LMFDB - Embedded newform 104.2.r.a.61.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [104,2,Mod(29,104)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("104.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(104, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	104.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.830444181021$
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			61.11
Character	$\chi$	$=$	104.61
Dual form			104.2.r.a.29.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24938 + 0.662601i) q^{2} +(-0.509400 - 0.294102i) q^{3} +(1.12192 + 1.65569i) q^{4} -1.78237i q^{5} +(-0.441564 - 0.704976i) q^{6} +(1.65832 + 2.87229i) q^{7} +(0.304647 + 2.81197i) q^{8} +(-1.32701 - 2.29844i) q^{9} +(1.18100 - 2.22687i) q^{10} +(-2.13570 - 1.23305i) q^{11} +(-0.0845644 - 1.17337i) q^{12} +(-3.57591 + 0.461374i) q^{13} +(0.168691 + 4.68739i) q^{14} +(-0.524200 + 0.907941i) q^{15} +(-1.48260 + 3.71509i) q^{16} +(-2.79947 - 4.84883i) q^{17} +(-0.134989 - 3.75092i) q^{18} +(2.54173 - 1.46747i) q^{19} +(2.95105 - 1.99968i) q^{20} -1.95086i q^{21} +(-1.85129 - 2.95566i) q^{22} +(-1.21868 + 2.11082i) q^{23} +(0.671821 - 1.52202i) q^{24} +1.82314 q^{25} +(-4.77339 - 1.79297i) q^{26} +3.32572i q^{27} +(-2.89511 + 5.96813i) q^{28} +(6.28420 + 3.62819i) q^{29} +(-1.25653 + 0.787031i) q^{30} -4.42876 q^{31} +(-4.31396 + 3.65920i) q^{32} +(0.725283 + 1.25623i) q^{33} +(-0.284775 - 7.91298i) q^{34} +(5.11949 - 2.95574i) q^{35} +(2.31671 - 4.77578i) q^{36} +(3.62746 + 2.09432i) q^{37} +(4.14794 - 0.149277i) q^{38} +(1.95726 + 0.816660i) q^{39} +(5.01199 - 0.542994i) q^{40} +(1.19018 - 2.06145i) q^{41} +(1.29264 - 2.43737i) q^{42} +(-9.41391 + 5.43512i) q^{43} +(-0.354542 - 4.91942i) q^{44} +(-4.09669 + 2.36522i) q^{45} +(-2.92123 + 1.82972i) q^{46} +8.82426 q^{47} +(1.84785 - 1.45643i) q^{48} +(-2.00003 + 3.46415i) q^{49} +(2.27781 + 1.20802i) q^{50} +3.29333i q^{51} +(-4.77577 - 5.40296i) q^{52} +1.32698i q^{53} +(-2.20363 + 4.15510i) q^{54} +(-2.19775 + 3.80661i) q^{55} +(-7.57160 + 5.53817i) q^{56} -1.72634 q^{57} +(5.44734 + 8.69692i) q^{58} +(4.50116 - 2.59874i) q^{59} +(-2.09138 + 0.150725i) q^{60} +(1.38839 - 0.801590i) q^{61} +(-5.53322 - 2.93450i) q^{62} +(4.40120 - 7.62310i) q^{63} +(-7.81438 + 1.71332i) q^{64} +(0.822340 + 6.37361i) q^{65} +(0.0737790 + 2.05008i) q^{66} +(10.0039 + 5.77577i) q^{67} +(4.88736 - 10.0750i) q^{68} +(1.24159 - 0.716834i) q^{69} +(8.35469 - 0.300671i) q^{70} +(-5.07044 - 8.78227i) q^{71} +(6.05889 - 4.43172i) q^{72} +12.1620 q^{73} +(3.14439 + 5.02016i) q^{74} +(-0.928710 - 0.536191i) q^{75} +(5.28128 + 2.56193i) q^{76} -8.17912i q^{77} +(1.90425 + 2.31720i) q^{78} -7.72073 q^{79} +(6.62168 + 2.64254i) q^{80} +(-3.00292 + 5.20121i) q^{81} +(2.85291 - 1.78693i) q^{82} -6.77111i q^{83} +(3.23001 - 2.18871i) q^{84} +(-8.64243 + 4.98971i) q^{85} +(-15.3629 + 0.552885i) q^{86} +(-2.13412 - 3.69640i) q^{87} +(2.81666 - 6.38117i) q^{88} +(-5.89082 + 10.2032i) q^{89} +(-6.68553 + 0.240601i) q^{90} +(-7.25519 - 9.50594i) q^{91} +(-4.86211 + 0.350412i) q^{92} +(2.25601 + 1.30251i) q^{93} +(11.0249 + 5.84696i) q^{94} +(-2.61558 - 4.53031i) q^{95} +(3.27371 - 0.595255i) q^{96} +(-3.17980 - 5.50758i) q^{97} +(-4.79415 + 3.00283i) q^{98} +6.54505i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) $ 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.24938	+	0.662601i	0.883448	+	0.468530i
$2$	1.24938	+	0.662601i	0.883448	+	0.468530i
$3$	−0.509400	−	0.294102i	−0.294102	−	0.169800i	0.345688	−	0.938349i	$-0.387646\pi$
$3$	−0.509400	−	0.294102i	−0.294102	−	0.169800i	−0.639790	+	0.768549i	$0.720979\pi$
$4$	1.12192	+	1.65569i	0.560959	+	0.827843i
$5$		−	1.78237i		−	0.797102i	−0.917146	−	0.398551i	$-0.869513\pi$
$5$		−	1.78237i		−	0.797102i	0.917146	−	0.398551i	$-0.130487\pi$
$6$	−0.441564	−	0.704976i	−0.180268	−	0.287805i
$7$	1.65832	+	2.87229i	0.626785	+	1.08562i	0.988193	+	0.153215i	$0.0489628\pi$
$7$	1.65832	+	2.87229i	0.626785	+	1.08562i	−0.361408	+	0.932408i	$0.617704\pi$
$8$	0.304647	+	2.81197i	0.107709	+	0.994182i
$9$	−1.32701	−	2.29844i	−0.442336	−	0.766148i
$10$	1.18100	−	2.22687i	0.373466	−	0.704198i
$11$	−2.13570	−	1.23305i	−0.643937	−	0.371777i	0.142192	−	0.989839i	$-0.454585\pi$
$11$	−2.13570	−	1.23305i	−0.643937	−	0.371777i	−0.786130	+	0.618062i	$0.787918\pi$
$12$	−0.0845644	−	1.17337i	−0.0244116	−	0.338722i
$13$	−3.57591	+	0.461374i	−0.991779	+	0.127962i
$13$	−3.57591	+	0.461374i	−0.991779	+	0.127962i
$14$	0.168691	+	4.68739i	0.0450846	+	1.25276i
$15$	−0.524200	+	0.907941i	−0.135348	+	0.234429i
$16$	−1.48260	+	3.71509i	−0.370649	+	0.928773i
$17$	−2.79947	−	4.84883i	−0.678972	−	1.17601i	−0.975291	−	0.220925i	$-0.929092\pi$
$17$	−2.79947	−	4.84883i	−0.678972	−	1.17601i	0.296319	−	0.955089i	$-0.404241\pi$
$18$	−0.134989	−	3.75092i	−0.0318172	−	0.884099i
$19$	2.54173	−	1.46747i	0.583113	−	0.336660i	−0.179257	−	0.983802i	$-0.557369\pi$
$19$	2.54173	−	1.46747i	0.583113	−	0.336660i	0.762369	+	0.647142i	$0.224036\pi$
$20$	2.95105	−	1.99968i	0.659875	−	0.447142i
$21$		−	1.95086i		−	0.425712i
$22$	−1.85129	−	2.95566i	−0.394696	−	0.630150i
$23$	−1.21868	+	2.11082i	−0.254112	+	0.440136i	−0.964654	−	0.263519i	$-0.915117\pi$
$23$	−1.21868	+	2.11082i	−0.254112	+	0.440136i	0.710542	+	0.703655i	$0.248450\pi$
$24$	0.671821	−	1.52202i	0.137135	−	0.310680i
$25$	1.82314			0.364629
$26$	−4.77339	−	1.79297i	−0.936139	−	0.351630i
$27$			3.32572i			0.640035i
$28$	−2.89511	+	5.96813i	−0.547125	+	1.12787i
$29$	6.28420	+	3.62819i	1.16695	+	0.673737i	0.952959	−	0.303099i	$-0.0980212\pi$
$29$	6.28420	+	3.62819i	1.16695	+	0.673737i	0.213988	+	0.976836i	$0.431355\pi$
$30$	−1.25653	+	0.787031i	−0.229410	+	0.143692i
$31$	−4.42876			−0.795429			−0.397714	−	0.917509i	$-0.630196\pi$
$31$	−4.42876			−0.795429			−0.397714	+	0.917509i	$0.630196\pi$
$32$	−4.31396	+	3.65920i	−0.762607	+	0.646862i
$33$	0.725283	+	1.25623i	0.126256	+	0.218681i
$34$	−0.284775	−	7.91298i	−0.0488384	−	1.35707i
$35$	5.11949	−	2.95574i	0.865352	−	0.499611i
$36$	2.31671	−	4.77578i	0.386118	−	0.795963i
$37$	3.62746	+	2.09432i	0.596351	+	0.344303i	0.767605	−	0.640924i	$-0.221448\pi$
$37$	3.62746	+	2.09432i	0.596351	+	0.344303i	−0.171254	+	0.985227i	$0.554782\pi$
$38$	4.14794	−	0.149277i	0.672885	−	0.0242160i
$39$	1.95726	+	0.816660i	0.313412	+	0.130770i
$40$	5.01199	−	0.542994i	0.792465	−	0.0858550i
$41$	1.19018	−	2.06145i	0.185875	−	0.321945i	−0.757996	−	0.652259i	$-0.773821\pi$
$41$	1.19018	−	2.06145i	0.185875	−	0.321945i	0.943871	+	0.330314i	$0.107155\pi$
$42$	1.29264	−	2.43737i	0.199459	−	0.376095i
$43$	−9.41391	+	5.43512i	−1.43561	+	0.828848i	−0.997540	−	0.0700937i	$-0.977670\pi$
$43$	−9.41391	+	5.43512i	−1.43561	+	0.828848i	−0.438067	+	0.898942i	$0.644337\pi$
$44$	−0.354542	−	4.91942i	−0.0534493	−	0.741631i
$45$	−4.09669	+	2.36522i	−0.610698	+	0.352587i
$46$	−2.92123	+	1.82972i	−0.430712	+	0.269778i
$47$	8.82426			1.28715			0.643575	−	0.765383i	$-0.277450\pi$
$47$	8.82426			1.28715			0.643575	+	0.765383i	$0.277450\pi$
$48$	1.84785	−	1.45643i	0.266714	−	0.210218i
$49$	−2.00003	+	3.46415i	−0.285718	+	0.494878i
$50$	2.27781	+	1.20802i	0.322130	+	0.170840i
$51$			3.29333i			0.461158i
$52$	−4.77577	−	5.40296i	−0.662280	−	0.749256i
$53$			1.32698i			0.182274i	0.995838	+	0.0911371i	$0.0290501\pi$
$53$			1.32698i			0.182274i	−0.995838	+	0.0911371i	$0.970950\pi$
$54$	−2.20363	+	4.15510i	−0.299875	+	0.565437i
$55$	−2.19775	+	3.80661i	−0.296344	+	0.513283i
$56$	−7.57160	+	5.53817i	−1.01180	+	0.740070i
$57$	−1.72634			−0.228660
$58$	5.44734	+	8.69692i	0.715271	+	1.14196i
$59$	4.50116	−	2.59874i	0.586001	−	0.338328i	−0.177514	−	0.984118i	$-0.556805\pi$
$59$	4.50116	−	2.59874i	0.586001	−	0.338328i	0.763514	+	0.645791i	$0.223472\pi$
$60$	−2.09138	+	0.150725i	−0.269996	+	0.0194586i
$61$	1.38839	−	0.801590i	0.177766	−	0.102633i	−0.408477	−	0.912769i	$-0.633940\pi$
$61$	1.38839	−	0.801590i	0.177766	−	0.102633i	0.586242	+	0.810136i	$0.300607\pi$
$62$	−5.53322	−	2.93450i	−0.702719	−	0.372682i
$63$	4.40120	−	7.62310i	0.554499	−	0.960420i
$64$	−7.81438	+	1.71332i	−0.976798	+	0.214165i
$65$	0.822340	+	6.37361i	0.101999	+	0.790549i
$66$	0.0737790	+	2.05008i	0.00908157	+	0.252348i
$67$	10.0039	+	5.77577i	1.22217	+	0.705622i	0.965381	−	0.260844i	$-0.0840008\pi$
$67$	10.0039	+	5.77577i	1.22217	+	0.705622i	0.256793	+	0.966466i	$0.417334\pi$
$68$	4.88736	−	10.0750i	0.592679	−	1.22178i
$69$	1.24159	−	0.716834i	0.149470	−	0.0862966i
$70$	8.35469	−	0.300671i	0.998576	−	0.0359370i
$71$	−5.07044	−	8.78227i	−0.601751	−	1.04226i	−0.992556	−	0.121790i	$-0.961137\pi$
$71$	−5.07044	−	8.78227i	−0.601751	−	1.04226i	0.390805	−	0.920474i	$-0.372197\pi$
$72$	6.05889	−	4.43172i	0.714048	−	0.522284i
$73$	12.1620			1.42345			0.711727	−	0.702456i	$-0.247913\pi$
$73$	12.1620			1.42345			0.711727	+	0.702456i	$0.247913\pi$
$74$	3.14439	+	5.02016i	0.365528	+	0.583582i
$75$	−0.928710	−	0.536191i	−0.107238	−	0.0619140i
$76$	5.28128	+	2.56193i	0.605805	+	0.293873i
$77$		−	8.17912i		−	0.932097i
$78$	1.90425	+	2.31720i	0.215614	+	0.262372i
