LMFDB - Embedded newform 162.2.g.b.103.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			103.3
Character	$\chi$	$=$	162.103
Dual form			162.2.g.b.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686242 - 0.727374i) q^{2} +(0.851057 - 1.50854i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.77668 + 0.441430i) q^{5} +(-1.68131 + 0.416189i) q^{6} +(-3.13446 - 1.57418i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.55140 - 2.56771i) q^{9} +O(q^{10})$	\(q+(-0.686242 - 0.727374i) q^{2} +(0.851057 - 1.50854i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.77668 + 0.441430i) q^{5} +(-1.68131 + 0.416189i) q^{6} +(-3.13446 - 1.57418i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.55140 - 2.56771i) q^{9} +(2.91280 + 2.44413i) q^{10} +(-1.41437 - 3.27887i) q^{11} +(1.45651 + 0.937331i) q^{12} +(6.00411 + 1.42300i) q^{13} +(1.00598 + 3.36019i) q^{14} +(-2.54825 + 6.07296i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.0237611 + 0.134756i) q^{17} +(-0.803048 + 2.89052i) q^{18} +(-0.591493 - 3.35452i) q^{19} +(-0.221089 - 3.79596i) q^{20} +(-5.04232 + 3.38874i) q^{21} +(-1.41437 + 3.27887i) q^{22} +(1.62119 - 0.814194i) q^{23} +(-0.317725 - 1.70266i) q^{24} +(9.20321 - 2.18120i) q^{25} +(-3.08522 - 5.34375i) q^{26} +(-5.19384 + 0.155090i) q^{27} +(1.75377 - 3.03762i) q^{28} +(-0.375745 + 1.25508i) q^{29} +(6.16603 - 2.31399i) q^{30} +(0.265030 + 0.174313i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-6.15002 - 0.656872i) q^{33} +(0.114324 - 0.0751919i) q^{34} +(12.5327 + 4.56154i) q^{35} +(2.65357 - 1.39948i) q^{36} +(-7.16975 + 2.60958i) q^{37} +(-2.03408 + 2.73225i) q^{38} +(7.25649 - 7.84640i) q^{39} +(-2.60936 + 2.76576i) q^{40} +(4.36125 - 4.62265i) q^{41} +(5.92513 + 1.34216i) q^{42} +(1.92691 - 2.58828i) q^{43} +(3.35556 - 1.22132i) q^{44} +(6.99262 + 9.01259i) q^{45} +(-1.70475 - 0.620480i) q^{46} +(3.99017 - 2.62437i) q^{47} +(-1.02043 + 1.39954i) q^{48} +(3.16665 + 4.25355i) q^{49} +(-7.90218 - 5.19734i) q^{50} +(0.183063 + 0.150530i) q^{51} +(-1.76970 + 5.91121i) q^{52} +(-2.78294 + 4.82020i) q^{53} +(3.67704 + 3.67143i) q^{54} +(6.78900 + 11.7589i) q^{55} +(-3.41300 + 0.808895i) q^{56} +(-5.56384 - 1.96260i) q^{57} +(1.17076 - 0.587978i) q^{58} +(1.85601 - 4.30271i) q^{59} +(-5.91452 - 2.89705i) q^{60} +(-0.784513 - 13.4696i) q^{61} +(-0.0550839 - 0.312396i) q^{62} +(0.820759 + 10.4906i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-23.3037 - 2.72382i) q^{65} +(3.74261 + 4.92414i) q^{66} +(-2.79770 - 9.34496i) q^{67} +(-0.133146 - 0.0315562i) q^{68} +(0.151481 - 3.13857i) q^{69} +(-5.28253 - 12.2463i) q^{70} +(3.05189 + 2.56084i) q^{71} +(-2.83894 - 0.969758i) q^{72} +(-10.7055 + 8.98301i) q^{73} +(6.81832 + 3.42429i) q^{74} +(4.54202 - 15.7398i) q^{75} +(3.38324 - 0.395444i) q^{76} +(-0.728272 + 12.5039i) q^{77} +(-10.6870 + 0.106345i) q^{78} +(2.36891 + 2.51090i) q^{79} +3.80239 q^{80} +(-4.18629 + 7.96712i) q^{81} -6.35527 q^{82} +(0.597161 + 0.632954i) q^{83} +(-3.08982 - 5.23083i) q^{84} +(0.0302527 - 0.519418i) q^{85} +(-3.20497 + 0.374608i) q^{86} +(1.57355 + 1.63497i) q^{87} +(-3.19108 - 1.60262i) q^{88} +(6.42404 - 5.39041i) q^{89} +(1.75689 - 11.2711i) q^{90} +(-16.5795 - 13.9119i) q^{91} +(0.718553 + 1.66579i) q^{92} +(0.488514 - 0.251459i) q^{93} +(-4.64712 - 1.10139i) q^{94} +(3.71467 + 12.4078i) q^{95} +(1.71825 - 0.218187i) q^{96} +(-6.91065 - 0.807739i) q^{97} +(0.920833 - 5.22230i) q^{98} +(-6.22494 + 8.71853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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 $

$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$2$	−0.686242	−	0.727374i	−0.485246	−	0.514331i
$3$	0.851057	−	1.50854i	0.491358	−	0.870958i
$3$	0.851057	−	1.50854i	0.491358	−	0.870958i
$4$	−0.0581448	+	0.998308i	−0.0290724	+	0.499154i
$5$	−3.77668	+	0.441430i	−1.68898	+	0.197414i	−0.905602	−	0.424129i	$-0.860580\pi$
$5$	−3.77668	+	0.441430i	−1.68898	+	0.197414i	−0.783380	+	0.621543i	$0.786506\pi$
$6$	−1.68131	+	0.416189i	−0.686390	+	0.169908i
$7$	−3.13446	−	1.57418i	−1.18471	−	0.594985i	−0.256323	−	0.966591i	$-0.582511\pi$
$7$	−3.13446	−	1.57418i	−1.18471	−	0.594985i	−0.928391	+	0.371606i	$0.878807\pi$
$8$	0.766044	−	0.642788i	0.270838	−	0.227260i
$9$	−1.55140	−	2.56771i	−0.517135	−	0.855904i
$10$	2.91280	+	2.44413i	0.921108	+	0.772901i
$11$	−1.41437	−	3.27887i	−0.426447	−	0.988616i	−0.987033	−	0.160519i	$-0.948683\pi$
$11$	−1.41437	−	3.27887i	−0.426447	−	0.988616i	0.560585	−	0.828097i	$-0.310576\pi$
$12$	1.45651	+	0.937331i	0.420457	+	0.270584i
$13$	6.00411	+	1.42300i	1.66524	+	0.394669i	0.951963	−	0.306214i	$-0.0990621\pi$
$13$	6.00411	+	1.42300i	1.66524	+	0.394669i	0.713277	+	0.700883i	$0.247210\pi$
$14$	1.00598	+	3.36019i	0.268858	+	0.898049i
$15$	−2.54825	+	6.07296i	−0.657956	+	1.56803i
$16$	−0.993238	−	0.116093i	−0.248310	−	0.0290232i
$17$	−0.0237611	+	0.134756i	−0.00576291	+	0.0326831i	−0.987554	−	0.157283i	$-0.949727\pi$
$17$	−0.0237611	+	0.134756i	−0.00576291	+	0.0326831i	0.981791	+	0.189966i	$0.0608377\pi$
$18$	−0.803048	+	2.89052i	−0.189280	+	0.681302i
$19$	−0.591493	−	3.35452i	−0.135698	−	0.769580i	−0.974371	−	0.224946i	$-0.927780\pi$
$19$	−0.591493	−	3.35452i	−0.135698	−	0.769580i	0.838674	−	0.544634i	$-0.183332\pi$
$20$	−0.221089	−	3.79596i	−0.0494371	−	0.848802i
$21$	−5.04232	+	3.38874i	−1.10033	+	0.739484i
$22$	−1.41437	+	3.27887i	−0.301544	+	0.699057i
$23$	1.62119	−	0.814194i	0.338042	−	0.169771i	−0.271677	−	0.962388i	$-0.587578\pi$
$23$	1.62119	−	0.814194i	0.338042	−	0.169771i	0.609720	+	0.792617i	$0.291282\pi$
$24$	−0.317725	−	1.70266i	−0.0648554	−	0.347554i
$25$	9.20321	−	2.18120i	1.84064	−	0.436240i
$26$	−3.08522	−	5.34375i	−0.605061	−	1.04800i
$27$	−5.19384	+	0.155090i	−0.999554	+	0.0298472i
$28$	1.75377	−	3.03762i	0.331432	−	0.574057i
$29$	−0.375745	+	1.25508i	−0.0697741	+	0.233062i	−0.985763	−	0.168143i	$-0.946223\pi$
$29$	−0.375745	+	1.25508i	−0.0697741	+	0.233062i	0.915989	+	0.401204i	$0.131408\pi$
$30$	6.16603	−	2.31399i	1.12576	−	0.422475i
$31$	0.265030	+	0.174313i	0.0476007	+	0.0313075i	0.573086	−	0.819495i	$-0.305746\pi$
$31$	0.265030	+	0.174313i	0.0476007	+	0.0313075i	−0.525486	+	0.850802i	$0.676116\pi$
$32$	0.597159	+	0.802123i	0.105564	+	0.141797i
$33$	−6.15002	−	0.656872i	−1.07058	−	0.114347i
$34$	0.114324	−	0.0751919i	0.0196064	−	0.0128953i
$35$	12.5327	+	4.56154i	2.11842	+	0.771041i
$36$	2.65357	−	1.39948i	0.442262	−	0.233247i
$37$	−7.16975	+	2.60958i	−1.17870	+	0.429012i	−0.855743	−	0.517402i	$-0.826899\pi$
$37$	−7.16975	+	2.60958i	−1.17870	+	0.429012i	−0.322958	+	0.946413i	$0.604677\pi$
$38$	−2.03408	+	2.73225i	−0.329972	+	0.443229i
$39$	7.25649	−	7.84640i	1.16197	−	1.25643i
$40$	−2.60936	+	2.76576i	−0.412576	+	0.437305i
$41$	4.36125	−	4.62265i	0.681112	−	0.721937i	−0.290929	−	0.956745i	$-0.593964\pi$
$41$	4.36125	−	4.62265i	0.681112	−	0.721937i	0.972042	+	0.234807i	$0.0754460\pi$
$42$	5.92513	+	1.34216i	0.914268	+	0.207099i
$43$	1.92691	−	2.58828i	0.293850	−	0.394710i	−0.630540	−	0.776157i	$-0.717167\pi$
$43$	1.92691	−	2.58828i	0.293850	−	0.394710i	0.924391	+	0.381447i	$0.124574\pi$
$44$	3.35556	−	1.22132i	0.505870	−	0.184121i
$45$	6.99262	+	9.01259i	1.04240	+	1.34352i
$46$	−1.70475	−	0.620480i	−0.251352	−	0.0914848i
$47$	3.99017	−	2.62437i	0.582026	−	0.382804i	−0.224085	−	0.974570i	$-0.571939\pi$
$47$	3.99017	−	2.62437i	0.582026	−	0.382804i	0.806110	+	0.591765i	$0.201569\pi$
