LMFDB - Embedded newform 189.2.w.a.25.13

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			25.13
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456477 - 0.166144i) q^{2} +(1.72709 - 0.131048i) q^{3} +(-1.35132 + 1.13389i) q^{4} +(1.44421 + 0.525651i) q^{5} +(0.766603 - 0.346766i) q^{6} +(-1.09247 + 2.40967i) q^{7} +(-0.914231 + 1.58349i) q^{8} +(2.96565 - 0.452662i) q^{9} +O(q^{10})$	\(q+(0.456477 - 0.166144i) q^{2} +(1.72709 - 0.131048i) q^{3} +(-1.35132 + 1.13389i) q^{4} +(1.44421 + 0.525651i) q^{5} +(0.766603 - 0.346766i) q^{6} +(-1.09247 + 2.40967i) q^{7} +(-0.914231 + 1.58349i) q^{8} +(2.96565 - 0.452662i) q^{9} +0.746585 q^{10} +(2.05246 - 0.747035i) q^{11} +(-2.18525 + 2.13542i) q^{12} +(-1.09206 - 6.19341i) q^{13} +(-0.0983346 + 1.28147i) q^{14} +(2.56317 + 0.718583i) q^{15} +(0.458402 - 2.59973i) q^{16} -5.28914 q^{17} +(1.27855 - 0.699356i) q^{18} +2.33437 q^{19} +(-2.54763 + 0.927262i) q^{20} +(-1.57101 + 4.30487i) q^{21} +(0.812787 - 0.682009i) q^{22} +(-0.500144 - 2.83646i) q^{23} +(-1.37144 + 2.85464i) q^{24} +(-2.02077 - 1.69563i) q^{25} +(-1.52750 - 2.64571i) q^{26} +(5.06262 - 1.17043i) q^{27} +(-1.25603 - 4.49498i) q^{28} +(-1.64020 + 9.30205i) q^{29} +(1.28942 - 0.0978385i) q^{30} +(2.04679 - 1.71746i) q^{31} +(-0.857698 - 4.86424i) q^{32} +(3.44688 - 1.55916i) q^{33} +(-2.41438 + 0.878761i) q^{34} +(-2.84441 + 2.90582i) q^{35} +(-3.49428 + 3.97443i) q^{36} +(-0.229261 + 0.397091i) q^{37} +(1.06559 - 0.387842i) q^{38} +(-2.69772 - 10.5534i) q^{39} +(-2.15271 + 1.80634i) q^{40} +(0.513695 + 2.91331i) q^{41} +(-0.00189857 + 2.22609i) q^{42} +(-4.87748 - 4.09269i) q^{43} +(-1.92648 + 3.33675i) q^{44} +(4.52098 + 0.905157i) q^{45} +(-0.699565 - 1.21168i) q^{46} +(5.09935 + 4.27886i) q^{47} +(0.451011 - 4.55002i) q^{48} +(-4.61302 - 5.26498i) q^{49} +(-1.20416 - 0.438277i) q^{50} +(-9.13481 + 0.693132i) q^{51} +(8.49839 + 7.13100i) q^{52} +(-4.80829 + 8.32820i) q^{53} +(2.11651 - 1.37540i) q^{54} +3.35687 q^{55} +(-2.81693 - 3.93291i) q^{56} +(4.03166 - 0.305915i) q^{57} +(0.796766 + 4.51869i) q^{58} +(-1.69936 - 9.63755i) q^{59} +(-4.27846 + 1.93532i) q^{60} +(4.29653 + 3.60521i) q^{61} +(0.648966 - 1.12404i) q^{62} +(-2.14912 + 7.64077i) q^{63} +(1.44015 + 2.49441i) q^{64} +(1.67840 - 9.51865i) q^{65} +(1.31438 - 1.28440i) q^{66} +(-8.51828 - 3.10040i) q^{67} +(7.14733 - 5.99732i) q^{68} +(-1.23550 - 4.83326i) q^{69} +(-0.815621 + 1.79902i) q^{70} +(-1.42313 - 2.46494i) q^{71} +(-1.99450 + 5.10993i) q^{72} +(-2.73297 - 4.73365i) q^{73} +(-0.0386779 + 0.219353i) q^{74} +(-3.71226 - 2.66368i) q^{75} +(-3.15448 + 2.64693i) q^{76} +(-0.442142 + 5.76187i) q^{77} +(-2.98484 - 4.36919i) q^{78} +(3.00687 - 1.09441i) q^{79} +(2.02858 - 3.51360i) q^{80} +(8.59019 - 2.68488i) q^{81} +(0.718519 + 1.24451i) q^{82} +(-0.920085 + 5.21806i) q^{83} +(-2.75833 - 7.59862i) q^{84} +(-7.63866 - 2.78025i) q^{85} +(-2.90644 - 1.05786i) q^{86} +(-1.61376 + 16.2804i) q^{87} +(-0.693498 + 3.93302i) q^{88} +17.9742 q^{89} +(2.21411 - 0.337951i) q^{90} +(16.1171 + 4.13459i) q^{91} +(3.89209 + 3.26585i) q^{92} +(3.30991 - 3.23443i) q^{93} +(3.03865 + 1.10598i) q^{94} +(3.37133 + 1.22706i) q^{95} +(-2.11877 - 8.28857i) q^{96} +(10.6549 + 8.94050i) q^{97} +(-2.98049 - 1.63692i) q^{98} +(5.74873 - 3.14452i) 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 $

$2$	0.456477	−	0.166144i	0.322778	−	0.117482i	−0.175549	−	0.984471i	$-0.556170\pi$
$2$	0.456477	−	0.166144i	0.322778	−	0.117482i	0.498327	+	0.866989i	$0.333948\pi$
$3$	1.72709	−	0.131048i	0.997134	−	0.0756606i
$3$	1.72709	−	0.131048i	0.997134	−	0.0756606i
$4$	−1.35132	+	1.13389i	−0.675661	+	0.566947i
$5$	1.44421	+	0.525651i	0.645873	+	0.235078i	0.644125	−	0.764920i	$-0.277222\pi$
$5$	1.44421	+	0.525651i	0.645873	+	0.235078i	0.00174734	+	0.999998i	$0.499444\pi$
$6$	0.766603	−	0.346766i	0.312964	−	0.141567i
$7$	−1.09247	+	2.40967i	−0.412914	+	0.910770i
$7$	−1.09247	+	2.40967i	−0.412914	+	0.910770i
$8$	−0.914231	+	1.58349i	−0.323229	+	0.559850i
$9$	2.96565	−	0.452662i	0.988551	−	0.150887i
$10$	0.746585			0.236091
$11$	2.05246	−	0.747035i	0.618840	−	0.225239i	−0.0135266	−	0.999909i	$-0.504306\pi$
$11$	2.05246	−	0.747035i	0.618840	−	0.225239i	0.632367	+	0.774669i	$0.282084\pi$
$12$	−2.18525	+	2.13542i	−0.630828	+	0.616442i
$13$	−1.09206	−	6.19341i	−0.302884	−	1.71774i	−0.633300	−	0.773906i	$-0.718300\pi$
$13$	−1.09206	−	6.19341i	−0.302884	−	1.71774i	0.330416	−	0.943835i	$-0.392811\pi$
$14$	−0.0983346	+	1.28147i	−0.0262810	+	0.342487i
$15$	2.56317	+	0.718583i	0.661807	+	0.185537i
$16$	0.458402	−	2.59973i	0.114600	−	0.649932i
$17$	−5.28914			−1.28281			−0.641403	−	0.767204i	$-0.721647\pi$
$17$	−5.28914			−1.28281			−0.641403	+	0.767204i	$0.721647\pi$
$18$	1.27855	−	0.699356i	0.301356	−	0.164840i
$19$	2.33437			0.535541			0.267771	−	0.963483i	$-0.413713\pi$
$19$	2.33437			0.535541			0.267771	+	0.963483i	$0.413713\pi$
$20$	−2.54763	+	0.927262i	−0.569667	+	0.207342i
$21$	−1.57101	+	4.30487i	−0.342821	+	0.939401i
$22$	0.812787	−	0.682009i	0.173287	−	0.145405i
$23$	−0.500144	−	2.83646i	−0.104287	−	0.591442i	−0.991503	−	0.130087i	$-0.958474\pi$
$23$	−0.500144	−	2.83646i	−0.104287	−	0.591442i	0.887216	−	0.461355i	$-0.152637\pi$
$24$	−1.37144	+	2.85464i	−0.279944	+	0.582701i
$25$	−2.02077	−	1.69563i	−0.404155	−	0.339126i
$26$	−1.52750	−	2.64571i	−0.299568	−	0.518866i
$27$	5.06262	−	1.17043i	0.974301	−	0.225249i
$28$	−1.25603	−	4.49498i	−0.237368	−	0.849472i
$29$	−1.64020	+	9.30205i	−0.304578	+	1.72735i	0.320907	+	0.947111i	$0.396012\pi$
$29$	−1.64020	+	9.30205i	−0.304578	+	1.72735i	−0.625485	+	0.780237i	$0.715099\pi$
$30$	1.28942	−	0.0978385i	0.235414	−	0.0178628i
$31$	2.04679	−	1.71746i	0.367614	−	0.308465i	−0.440203	−	0.897898i	$-0.645094\pi$
$31$	2.04679	−	1.71746i	0.367614	−	0.308465i	0.807817	+	0.589434i	$0.200649\pi$
$32$	−0.857698	−	4.86424i	−0.151621	−	0.859885i
$33$	3.44688	−	1.55916i	0.600025	−	0.271416i
$34$	−2.41438	+	0.878761i	−0.414062	+	0.150706i
$35$	−2.84441	+	2.90582i	−0.480792	+	0.491174i
$36$	−3.49428	+	3.97443i	−0.582380	+	0.662404i
$37$	−0.229261	+	0.397091i	−0.0376902	+	0.0652814i	−0.884255	−	0.467004i	$-0.845333\pi$
$37$	−0.229261	+	0.397091i	−0.0376902	+	0.0652814i	0.846565	+	0.532285i	$0.178667\pi$
$38$	1.06559	−	0.387842i	0.172861	−	0.0629163i
$39$	−2.69772	−	10.5534i	−0.431981	−	1.68990i
$40$	−2.15271	+	1.80634i	−0.340374	+	0.285607i
$41$	0.513695	+	2.91331i	0.0802256	+	0.454982i	0.998285	+	0.0585394i	$0.0186443\pi$
$41$	0.513695	+	2.91331i	0.0802256	+	0.454982i	−0.918059	+	0.396443i	$0.870245\pi$
$42$	−0.00189857	+	2.22609i	−0.000292956	+	0.343493i
$43$	−4.87748	−	4.09269i	−0.743809	−	0.624130i	0.190049	−	0.981775i	$-0.439135\pi$
$43$	−4.87748	−	4.09269i	−0.743809	−	0.624130i	−0.933858	+	0.357645i	$0.883580\pi$
$44$	−1.92648	+	3.33675i	−0.290427	+	0.503035i
$45$	4.52098	+	0.905157i	0.673948	+	0.134933i
$46$	−0.699565	−	1.21168i	−0.103145	−	0.178653i
$47$	5.09935	+	4.27886i	0.743816	+	0.624136i	0.933860	−	0.357640i	$-0.116418\pi$
$47$	5.09935	+	4.27886i	0.743816	+	0.624136i	−0.190043	+	0.981776i	$0.560863\pi$
$48$	0.451011	−	4.55002i	0.0650978	−	0.656739i
$49$	−4.61302	−	5.26498i	−0.659003	−	0.752140i
$50$	−1.20416	−	0.438277i	−0.170294	−	0.0619818i
$51$	−9.13481	+	0.693132i	−1.27913	+	0.0970579i
$52$	8.49839	+	7.13100i	1.17851	+	0.988891i
$53$	−4.80829	+	8.32820i	−0.660469	+	1.14397i	0.320023	+	0.947410i	$0.396309\pi$
$53$	−4.80829	+	8.32820i	−0.660469	+	1.14397i	−0.980492	+	0.196557i	$0.937024\pi$
$54$	2.11651	−	1.37540i	0.288021	−	0.187168i
$55$	3.35687			0.452641
$56$	−2.81693	−	3.93291i	−0.376428	−	0.525558i
$57$	4.03166	−	0.305915i	0.534006	−	0.0405194i
$58$	0.796766	+	4.51869i	0.104621	+	0.593333i
$59$	−1.69936	−	9.63755i	−0.221238	−	1.25470i	−0.869748	−	0.493496i	$-0.835719\pi$
$59$	−1.69936	−	9.63755i	−0.221238	−	1.25470i	0.648510	−	0.761206i	$-0.275392\pi$
$60$	−4.27846	+	1.93532i	−0.552347	+	0.249849i
$61$	4.29653	+	3.60521i	0.550114	+	0.461600i	0.874980	−	0.484160i	$-0.160875\pi$
$61$	4.29653	+	3.60521i	0.550114	+	0.461600i	−0.324866	+	0.945760i	$0.605319\pi$
$62$	0.648966	−	1.12404i	0.0824188	−	0.142754i
$63$	−2.14912	+	7.64077i	−0.270763	+	0.962646i
$64$	1.44015	+	2.49441i	0.180018	+	0.311801i
$65$	1.67840	−	9.51865i	0.208179	−	1.18064i
$66$	1.31438	−	1.28440i	0.161789	−	0.158099i
$67$	−8.51828	−	3.10040i	−1.04067	−	0.378774i	−0.235538	−	0.971865i	$-0.575685\pi$
$67$	−8.51828	−	3.10040i	−1.04067	−	0.378774i	−0.805136	+	0.593091i	$0.797908\pi$
$68$	7.14733	−	5.99732i	0.866741	−	0.727282i
$69$	−1.23550	−	4.83326i	−0.148737	−	0.581856i
$70$	−0.815621	+	1.79902i	−0.0974854	+	0.215025i
$71$	−1.42313	−	2.46494i	−0.168895	−	0.292535i	0.769137	−	0.639084i	$-0.220687\pi$
$71$	−1.42313	−	2.46494i	−0.168895	−	0.292535i	−0.938032	+	0.346550i	$0.887353\pi$
$72$	−1.99450	+	5.10993i	−0.235054	+	0.602211i
$73$	−2.73297	−	4.73365i	−0.319870	−	0.554031i	0.660591	−	0.750746i	$-0.270306\pi$
$73$	−2.73297	−	4.73365i	−0.319870	−	0.554031i	−0.980461	+	0.196715i	$0.936973\pi$
$74$	−0.0386779	+	0.219353i	−0.00449622	+	0.0254993i
$75$	−3.71226	−	2.66368i	−0.428655	−	0.307576i
$76$	−3.15448	+	2.64693i	−0.361844	+	0.303623i
$77$	−0.442142	+	5.76187i	−0.0503868	+	0.656626i
