LMFDB - Embedded newform 546.2.q.i.251.11

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			251.11
Character	$\chi$	$=$	546.251
Dual form			546.2.q.i.335.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.65284 - 0.517794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-0.377999 + 1.69030i) q^{6} +(-2.53047 + 0.772472i) q^{7} +1.00000 q^{8} +(2.46378 - 1.71166i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.65284 - 0.517794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-0.377999 + 1.69030i) q^{6} +(-2.53047 + 0.772472i) q^{7} +1.00000 q^{8} +(2.46378 - 1.71166i) 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} +(0.0978120 + 0.312224i) 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} +(1.65284 - 0.517794i) q^{24} +4.96432 q^{25} +(-2.01311 + 2.99122i) q^{26} +(3.18595 - 4.10484i) q^{27} +(1.93422 + 1.80522i) q^{28} +(5.72445 + 3.30501i) q^{29} +(-0.319300 - 0.0714045i) q^{30} -7.73989 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.26251 - 10.1173i) q^{33} +4.32488 q^{34} +(-0.145921 - 0.478010i) q^{35} +(-2.71423 - 1.27786i) q^{36} +(1.21090 + 0.699114i) q^{37} -5.41886 q^{38} +(6.07362 - 1.45296i) q^{39} +0.188901i q^{40} +(-7.23531 - 4.17731i) q^{41} +(-0.349194 - 4.56925i) q^{42} +(-2.00968 - 3.48087i) q^{43} -5.98549 q^{44} +(0.323336 + 0.465411i) q^{45} +(-2.12062 + 1.22434i) q^{46} +3.00234i q^{47} +(-0.377999 + 1.69030i) q^{48} +(5.80657 - 3.90944i) q^{49} +(-2.48216 + 4.29922i) q^{50} +(-5.51355 - 5.07095i) q^{51} +(-1.58392 - 3.23901i) q^{52} +0.440865i q^{53} +(1.96192 + 4.81154i) q^{54} +(0.979187 + 0.565334i) q^{55} +(-2.53047 + 0.772472i) 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} +(-4.91231 + 6.23452i) 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} +(4.13902 + 0.925601i) q^{69} +(0.486929 + 0.112634i) q^{70} +(-1.71090 - 2.96337i) q^{71} +(2.46378 - 1.71166i) q^{72} -7.64136 q^{73} +(-1.21090 + 0.699114i) q^{74} +(8.20523 - 2.57049i) q^{75} +(2.70943 - 4.69287i) q^{76} +(-3.56888 + 15.4287i) q^{77} +(-1.77851 + 5.98639i) q^{78} -12.8725 q^{79} +(-0.163593 - 0.0944507i) q^{80} +(3.14042 - 8.43432i) q^{81} +(7.23531 - 4.17731i) q^{82} +16.1727i q^{83} +(4.13169 + 1.98222i) q^{84} +(0.707522 - 0.408488i) q^{85} +4.01936 q^{86} +(11.1729 + 2.49858i) q^{87} +(2.99275 - 5.18359i) q^{88} +(-12.3724 - 7.14320i) q^{89} +(-0.564726 + 0.0473112i) q^{90} +(-9.29358 + 2.15158i) q^{91} -2.44869i q^{92} +(-12.7928 + 4.00767i) 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} +(0.482384 + 6.98336i) 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} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 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 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * 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
$3$	1.65284	−	0.517794i	0.954269	−	0.298948i
$3$	1.65284	−	0.517794i	0.954269	−	0.298948i
$4$	−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	$0.986551\pi$
$6$	−0.377999	+	1.69030i	−0.154317	+	0.690062i
$7$	−2.53047	+	0.772472i	−0.956428	+	0.291967i
$7$	−2.53047	+	0.772472i	−0.956428	+	0.291967i
$8$	1.00000			0.353553
$9$	2.46378	−	1.71166i	0.821260	−	0.570554i
$10$	−0.163593	−	0.0944507i	−0.0517328	−	0.0298679i
$11$	2.99275	−	5.18359i	0.902347	−	1.56291i	0.0779069	−	0.996961i	$-0.475176\pi$
$11$	2.99275	−	5.18359i	0.902347	−	1.56291i	0.824440	−	0.565950i	$-0.191490\pi$
$12$	−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
$15$	0.0978120	+	0.312224i	0.0252549	+	0.0806160i
$16$	−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	$0.0468447\pi$
$19$	2.70943	+	4.69287i	0.621586	+	1.07662i	−0.367605	+	0.929982i	$0.619822\pi$
$20$	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	0.704522	−	0.709682i	$-0.251161\pi$
$23$	2.12062	+	1.22434i	0.442181	+	0.255293i	−0.262342	+	0.964975i	$0.584495\pi$
$24$	1.65284	−	0.517794i	0.337385	−	0.105694i
$25$	4.96432			0.992863
$26$	−2.01311	+	2.99122i	−0.394802	+	0.586627i
$27$	3.18595	−	4.10484i	0.613137	−	0.789977i
$28$	1.93422	+	1.80522i	0.365532	+	0.341154i
$29$	5.72445	+	3.30501i	1.06300	+	0.613725i	0.926262	−	0.376881i	$-0.123004\pi$
$29$	5.72445	+	3.30501i	1.06300	+	0.613725i	0.136742	+	0.990607i	$0.456337\pi$
$30$	−0.319300	−	0.0714045i	−0.0582960	−	0.0130366i
$31$	−7.73989			−1.39013			−0.695063	−	0.718949i	$-0.744624\pi$
$31$	−7.73989			−1.39013			−0.695063	+	0.718949i	$0.744624\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.26251	−	10.1173i	0.393852	−	1.76119i
$34$	4.32488			0.741711
$35$	−0.145921	−	0.478010i	−0.0246652	−	0.0807984i
$36$	−2.71423	−	1.27786i	−0.452372	−	0.212977i
$37$	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
$39$	6.07362	−	1.45296i	0.972558	−	0.232660i
$40$			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	$0.892898\pi$
$42$	−0.349194	−	4.56925i	−0.0538818	−	0.705051i
$43$	−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
$45$	0.323336	+	0.465411i	0.0482000	+	0.0693794i
$46$	−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	$0.929731\pi$
$48$	−0.377999	+	1.69030i	−0.0545594	+	0.243974i
$49$	5.80657	−	3.90944i	0.829511	−	0.558491i
$50$	−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	$0.00963949\pi$
$53$			0.440865i			0.0605574i	−0.999541	+	0.0302787i	$0.990361\pi$
$54$	1.96192	+	4.81154i	0.266983	+	0.654767i
$55$	0.979187	+	0.565334i	0.132034	+	0.0762296i
$56$	−2.53047	+	0.772472i	−0.338149	+	0.103226i
$57$	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	−0.387776	−	0.921754i	$-0.626756\pi$
$61$	1.69169	−	0.976699i	0.216599	−	0.125053i	0.604374	+	0.796700i	$0.293423\pi$
$62$	3.86995	−	6.70294i	0.491484	−	0.851275i
$63$	−4.91231	+	6.23452i	−0.618893	+	0.785475i
$64$	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
$69$	4.13902	+	0.925601i	0.498279	+	0.111429i
$70$	0.486929	+	0.112634i	0.0581992	+	0.0134623i
$71$	−1.71090	−	2.96337i	−0.203047	−	0.351687i	0.746462	−	0.665428i	$-0.231751\pi$
$71$	−1.71090	−	2.96337i	−0.203047	−	0.351687i	−0.949509	+	0.313741i	$0.898418\pi$
$72$	2.46378	−	1.71166i	0.290359	−	0.201721i
$73$	−7.64136			−0.894354			−0.447177	−	0.894446i	$-0.647571\pi$