$48$	−1.02043	+	1.39954i	−0.147287	+	0.202006i
$49$	3.16665	+	4.25355i	0.452379	+	0.607650i
$50$	−7.90218	−	5.19734i	−1.11754	−	0.735015i
$51$	0.183063	+	0.150530i	0.0256339	+	0.0210783i
$52$	−1.76970	+	5.91121i	−0.245413	+	0.819737i
$53$	−2.78294	+	4.82020i	−0.382266	+	0.662105i	−0.991386	−	0.130974i	$-0.958190\pi$
$53$	−2.78294	+	4.82020i	−0.382266	+	0.662105i	0.609119	+	0.793078i	$0.291523\pi$
$54$	3.67704	+	3.67143i	0.500381	+	0.499618i
$55$	6.78900	+	11.7589i	0.915428	+	1.58557i
$56$	−3.41300	+	0.808895i	−0.456081	+	0.108093i
$57$	−5.56384	−	1.96260i	−0.736948	−	0.259952i
$58$	1.17076	−	0.587978i	0.153728	−	0.0772053i
$59$	1.85601	−	4.30271i	0.241631	−	0.560165i	−0.753641	−	0.657286i	$-0.771704\pi$
$59$	1.85601	−	4.30271i	0.241631	−	0.560165i	0.995273	+	0.0971215i	$0.0309635\pi$
$60$	−5.91452	−	2.89705i	−0.763562	−	0.374008i
$61$	−0.784513	−	13.4696i	−0.100447	−	1.72460i	−0.553270	−	0.833002i	$-0.686620\pi$
$61$	−0.784513	−	13.4696i	−0.100447	−	1.72460i	0.452824	−	0.891600i	$-0.350417\pi$
$62$	−0.0550839	−	0.312396i	−0.00699566	−	0.0396744i
$63$	0.820759	+	10.4906i	0.103406	+	1.32169i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	−23.3037	−	2.72382i	−2.89047	−	0.337848i
$66$	3.74261	+	4.92414i	0.460683	+	0.606119i
$67$	−2.79770	−	9.34496i	−0.341793	−	1.14167i	−0.940242	−	0.340507i	$-0.889401\pi$
$67$	−2.79770	−	9.34496i	−0.341793	−	1.14167i	0.598449	−	0.801161i	$-0.295784\pi$
$68$	−0.133146	−	0.0315562i	−0.0161464	−	0.00382676i
$69$	0.151481	−	3.13857i	0.0182362	−	0.377839i
$70$	−5.28253	−	12.2463i	−0.631384	−	1.46371i
$71$	3.05189	+	2.56084i	0.362193	+	0.303916i	0.805664	−	0.592373i	$-0.201809\pi$
$71$	3.05189	+	2.56084i	0.362193	+	0.303916i	−0.443471	+	0.896289i	$0.646253\pi$
$72$	−2.83894	−	0.969758i	−0.334572	−	0.114287i
$73$	−10.7055	+	8.98301i	−1.25299	+	1.05138i	−0.256595	+	0.966519i	$0.582601\pi$
$73$	−10.7055	+	8.98301i	−1.25299	+	1.05138i	−0.996393	+	0.0848624i	$0.972955\pi$
$74$	6.81832	+	3.42429i	0.792614	+	0.398066i
$75$	4.54202	−	15.7398i	0.524468	−	1.81747i
$76$	3.38324	−	0.395444i	0.388084	−	0.0453605i
$77$	−0.728272	+	12.5039i	−0.0829942	+	1.42496i
$78$	−10.6870	+	0.106345i	−1.21006	+	0.0120412i
$79$	2.36891	+	2.51090i	0.266523	+	0.282498i	0.846789	−	0.531929i	$-0.178533\pi$
$79$	2.36891	+	2.51090i	0.266523	+	0.282498i	−0.580266	+	0.814427i	$0.697051\pi$
$80$	3.80239			0.425120
$81$	−4.18629	+	7.96712i	−0.465143	+	0.885235i
$82$	−6.35527			−0.701822
$83$	0.597161	+	0.632954i	0.0655470	+	0.0694757i	0.759317	−	0.650721i	$-0.225533\pi$
$83$	0.597161	+	0.632954i	0.0655470	+	0.0694757i	−0.693770	+	0.720196i	$0.744052\pi$
$84$	−3.08982	−	5.23083i	−0.337127	−	0.570730i
$85$	0.0302527	−	0.519418i	0.00328136	−	0.0563388i
$86$	−3.20497	+	0.374608i	−0.345601	+	0.0403950i
$87$	1.57355	+	1.63497i	0.168703	+	0.175287i
$88$	−3.19108	−	1.60262i	−0.340171	−	0.170840i
$89$	6.42404	−	5.39041i	0.680947	−	0.571382i	−0.235336	−	0.971914i	$-0.575619\pi$
$89$	6.42404	−	5.39041i	0.680947	−	0.571382i	0.916283	+	0.400532i	$0.131175\pi$
$90$	1.75689	−	11.2711i	0.185192	−	1.18807i
$91$	−16.5795	−	13.9119i	−1.73801	−	1.45836i
$92$	0.718553	+	1.66579i	0.0749143	+	0.173671i
$93$	0.488514	−	0.251459i	0.0506565	−	0.0260750i
$94$	−4.64712	−	1.10139i	−0.479314	−	0.113599i
$95$	3.71467	+	12.4078i	0.381117	+	1.27302i
$96$	1.71825	−	0.218187i	0.175368	−	0.0222686i
$97$	−6.91065	−	0.807739i	−0.701670	−	0.0820134i	−0.242225	−	0.970220i	$-0.577877\pi$
$97$	−6.91065	−	0.807739i	−0.701670	−	0.0820134i	−0.459444	+	0.888207i	$0.651951\pi$
$98$	0.920833	−	5.22230i	0.0930182	−	0.527532i
$99$	−6.22494	+	8.71853i	−0.625630	+	0.876246i
$100$	1.64239	+	9.31447i	0.164239	+	0.931447i
$101$	0.234720	+	4.03000i	0.0233556	+	0.400999i	0.989645	+	0.143540i	$0.0458485\pi$
$101$	0.234720	+	4.03000i	0.0233556	+	0.400999i	−0.966289	+	0.257460i	$0.917114\pi$
$102$	−0.0161342	−	0.236455i	−0.00159752	−	0.0234125i
$103$	0.547289	−	1.26876i	0.0539260	−	0.125015i	−0.889123	−	0.457668i	$-0.848685\pi$
$103$	0.547289	−	1.26876i	0.0539260	−	0.125015i	0.943049	+	0.332654i	$0.107944\pi$
$104$	5.51410	−	2.76928i	0.540702	−	0.271551i
$105$	17.5473	−	15.0240i	1.71245	−	1.46619i
$106$	5.41585	−	1.28358i	0.526034	−	0.124672i
$107$	7.35361	+	12.7368i	0.710900	+	1.23132i	0.964520	+	0.264011i	$0.0850456\pi$
$107$	7.35361	+	12.7368i	0.710900	+	1.23132i	−0.253619	+	0.967304i	$0.581621\pi$
$108$	0.147167	−	5.19407i	0.0141611	−	0.499799i
$109$	1.46896	−	2.54431i	0.140700	−	0.243700i	−0.787060	−	0.616876i	$-0.788398\pi$
$109$	1.46896	−	2.54431i	0.140700	−	0.243700i	0.927761	+	0.373176i	$0.121731\pi$
$110$	3.89421	−	13.0076i	0.371299	−	1.24022i
$111$	−2.16521	+	13.0368i	−0.205513	+	1.23740i
$112$	2.93051	+	1.92743i	0.276907	+	0.182125i
$113$	10.8899	+	14.6277i	1.02444	+	1.37606i	0.924551	+	0.381059i	$0.124440\pi$
$113$	10.8899	+	14.6277i	1.02444	+	1.37606i	0.0998862	+	0.994999i	$0.468152\pi$
$114$	2.39059	+	5.39380i	0.223900	+	0.505176i
$115$	−5.76332	+	3.79059i	−0.537432	+	0.353475i
$116$	−1.23110	−	0.448085i	−0.114305	−	0.0416037i
$117$	−5.66094	−	17.6245i	−0.523354	−	1.62938i
$118$	−4.40334	+	1.60269i	−0.405361	+	0.147539i
$119$	0.286608	−	0.384982i	0.0262734	−	0.0352912i
$120$	1.95155	+	6.29015i	0.178152	+	0.574209i
$121$	−1.20189	+	1.27393i	−0.109263	+	0.115812i
$122$	−9.25904	+	9.81401i	−0.838274	+	0.888519i
$123$	−3.26180	−	10.5133i	−0.294107	−	0.947950i
$124$	−0.189428	+	0.254446i	−0.0170111	+	0.0228499i
$125$	−15.9293	+	5.79781i	−1.42476	+	0.518572i
$126$	7.06733	−	7.79607i	0.629608	−	0.694529i
$127$	9.76218	+	3.55314i	0.866254	+	0.315291i	0.736649	−	0.676275i	$-0.236407\pi$
$127$	9.76218	+	3.55314i	0.866254	+	0.315291i	0.129605	+	0.991566i	$0.458629\pi$
$128$	−0.835488	+	0.549509i	−0.0738474	+	0.0485702i
$129$	−2.26463	−	5.10960i	−0.199390	−	0.449875i
$130$	14.0108	+	18.8197i	1.22883	+	1.65060i
$131$	−14.5872	−	9.59417i	−1.27449	−	0.838246i	−0.281864	−	0.959454i	$-0.590953\pi$
$131$	−14.5872	−	9.59417i	−1.27449	−	0.838246i	−0.992627	+	0.121208i	$0.961323\pi$
$132$	1.01335	−	6.10142i	0.0882010	−	0.531061i
$133$	−3.42662	+	11.4457i	−0.297126	+	0.992470i
$134$	−4.87738	+	8.44787i	−0.421341	+	0.729785i
$135$	19.5470	−	2.87844i	1.68234	−	0.247737i
$136$	0.0684173	+	0.118502i	0.00586674	+	0.0101615i
$137$	15.7191	−	3.72549i	1.34297	−	0.318290i	0.504583	−	0.863363i	$-0.331646\pi$
$137$	15.7191	−	3.72549i	1.34297	−	0.318290i	0.838388	+	0.545073i	$0.183498\pi$
$138$	−2.38686	+	2.04363i	−0.203183	+	0.173965i
$139$	14.7919	−	7.42880i	1.25464	−	0.630102i	0.307688	−	0.951487i	$-0.400445\pi$
$139$	14.7919	−	7.42880i	1.25464	−	0.630102i	0.946949	+	0.321385i	$0.104148\pi$
$140$	−5.28253	+	12.2463i	−0.446456	+	1.03500i
$141$	−0.563122	−	8.25283i	−0.0474234	−	0.695014i
$142$	−0.231647	−	3.97722i	−0.0194394	−	0.333761i
$143$	−3.82618	−	21.6993i	−0.319961	−	1.81459i
$144$	1.24282	+	2.73046i	0.103568	+	0.227538i
$145$	0.865039	−	4.90588i	0.0718376	−	0.407411i
$146$	13.8806	+	1.62241i	1.14877	+	0.134271i
$147$	9.11167	−	1.15702i	0.751518	−	0.0954291i
$148$	−2.18828	−	7.30936i	−0.179875	−	0.600825i
$149$	−5.44321	−	1.29006i	−0.445925	−	0.105686i	0.00151744	−	0.999999i	$-0.499517\pi$
$149$	−5.44321	−	1.29006i	−0.445925	−	0.105686i	−0.447443	+	0.894313i	$0.647665\pi$
$150$	−14.5656	+	7.49754i	−1.18928	+	0.612172i
$151$	4.67318	+	10.8336i	0.380298	+	0.881630i	0.995632	+	0.0933632i	$0.0297618\pi$
$151$	4.67318	+	10.8336i	0.380298	+	0.881630i	−0.615334	+	0.788266i	$0.710979\pi$
$152$	−2.60936	−	2.18951i	−0.211647	−	0.177593i
