LMFDB - Embedded newform 384.2.v.a.349.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			349.28
Character	$\chi$	$=$	384.349
Dual form			384.2.v.a.373.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27565 + 0.610503i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.25457 + 1.55758i) q^{4} +(-1.28161 - 2.39773i) q^{5} +(-1.20967 - 0.732599i) q^{6} +(0.997543 + 5.01499i) q^{7} +(0.649491 + 2.75285i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(1.27565 + 0.610503i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.25457 + 1.55758i) q^{4} +(-1.28161 - 2.39773i) q^{5} +(-1.20967 - 0.732599i) q^{6} +(0.997543 + 5.01499i) q^{7} +(0.649491 + 2.75285i) q^{8} +(0.980785 + 0.195090i) q^{9} +(-0.171071 - 3.84110i) q^{10} +(0.439216 + 0.360455i) q^{11} +(-1.09586 - 1.67305i) q^{12} +(3.44526 + 1.84153i) q^{13} +(-1.78915 + 7.00638i) q^{14} +(1.04042 + 2.51181i) q^{15} +(-0.852096 + 3.90819i) q^{16} +(-0.200696 + 0.484523i) q^{17} +(1.13204 + 0.847639i) q^{18} +(4.89393 - 1.48456i) q^{19} +(2.12677 - 5.00434i) q^{20} +(-0.501185 - 5.08862i) q^{21} +(0.340227 + 0.727957i) q^{22} +(-4.43892 + 2.96599i) q^{23} +(-0.376538 - 2.80325i) q^{24} +(-1.32873 + 1.98858i) q^{25} +(3.27069 + 4.45250i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(-6.55974 + 7.84542i) q^{28} +(-2.77722 - 3.38405i) q^{29} +(-0.206246 + 3.83937i) q^{30} +(3.56394 - 3.56394i) q^{31} +(-3.47294 + 4.46528i) q^{32} +(-0.401770 - 0.401770i) q^{33} +(-0.551821 + 0.495557i) q^{34} +(10.7461 - 8.81912i) q^{35} +(0.926598 + 1.77240i) q^{36} +(0.893489 - 2.94544i) q^{37} +(7.14928 + 1.09398i) q^{38} +(-3.24817 - 2.17036i) q^{39} +(5.76819 - 5.08539i) q^{40} +(-5.07322 - 7.59261i) q^{41} +(2.46728 - 6.79728i) q^{42} +(-10.6540 + 1.04932i) q^{43} +(-0.0104087 + 1.13633i) q^{44} +(-0.789214 - 2.60169i) q^{45} +(-7.47326 + 1.07360i) q^{46} +(4.81689 + 1.99522i) q^{47} +(1.23106 - 3.80585i) q^{48} +(-17.6879 + 7.32655i) q^{49} +(-2.90903 + 1.72555i) q^{50} +(0.247221 - 0.462518i) q^{51} +(1.45400 + 7.67660i) q^{52} +(-0.501822 + 0.611472i) q^{53} +(-1.04350 - 0.954517i) q^{54} +(0.301369 - 1.51508i) q^{55} +(-13.1576 + 6.00328i) q^{56} +(-5.01588 + 0.997720i) q^{57} +(-1.47679 - 6.01237i) q^{58} +(9.69215 - 5.18056i) q^{59} +(-2.60704 + 4.77178i) q^{60} +(-0.0767350 + 0.779103i) q^{61} +(6.72214 - 2.37055i) q^{62} +5.11324i q^{63} +(-7.15632 + 3.57590i) q^{64} -10.6209i q^{65} +(-0.267237 - 0.757800i) q^{66} +(1.28819 - 13.0792i) q^{67} +(-1.00647 + 0.295270i) q^{68} +(4.70826 - 2.51662i) q^{69} +(19.0924 - 4.68958i) q^{70} +(10.4385 - 2.07635i) q^{71} +(0.0999580 + 2.82666i) q^{72} +(-0.349590 + 1.75751i) q^{73} +(2.93798 - 3.21188i) q^{74} +(1.51725 - 1.84877i) q^{75} +(8.45211 + 5.76019i) q^{76} +(-1.36954 + 2.56223i) q^{77} +(-2.81852 - 4.75164i) q^{78} +(8.80664 - 3.64783i) q^{79} +(10.4628 - 2.96569i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-1.83635 - 12.7827i) q^{82} +(1.74636 + 5.75698i) q^{83} +(7.29714 - 7.16467i) q^{84} +(1.41897 - 0.139756i) q^{85} +(-14.2314 - 5.16571i) q^{86} +(2.43215 + 3.63997i) q^{87} +(-0.707010 + 1.44321i) q^{88} +(-1.79157 - 1.19709i) q^{89} +(0.581577 - 3.80067i) q^{90} +(-5.79846 + 19.1150i) q^{91} +(-10.1887 - 3.19291i) q^{92} +(-3.89610 + 3.19745i) q^{93} +(4.92658 + 5.48593i) q^{94} +(-9.83170 - 9.83170i) q^{95} +(3.89389 - 4.10337i) q^{96} +(8.59524 - 8.59524i) q^{97} +(-27.0364 - 1.45236i) q^{98} +(0.360455 + 0.439216i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	1.27565	+	0.610503i	0.902022	+	0.431691i
$2$	1.27565	+	0.610503i	0.902022	+	0.431691i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$4$	1.25457	+	1.55758i	0.627286	+	0.778789i
$5$	−1.28161	−	2.39773i	−0.573155	−	1.07230i	−0.986813	−	0.161865i	$-0.948249\pi$
$5$	−1.28161	−	2.39773i	−0.573155	−	1.07230i	0.413658	−	0.910432i	$-0.364251\pi$
$6$	−1.20967	−	0.732599i	−0.493845	−	0.299082i
$7$	0.997543	+	5.01499i	0.377036	+	1.89549i	0.440949	+	0.897532i	$0.354642\pi$
$7$	0.997543	+	5.01499i	0.377036	+	1.89549i	−0.0639132	+	0.997955i	$0.520358\pi$
$8$	0.649491	+	2.75285i	0.229630	+	0.973278i
$9$	0.980785	+	0.195090i	0.326928	+	0.0650301i
$10$	−0.171071	−	3.84110i	−0.0540973	−	1.21466i
$11$	0.439216	+	0.360455i	0.132428	+	0.108681i	0.698276	−	0.715829i	$-0.253951\pi$
$11$	0.439216	+	0.360455i	0.132428	+	0.108681i	−0.565847	+	0.824510i	$0.691451\pi$
$12$	−1.09586	−	1.67305i	−0.316348	−	0.482967i
$13$	3.44526	+	1.84153i	0.955544	+	0.510749i	0.874003	−	0.485921i	$-0.161516\pi$
$13$	3.44526	+	1.84153i	0.955544	+	0.510749i	0.0815414	+	0.996670i	$0.474016\pi$
$14$	−1.78915	+	7.00638i	−0.478170	+	1.87253i
$15$	1.04042	+	2.51181i	0.268636	+	0.648545i
$16$	−0.852096	+	3.90819i	−0.213024	+	0.977047i
$17$	−0.200696	+	0.484523i	−0.0486759	+	0.117514i	−0.946347	−	0.323152i	$-0.895258\pi$
$17$	−0.200696	+	0.484523i	−0.0486759	+	0.117514i	0.897671	+	0.440666i	$0.145258\pi$
$18$	1.13204	+	0.847639i	0.266824	+	0.199791i
$19$	4.89393	−	1.48456i	1.12274	−	0.340581i	0.326285	−	0.945272i	$-0.394203\pi$
$19$	4.89393	−	1.48456i	1.12274	−	0.340581i	0.796460	+	0.604691i	$0.206703\pi$
$20$	2.12677	−	5.00434i	0.475561	−	1.11900i
$21$	−0.501185	−	5.08862i	−0.109368	−	1.11043i
$22$	0.340227	+	0.727957i	0.0725367	+	0.155201i
$23$	−4.43892	+	2.96599i	−0.925579	+	0.618452i	−0.924349	−	0.381547i	$-0.875391\pi$
$23$	−4.43892	+	2.96599i	−0.925579	+	0.618452i	−0.00122953	+	0.999999i	$0.500391\pi$
$24$	−0.376538	−	2.80325i	−0.0768605	−	0.572211i
$25$	−1.32873	+	1.98858i	−0.265746	+	0.397716i
$26$	3.27069	+	4.45250i	0.641436	+	0.873206i
$27$	−0.956940	−	0.290285i	−0.184163	−	0.0558653i
$28$	−6.55974	+	7.84542i	−1.23968	+	1.48264i
$29$	−2.77722	−	3.38405i	−0.515717	−	0.628403i	0.448416	−	0.893825i	$-0.351988\pi$
$29$	−2.77722	−	3.38405i	−0.515717	−	0.628403i	−0.964132	+	0.265423i	$0.914488\pi$
$30$	−0.206246	+	3.83937i	−0.0376553	+	0.700970i
$31$	3.56394	−	3.56394i	0.640102	−	0.640102i	−0.310478	−	0.950580i	$-0.600489\pi$
$31$	3.56394	−	3.56394i	0.640102	−	0.640102i	0.950580	+	0.310478i	$0.100489\pi$
$32$	−3.47294	+	4.46528i	−0.613934	+	0.789357i
$33$	−0.401770	−	0.401770i	−0.0699392	−	0.0699392i
$34$	−0.551821	+	0.495557i	−0.0946365	+	0.0849873i
$35$	10.7461	−	8.81912i	1.81643	−	1.49070i
$36$	0.926598	+	1.77240i	0.154433	+	0.295401i
$37$	0.893489	−	2.94544i	0.146889	−	0.484227i	−0.852361	−	0.522954i	$-0.824830\pi$
$37$	0.893489	−	2.94544i	0.146889	−	0.484227i	0.999250	+	0.0387264i	$0.0123301\pi$
$38$	7.14928	+	1.09398i	1.15977	+	0.177467i
$39$	−3.24817	−	2.17036i	−0.520124	−	0.347536i
$40$	5.76819	−	5.08539i	0.912030	−	0.804071i
$41$	−5.07322	−	7.59261i	−0.792304	−	1.18577i	−0.979102	−	0.203369i	$-0.934811\pi$
$41$	−5.07322	−	7.59261i	−0.792304	−	1.18577i	0.186798	−	0.982398i	$-0.440189\pi$
$42$	2.46728	−	6.79728i	0.380709	−	1.04884i
$43$	−10.6540	+	1.04932i	−1.62472	+	0.160021i	−0.868977	−	0.494853i	$-0.835222\pi$
$43$	−10.6540	+	1.04932i	−1.62472	+	0.160021i	−0.755739	+	0.654873i	$0.772722\pi$
$44$	−0.0104087	+	1.13633i	−0.00156917	+	0.171308i
$45$	−0.789214	−	2.60169i	−0.117649	−	0.387837i
$46$	−7.47326	+	1.07360i	−1.10187	+	0.158293i
$47$	4.81689	+	1.99522i	0.702615	+	0.291033i	0.705245	−	0.708964i	$-0.250837\pi$
$47$	4.81689	+	1.99522i	0.702615	+	0.291033i	−0.00262973	+	0.999997i	$0.500837\pi$
$48$	1.23106	−	3.80585i	0.177689	−	0.549327i
$49$	−17.6879	+	7.32655i	−2.52684	+	1.04665i
$50$	−2.90903	+	1.72555i	−0.411399	+	0.244029i
$51$	0.247221	−	0.462518i	0.0346179	−	0.0647655i
$52$	1.45400	+	7.67660i	0.201634	+	1.06455i
$53$	−0.501822	+	0.611472i	−0.0689306	+	0.0839922i	−0.806334	−	0.591460i	$-0.798552\pi$
$53$	−0.501822	+	0.611472i	−0.0689306	+	0.0839922i	0.737404	+	0.675452i	$0.236052\pi$
$54$	−1.04350	−	0.954517i	−0.142003	−	0.129893i
$55$	0.301369	−	1.51508i	0.0406366	−	0.204294i
$56$	−13.1576	+	6.00328i	−1.75826	+	0.802221i
$57$	−5.01588	+	0.997720i	−0.664369	+	0.132151i
$58$	−1.47679	−	6.01237i	−0.193912	−	0.789463i
$59$	9.69215	−	5.18056i	1.26181	−	0.674451i	0.301521	−	0.953460i	$-0.402506\pi$
$59$	9.69215	−	5.18056i	1.26181	−	0.674451i	0.960289	+	0.279008i	$0.0900056\pi$
$60$	−2.60704	+	4.77178i	−0.336568	+	0.616034i
$61$	−0.0767350	+	0.779103i	−0.00982491	+	0.0997540i	−0.998847	−	0.0480170i	$-0.984710\pi$
$61$	−0.0767350	+	0.779103i	−0.00982491	+	0.0997540i	0.989022	+	0.147771i	$0.0472098\pi$
$62$	6.72214	−	2.37055i	0.853712	−	0.301060i
$63$			5.11324i			0.644207i
$64$	−7.15632	+	3.57590i	−0.894540	+	0.446987i
$65$		−	10.6209i		−	1.31737i
$66$	−0.267237	−	0.757800i	−0.0328946	−	0.0932787i
$67$	1.28819	−	13.0792i	0.157377	−	1.59788i	−0.514681	−	0.857382i	$-0.672090\pi$
$67$	1.28819	−	13.0792i	0.157377	−	1.59788i	0.672058	−	0.740498i	$-0.265410\pi$
$68$	−1.00647	+	0.295270i	−0.122052	+	0.0358067i
$69$	4.70826	−	2.51662i	0.566808	−	0.302965i
$70$	19.0924	−	4.68958i	2.28198	−	0.560512i
$71$	10.4385	−	2.07635i	1.23882	−	0.246417i	0.468150	−	0.883649i	$-0.344921\pi$
$71$	10.4385	−	2.07635i	1.23882	−	0.246417i	0.770672	+	0.637232i	$0.219921\pi$
$72$	0.0999580	+	2.82666i	0.0117802	+	0.333125i
$73$	−0.349590	+	1.75751i	−0.0409164	+	0.205701i	−0.995836	−	0.0911643i	$-0.970941\pi$
$73$	−0.349590	+	1.75751i	−0.0409164	+	0.205701i	0.954919	+	0.296865i	$0.0959411\pi$
$74$	2.93798	−	3.21188i	0.341533	−	0.373373i
$75$	1.51725	−	1.84877i	0.175196	−	0.213477i
