LMFDB - Embedded newform 81.2.g.a.40.8

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			40.8
Character	$\chi$	$=$	81.40
Dual form			81.2.g.a.79.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.155203 + 2.66473i) q^{2} +(-1.72840 - 0.112415i) q^{3} +(-5.09021 + 0.594960i) q^{4} +(1.76667 + 0.418708i) q^{5} +(0.0313040 - 4.62316i) q^{6} +(-1.54209 + 2.07139i) q^{7} +(-1.44840 - 8.21430i) q^{8} +(2.97473 + 0.388597i) q^{9} +O(q^{10})$	\(q+(0.155203 + 2.66473i) q^{2} +(-1.72840 - 0.112415i) q^{3} +(-5.09021 + 0.594960i) q^{4} +(1.76667 + 0.418708i) q^{5} +(0.0313040 - 4.62316i) q^{6} +(-1.54209 + 2.07139i) q^{7} +(-1.44840 - 8.21430i) q^{8} +(2.97473 + 0.388597i) q^{9} +(-0.841551 + 4.77267i) q^{10} +(2.51185 + 2.66241i) q^{11} +(8.86480 - 0.456111i) q^{12} +(0.338219 - 0.169860i) q^{13} +(-5.75903 - 3.78777i) q^{14} +(-3.00644 - 0.922295i) q^{15} +(11.6906 - 2.77073i) q^{16} +(2.13907 - 0.778557i) q^{17} +(-0.573820 + 7.98715i) q^{18} +(-1.32149 - 0.480985i) q^{19} +(-9.24183 - 1.08021i) q^{20} +(2.89821 - 3.40683i) q^{21} +(-6.70474 + 7.10661i) q^{22} +(2.11397 + 2.83955i) q^{23} +(1.58001 + 14.3604i) q^{24} +(-1.52236 - 0.764560i) q^{25} +(0.505123 + 0.874898i) q^{26} +(-5.09783 - 1.00606i) q^{27} +(6.61718 - 11.4613i) q^{28} +(5.52098 - 3.63121i) q^{29} +(1.99106 - 8.15448i) q^{30} +(3.87125 - 8.97457i) q^{31} +(4.41321 + 14.7411i) q^{32} +(-4.04218 - 4.88407i) q^{33} +(2.40663 + 5.57920i) q^{34} +(-3.59167 + 3.01377i) q^{35} +(-15.3732 - 0.208197i) q^{36} +(-0.463728 - 0.389114i) q^{37} +(1.07659 - 3.59607i) q^{38} +(-0.603672 + 0.255565i) q^{39} +(0.880547 - 15.1184i) q^{40} +(0.194779 - 3.34423i) q^{41} +(9.52810 + 7.19419i) q^{42} +(-0.765225 + 2.55603i) q^{43} +(-14.3699 - 12.0578i) q^{44} +(5.09264 + 1.93206i) q^{45} +(-7.23854 + 6.07386i) q^{46} +(0.0597051 + 0.138412i) q^{47} +(-20.5176 + 3.47473i) q^{48} +(0.0950155 + 0.317374i) q^{49} +(1.80107 - 4.17535i) q^{50} +(-3.78469 + 1.10519i) q^{51} +(-1.62055 + 1.06585i) q^{52} +(-6.72572 + 11.6493i) q^{53} +(1.88967 - 13.7405i) q^{54} +(3.32284 + 5.75532i) q^{55} +(19.2486 + 9.66701i) q^{56} +(2.23000 + 0.979890i) q^{57} +(10.5331 + 14.1483i) q^{58} +(2.91546 - 3.09020i) q^{59} +(15.8521 + 2.90596i) q^{60} +(-7.39981 - 0.864914i) q^{61} +(24.5156 + 8.92296i) q^{62} +(-5.39224 + 5.56257i) q^{63} +(-16.0163 + 5.82946i) q^{64} +(0.668642 - 0.158471i) q^{65} +(12.3874 - 11.5293i) q^{66} +(-8.43131 - 5.54536i) q^{67} +(-10.4251 + 5.23568i) q^{68} +(-3.33457 - 5.14552i) q^{69} +(-8.58832 - 9.10309i) q^{70} +(-0.305263 + 1.73123i) q^{71} +(-1.11655 - 24.9981i) q^{72} +(0.930968 + 5.27978i) q^{73} +(0.964911 - 1.29610i) q^{74} +(2.54530 + 1.49260i) q^{75} +(7.01285 + 1.66208i) q^{76} +(-9.38839 + 1.09735i) q^{77} +(-0.774702 - 1.56896i) q^{78} +(-0.247092 - 4.24240i) q^{79} +21.8136 q^{80} +(8.69798 + 2.31194i) q^{81} +8.94171 q^{82} +(-0.151445 - 2.60022i) q^{83} +(-12.7256 + 19.0658i) q^{84} +(4.10501 - 0.479807i) q^{85} +(-6.92989 - 1.64241i) q^{86} +(-9.95066 + 5.65553i) q^{87} +(18.2316 - 24.4893i) q^{88} +(-0.553979 - 3.14177i) q^{89} +(-4.35803 + 13.8704i) q^{90} +(-0.169719 + 0.962523i) q^{91} +(-12.4500 - 13.1962i) q^{92} +(-7.69995 + 15.0765i) q^{93} +(-0.359564 + 0.180580i) q^{94} +(-2.13325 - 1.40306i) q^{95} +(-5.97065 - 25.9747i) q^{96} +(14.9574 - 3.54497i) q^{97} +(-0.830968 + 0.302448i) q^{98} +(6.43746 + 8.89603i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{27}\right)$

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 $

$2$	0.155203	+	2.66473i	0.109745	+	1.88425i	0.385058	+	0.922893i	$0.374182\pi$
$2$	0.155203	+	2.66473i	0.109745	+	1.88425i	−0.275313	+	0.961355i	$0.588781\pi$
$3$	−1.72840	−	0.112415i	−0.997892	−	0.0649030i
$3$	−1.72840	−	0.112415i	−0.997892	−	0.0649030i
$4$	−5.09021	+	0.594960i	−2.54511	+	0.297480i
$5$	1.76667	+	0.418708i	0.790078	+	0.187252i	0.605794	−	0.795621i	$-0.292855\pi$
$5$	1.76667	+	0.418708i	0.790078	+	0.187252i	0.184284	+	0.982873i	$0.441004\pi$
$6$	0.0313040	−	4.62316i	0.0127798	−	1.88740i
$7$	−1.54209	+	2.07139i	−0.582856	+	0.782912i	−0.991545	−	0.129762i	$-0.958579\pi$
$7$	−1.54209	+	2.07139i	−0.582856	+	0.782912i	0.408689	+	0.912674i	$0.365986\pi$
$8$	−1.44840	−	8.21430i	−0.512088	−	2.90419i
$9$	2.97473	+	0.388597i	0.991575	+	0.129532i
$10$	−0.841551	+	4.77267i	−0.266122	+	1.50925i
$11$	2.51185	+	2.66241i	0.757351	+	0.802746i	0.985283	−	0.170932i	$-0.0546777\pi$
$11$	2.51185	+	2.66241i	0.757351	+	0.802746i	−0.227931	+	0.973677i	$0.573196\pi$
$12$	8.86480	−	0.456111i	2.55905	−	0.131668i
$13$	0.338219	−	0.169860i	0.0938050	−	0.0471107i	−0.401278	−	0.915956i	$-0.631434\pi$
$13$	0.338219	−	0.169860i	0.0938050	−	0.0471107i	0.495083	+	0.868846i	$0.335138\pi$
$14$	−5.75903	−	3.78777i	−1.53917	−	1.01232i
$15$	−3.00644	−	0.922295i	−0.776259	−	0.238136i
$16$	11.6906	−	2.77073i	2.92266	−	0.692683i
$17$	2.13907	−	0.778557i	0.518800	−	0.188828i	−0.0693304	−	0.997594i	$-0.522086\pi$
$17$	2.13907	−	0.778557i	0.518800	−	0.188828i	0.588131	+	0.808766i	$0.299864\pi$
$18$	−0.573820	+	7.98715i	−0.135251	+	1.88259i
$19$	−1.32149	−	0.480985i	−0.303172	−	0.110345i	0.185955	−	0.982558i	$-0.440462\pi$
$19$	−1.32149	−	0.480985i	−0.303172	−	0.110345i	−0.489127	+	0.872213i	$0.662684\pi$
$20$	−9.24183	−	1.08021i	−2.06654	−	0.241543i