$73$	−7.64136			−0.894354			−0.447177	+	0.894446i	$0.647571\pi$
$74$	−1.21090	+	0.699114i	−0.140764	+	0.0812704i
$75$	8.20523	−	2.57049i	0.947459	−	0.296815i
$76$	2.70943	−	4.69287i	0.310793	−	0.538309i
$77$	−3.56888	+	15.4287i	−0.406712	+	1.75827i
$78$	−1.77851	+	5.98639i	−0.201377	+	0.677825i
$79$	−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
$81$	3.14042	−	8.43432i	0.348935	−	0.937147i
$82$	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	$0.652377\pi$
$84$	4.13169	+	1.98222i	0.450804	+	0.216277i
$85$	0.707522	−	0.408488i	0.0767415	−	0.0443067i
$86$	4.01936			0.433418
$87$	11.1729	+	2.49858i	1.19786	+	0.267876i
$88$	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
$91$	−9.29358	+	2.15158i	−0.974232	+	0.225546i
$92$		−	2.44869i		−	0.255293i
$93$	−12.7928	+	4.00767i	−1.32655	+	0.415576i
$94$	−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	$0.144030\pi$
$97$	8.15789	+	14.1299i	0.828308	+	1.43467i	−0.0710561	+	0.997472i	$0.522637\pi$
$98$	0.482384	+	6.98336i	0.0487281	+	0.705426i
$99$	−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	$0.249222\pi$
$102$	7.14835	−	2.23940i	0.707792	−	0.221733i
$103$		−	0.491580i		−	0.0484368i	−0.999707	−	0.0242184i	$-0.992290\pi$
$103$		−	0.491580i		−	0.0484368i	0.999707	−	0.0242184i	$-0.00770971\pi$
$104$	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	−0.0783719	−	0.996924i	$-0.524972\pi$
$107$	−10.1467	−	5.85821i	−0.980920	−	0.566334i	−0.902548	+	0.430590i	$0.858306\pi$
$108$	−5.14787	−	0.706695i	−0.495354	−	0.0680018i
$109$			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
$111$	2.36343	+	0.528529i	0.224326	+	0.0501657i
$112$	0.596256	−	2.57769i	0.0563409	−	0.243569i
$113$	2.91954	−	1.68560i	0.274647	−	0.158567i	−0.356351	−	0.934352i	$-0.615979\pi$
$113$	2.91954	−	1.68560i	0.274647	−	0.158567i	0.630998	+	0.775785i	$0.282646\pi$
$114$	−8.95652	+	2.80585i	−0.838855	+	0.262792i
$115$	−0.231280	+	0.400589i	−0.0215670	+	0.0373551i
$116$		−	6.61002i		−	0.613725i
$117$	9.28641	−	5.54640i	0.858529	−	0.512765i
$118$		−	1.85912i		−	0.171146i
$119$	8.36525	+	7.80735i	0.766842	+	0.715698i
$120$	0.0978120	+	0.312224i	0.00892897	+	0.0285021i
$121$	−12.4130	−	21.5000i	−1.12846	−	1.95455i
$122$			1.95340i			0.176852i
$123$	−14.1218	−	3.15803i	−1.27332	−	0.284750i
$124$	3.86995	+	6.70294i	0.347531	+	0.601942i
$125$			1.88227i			0.168356i
$126$	−2.94309	−	7.37145i	−0.262192	−	0.656701i
$127$	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	$0.664451\pi$
$132$	−9.89308	+	3.09925i	−0.861082	+	0.269755i
$133$	−10.4812	−	9.78222i	−0.908839	−	0.848226i
$134$	−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	0.687732	−	0.725965i	$-0.258607\pi$
$137$	−3.33395	−	5.77457i	−0.284839	−	0.493355i	−0.972570	+	0.232610i	$0.925273\pi$
$138$	−2.87110	+	3.12169i	−0.244404	+	0.265736i
$139$	1.01358	−	0.585188i	0.0859704	−	0.0496350i	−0.456399	−	0.889775i	$-0.650861\pi$
$139$	1.01358	−	0.585188i	0.0859704	−	0.0496350i	0.542369	+	0.840140i	$0.317528\pi$
$140$	−0.341008	+	0.365376i	−0.0288204	+	0.0308799i
$141$	1.55459	+	4.96240i	0.130920	+	0.417909i
$142$	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
$147$	7.57307	−	9.46829i	0.624617	−	0.780932i
$148$		−	1.39823i		−	0.114934i
$149$	2.76256	+	4.78489i	0.226317	+	0.391993i	0.956714	−	0.291030i	$-0.0939980\pi$
$149$	2.76256	+	4.78489i	0.226317	+	0.391993i	−0.730396	+	0.683023i	$0.760665\pi$
$150$	−1.87651	+	8.39119i	−0.153216	+	0.685138i
$151$			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
$153$	−11.7387	−	5.52661i	−0.949021	−	0.446800i
$154$	−11.5772	−	10.8051i	−0.932920	−	0.870701i
$155$		−	1.46208i		−	0.117437i
$156$	−4.29511	−	4.53343i	−0.343884	−	0.362965i
$157$			16.0563i			1.28143i	0.767777	+	0.640717i	$0.221363\pi$
$157$			16.0563i			1.28143i	−0.767777	+	0.640717i	$0.778637\pi$
$158$	6.43626	−	11.1479i	0.512041	−	0.886881i
$159$	0.228277	+	0.728680i	0.0181035	+	0.0577881i
$160$	0.163593	−	0.0944507i	0.0129332	−	0.00746698i
$161$	−6.31195	−	1.46004i	−0.497451	−	0.115067i
$162$	5.73413	+	6.93684i	0.450516	+	0.545010i
$163$	−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
$165$	1.91117	+	0.427391i	0.148784	+	0.0332724i
$166$	−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
$171$	14.7081	+	6.92457i	1.12475	+	0.529535i
$172$	−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
$175$	−12.5621	+	3.83479i	−0.949603	+	0.289883i
$176$	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	0.877507	−	0.479564i	$-0.159205\pi$
$179$	12.0538	+	6.95929i	0.900946	+	0.520162i	0.0234391	+	0.999725i	$0.492538\pi$
$180$	0.241390	−	0.512723i	0.0179922	−	0.0382161i
$181$		−	19.5377i		−	1.45222i	−0.687576	−	0.726112i	$-0.741325\pi$
$181$		−	19.5377i		−	1.45222i	0.687576	−	0.726112i	$-0.258675\pi$
$182$	2.78347	−	9.12427i	0.206325	−	0.676336i
$183$	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
$186$	2.92567	−	13.0827i	0.214521	−	0.959274i
$187$	−25.8865			−1.89301
$188$	2.60010	−	1.50117i	0.189632	−	0.109484i
$189$	−4.89109	+	12.8482i	−0.355774	+	0.934572i
$190$		−	1.02363i		−	0.0742620i
$191$	−7.34535	+	4.24084i	−0.531491	+	0.306856i	−0.741623	−	0.670817i	$-0.765944\pi$
$191$	−7.34535	+	4.24084i	−0.531491	+	0.306856i	0.210133	+	0.977673i	$0.432610\pi$
$192$	1.65284	−	0.517794i	0.119284	−	0.0373685i
$193$	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
$195$	0.274466	+	1.14732i	0.0196549	+	0.0821610i
$196$	−6.28896	−	3.07392i	−0.449211	−	0.219566i
$197$	5.48398	−	9.49852i	0.390717	−	0.676742i	−0.601827	−	0.798626i	$-0.705560\pi$
$197$	5.48398	−	9.49852i	0.390717	−	0.676742i	0.992544	+	0.121885i	$0.0388938\pi$
$198$	16.2460	+	7.64864i	1.15455	+	0.543565i
$199$	6.56897	−	3.79260i	0.465662	−	0.268850i	−0.248760	−	0.968565i	$-0.580023\pi$
$199$	6.56897	−	3.79260i	0.465662	−	0.268850i	0.714422	+	0.699715i	$0.246690\pi$
$200$	4.96432			0.351030
$201$	18.3516	+	4.10395i	1.29443	+	0.289470i
$202$	−2.57737	−	4.46413i	−0.181343	−	0.314095i
$203$	−17.0386	−	3.94126i	−1.19587	−	0.276623i
$204$	−1.63480	+	7.31035i	−0.114459	+	0.511827i
$205$	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
$210$	0.863138	−	0.0659632i	0.0595622	−	0.00455190i