$76$	8.45211	+	5.76019i	0.969523	+	0.660739i
$77$	−1.36954	+	2.56223i	−0.156074	+	0.291993i
$78$	−2.81852	−	4.75164i	−0.319135	−	0.538017i
$79$	8.80664	−	3.64783i	0.990825	−	0.410413i	0.172400	−	0.985027i	$-0.444848\pi$
$79$	8.80664	−	3.64783i	0.990825	−	0.410413i	0.818425	+	0.574614i	$0.194848\pi$
$80$	10.4628	−	2.96569i	1.16978	−	0.331574i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−1.83635	−	12.7827i	−0.202791	−	1.41162i
$83$	1.74636	+	5.75698i	0.191688	+	0.631910i	0.999120	+	0.0419494i	$0.0133568\pi$
$83$	1.74636	+	5.75698i	0.191688	+	0.631910i	−0.807432	+	0.589961i	$0.799143\pi$
$84$	7.29714	−	7.16467i	0.796183	−	0.781730i
$85$	1.41897	−	0.139756i	0.153909	−	0.0151587i
$86$	−14.2314	−	5.16571i	−1.53461	−	0.557033i
$87$	2.43215	+	3.63997i	0.260754	+	0.390246i
$88$	−0.707010	+	1.44321i	−0.0753675	+	0.153846i
$89$	−1.79157	−	1.19709i	−0.189906	−	0.126891i	0.456983	−	0.889476i	$-0.348930\pi$
$89$	−1.79157	−	1.19709i	−0.189906	−	0.126891i	−0.646889	+	0.762585i	$0.723930\pi$
$90$	0.581577	−	3.80067i	0.0613036	−	0.400625i
$91$	−5.79846	+	19.1150i	−0.607844	+	2.00379i
$92$	−10.1887	−	3.19291i	−1.06225	−	0.332884i
$93$	−3.89610	+	3.19745i	−0.404007	+	0.331560i
$94$	4.92658	+	5.48593i	0.508138	+	0.565830i
$95$	−9.83170	−	9.83170i	−1.00871	−	1.00871i
$96$	3.89389	−	4.10337i	0.397418	−	0.418798i
$97$	8.59524	−	8.59524i	0.872715	−	0.872715i	−0.120053	−	0.992768i	$-0.538306\pi$
$97$	8.59524	−	8.59524i	0.872715	−	0.872715i	0.992768	+	0.120053i	$0.0383064\pi$
$98$	−27.0364	−	1.45236i	−2.73109	−	0.146711i
$99$	0.360455	+	0.439216i	0.0362271	+	0.0441428i
$100$	−4.76436	+	0.425223i	−0.476436	+	0.0425223i
$101$	4.52804	+	1.37357i	0.450557	+	0.136675i	0.507405	−	0.861708i	$-0.330605\pi$
$101$	4.52804	+	1.37357i	0.450557	+	0.136675i	−0.0568476	+	0.998383i	$0.518105\pi$
$102$	0.597737	−	0.439083i	0.0591847	−	0.0434757i
$103$	−8.46172	+	12.6639i	−0.833758	+	1.24781i	0.132744	+	0.991150i	$0.457621\pi$
$103$	−8.46172	+	12.6639i	−0.833758	+	1.24781i	−0.966503	+	0.256657i	$0.917379\pi$
$104$	−2.83178	+	10.6803i	−0.277679	+	1.04729i
$105$	−11.5588	+	7.72335i	−1.12802	+	0.753722i
$106$	−1.01346	+	0.473661i	−0.0984355	+	0.0460061i
$107$	0.226148	+	2.29612i	0.0218625	+	0.221974i	0.999908	+	0.0135814i	$0.00432322\pi$
$107$	0.226148	+	2.29612i	0.0218625	+	0.221974i	−0.978045	+	0.208393i	$0.933177\pi$
$108$	−0.748410	−	1.85469i	−0.0720158	−	0.178468i
$109$	12.9330	−	3.92317i	1.23875	−	0.375772i	0.398099	−	0.917343i	$-0.369670\pi$
$109$	12.9330	−	3.92317i	1.23875	−	0.375772i	0.840655	+	0.541571i	$0.182170\pi$
$110$	1.30941	−	1.74873i	0.124847	−	0.166735i
$111$	−1.17789	+	2.84368i	−0.111800	+	0.269910i
$112$	−20.4495	−	0.374664i	−1.93230	−	0.0354024i
$113$	−3.11965	−	7.53151i	−0.293472	−	0.708505i	−1.00000		0.000818939i	$-0.999739\pi$
$113$	−3.11965	−	7.53151i	−0.293472	−	0.708505i	0.706527	−	0.707686i	$-0.250261\pi$
$114$	−7.00762	−	1.78947i	−0.656324	−	0.167599i
$115$	12.8006	+	6.84208i	1.19367	+	0.638027i
$116$	1.78670	−	8.57127i	0.165891	−	0.795823i
$117$	3.01980	+	2.47828i	0.279181	+	0.229118i
$118$	15.5265	−	0.691505i	1.42933	−	0.0636582i
$119$	−2.63008	−	0.523155i	−0.241099	−	0.0479576i
$120$	−6.23887	+	4.49552i	−0.569528	+	0.410383i
$121$	−2.08301	−	10.4720i	−0.189365	−	0.952000i
$122$	−0.573532	+	0.947017i	−0.0519251	+	0.0857389i
$123$	4.30459	+	8.05332i	0.388132	+	0.726143i
$124$	10.0223	+	1.07989i	0.900031	+	0.0969771i
$125$	−7.05733	−	0.695087i	−0.631227	−	0.0621704i
$126$	−3.12165	+	6.52271i	−0.278098	+	0.581089i
$127$	−14.9373			−1.32547			−0.662734	−	0.748855i	$-0.730604\pi$
$127$	−14.9373			−1.32547			−0.662734	+	0.748855i	$0.730604\pi$
$128$	−11.3121	+	0.192646i	−0.999855	+	0.0170277i
$129$	10.7055			0.942569
$130$	6.48412	−	13.5486i	0.568695	−	1.18829i
$131$	−17.0922	−	1.68344i	−1.49336	−	0.147083i	−0.681878	−	0.731465i	$-0.738837\pi$
$131$	−17.0922	−	1.68344i	−1.49336	−	0.147083i	−0.811478	+	0.584383i	$0.801337\pi$
$132$	0.121738	−	1.12984i	0.0105960	−	0.0983397i
$133$	12.3270	+	23.0621i	1.06888	+	1.99974i
$134$	9.62818	−	15.8981i	0.831748	−	1.37338i
$135$	0.530403	+	2.66652i	0.0456499	+	0.229497i
$136$	−1.46417	−	0.237792i	−0.125551	−	0.0203905i
$137$	16.5963	+	3.30120i	1.41792	+	0.282041i	0.843767	−	0.536710i	$-0.180333\pi$
$137$	16.5963	+	3.30120i	1.41792	+	0.282041i	0.574148	+	0.818751i	$0.305333\pi$
$138$	7.54251	−	0.335920i	0.642061	−	0.0285954i
$139$	−7.08961	−	5.81829i	−0.601333	−	0.493501i	0.283773	−	0.958892i	$-0.408414\pi$
$139$	−7.08961	−	5.81829i	−0.601333	−	0.493501i	−0.885105	+	0.465391i	$0.845914\pi$
$140$	27.2183	+	5.67370i	2.30036	+	0.479515i
$141$	−4.59813	−	2.45775i	−0.387232	−	0.206980i
$142$	14.5835	+	3.72404i	1.22382	+	0.312515i
$143$	0.849424	+	2.05069i	0.0710324	+	0.171487i
$144$	−1.59817	+	3.66686i	−0.133181	+	0.305571i
$145$	−4.55472	+	10.9961i	−0.378249	+	0.913174i
$146$	−1.51892	+	2.02854i	−0.125707	+	0.167883i
$147$	18.3208	−	5.55756i	1.51108	−	0.458380i
$148$	5.70870	−	2.30359i	0.469252	−	0.189354i
$149$	1.65497	+	16.8032i	0.135581	+	1.37657i	0.786577	+	0.617492i	$0.211851\pi$
$149$	1.65497	+	16.8032i	0.135581	+	1.37657i	−0.650997	+	0.759081i	$0.725649\pi$
$150$	3.06415	−	1.43210i	0.250187	−	0.116931i
$151$	−12.0822	+	8.07305i	−0.983233	+	0.656976i	−0.939673	−	0.342075i	$-0.888870\pi$
$151$	−12.0822	+	8.07305i	−0.983233	+	0.656976i	−0.0435608	+	0.999051i	$0.513870\pi$
$152$	7.26533	+	12.5080i	0.589296	+	1.01454i
$153$	−0.291365	+	0.436059i	−0.0235555	+	0.0352533i
$154$	−3.31131	+	2.43240i	−0.266833	+	0.196009i
$155$	−13.1130	−	3.97777i	−1.05326	−	0.319502i
$156$	−0.694564	−	7.78215i	−0.0556097	−	0.623071i
$157$	2.17928	+	2.65546i	0.173926	+	0.211929i	0.852676	−	0.522440i	$-0.174978\pi$
$157$	2.17928	+	2.65546i	0.173926	+	0.211929i	−0.678750	+	0.734369i	$0.737478\pi$
$158$	13.4612	+	0.723121i	1.07092	+	0.0575284i
$159$	0.559341	−	0.559341i	0.0443586	−	0.0443586i
$160$	15.1575	+	2.60441i	1.19831	+	0.205896i
$161$	−19.3024	−	19.3024i	−1.52124	−	1.52124i
$162$	0.944919	+	1.05220i	0.0742398	+	0.0826688i
$163$	−1.59054	+	1.30532i	−0.124581	+	0.102241i	−0.694621	−	0.719376i	$-0.744428\pi$
$163$	−1.59054	+	1.30532i	−0.124581	+	0.102241i	0.570040	+	0.821617i	$0.306928\pi$
$164$	5.46136	−	17.4274i	0.426461	−	1.36085i
$165$	−0.448422	+	1.47825i	−0.0349096	+	0.115082i
$166$	−1.28690	+	8.41005i	−0.0998832	+	0.652747i
$167$	15.7096	+	10.4968i	1.21564	+	0.812266i	0.986918	−	0.161225i	$-0.0515446\pi$
$167$	15.7096	+	10.4968i	1.21564	+	0.812266i	0.228724	+	0.973491i	$0.426545\pi$
$168$	13.6827	−	4.68470i	1.05564	−	0.361432i
$169$	1.25619	+	1.88002i	0.0966300	+	0.144617i
$170$	1.89543	+	0.688005i	0.145373	+	0.0527676i
$171$	5.08952	−	0.501274i	0.389205	−	0.0383334i
$172$	−15.0006	−	15.2779i	−1.14378	−	1.16493i
$173$	−4.61275	−	15.2062i	−0.350701	−	1.15611i	−0.937971	−	0.346715i	$-0.887297\pi$
$173$	−4.61275	−	15.2062i	−0.350701	−	1.15611i	0.587270	−	0.809391i	$-0.300203\pi$
$174$	0.880364	+	6.12817i	0.0667402	+	0.464575i
$175$	−11.2982	−	4.67986i	−0.854062	−	0.353764i
$176$	−1.78298	+	1.40940i	−0.134397	+	0.106237i
$177$	−10.1533	+	4.20562i	−0.763166	+	0.316114i
$178$	−1.55459	−	2.62082i	−0.116522	−	0.196439i
$179$	−4.57641	+	8.56186i	−0.342057	+	0.639943i	−0.992858	−	0.119305i	$-0.961933\pi$
$179$	−4.57641	+	8.56186i	−0.342057	+	0.639943i	0.650801	+	0.759248i	$0.274433\pi$
$180$	3.06221	−	4.49327i	0.228243	−	0.334909i
$181$	11.0282	−	13.4380i	0.819723	−	0.998836i	−0.180161	−	0.983637i	$-0.557662\pi$
$181$	11.0282	−	13.4380i	0.819723	−	0.998836i	0.999884	−	0.0151986i	$-0.00483805\pi$
$182$	−19.0666	+	20.8441i	−1.41331	+	1.54506i
$183$	0.152731	−	0.767830i	0.0112902	−	0.0567597i
$184$	−11.0480	−	10.2933i	−0.814466	−	0.758831i
$185$	−8.20748	+	1.63257i	−0.603426	+	0.120029i
$186$	−6.92212	+	1.70025i	−0.507554	+	0.124668i
$187$	−0.262798	+	0.140468i	−0.0192177	+	0.0102721i
$188$	2.93542	+	10.0058i	0.214088	+	0.729750i
$189$	0.501185	−	5.08862i	0.0364558	−	0.370142i
$190$	−6.53954	−	18.5441i	−0.474428	−	1.34533i
$191$			8.52134i			0.616582i	0.951292	+	0.308291i	$0.0997571\pi$
$191$			8.52134i			0.616582i	−0.951292	+	0.308291i	$0.900243\pi$
$192$	7.47236	−	2.85724i	0.539271	−	0.206203i
$193$			3.54347i			0.255064i	0.991834	+	0.127532i	$0.0407056\pi$
$193$			3.54347i			0.255064i	−0.991834	+	0.127532i	$0.959294\pi$
$194$	16.2120	−	5.71711i	1.16395	−	0.410465i
$195$	−1.04103	+	10.5698i	−0.0745501	+	0.756919i
$196$	−33.6024	−	18.3585i	−2.40017	−	1.31132i
$197$	−4.55570	+	2.43507i	−0.324580	+	0.173492i	−0.625637	−	0.780115i	$-0.715161\pi$
$197$	−4.55570	+	2.43507i	−0.324580	+	0.173492i	0.301057	+	0.953606i	$0.402661\pi$
$198$	0.191672	+	0.780345i	0.0136216	+	0.0554567i
$199$	7.44356	−	1.48062i	0.527660	−	0.104958i	0.0759305	−	0.997113i	$-0.475807\pi$
$199$	7.44356	−	1.48062i	0.527660	−	0.104958i	0.451729	+	0.892155i	$0.350807\pi$
$200$	−6.33726	−	2.36622i	−0.448112	−	0.167317i
$201$	−2.56397	+	12.8900i	−0.180849	+	0.909188i
$202$	4.93764	+	4.51658i	0.347411	+	0.317785i
$203$	14.2006	−	17.3035i	0.996685	−	1.21446i
$204$	1.03056	−	0.195197i	0.0721540	−	0.0136665i
$205$	−11.7031	+	21.8950i	−0.817382	+	1.52921i
$206$	−18.5255	+	10.9888i	−1.29073	+	0.765624i
$207$	−4.93226	+	2.04301i	−0.342816	+	0.141999i
$208$	−10.1327	+	11.8956i	−0.702580	+	0.824810i
$209$	2.68461	+	1.11200i	0.185698	+	0.0769187i
