LMFDB - Embedded newform 728.2.cz.a.309.73

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(309,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.309"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.cz (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.73
Character	$\chi$	$=$	728.309
Dual form			728.2.cz.a.589.73

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.30041 + 0.555811i) q^{2} +(-0.563630 + 0.325412i) q^{3} +(1.38215 + 1.44557i) q^{4} -2.56062 q^{5} +(-0.913819 + 0.109898i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.993899 + 2.64805i) q^{8} +(-1.28821 + 2.23125i) q^{9} +(-3.32987 - 1.42322i) q^{10} +(-2.93407 - 5.08197i) q^{11} +(-1.24943 - 0.364998i) q^{12} +(-2.06821 + 2.95339i) q^{13} +(0.848285 + 1.13155i) q^{14} +(1.44324 - 0.833257i) q^{15} +(-0.179336 + 3.99598i) q^{16} +(-0.197226 + 0.341605i) q^{17} +(-2.91537 + 2.18555i) q^{18} +(-4.11109 + 7.12062i) q^{19} +(-3.53916 - 3.70155i) q^{20} -0.650824 q^{21} +(-0.990894 - 8.23945i) q^{22} +(2.24361 + 3.88605i) q^{23} +(-1.42190 - 1.16909i) q^{24} +1.55679 q^{25} +(-4.33106 + 2.69109i) q^{26} -3.62927i q^{27} +(0.474191 + 1.94297i) q^{28} +(3.92800 - 2.26783i) q^{29} +(2.33995 - 0.281407i) q^{30} -4.34317i q^{31} +(-2.45422 + 5.09674i) q^{32} +(3.30747 + 1.90957i) q^{33} +(-0.446343 + 0.334607i) q^{34} +(-2.21756 - 1.28031i) q^{35} +(-5.00593 + 1.22172i) q^{36} +(-2.90510 - 5.03179i) q^{37} +(-9.30384 + 6.97476i) q^{38} +(0.204640 - 2.33764i) q^{39} +(-2.54500 - 6.78065i) q^{40} +(-7.40779 + 4.27689i) q^{41} +(-0.846340 - 0.361735i) q^{42} +(8.49000 + 4.90171i) q^{43} +(3.29101 - 11.2654i) q^{44} +(3.29863 - 5.71339i) q^{45} +(0.757712 + 6.30049i) q^{46} -7.44475i q^{47} +(-1.19926 - 2.31061i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.02447 + 0.865280i) q^{50} -0.256718i q^{51} +(-7.12790 + 1.09227i) q^{52} -0.739865i q^{53} +(2.01719 - 4.71955i) q^{54} +(7.51306 + 13.0130i) q^{55} +(-0.463282 + 2.79023i) q^{56} -5.35120i q^{57} +(6.36851 - 0.765891i) q^{58} +(-6.84105 + 11.8490i) q^{59} +(3.19931 + 0.934623i) q^{60} +(3.02363 + 1.74569i) q^{61} +(2.41398 - 5.64792i) q^{62} +(-2.23125 + 1.28821i) q^{63} +(-6.02433 + 5.26379i) q^{64} +(5.29591 - 7.56251i) q^{65} +(3.23971 + 4.32155i) q^{66} +(5.87298 + 10.1723i) q^{67} +(-0.766408 + 0.187045i) q^{68} +(-2.52913 - 1.46020i) q^{69} +(-2.17214 - 2.89748i) q^{70} +(10.3994 + 6.00409i) q^{71} +(-7.18882 - 1.19361i) q^{72} +4.41158i q^{73} +(-0.981111 - 8.15809i) q^{74} +(-0.877452 + 0.506597i) q^{75} +(-15.9755 + 3.89888i) q^{76} -5.86815i q^{77} +(1.56540 - 2.92615i) q^{78} +2.10138 q^{79} +(0.459211 - 10.2322i) q^{80} +(-2.68363 - 4.64819i) q^{81} +(-12.0103 + 1.44439i) q^{82} +3.25244 q^{83} +(-0.899535 - 0.940811i) q^{84} +(0.505021 - 0.874721i) q^{85} +(8.31609 + 11.0931i) q^{86} +(-1.47596 + 2.55644i) q^{87} +(10.5411 - 12.8205i) q^{88} +(7.13079 - 4.11696i) q^{89} +(7.46515 - 5.59636i) q^{90} +(-3.26782 + 1.52360i) q^{91} +(-2.51655 + 8.61439i) q^{92} +(1.41332 + 2.44794i) q^{93} +(4.13788 - 9.68125i) q^{94} +(10.5270 - 18.2332i) q^{95} +(-0.275269 - 3.67131i) q^{96} +(-1.67216 - 0.965421i) q^{97} +(0.168860 + 1.40410i) q^{98} +15.1189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) $ 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.30041	+	0.555811i	0.919531	+	0.393018i
$2$	1.30041	+	0.555811i	0.919531	+	0.393018i
$3$	−0.563630	+	0.325412i	−0.325412	+	0.187877i	−0.653802	−	0.756665i	$-0.726827\pi$
$3$	−0.563630	+	0.325412i	−0.325412	+	0.187877i	0.328390	+	0.944542i	$0.393494\pi$
$4$	1.38215	+	1.44557i	0.691074	+	0.722784i
$5$	−2.56062			−1.14515			−0.572573	−	0.819854i	$-0.694055\pi$
$5$	−2.56062			−1.14515			−0.572573	+	0.819854i	$0.694055\pi$
$6$	−0.913819	+	0.109898i	−0.373065	+	0.0448657i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$	0.993899	+	2.64805i	0.351397	+	0.936227i
$9$	−1.28821	+	2.23125i	−0.429405	+	0.743751i
$10$	−3.32987	−	1.42322i	−1.05300	−	0.450063i
$11$	−2.93407	−	5.08197i	−0.884657	−	1.53227i	−0.846106	−	0.533014i	$-0.821059\pi$
$11$	−2.93407	−	5.08197i	−0.884657	−	1.53227i	−0.0385504	−	0.999257i	$-0.512274\pi$
$12$	−1.24943	−	0.364998i	−0.360678	−	0.105366i
$13$	−2.06821	+	2.95339i	−0.573619	+	0.819122i
$13$	−2.06821	+	2.95339i	−0.573619	+	0.819122i
$14$	0.848285	+	1.13155i	0.226714	+	0.302420i
$15$	1.44324	−	0.833257i	0.372644	−	0.215146i
$16$	−0.179336	+	3.99598i	−0.0448340	+	0.998994i
$17$	−0.197226	+	0.341605i	−0.0478343	+	0.0828514i	−0.888951	−	0.458002i	$-0.848565\pi$
$17$	−0.197226	+	0.341605i	−0.0478343	+	0.0828514i	0.841117	+	0.540853i	$0.181899\pi$
$18$	−2.91537	+	2.18555i	−0.687158	+	0.515138i
$19$	−4.11109	+	7.12062i	−0.943149	+	1.63358i	−0.183734	+	0.982976i	$0.558819\pi$
$19$	−4.11109	+	7.12062i	−0.943149	+	1.63358i	−0.759415	+	0.650607i	$0.774515\pi$
$20$	−3.53916	−	3.70155i	−0.791380	−	0.827693i
$21$	−0.650824			−0.142021
$22$	−0.990894	−	8.23945i	−0.211259	−	1.75666i
$23$	2.24361	+	3.88605i	0.467825	+	0.810297i	0.999324	−	0.0367617i	$-0.0117042\pi$
$23$	2.24361	+	3.88605i	0.467825	+	0.810297i	−0.531499	+	0.847059i	$0.678371\pi$
$24$	−1.42190	−	1.16909i	−0.290244	−	0.238640i
$25$	1.55679			0.311357
$26$	−4.33106	+	2.69109i	−0.849390	+	0.527765i
$27$		−	3.62927i		−	0.698454i
$28$	0.474191	+	1.94297i	0.0896136	+	0.367187i
$29$	3.92800	−	2.26783i	0.729411	−	0.421126i	−0.0887955	−	0.996050i	$-0.528302\pi$
$29$	3.92800	−	2.26783i	0.729411	−	0.421126i	0.818207	+	0.574924i	$0.194968\pi$
$30$	2.33995	−	0.281407i	0.427214	−	0.0513777i
$31$		−	4.34317i		−	0.780056i	−0.920803	−	0.390028i	$-0.872465\pi$
$31$		−	4.34317i		−	0.780056i	0.920803	−	0.390028i	$-0.127535\pi$
$32$	−2.45422	+	5.09674i	−0.433849	+	0.900986i
$33$	3.30747	+	1.90957i	0.575756	+	0.332413i
$34$	−0.446343	+	0.334607i	−0.0765472	+	0.0573847i
$35$	−2.21756	−	1.28031i	−0.374837	−	0.216412i
$36$	−5.00593	+	1.22172i	−0.834322	+	0.203620i
$37$	−2.90510	−	5.03179i	−0.477596	−	0.827221i	0.522074	−	0.852900i	$-0.325158\pi$
$37$	−2.90510	−	5.03179i	−0.477596	−	0.827221i	−0.999670	+	0.0256792i	$0.991825\pi$
$38$	−9.30384	+	6.97476i	−1.50928	+	1.13145i
$39$	0.204640	−	2.33764i	0.0327686	−	0.374322i
$40$	−2.54500	−	6.78065i	−0.402400	−	1.07212i
$41$	−7.40779	+	4.27689i	−1.15690	+	0.667938i	−0.950560	−	0.310542i	$-0.899489\pi$
$41$	−7.40779	+	4.27689i	−1.15690	+	0.667938i	−0.206342	+	0.978480i	$0.566156\pi$
$42$	−0.846340	−	0.361735i	−0.130593	−	0.0558170i
$43$	8.49000	+	4.90171i	1.29471	+	0.747503i	0.979486	−	0.201513i	$-0.0645858\pi$
$43$	8.49000	+	4.90171i	1.29471	+	0.747503i	0.315228	+	0.949016i	$0.397919\pi$
$44$	3.29101	−	11.2654i	0.496138	−	1.69833i
$45$	3.29863	−	5.71339i	0.491731	−	0.851703i
$46$	0.757712	+	6.30049i	0.111718	+	0.928957i
$47$		−	7.44475i		−	1.08593i	−0.839756	−	0.542964i	$-0.817302\pi$
$47$		−	7.44475i		−	1.08593i	0.839756	−	0.542964i	$-0.182698\pi$
$48$	−1.19926	−	2.31061i	−0.173098	−	0.333508i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	2.02447	+	0.865280i	0.286303	+	0.122369i
$51$		−	0.256718i		−	0.0359478i
$52$	−7.12790	+	1.09227i	−0.988462	+	0.151471i
$53$		−	0.739865i		−	0.101628i	−0.998708	−	0.0508142i	$-0.983818\pi$
$53$		−	0.739865i		−	0.101628i	0.998708	−	0.0508142i	$-0.0161816\pi$
$54$	2.01719	−	4.71955i	0.274505	−	0.642250i
$55$	7.51306	+	13.0130i	1.01306	+	1.75467i
$56$	−0.463282	+	2.79023i	−0.0619087	+	0.372860i
$57$		−	5.35120i		−	0.708783i
$58$	6.36851	−	0.765891i	0.836226	−	0.100566i
$59$	−6.84105	+	11.8490i	−0.890629	+	1.54261i	−0.0515063	+	0.998673i	$0.516402\pi$
$59$	−6.84105	+	11.8490i	−0.890629	+	1.54261i	−0.839123	+	0.543942i	$0.816931\pi$
$60$	3.19931	+	0.934623i	0.413029	+	0.120659i
$61$	3.02363	+	1.74569i	0.387136	+	0.223513i	0.680918	−	0.732359i	$-0.261581\pi$
$61$	3.02363	+	1.74569i	0.387136	+	0.223513i	−0.293782	+	0.955872i	$0.594914\pi$
$62$	2.41398	−	5.64792i	0.306576	−	0.717286i
$63$	−2.23125	+	1.28821i	−0.281111	+	0.162300i
$64$	−6.02433	+	5.26379i	−0.753041	+	0.657974i
$65$	5.29591	−	7.56251i	0.656877	−	0.938014i
$66$	3.23971	+	4.32155i	0.398781	+	0.531946i
$67$	5.87298	+	10.1723i	0.717499	+	1.24275i	0.961988	+	0.273093i	$0.0880466\pi$
$67$	5.87298	+	10.1723i	0.717499	+	1.24275i	−0.244489	+	0.969652i	$0.578620\pi$
$68$	−0.766408	+	0.187045i	−0.0929407	+	0.0226826i
$69$	−2.52913	−	1.46020i	−0.304472	−	0.175787i
$70$	−2.17214	−	2.89748i	−0.259620	−	0.346315i
$71$	10.3994	+	6.00409i	1.23418	+	0.712555i	0.967899	−	0.251340i	$-0.0808713\pi$
$71$	10.3994	+	6.00409i	1.23418	+	0.712555i	0.266282	+	0.963895i	$0.414205\pi$
$72$	−7.18882	−	1.19361i	−0.847211	−	0.140669i
$73$			4.41158i			0.516337i	0.966100	+	0.258168i	$0.0831189\pi$
$73$			4.41158i			0.516337i	−0.966100	+	0.258168i	$0.916881\pi$
$74$	−0.981111	−	8.15809i	−0.114052	−	0.948359i
$75$	−0.877452	+	0.506597i	−0.101319	+	0.0584968i
$76$	−15.9755	+	3.89888i	−1.83251	+	0.447233i
$77$		−	5.86815i		−	0.668738i
$78$	1.56540	−	2.92615i	0.177247	−	0.331322i