$21$	2.89821	−	3.40683i	0.632441	−	0.743432i
$22$	−6.70474	+	7.10661i	−1.42946	+	1.51513i
$23$	2.11397	+	2.83955i	0.440793	+	0.592088i	0.965889	−	0.258955i	$-0.0833781\pi$
$23$	2.11397	+	2.83955i	0.440793	+	0.592088i	−0.525096	+	0.851043i	$0.675971\pi$
$24$	1.58001	+	14.3604i	0.322517	+	2.93131i
$25$	−1.52236	−	0.764560i	−0.304473	−	0.152912i
$26$	0.505123	+	0.874898i	0.0990627	+	0.171582i
$27$	−5.09783	−	1.00606i	−0.981078	−	0.193615i
$28$	6.61718	−	11.4613i	1.25053	−	2.16598i
$29$	5.52098	−	3.63121i	1.02522	−	0.674298i	0.0786857	−	0.996899i	$-0.474928\pi$
$29$	5.52098	−	3.63121i	1.02522	−	0.674298i	0.946535	+	0.322601i	$0.104557\pi$
$30$	1.99106	−	8.15448i	0.363516	−	1.48880i
$31$	3.87125	−	8.97457i	0.695298	−	1.61188i	−0.0923291	−	0.995729i	$-0.529431\pi$
$31$	3.87125	−	8.97457i	0.695298	−	1.61188i	0.787627	−	0.616153i	$-0.211310\pi$
$32$	4.41321	+	14.7411i	0.780152	+	2.60589i
$33$	−4.04218	−	4.88407i	−0.703654	−	0.850208i
$34$	2.40663	+	5.57920i	0.412734	+	0.956825i
$35$	−3.59167	+	3.01377i	−0.607104	+	0.509421i
$36$	−15.3732	−	0.208197i	−2.56220	−	0.0346995i
$37$	−0.463728	−	0.389114i	−0.0762364	−	0.0639699i	0.603873	−	0.797080i	$-0.293623\pi$
$37$	−0.463728	−	0.389114i	−0.0762364	−	0.0639699i	−0.680110	+	0.733111i	$0.738068\pi$
$38$	1.07659	−	3.59607i	0.174647	−	0.583360i
$39$	−0.603672	+	0.255565i	−0.0966649	+	0.0409231i
$40$	0.880547	−	15.1184i	0.139227	−	2.39043i
$41$	0.194779	−	3.34423i	0.0304194	−	0.522282i	−0.948338	−	0.317261i	$-0.897237\pi$
$41$	0.194779	−	3.34423i	0.0304194	−	0.522282i	0.978758	−	0.205021i	$-0.0657261\pi$
$42$	9.52810	+	7.19419i	1.47022	+	1.11009i
$43$	−0.765225	+	2.55603i	−0.116696	+	0.389791i	−0.996303	−	0.0859098i	$-0.972620\pi$
$43$	−0.765225	+	2.55603i	−0.116696	+	0.389791i	0.879607	+	0.475701i	$0.157805\pi$
$44$	−14.3699	−	12.0578i	−2.16634	−	1.81778i
$45$	5.09264	+	1.93206i	0.759167	+	0.288015i
$46$	−7.23854	+	6.07386i	−1.06726	+	0.895542i
$47$	0.0597051	+	0.138412i	0.00870888	+	0.0201895i	0.922515	−	0.385961i	$-0.126130\pi$
$47$	0.0597051	+	0.138412i	0.00870888	+	0.0201895i	−0.913806	+	0.406151i	$0.866871\pi$
$48$	−20.5176	+	3.47473i	−2.96146	+	0.501533i
$49$	0.0950155	+	0.317374i	0.0135736	+	0.0453391i
$50$	1.80107	−	4.17535i	0.254710	−	0.590483i
$51$	−3.78469	+	1.10519i	−0.529962	+	0.154758i
$52$	−1.62055	+	1.06585i	−0.224729	+	0.147807i
$53$	−6.72572	+	11.6493i	−0.923849	+	1.60015i	−0.130448	+	0.991455i	$0.541642\pi$
$53$	−6.72572	+	11.6493i	−0.923849	+	1.60015i	−0.793401	+	0.608699i	$0.791692\pi$
$54$	1.88967	−	13.7405i	0.257151	−	1.86984i
$55$	3.32284	+	5.75532i	0.448051	+	0.776047i
$56$	19.2486	+	9.66701i	2.57220	+	1.29181i
$57$	2.23000	+	0.979890i	0.295371	+	0.129790i
$58$	10.5331	+	14.1483i	1.38306	+	1.85777i
$59$	2.91546	−	3.09020i	0.379560	−	0.402310i	−0.509226	−	0.860633i	$-0.670068\pi$
$59$	2.91546	−	3.09020i	0.379560	−	0.402310i	0.888786	+	0.458323i	$0.151550\pi$
$60$	15.8521	+	2.90596i	2.04650	+	0.375158i
$61$	−7.39981	−	0.864914i	−0.947449	−	0.110741i	−0.371687	−	0.928358i	$-0.621220\pi$
$61$	−7.39981	−	0.864914i	−0.947449	−	0.110741i	−0.575762	+	0.817617i	$0.695295\pi$
$62$	24.5156	+	8.92296i	3.11349	+	1.13322i
$63$	−5.39224	+	5.56257i	−0.679358	+	0.700817i
$64$	−16.0163	+	5.82946i	−2.00204	+	0.728682i
$65$	0.668642	−	0.158471i	0.0829349	−	0.0196559i
$66$	12.3874	−	11.5293i	1.52478	−	1.41916i
$67$	−8.43131	−	5.54536i	−1.03005	−	0.677474i	−0.0823378	−	0.996604i	$-0.526239\pi$
$67$	−8.43131	−	5.54536i	−1.03005	−	0.677474i	−0.947711	+	0.319131i	$0.896609\pi$
$68$	−10.4251	+	5.23568i	−1.26423	+	0.634920i
$69$	−3.33457	−	5.14552i	−0.401435	−	0.619448i
$70$	−8.58832	−	9.10309i	−1.02650	−	1.08803i
$71$	−0.305263	+	1.73123i	−0.0362281	+	0.205460i	−0.997549	−	0.0699711i	$-0.977709\pi$
$71$	−0.305263	+	1.73123i	−0.0362281	+	0.205460i	0.961321	+	0.275431i	$0.0888204\pi$
$72$	−1.11655	−	24.9981i	−0.131587	−	2.94606i
$73$	0.930968	+	5.27978i	0.108962	+	0.617951i	0.989564	+	0.144095i	$0.0460272\pi$
$73$	0.930968	+	5.27978i	0.108962	+	0.617951i	−0.880602	+	0.473856i	$0.842862\pi$
$74$	0.964911	−	1.29610i	0.112169	−	0.150669i
$75$	2.54530	+	1.49260i	0.293906	+	0.172351i
$76$	7.01285	+	1.66208i	0.804429	+	0.190653i
$77$	−9.38839	+	1.09735i	−1.06991	+	0.125054i
$78$	−0.774702	−	1.56896i	−0.0877177	−	0.177649i
$79$	−0.247092	−	4.24240i	−0.0278000	−	0.477307i	−0.983262	−	0.182195i	$-0.941680\pi$
$79$	−0.247092	−	4.24240i	−0.0278000	−	0.477307i	0.955462	−	0.295113i	$-0.0953572\pi$
$80$	21.8136			2.43884
$81$	8.69798	+	2.31194i	0.966443	+	0.256882i
$82$	8.94171			0.987446
$83$	−0.151445	−	2.60022i	−0.0166233	−	0.285411i	−0.996367	−	0.0851577i	$-0.972861\pi$
$83$	−0.151445	−	2.60022i	−0.0166233	−	0.285411i	0.979744	−	0.200253i	$-0.0641764\pi$
$84$	−12.7256	+	19.0658i	−1.38847	+	2.08025i
$85$	4.10501	−	0.479807i	0.445251	−	0.0520424i
$86$	−6.92989	−	1.64241i	−0.747269	−	0.177106i
$87$	−9.95066	+	5.65553i	−1.06682	+	0.606337i
$88$	18.2316	−	24.4893i	1.94350	−	2.61057i
$89$	−0.553979	−	3.14177i	−0.0587216	−	0.333027i	0.941268	−	0.337661i	$-0.109636\pi$
$89$	−0.553979	−	3.14177i	−0.0587216	−	0.333027i	−0.999989	+	0.00463450i	$0.998525\pi$
$90$	−4.35803	+	13.8704i	−0.459377	+	1.46207i
$91$	−0.169719	+	0.962523i	−0.0177914	+	0.100900i
$92$	−12.4500	−	13.1962i	−1.29800	−	1.37580i
$93$	−7.69995	+	15.0765i	−0.798448	+	1.56336i