$153$	0.382877	−	0.148049i	0.0309538	−	0.0119691i
$154$	9.59481	−	8.05100i	0.773172	−	0.648768i
$155$	−1.07788	−	0.541331i	−0.0865773	−	0.0434808i
$156$	7.41120	+	7.70044i	0.593371	+	0.616529i
$157$	−4.03153	+	0.471218i	−0.321751	+	0.0376073i	−0.275436	−	0.961320i	$-0.588822\pi$
$157$	−4.03153	+	0.471218i	−0.321751	+	0.0376073i	−0.0463156	+	0.998927i	$0.514748\pi$
$158$	0.200716	−	3.44617i	0.0159681	−	0.274162i
$159$	4.90303	+	8.30045i	0.388836	+	0.658268i
$160$	−2.60936	−	2.76576i	−0.206288	−	0.218652i
$161$	−6.36325			−0.501494
$162$	8.66788	−	2.42237i	0.681013	−	0.190319i
$163$	−3.63802			−0.284951			−0.142476	−	0.989798i	$-0.545506\pi$
$163$	−3.63802			−0.284951			−0.142476	+	0.989798i	$0.545506\pi$
$164$	4.36125	+	4.62265i	0.340556	+	0.360969i
$165$	23.5166	−	0.234011i	1.83077	−	0.0182177i
$166$	0.0505971	−	0.868719i	0.00392710	−	0.0674257i
$167$	−9.37145	+	1.09537i	−0.725185	+	0.0847619i	−0.470673	−	0.882308i	$-0.655989\pi$
$167$	−9.37145	+	1.09537i	−0.725185	+	0.0847619i	−0.254512	+	0.967070i	$0.581915\pi$
$168$	−1.68440	+	5.83707i	−0.129954	+	0.450340i
$169$	22.4071	+	11.2533i	1.72363	+	0.865638i
$170$	−0.398572	+	0.334441i	−0.0305691	+	0.0256505i
$171$	−7.69580	+	6.72300i	−0.588513	+	0.514121i
$172$	2.47187	+	2.07414i	0.188478	+	0.158152i
$173$	−5.23397	−	12.1337i	−0.397931	−	0.922508i	−0.992921	−	0.118775i	$-0.962103\pi$
$173$	−5.23397	−	12.1337i	−0.397931	−	0.922508i	0.594990	−	0.803733i	$-0.297156\pi$
$174$	0.109394	−	2.26655i	0.00829312	−	0.171826i
$175$	−32.2807	−	7.65066i	−2.44019	−	0.578336i
$176$	1.02415	+	3.42090i	0.0771981	+	0.257860i
$177$	−4.91125	−	6.46172i	−0.369152	−	0.485692i
$178$	−8.32928	−	0.973553i	−0.624306	−	0.0729709i
$179$	2.39591	−	13.5879i	0.179079	−	1.01561i	−0.754251	−	0.656586i	$-0.772000\pi$
$179$	2.39591	−	13.5879i	0.179079	−	1.01561i	0.933330	−	0.359020i	$-0.116889\pi$
$180$	−9.40392	+	6.45675i	−0.700927	+	0.481258i
$181$	−1.34675	−	7.63781i	−0.100103	−	0.567714i	−0.993064	−	0.117578i	$-0.962487\pi$
$181$	−1.34675	−	7.63781i	−0.100103	−	0.567714i	0.892960	−	0.450135i	$-0.148624\pi$
$182$	1.25843	+	21.6064i	0.0932812	+	1.60158i
$183$	−20.9871	−	10.2799i	−1.55141	−	0.759912i
$184$	0.718553	−	1.66579i	0.0529724	−	0.122804i
$185$	25.9259	−	13.0205i	1.90611	−	0.957285i
$186$	−0.518143	−	0.182771i	−0.0379921	−	0.0134014i
$187$	0.475454	−	0.112685i	0.0347686	−	0.00824031i
$188$	2.38793	+	4.13601i	0.174157	+	0.301650i
$189$	16.5240	+	7.68993i	1.20194	+	0.559360i
$190$	6.47598	−	11.2167i	0.469817	−	0.813747i
$191$	−0.167520	+	0.559557i	−0.0121213	+	0.0404881i	−0.963836	−	0.266495i	$-0.914134\pi$
$191$	−0.167520	+	0.559557i	−0.0121213	+	0.0404881i	0.951715	+	0.306983i	$0.0993196\pi$
$192$	−1.33784	−	1.10008i	−0.0965503	−	0.0793917i
$193$	17.7592	+	11.6804i	1.27834	+	0.840775i	0.993053	−	0.117668i	$-0.0375420\pi$
$193$	17.7592	+	11.6804i	1.27834	+	0.840775i	0.285283	+	0.958443i	$0.407912\pi$
$194$	4.15485	+	5.58093i	0.298300	+	0.400687i
$195$	−23.9418	+	32.8366i	−1.71451	+	2.35148i
$196$	−4.43048	+	2.91397i	−0.316463	+	0.208141i
$197$	0.511789	+	0.186276i	0.0364634	+	0.0132716i	0.360187	−	0.932880i	$-0.382713\pi$
$197$	0.511789	+	0.186276i	0.0364634	+	0.0132716i	−0.323724	+	0.946152i	$0.604935\pi$
$198$	10.6134	−	1.45517i	0.754265	−	0.103414i
$199$	2.08507	−	0.758905i	0.147807	−	0.0537973i	−0.267057	−	0.963681i	$-0.586051\pi$
$199$	2.08507	−	0.758905i	0.147807	−	0.0537973i	0.414864	+	0.909883i	$0.363829\pi$
$200$	5.64802	−	7.58661i	0.399375	−	0.536454i
$201$	−16.4783	−	3.73265i	−1.16229	−	0.263281i
$202$	2.77024	−	2.93628i	0.194913	−	0.206596i
$203$	3.15347	−	3.34249i	0.221331	−	0.234597i
$204$	−0.160919	+	0.174001i	−0.0112666	+	0.0121825i
$205$	−14.4305	+	19.3835i	−1.00787	+	1.35380i
$206$	−1.29843	+	0.472592i	−0.0904662	+	0.0329270i
$207$	−4.60574	−	2.89962i	−0.320121	−	0.201537i
$208$	−5.79831	−	2.11041i	−0.402040	−	0.146331i
$209$	−10.1624	+	6.68395i	−0.702951	+	0.462338i
$210$	−22.9698	−	2.45336i	−1.58507	−	0.169298i
$211$	−2.25553	−	3.02970i	−0.155277	−	0.208573i	0.717677	−	0.696377i	$-0.245206\pi$
$211$	−2.25553	−	3.02970i	−0.155277	−	0.208573i	−0.872953	+	0.487804i	$0.837798\pi$
$212$	−4.65023	−	3.05850i	−0.319379	−	0.210059i
$213$	6.46047	−	2.42449i	0.442664	−	0.166123i
$214$	4.21808	−	14.0894i	0.288342	−	0.963129i
$215$	−6.13476	+	10.6257i	−0.418387	+	0.724668i
$216$	−3.87902	+	3.45734i	−0.263934	+	0.235242i
$217$	−0.556324	−	0.963581i	−0.0377657	−	0.0654122i
$218$	−2.85872	+	0.677529i	−0.193617	+	0.0458880i
$219$	4.44024	+	23.7948i	0.300043	+	1.60790i
$220$	−12.1337	+	6.09379i	−0.818056	+	0.410843i
$221$	−0.334422	+	0.775276i	−0.0224956	+	0.0521507i
$222$	10.9685	−	7.37146i	0.736155	−	0.494740i
$223$	−1.16390	−	19.9834i	−0.0779407	−	1.33819i	−0.779869	−	0.625943i	$-0.784714\pi$
$223$	−1.16390	−	19.9834i	−0.0779407	−	1.33819i	0.701928	−	0.712248i	$-0.252323\pi$
$224$	−0.609079	−	3.45426i	−0.0406958	−	0.230797i
$225$	−19.8786	−	20.2473i	−1.32524	−	1.34982i
$226$	3.16669	−	17.9592i	0.210645	−	1.19463i
$227$	7.26607	+	0.849281i	0.482266	+	0.0563688i	0.353753	−	0.935339i	$-0.384905\pi$
$227$	7.26607	+	0.849281i	0.482266	+	0.0563688i	0.128513	+	0.991708i	$0.458980\pi$
$228$	2.28279	−	5.44031i	0.151181	−	0.360293i
$229$	2.65299	+	8.86162i	0.175315	+	0.585592i	0.999806	+	0.0197168i	$0.00627644\pi$
$229$	2.65299	+	8.86162i	0.175315	+	0.585592i	−0.824491	+	0.565875i	$0.808538\pi$
$230$	6.71221	+	1.59082i	0.442590	+	0.104896i
$231$	18.2429	+	11.7402i	1.20030	+	0.772448i
$232$	0.518910	+	1.20297i	0.0340681	+	0.0789787i
$233$	6.59355	+	5.53265i	0.431958	+	0.362456i	0.832690	−	0.553740i	$-0.186800\pi$
$233$	6.59355	+	5.53265i	0.431958	+	0.362456i	−0.400732	+	0.916195i	$0.631244\pi$
$234$	−8.93480	+	16.2123i	−0.584086	+	1.05983i
$235$	−13.9111	+	11.6728i	−0.907460	+	0.761449i
$236$	4.18751	+	2.10305i	0.272584	+	0.136897i
$237$	5.80387	−	1.43669i	0.377002	−	0.0933227i
$238$	−0.476708	+	0.0557192i	−0.0309004	+	0.00361174i
$239$	1.65960	−	28.4943i	0.107351	−	1.84314i	−0.330155	−	0.943927i	$-0.607101\pi$
$239$	1.65960	−	28.4943i	0.107351	−	1.84314i	0.437506	−	0.899216i	$-0.355862\pi$
$240$	3.23605	−	5.73607i	0.208886	−	0.370262i
$241$	4.35262	+	4.61351i	0.280377	+	0.297182i	0.852223	−	0.523179i	$-0.175254\pi$
$241$	4.35262	+	4.61351i	0.280377	+	0.297182i	−0.571846	+	0.820361i	$0.693773\pi$
$242$	1.75141			0.112585
$243$	8.45597	+	13.0957i	0.542451	+	0.840088i
$244$	13.4924			0.863762
$245$	−13.8371	−	14.6664i	−0.884018	−	0.937005i
$246$	−5.40869	+	9.58719i	−0.344846	+	0.611257i
$247$	1.22210	−	20.9826i	0.0777602	−	1.33509i
$248$	0.315071	−	0.0368265i	0.0200070	−	0.00233848i
$249$	1.46306	−	0.362164i	0.0927174	−	0.0229512i
$250$	15.1486	+	7.60789i	0.958079	+	0.481165i
$251$	6.55985	−	5.50437i	0.414054	−	0.347433i	−0.411842	−	0.911255i	$-0.635114\pi$
$251$	6.55985	−	5.50437i	0.414054	−	0.347433i	0.825896	+	0.563823i	$0.190670\pi$
$252$	−10.5205	+	0.209398i	−0.662732	+	0.0131908i
$253$	−4.96260	−	4.16411i	−0.311996	−	0.261796i
$254$	−4.11475	−	9.53907i	−0.258183	−	0.598535i
$255$	−0.757818	−	0.487692i	−0.0474564	−	0.0305405i
$256$	0.973045	+	0.230616i	0.0608153	+	0.0144135i
$257$	−0.974583	−	3.25533i	−0.0607928	−	0.203062i	0.922198	−	0.386719i	$-0.126392\pi$
$257$	−0.974583	−	3.25533i	−0.0607928	−	0.203062i	−0.982990	+	0.183657i	$0.941206\pi$
$258$	−2.16250	+	5.15365i	−0.134632	+	0.320852i
$259$	26.5812	+	3.10690i	1.65168	+	0.193053i
$260$	4.07420	−	23.1059i	0.252671	−	1.43297i
