LMFDB - Embedded newform 192.2.r.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

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("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.3
Character	$\chi$	$=$	192.37
Dual form			192.2.r.a.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27221 + 0.617652i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.23701 - 1.57156i) q^{4} +(-0.108368 + 0.544803i) q^{5} +(-0.193240 + 1.40095i) q^{6} +(0.796770 - 1.92357i) q^{7} +(-0.603056 + 2.76339i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(-1.27221 + 0.617652i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.23701 - 1.57156i) q^{4} +(-0.108368 + 0.544803i) q^{5} +(-0.193240 + 1.40095i) q^{6} +(0.796770 - 1.92357i) q^{7} +(-0.603056 + 2.76339i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-0.198632 - 0.760034i) q^{10} +(2.39842 - 1.60257i) q^{11} +(-0.619458 - 1.90165i) q^{12} +(-0.531254 - 2.67079i) q^{13} +(0.174444 + 2.93931i) q^{14} +(0.392781 + 0.392781i) q^{15} +(-0.939603 - 3.88808i) q^{16} +(-0.676832 + 0.676832i) q^{17} +(1.05749 + 0.938999i) q^{18} +(4.60425 - 0.915842i) q^{19} +(0.722137 + 0.844234i) q^{20} +(-1.15673 - 1.73117i) q^{21} +(-2.06145 + 3.52019i) q^{22} +(2.60094 - 1.07735i) q^{23} +(1.96264 + 2.03668i) q^{24} +(4.33433 + 1.79534i) q^{25} +(2.32548 + 3.06967i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-2.03740 - 3.63166i) q^{28} +(-2.22114 - 1.48412i) q^{29} +(-0.742299 - 0.257096i) q^{30} +7.62911i q^{31} +(3.59685 + 4.36608i) q^{32} -2.88455i q^{33} +(0.443022 - 1.27912i) q^{34} +(0.961624 + 0.642536i) q^{35} +(-1.92532 - 0.541440i) q^{36} +(-10.2826 - 2.04534i) q^{37} +(-5.29188 + 4.00896i) q^{38} +(-2.51583 - 1.04209i) q^{39} +(-1.44015 - 0.628009i) q^{40} +(-5.30103 + 2.19576i) q^{41} +(2.54086 + 1.48795i) q^{42} +(-0.0728853 - 0.109081i) q^{43} +(0.448334 - 5.75166i) q^{44} +(0.544803 - 0.108368i) q^{45} +(-2.64351 + 2.97708i) q^{46} +(-0.682968 + 0.682968i) q^{47} +(-3.75483 - 1.37885i) q^{48} +(1.88445 + 1.88445i) q^{49} +(-6.62305 + 0.393069i) q^{50} +(0.186737 + 0.938792i) q^{51} +(-4.85448 - 2.46890i) q^{52} +(-10.3647 + 6.92544i) q^{53} +(1.36826 - 0.357589i) q^{54} +(0.613173 + 1.48033i) q^{55} +(4.83509 + 3.36181i) q^{56} +(1.79649 - 4.33711i) q^{57} +(3.74241 + 0.516211i) q^{58} +(1.21458 - 6.10609i) q^{59} +(1.10315 - 0.131404i) q^{60} +(-0.771532 + 1.15468i) q^{61} +(-4.71214 - 9.70580i) q^{62} -2.08206 q^{63} +(-7.27265 - 3.33296i) q^{64} +1.51263 q^{65} +(1.78165 + 3.66974i) q^{66} +(-5.47173 + 8.18903i) q^{67} +(0.226433 + 1.90093i) q^{68} +(0.549226 - 2.76114i) q^{69} +(-1.62025 - 0.223489i) q^{70} +(-1.40681 + 3.39634i) q^{71} +(2.78382 - 0.500353i) q^{72} +(4.16035 + 10.0440i) q^{73} +(14.3449 - 3.74899i) q^{74} +(3.90080 - 2.60643i) q^{75} +(4.25621 - 8.36876i) q^{76} +(-1.17168 - 5.89041i) q^{77} +(3.84430 - 0.228154i) q^{78} +(8.78791 + 8.78791i) q^{79} +(2.22006 - 0.0905551i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(5.38778 - 6.06765i) q^{82} +(17.2415 - 3.42954i) q^{83} +(-4.15153 - 0.323606i) q^{84} +(-0.295393 - 0.442086i) q^{85} +(0.160099 + 0.0937551i) q^{86} +(-2.46800 + 1.02228i) q^{87} +(2.98215 + 7.59420i) q^{88} +(4.29996 + 1.78110i) q^{89} +(-0.626167 + 0.474365i) q^{90} +(-5.56075 - 1.10610i) q^{91} +(1.52428 - 5.42023i) q^{92} +(6.34338 + 4.23851i) q^{93} +(0.447039 - 1.29071i) q^{94} +2.60765i q^{95} +(5.62857 - 0.565002i) q^{96} +1.62903i q^{97} +(-3.56135 - 1.23347i) q^{98} +(-2.39842 - 1.60257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	−1.27221	+	0.617652i	−0.899585	+	0.436746i
$2$	−1.27221	+	0.617652i	−0.899585	+	0.436746i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$4$	1.23701	−	1.57156i	0.618506	−	0.785780i
$5$	−0.108368	+	0.544803i	−0.0484636	+	0.243643i	−0.997422	−	0.0717580i	$-0.977139\pi$
$5$	−0.108368	+	0.544803i	−0.0484636	+	0.243643i	0.948958	+	0.315401i	$0.102139\pi$
$6$	−0.193240	+	1.40095i	−0.0788901	+	0.571935i
$7$	0.796770	−	1.92357i	0.301151	−	0.727043i	−0.698781	−	0.715336i	$-0.746274\pi$
$7$	0.796770	−	1.92357i	0.301151	−	0.727043i	0.999931	−	0.0117066i	$-0.00372640\pi$
$8$	−0.603056	+	2.76339i	−0.213212	+	0.977006i
$9$	−0.382683	−	0.923880i	−0.127561	−	0.307960i
$10$	−0.198632	−	0.760034i	−0.0628130	−	0.240344i
$11$	2.39842	−	1.60257i	0.723150	−	0.483193i	−0.138714	−	0.990332i	$-0.544297\pi$
$11$	2.39842	−	1.60257i	0.723150	−	0.483193i	0.861864	+	0.507139i	$0.169297\pi$
$12$	−0.619458	−	1.90165i	−0.178822	−	0.548959i
$13$	−0.531254	−	2.67079i	−0.147343	−	0.740744i	−0.981837	−	0.189727i	$-0.939240\pi$
$13$	−0.531254	−	2.67079i	−0.147343	−	0.740744i	0.834494	−	0.551018i	$-0.185760\pi$
$14$	0.174444	+	2.93931i	0.0466221	+	0.785563i
$15$	0.392781	+	0.392781i	0.101416	+	0.101416i
$16$	−0.939603	−	3.88808i	−0.234901	−	0.972019i
$17$	−0.676832	+	0.676832i	−0.164156	+	0.164156i	−0.784405	−	0.620249i	$-0.787032\pi$
$17$	−0.676832	+	0.676832i	−0.164156	+	0.164156i	0.620249	+	0.784405i	$0.287032\pi$
$18$	1.05749	+	0.938999i	0.249252	+	0.221324i
$19$	4.60425	−	0.915842i	1.05629	−	0.210109i	0.363754	−	0.931495i	$-0.381495\pi$
$19$	4.60425	−	0.915842i	1.05629	−	0.210109i	0.692533	+	0.721387i	$0.256495\pi$
$20$	0.722137	+	0.844234i	0.161475	+	0.188776i
$21$	−1.15673	−	1.73117i	−0.252419	−	0.377772i
$22$	−2.06145	+	3.52019i	−0.439502	+	0.750506i
$23$	2.60094	−	1.07735i	0.542334	−	0.224642i	−0.0946618	−	0.995509i	$-0.530177\pi$
$23$	2.60094	−	1.07735i	0.542334	−	0.224642i	0.636996	+	0.770867i	$0.280177\pi$
$24$	1.96264	+	2.03668i	0.400621	+	0.415735i
$25$	4.33433	+	1.79534i	0.866866	+	0.359068i
$26$	2.32548	+	3.06967i	0.456065	+	0.602011i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	−2.03740	−	3.63166i	−0.385032	−	0.686319i
$29$	−2.22114	−	1.48412i	−0.412455	−	0.275594i	0.331983	−	0.943285i	$-0.392282\pi$
$29$	−2.22114	−	1.48412i	−0.412455	−	0.275594i	−0.744438	+	0.667692i	$0.767282\pi$
$30$	−0.742299	−	0.257096i	−0.135525	−	0.0469391i
$31$			7.62911i			1.37023i	0.728435	+	0.685115i	$0.240248\pi$
$31$			7.62911i			1.37023i	−0.728435	+	0.685115i	$0.759752\pi$
$32$	3.59685	+	4.36608i	0.635839	+	0.771822i
$33$		−	2.88455i		−	0.502136i
$34$	0.443022	−	1.27912i	0.0759777	−	0.219366i
$35$	0.961624	+	0.642536i	0.162544	+	0.108608i
$36$	−1.92532	−	0.541440i	−0.320886	−	0.0902400i
$37$	−10.2826	−	2.04534i	−1.69045	−	0.336252i	−0.746262	−	0.665652i	$-0.768153\pi$
$37$	−10.2826	−	2.04534i	−1.69045	−	0.336252i	−0.944190	+	0.329400i	$0.893153\pi$
$38$	−5.29188	+	4.00896i	−0.858456	+	0.650339i
$39$	−2.51583	−	1.04209i	−0.402855	−	0.166868i
$40$	−1.44015	−	0.628009i	−0.227708	−	0.0992970i
$41$	−5.30103	+	2.19576i	−0.827882	+	0.342920i	−0.756064	−	0.654498i	$-0.772880\pi$
$41$	−5.30103	+	2.19576i	−0.827882	+	0.342920i	−0.0718179	+	0.997418i	$0.522880\pi$
$42$	2.54086	+	1.48795i	0.392063	+	0.229595i
$43$	−0.0728853	−	0.109081i	−0.0111149	−	0.0166346i	0.825871	−	0.563860i	$-0.190684\pi$
$43$	−0.0728853	−	0.109081i	−0.0111149	−	0.0166346i	−0.836985	+	0.547225i	$0.815684\pi$
$44$	0.448334	−	5.75166i	0.0675888	−	0.867095i
$45$	0.544803	−	0.108368i	0.0812144	−	0.0161545i
$46$	−2.64351	+	2.97708i	−0.389764	+	0.438947i
$47$	−0.682968	+	0.682968i	−0.0996212	+	0.0996212i	−0.755161	−	0.655540i	$-0.772441\pi$
$47$	−0.682968	+	0.682968i	−0.0996212	+	0.0996212i	0.655540	+	0.755161i	$0.272441\pi$
$48$	−3.75483	−	1.37885i	−0.541964	−	0.199020i
$49$	1.88445	+	1.88445i	0.269208	+	0.269208i
$50$	−6.62305	+	0.393069i	−0.936641	+	0.0555884i
$51$	0.186737	+	0.938792i	0.0261485	+	0.131457i
$52$	−4.85448	−	2.46890i	−0.673195	−	0.342376i
$53$	−10.3647	+	6.92544i	−1.42370	+	0.951283i	−0.424753	+	0.905309i	$0.639639\pi$
$53$	−10.3647	+	6.92544i	−1.42370	+	0.951283i	−0.998943	+	0.0459737i	$0.985361\pi$
$54$	1.36826	−	0.357589i	0.186196	−	0.0486617i
$55$	0.613173	+	1.48033i	0.0826803	+	0.199608i
$56$	4.83509	+	3.36181i	0.646116	+	0.449241i
$57$	1.79649	−	4.33711i	0.237951	−	0.574464i
$58$	3.74241	+	0.516211i	0.491403	+	0.0677818i
$59$	1.21458	−	6.10609i	0.158125	−	0.794946i	−0.817573	−	0.575825i	$-0.804681\pi$
$59$	1.21458	−	6.10609i	0.158125	−	0.794946i	0.975698	−	0.219121i	$-0.0703189\pi$
$60$	1.10315	−	0.131404i	0.142416	−	0.0169642i
$61$	−0.771532	+	1.15468i	−0.0987845	+	0.147842i	−0.877569	−	0.479450i	$-0.840836\pi$
$61$	−0.771532	+	1.15468i	−0.0987845	+	0.147842i	0.778785	+	0.627291i	$0.215836\pi$
$62$	−4.71214	−	9.70580i	−0.598442	−	1.23264i
$63$	−2.08206			−0.262315
$64$	−7.27265	−	3.33296i	−0.909081	−	0.416619i
$65$	1.51263			0.187618
$66$	1.78165	+	3.66974i	0.219306	+	0.451714i
$67$	−5.47173	+	8.18903i	−0.668479	+	1.00045i	0.329927	+	0.944006i	$0.392976\pi$
$67$	−5.47173	+	8.18903i	−0.668479	+	1.00045i	−0.998406	+	0.0564425i	$0.982024\pi$
$68$	0.226433	+	1.90093i	0.0274590	+	0.230522i
$69$	0.549226	−	2.76114i	0.0661190	−	0.332403i
$70$	−1.62025	−	0.223489i	−0.193656	−	0.0267121i
$71$	−1.40681	+	3.39634i	−0.166958	+	0.403071i	−0.985109	−	0.171932i	$-0.944999\pi$
$71$	−1.40681	+	3.39634i	−0.166958	+	0.403071i	0.818151	+	0.575003i	$0.194999\pi$
$72$	2.78382	−	0.500353i	0.328076	−	0.0589671i
$73$	4.16035	+	10.0440i	0.486932	+	1.17556i	0.956256	+	0.292531i	$0.0944975\pi$
$73$	4.16035	+	10.0440i	0.486932	+	1.17556i	−0.469324	+	0.883026i	$0.655502\pi$
$74$	14.3449	−	3.74899i	1.66756	−	0.435811i
