LMFDB - Embedded newform 546.2.q.j.251.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.6
Character	$\chi$	$=$	546.251
Dual form			546.2.q.j.335.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.377999 - 1.69030i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-1.65284 - 0.517794i) q^{6} +(-1.93422 + 1.80522i) q^{7} -1.00000 q^{8} +(-2.71423 + 1.27786i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.377999 - 1.69030i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-1.65284 - 0.517794i) q^{6} +(-1.93422 + 1.80522i) q^{7} -1.00000 q^{8} +(-2.71423 + 1.27786i) q^{9} +(0.163593 + 0.0944507i) q^{10} +(-2.99275 + 5.18359i) q^{11} +(-1.27484 + 1.17251i) q^{12} +(-3.59703 - 0.247790i) q^{13} +(0.596256 + 2.57769i) q^{14} +(0.319300 - 0.0714045i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.16244 - 3.74546i) q^{17} +(-0.250454 + 2.98953i) q^{18} +(-2.70943 - 4.69287i) q^{19} +(0.163593 - 0.0944507i) q^{20} +(3.78249 + 2.58704i) q^{21} +(2.99275 + 5.18359i) q^{22} +(-2.12062 - 1.22434i) q^{23} +(0.377999 + 1.69030i) q^{24} +4.96432 q^{25} +(-2.01311 + 2.99122i) q^{26} +(3.18595 + 4.10484i) q^{27} +(2.53047 + 0.772472i) q^{28} +(-5.72445 - 3.30501i) q^{29} +(0.0978120 - 0.312224i) q^{30} +7.73989 q^{31} +(0.500000 + 0.866025i) q^{32} +(9.89308 + 3.09925i) q^{33} -4.32488 q^{34} +(-0.341008 - 0.365376i) q^{35} +(2.46378 + 1.71166i) q^{36} +(1.21090 + 0.699114i) q^{37} -5.41886 q^{38} +(0.940833 + 6.17372i) q^{39} -0.188901i q^{40} +(-7.23531 - 4.17731i) q^{41} +(4.13169 - 1.98222i) q^{42} +(-2.00968 - 3.48087i) q^{43} +5.98549 q^{44} +(-0.241390 - 0.512723i) q^{45} +(-2.12062 + 1.22434i) q^{46} +3.00234i q^{47} +(1.65284 + 0.517794i) q^{48} +(0.482384 - 6.98336i) q^{49} +(2.48216 - 4.29922i) q^{50} +(-5.51355 + 5.07095i) q^{51} +(1.58392 + 3.23901i) q^{52} -0.440865i q^{53} +(5.14787 - 0.706695i) q^{54} +(-0.979187 - 0.565334i) q^{55} +(1.93422 - 1.80522i) q^{56} +(-6.90820 + 6.35365i) q^{57} +(-5.72445 + 3.30501i) q^{58} +(-1.61004 + 0.929559i) q^{59} +(-0.221488 - 0.240820i) q^{60} +(-1.69169 + 0.976699i) q^{61} +(3.86995 - 6.70294i) q^{62} +(2.94309 - 7.37145i) q^{63} +1.00000 q^{64} +(0.0468079 - 0.679483i) q^{65} +(7.63057 - 7.01803i) q^{66} +(9.40246 + 5.42851i) q^{67} +(-2.16244 + 3.74546i) q^{68} +(-1.26791 + 4.04729i) q^{69} +(-0.486929 + 0.112634i) q^{70} +(1.71090 + 2.96337i) q^{71} +(2.71423 - 1.27786i) q^{72} +7.64136 q^{73} +(1.21090 - 0.699114i) q^{74} +(-1.87651 - 8.39119i) q^{75} +(-2.70943 + 4.69287i) q^{76} +(-3.56888 - 15.4287i) q^{77} +(5.81702 + 2.27208i) q^{78} -12.8725 q^{79} +(-0.163593 - 0.0944507i) q^{80} +(5.73413 - 6.93684i) q^{81} +(-7.23531 + 4.17731i) q^{82} +16.1727i q^{83} +(0.349194 - 4.56925i) q^{84} +(0.707522 - 0.408488i) q^{85} -4.01936 q^{86} +(-3.42263 + 10.9253i) q^{87} +(2.99275 - 5.18359i) q^{88} +(-12.3724 - 7.14320i) q^{89} +(-0.564726 - 0.0473112i) q^{90} +(7.40474 - 6.01413i) q^{91} +2.44869i q^{92} +(-2.92567 - 13.0827i) q^{93} +(2.60010 + 1.50117i) q^{94} +(0.886490 - 0.511815i) q^{95} +(1.27484 - 1.17251i) q^{96} +(-8.15789 - 14.1299i) q^{97} +(-5.80657 - 3.90944i) q^{98} +(1.49909 - 17.8938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.377999	−	1.69030i	−0.218238	−	0.975896i
$3$	−0.377999	−	1.69030i	−0.218238	−	0.975896i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$			0.188901i			0.0844793i	0.999108	+	0.0422396i	$0.0134493\pi$
$5$			0.188901i			0.0844793i	−0.999108	+	0.0422396i	$0.986551\pi$
$6$	−1.65284	−	0.517794i	−0.674770	−	0.211388i
$7$	−1.93422	+	1.80522i	−0.731065	+	0.682308i
$7$	−1.93422	+	1.80522i	−0.731065	+	0.682308i
$8$	−1.00000			−0.353553
$9$	−2.71423	+	1.27786i	−0.904745	+	0.425955i
$10$	0.163593	+	0.0944507i	0.0517328	+	0.0298679i
$11$	−2.99275	+	5.18359i	−0.902347	+	1.56291i	−0.0779069	+	0.996961i	$0.524824\pi$
$11$	−2.99275	+	5.18359i	−0.902347	+	1.56291i	−0.824440	+	0.565950i	$0.808510\pi$
$12$	−1.27484	+	1.17251i	−0.368016	+	0.338474i
$13$	−3.59703	−	0.247790i	−0.997636	−	0.0687246i
$13$	−3.59703	−	0.247790i	−0.997636	−	0.0687246i
$14$	0.596256	+	2.57769i	0.159356	+	0.688916i
$15$	0.319300	−	0.0714045i	0.0824430	−	0.0184366i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.16244	−	3.74546i	−0.524469	−	0.908407i	−0.999594	−	0.0284885i	$-0.990931\pi$
$17$	−2.16244	−	3.74546i	−0.524469	−	0.908407i	0.475125	−	0.879918i	$-0.342403\pi$
$18$	−0.250454	+	2.98953i	−0.0590326	+	0.704638i
$19$	−2.70943	−	4.69287i	−0.621586	−	1.07662i	−0.989190	−	0.146636i	$-0.953155\pi$
$19$	−2.70943	−	4.69287i	−0.621586	−	1.07662i	0.367605	−	0.929982i	$-0.380178\pi$
$20$	0.163593	−	0.0944507i	0.0365806	−	0.0211198i
$21$	3.78249	+	2.58704i	0.825407	+	0.564538i
$22$	2.99275	+	5.18359i	0.638055	+	1.10514i
$23$	−2.12062	−	1.22434i	−0.442181	−	0.255293i	0.262342	−	0.964975i	$-0.415505\pi$
$23$	−2.12062	−	1.22434i	−0.442181	−	0.255293i	−0.704522	+	0.709682i	$0.748839\pi$
$24$	0.377999	+	1.69030i	0.0771587	+	0.345031i
$25$	4.96432			0.992863
$26$	−2.01311	+	2.99122i	−0.394802	+	0.586627i
$27$	3.18595	+	4.10484i	0.613137	+	0.789977i
$28$	2.53047	+	0.772472i	0.478214	+	0.145983i
$29$	−5.72445	−	3.30501i	−1.06300	−	0.613725i	−0.136742	−	0.990607i	$-0.543663\pi$
$29$	−5.72445	−	3.30501i	−1.06300	−	0.613725i	−0.926262	+	0.376881i	$0.876996\pi$
$30$	0.0978120	−	0.312224i	0.0178579	−	0.0570041i
$31$	7.73989			1.39013			0.695063	−	0.718949i	$-0.255376\pi$
$31$	7.73989			1.39013			0.695063	+	0.718949i	$0.255376\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	9.89308	+	3.09925i	1.72216	+	0.539510i
$34$	−4.32488			−0.741711
$35$	−0.341008	−	0.365376i	−0.0576409	−	0.0617598i
$36$	2.46378	+	1.71166i	0.410630	+	0.285277i
$37$	1.21090	+	0.699114i	0.199071	+	0.114934i	0.596222	−	0.802820i	$-0.296668\pi$
$37$	1.21090	+	0.699114i	0.199071	+	0.114934i	−0.397151	+	0.917753i	$0.630001\pi$
$38$	−5.41886			−0.879055
$39$	0.940833	+	6.17372i	0.150654	+	0.988587i
$40$		−	0.188901i		−	0.0298679i
$41$	−7.23531	−	4.17731i	−1.12996	−	0.652386i	−0.186039	−	0.982542i	$-0.559565\pi$
$41$	−7.23531	−	4.17731i	−1.12996	−	0.652386i	−0.943926	+	0.330157i	$0.892898\pi$
$42$	4.13169	−	1.98222i	0.637533	−	0.305862i
$43$	−2.00968	−	3.48087i	−0.306473	−	0.530827i	0.671115	−	0.741353i	$-0.265816\pi$
$43$	−2.00968	−	3.48087i	−0.306473	−	0.530827i	−0.977588	+	0.210526i	$0.932482\pi$
$44$	5.98549			0.902347
$45$	−0.241390	−	0.512723i	−0.0359843	−	0.0764322i
$46$	−2.12062	+	1.22434i	−0.312669	+	0.180520i
$47$			3.00234i			0.437936i	0.975732	+	0.218968i	$0.0702691\pi$
$47$			3.00234i			0.437936i	−0.975732	+	0.218968i	$0.929731\pi$
$48$	1.65284	+	0.517794i	0.238567	+	0.0747371i
$49$	0.482384	−	6.98336i	0.0689119	−	0.997623i
$50$	2.48216	−	4.29922i	0.351030	−	0.608002i
$51$	−5.51355	+	5.07095i	−0.772051	+	0.710076i
$52$	1.58392	+	3.23901i	0.219650	+	0.449170i
$53$		−	0.440865i		−	0.0605574i	−0.999541	−	0.0302787i	$-0.990361\pi$
$53$		−	0.440865i		−	0.0605574i	0.999541	−	0.0302787i	$-0.00963949\pi$
$54$	5.14787	−	0.706695i	0.700537	−	0.0961690i
$55$	−0.979187	−	0.565334i	−0.132034	−	0.0762296i
$56$	1.93422	−	1.80522i	0.258470	−	0.241232i
$57$	−6.90820	+	6.35365i	−0.915014	+	0.841562i
$58$	−5.72445	+	3.30501i	−0.751657	+	0.433969i
$59$	−1.61004	+	0.929559i	−0.209610	+	0.121018i	−0.601130	−	0.799151i	$-0.705283\pi$
$59$	−1.61004	+	0.929559i	−0.209610	+	0.121018i	0.391520	+	0.920170i	$0.371949\pi$
$60$	−0.221488	−	0.240820i	−0.0285940	−	0.0310897i
$61$	−1.69169	+	0.976699i	−0.216599	+	0.125053i	−0.604374	−	0.796700i	$-0.706577\pi$
$61$	−1.69169	+	0.976699i	−0.216599	+	0.125053i	0.387776	+	0.921754i	$0.373244\pi$
$62$	3.86995	−	6.70294i	0.491484	−	0.851275i
$63$	2.94309	−	7.37145i	0.370795	−	0.928715i
$64$	1.00000			0.125000
$65$	0.0468079	−	0.679483i	0.00580580	−	0.0842795i
$66$	7.63057	−	7.01803i	0.939258	−	0.863860i
$67$	9.40246	+	5.42851i	1.14869	+	0.663199i	0.948569	−	0.316572i	$-0.102532\pi$
$67$	9.40246	+	5.42851i	1.14869	+	0.663199i	0.200125	+	0.979770i	$0.435865\pi$
$68$	−2.16244	+	3.74546i	−0.262234	+	0.454203i
$69$	−1.26791	+	4.04729i	−0.152639	+	0.487237i
$70$	−0.486929	+	0.112634i	−0.0581992	+	0.0134623i
$71$	1.71090	+	2.96337i	0.203047	+	0.351687i	0.949509	−	0.313741i	$-0.101582\pi$
$71$	1.71090	+	2.96337i	0.203047	+	0.351687i	−0.746462	+	0.665428i	$0.768249\pi$
$72$	2.71423	−	1.27786i	0.319875	−	0.150598i
$73$	7.64136			0.894354			0.447177	−	0.894446i	$-0.352429\pi$
$73$	7.64136			0.894354			0.447177	+	0.894446i	$0.352429\pi$
$74$	1.21090	−	0.699114i	0.140764	−	0.0812704i
$75$	−1.87651	−	8.39119i	−0.216680	−	0.968931i
$76$	−2.70943	+	4.69287i	−0.310793	+	0.538309i
$77$	−3.56888	−	15.4287i	−0.406712	−	1.75827i
$78$	5.81702	+	2.27208i	0.658647	+	0.257262i
$79$	−12.8725			−1.44827			−0.724136	−	0.689658i	$-0.757761\pi$
$79$	−12.8725			−1.44827			−0.724136	+	0.689658i	$0.757761\pi$
$80$	−0.163593	−	0.0944507i	−0.0182903	−	0.0105599i