$79$	−7.72073			−0.868650			−0.434325	−	0.900756i	$-0.643013\pi$
$79$	−7.72073			−0.868650			−0.434325	+	0.900756i	$0.643013\pi$
$80$	6.62168	+	2.64254i	0.740327	+	0.295445i
$81$	−3.00292	+	5.20121i	−0.333658	+	0.577913i
$82$	2.85291	−	1.78693i	0.315051	−	0.197333i
$83$		−	6.77111i		−	0.743225i	−0.928388	−	0.371613i	$-0.878805\pi$
$83$		−	6.77111i		−	0.743225i	0.928388	−	0.371613i	$-0.121195\pi$
$84$	3.23001	−	2.18871i	0.352423	−	0.238807i
$85$	−8.64243	+	4.98971i	−0.937403	+	0.541210i
$86$	−15.3629	+	0.552885i	−1.65662	+	0.0596191i
$87$	−2.13412	−	3.69640i	−0.228801	−	0.396295i
$88$	2.81666	−	6.38117i	0.300257	−	0.680235i
$89$	−5.89082	+	10.2032i	−0.624426	+	1.08154i	0.364226	+	0.931311i	$0.381334\pi$
$89$	−5.89082	+	10.2032i	−0.624426	+	1.08154i	−0.988652	+	0.150227i	$0.952000\pi$
$90$	−6.68553	+	0.240601i	−0.704717	+	0.0253616i
$91$	−7.25519	−	9.50594i	−0.760550	−	0.996493i
$92$	−4.86211	+	0.350412i	−0.506910	+	0.0365330i
$93$	2.25601	+	1.30251i	0.233937	+	0.135064i
$94$	11.0249	+	5.84696i	1.13713	+	0.603068i
$95$	−2.61558	−	4.53031i	−0.268353	−	0.464800i
$96$	3.27371	−	0.595255i	0.334122	−	0.0607529i
$97$	−3.17980	−	5.50758i	−0.322860	−	0.559210i	0.658217	−	0.752828i	$-0.271311\pi$
$97$	−3.17980	−	5.50758i	−0.322860	−	0.559210i	−0.981077	+	0.193618i	$0.937978\pi$
$98$	−4.79415	+	3.00283i	−0.484282	+	0.303332i
$99$			6.54505i			0.657802i
$100$	2.04542	+	3.01856i	0.204542	+	0.301856i
$101$	−10.0401	−	5.79665i	−0.999027	−	0.576788i	−0.0910665	−	0.995845i	$-0.529028\pi$
$101$	−10.0401	−	5.79665i	−0.999027	−	0.576788i	−0.907960	+	0.419056i	$0.862361\pi$
$102$	−2.18216	+	4.11463i	−0.216066	+	0.407409i
$103$	2.03907			0.200915			0.100458	−	0.994941i	$-0.467969\pi$
$103$	2.03907			0.200915			0.100458	+	0.994941i	$0.467969\pi$
$104$	−2.38676	−	9.91481i	−0.234041	−	0.972227i
$105$	−3.47716			−0.339336
$106$	−0.879256	+	1.65790i	−0.0854009	+	0.161030i
$107$	−10.5701	−	6.10265i	−1.02185	−	0.589965i	−0.107210	−	0.994236i	$-0.534192\pi$
$107$	−10.5701	−	6.10265i	−1.02185	−	0.589965i	−0.914639	+	0.404271i	$0.867525\pi$
$108$	−5.50635	+	3.73119i	−0.529848	+	0.359034i
$109$		−	7.39858i		−	0.708656i	−0.935121	−	0.354328i	$-0.884710\pi$
$109$		−	7.39858i		−	0.708656i	0.935121	−	0.354328i	$-0.115290\pi$
$110$	−5.26810	+	3.29969i	−0.502293	+	0.314613i
$111$	−1.23189	−	2.13369i	−0.116925	−	0.202521i
$112$	−13.1294	+	1.90235i	−1.24061	+	0.179756i
$113$	4.78047	+	8.28002i	0.449709	+	0.778918i	0.998367	−	0.0571285i	$-0.0181945\pi$
$113$	4.78047	+	8.28002i	0.449709	+	0.778918i	−0.548658	+	0.836047i	$0.684861\pi$
$114$	−2.15686	−	1.14388i	−0.202009	−	0.107134i
$115$	3.76226	+	2.17214i	0.350833	+	0.202553i
$116$	1.04323	+	14.4752i	0.0968611	+	1.34399i
$117$	5.80570	+	7.60679i	0.536737	+	0.703248i
$118$	7.34560	−	0.264356i	0.676217	−	0.0243359i
$119$	9.28482	−	16.0818i	0.851138	−	1.47421i
$120$	−2.71280	−	1.19744i	−0.247644	−	0.109310i
$121$	−2.45920	−	4.25945i	−0.223563	−	0.387223i
$122$	2.26577	−	0.0815412i	0.205133	−	0.00738239i
$123$	−1.21255	+	0.700069i	−0.109332	+	0.0631231i
$124$	−4.96871	−	7.33264i	−0.446203	−	0.658490i
$125$		−	12.1614i		−	1.08775i
$126$	10.5499	−	6.60793i	0.939856	−	0.588682i
$127$	−7.87951	+	13.6477i	−0.699193	+	1.21104i	0.269553	+	0.962985i	$0.413124\pi$
$127$	−7.87951	+	13.6477i	−0.699193	+	1.21104i	−0.968747	+	0.248053i	$0.920209\pi$
$128$	−10.8984	−	3.03723i	−0.963292	−	0.268456i
$129$	6.39393			0.562954
$130$	−3.19574	+	8.50797i	−0.280285	+	0.746198i
$131$		−	11.1215i		−	0.971688i	−0.874045	−	0.485844i	$-0.838512\pi$
$131$		−	11.1215i		−	0.971688i	0.874045	−	0.485844i	$-0.161488\pi$
$132$	−1.26621	+	2.61023i	−0.110209	+	0.227191i
$133$	8.42998	+	4.86705i	0.730972	+	0.422027i
$134$	8.67171	+	13.8448i	0.749121	+	1.19601i
$135$	5.92767			0.510173
$136$	12.7819	−	9.34922i	1.09604	−	0.801689i
$137$	−0.0304295	−	0.0527055i	−0.00259977	−	0.00450293i	0.864723	−	0.502250i	$-0.167494\pi$
$137$	−0.0304295	−	0.0527055i	−0.00259977	−	0.00450293i	−0.867322	+	0.497747i	$0.834161\pi$
$138$	2.02620	−	0.0729194i	0.172482	−	0.00620732i
$139$	−13.1191	+	7.57434i	−1.11275	+	0.642447i	−0.939540	−	0.342438i	$-0.888747\pi$
$139$	−13.1191	+	7.57434i	−1.11275	+	0.642447i	−0.173210	+	0.984885i	$0.555414\pi$
$140$	10.6374	+	5.16017i	0.899027	+	0.436114i
$141$	−4.49508	−	2.59523i	−0.378554	−	0.218558i
$142$	−0.515788	−	14.3321i	−0.0432840	−	1.20272i
$143$	8.20596	+	3.42391i	0.686217	+	0.286321i
$144$	10.5063	−	1.52229i	0.875529	−	0.126858i
$145$	6.46678	−	11.2008i	0.537037	−	0.930176i
$146$	15.1950	+	8.05856i	1.25755	+	0.666931i
$147$	2.03763	−	1.17643i	0.168061	−	0.0970299i
$148$	0.602187	+	8.35559i	0.0494994	+	0.686825i
$149$	−0.971793	+	0.561065i	−0.0796123	+	0.0459642i	−0.539278	−	0.842128i	$-0.681303\pi$
$149$	−0.971793	+	0.561065i	−0.0796123	+	0.0459642i	0.459665	+	0.888092i	$0.347969\pi$
$150$	−0.805034	−	1.28527i	−0.0657308	−	0.104942i
$151$	−2.07494			−0.168856			−0.0844281	−	0.996430i	$-0.526906\pi$
$151$	−2.07494			−0.168856			−0.0844281	+	0.996430i	$0.526906\pi$
$152$	4.90081	+	6.70021i	0.397508	+	0.543459i
$153$	−7.42984	+	12.8689i	−0.600667	+	1.04039i
$154$	5.41950	−	10.2189i	0.436715	−	0.823459i
$155$			7.89370i			0.634038i
$156$	0.843755	+	4.15684i	0.0675545	+	0.332813i
$157$			23.8908i			1.90669i	0.301875	+	0.953347i	$0.402387\pi$
$157$			23.8908i			1.90669i	−0.301875	+	0.953347i	$0.597613\pi$
$158$	−9.64616	−	5.11577i	−0.767407	−	0.406989i
$159$	0.390267	−	0.675962i	0.0309502	−	0.0536072i
$160$	6.52207	+	7.68908i	0.515615	+	0.607875i
$161$	−8.08383			−0.637095
$162$	−7.19813	+	4.50857i	−0.565539	+	0.354227i
$163$	19.7876	−	11.4244i	1.54988	−	0.894825i	0.551732	−	0.834022i	$-0.313967\pi$
$163$	19.7876	−	11.4244i	1.54988	−	0.894825i	0.998150	−	0.0608031i	$-0.0193662\pi$
$164$	4.74840	−	0.342217i	0.370788	−	0.0267226i
$165$	2.23907	−	1.29273i	0.174311	−	0.100639i
$166$	4.48654	−	8.45971i	0.348223	−	0.656601i
$167$	−8.93203	+	15.4707i	−0.691181	+	1.19716i	0.280270	+	0.959921i	$0.409576\pi$
$167$	−8.93203	+	15.4707i	−0.691181	+	1.19716i	−0.971451	+	0.237239i	$0.923757\pi$
$168$	5.48576	−	0.594323i	0.423236	−	0.0458530i
$169$	12.5743	−	3.29966i	0.967251	−	0.253820i
$170$	−14.1039	+	0.507575i	−1.08172	+	0.0389292i
$171$	−6.74579	−	3.89468i	−0.515863	−	0.297834i
$172$	−19.5605	−	9.48872i	−1.49147	−	0.723508i
$173$	9.62750	−	5.55844i	0.731965	−	0.422600i	−0.0871756	−	0.996193i	$-0.527784\pi$
$173$	9.62750	−	5.55844i	0.731965	−	0.422600i	0.819141	+	0.573593i	$0.194451\pi$
$174$	−0.217092	−	6.03229i	−0.0164577	−	0.457307i
$175$	3.02335	+	5.23660i	0.228544	+	0.395849i
$176$	7.74726	−	6.10621i	0.583971	−	0.460273i
$177$	−3.05719			−0.229792
$178$	−14.1206	+	8.84445i	−1.05838	+	0.662919i
$179$	20.1700	+	11.6452i	1.50758	+	0.870400i	0.999961	+	0.00881628i	$0.00280635\pi$
$179$	20.1700	+	11.6452i	1.50758	+	0.870400i	0.507616	+	0.861584i	$0.330527\pi$
$180$	−8.51222	−	4.12924i	−0.634463	−	0.307775i
$181$		−	6.40510i		−	0.476088i	−0.971254	−	0.238044i	$-0.923494\pi$
$181$		−	6.40510i		−	0.476088i	0.971254	−	0.238044i	$-0.0765062\pi$
$182$	−2.76586	−	16.6839i	−0.205020	−	1.23669i
$183$	−0.942997			−0.0697084
$184$	−6.30683	−	2.78384i	−0.464945	−	0.205228i
$185$	3.73285	−	6.46549i	0.274445	−	0.475352i
$186$	1.95558	+	3.12217i	0.143390	+	0.228928i
$187$			13.8075i			1.00971i
$188$	9.90010	+	14.6102i	0.722039	+	1.06556i
$189$	−9.55242	+	5.51509i	−0.694836	+	0.401164i
$190$	−0.266068	−	7.39318i	−0.0193026	−	0.536358i
$191$	4.09795	+	7.09786i	0.296517	+	0.513583i	0.975337	−	0.220722i	$-0.0708414\pi$
$191$	4.09795	+	7.09786i	0.296517	+	0.513583i	−0.678819	+	0.734305i	$0.737508\pi$
$192$	4.48454	+	1.42546i	0.323644	+	0.102874i
$193$	8.77012	−	15.1903i	0.631287	−	1.09342i	−0.356002	−	0.934485i	$-0.615860\pi$
$193$	8.77012	−	15.1903i	0.631287	−	1.09342i	0.987289	−	0.158936i	$-0.0508064\pi$
$194$	−0.323464	−	8.98803i	−0.0232233	−	0.645303i
$195$	1.45559	−	3.48857i	0.104237	−	0.249822i
$196$	−7.97941	+	0.575075i	−0.569958	+	0.0410768i
$197$	−3.84294	−	2.21872i	−0.273798	−	0.158078i	0.356814	−	0.934175i	$-0.383863\pi$
$197$	−3.84294	−	2.21872i	−0.273798	−	0.158078i	−0.630612	+	0.776098i	$0.717196\pi$
$198$	−4.33676	+	8.17727i	−0.308200	+	0.581133i
$199$	−6.11231	−	10.5868i	−0.433290	−	0.750480i	0.563864	−	0.825867i	$-0.309314\pi$
$199$	−6.11231	−	10.5868i	−0.433290	−	0.750480i	−0.997154	+	0.0753871i	$0.975981\pi$
$200$	0.555415	+	5.12663i	0.0392738	+	0.362508i
$201$	−3.39733	−	5.88435i	−0.239629	−	0.415050i
$202$	−8.70306	−	13.8948i	−0.612345	−	0.977636i
$203$			24.0667i			1.68915i
$204$	−5.45272	+	3.69484i	−0.381766	+	0.258691i
$205$	−3.67428	−	2.12134i	−0.256623	−	0.148161i
$206$	2.54758	+	1.35109i	0.177498	+	0.0941348i
$207$	6.46879			0.449612
$208$	3.58759	−	13.9689i	0.248754	−	0.968567i
$209$	−7.23782			−0.500651
$210$	−4.34431	−	2.30397i	−0.299786	−	0.158989i
$211$	−9.32352	−	5.38294i	−0.641858	−	0.370577i	0.143472	−	0.989654i	$-0.454173\pi$
$211$	−9.32352	−	5.38294i	−0.641858	−	0.370577i	−0.785330	+	0.619078i	$0.787507\pi$
$212$	−2.19706	+	1.48876i	−0.150894	+	0.102248i
