LMFDB - Embedded newform 544.2.bd.b.69.7

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			69.7
Character	$\chi$	$=$	544.69
Dual form			544.2.bd.b.205.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.21759 + 0.719358i) q^{2} +(-1.28383 - 3.09944i) q^{3} +(0.965047 - 1.75177i) q^{4} +(2.78329 + 1.15288i) q^{5} +(3.79278 + 2.85031i) q^{6} +(-2.24686 - 2.24686i) q^{7} +(0.0851164 + 2.82715i) q^{8} +(-5.83697 + 5.83697i) q^{9} +(-4.21824 + 0.598454i) q^{10} +(-1.16535 + 2.81340i) q^{11} +(-6.66844 - 0.742135i) q^{12} +(-2.69948 + 1.11816i) q^{13} +(4.35205 + 1.11946i) q^{14} -10.1067i q^{15} +(-2.13737 - 3.38107i) q^{16} +1.00000i q^{17} +(2.90816 - 11.3059i) q^{18} +(-4.59445 + 1.90308i) q^{19} +(4.70558 - 3.76310i) q^{20} +(-4.07942 + 9.84859i) q^{21} +(-0.604928 - 4.26388i) q^{22} +(-0.421361 + 0.421361i) q^{23} +(8.65328 - 3.89338i) q^{24} +(2.88206 + 2.88206i) q^{25} +(2.48250 - 3.30335i) q^{26} +(16.2867 + 6.74615i) q^{27} +(-6.10430 + 1.76765i) q^{28} +(-1.28152 - 3.09387i) q^{29} +(7.27036 + 12.3059i) q^{30} -1.48342 q^{31} +(5.03464 + 2.57923i) q^{32} +10.2161 q^{33} +(-0.719358 - 1.21759i) q^{34} +(-3.66332 - 8.84403i) q^{35} +(4.59205 + 15.8579i) q^{36} +(-4.77154 - 1.97644i) q^{37} +(4.22516 - 5.62223i) q^{38} +(6.93133 + 6.93133i) q^{39} +(-3.02245 + 7.96691i) q^{40} +(-6.31308 + 6.31308i) q^{41} +(-2.11761 - 14.9261i) q^{42} +(0.202757 - 0.489500i) q^{43} +(3.80381 + 4.75649i) q^{44} +(-22.9753 + 9.51668i) q^{45} +(0.209935 - 0.816154i) q^{46} +6.36307i q^{47} +(-7.73541 + 10.9654i) q^{48} +3.09677i q^{49} +(-5.58240 - 1.43593i) q^{50} +(3.09944 - 1.28383i) q^{51} +(-0.646368 + 5.80793i) q^{52} +(2.42966 - 5.86572i) q^{53} +(-24.6834 + 3.50190i) q^{54} +(-6.48702 + 6.48702i) q^{55} +(6.16096 - 6.54345i) q^{56} +(11.7970 + 11.7970i) q^{57} +(3.78597 + 2.84519i) q^{58} +(-12.2448 - 5.07197i) q^{59} +(-17.7046 - 9.75348i) q^{60} +(5.30909 + 12.8173i) q^{61} +(1.80619 - 1.06711i) q^{62} +26.2297 q^{63} +(-7.98551 + 0.481273i) q^{64} -8.80254 q^{65} +(-12.4390 + 7.34902i) q^{66} +(-3.42100 - 8.25902i) q^{67} +(1.75177 + 0.965047i) q^{68} +(1.84694 + 0.765026i) q^{69} +(10.8224 + 8.13316i) q^{70} +(1.70472 + 1.70472i) q^{71} +(-16.9988 - 16.0051i) q^{72} +(10.3859 - 10.3859i) q^{73} +(7.23154 - 1.02596i) q^{74} +(5.23269 - 12.6328i) q^{75} +(-1.10010 + 9.88497i) q^{76} +(8.93971 - 3.70295i) q^{77} +(-13.4256 - 3.45340i) q^{78} +11.7357i q^{79} +(-2.05096 - 11.8746i) q^{80} -34.3762i q^{81} +(3.14537 - 12.2281i) q^{82} +(11.4040 - 4.72367i) q^{83} +(13.3156 + 16.6505i) q^{84} +(-1.15288 + 2.78329i) q^{85} +(0.105250 + 0.741865i) q^{86} +(-7.94400 + 7.94400i) q^{87} +(-8.05310 - 3.05515i) q^{88} +(2.86201 + 2.86201i) q^{89} +(21.1286 - 28.1149i) q^{90} +(8.57770 + 3.55300i) q^{91} +(0.331493 + 1.14476i) q^{92} +(1.90445 + 4.59776i) q^{93} +(-4.57732 - 7.74760i) q^{94} -14.9817 q^{95} +(1.53053 - 18.9158i) q^{96} -4.52492 q^{97} +(-2.22769 - 3.77060i) q^{98} +(-9.61964 - 23.2239i) 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 $

$2$	−1.21759	+	0.719358i	−0.860966	+	0.508663i
$2$	−1.21759	+	0.719358i	−0.860966	+	0.508663i
$3$	−1.28383	−	3.09944i	−0.741219	−	1.78946i	−0.600852	−	0.799360i	$-0.705172\pi$
$3$	−1.28383	−	3.09944i	−0.741219	−	1.78946i	−0.140367	−	0.990100i	$-0.544828\pi$
$4$	0.965047	−	1.75177i	0.482524	−	0.875883i
$5$	2.78329	+	1.15288i	1.24473	+	0.515583i	0.905189	−	0.425010i	$-0.139729\pi$
$5$	2.78329	+	1.15288i	1.24473	+	0.515583i	0.339538	+	0.940592i	$0.389729\pi$
$6$	3.79278	+	2.85031i	1.54840	+	1.16363i
$7$	−2.24686	−	2.24686i	−0.849234	−	0.849234i	0.140804	−	0.990038i	$-0.455031\pi$
$7$	−2.24686	−	2.24686i	−0.849234	−	0.849234i	−0.990038	+	0.140804i	$0.955031\pi$
$8$	0.0851164	+	2.82715i	0.0300932	+	0.999547i
$9$	−5.83697	+	5.83697i	−1.94566	+	1.94566i
$10$	−4.21824	+	0.598454i	−1.33392	+	0.189248i
$11$	−1.16535	+	2.81340i	−0.351366	+	0.848273i	0.645086	+	0.764110i	$0.276822\pi$
$11$	−1.16535	+	2.81340i	−0.351366	+	0.848273i	−0.996452	+	0.0841632i	$0.973178\pi$
$12$	−6.66844	−	0.742135i	−1.92501	−	0.214236i
$13$	−2.69948	+	1.11816i	−0.748700	+	0.310122i	−0.724211	−	0.689578i	$-0.757796\pi$
$13$	−2.69948	+	1.11816i	−0.748700	+	0.310122i	−0.0244891	+	0.999700i	$0.507796\pi$
$14$	4.35205	+	1.11946i	1.16314	+	0.299187i
$15$		−	10.1067i		−	2.60955i
$16$	−2.13737	−	3.38107i	−0.534342	−	0.845268i
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$	2.90816	−	11.3059i	0.685459	−	2.66483i
$19$	−4.59445	+	1.90308i	−1.05404	+	0.436597i	−0.841332	−	0.540518i	$-0.818228\pi$
$19$	−4.59445	+	1.90308i	−1.05404	+	0.436597i	−0.212707	+	0.977116i	$0.568228\pi$
$20$	4.70558	−	3.76310i	1.05220	−	0.841454i
$21$	−4.07942	+	9.84859i	−0.890202	+	2.14914i
$22$	−0.604928	−	4.26388i	−0.128971	−	0.909061i
$23$	−0.421361	+	0.421361i	−0.0878599	+	0.0878599i	−0.749671	−	0.661811i	$-0.769788\pi$
$23$	−0.421361	+	0.421361i	−0.0878599	+	0.0878599i	0.661811	+	0.749671i	$0.269788\pi$
$24$	8.65328	−	3.89338i	1.76634	−	0.794733i
$25$	2.88206	+	2.88206i	0.576412	+	0.576412i
$26$	2.48250	−	3.30335i	0.486858	−	0.647840i
$27$	16.2867	+	6.74615i	3.13437	+	1.29830i
$28$	−6.10430	+	1.76765i	−1.15360	+	0.334054i
$29$	−1.28152	−	3.09387i	−0.237973	−	0.574517i	0.759100	−	0.650974i	$-0.225639\pi$
$29$	−1.28152	−	3.09387i	−0.237973	−	0.574517i	−0.997073	+	0.0764567i	$0.975639\pi$
$30$	7.27036	+	12.3059i	1.32738	+	2.24673i
$31$	−1.48342			−0.266430			−0.133215	−	0.991087i	$-0.542530\pi$
$31$	−1.48342			−0.266430			−0.133215	+	0.991087i	$0.542530\pi$
$32$	5.03464	+	2.57923i	0.890007	+	0.455947i
$33$	10.2161			1.77839
$34$	−0.719358	−	1.21759i	−0.123369	−	0.208815i
$35$	−3.66332	−	8.84403i	−0.619214	−	1.49491i
$36$	4.59205	+	15.8579i	0.765342	+	2.64299i
$37$	−4.77154	−	1.97644i	−0.784437	−	0.324924i	−0.0457322	−	0.998954i	$-0.514562\pi$
$37$	−4.77154	−	1.97644i	−0.784437	−	0.324924i	−0.738704	+	0.674029i	$0.764562\pi$
$38$	4.22516	−	5.62223i	0.685411	−	0.912046i
$39$	6.93133	+	6.93133i	1.10990	+	1.10990i
$40$	−3.02245	+	7.96691i	−0.477891	+	1.25968i
$41$	−6.31308	+	6.31308i	−0.985937	+	0.985937i	−0.999902	−	0.0139651i	$-0.995555\pi$
$41$	−6.31308	+	6.31308i	−0.985937	+	0.985937i	0.0139651	+	0.999902i	$0.495555\pi$
$42$	−2.11761	−	14.9261i	−0.326754	−	2.30315i
$43$	0.202757	−	0.489500i	0.0309202	−	0.0746480i	−0.907665	−	0.419695i	$-0.862137\pi$
$43$	0.202757	−	0.489500i	0.0309202	−	0.0746480i	0.938585	+	0.345047i	$0.112137\pi$
$44$	3.80381	+	4.75649i	0.573446	+	0.717068i
$45$	−22.9753	+	9.51668i	−3.42495	+	1.41866i
$46$	0.209935	−	0.816154i	0.0309532	−	0.120335i
$47$			6.36307i			0.928148i	0.885796	+	0.464074i	$0.153613\pi$
$47$			6.36307i			0.928148i	−0.885796	+	0.464074i	$0.846387\pi$
$48$	−7.73541	+	10.9654i	−1.11651	+	1.58271i
$49$			3.09677i			0.442396i
$50$	−5.58240	−	1.43593i	−0.789471	−	0.203071i
$51$	3.09944	−	1.28383i	0.434008	−	0.179772i
$52$	−0.646368	+	5.80793i	−0.0896351	+	0.805415i
$53$	2.42966	−	5.86572i	0.333740	−	0.805719i	−0.664549	−	0.747244i	$-0.731376\pi$
$53$	2.42966	−	5.86572i	0.333740	−	0.805719i	0.998289	−	0.0584743i	$-0.0186236\pi$
$54$	−24.6834	+	3.50190i	−3.35898	+	0.476548i
$55$	−6.48702	+	6.48702i	−0.874710	+	0.874710i
$56$	6.16096	−	6.54345i	0.823293	−	0.874405i
$57$	11.7970	+	11.7970i	1.56255	+	1.56255i
$58$	3.78597	+	2.84519i	0.497122	+	0.373592i
$59$	−12.2448	−	5.07197i	−1.59414	−	0.660315i	−0.603569	−	0.797311i	$-0.706255\pi$
$59$	−12.2448	−	5.07197i	−1.59414	−	0.660315i	−0.990572	+	0.136996i	$0.956255\pi$
$60$	−17.7046	−	9.75348i	−2.28566	−	1.25917i
$61$	5.30909	+	12.8173i	0.679759	+	1.64108i	0.764455	+	0.644677i	$0.223008\pi$
$61$	5.30909	+	12.8173i	0.679759	+	1.64108i	−0.0846959	+	0.996407i	$0.526992\pi$
$62$	1.80619	−	1.06711i	0.229387	−	0.135523i
$63$	26.2297			3.30463
$64$	−7.98551	+	0.481273i	−0.998189	+	0.0601591i
$65$	−8.80254			−1.09182
$66$	−12.4390	+	7.34902i	−1.53113	+	0.904602i
$67$	−3.42100	−	8.25902i	−0.417941	−	1.00900i	−0.982943	−	0.183910i	$-0.941125\pi$
$67$	−3.42100	−	8.25902i	−0.417941	−	1.00900i	0.565002	−	0.825090i	$-0.308875\pi$
$68$	1.75177	+	0.965047i	0.212433	+	0.117029i
$69$	1.84694	+	0.765026i	0.222345	+	0.0920983i
$70$	10.8224	+	8.13316i	1.29353	+	0.972099i
$71$	1.70472	+	1.70472i	0.202313	+	0.202313i	0.800990	−	0.598677i	$-0.204307\pi$
$71$	1.70472	+	1.70472i	0.202313	+	0.202313i	−0.598677	+	0.800990i	$0.704307\pi$
$72$	−16.9988	−	16.0051i	−2.00332	−	1.88622i
$73$	10.3859	−	10.3859i	1.21558	−	1.21558i	0.246418	−	0.969164i	$-0.420746\pi$
$73$	10.3859	−	10.3859i	1.21558	−	1.21558i	0.969164	−	0.246418i	$-0.0792536\pi$
$74$	7.23154	−	1.02596i	0.840650	−	0.119265i
$75$	5.23269	−	12.6328i	0.604219	−	1.45871i
$76$	−1.10010	+	9.88497i	−0.126191	+	1.13388i
$77$	8.93971	−	3.70295i	1.01877	−	0.421990i
$78$	−13.4256	−	3.45340i	−1.52015	−	0.391021i
$79$			11.7357i			1.32037i	0.751103	+	0.660185i	$0.229522\pi$
