LMFDB - Embedded newform 189.2.u.a.4.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.19
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.371090 + 2.10456i) q^{2} +(0.871315 - 1.49693i) q^{3} +(-2.41207 + 0.877922i) q^{4} +(2.18602 - 0.795646i) q^{5} +(3.47372 + 1.27824i) q^{6} +(1.27150 - 2.32019i) q^{7} +(-0.605711 - 1.04912i) q^{8} +(-1.48162 - 2.60860i) q^{9} +O(q^{10})$	\(q+(0.371090 + 2.10456i) q^{2} +(0.871315 - 1.49693i) q^{3} +(-2.41207 + 0.877922i) q^{4} +(2.18602 - 0.795646i) q^{5} +(3.47372 + 1.27824i) q^{6} +(1.27150 - 2.32019i) q^{7} +(-0.605711 - 1.04912i) q^{8} +(-1.48162 - 2.60860i) q^{9} +(2.48569 + 4.30535i) q^{10} +(-1.37492 - 0.500429i) q^{11} +(-0.787484 + 4.37566i) q^{12} +(-5.79948 + 2.11084i) q^{13} +(5.35482 + 1.81494i) q^{14} +(0.713683 - 3.96558i) q^{15} +(-1.94951 + 1.63584i) q^{16} +(3.15768 + 5.46926i) q^{17} +(4.94014 - 4.08618i) q^{18} +(-2.94716 + 5.10463i) q^{19} +(-4.57432 + 3.83831i) q^{20} +(-2.36530 - 3.92497i) q^{21} +(0.542963 - 3.07930i) q^{22} +(0.628803 - 3.56612i) q^{23} +(-2.09823 - 0.00740721i) q^{24} +(0.315402 - 0.264654i) q^{25} +(-6.59451 - 11.4220i) q^{26} +(-5.19586 - 0.0550294i) q^{27} +(-1.02999 + 6.71275i) q^{28} +(-2.39036 - 0.870020i) q^{29} +(8.61064 + 0.0303974i) q^{30} +(5.82200 - 2.11903i) q^{31} +(-6.02216 - 5.05319i) q^{32} +(-1.94710 + 1.62213i) q^{33} +(-10.3386 + 8.67511i) q^{34} +(0.933465 - 6.08365i) q^{35} +(5.86392 + 4.99139i) q^{36} +0.375316 q^{37} +(-11.8366 - 4.30819i) q^{38} +(-1.89339 + 10.5206i) q^{39} +(-2.15882 - 1.81147i) q^{40} +(6.70424 - 2.44014i) q^{41} +(7.38258 - 6.43443i) q^{42} +(0.123419 + 0.699942i) q^{43} +3.75574 q^{44} +(-5.31437 - 4.52361i) q^{45} +7.73844 q^{46} +(7.13729 + 2.59776i) q^{47} +(0.750096 + 4.34362i) q^{48} +(-3.76659 - 5.90024i) q^{49} +(0.674022 + 0.565571i) q^{50} +(10.9385 + 0.0386151i) q^{51} +(12.1356 - 10.1830i) q^{52} +(-0.517201 + 0.895818i) q^{53} +(-1.81232 - 10.9554i) q^{54} -3.40376 q^{55} +(-3.20433 + 0.0714101i) q^{56} +(5.07338 + 8.85944i) q^{57} +(0.943968 - 5.35351i) q^{58} +(-2.58481 - 2.16891i) q^{59} +(1.76002 + 10.1918i) q^{60} +(-5.48842 - 1.99762i) q^{61} +(6.62011 + 11.4664i) q^{62} +(-7.93633 + 0.120812i) q^{63} +(5.85507 - 10.1413i) q^{64} +(-10.9983 + 9.22866i) q^{65} +(-4.13641 - 3.49582i) q^{66} +(1.04873 - 5.94764i) q^{67} +(-12.4181 - 10.4201i) q^{68} +(-4.79035 - 4.04849i) q^{69} +(13.1498 - 0.293050i) q^{70} +(3.69767 - 6.40455i) q^{71} +(-1.83931 + 3.13446i) q^{72} -6.77172 q^{73} +(0.139276 + 0.789875i) q^{74} +(-0.121354 - 0.702733i) q^{75} +(2.62729 - 14.9001i) q^{76} +(-2.90930 + 2.55378i) q^{77} +(-22.8439 - 0.0806439i) q^{78} +(0.0335365 + 0.190195i) q^{79} +(-2.96013 + 5.12709i) q^{80} +(-4.60961 + 7.72991i) q^{81} +(7.62331 + 13.2040i) q^{82} +(9.88619 + 3.59828i) q^{83} +(9.15109 + 7.39075i) q^{84} +(11.2543 + 9.44351i) q^{85} +(-1.42727 + 0.519483i) q^{86} +(-3.38512 + 2.82015i) q^{87} +(0.307791 + 1.74557i) q^{88} +(-1.46082 + 2.53022i) q^{89} +(7.54808 - 12.8631i) q^{90} +(-2.47647 + 16.1398i) q^{91} +(1.61406 + 9.15377i) q^{92} +(1.90074 - 10.5615i) q^{93} +(-2.81856 + 15.9848i) q^{94} +(-2.38107 + 13.5037i) q^{95} +(-12.8115 + 4.61185i) q^{96} +(-2.44666 - 13.8757i) q^{97} +(11.0196 - 10.1165i) q^{98} +(0.731684 + 4.32806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.371090	+	2.10456i	0.262401	+	1.48815i	0.776336	+	0.630319i	$0.217076\pi$
$2$	0.371090	+	2.10456i	0.262401	+	1.48815i	−0.513936	+	0.857829i	$0.671813\pi$
$3$	0.871315	−	1.49693i	0.503054	−	0.864255i
$3$	0.871315	−	1.49693i	0.503054	−	0.864255i
$4$	−2.41207	+	0.877922i	−1.20604	+	0.438961i
$5$	2.18602	−	0.795646i	0.977617	−	0.355824i	0.196704	−	0.980463i	$-0.436976\pi$
$5$	2.18602	−	0.795646i	0.977617	−	0.355824i	0.780913	+	0.624639i	$0.214754\pi$
$6$	3.47372	+	1.27824i	1.41814	+	0.521838i
$7$	1.27150	−	2.32019i	0.480581	−	0.876950i
$7$	1.27150	−	2.32019i	0.480581	−	0.876950i
$8$	−0.605711	−	1.04912i	−0.214151	−	0.370921i
$9$	−1.48162	−	2.60860i	−0.493873	−	0.869534i
$10$	2.48569	+	4.30535i	0.786045	+	1.36147i
$11$	−1.37492	−	0.500429i	−0.414553	−	0.150885i	0.126319	−	0.991990i	$-0.459684\pi$
$11$	−1.37492	−	0.500429i	−0.414553	−	0.150885i	−0.540872	+	0.841105i	$0.681906\pi$
$12$	−0.787484	+	4.37566i	−0.227327	+	1.26314i
$13$	−5.79948	+	2.11084i	−1.60849	+	0.585441i	−0.981140	−	0.193300i	$-0.938081\pi$
$13$	−5.79948	+	2.11084i	−1.60849	+	0.585441i	−0.627346	+	0.778741i	$0.715859\pi$
$14$	5.35482	+	1.81494i	1.43114	+	0.485063i
$15$	0.713683	−	3.96558i	0.184272	−	1.02391i
$16$	−1.94951	+	1.63584i	−0.487378	+	0.408959i
$17$	3.15768	+	5.46926i	0.765850	+	1.32649i	0.939796	+	0.341736i	$0.111015\pi$
$17$	3.15768	+	5.46926i	0.765850	+	1.32649i	−0.173946	+	0.984755i	$0.555652\pi$
$18$	4.94014	−	4.08618i	1.16440	−	0.963122i
$19$	−2.94716	+	5.10463i	−0.676124	+	1.17108i	0.300015	+	0.953935i	$0.403008\pi$
$19$	−2.94716	+	5.10463i	−0.676124	+	1.17108i	−0.976139	+	0.217147i	$0.930325\pi$
$20$	−4.57432	+	3.83831i	−1.02285	+	0.858272i
$21$	−2.36530	−	3.92497i	−0.516151	−	0.856498i
$22$	0.542963	−	3.07930i	0.115760	−	0.656509i
$23$	0.628803	−	3.56612i	0.131114	−	0.743587i	−0.846373	−	0.532591i	$-0.821218\pi$
$23$	0.628803	−	3.56612i	0.131114	−	0.743587i	0.977487	−	0.210996i	$-0.0676706\pi$
$24$	−2.09823	−	0.00740721i	−0.428300	−	0.00151199i
$25$	0.315402	−	0.264654i	0.0630804	−	0.0529307i
$26$	−6.59451	−	11.4220i	−1.29329	−	2.24004i
$27$	−5.19586	−	0.0550294i	−0.999944	−	0.0105904i
$28$	−1.02999	+	6.71275i	−0.194651	+	1.26859i
$29$	−2.39036	−	0.870020i	−0.443879	−	0.161559i	0.110405	−	0.993887i	$-0.464785\pi$
$29$	−2.39036	−	0.870020i	−0.443879	−	0.161559i	−0.554283	+	0.832328i	$0.687008\pi$
$30$	8.61064	+	0.0303974i	1.57208	+	0.00554978i
$31$	5.82200	−	2.11903i	1.04566	−	0.380590i	0.238638	−	0.971109i	$-0.423299\pi$
$31$	5.82200	−	2.11903i	1.04566	−	0.380590i	0.807024	+	0.590519i	$0.201077\pi$
$32$	−6.02216	−	5.05319i	−1.06458	−	0.893287i
$33$	−1.94710	+	1.62213i	−0.338946	+	0.282376i
$34$	−10.3386	+	8.67511i	−1.77305	+	1.48777i
$35$	0.933465	−	6.08365i	0.157784	−	1.02832i
$36$	5.86392	+	4.99139i	0.977320	+	0.831898i
$37$	0.375316			0.0617016			0.0308508	−	0.999524i	$-0.490178\pi$
$37$	0.375316			0.0617016			0.0308508	+	0.999524i	$0.490178\pi$
$38$	−11.8366	−	4.30819i	−1.92016	−	0.698880i
$39$	−1.89339	+	10.5206i	−0.303185	+	1.68465i
$40$	−2.15882	−	1.81147i	−0.341340	−	0.286418i
$41$	6.70424	−	2.44014i	1.04703	−	0.381087i	0.239487	−	0.970900i	$-0.423021\pi$
$41$	6.70424	−	2.44014i	1.04703	−	0.381087i	0.807540	+	0.589813i	$0.200799\pi$
$42$	7.38258	−	6.43443i	1.13916	−	0.992854i
$43$	0.123419	+	0.699942i	0.0188212	+	0.106740i	0.992771	−	0.120023i	$-0.0382968\pi$
$43$	0.123419	+	0.699942i	0.0188212	+	0.106740i	−0.973950	+	0.226763i	$0.927186\pi$
$44$	3.75574			0.566199
$45$	−5.31437	−	4.52361i	−0.792219	−	0.674340i
$46$	7.73844			1.14097
$47$	7.13729	+	2.59776i	1.04108	+	0.378922i	0.805290	−	0.592882i	$-0.202010\pi$
$47$	7.13729	+	2.59776i	1.04108	+	0.378922i	0.235791	+	0.971804i	$0.424232\pi$
$48$	0.750096	+	4.34362i	0.108267	+	0.626947i
$49$	−3.76659	−	5.90024i	−0.538084	−	0.842891i
$50$	0.674022	+	0.565571i	0.0953211	+	0.0799839i
$51$	10.9385	+	0.0386151i	1.53169	+	0.00540720i
$52$	12.1356	−	10.1830i	1.68291	−	1.41213i
$53$	−0.517201	+	0.895818i	−0.0710430	+	0.123050i	−0.899359	−	0.437212i	$-0.855966\pi$
$53$	−0.517201	+	0.895818i	−0.0710430	+	0.123050i	0.828316	+	0.560262i	$0.189299\pi$
$54$	−1.81232	−	10.9554i	−0.246626	−	1.49084i
$55$	−3.40376			−0.458963
$56$	−3.20433	+	0.0714101i	−0.428196	+	0.00954257i
$57$	5.07338	+	8.85944i	0.671986	+	1.17346i
$58$	0.943968	−	5.35351i	0.123949	−	0.702950i
$59$	−2.58481	−	2.16891i	−0.336514	−	0.282369i	0.458834	−	0.888522i	$-0.348267\pi$
$59$	−2.58481	−	2.16891i	−0.336514	−	0.282369i	−0.795348	+	0.606154i	$0.792712\pi$
$60$	1.76002	+	10.1918i	0.227217	+	1.31576i
$61$	−5.48842	−	1.99762i	−0.702720	−	0.255769i	−0.0341481	−	0.999417i	$-0.510872\pi$
$61$	−5.48842	−	1.99762i	−0.702720	−	0.255769i	−0.668572	+	0.743648i	$0.733094\pi$
$62$	6.62011	+	11.4664i	0.840755	+	1.45623i
$63$	−7.93633	+	0.120812i	−0.999884	+	0.0152208i
$64$	5.85507	−	10.1413i	0.731883	−	1.26766i
$65$	−10.9983	+	9.22866i	−1.36417	+	1.14467i
$66$	−4.13641	−	3.49582i	−0.509157	−	0.430306i
$67$	1.04873	−	5.94764i	0.128123	−	0.726619i	−0.851281	−	0.524709i	$-0.824174\pi$
$67$	1.04873	−	5.94764i	0.128123	−	0.726619i	0.979404	−	0.201910i	$-0.0647149\pi$
$68$	−12.4181	−	10.4201i	−1.50592	−	1.26362i
$69$	−4.79035	−	4.04849i	−0.576691	−	0.487381i
$70$	13.1498	−	0.293050i	1.57170	−	0.0350262i
$71$	3.69767	−	6.40455i	0.438833	−	0.760080i	−0.558767	−	0.829325i	$-0.688725\pi$
$71$	3.69767	−	6.40455i	0.438833	−	0.760080i	0.997600	+	0.0692443i	$0.0220588\pi$
$72$	−1.83931	+	3.13446i	−0.216765	+	0.369399i
$73$	−6.77172			−0.792570			−0.396285	−	0.918127i	$-0.629701\pi$
$73$	−6.77172			−0.792570			−0.396285	+	0.918127i	$0.629701\pi$
$74$	0.139276	+	0.789875i	0.0161905	+	0.0918210i
$75$	−0.121354	−	0.702733i	−0.0140128	−	0.0811446i
$76$	2.62729	−	14.9001i	0.301371	−	1.70916i
$77$	−2.90930	+	2.55378i	−0.331545	+	0.291030i
$78$	−22.8439	−	0.0806439i	−2.58656	−	0.00913113i