$75$	3.90080	−	2.60643i	0.450425	−	0.300964i
$76$	4.25621	−	8.36876i	0.488221	−	0.959962i
$77$	−1.17168	−	5.89041i	−0.133525	−	0.671275i
$78$	3.84430	−	0.228154i	0.435282	−	0.0258334i
$79$	8.78791	+	8.78791i	0.988717	+	0.988717i	0.999937	−	0.0112205i	$-0.00357166\pi$
$79$	8.78791	+	8.78791i	0.988717	+	0.988717i	−0.0112205	+	0.999937i	$0.503572\pi$
$80$	2.22006	−	0.0905551i	0.248210	−	0.0101244i
$81$	−0.707107	+	0.707107i	−0.0785674	+	0.0785674i
$82$	5.38778	−	6.06765i	0.594981	−	0.670059i
$83$	17.2415	−	3.42954i	1.89250	−	0.376441i	0.894932	−	0.446203i	$-0.147224\pi$
$83$	17.2415	−	3.42954i	1.89250	−	0.376441i	0.997564	+	0.0697620i	$0.0222240\pi$
$84$	−4.15153	−	0.323606i	−0.452969	−	0.0353083i
$85$	−0.295393	−	0.442086i	−0.0320398	−	0.0479510i
$86$	0.160099	+	0.0937551i	0.0172639	+	0.0101099i
$87$	−2.46800	+	1.02228i	−0.264597	+	0.109600i
$88$	2.98215	+	7.59420i	0.317898	+	0.809545i
$89$	4.29996	+	1.78110i	0.455795	+	0.188796i	0.598755	−	0.800932i	$-0.295662\pi$
$89$	4.29996	+	1.78110i	0.455795	+	0.188796i	−0.142960	+	0.989728i	$0.545662\pi$
$90$	−0.626167	+	0.474365i	−0.0660038	+	0.0500024i
$91$	−5.56075	−	1.10610i	−0.582925	−	0.115951i
$92$	1.52428	−	5.42023i	0.158917	−	0.565098i
$93$	6.34338	+	4.23851i	0.657778	+	0.439513i
$94$	0.447039	−	1.29071i	0.0461086	−	0.133127i
$95$			2.60765i			0.267540i
$96$	5.62857	−	0.565002i	0.574463	−	0.0576653i
$97$			1.62903i			0.165403i	0.996574	+	0.0827016i	$0.0263548\pi$
$97$			1.62903i			0.165403i	−0.996574	+	0.0827016i	$0.973645\pi$
$98$	−3.56135	−	1.23347i	−0.359750	−	0.124600i
$99$	−2.39842	−	1.60257i	−0.241050	−	0.161064i
$100$	8.18310	−	4.59081i	0.818310	−	0.459081i
$101$	−1.08125	−	0.215074i	−0.107588	−	0.0214006i	0.141003	−	0.990009i	$-0.454967\pi$
$101$	−1.08125	−	0.215074i	−0.107588	−	0.0214006i	−0.248591	+	0.968609i	$0.579967\pi$
$102$	−0.817415	−	1.07900i	−0.0809362	−	0.106837i
$103$	−4.73798	−	1.96253i	−0.466847	−	0.193374i	0.136844	−	0.990593i	$-0.456304\pi$
$103$	−4.73798	−	1.96253i	−0.466847	−	0.193374i	−0.603691	+	0.797218i	$0.706304\pi$
$104$	7.70082	+	0.142575i	0.755127	+	0.0139807i
$105$	1.06850	−	0.442587i	0.104275	−	0.0431920i
$106$	8.90846	−	15.2123i	0.865266	−	1.47755i
$107$	−10.8231	−	16.1979i	−1.04631	−	1.56591i	−0.803015	−	0.595959i	$-0.796772\pi$
$107$	−10.8231	−	16.1979i	−1.04631	−	1.56591i	−0.243294	−	0.969953i	$-0.578228\pi$
$108$	−1.51984	+	1.30003i	−0.146247	+	0.125096i
$109$	15.4025	−	3.06375i	1.47530	−	0.293454i	0.609073	−	0.793114i	$-0.291542\pi$
$109$	15.4025	−	3.06375i	1.47530	−	0.293454i	0.866222	+	0.499660i	$0.166542\pi$
$110$	−1.69441	−	1.50456i	−0.161556	−	0.143454i
$111$	−7.41336	+	7.41336i	−0.703645	+	0.703645i
$112$	−8.22765	−	1.29051i	−0.777440	−	0.121942i
$113$	−8.40952	−	8.40952i	−0.791101	−	0.791101i	0.190572	−	0.981673i	$-0.438966\pi$
$113$	−8.40952	−	8.40952i	−0.791101	−	0.791101i	−0.981673	+	0.190572i	$0.938966\pi$
$114$	0.393321	+	6.62729i	0.0368379	+	0.620703i
$115$	0.305082	+	1.53375i	0.0284490	+	0.143023i
$116$	−5.07995	+	1.65478i	−0.471662	+	0.153643i
$117$	−2.26419	+	1.51288i	−0.209324	+	0.139866i
$118$	2.22625	+	8.51839i	0.204943	+	0.784181i
$119$	0.762656	+	1.84122i	0.0699126	+	0.168784i
$120$	−1.32227	+	0.848538i	−0.120707	+	0.0774605i
$121$	−1.02535	+	2.47541i	−0.0932134	+	0.225037i
$122$	0.268357	−	1.94553i	0.0242959	−	0.176140i
$123$	−1.11939	+	5.62754i	−0.100932	+	0.507418i
$124$	11.9896	+	9.43731i	1.07670	+	0.847495i
$125$	−2.99084	+	4.47610i	−0.267509	+	0.400355i
$126$	2.64881	−	1.28599i	0.235975	−	0.114565i
$127$	−16.4170			−1.45678			−0.728389	−	0.685164i	$-0.759730\pi$
$127$	−16.4170			−1.45678			−0.728389	+	0.685164i	$0.759730\pi$
$128$	11.3109	−	0.251763i	0.999752	−	0.0222529i
$129$	−0.131190			−0.0115506
$130$	−1.92437	+	0.934276i	−0.168778	+	0.0819414i
$131$	6.24550	−	9.34705i	0.545672	−	0.816655i	−0.451464	−	0.892289i	$-0.649098\pi$
$131$	6.24550	−	9.34705i	0.545672	−	0.816655i	0.997136	+	0.0756341i	$0.0240981\pi$
$132$	−4.53325	−	3.56822i	−0.394568	−	0.310574i
$133$	1.90684	−	9.58633i	0.165344	−	0.831240i
$134$	1.90320	−	13.7977i	0.164411	−	1.19194i
$135$	0.212571	−	0.513193i	0.0182952	−	0.0441686i
$136$	−1.46218	−	2.27852i	−0.125381	−	0.195381i
$137$	7.14431	+	17.2479i	0.610379	+	1.47359i	0.862585	+	0.505912i	$0.168844\pi$
$137$	7.14431	+	17.2479i	0.610379	+	1.47359i	−0.252206	+	0.967674i	$0.581156\pi$
$138$	1.00670	+	3.85197i	0.0856959	+	0.327902i
$139$	−8.27222	+	5.52732i	−0.701640	+	0.468821i	−0.854516	−	0.519424i	$-0.826146\pi$
$139$	−8.27222	+	5.52732i	−0.701640	+	0.468821i	0.152876	+	0.988245i	$0.451146\pi$
$140$	2.19932	−	0.716424i	0.185877	−	0.0605489i
$141$	0.188431	+	0.947305i	0.0158687	+	0.0797774i
$142$	−0.308005	−	5.18976i	−0.0258472	−	0.435515i
$143$	−5.55430	−	5.55430i	−0.464474	−	0.464474i
$144$	−3.23254	+	2.35598i	−0.269379	+	0.196332i
$145$	1.04925	−	1.04925i	0.0871355	−	0.0871355i
$146$	−11.4965	−	10.2083i	−0.951456	−	0.844848i
$147$	2.61381	−	0.519920i	0.215584	−	0.0428822i
$148$	−15.9341	+	13.6296i	−1.30978	+	1.12035i
$149$	7.31402	+	10.9462i	0.599187	+	0.896747i	0.999810	−	0.0194958i	$-0.00620610\pi$
$149$	7.31402	+	10.9462i	0.599187	+	0.896747i	−0.400622	+	0.916243i	$0.631206\pi$
$150$	−3.35275	+	5.72525i	−0.273751	+	0.467464i
$151$	16.7940	−	6.95629i	1.36667	−	0.566095i	0.425789	−	0.904822i	$-0.359996\pi$
$151$	16.7940	−	6.95629i	1.36667	−	0.566095i	0.940885	+	0.338727i	$0.109996\pi$
$152$	−0.245789	+	13.2756i	−0.0199361	+	1.07680i
$153$	0.884323	+	0.366299i	0.0714933	+	0.0296135i
$154$	5.12884	+	6.77013i	0.413294	+	0.545552i
$155$	−4.15636	−	0.826752i	−0.333847	−	0.0664063i
$156$	−4.74982	+	2.66470i	−0.380290	+	0.213347i
$157$	−9.83267	−	6.56998i	−0.784732	−	0.524341i	0.0974552	−	0.995240i	$-0.468930\pi$
$157$	−9.83267	−	6.56998i	−0.784732	−	0.524341i	−0.882187	+	0.470899i	$0.843930\pi$
$158$	−16.6079	−	5.75215i	−1.32125	−	0.457617i
$159$			12.4655i			0.988576i
$160$	−2.76844	+	1.48643i	−0.218864	+	0.117512i
$161$		−	5.86150i		−	0.461951i
$162$	0.462839	−	1.33633i	0.0363641	−	0.104992i
$163$	−11.7295	−	7.83743i	−0.918729	−	0.613875i	0.00372057	−	0.999993i	$-0.498816\pi$
$163$	−11.7295	−	7.83743i	−0.918729	−	0.613875i	−0.922449	+	0.386118i	$0.873816\pi$
$164$	−3.10667	+	11.0471i	−0.242590	+	0.862631i
$165$	1.57151	+	0.312593i	0.122342	+	0.0243353i
$166$	−19.8164	+	15.0123i	−1.53805	+	1.16518i
$167$	−8.29440	−	3.43565i	−0.641840	−	0.265859i	0.0379345	−	0.999280i	$-0.487922\pi$
$167$	−8.29440	−	3.43565i	−0.641840	−	0.265859i	−0.679774	+	0.733422i	$0.737922\pi$
$168$	5.48147	−	2.15251i	0.422905	−	0.166070i
$169$	5.15953	−	2.13715i	0.396887	−	0.164396i
$170$	0.648856	+	0.379975i	0.0497650	+	0.0291427i
$171$	−2.60810	−	3.90329i	−0.199446	−	0.298492i
$172$	−0.261587	−	0.0203903i	−0.0199458	−	0.00155475i
$173$	15.6867	−	3.12028i	1.19264	−	0.237231i	0.441430	−	0.897296i	$-0.354471\pi$
$173$	15.6867	−	3.12028i	1.19264	−	0.237231i	0.751208	+	0.660065i	$0.229471\pi$
$174$	2.50839	−	2.82491i	0.190160	−	0.214156i
$175$	6.90693	−	6.90693i	0.522115	−	0.522115i
$176$	−8.48448	−	7.81945i	−0.639542	−	0.589413i
$177$	−4.40225	−	4.40225i	−0.330893	−	0.330893i
$178$	−6.57053	+	0.389952i	−0.492482	+	0.0292282i
$179$	1.36502	+	6.86243i	0.102026	+	0.512922i	0.997675	+	0.0681583i	$0.0217123\pi$
$179$	1.36502	+	6.86243i	0.102026	+	0.512922i	−0.895648	+	0.444764i	$0.853288\pi$
$180$	0.503620	−	0.990242i	0.0375377	−	0.0738083i
$181$	2.65398	−	1.77333i	0.197269	−	0.131811i	−0.453013	−	0.891504i	$-0.649651\pi$
$181$	2.65398	−	1.77333i	0.197269	−	0.131811i	0.650282	+	0.759693i	$0.274651\pi$
$182$	7.75761	−	2.02742i	0.575032	−	0.150282i
$183$	0.531440	+	1.28301i	0.0392852	+	0.0948429i
$184$	1.40861	+	7.83711i	0.103844	+	0.577760i
$185$	2.22861	−	5.38035i	0.163851	−	0.395571i
$186$	−10.6880	−	1.47425i	−0.783682	−	0.108097i
$187$	−0.538654	+	2.70800i	−0.0393903	+	0.198028i
$188$	0.228486	+	1.91817i	0.0166640	+	0.139897i
$189$	−1.15673	+	1.73117i	−0.0841398	+	0.125924i
$190$	−1.61062	−	3.31747i	−0.116847	−	0.240675i
$191$	−10.9059			−0.789125			−0.394562	−	0.918869i	$-0.629104\pi$
$191$	−10.9059			−0.789125			−0.394562	+	0.918869i	$0.629104\pi$
$192$	−6.81172	+	4.19529i	−0.491593	+	0.302769i
$193$	12.9626			0.933066			0.466533	−	0.884504i	$-0.345503\pi$
$193$	12.9626			0.933066			0.466533	+	0.884504i	$0.345503\pi$
$194$	−1.00617	−	2.07246i	−0.0722392	−	0.148794i
$195$	0.840370	−	1.25770i	0.0601801	−	0.0900659i
$196$	5.29262	−	0.630441i	0.378045	−	0.0450315i
$197$	−1.44648	+	7.27197i	−0.103058	+	0.518106i	0.894426	+	0.447215i	$0.147584\pi$
$197$	−1.44648	+	7.27197i	−0.103058	+	0.518106i	−0.997484	+	0.0708910i	$0.977416\pi$
$198$	4.04111	+	0.557412i	0.287189	+	0.0396135i
$199$	5.39564	−	13.0262i	0.382487	−	0.923404i	−0.608997	−	0.793173i	$-0.708428\pi$
$199$	5.39564	−	13.0262i	0.382487	−	0.923404i	0.991484	−	0.130232i	$-0.0415722\pi$
$200$	−7.57506	+	10.8948i	−0.535638	+	0.770376i
$201$	3.76900	+	9.09916i	0.265844	+	0.641805i
$202$	1.50841	−	0.394217i	0.106131	−	0.0277370i
$203$	−4.62455	+	3.09002i	−0.324579	+	0.216877i
$204$	1.70637	+	0.867828i	0.119469	+	0.0607601i
$205$	−0.621793	−	3.12596i	−0.0434279	−	0.218327i
$206$	7.23984	−	0.429675i	0.504424	−	0.0299369i
$207$	−1.99067	−	1.99067i	−0.138361	−	0.138361i
$208$	−9.88508	+	4.57504i	−0.685407	+	0.317222i