$79$	2.10138			0.236424			0.118212	−	0.992988i	$-0.462284\pi$
$79$	2.10138			0.236424			0.118212	+	0.992988i	$0.462284\pi$
$80$	0.459211	−	10.2322i	0.0513414	−	1.14399i
$81$	−2.68363	−	4.64819i	−0.298181	−	0.516465i
$82$	−12.0103	+	1.44439i	−1.32632	+	0.159506i
$83$	3.25244			0.357002			0.178501	−	0.983940i	$-0.442875\pi$
$83$	3.25244			0.357002			0.178501	+	0.983940i	$0.442875\pi$
$84$	−0.899535	−	0.940811i	−0.0981473	−	0.102651i
$85$	0.505021	−	0.874721i	0.0547772	−	0.0948769i
$86$	8.31609	+	11.0931i	0.896747	+	1.19620i
$87$	−1.47596	+	2.55644i	−0.158239	+	0.274079i
$88$	10.5411	−	12.8205i	1.12369	−	1.36667i
$89$	7.13079	−	4.11696i	0.755862	−	0.436397i	−0.0719460	−	0.997409i	$-0.522921\pi$
$89$	7.13079	−	4.11696i	0.755862	−	0.436397i	0.827808	+	0.561011i	$0.189588\pi$
$90$	7.46515	−	5.59636i	0.786896	−	0.589908i
$91$	−3.26782	+	1.52360i	−0.342560	+	0.159717i
$92$	−2.51655	+	8.61439i	−0.262368	+	0.898112i
$93$	1.41332	+	2.44794i	0.146554	+	0.253840i
$94$	4.13788	−	9.68125i	0.426789	−	0.998544i
$95$	10.5270	−	18.2332i	1.08004	−	1.87069i
$96$	−0.275269	−	3.67131i	−0.0280946	−	0.374702i
$97$	−1.67216	−	0.965421i	−0.169782	−	0.0980236i	0.412701	−	0.910867i	$-0.364585\pi$
$97$	−1.67216	−	0.965421i	−0.169782	−	0.0980236i	−0.582483	+	0.812843i	$0.697919\pi$
$98$	0.168860	+	1.40410i	0.0170574	+	0.141835i
$99$	15.1189			1.51950
$100$	2.15171	+	2.25044i	0.215171	+	0.225044i
$101$	11.2580	−	6.49981i	1.12021	−	0.646755i	0.178757	−	0.983893i	$-0.442792\pi$
$101$	11.2580	−	6.49981i	1.12021	−	0.646755i	0.941455	+	0.337138i	$0.109459\pi$
$102$	0.142687	−	0.333840i	0.0141281	−	0.0330551i
$103$	3.15101			0.310478			0.155239	−	0.987877i	$-0.450385\pi$
$103$	3.15101			0.310478			0.155239	+	0.987877i	$0.450385\pi$
$104$	−9.87631	−	2.54136i	−0.968452	−	0.249201i
$105$	1.66651			0.162635
$106$	0.411225	−	0.962130i	0.0399417	−	0.0934504i
$107$	11.4040	−	6.58413i	1.10247	−	0.636512i	0.165602	−	0.986193i	$-0.447043\pi$
$107$	11.4040	−	6.58413i	1.10247	−	0.636512i	0.936869	+	0.349681i	$0.113710\pi$
$108$	5.24636	−	5.01619i	0.504831	−	0.482683i
$109$	−11.1674			−1.06964			−0.534821	−	0.844965i	$-0.679621\pi$
$109$	−11.1674			−1.06964			−0.534821	+	0.844965i	$0.679621\pi$
$110$	2.53731	+	21.0981i	0.241923	+	2.01163i
$111$	3.27481	+	1.89071i	0.310831	+	0.179458i
$112$	−2.15330	+	3.37095i	−0.203468	+	0.318525i
$113$	−1.99568	+	3.45662i	−0.187738	+	0.325171i	−0.944496	−	0.328524i	$-0.893449\pi$
$113$	−1.99568	+	3.45662i	−0.187738	+	0.325171i	0.756758	+	0.653695i	$0.226782\pi$
$114$	2.97425	−	6.95876i	0.278564	−	0.651748i
$115$	−5.74504	−	9.95071i	−0.535728	−	0.927908i
$116$	8.70738	+	2.54371i	0.808460	+	0.236178i
$117$	−3.92545	−	8.41930i	−0.362908	−	0.778365i
$118$	−15.4820	+	11.6063i	−1.42524	+	1.06845i
$119$	−0.341605	+	0.197226i	−0.0313149	+	0.0180797i
$120$	3.64095	+	2.99361i	0.332371	+	0.273278i
$121$	−11.7176	+	20.2955i	−1.06524	+	1.84504i
$122$	2.96169	+	3.95069i	0.268139	+	0.357678i
$123$	2.78350	−	4.82117i	0.250980	−	0.434710i
$124$	6.27835	−	6.00290i	0.563812	−	0.539077i
$125$	8.81677			0.788596
$126$	−3.61755	+	0.435055i	−0.322277	+	0.0387578i
$127$	3.29696	+	5.71049i	0.292557	+	0.506724i	0.974414	−	0.224762i	$-0.0721604\pi$
$127$	3.29696	+	5.71049i	0.292557	+	0.506724i	−0.681856	+	0.731486i	$0.738827\pi$
$128$	−10.7598	+	3.49671i	−0.951040	+	0.309068i
$129$	−6.38029			−0.561754
$130$	11.0902	−	6.89086i	0.972675	−	0.604368i
$131$		−	4.89126i		−	0.427351i	−0.976905	−	0.213676i	$-0.931456\pi$
$131$		−	4.89126i		−	0.427351i	0.976905	−	0.213676i	$-0.0685435\pi$
$132$	1.81100	+	7.42047i	0.157627	+	0.645869i
$133$	−7.12062	+	4.11109i	−0.617436	+	0.356477i
$134$	1.98342	+	16.4925i	0.171342	+	1.42473i
$135$			9.29320i			0.799831i
$136$	−1.10061	−	0.182742i	−0.0943765	−	0.0156700i
$137$	−8.18491	−	4.72556i	−0.699284	−	0.403732i	0.107796	−	0.994173i	$-0.465621\pi$
$137$	−8.18491	−	4.72556i	−0.699284	−	0.403732i	−0.807081	+	0.590441i	$0.798954\pi$
$138$	−2.47733	−	3.30458i	−0.210884	−	0.281305i
$139$	8.08753	+	4.66934i	0.685976	+	0.396048i	0.802103	−	0.597186i	$-0.203715\pi$
$139$	8.08753	+	4.66934i	0.685976	+	0.396048i	−0.116127	+	0.993234i	$0.537048\pi$
$140$	−1.21422	−	4.97522i	−0.102621	−	0.420483i
$141$	2.42261	+	4.19608i	0.204021	+	0.353374i
$142$	10.1864	+	13.5879i	0.854821	+	1.14027i
$143$	21.0773	+	1.84513i	1.76257	+	0.154298i
$144$	−8.68501	−	5.54782i	−0.723751	−	0.462318i
$145$	−10.0581	+	5.80706i	−0.835282	+	0.482250i
$146$	−2.45201	+	5.73688i	−0.202930	+	0.474788i
$147$	−0.563630	−	0.325412i	−0.0464874	−	0.0268395i
$148$	3.25851	−	11.1542i	0.267848	−	0.916870i
$149$	−2.62068	+	4.53916i	−0.214695	+	0.371862i	−0.953178	−	0.302409i	$-0.902209\pi$
$149$	−2.62068	+	4.53916i	−0.214695	+	0.371862i	0.738483	+	0.674272i	$0.235542\pi$
$150$	−1.42262	+	0.171088i	−0.116157	+	0.0139693i
$151$			10.6953i			0.870370i	0.900341	+	0.435185i	$0.143317\pi$
$151$			10.6953i			0.870370i	−0.900341	+	0.435185i	$0.856683\pi$
$152$	−22.9418	−	3.80919i	−1.86082	−	0.308966i
$153$	−0.508138	−	0.880121i	−0.0410805	−	0.0711535i
$154$	3.26158	−	7.63102i	0.262826	−	0.614925i
$155$			11.1212i			0.893278i
$156$	3.66206	−	2.93514i	0.293199	−	0.234999i
$157$			10.6673i			0.851346i	0.904877	+	0.425673i	$0.139963\pi$
$157$			10.6673i			0.851346i	−0.904877	+	0.425673i	$0.860037\pi$
$158$	2.73266	+	1.16797i	0.217399	+	0.0929187i
$159$	0.240761	+	0.417010i	0.0190936	+	0.0330711i
$160$	6.28433	−	13.0508i	0.496820	−	1.03176i
$161$			4.48722i			0.353643i
$162$	−0.906315	−	7.53616i	−0.0712069	−	0.592097i
$163$	5.99743	−	10.3879i	0.469755	−	0.813640i	−0.529647	−	0.848218i	$-0.677675\pi$
$163$	5.99743	−	10.3879i	0.469755	−	0.813640i	0.999402	+	0.0345783i	$0.0110088\pi$
$164$	−16.4212	−	4.79717i	−1.28228	−	0.374596i
$165$	−8.46917	−	4.88968i	−0.659324	−	0.380661i
$166$	4.22952	+	1.80774i	0.328274	+	0.140308i
$167$	−0.260301	+	0.150285i	−0.0201427	+	0.0116294i	−0.510038	−	0.860152i	$-0.670369\pi$
$167$	−0.260301	+	0.150285i	−0.0201427	+	0.0116294i	0.489895	+	0.871782i	$0.337035\pi$
$168$	−0.646854	−	1.72341i	−0.0499058	−	0.132964i
$169$	−4.44499	−	12.2165i	−0.341922	−	0.939728i
$170$	1.14292	−	0.856803i	0.0876576	−	0.0657138i
$171$	−10.5919	−	18.3458i	−0.809986	−	1.40294i
$172$	4.64869	+	19.0478i	0.354459	+	1.45238i
$173$	−8.22686	−	4.74978i	−0.625477	−	0.361119i	0.153521	−	0.988145i	$-0.450939\pi$
$173$	−8.22686	−	4.74978i	−0.625477	−	0.361119i	−0.778998	+	0.627026i	$0.784272\pi$
$174$	−3.34025	+	2.50407i	−0.253224	+	0.189833i
$175$	1.34822	+	0.778394i	0.101916	+	0.0588410i
$176$	20.8336	−	10.8131i	1.57039	−	0.815070i
$177$		−	8.90464i		−	0.669314i
$178$	11.5612	−	1.39038i	0.866550	−	0.104213i
$179$	−13.7278	+	7.92576i	−1.02607	+	0.592399i	−0.915855	−	0.401509i	$-0.868486\pi$
$179$	−13.7278	+	7.92576i	−1.02607	+	0.592399i	−0.110211	+	0.993908i	$0.535153\pi$
$180$	12.8183	−	3.12836i	0.955419	−	0.233174i
$181$		−	0.150002i		−	0.0111495i	−0.999984	−	0.00557477i	$-0.998225\pi$
$181$		−	0.150002i		−	0.0111495i	0.999984	−	0.00557477i	$-0.00177451\pi$
$182$	−5.09635	+	0.165020i	−0.377766	+	0.0122321i
$183$	−2.27228			−0.167972
$184$	−8.06053	+	9.80354i	−0.594230	+	0.722726i
$185$	7.43888	+	12.8845i	0.546917	+	0.947288i
$186$	0.477306	+	3.96887i	0.0349978	+	0.291012i
$187$	2.31470			0.169268
$188$	10.7619	−	10.2897i	0.784892	−	0.750457i
$189$	1.81464	−	3.14304i	0.131995	−	0.228623i
$190$	23.8236	−	17.8597i	1.72835	−	1.29568i
$191$	5.79740	−	10.0414i	0.419485	−	0.726570i	−0.576402	−	0.817166i	$-0.695544\pi$
$191$	5.79740	−	10.0414i	0.419485	−	0.726570i	0.995888	+	0.0905962i	$0.0288772\pi$
$192$	1.68259	−	4.92722i	0.121431	−	0.355591i
$193$	−7.03458	+	4.06142i	−0.506360	+	0.292347i	−0.731336	−	0.682017i	$-0.761103\pi$
$193$	−7.03458	+	4.06142i	−0.506360	+	0.292347i	0.224976	+	0.974364i	$0.427770\pi$
$194$	−1.63790	−	2.18485i	−0.117595	−	0.156863i
$195$	−0.524005	+	5.98581i	−0.0375248	+	0.428653i
$196$	−0.560825	+	1.91976i	−0.0400589	+	0.137126i
$197$	−8.05372	−	13.9495i	−0.573804	−	0.993857i	−0.996170	−	0.0874323i	$-0.972134\pi$
$197$	−8.05372	−	13.9495i	−0.573804	−	0.993857i	0.422367	−	0.906425i	$-0.361199\pi$
$198$	19.6608	+	8.40324i	1.39723	+	0.597192i
$199$	7.37114	−	12.7672i	0.522526	−	0.905042i	−0.477130	−	0.878833i	$-0.658323\pi$
$199$	7.37114	−	12.7672i	0.522526	−	0.905042i	0.999656	−	0.0262096i	$-0.00834372\pi$
$200$	1.54729	+	4.12245i	0.109410	+	0.291501i
$201$	−6.62038	−	3.82228i	−0.466966	−	0.269603i
$202$	18.2527	−	2.19511i	1.28426	−	0.154448i
$203$	4.53566			0.318341
$204$	0.371104	−	0.354823i	0.0259825	−	0.0248426i
$205$	18.9685	−	10.9515i	1.32482	−	0.764886i
$206$	4.09762	+	1.75137i	0.285494	+	0.122024i
$207$	−11.5610			−0.803546
$208$	−11.4308	−	8.79418i	−0.792581	−	0.609767i
$209$	48.2490			3.33745
$210$	2.16716	+	0.926268i	0.149548	+	0.0639185i
$211$	−18.3088	+	10.5706i	−1.26043	+	0.727709i	−0.973157	−	0.230141i	$-0.926081\pi$
$211$	−18.3088	+	10.5706i	−1.26043	+	0.727709i	−0.287271	+	0.957849i	$0.592748\pi$