$79$			11.7357i			1.32037i	−0.751103	+	0.660185i	$0.770478\pi$
$80$	−2.05096	−	11.8746i	−0.229304	−	1.32763i
$81$		−	34.3762i		−	3.81958i
$82$	3.14537	−	12.2281i	0.347348	−	1.35037i
$83$	11.4040	−	4.72367i	1.25175	−	0.518490i	0.344380	−	0.938830i	$-0.388089\pi$
$83$	11.4040	−	4.72367i	1.25175	−	0.518490i	0.907367	+	0.420340i	$0.138089\pi$
$84$	13.3156	+	16.6505i	1.45285	+	1.81672i
$85$	−1.15288	+	2.78329i	−0.125047	+	0.301891i
$86$	0.105250	+	0.741865i	0.0113494	+	0.0799974i
$87$	−7.94400	+	7.94400i	−0.851686	+	0.851686i
$88$	−8.05310	−	3.05515i	−0.858463	−	0.325680i
$89$	2.86201	+	2.86201i	0.303373	+	0.303373i	0.842332	−	0.538959i	$-0.181182\pi$
$89$	2.86201	+	2.86201i	0.303373	+	0.303373i	−0.538959	+	0.842332i	$0.681182\pi$
$90$	21.1286	−	28.1149i	2.22715	−	2.96357i
$91$	8.57770	+	3.55300i	0.899187	+	0.372456i
$92$	0.331493	+	1.14476i	0.0345605	+	0.119349i
$93$	1.90445	+	4.59776i	0.197483	+	0.476765i
$94$	−4.57732	−	7.74760i	−0.472115	−	0.799104i
$95$	−14.9817			−1.53709
$96$	1.53053	−	18.9158i	0.156209	−	1.93059i
$97$	−4.52492			−0.459436			−0.229718	−	0.973257i	$-0.573780\pi$
$97$	−4.52492			−0.459436			−0.229718	+	0.973257i	$0.573780\pi$
$98$	−2.22769	−	3.77060i	−0.225031	−	0.380888i
$99$	−9.61964	−	23.2239i	−0.966810	−	2.33409i
$100$	7.83002	−	2.26737i	0.783002	−	0.226737i
$101$	−12.3169	−	5.10183i	−1.22558	−	0.507651i	−0.326400	−	0.945232i	$-0.605836\pi$
$101$	−12.3169	−	5.10183i	−1.22558	−	0.507651i	−0.899179	+	0.437580i	$0.855836\pi$
$102$	−2.85031	+	3.79278i	−0.282222	+	0.375541i
$103$	0.741072	+	0.741072i	0.0730200	+	0.0730200i	0.742674	−	0.669654i	$-0.233557\pi$
$103$	0.741072	+	0.741072i	0.0730200	+	0.0730200i	−0.669654	+	0.742674i	$0.733557\pi$
$104$	−3.39097	−	7.53664i	−0.332512	−	0.739029i
$105$	−22.7084	+	22.7084i	−2.21612	+	2.21612i
$106$	1.26123	+	8.88984i	0.122501	+	0.863457i
$107$	−6.34755	+	15.3243i	−0.613641	+	1.48146i	0.245333	+	0.969439i	$0.421103\pi$
$107$	−6.34755	+	15.3243i	−0.613641	+	1.48146i	−0.858973	+	0.512020i	$0.828897\pi$
$108$	27.5351	−	22.0200i	2.64956	−	2.11888i
$109$	5.69427	−	2.35864i	0.545412	−	0.225917i	−0.0929262	−	0.995673i	$-0.529622\pi$
$109$	5.69427	−	2.35864i	0.545412	−	0.225917i	0.638338	+	0.769756i	$0.279622\pi$
$110$	3.23204	−	12.5650i	0.308163	−	1.19803i
$111$			17.3265i			1.64456i
$112$	−2.79443	+	12.3992i	−0.264049	+	1.17161i
$113$		−	2.92892i		−	0.275530i	−0.990465	−	0.137765i	$-0.956008\pi$
$113$		−	2.92892i		−	0.275530i	0.990465	−	0.137765i	$-0.0439918\pi$
$114$	−22.8501	−	5.87762i	−2.14011	−	0.550489i
$115$	−1.65855	+	0.686994i	−0.154661	+	0.0640625i
$116$	−6.65647	−	0.740802i	−0.618037	−	0.0687818i
$117$	9.23009	−	22.2834i	0.853322	−	2.06010i
$118$	18.5577	−	2.63284i	1.70838	−	0.242372i
$119$	2.24686	−	2.24686i	0.205969	−	0.205969i
$120$	28.5732	−	0.860249i	2.60837	−	0.0785296i
$121$	1.22097	+	1.22097i	0.110997	+	0.110997i
$122$	−15.6845	−	11.7870i	−1.42001	−	1.06715i
$123$	27.6719	+	11.4621i	2.49509	+	1.03350i
$124$	−1.43157	+	2.59860i	−0.128559	+	0.233361i
$125$	−1.06543	−	2.57218i	−0.0952952	−	0.230063i
$126$	−31.9370	+	18.8686i	−2.84517	+	1.68094i
$127$	−19.9988			−1.77460			−0.887301	−	0.461190i	$-0.847423\pi$
$127$	−19.9988			−1.77460			−0.887301	+	0.461190i	$0.847423\pi$
$128$	9.37686	−	6.33044i	0.828806	−	0.559537i
$129$	−1.77748			−0.156498
$130$	10.7179	−	6.33218i	0.940020	−	0.555369i
$131$	−6.55605	−	15.8277i	−0.572804	−	1.38287i	−0.899158	−	0.437624i	$-0.855820\pi$
$131$	−6.55605	−	15.8277i	−0.572804	−	1.38287i	0.326353	−	0.945248i	$-0.394180\pi$
$132$	9.85900	−	17.8962i	0.858115	−	1.55766i
$133$	14.5991	+	6.04713i	1.26590	+	0.524353i
$134$	10.1066	+	7.59517i	0.873074	+	0.656123i
$135$	37.5530	+	37.5530i	3.23205	+	3.23205i
$136$	−2.82715	+	0.0851164i	−0.242426	+	0.00729867i
$137$	1.80744	−	1.80744i	0.154420	−	0.154420i	−0.625669	−	0.780089i	$-0.715174\pi$
$137$	1.80744	−	1.80744i	0.154420	−	0.154420i	0.780089	+	0.625669i	$0.215174\pi$
$138$	−2.79914	+	0.397122i	−0.238278	+	0.0338052i
$139$	−1.12601	+	2.71844i	−0.0955073	+	0.230575i	−0.964412	−	0.264405i	$-0.914825\pi$
$139$	−1.12601	+	2.71844i	−0.0955073	+	0.230575i	0.868904	+	0.494980i	$0.164825\pi$
$140$	−19.0279	−	2.11763i	−1.60816	−	0.178973i
$141$	19.7219	−	8.16908i	1.66088	−	0.687961i
$142$	−3.30195	−	0.849343i	−0.277093	−	0.0712753i
$143$		−	8.89777i		−	0.744069i
$144$	32.2110	+	7.25947i	2.68425	+	0.604956i
$145$		−	10.0886i		−	0.837812i
$146$	−5.17459	+	20.1170i	−0.428252	+	1.66490i
$147$	9.59825	−	3.97573i	0.791650	−	0.327912i
$148$	−8.06702	+	6.45127i	−0.663105	+	0.530291i
$149$	0.520496	−	1.25659i	0.0426407	−	0.102944i	−0.901124	−	0.433561i	$-0.857257\pi$
$149$	0.520496	−	1.25659i	0.0426407	−	0.102944i	0.943765	+	0.330617i	$0.107257\pi$
$150$	2.71627	+	19.1458i	0.221782	+	1.56325i
$151$	−6.46632	+	6.46632i	−0.526222	+	0.526222i	−0.919444	−	0.393222i	$-0.871361\pi$
$151$	−6.46632	+	6.46632i	−0.526222	+	0.526222i	0.393222	+	0.919444i	$0.371361\pi$
$152$	−5.77136	−	12.8272i	−0.468119	−	1.04042i
$153$	−5.83697	−	5.83697i	−0.471891	−	0.471891i
$154$	−8.22115	+	10.9395i	−0.662479	+	0.881532i
$155$	−4.12879	−	1.71020i	−0.331632	−	0.137367i
$156$	18.8311	−	5.45301i	1.50770	−	0.436590i
$157$	−4.81102	−	11.6148i	−0.383961	−	0.926964i	−0.991191	−	0.132438i	$-0.957719\pi$
$157$	−4.81102	−	11.6148i	−0.383961	−	0.926964i	0.607230	−	0.794526i	$-0.292281\pi$
$158$	−8.44218	−	14.2893i	−0.671624	−	1.13679i
$159$	−21.2997			−1.68918
$160$	11.0393	+	12.9831i	0.872737	+	1.02640i
$161$	1.89348			0.149227
$162$	24.7288	+	41.8561i	1.94288	+	3.28852i
$163$	−5.60879	−	13.5408i	−0.439314	−	1.06060i	−0.976186	−	0.216934i	$-0.930394\pi$
$163$	−5.60879	−	13.5408i	−0.439314	−	1.06060i	0.536872	−	0.843664i	$-0.319606\pi$
$164$	4.96662	+	17.1515i	0.387828	+	1.33930i
$165$	28.4343	+	11.7779i	2.21361	+	0.916907i
$166$	−10.4873	+	13.9550i	−0.813974	+	1.08312i
$167$	1.00381	+	1.00381i	0.0776772	+	0.0776772i	0.744878	−	0.667201i	$-0.232508\pi$
$167$	1.00381	+	1.00381i	0.0776772	+	0.0776772i	−0.667201	+	0.744878i	$0.732508\pi$
$168$	−28.1906	−	10.6948i	−2.17495	−	0.825124i
$169$	−3.15549	+	3.15549i	−0.242730	+	0.242730i
$170$	−0.598454	−	4.21824i	−0.0458993	−	0.323524i
$171$	15.7094	−	37.9259i	1.20133	−	2.90027i
$172$	−0.661819	−	0.827574i	−0.0504632	−	0.0631019i
$173$	−6.72929	+	2.78736i	−0.511618	+	0.211919i	−0.623531	−	0.781799i	$-0.714302\pi$
$173$	−6.72929	+	2.78736i	−0.511618	+	0.211919i	0.111913	+	0.993718i	$0.464302\pi$
$174$	3.95794	−	15.3871i	0.300051	−	1.16649i
$175$		−	12.9512i		−	0.979018i
$176$	12.0031	−	2.07315i	0.904769	−	0.156269i
$177$			44.4636i			3.34209i
$178$	−5.54356	−	1.42594i	−0.415508	−	0.106879i
$179$	2.96704	−	1.22899i	0.221767	−	0.0918589i	−0.269034	−	0.963131i	$-0.586704\pi$
$179$	2.96704	−	1.22899i	0.221767	−	0.0918589i	0.490801	+	0.871272i	$0.336704\pi$
$180$	−5.50125	+	49.4314i	−0.410039	+	3.68440i
$181$	−3.69176	+	8.91269i	−0.274406	+	0.662475i	−0.999662	−	0.0260046i	$-0.991722\pi$
$181$	−3.69176	+	8.91269i	−0.274406	+	0.662475i	0.725256	+	0.688480i	$0.241722\pi$
$182$	−13.0000	+	1.84435i	−0.963624	+	0.136712i
$183$	32.9104	−	32.9104i	2.43280	−	2.43280i
$184$	−1.22711	−	1.15538i	−0.0904641	−	0.0851761i
$185$	−11.0020	−	11.0020i	−0.808884	−	0.808884i
$186$	−5.62628	−	4.22820i	−0.412539	−	0.310026i
$187$	−2.81340	−	1.16535i	−0.205737	−	0.0852189i
$188$	11.1466	+	6.14066i	0.812949	+	0.447854i
$189$	−21.4362	−	51.7515i	−1.55925	−	3.76437i
$190$	18.2416	−	10.7772i	1.32338	−	0.781863i
$191$	8.12413			0.587841			0.293921	−	0.955830i	$-0.405040\pi$
$191$	8.12413			0.587841			0.293921	+	0.955830i	$0.405040\pi$
$192$	11.7437	+	24.1327i	0.847528	+	1.74163i
$193$	−17.0107			−1.22445			−0.612227	−	0.790682i	$-0.709726\pi$
$193$	−17.0107			−1.22445			−0.612227	+	0.790682i	$0.709726\pi$
$194$	5.50949	−	3.25504i	0.395559	−	0.233698i
$195$	11.3009	+	27.2829i	0.809278	+	1.95377i
$196$	5.42482	+	2.98853i	0.387487	+	0.213467i
$197$	−7.65589	−	3.17117i	−0.545460	−	0.225937i	0.0928994	−	0.995676i	$-0.470387\pi$
$197$	−7.65589	−	3.17117i	−0.545460	−	0.225937i	−0.638359	+	0.769739i	$0.720387\pi$
$198$	28.4190	+	21.3572i	2.01965	+	1.51779i
$199$	7.90909	+	7.90909i	0.560660	+	0.560660i	0.929495	−	0.368835i	$-0.120243\pi$
$199$	7.90909	+	7.90909i	0.560660	+	0.560660i	−0.368835	+	0.929495i	$0.620243\pi$
$200$	−7.90270	+	8.39332i	−0.558805	+	0.593497i
$201$	−21.2063	+	21.2063i	−1.49578	+	1.49578i
$202$	18.6670	−	2.64834i	1.31340	−	0.186336i
$203$	−4.07209	+	9.83090i	−0.285805	+	0.689994i
$204$	0.742135	−	6.66844i	0.0519598	−	0.466884i
$205$	−24.8494	+	10.2929i	−1.73555	+	0.718890i
$206$	−1.43542	−	0.369225i	−0.100010	−	0.0257251i
$207$		−	4.91894i		−	0.341890i
$208$	9.55036	+	6.73721i	0.662198	+	0.467142i
$209$		−	15.1438i		−	1.04752i
$210$	11.3140	−	43.9851i	0.780743	−	3.03526i
