LMFDB - Embedded newform 187.2.j.a.16.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,2,Mod(16,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.12
Character	$\chi$	$=$	187.16
Dual form			187.2.j.a.152.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.418751 + 1.28878i) q^{2} +(0.465953 - 0.641330i) q^{3} +(0.132428 - 0.0962145i) q^{4} +(-0.416272 - 0.135255i) q^{5} +(1.02165 + 0.331955i) q^{6} +(-0.474970 - 0.653740i) q^{7} +(2.37206 + 1.72340i) q^{8} +(0.732860 + 2.25551i) q^{9} -0.593122i q^{10} +(3.31215 + 0.172256i) q^{11} -0.129761i q^{12} +(-0.428750 - 1.31956i) q^{13} +(0.643634 - 0.885886i) q^{14} +(-0.280707 + 0.203945i) q^{15} +(-1.12662 + 3.46739i) q^{16} +(-3.01650 - 2.81082i) q^{17} +(-2.59997 + 1.88899i) q^{18} +(-3.59995 - 2.61551i) q^{19} +(-0.0681395 + 0.0221399i) q^{20} -0.640577 q^{21} +(1.16496 + 4.34077i) q^{22} +5.16908i q^{23} +(2.21054 - 0.718248i) q^{24} +(-3.89010 - 2.82632i) q^{25} +(1.52108 - 1.10513i) q^{26} +(4.04979 + 1.31586i) q^{27} +(-0.125798 - 0.0408744i) q^{28} +(-4.81250 - 6.62383i) q^{29} +(-0.380387 - 0.276367i) q^{30} +(-10.1950 + 3.31255i) q^{31} +0.923577 q^{32} +(1.65378 - 2.04392i) q^{33} +(2.35937 - 5.06465i) q^{34} +(0.109295 + 0.336376i) q^{35} +(0.314064 + 0.228181i) q^{36} +(4.82897 + 6.64650i) q^{37} +(1.86335 - 5.73479i) q^{38} +(-1.04605 - 0.339882i) q^{39} +(-0.754324 - 1.03824i) q^{40} +(1.49500 - 2.05769i) q^{41} +(-0.268242 - 0.825563i) q^{42} -2.51389 q^{43} +(0.455194 - 0.295865i) q^{44} -1.03803i q^{45} +(-6.66182 + 2.16456i) q^{46} +(-3.05225 - 2.21759i) q^{47} +(1.69879 + 2.33818i) q^{48} +(1.96134 - 6.03638i) q^{49} +(2.01353 - 6.19701i) q^{50} +(-3.20821 + 0.624862i) q^{51} +(-0.183739 - 0.133494i) q^{52} +(1.62238 + 4.99316i) q^{53} +5.77031i q^{54} +(-1.35546 - 0.519690i) q^{55} -2.36927i q^{56} +(-3.35482 + 1.09005i) q^{57} +(6.52144 - 8.97599i) q^{58} +(8.41513 - 6.11395i) q^{59} +(-0.0175509 + 0.0540161i) q^{60} +(5.92389 + 1.92479i) q^{61} +(-8.53831 - 11.7520i) q^{62} +(1.12643 - 1.55040i) q^{63} +(2.63999 + 8.12506i) q^{64} +0.607285i q^{65} +(3.32668 + 1.27547i) q^{66} -11.2844 q^{67} +(-0.669911 - 0.0819997i) q^{68} +(3.31509 + 2.40855i) q^{69} +(-0.387748 + 0.281715i) q^{70} +(10.6809 + 3.47044i) q^{71} +(-2.14876 + 6.61322i) q^{72} +(-0.324968 - 0.447281i) q^{73} +(-6.54376 + 9.00671i) q^{74} +(-3.62521 + 1.17790i) q^{75} -0.728384 q^{76} +(-1.46056 - 2.24710i) q^{77} -1.49045i q^{78} +(1.87476 - 0.609146i) q^{79} +(0.937963 - 1.29100i) q^{80} +(-3.02504 + 2.19782i) q^{81} +(3.27795 + 1.06507i) q^{82} +(-3.42133 + 10.5298i) q^{83} +(-0.0848302 + 0.0616327i) q^{84} +(0.875509 + 1.57806i) q^{85} +(-1.05269 - 3.23985i) q^{86} -6.49046 q^{87} +(7.55975 + 6.11677i) q^{88} +10.0076 q^{89} +(1.33779 - 0.434675i) q^{90} +(-0.659003 + 0.907040i) q^{91} +(0.497341 + 0.684531i) q^{92} +(-2.62595 + 8.08184i) q^{93} +(1.57986 - 4.86230i) q^{94} +(1.14480 + 1.57568i) q^{95} +(0.430344 - 0.592317i) q^{96} +(-6.68319 + 2.17150i) q^{97} +8.60089 q^{98} +(2.03882 + 7.59682i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	0.418751	+	1.28878i	0.296101	+	0.911306i	0.982849	+	0.184411i	$0.0590376\pi$
$2$	0.418751	+	1.28878i	0.296101	+	0.911306i	−0.686748	+	0.726896i	$0.740962\pi$
$3$	0.465953	−	0.641330i	0.269018	−	0.370272i	−0.653040	−	0.757324i	$-0.726507\pi$
$3$	0.465953	−	0.641330i	0.269018	−	0.370272i	0.922058	+	0.387052i	$0.126507\pi$
$4$	0.132428	−	0.0962145i	0.0662139	−	0.0481072i
$5$	−0.416272	−	0.135255i	−0.186163	−	0.0604879i	0.214452	−	0.976735i	$-0.431203\pi$
$5$	−0.416272	−	0.135255i	−0.186163	−	0.0604879i	−0.400615	+	0.916247i	$0.631203\pi$
$6$	1.02165	+	0.331955i	0.417088	+	0.135520i
$7$	−0.474970	−	0.653740i	−0.179522	−	0.247090i	0.709767	−	0.704436i	$-0.248800\pi$
$7$	−0.474970	−	0.653740i	−0.179522	−	0.247090i	−0.889289	+	0.457346i	$0.848800\pi$
$8$	2.37206	+	1.72340i	0.838650	+	0.609315i
$9$	0.732860	+	2.25551i	0.244287	+	0.751837i
$10$		−	0.593122i		−	0.187562i
$11$	3.31215	+	0.172256i	0.998650	+	0.0519371i
$11$	3.31215	+	0.172256i	0.998650	+	0.0519371i
$12$		−	0.129761i		−	0.0374589i
$13$	−0.428750	−	1.31956i	−0.118914	−	0.365979i	0.873829	−	0.486233i	$-0.161629\pi$
$13$	−0.428750	−	1.31956i	−0.118914	−	0.365979i	−0.992743	+	0.120254i	$0.961629\pi$
$14$	0.643634	−	0.885886i	0.172018	−	0.236763i
$15$	−0.280707	+	0.203945i	−0.0724781	+	0.0526584i
$16$	−1.12662	+	3.46739i	−0.281656	+	0.866847i
$17$	−3.01650	−	2.81082i	−0.731609	−	0.681724i
$17$	−3.01650	−	2.81082i	−0.731609	−	0.681724i
$18$	−2.59997	+	1.88899i	−0.612820	+	0.445240i
$19$	−3.59995	−	2.61551i	−0.825885	−	0.600040i	0.0925075	−	0.995712i	$-0.470512\pi$
$19$	−3.59995	−	2.61551i	−0.825885	−	0.600040i	−0.918392	+	0.395672i	$0.870512\pi$
$20$	−0.0681395	+	0.0221399i	−0.0152365	+	0.00495063i
$21$	−0.640577			−0.139785
$22$	1.16496	+	4.34077i	0.248371	+	0.925455i
$23$			5.16908i			1.07783i	0.842361	+	0.538914i	$0.181165\pi$
$23$			5.16908i			1.07783i	−0.842361	+	0.538914i	$0.818835\pi$
$24$	2.21054	−	0.718248i	0.451224	−	0.146612i
$25$	−3.89010	−	2.82632i	−0.778019	−	0.565264i
$26$	1.52108	−	1.10513i	0.298308	−	0.216734i
$27$	4.04979	+	1.31586i	0.779382	+	0.253237i
$28$	−0.125798	−	0.0408744i	−0.0237737	−	0.00772454i
$29$	−4.81250	−	6.62383i	−0.893658	−	1.23001i	−0.972447	−	0.233124i	$-0.925105\pi$
$29$	−4.81250	−	6.62383i	−0.893658	−	1.23001i	0.0787890	−	0.996891i	$-0.474895\pi$
$30$	−0.380387	−	0.276367i	−0.0694488	−	0.0504575i
$31$	−10.1950	+	3.31255i	−1.83107	+	0.594952i	−0.831873	+	0.554967i	$0.812731\pi$
$31$	−10.1950	+	3.31255i	−1.83107	+	0.594952i	−0.999200	+	0.0399849i	$0.987269\pi$
$32$	0.923577			0.163267
$33$	1.65378	−	2.04392i	0.287886	−	0.355800i
$34$	2.35937	−	5.06465i	0.404629	−	0.868580i
$35$	0.109295	+	0.336376i	0.0184742	+	0.0568579i
$36$	0.314064	+	0.228181i	0.0523440	+	0.0380301i
$37$	4.82897	+	6.64650i	0.793877	+	1.09268i	0.993614	+	0.112828i	$0.0359911\pi$
$37$	4.82897	+	6.64650i	0.793877	+	1.09268i	−0.199737	+	0.979849i	$0.564009\pi$
$38$	1.86335	−	5.73479i	0.302275	−	0.930306i
$39$	−1.04605	−	0.339882i	−0.167502	−	0.0544246i
$40$	−0.754324	−	1.03824i	−0.119269	−	0.164160i
$41$	1.49500	−	2.05769i	0.233480	−	0.321358i	−0.676160	−	0.736755i	$-0.736357\pi$
$41$	1.49500	−	2.05769i	0.233480	−	0.321358i	0.909640	+	0.415397i	$0.136357\pi$
$42$	−0.268242	−	0.825563i	−0.0413906	−	0.127387i
$43$	−2.51389			−0.383364			−0.191682	−	0.981457i	$-0.561394\pi$
$43$	−2.51389			−0.383364			−0.191682	+	0.981457i	$0.561394\pi$
$44$	0.455194	−	0.295865i	0.0686231	−	0.0446034i
$45$		−	1.03803i		−	0.154740i
$46$	−6.66182	+	2.16456i	−0.982232	+	0.319146i
$47$	−3.05225	−	2.21759i	−0.445216	−	0.323469i	0.342488	−	0.939522i	$-0.388730\pi$
$47$	−3.05225	−	2.21759i	−0.445216	−	0.323469i	−0.787704	+	0.616054i	$0.788730\pi$
$48$	1.69879	+	2.33818i	0.245198	+	0.337487i
$49$	1.96134	−	6.03638i	0.280191	−	0.862340i
$50$	2.01353	−	6.19701i	0.284756	−	0.876389i
$51$	−3.20821	+	0.624862i	−0.449240	+	0.0874982i
$52$	−0.183739	−	0.133494i	−0.0254800	−	0.0185123i
$53$	1.62238	+	4.99316i	0.222851	+	0.685864i	0.998503	+	0.0547031i	$0.0174212\pi$
$53$	1.62238	+	4.99316i	0.222851	+	0.685864i	−0.775652	+	0.631161i	$0.782579\pi$
$54$			5.77031i			0.785240i
$55$	−1.35546	−	0.519690i	−0.182770	−	0.0700750i
$56$		−	2.36927i		−	0.316608i
$57$	−3.35482	+	1.09005i	−0.444356	+	0.144380i
$58$	6.52144	−	8.97599i	0.856307	−	1.17861i
$59$	8.41513	−	6.11395i	1.09556	−	0.795969i	0.115228	−	0.993339i	$-0.463240\pi$
$59$	8.41513	−	6.11395i	1.09556	−	0.795969i	0.980329	+	0.197370i	$0.0632401\pi$
$60$	−0.0175509	+	0.0540161i	−0.00226581	+	0.00697344i
$61$	5.92389	+	1.92479i	0.758476	+	0.246444i	0.662625	−	0.748952i	$-0.269443\pi$
$61$	5.92389	+	1.92479i	0.758476	+	0.246444i	0.0958518	+	0.995396i	$0.469443\pi$
$62$	−8.53831	−	11.7520i	−1.08437	−	1.49250i
$63$	1.12643	−	1.55040i	0.141917	−	0.195332i
$64$	2.63999	+	8.12506i	0.329999	+	1.01563i
$65$			0.607285i			0.0753244i
$66$	3.32668	+	1.27547i	0.409486	+	0.156999i
$67$	−11.2844			−1.37861			−0.689306	−	0.724470i	$-0.742085\pi$
$67$	−11.2844			−1.37861			−0.689306	+	0.724470i	$0.742085\pi$
$68$	−0.669911	−	0.0819997i	−0.0812386	−	0.00994393i
$69$	3.31509	+	2.40855i	0.399090	+	0.289956i
$70$	−0.387748	+	0.281715i	−0.0463447	+	0.0336714i
$71$	10.6809	+	3.47044i	1.26759	+	0.411865i	0.864194	−	0.503159i	$-0.167829\pi$
$71$	10.6809	+	3.47044i	1.26759	+	0.411865i	0.403398	+	0.915025i	$0.367829\pi$
$72$	−2.14876	+	6.61322i	−0.253234	+	0.779375i
$73$	−0.324968	−	0.447281i	−0.0380347	−	0.0523502i	0.789576	−	0.613653i	$-0.210300\pi$
$73$	−0.324968	−	0.447281i	−0.0380347	−	0.0523502i	−0.827611	+	0.561302i	$0.810300\pi$
$74$	−6.54376	+	9.00671i	−0.760696	+	1.04701i
$75$	−3.62521	+	1.17790i	−0.418603	+	0.136012i
$76$	−0.728384			−0.0835513
$77$	−1.46056	−	2.24710i	−0.166446	−	0.256081i
$78$		−	1.49045i		−	0.168761i