$210$	−19.4601	+	2.79561i	−1.34288	+	0.192916i
$211$	−5.77365	−	19.0332i	−0.397475	−	1.31030i	−0.896243	−	0.443563i	$-0.853714\pi$
$211$	−5.77365	−	19.0332i	−0.397475	−	1.31030i	0.498768	−	0.866735i	$-0.333786\pi$
$212$	−1.58199	−	0.0144909i	−0.108651	−	0.000995240i
$213$	−10.5918	+	1.04320i	−0.725735	+	0.0714787i
$214$	−1.11330	+	3.06711i	−0.0761037	+	0.209663i
$215$	16.1703	+	24.2005i	1.10280	+	1.65046i
$216$	0.177584	−	2.82285i	0.0120831	−	0.192070i
$217$	21.4283	+	14.3179i	1.45465	+	0.971964i
$218$	18.8931	+	2.89101i	1.27960	+	0.195804i
$219$	0.520172	−	1.71478i	0.0351500	−	0.115874i
$220$	2.73795	−	1.43138i	0.184593	−	0.0965035i
$221$	−1.58372	+	1.29972i	−0.106532	+	0.0874287i
$222$	−3.23865	+	2.90844i	−0.217364	+	0.195202i
$223$	−8.96043	−	8.96043i	−0.600035	−	0.600035i	0.340287	−	0.940322i	$-0.389476\pi$
$223$	−8.96043	−	8.96043i	−0.600035	−	0.600035i	−0.940322	+	0.340287i	$0.889476\pi$
$224$	−25.8577	−	12.9624i	−1.72769	−	0.866089i
$225$	−1.69115	+	1.69115i	−0.112743	+	0.112743i
$226$	0.618418	−	11.5121i	0.0411366	−	0.765776i
$227$	−8.96592	−	10.9250i	−0.595089	−	0.725118i	0.385168	−	0.922847i	$-0.374144\pi$
$227$	−8.96592	−	10.9250i	−0.595089	−	0.725118i	−0.980257	+	0.197728i	$0.936644\pi$
$228$	−7.84681	−	6.56091i	−0.519668	−	0.434507i
$229$	7.67239	+	2.32739i	0.507006	+	0.153799i	0.533417	−	0.845853i	$-0.320908\pi$
$229$	7.67239	+	2.32739i	0.507006	+	0.153799i	−0.0264109	+	0.999651i	$0.508408\pi$
$230$	12.1520	+	16.5429i	0.801281	+	1.09081i
$231$	1.61409	−	2.41565i	0.106199	−	0.158938i
$232$	7.51199	−	9.84317i	0.493186	−	0.646236i
$233$	0.747487	−	0.499455i	0.0489695	−	0.0327204i	−0.530845	−	0.847469i	$-0.678125\pi$
$233$	0.747487	−	0.499455i	0.0489695	−	0.0327204i	0.579814	+	0.814749i	$0.303125\pi$
$234$	2.33921	+	5.00502i	0.152919	+	0.327189i
$235$	−1.38939	−	14.1067i	−0.0906337	−	0.920220i
$236$	20.2286	+	8.59688i	1.31677	+	0.559609i
$237$	−9.12179	+	2.76706i	−0.592524	+	0.179740i
$238$	−3.03568	−	2.27304i	−0.196774	−	0.147339i
$239$	−6.02744	+	14.5515i	−0.389882	+	0.941259i	0.600081	+	0.799939i	$0.295135\pi$
$239$	−6.02744	+	14.5515i	−0.389882	+	0.941259i	−0.989964	+	0.141321i	$0.954865\pi$
$240$	−10.7031	+	1.92587i	−0.690885	+	0.124315i
$241$	−1.11994	−	2.70377i	−0.0721415	−	0.174165i	0.883696	−	0.468062i	$-0.155048\pi$
$241$	−1.11994	−	2.70377i	−0.0721415	−	0.174165i	−0.955837	+	0.293897i	$0.905048\pi$
$242$	3.73599	−	14.6303i	0.240159	−	0.940472i
$243$	−0.881921	−	0.471397i	−0.0565753	−	0.0302401i
$244$	−1.30978	+	0.857921i	−0.0838503	+	0.0549228i
$245$	40.2361	+	33.0209i	2.57059	+	2.10963i
$246$	0.574580	+	12.9012i	0.0366339	+	0.822550i
$247$	19.5947	+	3.89764i	1.24678	+	0.248001i
$248$	12.1257	+	7.49622i	0.769984	+	0.476011i
$249$	−1.17367	−	5.90043i	−0.0743782	−	0.373924i
$250$	−8.57834	−	5.19521i	−0.542542	−	0.328574i
$251$	−6.94640	−	12.9958i	−0.438453	−	0.820288i	0.561521	−	0.827462i	$-0.310216\pi$
$251$	−6.94640	−	12.9958i	−0.438453	−	0.820288i	−0.999974	+	0.00717424i	$0.997716\pi$
$252$	−7.96426	+	6.41493i	−0.501702	+	0.404102i
$253$	−3.01875	−	0.297321i	−0.189787	−	0.0186924i
$254$	−19.0547	−	9.11924i	−1.19560	−	0.572192i
$255$	−1.42584			−0.0892893
$256$	−14.5479	−	6.66030i	−0.909242	−	0.416269i
$257$	13.3276			0.831355			0.415678	−	0.909512i	$-0.363544\pi$
$257$	13.3276			0.831355			0.415678	+	0.909512i	$0.363544\pi$
$258$	13.6565	+	6.53575i	0.850217	+	0.406898i
$259$	15.6626	+	1.54264i	0.973229	+	0.0958547i
$260$	16.5430	−	13.3247i	1.02595	−	0.826366i
$261$	−2.06366	−	3.86084i	−0.127737	−	0.238980i
$262$	−20.7760	−	12.5823i	−1.28355	−	0.777340i
$263$	4.10516	+	20.6380i	0.253135	+	1.27260i	0.872935	+	0.487836i	$0.162213\pi$
$263$	4.10516	+	20.6380i	0.253135	+	1.27260i	−0.619801	+	0.784759i	$0.712787\pi$
$264$	0.845065	−	1.36696i	0.0520101	−	0.0841304i
$265$	2.10929	+	0.419564i	0.129573	+	0.0257736i
$266$	1.64541	+	36.9448i	0.100887	+	2.26523i
$267$	1.66561	+	1.36693i	0.101933	+	0.0836546i
$268$	21.9880	−	14.4024i	1.34313	−	0.879764i
$269$	−6.85537	−	3.66427i	−0.417979	−	0.223415i	0.248980	−	0.968509i	$-0.419905\pi$
$269$	−6.85537	−	3.66427i	−0.417979	−	0.223415i	−0.666960	+	0.745094i	$0.732405\pi$
$270$	−0.951307	+	3.72536i	−0.0578947	+	0.226718i
$271$	6.75101	+	16.2984i	0.410095	+	0.990057i	0.985112	+	0.171915i	$0.0549955\pi$
$271$	6.75101	+	16.2984i	0.410095	+	0.990057i	−0.575017	+	0.818142i	$0.695005\pi$
$272$	−1.72259	−	1.19722i	−0.104448	−	0.0725920i
$273$	7.64413	−	18.4546i	0.462644	−	1.11692i
$274$	19.1557	+	14.3433i	1.15724	+	0.866508i
$275$	−1.30039	+	0.394470i	−0.0784166	+	0.0237874i
$276$	9.82669	+	4.17620i	0.591497	+	0.251378i
$277$	0.622873	+	6.32413i	0.0374248	+	0.379980i	0.995593	+	0.0937758i	$0.0298937\pi$
$277$	0.622873	+	6.32413i	0.0374248	+	0.379980i	−0.958169	+	0.286205i	$0.907606\pi$
$278$	−5.49178	−	11.7503i	−0.329375	−	0.704738i
$279$	4.19075	−	2.80017i	0.250893	−	0.167642i
$280$	31.2572	+	23.8545i	1.86797	+	1.42558i
$281$	−10.3311	+	15.4616i	−0.616304	+	0.922364i	−0.999999	−	0.00109568i	$-0.999651\pi$
$281$	−10.3311	+	15.4616i	−0.616304	+	0.922364i	0.383695	+	0.923460i	$0.374651\pi$
$282$	−4.36514	−	5.94240i	−0.259940	−	0.353865i
$283$	3.17622	+	0.963497i	0.188807	+	0.0572739i	0.383272	−	0.923635i	$-0.374797\pi$
$283$	3.17622	+	0.963497i	0.188807	+	0.0572739i	−0.194465	+	0.980909i	$0.562297\pi$
$284$	16.3299	+	13.6539i	0.969003	+	0.810207i
$285$	8.82068	+	10.7480i	0.522492	+	0.636659i
$286$	−0.168384	+	3.13454i	−0.00995675	+	0.185349i
$287$	33.0161	−	33.0161i	1.94888	−	1.94888i
$288$	−4.27734	+	3.70194i	−0.252045	+	0.218139i
$289$	11.8263	+	11.8263i	0.695667	+	0.695667i
$290$	−12.5234	+	11.2465i	−0.735398	+	0.660416i
$291$	−9.39634	+	7.71137i	−0.550823	+	0.452049i
$292$	−3.17604	+	1.66041i	−0.185864	+	0.0971680i
$293$	5.29450	−	17.4536i	0.309308	−	1.01965i	−0.655168	−	0.755483i	$-0.727402\pi$
$293$	5.29450	−	17.4536i	0.309308	−	1.01965i	0.964476	−	0.264169i	$-0.0850978\pi$
$294$	26.7639	+	4.09540i	1.56090	+	0.238849i
$295$	−24.8432	−	16.5997i	−1.44643	−	0.966471i
$296$	8.68865	+	0.546601i	0.505018	+	0.0317705i
$297$	−0.315669	−	0.472431i	−0.0183170	−	0.0274133i
$298$	−8.14724	+	22.4454i	−0.471957	+	1.30023i
$299$	−20.7552	+	2.04421i	−1.20031	+	0.118220i
$300$	4.78309	+	0.0438129i	0.276152	+	0.00252954i
$301$	−15.8901	−	52.3828i	−0.915893	−	3.01929i
$302$	−20.3413	+	2.92220i	−1.17051	+	0.168153i
$303$	−4.37161	−	1.81078i	−0.251142	−	0.104027i
$304$	1.63183	+	20.3914i	0.0935920	+	1.16953i
$305$	1.96642	−	0.814520i	0.112597	−	0.0466393i
$306$	−0.637896	+	0.378380i	−0.0364661	+	0.0216305i
$307$	11.3989	−	21.3259i	0.650570	−	1.21713i	−0.313019	−	0.949747i	$-0.601340\pi$
$307$	11.3989	−	21.3259i	0.650570	−	1.21713i	0.963590	−	0.267385i	$-0.0861595\pi$
$308$	−5.70906	+	1.08134i	−0.325304	+	0.0616150i
$309$	9.66225	−	11.7735i	0.549666	−	0.669770i
$310$	−14.2991	−	13.0797i	−0.812135	−	0.742880i
$311$	−1.80796	+	9.08925i	−0.102520	+	0.515404i	0.895064	+	0.445937i	$0.147130\pi$
$311$	−1.80796	+	9.08925i	−0.102520	+	0.515404i	−0.997584	+	0.0694663i	$0.977870\pi$
$312$	3.86500	−	10.3513i	0.218813	−	0.586030i
$313$	−14.3359	+	2.85159i	−0.810313	+	0.161181i	−0.582823	−	0.812599i	$-0.698052\pi$
$313$	−14.3359	+	2.85159i	−0.810313	+	0.161181i	−0.227490	+	0.973780i	$0.573052\pi$
$314$	1.15884	+	4.71790i	0.0653969	+	0.266247i
$315$	12.2602	−	6.55320i	0.690782	−	0.369231i
$316$	16.7304	+	9.14056i	0.941156	+	0.514197i
$317$	−0.207362	+	2.10538i	−0.0116466	+	0.118250i	−0.999250	−	0.0387191i	$-0.987672\pi$
$317$	−0.207362	+	2.10538i	−0.0116466	+	0.118250i	0.987604	+	0.156969i	$0.0501722\pi$
$318$	1.05500	−	0.372045i	0.0591616	−	0.0208632i
$319$		−	2.48739i		−	0.139267i
$320$	17.7457	+	12.5760i	0.992014	+	0.703020i
$321$		−	2.30723i		−	0.128777i
$322$	−12.8390	−	36.4074i	−0.715488	−	2.02890i
$323$	−0.262890	+	2.66917i	−0.0146276	+	0.148516i
$324$	0.563015	+	1.91912i	0.0312786	+	0.106618i
$325$	−8.23986	+	4.40429i	−0.457065	+	0.244306i
$326$	−2.82588	+	0.694106i	−0.156511	+	0.0384430i
$327$	−13.2552	+	2.63663i	−0.733016	+	0.145806i
$328$	17.6063	−	18.8971i	0.972144	−	1.04342i
$329$	−5.20095	+	26.1469i	−0.286738	+	1.44153i
$330$	−1.47451	+	1.61197i	−0.0811689	+	0.0887359i
$331$	−8.40419	+	10.2405i	−0.461936	+	0.562870i	−0.950926	−	0.309419i	$-0.899865\pi$
$331$	−8.40419	+	10.2405i	−0.461936	+	0.562870i	0.488990	+	0.872289i	$0.337365\pi$
$332$	−6.77600	+	9.94263i	−0.371881	+	0.545673i
$333$	1.45095	−	2.71453i	0.0795114	−	0.148755i
$334$	13.6316	+	22.9810i	0.745888	+	1.25746i
$335$	−33.0114	+	13.6738i	−1.80360	+	0.747078i
$336$	20.3143	+	2.37726i	1.10824	+	0.129690i
$337$	−18.8954	−	7.82674i	−1.02930	−	0.426350i	−0.196840	−	0.980436i	$-0.563068\pi$
$337$	−18.8954	−	7.82674i	−1.02930	−	0.426350i	−0.832459	+	0.554086i	$0.813068\pi$
$338$	0.454702	+	3.16516i	0.0247325	+	0.172162i
$339$	2.36641	+	7.80102i	0.128526	+	0.423693i
$340$	1.99788	+	2.03482i	0.108350	+	0.110354i
$341$	2.84998	−	0.280698i	0.154335	−	0.0152007i
$342$	6.79848	+	2.46772i	0.367620	+	0.133439i
$343$	−34.5016	−	51.6354i	−1.86291	−	2.78805i
$344$	−9.80829	−	28.6472i	−0.528828	−	1.54455i
$345$	−12.0684	−	8.06382i	−0.649738	−	0.434141i
$346$	3.39917	−	22.2139i	0.182740	−	1.19423i
$347$	−7.96942	+	26.2716i	−0.427821	+	1.41034i	0.432985	+	0.901401i	$0.357460\pi$
$347$	−7.96942	+	26.2716i	−0.427821	+	1.41034i	−0.860805	+	0.508934i	$0.830040\pi$