$79$	0.0335365	+	0.190195i	0.00377315	+	0.0213986i	0.986636	−	0.162939i	$-0.0520973\pi$
$79$	0.0335365	+	0.190195i	0.00377315	+	0.0213986i	−0.982863	+	0.184337i	$0.940986\pi$
$80$	−2.96013	+	5.12709i	−0.330952	+	0.573226i
$81$	−4.60961	+	7.72991i	−0.512179	+	0.858879i
$82$	7.62331	+	13.2040i	0.841853	+	1.45813i
$83$	9.88619	+	3.59828i	1.08515	+	0.394963i	0.821822	−	0.569744i	$-0.192958\pi$
$83$	9.88619	+	3.59828i	1.08515	+	0.394963i	0.263328	+	0.964706i	$0.415180\pi$
$84$	9.15109	+	7.39075i	0.998465	+	0.806397i
$85$	11.2543	+	9.44351i	1.22070	+	1.02429i
$86$	−1.42727	+	0.519483i	−0.153906	+	0.0560173i
$87$	−3.38512	+	2.82015i	−0.362923	+	0.302352i
$88$	0.307791	+	1.74557i	0.0328107	+	0.186079i
$89$	−1.46082	+	2.53022i	−0.154847	+	0.268203i	−0.933003	−	0.359868i	$-0.882822\pi$
$89$	−1.46082	+	2.53022i	−0.154847	+	0.268203i	0.778156	+	0.628071i	$0.216155\pi$
$90$	7.54808	−	12.8631i	0.795638	−	1.35589i
$91$	−2.47647	+	16.1398i	−0.259605	+	1.69191i
$92$	1.61406	+	9.15377i	0.168277	+	0.954346i
$93$	1.90074	−	10.5615i	0.197098	−	1.09517i
$94$	−2.81856	+	15.9848i	−0.290712	+	1.64871i
$95$	−2.38107	+	13.5037i	−0.244292	+	1.38545i
$96$	−12.8115	+	4.61185i	−1.30757	+	0.470695i
$97$	−2.44666	−	13.8757i	−0.248420	−	1.40886i	−0.812413	−	0.583082i	$-0.801847\pi$
$97$	−2.44666	−	13.8757i	−0.248420	−	1.40886i	0.563993	−	0.825780i	$-0.309265\pi$
$98$	11.0196	−	10.1165i	1.11315	−	1.02192i
$99$	0.731684	+	4.32806i	0.0735370	+	0.434986i
$100$	−0.528427	+	0.915262i	−0.0528427	+	0.0915262i
$101$	1.67945	+	9.52463i	0.167111	+	0.947736i	0.946861	+	0.321644i	$0.104235\pi$
$101$	1.67945	+	9.52463i	0.167111	+	0.947736i	−0.779749	+	0.626092i	$0.784653\pi$
$102$	3.97789	+	23.0350i	0.393870	+	2.28080i
$103$	1.60902	−	0.585637i	0.158542	−	0.0577045i	−0.261530	−	0.965195i	$-0.584227\pi$
$103$	1.60902	−	0.585637i	0.158542	−	0.0577045i	0.420072	+	0.907491i	$0.362005\pi$
$104$	5.72733	+	4.80580i	0.561611	+	0.471248i
$105$	−8.29347	−	6.69811i	−0.809360	−	0.653668i
$106$	−2.07723	−	0.756050i	−0.201758	−	0.0734341i
$107$	−1.53920	−	2.66597i	−0.148800	−	0.257729i	0.781984	−	0.623298i	$-0.214208\pi$
$107$	−1.53920	−	2.66597i	−0.148800	−	0.257729i	−0.930784	+	0.365569i	$0.880874\pi$
$108$	12.5811	−	4.42883i	1.21062	−	0.426164i
$109$	−0.812082	+	1.40657i	−0.0777833	+	0.134725i	−0.902293	−	0.431123i	$-0.858118\pi$
$109$	−0.812082	+	1.40657i	−0.0777833	+	0.134725i	0.824510	+	0.565847i	$0.191451\pi$
$110$	−1.26310	−	7.16341i	−0.120432	−	0.683004i
$111$	0.327019	−	0.561823i	0.0310392	−	0.0533259i
$112$	1.31665	+	6.60321i	0.124412	+	0.623944i
$113$	−0.388718	+	2.20453i	−0.0365675	+	0.207385i	−0.997617	−	0.0689905i	$-0.978022\pi$
$113$	−0.388718	+	2.20453i	−0.0365675	+	0.207385i	0.961050	+	0.276375i	$0.0891333\pi$
$114$	−16.7625	+	13.9649i	−1.56995	+	1.30793i
$115$	−1.46279	−	8.29590i	−0.136406	−	0.773597i
$116$	6.52953			0.606252
$117$	14.0989	+	12.0011i	1.30345	+	1.10950i
$118$	3.60541	−	6.24475i	0.331905	−	0.574876i
$119$	16.7047	−	0.372274i	1.53132	−	0.0341263i
$120$	−4.59267	+	1.65326i	−0.419251	+	0.150921i
$121$	−6.78652	−	5.69457i	−0.616956	−	0.517688i
$122$	2.16741	−	12.2920i	0.196228	−	1.11286i
$123$	2.18877	−	12.1619i	0.197355	−	1.09661i
$124$	−12.1827	+	10.2225i	−1.09404	+	0.918009i
$125$	−5.33688	+	9.24374i	−0.477345	+	0.826785i
$126$	−3.19935	−	16.6576i	−0.285021	−	1.48398i
$127$	−9.92699	−	17.1940i	−0.880878	−	1.52572i	−0.850367	−	0.526190i	$-0.823620\pi$
$127$	−9.92699	−	17.1940i	−0.880878	−	1.52572i	−0.0305106	−	0.999534i	$-0.509713\pi$
$128$	8.74111	+	3.18150i	0.772612	+	0.281208i
$129$	1.15530	+	0.425121i	0.101719	+	0.0374298i
$130$	−23.5036	−	19.7219i	−2.06140	−	1.72972i
$131$	0.874588	−	4.96003i	0.0764131	−	0.433360i	−0.922468	−	0.386073i	$-0.873831\pi$
$131$	0.874588	−	4.96003i	0.0764131	−	0.433360i	0.998881	−	0.0472872i	$-0.0150576\pi$
$132$	3.27243	−	5.62209i	0.284829	−	0.489340i
$133$	8.09641	+	13.3285i	0.702048	+	1.15573i
$134$	12.9063			1.11494
$135$	−11.4020	+	4.01377i	−0.981331	+	0.345450i
$136$	3.82528	−	6.62558i	0.328015	−	0.568139i
$137$	6.55693	−	5.50192i	0.560196	−	0.470061i	−0.318180	−	0.948030i	$-0.603072\pi$
$137$	6.55693	−	5.50192i	0.560196	−	0.470061i	0.878376	+	0.477970i	$0.158627\pi$
$138$	6.74262	−	11.5839i	0.573970	−	0.986090i
$139$	8.63861	+	7.24866i	0.732718	+	0.614823i	0.930871	−	0.365348i	$-0.119050\pi$
$139$	8.63861	+	7.24866i	0.732718	+	0.614823i	−0.198153	+	0.980171i	$0.563494\pi$
$140$	3.08938	+	15.4937i	0.261100	+	1.30946i
$141$	10.1075	−	8.42058i	0.851205	−	0.709140i
$142$	14.8509	+	5.40529i	1.24626	+	0.453602i
$143$	9.03012			0.755137
$144$	7.15568	+	2.66182i	0.596307	+	0.221818i
$145$	−5.91760			−0.491430
$146$	−2.51292	−	14.2515i	−0.207971	−	1.17946i
$147$	−12.1141	+	0.497365i	−0.999158	+	0.0410220i
$148$	−0.905289	+	0.329498i	−0.0744143	+	0.0270846i
$149$	−10.8257	−	9.08381i	−0.886873	−	0.744175i	0.0807075	−	0.996738i	$-0.474282\pi$
$149$	−10.8257	−	9.08381i	−0.886873	−	0.744175i	−0.967580	+	0.252563i	$0.918726\pi$
$150$	1.43391	−	0.516175i	0.117078	−	0.0421455i
$151$	14.9078	+	5.42601i	1.21318	+	0.441563i	0.867807	−	0.496902i	$-0.165529\pi$
$151$	14.9078	+	5.42601i	1.21318	+	0.441563i	0.345376	+	0.938464i	$0.387751\pi$
$152$	7.14050			0.579171
$153$	9.58865	−	16.3405i	0.775196	−	1.32105i
$154$	−6.45419	−	5.17510i	−0.520093	−	0.417021i
$155$	11.0410	−	9.26449i	0.886834	−	0.744142i
$156$	−4.66931	−	27.0388i	−0.373844	−	2.16483i
$157$	1.05236	+	0.883038i	0.0839877	+	0.0704741i	0.683815	−	0.729656i	$-0.260320\pi$
$157$	1.05236	+	0.883038i	0.0839877	+	0.0704741i	−0.599827	+	0.800130i	$0.704764\pi$
$158$	−0.387832	+	0.141159i	−0.0308542	+	0.0112300i
$159$	0.890335	+	1.55476i	0.0706082	+	0.123300i
$160$	−17.1851	−	6.25487i	−1.35860	−	0.494491i
$161$	−7.47456	−	5.99325i	−0.589078	−	0.472334i
$162$	−17.9786	−	6.83269i	−1.41253	−	0.536827i
$163$	−8.15141	−	14.1187i	−0.638468	−	1.10586i	−0.985769	−	0.168105i	$-0.946235\pi$
$163$	−8.15141	−	14.1187i	−0.638468	−	1.10586i	0.347302	−	0.937753i	$-0.387098\pi$
$164$	−14.0289	+	11.7716i	−1.09547	+	0.919208i
$165$	−2.96575	+	5.09520i	−0.230883	+	0.396661i
$166$	−3.90412	+	22.1414i	−0.303018	+	1.71850i
$167$	−1.93682	+	10.9843i	−0.149876	+	0.849988i	0.813446	+	0.581640i	$0.197589\pi$
$167$	−1.93682	+	10.9843i	−0.149876	+	0.849988i	−0.963322	+	0.268348i	$0.913522\pi$
$168$	−2.68508	+	4.85888i	−0.207159	+	0.374871i
$169$	19.2197	−	16.1273i	1.47844	−	1.24056i
$170$	−15.6980	+	27.1898i	−1.20399	+	2.08536i
$171$	17.6825	+	0.124848i	1.35221	+	0.00954734i
$172$	−0.912189	−	1.57996i	−0.0695538	−	0.120471i
$173$	9.41636	−	7.90126i	0.715912	−	0.600722i	−0.210339	−	0.977629i	$-0.567457\pi$
$173$	9.41636	−	7.90126i	0.715912	−	0.600722i	0.926251	+	0.376907i	$0.123012\pi$
$174$	−7.19135	−	6.07765i	−0.545175	−	0.460746i
$175$	−0.213015	−	1.06830i	−0.0161024	−	0.0807559i
$176$	3.49904	−	1.27355i	0.263750	−	0.0959971i
$177$	−5.49890	+	1.97948i	−0.413323	+	0.148787i
$178$	−5.86709	−	2.13545i	−0.439757	−	0.160058i
$179$	10.4647	+	18.1254i	0.782171	+	1.35476i	0.930675	+	0.365848i	$0.119221\pi$
$179$	10.4647	+	18.1254i	0.782171	+	1.35476i	−0.148504	+	0.988912i	$0.547446\pi$
$180$	16.7900	+	6.24566i	1.25145	+	0.465524i
$181$	10.3316	+	17.8949i	0.767942	+	1.33012i	0.938677	+	0.344798i	$0.112053\pi$
$181$	10.3316	+	17.8949i	0.767942	+	1.33012i	−0.170734	+	0.985317i	$0.554614\pi$
$182$	−34.8862	+	0.777457i	−2.58594	+	0.0576290i
$183$	−7.77245	+	6.47524i	−0.574556	+	0.478663i
$184$	−4.12216	+	1.50035i	−0.303890	+	0.110607i
$185$	0.820448	−	0.298619i	0.0603205	−	0.0219549i
$186$	22.9326	+	0.0809571i	1.68150	+	0.00593606i
$187$	−1.60457	−	9.09998i	−0.117338	−	0.665456i
$188$	−19.4963			−1.42191
$189$	−6.73420	+	11.9854i	−0.489841	+	0.871812i
$190$	−29.3029			−2.12586
$191$	2.33173	+	13.2239i	0.168718	+	0.956846i	0.945148	+	0.326643i	$0.105917\pi$
$191$	2.33173	+	13.2239i	0.168718	+	0.956846i	−0.776430	+	0.630203i	$0.782971\pi$
$192$	−10.0792	−	17.6009i	−0.727404	−	1.27023i
$193$	−14.3151	+	5.21028i	−1.03043	+	0.375044i	−0.801243	−	0.598339i	$-0.795828\pi$
$193$	−14.3151	+	5.21028i	−1.03043	+	0.375044i	−0.229183	+	0.973383i	$0.573605\pi$
$194$	28.2942	−	10.2983i	2.03141	−	0.739372i
$195$	4.23171	+	24.5048i	0.303039	+	1.75482i
$196$	14.2652	+	10.9250i	1.01895	+	0.780359i
$197$	4.15038	+	7.18868i	0.295703	+	0.512172i	0.975148	−	0.221554i	$-0.0711129\pi$
$197$	4.15038	+	7.18868i	0.295703	+	0.512172i	−0.679446	+	0.733726i	$0.737780\pi$
$198$	−8.83713	+	3.14597i	−0.628027	+	0.223575i
$199$	0.0177052	+	0.0306663i	0.00125509	+	0.00217388i	0.866652	−	0.498913i	$-0.166267\pi$
$199$	0.0177052	+	0.0306663i	0.00125509	+	0.00217388i	−0.865397	+	0.501087i	$0.832934\pi$
$200$	−0.468696	−	0.170592i	−0.0331418	−	0.0120626i
$201$	−7.98944	−	6.75214i	−0.563532	−	0.476259i
$202$	−19.4219	+	7.06900i	−1.36652	+	0.497373i
$203$	−5.05795	+	4.43987i	−0.354999	+	0.311618i
$204$	−26.4182	+	9.50997i	−1.84965	+	0.665831i
$205$	12.7141	−	10.6684i	0.887992	−	0.745114i
$206$	1.82960	+	3.16896i	0.127474	+	0.220792i
$207$	−10.2342	+	3.64333i	−0.711328	+	0.253229i
$208$	7.85317	−	13.6021i	0.544520	−	0.943135i
$209$	6.60660	−	5.54360i	0.456988	−	0.383458i
$210$	11.0189	−	19.9397i	0.760379	−	1.37597i
