LMFDB - Embedded newform 81.2.g.a.4.8

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			4.8
Character	$\chi$	$=$	81.4
Dual form			81.2.g.a.61.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43604 + 0.284732i) q^{2} +(-1.18775 - 1.26065i) q^{3} +(3.90713 + 0.926007i) q^{4} +(-3.57352 + 1.79469i) q^{5} +(-2.53446 - 3.40919i) q^{6} +(0.377600 - 1.26127i) q^{7} +(4.64483 + 1.69058i) q^{8} +(-0.178488 + 2.99469i) q^{9} +O(q^{10})$	\(q+(2.43604 + 0.284732i) q^{2} +(-1.18775 - 1.26065i) q^{3} +(3.90713 + 0.926007i) q^{4} +(-3.57352 + 1.79469i) q^{5} +(-2.53446 - 3.40919i) q^{6} +(0.377600 - 1.26127i) q^{7} +(4.64483 + 1.69058i) q^{8} +(-0.178488 + 2.99469i) q^{9} +(-9.21624 + 3.35444i) q^{10} +(-0.142583 - 2.44806i) q^{11} +(-3.47333 - 6.02540i) q^{12} +(0.783462 + 1.05237i) q^{13} +(1.27897 - 2.96500i) q^{14} +(6.50693 + 2.37332i) q^{15} +(3.65712 + 1.83667i) q^{16} +(0.206593 + 0.173352i) q^{17} +(-1.28749 + 7.24435i) q^{18} +(1.02778 - 0.862409i) q^{19} +(-15.6241 + 3.70298i) q^{20} +(-2.03852 + 1.02206i) q^{21} +(0.349704 - 6.00418i) q^{22} +(1.71576 + 5.73105i) q^{23} +(-3.38568 - 7.86351i) q^{24} +(6.56334 - 8.81609i) q^{25} +(1.60890 + 2.78670i) q^{26} +(3.98726 - 3.33193i) q^{27} +(2.64328 - 4.57830i) q^{28} +(-2.19520 - 5.08906i) q^{29} +(15.1754 + 7.63423i) q^{30} +(0.884536 - 0.937554i) q^{31} +(0.126410 + 0.0831411i) q^{32} +(-2.91680 + 3.08744i) q^{33} +(0.453909 + 0.481116i) q^{34} +(0.914230 + 5.18486i) q^{35} +(-3.47047 + 11.5353i) q^{36} +(-0.00841562 + 0.0477273i) q^{37} +(2.74927 - 1.80822i) q^{38} +(0.396116 - 2.23763i) q^{39} +(-19.6325 + 2.29471i) q^{40} +(-4.11791 + 0.481314i) q^{41} +(-5.25693 + 1.90934i) q^{42} +(-5.22957 + 3.43954i) q^{43} +(1.70983 - 9.69693i) q^{44} +(-4.73670 - 11.0219i) q^{45} +(2.54785 + 14.4496i) q^{46} +(5.69554 + 6.03692i) q^{47} +(-2.02834 - 6.79186i) q^{48} +(4.40019 + 2.89405i) q^{49} +(18.4988 - 19.6076i) q^{50} +(-0.0268446 - 0.466341i) q^{51} +(2.08658 + 4.83724i) q^{52} +(-5.79529 + 10.0377i) q^{53} +(10.6618 - 6.98142i) q^{54} +(4.90304 + 8.49231i) q^{55} +(3.88617 - 5.22004i) q^{56} +(-2.30794 - 0.271343i) q^{57} +(-3.89859 - 13.0222i) q^{58} +(0.567212 - 9.73865i) q^{59} +(23.2257 + 15.2983i) q^{60} +(-4.15895 + 0.985689i) q^{61} +(2.42172 - 2.03206i) q^{62} +(3.70972 + 1.35592i) q^{63} +(-5.98568 - 5.02258i) q^{64} +(-4.68839 - 2.35460i) q^{65} +(-7.98454 + 6.69062i) q^{66} +(-0.525148 + 1.21743i) q^{67} +(0.646660 + 0.868614i) q^{68} +(5.18696 - 8.97004i) q^{69} +(0.750805 + 12.8908i) q^{70} +(7.40721 - 2.69600i) q^{71} +(-5.89181 + 13.6081i) q^{72} +(-8.12155 - 2.95600i) q^{73} +(-0.0340903 + 0.113869i) q^{74} +(-18.9096 + 2.19725i) q^{75} +(4.81426 - 2.41781i) q^{76} +(-3.14152 - 0.744553i) q^{77} +(1.60208 - 5.33817i) q^{78} +(-5.19362 - 0.607048i) q^{79} -16.3650 q^{80} +(-8.93628 - 1.06903i) q^{81} -10.1684 q^{82} +(5.64086 + 0.659323i) q^{83} +(-8.91120 + 2.10562i) q^{84} +(-1.04938 - 0.248707i) q^{85} +(-13.7188 + 6.88984i) q^{86} +(-3.80817 + 8.81193i) q^{87} +(3.47637 - 11.6119i) q^{88} +(-8.61170 - 3.13440i) q^{89} +(-8.40049 - 28.1985i) q^{90} +(1.62316 - 0.590783i) q^{91} +(1.39672 + 23.9807i) q^{92} +(-2.23254 - 0.00151097i) q^{93} +(12.1557 + 16.3279i) q^{94} +(-2.12503 + 4.92638i) q^{95} +(-0.0453316 - 0.258110i) q^{96} +(11.0880 + 5.56859i) q^{97} +(9.89500 + 8.30289i) q^{98} +(7.35663 + 0.00995784i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{27}\right)$

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 $

$2$	2.43604	+	0.284732i	1.72254	+	0.201336i	0.919093	−	0.394040i	$-0.128923\pi$
$2$	2.43604	+	0.284732i	1.72254	+	0.201336i	0.803447	+	0.595376i	$0.202997\pi$
$3$	−1.18775	−	1.26065i	−0.685749	−	0.727838i
$3$	−1.18775	−	1.26065i	−0.685749	−	0.727838i
$4$	3.90713	+	0.926007i	1.95356	+	0.463003i
$5$	−3.57352	+	1.79469i	−1.59813	+	0.802609i	−0.598127	+	0.801401i	$0.704088\pi$
$5$	−3.57352	+	1.79469i	−1.59813	+	0.802609i	−0.999999	+	0.00120769i	$0.999616\pi$
$6$	−2.53446	−	3.40919i	−1.03469	−	1.39180i
$7$	0.377600	−	1.26127i	0.142720	−	0.476716i	−0.856503	−	0.516142i	$-0.827368\pi$
$7$	0.377600	−	1.26127i	0.142720	−	0.476716i	0.999223	+	0.0394257i	$0.0125528\pi$
$8$	4.64483	+	1.69058i	1.64220	+	0.597711i
$9$	−0.178488	+	2.99469i	−0.0594961	+	0.998229i
$10$	−9.21624	+	3.35444i	−2.91443	+	1.06077i
$11$	−0.142583	−	2.44806i	−0.0429905	−	0.738119i	−0.949080	−	0.315034i	$-0.897984\pi$
$11$	−0.142583	−	2.44806i	−0.0429905	−	0.738119i	0.906090	−	0.423085i	$-0.139053\pi$
$12$	−3.47333	−	6.02540i	−1.00266	−	1.73938i
$13$	0.783462	+	1.05237i	0.217293	+	0.291875i	0.897382	−	0.441254i	$-0.145466\pi$
$13$	0.783462	+	1.05237i	0.217293	+	0.291875i	−0.680089	+	0.733130i	$0.738059\pi$
$14$	1.27897	−	2.96500i	0.341820	−	0.792429i
$15$	6.50693	+	2.37332i	1.68008	+	0.612788i
$16$	3.65712	+	1.83667i	0.914279	+	0.459168i
$17$	0.206593	+	0.173352i	0.0501061	+	0.0420440i	0.667497	−	0.744613i	$-0.267366\pi$
$17$	0.206593	+	0.173352i	0.0501061	+	0.0420440i	−0.617391	+	0.786657i	$0.711810\pi$
$18$	−1.28749	+	7.24435i	−0.303464	+	1.70751i
$19$	1.02778	−	0.862409i	0.235789	−	0.197850i	−0.517235	−	0.855843i	$-0.673039\pi$
$19$	1.02778	−	0.862409i	0.235789	−	0.197850i	0.753024	+	0.657993i	$0.228594\pi$
$20$	−15.6241	+	3.70298i	−3.49365	+	0.828011i
$21$	−2.03852	+	1.02206i	−0.444842	+	0.223031i
$22$	0.349704	−	6.00418i	0.0745570	−	1.28010i
$23$	1.71576	+	5.73105i	0.357761	+	1.19501i	0.927702	+	0.373320i	$0.121781\pi$
$23$	1.71576	+	5.73105i	0.357761	+	1.19501i	−0.569941	+	0.821685i	$0.693034\pi$
$24$	−3.38568	−	7.86351i	−0.691098	−	1.60513i
$25$	6.56334	−	8.81609i	1.31267	−	1.76322i
$26$	1.60890	+	2.78670i	0.315531	+	0.546516i
$27$	3.98726	−	3.33193i	0.767348	−	0.641231i
$28$	2.64328	−	4.57830i	0.499533	−	0.865216i
$29$	−2.19520	−	5.08906i	−0.407639	−	0.945014i	−0.991130	−	0.132894i	$-0.957573\pi$
$29$	−2.19520	−	5.08906i	−0.407639	−	0.945014i	0.583491	−	0.812120i	$-0.301686\pi$
$30$	15.1754	+	7.63423i	2.77063	+	1.39381i
$31$	0.884536	−	0.937554i	0.158867	−	0.168390i	−0.643051	−	0.765824i	$-0.722332\pi$
$31$	0.884536	−	0.937554i	0.158867	−	0.168390i	0.801918	+	0.597434i	$0.203813\pi$
$32$	0.126410	+	0.0831411i	0.0223463	+	0.0146974i
$33$	−2.91680	+	3.08744i	−0.507750	+	0.537455i
$34$	0.453909	+	0.481116i	0.0778448	+	0.0825107i
$35$	0.914230	+	5.18486i	0.154533	+	0.876401i
$36$	−3.47047	+	11.5353i	−0.578412	+	1.92256i
$37$	−0.00841562	+	0.0477273i	−0.00138352	+	0.00784632i	−0.985492	−	0.169724i	$-0.945712\pi$
$37$	−0.00841562	+	0.0477273i	−0.00138352	+	0.00784632i	0.984108	+	0.177570i	$0.0568236\pi$
$38$	2.74927	−	1.80822i	0.445990	−	0.293332i
$39$	0.396116	−	2.23763i	0.0634294	−	0.358308i
$40$	−19.6325	+	2.29471i	−3.10417	+	0.362825i
$41$	−4.11791	+	0.481314i	−0.643109	+	0.0751686i	−0.431395	−	0.902163i	$-0.641978\pi$
$41$	−4.11791	+	0.481314i	−0.643109	+	0.0751686i	−0.211714	+	0.977332i	$0.567904\pi$
$42$	−5.25693	+	1.90934i	−0.811163	+	0.294617i
$43$	−5.22957	+	3.43954i	−0.797502	+	0.524525i	−0.881637	−	0.471929i	$-0.843558\pi$
$43$	−5.22957	+	3.43954i	−0.797502	+	0.524525i	0.0841345	+	0.996454i	$0.473187\pi$
$44$	1.70983	−	9.69693i	0.257767	−	1.46187i
$45$	−4.73670	−	11.0219i	−0.706105	−	1.64305i
$46$	2.54785	+	14.4496i	0.375660	+	2.13048i
$47$	5.69554	+	6.03692i	0.830780	+	0.880575i	0.994371	−	0.105953i	$-0.0337894\pi$
$47$	5.69554	+	6.03692i	0.830780	+	0.880575i	−0.163592	+	0.986528i	$0.552308\pi$