$81$	5.73413	−	6.93684i	0.637125	−	0.770760i
$82$	−7.23531	+	4.17731i	−0.799006	+	0.461306i
$83$			16.1727i			1.77518i	0.460633	+	0.887591i	$0.347623\pi$
$83$			16.1727i			1.77518i	−0.460633	+	0.887591i	$0.652377\pi$
$84$	0.349194	−	4.56925i	0.0381002	−	0.498546i
$85$	0.707522	−	0.408488i	0.0767415	−	0.0443067i
$86$	−4.01936			−0.433418
$87$	−3.42263	+	10.9253i	−0.366944	+	1.17132i
$88$	2.99275	−	5.18359i	0.319028	−	0.552572i
$89$	−12.3724	−	7.14320i	−1.31147	−	0.757178i	−0.329131	−	0.944284i	$-0.606756\pi$
$89$	−12.3724	−	7.14320i	−1.31147	−	0.757178i	−0.982340	+	0.187107i	$0.940089\pi$
$90$	−0.564726	−	0.0473112i	−0.0595273	−	0.00498703i
$91$	7.40474	−	6.01413i	0.776228	−	0.630453i
$92$			2.44869i			0.255293i
$93$	−2.92567	−	13.0827i	−0.303378	−	1.35662i
$94$	2.60010	+	1.50117i	0.268180	+	0.154834i
$95$	0.886490	−	0.511815i	0.0909519	−	0.0525111i
$96$	1.27484	−	1.17251i	0.130113	−	0.119669i
$97$	−8.15789	−	14.1299i	−0.828308	−	1.43467i	−0.899364	−	0.437200i	$-0.855970\pi$
$97$	−8.15789	−	14.1299i	−0.828308	−	1.43467i	0.0710561	−	0.997472i	$-0.477363\pi$
$98$	−5.80657	−	3.90944i	−0.586553	−	0.394913i
$99$	1.49909	−	17.8938i	0.150664	−	1.79839i
$100$	−2.48216	−	4.29922i	−0.248216	−	0.429922i
$101$	−2.57737	+	4.46413i	−0.256458	+	0.444198i	−0.965290	−	0.261179i	$-0.915889\pi$
$101$	−2.57737	+	4.46413i	−0.256458	+	0.444198i	0.708833	+	0.705377i	$0.249222\pi$
$102$	1.63480	+	7.31035i	0.161869	+	0.723832i
$103$			0.491580i			0.0484368i	0.999707	+	0.0242184i	$0.00770971\pi$
$103$			0.491580i			0.0484368i	−0.999707	+	0.0242184i	$0.992290\pi$
$104$	3.59703	+	0.247790i	0.352717	+	0.0242978i
$105$	−0.488695	+	0.714518i	−0.0476917	+	0.0697298i
$106$	−0.381800	−	0.220432i	−0.0370837	−	0.0214103i
$107$	10.1467	+	5.85821i	0.980920	+	0.566334i	0.902548	−	0.430590i	$-0.141694\pi$
$107$	10.1467	+	5.85821i	0.980920	+	0.566334i	0.0783719	+	0.996924i	$0.475028\pi$
$108$	1.96192	−	4.81154i	0.188786	−	0.462990i
$109$			2.68217i			0.256905i	0.991716	+	0.128453i	$0.0410010\pi$
$109$			2.68217i			0.256905i	−0.991716	+	0.128453i	$0.958999\pi$
$110$	−0.979187	+	0.565334i	−0.0933618	+	0.0539025i
$111$	0.723994	−	2.31105i	0.0687184	−	0.219355i
$112$	−0.596256	−	2.57769i	−0.0563409	−	0.243569i
$113$	−2.91954	+	1.68560i	−0.274647	+	0.158567i	−0.630998	−	0.775785i	$-0.717354\pi$
$113$	−2.91954	+	1.68560i	−0.274647	+	0.158567i	0.356351	+	0.934352i	$0.384021\pi$
$114$	2.04832	+	9.15950i	0.191843	+	0.857866i
$115$	0.231280	−	0.400589i	0.0215670	−	0.0373551i
$116$			6.61002i			0.613725i
$117$	10.0798	−	3.92395i	0.931879	−	0.362769i
$118$			1.85912i			0.171146i
$119$	10.9440	+	3.34085i	1.00323	+	0.306255i
$120$	−0.319300	+	0.0714045i	−0.0291480	+	0.00651831i
$121$	−12.4130	−	21.5000i	−1.12846	−	1.95455i
$122$			1.95340i			0.176852i
$123$	−4.32597	+	13.8089i	−0.390059	+	1.24510i
$124$	−3.86995	−	6.70294i	−0.347531	−	0.601942i
$125$			1.88227i			0.168356i
$126$	−4.91231	−	6.23452i	−0.437624	−	0.555415i
$127$	1.88905	−	3.27194i	0.167626	−	0.290338i	−0.769958	−	0.638094i	$-0.779723\pi$
$127$	1.88905	−	3.27194i	0.167626	−	0.290338i	0.937585	+	0.347756i	$0.113056\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.12405	+	4.71273i	−0.451148	+	0.414932i
$130$	−0.565046	−	0.380279i	−0.0495578	−	0.0333526i
$131$	−11.3072			−0.987918			−0.493959	−	0.869485i	$-0.664451\pi$
$131$	−11.3072			−0.987918			−0.493959	+	0.869485i	$0.664451\pi$
$132$	−2.26251	−	10.1173i	−0.196926	−	0.880596i
$133$	13.7123	+	4.18592i	1.18900	+	0.362965i
$134$	9.40246	−	5.42851i	0.812249	−	0.468952i
$135$	−0.775410	+	0.601831i	−0.0667367	+	0.0517973i
$136$	2.16244	+	3.74546i	0.185428	+	0.321170i
$137$	3.33395	+	5.77457i	0.284839	+	0.493355i	0.972570	−	0.232610i	$-0.0747267\pi$
$137$	3.33395	+	5.77457i	0.284839	+	0.493355i	−0.687732	+	0.725965i	$0.741393\pi$
$138$	2.87110	+	3.12169i	0.244404	+	0.265736i
$139$	−1.01358	+	0.585188i	−0.0859704	+	0.0496350i	−0.542369	−	0.840140i	$-0.682472\pi$
$139$	−1.01358	+	0.585188i	−0.0859704	+	0.0496350i	0.456399	+	0.889775i	$0.349139\pi$
$140$	−0.145921	+	0.478010i	−0.0123326	+	0.0403992i
$141$	5.07486	−	1.13488i	0.427380	−	0.0955743i
$142$	3.42180			0.287151
$143$	12.0494	−	17.9039i	1.00762	−	1.49720i
$144$	0.250454	−	2.98953i	0.0208712	−	0.249127i
$145$	0.624321	−	1.08136i	0.0518471	−	0.0898018i
$146$	3.82068	−	6.61761i	0.316202	−	0.547678i
$147$	−11.9863	+	1.82433i	−0.988615	+	0.150468i
$148$		−	1.39823i		−	0.114934i
$149$	−2.76256	−	4.78489i	−0.226317	−	0.391993i	0.730396	−	0.683023i	$-0.239335\pi$
$149$	−2.76256	−	4.78489i	−0.226317	−	0.391993i	−0.956714	+	0.291030i	$0.906002\pi$
$150$	−8.20523	−	2.57049i	−0.669955	−	0.209880i
$151$			13.2681i			1.07974i	0.841748	+	0.539871i	$0.181527\pi$
$151$			13.2681i			1.07974i	−0.841748	+	0.539871i	$0.818473\pi$
$152$	2.70943	+	4.69287i	0.219764	+	0.380642i
$153$	10.6556	+	7.40274i	0.861450	+	0.598476i
$154$	−15.1461	−	4.62362i	−1.22051	−	0.372582i
$155$			1.46208i			0.117437i
$156$	4.87618	−	3.90165i	0.390407	−	0.312382i
$157$		−	16.0563i		−	1.28143i	−0.767777	−	0.640717i	$-0.778637\pi$
$157$		−	16.0563i		−	1.28143i	0.767777	−	0.640717i	$-0.221363\pi$
$158$	−6.43626	+	11.1479i	−0.512041	+	0.886881i
$159$	−0.745194	+	0.166646i	−0.0590977	+	0.0132159i
$160$	−0.163593	+	0.0944507i	−0.0129332	+	0.00746698i
$161$	6.31195	−	1.46004i	0.497451	−	0.115067i
$162$	−3.14042	−	8.43432i	−0.246734	−	0.662663i
$163$	−3.26377	+	1.88434i	−0.255638	+	0.147593i	−0.622343	−	0.782744i	$-0.713819\pi$
$163$	−3.26377	+	1.88434i	−0.255638	+	0.147593i	0.366705	+	0.930337i	$0.380486\pi$
$164$			8.35461i			0.652386i
$165$	−0.585453	+	1.86882i	−0.0455774	+	0.145487i
$166$	14.0059	+	8.08634i	1.08707	+	0.627622i
$167$	−17.4109	−	10.0522i	−1.34730	−	0.777862i	−0.359431	−	0.933172i	$-0.617029\pi$
$167$	−17.4109	−	10.0522i	−1.34730	−	0.777862i	−0.987866	+	0.155309i	$0.950363\pi$
$168$	−3.78249	−	2.58704i	−0.291826	−	0.199594i
$169$	12.8772	+	1.78261i	0.990554	+	0.137124i
$170$		−	0.816976i		−	0.0626592i
$171$	13.3509	+	9.27526i	1.02097	+	0.709297i
$172$	−2.00968	+	3.48087i	−0.153237	+	0.265414i
$173$	8.26915	+	14.3226i	0.628692	+	1.08893i	0.987815	+	0.155636i	$0.0497425\pi$
$173$	8.26915	+	14.3226i	0.628692	+	1.08893i	−0.359123	+	0.933290i	$0.616924\pi$
$174$	7.75030	+	8.42675i	0.587549	+	0.638830i
$175$	−9.60206	+	8.96167i	−0.725848	+	0.677438i
$176$	−2.99275	−	5.18359i	−0.225587	−	0.390728i
$177$	2.17983	+	2.37009i	0.163846	+	0.178147i
$178$	−12.3724	+	7.14320i	−0.927350	+	0.535406i
$179$	−12.0538	−	6.95929i	−0.900946	−	0.520162i	−0.0234391	−	0.999725i	$-0.507462\pi$
$179$	−12.0538	−	6.95929i	−0.900946	−	0.520162i	−0.877507	+	0.479564i	$0.840795\pi$
$180$	−0.323336	+	0.465411i	−0.0241000	+	0.0346897i
$181$			19.5377i			1.45222i	0.687576	+	0.726112i	$0.258675\pi$
$181$			19.5377i			1.45222i	−0.687576	+	0.726112i	$0.741325\pi$
$182$	−1.50602	−	9.41976i	−0.111634	−	0.698239i
$183$	2.29037	+	2.49028i	0.169309	+	0.184087i
$184$	2.12062	+	1.22434i	0.156334	+	0.0902598i
$185$	−0.132064	+	0.228741i	−0.00970951	+	0.0168174i
$186$	−12.7928	−	4.00767i	−0.938016	−	0.293856i
$187$	25.8865			1.89301
$188$	2.60010	−	1.50117i	0.189632	−	0.109484i
$189$	−13.5724	−	2.18831i	−0.987250	−	0.159176i
$190$		−	1.02363i		−	0.0742620i
$191$	7.34535	−	4.24084i	0.531491	−	0.306856i	−0.210133	−	0.977673i	$-0.567390\pi$
$191$	7.34535	−	4.24084i	0.531491	−	0.306856i	0.741623	+	0.670817i	$0.234056\pi$
$192$	−0.377999	−	1.69030i	−0.0272797	−	0.121987i
$193$	0.941626	+	0.543648i	0.0677797	+	0.0391327i	0.533507	−	0.845796i	$-0.320874\pi$
$193$	0.941626	+	0.543648i	0.0677797	+	0.0391327i	−0.465727	+	0.884928i	$0.654207\pi$
$194$	−16.3158			−1.17140
$195$	−1.16622	+	0.177725i	−0.0835151	+	0.0127271i
$196$	−6.28896	+	3.07392i	−0.449211	+	0.219566i
$197$	−5.48398	+	9.49852i	−0.390717	+	0.676742i	−0.992544	−	0.121885i	$-0.961106\pi$
$197$	−5.48398	+	9.49852i	−0.390717	+	0.676742i	0.601827	+	0.798626i	$0.294440\pi$
$198$	−14.7469	−	10.2451i	−1.04802	−	0.728091i
$199$	−6.56897	+	3.79260i	−0.465662	+	0.268850i	−0.714422	−	0.699715i	$-0.753310\pi$
$199$	−6.56897	+	3.79260i	−0.465662	+	0.268850i	0.248760	+	0.968565i	$0.419977\pi$
$200$	−4.96432			−0.351030
$201$	5.62170	−	17.9450i	0.396524	−	1.26574i
$202$	2.57737	+	4.46413i	0.181343	+	0.314095i
$203$	17.0386	−	3.94126i	1.19587	−	0.276623i
$204$	7.14835	+	2.23940i	0.500485	+	0.156789i
$205$	0.789099	−	1.36676i	0.0551131	−	0.0954586i
$206$	0.425721	+	0.245790i	0.0296614	+	0.0171250i
$207$	7.32041	+	0.613284i	0.508804	+	0.0426262i
$208$	2.01311	−	2.99122i	0.139584	−	0.207404i
$209$	32.4345			2.24354
$210$	0.374443	+	0.780481i	0.0258390	+	0.0538583i
$211$	−6.91977	+	11.9854i	−0.476376	+	0.825108i	−0.999634	−	0.0270666i	$-0.991383\pi$
$211$	−6.91977	+	11.9854i	−0.476376	+	0.825108i	0.523257	+	0.852175i	$0.324717\pi$
$212$	−0.381800	+	0.220432i	−0.0262221	+	0.0151394i
$213$	4.36226	−	4.01209i	0.298897	−	0.274904i