$348$	−2.61823	+	8.35487i	−0.140352	+	0.447868i
$349$	−1.44649	+	1.18710i	−0.0774287	+	0.0635441i	−0.672312	−	0.740268i	$-0.734698\pi$
$349$	−1.44649	+	1.18710i	−0.0774287	+	0.0635441i	0.594883	+	0.803812i	$0.297198\pi$
$350$	−11.5555	−	12.8674i	−0.617666	−	0.687794i
$351$	−2.76234	−	2.76234i	−0.147443	−	0.147443i
$352$	−3.13490	+	0.709383i	−0.167091	+	0.0378102i
$353$	15.6088	−	15.6088i	0.830774	−	0.830774i	−0.156849	−	0.987623i	$-0.550133\pi$
$353$	15.6088	−	15.6088i	0.830774	−	0.830774i	0.987623	+	0.156849i	$0.0501335\pi$
$354$	−15.5196	−	0.833692i	−0.824855	−	0.0443102i
$355$	−18.3567	−	22.3676i	−0.974270	−	1.18715i
$356$	−0.383095	−	4.29234i	−0.0203040	−	0.227494i
$357$	2.56614	+	0.778429i	0.135814	+	0.0411988i
$358$	−11.0649	+	8.12803i	−0.584800	+	0.429580i
$359$	11.5121	−	17.2290i	0.607584	−	0.909314i	−0.392361	−	0.919811i	$-0.628341\pi$
$359$	11.5121	−	17.2290i	0.607584	−	0.909314i	0.999945	+	0.0104974i	$0.00334148\pi$
$360$	6.64946	−	3.86236i	0.350457	−	0.203564i
$361$	5.94873	−	3.97482i	0.313091	−	0.209201i
$362$	22.2721	−	10.4094i	1.17060	−	0.547105i
$363$	1.04654	+	10.6257i	0.0549294	+	0.557707i
$364$	−37.0476	+	14.9496i	−1.94182	+	0.783570i
$365$	4.66207	−	1.41422i	0.244024	−	0.0740238i
$366$	0.663594	−	0.886241i	0.0346866	−	0.0463246i
$367$	−2.69263	+	6.50058i	−0.140554	+	0.339327i	−0.978444	−	0.206511i	$-0.933789\pi$
$367$	−2.69263	+	6.50058i	−0.140554	+	0.339327i	0.837890	+	0.545839i	$0.183789\pi$
$368$	−7.80927	−	19.8754i	−0.407086	−	1.03608i
$369$	−3.49450	−	8.43646i	−0.181916	−	0.439185i
$370$	−11.4666	−	2.92810i	−0.596119	−	0.152225i
$371$	−3.56712	−	1.90666i	−0.185195	−	0.0989890i
$372$	−9.86822	−	2.05705i	−0.511643	−	0.106653i
$373$	1.28913	+	1.05796i	0.0667487	+	0.0547792i	0.667176	−	0.744900i	$-0.267503\pi$
$373$	1.28913	+	1.05796i	0.0667487	+	0.0547792i	−0.600427	+	0.799679i	$0.705003\pi$
$374$	−0.420994	+	0.0187498i	−0.0217691	+	0.000969529i
$375$	6.95522	+	1.38348i	0.359166	+	0.0714426i
$376$	−2.36401	+	14.5560i	−0.121914	+	0.750670i
$377$	−3.33641	−	16.7733i	−0.171834	−	0.863868i
$378$	3.74595	−	6.18533i	0.192671	−	0.318139i
$379$	0.586681	+	1.09760i	0.0301358	+	0.0563800i	0.896538	−	0.442966i	$-0.146074\pi$
$379$	0.586681	+	1.09760i	0.0301358	+	0.0563800i	−0.866403	+	0.499346i	$0.833574\pi$
$380$	2.97906	−	27.6482i	0.152822	−	1.41832i
$381$	14.8653	+	1.46411i	0.761574	+	0.0750085i
$382$	−5.20230	+	10.8703i	−0.266173	+	0.556171i
$383$	33.1751			1.69517			0.847584	−	0.530662i	$-0.178056\pi$
$383$	33.1751			1.69517			0.847584	+	0.530662i	$0.178056\pi$
$384$	11.2765	+	0.917058i	0.575450	+	0.0467984i
$385$	7.89876			0.402558
$386$	−2.16330	+	4.52023i	−0.110109	+	0.230074i
$387$	−10.6540	−	1.04932i	−0.541572	−	0.0533402i
$388$	24.1711	+	2.60440i	1.22710	+	0.132219i
$389$	−15.8440	−	29.6420i	−0.803322	−	1.50291i	−0.863289	−	0.504710i	$-0.831599\pi$
$389$	−15.8440	−	29.6420i	−0.803322	−	1.50291i	0.0599663	−	0.998200i	$-0.480901\pi$
$390$	−7.78089	+	12.8478i	−0.394001	+	0.650575i
$391$	−0.546218	−	2.74602i	−0.0276234	−	0.138872i
$392$	−31.6570	−	43.9334i	−1.59892	−	2.21897i
$393$	16.8449	+	3.35067i	0.849715	+	0.169019i
$394$	−7.29810	+	0.325035i	−0.367673	+	0.0163750i
$395$	−20.0332	−	16.4409i	−1.00798	−	0.827229i
$396$	−0.231896	+	1.11246i	−0.0116532	+	0.0559034i
$397$	−2.31738	−	1.23866i	−0.116306	−	0.0621668i	0.412218	−	0.911085i	$-0.364754\pi$
$397$	−2.31738	−	1.23866i	−0.116306	−	0.0621668i	−0.528524	+	0.848919i	$0.677254\pi$
$398$	10.3993	+	2.65556i	0.521270	+	0.133111i
$399$	−10.0071	−	24.1593i	−0.500982	−	1.20948i
$400$	−6.63955	−	6.88738i	−0.331977	−	0.344369i
$401$	9.39909	−	22.6914i	0.469368	−	1.13315i	−0.495072	−	0.868852i	$-0.664858\pi$
$401$	9.39909	−	22.6914i	0.469368	−	1.13315i	0.964440	−	0.264302i	$-0.0851417\pi$
$402$	−11.1401	+	14.8778i	−0.555618	+	0.742037i
$403$	18.8418	−	5.71560i	0.938577	−	0.284714i
$404$	3.54132	+	8.77602i	0.176187	+	0.436623i
$405$	−0.266485	−	2.70567i	−0.0132417	−	0.134446i
$406$	28.6788	−	13.4037i	1.42331	−	0.665214i
$407$	1.45413	−	0.971620i	0.0720787	−	0.0481614i
$408$	1.43381	+	0.380160i	0.0709841	+	0.0188207i
$409$	−11.0806	+	16.5833i	−0.547900	+	0.819990i	−0.997307	−	0.0733369i	$-0.976635\pi$
$409$	−11.0806	+	16.5833i	−0.547900	+	0.819990i	0.449407	+	0.893327i	$0.351635\pi$
$410$	−28.2961	+	20.7856i	−1.39744	+	1.02653i
$411$	−16.1928	−	4.91203i	−0.798731	−	0.242292i
$412$	−30.3408	+	2.70794i	−1.49478	+	0.133411i
$413$	35.6488	+	43.4382i	1.75416	+	2.13745i
$414$	−7.53911	−	0.404992i	−0.370527	−	0.0199043i
$415$	11.5655	−	11.5655i	0.567729	−	0.567729i
$416$	−20.1881	+	8.98854i	−0.989805	+	0.440699i
$417$	6.48518	+	6.48518i	0.317581	+	0.317581i
$418$	2.74574	+	3.05749i	0.134299	+	0.149547i
$419$	−22.0952	+	18.1331i	−1.07942	+	0.885858i	−0.993879	−	0.110476i	$-0.964762\pi$
$419$	−22.0952	+	18.1331i	−1.07942	+	0.885858i	−0.0855429	+	0.996334i	$0.527262\pi$
$420$	−26.5311	−	8.31424i	−1.29458	−	0.405693i
$421$	1.55965	−	5.14148i	0.0760128	−	0.250580i	−0.910697	−	0.413076i	$-0.864454\pi$
$421$	1.55965	−	5.14148i	0.0760128	−	0.250580i	0.986709	+	0.162496i	$0.0519543\pi$
$422$	4.25465	−	27.8045i	0.207113	−	1.35350i
$423$	4.33508	+	2.89661i	0.210779	+	0.140838i
$424$	−2.00922	−	0.984293i	−0.0975763	−	0.0478015i
$425$	−0.696843	−	1.04290i	−0.0338019	−	0.0505881i
$426$	−14.1483	−	5.13554i	−0.685486	−	0.248818i
$427$	−3.98374	+	0.392364i	−0.192787	+	0.0189878i
$428$	−3.29266	+	3.23289i	−0.159157	+	0.156268i
$429$	−0.644331	−	2.12408i	−0.0311086	−	0.102551i
$430$	5.85314	+	40.7434i	0.282264	+	1.96482i
$431$	−26.1789	−	10.8437i	−1.26100	−	0.522321i	−0.350781	−	0.936458i	$-0.614084\pi$
$431$	−26.1789	−	10.8437i	−1.26100	−	0.522321i	−0.910215	+	0.414136i	$0.864084\pi$
$432$	1.94989	−	3.49255i	0.0938142	−	0.168036i
$433$	32.2616	−	13.3632i	1.55039	−	0.642194i	0.567006	−	0.823714i	$-0.308102\pi$
$433$	32.2616	−	13.3632i	1.55039	−	0.642194i	0.983387	+	0.181520i	$0.0581016\pi$
$434$	18.5939	+	31.3467i	0.892535	+	1.50469i
$435$	5.61059	−	10.4967i	0.269007	−	0.503277i
$436$	22.3360	+	15.2222i	1.06970	+	0.729011i
$437$	−17.3206	+	21.1052i	−0.828556	+	1.00960i
$438$	1.71044	−	1.86989i	0.0817278	−	0.0893469i
$439$	0.461478	−	2.32001i	0.0220251	−	0.110728i	−0.968209	−	0.250143i	$-0.919522\pi$
$439$	0.461478	−	2.32001i	0.0220251	−	0.110728i	0.990234	+	0.139415i	$0.0445223\pi$
$440$	4.36653	−	0.154412i	0.208166	−	0.00736130i
$441$	−18.7773	+	3.73504i	−0.894159	+	0.177859i
$442$	−2.81375	+	0.691129i	−0.133837	+	0.0328736i
$443$	−5.59019	+	2.98802i	−0.265598	+	0.141965i	−0.598821	−	0.800883i	$-0.704364\pi$
$443$	−5.59019	+	2.98802i	−0.265598	+	0.141965i	0.333223	+	0.942848i	$0.391864\pi$
$444$	−5.90700	+	1.73295i	−0.280334	+	0.0822420i
$445$	−0.574195	+	5.82990i	−0.0272195	+	0.276364i
$446$	−5.96002	−	16.9008i	−0.282215	−	0.800274i
$447$		−	16.8845i		−	0.798610i
$448$	−25.0718	−	32.3218i	−1.18453	−	1.52706i
$449$			5.78325i			0.272928i	0.990645	+	0.136464i	$0.0435738\pi$
$449$			5.78325i			0.272928i	−0.990645	+	0.136464i	$0.956426\pi$
$450$	−3.18977	+	1.12487i	−0.150367	+	0.0530267i
$451$	0.508557	−	5.16346i	0.0239470	−	0.243138i
$452$	7.81708	−	14.3079i	0.367684	−	0.672988i
$453$	12.8153	−	6.84992i	0.602115	−	0.321837i
$454$	−4.76764	−	19.4102i	−0.223756	−	0.910967i
$455$	53.2639	−	10.5949i	2.49705	−	0.496694i
$456$	−6.00434	−	13.1599i	−0.281179	−	0.616270i
$457$	−3.47141	+	17.4519i	−0.162386	+	0.816367i	0.810618	+	0.585576i	$0.199131\pi$
$457$	−3.47141	+	17.4519i	−0.162386	+	0.816367i	−0.973003	+	0.230791i	$0.925869\pi$
$458$	8.36641	+	7.65296i	0.390937	+	0.357599i
$459$	0.332704	−	0.405401i	0.0155293	−	0.0189225i
$460$	5.40225	+	28.5219i	0.251881	+	1.32984i
$461$	−5.75200	+	10.7612i	−0.267897	+	0.501201i	−0.979516	−	0.201365i	$-0.935462\pi$
$461$	−5.75200	+	10.7612i	−0.267897	+	0.501201i	0.711619	+	0.702566i	$0.247962\pi$
$462$	3.53378	−	2.09613i	0.164406	−	0.0975207i
$463$	16.2832	−	6.74473i	0.756745	−	0.313454i	0.0292546	−	0.999572i	$-0.490687\pi$
$463$	16.2832	−	6.74473i	0.756745	−	0.313454i	0.727490	+	0.686118i	$0.240687\pi$
$464$	15.5920	−	7.97036i	0.723839	−	0.370015i
$465$	12.6599	+	5.24391i	0.587090	+	0.243181i
$466$	1.25845	−	0.180787i	0.0582967	−	0.00837481i
$467$	−7.46526	−	24.6097i	−0.345451	−	1.13880i	−0.941828	−	0.336095i	$-0.890894\pi$
$467$	−7.46526	−	24.6097i	−0.345451	−	1.13880i	0.596377	−	0.802704i	$-0.296606\pi$
$468$	−0.0715644	+	7.81276i	−0.00330807	+	0.361145i
$469$	66.8771	−	6.58682i	3.08810	−	0.304151i
$470$	6.83980	−	18.8435i	0.315497	−	0.869184i
$471$	−1.90851	−	2.85628i	−0.0879394	−	0.131611i
$472$	20.5562	+	23.3163i	0.946178	+	1.07322i
$473$	−5.05763	−	3.37940i	−0.232550	−	0.155385i
$474$	−13.3255	−	2.03907i	−0.612061	−	0.0936575i
$475$	−3.55054	+	11.7046i	−0.162910	+	0.537042i
$476$	−2.48477	−	4.75289i	−0.113889	−	0.217848i
$477$	−0.611472	+	0.501822i	−0.0279974	+	0.0229769i
$478$	−16.5727	+	14.8829i	−0.758015	+	0.680728i
$479$	−11.2023	−	11.2023i	−0.511844	−	0.511844i	0.403247	−	0.915091i	$-0.367882\pi$
$479$	−11.2023	−	11.2023i	−0.511844	−	0.511844i	−0.915091	+	0.403247i	$0.867882\pi$
$480$	−14.8292	−	4.07756i	−0.676859	−	0.186114i
$481$	8.50243	−	8.50243i	0.387677	−	0.387677i
$482$	0.222008	−	4.13279i	0.0101122	−	0.188243i
$483$	17.3175	+	21.1015i	0.787974	+	0.960149i
$484$	13.6977	−	16.3823i	0.622621	−	0.744652i