$211$	0.173013	−	0.981208i	0.0119107	−	0.0675491i	−0.978273	−	0.207321i	$-0.933526\pi$
$211$	0.173013	−	0.981208i	0.0119107	−	0.0675491i	0.990184	+	0.139771i	$0.0446368\pi$
$212$	0.461067	−	2.61484i	0.0316662	−	0.179588i
$213$	−6.36535	−	11.1155i	−0.436147	−	0.761625i
$214$	5.03951	−	4.22865i	0.344494	−	0.289065i
$215$	0.826701	+	1.43189i	0.0563806	+	0.0976540i
$216$	3.08946	+	5.48442i	0.210211	+	0.373168i
$217$	2.48609	−	16.2025i	0.168767	−	1.09990i
$218$	−3.26156	−	1.18711i	−0.220901	−	0.0804012i
$219$	−5.90031	+	10.1368i	−0.398706	+	0.684983i
$220$	8.21011	−	2.98824i	0.553526	−	0.201467i
$221$	−29.8576	−	25.0535i	−2.00844	−	1.68528i
$222$	1.30374	+	0.479743i	0.0875015	+	0.0321982i
$223$	14.0014	−	11.7485i	0.937601	−	0.786741i	−0.0395650	−	0.999217i	$-0.512597\pi$
$223$	14.0014	−	11.7485i	0.937601	−	0.786741i	0.977166	+	0.212476i	$0.0681528\pi$
$224$	−19.3815	+	7.54745i	−1.29498	+	0.504286i
$225$	−1.15768	−	0.430642i	−0.0771788	−	0.0287095i
$226$	−4.78381			−0.318214
$227$	−4.94795	−	1.80091i	−0.328407	−	0.119530i	0.172554	−	0.985000i	$-0.444798\pi$
$227$	−4.94795	−	1.80091i	−0.328407	−	0.119530i	−0.500961	+	0.865470i	$0.667020\pi$
$228$	−20.0153	−	16.9156i	−1.32554	−	1.12026i
$229$	2.74297	+	2.30162i	0.181260	+	0.152096i	0.728903	−	0.684617i	$-0.240030\pi$
$229$	2.74297	+	2.30162i	0.181260	+	0.152096i	−0.547643	+	0.836712i	$0.684475\pi$
$230$	16.9164	−	6.15706i	1.11543	−	0.405984i
$231$	1.28792	+	6.58017i	0.0847392	+	0.432943i
$232$	0.535110	+	3.03476i	0.0351317	+	0.199242i
$233$	1.43067			0.0937262			0.0468631	−	0.998901i	$-0.485078\pi$
$233$	1.43067			0.0937262			0.0468631	+	0.998901i	$0.485078\pi$
$234$	−20.0250	+	34.1255i	−1.30907	+	2.23086i
$235$	17.6691			1.15261
$236$	8.13889	+	2.96231i	0.529796	+	0.192830i
$237$	0.313930	+	0.115518i	0.0203920	+	0.00750370i
$238$	6.98244	+	35.0179i	0.452604	+	2.26987i
$239$	10.1253	+	8.49612i	0.654950	+	0.549569i	0.908569	−	0.417736i	$-0.137176\pi$
$239$	10.1253	+	8.49612i	0.654950	+	0.549569i	−0.253618	+	0.967304i	$0.581621\pi$
$240$	5.09571	+	8.89842i	0.328926	+	0.574391i
$241$	−22.2596	+	18.6780i	−1.43386	+	1.20316i	−0.490481	+	0.871452i	$0.663179\pi$
$241$	−22.2596	+	18.6780i	−1.43386	+	1.20316i	−0.943384	+	0.331703i	$0.892377\pi$
$242$	9.46613	−	16.3958i	0.608506	−	1.05396i
$243$	7.55474	+	13.6355i	0.484637	+	0.874716i
$244$	14.9922			0.959778
$245$	−12.9283	−	9.90116i	−0.825961	−	0.632562i
$246$	26.4077	+	0.0932251i	1.68370	+	0.00594381i
$247$	6.31694	−	35.8251i	0.401937	−	2.27950i
$248$	−5.74957	−	4.82446i	−0.365098	−	0.306354i
$249$	14.0004	−	11.6637i	0.887238	−	0.739159i
$250$	−21.4345	−	7.80150i	−1.35563	−	0.493410i
$251$	2.58209	+	4.47231i	0.162980	+	0.282290i	0.935936	−	0.352170i	$-0.114556\pi$
$251$	2.58209	+	4.47231i	0.162980	+	0.282290i	−0.772956	+	0.634460i	$0.781223\pi$
$252$	19.0369	−	7.25889i	1.19921	−	0.457267i
$253$	−2.64914	+	4.58844i	−0.166550	+	0.288473i
$254$	32.5021	−	27.2725i	2.03936	−	1.71123i
$255$	23.9424	−	8.61872i	1.49933	−	0.539725i
$256$	0.614970	−	3.48767i	0.0384356	−	0.217979i
$257$	−22.7350	−	19.0769i	−1.41817	−	1.18998i	−0.952313	−	0.305123i	$-0.901302\pi$
$257$	−22.7350	−	19.0769i	−1.41817	−	1.18998i	−0.465855	−	0.884861i	$-0.654253\pi$
$258$	−0.465969	+	2.58916i	−0.0290100	+	0.161194i
$259$	0.477213	−	0.870806i	0.0296526	−	0.0541092i
$260$	18.4266	−	31.9158i	1.14277	−	1.97934i
$261$	1.27207	+	7.52454i	0.0787390	+	0.465757i
$262$	10.7632			0.664955
$263$	−4.58677	−	26.0129i	−0.282833	−	1.60402i	−0.712926	−	0.701239i	$-0.752631\pi$
$263$	−4.58677	−	26.0129i	−0.282833	−	1.60402i	0.430094	−	0.902784i	$-0.358480\pi$
$264$	2.88119	+	1.06020i	0.177325	+	0.0652508i
$265$	−0.417857	+	2.36978i	−0.0256687	+	0.145575i
$266$	−25.0461	+	21.9854i	−1.53567	+	1.34801i
$267$	2.51473	+	4.39137i	0.153899	+	0.268747i
$268$	2.69195	+	15.2668i	0.164437	+	0.932570i
$269$	4.17652	−	7.23394i	0.254647	−	0.441061i	−0.710153	−	0.704048i	$-0.751374\pi$
$269$	4.17652	−	7.23394i	0.254647	−	0.441061i	0.964800	+	0.262986i	$0.0847075\pi$
$270$	−12.6784	−	22.5068i	−0.771582	−	1.36972i
$271$	11.6652	+	20.2047i	0.708609	+	1.22735i	0.965373	+	0.260873i	$0.0840104\pi$
$271$	11.6652	+	20.2047i	0.708609	+	1.22735i	−0.256764	+	0.966474i	$0.582656\pi$
$272$	−15.1028	−	5.49695i	−0.915739	−	0.333302i
$273$	22.0025	+	17.7700i	1.33165	+	1.07549i
$274$	14.0123	+	11.7577i	0.846515	+	0.710311i
$275$	−0.566092	+	0.206041i	−0.0341366	+	0.0124247i
$276$	15.1089	+	5.55968i	0.909451	+	0.334654i
$277$	3.78966	+	21.4922i	0.227699	+	1.29134i	0.857459	+	0.514553i	$0.172042\pi$
$277$	3.78966	+	21.4922i	0.227699	+	1.29134i	−0.629760	+	0.776790i	$0.716847\pi$
$278$	−12.0495	+	20.8704i	−0.722682	+	1.25172i
$279$	−14.1537	−	12.0477i	−0.847359	−	0.721275i
$280$	−6.94790	+	2.70561i	−0.415216	+	0.161691i
$281$	4.66276	+	26.4438i	0.278157	+	1.57751i	0.728751	+	0.684778i	$0.240101\pi$
$281$	4.66276	+	26.4438i	0.278157	+	1.57751i	−0.450594	+	0.892729i	$0.648788\pi$
$282$	21.4724	+	18.1470i	1.27866	+	1.08064i
$283$	−2.25911	+	12.8120i	−0.134290	+	0.761597i	0.841061	+	0.540940i	$0.181931\pi$
$283$	−2.25911	+	12.8120i	−0.134290	+	0.761597i	−0.975351	+	0.220657i	$0.929180\pi$
$284$	−3.29634	+	18.6945i	−0.195602	+	1.10931i
$285$	18.1395	+	15.3303i	1.07449	+	0.908087i
$286$	3.35099	+	19.0044i	0.198148	+	1.12376i
$287$	2.86282	−	18.6578i	0.168987	−	1.10133i
$288$	−4.25922	+	23.1963i	−0.250977	+	1.36686i
$289$	−11.4419	+	19.8179i	−0.673053	+	1.16576i
$290$	−2.19596	−	12.4539i	−0.128951	−	0.731320i
$291$	−22.9028	−	8.42761i	−1.34258	−	0.494035i
$292$	16.3339	−	5.94505i	0.955868	−	0.347908i
$293$	−16.5967	−	13.9263i	−0.969592	−	0.813584i	0.0128946	−	0.999917i	$-0.495895\pi$
$293$	−16.5967	−	13.9263i	−0.969592	−	0.813584i	−0.982487	+	0.186332i	$0.940340\pi$
$294$	−5.54218	−	25.3104i	−0.323226	−	1.47613i
$295$	−7.37613	−	2.68469i	−0.429455	−	0.156309i
$296$	−0.227333	−	0.393752i	−0.0132135	−	0.0228864i
$297$	7.11634	+	2.67582i	0.412932	+	0.155267i
$298$	15.1001	−	26.1542i	0.874726	−	1.51507i
$299$	3.88076	+	22.0089i	0.224430	+	1.27281i
$300$	0.909660	+	1.58850i	0.0525192	+	0.0917122i
$301$	1.78093	+	0.603619i	0.102651	+	0.0347920i
$302$	−5.88720	+	33.3880i	−0.338770	+	1.92126i
$303$	15.7211	+	5.78493i	0.903152	+	0.332336i
$304$	−2.60481	−	14.7726i	−0.149396	−	0.847266i
$305$	−13.5872			−0.778000
$306$	37.9478	+	14.1161i	2.16933	+	0.806962i
$307$	2.66936	−	4.62347i	0.152348	−	0.263875i	−0.779742	−	0.626101i	$-0.784650\pi$
$307$	2.66936	−	4.62347i	0.152348	−	0.263875i	0.932090	+	0.362226i	$0.117983\pi$
$308$	4.77541	−	8.71403i	0.272104	−	0.496528i
$309$	0.525308	−	2.91888i	0.0298837	−	0.166049i
$310$	23.5949	+	19.7984i	1.34010	+	1.12448i
$311$	−2.63744	+	14.9577i	−0.149556	+	0.848172i	0.814040	+	0.580809i	$0.197264\pi$
$311$	−2.63744	+	14.9577i	−0.149556	+	0.848172i	−0.963596	+	0.267364i	$0.913848\pi$
$312$	12.1843	−	4.38607i	0.689799	−	0.248312i
$313$	−5.78325	+	4.85272i	−0.326889	+	0.274292i	−0.791431	−	0.611259i	$-0.790663\pi$
$313$	−5.78325	+	4.85272i	−0.326889	+	0.274292i	0.464542	+	0.885551i	$0.346219\pi$
$314$	−1.46788	+	2.54245i	−0.0828374	+	0.143479i
$315$	−17.2528	+	6.57861i	−0.972088	+	0.370662i
$316$	−0.247869	−	0.429322i	−0.0139437	−	0.0241512i
$317$	−3.63433	−	1.32279i	−0.204125	−	0.0742953i	0.237935	−	0.971281i	$-0.423530\pi$
$317$	−3.63433	−	1.32279i	−0.204125	−	0.0742953i	−0.442059	+	0.896986i	$0.645752\pi$
$318$	−2.94168	+	2.45072i	−0.164961	+	0.137429i
$319$	2.85116	+	2.39241i	0.159635	+	0.133949i
$320$	4.73042	−	26.8276i	0.264439	−	1.49971i
$321$	−5.33191	−	0.0188228i	−0.297598	−	0.00105059i
$322$	9.83941	−	17.9547i	0.548329	−	1.00058i
$323$	−37.2247			−2.07124
$324$	4.33245	−	22.6920i	0.240691	−	1.26067i
$325$	−1.27053	+	2.20061i	−0.0704761	+	0.122068i
$326$	26.6886	−	22.3944i	1.47815	−	1.24031i
$327$	1.39796	+	2.44120i	0.0773072	+	0.134998i
$328$	−6.62084	−	5.55555i	−0.365575	−	0.306754i
$329$	15.1023	−	13.2568i	0.832619	−	0.730873i
$330$	−11.8237	−	4.35081i	−0.650874	−	0.239504i
$331$	−12.9416	−	4.71035i	−0.711333	−	0.258904i	−0.0390912	−	0.999236i	$-0.512446\pi$
$331$	−12.9416	−	4.71035i	−0.711333	−	0.258904i	−0.672242	+	0.740332i	$0.734669\pi$
$332$	−27.0052			−1.48210
$333$	−0.556076	−	0.979050i	−0.0304728	−	0.0536516i
$334$	−23.8358			−1.30423
$335$	−2.43967	−	13.8361i	−0.133293	−	0.755945i
$336$	11.0318	+	3.78253i	0.601833	+	0.206354i
$337$	−5.07604	+	1.84753i	−0.276509	+	0.100641i	−0.476553	−	0.879146i	$-0.658114\pi$
$337$	−5.07604	+	1.84753i	−0.276509	+	0.100641i	0.200043	+	0.979787i	$0.435892\pi$
$338$	41.0730	+	34.4643i	2.23408	+	1.87461i
$339$	2.96134	+	2.50273i	0.160838	+	0.135929i
$340$	−35.4370	−	12.8980i	−1.92184	−	0.699492i
$341$	−9.06519			−0.490907
$342$	6.29906	+	37.2602i	0.340614	+	2.01480i
$343$	−18.4789	+	1.23707i	−0.997767	+	0.0667958i
$344$	0.659569	−	0.553444i	0.0355616	−	0.0298397i
$345$	−13.6930	−	5.03864i	−0.737204	−	0.271271i
$346$	20.1230	+	16.8852i	1.08182	+	0.907753i
$347$	9.33144	−	3.39636i	0.500938	−	0.182326i	−0.0791780	−	0.996860i	$-0.525230\pi$
$347$	9.33144	−	3.39636i	0.500938	−	0.182326i	0.580116	+	0.814534i	$0.303007\pi$
$348$	5.68928	−	9.77427i	0.304977	−	0.523956i
$349$	11.9746	+	4.35840i	0.640986	+	0.233300i	0.642006	−	0.766700i	$-0.278103\pi$
