LMFDB - Embedded newform 572.2.j.a.463.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(463,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("572.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.j (of order $4$, degree $2$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			463.11
Character	$\chi$	$=$	572.463
Dual form			572.2.j.a.551.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22033 - 0.714703i) q^{2} -0.940195i q^{3} +(0.978400 + 1.74434i) q^{4} +(-2.27069 - 2.27069i) q^{5} +(-0.671960 + 1.14735i) q^{6} +(2.86451 + 2.86451i) q^{7} +(0.0527177 - 2.82794i) q^{8} +2.11603 q^{9} +O(q^{10})$	\(q+(-1.22033 - 0.714703i) q^{2} -0.940195i q^{3} +(0.978400 + 1.74434i) q^{4} +(-2.27069 - 2.27069i) q^{5} +(-0.671960 + 1.14735i) q^{6} +(2.86451 + 2.86451i) q^{7} +(0.0527177 - 2.82794i) q^{8} +2.11603 q^{9} +(1.14812 + 4.39385i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.64002 - 0.919887i) q^{12} +(-0.0766142 + 3.60474i) q^{13} +(-1.44837 - 5.54291i) q^{14} +(-2.13489 + 2.13489i) q^{15} +(-2.08547 + 3.41333i) q^{16} +5.12990i q^{17} +(-2.58225 - 1.51233i) q^{18} +(0.0110629 - 0.0110629i) q^{19} +(1.73922 - 6.18250i) q^{20} +(2.69320 - 2.69320i) q^{21} +(-0.357531 - 1.36827i) q^{22} +3.36033 q^{23} +(-2.65881 - 0.0495650i) q^{24} +5.31204i q^{25} +(2.66981 - 4.34420i) q^{26} -4.81007i q^{27} +(-2.19405 + 7.79933i) q^{28} +1.93627 q^{29} +(4.13108 - 1.07945i) q^{30} +(5.61682 - 5.61682i) q^{31} +(4.98447 - 2.67490i) q^{32} +(0.664818 - 0.664818i) q^{33} +(3.66635 - 6.26016i) q^{34} -13.0088i q^{35} +(2.07033 + 3.69109i) q^{36} +(-4.08456 + 4.08456i) q^{37} +(-0.0214071 + 0.00559370i) q^{38} +(3.38916 + 0.0720323i) q^{39} +(-6.54106 + 6.30165i) q^{40} +(-0.879678 - 0.879678i) q^{41} +(-5.21142 + 1.36175i) q^{42} +8.98914 q^{43} +(-0.541603 + 1.92527i) q^{44} +(-4.80485 - 4.80485i) q^{45} +(-4.10071 - 2.40164i) q^{46} +(-2.40145 - 2.40145i) q^{47} +(3.20920 + 1.96075i) q^{48} +9.41083i q^{49} +(3.79653 - 6.48243i) q^{50} +4.82310 q^{51} +(-6.36286 + 3.39323i) q^{52} +10.4363 q^{53} +(-3.43777 + 5.86986i) q^{54} -3.21124i q^{55} +(8.25166 - 7.94964i) q^{56} +(-0.0104013 - 0.0104013i) q^{57} +(-2.36289 - 1.38386i) q^{58} +(-4.50422 - 4.50422i) q^{59} +(-5.81276 - 1.63520i) q^{60} -11.4979 q^{61} +(-10.8687 + 2.84000i) q^{62} +(6.06140 + 6.06140i) q^{63} +(-7.99444 - 0.298165i) q^{64} +(8.35920 - 8.01126i) q^{65} +(-1.28644 + 0.336149i) q^{66} +(7.96420 - 7.96420i) q^{67} +(-8.94830 + 5.01909i) q^{68} -3.15937i q^{69} +(-9.29743 + 15.8750i) q^{70} +(-9.04867 + 9.04867i) q^{71} +(0.111552 - 5.98401i) q^{72} +(9.96352 - 9.96352i) q^{73} +(7.90376 - 2.06526i) q^{74} +4.99436 q^{75} +(0.0301216 + 0.00847358i) q^{76} +4.05103i q^{77} +(-4.08440 - 2.51014i) q^{78} +12.0289i q^{79} +(12.4860 - 3.01517i) q^{80} +1.82570 q^{81} +(0.444788 + 1.70220i) q^{82} +(8.42595 - 8.42595i) q^{83} +(7.33289 + 2.06284i) q^{84} +(11.6484 - 11.6484i) q^{85} +(-10.9697 - 6.42456i) q^{86} -1.82048i q^{87} +(2.03693 - 1.96238i) q^{88} +(-4.41534 + 4.41534i) q^{89} +(2.42945 + 9.29753i) q^{90} +(-10.5453 + 10.1063i) q^{91} +(3.28775 + 5.86158i) q^{92} +(-5.28090 - 5.28090i) q^{93} +(1.21423 + 4.64688i) q^{94} -0.0502410 q^{95} +(-2.51492 - 4.68637i) q^{96} +(3.43982 + 3.43982i) q^{97} +(6.72595 - 11.4843i) q^{98} +(1.49626 + 1.49626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	$ 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) $ 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.22033	−	0.714703i	−0.862902	−	0.505371i
$2$	−1.22033	−	0.714703i	−0.862902	−	0.505371i
$3$		−	0.940195i		−	0.542822i	−0.962464	−	0.271411i	$-0.912510\pi$
$3$		−	0.940195i		−	0.542822i	0.962464	−	0.271411i	$-0.0874902\pi$
$4$	0.978400	+	1.74434i	0.489200	+	0.872172i
$5$	−2.27069	−	2.27069i	−1.01548	−	1.01548i	−0.999878	−	0.0156040i	$-0.995033\pi$
$5$	−2.27069	−	2.27069i	−1.01548	−	1.01548i	−0.0156040	−	0.999878i	$-0.504967\pi$
$6$	−0.671960	+	1.14735i	−0.274327	+	0.468402i
$7$	2.86451	+	2.86451i	1.08268	+	1.08268i	0.996258	+	0.0864246i	$0.0275442\pi$
$7$	2.86451	+	2.86451i	1.08268	+	1.08268i	0.0864246	+	0.996258i	$0.472456\pi$
$8$	0.0527177	−	2.82794i	0.0186385	−	0.999826i
$9$	2.11603			0.705344
$10$	1.14812	+	4.39385i	0.363066	+	1.38946i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$11$	0.707107	+	0.707107i	0.213201	+	0.213201i
$12$	1.64002	−	0.919887i	0.473434	−	0.265549i
$13$	−0.0766142	+	3.60474i	−0.0212490	+	0.999774i
$13$	−0.0766142	+	3.60474i	−0.0212490	+	0.999774i
$14$	−1.44837	−	5.54291i	−0.387093	−	1.48141i
$15$	−2.13489	+	2.13489i	−0.551226	+	0.551226i
$16$	−2.08547	+	3.41333i	−0.521367	+	0.853333i
$17$			5.12990i			1.24418i	0.782945	+	0.622091i	$0.213717\pi$
$17$			5.12990i			1.24418i	−0.782945	+	0.622091i	$0.786283\pi$
$18$	−2.58225	−	1.51233i	−0.608643	−	0.356461i
$19$	0.0110629	−	0.0110629i	0.00253801	−	0.00253801i	−0.705837	−	0.708375i	$-0.749429\pi$
$19$	0.0110629	−	0.0110629i	0.00253801	−	0.00253801i	0.708375	+	0.705837i	$0.249429\pi$
$20$	1.73922	−	6.18250i	0.388901	−	1.38245i
$21$	2.69320	−	2.69320i	0.587704	−	0.587704i
$22$	−0.357531	−	1.36827i	−0.0762259	−	0.291717i
$23$	3.36033			0.700678			0.350339	−	0.936623i	$-0.386066\pi$
$23$	3.36033			0.700678			0.350339	+	0.936623i	$0.386066\pi$
$24$	−2.65881	−	0.0495650i	−0.542728	−	0.0101174i
$25$			5.31204i			1.06241i
$26$	2.66981	−	4.34420i	0.523593	−	0.851969i
$27$		−	4.81007i		−	0.925698i
$28$	−2.19405	+	7.79933i	−0.414637	+	1.47393i
$29$	1.93627			0.359557			0.179779	−	0.983707i	$-0.442462\pi$
$29$	1.93627			0.359557			0.179779	+	0.983707i	$0.442462\pi$
$30$	4.13108	−	1.07945i	0.754228	−	0.197080i
$31$	5.61682	−	5.61682i	1.00881	−	1.00881i	0.00884942	−	0.999961i	$-0.497183\pi$
$31$	5.61682	−	5.61682i	1.00881	−	1.00881i	0.999961	−	0.00884942i	$-0.00281690\pi$
$32$	4.98447	−	2.67490i	0.881138	−	0.472859i
$33$	0.664818	−	0.664818i	0.115730	−	0.115730i
$34$	3.66635	−	6.26016i	0.628774	−	1.07361i
$35$		−	13.0088i		−	2.19889i
$36$	2.07033	+	3.69109i	0.345055	+	0.615181i
$37$	−4.08456	+	4.08456i	−0.671498	+	0.671498i	−0.958061	−	0.286563i	$-0.907487\pi$
$37$	−4.08456	+	4.08456i	−0.671498	+	0.671498i	0.286563	+	0.958061i	$0.407487\pi$
$38$	−0.0214071	+	0.00559370i	−0.00347269	+	0.000907418i
$39$	3.38916	+	0.0720323i	0.542699	+	0.0115344i
$40$	−6.54106	+	6.30165i	−1.03423	+	0.996379i
$41$	−0.879678	−	0.879678i	−0.137383	−	0.137383i	0.635071	−	0.772454i	$-0.280971\pi$
$41$	−0.879678	−	0.879678i	−0.137383	−	0.137383i	−0.772454	+	0.635071i	$0.780971\pi$
$42$	−5.21142	+	1.36175i	−0.804140	+	0.210122i
$43$	8.98914			1.37083			0.685415	−	0.728152i	$-0.259621\pi$
$43$	8.98914			1.37083			0.685415	+	0.728152i	$0.259621\pi$
$44$	−0.541603	+	1.92527i	−0.0816498	+	0.290245i
$45$	−4.80485	−	4.80485i	−0.716265	−	0.716265i
$46$	−4.10071	−	2.40164i	−0.604617	−	0.354103i
$47$	−2.40145	−	2.40145i	−0.350287	−	0.350287i	0.509929	−	0.860216i	$-0.329672\pi$
$47$	−2.40145	−	2.40145i	−0.350287	−	0.350287i	−0.860216	+	0.509929i	$0.829672\pi$
$48$	3.20920	+	1.96075i	0.463208	+	0.283009i
$49$			9.41083i			1.34440i
$50$	3.79653	−	6.48243i	0.536910	−	0.916754i
$51$	4.82310			0.675370
$52$	−6.36286	+	3.39323i	−0.882370	+	0.470557i
$53$	10.4363			1.43354			0.716769	−	0.697310i	$-0.245620\pi$
$53$	10.4363			1.43354			0.716769	+	0.697310i	$0.245620\pi$
$54$	−3.43777	+	5.86986i	−0.467821	+	0.798787i
$55$		−	3.21124i		−	0.433003i
$56$	8.25166	−	7.94964i	1.10267	−	1.06232i
$57$	−0.0104013	−	0.0104013i	−0.00137769	−	0.00137769i
$58$	−2.36289	−	1.38386i	−0.310263	−	0.181710i
$59$	−4.50422	−	4.50422i	−0.586400	−	0.586400i	0.350255	−	0.936655i	$-0.386095\pi$
$59$	−4.50422	−	4.50422i	−0.586400	−	0.586400i	−0.936655	+	0.350255i	$0.886095\pi$
$60$	−5.81276	−	1.63520i	−0.750423	−	0.211104i
$61$	−11.4979			−1.47215			−0.736075	−	0.676900i	$-0.763323\pi$
$61$	−11.4979			−1.47215			−0.736075	+	0.676900i	$0.763323\pi$
$62$	−10.8687	+	2.84000i	−1.38033	+	0.360681i
$63$	6.06140	+	6.06140i	0.763664	+	0.763664i
$64$	−7.99444	−	0.298165i	−0.999305	−	0.0372706i
$65$	8.35920	−	8.01126i	1.03683	−	0.993675i
$66$	−1.28644	+	0.336149i	−0.158350	+	0.0413771i
$67$	7.96420	−	7.96420i	0.972982	−	0.972982i	−0.0266627	−	0.999644i	$-0.508488\pi$
$67$	7.96420	−	7.96420i	0.972982	−	0.972982i	0.999644	+	0.0266627i	$0.00848800\pi$
$68$	−8.94830	+	5.01909i	−1.08514	+	0.608654i
$69$		−	3.15937i		−	0.380343i
$70$	−9.29743	+	15.8750i	−1.11126	+	1.89743i
$71$	−9.04867	+	9.04867i	−1.07388	+	1.07388i	−0.0768363	+	0.997044i	$0.524482\pi$
$71$	−9.04867	+	9.04867i	−1.07388	+	1.07388i	−0.997044	+	0.0768363i	$0.975518\pi$
$72$	0.111552	−	5.98401i	0.0131466	−	0.705222i
$73$	9.96352	−	9.96352i	1.16614	−	1.16614i	0.183036	−	0.983106i	$-0.441407\pi$
$73$	9.96352	−	9.96352i	1.16614	−	1.16614i	0.983106	−	0.183036i	$-0.0585925\pi$