$211$	0.540822	−	0.224016i	0.0372317	−	0.0154219i	−0.363990	−	0.931403i	$-0.618586\pi$
$211$	0.540822	−	0.224016i	0.0372317	−	0.0154219i	0.401222	+	0.915981i	$0.368586\pi$
$212$	−7.93063	−	9.91690i	−0.544678	−	0.681095i
$213$	3.09510	−	7.47223i	0.212073	−	0.511989i
$214$	−3.29498	−	23.2249i	−0.225240	−	1.58762i
$215$	1.12867	−	1.12867i	0.0769745	−	0.0769745i
$216$	−17.6861	+	46.6190i	−1.20339	+	3.17202i
$217$	3.33303	+	3.33303i	0.226261	+	0.226261i
$218$	−5.23657	+	6.96808i	−0.354665	+	0.471938i
$219$	−45.5243	−	18.8568i	−3.07625	−	1.27422i
$220$	5.10346	+	17.6240i	0.344075	+	1.18821i
$221$	−1.11816	−	2.69948i	−0.0752156	−	0.181586i
$222$	−12.4640	−	21.0966i	−0.836526	−	1.41591i
$223$	−2.04171			−0.136723			−0.0683614	−	0.997661i	$-0.521777\pi$
$223$	−2.04171			−0.136723			−0.0683614	+	0.997661i	$0.521777\pi$
$224$	−5.51698	−	17.1073i	−0.368618	−	1.14303i
$225$	−33.6450			−2.24300
$226$	2.10694	+	3.56622i	0.140152	+	0.237222i
$227$	−3.09886	−	7.48131i	−0.205679	−	0.496552i	0.787055	−	0.616882i	$-0.211605\pi$
$227$	−3.09886	−	7.48131i	−0.205679	−	0.496552i	−0.992734	+	0.120331i	$0.961605\pi$
$228$	32.0502	−	9.28090i	2.12257	−	0.614643i
$229$	−18.0468	−	7.47524i	−1.19257	−	0.493978i	−0.303977	−	0.952679i	$-0.598315\pi$
$229$	−18.0468	−	7.47524i	−1.19257	−	0.493978i	−0.888590	+	0.458701i	$0.848315\pi$
$230$	1.52524	−	2.02957i	0.100571	−	0.133826i
$231$	−22.9541	−	22.9541i	−1.51027	−	1.51027i
$232$	8.63775	−	3.88639i	0.567096	−	0.255154i
$233$	−1.07683	+	1.07683i	−0.0705457	+	0.0705457i	−0.741499	−	0.670954i	$-0.765885\pi$
$233$	−1.07683	+	1.07683i	−0.0705457	+	0.0705457i	0.670954	+	0.741499i	$0.265885\pi$
$234$	4.79130	+	33.7718i	0.313217	+	2.20773i
$235$	−7.33584	+	17.7103i	−0.478537	+	1.15529i
$236$	−20.7017	+	16.5554i	−1.34757	+	1.07766i
$237$	36.3741	−	15.0666i	2.36275	−	0.978683i
$238$	−1.11946	+	4.35205i	−0.0725635	+	0.282102i
$239$		−	8.78507i		−	0.568259i	−0.958786	−	0.284130i	$-0.908295\pi$
$239$		−	8.78507i		−	0.568259i	0.958786	−	0.284130i	$-0.0917046\pi$
$240$	−34.1716	+	21.6018i	−2.20577	+	1.39439i
$241$		−	13.6008i		−	0.876102i	−0.898950	−	0.438051i	$-0.855669\pi$
$241$		−	13.6008i		−	0.876102i	0.898950	−	0.438051i	$-0.144331\pi$
$242$	−2.36495	−	0.608325i	−0.152025	−	0.0391046i
$243$	−57.6868	+	23.8947i	−3.70061	+	1.53284i
$244$	27.5764	+	3.06899i	1.76540	+	0.196472i
$245$	−3.57020	+	8.61923i	−0.228092	+	0.550662i
$246$	−41.9383	+	5.94991i	−2.67389	+	0.379352i
$247$	10.2747	−	10.2747i	0.653761	−	0.653761i
$248$	−0.126263	−	4.19384i	−0.00801772	−	0.266309i
$249$	−29.2814	−	29.2814i	−1.85564	−	1.85564i
$250$	3.14758	+	2.36543i	0.199070	+	0.149603i
$251$	−7.95348	−	3.29444i	−0.502019	−	0.207943i	0.117279	−	0.993099i	$-0.462583\pi$
$251$	−7.95348	−	3.29444i	−0.502019	−	0.207943i	−0.619298	+	0.785156i	$0.712583\pi$
$252$	25.3129	−	45.9483i	1.59456	−	2.89447i
$253$	−0.694426	−	1.67649i	−0.0436582	−	0.105400i
$254$	24.3503	−	14.3863i	1.52787	−	0.902675i
$255$	10.1067			0.632908
$256$	−6.86332	+	14.4532i	−0.428957	+	0.903325i
$257$	11.6832			0.728780			0.364390	−	0.931246i	$-0.381278\pi$
$257$	11.6832			0.728780			0.364390	+	0.931246i	$0.381278\pi$
$258$	2.16424	−	1.27864i	0.134740	−	0.0796049i
$259$	6.28021	+	15.1618i	0.390233	+	0.942107i
$260$	−8.49486	+	15.4200i	−0.526829	+	0.956307i
$261$	25.5390	+	10.5786i	1.58083	+	0.654799i
$262$	19.3684	+	14.5555i	1.19658	+	0.899241i
$263$	17.2663	+	17.2663i	1.06468	+	1.06468i	0.997758	+	0.0669249i	$0.0213188\pi$
$263$	17.2663	+	17.2663i	1.06468	+	1.06468i	0.0669249	+	0.997758i	$0.478681\pi$
$264$	0.869555	+	28.8823i	0.0535174	+	1.77759i
$265$	13.5249	−	13.5249i	0.830829	−	0.830829i
$266$	−22.1257	+	3.13904i	−1.35661	+	0.192467i
$267$	5.19629	−	12.5449i	0.318008	−	0.767738i
$268$	−17.7693	−	1.97756i	−1.08543	−	0.120798i
$269$	13.1465	−	5.44545i	0.801556	−	0.332015i	0.0559763	−	0.998432i	$-0.482173\pi$
$269$	13.1465	−	5.44545i	0.801556	−	0.332015i	0.745579	+	0.666417i	$0.232173\pi$
$270$	−72.7383	−	18.7101i	−4.42671	−	1.13866i
$271$			4.33985i			0.263627i	0.991275	+	0.131814i	$0.0420801\pi$
$271$			4.33985i			0.263627i	−0.991275	+	0.131814i	$0.957920\pi$
$272$	3.38107	−	2.13737i	0.205008	−	0.129597i
$273$		−	31.1475i		−	1.88513i
$274$	−0.900522	+	3.50091i	−0.0544025	+	0.211498i
$275$	−11.4670	+	4.74979i	−0.691487	+	0.286423i
$276$	3.12253	−	2.49711i	0.187954	−	0.150309i
$277$	−7.14408	+	17.2473i	−0.429246	+	1.03629i	0.550281	+	0.834980i	$0.314521\pi$
$277$	−7.14408	+	17.2473i	−0.429246	+	1.03629i	−0.979527	+	0.201313i	$0.935479\pi$
$278$	−0.584509	−	4.11995i	−0.0350565	−	0.247098i
$279$	8.65866	−	8.65866i	0.518380	−	0.518380i
$280$	24.6916	−	11.1095i	1.47560	−	0.663920i
$281$	7.12723	+	7.12723i	0.425175	+	0.425175i	0.886981	−	0.461806i	$-0.152798\pi$
$281$	7.12723	+	7.12723i	0.425175	+	0.425175i	−0.461806	+	0.886981i	$0.652798\pi$
$282$	−18.1367	+	24.1337i	−1.08002	+	1.43714i
$283$	13.0940	+	5.42370i	0.778355	+	0.322405i	0.736252	−	0.676708i	$-0.236594\pi$
$283$	13.0940	+	5.42370i	0.778355	+	0.322405i	0.0421036	+	0.999113i	$0.486594\pi$
$284$	4.63140	−	1.34113i	0.274823	−	0.0795816i
$285$	19.2340	+	46.4349i	1.13932	+	2.75057i
$286$	6.40068	+	10.8338i	0.378480	+	0.640618i
$287$	28.3692			1.67458
$288$	−44.4419	+	14.3322i	−2.61876	+	0.844531i
$289$	−1.00000			−0.0588235
$290$	7.25731	+	12.2838i	0.426164	+	0.721327i
$291$	5.80922	+	14.0247i	0.340543	+	0.822142i
$292$	−8.17081	−	28.2166i	−0.478160	−	1.65125i
$293$	−20.0602	−	8.30922i	−1.17193	−	0.485430i	−0.290100	−	0.956996i	$-0.593689\pi$
$293$	−20.0602	−	8.30922i	−1.17193	−	0.485430i	−0.881830	+	0.471567i	$0.843689\pi$
$294$	−8.82676	+	11.7454i	−0.514787	+	0.685005i
$295$	−28.2336	−	28.2336i	−1.64382	−	1.64382i
$296$	5.18154	−	13.6581i	0.301171	−	0.793859i
$297$	−37.9593	+	37.9593i	−2.20262	+	2.20262i
$298$	0.270187	+	1.90443i	0.0156515	+	0.110321i
$299$	0.666305	−	1.60860i	0.0385334	−	0.0930280i
$300$	−17.0800	−	21.3577i	−0.986113	−	1.23309i
$301$	−1.55541	+	0.644270i	−0.0896521	+	0.0371351i
$302$	3.22172	−	12.5249i	0.185389	−	0.720729i
$303$			44.7254i			2.56940i
$304$	16.2545	+	11.4666i	0.932260	+	0.657654i
$305$			41.7950i			2.39317i
$306$	11.3059	+	2.90816i	0.646315	+	0.166248i
$307$	1.91987	−	0.795234i	0.109573	−	0.0453864i	−0.327224	−	0.944947i	$-0.606113\pi$
$307$	1.91987	−	0.795234i	0.109573	−	0.0453864i	0.436796	+	0.899560i	$0.356113\pi$
$308$	2.14054	−	19.2338i	0.121969	−	1.09595i
$309$	1.34550	−	3.24831i	0.0765426	−	0.184790i
$310$	6.25741	−	0.887757i	0.355397	−	0.0504212i
$311$	−7.42028	+	7.42028i	−0.420765	+	0.420765i	−0.885467	−	0.464702i	$-0.846162\pi$
$311$	−7.42028	+	7.42028i	−0.420765	+	0.420765i	0.464702	+	0.885467i	$0.346162\pi$
$312$	−19.0059	+	20.1859i	−1.07600	+	1.14280i
$313$	2.28402	+	2.28402i	0.129101	+	0.129101i	0.768705	−	0.639604i	$-0.220902\pi$
$313$	2.28402	+	2.28402i	0.129101	+	0.129101i	−0.639604	+	0.768705i	$0.720902\pi$
$314$	14.2131	+	10.6812i	0.802090	+	0.602777i
$315$	73.0050	+	30.2396i	4.11336	+	1.70381i
$316$	20.5582	+	11.3255i	1.15649	+	0.637110i
$317$	3.65879	+	8.83311i	0.205498	+	0.496117i	0.992704	−	0.120573i	$-0.0384733\pi$
$317$	3.65879	+	8.83311i	0.205498	+	0.496117i	−0.787206	+	0.616690i	$0.788473\pi$
$318$	25.9343	−	15.3221i	1.45432	−	0.859221i
$319$	10.1977			0.570963
$320$	−22.7809	−	7.86679i	−1.27349	−	0.439767i
$321$	55.6459			3.10585
$322$	−2.30548	+	1.36209i	−0.128479	+	0.0759063i
$323$	−1.90308	−	4.59445i	−0.105890	−	0.255642i
$324$	−60.2190	−	33.1746i	−3.34550	−	1.84304i
$325$	−11.0027	−	4.55745i	−0.610318	−	0.252802i
$326$	16.5699	+	12.4524i	0.917721	+	0.689675i
$327$	−14.6209	−	14.6209i	−0.808539	−	0.808539i
$328$	−18.3853	−	17.3107i	−1.01516	−	0.955821i
$329$	14.2969	−	14.2969i	0.788215	−	0.788215i
$330$	−43.0939	+	6.11385i	−2.37224	+	0.336556i
$331$	9.77337	−	23.5950i	0.537193	−	1.29690i	−0.389481	−	0.921034i	$-0.627346\pi$
$331$	9.77337	−	23.5950i	0.537193	−	1.29690i	0.926674	−	0.375865i	$-0.122654\pi$
$332$	2.73059	−	24.5356i	0.149860	−	1.34657i
$333$	39.3877	−	16.3149i	2.15843	−	0.894052i
$334$	−1.94433	−	0.500129i	−0.106389	−	0.0273659i
$335$		−	26.9313i		−	1.47141i
$336$	42.0180	−	7.25724i	2.29227	−	0.395915i
$337$			33.0237i			1.79891i	0.437009	+	0.899457i	$0.356038\pi$
$337$			33.0237i			1.79891i	−0.437009	+	0.899457i	$0.643962\pi$
$338$	1.57216	−	6.11203i	0.0855145	−	0.332450i
$339$	−9.07800	+	3.76023i	−0.493049	+	0.204228i
$340$	3.76310	+	4.70558i	0.204083	+	0.255196i
$341$	1.72870	−	4.17346i	0.0936144	−	0.226005i
$342$	8.15469	+	57.4789i	0.440955	+	3.10810i
$343$	−8.77001	+	8.77001i	−0.473536	+	0.473536i
$344$	1.40115	+	0.531561i	0.0755447	+	0.0286598i
$345$	4.25859	+	4.25859i	0.229275	+	0.229275i
$346$	6.18839	−	8.23463i	0.332690	−	0.442696i
$347$	−10.8349	−	4.48797i	−0.581649	−	0.240927i	0.0724041	−	0.997375i	$-0.476933\pi$
$347$	−10.8349	−	4.48797i	−0.581649	−	0.240927i	−0.654053	+	0.756448i	$0.726933\pi$