$212$	1.06953	−	1.02260i	0.0734553	−	0.0702327i
$213$	−7.81522			−0.535490
$214$	18.4895	−	2.22359i	1.26392	−	0.152001i
$215$	−21.7397	−	12.5514i	−1.48263	−	0.856000i
$216$	9.61049	−	3.60713i	0.653911	−	0.245434i
$217$	2.17159	−	3.76130i	0.147417	−	0.255333i
$218$	−14.5222	−	6.20697i	−0.983569	−	0.420389i
$219$	−1.43558	−	2.48650i	−0.0970076	−	0.168022i
$220$	−8.42702	+	28.8465i	−0.568150	+	1.94483i
$221$	−0.600987	−	1.28900i	−0.0404267	−	0.0867072i
$222$	3.20772	+	4.27888i	0.215288	+	0.287180i
$223$	−9.42034	+	5.43883i	−0.630832	+	0.364211i	−0.781074	−	0.624438i	$-0.785328\pi$
$223$	−9.42034	+	5.43883i	−0.630832	+	0.364211i	0.150242	+	0.988649i	$0.451995\pi$
$224$	−4.67379	+	3.18680i	−0.312281	+	0.212927i
$225$	−2.00548	+	3.47359i	−0.133698	+	0.231572i
$226$	−4.51643	+	3.38581i	−0.300429	+	0.225221i
$227$	−5.45306	+	9.44498i	−0.361932	+	0.626885i	−0.988279	−	0.152660i	$-0.951216\pi$
$227$	−5.45306	+	9.44498i	−0.361932	+	0.626885i	0.626346	+	0.779545i	$0.284550\pi$
$228$	7.73552	−	7.39614i	0.512297	−	0.489821i
$229$	5.54336			0.366315			0.183158	−	0.983084i	$-0.441368\pi$
$229$	5.54336			0.366315			0.183158	+	0.983084i	$0.441368\pi$
$230$	−1.94021	−	16.1332i	−0.127934	−	1.06379i
$231$	1.90957	+	3.30747i	0.125640	+	0.217615i
$232$	9.90937	+	8.14754i	0.650582	+	0.534912i
$233$	−29.2079			−1.91347			−0.956737	−	0.290953i	$-0.906028\pi$
$233$	−29.2079			−1.91347			−0.956737	+	0.290953i	$0.906028\pi$
$234$	−0.425163	−	13.1304i	−0.0277938	−	0.858360i
$235$			19.0632i			1.24355i
$236$	−26.5840	+	6.48793i	−1.73047	+	0.422328i
$237$	−1.18440	+	0.683814i	−0.0769350	+	0.0444185i
$238$	−0.553848	+	0.0666070i	−0.0359006	+	0.00431749i
$239$			28.3648i			1.83477i	0.398003	+	0.917384i	$0.369703\pi$
$239$			28.3648i			1.83477i	−0.398003	+	0.917384i	$0.630297\pi$
$240$	3.07085	+	5.91660i	0.198223	+	0.381915i
$241$	−19.5726	−	11.3002i	−1.26078	−	0.727912i	−0.287555	−	0.957764i	$-0.592842\pi$
$241$	−19.5726	−	11.3002i	−1.26078	−	0.727912i	−0.973226	+	0.229852i	$0.926176\pi$
$242$	−26.5182	+	19.8797i	−1.70465	+	1.27792i
$243$	12.4543	+	7.19048i	0.798942	+	0.461270i
$244$	1.65558	+	6.78367i	0.105988	+	0.434280i
$245$	−1.28031	−	2.21756i	−0.0817961	−	0.141675i
$246$	6.29936	−	4.72240i	0.401632	−	0.301089i
$247$	−12.5273	−	26.8686i	−0.797095	−	1.70961i
$248$	11.5009	−	4.31667i	0.730310	−	0.274109i
$249$	−1.83317	+	1.05838i	−0.116173	+	0.0670723i
$250$	11.4654	+	4.90046i	0.725138	+	0.309932i
$251$	10.8924	+	6.28872i	0.687521	+	0.396940i	0.802683	−	0.596407i	$-0.203405\pi$
$251$	10.8924	+	6.28872i	0.687521	+	0.396940i	−0.115162	+	0.993347i	$0.536739\pi$
$252$	−4.94612	−	1.44493i	−0.311576	−	0.0910218i
$253$	13.1659	−	22.8039i	0.827730	−	1.43367i
$254$	1.11345	+	9.25848i	0.0698638	+	0.580929i
$255$			0.657359i			0.0411654i
$256$	−15.9357	−	1.43324i	−0.995980	−	0.0895778i
$257$	2.74185	+	4.74903i	0.171032	+	0.296236i	0.938781	−	0.344515i	$-0.111957\pi$
$257$	2.74185	+	4.74903i	0.171032	+	0.296236i	−0.767749	+	0.640751i	$0.778623\pi$
$258$	−8.29702	−	3.54624i	−0.516550	−	0.220779i
$259$		−	5.81021i		−	0.361029i
$260$	18.2519	−	2.79690i	1.13193	−	0.173456i
$261$			11.6858i			0.723333i
$262$	2.71862	−	6.36065i	0.167957	−	0.392963i
$263$	−4.82980	−	8.36546i	−0.297818	−	0.515836i	0.677818	−	0.735229i	$-0.262926\pi$
$263$	−4.82980	−	8.36546i	−0.297818	−	0.515836i	−0.975637	+	0.219393i	$0.929592\pi$
$264$	−1.76934	+	10.6562i	−0.108895	+	0.655847i
$265$			1.89452i			0.116379i
$266$	−11.5447	+	1.38840i	−0.707853	+	0.0851280i
$267$	−2.67942	+	4.64089i	−0.163978	+	0.284018i
$268$	−6.58743	+	22.5494i	−0.402392	+	1.37743i
$269$	19.4843	+	11.2493i	1.18798	+	0.685880i	0.957847	−	0.287280i	$-0.0927509\pi$
$269$	19.4843	+	11.2493i	1.18798	+	0.685880i	0.230132	+	0.973159i	$0.426084\pi$
$270$	−5.16526	+	12.0850i	−0.314348	+	0.735469i
$271$	−11.2983	+	6.52308i	−0.686323	+	0.396249i	−0.802233	−	0.597011i	$-0.796355\pi$
$271$	−11.2983	+	6.52308i	−0.686323	+	0.396249i	0.115910	+	0.993260i	$0.463022\pi$
$272$	−1.32968	−	0.849372i	−0.0806235	−	0.0515007i
$273$	1.34604	−	1.92213i	0.0814662	−	0.116333i
$274$	−8.01725	−	10.6944i	−0.484340	−	0.646075i
$275$	−4.56773	−	7.91154i	−0.275445	−	0.477084i
$276$	−1.38482	−	5.67424i	−0.0833566	−	0.341549i
$277$	−5.77332	−	3.33323i	−0.346885	−	0.200274i	0.316427	−	0.948617i	$-0.397517\pi$
$277$	−5.77332	−	3.33323i	−0.346885	−	0.200274i	−0.663313	+	0.748342i	$0.730850\pi$
$278$	7.92186	+	10.5672i	0.475122	+	0.633779i
$279$	9.69071	+	5.59493i	0.580168	+	0.334960i
$280$	1.18629	−	7.14472i	0.0708945	−	0.426979i
$281$		−	5.96013i		−	0.355552i	−0.984071	−	0.177776i	$-0.943110\pi$
$281$		−	5.96013i		−	0.355552i	0.984071	−	0.177776i	$-0.0568902\pi$
$282$	0.818163	+	6.80316i	0.0487209	+	0.405122i
$283$	−11.5734	+	6.68191i	−0.687968	+	0.397198i	−0.802850	−	0.596181i	$-0.796684\pi$
$283$	−11.5734	+	6.68191i	−0.687968	+	0.397198i	0.114882	+	0.993379i	$0.463351\pi$
$284$	5.69417	+	23.3316i	0.337887	+	1.38447i
$285$			13.7024i			0.811660i
$286$	26.3837	+	14.1144i	1.56010	+	0.834604i
$287$	−8.55378			−0.504913
$288$	−8.21056	−	12.0417i	−0.483812	−	0.709563i
$289$	8.42220	+	14.5877i	0.495424	+	0.858099i
$290$	−16.3073	+	1.96116i	−0.957600	+	0.115163i
$291$	1.25664			0.0736654
$292$	−6.37724	+	6.09746i	−0.373200	+	0.356827i
$293$	1.19393	−	2.06795i	0.0697502	−	0.120811i	−0.829041	−	0.559188i	$-0.811113\pi$
$293$	1.19393	−	2.06795i	0.0697502	−	0.120811i	0.898791	+	0.438377i	$0.144446\pi$
$294$	−0.552084	−	0.736442i	−0.0321982	−	0.0429502i
$295$	17.5174	−	30.3409i	1.01990	−	1.76652i
$296$	10.4370	−	12.6940i	0.606641	−	0.737821i
$297$	−18.4438	+	10.6486i	−1.07022	+	0.617892i
$298$	−5.93089	+	4.44617i	−0.343567	+	0.257560i
$299$	−16.1173	−	1.41093i	−0.932086	−	0.0815960i
$300$	−1.94509	−	0.568225i	−0.112300	−	0.0328065i
$301$	4.90171	+	8.49000i	0.282530	+	0.489356i
$302$	−5.94456	+	13.9083i	−0.342071	+	0.800332i
$303$	−4.23023	+	7.32697i	−0.243020	+	0.420924i
$304$	−27.7166	−	17.7048i	−1.58965	−	1.01544i
$305$	−7.74237	−	4.47006i	−0.443327	−	0.255955i
$306$	−0.171608	−	1.42695i	−0.00981018	−	0.0815733i
$307$	13.2970			0.758898			0.379449	−	0.925213i	$-0.376114\pi$
$307$	13.2970			0.758898			0.379449	+	0.925213i	$0.376114\pi$
$308$	8.48281	−	8.11065i	0.483353	−	0.462147i
$309$	−1.77600	+	1.02538i	−0.101033	+	0.0583316i
$310$	−6.18130	+	14.4622i	−0.351074	+	0.821397i
$311$	10.1140			0.573510			0.286755	−	0.958004i	$-0.407423\pi$
$311$	10.1140			0.573510			0.286755	+	0.958004i	$0.407423\pi$
$312$	6.39357	−	1.78148i	0.361965	−	0.100857i
$313$	−12.5614			−0.710011			−0.355006	−	0.934864i	$-0.615521\pi$
$313$	−12.5614			−0.710011			−0.355006	+	0.934864i	$0.615521\pi$
$314$	−5.92902	+	13.8719i	−0.334594	+	0.782839i
$315$	5.71339	−	3.29863i	0.321913	−	0.185857i
$316$	2.90442	+	3.03769i	0.163386	+	0.170883i
$317$	22.5044			1.26397			0.631986	−	0.774980i	$-0.282240\pi$
$317$	22.5044			1.26397			0.631986	+	0.774980i	$0.282240\pi$
$318$	0.0813097	+	0.676103i	0.00455962	+	0.0379140i
$319$	−23.0501	−	13.3080i	−1.29056	−	0.745104i
$320$	15.4260	−	13.4786i	0.862341	−	0.753475i
$321$	−4.28511	+	7.42203i	−0.239171	+	0.414257i
$322$	−2.49405	+	5.83524i	−0.138988	+	0.325185i
$323$	−1.62163	−	2.80874i	−0.0902297	−	0.156282i
$324$	3.01010	−	10.3039i	0.167228	−	0.572437i
$325$	−3.21977	+	4.59780i	−0.178601	+	0.255040i
$326$	13.5728	−	10.1751i	0.751730	−	0.563545i
$327$	6.29428	−	3.63400i	0.348075	−	0.200961i
$328$	−18.6880	−	15.3654i	−1.03187	−	0.848412i
$329$	3.72237	−	6.44734i	0.205221	−	0.355453i
$330$	−8.29568	−	11.0659i	−0.456662	−	0.609156i
$331$	0.163546	−	0.283269i	0.00898928	−	0.0155699i	−0.861496	−	0.507765i	$-0.830472\pi$
$331$	0.163546	−	0.283269i	0.00898928	−	0.0155699i	0.870485	+	0.492195i	$0.163805\pi$
$332$	4.49536	+	4.70163i	0.246715	+	0.258035i
$333$	14.9696			0.820328
$334$	−0.422030	+	0.0507542i	−0.0230924	+	0.00277715i
$335$	−15.0385	−	26.0474i	−0.821641	−	1.42312i
$336$	0.116716	−	2.60068i	0.00636738	−	0.141879i
$337$	−13.2569			−0.722148			−0.361074	−	0.932537i	$-0.617590\pi$
$337$	−13.2569			−0.722148			−0.361074	+	0.932537i	$0.617590\pi$
$338$	1.00973	−	18.3570i	0.0549221	−	0.998491i
$339$		−	2.59767i		−	0.141086i
$340$	1.96248	−	0.478952i	0.106431	−	0.0259748i
$341$	−22.0718	+	12.7432i	−1.19526	+	0.690082i
$342$	−3.57710	−	29.7442i	−0.193428	−	1.60838i
$343$			1.00000i			0.0539949i
$344$	−4.54175	+	27.3537i	−0.244875	+	1.47482i
$345$	6.47616	+	3.73901i	0.348665	+	0.201302i
$346$	−8.05834	−	10.7493i	−0.433219	−	0.577884i
$347$	−15.3274	−	8.84928i	−0.822818	−	0.475054i	0.0285692	−	0.999592i	$-0.490905\pi$
$347$	−15.3274	−	8.84928i	−0.822818	−	0.475054i	−0.851387	+	0.524538i	$0.824238\pi$
$348$	−5.73550	+	1.39977i	−0.307455	+	0.0750357i
$349$	−4.56778	−	7.91163i	−0.244508	−	0.423500i	0.717485	−	0.696574i	$-0.245293\pi$
$349$	−4.56778	−	7.91163i	−0.244508	−	0.423500i	−0.961993	+	0.273074i	$0.911960\pi$
$350$	1.32060	+	1.76159i	0.0705890	+	0.0941608i
$351$	10.7186	+	7.50611i	0.572119	+	0.400647i