$48$	−2.02834	−	6.79186i	−0.292766	−	0.980321i
$49$	4.40019	+	2.89405i	0.628598	+	0.413436i
$50$	18.4988	−	19.6076i	2.61612	−	2.77293i
$51$	−0.0268446	−	0.466341i	−0.00375899	−	0.0653008i
$52$	2.08658	+	4.83724i	0.289357	+	0.670805i
$53$	−5.79529	+	10.0377i	−0.796044	+	1.37879i	0.126130	+	0.992014i	$0.459744\pi$
$53$	−5.79529	+	10.0377i	−0.796044	+	1.37879i	−0.922174	+	0.386775i	$0.873589\pi$
$54$	10.6618	−	6.98142i	1.45089	−	0.950051i
$55$	4.90304	+	8.49231i	0.661125	+	1.14510i
$56$	3.88617	−	5.22004i	0.519312	−	0.697557i
$57$	−2.30794	−	0.271343i	−0.305695	−	0.0359403i
$58$	−3.89859	−	13.0222i	−0.511910	−	1.70990i
$59$	0.567212	−	9.73865i	0.0738447	−	1.26786i	−0.734277	−	0.678850i	$-0.762479\pi$
$59$	0.567212	−	9.73865i	0.0738447	−	1.26786i	0.808122	−	0.589015i	$-0.200484\pi$
$60$	23.2257	+	15.2983i	2.99843	+	1.97501i
$61$	−4.15895	+	0.985689i	−0.532499	+	0.126205i	−0.488064	−	0.872808i	$-0.662297\pi$
$61$	−4.15895	+	0.985689i	−0.532499	+	0.126205i	−0.0444347	+	0.999012i	$0.514149\pi$
$62$	2.42172	−	2.03206i	0.307558	−	0.258072i
$63$	3.70972	+	1.35592i	0.467381	+	0.170829i
$64$	−5.98568	−	5.02258i	−0.748210	−	0.627823i
$65$	−4.68839	−	2.35460i	−0.581524	−	0.292052i
$66$	−7.98454	+	6.69062i	−0.982829	+	0.823559i
$67$	−0.525148	+	1.21743i	−0.0641571	+	0.148733i	−0.947278	−	0.320412i	$-0.896179\pi$
$67$	−0.525148	+	1.21743i	−0.0641571	+	0.148733i	0.883121	+	0.469145i	$0.155438\pi$
$68$	0.646660	+	0.868614i	0.0784190	+	0.105335i
$69$	5.18696	−	8.97004i	0.624436	−	1.07987i
$70$	0.750805	+	12.8908i	0.0897384	+	1.54075i
$71$	7.40721	−	2.69600i	0.879074	−	0.319957i	0.137238	−	0.990538i	$-0.456177\pi$
$71$	7.40721	−	2.69600i	0.879074	−	0.319957i	0.741836	+	0.670581i	$0.233955\pi$
$72$	−5.89181	+	13.6081i	−0.694356	+	1.60373i
$73$	−8.12155	−	2.95600i	−0.950556	−	0.345974i	−0.180230	−	0.983624i	$-0.557684\pi$
$73$	−8.12155	−	2.95600i	−0.950556	−	0.345974i	−0.770326	+	0.637650i	$0.779906\pi$
$74$	−0.0340903	+	0.113869i	−0.00396292	+	0.0132371i
$75$	−18.9096	+	2.19725i	−2.18350	+	0.253716i
$76$	4.81426	−	2.41781i	0.552234	−	0.277342i
$77$	−3.14152	−	0.744553i	−0.358009	−	0.0848497i
$78$	1.60208	−	5.33817i	0.181400	−	0.604429i
$79$	−5.19362	−	0.607048i	−0.584328	−	0.0682982i	−0.181207	−	0.983445i	$-0.558001\pi$
$79$	−5.19362	−	0.607048i	−0.584328	−	0.0682982i	−0.403121	+	0.915147i	$0.632075\pi$
$80$	−16.3650			−1.82967
$81$	−8.93628	−	1.06903i	−0.992920	−	0.118781i
$82$	−10.1684			−1.12291
$83$	5.64086	+	0.659323i	0.619165	+	0.0723700i	0.419892	−	0.907574i	$-0.362068\pi$
$83$	5.64086	+	0.659323i	0.619165	+	0.0723700i	0.199273	+	0.979944i	$0.436142\pi$
$84$	−8.91120	+	2.10562i	−0.972292	+	0.229742i
$85$	−1.04938	−	0.248707i	−0.113821	−	0.0269760i
$86$	−13.7188	+	6.88984i	−1.47934	+	0.742950i
$87$	−3.80817	+	8.81193i	−0.408279	+	0.944738i
$88$	3.47637	−	11.6119i	0.370583	−	1.23783i
$89$	−8.61170	−	3.13440i	−0.912838	−	0.332246i	−0.157453	−	0.987527i	$-0.550328\pi$
$89$	−8.61170	−	3.13440i	−0.912838	−	0.332246i	−0.755385	+	0.655281i	$0.772550\pi$
$90$	−8.40049	−	28.1985i	−0.885490	−	2.97238i
$91$	1.62316	−	0.590783i	0.170154	−	0.0619309i
$92$	1.39672	+	23.9807i	0.145618	+	2.50017i
$93$	−2.23254	−	0.00151097i	−0.231504	−	0.000156680i
$94$	12.1557	+	16.3279i	1.25376	+	1.68409i
$95$	−2.12503	+	4.92638i	−0.218024	+	0.505436i
$96$	−0.0453316	−	0.258110i	−0.00462664	−	0.0263432i
$97$	11.0880	+	5.56859i	1.12581	+	0.565405i	0.911475	−	0.411355i	$-0.134944\pi$
$97$	11.0880	+	5.56859i	1.12581	+	0.565405i	0.214338	+	0.976759i	$0.431241\pi$
$98$	9.89500	+	8.30289i	0.999546	+	0.838719i
$99$	7.35663	+	0.00995784i	0.739369	+	0.00100080i
$100$	33.8076	−	28.3679i	3.38076	−	2.83679i
$101$	12.1161	−	2.87156i	1.20560	−	0.285731i	0.421764	−	0.906705i	$-0.361411\pi$
$101$	12.1161	−	2.87156i	1.20560	−	0.285731i	0.783831	+	0.620974i	$0.213263\pi$
$102$	0.0673878	−	1.14367i	0.00667238	−	0.113240i
$103$	0.363442	−	6.24005i	0.0358110	−	0.614851i	−0.931889	−	0.362745i	$-0.881840\pi$
$103$	0.363442	−	6.24005i	0.0358110	−	0.614851i	0.967700	−	0.252106i	$-0.0811232\pi$
$104$	1.85993	+	6.21260i	0.182381	+	0.609195i
$105$	5.45042	−	7.31085i	0.531907	−	0.713466i
$106$	−16.9756	+	22.8022i	−1.64882	+	2.21475i
$107$	−9.92075	−	17.1832i	−0.959075	−	1.66117i	−0.724755	−	0.689007i	$-0.758047\pi$
$107$	−9.92075	−	17.1832i	−0.959075	−	1.66117i	−0.234320	−	0.972159i	$-0.575286\pi$
$108$	18.6641	−	9.32607i	1.79596	−	0.897401i
$109$	−1.91684	+	3.32007i	−0.183600	+	0.318005i	−0.943104	−	0.332498i	$-0.892109\pi$
$109$	−1.91684	+	3.32007i	−0.183600	+	0.318005i	0.759504	+	0.650503i	$0.225442\pi$
$110$	9.52596	+	22.0837i	0.908264	+	2.10559i
$111$	0.0701632	−	0.0460791i	0.00665960	−	0.00437363i
$112$	3.69747	−	3.91909i	0.349378	−	0.370320i
$113$	2.91572	+	1.91770i	0.274288	+	0.180402i	0.679199	−	0.733954i	$-0.262327\pi$
$113$	2.91572	+	1.91770i	0.274288	+	0.180402i	−0.404911	+	0.914356i	$0.632698\pi$
$114$	−5.54498	−	1.31815i	−0.519335	−	0.123456i
$115$	−16.4168	−	17.4007i	−1.53087	−	1.62263i
$116$	−3.86445	−	21.9164i	−0.358805	−	2.03488i
$117$	−3.29136	+	2.15839i	−0.304286	+	0.199543i
$118$	4.15466	−	23.5622i	0.382467	−	2.16908i
$119$	0.296654	−	0.195112i	0.0271942	−	0.0178859i
$120$	26.2113	+	22.0242i	2.39276	+	2.01052i
$121$	4.95294	−	0.578916i	0.450267	−	0.0526287i
$122$	−10.4120	+	1.21699i	−0.942660	+	0.110181i
$123$	5.49782	+	4.61956i	0.495722	+	0.416532i
$124$	4.32418	−	2.84406i	0.388323	−	0.255404i
$125$	−4.16009	+	23.5930i	−0.372090	+	2.11022i
$126$	8.65095	+	4.35934i	0.770688	+	0.388361i
$127$	2.28154	+	12.9392i	0.202454	+	1.14817i	0.901397	+	0.432994i	$0.142543\pi$
$127$	2.28154	+	12.9392i	0.202454	+	1.14817i	−0.698943	+	0.715177i	$0.746346\pi$
$128$	−13.3589	−	14.1596i	−1.18077	−	1.25155i
$129$	10.5475	+	2.50734i	0.928656	+	0.220759i
$130$	−10.7507	−	7.07084i	−0.942897	−	0.620153i
$131$	2.97214	−	3.15028i	0.259677	−	0.275241i	−0.584398	−	0.811467i	$-0.698669\pi$
$131$	2.97214	−	3.15028i	0.259677	−	0.275241i	0.844074	+	0.536226i	$0.180151\pi$
$132$	−14.2553	+	9.36205i	−1.24077	+	0.814862i
$133$	−0.699643	−	1.62196i	−0.0606668	−	0.140641i
$134$	−1.62592	+	2.81618i	−0.140458	+	0.243281i
$135$	−8.26875	+	19.0626i	−0.711661	+	1.64065i
$136$	0.666523	+	1.15445i	0.0571539	+	0.0989935i
$137$	13.3885	−	17.9839i	1.14386	−	1.53647i	0.341241	−	0.939976i	$-0.389153\pi$
$137$	13.3885	−	17.9839i	1.14386	−	1.53647i	0.802618	−	0.596493i	$-0.203440\pi$
$138$	15.1897	−	20.3745i	1.29303	−	1.73439i
$139$	2.75308	+	9.19593i	0.233513	+	0.779989i	0.991770	+	0.128033i	$0.0408663\pi$
$139$	2.75308	+	9.19593i	0.233513	+	0.779989i	−0.758257	+	0.651956i	$0.773949\pi$
$140$	−1.22920	+	21.1045i	−0.103886	+	1.78365i
$141$	0.845565	−	14.3505i	0.0712094	−	1.20853i
$142$	18.8119	−	4.45850i	1.57866	−	0.374149i
$143$	2.46456	−	2.06801i	0.206097	−	0.172936i
$144$	−6.15301	+	10.6241i	−0.512751	+	0.885341i
$145$	16.9779	+	14.2461i	1.40994	+	1.18308i
$146$	−18.9428	−	9.51341i	−1.56771	−	0.787336i
$147$	−1.57794	−	8.98452i	−0.130147	−	0.741031i
$148$	−0.0770767	+	0.178684i	−0.00633567	+	0.0146877i
$149$	9.93888	+	13.3502i	0.814225	+	1.09369i	0.993934	+	0.109974i	$0.0350768\pi$
$149$	9.93888	+	13.3502i	0.814225	+	1.09369i	−0.179710	+	0.983720i	$0.557516\pi$
$150$	−46.6903	−	0.0315997i	−3.81224	−	0.00258010i
$151$	0.106543	+	1.82928i	0.00867039	+	0.148865i	0.999865	+	0.0164494i	$0.00523624\pi$
$151$	0.106543	+	1.82928i	0.00867039	+	0.148865i	−0.991194	+	0.132415i	$0.957727\pi$