$74$	7.90376	−	2.06526i	0.918793	−	0.240081i
$75$	4.99436			0.576698
$76$	0.0301216	+	0.00847358i	0.00345518	+	0.000971987i
$77$			4.05103i			0.461658i
$78$	−4.08440	−	2.51014i	−0.462467	−	0.284218i
$79$			12.0289i			1.35336i	0.736277	+	0.676680i	$0.236582\pi$
$79$			12.0289i			1.35336i	−0.736277	+	0.676680i	$0.763418\pi$
$80$	12.4860	−	3.01517i	1.39598	−	0.337106i
$81$	1.82570			0.202855
$82$	0.444788	+	1.70220i	0.0491186	+	0.187977i
$83$	8.42595	−	8.42595i	0.924868	−	0.924868i	−0.0725007	−	0.997368i	$-0.523098\pi$
$83$	8.42595	−	8.42595i	0.924868	−	0.924868i	0.997368	+	0.0725007i	$0.0230980\pi$
$84$	7.33289	+	2.06284i	0.800084	+	0.225074i
$85$	11.6484	−	11.6484i	1.26345	−	1.26345i
$86$	−10.9697	−	6.42456i	−1.18289	−	0.692778i
$87$		−	1.82048i		−	0.195176i
$88$	2.03693	−	1.96238i	0.217137	−	0.209190i
$89$	−4.41534	+	4.41534i	−0.468025	+	0.468025i	−0.901274	−	0.433249i	$-0.857367\pi$
$89$	−4.41534	+	4.41534i	−0.468025	+	0.468025i	0.433249	+	0.901274i	$0.357367\pi$
$90$	2.42945	+	9.29753i	0.256087	+	0.980046i
$91$	−10.5453	+	10.1063i	−1.10544	+	1.05943i
$92$	3.28775	+	5.86158i	0.342772	+	0.611112i
$93$	−5.28090	−	5.28090i	−0.547604	−	0.547604i
$94$	1.21423	+	4.64688i	0.125239	+	0.479289i
$95$	−0.0502410			−0.00515461
$96$	−2.51492	−	4.68637i	−0.256678	−	0.478301i
$97$	3.43982	+	3.43982i	0.349261	+	0.349261i	0.859834	−	0.510573i	$-0.170567\pi$
$97$	3.43982	+	3.43982i	0.349261	+	0.349261i	−0.510573	+	0.859834i	$0.670567\pi$
$98$	6.72595	−	11.4843i	0.679423	−	1.16009i
$99$	1.49626	+	1.49626i	0.150380	+	0.150380i
$100$	−9.26602	+	5.19730i	−0.926602	+	0.519730i
$101$			5.94197i			0.591248i	0.955304	+	0.295624i	$0.0955276\pi$
$101$			5.94197i			0.591248i	−0.955304	+	0.295624i	$0.904472\pi$
$102$	−5.88577	−	3.44709i	−0.582778	−	0.341312i
$103$	−8.49196			−0.836737			−0.418369	−	0.908277i	$-0.637398\pi$
$103$	−8.49196			−0.836737			−0.418369	+	0.908277i	$0.637398\pi$
$104$	10.1899	+	0.406694i	0.999204	+	0.0398796i
$105$	−12.2308			−1.19361
$106$	−12.7357	−	7.45886i	−1.23700	−	0.724469i
$107$		−	6.21897i		−	0.601210i	−0.953749	−	0.300605i	$-0.902811\pi$
$107$		−	6.21897i		−	0.601210i	0.953749	−	0.300605i	$-0.0971887\pi$
$108$	8.39041	−	4.70617i	0.807368	−	0.452852i
$109$	−8.58423	−	8.58423i	−0.822220	−	0.822220i	0.164206	−	0.986426i	$-0.447494\pi$
$109$	−8.58423	−	8.58423i	−0.822220	−	0.822220i	−0.986426	+	0.164206i	$0.947494\pi$
$110$	−2.29508	+	3.91876i	−0.218827	+	0.373639i
$111$	3.84029	+	3.84029i	0.364504	+	0.364504i
$112$	−15.7514	+	3.80368i	−1.48836	+	0.359414i
$113$	1.33087			0.125197			0.0625987	−	0.998039i	$-0.480061\pi$
$113$	1.33087			0.125197			0.0625987	+	0.998039i	$0.480061\pi$
$114$	0.00525917	+	0.0201269i	0.000492567	+	0.00188505i
$115$	−7.63027	−	7.63027i	−0.711526	−	0.711526i
$116$	1.89445	+	3.37753i	0.175895	+	0.313596i
$117$	−0.162118	+	7.62774i	−0.0149878	+	0.705185i
$118$	2.27745	+	8.71581i	0.209656	+	0.802355i
$119$	−14.6946	+	14.6946i	−1.34706	+	1.34706i
$120$	5.92478	+	6.14988i	0.540856	+	0.561404i
$121$			1.00000i			0.0909091i
$122$	14.0311	+	8.21755i	1.27032	+	0.743982i
$123$	−0.827069	+	0.827069i	−0.0745743	+	0.0745743i
$124$	15.2932	+	4.30216i	1.37337	+	0.386346i
$125$	0.708548	−	0.708548i	0.0633745	−	0.0633745i
$126$	−3.06480	−	11.7290i	−0.273034	−	1.04490i
$127$	15.8822			1.40932			0.704660	−	0.709545i	$-0.251100\pi$
$127$	15.8822			1.40932			0.704660	+	0.709545i	$0.251100\pi$
$128$	9.54274	+	6.07751i	0.843467	+	0.537181i
$129$		−	8.45155i		−	0.744117i
$130$	−15.9266	+	3.80203i	−1.39686	+	0.333460i
$131$			22.2907i			1.94755i	0.227514	+	0.973775i	$0.426940\pi$
$131$			22.2907i			1.94755i	−0.227514	+	0.973775i	$0.573060\pi$
$132$	1.81013	+	0.509213i	0.157552	+	0.0443213i
$133$	0.0633798			0.00549573
$134$	−15.4110	+	4.02690i	−1.33130	+	0.347871i
$135$	−10.9222	+	10.9222i	−0.940030	+	0.940030i
$136$	14.5070	+	0.270437i	1.24397	+	0.0231897i
$137$	−13.9655	+	13.9655i	−1.19315	+	1.19315i	−0.216976	+	0.976177i	$0.569619\pi$
$137$	−13.9655	+	13.9655i	−1.19315	+	1.19315i	−0.976177	+	0.216976i	$0.930381\pi$
$138$	−2.25801	+	3.85547i	−0.192215	+	0.328199i
$139$		−	3.36575i		−	0.285479i	−0.989760	−	0.142739i	$-0.954409\pi$
$139$		−	3.36575i		−	0.285479i	0.989760	−	0.142739i	$-0.0455911\pi$
$140$	22.6918	−	12.7278i	1.91781	−	1.07570i
$141$	−2.25783	+	2.25783i	−0.190144	+	0.190144i
$142$	17.5095	−	4.57524i	1.46936	−	0.383945i
$143$	−2.60311	+	2.49476i	−0.217683	+	0.208622i
$144$	−4.41292	+	7.22272i	−0.367743	+	0.601894i
$145$	−4.39667	−	4.39667i	−0.365124	−	0.365124i
$146$	−19.2797	+	5.03781i	−1.59560	+	0.416932i
$147$	8.84802			0.729772
$148$	−11.1212	−	3.12854i	−0.914159	−	0.257165i
$149$	−11.6376	−	11.6376i	−0.953391	−	0.953391i	0.0455700	−	0.998961i	$-0.485490\pi$
$149$	−11.6376	−	11.6376i	−0.953391	−	0.953391i	−0.998961	+	0.0455700i	$0.985490\pi$
$150$	−6.09475	−	3.56948i	−0.497634	−	0.291447i
$151$	9.26516	+	9.26516i	0.753988	+	0.753988i	0.975221	−	0.221233i	$-0.0710082\pi$
$151$	9.26516	+	9.26516i	0.753988	+	0.753988i	−0.221233	+	0.975221i	$0.571008\pi$
$152$	−0.0307021	−	0.0318685i	−0.00249027	−	0.00258488i
$153$			10.8550i			0.877577i
$154$	2.89528	−	4.94358i	0.233308	−	0.398365i
$155$	−25.5081			−2.04886
$156$	3.19030	+	5.98233i	0.255429	+	0.478970i
$157$	−8.88667			−0.709233			−0.354617	−	0.935012i	$-0.615389\pi$
$157$	−8.88667			−0.709233			−0.354617	+	0.935012i	$0.615389\pi$
$158$	8.59711	−	14.6792i	0.683949	−	1.16782i
$159$		−	9.81217i		−	0.778156i
$160$	−17.3920	−	5.24432i	−1.37496	−	0.414600i
$161$	9.62571	+	9.62571i	0.758612	+	0.758612i
$162$	−2.22795	−	1.30483i	−0.175044	−	0.102517i
$163$	−0.937356	−	0.937356i	−0.0734194	−	0.0734194i	0.669444	−	0.742863i	$-0.266533\pi$
$163$	−0.937356	−	0.937356i	−0.0734194	−	0.0734194i	−0.742863	+	0.669444i	$0.766533\pi$
$164$	0.673783	−	2.39514i	0.0526137	−	0.187029i
$165$	−3.01919			−0.235044
$166$	−16.3045	+	4.26037i	−1.26547	+	0.330669i
$167$	2.01307	+	2.01307i	0.155776	+	0.155776i	0.780692	−	0.624916i	$-0.214867\pi$
$167$	2.01307	+	2.01307i	0.155776	+	0.155776i	−0.624916	+	0.780692i	$0.714867\pi$
$168$	−7.47421	−	7.75817i	−0.576648	−	0.598556i
$169$	−12.9883	−	0.552348i	−0.999097	−	0.0424883i
$170$	−22.5400	+	5.88972i	−1.72874	+	0.451721i
$171$	0.0234096	−	0.0234096i	0.00179017	−	0.00179017i
$172$	8.79498	+	15.6801i	0.670611	+	1.19560i
$173$			14.4393i			1.09780i	0.835888	+	0.548900i	$0.184953\pi$
$173$			14.4393i			1.09780i	−0.835888	+	0.548900i	$0.815047\pi$
$174$	−1.30110	+	2.22158i	−0.0986361	+	0.168417i
$175$	−15.2164	+	15.2164i	−1.15025	+	1.15025i
$176$	−3.88824	+	0.938942i	−0.293087	+	0.0707754i
$177$	−4.23485	+	4.23485i	−0.318311	+	0.318311i
$178$	8.54382	−	2.23251i	0.640386	−	0.167333i
$179$	12.3850			0.925700			0.462850	−	0.886437i	$-0.346827\pi$
$179$	12.3850			0.925700			0.462850	+	0.886437i	$0.346827\pi$
$180$	3.68024	−	13.0824i	0.274309	−	0.975102i
$181$			1.83007i			0.136028i	0.997684	+	0.0680139i	$0.0216662\pi$
$181$			1.83007i			0.136028i	−0.997684	+	0.0680139i	$0.978334\pi$
$182$	20.0917	−	4.79632i	1.48930	−	0.355527i
$183$			10.8102i			0.799115i
$184$	0.177149	−	9.50281i	0.0130596	−	0.700557i
$185$	18.5495			1.36379
$186$	2.67016	+	10.2187i	0.195786	+	0.749272i
$187$	−3.62739	+	3.62739i	−0.265261	+	0.265261i
$188$	1.83937	−	6.53853i	0.134150	−	0.476871i
$189$	13.7785	−	13.7785i	1.00224	−	1.00224i
$190$	0.0613104	+	0.0359073i	0.00444793	+	0.00260499i
$191$		−	9.30716i		−	0.673442i	−0.941604	−	0.336721i	$-0.890682\pi$
$191$		−	9.30716i		−	0.673442i	0.941604	−	0.336721i	$-0.109318\pi$
$192$	−0.280333	+	7.51634i	−0.0202313	+	0.542445i
$193$	−3.15454	+	3.15454i	−0.227069	+	0.227069i	−0.811467	−	0.584398i	$-0.801331\pi$
$193$	−3.15454	+	3.15454i	−0.227069	+	0.227069i	0.584398	+	0.811467i	$0.301331\pi$
$194$	−1.73926	−	6.65616i	−0.124872	−	0.477885i
$195$	−7.53215	−	7.85928i	−0.539389	−	0.562815i
$196$	−16.4157	+	9.20756i	−1.17255	+	0.657683i
$197$	−1.89696	−	1.89696i	−0.135153	−	0.135153i	0.636294	−	0.771447i	$-0.280467\pi$
$197$	−1.89696	−	1.89696i	−0.135153	−	0.135153i	−0.771447	+	0.636294i	$0.780467\pi$
$198$	−0.756547	−	2.89531i	−0.0537655	−	0.205761i
$199$	4.30675			0.305297			0.152649	−	0.988281i	$-0.451220\pi$
$199$	4.30675			0.305297			0.152649	+	0.988281i	$0.451220\pi$
$200$	15.0221	+	0.280039i	1.06222	+	0.0198017i
$201$	−7.48790	−	7.48790i	−0.528156	−	0.528156i
$202$	4.24674	−	7.25115i	0.298800	−	0.510189i
$203$	5.54648	+	5.54648i	0.389286	+	0.389286i
$204$	4.71893	+	8.41315i	0.330391	+	0.589038i
$205$			3.99495i			0.279019i
$206$	10.3630	+	6.06922i	0.722022	+	0.422863i
$207$	7.11058			0.494219
$208$	−12.1444	−	7.77907i	−0.842062	−	0.539381i
$209$	0.0156454			0.00108221
$210$	14.9256	+	8.74140i	1.02997	+	0.603214i
$211$		−	21.7740i		−	1.49898i	−0.662014	−	0.749491i	$-0.730298\pi$
$211$		−	21.7740i		−	1.49898i	0.662014	−	0.749491i	$-0.269702\pi$
