LMFDB - Embedded newform 81.2.g.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

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

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	81.7
Dual form			81.2.g.a.58.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.925932 + 1.24374i) q^{2} +(1.03494 - 1.38884i) q^{3} +(-0.115939 + 0.387262i) q^{4} +(-2.65494 + 1.74618i) q^{5} +(2.68565 + 0.00122935i) q^{6} +(-0.200969 + 0.213014i) q^{7} +(2.32510 - 0.846267i) q^{8} +(-0.857778 - 2.87476i) q^{9} +O(q^{10})$	\(q+(0.925932 + 1.24374i) q^{2} +(1.03494 - 1.38884i) q^{3} +(-0.115939 + 0.387262i) q^{4} +(-2.65494 + 1.74618i) q^{5} +(2.68565 + 0.00122935i) q^{6} +(-0.200969 + 0.213014i) q^{7} +(2.32510 - 0.846267i) q^{8} +(-0.857778 - 2.87476i) q^{9} +(-4.63010 - 1.68522i) q^{10} +(-5.19744 + 2.61025i) q^{11} +(0.417857 + 0.561816i) q^{12} +(0.0996078 + 0.230917i) q^{13} +(-0.451018 - 0.0527165i) q^{14} +(-0.322542 + 5.49450i) q^{15} +(3.88090 + 2.55251i) q^{16} +(3.14189 - 2.63636i) q^{17} +(2.78121 - 3.72868i) q^{18} +(-3.55906 - 2.98641i) q^{19} +(-0.368420 - 1.23061i) q^{20} +(0.0878524 + 0.499573i) q^{21} +(-8.05895 - 4.04736i) q^{22} +(3.14672 + 3.33533i) q^{23} +(1.23102 - 4.10504i) q^{24} +(2.01916 - 4.68094i) q^{25} +(-0.194971 + 0.337700i) q^{26} +(-4.88034 - 1.78389i) q^{27} +(-0.0591924 - 0.102524i) q^{28} +(5.08083 - 0.593863i) q^{29} +(-7.13240 + 4.68638i) q^{30} +(5.76404 - 1.36610i) q^{31} +(0.131049 + 2.25003i) q^{32} +(-1.75383 + 9.91990i) q^{33} +(6.18813 + 1.46661i) q^{34} +(0.161598 - 0.916469i) q^{35} +(1.21273 + 0.00111025i) q^{36} +(0.850864 + 4.82549i) q^{37} +(0.418873 - 7.19176i) q^{38} +(0.423796 + 0.100646i) q^{39} +(-4.69526 + 6.30683i) q^{40} +(-1.08777 + 1.46113i) q^{41} +(-0.539994 + 0.571836i) q^{42} +(-0.127010 + 2.18068i) q^{43} +(-0.408268 - 2.31540i) q^{44} +(7.29720 + 6.13447i) q^{45} +(-1.23464 + 7.00200i) q^{46} +(-7.45323 - 1.76645i) q^{47} +(7.56156 - 2.74826i) q^{48} +(0.402027 + 6.90254i) q^{49} +(7.69149 - 1.82292i) q^{50} +(-0.409810 - 7.09209i) q^{51} +(-0.100974 + 0.0118021i) q^{52} +(-3.52502 - 6.10552i) q^{53} +(-2.30016 - 7.72165i) q^{54} +(9.24092 - 16.0057i) q^{55} +(-0.287005 + 0.665353i) q^{56} +(-7.83109 + 1.85222i) q^{57} +(5.44311 + 5.76936i) q^{58} +(-8.21945 - 4.12796i) q^{59} +(-2.09042 - 0.761934i) q^{60} +(0.893301 + 2.98383i) q^{61} +(7.03618 + 5.90406i) q^{62} +(0.784751 + 0.395017i) q^{63} +(4.43955 - 3.72523i) q^{64} +(-0.667676 - 0.439137i) q^{65} +(-13.9617 + 7.00384i) q^{66} +(6.79169 + 0.793835i) q^{67} +(0.656696 + 1.52239i) q^{68} +(7.88894 - 0.918424i) q^{69} +(1.28948 - 0.647601i) q^{70} +(4.71278 + 1.71531i) q^{71} +(-4.42723 - 5.95818i) q^{72} +(-1.71510 + 0.624247i) q^{73} +(-5.21382 + 5.52633i) q^{74} +(-4.41138 - 7.64882i) q^{75} +(1.56916 - 1.03205i) q^{76} +(0.488501 - 1.63171i) q^{77} +(0.267228 + 0.620285i) q^{78} +(-6.45435 - 8.66969i) q^{79} -14.7607 q^{80} +(-7.52843 + 4.93180i) q^{81} -2.82447 q^{82} +(-6.02991 - 8.09957i) q^{83} +(-0.203651 - 0.0238979i) q^{84} +(-3.73797 + 12.4857i) q^{85} +(-2.82981 + 1.86120i) q^{86} +(4.43359 - 7.67109i) q^{87} +(-9.87559 + 10.4675i) q^{88} +(9.79723 - 3.56590i) q^{89} +(-0.872991 + 14.7559i) q^{90} +(-0.0692067 - 0.0251892i) q^{91} +(-1.65647 + 0.831912i) q^{92} +(4.06816 - 9.41919i) q^{93} +(-4.70418 - 10.9055i) q^{94} +(14.6639 + 1.71396i) q^{95} +(3.26057 + 2.14665i) q^{96} +(-5.45395 - 3.58712i) q^{97} +(-8.21273 + 6.89130i) q^{98} +(11.9621 + 12.7023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	0.925932	+	1.24374i	0.654733	+	0.879459i	0.998216	−	0.0597000i	$-0.0190144\pi$
$2$	0.925932	+	1.24374i	0.654733	+	0.879459i	−0.343484	+	0.939159i	$0.611607\pi$
$3$	1.03494	−	1.38884i	0.597526	−	0.801850i
$3$	1.03494	−	1.38884i	0.597526	−	0.801850i
$4$	−0.115939	+	0.387262i	−0.0579693	+	0.193631i
$5$	−2.65494	+	1.74618i	−1.18733	+	0.780916i	−0.980318	−	0.197423i	$-0.936743\pi$
$5$	−2.65494	+	1.74618i	−1.18733	+	0.780916i	−0.207007	+	0.978339i	$0.566372\pi$
$6$	2.68565	+	0.00122935i	1.09641	+	0.000501881i
$7$	−0.200969	+	0.213014i	−0.0759591	+	0.0805119i	−0.764238	−	0.644934i	$-0.776885\pi$
$7$	−0.200969	+	0.213014i	−0.0759591	+	0.0805119i	0.688279	+	0.725446i	$0.258366\pi$
$8$	2.32510	−	0.846267i	0.822047	−	0.299200i
$9$	−0.857778	−	2.87476i	−0.285926	−	0.958252i
$10$	−4.63010	−	1.68522i	−1.46416	−	0.532912i
$11$	−5.19744	+	2.61025i	−1.56709	+	0.787020i	−0.999345	−	0.0361867i	$-0.988479\pi$
$11$	−5.19744	+	2.61025i	−1.56709	+	0.787020i	−0.567741	+	0.823207i	$0.692183\pi$
$12$	0.417857	+	0.561816i	0.120625	+	0.162182i
$13$	0.0996078	+	0.230917i	0.0276262	+	0.0640448i	0.931471	−	0.363816i	$-0.118526\pi$
$13$	0.0996078	+	0.230917i	0.0276262	+	0.0640448i	−0.903844	+	0.427861i	$0.859267\pi$
$14$	−0.451018	−	0.0527165i	−0.120540	−	0.0140891i
$15$	−0.322542	+	5.49450i	−0.0832800	+	1.41867i
$16$	3.88090	+	2.55251i	0.970226	+	0.638128i
$17$	3.14189	−	2.63636i	0.762021	−	0.639411i	−0.176631	−	0.984277i	$-0.556520\pi$
$17$	3.14189	−	2.63636i	0.762021	−	0.639411i	0.938652	+	0.344866i	$0.112076\pi$
$18$	2.78121	−	3.72868i	0.655538	−	0.878859i
$19$	−3.55906	−	2.98641i	−0.816505	−	0.685129i	0.135646	−	0.990757i	$-0.456689\pi$
$19$	−3.55906	−	2.98641i	−0.816505	−	0.685129i	−0.952151	+	0.305629i	$0.901133\pi$
$20$	−0.368420	−	1.23061i	−0.0823812	−	0.275172i
$21$	0.0878524	+	0.499573i	0.0191710	+	0.109016i
$22$	−8.05895	−	4.04736i	−1.71817	−	0.862900i
$23$	3.14672	+	3.33533i	0.656137	+	0.695464i	0.966938	−	0.255011i	$-0.0820789\pi$
$23$	3.14672	+	3.33533i	0.656137	+	0.695464i	−0.310802	+	0.950475i	$0.600597\pi$
$24$	1.23102	−	4.10504i	0.251280	−	0.837938i
$25$	2.01916	−	4.68094i	0.403832	−	0.936188i
$26$	−0.194971	+	0.337700i	−0.0382370	+	0.0662284i
$27$	−4.88034	−	1.78389i	−0.939222	−	0.343310i
$28$	−0.0591924	−	0.102524i	−0.0111863	−	0.0193753i
$29$	5.08083	−	0.593863i	0.943486	−	0.110278i	0.369580	−	0.929199i	$-0.379502\pi$
$29$	5.08083	−	0.593863i	0.943486	−	0.110278i	0.573906	+	0.818921i	$0.305428\pi$
$30$	−7.13240	+	4.68638i	−1.30219	+	0.855611i
$31$	5.76404	−	1.36610i	1.03525	−	0.245359i	0.322348	−	0.946621i	$-0.395528\pi$
$31$	5.76404	−	1.36610i	1.03525	−	0.245359i	0.712904	+	0.701262i	$0.247380\pi$
$32$	0.131049	+	2.25003i	0.0231665	+	0.397753i
$33$	−1.75383	+	9.91990i	−0.305302	+	1.72683i
$34$	6.18813	+	1.46661i	1.06126	+	0.251522i
$35$	0.161598	−	0.916469i	0.0273151	−	0.154912i
$36$	1.21273	+	0.00111025i	0.202122	+	0.000185042i
$37$	0.850864	+	4.82549i	0.139881	+	0.793306i	0.971336	+	0.237713i	$0.0763977\pi$
$37$	0.850864	+	4.82549i	0.139881	+	0.793306i	−0.831454	+	0.555593i	$0.812491\pi$
$38$	0.418873	−	7.19176i	0.0679501	−	1.16666i
$39$	0.423796	+	0.100646i	0.0678617	+	0.0161163i
$40$	−4.69526	+	6.30683i	−0.742387	+	0.997198i
$41$	−1.08777	+	1.46113i	−0.169881	+	0.228190i	−0.878908	−	0.476992i	$-0.841727\pi$
$41$	−1.08777	+	1.46113i	−0.169881	+	0.228190i	0.709027	+	0.705182i	$0.249135\pi$
$42$	−0.539994	+	0.571836i	−0.0833229	+	0.0882362i
$43$	−0.127010	+	2.18068i	−0.0193689	+	0.332551i	0.974679	+	0.223608i	$0.0717836\pi$
$43$	−0.127010	+	2.18068i	−0.0193689	+	0.332551i	−0.994048	+	0.108943i	$0.965253\pi$
$44$	−0.408268	−	2.31540i	−0.0615486	−	0.349060i
$45$	7.29720	+	6.13447i	1.08780	+	0.914473i
$46$	−1.23464	+	7.00200i	−0.182038	+	1.03239i
$47$	−7.45323	−	1.76645i	−1.08717	−	0.257663i	−0.352308	−	0.935884i	$-0.614603\pi$
$47$	−7.45323	−	1.76645i	−1.08717	−	0.257663i	−0.734858	+	0.678221i	$0.762751\pi$