$213$			5.96492i			0.408709i
$214$	−9.16248	−	14.6283i	−0.626334	−	0.999970i
$215$	9.68742	+	16.7791i	0.660677	+	1.14433i
$216$	−9.35183	+	1.01317i	−0.636311	+	0.0689374i
$217$	−7.34428	−	12.7207i	−0.498562	−	0.863536i
$218$	4.90231	−	9.24367i	0.332026	−	0.626060i
$219$	−6.19533	−	3.57687i	−0.418641	−	0.241703i
$220$	−8.76825	+	0.631927i	−0.591155	+	0.0426045i
$221$	12.2478	+	16.0474i	0.823875	+	1.07946i
$222$	−0.125313	−	3.48205i	−0.00841045	−	0.233700i
$223$	−3.59038	+	6.21873i	−0.240430	+	0.416437i	−0.960837	−	0.277115i	$-0.910622\pi$
$223$	−3.59038	+	6.21873i	−0.240430	+	0.416437i	0.720407	+	0.693552i	$0.243955\pi$
$224$	−17.6642	−	6.32281i	−1.18024	−	0.422460i
$225$	−2.41933	−	4.19040i	−0.161288	−	0.279360i
$226$	0.486290	+	13.5125i	0.0323475	+	0.898836i
$227$	−0.276361	+	0.159557i	−0.0183427	+	0.0105902i	−0.509143	−	0.860682i	$-0.670038\pi$
$227$	−0.276361	+	0.159557i	−0.0183427	+	0.0105902i	0.490801	+	0.871272i	$0.336704\pi$
$228$	−1.93682	−	2.85828i	−0.128269	−	0.189294i
$229$		−	9.18620i		−	0.607041i	−0.952825	−	0.303521i	$-0.901838\pi$
$229$		−	9.18620i		−	0.607041i	0.952825	−	0.303521i	$-0.0981622\pi$
$230$	3.26125	+	5.20672i	0.215040	+	0.343321i
$231$	−2.40550	+	4.16645i	−0.158270	+	0.274132i
$232$	−8.28790	+	18.7763i	−0.544127	+	1.23273i
$233$	−21.0081			−1.37628			−0.688142	−	0.725576i	$-0.741573\pi$
$233$	−21.0081			−1.37628			−0.688142	+	0.725576i	$0.741573\pi$
$234$	2.21328	+	13.3507i	0.144687	+	0.872760i
$235$		−	15.7281i		−	1.02599i
$236$	9.35264	+	4.53692i	0.608805	+	0.295329i
$237$	3.93294	+	2.27069i	0.255472	+	0.147497i
$238$	22.2561	−	13.9402i	1.44265	−	0.903608i
$239$	−14.3918			−0.930929			−0.465464	−	0.885067i	$-0.654113\pi$
$239$	−14.3918			−0.930929			−0.465464	+	0.885067i	$0.654113\pi$
$240$	−2.59591	−	3.29356i	−0.167565	−	0.212599i
$241$	1.04373	+	1.80780i	0.0672328	+	0.116451i	0.897682	−	0.440643i	$-0.145250\pi$
$241$	1.04373	+	1.80780i	0.0672328	+	0.116451i	−0.830449	+	0.557094i	$0.811916\pi$
$242$	−0.250160	−	6.95116i	−0.0160809	−	0.446837i
$243$	11.6998	−	6.75491i	0.750545	−	0.433328i
$244$	2.88485	+	1.39943i	0.184683	+	0.0895891i
$245$	6.17441	+	3.56480i	0.394468	+	0.227746i
$246$	−1.97881	+	0.0712141i	−0.126165	+	0.00454044i
$247$	−8.41195	+	6.42022i	−0.535239	+	0.408509i
$248$	−1.34921	−	12.4535i	−0.0856748	−	0.790801i
$249$	−1.99140	+	3.44920i	−0.126200	+	0.218584i
$250$	8.05816	−	15.1942i	0.509642	−	0.960968i
$251$	−6.27541	+	3.62311i	−0.396100	+	0.228688i	−0.684800	−	0.728731i	$-0.740110\pi$
$251$	−6.27541	+	3.62311i	−0.396100	+	0.228688i	0.288700	+	0.957420i	$0.406777\pi$
$252$	17.5592	−	1.26549i	1.10613	−	0.0797186i
$253$	5.20547	−	3.00538i	0.327265	−	0.188947i
$254$	−18.8875	+	11.8303i	−1.18511	+	0.742296i
$255$	5.86994			0.367590
$256$	−11.6038	−	11.0160i	−0.725239	−	0.688498i
$257$	9.08570	−	15.7369i	0.566750	−	0.981640i	−0.430134	−	0.902765i	$-0.641534\pi$
$257$	9.08570	−	15.7369i	0.566750	−	0.981640i	0.996885	−	0.0788752i	$-0.0251328\pi$
$258$	7.98847	+	4.23663i	0.497340	+	0.263761i
$259$			13.8922i			0.863216i
$260$	−9.63010	+	8.51221i	−0.597233	+	0.527905i
$261$		−	19.2585i		−	1.19207i
$262$	7.36911	−	13.8950i	0.455265	−	0.858436i
$263$	3.91017	−	6.77261i	0.241111	−	0.417617i	−0.719920	−	0.694057i	$-0.755821\pi$
$263$	3.91017	−	6.77261i	0.241111	−	0.417617i	0.961031	+	0.276440i	$0.0891548\pi$
$264$	−3.31152	+	2.42218i	−0.203810	+	0.149075i
$265$	2.36517			0.145291
$266$	7.30737	+	11.6665i	0.448043	+	0.715321i
$267$	6.00157	−	3.46501i	0.367290	−	0.212055i
$268$	1.66073	+	23.0433i	0.101445	+	1.40759i
$269$	−10.5009	+	6.06272i	−0.640253	+	0.369650i	−0.784712	−	0.619860i	$-0.787189\pi$
$269$	−10.5009	+	6.06272i	−0.640253	+	0.369650i	0.144459	+	0.989511i	$0.453856\pi$
$270$	7.40594	+	3.92768i	0.450711	+	0.239031i
$271$	2.50994	−	4.34734i	0.152468	−	0.264082i	−0.779666	−	0.626195i	$-0.784611\pi$
$271$	2.50994	−	4.34734i	0.152468	−	0.264082i	0.932134	+	0.362113i	$0.117945\pi$
$272$	22.1643	−	3.21144i	1.34391	−	0.194722i
$273$	0.900075	+	6.97610i	0.0544750	+	0.422213i
$274$	−0.00309542	−	0.0860120i	−0.000187001	−	0.00519617i
$275$	−3.89369	−	2.24802i	−0.234798	−	0.135561i
$276$	2.57982	+	1.25146i	0.155287	+	0.0753289i
$277$	24.9286	−	14.3925i	1.49781	−	0.864762i	0.497816	−	0.867283i	$-0.334136\pi$
$277$	24.9286	−	14.3925i	1.49781	−	0.864762i	0.999997	+	0.00252032i	$0.000802244\pi$
$278$	−21.4096	+	0.770495i	−1.28406	+	0.0462112i
$279$	5.87700	+	10.1793i	0.351847	+	0.609416i
$280$	9.87110	+	13.4954i	0.589911	+	0.806505i
$281$	13.5594			0.808884			0.404442	−	0.914564i	$-0.367466\pi$
$281$	13.5594			0.808884			0.404442	+	0.914564i	$0.367466\pi$
$282$	−3.89647	−	6.22089i	−0.232031	−	0.370448i
$283$	−18.4454	−	10.6494i	−1.09646	−	0.633043i	−0.161173	−	0.986926i	$-0.551528\pi$
$283$	−18.4454	−	10.6494i	−1.09646	−	0.633043i	−0.935290	+	0.353883i	$0.884861\pi$
$284$	8.85206	−	18.2481i	0.525273	−	1.08282i
$285$			3.07699i			0.182265i
$286$	7.98371	+	9.71505i	0.472086	+	0.574463i
$287$	7.89478			0.466014
$288$	14.1351	+	5.05960i	0.832921	+	0.298140i
$289$	−7.17410	+	12.4259i	−0.422006	+	0.730935i
$290$	15.5012	−	9.70920i	0.910259	−	0.570144i
$291$			3.74075i			0.219287i
$292$	13.6448	+	20.1365i	0.798500	+	1.17840i
$293$	−23.7670	+	13.7219i	−1.38848	+	0.801640i	−0.993144	−	0.116896i	$-0.962706\pi$
$293$	−23.7670	+	13.7219i	−1.38848	+	0.801640i	−0.395337	+	0.918536i	$0.629372\pi$
$294$	3.32528	−	0.119671i	0.193934	−	0.00697936i
$295$	−4.63193	−	8.02274i	−0.269681	−	0.467102i
$296$	−4.78406	+	10.8383i	−0.278068	+	0.629966i
$297$	4.10076	−	7.10273i	0.237950	−	0.412142i
$298$	−1.58590	+	0.0570740i	−0.0918689	+	0.00330621i
$299$	3.38402	−	8.11036i	0.195703	−	0.469034i
$300$	−0.154173	−	2.13922i	−0.00890118	−	0.123508i
$301$	−31.2225	−	18.0263i	−1.79963	−	1.03902i
$302$	−2.59240	−	1.37486i	−0.149176	−	0.0791142i
$303$	3.40962	+	5.90563i	0.195877	+	0.339270i
$304$	1.68342	+	11.6184i	0.0965508	+	0.666362i
$305$	−1.42873	−	2.47464i	−0.0818090	−	0.141697i
$306$	−17.8097	+	11.1551i	−1.01811	+	0.637696i
$307$			4.96158i			0.283173i	0.989926	+	0.141586i	$0.0452203\pi$
$307$			4.96158i			0.283173i	−0.989926	+	0.141586i	$0.954780\pi$
$308$	13.5421	−	9.17631i	0.771631	−	0.522869i
$309$	−1.03870	−	0.599694i	−0.0590896	−	0.0341154i
$310$	−5.23038	+	9.86226i	−0.297066	+	0.560139i
$311$	1.03478			0.0586768			0.0293384	−	0.999570i	$-0.490660\pi$
$311$	1.03478			0.0586768			0.0293384	+	0.999570i	$0.490660\pi$
$312$	−1.70015	+	5.75256i	−0.0962521	+	0.325674i
$313$	6.17484			0.349023			0.174511	−	0.984655i	$-0.444165\pi$
$313$	6.17484			0.349023			0.174511	+	0.984655i	$0.444165\pi$
$314$	−15.8301	+	29.8488i	−0.893344	+	1.68447i
$315$	−13.5872	−	7.84458i	−0.765552	−	0.441992i
$316$	−8.66203	−	12.7831i	−0.487278	−	0.719106i
$317$			11.6534i			0.654523i	0.944934	+	0.327261i	$0.106126\pi$
$317$			11.6534i			0.654523i	−0.944934	+	0.327261i	$0.893874\pi$
$318$	0.935486	−	0.585944i	0.0524594	−	0.0328581i
$319$	−8.94744	−	15.4974i	−0.500961	−	0.867689i
$320$	3.05377	+	13.9281i	0.170711	+	0.778607i
$321$	3.58960	+	6.21738i	0.200352	+	0.347020i
$322$	−10.0998	−	5.35636i	−0.562840	−	0.298498i
$323$	−14.2310	−	8.21628i	−0.791834	−	0.457166i
$324$	−11.9806	+	0.863442i	−0.665590	+	0.0479690i
$325$	−6.51940	+	0.841151i	−0.361631	+	0.0466587i
$326$	32.2921	−	1.16214i	1.78849	−	0.0643647i
$327$	−2.17594	+	3.76884i	−0.120330	+	0.208417i
$328$	6.15933	+	2.71874i	0.340092	+	0.150117i
$329$	14.6334	+	25.3458i	0.806766	+	1.39736i
$330$	3.65402	−	0.131502i	0.201147	−	0.00723893i
$331$	26.0340	−	15.0307i	1.43096	−	0.826163i	0.433762	−	0.901028i	$-0.357186\pi$
$331$	26.0340	−	15.0307i	1.43096	−	0.826163i	0.997194	+	0.0748651i	$0.0238526\pi$
$332$	11.2108	−	7.59663i	0.615274	−	0.416919i
$333$		−	11.1167i		−	0.609191i
$334$	−21.4105	+	13.4105i	−1.17153	+	0.733790i
$335$	10.2946	−	17.8307i	0.562453	−	0.974197i
$336$	7.24762	+	2.89234i	0.395390	+	0.157790i
$337$	17.7875			0.968946			0.484473	−	0.874806i	$-0.339011\pi$
$337$	17.7875			0.968946			0.484473	+	0.874806i	$0.339011\pi$
$338$	17.8964	+	4.20918i	0.973438	+	0.228949i
$339$		−	5.62379i		−	0.305442i
$340$	−17.9575	−	8.71110i	−0.973882	−	0.472426i
$341$	9.45849	+	5.46086i	0.512206	+	0.295722i
$342$	−5.84746	−	9.33572i	−0.316194	−	0.504818i
$343$	9.94972			0.537234
$344$	−18.1513	−	24.8159i	−0.978654	−	1.33798i
$345$	−1.27767	−	2.21298i	−0.0687872	−	0.119143i
$346$	15.7115	−	0.565429i	0.844654	−	0.0303976i
$347$	1.27962	−	0.738791i	0.0686938	−	0.0396604i	−0.465260	−	0.885174i	$-0.654039\pi$
$347$	1.27962	−	0.738791i	0.0686938	−	0.0396604i	0.533954	+	0.845514i	$0.320706\pi$
$348$	3.72577	−	7.68049i	0.199722	−	0.411717i
$349$	12.1744	+	7.02888i	0.651679	+	0.376247i	0.789099	−	0.614266i	$-0.210548\pi$
$349$	12.1744	+	7.02888i	0.651679	+	0.376247i	−0.137420	+	0.990513i	$0.543881\pi$
$350$	0.307548	+	8.54579i	0.0164392	+	0.456792i
$351$	−1.53440	−	11.8925i	−0.0819002	−	0.634773i
$352$	13.7253	−	2.49565i	0.731560	−	0.133019i
$353$	−7.52945	+	13.0414i	−0.400752	+	0.694123i	−0.993817	−	0.111032i	$-0.964585\pi$
