LMFDB - Embedded newform 544.2.bd.b.69.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(69,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bd (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,0,0,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			69.18
Character	$\chi$	$=$	544.69
Dual form			544.2.bd.b.205.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.433377 - 1.34617i) q^{2} +(-0.497273 - 1.20052i) q^{3} +(-1.62437 - 1.16680i) q^{4} +(1.36390 + 0.564945i) q^{5} +(-1.83162 + 0.149136i) q^{6} +(-3.09184 - 3.09184i) q^{7} +(-2.27468 + 1.68102i) q^{8} +(0.927343 - 0.927343i) q^{9} +(1.35160 - 1.59121i) q^{10} +(0.253587 - 0.612214i) q^{11} +(-0.593020 + 2.53031i) q^{12} +(-2.08308 + 0.862840i) q^{13} +(-5.50210 + 2.82222i) q^{14} -1.91832i q^{15} +(1.27714 + 3.79063i) q^{16} +1.00000i q^{17} +(-0.846475 - 1.65025i) q^{18} +(-1.88809 + 0.782072i) q^{19} +(-1.55629 - 2.50908i) q^{20} +(-2.17434 + 5.24933i) q^{21} +(-0.714248 - 0.606693i) q^{22} +(2.80753 - 2.80753i) q^{23} +(3.14924 + 1.89489i) q^{24} +(-1.99448 - 1.99448i) q^{25} +(0.258773 + 3.17812i) q^{26} +(-5.17601 - 2.14397i) q^{27} +(1.41472 + 8.62987i) q^{28} +(2.44946 + 5.91351i) q^{29} +(-2.58240 - 0.831358i) q^{30} -6.38695 q^{31} +(5.65634 - 0.0764819i) q^{32} -0.861080 q^{33} +(1.34617 + 0.433377i) q^{34} +(-2.47024 - 5.96368i) q^{35} +(-2.58837 + 0.424320i) q^{36} +(-2.77614 - 1.14992i) q^{37} +(0.234550 + 2.88063i) q^{38} +(2.07172 + 2.07172i) q^{39} +(-4.05212 + 1.00766i) q^{40} +(2.40345 - 2.40345i) q^{41} +(6.12419 + 5.20198i) q^{42} +(4.37994 - 10.5741i) q^{43} +(-1.12625 + 0.698575i) q^{44} +(1.78870 - 0.740903i) q^{45} +(-2.56270 - 4.99614i) q^{46} +7.25430i q^{47} +(3.91566 - 3.41822i) q^{48} +12.1190i q^{49} +(-3.54928 + 1.82055i) q^{50} +(1.20052 - 0.497273i) q^{51} +(4.39045 + 1.02897i) q^{52} +(3.01243 - 7.27264i) q^{53} +(-5.12933 + 6.03866i) q^{54} +(0.691734 - 0.691734i) q^{55} +(12.2304 + 1.83553i) q^{56} +(1.87779 + 1.87779i) q^{57} +(9.02216 - 0.734613i) q^{58} +(8.24947 + 3.41704i) q^{59} +(-2.23830 + 3.11606i) q^{60} +(-1.92737 - 4.65309i) q^{61} +(-2.76796 + 8.59794i) q^{62} -5.73440 q^{63} +(2.34837 - 7.64756i) q^{64} -3.32857 q^{65} +(-0.373173 + 1.15916i) q^{66} +(2.11500 + 5.10607i) q^{67} +(1.16680 - 1.62437i) q^{68} +(-4.76662 - 1.97440i) q^{69} +(-9.09869 + 0.740845i) q^{70} +(-4.13323 - 4.13323i) q^{71} +(-0.550534 + 3.66829i) q^{72} +(9.57223 - 9.57223i) q^{73} +(-2.75110 + 3.23882i) q^{74} +(-1.40262 + 3.38622i) q^{75} +(3.97948 + 0.932655i) q^{76} +(-2.67692 + 1.10882i) q^{77} +(3.68673 - 1.89106i) q^{78} -7.78493i q^{79} +(-0.399606 + 5.89155i) q^{80} +3.34569i q^{81} +(-2.19386 - 4.27706i) q^{82} +(1.16318 - 0.481806i) q^{83} +(9.65686 - 5.98981i) q^{84} +(-0.564945 + 1.36390i) q^{85} +(-12.3364 - 10.4788i) q^{86} +(5.88127 - 5.88127i) q^{87} +(0.452311 + 1.81888i) q^{88} +(-9.86807 - 9.86807i) q^{89} +(-0.222203 - 2.72899i) q^{90} +(9.10833 + 3.77279i) q^{91} +(-7.83629 + 1.28463i) q^{92} +(3.17606 + 7.66769i) q^{93} +(9.76555 + 3.14385i) q^{94} -3.01699 q^{95} +(-2.90456 - 6.75254i) q^{96} -7.43886 q^{97} +(16.3143 + 5.25210i) q^{98} +(-0.332570 - 0.802895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) $ 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.433377	−	1.34617i	0.306444	−	0.951889i
$2$	0.433377	−	1.34617i	0.306444	−	0.951889i
$3$	−0.497273	−	1.20052i	−0.287101	−	0.693123i	0.712866	−	0.701301i	$-0.247397\pi$
$3$	−0.497273	−	1.20052i	−0.287101	−	0.693123i	−0.999967	+	0.00817771i	$0.997397\pi$
$4$	−1.62437	−	1.16680i	−0.812184	−	0.583401i
$5$	1.36390	+	0.564945i	0.609953	+	0.252651i	0.666209	−	0.745765i	$-0.267916\pi$
$5$	1.36390	+	0.564945i	0.609953	+	0.252651i	−0.0562552	+	0.998416i	$0.517916\pi$
$6$	−1.83162	+	0.149136i	−0.747756	+	0.0608847i
$7$	−3.09184	−	3.09184i	−1.16861	−	1.16861i	−0.982536	−	0.186071i	$-0.940424\pi$
$7$	−3.09184	−	3.09184i	−1.16861	−	1.16861i	−0.186071	−	0.982536i	$-0.559576\pi$
$8$	−2.27468	+	1.68102i	−0.804222	+	0.594329i
$9$	0.927343	−	0.927343i	0.309114	−	0.309114i
$10$	1.35160	−	1.59121i	0.427412	−	0.503184i
$11$	0.253587	−	0.612214i	0.0764595	−	0.184590i	−0.881028	−	0.473064i	$-0.843148\pi$
$11$	0.253587	−	0.612214i	0.0764595	−	0.184590i	0.957488	+	0.288474i	$0.0931480\pi$
$12$	−0.593020	+	2.53031i	−0.171190	+	0.730438i
$13$	−2.08308	+	0.862840i	−0.577743	+	0.239309i	−0.652367	−	0.757903i	$-0.726224\pi$
$13$	−2.08308	+	0.862840i	−0.577743	+	0.239309i	0.0746247	+	0.997212i	$0.476224\pi$
$14$	−5.50210	+	2.82222i	−1.47050	+	0.754271i
$15$		−	1.91832i		−	0.495309i
$16$	1.27714	+	3.79063i	0.319286	+	0.947658i
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$	−0.846475	−	1.65025i	−0.199516	−	0.388969i
$19$	−1.88809	+	0.782072i	−0.433158	+	0.179420i	−0.588599	−	0.808425i	$-0.700320\pi$
$19$	−1.88809	+	0.782072i	−0.433158	+	0.179420i	0.155441	+	0.987845i	$0.450320\pi$
$20$	−1.55629	−	2.50908i	−0.347998	−	0.561047i
$21$	−2.17434	+	5.24933i	−0.474480	+	1.14550i
$22$	−0.714248	−	0.606693i	−0.152278	−	0.129347i
$23$	2.80753	−	2.80753i	0.585410	−	0.585410i	−0.350975	−	0.936385i	$-0.614150\pi$
$23$	2.80753	−	2.80753i	0.585410	−	0.585410i	0.936385	+	0.350975i	$0.114150\pi$
$24$	3.14924	+	1.89489i	0.642836	+	0.386792i
$25$	−1.99448	−	1.99448i	−0.398896	−	0.398896i
$26$	0.258773	+	3.17812i	0.0507496	+	0.623282i
$27$	−5.17601	−	2.14397i	−0.996124	−	0.412608i
$28$	1.41472	+	8.62987i	0.267357	+	1.63089i
$29$	2.44946	+	5.91351i	0.454853	+	1.09811i	0.970455	+	0.241284i	$0.0775684\pi$
$29$	2.44946	+	5.91351i	0.454853	+	1.09811i	−0.515602	+	0.856828i	$0.672432\pi$
$30$	−2.58240	−	0.831358i	−0.471479	−	0.151785i
$31$	−6.38695			−1.14713			−0.573565	−	0.819160i	$-0.694440\pi$
$31$	−6.38695			−1.14713			−0.573565	+	0.819160i	$0.694440\pi$
$32$	5.65634	−	0.0764819i	0.999909	−	0.0135202i
$33$	−0.861080			−0.149895
$34$	1.34617	+	0.433377i	0.230867	+	0.0743236i
$35$	−2.47024	−	5.96368i	−0.417546	−	1.00805i
$36$	−2.58837	+	0.424320i	−0.431395	+	0.0707200i
$37$	−2.77614	−	1.14992i	−0.456395	−	0.189045i	0.142629	−	0.989776i	$-0.454445\pi$
$37$	−2.77614	−	1.14992i	−0.456395	−	0.189045i	−0.599024	+	0.800731i	$0.704445\pi$
$38$	0.234550	+	2.88063i	0.0380490	+	0.467300i
$39$	2.07172	+	2.07172i	0.331741	+	0.331741i
$40$	−4.05212	+	1.00766i	−0.640696	+	0.159325i
$41$	2.40345	−	2.40345i	0.375356	−	0.375356i	−0.494068	−	0.869423i	$-0.664491\pi$
$41$	2.40345	−	2.40345i	0.375356	−	0.375356i	0.869423	+	0.494068i	$0.164491\pi$
$42$	6.12419	+	5.20198i	0.944984	+	0.802683i
$43$	4.37994	−	10.5741i	0.667935	−	1.61254i	−0.117124	−	0.993117i	$-0.537367\pi$
$43$	4.37994	−	10.5741i	0.667935	−	1.61254i	0.785059	−	0.619421i	$-0.212633\pi$
$44$	−1.12625	+	0.698575i	−0.169789	+	0.105314i
$45$	1.78870	−	0.740903i	0.266643	−	0.110447i
$46$	−2.56270	−	4.99614i	−0.377850	−	0.736641i
$47$			7.25430i			1.05815i	0.848576	+	0.529074i	$0.177461\pi$
$47$			7.25430i			1.05815i	−0.848576	+	0.529074i	$0.822539\pi$
$48$	3.91566	−	3.41822i	0.565177	−	0.493378i
$49$			12.1190i			1.73129i
$50$	−3.54928	+	1.82055i	−0.501944	+	0.257465i
$51$	1.20052	−	0.497273i	0.168107	−	0.0696322i
$52$	4.39045	+	1.02897i	0.608847	+	0.142693i
$53$	3.01243	−	7.27264i	0.413789	−	0.998975i	−0.570322	−	0.821421i	$-0.693182\pi$
$53$	3.01243	−	7.27264i	0.413789	−	0.998975i	0.984111	−	0.177554i	$-0.0568183\pi$
$54$	−5.12933	+	6.03866i	−0.698013	+	0.821758i
$55$	0.691734	−	0.691734i	0.0932734	−	0.0932734i
$56$	12.2304	+	1.83553i	1.63436	+	0.245283i
$57$	1.87779	+	1.87779i	0.248720	+	0.248720i
$58$	9.02216	−	0.734613i	1.18467	−	0.0964594i
$59$	8.24947	+	3.41704i	1.07399	+	0.444861i	0.848397	−	0.529361i	$-0.177568\pi$
$59$	8.24947	+	3.41704i	1.07399	+	0.444861i	0.225593	+	0.974222i	$0.427568\pi$
$60$	−2.23830	+	3.11606i	−0.288964	+	0.402282i
$61$	−1.92737	−	4.65309i	−0.246775	−	0.595767i	0.751152	−	0.660129i	$-0.229499\pi$
$61$	−1.92737	−	4.65309i	−0.246775	−	0.595767i	−0.997927	+	0.0643627i	$0.979499\pi$
$62$	−2.76796	+	8.59794i	−0.351531	+	1.09194i
$63$	−5.73440			−0.722467
$64$	2.34837	−	7.64756i	0.293546	−	0.955945i
$65$	−3.32857			−0.412858
$66$	−0.373173	+	1.15916i	−0.0459344	+	0.142683i
$67$	2.11500	+	5.10607i	0.258389	+	0.623805i	0.998832	−	0.0483133i	$-0.0153846\pi$
$67$	2.11500	+	5.10607i	0.258389	+	0.623805i	−0.740444	+	0.672118i	$0.765385\pi$
$68$	1.16680	−	1.62437i	0.141496	−	0.196984i
$69$	−4.76662	−	1.97440i	−0.573833	−	0.237689i
$70$	−9.09869	+	0.740845i	−1.08750	+	0.0885479i
$71$	−4.13323	−	4.13323i	−0.490524	−	0.490524i	0.417947	−	0.908471i	$-0.362750\pi$
$71$	−4.13323	−	4.13323i	−0.490524	−	0.490524i	−0.908471	+	0.417947i	$0.862750\pi$
$72$	−0.550534	+	3.66829i	−0.0648810	+	0.432312i
$73$	9.57223	−	9.57223i	1.12034	−	1.12034i	0.128655	−	0.991689i	$-0.458934\pi$
$73$	9.57223	−	9.57223i	1.12034	−	1.12034i	0.991689	−	0.128655i	$-0.0410660\pi$
$74$	−2.75110	+	3.23882i	−0.319809	+	0.376506i
$75$	−1.40262	+	3.38622i	−0.161961	+	0.391008i
$76$	3.97948	+	0.932655i	0.456477	+	0.106983i
$77$	−2.67692	+	1.10882i	−0.305064	+	0.126362i