$348$	6.24969	+	21.5824i	0.335019	+	1.15694i
$349$	−4.00115	−	9.65963i	−0.214177	−	0.517068i	0.779880	−	0.625928i	$-0.215280\pi$
$349$	−4.00115	−	9.65963i	−0.214177	−	0.517068i	−0.994057	+	0.108861i	$0.965280\pi$
$350$	9.31654	+	15.7692i	0.497990	+	0.842900i
$351$	−51.5087			−2.74933
$352$	−13.1235	+	11.1588i	−0.699486	+	0.594765i
$353$	2.84599			0.151477			0.0757383	−	0.997128i	$-0.475869\pi$
$353$	2.84599			0.151477			0.0757383	+	0.997128i	$0.475869\pi$
$354$	−31.9853	−	54.1384i	−1.70000	−	2.87742i
$355$	2.77940	+	6.71006i	0.147515	+	0.356133i
$356$	7.77555	−	2.25160i	0.412103	−	0.119334i
$357$	−9.84859	−	4.07942i	−0.521242	−	0.215906i
$358$	−2.72855	+	3.63077i	−0.144208	+	0.191892i
$359$	19.2860	+	19.2860i	1.01788	+	1.01788i	0.999837	+	0.0180409i	$0.00574292\pi$
$359$	19.2860	+	19.2860i	1.01788	+	1.01788i	0.0180409	+	0.999837i	$0.494257\pi$
$360$	−28.8606	−	64.1445i	−1.52109	−	3.38071i
$361$	4.05223	−	4.05223i	0.213275	−	0.213275i
$362$	−1.91637	−	13.5077i	−0.100722	−	0.709948i
$363$	2.21680	−	5.35183i	0.116352	−	0.280898i
$364$	14.5019	−	11.5973i	0.760107	−	0.607864i
$365$	40.8808	−	16.9334i	2.13980	−	0.886334i
$366$	−16.3970	+	63.7456i	−0.857083	+	3.33204i
$367$			7.12896i			0.372129i	0.982538	+	0.186064i	$0.0595733\pi$
$367$			7.12896i			0.372129i	−0.982538	+	0.186064i	$0.940427\pi$
$368$	2.32526	+	0.524049i	0.121212	+	0.0273180i
$369$		−	73.6985i		−	3.83659i
$370$	21.3103	+	5.48154i	1.10787	+	0.284972i
$371$	−18.6386	+	7.72035i	−0.967667	+	0.400821i
$372$	9.89208	+	1.10090i	0.512881	+	0.0570788i
$373$	−5.45284	+	13.1643i	−0.282337	+	0.681623i	−0.999889	−	0.0148822i	$-0.995263\pi$
$373$	−5.45284	+	13.1643i	−0.282337	+	0.681623i	0.717552	+	0.696505i	$0.245263\pi$
$374$	4.26388	−	0.604928i	0.220480	−	0.0312801i
$375$	−6.60448	+	6.60448i	−0.341054	+	0.341054i
$376$	−17.9893	+	0.541601i	−0.927728	+	0.0279309i
$377$	6.91888	+	6.91888i	0.356341	+	0.356341i
$378$	63.3284	+	47.5918i	3.25726	+	2.44786i
$379$	−17.5199	−	7.25699i	−0.899938	−	0.372766i	−0.115742	−	0.993279i	$-0.536924\pi$
$379$	−17.5199	−	7.25699i	−0.899938	−	0.372766i	−0.784196	+	0.620513i	$0.786924\pi$
$380$	−14.4581	+	26.2445i	−0.741684	+	1.34631i
$381$	25.6750	+	61.9848i	1.31537	+	3.17558i
$382$	−9.89185	+	5.84416i	−0.506111	+	0.299013i
$383$	−17.1818			−0.877948			−0.438974	−	0.898500i	$-0.644658\pi$
$383$	−17.1818			−0.877948			−0.438974	+	0.898500i	$0.644658\pi$
$384$	−31.6591	−	20.9358i	−1.61559	−	1.06838i
$385$	29.1509			1.48567
$386$	20.7120	−	12.2368i	1.05421	−	0.622835i
$387$	1.67371	+	4.04068i	0.0850792	+	0.205399i
$388$	−4.36676	+	7.92660i	−0.221689	+	0.402412i
$389$	35.2901	+	14.6176i	1.78928	+	0.741143i	0.990155	+	0.139974i	$0.0447019\pi$
$389$	35.2901	+	14.6176i	1.78928	+	0.741143i	0.799122	+	0.601169i	$0.205298\pi$
$390$	−33.3861	−	25.0899i	−1.69057	−	1.27048i
$391$	−0.421361	−	0.421361i	−0.0213091	−	0.0213091i
$392$	−8.75503	+	0.263586i	−0.442196	+	0.0133131i
$393$	−40.6401	+	40.6401i	−2.05002	+	2.05002i
$394$	11.6029	−	1.64614i	0.584548	−	0.0829314i
$395$	−13.5298	+	32.6639i	−0.680760	+	1.64350i
$396$	−49.9662	−	5.56077i	−2.51089	−	0.279439i
$397$	−19.0382	+	7.88588i	−0.955500	+	0.395781i	−0.805295	−	0.592874i	$-0.797993\pi$
$397$	−19.0382	+	7.88588i	−0.955500	+	0.395781i	−0.150205	+	0.988655i	$0.547993\pi$
$398$	−15.3195	−	3.94055i	−0.767897	−	0.197522i
$399$		−	53.0123i		−	2.65394i
$400$	3.58444	−	15.9045i	0.179222	−	0.795224i
$401$		−	1.41560i		−	0.0706919i	−0.999375	−	0.0353459i	$-0.988747\pi$
$401$		−	1.41560i		−	0.0706919i	0.999375	−	0.0353459i	$-0.0112533\pi$
$402$	10.5656	−	41.0755i	0.526967	−	2.04866i
$403$	4.00445	−	1.65870i	0.199476	−	0.0826257i
$404$	−20.8236	+	16.6528i	−1.03601	+	0.828510i
$405$	39.6315	−	95.6790i	1.96931	−	4.75433i
$406$	−2.11381	−	14.8993i	−0.104906	−	0.739440i
$407$	11.1210	−	11.1210i	0.551249	−	0.551249i
$408$	3.89338	+	8.65328i	0.192751	+	0.428401i
$409$	−7.01681	−	7.01681i	−0.346959	−	0.346959i	0.512017	−	0.858975i	$-0.328899\pi$
$409$	−7.01681	−	7.01681i	−0.346959	−	0.346959i	−0.858975	+	0.512017i	$0.828899\pi$
$410$	22.8520	−	30.4082i	1.12858	−	1.50175i
$411$	−7.92248	−	3.28160i	−0.390787	−	0.161869i
$412$	2.01335	−	0.583015i	0.0991908	−	0.0287231i
$413$	16.1164	+	38.9084i	0.793037	+	1.91456i
$414$	3.53848	+	5.98925i	0.173907	+	0.294356i
$415$	37.1864			1.82541
$416$	−16.4749	−	1.33303i	−0.807747	−	0.0653570i
$417$	9.87124			0.483397
$418$	10.8938	+	18.4389i	0.532835	+	0.901878i
$419$	5.81966	+	14.0499i	0.284309	+	0.686383i	0.999927	−	0.0121096i	$-0.00385469\pi$
$419$	5.81966	+	14.0499i	0.284309	+	0.686383i	−0.715618	+	0.698492i	$0.753855\pi$
$420$	17.8652	+	61.6946i	0.871730	+	3.01039i
$421$	7.77684	+	3.22127i	0.379020	+	0.156995i	0.564056	−	0.825737i	$-0.309240\pi$
$421$	7.77684	+	3.22127i	0.379020	+	0.156995i	−0.185036	+	0.982732i	$0.559240\pi$
$422$	−0.497351	+	0.661804i	−0.0242107	+	0.0322161i
$423$	−37.1410	−	37.1410i	−1.80586	−	1.80586i
$424$	16.7901	+	6.36974i	0.815397	+	0.309342i
$425$	−2.88206	+	2.88206i	−0.139800	+	0.139800i
$426$	1.60665	+	11.3246i	0.0778425	+	0.548678i
$427$	16.8699	−	40.7274i	0.816389	−	1.97094i
$428$	20.7190	+	25.9081i	1.00149	+	1.25232i
$429$	−27.5781	+	11.4232i	−1.33148	+	0.551518i
$430$	−0.562337	+	2.18617i	−0.0271183	+	0.105426i
$431$			29.5182i			1.42184i	0.703271	+	0.710922i	$0.251722\pi$
$431$			29.5182i			1.42184i	−0.703271	+	0.710922i	$0.748278\pi$
$432$	−12.0013	−	69.4854i	−0.577414	−	3.34312i
$433$		−	11.3967i		−	0.547689i	−0.961774	−	0.273845i	$-0.911705\pi$
$433$		−	11.3967i		−	0.547689i	0.961774	−	0.273845i	$-0.0882954\pi$
$434$	−6.45591	−	1.66062i	−0.309894	−	0.0797124i
$435$	−31.2689	+	12.9520i	−1.49923	+	0.621002i
$436$	1.36345	−	12.2512i	0.0652973	−	0.586728i
$437$	1.13404	−	2.73781i	0.0542484	−	0.130967i
$438$	68.9947	−	9.78847i	3.29669	−	0.467711i
$439$	0.804103	−	0.804103i	0.0383777	−	0.0383777i	−0.687658	−	0.726035i	$-0.741361\pi$
$439$	0.804103	−	0.804103i	0.0383777	−	0.0383777i	0.726035	+	0.687658i	$0.241361\pi$
$440$	−18.8919	−	17.7876i	−0.900637	−	0.847991i
$441$	−18.0758	−	18.0758i	−0.860751	−	0.860751i
$442$	3.30335	+	2.48250i	0.157124	+	0.118080i
$443$	14.6457	+	6.06645i	0.695839	+	0.288226i	0.702430	−	0.711753i	$-0.252098\pi$
$443$	14.6457	+	6.06645i	0.695839	+	0.288226i	−0.00659180	+	0.999978i	$0.502098\pi$
$444$	30.3520	+	16.7209i	1.44044	+	0.793538i
$445$	4.66627	+	11.2654i	0.221202	+	0.534029i
$446$	2.48596	−	1.46872i	0.117714	−	0.0695458i
$447$	−4.56294			−0.215820
$448$	19.0237	+	16.8610i	0.898785	+	0.796607i
$449$	4.69194			0.221426			0.110713	−	0.993852i	$-0.464687\pi$
$449$	4.69194			0.221426			0.110713	+	0.993852i	$0.464687\pi$
$450$	40.9658	−	24.2028i	1.93114	−	1.14093i
$451$	−10.4043	−	25.1182i	−0.489919	−	1.18277i
$452$	−5.13078	−	2.82655i	−0.241332	−	0.132950i
$453$	28.3436	+	11.7403i	1.33170	+	0.551608i
$454$	9.15488	+	6.87997i	0.429660	+	0.322893i
$455$	19.7781	+	19.7781i	0.927211	+	0.927211i
$456$	−32.3477	+	34.3559i	−1.51482	+	1.60886i
$457$	18.8135	−	18.8135i	0.880058	−	0.880058i	−0.113482	−	0.993540i	$-0.536200\pi$
$457$	18.8135	−	18.8135i	0.880058	−	0.880058i	0.993540	+	0.113482i	$0.0362005\pi$
$458$	27.3510	−	3.88036i	1.27803	−	0.181317i
$459$	−6.74615	+	16.2867i	−0.314883	+	0.760196i
$460$	−0.397126	+	3.56837i	−0.0185161	+	0.166376i
$461$	26.9787	−	11.1750i	1.25653	−	0.520470i	0.347684	−	0.937612i	$-0.386968\pi$
$461$	26.9787	−	11.1750i	1.25653	−	0.520470i	0.908841	+	0.417142i	$0.136968\pi$
$462$	44.4609	+	11.4364i	2.06851	+	0.532072i
$463$		−	19.5490i		−	0.908519i	−0.890869	−	0.454260i	$-0.849904\pi$
$463$		−	19.5490i		−	0.908519i	0.890869	−	0.454260i	$-0.150096\pi$
$464$	−7.72152	+	10.9457i	−0.358462	+	0.508140i
$465$			14.9925i			0.695261i
$466$	0.536512	−	2.08577i	0.0248534	−	0.0966215i
$467$	3.09525	−	1.28209i	0.143231	−	0.0593283i	−0.309916	−	0.950764i	$-0.600301\pi$
$467$	3.09525	−	1.28209i	0.143231	−	0.0593283i	0.453148	+	0.891436i	$0.350301\pi$
$468$	−30.1279	−	37.6735i	−1.39266	−	1.74146i
$469$	−10.8704	+	26.2434i	−0.501947	+	1.21181i
$470$	−3.80800	−	26.8409i	−0.175650	−	1.23808i
$471$	−29.8229	+	29.8229i	−1.37417	+	1.37417i
$472$	13.2970	−	35.0496i	0.612043	−	1.61329i
$473$	1.14088	+	1.14088i	0.0524576	+	0.0524576i
$474$	−33.4504	+	44.5110i	−1.53643	+	2.04446i
$475$	−18.7263	−	7.75669i	−0.859221	−	0.355901i
$476$	−1.76765	−	6.10430i	−0.0810200	−	0.279790i
$477$	20.0562	+	48.4199i	0.918309	+	2.21699i
$478$	6.31962	+	10.6966i	0.289053	+	0.489252i
$479$	3.92726			0.179441			0.0897205	−	0.995967i	$-0.471403\pi$
$479$	3.92726			0.179441			0.0897205	+	0.995967i	$0.471403\pi$
$480$	26.0675	−	50.8838i	1.18982	−	2.32252i
$481$	15.0906			0.688074
$482$	9.78383	+	16.5601i	0.445641	+	0.754294i
$483$	−2.43090	−	5.86872i	−0.110610	−	0.267036i
$484$	3.31715	−	0.960560i	0.150779	−	0.0436618i
$485$	−12.5942	−	5.21668i	−0.571872	−	0.236877i