$209$	9.57520	−	9.57520i	0.662331	−	0.662331i
$210$	−1.08599	+	1.22302i	−0.0749401	+	0.0843965i
$211$	−1.70710	+	0.339562i	−0.117521	+	0.0233764i	−0.253501	−	0.967335i	$-0.581582\pi$
$211$	−1.70710	+	0.339562i	−0.117521	+	0.0233764i	0.135979	+	0.990712i	$0.456582\pi$
$212$	−1.93746	+	24.8555i	−0.133065	+	1.70709i
$213$	2.04237	+	3.05662i	0.139941	+	0.209436i
$214$	23.7739	+	13.9222i	1.62515	+	0.951699i
$215$	0.0673258	−	0.0278873i	0.00459158	−	0.00190190i
$216$	1.13058	−	2.59264i	0.0769261	−	0.176407i
$217$	14.6752	+	6.07865i	0.996215	+	0.412646i
$218$	−17.7028	+	13.4111i	−1.19899	+	0.908316i
$219$	10.6626	+	2.12093i	0.720513	+	0.143319i
$220$	3.08493	+	0.867549i	0.207986	+	0.0584901i
$221$	2.16725	+	1.44811i	0.145785	+	0.0974103i
$222$	4.85244	−	14.0102i	0.325674	−	0.940302i
$223$		−	4.10607i		−	0.274963i	−0.990504	−	0.137481i	$-0.956099\pi$
$223$		−	4.10607i		−	0.274963i	0.990504	−	0.137481i	$-0.0439007\pi$
$224$	11.2643	−	3.44003i	0.752631	−	0.229847i
$225$		−	4.69145i		−	0.312763i
$226$	15.8928	+	5.50448i	1.05717	+	0.366153i
$227$	11.4843	+	7.67359i	0.762243	+	0.509314i	0.874891	−	0.484321i	$-0.160933\pi$
$227$	11.4843	+	7.67359i	0.762243	+	0.509314i	−0.112648	+	0.993635i	$0.535933\pi$
$228$	−4.59375	−	8.18834i	−0.304228	−	0.542286i
$229$	−13.6900	−	2.72311i	−0.904659	−	0.179948i	−0.279226	−	0.960225i	$-0.590078\pi$
$229$	−13.6900	−	2.72311i	−0.904659	−	0.179948i	−0.625433	+	0.780278i	$0.715078\pi$
$230$	−1.33545	−	1.76281i	−0.0880570	−	0.116236i
$231$	−5.54865	−	2.29833i	−0.365074	−	0.151219i
$232$	5.44066	−	5.24286i	0.357197	−	0.344211i
$233$	−23.3346	+	9.66550i	−1.52870	+	0.633208i	−0.979311	−	0.202360i	$-0.935139\pi$
$233$	−23.3346	+	9.66550i	−1.52870	+	0.633208i	−0.549387	+	0.835568i	$0.685139\pi$
$234$	1.94608	−	3.32318i	0.127219	−	0.217243i
$235$	−0.298071	−	0.446095i	−0.0194440	−	0.0291000i
$236$	−8.09365	−	9.46209i	−0.526852	−	0.615930i
$237$	12.1892	−	2.42458i	0.791772	−	0.157493i
$238$	−2.10749	−	1.87135i	−0.136608	−	0.121301i
$239$	16.5591	−	16.5591i	1.07112	−	1.07112i	0.0738503	−	0.997269i	$-0.476471\pi$
$239$	16.5591	−	16.5591i	1.07112	−	1.07112i	0.997269	−	0.0738503i	$-0.0235287\pi$
$240$	1.15810	−	1.89622i	0.0747553	−	0.122400i
$241$	−19.4817	−	19.4817i	−1.25493	−	1.25493i	−0.953484	−	0.301445i	$-0.902531\pi$
$241$	−19.4817	−	19.4817i	−1.25493	−	1.25493i	−0.301445	−	0.953484i	$-0.597469\pi$
$242$	−0.224488	−	3.78253i	−0.0144306	−	0.243150i
$243$	0.195090	+	0.980785i	0.0125150	+	0.0629174i
$244$	0.860254	+	2.64086i	0.0550721	+	0.169064i
$245$	−1.23087	+	0.822441i	−0.0786374	+	0.0525438i
$246$	−2.05177	−	7.85078i	−0.130816	−	0.500547i
$247$	−4.89205	−	11.8104i	−0.311273	−	0.751481i
$248$	−21.0822	−	4.60078i	−1.33872	−	0.292150i
$249$	6.72728	−	16.2411i	0.426324	−	1.02924i
$250$	1.04028	−	7.54182i	0.0657933	−	0.476987i
$251$	−5.89441	+	29.6332i	−0.372052	+	1.87043i	0.109460	+	0.993991i	$0.465088\pi$
$251$	−5.89441	+	29.6332i	−0.372052	+	1.87043i	−0.481512	+	0.876440i	$0.659912\pi$
$252$	−2.57554	+	3.27209i	−0.162243	+	0.206122i
$253$	4.51162	−	6.75212i	0.283643	−	0.424502i
$254$	20.8859	−	10.1400i	1.31049	−	0.636242i
$255$	−0.531693			−0.0332959
$256$	−14.2343	+	7.30650i	−0.889643	+	0.456656i
$257$	17.2185			1.07406			0.537031	−	0.843562i	$-0.319546\pi$
$257$	17.2185			1.07406			0.537031	+	0.843562i	$0.319546\pi$
$258$	0.166901	−	0.0810298i	0.0103908	−	0.00504470i
$259$	−12.1273	+	18.1497i	−0.753551	+	1.12777i
$260$	1.87114	−	2.37718i	0.116043	−	0.147427i
$261$	−0.521153	+	2.62001i	−0.0322585	+	0.162175i
$262$	−2.17233	+	15.7489i	−0.134207	+	0.972970i
$263$	3.42451	−	8.26750i	0.211164	−	0.509796i	−0.782438	−	0.622728i	$-0.786024\pi$
$263$	3.42451	−	8.26750i	0.211164	−	0.509796i	0.993603	+	0.112932i	$0.0360243\pi$
$264$	7.97114	+	1.73955i	0.490590	+	0.107062i
$265$	−2.64980	−	6.39719i	−0.162776	−	0.392976i
$266$	3.49512	+	13.3735i	0.214300	+	0.819984i
$267$	3.86986	−	2.58576i	0.236832	−	0.158246i
$268$	6.10095	+	18.7291i	0.372675	+	1.14406i
$269$	−1.33208	−	6.69680i	−0.0812182	−	0.408311i	−0.999911	−	0.0133386i	$-0.995754\pi$
$269$	−1.33208	−	6.69680i	−0.0812182	−	0.408311i	0.918693	−	0.394973i	$-0.129246\pi$
$270$	0.0465401	+	0.784182i	0.00283234	+	0.0477238i
$271$	1.64858	+	1.64858i	0.100144	+	0.100144i	0.755404	−	0.655260i	$-0.227441\pi$
$271$	1.64858	+	1.64858i	0.100144	+	0.100144i	−0.655260	+	0.755404i	$0.727441\pi$
$272$	3.26753	+	1.99562i	0.198123	+	0.121002i
$273$	−4.00908	+	4.00908i	−0.242641	+	0.242641i
$274$	−19.7422	−	17.5301i	−1.19267	−	1.05903i
$275$	13.2727	−	2.64010i	0.800374	−	0.159204i
$276$	−3.65991	−	4.27871i	−0.220300	−	0.257548i
$277$	−0.0147682	−	0.0221021i	−0.000887332	−	0.00132799i	0.831026	−	0.556234i	$-0.187754\pi$
$277$	−0.0147682	−	0.0221021i	−0.000887332	−	0.00132799i	−0.831913	+	0.554906i	$0.812754\pi$
$278$	7.11000	−	12.1412i	0.426429	−	0.728183i
$279$	7.04838	−	2.91954i	0.421976	−	0.174788i
$280$	−2.35549	+	2.26986i	−0.140768	+	0.135650i
$281$	−26.3657	−	10.9210i	−1.57285	−	0.651494i	−0.585586	−	0.810610i	$-0.699136\pi$
$281$	−26.3657	−	10.9210i	−1.57285	−	0.651494i	−0.987260	+	0.159116i	$0.949136\pi$
$282$	−0.824827	−	1.08878i	−0.0491177	−	0.0648360i
$283$	−13.8835	−	2.76160i	−0.825290	−	0.164160i	−0.235662	−	0.971835i	$-0.575726\pi$
$283$	−13.8835	−	2.76160i	−0.825290	−	0.164160i	−0.589628	+	0.807675i	$0.700726\pi$
$284$	3.59731	+	6.41220i	0.213461	+	0.380494i
$285$	2.16818	+	1.44873i	0.128432	+	0.0858156i
$286$	10.4968	+	3.63559i	0.620691	+	0.214977i
$287$			11.9464i			0.705176i
$288$	2.65728	−	4.99388i	0.156582	−	0.294267i
$289$			16.0838i			0.946106i
$290$	−0.686790	+	1.98293i	−0.0403297	+	0.116442i
$291$	1.35449	+	0.905042i	0.0794016	+	0.0530545i
$292$	20.9311	+	5.88627i	1.22490	+	0.344468i
$293$	18.4573	+	3.67138i	1.07829	+	0.214484i	0.702113	−	0.712065i	$-0.252240\pi$
$293$	18.4573	+	3.67138i	1.07829	+	0.214484i	0.376172	+	0.926550i	$0.377240\pi$
$294$	−3.00418	+	2.27587i	−0.175207	+	0.132731i
$295$	3.19499	+	1.32341i	0.186020	+	0.0770519i
$296$	11.8531	−	27.1814i	0.688945	−	1.57989i
$297$	−2.66498	+	1.10387i	−0.154638	+	0.0640530i
$298$	−16.0659	−	9.40829i	−0.930671	−	0.545008i
$299$	−4.25912	−	6.37423i	−0.246312	−	0.368631i
$300$	0.729172	−	9.35452i	0.0420987	−	0.540083i
$301$	−0.267897	+	0.0532881i	−0.0154414	+	0.00307148i
$302$	−17.0688	+	19.2227i	−0.982200	+	1.10614i
$303$	−0.779536	+	0.779536i	−0.0447832	+	0.0447832i
$304$	−7.88703	−	17.0411i	−0.452352	−	0.977377i
$305$	−0.545463	−	0.545463i	−0.0312331	−	0.0312331i
$306$	−1.35129	+	0.0801970i	−0.0772479	+	0.00458456i
$307$	−1.93563	−	9.73104i	−0.110472	−	0.555380i	−0.995889	−	0.0905825i	$-0.971127\pi$
$307$	−1.93563	−	9.73104i	−0.110472	−	0.555380i	0.885417	−	0.464798i	$-0.153873\pi$
$308$	−10.7065	−	5.44515i	−0.610061	−	0.310266i
$309$	−4.26407	+	2.84916i	−0.242574	+	0.162083i
$310$	5.79839	−	1.51539i	0.329326	−	0.0860682i
$311$	11.5916	+	27.9846i	0.657299	+	1.58686i	0.801959	+	0.597379i	$0.203791\pi$
$311$	11.5916	+	27.9846i	0.657299	+	1.58686i	−0.144660	+	0.989481i	$0.546209\pi$
$312$	4.39689	−	6.32378i	0.248925	−	0.358014i
$313$	−0.773213	+	1.86670i	−0.0437046	+	0.105512i	−0.944224	−	0.329303i	$-0.893186\pi$
$313$	−0.773213	+	1.86670i	−0.0437046	+	0.105512i	0.900520	+	0.434815i	$0.143186\pi$
$314$	16.5671	+	2.28519i	0.934937	+	0.128961i
$315$	0.225629	−	1.13431i	0.0127127	−	0.0639113i
$316$	24.6815	−	2.93998i	1.38844	−	0.165387i
$317$	−11.2955	+	16.9049i	−0.634419	+	0.949476i	0.365407	+	0.930848i	$0.380930\pi$
$317$	−11.2955	+	16.9049i	−0.634419	+	0.949476i	−0.999826	+	0.0186279i	$0.994070\pi$
$318$	−7.69932	−	15.8586i	−0.431757	−	0.889308i
$319$	−7.70562			−0.431432
$320$	2.60392	−	3.60097i	0.145564	−	0.201300i
$321$	−19.4811			−1.08733
$322$	3.62037	+	7.45703i	0.201755	+	0.415564i
$323$	−2.49643	+	3.73617i	−0.138905	+	0.207886i
$324$	0.236561	+	1.98596i	0.0131423	+	0.110331i
$325$	2.49235	−	12.5299i	0.138251	−	0.695033i
$326$	19.7632	+	2.72604i	1.09458	+	0.150982i
$327$	6.00977	−	14.5089i	0.332341	−	0.802342i
$328$	−2.87092	−	15.9730i	−0.158520	−	0.881960i
$329$	0.769571	+	1.85791i	0.0424278	+	0.102430i
$330$	−2.19236	+	0.572965i	−0.120685	+	0.0315407i
$331$	11.8874	−	7.94290i	0.653390	−	0.436581i	−0.184194	−	0.982890i	$-0.558967\pi$
$331$	11.8874	−	7.94290i	0.653390	−	0.436581i	0.837584	+	0.546309i	$0.183967\pi$
$332$	15.9382	−	31.3384i	0.874720	−	1.71992i
$333$	2.04534	+	10.2826i	0.112084	+	0.563484i
$334$	12.6742	−	0.752197i	0.693502	−	0.0411584i
$335$	−3.86844	−	3.86844i	−0.211356	−	0.211356i
$336$	−5.64406	+	6.12407i	−0.307909	+	0.334096i
$337$	−20.9053	+	20.9053i	−1.13878	+	1.13878i	−0.150113	+	0.988669i	$0.547964\pi$
$337$	−20.9053	+	20.9053i	−1.13878	+	1.13878i	−0.988669	+	0.150113i	$0.952036\pi$
$338$	−5.24397	+	5.90569i	−0.285234	+	0.321227i
$339$	−11.6643	+	2.32018i	−0.633520	+	0.126015i
$340$	−1.06017	−	0.0826388i	−0.0574958	−	0.00448172i
$341$	12.2262	+	18.2978i	0.662086	+	0.990881i
$342$	5.72891	+	3.35489i	0.309784	+	0.181412i
$343$	18.5914	−	7.70080i	1.00384	−	0.415804i
$344$	0.345386	−	0.135629i	0.0186220	−	0.00731262i
$345$	1.44476	+	0.598439i	0.0777833	+	0.0322189i
$346$	−18.0295	+	13.6586i	−0.969270	+	0.734289i
$347$	−5.39350	−	1.07283i	−0.289538	−	0.0575928i	0.0481842	−	0.998838i	$-0.484657\pi$
$347$	−5.39350	−	1.07283i	−0.289538	−	0.0575928i	−0.337723	+	0.941246i	$0.609657\pi$