$79$	1.87476	−	0.609146i	0.210927	−	0.0685343i	−0.201648	−	0.979458i	$-0.564630\pi$
$79$	1.87476	−	0.609146i	0.210927	−	0.0685343i	0.412575	+	0.910924i	$0.364630\pi$
$80$	0.937963	−	1.29100i	0.104867	−	0.144338i
$81$	−3.02504	+	2.19782i	−0.336116	+	0.244202i
$82$	3.27795	+	1.06507i	0.361989	+	0.117617i
$83$	−3.42133	+	10.5298i	−0.375539	+	1.15579i	0.567575	+	0.823322i	$0.307882\pi$
$83$	−3.42133	+	10.5298i	−0.375539	+	1.15579i	−0.943114	+	0.332469i	$0.892118\pi$
$84$	−0.0848302	+	0.0616327i	−0.00925573	+	0.00672468i
$85$	0.875509	+	1.57806i	0.0949623	+	0.171165i
$86$	−1.05269	−	3.23985i	−0.113515	−	0.349362i
$87$	−6.49046			−0.695850
$88$	7.55975	+	6.11677i	0.805872	+	0.652049i
$89$	10.0076			1.06080			0.530400	−	0.847748i	$-0.322042\pi$
$89$	10.0076			1.06080			0.530400	+	0.847748i	$0.322042\pi$
$90$	1.33779	−	0.434675i	0.141016	−	0.0458188i
$91$	−0.659003	+	0.907040i	−0.0690823	+	0.0950836i
$92$	0.497341	+	0.684531i	0.0518513	+	0.0713672i
$93$	−2.62595	+	8.08184i	−0.272298	+	0.838048i
$94$	1.57986	−	4.86230i	0.162950	−	0.501508i
$95$	1.14480	+	1.57568i	0.117454	+	0.161661i
$96$	0.430344	−	0.592317i	0.0439218	−	0.0604532i
$97$	−6.68319	+	2.17150i	−0.678576	+	0.220483i	−0.627972	−	0.778236i	$-0.716115\pi$
$97$	−6.68319	+	2.17150i	−0.678576	+	0.220483i	−0.0506040	+	0.998719i	$0.516115\pi$
$98$	8.60089			0.868821
$99$	2.03882	+	7.59682i	0.204909	+	0.763509i
$100$	−0.787090			−0.0787090
$101$	3.74738	+	11.5333i	0.372879	+	1.14760i	0.944899	+	0.327363i	$0.106160\pi$
$101$	3.74738	+	11.5333i	0.372879	+	1.14760i	−0.572020	+	0.820240i	$0.693840\pi$
$102$	−2.14875	−	3.87302i	−0.212758	−	0.383487i
$103$	−9.50934	+	6.90894i	−0.936984	+	0.680758i	−0.947693	−	0.319184i	$-0.896591\pi$
$103$	−9.50934	+	6.90894i	−0.936984	+	0.680758i	0.0107091	+	0.999943i	$0.496591\pi$
$104$	1.25711	−	3.86897i	0.123269	−	0.379384i
$105$	0.266654	+	0.0866412i	0.0260228	+	0.00845532i
$106$	−5.75573	+	4.18178i	−0.559046	+	0.406170i
$107$	−2.65906	+	3.65988i	−0.257061	+	0.353814i	−0.917969	−	0.396653i	$-0.870172\pi$
$107$	−2.65906	+	3.65988i	−0.257061	+	0.353814i	0.660908	+	0.750467i	$0.270172\pi$
$108$	0.662909	−	0.215392i	0.0637885	−	0.0207261i
$109$		−	16.6540i		−	1.59516i	−0.603210	−	0.797582i	$-0.706112\pi$
$109$		−	16.6540i		−	1.59516i	0.603210	−	0.797582i	$-0.293888\pi$
$110$	0.102169	−	1.96451i	0.00974141	−	0.187309i
$111$	6.51267			0.618155
$112$	2.80188	−	0.910386i	0.264753	−	0.0860234i
$113$	8.86668	−	12.2039i	0.834108	−	1.14805i	−0.153037	−	0.988220i	$-0.548905\pi$
$113$	8.86668	−	12.2039i	0.834108	−	1.14805i	0.987145	−	0.159830i	$-0.0510946\pi$
$114$	−2.80966	−	3.86717i	−0.263149	−	0.362193i
$115$	0.699145	−	2.15175i	0.0651956	−	0.200651i
$116$	−1.27462	−	0.414148i	−0.118345	−	0.0384527i
$117$	2.66206	−	1.93410i	0.246107	−	0.178807i
$118$	11.4034	+	8.28505i	1.04977	+	0.762701i
$119$	−0.404798	+	3.30706i	−0.0371077	+	0.303158i
$120$	−1.01733			−0.0928693
$121$	10.9407	+	1.14107i	0.994605	+	0.103734i
$122$			8.44061i			0.764177i
$123$	−0.623059	−	1.91758i	−0.0561794	−	0.172902i
$124$	−1.03138	+	1.41958i	−0.0926210	+	0.127482i
$125$	2.52342	+	3.47319i	0.225701	+	0.310651i
$126$	2.46982	+	0.802493i	0.220029	+	0.0714917i
$127$	−0.233775	+	0.719485i	−0.0207442	+	0.0638440i	−0.960893	−	0.276921i	$-0.910686\pi$
$127$	−0.233775	+	0.719485i	−0.0207442	+	0.0638440i	0.940149	+	0.340765i	$0.110686\pi$
$128$	−7.87155	+	5.71902i	−0.695754	+	0.505495i
$129$	−1.17135	+	1.61223i	−0.103132	+	0.141949i
$130$	−0.782658	+	0.254301i	−0.0686436	+	0.0223037i
$131$		−	14.1076i		−	1.23259i	−0.787516	−	0.616294i	$-0.788633\pi$
$131$		−	14.1076i		−	1.23259i	0.787516	−	0.616294i	$-0.211367\pi$
$132$	0.0223522	−	0.429789i	0.00194551	−	0.0374083i
$133$			3.59572i			0.311788i
$134$	−4.72536	−	14.5432i	−0.408209	−	1.25634i
$135$	−1.50784	−	1.09551i	−0.129774	−	0.0942864i
$136$	−2.31115	−	11.8661i	−0.198180	−	1.01751i
$137$	3.71150	−	11.4228i	0.317095	−	0.975918i	−0.657789	−	0.753203i	$-0.728508\pi$
$137$	3.71150	−	11.4228i	0.317095	−	0.975918i	0.974884	−	0.222715i	$-0.0714920\pi$
$138$	−1.71590	+	5.28101i	−0.146067	+	0.449549i
$139$	2.90005	+	3.99158i	0.245979	+	0.338561i	0.914098	−	0.405493i	$-0.132900\pi$
$139$	2.90005	+	3.99158i	0.245979	+	0.338561i	−0.668119	+	0.744055i	$0.732900\pi$
$140$	0.0468379	+	0.0340298i	0.00395853	+	0.00287604i
$141$	−2.84441	+	0.924205i	−0.239543	+	0.0778321i
$142$			15.2186i			1.27712i
$143$	−1.19278	−	4.44442i	−0.0997454	−	0.371661i
$144$	−8.64638			−0.720532
$145$	1.10740	+	3.40823i	0.0919647	+	0.283038i
$146$	0.440366	−	0.606112i	0.0364450	−	0.0501622i
$147$	−2.95742	−	4.07054i	−0.243924	−	0.335732i
$148$	1.27898	+	0.415565i	0.105131	+	0.0341593i
$149$	1.91407	−	5.89091i	0.156807	−	0.482602i	−0.841533	−	0.540206i	$-0.818346\pi$
$149$	1.91407	−	5.89091i	0.156807	−	0.482602i	0.998339	+	0.0576043i	$0.0183462\pi$
$150$	−3.03612	−	4.17885i	−0.247898	−	0.341202i
$151$	5.24491	+	3.81065i	0.426825	+	0.310106i	0.780378	−	0.625308i	$-0.215027\pi$
$151$	5.24491	+	3.81065i	0.426825	+	0.310106i	−0.353553	+	0.935414i	$0.615027\pi$
$152$	−4.03171	−	12.4083i	−0.327015	−	1.00645i
$153$	4.12916	−	8.86369i	0.333823	−	0.716587i
$154$	2.28441	−	2.82332i	0.184083	−	0.227509i
$155$	4.69193			0.376865
$156$	−0.171227	+	0.0556352i	−0.0137092	+	0.00445438i
$157$	2.64818	+	1.92402i	0.211348	+	0.153553i	0.688423	−	0.725309i	$-0.258303\pi$
$157$	2.64818	+	1.92402i	0.211348	+	0.153553i	−0.477075	+	0.878862i	$0.658303\pi$
$158$	1.57011	+	2.16107i	0.124911	+	0.171926i
$159$	3.95822	+	1.28610i	0.313907	+	0.101995i
$160$	−0.384459	−	0.124918i	−0.0303942	−	0.00987567i
$161$	3.37924	−	2.45516i	0.266321	−	0.193494i
$162$	−4.09925	−	2.97828i	−0.322068	−	0.233996i
$163$	7.51003	−	2.44016i	0.588231	−	0.191128i	0.000246530	−	1.00000i	$-0.499922\pi$
$163$	7.51003	−	2.44016i	0.588231	−	0.191128i	0.587985	+	0.808872i	$0.299922\pi$
$164$		−	0.416337i		−	0.0325104i
$165$	−0.964873	+	0.627144i	−0.0751152	+	0.0488231i
$166$	−15.0032			−1.16448
$167$	−9.36064	+	3.04146i	−0.724348	+	0.235355i	−0.647907	−	0.761719i	$-0.724356\pi$
$167$	−9.36064	+	3.04146i	−0.724348	+	0.235355i	−0.0764407	+	0.997074i	$0.524356\pi$
$168$	−1.51949	−	1.10397i	−0.117231	−	0.0851732i
$169$	8.95982	−	6.50969i	0.689217	−	0.500745i
$170$	−1.66716	+	1.78915i	−0.127865	+	0.137222i
$171$	3.26106	−	10.0365i	0.249380	−	0.767512i
$172$	−0.332908	+	0.241872i	−0.0253840	+	0.0184426i
$173$	−9.92862	+	13.6656i	−0.754859	+	1.03897i	0.242765	+	0.970085i	$0.421946\pi$
$173$	−9.92862	+	13.6656i	−0.754859	+	1.03897i	−0.997624	+	0.0688895i	$0.978054\pi$
$174$	−2.71788	−	8.36479i	−0.206042	−	0.634133i
$175$			3.88553i			0.293718i
$176$	−4.32882	+	11.2904i	−0.326297	+	0.851048i
$177$		−	8.24569i		−	0.619784i
$178$	4.19067	+	12.8976i	0.314104	+	0.966713i
$179$	−3.60090	−	2.61621i	−0.269144	−	0.195545i	0.445024	−	0.895518i	$-0.353195\pi$
$179$	−3.60090	−	2.61621i	−0.269144	−	0.195545i	−0.714169	+	0.699974i	$0.753195\pi$
$180$	−0.0998734	−	0.137464i	−0.00744413	−	0.0102460i
$181$	5.82449	+	1.89249i	0.432931	+	0.140668i	0.517372	−	0.855761i	$-0.326910\pi$
$181$	5.82449	+	1.89249i	0.432931	+	0.140668i	−0.0844411	+	0.996428i	$0.526910\pi$
$182$	−1.44493	−	0.469488i	−0.107106	−	0.0348007i
$183$	3.99468	−	2.90231i	0.295295	−	0.214545i
$184$	−8.90841	+	12.2614i	−0.656737	+	0.903920i
$185$	−1.11119	−	3.41990i	−0.0816964	−	0.251436i
$186$	−11.5153			−0.844346
$187$	−9.50692	−	9.82946i	−0.695215	−	0.718802i
$188$	−0.617567			−0.0450407
$189$	−1.06330	−	3.27250i	−0.0773437	−	0.238039i
$190$	−1.55132	+	2.13521i	−0.112545	+	0.154904i
$191$	−12.8118	+	9.30831i	−0.927029	+	0.673526i	−0.945264	−	0.326308i	$-0.894195\pi$
$191$	−12.8118	+	9.30831i	−0.927029	+	0.673526i	0.0182347	+	0.999834i	$0.494195\pi$
$192$	6.44096	+	2.09279i	0.464836	+	0.151034i
$193$	7.14405	+	2.32124i	0.514240	+	0.167087i	0.554630	−	0.832097i	$-0.312860\pi$
$193$	7.14405	+	2.32124i	0.514240	+	0.167087i	−0.0403898	+	0.999184i	$0.512860\pi$
$194$	−5.59718	−	7.70386i	−0.401854	−	0.553105i
$195$	0.389470	+	0.282967i	0.0278905	+	0.0202637i
$196$	−0.321051	−	0.988094i	−0.0229322	−	0.0705782i
$197$		−	1.63785i		−	0.116692i	−0.998296	−	0.0583461i	$-0.981417\pi$
$197$		−	1.63785i		−	0.116692i	0.998296	−	0.0583461i	$-0.0185827\pi$
$198$	−8.93689	+	5.80876i	−0.635117	+	0.412811i
$199$		−	9.94586i		−	0.705043i	−0.935804	−	0.352522i	$-0.885324\pi$
$199$		−	9.94586i		−	0.705043i	0.935804	−	0.352522i	$-0.114676\pi$
$200$	−4.35665	−	13.4084i	−0.308062	−	0.948117i
$201$	−5.25802	+	7.23704i	−0.370872	+	0.510462i
$202$	−13.2946	+	9.65912i	−0.935407	+	0.679613i
$203$	−2.04447	+	6.29224i	−0.143494	+	0.441629i
$204$	−0.364736	+	0.391426i	−0.0255366	+	0.0274053i
$205$	−0.900641	+	0.654354i	−0.0629035	+	0.0457021i
$206$	−12.8862	−	9.36235i	−0.897822	−	0.652306i
$207$	−11.6589	+	3.78821i	−0.810351	+	0.263299i
$208$	5.05845			0.350740
$209$	−11.4730	−	9.28308i	−0.793606	−	0.642124i
$210$			0.379940i			0.0262184i