$94$	−0.359564	+	0.180580i	−0.0370862	+	0.0186254i
$95$	−2.13325	−	1.40306i	−0.218867	−	0.143951i
$96$	−5.97065	−	25.9747i	−0.609377	−	2.65103i
$97$	14.9574	−	3.54497i	1.51869	−	0.359937i	0.615142	−	0.788416i	$-0.289099\pi$
$97$	14.9574	−	3.54497i	1.51869	−	0.359937i	0.903552	+	0.428479i	$0.140951\pi$
$98$	−0.830968	+	0.302448i	−0.0839405	+	0.0305518i
$99$	6.43746	+	8.89603i	0.646989	+	0.894084i
$100$	8.20403	+	2.98602i	0.820403	+	0.298602i
$101$	12.9566	+	1.51441i	1.28923	+	0.150690i	0.732937	−	0.680296i	$-0.238149\pi$
$101$	12.9566	+	1.51441i	1.28923	+	0.150690i	0.556294	+	0.830986i	$0.312223\pi$
$102$	−3.53243	−	9.91363i	−0.349763	−	0.981595i
$103$	9.41575	−	9.98011i	0.927761	−	0.983370i	−0.0721402	−	0.997395i	$-0.522983\pi$
$103$	9.41575	−	9.98011i	0.927761	−	0.983370i	0.999902	+	0.0140248i	$0.00446438\pi$
$104$	−1.88516	−	2.53221i	−0.184855	−	0.248303i
$105$	6.54664	−	4.80524i	0.638887	−	0.468944i
$106$	−32.0861	−	16.1142i	−3.11647	−	1.56515i
$107$	−1.15268	−	1.99650i	−0.111434	−	0.193009i	0.804915	−	0.593390i	$-0.202211\pi$
$107$	−1.15268	−	1.99650i	−0.111434	−	0.193009i	−0.916349	+	0.400381i	$0.868878\pi$
$108$	26.5476	+	2.08803i	2.55454	+	0.200921i
$109$	−4.62468	+	8.01018i	−0.442964	+	0.767236i	−0.997908	−	0.0646518i	$-0.979406\pi$
$109$	−4.62468	+	8.01018i	−0.442964	+	0.767236i	0.554944	+	0.831888i	$0.312740\pi$
$110$	−14.8206	+	9.74769i	−1.41309	+	0.929406i
$111$	0.757765	+	0.724674i	0.0719238	+	0.0687830i
$112$	−12.2888	+	28.4886i	−1.16118	+	2.69192i
$113$	−2.72429	−	9.09977i	−0.256280	−	0.856034i	−0.985196	−	0.171431i	$-0.945161\pi$
$113$	−2.72429	−	9.09977i	−0.256280	−	0.856034i	0.728916	−	0.684603i	$-0.240024\pi$
$114$	−2.26504	+	6.09443i	−0.212140	+	0.570795i
$115$	2.54574	+	5.90168i	0.237391	+	0.550335i
$116$	−25.9425	+	21.7684i	−2.40870	+	2.02114i
$117$	1.07212	−	0.373856i	0.0991171	−	0.0345630i
$118$	8.68704	+	7.28929i	0.799706	+	0.671033i
$119$	−1.68595	+	5.63145i	−0.154550	+	0.516235i
$120$	−3.22148	+	26.0316i	−0.294079	+	2.37635i
$121$	−0.139420	+	2.39374i	−0.0126745	+	0.217613i
$122$	1.15629	−	19.8527i	0.104686	−	1.79738i
$123$	−0.712600	+	5.75828i	−0.0642530	+	0.519206i
$124$	−14.3660	+	47.9857i	−1.29010	+	4.30924i
$125$	−9.32357	−	7.82340i	−0.833925	−	0.699746i
$126$	−15.6596	−	13.5055i	−1.39507	−	1.20317i
$127$	9.69030	−	8.13112i	0.859875	−	0.721521i	−0.102066	−	0.994778i	$-0.532545\pi$
$127$	9.69030	−	8.13112i	0.859875	−	0.721521i	0.961941	+	0.273257i	$0.0881009\pi$
$128$	−5.83028	−	13.5161i	−0.515329	−	1.19467i
$129$	1.60995	−	4.33182i	0.141748	−	0.381395i
$130$	0.526057	+	1.75715i	0.0461383	+	0.154113i
$131$	−5.89321	+	13.6620i	−0.514892	+	1.19365i	0.440350	+	0.897826i	$0.354854\pi$
$131$	−5.89321	+	13.6620i	−0.514892	+	1.19365i	−0.955242	+	0.295827i	$0.904405\pi$
$132$	23.4814	+	22.4560i	2.04379	+	1.95454i
$133$	3.03417	−	1.99561i	0.263096	−	0.173041i
$134$	13.4683	−	23.3278i	1.16349	−	2.01522i
$135$	−8.58493	−	3.91187i	−0.738873	−	0.336680i
$136$	−9.49354	−	16.4433i	−0.814064	−	1.41000i
$137$	−14.5193	−	7.29189i	−1.24047	−	0.622988i	−0.297138	−	0.954835i	$-0.596032\pi$
$137$	−14.5193	−	7.29189i	−1.24047	−	0.622988i	−0.943333	+	0.331847i	$0.892328\pi$
$138$	13.1939	−	9.68433i	1.12314	−	0.824385i
$139$	−9.85759	−	13.2410i	−0.836110	−	1.12309i	−0.990828	−	0.135132i	$-0.956854\pi$
$139$	−9.85759	−	13.2410i	−0.836110	−	1.12309i	0.154718	−	0.987959i	$-0.450553\pi$
$140$	16.4893	−	17.4776i	1.39360	−	1.47713i
$141$	−0.0876346	−	0.245943i	−0.00738016	−	0.0207121i
$142$	−4.66064	−	0.544751i	−0.391112	−	0.0457145i
$143$	1.30179	+	0.473813i	0.108861	+	0.0396223i
$144$	35.8532	−	3.69922i	2.98776	−	0.308269i
$145$	11.2742	−	4.10346i	0.936268	−	0.340774i
$146$	−13.9247	+	3.30021i	−1.15242	+	0.273127i
$147$	−0.128547	−	0.559230i	−0.0106024	−	0.0461245i
$148$	2.59198	+	1.70477i	0.213059	+	0.140131i
$149$	−3.04503	+	1.52927i	−0.249458	+	0.125283i	−0.569135	−	0.822244i	$-0.692722\pi$
$149$	−3.04503	+	1.52927i	−0.249458	+	0.125283i	0.319677	+	0.947527i	$0.396426\pi$
$150$	−3.58234	+	7.01420i	−0.292497	+	0.572707i
$151$	5.92981	+	6.28524i	0.482561	+	0.511485i	0.922213	−	0.386683i	$-0.126379\pi$
$151$	5.92981	+	6.28524i	0.482561	+	0.511485i	−0.439651	+	0.898169i	$0.644898\pi$
$152$	−2.03690	+	11.5518i	−0.165214	+	0.936976i
$153$	6.66569	−	1.48476i	0.538889	−	0.120036i
$154$	−4.38123	−	24.8472i	−0.353050	−	2.00224i
$155$	10.5969	−	14.2342i	0.851167	−	1.14332i
$156$	2.92077	−	1.66004i	0.233848	−	0.132909i
$157$	3.77987	+	0.895846i	0.301667	+	0.0714963i	0.378662	−	0.925535i	$-0.376384\pi$
$157$	3.77987	+	0.895846i	0.301667	+	0.0714963i	−0.0769950	+	0.997031i	$0.524533\pi$
$158$	11.2665	−	1.31686i	0.896314	−	0.104764i
$159$	12.9343	−	19.3786i	1.02576	−	1.53682i
$160$	1.62444	+	27.8905i	0.128423	+	2.20494i
$161$	−9.14176			−0.720472
$162$	−4.81074	+	23.5366i	−0.377967	+	1.84921i
$163$	−23.8379			−1.86713			−0.933564	−	0.358412i	$-0.883318\pi$
$163$	−23.8379			−1.86713			−0.933564	+	0.358412i	$0.883318\pi$
$164$	0.998218	+	17.1387i	0.0779477	+	1.33831i
$165$	−5.09620	−	10.3210i	−0.396739	−	0.803491i
$166$	6.90536	−	0.807121i	0.535960	−	0.0626447i
$167$	12.4436	+	2.94918i	0.962912	+	0.228214i	0.681864	−	0.731479i	$-0.261170\pi$
$167$	12.4436	+	2.94918i	0.962912	+	0.228214i	0.281049	+	0.959694i	$0.409318\pi$
$168$	−32.1825	−	18.8723i	−2.48294	−	1.45603i