$78$	−2.98484	−	4.36919i	−0.337967	−	0.494714i
$79$	3.00687	−	1.09441i	0.338300	−	0.123131i	−0.167284	−	0.985909i	$-0.553500\pi$
$79$	3.00687	−	1.09441i	0.338300	−	0.123131i	0.505583	+	0.862778i	$0.331277\pi$
$80$	2.02858	−	3.51360i	0.226802	−	0.392833i
$81$	8.59019	−	2.68488i	0.954466	−	0.298320i
$82$	0.718519	+	1.24451i	0.0793471	+	0.137433i
$83$	−0.920085	+	5.21806i	−0.100992	+	0.572757i	0.891753	+	0.452522i	$0.149476\pi$
$83$	−0.920085	+	5.21806i	−0.100992	+	0.572757i	−0.992746	+	0.120234i	$0.961635\pi$
$84$	−2.75833	−	7.59862i	−0.300959	−	0.829077i
$85$	−7.63866	−	2.78025i	−0.828529	−	0.301560i
$86$	−2.90644	−	1.05786i	−0.313409	−	0.114072i
$87$	−1.61376	+	16.2804i	−0.173013	+	1.74544i
$88$	−0.693498	+	3.93302i	−0.0739271	+	0.419262i
$89$	17.9742			1.90526			0.952629	−	0.304134i	$-0.0983669\pi$
$89$	17.9742			1.90526			0.952629	+	0.304134i	$0.0983669\pi$
$90$	2.21411	−	0.337951i	0.233388	−	0.0356232i
$91$	16.1171	+	4.13459i	1.68953	+	0.433423i
$92$	3.89209	+	3.26585i	0.405779	+	0.340489i
$93$	3.30991	−	3.23443i	0.343221	−	0.335394i
$94$	3.03865	+	1.10598i	0.313412	+	0.114073i
$95$	3.37133	+	1.22706i	0.345891	+	0.125894i
$96$	−2.11877	−	8.28857i	−0.216246	−	0.845949i
$97$	10.6549	+	8.94050i	1.08184	+	0.907771i	0.996072	−	0.0885447i	$-0.0282216\pi$
$97$	10.6549	+	8.94050i	1.08184	+	0.907771i	0.0857666	+	0.996315i	$0.472666\pi$
$98$	−2.98049	−	1.63692i	−0.301075	−	0.165354i
$99$	5.74873	−	3.14452i	0.577769	−	0.316036i
$100$	4.65338			0.465338
$101$	−2.52652	+	14.3286i	−0.251398	+	1.42575i	0.553753	+	0.832681i	$0.313195\pi$
$101$	−2.52652	+	14.3286i	−0.251398	+	1.42575i	−0.805151	+	0.593069i	$0.797916\pi$
$102$	−4.05467	+	1.83409i	−0.401473	+	0.181602i
$103$	1.52675	+	0.555691i	0.150435	+	0.0547539i	0.416140	−	0.909300i	$-0.363383\pi$
$103$	1.52675	+	0.555691i	0.150435	+	0.0547539i	−0.265705	+	0.964054i	$0.585605\pi$
$104$	10.8056	+	3.93293i	1.05958	+	0.385655i
$105$	−4.53173	+	5.39136i	−0.442252	+	0.526143i
$106$	−0.811193	+	4.60051i	−0.0787901	+	0.446841i
$107$	5.06054	+	8.76511i	0.489221	+	0.847356i	0.999923	−	0.0124021i	$-0.00394782\pi$
$107$	5.06054	+	8.76511i	0.489221	+	0.847356i	−0.510702	+	0.859758i	$0.670614\pi$
$108$	−5.51408	+	7.32209i	−0.530593	+	0.704569i
$109$	−2.46881	+	4.27611i	−0.236469	+	0.409577i	−0.959699	−	0.281031i	$-0.909324\pi$
$109$	−2.46881	+	4.27611i	−0.236469	+	0.409577i	0.723229	+	0.690608i	$0.242657\pi$
$110$	1.53234	−	0.557725i	0.146103	−	0.0531770i
$111$	−0.343915	+	0.715855i	−0.0326429	+	0.0679459i
$112$	5.76369	+	3.94472i	0.544618	+	0.372741i
$113$	3.75536	−	3.15112i	0.353274	−	0.296432i	−0.448829	−	0.893618i	$-0.648159\pi$
$113$	3.75536	−	3.15112i	0.353274	−	0.296432i	0.802103	+	0.597185i	$0.203714\pi$
$114$	1.78953	−	0.809480i	0.167605	−	0.0758147i
$115$	0.768671	−	4.35935i	0.0716790	−	0.406512i
$116$	−8.33109	−	14.4299i	−0.773522	−	1.33978i
$117$	−6.04221	−	17.8732i	−0.558602	−	1.65237i
$118$	−2.37694	−	4.11698i	−0.218815	−	0.378999i
$119$	5.77823	−	12.7451i	0.529689	−	1.16834i
$120$	−3.48120	+	3.40181i	−0.317789	+	0.310542i
$121$	−4.77195	+	4.00414i	−0.433814	+	0.364013i
$122$	2.56025	+	0.931856i	0.231794	+	0.0843663i
$123$	1.26898	+	4.96421i	0.114420	+	0.447608i
$124$	−0.818453	+	4.64168i	−0.0734992	+	0.416835i
$125$	−5.86938	−	10.1661i	−0.524973	−	0.909280i
$126$	0.288446	+	3.84490i	0.0256968	+	0.342531i
$127$	1.46479	−	2.53708i	0.129979	−	0.225130i	−0.793689	−	0.608323i	$-0.791842\pi$
$127$	1.46479	−	2.53708i	0.129979	−	0.225130i	0.923668	+	0.383194i	$0.125176\pi$
$128$	8.63925	+	7.24919i	0.763609	+	0.640744i
$129$	−8.96017	−	6.42925i	−0.788899	−	0.566064i
$130$	−0.815319	−	4.62391i	−0.0715082	−	0.405543i
$131$	−0.791396	−	4.48823i	−0.0691446	−	0.392138i	−0.999665	−	0.0258974i	$-0.991756\pi$
$131$	−0.791396	−	4.48823i	−0.0691446	−	0.392138i	0.930520	−	0.366241i	$-0.119355\pi$
$132$	−2.88992	+	6.01532i	−0.251535	+	0.523567i
$133$	−2.55023	+	5.62506i	−0.221133	+	0.487755i
$134$	−4.40352			−0.380406
$135$	7.92674	+	0.970819i	0.682226	+	0.0835548i
$136$	4.83550	−	8.37533i	0.414641	−	0.718179i
$137$	−3.68378	−	3.09106i	−0.314727	−	0.264087i	0.471716	−	0.881751i	$-0.343635\pi$
$137$	−3.68378	−	3.09106i	−0.314727	−	0.264087i	−0.786442	+	0.617664i	$0.788079\pi$
$138$	−1.36700	−	2.00100i	−0.116367	−	0.170337i
$139$	−2.85026	−	1.03741i	−0.241756	−	0.0879919i	0.218301	−	0.975882i	$-0.429949\pi$
$139$	−2.85026	−	1.03741i	−0.241756	−	0.0879919i	−0.460057	+	0.887890i	$0.652171\pi$
$140$	0.548812	−	7.15195i	0.0463831	−	0.604450i
$141$	9.36775	+	6.72170i	0.788907	+	0.566069i
$142$	−1.05916	−	0.888744i	−0.0888831	−	0.0745818i
$143$	−6.86811	−	11.8959i	−0.574340	−	0.994786i
$144$	0.182662	−	7.91739i	0.0152219	−	0.659782i
$145$	−7.25844	+	12.5720i	−0.602781	+	1.04405i
$146$	−2.03401	−	1.70673i	−0.168336	−	0.141250i
$147$	−8.65705	−	8.48855i	−0.714022	−	0.700123i
$148$	−0.140454	−	0.796554i	−0.0115453	−	0.0654764i
$149$	−11.4102	+	9.57426i	−0.934756	+	0.784354i	−0.976665	−	0.214768i	$-0.931101\pi$
$149$	−11.4102	+	9.57426i	−0.934756	+	0.784354i	0.0419090	+	0.999121i	$0.486656\pi$
$150$	−2.13712	−	0.599141i	−0.174495	−	0.0489196i
$151$	−9.00836	+	3.27878i	−0.733090	+	0.266823i	−0.681472	−	0.731844i	$-0.738660\pi$
$151$	−9.00836	+	3.27878i	−0.733090	+	0.266823i	−0.0516179	+	0.998667i	$0.516438\pi$
$152$	−2.13415	+	3.69646i	−0.173103	+	0.299823i
$153$	−15.6858	+	2.39420i	−1.26812	+	0.193559i
$154$	0.755473	+	2.70362i	0.0608777	+	0.217864i
$155$	3.85878	−	1.40448i	0.309945	−	0.112811i
$156$	15.6120	+	11.2021i	1.24996	+	0.896890i
$157$	1.61925	+	9.18321i	0.129230	+	0.732900i	0.978705	+	0.205271i	$0.0658077\pi$
$157$	1.61925	+	9.18321i	0.129230	+	0.732900i	−0.849475	+	0.527629i	$0.823081\pi$
$158$	1.19074	−	0.999150i	0.0947302	−	0.0794881i
$159$	−7.21294	+	15.0136i	−0.572023	+	1.19066i
$160$	1.31820	−	7.47586i	0.104213	−	0.591019i
$161$	7.38131	+	1.89356i	0.581729	+	0.149233i
$162$	3.47515	−	2.65280i	0.273034	−	0.208423i
$163$	−8.18715	−	14.1806i	−0.641267	−	1.11071i	−0.985150	−	0.171694i	$-0.945076\pi$
$163$	−8.18715	−	14.1806i	−0.641267	−	1.11071i	0.343883	−	0.939012i	$-0.388257\pi$
$164$	−3.99754	−	3.35434i	−0.312156	−	0.261930i
$165$	5.79761	−	0.439912i	0.451343	−	0.0342471i
$166$	0.446953	+	2.53479i	0.0346903	+	0.196738i
$167$	0.526404	−	0.441705i	0.0407344	−	0.0341802i	−0.622193	−	0.782864i	$-0.713758\pi$
$167$	0.526404	−	0.441705i	0.0407344	−	0.0341802i	0.662928	+	0.748684i	$0.269314\pi$
$168$	−5.38048	−	6.42333i	−0.415113	−	0.495570i
$169$	−24.9497	+	9.08094i	−1.91921	+	0.698534i
$170$	−3.94880			−0.302859
$171$	6.92293	−	1.05668i	0.529410	−	0.0808065i
$172$	11.2317			0.856411
$173$	1.43439	−	8.13481i	0.109054	−	0.618478i	−0.880469	−	0.474104i	$-0.842772\pi$
$173$	1.43439	−	8.13481i	0.109054	−	0.618478i	0.989523	−	0.144374i	$-0.0461168\pi$
$174$	1.96825	+	7.69975i	0.149213	+	0.583716i
$175$	6.29355	−	3.01698i	0.475747	−	0.228062i
$176$	−1.00123	−	5.67828i	−0.0754708	−	0.428016i
$177$	−4.19792	−	16.4222i	−0.315535	−	1.23437i
$178$	8.20481	−	2.98630i	0.614976	−	0.223833i
$179$	23.9893			1.79304			0.896521	−	0.443001i	$-0.146086\pi$
$179$	23.9893			1.79304			0.896521	+	0.443001i	$0.146086\pi$
$180$	−7.13565	+	3.90315i	−0.531860	+	0.290924i
$181$	1.13840	−	1.97177i	0.0846166	−	0.146560i	−0.820611	−	0.571487i	$-0.806367\pi$
$181$	1.13840	−	1.97177i	0.0846166	−	0.146560i	0.905228	+	0.424927i	$0.139700\pi$
$182$	8.04404	−	0.790419i	0.596264	−	0.0585898i
$183$	7.89293	+	5.66346i	0.583462	+	0.418655i
$184$	4.94876	+	1.80120i	0.364827	+	0.132786i
$185$	−0.539833	+	0.452974i	−0.0396893	+	0.0333033i
$186$	0.973517	−	2.02636i	0.0713817	−	0.148580i
$187$	−10.8558	+	3.95117i	−0.793852	+	0.288938i
$188$	−11.7426			−0.856419
$189$	−2.71040	+	13.4779i	−0.197153	+	0.980373i
$190$	1.74281			0.126436
$191$	−16.8937	+	6.14879i	−1.22238	+	0.444911i	−0.870982	−	0.491315i	$-0.836516\pi$
$191$	−16.8937	+	6.14879i	−1.22238	+	0.444911i	−0.351400	+	0.936225i	$0.614294\pi$
$192$	2.81414	+	4.11932i	0.203093	+	0.297287i
$193$	−0.0720593	+	0.0604649i	−0.00518694	+	0.00435236i	−0.645377	−	0.763864i	$-0.723300\pi$
$193$	−0.0720593	+	0.0604649i	−0.00518694	+	0.00435236i	0.640190	+	0.768216i	$0.278855\pi$
$194$	6.34912	+	2.31089i	0.455841	+	0.165912i
$195$	1.65133	−	16.6595i	0.118254	−	1.19301i
$196$	12.2036	+	1.88400i	0.871686	+	0.134572i
$197$	−12.1146	+	20.9832i	−0.863132	+	1.49499i	0.00575743	+	0.999983i	$0.498167\pi$
$197$	−12.1146	+	20.9832i	−0.863132	+	1.49499i	−0.868890	+	0.495006i	$0.835166\pi$
$198$	2.10172	−	2.39052i	0.149363	−	0.169887i
$199$	−11.4240			−0.809823			−0.404912	−	0.914356i	$-0.632698\pi$
$199$	−11.4240			−0.809823			−0.404912	+	0.914356i	$0.632698\pi$
$200$	4.53248	−	1.64969i	0.320495	−	0.116651i
$201$	−15.1181	−	4.23836i	−1.06635	−	0.298951i
$202$	1.22732	+	6.96046i	0.0863537	+	0.489736i
$203$	−20.6230	−	14.1145i	−1.44745	−	0.990647i
$204$	11.5581	−	11.2945i	0.809230	−	0.790776i
$205$	−0.789498	+	4.47746i	−0.0551409	+	0.312720i
$206$	0.789251			0.0549897
$207$	−2.76721	−	8.18554i	−0.192334	−	0.568935i
$208$	−16.6018			−1.15113
$209$	4.79120	−	1.74386i	0.331414	−	0.120625i
$210$	−1.17289	+	3.21396i	−0.0809371	+	0.221784i
$211$	18.8128	−	15.7858i	1.29513	−	1.08674i	0.304165	−	0.952619i	$-0.401623\pi$
$211$	18.8128	−	15.7858i	1.29513	−	1.08674i	0.990965	−	0.134123i	$-0.0428218\pi$