$349$	11.9746	+	4.35840i	0.640986	+	0.233300i	−0.00102019	+	0.999999i	$0.500325\pi$
$350$	2.16925	−	0.844738i	0.115951	−	0.0451531i
$351$	30.2494	−	10.6485i	1.61460	−	0.568373i
$352$	5.75121	+	9.96139i	0.306541	+	0.530944i
$353$	−11.9407	+	10.0194i	−0.635540	+	0.533281i	−0.902645	−	0.430386i	$-0.858377\pi$
$353$	−11.9407	+	10.0194i	−0.635540	+	0.533281i	0.267105	+	0.963667i	$0.413933\pi$
$354$	−6.20653	−	10.8382i	−0.329873	−	0.576044i
$355$	2.98742	−	16.9425i	0.158556	−	0.899214i
$356$	1.30227	−	7.38555i	0.0690203	−	0.391434i
$357$	13.9978	−	25.3302i	0.740843	−	1.34062i
$358$	−34.2627	+	28.7498i	−1.81084	+	1.51948i
$359$	7.46084	−	12.9226i	0.393768	−	0.682026i	−0.599175	−	0.800618i	$-0.704505\pi$
$359$	7.46084	−	12.9226i	0.393768	−	0.682026i	0.992943	+	0.118592i	$0.0378380\pi$
$360$	−1.52685	+	8.31542i	−0.0804718	+	0.438261i
$361$	−7.87146	−	13.6338i	−0.414288	−	0.717567i
$362$	−33.8268	+	28.3841i	−1.77790	+	1.49183i
$363$	−14.4376	+	5.19721i	−0.757777	+	0.272783i
$364$	−8.19609	−	41.1046i	−0.429592	−	2.15446i
$365$	−14.8031	+	5.38789i	−0.774830	+	0.282015i
$366$	−16.5118	−	13.9547i	−0.863085	−	0.729422i
$367$	9.93599	+	3.61640i	0.518654	+	0.188775i	0.588065	−	0.808813i	$-0.299890\pi$
$367$	9.93599	+	3.61640i	0.518654	+	0.188775i	−0.0694110	+	0.997588i	$0.522112\pi$
$368$	4.60772	+	7.98081i	0.240194	+	0.416028i
$369$	−16.2985	−	13.8733i	−0.848466	−	0.722217i
$370$	0.932920	+	1.61587i	0.0485002	+	0.0840049i
$371$	1.42085	+	2.33904i	0.0737669	+	0.121437i
$372$	4.68744	+	27.1438i	0.243032	+	1.40734i
$373$	22.5189	−	8.19620i	1.16598	−	0.424383i	0.314752	−	0.949174i	$-0.398079\pi$
$373$	22.5189	−	8.19620i	1.16598	−	0.424383i	0.851231	+	0.524791i	$0.175856\pi$
$374$	18.5560	−	6.75383i	0.959508	−	0.349232i
$375$	9.18716	+	16.0432i	0.474423	+	0.828465i
$376$	−1.59777	−	9.06138i	−0.0823985	−	0.467305i
$377$	15.6993			0.808556
$378$	−27.7230	−	9.72484i	−1.42592	−	0.500192i
$379$	−37.7717			−1.94020			−0.970102	−	0.242698i	$-0.921968\pi$
$379$	−37.7717			−1.94020			−0.970102	+	0.242698i	$0.921968\pi$
$380$	−6.11189	−	34.6623i	−0.313534	−	1.77814i
$381$	−34.3879	−	0.121397i	−1.76174	−	0.00621934i
$382$	−26.9651	+	9.81451i	−1.37966	+	0.502154i
$383$	−4.79996	+	1.74704i	−0.245267	+	0.0892698i	−0.461728	−	0.887021i	$-0.652771\pi$
$383$	−4.79996	+	1.74704i	−0.245267	+	0.0892698i	0.216462	+	0.976291i	$0.430548\pi$
$384$	12.3788	−	10.3128i	0.631701	−	0.526271i
$385$	−4.32787	+	7.89738i	−0.220569	+	0.402488i
$386$	−16.2775	−	28.1935i	−0.828505	−	1.43501i
$387$	1.64301	−	1.35900i	0.0835189	−	0.0690817i
$388$	18.0833	+	31.3212i	0.918039	+	1.59009i
$389$	4.76924	+	1.73586i	0.241810	+	0.0880117i	0.460082	−	0.887876i	$-0.347820\pi$
$389$	4.76924	+	1.73586i	0.241810	+	0.0880117i	−0.218272	+	0.975888i	$0.570042\pi$
$390$	−50.0014	+	17.9994i	−2.53192	+	0.911433i
$391$	21.4896	−	7.82157i	1.08678	−	0.395554i
$392$	−3.90861	+	7.52545i	−0.197414	+	0.380093i
$393$	−6.66280	−	5.63095i	−0.336094	−	0.284044i
$394$	−13.5888	+	11.4024i	−0.684595	+	0.574443i
$395$	0.224639	+	0.389087i	0.0113028	+	0.0195771i
$396$	−5.56457	−	9.79722i	−0.279630	−	0.492329i
$397$	6.93068	−	12.0043i	0.347841	−	0.602478i	−0.638025	−	0.770016i	$-0.720248\pi$
$397$	6.93068	−	12.0043i	0.347841	−	0.602478i	0.985866	+	0.167538i	$0.0535817\pi$
$398$	−0.0579688	+	0.0486416i	−0.00290572	+	0.00243818i
$399$	27.0064	−	0.506473i	1.35201	−	0.0253554i
$400$	−0.181950	+	1.03189i	−0.00909752	+	0.0515946i
$401$	−0.514490	+	2.91782i	−0.0256924	+	0.145709i	−0.994955	−	0.100318i	$-0.968014\pi$
$401$	−0.514490	+	2.91782i	−0.0256924	+	0.145709i	0.969263	+	0.246027i	$0.0791251\pi$
$402$	11.2455	−	19.3199i	0.560873	−	0.963589i
$403$	−29.2916	+	24.5786i	−1.45912	+	1.22435i
$404$	−12.4128	−	21.4997i	−0.617562	−	1.06965i
$405$	−3.92642	+	20.5653i	−0.195105	+	1.02190i
$406$	−11.2209	−	8.99716i	−0.556885	−	0.446522i
$407$	−0.516029	−	0.187819i	−0.0255786	−	0.00930984i
$408$	−6.58503	−	11.4992i	−0.326008	−	0.569294i
$409$	−5.65537	+	2.05839i	−0.279640	+	0.101781i	−0.478033	−	0.878342i	$-0.658650\pi$
$409$	−5.65537	+	2.05839i	−0.279640	+	0.101781i	0.198393	+	0.980123i	$0.436428\pi$
$410$	27.1704	+	22.7986i	1.34185	+	1.12594i
$411$	−2.52285	−	14.6092i	−0.124443	−	0.720618i
$412$	−3.36694	+	2.82520i	−0.165877	+	0.139187i
$413$	−8.31888	+	3.23949i	−0.409345	+	0.159405i
$414$	−11.4654	−	20.1865i	−0.563495	−	0.992113i
$415$	24.4744			1.20140
$416$	45.5919	+	16.5941i	2.23532	+	0.813592i
$417$	18.3777	−	6.61556i	0.899961	−	0.323966i
$418$	14.1185	+	11.8468i	0.690557	+	0.579446i
$419$	−7.39201	+	2.69047i	−0.361123	+	0.131438i	−0.516209	−	0.856463i	$-0.672657\pi$
$419$	−7.39201	+	2.69047i	−0.361123	+	0.131438i	0.155085	+	0.987901i	$0.450435\pi$
$420$	25.8849	+	8.87530i	1.26305	+	0.433070i
$421$	0.794417	+	4.50536i	0.0387175	+	0.219578i	0.998028	−	0.0627768i	$-0.0199956\pi$
$421$	0.794417	+	4.50536i	0.0387175	+	0.219578i	−0.959310	+	0.282355i	$0.908885\pi$
$422$	2.12921			0.103648
$423$	−3.79822	−	22.4672i	−0.184676	−	1.09239i
$424$	1.25310			0.0608558
$425$	2.44340	+	0.889325i	0.118522	+	0.0431386i
$426$	21.0312	−	17.5211i	1.01896	−	0.848901i
$427$	−11.6134	+	10.1942i	−0.562011	+	0.493333i
$428$	6.05318	+	5.07922i	0.292591	+	0.245513i
$429$	7.86809	−	13.5175i	0.379875	−	0.652631i
$430$	−2.70671	+	2.27120i	−0.130529	+	0.109527i
$431$	−7.55944	+	13.0933i	−0.364126	+	0.630684i	−0.988635	−	0.150333i	$-0.951965\pi$
$431$	−7.55944	+	13.0933i	−0.364126	+	0.630684i	0.624510	+	0.781017i	$0.285299\pi$
$432$	10.2194	−	8.39229i	0.491682	−	0.403774i
$433$	23.9348			1.15024			0.575118	−	0.818071i	$-0.304956\pi$
$433$	23.9348			1.15024			0.575118	+	0.818071i	$0.304956\pi$
$434$	35.0217	−	0.780476i	1.68109	−	0.0374641i
$435$	−5.15609	+	8.85825i	−0.247216	+	0.424721i
$436$	0.723943	−	4.10568i	0.0346706	−	0.196627i
$437$	16.3505	+	13.7197i	0.782151	+	0.656303i
$438$	−23.5231	−	8.65586i	−1.12398	−	0.413593i
$439$	−12.4086	−	4.51635i	−0.592229	−	0.215554i	0.0284806	−	0.999594i	$-0.490933\pi$
$439$	−12.4086	−	4.51635i	−0.592229	−	0.215554i	−0.620709	+	0.784041i	$0.713155\pi$
$440$	2.06169	+	3.57096i	0.0982874	+	0.170239i
$441$	−9.81072	+	18.5674i	−0.467177	+	0.884164i
$442$	41.6467	−	72.1342i	1.98093	−	3.43107i
$443$	−24.7912	+	20.8023i	−1.17787	+	0.988346i	−0.177874	+	0.984053i	$0.556922\pi$
$443$	−24.7912	+	20.8023i	−1.17787	+	0.988346i	−0.999991	+	0.00429310i	$0.998633\pi$
$444$	−0.295555	+	1.64225i	−0.0140264	+	0.0779380i
$445$	−1.18023	+	6.69340i	−0.0559481	+	0.317298i
$446$	29.9213	+	25.1069i	1.41681	+	1.18885i
$447$	−23.0304	+	8.29043i	−1.08930	+	0.392124i
$448$	−16.0850	−	26.4795i	−0.759945	−	1.25104i
$449$	8.34855	−	14.4601i	0.393992	−	0.682415i	−0.598980	−	0.800764i	$-0.704427\pi$
$449$	8.34855	−	14.4601i	0.393992	−	0.682415i	0.992972	+	0.118349i	$0.0377603\pi$
$450$	0.476707	−	2.59622i	0.0224722	−	0.122387i
$451$	−10.4389			−0.491549
$452$	−0.997790	−	5.65875i	−0.0469321	−	0.266165i
$453$	21.1118	−	17.5883i	0.991919	−	0.826370i
$454$	1.95398	−	11.0816i	0.0917047	−	0.520083i
$455$	7.42797	+	37.2524i	0.348229	+	1.74642i
$456$	6.22163	−	10.6889i	0.291354	−	0.500551i
$457$	0.0143321	+	0.0812812i	0.000670426	+	0.00380217i	0.985141	−	0.171747i	$-0.0549411\pi$
$457$	0.0143321	+	0.0812812i	0.000670426	+	0.00380217i	−0.984471	+	0.175549i	$0.943830\pi$
$458$	−3.82601	+	6.62685i	−0.178778	+	0.309652i
$459$	−16.1059	−	28.5913i	−0.751759	−	1.33453i
$460$	10.8115	+	18.7261i	0.504089	+	0.873108i
$461$	33.5842	+	12.2237i	1.56417	+	0.569312i	0.971688	−	0.236269i	$-0.0759247\pi$
$461$	33.5842	+	12.2237i	1.56417	+	0.569312i	0.592485	+	0.805581i	$0.298147\pi$
$462$	−13.3704	+	5.15235i	−0.622048	+	0.239709i
$463$	−17.9836	−	15.0900i	−0.835768	−	0.701292i	0.120840	−	0.992672i	$-0.461441\pi$
$463$	−17.9836	−	15.0900i	−0.835768	−	0.701292i	−0.956607	+	0.291380i	$0.905886\pi$
$464$	6.08325	−	2.21412i	0.282408	−	0.102788i
$465$	−4.24814	−	24.5999i	−0.197003	−	1.14079i
$466$	0.530907	+	3.01092i	0.0245938	+	0.139478i
$467$	7.82703	−	13.5568i	0.362192	−	0.627334i	−0.626130	−	0.779719i	$-0.715362\pi$
$467$	7.82703	−	13.5568i	0.362192	−	0.627334i	0.988321	+	0.152385i	$0.0486953\pi$
$468$	−44.5437	−	16.5697i	−2.05903	−	0.765933i
$469$	−12.4662	−	9.99566i	−0.575636	−	0.461557i
$470$	6.55685	+	37.1857i	0.302445	+	1.71525i
$471$	2.23879	−	0.805914i	0.103158	−	0.0371345i
$472$	−0.709807	+	4.02552i	−0.0326715	+	0.185289i
$473$	0.180581	−	1.02412i	0.00830311	−	0.0470893i
$474$	−0.126618	+	0.703552i	−0.00581574	+	0.0323152i
$475$	0.421419	+	2.38998i	0.0193360	+	0.109660i
$476$	−39.9662	+	15.5634i	−1.83185	+	0.713347i
$477$	3.10313	+	0.0219097i	0.142082	+	0.00100318i
$478$	−14.1232	+	24.4621i	−0.645980	+	1.11887i
$479$	−0.769741	−	4.36542i	−0.0351704	−	0.199461i	0.962160	−	0.272486i	$-0.0878459\pi$
$479$	−0.769741	−	4.36542i	−0.0351704	−	0.199461i	−0.997330	+	0.0730249i	$0.976735\pi$
$480$	−24.3368	+	20.2750i	−1.11082	+	0.925423i
$481$	−2.17664	+	0.792231i	−0.0992461	+	0.0361226i
$482$	−47.5692	−	39.9153i	−2.16672	−	1.81809i
$483$	−15.4842	+	5.96690i	−0.704555	+	0.271503i
$484$	21.3690	+	7.77767i	0.971316	+	0.353530i
$485$	−16.3886	−	28.3858i	−0.744166	−	1.28893i
$486$	−25.8931	+	20.9594i	−1.17454	+	0.950737i