$212$	10.2109	+	18.2045i	0.701287	+	1.25029i
$213$	8.50752	+	8.50752i	0.582926	+	0.582926i
$214$	−4.44471	+	7.58918i	−0.303834	+	0.518786i
$215$	−20.4115	−	20.4115i	−1.39205	−	1.39205i
$216$	−13.6026	−	0.253576i	−0.925537	−	0.0172537i
$217$	32.1789			2.18444
$218$	4.34040	+	16.6107i	0.293969	+	1.12502i
$219$	−9.36766	−	9.36766i	−0.633008	−	0.633008i
$220$	5.60150	−	3.14187i	0.377653	−	0.211825i
$221$	−18.4919	−	0.393023i	−1.24390	−	0.0264376i
$222$	−1.94175	−	7.43107i	−0.130321	−	0.498741i
$223$	2.72263	−	2.72263i	0.182321	−	0.182321i	−0.610046	−	0.792366i	$-0.708849\pi$
$223$	2.72263	−	2.72263i	0.182321	−	0.182321i	0.792366	+	0.610046i	$0.208849\pi$
$224$	21.9403	+	6.61580i	1.46595	+	0.442037i
$225$			11.2405i			0.749364i
$226$	−1.62409	−	0.951174i	−0.108033	−	0.0632711i
$227$	7.65828	−	7.65828i	0.508298	−	0.508298i	−0.405706	−	0.914004i	$-0.632974\pi$
$227$	7.65828	−	7.65828i	0.508298	−	0.508298i	0.914004	+	0.405706i	$0.132974\pi$
$228$	0.00796682	−	0.0283201i	0.000527616	−	0.00187555i
$229$	1.99683	−	1.99683i	0.131954	−	0.131954i	−0.638045	−	0.769999i	$-0.720257\pi$
$229$	1.99683	−	1.99683i	0.131954	−	0.131954i	0.769999	+	0.638045i	$0.220257\pi$
$230$	3.85806	+	14.7648i	0.254393	+	0.973562i
$231$	3.80876			0.250598
$232$	0.102076	−	5.47566i	0.00670162	−	0.359495i
$233$		−	19.3332i		−	1.26656i	−0.773923	−	0.633279i	$-0.781708\pi$
$233$		−	19.3332i		−	1.26656i	0.773923	−	0.633279i	$-0.218292\pi$
$234$	5.64941	−	9.19248i	0.369313	−	0.600931i
$235$			10.9059i			0.711421i
$236$	3.44998	−	12.2638i	0.224574	−	0.798308i
$237$	11.3095			0.734634
$238$	28.4346	−	7.42998i	1.84314	−	0.481614i
$239$	2.64380	−	2.64380i	0.171013	−	0.171013i	−0.616411	−	0.787424i	$-0.711414\pi$
$239$	2.64380	−	2.64380i	0.171013	−	0.171013i	0.787424	+	0.616411i	$0.211414\pi$
$240$	−2.83484	−	11.7393i	−0.182988	−	0.757770i
$241$	6.16295	−	6.16295i	0.396990	−	0.396990i	−0.480180	−	0.877170i	$-0.659429\pi$
$241$	6.16295	−	6.16295i	0.396990	−	0.396990i	0.877170	+	0.480180i	$0.159429\pi$
$242$	0.714703	−	1.22033i	0.0459428	−	0.0784456i
$243$		−	16.1467i		−	1.03581i
$244$	−11.2495	−	20.0562i	−0.720175	−	1.28397i
$245$	21.3691	−	21.3691i	1.36522	−	1.36522i
$246$	1.60040	−	0.418187i	0.102038	−	0.0266626i
$247$	0.0390314	+	0.0407266i	0.00248351	+	0.00259137i
$248$	−15.5879	−	16.1801i	−0.989832	−	1.02744i
$249$	−7.92203	−	7.92203i	−0.502038	−	0.502038i
$250$	−1.37106	+	0.358260i	−0.0867136	+	0.0226583i
$251$	−10.3492			−0.653233			−0.326617	−	0.945157i	$-0.605909\pi$
$251$	−10.3492			−0.653233			−0.326617	+	0.945157i	$0.605909\pi$
$252$	−4.64269	+	16.5036i	−0.292462	+	1.03963i
$253$	2.37612	+	2.37612i	0.149385	+	0.149385i
$254$	−19.3815	−	11.3511i	−1.21610	−	0.712229i
$255$	−10.9518	−	10.9518i	−0.685826	−	0.685826i
$256$	−7.30166	−	14.2368i	−0.456354	−	0.889798i
$257$		−	23.0795i		−	1.43966i	−0.694150	−	0.719830i	$-0.744220\pi$
$257$		−	23.0795i		−	1.43966i	0.694150	−	0.719830i	$-0.255780\pi$
$258$	−6.04034	+	10.3137i	−0.376055	+	0.642100i
$259$	−23.4006			−1.45404
$260$	22.1530	+	6.74309i	1.37387	+	0.418189i
$261$	4.09722			0.253612
$262$	15.9312	−	27.2020i	0.984235	−	1.68054i
$263$			4.23928i			0.261405i	0.991422	+	0.130703i	$0.0417233\pi$
$263$			4.23928i			0.261405i	−0.991422	+	0.130703i	$0.958277\pi$
$264$	−1.84502	−	1.91511i	−0.113553	−	0.117867i
$265$	−23.6976	−	23.6976i	−1.45573	−	1.45573i
$266$	−0.0773442	−	0.0452977i	−0.00474227	−	0.00277738i
$267$	4.15128	+	4.15128i	0.254054	+	0.254054i
$268$	21.6845	+	6.10012i	1.32459	+	0.372624i
$269$	3.66320			0.223349			0.111675	−	0.993745i	$-0.464379\pi$
$269$	3.66320			0.223349			0.111675	+	0.993745i	$0.464379\pi$
$270$	21.1347	−	5.52252i	1.28622	−	0.336090i
$271$	4.14460	+	4.14460i	0.251766	+	0.251766i	0.821694	−	0.569928i	$-0.193029\pi$
$271$	4.14460	+	4.14460i	0.251766	+	0.251766i	−0.569928	+	0.821694i	$0.693029\pi$
$272$	−17.5100	−	10.6982i	−1.06170	−	0.648675i
$273$	9.50193	+	9.91461i	0.575083	+	0.600059i
$274$	27.0237	−	7.06131i	1.63256	−	0.426589i
$275$	−3.75618	+	3.75618i	−0.226506	+	0.226506i
$276$	5.51103	−	3.09113i	0.331725	−	0.186064i
$277$			21.2431i			1.27638i	0.769880	+	0.638188i	$0.220316\pi$
$277$			21.2431i			1.27638i	−0.769880	+	0.638188i	$0.779684\pi$
$278$	−2.40551	+	4.10731i	−0.144273	+	0.246340i
$279$	11.8854	−	11.8854i	0.711559	−	0.711559i
$280$	−36.7881	−	0.685795i	−2.19851	−	0.0409841i
$281$	7.43515	−	7.43515i	0.443544	−	0.443544i	−0.449657	−	0.893201i	$-0.648454\pi$
$281$	7.43515	−	7.43515i	0.443544	−	0.443544i	0.893201	+	0.449657i	$0.148454\pi$
$282$	4.36897	−	1.14162i	0.260168	−	0.0679822i
$283$	−8.03719			−0.477761			−0.238881	−	0.971049i	$-0.576780\pi$
$283$	−8.03719			−0.477761			−0.238881	+	0.971049i	$0.576780\pi$
$284$	−24.6372	−	6.93077i	−1.46195	−	0.411265i
$285$			0.0472363i			0.00279804i
$286$	4.95966	−	1.18398i	0.293271	−	0.0700100i
$287$		−	5.03969i		−	0.297484i
$288$	10.5473	−	5.66017i	0.621506	−	0.333529i
$289$	−9.31585			−0.547991
$290$	2.22307	+	8.50770i	0.130543	+	0.499589i
$291$	3.23411	−	3.23411i	0.189587	−	0.189587i
$292$	27.1281	+	7.63149i	1.58755	+	0.446599i
$293$	−3.94985	+	3.94985i	−0.230753	+	0.230753i	−0.813007	−	0.582254i	$-0.802171\pi$
$293$	−3.94985	+	3.94985i	−0.230753	+	0.230753i	0.582254	+	0.813007i	$0.302171\pi$
$294$	−10.7975	−	6.32370i	−0.629722	−	0.368806i
$295$			20.4554i			1.19096i
$296$	11.3356	+	11.7662i	0.658866	+	0.683897i
$297$	3.40123	−	3.40123i	0.197360	−	0.197360i
$298$	5.88427	+	22.5192i	0.340867	+	1.30450i
$299$	−0.257449	+	12.1131i	−0.0148887	+	0.700520i
$300$	4.88648	+	8.71187i	0.282121	+	0.502980i
$301$	25.7495	+	25.7495i	1.48418	+	1.48418i
$302$	−4.68470	−	17.9284i	−0.269574	−	1.03166i
$303$	5.58661			0.320942
$304$	0.0146901	+	0.0608329i	0.000842535	+	0.00348900i
$305$	26.1080	+	26.1080i	1.49494	+	1.49494i
$306$	7.75812	−	13.2467i	0.443502	−	0.757263i
$307$	−4.27138	−	4.27138i	−0.243780	−	0.243780i	0.574632	−	0.818412i	$-0.305145\pi$
$307$	−4.27138	−	4.27138i	−0.243780	−	0.243780i	−0.818412	+	0.574632i	$0.805145\pi$
$308$	−7.06638	+	3.96353i	−0.402645	+	0.225843i
$309$			7.98410i			0.454199i
$310$	31.1282	+	18.2307i	1.76796	+	1.03543i
$311$	−13.6387			−0.773379			−0.386689	−	0.922210i	$-0.626381\pi$
$311$	−13.6387			−0.773379			−0.386689	+	0.922210i	$0.626381\pi$
$312$	0.382371	−	9.58052i	0.0216475	−	0.542390i
$313$	−13.3757			−0.756041			−0.378020	−	0.925797i	$-0.623395\pi$
$313$	−13.3757			−0.756041			−0.378020	+	0.925797i	$0.623395\pi$
$314$	10.8446	+	6.35133i	0.611999	+	0.358426i
$315$		−	27.5271i		−	1.55098i
$316$	−20.9826	+	11.7691i	−1.18036	+	0.662064i
$317$	4.56596	+	4.56596i	0.256450	+	0.256450i	0.823608	−	0.567159i	$-0.191957\pi$
$317$	4.56596	+	4.56596i	0.256450	+	0.256450i	−0.567159	+	0.823608i	$0.691957\pi$
$318$	−7.01279	+	11.9741i	−0.393258	+	0.671473i
$319$	1.36915	+	1.36915i	0.0766578	+	0.0766578i
$320$	17.4758	+	18.8299i	0.976929	+	1.05262i
$321$	−5.84704			−0.326350
$322$	−4.86700	−	18.6260i	−0.271227	−	1.03799i
$323$	0.0567518	+	0.0567518i	0.00315775	+	0.00315775i
$324$	1.78626	+	3.18464i	0.0992367	+	0.176924i
$325$	−19.1485	−	0.406978i	−1.06217	−	0.0225751i
$326$	0.473951	+	1.81381i	0.0262497	+	0.100458i
$327$	−8.07085	+	8.07085i	−0.446319	+	0.446319i
$328$	−2.53405	+	2.44130i	−0.139919	+	0.134798i
$329$		−	13.7579i		−	0.758500i
$330$	3.68440	+	2.15782i	0.202820	+	0.118784i
$331$	−10.1102	+	10.1102i	−0.555709	+	0.555709i	−0.928083	−	0.372374i	$-0.878544\pi$
$331$	−10.1102	+	10.1102i	−0.555709	+	0.555709i	0.372374	+	0.928083i	$0.378544\pi$
$332$	22.9417	+	6.45379i	1.25909	+	0.354198i
$333$	−8.64307	+	8.64307i	−0.473638	+	0.473638i
$334$	−1.01786	−	3.89536i	−0.0556948	−	0.213144i
$335$	−36.1684			−1.97609
$336$	3.57620	+	14.8094i	0.195098	+	0.807916i
$337$		−	28.6500i		−	1.56066i	−0.625366	−	0.780332i	$-0.715050\pi$
$337$		−	28.6500i		−	1.56066i	0.625366	−	0.780332i	$-0.284950\pi$
$338$	15.4552	+	9.95679i	0.840650	+	0.541578i
$339$		−	1.25127i		−	0.0679599i
$340$	31.7156	+	8.92201i	1.72002	+	0.483864i
$341$	7.94338			0.430158
$342$	−0.0452982	+	0.0118365i	−0.00244945	+	0.000640042i
$343$	−6.90586	+	6.90586i	−0.372881	+	0.372881i
$344$	0.473887	−	25.4207i	0.0255503	−	1.37059i
$345$	−7.17394	+	7.17394i	−0.386232	+	0.386232i
$346$	10.3198	−	17.6207i	0.554797	−	0.947295i
$347$			36.6371i			1.96678i	0.181502	+	0.983390i	$0.441904\pi$
$347$			36.6371i			1.96678i	−0.181502	+	0.983390i	$0.558096\pi$
$348$	3.17553	−	1.78115i	0.170227	−	0.0954799i
$349$	−16.8266	+	16.8266i	−0.900708	+	0.900708i	−0.995497	−	0.0947890i	$-0.969782\pi$
$349$	−16.8266	+	16.8266i	−0.900708	+	0.900708i	0.0947890	+	0.995497i	$0.469782\pi$
$350$	29.4442	−	7.69379i	1.57386	−	0.411251i
$351$	17.3390	+	0.368520i	0.925489	+	0.0196701i
$352$	5.41599	+	1.63312i	0.288673	+	0.0870454i