$212$	−2.94575	−	16.7062i	−0.202315	−	1.14738i
$213$	−2.78090	−	4.07067i	−0.190544	−	0.278917i
$214$	3.76630	+	3.16030i	0.257459	+	0.216033i
$215$	−4.89280	−	8.47458i	−0.333686	−	0.577962i
$216$	−2.77503	+	9.08667i	−0.188817	+	0.618270i
$217$	1.90246	+	6.80835i	0.129147	+	0.462181i
$218$	−0.416507	+	2.36213i	−0.0282094	+	0.159983i
$219$	−5.34041	−	7.81726i	−0.360872	−	0.528242i
$220$	−4.53622	+	3.80634i	−0.305832	+	0.256623i
$221$	5.77609	+	32.7578i	0.388542	+	2.20353i
$222$	−0.0380543	+	0.383911i	−0.00255404	+	0.0257664i
$223$	14.7349	−	5.36308i	0.986724	−	0.359138i	0.202273	−	0.979329i	$-0.435167\pi$
$223$	14.7349	−	5.36308i	0.986724	−	0.359138i	0.784451	+	0.620191i	$0.212945\pi$
$224$	12.6582	+	3.24727i	0.845764	+	0.216967i
$225$	−6.76047	−	4.11393i	−0.450698	−	0.274262i
$226$	1.19070	−	2.06235i	0.0792039	−	0.137185i
$227$	2.28216	−	0.830637i	0.151472	−	0.0551313i	−0.265171	−	0.964201i	$-0.585429\pi$
$227$	2.28216	−	0.830637i	0.151472	−	0.0551313i	0.416643	+	0.909070i	$0.363206\pi$
$228$	−5.10119	+	4.98486i	−0.337835	+	0.330130i
$229$	−0.542584	+	0.455282i	−0.0358550	+	0.0300859i	−0.660539	−	0.750792i	$-0.729672\pi$
$229$	−0.542584	+	0.455282i	−0.0358550	+	0.0300859i	0.624684	+	0.780878i	$0.285228\pi$
$230$	−0.373400	−	2.11766i	−0.0246213	−	0.139634i
$231$	−0.00853655	+	10.0092i	−0.000561663	+	0.658556i
$232$	−13.2302	−	11.1015i	−0.868607	−	0.728847i
$233$	0.118804	−	0.205774i	0.00778310	−	0.0134807i	−0.862108	−	0.506725i	$-0.830856\pi$
$233$	0.118804	−	0.205774i	0.00778310	−	0.0134807i	0.869891	+	0.493244i	$0.164189\pi$
$234$	−5.72765	−	7.15481i	−0.374428	−	0.467725i
$235$	5.11537	+	8.86007i	0.333690	+	0.577967i
$236$	13.2243	+	11.0965i	0.860830	+	0.722322i
$237$	5.04971	−	2.28419i	0.328014	−	0.148374i
$238$	0.520106	−	6.77787i	0.0337135	−	0.439344i
$239$	−1.95296	−	0.710821i	−0.126327	−	0.0459792i	0.278083	−	0.960557i	$-0.410301\pi$
$239$	−1.95296	−	0.710821i	−0.126327	−	0.0459792i	−0.404410	+	0.914578i	$0.632523\pi$
$240$	3.04308	−	6.33414i	0.196430	−	0.408867i
$241$	−13.2360	−	11.1063i	−0.852603	−	0.715419i	0.107758	−	0.994177i	$-0.465633\pi$
$241$	−13.2360	−	11.1063i	−0.852603	−	0.715419i	−0.960361	+	0.278758i	$0.910077\pi$
$242$	−1.51302	+	2.62063i	−0.0972609	+	0.168461i
$243$	14.4842	−	5.76275i	0.929159	−	0.369680i
$244$	−9.89391			−0.633393
$245$	−3.89465	−	10.0286i	−0.248820	−	0.640704i
$246$	1.40403	+	2.05522i	0.0895180	+	0.131036i
$247$	−2.54928	−	14.4577i	−0.162207	−	0.919921i
$248$	0.848350	+	4.81123i	0.0538703	+	0.305513i
$249$	−0.905250	+	9.13262i	−0.0573679	+	0.578756i
$250$	−4.36827	−	3.66541i	−0.276274	−	0.231821i
$251$	−3.32513	+	5.75929i	−0.209880	+	0.363523i	−0.951677	−	0.307102i	$-0.900641\pi$
$251$	−3.32513	+	5.75929i	−0.209880	+	0.363523i	0.741796	+	0.670625i	$0.233974\pi$
$252$	−5.75967	−	12.7620i	−0.362825	−	0.803930i
$253$	−3.14546	−	5.44809i	−0.197753	−	0.342518i
$254$	0.247120	−	1.40149i	0.0155057	−	0.0879371i
$255$	−13.5570	−	3.80069i	−0.848970	−	0.238009i
$256$	−0.265146	−	0.0965051i	−0.0165716	−	0.00603157i
$257$	−4.56803	+	3.83304i	−0.284946	+	0.239098i	−0.774046	−	0.633130i	$-0.781770\pi$
$257$	−4.56803	+	3.83304i	−0.284946	+	0.239098i	0.489100	+	0.872228i	$0.337325\pi$
$258$	−5.15830	−	1.44613i	−0.321142	−	0.0900319i
$259$	−0.706398	−	0.986252i	−0.0438935	−	0.0612827i
$260$	8.52508	+	14.7659i	0.528703	+	0.915741i
$261$	−0.653582	+	28.3291i	−0.0404557	+	1.75353i
$262$	−1.10695	−	1.91729i	−0.0683875	−	0.118451i
$263$	−1.90757	+	10.8184i	−0.117626	+	0.667089i	0.867791	+	0.496930i	$0.165539\pi$
$263$	−1.90757	+	10.8184i	−0.117626	+	0.667089i	−0.985417	+	0.170159i	$0.945572\pi$
$264$	−0.682316	+	6.88355i	−0.0419936	+	0.423653i
$265$	−11.3219	+	9.50023i	−0.695501	+	0.583594i
$266$	−0.229549	+	2.99142i	−0.0140746	+	0.183416i
$267$	31.0429	−	2.35548i	1.89980	−	0.144153i
$268$	15.0265	−	5.46918i	0.917887	−	0.334084i
$269$	6.36322	−	11.0214i	0.387972	−	0.671988i	−0.604204	−	0.796829i	$-0.706509\pi$
$269$	6.36322	−	11.0214i	0.387972	−	0.671988i	0.992177	+	0.124841i	$0.0398422\pi$
$270$	3.77968	−	0.873826i	0.230024	−	0.0531793i
$271$	8.08647	+	14.0062i	0.491218	+	0.850815i	0.999949	−	0.0101110i	$-0.00321849\pi$
$271$	8.08647	+	14.0062i	0.491218	+	0.850815i	−0.508731	+	0.860926i	$0.669885\pi$
$272$	−2.42455	+	13.7503i	−0.147010	+	0.833736i
$273$	28.3775	+	5.02867i	1.71748	+	0.304349i
$274$	−2.19513	−	0.798961i	−0.132612	−	0.0482670i
$275$	−5.41426	−	1.97063i	−0.326492	−	0.118833i
$276$	7.14996	+	5.13036i	0.430377	+	0.308811i
$277$	3.29339	−	18.6778i	0.197881	−	1.12224i	−0.710375	−	0.703823i	$-0.751475\pi$
$277$	3.29339	−	18.6778i	0.197881	−	1.12224i	0.908256	−	0.418414i	$-0.137414\pi$
$278$	−1.47344			−0.0883710
$279$	5.29263	−	6.01989i	0.316862	−	0.360401i
$280$	−2.00091	−	7.16070i	−0.119577	−	0.427933i
$281$	2.90607	+	2.43848i	0.173361	+	0.145467i	0.725340	−	0.688391i	$-0.241683\pi$
$281$	2.90607	+	2.43848i	0.173361	+	0.145467i	−0.551979	+	0.833858i	$0.686127\pi$
$282$	5.39294	+	1.51191i	0.321145	+	0.0900328i
$283$	30.2958	+	11.0268i	1.80090	+	0.655474i	0.998257	+	0.0590144i	$0.0187958\pi$
$283$	30.2958	+	11.0268i	1.80090	+	0.655474i	0.802643	+	0.596460i	$0.203426\pi$
$284$	4.71809	+	1.71724i	0.279967	+	0.101900i
$285$	5.98338	+	1.67744i	0.354425	+	0.0993629i
$286$	−5.11157	−	4.28912i	−0.302254	−	0.253621i
$287$	−7.58130	−	1.94486i	−0.447510	−	0.114802i
$288$	−4.74549	−	14.0374i	−0.279631	−	0.827162i
$289$	10.9750			0.645591
$290$	−1.22455	+	6.94477i	−0.0719081	+	0.407811i
$291$	19.5735	+	14.0447i	1.14742	+	0.823316i
$292$	9.06057	+	3.29778i	0.530230	+	0.192988i
$293$	1.19797	+	0.436026i	0.0699863	+	0.0254729i	0.376776	−	0.926304i	$-0.377033\pi$
$293$	1.19797	+	0.436026i	0.0699863	+	0.0254729i	−0.306790	+	0.951777i	$0.599255\pi$
$294$	−5.36207	−	2.43651i	−0.312722	−	0.142100i
$295$	2.61175	−	14.8120i	0.152062	−	0.862385i
$296$	−0.419194	−	0.726066i	−0.0243652	−	0.0422017i
$297$	9.51647	−	6.18421i	0.552202	−	0.358844i
$298$	−3.61777	+	6.26616i	−0.209572	+	0.362989i
$299$	−17.0211	+	6.19518i	−0.984357	+	0.358277i
$300$	8.03679	−	0.609816i	0.464004	−	0.0352078i
$301$	15.1905	−	7.28198i	0.875568	−	0.419727i
$302$	−3.56736	+	2.99337i	−0.205279	+	0.172249i
$303$	−2.48578	+	25.0778i	−0.142805	+	1.44068i
$304$	1.07008	−	6.06872i	0.0613733	−	0.348065i
$305$	4.31002	+	7.46518i	0.246791	+	0.427455i
$306$	−6.76242	+	3.69900i	−0.386582	+	0.211458i
$307$	−6.90602	−	11.9616i	−0.394147	−	0.682683i	0.598845	−	0.800865i	$-0.295627\pi$
$307$	−6.90602	−	11.9616i	−0.394147	−	0.682683i	−0.992992	+	0.118182i	$0.962293\pi$
$308$	−5.93586	−	8.28747i	−0.338227	−	0.472223i
$309$	2.70965	+	0.759649i	0.154147	+	0.0432149i
$310$	1.52810	−	1.28223i	0.0867903	−	0.0728257i
$311$	22.3094	+	8.11995i	1.26505	+	0.460440i	0.885460	−	0.464715i	$-0.153843\pi$
$311$	22.3094	+	8.11995i	1.26505	+	0.460440i	0.379589	+	0.925155i	$0.376065\pi$
$312$	19.1776	+	5.37645i	1.08572	+	0.304381i
$313$	1.96616	−	11.1506i	0.111134	−	0.630271i	−0.877458	−	0.479653i	$-0.840763\pi$
$313$	1.96616	−	11.1506i	0.111134	−	0.630271i	0.988592	−	0.150618i	$-0.0481264\pi$
$314$	2.26489	+	3.92290i	0.127815	+	0.221382i
$315$	−7.12016	+	9.90522i	−0.401176	+	0.558096i
$316$	−2.82231	+	4.88838i	−0.158767	+	0.274993i
$317$	−6.97317	−	5.85118i	−0.391652	−	0.328635i	0.425604	−	0.904909i	$-0.360062\pi$
$317$	−6.97317	−	5.85118i	−0.391652	−	0.328635i	−0.817256	+	0.576274i	$0.804506\pi$
$318$	−0.798114	+	8.05178i	−0.0447560	+	0.451521i
$319$	3.58250	+	20.3174i	0.200582	+	1.13756i
$320$	0.768692	+	4.35947i	0.0429712	+	0.243702i
$321$	9.88864	+	14.4749i	0.551930	+	0.807912i
$322$	3.68401	−	0.361996i	0.205302	−	0.0201732i
$323$	−12.3468			−0.686995
$324$	−8.56374	+	13.3685i	−0.475764	+	0.742694i
$325$	−8.29492	+	14.3672i	−0.460119	+	0.796950i
$326$	−6.09326	−	5.11286i	−0.337475	−	0.283175i
$327$	−3.70348	+	7.70874i	−0.204803	+	0.426294i
$328$	−5.08284	−	1.85000i	−0.280653	−	0.102149i
$329$	−15.8815	+	7.61323i	−0.875577	+	0.419731i
$330$	2.57339	−	1.16405i	0.141660	−	0.0640788i
$331$	1.07979	+	0.906048i	0.0593504	+	0.0498009i	0.671980	−	0.740569i	$-0.265444\pi$
$331$	1.07979	+	0.906048i	0.0593504	+	0.0498009i	−0.612630	+	0.790370i	$0.709888\pi$
$332$	−4.67339	−	8.09456i	−0.256486	−	0.444246i
$333$	−0.500159	+	1.28141i	−0.0274086	+	0.0702209i
$334$	0.166905	−	0.289087i	0.00913262	−	0.0158182i
$335$	−10.6725	−	8.95529i	−0.583101	−	0.489280i
$336$	10.4713	+	6.05755i	0.571259	+	0.330466i
$337$	−4.68879	−	26.5914i	−0.255414	−	1.44853i	−0.795007	−	0.606601i	$-0.792533\pi$
$337$	−4.68879	−	26.5914i	−0.255414	−	1.44853i	0.539592	−	0.841926i	$-0.318578\pi$
$338$	−9.88021	+	8.29048i	−0.537413	+	0.450943i
$339$	6.07288	−	5.93439i	0.329833	−	0.322312i
$340$	13.4748	−	4.90442i	0.730773	−	0.265980i
$341$	2.91795	−	5.05404i	0.158016	−	0.273691i
$342$	2.98460	−	1.63256i	0.161389	−	0.0882785i
$343$	17.7265	−	5.36404i	0.957138	−	0.289631i
$344$	10.9399	−	3.98180i	0.589840	−	0.214684i
$345$	0.756277	−	7.62971i	0.0407166	−	0.410770i
$346$	−0.696786	−	3.95167i	−0.0374594	−	0.212443i
$347$	−5.02217	+	4.21410i	−0.269604	+	0.226225i	−0.767559	−	0.640978i	$-0.778529\pi$
$347$	−5.02217	+	4.21410i	−0.269604	+	0.226225i	0.497955	+	0.867203i	$0.334084\pi$
$348$	−16.2795	−	23.8299i	−0.872674	−	1.27741i