$487$	−2.36648	+	4.09887i	−0.107236	+	0.185737i	−0.914649	−	0.404248i	$-0.867533\pi$
$487$	−2.36648	+	4.09887i	−0.107236	+	0.185737i	0.807414	+	0.589986i	$0.200867\pi$
$488$	1.22865	+	6.96800i	0.0556182	+	0.315427i
$489$	−28.2371	−	0.0996832i	−1.27693	−	0.00450783i
$490$	16.0400	−	30.8826i	0.724613	−	1.39514i
$491$	5.47411	−	31.0452i	0.247043	−	1.40105i	−0.568656	−	0.822575i	$-0.692536\pi$
$491$	5.47411	−	31.0452i	0.247043	−	1.40105i	0.815699	−	0.578476i	$-0.196352\pi$
$492$	5.39776	+	31.2570i	0.243350	+	1.40918i
$493$	−2.78963	−	15.8208i	−0.125638	−	0.712531i
$494$	77.7402			3.49770
$495$	5.04307	+	8.87905i	0.226669	+	0.399084i
$496$	−7.88367	+	13.6549i	−0.353987	+	0.613124i
$497$	−10.1582	−	16.7227i	−0.455658	−	0.750114i
$498$	29.7424	+	25.1363i	1.33279	+	1.12638i
$499$	−7.99879	−	6.71178i	−0.358075	−	0.300461i	0.445948	−	0.895059i	$-0.352867\pi$
$499$	−7.99879	−	6.71178i	−0.358075	−	0.300461i	−0.804023	+	0.594598i	$0.797311\pi$
$500$	4.75764	−	26.9819i	0.212768	−	1.20667i
$501$	14.7551	+	12.4701i	0.659211	+	0.557121i
$502$	−8.45406	+	7.09380i	−0.377323	+	0.316612i
$503$	17.1453	−	29.6965i	0.764470	−	1.32410i	−0.176057	−	0.984380i	$-0.556334\pi$
$503$	17.1453	−	29.6965i	0.764470	−	1.32410i	0.940526	−	0.339720i	$-0.110332\pi$
$504$	4.93387	+	8.25301i	0.219772	+	0.367618i
$505$	11.2495	+	19.4848i	0.500598	+	0.867061i
$506$	−10.6397	−	3.87254i	−0.472993	−	0.172155i
$507$	−7.39500	−	42.8226i	−0.328423	−	1.90182i
$508$	39.0396	+	32.7581i	1.73210	+	1.45341i
$509$	−5.41332	+	30.7005i	−0.239941	+	1.36077i	0.592012	+	0.805929i	$0.298334\pi$
$509$	−5.41332	+	30.7005i	−0.239941	+	1.36077i	−0.831953	+	0.554846i	$0.812777\pi$
$510$	27.0234	+	47.1898i	1.19662	+	2.08960i
$511$	−8.61023	+	15.7117i	−0.380894	+	0.695045i
$512$	26.1724			1.15667
$513$	15.5939	−	26.3607i	0.688488	−	1.16386i
$514$	31.7117	−	54.9263i	1.39874	−	2.42270i
$515$	3.05140	−	2.56043i	0.134461	−	0.112826i
$516$	−3.15990	−	0.0111551i	−0.139107	−	0.000491077i
$517$	−8.51319	−	7.14341i	−0.374410	−	0.314167i
$518$	2.00975	+	0.681176i	0.0883034	+	0.0299291i
$519$	−3.62305	−	20.9802i	−0.159034	−	0.920926i
$520$	16.3438	+	5.94864i	0.716722	+	0.260865i
$521$	6.87522			0.301209			0.150604	−	0.988594i	$-0.451878\pi$
$521$	6.87522			0.301209			0.150604	+	0.988594i	$0.451878\pi$
$522$	−15.3638	+	5.46942i	−0.672454	+	0.239390i
$523$	−34.3434			−1.50173			−0.750865	−	0.660456i	$-0.770363\pi$
$523$	−34.3434			−1.50173			−0.750865	+	0.660456i	$0.770363\pi$
$524$	2.24496	+	12.7318i	0.0980713	+	0.556190i
$525$	−1.78478	−	0.611957i	−0.0778940	−	0.0267080i
$526$	53.0435	−	19.3063i	2.31281	−	0.841793i
$527$	29.9735	+	25.1508i	1.30567	+	1.09559i
$528$	1.14235	−	6.34749i	0.0497145	−	0.276239i
$529$	9.29113	+	3.38170i	0.403962	+	0.147030i
$530$	−5.14241			−0.223372
$531$	−1.82813	+	9.95625i	−0.0793340	+	0.432064i
$532$	−31.2305	−	25.0413i	−1.35401	−	1.08568i
$533$	−33.7303	+	28.3031i	−1.46102	+	1.22594i
$534$	−8.30870	+	6.92199i	−0.359553	+	0.299544i
$535$	−5.48589	−	4.60321i	−0.237176	−	0.199014i
$536$	−6.87502	+	2.50230i	−0.296956	+	0.108083i
$537$	36.2507	+	0.127973i	1.56433	+	0.00552243i
$538$	16.7741	+	6.10528i	0.723184	+	0.263217i
$539$	2.22610	+	9.99725i	0.0958848	+	0.430612i
$540$	23.9787	−	19.6916i	1.03188	−	0.847391i
$541$	20.9638	+	36.3104i	0.901306	+	1.56111i	0.825800	+	0.563963i	$0.190724\pi$
$541$	20.9638	+	36.3104i	0.901306	+	1.56111i	0.0755060	+	0.997145i	$0.475943\pi$
$542$	−38.1931	+	32.0478i	−1.64053	+	1.37657i
$543$	35.7895	+	0.126345i	1.53588	+	0.00542197i
$544$	8.62118	−	48.8932i	0.369630	−	2.09628i
$545$	−0.656097	+	3.72091i	−0.0281041	+	0.159386i
$546$	−29.2331	+	52.8997i	−1.25106	+	2.26390i
$547$	−9.91952	+	8.32346i	−0.424128	+	0.355886i	−0.829731	−	0.558164i	$-0.811506\pi$
$547$	−9.91952	+	8.32346i	−0.424128	+	0.355886i	0.405603	+	0.914049i	$0.367062\pi$
$548$	−10.9855	+	19.0275i	−0.469279	+	0.812814i
$549$	2.92075	+	17.2768i	0.124654	+	0.737356i
$550$	−0.643696	−	1.11491i	−0.0274473	−	0.0475401i
$551$	11.4859	−	9.63781i	0.489315	−	0.410584i
$552$	−1.34579	+	7.47788i	−0.0572805	+	0.318280i
$553$	0.483931	+	0.164021i	0.0205788	+	0.00697490i
$554$	−43.8253	+	15.9511i	−1.86196	+	0.677698i
$555$	0.267857	−	1.48835i	0.0113699	−	0.0631768i
$556$	−27.2007	−	9.90025i	−1.15357	−	0.419864i
$557$	−5.97287	−	10.3453i	−0.253079	−	0.438345i	0.711293	−	0.702895i	$-0.248110\pi$
$557$	−5.97287	−	10.3453i	−0.253079	−	0.438345i	−0.964372	+	0.264550i	$0.914777\pi$
$558$	20.1027	−	34.2580i	0.851016	−	1.45026i
$559$	−2.19323	−	3.79878i	−0.0927636	−	0.160671i
$560$	8.13204	+	13.3871i	0.343641	+	0.565710i
$561$	−15.0202	−	5.52701i	−0.634151	−	0.233351i
$562$	−53.9223	+	19.6261i	−2.27457	+	0.827877i
$563$	32.0705	−	11.6727i	1.35161	−	0.491946i	0.438160	−	0.898897i	$-0.355630\pi$
$563$	32.0705	−	11.6727i	1.35161	−	0.491946i	0.913450	+	0.406951i	$0.133408\pi$
$564$	−16.9874	+	29.1846i	−0.715299	+	1.22889i
$565$	0.904280	+	5.12843i	0.0380433	+	0.215754i
$566$	−27.8020			−1.16861
$567$	12.0738	+	20.5237i	0.507051	+	0.861916i
$568$	−8.95887			−0.375906
$569$	−6.21554	−	35.2501i	−0.260569	−	1.47776i	−0.781362	−	0.624077i	$-0.785475\pi$
$569$	−6.21554	−	35.2501i	−0.260569	−	1.47776i	0.520793	−	0.853683i	$-0.325636\pi$
$570$	−25.5321	+	43.8645i	−1.06942	+	1.83728i
$571$	−10.8944	+	3.96523i	−0.455916	+	0.165940i	−0.559762	−	0.828654i	$-0.689107\pi$
$571$	−10.8944	+	3.96523i	−0.455916	+	0.165940i	0.103846	+	0.994593i	$0.466885\pi$
$572$	−21.7813	+	7.92775i	−0.910722	+	0.331476i
$573$	21.8269	+	8.03173i	0.911833	+	0.335530i
$574$	40.3287	−	0.898747i	1.68329	−	0.0375130i
$575$	−0.745460	−	1.29118i	−0.0310878	−	0.0538457i
$576$	−35.1295	−	0.248033i	−1.46373	−	0.0103347i
$577$	17.5190	+	30.3437i	0.729324	+	1.26323i	0.957169	+	0.289529i	$0.0934985\pi$
$577$	17.5190	+	30.3437i	0.729324	+	1.26323i	−0.227846	+	0.973697i	$0.573168\pi$
$578$	−45.9540	−	16.7259i	−1.91143	−	0.695705i
$579$	−4.67355	+	25.9686i	−0.194226	+	1.07922i
$580$	14.2737	−	5.19519i	0.592682	−	0.215719i
$581$	20.9190	−	18.3627i	0.867865	−	0.761812i
$582$	9.23739	−	51.3276i	0.382902	−	2.12760i
$583$	1.15940	−	0.972854i	0.0480175	−	0.0402915i
$584$	4.10171	+	7.10436i	0.169730	+	0.293981i
$585$	40.3692	+	15.0168i	1.66906	+	0.620868i
$586$	23.1499	−	40.0967i	0.956312	−	1.65638i
$587$	−1.35689	+	1.13856i	−0.0560047	+	0.0469935i	−0.670360	−	0.742036i	$-0.733860\pi$
$587$	−1.35689	+	1.13856i	−0.0560047	+	0.0469935i	0.614356	+	0.789029i	$0.289416\pi$
$588$	28.7836	−	11.8350i	1.18701	−	0.488066i
$589$	−6.34146	+	35.9642i	−0.261295	+	1.48188i
$590$	2.91288	−	16.5198i	0.119921	−	0.680108i
$591$	14.3773	+	0.0507548i	0.591401	+	0.00208778i
$592$	−0.731684	+	0.613955i	−0.0300720	+	0.0252334i
$593$	9.36976	+	16.2289i	0.384770	+	0.666441i	0.991737	−	0.128286i	$-0.0409475\pi$
$593$	9.36976	+	16.2289i	0.384770	+	0.666441i	−0.606967	+	0.794727i	$0.707614\pi$
$594$	−2.99061	+	15.9697i	−0.122706	+	0.655246i
$595$	36.2206	−	14.1048i	1.48490	−	0.578242i
$596$	34.0872	+	12.4067i	1.39626	+	0.508199i
$597$	0.0613323		0.000216516i	0.00251016		8.86142e-6i
$598$	−44.8789	+	16.3346i	−1.83524	+	0.667971i
$599$	−1.75555	−	1.47308i	−0.0717297	−	0.0601883i	0.606218	−	0.795299i	$-0.292686\pi$
$599$	−1.75555	−	1.47308i	−0.0717297	−	0.0601883i	−0.677948	+	0.735110i	$0.737130\pi$
$600$	−0.663747	+	0.552968i	−0.0270973	+	0.0225748i
$601$	11.9327	−	10.0128i	0.486746	−	0.408429i	−0.366112	−	0.930571i	$-0.619311\pi$
$601$	11.9327	−	10.0128i	0.486746	−	0.408429i	0.852859	+	0.522142i	$0.174867\pi$
$602$	−0.609467	+	3.97206i	−0.0248400	+	0.161889i
$603$	−17.0688	+	6.07642i	−0.695097	+	0.247451i
$604$	−40.7224			−1.65697
$605$	−19.3663	−	7.04876i	−0.787353	−	0.286573i
$606$	−6.34079	+	35.2326i	−0.257577	+	1.43123i
$607$	−5.53515	−	4.64454i	−0.224665	−	0.188516i	0.523507	−	0.852022i	$-0.324623\pi$
$607$	−5.53515	−	4.64454i	−0.224665	−	0.188516i	−0.748171	+	0.663505i	$0.769068\pi$
$608$	43.5429	−	15.8483i	1.76590	−	0.642735i
$609$	2.23912	+	11.4399i	0.0907336	+	0.463570i
$610$	−5.04207	−	28.5950i	−0.204148	−	1.15778i
$611$	−46.8760			−1.89640
$612$	−8.78282	+	47.8325i	−0.355025	+	1.93352i
$613$	24.6669			0.996285			0.498143	−	0.867095i	$-0.334016\pi$
$613$	24.6669			0.996285			0.498143	+	0.867095i	$0.334016\pi$
$614$	10.7209	+	3.90210i	0.432661	+	0.157476i
$615$	−4.89189	−	28.3277i	−0.197260	−	1.14228i
$616$	4.44142	+	1.50535i	0.178950	+	0.0606525i
$617$	17.0382	+	14.2967i	0.685931	+	0.575564i	0.917733	−	0.397199i	$-0.130018\pi$
$617$	17.0382	+	14.2967i	0.685931	+	0.575564i	−0.231802	+	0.972763i	$0.574462\pi$
$618$	6.33788	+	0.0223741i	0.254947	+	0.000900018i
$619$	23.2093	−	19.4749i	0.932860	−	0.782762i	−0.0434687	−	0.999055i	$-0.513841\pi$
$619$	23.2093	−	19.4749i	0.932860	−	0.782762i	0.976329	+	0.216292i	$0.0693964\pi$
$620$	−18.4982	+	32.0397i	−0.742904	+	1.28675i
$621$	−3.46341	+	18.4944i	−0.138982	+	0.742156i
$622$	−32.4580			−1.30145
$623$	4.01316	+	6.60655i	0.160784	+	0.264686i
$624$	−13.5188	−	23.6074i	−0.541187	−	0.945052i
$625$	−4.66925	+	26.4806i	−0.186770	+	1.05922i
$626$	−12.3589	−	10.3704i	−0.493963	−	0.414484i
$627$	−2.54196	−	14.7199i	−0.101516	−	0.587855i
$628$	−3.31361	−	1.20606i	−0.132228	−	0.0481269i
$629$	1.18513	+	2.05270i	0.0472542	+	0.0818466i
$630$	−20.2474	−	33.8684i	−0.806677	−	1.34935i