$214$	10.1467	−	5.85821i	0.693615	−	0.400459i
$215$	0.657540	−	0.379631i	0.0448439	−	0.0258906i
$216$	−3.18595	−	4.10484i	−0.216777	−	0.279299i
$217$	−14.9706	+	13.9722i	−1.01627	+	0.948494i
$218$	2.32283	+	1.34108i	0.157322	+	0.0908296i
$219$	−2.88843	−	12.9162i	−0.195182	−	0.872796i
$220$			1.13067i			0.0762296i
$221$	6.85027	+	14.0083i	0.460799	+	0.942303i
$222$	−1.63943	−	1.78252i	−0.110031	−	0.119635i
$223$	12.0097	−	20.8015i	0.804231	−	1.39297i	−0.112578	−	0.993643i	$-0.535911\pi$
$223$	12.0097	−	20.8015i	0.804231	−	1.39297i	0.916809	−	0.399326i	$-0.130756\pi$
$224$	−2.53047	−	0.772472i	−0.169074	−	0.0516129i
$225$	−13.4743	+	6.34372i	−0.898288	+	0.422915i
$226$			3.37119i			0.224248i
$227$	−13.1216	+	7.57576i	−0.870911	+	0.502821i	−0.867651	−	0.497174i	$-0.834371\pi$
$227$	−13.1216	+	7.57576i	−0.870911	+	0.502821i	−0.00326046	+	0.999995i	$0.501038\pi$
$228$	8.95652	+	2.80585i	0.593160	+	0.185822i
$229$	−14.1118			−0.932534			−0.466267	−	0.884644i	$-0.654401\pi$
$229$	−14.1118			−0.932534			−0.466267	+	0.884644i	$0.654401\pi$
$230$	−0.231280	−	0.400589i	−0.0152502	−	0.0264140i
$231$	−24.7302	+	11.8645i	−1.62713	+	0.780629i
$232$	5.72445	+	3.30501i	0.375829	+	0.216985i
$233$		−	25.4597i		−	1.66792i	−0.551827	−	0.833959i	$-0.686069\pi$
$233$		−	25.4597i		−	1.66792i	0.551827	−	0.833959i	$-0.313931\pi$
$234$	1.64167	−	10.6913i	0.107319	−	0.698915i
$235$	−0.567146			−0.0369966
$236$	1.61004	+	0.929559i	0.104805	+	0.0605092i
$237$	4.86580	+	21.7584i	0.316068	+	1.41336i
$238$	8.36525	−	7.80735i	0.542239	−	0.506075i
$239$	13.2140			0.854746			0.427373	−	0.904075i	$-0.359439\pi$
$239$	13.2140			0.854746			0.427373	+	0.904075i	$0.359439\pi$
$240$	−0.0978120	+	0.312224i	−0.00631374	+	0.0201540i
$241$	2.98003	+	5.16157i	0.191961	+	0.332486i	0.945900	−	0.324458i	$-0.105182\pi$
$241$	2.98003	+	5.16157i	0.191961	+	0.332486i	−0.753939	+	0.656944i	$0.771849\pi$
$242$	−24.8261			−1.59588
$243$	−13.8928	−	7.07028i	−0.891226	−	0.453559i
$244$	1.69169	+	0.976699i	0.108299	+	0.0625267i
$245$	1.31917	+	0.0911229i	0.0842785	+	0.00582163i
$246$	9.79584	+	10.6508i	0.624560	+	0.679072i
$247$	8.58305	+	17.5517i	0.546126	+	1.11679i
$248$	−7.73989			−0.491484
$249$	27.3367	−	6.11325i	1.73239	−	0.387412i
$250$	1.63010	+	0.941137i	0.103096	+	0.0595227i
$251$	−6.39264	−	11.0724i	−0.403500	−	0.698882i	0.590646	−	0.806931i	$-0.298873\pi$
$251$	−6.39264	−	11.0724i	−0.403500	−	0.698882i	−0.994146	+	0.108049i	$0.965540\pi$
$252$	−7.85541	+	1.13693i	−0.494844	+	0.0716198i
$253$	12.6930	−	7.32829i	0.798001	−	0.460726i
$254$	−1.88905	−	3.27194i	−0.118530	−	0.205300i
$255$	−0.957910	−	1.04152i	−0.0599867	−	0.0652223i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.37346	−	9.30710i	0.335187	−	0.580561i	−0.648334	−	0.761356i	$-0.724534\pi$
$257$	5.37346	−	9.30710i	0.335187	−	0.580561i	0.983521	+	0.180795i	$0.0578672\pi$
$258$	1.51931	+	6.79392i	0.0945883	+	0.422971i
$259$	−3.60420	+	0.833701i	−0.223954	+	0.0518037i
$260$	−0.611854	+	0.299205i	−0.0379456	+	0.0185559i
$261$	19.7608	+	1.65551i	1.22317	+	0.102473i
$262$	−5.65362	+	9.79235i	−0.349282	+	0.604974i
$263$	9.20947	+	5.31709i	0.567880	+	0.327866i	0.756302	−	0.654222i	$-0.227004\pi$
$263$	9.20947	+	5.31709i	0.567880	+	0.327866i	−0.188422	+	0.982088i	$0.560337\pi$
$264$	−9.89308	−	3.09925i	−0.608877	−	0.190746i
$265$	0.0832800			0.00511585
$266$	10.4812	−	9.78222i	0.642646	−	0.599786i
$267$	−7.39741	+	23.6132i	−0.452714	+	1.44510i
$268$		−	10.8570i		−	0.663199i
$269$	2.47776	+	4.29161i	0.151072	+	0.261664i	0.931622	−	0.363429i	$-0.118394\pi$
$269$	2.47776	+	4.29161i	0.151072	+	0.261664i	−0.780550	+	0.625093i	$0.785061\pi$
$270$	0.133496	+	0.972440i	0.00812429	+	0.0591808i
$271$	−9.08097	+	15.7287i	−0.551629	+	0.955450i	0.446528	+	0.894770i	$0.352660\pi$
$271$	−9.08097	+	15.7287i	−0.551629	+	0.955450i	−0.998157	+	0.0606805i	$0.980673\pi$
$272$	4.32488			0.262234
$273$	−12.9647	−	10.2429i	−0.784658	−	0.619929i
$274$	6.66790			0.402822
$275$	−14.8569	+	25.7330i	−0.895907	+	1.55176i
$276$	4.13902	−	0.925601i	0.249139	−	0.0557146i
$277$	16.5270	+	28.6255i	0.993009	+	1.71994i	0.598732	+	0.800949i	$0.295671\pi$
$277$	16.5270	+	28.6255i	0.993009	+	1.71994i	0.394276	+	0.918992i	$0.370995\pi$
$278$			1.17038i			0.0701945i
$279$	−21.0079	+	9.89053i	−1.25771	+	0.592131i
$280$	0.341008	+	0.365376i	0.0203791	+	0.0218354i
$281$	−15.9870			−0.953706			−0.476853	−	0.878983i	$-0.658223\pi$
$281$	−15.9870			−0.953706			−0.476853	+	0.878983i	$0.658223\pi$
$282$	1.55459	−	4.96240i	0.0925747	−	0.295506i
$283$	−22.9867	−	13.2714i	−1.36641	−	0.788900i	−0.375947	−	0.926641i	$-0.622682\pi$
$283$	−22.9867	−	13.2714i	−1.36641	−	0.788900i	−0.990468	+	0.137741i	$0.956016\pi$
$284$	1.71090	−	2.96337i	0.101523	−	0.175844i
$285$	−1.20021	−	1.30497i	−0.0710945	−	0.0772997i
$286$	−9.48054	−	19.3871i	−0.560596	−	1.14638i
$287$	21.5356	−	4.98148i	1.27121	−	0.294048i
$288$	−2.46378	−	1.71166i	−0.145180	−	0.100861i
$289$	−0.852297	+	1.47622i	−0.0501351	+	0.0868366i
$290$	−0.624321	−	1.08136i	−0.0366614	−	0.0634994i
$291$	−20.8001	+	19.1304i	−1.21932	+	1.12144i
$292$	−3.82068	−	6.61761i	−0.223588	−	0.387267i
$293$	25.7332	−	14.8571i	1.50335	−	0.867960i	0.503358	−	0.864078i	$-0.332098\pi$
$293$	25.7332	−	14.8571i	1.50335	−	0.867960i	0.999992	−	0.00388166i	$-0.00123557\pi$
$294$	−4.41324	+	11.2926i	−0.257386	+	0.658599i
$295$	−0.175595	−	0.304140i	−0.0102235	−	0.0177077i
$296$	−1.21090	−	0.699114i	−0.0703822	−	0.0406352i
$297$	−30.8125	+	4.22992i	−1.78792	+	0.245445i
$298$	−5.52511			−0.320061
$299$	7.32456	+	4.92946i	0.423590	+	0.285078i
$300$	−6.32873	+	5.82070i	−0.365389	+	0.336058i
$301$	10.1709	+	3.10484i	0.586239	+	0.178960i
$302$	11.4905	+	6.63404i	0.661204	+	0.381746i
$303$	8.51996	+	2.66909i	0.489459	+	0.153335i
$304$	5.41886			0.310793
$305$	−0.184500	−	0.319563i	−0.0105644	−	0.0182981i
$306$	11.7387	−	5.52661i	0.671059	−	0.315935i
$307$	−0.176409			−0.0100682			−0.00503408	−	0.999987i	$-0.501602\pi$
$307$	−0.176409			−0.0100682			−0.00503408	+	0.999987i	$0.501602\pi$
$308$	−11.5772	+	10.8051i	−0.659674	+	0.615678i
$309$	0.830918	−	0.185817i	0.0472693	−	0.0105707i
$310$	1.26620	+	0.731038i	0.0719151	+	0.0415202i
$311$	−11.5151			−0.652960			−0.326480	−	0.945204i	$-0.605863\pi$
$311$	−11.5151			−0.652960			−0.326480	+	0.945204i	$0.605863\pi$
$312$	−0.940833	−	6.17372i	−0.0532642	−	0.349518i
$313$		−	9.52231i		−	0.538233i	−0.963108	−	0.269116i	$-0.913268\pi$
$313$		−	9.52231i		−	0.538233i	0.963108	−	0.269116i	$-0.0867316\pi$
$314$	−13.9052	−	8.02816i	−0.784715	−	0.453055i
$315$	1.39248	+	0.555954i	0.0784572	+	0.0313245i
$316$	6.43626	+	11.1479i	0.362068	+	0.627120i
$317$	−20.9814			−1.17843			−0.589217	−	0.807975i	$-0.700564\pi$
$317$	−20.9814			−1.17843			−0.589217	+	0.807975i	$0.700564\pi$
$318$	−0.228277	+	0.728680i	−0.0128011	+	0.0408623i
$319$	34.2636	−	19.7821i	1.91840	−	1.10759i
$320$			0.188901i			0.0105599i
$321$	6.06668	−	19.3654i	0.338609	−	1.08087i
$322$	1.89154	−	6.19633i	0.105411	−	0.345308i
$323$	−11.7180	+	20.2961i	−0.652005	+	1.12931i
$324$	−8.87455	−	1.49748i	−0.493030	−	0.0831933i
$325$	−17.8568	−	1.23011i	−0.990516	−	0.0682341i
$326$			3.76868i			0.208728i
$327$	4.53367	−	1.01386i	0.250713	−	0.0560664i
$328$	7.23531	+	4.17731i	0.399503	+	0.230653i
$329$	−5.41988	−	5.80718i	−0.298807	−	0.320160i
$330$	1.32572	+	1.44142i	0.0729783	+	0.0793478i
$331$	4.41038	−	2.54633i	0.242416	−	0.139959i	−0.373871	−	0.927481i	$-0.621970\pi$
$331$	4.41038	−	2.54633i	0.242416	−	0.139959i	0.616287	+	0.787522i	$0.288636\pi$
$332$	14.0059	−	8.08634i	0.768676	−	0.443795i
$333$	−4.18004	−	0.350192i	−0.229065	−	0.0191904i
$334$	−17.4109	+	10.0522i	−0.952683	+	0.550032i
$335$	−1.02545	+	1.77614i	−0.0560265	+	0.0970408i
$336$	−4.13169	+	1.98222i	−0.225402	+	0.108139i
$337$	−24.2673			−1.32192			−0.660961	−	0.750420i	$-0.729851\pi$
$337$	−24.2673			−1.32192			−0.660961	+	0.750420i	$0.729851\pi$
$338$	7.98239	−	10.2607i	0.434185	−	0.558107i
$339$	3.95274	+	4.29774i	0.214684	+	0.233421i
$340$	−0.707522	−	0.408488i	−0.0383708	−	0.0221534i
$341$	−23.1635	+	40.1204i	−1.25438	+	2.17264i
$342$	14.7081	−	6.92457i	0.795320	−	0.374438i
$343$	11.6734	+	14.3781i	0.630307	+	0.776346i
$344$	2.00968	+	3.48087i	0.108355	+	0.187676i
$345$	−0.764539	−	0.239511i	−0.0411614	−	0.0128948i
$346$	16.5383			0.889104
$347$	−0.124936	+	0.0721316i	−0.00670689	+	0.00387223i	−0.503350	−	0.864083i	$-0.667899\pi$
$347$	−0.124936	+	0.0721316i	−0.00670689	+	0.00387223i	0.496643	+	0.867955i	$0.334566\pi$
$348$	11.1729	−	2.49858i	0.598932	−	0.133938i
$349$	13.3482	−	23.1197i	0.714511	−	1.23757i	−0.248636	−	0.968597i	$-0.579982\pi$
$349$	13.3482	−	23.1197i	0.714511	−	1.23757i	0.963148	−	0.268973i	$-0.0866843\pi$
$350$	2.96000	+	12.7965i	0.158219	+	0.684000i
$351$	−10.4428	−	15.5547i	−0.557396	−	0.830247i
$352$	−5.98549			−0.319028