$348$	−1.44637	+	5.14317i	−0.0775336	+	0.275703i
$349$	−2.47890	−	1.65635i	−0.132693	−	0.0886624i	0.487452	−	0.873150i	$-0.337926\pi$
$349$	−2.47890	−	1.65635i	−0.132693	−	0.0886624i	−0.620145	+	0.784487i	$0.712926\pi$
$350$	−4.52096	+	13.0531i	−0.241655	+	0.697719i
$351$			2.72312i			0.145349i
$352$	15.6237	+	4.70749i	0.832746	+	0.250910i
$353$		−	22.5962i		−	1.20268i	−0.798995	−	0.601338i	$-0.794635\pi$
$353$		−	22.5962i		−	1.20268i	0.798995	−	0.601338i	$-0.205365\pi$
$354$	8.31962	+	2.88151i	0.442183	+	0.153150i
$355$	−1.69788	−	1.13449i	−0.0901141	−	0.0602123i
$356$	8.11821	−	4.55440i	0.430264	−	0.241383i
$357$	1.95462	+	0.388799i	0.103450	+	0.0205774i
$358$	−5.97518	−	7.88731i	−0.315798	−	0.416857i
$359$	−4.93156	−	2.04272i	−0.260278	−	0.107811i	0.248729	−	0.968573i	$-0.419987\pi$
$359$	−4.93156	−	2.04272i	−0.260278	−	0.107811i	−0.509007	+	0.860763i	$0.669987\pi$
$360$	−0.0290833	+	1.57085i	−0.00153282	+	0.0827913i
$361$	2.80662	−	1.16254i	0.147717	−	0.0611862i
$362$	−2.28111	+	3.89528i	−0.119892	+	0.204732i
$363$	1.48857	+	2.22781i	0.0781298	+	0.116930i
$364$	−8.61703	+	7.37080i	−0.451655	+	0.386335i
$365$	−5.92282	+	1.17812i	−0.310015	+	0.0616658i
$366$	−1.46856	−	1.30401i	−0.0767626	−	0.0681616i
$367$	19.3944	−	19.3944i	1.01238	−	1.01238i	0.0124570	−	0.999922i	$-0.496035\pi$
$367$	19.3944	−	19.3944i	1.01238	−	1.01238i	0.999922	−	0.0124570i	$-0.00396527\pi$
$368$	−6.63265	−	9.10039i	−0.345751	−	0.474390i
$369$	4.05723	+	4.05723i	0.211211	+	0.211211i
$370$	0.487930	+	8.22141i	0.0253663	+	0.427411i
$371$	5.06335	+	25.4552i	0.262876	+	1.32157i
$372$	14.5079	−	4.72591i	0.752200	−	0.245027i
$373$	8.91901	−	5.95949i	0.461809	−	0.308571i	−0.302813	−	0.953050i	$-0.597926\pi$
$373$	8.91901	−	5.95949i	0.461809	−	0.308571i	0.764622	+	0.644479i	$0.222926\pi$
$374$	−0.987321	−	3.77783i	−0.0510531	−	0.195347i
$375$	2.06012	+	4.97358i	0.106384	+	0.256835i
$376$	−1.47544	−	2.29918i	−0.0760900	−	0.118571i
$377$	−2.78378	+	6.72064i	−0.143372	+	0.346131i
$378$	0.402338	−	2.91686i	0.0206941	−	0.150027i
$379$	−4.00989	+	20.1591i	−0.205974	+	1.03550i	0.730003	+	0.683444i	$0.239519\pi$
$379$	−4.00989	+	20.1591i	−0.205974	+	1.03550i	−0.935978	+	0.352060i	$0.885481\pi$
$380$	4.09808	+	3.22570i	0.210227	+	0.165475i
$381$	−9.12082	+	13.6503i	−0.467274	+	0.699325i
$382$	13.8746	−	6.73606i	0.709884	−	0.344647i
$383$	13.6892			0.699488			0.349744	−	0.936845i	$-0.386269\pi$
$383$	13.6892			0.699488			0.349744	+	0.936845i	$0.386269\pi$
$384$	6.07467	−	9.54455i	0.309997	−	0.487068i
$385$	3.33608			0.170023
$386$	−16.4910	+	8.00635i	−0.839372	+	0.407513i
$387$	−0.0728853	+	0.109081i	−0.00370497	+	0.00554488i
$388$	2.56012	+	2.01513i	0.129971	+	0.102303i
$389$	0.0124235	−	0.0624573i	0.000629898	−	0.00316671i	−0.980469	−	0.196673i	$-0.936986\pi$
$389$	0.0124235	−	0.0624573i	0.000629898	−	0.00316671i	0.981099	+	0.193507i	$0.0619861\pi$
$390$	−0.292300	+	2.11911i	−0.0148012	+	0.107305i
$391$	−1.03122	+	2.48958i	−0.0521509	+	0.125904i
$392$	−6.34391	+	4.07105i	−0.320416	+	0.205619i
$393$	−4.30197	−	10.3859i	−0.217006	−	0.523898i
$394$	−2.65132	−	10.1449i	−0.133572	−	0.511091i
$395$	−5.74000	+	3.83535i	−0.288811	+	0.192977i
$396$	−5.48541	+	1.78686i	−0.275652	+	0.0897930i
$397$	6.17909	+	31.0644i	0.310120	+	1.55908i	0.750257	+	0.661146i	$0.229930\pi$
$397$	6.17909	+	31.0644i	0.310120	+	1.55908i	−0.440138	+	0.897930i	$0.645070\pi$
$398$	1.18131	+	19.9047i	0.0592139	+	0.997730i
$399$	−6.91136	−	6.91136i	−0.346001	−	0.346001i
$400$	2.90787	−	18.5391i	0.145393	−	0.926956i
$401$	−4.54843	+	4.54843i	−0.227138	+	0.227138i	−0.811496	−	0.584358i	$-0.801346\pi$
$401$	−4.54843	+	4.54843i	−0.227138	+	0.227138i	0.584358	+	0.811496i	$0.301346\pi$
$402$	−10.4150	−	9.24807i	−0.519455	−	0.461252i
$403$	20.3758	−	4.05299i	1.01499	−	0.201894i
$404$	−1.67552	+	1.43320i	−0.0833601	+	0.0713043i
$405$	−0.308606	−	0.461861i	−0.0153347	−	0.0229501i
$406$	3.97481	−	6.78750i	0.197267	−	0.336858i
$407$	−27.9398	+	11.5731i	−1.38493	+	0.573655i
$408$	−2.70686	−	0.0501157i	−0.134010	−	0.00248110i
$409$	−20.0810	−	8.31781i	−0.992940	−	0.411289i	−0.173736	−	0.984792i	$-0.555584\pi$
$409$	−20.0810	−	8.31781i	−0.992940	−	0.411289i	−0.819203	+	0.573503i	$0.805584\pi$
$410$	2.72181	+	3.59282i	0.134420	+	0.177437i
$411$	18.3103	+	3.64214i	0.903178	+	0.179653i
$412$	−8.94517	+	5.01834i	−0.440697	+	0.247236i
$413$	−10.7778	−	7.20149i	−0.530340	−	0.354362i
$414$	3.76209	+	1.30300i	0.184897	+	0.0640391i
$415$			9.76484i			0.479337i
$416$	9.75007	−	11.9259i	0.478036	−	0.584717i
$417$			9.94891i			0.487200i
$418$	−6.26748	+	18.0958i	−0.306552	+	0.885093i
$419$	−11.1206	−	7.43054i	−0.543276	−	0.363006i	0.253448	−	0.967349i	$-0.418435\pi$
$419$	−11.1206	−	7.43054i	−0.543276	−	0.363006i	−0.796724	+	0.604343i	$0.793435\pi$
$420$	0.626194	−	2.22670i	0.0305551	−	0.108652i
$421$	−35.3436	−	7.03028i	−1.72254	−	0.342635i	−0.767941	−	0.640521i	$-0.778718\pi$
$421$	−35.3436	−	7.03028i	−1.72254	−	0.342635i	−0.954601	+	0.297886i	$0.903718\pi$
$422$	1.96204	−	1.48638i	0.0955108	−	0.0723560i
$423$	0.892341	+	0.369620i	0.0433871	+	0.0179715i
$424$	−12.8872	−	32.8180i	−0.625860	−	1.59378i
$425$	−4.14875	+	1.71847i	−0.201244	+	0.0833581i
$426$	−4.48624	−	2.62718i	−0.217359	−	0.127287i
$427$	1.60638	+	2.40411i	0.0777380	+	0.116343i
$428$	−38.8443	−	3.02786i	−1.87761	−	0.146357i
$429$	−7.70404	+	1.53243i	−0.371954	+	0.0739863i
$430$	−0.0684276	+	0.0770622i	−0.00329987	+	0.00371627i
$431$	−3.33895	+	3.33895i	−0.160831	+	0.160831i	−0.782935	−	0.622104i	$-0.786278\pi$
$431$	−3.33895	+	3.33895i	−0.160831	+	0.160831i	0.622104	+	0.782935i	$0.286278\pi$
$432$	0.163023	+	3.99668i	0.00784342	+	0.192290i
$433$	−21.0806	−	21.0806i	−1.01307	−	1.01307i	−0.999913	−	0.0131539i	$-0.995813\pi$
$433$	−21.0806	−	21.0806i	−1.01307	−	1.01307i	−0.0131539	−	0.999913i	$-0.504187\pi$
$434$	−22.4243	+	1.33085i	−1.07640	+	0.0638830i
$435$	−0.289488	−	1.45535i	−0.0138799	−	0.0697788i
$436$	14.2382	−	27.9959i	0.681888	−	1.34076i
$437$	10.9887	−	7.34241i	0.525661	−	0.351235i
$438$	−14.8750	+	3.88753i	−0.710756	+	0.185754i
$439$	−0.603287	−	1.45646i	−0.0287933	−	0.0695132i	0.908829	−	0.417169i	$-0.136978\pi$
$439$	−0.603287	−	1.45646i	−0.0287933	−	0.0695132i	−0.937622	+	0.347656i	$0.886978\pi$
$440$	−4.46051	+	0.801715i	−0.212646	+	0.0382203i
$441$	1.01986	−	2.46216i	0.0485647	−	0.117246i
$442$	−3.65161	−	0.503686i	−0.173689	−	0.0239579i
$443$	−1.73511	+	8.72300i	−0.0824377	+	0.414442i	0.917426	+	0.397907i	$0.130263\pi$
$443$	−1.73511	+	8.72300i	−0.0824377	+	0.414442i	−0.999863	+	0.0165348i	$0.994737\pi$
$444$	2.48013	+	20.8209i	0.117702	+	0.988118i
$445$	−1.43633	+	2.14961i	−0.0680884	+	0.101902i
$446$	2.53612	+	5.22376i	0.120089	+	0.247352i
$447$	13.1649			0.622677
$448$	−12.2058	+	11.3339i	−0.576671	+	0.535475i
$449$	1.07049			0.0505196			0.0252598	−	0.999681i	$-0.491959\pi$
$449$	1.07049			0.0505196			0.0252598	+	0.999681i	$0.491959\pi$
$450$	2.89768	+	5.96848i	0.136598	+	0.281357i
$451$	−9.19522	+	13.7616i	−0.432986	+	0.648009i
$452$	−23.6188	+	2.81339i	−1.11093	+	0.132331i
$453$	3.54629	−	17.8284i	0.166619	−	0.837651i
$454$	−19.3501	−	2.66906i	−0.908143	−	0.125265i
$455$	1.20522	−	2.90965i	0.0565014	−	0.136406i
$456$	10.9017	+	7.57991i	0.510520	+	0.354962i
$457$	1.44746	+	3.49447i	0.0677093	+	0.163465i	0.954112	−	0.299451i	$-0.0968034\pi$
$457$	1.44746	+	3.49447i	0.0677093	+	0.163465i	−0.886403	+	0.462915i	$0.846803\pi$
$458$	19.0984	−	4.99129i	0.892409	−	0.233228i
$459$	0.795870	−	0.531783i	0.0371480	−	0.0248215i
$460$	2.78777	+	1.41781i	0.129980	+	0.0661058i
$461$	−3.78086	−	19.0076i	−0.176092	−	0.885275i	−0.963267	−	0.268545i	$-0.913457\pi$
$461$	−3.78086	−	19.0076i	−0.176092	−	0.885275i	0.787175	−	0.616730i	$-0.211543\pi$
$462$	8.47859	−	0.503193i	0.394459	−	0.0234106i
$463$	4.11236	+	4.11236i	0.191118	+	0.191118i	0.796179	−	0.605061i	$-0.206851\pi$
$463$	4.11236	+	4.11236i	0.191118	+	0.191118i	−0.605061	+	0.796179i	$0.706851\pi$
$464$	−3.68337	+	10.0304i	−0.170996	+	0.465651i
$465$	−2.99657	+	2.99657i	−0.138963	+	0.138963i
$466$	23.7164	−	26.7091i	1.09864	−	1.23728i
$467$	−6.84555	+	1.36166i	−0.316774	+	0.0630103i	−0.350917	−	0.936407i	$-0.614130\pi$
$467$	−6.84555	+	1.36166i	−0.316774	+	0.0630103i	0.0341426	+	0.999417i	$0.489130\pi$
$468$	−0.423242	+	5.42976i	−0.0195644	+	0.250991i
$469$	11.3925	+	17.0501i	0.526056	+	0.787299i
$470$	0.654739	+	0.383420i	0.0302009	+	0.0176858i
$471$	−10.9255	+	4.52548i	−0.503419	+	0.208523i
$472$	16.1411	+	7.03867i	0.742953	+	0.323981i
$473$	−0.349619	−	0.144817i	−0.0160755	−	0.00665869i
$474$	−14.0096	+	10.6132i	−0.643482	+	0.487482i
$475$	21.6006	+	4.29662i	0.991103	+	0.197143i
$476$	3.83700	+	1.07904i	0.175868	+	0.0494579i
$477$	10.3647	+	6.92544i	0.474565	+	0.317094i
$478$	−10.8388	+	31.2943i	−0.495756	+	1.43137i
$479$		−	32.5847i		−	1.48883i	−0.667715	−	0.744417i	$-0.732728\pi$
$479$		−	32.5847i		−	1.48883i	0.667715	−	0.744417i	$-0.267272\pi$
$480$	−0.302142	+	3.12769i	−0.0137908	+	0.142759i
$481$			28.5493i			1.30174i
$482$	36.8177	+	12.7518i	1.67700	+	0.580830i
$483$	−4.87366	−	3.25648i	−0.221759	−	0.148175i
$484$	2.62188	+	4.67350i	0.119177	+	0.212432i
$485$	−0.887501	−	0.176535i	−0.0402993	−	0.00801604i
$486$	−0.853979	−	1.12726i	−0.0387373	−	0.0511336i