$48$	7.56156	−	2.74826i	1.09142	−	0.396678i
$49$	0.402027	+	6.90254i	0.0574324	+	0.986077i
$50$	7.69149	−	1.82292i	1.08774	−	0.257799i
$51$	−0.409810	−	7.09209i	−0.0573849	−	0.993091i
$52$	−0.100974	+	0.0118021i	−0.0140025	+	0.00163666i
$53$	−3.52502	−	6.10552i	−0.484199	−	0.838657i	0.515636	−	0.856808i	$-0.327556\pi$
$53$	−3.52502	−	6.10552i	−0.484199	−	0.838657i	−0.999835	+	0.0181502i	$0.994222\pi$
$54$	−2.30016	−	7.72165i	−0.313012	−	1.05078i
$55$	9.24092	−	16.0057i	1.24604	−	2.15821i
$56$	−0.287005	+	0.665353i	−0.0383527	+	0.0889115i
$57$	−7.83109	+	1.85222i	−1.03725	+	0.245332i
$58$	5.44311	+	5.76936i	0.714716	+	0.757554i
$59$	−8.21945	−	4.12796i	−1.07008	−	0.537415i	−0.175573	−	0.984466i	$-0.556178\pi$
$59$	−8.21945	−	4.12796i	−1.07008	−	0.537415i	−0.894508	+	0.447051i	$0.852474\pi$
$60$	−2.09042	−	0.761934i	−0.269872	−	0.0983652i
$61$	0.893301	+	2.98383i	0.114375	+	0.382041i	0.995940	−	0.0900236i	$-0.0286943\pi$
$61$	0.893301	+	2.98383i	0.114375	+	0.382041i	−0.881564	+	0.472064i	$0.843509\pi$
$62$	7.03618	+	5.90406i	0.893596	+	0.749816i
$63$	0.784751	+	0.395017i	0.0988693	+	0.0497674i
$64$	4.43955	−	3.72523i	0.554944	−	0.465653i
$65$	−0.667676	−	0.439137i	−0.0828150	−	0.0544683i
$66$	−13.9617	+	7.00384i	−1.71857	+	0.862113i
$67$	6.79169	+	0.793835i	0.829738	+	0.0969824i	0.520349	−	0.853953i	$-0.325802\pi$
$67$	6.79169	+	0.793835i	0.829738	+	0.0969824i	0.309388	+	0.950936i	$0.399876\pi$
$68$	0.656696	+	1.52239i	0.0796361	+	0.184617i
$69$	7.88894	−	0.918424i	0.949716	−	0.110565i
$70$	1.28948	−	0.647601i	0.154122	−	0.0774032i
$71$	4.71278	+	1.71531i	0.559304	+	0.203570i	0.606175	−	0.795331i	$-0.292703\pi$
$71$	4.71278	+	1.71531i	0.559304	+	0.203570i	−0.0468717	+	0.998901i	$0.514925\pi$
$72$	−4.42723	−	5.95818i	−0.521754	−	0.702178i
$73$	−1.71510	+	0.624247i	−0.200738	+	0.0730626i	−0.440432	−	0.897786i	$-0.645175\pi$
$73$	−1.71510	+	0.624247i	−0.200738	+	0.0730626i	0.239695	+	0.970848i	$0.422953\pi$
$74$	−5.21382	+	5.52633i	−0.606095	+	0.642423i
$75$	−4.41138	−	7.64882i	−0.509382	−	0.883209i
$76$	1.56916	−	1.03205i	0.179994	−	0.118384i
$77$	0.488501	−	1.63171i	0.0556699	−	0.185950i
$78$	0.267228	+	0.620285i	0.0302576	+	0.0702335i
$79$	−6.45435	−	8.66969i	−0.726171	−	0.975417i	−0.999907	−	0.0136119i	$-0.995667\pi$
$79$	−6.45435	−	8.66969i	−0.726171	−	0.975417i	0.273737	−	0.961805i	$-0.411740\pi$
$80$	−14.7607			−1.65030
$81$	−7.52843	+	4.93180i	−0.836493	+	0.547978i
$82$	−2.82447			−0.311911
$83$	−6.02991	−	8.09957i	−0.661868	−	0.889043i	0.336750	−	0.941594i	$-0.390672\pi$
$83$	−6.02991	−	8.09957i	−0.661868	−	0.889043i	−0.998618	+	0.0525508i	$0.983265\pi$
$84$	−0.203651	−	0.0238979i	−0.0222202	−	0.00260747i
$85$	−3.73797	+	12.4857i	−0.405440	+	1.35426i
$86$	−2.82981	+	1.86120i	−0.305147	+	0.200698i
$87$	4.43359	−	7.67109i	0.475331	−	0.822427i
$88$	−9.87559	+	10.4675i	−1.05274	+	1.11584i
$89$	9.79723	−	3.56590i	1.03850	−	0.377985i	0.234192	−	0.972190i	$-0.424756\pi$
$89$	9.79723	−	3.56590i	1.03850	−	0.377985i	0.804313	+	0.594206i	$0.202533\pi$
$90$	−0.872991	+	14.7559i	−0.0920213	+	1.55541i
$91$	−0.0692067	−	0.0251892i	−0.00725483	−	0.00264054i
$92$	−1.65647	+	0.831912i	−0.172699	+	0.0867329i
$93$	4.06816	−	9.41919i	0.421848	−	0.976725i
$94$	−4.70418	−	10.9055i	−0.485199	−	1.12482i
$95$	14.6639	+	1.71396i	1.50449	+	0.175849i
$96$	3.26057	+	2.14665i	0.332781	+	0.219092i
$97$	−5.45395	−	3.58712i	−0.553765	−	0.364217i	0.241574	−	0.970382i	$-0.422336\pi$
$97$	−5.45395	−	3.58712i	−0.553765	−	0.364217i	−0.795338	+	0.606166i	$0.792707\pi$
$98$	−8.21273	+	6.89130i	−0.829611	+	0.696126i
$99$	11.9621	+	12.7023i	1.20223	+	1.27663i
$100$	1.57865	+	1.32465i	0.157865	+	0.132465i
$101$	−0.0889104	−	0.296981i	−0.00884692	−	0.0295508i	0.953452	−	0.301545i	$-0.0975022\pi$
$101$	−0.0889104	−	0.296981i	−0.00884692	−	0.0295508i	−0.962299	+	0.271994i	$0.912317\pi$
$102$	8.44128	−	7.07649i	0.835811	−	0.700677i
$103$	−8.62814	−	4.33322i	−0.850156	−	0.426964i	−0.0303046	−	0.999541i	$-0.509648\pi$
$103$	−8.62814	−	4.33322i	−0.850156	−	0.426964i	−0.819851	+	0.572576i	$0.805944\pi$
$104$	0.427015	+	0.452610i	0.0418723	+	0.0443820i
$105$	−1.10559	−	1.17293i	−0.107894	−	0.114466i
$106$	4.32976	−	10.0375i	0.420544	−	0.974929i
$107$	−5.31399	+	9.20410i	−0.513723	+	0.889794i	0.486150	+	0.873875i	$0.338401\pi$
$107$	−5.31399	+	9.20410i	−0.513723	+	0.889794i	−0.999873	+	0.0159189i	$0.994933\pi$
$108$	1.25665	−	1.68315i	0.120922	−	0.161961i
$109$	8.57766	+	14.8569i	0.821590	+	1.42304i	0.904497	+	0.426479i	$0.140246\pi$
$109$	8.57766	+	14.8569i	0.821590	+	1.42304i	−0.0829070	+	0.996557i	$0.526420\pi$
$110$	28.4635	−	3.32690i	2.71389	−	0.317208i
$111$	7.58245	+	3.81240i	0.719695	+	0.361857i
$112$	−1.32366	+	0.313714i	−0.125074	+	0.0296432i
$113$	−0.615864	−	10.5740i	−0.0579356	−	0.994717i	−0.894562	−	0.446943i	$-0.852513\pi$
$113$	−0.615864	−	10.5740i	−0.0579356	−	0.994717i	0.836627	−	0.547773i	$-0.184524\pi$
$114$	−9.55473	−	8.02483i	−0.894883	−	0.751594i
$115$	−14.1785	−	3.36036i	−1.32215	−	0.313355i
$116$	−0.359083	+	2.03646i	−0.0333401	+	0.189081i
$117$	0.578388	−	0.484424i	0.0534720	−	0.0447850i
$118$	−2.47653	−	14.0451i	−0.227983	−	1.29296i
$119$	−0.0698393	+	1.19909i	−0.00640216	+	0.109921i
$120$	3.89987	+	13.0482i	0.356008	+	1.19113i
$121$	13.6312	−	18.3099i	1.23920	−	1.66453i
$122$	−2.88398	+	3.87386i	−0.261104	+	0.350723i
$123$	0.903500	+	3.02293i	0.0814658	+	0.272569i
$124$	−0.139235	+	2.39058i	−0.0125037	+	0.214680i
$125$	0.0540020	+	0.306261i	0.00483008	+	0.0273928i
$126$	0.235327	+	1.34179i	0.0209646	+	0.119536i
$127$	−2.51136	+	14.2427i	−0.222848	+	1.26383i	0.643910	+	0.765101i	$0.277311\pi$
$127$	−2.51136	+	14.2427i	−0.222848	+	1.26383i	−0.866757	+	0.498730i	$0.833800\pi$
$128$	13.1301	+	3.11190i	1.16055	+	0.275056i
$129$	2.89718	+	2.43329i	0.255083	+	0.214239i
$130$	−0.0720487	−	1.23703i	−0.00631909	−	0.108495i
$131$	−3.72370	+	0.882534i	−0.325342	+	0.0771074i	−0.390041	−	0.920797i	$-0.627539\pi$
$131$	−3.72370	+	0.882534i	−0.325342	+	0.0771074i	0.0646996	+	0.997905i	$0.479391\pi$
$132$	−3.63827	−	1.82929i	−0.316670	−	0.159219i
$133$	1.35141	−	0.157957i	0.117182	−	0.0136966i
$134$	5.30132	+	9.18216i	0.457964	+	0.793217i
$135$	16.0720	−	3.78584i	1.38326	−	0.325833i
$136$	5.07415	−	8.78868i	0.435104	−	0.753623i
$137$	−5.65021	+	13.0987i	−0.482730	+	1.11909i	0.486666	+	0.873588i	$0.338213\pi$
$137$	−5.65021	+	13.0987i	−0.482730	+	1.11909i	−0.969395	+	0.245505i	$0.921046\pi$
$138$	8.44690	+	8.96141i	0.719048	+	0.762846i
$139$	−4.04427	−	4.28668i	−0.343031	−	0.363591i	0.532773	−	0.846258i	$-0.321150\pi$
$139$	−4.04427	−	4.28668i	−0.343031	−	0.363591i	−0.875804	+	0.482667i	$0.839668\pi$
$140$	0.336178	+	0.168835i	0.0284123	+	0.0142692i
$141$	−10.1670	+	8.52320i	−0.856216	+	0.717783i
$142$	2.23031	+	7.44974i	0.187163	+	0.625168i
$143$	−1.12046	−	0.940175i	−0.0936973	−	0.0786213i
$144$	4.00889	−	13.3461i	0.334074	−	1.11218i
$145$	−12.4523	+	10.4487i	−1.03411	+	0.867719i
$146$	−2.36447	−	1.55514i	−0.195685	−	0.128704i
$147$	10.0026	+	6.58539i	0.825003	+	0.543154i
$148$	−1.96738	−	0.229954i	−0.161717	−	0.0189021i
$149$	5.58042	+	12.9369i	0.457166	+	1.05983i	0.978457	+	0.206451i	$0.0661913\pi$
$149$	5.58042	+	12.9369i	0.457166	+	1.05983i	−0.521291	+	0.853379i	$0.674549\pi$
$150$	5.42852	−	12.5689i	0.443237	−	1.02625i
$151$	1.41535	−	0.710815i	0.115180	−	0.0578453i	−0.390276	−	0.920698i	$-0.627621\pi$
$151$	1.41535	−	0.710815i	0.115180	−	0.0578453i	0.505456	+	0.862852i	$0.331324\pi$