$169$	−7.67752	+	10.3127i	−0.590579	+	0.793285i
$170$	1.91566	+	10.8643i	0.146925	+	0.833252i
$171$	−3.74418	−	1.94433i	−0.286324	−	0.148686i
$172$	2.37442	−	13.4660i	0.181048	−	1.02677i
$173$	3.49885	+	3.70856i	0.266013	+	0.281957i	0.846587	−	0.532250i	$-0.178653\pi$
$173$	3.49885	+	3.70856i	0.266013	+	0.281957i	−0.580574	+	0.814207i	$0.697172\pi$
$174$	−16.6148	−	25.6381i	−1.25957	−	1.94362i
$175$	3.93133	−	1.97439i	0.297180	−	0.149250i
$176$	36.7420	+	24.1656i	2.76953	+	1.82155i
$177$	−5.38646	+	5.01336i	−0.404871	+	0.376827i
$178$	8.28598	−	1.96381i	0.621061	−	0.147194i
$179$	1.10838	−	0.403418i	0.0828444	−	0.0301529i	−0.300266	−	0.953856i	$-0.597075\pi$
$179$	1.10838	−	0.403418i	0.0828444	−	0.0301529i	0.383110	+	0.923703i	$0.374853\pi$
$180$	−27.0721	−	6.80469i	−2.01784	−	0.507192i
$181$	−10.7631	−	3.91744i	−0.800013	−	0.291181i	−0.0905211	−	0.995895i	$-0.528853\pi$
$181$	−10.7631	−	3.91744i	−0.800013	−	0.291181i	−0.709492	+	0.704714i	$0.751075\pi$
$182$	−2.59120	−	0.302868i	−0.192073	−	0.0224501i
$183$	12.6926	+	2.32677i	0.938264	+	0.172000i
$184$	20.2631	−	21.4776i	1.49381	−	1.58335i
$185$	−0.656328	−	0.881602i	−0.0482542	−	0.0648167i
$186$	−41.3697	−	18.1784i	−3.03337	−	1.33290i
$187$	7.44586	+	3.73945i	0.544495	+	0.273456i
$188$	−0.386261	−	0.669024i	−0.0281710	−	0.0487936i
$189$	9.94526	−	9.00816i	0.723411	−	0.655247i
$190$	3.40769	−	5.90229i	0.247220	−	0.428197i
$191$	12.8526	−	8.45332i	0.929985	−	0.611661i	0.00845319	−	0.999964i	$-0.497309\pi$
$191$	12.8526	−	8.45332i	0.929985	−	0.611661i	0.921531	+	0.388304i	$0.126939\pi$
$192$	28.3379	−	8.27515i	2.04511	−	0.597208i
$193$	−6.91049	+	16.0203i	−0.497428	+	1.15317i	0.465899	+	0.884838i	$0.345731\pi$
$193$	−6.91049	+	16.0203i	−0.497428	+	1.15317i	−0.963327	+	0.268330i	$0.913528\pi$
$194$	11.7678	+	39.3072i	0.844879	+	2.82209i
$195$	−1.17349	+	0.198736i	−0.0840357	+	0.0142318i
$196$	−0.672474	−	1.55897i	−0.0480338	−	0.111355i
$197$	7.01270	−	5.88435i	0.499634	−	0.419243i	−0.357830	−	0.933787i	$-0.616483\pi$
$197$	7.01270	−	5.88435i	0.499634	−	0.419243i	0.857464	+	0.514544i	$0.172039\pi$
$198$	−22.7064	+	18.5348i	−1.61367	+	1.31721i
$199$	−17.7580	−	14.9007i	−1.25883	−	1.05629i	−0.995805	−	0.0914967i	$-0.970835\pi$
$199$	−17.7580	−	14.9007i	−1.25883	−	1.05629i	−0.263026	−	0.964789i	$-0.584721\pi$
$200$	−4.07533	+	13.6125i	−0.288169	+	0.962552i
$201$	13.9493	+	10.5324i	0.983907	+	0.742898i
$202$	−2.02459	+	34.7609i	−0.142450	+	2.44577i
$203$	−0.992220	+	17.0358i	−0.0696402	+	1.19568i
$204$	18.6073	−	7.87741i	1.30277	−	0.551529i
$205$	1.74437	−	5.82660i	0.121832	−	0.406947i
$206$	28.0556	+	23.5415i	1.95473	+	1.64021i
$207$	5.18504	+	9.26837i	0.360385	+	0.644196i
$208$	3.48336	−	2.92289i	0.241527	−	0.202666i
$209$	−2.03882	−	4.72652i	−0.141028	−	0.326940i
$210$	13.8207	+	16.6992i	0.953720	+	1.15236i
$211$	7.40749	+	24.7427i	0.509953	+	1.70336i	0.693593	+	0.720367i	$0.256027\pi$
$211$	7.40749	+	24.7427i	0.509953	+	1.70336i	−0.183640	+	0.982994i	$0.558788\pi$
$212$	27.3045	−	63.2989i	1.87528	−	4.34739i
$213$	0.722233	−	2.95794i	0.0494866	−	0.202675i
$214$	5.14123	−	3.38144i	0.351447	−	0.231150i
$215$	−2.42213	+	4.19525i	−0.165188	+	0.286114i
$216$	−0.880332	+	43.3323i	−0.0598990	+	2.94839i
$217$	12.6200	+	21.8585i	0.856702	+	1.48385i
$218$	−22.0627	−	11.0803i	−1.49428	−	0.750453i
$219$	−1.01556	−	9.23022i	−0.0686249	−	0.623720i
$220$	−20.3381	−	27.3188i	−1.37120	−	1.84184i
$221$	0.591228	−	0.626665i	0.0397703	−	0.0421540i
$222$	−1.81345	+	2.13171i	−0.121711	+	0.143071i
$223$	−4.05151	−	0.473554i	−0.271309	−	0.0317115i	−0.0206496	−	0.999787i	$-0.506573\pi$
$223$	−4.05151	−	0.473554i	−0.271309	−	0.0317115i	−0.250660	+	0.968075i	$0.580647\pi$
$224$	−37.3402	−	13.5907i	−2.49490	−	0.908069i
$225$	−4.23151	−	2.86594i	−0.282100	−	0.191063i
$226$	23.8256	−	8.67180i	1.58485	−	0.576840i
$227$	−20.7134	+	4.90916i	−1.37479	+	0.325832i	−0.850621	−	0.525780i	$-0.823774\pi$
$227$	−20.7134	+	4.90916i	−1.37479	+	0.325832i	−0.524173	+	0.851612i	$0.675625\pi$
$228$	−11.9342	−	3.66108i	−0.790359	−	0.242461i
$229$	−10.1269	−	6.66057i	−0.669204	−	0.440143i	0.168914	−	0.985631i	$-0.445974\pi$
$229$	−10.1269	−	6.66057i	−0.669204	−	0.440143i	−0.838119	+	0.545488i	$0.816344\pi$
$230$	−15.3313	+	7.69966i	−1.01091	+	0.507700i
$231$	16.3502	−	0.841252i	1.07577	−	0.0553503i
$232$	−37.8244	−	40.0916i	−2.48330	−	2.63214i
$233$	4.18661	−	23.7435i	0.274274	−	1.55549i	−0.466984	−	0.884266i	$-0.654659\pi$
$233$	4.18661	−	23.7435i	0.274274	−	1.55549i	0.741258	−	0.671220i	$-0.234229\pi$
$234$	1.16262	+	2.79887i	0.0760028	+	0.182968i
$235$	0.0475249	+	0.269527i	0.00310018	+	0.0175820i
$236$	−13.0017	+	17.4644i	−0.846341	+	1.13683i
$237$	−0.0498377	+	7.36034i	−0.00323731	+	0.478105i
$238$	−15.2680	−	3.61857i	−0.989675	−	0.234557i
$239$	23.5780	−	2.75588i	1.52514	−	0.178263i	0.688183	−	0.725537i	$-0.258409\pi$
$239$	23.5780	−	2.75588i	1.52514	−	0.178263i	0.836953	+	0.547274i	$0.184335\pi$
$240$	−37.7026	−	2.45218i	−2.43369	−	0.158288i
$241$	0.736982	+	12.6535i	0.0474732	+	0.815084i	0.935070	+	0.354463i	$0.115336\pi$
$241$	0.736982	+	12.6535i	0.0474732	+	0.815084i	−0.887597	+	0.460621i	$0.847627\pi$
$242$	−6.40031			−0.411428
$243$	−14.7737	−	4.97374i	−0.947733	−	0.319066i
$244$	38.1812			2.44430