$485$	−31.6249	−	9.59330i	−1.43601	−	0.435609i
$486$	−0.837235	−	1.13975i	−0.0379777	−	0.0517003i
$487$	−20.7766	+	31.0944i	−0.941479	+	1.40902i	−0.0291454	+	0.999575i	$0.509279\pi$
$487$	−20.7766	+	31.0944i	−0.941479	+	1.40902i	−0.912334	+	0.409448i	$0.865721\pi$
$488$	−2.19459	+	0.294781i	−0.0993444	+	0.0133441i
$489$	1.71082	−	1.14314i	0.0773661	−	0.0516944i
$490$	31.1679	+	66.6874i	1.40802	+	3.01263i
$491$	3.13113	+	31.7909i	0.141306	+	1.43470i	0.760436	+	0.649413i	$0.224985\pi$
$491$	3.13113	+	31.7909i	0.141306	+	1.43470i	−0.619130	+	0.785288i	$0.712515\pi$
$492$	−7.14325	+	16.8082i	−0.322042	+	0.757772i
$493$	2.19703	−	0.666461i	0.0989491	−	0.0300159i
$494$	22.6165	+	16.9347i	1.01757	+	0.761927i
$495$	0.591157	−	1.42718i	0.0265705	−	0.0641469i
$496$	10.8917	+	16.9654i	0.489053	+	0.761767i
$497$	20.8257	+	50.2777i	0.934161	+	2.25526i
$498$	2.10504	−	8.24342i	0.0943290	−	0.369396i
$499$	16.3568	+	8.74288i	0.732230	+	0.391385i	0.794973	−	0.606645i	$-0.207485\pi$
$499$	16.3568	+	8.74288i	0.732230	+	0.391385i	−0.0627432	+	0.998030i	$0.519985\pi$
$500$	−7.77128	−	11.8644i	−0.347542	−	0.530591i
$501$	−14.6050	−	11.9861i	−0.652505	−	0.535497i
$502$	−0.927211	−	20.8189i	−0.0413835	−	0.929194i
$503$	−17.6773	−	3.51623i	−0.788191	−	0.156781i	−0.215448	−	0.976515i	$-0.569121\pi$
$503$	−17.6773	−	3.51623i	−0.788191	−	0.156781i	−0.572744	+	0.819734i	$0.694121\pi$
$504$	−14.0760	+	3.32100i	−0.626993	+	0.147929i
$505$	−2.50976	−	12.6174i	−0.111683	−	0.561468i
$506$	−3.66936	−	2.22223i	−0.163123	−	0.0987903i
$507$	−1.06587	−	1.99410i	−0.0473368	−	0.0885609i
$508$	−18.7399	−	23.2660i	−0.831448	−	1.03226i
$509$	−21.9906	−	2.16589i	−0.974718	−	0.0960013i	−0.401900	−	0.915684i	$-0.631650\pi$
$509$	−21.9906	−	2.16589i	−0.974718	−	0.0960013i	−0.572818	+	0.819682i	$0.694150\pi$
$510$	−1.81887	−	0.870477i	−0.0805409	−	0.0385454i
$511$	−9.16261			−0.405330
$512$	−14.4919	−	17.3777i	−0.640456	−	0.767995i
$513$	−5.11415			−0.225795
$514$	17.0014	+	8.13656i	0.749900	+	0.358888i
$515$	41.2092	+	4.05875i	1.81589	+	0.178850i
$516$	13.4309	+	16.6747i	0.591260	+	0.734062i
$517$	1.39647	+	2.61260i	0.0614165	+	0.114902i
$518$	19.0383	+	11.5300i	0.836494	+	0.506597i
$519$	3.10007	+	15.5851i	0.136078	+	0.684110i
$520$	29.2378	−	6.89821i	1.28216	−	0.302507i
$521$	−26.6839	−	5.30775i	−1.16904	−	0.232537i	−0.427862	−	0.903844i	$-0.640733\pi$
$521$	−26.6839	−	5.30775i	−1.16904	−	0.232537i	−0.741179	+	0.671307i	$0.765733\pi$
$522$	−0.275459	−	6.18495i	−0.0120565	−	0.270708i
$523$	10.3429	+	8.48817i	0.452262	+	0.371162i	0.832773	−	0.553615i	$-0.186752\pi$
$523$	10.3429	+	8.48817i	0.452262	+	0.371162i	−0.380511	+	0.924776i	$0.624252\pi$
$524$	−18.8214	−	28.7345i	−0.822216	−	1.25527i
$525$	10.7851	+	5.76474i	0.470699	+	0.251594i
$526$	−7.36282	+	28.8331i	−0.321034	+	1.25718i
$527$	1.01154	+	2.44208i	0.0440634	+	0.106379i
$528$	1.91254	−	1.22785i	0.0832326	−	0.0534351i
$529$	2.10519	−	5.08237i	0.0915299	−	0.220973i
$530$	2.43457	+	1.82294i	0.105751	+	0.0791836i
$531$	10.5166	−	3.19017i	0.456381	−	0.138442i
$532$	−20.4560	+	48.1333i	−0.886878	+	2.08684i
$533$	−3.49655	−	35.5011i	−0.151452	−	1.53772i
$534$	1.29022	+	2.76058i	0.0558333	+	0.119462i
$535$	5.21564	−	3.48498i	0.225492	−	0.150669i
$536$	36.8417	−	4.94865i	1.59132	−	0.213749i
$537$	5.39358	−	8.07206i	0.232750	−	0.348335i
$538$	−6.50802	−	8.85956i	−0.280580	−	0.381963i
$539$	−10.4097	−	3.15774i	−0.448377	−	0.136014i
$540$	−3.48788	+	4.17148i	−0.150094	+	0.179512i
$541$	−9.51728	−	11.5968i	−0.409180	−	0.498587i	0.527119	−	0.849791i	$-0.323272\pi$
$541$	−9.51728	−	11.5968i	−0.409180	−	0.498587i	−0.936299	+	0.351204i	$0.885772\pi$
$542$	−1.33827	+	24.9126i	−0.0574838	+	1.07009i
$543$	−12.2923	+	12.2923i	−0.527513	+	0.527513i
$544$	−1.46653	−	2.57888i	−0.0628767	−	0.110569i
$545$	−25.9818	−	25.9818i	−1.11294	−	1.11294i
$546$	21.0178	−	18.8748i	0.899480	−	0.807768i
$547$	−31.4446	+	25.8059i	−1.34447	+	1.10338i	−0.359041	+	0.933322i	$0.616896\pi$
$547$	−31.4446	+	25.8059i	−1.34447	+	1.10338i	−0.985434	+	0.170060i	$0.945604\pi$
$548$	15.6793	+	29.9916i	0.669788	+	1.28118i
$549$	−0.227256	+	0.749163i	−0.00969905	+	0.0319735i
$550$	−1.89967	−	0.290688i	−0.0810023	−	0.0123950i
$551$	−18.6153	−	12.4384i	−0.793040	−	0.529893i
$552$	9.98584	+	11.3266i	0.425026	+	0.482092i
$553$	27.0788	+	40.5263i	1.15151	+	1.72336i
$554$	−3.06633	+	8.44766i	−0.130276	+	0.358907i
$555$	8.32798	−	0.820234i	0.353503	−	0.0348170i
$556$	0.168012	−	18.3421i	0.00712531	−	0.777878i
$557$	12.5094	+	41.2380i	0.530041	+	1.74731i	0.655483	+	0.755210i	$0.272465\pi$
$557$	12.5094	+	41.2380i	0.530041	+	1.74731i	−0.125442	+	0.992101i	$0.540035\pi$
$558$	7.05544	−	1.01357i	0.298681	−	0.0429080i
$559$	−38.6381	−	16.0044i	−1.63422	−	0.676915i
$560$	25.3100	+	49.5126i	1.06954	+	2.09229i
$561$	0.275300	−	0.114033i	0.0116232	−	0.00481448i
$562$	−22.6183	+	13.4165i	−0.954095	+	0.565940i
$563$	−0.569141	+	1.06479i	−0.0239865	+	0.0448755i	−0.893629	−	0.448806i	$-0.851849\pi$
$563$	−0.569141	+	1.06479i	−0.0239865	+	0.0448755i	0.869643	+	0.493682i	$0.164349\pi$
$564$	−1.94055	−	10.2454i	−0.0817118	−	0.431408i
$565$	−14.0603	+	17.1326i	−0.591523	+	0.720773i
$566$	3.46354	+	3.16818i	0.145583	+	0.133168i
$567$	−0.997543	+	5.01499i	−0.0418929	+	0.210610i
$568$	12.4956	+	27.3870i	0.524303	+	1.14913i
$569$	10.3008	−	2.04895i	0.431831	−	0.0858966i	0.0256114	−	0.999672i	$-0.491847\pi$
$569$	10.3008	−	2.04895i	0.431831	−	0.0858966i	0.406220	+	0.913775i	$0.366847\pi$
$570$	4.69041	+	19.0958i	0.196460	+	0.799835i
$571$	0.122852	−	0.0656659i	0.00514121	−	0.00274803i	−0.468824	−	0.883292i	$-0.655322\pi$
$571$	0.122852	−	0.0656659i	0.00514121	−	0.00274803i	0.473965	+	0.880544i	$0.342822\pi$
$572$	−2.12845	+	3.89579i	−0.0889949	+	0.162891i
$573$	0.835237	−	8.48030i	0.0348925	−	0.354270i
$574$	62.2735	−	21.9606i	2.59924	−	0.916618i
$575$		−	12.7682i		−	0.532469i
$576$	−7.71644	+	2.11106i	−0.321518	+	0.0879609i
$577$		−	9.62647i		−	0.400755i	−0.979719	−	0.200378i	$-0.935783\pi$
$577$		−	9.62647i		−	0.400755i	0.979719	−	0.200378i	$-0.0642169\pi$
$578$	7.86627	+	22.3063i	0.327194	+	0.927819i
$579$	0.347321	−	3.52640i	0.0144341	−	0.146552i
$580$	−22.8415	+	6.70104i	−0.948440	+	0.278245i
$581$	−27.1291	+	14.5008i	−1.12550	+	0.601595i
$582$	−16.6943	+	4.10053i	−0.692000	+	0.169973i
$583$	−0.440816	+	0.0876838i	−0.0182567	+	0.00363149i
$584$	−5.06520	+	0.179119i	−0.209600	+	0.00741198i
$585$	2.07204	−	10.4169i	0.0856685	−	0.430685i
$586$	17.4094	−	19.0324i	0.719177	−	0.786223i
$587$	15.1265	−	18.4316i	0.624336	−	0.760755i	−0.360780	−	0.932651i	$-0.617489\pi$
$587$	15.1265	−	18.4316i	0.624336	−	0.760755i	0.985115	+	0.171896i	$0.0549893\pi$
$588$	31.6411	+	21.5637i	1.30486	+	0.889273i
$589$	12.1508	−	22.7325i	0.500665	−	0.936678i
$590$	−21.5571	−	36.3422i	−0.887491	−	1.49619i
$591$	4.77244	−	1.97681i	0.196312	−	0.0813150i
$592$	10.7500	+	6.00172i	0.441822	+	0.246669i
$593$	−3.52898	−	1.46175i	−0.144918	−	0.0600269i	0.309046	−	0.951047i	$-0.399990\pi$
$593$	−3.52898	−	1.46175i	−0.144918	−	0.0600269i	−0.453964	+	0.891020i	$0.649990\pi$
$594$	−0.114262	−	0.795374i	−0.00468824	−	0.0326346i
$595$	2.11636	+	6.97671i	0.0867623	+	0.286017i
$596$	−24.0960	+	23.6586i	−0.987011	+	0.969094i
$597$	−7.55284	+	0.743890i	−0.309117	+	0.0304454i
$598$	−27.7244	−	10.0634i	−1.13374	−	0.411524i
$599$	−1.87920	−	2.81242i	−0.0767821	−	0.114913i	0.791091	−	0.611698i	$-0.209513\pi$
$599$	−1.87920	−	2.81242i	−0.0767821	−	0.114913i	−0.867873	+	0.496786i	$0.834513\pi$
$600$	6.07481	+	2.97598i	0.248003	+	0.121494i
$601$	19.2711	+	12.8766i	0.786086	+	0.525246i	0.882622	−	0.470083i	$-0.155776\pi$
$601$	19.2711	+	12.8766i	0.786086	+	0.525246i	−0.0965357	+	0.995330i	$0.530776\pi$
$602$	11.7096	−	76.5232i	0.477246	−	3.11885i
$603$	3.81506	−	12.5766i	0.155361	−	0.512158i
$604$	−27.7324	−	8.69070i	−1.12841	−	0.353619i
$605$	−22.4394	+	18.4156i	−0.912293	+	0.748699i
$606$	−4.47116	−	4.97880i	−0.181628	−	0.202250i
$607$	24.2831	+	24.2831i	0.985620	+	0.985620i	0.999898	−	0.0142778i	$-0.00454493\pi$
$607$	24.2831	+	24.2831i	0.985620	+	0.985620i	−0.0142778	+	0.999898i	$0.504545\pi$
$608$	−10.3674	+	27.0085i	−0.420452	+	1.09534i
$609$	−15.8282	+	15.8282i	−0.641393	+	0.641393i
$610$	3.00574	+	0.161465i	0.121699	+	0.00653752i
$611$	12.9212	+	15.7445i	0.522735	+	0.636955i
$612$	−1.04473	+	0.0932436i	−0.0422309	+	0.00376915i
$613$	−38.5560	−	11.6958i	−1.55726	−	0.472390i	−0.609879	−	0.792495i	$-0.708782\pi$
$613$	−38.5560	−	11.6958i	−1.55726	−	0.472390i	−0.947382	+	0.320105i	$0.896282\pi$
$614$	27.5605	−	20.2453i	1.11225	−	0.817034i
$615$	13.7929	−	20.6425i	0.556182	−	0.832385i
$616$	−7.94293	−	2.10599i	−0.320030	−	0.0848527i
$617$	16.2110	−	10.8319i	0.652631	−	0.436074i	−0.184681	−	0.982798i	$-0.559125\pi$
$617$	16.2110	−	10.8319i	0.652631	−	0.436074i	0.837313	+	0.546724i	$0.184125\pi$
$618$	19.5134	−	9.12003i	0.784945	−	0.366862i
$619$	1.12330	+	11.4051i	0.0451494	+	0.458410i	0.991005	+	0.133823i	$0.0427253\pi$
$619$	1.12330	+	11.4051i	0.0451494	+	0.458410i	−0.945856	+	0.324587i	$0.894775\pi$
$620$	−10.2555	−	25.4148i	−0.411869	−	1.02068i
$621$	5.10876	−	1.54973i	0.205008	−	0.0621884i
$622$	−7.85534	+	10.4909i	−0.314970	+	0.420648i
$623$	4.21621	−	10.1788i	0.168919	−	0.407807i
$624$	11.2499	−	10.8451i	0.450357	−	0.434152i