$261$	3.80560	−	0.982324i	0.235561	−	0.0608043i
$262$	3.03182	+	17.1943i	0.187306	+	1.06227i
$263$	−0.0936222	−	1.60743i	−0.00577299	−	0.0991185i	0.994191	−	0.107632i	$-0.0343269\pi$
$263$	−0.0936222	−	1.60743i	−0.00577299	−	0.0991185i	−0.999964	+	0.00851389i	$0.997290\pi$
$264$	−5.13342	+	3.44996i	−0.315940	+	0.212331i
$265$	8.38249	−	19.4328i	0.514932	−	1.19375i
$266$	10.6768	−	5.36209i	0.654637	−	0.328771i
$267$	−2.66444	−	14.2785i	−0.163061	−	0.873829i
$268$	9.49182	−	2.24960i	0.579805	−	0.137416i
$269$	−13.8706	−	24.0246i	−0.845706	−	1.46481i	−0.885007	−	0.465578i	$-0.845846\pi$
$269$	−13.8706	−	24.0246i	−0.845706	−	1.46481i	0.0393011	−	0.999227i	$-0.487487\pi$
$270$	−15.5077	−	12.2427i	−0.943766	−	0.745064i
$271$	−15.3007	+	26.5016i	−0.929450	+	1.60985i	−0.145207	+	0.989401i	$0.546385\pi$
$271$	−15.3007	+	26.5016i	−0.929450	+	1.60985i	−0.784243	+	0.620454i	$0.786948\pi$
$272$	0.0392446	−	0.131086i	0.00237955	−	0.00794827i
$273$	−35.0968	+	13.1711i	−2.12416	+	0.797154i
$274$	−13.4969	−	8.87706i	−0.815378	−	0.536283i
$275$	−20.1686	−	27.0911i	−1.21621	−	1.63366i
$276$	3.12445	+	0.333717i	0.188070	+	0.0200874i
$277$	−1.61396	+	1.06152i	−0.0969732	+	0.0637803i	−0.597069	−	0.802190i	$-0.703668\pi$
$277$	−1.61396	+	1.06152i	−0.0969732	+	0.0637803i	0.500096	+	0.865970i	$0.333298\pi$
$278$	−15.5544	−	5.66133i	−0.932889	−	0.339544i
$279$	0.0364169	−	0.950950i	0.00218022	−	0.0569319i
$280$	12.5327	−	4.56154i	0.748974	−	0.272604i
$281$	−9.34931	+	12.5583i	−0.557733	+	0.749166i	−0.988155	−	0.153462i	$-0.950958\pi$
$281$	−9.34931	+	12.5583i	−0.557733	+	0.749166i	0.430421	+	0.902628i	$0.358365\pi$
$282$	−5.61645	+	6.07304i	−0.334455	+	0.361644i
$283$	−9.87257	+	10.4643i	−0.586863	+	0.622039i	−0.950957	−	0.309324i	$-0.899897\pi$
$283$	−9.87257	+	10.4643i	−0.586863	+	0.622039i	0.364094	+	0.931362i	$0.381379\pi$
$284$	−2.73396	+	2.89783i	−0.162231	+	0.171955i
$285$	21.8792	+	4.95605i	1.29601	+	0.293571i
$286$	−13.1578	+	17.6740i	−0.778039	+	1.04509i
$287$	−20.9470	+	7.62410i	−1.23646	+	0.450036i
$288$	1.13319	−	2.77775i	0.0667737	−	0.163680i
$289$	15.9572	+	5.80794i	0.938658	+	0.341643i
$290$	−4.16203	+	2.73741i	−0.244403	+	0.160746i
$291$	−7.09986	+	9.73757i	−0.416201	+	0.570827i
$292$	−8.34534	−	11.2097i	−0.488374	−	0.656000i
$293$	−9.37716	−	6.16746i	−0.547820	−	0.360307i	0.245229	−	0.969465i	$-0.421137\pi$
$293$	−9.37716	−	6.16746i	−0.547820	−	0.360307i	−0.793048	+	0.609159i	$0.791507\pi$
$294$	−7.09439	−	5.83359i	−0.413753	−	0.340222i
$295$	−5.11019	+	17.0692i	−0.297527	+	0.993810i
$296$	−3.81495	+	6.60768i	−0.221739	+	0.384064i
$297$	7.85451	+	16.8106i	0.455765	+	0.975447i
$298$	2.79700	+	4.84454i	0.162026	+	0.280637i
$299$	10.8924	−	2.58155i	0.629925	−	0.149295i
$300$	15.4490	+	5.44953i	0.891951	+	0.314628i
$301$	−10.1142	+	5.07956i	−0.582975	+	0.292781i
$302$	4.67318	−	10.8336i	0.268911	−	0.623406i
$303$	6.27918	+	3.07567i	0.360730	+	0.176693i
$304$	0.198057	+	3.40051i	0.0113594	+	0.195033i
$305$	8.90873	+	50.5239i	0.510112	+	2.89299i
$306$	−0.370433	−	0.176897i	−0.0211763	−	0.0101125i
$307$	1.10143	−	6.24651i	0.0628618	−	0.356507i	−0.937110	−	0.349034i	$-0.886510\pi$
$307$	1.10143	−	6.24651i	0.0628618	−	0.356507i	0.999972	−	0.00747364i	$-0.00237896\pi$
$308$	−12.4404	−	1.45408i	−0.708860	−	0.0828538i
$309$	−1.44820	−	1.90540i	−0.0823854	−	0.108394i
$310$	0.345935	+	1.15550i	0.0196478	+	0.0656283i
$311$	31.9847	+	7.58051i	1.81369	+	0.429851i	0.990453	−	0.137853i	$-0.0440201\pi$
$311$	31.9847	+	7.58051i	1.81369	+	0.429851i	0.823233	+	0.567704i	$0.192168\pi$
$312$	0.515227	−	10.6751i	0.0291690	−	0.604357i
$313$	−5.58611	−	12.9501i	−0.315746	−	0.731981i	−0.999996	−	0.00273378i	$-0.999130\pi$
$313$	−5.58611	−	12.9501i	−0.315746	−	0.731981i	0.684251	−	0.729247i	$-0.260129\pi$
$314$	3.10935	+	2.60906i	0.175471	+	0.147238i
$315$	−7.73060	−	39.2572i	−0.435570	−	2.21189i
$316$	−2.64439	+	2.21891i	−0.148759	+	0.124823i
$317$	15.2914	+	7.67964i	0.858852	+	0.431332i	0.823011	−	0.568026i	$-0.192293\pi$
$317$	15.2914	+	7.67964i	0.858852	+	0.431332i	0.0358411	+	0.999358i	$0.488589\pi$
$318$	2.67286	−	9.26245i	0.149887	−	0.519412i
$319$	4.64667	−	0.543118i	0.260163	−	0.0304087i
$320$	−0.221089	+	3.79596i	−0.0123593	+	0.212200i
$321$	25.4724	−	0.253472i	1.42173	−	0.0141474i
$322$	4.36673	+	4.62846i	0.243348	+	0.257934i
$323$	0.466096			0.0259343
$324$	−7.71023	−	4.64246i	−0.428346	−	0.257914i
$325$	58.3609			3.23728
$326$	2.49656	+	2.64620i	0.138272	+	0.146559i
$327$	−2.58803	−	4.38133i	−0.143118	−	0.242288i
$328$	0.369526	−	6.34451i	0.0204036	−	0.350317i
$329$	−16.6382	+	1.94473i	−0.917296	+	0.107217i
$330$	−16.3083	−	16.9448i	−0.897742	−	0.932779i
$331$	5.61386	+	2.81938i	0.308565	+	0.154967i	0.596343	−	0.802730i	$-0.296620\pi$
$331$	5.61386	+	2.81938i	0.308565	+	0.154967i	−0.287777	+	0.957697i	$0.592916\pi$
$332$	−0.666605	+	0.559348i	−0.0365847	+	0.0306982i
$333$	17.8238	+	14.3614i	0.976740	+	0.786997i
$334$	7.22782	+	6.06486i	0.395489	+	0.331854i
$335$	14.6911	+	34.0579i	0.802663	+	1.86078i
$336$	5.40164	−	2.78045i	0.294684	−	0.151686i
$337$	2.27688	+	0.539631i	0.124030	+	0.0293956i	0.292162	−	0.956369i	$-0.405625\pi$
$337$	2.27688	+	0.539631i	0.124030	+	0.0293956i	−0.168132	+	0.985764i	$0.553774\pi$
$338$	−7.19137	−	24.0208i	−0.391159	−	1.30656i
$339$	31.3344	−	3.97890i	1.70185	−	0.216104i
$340$	0.516781	+	0.0604030i	0.0280264	+	0.00327581i
$341$	0.196700	−	1.11554i	0.0106519	−	0.0604099i
$342$	10.1713	+	0.984120i	0.550002	+	0.0532151i
$343$	1.03369	+	5.86233i	0.0558139	+	0.316536i
$344$	−0.187621	−	3.22133i	−0.0101159	−	0.173683i
$345$	0.813362	+	11.9202i	0.0437899	+	0.641763i
$346$	−5.23397	+	12.1337i	−0.281380	+	0.652312i
$347$	−30.3340	+	15.2343i	−1.62841	+	0.817819i	−0.629237	+	0.777214i	$0.716632\pi$
$347$	−30.3340	+	15.2343i	−1.62841	+	0.817819i	−0.999175	+	0.0406056i	$0.987071\pi$
$348$	−1.72370	+	1.47583i	−0.0923998	+	0.0791127i
$349$	−18.0733	+	4.28345i	−0.967441	+	0.229288i	−0.683821	−	0.729649i	$-0.739683\pi$
$349$	−18.0733	+	4.28345i	−0.967441	+	0.229288i	−0.283619	+	0.958937i	$0.591535\pi$
$350$	16.5875	+	28.7303i	0.886637	+	1.53570i
$351$	−31.4050	−	6.45965i	−1.67628	−	0.344791i
$352$	1.78546	−	3.09250i	0.0951651	−	0.164831i
$353$	0.522544	−	1.74542i	0.0278122	−	0.0928992i	−0.942957	−	0.332915i	$-0.891968\pi$
$353$	0.522544	−	1.74542i	0.0278122	−	0.0928992i	0.970769	+	0.240016i	$0.0771528\pi$
$354$	−1.32978	+	8.00661i	−0.0706768	+	0.425547i
$355$	−12.6565	−	8.32428i	−0.671735	−	0.441807i
$356$	5.00776	+	6.72659i	0.265411	+	0.356509i
$357$	−0.336842	−	0.760003i	−0.0178276	−	0.0402236i
$358$	−11.5276	+	7.58185i	−0.609255	+	0.400713i
$359$	10.6366	+	3.87139i	0.561376	+	0.204324i	0.607094	−	0.794630i	$-0.292335\pi$
$359$	10.6366	+	3.87139i	0.561376	+	0.204324i	−0.0457175	+	0.998954i	$0.514557\pi$
$360$	11.1498	+	2.40927i	0.587648	+	0.126980i
$361$	6.95120	−	2.53003i	0.365853	−	0.133160i
$362$	−4.63134	+	6.22097i	−0.243418	+	0.326967i
$363$	0.898899	+	2.89729i	0.0471800	+	0.152068i
$364$	14.8524	−	15.7426i	0.778476	−	0.825136i
$365$	36.4660	−	38.6517i	1.90872	−	2.02312i
$366$	6.92489	+	22.3200i	0.361970	+	1.16668i
$367$	−2.86793	+	3.85230i	−0.149705	+	0.201088i	−0.870649	−	0.491905i	$-0.836301\pi$
$367$	−2.86793	+	3.85230i	−0.149705	+	0.201088i	0.720944	+	0.692993i	$0.243708\pi$
$368$	−1.70475	+	0.620480i	−0.0888665	+	0.0323447i
$369$	−18.6357	−	4.02683i	−0.970136	−	0.209628i
$370$	−27.2622	−	9.92263i	−1.41729	−	0.515853i