$211$	−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
$217$	19.5856	−	5.97885i	1.32956	−	0.405871i
$218$	−2.32283	−	1.34108i	−0.157322	−	0.0908296i
$219$	−12.6300	+	3.95665i	−0.853454	+	0.267366i
$220$		−	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	$0.464089\pi$
$223$	−12.0097	+	20.8015i	−0.804231	+	1.39297i	−0.916809	+	0.399326i	$0.869244\pi$
$224$	1.93422	+	1.80522i	0.129235	+	0.120616i
$225$	12.2310	−	8.49724i	0.815399	−	0.566483i
$226$			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	$0.501038\pi$
$228$	2.04832	−	9.15950i	0.135654	−	0.606603i
$229$	14.1118			0.932534			0.466267	−	0.884644i	$-0.345599\pi$
$229$	14.1118			0.932534			0.466267	+	0.884644i	$0.345599\pi$
$230$	−0.231280	−	0.400589i	−0.0152502	−	0.0264140i
$231$	2.09010	+	27.3492i	0.137518	+	1.79945i
$232$	5.72445	+	3.30501i	0.375829	+	0.216985i
$233$			25.4597i			1.66792i	0.551827	+	0.833959i	$0.313931\pi$
$233$			25.4597i			1.66792i	−0.551827	+	0.833959i	$0.686069\pi$
$234$	0.160116	+	10.8155i	0.0104671	+	0.707029i
$235$	−0.567146			−0.0369966
$236$	1.61004	+	0.929559i	0.104805	+	0.0605092i
$237$	−21.2762	+	6.66531i	−1.38204	+	0.432958i
$238$	−10.9440	+	3.34085i	−0.709393	+	0.216555i
$239$	−13.2140			−0.854746			−0.427373	−	0.904075i	$-0.640561\pi$
$239$	−13.2140			−0.854746			−0.427373	+	0.904075i	$0.640561\pi$
$240$	−0.319300	−	0.0714045i	−0.0206107	−	0.00460914i
$241$	−2.98003	−	5.16157i	−0.191961	−	0.332486i	0.753939	−	0.656944i	$-0.228151\pi$
$241$	−2.98003	−	5.16157i	−0.191961	−	0.332486i	−0.945900	+	0.324458i	$0.894818\pi$
$242$	24.8261			1.59588
$243$	0.823378	−	15.5667i	0.0528197	−	0.998604i
$244$	−1.69169	−	0.976699i	−0.108299	−	0.0625267i
$245$	0.738498	+	1.09687i	0.0471809	+	0.0700765i
$246$	9.79584	−	10.6508i	0.624560	−	0.679072i
$247$	8.58305	+	17.5517i	0.546126	+	1.11679i
$248$	−7.73989			−0.491484
$249$	8.37411	+	26.7309i	0.530688	+	1.69400i
$250$	−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	$0.0578672\pi$
$258$	6.64337	−	2.08120i	0.413598	−	0.129570i
$259$	−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	0.188422	−	0.982088i	$-0.439663\pi$
$263$	−9.20947	−	5.31709i	−0.567880	−	0.327866i	−0.756302	+	0.654222i	$0.772996\pi$
$264$	2.26251	−	10.1173i	0.139248	−	0.622676i
$265$	−0.0832800			−0.00511585
$266$	13.7123	−	4.18592i	0.840753	−	0.256655i
$267$	−24.1483	−	5.40024i	−1.47785	−	0.330490i
$268$		−	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	$0.785061\pi$
$270$	−0.908906	+	0.370609i	−0.0553142	+	0.0225546i
$271$	9.08097	−	15.7287i	0.551629	−	0.955450i	−0.446528	−	0.894770i	$-0.647340\pi$
$271$	9.08097	−	15.7287i	0.551629	−	0.955450i	0.998157	−	0.0606805i	$-0.0193271\pi$
$272$	4.32488			0.262234
$273$	−14.2468	+	8.36838i	−0.862253	+	0.506477i
$274$	6.66790			0.402822
$275$	14.8569	−	25.7330i	0.895907	−	1.55176i
$276$	−1.26791	−	4.04729i	−0.0763195	−	0.243618i
$277$	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
$279$	−19.0694	+	13.2481i	−1.14165	+	0.793142i
$280$	−0.145921	−	0.478010i	−0.00872045	−	0.0285665i
$281$	15.9870			0.953706			0.476853	−	0.878983i	$-0.341777\pi$
$281$	15.9870			0.953706			0.476853	+	0.878983i	$0.341777\pi$
$282$	−5.07486	−	1.13488i	−0.302203	−	0.0675812i
$283$	22.9867	+	13.2714i	1.36641	+	0.788900i	0.990468	−	0.137741i	$-0.0439842\pi$
$283$	22.9867	+	13.2714i	1.36641	+	0.788900i	0.375947	+	0.926641i	$0.377318\pi$
$284$	−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
$288$	−2.71423	−	1.27786i	−0.159938	−	0.0752988i
$289$	−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
$297$	−11.7431	−	28.7994i	−0.681401	−	1.67111i
$298$	−5.52511			−0.320061
$299$	7.32456	+	4.92946i	0.423590	+	0.285078i
$300$	−6.32873	−	5.82070i	−0.365389	−	0.336058i
$301$	7.77431	+	7.25581i	0.448104	+	0.418218i
$302$	−11.4905	−	6.63404i	−0.661204	−	0.381746i
$303$	−1.94848	+	8.71305i	−0.111937	+	0.500552i
$304$	−5.41886			−0.310793
$305$	0.184500	+	0.319563i	0.0105644	+	0.0182981i
$306$	10.6556	−	7.40274i	0.609137	−	0.423186i
$307$	0.176409			0.0100682			0.00503408	−	0.999987i	$-0.498398\pi$
$307$	0.176409			0.0100682			0.00503408	+	0.999987i	$0.498398\pi$
$308$	15.1461	−	4.62362i	0.863030	−	0.263455i
$309$	−0.254537	−	0.812504i	−0.0144801	−	0.0462218i
$310$	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	$0.605863\pi$
$312$	6.07362	−	1.45296i	0.343851	−	0.0822577i
$313$			9.52231i			0.538233i	0.963108	+	0.269116i	$0.0867316\pi$
$313$			9.52231i			0.538233i	−0.963108	+	0.269116i	$0.913268\pi$
$314$	−13.9052	−	8.02816i	−0.784715	−	0.453055i
$315$	−1.17771	−	0.927943i	−0.0663564	−	0.0522837i
$316$	6.43626	+	11.1479i	0.362068	+	0.627120i
$317$	20.9814			1.17843			0.589217	−	0.807975i	$-0.299436\pi$
$317$	20.9814			1.17843			0.589217	+	0.807975i	$0.299436\pi$
$318$	−0.745194	−	0.166646i	−0.0417884	−	0.00934507i
$319$	34.2636	−	19.7821i	1.91840	−	1.10759i
$320$			0.188901i			0.0105599i
$321$	−19.8043	−	4.42879i	−1.10537	−	0.247191i
$322$	4.42041	−	4.73629i	0.246340	−	0.263943i
$323$	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
$327$	1.38881	+	4.43320i	0.0768013	+	0.245157i
$328$	−7.23531	−	4.17731i	−0.399503	−	0.230653i
$329$	−2.31922	−	7.59734i	−0.127863	−	0.418855i
$330$	−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
$336$	−0.349194	−	4.56925i	−0.0190501	−	0.249273i
$337$	−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
$342$	−13.3509	+	9.27526i	−0.721933	+	0.501549i
$343$	−11.6734	+	14.3781i	−0.630307	+	0.776346i
$344$	−2.00968	−	3.48087i	−0.108355	−	0.187676i
$345$	−0.174847	+	0.781866i	−0.00941346	+	0.0420942i
$346$	−16.5383			−0.889104
$347$	0.124936	−	0.0721316i	0.00670689	−	0.00387223i	−0.496643	−	0.867955i	$-0.665434\pi$
$347$	0.124936	−	0.0721316i	0.00670689	−	0.00387223i	0.503350	+	0.864083i	$0.332101\pi$
$348$	−3.42263	−	10.9253i	−0.183472	−	0.585659i
$349$	−13.3482	+	23.1197i	−0.714511	+	1.23757i	0.248636	+	0.968597i	$0.420018\pi$
$349$	−13.3482	+	23.1197i	−0.714511	+	1.23757i	−0.963148	+	0.268973i	$0.913316\pi$
$350$	2.96000	−	12.7965i	0.158219	−	0.684000i
$351$	12.4771	−	13.9758i	0.665978	−	0.745972i