$211$	−7.86558	+	2.55568i	−0.541489	+	0.175940i	−0.566975	−	0.823735i	$-0.691886\pi$
$211$	−7.86558	+	2.55568i	−0.541489	+	0.175940i	0.0254866	+	0.999675i	$0.491886\pi$
$212$	0.695263	+	0.505138i	0.0477508	+	0.0346930i
$213$	7.20251	−	5.23293i	0.493508	−	0.358554i
$214$	−5.83027	−	1.89437i	−0.398549	−	0.129496i
$215$	1.04646	+	0.340016i	0.0713680	+	0.0231889i
$216$	7.33859	+	10.1007i	0.499328	+	0.687266i
$217$	7.00785	+	5.09150i	0.475724	+	0.345634i
$218$	21.4634	−	6.97387i	1.45368	−	0.472330i
$219$	−0.438275			−0.0296159
$220$	−0.229502	+	0.0615931i	−0.0154730	+	0.00415261i
$221$	−2.41571	+	5.18558i	−0.162498	+	0.348820i
$222$	2.72718	+	8.39341i	0.183037	+	0.563329i
$223$	−2.88712	−	2.09762i	−0.193336	−	0.140467i	0.486906	−	0.873454i	$-0.338125\pi$
$223$	−2.88712	−	2.09762i	−0.193336	−	0.140467i	−0.680242	+	0.732988i	$0.738125\pi$
$224$	−0.438671	−	0.603779i	−0.0293100	−	0.0403417i
$225$	3.52390	−	10.8454i	0.234927	−	0.723030i
$226$	19.4411	+	6.31681i	1.29321	+	0.420188i
$227$	13.9360	+	19.1812i	0.924963	+	1.27310i	0.961792	+	0.273780i	$0.0882741\pi$
$227$	13.9360	+	19.1812i	0.924963	+	1.27310i	−0.0368298	+	0.999322i	$0.511726\pi$
$228$	−0.339393	+	0.467134i	−0.0224768	+	0.0309367i
$229$	−2.52781	−	7.77980i	−0.167042	−	0.514104i	0.832139	−	0.554568i	$-0.187116\pi$
$229$	−2.52781	−	7.77980i	−0.167042	−	0.514104i	−0.999181	+	0.0404640i	$0.987116\pi$
$230$	3.06590			0.202159
$231$	−2.12169	−	0.110343i	−0.139597	−	0.00726004i
$232$		−	24.0060i		−	1.57607i
$233$	17.3143	−	5.62577i	1.13430	−	0.368556i	0.319091	−	0.947724i	$-0.396622\pi$
$233$	17.3143	−	5.62577i	1.13430	−	0.368556i	0.815208	+	0.579168i	$0.196622\pi$
$234$	3.60737	+	2.62091i	0.235821	+	0.171334i
$235$	0.970626	+	1.33595i	0.0633167	+	0.0871479i
$236$	0.526147	−	1.61932i	0.0342493	−	0.105408i
$237$	0.482887	−	1.48617i	0.0313668	−	0.0965372i
$238$	−4.43159	+	0.863139i	−0.287257	+	0.0559490i
$239$	13.1505	+	9.55438i	0.850634	+	0.618022i	0.925321	−	0.379185i	$-0.123796\pi$
$239$	13.1505	+	9.55438i	0.850634	+	0.618022i	−0.0746868	+	0.997207i	$0.523796\pi$
$240$	−0.390907	−	1.20309i	−0.0252329	−	0.0776590i
$241$		−	18.7543i		−	1.20807i	−0.796957	−	0.604037i	$-0.793558\pi$
$241$		−	18.7543i		−	1.20807i	0.796957	−	0.604037i	$-0.206442\pi$
$242$	3.11081	+	14.5779i	0.199971	+	0.937106i
$243$			15.7387i			1.00964i
$244$	0.969681	−	0.315068i	0.0620774	−	0.0201702i
$245$	−1.63290	+	2.24750i	−0.104322	+	0.143587i
$246$	2.21043	−	1.60597i	0.140932	−	0.102393i
$247$	−1.90784	+	5.87173i	−0.121393	+	0.373609i
$248$	−29.8920	−	9.71249i	−1.89814	−	0.616744i
$249$	5.15887	+	7.10058i	0.326930	+	0.449981i
$250$	−3.41950	+	4.70653i	−0.216268	+	0.297667i
$251$	7.25769	+	22.3369i	0.458101	+	1.40989i	0.867455	+	0.497515i	$0.165754\pi$
$251$	7.25769	+	22.3369i	0.458101	+	1.40989i	−0.409354	+	0.912376i	$0.634246\pi$
$252$		−	0.313695i		−	0.0197609i
$253$	−0.890404	+	17.1208i	−0.0559792	+	1.07637i
$254$	−1.02515			−0.0643238
$255$	1.42001	+	0.173814i	0.0889242	+	0.0108847i
$256$	3.15640	+	2.29326i	0.197275	+	0.143329i
$257$	9.71169	−	7.05596i	0.605799	−	0.440138i	−0.242134	−	0.970243i	$-0.577847\pi$
$257$	9.71169	−	7.05596i	0.605799	−	0.440138i	0.847932	+	0.530104i	$0.177847\pi$
$258$	−2.56832	−	0.834497i	−0.159896	−	0.0519535i
$259$	2.05147	−	6.31377i	0.127472	−	0.392319i
$260$	0.0584296	+	0.0804215i	0.00362365	+	0.00498753i
$261$	11.4132	−	15.7090i	0.706462	−	0.972361i
$262$	18.1816	−	5.90757i	1.12326	−	0.364971i
$263$	−22.7422			−1.40234			−0.701171	−	0.712993i	$-0.747339\pi$
$263$	−22.7422			−1.40234			−0.701171	+	0.712993i	$0.747339\pi$
$264$	7.44536	−	1.99816i	0.458230	−	0.122979i
$265$		−	2.29795i		−	0.141162i
$266$	−4.63410	+	1.50571i	−0.284135	+	0.0923210i
$267$	4.66306	−	6.41815i	0.285375	−	0.392784i
$268$	−1.49437	+	1.08573i	−0.0912834	+	0.0663213i
$269$	17.2211	+	5.59549i	1.04999	+	0.341163i	0.782665	−	0.622443i	$-0.213860\pi$
$269$	17.2211	+	5.59549i	1.04999	+	0.341163i	0.267327	+	0.963606i	$0.413860\pi$
$270$	0.780464	−	2.40202i	0.0474975	−	0.146182i
$271$	18.0538	−	13.1168i	1.09669	−	0.796791i	0.116173	−	0.993229i	$-0.462937\pi$
$271$	18.0538	−	13.1168i	1.09669	−	0.796791i	0.980516	+	0.196437i	$0.0629373\pi$
$272$	13.1447	−	7.29265i	0.797012	−	0.442182i
$273$	0.274647	+	0.845277i	0.0166224	+	0.0511585i
$274$	16.2757			0.983252
$275$	−12.3977	−	10.0313i	−0.747611	−	0.604909i
$276$	0.670747			0.0403742
$277$	−9.95015	+	3.23300i	−0.597847	+	0.194252i	−0.592280	−	0.805732i	$-0.701772\pi$
$277$	−9.95015	+	3.23300i	−0.597847	+	0.194252i	−0.00556691	+	0.999985i	$0.501772\pi$
$278$	−3.92988	+	5.40901i	−0.235698	+	0.324411i
$279$	−14.9430	−	20.5672i	−0.894613	−	1.23133i
$280$	−0.320456	+	0.986263i	−0.0191509	+	0.0589405i
$281$	−6.56105	+	20.1928i	−0.391399	+	1.20460i	0.540331	+	0.841452i	$0.318299\pi$
$281$	−6.56105	+	20.1928i	−0.391399	+	1.20460i	−0.931730	+	0.363151i	$0.881701\pi$
$282$	−2.38220	−	3.27881i	−0.141858	−	0.195251i
$283$	−5.18919	+	7.14231i	−0.308465	+	0.424566i	−0.934902	−	0.354906i	$-0.884513\pi$
$283$	−5.18919	+	7.14231i	−0.308465	+	0.424566i	0.626436	+	0.779472i	$0.284513\pi$
$284$	1.74836	−	0.568076i	0.103746	−	0.0337091i
$285$	1.54395			0.0914557
$286$	5.22841	−	3.39834i	0.309162	−	0.200948i
$287$	−2.05528			−0.121319
$288$	0.676852	+	2.08314i	0.0398839	+	0.122750i
$289$	1.19858	+	16.9577i	0.0705045	+	0.997511i
$290$	−3.92874	+	2.85440i	−0.230704	+	0.167616i
$291$	−1.72141	+	5.29795i	−0.100911	+	0.310571i
$292$	−0.0860697	−	0.0279658i	−0.00503685	−	0.00163657i
$293$	1.03648	−	0.753050i	0.0605520	−	0.0439936i	−0.557097	−	0.830447i	$-0.688085\pi$
$293$	1.03648	−	0.753050i	0.0605520	−	0.0439936i	0.617650	+	0.786453i	$0.288085\pi$
$294$	4.00761	−	5.51601i	0.233729	−	0.321700i
$295$	−4.32993	+	1.40688i	−0.252098	+	0.0819117i
$296$			24.0881i			1.40010i
$297$	13.1868	+	5.05591i	0.765178	+	0.293374i
$298$	8.39361			0.486229
$299$	6.82089	−	2.21624i	0.394462	−	0.128169i
$300$	−0.366747	+	0.504784i	−0.0211742	+	0.0291437i
$301$	1.19402	+	1.64343i	0.0688221	+	0.0947255i
$302$	−2.71479	+	8.35526i	−0.156218	+	0.480791i
$303$	9.14273	+	2.97065i	0.525236	+	0.170660i
$304$	13.1248	−	9.53571i	0.752758	−	0.546911i
$305$	−2.20561	−	1.60247i	−0.126293	−	0.0917573i
$306$	13.1524	+	1.60991i	0.751875	+	0.0920325i
$307$	12.4738			0.711916			0.355958	−	0.934502i	$-0.384155\pi$
$307$	12.4738			0.711916			0.355958	+	0.934502i	$0.384155\pi$
$308$	−0.409622	−	0.157052i	−0.0233404	−	0.00894885i
$309$			9.31787i			0.530075i
$310$	1.96475	+	6.04687i	0.111590	+	0.343439i
$311$	9.24667	−	12.7269i	0.524330	−	0.721679i	−0.461923	−	0.886920i	$-0.652840\pi$
$311$	9.24667	−	12.7269i	0.524330	−	0.721679i	0.986253	+	0.165241i	$0.0528403\pi$
$312$	−1.89554	−	2.60898i	−0.107314	−	0.147704i
$313$	−15.4467	−	5.01894i	−0.873099	−	0.283687i	−0.162010	−	0.986789i	$-0.551798\pi$
$313$	−15.4467	−	5.01894i	−0.873099	−	0.283687i	−0.711089	+	0.703102i	$0.751798\pi$
$314$	−1.37071	+	4.21861i	−0.0773537	+	0.238070i
$315$	−0.678601	+	0.493032i	−0.0382348	+	0.0277792i
$316$	0.189662	−	0.261047i	0.0106693	−	0.0146850i
$317$	9.64043	−	3.13236i	0.541460	−	0.175931i	−0.0255021	−	0.999675i	$-0.508118\pi$
$317$	9.64043	−	3.13236i	0.541460	−	0.175931i	0.566962	+	0.823744i	$0.308118\pi$
$318$			5.63983i			0.316266i
$319$	−14.7987	−	22.7681i	−0.828569	−	1.27477i
$320$		−	3.73931i		−	0.209034i
$321$	1.10819	+	3.41067i	0.0618533	+	0.190365i
$322$	4.57922	+	3.32700i	0.255190	+	0.185406i
$323$	3.50751	+	18.0085i	0.195163	+	1.00202i
$324$	−0.189138	+	0.582106i	−0.0105076	+	0.0323392i
$325$	−2.06161	+	6.34498i	−0.114358	+	0.351956i
$326$	6.28966	+	8.65698i	0.348352	+	0.479466i
$327$	−10.6807	−	7.75999i	−0.590645	−	0.429129i
$328$	7.09247	−	2.30448i	0.391616	−	0.127244i
$329$			3.04866i			0.168078i
$330$	−1.21229	−	0.980893i	−0.0667345	−	0.0539964i
$331$	5.10089			0.280370			0.140185	−	0.990125i	$-0.455230\pi$
$331$	5.10089			0.280370			0.140185	+	0.990125i	$0.455230\pi$
$332$	0.560036	+	1.72361i	0.0307360	+	0.0945956i
$333$	−11.4523	+	15.7627i	−0.627582	+	0.863792i
$334$	−7.83955	−	10.7902i	−0.428961	−	0.590414i
$335$	4.69740	+	1.52628i	0.256646	+	0.0833894i
$336$	0.721688	−	2.22113i	0.0393713	−	0.121172i
$337$	6.27187	+	8.63249i	0.341651	+	0.470242i	0.944923	−	0.327294i	$-0.106137\pi$
$337$	6.27187	+	8.63249i	0.341651	+	0.470242i	−0.603272	+	0.797536i	$0.706137\pi$
$338$	12.1415	+	8.82132i	0.660410	+	0.479816i
$339$	−3.69529	−	11.3729i	−0.200701	−	0.617693i
$340$	0.267774	+	0.124743i	0.0145221	+	0.00676514i
$341$	−34.3379	+	9.21551i	−1.85950	+	0.499048i
$342$	14.3005			0.773280
$343$	−10.2574	+	3.33284i	−0.553849	+	0.179956i
$344$	−5.96309	−	4.33244i	−0.321508	−	0.233589i
$345$	−1.05421	−	1.45100i	−0.0567568	−	0.0781190i
$346$	−21.7696	−	7.07336i	−1.17034	−	0.380266i
$347$	−4.45330	−	1.44696i	−0.239065	−	0.0776771i	0.187034	−	0.982353i	$-0.440113\pi$
$347$	−4.45330	−	1.44696i	−0.239065	−	0.0776771i	−0.426099	+	0.904676i	$0.640113\pi$