$371$	16.3109	−	10.7278i	0.846819	−	0.556961i
$372$	0.222629	+	0.502308i	0.0115428	+	0.0260435i
$373$	12.6149	+	16.9448i	0.653176	+	0.877368i	0.998122	−	0.0612544i	$-0.0195101\pi$
$373$	12.6149	+	16.9448i	0.653176	+	0.877368i	−0.344946	+	0.938623i	$0.612103\pi$
$374$	−0.408240	−	0.268504i	−0.0211096	−	0.0138840i
$375$	−4.81054	+	28.9644i	−0.248415	+	1.49571i
$376$	1.36973	−	4.57522i	0.0706384	−	0.235949i
$377$	−4.04198	+	7.00092i	−0.208173	+	0.360566i
$378$	−5.74600	−	17.2963i	−0.295543	−	0.889624i
$379$	−8.13502	−	14.0903i	−0.417868	−	0.723768i	0.577857	−	0.816138i	$-0.303889\pi$
$379$	−8.13502	−	14.0903i	−0.417868	−	0.723768i	−0.995725	+	0.0923698i	$0.970556\pi$
$380$	−12.6028	+	2.98693i	−0.646512	+	0.153226i
$381$	13.6682	−	11.7027i	0.700246	−	0.599550i
$382$	0.521966	−	0.262141i	0.0267061	−	0.0134123i
$383$	−4.74133	+	10.9916i	−0.242270	+	0.561646i	−0.995354	−	0.0962784i	$-0.969306\pi$
$383$	−4.74133	+	10.9916i	−0.242270	+	0.561646i	0.753084	+	0.657924i	$0.228565\pi$
$384$	0.117910	+	1.72803i	0.00601708	+	0.0881833i
$385$	−2.76917	−	47.5448i	−0.141130	−	2.42311i
$386$	−3.69108	−	20.9332i	−0.187871	−	1.06547i
$387$	−9.63538	−	0.932266i	−0.489794	−	0.0473897i
$388$	1.20819	−	6.85199i	0.0613366	−	0.347857i
$389$	−8.21291	−	0.959952i	−0.416411	−	0.0486715i	−0.0946920	−	0.995507i	$-0.530187\pi$
$389$	−8.21291	−	0.959952i	−0.416411	−	0.0486715i	−0.321719	+	0.946835i	$0.604261\pi$
$390$	40.3143	−	5.11918i	2.04139	−	0.259220i
$391$	0.0711961	+	0.237811i	0.00360054	+	0.0120266i
$392$	5.15993	+	1.22293i	0.260616	+	0.0617671i
$393$	−26.8878	+	13.8403i	−1.35631	+	0.698149i
$394$	−0.215719	−	0.500092i	−0.0108677	−	0.0251943i
$395$	−10.0550	−	8.43714i	−0.505922	−	0.424519i
$396$	−8.34184	−	6.72134i	−0.419193	−	0.337760i
$397$	25.2439	−	21.1822i	1.26696	−	1.06310i	0.272051	−	0.962283i	$-0.412298\pi$
$397$	25.2439	−	21.1822i	1.26696	−	1.06310i	0.994905	−	0.100820i	$-0.0321465\pi$
$398$	−1.98287	−	0.995835i	−0.0993923	−	0.0499167i
$399$	14.3501	+	14.9102i	0.718404	+	0.746442i
$400$	−9.39421	+	1.09803i	−0.469710	+	0.0549013i
$401$	0.849467	−	14.5848i	0.0424204	−	0.728330i	−0.908307	−	0.418303i	$-0.862625\pi$
$401$	0.849467	−	14.5848i	0.0424204	−	0.728330i	0.950728	−	0.310027i	$-0.100338\pi$
$402$	8.59305	+	14.5474i	0.428582	+	0.725556i
$403$	1.34322	+	1.42373i	0.0669105	+	0.0709210i
$404$	−4.03682			−0.200840
$405$	12.2933	−	31.9372i	0.610861	−	1.58697i
$406$	−4.59528			−0.228060
$407$	18.6971	+	19.8178i	0.926781	+	0.982331i
$408$	0.236993	−	0.00235828i	0.0117329	−	0.000116752i
$409$	0.296826	−	5.09630i	0.0146771	−	0.251996i	−0.982986	−	0.183678i	$-0.941200\pi$
$409$	0.296826	−	5.09630i	0.0146771	−	0.251996i	0.997664	−	0.0683181i	$-0.0217633\pi$
$410$	24.0018	−	2.80541i	1.18536	−	0.138549i
$411$	7.75777	−	26.8835i	0.382663	−	1.32607i
$412$	1.23479	+	0.620135i	0.0608338	+	0.0305519i
$413$	−12.5908	+	10.5650i	−0.619554	+	0.519867i
$414$	1.05155	+	5.33993i	0.0516808	+	0.262443i
$415$	−2.53469	−	2.12686i	−0.124423	−	0.104403i
$416$	2.44398	+	5.66579i	0.119826	+	0.277788i
$417$	1.38213	−	28.6366i	0.0676834	−	1.40234i
$418$	11.8356	+	2.80509i	0.578899	+	0.137202i
$419$	7.80974	+	26.0864i	0.381531	+	1.27440i	0.906111	+	0.423041i	$0.139037\pi$
$419$	7.80974	+	26.0864i	0.381531	+	1.27440i	−0.524580	+	0.851361i	$0.675777\pi$
$420$	13.9783	+	18.3912i	0.682072	+	0.897400i
$421$	−3.94940	−	0.461619i	−0.192482	−	0.0224979i	0.0193056	−	0.999814i	$-0.493854\pi$
$421$	−3.94940	−	0.461619i	−0.192482	−	0.0224979i	−0.211788	+	0.977316i	$0.567929\pi$
$422$	−0.655887	+	3.71972i	−0.0319281	+	0.181073i
$423$	−12.9290	−	6.17414i	−0.628629	−	0.300197i
$424$	0.966505	+	5.48132i	0.0469376	+	0.266197i
$425$	0.0752513	+	1.29201i	0.00365022	+	0.0626719i
$426$	−6.19696	−	3.03539i	−0.300244	−	0.147065i
$427$	−18.7445	+	43.4547i	−0.907112	+	2.10292i
$428$	−13.1429	+	6.60059i	−0.635284	+	0.319051i
$429$	−35.9906	−	12.6954i	−1.73764	−	0.612940i
$430$	11.9388	−	2.82955i	0.575740	−	0.136453i
$431$	−20.1905	−	34.9710i	−0.972542	−	1.68449i	−0.687818	−	0.725883i	$-0.741431\pi$
$431$	−20.1905	−	34.9710i	−0.972542	−	1.68449i	−0.284724	−	0.958610i	$-0.591902\pi$
$432$	5.17672	+	0.448926i	0.249065	+	0.0215990i
$433$	16.5183	−	28.6105i	0.793818	−	1.37493i	−0.129770	−	0.991544i	$-0.541424\pi$
$433$	16.5183	−	28.6105i	0.793818	−	1.37493i	0.923587	−	0.383388i	$-0.125243\pi$
$434$	−0.319111	+	1.06590i	−0.0153178	+	0.0511651i
$435$	−6.66454	−	5.48013i	−0.319540	−	0.262752i
$436$	2.45459	+	1.61441i	0.117553	+	0.0773161i
$437$	−3.69016	−	4.95674i	−0.176524	−	0.237113i
$438$	14.2606	−	19.5587i	0.681400	−	0.934551i
$439$	−31.1967	+	20.5184i	−1.48894	+	0.979291i	−0.495055	+	0.868862i	$0.664852\pi$
$439$	−31.1967	+	20.5184i	−1.48894	+	0.979291i	−0.993884	+	0.110429i	$0.964778\pi$
$440$	12.7591	+	4.64395i	0.608268	+	0.221392i
$441$	6.00914	−	14.7300i	0.286150	−	0.701430i
$442$	0.793410	−	0.288778i	0.0377386	−	0.0137357i
$443$	−12.0343	+	16.1649i	−0.571767	+	0.768017i	−0.990113	−	0.140271i	$-0.955203\pi$
$443$	−12.0343	+	16.1649i	−0.571767	+	0.768017i	0.418346	+	0.908288i	$0.362610\pi$
$444$	−12.8888	−	2.91957i	−0.611677	−	0.138557i
$445$	−21.8820	+	23.1936i	−1.03731	+	1.09948i
$446$	−13.7367	+	14.5601i	−0.650452	+	0.689439i
$447$	−6.57860	+	7.11340i	−0.311157	+	0.336452i
$448$	−2.09456	+	2.81348i	−0.0989587	+	0.132925i
$449$	−16.4473	+	5.98634i	−0.776198	+	0.282513i	−0.699586	−	0.714548i	$-0.746632\pi$
$449$	−16.4473	+	5.98634i	−0.776198	+	0.282513i	−0.0766114	+	0.997061i	$0.524410\pi$
$450$	−1.08581	+	28.3537i	−0.0511857	+	1.33661i
$451$	−21.3255	−	7.76184i	−1.00418	−	0.365491i
$452$	−15.2361	+	10.0210i	−0.716648	+	0.471347i
$453$	20.3202	+	2.17036i	0.954724	+	0.101972i
$454$	−4.36853	−	5.86796i	−0.205025	−	0.275397i
$455$	68.7567	+	45.2220i	3.22337	+	2.12004i
$456$	−5.52368	+	2.07293i	−0.258670	+	0.0970737i
$457$	−7.98243	+	26.6632i	−0.373402	+	1.24725i	0.540509	+	0.841338i	$0.318232\pi$
$457$	−7.98243	+	26.6632i	−0.373402	+	1.24725i	−0.913912	+	0.405913i	$0.866954\pi$
$458$	4.62511	−	8.01093i	0.216117	−	0.374326i
$459$	0.102512	−	0.703585i	0.00478485	−	0.0328405i
$460$	−3.44907	−	5.97397i	−0.160814	−	0.278538i
$461$	−0.638507	+	0.151329i	−0.0297382	+	0.00704809i	−0.245458	−	0.969407i	$-0.578938\pi$
$461$	−0.638507	+	0.151329i	−0.0297382	+	0.00704809i	0.215720	+	0.976455i	$0.430790\pi$
$462$	−3.97955	−	21.3260i	−0.185145	−	0.992177i
$463$	35.7204	−	17.9395i	1.66007	−	0.833718i	0.663754	−	0.747951i	$-0.268962\pi$
$463$	35.7204	−	17.9395i	1.66007	−	0.833718i	0.996315	−	0.0857667i	$-0.0273340\pi$
$464$	0.518910	−	1.20297i	0.0240898	−	0.0558464i
$465$	−1.73396	+	1.16532i	−0.0804104	+	0.0540406i
$466$	−0.500468	−	8.59271i	−0.0231837	−	0.398050i
$467$	−3.49400	−	19.8154i	−0.161683	−	0.916949i	−0.952419	−	0.304792i	$-0.901413\pi$
$467$	−3.49400	−	19.8154i	−0.161683	−	0.916949i	0.790736	−	0.612157i	$-0.209698\pi$
$468$	17.9238	−	4.62659i	0.828528	−	0.213864i
$469$	−5.94142	+	33.6954i	−0.274349	+	1.55591i
$470$	18.0369	+	2.10821i	0.831978	+	0.0972443i
$471$	−2.72021	+	6.48277i	−0.125341	+	0.298710i
$472$	−1.34394	−	4.48908i	−0.0618600	−	0.206627i
$473$	−11.2120	−	2.65729i	−0.515528	−	0.122182i
$474$	−5.02787	−	3.23567i	−0.230938	−	0.148619i
$475$	−12.7605	−	29.5822i	−0.585493	−	1.35733i
$476$	0.367666	+	0.308508i	0.0168519	+	0.0141405i
$477$	16.6943	−	0.332279i	0.764381	−	0.0152140i
$478$	−21.8649	+	18.3468i	−1.00008	+	0.839164i
$479$	−14.7708	−	7.41817i	−0.674894	−	0.338945i	0.0781245	−	0.996944i	$-0.475107\pi$