$152$	−10.8025	−	3.93178i	−0.876196	−	0.318909i
$153$	−10.2739	−	6.77076i	−0.830599	−	0.547383i
$154$	2.48174	−	0.903281i	0.199985	−	0.0727884i
$155$	−12.9177	+	13.6920i	−1.03758	+	1.09977i
$156$	−0.0881110	+	0.152451i	−0.00705452	+	0.0122059i
$157$	−4.28135	+	2.81589i	−0.341689	+	0.224732i	−0.708742	−	0.705468i	$-0.750737\pi$
$157$	−4.28135	+	2.81589i	−0.341689	+	0.224732i	0.367053	+	0.930200i	$0.380367\pi$
$158$	4.80658	−	16.0551i	0.382391	−	1.27727i
$159$	−12.1278	−	1.42317i	−0.961799	−	0.112864i
$160$	−4.27689	−	5.74486i	−0.338118	−	0.454171i
$161$	−1.34287			−0.105833
$162$	−13.1047	−	4.79692i	−1.02960	−	0.376881i
$163$	−17.6764			−1.38452			−0.692262	−	0.721646i	$-0.743386\pi$
$163$	−17.6764			−1.38452			−0.692262	+	0.721646i	$0.743386\pi$
$164$	−0.439726	−	0.590654i	−0.0343368	−	0.0461223i
$165$	−12.6656	−	29.3992i	−0.986019	−	2.28873i
$166$	4.49050	−	14.9993i	0.348530	−	1.16417i
$167$	−1.15161	+	0.757426i	−0.0891143	+	0.0586114i	−0.593284	−	0.804993i	$-0.702169\pi$
$167$	−1.15161	+	0.757426i	−0.0891143	+	0.0586114i	0.504170	+	0.863605i	$0.331799\pi$
$168$	0.627037	+	1.08721i	0.0483770	+	0.0838800i
$169$	8.87774	−	9.40986i	0.682903	−	0.723835i
$170$	−18.9901	+	6.91183i	−1.45647	+	0.530113i
$171$	−5.53230	+	12.7931i	−0.423066	+	0.978313i
$172$	−0.829771	−	0.302012i	−0.0632695	−	0.0230282i
$173$	11.6171	−	5.83431i	0.883230	−	0.443575i	0.0514468	−	0.998676i	$-0.483617\pi$
$173$	11.6171	−	5.83431i	0.883230	−	0.443575i	0.831783	+	0.555101i	$0.187320\pi$
$174$	13.6461	−	1.58866i	1.03451	−	0.120436i
$175$	0.591320	+	1.37083i	0.0446996	+	0.103625i
$176$	−26.8335	−	3.13638i	−2.02265	−	0.236414i
$177$	−14.2398	+	7.14333i	−1.07033	+	0.536925i
$178$	13.5066	+	8.88345i	1.01237	+	0.665843i
$179$	19.1637	−	16.0803i	1.43237	−	1.20190i	0.488067	−	0.872806i	$-0.337702\pi$
$179$	19.1637	−	16.0803i	1.43237	−	1.20190i	0.944298	−	0.329091i	$-0.106742\pi$
$180$	−3.22168	+	2.11471i	−0.240129	+	0.157621i
$181$	3.52910	+	2.96126i	0.262316	+	0.220109i	0.764454	−	0.644678i	$-0.223009\pi$
$181$	3.52910	+	2.96126i	0.262316	+	0.220109i	−0.502138	+	0.864787i	$0.667453\pi$
$182$	−0.0327518	−	0.109399i	−0.00242773	−	0.00810917i
$183$	5.06860	+	1.84745i	0.374681	+	0.136567i
$184$	10.1390	+	5.09201i	0.747458	+	0.375388i
$185$	−10.6852	−	11.3256i	−0.785590	−	0.832677i
$186$	15.4819	−	3.66179i	1.13519	−	0.268495i
$187$	−9.44823	+	21.9035i	−0.690923	+	1.60174i
$188$	1.54820	−	2.68156i	0.112914	−	0.195573i
$189$	1.36079	−	0.681076i	0.0989830	−	0.0495410i
$190$	11.4460	+	19.8251i	0.830384	+	1.43827i
$191$	−2.66989	+	0.312065i	−0.193186	+	0.0225803i	−0.212136	−	0.977240i	$-0.568042\pi$
$191$	−2.66989	+	0.312065i	−0.193186	+	0.0225803i	0.0189494	+	0.999820i	$0.493968\pi$
$192$	−0.579069	−	10.0213i	−0.0417907	−	0.723222i
$193$	6.42800	−	1.52346i	0.462697	−	0.109661i	0.00734588	−	0.999973i	$-0.497662\pi$
$193$	6.42800	−	1.52346i	0.462697	−	0.109661i	0.455352	+	0.890312i	$0.349514\pi$
$194$	−0.588534	−	10.1047i	−0.0422543	−	0.725478i
$195$	−1.30090	+	0.472815i	−0.0931595	+	0.0338590i
$196$	−2.71970	−	0.644581i	−0.194264	−	0.0460415i
$197$	−2.65657	+	15.0662i	−0.189273	+	1.07342i	0.731068	+	0.682304i	$0.239022\pi$
$197$	−2.65657	+	15.0662i	−0.189273	+	1.07342i	−0.920341	+	0.391116i	$0.872089\pi$
$198$	−4.72237	+	26.6393i	−0.335604	+	1.89317i
$199$	2.44426	+	13.8621i	0.173269	+	0.982657i	0.940123	+	0.340835i	$0.110710\pi$
$199$	2.44426	+	13.8621i	0.173269	+	0.982657i	−0.766854	+	0.641821i	$0.778179\pi$
$200$	0.733424	−	12.5924i	0.0518609	−	0.890417i
$201$	8.13154	−	8.61103i	0.573555	−	0.607375i
$202$	0.287043	−	0.385566i	0.0201963	−	0.0271283i
$203$	−0.894586	+	1.20164i	−0.0627876	+	0.0843384i
$204$	2.79401	+	0.663544i	0.195620	+	0.0464574i
$205$	0.336569	−	5.77866i	0.0235070	−	0.403599i
$206$	−2.59967	−	14.7434i	−0.181127	−	1.02722i
$207$	6.88907	−	11.9070i	0.478823	−	0.827596i
$208$	−0.202849	+	1.15042i	−0.0140651	+	0.0797670i
$209$	26.2933	+	6.23162i	1.81874	+	0.431050i
$210$	0.435123	−	2.46112i	0.0300264	−	0.169833i
$211$	−0.898645	−	15.4291i	−0.0618653	−	1.06219i	−0.876249	−	0.481859i	$-0.839962\pi$
$211$	−0.898645	−	15.4291i	−0.0618653	−	1.06219i	0.814384	−	0.580327i	$-0.197075\pi$
$212$	2.77312	−	0.657242i	0.190459	−	0.0451396i
$213$	7.25976	−	4.77006i	0.497431	−	0.326839i
$214$	−16.3679	+	1.91314i	−1.11889	+	0.130779i
$215$	−3.47067	−	6.01137i	−0.236698	−	0.409972i
$216$	−12.8569	−	0.0176557i	−0.874803	−	0.00120132i
$217$	−0.867392	+	1.50237i	−0.0588824	+	0.101987i
$218$	−10.5359	+	24.4249i	−0.713579	+	1.65426i
$219$	−0.908056	+	3.02807i	−0.0613608	+	0.204618i
$220$	5.12704	+	5.43434i	0.345665	+	0.366383i
$221$	0.921737	+	0.462914i	0.0620028	+	0.0311390i
$222$	2.27919	+	12.9606i	0.152969	+	0.869861i
$223$	−1.39226	−	4.65047i	−0.0932325	−	0.311418i	0.898634	−	0.438699i	$-0.144560\pi$
$223$	−1.39226	−	4.65047i	−0.0932325	−	0.311418i	−0.991867	+	0.127280i	$0.959375\pi$
$224$	−0.505626	−	0.424270i	−0.0337836	−	0.0283478i
$225$	−15.1886	−	1.78938i	−1.01257	−	0.119292i
$226$	12.5811	−	10.5568i	0.836880	−	0.702225i
$227$	16.1686	+	10.6342i	1.07315	+	0.705820i	0.957780	−	0.287503i	$-0.0928252\pi$
$227$	16.1686	+	10.6342i	1.07315	+	0.705820i	0.115367	+	0.993323i	$0.463196\pi$
$228$	0.190633	−	3.24743i	0.0126250	−	0.215066i
$229$	3.65865	+	0.427635i	0.241770	+	0.0282589i	0.236115	−	0.971725i	$-0.424126\pi$
$229$	3.65865	+	0.427635i	0.241770	+	0.0282589i	0.00565534	+	0.999984i	$0.498200\pi$
$230$	−8.94887	−	20.7458i	−0.590071	−	1.36794i
$231$	−1.76062	−	2.36718i	−0.115840	−	0.155749i
$232$	11.3109	−	5.68053i	0.742594	−	0.372945i
$233$	−1.43618	−	0.522727i	−0.0940872	−	0.0342450i	0.294548	−	0.955637i	$-0.404831\pi$
$233$	−1.43618	−	0.522727i	−0.0940872	−	0.0342450i	−0.388635	+	0.921392i	$0.627053\pi$
$234$	1.13805	+	0.270822i	0.0743964	+	0.0177042i
$235$	22.8724	−	8.32488i	1.49203	−	0.543056i
$236$	2.55156	−	2.70449i	0.166092	−	0.176047i
$237$	−18.7207	−	0.00856939i	−1.21604	−	0.000556642i
$238$	−1.55603	+	1.02342i	−0.100863	+	0.0663383i
$239$	−1.36488	+	4.55903i	−0.0882871	+	0.294899i	−0.990718	−	0.135936i	$-0.956596\pi$
$239$	−1.36488	+	4.55903i	−0.0882871	+	0.294899i	0.902431	+	0.430835i	$0.141781\pi$
$240$	−15.2765	+	20.5003i	−0.986096	+	1.32329i
$241$	15.1105	+	20.2969i	0.973350	+	1.30744i	0.951491	+	0.307675i	$0.0995511\pi$
$241$	15.1105	+	20.2969i	0.973350	+	1.30744i	0.0218591	+	0.999761i	$0.493041\pi$
$242$	35.3943			2.27523
$243$	−0.942003	+	15.5600i	−0.0604295	+	0.998172i
$244$	−1.25909			−0.0806052
$245$	−13.1204	−	17.6238i	−0.838235	−	1.12594i
$246$	−2.92317	+	3.92275i	−0.186375	+	0.250106i
$247$	0.335101	−	1.11932i	0.0213220	−	0.0712204i
$248$	12.2459	−	8.05424i	0.777614	−	0.511444i
$249$	−17.4897	−	0.00800586i	−1.10836	−	0.000507351i
$250$	−0.330907	+	0.350741i	−0.0209284	+	0.0221828i
$251$	−2.06755	+	0.752528i	−0.130503	+	0.0474991i	−0.406446	−	0.913675i	$-0.633232\pi$
$251$	−2.06755	+	0.752528i	−0.130503	+	0.0474991i	0.275943	+	0.961174i	$0.411010\pi$
$252$	−0.243958	+	0.258107i	−0.0153679	+	0.0162592i
$253$	−25.0609	−	9.12143i	−1.57557	−	0.573460i
$254$	−20.0395	+	10.0642i	−1.25739	+	0.631487i
$255$	13.4721	+	18.1135i	0.843656	+	1.13431i
$256$	3.69630	+	8.56900i	0.231019	+	0.535562i
$257$	10.1971	+	1.19186i	0.636075	+	0.0743465i	0.428018	−	0.903770i	$-0.359212\pi$
$257$	10.1971	+	1.19186i	0.636075	+	0.0743465i	0.208057	+	0.978117i	$0.433286\pi$
$258$	−0.343787	+	5.85641i	−0.0214032	+	0.364604i
$259$	−1.19890	−	0.788527i	−0.0744958	−	0.0489967i