$348$	−0.859518	+	0.624476i	−0.0460750	+	0.0334754i
$349$	−20.7485	−	15.0747i	−1.11064	−	0.806930i	−0.127879	−	0.991790i	$-0.540817\pi$
$349$	−20.7485	−	15.0747i	−1.11064	−	0.806930i	−0.982765	+	0.184860i	$0.940817\pi$
$350$	−5.00760	+	1.62707i	−0.267667	+	0.0869704i
$351$		−	5.90810i		−	0.315351i
$352$	3.05902	+	0.159091i	0.163047	+	0.00847960i
$353$	−1.95795			−0.104211			−0.0521055	−	0.998642i	$-0.516593\pi$
$353$	−1.95795			−0.104211			−0.0521055	+	0.998642i	$0.516593\pi$
$354$	10.6269	−	3.45289i	0.564813	−	0.183519i
$355$	−3.97677	−	2.88930i	−0.211065	−	0.153348i
$356$	1.32528	−	0.962872i	0.0702397	−	0.0510321i
$357$	1.93230	+	1.80055i	0.102268	+	0.0952950i
$358$	1.86384	−	5.73632i	0.0985071	−	0.303174i
$359$	−13.7484	+	9.98877i	−0.725611	+	0.527187i	−0.888172	−	0.459511i	$-0.848025\pi$
$359$	−13.7484	+	9.98877i	−0.725611	+	0.527187i	0.162561	+	0.986698i	$0.448025\pi$
$360$	1.78894	−	2.46227i	0.0942855	−	0.129773i
$361$	0.247379	+	0.761355i	0.0130200	+	0.0400713i
$362$			8.29897i			0.436184i
$363$	5.82964	−	6.48488i	0.305977	−	0.340368i
$364$			0.183523i			0.00961922i
$365$	0.0747784	+	0.230144i	0.00391408	+	0.0120463i
$366$	5.41321	+	3.93293i	0.282953	+	0.205578i
$367$	7.91857	+	10.8990i	0.413346	+	0.568922i	0.964031	−	0.265791i	$-0.0856333\pi$
$367$	7.91857	+	10.8990i	0.413346	+	0.568922i	−0.550685	+	0.834713i	$0.685633\pi$
$368$	−17.9232	−	5.82360i	−0.934312	−	0.303576i
$369$	5.73678	+	1.86399i	0.298645	+	0.0970355i
$370$	3.94219	−	2.86417i	0.204945	−	0.148901i
$371$	2.49365	−	3.43222i	0.129464	−	0.178192i
$372$	0.429841	+	1.32292i	0.0222862	+	0.0685900i
$373$	−38.4166			−1.98913			−0.994567	−	0.104096i	$-0.966805\pi$
$373$	−38.4166			−1.98913			−0.994567	+	0.104096i	$0.966805\pi$
$374$	8.68700	−	16.3684i	0.449194	−	0.846392i
$375$	3.40325			0.175743
$376$	−3.41832	−	10.5205i	−0.176286	−	0.542554i
$377$	−6.67716	+	9.19032i	−0.343891	+	0.473326i
$378$	3.77228	−	2.74072i	0.194025	−	0.140968i
$379$	−32.5678	−	10.5819i	−1.67290	−	0.543557i	−0.689384	−	0.724396i	$-0.742119\pi$
$379$	−32.5678	−	10.5819i	−1.67290	−	0.543557i	−0.983513	+	0.180840i	$0.942119\pi$
$380$	0.303206	+	0.0985176i	0.0155541	+	0.00505384i
$381$	0.352499	+	0.485174i	0.0180591	+	0.0248562i
$382$	−17.3613	−	12.6137i	−0.888283	−	0.645375i
$383$	−1.90622	−	5.86675i	−0.0974034	−	0.299777i	0.890469	−	0.455044i	$-0.150376\pi$
$383$	−1.90622	−	5.86675i	−0.0974034	−	0.299777i	−0.987873	+	0.155267i	$0.950376\pi$
$384$			7.71306i			0.393605i
$385$	0.304059	+	1.13295i	0.0154963	+	0.0577407i
$386$			10.1791i			0.518105i
$387$	−1.84232	−	5.67009i	−0.0936506	−	0.288227i
$388$	−0.676111	+	0.930587i	−0.0343243	+	0.0472434i
$389$	−20.0614	+	14.5754i	−1.01715	+	0.739004i	−0.965697	−	0.259671i	$-0.916386\pi$
$389$	−20.0614	+	14.5754i	−1.01715	+	0.739004i	−0.0514550	+	0.998675i	$0.516386\pi$
$390$	−0.201591	+	0.620434i	−0.0102080	+	0.0314169i
$391$	14.5294	−	15.5926i	0.734781	−	0.788549i
$392$	15.0555	−	10.9385i	0.760419	−	0.552477i
$393$	−9.04763	−	6.57349i	−0.456392	−	0.331589i
$394$	2.11083	−	0.685851i	0.106342	−	0.0345527i
$395$	−0.862800			−0.0434122
$396$	1.00092	+	0.809868i	0.0502981	+	0.0406974i
$397$		−	1.05100i		−	0.0527482i	−0.999652	−	0.0263741i	$-0.991604\pi$
$397$		−	1.05100i		−	0.0527482i	0.999652	−	0.0263741i	$-0.00839611\pi$
$398$	12.8180	−	4.16483i	0.642510	−	0.208764i
$399$	2.30604	+	1.67544i	0.115447	+	0.0838768i
$400$	14.1826	−	10.3043i	0.709131	−	0.515214i
$401$	−18.5129	−	6.01520i	−0.924489	−	0.300385i	−0.192182	−	0.981359i	$-0.561556\pi$
$401$	−18.5129	−	6.01520i	−0.924489	−	0.300385i	−0.732307	+	0.680975i	$0.761556\pi$
$402$	−11.5288	−	3.74592i	−0.575003	−	0.186830i
$403$	8.74219	+	12.0326i	0.435479	+	0.599386i
$404$	1.60592	+	1.16677i	0.0798977	+	0.0580491i
$405$	1.55651	−	0.505740i	0.0773435	−	0.0251304i
$406$	−8.96545			−0.444948
$407$	14.8494	+	22.8460i	0.736055	+	1.13243i
$408$	−8.68696	−	4.04683i	−0.430069	−	0.200348i
$409$	−9.36758	−	28.8304i	−0.463197	−	1.42557i	−0.861236	−	0.508205i	$-0.830309\pi$
$409$	−9.36758	−	28.8304i	−0.463197	−	1.42557i	0.398039	−	0.917368i	$-0.369691\pi$
$410$	−1.22046	−	0.886719i	−0.0602744	−	0.0437919i
$411$	−5.59641	−	7.70280i	−0.276051	−	0.379951i
$412$	−0.594562	+	1.82987i	−0.0292920	+	0.0901514i
$413$	−7.99387	−	2.59737i	−0.393353	−	0.127808i
$414$	−9.76436	−	13.4395i	−0.479892	−	0.660515i
$415$	2.84841	−	3.92049i	0.139823	−	0.192450i
$416$	−0.395983	−	1.21871i	−0.0194147	−	0.0597522i
$417$	3.91121			0.191533
$418$	7.15954	−	18.6735i	0.350184	−	0.913352i
$419$			31.9025i			1.55854i	0.626688	+	0.779271i	$0.284410\pi$
$419$			31.9025i			1.55854i	−0.626688	+	0.779271i	$0.715590\pi$
$420$	0.0436486	−	0.0141823i	0.00212983	−	0.000692025i
$421$	4.47586	+	3.25190i	0.218140	+	0.158488i	0.691489	−	0.722387i	$-0.256955\pi$
$421$	4.47586	+	3.25190i	0.218140	+	0.158488i	−0.473349	+	0.880875i	$0.656955\pi$
$422$	−6.58743	−	9.06682i	−0.320671	−	0.441366i
$423$	2.76492	−	8.50956i	0.134435	−	0.413749i
$424$	−4.75686	+	14.6401i	−0.231013	+	0.710986i
$425$	3.79021	+	19.4600i	0.183852	+	0.943947i
$426$	9.76015	+	7.09117i	0.472881	+	0.343568i
$427$	−1.55536	−	4.78690i	−0.0752690	−	0.231654i
$428$			0.740510i			0.0357939i
$429$	−3.40612	−	1.30593i	−0.164449	−	0.0630507i
$430$			1.49104i			0.0719044i
$431$	16.8362	−	5.47041i	0.810971	−	0.263500i	0.125962	−	0.992035i	$-0.459798\pi$
$431$	16.8362	−	5.47041i	0.810971	−	0.263500i	0.685009	+	0.728535i	$0.259798\pi$
$432$	−9.12517	+	12.5597i	−0.439035	+	0.604279i
$433$	16.9027	−	12.2805i	0.812293	−	0.590165i	−0.102201	−	0.994764i	$-0.532589\pi$
$433$	16.9027	−	12.2805i	0.812293	−	0.590165i	0.914495	+	0.404598i	$0.132589\pi$
$434$	−3.62729	+	11.1637i	−0.174116	+	0.535873i
$435$	2.70180	+	0.877868i	0.129541	+	0.0420905i
$436$	−1.60236	−	2.20545i	−0.0767390	−	0.105622i
$437$	13.5198	−	18.6084i	0.646740	−	0.890162i
$438$	−0.183528	−	0.564840i	−0.00876929	−	0.0269891i
$439$			9.97116i			0.475897i	0.971278	+	0.237949i	$0.0764750\pi$
$439$			9.97116i			0.475897i	−0.971278	+	0.237949i	$0.923525\pi$
$440$	−2.31959	−	3.56873i	−0.110582	−	0.170133i
$441$	15.0525			0.716786
$442$	−7.69466	−	0.941857i	−0.365998	−	0.0447996i
$443$	−5.88357	−	4.27466i	−0.279537	−	0.203095i	0.439178	−	0.898400i	$-0.355270\pi$
$443$	−5.88357	−	4.27466i	−0.279537	−	0.203095i	−0.718715	+	0.695304i	$0.755270\pi$
$444$	0.862459	−	0.626613i	0.0409305	−	0.0297378i
$445$	−4.16587	−	1.35357i	−0.197481	−	0.0641655i
$446$	1.49439	−	4.59925i	0.0707612	−	0.217781i
$447$	−2.88615	−	3.97244i	−0.136510	−	0.187890i
$448$	4.05776	−	5.58503i	0.191711	−	0.263868i
$449$	−31.4284	+	10.2117i	−1.48320	+	0.481921i	−0.935067	−	0.354471i	$-0.884661\pi$
$449$	−31.4284	+	10.2117i	−1.48320	+	0.481921i	−0.548133	+	0.836391i	$0.684661\pi$
$450$	15.4530			0.728464
$451$	5.30612	−	6.55786i	0.249855	−	0.308798i
$452$		−	2.46925i		−	0.116144i
$453$	4.88777	−	1.58813i	0.229647	−	0.0746169i
$454$	−18.8847	+	25.9926i	−0.886303	+	1.21989i
$455$	0.397006	−	0.288442i	0.0186119	−	0.0135224i
$456$	−9.83641	−	3.19604i	−0.460632	−	0.149668i
$457$	11.9048	−	36.6391i	0.556881	−	1.71390i	−0.134041	−	0.990976i	$-0.542795\pi$
$457$	11.9048	−	36.6391i	0.556881	−	1.71390i	0.690922	−	0.722929i	$-0.257205\pi$
$458$	8.96794	−	6.51559i	0.419044	−	0.304454i
$459$	−8.51756	−	15.3525i	−0.397566	−	0.716594i
$460$	−0.114443	−	0.352219i	−0.00533593	−	0.0164223i
$461$	10.2763			0.478617			0.239308	−	0.970944i	$-0.423079\pi$
$461$	10.2763			0.478617			0.239308	+	0.970944i	$0.423079\pi$
$462$	−0.746249	−	2.78059i	−0.0347186	−	0.129365i
$463$	1.22150			0.0567680			0.0283840	−	0.999597i	$-0.490964\pi$
$463$	1.22150			0.0567680			0.0283840	+	0.999597i	$0.490964\pi$
$464$	28.3893	−	9.22423i	1.31794	−	0.428224i
$465$	2.18622	−	3.00907i	0.101384	−	0.139542i
$466$	14.5008	+	19.9586i	0.671735	+	0.924564i
$467$	−4.26833	+	13.1366i	−0.197515	+	0.607888i	0.802423	+	0.596755i	$0.203544\pi$
$467$	−4.26833	+	13.1366i	−0.197515	+	0.607888i	−0.999938	+	0.0111325i	$0.996456\pi$
$468$	0.166442	−	0.512257i	0.00769380	−	0.0236791i
$469$	5.35976	+	7.37708i	0.247491	+	0.340642i
$470$	−1.31530	+	1.81036i	−0.0606703	+	0.0835055i
$471$	2.46786	−	0.801857i	0.113713	−	0.0369476i
$472$	30.4980			1.40378
$473$	−8.32636	−	0.433031i	−0.382846	−	0.0199108i
$474$	2.11756			0.0972628
$475$	6.61186	+	20.3492i	0.303373	+	0.933686i
$476$	0.264581	+	0.476895i	0.0121270	+	0.0218584i
$477$	−10.0732	+	7.31858i	−0.461218	+	0.335095i
$478$	−6.80674	+	20.9490i	−0.311333	+	0.958185i
$479$	−27.4921	−	8.93272i	−1.25615	−	0.408146i	−0.396026	−	0.918239i	$-0.629611\pi$
$479$	−27.4921	−	8.93272i	−1.25615	−	0.408146i	−0.860119	+	0.510093i	$0.829611\pi$
$480$	−0.259254	+	0.188359i	−0.0118333	+	0.00859738i
$481$	6.70001	−	9.22177i	0.305494	−	0.420477i
$482$	24.1702	−	7.85339i	1.10092	−	0.357712i
$483$		−	3.31119i		−	0.150665i
$484$	1.55864	−	0.901540i	0.0708471	−	0.0409791i
$485$	3.07574			0.139662