$625$	11.9544	+	28.8604i	0.478175	+	1.15442i
$626$	−20.0285	−	5.11448i	−0.800501	−	0.204416i
$627$	−2.56269	−	1.36978i	−0.102344	−	0.0547039i
$628$	−1.40202	+	6.72587i	−0.0559468	+	0.268392i
$629$	1.24781	+	1.02405i	0.0497536	+	0.0408317i
$630$	19.6404	−	0.874726i	0.782494	−	0.0348499i
$631$	−39.3222	−	7.82167i	−1.56539	−	0.311376i	−0.665131	−	0.746727i	$-0.731624\pi$
$631$	−39.3222	−	7.82167i	−1.56539	−	0.311376i	−0.900261	+	0.435351i	$0.856624\pi$
$632$	15.7618	+	21.8741i	0.626969	+	0.870105i
$633$	3.88027	+	19.5075i	0.154227	+	0.775352i
$634$	−1.54986	+	2.55913i	−0.0615528	+	0.101636i
$635$	19.1438	+	35.8155i	0.759699	+	1.42130i
$636$	1.57295	+	0.169483i	0.0623715	+	0.00672044i
$637$	−74.4314	−	7.33086i	−2.94908	−	0.290459i
$638$	1.51856	−	3.17304i	0.0601203	−	0.125622i
$639$	10.6430			0.421031
$640$	14.9596	+	26.8764i	0.591331	+	1.06238i
$641$	43.4247			1.71517			0.857586	−	0.514341i	$-0.171963\pi$
$641$	43.4247			1.71517			0.857586	+	0.514341i	$0.171963\pi$
$642$	1.40857	−	2.94322i	0.0555918	−	0.116160i
$643$	25.6789	+	2.52916i	1.01268	+	0.0997402i	0.590721	−	0.806876i	$-0.298843\pi$
$643$	25.6789	+	2.52916i	1.01268	+	0.0997402i	0.421957	+	0.906616i	$0.361343\pi$
$644$	5.84873	−	54.2813i	0.230472	−	2.13898i
$645$	−13.7203	−	25.6690i	−0.540238	−	1.01071i
$646$	−1.96489	+	3.24443i	−0.0773076	+	0.127650i
$647$	1.82675	+	9.18369i	0.0718169	+	0.361048i	0.999937	−	0.0112331i	$-0.00357568\pi$
$647$	1.82675	+	9.18369i	0.0718169	+	0.361048i	−0.928120	+	0.372281i	$0.878576\pi$
$648$	−0.453417	+	2.79185i	−0.0178119	+	0.109674i
$649$	6.12430	+	1.21820i	0.240400	+	0.0478185i
$650$	−13.2000	+	0.587889i	−0.517747	+	0.0230589i
$651$	−19.9217	−	16.3493i	−0.780793	−	0.640780i
$652$	−4.02859	−	0.839767i	−0.157772	−	0.0328878i
$653$	−22.0645	−	11.7937i	−0.863452	−	0.461525i	−0.0206741	−	0.999786i	$-0.506581\pi$
$653$	−22.0645	−	11.7937i	−0.863452	−	0.461525i	−0.842778	+	0.538262i	$0.819081\pi$
$654$	−18.5187	−	4.72894i	−0.724139	−	0.184916i
$655$	17.8692	+	43.1401i	0.698209	+	1.68562i
$656$	33.9962	−	13.3575i	1.32733	−	0.521522i
$657$	−0.685745	+	1.65554i	−0.0267535	+	0.0645886i
$658$	−22.5974	+	30.1792i	−0.880938	+	1.17651i
$659$	1.29856	−	0.393914i	0.0505847	−	0.0153447i	−0.264891	−	0.964278i	$-0.585336\pi$
$659$	1.29856	−	0.393914i	0.0505847	−	0.0153447i	0.315476	+	0.948934i	$0.397836\pi$
$660$	−2.86507	+	1.15612i	−0.111523	+	0.0450019i
$661$	0.113501	+	1.15239i	0.00441466	+	0.0448228i	0.997140	−	0.0755809i	$-0.0240811\pi$
$661$	0.113501	+	1.15239i	0.00441466	+	0.0448228i	−0.992725	+	0.120404i	$0.961581\pi$
$662$	−16.9727	+	7.93257i	−0.659662	+	0.308308i
$663$	1.70348	−	1.13823i	0.0661578	−	0.0442053i
$664$	−14.7138	+	8.54657i	−0.571007	+	0.331671i
$665$	39.4983	−	59.1134i	1.53168	−	2.29232i
$666$	3.50813	−	2.57699i	0.135937	−	0.0998563i
$667$	22.3649	+	6.78432i	0.865973	+	0.262690i
$668$	3.35921	+	37.6378i	0.129972	+	1.45625i
$669$	8.03901	+	9.79556i	0.310806	+	0.378718i
$670$	−50.4589	−	2.71059i	−1.94940	−	0.104719i
$671$	−0.314535	+	0.314535i	−0.0121425	+	0.0121425i
$672$	24.4627	+	15.4345i	0.943668	+	0.595399i
$673$	16.8752	+	16.8752i	0.650493	+	0.650493i	0.953112	−	0.302619i	$-0.0978610\pi$
$673$	16.8752	+	16.8752i	0.650493	+	0.650493i	−0.302619	+	0.953112i	$0.597861\pi$
$674$	−19.3257	−	21.5199i	−0.744399	−	0.828916i
$675$	1.84877	−	1.51725i	0.0711591	−	0.0583988i
$676$	−1.35230	+	4.31523i	−0.0520114	+	0.165971i
$677$	−14.0259	+	46.2372i	−0.539059	+	1.77704i	0.0858138	+	0.996311i	$0.472651\pi$
$677$	−14.0259	+	46.2372i	−0.539059	+	1.77704i	−0.624872	+	0.780727i	$0.714849\pi$
$678$	−1.74383	+	11.3961i	−0.0669713	+	0.437664i
$679$	51.6792	+	34.5309i	1.98326	+	1.32518i
$680$	1.30634	+	3.81544i	0.0500957	+	0.146315i
$681$	7.85191	+	11.7512i	0.300886	+	0.450307i
$682$	3.80694	+	1.38185i	0.145775	+	0.0529136i
$683$	−20.2974	+	1.99912i	−0.776658	+	0.0764941i	−0.478576	−	0.878046i	$-0.658847\pi$
$683$	−20.2974	+	1.99912i	−0.776658	+	0.0764941i	−0.298082	+	0.954540i	$0.596347\pi$
$684$	7.16594	+	7.29844i	0.273997	+	0.279063i
$685$	−13.3546	−	44.0243i	−0.510254	−	1.68208i
$686$	−12.4885	−	86.9321i	−0.476814	−	3.31908i
$687$	−7.40732	−	3.06821i	−0.282607	−	0.117060i
$688$	4.97725	−	42.5318i	0.189756	−	1.62151i
$689$	−2.85496	+	1.18256i	−0.108765	+	0.0450520i
$690$	−10.4720	−	17.6544i	−0.398663	−	0.672091i
$691$	−6.46334	+	12.0921i	−0.245877	+	0.460004i	−0.974340	−	0.225082i	$-0.927735\pi$
$691$	−6.46334	+	12.0921i	−0.245877	+	0.460004i	0.728463	+	0.685085i	$0.240235\pi$
$692$	17.8978	−	26.2620i	0.680373	−	0.998331i
$693$	−1.84309	+	2.24581i	−0.0700133	+	0.0853114i
$694$	−26.2051	+	28.6481i	−0.994732	+	1.08747i
$695$	−4.86456	+	24.4558i	−0.184523	+	0.927660i
$696$	−8.44062	+	9.05947i	−0.319941	+	0.343398i
$697$	4.69697	−	0.934286i	0.177910	−	0.0353886i
$698$	−2.56994	+	0.631243i	−0.0972738	+	0.0238929i
$699$	−0.792843	+	0.423784i	−0.0299881	+	0.0160290i
$700$	−6.88514	−	23.4690i	−0.260234	−	0.887045i
$701$	−3.86005	+	39.1918i	−0.145792	+	1.48025i	0.592390	+	0.805652i	$0.298185\pi$
$701$	−3.86005	+	39.1918i	−0.145792	+	1.48025i	−0.738182	+	0.674602i	$0.764315\pi$
$702$	−1.83737	−	5.21021i	−0.0693470	−	0.196647i
$703$		−	15.7412i		−	0.593691i
$704$	−4.43212	−	1.00894i	−0.167042	−	0.0380259i
$705$			14.1750i			0.533860i
$706$	29.4407	−	10.3822i	1.10801	−	0.390739i
$707$	−2.37150	+	24.0783i	−0.0891896	+	0.905557i
$708$	−19.2886	−	10.5382i	−0.724909	−	0.396051i
$709$	16.3700	−	8.74995i	0.614789	−	0.328611i	−0.134441	−	0.990922i	$-0.542924\pi$
$709$	16.3700	−	8.74995i	0.614789	−	0.328611i	0.749230	+	0.662310i	$0.230424\pi$
$710$	−9.76118	−	39.7401i	−0.366330	−	1.49142i
$711$	9.34908	−	1.85965i	0.350618	−	0.0697423i
$712$	2.13179	−	5.70941i	0.0798922	−	0.213969i
$713$	−5.24943	+	26.3906i	−0.196593	+	0.988337i
$714$	2.79826	+	2.55964i	0.104722	+	0.0957921i
$715$	3.82837	−	4.66489i	0.143173	−	0.174457i
$716$	−19.0772	+	3.61336i	−0.712948	+	0.135038i
$717$	7.42471	−	13.8907i	0.277281	−	0.518756i
$718$	25.2038	−	14.9501i	0.940597	−	0.557933i
$719$	−6.76249	+	2.80112i	−0.252198	+	0.104464i	−0.505201	−	0.863002i	$-0.668582\pi$
$719$	−6.76249	+	2.80112i	−0.252198	+	0.104464i	0.253003	+	0.967466i	$0.418582\pi$
$720$	10.8404	−	0.867507i	0.403997	−	0.0323301i
$721$	−71.9501	−	29.8027i	−2.67956	−	1.10991i
$722$	10.0151	−	1.43876i	0.372725	−	0.0535452i
$723$	0.849529	+	2.80052i	0.0315943	+	0.104152i
$724$	34.7664	+	0.318458i	1.29208	+	0.0118354i
$725$	10.4196	−	1.02624i	0.386975	−	0.0381138i
$726$	−5.15202	+	14.1937i	−0.191210	+	0.526776i
$727$	−2.09070	−	3.12895i	−0.0775396	−	0.116046i	0.790673	−	0.612239i	$-0.209731\pi$
$727$	−2.09070	−	3.12895i	−0.0775396	−	0.116046i	−0.868212	+	0.496193i	$0.834731\pi$
$728$	−56.3866	−	3.54727i	−2.08983	−	0.131470i
$729$	0.831470	+	0.555570i	0.0307952	+	0.0205767i
$730$	6.81056	+	1.04215i	0.252070	+	0.0385717i
$731$	1.62979	−	5.37269i	0.0602799	−	0.198716i
$732$	1.38757	−	0.725409i	0.0512860	−	0.0268119i
$733$	24.2611	−	19.9106i	0.896104	−	0.735414i	−0.0689067	−	0.997623i	$-0.521951\pi$
$733$	24.2611	−	19.9106i	0.896104	−	0.735414i	0.965011	+	0.262209i	$0.0844511\pi$
$734$	−7.40348	+	6.64861i	−0.273267	+	0.245405i
$735$	−36.8057	−	36.8057i	−1.35760	−	1.35760i
$736$	2.17211	−	30.1217i	0.0800652	−	1.11030i
$737$	5.28026	−	5.28026i	0.194501	−	0.194501i
$738$	0.692725	−	12.8954i	0.0254995	−	0.474686i
$739$	23.3058	+	28.3983i	0.857320	+	1.04465i	0.998505	+	0.0546637i	$0.0174087\pi$
$739$	23.3058	+	28.3983i	0.857320	+	1.04465i	−0.141185	+	0.989983i	$0.545091\pi$
$740$	−12.8397	−	10.7356i	−0.471998	−	0.394649i
$741$	−19.1184	−	5.79949i	−0.702330	−	0.213050i
$742$	−3.38637	−	4.60997i	−0.124318	−	0.169237i
$743$	−15.3541	+	22.9791i	−0.563288	+	0.843020i	−0.998352	−	0.0573793i	$-0.981726\pi$
$743$	−15.3541	+	22.9791i	−0.563288	+	0.843020i	0.435065	+	0.900399i	$0.356726\pi$
$744$	−11.3326	−	8.64866i	−0.415472	−	0.317075i
$745$	38.1685	−	25.5034i	1.39839	−	0.934372i
$746$	0.998592	+	2.13661i	0.0365611	+	0.0782268i
$747$	0.589673	+	5.98706i	0.0215750	+	0.219055i
$748$	−0.548489	−	0.233100i	−0.0200547	−	0.00852298i
$749$	−11.2894	+	3.42461i	−0.412506	+	0.125132i
$750$	8.02782	+	6.01102i	0.293134	+	0.219491i
$751$	5.86891	−	14.1688i	0.214159	−	0.517027i	−0.779895	−	0.625910i	$-0.784728\pi$
$751$	5.86891	−	14.1688i	0.214159	−	0.517027i	0.994054	+	0.108884i	$0.0347276\pi$
$752$	−11.9021	+	17.1252i	−0.434026	+	0.624491i
$753$	5.63914	+	13.6141i	0.205502	+	0.496125i
$754$	5.98404	−	23.4338i	0.217926	−	0.853407i
$755$	34.8417	+	18.6233i	1.26802	+	0.677770i
$756$	8.55469	−	5.60340i	0.311131	−	0.203794i
$757$	0.467130	+	0.383364i	0.0169781	+	0.0139336i	0.642844	−	0.765997i	$-0.277754\pi$
$757$	0.467130	+	0.383364i	0.0169781	+	0.0139336i	−0.625866	+	0.779931i	$0.715254\pi$
$758$	0.0783106	+	1.75833i	0.00284437	+	0.0638653i
$759$	2.97507	+	0.591778i	0.107988	+	0.0214802i
$760$	20.6796	−	33.4508i	0.750126	−	1.21339i
$761$	5.43639	+	27.3306i	0.197069	+	0.990733i	0.945028	+	0.326988i	$0.106034\pi$
$761$	5.43639	+	27.3306i	0.197069	+	0.990733i	−0.747959	+	0.663745i	$0.768966\pi$
$762$	18.0691	+	10.9430i	0.654576	+	0.396424i
$763$	32.5759	+	60.9452i	1.17933	+	2.20636i
$764$	−13.2726	+	10.6906i	−0.480187	+	0.386774i
$765$	1.41897	+	0.139756i	0.0513030	+	0.00505290i
$766$	42.3198	+	20.2535i	1.52908	+	0.731788i