$78$	3.68673	−	1.89106i	0.417440	−	0.214120i
$79$		−	7.78493i		−	0.875874i	−0.899006	−	0.437937i	$-0.855709\pi$
$79$		−	7.78493i		−	0.875874i	0.899006	−	0.437937i	$-0.144291\pi$
$80$	−0.399606	+	5.89155i	−0.0446774	+	0.658695i
$81$			3.34569i			0.371743i
$82$	−2.19386	−	4.27706i	−0.242271	−	0.472322i
$83$	1.16318	−	0.481806i	0.127676	−	0.0528851i	−0.317931	−	0.948114i	$-0.602988\pi$
$83$	1.16318	−	0.481806i	0.127676	−	0.0528851i	0.445607	+	0.895229i	$0.352988\pi$
$84$	9.65686	−	5.98981i	1.05365	−	0.653542i
$85$	−0.564945	+	1.36390i	−0.0612769	+	0.147935i
$86$	−12.3364	−	10.4788i	−1.33027	−	1.12995i
$87$	5.88127	−	5.88127i	0.630538	−	0.630538i
$88$	0.452311	+	1.81888i	0.0482165	+	0.193893i
$89$	−9.86807	−	9.86807i	−1.04601	−	1.04601i	−0.998889	−	0.0471247i	$-0.984994\pi$
$89$	−9.86807	−	9.86807i	−1.04601	−	1.04601i	−0.0471247	−	0.998889i	$-0.515006\pi$
$90$	−0.222203	−	2.72899i	−0.0234222	−	0.287661i
$91$	9.10833	+	3.77279i	0.954813	+	0.395496i
$92$	−7.83629	+	1.28463i	−0.816990	+	0.133932i
$93$	3.17606	+	7.66769i	0.329342	+	0.795102i
$94$	9.76555	+	3.14385i	1.00724	+	0.324263i
$95$	−3.01699			−0.309536
$96$	−2.90456	−	6.75254i	−0.296446	−	0.689178i
$97$	−7.43886			−0.755302			−0.377651	−	0.925948i	$-0.623268\pi$
$97$	−7.43886			−0.755302			−0.377651	+	0.925948i	$0.623268\pi$
$98$	16.3143	+	5.25210i	1.64799	+	0.530543i
$99$	−0.332570	−	0.802895i	−0.0334245	−	0.0806940i
$100$	0.912606	+	5.56694i	0.0912606	+	0.556694i
$101$	3.21312	+	1.33092i	0.319717	+	0.132431i	0.536770	−	0.843729i	$-0.319644\pi$
$101$	3.21312	+	1.33092i	0.319717	+	0.132431i	−0.217053	+	0.976160i	$0.569644\pi$
$102$	−0.149136	−	1.83162i	−0.0147667	−	0.181358i
$103$	−5.75020	−	5.75020i	−0.566584	−	0.566584i	0.364586	−	0.931170i	$-0.381211\pi$
$103$	−5.75020	−	5.75020i	−0.566584	−	0.566584i	−0.931170	+	0.364586i	$0.881211\pi$
$104$	3.28790	−	5.46438i	0.322405	−	0.535827i
$105$	−5.93116	+	5.93116i	−0.578822	+	0.578822i
$106$	−8.48473	−	7.20705i	−0.824109	−	0.700011i
$107$	6.17502	−	14.9078i	0.596962	−	1.44119i	−0.279700	−	0.960087i	$-0.590235\pi$
$107$	6.17502	−	14.9078i	0.596962	−	1.44119i	0.876662	−	0.481107i	$-0.159765\pi$
$108$	5.90615	+	9.52199i	0.568320	+	0.916254i
$109$	9.59365	−	3.97382i	0.918905	−	0.380623i	0.127446	−	0.991846i	$-0.459322\pi$
$109$	9.59365	−	3.97382i	0.918905	−	0.380623i	0.791459	+	0.611223i	$0.209322\pi$
$110$	−0.631413	−	1.23098i	−0.0602028	−	0.117369i
$111$			3.90465i			0.370613i
$112$	7.77132	−	15.6688i	0.734321	−	1.48056i
$113$		−	5.69843i		−	0.536063i	−0.963410	−	0.268032i	$-0.913627\pi$
$113$		−	5.69843i		−	0.536063i	0.963410	−	0.268032i	$-0.0863732\pi$
$114$	3.34163	−	1.71404i	0.312972	−	0.160535i
$115$	5.41528	−	2.24308i	0.504977	−	0.209169i
$116$	2.92108	−	12.4638i	0.271216	−	1.15723i
$117$	−1.13158	+	2.73188i	−0.104615	+	0.252562i
$118$	8.17507	−	9.62435i	0.752576	−	0.885994i
$119$	3.09184	−	3.09184i	0.283429	−	0.283429i
$120$	3.22473	+	4.36358i	0.294376	+	0.398338i
$121$	7.46767	+	7.46767i	0.678880	+	0.678880i
$122$	−7.09914	+	0.578035i	−0.642726	+	0.0523328i
$123$	−4.08057	−	1.69023i	−0.367932	−	0.152403i
$124$	10.3748	+	7.45231i	0.931681	+	0.669237i
$125$	−4.41822	−	10.6665i	−0.395178	−	0.954043i
$126$	−2.48516	+	7.71950i	−0.221396	+	0.687708i
$127$	0.161365			0.0143189			0.00715943	−	0.999974i	$-0.497721\pi$
$127$	0.161365			0.0143189			0.00715943	+	0.999974i	$0.497721\pi$
$128$	−9.27721	−	6.47559i	−0.819998	−	0.572367i
$129$	−14.8725			−1.30945
$130$	−1.44253	+	4.48083i	−0.126518	+	0.392995i
$131$	1.41608	+	3.41873i	0.123724	+	0.298696i	0.973590	−	0.228302i	$-0.0733175\pi$
$131$	1.41608	+	3.41873i	0.123724	+	0.298696i	−0.849866	+	0.526998i	$0.823318\pi$
$132$	1.39871	+	1.00471i	0.121742	+	0.0874488i
$133$	8.25573	+	3.41963i	0.715862	+	0.296520i
$134$	7.79025	−	0.634306i	0.672975	−	0.0547957i
$135$	−5.84832	−	5.84832i	−0.503343	−	0.503343i
$136$	−1.68102	−	2.27468i	−0.144146	−	0.195053i
$137$	4.03768	−	4.03768i	0.344962	−	0.344962i	−0.513267	−	0.858229i	$-0.671565\pi$
$137$	4.03768	−	4.03768i	0.344962	−	0.344962i	0.858229	+	0.513267i	$0.171565\pi$
$138$	−4.72363	+	5.56103i	−0.402102	+	0.473387i
$139$	6.14543	−	14.8364i	0.521249	−	1.25841i	−0.415879	−	0.909420i	$-0.636526\pi$
$139$	6.14543	−	14.8364i	0.521249	−	1.25841i	0.937128	−	0.348986i	$-0.113474\pi$
$140$	−2.94586	+	12.5695i	−0.248971	+	1.06232i
$141$	8.70896	−	3.60737i	0.733427	−	0.303795i
$142$	−7.35529	+	3.77280i	−0.617243	+	0.316606i
$143$			1.49410i			0.124943i
$144$	4.69957	+	2.33087i	0.391631	+	0.194239i
$145$			9.44923i			0.784716i
$146$	−8.73750	−	17.0343i	−0.723120	−	1.40977i
$147$	14.5492	−	6.02646i	1.19999	−	0.497054i
$148$	3.16775	+	5.10710i	0.260388	+	0.419801i
$149$	−6.03524	+	14.5704i	−0.494426	+	1.19365i	0.458019	+	0.888942i	$0.348559\pi$
$149$	−6.03524	+	14.5704i	−0.494426	+	1.19365i	−0.952446	+	0.304708i	$0.901441\pi$
$150$	3.95058	+	3.35568i	0.322564	+	0.273990i
$151$	−15.5491	+	15.5491i	−1.26537	+	1.26537i	−0.316909	+	0.948456i	$0.602645\pi$
$151$	−15.5491	+	15.5491i	−1.26537	+	1.26537i	−0.948456	+	0.316909i	$0.897355\pi$
$152$	2.98013	−	4.95288i	0.241721	−	0.401731i
$153$	0.927343	+	0.927343i	0.0749712	+	0.0749712i
$154$	0.332544	+	4.08414i	0.0267971	+	0.329110i
$155$	−8.71114	−	3.60827i	−0.699696	−	0.289823i
$156$	−0.947948	−	5.78253i	−0.0758966	−	0.462973i
$157$	2.48736	+	6.00502i	0.198513	+	0.479252i	0.991519	−	0.129961i	$-0.0414852\pi$
$157$	2.48736	+	6.00502i	0.198513	+	0.479252i	−0.793006	+	0.609213i	$0.791485\pi$
$158$	−10.4799	−	3.37381i	−0.833734	−	0.268406i
$159$	−10.2290			−0.811211
$160$	7.75787	+	3.09120i	0.613314	+	0.244381i
$161$	−17.3609			−1.36823
$162$	4.50388	+	1.44994i	0.353858	+	0.113918i
$163$	6.57827	+	15.8813i	0.515250	+	1.24392i	0.940792	+	0.338984i	$0.110083\pi$
$163$	6.57827	+	15.8813i	0.515250	+	1.24392i	−0.425542	+	0.904939i	$0.639917\pi$
$164$	−6.70843	+	1.09973i	−0.523841	+	0.0858749i
$165$	−1.17442	−	0.486463i	−0.0914288	−	0.0378711i
$166$	−0.144498	−	1.77465i	−0.0112152	−	0.137740i
$167$	−10.2011	−	10.2011i	−0.789387	−	0.789387i	0.192006	−	0.981394i	$-0.438501\pi$
$167$	−10.2011	−	10.2011i	−0.789387	−	0.789387i	−0.981394	+	0.192006i	$0.938501\pi$
$168$	−3.87826	−	15.5957i	−0.299214	−	1.20323i
$169$	−5.59766	+	5.59766i	−0.430589	+	0.430589i
$170$	1.59121	+	1.35160i	0.122040	+	0.103663i
$171$	−1.02566	+	2.47616i	−0.0784340	+	0.189356i
$172$	−19.4526	+	12.0657i	−1.48324	+	0.920004i
$173$	−6.46059	+	2.67606i	−0.491190	+	0.203457i	−0.614509	−	0.788910i	$-0.710646\pi$
$173$	−6.46059	+	2.67606i	−0.491190	+	0.203457i	0.123320	+	0.992367i	$0.460646\pi$
$174$	−5.36840	−	10.4660i	−0.406977	−	0.793426i
$175$			12.3332i			0.932306i
$176$	2.64455	+	0.179372i	0.199340	+	0.0135207i
$177$		−	11.6029i		−	0.872127i
$178$	−17.5607	+	9.00754i	−1.31623	+	0.675144i
$179$	16.8298	−	6.97111i	1.25792	−	0.521045i	0.348646	−	0.937254i	$-0.386642\pi$
$179$	16.8298	−	6.97111i	1.25792	−	0.521045i	0.909269	+	0.416209i	$0.136642\pi$
$180$	−3.76999	−	0.883558i	−0.280999	−	0.0658566i
$181$	−3.63701	+	8.78051i	−0.270337	+	0.652650i	−0.999498	−	0.0316919i	$-0.989910\pi$
$181$	−3.63701	+	8.78051i	−0.270337	+	0.652650i	0.729161	+	0.684342i	$0.239910\pi$
$182$	9.02618	−	10.6264i	0.669065	−	0.787678i
$183$	−4.62771	+	4.62771i	−0.342090	+	0.342090i
$184$	−1.66674	+	11.1057i	−0.122874	+	0.818726i
$185$	−3.13673	−	3.13673i	−0.230617	−	0.230617i
$186$	11.6985	−	0.952527i	0.857774	−	0.0698426i
$187$	0.612214	+	0.253587i	0.0447695	+	0.0185441i
$188$	8.46434	−	11.7837i	0.617325	−	0.859411i
$189$	9.37459	+	22.6323i	0.681901	+	1.64626i
$190$	−1.30749	+	4.06139i	−0.0948556	+	0.294644i
$191$	4.67577			0.338327			0.169164	−	0.985588i	$-0.445893\pi$
$191$	4.67577			0.338327			0.169164	+	0.985588i	$0.445893\pi$
$192$	−10.3489	+	0.983652i	−0.746865	+	0.0709889i
$193$	22.9075			1.64892			0.824460	−	0.565921i	$-0.191479\pi$
$193$	22.9075			1.64892			0.824460	+	0.565921i	$0.191479\pi$
$194$	−3.22384	+	10.0140i	−0.231458	+	0.718964i
$195$	1.65521	+	3.99602i	0.118532	+	0.286161i
$196$	14.1405	−	19.6857i	1.01004	−	1.40612i
$197$	18.4352	+	7.63610i	1.31345	+	0.544049i	0.925889	−	0.377794i	$-0.123317\pi$
$197$	18.4352	+	7.63610i	1.31345	+	0.544049i	0.387562	+	0.921844i	$0.373317\pi$
$198$	−1.22496	+	0.0997405i	−0.0870544	+	0.00708825i
$199$	12.8282	+	12.8282i	0.909366	+	0.909366i	0.996221	−	0.0868554i	$-0.0276818\pi$
$199$	12.8282	+	12.8282i	0.909366	+	0.909366i	−0.0868554	+	0.996221i	$0.527682\pi$
$200$	7.88957	+	1.18406i	0.557877	+	0.0837256i
$201$	5.07822	−	5.07822i	0.358190	−	0.358190i
$202$	3.18414	−	3.74863i	0.224035	−	0.263752i
$203$	10.7103	−	25.8570i	0.751717	−	1.81481i
$204$	−2.53031	−	0.593020i	−0.177157	−	0.0415197i
$205$	4.63587	−	1.92024i	0.323783	−	0.134115i
$206$	−10.2328	+	5.24876i	−0.712951	+	0.365699i
$207$		−	5.20709i		−	0.361917i
$208$	−5.93111	−	6.79423i	−0.411248	−	0.471095i
$209$			1.35424i			0.0936747i
$210$	5.41394	+	10.5548i	0.373597	+	0.728350i
$211$	7.55192	−	3.12811i	0.519895	−	0.215348i	−0.107276	−	0.994229i	$-0.534213\pi$