$486$	−20.2838	+	6.59060i	−0.920092	+	0.298956i
$487$	−2.89130	+	3.97954i	−0.131017	+	0.180330i	−0.869486	−	0.493958i	$-0.835550\pi$
$487$	−2.89130	+	3.97954i	−0.131017	+	0.180330i	0.738468	+	0.674288i	$0.235550\pi$
$488$	10.7346	+	14.7750i	0.485934	+	0.668831i
$489$	1.93438	−	5.95341i	0.0874757	−	0.269222i
$490$	−3.58031	−	1.16331i	−0.161742	−	0.0525532i
$491$	11.6863	−	8.49060i	0.527396	−	0.383175i	−0.291987	−	0.956422i	$-0.594316\pi$
$491$	11.6863	−	8.49060i	0.527396	−	0.383175i	0.819383	+	0.573247i	$0.194316\pi$
$492$	−0.267009	−	0.193994i	−0.0120377	−	0.00874591i
$493$	−4.10150	+	33.5079i	−0.184722	+	1.50912i
$494$	−8.36629			−0.376417
$495$	0.178807	−	3.43811i	0.00803676	−	0.154531i
$496$		−	39.0819i		−	1.75483i
$497$	−2.80435	−	8.63089i	−0.125792	−	0.387149i
$498$	−6.99081	+	9.62203i	−0.313266	+	0.431173i
$499$	−1.88041	−	2.58816i	−0.0841786	−	0.115862i	0.764851	−	0.644207i	$-0.222813\pi$
$499$	−1.88041	−	2.58816i	−0.0841786	−	0.115862i	−0.849030	+	0.528345i	$0.822813\pi$
$500$	0.668341	+	0.217157i	0.0298891	+	0.00971157i
$501$	−2.41105	+	7.42043i	−0.107718	+	0.331521i
$502$	−25.7482	+	18.7072i	−1.14920	+	0.834941i
$503$	13.1140	−	18.0498i	0.584722	−	0.804801i	−0.409481	−	0.912319i	$-0.634290\pi$
$503$	13.1140	−	18.0498i	0.584722	−	0.804801i	0.994203	+	0.107517i	$0.0342901\pi$
$504$	5.34392	−	1.73635i	0.238037	−	0.0773430i
$505$		−	5.30783i		−	0.236195i
$506$	−22.4378	+	6.02179i	−0.997481	+	0.267701i
$507$		−	8.77941i		−	0.389907i
$508$	0.0382666	+	0.117772i	0.00169781	+	0.00522531i
$509$	−7.24024	−	5.26034i	−0.320918	−	0.233161i	0.415649	−	0.909525i	$-0.363554\pi$
$509$	−7.24024	−	5.26034i	−0.320918	−	0.233161i	−0.736567	+	0.676365i	$0.763554\pi$
$510$	0.370619	+	1.90286i	0.0164113	+	0.0842602i
$511$	−0.138055	+	0.424890i	−0.00610719	+	0.0187960i
$512$	−7.64710	+	23.5353i	−0.337957	+	1.04013i
$513$	−11.1374	−	15.3293i	−0.491728	−	0.676805i
$514$	13.1604	+	9.56156i	0.580479	+	0.421743i
$515$	4.89295	−	1.58981i	0.215609	−	0.0700556i
$516$			0.326205i			0.0143604i
$517$	−9.72751	−	7.87075i	−0.427815	−	0.346155i
$518$	8.99613			0.395267
$519$	4.13787	+	12.7350i	0.181632	+	0.559006i
$520$	−1.04660	+	1.44052i	−0.0458963	+	0.0631708i
$521$	16.4296	+	22.6134i	0.719792	+	0.990709i	0.999531	+	0.0306328i	$0.00975224\pi$
$521$	16.4296	+	22.6134i	0.719792	+	0.990709i	−0.279738	+	0.960076i	$0.590248\pi$
$522$	25.0247	+	8.13103i	1.09530	+	0.355885i
$523$	−0.840817	+	2.58777i	−0.0367664	+	0.113155i	−0.967755	−	0.251892i	$-0.918947\pi$
$523$	−0.840817	+	2.58777i	−0.0367664	+	0.113155i	0.930989	+	0.365047i	$0.118947\pi$
$524$	−1.35736	−	1.86824i	−0.0592964	−	0.0816144i
$525$	2.49190	+	1.81047i	0.108756	+	0.0790156i
$526$	−9.52329	−	29.3097i	−0.415235	−	1.27796i
$527$	40.0642	+	18.6639i	1.74522	+	0.813014i
$528$	5.22386	+	8.03702i	0.227339	+	0.349766i
$529$	−3.71942			−0.161714
$530$	2.96156	−	0.962268i	0.128642	−	0.0417983i
$531$	19.9572	+	14.4997i	0.866068	+	0.629236i
$532$	0.345960	+	0.476173i	0.0149993	+	0.0206447i
$533$	−3.35622	−	1.09050i	−0.145374	−	0.0472349i
$534$	10.2243	+	3.32206i	0.442447	+	0.143760i
$535$	1.60191	−	1.16386i	0.0692566	−	0.0503179i
$536$	−26.7673	−	19.4476i	−1.15617	−	0.840009i
$537$	−3.35571	+	1.09034i	−0.144809	+	0.0470514i
$538$			24.5374i			1.05788i
$539$	7.53605	−	19.6555i	0.324601	−	0.846624i
$540$	−0.305084			−0.0131287
$541$	5.45137	−	1.77126i	0.234373	−	0.0761523i	−0.189476	−	0.981885i	$-0.560679\pi$
$541$	5.45137	−	1.77126i	0.234373	−	0.0761523i	0.423849	+	0.905733i	$0.360679\pi$
$542$	24.4648	+	17.7747i	1.05085	+	0.763489i
$543$	3.92765	−	2.85360i	0.168552	−	0.122460i
$544$	−2.78597	−	2.59601i	−0.119448	−	0.111303i
$545$	−2.25254	+	6.93260i	−0.0964882	+	0.296960i
$546$	−0.974368	+	0.707920i	−0.0416991	+	0.0302962i
$547$	21.6045	−	29.7361i	0.923743	−	1.27142i	−0.0385077	−	0.999258i	$-0.512260\pi$
$547$	21.6045	−	29.7361i	0.923743	−	1.27142i	0.962251	−	0.272165i	$-0.0877396\pi$
$548$	−0.607535	−	1.86980i	−0.0259526	−	0.0798739i
$549$			14.7720i			0.630453i
$550$	7.73658	−	20.1786i	0.329889	−	0.860417i
$551$			36.4326i			1.55208i
$552$	3.71268	+	11.4265i	0.158022	+	0.486342i
$553$	−1.28868	−	0.936278i	−0.0548001	−	0.0398146i
$554$	−8.33326	−	11.4698i	−0.354046	−	0.487303i
$555$	−2.71104	−	0.880872i	−0.115077	−	0.0373909i
$556$	0.768096	+	0.249569i	0.0325745	+	0.0105841i
$557$	−23.2024	+	16.8575i	−0.983118	+	0.714277i	−0.958403	−	0.285417i	$-0.907868\pi$
$557$	−23.2024	+	16.8575i	−0.983118	+	0.714277i	−0.0247149	+	0.999695i	$0.507868\pi$
$558$	20.2493	−	27.8708i	0.857222	−	1.17986i
$559$	1.07783	+	3.31721i	0.0455872	+	0.140303i
$560$	−1.28948			−0.0544904
$561$	−10.7337	+	1.51700i	−0.453178	+	0.0640479i
$562$	−28.7716			−1.21366
$563$	2.85353	+	8.78228i	0.120262	+	0.370129i	0.993008	−	0.118046i	$-0.0376629\pi$
$563$	2.85353	+	8.78228i	0.120262	+	0.370129i	−0.872746	+	0.488175i	$0.837663\pi$
$564$	−0.287757	+	0.396064i	−0.0121168	+	0.0166773i
$565$	−5.34160	+	3.88090i	−0.224723	+	0.163271i
$566$	−11.3779	−	3.69689i	−0.478247	−	0.155392i
$567$	2.87361	+	0.933692i	0.120680	+	0.0392114i
$568$	19.3548	+	26.6396i	0.812110	+	1.11777i
$569$	−17.6536	−	12.8261i	−0.740079	−	0.537699i	0.152657	−	0.988279i	$-0.451217\pi$
$569$	−17.6536	−	12.8261i	−0.740079	−	0.537699i	−0.892736	+	0.450580i	$0.851217\pi$
$570$	0.646530	+	1.98982i	0.0270802	+	0.0833442i
$571$			12.6164i			0.527978i	0.964526	+	0.263989i	$0.0850383\pi$
$571$			12.6164i			0.527978i	−0.964526	+	0.263989i	$0.914962\pi$
$572$	−0.585575	−	0.473802i	−0.0244841	−	0.0198107i
$573$			12.5538i			0.524444i
$574$	−0.860648	−	2.64880i	−0.0359228	−	0.110559i
$575$	14.6095	−	20.1082i	0.609258	−	0.838571i
$576$	−16.3914	+	11.9091i	−0.682976	+	0.496211i
$577$	−1.60855	+	4.95059i	−0.0669646	+	0.206096i	−0.978940	−	0.204150i	$-0.934557\pi$
$577$	−1.60855	+	4.95059i	−0.0669646	+	0.206096i	0.911975	+	0.410246i	$0.134557\pi$
$578$	−21.3529	+	8.64575i	−0.888162	+	0.359616i
$579$	4.81748	−	3.50010i	0.200207	−	0.145459i
$580$	0.474572	+	0.344797i	0.0197055	+	0.0143169i
$581$	8.50875	−	2.76466i	0.353002	−	0.114697i
$582$	−7.54874			−0.312905
$583$	4.51345	+	16.8176i	0.186928	+	0.696512i
$584$		−	1.62103i		−	0.0670786i
$585$	−1.36974	+	0.445055i	−0.0566317	+	0.0184007i
$586$	1.40454	+	1.02046i	0.0580212	+	0.0421549i
$587$	32.7803	−	23.8162i	1.35299	−	0.983002i	0.354129	−	0.935196i	$-0.384777\pi$
$587$	32.7803	−	23.8162i	1.35299	−	0.983002i	0.998857	−	0.0478053i	$-0.0152227\pi$
$588$	−0.783289	−	0.254506i	−0.0323023	−	0.0104957i
$589$	45.3654	+	14.7401i	1.86925	+	0.607356i
$590$	−3.62632	−	4.99120i	−0.149293	−	0.205485i
$591$	−1.05040	−	0.763163i	−0.0432078	−	0.0313923i
$592$	−28.4864	+	9.25579i	−1.17078	+	0.380411i
$593$	−6.02907			−0.247584			−0.123792	−	0.992308i	$-0.539506\pi$
$593$	−6.02907			−0.247584			−0.123792	+	0.992308i	$0.539506\pi$
$594$	−0.993969	+	19.1121i	−0.0407831	+	0.784180i
$595$	0.615803	−	1.32189i	0.0252455	−	0.0541921i
$596$	−0.313314	−	0.964282i	−0.0128339	−	0.0394985i
$597$	−6.37857	−	4.63431i	−0.261058	−	0.189670i
$598$	5.71250	+	7.86259i	0.233602	+	0.321525i
$599$	−7.11312	+	21.8919i	−0.290634	+	0.894480i	0.694019	+	0.719957i	$0.255838\pi$
$599$	−7.11312	+	21.8919i	−0.290634	+	0.894480i	−0.984653	+	0.174523i	$0.944162\pi$
$600$	−10.6292	−	3.45364i	−0.433936	−	0.140994i
$601$	−18.6504	−	25.6700i	−0.760765	−	1.04710i	−0.997150	−	0.0754433i	$-0.975963\pi$
$601$	−18.6504	−	25.6700i	−0.760765	−	1.04710i	0.236385	−	0.971659i	$-0.424037\pi$
$602$	−1.61802	+	2.22702i	−0.0659457	+	0.0907664i
$603$	−8.26990	−	25.4521i	−0.336777	−	1.03649i
$604$	1.06121			0.0431801
$605$	−4.39996	−	1.95478i	−0.178884	−	0.0794730i
$606$			13.0269i			0.529184i
$607$	−42.7133	+	13.8784i	−1.73368	+	0.563307i	−0.993973	−	0.109623i	$-0.965036\pi$
$607$	−42.7133	+	13.8784i	−1.73368	+	0.563307i	−0.739706	+	0.672930i	$0.765036\pi$
$608$	−3.32483	−	2.41563i	−0.134840	−	0.0979667i
$609$	3.08277	+	4.24307i	0.124920	+	0.171938i
$610$	1.14163	−	3.51359i	0.0462234	−	0.142261i
$611$	−1.61758	+	4.97840i	−0.0654403	+	0.201405i
$612$	−0.305999	−	1.57108i	−0.0123693	−	0.0635073i
$613$	26.6627	+	19.3716i	1.07690	+	0.782412i	0.977139	−	0.212600i	$-0.0681930\pi$
$613$	26.6627	+	19.3716i	1.07690	+	0.782412i	0.0997585	+	0.995012i	$0.468193\pi$
$614$	5.22340	+	16.0760i	0.210799	+	0.648774i
$615$			0.882507i			0.0355861i
$616$	0.408121	−	7.84739i	0.0164437	−	0.316180i
$617$		−	30.4805i		−	1.22710i	−0.789656	−	0.613550i	$-0.789741\pi$
$617$		−	30.4805i		−	1.22710i	0.789656	−	0.613550i	$-0.210259\pi$
$618$	−12.0087	+	3.90186i	−0.483061	+	0.156956i
$619$	10.7025	−	14.7308i	0.430171	−	0.592080i	−0.537821	−	0.843059i	$-0.680753\pi$
$619$	10.7025	−	14.7308i	0.430171	−	0.592080i	0.967992	+	0.250979i	$0.0807526\pi$
$620$	0.621342	−	0.451431i	0.0249537	−	0.0181299i
$621$	−6.80177	+	20.9337i	−0.272946	+	0.840040i
$622$	20.2743	+	6.58752i	0.812925	+	0.264135i
$623$	−4.75329	−	6.54234i	−0.190437	−	0.262113i