$352$	−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	$0.508030\pi$
$354$	−0.962640	−	3.07283i	−0.0511637	−	0.163319i
$355$	0.559784	−	0.323192i	0.0297103	−	0.0171532i
$356$			14.2864i			0.757178i
$357$	17.8690	+	8.57284i	0.945730	+	0.453723i
$358$	−12.0538	+	6.95929i	−0.637065	+	0.367810i
$359$	−23.0451			−1.21627			−0.608137	−	0.793832i	$-0.708083\pi$
$359$	−23.0451			−1.21627			−0.608137	+	0.793832i	$0.708083\pi$
$360$	0.323336	+	0.465411i	0.0170413	+	0.0245293i
$361$	−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
$364$	6.51011	+	6.97269i	0.341223	+	0.365468i
$365$		−	1.44346i		−	0.0755544i
$366$	1.01146	+	3.22866i	0.0528697	+	0.168765i
$367$	−13.8828	−	8.01521i	−0.724674	−	0.418391i	0.0917966	−	0.995778i	$-0.470739\pi$
$367$	−13.8828	−	8.01521i	−0.724674	−	0.418391i	−0.816471	+	0.577387i	$0.804072\pi$
$368$	−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
$371$	−0.340556	−	1.11560i	−0.0176808	−	0.0579188i
$372$	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
$375$	0.974629	+	3.11110i	0.0503296	+	0.160657i
$376$			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
$381$	1.42812	−	6.38614i	0.0731649	−	0.327172i
$382$		−	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	$0.392184\pi$
$384$	−0.377999	+	1.69030i	−0.0192897	+	0.0862578i
$385$	−2.91451	−	0.674167i	−0.148537	−	0.0343587i
$386$	−0.941626	+	0.543648i	−0.0479275	+	0.0276710i
$387$	−10.9095	−	5.13619i	−0.554560	−	0.261087i
$388$	8.15789	−	14.1299i	0.414154	−	0.717336i
$389$			3.50651i			0.177787i	0.996041	+	0.0888936i	$0.0283331\pi$
$389$			3.50651i			0.177787i	−0.996041	+	0.0888936i	$0.971667\pi$
$390$	−1.13084	−	0.335963i	−0.0572622	−	0.0170122i
$391$		−	10.5903i		−	0.535573i
$392$	5.80657	−	3.90944i	0.293276	−	0.197456i
$393$	−18.6891	+	5.85482i	−0.942740	+	0.295336i
$394$	5.48398	+	9.49852i	0.276279	+	0.478529i
$395$		−	2.43164i		−	0.122349i
$396$	−14.7469	+	10.2451i	−0.741061	+	0.514838i
$397$	−13.1380	−	22.7557i	−0.659378	−	1.14208i	−0.980777	−	0.195133i	$-0.937486\pi$
$397$	−13.1380	−	22.7557i	−0.659378	−	1.14208i	0.321399	−	0.946944i	$-0.395847\pi$
$398$			7.58519i			0.380211i
$399$	−22.3890	−	10.7413i	−1.12085	−	0.537740i
$400$	−2.48216	+	4.29922i	−0.124108	+	0.214961i
$401$	−5.37427	+	9.30851i	−0.268378	+	0.464845i	−0.968443	−	0.249234i	$-0.919821\pi$
$401$	−5.37427	+	9.30851i	−0.268378	+	0.464845i	0.700065	+	0.714079i	$0.253154\pi$
$402$	−12.7299	+	13.8410i	−0.634912	+	0.690327i
$403$	−27.8406	−	1.91787i	−1.38684	−	0.0955358i
$404$	5.15473			0.256458
$405$	1.59326	+	0.593229i	0.0791695	+	0.0294778i
$406$	11.9325	−	12.7852i	0.592201	−	0.634520i
$407$	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	0.989893	−	0.141815i	$-0.0452938\pi$
$409$	7.52589	+	13.0352i	0.372131	+	0.644550i	−0.617762	+	0.786365i	$0.711961\pi$
$410$	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
$413$	3.35611	−	3.59594i	0.165144	−	0.176945i
$414$	−3.12909	+	6.64631i	−0.153786	+	0.326648i
$415$	−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	$-0.0279518\pi$
$420$	−0.374443	+	0.780481i	−0.0182710	+	0.0380836i
$421$		−	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
$423$	5.13900	+	7.39711i	0.249867	+	0.359660i
$424$			0.440865i			0.0214103i
$425$	−10.7350	−	18.5936i	−0.520726	−	0.901924i
$426$	5.65570	−	1.77179i	0.274020	−	0.0858434i
$427$	−3.52631	+	3.77829i	−0.170650	+	0.182844i
$428$			11.7164i			0.566334i
$429$	10.6453	−	35.8315i	0.513958	−	1.72996i
$430$			0.759262i			0.0366149i
$431$	−0.197300	+	0.341734i	−0.00950362	+	0.0164607i	−0.870738	−	0.491747i	$-0.836358\pi$
$431$	−0.197300	+	0.341734i	−0.00950362	+	0.0164607i	0.861234	+	0.508208i	$0.169692\pi$
$432$	1.96192	+	4.81154i	0.0943929	+	0.231495i
$433$	20.3742	−	11.7631i	0.979122	−	0.565296i	0.0771170	−	0.997022i	$-0.475428\pi$
$433$	20.3742	−	11.7631i	0.979122	−	0.565296i	0.902005	+	0.431726i	$0.142095\pi$
$434$	−4.61496	+	19.9510i	−0.221525	+	0.957680i
$435$	−0.471986	+	2.11058i	−0.0226300	+	0.101195i
$436$	2.32283	−	1.34108i	0.111243	−	0.0642263i
$437$			13.2691i			0.634746i
$438$	2.88843	−	12.9162i	0.138014	−	0.617160i
$439$	4.95314	+	2.85970i	0.236400	+	0.136486i	0.613521	−	0.789678i	$-0.289753\pi$
$439$	4.95314	+	2.85970i	0.236400	+	0.136486i	−0.377121	+	0.926164i	$0.623086\pi$
$440$	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	$-0.981251\pi$
$443$		−	2.47810i		−	0.117738i	0.998266	−	0.0588690i	$-0.0187494\pi$
$444$	−0.723994	−	2.31105i	−0.0343592	−	0.109678i
$445$	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
$448$	−2.53047	+	0.772472i	−0.119554	+	0.0364959i
$449$	5.34379	+	9.25571i	0.252189	+	0.436804i	0.964128	−	0.265437i	$-0.0855162\pi$
$449$	5.34379	+	9.25571i	0.252189	+	0.436804i	−0.711939	+	0.702241i	$0.752183\pi$
$450$	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
$453$	6.87013	+	21.9301i	0.322787	+	1.03036i
$454$		−	15.1515i		−	0.711096i
$455$	−0.406436	−	1.75557i	−0.0190540	−	0.0823025i
$456$	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
$459$	−22.2639	−	3.05637i	−1.03919	−	0.142659i
$460$	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	$0.129218\pi$
$462$	−24.7302	−	11.8645i	−1.15055	−	0.551988i
$463$			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
$465$	−0.757054	−	2.41658i	−0.0351075	−	0.112066i
$466$	−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	$0.602524\pi$
$468$	−9.44653	−	5.26907i	−0.436666	−	0.243563i
$469$	−27.9860	−	6.47356i	−1.29228	−	0.298921i
$470$	0.283573	−	0.491163i	0.0130803	−	0.0226557i
$471$	8.31386	+	26.5386i	0.383083	+	1.22283i
$472$	−1.61004	+	0.929559i	−0.0741083	+	0.0427864i
$473$	−24.0578			−1.10618
$474$	4.86580	−	21.7584i	0.223494	−	0.999398i
$475$	13.4505	+	23.2969i	0.617150	+	1.06893i
$476$	2.57873	−	11.1482i	0.118196	−	0.510977i
$477$	0.754612	+	1.08619i	0.0345513	+	0.0497334i
$478$	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
$483$	−11.1887	+	0.855066i	−0.509102	+	0.0389069i
$484$	−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
$490$	−1.31917	+	0.0911229i	−0.0595939	+	0.00411651i
$491$	25.7266	+	14.8533i	1.16102	+	0.670318i	0.951549	−	0.307496i	$-0.0994911\pi$
$491$	25.7266	+	14.8533i	1.16102	+	0.670318i	0.209475	+	0.977814i	$0.432824\pi$