$487$	−9.81243	−	4.06444i	−0.444644	−	0.184177i	0.149116	−	0.988820i	$-0.452357\pi$
$487$	−9.81243	−	4.06444i	−0.444644	−	0.184177i	−0.593760	+	0.804642i	$0.702357\pi$
$488$	−2.72555	−	2.82838i	−0.123380	−	0.128035i
$489$	−13.0332	+	5.39852i	−0.589380	+	0.244129i
$490$	1.05794	−	1.80656i	0.0477927	−	0.0816122i
$491$	−8.36427	−	12.5180i	−0.377474	−	0.564930i	0.593283	−	0.804994i	$-0.297832\pi$
$491$	−8.36427	−	12.5180i	−0.377474	−	0.564930i	−0.970757	+	0.240064i	$0.922832\pi$
$492$	7.45933	+	8.72052i	0.336292	+	0.393151i
$493$	2.50783	−	0.498839i	0.112947	−	0.0224666i
$494$	13.5184	+	12.0037i	0.608223	+	0.540073i
$495$	1.13300	−	1.13300i	0.0509244	−	0.0509244i
$496$	29.6626	−	7.16834i	1.33189	−	0.321868i
$497$	5.41220	+	5.41220i	0.242771	+	0.242771i
$498$	1.47286	+	24.8171i	0.0660006	+	1.11208i
$499$	0.291600	+	1.46597i	0.0130538	+	0.0656259i	0.986763	−	0.162168i	$-0.0518487\pi$
$499$	0.291600	+	1.46597i	0.0130538	+	0.0656259i	−0.973709	+	0.227794i	$0.926849\pi$
$500$	3.33477	+	10.2373i	0.149135	+	0.457825i
$501$	−7.46476	+	4.98779i	−0.333501	+	0.222838i
$502$	−10.8041	−	41.3402i	−0.482211	−	1.84510i
$503$	11.7573	+	28.3846i	0.524231	+	1.26561i	0.935253	+	0.353980i	$0.115172\pi$
$503$	11.7573	+	28.3846i	0.524231	+	1.26561i	−0.411022	+	0.911625i	$0.634828\pi$
$504$	1.25560	−	5.75355i	0.0559288	−	0.256283i
$505$	0.234345	−	0.565760i	0.0104282	−	0.0251760i
$506$	−1.56925	+	11.3767i	−0.0697616	+	0.505756i
$507$	1.08951	−	5.47733i	0.0483868	−	0.243257i
$508$	−20.3081	+	25.8004i	−0.901025	+	1.14471i
$509$	23.4657	−	35.1189i	1.04010	−	1.55662i	0.227516	−	0.973774i	$-0.426940\pi$
$509$	23.4657	−	35.1189i	1.04010	−	1.55662i	0.812584	−	0.582844i	$-0.198060\pi$
$510$	0.676422	−	0.328401i	0.0299525	−	0.0145418i
$511$	22.6351			1.00132
$512$	13.5961	−	18.0872i	0.600867	−	0.799349i
$513$	−4.69445			−0.207265
$514$	−21.9055	+	10.6351i	−0.966210	+	0.469092i
$515$	1.58264	−	2.36859i	0.0697394	−	0.104372i
$516$	−0.162284	+	0.206173i	−0.00714414	+	0.00907627i
$517$	−0.543538	+	2.73255i	−0.0239048	+	0.120177i
$518$	4.21814	−	30.5806i	0.185335	−	1.34363i
$519$	6.12065	−	14.7766i	0.268667	−	0.648619i
$520$	−0.912197	+	4.17997i	−0.0400025	+	0.183304i
$521$	−10.5955	−	25.5799i	−0.464199	−	1.12068i	−0.966657	−	0.256075i	$-0.917571\pi$
$521$	−10.5955	−	25.5799i	−0.464199	−	1.12068i	0.502458	−	0.864602i	$-0.332429\pi$
$522$	−0.955242	−	3.65508i	−0.0418098	−	0.159979i
$523$	15.7045	−	10.4934i	0.686710	−	0.458845i	−0.162633	−	0.986687i	$-0.551999\pi$
$523$	15.7045	−	10.4934i	0.686710	−	0.458845i	0.849343	+	0.527842i	$0.176999\pi$
$524$	−6.96369	−	21.3776i	−0.304210	−	0.933884i
$525$	−1.90562	−	9.58019i	−0.0831680	−	0.418114i
$526$	0.749758	+	12.6331i	0.0326910	+	0.550830i
$527$	−5.16363	−	5.16363i	−0.224931	−	0.224931i
$528$	−11.2154	+	2.71033i	−0.488086	+	0.117952i
$529$	−10.6592	+	10.6592i	−0.463445	+	0.463445i
$530$	7.32233	+	6.50188i	0.318062	+	0.282424i
$531$	−6.10609	+	1.21458i	−0.264982	+	0.0527082i
$532$	−12.7067	−	14.8551i	−0.550906	−	0.644051i
$533$	8.68060	+	12.9914i	0.375999	+	0.562722i
$534$	−3.32616	+	5.67984i	−0.143937	+	0.245791i
$535$	9.99754	−	4.14112i	0.432231	−	0.179036i
$536$	−19.3297	−	20.0590i	−0.834917	−	0.866416i
$537$	6.46426	+	2.67759i	0.278954	+	0.115546i
$538$	5.83097	+	7.69695i	0.251391	+	0.331839i
$539$	7.53968	+	1.49973i	0.324757	+	0.0645982i
$540$	−0.543560	−	0.968894i	−0.0233911	−	0.0416946i
$541$	−15.2245	−	10.1727i	−0.654554	−	0.437359i	0.183446	−	0.983030i	$-0.441275\pi$
$541$	−15.2245	−	10.1727i	−0.654554	−	0.437359i	−0.838000	+	0.545671i	$0.816275\pi$
$542$	−3.11558	−	1.07908i	−0.133826	−	0.0463506i
$543$		−	3.19192i		−	0.136978i
$544$	−5.38956	−	0.520644i	−0.231076	−	0.0223224i
$545$			8.72335i			0.373667i
$546$	2.62416	−	7.57659i	0.112304	−	0.324248i
$547$	−15.3353	−	10.2467i	−0.655690	−	0.438118i	0.182715	−	0.983166i	$-0.441511\pi$
$547$	−15.3353	−	10.2467i	−0.655690	−	0.438118i	−0.838405	+	0.545048i	$0.816511\pi$
$548$	35.9437	+	10.1081i	1.53544	+	0.431798i
$549$	1.36204	+	0.270926i	0.0581303	+	0.0115628i
$550$	−15.2549	+	11.5567i	−0.650472	+	0.492778i
$551$	−11.5859	−	4.79903i	−0.493575	−	0.204446i
$552$	7.29891	+	3.18285i	0.310662	+	0.135471i
$553$	23.9061	−	9.90224i	1.01659	−	0.421086i
$554$	0.0324395	+	0.0189968i	0.00137822	+	0.000807098i
$555$	−3.23545	−	4.84219i	−0.137337	−	0.205539i
$556$	−1.54632	+	19.8376i	−0.0655784	+	0.841304i
$557$	6.09288	−	1.21195i	0.258164	−	0.0513519i	−0.0643115	−	0.997930i	$-0.520485\pi$
$557$	6.09288	−	1.21195i	0.258164	−	0.0513519i	0.322475	+	0.946578i	$0.395485\pi$
$558$	−7.16373	+	8.06770i	−0.303265	+	0.341533i
$559$	−0.252611	+	0.252611i	−0.0106843	+	0.0106843i
$560$	1.59469	−	4.34260i	0.0673878	−	0.183508i
$561$	1.95236	+	1.95236i	0.0824285	+	0.0824285i
$562$	40.2880	−	2.39104i	1.69945	−	0.100860i
$563$	−4.63282	−	23.2908i	−0.195250	−	0.981588i	−0.946778	−	0.321887i	$-0.895683\pi$
$563$	−4.63282	−	23.2908i	−0.195250	−	0.981588i	0.751528	−	0.659701i	$-0.229317\pi$
$564$	1.72184	+	0.875697i	0.0725024	+	0.0368735i
$565$	5.49285	−	3.67021i	0.231086	−	0.154407i
$566$	19.3684	−	5.06186i	0.814115	−	0.212766i
$567$	0.796770	+	1.92357i	0.0334612	+	0.0807825i
$568$	−8.53702	−	5.93574i	−0.358206	−	0.249058i
$569$	14.7599	−	35.6336i	0.618768	−	1.49384i	−0.234366	−	0.972148i	$-0.575301\pi$
$569$	14.7599	−	35.6336i	0.618768	−	1.49384i	0.853135	−	0.521691i	$-0.174699\pi$
$570$	−3.65319	−	0.503904i	−0.153015	−	0.0211062i
$571$	3.77661	−	18.9863i	0.158046	−	0.794552i	−0.817700	−	0.575645i	$-0.804751\pi$
$571$	3.77661	−	18.9863i	0.158046	−	0.794552i	0.975746	−	0.218907i	$-0.0702490\pi$
$572$	−15.5997	+	1.85818i	−0.652254	+	0.0776945i
$573$	−6.05900	+	9.06794i	−0.253118	+	0.378819i
$574$	−7.37874	−	15.1983i	−0.307983	−	0.634366i
$575$	13.2075			0.550793
$576$	−0.296127	+	7.99452i	−0.0123386	+	0.333105i
$577$	36.5879			1.52318			0.761588	−	0.648062i	$-0.224420\pi$
$577$	36.5879			1.52318			0.761588	+	0.648062i	$0.224420\pi$
$578$	−9.93419	−	20.4619i	−0.413208	−	0.851102i
$579$	7.20161	−	10.7780i	0.299289	−	0.447917i
$580$	−0.351025	−	2.94690i	−0.0145755	−	0.122363i
$581$	7.14051	−	35.8978i	0.296238	−	1.48929i
$582$	−2.28219	−	0.314795i	−0.0945999	−	0.0130487i
$583$	−13.7603	+	33.2202i	−0.569892	+	1.37584i
$584$	−30.2643	+	5.43959i	−1.25235	+	0.225092i
$585$	−0.578857	−	1.39748i	−0.0239328	−	0.0577788i
$586$	−25.7491	+	6.72942i	−1.06368	+	0.277990i
$587$	12.2710	−	8.19922i	0.506478	−	0.338418i	−0.275936	−	0.961176i	$-0.588988\pi$
$587$	12.2710	−	8.19922i	0.506478	−	0.338418i	0.782415	+	0.622758i	$0.213988\pi$
$588$	2.41623	−	4.75091i	0.0996437	−	0.195924i
$589$	6.98706	+	35.1263i	0.287897	+	1.44736i
$590$	−4.88209	+	0.289746i	−0.200993	+	0.0119286i
$591$	5.24280	+	5.24280i	0.215660	+	0.215660i
$592$	1.70914	+	41.9014i	0.0702452	+	1.72214i
$593$	23.9334	−	23.9334i	0.982828	−	0.982828i	−0.0170268	−	0.999855i	$-0.505420\pi$
$593$	23.9334	−	23.9334i	0.982828	−	0.982828i	0.999855	+	0.0170268i	$0.00542006\pi$
$594$	2.70859	−	3.05038i	0.111135	−	0.125159i
$595$	−1.08575	+	0.215968i	−0.0445113	+	0.00885384i
$596$	26.2501	+	2.04616i	1.07525	+	0.0838140i
$597$	−7.83325	−	11.7233i	−0.320594	−	0.479802i
$598$	9.35554	+	5.47867i	0.382576	+	0.224040i
$599$	−6.48478	+	2.68609i	−0.264961	+	0.109750i	−0.511209	−	0.859456i	$-0.670802\pi$
$599$	−6.48478	+	2.68609i	−0.264961	+	0.109750i	0.246248	+	0.969207i	$0.420802\pi$
$600$	4.85018	+	12.3512i	0.198008	+	0.504237i
$601$	−10.2410	−	4.24195i	−0.417738	−	0.173033i	0.163907	−	0.986476i	$-0.447590\pi$
$601$	−10.2410	−	4.24195i	−0.417738	−	0.173033i	−0.581644	+	0.813443i	$0.697590\pi$
$602$	0.307907	−	0.233261i	0.0125494	−	0.00950700i
$603$	9.65962	+	1.92142i	0.393370	+	0.0782462i
$604$	9.84211	−	34.9978i	0.400470	−	1.42404i
$605$	−1.23749	−	0.826866i	−0.0503112	−	0.0336169i
$606$	0.510248	−	1.47321i	0.0207274	−	0.0598452i
$607$			5.48744i			0.222728i	0.993780	+	0.111364i	$0.0355220\pi$
$607$			5.48744i			0.222728i	−0.993780	+	0.111364i	$0.964478\pi$
$608$	20.5594	+	16.8084i	0.833794	+	0.681670i
$609$			5.56189i			0.225379i
$610$	1.03085	+	0.357034i	0.0417378	+	0.0144559i
$611$	2.18690	+	1.46124i	0.0884724	+	0.0591153i
$612$	1.66958	−	0.936651i	0.0674887	−	0.0378619i
$613$	21.1553	+	4.20805i	0.854453	+	0.169961i	0.602836	−	0.797865i	$-0.294037\pi$
$613$	21.1553	+	4.20805i	0.854453	+	0.169961i	0.251618	+	0.967827i	$0.419037\pi$
$614$	8.47291	+	11.1843i	0.341939	+	0.451363i
$615$	−2.94459	−	1.21969i	−0.118737	−	0.0491827i
$616$	16.9841	+	0.314449i	0.684309	+	0.0126695i
$617$	−4.08264	+	1.69108i	−0.164361	+	0.0680804i	−0.463347	−	0.886177i	$-0.653352\pi$
$617$	−4.08264	+	1.69108i	−0.164361	+	0.0680804i	0.298986	+	0.954257i	$0.403352\pi$
$618$	3.66498	−	6.25842i	0.147427	−	0.251751i
$619$	24.8506	+	37.1915i	0.998829	+	1.49485i	0.863688	+	0.504027i	$0.168149\pi$
$619$	24.8506	+	37.1915i	0.998829	+	1.49485i	0.135141	+	0.990826i	$0.456851\pi$
$620$	−6.44076	+	5.50927i	−0.258667	+	0.221258i
$621$	−2.76114	+	0.549226i	−0.110801	+	0.0220397i
$622$	−32.0316	−	28.4426i	−1.28435	−	1.14044i
$623$	6.85216	−	6.85216i	0.274526	−	0.274526i
$624$	−1.68785	+	10.7609i	−0.0675681	+	0.430781i
$625$	14.4723	+	14.4723i	0.578891	+	0.578891i
$626$	−0.169286	−	2.85240i	−0.00676604	−	0.114005i
$627$	−2.64179	−	13.2812i	−0.105503	−	0.530400i