$624$	2.35700	−	3.24413i	0.0943556	−	0.129869i
$625$	6.84876	+	21.0783i	0.273950	+	0.843133i
$626$		−	22.0091i		−	0.879661i
$627$	−11.2994	+	3.03251i	−0.451255	+	0.121107i
$628$	0.535812			0.0213812
$629$	4.11553	−	33.6225i	0.164097	−	1.34062i
$630$	−0.919576	−	0.668111i	−0.0366368	−	0.0266182i
$631$	25.6620	−	18.6445i	1.02159	−	0.742226i	0.0549792	−	0.998487i	$-0.482491\pi$
$631$	25.6620	−	18.6445i	1.02159	−	0.742226i	0.966608	+	0.256261i	$0.0824907\pi$
$632$	5.49684	+	1.78603i	0.218653	+	0.0710445i
$633$	−2.02596	+	6.23526i	−0.0805246	+	0.247829i
$634$	8.07387	+	11.1127i	0.320654	+	0.441343i
$635$	0.194628	−	0.267883i	0.00772358	−	0.0106306i
$636$	0.647920	−	0.210522i	0.0256917	−	0.00834774i
$637$	−8.80627			−0.348917
$638$	23.1461	−	28.6065i	0.916364	−	1.13254i
$639$			26.6343i			1.05363i
$640$	4.05024	−	1.31600i	0.160100	−	0.0520195i
$641$	−5.86702	+	8.07526i	−0.231733	+	0.318953i	−0.909010	−	0.416775i	$-0.863160\pi$
$641$	−5.86702	+	8.07526i	−0.231733	+	0.318953i	0.677276	+	0.735729i	$0.263160\pi$
$642$	−3.93155	+	2.85644i	−0.155166	+	0.112735i
$643$	−39.1753	−	12.7288i	−1.54492	−	0.501976i	−0.592193	−	0.805796i	$-0.701738\pi$
$643$	−39.1753	−	12.7288i	−1.54492	−	0.501976i	−0.952729	+	0.303821i	$0.901738\pi$
$644$	0.211283	−	0.650263i	0.00832572	−	0.0256239i
$645$	0.705664	−	0.512695i	0.0277855	−	0.0201873i
$646$	−21.7403	+	12.0615i	−0.855359	+	0.474553i
$647$	7.48099	+	23.0241i	0.294108	+	0.905171i	0.983520	+	0.180801i	$0.0578691\pi$
$647$	7.48099	+	23.0241i	0.294108	+	0.905171i	−0.689412	+	0.724370i	$0.742131\pi$
$648$	−10.9633			−0.430680
$649$	28.9253	−	18.8008i	1.13542	−	0.737995i
$650$	−9.04060			−0.354601
$651$	6.53067	−	2.12194i	0.255957	−	0.0831655i
$652$	0.759759	−	1.04572i	0.0297545	−	0.0409535i
$653$	19.5734	+	26.9405i	0.765967	+	1.05426i	0.996694	+	0.0812444i	$0.0258894\pi$
$653$	19.5734	+	26.9405i	0.765967	+	1.05426i	−0.230727	+	0.973018i	$0.574111\pi$
$654$	5.52838	−	17.0146i	0.216177	−	0.665324i
$655$	−1.90813	+	5.87260i	−0.0745566	+	0.229462i
$656$	5.45052	+	7.50199i	0.212807	+	0.292904i
$657$	0.770690	−	1.06076i	0.0300675	−	0.0413843i
$658$	−3.92906	+	1.27663i	−0.153171	+	0.0497682i
$659$	24.9073			0.970249			0.485124	−	0.874445i	$-0.338774\pi$
$659$	24.9073			0.970249			0.485124	+	0.874445i	$0.338774\pi$
$660$	−0.0674357	+	0.175886i	−0.00262493	+	0.00684635i
$661$	−16.6703			−0.648398			−0.324199	−	0.945989i	$-0.605095\pi$
$661$	−16.6703			−0.648398			−0.324199	+	0.945989i	$0.605095\pi$
$662$	2.13600	+	6.57393i	0.0830180	+	0.255503i
$663$	2.20006	+	3.96551i	0.0854433	+	0.154007i
$664$	−26.2626	+	19.0809i	−1.01919	+	0.740482i
$665$	0.486339	−	1.49680i	0.0188594	−	0.0580433i
$666$	−25.1104	−	8.15885i	−0.973007	−	0.316149i
$667$	34.2391	−	24.8762i	1.32574	−	0.963210i
$668$	−0.946977	+	1.30340i	−0.0366397	+	0.0504302i
$669$	−2.69053	+	0.874205i	−0.104022	+	0.0337987i
$670$			6.69305i			0.258575i
$671$	19.2892	+	7.39561i	0.744653	+	0.285504i
$672$	−0.591622			−0.0228223
$673$	16.5477	−	5.37668i	0.637867	−	0.207256i	0.0278103	−	0.999613i	$-0.491147\pi$
$673$	16.5477	−	5.37668i	0.637867	−	0.207256i	0.610057	+	0.792358i	$0.291147\pi$
$674$	−8.49905	+	11.6979i	−0.327371	+	0.450588i
$675$	−12.0350	−	16.5648i	−0.463229	−	0.637580i
$676$	0.560203	−	1.72413i	0.0215463	−	0.0663126i
$677$	−5.83750	−	1.89672i	−0.224353	−	0.0728969i	0.194683	−	0.980866i	$-0.437632\pi$
$677$	−5.83750	−	1.89672i	−0.224353	−	0.0728969i	−0.419037	+	0.907969i	$0.637632\pi$
$678$	13.1098	−	9.52485i	0.503480	−	0.365800i
$679$	4.59391	+	3.33767i	0.176298	+	0.128088i
$680$	−0.642880	+	5.25212i	−0.0246533	+	0.201409i
$681$	18.7950			0.720226
$682$	−26.2558	−	40.3951i	−1.00539	−	1.54681i
$683$			6.28700i			0.240565i	0.992740	+	0.120283i	$0.0383801\pi$
$683$			6.28700i			0.240565i	−0.992740	+	0.120283i	$0.961620\pi$
$684$	−0.533803	−	1.64288i	−0.0204105	−	0.0628170i
$685$	−3.08999	+	4.25301i	−0.118062	+	0.162499i
$686$	−8.59060	−	11.8239i	−0.327991	−	0.451440i
$687$	−6.16726	−	2.00386i	−0.235296	−	0.0764522i
$688$	2.83220	−	8.71661i	0.107977	−	0.332318i
$689$	5.89317	−	4.28164i	0.224512	−	0.163117i
$690$	1.42857	−	1.96625i	0.0543846	−	0.0748539i
$691$	−7.17172	+	2.33023i	−0.272825	+	0.0886463i	−0.442234	−	0.896900i	$-0.645814\pi$
$691$	−7.17172	+	2.33023i	−0.272825	+	0.0886463i	0.169409	+	0.985546i	$0.445814\pi$
$692$			2.76498i			0.105109i
$693$	3.99797	−	4.94112i	0.151870	−	0.187697i
$694$		−	6.34524i		−	0.240862i
$695$	−0.667330	−	2.05383i	−0.0253133	−	0.0779062i
$696$	−15.3958	−	11.1857i	−0.583575	−	0.423992i
$697$	−10.2935	+	2.00486i	−0.389894	+	0.0759394i
$698$	10.7395	−	33.0529i	0.406497	−	1.25107i
$699$	4.45970	−	13.7255i	0.168681	−	0.519148i
$700$	0.373844	+	0.514552i	0.0141300	+	0.0194482i
$701$	9.88642	+	7.18290i	0.373405	+	0.271294i	0.758621	−	0.651532i	$-0.225873\pi$
$701$	9.88642	+	7.18290i	0.373405	+	0.271294i	−0.385217	+	0.922826i	$0.625873\pi$
$702$	7.61425	−	2.47402i	0.287381	−	0.0933758i
$703$		−	36.5573i		−	1.37878i
$704$	7.34446	+	27.3662i	0.276805	+	1.03140i
$705$	1.30905			0.0493018
$706$	−0.819891	−	2.52337i	−0.0308570	−	0.0949682i
$707$	5.75986	−	7.92777i	0.216622	−	0.298154i
$708$	−0.793355	−	1.09196i	−0.0298161	−	0.0410384i
$709$	−31.1221	−	10.1122i	−1.16881	−	0.379771i	−0.340614	−	0.940203i	$-0.610635\pi$
$709$	−31.1221	−	10.1122i	−1.16881	−	0.379771i	−0.828200	+	0.560432i	$0.810635\pi$
$710$	2.05839	−	6.33509i	0.0772502	−	0.237752i
$711$	2.74787	+	3.78212i	0.103053	+	0.141840i
$712$	23.7385	+	17.2471i	0.889639	+	0.646361i
$713$	−17.1228	−	52.6987i	−0.641256	−	1.97358i
$714$	−1.51136	+	3.24429i	−0.0565612	+	0.121415i
$715$	−0.104608	+	2.01142i	−0.00391213	+	0.0752228i
$716$	−0.728577			−0.0272282
$717$	12.2550	−	3.98190i	0.457672	−	0.148707i
$718$	−18.6305	−	13.5358i	−0.695283	−	0.505153i
$719$	−22.3554	−	30.7695i	−0.833715	−	1.14751i	−0.987220	−	0.159363i	$-0.949056\pi$
$719$	−22.3554	−	30.7695i	−0.833715	−	1.14751i	0.153505	−	0.988148i	$-0.450944\pi$
$720$	3.59925	+	1.16947i	0.134136	+	0.0435834i
$721$	9.03330	+	2.93510i	0.336418	+	0.109309i
$722$	−0.877631	+	0.637636i	−0.0326620	+	0.0237304i
$723$	−12.0277	−	8.73865i	−0.447316	−	0.324994i
$724$	0.953409	−	0.309781i	0.0354332	−	0.0115129i
$725$			39.3690i			1.46213i
$726$	10.7988	+	4.79759i	0.400780	+	0.178055i
$727$	20.2530			0.751141			0.375570	−	0.926794i	$-0.377447\pi$
$727$	20.2530			0.751141			0.375570	+	0.926794i	$0.377447\pi$
$728$	−3.12639	+	1.01583i	−0.115872	+	0.0376490i
$729$	1.01859	+	0.740051i	0.0377257	+	0.0274093i
$730$	−0.265292	+	0.192746i	−0.00981890	+	0.00713385i
$731$	7.58314	+	7.06608i	0.280473	+	0.261348i
$732$	0.249763	−	0.768692i	0.00923152	−	0.0284117i
$733$	−32.1540	+	23.3612i	−1.18763	+	0.862866i	−0.993012	−	0.118012i	$-0.962348\pi$
$733$	−32.1540	+	23.3612i	−1.18763	+	0.862866i	−0.194621	+	0.980878i	$0.562348\pi$
$734$	−10.7305	+	14.7693i	−0.396070	+	0.545143i
$735$	0.680531	+	2.09446i	0.0251018	+	0.0772553i
$736$			4.77405i			0.175974i
$737$	−37.3757	−	1.94381i	−1.37675	−	0.0716011i
$738$			8.17400i			0.300889i
$739$	9.70184	+	29.8592i	0.356888	+	1.09839i	0.954907	+	0.296906i	$0.0959549\pi$
$739$	9.70184	+	29.8592i	0.356888	+	1.09839i	−0.598019	+	0.801482i	$0.704045\pi$
$740$	−0.476196	−	0.345977i	−0.0175053	−	0.0127184i
$741$	2.87675	+	3.95951i	0.105680	+	0.145456i
$742$	5.46759	+	1.77653i	0.200722	+	0.0652184i
$743$	−23.7139	−	7.70511i	−0.869979	−	0.282673i	−0.160189	−	0.987086i	$-0.551210\pi$
$743$	−23.7139	−	7.70511i	−0.869979	−	0.282673i	−0.709790	+	0.704413i	$0.751210\pi$
$744$	−20.1572	+	14.6450i	−0.738998	+	0.536913i
$745$	−1.59355	+	2.19333i	−0.0583832	+	0.0803575i
$746$	−16.0870	−	49.5106i	−0.588985	−	1.81271i
$747$	−26.2573			−0.960705
$748$	−2.20472	−	0.386991i	−0.0806125	−	0.0141498i
$749$	3.65558			0.133572
$750$	1.42511	+	4.38605i	0.0520378	+	0.160156i
$751$	14.8376	−	20.4222i	0.541432	−	0.745217i	−0.447387	−	0.894340i	$-0.647645\pi$
$751$	14.8376	−	20.4222i	0.541432	−	0.745217i	0.988819	+	0.149124i	$0.0476453\pi$
$752$	11.1280	−	8.08494i	0.405795	−	0.294827i
$753$	17.7070	+	5.75337i	0.645281	+	0.209664i
$754$	−14.6404	−	4.75695i	−0.533171	−	0.173238i
$755$	−1.66790	−	2.29567i	−0.0607011	−	0.0835479i
$756$	−0.455672	−	0.331065i	−0.0165726	−	0.0120407i
$757$	5.90367	+	18.1696i	0.214572	+	0.660386i	0.999184	+	0.0403981i	$0.0128626\pi$
$757$	5.90367	+	18.1696i	0.214572	+	0.660386i	−0.784611	+	0.619988i	$0.787137\pi$
$758$		−	46.4040i		−	1.68547i
$759$	10.5652	+	8.54852i	0.383492	+	0.310292i
$760$			5.71055i			0.207143i
$761$	−7.44457	−	22.9120i	−0.269865	−	0.830560i	−0.990532	−	0.137279i	$-0.956164\pi$
$761$	−7.44457	−	22.9120i	−0.269865	−	0.830560i	0.720667	−	0.693281i	$-0.243836\pi$
$762$	−0.477674	+	0.657461i	−0.0173043	+	0.0238173i
$763$	−10.8874	+	7.91015i	−0.394150	+	0.286367i
$764$	−0.801044	+	2.46536i	−0.0289808	+	0.0891936i
$765$	−2.91771	+	3.13122i	−0.105490	+	0.113209i