$245$	0.0349739	+	0.600478i	0.00223440	+	0.0383631i
$246$	−15.4548	−	1.00518i	−0.985364	−	0.0640882i
$247$	−0.528654	+	0.0617908i	−0.0336375	+	0.00393166i
$248$	−79.3270	−	18.8008i	−5.03727	−	1.19385i
$249$	−0.0305461	+	4.51123i	−0.00193578	+	0.285888i
$250$	19.4002	−	26.0590i	1.22698	−	1.64811i
$251$	2.35563	+	13.3595i	0.148686	+	0.843242i	0.964333	+	0.264692i	$0.0852702\pi$
$251$	2.35563	+	13.3595i	0.148686	+	0.843242i	−0.815647	+	0.578550i	$0.803619\pi$
$252$	24.1381	−	31.5228i	1.52056	−	1.98575i
$253$	−2.25007	+	12.7608i	−0.141461	+	0.802263i
$254$	23.1712	+	24.5600i	1.45389	+	1.54103i
$255$	−7.14904	+	0.367832i	−0.447690	+	0.0230345i
$256$	4.64940	−	2.33502i	0.290587	−	0.145938i
$257$	−2.33857	−	1.53810i	−0.145876	−	0.0959442i	0.474473	−	0.880270i	$-0.342639\pi$
$257$	−2.33857	−	1.53810i	−0.145876	−	0.0959442i	−0.620349	+	0.784326i	$0.713009\pi$
$258$	11.7930	+	3.61777i	0.734199	+	0.225233i
$259$	1.52112	−	0.360512i	0.0945177	−	0.0224011i
$260$	−3.30925	+	1.20447i	−0.205231	+	0.0746979i
$261$	17.8345	−	8.65641i	1.10393	−	0.535818i
$262$	−37.3201	−	13.5834i	−2.30564	−	0.839186i
$263$	1.47542	+	0.172452i	0.0909781	+	0.0106338i	0.161460	−	0.986879i	$-0.448380\pi$
$263$	1.47542	+	0.172452i	0.0909781	+	0.0106338i	−0.0704820	+	0.997513i	$0.522454\pi$
$264$	−34.2645	+	40.2778i	−2.10884	+	2.47893i
$265$	−16.7598	+	17.7643i	−1.02954	+	1.09125i
$266$	5.78867	+	7.77553i	0.354926	+	0.476748i
$267$	0.604313	+	5.49251i	0.0369834	+	0.336136i
$268$	46.2164	+	23.2108i	2.82312	+	1.41782i
$269$	−4.56187	−	7.90140i	−0.278142	−	0.481757i	0.692781	−	0.721148i	$-0.256385\pi$
$269$	−4.56187	−	7.90140i	−0.278142	−	0.481757i	−0.970923	+	0.239392i	$0.923052\pi$
$270$	9.09166	−	23.4836i	0.553301	−	1.42917i
$271$	−2.94843	+	5.10683i	−0.179105	+	0.310218i	−0.941574	−	0.336806i	$-0.890653\pi$
$271$	−2.94843	+	5.10683i	−0.179105	+	0.310218i	0.762470	+	0.647024i	$0.223987\pi$
$272$	22.8499	−	15.0286i	1.38548	−	0.911244i
$273$	0.401544	−	1.64454i	0.0243026	−	0.0995324i
$274$	17.1775	−	39.8218i	1.03773	−	2.40572i
$275$	−1.78838	−	5.97361i	−0.107843	−	0.360222i
$276$	20.0351	+	24.2079i	1.20597	+	1.45714i
$277$	−1.96051	−	4.54498i	−0.117796	−	0.273081i	0.849110	−	0.528217i	$-0.177139\pi$
$277$	−1.96051	−	4.54498i	−0.117796	−	0.273081i	−0.966905	+	0.255136i	$0.917880\pi$
$278$	33.7538	−	28.3228i	2.02442	−	1.69869i
$279$	15.0034	−	25.1925i	0.898231	−	1.50824i
$280$	29.9582	+	25.1379i	1.79035	+	1.50228i
$281$	−3.90301	+	13.0370i	−0.232834	+	0.777719i	0.759101	+	0.650973i	$0.225639\pi$
$281$	−3.90301	+	13.0370i	−0.232834	+	0.777719i	−0.991935	+	0.126747i	$0.959546\pi$
$282$	0.641769	−	0.271693i	0.0382168	−	0.0161791i
$283$	0.687609	−	11.8058i	0.0408741	−	0.701781i	−0.914173	−	0.405325i	$-0.867158\pi$
$283$	0.687609	−	11.8058i	0.0408741	−	0.701781i	0.955047	−	0.296456i	$-0.0958047\pi$
$284$	0.523838	−	8.99396i	0.0310841	−	0.533693i
$285$	3.52938	+	2.66486i	0.209063	+	0.157853i
$286$	−1.06054	+	3.54246i	−0.0627112	+	0.209470i
$287$	6.62685	+	5.56058i	0.391170	+	0.328231i
$288$	7.39972	+	45.5658i	0.436032	+	2.68499i
$289$	−9.05329	+	7.59661i	−0.532547	+	0.446860i
$290$	12.6844	+	29.4057i	0.744852	+	1.72676i
$291$	−26.2509	+	4.44568i	−1.53885	+	0.260610i
$292$	−7.88008	−	26.3213i	−0.461147	−	1.54034i
$293$	−6.44781	+	14.9477i	−0.376685	+	0.873254i	0.619418	+	0.785061i	$0.287368\pi$
$293$	−6.44781	+	14.9477i	−0.376685	+	0.873254i	−0.996103	+	0.0881929i	$0.971891\pi$
$294$	1.47024	−	0.429337i	0.0857464	−	0.0250394i
$295$	6.44454	−	4.23864i	0.375215	−	0.246783i
$296$	−2.52464	+	4.37280i	−0.146741	+	0.254164i
$297$	−10.1265	−	16.0995i	−0.587597	−	0.934191i
$298$	−4.54769	−	7.87683i	−0.263440	−	0.456292i
$299$	1.19731	+	0.601312i	0.0692422	+	0.0347748i
$300$	−13.8442	−	6.08330i	−0.799293	−	0.351219i
$301$	−4.11449	−	5.52672i	−0.237155	−	0.318555i
$302$	−15.8281	+	16.7768i	−0.910806	+	0.965398i
$303$	−22.2240	−	4.07403i	−1.27673	−	0.234047i
$304$	−16.7818	−	1.96151i	−0.962502	−	0.112500i
$305$	−12.7109	−	4.62638i	−0.727822	−	0.264906i
$306$	4.99101	+	17.5318i	0.285317	+	1.00223i
$307$	23.4445	−	8.53312i	1.33805	−	0.487011i	0.428853	−	0.903374i	$-0.358918\pi$
$307$	23.4445	−	8.53312i	1.33805	−	0.487011i	0.909198	+	0.416364i	$0.136696\pi$
$308$	47.1360	−	11.1714i	2.68582	−	0.636552i
$309$	−17.3961	+	16.1911i	−0.989629	+	0.921082i
$310$	39.5749	+	26.0288i	2.24770	+	1.47834i
$311$	7.41173	−	3.72231i	0.420281	−	0.211073i	−0.226074	−	0.974110i	$-0.572589\pi$
$311$	7.41173	−	3.72231i	0.420281	−	0.211073i	0.646354	+	0.763037i	$0.276293\pi$
$312$	2.97365	+	4.58858i	0.168350	+	0.259777i
$313$	−3.79792	−	4.02556i	−0.214671	−	0.227538i	0.611086	−	0.791565i	$-0.290733\pi$
$313$	−3.79792	−	4.02556i	−0.214671	−	0.227538i	−0.825757	+	0.564026i	$0.809252\pi$
$314$	−1.80054	+	10.2114i	−0.101610	+	0.576261i
$315$	−11.8554	+	7.56943i	−0.667975	+	0.426489i
$316$	3.78181	+	21.4477i	0.212743	+	1.20653i
$317$	−13.1931	+	17.7214i	−0.741000	+	0.995335i	0.258570	+	0.965993i	$0.416749\pi$
$317$	−13.1931	+	17.7214i	−0.741000	+	0.995335i	−0.999569	+	0.0293426i	$0.990659\pi$
$318$	53.6460	+	31.4588i	3.00832	+	1.76412i
$319$	23.5356	+	5.57805i	1.31774	+	0.312311i
$320$	−30.7363	+	3.59256i	−1.71821	+	0.200830i
$321$	1.76785	+	3.58033i	0.0986719	+	0.199834i
$322$	−1.41883	−	24.3603i	−0.0790681	−	1.35755i
$323$	−3.20124			−0.178122