$631$	−5.86210	+	10.1534i	−0.233366	+	0.404202i	−0.958797	−	0.284093i	$-0.908307\pi$
$631$	−5.86210	+	10.1534i	−0.233366	+	0.404202i	0.725430	+	0.688296i	$0.241641\pi$
$632$	0.179224	−	0.150387i	0.00712917	−	0.00598208i
$633$	−1.31805	−	1.11393i	−0.0523879	−	0.0442748i
$634$	1.43522	−	8.13954i	0.0569999	−	0.323263i
$635$	−35.3809	−	29.6881i	−1.40405	−	1.17814i
$636$	−3.51251	−	2.96854i	−0.139280	−	0.117710i
$637$	34.2987	+	26.2676i	1.35896	+	1.04076i
$638$	−3.97693	+	6.88824i	−0.157448	+	0.272708i
$639$	−22.1855	−	0.156641i	−0.877643	−	0.00619662i
$640$	21.6396			0.855379
$641$	6.21595	+	35.2524i	0.245515	+	1.39239i	0.819293	+	0.573375i	$0.194366\pi$
$641$	6.21595	+	35.2524i	0.245515	+	1.39239i	−0.573778	+	0.819011i	$0.694523\pi$
$642$	−1.93901	−	11.2283i	−0.0765265	−	0.443146i
$643$	3.10936	−	17.6340i	0.122621	−	0.695419i	−0.860071	−	0.510174i	$-0.829581\pi$
$643$	3.10936	−	17.6340i	0.122621	−	0.695419i	0.982692	−	0.185245i	$-0.0593078\pi$
$644$	23.2908	+	7.89407i	0.917785	+	0.311070i
$645$	2.86376	+	0.0101097i	0.112760	+	0.000398069i
$646$	−13.8137	−	78.3416i	−0.543494	−	3.08231i
$647$	9.02096	−	15.6248i	0.354651	−	0.614273i	−0.632407	−	0.774636i	$-0.717933\pi$
$647$	9.02096	−	15.6248i	0.354651	−	0.614273i	0.987058	+	0.160363i	$0.0512665\pi$
$648$	10.9017	+	0.153951i	0.428260	+	0.00604777i
$649$	2.46851	+	4.27559i	0.0968976	+	0.167832i
$650$	−5.10280	−	1.85727i	−0.200148	−	0.0728480i
$651$	−22.0879	−	17.8390i	−0.865693	−	0.699165i
$652$	32.0569	+	26.8989i	1.25544	+	1.05344i
$653$	−1.36691	+	0.497513i	−0.0534912	+	0.0194692i	−0.368627	−	0.929577i	$-0.620172\pi$
$653$	−1.36691	+	0.497513i	−0.0534912	+	0.0194692i	0.315136	+	0.949047i	$0.397950\pi$
$654$	−4.61887	+	3.84799i	−0.180612	+	0.150468i
$655$	−2.03456	−	11.5386i	−0.0794970	−	0.450850i
$656$	−9.07833	+	15.7241i	−0.354449	+	0.613924i
$657$	10.0331	+	17.6647i	0.391429	+	0.689167i
$658$	33.5041	+	26.8643i	1.30613	+	1.04728i
$659$	−6.17337	−	35.0109i	−0.240480	−	1.36383i	−0.830759	−	0.556632i	$-0.812093\pi$
$659$	−6.17337	−	35.0109i	−0.240480	−	1.36383i	0.590278	−	0.807200i	$-0.299018\pi$
$660$	2.68040	−	14.8937i	0.104335	−	0.579736i
$661$	4.28997	−	24.3296i	0.166861	−	0.946313i	−0.780265	−	0.625449i	$-0.784916\pi$
$661$	4.28997	−	24.3296i	0.166861	−	0.946313i	0.947125	−	0.320864i	$-0.103973\pi$
$662$	5.11071	−	28.9843i	0.198633	−	1.12651i
$663$	−63.5188	+	22.8654i	−2.46687	+	0.888017i
$664$	−2.21314	−	12.5513i	−0.0858865	−	0.487087i
$665$	28.3037	+	22.6944i	1.09757	+	0.880053i
$666$	1.85411	−	1.53361i	0.0718455	−	0.0594262i
$667$	−4.60566	+	7.97723i	−0.178332	+	0.308880i
$668$	−4.97158	−	28.1952i	−0.192356	−	1.09091i
$669$	−5.38718	−	31.1958i	−0.208280	−	1.20610i
$670$	28.2135	−	10.2689i	1.08998	−	0.396721i
$671$	6.54645	+	5.49313i	0.252723	+	0.212060i
$672$	−5.58940	+	35.5891i	−0.215616	+	1.37288i
$673$	−0.751164	−	0.273401i	−0.0289552	−	0.0105388i	0.327502	−	0.944851i	$-0.393793\pi$
$673$	−0.751164	−	0.273401i	−0.0289552	−	0.0105388i	−0.356457	+	0.934312i	$0.616015\pi$
$674$	−5.77190	−	9.99722i	−0.222325	−	0.385079i
$675$	−1.65335	+	1.35775i	−0.0636374	+	0.0522597i
$676$	−32.2009	+	55.7735i	−1.23849	+	2.14514i
$677$	−2.34890	−	13.3213i	−0.0902756	−	0.511979i	−0.996093	−	0.0883102i	$-0.971853\pi$
$677$	−2.34890	−	13.3213i	−0.0902756	−	0.511979i	0.905817	−	0.423668i	$-0.139258\pi$
$678$	−4.16821	+	7.16105i	−0.160079	+	0.275018i
$679$	−35.3052	−	11.9662i	−1.35489	−	0.459220i
$680$	3.09052	−	17.5272i	0.118516	−	0.672138i
$681$	−7.00706	+	5.83760i	−0.268511	+	0.223697i
$682$	−3.36400	−	19.0782i	−0.128814	−	0.730543i
$683$	−50.1795			−1.92006			−0.960032	−	0.279889i	$-0.909702\pi$
$683$	−50.1795			−1.92006			−0.960032	+	0.279889i	$0.909702\pi$
$684$	−42.7611	+	15.2227i	−1.63501	+	0.582055i
$685$	9.95599	−	17.2443i	0.380399	−	0.658870i
$686$	−9.46084	−	38.4308i	−0.361216	−	1.46730i
$687$	5.83537	−	2.10060i	0.222633	−	0.0801429i
$688$	−1.38560	−	1.16265i	−0.0528254	−	0.0443257i
$689$	1.10857	−	6.28700i	0.0422331	−	0.239516i
$690$	5.52279	−	30.6874i	0.210249	−	1.16825i
$691$	22.9191	−	19.2314i	0.871884	−	0.731597i	−0.0926102	−	0.995702i	$-0.529521\pi$
$691$	22.9191	−	19.2314i	0.871884	−	0.731597i	0.964494	+	0.264105i	$0.0850766\pi$
$692$	−15.7762	+	27.3252i	−0.599723	+	1.03875i
$693$	10.9723	+	3.80547i	0.416802	+	0.144558i
$694$	10.6107	+	18.3782i	0.402775	+	0.697627i
$695$	24.6515	+	8.97242i	0.935086	+	0.340343i
$696$	5.00908	+	1.84321i	0.189869	+	0.0698667i
$697$	34.5156	+	28.9621i	1.30737	+	1.09702i
$698$	−4.72884	+	26.8186i	−0.178989	+	1.01510i
$699$	1.24656	−	2.14162i	0.0471493	−	0.0810033i
$700$	1.45169	+	2.38981i	0.0548688	+	0.0903262i
$701$	43.0198			1.62484			0.812418	−	0.583076i	$-0.198151\pi$
$701$	43.0198			1.62484			0.812418	+	0.583076i	$0.198151\pi$
$702$	33.6356	+	59.7101i	1.26949	+	2.25361i
$703$	−1.10612	+	1.91585i	−0.0417179	+	0.0722576i
$704$	−13.1252	+	11.0134i	−0.494675	+	0.415082i
$705$	15.3954	−	26.4495i	0.579824	−	0.996147i
$706$	−25.5176	−	21.4118i	−0.960367	−	0.805844i
$707$	24.2344	+	8.21389i	0.911428	+	0.308915i
$708$	11.5259	−	9.60226i	0.433171	−	0.360875i
$709$	0.592841	+	0.215777i	0.0222646	+	0.00810366i	0.353128	−	0.935575i	$-0.385118\pi$
$709$	0.592841	+	0.215777i	0.0222646	+	0.00810366i	−0.330864	+	0.943679i	$0.607340\pi$
$710$	36.7651			1.37977
$711$	0.446455	−	0.369280i	0.0167434	−	0.0138491i
$712$	3.53934			0.132642
$713$	−3.89583	−	22.0944i	−0.145900	−	0.827441i
$714$	58.5034	+	20.0594i	2.18943	+	0.750705i
$715$	19.7400	−	7.18478i	0.738235	−	0.268696i
$716$	−41.1544	−	34.5327i	−1.53801	−	1.29055i
$717$	21.5404	−	7.75408i	0.804443	−	0.289581i
$718$	29.9649	+	10.9063i	1.11828	+	0.407021i
$719$	24.1094			0.899128			0.449564	−	0.893248i	$-0.351579\pi$
$719$	24.1094			0.899128			0.449564	+	0.893248i	$0.351579\pi$
$720$	17.7603	+	0.125397i	0.661888	+	0.00467327i
$721$	0.687079	−	4.47788i	0.0255882	−	0.166765i
$722$	25.7721	−	21.6253i	0.959136	−	0.804811i
$723$	8.56461	+	49.5955i	0.318521	+	1.84448i
$724$	−40.6309	−	34.0934i	−1.51004	−	1.26707i
$725$	−0.984178	+	0.358212i	−0.0365515	+	0.0133036i
$726$	−16.2955	−	28.4561i	−0.604782	−	1.05611i
$727$	35.9584	+	13.0878i	1.33362	+	0.485399i	0.907798	−	0.419408i	$-0.137762\pi$
$727$	35.9584	+	13.0878i	1.33362	+	0.485399i	0.425824	+	0.904806i	$0.359984\pi$
$728$	18.4327	−	7.17795i	0.683160	−	0.266032i
$729$	26.9939	+	0.571850i	0.999776	+	0.0211796i
$730$	−16.8324	−	29.1546i	−0.622996	−	1.07906i
$731$	−3.43845	+	2.88520i	−0.127176	+	0.106713i
$732$	13.0629	−	22.4423i	0.482820	−	0.829493i
$733$	−4.56217	+	25.8734i	−0.168508	+	0.955654i	0.776866	+	0.629666i	$0.216808\pi$
$733$	−4.56217	+	25.8734i	−0.168508	+	0.955654i	−0.945374	+	0.325989i	$0.894303\pi$
$734$	−3.92378	+	22.2529i	−0.144829	+	0.821369i
$735$	−26.0860	+	10.7258i	−0.962198	+	0.395628i
$736$	−21.8070	+	18.2983i	−0.803818	+	0.674483i
$737$	−4.41828	+	7.65269i	−0.162750	+	0.281891i
$738$	23.1490	−	39.4494i	0.852127	−	1.45215i
$739$	−15.9719	−	27.6642i	−0.587536	−	1.01764i	−0.994554	−	0.104222i	$-0.966765\pi$
$739$	−15.9719	−	27.6642i	−0.587536	−	1.01764i	0.407018	−	0.913420i	$-0.366569\pi$
$740$	−1.71682	+	1.44058i	−0.0631114	+	0.0529567i
$741$	−48.1238	−	40.6710i	−1.76787	−	1.49409i
$742$	−4.39537	+	3.85826i	−0.161359	+	0.141641i
$743$	−29.0519	+	10.5740i	−1.06581	+	0.387923i	−0.814608	−	0.580012i	$-0.803048\pi$
$743$	−29.0519	+	10.5740i	−1.06581	+	0.387923i	−0.251202	+	0.967935i	$0.580826\pi$
$744$	−12.2316	+	4.40310i	−0.448432	+	0.161425i
$745$	−30.8926	−	11.2440i	−1.13182	−	0.411948i
$746$	25.6059	+	44.3507i	0.937499	+	1.62380i
$747$	−5.26109	−	31.1204i	−0.192493	−	1.13864i
$748$	11.8594	+	20.5411i	0.433623	+	0.751058i
$749$	−8.14266	+	0.181463i	−0.297526	+	0.00663053i
$750$	−30.3545	+	25.2884i	−1.10839	+	0.923401i
$751$	−6.13940	+	2.23456i	−0.224030	+	0.0815402i	−0.451596	−	0.892222i	$-0.649145\pi$
$751$	−6.13940	+	2.23456i	−0.224030	+	0.0815402i	0.227567	+	0.973763i	$0.426923\pi$
$752$	−18.1637	+	6.61106i	−0.662364	+	0.241081i
$753$	8.94457	+	0.0315763i	0.325958	+	0.00115070i
$754$	5.82586	+	33.0401i	0.212165	+	1.20325i
$755$	36.9060			1.34315
$756$	5.72110	−	34.8218i	0.208075	−	1.26646i
$757$	−18.2609			−0.663705			−0.331852	−	0.943331i	$-0.607674\pi$
$757$	−18.2609			−0.663705			−0.331852	+	0.943331i	$0.607674\pi$
$758$	−14.0167	−	79.4928i	−0.509110	−	2.88731i
$759$	4.56036	+	7.96357i	0.165531	+	0.289059i
$760$	15.6093	−	5.68131i	0.566208	−	0.206083i
$761$	−17.9032	+	6.51622i	−0.648990	+	0.236213i	−0.645476	−	0.763781i	$-0.723341\pi$
$761$	−17.9032	+	6.51622i	−0.648990	+	0.236213i	−0.00351399	+	0.999994i	$0.501119\pi$
$762$	−12.5055	−	72.4163i	−0.453027	−	2.62337i
$763$	2.23095	+	3.67263i	0.0807657	+	0.132958i
$764$	−17.2338	−	29.8499i	−0.623498	−	1.07993i
$765$	7.95972	−	43.3498i	0.287784	−	1.56732i
$766$	−5.45797	−	9.45349i	−0.197205	−	0.341568i
$767$	19.5688	+	7.12245i	0.706587	+	0.257177i
$768$	−4.68498	−	3.95943i	−0.169055	−	0.142874i
$769$	−46.6359	+	16.9741i	−1.68173	+	0.612101i	−0.993546	−	0.113431i	$-0.963816\pi$
$769$	−46.6359	+	16.9741i	−1.68173	+	0.612101i	−0.688189	+	0.725532i	$0.741594\pi$
$770$	−18.2265	−	6.17761i	−0.656838	−	0.222626i
$771$	−48.3662	+	17.4107i	−1.74187	+	0.627032i