$486$	53.0500	−	70.5913i	2.40640	−	3.20209i
$487$	−12.4711	−	12.4711i	−0.565120	−	0.565120i	0.365637	−	0.930757i	$-0.380851\pi$
$487$	−12.4711	−	12.4711i	−0.565120	−	0.565120i	−0.930757	+	0.365637i	$0.880851\pi$
$488$	−35.7844	+	16.1005i	−1.61988	+	0.728837i
$489$	−34.7681	+	34.7681i	−1.57227	+	1.57227i
$490$	−1.85328	−	13.0629i	−0.0837225	−	0.590123i
$491$	−9.61259	+	23.2068i	−0.433810	+	1.04731i	0.544238	+	0.838931i	$0.316819\pi$
$491$	−9.61259	+	23.2068i	−0.433810	+	1.04731i	−0.978048	+	0.208379i	$0.933181\pi$
$492$	46.7836	−	37.4132i	2.10917	−	1.68672i
$493$	3.09387	−	1.28152i	0.139341	−	0.0577169i
$494$	−5.11916	+	19.9015i	−0.230322	+	0.895410i
$495$		−	75.7291i		−	3.40377i
$496$	3.17061	+	5.01555i	0.142365	+	0.225205i
$497$		−	7.66053i		−	0.343622i
$498$	56.7166	+	14.5889i	2.54153	+	0.653745i
$499$	−27.0887	+	11.2205i	−1.21266	+	0.502299i	−0.895068	−	0.445930i	$-0.852873\pi$
$499$	−27.0887	+	11.2205i	−1.21266	+	0.502299i	−0.317588	+	0.948229i	$0.602873\pi$
$500$	−5.53405	−	0.615888i	−0.247490	−	0.0275433i
$501$	1.82252	−	4.39996i	0.0814244	−	0.196576i
$502$	12.0539	−	1.71013i	0.537994	−	0.0763267i
$503$	7.43608	−	7.43608i	0.331559	−	0.331559i	−0.521620	−	0.853178i	$-0.674672\pi$
$503$	7.43608	−	7.43608i	0.331559	−	0.331559i	0.853178	+	0.521620i	$0.174672\pi$
$504$	2.23258	+	74.1552i	0.0994469	+	3.30314i
$505$	−28.3998	−	28.3998i	−1.26377	−	1.26377i
$506$	2.05152	+	1.54174i	0.0912014	+	0.0685386i
$507$	13.8314	+	5.72914i	0.614272	+	0.254440i
$508$	−19.2997	+	35.0331i	−0.856288	+	1.55434i
$509$	−8.17333	−	19.7322i	−0.362276	−	0.874612i	−0.994967	−	0.100207i	$-0.968049\pi$
$509$	−8.17333	−	19.7322i	−0.362276	−	0.874612i	0.632690	−	0.774405i	$-0.281951\pi$
$510$	−12.3059	+	7.27036i	−0.544912	+	0.321937i
$511$	−46.6715			−2.06463
$512$	−2.04033	−	22.5352i	−0.0901705	−	0.995926i
$513$	−87.6667			−3.87058
$514$	−14.2254	+	8.40443i	−0.627454	+	0.370703i
$515$	1.20826	+	2.91699i	0.0532421	+	0.128538i
$516$	−1.71535	+	3.11373i	−0.0755141	+	0.137074i
$517$	−17.9019	−	7.41520i	−0.787324	−	0.326120i
$518$	−18.5535	−	13.9431i	−0.815193	−	0.612624i
$519$	17.2785	+	17.2785i	0.758442	+	0.758442i
$520$	−0.749240	−	24.8861i	−0.0328564	−	1.09133i
$521$	27.3920	−	27.3920i	1.20007	−	1.20007i	0.225922	−	0.974145i	$-0.427461\pi$
$521$	27.3920	−	27.3920i	1.20007	−	1.20007i	0.974145	−	0.225922i	$-0.0725395\pi$
$522$	−38.7058	+	5.49131i	−1.69411	+	0.240348i
$523$	2.16741	−	5.23259i	0.0947742	−	0.228805i	−0.869382	−	0.494141i	$-0.835483\pi$
$523$	2.16741	−	5.23259i	0.0947742	−	0.228805i	0.964156	+	0.265336i	$0.0854827\pi$
$524$	−34.0533	−	3.78981i	−1.48763	−	0.165559i
$525$	−40.1414	+	16.6271i	−1.75191	+	0.725666i
$526$	−33.4438	−	8.60258i	−1.45822	−	0.375090i
$527$		−	1.48342i		−	0.0646187i
$528$	−21.8355	−	34.5413i	−0.950269	−	1.50322i
$529$			22.6449i			0.984561i
$530$	−6.73853	+	26.1971i	−0.292703	+	1.13793i
$531$	101.078	−	41.8677i	4.38639	−	1.81690i
$532$	24.6819	−	19.7384i	1.07010	−	0.855767i
$533$	9.98298	−	24.1010i	0.432411	−	1.04393i
$534$	2.69737	+	19.0126i	0.116727	+	0.822755i
$535$	−35.3342	+	35.3342i	−1.52763	+	1.52763i
$536$	23.0583	−	10.3746i	0.995966	−	0.448116i
$537$	−7.61834	−	7.61834i	−0.328756	−	0.328756i
$538$	−12.0898	+	16.0874i	−0.521228	+	0.693576i
$539$	−8.71248	−	3.60883i	−0.375273	−	0.155443i
$540$	102.025	−	29.5437i	4.39044	−	1.27136i
$541$	6.38949	+	15.4256i	0.274706	+	0.663198i	0.999673	−	0.0255854i	$-0.00814498\pi$
$541$	6.38949	+	15.4256i	0.274706	+	0.663198i	−0.724967	+	0.688784i	$0.758145\pi$
$542$	−3.12191	−	5.28416i	−0.134098	−	0.226974i
$543$	32.3639			1.38887
$544$	−2.57923	+	5.03464i	−0.110583	+	0.215858i
$545$	18.5681			0.795368
$546$	22.4062	+	37.9248i	0.958897	+	1.62303i
$547$	−14.3425	−	34.6259i	−0.613241	−	1.48050i	−0.859420	−	0.511271i	$-0.829175\pi$
$547$	−14.3425	−	34.6259i	−0.613241	−	1.48050i	0.246178	−	0.969225i	$-0.420825\pi$
$548$	−1.42195	−	4.91047i	−0.0607425	−	0.209765i
$549$	−105.803	−	43.8250i	−4.51556	−	1.87041i
$550$	10.5453	−	14.0322i	0.449654	−	0.598335i
$551$	11.7758	+	11.7758i	0.501666	+	0.501666i
$552$	−2.00564	+	5.28668i	−0.0853656	+	0.225016i
$553$	26.3685	−	26.3685i	1.12130	−	1.12130i
$554$	−3.70846	−	26.1393i	−0.157557	−	1.11055i
$555$	−19.9753	+	48.2247i	−0.847906	+	2.04702i
$556$	3.67541	+	4.59594i	0.155872	+	0.194911i
$557$	−19.4173	+	8.04291i	−0.822738	+	0.340789i	−0.754024	−	0.656847i	$-0.771890\pi$
$557$	−19.4173	+	8.04291i	−0.822738	+	0.340789i	−0.0687140	+	0.997636i	$0.521890\pi$
$558$	−4.31401	+	16.7714i	−0.182627	+	0.709989i
$559$			1.54811i			0.0654780i
$560$	−22.0725	+	31.2889i	−0.932732	+	1.32220i
$561$			10.2161i			0.431323i
$562$	−13.8051	−	3.55101i	−0.582332	−	0.149790i
$563$	−4.10874	+	1.70190i	−0.173163	+	0.0717263i	−0.467581	−	0.883950i	$-0.654874\pi$
$563$	−4.10874	+	1.70190i	−0.173163	+	0.0717263i	0.294418	+	0.955677i	$0.404874\pi$
$564$	4.72225	−	42.4317i	0.198843	−	1.78670i
$565$	3.37669	−	8.15205i	0.142058	−	0.342959i
$566$	−19.8446	+	2.81542i	−0.834133	+	0.118341i
$567$	−77.2385	+	77.2385i	−3.24371	+	3.24371i
$568$	−4.67439	+	4.96459i	−0.196133	+	0.208309i
$569$	29.4002	+	29.4002i	1.23252	+	1.23252i	0.962993	+	0.269527i	$0.0868673\pi$
$569$	29.4002	+	29.4002i	1.23252	+	1.23252i	0.269527	+	0.962993i	$0.413133\pi$
$570$	−56.8224	−	42.7025i	−2.38003	−	1.78861i
$571$	−11.1667	−	4.62541i	−0.467313	−	0.193567i	0.136586	−	0.990628i	$-0.456387\pi$
$571$	−11.1667	−	4.62541i	−0.467313	−	0.193567i	−0.603899	+	0.797061i	$0.706387\pi$
$572$	−15.5868	−	8.58677i	−0.651717	−	0.359031i
$573$	−10.4300	−	25.1802i	−0.435719	−	1.05192i
$574$	−34.5421	+	20.4076i	−1.44176	+	0.851799i
$575$	−2.42878			−0.101287
$576$	43.8020	−	49.4203i	1.82508	−	2.05918i
$577$	18.2628			0.760289			0.380144	−	0.924927i	$-0.375874\pi$
$577$	18.2628			0.760289			0.380144	+	0.924927i	$0.375874\pi$
$578$	1.21759	−	0.719358i	0.0506450	−	0.0299214i
$579$	21.8388	+	52.7235i	0.907588	+	2.19111i
$580$	−17.6728	−	9.73596i	−0.733825	−	0.404264i
$581$	−36.2365	−	15.0097i	−1.50335	−	0.622706i
$582$	−17.1620	−	12.8974i	−0.711389	−	0.534615i
$583$	13.6712	+	13.6712i	0.566205	+	0.566205i
$584$	30.2466	+	28.4785i	1.25161	+	1.17845i
$585$	51.3801	−	51.3801i	2.12431	−	2.12431i
$586$	30.4024	−	4.31328i	1.25591	−	0.178180i
$587$	13.3694	−	32.2765i	0.551813	−	1.33219i	−0.364303	−	0.931280i	$-0.618693\pi$
$587$	13.3694	−	32.2765i	0.551813	−	1.33219i	0.916116	−	0.400913i	$-0.131307\pi$
$588$	2.29822	−	20.6507i	0.0947772	−	0.851619i
$589$	6.81549	−	2.82307i	0.280827	−	0.116323i
$590$	54.6870	+	14.0668i	2.25143	+	0.579123i
$591$			27.8002i			1.14355i
$592$	3.51606	+	20.3573i	0.144509	+	0.836680i
$593$		−	38.1497i		−	1.56662i	−0.621631	−	0.783310i	$-0.713530\pi$
$593$		−	38.1497i		−	1.56662i	0.621631	−	0.783310i	$-0.286470\pi$
$594$	18.9125	−	73.5252i	0.775989	−	3.01678i
$595$	8.84403	−	3.66332i	0.362570	−	0.150181i
$596$	−1.69895	−	2.12445i	−0.0695915	−	0.0870210i
$597$	14.3598	−	34.6676i	0.587707	−	1.41885i
$598$	0.345876	+	2.43793i	0.0141439	+	0.0996944i
$599$	−21.7920	+	21.7920i	−0.890395	+	0.890395i	−0.994560	−	0.104165i	$-0.966783\pi$
$599$	−21.7920	+	21.7920i	−0.890395	+	0.890395i	0.104165	+	0.994560i	$0.466783\pi$
$600$	36.1603	+	13.7183i	1.47624	+	0.560048i
$601$	−9.68422	−	9.68422i	−0.395028	−	0.395028i	0.481447	−	0.876475i	$-0.340111\pi$
$601$	−9.68422	−	9.68422i	−0.395028	−	0.395028i	−0.876475	+	0.481447i	$0.840111\pi$
$602$	1.43038	−	1.90335i	0.0582981	−	0.0775748i
$603$	68.1758	+	28.2394i	2.77634	+	1.15000i
$604$	5.08718	+	17.5678i	0.206994	+	0.714823i
$605$	1.99069	+	4.80595i	0.0809330	+	0.195389i
$606$	−32.1736	−	54.4571i	−1.30696	−	2.21217i
$607$	41.8081			1.69694			0.848469	−	0.529245i	$-0.177525\pi$
$607$	41.8081			1.69694			0.848469	+	0.529245i	$0.177525\pi$
$608$	−28.0399	−	2.26878i	−1.13717	−	0.0920113i
$609$	35.6981			1.44656
$610$	−30.0656	−	50.8891i	−1.21732	−	2.06044i
$611$	−7.11492	−	17.1769i	−0.287839	−	0.694905i
$612$	−15.8579	+	4.59205i	−0.641019	+	0.185623i
$613$	−14.8196	−	6.13850i	−0.598560	−	0.247932i	0.0627687	−	0.998028i	$-0.480007\pi$
$613$	−14.8196	−	6.13850i	−0.598560	−	0.247932i	−0.661328	+	0.750097i	$0.730007\pi$
$614$	−1.76555	+	2.34934i	−0.0712518	+	0.0948117i
$615$	63.8046	+	63.8046i	2.57285	+	2.57285i
$616$	11.2297	+	24.9587i	0.452457	+	1.00561i
$617$	−7.14338	+	7.14338i	−0.287582	+	0.287582i	−0.836123	−	0.548542i	$-0.815183\pi$
$617$	−7.14338	+	7.14338i	−0.287582	+	0.287582i	0.548542	+	0.836123i	$0.315183\pi$
$618$	0.698441	+	4.92301i	0.0280954	+	0.198032i
$619$	11.9929	−	28.9534i	0.482034	−	1.16373i	−0.476607	−	0.879116i	$-0.658134\pi$
$619$	11.9929	−	28.9534i	0.482034	−	1.16373i	0.958641	−	0.284617i	$-0.0918665\pi$
$620$	−6.98034	+	5.58225i	−0.280337	+	0.224188i
$621$	−9.70513	+	4.02000i	−0.389453	+	0.161317i
$622$	3.69701	−	14.3727i	0.148237	−	0.576292i