$353$	−4.09342	−	4.09342i	−0.217871	−	0.217871i	0.589730	−	0.807601i	$-0.299234\pi$
$353$	−4.09342	−	4.09342i	−0.217871	−	0.217871i	−0.807601	+	0.589730i	$0.799234\pi$
$354$	8.19456	−	2.14125i	0.435536	−	0.113806i
$355$	41.0934			2.18101
$356$	−12.0218	−	3.38190i	−0.637156	−	0.179240i
$357$	13.8158	+	13.8158i	0.731211	+	0.731211i
$358$	−15.1138	−	8.85161i	−0.798788	−	0.467822i
$359$	−21.4101	−	21.4101i	−1.12998	−	1.12998i	−0.990180	−	0.139801i	$-0.955354\pi$
$359$	−21.4101	−	21.4101i	−1.12998	−	1.12998i	−0.139801	−	0.990180i	$-0.544646\pi$
$360$	−13.8411	+	13.3345i	−0.729490	+	0.702790i
$361$			18.9998i			0.999987i
$362$	1.30795	−	2.23328i	0.0687445	−	0.117379i
$363$	0.940195			0.0493474
$364$	−27.9464	−	8.50652i	−1.46479	−	0.445863i
$365$	−45.2481			−2.36839
$366$	7.72610	−	13.1920i	0.403850	−	0.689558i
$367$			2.56826i			0.134062i	0.997751	+	0.0670311i	$0.0213527\pi$
$367$			2.56826i			0.134062i	−0.997751	+	0.0670311i	$0.978647\pi$
$368$	−7.00786	+	11.4699i	−0.365310	+	0.597912i
$369$	−1.86143	−	1.86143i	−0.0969021	−	0.0969021i
$370$	−22.6365	−	13.2574i	−1.17682	−	0.689220i
$371$	29.8949	+	29.8949i	1.55207	+	1.55207i
$372$	4.04487	−	14.3785i	0.209717	−	0.745493i
$373$	−8.16268			−0.422648			−0.211324	−	0.977416i	$-0.567777\pi$
$373$	−8.16268			−0.422648			−0.211324	+	0.977416i	$0.567777\pi$
$374$	7.01910	−	1.83410i	0.362949	−	0.0948389i
$375$	−0.666173	−	0.666173i	−0.0344010	−	0.0344010i
$376$	−6.91774	+	6.66454i	−0.356755	+	0.343698i
$377$	−0.148346	+	6.97976i	−0.00764022	+	0.359476i
$378$	−26.6618	+	6.96675i	−1.37134	+	0.358331i
$379$	17.0421	−	17.0421i	0.875392	−	0.875392i	−0.117662	−	0.993054i	$-0.537540\pi$
$379$	17.0421	−	17.0421i	0.875392	−	0.875392i	0.993054	+	0.117662i	$0.0375399\pi$
$380$	−0.0491558	−	0.0876375i	−0.00252164	−	0.00449571i
$381$		−	14.9324i		−	0.765009i
$382$	−6.65185	+	11.3578i	−0.340338	+	0.581115i
$383$	−8.12540	+	8.12540i	−0.415189	+	0.415189i	−0.883541	−	0.468353i	$-0.844848\pi$
$383$	−8.12540	+	8.12540i	−0.415189	+	0.415189i	0.468353	+	0.883541i	$0.344848\pi$
$384$	5.71404	−	8.97204i	0.291594	−	0.457852i
$385$	9.19862	−	9.19862i	0.468805	−	0.468805i
$386$	6.10414	−	1.59502i	0.310693	−	0.0811842i
$387$	19.0213			0.966908
$388$	−2.63471	+	9.36576i	−0.133757	+	0.475474i
$389$		−	25.9505i		−	1.31574i	−0.753131	−	0.657871i	$-0.771457\pi$
$389$		−	25.9505i		−	1.31574i	0.753131	−	0.657871i	$-0.228543\pi$
$390$	3.57465	+	14.9741i	0.181009	+	0.758245i
$391$			17.2382i			0.871772i
$392$	26.6132	+	0.496118i	1.34417	+	0.0250577i
$393$	20.9576			1.05717
$394$	0.959151	+	3.67068i	0.0483213	+	0.184926i
$395$	27.3139	−	27.3139i	1.37431	−	1.37431i
$396$	−1.14605	+	4.07394i	−0.0575912	+	0.204723i
$397$	−11.2521	+	11.2521i	−0.564726	+	0.564726i	−0.930646	−	0.365920i	$-0.880754\pi$
$397$	−11.2521	+	11.2521i	−0.564726	+	0.564726i	0.365920	+	0.930646i	$0.380754\pi$
$398$	−5.25564	−	3.07804i	−0.263442	−	0.154288i
$399$		−	0.0595894i		−	0.00298320i
$400$	−18.1318	−	11.0781i	−0.906588	−	0.553904i
$401$	3.98655	−	3.98655i	0.199079	−	0.199079i	−0.600526	−	0.799605i	$-0.705042\pi$
$401$	3.98655	−	3.98655i	0.199079	−	0.199079i	0.799605	+	0.600526i	$0.205042\pi$
$402$	3.78607	+	14.4893i	0.188832	+	0.722661i
$403$	19.8168	+	20.6775i	0.987146	+	1.03002i
$404$	−10.3648	+	5.81362i	−0.515670	+	0.289239i
$405$	−4.14558	−	4.14558i	−0.205996	−	0.205996i
$406$	−2.80444	−	10.7326i	−0.139182	−	0.532650i
$407$	−5.77645			−0.286328
$408$	0.254263	−	13.6394i	0.0125879	−	0.675252i
$409$	−0.0666634	−	0.0666634i	−0.00329629	−	0.00329629i	0.705457	−	0.708753i	$-0.250742\pi$
$409$	−0.0666634	−	0.0666634i	−0.00329629	−	0.00329629i	−0.708753	+	0.705457i	$0.750742\pi$
$410$	2.85520	−	4.87515i	0.141008	−	0.240766i
$411$	13.1303	+	13.1303i	0.647669	+	0.647669i
$412$	−8.30853	−	14.8129i	−0.409332	−	0.729779i
$413$		−	25.8048i		−	1.26977i
$414$	−8.67724	−	5.08195i	−0.426463	−	0.249764i
$415$	−38.2654			−1.87837
$416$	9.26041	+	18.1726i	0.454029	+	0.890987i
$417$	−3.16446			−0.154964
$418$	−0.0190925	−	0.0111818i	−0.000933843	−	0.000546919i
$419$		−	5.75122i		−	0.280966i	−0.990083	−	0.140483i	$-0.955135\pi$
$419$		−	5.75122i		−	0.280966i	0.990083	−	0.140483i	$-0.0448655\pi$
$420$	−11.9666	−	21.3348i	−0.583912	−	1.04103i
$421$	−9.09520	−	9.09520i	−0.443273	−	0.443273i	0.449838	−	0.893110i	$-0.351482\pi$
$421$	−9.09520	−	9.09520i	−0.443273	−	0.443273i	−0.893110	+	0.449838i	$0.851482\pi$
$422$	−15.5619	+	26.5714i	−0.757542	+	1.29348i
$423$	−5.08155	−	5.08155i	−0.247073	−	0.247073i
$424$	0.550179	−	29.5132i	0.0267191	−	1.43329i
$425$	−27.2502			−1.32183
$426$	−4.30162	−	16.4623i	−0.208414	−	0.797601i
$427$	−32.9357	−	32.9357i	−1.59387	−	1.59387i
$428$	10.8480	−	6.08464i	0.524359	−	0.294112i
$429$	2.34556	+	2.44743i	0.113245	+	0.118163i
$430$	10.3206	+	39.4969i	0.497703	+	1.90471i
$431$	−3.53423	+	3.53423i	−0.170238	+	0.170238i	−0.787084	−	0.616846i	$-0.788410\pi$
$431$	−3.53423	+	3.53423i	−0.170238	+	0.170238i	0.616846	+	0.787084i	$0.288410\pi$
$432$	16.4184	+	10.0312i	0.789929	+	0.482628i
$433$		−	30.9425i		−	1.48700i	−0.668736	−	0.743500i	$-0.733164\pi$
$433$		−	30.9425i		−	1.48700i	0.668736	−	0.743500i	$-0.266836\pi$
$434$	−39.2688	−	22.9983i	−1.88496	−	1.10395i
$435$	−4.13373	+	4.13373i	−0.198197	+	0.198197i
$436$	6.57503	−	23.3726i	0.314887	−	1.11935i
$437$	0.0371752	−	0.0371752i	0.00177833	−	0.00177833i
$438$	4.73652	+	18.1267i	0.226320	+	0.866127i
$439$	−31.6700			−1.51152			−0.755762	−	0.654846i	$-0.772733\pi$
$439$	−31.6700			−1.51152			−0.755762	+	0.654846i	$0.772733\pi$
$440$	−9.08117	−	0.169289i	−0.432928	−	0.00807054i
$441$			19.9136i			0.948268i
$442$	22.2853	+	13.6959i	1.06000	+	0.651445i
$443$		−	30.9887i		−	1.47232i	−0.676809	−	0.736159i	$-0.736638\pi$
$443$		−	30.9887i		−	1.47232i	0.676809	−	0.736159i	$-0.263362\pi$
$444$	−2.94144	+	10.4561i	−0.139595	+	0.496225i
$445$	20.0517			0.950542
$446$	−5.26837	+	1.37663i	−0.249464	+	0.0651853i
$447$	−10.9416	+	10.9416i	−0.517522	+	0.517522i
$448$	−22.0461	−	23.7543i	−1.04158	−	1.12228i
$449$	−10.3240	+	10.3240i	−0.487219	+	0.487219i	−0.907427	−	0.420209i	$-0.861957\pi$
$449$	−10.3240	+	10.3240i	−0.487219	+	0.487219i	0.420209	+	0.907427i	$0.361957\pi$
$450$	8.03358	−	13.7170i	0.378707	−	0.646627i
$451$		−	1.24405i		−	0.0585802i
$452$	1.30212	+	2.32149i	0.0612466	+	0.109194i
$453$	8.71105	−	8.71105i	0.409281	−	0.409281i
$454$	−14.8190	+	3.87222i	−0.695490	+	0.181732i
$455$	46.8934	+	0.996660i	2.19839	+	0.0467241i
$456$	−0.0299626	+	0.0288659i	−0.00140313	+	0.00135177i
$457$	6.14871	+	6.14871i	0.287624	+	0.287624i	0.836140	−	0.548516i	$-0.184807\pi$
$457$	6.14871	+	6.14871i	0.287624	+	0.287624i	−0.548516	+	0.836140i	$0.684807\pi$
$458$	−3.86393	+	1.00965i	−0.180550	+	0.0471778i
$459$	24.6752			1.15174
$460$	5.84435	−	20.7753i	0.272494	−	0.968652i
$461$	−9.16426	−	9.16426i	−0.426822	−	0.426822i	0.460722	−	0.887544i	$-0.347590\pi$
$461$	−9.16426	−	9.16426i	−0.426822	−	0.426822i	−0.887544	+	0.460722i	$0.847590\pi$
$462$	−4.64793	−	2.72213i	−0.216241	−	0.126645i
$463$	−6.26102	−	6.26102i	−0.290974	−	0.290974i	0.546491	−	0.837465i	$-0.315963\pi$
$463$	−6.26102	−	6.26102i	−0.290974	−	0.290974i	−0.837465	+	0.546491i	$0.815963\pi$
$464$	−4.03804	+	6.60915i	−0.187461	+	0.306822i
$465$			23.9826i			1.11216i
$466$	−13.8175	+	23.5928i	−0.640082	+	1.09292i
$467$	1.75529			0.0812252			0.0406126	−	0.999175i	$-0.487069\pi$
$467$	1.75529			0.0812252			0.0406126	+	0.999175i	$0.487069\pi$
$468$	−13.4640	+	7.18020i	−0.622374	+	0.331905i
$469$	45.6271			2.10686
$470$	7.79446	−	13.3087i	0.359532	−	0.613887i
$471$			8.35520i			0.384987i
$472$	−12.9751	+	12.5002i	−0.597228	+	0.575368i
$473$	6.35628	+	6.35628i	0.292262	+	0.292262i
$474$	−13.8013	−	8.08296i	−0.633917	−	0.371263i
$475$	0.0587668	+	0.0587668i	0.00269641	+	0.00269641i
$476$	−40.0097	−	11.2553i	−1.83384	−	0.515884i
$477$	22.0836			1.01114
$478$	−5.11583	+	1.33677i	−0.233993	+	0.0611425i
$479$	−24.2077	−	24.2077i	−1.10608	−	1.10608i	−0.993661	−	0.112417i	$-0.964141\pi$
$479$	−24.2077	−	24.2077i	−1.10608	−	1.10608i	−0.112417	−	0.993661i	$-0.535859\pi$
$480$	−4.93069	+	16.3519i	−0.225054	+	0.746358i
$481$	−14.4108	−	15.0367i	−0.657078	−	0.685615i
$482$	−11.9255	+	3.11614i	−0.543191	+	0.141936i
$483$	9.05005	−	9.05005i	0.411791	−	0.411791i
$484$	−1.74434	+	0.978400i	−0.0792883	+	0.0444727i
$485$		−	15.6215i		−	0.709337i
$486$	−11.5401	+	19.7043i	−0.523470	+	0.893805i
$487$	23.6062	−	23.6062i	1.06970	−	1.06970i	0.0723151	−	0.997382i	$-0.476961\pi$
$487$	23.6062	−	23.6062i	1.06970	−	1.06970i	0.997382	−	0.0723151i	$-0.0230387\pi$
$488$	−0.606141	+	32.5152i	−0.0274387	+	1.47189i
$489$	−0.881297	+	0.881297i	−0.0398536	+	0.0398536i
$490$	−41.3498	+	10.8047i	−1.86799	+	0.488108i
$491$	−2.63396			−0.118869			−0.0594344	−	0.998232i	$-0.518930\pi$
$491$	−2.63396			−0.118869			−0.0594344	+	0.998232i	$0.518930\pi$