$772$	29.9549	−	25.1351i	1.07810	−	0.904634i
$773$	4.81995	+	8.34840i	0.173362	+	0.300271i	0.939593	−	0.342294i	$-0.111204\pi$
$773$	4.81995	+	8.34840i	0.173362	+	0.300271i	−0.766231	+	0.642565i	$0.777870\pi$
$774$	3.46979	+	2.95350i	0.124719	+	0.106161i
$775$	1.27546	−	2.20916i	0.0458158	−	0.0793554i
$776$	−13.0753	+	10.9715i	−0.469376	+	0.393854i
$777$	−0.887735	−	1.47310i	−0.0318473	−	0.0528473i
$778$	−1.88340	+	10.6813i	−0.0675233	+	0.382943i
$779$	−7.30243	+	41.4141i	−0.261637	+	1.48382i
$780$	−31.7205	−	55.3921i	−1.13578	−	1.98336i
$781$	−8.28901	+	6.95531i	−0.296604	+	0.248880i
$782$	24.4355	+	42.3236i	0.873813	+	1.51349i
$783$	12.3721	+	4.65204i	0.442143	+	0.166250i
$784$	16.9948	+	5.34107i	0.606958	+	0.190753i
$785$	3.00307	+	1.09303i	0.107184	+	0.0390119i
$786$	9.37817	−	16.1118i	0.334508	−	0.574690i
$787$	−25.7236	+	9.36263i	−0.916948	+	0.333742i	−0.757024	−	0.653388i	$-0.773347\pi$
$787$	−25.7236	+	9.36263i	−0.916948	+	0.333742i	−0.159924	+	0.987129i	$0.551125\pi$
$788$	−16.3221	−	13.6959i	−0.581452	−	0.487896i
$789$	−42.9361	−	15.7993i	−1.52856	−	0.562471i
$790$	−0.735494	+	0.617153i	−0.0261677	+	0.0219573i
$791$	4.62068	+	3.70496i	0.164293	+	0.131733i
$792$	4.09747	−	3.38918i	0.145597	−	0.120429i
$793$	36.0466			1.28005
$794$	27.8356	+	10.1313i	0.987849	+	0.359548i
$795$	3.18332	+	2.69033i	0.112901	+	0.0954163i
$796$	−0.0696289	−	0.0584256i	−0.00246793	−	0.00207084i
$797$	−46.2445	+	16.8316i	−1.63806	+	0.596206i	−0.986699	−	0.162559i	$-0.948025\pi$
$797$	−46.2445	+	16.8316i	−1.63806	+	0.596206i	−0.651364	+	0.758765i	$0.725803\pi$
$798$	11.0877	+	56.6486i	0.392501	+	2.00534i
$799$	8.32944	+	47.2386i	0.294674	+	1.67118i
$800$	−3.23675			−0.114436
$801$	8.76471	+	0.0618834i	0.309686	+	0.00218654i
$802$	−6.33165			−0.223578
$803$	9.31056	+	3.38877i	0.328563	+	0.119587i
$804$	25.1990	+	9.27255i	0.888699	+	0.327017i
$805$	−21.1080	−	7.15426i	−0.743960	−	0.252154i
$806$	−62.5968	−	52.5250i	−2.20488	−	1.85011i
$807$	−7.18967	−	12.5550i	−0.253088	−	0.441957i
$808$	8.97524	−	7.53112i	0.315748	−	0.264944i
$809$	6.03274	−	10.4490i	0.212100	−	0.367368i	−0.740272	−	0.672308i	$-0.765303\pi$
$809$	6.03274	−	10.4490i	0.212100	−	0.367368i	0.952372	+	0.304940i	$0.0986364\pi$
$810$	−44.7380	−	0.631779i	−1.57193	−	0.0221984i
$811$	−46.4263			−1.63025			−0.815123	−	0.579287i	$-0.803331\pi$
$811$	−46.4263			−1.63025			−0.815123	+	0.579287i	$0.803331\pi$
$812$	8.30228	−	15.1498i	0.291353	−	0.531653i
$813$	40.4091	+	0.142653i	1.41721	+	0.00500306i
$814$	0.203783	−	1.15571i	0.00714259	−	0.0405076i
$815$	−29.0526	−	24.3780i	−1.01767	−	0.853924i
$816$	−21.3878	+	17.8182i	−0.748724	+	0.623763i
$817$	−3.93668	−	1.43283i	−0.137727	−	0.0501285i
$818$	−6.43065	−	11.1382i	−0.224842	−	0.389438i
$819$	45.7716	−	17.4530i	1.59939	−	0.609855i
$820$	−21.3013	+	36.8949i	−0.743874	+	1.28843i
$821$	−9.36189	+	7.85556i	−0.326732	+	0.274161i	−0.791367	−	0.611342i	$-0.790630\pi$
$821$	−9.36189	+	7.85556i	−0.326732	+	0.274161i	0.464635	+	0.885502i	$0.346186\pi$
$822$	29.8097	−	10.7308i	1.03973	−	0.374280i
$823$	0.712473	−	4.04064i	0.0248353	−	0.140848i	−0.969869	−	0.243628i	$-0.921663\pi$
$823$	0.712473	−	4.04064i	0.0248353	−	0.140848i	0.994704	+	0.102780i	$0.0327737\pi$
$824$	−1.58901	−	1.33334i	−0.0553557	−	0.0464490i
$825$	−0.184816	+	1.02693i	−0.00643445	+	0.0357531i
$826$	−9.90475	−	16.3054i	−0.344630	−	0.567338i
$827$	14.8424	−	25.7078i	0.516121	−	0.893947i	−0.483704	−	0.875232i	$-0.660709\pi$
$827$	14.8424	−	25.7078i	0.516121	−	0.893947i	0.999825	−	0.0187156i	$-0.00595770\pi$
$828$	21.4871	−	17.7728i	0.746729	−	0.617649i
$829$	−30.0386			−1.04328			−0.521641	−	0.853165i	$-0.674680\pi$
$829$	−30.0386			−1.04328			−0.521641	+	0.853165i	$0.674680\pi$
$830$	9.08220	+	51.5077i	0.315248	+	1.78786i
$831$	35.4744	+	13.0536i	1.23059	+	0.452826i
$832$	−12.5497	+	71.1732i	−0.435084	+	2.46749i
$833$	20.3763	−	39.2315i	0.705996	−	1.35929i
$834$	20.7426	+	36.2220i	0.718259	+	1.25427i
$835$	4.50565	+	25.5528i	0.155925	+	0.884292i
$836$	−11.0687	+	19.1716i	−0.382821	+	0.663065i
$837$	−30.3669	+	10.6898i	−1.04963	+	0.369494i
$838$	−8.40536	−	14.5585i	−0.290358	−	0.502916i
$839$	−32.9214	−	11.9824i	−1.13657	−	0.413678i	−0.295898	−	0.955220i	$-0.595619\pi$
$839$	−32.9214	−	11.9824i	−1.13657	−	0.413678i	−0.840674	+	0.541541i	$0.817841\pi$
$840$	−2.00369	+	12.7580i	−0.0691338	+	0.440192i
$841$	−17.2584	−	14.4815i	−0.595117	−	0.499363i
$842$	−9.18699	+	3.34379i	−0.316605	+	0.115235i
$843$	43.6474	+	16.0611i	1.50330	+	0.553173i
$844$	0.444103	+	2.51864i	0.0152867	+	0.0866950i
$845$	29.1831	−	50.5466i	1.00393	−	1.73885i
$846$	45.8741	−	16.3310i	1.57718	−	0.561470i
$847$	−21.8415	+	8.50541i	−0.750484	+	0.292249i
$848$	−0.457122	−	2.59247i	−0.0156976	−	0.0890256i
$849$	17.2104	+	14.5451i	0.590659	+	0.499186i
$850$	−0.964913	+	5.47230i	−0.0330963	+	0.187698i
$851$	0.236000	−	1.33842i	0.00808997	−	0.0458805i
$852$	25.1123	+	21.2232i	0.860332	+	0.727095i
$853$	−2.07548	−	11.7706i	−0.0710630	−	0.403018i	−0.999503	−	0.0315351i	$-0.989960\pi$
$853$	−2.07548	−	11.7706i	−0.0710630	−	0.403018i	0.928440	−	0.371483i	$-0.121151\pi$
$854$	−25.7639	−	20.6580i	−0.881624	−	0.706904i
$855$	38.7536	−	13.7961i	1.32535	−	0.471816i
$856$	−1.86462	+	3.22962i	−0.0637314	+	0.110386i
$857$	0.324126	+	1.83821i	0.0110719	+	0.0627921i	0.989843	−	0.142164i	$-0.0454060\pi$
$857$	0.324126	+	1.83821i	0.0110719	+	0.0627921i	−0.978771	+	0.204956i	$0.934295\pi$
$858$	31.3681	+	11.5426i	1.07089	+	0.394059i
$859$	−16.1835	+	5.89030i	−0.552172	+	0.200974i	−0.603011	−	0.797733i	$-0.706033\pi$
$859$	−16.1835	+	5.89030i	−0.552172	+	0.200974i	0.0508390	+	0.998707i	$0.483810\pi$
$860$	−3.25115	−	2.72804i	−0.110863	−	0.0930253i
$861$	−25.4350	−	20.5423i	−0.866823	−	0.700078i
$862$	−30.3609	−	11.0505i	−1.03410	−	0.376381i
$863$	15.8433	+	27.4413i	0.539311	+	0.934114i	0.998941	+	0.0460035i	$0.0146486\pi$
$863$	15.8433	+	27.4413i	0.539311	+	0.934114i	−0.459630	+	0.888110i	$0.652018\pi$
$864$	31.0122	+	26.5871i	1.05506	+	0.904511i
$865$	14.2977	−	24.7644i	0.486137	−	0.842014i
$866$	8.88199	+	50.3723i	0.301822	+	1.71172i
$867$	19.6966	+	34.3954i	0.668933	+	1.16813i
$868$	8.22791	+	41.2642i	0.279274	+	1.40060i
$869$	0.0490692	−	0.278285i	0.00166456	−	0.00944018i
$870$	−20.5561	−	7.56409i	−0.696917	−	0.256447i
$871$	6.47241	+	36.7069i	0.219309	+	1.24376i
$872$	1.96755			0.0666295
$873$	−32.5711	+	26.9408i	−1.10237	+	0.911809i
$874$	−22.8064	+	39.5018i	−0.771438	+	1.33617i
$875$	14.6614	+	24.1360i	0.495647	+	0.815945i
$876$	5.33262	−	29.6307i	0.180173	−	1.00113i
$877$	−5.87032	−	4.92579i	−0.198227	−	0.166332i	0.538271	−	0.842772i	$-0.319078\pi$
$877$	−5.87032	−	4.92579i	−0.198227	−	0.166332i	−0.736498	+	0.676440i	$0.763522\pi$
$878$	4.90022	−	27.7905i	0.165374	−	0.937885i
$879$	−35.3078	+	12.7100i	−1.19090	+	0.428698i
$880$	6.63567	−	5.56799i	0.223688	−	0.187697i
$881$	−14.1075	+	24.4350i	−0.475295	+	0.823235i	−0.999600	−	0.0282959i	$-0.990992\pi$
$881$	−14.1075	+	24.4350i	−0.475295	+	0.823235i	0.524305	+	0.851531i	$0.324325\pi$
$882$	−42.7169	−	13.7570i	−1.43835	−	0.463224i
$883$	−5.20487	−	9.01509i	−0.175158	−	0.303382i	0.765058	−	0.643961i	$-0.222710\pi$
$883$	−5.20487	−	9.01509i	−0.175158	−	0.303382i	−0.940216	+	0.340579i	$0.889377\pi$
$884$	94.0138	+	34.2182i	3.16202	+	1.15088i
$885$	−10.4457	+	8.70236i	−0.351130	+	0.292527i
$886$	−52.9794	−	44.4550i	−1.77988	−	1.49349i
$887$	8.25187	−	46.7987i	0.277071	−	1.57135i	−0.455235	−	0.890371i	$-0.650445\pi$
$887$	8.25187	−	46.7987i	0.277071	−	1.57135i	0.732306	−	0.680976i	$-0.238444\pi$
$888$	−0.787500	−	0.00278005i	−0.0264268	−	9.32922e-5i
$889$	−52.5156	+	1.17034i	−1.76132	+	0.0392519i
$890$	−14.5246			−0.486866
$891$	10.2061	−	8.32121i	0.341917	−	0.278771i
$892$	−23.4580	+	40.6305i	−0.785432	+	1.36041i
$893$	−34.2953	+	28.7772i	−1.14765	+	0.962991i
$894$	−25.9941	−	45.3924i	−0.869372	−	1.51815i
$895$	37.2975	+	31.2963i	1.24672	+	1.04612i
$896$	18.4960	−	16.2358i	0.617908	−	0.542399i
$897$	36.3272	+	13.3675i	1.21293	+	0.446326i
$898$	33.5302	+	12.2040i	1.11892	+	0.407253i
$899$	−15.7603			−0.525634
$900$	3.17048	+	0.0223853i	0.105683	+	0.000746175i
$901$	−6.53262			−0.217633
$902$	−3.87377	−	21.9693i	−0.128983	−	0.731497i
$903$	2.45533	−	2.13999i	0.0817082	−	0.0712143i
$904$	2.54827	−	0.927495i	0.0847543	−	0.0308480i
$905$	36.8231	+	30.8982i	1.22404	+	1.02709i
$906$	44.8500	+	37.9042i	1.49004	+	1.25928i
$907$	15.4104	+	5.60891i	0.511692	+	0.186241i	0.584946	−	0.811073i	$-0.301116\pi$
$907$	15.4104	+	5.60891i	0.511692	+	0.186241i	−0.0732531	+	0.997313i	$0.523338\pi$
$908$	13.5159			0.448540
$909$	22.3577	−	18.4929i	0.741557	−	0.613370i
$910$	−75.6433	+	29.4566i	−2.50755	+	0.976476i
$911$	2.90818	−	2.44025i	0.0963523	−	0.0808492i	−0.593339	−	0.804953i	$-0.702191\pi$
$911$	2.90818	−	2.44025i	0.0963523	−	0.0808492i	0.689691	+	0.724103i	$0.257746\pi$
$912$	−24.3832	−	8.97237i	−0.807408	−	0.297105i
$913$	−11.7920	−	9.89468i	−0.390259	−	0.327466i
$914$	−0.165742	+	0.0603253i	−0.00548227	+	0.00199538i
$915$	−11.8387	+	20.3391i	−0.391376	+	0.672390i
$916$	−8.63688	−	3.14357i	−0.285371	−	0.103866i
$917$	−10.3962	−	8.33588i	−0.343313	−	0.275275i