$324$	−45.6501	−	6.59330i	−2.53612	−	0.366294i
$325$	−0.644760			−0.0357648
$326$	−3.69970	−	63.5215i	−0.204908	−	3.51813i
$327$	8.89376	−	13.3249i	0.491826	−	0.736869i
$328$	−27.7527	+	3.24382i	−1.53239	+	0.179110i
$329$	−0.378776	−	0.0897715i	−0.0208826	−	0.00494926i
$330$	26.7118	−	15.1818i	1.47044	−	0.835733i
$331$	1.70974	−	2.29658i	0.0939760	−	0.126232i	−0.752648	−	0.658423i	$-0.771224\pi$
$331$	1.70974	−	2.29658i	0.0939760	−	0.126232i	0.846624	+	0.532191i	$0.178631\pi$
$332$	2.31791	+	13.1455i	0.127212	+	0.721455i
$333$	−1.22826	−	1.33771i	−0.0673080	−	0.0733061i
$334$	−5.92749	+	33.6165i	−0.324338	+	1.83941i
$335$	−12.5734	−	13.3271i	−0.686960	−	0.728135i
$336$	24.4425	−	47.8582i	1.33345	−	2.61088i
$337$	−14.4460	+	7.25506i	−0.786925	+	0.395208i	−0.796418	−	0.604746i	$-0.793274\pi$
$337$	−14.4460	+	7.25506i	−0.786925	+	0.395208i	0.00949332	+	0.999955i	$0.496978\pi$
$338$	−28.6721	−	18.8579i	−1.55956	−	1.02574i
$339$	3.68571	+	16.0343i	0.200180	+	0.870863i
$340$	−20.6099	+	4.88464i	−1.11773	+	0.264907i
$341$	33.6180	−	12.2359i	1.82052	−	0.662613i
$342$	4.60000	−	10.2790i	0.248739	−	0.555823i
$343$	−17.7905	−	6.47520i	−0.960595	−	0.349628i
$344$	22.1044	+	2.58363i	1.19179	+	0.139300i
$345$	−3.73661	−	10.4866i	−0.201172	−	0.564582i
$346$	−9.33928	+	9.89906i	−0.502083	+	0.532177i
$347$	8.80217	+	11.8234i	0.472525	+	0.634711i	0.972935	−	0.231077i	$-0.0742249\pi$
$347$	8.80217	+	11.8234i	0.472525	+	0.634711i	−0.500410	+	0.865788i	$0.666817\pi$
$348$	47.2862	−	34.7081i	2.53480	−	1.86055i
$349$	−2.21059	−	1.11020i	−0.118330	−	0.0594277i	0.388649	−	0.921386i	$-0.372942\pi$
$349$	−2.21059	−	1.11020i	−0.118330	−	0.0594277i	−0.506980	+	0.861958i	$0.669238\pi$
$350$	5.87136	+	10.1695i	0.313837	+	0.543582i
$351$	−1.89507	+	0.525650i	−0.101151	+	0.0280571i
$352$	−28.1616	+	48.7773i	−1.50102	+	2.59984i
$353$	−13.0877	+	8.60791i	−0.696588	+	0.458153i	−0.847778	−	0.530352i	$-0.822060\pi$
$353$	−13.0877	+	8.60791i	−0.696588	+	0.458153i	0.151190	+	0.988505i	$0.451690\pi$
$354$	−14.1952	−	13.5754i	−0.754468	−	0.721522i
$355$	−1.26418	+	2.93070i	−0.0670957	+	0.155545i
$356$	4.68910	+	15.6627i	0.248522	+	0.830120i
$357$	3.54705	−	9.54387i	0.187730	−	0.505115i
$358$	1.24702	+	2.89093i	0.0659072	+	0.152790i
$359$	−0.180567	+	0.151513i	−0.00952994	+	0.00799657i	−0.647540	−	0.762031i	$-0.724202\pi$
$359$	−0.180567	+	0.151513i	−0.00952994	+	0.00799657i	0.638010	+	0.770028i	$0.279758\pi$
$360$	8.49435	−	44.6309i	0.447692	−	2.35226i
$361$	−13.0398	−	10.9417i	−0.686307	−	0.575880i
$362$	8.76845	−	29.2887i	0.460860	−	1.53938i
$363$	0.510066	−	4.12167i	0.0267715	−	0.216332i
$364$	0.291241	−	5.00042i	0.0152652	−	0.262093i
$365$	−0.565975	+	9.71742i	−0.0296245	+	0.508633i
$366$	−4.23028	+	34.1834i	−0.221120	+	1.78680i
$367$	2.76321	−	9.22975i	0.144238	−	0.481789i	−0.855088	−	0.518482i	$-0.826497\pi$
$367$	2.76321	−	9.22975i	0.144238	−	0.481789i	0.999327	+	0.0366932i	$0.0116824\pi$
$368$	32.5813	+	27.3390i	1.69842	+	1.42514i
$369$	1.87897	−	9.87249i	0.0978155	−	0.513941i
$370$	2.24737	−	1.88576i	0.116835	−	0.0980362i
$371$	−13.7585	−	31.8959i	−0.714308	−	1.65595i
$372$	30.2245	−	81.3235i	1.56707	−	4.21643i
$373$	0.0172675	+	0.0576774i	0.000894076	+	0.00298642i	0.958435	−	0.285310i	$-0.0920964\pi$
$373$	0.0172675	+	0.0576774i	0.000894076	+	0.00298642i	−0.957541	+	0.288296i	$0.906911\pi$
$374$	−8.80900	+	20.4216i	−0.455502	+	1.05597i
$375$	15.2354	+	14.5701i	0.786751	+	0.752395i
$376$	1.05048	−	0.690912i	0.0541744	−	0.0356311i
$377$	1.25050	−	2.16594i	0.0644042	−	0.111551i
$378$	25.5478	+	25.1033i	1.31404	+	1.29118i
$379$	−1.23614	−	2.14105i	−0.0634961	−	0.109979i	0.832530	−	0.553980i	$-0.186892\pi$
$379$	−1.23614	−	2.14105i	−0.0634961	−	0.109979i	−0.896026	+	0.444002i	$0.853558\pi$
$380$	11.6935	+	5.87268i	0.599862	+	0.301262i
$381$	−17.6628	+	12.9645i	−0.904891	+	0.664191i
$382$	24.5206	+	32.9368i	1.25458	+	1.68519i
$383$	18.9333	−	20.0682i	0.967448	−	1.02543i	−0.0322153	−	0.999481i	$-0.510256\pi$
$383$	18.9333	−	20.0682i	0.967448	−	1.02543i	0.999663	−	0.0259538i	$-0.00826228\pi$
$384$	8.55764	+	24.0167i	0.436705	+	1.22559i
$385$	−17.0456	−	1.99235i	−0.868726	−	0.101540i
$386$	−43.7623	−	15.9282i	−2.22744	−	0.810723i
$387$	−3.26960	+	7.30612i	−0.166203	+	0.371391i
$388$	−74.0272	+	26.9437i	−3.75816	+	1.36786i
$389$	10.5158	−	2.49230i	0.533174	−	0.126365i	0.0447950	−	0.998996i	$-0.485737\pi$
$389$	10.5158	−	2.49230i	0.533174	−	0.126365i	0.488379	+	0.872632i	$0.337588\pi$
$390$	−0.711706	−	3.09620i	−0.0360386	−	0.156782i
$391$	6.73268	+	4.42815i	0.340486	+	0.223941i
$392$	2.46938	−	1.24017i	0.124723	−	0.0626381i
$393$	11.7216	−	22.9509i	0.591278	−	1.15772i
$394$	16.7686	+	17.7737i	0.844789	+	0.895424i
$395$	1.33980	−	7.59837i	0.0674126	−	0.382316i
$396$	−38.0608	−	41.4526i	−1.91263	−	2.08307i
$397$	−3.32712	−	18.8690i	−0.166983	−	0.947010i	−0.946996	−	0.321246i	$-0.895898\pi$
$397$	−3.32712	−	18.8690i	−0.166983	−	0.947010i	0.780012	−	0.625764i	$-0.215213\pi$
$398$	36.9503	−	49.6329i	1.85215	−	2.48787i
$399$	−5.46860	+	3.10812i	−0.273773	+	0.155601i
$400$	−19.9158	−	4.72013i	−0.995790	−	0.236007i
$401$	−31.2938	+	3.65772i	−1.56274	+	0.182658i	−0.853038	−	0.521848i	$-0.825243\pi$
$401$	−31.2938	+	3.65772i	−1.56274	+	0.182658i	−0.709698	+	0.704506i	$0.751169\pi$