$492$	4.32597	+	13.8089i	0.195030	+	0.622552i
$493$		−	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
$497$	6.61850	+	6.17710i	0.296881	+	0.277081i
$498$	−27.3367	−	6.11325i	−1.22499	−	0.273941i
$499$		−	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
$501$	−33.9825	−	7.59944i	−1.51822	−	0.339518i
$502$	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	$0.927679\pi$
$504$	−4.91231	+	6.23452i	−0.218812	+	0.277707i
$505$	−0.843280	−	0.486868i	−0.0375255	−	0.0216653i
$506$			14.6566i			0.651565i
$507$	22.2070	−	3.72135i	0.986248	−	0.165271i
$508$	−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	$0.667359\pi$
$510$	0.423025	+	1.35033i	0.0187319	+	0.0597938i
$511$	19.3362	−	5.90274i	0.855385	−	0.261122i
$512$	1.00000			0.0441942
$513$	27.8956	+	3.82948i	1.23162	+	0.169076i
$514$	5.37346	+	9.30710i	0.237013	+	0.410519i
$515$	0.0928601			0.00409191
$516$	−1.51931	+	6.79392i	−0.0668840	+	0.299086i
$517$	15.5629	+	8.98524i	0.684455	+	0.395170i
$518$	2.52411	−	2.70448i	0.110903	−	0.118828i
$519$	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	$0.610442\pi$
$522$	−8.44671	+	17.9412i	−0.369703	+	0.785263i
$523$	17.2591	+	9.96453i	0.754687	+	0.435719i	0.827385	−	0.561635i	$-0.189828\pi$
$523$	17.2591	+	9.96453i	0.754687	+	0.435719i	−0.0726981	+	0.997354i	$0.523161\pi$
$524$	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
$531$	−2.37570	+	5.04608i	−0.103097	+	0.218981i
$532$	−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
$537$	23.5266	+	5.26121i	1.01525	+	0.227038i
$538$	−4.95553			−0.213648
$539$	−2.88730	−	41.7988i	−0.124365	−	1.80040i
$540$	0.133496	−	0.972440i	0.00574474	−	0.0418472i
$541$		−	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
$543$	−10.1165	−	32.2927i	−0.434140	−	1.38581i
$544$	−2.16244	+	3.74546i	−0.0927139	+	0.160585i
$545$	−0.506665			−0.0217032
$546$	−0.123846	−	16.5222i	−0.00530010	−	0.707087i
$547$	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
$549$	2.49618	−	5.30198i	0.106534	−	0.226283i
$550$	14.8569	+	25.7330i	0.633502	+	1.09726i
$551$			35.8188i			1.52593i
$552$	4.13902	+	0.925601i	0.176168	+	0.0393962i
$553$	32.5735	−	9.94366i	1.38517	−	0.422847i
$554$	−33.0539			−1.40433
$555$	−0.0998398	+	0.446455i	−0.00423796	+	0.0189509i
$556$	−1.01358	−	0.585188i	−0.0429852	−	0.0248175i
$557$	−1.86994	+	3.23883i	−0.0792319	+	0.137234i	−0.902919	−	0.429811i	$-0.858580\pi$
$557$	−1.86994	+	3.23883i	−0.0792319	+	0.137234i	0.823687	+	0.567045i	$0.191913\pi$
$558$	−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
$561$	−42.7864	+	13.4039i	−1.80644	+	0.565912i
$562$	−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	0.367369	−	0.930075i	$-0.380259\pi$
$569$	−6.06874	−	3.50379i	−0.254415	−	0.146886i	−0.621784	+	0.783189i	$0.713592\pi$
$570$	−0.530029	−	1.69190i	−0.0222005	−	0.0708659i
$571$	−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
$574$	−15.0819	+	16.1596i	−0.629506	+	0.674490i
$575$	10.5274	+	6.07803i	0.439025	+	0.253471i
$576$	2.46378	−	1.71166i	0.102657	−	0.0713193i
$577$	−13.4291			−0.559059			−0.279530	−	0.960137i	$-0.590179\pi$
$577$	−13.4291			−0.559059			−0.279530	+	0.960137i	$0.590179\pi$
$578$	−0.852297	−	1.47622i	−0.0354509	−	0.0614027i
$579$	1.83786	+	0.410997i	0.0763788	+	0.0170804i
$580$	1.24864			0.0518471
$581$	−12.4929	−	40.9245i	−0.518294	−	1.69783i
$582$	−26.9674	+	8.44821i	−1.11784	+	0.350190i
$583$	2.28526	+	1.31940i	0.0946458	+	0.0546438i
$584$	−7.64136			−0.316202
$585$	1.04772	+	1.75422i	0.0433180	+	0.0725279i
$586$			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	$0.467100\pi$
$588$	−11.9863	−	1.82433i	−0.494307	−	0.0752341i
$589$	−20.9707	−	36.3223i	−0.864083	−	1.49664i
$590$	0.351190			0.0144583
$591$	4.14587	−	18.5391i	0.170538	−	0.762598i
$592$	−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	$-0.152834\pi$
$594$	30.8125	+	4.22992i	1.26425	+	0.173556i
$595$	−1.47482	+	1.58021i	−0.0604617	+	0.0647822i
$596$	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	$0.208486\pi$
$599$			29.8169i			1.21829i	−0.793060	+	0.609143i	$0.791514\pi$
$600$	8.20523	−	2.57049i	0.334977	−	0.104940i
$601$	15.1795	+	8.76391i	0.619186	+	0.357487i	0.776552	−	0.630053i	$-0.216967\pi$
$601$	15.1795	+	8.76391i	0.619186	+	0.357487i	−0.157366	+	0.987540i	$0.550300\pi$
$602$	−10.1709	+	3.10484i	−0.414534	+	0.126544i
$603$	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	−0.263438	−	0.964676i	$-0.584856\pi$
$607$	10.8473	−	6.26269i	0.440278	−	0.254195i	0.703716	+	0.710482i	$0.251523\pi$
$608$	2.70943	−	4.69287i	0.109882	−	0.190321i
$609$	−30.2029	+	2.30818i	−1.22388	+	0.0935322i
$610$	−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
$615$	0.596557	−	2.66763i	0.0240555	−	0.107569i
$616$	−3.56888	+	15.4287i	−0.143794	+	0.621641i
$617$	−12.5067	−	21.6622i	−0.503499	−	0.872086i	−0.999992	−	0.00404517i	$-0.998712\pi$
$617$	−12.5067	−	21.6622i	−0.503499	−	0.872086i	0.496493	−	0.868041i	$-0.334621\pi$
$618$	0.830918	+	0.185817i	0.0334244	+	0.00747464i
$619$	−30.6669			−1.23261			−0.616303	−	0.787509i	$-0.711370\pi$
$619$	−30.6669			−1.23261			−0.616303	+	0.787509i	$0.711370\pi$
$620$	−1.26620	+	0.731038i	−0.0508516	+	0.0293592i
$621$	11.7819	−	4.80413i	0.472793	−	0.192783i
$622$	5.75754	−	9.97235i	0.230856	−	0.399855i
$623$	36.8259	+	8.51835i	1.47540	+	0.341280i
$624$	−1.77851	+	5.98639i	−0.0711975	+	0.239647i
$625$	24.4660			0.978641
$626$	−8.24656	−	4.76115i	−0.329599	−	0.190294i
$627$	53.6092	−	16.7944i	2.14095	−	0.670704i
$628$	13.9052	−	8.02816i	0.554877	−	0.320358i
$629$		−	6.04717i		−	0.241116i
$630$	1.39248	−	0.555954i	0.0554776	−	0.0221498i
$631$	−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
$633$	−5.23133	+	23.3930i	−0.207927	+	0.929787i
$634$	−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
$637$	21.8551	−	12.6235i	0.865931	−	0.500163i
$638$			39.5642i			1.56636i
$639$	−9.28757	−	4.37260i	−0.367411	−	0.172977i
$640$	−0.163593	−	0.0944507i	−0.00646660	−	0.00373349i
$641$	−14.5471	+	8.39874i	−0.574574	+	0.331730i	−0.758974	−	0.651121i	$-0.774299\pi$