$918$	54.1953	−	44.5058i	1.78871	−	1.46891i
$919$	−1.95723	−	3.39003i	−0.0645632	−	0.111827i	0.831937	−	0.554870i	$-0.187232\pi$
$919$	−1.95723	−	3.39003i	−0.0645632	−	0.111827i	−0.896500	+	0.443043i	$0.853899\pi$
$920$	−7.81738	+	6.55956i	−0.257732	+	0.216262i
$921$	−4.59517	−	8.02435i	−0.151416	−	0.264411i
$922$	−13.2626	+	75.2160i	−0.436781	+	2.47711i
$923$	−7.92558	+	44.9482i	−0.260874	+	1.47949i
$924$	−8.88344	−	14.7411i	−0.292244	−	0.484948i
$925$	0.118375	−	0.0993288i	0.00389216	−	0.00326591i
$926$	25.0843	−	43.4472i	0.824320	−	1.42776i
$927$	−3.91165	−	3.32961i	−0.128476	−	0.109359i
$928$	9.99876	+	17.3184i	0.328225	+	0.568503i
$929$	−23.2641	+	19.5209i	−0.763272	+	0.640461i	−0.938976	−	0.343982i	$-0.888224\pi$
$929$	−23.2641	+	19.5209i	−0.763272	+	0.640461i	0.175704	+	0.984443i	$0.443780\pi$
$930$	50.1955	−	18.0693i	1.64598	−	0.592514i
$931$	41.2192	−	1.83810i	1.35091	−	0.0602412i
$932$	−3.45087	+	1.25602i	−0.113037	+	0.0411422i
$933$	20.0926	+	16.9809i	0.657802	+	0.555931i
$934$	31.4356	+	11.4416i	1.02860	+	0.374382i
$935$	−10.7480	−	18.6161i	−0.351497	−	0.608810i
$936$	4.05070	−	22.0607i	0.132401	−	0.721076i
$937$	−13.9312	−	24.1295i	−0.455111	−	0.788276i	0.543583	−	0.839355i	$-0.317067\pi$
$937$	−13.9312	−	24.1295i	−0.455111	−	0.788276i	−0.998695	+	0.0510795i	$0.983734\pi$
$938$	16.4104	−	29.9451i	0.535817	−	0.977744i
$939$	2.22517	+	12.8854i	0.0726157	+	0.420499i
$940$	−42.6192	+	15.5121i	−1.39009	+	0.505950i
$941$	25.2359	−	9.18512i	0.822667	−	0.299426i	0.103821	−	0.994596i	$-0.466893\pi$
$941$	25.2359	−	9.18512i	0.822667	−	0.299426i	0.718846	+	0.695170i	$0.244671\pi$
$942$	2.52689	+	4.41260i	0.0823304	+	0.143770i
$943$	−4.48620	−	25.4425i	−0.146091	−	0.828521i
$944$	8.58711			0.279487
$945$	−5.18494	+	31.5584i	−0.168666	+	1.02660i
$946$	2.22234			0.0722546
$947$	1.46748	+	8.32249i	0.0476867	+	0.270445i	0.999323	−	0.0367811i	$-0.0117104\pi$
$947$	1.46748	+	8.32249i	0.0476867	+	0.270445i	−0.951637	+	0.307226i	$0.900599\pi$
$948$	−0.858638	−	0.00303118i	−0.0278873	−	9.84481e-5i
$949$	39.2725	−	14.2940i	1.27484	−	0.464003i
$950$	−4.87348	+	1.77380i	−0.158116	+	0.0575497i
$951$	−5.14678	+	4.28779i	−0.166896	+	0.139041i
$952$	−10.5088	−	17.2998i	−0.340592	−	0.560690i
$953$	9.42362	+	16.3222i	0.305261	+	0.528727i	0.977319	−	0.211771i	$-0.0679230\pi$
$953$	9.42362	+	16.3222i	0.305261	+	0.528727i	−0.672058	+	0.740498i	$0.734590\pi$
$954$	1.10543	+	6.53885i	0.0357896	+	0.211703i
$955$	15.6187	+	27.0524i	0.505410	+	0.875395i
$956$	−31.8819	−	11.6040i	−1.03113	−	0.375302i
$957$	6.06554	−	2.18346i	0.196071	−	0.0705812i
$958$	8.90164	−	3.23993i	0.287599	−	0.104677i
$959$	−4.42839	−	22.2090i	−0.143000	−	0.717167i
$960$	−36.0374	−	30.4564i	−1.16310	−	0.982976i
$961$	5.65795	−	4.74758i	0.182514	−	0.153148i
$962$	−2.47503	−	4.28687i	−0.0797980	−	0.138214i
$963$	−4.67395	+	7.96512i	−0.150616	+	0.256672i
$964$	37.2938	−	64.5948i	1.20115	−	2.08046i
$965$	−27.1476	+	22.7795i	−0.873912	+	0.733299i
$966$	−18.3037	−	30.3731i	−0.588913	−	0.977239i
$967$	6.86487	−	38.9326i	0.220759	−	1.25199i	−0.649868	−	0.760047i	$-0.725176\pi$
$967$	6.86487	−	38.9326i	0.220759	−	1.25199i	0.870628	−	0.491942i	$-0.163713\pi$
$968$	−1.86363	+	10.5691i	−0.0598992	+	0.339705i
$969$	−32.4345	+	55.7229i	−1.04195	+	1.79008i
$970$	53.6580	−	45.0244i	1.72285	−	1.44565i
$971$	13.0672	+	22.6331i	0.419347	+	0.726330i	0.995874	−	0.0907479i	$-0.0289258\pi$
$971$	13.0672	+	22.6331i	0.419347	+	0.726330i	−0.576527	+	0.817078i	$0.695592\pi$
$972$	−30.1935	−	26.2572i	−0.968455	−	0.842202i
$973$	27.8023	−	10.8266i	0.891299	−	0.347085i
$974$	−9.50449	−	3.45935i	−0.304543	−	0.110845i
$975$	2.18715	+	3.81932i	0.0700447	+	0.122316i
$976$	13.9675	−	5.08376i	0.447089	−	0.162727i
$977$	−8.41700	−	7.06270i	−0.269284	−	0.225956i	0.498139	−	0.867097i	$-0.334017\pi$
$977$	−8.41700	−	7.06270i	−0.269284	−	0.225956i	−0.767423	+	0.641141i	$0.778461\pi$
$978$	−10.2687	−	59.4637i	−0.328358	−	1.90144i
$979$	3.27470	−	2.74780i	0.104660	−	0.0878201i
$980$	39.8765	+	12.5322i	1.27381	+	0.400328i
$981$	4.87237	+	0.0344015i	0.155563	+	0.00109835i
$982$	67.3679			2.14980
$983$	26.8263	+	9.76399i	0.855628	+	0.311423i	0.732333	−	0.680947i	$-0.238432\pi$
$983$	26.8263	+	9.76399i	0.855628	+	0.311423i	0.123295	+	0.992370i	$0.460654\pi$
$984$	−14.0851	+	5.07033i	−0.449017	+	0.161636i
$985$	14.7925	+	12.4123i	0.471327	+	0.395490i
$986$	32.2605	−	11.7419i	1.02738	−	0.373937i
$987$	−6.68570	−	34.1581i	−0.212808	−	1.08726i
$988$	16.2148	+	91.9585i	0.515861	+	2.92559i
$989$	2.57368			0.0818383
$990$	−16.8150	+	13.9084i	−0.534417	+	0.442037i
$991$	37.6166			1.19493			0.597465	−	0.801895i	$-0.296175\pi$
$991$	37.6166			1.19493			0.597465	+	0.801895i	$0.296175\pi$
$992$	−45.7689	−	16.6585i	−1.45316	−	0.528908i
$993$	−18.3273	+	15.2685i	−0.581598	+	0.484530i
$994$	31.4242	−	27.5842i	0.996716	−	0.874917i
$995$	0.0631035	+	0.0529501i	0.00200051	+	0.00167863i
$996$	−23.5301	+	40.4250i	−0.745578	+	1.28092i
$997$	20.6930	−	17.3635i	0.655354	−	0.549907i	−0.253336	−	0.967378i	$-0.581528\pi$
$997$	20.6930	−	17.3635i	0.655354	−	0.549907i	0.908690	+	0.417471i	$0.137084\pi$
$998$	11.1571	−	19.3246i	0.353171	−	0.611710i
$999$	−1.95009	−	0.0206534i	−0.0616981	−	0.000653445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.19	✓	132
3.2	odd	2		567.2.u.a.550.4		132
7.2	even	3		189.2.w.a.58.19	yes	132
21.2	odd	6		567.2.w.a.226.4		132
27.7	even	9		189.2.w.a.88.19	yes	132
27.20	odd	18		567.2.w.a.424.4		132
189.128	odd	18		567.2.u.a.100.4		132
189.142	even	9	inner	189.2.u.a.142.19	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.19	✓	132	1.1	even	1	trivial
189.2.u.a.142.19	yes	132	189.142	even	9	inner
189.2.w.a.58.19	yes	132	7.2	even	3
189.2.w.a.88.19	yes	132	27.7	even	9
567.2.u.a.100.4		132	189.128	odd	18
567.2.u.a.550.4		132	3.2	odd	2
567.2.w.a.226.4		132	21.2	odd	6
567.2.w.a.424.4		132	27.20	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.371090 + 2.10456i) q^{2} +(0.871315 - 1.49693i) q^{3} +(-2.41207 + 0.877922i) q^{4} +(2.18602 - 0.795646i) q^{5} +(3.47372 + 1.27824i) q^{6} +(1.27150 - 2.32019i) q^{7} +(-0.605711 - 1.04912i) q^{8} +(-1.48162 - 2.60860i) q^{9} +O(q^{10})\)	\(q+(0.371090 + 2.10456i) q^{2} +(0.871315 - 1.49693i) q^{3} +(-2.41207 + 0.877922i) q^{4} +(2.18602 - 0.795646i) q^{5} +(3.47372 + 1.27824i) q^{6} +(1.27150 - 2.32019i) q^{7} +(-0.605711 - 1.04912i) q^{8} +(-1.48162 - 2.60860i) q^{9} +(2.48569 + 4.30535i) q^{10} +(-1.37492 - 0.500429i) q^{11} +(-0.787484 + 4.37566i) q^{12} +(-5.79948 + 2.11084i) q^{13} +(5.35482 + 1.81494i) q^{14} +(0.713683 - 3.96558i) q^{15} +(-1.94951 + 1.63584i) q^{16} +(3.15768 + 5.46926i) q^{17} +(4.94014 - 4.08618i) q^{18} +(-2.94716 + 5.10463i) q^{19} +(-4.57432 + 3.83831i) q^{20} +(-2.36530 - 3.92497i) q^{21} +(0.542963 - 3.07930i) q^{22} +(0.628803 - 3.56612i) q^{23} +(-2.09823 - 0.00740721i) q^{24} +(0.315402 - 0.264654i) q^{25} +(-6.59451 - 11.4220i) q^{26} +(-5.19586 - 0.0550294i) q^{27} +(-1.02999 + 6.71275i) q^{28} +(-2.39036 - 0.870020i) q^{29} +(8.61064 + 0.0303974i) q^{30} +(5.82200 - 2.11903i) q^{31} +(-6.02216 - 5.05319i) q^{32} +(-1.94710 + 1.62213i) q^{33} +(-10.3386 + 8.67511i) q^{34} +(0.933465 - 6.08365i) q^{35} +(5.86392 + 4.99139i) q^{36} +0.375316 q^{37} +(-11.8366 - 4.30819i) q^{38} +(-1.89339 + 10.5206i) q^{39} +(-2.15882 - 1.81147i) q^{40} +(6.70424 - 2.44014i) q^{41} +(7.38258 - 6.43443i) q^{42} +(0.123419 + 0.699942i) q^{43} +3.75574 q^{44} +(-5.31437 - 4.52361i) q^{45} +7.73844 q^{46} +(7.13729 + 2.59776i) q^{47} +(0.750096 + 4.34362i) q^{48} +(-3.76659 - 5.90024i) q^{49} +(0.674022 + 0.565571i) q^{50} +(10.9385 + 0.0386151i) q^{51} +(12.1356 - 10.1830i) q^{52} +(-0.517201 + 0.895818i) q^{53} +(-1.81232 - 10.9554i) q^{54} -3.40376 q^{55} +(-3.20433 + 0.0714101i) q^{56} +(5.07338 + 8.85944i) q^{57} +(0.943968 - 5.35351i) q^{58} +(-2.58481 - 2.16891i) q^{59} +(1.76002 + 10.1918i) q^{60} +(-5.48842 - 1.99762i) q^{61} +(6.62011 + 11.4664i) q^{62} +(-7.93633 + 0.120812i) q^{63} +(5.85507 - 10.1413i) q^{64} +(-10.9983 + 9.22866i) q^{65} +(-4.13641 - 3.49582i) q^{66} +(1.04873 - 5.94764i) q^{67} +(-12.4181 - 10.4201i) q^{68} +(-4.79035 - 4.04849i) q^{69} +(13.1498 - 0.293050i) q^{70} +(3.69767 - 6.40455i) q^{71} +(-1.83931 + 3.13446i) q^{72} -6.77172 q^{73} +(0.139276 + 0.789875i) q^{74} +(-0.121354 - 0.702733i) q^{75} +(2.62729 - 14.9001i) q^{76} +(-2.90930 + 2.55378i) q^{77} +(-22.8439 - 0.0806439i) q^{78} +(0.0335365 + 0.190195i) q^{79} +(-2.96013 + 5.12709i) q^{80} +(-4.60961 + 7.72991i) q^{81} +(7.62331 + 13.2040i) q^{82} +(9.88619 + 3.59828i) q^{83} +(9.15109 + 7.39075i) q^{84} +(11.2543 + 9.44351i) q^{85} +(-1.42727 + 0.519483i) q^{86} +(-3.38512 + 2.82015i) q^{87} +(0.307791 + 1.74557i) q^{88} +(-1.46082 + 2.53022i) q^{89} +(7.54808 - 12.8631i) q^{90} +(-2.47647 + 16.1398i) q^{91} +(1.61406 + 9.15377i) q^{92} +(1.90074 - 10.5615i) q^{93} +(-2.81856 + 15.9848i) q^{94} +(-2.38107 + 13.5037i) q^{95} +(-12.8115 + 4.61185i) q^{96} +(-2.44666 - 13.8757i) q^{97} +(11.0196 - 10.1165i) q^{98} +(0.731684 + 4.32806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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