$352$	33.1024	−	2.48196i	1.76436	−	0.132289i
$353$	9.89278	−	5.71160i	0.526539	−	0.303998i	−0.213067	−	0.977038i	$-0.568345\pi$
$353$	9.89278	−	5.71160i	0.526539	−	0.303998i	0.739606	+	0.673040i	$0.235012\pi$
$354$	4.94930	−	11.5797i	0.263052	−	0.615455i
$355$	−26.6289	−	15.3742i	−1.41332	−	0.815979i
$356$	15.8072	+	4.61779i	0.837777	+	0.244742i
$357$	0.128359	−	0.222325i	0.00679349	−	0.0117667i
$358$	−22.2571	+	2.67668i	−1.17632	+	0.141467i
$359$		−	9.61189i		−	0.507296i	−0.967297	−	0.253648i	$-0.918369\pi$
$359$		−	9.61189i		−	0.507296i	0.967297	−	0.253648i	$-0.0816306\pi$
$360$	18.4079	+	3.05639i	0.970179	+	0.161086i
$361$	−24.3022	−	42.0926i	−1.27906	−	2.21540i
$362$	0.0833727	−	0.195064i	0.00438197	−	0.0102523i
$363$		−	15.2522i		−	0.800532i
$364$	−6.71908	−	2.61801i	−0.352175	−	0.137221i
$365$		−	11.2964i		−	0.591281i
$366$	−2.95490	−	1.26296i	−0.154455	−	0.0660158i
$367$	9.64903	+	16.7126i	0.503675	+	0.872391i	0.999991	+	0.00424925i	$0.00135258\pi$
$367$	9.64903	+	16.7126i	0.503675	+	0.872391i	−0.496316	+	0.868142i	$0.665314\pi$
$368$	−15.9309	+	8.26852i	−0.830457	+	0.431026i
$369$		−	22.0382i		−	1.14726i
$370$	2.51225	+	20.8898i	0.130606	+	1.08601i
$371$	0.369933	−	0.640742i	0.0192059	−	0.0332657i
$372$	−1.58525	+	5.42647i	−0.0821914	+	0.281349i
$373$	20.4823	+	11.8255i	1.06053	+	0.612300i	0.925580	−	0.378552i	$-0.123578\pi$
$373$	20.4823	+	11.8255i	1.06053	+	0.612300i	0.134954	+	0.990852i	$0.456911\pi$
$374$	3.01007	+	1.28654i	0.155647	+	0.0665252i
$375$	−4.96940	+	2.86908i	−0.256618	+	0.148159i
$376$	19.7141	−	7.39933i	1.01667	−	0.381591i
$377$	−1.42616	+	16.2913i	−0.0734508	+	0.839043i
$378$	4.10672	−	3.07866i	0.211227	−	0.158349i
$379$	1.67395	+	2.89937i	0.0859850	+	0.148930i	0.905811	−	0.423683i	$-0.139263\pi$
$379$	1.67395	+	2.89937i	0.0859850	+	0.148930i	−0.819825	+	0.572613i	$0.805930\pi$
$380$	40.9072	−	9.98357i	2.09849	−	0.512146i
$381$	−3.71653	−	2.14574i	−0.190403	−	0.109929i
$382$	13.1201	−	9.83570i	0.671285	−	0.503238i
$383$	4.74278	+	2.73824i	0.242344	+	0.139918i	0.616254	−	0.787548i	$-0.288650\pi$
$383$	4.74278	+	2.73824i	0.242344	+	0.139918i	−0.373909	+	0.927465i	$0.621983\pi$
$384$	4.92667	−	5.47221i	0.251413	−	0.279253i
$385$			15.0261i			0.765802i
$386$	−11.4052	+	1.37162i	−0.580511	+	0.0698136i
$387$	−21.8739	+	12.6289i	−1.11191	+	0.641963i
$388$	−0.915587	−	3.75157i	−0.0464819	−	0.190457i
$389$			11.4991i			0.583028i	0.956567	+	0.291514i	$0.0941591\pi$
$389$			11.4991i			0.583028i	−0.956567	+	0.291514i	$0.905841\pi$
$390$	−4.00840	+	7.49278i	−0.202973	+	0.379412i
$391$	−1.76999			−0.0895124
$392$	−1.79633	+	2.18477i	−0.0907283	+	0.110347i
$393$	1.59167	+	2.75686i	0.0802893	+	0.139065i
$394$	−2.71990	−	22.6164i	−0.137027	−	1.13940i
$395$	−5.38084			−0.270739
$396$	20.8965	+	21.8554i	1.05009	+	1.09827i
$397$	−18.1313	+	31.4043i	−0.909982	+	1.57613i	−0.0958950	+	0.995391i	$0.530571\pi$
$397$	−18.1313	+	31.4043i	−0.909982	+	1.57613i	−0.814087	+	0.580743i	$0.802762\pi$
$398$	16.6817	−	12.5057i	0.836177	−	0.626852i
$399$	2.67560	−	4.63427i	0.133947	−	0.232004i
$400$	−0.279188	+	6.22089i	−0.0139594	+	0.311044i
$401$	26.5138	−	15.3078i	1.32404	−	0.764433i	0.339666	−	0.940546i	$-0.389686\pi$
$401$	26.5138	−	15.3078i	1.32404	−	0.764433i	0.984370	+	0.176114i	$0.0563526\pi$
$402$	−6.48476	−	8.65022i	−0.323431	−	0.431434i
$403$	12.8271	+	8.98260i	0.638962	+	0.447455i
$404$	24.9561	+	7.29051i	1.24161	+	0.362716i
$405$	6.87177	+	11.9023i	0.341461	+	0.591428i
$406$	5.89823	+	2.52097i	0.292724	+	0.125114i
$407$	−17.0476	+	29.5273i	−0.845018	+	1.46361i
$408$	0.679803	−	0.255152i	0.0336553	−	0.0126319i
$409$	11.1791	+	6.45426i	0.552771	+	0.319142i	0.750239	−	0.661167i	$-0.229938\pi$
$409$	11.1791	+	6.45426i	0.552771	+	0.319142i	−0.197468	+	0.980309i	$0.563272\pi$
$410$	30.7539	−	3.69853i	1.51883	−	0.182658i
$411$	6.15102			0.303407
$412$	4.35516	+	4.55500i	0.214563	+	0.224409i
$413$	−11.8490	+	6.84105i	−0.583054	+	0.336626i
$414$	−15.0341	−	6.42574i	−0.738885	−	0.315808i
$415$	−8.32828			−0.408819
$416$	−9.97681	−	17.7894i	−0.489153	−	0.872198i
$417$	−6.07784			−0.297633
$418$	62.7436	+	26.8173i	3.06889	+	1.31168i
$419$	−2.29409	+	1.32449i	−0.112074	+	0.0647057i	−0.554989	−	0.831858i	$-0.687278\pi$
$419$	−2.29409	+	1.32449i	−0.112074	+	0.0647057i	0.442915	+	0.896563i	$0.353944\pi$
$420$	2.30337	+	2.40906i	0.112393	+	0.117550i
$421$	−15.9396			−0.776850			−0.388425	−	0.921480i	$-0.626981\pi$
$421$	−15.9396			−0.776850			−0.388425	+	0.921480i	$0.626981\pi$
$422$	−29.6842	+	3.56989i	−1.44501	+	0.173780i
$423$	16.6111	+	9.59043i	0.807660	+	0.466303i
$424$	1.95920	−	0.735352i	0.0951471	−	0.0357118i
$425$	−0.307039	+	0.531806i	−0.0148936	+	0.0257964i
$426$	−10.1630	−	4.34379i	−0.492399	−	0.210457i
$427$	1.74569	+	3.02363i	0.0844800	+	0.146324i
$428$	25.2799	+	7.38509i	1.22195	+	0.356972i
$429$	−12.4802	+	5.81884i	−0.602551	+	0.280936i
$430$	−21.2944	−	28.4052i	−1.02691	−	1.36982i
$431$	−3.08056	+	1.77856i	−0.148385	+	0.0856702i	−0.572354	−	0.820006i	$-0.693970\pi$
$431$	−3.08056	+	1.77856i	−0.148385	+	0.0856702i	0.423969	+	0.905677i	$0.360636\pi$
$432$	14.5025	+	0.650859i	0.697752	+	0.0313145i
$433$	−5.75684	+	9.97114i	−0.276656	+	0.479182i	−0.970552	−	0.240893i	$-0.922560\pi$
$433$	−5.75684	+	9.97114i	−0.276656	+	0.479182i	0.693896	+	0.720076i	$0.255893\pi$
$434$	4.91453	−	3.68425i	0.235905	−	0.176849i
$435$	3.77937	−	6.54607i	0.181207	−	0.313860i
$436$	−15.4350	−	16.1432i	−0.739202	−	0.773121i
$437$	−36.8948			−1.76492
$438$	−0.484824	−	4.03139i	−0.0231658	−	0.192627i
$439$	−19.5307	−	33.8282i	−0.932150	−	1.61453i	−0.779639	−	0.626229i	$-0.784597\pi$
$439$	−19.5307	−	33.8282i	−0.932150	−	1.61453i	−0.152511	−	0.988302i	$-0.548736\pi$
$440$	−26.9918	+	32.8286i	−1.28679	+	1.56504i
$441$	−2.57643			−0.122687
$442$	−0.0650926	−	2.01026i	−0.00309614	−	0.0956184i
$443$			20.4439i			0.971317i	0.874149	+	0.485658i	$0.161420\pi$
$443$			20.4439i			0.971317i	−0.874149	+	0.485658i	$0.838580\pi$
$444$	1.79312	+	7.34720i	0.0850975	+	0.348683i
$445$	−18.2593	+	10.5420i	−0.865572	+	0.499738i
$446$	−15.2733	+	1.83680i	−0.723211	+	0.0869750i
$447$		−	3.41121i		−	0.161345i
$448$	−7.84912	+	1.54641i	−0.370836	+	0.0730611i
$449$	−2.46737	−	1.42454i	−0.116442	−	0.0672280i	0.440648	−	0.897680i	$-0.354749\pi$
$449$	−2.46737	−	1.42454i	−0.116442	−	0.0672280i	−0.557090	+	0.830452i	$0.688082\pi$
$450$	−4.53860	+	3.40243i	−0.213952	+	0.160392i
$451$	43.4700	+	25.0974i	2.04692	+	1.18179i
$452$	−7.75510	+	1.89267i	−0.364769	+	0.0890235i
$453$	−3.48037	−	6.02818i	−0.163522	−	0.283229i
$454$	−12.3409	+	9.25150i	−0.579185	+	0.434194i
$455$	8.36765	−	3.90137i	0.392281	−	0.182899i
$456$	14.1702	−	5.31855i	0.663582	−	0.249064i
$457$	8.89367	−	5.13476i	0.416028	−	0.240194i	−0.277348	−	0.960769i	$-0.589456\pi$
$457$	8.89367	−	5.13476i	0.416028	−	0.240194i	0.693377	+	0.720575i	$0.256122\pi$
$458$	7.20865	+	3.08106i	0.336838	+	0.143969i
$459$	1.23978	+	0.715786i	0.0578679	+	0.0334100i
$460$	6.44393	−	22.0582i	0.300450	−	1.02847i
$461$	17.6759	−	30.6156i	0.823249	−	1.42591i	−0.0800005	−	0.996795i	$-0.525492\pi$
$461$	17.6759	−	30.6156i	0.823249	−	1.42591i	0.903250	−	0.429115i	$-0.141174\pi$
$462$	0.644898	+	5.36243i	0.0300034	+	0.249483i
$463$		−	8.66328i		−	0.402617i	−0.979528	−	0.201308i	$-0.935481\pi$
$463$		−	8.66328i		−	0.402617i	0.979528	−	0.201308i	$-0.0645193\pi$
$464$	8.35777	+	16.1029i	0.388000	+	0.747558i
$465$	−3.61898	−	6.26825i	−0.167826	−	0.290683i
$466$	−37.9824	−	16.2341i	−1.75950	−	0.752030i
$467$		−	12.2682i		−	0.567703i	−0.958868	−	0.283852i	$-0.908388\pi$
$467$		−	12.2682i		−	0.567703i	0.958868	−	0.283852i	$-0.0916123\pi$
$468$	6.74512	−	17.3112i	0.311793	−	0.800211i
$469$			11.7460i			0.542378i
$470$	−10.5955	+	24.7900i	−0.488736	+	1.14348i
$471$	−3.47128	−	6.01243i	−0.159948	−	0.277038i
$472$	−38.1762	−	6.33868i	−1.75720	−	0.291761i
$473$		−	57.5279i		−	2.64513i
$474$	−1.92028	+	0.230937i	−0.0882014	+	0.0106073i
$475$	−6.40010	+	11.0853i	−0.293657	+	0.508628i
$476$	−0.757252	−	0.221218i	−0.0347086	−	0.0101395i
$477$	1.65083	+	0.953105i	0.0755861	+	0.0436397i
$478$	−15.7655	+	36.8860i	−0.721097	+	1.68713i
$479$	−14.1707	+	8.18145i	−0.647475	+	0.373820i	−0.787488	−	0.616330i	$-0.788619\pi$
$479$	−14.1707	+	8.18145i	−0.647475	+	0.373820i	0.140013	+	0.990150i	$0.455286\pi$
$480$	0.704861	+	9.40084i	0.0321723	+	0.429088i
$481$	20.8692	+	1.82691i	0.951553	+	0.0833001i
$482$	−19.1716	−	25.5736i	−0.873244	−	1.16485i
$483$	−1.46020	−	2.52913i	−0.0664412	−	0.115080i
$484$	−45.5339	+	11.1127i	−2.06972	+	0.505125i
$485$	4.28176	+	2.47208i	0.194425	+	0.112251i
$486$	12.1992	+	16.2728i	0.553365	+	0.738150i
$487$	−3.57047	−	2.06141i	−0.161794	−	0.0934116i	0.416917	−	0.908945i	$-0.363111\pi$
$487$	−3.57047	−	2.06141i	−0.161794	−	0.0934116i	−0.578711	+	0.815533i	$0.696444\pi$
$488$	−1.61750	+	9.74176i	−0.0732207	+	0.440989i
$489$			7.80655i			0.353024i