$211$	7.55192	−	3.12811i	0.519895	−	0.215348i	0.627171	+	0.778882i	$0.284213\pi$
$212$	−13.3790	+	8.29854i	−0.918876	+	0.569946i
$213$	−2.90670	+	7.01739i	−0.199164	+	0.480823i
$214$	−17.3924	−	14.7734i	−1.18892	−	1.00989i
$215$	11.9476	−	11.9476i	0.814819	−	0.814819i
$216$	15.3778	−	3.82410i	1.04633	−	0.260197i
$217$	19.7475	+	19.7475i	1.34054	+	1.34054i
$218$	−1.19178	−	14.6369i	−0.0807176	−	0.991335i
$219$	−16.2517	−	6.73168i	−1.09819	−	0.454884i
$220$	−1.93075	+	0.316514i	−0.130171	+	0.0213394i
$221$	−0.862840	−	2.08308i	−0.0580409	−	0.140123i
$222$	5.25634	+	1.69219i	0.352782	+	0.113572i
$223$	−1.25695			−0.0841719			−0.0420860	−	0.999114i	$-0.513400\pi$
$223$	−1.25695			−0.0841719			−0.0420860	+	0.999114i	$0.513400\pi$
$224$	−17.7250	−	17.2520i	−1.18430	−	1.15270i
$225$	−3.69914			−0.246609
$226$	−7.67108	−	2.46957i	−0.510273	−	0.164273i
$227$	6.64427	+	16.0407i	0.440995	+	1.06466i	0.975600	+	0.219555i	$0.0704605\pi$
$227$	6.64427	+	16.0407i	0.440995	+	1.06466i	−0.534605	+	0.845102i	$0.679540\pi$
$228$	−0.859213	−	5.24124i	−0.0569028	−	0.347110i
$229$	6.59234	+	2.73064i	0.435634	+	0.180446i	0.589713	−	0.807613i	$-0.299241\pi$
$229$	6.59234	+	2.73064i	0.435634	+	0.180446i	−0.154079	+	0.988059i	$0.549241\pi$
$230$	−0.672719	−	8.26201i	−0.0443578	−	0.544781i
$231$	2.66233	+	2.66233i	0.175168	+	0.175168i
$232$	−15.5125	−	9.33380i	−1.01844	−	0.612794i
$233$	2.40864	−	2.40864i	0.157795	−	0.157795i	−0.623794	−	0.781589i	$-0.714410\pi$
$233$	2.40864	−	2.40864i	0.157795	−	0.157795i	0.781589	+	0.623794i	$0.214410\pi$
$234$	3.18718	+	2.70724i	0.208353	+	0.176978i
$235$	−4.09828	+	9.89412i	−0.267342	+	0.645421i
$236$	−9.41316	−	15.1760i	−0.612745	−	0.987876i
$237$	−9.34600	+	3.87124i	−0.607088	+	0.251464i
$238$	−2.82222	−	5.50210i	−0.182938	−	0.356648i
$239$			24.3216i			1.57323i	0.617442	+	0.786616i	$0.288169\pi$
$239$			24.3216i			1.57323i	−0.617442	+	0.786616i	$0.711831\pi$
$240$	7.27166	−	2.44997i	0.469384	−	0.158145i
$241$		−	14.8760i		−	0.958247i	−0.877748	−	0.479123i	$-0.840955\pi$
$241$		−	14.8760i		−	0.958247i	0.877748	−	0.479123i	$-0.159045\pi$
$242$	13.2891	−	6.81647i	0.854256	−	0.438179i
$243$	−11.5115	+	4.76820i	−0.738461	+	0.305880i
$244$	−2.29847	+	9.80719i	−0.147145	+	0.627841i
$245$	−6.84657	+	16.5291i	−0.437411	+	1.05600i
$246$	−4.04376	+	4.76065i	−0.257821	+	0.303528i
$247$	3.25824	−	3.25824i	0.207317	−	0.207317i
$248$	14.5283	−	10.7366i	0.922547	−	0.681772i
$249$	−1.15684	−	1.15684i	−0.0733117	−	0.0733117i
$250$	−16.2738	+	1.32506i	−1.02924	+	0.0838042i
$251$	8.23121	+	3.40948i	0.519549	+	0.215204i	0.627019	−	0.779004i	$-0.284275\pi$
$251$	8.23121	+	3.40948i	0.519549	+	0.215204i	−0.107470	+	0.994208i	$0.534275\pi$
$252$	9.31478	+	6.69091i	0.586776	+	0.421488i
$253$	−1.00686	−	2.43076i	−0.0633004	−	0.152821i
$254$	0.0699321	−	0.217226i	0.00438793	−	0.0136300i
$255$	1.91832			0.120130
$256$	−12.7378	+	9.68237i	−0.796113	+	0.605148i
$257$	−28.7527			−1.79355			−0.896773	−	0.442491i	$-0.854095\pi$
$257$	−28.7527			−1.79355			−0.896773	+	0.442491i	$0.854095\pi$
$258$	−6.44541	+	20.0210i	−0.401274	+	1.24645i
$259$	5.02804	+	12.1388i	0.312427	+	0.754266i
$260$	5.40682	+	3.88378i	0.335316	+	0.240862i
$261$	7.75534	+	3.21237i	0.480044	+	0.198841i
$262$	5.21590	−	0.424695i	0.322239	−	0.0262377i
$263$	−2.87166	−	2.87166i	−0.177074	−	0.177074i	0.613005	−	0.790079i	$-0.289961\pi$
$263$	−2.87166	−	2.87166i	−0.177074	−	0.177074i	−0.790079	+	0.613005i	$0.789961\pi$
$264$	1.95868	−	1.44749i	0.120549	−	0.0890868i
$265$	8.21728	−	8.21728i	0.504784	−	0.504784i
$266$	8.18127	−	9.63165i	0.501626	−	0.590554i
$267$	−6.93973	+	16.7540i	−0.424705	+	1.02533i
$268$	2.52223	−	10.7619i	0.154070	−	0.657389i
$269$	7.81137	−	3.23558i	0.476268	−	0.197277i	−0.131619	−	0.991300i	$-0.542018\pi$
$269$	7.81137	−	3.23558i	0.476268	−	0.197277i	0.607887	+	0.794024i	$0.292018\pi$
$270$	−10.4074	+	5.33833i	−0.633374	+	0.324880i
$271$			21.2142i			1.28867i	0.764742	+	0.644336i	$0.222866\pi$
$271$			21.2142i			1.28867i	−0.764742	+	0.644336i	$0.777134\pi$
$272$	−3.79063	+	1.27714i	−0.229841	+	0.0774382i
$273$		−	12.8109i		−	0.775350i
$274$	−3.68558	−	7.18526i	−0.222654	−	0.434077i
$275$	−1.72682	+	0.715274i	−0.104131	+	0.0431327i
$276$	5.43901	+	8.76885i	0.327390	+	0.527823i
$277$	3.80060	−	9.17547i	0.228356	−	0.551301i	−0.767621	−	0.640904i	$-0.778560\pi$
$277$	3.80060	−	9.17547i	0.228356	−	0.551301i	0.995978	+	0.0896030i	$0.0285598\pi$
$278$	−17.3091	−	14.7026i	−1.03813	−	0.881802i
$279$	−5.92289	+	5.92289i	−0.354594	+	0.354594i
$280$	15.6440	+	9.41298i	0.934911	+	0.562533i
$281$	−13.5300	−	13.5300i	−0.807134	−	0.807134i	0.177065	−	0.984199i	$-0.443340\pi$
$281$	−13.5300	−	13.5300i	−0.807134	−	0.807134i	−0.984199	+	0.177065i	$0.943340\pi$
$282$	−1.08188	−	13.2871i	−0.0644250	−	0.791237i
$283$	−12.5210	−	5.18637i	−0.744296	−	0.308298i	−0.0218842	−	0.999761i	$-0.506966\pi$
$283$	−12.5210	−	5.18637i	−0.744296	−	0.308298i	−0.722412	+	0.691463i	$0.756966\pi$
$284$	1.89122	+	11.5365i	0.112223	+	0.684568i
$285$	1.50027	+	3.62197i	0.0888682	+	0.214547i
$286$	2.01131	+	0.647508i	0.118932	+	0.0382879i
$287$	−14.8622			−0.877287
$288$	5.17444	−	5.31629i	0.304907	−	0.313265i
$289$	−1.00000			−0.0588235
$290$	12.7203	+	4.09508i	0.746962	+	0.240472i
$291$	3.69915	+	8.93054i	0.216848	+	0.523517i
$292$	−26.7177	+	4.37992i	−1.56354	+	0.256315i
$293$	8.65930	+	3.58680i	0.505882	+	0.209543i	0.621003	−	0.783808i	$-0.286726\pi$
$293$	8.65930	+	3.58680i	0.505882	+	0.209543i	−0.115121	+	0.993351i	$0.536726\pi$
$294$	−1.80739	−	22.1974i	−0.105409	−	1.29458i
$295$	9.32099	+	9.32099i	0.542689	+	0.542689i
$296$	8.24787	−	2.05105i	0.479398	−	0.119215i
$297$	−2.62514	+	2.62514i	−0.152326	+	0.152326i
$298$	16.9987	+	14.4389i	0.984708	+	0.836426i
$299$	−3.42586	+	8.27076i	−0.198123	+	0.478310i
$300$	6.22943	−	3.86389i	0.359656	−	0.223082i
$301$	−46.2357	+	19.1514i	−2.66498	+	1.10387i
$302$	14.1931	+	27.6704i	0.816723	+	1.59225i
$303$		−	4.51925i		−	0.259624i
$304$	−5.37591	−	6.15824i	−0.308330	−	0.353199i
$305$		−	7.43519i		−	0.425738i
$306$	1.65025	−	0.846475i	0.0943388	−	0.0483898i
$307$	15.9220	−	6.59512i	0.908718	−	0.376403i	0.121152	−	0.992634i	$-0.461341\pi$
$307$	15.9220	−	6.59512i	0.908718	−	0.376403i	0.787566	+	0.616230i	$0.211341\pi$
$308$	5.64208	+	1.32231i	0.321487	+	0.0753458i
$309$	−4.04383	+	9.76267i	−0.230046	+	0.555379i
$310$	−8.63258	+	10.1630i	−0.490297	+	0.577218i
$311$	−15.4201	+	15.4201i	−0.874396	+	0.874396i	−0.992948	−	0.118552i	$-0.962175\pi$
$311$	−15.4201	+	15.4201i	−0.874396	+	0.874396i	0.118552	+	0.992948i	$0.462175\pi$
$312$	−8.19511	−	1.22991i	−0.463957	−	0.0696302i
$313$	15.3630	+	15.3630i	0.868368	+	0.868368i	0.992292	−	0.123923i	$-0.0395477\pi$
$313$	15.3630	+	15.3630i	0.868368	+	0.868368i	−0.123923	+	0.992292i	$0.539548\pi$
$314$	9.16176	−	0.745979i	0.517028	−	0.0420981i
$315$	−7.82113	−	3.23962i	−0.440671	−	0.182532i
$316$	−9.08348	+	12.6456i	−0.510986	+	0.711370i
$317$	−4.95546	−	11.9635i	−0.278327	−	0.671940i	0.721463	−	0.692453i	$-0.243470\pi$
$317$	−4.95546	−	11.9635i	−0.278327	−	0.671940i	−0.999790	+	0.0205132i	$0.993470\pi$
$318$	−4.43301	+	13.7700i	−0.248591	+	0.772183i
$319$	4.24149			0.237478
$320$	7.52338	−	9.10378i	0.420570	−	0.508917i
$321$	−20.9679			−1.17031
$322$	−7.52382	+	23.3708i	−0.419286	+	1.30240i
$323$	−0.782072	−	1.88809i	−0.0435157	−	0.105056i
$324$	3.90376	−	5.43463i	0.216875	−	0.301924i
$325$	5.87558	+	2.43375i	0.325919	+	0.135000i
$326$	24.2299	−	1.97288i	1.34197	−	0.109268i
$327$	−9.54133	−	9.54133i	−0.527637	−	0.527637i
$328$	−1.42685	+	9.50732i	−0.0787846	+	0.524954i
$329$	22.4292	−	22.4292i	1.23656	−	1.23656i
$330$	−1.16383	+	1.37016i	−0.0640669	+	0.0754247i
$331$	−5.44764	+	13.1518i	−0.299430	+	0.722887i	0.700527	+	0.713625i	$0.252948\pi$
$331$	−5.44764	+	13.1518i	−0.299430	+	0.722887i	−0.999957	+	0.00926165i	$0.997052\pi$
$332$	−2.45161	−	0.574574i	−0.134550	−	0.0315339i
$333$	−3.64080	+	1.50807i	−0.199515	+	0.0826417i
$334$	−18.1534	+	9.31156i	−0.993312	+	0.509506i
$335$			8.15901i			0.445774i
$336$	−22.6752	−	1.53799i	−1.23703	−	0.0839044i
$337$		−	23.9106i		−	1.30249i	−0.758866	−	0.651247i	$-0.774246\pi$
$337$		−	23.9106i		−	1.30249i	0.758866	−	0.651247i	$-0.225754\pi$
$338$	5.10952	+	9.96131i	0.277921	+	0.541824i
$339$	−6.84110	+	2.83368i	−0.371558	+	0.153904i
$340$	2.50908	−	1.55629i	0.136074	−	0.0844018i
$341$	−1.61965	+	3.91018i	−0.0877090	+	0.211748i
$342$	2.88884	+	2.45382i	0.156211	+	0.132688i
$343$	15.8272	−	15.8272i	0.854587	−	0.854587i
$344$	7.81228	+	31.4155i	0.421210	+	1.69381i
$345$	−5.38575	−	5.38575i	−0.289959	−	0.289959i
$346$	0.802574	+	9.85683i	0.0431466	+	0.529906i
$347$	−20.8689	−	8.64418i	−1.12030	−	0.464044i	−0.255828	−	0.966722i	$-0.582348\pi$
$347$	−20.8689	−	8.64418i	−1.12030	−	0.464044i	−0.864474	+	0.502678i	$0.832348\pi$
$348$	−16.4156	+	2.69106i	−0.879969	+	0.144256i
$349$	4.28894	+	10.3544i	0.229582	+	0.554260i	0.996127	−	0.0879313i	$-0.0280256\pi$
$349$	4.28894	+	10.3544i	0.229582	+	0.554260i	−0.766545	+	0.642191i	$0.778026\pi$