$353$	15.5551	+	8.98072i	0.827912	+	0.477995i	0.853137	−	0.521686i	$-0.174697\pi$
$353$	15.5551	+	8.98072i	0.827912	+	0.477995i	−0.0252249	+	0.999682i	$0.508030\pi$
$354$	3.14247	−	0.702745i	0.167020	−	0.0373505i
$355$	−0.559784	+	0.323192i	−0.0297103	+	0.0171532i
$356$			14.2864i			0.757178i
$357$	1.51022	−	19.7615i	0.0799294	−	1.04589i
$358$	−12.0538	+	6.95929i	−0.637065	+	0.367810i
$359$	23.0451			1.21627			0.608137	−	0.793832i	$-0.291917\pi$
$359$	23.0451			1.21627			0.608137	+	0.793832i	$0.291917\pi$
$360$	0.241390	+	0.512723i	0.0127224	+	0.0270229i
$361$	−5.18202	+	8.97553i	−0.272738	+	0.472396i
$362$	16.9201	+	9.76884i	0.889303	+	0.513439i
$363$	−31.6494	+	29.1088i	−1.66116	+	1.52781i
$364$	−8.91076	−	3.40563i	−0.467051	−	0.178503i
$365$			1.44346i			0.0755544i
$366$	3.30183	−	0.738382i	0.172589	−	0.0385959i
$367$	13.8828	+	8.01521i	0.724674	+	0.418391i	0.816471	−	0.577387i	$-0.195928\pi$
$367$	13.8828	+	8.01521i	0.724674	+	0.418391i	−0.0917966	+	0.995778i	$0.529261\pi$
$368$	2.12062	−	1.22434i	0.110545	−	0.0638233i
$369$	24.9763	+	2.09245i	1.30022	+	0.108928i
$370$	0.132064	+	0.228741i	0.00686566	+	0.0118917i
$371$	0.795856	+	0.852728i	0.0413188	+	0.0442714i
$372$	−9.86716	+	9.07508i	−0.511588	+	0.470521i
$373$	2.79520	+	4.84143i	0.144730	+	0.250680i	0.929272	−	0.369396i	$-0.120435\pi$
$373$	2.79520	+	4.84143i	0.144730	+	0.250680i	−0.784542	+	0.620076i	$0.787102\pi$
$374$	12.9433	−	22.4184i	0.669280	−	1.15923i
$375$	3.18161	−	0.711497i	0.164298	−	0.0367416i
$376$		−	3.00234i		−	0.154834i
$377$	19.7720	+	13.3067i	1.01831	+	0.685329i
$378$	−8.68136	+	10.6599i	−0.446521	+	0.548287i
$379$	−28.6697	−	16.5524i	−1.47266	−	0.850241i	−0.473134	−	0.880991i	$-0.656877\pi$
$379$	−28.6697	−	16.5524i	−1.47266	−	0.850241i	−0.999527	+	0.0307493i	$0.990211\pi$
$380$	−0.886490	−	0.511815i	−0.0454760	−	0.0262556i
$381$	−6.24462	−	1.95628i	−0.319922	−	0.100223i
$382$		−	8.48168i		−	0.433960i
$383$	−6.23135	+	3.59767i	−0.318407	+	0.183832i	−0.650682	−	0.759350i	$-0.725517\pi$
$383$	−6.23135	+	3.59767i	−0.318407	+	0.183832i	0.332275	+	0.943182i	$0.392184\pi$
$384$	−1.65284	−	0.517794i	−0.0843463	−	0.0264235i
$385$	2.91451	−	0.674167i	0.148537	−	0.0343587i
$386$	0.941626	−	0.543648i	0.0479275	−	0.0276710i
$387$	9.90281	+	6.87979i	0.503388	+	0.349719i
$388$	−8.15789	+	14.1299i	−0.414154	+	0.717336i
$389$		−	3.50651i		−	0.177787i	−0.996041	−	0.0888936i	$-0.971667\pi$
$389$		−	3.50651i		−	0.177787i	0.996041	−	0.0888936i	$-0.0283331\pi$
$390$	−0.429198	+	1.09884i	−0.0217333	+	0.0556421i
$391$			10.5903i			0.535573i
$392$	−0.482384	+	6.98336i	−0.0243640	+	0.352713i
$393$	4.27412	+	19.1126i	0.215601	+	0.964105i
$394$	5.48398	+	9.49852i	0.276279	+	0.478529i
$395$		−	2.43164i		−	0.122349i
$396$	−16.2460	+	7.64864i	−0.816393	+	0.384359i
$397$	13.1380	+	22.7557i	0.659378	+	1.14208i	0.980777	+	0.195133i	$0.0625137\pi$
$397$	13.1380	+	22.7557i	0.659378	+	1.14208i	−0.321399	+	0.946944i	$0.604153\pi$
$398$			7.58519i			0.380211i
$399$	1.89223	−	24.7601i	0.0947302	−	1.23956i
$400$	−2.48216	+	4.29922i	−0.124108	+	0.214961i
$401$	5.37427	−	9.30851i	0.268378	−	0.464845i	−0.700065	−	0.714079i	$-0.746846\pi$
$401$	5.37427	−	9.30851i	0.268378	−	0.464845i	0.968443	+	0.249234i	$0.0801790\pi$
$402$	−12.7299	−	13.8410i	−0.634912	−	0.690327i
$403$	−27.8406	−	1.91787i	−1.38684	−	0.0955358i
$404$	5.15473			0.256458
$405$	1.31038	+	1.08318i	0.0651133	+	0.0538239i
$406$	5.10606	−	16.7265i	0.253409	−	0.830121i
$407$	−7.24784	+	4.18454i	−0.359262	+	0.207420i
$408$	5.51355	−	5.07095i	0.272961	−	0.251050i
$409$	−7.52589	−	13.0352i	−0.372131	−	0.644550i	0.617762	−	0.786365i	$-0.288039\pi$
$409$	−7.52589	−	13.0352i	−0.372131	−	0.644550i	−0.989893	+	0.141815i	$0.954706\pi$
$410$	−0.789099	−	1.36676i	−0.0389708	−	0.0674994i
$411$	8.50053	−	7.81816i	0.419300	−	0.385641i
$412$	0.425721	−	0.245790i	0.0209738	−	0.0121092i
$413$	1.43612	−	4.70445i	0.0706667	−	0.231491i
$414$	4.19133	−	6.03302i	0.205992	−	0.296507i
$415$	−3.05504			−0.149966
$416$	−1.58392	−	3.23901i	−0.0776581	−	0.158806i
$417$	1.37227	+	1.49205i	0.0672006	+	0.0730659i
$418$	16.2173	−	28.0891i	0.793213	−	1.37388i
$419$	11.7500	−	20.3516i	0.574024	−	0.994239i	−0.422123	−	0.906539i	$-0.638715\pi$
$419$	11.7500	−	20.3516i	0.574024	−	0.994239i	0.996147	−	0.0877004i	$-0.0279518\pi$
$420$	0.863138	+	0.0659632i	0.0421168	+	0.00321868i
$421$		−	34.1950i		−	1.66656i	−0.552851	−	0.833280i	$-0.686460\pi$
$421$		−	34.1950i		−	1.66656i	0.552851	−	0.833280i	$-0.313540\pi$
$422$	6.91977	+	11.9854i	0.336849	+	0.583440i
$423$	−3.83658	−	8.14905i	−0.186541	−	0.396221i
$424$			0.440865i			0.0214103i
$425$	−10.7350	−	18.5936i	−0.520726	−	0.901924i
$426$	−1.29344	−	5.78387i	−0.0626673	−	0.280230i
$427$	1.50894	−	4.94302i	0.0730230	−	0.239209i
$428$		−	11.7164i		−	0.566334i
$429$	−34.8177	−	13.5995i	−1.68101	−	0.656589i
$430$		−	0.759262i		−	0.0366149i
$431$	0.197300	−	0.341734i	0.00950362	−	0.0164607i	−0.861234	−	0.508208i	$-0.830308\pi$
$431$	0.197300	−	0.341734i	0.00950362	−	0.0164607i	0.870738	+	0.491747i	$0.163642\pi$
$432$	−5.14787	+	0.706695i	−0.247677	+	0.0340009i
$433$	−20.3742	+	11.7631i	−0.979122	+	0.565296i	−0.902005	−	0.431726i	$-0.857905\pi$
$433$	−20.3742	+	11.7631i	−0.979122	+	0.565296i	−0.0771170	+	0.997022i	$0.524572\pi$
$434$	4.61496	+	19.9510i	0.221525	+	0.957680i
$435$	−2.06381	−	0.646539i	−0.0989521	−	0.0309992i
$436$	2.32283	−	1.34108i	0.111243	−	0.0642263i
$437$			13.2691i			0.634746i
$438$	−12.6300	−	3.95665i	−0.603483	−	0.189056i
$439$	−4.95314	−	2.85970i	−0.236400	−	0.136486i	0.377121	−	0.926164i	$-0.376914\pi$
$439$	−4.95314	−	2.85970i	−0.236400	−	0.136486i	−0.613521	+	0.789678i	$0.710247\pi$
$440$	0.979187	+	0.565334i	0.0466809	+	0.0269512i
$441$	7.61448	+	19.5709i	0.362594	+	0.931947i
$442$	15.5567	+	1.07166i	0.739957	+	0.0509738i
$443$			2.47810i			0.117738i	0.998266	+	0.0588690i	$0.0187494\pi$
$443$			2.47810i			0.117738i	−0.998266	+	0.0588690i	$0.981251\pi$
$444$	−2.36343	+	0.528529i	−0.112163	+	0.0250829i
$445$	1.34936	−	2.33716i	0.0639658	−	0.110792i
$446$	−12.0097	−	20.8015i	−0.568677	−	0.984978i
$447$	−7.04366	+	6.47824i	−0.333154	+	0.306410i
$448$	−1.93422	+	1.80522i	−0.0913831	+	0.0852885i
$449$	−5.34379	−	9.25571i	−0.252189	−	0.436804i	0.711939	−	0.702241i	$-0.247817\pi$
$449$	−5.34379	−	9.25571i	−0.252189	−	0.436804i	−0.964128	+	0.265437i	$0.914484\pi$
$450$	−1.24333	+	14.8410i	−0.0586113	+	0.699609i
$451$	43.3069	−	25.0032i	2.03924	−	1.17736i
$452$	2.91954	+	1.68560i	0.137323	+	0.0792837i
$453$	22.4271	−	5.01532i	1.05372	−	0.235640i
$454$			15.1515i			0.711096i
$455$	1.13608	+	1.39877i	0.0532602	+	0.0655752i
$456$	6.90820	−	6.35365i	0.323506	−	0.297537i
$457$	6.26295	+	3.61591i	0.292968	+	0.169145i	0.639280	−	0.768974i	$-0.279233\pi$
$457$	6.26295	+	3.61591i	0.292968	+	0.169145i	−0.346311	+	0.938120i	$0.612566\pi$
$458$	−7.05590	+	12.2212i	−0.329700	+	0.571058i
$459$	8.48507	−	20.8093i	0.396049	−	0.971296i
$460$	−0.462560			−0.0215670
$461$	22.2461	−	12.8438i	1.03610	−	0.598195i	0.117376	−	0.993088i	$-0.462552\pi$
$461$	22.2461	−	12.8438i	1.03610	−	0.598195i	0.918727	+	0.394893i	$0.129218\pi$
$462$	−2.09010	+	27.3492i	−0.0972401	+	1.27240i
$463$			17.8625i			0.830141i	0.909789	+	0.415070i	$0.136243\pi$
$463$			17.8625i			0.830141i	−0.909789	+	0.415070i	$0.863757\pi$
$464$	5.72445	−	3.30501i	0.265751	−	0.153431i
$465$	2.47135	−	0.552663i	0.114606	−	0.0256292i
$466$	−22.0487	−	12.7298i	−1.02139	−	0.589698i
$467$	−13.6813			−0.633095			−0.316547	−	0.948577i	$-0.602524\pi$
$467$	−13.6813			−0.633095			−0.316547	+	0.948577i	$0.602524\pi$
$468$	−8.43815	−	6.76740i	−0.390053	−	0.312823i
$469$	−27.9860	+	6.47356i	−1.29228	+	0.298921i
$470$	−0.283573	+	0.491163i	−0.0130803	+	0.0226557i
$471$	−27.1400	+	6.06927i	−1.25055	+	0.279657i
$472$	1.61004	−	0.929559i	0.0741083	−	0.0427864i
$473$	24.0578			1.10618
$474$	21.2762	+	6.66531i	0.977250	+	0.306148i
$475$	−13.4505	−	23.2969i	−0.617150	−	1.06893i
$476$	−2.57873	−	11.1482i	−0.118196	−	0.510977i
$477$	0.563365	+	1.19661i	0.0257947	+	0.0547890i
$478$	6.60702	−	11.4437i	0.302198	−	0.523423i
$479$	−2.54639	−	1.47016i	−0.116348	−	0.0671733i	0.440697	−	0.897656i	$-0.354731\pi$
$479$	−2.54639	−	1.47016i	−0.116348	−	0.0671733i	−0.557044	+	0.830483i	$0.688065\pi$
$480$	0.221488	+	0.240820i	0.0101095	+	0.0109919i
$481$	−4.18241	−	2.81478i	−0.190701	−	0.128343i
$482$	5.96007			0.271474
$483$	−4.85382	−	10.1172i	−0.220857	−	0.460348i
$484$	−12.4130	+	21.5000i	−0.564230	+	0.977274i
$485$	2.66915	−	1.54104i	0.121200	−	0.0699749i
$486$	−13.0695	+	8.49641i	−0.592843	+	0.385405i
$487$	36.7588	−	21.2227i	1.66570	−	0.961694i	0.695788	−	0.718247i	$-0.255055\pi$
$487$	36.7588	−	21.2227i	1.66570	−	0.961694i	0.969914	−	0.243446i	$-0.0782779\pi$
$488$	1.69169	−	0.976699i	0.0765793	−	0.0442131i
$489$	4.41880	+	4.80448i	0.199825	+	0.217266i