$492$	−2.25190	−	0.633488i	−0.101523	−	0.0285598i
$493$			9.93289i			0.447355i
$494$	−0.0185237	−	0.0775956i	−0.000833422	−	0.00349119i
$495$		−	6.79508i		−	0.305416i
$496$	7.45838	+	30.8857i	0.334891	+	1.38681i
$497$	−51.8400			−2.32534
$498$	4.00558	+	15.3294i	0.179494	+	0.686926i
$499$	−27.1607	+	27.1607i	−1.21588	+	1.21588i	−0.246816	+	0.969062i	$0.579384\pi$
$499$	−27.1607	+	27.1607i	−1.21588	+	1.21588i	−0.969062	+	0.246816i	$0.920616\pi$
$500$	1.92919	+	0.542707i	0.0862762	+	0.0242706i
$501$	1.89268	−	1.89268i	0.0845587	−	0.0845587i
$502$	12.6294	+	7.39657i	0.563676	+	0.330125i
$503$		−	14.6794i		−	0.654524i	−0.944934	−	0.327262i	$-0.893874\pi$
$503$		−	14.6794i		−	0.654524i	0.944934	−	0.327262i	$-0.106126\pi$
$504$	17.4608	−	16.8217i	0.777765	−	0.749298i
$505$	13.4924	−	13.4924i	0.600402	−	0.600402i
$506$	−1.20142	−	4.59786i	−0.0534098	−	0.204400i
$507$	−0.519315	+	12.2115i	−0.0230636	+	0.542332i
$508$	15.5392	+	27.7040i	0.689439	+	1.22917i
$509$	16.1875	+	16.1875i	0.717501	+	0.717501i	0.968093	−	0.250592i	$-0.0806253\pi$
$509$	16.1875	+	16.1875i	0.717501	+	0.717501i	−0.250592	+	0.968093i	$0.580625\pi$
$510$	5.53749	+	21.1920i	0.245204	+	0.938397i
$511$	57.0812			2.52512
$512$	−1.26464	+	22.5920i	−0.0558897	+	0.998437i
$513$	−0.0532135	−	0.0532135i	−0.00234943	−	0.00234943i
$514$	−16.4950	+	28.1646i	−0.727563	+	1.24229i
$515$	19.2826	+	19.2826i	0.849692	+	0.849692i
$516$	14.7424	−	8.26899i	0.648998	−	0.364022i
$517$		−	3.39616i		−	0.149363i
$518$	28.5563	+	16.7244i	1.25469	+	0.734830i
$519$	13.5758			0.595910
$520$	−22.2147	−	24.0616i	−0.974177	−	1.05517i
$521$	33.6507			1.47426			0.737131	−	0.675750i	$-0.236180\pi$
$521$	33.6507			1.47426			0.737131	+	0.675750i	$0.236180\pi$
$522$	−4.99995	−	2.92829i	−0.218842	−	0.128168i
$523$		−	17.3244i		−	0.757544i	−0.925490	−	0.378772i	$-0.876346\pi$
$523$		−	17.3244i		−	0.757544i	0.925490	−	0.378772i	$-0.123654\pi$
$524$	−38.8827	+	21.8092i	−1.69860	+	0.952741i
$525$	14.3064	+	14.3064i	0.624382	+	0.624382i
$526$	3.02983	−	5.17331i	0.132107	−	0.225567i
$527$	28.8137	+	28.8137i	1.25514	+	1.25514i
$528$	0.882789	+	3.65570i	0.0384185	+	0.159094i
$529$	−11.7082			−0.509050
$530$	11.9821	+	45.8556i	0.520470	+	1.99184i
$531$	−9.53108	−	9.53108i	−0.413614	−	0.413614i
$532$	0.0620108	+	0.110556i	0.00268851	+	0.00479322i
$533$	3.23841	−	3.10361i	0.140271	−	0.134432i
$534$	−2.09899	−	8.03286i	−0.0908323	−	0.347616i
$535$	−14.1213	+	14.1213i	−0.610519	+	0.610519i
$536$	−22.1024	−	22.9421i	−0.954678	−	0.990948i
$537$		−	11.6443i		−	0.502490i
$538$	−4.47031	−	2.61810i	−0.192729	−	0.112874i
$539$	−6.65447	+	6.65447i	−0.286628	+	0.286628i
$540$	−29.7382	−	8.36575i	−1.27973	−	0.360005i
$541$	−15.3514	+	15.3514i	−0.660007	+	0.660007i	−0.955382	−	0.295375i	$-0.904556\pi$
$541$	−15.3514	+	15.3514i	−0.660007	+	0.660007i	0.295375	+	0.955382i	$0.404556\pi$
$542$	−2.09561	−	8.01992i	−0.0900143	−	0.344485i
$543$	1.72062			0.0738389
$544$	13.7219	+	25.5698i	0.588323	+	1.09630i
$545$			38.9842i			1.66990i
$546$	−4.50948	−	18.8901i	−0.192988	−	0.808423i
$547$			21.4750i			0.918203i	0.888384	+	0.459102i	$0.151829\pi$
$547$			21.4750i			0.918203i	−0.888384	+	0.459102i	$0.848171\pi$
$548$	−38.0245	−	10.6968i	−1.62432	−	0.456943i
$549$	−24.3298			−1.03837
$550$	7.26832	−	1.89922i	0.309922	−	0.0809830i
$551$	0.0214209	−	0.0214209i	0.000912561	−	0.000912561i
$552$	−8.93450	−	0.166555i	−0.380277	−	0.00708905i
$553$	−34.4570	+	34.4570i	−1.46526	+	1.46526i
$554$	15.1825	−	25.9236i	0.645044	−	1.10139i
$555$		−	17.4402i		−	0.740295i
$556$	5.87102	−	3.29305i	0.248987	−	0.139656i
$557$	−23.8771	+	23.8771i	−1.01171	+	1.01171i	−0.0117765	+	0.999931i	$0.503749\pi$
$557$	−23.8771	+	23.8771i	−1.01171	+	1.01171i	−0.999931	+	0.0117765i	$0.996251\pi$
$558$	−22.9986	+	6.00954i	−0.973607	+	0.254404i
$559$	−0.688696	+	32.4035i	−0.0291287	+	1.37052i
$560$	44.4034	+	27.1294i	1.87639	+	1.14643i
$561$	3.41045	+	3.41045i	0.143989	+	0.143989i
$562$	−14.3873	+	3.75940i	−0.606890	+	0.158581i
$563$	−4.48935			−0.189203			−0.0946017	−	0.995515i	$-0.530158\pi$
$563$	−4.48935			−0.189203			−0.0946017	+	0.995515i	$0.530158\pi$
$564$	−6.14749	−	1.72937i	−0.258856	−	0.0728196i
$565$	−3.02198	−	3.02198i	−0.127136	−	0.127136i
$566$	9.80801	+	5.74420i	0.412261	+	0.241447i
$567$	5.22972	+	5.22972i	0.219628	+	0.219628i
$568$	25.1120	+	26.0661i	1.05368	+	1.09371i
$569$		−	23.1735i		−	0.971482i	−0.874103	−	0.485741i	$-0.838550\pi$
$569$		−	23.1735i		−	0.971482i	0.874103	−	0.485741i	$-0.161450\pi$
$570$	0.0337599	−	0.0576438i	0.00141405	−	0.00241443i
$571$	3.76724			0.157654			0.0788271	−	0.996888i	$-0.474882\pi$
$571$	3.76724			0.157654			0.0788271	+	0.996888i	$0.474882\pi$
$572$	−6.89860	−	2.09984i	−0.288445	−	0.0877988i
$573$	−8.75055			−0.365559
$574$	−3.60188	+	6.15008i	−0.150340	+	0.256699i
$575$			17.8502i			0.744406i
$576$	−16.9165	−	0.630927i	−0.704854	−	0.0262886i
$577$	5.48548	+	5.48548i	0.228364	+	0.228364i	0.812009	−	0.583645i	$-0.198374\pi$
$577$	5.48548	+	5.48548i	0.228364	+	0.228364i	−0.583645	+	0.812009i	$0.698374\pi$
$578$	11.3684	+	6.65806i	0.472863	+	0.276939i
$579$	2.96589	+	2.96589i	0.123258	+	0.123258i
$580$	3.36760	−	11.9710i	0.139832	−	0.497069i
$581$	48.2724			2.00268
$582$	−6.25809	+	1.63525i	−0.259406	+	0.0677831i
$583$	7.37959	+	7.37959i	0.305631	+	0.305631i
$584$	−27.6510	−	28.7015i	−1.14420	−	1.18767i
$585$	17.6883	−	16.9521i	0.731323	−	0.700883i
$586$	7.64308	−	1.99714i	0.315733	−	0.0825013i
$587$	−26.4782	+	26.4782i	−1.09287	+	1.09287i	−0.0976531	+	0.995221i	$0.531134\pi$
$587$	−26.4782	+	26.4782i	−1.09287	+	1.09287i	−0.995221	+	0.0976531i	$0.968866\pi$
$588$	8.65691	+	15.4340i	0.357005	+	0.636487i
$589$		−	0.124277i		−	0.00512075i
$590$	14.6195	−	24.9622i	0.601875	−	1.02768i
$591$	−1.78351	+	1.78351i	−0.0733639	+	0.0733639i
$592$	−5.42375	−	22.4602i	−0.222915	−	0.923108i
$593$	0.0273214	−	0.0273214i	0.00112195	−	0.00112195i	−0.706546	−	0.707668i	$-0.749747\pi$
$593$	0.0273214	−	0.0273214i	0.00112195	−	0.00112195i	0.707668	+	0.706546i	$0.249747\pi$
$594$	−6.58149	+	1.71975i	−0.270042	+	0.0705622i
$595$	66.7339			2.73582
$596$	8.91375	−	31.6863i	0.365122	−	1.29792i
$597$		−	4.04918i		−	0.165722i
$598$	8.97145	−	14.5980i	0.366870	−	0.596956i
$599$			3.13127i			0.127940i	0.997952	+	0.0639701i	$0.0203762\pi$
$599$			3.13127i			0.127940i	−0.997952	+	0.0639701i	$0.979624\pi$
$600$	0.263291	−	14.1237i	0.0107488	−	0.576598i
$601$	−24.9666			−1.01841			−0.509204	−	0.860646i	$-0.670060\pi$
$601$	−24.9666			−1.01841			−0.509204	+	0.860646i	$0.670060\pi$
$602$	−13.0196	−	49.8260i	−0.530639	−	2.03076i
$603$	16.8525	−	16.8525i	0.686287	−	0.686287i
$604$	−7.09658	+	25.2266i	−0.288756	+	1.02646i
$605$	2.27069	−	2.27069i	0.0923166	−	0.0923166i
$606$	−6.81750	−	3.99277i	−0.276942	−	0.162195i
$607$		−	5.10274i		−	0.207114i	−0.994624	−	0.103557i	$-0.966978\pi$
$607$		−	5.10274i		−	0.207114i	0.994624	−	0.103557i	$-0.0330224\pi$
$608$	0.0255507	−	0.0847351i	0.00103622	−	0.00343646i
$609$	5.21477	−	5.21477i	0.211313	−	0.211313i
$610$	−13.2009	−	50.5198i	−0.534488	−	2.04549i
$611$	8.84058	−	8.47261i	0.357651	−	0.342765i
$612$	−18.9349	+	10.6206i	−0.765398	+	0.429311i
$613$	15.6906	+	15.6906i	0.633735	+	0.633735i	0.949003	−	0.315268i	$-0.102094\pi$
$613$	15.6906	+	15.6906i	0.633735	+	0.633735i	−0.315268	+	0.949003i	$0.602094\pi$
$614$	2.15972	+	8.26524i	0.0871590	+	0.333558i
$615$	3.75603			0.151458
$616$	11.4560	+	0.213561i	0.461577	+	0.00860462i
$617$	22.4908	+	22.4908i	0.905445	+	0.905445i	0.995900	−	0.0904559i	$-0.0288324\pi$
$617$	22.4908	+	22.4908i	0.905445	+	0.905445i	−0.0904559	+	0.995900i	$0.528832\pi$
$618$	5.70626	−	9.74322i	0.229539	−	0.391930i
$619$	−29.1785	−	29.1785i	−1.17278	−	1.17278i	−0.981543	−	0.191241i	$-0.938749\pi$
$619$	−29.1785	−	29.1785i	−1.17278	−	1.17278i	−0.191241	−	0.981543i	$-0.561251\pi$
$620$	−24.9571	−	44.4948i	−1.00230	−	1.78696i
$621$		−	16.1634i		−	0.648617i
$622$	16.6437	+	9.74761i	0.667350	+	0.390843i
$623$	−25.2956			−1.01345
$624$	−7.31384	+	11.4181i	−0.292788	+	0.457090i
$625$	23.3424			0.933697
$626$	16.3228	+	9.55967i	0.652389	+	0.382081i
$627$		−	0.0147097i		−	0.000587449i
$628$	−8.69472	−	15.5014i	−0.346957	−	0.618573i
$629$	−20.9534	−	20.9534i	−0.835467	−	0.835467i
$630$	−19.6737	+	33.5921i	−0.783818	+	1.33834i
$631$	3.73243	+	3.73243i	0.148586	+	0.148586i	0.777486	−	0.628900i	$-0.216495\pi$
$631$	3.73243	+	3.73243i	0.148586	+	0.148586i	−0.628900	+	0.777486i	$0.716495\pi$
$632$	34.0170	+	0.634138i	1.35313	+	0.0252247i
$633$	−20.4718			−0.813680
$634$	−2.30866	−	8.83527i	−0.0916887	−	0.350893i
$635$	−36.0636	−	36.0636i	−1.43114	−	1.43114i
$636$	17.1158	−	9.60023i	0.678686	−	0.380674i
$637$	−33.9236	−	0.721004i	−1.34410	−	0.0285672i
$638$	−0.692278	−	2.64935i	−0.0274076	−	0.104889i
