LMFDB - Embedded newform 189.2.w.a.25.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (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			25.15
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00414 - 0.365478i) q^{2} +(-0.803391 + 1.53446i) q^{3} +(-0.657360 + 0.551590i) q^{4} +(0.354797 + 0.129136i) q^{5} +(-0.245908 + 1.83444i) q^{6} +(1.55771 + 2.13859i) q^{7} +(-1.52708 + 2.64497i) q^{8} +(-1.70913 - 2.46554i) q^{9} +O(q^{10})$	\(q+(1.00414 - 0.365478i) q^{2} +(-0.803391 + 1.53446i) q^{3} +(-0.657360 + 0.551590i) q^{4} +(0.354797 + 0.129136i) q^{5} +(-0.245908 + 1.83444i) q^{6} +(1.55771 + 2.13859i) q^{7} +(-1.52708 + 2.64497i) q^{8} +(-1.70913 - 2.46554i) q^{9} +0.403463 q^{10} +(-1.26884 + 0.461820i) q^{11} +(-0.318275 - 1.45183i) q^{12} +(0.253416 + 1.43719i) q^{13} +(2.34577 + 1.57814i) q^{14} +(-0.483194 + 0.440675i) q^{15} +(-0.268700 + 1.52387i) q^{16} +4.22631 q^{17} +(-2.61731 - 1.85111i) q^{18} +7.17641 q^{19} +(-0.304459 + 0.110814i) q^{20} +(-4.53302 + 0.672117i) q^{21} +(-1.10531 + 0.927466i) q^{22} +(-0.904031 - 5.12702i) q^{23} +(-2.83176 - 4.46818i) q^{24} +(-3.72102 - 3.12230i) q^{25} +(0.779728 + 1.35053i) q^{26} +(5.15637 - 0.641790i) q^{27} +(-2.20360 - 0.546604i) q^{28} +(0.957325 - 5.42926i) q^{29} +(-0.324139 + 0.619097i) q^{30} +(-4.18842 + 3.51450i) q^{31} +(-0.773566 - 4.38711i) q^{32} +(0.310731 - 2.31800i) q^{33} +(4.24382 - 1.54462i) q^{34} +(0.276502 + 0.959919i) q^{35} +(2.48348 + 0.678009i) q^{36} +(-1.08910 + 1.88637i) q^{37} +(7.20615 - 2.62282i) q^{38} +(-2.40890 - 0.765771i) q^{39} +(-0.883362 + 0.741228i) q^{40} +(-1.68852 - 9.57606i) q^{41} +(-4.30616 + 2.33162i) q^{42} +(7.70916 + 6.46875i) q^{43} +(0.579348 - 1.00346i) q^{44} +(-0.288004 - 1.09547i) q^{45} +(-2.78159 - 4.81785i) q^{46} +(7.10294 + 5.96008i) q^{47} +(-2.12245 - 1.63658i) q^{48} +(-2.14710 + 6.66258i) q^{49} +(-4.87757 - 1.77529i) q^{50} +(-3.39538 + 6.48509i) q^{51} +(-0.959326 - 0.804970i) q^{52} +(-1.05253 + 1.82303i) q^{53} +(4.94317 - 2.52899i) q^{54} -0.509818 q^{55} +(-8.03524 + 0.854311i) q^{56} +(-5.76547 + 11.0119i) q^{57} +(-1.02298 - 5.80163i) q^{58} +(-0.445729 - 2.52786i) q^{59} +(0.0745601 - 0.556207i) q^{60} +(-1.04747 - 0.878929i) q^{61} +(-2.92130 + 5.05984i) q^{62} +(2.61045 - 7.49570i) q^{63} +(-3.92755 - 6.80271i) q^{64} +(-0.0956814 + 0.542636i) q^{65} +(-0.535161 - 2.44117i) q^{66} +(-2.49507 - 0.908131i) q^{67} +(-2.77820 + 2.33119i) q^{68} +(8.59348 + 2.73180i) q^{69} +(0.628477 + 0.862840i) q^{70} +(1.85480 + 3.21260i) q^{71} +(9.13125 - 0.755525i) q^{72} +(4.78086 + 8.28069i) q^{73} +(-0.404182 + 2.29223i) q^{74} +(7.78048 - 3.20132i) q^{75} +(-4.71748 + 3.95844i) q^{76} +(-2.96412 - 1.99414i) q^{77} +(-2.69876 + 0.111458i) q^{78} +(2.26722 - 0.825202i) q^{79} +(-0.292120 + 0.505967i) q^{80} +(-3.15778 + 8.42784i) q^{81} +(-5.19535 - 8.99862i) q^{82} +(2.04308 - 11.5869i) q^{83} +(2.60909 - 2.94219i) q^{84} +(1.49948 + 0.545766i) q^{85} +(10.1053 + 3.67802i) q^{86} +(7.56187 + 5.83079i) q^{87} +(0.716113 - 4.06128i) q^{88} -8.42555 q^{89} +(-0.689569 - 0.994755i) q^{90} +(-2.67881 + 2.78068i) q^{91} +(3.42228 + 2.87164i) q^{92} +(-2.02792 - 9.25048i) q^{93} +(9.31065 + 3.38880i) q^{94} +(2.54617 + 0.926730i) q^{95} +(7.35332 + 2.33756i) q^{96} +(-2.67184 - 2.24194i) q^{97} +(0.279036 + 7.47490i) q^{98} +(3.30724 + 2.33907i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00414	−	0.365478i	0.710037	−	0.258432i	0.0383465	−	0.999265i	$-0.487791\pi$
$2$	1.00414	−	0.365478i	0.710037	−	0.258432i	0.671690	+	0.740832i	$0.265569\pi$
$3$	−0.803391	+	1.53446i	−0.463838	+	0.885920i
$3$	−0.803391	+	1.53446i	−0.463838	+	0.885920i
$4$	−0.657360	+	0.551590i	−0.328680	+	0.275795i
$5$	0.354797	+	0.129136i	0.158670	+	0.0577512i	0.420134	−	0.907462i	$-0.361983\pi$
$5$	0.354797	+	0.129136i	0.158670	+	0.0577512i	−0.261464	+	0.965213i	$0.584205\pi$
$6$	−0.245908	+	1.83444i	−0.100392	+	0.748906i
$7$	1.55771	+	2.13859i	0.588758	+	0.808309i
$7$	1.55771	+	2.13859i	0.588758	+	0.808309i
$8$	−1.52708	+	2.64497i	−0.539903	+	0.935139i
$9$	−1.70913	−	2.46554i	−0.569709	−	0.821847i
$10$	0.403463			0.127586
$11$	−1.26884	+	0.461820i	−0.382569	+	0.139244i	−0.526144	−	0.850396i	$-0.676363\pi$
$11$	−1.26884	+	0.461820i	−0.382569	+	0.139244i	0.143574	+	0.989640i	$0.454140\pi$
$12$	−0.318275	−	1.45183i	−0.0918782	−	0.419108i
$13$	0.253416	+	1.43719i	0.0702849	+	0.398605i	0.999572	+	0.0292477i	$0.00931117\pi$
$13$	0.253416	+	1.43719i	0.0702849	+	0.398605i	−0.929287	+	0.369358i	$0.879578\pi$
$14$	2.34577	+	1.57814i	0.626933	+	0.421775i
$15$	−0.483194	+	0.440675i	−0.124760	+	0.113782i
$16$	−0.268700	+	1.52387i	−0.0671751	+	0.380969i
$17$	4.22631			1.02503			0.512515	−	0.858678i	$-0.328714\pi$
$17$	4.22631			1.02503			0.512515	+	0.858678i	$0.328714\pi$
$18$	−2.61731	−	1.85111i	−0.616906	−	0.436310i
$19$	7.17641			1.64638			0.823191	−	0.567765i	$-0.192192\pi$
$19$	7.17641			1.64638			0.823191	+	0.567765i	$0.192192\pi$
$20$	−0.304459	+	0.110814i	−0.0680791	+	0.0247788i
$21$	−4.53302	+	0.672117i	−0.989186	+	0.146668i
$22$	−1.10531	+	0.927466i	−0.235653	+	0.197737i
$23$	−0.904031	−	5.12702i	−0.188504	−	1.06906i	−0.921371	−	0.388685i	$-0.872929\pi$
$23$	−0.904031	−	5.12702i	−0.188504	−	1.06906i	0.732867	−	0.680372i	$-0.238182\pi$
$24$	−2.83176	−	4.46818i	−0.578031	−	0.912064i
$25$	−3.72102	−	3.12230i	−0.744203	−	0.624461i
$26$	0.779728	+	1.35053i	0.152917	+	0.264861i
$27$	5.15637	−	0.641790i	0.992343	−	0.123513i
$28$	−2.20360	−	0.546604i	−0.416441	−	0.103298i
$29$	0.957325	−	5.42926i	0.177771	−	1.00819i	−0.757126	−	0.653269i	$-0.773397\pi$
$29$	0.957325	−	5.42926i	0.177771	−	1.00819i	0.934897	−	0.354919i	$-0.115492\pi$
$30$	−0.324139	+	0.619097i	−0.0591793	+	0.113031i
$31$	−4.18842	+	3.51450i	−0.752263	+	0.631223i	−0.936100	−	0.351733i	$-0.885592\pi$
$31$	−4.18842	+	3.51450i	−0.752263	+	0.631223i	0.183838	+	0.982957i	$0.441148\pi$
$32$	−0.773566	−	4.38711i	−0.136748	−	0.775539i
$33$	0.310731	−	2.31800i	0.0540913	−	0.403513i
$34$	4.24382	−	1.54462i	0.727808	−	0.264901i
$35$	0.276502	+	0.959919i	0.0467374	+	0.162256i
$36$	2.48348	+	0.678009i	0.413913	+	0.113002i
$37$	−1.08910	+	1.88637i	−0.179047	+	0.310118i	−0.941554	−	0.336861i	$-0.890635\pi$
$37$	−1.08910	+	1.88637i	−0.179047	+	0.310118i	0.762508	+	0.646979i	$0.223968\pi$
$38$	7.20615	−	2.62282i	1.16899	−	0.425478i
$39$	−2.40890	−	0.765771i	−0.385733	−	0.122622i
$40$	−0.883362	+	0.741228i	−0.139672	+	0.117199i
$41$	−1.68852	−	9.57606i	−0.263702	−	1.49553i	−0.772706	−	0.634764i	$-0.781097\pi$
$41$	−1.68852	−	9.57606i	−0.263702	−	1.49553i	0.509004	−	0.860764i	$-0.330014\pi$
$42$	−4.30616	+	2.33162i	−0.664454	+	0.359777i
$43$	7.70916	+	6.46875i	1.17564	+	0.986476i	0.999998	+	0.00202064i	$0.000643190\pi$
$43$	7.70916	+	6.46875i	1.17564	+	0.986476i	0.175638	+	0.984455i	$0.443801\pi$
$44$	0.579348	−	1.00346i	0.0873401	−	0.151277i
$45$	−0.288004	−	1.09547i	−0.0429331	−	0.163304i
$46$	−2.78159	−	4.81785i	−0.410123	−	0.710354i
$47$	7.10294	+	5.96008i	1.03607	+	0.869366i	0.991561	−	0.129642i	$-0.0413830\pi$
$47$	7.10294	+	5.96008i	1.03607	+	0.869366i	0.0445098	+	0.999009i	$0.485827\pi$
$48$	−2.12245	−	1.63658i	−0.306349	−	0.236219i
$49$	−2.14710	+	6.66258i	−0.306728	+	0.951797i
$50$	−4.87757	−	1.77529i	−0.689792	−	0.251064i
$51$	−3.39538	+	6.48509i	−0.475448	+	0.908094i
$52$	−0.959326	−	0.804970i	−0.133035	−	0.111629i
$53$	−1.05253	+	1.82303i	−0.144576	+	0.250412i	−0.929215	−	0.369541i	$-0.879515\pi$
$53$	−1.05253	+	1.82303i	−0.144576	+	0.250412i	0.784639	+	0.619953i	$0.212848\pi$
$54$	4.94317	−	2.52899i	0.672680	−	0.344152i
$55$	−0.509818			−0.0687438
$56$	−8.03524	+	0.854311i	−1.07375	+	0.114162i
$57$	−5.76547	+	11.0119i	−0.763655	+	1.45856i
$58$	−1.02298	−	5.80163i	−0.134324	−	0.761792i
$59$	−0.445729	−	2.52786i	−0.0580290	−	0.329099i	0.941949	−	0.335756i	$-0.108992\pi$
$59$	−0.445729	−	2.52786i	−0.0580290	−	0.329099i	−0.999978	+	0.00665763i	$0.997881\pi$
$60$	0.0745601	−	0.556207i	0.00962567	−	0.0718060i
$61$	−1.04747	−	0.878929i	−0.134114	−	0.112535i	0.573263	−	0.819371i	$-0.305677\pi$
$61$	−1.04747	−	0.878929i	−0.134114	−	0.112535i	−0.707377	+	0.706836i	$0.750122\pi$
$62$	−2.92130	+	5.05984i	−0.371006	+	0.642601i
$63$	2.61045	−	7.49570i	0.328886	−	0.944370i
$64$	−3.92755	−	6.80271i	−0.490944	−	0.850339i
$65$	−0.0956814	+	0.542636i	−0.0118678	+	0.0673058i
$66$	−0.535161	−	2.44117i	−0.0658738	−	0.300488i
$67$	−2.49507	−	0.908131i	−0.304821	−	0.110946i	0.185081	−	0.982723i	$-0.440745\pi$
$67$	−2.49507	−	0.908131i	−0.304821	−	0.110946i	−0.489902	+	0.871777i	$0.662967\pi$
$68$	−2.77820	+	2.33119i	−0.336906	+	0.282698i
$69$	8.59348	+	2.73180i	1.03453	+	0.328870i
$70$	0.628477	+	0.862840i	0.0751174	+	0.103129i
$71$	1.85480	+	3.21260i	0.220124	+	0.381265i	0.954845	−	0.297103i	$-0.0960206\pi$
$71$	1.85480	+	3.21260i	0.220124	+	0.381265i	−0.734722	+	0.678369i	$0.762687\pi$
$72$	9.13125	−	0.755525i	1.07613	−	0.0890394i
$73$	4.78086	+	8.28069i	0.559557	+	0.969182i	0.997533	+	0.0701950i	$0.0223622\pi$
$73$	4.78086	+	8.28069i	0.559557	+	0.969182i	−0.437976	+	0.898987i	$0.644305\pi$
$74$	−0.404182	+	2.29223i	−0.0469852	+	0.266466i
$75$	7.78048	−	3.20132i	0.898412	−	0.369656i
$76$	−4.71748	+	3.95844i	−0.541132	+	0.454064i