$490$	0.738498	−	1.09687i	0.0333619	−	0.0495515i
$491$	−25.7266	−	14.8533i	−1.16102	−	0.670318i	−0.209475	−	0.977814i	$-0.567176\pi$
$491$	−25.7266	−	14.8533i	−1.16102	−	0.670318i	−0.951549	+	0.307496i	$0.900509\pi$
$492$	14.1218	−	3.15803i	0.636660	−	0.142375i
$493$			28.5876i			1.28752i
$494$	19.4918	+	1.34274i	0.876977	+	0.0604127i
$495$	3.38016	+	0.283181i	0.151927	+	0.0127280i
$496$	−3.86995	+	6.70294i	−0.173766	+	0.300971i
$497$	−8.65877	−	2.64325i	−0.388399	−	0.118566i
$498$	8.37411	−	26.7309i	0.375253	−	1.19784i
$499$		−	20.3400i		−	0.910543i	−0.890353	−	0.455272i	$-0.849542\pi$
$499$		−	20.3400i		−	0.910543i	0.890353	−	0.455272i	$-0.150458\pi$
$500$	1.63010	−	0.941137i	0.0729001	−	0.0420889i
$501$	−10.4099	+	33.2294i	−0.465081	+	1.48458i
$502$	−12.7853			−0.570635
$503$	−6.55055	−	11.3459i	−0.292075	−	0.505888i	0.682226	−	0.731142i	$-0.261012\pi$
$503$	−6.55055	−	11.3459i	−0.292075	−	0.505888i	−0.974300	+	0.225254i	$0.927679\pi$
$504$	−2.94309	+	7.37145i	−0.131096	+	0.328350i
$505$	−0.843280	−	0.486868i	−0.0375255	−	0.0216653i
$506$		−	14.6566i		−	0.651565i
$507$	−1.85441	−	22.4402i	−0.0823574	−	0.996603i
$508$	−3.77811			−0.167626
$509$	−0.0849695	−	0.0490572i	−0.00376621	−	0.00217442i	0.498116	−	0.867111i	$-0.334025\pi$
$509$	−0.0849695	−	0.0490572i	−0.00376621	−	0.00217442i	−0.501882	+	0.864936i	$0.667359\pi$
$510$	−1.38094	+	0.308816i	−0.0611488	+	0.0136746i
$511$	−14.7800	+	13.7943i	−0.653831	+	0.610225i
$512$	−1.00000			−0.0441942
$513$	10.6314	−	26.0730i	0.469386	−	1.15115i
$514$	−5.37346	−	9.30710i	−0.237013	−	0.410519i
$515$	−0.0928601			−0.00409191
$516$	6.64337	+	2.08120i	0.292458	+	0.0916196i
$517$	−15.5629	−	8.98524i	−0.684455	−	0.395170i
$518$	−1.08009	+	3.53818i	−0.0474565	+	0.155459i
$519$	21.0837	−	19.3913i	0.925474	−	0.851182i
$520$	−0.0468079	+	0.679483i	−0.00205266	+	0.0297973i
$521$	−15.5234			−0.680091			−0.340045	−	0.940409i	$-0.610442\pi$
$521$	−15.5234			−0.680091			−0.340045	+	0.940409i	$0.610442\pi$
$522$	11.3141	−	16.2856i	0.495206	−	0.712803i
$523$	−17.2591	−	9.96453i	−0.754687	−	0.435719i	0.0726981	−	0.997354i	$-0.476839\pi$
$523$	−17.2591	−	9.96453i	−0.754687	−	0.435719i	−0.827385	+	0.561635i	$0.810172\pi$
$524$	5.65362	+	9.79235i	0.246979	+	0.427781i
$525$	18.7775	+	12.8429i	0.819517	+	0.560509i
$526$	9.20947	−	5.31709i	0.401552	−	0.231836i
$527$	−16.7371	−	28.9894i	−0.729078	−	1.26280i
$528$	−7.63057	+	7.01803i	−0.332078	+	0.305421i
$529$	−8.50197	−	14.7258i	−0.369651	−	0.640254i
$530$	0.0416400	−	0.0721226i	0.00180873	−	0.00313280i
$531$	3.18219	−	4.58046i	0.138095	−	0.198775i
$532$	−3.23103	−	13.9681i	−0.140083	−	0.605595i
$533$	24.9905	+	16.8187i	1.08246	+	0.728499i
$534$	16.7509	+	18.2129i	0.724883	+	0.788151i
$535$	−1.10662	+	1.91673i	−0.0478435	+	0.0828674i
$536$	−9.40246	−	5.42851i	−0.406125	−	0.234476i
$537$	−7.20695	+	23.0052i	−0.311003	+	0.992748i
$538$	4.95553			0.213648
$539$	34.7552	+	23.3999i	1.49701	+	1.00790i
$540$	0.908906	+	0.370609i	0.0391131	+	0.0159485i
$541$		−	14.9102i		−	0.641039i	−0.947242	−	0.320520i	$-0.896143\pi$
$541$		−	14.9102i		−	0.641039i	0.947242	−	0.320520i	$-0.103857\pi$
$542$	9.08097	+	15.7287i	0.390061	+	0.675605i
$543$	33.0246	−	7.38523i	1.41722	−	0.316930i
$544$	2.16244	−	3.74546i	0.0927139	−	0.160585i
$545$	−0.506665			−0.0217032
$546$	−15.3530	+	6.10629i	−0.657046	+	0.261325i
$547$	18.1583			0.776395			0.388197	−	0.921576i	$-0.373098\pi$
$547$	18.1583			0.776395			0.388197	+	0.921576i	$0.373098\pi$
$548$	3.33395	−	5.77457i	0.142419	−	0.246677i
$549$	3.34356	−	4.81274i	0.142700	−	0.205403i
$550$	14.8569	+	25.7330i	0.633502	+	1.09726i
$551$			35.8188i			1.52593i
$552$	1.26791	−	4.04729i	0.0539660	−	0.172264i
$553$	24.8982	−	23.2377i	1.05878	−	0.988167i
$554$	33.0539			1.40433
$555$	0.436561	+	0.136763i	0.0185310	+	0.00580528i
$556$	1.01358	+	0.585188i	0.0429852	+	0.0248175i
$557$	1.86994	−	3.23883i	0.0792319	−	0.137234i	−0.823687	−	0.567045i	$-0.808087\pi$
$557$	1.86994	−	3.23883i	0.0792319	−	0.137234i	0.902919	+	0.429811i	$0.141420\pi$
$558$	−1.93849	+	23.1386i	−0.0820628	+	0.979536i
$559$	6.36634	+	13.0187i	0.269268	+	0.550634i
$560$	0.486929	−	0.112634i	0.0205765	−	0.00475964i
$561$	−9.78508	−	43.7560i	−0.413127	−	1.84738i
$562$	−7.99351	+	13.8452i	−0.337186	+	0.584023i
$563$	11.4570	+	19.8442i	0.482856	+	0.836331i	0.999806	−	0.0196842i	$-0.00626607\pi$
$563$	11.4570	+	19.8442i	0.482856	+	0.836331i	−0.516950	+	0.856016i	$0.672933\pi$
$564$	−3.52027	−	3.82752i	−0.148230	−	0.161168i
$565$	−0.318411	−	0.551505i	−0.0133957	−	0.0232020i
$566$	−22.9867	+	13.2714i	−0.966201	+	0.557837i
$567$	1.43146	+	23.7687i	0.0601158	+	0.998191i
$568$	−1.71090	−	2.96337i	−0.0717878	−	0.124340i
$569$	6.06874	+	3.50379i	0.254415	+	0.146886i	0.621784	−	0.783189i	$-0.286408\pi$
$569$	6.06874	+	3.50379i	0.254415	+	0.146886i	−0.367369	+	0.930075i	$0.619741\pi$
$570$	−1.73024	+	0.386931i	−0.0724719	+	0.0162068i
$571$	−37.6484			−1.57554			−0.787769	−	0.615971i	$-0.788764\pi$
$571$	−37.6484			−1.57554			−0.787769	+	0.615971i	$0.788764\pi$
$572$	−21.5300	−	1.48314i	−0.900213	−	0.0620134i
$573$	−9.94483	−	10.8128i	−0.415451	−	0.451712i
$574$	6.45370	−	21.1411i	0.269372	−	0.882413i
$575$	−10.5274	−	6.07803i	−0.439025	−	0.253471i
$576$	−2.71423	+	1.27786i	−0.113093	+	0.0532443i
$577$	13.4291			0.559059			0.279530	−	0.960137i	$-0.409821\pi$
$577$	13.4291			0.559059			0.279530	+	0.960137i	$0.409821\pi$
$578$	0.852297	+	1.47622i	0.0354509	+	0.0614027i
$579$	0.562995	−	1.79713i	0.0233973	−	0.0746862i
$580$	−1.24864			−0.0518471
$581$	−29.1952	−	31.2814i	−1.21122	−	1.29777i
$582$	6.16735	+	27.5786i	0.255645	+	1.14317i
$583$	2.28526	+	1.31940i	0.0946458	+	0.0546438i
$584$	−7.64136			−0.316202
$585$	0.741240	+	1.90409i	0.0306465	+	0.0787245i
$586$		−	29.7142i		−	1.22748i
$587$	24.6198	+	14.2142i	1.01617	+	0.586684i	0.912991	−	0.407979i	$-0.133766\pi$
$587$	24.6198	+	14.2142i	1.01617	+	0.586684i	0.103175	+	0.994663i	$0.467100\pi$
$588$	7.57307	+	9.46829i	0.312308	+	0.390466i
$589$	−20.9707	−	36.3223i	−0.864083	−	1.49664i
$590$	−0.351190			−0.0144583
$591$	18.1283	+	5.67914i	0.745699	+	0.233608i
$592$	−1.21090	+	0.699114i	−0.0497677	+	0.0287334i
$593$		−	22.4962i		−	0.923810i	−0.886929	−	0.461905i	$-0.847166\pi$
$593$		−	22.4962i		−	0.923810i	0.886929	−	0.461905i	$-0.152834\pi$
$594$	−11.7431	+	28.7994i	−0.481823	+	1.18165i
$595$	−0.631091	+	2.06733i	−0.0258722	+	0.0847525i
$596$	−2.76256	+	4.78489i	−0.113159	+	0.195997i
$597$	8.89369	+	9.66994i	0.363995	+	0.395764i
$598$	7.93132	−	3.87852i	0.324336	−	0.158605i
$599$		−	29.8169i		−	1.21829i	−0.793060	−	0.609143i	$-0.791514\pi$
$599$		−	29.8169i		−	1.21829i	0.793060	−	0.609143i	$-0.208486\pi$
$600$	1.87651	+	8.39119i	0.0766080	+	0.342569i
$601$	−15.1795	−	8.76391i	−0.619186	−	0.357487i	0.157366	−	0.987540i	$-0.449700\pi$
$601$	−15.1795	−	8.76391i	−0.619186	−	0.357487i	−0.776552	+	0.630053i	$0.783033\pi$
$602$	7.77431	−	7.25581i	0.316857	−	0.295725i
$603$	−32.4574	−	2.71919i	−1.32177	−	0.110734i
$604$	11.4905	−	6.63404i	0.467542	−	0.269935i
$605$	4.06139	−	2.34484i	0.165119	−	0.0953314i
$606$	6.57148	−	6.04396i	0.266948	−	0.245519i
$607$	−10.8473	+	6.26269i	−0.440278	+	0.254195i	−0.703716	−	0.710482i	$-0.748477\pi$
$607$	−10.8473	+	6.26269i	−0.440278	+	0.254195i	0.263438	+	0.964676i	$0.415144\pi$
$608$	2.70943	−	4.69287i	0.109882	−	0.190321i
$609$	−13.1025	−	27.3105i	−0.530940	−	1.10668i
$610$	−0.369000			−0.0149404
$611$	0.743950	−	10.7995i	0.0300970	−	0.436901i
$612$	1.08318	−	12.9293i	0.0437851	−	0.522638i
$613$	−14.4298	−	8.33108i	−0.582816	−	0.336489i	0.179436	−	0.983770i	$-0.442573\pi$
$613$	−14.4298	−	8.33108i	−0.582816	−	0.336489i	−0.762252	+	0.647281i	$0.775906\pi$
$614$	−0.0882043	+	0.152774i	−0.00355964	+	0.00616547i
$615$	−2.60851	−	0.817181i	−0.105185	−	0.0329519i
$616$	3.56888	+	15.4287i	0.143794	+	0.621641i
$617$	12.5067	+	21.6622i	0.503499	+	0.872086i	0.999992	+	0.00404517i	$0.00128762\pi$
$617$	12.5067	+	21.6622i	0.503499	+	0.872086i	−0.496493	+	0.868041i	$0.665379\pi$
$618$	0.254537	−	0.812504i	0.0102390	−	0.0326837i
$619$	30.6669			1.23261			0.616303	−	0.787509i	$-0.288630\pi$
$619$	30.6669			1.23261			0.616303	+	0.787509i	$0.288630\pi$
$620$	1.26620	−	0.731038i	0.0508516	−	0.0293592i
$621$	−1.73047	−	12.6055i	−0.0694415	−	0.505842i
$622$	−5.75754	+	9.97235i	−0.230856	+	0.399855i
$623$	36.8259	−	8.51835i	1.47540	−	0.341280i
$624$	−5.81702	−	2.27208i	−0.232867	−	0.0909558i
$625$	24.4660			0.978641
$626$	−8.24656	−	4.76115i	−0.329599	−	0.190294i
$627$	−12.2602	−	54.8241i	−0.489626	−	2.18946i
$628$	−13.9052	+	8.02816i	−0.554877	+	0.320358i
$629$		−	6.04717i		−	0.241116i
$630$	1.17771	−	0.927943i	0.0469210	−	0.0369701i
$631$	−10.3667	+	5.98521i	−0.412691	+	0.238268i	−0.691945	−	0.721950i	$-0.743246\pi$
$631$	−10.3667	+	5.98521i	−0.412691	+	0.238268i	0.279254	+	0.960217i	$0.409913\pi$