$349$	−1.35955	+	7.71038i	−0.0727749	+	0.412727i	0.926556	+	0.376156i	$0.122754\pi$
$349$	−1.35955	+	7.71038i	−0.0727749	+	0.412727i	−0.999331	+	0.0365706i	$0.988357\pi$
$350$	2.37161	−	2.42282i	0.126768	−	0.129505i
$351$	−12.7777	−	30.0767i	−0.682021	−	1.60537i
$352$	−5.39415	−	9.34294i	−0.287509	−	0.497980i
$353$	−24.6564	−	20.6891i	−1.31233	−	1.10117i	−0.987872	−	0.155271i	$-0.950375\pi$
$353$	−24.6564	−	20.6891i	−1.31233	−	1.10117i	−0.324454	−	0.945902i	$-0.605180\pi$
$354$	−4.64471	−	6.79889i	−0.246863	−	0.361357i
$355$	−0.759612	−	4.30798i	−0.0403160	−	0.228644i
$356$	−24.2889	+	20.3808i	−1.28731	+	1.08018i
$357$	8.30927	−	22.7691i	0.439773	−	1.20507i
$358$	10.9506	−	3.98568i	0.578755	−	0.210650i
$359$	15.2489			0.804807			0.402403	−	0.915462i	$-0.368175\pi$
$359$	15.2489			0.804807			0.402403	+	0.915462i	$0.368175\pi$
$360$	−5.56653	+	6.33143i	−0.293382	+	0.333696i
$361$	−13.5507			−0.713196
$362$	0.192056	−	1.08921i	0.0100943	−	0.0572474i
$363$	−7.71684	+	7.54086i	−0.405029	+	0.395792i
$364$	−26.4676	+	12.6879i	−1.38728	+	0.665028i
$365$	−1.45875	−	8.27299i	−0.0763545	−	0.433028i
$366$	4.54389	+	1.27388i	0.237513	+	0.0665867i
$367$	11.6333	−	4.23418i	0.607254	−	0.221023i	−0.0200471	−	0.999799i	$-0.506382\pi$
$367$	11.6333	−	4.23418i	0.607254	−	0.221023i	0.627301	+	0.778777i	$0.284159\pi$
$368$	−7.60327			−0.396348
$369$	2.84218	+	8.40733i	0.147958	+	0.437668i
$370$	−0.171163	+	0.296462i	−0.00889832	+	0.0154123i
$371$	−14.8153	−	20.6847i	−0.769173	−	1.07390i
$372$	−0.805256	+	8.12383i	−0.0417506	+	0.421201i
$373$	−21.9719	−	7.99711i	−1.13766	−	0.414075i	−0.296593	−	0.955004i	$-0.595850\pi$
$373$	−21.9719	−	7.99711i	−1.13766	−	0.414075i	−0.841068	+	0.540929i	$0.818073\pi$
$374$	−4.29895	+	3.60724i	−0.222293	+	0.186526i
$375$	−11.4692	−	16.7885i	−0.592265	−	0.866954i
$376$	−11.4375	+	4.16292i	−0.589846	+	0.214686i
$377$	59.4026			3.05939
$378$	1.00204	+	6.60267i	0.0515392	+	0.339605i
$379$	0.0616475			0.00316662			0.00158331	−	0.999999i	$-0.499496\pi$
$379$	0.0616475			0.00316662			0.00158331	+	0.999999i	$0.499496\pi$
$380$	−5.94711	+	2.16457i	−0.305080	+	0.111040i
$381$	2.19733	−	4.57372i	0.112573	−	0.234319i
$382$	−6.68999	+	5.61357i	−0.342289	+	0.287215i
$383$	1.50770	+	0.548758i	0.0770398	+	0.0280402i	0.380253	−	0.924883i	$-0.375837\pi$
$383$	1.50770	+	0.548758i	0.0770398	+	0.0280402i	−0.303213	+	0.952923i	$0.598059\pi$
$384$	15.8707	+	11.3878i	0.809899	+	0.581132i
$385$	−3.66728	+	8.08896i	−0.186902	+	0.412252i
$386$	−0.0228475	+	0.0395731i	−0.00116291	+	0.00201422i
$387$	−16.3175	−	9.92965i	−0.829466	−	0.504753i
$388$	−24.5357			−1.24561
$389$	13.0227	−	4.73988i	0.660278	−	0.240322i	0.00992168	−	0.999951i	$-0.496842\pi$
$389$	13.0227	−	4.73988i	0.660278	−	0.240322i	0.650356	+	0.759629i	$0.274620\pi$
$390$	−2.01408	−	7.87904i	−0.101987	−	0.398971i
$391$	2.64533	+	15.0024i	0.133780	+	0.758705i
$392$	12.5544	−	2.49129i	0.634095	−	0.125829i
$393$	−1.95498	−	7.64785i	−0.0986158	−	0.385783i
$394$	−2.04383	+	11.5911i	−0.102967	+	0.583952i
$395$	4.91785			0.247444
$396$	−4.20284	+	10.7677i	−0.211200	+	0.541097i
$397$	−6.08479			−0.305387			−0.152693	−	0.988274i	$-0.548795\pi$
$397$	−6.08479			−0.305387			−0.152693	+	0.988274i	$0.548795\pi$
$398$	−5.21478	+	1.89803i	−0.261393	+	0.0951394i
$399$	−3.66731	+	10.0492i	−0.183595	+	0.503088i
$400$	−5.33450	+	4.47618i	−0.266725	+	0.223809i
$401$	4.07713	+	23.1226i	0.203602	+	1.15469i	0.899624	+	0.436665i	$0.143840\pi$
$401$	4.07713	+	23.1226i	0.203602	+	1.15469i	−0.696022	+	0.718020i	$0.745048\pi$
$402$	−7.60526	+	0.577072i	−0.379316	+	0.0287818i
$403$	−12.8721	−	10.8010i	−0.641207	−	0.538037i
$404$	−12.8330	−	22.2274i	−0.638464	−	1.10585i
$405$	13.8174	+	0.637903i	0.686592	+	0.0316977i
$406$	−11.7590	−	3.01658i	−0.583589	−	0.149710i
$407$	−0.173908	+	0.986279i	−0.00862028	+	0.0488881i
$408$	7.25375	−	15.0986i	0.359114	−	0.747492i
$409$	−1.39144	+	1.16755i	−0.0688021	+	0.0577319i	−0.676540	−	0.736406i	$-0.736522\pi$
$409$	−1.39144	+	1.16755i	−0.0688021	+	0.0577319i	0.607738	+	0.794138i	$0.292077\pi$
$410$	0.383517	+	2.17503i	0.0189405	+	0.107417i
$411$	−6.76729	−	4.85578i	−0.333806	−	0.239518i
$412$	−2.69322	+	0.980253i	−0.132686	+	0.0482936i
$413$	25.0798	+	6.43382i	1.23410	+	0.316588i
$414$	−2.62315	−	3.27676i	−0.128921	−	0.161044i
$415$	−4.07168	+	7.05236i	−0.199871	+	0.346187i
$416$	−29.1896	+	10.6241i	−1.43114	+	0.520891i
$417$	−5.05859	−	1.41818i	−0.247720	−	0.0694483i
$418$	1.89734	−	1.59206i	0.0928022	−	0.0778703i
$419$	0.303043	+	1.71864i	0.0148046	+	0.0839611i	0.991315	−	0.131510i	$-0.0419825\pi$
$419$	0.303043	+	1.71864i	0.0148046	+	0.0839611i	−0.976510	+	0.215471i	$0.930871\pi$
$420$	0.0105960	−	12.4240i	0.000517034	−	0.606227i
$421$	10.8495	+	9.10383i	0.528773	+	0.443693i	0.867678	−	0.497127i	$-0.165612\pi$
$421$	10.8495	+	9.10383i	0.528773	+	0.443693i	−0.338904	+	0.940821i	$0.610056\pi$
$422$	5.96491	−	10.3315i	0.290367	−	0.502931i
$423$	17.0598	+	10.3813i	0.829475	+	0.504758i
$424$	−8.79178	−	15.2278i	−0.426966	−	0.739527i
$425$	10.6882	+	8.96844i	0.518452	+	0.435033i
$426$	−1.94574	−	1.39614i	−0.0942712	−	0.0676430i
$427$	−13.3812	+	6.41463i	−0.647562	+	0.310426i
$428$	−16.7771	−	6.10637i	−0.810953	−	0.295163i
$429$	−13.4208	−	19.6452i	−0.647960	−	0.948480i
$430$	−3.64146	−	3.05554i	−0.175607	−	0.147351i
$431$	5.63358	−	9.75765i	0.271360	−	0.470009i	−0.697850	−	0.716244i	$-0.745860\pi$
$431$	5.63358	−	9.75765i	0.271360	−	0.470009i	0.969210	+	0.246234i	$0.0791933\pi$
$432$	−0.722084	−	13.6979i	−0.0347413	−	0.659043i
$433$	11.4819			0.551785			0.275892	−	0.961189i	$-0.411027\pi$
$433$	11.4819			0.551785			0.275892	+	0.961189i	$0.411027\pi$
$434$	1.99960	+	2.79178i	0.0959837	+	0.134010i
$435$	−10.8884	+	22.6641i	−0.522060	+	1.08666i
$436$	−1.51249	−	8.57777i	−0.0724352	−	0.410801i
$437$	−1.16752	−	6.62134i	−0.0558501	−	0.316741i
$438$	−3.73657	−	2.68113i	−0.178540	−	0.128109i
$439$	13.2011	+	11.0771i	0.630056	+	0.528680i	0.900946	−	0.433930i	$-0.142874\pi$
$439$	13.2011	+	11.0771i	0.630056	+	0.528680i	−0.270890	+	0.962610i	$0.587318\pi$
$440$	−3.06896	+	5.31559i	−0.146307	+	0.253411i
$441$	−16.0639	−	13.5260i	−0.764947	−	0.644093i
$442$	8.07917	+	13.9935i	0.384287	+	0.665605i
$443$	6.23573	−	35.3646i	0.296268	−	1.68022i	−0.365734	−	0.930719i	$-0.619182\pi$
$443$	6.23573	−	35.3646i	0.296268	−	1.68022i	0.662003	−	0.749502i	$-0.269707\pi$
$444$	−0.346963	−	1.35731i	−0.0164661	−	0.0644152i
$445$	25.9586	+	9.44815i	1.23055	+	0.447885i
$446$	5.83512	−	4.89625i	0.276301	−	0.231844i
$447$	−18.4516	+	18.0308i	−0.872732	+	0.852830i
$448$	−7.58401	+	0.745216i	−0.358311	+	0.0352082i
$449$	8.11520	+	14.0559i	0.382980	+	0.663341i	0.991487	−	0.130208i	$-0.0415645\pi$
$449$	8.11520	+	14.0559i	0.382980	+	0.663341i	−0.608507	+	0.793549i	$0.708231\pi$
$450$	−3.76950	−	0.754702i	−0.177696	−	0.0355770i
$451$	3.23068	+	5.59570i	0.152127	+	0.263491i
$452$	−1.50166	+	8.51635i	−0.0706322	+	0.400575i
$453$	−15.1285	+	6.84326i	−0.710801	+	0.321524i
$454$	0.903747	−	0.758334i	0.0424150	−	0.0355904i
$455$	21.1032	+	14.4432i	0.989334	+	0.677108i
$456$	−3.20145	+	6.66378i	−0.149922	+	0.312060i
$457$	−16.9019	+	6.15181i	−0.790640	+	0.287769i	−0.705602	−	0.708608i	$-0.749323\pi$
$457$	−16.9019	+	6.15181i	−0.790640	+	0.287769i	−0.0850377	+	0.996378i	$0.527101\pi$
$458$	−0.172035	+	0.297973i	−0.00803866	+	0.0139234i
$459$	−26.7769	+	6.19057i	−1.24984	+	0.288951i
$460$	3.90432	+	6.76247i	0.182040	+	0.315302i
$461$	6.39959	−	36.2939i	0.298059	−	1.69037i	−0.356445	−	0.934316i	$-0.616011\pi$
$461$	6.39959	−	36.2939i	0.298059	−	1.69037i	0.654504	−	0.756059i	$-0.272878\pi$
$462$	1.65907	+	4.57038i	0.0771870	+	0.212634i
$463$	31.3099	+	11.3959i	1.45509	+	0.529611i	0.944009	−	0.329920i	$-0.107022\pi$
$463$	31.3099	+	11.3959i	1.45509	+	0.529611i	0.511084	+	0.859531i	$0.329244\pi$
$464$	23.4309	+	8.52815i	1.08775	+	0.395910i
$465$	6.48040	−	2.93135i	0.300521	−	0.135938i
$466$	0.0200431	−	0.113670i	0.000928477	−	0.00526566i
$467$	−26.2715			−1.21570			−0.607850	−	0.794052i	$-0.707968\pi$
$467$	−26.2715			−1.21570			−0.607850	+	0.794052i	$0.707968\pi$
$468$	28.4312	+	17.3012i	1.31423	+	0.799746i
$469$	16.7769	−	17.1392i	0.774686	−	0.791413i
$470$	3.80710	+	3.19453i	0.175608	+	0.147353i
$471$	4.00002	+	15.6480i	0.184311	+	0.721022i
$472$	16.8146	+	6.12002i	0.773955	+	0.281697i
$473$	−13.0682	−	4.75644i	−0.600878	−	0.218702i
$474$	1.92557	−	1.88166i	0.0884446	−	0.0864276i
$475$	−4.71724	−	3.95823i	−0.216442	−	0.181616i
$476$	6.64334	+	23.7746i	0.304497	+	1.08971i
$477$	−10.4899	+	26.8751i	−0.480297	+	1.23053i
$478$	−1.00958			−0.0461772
$479$	1.33725	−	7.58393i	0.0611006	−	0.346519i	−0.938897	−	0.344199i	$-0.888151\pi$
$479$	1.33725	−	7.58393i	0.0611006	−	0.346519i	0.999997	−	0.00231964i	$-0.000738365\pi$
$480$	1.29694	−	13.0842i	0.0591970	−	0.597210i
$481$	2.70971	+	0.986255i	0.123552	+	0.0449694i
$482$	−7.88716	−	2.87069i	−0.359250	−	0.130756i
$483$	12.9963	+	2.30303i	0.591353	+	0.104792i
$484$	1.90817	−	10.8218i	0.0867350	−	0.491899i
$485$	10.6883	+	18.5128i	0.485333	+	0.840621i
$486$	5.65424	−	5.03702i	0.256482	−	0.228484i
$487$	−14.0607	+	24.3538i	−0.637150	+	1.10358i	0.348906	+	0.937158i	$0.386553\pi$