$350$	16.6027	+	5.34495i	0.887452	+	0.285700i
$351$	12.6320			0.674244
$352$	1.38755	−	3.48228i	0.0739568	−	0.185606i
$353$	−2.04488			−0.108838			−0.0544190	−	0.998518i	$-0.517331\pi$
$353$	−2.04488			−0.108838			−0.0544190	+	0.998518i	$0.517331\pi$
$354$	−15.6195	−	5.02843i	−0.830168	−	0.267258i
$355$	−3.30225	−	7.97235i	−0.175265	−	0.423128i
$356$	4.51529	+	27.5435i	0.239310	+	1.45980i
$357$	−5.24933	−	2.17434i	−0.277824	−	0.115078i
$358$	−2.09069	−	25.6769i	−0.110497	−	1.35707i
$359$	14.4729	+	14.4729i	0.763849	+	0.763849i	0.977016	−	0.213167i	$-0.0683778\pi$
$359$	14.4729	+	14.4729i	0.763849	+	0.763849i	−0.213167	+	0.977016i	$0.568378\pi$
$360$	−2.82325	+	4.69215i	−0.148798	+	0.247298i
$361$	−10.4818	+	10.4818i	−0.551673	+	0.551673i
$362$	10.2439	+	8.70132i	0.538407	+	0.457331i
$363$	5.25165	−	12.6786i	0.275640	−	0.665454i
$364$	−10.3932	−	16.7560i	−0.544750	−	0.878255i
$365$	18.4633	−	7.64775i	0.966414	−	0.400302i
$366$	4.22416	+	8.23525i	0.220800	+	0.430463i
$367$		−	27.8863i		−	1.45565i	−0.685762	−	0.727826i	$-0.740531\pi$
$367$		−	27.8863i		−	1.45565i	0.685762	−	0.727826i	$-0.259469\pi$
$368$	14.2279	+	7.05670i	0.741682	+	0.367856i
$369$		−	4.45764i		−	0.232056i
$370$	−5.58198	+	2.86320i	−0.290193	+	0.148851i
$371$	−31.7998	+	13.1719i	−1.65097	+	0.683852i
$372$	3.78759	−	16.1610i	0.196377	−	0.837908i
$373$	−4.48053	+	10.8169i	−0.231993	+	0.560080i	−0.996412	−	0.0846398i	$-0.973026\pi$
$373$	−4.48053	+	10.8169i	−0.231993	+	0.560080i	0.764419	+	0.644720i	$0.223026\pi$
$374$	0.606693	−	0.714248i	0.0313713	−	0.0369329i
$375$	−10.6084	+	10.6084i	−0.547813	+	0.547813i
$376$	−12.1946	−	16.5012i	−0.628888	−	0.850986i
$377$	−10.2048	−	10.2048i	−0.525576	−	0.525576i
$378$	34.5297	−	2.81152i	1.77602	−	0.144609i
$379$	−11.5250	−	4.77380i	−0.591998	−	0.245213i	0.0665122	−	0.997786i	$-0.478813\pi$
$379$	−11.5250	−	4.77380i	−0.591998	−	0.245213i	−0.658510	+	0.752572i	$0.728813\pi$
$380$	4.90070	+	3.52023i	0.251401	+	0.180584i
$381$	−0.0802427	−	0.193723i	−0.00411096	−	0.00992473i
$382$	2.02637	−	6.29440i	0.103678	−	0.322050i
$383$	−7.90575			−0.403965			−0.201983	−	0.979389i	$-0.564738\pi$
$383$	−7.90575			−0.403965			−0.201983	+	0.979389i	$0.564738\pi$
$384$	−3.16080	+	14.3577i	−0.161299	+	0.732686i
$385$	−4.27747			−0.218000
$386$	9.92760	−	30.8375i	0.505302	−	1.56959i
$387$	−5.74413	−	13.8675i	−0.291990	−	0.704927i
$388$	12.0835	+	8.67969i	0.613444	+	0.440644i
$389$	−13.6987	−	5.67419i	−0.694552	−	0.287693i	0.00734332	−	0.999973i	$-0.497663\pi$
$389$	−13.6987	−	5.67419i	−0.694552	−	0.287693i	−0.701895	+	0.712280i	$0.747663\pi$
$390$	6.09667	−	0.496410i	0.308717	−	0.0251367i
$391$	2.80753	+	2.80753i	0.141983	+	0.141983i
$392$	−20.3722	−	27.5669i	−1.02895	−	1.39234i
$393$	3.40008	−	3.40008i	0.171512	−	0.171512i
$394$	18.2689	−	21.5076i	0.920374	−	1.08354i
$395$	4.39806	−	10.6179i	0.221290	−	0.534242i
$396$	−0.396604	+	1.69224i	−0.0199301	+	0.0850383i
$397$	9.96018	−	4.12564i	0.499887	−	0.207060i	−0.118469	−	0.992958i	$-0.537799\pi$
$397$	9.96018	−	4.12564i	0.499887	−	0.207060i	0.618357	+	0.785898i	$0.287799\pi$
$398$	22.8284	−	11.7095i	1.14428	−	0.586945i
$399$		−	11.6117i		−	0.581312i
$400$	5.01311	−	10.1076i	0.250655	−	0.505379i
$401$		−	21.6098i		−	1.07914i	−0.841939	−	0.539572i	$-0.818586\pi$
$401$		−	21.6098i		−	1.07914i	0.841939	−	0.539572i	$-0.181414\pi$
$402$	−4.63538	−	9.03695i	−0.231192	−	0.450722i
$403$	13.3045	−	5.51092i	0.662746	−	0.274518i
$404$	−3.66637	−	5.91097i	−0.182409	−	0.294082i
$405$	−1.89013	+	4.56317i	−0.0939212	+	0.226746i
$406$	−30.1664	−	25.6238i	−1.49713	−	1.27169i
$407$	−1.40799	+	1.40799i	−0.0697914	+	0.0697914i
$408$	−1.89489	+	3.14924i	−0.0938109	+	0.155911i
$409$	17.4791	+	17.4791i	0.864284	+	0.864284i	0.991832	−	0.127548i	$-0.0407108\pi$
$409$	17.4791	+	17.4791i	0.864284	+	0.864284i	−0.127548	+	0.991832i	$0.540711\pi$
$410$	−0.575896	−	7.07288i	−0.0284415	−	0.349305i
$411$	−6.85516	−	2.83950i	−0.338140	−	0.140062i
$412$	2.63109	+	16.0498i	0.129625	+	0.790716i
$413$	−14.9411	−	36.0711i	−0.735204	−	1.77494i
$414$	−7.00964	−	2.25663i	−0.344505	−	0.110907i
$415$	1.85866			0.0912378
$416$	−11.7166	+	5.03983i	−0.574454	+	0.247098i
$417$	−20.8674			−1.02188
$418$	1.82304	+	0.586897i	0.0891679	+	0.0287061i
$419$	3.48225	+	8.40689i	0.170119	+	0.410704i	0.985828	−	0.167759i	$-0.0536530\pi$
$419$	3.48225	+	8.40689i	0.170119	+	0.410704i	−0.815709	+	0.578462i	$0.803653\pi$
$420$	16.5549	−	2.71389i	0.807795	−	0.132424i
$421$	9.96012	+	4.12562i	0.485426	+	0.201070i	0.611955	−	0.790893i	$-0.290383\pi$
$421$	9.96012	+	4.12562i	0.485426	+	0.201070i	−0.126528	+	0.991963i	$0.540383\pi$
$422$	−0.938145	−	11.5218i	−0.0456682	−	0.560875i
$423$	6.72723	+	6.72723i	0.327089	+	0.327089i
$424$	5.37311	+	21.6069i	0.260941	+	1.04932i
$425$	1.99448	−	1.99448i	0.0967465	−	0.0967465i
$426$	8.18693	+	6.95410i	0.396658	+	0.336927i
$427$	−8.42749	+	20.3458i	−0.407835	+	0.984600i
$428$	−27.4250	+	17.0108i	−1.32564	+	0.822246i
$429$	1.79370	−	0.742975i	0.0866006	−	0.0358712i
$430$	−10.9057	−	21.2613i	−0.525920	−	1.02531i
$431$			21.9612i			1.05783i	0.848674	+	0.528916i	$0.177401\pi$
$431$			21.9612i			1.05783i	−0.848674	+	0.528916i	$0.822599\pi$
$432$	1.51651	−	22.3585i	0.0729633	−	1.07573i
$433$			3.36141i			0.161539i	0.996733	+	0.0807696i	$0.0257378\pi$
$433$			3.36141i			0.161539i	−0.996733	+	0.0807696i	$0.974262\pi$
$434$	35.1416	−	18.0254i	1.68685	−	0.865247i
$435$	11.3440	−	4.69885i	0.543905	−	0.225293i
$436$	−20.2203	−	4.73895i	−0.968376	−	0.226954i
$437$	−3.10518	+	7.49656i	−0.148541	+	0.358609i
$438$	−16.1051	+	18.9603i	−0.769533	+	0.905956i
$439$	5.90005	−	5.90005i	0.281594	−	0.281594i	−0.552151	−	0.833744i	$-0.686193\pi$
$439$	5.90005	−	5.90005i	0.281594	−	0.281594i	0.833744	+	0.552151i	$0.186193\pi$
$440$	−0.410660	+	2.73629i	−0.0195775	+	0.130448i
$441$	11.2385	+	11.2385i	0.535166	+	0.535166i
$442$	−3.17812	+	0.258773i	−0.151168	+	0.0123086i
$443$	−0.102611	−	0.0425030i	−0.00487521	−	0.00201938i	0.380244	−	0.924886i	$-0.375840\pi$
$443$	−0.102611	−	0.0425030i	−0.00487521	−	0.00201938i	−0.385120	+	0.922867i	$0.625840\pi$
$444$	4.55595	−	6.34259i	0.216216	−	0.301006i
$445$	−7.88412	−	19.0340i	−0.373743	−	0.902296i
$446$	−0.544736	+	1.69208i	−0.0257940	+	0.0801223i
$447$	20.4932			0.969297
$448$	−30.9059	+	16.3843i	−1.46016	+	0.774084i
$449$	26.1153			1.23246			0.616228	−	0.787567i	$-0.288660\pi$
$449$	26.1153			1.23246			0.616228	+	0.787567i	$0.288660\pi$
$450$	−1.60312	+	4.97968i	−0.0755719	+	0.234744i
$451$	−0.861941	−	2.08091i	−0.0405872	−	0.0979862i
$452$	−6.64894	+	9.25635i	−0.312740	+	0.435382i
$453$	26.3992	+	10.9349i	1.24034	+	0.513766i
$454$	24.4730	−	1.99267i	1.14858	−	0.0935206i
$455$	10.2914	+	10.2914i	0.482469	+	0.482469i
$456$	−7.42799	−	1.11479i	−0.347847	−	0.0522046i
$457$	22.4544	−	22.4544i	1.05037	−	1.05037i	0.0517101	−	0.998662i	$-0.483533\pi$
$457$	22.4544	−	22.4544i	1.05037	−	1.05037i	0.998662	−	0.0517101i	$-0.0164672\pi$
$458$	6.53288	−	7.69104i	0.305262	−	0.359379i
$459$	2.14397	−	5.17601i	0.100072	−	0.241596i
$460$	−11.4136	−	2.67497i	−0.532164	−	0.124721i
$461$	38.9253	−	16.1234i	1.81293	−	0.750942i	0.832520	−	0.553995i	$-0.186897\pi$
$461$	38.9253	−	16.1234i	1.81293	−	0.750942i	0.980414	−	0.196947i	$-0.0631027\pi$
$462$	4.73775	−	2.43016i	0.220420	−	0.113061i
$463$			12.6977i			0.590112i	0.955480	+	0.295056i	$0.0953383\pi$
$463$			12.6977i			0.590112i	−0.955480	+	0.295056i	$0.904662\pi$
$464$	−19.2877	+	16.8374i	−0.895407	+	0.781657i
$465$			12.2522i			0.568184i
$466$	−2.19860	−	4.28629i	−0.101848	−	0.198559i
$467$	−20.9969	+	8.69722i	−0.971623	+	0.402459i	−0.811316	−	0.584608i	$-0.801248\pi$
$467$	−20.9969	+	8.69722i	−0.971623	+	0.402459i	−0.160307	+	0.987067i	$0.551248\pi$
$468$	5.02567	−	3.11725i	0.232312	−	0.144095i
$469$	9.24790	−	22.3264i	0.427029	−	1.03094i
$470$	11.5431	+	9.80488i	0.532444	+	0.452266i
$471$	5.97227	−	5.97227i	0.275188	−	0.275188i
$472$	−24.5090	+	6.09480i	−1.12812	+	0.280536i
$473$	−5.36293	−	5.36293i	−0.246588	−	0.246588i
$474$	1.16102	+	14.2591i	0.0533273	+	0.654940i
$475$	5.32559	+	2.20593i	0.244355	+	0.101215i
$476$	−8.62987	+	1.41472i	−0.395549	+	0.0648436i
$477$	−3.95068	−	9.53779i	−0.180889	−	0.436705i
$478$	32.7411	+	10.5404i	1.49754	+	0.482108i
$479$	8.65149			0.395297			0.197648	−	0.980273i	$-0.436670\pi$
$479$	8.65149			0.395297			0.197648	+	0.980273i	$0.436670\pi$
$480$	−0.146717	−	10.8507i	−0.00669669	−	0.495264i
$481$	6.77512			0.308919
$482$	−20.0257	−	6.44692i	−0.912144	−	0.293649i
$483$	8.63311	+	20.8422i	0.392820	+	0.948351i
$484$	−3.41695	−	20.8436i	−0.155316	−	0.947434i
$485$	−10.1458	−	4.20255i	−0.460699	−	0.190828i
$486$	1.43002	+	17.5629i	0.0648672	+	0.796668i
$487$	−29.7966	−	29.7966i	−1.35021	−	1.35021i	−0.885420	−	0.464791i	$-0.846129\pi$
$487$	−29.7966	−	29.7966i	−1.35021	−	1.35021i	−0.464791	−	0.885420i	$-0.653871\pi$
$488$	12.2061	+	7.34436i	0.552543	+	0.332463i
$489$	15.7947	−	15.7947i	0.714263	−	0.714263i