$479$	−14.7708	−	7.41817i	−0.674894	−	0.338945i	−0.753019	+	0.657999i	$0.771403\pi$
$480$	−6.39298	+	1.58251i	−0.291798	+	0.0722314i
$481$	−46.7614	+	5.46562i	−2.13214	+	0.249211i
$482$	0.368795	−	6.33196i	0.0167981	−	0.288413i
$483$	−5.41549	+	9.59924i	−0.246413	+	0.436780i
$484$	−1.20189	−	1.27393i	−0.0546313	−	0.0579058i
$485$	26.4558			1.20130
$486$	3.72261	−	15.1374i	0.168861	−	0.686648i
$487$	−22.8688			−1.03628			−0.518142	−	0.855295i	$-0.673376\pi$
$487$	−22.8688			−1.03628			−0.518142	+	0.855295i	$0.673376\pi$
$488$	−9.25904	−	9.81401i	−0.419137	−	0.444260i
$489$	−3.09616	+	5.48810i	−0.140013	+	0.248181i
$490$	−1.17241	+	20.1294i	−0.0529639	+	0.909356i
$491$	−20.7899	+	2.42999i	−0.938236	+	0.109664i	−0.571446	−	0.820640i	$-0.693617\pi$
$491$	−20.7899	+	2.42999i	−0.938236	+	0.109664i	−0.366790	+	0.930304i	$0.619543\pi$
$492$	10.6851	−	2.64499i	0.481723	−	0.119245i
$493$	−0.160201	−	0.0804558i	−0.00721507	−	0.00362355i
$494$	−16.1008	+	13.5102i	−0.724411	+	0.607853i
$495$	19.6610	−	35.6750i	0.883694	−	1.60347i
$496$	−0.243001	−	0.203902i	−0.0109111	−	0.00915548i
$497$	−5.53479	−	12.8311i	−0.248269	−	0.575553i
$498$	−1.26744	−	0.815657i	−0.0567953	−	0.0365505i
$499$	17.5900	+	4.16891i	0.787436	+	0.186626i	0.604612	−	0.796520i	$-0.293328\pi$
$499$	17.5900	+	4.16891i	0.787436	+	0.186626i	0.182824	+	0.983146i	$0.441476\pi$
$500$	−4.86179	−	16.2395i	−0.217426	−	0.726253i
$501$	−6.32323	+	15.0695i	−0.282501	+	0.673254i
$502$	−8.50538	−	0.994136i	−0.379614	−	0.0443705i
$503$	−2.56772	+	14.5622i	−0.114489	+	0.649298i	0.872513	+	0.488590i	$0.162489\pi$
$503$	−2.56772	+	14.5622i	−0.114489	+	0.649298i	−0.987002	+	0.160708i	$0.948622\pi$
$504$	7.37195	+	7.50867i	0.328373	+	0.334463i
$505$	−2.66543	−	15.1164i	−0.118610	−	0.672670i
$506$	0.376674	+	6.46725i	0.0167452	+	0.287504i
$507$	36.0458	−	24.2249i	1.60085	−	1.07587i
$508$	−4.11475	+	9.53907i	−0.182563	+	0.423228i
$509$	−32.6449	+	16.3949i	−1.44696	+	0.726690i	−0.986920	−	0.161210i	$-0.948460\pi$
$509$	−32.6449	+	16.3949i	−1.44696	+	0.726690i	−0.460038	+	0.887899i	$0.652164\pi$
$510$	0.165312	+	0.885892i	0.00732014	+	0.0392279i
$511$	47.6969	−	11.3044i	2.10999	−	0.500076i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	3.59237	+	17.3311i	0.158607	+	0.765187i
$514$	−1.69904	+	2.94283i	−0.0749417	+	0.129803i
$515$	−1.50687	+	5.03329i	−0.0664005	+	0.221793i
$516$	5.23263	−	1.96370i	0.230354	−	0.0864472i
$517$	−14.2485	−	9.37141i	−0.626650	−	0.412154i
$518$	−15.9813	−	21.4666i	−0.702177	−	0.943187i
$519$	−22.7586	−	2.43080i	−0.998992	−	0.106700i
$520$	−19.6025	+	12.8928i	−0.859628	+	0.565386i
$521$	10.0480	+	3.65717i	0.440210	+	0.160223i	0.552611	−	0.833440i	$-0.313632\pi$
$521$	10.0480	+	3.65717i	0.440210	+	0.160223i	−0.112400	+	0.993663i	$0.535854\pi$
$522$	−3.32608	−	2.09398i	−0.145579	−	0.0916512i
$523$	27.4132	−	9.97760i	1.19870	−	0.436290i	0.335927	−	0.941888i	$-0.390950\pi$
$523$	27.4132	−	9.97760i	1.19870	−	0.436290i	0.862769	+	0.505598i	$0.168728\pi$
$524$	10.4261	−	14.0047i	0.455467	−	0.611798i
$525$	−39.0141	+	42.1856i	−1.70271	+	1.84113i
$526$	−1.10496	+	1.17118i	−0.0481784	+	0.0510661i
$527$	−0.0297871	+	0.0315724i	−0.00129754	+	0.00137532i
$528$	6.03218	+	1.36640i	0.262517	+	0.0594651i
$529$	−11.7693	+	15.8089i	−0.511708	+	0.687343i
$530$	−19.8873	+	7.23839i	−0.863850	+	0.314416i
$531$	−13.9275	+	1.90955i	−0.604403	+	0.0828673i
$532$	−11.2271	−	4.08634i	−0.486757	−	0.177165i
$533$	32.7634	−	21.5488i	1.41914	−	0.933384i
$534$	−8.55734	+	11.7365i	−0.370312	+	0.507889i
$535$	−33.3946	−	44.8568i	−1.44378	−	1.93933i
$536$	−8.14998	−	5.36033i	−0.352026	−	0.231531i
$537$	−18.4589	−	15.1784i	−0.796558	−	0.654996i
$538$	−7.95627	+	26.5758i	−0.343019	+	1.14576i
$539$	9.46803	−	16.3991i	0.407817	−	0.706360i
$540$	1.73702	+	19.6813i	0.0747493	+	0.846948i
$541$	−12.5176	−	21.6812i	−0.538175	−	0.932147i	−0.999002	−	0.0446570i	$-0.985781\pi$
$541$	−12.5176	−	21.6812i	−0.538175	−	0.932147i	0.460827	−	0.887490i	$-0.347553\pi$
$542$	29.7765	−	7.05716i	1.27901	−	0.303131i
$543$	−12.6681	−	4.46858i	−0.543641	−	0.191765i
$544$	−0.122280	+	0.0614113i	−0.00524271	+	0.00263299i
$545$	−4.42464	+	10.2575i	−0.189531	+	0.439382i
$546$	33.6652	+	16.4899i	1.44074	+	0.705703i
$547$	−0.200489	−	3.44227i	−0.00857231	−	0.147181i	−0.999878	−	0.0156038i	$-0.995033\pi$
$547$	−0.200489	−	3.44227i	−0.00857231	−	0.147181i	0.991306	−	0.131577i	$-0.0420041\pi$
$548$	2.80520	+	15.9091i	0.119832	+	0.679603i
$549$	−33.3689	+	22.9111i	−1.42415	+	0.977824i
$550$	−5.86484	+	33.2611i	−0.250078	+	1.41826i
$551$	4.43243	+	0.518077i	0.188828	+	0.0220708i
$552$	−1.90139	−	2.50165i	−0.0809285	−	0.106477i
$553$	−3.47263	−	11.5994i	−0.147671	−	0.493257i
$554$	1.87968	+	0.445493i	0.0798600	+	0.0189272i
$555$	2.42247	−	50.1915i	0.102828	−	2.13051i
$556$	6.55615	+	15.1989i	0.278043	+	0.644576i
$557$	6.01226	+	5.04489i	0.254748	+	0.213759i	0.761213	−	0.648501i	$-0.224604\pi$
$557$	6.01226	+	5.04489i	0.254748	+	0.213759i	−0.506466	+	0.862260i	$0.669048\pi$
$558$	−0.716687	+	0.626093i	−0.0303398	+	0.0265046i
$559$	15.2525	−	12.7984i	0.645111	−	0.541313i
$560$	−11.9184	−	5.98566i	−0.503645	−	0.252940i
$561$	0.234649	−	0.813143i	0.00990687	−	0.0343309i
$562$	15.5505	−	1.81759i	0.655957	−	0.0766704i
$563$	−1.20456	+	20.6815i	−0.0507660	+	0.871619i	0.872776	+	0.488121i	$0.162318\pi$
$563$	−1.20456	+	20.6815i	−0.0507660	+	0.871619i	−0.923542	+	0.383498i	$0.874719\pi$
$564$	8.27161	−	0.0823096i	0.348298	−	0.00346586i
$565$	−47.5848	−	50.4370i	−2.00191	−	2.12190i
$566$	14.3864			0.604707
$567$	25.6634	−	18.3826i	1.07776	−	0.771996i
$568$	3.98396			0.167163
$569$	17.7236	+	18.7859i	0.743010	+	0.787545i	0.983073	−	0.183213i	$-0.0586497\pi$
$569$	17.7236	+	18.7859i	0.743010	+	0.787545i	−0.240063	+	0.970757i	$0.577168\pi$
$570$	−11.4095	−	19.3154i	−0.477891	−	0.809032i
$571$	0.326901	−	5.61267i	0.0136804	−	0.234883i	−0.984536	−	0.175183i	$-0.943948\pi$
$571$	0.326901	−	5.61267i	0.0136804	−	0.234883i	0.998216	−	0.0597005i	$-0.0190146\pi$
$572$	21.8851	−	2.55800i	0.915061	−	0.106955i
$573$	0.701546	+	0.728926i	0.0293075	+	0.0304513i
$574$	19.9203	+	10.0044i	0.831457	+	0.417574i
$575$	13.1443	−	11.0294i	0.548154	−	0.459956i
$576$	−2.79810	+	1.08196i	−0.116588	+	0.0450815i
$577$	4.53375	+	3.80427i	0.188743	+	0.158374i	0.732263	−	0.681022i	$-0.238464\pi$
$577$	4.53375	+	3.80427i	0.188743	+	0.158374i	−0.543520	+	0.839396i	$0.682909\pi$
$578$	−6.72594	−	15.5925i	−0.279762	−	0.648562i
$579$	32.7345	−	16.8498i	1.36040	−	0.700255i
$580$	4.84728	+	1.14883i	0.201273	+	0.0477025i
$581$	−0.875390	−	2.92401i	−0.0363173	−	0.121308i
$582$	11.9551	−	1.51808i	0.495554	−	0.0629263i
$583$	19.7409	+	2.30738i	0.817584	+	0.0955619i
$584$	−2.42675	+	13.7628i	−0.100419	+	0.569507i
$585$	29.1595	+	64.0630i	1.20560	+	2.64868i
$586$	1.94895	+	11.0531i	0.0805105	+	0.456598i
$587$	0.583214	+	10.0134i	0.0240718	+	0.413297i	0.988722	+	0.149763i	$0.0478511\pi$
$587$	0.583214	+	10.0134i	0.0240718	+	0.413297i	−0.964650	+	0.263534i	$0.915112\pi$
$588$	0.625262	+	9.16353i	0.0257854	+	0.377897i
$589$	0.427973	−	0.992153i	0.0176343	−	0.0408810i
$590$	15.9225	−	7.99660i	0.655521	−	0.329215i
$591$	0.716567	−	0.613524i	0.0294756	−	0.0252370i
$592$	7.42423	−	1.75957i	0.305134	−	0.0723181i
$593$	14.9501	+	25.8943i	0.613927	+	1.06335i	0.990572	+	0.136995i	$0.0437445\pi$
$593$	14.9501	+	25.8943i	0.613927	+	1.06335i	−0.376644	+	0.926358i	$0.622922\pi$