$487$	−14.0607	+	24.3538i	−0.637150	+	1.10358i	−0.986055	+	0.166418i	$0.946780\pi$
$488$	−9.63685	+	3.50753i	−0.436240	+	0.158778i
$489$	−15.9982	−	23.4181i	−0.723465	−	1.05900i
$490$	−3.44402	−	3.93076i	−0.155585	−	0.177574i
$491$	29.8391	−	25.0380i	1.34662	−	1.12995i	0.366747	−	0.930321i	$-0.380471\pi$
$491$	29.8391	−	25.0380i	1.34662	−	1.12995i	0.979872	−	0.199627i	$-0.0639730\pi$
$492$	−7.34368	−	5.26936i	−0.331079	−	0.237561i
$493$	8.67527	−	49.1999i	0.390714	−	2.21585i
$494$	−3.56575	−	6.17606i	−0.160431	−	0.277874i
$495$	9.95532	−	1.51953i	0.447459	−	0.0682978i
$496$	−3.52667	−	6.10837i	−0.158352	−	0.274274i
$497$	7.49442	−	0.736413i	0.336171	−	0.0330327i
$498$	1.10411	+	4.31924i	0.0494761	+	0.193550i
$499$	−11.3677	+	9.53865i	−0.508889	+	0.427008i	−0.860738	−	0.509048i	$-0.829997\pi$
$499$	−11.3677	+	9.53865i	−0.508889	+	0.427008i	0.351849	+	0.936057i	$0.385553\pi$
$500$	19.4586	+	7.08236i	0.870217	+	0.316733i
$501$	0.851260	−	0.831847i	0.0380315	−	0.0371642i
$502$	−0.560973	+	3.18144i	−0.0250375	+	0.141994i
$503$	−13.9372	−	24.1400i	−0.621430	−	1.07635i	−0.989220	−	0.146439i	$-0.953219\pi$
$503$	−13.9372	−	24.1400i	−0.621430	−	1.07635i	0.367790	−	0.929909i	$-0.380114\pi$
$504$	−10.1343	−	10.3885i	−0.451419	−	0.462742i
$505$	−11.1807	+	19.3655i	−0.497534	+	0.861755i
$506$	−2.34100	−	1.96433i	−0.104070	−	0.0873251i
$507$	−41.9002	+	18.9532i	−1.86085	+	0.841739i
$508$	0.897385	+	5.08932i	0.0398150	+	0.225802i
$509$	−4.32896	−	24.5508i	−0.191878	−	1.08819i	−0.916795	−	0.399357i	$-0.869233\pi$
$509$	−4.32896	−	24.5508i	−0.191878	−	1.08819i	0.724918	−	0.688836i	$-0.241878\pi$
$510$	−6.81991	+	0.517482i	−0.301991	+	0.0229145i
$511$	14.3922	−	1.41420i	0.636674	−	0.0625605i
$512$	−22.6925			−1.00288
$513$	11.8180	−	2.73222i	0.521778	−	0.120630i
$514$	−1.44837	+	2.50865i	−0.0638848	+	0.110652i
$515$	1.91285	+	1.60507i	0.0842904	+	0.0707281i
$516$	19.3981	−	1.47189i	0.853956	−	0.0647966i
$517$	13.6627	+	4.97280i	0.600884	+	0.218704i
$518$	−0.486315	−	0.332838i	−0.0213675	−	0.0146241i
$519$	1.41126	−	14.2375i	0.0619473	−	0.624956i
$520$	13.5383	+	11.3600i	0.593693	+	0.498168i
$521$	−5.35420	−	9.27374i	−0.234572	−	0.406290i	0.724576	−	0.689194i	$-0.242035\pi$
$521$	−5.35420	−	9.27374i	−0.234572	−	0.406290i	−0.959148	+	0.282904i	$0.908702\pi$
$522$	4.40837	+	13.0402i	0.192949	+	0.570754i
$523$	3.36993	−	5.83689i	0.147357	−	0.255229i	−0.782893	−	0.622156i	$-0.786257\pi$
$523$	3.36993	−	5.83689i	0.147357	−	0.255229i	0.930250	+	0.366927i	$0.119590\pi$
$524$	6.15860	+	5.16768i	0.269040	+	0.225751i
$525$	10.4741	−	6.03534i	0.457128	−	0.263404i
$526$	0.926646	+	5.25527i	0.0404037	+	0.229141i
$527$	−10.8258	+	9.08388i	−0.471577	+	0.395700i
$528$	−2.47334	−	9.67567i	−0.107638	−	0.421079i
$529$	13.8176	−	5.02919i	0.600765	−	0.218661i
$530$	−3.58980	+	6.21771i	−0.155931	+	0.270080i
$531$	−9.40226	−	27.8124i	−0.408024	−	1.20695i
$532$	−2.93204	−	10.4929i	−0.127120	−	0.454927i
$533$	17.4823	−	6.36304i	0.757243	−	0.275614i
$534$	13.7791	−	6.23283i	0.596278	−	0.269721i
$535$	2.70112	+	15.3188i	0.116779	+	0.662289i
$536$	12.6971	−	10.6542i	0.548433	−	0.460190i
$537$	41.4315	−	3.14375i	1.78790	−	0.135663i
$538$	1.07352	−	6.08824i	0.0462828	−	0.262483i
$539$	−13.4012	−	7.36008i	−0.577229	−	0.317021i
$540$	−11.8124	+	7.67619i	−0.508324	+	0.330331i
$541$	9.86926	+	17.0941i	0.424312	+	0.734931i	0.996356	−	0.0852926i	$-0.0271825\pi$
$541$	9.86926	+	17.0941i	0.424312	+	0.734931i	−0.572043	+	0.820223i	$0.693849\pi$
$542$	6.01834	+	5.04998i	0.258510	+	0.216915i
$543$	1.70772	−	3.55460i	0.0732852	−	0.152542i
$544$	4.53649	+	25.7277i	0.194500	+	1.10307i
$545$	−5.81324	+	4.87789i	−0.249012	+	0.208946i
$546$	13.7892	−	2.41928i	0.590122	−	0.103535i
$547$	−33.7755	+	12.2933i	−1.44413	+	0.525622i	−0.940947	−	0.338555i	$-0.890062\pi$
$547$	−33.7755	+	12.2933i	−1.44413	+	0.525622i	−0.503188	+	0.864177i	$0.667840\pi$
$548$	8.48291			0.362372
$549$	14.3740	+	8.74694i	0.613465	+	0.373310i
$550$	−2.79889			−0.119345
$551$	−3.82884	+	21.7144i	−0.163114	+	0.925066i
$552$	8.78297	+	2.46230i	0.373828	+	0.104803i
$553$	−0.647743	+	8.44119i	−0.0275448	+	0.358956i
$554$	−1.59984	−	9.07315i	−0.0679707	−	0.385481i
$555$	−0.872977	+	0.853068i	−0.0370558	+	0.0362107i
$556$	5.02793	−	1.83002i	0.213232	−	0.0776100i
$557$	−19.1669			−0.812127			−0.406064	−	0.913845i	$-0.633099\pi$
$557$	−19.1669			−0.812127			−0.406064	+	0.913845i	$0.633099\pi$
$558$	1.41580	−	3.62728i	0.0599355	−	0.153555i
$559$	−20.0212	+	34.6777i	−0.846806	+	1.46671i
$560$	6.25047	+	8.72671i	0.264130	+	0.368771i
$561$	−18.2310	+	8.24664i	−0.769715	+	0.348174i
$562$	1.73169	+	0.630285i	0.0730471	+	0.0265870i
$563$	−25.8828	+	21.7182i	−1.09083	+	0.915314i	−0.996775	−	0.0802526i	$-0.974427\pi$
$563$	−25.8828	+	21.7182i	−1.09083	+	0.915314i	−0.0940547	+	0.995567i	$0.529983\pi$
$564$	−20.2805	+	1.53885i	−0.853964	+	0.0647972i
$565$	7.07993	−	2.57688i	0.297855	−	0.108410i
$566$	15.6614			0.658298
$567$	−2.91484	+	23.6327i	−0.122412	+	0.992479i
$568$	5.20429			0.218367
$569$	29.9091	−	10.8860i	1.25386	−	0.456366i	0.372153	−	0.928171i	$-0.378620\pi$
$569$	29.9091	−	10.8860i	1.25386	−	0.456366i	0.881703	+	0.471805i	$0.156397\pi$
$570$	3.00998	−	0.228391i	0.126074	−	0.00956626i
$571$	12.8562	−	10.7876i	0.538013	−	0.451447i	−0.332845	−	0.942982i	$-0.608008\pi$
$571$	12.8562	−	10.7876i	0.538013	−	0.451447i	0.870858	+	0.491535i	$0.163564\pi$
$572$	22.7697	+	8.28750i	0.952050	+	0.346518i
$573$	−28.3710	+	12.8334i	−1.18522	+	0.536121i
$574$	−3.78382	+	0.371804i	−0.157934	+	0.0155188i
$575$	−3.79891	+	6.57990i	−0.158425	+	0.274401i
$576$	5.40010	+	6.74564i	0.225004	+	0.281068i
$577$	2.10159			0.0874905			0.0437453	−	0.999043i	$-0.486071\pi$
$577$	2.10159			0.0874905			0.0437453	+	0.999043i	$0.486071\pi$
$578$	5.00986	−	1.82344i	0.208383	−	0.0758451i
$579$	−0.116529	+	0.113871i	−0.00484277	+	0.00473233i
$580$	−4.44680	−	25.2191i	−0.184644	−	1.04717i
$581$	−11.5686	−	7.91767i	−0.479948	−	0.328480i
$582$	11.2683	+	3.15907i	0.467087	+	0.130948i
$583$	−3.64737	+	20.6853i	−0.151059	+	0.856696i
$584$	9.99427			0.413566
$585$	0.668801	−	28.9888i	0.0276515	−	1.19854i
$586$	0.619291			0.0255827
$587$	11.2216	−	4.08433i	0.463165	−	0.168578i	−0.0998888	−	0.994999i	$-0.531849\pi$
$587$	11.2216	−	4.08433i	0.463165	−	0.168578i	0.563054	+	0.826420i	$0.309626\pi$
$588$	21.3236	+	1.65458i	0.879369	+	0.0682337i
$589$	4.77796	−	4.00918i	0.196872	−	0.165195i
$590$	−1.26872	−	7.19525i	−0.0522322	−	0.296224i
$591$	−18.1732	+	37.8273i	−0.747546	+	1.55601i
$592$	0.927234	+	0.778042i	0.0381091	+	0.0319773i
$593$	13.9411	+	24.1467i	0.572493	+	0.991587i	0.996309	+	0.0858390i	$0.0273571\pi$
$593$	13.9411	+	24.1467i	0.572493	+	0.991587i	−0.423816	+	0.905748i	$0.639310\pi$
$594$	3.31658	−	4.40406i	0.136081	−	0.180701i
$595$	15.0445	−	15.3693i	0.616763	−	0.630081i
$596$	4.56260	−	25.8758i	0.186891	−	1.05991i
$597$	−19.7302	+	1.49709i	−0.807502	+	0.0612717i
$598$	−6.74047	+	5.65592i	−0.275638	+	0.231288i
$599$	−0.994447	−	5.63979i	−0.0406320	−	0.230436i	0.957729	−	0.287673i	$-0.0928818\pi$
$599$	−0.994447	−	5.63979i	−0.0406320	−	0.230436i	−0.998361	+	0.0572379i	$0.981771\pi$
$600$	7.61179	−	3.44312i	0.310750	−	0.140565i
$601$	−10.6243	+	3.86694i	−0.433375	+	0.157736i	−0.549490	−	0.835500i	$-0.685178\pi$
$601$	−10.6243	+	3.86694i	−0.433375	+	0.157736i	0.116115	+	0.993236i	$0.462956\pi$
$602$	5.72428	−	5.84788i	0.233304	−	0.238342i
$603$	−26.6657	−	5.33881i	−1.08591	−	0.217413i
$604$	8.45541	−	14.6452i	0.344046	−	0.595905i
$605$	−8.99651	+	3.27446i	−0.365760	+	0.133126i
$606$	3.03183	+	11.8605i	0.123160	+	0.481799i
$607$	29.2992	−	24.5850i	1.18922	−	0.997873i	0.189347	−	0.981910i	$-0.439363\pi$
$607$	29.2992	−	24.5850i	1.18922	−	0.997873i	0.999873	−	0.0159631i	$-0.00508144\pi$
$608$	−2.00218	−	11.3549i	−0.0811992	−	0.460504i
$609$	−37.4674	−	21.6744i	−1.51826	−	0.878292i
$610$	3.20772	+	2.69160i	0.129877	+	0.108980i
$611$	20.9319	−	36.2551i	0.846814	−	1.46673i
$612$	18.4817	−	21.0213i	0.747080	−	0.849736i
$613$	−9.64658	−	16.7084i	−0.389622	−	0.674845i	0.602777	−	0.797910i	$-0.294061\pi$
$613$	−9.64658	−	16.7084i	−0.389622	−	0.674845i	−0.992399	+	0.123065i	$0.960728\pi$
$614$	−5.13979	−	4.31279i	−0.207425	−	0.174050i
$615$	−0.776768	+	7.83643i	−0.0313223	+	0.315995i
$616$	−8.71966	−	5.96781i	−0.351325	−	0.240450i
$617$	−22.5923	−	8.22291i	−0.909531	−	0.331042i	−0.155465	−	0.987841i	$-0.549688\pi$
$617$	−22.5923	−	8.22291i	−0.909531	−	0.331042i	−0.754065	+	0.656799i	$0.771910\pi$
$618$	1.36311	−	0.103430i	0.0548321	−	0.00416056i
$619$	28.4470	+	23.8699i	1.14338	+	0.959412i	0.999544	−	0.0301893i	$-0.00961101\pi$
$619$	28.4470	+	23.8699i	1.14338	+	0.959412i	0.143838	+	0.989601i	$0.454055\pi$
$620$	−3.62192	+	6.27336i	−0.145460	+	0.251944i
$621$	−5.85191	−	13.7745i	−0.234829	−	0.552752i
$622$	11.5328			0.462424
$623$	−19.6362	+	43.3118i	−0.786709	+	1.73525i
$624$	−28.6727	+	2.17563i	−1.14783	+	0.0870948i
$625$	−0.842477	−	4.77792i	−0.0336991	−	0.191117i
$626$	−0.955107	−	5.41668i	−0.0381737	−	0.216494i
$627$	8.04629	−	3.63967i	0.321338	−	0.145354i
$628$	−12.6009	−	10.5734i	−0.502831	−	0.421925i
$629$	1.21259	−	2.10027i	0.0483492	−	0.0837433i
$630$	−1.60450	+	5.70448i	−0.0639248	+	0.227272i