$628$	−22.4882	+	7.32549i	−0.897378	+	0.292319i
$629$	8.34395	−	5.57525i	0.332695	−	0.222300i
$630$	0.413564	+	1.58244i	0.0164768	+	0.0630458i
$631$	−2.71634	−	6.55782i	−0.108136	−	0.261063i	0.860544	−	0.509376i	$-0.170124\pi$
$631$	−2.71634	−	6.55782i	−0.108136	−	0.261063i	−0.968680	+	0.248313i	$0.920124\pi$
$632$	−29.5840	+	18.9848i	−1.17679	+	0.755175i
$633$	−0.666075	+	1.60805i	−0.0264741	+	0.0639142i
$634$	3.92885	−	28.4832i	0.156034	−	1.13121i
$635$	1.77908	−	8.94405i	0.0706007	−	0.354934i
$636$	19.5902	+	15.4199i	0.776804	+	0.611440i
$637$	4.03186	−	6.03411i	0.159748	−	0.239080i
$638$	9.80313	−	4.75939i	0.388109	−	0.188426i
$639$	3.67617			0.145427
$640$	−1.08858	+	6.18949i	−0.0430299	+	0.244661i
$641$	6.68514			0.264047			0.132024	−	0.991247i	$-0.457853\pi$
$641$	6.68514			0.264047			0.132024	+	0.991247i	$0.457853\pi$
$642$	24.7839	−	12.0325i	0.978143	−	0.474886i
$643$	−0.406258	+	0.608007i	−0.0160212	+	0.0239775i	−0.839394	−	0.543524i	$-0.817090\pi$
$643$	−0.406258	+	0.608007i	−0.0160212	+	0.0239775i	0.823373	+	0.567501i	$0.192090\pi$
$644$	−9.21170	−	7.25075i	−0.362992	−	0.285719i
$645$	0.0142168	−	0.0714727i	0.000559786	−	0.00281423i
$646$	0.868317	−	6.29510i	0.0341635	−	0.247677i
$647$	−9.19100	+	22.1890i	−0.361336	+	0.872341i	0.633770	+	0.773522i	$0.281507\pi$
$647$	−9.19100	+	22.1890i	−0.361336	+	0.872341i	−0.995105	+	0.0988197i	$0.968493\pi$
$648$	−1.52759	−	2.38044i	−0.0600093	−	0.0935124i
$649$	−6.87239	−	16.5914i	−0.269765	−	0.651270i
$650$	4.56833	+	17.4800i	0.179185	+	0.685621i
$651$	13.2073	−	8.82484i	0.517635	−	0.345873i
$652$	−26.8266	+	8.73869i	−1.05061	+	0.342233i
$653$	−6.40052	−	32.1776i	−0.250472	−	1.25921i	−0.877259	−	0.480017i	$-0.840631\pi$
$653$	−6.40052	−	32.1776i	−0.250472	−	1.25921i	0.626788	−	0.779190i	$-0.284369\pi$
$654$	1.31577	+	22.1702i	0.0514507	+	0.866924i
$655$	4.41548	+	4.41548i	0.172527	+	0.172527i
$656$	13.5181	+	18.5477i	0.527795	+	0.724165i
$657$	7.68732	−	7.68732i	0.299911	−	0.299911i
$658$	−2.12659	−	1.88831i	−0.0829033	−	0.0736142i
$659$	−29.2554	+	5.81927i	−1.13963	+	0.226687i	−0.728603	−	0.684936i	$-0.759830\pi$
$659$	−29.2554	+	5.81927i	−1.13963	+	0.226687i	−0.411027	+	0.911623i	$0.634830\pi$
$660$	2.43524	−	2.08304i	0.0947915	−	0.0810823i
$661$	2.64175	+	3.95366i	0.102752	+	0.153780i	0.879283	−	0.476300i	$-0.158022\pi$
$661$	2.64175	+	3.95366i	0.102752	+	0.153780i	−0.776531	+	0.630079i	$0.783022\pi$
$662$	−10.2173	+	17.4473i	−0.397105	+	0.678107i
$663$	2.40811	−	0.997474i	0.0935234	−	0.0387387i
$664$	−0.920403	+	49.7131i	−0.0357186	+	1.92924i
$665$	5.01601	+	2.07770i	0.194513	+	0.0805698i
$666$	−8.95317	−	11.8183i	−0.346928	−	0.457950i
$667$	−7.37596	−	1.46717i	−0.285598	−	0.0568090i
$668$	−15.6596	+	8.78520i	−0.605888	+	0.339910i
$669$	−3.41407	−	2.28121i	−0.131996	−	0.0881966i
$670$	7.31080	+	2.53210i	0.282441	+	0.0978236i
$671$			4.00584i			0.154644i
$672$	3.39785	−	11.2771i	0.131075	−	0.435025i
$673$			3.28270i			0.126539i	0.997996	+	0.0632694i	$0.0201527\pi$
$673$			3.28270i			0.126539i	−0.997996	+	0.0632694i	$0.979847\pi$
$674$	13.6836	−	39.5080i	0.527073	−	1.52179i
$675$	−3.90080	−	2.60643i	−0.150142	−	0.100321i
$676$	3.02375	−	10.7522i	0.116298	−	0.413546i
$677$	5.56249	+	1.10645i	0.213784	+	0.0425242i	0.300820	−	0.953681i	$-0.402740\pi$
$677$	5.56249	+	1.10645i	0.213784	+	0.0425242i	−0.0870364	+	0.996205i	$0.527740\pi$
$678$	13.4064	−	10.1563i	0.514869	−	0.390049i
$679$	3.13356	+	1.29796i	0.120255	+	0.0498113i
$680$	1.39980	−	0.549683i	0.0536797	−	0.0210794i
$681$	12.7607	−	5.28566i	0.488992	−	0.202547i
$682$	−26.8559	−	15.7270i	−1.02837	−	0.602219i
$683$	−6.55256	−	9.80659i	−0.250727	−	0.375239i	0.684662	−	0.728861i	$-0.259950\pi$
$683$	−6.55256	−	9.80659i	−0.250727	−	0.375239i	−0.935388	+	0.353622i	$0.884950\pi$
$684$	−9.36051	−	0.729638i	−0.357908	−	0.0278984i
$685$	−10.1709	+	2.02312i	−0.388610	+	0.0772994i
$686$	−18.8956	+	21.2800i	−0.721439	+	0.812474i
$687$	−9.86992	+	9.86992i	−0.376561	+	0.376561i
$688$	−0.355630	+	0.385876i	−0.0135583	+	0.0147114i
$689$	24.0027	+	24.0027i	0.914430	+	0.914430i
$690$	−2.20766	+	0.131022i	−0.0840441	+	0.00498791i
$691$	−1.50400	−	7.56114i	−0.0572150	−	0.287639i	0.941576	−	0.336801i	$-0.109345\pi$
$691$	−1.50400	−	7.56114i	−0.0572150	−	0.287639i	−0.998791	+	0.0491618i	$0.984345\pi$
$692$	14.5009	−	28.5124i	0.551243	−	1.08388i
$693$	−4.99365	+	3.33665i	−0.189693	+	0.126749i
$694$	7.52428	−	1.96644i	0.285618	−	0.0746451i
$695$	−2.11485	−	5.10571i	−0.0802210	−	0.193671i
$696$	−1.33661	−	7.43653i	−0.0506642	−	0.281881i
$697$	2.10175	−	5.07406i	0.0796093	−	0.192194i
$698$	4.17672	+	0.576117i	0.158091	+	0.0218064i
$699$	−4.92743	+	24.7718i	−0.186372	+	0.936957i
$700$	−2.31070	−	19.3986i	−0.0873364	−	0.733199i
$701$	−22.4684	+	33.6263i	−0.848619	+	1.27005i	0.112427	+	0.993660i	$0.464138\pi$
$701$	−22.4684	+	33.6263i	−0.848619	+	1.27005i	−0.961046	+	0.276388i	$0.910862\pi$
$702$	−1.68194	−	3.46436i	−0.0634807	−	0.130754i
$703$	−49.2169			−1.85625
$704$	−22.7841	+	3.66112i	−0.858710	+	0.137984i
$705$	−0.536514			−0.0202063
$706$	13.9566	+	28.7470i	0.525264	+	1.08191i
$707$	−1.27522	+	1.90850i	−0.0479595	+	0.0717764i
$708$	−12.3640	+	1.47276i	−0.464669	+	0.0553499i
$709$	−7.46087	+	37.5083i	−0.280199	+	1.40865i	0.542442	+	0.840093i	$0.317500\pi$
$709$	−7.46087	+	37.5083i	−0.280199	+	1.40865i	−0.822641	+	0.568561i	$0.807500\pi$
$710$	2.86077	+	0.394602i	0.107363	+	0.0148091i
$711$	4.75598	−	11.4820i	0.178363	−	0.430607i
$712$	−7.51499	+	10.8084i	−0.281636	+	0.405061i
$713$	8.21919	+	19.8429i	0.307811	+	0.743122i
$714$	−2.72682	+	0.712645i	−0.102049	+	0.0266701i
$715$	3.62791	−	2.42409i	0.135676	−	0.0906558i
$716$	12.4733	+	6.34369i	0.466148	+	0.237075i
$717$	−4.56865	−	22.9681i	−0.170619	−	0.857761i
$718$	7.53565	−	0.447231i	0.281228	−	0.0166905i
$719$	−25.4364	−	25.4364i	−0.948616	−	0.948616i	0.0501266	−	0.998743i	$-0.484038\pi$
$719$	−25.4364	−	25.4364i	−0.948616	−	0.948616i	−0.998743	+	0.0501266i	$0.984038\pi$
$720$	−0.933241	−	2.01641i	−0.0347798	−	0.0751472i
$721$	−7.55016	+	7.55016i	−0.281183	+	0.281183i
$722$	−2.85255	+	3.21250i	−0.106161	+	0.119557i
$723$	−27.0219	+	5.37500i	−1.00496	+	0.199898i
$724$	0.496106	−	6.36453i	0.0184376	−	0.236536i
$725$	−6.96265	−	10.4203i	−0.258587	−	0.387002i
$726$	−3.26978	−	1.91481i	−0.121353	−	0.0710652i
$727$	−28.6361	+	11.8615i	−1.06205	+	0.439918i	−0.844180	−	0.536059i	$-0.819912\pi$
$727$	−28.6361	+	11.8615i	−1.06205	+	0.439918i	−0.217875	+	0.975977i	$0.569912\pi$
$728$	6.41004	−	14.6995i	0.237572	−	0.544799i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	6.80738	−	5.15706i	0.251952	−	0.190871i
$731$	0.123160	+	0.0244981i	0.00455525	+	0.000906095i
$732$	2.67373	+	0.751909i	0.0988238	+	0.0277914i
$733$	14.7780	+	9.87431i	0.545836	+	0.364716i	0.797707	−	0.603045i	$-0.206046\pi$
$733$	14.7780	+	9.87431i	0.545836	+	0.364716i	−0.251871	+	0.967761i	$0.581046\pi$
$734$	−12.6947	+	36.6526i	−0.468569	+	1.35287i
$735$			1.48035i			0.0546037i
$736$	14.0590	+	7.48088i	0.518220	+	0.275749i
$737$			28.4095i			1.04648i
$738$	−7.66759	−	2.65567i	−0.282248	−	0.0977567i
$739$	−41.0667	−	27.4399i	−1.51066	−	1.00939i	−0.987581	−	0.157111i	$-0.949782\pi$
$739$	−41.0667	−	27.4399i	−1.51066	−	1.00939i	−0.523083	−	0.852282i	$-0.675218\pi$
$740$	−5.69872	−	10.1580i	−0.209489	−	0.373414i
$741$	−12.5379	−	2.49394i	−0.460591	−	0.0916173i
$742$	−22.1641	−	29.2568i	−0.813668	−	1.07405i
$743$	18.4101	+	7.62571i	0.675401	+	0.279760i	0.693903	−	0.720069i	$-0.255890\pi$
$743$	18.4101	+	7.62571i	0.675401	+	0.279760i	−0.0185020	+	0.999829i	$0.505890\pi$
$744$	−15.5381	+	14.9732i	−0.569653	+	0.548943i
$745$	−6.75612	+	2.79848i	−0.247525	+	0.102528i
$746$	−7.66592	+	13.0905i	−0.280669	+	0.479279i
$747$	−9.76650	−	14.6166i	−0.357338	−	0.534793i
$748$	3.58946	+	4.19635i	0.131244	+	0.153434i
$749$	−39.7814	+	7.91302i	−1.45358	+	0.289135i
$750$	−5.69284	−	5.05497i	−0.207873	−	0.184582i
$751$	−5.80705	+	5.80705i	−0.211902	+	0.211902i	−0.805075	−	0.593173i	$-0.797875\pi$
$751$	−5.80705	+	5.80705i	−0.211902	+	0.211902i	0.593173	+	0.805075i	$0.297875\pi$
$752$	3.29715	+	2.01372i	0.120235	+	0.0734326i
$753$	21.3643	+	21.3643i	0.778560	+	0.778560i
$754$	−0.609477	−	10.2694i	−0.0221959	−	0.373991i
$755$	1.96988	+	9.90324i	0.0716911	+	0.360416i
$756$	1.28975	+	3.95935i	0.0469077	+	0.144000i
$757$	33.5924	−	22.4457i	1.22094	−	0.815804i	0.233276	−	0.972411i	$-0.425056\pi$
$757$	33.5924	−	22.4457i	1.22094	−	0.815804i	0.987661	+	0.156607i	$0.0500556\pi$
$758$	−7.34990	−	28.1232i	−0.266960	−	1.02148i
$759$	−3.10766	−	7.50255i	−0.112801	−	0.272325i
$760$	−7.20596	−	1.57256i	−0.261388	−	0.0570427i
$761$	−5.59045	+	13.4965i	−0.202654	+	0.489249i	−0.992232	−	0.124400i	$-0.960299\pi$
$761$	−5.59045	+	13.4965i	−0.202654	+	0.489249i	0.789578	+	0.613650i	$0.210299\pi$
$762$	3.17244	−	22.9994i	0.114925	−	0.833182i
$763$	6.37893	−	32.0690i	0.230933	−	1.16098i
$764$	−13.4908	+	17.1393i	−0.488078	+	0.620078i
$765$	−0.295393	+	0.442086i	−0.0106799	+	0.0159837i
$766$	−17.4155	+	8.45519i	−0.629249	+	0.305499i
$767$	−16.9534			−0.612150
$768$	−1.83302	+	15.8947i	−0.0661433	+	0.573549i
$769$	12.3574			0.445620			0.222810	−	0.974862i	$-0.428477\pi$
$769$	12.3574			0.445620			0.222810	+	0.974862i	$0.428477\pi$