$632$	12.8725			0.512041
$633$	22.8746	+	7.16602i	0.909183	+	0.284824i
$634$	−10.4907	+	18.1705i	−0.416640	+	0.721641i
$635$	0.618074	+	0.356845i	0.0245275	+	0.0141610i
$636$	0.516917	+	0.562034i	0.0204971	+	0.0222861i
$637$	−3.46555	+	24.9998i	−0.137310	+	0.990528i
$638$		−	39.5642i		−	1.56636i
$639$	−8.43057	−	5.85697i	−0.333508	−	0.231698i
$640$	0.163593	+	0.0944507i	0.00646660	+	0.00373349i
$641$	14.5471	−	8.39874i	0.574574	−	0.331730i	−0.184400	−	0.982851i	$-0.559034\pi$
$641$	14.5471	−	8.39874i	0.574574	−	0.331730i	0.758974	+	0.651121i	$0.225701\pi$
$642$	−13.7376	−	14.9366i	−0.542179	−	0.589500i
$643$	10.4978	+	18.1827i	0.413993	+	0.717057i	0.995322	−	0.0966114i	$-0.0308004\pi$
$643$	10.4978	+	18.1827i	0.413993	+	0.717057i	−0.581329	+	0.813669i	$0.697467\pi$
$644$	−4.42041	−	4.73629i	−0.174189	−	0.186636i
$645$	−0.890240	−	0.967941i	−0.0350532	−	0.0381126i
$646$	11.7180	+	20.2961i	0.461037	+	0.798540i
$647$	0.217879	−	0.377377i	0.00856570	−	0.0148362i	−0.861711	−	0.507400i	$-0.830607\pi$
$647$	0.217879	−	0.377377i	0.00856570	−	0.0148362i	0.870276	+	0.492564i	$0.163940\pi$
$648$	−5.73413	+	6.93684i	−0.225258	+	0.272505i
$649$		−	11.1277i		−	0.436802i
$650$	−9.99369	+	14.8494i	−0.391985	+	0.582440i
$651$	29.2761	+	20.0234i	1.14742	+	0.784778i
$652$	3.26377	+	1.88434i	0.127819	+	0.0737964i
$653$	16.0308	+	9.25537i	0.627333	+	0.362191i	0.779718	−	0.626130i	$-0.215362\pi$
$653$	16.0308	+	9.25537i	0.627333	+	0.362191i	−0.152386	+	0.988321i	$0.548696\pi$
$654$	1.38881	−	4.43320i	0.0543067	−	0.173352i
$655$		−	2.13595i		−	0.0834586i
$656$	7.23531	−	4.17731i	0.282491	−	0.163096i
$657$	−20.7404	+	9.76462i	−0.809162	+	0.380954i
$658$	−7.73910	+	1.79016i	−0.301702	+	0.0697878i
$659$	0.282523	−	0.163115i	0.0110055	−	0.00635405i	−0.494487	−	0.869185i	$-0.664644\pi$
$659$	0.282523	−	0.163115i	0.0110055	−	0.00635405i	0.505493	+	0.862831i	$0.331311\pi$
$660$	1.91117	−	0.427391i	0.0743921	−	0.0166362i
$661$	−4.09057	+	7.08508i	−0.159105	+	0.275578i	−0.934546	−	0.355842i	$-0.884194\pi$
$661$	−4.09057	+	7.08508i	−0.159105	+	0.275578i	0.775441	+	0.631420i	$0.217527\pi$
$662$		−	5.09266i		−	0.197932i
$663$	21.0889	−	16.8742i	0.819025	−	0.655338i
$664$		−	16.1727i		−	0.627622i
$665$	−0.790726	+	2.59027i	−0.0306630	+	0.100446i
$666$	−2.39330	+	3.44493i	−0.0927383	+	0.133488i
$667$	8.09294	+	14.0174i	0.313360	+	0.542755i
$668$			20.1044i			0.777862i
$669$	−39.7004	−	12.4371i	−1.53491	−	0.480847i
$670$	1.02545	+	1.77614i	0.0396167	+	0.0686182i
$671$		−	11.6920i		−	0.451366i
$672$	−0.349194	+	4.56925i	−0.0134705	+	0.176263i
$673$	−4.89481	+	8.47806i	−0.188681	+	0.326805i	−0.944811	−	0.327617i	$-0.893755\pi$
$673$	−4.89481	+	8.47806i	−0.188681	+	0.326805i	0.756130	+	0.654422i	$0.227088\pi$
$674$	−12.1336	+	21.0161i	−0.467370	+	0.809509i
$675$	15.8161	+	20.3777i	0.608761	+	0.784339i
$676$	−4.89481	−	12.0433i	−0.188262	−	0.463203i
$677$	−32.9389			−1.26595			−0.632973	−	0.774174i	$-0.718166\pi$
$677$	−32.9389			−1.26595			−0.632973	+	0.774174i	$0.718166\pi$
$678$	5.69833	−	1.27431i	0.218843	−	0.0489394i
$679$	41.2866	+	12.6035i	1.58444	+	0.483677i
$680$	−0.707522	+	0.408488i	−0.0271322	+	0.0156648i
$681$	17.7653	+	19.3158i	0.680767	+	0.740184i
$682$	23.1635	+	40.1204i	0.886977	+	1.53629i
$683$	−22.0625	−	38.2134i	−0.844198	−	1.46219i	−0.886316	−	0.463081i	$-0.846744\pi$
$683$	−22.0625	−	38.2134i	−0.844198	−	1.46219i	0.0421178	−	0.999113i	$-0.486590\pi$
$684$	1.35718	−	16.1998i	0.0518929	−	0.619416i
$685$	−1.09082	+	0.629788i	−0.0416783	+	0.0240630i
$686$	18.2886	−	2.92043i	0.698260	−	0.111503i
$687$	5.33424	+	23.8532i	0.203514	+	0.910056i
$688$	4.01936			0.153237
$689$	−0.109242	+	1.58580i	−0.00416178	+	0.0604142i
$690$	−0.589692	+	0.542355i	−0.0224492	+	0.0206471i
$691$	−21.4006	+	37.0670i	−0.814118	+	1.41009i	0.0958414	+	0.995397i	$0.469446\pi$
$691$	−21.4006	+	37.0670i	−0.814118	+	1.41009i	−0.909959	+	0.414697i	$0.863888\pi$
$692$	8.26915	−	14.3226i	0.314346	−	0.544463i
$693$	29.4026	+	37.3166i	1.11691	+	1.41754i
$694$			0.144263i			0.00547616i
$695$	−0.110543	−	0.191466i	−0.00419313	−	0.00726272i
$696$	3.42263	−	10.9253i	0.129734	−	0.414124i
$697$			36.1327i			1.36862i
$698$	−13.3482	−	23.1197i	−0.505236	−	0.875094i
$699$	−43.0345	+	9.62373i	−1.62771	+	0.364003i
$700$	12.5621	+	3.83479i	0.474801	+	0.144942i
$701$			8.82186i			0.333197i	0.986025	+	0.166598i	$0.0532784\pi$
$701$			8.82186i			0.333197i	−0.986025	+	0.166598i	$0.946722\pi$
$702$	−18.6921	+	1.26641i	−0.705489	+	0.0477976i
$703$		−	7.57680i		−	0.285765i
$704$	−2.99275	+	5.18359i	−0.112793	+	0.195364i
$705$	0.214381	+	0.958648i	0.00807405	+	0.0361048i
$706$	15.5551	−	8.98072i	0.585422	−	0.337994i
$707$	−3.07354	−	13.2873i	−0.115592	−	0.499720i
$708$	0.962640	−	3.07283i	0.0361782	−	0.115484i
$709$	−1.61792	+	0.934109i	−0.0607624	+	0.0350812i	−0.530073	−	0.847952i	$-0.677836\pi$
$709$	−1.61792	+	0.934109i	−0.0607624	+	0.0350812i	0.469311	+	0.883033i	$0.344502\pi$
$710$			0.646383i			0.0242583i
$711$	34.9390	−	16.4493i	1.31032	−	0.616898i
$712$	12.3724	+	7.14320i	0.463675	+	0.267703i
$713$	−16.4134	−	9.47628i	−0.614687	−	0.354890i
$714$	−16.3588	−	11.1886i	−0.612214	−	0.418724i
$715$	3.38208	+	2.27615i	0.126483	+	0.0851233i
$716$			13.9186i			0.520162i
$717$	−4.99490	−	22.3357i	−0.186538	−	0.834143i
$718$	11.5225	−	19.9576i	0.430018	−	0.744813i
$719$	2.94341	+	5.09814i	0.109771	+	0.190129i	0.915677	−	0.401914i	$-0.131655\pi$
$719$	2.94341	+	5.09814i	0.109771	+	0.190129i	−0.805907	+	0.592043i	$0.798322\pi$
$720$	0.564726	+	0.0473112i	0.0210461	+	0.00176318i
$721$	−0.887408	−	0.950822i	−0.0330488	−	0.0354105i
$722$	5.18202	+	8.97553i	0.192855	+	0.334035i
$723$	7.59816	−	6.98822i	0.282578	−	0.259895i
$724$	16.9201	−	9.76884i	0.628832	−	0.363056i
$725$	−28.4180	−	16.4071i	−1.05542	−	0.609345i
$726$	9.38424	+	41.9636i	0.348282	+	1.55741i
$727$			12.7622i			0.473322i	0.971592	+	0.236661i	$0.0760531\pi$
$727$			12.7622i			0.473322i	−0.971592	+	0.236661i	$0.923947\pi$
$728$	−7.40474	+	6.01413i	−0.274438	+	0.222899i
$729$	−6.69942	+	26.1556i	−0.248127	+	0.968728i
$730$	1.25008	+	0.721732i	0.0462674	+	0.0267125i
$731$	−8.69162	+	15.0543i	−0.321471	+	0.556804i
$732$	1.01146	−	3.22866i	0.0373845	−	0.119335i
$733$	8.94011			0.330210			0.165105	−	0.986276i	$-0.447204\pi$
$733$	8.94011			0.330210			0.165105	+	0.986276i	$0.447204\pi$
$734$	13.8828	−	8.01521i	0.512422	−	0.295847i
$735$	−0.344618	−	2.26423i	−0.0127114	−	0.0835175i
$736$		−	2.44869i		−	0.0902598i
$737$	−56.2783	+	32.4923i	−2.07304	+	1.19687i
$738$	14.3003	−	20.5839i	0.526401	−	0.757705i
$739$	−21.6281	−	12.4870i	−0.795601	−	0.459340i	0.0463298	−	0.998926i	$-0.485247\pi$
$739$	−21.6281	−	12.4870i	−0.795601	−	0.459340i	−0.841931	+	0.539586i	$0.818581\pi$
$740$	0.264127			0.00970951
$741$	26.4234	−	21.1425i	0.970686	−	0.776688i
$742$	1.13641	−	0.262868i	0.0417190	−	0.00965019i
$743$	−11.5885	+	20.0719i	−0.425142	+	0.736368i	−0.996434	−	0.0843791i	$-0.973109\pi$
$743$	−11.5885	+	20.0719i	−0.425142	+	0.736368i	0.571291	+	0.820747i	$0.306443\pi$
$744$	2.92567	+	13.0827i	0.107260	+	0.479637i
$745$	0.903872	−	0.521851i	0.0331153	−	0.0191191i
$746$	5.59041			0.204679
$747$	−20.6665	−	43.8964i	−0.756147	−	1.60609i
$748$	−12.9433	−	22.4184i	−0.473253	−	0.819698i
$749$	−30.2013	+	6.98598i	−1.10353	+	0.255262i
$750$	0.974629	−	3.11110i	0.0355884	−	0.113601i
$751$	0.120286	−	0.208341i	0.00438929	−	0.00760248i	−0.863822	−	0.503796i	$-0.831936\pi$
$751$	0.120286	−	0.208341i	0.00438929	−	0.00760248i	0.868212	+	0.496194i	$0.165270\pi$
$752$	−2.60010	−	1.50117i	−0.0948160	−	0.0547421i
$753$	−16.2992	+	14.9908i	−0.593977	+	0.546296i
$754$	21.4099	−	10.4698i	0.779704	−	0.381286i
$755$	−2.50636			−0.0912158
$756$	4.89109	+	12.8482i	0.177887	+	0.467286i
$757$	−23.1169	+	40.0396i	−0.840197	+	1.45526i	0.0495307	+	0.998773i	$0.484227\pi$
$757$	−23.1169	+	40.0396i	−0.840197	+	1.45526i	−0.889728	+	0.456491i	$0.849106\pi$
$758$	−28.6697	+	16.5524i	−1.04133	+	0.601211i
$759$	−17.1850	−	18.6849i	−0.623774	−	0.678217i
$760$	−0.886490	+	0.511815i	−0.0321564	+	0.0185655i
$761$	−19.1333	+	11.0466i	−0.693582	+	0.400440i	−0.804952	−	0.593339i	$-0.797809\pi$
$761$	−19.1333	+	11.0466i	−0.693582	+	0.400440i	0.111371	+	0.993779i	$0.464476\pi$
$762$	−4.81650	+	4.42986i	−0.174483	+	0.160477i
$763$	−4.84189	−	5.18789i	−0.175288	−	0.187814i
$764$	−7.34535	−	4.24084i	−0.265745	−	0.153428i
$765$	−1.39839	+	2.01285i	−0.0505588	+	0.0727747i
$766$			7.19534i			0.259978i
$767$	6.02171	−	2.94470i	0.217431	−	0.106327i
$768$	−1.27484	+	1.17251i	−0.0460020	+	0.0423092i
$769$	−27.1219	+	46.9765i	−0.978040	+	1.69402i	−0.308528	+	0.951215i	$0.599836\pi$
$769$	−27.1219	+	46.9765i	−0.978040	+	1.69402i	−0.669513	+	0.742800i	$0.733497\pi$
$770$	0.873409	−	2.86112i	0.0314755	−	0.103108i
$771$	−17.7630	−	5.56468i	−0.639717	−	0.200407i