$766$	6.76273	−	4.91341i	0.244347	−	0.177529i
$767$	−11.6757	−	8.48288i	−0.421585	−	0.306299i
$768$	2.94147	−	0.955741i	0.106141	−	0.0344873i
$769$	−13.0713			−0.471363			−0.235682	−	0.971830i	$-0.575732\pi$
$769$	−13.0713			−0.471363			−0.235682	+	0.971830i	$0.575732\pi$
$770$	−1.33280	+	0.866291i	−0.0480309	+	0.0312189i
$771$		−	9.51614i		−	0.342716i
$772$	1.16941	−	0.379964i	0.0420879	−	0.0136752i
$773$	4.40788	+	3.20251i	0.158540	+	0.115186i	0.664227	−	0.747531i	$-0.268761\pi$
$773$	4.40788	+	3.20251i	0.158540	+	0.115186i	−0.505687	+	0.862717i	$0.668761\pi$
$774$	6.53604	−	4.74871i	0.234933	−	0.170689i
$775$	49.0218	+	15.9281i	1.76091	+	0.572156i
$776$	−19.5953	−	6.36690i	−0.703431	−	0.228558i
$777$	−3.09332	−	4.25759i	−0.110972	−	0.152740i
$778$	−27.1853	−	19.7513i	−0.974639	−	0.708117i
$779$	−10.7639	+	3.49739i	−0.385655	+	0.125307i
$780$	0.0788022			0.00282157
$781$	34.7790	+	13.3345i	1.24449	+	0.477145i
$782$	26.1796	+	12.1958i	0.936180	+	0.436120i
$783$	−10.7736	−	33.1577i	−0.385016	−	1.18496i
$784$	18.7208	+	13.6014i	0.668599	+	0.485766i
$785$	−0.842132	−	1.15910i	−0.0300570	−	0.0413699i
$786$	4.68309	−	14.4131i	0.167040	−	0.514097i
$787$	28.6510	+	9.30927i	1.02130	+	0.331840i	0.771344	−	0.636418i	$-0.219585\pi$
$787$	28.6510	+	9.30927i	1.02130	+	0.331840i	0.249953	+	0.968258i	$0.419585\pi$
$788$	−0.157585	−	0.216897i	−0.00561374	−	0.00772664i
$789$	−10.5968	+	14.5852i	−0.377256	+	0.519248i
$790$	−0.361298	−	1.11196i	−0.0128544	−	0.0395618i
$791$	−12.1896			−0.433413
$792$	−8.25619	+	21.5338i	−0.293371	+	0.765171i
$793$		−	8.64215i		−	0.306892i
$794$	1.35451	−	0.440107i	0.0480698	−	0.0156188i
$795$	−1.47374	−	1.07074i	−0.0522683	−	0.0379752i
$796$	−0.956935	−	1.31711i	−0.0339177	−	0.0466837i
$797$	11.6803	−	35.9483i	0.413738	−	1.27336i	−0.499636	−	0.866235i	$-0.666533\pi$
$797$	11.6803	−	35.9483i	0.413738	−	1.27336i	0.913375	−	0.407120i	$-0.133467\pi$
$798$	−1.19362	+	3.67358i	−0.0422536	+	0.130043i
$799$	2.97387	+	15.2687i	0.105208	+	0.540167i
$800$	−3.59280	−	2.61032i	−0.127025	−	0.0922889i
$801$	7.33414	+	22.5722i	0.259139	+	0.797548i
$802$		−	26.3779i		−	0.931437i
$803$	−0.999297	−	1.53744i	−0.0352644	−	0.0542550i
$804$			1.46428i			0.0516413i
$805$	−1.73875	+	0.564956i	−0.0612830	+	0.0199121i
$806$	−11.8466	+	16.3054i	−0.417278	+	0.574334i
$807$	11.6128	−	8.43720i	0.408790	−	0.297003i
$808$	−10.9874	+	33.8158i	−0.386537	+	1.18964i
$809$	5.40614	+	1.75656i	0.190070	+	0.0617574i	0.402505	−	0.915418i	$-0.368140\pi$
$809$	5.40614	+	1.75656i	0.190070	+	0.0617574i	−0.212436	+	0.977175i	$0.568140\pi$
$810$	1.30358	+	1.79422i	0.0458030	+	0.0630425i
$811$	−26.1432	+	35.9830i	−0.918012	+	1.26353i	0.0463439	+	0.998926i	$0.485243\pi$
$811$	−26.1432	+	35.9830i	−0.918012	+	1.26353i	−0.964356	+	0.264609i	$0.914757\pi$
$812$	0.334659	+	1.02998i	0.0117442	+	0.0361451i
$813$		−	17.6903i		−	0.620425i
$814$	−23.2253	+	28.7044i	−0.814048	+	1.00609i
$815$	−3.45626			−0.121068
$816$	1.44781	−	11.8281i	0.0506834	−	0.414066i
$817$	9.04985	+	6.57510i	0.316614	+	0.230034i
$818$	33.2335	−	24.1455i	1.16198	−	0.844228i
$819$	−2.52879	−	0.821655i	−0.0883632	−	0.0287109i
$820$	−0.0563117	+	0.173309i	−0.00196649	+	0.00605223i
$821$	−20.9457	−	28.8293i	−0.731010	−	1.00615i	−0.999086	−	0.0427513i	$-0.986388\pi$
$821$	−20.9457	−	28.8293i	−0.731010	−	1.00615i	0.268076	−	0.963398i	$-0.413612\pi$
$822$	7.58373	−	10.4381i	0.264513	−	0.364071i
$823$	37.7115	−	12.2532i	1.31454	−	0.427120i	0.433923	−	0.900950i	$-0.357129\pi$
$823$	37.7115	−	12.2532i	1.31454	−	0.427120i	0.880616	+	0.473830i	$0.157129\pi$
$824$	−34.4636			−1.20060
$825$	−12.2101	+	3.27692i	−0.425102	+	0.114088i
$826$		−	11.3900i		−	0.396309i
$827$	−12.4820	+	4.05564i	−0.434040	+	0.141028i	−0.517884	−	0.855451i	$-0.673280\pi$
$827$	−12.4820	+	4.05564i	−0.434040	+	0.141028i	0.0838440	+	0.996479i	$0.473280\pi$
$828$	−1.17948	+	1.62342i	−0.0409899	+	0.0564178i
$829$	−37.0413	+	26.9121i	−1.28650	+	0.934696i	−0.999728	−	0.0233037i	$-0.992582\pi$
$829$	−37.0413	+	26.9121i	−1.28650	+	0.934696i	−0.286770	+	0.957999i	$0.592582\pi$
$830$	6.24543	+	2.02926i	0.216782	+	0.0704368i
$831$	−2.56289	+	7.88776i	−0.0889056	+	0.273623i
$832$	9.58958	−	6.96723i	0.332459	−	0.241545i
$833$	−22.8836	+	12.6958i	−0.792869	+	0.439883i
$834$	1.63782	+	5.04069i	0.0567131	+	0.174545i
$835$	4.30795			0.149083
$836$	−2.41251	−	0.125468i	−0.0834386	−	0.00433941i
$837$	−45.6464			−1.57777
$838$	−41.1154	+	13.3592i	−1.42031	+	0.461486i
$839$	19.1116	−	26.3048i	0.659804	−	0.908143i	−0.339671	−	0.940544i	$-0.610316\pi$
$839$	19.1116	−	26.3048i	0.659804	−	0.908143i	0.999475	+	0.0324018i	$0.0103156\pi$
$840$	0.483202	+	0.665071i	0.0166721	+	0.0229471i
$841$	−11.7535	+	36.1737i	−0.405295	+	1.24737i
$842$	−2.31672	+	7.13014i	−0.0798396	+	0.245721i
$843$	9.89312	+	13.6167i	0.340737	+	0.468984i
$844$	−0.795728	+	1.09523i	−0.0273901	+	0.0376992i
$845$	−4.61019	+	1.49794i	−0.158595	+	0.0515308i
$846$	12.1248			0.416858
$847$	−4.45052	−	7.69432i	−0.152922	−	0.264380i
$848$	−19.1410			−0.657306
$849$	2.16265	+	6.65597i	0.0742221	+	0.228432i
$850$	−23.4925	+	13.0336i	−0.805786	+	0.447049i
$851$	−34.3563	+	24.9613i	−1.17772	+	0.855663i
$852$	0.450329	−	1.38597i	0.0154280	−	0.0474826i
$853$	52.4822	+	17.0525i	1.79696	+	0.583866i	0.999802	−	0.0199093i	$-0.00633775\pi$
$853$	52.4822	+	17.0525i	1.79696	+	0.583866i	0.797154	+	0.603776i	$0.206338\pi$
$854$	5.51796	−	4.00903i	0.188821	−	0.137186i
$855$	−2.71498	+	3.73685i	−0.0928504	+	0.127798i
$856$	−12.6149	+	4.09883i	−0.431168	+	0.140095i
$857$			27.0934i			0.925493i	0.886491	+	0.462746i	$0.153136\pi$
$857$			27.0934i			0.925493i	−0.886491	+	0.462746i	$0.846864\pi$
$858$	0.256739	−	4.93660i	0.00876493	−	0.168533i
$859$	0.107909			0.00368180			0.00184090	−	0.999998i	$-0.499414\pi$
$859$	0.107909			0.00368180			0.00184090	+	0.999998i	$0.499414\pi$
$860$	0.171295	−	0.0556571i	0.00584111	−	0.00189789i
$861$	−0.957663	+	1.31811i	−0.0326371	+	0.0449211i
$862$	14.1003	+	19.4074i	0.480259	+	0.661020i
$863$	16.5339	−	50.8862i	0.562821	−	1.73219i	−0.111517	−	0.993763i	$-0.535571\pi$
$863$	16.5339	−	50.8862i	0.562821	−	1.73219i	0.674338	−	0.738423i	$-0.264429\pi$
$864$	3.74029	+	1.21529i	0.127247	+	0.0413452i
$865$	5.98135	−	4.34570i	0.203372	−	0.147758i
$866$	22.9050	+	16.6414i	0.778342	+	0.565499i
$867$	11.4340	+	7.13281i	0.388318	+	0.242243i
$868$	1.41791			0.0481271
$869$	6.31441	−	1.69464i	0.214202	−	0.0574868i
$870$			3.84964i			0.130515i
$871$	4.83820	+	14.8904i	0.163936	+	0.504543i
$872$	28.7016	−	39.5043i	0.971957	−	1.33778i
$873$	−9.79569	−	13.4826i	−0.331534	−	0.456317i
$874$	29.6436	+	9.63180i	1.00271	+	0.325800i
$875$	1.07201	−	3.29932i	0.0362407	−	0.111537i
$876$	−0.0580398	+	0.0421684i	−0.00196098	+	0.00142474i
$877$	−25.1893	+	34.6701i	−0.850583	+	1.17073i	0.133151	+	0.991096i	$0.457490\pi$
$877$	−25.1893	+	34.6701i	−0.850583	+	1.17073i	−0.983734	+	0.179631i	$0.942510\pi$
$878$	−12.8506	+	4.17543i	−0.433688	+	0.140914i
$879$		−	1.01561i		−	0.0342558i
$880$	3.32905	−	4.11440i	0.112222	−	0.138696i
$881$			12.4153i			0.418283i	0.977885	+	0.209141i	$0.0670669\pi$
$881$			12.4153i			0.418283i	−0.977885	+	0.209141i	$0.932933\pi$
$882$	6.30325	+	19.3994i	0.212241	+	0.653212i
$883$	14.6500	+	10.6439i	0.493013	+	0.358195i	0.806342	−	0.591450i	$-0.201444\pi$
$883$	14.6500	+	10.6439i	0.493013	+	0.358195i	−0.313329	+	0.949645i	$0.601444\pi$
$884$	0.179021	+	0.919142i	0.00602112	+	0.0309141i
$885$	−1.11527	+	3.43245i	−0.0374894	+	0.115381i
$886$	3.04536	−	9.37266i	0.102311	−	0.314881i
$887$	1.03093	+	1.41896i	0.0346154	+	0.0476439i	0.825974	−	0.563708i	$-0.190626\pi$
$887$	1.03093	+	1.41896i	0.0346154	+	0.0476439i	−0.791359	+	0.611352i	$0.790626\pi$
$888$	15.4484	+	11.2240i	0.518416	+	0.376651i
$889$	0.581392	−	0.188906i	0.0194993	−	0.00633570i
$890$		−	5.93571i		−	0.198965i
$891$	−10.3980	+	6.75843i	−0.348345	+	0.226416i
$892$	−0.584156			−0.0195590
$893$	5.18780	+	15.9664i	0.173603	+	0.534295i
$894$	3.91103	−	5.38308i	0.130805	−	0.180037i
$895$	1.14510	+	1.57610i	0.0382765	+	0.0526831i
$896$	7.47750	+	2.42959i	0.249806	+	0.0811668i
$897$	1.75688	−	5.40711i	0.0586604	−	0.180538i
$898$	−26.3214	−	36.2282i	−0.878355	−	1.20895i
$899$	71.0051	+	51.5882i	2.36815	+	1.72056i
$900$	−0.576826	−	1.77529i	−0.0192275	−	0.0591763i
$901$	9.14098	−	19.6221i	0.304530	−	0.653707i
$902$	10.6736	+	4.09232i	0.355392	+	0.136259i
$903$	1.61034			0.0535886
$904$	42.0646	−	13.6676i	1.39905	−	0.454578i
$905$	−2.16860	−	1.57558i	−0.0720868	−	0.0523741i
$906$	4.09351	+	5.63423i	0.135998	+	0.187185i
$907$	−16.4130	−	5.33291i	−0.544985	−	0.177076i	0.0235693	−	0.999722i	$-0.492497\pi$
$907$	−16.4130	−	5.33291i	−0.544985	−	0.177076i	−0.568554	+	0.822646i	$0.692497\pi$
$908$	3.69102	+	1.19929i	0.122491	+	0.0397997i
$909$	−23.2671	+	16.9045i	−0.771720	+	0.560688i
$910$	0.537985	+	0.390869i	0.0178340	+	0.0129572i