$353$	−7.52945	+	13.0414i	−0.400752	+	0.694123i	0.593065	+	0.805155i	$0.297918\pi$
$354$	−3.81960	−	2.02570i	−0.203009	−	0.107664i
$355$	−15.6533	+	9.03743i	−0.830790	+	0.479657i
$356$	−23.5023	+	1.69381i	−1.24562	+	0.0897718i
$357$	−9.45938	+	5.46138i	−0.500644	+	0.289047i
$358$	17.4840	+	27.9139i	0.924057	+	1.47530i
$359$	−0.213296			−0.0112573			−0.00562866	−	0.999984i	$-0.501792\pi$
$359$	−0.213296			−0.0112573			−0.00562866	+	0.999984i	$0.501792\pi$
$360$	−7.89899	−	10.7992i	−0.416313	−	0.569169i
$361$	−5.19307	+	8.99467i	−0.273320	+	0.473404i
$362$	4.24403	−	8.00243i	0.223061	−	0.420598i
$363$			2.89302i			0.151844i
$364$	7.59913	−	22.6772i	0.398302	−	1.18861i
$365$		−	21.6772i		−	1.13464i
$366$	−1.17817	−	0.624831i	−0.0615837	−	0.0326605i
$367$	−5.55712	+	9.62522i	−0.290079	+	0.502432i	−0.973828	−	0.227285i	$-0.927015\pi$
$367$	−5.55712	+	9.62522i	−0.290079	+	0.502432i	0.683749	+	0.729717i	$0.260348\pi$
$368$	−6.03507	−	7.65700i	−0.314600	−	0.399149i
$369$	−6.31751			−0.328876
$370$	8.94781	−	5.60448i	0.465174	−	0.291363i
$371$	−3.81146	+	2.20055i	−0.197881	+	0.114247i
$372$	0.374515	+	5.19655i	0.0194177	+	0.269429i
$373$	−6.29802	+	3.63616i	−0.326099	+	0.188273i	−0.654108	−	0.756401i	$-0.726956\pi$
$373$	−6.29802	+	3.63616i	−0.326099	+	0.188273i	0.328009	+	0.944675i	$0.393622\pi$
$374$	−9.14888	+	17.2509i	−0.473077	+	0.892022i
$375$	−3.57669	+	6.19502i	−0.184700	+	0.319909i
$376$	2.68828	+	24.8136i	0.138638	+	1.27966i
$377$	−24.1457	−	10.0747i	−1.24357	−	0.518874i
$378$	−15.5889	+	0.561019i	−0.801809	+	0.0288557i
$379$	8.29446	+	4.78881i	0.426058	+	0.245984i	0.697666	−	0.716423i	$-0.254222\pi$
$379$	8.29446	+	4.78881i	0.426058	+	0.245984i	−0.271608	+	0.962408i	$0.587555\pi$
$380$	4.56631	−	9.41322i	0.234247	−	0.482888i
$381$	8.02765	−	4.63476i	0.411269	−	0.237446i
$382$	0.416862	+	11.5833i	0.0213285	+	0.592651i
$383$	−13.7992	−	23.9008i	−0.705104	−	1.22128i	−0.966654	−	0.256086i	$-0.917567\pi$
$383$	−13.7992	−	23.9008i	−0.705104	−	1.22128i	0.261550	−	0.965190i	$-0.415766\pi$
$384$	4.65839	+	4.75241i	0.237723	+	0.242520i
$385$	−14.5783			−0.742976
$386$	21.0224	−	13.1674i	1.07001	−	0.670204i
$387$	24.9847	+	14.4249i	1.27004	+	0.733259i
$388$	5.55135	−	11.4438i	0.281827	−	0.580972i
$389$		−	3.20160i		−	0.162328i	−0.996701	−	0.0811638i	$-0.974136\pi$
$389$		−	3.20160i		−	0.162328i	0.996701	−	0.0811638i	$-0.0258637\pi$
$390$	4.13012	−	3.39408i	0.209137	−	0.171866i
$391$	13.6467			0.690141
$392$	−10.3504	−	4.56868i	−0.522774	−	0.230753i
$393$	−3.27085	+	5.66528i	−0.164993	+	0.285776i
$394$	−3.33118	−	5.31838i	−0.167822	−	0.267936i
$395$			13.7612i			0.692403i
$396$	−10.8365	+	7.34301i	−0.544557	+	0.369000i
$397$	2.89755	−	1.67290i	0.145424	−	0.0839605i	−0.425523	−	0.904948i	$-0.639910\pi$
$397$	2.89755	−	1.67290i	0.145424	−	0.0839605i	0.570946	+	0.820987i	$0.306576\pi$
$398$	−0.621771	−	17.2770i	−0.0311666	−	0.866020i
$399$	−2.86282	−	4.95856i	−0.143320	−	0.248238i
$400$	−2.70299	+	6.77315i	−0.135149	+	0.338657i
$401$	−3.35071	+	5.80359i	−0.167326	+	0.289818i	−0.937479	−	0.348042i	$-0.886847\pi$
$401$	−3.35071	+	5.80359i	−0.167326	+	0.289818i	0.770153	+	0.637860i	$0.220180\pi$
$402$	−0.345592	−	9.60289i	−0.0172365	−	0.478949i
$403$	15.8368	−	2.04331i	0.788889	−	0.101785i
$404$	−1.66673	−	23.1266i	−0.0829231	−	1.15059i
$405$	9.27050	+	5.35233i	0.460655	+	0.265959i
$406$	−15.9466	+	30.0686i	−0.791419	+	1.49228i
$407$	−5.16477	−	8.94565i	−0.256008	−	0.443419i
$408$	−9.26074	+	1.00330i	−0.458475	+	0.0496708i
$409$	10.5468	+	18.2676i	0.521506	+	0.903274i	0.999687	+	0.0250132i	$0.00796277\pi$
$409$	10.5468	+	18.2676i	0.521506	+	0.903274i	−0.478182	+	0.878261i	$0.658704\pi$
$410$	−3.18497	−	5.08495i	−0.157295	−	0.251128i
$411$			0.0357976i			0.00176576i
$412$	2.28767	+	3.37605i	0.112705	+	0.166326i
$413$	14.9287	+	8.61908i	0.734592	+	0.424117i
$414$	8.08201	+	4.28623i	0.397209	+	0.210657i
$415$	−12.0686			−0.592426
$416$	13.7381	−	15.0753i	0.673564	−	0.739129i
$417$	8.91052			0.436350
$418$	−9.04282	−	4.79579i	−0.442299	−	0.234570i
$419$	−26.6905	−	15.4098i	−1.30392	−	0.752817i	−0.322843	−	0.946453i	$-0.604639\pi$
$419$	−26.6905	−	15.4098i	−1.30392	−	0.752817i	−0.981073	+	0.193636i	$0.937972\pi$
$420$	−3.90109	−	5.75709i	−0.190354	−	0.280917i
$421$		−	5.77781i		−	0.281593i	−0.990039	−	0.140796i	$-0.955034\pi$
$421$		−	5.77781i		−	0.281593i	0.990039	−	0.140796i	$-0.0449663\pi$
$422$	−8.08191	−	12.9031i	−0.393421	−	0.628115i
$423$	−11.7099	−	20.2821i	−0.569353	−	0.986148i
$424$	−3.73142	+	0.404259i	−0.181214	+	0.0196325i
$425$	−5.10384	−	8.84011i	−0.247573	−	0.428809i
$426$	−3.95236	+	7.45247i	−0.191493	+	0.361073i
$427$	4.60479	+	2.65858i	0.222842	+	0.128658i
$428$	−1.75472	−	24.3474i	−0.0848174	−	1.17688i
$429$	−3.17314	−	4.15753i	−0.153201	−	0.200727i
$430$	0.985447	+	27.3824i	0.0475225	+	1.32050i
$431$	−3.25712	+	5.64150i	−0.156890	+	0.271741i	−0.933746	−	0.357937i	$-0.883480\pi$
$431$	−3.25712	+	5.64150i	−0.156890	+	0.271741i	0.776856	+	0.629679i	$0.216813\pi$
$432$	−12.3553	−	4.93070i	−0.594447	−	0.237228i
$433$	0.570484	+	0.988107i	0.0274157	+	0.0474854i	0.879408	−	0.476069i	$-0.157939\pi$
$433$	0.570484	+	0.988107i	0.0274157	+	0.0474854i	−0.851992	+	0.523555i	$0.824606\pi$
$434$	−0.747093	−	20.7593i	−0.0358616	−	0.996480i
$435$	−6.58836	+	3.80379i	−0.315888	+	0.182378i
$436$	12.2497	−	8.30061i	0.586656	−	0.397527i
$437$			7.15350i			0.342198i
$438$	−5.37030	−	8.57392i	−0.256603	−	0.409678i
$439$	11.9751	−	20.7415i	0.571540	−	0.989936i	−0.424868	−	0.905255i	$-0.639680\pi$
$439$	11.9751	−	20.7415i	0.571540	−	0.989936i	0.996408	−	0.0846810i	$-0.0269871\pi$
$440$	−11.3736	−	5.02034i	−0.542216	−	0.239335i
$441$	10.6162			0.505534
$442$	4.66917	+	28.1647i	0.222090	+	1.33966i
$443$			24.5182i			1.16489i	0.812868	+	0.582447i	$0.197905\pi$
$443$			24.5182i			1.16489i	−0.812868	+	0.582447i	$0.802095\pi$
$444$	2.15064	−	4.43344i	0.102065	−	0.210402i
$445$	18.1859	+	10.4996i	0.862095	+	0.497731i
$446$	−8.60630	+	5.39058i	−0.407520	+	0.255251i
$447$	0.660042			0.0312189
$448$	−17.8799	−	19.6039i	−0.844744	−	0.926199i
$449$	9.86244	+	17.0822i	0.465437	+	0.806161i	0.999221	−	0.0394599i	$-0.0125637\pi$
$449$	9.86244	+	17.0822i	0.465437	+	0.806161i	−0.533784	+	0.845621i	$0.679230\pi$
$450$	−0.246104	−	6.83846i	−0.0116015	−	0.322368i
$451$	−5.08373	+	2.93509i	−0.239383	+	0.138208i
$452$	−8.34581	+	17.2045i	−0.392554	+	0.809230i
$453$	1.05697	+	0.610244i	0.0496610	+	0.0286718i
$454$	−0.451004	+	0.0162309i	−0.0211667	+	0.000761752i
$455$	−16.9431	+	12.9315i	−0.794307	+	0.606236i
$456$	−0.525925	−	4.85443i	−0.0246287	−	0.227330i
$457$	−5.33778	+	9.24531i	−0.249691	+	0.432477i	−0.963440	−	0.267924i	$-0.913662\pi$
$457$	−5.33778	+	9.24531i	−0.249691	+	0.432477i	0.713749	+	0.700401i	$0.246996\pi$
$458$	6.08679	−	11.4771i	0.284417	−	0.536289i
$459$	16.1258	−	9.31026i	0.752690	−	0.434566i
$460$	0.624565	+	8.66610i	0.0291205	+	0.404059i
$461$	−22.4467	+	12.9596i	−1.04545	+	0.603590i	−0.921372	−	0.388683i	$-0.872930\pi$
$461$	−22.4467	+	12.9596i	−1.04545	+	0.603590i	−0.124077	+	0.992273i	$0.539597\pi$
$462$	−5.76608	+	3.61160i	−0.268262	+	0.168027i
$463$	−20.4817			−0.951867			−0.475933	−	0.879481i	$-0.657890\pi$
$463$	−20.4817			−0.951867			−0.475933	+	0.879481i	$0.657890\pi$
$464$	−22.7960	+	17.9673i	−1.05828	+	0.834109i
$465$	2.32156	−	4.02105i	0.107660	−	0.186472i
$466$	−26.2471	−	13.9200i	−1.21588	−	0.644830i
$467$			2.02585i			0.0937453i	0.998901	+	0.0468726i	$0.0149255\pi$
$467$			2.02585i			0.0937453i	−0.998901	+	0.0468726i	$0.985075\pi$
$468$	−6.08093	+	18.1466i	−0.281091	+	0.838828i
$469$			38.3122i			1.76909i
$470$	10.4215	−	19.6505i	0.480707	−	0.906408i
$471$	7.02635	−	12.1700i	0.323757	−	0.560763i
$472$	8.67886	+	11.8654i	0.399477	+	0.546151i
$473$	26.8070			1.23259
$474$	3.40919	+	5.44293i	0.156589	+	0.250002i
$475$	4.63394	−	2.67541i	0.212620	−	0.122756i
$476$	37.0432	−	2.66970i	1.69787	−	0.122366i
$477$	3.04998	−	1.76091i	0.139649	−	0.0806264i
$478$	−17.9809	−	9.53603i	−0.822427	−	0.436168i
$479$	9.72335	−	16.8413i	0.444271	−	0.769500i	−0.553730	−	0.832696i	$-0.686796\pi$
$479$	9.72335	−	16.8413i	0.444271	−	0.769500i	0.998001	+	0.0631961i	$0.0201294\pi$
$480$	−1.06097	−	5.83498i	−0.0484263	−	0.266329i
$481$	−13.9377	−	5.81547i	−0.635506	−	0.265163i
$482$	0.106173	+	2.95021i	0.00483605	+	0.134379i
$483$	4.11791	+	2.37747i	0.187371	+	0.108179i
$484$	4.29330	−	8.85042i	0.195150	−	0.402292i
$485$	−9.81657	+	5.66760i	−0.445748	+	0.257352i
$486$	19.0934	−	0.687139i	0.866095	−	0.0311693i
$487$	14.9615	+	25.9141i	0.677971	+	1.17428i	0.975591	+	0.219596i	$0.0704740\pi$
$487$	14.9615	+	25.9141i	0.677971	+	1.17428i	−0.297620	+	0.954685i	$0.596193\pi$
$488$	2.67702	+	3.65992i	0.121183	+	0.165677i
$489$	−13.4397			−0.607765
$490$	5.35216	+	8.54497i	0.241786	+	0.386022i
$491$	11.5127	+	6.64683i	0.519559	+	0.299967i	0.736754	−	0.676161i	$-0.236358\pi$
$491$	11.5127	+	6.64683i	0.519559	+	0.299967i	−0.217195	+	0.976128i	$0.569691\pi$
$492$	−2.51948	−	1.22219i	−0.113587	−	0.0551006i
$493$		−	40.6280i		−	1.82979i