$639$	−19.1473	+	19.1473i	−0.757455	+	0.757455i
$640$	−7.86846	−	35.4687i	−0.311028	−	1.40202i
$641$			13.3136i			0.525854i	0.964816	+	0.262927i	$0.0846878\pi$
$641$			13.3136i			0.525854i	−0.964816	+	0.262927i	$0.915312\pi$
$642$	7.13531	+	4.17890i	0.281608	+	0.164928i
$643$	−12.3485	+	12.3485i	−0.486979	+	0.486979i	−0.907351	−	0.420373i	$-0.861899\pi$
$643$	−12.3485	+	12.3485i	−0.486979	+	0.486979i	0.420373	+	0.907351i	$0.361899\pi$
$644$	−7.37275	+	26.2083i	−0.290527	+	1.03275i
$645$	−19.1908	+	19.1908i	−0.755638	+	0.755638i
$646$	−0.0286951	−	0.109816i	−0.00112899	−	0.00432067i
$647$	−6.43859			−0.253127			−0.126564	−	0.991959i	$-0.540395\pi$
$647$	−6.43859			−0.253127			−0.126564	+	0.991959i	$0.540395\pi$
$648$	0.0962465	−	5.16295i	0.00378092	−	0.202820i
$649$		−	6.36993i		−	0.250042i
$650$	23.0766	+	14.1821i	0.905139	+	0.556269i
$651$		−	30.2544i		−	1.18576i
$652$	0.717961	−	2.55218i	0.0281175	−	0.0999511i
$653$	−9.12938			−0.357260			−0.178630	−	0.983916i	$-0.557167\pi$
$653$	−9.12938			−0.357260			−0.178630	+	0.983916i	$0.557167\pi$
$654$	15.6173	−	4.08082i	0.610686	−	0.159573i
$655$	50.6153	−	50.6153i	1.97770	−	1.97770i
$656$	4.83717	−	1.16809i	0.188860	−	0.0456064i
$657$	21.0831	−	21.0831i	0.822532	−	0.822532i
$658$	−9.83284	+	16.7892i	−0.383324	+	0.654511i
$659$		−	28.4730i		−	1.10915i	−0.832133	−	0.554576i	$-0.812881\pi$
$659$		−	28.4730i		−	1.10915i	0.832133	−	0.554576i	$-0.187119\pi$
$660$	−2.95398	−	5.26650i	−0.114983	−	0.204998i
$661$	18.5153	−	18.5153i	0.720160	−	0.720160i	−0.248477	−	0.968638i	$-0.579930\pi$
$661$	18.5153	−	18.5153i	0.720160	−	0.720160i	0.968638	+	0.248477i	$0.0799301\pi$
$662$	19.5636	−	5.11199i	0.760362	−	0.198683i
$663$	−0.369518	+	17.3860i	−0.0143509	+	0.675217i
$664$	−23.3838	−	24.2722i	−0.907469	−	0.941945i
$665$	−0.143916	−	0.143916i	−0.00558081	−	0.00558081i
$666$	16.7246	−	4.37016i	0.648066	−	0.169340i
$667$	6.50653			0.251934
$668$	−1.54190	+	5.48108i	−0.0596578	+	0.212069i
$669$	−2.55980	−	2.55980i	−0.0989676	−	0.0989676i
$670$	44.1373	+	25.8497i	1.70517	+	0.998660i
$671$	−8.13021	−	8.13021i	−0.313863	−	0.313863i
$672$	6.22014	−	20.6282i	0.239947	−	0.795750i
$673$			32.2629i			1.24364i	0.783159	+	0.621821i	$0.213607\pi$
$673$			32.2629i			1.24364i	−0.783159	+	0.621821i	$0.786393\pi$
$674$	−20.4762	+	34.9624i	−0.788714	+	1.34670i
$675$	25.5513			0.983469
$676$	−11.7442	−	23.1964i	−0.451701	−	0.892169i
$677$	−35.7337			−1.37336			−0.686678	−	0.726961i	$-0.740932\pi$
$677$	−35.7337			−1.37336			−0.686678	+	0.726961i	$0.740932\pi$
$678$	−0.894289	+	1.52696i	−0.0343450	+	0.0586427i
$679$			19.7068i			0.756278i
$680$	−32.3268	−	33.5550i	−1.23968	−	1.28677i
$681$	−7.20028	−	7.20028i	−0.275915	−	0.275915i
$682$	−9.69353	−	5.67715i	−0.371184	−	0.217389i
$683$	−1.56157	−	1.56157i	−0.0597519	−	0.0597519i	0.676599	−	0.736351i	$-0.263453\pi$
$683$	−1.56157	−	1.56157i	−0.0597519	−	0.0597519i	−0.736351	+	0.676599i	$0.763453\pi$
$684$	0.0637382	+	0.0179304i	0.00243709	+	0.000685585i
$685$	63.4225			2.42325
$686$	13.3631	−	3.49178i	0.510204	−	0.133317i
$687$	−1.87741	−	1.87741i	−0.0716278	−	0.0716278i
$688$	−18.7465	+	30.6829i	−0.714705	+	1.16978i
$689$	−0.799570	+	37.6202i	−0.0304612	+	1.43321i
$690$	13.8818	−	3.62733i	0.528471	−	0.138090i
$691$	23.2395	−	23.2395i	0.884071	−	0.884071i	−0.109875	−	0.993945i	$-0.535045\pi$
$691$	23.2395	−	23.2395i	0.884071	−	0.884071i	0.993945	+	0.109875i	$0.0350449\pi$
$692$	−25.1871	+	14.1274i	−0.957471	+	0.537044i
$693$			8.57211i			0.325628i
$694$	26.1846	−	44.7092i	0.993954	−	1.69714i
$695$	−7.64256	+	7.64256i	−0.289899	+	0.289899i
$696$	−5.14819	−	0.0959714i	−0.195142	−	0.00363779i
$697$	4.51266	−	4.51266i	0.170929	−	0.170929i
$698$	32.5600	−	8.50796i	1.23242	−	0.322031i
$699$	−18.1770			−0.687516
$700$	−41.4303	−	11.6549i	−1.56592	−	0.440513i
$701$			15.0950i			0.570130i	0.958508	+	0.285065i	$0.0920152\pi$
$701$			15.0950i			0.570130i	−0.958508	+	0.285065i	$0.907985\pi$
$702$	−20.8959	−	12.8420i	−0.788666	−	0.484689i
$703$			0.0903746i			0.00340854i
$704$	−5.44209	−	5.86376i	−0.205106	−	0.220999i
$705$	10.2537			0.386175
$706$	2.06974	+	7.92090i	0.0778956	+	0.298107i
$707$	−17.0208	+	17.0208i	−0.640134	+	0.640134i
$708$	−11.5304	−	3.24365i	−0.433339	−	0.121904i
$709$	25.4387	−	25.4387i	0.955371	−	0.955371i	−0.0436744	−	0.999046i	$-0.513906\pi$
$709$	25.4387	−	25.4387i	0.955371	−	0.955371i	0.999046	+	0.0436744i	$0.0139064\pi$
$710$	−50.1474	−	29.3696i	−1.88200	−	1.10222i
$711$			25.4536i			0.954585i
$712$	12.2535	+	12.7191i	0.459220	+	0.476667i
$713$	18.8744	−	18.8744i	0.706851	−	0.706851i
$714$	−6.98563	−	26.7341i	−0.261431	−	1.00050i
$715$	11.5757	+	0.246026i	0.432905	+	0.00920087i
$716$	12.1175	+	21.6037i	0.452852	+	0.807369i
$717$	−2.48569	−	2.48569i	−0.0928297	−	0.0928297i
$718$	10.8255	+	41.4292i	0.404003	+	1.54612i
$719$	4.26512			0.159062			0.0795310	−	0.996832i	$-0.474658\pi$
$719$	4.26512			0.159062			0.0795310	+	0.996832i	$0.474658\pi$
$720$	26.4209	−	6.38019i	0.984649	−	0.237776i
$721$	−24.3253	−	24.3253i	−0.905921	−	0.905921i
$722$	13.5792	−	23.1859i	0.505365	−	0.862891i
$723$	−5.79437	−	5.79437i	−0.215495	−	0.215495i
$724$	−3.19226	+	1.79054i	−0.118640	+	0.0665448i
$725$			10.2856i			0.381997i
$726$	−1.14735	−	0.671960i	−0.0425820	−	0.0249388i
$727$	10.0764			0.373715			0.186857	−	0.982387i	$-0.440170\pi$
$727$	10.0764			0.373715			0.186857	+	0.982387i	$0.440170\pi$
$728$	28.0242	+	30.3541i	1.03864	+	1.12500i
$729$	−9.70398			−0.359407
$730$	55.2175	+	32.3389i	2.04369	+	1.19692i
$731$			46.1134i			1.70556i
$732$	−18.8567	+	10.5767i	−0.696965	+	0.390927i
$733$	15.1943	+	15.1943i	0.561216	+	0.561216i	0.929653	−	0.368437i	$-0.120107\pi$
$733$	15.1943	+	15.1943i	0.561216	+	0.561216i	−0.368437	+	0.929653i	$0.620107\pi$
$734$	1.83554	−	3.13412i	0.0677512	−	0.115683i
$735$	−20.0911	−	20.0911i	−0.741071	−	0.741071i
$736$	16.7495	−	8.98854i	0.617394	−	0.331322i
$737$	11.2631			0.414881
$738$	0.941185	+	3.60192i	0.0346455	+	0.132589i
$739$	8.08048	+	8.08048i	0.297245	+	0.297245i	0.839934	−	0.542689i	$-0.182594\pi$
$739$	8.08048	+	8.08048i	0.297245	+	0.297245i	−0.542689	+	0.839934i	$0.682594\pi$
$740$	18.1489	+	32.3568i	0.667166	+	1.18946i
$741$	0.0382909	−	0.0366971i	0.00140665	−	0.00134810i
$742$	−15.1156	−	57.8476i	−0.554912	−	2.12365i
$743$	−33.2244	+	33.2244i	−1.21889	+	1.21889i	−0.250864	+	0.968022i	$0.580715\pi$
$743$	−33.2244	+	33.2244i	−1.21889	+	1.21889i	−0.968022	+	0.250864i	$0.919285\pi$
$744$	−15.2125	+	14.6557i	−0.557716	+	0.537303i
$745$			52.8508i			1.93630i
$746$	9.96115	+	5.83389i	0.364704	+	0.213594i
$747$	17.8296	−	17.8296i	0.652350	−	0.652350i
$748$	−9.87644	−	2.77837i	−0.361118	−	0.101587i
$749$	17.8143	−	17.8143i	0.650920	−	0.650920i
$750$	0.336834	+	1.28907i	0.0122994	+	0.0470700i
$751$	−16.8846			−0.616127			−0.308064	−	0.951366i	$-0.599681\pi$
$751$	−16.8846			−0.616127			−0.308064	+	0.951366i	$0.599681\pi$
$752$	13.2051	−	3.18880i	0.481540	−	0.116284i
$753$			9.73023i			0.354589i
$754$	5.16948	−	8.41157i	0.188262	−	0.306331i
$755$		−	42.0765i		−	1.53132i
$756$	37.5153	+	10.5535i	1.36442	+	0.383829i
$757$	−31.5957			−1.14836			−0.574182	−	0.818728i	$-0.694680\pi$
$757$	−31.5957			−1.14836			−0.574182	+	0.818728i	$0.694680\pi$
$758$	−32.9769	+	8.61690i	−1.19778	+	0.312980i
$759$	2.23401	−	2.23401i	0.0810895	−	0.0810895i
$760$	−0.00264859	+	0.142078i	−9.60745e−5	+	0.00515372i
$761$	−13.2612	+	13.2612i	−0.480717	+	0.480717i	−0.905361	−	0.424644i	$-0.860399\pi$
$761$	−13.2612	+	13.2612i	−0.480717	+	0.480717i	0.424644	+	0.905361i	$0.360399\pi$
$762$	−10.6722	+	18.2224i	−0.386614	+	0.660128i
$763$		−	49.1792i		−	1.78041i
$764$	16.2349	−	9.10613i	0.587357	−	0.329448i
$765$	24.6484	−	24.6484i	0.891164	−	0.891164i
$766$	15.7229	−	4.10841i	0.568091	−	0.148443i
$767$	16.5816	−	15.8915i	0.598728	−	0.573807i
$768$	−13.3853	+	6.86499i	−0.483002	+	0.247719i
$769$	−30.2775	−	30.2775i	−1.09184	−	1.09184i	−0.995333	−	0.0965035i	$-0.969234\pi$
$769$	−30.2775	−	30.2775i	−1.09184	−	1.09184i	−0.0965035	−	0.995333i	$-0.530766\pi$
$770$	−17.7996	+	4.65105i	−0.641453	+	0.167612i
$771$	−21.6992			−0.781479
$772$	−8.58901	−	2.41620i	−0.309125	−	0.0869610i
$773$	−32.6016	−	32.6016i	−1.17260	−	1.17260i	−0.981588	−	0.191012i	$-0.938823\pi$
$773$	−32.6016	−	32.6016i	−1.17260	−	1.17260i	−0.191012	−	0.981588i	$-0.561177\pi$
$774$	−23.2122	−	13.5946i	−0.834347	−	0.488647i
$775$	29.8368	+	29.8368i	1.07177	+	1.07177i
$776$	9.90894	−	9.54626i	0.355710	−	0.342691i
$777$			22.0011i			0.789285i
$778$	−18.5469	+	31.6681i	−0.664938	+	1.13536i
$779$	−0.0194637			−0.000697358
$780$	6.33982	−	20.8282i	0.227002	−	0.745768i
$781$	−12.7968			−0.457904
$782$	12.3202	−	21.0362i	0.440568	−	0.752254i
$783$		−	9.31362i		−	0.332841i