$772$		−	1.08730i		−	0.0391327i
$773$	−38.1638	+	22.0339i	−1.37266	+	0.792504i	−0.991262	−	0.131909i	$-0.957889\pi$
$773$	−38.1638	+	22.0339i	−1.37266	+	0.792504i	−0.381395	+	0.924412i	$0.624556\pi$
$774$	10.9095	−	5.13619i	0.392133	−	0.184617i
$775$	38.4233			1.38020
$776$	8.15789	+	14.1299i	0.292851	+	0.507233i
$777$	2.77159	+	5.77704i	0.0994302	+	0.207250i
$778$	−3.03673	−	1.75325i	−0.108872	−	0.0628572i
$779$			45.2725i			1.62205i
$780$	0.737026	+	0.921118i	0.0263898	+	0.0329813i
$781$	−20.4812			−0.732874
$782$	9.17145	+	5.29514i	0.327970	+	0.189354i
$783$	−4.67127	−	34.0276i	−0.166938	−	1.21605i
$784$	5.80657	+	3.90944i	0.207378	+	0.139623i
$785$	3.03306			0.108255
$786$	18.6891	+	5.85482i	0.666618	+	0.208834i
$787$	0.125526	+	0.217418i	0.00447452	+	0.00775010i	0.868254	−	0.496120i	$-0.165242\pi$
$787$	0.125526	+	0.217418i	0.00447452	+	0.00775010i	−0.863779	+	0.503870i	$0.831909\pi$
$788$	10.9680			0.390717
$789$	5.50631	−	17.5766i	0.196030	−	0.625745i
$790$	−2.10586	−	1.21582i	−0.0749231	−	0.0432569i
$791$	2.60415	−	8.53070i	0.0925929	−	0.303317i
$792$	−1.49909	+	17.8938i	−0.0532679	+	0.635828i
$793$	6.32708	−	3.09403i	0.224681	−	0.109872i
$794$	26.2760			0.932502
$795$	−0.0314797	−	0.140768i	−0.00111647	−	0.00499253i
$796$	6.56897	+	3.79260i	0.232831	+	0.134425i
$797$	−14.5879	−	25.2669i	−0.516728	−	0.895000i	−0.999811	−	0.0194252i	$-0.993816\pi$
$797$	−14.5879	−	25.2669i	−0.516728	−	0.895000i	0.483083	−	0.875575i	$-0.339517\pi$
$798$	−20.4968	−	14.0188i	−0.725579	−	0.496260i
$799$	11.2451	−	6.49238i	0.397824	−	0.229684i
$800$	2.48216	+	4.29922i	0.0877575	+	0.152001i
$801$	42.7096	+	3.57809i	1.50907	+	0.126426i
$802$	−5.37427	−	9.30851i	−0.189772	−	0.328695i
$803$	−22.8686	+	39.6097i	−0.807017	+	1.39779i
$804$	−18.3516	+	4.10395i	−0.647213	+	0.144735i
$805$	0.275804	+	1.19234i	0.00972082	+	0.0420243i
$806$	−15.5812	+	23.1517i	−0.548825	+	0.815485i
$807$	6.31752	−	5.81039i	0.222387	−	0.204535i
$808$	2.57737	−	4.46413i	0.0906714	−	0.157048i
$809$	25.3578	+	14.6403i	0.891532	+	0.514727i	0.874443	−	0.485127i	$-0.161227\pi$
$809$	25.3578	+	14.6403i	0.891532	+	0.514727i	0.0170890	+	0.999854i	$0.494560\pi$
$810$	1.59326	−	0.593229i	0.0559813	−	0.0208440i
$811$	6.42322			0.225550			0.112775	−	0.993621i	$-0.464026\pi$
$811$	6.42322			0.225550			0.112775	+	0.993621i	$0.464026\pi$
$812$	−11.9325	−	12.7852i	−0.418750	−	0.448673i
$813$	30.0188	+	9.40414i	1.05281	+	0.329817i
$814$			8.36908i			0.293336i
$815$	−0.355954	−	0.616531i	−0.0124685	−	0.0215961i
$816$	−1.63480	−	7.31035i	−0.0572295	−	0.255913i
$817$	−10.8902	+	18.8623i	−0.380999	+	0.659909i
$818$	−15.0518			−0.526273
$819$	−12.4130	+	25.7860i	−0.433744	+	0.901036i
$820$	−1.57820			−0.0551131
$821$	−14.9385	+	25.8742i	−0.521356	+	0.903015i	0.478335	+	0.878177i	$0.341240\pi$
$821$	−14.9385	+	25.8742i	−0.521356	+	0.903015i	−0.999691	+	0.0248379i	$0.992093\pi$
$822$	−2.52046	−	11.2708i	−0.0879111	−	0.393113i
$823$	−3.08977	−	5.35164i	−0.107703	−	0.186546i	0.807137	−	0.590365i	$-0.201016\pi$
$823$	−3.08977	−	5.35164i	−0.107703	−	0.186546i	−0.914839	+	0.403818i	$0.867683\pi$
$824$		−	0.491580i		−	0.0171250i
$825$	49.1124	+	15.3857i	1.70987	+	0.535660i
$826$	−3.35611	−	3.59594i	−0.116774	−	0.125119i
$827$	−9.74990			−0.339037			−0.169519	−	0.985527i	$-0.554221\pi$
$827$	−9.74990			−0.339037			−0.169519	+	0.985527i	$0.554221\pi$
$828$	−3.12909	−	6.64631i	−0.108743	−	0.230975i
$829$	−1.71389	−	0.989516i	−0.0595259	−	0.0343673i	0.469942	−	0.882697i	$-0.344275\pi$
$829$	−1.71389	−	0.989516i	−0.0595259	−	0.0343673i	−0.529468	+	0.848330i	$0.677608\pi$
$830$	−1.52752	+	2.64574i	−0.0530210	+	0.0918351i
$831$	42.1386	−	38.7559i	1.46177	−	1.34443i
$832$	−3.59703	−	0.247790i	−0.124704	−	0.00859057i
$833$	−27.1990	+	13.2944i	−0.942389	+	0.460622i
$834$	1.97829	−	0.442401i	0.0685025	−	0.0153191i
$835$	1.89887	−	3.28895i	0.0657132	−	0.113819i
$836$	−16.2173	−	28.0891i	−0.560886	−	0.971483i
$837$	24.6589	+	31.7710i	0.852337	+	1.09817i
$838$	−11.7500	−	20.3516i	−0.405896	−	0.703033i
$839$	−7.69610	+	4.44334i	−0.265699	+	0.153401i	−0.626931	−	0.779074i	$-0.715689\pi$
$839$	−7.69610	+	4.44334i	−0.265699	+	0.153401i	0.361233	+	0.932476i	$0.382356\pi$
$840$	0.488695	−	0.714518i	0.0168616	−	0.0246532i
$841$	7.34621	+	12.7240i	0.253318	+	0.438759i
$842$	−29.6137	−	17.0975i	−1.02056	−	0.589218i
$843$	6.04308	+	27.0229i	0.208135	+	0.930718i
$844$	13.8395			0.476376
$845$	−0.336738	+	2.43252i	−0.0115841	+	0.0836813i
$846$	−8.97558	−	0.751949i	−0.308587	−	0.0258525i
$847$	62.8217	+	19.1775i	2.15858	+	0.658945i
$848$	0.381800	+	0.220432i	0.0131111	+	0.00756968i
$849$	−13.7436	+	43.8709i	−0.471681	+	1.50565i
$850$	−21.4701			−0.736418
$851$	−1.71191	−	2.96512i	−0.0586835	−	0.101643i
$852$	−5.65570	−	1.77179i	−0.193761	−	0.0607004i
$853$	−19.7131			−0.674964			−0.337482	−	0.941332i	$-0.609575\pi$
$853$	−19.7131			−0.674964			−0.337482	+	0.941332i	$0.609575\pi$
$854$	−3.52631	−	3.77829i	−0.120668	−	0.129291i
$855$	−1.75211	+	2.52200i	−0.0599209	+	0.0862506i
$856$	−10.1467	−	5.85821i	−0.346807	−	0.200229i
$857$	−0.359437			−0.0122781			−0.00613906	−	0.999981i	$-0.501954\pi$
$857$	−0.359437			−0.0122781			−0.00613906	+	0.999981i	$0.501954\pi$
$858$	−29.1863	+	23.3533i	−0.996405	+	0.797267i
$859$			38.7509i			1.32216i	0.750314	+	0.661081i	$0.229902\pi$
$859$			38.7509i			1.32216i	−0.750314	+	0.661081i	$0.770098\pi$
$860$	−0.657540	−	0.379631i	−0.0224219	−	0.0129453i
$861$	−16.5606	−	34.5186i	−0.564385	−	1.17639i
$862$	−0.197300	−	0.341734i	−0.00672007	−	0.0116395i
$863$	16.1927			0.551207			0.275603	−	0.961271i	$-0.411122\pi$
$863$	16.1927			0.551207			0.275603	+	0.961271i	$0.411122\pi$
$864$	−1.96192	+	4.81154i	−0.0667459	+	0.163692i
$865$	−2.70556	+	1.56205i	−0.0919917	+	0.0531114i
$866$			23.5261i			0.799450i
$867$	2.81743	+	0.882628i	0.0956848	+	0.0299756i
$868$	19.5856	+	5.97885i	0.664778	+	0.202935i
$869$	38.5242	−	66.7258i	1.30684	−	2.26352i
$870$	−1.59182	+	1.46404i	−0.0539679	+	0.0496357i
$871$	−32.4758	−	21.8563i	−1.10040	−	0.740574i
$872$		−	2.68217i		−	0.0908296i
$873$	40.1985	+	27.9271i	1.36051	+	0.945190i
$874$	11.4914	+	6.63454i	0.388701	+	0.224417i
$875$	−3.39791	−	3.64072i	−0.114870	−	0.123079i
$876$	−9.74154	+	8.95955i	−0.329136	+	0.302715i
$877$	−42.5792	+	24.5831i	−1.43780	+	0.830114i	−0.997697	−	0.0678340i	$-0.978391\pi$
$877$	−42.5792	+	24.5831i	−1.43780	+	0.830114i	−0.440102	+	0.897948i	$0.645058\pi$
$878$	−4.95314	+	2.85970i	−0.167160	+	0.0965100i
$879$	−34.8401	−	37.8809i	−1.17513	−	1.27769i
$880$	0.979187	−	0.565334i	0.0330084	−	0.0190574i
$881$	−17.5774	+	30.4450i	−0.592199	+	1.02572i	0.401737	+	0.915755i	$0.368407\pi$
$881$	−17.5774	+	30.4450i	−0.592199	+	1.02572i	−0.993936	+	0.109963i	$0.964927\pi$
$882$	20.7561	+	3.19111i	0.698895	+	0.107450i
$883$	27.8767			0.938125			0.469062	−	0.883165i	$-0.344592\pi$
$883$	27.8767			0.938125			0.469062	+	0.883165i	$0.344592\pi$
$884$	8.70644	−	12.9367i	0.292829	−	0.435108i
$885$	−0.447713	+	0.411773i	−0.0150497	+	0.0138416i
$886$	2.14610	+	1.23905i	0.0720995	+	0.0416267i
$887$	−10.2666	+	17.7823i	−0.344719	+	0.597070i	−0.985303	−	0.170818i	$-0.945359\pi$
$887$	−10.2666	+	17.7823i	−0.344719	+	0.597070i	0.640584	+	0.767888i	$0.278692\pi$
$888$	−0.723994	+	2.31105i	−0.0242956	+	0.0775538i
$889$	2.25272	+	9.73879i	0.0755538	+	0.326629i
$890$	−1.34936	−	2.33716i	−0.0452307	−	0.0783418i
$891$	18.7969	+	50.4836i	0.629721	+	1.69126i
$892$	−24.0195			−0.804231
$893$	14.0896	−	8.13463i	0.471490	−	0.272215i
$894$	2.08849	+	9.33910i	0.0698495	+	0.312346i
$895$	1.31462	−	2.27699i	0.0439429	−	0.0761113i
$896$	0.596256	+	2.57769i	0.0199195	+	0.0861145i
$897$	5.56360	−	14.2440i	0.185763	−	0.475595i
$898$	−10.6876			−0.356649
$899$	−44.3066	−	25.5804i	−1.47771	−	0.853156i
$900$	12.2310	+	8.49724i	0.407699	+	0.283241i
$901$	−1.65124	+	0.953344i	−0.0550108	+	0.0317605i
$902$		−	50.0065i		−	1.66503i
$903$	1.40354	−	18.3655i	0.0467067	−	0.611164i
$904$	2.91954	−	1.68560i	0.0971023	−	0.0560621i
$905$	−3.69070			−0.122683
$906$	6.87013	−	21.9301i	0.228245	−	0.728578i
$907$	9.72098	−	16.8372i	0.322780	−	0.559071i	−0.658281	−	0.752772i	$-0.728716\pi$
$907$	9.72098	−	16.8372i	0.322780	−	0.559071i	0.981060	+	0.193702i	$0.0620494\pi$
$908$	13.1216	+	7.57576i	0.435456	+	0.251410i
$909$	1.29102	−	15.4102i	0.0428206	−	0.511125i
$910$	1.77941	−	0.284490i	0.0589867	−	0.00943074i
$911$		−	38.8818i		−	1.28821i	−0.764936	−	0.644106i	$-0.777229\pi$
$911$		−	38.8818i		−	1.28821i	0.764936	−	0.644106i	$-0.222771\pi$
$912$	−2.04832	−	9.15950i	−0.0678268	−	0.303301i
$913$	−83.8325	−	48.4007i	−2.77445	−	1.60183i
$914$	6.26295	−	3.61591i	0.207160	−	0.119604i
$915$	−0.470417	+	0.432655i	−0.0155515	+	0.0143031i
$916$	7.05590	+	12.2212i	0.233133	+	0.403799i
$917$	21.8706	−	20.4120i	0.722232	−	0.674064i
$918$	−13.7789	−	17.7529i	−0.454770	−	0.585934i