$494$	−14.7638	+	2.44755i	−0.664255	+	0.110121i
$495$	11.6657			0.524335
$496$	6.56606	−	16.4532i	0.294825	−	0.738773i
$497$	16.8168	−	29.1276i	0.754337	−	1.30655i
$498$	−4.77347	+	2.98987i	−0.213904	+	0.133979i
$499$			4.06334i			0.181900i	0.995855	+	0.0909501i	$0.0289904\pi$
$499$			4.06334i			0.181900i	−0.995855	+	0.0909501i	$0.971010\pi$
$500$	20.1355	−	13.6441i	0.900485	−	0.610182i
$501$	9.09995	−	5.25386i	0.406556	−	0.234725i
$502$	−10.2411	+	0.368558i	−0.457081	+	0.0164496i
$503$	−0.391329	−	0.677801i	−0.0174485	−	0.0302217i	0.857169	−	0.515035i	$-0.172221\pi$
$503$	−0.391329	−	0.677801i	−0.0174485	−	0.0302217i	−0.874618	+	0.484813i	$0.838888\pi$
$504$	22.7768	+	10.0537i	1.01456	+	0.447827i
$505$	−10.3318	+	17.8952i	−0.459759	+	0.796326i
$506$	8.49499	−	0.305720i	0.377649	−	0.0135909i
$507$	−7.37577	−	2.01727i	−0.327570	−	0.0895902i
$508$	−31.4365	+	2.26563i	−1.39477	+	0.100521i
$509$	16.5487	+	9.55438i	0.733507	+	0.423491i	0.819704	−	0.572788i	$-0.194138\pi$
$509$	16.5487	+	9.55438i	0.733507	+	0.423491i	−0.0861967	+	0.996278i	$0.527471\pi$
$510$	7.33380	+	3.88943i	0.324746	+	0.172227i
$511$	20.1685	+	34.9328i	0.892200	+	1.54534i
$512$	−7.19843	−	21.4519i	−0.318129	−	0.948048i
$513$	4.88039	+	8.45308i	0.215474	+	0.373212i
$514$	21.7788	−	13.6412i	0.960622	−	0.601688i
$515$		−	3.63438i		−	0.160150i
$516$	7.17347	+	10.5863i	0.315794	+	0.466038i
$517$	−18.8459	−	10.8807i	−0.828844	−	0.478533i
$518$	−9.20496	+	17.3566i	−0.404443	+	0.762606i
$519$	−6.53900			−0.287030
$520$	−17.6719	+	4.25410i	−0.774964	+	0.186555i
$521$	−3.23410			−0.141688			−0.0708441	−	0.997487i	$-0.522569\pi$
$521$	−3.23410			−0.141688			−0.0708441	+	0.997487i	$0.522569\pi$
$522$	12.7607	−	24.0613i	0.558522	−	1.05313i
$523$	16.6431	+	9.60888i	0.727750	+	0.420167i	0.817599	−	0.575789i	$-0.195305\pi$
$523$	16.6431	+	9.60888i	0.727750	+	0.420167i	−0.0898482	+	0.995955i	$0.528638\pi$
$524$	18.4137	−	12.4774i	0.804406	−	0.545078i
$525$		−	3.55670i		−	0.155227i
$526$	9.37283	−	5.87070i	0.408675	−	0.255975i
$527$	12.3982	+	21.4743i	0.540074	+	0.935435i
$528$	−5.74230	+	0.832016i	−0.249902	+	0.0362088i
$529$	8.52964	+	14.7738i	0.370854	+	0.642337i
$530$	2.95500	+	1.56716i	0.128357	+	0.0680732i
$531$	−11.9461	−	6.89710i	−0.518418	−	0.299309i
$532$	1.39944	+	19.4179i	0.0606735	+	0.841871i
$533$	−3.30487	+	7.92068i	−0.143150	+	0.343083i
$534$	9.79419	−	0.352476i	0.423836	−	0.0152531i
$535$	−10.8772	+	18.8399i	−0.470262	+	0.814518i
$536$	−13.1936	+	29.8903i	−0.569878	+	1.29107i
$537$	−6.84974	−	11.8641i	−0.295588	−	0.511973i
$538$	−17.1369	+	0.616726i	−0.738823	+	0.0265890i
$539$	8.54291	−	4.93225i	0.367969	−	0.212447i
$540$	6.65037	+	9.81437i	0.286186	+	0.422343i
$541$			17.5473i			0.754417i	0.926128	+	0.377208i	$0.123116\pi$
$541$			17.5473i			0.754417i	−0.926128	+	0.377208i	$0.876884\pi$
$542$	6.01643	−	3.76841i	0.258428	−	0.161867i
$543$	−1.88376	+	3.26276i	−0.0808397	+	0.140018i
$544$	29.8197	+	10.6738i	1.27851	+	0.457635i
$545$	−13.1870			−0.564871
$546$	−3.49783	+	9.31221i	−0.149693	+	0.398526i
$547$		−	10.8081i		−	0.462121i	−0.972939	−	0.231061i	$-0.925780\pi$
$547$		−	10.8081i		−	0.462121i	0.972939	−	0.231061i	$-0.0742196\pi$
$548$	0.0531243	−	0.109513i	0.00226936	−	0.00467816i
$549$	−3.68482	−	2.12743i	−0.157264	−	0.0907965i
$550$	−3.37517	−	5.38860i	−0.143918	−	0.229771i
$551$	21.2970			0.907283
$552$	2.39396	+	3.27294i	0.101894	+	0.139306i
$553$	−12.8034	−	22.1762i	−0.544457	−	0.943027i
$554$	40.6818	−	1.46407i	1.72841	−	0.0622024i
$555$	−3.80303	+	2.19568i	−0.161430	+	0.0932015i
$556$	−27.2593	−	13.2234i	−1.15605	−	0.560797i
$557$	−8.61540	−	4.97411i	−0.365046	−	0.210760i	0.306246	−	0.951952i	$-0.400927\pi$
$557$	−8.61540	−	4.97411i	−0.365046	−	0.210760i	−0.671292	+	0.741193i	$0.734260\pi$
$558$	0.597834	+	16.6119i	0.0253083	+	0.703238i
$559$	31.1557	−	23.7788i	1.31774	−	1.00574i
$560$	3.39071	+	23.4015i	0.143283	+	0.988896i
$561$	4.06082	−	7.03355i	0.171448	−	0.296957i
$562$	16.9409	+	8.98446i	0.714607	+	0.378986i
$563$	−7.22674	+	4.17236i	−0.304571	+	0.175844i	−0.644494	−	0.764609i	$-0.722932\pi$
$563$	−7.22674	+	4.17236i	−0.304571	+	0.175844i	0.339924	+	0.940453i	$0.389599\pi$
$564$	−0.746218	−	10.3541i	−0.0314214	−	0.435985i
$565$	14.7581	−	8.52058i	0.620877	−	0.358464i
$566$	−15.9890	−	25.5272i	−0.672068	−	1.07299i
$567$	−19.9192			−0.836527
$568$	23.1508	−	16.9334i	0.971386	−	0.710511i
$569$	17.5793	−	30.4482i	0.736961	−	1.27645i	−0.216896	−	0.976195i	$-0.569593\pi$
$569$	17.5793	−	30.4482i	0.736961	−	1.27645i	0.953858	−	0.300260i	$-0.0970733\pi$
$570$	−2.03882	+	3.84434i	−0.0853966	+	0.161022i
$571$		−	19.3907i		−	0.811474i	−0.913990	−	0.405737i	$-0.867015\pi$
$571$		−	19.3907i		−	0.811474i	0.913990	−	0.405737i	$-0.132985\pi$
$572$	3.53751	+	17.4278i	0.147911	+	0.728695i
$573$		−	4.82087i		−	0.201395i
$574$	9.86360	+	5.23109i	0.411699	+	0.218341i
$575$	−2.22183	+	3.84832i	−0.0926567	+	0.160486i
$576$	14.3077	+	15.6873i	0.596154	+	0.653639i
$577$	5.44279			0.226586			0.113293	−	0.993562i	$-0.463860\pi$
$577$	5.44279			0.226586			0.113293	+	0.993562i	$0.463860\pi$
$578$	−17.1966	+	10.7711i	−0.715285	+	0.448021i
$579$	−8.93500	+	5.15863i	−0.371326	+	0.214385i
$580$	25.8002	−	1.85942i	1.07130	−	0.0772082i
$581$	19.4486	−	11.2286i	0.806863	−	0.465842i
$582$	−2.47863	+	4.67363i	−0.102742	+	0.193728i
$583$	1.63622	−	2.83402i	0.0677654	−	0.117373i
$584$	3.70512	+	34.1992i	0.153319	+	1.41517i
$585$	13.5581	−	10.3479i	0.560560	−	0.427834i
$586$	−38.7862	+	1.39585i	−1.60224	+	0.0576620i
$587$	6.70704	+	3.87231i	0.276829	+	0.159827i	0.631987	−	0.774979i	$-0.282240\pi$
$587$	6.70704	+	3.87231i	0.276829	+	0.159827i	−0.355158	+	0.934806i	$0.615573\pi$
$588$	4.23384	+	2.05382i	0.174601	+	0.0846981i
$589$	−11.2567	+	6.49906i	−0.463825	+	0.267789i
$590$	−0.471180	−	13.0926i	−0.0193982	−	0.539014i
$591$	1.30506	+	2.26044i	0.0536831	+	0.0929819i
$592$	−13.1586	+	10.3713i	−0.540817	+	0.426259i
$593$	−41.9381			−1.72219			−0.861095	−	0.508444i	$-0.830221\pi$
$593$	−41.9381			−1.72219			−0.861095	+	0.508444i	$0.830221\pi$
$594$	9.82970	−	6.15686i	0.403318	−	0.252619i
$595$	−28.6638	−	16.5490i	−1.17510	−	0.678444i
$596$	−2.01922	−	0.979515i	−0.0827105	−	0.0401225i
$597$			7.19058i			0.294291i
$598$	9.60187	−	7.89069i	0.392650	−	0.322674i
$599$	−28.4843			−1.16384			−0.581919	−	0.813246i	$-0.697698\pi$
$599$	−28.4843			−1.16384			−0.581919	+	0.813246i	$0.697698\pi$
$600$	1.22483	−	2.77486i	0.0500033	−	0.113283i
$601$	10.3349	−	17.9005i	0.421569	−	0.730178i	−0.574525	−	0.818487i	$-0.694813\pi$
$601$	10.3349	−	17.9005i	0.421569	−	0.730178i	0.996093	+	0.0883092i	$0.0281464\pi$
$602$	−27.0646	−	43.2098i	−1.10307	−	1.76110i
$603$		−	30.6580i		−	1.24849i
$604$	−2.32791	−	3.43545i	−0.0947215	−	0.139786i
$605$	−7.59194	+	4.38321i	−0.308656	+	0.178203i
$606$	0.346841	+	9.63761i	0.0140895	+	0.391501i
$607$	21.0555	+	36.4693i	0.854618	+	1.48024i	0.876999	+	0.480492i	$0.159542\pi$
$607$	21.0555	+	36.4693i	0.854618	+	1.48024i	−0.0223811	+	0.999750i	$0.507125\pi$
$608$	−5.59514	+	15.6313i	−0.226913	+	0.633933i
$609$	7.07808	−	12.2596i	0.286818	−	0.496784i
$610$	−0.145337	−	4.03845i	−0.00588452	−	0.163512i
$611$	−31.5547	+	4.07128i	−1.27657	+	0.164706i
$612$	−29.6425	+	2.13633i	−1.19823	+	0.0863561i
$613$	2.45743	+	1.41880i	0.0992548	+	0.0573048i	0.548806	−	0.835950i	$-0.315083\pi$
$613$	2.45743	+	1.41880i	0.0992548	+	0.0573048i	−0.449551	+	0.893255i	$0.648416\pi$
$614$	−3.28755	+	6.19892i	−0.132675	+	0.250168i
$615$	1.24778	+	2.16123i	0.0503155	+	0.0871490i
$616$	22.9995	−	2.49174i	0.926675	−	0.100395i
$617$	4.20136	+	7.27696i	0.169140	+	0.292960i	0.938118	−	0.346316i	$-0.112568\pi$
$617$	4.20136	+	7.27696i	0.169140	+	0.292960i	−0.768978	+	0.639276i	$0.779234\pi$
$618$	−0.900377	−	1.43749i	−0.0362185	−	0.0578244i
$619$		−	20.3468i		−	0.817806i	−0.912578	−	0.408903i	$-0.865911\pi$
$619$		−	20.3468i		−	0.817806i	0.912578	−	0.408903i	$-0.134089\pi$
$620$	−13.0695	+	8.85609i	−0.524884	+	0.355669i
$621$	−7.01998	−	4.05299i	−0.281702	−	0.162641i
$622$	1.29283	+	0.685644i	0.0518379	+	0.0274918i
$623$	−39.0754			−1.56552
$624$	−5.93579	+	6.06063i	−0.237622	+	0.242619i
$625$	−12.5604			−0.502417
$626$	7.71475	+	4.09146i	0.308343	+	0.163528i
$627$	3.68695	+	2.12866i	0.147243	+	0.0850105i
$628$	−39.5557	+	26.8036i	−1.57844	+	1.06958i
$629$		−	23.4519i		−	0.935089i
$630$	−11.7778	−	18.8038i	−0.469239	−	0.749161i
$631$	−9.63472	−	16.6878i	−0.383552	−	0.664332i	0.608015	−	0.793925i	$-0.291966\pi$
$631$	−9.63472	−	16.6878i	−0.383552	−	0.664332i	−0.991567	+	0.129594i	$0.958633\pi$
$632$	−2.35210	−	21.7105i	−0.0935614	−	0.863597i
$633$	3.16627	+	5.48414i	0.125848	+	0.217975i
$634$	−7.72159	+	14.5596i	−0.306663	+	0.578237i
$635$	24.3253	+	14.0442i	0.965321	+	0.557328i
$636$	1.55703	−	0.112215i	0.0617402	−	0.00444961i
$637$	5.55365	−	13.3102i	0.220044	−	0.527371i
$638$	−0.910173	−	25.2908i	−0.0360341	−	1.00127i
$639$	−13.4570	+	23.3083i	−0.532352	+	0.922061i
$640$	−5.41348	+	19.4250i	−0.213986	+	0.767842i