$490$	19.2839	+	16.3800i	0.871156	+	0.739973i
$491$	−10.8584	+	26.2144i	−0.490031	+	1.18304i	0.464673	+	0.885483i	$0.346172\pi$
$491$	−10.8584	+	26.2144i	−0.490031	+	1.18304i	−0.954704	+	0.297558i	$0.903828\pi$
$492$	4.65618	+	7.50677i	0.209917	+	0.338431i
$493$	−5.91351	+	2.44946i	−0.266331	+	0.110318i
$494$	−2.97411	−	5.79821i	−0.133812	−	0.260874i
$495$		−	1.28295i		−	0.0576643i
$496$	−8.15705	−	24.2106i	−0.366262	−	1.08709i
$497$			25.5586i			1.14646i
$498$	−2.05865	+	1.05596i	−0.0922505	+	0.0473186i
$499$	8.40567	−	3.48174i	0.376289	−	0.155864i	−0.186519	−	0.982451i	$-0.559721\pi$
$499$	8.40567	−	3.48174i	0.376289	−	0.155864i	0.562809	+	0.826587i	$0.309721\pi$
$500$	−5.26891	+	22.4816i	−0.235633	+	1.00541i
$501$	−7.17395	+	17.3195i	−0.320509	+	0.773776i
$502$	8.15697	−	9.60305i	0.364063	−	0.428605i
$503$	3.52282	−	3.52282i	0.157075	−	0.157075i	−0.624194	−	0.781269i	$-0.714573\pi$
$503$	3.52282	−	3.52282i	0.157075	−	0.157075i	0.781269	+	0.624194i	$0.214573\pi$
$504$	13.0439	−	9.63962i	0.581024	−	0.429383i
$505$	3.63047	+	3.63047i	0.161554	+	0.161554i
$506$	−3.70858	+	0.301964i	−0.164866	+	0.0134239i
$507$	9.50368	+	3.93656i	0.422073	+	0.174829i
$508$	−0.262117	−	0.188282i	−0.0116296	−	0.00835364i
$509$	−12.8075	−	30.9200i	−0.567682	−	1.37051i	−0.903504	−	0.428580i	$-0.859014\pi$
$509$	−12.8075	−	30.9200i	−0.567682	−	1.37051i	0.335822	−	0.941925i	$-0.390986\pi$
$510$	0.831358	−	2.58240i	0.0368132	−	0.114350i
$511$	−59.1917			−2.61849
$512$	7.51387	+	21.3434i	0.332069	+	0.943255i
$513$	11.4495			0.505509
$514$	−12.4608	+	38.7062i	−0.549622	+	1.70726i
$515$	−4.59414	−	11.0912i	−0.202442	−	0.488738i
$516$	24.1584	+	17.3533i	1.06352	+	0.763936i
$517$	4.44119	+	1.83960i	0.195323	+	0.0809055i
$518$	18.5199	−	1.50795i	0.813719	−	0.0662556i
$519$	6.42536	+	6.42536i	0.282042	+	0.282042i
$520$	7.57143	−	5.59537i	0.332029	−	0.245373i
$521$	3.84108	−	3.84108i	0.168281	−	0.168281i	−0.617943	−	0.786223i	$-0.712034\pi$
$521$	3.84108	−	3.84108i	0.168281	−	0.168281i	0.786223	+	0.617943i	$0.212034\pi$
$522$	7.68540	−	9.04787i	0.336381	−	0.396015i
$523$	3.36698	−	8.12861i	0.147228	−	0.355439i	−0.833011	−	0.553256i	$-0.813385\pi$
$523$	3.36698	−	8.12861i	0.147228	−	0.355439i	0.980239	+	0.197817i	$0.0633851\pi$
$524$	1.68874	−	7.20556i	0.0737729	−	0.314776i
$525$	14.8064	−	6.13300i	0.646203	−	0.267666i
$526$	−5.11027	+	2.62124i	−0.222818	+	0.114292i
$527$		−	6.38695i		−	0.278220i
$528$	−1.09972	−	3.26404i	−0.0478593	−	0.142049i
$529$			7.23556i			0.314590i
$530$	−7.50071	−	14.6231i	−0.325810	−	0.635186i
$531$	10.8189	−	4.48132i	0.469499	−	0.194473i
$532$	−9.42030	−	15.1875i	−0.408422	−	0.658464i
$533$	−2.93278	+	7.08037i	−0.127033	+	0.306685i
$534$	19.5463	+	16.6029i	0.845849	+	0.718477i
$535$	16.8442	−	16.8442i	0.728238	−	0.728238i
$536$	−13.3943	−	8.05933i	−0.578547	−	0.348110i
$537$	−16.7380	−	16.7380i	−0.722297	−	0.722297i
$538$	−0.970376	−	11.9177i	−0.0418359	−	0.513808i
$539$	7.41943	+	3.07323i	0.319577	+	0.132373i
$540$	2.67599	+	16.3237i	0.115156	+	0.702459i
$541$	−10.7140	−	25.8658i	−0.460630	−	1.11206i	−0.968139	−	0.250413i	$-0.919434\pi$
$541$	−10.7140	−	25.8658i	−0.460630	−	1.11206i	0.507509	−	0.861646i	$-0.330566\pi$
$542$	28.5580	+	9.19377i	1.22667	+	0.394906i
$543$	12.3498			0.529981
$544$	0.0764819	+	5.65634i	0.00327913	+	0.242513i
$545$	15.3297			0.656654
$546$	−17.2457	−	5.55195i	−0.738047	−	0.237601i
$547$	3.75795	+	9.07250i	0.160678	+	0.387912i	0.983630	−	0.180199i	$-0.0576743\pi$
$547$	3.75795	+	9.07250i	0.160678	+	0.387912i	−0.822952	+	0.568111i	$0.807674\pi$
$548$	−11.2699	+	1.84750i	−0.481424	+	0.0789214i
$549$	−6.10234	−	2.52767i	−0.260442	−	0.107878i
$550$	0.214517	+	2.63459i	0.00914702	+	0.112339i
$551$	−9.24959	−	9.24959i	−0.394046	−	0.394046i
$552$	14.1615	−	3.52163i	0.602755	−	0.149890i
$553$	−24.0698	+	24.0698i	−1.02355	+	1.02355i
$554$	−10.7047	−	9.09272i	−0.454798	−	0.386312i
$555$	−2.20591	+	5.32554i	−0.0936357	+	0.226057i
$556$	−27.2936	+	16.9292i	−1.15751	+	0.717960i
$557$	28.9421	−	11.9882i	1.22631	−	0.507956i	0.326902	−	0.945058i	$-0.393995\pi$
$557$	28.9421	−	11.9882i	1.22631	−	0.507956i	0.899412	+	0.437102i	$0.143995\pi$
$558$	5.40640	+	10.5401i	0.228871	+	0.446198i
$559$			25.8059i			1.09148i
$560$	19.4513	−	16.9802i	0.821967	−	0.717546i
$561$		−	0.861080i		−	0.0363548i
$562$	−24.0774	+	12.3502i	−1.01564	+	0.520960i
$563$	37.6595	−	15.5991i	1.58716	−	0.657422i	0.597631	−	0.801772i	$-0.296109\pi$
$563$	37.6595	−	15.5991i	1.58716	−	0.657422i	0.989527	+	0.144349i	$0.0461089\pi$
$564$	−18.3557	−	4.30194i	−0.772912	−	0.181144i
$565$	3.21930	−	7.77207i	0.135437	−	0.326974i
$566$	−12.4081	+	14.6078i	−0.521550	+	0.614011i
$567$	10.3443	−	10.3443i	0.434422	−	0.434422i
$568$	16.3498	+	2.45376i	0.686023	+	0.102958i
$569$	−15.4108	−	15.4108i	−0.646056	−	0.646056i	0.305982	−	0.952037i	$-0.401015\pi$
$569$	−15.4108	−	15.4108i	−0.646056	−	0.646056i	−0.952037	+	0.305982i	$0.901015\pi$
$570$	5.52598	−	0.449943i	0.231458	−	0.0188460i
$571$	13.3372	+	5.52446i	0.558145	+	0.231191i	0.643880	−	0.765127i	$-0.277324\pi$
$571$	13.3372	+	5.52446i	0.558145	+	0.231191i	−0.0857345	+	0.996318i	$0.527324\pi$
$572$	1.74332	−	2.42696i	0.0728917	−	0.101476i
$573$	−2.32514	−	5.61338i	−0.0971340	−	0.234502i
$574$	−6.44093	+	20.0071i	−0.268839	+	0.835079i
$575$	−11.1991			−0.467036
$576$	−4.91417	−	9.26966i	−0.204757	−	0.386236i
$577$	33.8790			1.41040			0.705201	−	0.709007i	$-0.250857\pi$
$577$	33.8790			1.41040			0.705201	+	0.709007i	$0.250857\pi$
$578$	−0.433377	+	1.34617i	−0.0180261	+	0.0559935i
$579$	−11.3913	−	27.5010i	−0.473406	−	1.14290i
$580$	11.0254	−	15.3490i	0.457804	−	0.637334i
$581$	−5.08605	−	2.10671i	−0.211005	−	0.0874011i
$582$	13.6252	−	1.10941i	0.564782	−	0.0459863i
$583$	−3.68850	−	3.68850i	−0.152762	−	0.152762i
$584$	−5.68272	+	37.8649i	−0.235153	+	1.56686i
$585$	−3.08672	+	3.08672i	−0.127620	+	0.127620i
$586$	8.58120	−	10.1025i	0.354486	−	0.417330i
$587$	−13.0146	+	31.4200i	−0.537169	+	1.29684i	0.389521	+	0.921017i	$0.372640\pi$
$587$	−13.0146	+	31.4200i	−0.537169	+	1.29684i	−0.926691	+	0.375824i	$0.877360\pi$
$588$	−30.6649	−	7.18681i	−1.26460	−	0.296379i
$589$	12.0591	−	4.99506i	0.496888	−	0.205818i
$590$	16.5872	−	8.50817i	0.682883	−	0.350276i
$591$		−	25.9291i		−	1.06658i
$592$	0.813378	−	11.9919i	0.0334296	−	0.492866i
$593$		−	0.714191i		−	0.0293283i	−0.999892	−	0.0146641i	$-0.995332\pi$
$593$		−	0.714191i		−	0.0293283i	0.999892	−	0.0146641i	$-0.00466791\pi$
$594$	2.39622	+	4.67158i	0.0983182	+	0.191677i
$595$	5.96368	−	2.47024i	0.244487	−	0.101270i
$596$	26.8042	−	16.6257i	1.09794	−	0.681015i
$597$	9.02143	−	21.7797i	0.369222	−	0.891382i
$598$	9.64919	+	8.19617i	0.394585	+	0.335166i
$599$	32.8980	−	32.8980i	1.34418	−	1.34418i	0.452324	−	0.891854i	$-0.350595\pi$
$599$	32.8980	−	32.8980i	1.34418	−	1.34418i	0.891854	−	0.452324i	$-0.149405\pi$
$600$	−2.50178	−	10.0604i	−0.102135	−	0.410715i
$601$	−3.09648	−	3.09648i	−0.126308	−	0.126308i	0.641127	−	0.767435i	$-0.278467\pi$
$601$	−3.09648	−	3.09648i	−0.126308	−	0.126308i	−0.767435	+	0.641127i	$0.778467\pi$
$602$	5.74367	+	70.5410i	0.234095	+	2.87504i
$603$	6.69641	+	2.77374i	0.272699	+	0.112956i
$604$	43.4001	−	7.11472i	1.76592	−	0.289494i
$605$	5.96632	+	14.4040i	0.242565	+	0.585604i
$606$	−6.08370	−	1.95854i	−0.247134	−	0.0795604i
$607$	−37.9158			−1.53895			−0.769477	−	0.638675i	$-0.779483\pi$
$607$	−37.9158			−1.53895			−0.769477	+	0.638675i	$0.779483\pi$
$608$	−10.6199	+	4.56807i	−0.430692	+	0.185260i
$609$	−36.3679			−1.47370
$610$	−10.0091	−	3.22224i	−0.405255	−	0.130465i
$611$	−6.25930	−	15.1113i	−0.253224	−	0.611338i
$612$	−0.424320	−	2.58837i	−0.0171521	−	0.104629i
$613$	−21.9323	−	9.08466i	−0.885838	−	0.366926i	−0.107080	−	0.994250i	$-0.534150\pi$
$613$	−21.9323	−	9.08466i	−0.885838	−	0.366926i	−0.778758	+	0.627324i	$0.784150\pi$
$614$	−1.97793	−	24.2920i	−0.0798228	−	0.980345i
$615$	−4.61059	−	4.61059i	−0.185917	−	0.185917i
$616$	4.22521	−	7.02216i	0.170239	−	0.282931i
$617$	−23.3794	+	23.3794i	−0.941220	+	0.941220i	−0.998366	−	0.0571454i	$-0.981800\pi$
$617$	−23.3794	+	23.3794i	−0.941220	+	0.941220i	0.0571454	+	0.998366i	$0.481800\pi$
$618$	11.3898	+	9.67462i	0.458163	+	0.389170i
$619$	−10.5171	+	25.3905i	−0.422718	+	1.02053i	0.558825	+	0.829286i	$0.311252\pi$
$619$	−10.5171	+	25.3905i	−0.422718	+	1.02053i	−0.981542	+	0.191245i	$0.938748\pi$
$620$	9.93996	+	16.0253i	0.399198	+	0.643593i
$621$	−20.5511	+	8.51254i	−0.824686	+	0.341596i
$622$	14.0754	+	27.4409i	0.564374	+	1.10028i
$623$			61.0211i			2.44476i
$624$	−5.20725	+	10.4990i	−0.208457	+	0.420297i
$625$		−	2.94098i		−	0.117639i
$626$	27.3393	−	14.0233i	1.09270	−	0.560484i
$627$	1.62580	−	0.673427i	0.0649281	−	0.0268941i
$628$	2.96628	−	12.6566i	0.118368	−	0.505054i
$629$	1.14992	−	2.77614i	0.0458501	−	0.110692i
$630$	−7.75059	+	9.12463i	−0.308791	+	0.363534i
$631$	19.1142	−	19.1142i	0.760922	−	0.760922i	−0.215567	−	0.976489i	$-0.569160\pi$
$631$	19.1142	−	19.1142i	0.760922	−	0.760922i	0.976489	+	0.215567i	$0.0691599\pi$