$919$	15.9286	+	27.5891i	0.525435	+	0.910080i	0.999561	+	0.0296229i	$0.00943065\pi$
$919$	15.9286	+	27.5891i	0.525435	+	0.910080i	−0.474126	+	0.880457i	$0.657236\pi$
$920$	−0.231280	+	0.400589i	−0.00762508	+	0.0132070i
$921$	0.0666823	+	0.298184i	0.00219726	+	0.00982548i
$922$		−	25.6876i		−	0.845975i
$923$	−5.41986	−	11.0833i	−0.178397	−	0.364810i
$924$	22.6401	+	15.4847i	0.744804	+	0.509409i
$925$	6.01130	+	3.47062i	0.197650	+	0.114113i
$926$	15.4694	+	8.93125i	0.508355	+	0.293499i
$927$	−0.628172	−	1.33426i	−0.0206319	−	0.0438229i
$928$		−	6.61002i		−	0.216985i
$929$	−2.19851	+	1.26931i	−0.0721307	+	0.0416447i	−0.535632	−	0.844452i	$-0.679926\pi$
$929$	−2.19851	+	1.26931i	−0.0721307	+	0.0416447i	0.463501	+	0.886096i	$0.346593\pi$
$930$	0.757054	−	2.41658i	0.0248248	−	0.0792429i
$931$	−34.0790	+	16.6572i	−1.11689	+	0.545916i
$932$	−22.0487	+	12.7298i	−0.722230	+	0.416979i
$933$	4.35269	+	19.4639i	0.142501	+	0.637221i
$934$	−6.84064	+	11.8483i	−0.223833	+	0.387690i
$935$			4.89000i			0.159920i
$936$	−10.0798	+	3.92395i	−0.329469	+	0.128258i
$937$		−	8.65434i		−	0.282725i	−0.989958	−	0.141362i	$-0.954852\pi$
$937$		−	8.65434i		−	0.282725i	0.989958	−	0.141362i	$-0.0451483\pi$
$938$	−8.38675	+	27.4734i	−0.273837	+	0.897038i
$939$	−16.0956	+	3.59942i	−0.525259	+	0.117463i
$940$	0.283573	+	0.491163i	0.00924914	+	0.0160200i
$941$		−	31.5060i		−	1.02707i	−0.858070	−	0.513533i	$-0.828337\pi$
$941$		−	31.5060i		−	1.02707i	0.858070	−	0.513533i	$-0.171663\pi$
$942$	−8.31386	+	26.5386i	−0.270880	+	0.864674i
$943$	10.2289	+	17.7170i	0.333099	+	0.576945i
$944$		−	1.85912i		−	0.0605092i
$945$	0.413376	−	2.56385i	0.0134471	−	0.0834022i
$946$	12.0289	−	20.8347i	0.391094	−	0.677394i
$947$	−22.7880	+	39.4700i	−0.740510	+	1.28260i	0.211753	+	0.977323i	$0.432083\pi$
$947$	−22.7880	+	39.4700i	−0.740510	+	1.28260i	−0.952263	+	0.305278i	$0.901250\pi$
$948$	16.4105	−	15.0931i	0.532987	−	0.490202i
$949$	−27.4862	−	1.89345i	−0.892239	−	0.0614641i
$950$	−26.9009			−0.872782
$951$	7.93096	+	35.4649i	0.257179	+	1.15003i
$952$	−10.9440	−	3.34085i	−0.354697	−	0.108278i
$953$	18.5089	−	10.6861i	0.599562	−	0.346157i	−0.169307	−	0.985563i	$-0.554153\pi$
$953$	18.5089	−	10.6861i	0.599562	−	0.346157i	0.768869	+	0.639406i	$0.220820\pi$
$954$	1.31798	+	0.110416i	0.0426711	+	0.00357486i
$955$	0.801100	+	1.38755i	0.0259230	+	0.0449000i
$956$	−6.60702	−	11.4437i	−0.213686	−	0.370116i
$957$	−46.3894	−	50.4382i	−1.49955	−	1.63044i
$958$	−2.54639	+	1.47016i	−0.0822702	+	0.0474987i
$959$	−16.8729	−	5.15076i	−0.544855	−	0.166327i
$960$	0.319300	−	0.0714045i	0.0103054	−	0.00230457i
$961$	28.9059			0.932450
$962$	−4.52888	+	2.21468i	−0.146017	+	0.0714042i
$963$	−35.0265	−	2.93443i	−1.12871	−	0.0945605i
$964$	2.98003	−	5.16157i	0.0959804	−	0.166243i
$965$	−0.102696	+	0.177875i	−0.00330590	+	0.00572598i
$966$	−11.1887	−	0.855066i	−0.359989	−	0.0275113i
$967$		−	42.7297i		−	1.37409i	−0.726613	−	0.687047i	$-0.758907\pi$
$967$		−	42.7297i		−	1.37409i	0.726613	−	0.687047i	$-0.241093\pi$
$968$	12.4130	+	21.5000i	0.398971	+	0.691037i
$969$	38.7359	+	12.1350i	1.24438	+	0.389832i
$970$		−	3.08207i		−	0.0989594i
$971$	−26.7342	−	46.3050i	−0.857942	−	1.48600i	−0.873888	−	0.486127i	$-0.838409\pi$
$971$	−26.7342	−	46.3050i	−0.857942	−	1.48600i	0.0159459	−	0.999873i	$-0.494924\pi$
$972$	0.823378	+	15.5667i	0.0264099	+	0.499302i
$973$	0.904083	−	2.96161i	0.0289836	−	0.0949447i
$974$		−	42.4455i		−	1.36004i
$975$	4.67059	+	30.6483i	0.149579	+	0.981531i
$976$		−	1.95340i		−	0.0625267i
$977$	−11.3661	+	19.6866i	−0.363633	+	0.629831i	−0.988556	−	0.150856i	$-0.951797\pi$
$977$	−11.3661	+	19.6866i	−0.363633	+	0.629831i	0.624923	+	0.780687i	$0.285130\pi$
$978$	6.37020	−	1.42456i	0.203697	−	0.0455523i
$979$	74.0548	−	42.7556i	2.36680	−	1.36647i
$980$	−0.580668	−	1.18799i	−0.0185488	−	0.0379490i
$981$	−3.42744	−	7.28003i	−0.109430	−	0.232433i
$982$	−25.7266	+	14.8533i	−0.820968	+	0.473986i
$983$			0.816341i			0.0260372i	0.999915	+	0.0130186i	$0.00414407\pi$
$983$			0.816341i			0.0260372i	−0.999915	+	0.0130186i	$0.995856\pi$
$984$	4.32597	−	13.8089i	0.137907	−	0.440210i
$985$	−1.79428	−	1.03593i	−0.0571707	−	0.0330075i
$986$	24.7576	+	14.2938i	0.788441	+	0.455207i
$987$	−7.76717	+	11.3563i	−0.247232	+	0.361476i
$988$	10.9087	−	16.2090i	0.347053	−	0.515677i
$989$			9.84214i			0.312962i
$990$	1.93532	−	2.78572i	0.0615086	−	0.0885359i
$991$	−6.09810	+	10.5622i	−0.193713	+	0.335520i	−0.946478	−	0.322769i	$-0.895386\pi$
$991$	−6.09810	+	10.5622i	−0.193713	+	0.335520i	0.752765	+	0.658289i	$0.228720\pi$
$992$	3.86995	+	6.70294i	0.122871	+	0.212819i
$993$	−5.97118	−	6.49235i	−0.189490	−	0.206029i
$994$	−6.61850	+	6.17710i	−0.209926	+	0.195926i
$995$	−0.716427	−	1.24089i	−0.0227123	−	0.0393388i
$996$	−18.9626	−	20.6176i	−0.600852	−	0.653295i
$997$	21.8790	−	12.6319i	0.692915	−	0.400055i	−0.111788	−	0.993732i	$-0.535658\pi$
$997$	21.8790	−	12.6319i	0.692915	−	0.400055i	0.804703	+	0.593677i	$0.202324\pi$
$998$	−17.6149	−	10.1700i	−0.557591	−	0.321926i
$999$	0.988121	+	7.19790i	0.0312628	+	0.227731i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.251.6	yes	24
3.2	odd	2		546.2.q.i.251.2	✓	24
7.6	odd	2	inner	546.2.q.j.251.7	yes	24
13.10	even	6		546.2.q.i.335.11	yes	24
21.20	even	2		546.2.q.i.251.11	yes	24
39.23	odd	6	inner	546.2.q.j.335.7	yes	24
91.62	odd	6		546.2.q.i.335.2	yes	24
273.62	even	6	inner	546.2.q.j.335.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.2	✓	24	3.2	odd	2
546.2.q.i.251.11	yes	24	21.20	even	2
546.2.q.i.335.2	yes	24	91.62	odd	6
546.2.q.i.335.11	yes	24	13.10	even	6
546.2.q.j.251.6	yes	24	1.1	even	1	trivial
546.2.q.j.251.7	yes	24	7.6	odd	2	inner
546.2.q.j.335.6	yes	24	273.62	even	6	inner
546.2.q.j.335.7	yes	24	39.23	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.377999 - 1.69030i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-1.65284 - 0.517794i) q^{6} +(-1.93422 + 1.80522i) q^{7} -1.00000 q^{8} +(-2.71423 + 1.27786i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.377999 - 1.69030i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-1.65284 - 0.517794i) q^{6} +(-1.93422 + 1.80522i) q^{7} -1.00000 q^{8} +(-2.71423 + 1.27786i) q^{9} +(0.163593 + 0.0944507i) q^{10} +(-2.99275 + 5.18359i) q^{11} +(-1.27484 + 1.17251i) q^{12} +(-3.59703 - 0.247790i) q^{13} +(0.596256 + 2.57769i) q^{14} +(0.319300 - 0.0714045i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.16244 - 3.74546i) q^{17} +(-0.250454 + 2.98953i) q^{18} +(-2.70943 - 4.69287i) q^{19} +(0.163593 - 0.0944507i) q^{20} +(3.78249 + 2.58704i) q^{21} +(2.99275 + 5.18359i) q^{22} +(-2.12062 - 1.22434i) q^{23} +(0.377999 + 1.69030i) q^{24} +4.96432 q^{25} +(-2.01311 + 2.99122i) q^{26} +(3.18595 + 4.10484i) q^{27} +(2.53047 + 0.772472i) q^{28} +(-5.72445 - 3.30501i) q^{29} +(0.0978120 - 0.312224i) q^{30} +7.73989 q^{31} +(0.500000 + 0.866025i) q^{32} +(9.89308 + 3.09925i) q^{33} -4.32488 q^{34} +(-0.341008 - 0.365376i) q^{35} +(2.46378 + 1.71166i) q^{36} +(1.21090 + 0.699114i) q^{37} -5.41886 q^{38} +(0.940833 + 6.17372i) q^{39} -0.188901i q^{40} +(-7.23531 - 4.17731i) q^{41} +(4.13169 - 1.98222i) q^{42} +(-2.00968 - 3.48087i) q^{43} +5.98549 q^{44} +(-0.241390 - 0.512723i) q^{45} +(-2.12062 + 1.22434i) q^{46} +3.00234i q^{47} +(1.65284 + 0.517794i) q^{48} +(0.482384 - 6.98336i) q^{49} +(2.48216 - 4.29922i) q^{50} +(-5.51355 + 5.07095i) q^{51} +(1.58392 + 3.23901i) q^{52} -0.440865i q^{53} +(5.14787 - 0.706695i) q^{54} +(-0.979187 - 0.565334i) q^{55} +(1.93422 - 1.80522i) q^{56} +(-6.90820 + 6.35365i) q^{57} +(-5.72445 + 3.30501i) q^{58} +(-1.61004 + 0.929559i) q^{59} +(-0.221488 - 0.240820i) q^{60} +(-1.69169 + 0.976699i) q^{61} +(3.86995 - 6.70294i) q^{62} +(2.94309 - 7.37145i) q^{63} +1.00000 q^{64} +(0.0468079 - 0.679483i) q^{65} +(7.63057 - 7.01803i) q^{66} +(9.40246 + 5.42851i) q^{67} +(-2.16244 + 3.74546i) q^{68} +(-1.26791 + 4.04729i) q^{69} +(-0.486929 + 0.112634i) q^{70} +(1.71090 + 2.96337i) q^{71} +(2.71423 - 1.27786i) q^{72} +7.64136 q^{73} +(1.21090 - 0.699114i) q^{74} +(-1.87651 - 8.39119i) q^{75} +(-2.70943 + 4.69287i) q^{76} +(-3.56888 - 15.4287i) q^{77} +(5.81702 + 2.27208i) q^{78} -12.8725 q^{79} +(-0.163593 - 0.0944507i) q^{80} +(5.73413 - 6.93684i) q^{81} +(-7.23531 + 4.17731i) q^{82} +16.1727i q^{83} +(0.349194 - 4.56925i) q^{84} +(0.707522 - 0.408488i) q^{85} -4.01936 q^{86} +(-3.42263 + 10.9253i) q^{87} +(2.99275 - 5.18359i) q^{88} +(-12.3724 - 7.14320i) q^{89} +(-0.564726 - 0.0473112i) q^{90} +(7.40474 - 6.01413i) q^{91} +2.44869i q^{92} +(-2.92567 - 13.0827i) q^{93} +(2.60010 + 1.50117i) q^{94} +(0.886490 - 0.511815i) q^{95} +(1.27484 - 1.17251i) q^{96} +(-8.15789 - 14.1299i) q^{97} +(-5.80657 - 3.90944i) q^{98} +(1.49909 - 17.8938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

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