$641$	6.64940	+	11.5171i	0.262636	+	0.454898i	0.966941	−	0.254998i	$-0.0820750\pi$
$641$	6.64940	+	11.5171i	0.262636	+	0.454898i	−0.704306	+	0.709897i	$0.748742\pi$
$642$	0.365150	+	10.1464i	0.0144113	+	0.400445i
$643$	−29.9292	+	17.2797i	−1.18029	+	0.681443i	−0.956083	−	0.293097i	$-0.905314\pi$
$643$	−29.9292	+	17.2797i	−1.18029	+	0.681443i	−0.224212	+	0.974540i	$0.571981\pi$
$644$	−9.06940	−	13.3843i	−0.357385	−	0.527415i
$645$		−	11.3964i		−	0.448732i
$646$	−12.3359	−	19.6948i	−0.485348	−	0.774880i
$647$	−2.33433	+	4.04318i	−0.0917721	+	0.158954i	−0.908257	−	0.418413i	$-0.862586\pi$
$647$	−2.33433	+	4.04318i	−0.0917721	+	0.158954i	0.816485	+	0.577367i	$0.195920\pi$
$648$	−15.5405	−	6.85960i	−0.610488	−	0.269471i
$649$	−12.8175			−0.503130
$650$	−8.70258	−	3.26884i	−0.341343	−	0.128215i
$651$			8.63988i			0.338624i
$652$	41.1152	+	19.9448i	1.61020	+	0.781099i
$653$	−16.4329	−	9.48755i	−0.643069	−	0.371276i	0.142726	−	0.989762i	$-0.454413\pi$
$653$	−16.4329	−	9.48755i	−0.643069	−	0.371276i	−0.785796	+	0.618486i	$0.787746\pi$
$654$	−5.21582	+	3.26695i	−0.203955	+	0.127748i
$655$	−19.8226			−0.774534
$656$	5.89392	+	7.47792i	0.230119	+	0.291964i
$657$	−16.1391	−	27.9537i	−0.629645	−	1.09058i
$658$	1.48857	+	41.3628i	0.0580307	+	1.61249i
$659$	−7.64797	+	4.41556i	−0.297923	+	0.172006i	−0.641509	−	0.767115i	$-0.721691\pi$
$659$	−7.64797	+	4.41556i	−0.297923	+	0.172006i	0.343587	+	0.939121i	$0.388358\pi$
$660$	4.65240	+	2.25686i	0.181094	+	0.0878481i
$661$	−26.5464	−	15.3266i	−1.03254	−	0.596135i	−0.114826	−	0.993386i	$-0.536631\pi$
$661$	−26.5464	−	15.3266i	−1.03254	−	0.596135i	−0.917710	+	0.397250i	$0.869965\pi$
$662$	42.4858	−	1.52899i	1.65126	−	0.0594259i
$663$	−1.51945	−	11.7766i	−0.0590107	−	0.457367i
$664$	19.0402	−	2.06280i	0.738902	−	0.0800520i
$665$	8.67491	−	15.0254i	0.336398	−	0.582659i
$666$	7.36593	−	13.8890i	0.285424	−	0.538188i
$667$	−15.3169	+	8.84320i	−0.593072	+	0.342410i
$668$	−35.6357	+	2.56826i	−1.37879	+	0.0993690i
$669$	3.65788	−	2.11188i	0.141422	−	0.0816500i
$670$	24.6765	−	15.4562i	0.953338	−	0.597126i
$671$	−3.95359			−0.152627
$672$	7.13859	+	8.41592i	0.275377	+	0.324651i
$673$	−0.586586	+	1.01600i	−0.0226112	+	0.0391638i	−0.877110	−	0.480290i	$-0.840531\pi$
$673$	−0.586586	+	1.01600i	−0.0226112	+	0.0391638i	0.854498	+	0.519454i	$0.173865\pi$
$674$	22.2234	+	11.7860i	0.856013	+	0.453980i
$675$			6.06326i			0.233375i
$676$	19.5705	+	17.1171i	0.752712	+	0.658350i
$677$		−	5.90986i		−	0.227134i	−0.993530	−	0.113567i	$-0.963772\pi$
$677$		−	5.90986i		−	0.227134i	0.993530	−	0.113567i	$-0.0362277\pi$
$678$	3.72633	−	7.02627i	0.143109	−	0.269842i
$679$	10.5462	−	18.2666i	0.404728	−	0.701009i
$680$	−16.6638	−	22.7822i	−0.639028	−	0.873656i
$681$	0.187705			0.00719286
$682$	8.19891	+	13.0899i	0.313952	+	0.501239i
$683$	22.0262	−	12.7169i	0.842811	−	0.486597i	−0.0154080	−	0.999881i	$-0.504905\pi$
$683$	22.0262	−	12.7169i	0.842811	−	0.486597i	0.858219	+	0.513284i	$0.171571\pi$
$684$	−1.11985	−	15.5384i	−0.0428187	−	0.594127i
$685$	−0.0939408	+	0.0542368i	−0.00358929	+	0.00207228i
$686$	12.4310	+	6.59270i	0.474618	+	0.251710i
$687$	−2.70168	+	4.67945i	−0.103076	+	0.178532i
$688$	−6.23496	−	43.0316i	−0.237705	−	1.64057i
$689$	−0.612232	−	4.74515i	−0.0233242	−	0.180776i
$690$	−0.129970	−	3.61145i	−0.00494786	−	0.137485i
$691$	2.50444	+	1.44594i	0.0952733	+	0.0550061i	0.546880	−	0.837211i	$-0.315816\pi$
$691$	2.50444	+	1.44594i	0.0952733	+	0.0550061i	−0.451606	+	0.892217i	$0.649149\pi$
$692$	20.0043	+	9.70400i	0.760449	+	0.368891i
$693$	−18.7993	+	10.8538i	−0.714125	+	0.412300i
$694$	2.08826	−	0.0751531i	0.0792694	−	0.00285277i
$695$	13.5003	+	23.3832i	0.512096	+	0.886976i
$696$	9.74402	−	7.12717i	0.369346	−	0.270155i
$697$	−13.3275			−0.504815
$698$	10.5531	+	16.8485i	0.399441	+	0.637726i
$699$	10.7015	+	6.17852i	0.404768	+	0.233693i
$700$	−5.27821	+	10.8808i	−0.199498	+	0.411254i
$701$			44.2006i			1.66943i	0.550679	+	0.834717i	$0.314369\pi$
$701$			44.2006i			1.66943i	−0.550679	+	0.834717i	$0.685631\pi$
$702$	5.96291	−	15.8750i	0.225056	−	0.599161i
$703$	12.2934			0.463653
$704$	18.8018	+	5.97636i	0.708618	+	0.225243i
$705$	−4.62568	+	8.01191i	−0.174213	+	0.301746i
$706$	−18.0484	+	11.3047i	−0.679261	+	0.425457i
$707$		−	38.4507i		−	1.44609i
$708$	−3.42991	−	5.06174i	−0.128904	−	0.190232i
$709$	24.1216	−	13.9266i	0.905904	−	0.523024i	0.0267929	−	0.999641i	$-0.491471\pi$
$709$	24.1216	−	13.9266i	0.905904	−	0.523024i	0.879111	+	0.476617i	$0.158137\pi$
$710$	−25.5452	+	0.919327i	−0.958693	+	0.0345017i
$711$	10.2455	+	17.7457i	0.384235	+	0.665515i
$712$	−30.4858	−	13.4565i	−1.14250	−	0.504302i
$713$	5.39724	−	9.34830i	0.202128	−	0.350097i
$714$	−15.4371	+	0.555555i	−0.577719	+	0.0207911i
$715$	6.10268	−	14.6261i	0.228227	−	0.546985i
$716$	3.34838	+	46.4601i	0.125135	+	1.73630i
$717$	7.33119	+	4.23266i	0.273788	+	0.158072i
$718$	−0.266488	−	0.141330i	−0.00994525	−	0.00527439i
$719$	24.2128	+	41.9378i	0.902984	+	1.56401i	0.823601	+	0.567170i	$0.191962\pi$
$719$	24.2128	+	41.9378i	0.902984	+	1.56401i	0.0793833	+	0.996844i	$0.474705\pi$
$720$	−2.71329	−	18.7262i	−0.101118	−	0.697886i
$721$	3.38142	+	5.85679i	0.125931	+	0.218118i
$722$	−12.4480	+	7.79685i	−0.463267	+	0.290169i
$723$		−	1.22786i		−	0.0456645i
$724$	10.6048	−	7.18601i	0.394126	−	0.267066i
$725$	11.4570	+	6.61471i	0.425503	+	0.245664i
$726$	−1.91692	+	3.61449i	−0.0711436	+	0.134146i
$727$	46.8805			1.73870			0.869351	−	0.494195i	$-0.164537\pi$
$727$	46.8805			1.73870			0.869351	+	0.494195i	$0.164537\pi$
$728$	24.5202	−	23.2973i	0.908778	−	0.863457i
$729$	10.0710			0.373000
$730$	14.3634	−	27.0832i	0.531612	−	1.00239i
$731$	52.7080	+	30.4310i	1.94947	+	1.12553i
$732$	−1.05797	−	1.56131i	−0.0391036	−	0.0577076i
$733$			27.5679i			1.01824i	0.860694	+	0.509122i	$0.170030\pi$
$733$			27.5679i			1.01824i	−0.860694	+	0.509122i	$0.829970\pi$
$734$	−13.3207	+	8.34343i	−0.491674	+	0.307962i
$735$	−2.09683	−	3.63181i	−0.0773427	−	0.133961i
$736$	−2.46658	−	13.5654i	−0.0909192	−	0.500026i
$737$	−14.2436	−	24.6706i	−0.524669	−	0.908753i
$738$	−7.89299	−	4.18599i	−0.290545	−	0.154088i
$739$	28.2348	+	16.3014i	1.03863	+	0.599655i	0.919446	−	0.393216i	$-0.128638\pi$
$739$	28.2348	+	16.3014i	1.03863	+	0.599655i	0.119188	+	0.992872i	$0.461971\pi$
$740$	14.8928	−	1.07332i	0.547470	−	0.0394561i
$741$	6.17325	−	0.796489i	0.226780	−	0.0292598i
$742$	−6.22006	+	0.223849i	−0.228345	+	0.00821776i
$743$	12.2924	−	21.2910i	0.450963	−	0.781091i	−0.547483	−	0.836817i	$-0.684414\pi$
$743$	12.2924	−	21.2910i	0.450963	−	0.781091i	0.998446	+	0.0557256i	$0.0177472\pi$
$744$	−2.97533	+	6.74064i	−0.109081	+	0.247124i
$745$	1.00003	+	1.73210i	0.0366382	+	0.0634591i
$746$	−10.2780	+	0.369887i	−0.376303	+	0.0135425i
$747$	−15.5630	+	8.98531i	−0.569421	+	0.328755i
$748$	−22.8609	+	15.4909i	−0.835878	+	0.566404i
$749$		−	40.4805i		−	1.47912i
$750$	−8.57349	+	5.37003i	−0.313060	+	0.196086i
$751$	22.5199	−	39.0057i	0.821764	−	1.42334i	−0.0826041	−	0.996582i	$-0.526324\pi$
$751$	22.5199	−	39.0057i	0.821764	−	1.42334i	0.904368	−	0.426754i	$-0.140343\pi$
$752$	−13.0828	+	32.7829i	−0.477081	+	1.19547i
$753$	4.26226			0.155325
$754$	−23.4917	−	28.5861i	−0.855518	−	1.04105i
$755$			3.69832i			0.134596i
$756$	−19.8483	−	9.62833i	−0.721876	−	0.350179i
$757$	−10.4986	−	6.06138i	−0.381579	−	0.220305i	0.296926	−	0.954900i	$-0.404038\pi$
$757$	−10.4986	−	6.06138i	−0.381579	−	0.220305i	−0.678505	+	0.734596i	$0.737372\pi$
$758$	7.18989	+	11.4790i	0.261148	+	0.416935i
$759$	−3.53555			−0.128333
$760$	11.9423	−	8.73508i	0.433192	−	0.316854i
$761$	12.0876	+	20.9363i	0.438174	+	0.758940i	0.997549	−	0.0699753i	$-0.0222921\pi$
$761$	12.0876	+	20.9363i	0.438174	+	0.758940i	−0.559375	+	0.828915i	$0.688959\pi$
$762$	13.1006	−	0.471468i	0.474585	−	0.0170795i
$763$	21.2509	−	12.2692i	0.769333	−	0.444175i
$764$	−7.15426	+	14.7481i	−0.258832	+	0.533569i
$765$	22.9371	+	13.2428i	0.829294	+	0.478793i
$766$	−1.40371	−	39.0046i	−0.0507181	−	1.40930i
$767$	−14.8967	+	11.3696i	−0.537890	+	0.410532i
$768$	2.67117	+	9.02424i	0.0963874	+	0.325634i
$769$	−17.0904	+	29.6015i	−0.616296	+	1.06746i	0.373859	+	0.927485i	$0.378034\pi$
$769$	−17.0904	+	29.6015i	−0.616296	+	1.06746i	−0.990156	+	0.139971i	$0.955299\pi$
$770$	−18.2138	−	9.65957i	−0.656381	−	0.348107i
$771$	−9.25651	+	5.34425i	−0.333365	+	0.192468i
$772$	34.9897	−	2.52171i	1.25931	−	0.0907582i
$773$	14.7695	−	8.52716i	0.531221	−	0.306701i	−0.210292	−	0.977639i	$-0.567442\pi$
$773$	14.7695	−	8.52716i	0.531221	−	0.306701i	0.741514	+	0.670938i	$0.234108\pi$
$774$	21.6575	+	34.5771i	0.778462	+	1.24285i
$775$	−8.07427			−0.290036
$776$	14.5185	−	10.6194i	0.521182	−	0.381214i
$777$	4.08571	−	7.07666i	0.146574	−	0.253874i
$778$	2.12138	−	4.00003i	0.0760553	−	0.143408i
$779$		−	6.98620i		−	0.250307i
$780$	7.40903	−	1.50389i	0.265286	−	0.0538478i
$781$			25.0084i			0.894870i
$782$	17.0499	+	9.04229i	0.609703	+	0.323352i
$783$	−12.0663	+	20.8995i	−0.431215	+	0.746887i
$784$	−9.90440	−	12.5662i	−0.353728	−	0.448793i
$785$	42.5824			1.51983