$260$	0.247471	−	0.207653i	0.0153475	−	0.0128781i
$261$	−6.06543	−	14.0967i	−0.375441	−	0.872565i
$262$	−4.54554	−	3.81416i	−0.280825	−	0.235640i
$263$	−0.455133	−	1.52025i	−0.0280647	−	0.0937426i	0.942810	−	0.333331i	$-0.108173\pi$
$263$	−0.455133	−	1.52025i	−0.0280647	−	0.0937426i	−0.970875	+	0.239588i	$0.922987\pi$
$264$	4.31706	+	24.5490i	0.265696	+	1.51088i
$265$	20.0201	+	10.0545i	1.22982	+	0.617641i
$266$	1.44777	+	1.53455i	0.0887684	+	0.0940890i
$267$	5.18711	−	17.2973i	0.317446	−	1.05858i
$268$	−1.09484	+	2.53813i	−0.0668782	+	0.155041i
$269$	2.49753	−	4.32585i	0.152277	−	0.263752i	−0.779787	−	0.626045i	$-0.784673\pi$
$269$	2.49753	−	4.32585i	0.152277	−	0.263752i	0.932064	+	0.362293i	$0.118006\pi$
$270$	19.5902	+	16.4840i	1.19222	+	1.00319i
$271$	−4.63580	−	8.02944i	−0.281605	−	0.487754i	0.690175	−	0.723642i	$-0.257533\pi$
$271$	−4.63580	−	8.02944i	−0.281605	−	0.487754i	−0.971780	+	0.235888i	$0.924200\pi$
$272$	18.9227	−	2.21175i	1.14736	−	0.134107i
$273$	−0.106609	+	0.0700479i	−0.00645227	+	0.00423949i
$274$	−21.5231	+	5.10106i	−1.30026	+	0.308166i
$275$	1.72397	+	29.5994i	0.103959	+	1.78491i
$276$	−0.558962	+	3.16157i	−0.0336456	+	0.190304i
$277$	−25.1474	−	5.96004i	−1.51096	−	0.358104i	−0.610139	−	0.792294i	$-0.708887\pi$
$277$	−25.1474	−	5.96004i	−1.51096	−	0.358104i	−0.900821	+	0.434190i	$0.857035\pi$
$278$	1.58680	−	8.99921i	0.0951701	−	0.539737i
$279$	−8.87147	−	15.3984i	−0.531121	−	0.921877i
$280$	−0.399845	−	2.26764i	−0.0238953	−	0.135517i
$281$	1.68385	−	28.9105i	0.100450	−	1.72466i	−0.452775	−	0.891625i	$-0.649566\pi$
$281$	1.68385	−	28.9105i	0.100450	−	1.72466i	0.553225	−	0.833032i	$-0.313397\pi$
$282$	−20.0146	−	4.75323i	−1.19185	−	0.283051i
$283$	0.616270	−	0.827794i	0.0366334	−	0.0492072i	−0.783429	−	0.621481i	$-0.786531\pi$
$283$	0.616270	−	0.827794i	0.0366334	−	0.0492072i	0.820062	+	0.572274i	$0.193939\pi$
$284$	−1.21067	+	1.62621i	−0.0718399	+	0.0964978i
$285$	17.5568	−	18.5920i	1.03997	−	1.10130i
$286$	0.131869	−	2.26410i	0.00779755	−	0.133879i
$287$	−0.0926338	−	0.525353i	−0.00546800	−	0.0310106i
$288$	6.35588	−	2.30676i	0.374524	−	0.135927i
$289$	−0.0309285	+	0.175404i	−0.00181932	+	0.0103179i
$290$	−24.5255	−	5.81265i	−1.44019	−	0.341331i
$291$	−10.6265	+	3.86222i	−0.622936	+	0.226407i
$292$	−0.0429003	−	0.736569i	−0.00251055	−	0.0431045i
$293$	6.75313	−	1.60052i	0.394522	−	0.0935035i	−0.0285661	−	0.999592i	$-0.509094\pi$
$293$	6.75313	−	1.60052i	0.394522	−	0.0935035i	0.423088	+	0.906088i	$0.360946\pi$
$294$	1.07122	+	18.5383i	0.0624748	+	1.08118i
$295$	29.0303	−	3.39316i	1.69021	−	0.197557i
$296$	6.06200	+	10.4997i	0.352346	+	0.610282i
$297$	30.0217	−	3.46725i	1.74203	−	0.201190i
$298$	−10.9230	+	18.9193i	−0.632755	+	1.09596i
$299$	−0.456746	+	1.05886i	−0.0264143	+	0.0612352i
$300$	3.47355	−	0.821567i	0.200545	−	0.0474332i
$301$	−0.438992	−	0.465305i	−0.0253031	−	0.0268197i
$302$	2.19459	+	1.10216i	0.126284	+	0.0634224i
$303$	−0.504479	−	0.183877i	−0.0289815	−	0.0105634i
$304$	−6.18954	−	20.6745i	−0.354994	−	1.18576i
$305$	−7.58197	−	6.36203i	−0.434143	−	0.364289i
$306$	−1.09189	−	19.0474i	−0.0624191	−	1.08887i
$307$	14.0395	−	11.7805i	0.801275	−	0.672350i	−0.147233	−	0.989102i	$-0.547037\pi$
$307$	14.0395	−	11.7805i	0.801275	−	0.672350i	0.948508	+	0.316752i	$0.102592\pi$
$308$	0.575263	+	0.378356i	0.0327786	+	0.0215588i
$309$	−14.9478	+	7.49851i	−0.850351	+	0.426575i
$310$	−28.9902	−	3.38847i	−1.64653	−	0.192452i
$311$	5.82070	+	13.4939i	0.330062	+	0.765169i	0.999746	+	0.0225232i	$0.00716997\pi$
$311$	5.82070	+	13.4939i	0.330062	+	0.765169i	−0.669685	+	0.742645i	$0.733571\pi$
$312$	1.07054	−	0.124632i	0.0606075	−	0.00705588i
$313$	5.05726	−	2.53985i	0.285853	−	0.143561i	−0.300095	−	0.953909i	$-0.597018\pi$
$313$	5.05726	−	2.53985i	0.285853	−	0.143561i	0.585948	+	0.810348i	$0.300722\pi$
$314$	−7.46647	−	2.71757i	−0.421358	−	0.153362i
$315$	−2.77324	+	0.321572i	−0.156254	+	0.0181185i
$316$	4.10575	−	1.49437i	0.230967	−	0.0840650i
$317$	15.7261	−	16.6687i	0.883267	−	0.936208i	−0.115099	−	0.993354i	$-0.536719\pi$
$317$	15.7261	−	16.6687i	0.883267	−	0.936208i	0.998366	+	0.0571458i	$0.0182000\pi$
$318$	−9.45948	−	16.4016i	−0.530461	−	0.919758i
$319$	−24.8571	+	16.3488i	−1.39173	+	0.915357i
$320$	−5.28183	+	17.6425i	−0.295263	+	0.986247i
$321$	7.28338	+	16.9060i	0.406519	+	0.943603i
$322$	−1.24340	−	1.67018i	−0.0692921	−	0.0930755i
$323$	−19.0554			−1.06027
$324$	−1.03706	−	3.48726i	−0.0576147	−	0.193737i
$325$	1.28203			0.0711144
$326$	−16.3672	−	21.9849i	−0.906493	−	1.21763i
$327$	29.5114	+	3.46308i	1.63198	+	0.191509i
$328$	−1.29267	+	4.31782i	−0.0713757	+	0.238412i
$329$	1.87415	−	1.23264i	0.103325	−	0.0679579i
$330$	24.8376	−	42.9745i	1.36726	−	2.36567i
$331$	−2.11190	+	2.23849i	−0.116081	+	0.123038i	−0.782808	−	0.622264i	$-0.786213\pi$
$331$	−2.11190	+	2.23849i	−0.116081	+	0.123038i	0.666727	+	0.745302i	$0.267695\pi$
$332$	3.83576	−	1.39610i	0.210515	−	0.0766210i
$333$	13.1423	−	6.58523i	0.720191	−	0.360868i
$334$	−2.00836	−	0.730982i	−0.109892	−	0.0399975i
$335$	−19.4177	+	9.75195i	−1.06090	+	0.532806i
$336$	−0.934218	+	2.16304i	−0.0509658	+	0.118003i
$337$	−1.62778	−	3.77363i	−0.0886711	−	0.205563i	0.868110	−	0.496372i	$-0.165335\pi$
$337$	−1.62778	−	3.77363i	−0.0886711	−	0.205563i	−0.956781	+	0.290809i	$0.906076\pi$
$338$	19.9236	+	2.32874i	1.08370	+	0.126667i
$339$	−15.3230	−	10.0881i	−0.832231	−	0.547913i
$340$	−4.40186	−	2.89515i	−0.238725	−	0.157012i
$341$	−26.3924	+	22.1458i	−1.42923	+	1.19926i
$342$	−21.0339	+	4.96478i	−1.13738	+	0.268465i
$343$	−3.12151	−	2.61926i	−0.168546	−	0.141427i
$344$	1.55013	+	5.17779i	0.0835774	+	0.279168i
$345$	−19.3409	+	16.2139i	−1.04128	+	0.872926i
$346$	18.0130	+	9.04647i	0.968385	+	0.486341i
$347$	6.14191	+	6.51005i	0.329715	+	0.349478i	0.870930	−	0.491407i	$-0.163517\pi$
$347$	6.14191	+	6.51005i	0.329715	+	0.349478i	−0.541215	+	0.840884i	$0.682036\pi$
$348$	2.45670	+	2.60634i	0.131693	+	0.139714i
$349$	1.96434	−	4.55386i	0.105149	−	0.243762i	−0.857517	−	0.514456i	$-0.827994\pi$
$349$	1.96434	−	4.55386i	0.105149	−	0.243762i	0.962666	+	0.270694i	$0.0872531\pi$
$350$	−1.15744	+	2.00475i	−0.0618679	+	0.107158i
$351$	−0.0741893	−	1.30464i	−0.00395993	−	0.0696367i
$352$	−6.55427	−	11.3523i	−0.349344	−	0.605081i
$353$	−20.1602	+	2.35639i	−1.07302	+	0.125418i	−0.634209	−	0.773161i	$-0.718674\pi$
$353$	−20.1602	+	2.35639i	−1.07302	+	0.125418i	−0.438811	+	0.898579i	$0.644600\pi$
$354$	−22.0695	−	11.0964i	−1.17298	−	0.589766i
$355$	−15.5074	+	3.67532i	−0.823047	+	0.195066i
$356$	0.245060	+	4.20752i	0.0129882	+	0.222998i
$357$	1.59308	+	1.33799i	0.0843145	+	0.0708141i
$358$	37.7441	+	8.94551i	1.99484	+	0.472785i
$359$	−1.35166	+	7.66566i	−0.0713380	+	0.404578i	0.928139	+	0.372234i	$0.121408\pi$
$359$	−1.35166	+	7.66566i	−0.0713380	+	0.404578i	−0.999477	+	0.0323438i	$0.989703\pi$
$360$	22.1581	+	8.08787i	1.16783	+	0.426268i
$361$	0.448974	+	2.54626i	0.0236302	+	0.134014i
$362$	−0.415346	+	7.13122i	−0.0218301	+	0.374808i
$363$	−11.3220	−	37.8813i	−0.594253	−	1.98825i
$364$	0.0177785	−	0.0238807i	0.000931849	−	0.00125169i
$365$	3.46345	−	4.65222i	0.181285	−	0.243508i
$366$	2.39543	+	8.01464i	0.125211	+	0.418932i
$367$	0.0112963	−	0.193950i	0.000589663	−	0.0101241i	−0.998000	−	0.0632061i	$-0.979867\pi$
$367$	0.0112963	−	0.193950i	0.000589663	−	0.0101241i	0.998590	+	0.0530820i	$0.0169045\pi$
$368$	3.69866	+	20.9761i	0.192806	+	1.09346i
$369$	5.13346	+	1.87375i	0.267237	+	0.0975435i