$631$	20.4388	+	35.4011i	0.813656	+	1.40929i	0.910289	+	0.413974i	$0.135859\pi$
$631$	20.4388	+	35.4011i	0.813656	+	1.40929i	−0.0966327	+	0.995320i	$0.530807\pi$
$632$	−1.01598	+	5.76192i	−0.0404136	+	0.229197i
$633$	30.4227	−	29.7289i	1.20919	−	1.18162i
$634$	−4.15523	−	1.51238i	−0.165025	−	0.0600643i
$635$	3.44909	−	2.89413i	0.136873	−	0.114850i
$636$	−7.27687	−	28.4669i	−0.288547	−	1.12879i
$637$	−27.5704	+	34.3200i	−1.09238	+	1.35981i
$638$	5.01095	+	8.67921i	0.198385	+	0.343613i
$639$	−5.33631	−	6.66596i	−0.211101	−	0.263701i
$640$	8.66638	+	15.0106i	0.342569	+	0.593347i
$641$	2.30656	−	13.0811i	0.0911036	−	0.516674i	−0.904768	−	0.425904i	$-0.859956\pi$
$641$	2.30656	−	13.0811i	0.0911036	−	0.516674i	0.995872	−	0.0907701i	$-0.0289328\pi$
$642$	6.91887	+	4.96454i	0.273066	+	0.195935i
$643$	10.9753	−	9.20939i	0.432825	−	0.363183i	−0.400192	−	0.916431i	$-0.631056\pi$
$643$	10.9753	−	9.20939i	0.432825	−	0.363183i	0.833016	+	0.553248i	$0.186612\pi$
$644$	−12.1216	+	5.81082i	−0.477659	+	0.228978i
$645$	−9.56087	−	13.9951i	−0.376459	−	0.551058i
$646$	−5.63604	+	2.05135i	−0.221747	+	0.0807094i
$647$	−2.12844	+	3.68657i	−0.0836777	+	0.144934i	−0.904827	−	0.425779i	$-0.860000\pi$
$647$	−2.12844	+	3.68657i	−0.0836777	+	0.144934i	0.821149	+	0.570713i	$0.193333\pi$
$648$	−3.60193	+	16.0571i	−0.141497	+	0.630783i
$649$	−10.6874	−	18.5112i	−0.419519	−	0.726628i
$650$	−1.39941	+	7.93646i	−0.0548895	+	0.311294i
$651$	4.17793	+	11.5093i	0.163746	+	0.451085i
$652$	27.1427	+	9.87913i	1.06299	+	0.386897i
$653$	11.2063	+	4.07877i	0.438538	+	0.159615i	0.551848	−	0.833945i	$-0.313923\pi$
$653$	11.2063	+	4.07877i	0.438538	+	0.159615i	−0.113310	+	0.993560i	$0.536145\pi$
$654$	−0.409791	+	4.13418i	−0.0160241	+	0.161659i
$655$	1.21630	−	6.89797i	0.0475247	−	0.269526i
$656$	7.80928			0.304901
$657$	−10.2478	−	12.8012i	−0.399804	−	0.499424i
$658$	−5.98466	+	6.11389i	−0.233306	+	0.238344i
$659$	23.1573	+	19.4313i	0.902082	+	0.756936i	0.970596	−	0.240714i	$-0.0773815\pi$
$659$	23.1573	+	19.4313i	0.902082	+	0.756936i	−0.0685145	+	0.997650i	$0.521826\pi$
$660$	−7.33562	+	7.16833i	−0.285539	+	0.279027i
$661$	−47.1756	−	17.1705i	−1.83492	−	0.667855i	−0.991419	−	0.130723i	$-0.958270\pi$
$661$	−47.1756	−	17.1705i	−1.83492	−	0.667855i	−0.843498	−	0.537132i	$-0.819508\pi$
$662$	0.643432	+	0.234190i	0.0250077	+	0.00910206i
$663$	14.2686	+	55.8186i	0.554148	+	2.16782i
$664$	−7.42160	−	6.22746i	−0.288014	−	0.241672i
$665$	−6.63990	+	6.78327i	−0.257484	+	0.263044i
$666$	−0.0154122	+	0.668034i	−0.000597213	+	0.0258858i
$667$	27.2052			1.05339
$668$	−0.210494	+	1.19377i	−0.00814426	+	0.0461884i
$669$	24.7457	−	11.1935i	0.956723	−	0.432765i
$670$	−6.35963	−	2.31471i	−0.245694	−	0.0894252i
$671$	11.5117	+	4.18991i	0.444403	+	0.161750i
$672$	22.2874	+	3.94947i	0.859755	+	0.152354i
$673$	−6.51850	+	36.9682i	−0.251270	+	1.42502i	0.554200	+	0.832384i	$0.313024\pi$
$673$	−6.51850	+	36.9682i	−0.251270	+	1.42502i	−0.805470	+	0.592637i	$0.798087\pi$
$674$	−6.55834	−	11.3594i	−0.252618	−	0.437547i
$675$	−12.2150	−	6.21916i	−0.470157	−	0.239376i
$676$	23.4182	−	40.5615i	0.900700	−	1.56006i
$677$	14.4836	−	5.27159i	0.556649	−	0.202604i	−0.0483491	−	0.998831i	$-0.515396\pi$
$677$	14.4836	−	5.27159i	0.556649	−	0.202604i	0.604998	+	0.796227i	$0.293174\pi$
$678$	1.78617	−	3.71789i	0.0685974	−	0.142785i
$679$	−33.1838	+	15.9075i	−1.27348	+	0.610475i
$680$	11.3860	−	9.55399i	0.436633	−	0.366379i
$681$	3.83263	−	1.73365i	0.146867	−	0.0664337i
$682$	0.492279	−	2.79185i	0.0188503	−	0.106906i
$683$	−5.51899	−	9.55917i	−0.211178	−	0.365771i	0.740905	−	0.671610i	$-0.234397\pi$
$683$	−5.51899	−	9.55917i	−0.211178	−	0.365771i	−0.952084	+	0.305838i	$0.901063\pi$
$684$	−8.15694	+	9.27778i	−0.311888	+	0.354745i
$685$	−3.69536	−	6.40054i	−0.141192	−	0.244552i
$686$	7.20052	−	5.39371i	0.274917	−	0.205933i
$687$	−0.877425	+	0.857416i	−0.0334759	+	0.0327125i
$688$	−12.8757	+	10.8040i	−0.490883	+	0.411899i
$689$	56.8309	+	20.6848i	2.16508	+	0.788026i
$690$	−0.922408	−	3.60844i	−0.0351155	−	0.137371i
$691$	7.63632	−	43.3077i	0.290499	−	1.64750i	−0.394454	−	0.918916i	$-0.629066\pi$
$691$	7.63632	−	43.3077i	0.290499	−	1.64750i	0.684953	−	0.728587i	$-0.259823\pi$
$692$	7.28568	+	12.6192i	0.276960	+	0.479709i
$693$	1.29694	+	17.2878i	0.0492667	+	0.656711i
$694$	−1.59236	+	2.75804i	−0.0604451	+	0.104694i
$695$	−3.57107	−	2.99649i	−0.135458	−	0.113663i
$696$	−24.3046	−	17.4394i	−0.921262	−	0.661039i
$697$	−2.71700	−	15.4089i	−0.102914	−	0.583654i
$698$	0.660432	+	3.74549i	0.0249977	+	0.141769i
$699$	0.178218	−	0.370959i	0.00674083	−	0.0140310i
$700$	−5.08367	+	11.2131i	−0.192145	+	0.423816i
$701$	−38.0205			−1.43601			−0.718007	−	0.696036i	$-0.754945\pi$
$701$	−38.0205			−1.43601			−0.718007	+	0.696036i	$0.754945\pi$
$702$	−10.8298	−	11.6064i	−0.408743	−	0.438055i
$703$	−0.535179	+	0.926957i	−0.0201847	+	0.0349609i
$704$	4.81925	+	4.04383i	0.181632	+	0.152408i
$705$	9.99577	+	14.6317i	0.376463	+	0.551064i
$706$	−14.6925	−	5.34762i	−0.552958	−	0.201260i
$707$	−31.7671	−	21.7416i	−1.19472	−	0.817679i
$708$	24.2937	+	17.4316i	0.913014	+	0.655121i
$709$	31.1106	+	26.1049i	1.16838	+	0.980391i	0.999986	−	0.00532808i	$-0.00169599\pi$
$709$	31.1106	+	26.1049i	1.16838	+	0.980391i	0.168399	+	0.985719i	$0.446140\pi$
$710$	−1.06249	−	1.84029i	−0.0398746	−	0.0690648i
$711$	8.42195	−	4.60675i	0.315848	−	0.172767i
$712$	−16.4325	+	28.4620i	−0.615836	+	1.06666i
$713$	−5.89518	−	4.94664i	−0.220776	−	0.185253i
$714$	0.0100418	−	11.7741i	0.000375805	−	0.440635i
$715$	−3.66592	−	20.7905i	−0.137098	−	0.777520i
$716$	−32.4172	+	27.2013i	−1.21149	+	1.01656i
$717$	−3.46609	−	0.971717i	−0.129443	−	0.0362894i
$718$	6.96078	−	2.53352i	0.259774	−	0.0945500i
$719$	−1.79288	+	3.10536i	−0.0668631	+	0.115810i	−0.897519	−	0.440976i	$-0.854632\pi$
$719$	−1.79288	+	3.10536i	−0.0668631	+	0.115810i	0.830656	+	0.556786i	$0.187966\pi$
$720$	4.42559	−	11.3384i	0.164932	−	0.422557i
$721$	−3.00696	+	3.07189i	−0.111985	+	0.114403i
$722$	−6.18560	+	2.25137i	−0.230204	+	0.0837874i
$723$	−24.3151	−	17.4470i	−0.904288	−	0.648860i
$724$	0.697429	+	3.95531i	0.0259197	+	0.146998i
$725$	19.0873	−	16.0162i	0.708886	−	0.594826i
$726$	−2.26969	+	4.72434i	−0.0842362	+	0.175337i
$727$	1.66588	−	9.44768i	0.0617841	−	0.350395i	−0.938207	−	0.346076i	$-0.887514\pi$
$727$	1.66588	−	9.44768i	0.0617841	−	0.350395i	0.999991	−	0.00431931i	$-0.00137488\pi$
$728$	−21.2819	+	21.7414i	−0.788758	+	0.805790i
$729$	24.2602	−	11.8509i	0.898525	−	0.438921i
$730$	−2.04040	−	3.53407i	−0.0755185	−	0.130802i
$731$	25.7977	+	21.6468i	0.954163	+	0.800637i
$732$	−17.0876	+	1.29658i	−0.631577	+	0.0479229i
$733$	−5.85559	−	33.2087i	−0.216281	−	1.22659i	−0.878669	−	0.477431i	$-0.841568\pi$
$733$	−5.85559	−	33.2087i	−0.216281	−	1.22659i	0.662388	−	0.749161i	$-0.269543\pi$
$734$	4.60686	−	3.86562i	0.170042	−	0.142683i
$735$	−8.04063	−	16.8099i	−0.296583	−	0.620042i
$736$	−13.3682	+	4.86564i	−0.492760	+	0.179350i
$737$	−19.7996			−0.729326
$738$	2.69422	+	3.36554i	0.0991757	+	0.123887i
$739$	−10.1081			−0.371833			−0.185916	−	0.982566i	$-0.559525\pi$
$739$	−10.1081			−0.371833			−0.185916	+	0.982566i	$0.559525\pi$
$740$	0.215864	−	1.22423i	0.00793532	−	0.0450034i
$741$	−6.29748	−	24.6356i	−0.231344	−	0.905012i
$742$	−10.1995	−	6.98062i	−0.374435	−	0.256267i
$743$	0.817980	+	4.63899i	0.0300088	+	0.170188i	0.996129	−	0.0879046i	$-0.0280171\pi$
$743$	0.817980	+	4.63899i	0.0300088	+	0.170188i	−0.966120	+	0.258093i	$0.916906\pi$
$744$	2.09567	+	8.19823i	0.0768312	+	0.300562i
$745$	−21.5114	+	7.82952i	−0.788118	+	0.286851i
$746$	−11.3583			−0.415859
$747$	−0.366632	+	15.8914i	−0.0134144	+	0.581438i
$748$	10.1894	−	17.6486i	0.372562	−	0.645296i
$749$	−26.6495	+	2.61862i	−0.973752	+	0.0956824i
$750$	−8.02472	−	5.75803i	−0.293021	−	0.210254i
$751$	−13.7464	−	5.00327i	−0.501612	−	0.182572i	0.0788067	−	0.996890i	$-0.474889\pi$
$751$	−13.7464	−	5.00327i	−0.501612	−	0.182572i	−0.580419	+	0.814318i	$0.697111\pi$
$752$	13.4614	−	11.2955i	0.490887	−	0.411903i
$753$	−4.98804	+	10.3825i	−0.181774	+	0.378361i
$754$	27.1159	−	9.86939i	0.987504	−	0.359422i
$755$	−14.7335			−0.536207
$756$	−11.6199	−	21.2863i	−0.422611	−	0.774174i
$757$	50.4233			1.83266			0.916332	−	0.400419i	$-0.131135\pi$
$757$	50.4233			1.83266			0.916332	+	0.400419i	$0.131135\pi$
$758$	0.0281407	−	0.0102424i	0.00102212	−	0.000372020i
$759$	−6.14643	−	8.99711i	−0.223101	−	0.326574i
$760$	−5.02523	+	4.21666i	−0.182284	+	0.152955i
$761$	−46.3273	−	16.8618i	−1.67936	−	0.611239i	−0.686142	−	0.727468i	$-0.740697\pi$
$761$	−46.3273	−	16.8618i	−1.67936	−	0.611239i	−0.993222	+	0.116229i	$0.962919\pi$
$762$	0.243135	−	2.45287i	0.00880786	−	0.0888582i
$763$	−7.60691	−	10.6205i	−0.275389	−	0.384489i
$764$	15.8567	−	27.4646i	0.573675	−	0.993634i
$765$	−23.9121	−	4.78751i	−0.864545	−	0.173093i
$766$	0.779404			0.0281610
$767$	−57.8334	+	21.0496i	−2.08824	+	0.760059i
$768$	−0.470576	−	0.131926i	−0.0169805	−	0.00476046i
$769$	5.95324	+	33.7625i	0.214679	+	1.21751i	0.881462	+	0.472255i	$0.156560\pi$
$769$	5.95324	+	33.7625i	0.214679	+	1.21751i	−0.666783	+	0.745252i	$0.732329\pi$
$770$	−0.330097	+	4.30173i	−0.0118959	+	0.155023i
$771$	−7.38708	+	7.21861i	−0.266039	+	0.259972i