$784$	−32.1223	−	19.6260i	−1.14722	−	0.700928i
$785$	20.1788	+	20.1788i	0.720214	+	0.720214i
$786$	−25.5752	−	14.9785i	−0.912236	−	0.534264i
$787$	13.9717	+	13.9717i	0.498038	+	0.498038i	0.910827	−	0.412789i	$-0.135445\pi$
$787$	13.9717	+	13.9717i	0.498038	+	0.498038i	−0.412789	+	0.910827i	$0.635445\pi$
$788$	1.45296	−	5.16494i	0.0517597	−	0.183993i
$789$	3.98575			0.141897
$790$	−52.8533	+	13.8106i	−1.88044	+	0.491360i
$791$	3.81228	+	3.81228i	0.135549	+	0.135549i
$792$	4.31021	−	4.15245i	0.153157	−	0.147551i
$793$	0.880899	−	41.4467i	0.0312816	−	1.47182i
$794$	21.7731	−	5.68934i	0.772700	−	0.201907i
$795$	−22.2804	+	22.2804i	−0.790204	+	0.790204i
$796$	4.21372	+	7.51244i	0.149351	+	0.266272i
$797$		−	30.8696i		−	1.09346i	−0.837309	−	0.546730i	$-0.815873\pi$
$797$		−	30.8696i		−	1.09346i	0.837309	−	0.546730i	$-0.184127\pi$
$798$	−0.0425887	+	0.0727186i	−0.00150762	+	0.00257421i
$799$	12.3192	−	12.3192i	0.435822	−	0.435822i
$800$	14.2092	+	26.4777i	0.502369	+	0.936128i
$801$	−9.34300	+	9.34300i	−0.330119	+	0.330119i
$802$	−7.71409	+	2.01570i	−0.272394	+	0.0711768i
$803$	14.0906			0.497245
$804$	5.73531	−	20.3876i	0.202269	−	0.719016i
$805$		−	43.7140i		−	1.54071i
$806$	−9.40477	−	39.3964i	−0.331269	−	1.38768i
$807$		−	3.44412i		−	0.121239i
$808$	16.8035	+	0.313247i	0.591145	+	0.0110200i
$809$	24.4625			0.860054			0.430027	−	0.902816i	$-0.358504\pi$
$809$	24.4625			0.860054			0.430027	+	0.902816i	$0.358504\pi$
$810$	2.09611	+	8.02183i	0.0736498	+	0.281858i
$811$	0.614981	−	0.614981i	0.0215949	−	0.0215949i	−0.696227	−	0.717822i	$-0.745139\pi$
$811$	0.614981	−	0.614981i	0.0215949	−	0.0215949i	0.717822	+	0.696227i	$0.245139\pi$
$812$	−4.24829	+	15.1016i	−0.149086	+	0.529964i
$813$	3.89673	−	3.89673i	0.136664	−	0.136664i
$814$	7.04916	+	4.12844i	0.247073	+	0.144702i
$815$			4.25688i			0.149112i
$816$	−10.0584	+	16.4629i	−0.352115	+	0.576315i
$817$	0.0994463	−	0.0994463i	0.00347919	−	0.00347919i
$818$	0.0337067	+	0.128996i	0.00117853	+	0.00451023i
$819$	−22.3141	+	21.3854i	−0.779719	+	0.747265i
$820$	−6.96856	+	3.90866i	−0.243353	+	0.136496i
$821$	1.72702	+	1.72702i	0.0602735	+	0.0602735i	0.736601	−	0.676328i	$-0.236430\pi$
$821$	1.72702	+	1.72702i	0.0602735	+	0.0602735i	−0.676328	+	0.736601i	$0.736430\pi$
$822$	−6.63901	−	25.4075i	−0.231562	−	0.886189i
$823$	38.9575			1.35797			0.678986	−	0.734151i	$-0.262420\pi$
$823$	38.9575			1.35797			0.678986	+	0.734151i	$0.262420\pi$
$824$	−0.447677	+	24.0147i	−0.0155956	+	0.836592i
$825$	3.53154	+	3.53154i	0.122953	+	0.122953i
$826$	−18.4427	+	31.4903i	−0.641705	+	1.09569i
$827$	33.4590	+	33.4590i	1.16348	+	1.16348i	0.983707	+	0.179777i	$0.0575375\pi$
$827$	33.4590	+	33.4590i	1.16348	+	1.16348i	0.179777	+	0.983707i	$0.442463\pi$
$828$	6.95699	+	12.4033i	0.241772	+	0.431044i
$829$		−	34.3267i		−	1.19222i	−0.802904	−	0.596108i	$-0.796713\pi$
$829$		−	34.3267i		−	1.19222i	0.802904	−	0.596108i	$-0.203287\pi$
$830$	46.6963	+	27.3484i	1.62085	+	0.949276i
$831$	19.9727			0.692845
$832$	1.68729	−	28.7950i	0.0584964	−	0.998288i
$833$	−48.2766			−1.67269
$834$	3.86168	+	2.26165i	0.133719	+	0.0783144i
$835$		−	9.14211i		−	0.316376i
$836$	0.0153074	+	0.0272909i	0.000529418	+	0.000943875i
$837$	−27.0173	−	27.0173i	−0.933854	−	0.933854i
$838$	−4.11042	+	7.01838i	−0.141992	+	0.242446i
$839$	7.37624	+	7.37624i	0.254656	+	0.254656i	0.822876	−	0.568220i	$-0.192368\pi$
$839$	7.37624	+	7.37624i	0.254656	+	0.254656i	−0.568220	+	0.822876i	$0.692368\pi$
$840$	−0.644781	+	34.5880i	−0.0222471	+	1.19340i
$841$	−25.2508			−0.870719
$842$	4.59876	+	17.5995i	0.158484	+	0.606518i
$843$	−6.99050	−	6.99050i	−0.240765	−	0.240765i
$844$	37.9813	−	21.3037i	1.30737	−	0.733302i
$845$	28.2381	+	30.7465i	0.971419	+	1.05771i
$846$	2.56936	+	9.83295i	0.0883363	+	0.338064i
$847$	−2.86451	+	2.86451i	−0.0984257	+	0.0984257i
$848$	−21.7646	+	35.6226i	−0.747399	+	1.22329i
$849$			7.55653i			0.259339i
$850$	33.2542	+	19.4758i	1.14061	+	0.668015i
$851$	−13.7255	+	13.7255i	−0.470504	+	0.470504i
$852$	−6.51627	+	23.1638i	−0.223244	+	0.793578i
$853$	−16.6410	+	16.6410i	−0.569777	+	0.569777i	−0.932066	−	0.362289i	$-0.881995\pi$
$853$	−16.6410	+	16.6410i	−0.569777	+	0.569777i	0.362289	+	0.932066i	$0.381995\pi$
$854$	16.6531	+	63.7316i	0.569858	+	2.18085i
$855$	−0.106312			−0.00363578
$856$	−17.5868	−	0.327850i	−0.601106	−	0.0112057i
$857$		−	27.7924i		−	0.949369i	−0.880156	−	0.474685i	$-0.842562\pi$
$857$		−	27.7924i		−	0.949369i	0.880156	−	0.474685i	$-0.157438\pi$
$858$	−1.11317	−	4.66305i	−0.0380029	−	0.159194i
$859$		−	48.8344i		−	1.66621i	−0.553116	−	0.833104i	$-0.686561\pi$
$859$		−	48.8344i		−	1.66621i	0.553116	−	0.833104i	$-0.313439\pi$
$860$	15.6341	−	55.5753i	0.533117	−	1.89510i
$861$	−4.73830			−0.161481
$862$	6.83885	−	1.78700i	0.232932	−	0.0608654i
$863$	15.3948	−	15.3948i	0.524044	−	0.524044i	−0.394746	−	0.918790i	$-0.629167\pi$
$863$	15.3948	−	15.3948i	0.524044	−	0.524044i	0.918790	+	0.394746i	$0.129167\pi$
$864$	−12.8664	−	23.9756i	−0.437725	−	0.815668i
$865$	32.7872	−	32.7872i	1.11480	−	1.11480i
$866$	−22.1147	+	37.7599i	−0.751487	+	1.28313i
$867$			8.75872i			0.297462i
$868$	31.4838	+	56.1310i	1.06863	+	1.90521i
$869$	−8.50574	+	8.50574i	−0.288537	+	0.288537i
$870$	7.99890	−	2.09012i	0.271188	−	0.0708617i
$871$	28.0987	+	29.3190i	0.952087	+	0.993437i
$872$	−24.7282	+	23.8231i	−0.837402	+	0.806752i
$873$	7.27878	+	7.27878i	0.246349	+	0.246349i
$874$	−0.0719351	+	0.0187967i	−0.00243324	+	0.000635808i
$875$	4.05929			0.137229
$876$	7.17509	−	25.5057i	0.242424	−	0.861759i
$877$	12.5866	+	12.5866i	0.425021	+	0.425021i	0.886928	−	0.461908i	$-0.152835\pi$
$877$	12.5866	+	12.5866i	0.425021	+	0.425021i	−0.461908	+	0.886928i	$0.652835\pi$
$878$	38.6477	+	22.6346i	1.30430	+	0.763881i
$879$	3.71363	+	3.71363i	0.125258	+	0.125258i
$880$	10.9610	+	6.69693i	0.369496	+	0.225753i
$881$		−	26.0147i		−	0.876456i	−0.898864	−	0.438228i	$-0.855606\pi$
$881$		−	26.0147i		−	0.876456i	0.898864	−	0.438228i	$-0.144394\pi$
$882$	14.2323	−	24.3012i	0.479227	−	0.818263i
$883$	−4.33991			−0.146049			−0.0730247	−	0.997330i	$-0.523265\pi$
$883$	−4.33991			−0.146049			−0.0730247	+	0.997330i	$0.523265\pi$
$884$	−17.4069	−	32.6408i	−0.585459	−	1.09783i
$885$	19.2320			0.646478
$886$	−22.1477	+	37.8164i	−0.744067	+	1.27047i
$887$		−	16.1437i		−	0.542052i	−0.962572	−	0.271026i	$-0.912637\pi$
$887$		−	16.1437i		−	0.542052i	0.962572	−	0.271026i	$-0.0873629\pi$
$888$	11.0625	−	10.6576i	0.371234	−	0.357647i
$889$	45.4948	+	45.4948i	1.52585	+	1.52585i
$890$	−24.4697	−	14.3310i	−0.820225	−	0.480377i
$891$	1.29096	+	1.29096i	0.0432488	+	0.0432488i
$892$	7.41301	+	2.08538i	0.248206	+	0.0698236i
$893$	−0.0531342			−0.00177807
$894$	21.1724	−	5.53237i	0.708111	−	0.185030i
$895$	−28.1225	−	28.1225i	−0.940032	−	0.940032i
$896$	9.92619	+	44.7444i	0.331611	+	1.49480i
$897$	11.3887	+	0.242053i	0.380258	+	0.00808190i
$898$	19.9772	−	5.22006i	0.666648	−	0.174196i
$899$	10.8757	−	10.8757i	0.362725	−	0.362725i
$900$	−19.6072	+	10.9977i	−0.653574	+	0.366589i
$901$			53.5372i			1.78358i
$902$	−0.889128	+	1.51815i	−0.0296047	+	0.0505490i
$903$	24.2095	−	24.2095i	0.805643	−	0.805643i
$904$	0.0701603	−	3.76360i	0.00233350	−	0.125176i
$905$	4.15551	−	4.15551i	0.138134	−	0.138134i
$906$	−16.8562	+	4.40453i	−0.560008	+	0.146331i
$907$	−2.94406			−0.0977558			−0.0488779	−	0.998805i	$-0.515565\pi$
$907$	−2.94406			−0.0977558			−0.0488779	+	0.998805i	$0.515565\pi$
$908$	20.8515	+	5.86581i	0.691982	+	0.194664i
$909$			12.5734i			0.417033i
$910$	−56.5129	−	34.7311i	−1.87339	−	1.15132i
$911$			56.9195i			1.88583i	0.333038	+	0.942913i	$0.391926\pi$
$911$			56.9195i			1.88583i	−0.333038	+	0.942913i	$0.608074\pi$
$912$	0.0571948	−	0.0138116i	0.00189391	−	0.000457346i
$913$	11.9161			0.394365
$914$	−3.10894	−	11.8979i	−0.102835	−	0.393549i
$915$	24.5466	−	24.5466i	0.811487	−	0.811487i
$916$	5.43687	+	1.52946i	0.179639	+	0.0505348i
$917$	−63.8520	+	63.8520i	−2.10858	+	2.10858i
$918$	−30.1118	−	17.6354i	−0.993837	−	0.582055i
$919$		−	47.6617i		−	1.57221i	−0.618091	−	0.786106i	$-0.712094\pi$
$919$		−	47.6617i		−	1.57221i	0.618091	−	0.786106i	$-0.287906\pi$
$920$	−21.9802	+	21.1757i	−0.724664	+	0.698141i
$921$	−4.01593	+	4.01593i	−0.132329	+	0.132329i
$922$	4.63368	+	17.7331i	0.152602	+	0.584009i
$923$	−31.9248	−	33.3113i	−1.05082	−	1.09646i
$924$	3.72649	+	6.64378i	0.122592	+	0.218564i
$925$	−21.6974	−	21.6974i	−0.713405	−	0.713405i
$926$	3.16573	+	12.1153i	0.104032	+	0.398133i
$927$	−17.9693			−0.590188
$928$	9.65130	−	5.17933i	0.316820	−	0.170020i
$929$	10.5200	+	10.5200i	0.345150	+	0.345150i	0.858300	−	0.513149i	$-0.171521\pi$
$929$	10.5200	+	10.5200i	0.345150	+	0.345150i	−0.513149	+	0.858300i	$0.671521\pi$
$930$	17.1404	−	29.2666i	0.562056	−	0.959689i
$931$	0.104112	+	0.104112i	0.00341212	+	0.00341212i