$77$	−2.96412	−	1.99414i	−0.337793	−	0.227254i
$78$	−2.69876	+	0.111458i	−0.305574	+	0.0126201i
$79$	2.26722	−	0.825202i	0.255083	−	0.0928424i	−0.211314	−	0.977418i	$-0.567774\pi$
$79$	2.26722	−	0.825202i	0.255083	−	0.0928424i	0.466396	+	0.884576i	$0.345552\pi$
$80$	−0.292120	+	0.505967i	−0.0326600	+	0.0565689i
$81$	−3.15778	+	8.42784i	−0.350864	+	0.936426i
$82$	−5.19535	−	8.99862i	−0.573731	−	0.993731i
$83$	2.04308	−	11.5869i	0.224257	−	1.27183i	−0.639842	−	0.768506i	$-0.721000\pi$
$83$	2.04308	−	11.5869i	0.224257	−	1.27183i	0.864100	−	0.503321i	$-0.167888\pi$
$84$	2.60909	−	2.94219i	0.284675	−	0.321019i
$85$	1.49948	+	0.545766i	0.162641	+	0.0591966i
$86$	10.1053	+	3.67802i	1.08968	+	0.396612i
$87$	7.56187	+	5.83079i	0.810717	+	0.625127i
$88$	0.716113	−	4.06128i	0.0763379	−	0.432934i
$89$	−8.42555			−0.893106			−0.446553	−	0.894757i	$-0.647349\pi$
$89$	−8.42555			−0.893106			−0.446553	+	0.894757i	$0.647349\pi$
$90$	−0.689569	−	0.994755i	−0.0726870	−	0.104856i
$91$	−2.67881	+	2.78068i	−0.280816	+	0.291494i
$92$	3.42228	+	2.87164i	0.356798	+	0.299389i
$93$	−2.02792	−	9.25048i	−0.210285	−	0.959230i
$94$	9.31065	+	3.38880i	0.960320	+	0.349528i
$95$	2.54617	+	0.926730i	0.261231	+	0.0950805i
$96$	7.35332	+	2.33756i	0.750495	+	0.238576i
$97$	−2.67184	−	2.24194i	−0.271284	−	0.227635i	0.496988	−	0.867757i	$-0.334439\pi$
$97$	−2.67184	−	2.24194i	−0.271284	−	0.227635i	−0.768273	+	0.640123i	$0.778884\pi$
$98$	0.279036	+	7.47490i	0.0281869	+	0.755079i
$99$	3.30724	+	2.33907i	0.332390	+	0.235085i
$100$	4.16828			0.416828
$101$	−1.00639	+	5.70752i	−0.100140	+	0.567920i	0.892911	+	0.450233i	$0.148659\pi$
$101$	−1.00639	+	5.70752i	−0.100140	+	0.567920i	−0.993051	+	0.117687i	$0.962452\pi$
$102$	−1.03928	+	7.75290i	−0.102904	+	0.767651i
$103$	−10.5421	−	3.83701i	−1.03874	−	0.378071i	−0.234339	−	0.972155i	$-0.575293\pi$
$103$	−10.5421	−	3.83701i	−1.03874	−	0.378071i	−0.804403	+	0.594083i	$0.797515\pi$
$104$	−4.18832	−	1.52442i	−0.410699	−	0.149482i
$105$	−1.69510	−	0.346909i	−0.165424	−	0.0338548i
$106$	−0.390610	+	2.21526i	−0.0379394	+	0.215165i
$107$	−2.48198	−	4.29892i	−0.239942	−	0.415592i	0.720755	−	0.693190i	$-0.243795\pi$
$107$	−2.48198	−	4.29892i	−0.239942	−	0.415592i	−0.960698	+	0.277597i	$0.910462\pi$
$108$	−3.03558	+	3.26609i	−0.292099	+	0.314279i
$109$	8.12244	−	14.0685i	0.777989	−	1.34752i	−0.155110	−	0.987897i	$-0.549573\pi$
$109$	8.12244	−	14.0685i	0.777989	−	1.34752i	0.933099	−	0.359619i	$-0.117093\pi$
$110$	−0.511930	+	0.186327i	−0.0488106	+	0.0177656i
$111$	−2.01959	−	3.18667i	−0.191691	−	0.302465i
$112$	−3.67749	+	1.79911i	−0.347490	+	0.170000i
$113$	−9.42690	+	7.91011i	−0.886808	+	0.744121i	−0.967567	−	0.252613i	$-0.918710\pi$
$113$	−9.42690	+	7.91011i	−0.886808	+	0.744121i	0.0807590	+	0.996734i	$0.474266\pi$
$114$	−1.76474	+	13.1647i	−0.165283	+	1.23299i
$115$	0.341332	−	1.93579i	0.0318294	−	0.180513i
$116$	2.36542	+	4.09703i	0.219624	+	0.380399i
$117$	3.11034	−	3.08115i	0.287551	−	0.284852i
$118$	−1.37145	−	2.37543i	−0.126252	−	0.218676i
$119$	6.58335	+	9.03832i	0.603494	+	0.828541i
$120$	−0.427700	−	1.95098i	−0.0390434	−	0.178099i
$121$	−7.02981	+	5.89871i	−0.639074	+	0.536247i
$122$	−1.37304	−	0.499745i	−0.124309	−	0.0452447i
$123$	16.0506	+	5.10236i	1.44723	+	0.460064i
$124$	0.814734	−	4.62058i	0.0731652	−	0.414941i
$125$	−1.86092	−	3.22321i	−0.166446	−	0.288293i
$126$	−0.118249	−	8.48082i	−0.0105345	−	0.755532i
$127$	7.89539	−	13.6752i	0.700602	−	1.21348i	−0.267653	−	0.963515i	$-0.586248\pi$
$127$	7.89539	−	13.6752i	0.700602	−	1.21348i	0.968255	−	0.249963i	$-0.0804186\pi$
$128$	0.395069	+	0.331503i	0.0349195	+	0.0293010i
$129$	−16.1195	+	6.63245i	−1.41924	+	0.583954i
$130$	0.102244	+	0.579854i	0.00896739	+	0.0508566i
$131$	2.18582	+	12.3964i	0.190976	+	1.08308i	0.918034	+	0.396502i	$0.129776\pi$
$131$	2.18582	+	12.3964i	0.190976	+	1.08308i	−0.727058	+	0.686576i	$0.759113\pi$
$132$	1.07433	+	1.69516i	0.0935081	+	0.147545i
$133$	11.1787	+	15.3474i	0.969321	+	1.33079i
$134$	−2.83731			−0.245106
$135$	1.91234	+	0.438165i	0.164588	+	0.0377112i
$136$	−6.45389	+	11.1785i	−0.553416	+	0.958545i
$137$	−13.7550	−	11.5418i	−1.17517	−	0.986083i	−0.999999	−	0.00154415i	$-0.999508\pi$
$137$	−13.7550	−	11.5418i	−1.17517	−	0.986083i	−0.175169	−	0.984538i	$-0.556047\pi$
$138$	9.62750	−	0.397613i	0.819547	−	0.0338471i
$139$	4.22446	+	1.53758i	0.358314	+	0.130416i	0.514903	−	0.857248i	$-0.327828\pi$
$139$	4.22446	+	1.53758i	0.358314	+	0.130416i	−0.156590	+	0.987664i	$0.550050\pi$
$140$	−0.711243	−	0.478496i	−0.0601110	−	0.0404403i
$141$	−14.8519	+	6.11090i	−1.25076	+	0.514631i
$142$	3.03662	+	2.54802i	0.254827	+	0.213825i
$143$	−0.985268	−	1.70653i	−0.0823922	−	0.142708i
$144$	4.21642	−	1.94200i	0.351368	−	0.161834i
$145$	1.04077	−	1.80266i	0.0864309	−	0.149703i
$146$	7.82708	+	6.56770i	0.647774	+	0.543547i
$147$	−8.49849	−	8.64729i	−0.700944	−	0.713216i
$148$	−0.324576	−	1.84076i	−0.0266800	−	0.151310i
$149$	−5.85372	+	4.91185i	−0.479555	+	0.402395i	−0.850266	−	0.526354i	$-0.823559\pi$
$149$	−5.85372	+	4.91185i	−0.479555	+	0.402395i	0.370710	+	0.928749i	$0.379114\pi$
$150$	6.64270	−	6.05818i	0.542374	−	0.494648i
$151$	−2.05435	+	0.747722i	−0.167181	+	0.0608488i	−0.424255	−	0.905543i	$-0.639464\pi$
$151$	−2.05435	+	0.747722i	−0.167181	+	0.0608488i	0.257074	+	0.966392i	$0.417242\pi$
$152$	−10.9589	+	18.9814i	−0.888886	+	1.53960i
$153$	−7.22329	−	10.4201i	−0.583968	−	0.842417i
$154$	−3.70522	−	0.919082i	−0.298575	−	0.0740617i
$155$	−1.93989	+	0.706061i	−0.155815	+	0.0567122i
$156$	2.00591	−	0.825341i	0.160601	−	0.0660801i
$157$	−3.10443	−	17.6061i	−0.247761	−	1.40512i	−0.813993	−	0.580875i	$-0.802710\pi$
$157$	−3.10443	−	17.6061i	−0.247761	−	1.40512i	0.566232	−	0.824246i	$-0.308401\pi$
$158$	1.97502	−	1.65724i	0.157124	−	0.131843i
$159$	−1.95177	−	3.07966i	−0.154786	−	0.244233i
$160$	0.292073	−	1.65643i	0.0230904	−	0.130952i
$161$	9.55635	−	9.91974i	0.753146	−	0.781785i
$162$	−0.0906699	+	9.61686i	−0.00712370	+	0.755572i
$163$	−2.71072	−	4.69511i	−0.212320	−	0.367749i	0.740120	−	0.672475i	$-0.234769\pi$
$163$	−2.71072	−	4.69511i	−0.212320	−	0.367749i	−0.952440	+	0.304725i	$0.901435\pi$
$164$	6.39202	+	5.36354i	0.499133	+	0.418822i
$165$	0.409583	−	0.782294i	0.0318860	−	0.0609015i
$166$	−2.18321	−	12.3816i	−0.169450	−	0.960999i
$167$	−1.87662	+	1.57467i	−0.145217	+	0.121852i	−0.712502	−	0.701670i	$-0.752438\pi$
$167$	−1.87662	+	1.57467i	−0.145217	+	0.121852i	0.567285	+	0.823522i	$0.307994\pi$
$168$	5.14453	−	13.0161i	0.396909	−	1.00421i
$169$	10.2147	−	3.71785i	0.785746	−	0.285988i
$170$	1.70516			0.130780
$171$	−12.2654	−	17.6937i	−0.937958	−	1.35307i
$172$	−8.63579			−0.658473
$173$	0.650712	−	3.69037i	0.0494727	−	0.280574i	−0.950028	−	0.312164i	$-0.898946\pi$
$173$	0.650712	−	3.69037i	0.0494727	−	0.280574i	0.999501	+	0.0315905i	$0.0100572\pi$
$174$	9.72422	+	3.09125i	0.737192	+	0.234347i
$175$	0.881059	−	12.8213i	0.0666018	−	0.969203i
$176$	−0.362818	−	2.05764i	−0.0273484	−	0.155101i
$177$	4.23698	+	1.34690i	0.318471	+	0.101239i
$178$	−8.46046	+	3.07936i	−0.634138	+	0.230807i
$179$	−3.06925			−0.229407			−0.114703	−	0.993400i	$-0.536592\pi$
$179$	−3.06925			−0.229407			−0.114703	+	0.993400i	$0.536592\pi$
$180$	0.793575	+	0.561261i	0.0591496	+	0.0418339i
$181$	−1.19587	+	2.07130i	−0.0888880	+	0.153958i	−0.907041	−	0.421042i	$-0.861665\pi$
$181$	−1.19587	+	2.07130i	−0.0888880	+	0.153958i	0.818153	+	0.575000i	$0.194998\pi$
$182$	−1.67363	+	3.77124i	−0.124058	+	0.279543i
$183$	2.19021	−	0.901171i	0.161905	−	0.0666165i
$184$	14.9413	+	5.43820i	1.10149	+	0.400910i
$185$	−0.630006	+	0.528638i	−0.0463190	+	0.0388663i
$186$	−5.41717	−	8.54765i	−0.397206	−	0.626744i
$187$	−5.36250	+	1.95179i	−0.392145	+	0.142729i
$188$	−7.95671			−0.580302
$189$	9.40463	+	10.0276i	0.684086	+	0.729401i
$190$	2.89542			0.210056
$191$	−10.7830	+	3.92467i	−0.780227	+	0.283979i	−0.701267	−	0.712898i	$-0.747382\pi$
$191$	−10.7830	+	3.92467i	−0.780227	+	0.283979i	−0.0789596	+	0.996878i	$0.525160\pi$
$192$	13.5938	−	0.561421i	0.981051	−	0.0405171i
$193$	12.9040	−	10.8278i	0.928853	−	0.779400i	−0.0467581	−	0.998906i	$-0.514889\pi$
$193$	12.9040	−	10.8278i	0.928853	−	0.779400i	0.975611	+	0.219506i	$0.0704445\pi$
$194$	−3.50229	−	1.27473i	−0.251450	−	0.0915203i
$195$	−0.755783	−	0.582768i	−0.0541228	−	0.0417329i
$196$	−2.26360	−	5.56403i	−0.161686	−	0.397431i
$197$	9.66211	−	16.7353i	0.688397	−	1.19234i	−0.283960	−	0.958836i	$-0.591648\pi$
$197$	9.66211	−	16.7353i	0.688397	−	1.19234i	0.972356	−	0.233502i	$-0.0750185\pi$
$198$	4.17582	+	1.14003i	0.296763	+	0.0810186i
$199$	−3.66722			−0.259962			−0.129981	−	0.991516i	$-0.541492\pi$
$199$	−3.66722			−0.259962			−0.129981	+	0.991516i	$0.541492\pi$
$200$	13.9407	−	5.07399i	0.985755	−	0.358786i
$201$	3.39800	−	3.09900i	0.239677	−	0.218586i
$202$	1.07542	+	6.09898i	0.0756660	+	0.429123i
$203$	13.1022	−	6.40987i	0.919592	−	0.449885i
$204$	−1.34513	−	6.13589i	−0.0941779	−	0.429598i
$205$	0.637528	−	3.61560i	0.0445269	−	0.252525i
$206$	−11.9881			−0.835251
$207$	−11.0958	+	10.9916i	−0.771209	+	0.763972i
$208$	−2.25819			−0.156578
$209$	−9.10571	+	3.31421i	−0.629855	+	0.229249i
$210$	−1.82891	+	0.271174i	−0.126207	+	0.0187128i