$772$	0.0288145	−	0.163415i	0.00103706	−	0.00588143i
$773$	15.3215			0.551075			0.275537	−	0.961290i	$-0.411144\pi$
$773$	15.3215			0.551075			0.275537	+	0.961290i	$0.411144\pi$
$774$	−9.09834	−	1.82160i	−0.327033	−	0.0654761i
$775$	−7.04827			−0.253181
$776$	−23.8983	+	8.69825i	−0.857897	+	0.312249i
$777$	−1.34926	−	1.61077i	−0.0484043	−	0.0577861i
$778$	5.15707	−	4.32730i	0.184890	−	0.155141i
$779$	1.19915	+	6.80073i	0.0429641	+	0.243662i
$780$	16.6586	+	24.3847i	0.596473	+	0.873114i
$781$	−4.76232	−	3.99606i	−0.170409	−	0.142990i
$782$	3.70010	+	6.40876i	0.132315	+	0.229177i
$783$	2.58368	+	49.0125i	0.0923332	+	1.75156i
$784$	−15.8021	+	9.57912i	−0.564362	+	0.342111i
$785$	−2.48862	+	14.1137i	−0.0888228	+	0.503739i
$786$	−2.16305	−	3.16626i	−0.0771535	−	0.112937i
$787$	−2.60259	+	2.18383i	−0.0927723	+	0.0778452i	−0.687994	−	0.725716i	$-0.741509\pi$
$787$	−2.60259	+	2.18383i	−0.0927723	+	0.0778452i	0.595222	+	0.803561i	$0.297064\pi$
$788$	−7.42190	−	42.0917i	−0.264394	−	1.49946i
$789$	−1.87681	+	18.9342i	−0.0668162	+	0.674076i
$790$	2.24489	−	0.817073i	0.0798696	−	0.0290701i
$791$	3.49055	+	12.4917i	0.124110	+	0.444153i
$792$	−0.276343	+	11.9779i	−0.00981941	+	0.425616i
$793$	17.6365	−	30.5473i	0.626289	−	1.08476i
$794$	−2.77757	+	1.01095i	−0.0985722	+	0.0358773i
$795$	−18.3090	+	17.8914i	−0.649352	+	0.634544i
$796$	15.4374	−	12.9536i	0.547166	−	0.459127i
$797$	−2.86495	−	16.2480i	−0.101482	−	0.575532i	−0.992567	−	0.121697i	$-0.961167\pi$
$797$	−2.86495	−	16.2480i	−0.101482	−	0.575532i	0.891086	−	0.453835i	$-0.149945\pi$
$798$	−0.00443196	+	5.19652i	−0.000156890	+	0.183955i
$799$	−26.9712	−	22.6315i	−0.954172	−	0.800645i
$800$	−6.51475	+	11.2839i	−0.230331	+	0.398945i
$801$	53.3052	−	8.13623i	1.88345	−	0.287480i
$802$	5.70280	+	9.87753i	0.201373	+	0.348788i
$803$	−9.14551	−	7.67400i	−0.322738	−	0.270809i
$804$	25.2353	−	11.4149i	0.889979	−	0.402574i
$805$	9.66485	+	6.61470i	0.340641	+	0.233138i
$806$	−7.67037	−	2.79178i	−0.270177	−	0.0983364i
$807$	9.54550	−	19.8688i	0.336017	−	0.699416i
$808$	−20.3795	−	17.1004i	−0.716947	−	0.601590i
$809$	10.8360	−	18.7686i	0.380975	−	0.659868i	−0.610227	−	0.792227i	$-0.708922\pi$
$809$	10.8360	−	18.7686i	0.380975	−	0.659868i	0.991202	+	0.132359i	$0.0422552\pi$
$810$	6.41331	−	2.00449i	0.225341	−	0.0704307i
$811$	−23.1731			−0.813716			−0.406858	−	0.913491i	$-0.633376\pi$
$811$	−23.1731			−0.813716			−0.406858	+	0.913491i	$0.633376\pi$
$812$	43.8727	−	4.31100i	1.53963	−	0.151286i
$813$	15.8015	+	23.1302i	0.554183	+	0.811210i
$814$	0.0844797	+	0.479108i	0.00296101	+	0.0167927i
$815$	−4.36997	−	24.7833i	−0.153073	−	0.868123i
$816$	−2.38546	+	24.0657i	−0.0835078	+	0.842469i
$817$	−11.3858	−	9.55386i	−0.398340	−	0.334247i
$818$	−0.441177	+	0.764142i	−0.0154254	+	0.0267176i
$819$	49.6693	+	4.96614i	1.73559	+	0.173531i
$820$	−4.01010	−	6.94570i	−0.140039	−	0.242554i
$821$	−4.26899	+	24.2107i	−0.148989	+	0.844958i	0.815089	+	0.579336i	$0.196688\pi$
$821$	−4.26899	+	24.2107i	−0.148989	+	0.844958i	−0.964077	+	0.265622i	$0.914423\pi$
$822$	−3.89587	−	1.09221i	−0.135884	−	0.0380951i
$823$	−20.6513	−	7.51646i	−0.719860	−	0.262007i	−0.0439934	−	0.999032i	$-0.514008\pi$
$823$	−20.6513	−	7.51646i	−0.719860	−	0.262007i	−0.675866	+	0.737024i	$0.736230\pi$
$824$	−2.27574	+	1.90957i	−0.0792790	+	0.0665230i
$825$	−9.60914	−	2.69392i	−0.334547	−	0.0937902i
$826$	12.5173	−	1.22997i	0.435533	−	0.0427961i
$827$	−18.1708	−	31.4727i	−0.631860	−	1.09441i	−0.987171	−	0.159666i	$-0.948958\pi$
$827$	−18.1708	−	31.4727i	−0.631860	−	1.09441i	0.355311	−	0.934748i	$-0.384375\pi$
$828$	13.0209	+	7.92358i	0.452508	+	0.275363i
$829$	−19.4445	−	33.6789i	−0.675336	−	1.16972i	−0.976371	−	0.216103i	$-0.930665\pi$
$829$	−19.4445	−	33.6789i	−0.675336	−	1.16972i	0.301035	−	0.953613i	$-0.402668\pi$
$830$	−0.686922	+	3.89573i	−0.0238434	+	0.135223i
$831$	3.24029	−	32.6897i	0.112404	−	1.13399i
$832$	13.8761	−	11.6435i	0.481068	−	0.403664i
$833$	24.3989	+	27.8472i	0.845373	+	0.964850i
$834$	−2.54476	+	0.193091i	−0.0881177	+	0.00668620i
$835$	0.992423	−	0.361213i	0.0343442	−	0.0125003i
$836$	−4.49711	+	7.78922i	−0.155536	+	0.269396i
$837$	8.35194	−	11.0905i	0.288685	−	0.383342i
$838$	0.423874	+	0.734172i	0.0146425	+	0.0253615i
$839$	−1.84595	+	10.4689i	−0.0637293	+	0.361427i	0.936221	+	0.351413i	$0.114299\pi$
$839$	−1.84595	+	10.4689i	−0.0637293	+	0.361427i	−0.999950	+	0.0100140i	$0.996812\pi$
$840$	−4.39414	−	12.1049i	−0.151612	−	0.417660i
$841$	−56.5868	−	20.5959i	−1.95127	−	0.710204i
$842$	6.46511	+	2.35311i	0.222802	+	0.0810934i
$843$	5.33858	+	3.83063i	0.183871	+	0.131934i
$844$	−7.52273	+	42.6635i	−0.258943	+	1.46854i
$845$	−40.8061			−1.40377
$846$	9.51220	+	1.90446i	0.327036	+	0.0654767i
$847$	−4.43546	−	15.8732i	−0.152404	−	0.545411i
$848$	19.4469	+	16.3179i	0.667810	+	0.560359i
$849$	53.7685	+	15.0740i	1.84533	+	0.517338i
$850$	6.36896	+	2.31811i	0.218454	+	0.0795106i
$851$	1.24099	+	0.451685i	0.0425407	+	0.0154836i
$852$	8.37359	+	2.34753i	0.286874	+	0.0804251i
$853$	23.3312	+	19.5772i	0.798847	+	0.670312i	0.947918	−	0.318515i	$-0.103184\pi$
$853$	23.3312	+	19.5772i	0.798847	+	0.670312i	−0.149071	+	0.988826i	$0.547628\pi$
$854$	−5.04246	+	5.15134i	−0.172549	+	0.176275i
$855$	10.5536	+	2.11297i	0.360927	+	0.0722621i
$856$	−18.5060			−0.632523
$857$	−5.66650	+	32.1363i	−0.193564	+	1.09776i	0.720885	+	0.693054i	$0.243735\pi$
$857$	−5.66650	+	32.1363i	−0.193564	+	1.09776i	−0.914449	+	0.404701i	$0.867376\pi$
$858$	−9.39021	−	6.73782i	−0.320576	−	0.230025i
$859$	22.2453	+	8.09664i	0.759001	+	0.276254i	0.692388	−	0.721525i	$-0.256559\pi$
$859$	22.2453	+	8.09664i	0.759001	+	0.276254i	0.0666128	+	0.997779i	$0.478781\pi$
$860$	16.2210	+	5.90397i	0.553132	+	0.201324i
$861$	−13.3484	−	2.36543i	−0.454913	−	0.0806136i
$862$	0.950426	−	5.39013i	0.0323716	−	0.183589i
$863$	12.7899	+	22.1527i	0.435372	+	0.754087i	0.997326	−	0.0730817i	$-0.0232834\pi$
$863$	12.7899	+	22.1527i	0.435372	+	0.754087i	−0.561954	+	0.827169i	$0.689950\pi$
$864$	−10.0355	−	23.6219i	−0.341413	−	0.803634i
$865$	6.34763	−	10.9944i	0.215826	−	0.373821i
$866$	5.24123	−	1.90765i	0.178104	−	0.0648246i
$867$	18.9549	−	1.43826i	0.643741	−	0.0488458i
$868$	−10.2908	−	7.04309i	−0.349292	−	0.239058i
$869$	5.35393	−	4.49248i	0.181620	−	0.152397i
$870$	−1.20481	+	12.1547i	−0.0408468	+	0.412083i
$871$	−9.89953	+	56.1430i	−0.335433	+	1.90233i
$872$	−4.51413	−	7.81870i	−0.152868	−	0.264775i
$873$	35.6457	+	21.6914i	1.20642	+	0.734142i
$874$	−1.63304	−	2.82851i	−0.0552385	−	0.0956759i
$875$	30.9090	−	3.03716i	1.04491	−	0.102675i
$876$	16.0806	+	4.50818i	0.543311	+	0.152317i
$877$	10.0205	−	8.40817i	0.338367	−	0.283924i	−0.457732	−	0.889090i	$-0.651338\pi$
$877$	10.0205	−	8.40817i	0.338367	−	0.283924i	0.796099	+	0.605167i	$0.206894\pi$
$878$	7.86642	+	2.86314i	0.265479	+	0.0966264i
$879$	2.12614	+	0.596063i	0.0717130	+	0.0201047i
$880$	1.53880	−	8.72695i	0.0518729	−	0.294186i
$881$	−10.1622	−	17.6014i	−0.342373	−	0.593007i	0.642500	−	0.766285i	$-0.277897\pi$
$881$	−10.1622	−	17.6014i	−0.342373	−	0.593007i	−0.984873	+	0.173279i	$0.944564\pi$
$882$	−9.58006	−	3.50537i	−0.322577	−	0.118032i
$883$	−11.6233	+	20.1321i	−0.391155	+	0.677500i	−0.992602	−	0.121412i	$-0.961258\pi$
$883$	−11.6233	+	20.1321i	−0.391155	+	0.677500i	0.601447	+	0.798913i	$0.294591\pi$
$884$	−44.9492	−	37.7169i	−1.51181	−	1.26856i
$885$	2.56964	−	25.9238i	0.0863773	−	0.871419i
$886$	−3.02915	−	17.1792i	−0.101766	−	0.577145i
$887$	−3.42234	−	19.4090i	−0.114911	−	0.651692i	−0.986794	−	0.161978i	$-0.948213\pi$
$887$	−3.42234	−	19.4090i	−0.114911	−	0.651692i	0.871884	−	0.489713i	$-0.162899\pi$
$888$	−0.819134	−	1.19904i	−0.0274883	−	0.0402373i
$889$	4.51330	+	6.30134i	0.151371	+	0.211340i
$890$	13.4193			0.449814
$891$	15.6253	−	11.9278i	0.523469	−	0.399596i
$892$	−13.8305	+	23.9551i	−0.463078	+	0.802075i
$893$	11.9038	+	9.98844i	0.398344	+	0.334251i
$894$	−5.42703	+	11.2963i	−0.181507	+	0.377805i
$895$	34.6457	+	12.6100i	1.15808	+	0.421505i
$896$	−26.9063	+	12.8982i	−0.898875	+	0.430899i
$897$	−28.5851	+	12.9302i	−0.954428	+	0.431727i
$898$	6.03972	+	5.06792i	0.201548	+	0.169119i
$899$	12.6187	+	21.8563i	0.420858	+	0.728948i
$900$	13.8003	−	2.10641i	0.460010	−	0.0702137i
$901$	25.4317	−	44.0491i	0.847254	−	1.46749i
$902$	2.40443	+	2.01755i	0.0800586	+	0.0671771i
$903$	25.2811	−	14.5673i	0.841302	−	0.484769i
$904$	1.55652	+	8.82744i	0.0517689	+	0.293596i
$905$	2.68056	−	2.24925i	0.0891047	−	0.0747677i
$906$	−5.76887	+	5.63731i	−0.191658	+	0.187287i
$907$	12.3320	−	4.48847i	0.409477	−	0.149037i	−0.129065	−	0.991636i	$-0.541198\pi$
$907$	12.3320	−	4.48847i	0.409477	−	0.149037i	0.538542	+	0.842599i	$0.318975\pi$
$908$	−2.14207	+	3.71018i	−0.0710872	+	0.123127i
$909$	−1.00676	+	43.6374i	−0.0333921	+	1.44736i
$910$	12.0328	+	3.08682i	0.398883	+	0.102327i
$911$	13.1943	−	4.80232i	0.437145	−	0.159108i	−0.114067	−	0.993473i	$-0.536388\pi$
$911$	13.1943	−	4.80232i	0.437145	−	0.159108i	0.551212	+	0.834365i	$0.314166\pi$
$912$	1.05283	−	10.6214i	0.0348625	−	0.351711i
$913$	2.00963	+	11.3972i	0.0665092	+	0.377192i
$914$	−6.69327	+	5.61632i	−0.221394	+	0.185771i
$915$	8.42208	+	12.3282i	0.278425	+	0.407557i
$916$	0.216964	−	1.23046i	0.00716870	−	0.0406557i