$594$	6.83746	−	17.2493i	0.280545	−	0.707746i
$595$	−0.912485	+	1.58047i	−0.0374082	+	0.0647930i
$596$	1.60438	−	5.35899i	0.0657178	−	0.219513i
$597$	0.629676	−	3.79129i	0.0257709	−	0.155167i
$598$	−9.35258	−	6.15129i	−0.382456	−	0.251545i
$599$	−9.81231	−	13.1802i	−0.400920	−	0.538529i	0.555118	−	0.831772i	$-0.312673\pi$
$599$	−9.81231	−	13.1802i	−0.400920	−	0.538529i	−0.956038	+	0.293242i	$0.905266\pi$
$600$	−6.63794	−	14.9769i	−0.270993	−	0.611430i
$601$	18.6165	−	12.2443i	0.759384	−	0.499455i	−0.109794	−	0.993954i	$-0.535019\pi$
$601$	18.6165	−	12.2443i	0.759384	−	0.499455i	0.869178	+	0.494499i	$0.164649\pi$
$602$	10.6355	+	3.87102i	0.433473	+	0.157771i
$603$	−19.6548	+	21.6815i	−0.800405	+	0.882938i
$604$	−11.0870	+	4.03535i	−0.451125	+	0.164196i
$605$	3.97680	−	5.34177i	0.161680	−	0.217174i
$606$	−2.07187	−	6.67796i	−0.0841642	−	0.271274i
$607$	11.7322	−	12.4354i	0.476193	−	0.504735i	−0.444093	−	0.895981i	$-0.646474\pi$
$607$	11.7322	−	12.4354i	0.476193	−	0.504735i	0.920286	+	0.391245i	$0.127956\pi$
$608$	2.33753	−	2.47763i	0.0947992	−	0.100481i
$609$	−2.35850	−	7.60180i	−0.0955712	−	0.308040i
$610$	30.6362	−	41.1516i	1.24042	−	1.66618i
$611$	27.6919	−	10.0790i	1.12029	−	0.407753i
$612$	0.125536	+	0.390838i	0.00507450	+	0.0157987i
$613$	18.3744	+	6.68772i	0.742133	+	0.270114i	0.685292	−	0.728269i	$-0.259675\pi$
$613$	18.3744	+	6.68772i	0.742133	+	0.270114i	0.0568418	+	0.998383i	$0.481897\pi$
$614$	−5.29939	+	3.48547i	−0.213866	+	0.140662i
$615$	16.9596	+	38.2654i	0.683879	+	1.54301i
$616$	7.47949	+	10.0467i	0.301357	+	0.404793i
$617$	28.7378	+	18.9012i	1.15694	+	0.760932i	0.974962	−	0.222370i	$-0.0713793\pi$
$617$	28.7378	+	18.9012i	1.15694	+	0.760932i	0.181979	+	0.983302i	$0.441750\pi$
$618$	−0.392117	+	2.36095i	−0.0157733	+	0.0949712i
$619$	−0.631086	+	2.10797i	−0.0253655	+	0.0847266i	−0.969735	−	0.244159i	$-0.921488\pi$
$619$	−0.631086	+	2.10797i	−0.0253655	+	0.0847266i	0.944370	+	0.328886i	$0.106673\pi$
$620$	0.603088	−	1.04458i	0.0242206	−	0.0419513i
$621$	−8.29394	+	4.48022i	−0.332825	+	0.179785i
$622$	−16.4354	−	28.4669i	−0.658998	−	1.14142i
$623$	−28.6213	+	6.78338i	−1.14669	+	0.271771i
$624$	−8.11834	+	6.95092i	−0.324994	+	0.278259i
$625$	15.3401	−	7.70409i	0.613604	−	0.308163i
$626$	−5.58611	+	12.9501i	−0.223266	+	0.517589i
$627$	1.43420	+	21.0189i	0.0572764	+	0.839415i
$628$	−0.236008	−	4.05211i	−0.00941776	−	0.161697i
$629$	−0.181295	−	1.02817i	−0.00722869	−	0.0409959i
$630$	−23.2496	+	32.5630i	−0.926286	+	1.29734i
$631$	−4.88620	+	27.7110i	−0.194517	+	1.10316i	0.718589	+	0.695435i	$0.244788\pi$
$631$	−4.88620	+	27.7110i	−0.194517	+	1.10316i	−0.913106	+	0.407723i	$0.866323\pi$
$632$	3.42866	+	0.400753i	0.136385	+	0.0159411i
$633$	−6.49001	+	0.824114i	−0.257955	+	0.0327556i
$634$	−4.90764	−	16.3927i	−0.194907	−	0.651036i
$635$	−38.4371	−	9.10976i	−1.52533	−	0.361510i
$636$	−8.57149	+	4.41211i	−0.339882	+	0.174951i
$637$	12.9601	+	30.0449i	0.513498	+	1.19042i
$638$	−3.58379	−	3.00715i	−0.141883	−	0.119054i
$639$	1.84079	−	11.8093i	0.0728204	−	0.467168i
$640$	2.91280	−	2.44413i	0.115138	−	0.0966127i
$641$	−11.9322	−	5.99260i	−0.471295	−	0.236693i	0.197267	−	0.980350i	$-0.436794\pi$
$641$	−11.9322	−	5.99260i	−0.471295	−	0.236693i	−0.668562	+	0.743656i	$0.733090\pi$
$642$	−17.6646	−	18.3540i	−0.697166	−	0.724375i
$643$	45.0701	−	5.26794i	1.77739	−	0.207747i	0.836852	−	0.547429i	$-0.184393\pi$
$643$	45.0701	−	5.26794i	1.77739	−	0.207747i	0.940540	+	0.339682i	$0.110319\pi$
$644$	0.369990	−	6.35249i	0.0145797	−	0.250323i
$645$	10.8083	+	18.2976i	0.425577	+	0.720469i
$646$	−0.319854	−	0.339026i	−0.0125845	−	0.0133388i
$647$	10.1080			0.397388			0.198694	−	0.980062i	$-0.436330\pi$
$647$	10.1080			0.397388			0.198694	+	0.980062i	$0.436330\pi$
$648$	1.91428	+	8.79406i	0.0752000	+	0.345463i
$649$	−16.7331			−0.656831
$650$	−40.0497	−	42.4502i	−1.57088	−	1.66503i
$651$	−1.92707	+	0.0191760i	−0.0755277	+	0.000751566i
$652$	0.211532	−	3.63186i	0.00828423	−	0.142235i
$653$	25.9543	−	3.03362i	1.01567	−	0.118715i	0.408064	−	0.912953i	$-0.366204\pi$
$653$	25.9543	−	3.03362i	1.01567	−	0.118715i	0.607606	+	0.794238i	$0.292130\pi$
$654$	−1.41085	+	4.88912i	−0.0551687	+	0.191180i
$655$	59.3264	+	29.7948i	2.31807	+	1.16418i
$656$	−4.86842	+	4.08509i	−0.190080	+	0.159496i
$657$	39.6744	+	13.5524i	1.54784	+	0.528731i
$658$	12.8324	+	10.7677i	0.500259	+	0.419767i
$659$	−8.94916	−	20.7465i	−0.348610	−	0.808168i	−0.998827	−	0.0484199i	$-0.984581\pi$
$659$	−8.94916	−	20.7465i	−0.348610	−	0.808168i	0.650217	−	0.759748i	$-0.274678\pi$
$660$	−1.13375	+	23.4904i	−0.0441313	+	0.914364i
$661$	36.7996	+	8.72168i	1.43134	+	0.339234i	0.871919	−	0.489650i	$-0.162875\pi$
$661$	36.7996	+	8.72168i	1.43134	+	0.339234i	0.559421	+	0.828884i	$0.311023\pi$
$662$	−1.80172	−	6.01815i	−0.0700257	−	0.233902i
$663$	0.884926	+	1.16429i	0.0343677	+	0.0452174i
$664$	0.864307	+	0.101023i	0.0335416	+	0.00392045i
$665$	7.88877	−	44.7394i	0.305913	−	1.73492i
$666$	−1.78538	−	22.8199i	−0.0691821	−	0.884255i
$667$	0.412720	+	2.34065i	0.0159806	+	0.0906303i
$668$	−0.548611	−	9.41929i	−0.0212264	−	0.364443i
$669$	−31.1364	−	15.2513i	−1.20380	−	0.589648i
$670$	14.6911	−	34.0579i	0.567569	−	1.31577i
$671$	−43.0554	+	21.6232i	−1.66213	+	0.834755i
$672$	−5.72926	−	2.02095i	−0.221011	−	0.0779598i
$673$	−43.4096	+	10.2883i	−1.67332	+	0.396584i	−0.954405	−	0.298516i	$-0.903509\pi$
$673$	−43.4096	+	10.2883i	−1.67332	+	0.396584i	−0.718914	+	0.695099i	$0.755360\pi$
$674$	−1.16998	−	2.02646i	−0.0450658	−	0.0780563i
$675$	−47.4617	+	12.7561i	−1.82680	+	0.490984i
$676$	−12.5371	+	21.7149i	−0.482197	+	0.835189i
$677$	2.60218	−	8.69190i	0.100010	−	0.334057i	−0.893311	−	0.449439i	$-0.851624\pi$
$677$	2.60218	−	8.69190i	0.100010	−	0.334057i	0.993321	+	0.115382i	$0.0368092\pi$
$678$	−24.3971	−	20.0614i	−0.936967	−	0.770452i
$679$	20.3896	+	13.4104i	0.782481	+	0.514646i
$680$	−0.310701	−	0.417344i	−0.0119148	−	0.0160044i
$681$	7.46501	−	10.2384i	0.286060	−	0.392336i
$682$	−0.946398	+	0.622456i	−0.0362394	+	0.0238351i
$683$	20.2951	+	7.38680i	0.776569	+	0.282648i	0.699741	−	0.714396i	$-0.253299\pi$
$683$	20.2951	+	7.38680i	0.776569	+	0.282648i	0.0768276	+	0.997044i	$0.475521\pi$
$684$	−6.26416	−	8.07369i	−0.239516	−	0.308705i
$685$	−57.7214	+	21.0089i	−2.20542	+	0.802707i
$686$	3.55475	−	4.77486i	0.135721	−	0.182305i
$687$	15.6260	+	3.53958i	0.596168	+	0.135044i
$688$	−2.21436	+	2.34708i	−0.0844216	+	0.0894817i
$689$	−23.5682	+	24.9808i	−0.897877	+	0.951694i
$690$	8.11229	−	8.77177i	0.308830	−	0.333936i
$691$	12.6379	−	16.9757i	0.480769	−	0.645784i	−0.493879	−	0.869531i	$-0.664421\pi$
$691$	12.6379	−	16.9757i	0.480769	−	0.645784i	0.974647	+	0.223746i	$0.0718288\pi$
$692$	12.4175	−	4.51960i	0.472042	−	0.171809i
$693$	33.2364	−	17.5287i	1.26254	−	0.665859i
$694$	31.8974	+	11.6097i	1.21081	+	0.440699i
$695$	−52.5851	+	34.5858i	−1.99467	+	1.31191i
$696$	2.25635	+	0.240997i	0.0855267	+	0.00913495i
$697$	0.519301	+	0.697543i	0.0196699	+	0.0264213i
$698$	15.5183	+	10.2065i	0.587376	+	0.386324i
$699$	13.9577	−	5.23806i	0.527930	−	0.198122i
$700$	9.51467	−	31.7812i	0.359621	−	1.20122i
$701$	9.63781	−	16.6932i	0.364015	−	0.630493i	−0.624602	−	0.780943i	$-0.714739\pi$
$701$	9.63781	−	16.6932i	0.364015	−	0.630493i	0.988618	+	0.150450i	$0.0480723\pi$
$702$	16.8529	+	27.2761i	0.636071	+	1.02947i
$703$	12.9947	+	22.5076i	0.490106	+	0.848888i
$704$	−3.47466	+	0.823509i	−0.130956	+	0.0310372i