$152$	6.23183	−	2.26820i	0.505468	−	0.183975i
$153$	−0.556009	+	0.587739i	−0.0449507	+	0.0475159i
$154$	−7.44086	−	2.70825i	−0.599601	−	0.218237i
$155$	−1.47829	+	4.93783i	−0.118739	+	0.396616i
$156$	3.61974	−	8.37590i	0.289811	−	0.670609i
$157$	−9.65812	+	4.85049i	−0.770802	+	0.387111i	−0.790317	−	0.612698i	$-0.790084\pi$
$157$	−9.65812	+	4.85049i	−0.770802	+	0.387111i	0.0195149	+	0.999810i	$0.493788\pi$
$158$	−12.4790	−	2.95758i	−0.992778	−	0.235293i
$159$	19.5375	−	4.61650i	1.54942	−	0.366112i
$160$	−0.600940	−	0.0702398i	−0.0475085	−	0.00555295i
$161$	7.87629			0.620738
$162$	−21.4648	−	5.14865i	−1.68643	−	0.404516i
$163$	3.76716			0.295067			0.147533	−	0.989057i	$-0.452867\pi$
$163$	3.76716			0.295067			0.147533	+	0.989057i	$0.452867\pi$
$164$	−16.5349	−	1.93265i	−1.29116	−	0.150915i
$165$	4.88225	−	16.2678i	0.380083	−	1.26644i
$166$	13.5536	+	3.21227i	1.05197	+	0.249321i
$167$	10.5761	−	5.31150i	0.818400	−	0.411016i	0.0102172	−	0.999948i	$-0.496748\pi$
$167$	10.5761	−	5.31150i	0.818400	−	0.411016i	0.808183	+	0.588932i	$0.200451\pi$
$168$	−11.1965	+	1.30100i	−0.863826	+	0.100374i
$169$	3.23477	−	10.8049i	0.248828	−	0.831144i
$170$	−2.48551	−	0.904650i	−0.190630	−	0.0693835i
$171$	2.39920	+	3.23180i	0.183471	+	0.247142i
$172$	−23.6176	+	8.59612i	−1.80083	+	0.655448i
$173$	0.556322	+	9.55169i	0.0422964	+	0.726201i	0.951082	+	0.308938i	$0.0999736\pi$
$173$	0.556322	+	9.55169i	0.0422964	+	0.726201i	−0.908786	+	0.417263i	$0.862989\pi$
$174$	−11.7859	+	20.3819i	−0.893487	+	1.54515i
$175$	−8.64118	−	11.6071i	−0.653212	−	0.877416i
$176$	3.97485	−	9.21473i	0.299615	−	0.694586i
$177$	−12.9508	+	10.8521i	−0.973439	+	0.815690i
$178$	−20.0860	−	10.0876i	−1.50551	−	0.756094i
$179$	−1.08723	−	0.912294i	−0.0812633	−	0.0681880i	0.601251	−	0.799060i	$-0.294669\pi$
$179$	−1.08723	−	0.912294i	−0.0812633	−	0.0681880i	−0.682514	+	0.730872i	$0.739114\pi$
$180$	−8.30054	−	47.4502i	−0.618686	−	3.53673i
$181$	−7.58350	+	6.36331i	−0.563677	+	0.472981i	−0.879541	−	0.475823i	$-0.842150\pi$
$181$	−7.58350	+	6.36331i	−0.563677	+	0.472981i	0.315864	+	0.948804i	$0.397706\pi$
$182$	4.12231	−	0.977004i	0.305566	−	0.0724204i
$183$	6.18241	+	4.07223i	0.457017	+	0.301028i
$184$	−1.71937	+	29.5204i	−0.126753	+	2.17627i
$185$	−0.0555823	−	0.185658i	−0.00408649	−	0.0136498i
$186$	−5.43812	−	0.639357i	−0.398743	−	0.0468799i
$187$	0.394920	−	0.530469i	0.0288794	−	0.0387918i
$188$	16.6630	+	28.8611i	1.21527	+	2.10491i
$189$	−2.69689	−	6.28716i	−0.196170	−	0.457323i
$190$	−6.57936	+	11.3958i	−0.477317	+	0.826737i
$191$	−7.05983	−	16.3665i	−0.510831	−	1.18424i	−0.957210	−	0.289396i	$-0.906546\pi$
$191$	−7.05983	−	16.3665i	−0.510831	−	1.18424i	0.446378	−	0.894844i	$-0.352714\pi$
$192$	0.777777	+	13.5114i	0.0561312	+	0.975104i
$193$	−18.9616	+	20.0981i	−1.36488	+	1.44669i	−0.605996	+	0.795468i	$0.707225\pi$
$193$	−18.9616	+	20.0981i	−1.36488	+	1.44669i	−0.758886	+	0.651223i	$0.774256\pi$
$194$	25.4252	+	16.7224i	1.82542	+	1.20060i
$195$	2.60032	+	8.70712i	0.186213	+	0.623530i
$196$	14.5122	+	15.3820i	1.03659	+	1.09872i
$197$	−1.04040	−	5.90042i	−0.0741256	−	0.420387i	−0.999178	−	0.0405468i	$-0.987090\pi$
$197$	−1.04040	−	5.90042i	−0.0741256	−	0.420387i	0.925052	−	0.379840i	$-0.124021\pi$
$198$	17.9182	+	2.11893i	1.27339	+	0.150586i
$199$	2.78863	−	15.8151i	0.197681	−	1.12110i	−0.710868	−	0.703326i	$-0.751698\pi$
$199$	2.78863	−	15.8151i	0.197681	−	1.12110i	0.908549	−	0.417779i	$-0.137191\pi$
$200$	45.3899	−	29.8534i	3.20955	−	2.11096i
$201$	2.15850	−	0.783977i	0.152249	−	0.0552974i
$202$	30.3329	−	3.54541i	2.13421	−	0.249454i
$203$	−7.24760	+	0.847123i	−0.508682	+	0.0594564i
$204$	0.326949	−	1.84691i	0.0228910	−	0.129310i
$205$	13.8516	−	9.11034i	0.967438	−	0.636294i
$206$	2.66210	−	15.0975i	0.185478	−	1.05190i
$207$	−17.4689	+	4.11525i	−1.21417	+	0.286029i
$208$	0.932348	+	5.28761i	0.0646467	+	0.366630i
$209$	−2.25778	−	2.39310i	−0.156174	−	0.165534i
$210$	15.3591	−	16.2576i	1.05988	−	1.12188i
$211$	8.41443	+	5.53426i	0.579273	+	0.380994i	0.805069	−	0.593181i	$-0.202128\pi$
$211$	8.41443	+	5.53426i	0.579273	+	0.380994i	−0.225796	+	0.974175i	$0.572498\pi$
$212$	−31.9380	+	33.8523i	−2.19351	+	2.32498i
$213$	−12.1967	−	6.13573i	−0.835701	−	0.420413i
$214$	−19.2747	−	44.6838i	−1.31759	−	3.05452i
$215$	12.5151	−	21.6767i	0.853520	−	1.47834i
$216$	24.1530	−	8.73549i	1.64341	−	0.594375i
$217$	−0.848510	−	1.46966i	−0.0576006	−	0.0997672i
$218$	−5.61484	+	7.54203i	−0.380285	+	0.510811i
$219$	5.91990	+	13.7495i	0.400030	+	0.929102i
$220$	11.2929	+	37.7208i	0.761364	+	2.54313i
$221$	−0.0205731	+	0.353227i	−0.00138390	+	0.0237606i
$222$	0.184041	−	0.0922728i	0.0123520	−	0.00619294i
$223$	−12.6909	+	3.00779i	−0.849844	+	0.201417i	−0.632386	−	0.774653i	$-0.717924\pi$
$223$	−12.6909	+	3.00779i	−0.849844	+	0.201417i	−0.217457	+	0.976070i	$0.569776\pi$
$224$	0.152596	−	0.128043i	0.0101957	−	0.00855525i
$225$	25.2299	+	21.2287i	1.68200	+	1.41525i
$226$	6.55678	+	5.50179i	0.436151	+	0.365974i
$227$	14.5592	+	7.31190i	0.966328	+	0.485308i	0.860708	−	0.509098i	$-0.170021\pi$
$227$	14.5592	+	7.31190i	0.966328	+	0.485308i	0.105620	+	0.994407i	$0.466317\pi$
$228$	−8.76617	−	3.19735i	−0.580554	−	0.211749i
$229$	−2.66861	+	6.18653i	−0.176347	+	0.408817i	−0.983348	−	0.181732i	$-0.941830\pi$
$229$	−2.66861	+	6.18653i	−0.176347	+	0.408817i	0.807002	+	0.590549i	$0.201089\pi$
$230$	−35.0373	−	47.0633i	−2.31029	−	3.10326i
$231$	2.79272	+	4.84470i	0.183748	+	0.318758i
$232$	−1.59290	−	27.3490i	−0.104579	−	1.79555i
$233$	−12.9692	+	4.72040i	−0.849641	+	0.309244i	−0.729894	−	0.683560i	$-0.760431\pi$
$233$	−12.9692	+	4.72040i	−0.849641	+	0.309244i	−0.119747	+	0.992804i	$0.538208\pi$
$234$	−8.63245	+	4.32076i	−0.564321	+	0.282457i
$235$	−31.1875	−	11.3513i	−2.03445	−	0.740479i
$236$	11.2342	−	37.5249i	0.731286	−	2.44266i
$237$	5.40346	+	7.26838i	0.350993	+	0.472132i
$238$	0.778215	−	0.390834i	0.0504442	−	0.0253340i
$239$	12.2001	+	2.89148i	0.789159	+	0.187034i	0.605383	−	0.795934i	$-0.293020\pi$
$239$	12.2001	+	2.89148i	0.789159	+	0.187034i	0.183776	+	0.982968i	$0.441168\pi$
$240$	19.4376	+	20.6306i	1.25469	+	1.33170i
$241$	−13.5982	−	1.58941i	−0.875940	−	0.102383i	−0.333773	−	0.942653i	$-0.608322\pi$
$241$	−13.5982	−	1.58941i	−0.875940	−	0.102383i	−0.542167	+	0.840271i	$0.682396\pi$
$242$	12.2304			0.786199
$243$	9.26642	+	12.5353i	0.594441	+	0.804139i
$244$	−17.1623			−1.09870
$245$	−20.9181	−	2.44497i	−1.33641	−	0.156203i
$246$	12.0776	+	12.8189i	0.770038	+	0.817300i
$247$	1.71280	+	0.405941i	0.108983	+	0.0258294i
$248$	5.69353	−	2.85940i	0.361540	−	0.181572i
$249$	−5.86877	−	7.89428i	−0.371918	−	0.500280i
$250$	−16.8518	+	56.2890i	−1.06580	+	3.56003i
$251$	−12.4879	−	4.54521i	−0.788226	−	0.286891i	−0.0836277	−	0.996497i	$-0.526651\pi$
$251$	−12.4879	−	4.54521i	−0.788226	−	0.286891i	−0.704599	+	0.709606i	$0.748873\pi$
$252$	13.2388	+	8.73296i	0.833964	+	0.550125i
$253$	13.7853	−	5.01745i	0.866676	−	0.315444i
$254$	1.87370	+	32.1701i	0.117566	+	2.01853i
$255$	0.932866	+	1.61830i	0.0584183	+	0.101342i
$256$	−19.1791	−	25.7620i	−1.19869	−	1.61012i
$257$	−1.33177	+	3.08739i	−0.0830736	+	0.192586i	−0.954690	−	0.297603i	$-0.903813\pi$
$257$	−1.33177	+	3.08739i	−0.0830736	+	0.192586i	0.871616	+	0.490189i	$0.163072\pi$
$258$	24.9802	+	9.11121i	1.55520	+	0.567239i
$259$	0.0570194	+	0.0286362i	0.00354302	+	0.00177937i
$260$	−16.1378	−	13.5412i	−1.00082	−	0.839790i