$641$	−14.5471	+	8.39874i	−0.574574	+	0.331730i	0.184400	+	0.982851i	$0.440966\pi$
$642$	13.7376	−	14.9366i	0.542179	−	0.589500i
$643$	−10.4978	−	18.1827i	−0.413993	−	0.717057i	0.581329	−	0.813669i	$-0.302533\pi$
$643$	−10.4978	−	18.1827i	−0.413993	−	0.717057i	−0.995322	+	0.0966114i	$0.969200\pi$
$644$	1.89154	+	6.19633i	0.0745371	+	0.244170i
$645$	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	$0.163940\pi$
$648$	3.14042	−	8.43432i	0.123367	−	0.331331i
$649$			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	0.152386	−	0.988321i	$-0.451304\pi$
$653$	−16.0308	−	9.25537i	−0.627333	−	0.362191i	−0.779718	+	0.626130i	$0.784638\pi$
$654$	−4.53367	−	1.01386i	−0.177281	−	0.0396449i
$655$		−	2.13595i		−	0.0834586i
$656$	7.23531	−	4.17731i	0.282491	−	0.163096i
$657$	−18.8266	+	13.0794i	−0.734497	+	0.510277i
$658$	7.73910	+	1.79016i	0.301702	+	0.0697878i
$659$	−0.282523	+	0.163115i	−0.0110055	+	0.00635405i	−0.505493	−	0.862831i	$-0.668689\pi$
$659$	−0.282523	+	0.163115i	−0.0110055	+	0.00635405i	0.494487	+	0.869185i	$0.335356\pi$
$660$	−0.585453	−	1.86882i	−0.0227887	−	0.0727436i
$661$	4.09057	−	7.08508i	0.159105	−	0.275578i	−0.775441	−	0.631420i	$-0.782473\pi$
$661$	4.09057	−	7.08508i	0.159105	−	0.275578i	0.934546	+	0.355842i	$0.115806\pi$
$662$			5.09266i			0.197932i
$663$	−18.5758	−	19.6066i	−0.721426	−	0.761456i
$664$			16.1727i			0.627622i
$665$	1.84787	−	1.97992i	0.0716575	−	0.0767781i
$666$	−1.78675	+	3.79512i	−0.0692350	+	0.147058i
$667$	8.09294	+	14.0174i	0.313360	+	0.542755i
$668$			20.1044i			0.777862i
$669$	−9.07933	+	40.6001i	−0.351027	+	1.56969i
$670$	−1.02545	−	1.77614i	−0.0396167	−	0.0686182i
$671$		−	11.6920i		−	0.451366i
$672$	4.13169	+	1.98222i	0.159383	+	0.0764656i
$673$	−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	$0.718166\pi$
$678$	1.74558	+	5.57205i	0.0670386	+	0.213993i
$679$	−31.5582	−	29.4535i	−1.21109	−	1.13032i
$680$	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	$0.153256\pi$
$683$	22.0625	+	38.2134i	0.844198	+	1.46219i	−0.0421178	+	0.999113i	$0.513410\pi$
$684$	−1.35718	−	16.1998i	−0.0518929	−	0.619416i
$685$	1.09082	−	0.629788i	0.0416783	−	0.0240630i
$686$	−6.61511	−	17.2986i	−0.252566	−	0.660462i
$687$	23.3246	−	7.30700i	0.889888	−	0.278779i
$688$	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	$-0.530554\pi$
$691$	21.4006	−	37.0670i	0.814118	−	1.41009i	0.909959	−	0.414697i	$-0.136112\pi$
$692$	8.26915	−	14.3226i	0.314346	−	0.544463i
$693$	17.6159	+	44.1217i	0.669171	+	1.67605i
$694$			0.144263i			0.00547616i
$695$	0.110543	+	0.191466i	0.00419313	+	0.00726272i
$696$	11.1729	+	2.49858i	0.423509	+	0.0947085i
$697$			36.1327i			1.36862i
$698$	−13.3482	−	23.1197i	−0.505236	−	0.875094i
$699$	13.1829	+	42.0808i	0.498621	+	1.59164i
$700$	9.60206	+	8.96167i	0.362924	+	0.338719i
$701$		−	8.82186i		−	0.333197i	−0.986025	−	0.166598i	$-0.946722\pi$
$701$		−	8.82186i		−	0.333197i	0.986025	−	0.166598i	$-0.0532784\pi$
$702$	5.86483	+	17.7934i	0.221354	+	0.671567i
$703$			7.57680i			0.285765i
$704$	2.99275	−	5.18359i	0.112793	−	0.195364i
$705$	−0.937404	+	0.293665i	−0.0353047	+	0.0110601i
$706$	−15.5551	+	8.98072i	−0.585422	+	0.337994i
$707$	3.07354	−	13.2873i	0.115592	−	0.499720i
$708$	3.14247	+	0.702745i	0.118101	+	0.0264108i
$709$	−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
$711$	−31.7150	+	22.0334i	−1.18941	+	0.826318i
$712$	−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
$717$	−21.8407	+	6.84215i	−0.815657	+	0.255525i
$718$	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
$721$	0.379732	+	1.24393i	0.0141419	+	0.0463263i
$722$	−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
$726$	41.0336	−	12.8548i	1.52290	−	0.477086i
$727$		−	12.7622i		−	0.473322i	−0.971592	−	0.236661i	$-0.923947\pi$
$727$		−	12.7622i		−	0.473322i	0.971592	−	0.236661i	$-0.0760531\pi$
$728$	−9.29358	+	2.15158i	−0.344443	+	0.0797427i
$729$	−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
$732$	−3.30183	−	0.738382i	−0.122039	−	0.0272914i
$733$	−8.94011			−0.330210			−0.165105	−	0.986276i	$-0.552796\pi$
$733$	−8.94011			−0.330210			−0.165105	+	0.986276i	$0.552796\pi$
$734$	13.8828	−	8.01521i	0.512422	−	0.295847i
$735$	1.78857	+	1.43056i	0.0659725	+	0.0527672i
$736$		−	2.44869i		−	0.0902598i
$737$	56.2783	−	32.4923i	2.07304	−	1.19687i
$738$	10.6761	−	22.6764i	0.392991	−	0.834729i
$739$	−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
$741$	23.2746	+	24.5660i	0.855014	+	0.902456i
$742$	1.13641	+	0.262868i	0.0417190	+	0.00965019i
$743$	11.5885	−	20.0719i	0.425142	−	0.736368i	−0.571291	−	0.820747i	$-0.693557\pi$
$743$	11.5885	−	20.0719i	0.425142	−	0.736368i	0.996434	+	0.0843791i	$0.0268907\pi$
$744$	−12.7928	+	4.00767i	−0.469008	+	0.146928i
$745$	−0.903872	+	0.521851i	−0.0331153	+	0.0191191i
$746$	−5.59041			−0.204679
$747$	27.6822	+	39.8459i	1.01284	+	1.45789i
$748$	12.9433	+	22.4184i	0.473253	+	0.819698i
$749$	30.2013	+	6.98598i	1.10353	+	0.255262i
$750$	−3.18161	−	0.711497i	−0.116176	−	0.0259802i
$751$	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
$756$	13.5724	−	2.18831i	0.493625	−	0.0795882i
$757$	−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
$763$	−2.07190	−	6.78715i	−0.0750078	−	0.245711i
$764$	7.34535	+	4.24084i	0.265745	+	0.153428i
$765$	1.04398	−	2.21746i	0.0377453	−	0.0801726i
$766$		−	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	$-0.400164\pi$
$769$	27.1219	−	46.9765i	0.978040	−	1.69402i	0.669513	−	0.742800i	$-0.266503\pi$
$770$	2.04110	−	2.18696i	0.0735562	−	0.0788124i
$771$	4.06232	−	18.1655i	0.146301	−	0.654215i
$772$		−	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	$0.624556\pi$
$774$	9.90281	−	6.87979i	0.355949	−	0.247289i
$775$	−38.4233			−1.38020
$776$	8.15789	+	14.1299i	0.292851	+	0.507233i
$777$	−6.38886	+	0.488253i	−0.229199	+	0.0175160i
$778$	−3.03673	−	1.75325i	−0.108872	−	0.0628572i
$779$		−	45.2725i		−	1.62205i
$780$	0.856372	−	0.811353i	0.0306630	−	0.0290511i
$781$	−20.4812			−0.732874
$782$	9.17145	+	5.29514i	0.327970	+	0.189354i
$783$	31.8044	−	12.9683i	1.13660	−	0.463451i
$784$	0.482384	+	6.98336i	0.0172280	+	0.249406i
$785$	−3.03306			−0.108255