$932$	33.7237	−	18.9156i	1.10466	−	0.619601i
$933$			12.8230i			0.419807i
$934$	−2.14203	−	1.25451i	−0.0700894	−	0.0410489i
$935$	16.4733			0.538735
$936$	21.5622	+	0.860577i	0.704783	+	0.0281289i
$937$	41.0205			1.34008			0.670041	−	0.742324i	$-0.266277\pi$
$937$	41.0205			1.34008			0.670041	+	0.742324i	$0.266277\pi$
$938$	−55.6800	−	32.6098i	−1.81802	−	1.06475i
$939$			12.5758i			0.410395i
$940$	−19.0236	+	10.6703i	−0.620481	+	0.348027i
$941$	22.0664	+	22.0664i	0.719343	+	0.719343i	0.968471	−	0.249127i	$-0.0801438\pi$
$941$	22.0664	+	22.0664i	0.719343	+	0.719343i	−0.249127	+	0.968471i	$0.580144\pi$
$942$	5.97148	−	10.1961i	0.194561	−	0.332206i
$943$	−2.95601	−	2.95601i	−0.0962611	−	0.0962611i
$944$	24.7678	−	5.98100i	0.806123	−	0.194665i
$945$	−62.5733			−2.03551
$946$	−3.21390	−	12.2996i	−0.104493	−	0.399894i
$947$	18.8942	+	18.8942i	0.613979	+	0.613979i	0.943981	−	0.330001i	$-0.107049\pi$
$947$	18.8942	+	18.8942i	0.613979	+	0.613979i	−0.330001	+	0.943981i	$0.607049\pi$
$948$	11.0653	+	19.7277i	0.359383	+	0.640727i
$949$	35.1525	+	36.6792i	1.14110	+	1.19066i
$950$	−0.0297140	−	0.113716i	−0.000964049	−	0.00368942i
$951$	4.29289	−	4.29289i	0.139207	−	0.139207i
$952$	40.7808	+	42.3302i	1.32171	+	1.37193i
$953$		−	15.3131i		−	0.496041i	−0.968755	−	0.248021i	$-0.920220\pi$
$953$		−	15.3131i		−	0.496041i	0.968755	−	0.248021i	$-0.0797801\pi$
$954$	−26.9492	−	15.7832i	−0.872513	−	0.511000i
$955$	−21.1336	+	21.1336i	−0.683869	+	0.683869i
$956$	7.19839	+	2.02500i	0.232813	+	0.0654932i
$957$	1.28727	−	1.28727i	0.0416116	−	0.0416116i
$958$	12.2400	+	46.8426i	0.395457	+	1.51342i
$959$	−80.0086			−2.58361
$960$	17.7038	−	16.4307i	0.571388	−	0.530298i
$961$		−	32.0973i		−	1.03540i
$962$	6.83917	+	28.6492i	0.220504	+	0.923687i
$963$		−	13.1595i		−	0.424060i
$964$	16.7801	+	4.72047i	0.540451	+	0.152036i
$965$	14.3260			0.461169
$966$	−17.5121	+	4.57593i	−0.563443	+	0.147228i
$967$	−8.26355	+	8.26355i	−0.265738	+	0.265738i	−0.827380	−	0.561642i	$-0.810170\pi$
$967$	−8.26355	+	8.26355i	−0.265738	+	0.265738i	0.561642	+	0.827380i	$0.310170\pi$
$968$	2.82794	+	0.0527177i	0.0908933	+	0.00169441i
$969$	0.0533577	−	0.0533577i	0.00171410	−	0.00171410i
$970$	−11.1647	+	19.0634i	−0.358478	+	0.612088i
$971$		−	18.5609i		−	0.595649i	−0.954621	−	0.297824i	$-0.903739\pi$
$971$		−	18.5609i		−	0.595649i	0.954621	−	0.297824i	$-0.0962610\pi$
$972$	28.1654	−	15.7980i	0.903406	−	0.506720i
$973$	9.64121	−	9.64121i	0.309083	−	0.309083i
$974$	−45.6786	+	11.9359i	−1.46364	+	0.382450i
$975$	−0.382639	+	18.0033i	−0.0122542	+	0.576568i
$976$	23.9784	−	39.2460i	0.767529	−	1.25623i
$977$	−25.2012	−	25.2012i	−0.806258	−	0.806258i	0.177808	−	0.984065i	$-0.443100\pi$
$977$	−25.2012	−	25.2012i	−0.806258	−	0.806258i	−0.984065	+	0.177808i	$0.943100\pi$
$978$	1.70534	−	0.445606i	0.0545307	−	0.0142489i
$979$	−6.24423			−0.199567
$980$	58.1825	+	16.3675i	1.85857	+	0.522840i
$981$	−18.1645	−	18.1645i	−0.579948	−	0.579948i
$982$	3.21429	+	1.88250i	0.102572	+	0.0600728i
$983$	−7.53294	−	7.53294i	−0.240264	−	0.240264i	0.576696	−	0.816959i	$-0.304342\pi$
$983$	−7.53294	−	7.53294i	−0.240264	−	0.240264i	−0.816959	+	0.576696i	$0.804342\pi$
$984$	2.29530	+	2.38250i	0.0731714	+	0.0759513i
$985$			8.61481i			0.274491i
$986$	7.09906	−	12.1214i	0.226080	−	0.386023i
$987$	−12.9352			−0.411731
$988$	−0.0328528	+	0.107931i	−0.00104519	+	0.00343374i
$989$	30.2065			0.960511
$990$	−4.85646	+	8.29223i	−0.154349	+	0.263544i
$991$		−	23.8997i		−	0.759198i	−0.925151	−	0.379599i	$-0.876062\pi$
$991$		−	23.8997i		−	0.759198i	0.925151	−	0.379599i	$-0.123938\pi$
$992$	12.9725	−	43.0213i	0.411876	−	1.36593i
$993$	9.50560	+	9.50560i	0.301651	+	0.301651i
$994$	63.2618	+	37.0502i	2.00654	+	1.17516i
$995$	−9.77928	−	9.77928i	−0.310024	−	0.310024i
$996$	6.06783	−	21.5697i	0.192266	−	0.683461i
$997$	8.55598			0.270971			0.135485	−	0.990779i	$-0.456741\pi$
$997$	8.55598			0.270971			0.135485	+	0.990779i	$0.456741\pi$
$998$	52.5567	−	13.7331i	1.66365	−	0.434714i
$999$	19.6470	+	19.6470i	0.621605	+	0.621605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.j.a.463.11	✓	140
4.3	odd	2	inner	572.2.j.a.463.25	yes	140
13.5	odd	4	inner	572.2.j.a.551.25	yes	140
52.31	even	4	inner	572.2.j.a.551.11	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.j.a.463.11	✓	140	1.1	even	1	trivial
572.2.j.a.463.25	yes	140	4.3	odd	2	inner
572.2.j.a.551.11	yes	140	52.31	even	4	inner
572.2.j.a.551.25	yes	140	13.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22033 - 0.714703i) q^{2} -0.940195i q^{3} +(0.978400 + 1.74434i) q^{4} +(-2.27069 - 2.27069i) q^{5} +(-0.671960 + 1.14735i) q^{6} +(2.86451 + 2.86451i) q^{7} +(0.0527177 - 2.82794i) q^{8} +2.11603 q^{9} +O(q^{10})\)	\(q+(-1.22033 - 0.714703i) q^{2} -0.940195i q^{3} +(0.978400 + 1.74434i) q^{4} +(-2.27069 - 2.27069i) q^{5} +(-0.671960 + 1.14735i) q^{6} +(2.86451 + 2.86451i) q^{7} +(0.0527177 - 2.82794i) q^{8} +2.11603 q^{9} +(1.14812 + 4.39385i) q^{10} +(0.707107 + 0.707107i) q^{11} +(1.64002 - 0.919887i) q^{12} +(-0.0766142 + 3.60474i) q^{13} +(-1.44837 - 5.54291i) q^{14} +(-2.13489 + 2.13489i) q^{15} +(-2.08547 + 3.41333i) q^{16} +5.12990i q^{17} +(-2.58225 - 1.51233i) q^{18} +(0.0110629 - 0.0110629i) q^{19} +(1.73922 - 6.18250i) q^{20} +(2.69320 - 2.69320i) q^{21} +(-0.357531 - 1.36827i) q^{22} +3.36033 q^{23} +(-2.65881 - 0.0495650i) q^{24} +5.31204i q^{25} +(2.66981 - 4.34420i) q^{26} -4.81007i q^{27} +(-2.19405 + 7.79933i) q^{28} +1.93627 q^{29} +(4.13108 - 1.07945i) q^{30} +(5.61682 - 5.61682i) q^{31} +(4.98447 - 2.67490i) q^{32} +(0.664818 - 0.664818i) q^{33} +(3.66635 - 6.26016i) q^{34} -13.0088i q^{35} +(2.07033 + 3.69109i) q^{36} +(-4.08456 + 4.08456i) q^{37} +(-0.0214071 + 0.00559370i) q^{38} +(3.38916 + 0.0720323i) q^{39} +(-6.54106 + 6.30165i) q^{40} +(-0.879678 - 0.879678i) q^{41} +(-5.21142 + 1.36175i) q^{42} +8.98914 q^{43} +(-0.541603 + 1.92527i) q^{44} +(-4.80485 - 4.80485i) q^{45} +(-4.10071 - 2.40164i) q^{46} +(-2.40145 - 2.40145i) q^{47} +(3.20920 + 1.96075i) q^{48} +9.41083i q^{49} +(3.79653 - 6.48243i) q^{50} +4.82310 q^{51} +(-6.36286 + 3.39323i) q^{52} +10.4363 q^{53} +(-3.43777 + 5.86986i) q^{54} -3.21124i q^{55} +(8.25166 - 7.94964i) q^{56} +(-0.0104013 - 0.0104013i) q^{57} +(-2.36289 - 1.38386i) q^{58} +(-4.50422 - 4.50422i) q^{59} +(-5.81276 - 1.63520i) q^{60} -11.4979 q^{61} +(-10.8687 + 2.84000i) q^{62} +(6.06140 + 6.06140i) q^{63} +(-7.99444 - 0.298165i) q^{64} +(8.35920 - 8.01126i) q^{65} +(-1.28644 + 0.336149i) q^{66} +(7.96420 - 7.96420i) q^{67} +(-8.94830 + 5.01909i) q^{68} -3.15937i q^{69} +(-9.29743 + 15.8750i) q^{70} +(-9.04867 + 9.04867i) q^{71} +(0.111552 - 5.98401i) q^{72} +(9.96352 - 9.96352i) q^{73} +(7.90376 - 2.06526i) q^{74} +4.99436 q^{75} +(0.0301216 + 0.00847358i) q^{76} +4.05103i q^{77} +(-4.08440 - 2.51014i) q^{78} +12.0289i q^{79} +(12.4860 - 3.01517i) q^{80} +1.82570 q^{81} +(0.444788 + 1.70220i) q^{82} +(8.42595 - 8.42595i) q^{83} +(7.33289 + 2.06284i) q^{84} +(11.6484 - 11.6484i) q^{85} +(-10.9697 - 6.42456i) q^{86} -1.82048i q^{87} +(2.03693 - 1.96238i) q^{88} +(-4.41534 + 4.41534i) q^{89} +(2.42945 + 9.29753i) q^{90} +(-10.5453 + 10.1063i) q^{91} +(3.28775 + 5.86158i) q^{92} +(-5.28090 - 5.28090i) q^{93} +(1.21423 + 4.64688i) q^{94} -0.0502410 q^{95} +(-2.51492 - 4.68637i) q^{96} +(3.43982 + 3.43982i) q^{97} +(6.72595 - 11.4843i) q^{98} +(1.49626 + 1.49626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9}+O(q^{10}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9	\( 140 q + 4 q^{5} - 12 q^{6} + 12 q^{8} - 140 q^{9} + 16 q^{14} - 12 q^{18} - 8 q^{20} - 16 q^{21} - 32 q^{26} - 20 q^{28} + 20 q^{32} - 8 q^{34} + 36 q^{37} - 80 q^{40} - 20 q^{41} - 20 q^{42} - 8 q^{44} - 20 q^{45} + 60 q^{46} + 20 q^{48} + 88 q^{50} - 8 q^{53} + 88 q^{54} - 80 q^{57} - 60 q^{58} + 12 q^{60} - 40 q^{61} - 20 q^{65} - 20 q^{66} - 80 q^{68} - 28 q^{70} + 20 q^{72} + 100 q^{73} - 136 q^{74} - 32 q^{76} - 88 q^{78} - 72 q^{80} + 140 q^{81} + 92 q^{84} + 24 q^{85} - 32 q^{86} - 60 q^{89} - 68 q^{92} - 80 q^{93} + 64 q^{94} + 100 q^{96} - 20 q^{97} + 92 q^{98}+O(q^{100}) \) 140 * q + 4 * q^5 - 12 * q^6 + 12 * q^8 - 140 * q^9 + 16 * q^14 - 12 * q^18 - 8 * q^20 - 16 * q^21 - 32 * q^26 - 20 * q^28 + 20 * q^32 - 8 * q^34 + 36 * q^37 - 80 * q^40 - 20 * q^41 - 20 * q^42 - 8 * q^44 - 20 * q^45 + 60 * q^46 + 20 * q^48 + 88 * q^50 - 8 * q^53 + 88 * q^54 - 80 * q^57 - 60 * q^58 + 12 * q^60 - 40 * q^61 - 20 * q^65 - 20 * q^66 - 80 * q^68 - 28 * q^70 + 20 * q^72 + 100 * q^73 - 136 * q^74 - 32 * q^76 - 88 * q^78 - 72 * q^80 + 140 * q^81 + 92 * q^84 + 24 * q^85 - 32 * q^86 - 60 * q^89 - 68 * q^92 - 80 * q^93 + 64 * q^94 + 100 * q^96 - 20 * q^97 + 92 * q^98

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