$211$	5.64404	−	4.73591i	0.388552	−	0.326034i	−0.427497	−	0.904017i	$-0.640604\pi$
$211$	5.64404	−	4.73591i	0.388552	−	0.326034i	0.816049	+	0.577983i	$0.196160\pi$
$212$	−0.313677	−	1.77895i	−0.0215434	−	0.122179i
$213$	−6.41973	+	0.265133i	−0.439872	+	0.0181666i
$214$	−4.06343	−	3.40962i	−0.277770	−	0.233077i
$215$	1.89984	+	3.29062i	0.129568	+	0.224418i
$216$	−6.17664	+	14.6185i	−0.420267	+	0.994664i
$217$	−14.0404	−	3.48273i	−0.953125	−	0.236423i
$218$	3.01437	−	17.0954i	0.204159	−	1.15784i
$219$	−16.5473	+	0.683398i	−1.11816	+	0.0461797i
$220$	0.335133	−	0.281210i	0.0225947	−	0.0189592i
$221$	1.07101	+	6.07401i	0.0720441	+	0.408582i
$222$	−3.19262	−	2.46176i	−0.214274	−	0.165222i
$223$	−13.2430	+	4.82007i	−0.886820	+	0.322776i	−0.744959	−	0.667111i	$-0.767531\pi$
$223$	−13.2430	+	4.82007i	−0.886820	+	0.322776i	−0.141861	+	0.989887i	$0.545309\pi$
$224$	8.17722	−	8.48817i	0.546364	−	0.567140i
$225$	−1.33848	+	14.5107i	−0.0892320	+	0.967382i
$226$	−6.57499	+	11.3882i	−0.437362	+	0.757533i
$227$	26.2874	−	9.56782i	1.74475	−	0.635039i	0.745258	−	0.666776i	$-0.232326\pi$
$227$	26.2874	−	9.56782i	1.74475	−	0.635039i	0.999496	+	0.0317379i	$0.0101042\pi$
$228$	−2.28408	−	10.4190i	−0.151267	−	0.690012i
$229$	−7.27754	+	6.10659i	−0.480914	+	0.403534i	−0.850757	−	0.525560i	$-0.823856\pi$
$229$	−7.27754	+	6.10659i	−0.480914	+	0.403534i	0.369843	+	0.929094i	$0.379411\pi$
$230$	−0.364743	−	2.06856i	−0.0240505	−	0.136397i
$231$	5.44128	−	2.94625i	0.358010	−	0.193849i
$232$	12.8983	+	10.8230i	0.846817	+	0.710564i
$233$	9.35095	−	16.1963i	0.612601	−	1.06106i	−0.378199	−	0.925724i	$-0.623457\pi$
$233$	9.35095	−	16.1963i	0.612601	−	1.06106i	0.990800	−	0.135332i	$-0.0432100\pi$
$234$	1.99713	−	4.23068i	0.130556	−	0.276568i
$235$	1.75044	+	3.03186i	0.114186	+	0.197777i
$236$	1.68734	+	1.41585i	0.109837	+	0.0921640i
$237$	−0.555229	+	4.14192i	−0.0360660	+	0.269047i
$238$	9.91393	+	6.66969i	0.642625	+	0.432332i
$239$	−25.0550	−	9.11928i	−1.62067	−	0.589877i	−0.637164	−	0.770728i	$-0.719893\pi$
$239$	−25.0550	−	9.11928i	−1.62067	−	0.589877i	−0.983510	+	0.180851i	$0.942115\pi$
$240$	−0.541699	−	0.854736i	−0.0349665	−	0.0551730i
$241$	2.08085	+	1.74604i	0.134039	+	0.112472i	0.707343	−	0.706871i	$-0.249894\pi$
$241$	2.08085	+	1.74604i	0.134039	+	0.112472i	−0.573303	+	0.819343i	$0.694338\pi$
$242$	−4.90309	+	8.49240i	−0.315182	+	0.545912i
$243$	−10.3952	−	11.6163i	−0.666855	−	0.745188i
$244$	1.17337			0.0751174
$245$	−1.62216	+	2.08660i	−0.103636	+	0.133308i
$246$	17.9819	−	0.742647i	1.14648	−	0.0473495i
$247$	1.81862	+	10.3139i	0.115716	+	0.656257i
$248$	−2.89973	−	16.4452i	−0.184133	−	1.04427i
$249$	16.1382	+	12.4438i	1.02272	+	0.788596i
$250$	−3.04665	−	2.55644i	−0.192687	−	0.161683i
$251$	−3.89375	+	6.74417i	−0.245771	+	0.425688i	−0.962348	−	0.271820i	$-0.912375\pi$
$251$	−3.89375	+	6.74417i	−0.245771	+	0.425688i	0.716577	+	0.697508i	$0.245708\pi$
$252$	2.41855	+	6.36727i	0.152354	+	0.401100i
$253$	3.51483	+	6.08786i	0.220975	+	0.382740i
$254$	2.93011	−	16.6175i	0.183851	−	1.04267i
$255$	−2.04212	+	1.86243i	−0.127883	+	0.116630i
$256$	15.2806	+	5.56169i	0.955039	+	0.347606i
$257$	−10.3928	+	8.72061i	−0.648287	+	0.543977i	−0.906550	−	0.422097i	$-0.861294\pi$
$257$	−10.3928	+	8.72061i	−0.648287	+	0.543977i	0.258264	+	0.966074i	$0.416850\pi$
$258$	−13.7623	+	12.5513i	−0.856802	+	0.781407i
$259$	−5.73067	+	0.609288i	−0.356086	+	0.0378593i
$260$	−0.236416	−	0.409484i	−0.0146619	−	0.0253951i
$261$	−15.0222	+	6.91896i	−0.929854	+	0.428273i
$262$	6.72549	+	11.6489i	0.415502	+	0.719671i
$263$	−5.21316	+	29.5653i	−0.321457	+	1.82307i	0.212026	+	0.977264i	$0.431994\pi$
$263$	−5.21316	+	29.5653i	−0.321457	+	1.82307i	−0.533484	+	0.845810i	$0.679117\pi$
$264$	5.65655	+	4.36164i	0.348136	+	0.268440i
$265$	−0.608851	+	0.510887i	−0.0374014	+	0.0313835i
$266$	16.8342	+	11.3254i	1.03217	+	0.694403i
$267$	6.76901	−	12.9287i	0.414257	−	0.791221i
$268$	2.14107	−	0.779287i	0.130787	−	0.0476025i
$269$	−4.17765	+	7.23590i	−0.254716	+	0.441181i	−0.964818	−	0.262918i	$-0.915315\pi$
$269$	−4.17765	+	7.23590i	−0.254716	+	0.441181i	0.710102	+	0.704098i	$0.248649\pi$
$270$	2.08040	−	0.258939i	0.126609	−	0.0157585i
$271$	12.1954	+	21.1230i	0.740817	+	1.28313i	0.952124	+	0.305713i	$0.0988949\pi$
$271$	12.1954	+	21.1230i	0.740817	+	1.28313i	−0.211306	+	0.977420i	$0.567772\pi$
$272$	−1.13561	+	6.44036i	−0.0688564	+	0.390504i
$273$	−2.11470	−	6.34449i	−0.127987	−	0.383986i
$274$	−18.0303	−	6.56247i	−1.08925	−	0.396454i
$275$	6.16331	+	2.24326i	0.371662	+	0.135274i
$276$	−7.15584	+	2.94431i	−0.430731	+	0.177226i
$277$	−5.66961	+	32.1539i	−0.340654	+	1.93194i	0.0213647	+	0.999772i	$0.493199\pi$
$277$	−5.66961	+	32.1539i	−0.340654	+	1.93194i	−0.362018	+	0.932171i	$0.617912\pi$
$278$	4.80391			0.288120
$279$	15.8237	+	4.31999i	0.947340	+	0.258631i
$280$	−2.96120	−	0.734528i	−0.176966	−	0.0438964i
$281$	−14.1740	−	11.8934i	−0.845553	−	0.709503i	0.113253	−	0.993566i	$-0.463873\pi$
$281$	−14.1740	−	11.8934i	−0.845553	−	0.709503i	−0.958806	+	0.284063i	$0.908317\pi$
$282$	−12.6801	+	11.5643i	−0.755087	+	0.688643i
$283$	−5.42158	−	1.97329i	−0.322279	−	0.117300i	0.175814	−	0.984423i	$-0.443744\pi$
$283$	−5.42158	−	1.97329i	−0.322279	−	0.117300i	−0.498094	+	0.867123i	$0.665966\pi$
$284$	−2.99131	−	1.08875i	−0.177501	−	0.0646052i
$285$	−3.46760	+	3.16246i	−0.205403	+	0.187328i
$286$	−1.61305	−	1.35351i	−0.0953817	−	0.0800347i
$287$	17.8490	−	18.5277i	1.05359	−	1.09366i
$288$	−9.49448	+	9.40539i	−0.559468	+	0.554218i
$289$	0.861657			0.0506857
$290$	0.386245	−	2.19051i	0.0226811	−	0.128631i
$291$	5.58670	−	2.29867i	0.327498	−	0.134751i
$292$	−7.71029	−	2.80632i	−0.451211	−	0.164227i
$293$	31.7641	+	11.5612i	1.85568	+	0.675412i	0.981991	+	0.188925i	$0.0605004\pi$
$293$	31.7641	+	11.5612i	1.85568	+	0.675412i	0.873688	+	0.486487i	$0.161722\pi$
$294$	−11.6941	−	5.57710i	−0.682014	−	0.325263i
$295$	0.168293	−	0.954435i	0.00979838	−	0.0555693i
$296$	−3.32627	−	5.76127i	−0.193336	−	0.334867i
$297$	−6.24621	+	3.19564i	−0.362442	+	0.185430i
$298$	−4.08280	+	7.07161i	−0.236510	+	0.409647i
$299$	7.13941	−	2.59853i	0.412883	−	0.150277i
$300$	−3.34876	+	6.39605i	−0.193341	+	0.369276i
$301$	−1.82537	+	26.5631i	−0.105212	+	1.53107i
$302$	−1.78959	+	1.50164i	−0.102979	+	0.0864097i
$303$	−7.94943	−	6.12964i	−0.456683	−	0.352138i
$304$	−1.92830	+	10.9360i	−0.110596	+	0.627220i
$305$	−0.258137	−	0.447107i	−0.0147809	−	0.0256013i
$306$	−11.0615	−	7.82335i	−0.632346	−	0.447231i
$307$	9.02902	+	15.6387i	0.515314	+	0.892549i	0.999842	+	0.0177739i	$0.00565790\pi$
$307$	9.02902	+	15.6387i	0.515314	+	0.892549i	−0.484528	+	0.874776i	$0.661009\pi$
$308$	3.04844	−	0.324112i	0.173701	−	0.0184680i
$309$	14.3571	−	13.0938i	0.816749	−	0.744879i
$310$	−1.68987	+	1.41797i	−0.0959784	+	0.0805354i
$311$	18.1173	+	6.59415i	1.02734	+	0.373920i	0.800066	−	0.599912i	$-0.204798\pi$
$311$	18.1173	+	6.59415i	1.02734	+	0.373920i	0.227270	+	0.973832i	$0.427020\pi$
$312$	5.70402	−	5.20209i	0.322927	−	0.294511i
$313$	4.28901	−	24.3242i	0.242429	−	1.37489i	−0.583958	−	0.811784i	$-0.698497\pi$
$313$	4.28901	−	24.3242i	0.242429	−	1.37489i	0.826388	−	0.563102i	$-0.190392\pi$
$314$	−9.55195	−	16.5445i	−0.539048	−	0.933658i
$315$	1.89414	−	2.32235i	0.106723	−	0.130850i
$316$	−1.03521	+	1.79303i	−0.0582350	+	0.100866i
$317$	−3.59407	−	3.01578i	−0.201863	−	0.169383i	0.536252	−	0.844058i	$-0.319840\pi$
$317$	−3.59407	−	3.01578i	−0.201863	−	0.169383i	−0.738115	+	0.674674i	$0.764284\pi$
$318$	−3.08541	−	2.37909i	−0.173021	−	0.133413i
$319$	1.29265	+	7.33097i	0.0723744	+	0.410455i
$320$	−0.515010	−	2.92077i	−0.0287899	−	0.163276i
$321$	8.59052	−	0.354786i	0.479476	−	0.0198022i
$322$	5.97049	−	13.4535i	0.332722	−	0.749733i
$323$	30.3297			1.68759
$324$	−2.57292	−	7.28192i	−0.142940	−	0.404551i
$325$	3.54439	−	6.13906i	0.196607	−	0.340534i
$326$	−4.43791	−	3.72385i	−0.245793	−	0.206245i
$327$	15.0620	+	23.7660i	0.832931	+	1.31427i
$328$	27.9069	+	10.1573i	1.54090	+	0.560842i
$329$	−1.68183	+	24.4743i	−0.0927222	+	1.34931i
$330$	0.125368	−	0.935229i	0.00690131	−	0.0514827i
$331$	−14.7548	−	12.3807i	−0.810996	−	0.680507i	0.139849	−	0.990173i	$-0.455338\pi$
$331$	−14.7548	−	12.3807i	−0.810996	−	0.680507i	−0.950845	+	0.309666i	$0.899783\pi$
$332$	5.04818	+	8.74370i	0.277055	+	0.479873i
$333$	6.51234	−	0.538834i	0.356874	−	0.0295279i
$334$	−1.30889	+	2.26706i	−0.0716192	+	0.124048i
$335$	−0.767971	−	0.644404i	−0.0419587	−	0.0352075i
$336$	0.193802	−	7.08835i	0.0105727	−	0.386701i
$337$	−3.88353	−	22.0246i	−0.211549	−	1.19975i	−0.886795	−	0.462162i	$-0.847074\pi$
$337$	−3.88353	−	22.0246i	−0.211549	−	1.19975i	0.675246	−	0.737592i	$-0.264037\pi$
$338$	8.89823	−	7.46650i	0.484000	−	0.406124i
$339$	−4.56425	−	20.8201i	−0.247896	−	1.13079i
$340$	−1.28674	+	0.468334i	−0.0697831	+	0.0253990i
$341$	3.69137	−	6.39364i	0.199899	−	0.346235i
$342$	−18.7829	−	13.2843i	−1.01566	−	0.718333i
$343$	−17.5930	+	5.78660i	−0.949935	+	0.312447i
$344$	−28.8821	+	10.5122i	−1.55722	+	0.566782i
$345$	2.69617	+	2.07896i	0.145157	+	0.111927i
$346$	−0.695342	−	3.94348i	−0.0373818	−	0.212003i
$347$	20.8243	−	17.4737i	1.11791	−	0.938036i	0.119411	−	0.992845i	$-0.461899\pi$
$347$	20.8243	−	17.4737i	1.11791	−	0.938036i	0.998497	+	0.0548091i	$0.0174550\pi$