$786$	4.27412	−	19.1126i	0.152453	−	0.681725i
$787$	−0.125526	−	0.217418i	−0.00447452	−	0.00775010i	0.863779	−	0.503870i	$-0.168091\pi$
$787$	−0.125526	−	0.217418i	−0.00447452	−	0.00775010i	−0.868254	+	0.496120i	$0.834758\pi$
$788$	−10.9680			−0.390717
$789$	−17.9750	−	4.01971i	−0.639926	−	0.143105i
$790$	2.10586	+	1.21582i	0.0749231	+	0.0432569i
$791$	−6.08573	+	6.52061i	−0.216384	+	0.231846i
$792$	−1.49909	−	17.8938i	−0.0532679	−	0.635828i
$793$	6.32708	−	3.09403i	0.224681	−	0.109872i
$794$	26.2760			0.932502
$795$	−0.137649	+	0.0431218i	−0.00488190	+	0.00152937i
$796$	−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
$804$	−5.62170	−	17.9450i	−0.198262	−	0.632870i
$805$	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	−0.0170890	−	0.999854i	$-0.505440\pi$
$809$	−25.3578	−	14.6403i	−0.891532	−	0.514727i	−0.874443	+	0.485127i	$0.838773\pi$
$810$	−1.31038	+	1.08318i	−0.0460420	+	0.0380592i
$811$	−6.42322			−0.225550			−0.112775	−	0.993621i	$-0.535974\pi$
$811$	−6.42322			−0.225550			−0.112775	+	0.993621i	$0.535974\pi$
$812$	5.10606	+	16.7265i	0.179187	+	0.586984i
$813$	6.86519	−	30.6991i	0.240773	−	1.07667i
$814$			8.36908i			0.293336i
$815$	−0.355954	−	0.616531i	−0.0124685	−	0.0215961i
$816$	7.14835	−	2.23940i	0.250242	−	0.0783945i
$817$	10.8902	−	18.8623i	0.380999	−	0.659909i
$818$	−15.0518			−0.526273
$819$	−19.2146	+	21.2085i	−0.671411	+	0.741085i
$820$	−1.57820			−0.0551131
$821$	14.9385	−	25.8742i	0.521356	−	0.903015i	−0.478335	−	0.878177i	$-0.658760\pi$
$821$	14.9385	−	25.8742i	0.521356	−	0.903015i	0.999691	−	0.0248379i	$-0.00790697\pi$
$822$	11.0210	−	3.45260i	0.384401	−	0.120423i
$823$	−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
$825$	11.2318	−	50.2254i	0.391041	−	1.74862i
$826$	1.43612	+	4.70445i	0.0499689	+	0.163689i
$827$	9.74990			0.339037			0.169519	−	0.985527i	$-0.445779\pi$
$827$	9.74990			0.339037			0.169519	+	0.985527i	$0.445779\pi$
$828$	−4.19133	−	6.03302i	−0.145659	−	0.209662i
$829$	1.71389	+	0.989516i	0.0595259	+	0.0343673i	0.529468	−	0.848330i	$-0.322392\pi$
$829$	1.71389	+	0.989516i	0.0595259	+	0.0343673i	−0.469942	+	0.882697i	$0.655725\pi$
$830$	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
$834$	0.606014	+	1.93445i	0.0209845	+	0.0669845i
$835$	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
$843$	26.4240	−	8.27798i	0.910092	−	0.285109i
$844$	13.8395			0.476376
$845$	−0.336738	+	2.43252i	−0.0115841	+	0.0836813i
$846$	−8.97558	+	0.751949i	−0.308587	+	0.0258525i
$847$	48.0190	+	44.8165i	1.64995	+	1.53991i
$848$	−0.381800	−	0.220432i	−0.0131111	−	0.00756968i
$849$	44.8652	+	10.0331i	1.53977	+	0.344336i
$850$	21.4701			0.736418
$851$	1.71191	+	2.96512i	0.0586835	+	0.101643i
$852$	−1.29344	+	5.78387i	−0.0443124	+	0.198152i
$853$	19.7131			0.674964			0.337482	−	0.941332i	$-0.390425\pi$
$853$	19.7131			0.674964			0.337482	+	0.941332i	$0.390425\pi$
$854$	−1.50894	−	4.94302i	−0.0516350	−	0.169147i
$855$	−1.30806	+	2.77837i	−0.0447347	+	0.0950183i
$856$	−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	$0.501954\pi$
$858$	25.7084	+	27.1348i	0.877669	+	0.926367i
$859$		−	38.7509i		−	1.32216i	−0.750314	−	0.661081i	$-0.770098\pi$
$859$		−	38.7509i		−	1.32216i	0.750314	−	0.661081i	$-0.229902\pi$
$860$	−0.657540	−	0.379631i	−0.0224219	−	0.0129453i
$861$	38.1743	−	2.91738i	1.30098	−	0.0994241i
$862$	−0.197300	−	0.341734i	−0.00672007	−	0.0116395i
$863$	−16.1927			−0.551207			−0.275603	−	0.961271i	$-0.588878\pi$
$863$	−16.1927			−0.551207			−0.275603	+	0.961271i	$0.588878\pi$
$864$	−5.14787	−	0.706695i	−0.175134	−	0.0240423i
$865$	−2.70556	+	1.56205i	−0.0919917	+	0.0531114i
$866$			23.5261i			0.799450i
$867$	−0.644335	+	2.88128i	−0.0218828	+	0.0978533i
$868$	−14.9706	−	13.9722i	−0.508136	−	0.474247i
$869$	−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
$873$	44.2848	+	20.8493i	1.49881	+	0.705644i
$874$	−11.4914	−	6.63454i	−0.388701	−	0.224417i
$875$	−1.45400	−	4.76304i	−0.0491543	−	0.161020i
$876$	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	$0.964927\pi$
$882$	13.1416	+	16.3798i	0.442502	+	0.551536i
$883$	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	$0.278692\pi$
$888$	2.36343	+	0.528529i	0.0793114	+	0.0177363i
$889$	−2.25272	+	9.73879i	−0.0755538	+	0.326629i
$890$	1.34936	+	2.33716i	0.0452307	+	0.0783418i
$891$	−34.3216	−	41.5204i	−1.14982	−	1.39099i
$892$	24.0195			0.804231
$893$	−14.0896	+	8.13463i	−0.471490	+	0.272215i
$894$	−9.13215	+	2.86087i	−0.305425	+	0.0956818i
$895$	−1.31462	+	2.27699i	−0.0439429	+	0.0761113i
$896$	0.596256	−	2.57769i	0.0199195	−	0.0861145i
$897$	14.6588	+	4.35502i	0.489443	+	0.145410i
$898$	−10.6876			−0.356649
$899$	−44.3066	−	25.5804i	−1.47771	−	0.853156i
$900$	−13.4743	−	6.34372i	−0.449144	−	0.211457i
$901$	1.65124	−	0.953344i	0.0550108	−	0.0317605i
$902$		−	50.0065i		−	1.66503i
$903$	16.6067	+	7.96723i	0.552637	+	0.265133i
$904$	2.91954	−	1.68560i	0.0971023	−	0.0560621i
$905$	3.69070			0.122683
$906$	−22.4271	−	5.01532i	−0.745089	−	0.166623i
$907$	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
$910$	1.72359	+	0.525802i	0.0571364	+	0.0174302i
$911$			38.8818i			1.28821i	0.764936	+	0.644106i	$0.222771\pi$
$911$			38.8818i			1.28821i	−0.764936	+	0.644106i	$0.777229\pi$
$912$	−8.95652	+	2.80585i	−0.296580	+	0.0929110i
$913$	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
$917$	28.6126	−	8.73452i	0.944873	−	0.288439i
$918$	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
$921$	0.291576	−	0.0913433i	0.00960775	−	0.00300986i
$922$			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
$927$	−0.841419	−	1.21114i	−0.0276358	−	0.0397792i
$928$		−	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	$0.346593\pi$
$930$	2.47135	+	0.552663i	0.0810387	+	0.0181225i
$931$	34.0790	+	16.6572i	1.11689	+	0.545916i
$932$	22.0487	−	12.7298i	0.722230	−	0.416979i
$933$	−19.0326	+	5.96243i	−0.623100	+	0.195201i
$934$	6.84064	−	11.8483i	0.223833	−	0.387690i
$935$		−	4.89000i		−	0.159920i
$936$	9.28641	−	5.54640i	0.303536	−	0.181290i
$937$			8.65434i			0.282725i	0.989958	+	0.141362i	$0.0451483\pi$
$937$			8.65434i			0.282725i	−0.989958	+	0.141362i	$0.954852\pi$