$770$	−4.24418	+	2.06054i	−0.152950	+	0.0742567i
$771$	9.56610	−	14.3167i	0.344515	−	0.515603i
$772$	16.0348	−	20.3714i	0.577107	−	0.733184i
$773$	−4.11151	+	20.6700i	−0.147881	+	0.743447i	0.833673	+	0.552259i	$0.186234\pi$
$773$	−4.11151	+	20.6700i	−0.147881	+	0.743447i	−0.981553	+	0.191188i	$0.938766\pi$
$774$	0.0253512	−	0.183791i	0.000911231	−	0.00660622i
$775$	−13.6968	+	33.0671i	−0.492005	+	1.18781i
$776$	−4.50165	−	0.982397i	−0.161600	−	0.0352660i
$777$	8.35340	+	20.1669i	0.299676	+	0.723483i
$778$	0.0227716	+	0.0871320i	0.000816402	+	0.00312383i
$779$	−22.3963	+	14.9647i	−0.802430	+	0.536167i
$780$	−0.937007	−	2.87648i	−0.0335502	−	0.102995i
$781$	2.06876	+	10.4003i	0.0740260	+	0.372154i
$782$	−0.225774	−	3.80419i	−0.00807365	−	0.136038i
$783$	1.88892	+	1.88892i	0.0675046	+	0.0675046i
$784$	5.55626	−	9.09754i	0.198438	−	0.324912i
$785$	4.64489	−	4.64489i	0.165783	−	0.165783i
$786$	11.8879	+	10.5558i	0.424026	+	0.376515i
$787$	23.7130	−	4.71681i	0.845278	−	0.168136i	0.246591	−	0.969120i	$-0.420690\pi$
$787$	23.7130	−	4.71681i	0.845278	−	0.168136i	0.598686	+	0.800983i	$0.295690\pi$
$788$	9.63902	+	11.2687i	0.343376	+	0.401433i
$789$	−4.97162	−	7.44055i	−0.176994	−	0.264891i
$790$	4.93355	−	8.42467i	0.175528	−	0.299736i
$791$	−22.8768	+	9.47588i	−0.813405	+	0.336924i
$792$	5.87491	−	5.66132i	0.208756	−	0.201166i
$793$	3.49379	+	1.44717i	0.124068	+	0.0513907i
$794$	−27.0480	−	35.7037i	−0.959899	−	1.26708i
$795$	−6.79122	−	1.35086i	−0.240860	−	0.0479100i
$796$	−13.7970	−	24.5932i	−0.489023	−	0.871681i
$797$	−20.7124	−	13.8396i	−0.733671	−	0.490223i	0.131741	−	0.991284i	$-0.457943\pi$
$797$	−20.7124	−	13.8396i	−0.733671	−	0.490223i	−0.865412	+	0.501061i	$0.832943\pi$
$798$	13.0615	+	4.52385i	0.462371	+	0.160143i
$799$		−	0.924509i		−	0.0327068i
$800$	7.75132	+	25.3816i	0.274051	+	0.897376i
$801$		−	4.65424i		−	0.164450i
$802$	2.97719	−	8.59588i	0.105128	−	0.303531i
$803$	26.0744	+	17.4224i	0.920146	+	0.614822i
$804$	18.9622	+	5.33257i	0.668744	+	0.188065i
$805$	3.19336	+	0.635199i	0.112551	+	0.0223878i
$806$	−23.4188	+	17.7414i	−0.824893	+	0.624914i
$807$	−6.30825	−	2.61296i	−0.222061	−	0.0919807i
$808$	1.24638	−	2.85821i	0.0438477	−	0.100551i
$809$	6.56369	−	2.71877i	0.230767	−	0.0955868i	−0.264304	−	0.964439i	$-0.585142\pi$
$809$	6.56369	−	2.71877i	0.230767	−	0.0955868i	0.495071	+	0.868853i	$0.335142\pi$
$810$	0.677879	+	0.396971i	0.0238183	+	0.0139481i
$811$	14.7913	+	22.1368i	0.519393	+	0.777327i	0.994736	−	0.102474i	$-0.0326757\pi$
$811$	14.7913	+	22.1368i	0.519393	+	0.777327i	−0.475342	+	0.879801i	$0.657676\pi$
$812$	−0.864462	+	11.0901i	−0.0303367	+	0.389188i
$813$	2.28664	−	0.454842i	0.0801961	−	0.0159520i
$814$	28.3971	−	31.9804i	0.995317	−	1.12091i
$815$	5.54096	−	5.54096i	0.194091	−	0.194091i
$816$	3.47464	−	1.60814i	0.121637	−	0.0562962i
$817$	−0.435483	−	0.435483i	−0.0152356	−	0.0152356i
$818$	30.6846	−	1.82109i	1.07286	−	0.0636729i
$819$	1.10610	+	5.56075i	0.0386504	+	0.194308i
$820$	−5.68181	−	2.88967i	−0.198417	−	0.100912i
$821$	−19.1940	+	12.8250i	−0.669876	+	0.447597i	−0.843438	−	0.537226i	$-0.819472\pi$
$821$	−19.1940	+	12.8250i	−0.669876	+	0.447597i	0.173562	+	0.984823i	$0.444472\pi$
$822$	−25.5440	+	6.67582i	−0.890948	+	0.232846i
$823$	−14.7626	−	35.6400i	−0.514590	−	1.24233i	−0.941186	−	0.337888i	$-0.890287\pi$
$823$	−14.7626	−	35.6400i	−0.514590	−	1.24233i	0.426596	−	0.904442i	$-0.359713\pi$
$824$	8.28051	−	11.9094i	0.288465	−	0.414882i
$825$	5.17875	−	12.5026i	0.180301	−	0.435285i
$826$	18.1596	+	2.50485i	0.631852	+	0.0871547i
$827$	−0.674904	+	3.39297i	−0.0234687	+	0.117985i	−0.990744	−	0.135745i	$-0.956657\pi$
$827$	−0.674904	+	3.39297i	−0.0234687	+	0.117985i	0.967275	+	0.253730i	$0.0816574\pi$
$828$	−5.59095	+	0.665977i	−0.194299	+	0.0231443i
$829$	−18.3833	+	27.5126i	−0.638480	+	0.955553i	0.361253	+	0.932468i	$0.382349\pi$
$829$	−18.3833	+	27.5126i	−0.638480	+	0.955553i	−0.999733	+	0.0230853i	$0.992651\pi$
$830$	−6.03127	−	12.4229i	−0.209349	−	0.431204i
$831$	−0.0265820			−0.000922118
$832$	−5.03801	+	21.1944i	−0.174662	+	0.734783i
$833$	−2.55092			−0.0883840
$834$	−6.14496	−	12.6571i	−0.212783	−	0.438278i
$835$	2.77060	−	4.14649i	0.0958805	−	0.143495i
$836$	−3.20337	−	26.8927i	−0.110791	−	0.930102i
$837$	1.48837	−	7.48252i	0.0514455	−	0.258634i
$838$	18.7372	+	2.58452i	0.647264	+	0.0892807i
$839$	−13.3235	+	32.1659i	−0.459979	+	1.11049i	0.508426	+	0.861106i	$0.330228\pi$
$839$	−13.3235	+	32.1659i	−0.459979	+	1.11049i	−0.968405	+	0.249383i	$0.919772\pi$
$840$	0.578676	+	3.21958i	0.0199662	+	0.111086i
$841$	−8.36697	−	20.1997i	−0.288516	−	0.696540i
$842$	49.3066	−	12.8861i	1.69922	−	0.444084i
$843$	−23.7285	+	15.8549i	−0.817253	+	0.546071i
$844$	−1.57805	+	3.10285i	−0.0543189	+	0.106804i
$845$	0.605196	+	3.04252i	0.0208194	+	0.104666i
$846$	−1.36354	+	0.0809241i	−0.0468794	+	0.00278223i
$847$	3.94466	+	3.94466i	0.135540	+	0.135540i
$848$	36.6653	+	33.7914i	1.25909	+	1.16040i
$849$	−10.0095	+	10.0095i	−0.343524	+	0.343524i
$850$	4.21665	−	4.74873i	0.144630	−	0.162880i
$851$	−28.9480	+	5.75812i	−0.992326	+	0.197386i
$852$	7.33011	+	0.571372i	0.251125	+	0.0195749i
$853$	−22.0779	−	33.0419i	−0.755934	−	1.13133i	−0.987362	−	0.158483i	$-0.949340\pi$
$853$	−22.0779	−	33.0419i	−0.755934	−	1.13133i	0.231428	−	0.972852i	$-0.425660\pi$
$854$	−3.52855	−	2.06634i	−0.120744	−	0.0707088i
$855$	2.40916	−	0.997906i	0.0823915	−	0.0341277i
$856$	51.2881	−	20.1402i	1.75299	−	0.688378i
$857$	44.7944	+	18.5544i	1.53015	+	0.633808i	0.979593	−	0.200992i	$-0.0644164\pi$
$857$	44.7944	+	18.5544i	1.53015	+	0.633808i	0.550554	+	0.834799i	$0.314416\pi$
$858$	8.85461	−	6.70798i	0.302291	−	0.229007i
$859$	5.29064	+	1.05237i	0.180514	+	0.0359065i	0.284520	−	0.958670i	$-0.408166\pi$
$859$	5.29064	+	1.05237i	0.180514	+	0.0359065i	−0.104005	+	0.994577i	$0.533166\pi$
$860$	0.0394563	−	0.140303i	0.00134545	−	0.00478431i
$861$	9.93310	+	6.63708i	0.338519	+	0.226191i
$862$	2.18552	−	6.31013i	0.0744390	−	0.214924i
$863$		−	20.0503i		−	0.682520i	−0.939969	−	0.341260i	$-0.889146\pi$
$863$		−	20.0503i		−	0.682520i	0.939969	−	0.341260i	$-0.110854\pi$
$864$	−2.67595	−	4.98390i	−0.0910378	−	0.169556i
$865$			8.88430i			0.302075i
$866$	39.8393	+	13.7984i	1.35379	+	0.468887i
$867$	13.3732	+	8.93568i	0.454177	+	0.303472i
$868$	27.7063	−	15.5435i	0.940414	−	0.527582i
$869$	35.1603	+	6.99382i	1.19273	+	0.237249i
$870$	1.26719	+	1.67270i	0.0429617	+	0.0567100i
$871$	24.7781	+	10.2634i	0.839573	+	0.347762i
$872$	−0.822236	+	44.4108i	−0.0278444	+	1.50394i
$873$	1.50503	−	0.623404i	0.0509375	−	0.0210990i
$874$	−9.44482	+	16.1283i	−0.319476	+	0.545546i
$875$	6.22711	+	9.31952i	0.210515	+	0.315057i
$876$	16.5229	−	14.1333i	0.558259	−	0.477521i
$877$	−18.5626	+	3.69233i	−0.626814	+	0.124681i	−0.498269	−	0.867023i	$-0.666031\pi$
$877$	−18.5626	+	3.69233i	−0.626814	+	0.124681i	−0.128545	+	0.991704i	$0.541031\pi$
$878$	1.66709	+	1.48030i	0.0562616	+	0.0499577i
$879$	13.3070	−	13.3070i	0.448832	−	0.448832i
$880$	5.17950	−	3.77499i	0.174601	−	0.127255i
$881$	16.4990	+	16.4990i	0.555866	+	0.555866i	0.928128	−	0.372262i	$-0.121418\pi$
$881$	16.4990	+	16.4990i	0.555866	+	0.555866i	−0.372262	+	0.928128i	$0.621418\pi$
$882$	0.223287	+	3.76229i	0.00751845	+	0.126683i
$883$	−5.59024	−	28.1040i	−0.188126	−	0.945775i	−0.953317	−	0.301971i	$-0.902355\pi$
$883$	−5.59024	−	28.1040i	−0.188126	−	0.945775i	0.765191	−	0.643804i	$-0.222645\pi$
$884$	4.95670	−	1.61463i	0.166712	−	0.0543059i
$885$	2.87542	−	1.92129i	0.0966561	−	0.0645836i
$886$	−3.18036	−	12.1691i	−0.106846	−	0.408830i
$887$	12.2463	+	29.5651i	0.411189	+	0.992698i	0.984819	+	0.173583i	$0.0555346\pi$
$887$	12.2463	+	29.5651i	0.411189	+	0.992698i	−0.573630	+	0.819114i	$0.694465\pi$
$888$	−16.0153	−	24.9567i	−0.537439	−	0.837491i
$889$	−13.0806	+	31.5794i	−0.438710	+	1.05914i
$890$	0.499588	−	3.62190i	0.0167462	−	0.121406i
$891$	−0.562748	+	2.82913i	−0.0188528	+	0.0947793i
$892$	−6.45293	−	5.07925i	−0.216060	−	0.170066i
$893$	−2.51906	+	3.77005i	−0.0842973	+	0.126160i
$894$	−16.7484	+	8.13131i	−0.560151	+	0.271952i
$895$	−3.88659			−0.129914
$896$	8.52791	−	21.9580i	0.284898	−	0.733564i
$897$	−7.66622			−0.255968
$898$	−1.36188	+	0.661191i	−0.0454467	+	0.0220642i
$899$	11.3225	−	16.9453i	0.377626	−	0.565158i
$900$	−7.37289	−	5.80338i	−0.245763	−	0.193446i
$901$	2.32777	−	11.7025i	0.0775493	−	0.389866i
$902$	3.19831	−	23.1870i	0.106492	−	0.772044i
$903$	−0.104528	+	0.252354i	−0.00347849	+	0.00839781i
$904$	28.3102	−	18.1674i	0.941583	−	0.604238i
$905$	0.678511	+	1.63807i	0.0225545	+	0.0544513i
$906$	6.50013	+	24.8717i	0.215953	+	0.826308i
$907$	26.1515	−	17.4739i	0.868346	−	0.580211i	−0.0396381	−	0.999214i	$-0.512621\pi$
$907$	26.1515	−	17.4739i	0.868346	−	0.580211i	0.907985	+	0.419004i	$0.137621\pi$
$908$	26.2658	−	8.55601i	0.871661	−	0.283941i
$909$	0.215074	+	1.08125i	0.00713354	+	0.0358627i
$910$	0.263868	+	4.44607i	0.00874715	+	0.147386i
$911$	7.06776	+	7.06776i	0.234165	+	0.234165i	0.814429	−	0.580263i	$-0.197050\pi$
$911$	7.06776	+	7.06776i	0.234165	+	0.234165i	−0.580263	+	0.814429i	$0.697050\pi$
$912$	−18.5510	−	2.90973i	−0.614285	−	0.0963507i
$913$	35.8561	−	35.8561i	1.18666	−	1.18666i
$914$	−3.99983	−	3.55166i	−0.132303	−	0.117479i
$915$	−0.756579	+	0.150493i	−0.0250117	+	0.00497514i