$767$	42.9322			1.55019
$768$	13.8250	+	8.05417i	0.498866	+	0.290630i
$769$	−40.9276			−1.47589			−0.737944	−	0.674862i	$-0.764203\pi$
$769$	−40.9276			−1.47589			−0.737944	+	0.674862i	$0.764203\pi$
$770$	10.0761	+	4.82222i	0.363116	+	0.173781i
$771$	−13.2635	−	1.30634i	−0.477672	−	0.0470466i
$772$	−5.51923	+	4.44554i	−0.198641	+	0.159998i
$773$	−8.69440	−	16.2661i	−0.312716	−	0.585050i	0.675636	−	0.737235i	$-0.263869\pi$
$773$	−8.69440	−	16.2661i	−0.312716	−	0.585050i	−0.988352	+	0.152185i	$0.951369\pi$
$774$	−12.9501	−	7.84285i	−0.465483	−	0.281906i
$775$	2.35168	+	11.8227i	0.0844748	+	0.424683i
$776$	29.2439	+	18.0788i	1.04980	+	0.648993i
$777$	−15.4360	−	3.07041i	−0.553764	−	0.110150i
$778$	−2.11487	−	47.4857i	−0.0758217	−	1.70244i
$779$	−36.0997	−	29.6262i	−1.29341	−	1.06147i
$780$	−17.7693	+	11.6391i	−0.636245	+	0.416746i
$781$	5.33318	+	2.85065i	0.190836	+	0.102004i
$782$	0.979671	−	3.83643i	0.0350330	−	0.137191i
$783$	1.67529	+	4.04452i	0.0598701	+	0.144539i
$784$	−13.5618	−	75.3704i	−0.484350	−	2.69180i
$785$	3.57409	−	8.62861i	0.127565	−	0.307968i
$786$	19.4427	+	14.5582i	0.693497	+	0.519273i
$787$	−16.7584	+	5.08362i	−0.597374	+	0.181211i	−0.574469	−	0.818526i	$-0.694791\pi$
$787$	−16.7584	+	5.08362i	−0.597374	+	0.181211i	−0.0229046	+	0.999738i	$0.507291\pi$
$788$	−9.50826	−	4.04088i	−0.338718	−	0.143950i
$789$	−2.06251	−	20.9410i	−0.0734273	−	0.745520i
$790$	−15.5182	−	33.2031i	−0.552114	−	1.18131i
$791$	34.6584	−	23.1580i	1.23231	−	0.823405i
$792$	−0.974981	+	1.27754i	−0.0346444	+	0.0453955i
$793$	−1.69912	+	2.54291i	−0.0603374	+	0.0903013i
$794$	−2.19996	−	2.99487i	−0.0780736	−	0.106284i
$795$	−2.05801	−	0.624290i	−0.0729900	−	0.0221413i
$796$	11.6447	+	9.73638i	0.412734	+	0.345097i
$797$	−6.01265	−	7.32643i	−0.212979	−	0.259515i	0.655553	−	0.755149i	$-0.272436\pi$
$797$	−6.01265	−	7.32643i	−0.212979	−	0.259515i	−0.868531	+	0.495634i	$0.834936\pi$
$798$	1.98374	−	36.9282i	0.0702236	−	1.30724i
$799$	−1.93346	+	1.93346i	−0.0684009	+	0.0684009i
$800$	−4.26498	−	12.8394i	−0.150790	−	0.453940i
$801$	−1.52360	−	1.52360i	−0.0538339	−	0.0538339i
$802$	25.8431	−	23.2081i	0.912552	−	0.819508i
$803$	−0.787048	+	0.645913i	−0.0277743	+	0.0227938i
$804$	−23.2938	+	12.1778i	−0.821509	+	0.429478i
$805$	−21.5438	+	71.0203i	−0.759318	+	2.50314i
$806$	27.5250	+	4.21187i	0.969526	+	0.148357i
$807$	6.46320	+	4.31857i	0.227515	+	0.152021i
$808$	−0.840293	+	13.3571i	−0.0295614	+	0.469902i
$809$	−8.15519	−	12.2051i	−0.286721	−	0.429108i	0.659950	−	0.751309i	$-0.270577\pi$
$809$	−8.15519	−	12.2051i	−0.286721	−	0.429108i	−0.946671	+	0.322201i	$0.895577\pi$
$810$	1.31188	−	3.61418i	0.0460946	−	0.126989i
$811$	−12.3827	+	1.21959i	−0.434815	+	0.0428256i	−0.313057	−	0.949734i	$-0.601353\pi$
$811$	−12.3827	+	1.21959i	−0.434815	+	0.0428256i	−0.121758	+	0.992560i	$0.538853\pi$
$812$	44.7671	+	0.410064i	1.57102	+	0.0143904i
$813$	−5.12098	−	16.8816i	−0.179601	−	0.592064i
$814$	2.44814	−	0.351697i	0.0858074	−	0.0123270i
$815$	5.16827	+	2.14077i	0.181036	+	0.0749878i
$816$	1.59695	+	1.36030i	0.0559045	+	0.0476199i
$817$	−50.5820	+	20.9518i	−1.76964	+	0.733009i
$818$	−24.2591	+	14.3897i	−0.848200	+	0.503125i
$819$	−9.41619	+	17.6165i	−0.329028	+	0.615569i
$820$	−48.7856	+	9.24035i	−1.70367	+	0.322687i
$821$	4.83217	−	5.88801i	0.168644	−	0.205493i	−0.681830	−	0.731511i	$-0.738816\pi$
$821$	4.83217	−	5.88801i	0.168644	−	0.205493i	0.850473	+	0.526018i	$0.176316\pi$
$822$	−17.6575	−	16.1518i	−0.615877	−	0.563358i
$823$	−0.466652	+	2.34602i	−0.0162665	+	0.0817771i	−0.988066	−	0.154032i	$-0.950774\pi$
$823$	−0.466652	+	2.34602i	−0.0162665	+	0.0817771i	0.971799	+	0.235809i	$0.0757741\pi$
$824$	−40.3575	−	15.0687i	−1.40592	−	0.524945i
$825$	1.33280	−	0.265110i	0.0464020	−	0.00922993i
$826$	18.9563	+	77.1756i	0.659574	+	2.68528i
$827$	−35.5497	+	19.0017i	−1.23618	+	0.660754i	−0.954345	−	0.298708i	$-0.903444\pi$
$827$	−35.5497	+	19.0017i	−1.23618	+	0.660754i	−0.281839	+	0.959462i	$0.590944\pi$
$828$	−9.37003	−	5.11928i	−0.325631	−	0.177907i
$829$	0.789524	−	8.01617i	0.0274213	−	0.278413i	−0.971690	−	0.236260i	$-0.924078\pi$
$829$	0.789524	−	8.01617i	0.0274213	−	0.278413i	0.999111	−	0.0421530i	$-0.0134217\pi$
$830$	21.8144	−	7.69279i	0.757187	−	0.267021i
$831$		−	6.35473i		−	0.220443i
$832$	−31.2405	−	0.858677i	−1.08307	−	0.0297693i
$833$		−	10.0406i		−	0.347886i
$834$	4.31361	+	12.2320i	0.149368	+	0.423561i
$835$	5.03489	−	51.1201i	0.174240	−	1.76908i
$836$	1.63601	+	5.57657i	0.0565825	+	0.192870i
$837$	−4.44503	+	2.37592i	−0.153643	+	0.0821238i
$838$	−39.2561	+	9.64229i	−1.35608	+	0.333087i
$839$	−27.9507	+	5.55974i	−0.964965	+	0.191943i	−0.652334	−	0.757931i	$-0.726210\pi$
$839$	−27.9507	+	5.55974i	−0.964965	+	0.191943i	−0.312631	+	0.949875i	$0.601210\pi$
$840$	−28.7685	−	26.8034i	−0.992609	−	0.924804i
$841$	1.91876	−	9.64627i	0.0661642	−	0.332630i
$842$	5.12846	−	5.60657i	0.176738	−	0.193215i
$843$	11.7969	−	14.3746i	0.406307	−	0.495086i
$844$	22.4022	−	32.8714i	0.771115	−	1.13148i
$845$	2.89783	−	5.42146i	0.0996885	−	0.186504i
$846$	3.76167	+	6.34165i	0.129329	+	0.218030i
$847$	50.4391	−	20.8926i	1.73311	−	0.717877i
$848$	−1.96215	−	2.48225i	−0.0673804	−	0.0852408i
$849$	−3.06649	−	1.27018i	−0.105242	−	0.0435925i
$850$	−0.252236	−	1.75580i	−0.00865162	−	0.0602235i
$851$	4.77002	+	15.7247i	0.163514	+	0.539034i
$852$	−14.9130	−	15.1887i	−0.510911	−	0.520357i
$853$	−49.8278	+	4.90761i	−1.70607	+	0.168033i	−0.903519	−	0.428549i	$-0.859025\pi$
$853$	−49.8278	+	4.90761i	−1.70607	+	0.168033i	−0.802552	+	0.596582i	$0.796525\pi$
$854$	−5.32140	−	1.93157i	−0.182095	−	0.0660968i
$855$	−7.72472	−	11.5609i	−0.264180	−	0.395373i
$856$	−6.17398	+	2.11386i	−0.211022	+	0.0722502i
$857$	−14.7908	−	9.88288i	−0.505243	−	0.337593i	0.276686	−	0.960960i	$-0.410764\pi$
$857$	−14.7908	−	9.88288i	−0.505243	−	0.337593i	−0.781929	+	0.623368i	$0.785764\pi$
$858$	0.474812	−	3.10295i	0.0162098	−	0.105933i
$859$	2.87475	−	9.47677i	0.0980851	−	0.323343i	−0.894142	−	0.447783i	$-0.852214\pi$
$859$	2.87475	−	9.47677i	0.0980851	−	0.323343i	0.992227	+	0.124440i	$0.0397135\pi$
$860$	−17.4074	+	55.5478i	−0.593588	+	1.89416i
$861$	−36.0933	+	29.6210i	−1.23006	+	1.00948i
$862$	−26.7751	−	29.8151i	−0.911964	−	1.01551i
$863$	−19.2126	−	19.2126i	−0.654003	−	0.654003i	0.299952	−	0.953954i	$-0.403029\pi$
$863$	−19.2126	−	19.2126i	−0.654003	−	0.654003i	−0.953954	+	0.299952i	$0.903029\pi$
$864$	4.61960	−	3.26486i	0.157162	−	0.111073i
$865$	−30.5486	+	30.5486i	−1.03868	+	1.03868i
$866$	49.3128	+	2.64903i	1.67572	+	0.0900176i
$867$	−10.6102	−	12.9286i	−0.360341	−	0.439077i
$868$	4.58206	+	51.3391i	0.155525	+	1.74256i
$869$	5.18289	+	1.57221i	0.175818	+	0.0533337i
$870$	13.5654	−	9.96482i	0.459911	−	0.337839i
$871$	28.5239	−	42.6891i	0.966497	−	1.44646i
$872$	19.1997	+	33.0544i	0.650185	+	1.11936i
$873$	10.1069	−	6.75324i	0.342068	−	0.228563i
$874$	−34.9798	+	16.3486i	−1.18321	+	0.553000i
$875$	−3.55414	−	36.0858i	−0.120152	−	1.21992i
$876$	3.32349	−	1.34111i	0.112290	−	0.0453117i
$877$	1.32868	−	0.403050i	0.0448663	−	0.0136100i	−0.267772	−	0.963482i	$-0.586287\pi$
$877$	1.32868	−	0.403050i	0.0448663	−	0.0136100i	0.312638	+	0.949872i	$0.398787\pi$
$878$	2.00506	−	2.67778i	0.0676673	−	0.0903709i
$879$	−6.97976	+	16.8506i	−0.235422	+	0.568358i
$880$	5.66444	+	2.46880i	0.190948	+	0.0832234i
$881$	4.63234	+	11.1835i	0.156067	+	0.376780i	0.982502	−	0.186253i	$-0.0596344\pi$
$881$	4.63234	+	11.1835i	0.156067	+	0.376780i	−0.826434	+	0.563033i	$0.809634\pi$
$882$	−26.2336	−	6.69900i	−0.883331	−	0.225567i
$883$	−29.4519	−	15.7423i	−0.991134	−	0.529772i	−0.105631	−	0.994405i	$-0.533686\pi$
$883$	−29.4519	−	15.7423i	−0.991134	−	0.529772i	−0.885503	+	0.464633i	$0.846186\pi$
$884$	−4.01130	−	0.836164i	−0.134915	−	0.0281233i
$885$	23.0965	+	18.9548i	0.776380	+	0.637159i
$886$	−8.95533	+	0.398843i	−0.300860	+	0.0133994i
$887$	7.87814	+	1.56706i	0.264522	+	0.0526167i	0.325569	−	0.945518i	$-0.394444\pi$
$887$	7.87814	+	1.56706i	0.264522	+	0.0526167i	−0.0610472	+	0.998135i	$0.519444\pi$
$888$	−8.59324	−	1.39561i	−0.288370	−	0.0468335i
$889$	−14.9006	−	74.9102i	−0.499749	−	2.51241i
$890$	−4.29165	+	7.08638i	−0.143856	+	0.237536i
$891$	0.267842	+	0.501098i	0.00897305	+	0.0167874i
$892$	2.71506	−	25.1981i	0.0909068	−	0.843694i
$893$	26.5355	+	2.61352i	0.887978	+	0.0874582i
$894$	10.3080	−	21.5388i	0.344753	−	0.720364i
$895$	26.3942			0.882261
$896$	−12.2504	−	56.5377i	−0.409257	−	1.88879i
$897$	20.8556			0.696350
$898$	−3.53069	+	7.37741i	−0.117821	+	0.246187i
$899$	−21.9584	−	2.16271i	−0.732353	−	0.0721305i
$900$	−4.75577	−	0.512427i	−0.158526	−	0.0170809i
$901$	−0.195559	−	0.365864i	−0.00651500	−	0.0121887i
$902$	3.80105	−	6.27630i	0.126561	−	0.208978i
$903$	10.6792	+	53.6881i	0.355382	+	1.78663i
$904$	18.7069	−	13.4796i	0.622182	−	0.448324i
$905$	−46.3546	−	9.22050i	−1.54088	−	0.306500i
$906$	20.5297	−	0.914332i	0.682055	−	0.0303766i
$907$	18.4506	+	15.1420i	0.612643	+	0.502783i	0.888779	−	0.458335i	$-0.151554\pi$
$907$	18.4506	+	15.1420i	0.612643	+	0.502783i	−0.276136	+	0.961118i	$0.589054\pi$
$908$	5.76815	−	27.6713i	0.191423	−	0.918305i
$909$	4.17307	+	2.23055i	0.138412	+	0.0739827i
$910$	74.4144	+	19.0024i	2.46681	+	0.629925i
$911$	−8.38137	−	20.2344i	−0.277687	−	0.670396i	0.722084	−	0.691806i	$-0.243185\pi$