$632$	13.0866	+	17.7083i	0.520557	+	0.704397i
$633$	−7.51073	−	7.51073i	−0.298525	−	0.298525i
$634$	−18.2526	+	1.48618i	−0.724903	+	0.0590239i
$635$	0.220086	+	0.0911625i	0.00873384	+	0.00361767i
$636$	16.6156	+	11.9352i	0.658853	+	0.473262i
$637$	−10.4568	−	25.2449i	−0.414312	−	1.00024i
$638$	1.83817	−	5.70978i	0.0727737	−	0.226052i
$639$	−7.66584			−0.303256
$640$	−8.99481	−	14.0732i	−0.355551	−	0.556290i
$641$	−28.9496			−1.14344			−0.571720	−	0.820449i	$-0.693723\pi$
$641$	−28.9496			−1.14344			−0.571720	+	0.820449i	$0.693723\pi$
$642$	−9.08701	+	28.2264i	−0.358635	+	1.11401i
$643$	7.79655	+	18.8225i	0.307466	+	0.742288i	0.999786	+	0.0206976i	$0.00658872\pi$
$643$	7.79655	+	18.8225i	0.307466	+	0.742288i	−0.692320	+	0.721591i	$0.743411\pi$
$644$	28.2005	+	20.2567i	1.11125	+	0.798227i
$645$	−20.2846	−	8.40215i	−0.798705	−	0.330834i
$646$	−2.88063	+	0.234550i	−0.113337	+	0.00922825i
$647$	−11.9813	−	11.9813i	−0.471032	−	0.471032i	0.431217	−	0.902248i	$-0.358084\pi$
$647$	−11.9813	−	11.9813i	−0.471032	−	0.471032i	−0.902248	+	0.431217i	$0.858084\pi$
$648$	−5.62415	−	7.61038i	−0.220938	−	0.298964i
$649$	4.18392	−	4.18392i	0.164233	−	0.164233i
$650$	5.82259	−	6.85483i	0.228381	−	0.268868i
$651$	13.8874	−	33.5272i	0.544291	−	1.31403i
$652$	7.84486	−	33.4727i	0.307229	−	1.31089i
$653$	−6.84104	+	2.83365i	−0.267711	+	0.110889i	−0.512501	−	0.858687i	$-0.671281\pi$
$653$	−6.84104	+	2.83365i	−0.267711	+	0.110889i	0.244790	+	0.969576i	$0.421281\pi$
$654$	−16.9793	+	8.70929i	−0.663943	+	0.340560i
$655$			5.46280i			0.213449i
$656$	12.1801	+	6.04104i	0.475555	+	0.235863i
$657$		−	17.7535i		−	0.692629i
$658$	−20.4733	−	39.9139i	−0.798131	−	1.55600i
$659$	25.2509	−	10.4593i	0.983636	−	0.407435i	0.167865	−	0.985810i	$-0.446313\pi$
$659$	25.2509	−	10.4593i	0.983636	−	0.407435i	0.815771	+	0.578375i	$0.196313\pi$
$660$	1.34009	+	2.16052i	0.0521630	+	0.0840980i
$661$	10.0330	−	24.2218i	0.390239	−	0.942121i	−0.599648	−	0.800264i	$-0.704693\pi$
$661$	10.0330	−	24.2218i	0.390239	−	0.942121i	0.989887	−	0.141857i	$-0.0453073\pi$
$662$	15.3437	+	13.0332i	0.596350	+	0.506548i
$663$	−2.07172	+	2.07172i	−0.0804590	+	0.0804590i
$664$	−1.83595	+	3.05128i	−0.0712486	+	0.118413i
$665$	9.32806	+	9.32806i	0.361727	+	0.361727i
$666$	0.452283	+	5.55472i	0.0175256	+	0.215241i
$667$	23.4793	+	9.72544i	0.909122	+	0.376570i
$668$	4.66769	+	28.4731i	0.180598	+	1.10166i
$669$	0.625050	+	1.50900i	0.0241658	+	0.0583415i
$670$	10.9834	+	3.53593i	0.424327	+	0.136605i
$671$	−3.33744			−0.128841
$672$	−11.8973	+	29.8583i	−0.458950	+	1.15181i
$673$	29.0367			1.11928			0.559641	−	0.828735i	$-0.310939\pi$
$673$	29.0367			1.11928			0.559641	+	0.828735i	$0.310939\pi$
$674$	−32.1878	−	10.3623i	−1.23983	−	0.399141i
$675$	6.04734	+	14.5996i	0.232762	+	0.561938i
$676$	15.6240	−	2.56129i	0.600923	−	0.0985113i
$677$	−6.92225	−	2.86729i	−0.266044	−	0.110199i	0.245674	−	0.969352i	$-0.420991\pi$
$677$	−6.92225	−	2.86729i	−0.266044	−	0.110199i	−0.511718	+	0.859154i	$0.670991\pi$
$678$	0.849843	+	10.4374i	0.0326380	+	0.400845i
$679$	22.9998	+	22.9998i	0.882652	+	0.882652i
$680$	−1.00766	−	4.05212i	−0.0386421	−	0.155392i
$681$	15.9532	−	15.9532i	0.611328	−	0.611328i
$682$	4.56186	+	3.87491i	0.174683	+	0.148378i
$683$	11.4015	−	27.5257i	0.436267	−	1.05324i	−0.540960	−	0.841048i	$-0.681939\pi$
$683$	11.4015	−	27.5257i	0.436267	−	1.05324i	0.977227	−	0.212195i	$-0.0680610\pi$
$684$	4.55523	−	2.82545i	0.174174	−	0.108034i
$685$	7.78805	−	3.22591i	0.297566	−	0.123256i
$686$	−14.4470	−	28.1653i	−0.551589	−	1.07536i
$687$		−	9.27214i		−	0.353754i
$688$	45.6764	+	3.09810i	1.74140	+	0.118114i
$689$			17.7488i			0.676174i
$690$	−9.58422	+	4.91609i	−0.364865	+	0.187152i
$691$	−36.1450	+	14.9717i	−1.37502	+	0.569552i	−0.943145	−	0.332381i	$-0.892148\pi$
$691$	−36.1450	+	14.9717i	−1.37502	+	0.569552i	−0.431875	+	0.901933i	$0.642148\pi$
$692$	13.6168	+	3.19132i	0.517634	+	0.121316i
$693$	−1.45417	+	3.51068i	−0.0552394	+	0.133360i
$694$	−20.6807	+	24.3470i	−0.785028	+	0.924199i
$695$	16.7635	−	16.7635i	0.635875	−	0.635875i
$696$	−3.49152	+	23.2645i	−0.132346	+	0.881839i
$697$	2.40345	+	2.40345i	0.0910371	+	0.0910371i
$698$	15.7976	−	1.28629i	0.597947	−	0.0486868i
$699$	−4.08938	−	1.69388i	−0.154674	−	0.0640683i
$700$	14.3905	−	20.0337i	0.543909	−	0.757204i
$701$	−18.1049	−	43.7091i	−0.683812	−	1.65087i	−0.756890	−	0.653543i	$-0.773282\pi$
$701$	−18.1049	−	43.7091i	−0.683812	−	1.65087i	0.0730773	−	0.997326i	$-0.476718\pi$
$702$	5.47441	−	17.0048i	0.206618	−	0.641805i
$703$	6.14092			0.231609
$704$	−4.08643	−	3.37703i	−0.154013	−	0.127277i
$705$	13.9161			0.524110
$706$	−0.886204	+	2.75276i	−0.0333527	+	0.103602i
$707$	−5.81947	−	14.0494i	−0.218864	−	0.528384i
$708$	−13.5383	+	18.8474i	−0.508800	+	0.708328i
$709$	−45.6738	−	18.9187i	−1.71532	−	0.710507i	−0.999931	−	0.0117772i	$-0.996251\pi$
$709$	−45.6738	−	18.9187i	−1.71532	−	0.710507i	−0.715385	−	0.698730i	$-0.753749\pi$
$710$	−12.1633	+	0.990373i	−0.456480	+	0.0371680i
$711$	−7.21930	−	7.21930i	−0.270745	−	0.270745i
$712$	39.0351	+	5.85836i	1.46290	+	0.219551i
$713$	−17.9315	+	17.9315i	−0.671542	+	0.671542i
$714$	−5.20198	+	6.12419i	−0.194679	+	0.229192i
$715$	−0.844082	+	2.03780i	−0.0315669	+	0.0762092i
$716$	−35.4716	−	8.31335i	−1.32564	−	0.310684i
$717$	29.1987	−	12.0945i	1.09044	−	0.451677i
$718$	25.7552	−	13.2108i	0.961176	−	0.493022i
$719$			33.7778i			1.25970i	0.776717	+	0.629850i	$0.216884\pi$
$719$			33.7778i			1.25970i	−0.776717	+	0.629850i	$0.783116\pi$
$720$	5.09292	+	5.83406i	0.189802	+	0.217423i
$721$			35.5574i			1.32423i
$722$	9.56773	+	18.6529i	0.356074	+	0.694188i
$723$	−17.8590	+	7.39743i	−0.664183	+	0.275114i
$724$	16.1530	−	10.0191i	0.600320	−	0.372357i
$725$	6.90899	−	16.6798i	0.256594	−	0.619472i
$726$	−14.7917	−	12.5642i	−0.548970	−	0.466303i
$727$	−19.6907	+	19.6907i	−0.730287	+	0.730287i	−0.970676	−	0.240390i	$-0.922725\pi$
$727$	−19.6907	+	19.6907i	−0.730287	+	0.730287i	0.240390	+	0.970676i	$0.422725\pi$
$728$	−27.0607	+	6.72934i	−1.00294	+	0.249406i
$729$	18.5460	+	18.5460i	0.686887	+	0.686887i
$730$	−2.29363	−	28.1692i	−0.0848909	−	1.04259i
$731$	10.5741	+	4.37994i	0.391098	+	0.161998i
$732$	12.9167	−	2.11748i	0.477416	−	0.0782643i
$733$	19.4987	+	47.0741i	0.720201	+	1.73872i	0.672777	+	0.739845i	$0.265101\pi$
$733$	19.4987	+	47.0741i	0.720201	+	1.73872i	0.0474241	+	0.998875i	$0.484899\pi$
$734$	−37.5398	−	12.0853i	−1.38562	−	0.446076i
$735$	23.2482			0.857522
$736$	15.6656	−	16.0951i	0.577442	−	0.593272i
$737$	3.66234			0.134904
$738$	−6.00076	−	1.93184i	−0.220891	−	0.0711120i
$739$	7.27330	+	17.5593i	0.267553	+	0.645929i	0.999367	−	0.0355748i	$-0.0113262\pi$
$739$	7.27330	+	17.5593i	0.267553	+	0.645929i	−0.731814	+	0.681504i	$0.761326\pi$
$740$	1.43526	+	8.75516i	0.0527613	+	0.321846i
$741$	−5.53183	−	2.29136i	−0.203217	−	0.0841752i
$742$	3.95037	+	48.5165i	0.145023	+	1.78110i
$743$	10.9409	+	10.9409i	0.401385	+	0.401385i	0.878721	−	0.477336i	$-0.158398\pi$
$743$	10.9409	+	10.9409i	0.401385	+	0.401385i	−0.477336	+	0.878721i	$0.658398\pi$
$744$	−20.1140	−	12.1026i	−0.737416	−	0.443701i
$745$	−16.4629	+	16.4629i	−0.603154	+	0.603154i
$746$	12.6197	+	10.7194i	0.462041	+	0.392465i
$747$	0.631870	−	1.52547i	0.0231189	−	0.0558140i
$748$	−0.698575	−	1.12625i	−0.0255424	−	0.0411799i
$749$	−65.1849	+	27.0005i	−2.38180	+	0.986576i
$750$	9.68327	+	18.8781i	0.353583	+	0.689331i
$751$		−	15.8520i		−	0.578449i	−0.957261	−	0.289224i	$-0.906603\pi$
$751$		−	15.8520i		−	0.578449i	0.957261	−	0.289224i	$-0.0933973\pi$
$752$	−27.4984	+	9.26478i	−1.00276	+	0.337852i
$753$		−	11.5772i		−	0.421897i
$754$	−18.1600	+	9.31494i	−0.661349	+	0.339230i
$755$	−29.9917	+	12.4230i	−1.09151	+	0.452118i
$756$	11.1796	−	47.7014i	0.406598	−	1.73488i
$757$	0.839324	−	2.02631i	0.0305057	−	0.0736474i	−0.907893	−	0.419203i	$-0.862310\pi$
$757$	0.839324	−	2.02631i	0.0305057	−	0.0736474i	0.938398	+	0.345556i	$0.112310\pi$
$758$	−11.4210	+	13.4457i	−0.414830	+	0.488372i
$759$	−2.41751	+	2.41751i	−0.0877500	+	0.0877500i
$760$	6.86269	−	5.07161i	0.248936	−	0.183966i
$761$	5.38144	+	5.38144i	0.195077	+	0.195077i	0.797886	−	0.602809i	$-0.205952\pi$
$761$	5.38144	+	5.38144i	0.195077	+	0.195077i	−0.602809	+	0.797886i	$0.705952\pi$
$762$	−0.295560	+	0.0240655i	−0.0107070	+	0.000871799i
$763$	−41.9485	−	17.3756i	−1.51864	−	0.629040i
$764$	−7.59518	−	5.45571i	−0.274784	−	0.197381i
$765$	0.740903	+	1.78870i	0.0267874	+	0.0646705i
$766$	−3.42617	+	10.6425i	−0.123793	+	0.384530i
$767$	−20.1327			−0.726949
$768$	17.9581	+	10.4773i	0.648007	+	0.378066i
$769$	−48.7211			−1.75693			−0.878464	−	0.477809i	$-0.841431\pi$
$769$	−48.7211			−1.75693			−0.878464	+	0.477809i	$0.841431\pi$
$770$	−1.85376	+	5.75822i	−0.0668048	+	0.207512i
$771$	14.2980	+	34.5184i	0.514929	+	1.24315i
$772$	−37.2102	−	26.7286i	−1.33923	−	0.961982i
$773$	33.6060	+	13.9201i	1.20873	+	0.500670i	0.893808	−	0.448449i	$-0.148023\pi$
$773$	33.6060	+	13.9201i	1.20873	+	0.500670i	0.314917	+	0.949119i	$0.398023\pi$