$490$	−0.432386	−	3.59536i	−0.0195332	−	0.162422i
$491$	14.6287	−	8.44590i	0.660186	−	0.381158i	−0.132162	−	0.991228i	$-0.542192\pi$
$491$	14.6287	−	8.44590i	0.660186	−	0.381158i	0.792348	+	0.610070i	$0.208859\pi$
$492$	10.8165	−	2.63982i	0.487647	−	0.119012i
$493$			1.78910i			0.0805770i
$494$	−1.35683	−	41.9031i	−0.0610466	−	1.88531i
$495$	−38.7137			−1.74005
$496$	17.3552	+	0.778886i	0.779272	+	0.0349730i
$497$	6.00409	+	10.3994i	0.269320	+	0.466477i
$498$	−2.97215	+	0.357437i	−0.133185	+	0.0160171i
$499$	9.73748			0.435909			0.217955	−	0.975959i	$-0.430061\pi$
$499$	9.73748			0.435909			0.217955	+	0.975959i	$0.430061\pi$
$500$	12.1861	+	12.7452i	0.544978	+	0.569984i
$501$	0.0978091	−	0.169410i	0.00436979	−	0.00756870i
$502$	10.6692	+	14.2320i	0.476192	+	0.635207i
$503$	−8.71964	+	15.1029i	−0.388789	+	0.673403i	−0.992287	−	0.123962i	$-0.960440\pi$
$503$	−8.71964	+	15.1029i	−0.388789	+	0.673403i	0.603498	+	0.797365i	$0.293773\pi$
$504$	−5.62889	−	4.62811i	−0.250731	−	0.206152i
$505$	−28.8275	+	16.6436i	−1.28281	+	0.740628i
$506$	29.7957	−	22.3368i	1.32458	−	0.992991i
$507$	6.48071	+	5.43912i	0.287819	+	0.241560i
$508$	−3.69803	+	12.6587i	−0.164074	+	0.561640i
$509$	−19.3856	−	33.5768i	−0.859251	−	1.48827i	−0.872644	−	0.488356i	$-0.837597\pi$
$509$	−19.3856	−	33.5768i	−0.859251	−	1.48827i	0.0133935	−	0.999910i	$-0.495737\pi$
$510$	−0.365368	+	0.854838i	−0.0161787	+	0.0378529i
$511$	−2.20579	+	3.82054i	−0.0975785	+	0.169011i
$512$	−19.9263	−	10.7210i	−0.880628	−	0.473807i
$513$	25.8427	+	14.9203i	1.14098	+	0.658746i
$514$	0.925977	+	7.69965i	0.0408431	+	0.339617i
$515$	−8.06855			−0.355543
$516$	−8.81851	−	9.22315i	−0.388213	−	0.406027i
$517$	−37.8340	+	21.8434i	−1.66394	+	0.960674i
$518$	3.22938	−	7.55567i	0.141891	−	0.331977i
$519$	6.18254			0.271384
$520$	25.2895	+	6.50747i	1.10902	+	0.285371i
$521$	26.7126			1.17030			0.585151	−	0.810924i	$-0.301035\pi$
$521$	26.7126			1.17030			0.585151	+	0.810924i	$0.301035\pi$
$522$	−6.49511	+	15.1964i	−0.284283	+	0.665127i
$523$	30.1920	−	17.4313i	1.32020	−	0.762220i	0.336442	−	0.941704i	$-0.390776\pi$
$523$	30.1920	−	17.4313i	1.32020	−	0.762220i	0.983761	+	0.179485i	$0.0574430\pi$
$524$	7.07065	−	6.76044i	0.308883	−	0.295331i
$525$	−1.01319			−0.0442194
$526$	−1.63112	−	13.5630i	−0.0711201	−	0.591375i
$527$	1.48365	+	0.856585i	0.0646288	+	0.0373134i
$528$	−8.22373	+	12.8741i	−0.357892	+	0.560274i
$529$	1.43241	−	2.48101i	0.0622787	−	0.107870i
$530$	−1.05299	+	2.46365i	−0.0457391	+	0.107014i
$531$	−17.6255	−	30.5282i	−0.764881	−	1.32481i
$532$	−15.7846	−	4.61121i	−0.684350	−	0.199921i
$533$	2.68958	−	30.7236i	0.116499	−	1.33079i
$534$	−6.06381	+	4.54582i	−0.262407	+	0.196717i
$535$	−29.2015	+	16.8595i	−1.26249	+	0.728898i
$536$	−21.0996	+	25.6622i	−0.911364	+	1.10844i
$537$	5.15828	−	8.93440i	0.222596	−	0.385548i
$538$	19.0852	+	25.4583i	0.822820	+	1.09758i
$539$	2.93407	−	5.08197i	0.126380	−	0.218896i
$540$	−13.4340	+	12.8446i	−0.578105	+	0.552742i
$541$	1.88293			0.0809534			0.0404767	−	0.999180i	$-0.487112\pi$
$541$	1.88293			0.0809534			0.0404767	+	0.999180i	$0.487112\pi$
$542$	−18.3181	+	2.20297i	−0.786828	+	0.0946257i
$543$	0.0488124	+	0.0845455i	0.00209474	+	0.00362819i
$544$	−1.25704	−	1.84358i	−0.0538951	−	0.0790430i
$545$	28.5955			1.22490
$546$	2.81876	−	1.75142i	0.120632	−	0.0749540i
$547$			8.04473i			0.343968i	0.985100	+	0.171984i	$0.0550177\pi$
$547$			8.04473i			0.343968i	−0.985100	+	0.171984i	$0.944982\pi$
$548$	−4.48164	−	18.3633i	−0.191446	−	0.784440i
$549$	−7.79016	+	4.49765i	−0.332476	+	0.191955i
$550$	−1.54261	−	12.8271i	−0.0657772	−	0.546948i
$551$			37.2931i			1.58874i
$552$	1.35297	−	8.14856i	0.0575861	−	0.346826i
$553$	1.81985	+	1.05069i	0.0773878	+	0.0446798i
$554$	−5.65506	−	7.54345i	−0.240260	−	0.320491i
$555$	−8.38555	−	4.84140i	−0.355947	−	0.205506i
$556$	4.42832	+	18.1448i	0.187802	+	0.769511i
$557$	19.4307	+	33.6550i	0.823307	+	1.42601i	0.903207	+	0.429206i	$0.141207\pi$
$557$	19.4307	+	33.6550i	0.823307	+	1.42601i	−0.0799002	+	0.996803i	$0.525460\pi$
$558$	9.49220	+	12.6619i	0.401837	+	0.536022i
$559$	−32.0358	+	14.9365i	−1.35497	+	0.631746i
$560$	5.51378	−	8.63173i	0.233000	−	0.364757i
$561$	−1.30463	+	0.753231i	−0.0550817	+	0.0318014i
$562$	3.31271	−	7.75064i	0.139738	−	0.326941i
$563$	−28.0201	−	16.1774i	−1.18091	−	0.681797i	−0.224683	−	0.974432i	$-0.572135\pi$
$563$	−28.0201	−	16.1774i	−1.18091	−	0.681797i	−0.956224	+	0.292634i	$0.905468\pi$
$564$	−2.71732	+	9.30166i	−0.114420	+	0.391670i
$565$	5.11018	−	8.85109i	0.214987	−	0.372368i
$566$	−18.7641	+	2.25661i	−0.788714	+	0.0948525i
$567$		−	5.36727i		−	0.225404i
$568$	−5.56318	+	33.5056i	−0.233426	+	1.40586i
$569$	12.1335	+	21.0158i	0.508661	+	0.881027i	0.999950	+	0.0100300i	$0.00319270\pi$
$569$	12.1335	+	21.0158i	0.508661	+	0.881027i	−0.491289	+	0.870997i	$0.663474\pi$
$570$	−7.61594	+	17.8188i	−0.318997	+	0.746346i
$571$		−	44.0313i		−	1.84265i	−0.388791	−	0.921326i	$-0.627107\pi$
$571$		−	44.0313i		−	1.84265i	0.388791	−	0.921326i	$-0.372893\pi$
$572$	26.4647	+	33.0189i	1.10654	+	1.38059i
$573$			7.54618i			0.315246i
$574$	−11.1234	−	4.75428i	−0.464283	−	0.198440i
$575$	3.49283	+	6.04975i	0.145661	+	0.252292i
$576$	−3.98422	−	20.2227i	−0.166009	−	0.842612i
$577$			15.4185i			0.641879i	0.947100	+	0.320939i	$0.103999\pi$
$577$			15.4185i			0.641879i	−0.947100	+	0.320939i	$0.896001\pi$
$578$	2.84434	+	23.6512i	0.118309	+	0.983759i
$579$	2.64327	−	4.57827i	0.109850	−	0.190267i
$580$	−22.2963	−	6.51349i	−0.925804	−	0.270458i
$581$	2.81670	+	1.62622i	0.116856	+	0.0674670i
$582$	1.63415	+	0.698453i	0.0677376	+	0.0289518i
$583$	−3.75997	+	2.17082i	−0.155722	+	0.0899062i
$584$	−11.6821	+	4.38467i	−0.483408	+	0.181439i
$585$	10.0516	+	21.5586i	0.415582	+	0.891340i
$586$	2.70199	−	2.02559i	0.111618	−	0.0836762i
$587$	2.86153	+	4.95632i	0.118108	+	0.204569i	0.919018	−	0.394216i	$-0.128984\pi$
$587$	2.86153	+	4.95632i	0.118108	+	0.204569i	−0.800910	+	0.598785i	$0.795650\pi$
$588$	−0.308615	−	1.26453i	−0.0127271	−	0.0521485i
$589$	30.9261	+	17.8552i	1.27429	+	0.735710i
$590$	39.6436	−	29.7194i	1.63210	−	1.22353i
$591$	9.07864	+	5.24155i	0.373445	+	0.215609i
$592$	20.6279	−	10.7064i	0.847802	−	0.440028i
$593$		−	36.2044i		−	1.48674i	−0.668882	−	0.743369i	$-0.733227\pi$
$593$		−	36.2044i		−	1.48674i	0.668882	−	0.743369i	$-0.266773\pi$
$594$	−29.9032	+	3.59623i	−1.22694	+	0.147555i
$595$	0.874721	−	0.505021i	0.0358601	−	0.0207038i
$596$	−10.1838	+	2.48541i	−0.417146	+	0.101806i
$597$			9.59463i			0.392682i
$598$	−20.1749	−	10.7930i	−0.825013	−	0.441357i
$599$	40.2012			1.64258			0.821288	−	0.570514i	$-0.193256\pi$
$599$	40.2012			1.64258			0.821288	+	0.570514i	$0.193256\pi$
$600$	−2.21359	−	1.82003i	−0.0903696	−	0.0743024i
$601$	14.0537	+	24.3417i	0.573263	+	0.992921i	0.996228	+	0.0867746i	$0.0276560\pi$
$601$	14.0537	+	24.3417i	0.573263	+	0.992921i	−0.422965	+	0.906146i	$0.639011\pi$
$602$	1.65540	+	13.7649i	0.0674691	+	0.561017i
$603$	−30.2626			−1.23239
$604$	−15.4608	+	14.7825i	−0.629090	+	0.601490i
$605$	30.0043	−	51.9690i	1.21985	−	2.11284i
$606$	−9.57346	+	7.17688i	−0.388895	+	0.291541i
$607$	11.3280	−	19.6207i	0.459789	−	0.796379i	−0.539160	−	0.842203i	$-0.681258\pi$
$607$	11.3280	−	19.6207i	0.459789	−	0.796379i	0.998949	+	0.0458247i	$0.0145916\pi$
$608$	−26.2025	−	38.4288i	−1.06265	−	1.55849i
$609$	−2.55644	+	1.47596i	−0.103592	+	0.0598089i
$610$	−7.58377	−	10.1162i	−0.307058	−	0.409594i
$611$	21.9872	+	15.3973i	0.889508	+	0.622909i
$612$	0.569953	−	1.95100i	0.0230390	−	0.0788647i
$613$	5.37441	+	9.30875i	0.217070	+	0.375977i	0.953911	−	0.300090i	$-0.0970166\pi$
$613$	5.37441	+	9.30875i	0.217070	+	0.375977i	−0.736841	+	0.676066i	$0.763683\pi$
$614$	17.2915	+	7.39060i	0.697830	+	0.298261i
$615$	−7.12749	+	12.3452i	−0.287408	+	0.497806i
$616$	15.5391	−	5.83235i	0.626090	−	0.234992i
$617$	−18.4619	−	10.6590i	−0.743248	−	0.429115i	0.0800008	−	0.996795i	$-0.474508\pi$
$617$	−18.4619	−	10.6590i	−0.743248	−	0.429115i	−0.823249	+	0.567680i	$0.807841\pi$
$618$	−2.87946	+	0.346290i	−0.115829	+	0.0139298i
$619$	33.9007			1.36258			0.681292	−	0.732012i	$-0.261419\pi$
$619$	33.9007			1.36258			0.681292	+	0.732012i	$0.261419\pi$
$620$	−16.0765	+	15.3712i	−0.645647	+	0.617321i
$621$	14.1035	−	8.14268i	0.565955	−	0.326755i
$622$	13.1523	+	5.62145i	0.527360	+	0.225400i
$623$	8.23393			0.329885
$624$	9.30445	+	1.23696i	0.372476	+	0.0495180i
$625$	−30.3603			−1.21441
$626$	−16.3350	−	6.98176i	−0.652877	−	0.279047i
$627$	−27.1946	+	15.7008i	−1.08605	+	0.627030i
$628$	−15.4204	+	14.7438i	−0.615339	+	0.588343i
$629$	2.29185			0.0913819
$630$	9.26319	−	1.11401i	0.369054	−	0.0443833i
$631$	40.7392	+	23.5208i	1.62180	+	0.936347i	0.986438	+	0.164133i	$0.0524827\pi$
$631$	40.7392	+	23.5208i	1.62180	+	0.936347i	0.635363	+	0.772214i	$0.280851\pi$
$632$	2.08856	+	5.56455i	0.0830784	+	0.221346i
$633$	6.87958	−	11.9158i	0.273439	−	0.473610i
$634$	29.2650	+	12.5082i	1.16226	+	0.496764i