$786$	−7.84038	+	4.91084i	−0.279657	+	0.175164i
$787$	−33.3134	+	19.2335i	−1.18749	+	0.685600i	−0.957736	−	0.287648i	$-0.907127\pi$
$787$	−33.3134	+	19.2335i	−1.18749	+	0.685600i	−0.229757	+	0.973248i	$0.573793\pi$
$788$	−0.637958	−	8.85194i	−0.0227263	−	0.315337i
$789$	−3.98368	+	2.29998i	−0.141823	+	0.0818814i
$790$	−9.11821	+	17.1931i	−0.324411	+	0.611701i
$791$	−15.8551	+	27.4618i	−0.563741	+	0.976428i
$792$	−18.4045	+	1.99393i	−0.653975	+	0.0708511i
$793$	−4.59494	+	3.50698i	−0.163171	+	0.124537i
$794$	4.72862	−	0.170175i	0.167812	−	0.00603928i
$795$	−1.20482	−	0.695601i	−0.0427304	−	0.0246704i
$796$	10.6710	−	21.9976i	0.378222	−	0.779685i
$797$	−38.4730	+	22.2124i	−1.36278	+	0.786804i	−0.989994	−	0.141111i	$-0.954933\pi$
$797$	−38.4730	+	22.2124i	−1.36278	+	0.786804i	−0.372791	+	0.927915i	$0.621599\pi$
$798$	−0.291219	−	8.09205i	−0.0103090	−	0.286455i
$799$	−24.7033	−	42.7873i	−0.873939	−	1.51371i
$800$	−7.86496	+	6.67126i	−0.278068	+	0.235865i
$801$	31.2687			1.10482
$802$	−8.03179	+	5.03073i	−0.283612	+	0.177641i
$803$	−25.9744	−	14.9963i	−0.916616	−	0.529208i
$804$	5.93111	−	12.2267i	0.209174	−	0.431202i
$805$			14.4084i			0.507830i
$806$	21.1402	+	7.94063i	0.744632	+	0.279697i
$807$	7.13224			0.251067
$808$	13.2413	−	29.9984i	0.465829	−	1.05534i
$809$	−15.4545	+	26.7681i	−0.543353	+	0.941115i	0.455356	+	0.890310i	$0.349512\pi$
$809$	−15.4545	+	26.7681i	−0.543353	+	0.941115i	−0.998709	+	0.0508052i	$0.983821\pi$
$810$	8.03596	+	12.8298i	0.282355	+	0.450792i
$811$			32.1542i			1.12909i	0.825403	+	0.564544i	$0.190948\pi$
$811$			32.1542i			1.12909i	−0.825403	+	0.564544i	$0.809052\pi$
$812$	−39.8470	+	27.0009i	−1.39835	+	0.947546i
$813$	−2.55712	+	1.47636i	−0.0896823	+	0.0517781i
$814$	−0.525383	−	14.5987i	−0.0184147	−	0.511685i
$815$	−20.3625	−	35.2688i	−0.713266	−	1.23541i
$816$	−12.2350	−	4.88267i	−0.428311	−	0.170928i
$817$	−15.9517	+	27.6292i	−0.558081	+	0.966624i
$818$	1.07287	+	29.8116i	0.0375119	+	1.04234i
$819$	−12.2212	+	29.2901i	−0.427043	+	1.02348i
$820$	−0.609958	−	8.46343i	−0.0213007	−	0.295556i
$821$	10.3465	+	5.97353i	0.361094	+	0.208478i	0.669561	−	0.742757i	$-0.266482\pi$
$821$	10.3465	+	5.97353i	0.361094	+	0.208478i	−0.308466	+	0.951235i	$0.599816\pi$
$822$	−0.0237195	+	0.0447249i	−0.000827313	+	0.00155996i
$823$	−19.2125	−	33.2770i	−0.669706	−	1.15996i	−0.977986	−	0.208669i	$-0.933087\pi$
$823$	−19.2125	−	33.2770i	−0.669706	−	1.15996i	0.308281	−	0.951295i	$-0.400246\pi$
$824$	0.621195	+	5.73380i	0.0216404	+	0.199746i
$825$	1.32230	+	2.29028i	0.0460364	+	0.0797374i
$826$	12.9406	+	20.6603i	0.450262	+	0.718864i
$827$		−	13.1098i		−	0.455872i	−0.973676	−	0.227936i	$-0.926802\pi$
$827$		−	13.1098i		−	0.455872i	0.973676	−	0.227936i	$-0.0731977\pi$
$828$	7.25746	+	10.7103i	0.252214	+	0.372208i
$829$	11.4829	+	6.62967i	0.398818	+	0.230258i	0.685974	−	0.727626i	$-0.259376\pi$
$829$	11.4829	+	6.62967i	0.398818	+	0.230258i	−0.287156	+	0.957884i	$0.592710\pi$
$830$	−15.0784	−	7.99670i	−0.523378	−	0.277569i
$831$	−16.9315			−0.587347
$832$	27.1530	−	9.73202i	0.941362	−	0.337397i
$833$	22.3961			0.775978
$834$	11.1327	+	5.90412i	0.385492	+	0.204443i
$835$	27.5746	+	15.9202i	0.954259	+	0.550942i
$836$	−8.12025	−	11.9836i	−0.280845	−	0.414460i
$837$		−	14.7288i		−	0.509102i
$838$	−23.1361	−	36.9379i	−0.799225	−	1.27600i
$839$	2.06865	+	3.58301i	0.0714179	+	0.123699i	0.899523	−	0.436874i	$-0.143914\pi$
$839$	2.06865	+	3.58301i	0.0714179	+	0.123699i	−0.828105	+	0.560573i	$0.810581\pi$
$840$	−1.05931	−	9.77768i	−0.0365495	−	0.337362i
$841$	11.8275	+	20.4858i	0.407844	+	0.706407i
$842$	3.82838	−	7.21870i	0.131935	−	0.248773i
$843$	−6.90715	−	3.98784i	−0.237895	−	0.137349i
$844$	−1.54778	−	21.4761i	−0.0532767	−	0.739236i
$845$	−5.88123	−	22.4120i	−0.202321	−	0.770998i
$846$	−1.19118	−	33.0990i	−0.0409535	−	1.13797i
$847$	8.15625	−	14.1270i	0.280252	−	0.485411i
$848$	−4.92984	−	1.96737i	−0.169291	−	0.0675597i
$849$	6.26405	+	10.8497i	0.214982	+	0.372359i
$850$	−0.519185	−	14.4265i	−0.0178079	−	0.494825i
$851$	−8.84143	+	5.10460i	−0.303080	+	0.174984i
$852$	−9.87603	+	6.69215i	−0.338347	+	0.229269i
$853$			38.2871i			1.31093i	0.755227	+	0.655463i	$0.227527\pi$
$853$			38.2871i			1.31093i	−0.755227	+	0.655463i	$0.772473\pi$
$854$	3.99157	+	6.37273i	0.136589	+	0.218070i
$855$	−6.94178	+	12.0235i	−0.237404	+	0.411196i
$856$	13.9403	−	31.5820i	0.476471	−	1.07945i
$857$	4.33857			0.148203			0.0741014	−	0.997251i	$-0.476391\pi$
$857$	4.33857			0.148203			0.0741014	+	0.997251i	$0.476391\pi$
$858$	−1.20968	−	7.29688i	−0.0412979	−	0.249111i
$859$		−	13.0557i		−	0.445453i	−0.974881	−	0.222727i	$-0.928504\pi$
$859$		−	13.0557i		−	0.445453i	0.974881	−	0.222727i	$-0.0714958\pi$
$860$	−16.9124	+	34.8641i	−0.576709	+	1.18886i
$861$	−4.02160	−	2.32187i	−0.137056	−	0.0791292i
$862$	−7.80745	+	4.89022i	−0.265923	+	0.166562i
$863$	40.9955			1.39550			0.697751	−	0.716340i	$-0.254184\pi$
$863$	40.9955			1.39550			0.697751	+	0.716340i	$0.254184\pi$
$864$	−12.1695	−	14.3470i	−0.414014	−	0.488095i
$865$	−9.90721	−	17.1598i	−0.336855	−	0.583451i
$866$	0.0580321	+	1.61253i	0.00197201	+	0.0547959i
$867$	7.30897	−	4.21984i	0.248226	−	0.143313i
$868$	12.8218	−	26.4314i	0.435199	−	0.897140i
$869$	16.4892	+	9.52002i	0.559356	+	0.322944i
$870$	−10.7518	+	0.386938i	−0.364520	+	0.0131184i
$871$	−38.4379	−	16.0381i	−1.30242	−	0.543430i
$872$	20.8046	−	2.25396i	0.704533	−	0.0763286i
$873$	−8.43925	+	14.6172i	−0.285625	+	0.494718i
$874$	−4.73992	+	8.93747i	−0.160330	+	0.302314i
$875$	34.9310	−	20.1674i	1.18088	−	0.681784i
$876$	−1.02847	−	14.2705i	−0.0347489	−	0.482155i
$877$	26.9990	−	15.5879i	0.911690	−	0.526365i	0.0307156	−	0.999528i	$-0.490221\pi$
$877$	26.9990	−	15.5879i	0.911690	−	0.526365i	0.880975	+	0.473164i	$0.156888\pi$
$878$	28.7048	−	17.9793i	0.968740	−	0.606773i
$879$	16.1425			0.544474
$880$	−10.8835	−	13.8085i	−0.366884	−	0.465485i
$881$	2.45718	−	4.25595i	0.0827844	−	0.143387i	−0.821661	−	0.569977i	$-0.806952\pi$
$881$	2.45718	−	4.25595i	0.0827844	−	0.143387i	0.904445	+	0.426590i	$0.140285\pi$
$882$	13.2637	+	7.03431i	0.446612	+	0.236858i
$883$		−	2.14194i		−	0.0720821i	−0.999350	−	0.0360411i	$-0.988525\pi$
$883$		−	2.14194i		−	0.0720821i	0.999350	−	0.0360411i	$-0.0114747\pi$
$884$	−12.8284	+	38.2823i	−0.431466	+	1.28757i
$885$			5.44905i			0.183168i
$886$	−16.2458	+	30.6326i	−0.545788	+	1.02912i
$887$	2.61724	−	4.53319i	0.0878783	−	0.152210i	−0.818736	−	0.574170i	$-0.805325\pi$
$887$	2.61724	−	4.53319i	0.0878783	−	0.152210i	0.906614	+	0.421961i	$0.138658\pi$
$888$	5.62459	−	4.11405i	0.188749	−	0.138059i
$889$	−52.2669			−1.75297
$890$	15.7641	+	25.1681i	0.528414	+	0.843637i
$891$	12.8267	−	7.40548i	0.429710	−	0.248093i
$892$	−14.3244	+	1.03236i	−0.479616	+	0.0345659i
$893$	22.4289	−	12.9493i	0.750554	−	0.433332i
$894$	0.824645	+	0.437345i	0.0275803	+	0.0146270i
$895$	20.7560	−	35.9505i	0.693797	−	1.20169i
$896$	−9.34921	−	36.3400i	−0.312335	−	1.21404i
$897$	−4.10909	+	3.13617i	−0.137199	+	0.104714i
$898$	1.00325	+	27.8771i	0.0334789	+	0.930272i
$899$	−27.8312	−	16.0684i	−0.928223	−	0.535910i
$900$	4.22369	−	8.70693i	0.140790	−	0.290231i
$901$	6.43428	−	3.71483i	0.214357	−	0.123759i
$902$	−8.29632	+	0.298570i	−0.276237	+	0.00994130i
$903$	10.6032	+	18.3652i	0.352851	+	0.611156i
$904$	−21.8268	+	15.9650i	−0.725949	+	0.530989i
$905$	−11.4163			−0.379490
$906$	0.916218	+	1.46278i	0.0304393	+	0.0485977i
$907$	−13.8926	−	8.02088i	−0.461296	−	0.266329i	0.251293	−	0.967911i	$-0.419144\pi$
$907$	−13.8926	−	8.02088i	−0.461296	−	0.266329i	−0.712589	+	0.701582i	$0.752477\pi$
$908$	−0.574232	−	0.278557i	−0.0190565	−	0.00924425i
$909$			30.7688i			1.02054i
$910$	−29.7369	+	4.92980i	−0.985768	+	0.163421i
$911$	−43.9693			−1.45677			−0.728384	−	0.685170i	$-0.759728\pi$
$911$	−43.9693			−1.45677			−0.728384	+	0.685170i	$0.759728\pi$
$912$	2.55947	−	6.41352i	0.0847525	−	0.212373i
$913$	−8.34908	+	14.4610i	−0.276314	+	0.478590i
$914$	−12.7949	+	8.01412i	−0.423217	+	0.265083i
$915$			1.68077i			0.0555647i
$916$	15.2095	−	10.3062i	0.502535	−	0.340526i
$917$	31.9441	−	18.4429i	1.05489	−	0.609039i
$918$	26.3163	−	0.947080i	0.868569	−	0.0312583i
$919$	−14.9889	−	25.9615i	−0.494437	−	0.856390i	0.505542	−	0.862802i	$-0.331292\pi$
$919$	−14.9889	−	25.9615i	−0.494437	−	0.856390i	−0.999979	+	0.00641145i	$0.997959\pi$
$920$	−4.96185	+	11.2411i	−0.163587	+	0.370609i
$921$	1.45921	−	2.52743i	0.0480827	−	0.0832817i
$922$	−36.6316	+	1.31831i	−1.20640	+	0.0434162i
$923$	22.1834	+	29.0652i	0.730174	+	0.956694i
$924$	−9.59710	+	0.691662i	−0.315721	+	0.0227540i
$925$	6.61338	+	3.81824i	0.217447	+	0.125543i
$926$	−25.5895	−	13.5712i	−0.840925	−	0.445978i
$927$	−2.70586	−	4.68668i	−0.0888720	−	0.153931i
$928$	−40.3861	+	7.34335i	−1.32574	+	0.241057i
$929$	−6.63588	−	11.4937i	−0.217716	−	0.377095i	0.736393	−	0.676554i	$-0.236527\pi$
$929$	−6.63588	−	11.4937i	−0.217716	−	0.377095i	−0.954109	+	0.299458i	$0.903194\pi$
$930$	5.56487	−	3.48557i	0.182479	−	0.114296i
$931$			11.7399i			0.384760i