$705$	5.76978	+	30.9197i	0.217302	+	1.16450i
$706$	−1.62816	+	0.817693i	−0.0612767	+	0.0307743i
$707$	5.60823	−	13.0013i	0.210919	−	0.488966i
$708$	6.73635	−	4.52723i	0.253167	−	0.170144i
$709$	0.694133	+	11.9178i	0.0260687	+	0.447582i	0.985936	+	0.167126i	$0.0534487\pi$
$709$	0.694133	+	11.9178i	0.0260687	+	0.447582i	−0.959867	+	0.280456i	$0.909514\pi$
$710$	2.63052	+	14.9184i	0.0987218	+	0.559879i
$711$	2.77213	−	9.97810i	0.103963	−	0.374208i
$712$	1.45621	−	8.25858i	0.0545738	−	0.309503i
$713$	0.571589	+	0.0668092i	0.0214062	+	0.00250202i
$714$	−0.321651	+	0.766555i	−0.0120375	+	0.0286876i
$715$	24.0290	+	80.2624i	0.898633	+	3.00164i
$716$	13.4256	+	3.18192i	0.501738	+	0.118914i
$717$	−41.5724	−	26.7538i	−1.55255	−	0.999141i
$718$	−4.48330	−	10.3935i	−0.167315	−	0.387881i
$719$	−0.280815	−	0.235632i	−0.0104726	−	0.00878758i	0.637536	−	0.770420i	$-0.279954\pi$
$719$	−0.280815	−	0.235632i	−0.0104726	−	0.00878758i	−0.648009	+	0.761633i	$0.724398\pi$
$720$	−5.89904	−	9.76344i	−0.219844	−	0.363862i
$721$	−3.71271	+	3.11534i	−0.138269	+	0.116021i
$722$	−6.61048	−	3.31991i	−0.246017	−	0.123554i
$723$	10.6640	−	2.63976i	0.396599	−	0.0981736i
$724$	7.70319	−	0.900374i	0.286287	−	0.0334621i
$725$	−0.720488	+	12.3703i	−0.0267583	+	0.459422i
$726$	1.49055	−	2.64208i	0.0553194	−	0.0980566i
$727$	−28.8159	−	30.5430i	−1.06872	−	1.13278i	−0.990733	−	0.135825i	$-0.956632\pi$
$727$	−28.8159	−	30.5430i	−1.06872	−	1.13278i	−0.0779889	−	0.996954i	$-0.524850\pi$
$728$	−21.6431			−0.802145
$729$	26.9519	−	1.61103i	0.998218	−	0.0596677i
$730$	−53.1387			−1.96675
$731$	0.303001	+	0.321162i	0.0112069	+	0.0118786i
$732$	11.4828	−	20.3539i	0.424416	−	0.752300i
$733$	−3.12616	+	53.6741i	−0.115467	+	1.98250i	0.0607694	+	0.998152i	$0.480645\pi$
$733$	−3.12616	+	53.6741i	−0.115467	+	1.98250i	−0.176237	+	0.984348i	$0.556392\pi$
$734$	4.77015	−	0.557551i	0.176070	−	0.0205796i
$735$	−33.9011	+	8.39184i	−1.25046	+	0.309538i
$736$	1.62119	+	0.814194i	0.0597580	+	0.0300116i
$737$	−26.6839	+	22.3905i	−0.982915	+	0.824763i
$738$	9.85958	+	16.3185i	0.362936	+	0.600692i
$739$	19.6431	+	16.4825i	0.722581	+	0.606318i	0.928098	−	0.372336i	$-0.121443\pi$
$739$	19.6431	+	16.4825i	0.722581	+	0.606318i	−0.205517	+	0.978654i	$0.565887\pi$
$740$	11.4910	+	26.6391i	0.422417	+	0.979273i
$741$	−30.6131	−	19.7010i	−1.12460	−	0.723733i
$742$	−18.9963	−	4.50222i	−0.697378	−	0.165282i
$743$	−10.9043	−	36.4229i	−0.400040	−	1.33623i	−0.886583	−	0.462570i	$-0.846927\pi$
$743$	−10.9043	−	36.4229i	−0.400040	−	1.33623i	0.486542	−	0.873657i	$-0.338258\pi$
$744$	0.212589	−	0.506639i	0.00779388	−	0.0185743i
$745$	21.1267	+	2.46936i	0.774023	+	0.0904704i
$746$	3.66831	−	20.8040i	0.134306	−	0.761688i
$747$	0.698805	−	2.51531i	0.0255679	−	0.0920302i
$748$	0.0848488	+	0.481201i	0.00310238	+	0.0175945i
$749$	−2.99947	−	51.4989i	−0.109598	−	1.88173i
$750$	24.3691	−	16.3775i	0.889834	−	0.598022i
$751$	7.83039	−	18.1529i	0.285735	−	0.662408i	−0.713535	−	0.700620i	$-0.752907\pi$
$751$	7.83039	−	18.1529i	0.285735	−	0.662408i	0.999270	+	0.0382118i	$0.0121661\pi$
$752$	−4.26786	+	2.14340i	−0.155633	+	0.0781617i
$753$	−2.72077	−	14.5804i	−0.0991504	−	0.531338i
$754$	7.86606	−	1.86429i	0.286465	−	0.0678935i
$755$	−22.4314	−	38.8523i	−0.816362	−	1.41398i
$756$	−8.63770	+	16.0489i	−0.314150	+	0.583693i
$757$	−22.2454	+	38.5302i	−0.808524	+	1.40040i	0.105362	+	0.994434i	$0.466400\pi$
$757$	−22.2454	+	38.5302i	−0.808524	+	1.40040i	−0.913886	+	0.405971i	$0.866933\pi$
$758$	−4.66630	+	15.5865i	−0.169488	+	0.566128i
$759$	−10.5052	+	3.94239i	−0.381314	+	0.143100i
$760$	10.8212	+	7.11722i	0.392527	+	0.258169i
$761$	19.9164	+	26.7523i	0.721968	+	0.969772i	0.999958	+	0.00918761i	$0.00292455\pi$
$761$	19.9164	+	26.7523i	0.721968	+	0.969772i	−0.277989	+	0.960584i	$0.589668\pi$
$762$	−17.8920	−	1.91101i	−0.648158	−	0.0692286i
$763$	−8.60958	+	5.66261i	−0.311688	+	0.205000i
$764$	−0.548869	−	0.199772i	−0.0198574	−	0.00722750i
$765$	−1.38065	+	0.728148i	−0.0499175	+	0.0263262i
$766$	11.2487	−	4.09420i	0.406433	−	0.147929i
$767$	17.2664	−	23.1928i	0.623454

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.851057 - 1.50854i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.77668 + 0.441430i) q^{5} +(-1.68131 + 0.416189i) q^{6} +(-3.13446 - 1.57418i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.55140 - 2.56771i) q^{9} +O(q^{10})\)	\(q+(-0.686242 - 0.727374i) q^{2} +(0.851057 - 1.50854i) q^{3} +(-0.0581448 + 0.998308i) q^{4} +(-3.77668 + 0.441430i) q^{5} +(-1.68131 + 0.416189i) q^{6} +(-3.13446 - 1.57418i) q^{7} +(0.766044 - 0.642788i) q^{8} +(-1.55140 - 2.56771i) q^{9} +(2.91280 + 2.44413i) q^{10} +(-1.41437 - 3.27887i) q^{11} +(1.45651 + 0.937331i) q^{12} +(6.00411 + 1.42300i) q^{13} +(1.00598 + 3.36019i) q^{14} +(-2.54825 + 6.07296i) q^{15} +(-0.993238 - 0.116093i) q^{16} +(-0.0237611 + 0.134756i) q^{17} +(-0.803048 + 2.89052i) q^{18} +(-0.591493 - 3.35452i) q^{19} +(-0.221089 - 3.79596i) q^{20} +(-5.04232 + 3.38874i) q^{21} +(-1.41437 + 3.27887i) q^{22} +(1.62119 - 0.814194i) q^{23} +(-0.317725 - 1.70266i) q^{24} +(9.20321 - 2.18120i) q^{25} +(-3.08522 - 5.34375i) q^{26} +(-5.19384 + 0.155090i) q^{27} +(1.75377 - 3.03762i) q^{28} +(-0.375745 + 1.25508i) q^{29} +(6.16603 - 2.31399i) q^{30} +(0.265030 + 0.174313i) q^{31} +(0.597159 + 0.802123i) q^{32} +(-6.15002 - 0.656872i) q^{33} +(0.114324 - 0.0751919i) q^{34} +(12.5327 + 4.56154i) q^{35} +(2.65357 - 1.39948i) q^{36} +(-7.16975 + 2.60958i) q^{37} +(-2.03408 + 2.73225i) q^{38} +(7.25649 - 7.84640i) q^{39} +(-2.60936 + 2.76576i) q^{40} +(4.36125 - 4.62265i) q^{41} +(5.92513 + 1.34216i) q^{42} +(1.92691 - 2.58828i) q^{43} +(3.35556 - 1.22132i) q^{44} +(6.99262 + 9.01259i) q^{45} +(-1.70475 - 0.620480i) q^{46} +(3.99017 - 2.62437i) q^{47} +(-1.02043 + 1.39954i) q^{48} +(3.16665 + 4.25355i) q^{49} +(-7.90218 - 5.19734i) q^{50} +(0.183063 + 0.150530i) q^{51} +(-1.76970 + 5.91121i) q^{52} +(-2.78294 + 4.82020i) q^{53} +(3.67704 + 3.67143i) q^{54} +(6.78900 + 11.7589i) q^{55} +(-3.41300 + 0.808895i) q^{56} +(-5.56384 - 1.96260i) q^{57} +(1.17076 - 0.587978i) q^{58} +(1.85601 - 4.30271i) q^{59} +(-5.91452 - 2.89705i) q^{60} +(-0.784513 - 13.4696i) q^{61} +(-0.0550839 - 0.312396i) q^{62} +(0.820759 + 10.4906i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-23.3037 - 2.72382i) q^{65} +(3.74261 + 4.92414i) q^{66} +(-2.79770 - 9.34496i) q^{67} +(-0.133146 - 0.0315562i) q^{68} +(0.151481 - 3.13857i) q^{69} +(-5.28253 - 12.2463i) q^{70} +(3.05189 + 2.56084i) q^{71} +(-2.83894 - 0.969758i) q^{72} +(-10.7055 + 8.98301i) q^{73} +(6.81832 + 3.42429i) q^{74} +(4.54202 - 15.7398i) q^{75} +(3.38324 - 0.395444i) q^{76} +(-0.728272 + 12.5039i) q^{77} +(-10.6870 + 0.106345i) q^{78} +(2.36891 + 2.51090i) q^{79} +3.80239 q^{80} +(-4.18629 + 7.96712i) q^{81} -6.35527 q^{82} +(0.597161 + 0.632954i) q^{83} +(-3.08982 - 5.23083i) q^{84} +(0.0302527 - 0.519418i) q^{85} +(-3.20497 + 0.374608i) q^{86} +(1.57355 + 1.63497i) q^{87} +(-3.19108 - 1.60262i) q^{88} +(6.42404 - 5.39041i) q^{89} +(1.75689 - 11.2711i) q^{90} +(-16.5795 - 13.9119i) q^{91} +(0.718553 + 1.66579i) q^{92} +(0.488514 - 0.251459i) q^{93} +(-4.64712 - 1.10139i) q^{94} +(3.71467 + 12.4078i) q^{95} +(1.71825 - 0.218187i) q^{96} +(-6.91065 - 0.807739i) q^{97} +(0.920833 - 5.22230i) q^{98} +(-6.22494 + 8.71853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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