$911$	12.0481	−	3.91465i	0.399170	−	0.129698i	−0.102551	−	0.994728i	$-0.532701\pi$
$911$	12.0481	−	3.91465i	0.399170	−	0.129698i	0.501721	+	0.865030i	$0.332701\pi$
$912$		−	12.8605i		−	0.425854i
$913$	−13.1458	+	34.2868i	−0.435061	+	1.13473i
$914$	52.2049			1.72679
$915$	−2.05543	+	0.667848i	−0.0679503	+	0.0220784i
$916$	−1.08328	−	0.787050i	−0.0357926	−	0.0260049i
$917$	−9.22270	+	6.70069i	−0.304561	+	0.221276i
$918$	16.2193	−	17.4062i	0.535317	−	0.574489i
$919$	1.19121	−	3.66618i	0.0392945	−	0.120936i	−0.929485	−	0.368860i	$-0.879748\pi$
$919$	1.19121	−	3.66618i	0.0392945	−	0.120936i	0.968780	+	0.247924i	$0.0797482\pi$
$920$	5.36674	−	3.89916i	0.176936	−	0.128552i
$921$	5.81220	−	7.99981i	0.191519	−	0.263603i
$922$	4.30322	+	13.2440i	0.141719	+	0.436166i
$923$		−	15.5820i		−	0.512888i
$924$	−0.291587	+	0.189524i	−0.00959250	+	0.00623489i
$925$		−	39.5037i		−	1.29887i
$926$	0.511504	+	1.57425i	0.0168091	+	0.0517330i
$927$	−22.5522	−	16.3851i	−0.740712	−	0.538158i
$928$	−4.44471	−	6.11762i	−0.145905	−	0.200821i
$929$	25.9583	+	8.43437i	0.851665	+	0.276723i	0.702143	−	0.712036i	$-0.252227\pi$
$929$	25.9583	+	8.43437i	0.851665	+	0.276723i	0.149522	+	0.988758i	$0.452227\pi$
$930$	4.79352	+	1.55751i	0.157186	+	0.0510727i
$931$	−22.8490	+	16.6007i	−0.748845	+	0.544067i
$932$	1.75162	−	2.41090i	0.0573762	−	0.0789716i
$933$	−3.85365	−	11.8603i	−0.126163	−	0.388290i
$934$	−18.7175			−0.612456
$935$	2.62798	+	5.37759i	0.0859443	+	0.175866i
$936$	9.64779			0.315348
$937$	13.4943	+	41.5313i	0.440840	+	1.35677i	0.886982	+	0.461804i	$0.152798\pi$
$937$	13.4943	+	41.5313i	0.440840	+	1.35677i	−0.446142	+	0.894962i	$0.647202\pi$
$938$	−7.26304	+	9.99672i	−0.237147	+	0.326405i
$939$	−10.4162	+	7.56784i	−0.339921	+	0.246967i
$940$	0.257076	+	0.0835290i	0.00838489	+	0.00272442i
$941$	6.64084	+	2.15774i	0.216485	+	0.0703403i	0.415252	−	0.909707i	$-0.363694\pi$
$941$	6.64084	+	2.15774i	0.216485	+	0.0703403i	−0.198766	+	0.980047i	$0.563694\pi$
$942$	2.06684	+	2.84476i	0.0673412	+	0.0926872i
$943$	10.6364	+	7.72779i	0.346368	+	0.251651i
$944$	11.7188	+	36.0666i	0.381413	+	1.17387i
$945$			1.50607i			0.0489924i
$946$	−2.92859	−	10.9122i	−0.0952165	−	0.354786i
$947$		−	31.4822i		−	1.02303i	−0.859274	−	0.511516i	$-0.829084\pi$
$947$		−	31.4822i		−	1.02303i	0.859274	−	0.511516i	$-0.170916\pi$
$948$	−0.0790436	−	0.243271i	−0.00256722	−	0.00790108i
$949$	−0.450882	+	0.620585i	−0.0146362	+	0.0201451i
$950$	−23.4570	+	17.0425i	−0.761044	+	0.552931i
$951$	2.48311	−	7.64223i	0.0805204	−	0.247816i
$952$	−6.65960	+	7.14692i	−0.215839	+	0.231633i
$953$	31.3440	−	22.7727i	1.01533	−	0.737681i	0.0500106	−	0.998749i	$-0.484074\pi$
$953$	31.3440	−	22.7727i	1.01533	−	0.737681i	0.965321	+	0.261067i	$0.0840745\pi$
$954$	−13.6502	−	9.91744i	−0.441941	−	0.321089i
$955$	6.59219	−	2.14193i	0.213318	−	0.0693113i
$956$	2.66076			0.0860551
$957$	−21.4974	−	1.11802i	−0.694911	−	0.0361404i
$958$		−	39.1719i		−	1.26559i
$959$	−9.23041	+	2.99914i	−0.298065	+	0.0968473i
$960$	−2.39813	−	1.74234i	−0.0773994	−	0.0562339i
$961$	67.8851	−	49.3214i	2.18984	−	1.59101i
$962$	14.6905	+	4.77323i	0.473640	+	0.153895i
$963$	−10.2036	−	3.31536i	−0.328807	−	0.106836i
$964$	−1.80444	−	2.48360i	−0.0581171	−	0.0799913i
$965$	−2.65991	−	1.93254i	−0.0856255	−	0.0622106i
$966$	4.26741	−	1.38656i	0.137302	−	0.0446120i
$967$	−19.0215			−0.611690			−0.305845	−	0.952081i	$-0.598939\pi$
$967$	−19.0215			−0.611690			−0.305845	+	0.952081i	$0.598939\pi$
$968$	23.9854	+	21.5618i	0.770919	+	0.693024i
$969$	13.1837	+	6.14166i	0.423522	+	0.197298i
$970$	1.28797	+	3.96395i	0.0413541	+	0.127275i
$971$	−20.5512	−	14.9313i	−0.659520	−	0.479169i	0.206981	−	0.978345i	$-0.433636\pi$
$971$	−20.5512	−	14.9313i	−0.659520	−	0.479169i	−0.866501	+	0.499176i	$0.833636\pi$
$972$	1.51429	+	2.08425i	0.0485710	+	0.0668523i
$973$	1.23202	−	3.79176i	0.0394967	−	0.121558i
$974$	−6.33949	−	2.05983i	−0.203130	−	0.0660011i
$975$	3.10861	+	4.27864i	0.0995553	+	0.137026i
$976$	−13.3480	+	18.3719i	−0.427258	+	0.588070i
$977$	−4.59730	−	14.1490i	−0.147081	−	0.452667i	0.850192	−	0.526473i	$-0.176486\pi$
$977$	−4.59730	−	14.1490i	−0.147081	−	0.452667i	−0.997273	+	0.0738051i	$0.976486\pi$
$978$	8.48267			0.271246
$979$	33.1465	+	1.72386i	1.05937	+	0.0550948i
$980$			0.454740i			0.0145261i
$981$	37.5633	−	12.2050i	1.19930	−	0.389677i
$982$	15.8362	+	11.5057i	0.505353	+	0.367160i
$983$	−17.4746	−	24.0518i	−0.557355	−	0.767133i	0.433632	−	0.901090i	$-0.357232\pi$
$983$	−17.4746	−	24.0518i	−0.557355	−	0.767133i	−0.990987	+	0.133957i	$0.957232\pi$
$984$	1.82683	−	5.62239i	0.0582371	−	0.179235i
$985$	−0.221528	+	0.681792i	−0.00705846	+	0.0217237i
$986$	−44.9018	+	8.74551i	−1.42997	+	0.278514i
$987$	1.95520	+	1.42054i	0.0622347	+	0.0452161i
$988$	0.312294	+	0.961143i	0.00993540	+	0.0305780i
$989$		−	12.9945i		−	0.413200i
$990$	4.50584	−	1.20927i	0.143205	−	0.0384330i
$991$		−	16.7200i		−	0.531128i	−0.964093	−	0.265564i	$-0.914442\pi$
$991$		−	16.7200i		−	0.531128i	0.964093	−	0.265564i	$-0.0855581\pi$
$992$	−9.41585	+	3.05940i	−0.298954	+	0.0971359i
$993$	2.37678	−	3.27135i	0.0754247	−	0.103813i
$994$	9.94902	−	7.22838i	0.315564	−	0.229270i
$995$	−1.34523	+	4.14018i	−0.0426466	+	0.131253i
$996$	1.36636	+	0.443956i	0.0432947	+	0.0140673i
$997$	19.1481	+	26.3550i	0.606425	+	0.834673i	0.996277	−	0.0862048i	$-0.0274739\pi$
$997$	19.1481	+	26.3550i	0.606425	+	0.834673i	−0.389852	+	0.920877i	$0.627474\pi$
$998$	2.54815	−	3.50723i	0.0806603	−	0.111019i
$999$	10.8105	+	33.2712i	0.342028	+	1.05265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.j.a.16.12	yes	64
11.9	even	5	inner	187.2.j.a.152.11	yes	64
17.16	even	2	inner	187.2.j.a.16.11	✓	64
187.152	even	10	inner	187.2.j.a.152.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.j.a.16.11	✓	64	17.16	even	2	inner
187.2.j.a.16.12	yes	64	1.1	even	1	trivial
187.2.j.a.152.11	yes	64	11.9	even	5	inner
187.2.j.a.152.12	yes	64	187.152	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.418751 + 1.28878i) q^{2} +(0.465953 - 0.641330i) q^{3} +(0.132428 - 0.0962145i) q^{4} +(-0.416272 - 0.135255i) q^{5} +(1.02165 + 0.331955i) q^{6} +(-0.474970 - 0.653740i) q^{7} +(2.37206 + 1.72340i) q^{8} +(0.732860 + 2.25551i) q^{9} -0.593122i q^{10} +(3.31215 + 0.172256i) q^{11} -0.129761i q^{12} +(-0.428750 - 1.31956i) q^{13} +(0.643634 - 0.885886i) q^{14} +(-0.280707 + 0.203945i) q^{15} +(-1.12662 + 3.46739i) q^{16} +(-3.01650 - 2.81082i) q^{17} +(-2.59997 + 1.88899i) q^{18} +(-3.59995 - 2.61551i) q^{19} +(-0.0681395 + 0.0221399i) q^{20} -0.640577 q^{21} +(1.16496 + 4.34077i) q^{22} +5.16908i q^{23} +(2.21054 - 0.718248i) q^{24} +(-3.89010 - 2.82632i) q^{25} +(1.52108 - 1.10513i) q^{26} +(4.04979 + 1.31586i) q^{27} +(-0.125798 - 0.0408744i) q^{28} +(-4.81250 - 6.62383i) q^{29} +(-0.380387 - 0.276367i) q^{30} +(-10.1950 + 3.31255i) q^{31} +0.923577 q^{32} +(1.65378 - 2.04392i) q^{33} +(2.35937 - 5.06465i) q^{34} +(0.109295 + 0.336376i) q^{35} +(0.314064 + 0.228181i) q^{36} +(4.82897 + 6.64650i) q^{37} +(1.86335 - 5.73479i) q^{38} +(-1.04605 - 0.339882i) q^{39} +(-0.754324 - 1.03824i) q^{40} +(1.49500 - 2.05769i) q^{41} +(-0.268242 - 0.825563i) q^{42} -2.51389 q^{43} +(0.455194 - 0.295865i) q^{44} -1.03803i q^{45} +(-6.66182 + 2.16456i) q^{46} +(-3.05225 - 2.21759i) q^{47} +(1.69879 + 2.33818i) q^{48} +(1.96134 - 6.03638i) q^{49} +(2.01353 - 6.19701i) q^{50} +(-3.20821 + 0.624862i) q^{51} +(-0.183739 - 0.133494i) q^{52} +(1.62238 + 4.99316i) q^{53} +5.77031i q^{54} +(-1.35546 - 0.519690i) q^{55} -2.36927i q^{56} +(-3.35482 + 1.09005i) q^{57} +(6.52144 - 8.97599i) q^{58} +(8.41513 - 6.11395i) q^{59} +(-0.0175509 + 0.0540161i) q^{60} +(5.92389 + 1.92479i) q^{61} +(-8.53831 - 11.7520i) q^{62} +(1.12643 - 1.55040i) q^{63} +(2.63999 + 8.12506i) q^{64} +0.607285i q^{65} +(3.32668 + 1.27547i) q^{66} -11.2844 q^{67} +(-0.669911 - 0.0819997i) q^{68} +(3.31509 + 2.40855i) q^{69} +(-0.387748 + 0.281715i) q^{70} +(10.6809 + 3.47044i) q^{71} +(-2.14876 + 6.61322i) q^{72} +(-0.324968 - 0.447281i) q^{73} +(-6.54376 + 9.00671i) q^{74} +(-3.62521 + 1.17790i) q^{75} -0.728384 q^{76} +(-1.46056 - 2.24710i) q^{77} -1.49045i q^{78} +(1.87476 - 0.609146i) q^{79} +(0.937963 - 1.29100i) q^{80} +(-3.02504 + 2.19782i) q^{81} +(3.27795 + 1.06507i) q^{82} +(-3.42133 + 10.5298i) q^{83} +(-0.0848302 + 0.0616327i) q^{84} +(0.875509 + 1.57806i) q^{85} +(-1.05269 - 3.23985i) q^{86} -6.49046 q^{87} +(7.55975 + 6.11677i) q^{88} +10.0076 q^{89} +(1.33779 - 0.434675i) q^{90} +(-0.659003 + 0.907040i) q^{91} +(0.497341 + 0.684531i) q^{92} +(-2.62595 + 8.08184i) q^{93} +(1.57986 - 4.86230i) q^{94} +(1.14480 + 1.57568i) q^{95} +(0.430344 - 0.592317i) q^{96} +(-6.68319 + 2.17150i) q^{97} +8.60089 q^{98} +(2.03882 + 7.59682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

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