$370$	4.19242	−	23.7764i	0.217953	−	1.23607i
$371$	2.00898	+	0.476138i	0.104301	+	0.0247198i
$372$	3.17604	+	2.66749i	0.164670	+	0.138303i
$373$	−0.132942	−	2.28253i	−0.00688350	−	0.118185i	−0.999999	−	0.00104965i	$-0.999666\pi$
$373$	−0.132942	−	2.28253i	−0.00688350	−	0.118185i	0.993116	−	0.117135i	$-0.0373712\pi$
$374$	−35.9907	+	8.52994i	−1.86103	+	0.441073i
$375$	0.481237	+	0.241962i	0.0248510	+	0.0124949i
$376$	−18.8244	+	2.20026i	−0.970794	+	0.113469i
$377$	0.643223	+	1.11409i	0.0331277	+	0.0573788i
$378$	2.10708	+	1.06184i	0.108377	+	0.0546153i
$379$	3.62704	−	6.28222i	0.186309	−	0.322696i	−0.757708	−	0.652594i	$-0.773681\pi$
$379$	3.62704	−	6.28222i	0.186309	−	0.322696i	0.944017	+	0.329898i	$0.107014\pi$
$380$	−2.36387	+	5.48006i	−0.121264	+	0.281121i
$381$	17.1817	+	18.2283i	0.880246	+	0.933862i
$382$	−2.86027	−	3.03170i	−0.146344	−	0.155115i
$383$	24.1849	+	12.1461i	1.23579	+	0.620637i	0.942122	−	0.335271i	$-0.108828\pi$
$383$	24.1849	+	12.1461i	1.23579	+	0.620637i	0.293667	+	0.955908i	$0.405124\pi$
$384$	17.9109	−	15.0151i	0.914012	−	0.766234i
$385$	1.55232	+	5.18510i	0.0791134	+	0.264257i
$386$	7.84669	+	6.58415i	0.399386	+	0.335124i
$387$	6.37788	−	1.50542i	0.324206	−	0.0765248i
$388$	2.02148	−	1.69622i	0.102625	−	0.0861126i
$389$	19.1210	+	12.5761i	0.969474	+	0.637633i	0.932304	−	0.361676i	$-0.117795\pi$
$389$	19.1210	+	12.5761i	0.969474	+	0.637633i	0.0371701	+	0.999309i	$0.488166\pi$
$390$	−1.79261	−	1.18019i	−0.0907721	−	0.0597613i
$391$	18.6798	+	2.18335i	0.944678	+	0.110417i
$392$	6.77614	+	15.7089i	0.342247	+	0.793417i
$393$	−2.62813	+	6.08502i	−0.132571	+	0.306949i
$394$	−21.1982	+	10.6462i	−1.06795	+	0.536346i
$395$	32.2748	+	11.7471i	1.62392	+	0.591059i
$396$	−6.30601	+	3.15977i	−0.316889	+	0.158784i
$397$	−16.8844	+	6.14542i	−0.847403	+	0.308430i	−0.728981	−	0.684534i	$-0.760006\pi$
$397$	−16.8844	+	6.14542i	−0.847403	+	0.308430i	−0.118422	+	0.992963i	$0.537784\pi$
$398$	−14.9776	+	15.8754i	−0.750761	+	0.795760i
$399$	1.17925	−	2.04037i	0.0590366	−	0.102146i
$400$	19.7843	−	13.0124i	0.989216	−	0.650618i
$401$	0.411776	−	1.37543i	0.0205631	−	0.0686856i	−0.947092	−	0.320962i	$-0.895994\pi$
$401$	0.411776	−	1.37543i	0.0205631	−	0.0686856i	0.967655	+	0.252276i	$0.0811791\pi$
$402$	18.2392	+	2.14032i	0.909687	+	0.106749i
$403$	0.889599	+	1.19494i	0.0443141	+	0.0595242i
$404$	0.125318			0.00623480
$405$	11.3757	−	26.2397i	0.565264	−	1.30386i
$406$	−2.32285			−0.115281
$407$	−17.0181	−	22.8592i	−0.843554	−	1.13309i
$408$	−6.95465	−	16.1430i	−0.344306	−	0.799198i
$409$	−3.73740	+	12.4838i	−0.184803	+	0.617284i	0.814508	+	0.580153i	$0.197007\pi$
$409$	−3.73740	+	12.4838i	−0.184803	+	0.617284i	−0.999310	+	0.0371312i	$0.988178\pi$
$410$	7.49881	−	4.93204i	0.370340	−	0.243576i
$411$	12.3443	+	21.4036i	0.608901	+	1.05576i
$412$	2.67843	−	2.83897i	0.131957	−	0.139866i
$413$	2.53117	−	0.921270i	0.124551	−	0.0453328i
$414$	21.1881	−	2.45687i	1.04134	−	0.120749i
$415$	30.1524	+	10.9746i	1.48012	+	0.538720i
$416$	−0.506517	+	0.254382i	−0.0248340	+	0.0124721i
$417$	−10.1391	+	1.18039i	−0.496515	+	0.0578040i
$418$	16.5952	+	38.4721i	0.811700	+	1.88173i
$419$	−29.7448	−	3.47667i	−1.45313	−	0.169846i	−0.647408	−	0.762143i	$-0.724147\pi$
$419$	−29.7448	−	3.47667i	−1.45313	−	0.169846i	−0.805720	+	0.592297i	$0.798221\pi$
$420$	0.582412	−	0.292164i	0.0284188	−	0.0142562i
$421$	−26.9903	−	17.7518i	−1.31543	−	0.865171i	−0.318849	−	0.947806i	$-0.603296\pi$
$421$	−26.9903	−	17.7518i	−1.31543	−	0.865171i	−0.996580	+	0.0826343i	$0.973667\pi$
$422$	18.3578	−	15.4040i	0.893643	−	0.749856i
$423$	1.31511	+	22.9414i	0.0639430	+	1.11545i
$424$	−13.3629	−	11.2128i	−0.648961	−	0.544543i
$425$	−5.99666	−	20.0303i	−0.290881	−	0.971610i
$426$	12.6548	+	4.61252i	0.613126	+	0.223477i
$427$	−0.815125	−	0.409371i	−0.0394467	−	0.0198109i
$428$	−2.94830	−	3.12502i	−0.142512	−	0.151053i
$429$	−2.46537	+	0.583111i	−0.119029	+	0.0281529i
$430$	4.26300	−	9.88274i	0.205580	−	0.476588i
$431$	15.3414	−	26.5721i	0.738970	−	1.27993i	−0.213989	−	0.976836i	$-0.568646\pi$
$431$	15.3414	−	26.5721i	0.738970	−	1.27993i	0.952960	−	0.303098i	$-0.0980208\pi$
$432$	−14.3867	−	19.3802i	−0.692182	−	0.932432i
$433$	−19.2517	−	33.3449i	−0.925176	−	1.60245i	−0.791277	−	0.611457i	$-0.790584\pi$
$433$	−19.2517	−	33.3449i	−0.925176	−	1.60245i	−0.133899	−	0.990995i	$-0.542750\pi$
$434$	−2.67170	+	0.312277i	−0.128246	+	0.0149898i
$435$	1.62420	+	28.1082i	0.0778746	+	1.34768i
$436$	−6.74801	+	1.59931i	−0.323171	+	0.0765930i
$437$	−1.23872	−	21.2680i	−0.0592561	−	1.01739i
$438$	−4.60694	+	1.67440i	−0.220128	+	0.0800060i
$439$	38.5142	+	9.12802i	1.83818	+	0.435657i	0.994817	−	0.101686i	$-0.0324237\pi$
$439$	38.5142	+	9.12802i	1.83818	+	0.435657i	0.843364	+	0.537343i	$0.180572\pi$
$440$	7.94092	−	45.0352i	0.378569	−	2.14697i
$441$	19.4983	−	7.07658i	0.928488	−	0.336980i
$442$	0.277720	+	1.57503i	0.0132098	+	0.0749166i
$443$	−0.351273	+	6.03112i	−0.0166895	+	0.286547i	0.979629	+	0.200816i	$0.0643595\pi$
$443$	−0.351273	+	6.03112i	−0.0166895	+	0.286547i	−0.996318	+	0.0857306i	$0.972678\pi$
$444$	−2.35550	+	2.49439i	−0.111787	+	0.118379i
$445$	−19.7844	+	26.5750i	−0.937869	+	1.25978i
$446$	4.49485	−	6.03763i	0.212837	−	0.285890i
$447$	23.7427	+	5.63861i	1.12299	+	0.266697i
$448$	−0.0986843	+	1.69434i	−0.00466239	+	0.0800502i
$449$	−0.417057	−	2.36525i	−0.0196821	−	0.111623i	0.973384	−	0.229181i	$-0.0736046\pi$
$449$	−0.417057	−	2.36525i	−0.0196821	−	0.111623i	−0.993066	+	0.117558i	$0.962494\pi$
$450$	−11.8380	−	20.5475i	−0.558050	−	0.968618i
$451$	1.83971	−	10.4335i	0.0866284	−	0.491294i
$452$	4.16631	+	0.987433i	0.195967	+	0.0464449i
$453$	0.477597	−	2.70136i	0.0224395	−	0.126921i
$454$	1.74475	+	29.9561i	0.0818850	+	1.40591i
$455$	0.227725	−	0.0539717i	0.0106759	−	0.00253023i
$456$	−16.6406	+	10.9338i	−0.779267	+	0.512021i
$457$	12.8119	−	1.49750i	0.599317	−	0.0700501i	0.188975	−	0.981982i	$-0.439483\pi$
$457$	12.8119	−	1.49750i	0.599317	−	0.0700501i	0.410342	+	0.911932i	$0.365409\pi$
$458$	2.85579	+	4.94638i	0.133442	+	0.231129i
$459$	−20.0365	+	7.26154i	−0.935223	+	0.338940i
$460$	2.94517	−	5.10118i	0.137319	−	0.237844i
$461$	−11.7178	+	27.1648i	−0.545750	+	1.26519i	0.392665	+	0.919682i	$0.371553\pi$
$461$	−11.7178	+	27.1648i	−0.545750	+	1.26519i	−0.938415	+	0.345510i	$0.887706\pi$
$462$	1.31395	−	4.38160i	0.0611305	−	0.203851i
$463$	−23.7270	−	25.1492i	−1.10269	−	1.16878i	−0.984426	−	0.175798i	$-0.943750\pi$
$463$	−23.7270	−	25.1492i	−1.10269	−	1.16878i	−0.118261	−	0.992983i	$-0.537732\pi$
$464$	21.2340	+	10.6641i	0.985766	+	0.495070i
$465$	5.64691	+	32.1111i	0.261869	+	1.48912i
$466$	−0.679667	−	2.27025i	−0.0314850	−	0.105167i
$467$	−24.0070	−	20.1443i	−1.11091	−	0.932165i	−0.112801	−	0.993618i	$-0.535982\pi$
$467$	−24.0070	−	20.1443i	−1.11091	−	0.932165i	−0.998110	+	0.0614529i	$0.980427\pi$
$468$	0.120541	+	0.280151i	0.00557203	+	0.0129500i
$469$	−1.53402	+	1.28719i	−0.0708343	+	0.0594371i
$470$	31.5323	+	20.7391i	1.45448	+	0.956625i
$471$	−0.520130	+	8.86041i	−0.0239663	+	0.408266i
$472$	−22.6044	−	2.64208i	−1.04045	−	0.121611i
$473$	−5.03201	−	11.6655i	−0.231372	−	0.536380i
$474$	−17.3235	−	23.2917i	−0.795694	−	1.06982i
$475$	−21.1655	+	10.6297i	−0.971140	+	0.487725i
$476$	−0.456267	−	0.166068i	−0.0209130	−	0.00761170i
$477$	−14.5282	+	15.3708i	−0.665200	+	0.703779i
$478$	−6.93405	+	2.52379i	−0.317156	+	0.115435i
$479$	6.50596	−	6.89591i	0.297265	−	0.315082i	−0.561475	−	0.827493i	$-0.689766\pi$