$774$	−21.1575	+	1.72271i	−0.760491	+	0.0619216i
$775$	12.7386	+	12.7386i	0.457586	+	0.457586i
$776$	16.9211	−	12.5049i	0.607431	−	0.448898i
$777$	12.0726	−	12.0726i	0.433101	−	0.433101i
$778$	−13.5752	+	15.9818i	−0.486693	+	0.572974i
$779$	−2.65826	+	6.41760i	−0.0952419	+	0.229934i
$780$	1.97390	−	8.42231i	0.0706771	−	0.301567i
$781$	−3.57856	+	1.48229i	−0.128051	+	0.0530404i
$782$	4.99614	−	2.56270i	0.178662	−	0.0916421i
$783$		−	35.8600i		−	1.28153i
$784$	−45.9387	+	15.4777i	−1.64067	+	0.552775i
$785$			9.59544i			0.342476i
$786$	−3.10358	−	6.05062i	−0.110701	−	0.215819i
$787$	20.3065	−	8.41122i	0.723848	−	0.299828i	0.00982692	−	0.999952i	$-0.496872\pi$
$787$	20.3065	−	8.41122i	0.723848	−	0.299828i	0.714021	+	0.700124i	$0.246872\pi$
$788$	−21.0357	−	33.9140i	−0.749365	−	1.20814i
$789$	−2.01950	+	4.87550i	−0.0718960	+	0.173572i
$790$	−12.3875	−	10.5221i	−0.440726	−	0.374359i
$791$	−17.6187	+	17.6187i	−0.626448	+	0.626448i
$792$	2.10617	+	1.26728i	0.0748395	+	0.0450307i
$793$	8.02974	+	8.02974i	0.285144	+	0.285144i
$794$	−1.23731	−	15.1961i	−0.0439106	−	0.539289i
$795$	−13.9513	−	5.77881i	−0.494801	−	0.204953i
$796$	−5.86973	−	35.8056i	−0.208047	−	1.26910i
$797$	−5.67489	−	13.7004i	−0.201015	−	0.485293i	0.790939	−	0.611895i	$-0.209593\pi$
$797$	−5.67489	−	13.7004i	−0.201015	−	0.485293i	−0.991954	+	0.126603i	$0.959593\pi$
$798$	−15.6314	−	5.03225i	−0.553344	−	0.178140i
$799$	−7.25430			−0.256639
$800$	−11.4340	−	11.1289i	−0.404253	−	0.393467i
$801$	−18.3022			−0.646676
$802$	−29.0906	−	9.36522i	−1.02723	−	0.330697i
$803$	−3.43286	−	8.28765i	−0.121143	−	0.292465i
$804$	−14.1742	+	2.32362i	−0.499885	+	0.0819477i
$805$	−23.6785	−	9.80794i	−0.834556	−	0.345685i
$806$	−1.65277	−	20.2985i	−0.0582163	−	0.714985i
$807$	−7.76877	−	7.76877i	−0.273474	−	0.273474i
$808$	−9.54612	+	2.37389i	−0.335831	+	0.0835131i
$809$	27.3048	−	27.3048i	0.959985	−	0.959985i	−0.0392450	−	0.999230i	$-0.512495\pi$
$809$	27.3048	−	27.3048i	0.959985	−	0.959985i	0.999230	+	0.0392450i	$0.0124953\pi$
$810$	5.32369	+	4.52202i	0.187055	+	0.158887i
$811$	6.32126	−	15.2609i	0.221969	−	0.535881i	−0.773188	−	0.634177i	$-0.781339\pi$
$811$	6.32126	−	15.2609i	0.221969	−	0.535881i	0.995157	+	0.0982955i	$0.0313390\pi$
$812$	−47.5675	+	29.5045i	−1.66929	+	1.03540i
$813$	25.4682	−	10.5493i	0.893208	−	0.369979i
$814$	1.28521	+	2.50559i	0.0450465	+	0.0878209i
$815$			25.3769i			0.888913i
$816$	3.41822	+	3.91566i	0.119662	+	0.137075i
$817$			23.3903i			0.818324i
$818$	31.1049	−	15.9548i	1.08756	−	0.557847i
$819$	11.9452	−	4.94787i	0.417400	−	0.172893i
$820$	−9.77090	−	2.28997i	−0.341215	−	0.0799692i
$821$	−10.5406	+	25.4474i	−0.367871	+	0.888119i	0.626228	+	0.779640i	$0.284598\pi$
$821$	−10.5406	+	25.4474i	−0.367871	+	0.888119i	−0.994099	+	0.108479i	$0.965402\pi$
$822$	−6.79333	+	7.99766i	−0.236945	+	0.278951i
$823$	13.9192	−	13.9192i	0.485192	−	0.485192i	−0.421593	−	0.906785i	$-0.638529\pi$
$823$	13.9192	−	13.9192i	0.485192	−	0.485192i	0.906785	+	0.421593i	$0.138529\pi$
$824$	22.7461	+	3.41371i	0.792397	+	0.118922i
$825$	1.71741	+	1.71741i	0.0597925	+	0.0597925i
$826$	−55.0331	+	4.48097i	−1.91484	+	0.155913i
$827$	16.3892	+	6.78862i	0.569907	+	0.236063i	0.648980	−	0.760805i	$-0.275196\pi$
$827$	16.3892	+	6.78862i	0.569907	+	0.236063i	−0.0790726	+	0.996869i	$0.525196\pi$
$828$	−6.07564	+	8.45822i	−0.211143	+	0.293944i
$829$	−7.98040	−	19.2664i	−0.277171	−	0.669150i	0.722584	−	0.691283i	$-0.242954\pi$
$829$	−7.98040	−	19.2664i	−0.277171	−	0.669150i	−0.999755	+	0.0221332i	$0.992954\pi$
$830$	0.805499	−	2.50207i	0.0279593	−	0.0868482i
$831$	−12.9053			−0.447680
$832$	1.70678	+	17.9568i	0.0591718	+	0.622538i
$833$	−12.1190			−0.419899
$834$	−9.04346	+	28.0911i	−0.313149	+	0.972717i
$835$	−8.15022	−	19.6764i	−0.282050	−	0.680929i
$836$	1.58013	−	2.19978i	0.0546499	−	0.0760811i
$837$	33.0589	+	13.6935i	1.14268	+	0.473315i
$838$	12.8263	−	1.04436i	0.443076	−	0.0360767i
$839$	5.73385	+	5.73385i	0.197955	+	0.197955i	0.799123	−	0.601168i	$-0.205298\pi$
$839$	5.73385	+	5.73385i	0.197955	+	0.197955i	−0.601168	+	0.799123i	$0.705298\pi$
$840$	3.52114	−	23.4619i	0.121491	−	0.809512i
$841$	−8.46371	+	8.46371i	−0.291852	+	0.291852i
$842$	9.87029	−	11.6201i	0.340153	−	0.400455i
$843$	−9.51500	+	22.9712i	−0.327714	+	0.791172i
$844$	−15.9170	−	3.73040i	−0.547885	−	0.128406i
$845$	−10.7970	+	4.47226i	−0.371428	+	0.153850i
$846$	11.9714	−	6.14059i	0.411587	−	0.211118i
$847$		−	46.1778i		−	1.58669i
$848$	31.4152	+	2.13080i	1.07880	+	0.0731720i
$849$			17.6108i			0.604401i
$850$	−1.82055	−	3.54928i	−0.0624445	−	0.121739i
$851$	−11.0225	+	4.56568i	−0.377847	+	0.156509i
$852$	12.9095	−	8.00728i	0.442270	−	0.274325i
$853$	−18.8493	+	45.5064i	−0.645389	+	1.55811i	0.173922	+	0.984759i	$0.444356\pi$
$853$	−18.8493	+	45.5064i	−0.645389	+	1.55811i	−0.819312	+	0.573348i	$0.805644\pi$
$854$	23.7366	+	20.1622i	0.812251	+	0.689938i
$855$	−2.79778	+	2.79778i	−0.0956822	+	0.0956822i
$856$	11.0141	+	44.2909i	0.376453	+	1.51383i
$857$	−21.2178	−	21.2178i	−0.724786	−	0.724786i	0.244790	−	0.969576i	$-0.421281\pi$
$857$	−21.2178	−	21.2178i	−0.724786	−	0.724786i	−0.969576	+	0.244790i	$0.921281\pi$
$858$	−0.222824	−	2.73662i	−0.00760710	−	0.0934267i
$859$	−34.3564	−	14.2309i	−1.17223	−	0.485552i	−0.290298	−	0.956936i	$-0.593754\pi$
$859$	−34.3564	−	14.2309i	−1.17223	−	0.485552i	−0.881928	+	0.471385i	$0.843754\pi$
$860$	−33.3478	+	5.46680i	−1.13715	+	0.186416i
$861$	7.39056	+	17.8424i	0.251870	+	0.608067i
$862$	29.5635	+	9.51747i	1.00694	+	0.324166i
$863$	13.0998			0.445923			0.222962	−	0.974827i	$-0.428428\pi$
$863$	13.0998			0.445923			0.222962	+	0.974827i	$0.428428\pi$
$864$	−29.4412	−	11.7312i	−1.00161	−	0.399103i
$865$	−10.3234			−0.351007
$866$	4.52504	+	1.45676i	0.153767	+	0.0495027i
$867$	0.497273	+	1.20052i	0.0168883	+	0.0407719i
$868$	−9.03575	−	55.1185i	−0.306693	−	1.87084i
$869$	−4.76605	−	1.97416i	−0.161677	−	0.0669688i
$870$	−1.40922	−	17.3074i	−0.0477772	−	0.586776i
$871$	−8.81144	−	8.81144i	−0.298564	−	0.298564i
$872$	−15.1425	+	25.1663i	−0.512788	+	0.852237i
$873$	−6.89838	+	6.89838i	−0.233475	+	0.233475i
$874$	8.74596	+	7.42895i	0.295836	+	0.251288i
$875$	−19.3188	+	46.6397i	−0.653094	+	1.57671i
$876$	18.5442	+	29.8972i	0.626551	+	1.01013i
$877$	−3.84578	+	1.59297i	−0.129863	+	0.0537909i	−0.446668	−	0.894700i	$-0.647390\pi$
$877$	−3.84578	+	1.59297i	−0.129863	+	0.0537909i	0.316806	+	0.948490i	$0.397390\pi$
$878$	−5.38554	−	10.4994i	−0.181753	−	0.354339i
$879$		−	12.1793i		−	0.410798i
$880$	3.50556	+	1.73867i	0.118172	+	0.0586105i
$881$			33.7139i			1.13585i	0.823081	+	0.567924i	$0.192253\pi$
$881$			33.7139i			1.13585i	−0.823081	+	0.567924i	$0.807747\pi$
$882$	19.9994	−	10.2584i	0.673416	−	0.345420i
$883$	−51.5358	+	21.3468i	−1.73432	+	0.718378i	−0.735137	+	0.677918i	$0.762882\pi$
$883$	−51.5358	+	21.3468i	−1.73432	+	0.718378i	−0.999181	+	0.0404601i	$0.987118\pi$
$884$	−1.02897	+	4.39045i	−0.0346081	+	0.147667i
$885$	6.55499	−	15.8252i	0.220344	−	0.531957i
$886$	−0.101686	+	0.119713i	−0.00341620	+	0.00402183i
$887$	−3.89766	+	3.89766i	−0.130871	+	0.130871i	−0.769508	−	0.638637i	$-0.779498\pi$
$887$	−3.89766	+	3.89766i	−0.130871	+	0.130871i	0.638637	+	0.769508i	$0.279498\pi$
$888$	−6.56378	−	8.88184i	−0.220266	−	0.298055i
$889$	−0.498917	−	0.498917i	−0.0167331	−	0.0167331i
$890$	−29.0398	+	2.36451i	−0.973417	+	0.0792587i
$891$	2.04828	+	0.848424i	0.0686199	+	0.0284233i
$892$	2.04176	+	1.46662i	0.0683631	+	0.0491060i
$893$	−5.67339	−	13.6968i	−0.189853	−	0.458345i
$894$	8.88130	−	27.5875i	0.297035	−	0.922663i
$895$	26.8924			0.898912
$896$	8.66217	+	48.7052i	0.289383	+	1.62713i
$897$	11.6328			0.388409
$898$	11.3178	−	35.1557i	0.377679	−	1.17316i
$899$	−15.6446	−	37.7693i	−0.521775	−	1.25968i
$900$	6.00876	+	4.31616i	0.200292	+	0.143872i
$901$	7.27264	+	3.01243i	0.242287	+	0.100359i
$902$	−3.17481	+	0.258503i	−0.105710	+	0.00860721i
$903$	45.9835	+	45.9835i	1.53024	+	1.53024i
$904$	9.57915	+	12.9621i	0.318598	+	0.431114i
$905$	−9.92100	+	9.92100i	−0.329785	+	0.329785i
$906$	26.1611	−	30.7989i	0.869143	−	1.02323i
$907$	−1.63873	+	3.95624i	−0.0544130	+	0.131365i	−0.948748	−	0.316033i	$-0.897649\pi$
$907$	−1.63873	+	3.95624i	−0.0544130	+	0.131365i	0.894335	+	0.447397i	$0.147649\pi$
$908$	7.92357	−	33.8085i	0.262953	−	1.12197i
$909$	4.21388	−	1.74545i	0.139766	−	0.0578928i
$910$	18.3141	−	9.39396i	0.607106	−	0.311407i
$911$		−	1.57673i		−	0.0522395i	−0.999659	−	0.0261198i	$-0.991685\pi$
$911$		−	1.57673i		−	0.0522395i	0.999659	−	0.0261198i	$-0.00831513\pi$
$912$	−4.71982	+	9.51624i	−0.156289	+	0.315114i
$913$		−	0.834297i		−	0.0276112i
$914$	−20.4963	−	39.9587i	−0.677957	−	1.32172i
$915$	−8.92612	+	3.69732i	−0.295089	+	0.122230i
$916$	−7.52227	−	12.1275i	−0.248543	−	0.400705i
$917$	6.19186	−	14.9485i	0.204473	−	0.493642i
$918$	−6.03866	−	5.12933i	−0.199306	−	0.169293i
$919$	12.8517	−	12.8517i	0.423938	−	0.423938i	−0.462619	−	0.886557i	$-0.653090\pi$
$919$	12.8517	−	12.8517i	0.423938	−	0.423938i	0.886557	+	0.462619i	$0.153090\pi$