$623$		−	12.8611i		−	0.515268i
$624$	8.62053	−	38.2501i	0.345098	−	1.53123i
$625$		−	28.7667i		−	1.15067i
$626$	−4.42403	−	1.13797i	−0.176820	−	0.0454825i
$627$	−46.9373	+	19.4421i	−1.87449	+	0.776441i
$628$	−24.9893	−	2.78108i	−0.997182	−	0.110977i
$629$	1.97644	−	4.77154i	0.0788057	−	0.190254i
$630$	−110.643	+	15.6973i	−4.40813	+	0.625394i
$631$	13.8913	−	13.8913i	0.553003	−	0.553003i	−0.374303	−	0.927306i	$-0.622118\pi$
$631$	13.8913	−	13.8913i	0.553003	−	0.553003i	0.927306	+	0.374303i	$0.122118\pi$
$632$	−33.1786	+	0.998901i	−1.31977	+	0.0397342i
$633$	−1.38864	−	1.38864i	−0.0551937	−	0.0551937i
$634$	−10.8091	−	8.12311i	−0.429283	−	0.322610i
$635$	−55.6624	−	23.0561i	−2.20889	−	0.914954i
$636$	−20.5552	+	37.3121i	−0.815067	+	1.47952i
$637$	−3.46269	−	8.35967i	−0.137197	−	0.331222i
$638$	−12.4167	+	7.33582i	−0.491580	+	0.290428i
$639$	−19.9008			−0.787262
$640$	33.3968	−	6.80908i	1.32012	−	0.269153i
$641$	1.45180			0.0573426			0.0286713	−	0.999589i	$-0.490872\pi$
$641$	1.45180			0.0573426			0.0286713	+	0.999589i	$0.490872\pi$
$642$	−67.7539	+	40.0294i	−2.67403	+	1.57983i
$643$	−2.02469	−	4.88803i	−0.0798459	−	0.192765i	0.878915	−	0.476978i	$-0.158268\pi$
$643$	−2.02469	−	4.88803i	−0.0798459	−	0.192765i	−0.958761	+	0.284213i	$0.908268\pi$
$644$	1.82730	−	3.31693i	0.0720056	−	0.130706i
$645$	−4.94725	−	2.04922i	−0.194798	−	0.0806878i
$646$	5.62223	+	4.22516i	0.221204	+	0.166237i
$647$	4.44382	+	4.44382i	0.174705	+	0.174705i	0.789043	−	0.614338i	$-0.210577\pi$
$647$	4.44382	+	4.44382i	0.174705	+	0.174705i	−0.614338	+	0.789043i	$0.710577\pi$
$648$	97.1865	−	2.92598i	3.81785	−	0.114943i
$649$	28.5390	−	28.5390i	1.12025	−	1.12025i
$650$	16.6752	−	2.36575i	0.654054	−	0.0927924i
$651$	6.05148	−	14.6096i	0.237176	−	0.572594i
$652$	−29.1331	−	3.24224i	−1.14094	−	0.126976i
$653$	−22.4226	+	9.28775i	−0.877464	+	0.363458i	−0.775513	−	0.631332i	$-0.782509\pi$
$653$	−22.4226	+	9.28775i	−0.877464	+	0.363458i	−0.101951	+	0.994789i	$0.532509\pi$
$654$	28.3200	+	7.28460i	1.10740	+	0.284850i
$655$		−	51.6114i		−	2.01663i
$656$	34.8384	+	7.85161i	1.36021	+	0.306554i
$657$			121.245i			4.73020i
$658$	−7.12317	+	27.6924i	−0.277690	+	1.07956i
$659$	1.51637	−	0.628102i	0.0590695	−	0.0244674i	−0.352953	−	0.935641i	$-0.614822\pi$
$659$	1.51637	−	0.628102i	0.0590695	−	0.0244674i	0.412023	+	0.911174i	$0.364822\pi$
$660$	48.0726	−	38.4441i	1.87122	−	1.49643i
$661$	−5.47330	+	13.2137i	−0.212887	+	0.513954i	−0.993864	−	0.110605i	$-0.964721\pi$
$661$	−5.47330	+	13.2137i	−0.212887	+	0.513954i	0.780978	+	0.624559i	$0.214721\pi$
$662$	5.07331	+	35.7596i	0.197180	+	1.38984i
$663$	−6.93133	+	6.93133i	−0.269191	+	0.269191i
$664$	14.3252	+	31.8386i	0.555925	+	1.23558i
$665$	33.6619	+	33.6619i	1.30535	+	1.30535i
$666$	−36.2218	+	48.1988i	−1.40357	+	1.86766i
$667$	1.84362	+	0.763653i	0.0713853	+	0.0295687i
$668$	2.72716	−	0.789716i	0.105517	−	0.0305550i
$669$	2.62120	+	6.32813i	0.101341	+	0.244660i
$670$	19.3732	+	32.7912i	0.748453	+	1.26684i
$671$	−42.2471			−1.63093
$672$	−45.9401	+	39.0623i	−1.77218	+	1.50686i
$673$	−2.43618			−0.0939078			−0.0469539	−	0.998897i	$-0.514951\pi$
$673$	−2.43618			−0.0939078			−0.0469539	+	0.998897i	$0.514951\pi$
$674$	−23.7559	−	40.2093i	−0.915042	−	1.54880i
$675$	27.4963	+	66.3819i	1.05833	+	2.55504i
$676$	2.48249	+	8.57289i	0.0954802	+	0.329726i
$677$	−3.52422	−	1.45978i	−0.135447	−	0.0561039i	0.313930	−	0.949446i	$-0.398354\pi$
$677$	−3.52422	−	1.45978i	−0.135447	−	0.0561039i	−0.449377	+	0.893342i	$0.648354\pi$
$678$	8.34832	−	11.1088i	0.320615	−	0.426629i
$679$	10.1669	+	10.1669i	0.390169	+	0.390169i
$680$	−7.96691	−	3.02245i	−0.305517	−	0.115906i
$681$	−19.2094	+	19.2094i	−0.736107	+	0.736107i
$682$	0.897361	+	6.32511i	0.0343617	+	0.242201i
$683$	15.1581	−	36.5948i	0.580007	−	1.40026i	−0.312798	−	0.949820i	$-0.601266\pi$
$683$	15.1581	−	36.5948i	0.580007	−	1.40026i	0.892806	−	0.450442i	$-0.148734\pi$
$684$	−51.2770	−	64.1195i	−1.96062	−	2.45167i
$685$	7.11439	−	2.94688i	0.271827	−	0.112594i
$686$	4.36949	−	16.9870i	0.166828	−	0.648568i
$687$			65.5319i			2.50020i
$688$	−2.08840	+	0.360703i	−0.0796196	+	0.0137517i
$689$			18.5511i			0.706742i
$690$	−8.24866	−	2.12176i	−0.314021	−	0.0807740i
$691$	31.4687	−	13.0348i	1.19713	−	0.495866i	0.307058	−	0.951691i	$-0.400656\pi$
$691$	31.4687	−	13.0348i	1.19713	−	0.495866i	0.890070	+	0.455825i	$0.150656\pi$
$692$	−1.61127	+	14.4781i	−0.0612514	+	0.550374i
$693$	−30.5668	+	73.7948i	−1.16114	+	2.80323i
$694$	16.4210	−	2.32969i	0.623331	−	0.0884337i
$695$	−6.26806	+	6.26806i	−0.237761	+	0.237761i
$696$	−23.1350	−	21.7827i	−0.876930	−	0.825670i
$697$	−6.31308	−	6.31308i	−0.239125	−	0.239125i
$698$	11.8205	+	8.88320i	0.447412	+	0.336234i
$699$	4.72005	+	1.95511i	0.178529	+	0.0739490i
$700$	−22.6874	−	12.4985i	−0.857505	−	0.472399i
$701$	7.12595	+	17.2036i	0.269143	+	0.649770i	0.999444	−	0.0333568i	$-0.0106198\pi$
$701$	7.12595	+	17.2036i	0.269143	+	0.649770i	−0.730300	+	0.683126i	$0.760620\pi$
$702$	62.7165	−	37.0532i	2.36708	−	1.39848i
$703$	25.6839			0.968688
$704$	7.95190	−	23.0273i	0.299699	−	0.867875i
$705$	64.3098			2.42205
$706$	−3.46524	+	2.04728i	−0.130416	+	0.0770506i
$707$	16.2113	+	39.1375i	0.609688	+	1.47192i
$708$	77.8898	+	42.9095i	2.92728	+	1.61264i
$709$	17.1135	+	7.08865i	0.642711	+	0.266220i	0.680143	−	0.733079i	$-0.261918\pi$
$709$	17.1135	+	7.08865i	0.642711	+	0.266220i	−0.0374317	+	0.999299i	$0.511918\pi$
$710$	−8.21111	−	6.17072i	−0.308157	−	0.231583i
$711$	−68.5009	−	68.5009i	−2.56899	−	2.56899i
$712$	−7.84772	+	8.33493i	−0.294106	+	0.312365i
$713$	0.625055	−	0.625055i	0.0234085	−	0.0234085i
$714$	14.9261	−	2.11761i	0.558595	−	0.0792495i
$715$	10.2580	−	24.7651i	0.383629	−	0.926162i
$716$	0.710434	−	6.38359i	0.0265502	−	0.238566i
$717$	−27.2288	+	11.2785i	−1.01688	+	0.421204i
$718$	−37.3560	−	9.60890i	−1.39412	−	0.358601i
$719$			39.8816i			1.48733i	0.668550	+	0.743667i	$0.266915\pi$
$719$			39.8816i			1.48733i	−0.668550	+	0.743667i	$0.733085\pi$
$720$	81.2832	+	57.3405i	3.02925	+	2.13695i
$721$		−	3.33017i		−	0.124022i
$722$	−2.01895	+	7.84896i	−0.0751374	+	0.292108i
$723$	−42.1547	+	17.4610i	−1.56775	+	0.649383i
$724$	12.0502	+	15.0683i	0.447843	+	0.560007i
$725$	5.22330	−	12.6102i	0.193988	−	0.468329i
$726$	1.15073	+	8.11101i	0.0427076	+	0.301028i
$727$	−31.3657	+	31.3657i	−1.16329	+	1.16329i	−0.179541	+	0.983751i	$0.557461\pi$
$727$	−31.3657	+	31.3657i	−1.16329	+	1.16329i	−0.983751	+	0.179541i	$0.942539\pi$
$728$	−9.31475	+	24.5528i	−0.345228	+	0.909989i
$729$	75.1970	+	75.1970i	2.78507	+	2.78507i
$730$	−37.5949	+	50.0259i	−1.39145	+	1.85154i
$731$	0.489500	+	0.202757i	0.0181048	+	0.00749926i
$732$	−25.8912	−	89.4113i	−0.956966	−	3.30474i
$733$	−3.44403	−	8.31463i	−0.127208	−	0.307108i	0.847425	−	0.530915i	$-0.178152\pi$
$733$	−3.44403	−	8.31463i	−0.127208	−	0.307108i	−0.974634	+	0.223807i	$0.928152\pi$
$734$	−5.12828	−	8.68014i	−0.189288	−	0.320390i
$735$	31.2983			1.15445
$736$	−3.20819	+	1.03462i	−0.118255	+	0.0381365i
$737$	27.2226			1.00276
$738$	53.0156	+	89.7344i	1.95153	+	3.30317i
$739$	14.3940	+	34.7502i	0.529492	+	1.27831i	0.931857	+	0.362826i	$0.118188\pi$
$739$	14.3940	+	34.7502i	0.529492	+	1.27831i	−0.402365	+	0.915479i	$0.631812\pi$
$740$	−29.8904	+	8.65549i	−1.09879	+	0.318182i
$741$	−45.0366	−	18.6548i	−1.65446	−	0.685300i
$742$	17.1404	−	22.8080i	0.629245	−	0.837309i
$743$	27.4023	+	27.4023i	1.00529	+	1.00529i	0.999986	+	0.00530514i	$0.00168869\pi$
$743$	27.4023	+	27.4023i	1.00529	+	1.00529i	0.00530514	+	0.999986i	$0.498311\pi$
$744$	−12.8364	+	5.77551i	−0.470607	+	0.211741i
$745$	2.89739	−	2.89739i	0.106152	−	0.106152i
$746$	−2.83055	−	19.9513i	−0.103634	−	0.730469i
$747$	−38.9926	+	94.1364i	−1.42666	+	3.44427i
$748$	−4.75649	+	3.80381i	−0.173914	+	0.139081i
$749$	48.6937	−	20.1696i	1.77923	−	0.736981i
$750$	3.29055	−	12.7925i	0.120154	−	0.467117i
$751$		−	35.8931i		−	1.30976i	−0.755733	−	0.654880i	$-0.772719\pi$
$751$		−	35.8931i		−	1.30976i	0.755733	−	0.654880i	$-0.227281\pi$
$752$	21.5140	−	13.6002i	0.784535	−	0.495949i
$753$			28.8808i			1.05247i
$754$	−13.4015	−	3.44720i	−0.488054	−	0.125540i
$755$	−25.4526	+	10.5428i	−0.926314	+	0.383692i
$756$	−111.343	−	12.3915i	−4.04952	−	0.450674i
$757$	−13.3280	+	32.1767i	−0.484415	+	1.16948i	0.473076	+	0.881022i	$0.343144\pi$
$757$	−13.3280	+	32.1767i	−0.484415	+	1.16948i	−0.957492	+	0.288461i	$0.906856\pi$
$758$	26.5524	−	3.76707i	0.964428	−	0.136826i
$759$	−4.30466	+	4.30466i	−0.156249	+	0.156249i
$760$	−1.27519	−	42.3555i	−0.0462560	−	1.53640i
$761$	−17.7964	−	17.7964i	−0.645119	−	0.645119i	0.306690	−	0.951809i	$-0.400778\pi$
$761$	−17.7964	−	17.7964i	−0.645119	−	0.645119i	−0.951809	+	0.306690i	$0.900778\pi$
$762$	−75.8509	−	57.0026i	−2.74779	−	2.06499i
$763$	−18.0938	−	7.49469i	−0.655039	−	0.271326i