$479$	6.50596	−	6.89591i	0.297265	−	0.315082i	0.858740	+	0.512411i	$0.171248\pi$
$480$	−12.4051	−	0.00567840i	−0.566211	−	0.000259182i
$481$	−1.02953	+	0.677135i	−0.0469427	+	0.0308747i
$482$	−11.2528	+	37.5870i	−0.512552	+	1.71204i
$483$	−1.38979	+	1.86503i	−0.0632377	+	0.0848619i
$484$	5.51034	+	7.40167i	0.250470	+	0.336440i
$485$	20.7437			0.941922
$486$	−20.2248	+	13.2359i	−0.917417	+	0.600391i
$487$	−16.8494			−0.763520			−0.381760	−	0.924261i	$-0.624682\pi$
$487$	−16.8494			−0.763520			−0.381760	+	0.924261i	$0.624682\pi$
$488$	4.60213	+	6.18173i	0.208329	+	0.279834i
$489$	−18.2941	+	24.5498i	−0.827288	+	1.11018i
$490$	9.77085	−	32.6369i	0.441402	−	1.47439i
$491$	−12.9995	+	8.54993i	−0.586661	+	0.385853i	−0.807859	−	0.589376i	$-0.799374\pi$
$491$	−12.9995	+	8.54993i	−0.586661	+	0.385853i	0.221198	+	0.975229i	$0.429003\pi$
$492$	−1.27542		0.000583821i	−0.0575003		2.63207e-5i
$493$	14.3978	−	15.2607i	0.648443	−	0.687309i
$494$	1.70242	−	0.619631i	0.0765956	−	0.0278785i
$495$	−53.9392	−	12.8360i	−2.42439	−	0.576935i
$496$	25.8567	+	9.41106i	1.16100	+	0.422569i
$497$	−1.31251	+	0.659166i	−0.0588740	+	0.0295676i
$498$	−16.1843	−	21.7600i	−0.725235	−	0.975091i
$499$	−7.23826	−	16.7802i	−0.324029	−	0.751184i	−0.999900	−	0.0141637i	$-0.995491\pi$
$499$	−7.23826	−	16.7802i	−0.324029	−	0.751184i	0.675871	−	0.737020i	$-0.263768\pi$
$500$	−0.124864	−	0.0145945i	−0.00558409	−	0.000652686i
$501$	−0.139906	+	2.38330i	−0.00625055	+	0.106478i
$502$	−2.85036	−	1.87471i	−0.127218	−	0.0836726i
$503$	−22.0539	+	18.5054i	−0.983333	+	0.825114i	−0.984589	−	0.174885i	$-0.944045\pi$
$503$	−22.0539	+	18.5054i	−0.983333	+	0.825114i	0.00125604	+	0.999999i	$0.499600\pi$
$504$	2.15891	+	0.254344i	0.0961656	+	0.0113294i
$505$	0.754636	+	0.633215i	0.0335808	+	0.0281777i
$506$	−11.8600	−	39.6152i	−0.527242	−	1.76111i
$507$	−3.88085	−	22.0685i	−0.172355	−	0.980096i
$508$	−5.22448	−	2.62383i	−0.231799	−	0.116414i
$509$	−6.35316	−	6.73395i	−0.281599	−	0.298477i	0.571100	−	0.820881i	$-0.306517\pi$
$509$	−6.35316	−	6.73395i	−0.281599	−	0.298477i	−0.852698	+	0.522404i	$0.825035\pi$
$510$	−10.0542	+	33.5277i	−0.445210	+	1.48463i
$511$	0.211709	−	0.490796i	0.00936545	−	0.0217115i
$512$	6.25876	−	10.8405i	0.276601	−	0.479086i
$513$	12.0420	+	20.9237i	0.531667	+	0.923802i
$514$	7.95941	+	13.7861i	0.351074	+	0.608079i
$515$	30.4738	−	3.56188i	1.34284	−	0.156955i
$516$	−1.27822	+	0.839858i	−0.0562703	+	0.0369727i
$517$	43.3486	−	10.2738i	1.90647	−	0.451841i
$518$	−0.129372	−	2.22124i	−0.00568430	−	0.0975957i
$519$	3.92008	−	22.1725i	0.172072	−	0.973265i
$520$	−1.92404	−	0.456006i	−0.0843747	−	0.0199972i
$521$	−0.982915	+	5.57439i	−0.0430623	+	0.244218i	−0.998739	−	0.0501990i	$-0.984014\pi$
$521$	−0.982915	+	5.57439i	−0.0430623	+	0.244218i	0.955677	+	0.294417i	$0.0951256\pi$
$522$	11.9165	−	20.5964i	0.521572	−	0.901482i
$523$	2.68166	+	15.2084i	0.117261	+	0.665018i	0.985606	+	0.169058i	$0.0540726\pi$
$523$	2.68166	+	15.2084i	0.117261	+	0.665018i	−0.868345	+	0.495960i	$0.834816\pi$
$524$	0.0899493	−	1.54437i	0.00392945	−	0.0674661i
$525$	2.51586	+	0.597486i	0.109801	+	0.0260764i
$526$	1.46938	−	1.97372i	0.0640679	−	0.0860581i
$527$	14.5084	−	19.4882i	0.631998	−	0.848921i
$528$	−32.1271	+	34.0215i	−1.39815	+	1.48060i
$529$	0.114762	−	1.97038i	0.00498964	−	0.0856687i
$530$	6.03207	+	34.2096i	0.262016	+	1.48597i
$531$	−4.81642	+	27.1698i	−0.209015	+	1.17907i
$532$	−0.0955097	+	0.541662i	−0.00414087	+	0.0234840i
$533$	−0.445750	−	0.105645i	−0.0193076	−	0.00457598i
$534$	26.3164	−	9.56473i	1.13882	−	0.413906i
$535$	−1.96371	−	33.7155i	−0.0848984	−	1.45765i
$536$	16.4632	−	3.90184i	0.711100	−	0.168534i
$537$	−2.49960	−	43.2577i	−0.107866	−	1.86671i
$538$	7.69278	−	0.899157i	0.331659	−	0.0387654i
$539$	−20.1069	−	34.8261i	−0.866064	−	1.50007i
$540$	−0.397258	+	6.66301i	−0.0170953	+	0.286730i
$541$	−19.5695	+	33.8953i	−0.841357	+	1.45727i	0.0473898	+	0.998876i	$0.484910\pi$
$541$	−19.5695	+	33.8953i	−0.841357	+	1.45727i	−0.888747	+	0.458397i	$0.848424\pi$
$542$	5.69412	−	13.2005i	0.244584	−	0.567008i
$543$	7.76516	−	1.83662i	0.333235	−	0.0788170i
$544$	6.34364	+	6.72386i	0.271981	+	0.288283i
$545$	−48.7161	−	24.4661i	−2.08677	−	1.04801i
$546$	−0.185834	−	0.0677345i	−0.00795297	−	0.00289877i
$547$	6.08425	+	20.3228i	0.260144	+	0.868941i	0.983875	+	0.178859i	$0.0572405\pi$
$547$	6.08425	+	20.3228i	0.260144	+	0.868941i	−0.723731	+	0.690082i	$0.757574\pi$
$548$	−4.41754	−	3.70675i	−0.188708	−	0.158345i
$549$	7.81153	−	5.12749i	0.333388	−	0.218836i
$550$	−35.2178	+	29.5512i	−1.50169	+	1.26007i
$551$	−19.8565	−	13.0598i	−0.845915	−	0.556367i
$552$	17.5653	−	8.81157i	0.747630	−	0.375045i
$553$	3.14389	+	0.367468i	0.133692	+	0.0156263i
$554$	−15.8720	−	36.7955i	−0.674337	−	1.56329i
$555$	−26.7881	+	3.11865i	−1.13709	+	0.132379i
$556$	2.12896	−	1.06920i	0.0902879	−	0.0453443i
$557$	2.55364	+	0.929451i	0.108201	+	0.0393821i	0.395554	−	0.918443i	$-0.370553\pi$
$557$	2.55364	+	0.929451i	0.108201	+	0.0393821i	−0.287352	+	0.957825i	$0.592775\pi$
$558$	10.9372	−	25.2917i	0.463010	−	1.07068i
$559$	−0.516208	+	0.187884i	−0.0218333	+	0.00794666i
$560$	2.96644	−	3.14425i	0.125355	−	0.132869i
$561$	20.6421	+	35.7910i	0.871510	+	1.51110i
$562$	37.5164	−	24.6749i	1.58253	−	1.04085i
$563$	5.25606	−	17.5564i	0.221516	−	0.739916i	−0.772913	−	0.634512i	$-0.781201\pi$
$563$	5.25606	−	17.5564i	0.221516	−	0.739916i	0.994429	−	0.105404i	$-0.0336136\pi$
$564$	−2.12196	−	4.92547i	−0.0893508	−	0.207400i
$565$	20.0992	+	26.9979i	0.845579	+	1.13581i
$566$	1.60019			0.0672608
$567$	0.462434	−	2.59480i	0.0194204	−	0.108972i
$568$	12.4093			0.520682
$569$	6.69263	+	8.98976i	0.280570	+	0.376870i	0.919960	−	0.392012i	$-0.128221\pi$
$569$	6.69263	+	8.98976i	0.280570	+	0.376870i	−0.639391	+	0.768882i	$0.720813\pi$
$570$	39.3801	+	4.62114i	1.64945	+	0.193558i
$571$	−0.125284	+	0.418478i	−0.00524298	+	0.0175128i	−0.960571	−	0.278035i	$-0.910317\pi$
$571$	−0.125284	+	0.418478i	−0.00524298	+	0.0175128i	0.955328	+	0.295548i	$0.0955021\pi$
$572$	0.493998	−	0.324908i	0.0206551	−	0.0135851i
$573$	−2.32978	+	4.03103i	−0.0973279	+	0.168399i
$574$	0.567631	−	0.601653i	0.0236924	−	0.0251125i
$575$	21.9662	−	7.99505i	0.916055	−	0.333417i
$576$	−14.5173	−	9.56721i	−0.604886	−	0.398634i
$577$	34.0165	+	12.3810i	1.41612	+	0.515427i	0.932921	−	0.360081i	$-0.117251\pi$
$577$	34.0165	+	12.3810i	1.41612	+	0.515427i	0.483203	+	0.875508i	$0.339473\pi$
$578$	−0.246795	+	0.123945i	−0.0102653	+	0.00515544i
$579$	4.53677	−	10.5042i	0.188542	−	0.436539i
$580$	−2.60269	−	6.03372i	−0.108071	−	0.250536i
$581$	2.93715	+	0.343303i	0.121853	+	0.0142426i
$582$	−14.6430	−	9.64046i	−0.606972	−	0.399610i
$583$	34.2580	+	22.5319i	1.41882	+	0.933174i
$584$	−3.45951	+	2.90287i	−0.143155	+	0.120122i
$585$	−0.689694	+	2.29609i	−0.0285154	+	0.0949315i
$586$	8.24358	+	6.91718i	0.340539	+	0.285746i
$587$	0.230578	+	0.770183i	0.00951696	+	0.0317889i	0.962616	−	0.270869i	$-0.0873111\pi$
$587$	0.230578	+	0.770183i	0.00951696	+	0.0317889i	−0.953099	+	0.302658i	$0.902126\pi$
$588$	−3.70997	+	3.11014i	−0.152996	+	0.128260i
$589$	−24.5943	−	12.3517i	−1.01339	−	0.508944i
$590$	31.1003	+	32.9644i	1.28038	+	1.35712i
$591$	18.1752	+	19.2822i	0.747626	+	0.793165i
$592$	−9.01499	+	20.8991i	−0.370514	+	0.858948i
$593$	−18.8891	+	32.7169i	−0.775683	+	1.34352i	0.158726	+	0.987323i	$0.449261\pi$
$593$	−18.8891	+	32.7169i	−0.775683	+	1.34352i	−0.934410	+	0.356200i	$0.884072\pi$
$594$	32.1104	+	34.1288i	1.31751	+	1.40032i