$348$	−8.18707	+	0.338124i	−0.438873	+	0.0181253i
$349$	3.70378	−	21.0052i	0.198259	−	1.12438i	−0.709442	−	0.704764i	$-0.751053\pi$
$349$	3.70378	−	21.0052i	0.198259	−	1.12438i	0.907701	−	0.419618i	$-0.137836\pi$
$350$	−3.80121	−	13.1965i	−0.203183	−	0.705382i
$351$	2.22908	+	7.24805i	0.118979	+	0.386872i
$352$	3.00759	+	5.20929i	0.160305	+	0.277656i
$353$	−15.0842	−	12.6571i	−0.802851	−	0.673672i	0.146039	−	0.989279i	$-0.453348\pi$
$353$	−15.0842	−	12.6571i	−0.802851	−	0.673672i	−0.948890	+	0.315607i	$0.897792\pi$
$354$	4.74680	−	0.196042i	0.252290	−	0.0104195i
$355$	0.243215	+	1.37934i	0.0129085	+	0.0732078i
$356$	5.53862	−	4.64745i	0.293546	−	0.246314i
$357$	−19.1579	+	2.84057i	−1.01394	+	0.150339i
$358$	−3.08197	+	1.12175i	−0.162887	+	0.0592861i
$359$	−21.3704			−1.12789			−0.563943	−	0.825814i	$-0.690716\pi$
$359$	−21.3704			−1.12789			−0.563943	+	0.825814i	$0.690716\pi$
$360$	3.33731	+	0.911111i	0.175891	+	0.0480198i
$361$	32.5009			1.71057
$362$	−0.443805	+	2.51694i	−0.0233259	+	0.132288i
$363$	−3.40364	−	15.5259i	−0.178645	−	0.814900i
$364$	0.227149	−	3.30551i	0.0119058	−	0.173256i
$365$	0.626903	+	3.55534i	0.0328136	+	0.186095i
$366$	1.86992	−	1.70538i	0.0977424	−	0.0891415i
$367$	−28.9852	+	10.5497i	−1.51301	+	0.550692i	−0.959392	−	0.282075i	$-0.908977\pi$
$367$	−28.9852	+	10.5497i	−1.51301	+	0.550692i	−0.553623	+	0.832768i	$0.686755\pi$
$368$	8.05584			0.419940
$369$	−20.7243	+	20.5298i	−1.07886	+	1.06874i
$370$	−0.439411	+	0.761082i	−0.0228439	+	0.0395668i
$371$	−5.53823	+	0.588828i	−0.287531	+	0.0305704i
$372$	6.43555	+	4.96231i	0.333667	+	0.257284i
$373$	18.3495	+	6.67867i	0.950101	+	0.345809i	0.770147	−	0.637866i	$-0.220183\pi$
$373$	18.3495	+	6.67867i	0.950101	+	0.345809i	0.179954	+	0.983675i	$0.442405\pi$
$374$	−4.67138	+	3.91976i	−0.241551	+	0.202686i
$375$	6.44093	−	0.266009i	0.332608	−	0.0137366i
$376$	−26.6110	+	9.68560i	−1.37236	+	0.499497i
$377$	8.04549			0.414364
$378$	13.1085	+	6.63197i	0.674227	+	0.341112i
$379$	13.5629			0.696678			0.348339	−	0.937369i	$-0.386746\pi$
$379$	13.5629			0.696678			0.348339	+	0.937369i	$0.386746\pi$
$380$	−2.18492	+	0.795247i	−0.112084	+	0.0407953i
$381$	14.6410	+	23.1017i	0.750079	+	1.18354i
$382$	−9.39324	+	7.88187i	−0.480600	+	0.403271i
$383$	4.65718	+	1.69507i	0.237971	+	0.0866142i	0.458253	−	0.888822i	$-0.348476\pi$
$383$	4.65718	+	1.69507i	0.237971	+	0.0866142i	−0.220282	+	0.975436i	$0.570698\pi$
$384$	−0.826072	+	0.339891i	−0.0421553	+	0.0173450i
$385$	−0.794146	−	1.09029i	−0.0404735	−	0.0555662i
$386$	9.00019	−	15.5888i	0.458098	−	0.793448i
$387$	2.77305	−	30.0632i	0.140962	−	1.52820i
$388$	2.99299			0.151946
$389$	−15.2344	+	5.54489i	−0.772417	+	0.281137i	−0.698007	−	0.716091i	$-0.745930\pi$
$389$	−15.2344	+	5.54489i	−0.772417	+	0.281137i	−0.0744101	+	0.997228i	$0.523707\pi$
$390$	−0.971904	−	0.308960i	−0.0492143	−	0.0156448i
$391$	−3.82071	−	21.6683i	−0.193222	−	1.09581i
$392$	−14.3436	−	15.8533i	−0.724459	−	0.800711i
$393$	−20.7778	−	6.60510i	−1.04810	−	0.333183i
$394$	3.58577	−	20.3359i	0.180648	−	1.02451i
$395$	0.910967			0.0458357
$396$	−3.46425	+	0.286634i	−0.174085	+	0.0144039i
$397$	−19.3528			−0.971289			−0.485645	−	0.874156i	$-0.661415\pi$
$397$	−19.3528			−0.971289			−0.485645	+	0.874156i	$0.661415\pi$
$398$	−3.68241	+	1.34029i	−0.184583	+	0.0671826i
$399$	−32.5308	+	4.82339i	−1.62858	+	0.241471i
$400$	5.75784	−	4.83140i	0.287892	−	0.241570i
$401$	3.91632	+	22.2106i	0.195572	+	1.10914i	0.911602	+	0.411074i	$0.134846\pi$
$401$	3.91632	+	22.2106i	0.195572	+	1.10914i	−0.716030	+	0.698069i	$0.754043\pi$
$402$	2.27947	−	4.35373i	0.113690	−	0.217144i
$403$	−6.11243	−	5.12894i	−0.304482	−	0.255491i
$404$	−2.48665	−	4.30701i	−0.123716	−	0.214282i
$405$	−2.20870	+	2.58239i	−0.109751	+	0.128320i
$406$	10.8138	−	11.2250i	0.536679	−	0.557087i
$407$	0.510726	−	2.89647i	0.0253158	−	0.143573i
$408$	−11.9679	−	18.8839i	−0.592499	−	0.934892i
$409$	17.2011	−	14.4334i	0.850537	−	0.713686i	−0.109371	−	0.994001i	$-0.534884\pi$
$409$	17.2011	−	14.4334i	0.850537	−	0.713686i	0.959908	+	0.280316i	$0.0904391\pi$
$410$	−0.681254	−	3.86359i	−0.0336448	−	0.190809i
$411$	28.7610	−	11.8339i	1.41868	−	0.583722i
$412$	9.04640	−	3.29262i	0.445684	−	0.162216i
$413$	4.71172	−	4.89089i	0.231849	−	0.240665i
$414$	−7.12453	+	15.0924i	−0.350151	+	0.741753i
$415$	2.22116	−	3.84716i	0.109032	−	0.188850i
$416$	6.10909	−	2.22353i	0.299523	−	0.109017i
$417$	−5.75324	+	5.24698i	−0.281737	+	0.256946i
$418$	−7.93217	+	6.65588i	−0.387975	+	0.325550i
$419$	4.65004	+	26.3717i	0.227169	+	1.28834i	0.858495	+	0.512823i	$0.171400\pi$
$419$	4.65004	+	26.3717i	0.227169	+	1.28834i	−0.631325	+	0.775518i	$0.717489\pi$
$420$	1.30564	−	0.706954i	0.0637086	−	0.0344958i
$421$	22.3981	+	18.7942i	1.09162	+	0.915974i	0.996833	−	0.0795237i	$-0.0253400\pi$
$421$	22.3981	+	18.7942i	1.09162	+	0.915974i	0.0947826	+	0.995498i	$0.469784\pi$
$422$	3.93655	−	6.81831i	0.191628	−	0.331910i
$423$	2.55499	−	27.6991i	0.124228	−	1.34678i
$424$	−3.21458	−	5.56781i	−0.156114	−	0.270397i
$425$	−15.7262	−	13.1958i	−0.762831	−	0.640091i
$426$	−6.34943	+	2.61250i	−0.307631	+	0.126576i
$427$	0.248018	−	3.60921i	0.0120025	−	0.174662i
$428$	4.00280	+	1.45690i	0.193483	+	0.0704219i
$429$	3.41016	−	0.140839i	0.164644	−	0.00679975i
$430$	3.11036	+	2.60990i	0.149995	+	0.125861i
$431$	−14.6758	+	25.4192i	−0.706908	+	1.22440i	0.259091	+	0.965853i	$0.416577\pi$
$431$	−14.6758	+	25.4192i	−0.706908	+	1.22440i	−0.965999	+	0.258547i	$0.916756\pi$
$432$	−0.407509	+	8.03010i	−0.0196063	+	0.386349i
$433$	3.99526			0.192000			0.0960000	−	0.995381i	$-0.469395\pi$
$433$	3.99526			0.192000			0.0960000	+	0.995381i	$0.469395\pi$
$434$	−15.3714	+	1.63430i	−0.737853	+	0.0784489i
$435$	1.92996	+	3.04525i	0.0925347	+	0.146009i
$436$	2.42067	+	13.7283i	0.115929	+	0.657467i
$437$	−6.48770	−	36.7936i	−0.310349	−	1.76008i
$438$	−16.3661	+	6.73390i	−0.782001	+	0.321758i
$439$	5.55909	+	4.66463i	0.265321	+	0.222631i	0.765736	−	0.643155i	$-0.222375\pi$
$439$	5.55909	+	4.66463i	0.265321	+	0.222631i	−0.500415	+	0.865786i	$0.666819\pi$
$440$	0.778530	−	1.34845i	0.0371150	−	0.0642850i
$441$	20.0965	−	6.09344i	0.956977	−	0.290164i
$442$	3.29537	+	5.70775i	0.156745	+	0.271490i
$443$	−5.56269	+	31.5476i	−0.264292	+	1.49887i	0.506753	+	0.862091i	$0.330846\pi$
$443$	−5.56269	+	31.5476i	−0.264292	+	1.49887i	−0.771045	+	0.636781i	$0.780266\pi$
$444$	3.08533	+	0.980803i	0.146423	+	0.0465468i
$445$	−2.98936	−	1.08804i	−0.141709	−	0.0515779i
$446$	−11.5363	+	9.68009i	−0.546259	+	0.458365i
$447$	−2.83421	−	12.9284i	−0.134053	−	0.611493i
$448$	8.43021	−	18.9960i	0.398290	−	0.897478i
$449$	6.83151	+	11.8325i	0.322399	+	0.558411i	0.980983	−	0.194096i	$-0.0621774\pi$
$449$	6.83151	+	11.8325i	0.322399	+	0.558411i	−0.658583	+	0.752508i	$0.728844\pi$
$450$	3.95933	+	15.0600i	0.186645	+	0.709937i
$451$	6.56487	+	11.3707i	0.309128	+	0.535425i
$452$	1.83373	−	10.3996i	0.0862512	−	0.489155i
$453$	0.503097	−	3.75303i	0.0236376	−	0.176333i
$454$	22.8995	−	19.2149i	1.07472	−	0.901801i
$455$	−1.30952	+	0.640646i	−0.0613911	+	0.0300339i
$456$	−20.3219	−	32.0655i	−0.951660	−	1.50161i
$457$	19.3777	−	7.05289i	0.906449	−	0.329920i	0.153615	−	0.988131i	$-0.450909\pi$
$457$	19.3777	−	7.05289i	0.906449	−	0.329920i	0.752834	+	0.658210i	$0.228686\pi$
$458$	−5.07587	+	8.79167i	−0.237180	+	0.410808i
$459$	21.7924	−	2.71240i	1.01718	−	0.126604i
$460$	0.843385	+	1.46079i	0.0393231	+	0.0681095i
$461$	−2.35546	+	13.3585i	−0.109705	+	0.622166i	0.879532	+	0.475840i	$0.157856\pi$
$461$	−2.35546	+	13.3585i	−0.109705	+	0.622166i	−0.989236	+	0.146326i	$0.953255\pi$
$462$	4.38703	−	4.94712i	0.204103	−	0.230161i
$463$	−29.2455	−	10.6445i	−1.35916	−	0.494692i	−0.443362	−	0.896342i	$-0.646215\pi$
$463$	−29.2455	−	10.6445i	−1.35916	−	0.494692i	−0.915793	+	0.401650i	$0.868437\pi$
$464$	8.01628	+	2.91769i	0.372146	+	0.135450i
$465$	0.475066	−	3.54392i	0.0220307	−	0.164345i
$466$	3.47029	−	19.6810i	0.160758	−	0.911704i
$467$	6.40650			0.296457			0.148229	−	0.988953i	$-0.452643\pi$
$467$	6.40650			0.296457			0.148229	+	0.988953i	$0.452643\pi$
$468$	−0.345077	+	3.74105i	−0.0159512	+	0.172930i
$469$	−1.94447	−	6.75052i	−0.0897873	−	0.311710i
$470$	2.86578	+	2.40467i	0.132188	+	0.110919i
$471$	29.5099	+	9.38097i	1.35975	+	0.432252i
$472$	7.36677	+	2.68129i	0.339083	+	0.123416i
$473$	−12.7691	−	4.64757i	−0.587123	−	0.213695i
$474$	0.956252	+	4.36200i	0.0439221	+	0.200354i
$475$	−26.7036	−	22.4069i	−1.22524	−	1.02810i
$476$	−9.31307	−	2.31011i	−0.426864	−	0.105884i
$477$	6.29365	−	0.520740i	0.288167	−	0.0238431i
$478$	−28.4917			−1.30318
$479$	−6.16462	+	34.9613i	−0.281669	+	1.59742i	0.435279	+	0.900296i	$0.356650\pi$
$479$	−6.16462	+	34.9613i	−0.281669	+	1.59742i	−0.716947	+	0.697127i	$0.754461\pi$
$480$	2.30707	+	1.77893i	0.105303	+	0.0811968i
$481$	−2.98708	−	1.08721i	−0.136199	−	0.0495724i
$482$	2.72761	+	0.992769i	0.124239	+	0.0452194i
$483$	7.54394	+	22.6332i	0.343261	+	1.02985i
$484$	1.36744	−	7.75515i	0.0621565	−	0.352507i
$485$	−0.658447	−	1.14046i	−0.0298985	−	0.0517858i
$486$	−14.6838	−	7.86522i	−0.666072	−	0.356774i
$487$	−4.73681	+	8.20439i	−0.214645	+	0.371776i	−0.953163	−	0.302458i	$-0.902193\pi$
$487$	−4.73681	+	8.20439i	−0.214645	+	0.371776i	0.738518	+	0.674234i	$0.235526\pi$