$920$	−8.54739	+	14.2055i	−0.281799	+	0.468341i
$921$	−15.8352	−	15.8352i	−0.521788	−	0.521788i
$922$	−4.83554	−	59.3878i	−0.159250	−	1.95583i
$923$	12.1762	+	5.04353i	0.400783	+	0.166010i
$924$	−1.21819	−	7.43101i	−0.0400755	−	0.244462i
$925$	3.24348	+	7.83045i	0.106645	+	0.257464i
$926$	17.0933	+	5.50289i	0.561721	+	0.180836i
$927$	−10.6648			−0.350278
$928$	14.3072	+	33.2615i	0.469658	+	1.09186i
$929$	39.1744			1.28527			0.642636	−	0.766172i	$-0.277841\pi$
$929$	39.1744			1.28527			0.642636	+	0.766172i	$0.277841\pi$
$930$	16.4936	+	5.30984i	0.540848	+	0.174117i
$931$	−9.47794	−	22.8818i	−0.310627	−	0.749920i
$932$	−6.72292	+	1.10211i	−0.220216	+	0.0361008i
$933$	26.1803	+	10.8442i	0.857104	+	0.355024i
$934$	2.60837	+	32.0347i	0.0853484	+	1.04821i
$935$	0.691734	+	0.691734i	0.0226221	+	0.0226221i
$936$	−2.01834	−	8.11637i	−0.0659716	−	0.265292i
$937$	−20.1865	+	20.1865i	−0.659465	+	0.659465i	−0.955253	−	0.295789i	$-0.904418\pi$
$937$	−20.1865	+	20.1865i	−0.659465	+	0.659465i	0.295789	+	0.955253i	$0.404418\pi$
$938$	−26.0474	−	22.1251i	−0.850478	−	0.722409i
$939$	10.8040	−	26.0833i	0.352577	−	0.851195i
$940$	18.2016	−	11.2898i	0.593671	−	0.368233i
$941$	7.75679	−	3.21297i	0.252864	−	0.104740i	−0.252651	−	0.967557i	$-0.581302\pi$
$941$	7.75679	−	3.21297i	0.252864	−	0.104740i	0.505515	+	0.862818i	$0.331302\pi$
$942$	−5.45147	−	10.6280i	−0.177618	−	0.346278i
$943$		−	13.4955i		−	0.439474i
$944$	−2.41700	+	35.6348i	−0.0786667	+	1.15981i
$945$			36.1642i			1.17642i
$946$	−9.54361	+	4.89526i	−0.310289	+	0.159159i
$947$	24.8890	−	10.3094i	0.808785	−	0.335010i	0.0603157	−	0.998179i	$-0.480789\pi$
$947$	24.8890	−	10.3094i	0.808785	−	0.335010i	0.748469	+	0.663170i	$0.230789\pi$
$948$	19.6983	+	4.61662i	0.639772	+	0.149941i
$949$	−11.6804	+	28.1990i	−0.379162	+	0.915379i
$950$	5.27756	−	6.21317i	0.171226	−	0.201582i
$951$	−11.8983	+	11.8983i	−0.385829	+	0.385829i
$952$	−1.83553	+	12.2304i	−0.0594898	+	0.396390i
$953$	22.4755	+	22.4755i	0.728051	+	0.728051i	0.970231	−	0.242180i	$-0.0778624\pi$
$953$	22.4755	+	22.4755i	0.728051	+	0.728051i	−0.242180	+	0.970231i	$0.577862\pi$
$954$	−14.5517	+	1.18484i	−0.471127	+	0.0383607i
$955$	6.37728	+	2.64155i	0.206364	+	0.0854787i
$956$	28.3785	−	39.5072i	0.917826	−	1.27775i
$957$	−2.10918	−	5.09201i	−0.0681801	−	0.164601i
$958$	3.74936	−	11.6464i	0.121136	−	0.376278i
$959$	−24.9678			−0.806251
$960$	−14.6705	−	4.50493i	−0.473488	−	0.145396i
$961$	9.79312			0.315907
$962$	2.93619	−	9.12049i	0.0946664	−	0.294057i
$963$	−8.09830	−	19.5510i	−0.260964	−	0.630023i
$964$	−17.3573	+	24.1641i	−0.559042	+	0.778273i
$965$	31.2435	+	12.9415i	1.00576	+	0.416601i
$966$	31.7986	−	2.58914i	1.02310	−	0.0833042i
$967$	12.0431	+	12.0431i	0.387280	+	0.387280i	0.873716	−	0.486436i	$-0.161703\pi$
$967$	12.0431	+	12.0431i	0.387280	+	0.387280i	−0.486436	+	0.873716i	$0.661703\pi$
$968$	−29.5399	−	4.43332i	−0.949448	−	0.142492i
$969$	−1.87779	+	1.87779i	−0.0603234	+	0.0603234i
$970$	−10.0543	+	11.8368i	−0.322825	+	0.380056i
$971$	8.94517	−	21.5955i	0.287064	−	0.693034i	−0.712902	−	0.701264i	$-0.752620\pi$
$971$	8.94517	−	21.5955i	0.287064	−	0.693034i	0.999966	+	0.00822958i	$0.00261959\pi$
$972$	24.2624	+	5.68629i	0.778217	+	0.182388i
$973$	−64.8725	+	26.8711i	−2.07972	+	0.861447i
$974$	−53.0245	+	27.1982i	−1.69902	+	0.871487i
$975$		−	8.26402i		−	0.264660i
$976$	15.1766	−	13.2486i	0.485792	−	0.424078i
$977$		−	37.0156i		−	1.18423i	−0.805852	−	0.592117i	$-0.798292\pi$
$977$		−	37.0156i		−	1.18423i	0.805852	−	0.592117i	$-0.201708\pi$
$978$	−14.4174	−	28.1075i	−0.461017	−	0.898780i
$979$	−8.54379	+	3.53896i	−0.273061	+	0.113105i
$980$	30.4075	−	18.8607i	0.971333	−	0.602484i
$981$	5.21151	−	12.5817i	0.166391	−	0.401703i
$982$	30.5834	+	25.9780i	0.975955	+	0.828991i
$983$	−14.5677	+	14.5677i	−0.464637	+	0.464637i	−0.900172	−	0.435535i	$-0.856559\pi$
$983$	−14.5677	+	14.5677i	−0.464637	+	0.464637i	0.435535	+	0.900172i	$0.356559\pi$
$984$	12.1233	−	3.01477i	0.386477	−	0.0961073i
$985$	20.8297	+	20.8297i	0.663689	+	0.663689i
$986$	0.734613	+	9.02216i	0.0233948	+	0.287324i
$987$	−38.0802	−	15.7733i	−1.21211	−	0.502071i
$988$	−9.09431	+	1.49086i	−0.289328	+	0.0474305i
$989$	−17.3903	−	41.9840i	−0.552980	−	1.33501i
$990$	−1.72707	−	0.556002i	−0.0548900	−	0.0176709i
$991$	46.7020			1.48354			0.741770	−	0.670655i	$-0.233987\pi$
$991$	46.7020			1.48354			0.741770	+	0.670655i	$0.233987\pi$
$992$	−36.1267	+	0.488486i	−1.14703	+	0.0155094i
$993$	18.4980			0.587016
$994$	34.4063	+	11.0765i	1.09130	+	0.351326i
$995$	10.2491	+	24.7435i	0.324919	+	0.784423i
$996$	0.529330	+	3.22894i	0.0167725	+	0.102313i
$997$	47.9860	+	19.8765i	1.51973	+	0.629494i	0.977538	−	0.210759i	$-0.0675934\pi$
$997$	47.9860	+	19.8765i	1.51973	+	0.629494i	0.542195	+	0.840253i	$0.317593\pi$
$998$	−1.04420	−	12.8244i	−0.0330537	−	0.405949i
$999$	11.9040	+	11.9040i	0.376625	+	0.376625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bd.b.69.18	✓	128
32.13	even	8	inner	544.2.bd.b.205.18	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.18	✓	128	1.1	even	1	trivial
544.2.bd.b.205.18	yes	128	32.13	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.433377 - 1.34617i) q^{2} +(-0.497273 - 1.20052i) q^{3} +(-1.62437 - 1.16680i) q^{4} +(1.36390 + 0.564945i) q^{5} +(-1.83162 + 0.149136i) q^{6} +(-3.09184 - 3.09184i) q^{7} +(-2.27468 + 1.68102i) q^{8} +(0.927343 - 0.927343i) q^{9} +(1.35160 - 1.59121i) q^{10} +(0.253587 - 0.612214i) q^{11} +(-0.593020 + 2.53031i) q^{12} +(-2.08308 + 0.862840i) q^{13} +(-5.50210 + 2.82222i) q^{14} -1.91832i q^{15} +(1.27714 + 3.79063i) q^{16} +1.00000i q^{17} +(-0.846475 - 1.65025i) q^{18} +(-1.88809 + 0.782072i) q^{19} +(-1.55629 - 2.50908i) q^{20} +(-2.17434 + 5.24933i) q^{21} +(-0.714248 - 0.606693i) q^{22} +(2.80753 - 2.80753i) q^{23} +(3.14924 + 1.89489i) q^{24} +(-1.99448 - 1.99448i) q^{25} +(0.258773 + 3.17812i) q^{26} +(-5.17601 - 2.14397i) q^{27} +(1.41472 + 8.62987i) q^{28} +(2.44946 + 5.91351i) q^{29} +(-2.58240 - 0.831358i) q^{30} -6.38695 q^{31} +(5.65634 - 0.0764819i) q^{32} -0.861080 q^{33} +(1.34617 + 0.433377i) q^{34} +(-2.47024 - 5.96368i) q^{35} +(-2.58837 + 0.424320i) q^{36} +(-2.77614 - 1.14992i) q^{37} +(0.234550 + 2.88063i) q^{38} +(2.07172 + 2.07172i) q^{39} +(-4.05212 + 1.00766i) q^{40} +(2.40345 - 2.40345i) q^{41} +(6.12419 + 5.20198i) q^{42} +(4.37994 - 10.5741i) q^{43} +(-1.12625 + 0.698575i) q^{44} +(1.78870 - 0.740903i) q^{45} +(-2.56270 - 4.99614i) q^{46} +7.25430i q^{47} +(3.91566 - 3.41822i) q^{48} +12.1190i q^{49} +(-3.54928 + 1.82055i) q^{50} +(1.20052 - 0.497273i) q^{51} +(4.39045 + 1.02897i) q^{52} +(3.01243 - 7.27264i) q^{53} +(-5.12933 + 6.03866i) q^{54} +(0.691734 - 0.691734i) q^{55} +(12.2304 + 1.83553i) q^{56} +(1.87779 + 1.87779i) q^{57} +(9.02216 - 0.734613i) q^{58} +(8.24947 + 3.41704i) q^{59} +(-2.23830 + 3.11606i) q^{60} +(-1.92737 - 4.65309i) q^{61} +(-2.76796 + 8.59794i) q^{62} -5.73440 q^{63} +(2.34837 - 7.64756i) q^{64} -3.32857 q^{65} +(-0.373173 + 1.15916i) q^{66} +(2.11500 + 5.10607i) q^{67} +(1.16680 - 1.62437i) q^{68} +(-4.76662 - 1.97440i) q^{69} +(-9.09869 + 0.740845i) q^{70} +(-4.13323 - 4.13323i) q^{71} +(-0.550534 + 3.66829i) q^{72} +(9.57223 - 9.57223i) q^{73} +(-2.75110 + 3.23882i) q^{74} +(-1.40262 + 3.38622i) q^{75} +(3.97948 + 0.932655i) q^{76} +(-2.67692 + 1.10882i) q^{77} +(3.68673 - 1.89106i) q^{78} -7.78493i q^{79} +(-0.399606 + 5.89155i) q^{80} +3.34569i q^{81} +(-2.19386 - 4.27706i) q^{82} +(1.16318 - 0.481806i) q^{83} +(9.65686 - 5.98981i) q^{84} +(-0.564945 + 1.36390i) q^{85} +(-12.3364 - 10.4788i) q^{86} +(5.88127 - 5.88127i) q^{87} +(0.452311 + 1.81888i) q^{88} +(-9.86807 - 9.86807i) q^{89} +(-0.222203 - 2.72899i) q^{90} +(9.10833 + 3.77279i) q^{91} +(-7.83629 + 1.28463i) q^{92} +(3.17606 + 7.66769i) q^{93} +(9.76555 + 3.14385i) q^{94} -3.01699 q^{95} +(-2.90456 - 6.75254i) q^{96} -7.43886 q^{97} +(16.3143 + 5.25210i) q^{98} +(-0.332570 - 0.802895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 20 q^{6} - 24 q^{8} - 16 q^{12} - 20 q^{16} - 20 q^{18} - 48 q^{22} - 8 q^{23} + 68 q^{24} + 20 q^{26} - 24 q^{27} + 20 q^{30} + 48 q^{31} - 24 q^{35} + 8 q^{36} + 68 q^{38} - 24 q^{39} - 36 q^{40}+ \cdots - 136 q^{99}+O(q^{100}) \) 128 * q + 20 * q^6 - 24 * q^8 - 16 * q^12 - 20 * q^16 - 20 * q^18 - 48 * q^22 - 8 * q^23 + 68 * q^24 + 20 * q^26 - 24 * q^27 + 20 * q^30 + 48 * q^31 - 24 * q^35 + 8 * q^36 + 68 * q^38 - 24 * q^39 - 36 * q^40 - 16 * q^42 - 8 * q^43 - 40 * q^44 - 80 * q^45 + 12 * q^50 + 56 * q^52 - 16 * q^53 - 136 * q^54 + 32 * q^55 + 128 * q^56 - 32 * q^58 + 20 * q^60 - 12 * q^62 - 80 * q^63 + 12 * q^64 - 8 * q^66 + 40 * q^67 - 4 * q^68 + 100 * q^70 - 44 * q^72 + 84 * q^74 + 32 * q^75 - 32 * q^76 - 16 * q^77 - 64 * q^78 + 44 * q^80 + 40 * q^82 + 84 * q^84 - 120 * q^86 - 56 * q^87 + 128 * q^88 - 68 * q^90 - 56 * q^91 - 40 * q^92 + 32 * q^95 - 72 * q^96 - 12 * q^98 - 136 * q^99

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