$911$	−8.38137	−	20.2344i	−0.277687	−	0.670396i	−0.999771	+	0.0214097i	$0.993185\pi$
$912$	0.374731	−	20.4531i	0.0124086	−	0.677271i
$913$	−1.30810	+	3.15804i	−0.0432919	+	0.104516i
$914$	−15.0828	+	20.1433i	−0.498893	+	0.666280i
$915$	−2.03679	+	0.617854i	−0.0673343	+	0.0204256i
$916$	6.00047	+	14.8702i	0.198261	+	0.491326i
$917$	−8.60783	−	87.3967i	−0.284256	−	2.88609i
$918$	0.671912	−	0.314033i	0.0221764	−	0.0103646i
$919$	47.2171	−	31.5494i	1.55755	−	1.04072i	0.584136	−	0.811656i	$-0.301434\pi$
$919$	47.2171	−	31.5494i	1.55755	−	1.04072i	0.973411	−	0.229064i	$-0.0735664\pi$
$920$	−10.5213	+	39.6820i	−0.346877	+	1.30828i
$921$	−13.4343	+	20.1059i	−0.442676	+	0.662512i
$922$	−13.9073	+	10.2160i	−0.458013	+	0.336445i
$923$	39.7871	+	12.0693i	1.30961	+	0.397265i
$924$	5.78756	−	0.516545i	0.190397	−	0.0169931i
$925$	4.67004	+	5.69046i	0.153550	+	0.187101i
$926$	24.8894	+	1.33703i	0.817915	+	0.0439374i
$927$	−10.7697	+	10.7697i	−0.353724	+	0.353724i
$928$	24.7558	−	0.648458i	0.812650	−	0.0212867i
$929$	16.8652	+	16.8652i	0.553330	+	0.553330i	0.927400	−	0.374070i	$-0.122038\pi$
$929$	16.8652	+	16.8652i	0.553330	+	0.553330i	−0.374070	+	0.927400i	$0.622038\pi$
$930$	12.9482	+	14.4183i	0.424589	+	0.472795i
$931$	−75.6865	+	62.1143i	−2.48052	+	2.03571i
$932$	1.71572	+	0.537667i	0.0562002	+	0.0176119i
$933$	2.69016	−	8.86827i	0.0880719	−	0.290334i
$934$	5.50120	−	35.9509i	0.180005	−	1.17635i
$935$	0.673610	+	0.450092i	0.0220294	+	0.0147196i
$936$	−4.86100	+	9.92267i	−0.158887	+	0.324332i
$937$	−23.2055	−	34.7295i	−0.758091	−	1.13456i	−0.986938	−	0.161101i	$-0.948496\pi$
$937$	−23.2055	−	34.7295i	−0.758091	−	1.13456i	0.228847	−	0.973462i	$-0.426504\pi$
$938$	89.3332	+	32.4262i	2.91683	+	1.05875i
$939$	14.5464	−	1.43269i	0.474703	−	0.0467542i
$940$	20.2292	−	19.8620i	0.659803	−	0.647826i
$941$	8.09653	+	26.6907i	0.263939	+	0.870091i	0.984302	+	0.176494i	$0.0564755\pi$
$941$	8.09653	+	26.6907i	0.263939	+	0.870091i	−0.720362	+	0.693598i	$0.756025\pi$
$942$	−0.690821	−	4.80877i	−0.0225082	−	0.156678i
$943$	45.0393	+	18.6559i	1.46668	+	0.607519i
$944$	11.9880	+	42.2931i	0.390175	+	1.37652i
$945$	−12.8435	+	5.31993i	−0.417798	+	0.173057i
$946$	−4.38863	−	7.39863i	−0.142687	−	0.240550i
$947$	0.271814	−	0.508528i	0.00883277	−	0.0165250i	−0.877466	−	0.479639i	$-0.840768\pi$
$947$	0.271814	−	0.508528i	0.00883277	−	0.0165250i	0.886299	+	0.463114i	$0.153268\pi$
$948$	−15.7539	−	10.7364i	−0.511662	−	0.348702i
$949$	−4.44094	+	5.41130i	−0.144159	+	0.175658i
$950$	−11.6749	+	12.7633i	−0.378784	+	0.414097i
$951$	0.412726	−	2.07491i	0.0133836	−	0.0672837i
$952$	−0.268048	−	7.57999i	−0.00868749	−	0.245669i
$953$	48.9391	−	9.73459i	1.58529	−	0.315334i	0.677750	−	0.735293i	$-0.262955\pi$
$953$	48.9391	−	9.73459i	1.58529	−	0.315334i	0.907543	+	0.419958i	$0.137955\pi$
$954$	−1.08639	+	0.266845i	−0.0351732	+	0.00863942i
$955$	20.4319	−	10.9211i	0.661160	−	0.353397i
$956$	−30.2270	+	8.86773i	−0.977610	+	0.286803i
$957$	−0.243807	+	2.47541i	−0.00788116	+	0.0800187i
$958$	−7.45116	−	21.1292i	−0.240736	−	0.682653i
$959$			86.5232i			2.79398i
$960$	−16.4276	−	14.2548i	−0.530198	−	0.460073i
$961$			5.59670i			0.180539i
$962$	16.0369	−	5.65538i	0.517050	−	0.182337i
$963$	−0.226148	+	2.29612i	−0.00728751	+	0.0739914i
$964$	2.80628	−	5.13646i	0.0903843	−	0.165434i
$965$	8.49628	−	4.54136i	0.273505	−	0.146191i
$966$	9.20861	+	37.4905i	0.296282	+	1.20624i
$967$	26.6988	−	5.31071i	0.858574	−	0.170781i	0.253877	−	0.967237i	$-0.418294\pi$
$967$	26.6988	−	5.31071i	0.858574	−	0.170781i	0.604697	+	0.796455i	$0.293294\pi$
$968$	27.4749	−	12.5357i	0.883077	−	0.402912i
$969$	0.523248	−	2.63055i	0.0168092	−	0.0845053i
$970$	−34.4856	−	31.5448i	−1.10726	−	1.01284i
$971$	19.4085	−	23.6494i	0.622850	−	0.758945i	−0.362033	−	0.932165i	$-0.617917\pi$
$971$	19.4085	−	23.6494i	0.622850	−	0.758945i	0.984883	+	0.173220i	$0.0554173\pi$
$972$	−0.372197	−	1.96506i	−0.0119382	−	0.0630294i
$973$	22.1065	−	41.3583i	0.708701	−	1.32589i
$974$	−45.4870	+	26.9815i	−1.45750	+	0.864541i
$975$	8.63188	−	3.57544i	0.276441	−	0.114506i
$976$	−2.97950	−	0.963765i	−0.0953714	−	0.0308494i
$977$	14.5970	+	6.04628i	0.467000	+	0.193438i	0.603759	−	0.797167i	$-0.293669\pi$
$977$	14.5970	+	6.04628i	0.467000	+	0.193438i	−0.136759	+	0.990604i	$0.543669\pi$
$978$	2.88030	−	0.413780i	0.0921019	−	0.0132312i
$979$	−0.355389	−	1.17156i	−0.0113583	−	0.0374432i
$980$	−0.953532	+	104.098i	−0.0304595	+	3.32529i
$981$	13.4498	−	1.32469i	0.429420	−	0.0422942i
$982$	−15.4142	+	42.4656i	−0.491886	+	1.35513i
$983$	−22.8167	−	34.1476i	−0.727739	−	1.08914i	−0.992190	−	0.124739i	$-0.960191\pi$
$983$	−22.8167	−	34.1476i	−0.727739	−	1.08914i	0.264450	−	0.964399i	$-0.414809\pi$
$984$	−19.3737	+	17.0804i	−0.617612	+	0.544504i
$985$	11.6773	+	7.80251i	0.372069	+	0.248609i
$986$	3.20952	+	0.491120i	0.102212	+	0.0156404i
$987$	7.73876	−	25.5113i	0.246327	−	0.812032i
$988$	18.5122	+	35.4102i	0.588950	+	1.12655i
$989$	44.1798	−	36.2575i	1.40484	−	1.15292i
$990$	1.62541	−	1.45968i	0.0516588	−	0.0463917i
$991$	−5.54321	−	5.54321i	−0.176086	−	0.176086i	0.613561	−	0.789647i	$-0.289736\pi$
$991$	−5.54321	−	5.54321i	−0.176086	−	0.176086i	−0.789647	+	0.613561i	$0.789736\pi$
$992$	3.53664	+	28.2913i	0.112288	+	0.898250i
$993$	9.36747	−	9.36747i	0.297268	−	0.297268i
$994$	−4.12835	+	76.8510i	−0.130943	+	2.43757i
$995$	−13.0899	−	15.9501i	−0.414977	−	0.505651i
$996$	7.71792	−	9.23059i	0.244552	−	0.292483i
$997$	14.7893	+	4.48630i	0.468383	+	0.142083i	0.515649	−	0.856800i	$-0.327551\pi$
$997$	14.7893	+	4.48630i	0.468383	+	0.142083i	−0.0472659	+	0.998882i	$0.515051\pi$
$998$	15.5280	+	21.1387i	0.491530	+	0.669135i
$999$	−1.71003	+	2.55924i	−0.0541030	+	0.0809709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.349.28	✓	512
128.117	even	32	inner	384.2.v.a.373.28	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.349.28	✓	512	1.1	even	1	trivial
384.2.v.a.373.28	yes	512	128.117	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27565 + 0.610503i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.25457 + 1.55758i) q^{4} +(-1.28161 - 2.39773i) q^{5} +(-1.20967 - 0.732599i) q^{6} +(0.997543 + 5.01499i) q^{7} +(0.649491 + 2.75285i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.27565 + 0.610503i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(1.25457 + 1.55758i) q^{4} +(-1.28161 - 2.39773i) q^{5} +(-1.20967 - 0.732599i) q^{6} +(0.997543 + 5.01499i) q^{7} +(0.649491 + 2.75285i) q^{8} +(0.980785 + 0.195090i) q^{9} +(-0.171071 - 3.84110i) q^{10} +(0.439216 + 0.360455i) q^{11} +(-1.09586 - 1.67305i) q^{12} +(3.44526 + 1.84153i) q^{13} +(-1.78915 + 7.00638i) q^{14} +(1.04042 + 2.51181i) q^{15} +(-0.852096 + 3.90819i) q^{16} +(-0.200696 + 0.484523i) q^{17} +(1.13204 + 0.847639i) q^{18} +(4.89393 - 1.48456i) q^{19} +(2.12677 - 5.00434i) q^{20} +(-0.501185 - 5.08862i) q^{21} +(0.340227 + 0.727957i) q^{22} +(-4.43892 + 2.96599i) q^{23} +(-0.376538 - 2.80325i) q^{24} +(-1.32873 + 1.98858i) q^{25} +(3.27069 + 4.45250i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(-6.55974 + 7.84542i) q^{28} +(-2.77722 - 3.38405i) q^{29} +(-0.206246 + 3.83937i) q^{30} +(3.56394 - 3.56394i) q^{31} +(-3.47294 + 4.46528i) q^{32} +(-0.401770 - 0.401770i) q^{33} +(-0.551821 + 0.495557i) q^{34} +(10.7461 - 8.81912i) q^{35} +(0.926598 + 1.77240i) q^{36} +(0.893489 - 2.94544i) q^{37} +(7.14928 + 1.09398i) q^{38} +(-3.24817 - 2.17036i) q^{39} +(5.76819 - 5.08539i) q^{40} +(-5.07322 - 7.59261i) q^{41} +(2.46728 - 6.79728i) q^{42} +(-10.6540 + 1.04932i) q^{43} +(-0.0104087 + 1.13633i) q^{44} +(-0.789214 - 2.60169i) q^{45} +(-7.47326 + 1.07360i) q^{46} +(4.81689 + 1.99522i) q^{47} +(1.23106 - 3.80585i) q^{48} +(-17.6879 + 7.32655i) q^{49} +(-2.90903 + 1.72555i) q^{50} +(0.247221 - 0.462518i) q^{51} +(1.45400 + 7.67660i) q^{52} +(-0.501822 + 0.611472i) q^{53} +(-1.04350 - 0.954517i) q^{54} +(0.301369 - 1.51508i) q^{55} +(-13.1576 + 6.00328i) q^{56} +(-5.01588 + 0.997720i) q^{57} +(-1.47679 - 6.01237i) q^{58} +(9.69215 - 5.18056i) q^{59} +(-2.60704 + 4.77178i) q^{60} +(-0.0767350 + 0.779103i) q^{61} +(6.72214 - 2.37055i) q^{62} +5.11324i q^{63} +(-7.15632 + 3.57590i) q^{64} -10.6209i q^{65} +(-0.267237 - 0.757800i) q^{66} +(1.28819 - 13.0792i) q^{67} +(-1.00647 + 0.295270i) q^{68} +(4.70826 - 2.51662i) q^{69} +(19.0924 - 4.68958i) q^{70} +(10.4385 - 2.07635i) q^{71} +(0.0999580 + 2.82666i) q^{72} +(-0.349590 + 1.75751i) q^{73} +(2.93798 - 3.21188i) q^{74} +(1.51725 - 1.84877i) q^{75} +(8.45211 + 5.76019i) q^{76} +(-1.36954 + 2.56223i) q^{77} +(-2.81852 - 4.75164i) q^{78} +(8.80664 - 3.64783i) q^{79} +(10.4628 - 2.96569i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-1.83635 - 12.7827i) q^{82} +(1.74636 + 5.75698i) q^{83} +(7.29714 - 7.16467i) q^{84} +(1.41897 - 0.139756i) q^{85} +(-14.2314 - 5.16571i) q^{86} +(2.43215 + 3.63997i) q^{87} +(-0.707010 + 1.44321i) q^{88} +(-1.79157 - 1.19709i) q^{89} +(0.581577 - 3.80067i) q^{90} +(-5.79846 + 19.1150i) q^{91} +(-10.1887 - 3.19291i) q^{92} +(-3.89610 + 3.19745i) q^{93} +(4.92658 + 5.48593i) q^{94} +(-9.83170 - 9.83170i) q^{95} +(3.89389 - 4.10337i) q^{96} +(8.59524 - 8.59524i) q^{97} +(-27.0364 - 1.45236i) q^{98} +(0.360455 + 0.439216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more