$488$	3.92431	−	1.42833i	0.177645	−	0.0646575i
$489$	9.38222	−	0.387483i	0.424279	−	0.0175226i
$490$	−0.866274	+	2.68811i	−0.0391343	+	0.121436i
$491$	−4.43446	+	3.72095i	−0.200124	+	0.167924i	−0.737343	−	0.675519i	$-0.763920\pi$
$491$	−4.43446	+	3.72095i	−0.200124	+	0.167924i	0.537218	+	0.843443i	$0.319475\pi$
$492$	−13.3654	+	5.49927i	−0.602560	+	0.247926i
$493$	4.04595	−	22.9457i	0.182220	−	1.03342i
$494$	5.59565	+	9.69195i	0.251760	+	0.436062i
$495$	0.871342	+	1.25698i	0.0391639	+	0.0564969i
$496$	−4.23023	−	7.32698i	−0.189943	−	0.328991i
$497$	−3.98119	+	8.97093i	−0.178581	+	0.402401i
$498$	20.7530	+	6.59722i	0.929965	+	0.295629i
$499$	9.74833	−	8.17982i	0.436395	−	0.366179i	−0.397963	−	0.917401i	$-0.630283\pi$
$499$	9.74833	−	8.17982i	0.436395	−	0.366179i	0.834358	+	0.551222i	$0.185838\pi$
$500$	3.00119	+	1.09234i	0.134217	+	0.0488511i
$501$	−0.908609	−	4.14467i	−0.0405936	−	0.185170i
$502$	−1.44503	+	8.19519i	−0.0644950	+	0.365769i
$503$	4.98471	+	8.63376i	0.222257	+	0.384960i	0.955493	−	0.295014i	$-0.0953243\pi$
$503$	4.98471	+	8.63376i	0.222257	+	0.384960i	−0.733236	+	0.679974i	$0.761991\pi$
$504$	15.8396	+	18.3511i	0.705551	+	0.817422i
$505$	−1.09411	+	1.89505i	−0.0486872	+	0.0843286i
$506$	5.75437	+	4.82849i	0.255813	+	0.214653i
$507$	−2.50152	+	18.6609i	−0.111096	+	0.828761i
$508$	2.35300	+	13.3445i	0.104398	+	0.592069i
$509$	−1.33197	−	7.55397i	−0.0590385	−	0.334824i	0.940955	−	0.338533i	$-0.109931\pi$
$509$	−1.33197	−	7.55397i	−0.0590385	−	0.334824i	−0.999993	+	0.00370882i	$0.998819\pi$
$510$	−1.36991	+	2.61649i	−0.0606606	+	0.115860i
$511$	−10.2618	+	23.1232i	−0.453955	+	1.02291i
$512$	16.3452			0.722360
$513$	37.0042	−	4.60575i	1.63378	−	0.203349i
$514$	−7.24869	+	12.5551i	−0.319726	+	0.553782i
$515$	−3.24481	−	2.72272i	−0.142983	−	0.119977i
$516$	6.93791	−	13.2513i	0.305425	−	0.583354i
$517$	−11.7650	−	4.28210i	−0.517423	−	0.188327i
$518$	−5.53173	+	2.70625i	−0.243050	+	0.118906i
$519$	5.13994	+	3.96330i	0.225618	+	0.173970i
$520$	−1.28915	−	1.08172i	−0.0565328	−	0.0474366i
$521$	−9.54267	−	16.5284i	−0.418072	−	0.724122i	0.577674	−	0.816268i	$-0.303961\pi$
$521$	−9.54267	−	16.5284i	−0.418072	−	0.724122i	−0.995745	+	0.0921461i	$0.970627\pi$
$522$	−12.5558	+	12.4379i	−0.549550	+	0.544394i
$523$	3.09640	−	5.36312i	0.135396	−	0.234513i	−0.790353	−	0.612652i	$-0.790103\pi$
$523$	3.09640	−	5.36312i	0.135396	−	0.234513i	0.925749	+	0.378139i	$0.123436\pi$
$524$	−8.27460	−	6.94321i	−0.361478	−	0.303316i
$525$	18.9660	+	11.6525i	0.827744	+	0.508557i
$526$	5.57071	+	31.5931i	0.242895	+	1.37752i
$527$	−17.7015	+	14.8534i	−0.771092	+	0.647023i
$528$	3.44885	+	1.09636i	0.150092	+	0.0477131i
$529$	−3.85608	+	1.40350i	−0.167656	+	0.0610217i
$530$	−0.424656	+	0.735525i	−0.0184459	+	0.0319492i
$531$	−5.47072	+	5.41939i	−0.237409	+	0.235181i
$532$	−15.8139	−	3.92265i	−0.685620	−	0.170069i
$533$	13.3347	−	4.85345i	0.577592	−	0.210226i
$534$	2.07191	−	15.4562i	0.0896605	−	0.668853i
$535$	−0.325457	−	1.84576i	−0.0140707	−	0.0797990i
$536$	6.21214	−	5.21261i	0.268324	−	0.225150i
$537$	2.46581	−	4.70964i	0.106408	−	0.203236i
$538$	−1.55039	+	8.79273i	−0.0668423	+	0.379081i
$539$	−0.352591	−	9.44532i	−0.0151871	−	0.406839i
$540$	−1.49878	+	0.766796i	−0.0644973	+	0.0329977i
$541$	−5.59269	−	9.68681i	−0.240448	−	0.416469i	0.720394	−	0.693565i	$-0.243961\pi$
$541$	−5.59269	−	9.68681i	−0.240448	−	0.416469i	−0.960842	+	0.277097i	$0.910628\pi$
$542$	19.9659	+	16.7534i	0.857610	+	0.719620i
$543$	−2.21758	−	3.49907i	−0.0951653	−	0.150159i
$544$	−3.26933	−	18.5413i	−0.140171	−	0.794951i
$545$	4.69856	−	3.94256i	0.201264	−	0.168881i
$546$	−4.44224	−	5.59790i	−0.190110	−	0.239568i
$547$	−26.7050	+	9.71983i	−1.14182	+	0.415590i	−0.842572	−	0.538584i	$-0.818959\pi$
$547$	−26.7050	+	9.71983i	−1.14182	+	0.415590i	−0.299252	+	0.954174i	$0.596737\pi$
$548$	15.4083			0.658210
$549$	−0.376782	+	4.08477i	−0.0160807	+	0.174334i
$550$	7.00872			0.298853
$551$	6.87016	−	38.9626i	0.292679	−	1.65986i
$552$	−20.3484	+	18.5579i	−0.866087	+	0.789875i
$553$	5.29643	+	3.56323i	0.225227	+	0.151524i
$554$	6.05847	+	34.3593i	0.257400	+	1.45979i
$555$	−0.305032	−	1.39142i	−0.0129479	−	0.0590626i
$556$	−3.62510	+	1.31943i	−0.153738	+	0.0559562i
$557$	−10.4724			−0.443729			−0.221864	−	0.975078i	$-0.571214\pi$
$557$	−10.4724			−0.443729			−0.221864	+	0.975078i	$0.571214\pi$
$558$	17.4681	−	1.44532i	0.739484	−	0.0611853i
$559$	−7.34322	+	12.7188i	−0.310585	+	0.537949i
$560$	−1.53709	+	0.163425i	−0.0649540	+	0.00690595i
$561$	1.31324	−	9.79659i	0.0554452	−	0.413612i
$562$	−18.5796	−	6.76241i	−0.783732	−	0.285255i
$563$	−12.2299	+	10.2621i	−0.515427	+	0.432495i	−0.863034	−	0.505145i	$-0.831439\pi$
$563$	−12.2299	+	10.2621i	−0.515427	+	0.432495i	0.347607	+	0.937640i	$0.386994\pi$
$564$	6.39235	−	12.2092i	0.269166	−	0.514102i
$565$	−4.36611	+	1.58913i	−0.183684	+	0.0668554i
$566$	−6.16524			−0.259144
$567$	−22.9425	+	6.37492i	−0.963496	+	0.267722i
$568$	−11.3297			−0.475382
$569$	−25.3759	+	9.23607i	−1.06381	+	0.387196i	−0.813859	−	0.581062i	$-0.802637\pi$
$569$	−25.3759	+	9.23607i	−1.06381	+	0.387196i	−0.249953	+	0.968258i	$0.580415\pi$
$570$	−2.32615	+	4.44290i	−0.0974318	+	0.186093i
$571$	13.4123	−	11.2542i	0.561286	−	0.470974i	−0.317456	−	0.948273i	$-0.602828\pi$
$571$	13.4123	−	11.2542i	0.561286	−	0.470974i	0.878741	+	0.477299i	$0.158384\pi$
$572$	1.58898	+	0.578342i	0.0664387	+	0.0241817i
$573$	2.64068	−	19.6990i	0.110316	−	0.822939i
$574$	11.1515	−	25.1279i	0.465453	−	1.04882i
$575$	−12.6442	+	21.9004i	−0.527299	+	0.913309i
$576$	−10.0597	+	21.3102i	−0.419154	+	0.887926i
$577$	31.5176			1.31209			0.656047	−	0.754720i	$-0.272227\pi$
$577$	31.5176			1.31209			0.656047	+	0.754720i	$0.272227\pi$
$578$	0.865227	−	0.314917i	0.0359887	−	0.0130988i
$579$	6.24778	+	28.4996i	0.259649	+	1.18441i
$580$	0.310172	+	1.75907i	0.0128792	+	0.0730415i
$581$	27.9621	−	13.6797i	1.16006	−	0.567529i
$582$	4.76973	−	4.35002i	0.197712	−	0.180314i
$583$	0.493576	−	2.79921i	0.0204418	−	0.115931i
$584$	−29.2029			−1.20843
$585$	1.50142	−	0.691527i	0.0620762	−	0.0285911i
$586$	36.1211			1.49215
$587$	−1.33160	+	0.484664i	−0.0549612	+	0.0200042i	−0.369354	−	0.929289i	$-0.620421\pi$
$587$	−1.33160	+	0.484664i	−0.0549612	+	0.0200042i	0.314393	+	0.949293i	$0.398199\pi$
$588$	10.3563	+	0.996691i	0.427088	+	0.0411028i
$589$	−30.0578	+	25.2215i	−1.23851	+	1.03923i
$590$	−0.179835	−	1.01990i	−0.00740370	−	0.0419885i
$591$	17.9171	+	28.2711i	0.737012	+	1.16292i
$592$	−2.58196	−	2.16652i	−0.106118	−	0.0890434i
$593$	4.35621	+	7.54518i	0.178888	+	0.309844i	0.941500	−	0.337013i	$-0.109417\pi$
$593$	4.35621	+	7.54518i	0.178888	+	0.309844i	−0.762612	+	0.646856i	$0.776083\pi$
$594$	−5.10415	+	5.49173i	−0.209426	+	0.225329i
$595$	1.16858	+	4.05691i	0.0479072	+	0.166317i
$596$	1.13867	−	6.45770i	0.0466416	−	0.264518i
$597$	2.94621	−	5.62720i	0.120580	−	0.230306i
$598$	6.21928	−	5.21860i	0.254325	−	0.213404i
$599$	−0.449291	−	2.54806i	−0.0183575	−	0.104111i	0.974252	−	0.225461i	$-0.0723888\pi$
$599$	−0.449291	−	2.54806i	−0.0183575	−	0.104111i	−0.992610	+	0.121350i	$0.961278\pi$
$600$	−3.41399	+	25.4678i	−0.139375	+	1.03972i
$601$	−18.2433	+	6.64003i	−0.744161	+	0.270852i	−0.686147	−	0.727463i	$-0.740699\pi$
$601$	−18.2433	+	6.64003i	−0.744161	+	0.270852i	−0.0580144	+	0.998316i	$0.518477\pi$
$602$	7.87531	+	27.3403i	0.320974	+	1.11431i
$603$	2.02535	+	7.70380i	0.0824788	+	0.313723i
$604$	0.938010	−	1.62468i	0.0381671	−	0.0661073i
$605$	−3.25589	+	1.18505i	−0.132371	+	0.0481790i
$606$	−10.2226	−	3.24969i	−0.415265	−	0.132010i
$607$	16.7002	−	14.0131i	0.677839	−	0.568774i	−0.237535	−	0.971379i	$-0.576340\pi$
$607$	16.7002	−	14.0131i	0.677839	−	0.568774i	0.915374	+	0.402605i	$0.131895\pi$
$608$	−5.55143	−	31.4837i	−0.225140	−	1.27683i
$609$	−0.690476	+	25.2544i	−0.0279795	+	1.02336i
$610$	−0.422614	−	0.354616i	−0.0171112	−	0.0143580i
$611$	−6.76578	+	11.7187i	−0.273714	+	0.474087i
$612$	10.4959	+	2.86547i	0.424273	+	0.115830i
$613$	−4.90821	−	8.50128i	−0.198241	−	0.343363i	0.749717	−	0.661758i	$-0.230190\pi$
$613$	−4.90821	−	8.50128i	−0.198241	−	0.343363i	−0.947958	+	0.318395i	$0.896856\pi$
$614$	14.7821	+	12.4036i	0.596555	+	0.500569i
$615$	5.03581	+	3.88300i	0.203063	+	0.156578i
$616$	9.80089	−	4.79482i	0.394889	−	0.193189i
$617$	−14.4286	−	5.25159i	−0.580874	−	0.211421i	0.0348367	−	0.999393i	$-0.488909\pi$
$617$	−14.4286	−	5.25159i	−0.580874	−	0.211421i	−0.615711	+	0.787972i	$0.711131\pi$
$618$	9.63114	−	18.3953i	0.387421	−	0.739966i
$619$	−5.19329	−	4.35769i	−0.208736	−	0.175150i	0.532426	−	0.846477i	$-0.321281\pi$
$619$	−5.19329	−	4.35769i	−0.208736	−	0.175150i	−0.741162	+	0.671326i	$0.765725\pi$
$620$	0.885746	−	1.53416i	0.0355724	−	0.0616133i
$621$	−7.95198	−	25.8566i	−0.319102	−	1.03759i
$622$	20.6024			0.826079
$623$	−13.1245	−	18.0188i	−0.525824	−	0.721906i
$624$	1.81421	−	3.46510i	0.0726266	−	0.138715i
$625$	3.97341	+	22.5343i	0.158936	+	0.901374i
$626$	−4.58318	−	25.9925i	−0.183181	−	1.03887i
$627$	2.22993	−	16.6349i	0.0890549	−	0.664336i
$628$	11.7521	+	9.86117i	0.468959	+	0.393504i
$629$	−4.60286	+	7.97239i	−0.183528	+	0.317880i
$630$	1.05322	−	3.02424i	0.0419613	−	0.120489i