$595$	−1.90842	−	3.30548i	−0.0782375	−	0.135511i
$596$	−5.65695	+	0.661202i	−0.231718	+	0.0270839i
$597$	21.7819	+	10.9518i	0.891476	+	0.448227i
$598$	−1.73986	+	0.412354i	−0.0711481	+	0.0168624i
$599$	1.70339	+	29.2461i	0.0695986	+	1.19496i	0.834571	+	0.550900i	$0.185715\pi$
$599$	1.70339	+	29.2461i	0.0695986	+	1.19496i	−0.764973	+	0.644063i	$0.777248\pi$
$600$	−16.7298	−	14.0511i	−0.682993	−	0.573632i
$601$	3.87462	+	0.918301i	0.158049	+	0.0374583i	0.308879	−	0.951101i	$-0.400046\pi$
$601$	3.87462	+	0.918301i	0.158049	+	0.0374583i	−0.150830	+	0.988560i	$0.548194\pi$
$602$	0.172242	−	0.976833i	0.00702006	−	0.0398128i
$603$	−3.54369	−	20.2054i	−0.144310	−	0.822827i
$604$	0.111178	+	0.630523i	0.00452377	+	0.0256556i
$605$	−4.21765	+	72.4142i	−0.171472	+	2.94406i
$606$	−0.238417	−	0.797699i	−0.00968505	−	0.0324043i
$607$	−20.1594	+	27.0788i	−0.818245	+	1.09909i	0.175171	+	0.984538i	$0.443952\pi$
$607$	−20.1594	+	27.0788i	−0.818245	+	1.09909i	−0.993417	+	0.114556i	$0.963455\pi$
$608$	6.25309	−	8.39936i	0.253596	−	0.340639i
$609$	0.743040	+	2.48607i	0.0301095	+	0.100741i
$610$	0.892337	−	15.3208i	0.0361297	−	0.620322i
$611$	−0.334497	−	1.89703i	−0.0135323	−	0.0767456i
$612$	3.81321	−	3.19372i	0.154140	−	0.129098i
$613$	7.41615	−	42.0591i	0.299536	−	1.69875i	−0.348637	−	0.937258i	$-0.613355\pi$
$613$	7.41615	−	42.0591i	0.299536	−	1.69875i	0.648173	−	0.761493i	$-0.275533\pi$
$614$	27.6515	+	6.55353i	1.11592	+	0.264479i
$615$	−7.67733	−	6.44804i	−0.309580	−	0.260010i
$616$	−0.245046	−	4.20729i	−0.00987320	−	0.169516i
$617$	−7.31208	+	1.73299i	−0.294373	+	0.0697677i	−0.375149	−	0.926965i	$-0.622408\pi$
$617$	−7.31208	+	1.73299i	−0.294373	+	0.0697677i	0.0807756	+	0.996732i	$0.474260\pi$
$618$	−23.1669	−	11.6481i	−0.931908	−	0.468556i
$619$	−20.8479	+	2.43677i	−0.837946	+	0.0979419i	−0.524232	−	0.851576i	$-0.675647\pi$
$619$	−20.8479	+	2.43677i	−0.837946	+	0.0979419i	−0.313714	+	0.949517i	$0.601573\pi$
$620$	−3.80472	−	6.58997i	−0.152801	−	0.264660i
$621$	−9.40720	−	21.8910i	−0.377498	−	0.878454i
$622$	−11.3934	+	19.7339i	−0.456832	+	0.791256i
$623$	−1.20935	+	2.80359i	−0.0484516	+	0.112323i
$624$	1.38781	+	1.47234i	0.0555569	+	0.0589409i
$625$	16.8137	+	17.8215i	0.672547	+	0.712858i
$626$	7.84160	+	3.93820i	0.313413	+	0.157402i
$627$	35.8668	−	30.0679i	1.43238	−	1.20080i
$628$	−0.594113	−	1.98447i	−0.0237077	−	0.0791892i
$629$	15.3951	+	12.9180i	0.613841	+	0.515074i
$630$	−2.96778	−	3.15144i	−0.118239	−	0.125556i
$631$	−23.1956	+	19.4634i	−0.923403	+	0.774827i	−0.974621	−	0.223860i	$-0.928134\pi$
$631$	−23.1956	+	19.4634i	−0.923403	+	0.774827i	0.0512179	+	0.998688i	$0.483690\pi$
$632$	−22.3439	−	14.6958i	−0.888791	−	0.584567i
$633$	−22.3587	−	14.7202i	−0.888679	−	0.585077i
$634$	35.2929	+	4.12515i	1.40166	+	0.163831i
$635$	−18.2028	−	42.1987i	−0.722354	−	1.67461i
$636$	1.95722	−	4.53165i	0.0776089	−	0.179691i
$637$	−1.55387	+	0.780382i	−0.0615665	+	0.0309198i
$638$	−43.3497	−	15.7780i	−1.71623	−	0.624657i
$639$	0.888580	−	15.0194i	0.0351517	−	0.594160i
$640$	−40.2937	+	14.6657i	−1.59275	+	0.579712i
$641$	11.3237	−	12.0024i	0.447258	−	0.474066i	−0.464039	−	0.885815i	$-0.653600\pi$
$641$	11.3237	−	12.0024i	0.447258	−	0.474066i	0.911297	+	0.411749i	$0.135082\pi$
$642$	−14.2828	+	24.7125i	−0.563699	+	0.975324i
$643$	15.0954	−	9.92841i	0.595305	−	0.391538i	−0.215801	−	0.976437i	$-0.569236\pi$
$643$	15.0954	−	9.92841i	0.595305	−	0.391538i	0.811106	+	0.584899i	$0.198866\pi$
$644$	0.155690	−	0.520041i	0.00613505	−	0.0204925i
$645$	−11.9408	−	1.40122i	−0.470169	−	0.0551730i
$646$	−17.6440	−	23.7000i	−0.694195	−	0.932466i
$647$	−4.14445			−0.162935			−0.0814676	−	0.996676i	$-0.525961\pi$
$647$	−4.14445			−0.162935			−0.0814676	+	0.996676i	$0.525961\pi$
$648$	−13.3307	+	17.8380i	−0.523681	+	0.700743i
$649$	53.4951			2.09987
$650$	1.18707	+	1.59452i	0.0465609	+	0.0625421i
$651$	1.18885	+	2.75954i	0.0465948	+	0.108155i
$652$	2.04938	−	6.84541i	0.0802599	−	0.268087i
$653$	−16.8784	+	11.1011i	−0.660503	+	0.434419i	−0.835009	−	0.550237i	$-0.814538\pi$
$653$	−16.8784	+	11.1011i	−0.660503	+	0.434419i	0.174506	+	0.984656i	$0.444167\pi$
$654$	23.0183	+	39.9111i	0.900088	+	1.56065i
$655$	8.34515	−	8.84534i	0.326072	−	0.345616i
$656$	−7.95109	+	2.89396i	−0.310438	+	0.112990i
$657$	3.26574	+	4.39504i	0.127408	+	0.171467i
$658$	3.26842	+	1.18961i	0.127416	+	0.0463758i
$659$	6.85612	−	3.44327i	0.267076	−	0.134131i	−0.310222	−	0.950664i	$-0.600403\pi$
$659$	6.85612	−	3.44327i	0.267076	−	0.134131i	0.577298	+	0.816533i	$0.304107\pi$
$660$	12.8537	−	1.49641i	0.500328	−	0.0582478i
$661$	−2.07836	−	4.81819i	−0.0808389	−	0.187406i	0.873003	−	0.487715i	$-0.162169\pi$
$661$	−2.07836	−	4.81819i	−0.0808389	−	0.187406i	−0.953842	+	0.300309i	$0.902910\pi$
$662$	−4.73958	−	0.553978i	−0.184209	−	0.0215310i
$663$	1.59686	−	0.801060i	0.0620170	−	0.0311106i
$664$	−20.8745	−	13.7294i	−0.810089	−	0.532804i
$665$	−3.31209	+	2.77917i	−0.128437	+	0.107772i
$666$	20.3592	+	10.2481i	0.788901	+	0.397106i
$667$	17.9687	+	15.0775i	0.695750	+	0.583803i
$668$	−0.159806	−	0.533790i	−0.00618309	−	0.0206530i
$669$	−7.89969	−	2.87935i	−0.305420	−	0.111322i
$670$	−30.1084	−	15.1210i	−1.16319	−	0.584176i
$671$	−12.4314	−	13.1765i	−0.479910	−	0.508675i
$672$	−1.11254	+	0.263139i	−0.0429172	+	0.0101508i
$673$	1.31913	−	3.05808i	0.0508486	−	0.117880i	−0.890898	−	0.454203i	$-0.849924\pi$
$673$	1.31913	−	3.05808i	0.0508486	−	0.117880i	0.941747	+	0.336323i	$0.109183\pi$
$674$	3.18620	−	5.51867i	0.122728	−	0.212571i
$675$	−18.2045	+	19.2426i	−0.700691	+	0.740649i
$676$	2.61481	+	4.52898i	0.100570	+	0.174192i
$677$	23.6194	−	2.76071i	0.907767	−	0.106103i	0.350621	−	0.936517i	$-0.385970\pi$
$677$	23.6194	−	2.76071i	0.907767	−	0.106103i	0.557146	+	0.830415i	$0.311896\pi$
$678$	−1.64100	−	28.3988i	−0.0630222	−	1.09065i
$679$	1.86018	−	0.440871i	0.0713872	−	0.0169191i
$680$	1.87508	+	32.1938i	0.0719059	+	1.23458i
$681$	31.5029	−	11.4498i	1.20719	−	0.438757i
$682$	−51.9812	−	12.3198i	−1.99046	−	0.471748i
$683$	−3.07677	+	17.4492i	−0.117729	+	0.667676i	0.867633	+	0.497205i	$0.165640\pi$
$683$	−3.07677	+	17.4492i	−0.117729	+	0.667676i	−0.985363	+	0.170472i	$0.945471\pi$
$684$	−4.31288	−	3.62567i	−0.164907	−	0.138631i
$685$	−7.87167	−	44.6424i	−0.300761	−	1.70570i
$686$	0.367376	−	6.30761i	0.0140265	−	0.240826i
$687$	4.38042	−	4.63872i	0.167123	−	0.176978i
$688$	−6.05914	+	8.13883i	−0.231002	+	0.310290i
$689$	1.05875	−	1.42214i	0.0403351	−	0.0541794i
$690$	−38.0743	−	9.04218i	−1.44946	−	0.344230i
$691$	−1.65085	+	28.3440i	−0.0628014	+	1.07826i	0.808813	+	0.588066i	$0.200110\pi$
$691$	−1.65085	+	28.3440i	−0.0628014	+	1.07826i	−0.871615	+	0.490192i	$0.836927\pi$
$692$	0.912541	+	5.17528i	0.0346896	+	0.196734i
$693$	−5.10979	−	0.00467799i	−0.194105	−	0.000177702i
$694$	−2.40983	+	13.6668i	−0.0914758	+	0.518785i
$695$	18.2226	+	4.31884i	0.691224	+	0.163823i
$696$	3.81675	−	21.5881i	0.144673	−	0.818293i
$697$	0.434407	+	7.45847i	0.0164543	+	0.282510i
$698$	7.48267	−	1.77343i	0.283223	−	0.0671252i
$699$	−2.21235	+	1.45364i	−0.0836788	+	0.0549816i
$700$	−0.599429	+	0.0700632i	−0.0226563	+	0.00264814i
$701$	19.6318	+	34.0032i	0.741482	+	1.28428i	0.951820	+	0.306656i	$0.0992102\pi$
$701$	19.6318	+	34.0032i	0.741482	+	1.28428i	−0.210338	+	0.977629i	$0.567456\pi$
$702$	1.55395	−	1.30028i	0.0586499	−	0.0490760i
$703$	11.3826	−	19.7152i	0.429303	−	0.743574i
$704$	−13.3505	+	30.9500i	−0.503167	+	1.16647i