$261$	15.6319	−	5.66561i	0.967593	−	0.350693i
$262$	8.13723	−	6.82794i	0.502720	−	0.421832i
$263$	−23.7653	+	5.63248i	−1.46543	+	0.347313i	−0.884462	−	0.466612i	$-0.845474\pi$
$263$	−23.7653	+	5.63248i	−1.46543	+	0.347313i	−0.580969	+	0.813926i	$0.697326\pi$
$264$	−18.7676	+	9.40956i	−1.15507	+	0.579118i
$265$	2.69497	−	46.2708i	0.165550	−	2.84239i
$266$	−1.24254	−	4.15036i	−0.0761848	−	0.254475i
$267$	6.27717	+	14.5792i	0.384157	+	0.892235i
$268$	−3.17917	+	4.27037i	−0.194199	+	0.260854i
$269$	0.417322	+	0.722824i	0.0254446	+	0.0440713i	0.878467	−	0.477802i	$-0.158567\pi$
$269$	0.417322	+	0.722824i	0.0254446	+	0.0440713i	−0.853023	+	0.521874i	$0.825233\pi$
$270$	−25.5708	+	44.0829i	−1.55619	+	2.68280i
$271$	14.1085	−	24.4366i	0.857029	−	1.48442i	−0.0177208	−	0.999843i	$-0.505641\pi$
$271$	14.1085	−	24.4366i	0.857029	−	1.48442i	0.874750	−	0.484575i	$-0.161026\pi$
$272$	0.437143	+	1.01341i	0.0265057	+	0.0614471i
$273$	−2.67269	−	1.34454i	−0.161758	−	0.0813753i
$274$	37.7356	−	39.9974i	2.27969	−	2.41633i
$275$	−22.5182	−	14.8104i	−1.35790	−	0.893103i
$276$	28.5724	−	30.2440i	1.71986	−	1.82047i
$277$	18.4055	+	19.5087i	1.10588	+	1.17217i	0.983730	+	0.179654i	$0.0574978\pi$
$277$	18.4055	+	19.5087i	1.10588	+	1.17217i	0.122151	+	0.992512i	$0.461021\pi$
$278$	4.08824	+	23.1856i	0.245196	+	1.39058i
$279$	2.64980	+	2.81625i	0.158639	+	0.168604i
$280$	−4.51897	+	25.6284i	−0.270060	+	1.53159i
$281$	−12.2272	+	8.04196i	−0.729414	+	0.479743i	−0.859097	−	0.511812i	$-0.828974\pi$
$281$	−12.2272	+	8.04196i	−0.729414	+	0.479743i	0.129683	+	0.991555i	$0.458604\pi$
$282$	6.14587	−	34.7175i	0.365981	−	2.06740i
$283$	−1.15958	+	0.135536i	−0.0689299	+	0.00805675i	−0.150488	−	0.988612i	$-0.548084\pi$
$283$	−1.15958	+	0.135536i	−0.0689299	+	0.00805675i	0.0815580	+	0.996669i	$0.474010\pi$
$284$	31.4374	−	3.67451i	1.86547	−	0.218042i
$285$	8.73446	−	3.17239i	0.517385	−	0.187916i
$286$	6.59261	−	4.33603i	0.389829	−	0.256395i
$287$	−0.947854	+	5.37555i	−0.0559500	+	0.317308i
$288$	−0.271544	+	0.363718i	−0.0160009	+	0.0214323i
$289$	−2.93939	−	16.6701i	−0.172905	−	0.980594i
$290$	37.3025	+	39.5383i	2.19048	+	2.32177i
$291$	−6.14972	−	20.5922i	−0.360503	−	1.20714i
$292$	−28.9947	−	19.0701i	−1.69679	−	1.11599i
$293$	−11.4840	+	12.1723i	−0.670902	+	0.711114i	−0.969999	−	0.243108i	$-0.921833\pi$
$293$	−11.4840	+	12.1723i	−0.670902	+	0.711114i	0.299097	+	0.954223i	$0.403314\pi$
$294$	−1.28575	−	22.3359i	−0.0749866	−	1.30266i
$295$	15.4509	+	35.8192i	0.899586	+	2.08548i
$296$	−0.119776	+	0.207458i	−0.00696184	+	0.0120583i
$297$	−8.72530	−	9.28598i	−0.506293	−	0.538827i
$298$	20.4103	+	35.3516i	1.18234	+	2.04786i
$299$	−4.68696	+	6.29568i	−0.271054	+	0.364088i
$300$	−75.9171	−	8.92552i	−4.38307	−	0.515315i
$301$	2.36351	+	7.89469i	0.136231	+	0.455042i
$302$	−0.261311	+	4.48654i	−0.0150368	+	0.258171i
$303$	−18.0110	−	11.8635i	−1.03470	−	0.681538i
$304$	5.34267	−	1.26624i	0.306423	−	0.0726236i
$305$	13.0931	−	10.9864i	0.749707	−	0.629079i
$306$	−1.52181	+	1.27344i	−0.0869960	+	0.0727979i
$307$	−15.6362	−	13.1204i	−0.892407	−	0.748818i	0.0762844	−	0.997086i	$-0.475694\pi$
$307$	−15.6362	−	13.1204i	−0.892407	−	0.748818i	−0.968691	+	0.248268i	$0.920139\pi$
$308$	−11.5848	−	5.81813i	−0.660108	−	0.331519i
$309$	−8.29822	+	6.95347i	−0.472069	+	0.395569i
$310$	−5.00713	+	11.6078i	−0.284386	+	0.659281i
$311$	3.96265	+	5.32276i	0.224701	+	0.301826i	0.900149	−	0.435581i	$-0.143457\pi$
$311$	3.96265	+	5.32276i	0.224701	+	0.301826i	−0.675448	+	0.737407i	$0.736050\pi$
$312$	5.62279	−	9.72375i	0.318328	−	0.550499i
$313$	0.533740	+	9.16397i	0.0301688	+	0.517978i	0.979213	+	0.202835i	$0.0650155\pi$
$313$	0.533740	+	9.16397i	0.0301688	+	0.517978i	−0.949044	+	0.315143i	$0.897947\pi$
$314$	−24.9087	+	9.06601i	−1.40568	+	0.511625i
$315$	−15.6902	+	1.81240i	−0.884042	+	0.102117i
$316$	−19.7300	−	7.18114i	−1.10990	−	0.403971i
$317$	−0.0143668	+	0.0479884i	−0.000806919	+	0.00269530i	−0.958392	−	0.285455i	$-0.907855\pi$
$317$	−0.0143668	+	0.0479884i	−0.000806919	+	0.00269530i	0.957585	+	0.288151i	$0.0930404\pi$
$318$	48.9085	−	5.68303i	2.74265	−	0.318689i
$319$	−12.1453	+	6.09962i	−0.680008	+	0.341513i
$320$	30.4039	+	7.20586i	1.69963	+	0.402820i
$321$	−9.87870	+	32.9161i	−0.551375	+	1.83719i
$322$	19.1869	+	2.24263i	1.06925	+	0.124977i
$323$	0.361832			0.0201329
$324$	−33.9253	−	12.4519i	−1.88474	−	0.691772i
$325$	14.4199			0.799874
$326$	9.17695	+	1.07263i	0.508264	+	0.0594076i
$327$	6.46219	−	1.52695i	0.357360	−	0.0844404i
$328$	−19.9407	−	4.72603i	−1.10104	−	0.260951i
$329$	9.76484	−	4.90409i	0.538353	−	0.270371i
$330$	16.5253	−	38.2388i	0.909689	−	2.10498i
$331$	5.30612	−	17.7237i	0.291651	−	0.974181i	−0.679091	−	0.734054i	$-0.737626\pi$
$331$	5.30612	−	17.7237i	0.291651	−	0.974181i	0.970742	−	0.240127i	$-0.0771890\pi$
$332$	21.4290	+	7.79954i	1.17607	+	0.428055i
$333$	−0.141426	−	0.0337209i	−0.00775011	−	0.00184789i
$334$	27.2761	−	9.92767i	1.49248	−	0.543218i
$335$	−0.308281	−	5.29299i	−0.0168432	−	0.289187i
$336$	−9.33230	−	0.00631604i	−0.509119	−	0.000344568i
$337$	−2.17944	−	2.92750i	−0.118722	−	0.159471i	0.738789	−	0.673936i	$-0.235398\pi$
$337$	−2.17944	−	2.92750i	−0.118722	−	0.159471i	−0.857511	+	0.514465i	$0.827990\pi$
$338$	10.9565	−	25.4001i	0.595956	−	1.38158i
$339$	−1.04560	−	5.95346i	−0.0567893	−	0.323348i
$340$	−3.86974	−	1.94346i	−0.209866	−	0.105399i
$341$	−2.42131	−	2.03172i	−0.131121	−	0.110024i
$342$	4.92434	+	8.55593i	0.266278	+	0.462652i
$343$	12.3716	−	10.3810i	0.668005	−	0.560523i
$344$	−30.1053	+	7.13509i	−1.62317	+	0.384698i
$345$	−2.43725	+	41.3636i	−0.131217	+	2.22694i
$346$	−1.36445	+	23.4267i	−0.0733533	+	1.25943i
$347$	−1.17599	−	3.92808i	−0.0631305	−	0.210870i	0.920605	−	0.390496i	$-0.127697\pi$
$347$	−1.17599	−	3.92808i	−0.0631305	−	0.210870i	−0.983735	+	0.179626i	$0.942511\pi$
$348$	−23.0389	+	30.9030i	−1.23502	+	1.65657i
$349$	4.51755	−	6.06813i	0.241819	−	0.324819i	−0.664600	−	0.747200i	$-0.731398\pi$
$349$	4.51755	−	6.06813i	0.241819	−	0.324819i	0.906419	+	0.422380i	$0.138805\pi$
$350$	−17.7453	−	30.7358i	−0.948528	−	1.64290i
$351$	6.63030	+	1.58563i	0.353899	+	0.0846349i
$352$	0.185511	−	0.321314i	0.00988775	−	0.0171261i
$353$	0.812133	+	1.88274i	0.0432255	+	0.100208i	0.938461	−	0.345386i	$-0.112252\pi$
$353$	0.812133	+	1.88274i	0.0432255	+	0.100208i	−0.895235	+	0.445594i	$0.852993\pi$
$354$	−34.6385	+	22.7485i	−1.84102	+	1.20907i
$355$	−21.6313	+	22.9279i	−1.14807	+	1.21688i
$356$	−30.7445	−	20.2210i	−1.62946	−	1.07171i
$357$	−0.598320	−	0.142232i	−0.0316664	−	0.00752772i
$358$	−2.38878	−	2.53195i	−0.126251	−	0.133818i
$359$	−1.74531	−	9.89817i	−0.0921141	−	0.522405i	−0.995594	−	0.0937737i	$-0.970107\pi$
$359$	−1.74531	−	9.89817i	−0.0921141	−	0.522405i	0.903479	−	0.428631i	$-0.141004\pi$
$360$	−3.36776	−	59.2026i	−0.177497	−	3.12025i
$361$	−2.98674	+	16.9386i	−0.157197	+	0.891506i
$362$	−20.2855	+	13.3420i	−1.06618	+	0.701240i
$363$	−6.61268	−	5.55633i	−0.347076	−	0.291631i
$364$	6.88898	−	0.805206i	0.361080	−	0.0422043i
$365$	34.3276	−	4.01232i	1.79679	−	0.210015i
$366$	13.9011	+	11.6805i	0.726623	+	0.610547i
$367$	−27.1341	+	17.8464i	−1.41639	+	0.931574i	−0.416643	+	0.909070i	$0.636794\pi$
$367$	−27.1341	+	17.8464i	−1.41639	+	0.931574i	−0.999747	+	0.0225041i	$0.992836\pi$
$368$	−4.25131	+	24.1104i	−0.221615	+	1.25684i
$369$	−0.706387	−	12.4177i	−0.0367730	−	0.646442i
$370$	−0.0825380	−	0.468096i	−0.00429095	−	0.0243352i