$938$	19.5993	−	20.9998i	0.639940	−	0.685669i
$939$	4.93059	+	15.7389i	0.160904	+	0.513619i
$940$	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	$-0.171663\pi$
$942$	−27.1400	−	6.06927i	−0.884269	−	0.197748i
$943$	−10.2289	−	17.7170i	−0.333099	−	0.576945i
$944$		−	1.85912i		−	0.0605092i
$945$	−2.42705	−	0.923933i	−0.0789520	−	0.0300556i
$946$	12.0289	−	20.8347i	0.391094	−	0.677394i
$947$	22.7880	−	39.4700i	0.740510	−	1.28260i	−0.211753	−	0.977323i	$-0.567917\pi$
$947$	22.7880	−	39.4700i	0.740510	−	1.28260i	0.952263	−	0.305278i	$-0.0987495\pi$
$948$	16.4105	+	15.0931i	0.532987	+	0.490202i
$949$	−27.4862	−	1.89345i	−0.892239	−	0.0614641i
$950$	−26.9009			−0.872782
$951$	34.6790	−	10.8641i	1.12454	−	0.352291i
$952$	8.36525	+	7.80735i	0.271119	+	0.253038i
$953$	−18.5089	+	10.6861i	−0.599562	+	0.346157i	−0.768869	−	0.639406i	$-0.779180\pi$
$953$	−18.5089	+	10.6861i	−0.599562	+	0.346157i	0.169307	+	0.985563i	$0.445847\pi$
$954$	−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
$959$	12.8972	+	12.0370i	0.416471	+	0.388695i
$960$	0.0978120	+	0.312224i	0.00315687	+	0.0100770i
$961$	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
$966$	4.85382	−	10.1172i	0.156169	−	0.325516i
$967$		−	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
$969$	8.85875	−	39.6138i	0.284584	−	1.27258i
$970$		−	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	$-0.494924\pi$
$972$	−13.8928	+	7.07028i	−0.445613	+	0.226779i
$973$	−2.11278	+	2.26376i	−0.0677327	+	0.0725729i
$974$			42.4455i			1.36004i
$975$	30.1514	−	7.21295i	0.965617	−	0.230999i
$976$			1.95340i			0.0625267i
$977$	11.3661	−	19.6866i	0.363633	−	0.629831i	−0.624923	−	0.780687i	$-0.714870\pi$
$977$	11.3661	−	19.6866i	0.363633	−	0.629831i	0.988556	+	0.150856i	$0.0482029\pi$
$978$	−1.95140	−	6.22903i	−0.0623988	−	0.199183i
$979$	−74.0548	+	42.7556i	−2.36680	+	1.36647i
$980$	0.580668	−	1.18799i	0.0185488	−	0.0379490i
$981$	4.59097	+	6.60827i	0.146578	+	0.210986i
$982$	−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	$0.995856\pi$
$984$	−14.1218	−	3.15803i	−0.450187	−	0.100674i
$985$	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
$990$	−1.44484	+	3.06890i	−0.0459200	+	0.0975359i
$991$	−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
$994$	−8.65877	+	2.64325i	−0.274640	+	0.0838387i
$995$	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	−0.804703	−	0.593677i	$-0.797676\pi$
$997$	−21.8790	+	12.6319i	−0.692915	+	0.400055i	0.111788	+	0.993732i	$0.464342\pi$
$998$	17.6149	+	10.1700i	0.557591	+	0.321926i
$999$	6.72762	−	2.74321i	0.212853	−	0.0867914i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.65284 - 0.517794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-0.377999 + 1.69030i) q^{6} +(-2.53047 + 0.772472i) q^{7} +1.00000 q^{8} +(2.46378 - 1.71166i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.65284 - 0.517794i) q^{3} +(-0.500000 - 0.866025i) q^{4} +0.188901i q^{5} +(-0.377999 + 1.69030i) q^{6} +(-2.53047 + 0.772472i) q^{7} +1.00000 q^{8} +(2.46378 - 1.71166i) 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} +(0.0978120 + 0.312224i) 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} +(1.65284 - 0.517794i) q^{24} +4.96432 q^{25} +(-2.01311 + 2.99122i) q^{26} +(3.18595 - 4.10484i) q^{27} +(1.93422 + 1.80522i) q^{28} +(5.72445 + 3.30501i) q^{29} +(-0.319300 - 0.0714045i) q^{30} -7.73989 q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.26251 - 10.1173i) q^{33} +4.32488 q^{34} +(-0.145921 - 0.478010i) q^{35} +(-2.71423 - 1.27786i) q^{36} +(1.21090 + 0.699114i) q^{37} -5.41886 q^{38} +(6.07362 - 1.45296i) q^{39} +0.188901i q^{40} +(-7.23531 - 4.17731i) q^{41} +(-0.349194 - 4.56925i) q^{42} +(-2.00968 - 3.48087i) q^{43} -5.98549 q^{44} +(0.323336 + 0.465411i) q^{45} +(-2.12062 + 1.22434i) q^{46} +3.00234i q^{47} +(-0.377999 + 1.69030i) q^{48} +(5.80657 - 3.90944i) q^{49} +(-2.48216 + 4.29922i) q^{50} +(-5.51355 - 5.07095i) q^{51} +(-1.58392 - 3.23901i) q^{52} +0.440865i q^{53} +(1.96192 + 4.81154i) q^{54} +(0.979187 + 0.565334i) q^{55} +(-2.53047 + 0.772472i) 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} +(-4.91231 + 6.23452i) 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} +(4.13902 + 0.925601i) q^{69} +(0.486929 + 0.112634i) q^{70} +(-1.71090 - 2.96337i) q^{71} +(2.46378 - 1.71166i) q^{72} -7.64136 q^{73} +(-1.21090 + 0.699114i) q^{74} +(8.20523 - 2.57049i) q^{75} +(2.70943 - 4.69287i) q^{76} +(-3.56888 + 15.4287i) q^{77} +(-1.77851 + 5.98639i) q^{78} -12.8725 q^{79} +(-0.163593 - 0.0944507i) q^{80} +(3.14042 - 8.43432i) q^{81} +(7.23531 - 4.17731i) q^{82} +16.1727i q^{83} +(4.13169 + 1.98222i) q^{84} +(0.707522 - 0.408488i) q^{85} +4.01936 q^{86} +(11.1729 + 2.49858i) q^{87} +(2.99275 - 5.18359i) q^{88} +(-12.3724 - 7.14320i) q^{89} +(-0.564726 + 0.0473112i) q^{90} +(-9.29358 + 2.15158i) q^{91} -2.44869i q^{92} +(-12.7928 + 4.00767i) 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} +(0.482384 + 6.98336i) q^{98} +(-1.49909 - 17.8938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} - 18 q^{7} + 24 q^{8} - 12 q^{9} + 6 q^{15} - 12 q^{16} + 6 q^{18} - 12 q^{21} + 36 q^{23} - 12 q^{25} + 18 q^{28} - 12 q^{30} - 12 q^{32} + 36 q^{35} + 6 q^{36} + 36 q^{37} + 12 q^{39} + 24 q^{42} - 42 q^{43} - 36 q^{46} + 6 q^{50} + 12 q^{51} - 18 q^{56} + 36 q^{57} + 6 q^{60} + 24 q^{63} + 24 q^{64} - 66 q^{65} - 54 q^{67} - 48 q^{71} - 12 q^{72} - 36 q^{74} - 42 q^{78} - 48 q^{79} + 84 q^{81} - 12 q^{84} + 84 q^{86} + 36 q^{91} - 18 q^{93} + 36 q^{95} - 36 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 - 18 * q^7 + 24 * q^8 - 12 * q^9 + 6 * q^15 - 12 * q^16 + 6 * q^18 - 12 * q^21 + 36 * q^23 - 12 * q^25 + 18 * q^28 - 12 * q^30 - 12 * q^32 + 36 * q^35 + 6 * q^36 + 36 * q^37 + 12 * q^39 + 24 * q^42 - 42 * q^43 - 36 * q^46 + 6 * q^50 + 12 * q^51 - 18 * q^56 + 36 * q^57 + 6 * q^60 + 24 * q^63 + 24 * q^64 - 66 * q^65 - 54 * q^67 - 48 * q^71 - 12 * q^72 - 36 * q^74 - 42 * q^78 - 48 * q^79 + 84 * q^81 - 12 * q^84 + 84 * q^86 + 36 * q^91 - 18 * q^93 + 36 * q^95 - 36 * q^99

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