$916$	−21.2142	+	18.1461i	−0.700937	+	0.599564i
$917$	−13.0035	−	19.4611i	−0.429414	−	0.642663i
$918$	−0.684053	+	1.16811i	−0.0225771	+	0.0385533i
$919$	−25.8203	+	10.6951i	−0.851733	+	0.352799i	−0.765469	−	0.643473i	$-0.777493\pi$
$919$	−25.8203	+	10.6951i	−0.851733	+	0.352799i	−0.0862641	+	0.996272i	$0.527493\pi$
$920$	−4.42233	−	0.0818764i	−0.145800	−	0.00269938i
$921$	−9.16644	−	3.79687i	−0.302045	−	0.125111i
$922$	16.5501	+	21.8464i	0.545050	+	0.719472i
$923$	9.81829	+	1.95298i	0.323173	+	0.0642831i
$924$	−10.4757	+	5.87698i	−0.344625	+	0.193338i
$925$	−40.8962	−	27.3260i	−1.34466	−	0.898472i
$926$	−7.77178	−	2.69176i	−0.255397	−	0.0884567i
$927$			5.12835i			0.168437i
$928$	−1.50931	−	15.0358i	−0.0495456	−	0.493575i
$929$		−	12.0795i		−	0.396317i	−0.980170	−	0.198158i	$-0.936504\pi$
$929$		−	12.0795i		−	0.396317i	0.980170	−	0.198158i	$-0.0634960\pi$
$930$	1.96141	−	5.66309i	0.0643173	−	0.185700i
$931$	10.4024	+	6.95063i	0.340923	+	0.227798i
$932$	−13.6752	+	48.6280i	−0.447947	+	1.59286i
$933$	29.7083	+	5.90934i	0.972605	+	0.193463i
$934$	7.86791	−	5.96048i	0.257446	−	0.195033i
$935$	−1.41695	−	0.586920i	−0.0463392	−	0.0191943i
$936$	−2.81525	−	7.16919i	−0.0920194	−	0.234332i
$937$	47.9234	−	19.8505i	1.56559	−	0.648488i	0.579540	−	0.814944i	$-0.303232\pi$
$937$	47.9234	−	19.8505i	1.56559	−	0.648488i	0.986049	+	0.166456i	$0.0532322\pi$
$938$	−25.0246	−	14.6546i	−0.817082	−	0.478489i
$939$	1.12253	+	1.67999i	0.0366324	+	0.0548243i
$940$	−1.06978	−	0.0833880i	−0.0348925	−	0.00271982i
$941$	8.91906	−	1.77411i	0.290753	−	0.0578344i	−0.0475587	−	0.998868i	$-0.515144\pi$
$941$	8.91906	−	1.77411i	0.290753	−	0.0578344i	0.338312	+	0.941034i	$0.390144\pi$
$942$	11.1043	−	12.5055i	0.361797	−	0.407450i
$943$	−11.4221	+	11.4221i	−0.371954	+	0.371954i
$944$	−24.8822	+	1.01493i	−0.809846	+	0.0330332i
$945$	−0.817794	−	0.817794i	−0.0266028	−	0.0266028i
$946$	0.534233	−	0.0317060i	0.0173694	−	0.00103085i
$947$	−5.09139	−	25.5962i	−0.165448	−	0.831763i	−0.970971	−	0.239198i	$-0.923115\pi$
$947$	−5.09139	−	25.5962i	−0.165448	−	0.831763i	0.805523	−	0.592565i	$-0.201885\pi$
$948$	11.2678	−	22.1553i	0.365961	−	0.719569i
$949$	24.6151	−	16.4473i	0.799041	−	0.533902i
$950$	−30.1342	+	7.87546i	−0.977682	+	0.255514i
$951$	7.78049	+	18.7838i	0.252300	+	0.609105i
$952$	−5.54792	+	0.997162i	−0.179809	+	0.0323182i
$953$	−6.08594	+	14.6928i	−0.197143	+	0.475945i	−0.991277	−	0.131798i	$-0.957925\pi$
$953$	−6.08594	+	14.6928i	−0.197143	+	0.475945i	0.794134	+	0.607743i	$0.207925\pi$
$954$	−17.4635	−	2.40883i	−0.565401	−	0.0779888i
$955$	1.18185	−	5.94157i	0.0382438	−	0.192265i
$956$	−5.53982	−	46.5074i	−0.179171	−	1.50416i
$957$	−4.28101	+	6.40699i	−0.138385	+	0.207108i
$958$	20.1260	+	41.4544i	0.650242	+	1.33933i
$959$	38.8699			1.25518
$960$	−1.54744	−	4.16568i	−0.0499433	−	0.134447i
$961$	−27.2034			−0.877529
$962$	−17.6336	−	36.3206i	−0.568529	−	1.17102i
$963$	−10.8231	+	16.1979i	−0.348770	+	0.521970i
$964$	−54.7158	+	6.51758i	−1.76228	+	0.209917i
$965$	−1.40473	+	7.06204i	−0.0452197	+	0.227335i
$966$	8.21166	+	1.13268i	0.264206	+	0.0364433i
$967$	−13.1749	+	31.8069i	−0.423675	+	1.02284i	0.557579	+	0.830124i	$0.311730\pi$
$967$	−13.1749	+	31.8069i	−0.423675	+	1.02284i	−0.981254	+	0.192718i	$0.938270\pi$
$968$	−6.22217	−	4.32624i	−0.199988	−	0.139051i
$969$	1.71957	+	4.15141i	0.0552406	+	0.133363i
$970$	1.23812	−	0.323578i	0.0397536	−	0.0103895i
$971$	1.90576	−	1.27339i	0.0611588	−	0.0408650i	−0.524615	−	0.851340i	$-0.675791\pi$
$971$	1.90576	−	1.27339i	0.0611588	−	0.0408650i	0.585774	+	0.810475i	$0.300791\pi$
$972$	1.78269	+	0.906647i	0.0571799	+	0.0290807i
$973$	4.04115	+	20.3162i	0.129553	+	0.651308i
$974$	14.9938	−	0.889864i	0.480433	−	0.0285131i
$975$	−9.03354	−	9.03354i	−0.289305	−	0.289305i
$976$	5.21442	+	1.91484i	0.166909	+	0.0612924i
$977$	−21.8800	+	21.8800i	−0.700002	+	0.700002i	−0.964411	−	0.264409i	$-0.914823\pi$
$977$	−21.8800	+	21.8800i	−0.700002	+	0.700002i	0.264409	+	0.964411i	$0.414823\pi$
$978$	13.2465	−	14.9180i	0.423575	−	0.477025i
$979$	13.1674	−	2.61917i	0.420833	−	0.0837089i
$980$	−0.230085	+	2.95175i	−0.00734980	+	0.0942903i
$981$	−8.72483	−	13.0576i	−0.278563	−	0.416898i
$982$	18.3728	+	10.7593i	0.586301	+	0.343342i
$983$	51.1366	−	21.1815i	1.63101	−	0.675585i	0.635661	−	0.771968i	$-0.280728\pi$
$983$	51.1366	−	21.1815i	1.63101	−	0.675585i	0.995344	+	0.0963836i	$0.0307276\pi$
$984$	−14.8760	−	6.48703i	−0.474231	−	0.206799i
$985$	−3.80503	−	1.57610i	−0.121238	−	0.0502186i
$986$	−2.88237	+	2.18359i	−0.0917934	+	0.0695398i
$987$	1.97235	+	0.392324i	0.0627805	+	0.0124878i
$988$	−24.6123	−	6.92151i	−0.783023	−	0.220203i
$989$	−0.307088	−	0.205190i	−0.00976483	−	0.00652465i
$990$	−0.741606	+	2.14120i	−0.0235698	+	0.0680518i
$991$		−	29.9078i		−	0.950053i	−0.879971	−	0.475027i	$-0.842438\pi$
$991$		−	29.9078i		−	0.950053i	0.879971	−	0.475027i	$-0.157562\pi$
$992$	−33.3094	+	27.4408i	−1.05757	+	0.871245i
$993$		−	14.2968i		−	0.453697i
$994$	−10.2283	−	3.54258i	−0.324422	−	0.112364i
$995$	6.51200	+	4.35118i	0.206444	+	0.137942i
$996$	−17.2021	−	30.6628i	−0.545070	−	0.971587i
$997$	−5.93228	−	1.18000i	−0.187877	−	0.0373711i	0.100255	−	0.994962i	$-0.468034\pi$
$997$	−5.93228	−	1.18000i	−0.187877	−	0.0373711i	−0.288132	+	0.957591i	$0.593034\pi$
$998$	−1.27644	−	1.68491i	−0.0404048	−	0.0533349i
$999$	9.68602	+	4.01208i	0.306452	+	0.126937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.37.3	✓	128
3.2	odd	2		576.2.bd.b.37.14		128
4.3	odd	2		768.2.r.a.241.4		128
64.19	odd	16		768.2.r.a.529.4		128
64.45	even	16	inner	192.2.r.a.109.3	yes	128
192.173	odd	16		576.2.bd.b.109.14		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.3	✓	128	1.1	even	1	trivial
192.2.r.a.109.3	yes	128	64.45	even	16	inner
576.2.bd.b.37.14		128	3.2	odd	2
576.2.bd.b.109.14		128	192.173	odd	16
768.2.r.a.241.4		128	4.3	odd	2
768.2.r.a.529.4		128	64.19	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27221 + 0.617652i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.23701 - 1.57156i) q^{4} +(-0.108368 + 0.544803i) q^{5} +(-0.193240 + 1.40095i) q^{6} +(0.796770 - 1.92357i) q^{7} +(-0.603056 + 2.76339i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(-1.27221 + 0.617652i) q^{2} +(0.555570 - 0.831470i) q^{3} +(1.23701 - 1.57156i) q^{4} +(-0.108368 + 0.544803i) q^{5} +(-0.193240 + 1.40095i) q^{6} +(0.796770 - 1.92357i) q^{7} +(-0.603056 + 2.76339i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-0.198632 - 0.760034i) q^{10} +(2.39842 - 1.60257i) q^{11} +(-0.619458 - 1.90165i) q^{12} +(-0.531254 - 2.67079i) q^{13} +(0.174444 + 2.93931i) q^{14} +(0.392781 + 0.392781i) q^{15} +(-0.939603 - 3.88808i) q^{16} +(-0.676832 + 0.676832i) q^{17} +(1.05749 + 0.938999i) q^{18} +(4.60425 - 0.915842i) q^{19} +(0.722137 + 0.844234i) q^{20} +(-1.15673 - 1.73117i) q^{21} +(-2.06145 + 3.52019i) q^{22} +(2.60094 - 1.07735i) q^{23} +(1.96264 + 2.03668i) q^{24} +(4.33433 + 1.79534i) q^{25} +(2.32548 + 3.06967i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-2.03740 - 3.63166i) q^{28} +(-2.22114 - 1.48412i) q^{29} +(-0.742299 - 0.257096i) q^{30} +7.62911i q^{31} +(3.59685 + 4.36608i) q^{32} -2.88455i q^{33} +(0.443022 - 1.27912i) q^{34} +(0.961624 + 0.642536i) q^{35} +(-1.92532 - 0.541440i) q^{36} +(-10.2826 - 2.04534i) q^{37} +(-5.29188 + 4.00896i) q^{38} +(-2.51583 - 1.04209i) q^{39} +(-1.44015 - 0.628009i) q^{40} +(-5.30103 + 2.19576i) q^{41} +(2.54086 + 1.48795i) q^{42} +(-0.0728853 - 0.109081i) q^{43} +(0.448334 - 5.75166i) q^{44} +(0.544803 - 0.108368i) q^{45} +(-2.64351 + 2.97708i) q^{46} +(-0.682968 + 0.682968i) q^{47} +(-3.75483 - 1.37885i) q^{48} +(1.88445 + 1.88445i) q^{49} +(-6.62305 + 0.393069i) q^{50} +(0.186737 + 0.938792i) q^{51} +(-4.85448 - 2.46890i) q^{52} +(-10.3647 + 6.92544i) q^{53} +(1.36826 - 0.357589i) q^{54} +(0.613173 + 1.48033i) q^{55} +(4.83509 + 3.36181i) q^{56} +(1.79649 - 4.33711i) q^{57} +(3.74241 + 0.516211i) q^{58} +(1.21458 - 6.10609i) q^{59} +(1.10315 - 0.131404i) q^{60} +(-0.771532 + 1.15468i) q^{61} +(-4.71214 - 9.70580i) q^{62} -2.08206 q^{63} +(-7.27265 - 3.33296i) q^{64} +1.51263 q^{65} +(1.78165 + 3.66974i) q^{66} +(-5.47173 + 8.18903i) q^{67} +(0.226433 + 1.90093i) q^{68} +(0.549226 - 2.76114i) q^{69} +(-1.62025 - 0.223489i) q^{70} +(-1.40681 + 3.39634i) q^{71} +(2.78382 - 0.500353i) q^{72} +(4.16035 + 10.0440i) q^{73} +(14.3449 - 3.74899i) q^{74} +(3.90080 - 2.60643i) q^{75} +(4.25621 - 8.36876i) q^{76} +(-1.17168 - 5.89041i) q^{77} +(3.84430 - 0.228154i) q^{78} +(8.78791 + 8.78791i) q^{79} +(2.22006 - 0.0905551i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(5.38778 - 6.06765i) q^{82} +(17.2415 - 3.42954i) q^{83} +(-4.15153 - 0.323606i) q^{84} +(-0.295393 - 0.442086i) q^{85} +(0.160099 + 0.0937551i) q^{86} +(-2.46800 + 1.02228i) q^{87} +(2.98215 + 7.59420i) q^{88} +(4.29996 + 1.78110i) q^{89} +(-0.626167 + 0.474365i) q^{90} +(-5.56075 - 1.10610i) q^{91} +(1.52428 - 5.42023i) q^{92} +(6.34338 + 4.23851i) q^{93} +(0.447039 - 1.29071i) q^{94} +2.60765i q^{95} +(5.62857 - 0.565002i) q^{96} +1.62903i q^{97} +(-3.56135 - 1.23347i) q^{98} +(-2.39842 - 1.60257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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