$402$	−25.9010	+	38.8057i	−1.29183	+	1.93545i
$403$	−0.215089	−	3.69294i	−0.0107144	−	0.183958i
$404$	−66.8529			−3.32606
$405$	14.3984	+	7.72634i	0.715464	+	0.383925i
$406$	−45.5497			−2.26059
$407$	−0.128836	−	2.21203i	−0.00638616	−	0.109646i
$408$	14.5601	+	29.4878i	0.720835	+	1.45986i
$409$	0.909506	−	0.106306i	0.0449722	−	0.00525649i	−0.0935771	−	0.995612i	$-0.529830\pi$
$409$	0.909506	−	0.106306i	0.0449722	−	0.00525649i	0.138549	+	0.990356i	$0.455756\pi$
$410$	15.7970	+	3.74396i	0.780160	+	0.184901i
$411$	24.2755	+	14.2355i	1.19742	+	0.702185i
$412$	−41.9904	+	56.4029i	−2.06872	+	2.77877i
$413$	1.90511	+	10.8044i	0.0937444	+	0.531651i
$414$	−23.8930	+	15.2552i	−1.17427	+	0.749752i
$415$	0.821178	−	4.65713i	0.0403100	−	0.228609i
$416$	3.99656	+	4.23610i	0.195947	+	0.207692i
$417$	15.5493	+	23.9939i	0.761455	+	1.17499i
$418$	12.2785	−	6.16647i	0.600559	−	0.301612i
$419$	10.1925	+	6.70374i	0.497938	+	0.327499i	0.773513	−	0.633781i	$-0.218498\pi$
$419$	10.1925	+	6.70374i	0.497938	+	0.327499i	−0.275575	+	0.961280i	$0.588868\pi$
$420$	−30.4648	+	28.3547i	−1.48653	+	1.38357i
$421$	30.4907	−	7.22644i	1.48603	−	0.352195i	0.594107	−	0.804386i	$-0.297506\pi$
$421$	30.4907	−	7.22644i	1.48603	−	0.352195i	0.891921	+	0.452191i	$0.149358\pi$
$422$	−64.7830	+	23.5791i	−3.15359	+	1.14781i
$423$	0.123820	+	0.434939i	0.00602032	+	0.0211474i
$424$	105.432	+	38.3743i	5.12025	+	1.86362i
$425$	−3.85169	−	0.450198i	−0.186835	−	0.0218378i
$426$	7.99421	+	1.46547i	0.387321	+	0.0710025i
$427$	13.2028	−	13.9941i	0.638927	−	0.677223i
$428$	7.05522	+	9.47681i	0.341027	+	0.458079i
$429$	−2.19675	−	0.965280i	−0.106060	−	0.0466041i
$430$	−11.5551	−	5.80320i	−0.557238	−	0.279855i
$431$	6.90324	+	11.9568i	0.332518	+	0.575937i	0.983005	−	0.183580i	$-0.0587686\pi$
$431$	6.90324	+	11.9568i	0.332518	+	0.575937i	−0.650487	+	0.759517i	$0.725435\pi$
$432$	−62.3844	+	2.36329i	−3.00147	+	0.113704i
$433$	12.1413	−	21.0293i	0.583472	−	1.01060i	−0.411592	−	0.911368i	$-0.635027\pi$
$433$	12.1413	−	21.0293i	0.583472	−	1.01060i	0.995064	−	0.0992354i	$-0.0316397\pi$
$434$	−56.2883	+	37.0214i	−2.70193	+	1.77708i
$435$	−19.9475	+	5.82502i	−0.956411	+	0.279289i
$436$	18.7748	−	43.5250i	0.899152	−	2.08447i
$437$	−1.42782	−	4.76924i	−0.0683018	−	0.228144i
$438$	24.4384	−	4.13873i	1.16771	−	0.197756i
$439$	5.03397	+	11.6701i	0.240258	+	0.556981i	0.995094	−	0.0989323i	$-0.0315427\pi$
$439$	5.03397	+	11.6701i	0.240258	+	0.556981i	−0.754836	+	0.655914i	$0.772283\pi$
$440$	42.4631	−	35.6308i	2.02435	−	1.69863i
$441$	0.159314	+	0.981023i	0.00758640	+	0.0467154i
$442$	1.76165	+	1.47820i	0.0837932	+	0.0703108i
$443$	−7.31849	+	24.4454i	−0.347712	+	1.16144i	0.588056	+	0.808820i	$0.299894\pi$
$443$	−7.31849	+	24.4454i	−0.347712	+	1.16144i	−0.935767	+	0.352618i	$0.885292\pi$
$444$	−4.28833	−	3.23791i	−0.203515	−	0.153664i
$445$	0.336788	−	5.78242i	0.0159653	−	0.274113i
$446$	0.633086	−	10.8697i	0.0299775	−	0.514694i
$447$	5.43494	−	2.30088i	0.257064	−	0.108828i
$448$	12.6235	−	42.1656i	0.596407	−	1.99214i
$449$	2.45881	+	2.06318i	0.116038	+	0.0973677i	0.698960	−	0.715160i	$-0.253646\pi$
$449$	2.45881	+	2.06318i	0.116038	+	0.0973677i	−0.582922	+	0.812528i	$0.698091\pi$
$450$	6.98021	−	11.7206i	0.329050	−	0.552515i
$451$	9.39297	−	7.88164i	0.442298	−	0.371132i
$452$	19.2812	+	44.6989i	0.906912	+	2.10246i
$453$	−9.54253	−	11.5300i	−0.448347	−	0.541726i
$454$	−16.2963	−	54.4335i	−0.764825	−	2.55469i
$455$	−0.702853	+	1.62940i	−0.0329502	+	0.0763873i
$456$	4.81917	−	19.7372i	0.225678	−	0.924278i
$457$	1.78221	−	1.17218i	0.0833682	−	0.0548321i	−0.507141	−	0.861863i	$-0.669297\pi$
$457$	1.78221	−	1.17218i	0.0833682	−	0.0548321i	0.590509	+	0.807031i	$0.298927\pi$
$458$	16.1769	−	28.0192i	0.755896	−	1.30925i
$459$	−11.6879	+	1.81693i	−0.545543	+	0.0848070i
$460$	−16.4696	−	28.5262i	−0.767899	−	1.33004i
$461$	20.4974	+	10.2942i	0.954661	+	0.479449i	0.856742	−	0.515746i	$-0.172485\pi$
$461$	20.4974	+	10.2942i	0.954661	+	0.479449i	0.0979192	+	0.995194i	$0.468781\pi$
$462$	4.77931	+	43.4384i	0.222354	+	2.02094i
$463$	17.2886	+	23.2226i	0.803467	+	1.07924i	0.995206	+	0.0977977i	$0.0311798\pi$
$463$	17.2886	+	23.2226i	0.803467	+	1.07924i	−0.191739	+	0.981446i	$0.561413\pi$
$464$	54.4827	−	57.7483i	2.52930	−	2.68090i
$465$	−19.9159	+	23.4111i	−0.923577	+	1.08566i
$466$	63.9196	+	7.47113i	2.96102	+	0.346094i
$467$	−1.96329	−	0.714577i	−0.0908500	−	0.0330667i	0.296195	−	0.955127i	$-0.404282\pi$
$467$	−1.96329	−	0.714577i	−0.0908500	−	0.0330667i	−0.387045	+	0.922061i	$0.626504\pi$
$468$	−5.23486	+	2.54087i	−0.241982	+	0.117452i
$469$	24.4885	−	8.91307i	1.13077	−	0.411567i
$470$	−0.710840	+	0.168472i	−0.0327886	+	0.00777104i
$471$	−6.43242	−	1.97329i	−0.296390	−	0.0909246i
$472$	−29.6066	−	19.4726i	−1.36275	−	0.896298i
$473$	−8.72732	+	4.38303i	−0.401283	+	0.201532i
$474$	−19.6210	+	1.00954i	−0.901224	+	0.0463697i
$475$	1.64405	+	1.74259i	0.0754344	+	0.0799557i
$476$	5.23133	−	29.6684i	0.239778	−	1.35985i
$477$	−24.5341	+	32.0399i	−1.12334	+	1.46700i
$478$	11.0030	+	62.4013i	0.503267	+	2.85417i
$479$	−12.9813	+	17.4369i	−0.593131	+	0.796713i	−0.992779	−	0.119955i	$-0.961725\pi$
$479$	−12.9813	+	17.4369i	−0.593131	+	0.796713i	0.399648	+	0.916669i	$0.369132\pi$
$480$	0.327645	−	48.3886i	0.0149549	−	2.20863i