$705$	12.1097	−	40.3820i	0.456079	−	1.52088i
$706$	−21.5977	−	22.8923i	−0.812841	−	0.861561i
$707$	0.0811296	+	0.0407448i	0.00305119	+	0.00153237i
$708$	−1.11540	−	6.34272i	−0.0419193	−	0.238374i
$709$	−14.3580	−	47.9591i	−0.539226	−	1.80114i	−0.596289	−	0.802770i	$-0.703359\pi$
$709$	−14.3580	−	47.9591i	−0.539226	−	1.80114i	0.0570631	−	0.998371i	$-0.481826\pi$
$710$	−18.9299	−	15.8841i	−0.710428	−	0.596120i
$711$	−19.3868	+	25.9913i	−0.727063	+	0.974751i
$712$	19.7618	−	16.5821i	0.740606	−	0.621442i
$713$	22.6942	+	14.9262i	0.849905	+	0.558991i
$714$	−0.189038	+	3.22027i	−0.00707458	+	0.120515i
$715$	4.61646	+	0.539587i	0.172646	+	0.0201794i
$716$	4.00547	+	9.28572i	0.149691	+	0.347024i
$717$	4.91921	+	6.61396i	0.183711	+	0.247003i
$718$	−10.7857	+	5.41676i	−0.402517	+	0.202152i
$719$	17.5102	+	6.37320i	0.653021	+	0.237680i	0.647220	−	0.762303i	$-0.275931\pi$
$719$	17.5102	+	6.37320i	0.653021	+	0.237680i	0.00580045	+	0.999983i	$0.498154\pi$
$720$	12.6614	+	42.4335i	0.471863	+	1.58140i
$721$	2.65702	−	0.967078i	0.0989528	−	0.0360159i
$722$	−2.75117	+	2.91607i	−0.102388	+	0.108525i
$723$	43.8277	+	0.0200621i	1.62997	+	0.000746116i
$724$	−1.55594	+	1.02336i	−0.0578262	+	0.0380329i
$725$	7.47917	−	24.9822i	0.277769	−	0.927814i
$726$	36.6312	−	49.1572i	1.35951	−	1.82440i
$727$	−25.0282	−	33.6187i	−0.928245	−	1.24685i	−0.968844	−	0.247673i	$-0.920334\pi$
$727$	−25.0282	−	33.6187i	−0.928245	−	1.24685i	0.0405990	−	0.999176i	$-0.487073\pi$
$728$	−0.182229			−0.00675386
$729$	20.6355	+	17.4120i	0.764276	+	0.644889i
$730$	8.99309			0.332849
$731$	5.35002	+	7.18632i	0.197878	+	0.265796i
$732$	−1.30309	+	1.74869i	−0.0481637	+	0.0646333i
$733$	−4.09420	+	13.6756i	−0.151223	+	0.505119i	−0.999710	−	0.0240976i	$-0.992329\pi$
$733$	−4.09420	+	13.6756i	−0.151223	+	0.505119i	0.848487	+	0.529216i	$0.177514\pi$
$734$	0.251684	−	0.165535i	0.00928982	−	0.00611001i
$735$	−38.0557	−	0.0174199i	−1.40371	−	0.000642544i
$736$	−7.09222	+	7.51731i	−0.261423	+	0.277092i
$737$	−37.3715	+	13.6021i	−1.37660	+	0.501041i
$738$	2.42277	+	8.11966i	0.0891834	+	0.298889i
$739$	−17.4197	−	6.34025i	−0.640794	−	0.233230i	0.00112859	−	0.999999i	$-0.499641\pi$
$739$	−17.4197	−	6.34025i	−0.640794	−	0.233230i	−0.641923	+	0.766769i	$0.721863\pi$
$740$	5.62481	−	2.82489i	0.206772	−	0.103845i
$741$	−1.20775	−	1.62383i	−0.0443676	−	0.0596531i
$742$	1.26799	+	2.93953i	0.0465493	+	0.107913i
$743$	29.2856	+	3.42299i	1.07438	+	0.125577i	0.634840	−	0.772644i	$-0.281066\pi$
$743$	29.2856	+	3.42299i	1.07438	+	0.125577i	0.439544	+	0.898221i	$0.355140\pi$
$744$	1.48772	−	25.3433i	0.0545424	−	0.929130i
$745$	−37.4058	−	24.6022i	−1.37044	−	0.901355i
$746$	2.71579	−	2.27882i	0.0994320	−	0.0834334i
$747$	−18.1120	+	24.2821i	−0.662682	+	0.888437i
$748$	−7.38696	−	6.19840i	−0.270094	−	0.226636i
$749$	−0.892660	−	2.98169i	−0.0326171	−	0.108949i
$750$	0.144654	+	0.822576i	0.00528202	+	0.0300362i
$751$	−14.9121	−	7.48913i	−0.544150	−	0.273282i	0.155418	−	0.987849i	$-0.450328\pi$
$751$	−14.9121	−	7.48913i	−0.544150	−	0.273282i	−0.699568	+	0.714567i	$0.746624\pi$
$752$	−24.4164	−	25.8799i	−0.890374	−	0.943742i
$753$	−1.09466	+	3.65033i	−0.0398916	+	0.133026i
$754$	−0.790066	+	1.83158i	−0.0287725	+	0.0667022i
$755$	−2.51646	+	4.35863i	−0.0915833	+	0.158627i
$756$	0.105987	+	0.605946i	0.00385470	+	0.0220380i
$757$	−16.3993	−	28.4044i	−0.596042	−	1.03237i	−0.993399	−	0.114710i	$-0.963406\pi$
$757$	−16.3993	−	28.4044i	−0.596042	−	1.03237i	0.397357	−	0.917664i	$-0.369927\pi$
$758$	11.1719	−	1.30580i	0.405780	−	0.0474289i
$759$	−38.6049	+	25.3656i	−1.40127	+	0.920712i
$760$	35.5455	−	8.42444i	1.28937	−	0.305587i
$761$	−1.96922	−	33.8102i	−0.0713841	−	1.22562i	−0.823781	−	0.566908i	$-0.808140\pi$
$761$	−1.96922	−	33.8102i	−0.0713841	−	1.22562i	0.752397	−	0.658710i	$-0.228897\pi$
$762$	−6.76216	+	38.2478i	−0.244967	+	1.38557i
$763$	−4.88858	−	1.15862i	−0.176979	−	0.0419447i
$764$	0.188692	−	1.07013i	0.00682665	−	0.0387159i
$765$	39.0997	+	0.0357956i	1.41365	+	0.00129419i
$766$	7.28693	+	41.3262i	0.263287	+	1.49318i
$767$	0.134495	−	2.30919i	0.00485633	−	0.0833799i

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.925932 + 1.24374i) q^{2} +(1.03494 - 1.38884i) q^{3} +(-0.115939 + 0.387262i) q^{4} +(-2.65494 + 1.74618i) q^{5} +(2.68565 + 0.00122935i) q^{6} +(-0.200969 + 0.213014i) q^{7} +(2.32510 - 0.846267i) q^{8} +(-0.857778 - 2.87476i) q^{9} +O(q^{10})\)	\(q+(0.925932 + 1.24374i) q^{2} +(1.03494 - 1.38884i) q^{3} +(-0.115939 + 0.387262i) q^{4} +(-2.65494 + 1.74618i) q^{5} +(2.68565 + 0.00122935i) q^{6} +(-0.200969 + 0.213014i) q^{7} +(2.32510 - 0.846267i) q^{8} +(-0.857778 - 2.87476i) q^{9} +(-4.63010 - 1.68522i) q^{10} +(-5.19744 + 2.61025i) q^{11} +(0.417857 + 0.561816i) q^{12} +(0.0996078 + 0.230917i) q^{13} +(-0.451018 - 0.0527165i) q^{14} +(-0.322542 + 5.49450i) q^{15} +(3.88090 + 2.55251i) q^{16} +(3.14189 - 2.63636i) q^{17} +(2.78121 - 3.72868i) q^{18} +(-3.55906 - 2.98641i) q^{19} +(-0.368420 - 1.23061i) q^{20} +(0.0878524 + 0.499573i) q^{21} +(-8.05895 - 4.04736i) q^{22} +(3.14672 + 3.33533i) q^{23} +(1.23102 - 4.10504i) q^{24} +(2.01916 - 4.68094i) q^{25} +(-0.194971 + 0.337700i) q^{26} +(-4.88034 - 1.78389i) q^{27} +(-0.0591924 - 0.102524i) q^{28} +(5.08083 - 0.593863i) q^{29} +(-7.13240 + 4.68638i) q^{30} +(5.76404 - 1.36610i) q^{31} +(0.131049 + 2.25003i) q^{32} +(-1.75383 + 9.91990i) q^{33} +(6.18813 + 1.46661i) q^{34} +(0.161598 - 0.916469i) q^{35} +(1.21273 + 0.00111025i) q^{36} +(0.850864 + 4.82549i) q^{37} +(0.418873 - 7.19176i) q^{38} +(0.423796 + 0.100646i) q^{39} +(-4.69526 + 6.30683i) q^{40} +(-1.08777 + 1.46113i) q^{41} +(-0.539994 + 0.571836i) q^{42} +(-0.127010 + 2.18068i) q^{43} +(-0.408268 - 2.31540i) q^{44} +(7.29720 + 6.13447i) q^{45} +(-1.23464 + 7.00200i) q^{46} +(-7.45323 - 1.76645i) q^{47} +(7.56156 - 2.74826i) q^{48} +(0.402027 + 6.90254i) q^{49} +(7.69149 - 1.82292i) q^{50} +(-0.409810 - 7.09209i) q^{51} +(-0.100974 + 0.0118021i) q^{52} +(-3.52502 - 6.10552i) q^{53} +(-2.30016 - 7.72165i) q^{54} +(9.24092 - 16.0057i) q^{55} +(-0.287005 + 0.665353i) q^{56} +(-7.83109 + 1.85222i) q^{57} +(5.44311 + 5.76936i) q^{58} +(-8.21945 - 4.12796i) q^{59} +(-2.09042 - 0.761934i) q^{60} +(0.893301 + 2.98383i) q^{61} +(7.03618 + 5.90406i) q^{62} +(0.784751 + 0.395017i) q^{63} +(4.43955 - 3.72523i) q^{64} +(-0.667676 - 0.439137i) q^{65} +(-13.9617 + 7.00384i) q^{66} +(6.79169 + 0.793835i) q^{67} +(0.656696 + 1.52239i) q^{68} +(7.88894 - 0.918424i) q^{69} +(1.28948 - 0.647601i) q^{70} +(4.71278 + 1.71531i) q^{71} +(-4.42723 - 5.95818i) q^{72} +(-1.71510 + 0.624247i) q^{73} +(-5.21382 + 5.52633i) q^{74} +(-4.41138 - 7.64882i) q^{75} +(1.56916 - 1.03205i) q^{76} +(0.488501 - 1.63171i) q^{77} +(0.267228 + 0.620285i) q^{78} +(-6.45435 - 8.66969i) q^{79} -14.7607 q^{80} +(-7.52843 + 4.93180i) q^{81} -2.82447 q^{82} +(-6.02991 - 8.09957i) q^{83} +(-0.203651 - 0.0238979i) q^{84} +(-3.73797 + 12.4857i) q^{85} +(-2.82981 + 1.86120i) q^{86} +(4.43359 - 7.67109i) q^{87} +(-9.87559 + 10.4675i) q^{88} +(9.79723 - 3.56590i) q^{89} +(-0.872991 + 14.7559i) q^{90} +(-0.0692067 - 0.0251892i) q^{91} +(-1.65647 + 0.831912i) q^{92} +(4.06816 - 9.41919i) q^{93} +(-4.70418 - 10.9055i) q^{94} +(14.6639 + 1.71396i) q^{95} +(3.26057 + 2.14665i) q^{96} +(-5.45395 - 3.58712i) q^{97} +(-8.21273 + 6.89130i) q^{98} +(11.9621 + 12.7023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

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