$764$	7.84016	−	14.2316i	0.283647	−	0.514880i
$765$	−9.51668	−	22.9753i	−0.344076	−	0.830674i
$766$	20.9204	−	12.3599i	0.755883	−	0.446580i
$767$	38.7259			1.39831
$768$	53.6081	+	2.71699i	1.93441	+	0.0980408i
$769$	10.8715			0.392036			0.196018	−	0.980600i	$-0.437199\pi$
$769$	10.8715			0.392036			0.196018	+	0.980600i	$0.437199\pi$
$770$	−35.4938	+	20.9699i	−1.27911	+	0.755704i
$771$	−14.9993	−	36.2114i	−0.540185	−	1.30412i
$772$	−16.4161	+	29.7987i	−0.590828	+	1.07248i
$773$	−4.16297	−	1.72436i	−0.149732	−	0.0620209i	0.306559	−	0.951852i	$-0.400822\pi$
$773$	−4.16297	−	1.72436i	−0.149732	−	0.0620209i	−0.456291	+	0.889831i	$0.650822\pi$
$774$	−4.94458	−	3.71590i	−0.177729	−	0.133565i
$775$	−4.27530	−	4.27530i	−0.153573	−	0.153573i
$776$	−0.385145	−	12.7926i	−0.0138259	−	0.459228i
$777$	38.9302	−	38.9302i	1.39661	−	1.39661i
$778$	−53.4841	+	7.58794i	−1.91750	+	0.272041i
$779$	16.9908	−	41.0195i	0.608759	−	1.46967i
$780$	58.6992	+	6.53267i	2.10177	+	0.233907i
$781$	−6.78266	+	2.80947i	−0.242703	+	0.100531i
$782$	0.816154	+	0.209935i	0.0291856	+	0.00750726i
$783$		−	59.0341i		−	2.10971i
$784$	10.4704	−	6.61895i	0.373944	−	0.236391i
$785$		−	37.8740i		−	1.35178i
$786$	20.2481	−	78.7177i	0.722227	−	2.80777i
$787$	3.99059	−	1.65296i	0.142249	−	0.0589215i	−0.310423	−	0.950598i	$-0.600471\pi$
$787$	3.99059	−	1.65296i	0.142249	−	0.0589215i	0.452672	+	0.891677i	$0.350471\pi$
$788$	−12.9435	+	10.3510i	−0.461091	+	0.368739i
$789$	31.3487	−	75.6826i	1.11604	−	2.69437i
$790$	−7.02328	−	49.5040i	−0.249877	−	1.76127i
$791$	−6.58088	+	6.58088i	−0.233989	+	0.233989i
$792$	64.8384	−	29.1728i	2.30393	−	1.03661i
$793$	−28.6635	−	28.6635i	−1.01787	−	1.01787i
$794$	17.5079	−	23.2971i	0.621333	−	0.826782i
$795$	−59.2833	−	24.5559i	−2.10256	−	0.870910i
$796$	21.4875	−	6.22223i	0.761605	−	0.220541i
$797$	0.365208	+	0.881689i	0.0129363	+	0.0312310i	0.930216	−	0.367013i	$-0.119620\pi$
$797$	0.365208	+	0.881689i	0.0129363	+	0.0312310i	−0.917279	+	0.398244i	$0.869620\pi$
$798$	38.1349	+	64.5472i	1.34996	+	2.28495i
$799$	−6.36307			−0.225109
$800$	7.07665	+	21.9436i	0.250198	+	0.775824i
$801$	−33.4109			−1.18052
$802$	1.01833	+	1.72362i	0.0359583	+	0.0608633i
$803$	17.1166	+	41.3231i	0.604031	+	1.45826i
$804$	16.6834	+	57.6136i	0.588379	+	2.03188i
$805$	5.27011	+	2.18295i	0.185747	+	0.0769389i
$806$	−3.68258	+	4.90025i	−0.129713	+	0.172604i
$807$	−33.7557	−	33.7557i	−1.18826	−	1.18826i
$808$	13.3753	−	35.2560i	0.470540	−	1.24030i
$809$	9.07340	−	9.07340i	0.319004	−	0.319004i	−0.529381	−	0.848384i	$-0.677576\pi$
$809$	9.07340	−	9.07340i	0.319004	−	0.319004i	0.848384	+	0.529381i	$0.177576\pi$
$810$	20.5725	+	145.007i	0.722846	+	5.09503i
$811$	−13.3079	+	32.1280i	−0.467302	+	1.12817i	0.498034	+	0.867157i	$0.334055\pi$
$811$	−13.3079	+	32.1280i	−0.467302	+	1.12817i	−0.965336	+	0.261009i	$0.915945\pi$
$812$	13.2917	+	16.6206i	0.466447	+	0.583270i
$813$	13.4511	−	5.57163i	0.471751	−	0.195405i
$814$	−5.54084	+	21.5409i	−0.194206	+	0.755007i
$815$		−	44.1543i		−	1.54666i
$816$	−10.9654	−	7.73541i	−0.383864	−	0.270793i
$817$			2.63485i			0.0921817i
$818$	13.5912	+	3.49599i	0.475205	+	0.122234i
$819$	−70.8065	+	29.3290i	−2.47418	+	1.02484i
$820$	−5.94998	+	53.4634i	−0.207782	+	1.86702i
$821$	10.9601	−	26.4600i	0.382510	−	0.923461i	−0.608969	−	0.793194i	$-0.708417\pi$
$821$	10.9601	−	26.4600i	0.382510	−	0.923461i	0.991479	−	0.130267i	$-0.0415834\pi$
$822$	12.0070	−	1.70346i	0.418791	−	0.0594151i
$823$	26.7282	−	26.7282i	0.931686	−	0.931686i	−0.0661254	−	0.997811i	$-0.521064\pi$
$823$	26.7282	−	26.7282i	0.931686	−	0.931686i	0.997811	+	0.0661254i	$0.0210637\pi$
$824$	−2.03204	+	2.15820i	−0.0707895	+	0.0751843i
$825$	29.4434	+	29.4434i	1.02509	+	1.02509i
$826$	−47.6123	−	35.7810i	−1.65664	−	1.24498i
$827$	−47.4945	−	19.6729i	−1.65155	−	0.684093i	−0.654160	−	0.756356i	$-0.726978\pi$
$827$	−47.4945	−	19.6729i	−1.65155	−	0.684093i	−0.997386	+	0.0722631i	$0.976978\pi$
$828$	−8.61683	−	4.74701i	−0.299456	−	0.164970i
$829$	6.75131	+	16.2991i	0.234483	+	0.566091i	0.996695	−	0.0812360i	$-0.0258867\pi$
$829$	6.75131	+	16.2991i	0.234483	+	0.566091i	−0.762212	+	0.647327i	$0.775887\pi$
$830$	−45.2777	+	26.7503i	−1.57161	+	0.928517i
$831$	62.6288			2.17257
$832$	21.0186	−	10.2283i	0.728688	−	0.354601i
$833$	−3.09677			−0.107297
$834$	−12.0191	+	7.10096i	−0.416188	+	0.245886i
$835$	1.63663	+	3.95117i	0.0566378	+	0.136736i
$836$	−26.5284	−	14.6145i	−0.917504	−	0.505453i
$837$	−24.1599	−	10.0074i	−0.835089	−	0.345905i
$838$	−17.1929	−	12.9206i	−0.593918	−	0.446334i
$839$	14.5876	+	14.5876i	0.503619	+	0.503619i	0.912560	−	0.408942i	$-0.134102\pi$
$839$	14.5876	+	14.5876i	0.503619	+	0.503619i	−0.408942	+	0.912560i	$0.634102\pi$
$840$	−66.1329	−	62.2672i	−2.28180	−	2.14842i
$841$	12.5764	−	12.5764i	0.433668	−	0.433668i
$842$	−11.7862	+	1.67215i	−0.406181	+	0.0576260i
$843$	12.9402	−	31.2405i	0.445686	−	1.07598i
$844$	0.129495	−	1.16358i	0.00445742	−	0.0400520i
$845$	−12.4206	+	5.14477i	−0.427280	+	0.176985i
$846$	71.9402	+	18.5048i	2.47335	+	0.636208i
$847$		−	5.48670i		−	0.188525i
$848$	−25.0255	+	4.32234i	−0.859380	+	0.148430i
$849$		−	47.5470i		−	1.63181i
$850$	1.43593	−	5.58240i	0.0492521	−	0.191475i
$851$	2.84334	−	1.17775i	0.0974683	−	0.0403727i
$852$	−10.1027	−	12.6329i	−0.346112	−	0.432797i
$853$	−15.3554	+	37.0712i	−0.525758	+	1.26929i	0.408520	+	0.912749i	$0.366045\pi$
$853$	−15.3554	+	37.0712i	−0.525758	+	1.26929i	−0.934279	+	0.356544i	$0.883955\pi$
$854$	8.75706	+	61.7248i	0.299661	+	2.11218i
$855$	87.4478	−	87.4478i	2.99065	−	2.99065i
$856$	−43.8644	−	16.6411i	−1.49925	−	0.568781i
$857$	−13.7151	−	13.7151i	−0.468500	−	0.468500i	0.432928	−	0.901428i	$-0.357480\pi$
$857$	−13.7151	−	13.7151i	−0.468500	−	0.468500i	−0.901428	+	0.432928i	$0.857480\pi$
$858$	25.3614	−	33.7473i	0.865823	−	1.15211i
$859$	20.3310	+	8.42137i	0.693684	+	0.287333i	0.701534	−	0.712636i	$-0.252499\pi$
$859$	20.3310	+	8.42137i	0.693684	+	0.287333i	−0.00785017	+	0.999969i	$0.502499\pi$
$860$	−0.887944	−	3.06638i	−0.0302786	−	0.104563i
$861$	−36.4212	−	87.9286i	−1.24123	−	2.99660i
$862$	−21.2342	−	35.9411i	−0.723239	−	1.22416i
$863$	11.3596			0.386685			0.193342	−	0.981131i	$-0.438067\pi$
$863$	11.3596			0.386685			0.193342	+	0.981131i	$0.438067\pi$
$864$	64.5976	+	75.9714i	2.19765	+	2.58460i
$865$	−21.9431			−0.746086
$866$	8.19829	+	13.8765i	0.278589	+	0.471542i
$867$	1.28383	+	3.09944i	0.0436011	+	0.105262i
$868$	9.05523	−	2.62216i	0.307355	−	0.0890019i
$869$	−33.0173	−	13.6762i	−1.12004	−	0.463934i
$870$	28.7556	−	38.2638i	0.974905	−	1.29726i
$871$	18.4698	+	18.4698i	0.625826	+	0.625826i
$872$	7.15291	+	15.8978i	0.242228	+	0.538367i
$873$	26.4118	−	26.4118i	0.893904	−	0.893904i
$874$	0.588674	+	4.14931i	0.0199122	+	0.140352i
$875$	−3.38546	+	8.17321i	−0.114449	+	0.276305i
$876$	−76.9657	+	61.5502i	−2.60043	+	2.07959i
$877$	12.6263	−	5.22999i	0.426361	−	0.176604i	−0.159176	−	0.987250i	$-0.550884\pi$
$877$	12.6263	−	5.22999i	0.426361	−	0.176604i	0.585537	+	0.810646i	$0.300884\pi$
$878$	−0.400629	+	1.55750i	−0.0135206	+	0.0525632i
$879$			72.8430i			2.45693i
$880$	35.7983	+	8.06795i	1.20676	+	0.271971i
$881$			32.1970i			1.08474i	0.840138	+	0.542372i	$0.182474\pi$
$881$			32.1970i			1.08474i	−0.840138	+	0.542372i	$0.817526\pi$
$882$	35.0118	+	9.00590i	1.17891	+	0.303245i
$883$	7.78361	−	3.22408i	0.261939	−	0.108499i	−0.247849	−	0.968799i	$-0.579724\pi$
$883$	7.78361	−	3.22408i	0.261939	−	0.108499i	0.509788	+	0.860300i	$0.329724\pi$
$884$	−5.80793	−	0.646368i	−0.195342	−	0.0217397i
$885$	−51.2611	+	123.755i	−1.72312	+	4.15999i
$886$	−22.1964	+	3.14907i	−0.745703	+	0.105795i
$887$	1.12901	−	1.12901i	0.0379084	−	0.0379084i	−0.687899	−	0.725807i	$-0.741467\pi$
$887$	1.12901	−	1.12901i	0.0379084	−	0.0379084i	0.725807	+	0.687899i	$0.241467\pi$
$888$	−48.9845	+	1.47477i	−1.64381	+	0.0494900i
$889$	44.9344	+	44.9344i	1.50705	+	1.50705i
$890$	−13.7854	−	10.3599i	−0.462089	−	0.347264i
$891$	96.7141	+	40.0603i	3.24004	+	1.34207i
$892$	−1.97034	+	3.57659i	−0.0659719	+	0.119753i
$893$	−12.1094	−	29.2348i	−0.405227	−	0.978305i
$894$	5.55579	−	3.28239i	0.185813	−	0.109780i
$895$	9.67501			0.323400
$896$	−35.2921	−	6.84490i	−1.17903	−	0.228672i
$897$	−5.84119			−0.195031
$898$	−5.71285	+	3.37518i	−0.190640	+	0.112631i
$899$	1.90103	+	4.58950i	0.0634030	+	0.153068i
$900$	−32.4690	+	58.9381i	−1.08230	+	1.96460i
$901$	5.86572	+	2.42966i	0.195416	+	0.0809438i
$902$	30.7371	+	23.0992i	1.02344	+	0.769120i
$903$	3.99375	+	3.99375i	0.132904	+	0.132904i
$904$	8.28049	−	0.249299i	0.275405	−	0.00829157i
$905$	−20.5505	+	20.5505i	−0.683121	+	0.683121i
$906$	−42.9564	+	6.09434i	−1.42713	+	0.202471i
$907$	−9.81485	+	23.6952i	−0.325897	+	0.786785i	0.672992	+	0.739650i	$0.265009\pi$
$907$	−9.81485	+	23.6952i	−0.325897	+	0.786785i	−0.998889	+	0.0471346i	$0.984991\pi$