$371$	10.4720	+	11.0997i	0.543680	+	0.576267i
$372$	−8.72142	−	2.07325i	−0.452184	−	0.107493i
$373$	−12.6178	−	8.29884i	−0.653324	−	0.429698i	0.179105	−	0.983830i	$-0.442680\pi$
$373$	−12.6178	−	8.29884i	−0.653324	−	0.429698i	−0.832429	+	0.554132i	$0.813050\pi$
$374$	1.11308	−	1.17980i	0.0575561	−	0.0610059i
$375$	34.6838	−	22.7783i	1.79106	−	1.17626i
$376$	16.2489	+	37.6692i	0.837974	+	1.94264i
$377$	3.63572	−	6.29725i	0.187249	−	0.324325i
$378$	−4.77957	−	16.0837i	−0.245835	−	0.827254i
$379$	1.32973	+	2.30316i	0.0683037	+	0.118305i	0.898155	−	0.439680i	$-0.144908\pi$
$379$	1.32973	+	2.30316i	0.0683037	+	0.118305i	−0.829851	+	0.557985i	$0.811575\pi$
$380$	−12.8646	+	17.2802i	−0.659942	+	0.886455i
$381$	13.6020	−	18.2448i	0.696850	−	0.934711i
$382$	−12.5380	−	41.8797i	−0.641497	−	2.14275i
$383$	0.0903647	−	1.55150i	0.00461742	−	0.0792780i	−0.995212	−	0.0977380i	$-0.968839\pi$
$383$	0.0903647	−	1.55150i	0.00461742	−	0.0792780i	0.999830	+	0.0184600i	$0.00587632\pi$
$384$	−1.98328	+	33.6591i	−0.101209	+	1.71766i
$385$	12.5625	−	2.97737i	0.640244	−	0.151741i
$386$	−51.9137	+	43.5607i	−2.64234	+	2.21718i
$387$	−9.36693	−	16.2748i	−0.476148	−	0.827297i
$388$	38.1656	+	32.0247i	1.93757	+	1.62581i
$389$	−3.28564	−	1.65011i	−0.166588	−	0.0836638i	0.363551	−	0.931574i	$-0.381564\pi$
$389$	−3.28564	−	1.65011i	−0.166588	−	0.0836638i	−0.530140	+	0.847910i	$0.677860\pi$
$390$	3.85529	+	21.9513i	0.195220	+	1.11155i
$391$	−0.639024	+	1.48142i	−0.0323168	+	0.0749188i
$392$	15.5455	+	20.8812i	0.785167	+	1.05466i
$393$	−7.50157	−	0.00507701i	−0.378404	−	0.000256101i
$394$	−0.854424	−	14.6699i	−0.0430452	−	0.739058i
$395$	19.6490	−	7.15164i	0.988647	−	0.359838i
$396$	28.7341	+	6.85119i	1.44394	+	0.344285i
$397$	36.1674	+	13.1638i	1.81519	+	0.660674i	0.996223	+	0.0868301i	$0.0276737\pi$
$397$	36.1674	+	13.1638i	1.81519	+	0.660674i	0.818965	+	0.573844i	$0.194548\pi$
$398$	11.2963	−	37.7323i	0.566232	−	1.89135i
$399$	−1.21372	+	2.80849i	−0.0607619	+	0.140600i
$400$	40.1952	−	20.1868i	2.00976	−	1.00934i
$401$	17.3252	+	4.10616i	0.865182	+	0.205052i	0.639163	−	0.769071i	$-0.279281\pi$
$401$	17.3252	+	4.10616i	0.865182	+	0.205052i	0.226018	+	0.974123i	$0.427429\pi$
$402$	5.48142	−	1.29520i	0.273388	−	0.0645989i
$403$	1.67965	+	0.196324i	0.0836696	+	0.00977957i
$404$	49.9982			2.48750
$405$	33.8526	−	12.2176i	1.68215	−	0.607099i
$406$	−17.8966			−0.888196
$407$	0.118039	+	0.0137968i	0.00585100	+	0.000683884i
$408$	0.663698	−	2.21146i	0.0328580	−	0.109483i
$409$	−17.8371	−	4.22746i	−0.881986	−	0.209035i	−0.235421	−	0.971893i	$-0.575647\pi$
$409$	−17.8371	−	4.22746i	−0.881986	−	0.209035i	−0.646565	+	0.762859i	$0.723795\pi$
$410$	36.3371	−	18.2492i	1.79456	−	0.901262i
$411$	−38.5737	+	4.48216i	−1.90270	+	0.221089i
$412$	7.19834	−	24.0441i	0.354637	−	1.18457i
$413$	−12.0689	−	4.39273i	−0.593873	−	0.216152i
$414$	−43.7267	+	5.05094i	−2.14905	+	0.248240i
$415$	−21.3410	+	7.76749i	−1.04759	+	0.381291i
$416$	0.0115420	+	0.198168i	0.000565892	+	0.00971598i
$417$	8.32290	−	14.3932i	0.407574	−	0.704837i
$418$	−4.81864	−	6.47255i	−0.235687	−	0.316583i
$419$	−4.94733	+	11.4692i	−0.241693	+	0.560308i	−0.995280	−	0.0970402i	$-0.969062\pi$
$419$	−4.94733	+	11.4692i	−0.241693	+	0.560308i	0.753587	+	0.657348i	$0.228322\pi$
$420$	28.0654	−	23.5173i	1.36945	−	1.14753i
$421$	19.3203	+	9.70302i	0.941614	+	0.472896i	0.852269	−	0.523104i	$-0.175226\pi$
$421$	19.3203	+	9.70302i	0.941614	+	0.472896i	0.0893456	+	0.996001i	$0.471522\pi$
$422$	18.9221	+	15.8775i	0.921114	+	0.772906i
$423$	−19.0953	+	15.9788i	−0.928443	+	0.776917i
$424$	−43.8878	+	36.8262i	−2.13138	+	1.78844i
$425$	2.88422	−	0.683574i	0.139905	−	0.0331582i
$426$	−27.9645	−	18.4197i	−1.35488	−	0.892436i
$427$	−0.327198	+	5.61777i	−0.0158342	+	0.271863i
$428$	−22.8498	−	76.3238i	−1.10449	−	3.68925i
$429$	−5.53434	−	0.650668i	−0.267200	−	0.0314146i
$430$	36.6592	−	49.2419i	1.76787	−	2.37466i
$431$	15.5400	+	26.9162i	0.748538	+	1.29651i	0.948524	+	0.316707i	$0.102577\pi$
$431$	15.5400	+	26.9162i	0.748538	+	1.29651i	−0.199986	+	0.979799i	$0.564090\pi$
$432$	20.7015	−	4.86198i	0.996003	−	0.233922i
$433$	−6.64480	+	11.5091i	−0.319329	+	0.553093i	−0.980348	−	0.197275i	$-0.936791\pi$
$433$	−6.64480	+	11.5091i	−0.319329	+	0.553093i	0.661019	+	0.750369i	$0.270124\pi$
$434$	−1.64854	−	3.82175i	−0.0791326	−	0.183450i
$435$	−2.20610	−	38.3241i	−0.105774	−	1.83750i
$436$	−10.5638	+	11.1969i	−0.505912	+	0.536236i
$437$	6.70593	+	4.41056i	0.320788	+	0.210986i
$438$	10.5062	+	35.1798i	0.502006	+	1.68096i
$439$	0.880146	+	0.932901i	0.0420071	+	0.0445249i	0.748036	−	0.663658i	$-0.230997\pi$
$439$	0.880146	+	0.932901i	0.0420071	+	0.0445249i	−0.706029	+	0.708183i	$0.749515\pi$
$440$	8.41685	+	47.7343i	0.401258	+	2.27564i
$441$	−9.45215	+	12.6606i	−0.450102	+	0.602887i
$442$	−0.150692	+	0.854617i	−0.00716769	+	0.0406500i
$443$	32.6702	−	21.4875i	1.55221	−	1.02090i	0.572637	−	0.819809i	$-0.305921\pi$
$443$	32.6702	−	21.4875i	1.55221	−	1.02090i	0.979572	−	0.201094i	$-0.0644498\pi$
$444$	0.316806	−	0.115065i	0.0150350	−	0.00546076i
$445$	36.3993	−	4.25447i	1.72549	−	0.201681i
$446$	−31.7719	+	3.71360i	−1.50444	+	0.175844i
$447$	5.02507	−	28.3862i	0.237678	−	1.34262i
$448$	−8.59504	+	5.65305i	−0.406077	+	0.267081i
$449$	−2.78437	+	15.7909i	−0.131403	+	0.745221i	0.845895	+	0.533349i	$0.179067\pi$
$449$	−2.78437	+	15.7909i	−0.131403	+	0.745221i	−0.977298	+	0.211871i	$0.932044\pi$
$450$	55.4166	+	58.8977i	2.61237	+	2.77647i
$451$	1.76543	+	10.0123i	0.0831310	+	0.471459i
$452$	9.61630	+	10.1927i	0.452313	+	0.479423i
$453$	2.17954	−	2.30705i	0.102404	−	0.108395i
$454$	33.3849	+	21.9576i	1.56683	+	1.03052i
$455$	−4.74013	+	5.02425i	−0.222221	+	0.235540i
$456$	−10.2613	−	5.16211i	−0.480529	−	0.241738i
$457$	−1.53118	−	3.54968i	−0.0716256	−	0.166047i	0.878642	−	0.477481i	$-0.158450\pi$
$457$	−1.53118	−	3.54968i	−0.0716256	−	0.166047i	−0.950268	+	0.311434i	$0.899191\pi$
$458$	−8.26234	+	14.3108i	−0.386074	+	0.668699i
$459$	1.40134	+	0.00284525i	0.0654087	+	0.000132805i
$460$	−48.0292	−	83.1890i	−2.23937	−	3.87871i
$461$	−12.6783	+	17.0299i	−0.590486	+	0.793160i	−0.992470	−	0.122486i	$-0.960913\pi$
$461$	−12.6783	+	17.0299i	−0.590486	+	0.793160i	0.401984	+	0.915647i	$0.368321\pi$
$462$	5.42374	+	12.5971i	0.252335	+	0.586069i
$463$	−5.53918	−	18.5021i	−0.257427	−	0.859867i	−0.984810	−	0.173635i	$-0.944449\pi$
$463$	−5.53918	−	18.5021i	−0.257427	−	0.859867i	0.727383	−	0.686232i	$-0.240737\pi$
$464$	1.31881	−	22.6431i	0.0612244	−	1.05118i
$465$	7.98073	−	4.00131i	0.370098	−	0.185556i
$466$	−32.9376	+	7.80634i	−1.52580	+	0.361622i
$467$	−3.15564	+	2.64790i	−0.146026	+	0.122530i	−0.712874	−	0.701292i	$-0.752607\pi$
$467$	−3.15564	+	2.64790i	−0.146026	+	0.122530i	0.566848	+	0.823822i	$0.308162\pi$
$468$	−14.8584	+	5.38527i	−0.686832	+	0.248934i
$469$	1.33722	+	1.12206i	0.0617469	+	0.0518118i
$470$	−72.7419	−	36.5324i	−3.35533	−	1.68511i
$471$	17.5862	+	6.41435i	0.810331	+	0.295558i
$472$	19.0986	−	44.2755i	0.879084	−	2.03794i
$473$	9.16587	+	12.3119i	0.421447	+	0.566102i
$474$	11.0935	+	19.2446i	0.509542	+	0.883934i
$475$	−0.857416	−	14.7213i	−0.0393410	−	0.675458i
$476$	1.33974	−	0.487625i	0.0614068	−	0.0223503i
$477$	−29.0255	−	19.1467i	−1.32899	−	0.876667i
$478$	28.8966	+	10.5175i	1.32170	+	0.481060i
$479$	−8.24624	+	27.5443i	−0.376780	+	1.25853i	0.533945	+	0.845520i	$0.320709\pi$