$635$	−8.44226	−	14.6224i	−0.335021	−	0.580273i
$636$	−0.270050	+	0.924406i	−0.0107082	+	0.0366551i
$637$	−3.59181	−	0.314432i	−0.142313	−	0.0124582i
$638$	−22.5779	−	30.1174i	−0.893868	−	1.19236i
$639$	−26.7933	+	15.4691i	−1.05993	+	0.611949i
$640$	27.5518	−	8.95375i	1.08908	−	0.353928i
$641$	−8.20891	+	14.2182i	−0.324232	+	0.561587i	−0.981357	−	0.192195i	$-0.938439\pi$
$641$	−8.20891	+	14.2182i	−0.324232	+	0.561587i	0.657124	+	0.753782i	$0.271773\pi$
$642$	−9.69766	+	7.26999i	−0.382736	+	0.286923i
$643$	18.6383	−	32.2825i	0.735022	−	1.27310i	−0.219691	−	0.975569i	$-0.570505\pi$
$643$	18.6383	−	32.2825i	0.735022	−	1.27310i	0.954714	−	0.297526i	$-0.0961616\pi$
$644$	−6.48659	+	6.20201i	−0.255607	+	0.244393i
$645$	16.3375			0.643289
$646$	−0.547655	−	4.55384i	−0.0215472	−	0.179168i
$647$	−11.1984	−	19.3963i	−0.440256	−	0.762546i	0.557452	−	0.830209i	$-0.311779\pi$
$647$	−11.1984	−	19.3963i	−0.440256	−	0.762546i	−0.997708	+	0.0676631i	$0.978446\pi$
$648$	9.64137	−	11.7262i	0.378749	−	0.460650i
$649$	80.2886			3.15160
$650$	−6.74253	+	4.18945i	−0.264464	+	0.164324i
$651$			2.82664i			0.110785i
$652$	23.3057	−	5.68786i	0.912722	−	0.222754i
$653$	−36.8599	+	21.2811i	−1.44244	+	0.832793i	−0.998012	−	0.0630219i	$-0.979926\pi$
$653$	−36.8599	+	21.2811i	−1.44244	+	0.832793i	−0.444427	+	0.895815i	$0.646593\pi$
$654$	10.2050	−	1.22727i	0.399046	−	0.0479902i
$655$			12.5247i			0.489379i
$656$	−15.7619	−	30.3684i	−0.615398	−	1.18568i
$657$	−9.84335	−	5.68306i	−0.384026	−	0.221717i
$658$	8.42413	−	6.31527i	0.328407	−	0.246195i
$659$	14.9454	+	8.62872i	0.582189	+	0.336127i	0.762003	−	0.647573i	$-0.224216\pi$
$659$	14.9454	+	8.62872i	0.582189	+	0.336127i	−0.179814	+	0.983701i	$0.557549\pi$
$660$	−4.63728	−	19.0010i	−0.180506	−	0.739614i
$661$	0.0864595	+	0.149752i	0.00336288	+	0.00582469i	0.867702	−	0.497085i	$-0.165596\pi$
$661$	0.0864595	+	0.149752i	0.00336288	+	0.00582469i	−0.864339	+	0.502910i	$0.832263\pi$
$662$	0.370121	−	0.277467i	0.0143852	−	0.0107840i
$663$	0.758189	+	0.530949i	0.0294456	+	0.0206203i
$664$	3.23260	+	8.61263i	0.125449	+	0.334235i
$665$	18.2332	−	10.5270i	0.707054	−	0.408218i
$666$	19.4666	+	8.32027i	0.754317	+	0.322404i
$667$	17.6258	+	10.1763i	0.682474	+	0.394027i
$668$	−0.577022	−	0.168567i	−0.0223257	−	0.00652207i
$669$	3.53972	−	6.13098i	0.136854	−	0.237037i
$670$	−5.07879	−	42.2310i	−0.196211	−	1.63153i
$671$		−	20.4880i		−	0.790929i
$672$	1.59727	−	3.31708i	0.0616158	−	0.127959i
$673$	20.3722	+	35.2857i	0.785291	+	1.36016i	0.928825	+	0.370518i	$0.120820\pi$
$673$	20.3722	+	35.2857i	0.785291	+	1.36016i	−0.143535	+	0.989645i	$0.545847\pi$
$674$	−17.2394	−	7.36832i	−0.664037	−	0.283817i
$675$		−	5.65001i		−	0.217469i
$676$	11.5161	−	23.3105i	0.442927	−	0.896558i
$677$			35.7998i			1.37590i	0.725758	+	0.687950i	$0.241489\pi$
$677$			35.7998i			1.37590i	−0.725758	+	0.687950i	$0.758511\pi$
$678$	1.44382	−	3.37805i	0.0554494	−	0.129733i
$679$	−0.965421	−	1.67216i	−0.0370494	−	0.0641715i
$680$	2.81825	+	0.467934i	0.108075	+	0.0179445i
$681$		−	7.09797i		−	0.271995i
$682$	−35.7853	+	4.30362i	−1.37029	+	0.164794i
$683$	−1.95916	+	3.39337i	−0.0749652	+	0.129844i	−0.901071	−	0.433671i	$-0.857218\pi$
$683$	−1.95916	+	3.39337i	−0.0749652	+	0.129844i	0.826106	+	0.563515i	$0.190551\pi$
$684$	11.8804	−	40.6679i	0.454260	−	1.55498i
$685$	20.9585	+	12.1004i	0.800782	+	0.462332i
$686$	−0.555811	+	1.30041i	−0.0212210	+	0.0496500i
$687$	−3.12440	+	1.80387i	−0.119203	+	0.0688221i
$688$	−21.1097	+	33.0468i	−0.804799	+	1.25990i
$689$	2.18511	+	1.53020i	0.0832460	+	0.0582959i
$690$	6.34350	+	8.46178i	0.241493	+	0.322135i
$691$	14.4215	+	24.9787i	0.548618	+	0.950235i	0.998370	+	0.0570807i	$0.0181792\pi$
$691$	14.4215	+	24.9787i	0.548618	+	0.950235i	−0.449751	+	0.893154i	$0.648487\pi$
$692$	−4.50461	−	18.4574i	−0.171239	−	0.701645i
$693$	13.0933	+	7.55943i	0.497374	+	0.287159i
$694$	−15.0134	−	20.0269i	−0.569902	−	0.760209i
$695$	−20.7091	−	11.9564i	−0.785542	−	0.453533i
$696$	−8.23652	−	1.36757i	−0.312205	−	0.0518377i
$697$		−	3.37405i		−	0.127801i
$698$	−1.54263	−	12.8272i	−0.0583894	−	0.485517i
$699$	16.4625	−	9.50461i	0.622668	−	0.359497i
$700$	0.738214	+	3.02480i	0.0279019	+	0.114327i
$701$			6.25079i			0.236089i	0.993008	+	0.118045i	$0.0376626\pi$
$701$			6.25079i			0.236089i	−0.993008	+	0.118045i	$0.962337\pi$
$702$	9.76669	+	15.7186i	0.368620	+	0.593260i
$703$	47.7726			1.80178
$704$	44.4262	+	15.1711i	1.67438	+	0.571782i
$705$	−6.20339	−	10.7446i	−0.233633	−	0.404665i
$706$	16.0393	−	1.92892i	0.603646	−	0.0725958i
$707$	12.9996			0.488901
$708$	12.8723	−	12.3075i	0.483769	−	0.462545i
$709$	−0.217747	+	0.377148i	−0.00817764	+	0.0141641i	−0.870085	−	0.492901i	$-0.835936\pi$
$709$	−0.217747	+	0.377148i	−0.00817764	+	0.0141641i	0.861908	+	0.507065i	$0.169270\pi$
$710$	−26.0834	−	34.7935i	−0.978894	−	1.30578i
$711$	−2.70703	+	4.68871i	−0.101521	+	0.175840i
$712$	17.9892	+	14.7908i	0.674174	+	0.554310i
$713$	16.8778	−	9.74439i	0.632078	−	0.364930i
$714$	0.290491	−	0.217770i	0.0108713	−	0.00814985i
$715$	−53.9710	−	4.72469i	−2.01840	−	0.176693i
$716$	−30.4311	−	8.88993i	−1.13726	−	0.332232i
$717$	−9.23025	−	15.9873i	−0.344710	−	0.597055i
$718$	5.34240	−	12.4994i	0.199377	−	0.466475i
$719$	−4.48502	+	7.76829i	−0.167263	+	0.289708i	−0.937457	−	0.348102i	$-0.886826\pi$
$719$	−4.48502	+	7.76829i	−0.167263	+	0.289708i	0.770193	+	0.637810i	$0.220160\pi$
$720$	22.2390	+	14.2059i	0.828800	+	0.529421i
$721$	2.72886	+	1.57551i	0.101628	+	0.0586749i
$722$	−8.20732	−	68.2452i	−0.305445	−	2.53982i
$723$	14.7089			0.547031
$724$	0.216838	−	0.207325i	0.00805871	−	0.00770516i
$725$	6.11506	−	3.53053i	0.227108	−	0.131121i
$726$	8.47733	−	19.8341i	0.314623	−	0.736114i
$727$	12.8658			0.477167			0.238583	−	0.971122i	$-0.423317\pi$
$727$	12.8658			0.477167			0.238583	+	0.971122i	$0.423317\pi$
$728$	−7.28245	−	7.13904i	−0.269906	−	0.264590i
$729$	6.74232			0.249716
$730$	6.27867	−	14.6900i	0.232384	−	0.543701i
$731$	−3.34889	+	1.93349i	−0.123863	+	0.0715125i
$732$	−3.14062	−	3.28473i	−0.116081	−	0.121407i
$733$	23.5196			0.868715			0.434358	−	0.900741i	$-0.356975\pi$
$733$	23.5196			0.868715			0.434358	+	0.900741i	$0.356975\pi$
$734$	3.25867	+	27.0963i	0.120280	+	1.00014i
$735$	1.44324	+	0.833257i	0.0532348	+	0.0307352i
$736$	−25.3125	+	1.89789i	−0.933032	+	0.0699573i
$737$	34.4635	−	59.6926i	1.26948	−	2.19881i
$738$	12.2491	−	28.6587i	0.450895	−	1.05494i
$739$	−2.40984	−	4.17397i	−0.0886476	−	0.153542i	0.818292	−	0.574803i	$-0.194921\pi$
$739$	−2.40984	−	4.17397i	−0.0886476	−	0.153542i	−0.906940	+	0.421260i	$0.861588\pi$
$740$	−8.34382	+	28.5617i	−0.306725	+	1.04995i
$741$	15.8041	+	11.0674i	0.580580	+	0.406572i
$742$	0.837197	−	0.627617i	0.0307345	−	0.0230405i
$743$	25.8545	−	14.9271i	0.948510	−	0.547622i	0.0558920	−	0.998437i	$-0.482200\pi$
$743$	25.8545	−	14.9271i	0.948510	−	0.547622i	0.892618	+	0.450814i	$0.148866\pi$
$744$	−5.07757	+	6.17555i	−0.186153	+	0.226407i
$745$	6.71058	−	11.6231i	0.245857	−	0.425836i
$746$	20.0627	+	26.7623i	0.734549	+	0.979838i
$747$	−4.18984	+	7.25702i	−0.153298	+	0.265520i
$748$	3.19926	+	3.34606i	0.116976	+	0.122344i
$749$	13.1683			0.481158
$750$	−8.05693	+	0.968945i	−0.294198	+	0.0353809i
$751$	21.2550	+	36.8148i	0.775607	+	1.34339i	0.934453	+	0.356087i	$0.115889\pi$
$751$	21.2550	+	36.8148i	0.775607	+	1.34339i	−0.158846	+	0.987303i	$0.550777\pi$
$752$	29.7490	+	1.33511i	1.08484	+	0.0486865i
$753$	−8.18569			−0.298303
$754$	−10.9095	+	20.3927i	−0.397299	+	0.742658i
$755$		−	27.3866i		−	0.996700i
$756$	7.05158	−	1.72097i	0.256463	−	0.0625910i
$757$	−31.4654	+	18.1666i	−1.14363	+	0.660275i	−0.947327	−	0.320269i	$-0.896227\pi$
$757$	−31.4654	+	18.1666i	−1.14363	+	0.660275i	−0.196303	+	0.980543i	$0.562894\pi$
$758$	0.565326	+	4.70077i	0.0205336	+	0.170740i
$759$			17.1373i			0.622045i
$760$	58.7452	+	9.75391i	2.13091	+	0.353811i
$761$	38.1369	+	22.0183i	1.38246	+	0.798164i	0.992450	−	0.122646i	$-0.0391381\pi$
$761$	38.1369	+	22.0183i	1.38246	+	0.798164i	0.390010	+	0.920810i	$0.372471\pi$
$762$	−3.64039	−	4.85603i	−0.131878	−	0.175915i
$763$	−9.67125	−	5.58370i	−0.350123	−	0.202143i
$764$	22.5284	−	5.49815i	0.815048	−	0.198916i
$765$	1.30115	+	2.25366i	0.0470432	+	0.0814811i
$766$	4.64562	+	6.19693i	0.167853	+	0.223904i
$767$	−20.8461	−	44.7106i	−0.752708	−	1.61441i
$768$	9.44822	−	4.37784i	0.340933	−	0.157972i
$769$	−13.0704	+	7.54618i	−0.471329	+	0.272122i	−0.716796	−	0.697283i	$-0.754392\pi$
$769$	−13.0704	+	7.54618i	−0.471329	+	0.272122i	0.245467	+	0.969405i	$0.421059\pi$
$770$	−8.35168	+	19.5402i	−0.300974	+	0.704178i
$771$	−3.09078	−	1.78446i	−0.111312	−	0.0642659i
$772$	−15.5939	−	4.55549i	−0.561236	−	0.163956i
$773$	7.62631	−	13.2092i	0.274299	−	0.475100i	−0.695659	−	0.718372i	$-0.744887\pi$
$773$	7.62631	−	13.2092i	0.274299	−	0.475100i	0.969958	+	0.243272i	$0.0782208\pi$
$774$	−35.4644	+	4.26502i	−1.27474	+	0.153303i