$631$	−21.7470	−	37.6669i	−0.865734	−	1.49950i	−0.866317	−	0.499495i	$-0.833519\pi$
$631$	−21.7470	−	37.6669i	−0.865734	−	1.49950i	0.000582574	−	1.00000i	$-0.499815\pi$
$632$	−1.27959	+	7.25689i	−0.0508992	+	0.288664i
$633$	2.73269	+	12.4653i	0.108615	+	0.495453i
$634$	−4.71117	−	1.71472i	−0.187104	−	0.0681004i
$635$	4.56721	−	3.83235i	0.181244	−	0.152082i
$636$	2.98173	+	0.947868i	0.118233	+	0.0375854i
$637$	−10.1195	−	1.39739i	−0.400950	−	0.0553665i
$638$	3.97731	+	6.88891i	0.157463	+	0.272734i
$639$	4.75072	−	10.0638i	0.187935	−	0.398118i
$640$	0.0973606	+	0.168634i	0.00384852	+	0.00666583i
$641$	6.75182	−	38.2915i	0.266681	−	1.51242i	−0.497524	−	0.867450i	$-0.665758\pi$
$641$	6.75182	−	38.2915i	0.266681	−	1.51242i	0.764205	−	0.644973i	$-0.223131\pi$
$642$	8.49645	−	3.49590i	0.335328	−	0.137972i
$643$	−14.0932	+	11.8256i	−0.555782	+	0.466357i	−0.876893	−	0.480685i	$-0.840388\pi$
$643$	−14.0932	+	11.8256i	−0.555782	+	0.466357i	0.321111	+	0.947041i	$0.395944\pi$
$644$	−0.810326	+	11.7920i	−0.0319313	+	0.464671i
$645$	−6.57563	+	0.271572i	−0.258915	+	0.0106931i
$646$	30.4554	−	11.0849i	1.19825	−	0.436128i
$647$	−7.39691	+	12.8118i	−0.290803	+	0.503685i	−0.974000	−	0.226549i	$-0.927256\pi$
$647$	−7.39691	+	12.8118i	−0.290803	+	0.503685i	0.683197	+	0.730234i	$0.260589\pi$
$648$	−17.4692	−	21.2222i	−0.686256	−	0.833686i
$649$	1.73297	+	3.00160i	0.0680251	+	0.117823i
$650$	1.31538	−	7.45989i	0.0515934	−	0.292601i
$651$	16.6240	−	18.7464i	0.651547	−	0.734730i
$652$	4.37170	+	1.59117i	0.171209	+	0.0623149i
$653$	35.3353	+	12.8610i	1.38278	+	0.503290i	0.923019	−	0.384755i	$-0.125714\pi$
$653$	35.3353	+	12.8610i	1.38278	+	0.503290i	0.459758	+	0.888044i	$0.347936\pi$
$654$	23.8104	+	18.3597i	0.931060	+	0.717920i
$655$	−0.825293	+	4.68047i	−0.0322469	+	0.182881i
$656$	15.0464			0.587464
$657$	12.2453	−	25.9401i	0.477734	−	1.01202i
$658$	7.25603	+	25.1904i	0.282869	+	0.982023i
$659$	−12.1274	−	10.1761i	−0.472416	−	0.396404i	0.375259	−	0.926920i	$-0.377554\pi$
$659$	−12.1274	−	10.1761i	−0.472416	−	0.396404i	−0.847675	+	0.530516i	$0.821998\pi$
$660$	0.162262	+	0.740170i	0.00631606	+	0.0288111i
$661$	−13.2952	−	4.83907i	−0.517124	−	0.188218i	0.0702558	−	0.997529i	$-0.477618\pi$
$661$	−13.2952	−	4.83907i	−0.517124	−	0.188218i	−0.587380	+	0.809311i	$0.699841\pi$
$662$	−19.3408	−	7.03948i	−0.751702	−	0.273597i
$663$	−10.1808	−	3.23638i	−0.395388	−	0.125691i
$664$	27.5271	+	23.0980i	1.06826	+	0.896375i
$665$	1.98429	+	6.88877i	0.0769477	+	0.267135i
$666$	6.34239	−	2.92118i	0.245762	−	0.113194i
$667$	−28.7013			−1.11132
$668$	0.365041	−	2.07025i	0.0141239	−	0.0801004i
$669$	3.24314	−	24.1933i	0.125387	−	0.935367i
$670$	−1.00667	−	0.366397i	−0.0388910	−	0.0141552i
$671$	1.73497	+	0.631479i	0.0669780	+	0.0243780i
$672$	6.45524	+	19.3669i	0.249016	+	0.747096i
$673$	−5.02113	+	28.4762i	−0.193550	+	1.09768i	0.720918	+	0.693021i	$0.243721\pi$
$673$	−5.02113	+	28.4762i	−0.193550	+	1.09768i	−0.914468	+	0.404658i	$0.867391\pi$
$674$	−11.9491	−	20.6965i	−0.460263	−	0.797199i
$675$	−21.1908	−	13.7116i	−0.815634	−	0.527761i
$676$	−4.66400	+	8.07829i	−0.179385	+	0.310704i
$677$	25.9423	−	9.44223i	0.997045	−	0.362895i	0.208600	−	0.978001i	$-0.433109\pi$
$677$	25.9423	−	9.44223i	0.997045	−	0.362895i	0.788444	+	0.615106i	$0.210887\pi$
$678$	−12.1925	−	19.2382i	−0.468248	−	0.738840i
$679$	0.632636	−	9.20625i	0.0242784	−	0.353303i
$680$	−3.73336	+	3.13266i	−0.143168	+	0.120132i
$681$	−6.43761	+	48.0236i	−0.246690	+	1.84027i
$682$	1.36993	−	7.76924i	0.0524572	−	0.297500i
$683$	−25.8157	−	44.7140i	−0.987808	−	1.71093i	−0.628722	−	0.777630i	$-0.716422\pi$
$683$	−25.8157	−	44.7140i	−0.987808	−	1.71093i	−0.359087	−	0.933304i	$-0.616912\pi$
$684$	17.8225	+	4.86568i	0.681459	+	0.186044i
$685$	−3.38977	−	5.87125i	−0.129516	−	0.224329i
$686$	−15.5511	+	12.2405i	−0.593742	+	0.467343i
$687$	−3.52359	−	16.0731i	−0.134433	−	0.613226i
$688$	−11.9290	+	10.0096i	−0.454790	+	0.381614i
$689$	−2.88677	−	1.05070i	−0.109977	−	0.0400284i
$690$	3.46715	+	1.10218i	0.131992	+	0.0419593i
$691$	−0.674442	+	3.82495i	−0.0256570	+	0.145508i	−0.994945	−	0.100420i	$-0.967981\pi$
$691$	−0.674442	+	3.82495i	−0.0256570	+	0.145508i	0.969288	+	0.245928i	$0.0790926\pi$
$692$	1.60782	+	2.78483i	0.0611201	+	0.105863i
$693$	0.149420	+	10.7164i	0.00567599	+	0.407082i
$694$	14.5243	−	25.1569i	0.551337	−	0.954943i
$695$	1.30027	+	1.09106i	0.0493220	+	0.0413861i
$696$	−26.9698	+	11.0969i	−1.02229	+	0.420626i
$697$	−7.13619	−	40.4713i	−0.270302	−	1.53296i
$698$	−3.95781	−	22.4459i	−0.149806	−	0.849589i
$699$	17.3401	+	27.3606i	0.655863	+	1.03487i
$700$	6.49296	+	8.91422i	0.245411	+	0.336926i
$701$	0.455895			0.0172189			0.00860946	−	0.999963i	$-0.497259\pi$
$701$	0.455895			0.0172189			0.00860946	+	0.999963i	$0.497259\pi$
$702$	4.88732	+	6.46340i	0.184460	+	0.243945i
$703$	−7.81582	+	13.5374i	−0.294779	+	0.510572i
$704$	8.12506	+	6.81773i	0.306225	+	0.256953i
$705$	−6.05855	+	0.250216i	−0.228178	+	0.00942369i
$706$	−19.7726	−	7.19664i	−0.744152	−	0.270849i
$707$	−13.7737	+	6.73840i	−0.518013	+	0.253424i
$708$	−3.52816	+	1.45168i	−0.132596	+	0.0545574i
$709$	−0.877410	−	0.736235i	−0.0329518	−	0.0276499i	0.626163	−	0.779692i	$-0.284624\pi$
$709$	−0.877410	−	0.736235i	−0.0329518	−	0.0276499i	−0.659115	+	0.752042i	$0.729069\pi$
$710$	0.748342	+	1.29617i	0.0280848	+	0.0486442i
$711$	−5.90954	−	4.17956i	−0.221625	−	0.156746i
$712$	12.8665	−	22.2854i	0.482191	−	0.835179i
$713$	21.8054	+	18.2969i	0.816618	+	0.685224i
$714$	−18.1991	+	9.85414i	−0.681085	+	0.368782i
$715$	−0.129196	−	0.732706i	−0.00483165	−	0.0274016i
$716$	2.01760	−	1.69297i	0.0754014	−	0.0632693i
$717$	34.1221	−	31.1195i	1.27431	−	1.16218i
$718$	−21.4589	+	7.81041i	−0.800840	+	0.291482i
$719$	−0.0655786	+	0.113585i	−0.00244567	+	0.00423602i	−0.867246	−	0.497880i	$-0.834112\pi$
$719$	−0.0655786	+	0.113585i	−0.00244567	+	0.00423602i	0.864800	+	0.502117i	$0.167445\pi$
$720$	1.74675	−	0.144527i	0.0650976	−	0.00538621i
$721$	−8.21572	−	28.5221i	−0.305969	−	1.06222i
$722$	32.6356	−	11.8784i	1.21457	−	0.442067i
$723$	−4.35096	+	1.79022i	−0.161814	+	0.0665791i
$724$	−0.356395	−	2.02122i	−0.0132453	−	0.0751179i
$725$	−20.5140	+	17.2133i	−0.761872	+	0.639286i
$726$	−9.09214	−	14.3463i	−0.337441	−	0.532441i
$727$	0.963416	−	5.46380i	0.0357311	−	0.202641i	−0.961716	−	0.274047i	$-0.911638\pi$
$727$	0.963416	−	5.46380i	0.0357311	−	0.202641i	0.997447	+	0.0714061i	$0.0227486\pi$
$728$	−3.26407	−	11.3317i	−0.120974	−	0.419980i
$729$	26.1762	−	6.61861i	0.969489	−	0.245134i
$730$	1.92890	+	3.34095i	0.0713918	+	0.123654i
$731$	32.5813	+	27.3389i	1.20506	+	1.01117i
$732$	−0.942676	+	1.80049i	−0.0348423	+	0.0665480i
$733$	3.37242	+	19.1260i	0.124563	+	0.706434i	0.981566	+	0.191122i	$0.0612126\pi$
$733$	3.37242	+	19.1260i	0.124563	+	0.706434i	−0.857003	+	0.515311i	$0.827676\pi$
$734$	−25.2496	+	21.1869i	−0.931979	+	0.782023i
$735$	−1.89857	−	4.16549i	−0.0700297	−	0.153646i
$736$	−21.7935	+	7.93217i	−0.803318	+	0.292384i
$737$	3.58523			0.132064
$738$	−13.3069	+	28.1891i	−0.489835	+	1.03766i
$739$	−29.6486			−1.09064			−0.545321	−	0.838227i	$-0.683592\pi$
$739$	−29.6486			−1.09064			−0.545321	+	0.838227i	$0.683592\pi$
$740$	0.122549	−	0.695011i	0.00450500	−	0.0255491i
$741$	−17.2873	−	5.49549i	−0.635064	−	0.201882i
$742$	−5.34598	+	2.61537i	−0.196257	+	0.0960133i
$743$	5.66975	+	32.1548i	0.208003	+	1.17964i	0.892644	+	0.450763i	$0.148848\pi$
$743$	5.66975	+	32.1548i	0.208003	+	1.17964i	−0.684641	+	0.728881i	$0.740041\pi$
$744$	27.5641	+	8.76239i	1.01055	+	0.321245i
$745$	−2.71118	+	0.986787i	−0.0993298	+	0.0361531i
$746$	20.8664			0.763975
$747$	−32.0598	+	14.7662i	−1.17301	+	0.540265i
$748$	2.44850	−	4.24093i	0.0895261	−	0.155064i
$749$	5.32741	−	12.0044i	0.194659	−	0.438631i
$750$	6.37040	−	2.62113i	0.232614	−	0.0957102i
$751$	−15.2829	−	5.56252i	−0.557681	−	0.202979i	0.0477749	−	0.998858i	$-0.484787\pi$
$751$	−15.2829	−	5.56252i	−0.557681	−	0.202979i	−0.605456	+	0.795879i	$0.707009\pi$
$752$	−10.9910	+	9.22252i	−0.400800	+	0.336311i
$753$	−7.22045	−	11.3930i	−0.263128	−	0.415184i
$754$	8.07882	−	2.94045i	0.294213	−	0.107085i
$755$	−0.825434			−0.0300406
$756$	−11.7134	−	1.40424i	−0.426011	−	0.0510718i
$757$	16.6281			0.604358			0.302179	−	0.953251i	$-0.402286\pi$
$757$	16.6281			0.604358			0.302179	+	0.953251i	$0.402286\pi$
$758$	13.6191	−	4.95694i	0.494667	−	0.180044i
$759$	−12.1653	+	0.502425i	−0.441574	+	0.0182369i
$760$	−6.33937	+	5.31936i	−0.229953	+	0.192954i
$761$	3.92501	+	1.42859i	0.142282	+	0.0517862i	0.412179	−	0.911103i	$-0.364768\pi$
$761$	3.92501	+	1.42859i	0.142282	+	0.0517862i	−0.269898	+	0.962889i	$0.586990\pi$
$762$	23.1448	+	17.8464i	0.838447	+	0.646509i
$763$	42.7390	−	4.54404i	1.54726	−	0.164505i
$764$	4.92346	−	8.52769i	0.178125	−	0.308521i
$765$	−1.21719	−	4.62981i	−0.0440077	−	0.167391i
$766$	5.29598			0.191352
$767$	3.52006	−	1.28120i	0.127102	−	0.0462613i
$768$	−20.8105	+	18.9793i	−0.750934	+	0.684855i
$769$	2.60549	+	14.7765i	0.0939563	+	0.532852i	0.995062	+	0.0992534i	$0.0316454\pi$
$769$	2.60549	+	14.7765i	0.0939563	+	0.532852i	−0.901106	+	0.433599i	$0.857243\pi$
$770$	−1.19591	−	0.804563i	−0.0430977	−	0.0289944i
$771$	−5.03192	−	22.9534i	−0.181220	−	0.826647i
$772$	−2.51010	+	14.2355i	−0.0903405	+	0.512346i