$479$	−8.24624	+	27.5443i	−0.376780	+	1.25853i	−0.910725	+	0.413014i	$0.864476\pi$
$480$	0.625220	+	0.841004i	0.0285373	+	0.0383864i
$481$	−0.0568202	+	0.0285362i	−0.00259078	+	0.00130114i
$482$	−32.6733	−	7.74372i	−1.48823	−	0.352717i
$483$	−9.35508	−	9.92926i	−0.425671	−	0.451797i
$484$	19.8878	+	2.32456i	0.903993	+	0.105662i
$485$	−49.6170			−2.25299
$486$	19.0042	+	33.1749i	0.862046	+	1.50484i
$487$	8.88765			0.402738			0.201369	−	0.979515i	$-0.435461\pi$
$487$	8.88765			0.402738			0.201369	+	0.979515i	$0.435461\pi$
$488$	−20.9840	−	2.45268i	−0.949901	−	0.111028i
$489$	−4.47445	−	4.74908i	−0.202342	−	0.214761i
$490$	−50.2611	−	11.9121i	−2.27056	−	0.538134i
$491$	−25.2009	+	12.6563i	−1.13730	+	0.571173i	−0.914859	−	0.403773i	$-0.867698\pi$
$491$	−25.2009	+	12.6563i	−1.13730	+	0.571173i	−0.222440	+	0.974946i	$0.571402\pi$
$492$	17.2030	+	23.1403i	0.775569	+	1.04324i
$493$	0.428684	−	1.43191i	0.0193070	−	0.0644898i
$494$	4.05686	+	1.47658i	0.182527	+	0.0664344i
$495$	−26.3069	+	13.1673i	−1.18241	+	0.591825i
$496$	4.95683	−	1.80414i	0.222568	−	0.0810082i
$497$	−0.603432	−	10.3605i	−0.0270676	−	0.464733i
$498$	−12.0488	−	20.9018i	−0.539920	−	0.936633i
$499$	0.710634	+	0.954547i	0.0318123	+	0.0427314i	0.817745	−	0.575581i	$-0.195224\pi$
$499$	0.710634	+	0.954547i	0.0318123	+	0.0427314i	−0.785932	+	0.618312i	$0.787817\pi$
$500$	−38.1013	+	88.3287i	−1.70394	+	3.95018i
$501$	−19.2577	−	7.02399i	−0.860370	−	0.313809i
$502$	−29.1267	−	14.6280i	−1.29999	−	0.652880i
$503$	4.59276	+	3.85379i	0.204781	+	0.171832i	0.739411	−	0.673255i	$-0.235104\pi$
$503$	4.59276	+	3.85379i	0.204781	+	0.171832i	−0.534629	+	0.845087i	$0.679549\pi$
$504$	14.9387	+	12.5696i	0.665424	+	0.559894i
$505$	−38.1435	+	32.0062i	−1.69736	+	1.42426i
$506$	35.0102	−	8.29758i	1.55639	−	0.368872i
$507$	−17.4633	+	8.75560i	−0.775572	+	0.388850i
$508$	−3.06756	+	52.6680i	−0.136101	+	2.33676i
$509$	−7.20888	−	24.0793i	−0.319528	−	1.06730i	−0.955354	−	0.295465i	$-0.904525\pi$
$509$	−7.20888	−	24.0793i	−0.319528	−	1.06730i	0.635826	−	0.771833i	$-0.280660\pi$
$510$	1.81172	+	4.20786i	0.0802242	+	0.186327i
$511$	−6.79503	+	9.12731i	−0.300594	+	0.403768i
$512$	−19.9189	−	34.5006i	−0.880300	−	1.52473i
$513$	1.22453	−	6.86314i	0.0540643	−	0.303015i
$514$	−4.12333	+	7.14181i	−0.181872	+	0.315012i
$515$	9.90019	+	22.9512i	0.436254	+	1.01135i
$516$	38.8886	+	19.5636i	1.71198	+	0.861238i
$517$	13.9667	−	14.8038i	0.614253	−	0.651070i
$518$	0.130748	+	0.0859943i	0.00574474	+	0.00377837i
$519$	11.3806	−	12.0464i	0.499552	−	0.528777i
$520$	−17.7962	−	18.8628i	−0.780414	−	0.827190i
$521$	−5.84968	−	33.1752i	−0.256279	−	1.45343i	−0.792768	−	0.609524i	$-0.791361\pi$
$521$	−5.84968	−	33.1752i	−0.256279	−	1.45343i	0.536488	−	0.843908i	$-0.319750\pi$
$522$	39.6932	−	9.35074i	1.73733	−	0.409271i
$523$	4.18478	−	23.7331i	0.182988	−	1.03778i	−0.745526	−	0.666477i	$-0.767801\pi$
$523$	4.18478	−	23.7331i	0.182988	−	1.03778i	0.928513	−	0.371299i	$-0.121087\pi$
$524$	14.5297	−	9.55633i	0.634733	−	0.417470i
$525$	−4.36896	+	24.6799i	−0.190677	+	1.07712i
$526$	−59.4970	+	6.95420i	−2.59419	+	0.303217i
$527$	0.345265	−	0.0403557i	0.0150400	−	0.00175792i
$528$	−16.3377	+	5.93392i	−0.711007	+	0.258241i
$529$	−10.6848	+	7.02753i	−0.464558	+	0.305545i
$530$	19.7398	−	111.950i	0.857443	−	4.86280i
$531$	29.0630	+	3.43686i	1.26123	+	0.149147i
$532$	−1.23166	−	6.98506i	−0.0533990	−	0.302841i
$533$	−3.73274	−	3.95648i	−0.161683	−	0.171374i
$534$	11.1403	+	37.3029i	0.482086	+	1.61426i
$535$	66.2905	+	43.6000i	2.86599	+	1.88499i
$536$	−4.49739	+	4.76696i	−0.194258	+	0.205901i
$537$	0.141274	+	2.45420i	0.00609643	+	0.105906i
$538$	0.810803	+	1.87965i	0.0349562	+	0.0810376i
$539$	6.45742	−	11.1846i	0.278141	−	0.481754i
$540$	−49.9592	+	66.8232i	−2.14990	+	2.87561i
$541$	−11.3703	−	19.6940i	−0.488849	−	0.846712i	0.511068	−	0.859540i	$-0.329250\pi$
$541$	−11.3703	−	19.6940i	−0.488849	−	0.846712i	−0.999918	+	0.0128282i	$0.995917\pi$
$542$	41.3267	−	55.5114i	1.77513	−	2.38442i
$543$	17.0292	+	2.00212i	0.730794	+	0.0859190i
$544$	0.0117027	+	0.0390897i	0.000501749	+	0.00167596i
$545$	0.891384	−	15.3045i	0.0381827	−	0.655571i
$546$	−6.12794	−	4.03635i	−0.262252	−	0.172740i
$547$	0.378936	−	0.0898095i	0.0162021	−	0.00383998i	−0.222507	−	0.974931i	$-0.571424\pi$
$547$	0.378936	−	0.0898095i	0.0162021	−	0.00383998i	0.238709	+	0.971091i	$0.423276\pi$
$548$	68.9639	−	57.8676i	2.94599	−	2.47198i
$549$	−2.20951	−	12.6307i	−0.0942994	−	0.539064i
$550$	−50.6382	−	42.4905i	−2.15922	−	1.81180i
$551$	−6.64503	−	3.33726i	−0.283088	−	0.142172i
$552$	39.2571	−	32.8954i	1.67089	−	1.40012i
$553$	−2.72677	+	6.32136i	−0.115954	+	0.268811i
$554$	39.2818	+	52.7647i	1.66893	+	2.24176i
$555$	−0.168032	+	0.290586i	−0.00713256	+	0.0123347i
$556$	2.24115	+	38.4791i	0.0950460	+	1.63188i
$557$	19.6611	−	7.15607i	0.833069	−	0.303212i	0.109951	−	0.993937i	$-0.464931\pi$
$557$	19.6611	−	7.15607i	0.833069	−	0.303212i	0.723118	+	0.690725i	$0.242708\pi$
$558$	5.65314	+	7.61498i	0.239316	+	0.322368i
$559$	−7.71685	−	2.80870i	−0.326388	−	0.118795i
$560$	−6.17944	+	20.6408i	−0.261129	+	0.872232i
$561$	−1.13780	+	0.132210i	−0.0480381	+	0.00558190i
$562$	−32.0758	+	16.1091i	−1.35303	+	0.679520i
$563$	−13.4939	−	3.19812i	−0.568701	−	0.134785i	−0.0638013	−	0.997963i	$-0.520322\pi$
$563$	−13.4939	−	3.19812i	−0.568701	−	0.134785i	−0.504900	+	0.863178i	$0.668471\pi$
$564$	16.5923	−	55.2861i	0.698664	−	2.32796i
$565$	−13.8611	−	1.62013i	−0.583139	−	0.0681592i
$566$	−2.86338			−0.120357
$567$	−4.72268	+	10.8674i	−0.198334	+	0.456389i
$568$	38.9631			1.63485
$569$	9.23784	+	1.07975i	0.387270	+	0.0452654i	0.307501	−	0.951548i	$-0.400507\pi$
$569$	9.23784	+	1.07975i	0.387270	+	0.0452654i	0.0797697	+	0.996813i	$0.474581\pi$
$570$	22.1808	−	5.24109i	0.929050	−	0.219525i
$571$	35.0608	+	8.30957i	1.46725	+	0.347745i	0.885125	−	0.465354i	$-0.154073\pi$
$571$	35.0608	+	8.30957i	1.46725	+	0.347745i	0.582126	+	0.813099i	$0.302221\pi$
$572$	11.5444	−	5.79780i	0.482694	−	0.242418i
$573$	−12.2472	+	28.3394i	−0.511633	+	1.18389i
$574$	−3.83960	+	12.8252i	−0.160262	+	0.535312i
$575$	61.7866	+	22.4885i	2.57668	+	0.937834i
$576$	16.1094	−	17.0288i	0.671226	−	0.709531i
$577$	8.15363	−	2.96768i	0.339440	−	0.123546i	−0.166675	−	0.986012i	$-0.553303\pi$
$577$	8.15363	−	2.96768i	0.339440	−	0.123546i	0.506115	+	0.862466i	$0.331081\pi$
$578$	−2.41395	−	41.4460i	−0.100407	−	1.72393i
$579$	47.8583	+	0.0323902i	1.98892	+	0.00134609i
$580$	53.1427	+	71.3831i	2.20663	+	2.96402i
$581$	2.96158	−	6.86571i	0.122867	−	0.284838i
$582$	−9.11769	−	51.9144i	−0.377940	−	2.15192i
$583$	25.3993	+	12.7560i	1.05193	+	0.528300i
$584$	−32.7259	−	27.4603i	−1.35421	−	1.13631i
$585$	7.88811	−	13.6200i	0.326133	−	0.563118i
$586$	−31.4413	+	26.3824i	−1.29883	+	1.08985i
$587$	9.00828	−	2.13500i	0.371812	−	0.0881210i	−0.0404620	−	0.999181i	$-0.512883\pi$
$587$	9.00828	−	2.13500i	0.371812	−	0.0881210i	0.412274	+	0.911060i	$0.364735\pi$
$588$	2.15449	−	36.5649i	0.0888498	−	1.50791i
$589$	0.100553	−	1.72643i	0.00414322	−	0.0711363i
$590$	27.4401	+	91.6564i	1.12969	+	3.77344i
$591$	−6.20263	+	8.31982i	−0.255142	+	0.342232i
$592$	−0.118436	+	0.159088i	−0.00486771	+	0.00653846i
$593$	18.3119	+	31.7171i	0.751979	+	1.30247i	0.946862	+	0.321639i	$0.104234\pi$
$593$	18.3119	+	31.7171i	0.751979	+	1.30247i	−0.194884	+	0.980826i	$0.562433\pi$
$594$	−18.6112	−	25.1054i	−0.763625	−	1.03009i
$595$	−0.709932	+	1.22964i	−0.0291044	+	0.0504102i