$775$		−	6.76139i		−	0.242876i
$776$	0.894525	−	5.38749i	0.0321116	−	0.193399i
$777$	1.89071	+	3.27481i	0.0678289	+	0.117483i
$778$	−6.39134	+	14.9536i	−0.229141	+	0.536113i
$779$		−	70.3307i		−	2.51986i
$780$	−9.37715	+	7.51579i	−0.335756	+	0.269108i
$781$		−	70.4658i		−	2.52147i
$782$	−2.30172	−	0.983782i	−0.0823094	−	0.0351800i
$783$	−8.23058	−	14.2558i	−0.294137	−	0.509460i
$784$	−3.55029	+	1.84268i	−0.126796	+	0.0658100i
$785$		−	27.3150i		−	0.974914i
$786$	0.537539	+	4.46973i	0.0191734	+	0.159430i
$787$	7.13152	−	12.3521i	0.254211	−	0.440307i	−0.710470	−	0.703728i	$-0.751518\pi$
$787$	7.13152	−	12.3521i	0.254211	−	0.440307i	0.964681	+	0.263421i	$0.0848509\pi$
$788$	9.03346	−	30.9224i	0.321804	−	1.10157i
$789$	5.44444	+	3.14335i	0.193827	+	0.111906i
$790$	−6.99731	−	2.99073i	−0.248953	−	0.106405i
$791$	−3.45662	+	1.99568i	−0.122903	+	0.0709582i
$792$	15.0266	+	40.0355i	0.533948	+	1.42260i
$793$	−11.4092	+	5.31948i	−0.405153	+	0.188900i
$794$	−41.0330	+	30.7610i	−1.45621	+	1.09167i
$795$	−0.616498	−	1.06781i	−0.0218649	−	0.0378712i
$796$	28.6439	−	6.99065i	1.01525	−	0.247777i
$797$	23.4643	+	13.5471i	0.831147	+	0.479863i	0.854245	−	0.519870i	$-0.174020\pi$
$797$	23.4643	+	13.5471i	0.831147	+	0.479863i	−0.0230979	+	0.999733i	$0.507353\pi$
$798$	6.05516	−	4.53934i	0.214350	−	0.160691i
$799$	2.54316	+	1.46830i	0.0899706	+	0.0519446i
$800$	−3.82070	+	7.93455i	−0.135082	+	0.280529i
$801$			21.2141i			0.749564i
$802$	42.9871	−	5.16973i	1.51793	−	0.182549i
$803$	22.4195	−	12.9439i	0.791168	−	0.456781i
$804$	−3.62498	−	14.8532i	−0.127843	−	0.523831i
$805$		−	11.4901i		−	0.404972i
$806$	11.6878	+	18.8105i	0.411687	+	0.662572i
$807$	−14.6426			−0.515443
$808$	28.4011	+	23.3516i	0.999148	+	0.821505i
$809$	7.54079	+	13.0610i	0.265120	+	0.459201i	0.967595	−	0.252507i	$-0.0812551\pi$
$809$	7.54079	+	13.0610i	0.265120	+	0.459201i	−0.702475	+	0.711708i	$0.747922\pi$
$810$	2.32073	+	19.2973i	0.0815422	+	0.678037i
$811$	32.0888			1.12679			0.563394	−	0.826188i	$-0.309495\pi$
$811$	32.0888			1.12679			0.563394	+	0.826188i	$0.309495\pi$
$812$	6.26896	+	6.55661i	0.219997	+	0.230092i
$813$	4.24538	−	7.35321i	0.148892	−	0.257888i
$814$	−38.5805	+	28.9224i	−1.35225	+	1.01373i
$815$	−15.3572	+	26.5994i	−0.537938	+	0.931736i
$816$	1.02584	+	0.0460388i	0.0359116	+	0.00161168i
$817$	−69.8064	+	40.3027i	−2.44222	+	1.41001i
$818$	10.9501	+	14.6067i	0.382861	+	0.510710i
$819$	0.810111	−	9.25405i	0.0283076	−	0.323363i
$820$	42.0485	+	12.2837i	1.46840	+	0.428967i
$821$	−21.1373	−	36.6109i	−0.737697	−	1.27773i	−0.953530	−	0.301299i	$-0.902580\pi$
$821$	−21.1373	−	36.6109i	−0.737697	−	1.27773i	0.215833	−	0.976430i	$-0.430753\pi$
$822$	7.99886	+	3.41880i	0.278992	+	0.119245i
$823$	19.8122	−	34.3157i	0.690609	−	1.19617i	−0.281029	−	0.959699i	$-0.590676\pi$
$823$	19.8122	−	34.3157i	0.690609	−	1.19617i	0.971639	−	0.236471i	$-0.0759908\pi$
$824$	3.13179	+	8.34403i	0.109101	+	0.290678i
$825$	5.14902	+	2.97279i	0.179266	+	0.103499i
$826$	−19.2110	+	2.31036i	−0.668436	+	0.0803876i
$827$	−28.1004			−0.977146			−0.488573	−	0.872523i	$-0.662482\pi$
$827$	−28.1004			−0.977146			−0.488573	+	0.872523i	$0.662482\pi$
$828$	−15.9790	−	16.7122i	−0.555309	−	0.580790i
$829$	15.6690	−	9.04650i	0.544207	−	0.314198i	−0.202575	−	0.979267i	$-0.564931\pi$
$829$	15.6690	−	9.04650i	0.544207	−	0.314198i	0.746782	+	0.665069i	$0.231598\pi$
$830$	−10.8302	−	4.62895i	−0.375922	−	0.160673i
$831$	4.33869			0.150508
$832$	−3.08641	−	28.6788i	−0.107002	−	0.994259i
$833$	−0.394451			−0.0136669
$834$	−7.90370	−	3.37813i	−0.273683	−	0.116975i
$835$	0.666534	−	0.384823i	0.0230663	−	0.0133174i
$836$	66.6873	+	69.7472i	2.30643	+	2.41226i
$837$	−15.7626			−0.544834
$838$	−3.71943	+	0.447307i	−0.128486	+	0.0154520i
$839$	24.4060	+	14.0908i	0.842589	+	0.486469i	0.858143	−	0.513410i	$-0.171618\pi$
$839$	24.4060	+	14.0908i	0.842589	+	0.486469i	−0.0155547	+	0.999879i	$0.504951\pi$
$840$	1.65635	+	4.41301i	0.0571494	+	0.152263i
$841$	−4.21388	+	7.29866i	−0.145306	+	0.251678i
$842$	−20.7281	−	8.85942i	−0.714337	−	0.305316i
$843$	1.93950	+	3.35931i	0.0667999	+	0.115701i
$844$	−40.5859	−	11.8565i	−1.39703	−	0.408117i
$845$	11.3819	+	31.2818i	0.391550	+	1.07613i
$846$	16.2708	+	21.7042i	0.559403	+	0.746204i
$847$	−20.2955	+	11.7176i	−0.697360	+	0.402621i
$848$	2.95648	+	0.132684i	0.101526	+	0.00455640i
$849$	4.34875	−	7.53225i	0.149249	−	0.258506i
$850$	−0.694861	+	0.520912i	−0.0238335	+	0.0178671i
$851$	13.0359	−	22.5788i	0.446863	−	0.773990i
$852$	−10.8018	−	11.2974i	−0.370063	−	0.387044i
$853$	−52.2710			−1.78973			−0.894863	−	0.446341i	$-0.852727\pi$
$853$	−52.2710			−1.78973			−0.894863	+	0.446341i	$0.852727\pi$
$854$	0.589555	+	4.90224i	0.0201741	+	0.167751i
$855$	27.1219	+	46.9766i	0.927551	+	1.60657i
$856$	28.7696	+	23.6545i	0.983324	+	0.808495i
$857$	−36.0636			−1.23191			−0.615954	−	0.787782i	$-0.711229\pi$
$857$	−36.0636			−1.23191			−0.615954	+	0.787782i	$0.711229\pi$
$858$	−19.4636	+	0.630235i	−0.664477	+	0.0215159i
$859$			19.3662i			0.660766i	0.943847	+	0.330383i	$0.107178\pi$
$859$			19.3662i			0.660766i	−0.943847	+	0.330383i	$0.892822\pi$
$860$	−11.9035	−	48.7741i	−0.405907	−	1.66318i
$861$	4.82117	−	2.78350i	0.164305	−	0.0948615i
$862$	−4.99454	+	0.600654i	−0.170115	+	0.0204584i
$863$		−	27.7762i		−	0.945512i	−0.881193	−	0.472756i	$-0.843259\pi$
$863$		−	27.7762i		−	0.945512i	0.881193	−	0.472756i	$-0.156741\pi$
$864$	18.4975	+	8.90704i	0.629297	+	0.303023i
$865$	21.0659	+	12.1624i	0.716262	+	0.413534i
$866$	−13.0283	+	9.76688i	−0.442721	+	0.331892i
$867$	−9.49401	−	5.48137i	−0.322434	−	0.186157i
$868$	8.43866	−	2.05949i	0.286427	−	0.0699037i
$869$	−6.16560	−	10.6791i	−0.209154	−	0.362265i
$870$	8.55312	−	6.41197i	0.289978	−	0.217386i
$871$	−42.1893	−	3.69331i	−1.42953	−	0.125143i
$872$	−11.0993	−	29.5718i	−0.375869	−	1.00143i
$873$	4.30819	−	2.48734i	0.145810	−	0.0841836i
$874$	−47.9785	−	20.5065i	−1.62290	−	0.693644i
$875$	7.63554	+	4.40838i	0.258129	+	0.149031i
$876$	1.61022	−	5.51194i	0.0544043	−	0.186231i
$877$	7.17456	−	12.4267i	0.242268	−	0.419620i	−0.719092	−	0.694915i	$-0.755442\pi$
$877$	7.17456	−	12.4267i	0.242268	−	0.419620i	0.961360	+	0.275295i	$0.0887755\pi$
$878$	−6.59590	−	54.8460i	−0.222601	−	1.85096i
$879$			1.55408i			0.0524177i
$880$	−53.3470	+	27.6883i	−1.79833	+	0.933373i
$881$	10.4270	+	18.0602i	0.351296	+	0.608463i	0.986477	−	0.163901i	$-0.0524077\pi$
$881$	10.4270	+	18.0602i	0.351296	+	0.608463i	−0.635181	+	0.772364i	$0.719074\pi$
$882$	−3.35042	−	1.43201i	−0.112815	−	0.0482182i
$883$			8.17190i			0.275006i	0.990501	+	0.137503i	$0.0439077\pi$
$883$			8.17190i			0.275006i	−0.990501	+	0.137503i	$0.956092\pi$
$884$	1.03268	−	2.65035i	0.0347328	−	0.0891409i
$885$			22.8014i			0.766461i
$886$	−11.3629	+	26.5854i	−0.381745	+	0.893156i
$887$	−6.68872	−	11.5852i	−0.224585	−	0.388993i	0.731610	−	0.681724i	$-0.238769\pi$
$887$	−6.68872	−	11.5852i	−0.224585	−	0.388993i	−0.956195	+	0.292731i	$0.905436\pi$
$888$	−1.75187	+	10.5510i	−0.0587888	+	0.354069i
$889$			6.59391i			0.221153i
$890$	−29.6039	+	3.56024i	−0.992326	+	0.119339i
$891$	−15.7480	+	27.2763i	−0.527577	+	0.913789i
$892$	−20.8825	−	6.10047i	−0.699198	−	0.204259i
$893$	53.0112	+	30.6060i	1.77395	+	1.02419i
$894$	1.89599	−	4.43598i	0.0634113	−	0.148361i
$895$	35.1518	−	20.2949i	1.17499	−	0.678383i
$896$	−11.0666	−	2.35165i	−0.369709	−	0.0785632i
$897$	9.54331	−	4.44951i	0.318642	−	0.148565i
$898$	−2.41682	−	3.22388i	−0.0806505	−	0.107582i
$899$	−9.84958	−	17.0600i	−0.328502	−	0.568982i
$900$	−7.79317	+	1.90196i	−0.259772	+	0.0633985i
$901$	0.252742	+	0.145920i	0.00842005	+	0.00486132i
$902$	42.5795	+	56.7981i	1.41774	+	1.89117i
$903$	−5.52550	−	3.19015i	−0.183877	−	0.106161i
$904$	−11.1368	−	1.84913i	−0.370404	−	0.0615010i
$905$			0.384098i			0.0127678i
$906$	−1.17539	−	9.77356i	−0.0390497	−	0.324705i
$907$	−20.2323	+	11.6811i	−0.671804	+	0.387866i	−0.796760	−	0.604296i	$-0.793454\pi$
$907$	−20.2323	+	11.6811i	−0.671804	+	0.387866i	0.124956	+	0.992162i	$0.460121\pi$
$908$	−21.1903	+	5.17158i	−0.703225	+	0.171625i
$909$			33.4926i			1.11088i
$910$	13.0498	−	0.422555i	0.432597	−	0.0140076i
$911$	−17.2641			−0.571985			−0.285993	−	0.958232i	$-0.592323\pi$
$911$	−17.2641			−0.571985			−0.285993	+	0.958232i	$0.592323\pi$
$912$	21.3833	+	0.959661i	0.708070	+	0.0317776i
$913$	−9.54291	−	16.5288i	−0.315824	−	0.547024i
$914$	14.4194	−	1.73411i	0.476951	−	0.0573592i
$915$	5.81844			0.192352
$916$	7.66174	+	8.01330i	0.253151	+	0.264767i
$917$	2.44563	−	4.23595i	0.0807618	−	0.139883i
$918$	1.21438	+	1.61990i	0.0400806	+	0.0534647i
$919$	8.82819	−	15.2909i	0.291215	−	0.504399i	−0.682882	−	0.730529i	$-0.739274\pi$
$919$	8.82819	−	15.2909i	0.291215	−	0.504399i	0.974097	+	0.226129i	$0.0726071\pi$
$920$	20.6400	−	25.1032i	0.680480	−	0.827627i
$921$	−7.49457	+	4.32699i	−0.246954	+	0.142579i
$922$	40.0025	−	29.9884i	1.31741	−	0.987616i