$917$	11.6797	+	2.99625i	0.385699	+	0.0989448i
$918$	−11.1945	+	7.27469i	−0.369475	+	0.240100i
$919$	−23.0349	−	39.8977i	−0.759852	−	1.31610i	−0.942926	−	0.333003i	$-0.891938\pi$
$919$	−23.0349	−	39.8977i	−0.759852	−	1.31610i	0.183074	−	0.983099i	$-0.441395\pi$
$920$	6.20027	+	5.20264i	0.204417	+	0.171526i
$921$	−13.4948	−	19.7536i	−0.444670	−	0.650905i
$922$	−3.10875	−	17.6306i	−0.102381	−	0.580633i
$923$	−13.7122	+	11.5059i	−0.451343	+	0.378722i
$924$	−11.3378	−	13.5353i	−0.372986	−	0.445279i
$925$	1.13660	−	0.413690i	0.0373713	−	0.0136020i
$926$	16.1856			0.531892
$927$	4.77935	+	0.956885i	0.156974	+	0.0314282i
$928$	46.6542			1.53150
$929$	−3.55949	+	20.1869i	−0.116783	+	0.662310i	0.869069	+	0.494691i	$0.164719\pi$
$929$	−3.55949	+	20.1869i	−0.116783	+	0.662310i	−0.985852	+	0.167619i	$0.946392\pi$
$930$	2.47113	−	2.41477i	0.0810315	−	0.0791836i
$931$	−10.7685	−	12.2904i	−0.352923	−	0.402802i
$932$	0.0727839	+	0.412778i	0.00238412	+	0.0135210i
$933$	39.5943	+	11.1003i	1.29626	+	0.363406i
$934$	−11.9923	+	4.36486i	−0.392401	+	0.142822i
$935$	−17.7550			−0.580650
$936$	33.8260	+	6.77239i	1.10564	+	0.221363i
$937$	23.3013	−	40.3591i	0.761222	−	1.31847i	−0.180999	−	0.983483i	$-0.557933\pi$
$937$	23.3013	−	40.3591i	0.761222	−	1.31847i	0.942221	−	0.334992i	$-0.108733\pi$
$938$	4.81071	−	10.6110i	0.157075	−	0.346462i
$939$	1.93446	−	19.5158i	0.0631286	−	0.636873i
$940$	−16.9589	−	6.17253i	−0.553138	−	0.201326i
$941$	−12.1406	+	10.1871i	−0.395771	+	0.332091i	−0.818856	−	0.573998i	$-0.805392\pi$
$941$	−12.1406	+	10.1871i	−0.395771	+	0.332091i	0.423085	+	0.906090i	$0.360947\pi$
$942$	4.42574	+	6.47838i	0.144199	+	0.211077i
$943$	8.00654	−	2.91414i	0.260729	−	0.0948976i
$944$	−25.8340			−0.840824
$945$	−10.9991	+	18.0403i	−0.357800	+	0.586849i
$946$	−6.75561			−0.219644
$947$	14.5676	−	5.30219i	0.473385	−	0.172298i	−0.0943002	−	0.995544i	$-0.530061\pi$
$947$	14.5676	−	5.30219i	0.473385	−	0.172298i	0.567685	+	0.823246i	$0.307839\pi$
$948$	−4.23375	+	8.81251i	−0.137506	+	0.286217i
$949$	−26.3328	+	22.0958i	−0.854799	+	0.717261i
$950$	−2.81095	−	1.02310i	−0.0911992	−	0.0331938i
$951$	−12.8100	−	9.19167i	−0.415394	−	0.298060i
$952$	14.8992	+	20.8017i	0.482884	+	0.674189i
$953$	−7.02346	+	12.1650i	−0.227512	+	0.394062i	−0.957070	−	0.289856i	$-0.906392\pi$
$953$	−7.02346	+	12.1650i	−0.227512	+	0.394062i	0.729558	+	0.683919i	$0.239726\pi$
$954$	−0.323242	+	14.0107i	−0.0104653	+	0.453613i
$955$	−27.6302			−0.894092
$956$	3.44508	−	1.25391i	0.111422	−	0.0405542i
$957$	8.84984	+	34.6204i	0.286075	+	1.11912i
$958$	−0.649601	−	3.68407i	−0.0209877	−	0.119027i
$959$	11.4729	−	5.49982i	0.370478	−	0.177598i
$960$	1.89890	+	7.42845i	0.0612867	+	0.239752i
$961$	−4.14342	+	23.4985i	−0.133659	+	0.758016i
$962$	1.40078			0.0451631
$963$	18.9754	+	23.7036i	0.611475	+	0.763837i
$964$	30.4794			0.981675
$965$	−0.135853	+	0.0494463i	−0.00437325	+	0.00159173i
$966$	6.31516	−	1.10798i	0.203187	−	0.0356487i
$967$	32.5537	−	27.3158i	1.04686	−	0.878417i	0.0540975	−	0.998536i	$-0.482772\pi$
$967$	32.5537	−	27.3158i	1.04686	−	0.878417i	0.992760	+	0.120118i	$0.0383274\pi$
$968$	−1.97787	−	11.2171i	−0.0635713	−	0.360530i
$969$	−21.3240	+	1.61803i	−0.685026	+	0.0519785i
$970$	7.95478	+	6.67485i	0.255412	+	0.214316i
$971$	−6.82904	−	11.8282i	−0.219154	−	0.379586i	0.735395	−	0.677638i	$-0.236996\pi$
$971$	−6.82904	−	11.8282i	−0.219154	−	0.379586i	−0.954550	+	0.298052i	$0.903663\pi$
$972$	−13.0384	+	24.2108i	−0.418207	+	0.776562i
$973$	5.61364	−	5.73485i	0.179965	−	0.183851i
$974$	−2.37214	+	13.4531i	−0.0760081	+	0.431064i
$975$	−12.4432	+	25.9005i	−0.398503	+	0.829478i
$976$	11.3421	−	9.51716i	0.363052	−	0.304637i
$977$	4.14125	+	23.4862i	0.132490	+	0.751390i	0.976575	+	0.215180i	$0.0690337\pi$
$977$	4.14125	+	23.4862i	0.132490	+	0.751390i	−0.844084	+	0.536211i	$0.819855\pi$
$978$	−11.1936	−	8.03183i	−0.357933	−	0.256830i
$979$	36.8913	−	13.4273i	1.17905	−	0.429139i
$980$	16.6343	+	9.13574i	0.531363	+	0.291831i
$981$	−5.38601	+	13.7990i	−0.171962	+	0.440568i
$982$	9.46096	−	16.3869i	0.301911	−	0.522926i
$983$	4.49239	−	1.63510i	0.143285	−	0.0521515i	−0.269382	−	0.963033i	$-0.586819\pi$
$983$	4.49239	−	1.63510i	0.143285	−	0.0521515i	0.412667	+	0.910882i	$0.364597\pi$
$984$	−9.02094	−	2.52902i	−0.287577	−	0.0806221i
$985$	−28.5260	+	23.9361i	−0.908913	+	0.762669i
$986$	−4.21421	−	23.9000i	−0.134208	−	0.761131i
$987$	−26.4311	+	15.2299i	−0.841310	+	0.484774i
$988$	19.8384	+	16.6464i	0.631143	+	0.529592i
$989$	−9.16930	+	15.8817i	−0.291567	+	0.505008i
$990$	4.29192	−	2.34765i	0.136406	−	0.0746132i
$991$	−4.52949	−	7.84530i	−0.143884	−	0.249214i	0.785072	−	0.619404i	$-0.212626\pi$
$991$	−4.52949	−	7.84530i	−0.143884	−	0.249214i	−0.928956	+	0.370190i	$0.879293\pi$
$992$	−10.1097	−	8.48301i	−0.320982	−	0.269336i
$993$	1.98362	+	1.42332i	0.0629482	+	0.0451677i
$994$	3.29868	−	1.58131i	0.104628	−	0.0501561i
$995$	−16.4987	−	6.00502i	−0.523043	−	0.190372i
$996$	−9.13213	−	13.3676i	−0.289363	−	0.423567i
$997$	1.50708	+	1.26459i	0.0477296	+	0.0400499i	0.666340	−	0.745648i	$-0.267860\pi$
$997$	1.50708	+	1.26459i	0.0477296	+	0.0400499i	−0.618611	+	0.785698i	$0.712304\pi$
$998$	−3.60432	+	6.24286i	−0.114093	+	0.197614i
$999$	−0.695892	+	2.27865i	−0.0220170	+	0.0720934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.13	yes	132
3.2	odd	2		567.2.w.a.235.10		132
7.2	even	3		189.2.u.a.79.10	yes	132
21.2	odd	6		567.2.u.a.478.13		132
27.13	even	9		189.2.u.a.67.10	✓	132
27.14	odd	18		567.2.u.a.172.13		132
189.121	even	9	inner	189.2.w.a.121.13	yes	132
189.149	odd	18		567.2.w.a.415.10		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.10	✓	132	27.13	even	9
189.2.u.a.79.10	yes	132	7.2	even	3
189.2.w.a.25.13	yes	132	1.1	even	1	trivial
189.2.w.a.121.13	yes	132	189.121	even	9	inner
567.2.u.a.172.13		132	27.14	odd	18
567.2.u.a.478.13		132	21.2	odd	6
567.2.w.a.235.10		132	3.2	odd	2
567.2.w.a.415.10		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)

\(f(q)\)	\(=\)	\(q+(0.456477 - 0.166144i) q^{2} +(1.72709 - 0.131048i) q^{3} +(-1.35132 + 1.13389i) q^{4} +(1.44421 + 0.525651i) q^{5} +(0.766603 - 0.346766i) q^{6} +(-1.09247 + 2.40967i) q^{7} +(-0.914231 + 1.58349i) q^{8} +(2.96565 - 0.452662i) q^{9} +O(q^{10})\)	\(q+(0.456477 - 0.166144i) q^{2} +(1.72709 - 0.131048i) q^{3} +(-1.35132 + 1.13389i) q^{4} +(1.44421 + 0.525651i) q^{5} +(0.766603 - 0.346766i) q^{6} +(-1.09247 + 2.40967i) q^{7} +(-0.914231 + 1.58349i) q^{8} +(2.96565 - 0.452662i) q^{9} +0.746585 q^{10} +(2.05246 - 0.747035i) q^{11} +(-2.18525 + 2.13542i) q^{12} +(-1.09206 - 6.19341i) q^{13} +(-0.0983346 + 1.28147i) q^{14} +(2.56317 + 0.718583i) q^{15} +(0.458402 - 2.59973i) q^{16} -5.28914 q^{17} +(1.27855 - 0.699356i) q^{18} +2.33437 q^{19} +(-2.54763 + 0.927262i) q^{20} +(-1.57101 + 4.30487i) q^{21} +(0.812787 - 0.682009i) q^{22} +(-0.500144 - 2.83646i) q^{23} +(-1.37144 + 2.85464i) q^{24} +(-2.02077 - 1.69563i) q^{25} +(-1.52750 - 2.64571i) q^{26} +(5.06262 - 1.17043i) q^{27} +(-1.25603 - 4.49498i) q^{28} +(-1.64020 + 9.30205i) q^{29} +(1.28942 - 0.0978385i) q^{30} +(2.04679 - 1.71746i) q^{31} +(-0.857698 - 4.86424i) q^{32} +(3.44688 - 1.55916i) q^{33} +(-2.41438 + 0.878761i) q^{34} +(-2.84441 + 2.90582i) q^{35} +(-3.49428 + 3.97443i) q^{36} +(-0.229261 + 0.397091i) q^{37} +(1.06559 - 0.387842i) q^{38} +(-2.69772 - 10.5534i) q^{39} +(-2.15271 + 1.80634i) q^{40} +(0.513695 + 2.91331i) q^{41} +(-0.00189857 + 2.22609i) q^{42} +(-4.87748 - 4.09269i) q^{43} +(-1.92648 + 3.33675i) q^{44} +(4.52098 + 0.905157i) q^{45} +(-0.699565 - 1.21168i) q^{46} +(5.09935 + 4.27886i) q^{47} +(0.451011 - 4.55002i) q^{48} +(-4.61302 - 5.26498i) q^{49} +(-1.20416 - 0.438277i) q^{50} +(-9.13481 + 0.693132i) q^{51} +(8.49839 + 7.13100i) q^{52} +(-4.80829 + 8.32820i) q^{53} +(2.11651 - 1.37540i) q^{54} +3.35687 q^{55} +(-2.81693 - 3.93291i) q^{56} +(4.03166 - 0.305915i) q^{57} +(0.796766 + 4.51869i) q^{58} +(-1.69936 - 9.63755i) q^{59} +(-4.27846 + 1.93532i) q^{60} +(4.29653 + 3.60521i) q^{61} +(0.648966 - 1.12404i) q^{62} +(-2.14912 + 7.64077i) q^{63} +(1.44015 + 2.49441i) q^{64} +(1.67840 - 9.51865i) q^{65} +(1.31438 - 1.28440i) q^{66} +(-8.51828 - 3.10040i) q^{67} +(7.14733 - 5.99732i) q^{68} +(-1.23550 - 4.83326i) q^{69} +(-0.815621 + 1.79902i) q^{70} +(-1.42313 - 2.46494i) q^{71} +(-1.99450 + 5.10993i) q^{72} +(-2.73297 - 4.73365i) q^{73} +(-0.0386779 + 0.219353i) q^{74} +(-3.71226 - 2.66368i) q^{75} +(-3.15448 + 2.64693i) q^{76} +(-0.442142 + 5.76187i) q^{77} +(-2.98484 - 4.36919i) q^{78} +(3.00687 - 1.09441i) q^{79} +(2.02858 - 3.51360i) q^{80} +(8.59019 - 2.68488i) q^{81} +(0.718519 + 1.24451i) q^{82} +(-0.920085 + 5.21806i) q^{83} +(-2.75833 - 7.59862i) q^{84} +(-7.63866 - 2.78025i) q^{85} +(-2.90644 - 1.05786i) q^{86} +(-1.61376 + 16.2804i) q^{87} +(-0.693498 + 3.93302i) q^{88} +17.9742 q^{89} +(2.21411 - 0.337951i) q^{90} +(16.1171 + 4.13459i) q^{91} +(3.89209 + 3.26585i) q^{92} +(3.30991 - 3.23443i) q^{93} +(3.03865 + 1.10598i) q^{94} +(3.37133 + 1.22706i) q^{95} +(-2.11877 - 8.28857i) q^{96} +(10.6549 + 8.94050i) q^{97} +(-2.98049 - 1.63692i) q^{98} +(5.74873 - 3.14452i) 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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