$596$	26.4701	+	61.3645i	1.08426	+	2.51359i
$597$	−23.2496	+	15.2690i	−0.951542	+	0.624917i
$598$	−13.2102	+	14.0020i	−0.540205	+	0.572584i
$599$	−20.6854	−	13.6050i	−0.845182	−	0.555885i	0.0514430	−	0.998676i	$-0.483618\pi$
$599$	−20.6854	−	13.6050i	−0.845182	−	0.555885i	−0.896625	+	0.442791i	$0.853988\pi$
$600$	−91.5468	−	21.7624i	−3.73738	−	0.888447i
$601$	−15.1593	−	16.0679i	−0.618359	−	0.655423i	0.340188	−	0.940358i	$-0.389509\pi$
$601$	−15.1593	−	16.0679i	−0.618359	−	0.655423i	−0.958547	+	0.284935i	$0.908028\pi$
$602$	3.50974	+	19.9047i	0.143046	+	0.811257i
$603$	−3.55209	−	1.78995i	−0.144652	−	0.0728924i
$604$	−1.27765	+	7.24590i	−0.0519867	+	0.294831i
$605$	−16.6604	+	10.9577i	−0.677343	+	0.445496i
$606$	−40.4975	−	34.0282i	−1.64510	−	1.38230i
$607$	9.50492	−	1.11097i	0.385793	−	0.0450927i	0.0790138	−	0.996874i	$-0.474823\pi$
$607$	9.50492	−	1.11097i	0.385793	−	0.0450927i	0.306779	+	0.951781i	$0.400749\pi$
$608$	0.201623	−	0.0235663i	0.00817689	−	0.000955741i
$609$	9.67628	+	8.13053i	0.392103	+	0.329466i
$610$	35.0234	−	23.0353i	1.41806	−	0.932671i
$611$	−1.89085	+	10.7235i	−0.0764954	+	0.433827i
$612$	−2.71665	+	1.78150i	−0.109814	+	0.0720131i
$613$	−2.38544	−	13.5285i	−0.0963469	−	0.546410i	−0.994326	−	0.106373i	$-0.966076\pi$
$613$	−2.38544	−	13.5285i	−0.0963469	−	0.546410i	0.897979	−	0.440037i	$-0.145035\pi$
$614$	−34.3547	−	36.4139i	−1.38644	−	1.46954i
$615$	−27.9372	−	6.64122i	−1.12654	−	0.267800i
$616$	−13.3331	−	8.76931i	−0.537205	−	0.353326i
$617$	9.33576	−	9.89532i	0.375843	−	0.398371i	−0.511648	−	0.859195i	$-0.670965\pi$
$617$	9.33576	−	9.89532i	0.375843	−	0.398371i	0.887491	+	0.460825i	$0.152446\pi$
$618$	−22.1947	+	14.5762i	−0.892800	+	0.586339i
$619$	−5.64861	−	13.0949i	−0.227037	−	0.526330i	0.766178	−	0.642629i	$-0.222156\pi$
$619$	−5.64861	−	13.0949i	−0.227037	−	0.526330i	−0.993214	+	0.116299i	$0.962897\pi$
$620$	−10.3483	+	17.9238i	−0.415599	+	0.719839i
$621$	25.9367	+	17.1343i	1.04080	+	0.687578i
$622$	8.13761	+	14.0947i	0.326288	+	0.565148i
$623$	−7.20511	+	9.67815i	−0.288667	+	0.387747i
$624$	5.55844	−	7.45574i	0.222516	−	0.298468i
$625$	−11.7148	−	39.1301i	−0.468592	−	1.56521i
$626$	−1.30906	+	22.4758i	−0.0523207	+	0.898312i
$627$	−0.335191	+	5.68868i	−0.0133863	+	0.227184i
$628$	−42.2271	+	10.0080i	−1.68505	+	0.399363i
$629$	−0.0100122	+	0.00840126i	−0.000399214	+	0.000334980i
$630$	−38.7380	−	0.0524353i	−1.54336	−	0.00208907i
$631$	−6.09157	−	5.11144i	−0.242502	−	0.203483i	0.513434	−	0.858129i	$-0.328373\pi$
$631$	−6.09157	−	5.11144i	−0.242502	−	0.203483i	−0.755935	+	0.654646i	$0.772818\pi$
$632$	−23.0973	−	11.5999i	−0.918759	−	0.461418i
$633$	−3.01749	−	17.1810i	−0.119934	−	0.682883i
$634$	−0.0486619	+	0.112811i	−0.00193261	+	0.00448030i
$635$	−31.3750	−	42.1440i	−1.24508	−	1.67243i
$636$	80.6103	+	0.0545565i	3.19641	+	0.00216331i
$637$	0.401763	+	6.89801i	0.0159184	+	0.273309i
$638$	−31.3233	+	11.4007i	−1.24010	+	0.451360i
$639$	6.75159	+	22.6635i	0.267089	+	0.896553i
$640$	73.1505	+	26.6246i	2.89153	+	1.05243i
$641$	−1.20559	+	4.02695i	−0.0476179	+	0.159055i	−0.978492	−	0.206286i	$-0.933862\pi$
$641$	−1.20559	+	4.02695i	−0.0476179	+	0.159055i	0.930874	+	0.365341i	$0.119048\pi$
$642$	−33.4372	+	77.3720i	−1.31966	+	3.05363i
$643$	17.1475	−	8.61180i	0.676232	−	0.339616i	−0.0773186	−	0.997006i	$-0.524636\pi$
$643$	17.1475	−	8.61180i	0.676232	−	0.339616i	0.753551	+	0.657390i	$0.228340\pi$
$644$	30.7737	+	7.29349i	1.21265	+	0.287404i
$645$	−42.1916	+	9.96944i	−1.66129	+	0.392546i
$646$	0.881437	+	0.103025i	0.0346797	+	0.00405347i
$647$	−33.3755			−1.31213			−0.656063	−	0.754706i	$-0.727779\pi$
$647$	−33.3755			−1.31213			−0.656063	+	0.754706i	$0.727779\pi$
$648$	−39.7003	−	20.0730i	−1.55957	−	0.788541i
$649$	−23.9217			−0.939009
$650$	35.1275	+	4.10582i	1.37781	+	0.161043i
$651$	−0.844913	+	2.81527i	−0.0331148	+	0.110339i
$652$	14.7188	+	3.48841i	0.576432	+	0.136617i
$653$	10.8992	−	5.47380i	0.426520	−	0.214206i	−0.222572	−	0.974916i	$-0.571445\pi$
$653$	10.8992	−	5.47380i	0.426520	−	0.214206i	0.649092	+	0.760710i	$0.275149\pi$
$654$	16.1769	−	1.87971i	0.632568	−	0.0735026i
$655$	−4.96721	+	16.5916i	−0.194085	+	0.648289i
$656$	−15.9437	−	5.80302i	−0.622496	−	0.226570i
$657$	10.3019	−	23.7939i	0.401916	−	0.928288i
$658$	25.1839	−	9.16619i	0.981770	−	0.357335i
$659$	1.36161	+	23.3779i	0.0530408	+	0.910675i	0.914939	+	0.403593i	$0.132239\pi$
$659$	1.36161	+	23.3779i	0.0530408	+	0.910675i	−0.861898	+	0.507082i	$0.830724\pi$
$660$	34.1397	−	59.0393i	1.32888	−	2.29810i
$661$	−20.1047	−	27.0053i	−0.781982	−	1.05038i	−0.997271	−	0.0738336i	$-0.976477\pi$
$661$	−20.1047	−	27.0053i	−0.781982	−	1.05038i	0.215289	−	0.976550i	$-0.430931\pi$
$662$	17.9724	−	41.6647i	0.698518	−	1.61935i
$663$	0.469732	−	0.393611i	0.0182429	−	0.0152866i
$664$	25.0862	+	12.5988i	0.973535	+	0.488928i
$665$	5.41109	+	4.54045i	0.209833	+	0.176071i
$666$	−0.334919	−	0.122414i	−0.0129778	−	0.00474345i
$667$	25.3992	−	21.3124i	0.983460	−	0.825221i
$668$	46.2405	−	10.9592i	1.78910	−	0.424024i
$669$	18.8654	+	12.4263i	0.729378	+	0.480427i
$670$	0.756098	−	12.9817i	0.0292106	−	0.501527i
$671$	3.00603	+	10.0408i	0.116046	+	0.387622i
$672$	−0.342664	−	0.0402868i	−0.0132186	−	0.00155410i
$673$	−7.41080	+	9.95443i	−0.285665	+	0.383715i	−0.921673	−	0.387968i	$-0.873177\pi$
$673$	−7.41080	+	9.95443i	−0.285665	+	0.383715i	0.636008	+	0.771683i	$0.280585\pi$
$674$	−4.47565	−	7.75205i	−0.172396	−	0.298598i
$675$	−3.20492	−	57.0206i	−0.123357	−	2.19472i
$676$	22.6440	−	39.2206i	0.870925	−	1.50849i
$677$	−5.86348	−	13.5931i	−0.225352	−	0.522425i	0.767602	−	0.640927i	$-0.221450\pi$
$677$	−5.86348	−	13.5931i	−0.225352	−	0.522425i	−0.992954	+	0.118502i	$0.962191\pi$
$678$	−0.851986	−	14.8006i	−0.0327203	−	0.568413i
$679$	11.2103	−	11.8823i	0.430213	−	0.455999i
$680$	−4.45372	−	2.92926i	−0.170792	−	0.112332i
$681$	−8.07495	−	27.0388i	−0.309433	−	1.03613i
$682$	−5.31991	−	5.63878i	−0.203710	−	0.215920i
$683$	6.94875	+	39.4083i	0.265887	+	1.50792i	0.766499	+	0.642246i	$0.221997\pi$
$683$	6.94875	+	39.4083i	0.265887	+	1.50792i	−0.500612	+	0.865672i	$0.666892\pi$
$684$	6.38130	+	14.8487i	0.243995	+	0.567756i
$685$	−15.5686	+	88.2941i	−0.594847	+	3.37354i
$686$	33.0936	−	21.7660i	1.26352	−	0.831030i
$687$	10.9687	−	3.98388i	0.418482	−	0.151994i
$688$	−25.4425	+	2.97380i	−0.969985	+	0.113375i
$689$	−15.1038	+	1.76538i	−0.575410	+	0.0672557i
$690$	−17.7148	+	100.069i	−0.674390	+	3.80958i
$691$	32.8873	−	21.6303i	1.25109	−	0.822857i	0.261285	−	0.965262i	$-0.415854\pi$
$691$	32.8873	−	21.6303i	1.25109	−	0.822857i	0.989809	+	0.142405i	$0.0454834\pi$
$692$	−6.67130	+	37.8348i	−0.253605	+	1.43826i
$693$	2.79042	−	9.27496i	0.105999	−	0.352326i
$694$	−1.74631	−	9.90380i	−0.0662889	−	0.375943i
$695$	−26.3420	−	27.9209i	−0.999210	−	1.05910i
$696$	−32.5856	+	34.4919i	−1.23515	+	1.30741i
$697$	−0.934166	−	0.614411i	−0.0353841	−	0.0232725i
$698$	12.7327	−	13.4959i	0.481941	−	0.510828i
$699$	21.3550	+	10.7430i	0.807720	+	0.406337i
$700$	−23.0139	−	53.3523i	−0.869845	−	2.01653i
$701$	−2.37301	+	4.11018i	−0.0896274	+	0.155239i	−0.907354	−	0.420368i	$-0.861901\pi$
$701$	−2.37301	+	4.11018i	−0.0896274	+	0.155239i	0.817726	+	0.575607i	$0.195234\pi$
$702$	15.7002	+	5.75053i	0.592565	+	0.217040i
$703$	0.0325111	+	0.0563108i	0.00122618	+	0.00212380i
$704$	−11.4421	+	15.3695i	−0.431242	+	0.579258i
$705$	22.7330	+	52.7992i	0.856173	+	1.98853i