$923$	−39.2406	+	18.2957i	−1.29162	+	0.602210i
$924$	−2.14187	+	7.33181i	−0.0704622	+	0.241199i
$925$	−4.52263	−	7.83343i	−0.148703	−	0.257561i
$926$	4.81515	−	11.2658i	0.158236	−	0.370218i
$927$	−4.05918	+	7.03070i	−0.133321	+	0.230919i
$928$	1.91838	+	25.5858i	0.0629740	+	0.839894i
$929$	0.949300	+	0.548079i	0.0311455	+	0.0179819i	0.515492	−	0.856894i	$-0.327609\pi$
$929$	0.949300	+	0.548079i	0.0311455	+	0.0179819i	−0.484346	+	0.874876i	$0.660943\pi$
$930$	−1.22220	−	10.1628i	−0.0400775	−	0.333251i
$931$	−8.22219			−0.269471
$932$	−40.3697	−	42.2220i	−1.32235	−	1.38303i
$933$	−5.70053	+	3.29120i	−0.186627	+	0.107749i
$934$	6.81879	−	15.9537i	0.223118	−	0.522021i
$935$	−5.92707			−0.193836
$936$	18.3932	−	18.7627i	0.601201	−	0.613279i
$937$	45.6620			1.49171			0.745855	−	0.666108i	$-0.232041\pi$
$937$	45.6620			1.49171			0.745855	+	0.666108i	$0.232041\pi$
$938$	−6.52854	+	15.2746i	−0.213164	+	0.498734i
$939$	7.07997	−	4.08762i	0.231046	−	0.133395i
$940$	−27.5571	+	26.3481i	−0.898815	+	0.859382i
$941$	−24.5540			−0.800436			−0.400218	−	0.916420i	$-0.631066\pi$
$941$	−24.5540			−0.800436			−0.400218	+	0.916420i	$0.631066\pi$
$942$	−1.17232	−	9.74802i	−0.0381962	−	0.317608i
$943$	−33.2404	−	19.1914i	−1.08246	−	0.624956i
$944$	−46.1217	−	29.4616i	−1.50113	−	0.958895i
$945$	−4.64660	+	8.04815i	−0.151154	+	0.261806i
$946$	31.9746	−	74.8100i	1.03959	−	2.43228i
$947$	−25.3132	−	43.8437i	−0.822568	−	1.42473i	−0.903764	−	0.428032i	$-0.859207\pi$
$947$	−25.3132	−	43.8437i	−0.822568	−	1.42473i	0.0811955	−	0.996698i	$-0.474126\pi$
$948$	−2.62552	−	0.767000i	−0.0852728	−	0.0249110i
$949$	−13.0291	−	9.12409i	−0.422943	−	0.296181i
$950$	−14.4841	+	10.8582i	−0.469926	+	0.352287i
$951$	−12.6842	+	7.32320i	−0.411312	+	0.237471i
$952$	−0.861784	−	0.708564i	−0.0279306	−	0.0229647i
$953$	−15.2891	+	26.4815i	−0.495262	+	0.857819i	−0.999985	−	0.00546260i	$-0.998261\pi$
$953$	−15.2891	+	26.4815i	−0.495262	+	0.857819i	0.504723	+	0.863281i	$0.331595\pi$
$954$	1.61701	+	2.15698i	0.0523526	+	0.0698347i
$955$	−14.8450	+	25.7122i	−0.480372	+	0.832028i
$956$	−41.0033	+	39.2044i	−1.32614	+	1.26796i
$957$	17.3223			0.559950
$958$	−22.9751	+	2.76303i	−0.742291	+	0.0892696i
$959$	−4.72556	−	8.18491i	−0.152596	−	0.264305i
$960$	−4.30848	+	12.6167i	−0.139056	+	0.407204i
$961$	12.1369			0.391512
$962$	26.1232	+	13.9751i	0.842244	+	0.450575i
$963$			33.9271i			1.09328i
$964$	−10.7169	−	43.9121i	−0.345169	−	1.41431i
$965$	18.0129	−	10.3998i	0.579856	−	0.334780i
$966$	−0.493137	−	4.10051i	−0.0158664	−	0.131932i
$967$		−	11.8629i		−	0.381486i	−0.981640	−	0.190743i	$-0.938910\pi$
$967$		−	11.8629i		−	0.381486i	0.981640	−	0.190743i	$-0.0610897\pi$
$968$	−65.3895	−	10.8571i	−2.10170	−	0.348961i
$969$	1.82800	+	1.05539i	0.0587237	+	0.0339041i
$970$	4.19405	+	5.59457i	0.134663	+	0.179631i
$971$	13.6965	+	7.90766i	0.439540	+	0.253769i	0.703403	−	0.710792i	$-0.251663\pi$
$971$	13.6965	+	7.90766i	0.439540	+	0.253769i	−0.263862	+	0.964560i	$0.584996\pi$
$972$	6.81932	+	27.9418i	0.218730	+	0.896234i
$973$	4.66934	+	8.08753i	0.149692	+	0.259274i
$974$	−3.49733	−	4.66520i	−0.112062	−	0.149483i
$975$	0.318581	−	3.63921i	0.0102027	−	0.116548i
$976$	−7.51799	+	11.7693i	−0.240645	+	0.376726i
$977$	−24.8295	+	14.3353i	−0.794366	+	0.458627i	−0.841497	−	0.540261i	$-0.818325\pi$
$977$	−24.8295	+	14.3353i	−0.794366	+	0.458627i	0.0471314	+	0.998889i	$0.484992\pi$
$978$	−4.33897	+	10.1517i	−0.138745	+	0.324617i
$979$	−41.8445	−	24.1590i	−1.33736	−	0.772123i
$980$	1.43606	−	4.91578i	0.0458733	−	0.157029i
$981$	14.3860	−	24.9173i	0.459310	−	0.795547i
$982$	23.7177	−	2.85235i	0.756863	−	0.0910221i
$983$			27.0986i			0.864310i	0.901799	+	0.432155i	$0.142247\pi$
$983$			27.0986i			0.864310i	−0.901799	+	0.432155i	$0.857753\pi$
$984$	15.5332	+	2.57909i	0.495180	+	0.0822185i
$985$	20.6225	+	35.7193i	0.657089	+	1.13811i
$986$	−0.994401	+	2.32657i	−0.0316682	+	0.0740930i
$987$			4.84522i			0.154225i
$988$	21.5258	−	55.2455i	0.684827	−	1.75759i
$989$			43.9901i			1.39880i
$990$	−50.3438	−	21.5175i	−1.60003	−	0.683872i
$991$	6.48763	+	11.2369i	0.206086	+	0.356952i	0.950478	−	0.310791i	$-0.100594\pi$
$991$	6.48763	+	11.2369i	0.206086	+	0.356952i	−0.744392	+	0.667743i	$0.767261\pi$
$992$	22.1360	+	10.6591i	0.702820	+	0.338427i
$993$			0.212879i			0.00675550i
$994$	2.02770	+	16.8607i	0.0643147	+	0.534787i
$995$	−18.8747	+	32.6920i	−0.598369	+	1.03640i
$996$	−4.06368	−	1.18714i	−0.128763	−	0.0376159i
$997$	−13.1543	−	7.59462i	−0.416600	−	0.240524i	0.277022	−	0.960864i	$-0.410653\pi$
$997$	−13.1543	−	7.59462i	−0.416600	−	0.240524i	−0.693622	+	0.720340i	$0.743986\pi$
$998$	12.6627	+	5.41220i	0.400832	+	0.171320i
$999$	−18.2617	+	10.5434i	−0.577776	+	0.333579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.cz.a.309.73	yes	168
8.5	even	2	inner	728.2.cz.a.309.45	✓	168
13.4	even	6	inner	728.2.cz.a.589.45	yes	168
104.69	even	6	inner	728.2.cz.a.589.73	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.cz.a.309.45	✓	168	8.5	even	2	inner
728.2.cz.a.309.73	yes	168	1.1	even	1	trivial
728.2.cz.a.589.45	yes	168	13.4	even	6	inner
728.2.cz.a.589.73	yes	168	104.69	even	6	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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30041 + 0.555811i) q^{2} +(-0.563630 + 0.325412i) q^{3} +(1.38215 + 1.44557i) q^{4} -2.56062 q^{5} +(-0.913819 + 0.109898i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.993899 + 2.64805i) q^{8} +(-1.28821 + 2.23125i) q^{9} +(-3.32987 - 1.42322i) q^{10} +(-2.93407 - 5.08197i) q^{11} +(-1.24943 - 0.364998i) q^{12} +(-2.06821 + 2.95339i) q^{13} +(0.848285 + 1.13155i) q^{14} +(1.44324 - 0.833257i) q^{15} +(-0.179336 + 3.99598i) q^{16} +(-0.197226 + 0.341605i) q^{17} +(-2.91537 + 2.18555i) q^{18} +(-4.11109 + 7.12062i) q^{19} +(-3.53916 - 3.70155i) q^{20} -0.650824 q^{21} +(-0.990894 - 8.23945i) q^{22} +(2.24361 + 3.88605i) q^{23} +(-1.42190 - 1.16909i) q^{24} +1.55679 q^{25} +(-4.33106 + 2.69109i) q^{26} -3.62927i q^{27} +(0.474191 + 1.94297i) q^{28} +(3.92800 - 2.26783i) q^{29} +(2.33995 - 0.281407i) q^{30} -4.34317i q^{31} +(-2.45422 + 5.09674i) q^{32} +(3.30747 + 1.90957i) q^{33} +(-0.446343 + 0.334607i) q^{34} +(-2.21756 - 1.28031i) q^{35} +(-5.00593 + 1.22172i) q^{36} +(-2.90510 - 5.03179i) q^{37} +(-9.30384 + 6.97476i) q^{38} +(0.204640 - 2.33764i) q^{39} +(-2.54500 - 6.78065i) q^{40} +(-7.40779 + 4.27689i) q^{41} +(-0.846340 - 0.361735i) q^{42} +(8.49000 + 4.90171i) q^{43} +(3.29101 - 11.2654i) q^{44} +(3.29863 - 5.71339i) q^{45} +(0.757712 + 6.30049i) q^{46} -7.44475i q^{47} +(-1.19926 - 2.31061i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.02447 + 0.865280i) q^{50} -0.256718i q^{51} +(-7.12790 + 1.09227i) q^{52} -0.739865i q^{53} +(2.01719 - 4.71955i) q^{54} +(7.51306 + 13.0130i) q^{55} +(-0.463282 + 2.79023i) q^{56} -5.35120i q^{57} +(6.36851 - 0.765891i) q^{58} +(-6.84105 + 11.8490i) q^{59} +(3.19931 + 0.934623i) q^{60} +(3.02363 + 1.74569i) q^{61} +(2.41398 - 5.64792i) q^{62} +(-2.23125 + 1.28821i) q^{63} +(-6.02433 + 5.26379i) q^{64} +(5.29591 - 7.56251i) q^{65} +(3.23971 + 4.32155i) q^{66} +(5.87298 + 10.1723i) q^{67} +(-0.766408 + 0.187045i) q^{68} +(-2.52913 - 1.46020i) q^{69} +(-2.17214 - 2.89748i) q^{70} +(10.3994 + 6.00409i) q^{71} +(-7.18882 - 1.19361i) q^{72} +4.41158i q^{73} +(-0.981111 - 8.15809i) q^{74} +(-0.877452 + 0.506597i) q^{75} +(-15.9755 + 3.89888i) q^{76} -5.86815i q^{77} +(1.56540 - 2.92615i) q^{78} +2.10138 q^{79} +(0.459211 - 10.2322i) q^{80} +(-2.68363 - 4.64819i) q^{81} +(-12.0103 + 1.44439i) q^{82} +3.25244 q^{83} +(-0.899535 - 0.940811i) q^{84} +(0.505021 - 0.874721i) q^{85} +(8.31609 + 11.0931i) q^{86} +(-1.47596 + 2.55644i) q^{87} +(10.5411 - 12.8205i) q^{88} +(7.13079 - 4.11696i) q^{89} +(7.46515 - 5.59636i) q^{90} +(-3.26782 + 1.52360i) q^{91} +(-2.51655 + 8.61439i) q^{92} +(1.41332 + 2.44794i) q^{93} +(4.13788 - 9.68125i) q^{94} +(10.5270 - 18.2332i) q^{95} +(-0.275269 - 3.67131i) q^{96} +(-1.67216 - 0.965421i) q^{97} +(0.168860 + 1.40410i) q^{98} +15.1189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 18 q^{6} + 84 q^{9} - 8 q^{10} - 4 q^{12} + 8 q^{16} + 4 q^{17} - 18 q^{22} + 24 q^{23} + 48 q^{24} + 160 q^{25} - 30 q^{26} - 8 q^{30} + 22 q^{36} - 20 q^{38} - 48 q^{39} + 4 q^{40} + 12 q^{41}+ \cdots - 104 q^{95}+O(q^{100}) \) 168 * q - 18 * q^6 + 84 * q^9 - 8 * q^10 - 4 * q^12 + 8 * q^16 + 4 * q^17 - 18 * q^22 + 24 * q^23 + 48 * q^24 + 160 * q^25 - 30 * q^26 - 8 * q^30 + 22 * q^36 - 20 * q^38 - 48 * q^39 + 4 * q^40 + 12 * q^41 - 54 * q^48 + 84 * q^49 - 30 * q^50 - 58 * q^52 + 24 * q^54 - 32 * q^55 - 12 * q^58 + 28 * q^62 - 36 * q^64 + 12 * q^65 - 60 * q^66 - 64 * q^68 - 132 * q^72 + 62 * q^74 - 78 * q^76 + 30 * q^78 - 80 * q^79 + 48 * q^80 - 84 * q^81 - 18 * q^82 - 42 * q^84 - 24 * q^87 + 42 * q^88 + 40 * q^90 - 24 * q^92 + 12 * q^94 - 104 * q^95

Introduction

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