$908$	−16.0960	−	1.79134i	−0.534166	−	0.0594477i
$909$	101.673	−	42.1142i	3.37227	−	1.39684i
$910$	−38.3091	−	9.85405i	−1.26993	−	0.326659i
$911$			19.3095i			0.639753i	0.947459	+	0.319877i	$0.103641\pi$
$911$			19.3095i			0.639753i	−0.947459	+	0.319877i	$0.896359\pi$
$912$	14.6720	−	65.1009i	0.485837	−	2.15571i
$913$			37.5887i			1.24400i
$914$	−9.37346	+	36.4407i	−0.310047	+	1.20535i
$915$	129.541	−	53.6576i	4.28249	−	1.77386i
$916$	−30.5109	+	24.3999i	−1.00811	+	0.806194i
$917$	−20.8321	+	50.2932i	−0.687937	+	1.66083i
$918$	−3.50190	−	24.6834i	−0.115580	−	0.814672i
$919$	−20.3520	+	20.3520i	−0.671351	+	0.671351i	−0.958028	−	0.286676i	$-0.907450\pi$
$919$	−20.3520	+	20.3520i	−0.671351	+	0.671351i	0.286676	+	0.958028i	$0.407450\pi$
$920$	−2.08340	−	4.63049i	−0.0686877	−	0.152663i
$921$	−4.92956	−	4.92956i	−0.162434	−	0.162434i
$922$	−24.8102	+	33.0139i	−0.817081	+	1.08725i
$923$	−6.50799	−	2.69570i	−0.214213	−	0.0887300i
$924$	−62.3620	+	18.0584i	−2.05156	+	0.594079i
$925$	−8.05566	−	19.4481i	−0.264869	−	0.639449i
$926$	14.0627	+	23.8027i	0.462130	+	0.782204i
$927$	−8.65122			−0.284143
$928$	1.52778	−	18.8819i	0.0501519	−	0.619827i
$929$	−42.3070			−1.38805			−0.694023	−	0.719953i	$-0.744163\pi$
$929$	−42.3070			−1.38805			−0.694023	+	0.719953i	$0.744163\pi$
$930$	−10.7850	−	18.2547i	−0.353654	−	0.598596i
$931$	−5.89342	−	14.2280i	−0.193149	−	0.466303i
$932$	0.847166	+	2.92556i	0.0277498	+	0.0958298i
$933$	32.5250	+	13.4723i	1.06482	+	0.441064i
$934$	−2.84646	+	3.78766i	−0.0931390	+	0.123936i
$935$	−6.48702	−	6.48702i	−0.212148	−	0.212148i
$936$	63.7841	+	24.1981i	2.08485	+	0.790941i
$937$	−42.2051	+	42.2051i	−1.37878	+	1.37878i	−0.532096	+	0.846684i	$0.678595\pi$
$937$	−42.2051	+	42.2051i	−1.37878	+	1.37878i	−0.846684	+	0.532096i	$0.821405\pi$
$938$	−5.64276	−	39.7733i	−0.184243	−	1.29865i
$939$	4.14689	−	10.0115i	0.135329	−	0.326712i
$940$	23.9448	+	29.9419i	0.780994	+	0.976598i
$941$	22.2267	−	9.20662i	0.724571	−	0.300127i	0.0102522	−	0.999947i	$-0.496737\pi$
$941$	22.2267	−	9.20662i	0.724571	−	0.300127i	0.714319	+	0.699820i	$0.246737\pi$
$942$	14.8587	−	57.7654i	0.484122	−	1.88210i
$943$		−	5.32017i		−	0.173249i
$944$	9.02298	+	52.2413i	0.293673	+	1.70031i
$945$		−	168.753i		−	5.48953i
$946$	−2.20982	−	0.568420i	−0.0718474	−	0.0184809i
$947$	32.6902	−	13.5407i	1.06229	−	0.440014i	0.218025	−	0.975943i	$-0.430039\pi$
$947$	32.6902	−	13.5407i	1.06229	−	0.440014i	0.844263	+	0.535929i	$0.180039\pi$
$948$	8.70948	−	78.2589i	0.282871	−	2.54173i
$949$	−16.4235	+	39.6497i	−0.533128	+	1.28708i
$950$	28.3808	−	4.02646i	0.920794	−	0.130636i
$951$	22.6804	−	22.6804i	0.735462	−	0.735462i
$952$	6.54345	+	6.16096i	0.212074	+	0.199678i
$953$	−25.0104	−	25.0104i	−0.810167	−	0.810167i	0.174492	−	0.984659i	$-0.444172\pi$
$953$	−25.0104	−	25.0104i	−0.810167	−	0.810167i	−0.984659	+	0.174492i	$0.944172\pi$
$954$	−59.2514	−	44.5279i	−1.91833	−	1.44165i
$955$	22.6118	+	9.36612i	0.731701	+	0.303081i
$956$	−15.3894	−	8.47801i	−0.497729	−	0.274198i
$957$	−13.0921	−	31.6072i	−0.423209	−	1.02172i
$958$	−4.78179	+	2.82511i	−0.154493	+	0.0912751i
$959$	−8.12213			−0.262277
$960$	4.86410	+	80.7074i	0.156988	+	2.60482i
$961$	−28.7995			−0.929015
$962$	−18.3742	+	10.8556i	−0.592408	+	0.349998i
$963$	−52.3972	−	126.498i	−1.68848	−	4.07634i
$964$	−23.8254	−	13.1254i	−0.767363	−	0.422740i
$965$	−47.3457	−	19.6112i	−1.52411	−	0.631308i
$966$	7.18155	+	5.39700i	0.231063	+	0.173646i
$967$	−28.1848	−	28.1848i	−0.906363	−	0.906363i	0.0896132	−	0.995977i	$-0.471437\pi$
$967$	−28.1848	−	28.1848i	−0.906363	−	0.906363i	−0.995977	+	0.0896132i	$0.971437\pi$
$968$	−3.34793	+	3.55578i	−0.107607	+	0.114287i
$969$	−11.7970	+	11.7970i	−0.378973	+	0.378973i
$970$	19.0872	−	2.70796i	0.612853	−	0.0869472i
$971$	12.3562	−	29.8304i	0.396528	−	0.957304i	−0.591954	−	0.805971i	$-0.701643\pi$
$971$	12.3562	−	29.8304i	0.396528	−	0.957304i	0.988483	−	0.151333i	$-0.0483565\pi$
$972$	−13.8126	+	124.113i	−0.443041	+	3.98093i
$973$	8.63796	−	3.57796i	0.276920	−	0.114704i
$974$	24.1559	+	6.21350i	0.774005	+	0.199093i
$975$			39.9530i			1.27952i
$976$	31.9887	−	45.3457i	1.02393	−	1.45148i
$977$		−	3.58181i		−	0.114592i	−0.998357	−	0.0572962i	$-0.981752\pi$
$977$		−	3.58181i		−	0.114592i	0.998357	−	0.0572962i	$-0.0182479\pi$
$978$	17.3226	−	67.3441i	0.553914	−	2.15343i
$979$	−11.3872	+	4.71675i	−0.363938	+	0.150748i
$980$	11.6535	+	14.5721i	0.372256	+	0.465489i
$981$	−19.4699	+	47.0046i	−0.621627	+	1.50074i
$982$	−4.98985	−	35.1713i	−0.159233	−	1.12236i
$983$	−2.29293	+	2.29293i	−0.0731330	+	0.0731330i	−0.742727	−	0.669594i	$-0.766468\pi$
$983$	−2.29293	+	2.29293i	−0.0731330	+	0.0731330i	0.669594	+	0.742727i	$0.266468\pi$
$984$	−30.0496	+	79.2081i	−0.957947	+	2.52506i
$985$	−17.6526	−	17.6526i	−0.562459	−	0.562459i
$986$	−2.84519	+	3.78597i	−0.0906093	+	0.120570i
$987$	−62.6672	−	25.9576i	−1.99472	−	0.826240i
$988$	−8.08327	−	27.9143i	−0.257163	−	0.888074i
$989$	0.120822	+	0.291690i	0.00384192	+	0.00927521i
$990$	54.4763	+	92.2069i	1.73137	+	2.93053i
$991$	−39.5207			−1.25542			−0.627709	−	0.778448i	$-0.716007\pi$
$991$	−39.5207			−1.25542			−0.627709	+	0.778448i	$0.716007\pi$
$992$	−7.46847	−	3.82607i	−0.237124	−	0.121478i
$993$	−85.6786			−2.71893
$994$	5.51067	+	9.32738i	0.174788	+	0.295847i
$995$	12.8951	+	31.1315i	0.408802	+	0.986936i
$996$	−79.5522	+	23.0363i	−2.52071	+	0.729932i
$997$	47.2401	+	19.5675i	1.49611	+	0.619709i	0.972636	−	0.232334i	$-0.0746361\pi$
$997$	47.2401	+	19.5675i	1.49611	+	0.619709i	0.523473	+	0.852042i	$0.324636\pi$
$998$	24.9113	−	33.1484i	0.788554	−	1.04930i
$999$	−64.3791	−	64.3791i	−2.03686	−	2.03686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bd.b.69.7	✓	128
32.13	even	8	inner	544.2.bd.b.205.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bd.b.69.7	✓	128	1.1	even	1	trivial
544.2.bd.b.205.7	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+(-1.21759 + 0.719358i) q^{2} +(-1.28383 - 3.09944i) q^{3} +(0.965047 - 1.75177i) q^{4} +(2.78329 + 1.15288i) q^{5} +(3.79278 + 2.85031i) q^{6} +(-2.24686 - 2.24686i) q^{7} +(0.0851164 + 2.82715i) q^{8} +(-5.83697 + 5.83697i) q^{9} +(-4.21824 + 0.598454i) q^{10} +(-1.16535 + 2.81340i) q^{11} +(-6.66844 - 0.742135i) q^{12} +(-2.69948 + 1.11816i) q^{13} +(4.35205 + 1.11946i) q^{14} -10.1067i q^{15} +(-2.13737 - 3.38107i) q^{16} +1.00000i q^{17} +(2.90816 - 11.3059i) q^{18} +(-4.59445 + 1.90308i) q^{19} +(4.70558 - 3.76310i) q^{20} +(-4.07942 + 9.84859i) q^{21} +(-0.604928 - 4.26388i) q^{22} +(-0.421361 + 0.421361i) q^{23} +(8.65328 - 3.89338i) q^{24} +(2.88206 + 2.88206i) q^{25} +(2.48250 - 3.30335i) q^{26} +(16.2867 + 6.74615i) q^{27} +(-6.10430 + 1.76765i) q^{28} +(-1.28152 - 3.09387i) q^{29} +(7.27036 + 12.3059i) q^{30} -1.48342 q^{31} +(5.03464 + 2.57923i) q^{32} +10.2161 q^{33} +(-0.719358 - 1.21759i) q^{34} +(-3.66332 - 8.84403i) q^{35} +(4.59205 + 15.8579i) q^{36} +(-4.77154 - 1.97644i) q^{37} +(4.22516 - 5.62223i) q^{38} +(6.93133 + 6.93133i) q^{39} +(-3.02245 + 7.96691i) q^{40} +(-6.31308 + 6.31308i) q^{41} +(-2.11761 - 14.9261i) q^{42} +(0.202757 - 0.489500i) q^{43} +(3.80381 + 4.75649i) q^{44} +(-22.9753 + 9.51668i) q^{45} +(0.209935 - 0.816154i) q^{46} +6.36307i q^{47} +(-7.73541 + 10.9654i) q^{48} +3.09677i q^{49} +(-5.58240 - 1.43593i) q^{50} +(3.09944 - 1.28383i) q^{51} +(-0.646368 + 5.80793i) q^{52} +(2.42966 - 5.86572i) q^{53} +(-24.6834 + 3.50190i) q^{54} +(-6.48702 + 6.48702i) q^{55} +(6.16096 - 6.54345i) q^{56} +(11.7970 + 11.7970i) q^{57} +(3.78597 + 2.84519i) q^{58} +(-12.2448 - 5.07197i) q^{59} +(-17.7046 - 9.75348i) q^{60} +(5.30909 + 12.8173i) q^{61} +(1.80619 - 1.06711i) q^{62} +26.2297 q^{63} +(-7.98551 + 0.481273i) q^{64} -8.80254 q^{65} +(-12.4390 + 7.34902i) q^{66} +(-3.42100 - 8.25902i) q^{67} +(1.75177 + 0.965047i) q^{68} +(1.84694 + 0.765026i) q^{69} +(10.8224 + 8.13316i) q^{70} +(1.70472 + 1.70472i) q^{71} +(-16.9988 - 16.0051i) q^{72} +(10.3859 - 10.3859i) q^{73} +(7.23154 - 1.02596i) q^{74} +(5.23269 - 12.6328i) q^{75} +(-1.10010 + 9.88497i) q^{76} +(8.93971 - 3.70295i) q^{77} +(-13.4256 - 3.45340i) q^{78} +11.7357i q^{79} +(-2.05096 - 11.8746i) q^{80} -34.3762i q^{81} +(3.14537 - 12.2281i) q^{82} +(11.4040 - 4.72367i) q^{83} +(13.3156 + 16.6505i) q^{84} +(-1.15288 + 2.78329i) q^{85} +(0.105250 + 0.741865i) q^{86} +(-7.94400 + 7.94400i) q^{87} +(-8.05310 - 3.05515i) q^{88} +(2.86201 + 2.86201i) q^{89} +(21.1286 - 28.1149i) q^{90} +(8.57770 + 3.55300i) q^{91} +(0.331493 + 1.14476i) q^{92} +(1.90445 + 4.59776i) q^{93} +(-4.57732 - 7.74760i) q^{94} -14.9817 q^{95} +(1.53053 - 18.9158i) q^{96} -4.52492 q^{97} +(-2.22769 - 3.77060i) q^{98} +(-9.61964 - 23.2239i) 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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