$706$	1.44231	+	4.81766i	0.0542822	+	0.181315i
$707$	0.953210	−	16.3660i	0.0358492	−	0.615506i
$708$	−60.6494	+	30.4079i	−2.27934	+	1.14280i
$709$	0.354156	−	0.0839366i	0.0133006	−	0.00315231i	−0.223960	−	0.974598i	$-0.571899\pi$
$709$	0.354156	−	0.0839366i	0.0133006	−	0.00315231i	0.237261	+	0.971446i	$0.423750\pi$
$710$	−59.2231	+	49.6940i	−2.22260	+	1.86498i
$711$	2.74492	−	15.4449i	0.102942	−	0.579230i
$712$	−34.7009	−	29.1175i	−1.30047	−	1.09123i
$713$	6.89082	+	3.46070i	0.258063	+	0.129604i
$714$	−1.41703	−	0.516844i	−0.0530311	−	0.0193424i
$715$	−5.09572	+	11.8132i	−0.190569	+	0.441789i
$716$	−3.40316	−	4.57123i	−0.127182	−	0.170835i
$717$	−10.8456	−	18.8144i	−0.405035	−	0.702638i
$718$	−1.43333	−	24.6093i	−0.0534913	−	0.918410i
$719$	−15.2471	+	5.54950i	−0.568622	+	0.206961i	−0.610301	−	0.792170i	$-0.708951\pi$
$719$	−15.2471	+	5.54950i	−0.568622	+	0.206961i	0.0416792	+	0.999131i	$0.486729\pi$
$720$	2.92096	−	49.0081i	0.108858	−	1.82642i
$721$	−7.73318	−	2.81465i	−0.287998	−	0.104823i
$722$	−12.0988	+	40.4127i	−0.450270	+	1.50401i
$723$	14.1477	+	19.0305i	0.526157	+	0.707751i
$724$	−35.5222	+	17.8399i	−1.32017	+	0.663015i
$725$	−59.2735	−	14.0481i	−2.20136	−	0.521732i
$726$	−14.5267	−	15.4183i	−0.539136	−	0.572226i
$727$	15.7245	+	1.83793i	0.583188	+	0.0681649i	0.402571	−	0.915389i	$-0.368117\pi$
$727$	15.7245	+	1.83793i	0.583188	+	0.0681649i	0.180617	+	0.983554i	$0.442191\pi$
$728$	8.53809			0.316443
$729$	4.79644	−	26.5706i	0.177646	−	0.984094i
$730$	84.7659			3.13733
$731$	−1.67664	−	0.195971i	−0.0620129	−	0.00724827i
$732$	20.3846	+	21.6357i	0.753435	+	0.799678i
$733$	44.4587	+	10.5369i	1.64212	+	0.389190i	0.944820	−	0.327589i	$-0.106236\pi$
$733$	44.4587	+	10.5369i	1.64212	+	0.389190i	0.697301	+	0.716779i	$0.254384\pi$
$734$	−71.1813	+	35.7486i	−2.62735	+	1.31950i
$735$	21.7632	+	29.2744i	0.802749	+	1.07980i
$736$	−0.259596	+	0.867111i	−0.00956884	+	0.0319621i
$737$	3.05522	+	1.11201i	0.112541	+	0.0409614i
$738$	1.81494	−	30.4512i	0.0668090	−	1.12093i
$739$	−2.12852	+	0.774717i	−0.0782987	+	0.0284984i	−0.380873	−	0.924628i	$-0.624376\pi$
$739$	−2.12852	+	0.774717i	−0.0782987	+	0.0284984i	0.302574	+	0.953126i	$0.402154\pi$
$740$	−0.0452469	−	0.776859i	−0.00166331	−	0.0285579i
$741$	−1.52263	−	2.64140i	−0.0559353	−	0.0970343i
$742$	22.3498	+	30.0210i	0.820488	+	1.10211i
$743$	−1.08128	+	2.50670i	−0.0396685	+	0.0919619i	−0.936898	−	0.349602i	$-0.886317\pi$
$743$	−1.08128	+	2.50670i	−0.0396685	+	0.0919619i	0.897230	+	0.441564i	$0.145576\pi$
$744$	−10.3672	−	3.78131i	−0.380081	−	0.138629i
$745$	−59.4763	−	29.8701i	−2.17904	−	1.09436i
$746$	−28.3745	−	23.8090i	−1.03886	−	0.871709i
$747$	−2.98129	+	16.7749i	−0.109080	+	0.613763i
$748$	2.03422	−	1.70691i	0.0743785	−	0.0624109i
$749$	−25.4188	+	6.02437i	−0.928784	+	0.220126i
$750$	90.9767	−	45.6132i	3.32200	−	1.66556i
$751$	2.50704	−	43.0442i	0.0914831	−	1.57070i	−0.570571	−	0.821248i	$-0.693278\pi$
$751$	2.50704	−	43.0442i	0.0914831	−	1.57070i	0.662054	−	0.749456i	$-0.269685\pi$
$752$	9.74140	+	32.5386i	0.355232	+	1.18656i
$753$	9.10255	+	21.1414i	0.331715	+	0.770436i
$754$	10.6498	−	14.3052i	0.387843	−	0.520963i
$755$	−3.66372	−	6.34576i	−0.133337	−	0.230946i
$756$	−4.71514	−	27.0621i	−0.171488	−	0.984238i
$757$	19.3916	−	33.5873i	0.704800	−	1.22075i	−0.261963	−	0.965078i	$-0.584370\pi$
$757$	19.3916	−	33.5873i	0.704800	−	1.22075i	0.966764	−	0.255672i	$-0.0822968\pi$
$758$	2.58349	+	5.98921i	0.0938367	+	0.217538i
$759$	−22.6988	−	11.4190i	−0.823915	−	0.414484i
$760$	−18.1989	+	19.2897i	−0.660142	+	0.699710i
$761$	36.1896	+	23.8023i	1.31187	+	0.862831i	0.996289	−	0.0860672i	$-0.0274300\pi$
$761$	36.1896	+	23.8023i	1.31187	+	0.862831i	0.315582	+	0.948898i	$0.397800\pi$
$762$	38.3299	−	40.5722i	1.38854	−	1.46978i
$763$	3.46371	+	3.67132i	0.125395	+	0.132911i
$764$	−12.4282	−	70.4836i	−0.449635	−	2.55001i
$765$	0.932099	−	3.09816i	0.0337001	−	0.112014i
$766$	0.661895	−	3.75379i	0.0239152	−	0.135630i
$767$	10.6931	−	7.03294i	0.386104	−	0.253945i
$768$

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)

\(f(q)\)	\(=\)	\(q+(2.43604 + 0.284732i) q^{2} +(-1.18775 - 1.26065i) q^{3} +(3.90713 + 0.926007i) q^{4} +(-3.57352 + 1.79469i) q^{5} +(-2.53446 - 3.40919i) q^{6} +(0.377600 - 1.26127i) q^{7} +(4.64483 + 1.69058i) q^{8} +(-0.178488 + 2.99469i) q^{9} +O(q^{10})\)	\(q+(2.43604 + 0.284732i) q^{2} +(-1.18775 - 1.26065i) q^{3} +(3.90713 + 0.926007i) q^{4} +(-3.57352 + 1.79469i) q^{5} +(-2.53446 - 3.40919i) q^{6} +(0.377600 - 1.26127i) q^{7} +(4.64483 + 1.69058i) q^{8} +(-0.178488 + 2.99469i) q^{9} +(-9.21624 + 3.35444i) q^{10} +(-0.142583 - 2.44806i) q^{11} +(-3.47333 - 6.02540i) q^{12} +(0.783462 + 1.05237i) q^{13} +(1.27897 - 2.96500i) q^{14} +(6.50693 + 2.37332i) q^{15} +(3.65712 + 1.83667i) q^{16} +(0.206593 + 0.173352i) q^{17} +(-1.28749 + 7.24435i) q^{18} +(1.02778 - 0.862409i) q^{19} +(-15.6241 + 3.70298i) q^{20} +(-2.03852 + 1.02206i) q^{21} +(0.349704 - 6.00418i) q^{22} +(1.71576 + 5.73105i) q^{23} +(-3.38568 - 7.86351i) q^{24} +(6.56334 - 8.81609i) q^{25} +(1.60890 + 2.78670i) q^{26} +(3.98726 - 3.33193i) q^{27} +(2.64328 - 4.57830i) q^{28} +(-2.19520 - 5.08906i) q^{29} +(15.1754 + 7.63423i) q^{30} +(0.884536 - 0.937554i) q^{31} +(0.126410 + 0.0831411i) q^{32} +(-2.91680 + 3.08744i) q^{33} +(0.453909 + 0.481116i) q^{34} +(0.914230 + 5.18486i) q^{35} +(-3.47047 + 11.5353i) q^{36} +(-0.00841562 + 0.0477273i) q^{37} +(2.74927 - 1.80822i) q^{38} +(0.396116 - 2.23763i) q^{39} +(-19.6325 + 2.29471i) q^{40} +(-4.11791 + 0.481314i) q^{41} +(-5.25693 + 1.90934i) q^{42} +(-5.22957 + 3.43954i) q^{43} +(1.70983 - 9.69693i) q^{44} +(-4.73670 - 11.0219i) q^{45} +(2.54785 + 14.4496i) q^{46} +(5.69554 + 6.03692i) q^{47} +(-2.02834 - 6.79186i) q^{48} +(4.40019 + 2.89405i) q^{49} +(18.4988 - 19.6076i) q^{50} +(-0.0268446 - 0.466341i) q^{51} +(2.08658 + 4.83724i) q^{52} +(-5.79529 + 10.0377i) q^{53} +(10.6618 - 6.98142i) q^{54} +(4.90304 + 8.49231i) q^{55} +(3.88617 - 5.22004i) q^{56} +(-2.30794 - 0.271343i) q^{57} +(-3.89859 - 13.0222i) q^{58} +(0.567212 - 9.73865i) q^{59} +(23.2257 + 15.2983i) q^{60} +(-4.15895 + 0.985689i) q^{61} +(2.42172 - 2.03206i) q^{62} +(3.70972 + 1.35592i) q^{63} +(-5.98568 - 5.02258i) q^{64} +(-4.68839 - 2.35460i) q^{65} +(-7.98454 + 6.69062i) q^{66} +(-0.525148 + 1.21743i) q^{67} +(0.646660 + 0.868614i) q^{68} +(5.18696 - 8.97004i) q^{69} +(0.750805 + 12.8908i) q^{70} +(7.40721 - 2.69600i) q^{71} +(-5.89181 + 13.6081i) q^{72} +(-8.12155 - 2.95600i) q^{73} +(-0.0340903 + 0.113869i) q^{74} +(-18.9096 + 2.19725i) q^{75} +(4.81426 - 2.41781i) q^{76} +(-3.14152 - 0.744553i) q^{77} +(1.60208 - 5.33817i) q^{78} +(-5.19362 - 0.607048i) q^{79} -16.3650 q^{80} +(-8.93628 - 1.06903i) q^{81} -10.1684 q^{82} +(5.64086 + 0.659323i) q^{83} +(-8.91120 + 2.10562i) q^{84} +(-1.04938 - 0.248707i) q^{85} +(-13.7188 + 6.88984i) q^{86} +(-3.80817 + 8.81193i) q^{87} +(3.47637 - 11.6119i) q^{88} +(-8.61170 - 3.13440i) q^{89} +(-8.40049 - 28.1985i) q^{90} +(1.62316 - 0.590783i) q^{91} +(1.39672 + 23.9807i) q^{92} +(-2.23254 - 0.00151097i) q^{93} +(12.1557 + 16.3279i) q^{94} +(-2.12503 + 4.92638i) q^{95} +(-0.0453316 - 0.258110i) q^{96} +(11.0880 + 5.56859i) q^{97} +(9.89500 + 8.30289i) q^{98} +(7.35663 + 0.00995784i) 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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