72} +(0.963861 + 0.644031i) q^{73} +(2.18699 - 3.09178i) q^{74} +(-1.36853 - 4.51143i) q^{75} +(3.61962 - 2.66150i) q^{76} +(11.3460 - 13.8252i) q^{77} +(-3.32432 + 3.83784i) q^{78} +(-3.81143 + 9.20161i) q^{79} +(2.09981 - 0.399765i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(3.34242 + 1.11181i) q^{82} +(-10.4553 + 1.02975i) q^{83} +(10.3733 - 0.466879i) q^{84} +(2.36338 + 1.26325i) q^{85} +(7.66931 - 4.83449i) q^{86} +(1.28741 + 6.47227i) q^{87} +(-9.27019 + 2.99920i) q^{88} +(14.4051 + 2.86536i) q^{89} +(0.307672 - 0.690265i) q^{90} +(-18.5505 - 1.82707i) q^{91} +(7.50756 + 8.35205i) q^{92} +(9.43243 + 2.86129i) q^{93} +(8.07031 + 1.01222i) q^{94} +(0.848835 - 0.848835i) q^{95} +(-4.89305 - 2.83868i) q^{96} +(9.74616 + 9.74616i) q^{97} +(17.3170 + 22.2840i) q^{98} +(-0.999964 + 3.29644i) 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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