$932$	−23.5693	−	34.7828i	−0.772040	−	1.13935i
$933$	−0.527115	−	0.304330i	−0.0172570	−	0.00996332i
$934$	−1.34233	+	2.53107i	−0.0439225	+	0.0828190i
$935$	24.6101			0.804838
$936$	−19.6214	+	18.6429i	−0.641345	+	0.609361i
$937$	2.64444			0.0863903			0.0431951	−	0.999067i	$-0.486246\pi$
$937$	2.64444			0.0863903			0.0431951	+	0.999067i	$0.486246\pi$
$938$	−25.3857	+	47.8666i	−0.828873	+	1.56290i
$939$	−3.14547	−	1.81604i	−0.102648	−	0.0592641i
$940$	26.0408	−	17.6457i	0.849359	−	0.575538i
$941$		−	28.1115i		−	0.916408i	−0.888847	−	0.458204i	$-0.848493\pi$
$941$		−	28.1115i		−	0.916408i	0.888847	−	0.458204i	$-0.151507\pi$
$942$	16.8425	−	10.5493i	0.548757	−	0.343715i
$943$	2.90090	+	5.02450i	0.0944662	+	0.163620i
$944$	2.98117	+	20.5751i	0.0970290	+	0.669662i
$945$	9.82996	+	17.0260i	0.319768	+	0.553855i
$946$	33.4923	+	17.7624i	1.08893	+	0.577504i
$947$	−39.4200	−	22.7591i	−1.28098	−	0.739573i	−0.303951	−	0.952688i	$-0.598306\pi$
$947$	−39.4200	−	22.7591i	−1.28098	−	0.739573i	−0.977027	+	0.213115i	$0.931639\pi$
$948$	0.652899	+	9.05924i	0.0212052	+	0.294231i
$949$	−43.4902	+	5.61123i	−1.41175	+	0.182148i
$950$	7.56230	−	0.272154i	0.245353	−	0.00882984i
$951$	3.42731	−	5.93627i	0.111138	−	0.192497i
$952$	48.0501	+	21.2094i	1.55731	+	0.687401i
$953$	3.59780	+	6.23157i	0.116544	+	0.201860i	0.918396	−	0.395663i	$-0.129485\pi$
$953$	3.59780	+	6.23157i	0.116544	+	0.201860i	−0.801852	+	0.597523i	$0.796152\pi$
$954$	4.97737	−	0.179127i	0.161148	−	0.00579946i
$955$	12.6510	−	7.30408i	0.409378	−	0.236355i
$956$	−16.1464	−	23.8283i	−0.522213	−	0.770663i
$957$			10.5259i			0.340253i
$958$	23.3073	−	14.5986i	0.753024	−	0.471659i
$959$	0.100924	−	0.174805i	0.00325899	−	0.00564474i
$960$	2.54071	−	7.99312i	0.0820010	−	0.257977i
$961$	−11.3861			−0.367293
$962$	−13.5602	−	16.5009i	−0.437200	−	0.532011i
$963$			32.3930i			1.04385i
$964$	−1.82216	+	3.75630i	−0.0586880	+	0.120982i
$965$	−27.0748	−	15.6316i	−0.871568	−	0.503200i
$966$	3.56953	+	5.69891i	0.114848	+	0.183359i
$967$	10.5233			0.338408			0.169204	−	0.985581i	$-0.445880\pi$
$967$	10.5233			0.338408			0.169204	+	0.985581i	$0.445880\pi$
$968$	11.2283	−	8.21282i	0.360890	−	0.263970i
$969$	4.83285	+	8.37074i	0.155254	+	0.268907i
$970$	−16.0200	+	0.576533i	−0.514372	+	0.0185114i
$971$	5.96165	−	3.44196i	0.191319	−	0.110458i	−0.401281	−	0.915955i	$-0.631435\pi$
$971$	5.96165	−	3.44196i	0.191319	−	0.110458i	0.592600	+	0.805497i	$0.298102\pi$
$972$	24.3103	+	11.7928i	0.779753	+	0.378255i
$973$	−43.5114	−	25.1213i	−1.39491	−	0.805352i
$974$	1.52195	+	42.2902i	0.0487665	+	1.35507i
$975$	3.56837	+	1.48889i	0.114279	+	0.0476826i
$976$	0.919551	+	6.34644i	0.0294341	+	0.203145i
$977$	4.89362	−	8.47599i	0.156561	−	0.271171i	−0.777066	−	0.629420i	$-0.783293\pi$
$977$	4.89362	−	8.47599i	0.156561	−	0.271171i	0.933626	+	0.358249i	$0.116626\pi$
$978$	−16.7914	−	8.90518i	−0.536929	−	0.284756i
$979$	25.1620	−	14.5273i	0.804182	−	0.464295i
$980$	1.02500	+	14.2223i	0.0327424	+	0.454314i
$981$	−17.0052	+	9.81798i	−0.542935	+	0.313464i
$982$	9.97952	+	15.9327i	0.318459	+	0.508434i
$983$	−19.2063			−0.612586			−0.306293	−	0.951937i	$-0.599089\pi$
$983$	−19.2063			−0.612586			−0.306293	+	0.951937i	$0.599089\pi$
$984$	−2.33798	−	3.19640i	−0.0745319	−	0.101897i
$985$	−3.95459	+	6.84956i	−0.126004	+	0.218245i
$986$	26.9202	−	50.7600i	0.857314	−	1.61653i
$987$		−	17.2149i		−	0.547956i
$988$	−20.0674	−	6.72458i	−0.638429	−	0.213937i
$989$		−	26.4947i		−	0.842483i
$990$	14.5750	+	7.72972i	0.463222	+	0.245667i
$991$	11.1847	−	19.3725i	0.355295	−	0.615389i	−0.631873	−	0.775072i	$-0.717714\pi$
$991$	11.1847	−	19.3725i	0.355295	−	0.615389i	0.987168	+	0.159683i	$0.0510471\pi$
$992$	19.1055	−	16.2057i	0.606599	−	0.514533i
$993$	−17.6823			−0.561130
$994$	40.3106	−	25.2487i	1.27857	−	0.800839i
$995$	−18.8697	+	10.8944i	−0.598209	+	0.345376i
$996$	−7.94498	+	0.572594i	−0.251746	+	0.0181433i
$997$	−39.2759	+	22.6759i	−1.24388	+	0.718154i	−0.969882	−	0.243576i	$-0.921679\pi$
$997$	−39.2759	+	22.6759i	−1.24388	+	0.718154i	−0.273998	+	0.961730i	$0.588346\pi$
$998$	−2.69238	+	5.07667i	−0.0852257	+	0.160699i
$999$	−6.96510	+	12.0639i	−0.220366	+	0.381685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.r.a.61.11	yes	24
3.2	odd	2		936.2.be.a.685.2		24
4.3	odd	2		416.2.z.a.113.7		24
8.3	odd	2		416.2.z.a.113.6		24
8.5	even	2	inner	104.2.r.a.61.3	yes	24
13.3	even	3	inner	104.2.r.a.29.3	✓	24
24.5	odd	2		936.2.be.a.685.10		24
39.29	odd	6		936.2.be.a.757.10		24
52.3	odd	6		416.2.z.a.81.6		24
104.3	odd	6		416.2.z.a.81.7		24
104.29	even	6	inner	104.2.r.a.29.11	yes	24
312.29	odd	6		936.2.be.a.757.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.3	✓	24	13.3	even	3	inner
104.2.r.a.29.11	yes	24	104.29	even	6	inner
104.2.r.a.61.3	yes	24	8.5	even	2	inner
104.2.r.a.61.11	yes	24	1.1	even	1	trivial
416.2.z.a.81.6		24	52.3	odd	6
416.2.z.a.81.7		24	104.3	odd	6
416.2.z.a.113.6		24	8.3	odd	2
416.2.z.a.113.7		24	4.3	odd	2
936.2.be.a.685.2		24	3.2	odd	2
936.2.be.a.685.10		24	24.5	odd	2
936.2.be.a.757.2		24	312.29	odd	6
936.2.be.a.757.10		24	39.29	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24938 + 0.662601i) q^{2} +(-0.509400 - 0.294102i) q^{3} +(1.12192 + 1.65569i) q^{4} -1.78237i q^{5} +(-0.441564 - 0.704976i) q^{6} +(1.65832 + 2.87229i) q^{7} +(0.304647 + 2.81197i) q^{8} +(-1.32701 - 2.29844i) q^{9} +(1.18100 - 2.22687i) q^{10} +(-2.13570 - 1.23305i) q^{11} +(-0.0845644 - 1.17337i) q^{12} +(-3.57591 + 0.461374i) q^{13} +(0.168691 + 4.68739i) q^{14} +(-0.524200 + 0.907941i) q^{15} +(-1.48260 + 3.71509i) q^{16} +(-2.79947 - 4.84883i) q^{17} +(-0.134989 - 3.75092i) q^{18} +(2.54173 - 1.46747i) q^{19} +(2.95105 - 1.99968i) q^{20} -1.95086i q^{21} +(-1.85129 - 2.95566i) q^{22} +(-1.21868 + 2.11082i) q^{23} +(0.671821 - 1.52202i) q^{24} +1.82314 q^{25} +(-4.77339 - 1.79297i) q^{26} +3.32572i q^{27} +(-2.89511 + 5.96813i) q^{28} +(6.28420 + 3.62819i) q^{29} +(-1.25653 + 0.787031i) q^{30} -4.42876 q^{31} +(-4.31396 + 3.65920i) q^{32} +(0.725283 + 1.25623i) q^{33} +(-0.284775 - 7.91298i) q^{34} +(5.11949 - 2.95574i) q^{35} +(2.31671 - 4.77578i) q^{36} +(3.62746 + 2.09432i) q^{37} +(4.14794 - 0.149277i) q^{38} +(1.95726 + 0.816660i) q^{39} +(5.01199 - 0.542994i) q^{40} +(1.19018 - 2.06145i) q^{41} +(1.29264 - 2.43737i) q^{42} +(-9.41391 + 5.43512i) q^{43} +(-0.354542 - 4.91942i) q^{44} +(-4.09669 + 2.36522i) q^{45} +(-2.92123 + 1.82972i) q^{46} +8.82426 q^{47} +(1.84785 - 1.45643i) q^{48} +(-2.00003 + 3.46415i) q^{49} +(2.27781 + 1.20802i) q^{50} +3.29333i q^{51} +(-4.77577 - 5.40296i) q^{52} +1.32698i q^{53} +(-2.20363 + 4.15510i) q^{54} +(-2.19775 + 3.80661i) q^{55} +(-7.57160 + 5.53817i) q^{56} -1.72634 q^{57} +(5.44734 + 8.69692i) q^{58} +(4.50116 - 2.59874i) q^{59} +(-2.09138 + 0.150725i) q^{60} +(1.38839 - 0.801590i) q^{61} +(-5.53322 - 2.93450i) q^{62} +(4.40120 - 7.62310i) q^{63} +(-7.81438 + 1.71332i) q^{64} +(0.822340 + 6.37361i) q^{65} +(0.0737790 + 2.05008i) q^{66} +(10.0039 + 5.77577i) q^{67} +(4.88736 - 10.0750i) q^{68} +(1.24159 - 0.716834i) q^{69} +(8.35469 - 0.300671i) q^{70} +(-5.07044 - 8.78227i) q^{71} +(6.05889 - 4.43172i) q^{72} +12.1620 q^{73} +(3.14439 + 5.02016i) q^{74} +(-0.928710 - 0.536191i) q^{75} +(5.28128 + 2.56193i) q^{76} -8.17912i q^{77} +(1.90425 + 2.31720i) q^{78} -7.72073 q^{79} +(6.62168 + 2.64254i) q^{80} +(-3.00292 + 5.20121i) q^{81} +(2.85291 - 1.78693i) q^{82} -6.77111i q^{83} +(3.23001 - 2.18871i) q^{84} +(-8.64243 + 4.98971i) q^{85} +(-15.3629 + 0.552885i) q^{86} +(-2.13412 - 3.69640i) q^{87} +(2.81666 - 6.38117i) q^{88} +(-5.89082 + 10.2032i) q^{89} +(-6.68553 + 0.240601i) q^{90} +(-7.25519 - 9.50594i) q^{91} +(-4.86211 + 0.350412i) q^{92} +(2.25601 + 1.30251i) q^{93} +(11.0249 + 5.84696i) q^{94} +(-2.61558 - 4.53031i) q^{95} +(3.27371 - 0.595255i) q^{96} +(-3.17980 - 5.50758i) q^{97} +(-4.79415 + 3.00283i) q^{98} +6.54505i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - q^{4} - 8 q^{6} - 2 q^{7} - 10 q^{8} + 6 q^{9} - 3 q^{10} - 12 q^{12} + 8 q^{14} + 4 q^{15} - q^{16} + 6 q^{18} - 11 q^{20} - 2 q^{22} - 14 q^{23} - 18 q^{24} - 12 q^{25} - 3 q^{26} - 4 q^{28}+ \cdots - 17 q^{98}+O(q^{100}) \) 24 * q - q^2 - q^4 - 8 * q^6 - 2 * q^7 - 10 * q^8 + 6 * q^9 - 3 * q^10 - 12 * q^12 + 8 * q^14 + 4 * q^15 - q^16 + 6 * q^18 - 11 * q^20 - 2 * q^22 - 14 * q^23 - 18 * q^24 - 12 * q^25 - 3 * q^26 - 4 * q^28 + 14 * q^30 - 8 * q^31 - 21 * q^32 - 14 * q^33 + 14 * q^34 + 5 * q^36 + 12 * q^38 - 34 * q^39 + 54 * q^40 - 4 * q^41 + 22 * q^42 + 24 * q^46 - 8 * q^47 - 8 * q^48 + 6 * q^49 + 32 * q^50 - 4 * q^52 + 22 * q^54 + 8 * q^55 + 8 * q^56 - 52 * q^57 + 33 * q^58 + 56 * q^60 - 14 * q^62 + 32 * q^63 + 26 * q^64 + 30 * q^65 - 104 * q^66 + 23 * q^68 - 16 * q^70 + 30 * q^71 + 17 * q^72 - 12 * q^73 - 7 * q^74 + 14 * q^76 - 8 * q^78 - 48 * q^79 + 29 * q^80 + 8 * q^81 - q^82 + 60 * q^84 - 96 * q^86 - 26 * q^87 + 4 * q^88 - 22 * q^89 - 50 * q^90 - 80 * q^92 - 42 * q^94 + 60 * q^95 - 40 * q^96 + 2 * q^97 - 17 * q^98

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