$773$	13.1524			0.473058			0.236529	−	0.971624i	$-0.423990\pi$
$773$	13.1524			0.473058			0.236529	+	0.971624i	$0.423990\pi$
$774$	−8.20289	−	31.2012i	−0.294847	−	1.12150i
$775$	26.5585			0.954011
$776$	10.0100	−	3.64333i	0.359337	−	0.130788i
$777$	3.66904	−	9.28297i	0.131626	−	0.333025i
$778$	−13.2710	+	11.1357i	−0.475790	+	0.399235i
$779$	−12.1175	−	68.7217i	−0.434154	−	2.46221i
$780$	0.818271	−	0.0337943i	0.0292988	−	0.00121003i
$781$	−3.83708	−	3.21969i	−0.137302	−	0.115210i
$782$	−11.7558	−	20.3617i	−0.420388	−	0.728134i
$783$	1.45187	−	28.6096i	0.0518857	−	1.02243i
$784$	−9.57601	−	5.06214i	−0.342000	−	0.180791i
$785$	1.17213	−	6.64749i	0.0418352	−	0.237259i
$786$	−23.2779	+	0.961372i	−0.830296	+	0.0342910i
$787$	19.4533	−	16.3232i	0.693434	−	0.581860i	−0.226463	−	0.974020i	$-0.572716\pi$
$787$	19.4533	−	16.3232i	0.693434	−	0.581860i	0.919897	+	0.392159i	$0.128272\pi$
$788$	2.87953	+	16.3306i	0.102579	+	0.581754i
$789$	−41.1785	−	31.7519i	−1.46599	−	1.13040i
$790$	0.914741	−	0.332938i	0.0325450	−	0.0118454i
$791$	−31.6008	−	7.83860i	−1.12360	−	0.278709i
$792$	−11.2372	+	5.17563i	−0.399296	+	0.183908i
$793$	0.997746	−	1.72815i	0.0354310	−	0.0613683i
$794$	−19.4330	+	7.07303i	−0.689651	+	0.251012i
$795$	−0.294789	−	1.34470i	−0.0104551	−	0.0476915i
$796$	2.41068	−	2.02280i	0.0854444	−	0.0716963i
$797$	−5.64992	−	32.0423i	−0.200130	−	1.13500i	−0.904921	−	0.425580i	$-0.860070\pi$
$797$	−5.64992	−	32.0423i	−0.200130	−	1.13500i	0.704791	−	0.709415i	$-0.251041\pi$
$798$	−30.9028	+	16.7327i	−1.09395	+	0.592330i
$799$	30.0192	+	25.1891i	1.06200	+	0.891126i
$800$	−10.8194	+	18.7398i	−0.382525	+	0.662553i
$801$	14.4003	+	20.7735i	0.508810	+	0.733997i
$802$	12.0500	+	20.8713i	0.425501	+	0.736990i
$803$	−9.89033	−	8.29897i	−0.349022	−	0.292864i
$804$	−0.524335	+	3.91146i	−0.0184919	+	0.137947i
$805$	4.67155	−	2.28543i	0.164651	−	0.0805508i
$806$	−8.01227	−	2.91623i	−0.282220	−	0.102720i
$807$	−7.74691	−	12.2237i	−0.272704	−	0.430294i
$808$	−13.5594	−	11.3777i	−0.477018	−	0.400266i
$809$	15.6576	−	27.1198i	0.550493	−	0.953481i	−0.447746	−	0.894161i	$-0.647773\pi$
$809$	15.6576	−	27.1198i	0.550493	−	0.953481i	0.998239	−	0.0593207i	$-0.0188935\pi$
$810$	−1.27405	+	3.40032i	−0.0447654	+	0.119475i
$811$	−35.6715			−1.25260			−0.626299	−	0.779583i	$-0.715431\pi$
$811$	−35.6715			−1.25260			−0.626299	+	0.779583i	$0.715431\pi$
$812$	−5.07721	+	11.4406i	−0.178175	+	0.401487i
$813$	−42.2101	+	1.74326i	−1.48037	+	0.0611389i
$814$	−0.545755	−	3.09513i	−0.0191287	−	0.108484i
$815$	−0.355451	−	2.01586i	−0.0124509	−	0.0706125i
$816$	−8.97013	−	6.91667i	−0.314017	−	0.242132i
$817$	55.3241	+	46.4224i	1.93555	+	1.62412i
$818$	11.9972	−	20.7798i	0.419473	−	0.726549i
$819$	11.4343	+	1.85219i	0.399547	+	0.0647208i
$820$	1.57525	+	2.72840i	0.0550099	+	0.0952800i
$821$	−1.99760	+	11.3290i	−0.0697168	+	0.395384i	0.929903	+	0.367805i	$0.119891\pi$
$821$	−1.99760	+	11.3290i	−0.0697168	+	0.395384i	−0.999620	+	0.0275784i	$0.991220\pi$
$822$	24.5552	−	22.3944i	0.856460	−	0.781096i
$823$	10.9531	+	3.98659i	0.381800	+	0.138964i	0.525788	−	0.850616i	$-0.323771\pi$
$823$	10.9531	+	3.98659i	0.381800	+	0.138964i	−0.143988	+	0.989579i	$0.545993\pi$
$824$	26.2473	−	22.0241i	0.914370	−	0.767247i
$825$	−8.39375	+	7.65513i	−0.292233	+	0.266518i
$826$	2.94373	−	6.63319i	0.102425	−	0.230798i
$827$	9.86611	+	17.0886i	0.343078	+	0.594229i	0.985003	−	0.172539i	$-0.0551971\pi$
$827$	9.86611	+	17.0886i	0.343078	+	0.594229i	−0.641924	+	0.766768i	$0.721864\pi$
$828$	1.23102	−	13.3458i	0.0427810	−	0.463798i
$829$	−9.66274	−	16.7364i	−0.335601	−	0.581278i	0.647999	−	0.761641i	$-0.275606\pi$
$829$	−9.66274	−	16.7364i	−0.335601	−	0.581278i	−0.983600	+	0.180363i	$0.942273\pi$
$830$	0.824308	−	4.67488i	0.0286122	−	0.162268i
$831$	−44.7840	−	34.5320i	−1.55354	−	1.19790i
$832$	8.78150	−	7.36856i	0.304444	−	0.255459i
$833$	−9.07429	+	28.1581i	−0.314405	+	0.975620i
$834$	−3.85942	+	7.37140i	−0.133641	+	0.255251i
$835$	−0.869165	+	0.316350i	−0.0300787	+	0.0109478i
$836$	4.15764	−	7.20125i	0.143795	−	0.249060i
$837$	−19.3415	+	20.8102i	−0.668539	+	0.719304i
$838$	14.3076	+	24.7815i	0.494247	+	0.856061i
$839$	−2.74718	+	15.5800i	−0.0948432	+	0.537883i	0.899952	+	0.435989i	$0.143601\pi$
$839$	−2.74718	+	15.5800i	−0.0948432	+	0.537883i	−0.994795	+	0.101894i	$0.967510\pi$
$840$	3.50610	−	3.95372i	0.120972	−	0.136416i
$841$	−1.30929	−	0.476542i	−0.0451479	−	0.0164325i
$842$	29.3598	+	10.6861i	1.01180	+	0.368267i
$843$	29.6373	−	12.1944i	1.02076	−	0.419998i
$844$	−1.09788	+	6.22640i	−0.0377907	+	0.214321i
$845$	4.10425			0.141191
$846$	−7.55785	−	28.7477i	−0.259844	−	0.988365i
$847$	−23.5653	−	5.84539i	−0.809713	−	0.200850i
$848$	−2.49525	−	2.09377i	−0.0856874	−	0.0719003i
$849$	7.38358	−	6.73386i	0.253404	−	0.231106i
$850$	−20.6141	−	7.50292i	−0.707058	−	0.257348i
$851$	10.6560	+	3.87848i	0.365284	+	0.132953i
$852$	4.07382	−	3.71535i	0.139567	−	0.127286i
$853$	23.9615	+	20.1061i	0.820427	+	0.688420i	0.953072	−	0.302743i	$-0.0979025\pi$
$853$	23.9615	+	20.1061i	0.820427	+	0.688420i	−0.132645	+	0.991164i	$0.542347\pi$
$854$	−1.07004	−	3.71481i	−0.0366161	−	0.127118i
$855$	−2.06683	−	7.86158i	−0.0706842	−	0.268860i
$856$	15.1607			0.518182
$857$	9.22357	−	52.3095i	0.315071	−	1.78686i	−0.256748	−	0.966478i	$-0.582651\pi$
$857$	9.22357	−	52.3095i	0.315071	−	1.78686i	0.571819	−	0.820379i	$-0.306238\pi$
$858$	3.37282	−	1.38776i	0.115146	−	0.0473774i
$859$	45.4796	+	16.5532i	1.55175	+	0.564789i	0.968826	−	0.247741i	$-0.0796883\pi$
$859$	45.4796	+	16.5532i	1.55175	+	0.564789i	0.582919	+	0.812530i	$0.301911\pi$
$860$	−3.06395	−	1.11519i	−0.104480	−	0.0380276i
$861$	14.0903	+	42.2736i	0.480196	+	1.44068i
$862$	−5.44642	+	30.8882i	−0.185506	+	1.05206i
$863$	11.7409	+	20.3358i	0.399664	+	0.692238i	0.993684	−	0.112212i	$-0.0357936\pi$
$863$	11.7409	+	20.3358i	0.399664	+	0.692238i	−0.594021	+	0.804450i	$0.702460\pi$
$864$	−6.80439	−	22.1251i	−0.231490	−	0.752711i
$865$	0.707428	−	1.22530i	0.0240533	−	0.0416615i
$866$	4.01182	−	1.46018i	0.136327	−	0.0496190i
$867$	−0.692248	+	1.32218i	−0.0235100	+	0.0449035i
$868$	11.1506	−	5.45514i	0.378477	−	0.185160i
$869$	−2.49565	+	2.09410i	−0.0846590	+	0.0710374i
$870$	3.05093	+	2.35251i	0.103436	+	0.0797575i
$871$	0.672869	−	3.81603i	0.0227993	−	0.129301i
$872$	24.8072	+	42.9673i	0.840077	+	1.45506i
$873$	−0.961083	+	10.4193i	−0.0325277	+	0.352640i
$874$	−19.9618	−	34.5749i	−0.675219	−	1.16951i
$875$	3.99434	−	9.00056i	0.135033	−	0.304275i
$876$	10.5006	−	9.57655i	0.354781	−	0.323562i
$877$	10.0175	−	8.40567i	0.338266	−	0.283839i	−0.457792	−	0.889060i	$-0.651359\pi$
$877$	10.0175	−	8.40567i	0.338266	−	0.283839i	0.796058	+	0.605220i	$0.206915\pi$
$878$	7.28695	+	2.65223i	0.245923	+	0.0895085i
$879$	−43.2592	+	39.4526i	−1.45910	+	1.33070i
$880$	0.136988	−	0.776898i	0.00461787	−	0.0261892i
$881$	−11.9823	−	20.7540i	−0.403695	−	0.699220i	0.590474	−	0.807057i	$-0.298941\pi$
$881$	−11.9823	−	20.7540i	−0.403695	−	0.699220i	−0.994169	+	0.107837i	$0.965608\pi$
$882$	17.9528	−	13.4635i	0.604501	−	0.453340i
$883$	5.29149	−	9.16513i	0.178073	−	0.308431i	−0.763148	−	0.646224i	$-0.776347\pi$
$883$	5.29149	−	9.16513i	0.178073	−	0.308431i	0.941220	+	0.337793i	$0.109680\pi$
$884$	−4.05441	−	3.40205i	−0.136364	−	0.114423i
$885$	1.32934	+	1.02502i	0.0446851	+	0.0344558i
$886$	5.94422	+	33.7114i	0.199700	+	1.13256i
$887$	−4.99859	−	28.3484i	−0.167836	−	0.951846i	−0.946092	−	0.323898i	$-0.895006\pi$
$887$	−4.99859	−	28.3484i	−0.167836	−	0.951846i	0.778256	−	0.627947i	$-0.216105\pi$
$888$	11.5127	−	0.475472i	0.386342	−	0.0159558i
$889$	41.5443	−	4.41701i	1.39335	−	0.148142i
$890$	−3.39940			−0.113948
$891$	0.114571	−	12.1519i	0.00383827	−	0.407104i
$892$	6.04673	−	10.4733i	0.202460	−	0.350670i
$893$	50.9736	+	42.7720i	1.70577	+	1.43131i
$894$	−7.57101	−	11.9461i	−0.253212	−	0.399539i
$895$	−1.08896	−	0.396350i	−0.0364000	−	0.0132485i
$896$	−0.0935442	+	1.36127i	−0.00312509	+	0.0454770i
$897$	−1.74840	+	13.0428i	−0.0583773	+	0.435485i
$898$	11.1843	+	9.38478i	0.373227	+	0.313174i
$899$	15.0715	+	26.1045i	0.502662	+	0.870635i
$900$	−7.12411	−	10.2771i	−0.237470	−	0.342569i
$901$	−4.44830	+	7.70468i	−0.148194	+	0.256680i
$902$	10.7478	+	9.01848i	0.357863	+	0.300283i
$903$	−39.2935	−	24.1415i	−1.30761	−	0.803380i
$904$	−6.52643	−	37.0132i	−0.217066	−	1.23104i
$905$	−0.691768	+	0.580462i	−0.0229951	+	0.0192952i
$906$	−0.866468	−	3.95245i	−0.0287865	−	0.131311i
$907$	23.8688	−	8.68755i	0.792552	−	0.288465i	0.0861556	−	0.996282i	$-0.472542\pi$
$907$	23.8688	−	8.68755i	0.792552	−	0.288465i	0.706397	+	0.707816i	$0.250320\pi$
$908$	−12.0027	+	20.7894i	−0.398325	+	0.689919i
$909$	15.7922	−	7.27358i	0.523793	−	0.241249i
$910$	−1.08080	+	1.12190i	−0.0358282	+	0.0371906i
$911$	45.9564	−	16.7268i	1.52260	−	0.554183i	0.560808	−	0.827946i	$-0.310491\pi$
$911$	45.9564	−	16.7268i	1.52260	−	0.554183i	0.961797	+	0.273763i	$0.0882685\pi$
$912$	−15.2316	−	11.7447i	−0.504368	−	0.388908i
$913$	2.75871	+	15.6454i	0.0913001	+	0.517788i
$914$	16.8803	−	14.1642i	0.558350	−	0.468511i
$915$	0.893452	−	0.0368993i	0.0295366	−	0.00121985i
$916$	1.41563	−	8.02844i	0.0467738	−	0.265267i
$917$	−23.1059	+	23.9845i	−0.763024	+	0.792039i
$918$	20.8913	−	10.6883i	0.689517	−	0.352766i
$919$	−1.15985	−	2.00892i	−0.0382600	−	0.0662682i	0.846261	−	0.532768i	$-0.178848\pi$
$919$	−1.15985	−	2.00892i	−0.0382600	−	0.0662682i	−0.884521	+	0.466500i	$0.845515\pi$
$920$	4.59888	+	3.85892i	0.151620	+	0.127225i
$921$	−31.2508	+	1.29065i	−1.02975	+	0.0425283i
$922$	2.51701	+	14.2747i	0.0828934	+	0.470112i
$923$	−4.14709	+	3.47982i	−0.136503	+	0.114540i
$924$	−1.95175	+	4.93810i	−0.0642080	+	0.162451i
$925$	9.94238	−	3.61873i	0.326904	−	0.118983i
$926$	−33.2571			−1.09289
$927$	8.55746	+	32.5499i	0.281064	+	1.06908i
$928$	−24.5593			−0.806199
$929$	−0.822152	+	4.66266i	−0.0269739	+	0.152977i	−0.995320	−	0.0966352i	$-0.969192\pi$
$929$	−0.822152	+	4.66266i	−0.0269739	+	0.152977i	0.968346	+	0.249612i	$0.0803031\pi$
$930$	−0.818191	−	3.73223i	−0.0268295	−	0.122385i
$931$	−15.4085	+	47.8134i	−0.504992	+	1.56702i
$932$	2.78679	+	15.8047i	0.0912845	+	0.517700i
$933$	−24.6737	+	22.5025i	−0.807781	+	0.736700i
$934$	6.43304	−	2.34143i	0.210495	−	0.0766141i
$935$	−2.15464			−0.0704644
$936$	3.39984	+	12.9319i	0.111127	+	0.422692i
$937$	0.549618	−	0.951966i	0.0179552	−	0.0310994i	−0.856908	−	0.515469i	$-0.827618\pi$
$937$	0.549618	−	0.951966i	0.0179552	−	0.0310994i	0.874863	+	0.484370i	$0.160951\pi$
$938$	−4.41970	−	6.06783i	−0.144308	−	0.198122i
$939$	33.8787	+	26.1232i	1.10559	+	0.852497i
$940$	−2.82301	−	1.02749i	−0.0920766	−	0.0335131i
$941$	−35.1954	+	29.5324i	−1.14734	+	0.962730i	−0.999654	−	0.0263053i	$-0.991626\pi$
$941$	−35.1954	+	29.5324i	−1.14734	+	0.962730i	−0.147682	+	0.989035i	$0.547181\pi$
$942$	33.0607	−	1.36540i	1.07718	−	0.0444871i
$943$	−47.5701	+	17.3141i	−1.54910	+	0.563825i
$944$	3.97190			0.129274
$945$	2.04181	+	4.77224i	0.0664202	+	0.155241i
$946$	−14.5206			−0.472105
$947$	3.06516	−	1.11563i	0.0996042	−	0.0362530i	−0.291737	−	0.956498i	$-0.594233\pi$
$947$	3.06516	−	1.11563i	0.0996042	−	0.0362530i	0.391342	+	0.920245i	$0.372011\pi$
$948$	−1.91966	−	3.02899i	−0.0623476	−	0.0983770i
$949$	−10.6894	+	8.96947i	−0.346993	+	0.291161i
$950$	−35.0034	−	12.7402i	−1.13566	−	0.413347i
$951$	7.51504	−	3.09210i	0.243692	−	0.100268i
$952$	−33.9594	+	3.61058i	−1.10063	+	0.117020i
$953$	−24.9115	+	43.1480i	−0.806963	+	1.39770i	0.107996	+	0.994151i	$0.465557\pi$
$953$	−24.9115	+	43.1480i	−0.806963	+	1.39770i	−0.914958	+	0.403549i	$0.867777\pi$
$954$	6.12941	−	2.82309i	0.198447	−	0.0914009i
$955$	−4.33257			−0.140199
$956$	21.5003	−	7.82545i	0.695368	−	0.253093i
$957$	−12.2876	−	3.90612i	−0.397201	−	0.126267i
$958$	6.58744	+	37.3592i	0.212830	+	1.20702i
$959$	3.25689	−	47.3950i	0.105171	−	1.53046i
$960$	4.89555	+	1.55626i	0.158003	+	0.0502280i
$961$	−0.191949	+	1.08860i	−0.00619189	+	0.0351160i
$962$	−3.39680			−0.109517
$963$	−6.35714	+	13.4668i	−0.204856	+	0.433962i
$964$	−2.33096			−0.0750753
$965$	5.97656	−	2.17529i	0.192392	−	0.0700251i
$966$	15.8472	+	19.9699i	0.509874	+	0.642520i
$967$	−34.7418	+	29.1519i	−1.11722	+	0.937461i	−0.998461	−	0.0554620i	$-0.982337\pi$
$967$	−34.7418	+	29.1519i	−1.11722	+	0.937461i	−0.118761	+	0.992923i	$0.537892\pi$
$968$	−4.86688	−	27.6014i	−0.156427	−	0.887144i
$969$	−24.3666	+	46.5397i	−0.782769	+	1.49507i
$970$	−1.07799	−	0.904541i	−0.0346122	−	0.0290430i
$971$	4.19782	+	7.27084i	0.134714	+	0.233332i	0.925488	−	0.378776i	$-0.123655\pi$
$971$	4.19782	+	7.27084i	0.134714	+	0.233332i	−0.790774	+	0.612108i	$0.790322\pi$
$972$	13.2409	+	1.90219i	0.424701	+	0.0610129i
$973$	3.29223	+	11.4295i	0.105544	+	0.366412i
$974$	−1.75791	+	9.96958i	−0.0563269	+	0.319446i
$975$	6.57260	+	10.3708i	0.210492	+	0.332131i
$976$	1.62083	−	1.36004i	0.0518816	−	0.0435338i
$977$	0.322816	+	1.83078i	0.0103278	+	0.0585719i	0.989536	−	0.144285i	$-0.0460884\pi$
$977$	0.322816	+	1.83078i	0.0103278	+	0.0585719i	−0.979208	+	0.202857i	$0.934977\pi$
$978$	9.27948	−	3.81809i	0.296725	−	0.122089i
$979$	10.6907	−	3.89109i	0.341675	−	0.124360i
$980$	−0.0846044	−	2.26641i	−0.00270259	−	0.0723978i
$981$	−48.5687	+	4.01860i	−1.55068	+	0.128304i
$982$	−3.09291	+	5.35707i	−0.0986986	+	0.170951i
$983$	−14.0543	+	5.11534i	−0.448262	+	0.163154i	−0.556280	−	0.830995i	$-0.687772\pi$
$983$	−14.0543	+	5.11534i	−0.448262	+	0.163154i	0.108018	+	0.994149i	$0.465550\pi$
$984$	−38.0061	+	34.6617i	−1.21159	+	1.10498i
$985$	5.58920	−	4.68990i	0.178087	−	0.149433i
$986$	−4.32345	−	24.5195i	−0.137687	−	0.780859i
$987$	−36.2036	−	22.2431i	−1.15237	−	0.708007i
$988$	−6.88452	−	5.77680i	−0.219026	−	0.183784i
$989$	26.1961	−	45.3729i	0.832987	−	1.44278i
$990$	1.33435	+	0.943727i	0.0424084	+	0.0299936i
$991$	12.6250	+	21.8672i	0.401047	+	0.694634i	0.993853	−	0.110712i	$-0.0353131\pi$
$991$	12.6250	+	21.8672i	0.401047	+	0.694634i	−0.592806	+	0.805346i	$0.701980\pi$
$992$	18.6585	+	15.6564i	0.592409	+	0.497090i
$993$	30.8516	−	12.6940i	0.979045	−	0.402833i
$994$	−0.719007	+	10.4631i	−0.0228055	+	0.331871i
$995$	−1.30112	−	0.473568i	−0.0412482	−	0.0150131i
$996$	−17.4725	+	0.721609i	−0.553637	+	0.0228651i
$997$	8.14440	+	6.83397i	0.257936	+	0.216434i	0.762581	−	0.646893i	$-0.223932\pi$
$997$	8.14440	+	6.83397i	0.257936	+	0.216434i	−0.504645	+	0.863327i	$0.668377\pi$
$998$	6.79918	−	11.7765i	0.215224	−	0.372779i
$999$	−4.40513	+	10.4258i	−0.139372	+	0.329858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.15	yes	132
3.2	odd	2		567.2.w.a.235.8		132
7.2	even	3		189.2.u.a.79.8	yes	132
21.2	odd	6		567.2.u.a.478.15		132
27.13	even	9		189.2.u.a.67.8	✓	132
27.14	odd	18		567.2.u.a.172.15		132
189.121	even	9	inner	189.2.w.a.121.15	yes	132
189.149	odd	18		567.2.w.a.415.8		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.8	✓	132	27.13	even	9
189.2.u.a.79.8	yes	132	7.2	even	3
189.2.w.a.25.15	yes	132	1.1	even	1	trivial
189.2.w.a.121.15	yes	132	189.121	even	9	inner
567.2.u.a.172.15		132	27.14	odd	18
567.2.u.a.478.15		132	21.2	odd	6
567.2.w.a.235.8		132	3.2	odd	2
567.2.w.a.415.8		132	189.149	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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00414 - 0.365478i) q^{2} +(-0.803391 + 1.53446i) q^{3} +(-0.657360 + 0.551590i) q^{4} +(0.354797 + 0.129136i) q^{5} +(-0.245908 + 1.83444i) q^{6} +(1.55771 + 2.13859i) q^{7} +(-1.52708 + 2.64497i) q^{8} +(-1.70913 - 2.46554i) q^{9} +O(q^{10})\)	\(q+(1.00414 - 0.365478i) q^{2} +(-0.803391 + 1.53446i) q^{3} +(-0.657360 + 0.551590i) q^{4} +(0.354797 + 0.129136i) q^{5} +(-0.245908 + 1.83444i) q^{6} +(1.55771 + 2.13859i) q^{7} +(-1.52708 + 2.64497i) q^{8} +(-1.70913 - 2.46554i) q^{9} +0.403463 q^{10} +(-1.26884 + 0.461820i) q^{11} +(-0.318275 - 1.45183i) q^{12} +(0.253416 + 1.43719i) q^{13} +(2.34577 + 1.57814i) q^{14} +(-0.483194 + 0.440675i) q^{15} +(-0.268700 + 1.52387i) q^{16} +4.22631 q^{17} +(-2.61731 - 1.85111i) q^{18} +7.17641 q^{19} +(-0.304459 + 0.110814i) q^{20} +(-4.53302 + 0.672117i) q^{21} +(-1.10531 + 0.927466i) q^{22} +(-0.904031 - 5.12702i) q^{23} +(-2.83176 - 4.46818i) q^{24} +(-3.72102 - 3.12230i) q^{25} +(0.779728 + 1.35053i) q^{26} +(5.15637 - 0.641790i) q^{27} +(-2.20360 - 0.546604i) q^{28} +(0.957325 - 5.42926i) q^{29} +(-0.324139 + 0.619097i) q^{30} +(-4.18842 + 3.51450i) q^{31} +(-0.773566 - 4.38711i) q^{32} +(0.310731 - 2.31800i) q^{33} +(4.24382 - 1.54462i) q^{34} +(0.276502 + 0.959919i) q^{35} +(2.48348 + 0.678009i) q^{36} +(-1.08910 + 1.88637i) q^{37} +(7.20615 - 2.62282i) q^{38} +(-2.40890 - 0.765771i) q^{39} +(-0.883362 + 0.741228i) q^{40} +(-1.68852 - 9.57606i) q^{41} +(-4.30616 + 2.33162i) q^{42} +(7.70916 + 6.46875i) q^{43} +(0.579348 - 1.00346i) q^{44} +(-0.288004 - 1.09547i) q^{45} +(-2.78159 - 4.81785i) q^{46} +(7.10294 + 5.96008i) q^{47} +(-2.12245 - 1.63658i) q^{48} +(-2.14710 + 6.66258i) q^{49} +(-4.87757 - 1.77529i) q^{50} +(-3.39538 + 6.48509i) q^{51} +(-0.959326 - 0.804970i) q^{52} +(-1.05253 + 1.82303i) q^{53} +(4.94317 - 2.52899i) q^{54} -0.509818 q^{55} +(-8.03524 + 0.854311i) q^{56} +(-5.76547 + 11.0119i) q^{57} +(-1.02298 - 5.80163i) q^{58} +(-0.445729 - 2.52786i) q^{59} +(0.0745601 - 0.556207i) q^{60} +(-1.04747 - 0.878929i) q^{61} +(-2.92130 + 5.05984i) q^{62} +(2.61045 - 7.49570i) q^{63} +(-3.92755 - 6.80271i) q^{64} +(-0.0956814 + 0.542636i) q^{65} +(-0.535161 - 2.44117i) q^{66} +(-2.49507 - 0.908131i) q^{67} +(-2.77820 + 2.33119i) q^{68} +(8.59348 + 2.73180i) q^{69} +(0.628477 + 0.862840i) q^{70} +(1.85480 + 3.21260i) q^{71} +(9.13125 - 0.755525i) q^{72} +(4.78086 + 8.28069i) q^{73} +(-0.404182 + 2.29223i) q^{74} +(7.78048 - 3.20132i) q^{75} +(-4.71748 + 3.95844i) q^{76} +(-2.96412 - 1.99414i) q^{77} +(-2.69876 + 0.111458i) q^{78} +(2.26722 - 0.825202i) q^{79} +(-0.292120 + 0.505967i) q^{80} +(-3.15778 + 8.42784i) q^{81} +(-5.19535 - 8.99862i) q^{82} +(2.04308 - 11.5869i) q^{83} +(2.60909 - 2.94219i) q^{84} +(1.49948 + 0.545766i) q^{85} +(10.1053 + 3.67802i) q^{86} +(7.56187 + 5.83079i) q^{87} +(0.716113 - 4.06128i) q^{88} -8.42555 q^{89} +(-0.689569 - 0.994755i) q^{90} +(-2.67881 + 2.78068i) q^{91} +(3.42228 + 2.87164i) q^{92} +(-2.02792 - 9.25048i) q^{93} +(9.31065 + 3.38880i) q^{94} +(2.54617 + 0.926730i) q^{95} +(7.35332 + 2.33756i) q^{96} +(-2.67184 - 2.24194i) q^{97} +(0.279036 + 7.47490i) q^{98} +(3.30724 + 2.33907i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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