$481$	−0.222936	−	0.0528369i	−0.0101650	−	0.00240916i
$482$	−33.6038	+	3.92772i	−1.53061	+	0.178903i
$483$	15.8006	+	1.02767i	0.718952	+	0.0467608i
$484$	−0.714507	−	12.2676i	−0.0324776	−	0.557618i
$485$	27.9091			1.26729
$486$	10.9607	−	40.1398i	0.497189	−	1.82078i
$487$	−3.65843			−0.165779			−0.0828896	−	0.996559i	$-0.526415\pi$
$487$	−3.65843			−0.165779			−0.0828896	+	0.996559i	$0.526415\pi$
$488$	3.61325	+	62.0370i	0.163564	+	2.80828i
$489$	41.2014	+	2.67974i	1.86319	+	0.121182i
$490$	−1.59468	+	0.186392i	−0.0720404	+	0.00842032i
$491$	−16.8990	−	4.00514i	−0.762642	−	0.180750i	−0.169151	−	0.985590i	$-0.554103\pi$
$491$	−16.8990	−	4.00514i	−0.762642	−	0.180750i	−0.593491	+	0.804841i	$0.702251\pi$
$492$	0.201338	−	29.7348i	0.00907701	−	1.34055i
$493$	8.98266	−	12.0658i	0.404558	−	0.543416i
$494$	−0.246704	−	1.39913i	−0.0110998	−	0.0629498i
$495$	7.64802	+	18.4117i	0.343753	+	0.827546i
$496$	20.3913	−	115.645i	0.915596	−	5.19260i
$497$	−3.11531	−	3.30204i	−0.139741	−	0.148117i
$498$	−12.0260	+	0.618759i	−0.538896	+	0.0277272i
$499$	−15.1185	+	7.59280i	−0.676797	+	0.339900i	−0.753775	−	0.657132i	$-0.771769\pi$
$499$	−15.1185	+	7.59280i	−0.676797	+	0.339900i	0.0769779	+	0.997033i	$0.475473\pi$
$500$	52.1135	+	34.2756i	2.33059	+	1.53285i
$501$	−21.1759	−	6.49621i	−0.946070	−	0.290229i
$502$	−35.2337	+	8.35055i	−1.57256	+	0.372703i
$503$	−27.0776	+	9.85546i	−1.20733	+	0.439433i	−0.865778	−	0.500429i	$-0.833176\pi$
$503$	−27.0776	+	9.85546i	−1.20733	+	0.439433i	−0.341555	+	0.939862i	$0.610953\pi$
$504$	53.5027	+	36.2366i	2.38320	+	1.61411i
$505$	22.2559	+	8.10050i	0.990377	+	0.360468i
$506$	−34.3532	−	4.01532i	−1.52719	−	0.178503i
$507$	14.4291	−	16.9614i	0.640820	−	0.753282i
$508$	−44.4880	+	47.1545i	−1.97383	+	2.09214i
$509$	−7.15272	−	9.60777i	−0.317039	−	0.425857i	0.614826	−	0.788663i	$-0.289226\pi$
$509$	−7.15272	−	9.60777i	−0.317039	−	0.425857i	−0.931865	+	0.362806i	$0.881819\pi$
$510$	−2.08972	−	18.9931i	−0.0925344	−	0.841031i
$511$	−12.3721	−	6.21351i	−0.547310	−	0.274870i
$512$	−7.77620	−	13.4688i	−0.343663	−	0.595241i
$513$	6.25286	+	3.78147i	0.276070	+	0.166956i
$514$	3.73567	−	6.47037i	0.164773	−	0.285396i
$515$	20.8133	−	13.6891i	0.917142	−	0.603214i
$516$	−5.61773	+	23.0077i	−0.247307	+	1.01286i
$517$	−0.218538	+	0.506629i	−0.00961131	+	0.0222815i
$518$	1.19675	+	3.99741i	0.0525821	+	0.175636i
$519$	−5.63051	−	6.80320i	−0.247152	−	0.298627i
$520$	−2.27019	−	5.26290i	−0.0995545	−	0.230793i
$521$	2.74519	−	2.30349i	0.120269	−	0.100918i	−0.580669	−	0.814139i	$-0.697209\pi$
$521$	2.74519	−	2.30349i	0.120269	−	0.100918i	0.700939	+	0.713222i	$0.252765\pi$
$522$	25.8349	+	46.1805i	1.13076	+	2.02127i
$523$	−20.6502	−	17.3276i	−0.902971	−	0.757683i	0.0677978	−	0.997699i	$-0.478403\pi$
$523$	−20.6502	−	17.3276i	−0.902971	−	0.757683i	−0.970769	+	0.240016i	$0.922847\pi$
$524$	21.8693	−	73.0486i	0.955366	−	3.19114i
$525$	−7.01685	+	2.97059i	−0.306241	+	0.129647i
$526$	−0.230548	+	3.95835i	−0.0100524	+	0.172592i
$527$	1.29366	−	22.2112i	0.0563526	−	0.967536i
$528$	−60.7882	−	45.8981i	−2.64547	−	1.99746i
$529$	3.00228	−	10.0283i	0.130534	−	0.436013i
$530$	−49.9383	−	41.9032i	−2.16918	−	1.82016i
$531$	9.87352	−	8.05957i	0.428474	−	0.349755i
$532$	−14.2573	+	11.9633i	−0.618132	+	0.518674i
$533$	−0.502173	−	1.16417i	−0.0217515	−	0.0504257i
$534$	−14.5422	+	2.46278i	−0.629305	+	0.106575i
$535$	−1.20045	−	4.00979i	−0.0519001	−	0.173358i
$536$	−33.3393	+	77.2892i	−1.44004	+	3.33839i
$537$	−1.96108	+	0.572668i	−0.0846267	+	0.0247125i
$538$	20.3471	−	13.3825i	0.877224	−	0.576959i
$539$	−0.606313	+	1.05017i	−0.0261158	+	0.0452338i
$540$	46.0265	+	14.8045i	1.98066	+	0.637086i
$541$	8.33503	+	14.4367i	0.358351	+	0.620682i	0.987685	−	0.156453i	$-0.0500058\pi$
$541$	8.33503	+	14.4367i	0.358351	+	0.620682i	−0.629335	+	0.777134i	$0.716672\pi$
$542$	−14.0659	−	7.06418i	−0.604183	−	0.303432i
$543$	18.1625	+	7.98083i	0.779428	+	0.342490i
$544$	20.9170	+	28.0964i	0.896808	+	1.20462i
$545$	−11.5242	+	12.2149i	−0.493642	+	0.523230i
$546$	4.44458	+	0.814768i	0.190211	+	0.0348688i
$547$	38.4603	+	4.49536i	1.64444	+	0.192208i	0.887349	−	0.461098i	$-0.152544\pi$
$547$	38.4603	+	4.49536i	1.64444	+	0.192208i	0.757094	+	0.653306i	$0.226618\pi$
$548$	78.2449	+	28.4788i	3.34246	+	1.21655i
$549$	−21.6763	−	5.44843i	−0.925122	−	0.232533i
$550$	15.6405	−	5.69267i	0.666912	−	0.242736i
$551$	−9.04250	+	2.14311i	−0.385224	+	0.0912997i
$552$	−37.4371	+	34.8440i	−1.59343	+	1.48306i
$553$	9.16871	+	6.03035i	0.389893	+	0.256437i
$554$	11.8069	−	5.92962i	0.501625	−	0.251926i
$555$	1.03529	+	1.59754i	0.0439457	+	0.0678118i
$556$	58.0551	+	61.5348i	2.46208	+	2.60966i
$557$	3.42298	−	19.4127i	0.145036	−	0.822542i	−0.822302	−	0.569052i	$-0.807310\pi$
$557$	3.42298	−	19.4127i	0.145036	−	0.822542i	0.967338	−	0.253490i	$-0.0815786\pi$
$558$	69.4598	+	36.0701i	2.94047	+	1.52697i
$559$	0.175353	+	0.994479i	0.00741666	+	0.0420620i
$560$	−33.6386	+	45.1845i	−1.42149	+	1.90939i
$561$	−12.4490	−	7.30029i	−0.525599	−	0.308218i
$562$	−35.3457	−	8.37708i	−1.49097	−	0.353366i
$563$	−0.729538	+	0.0852707i	−0.0307463	+	0.00359373i	−0.131452	−	0.991323i	$-0.541964\pi$
$563$	−0.729538	+	0.0852707i	−0.0307463	+	0.00359373i	0.100706	+	0.994916i	$0.467890\pi$
$564$	0.592404	+	1.19976i	0.0249447	+	0.0505191i
$565$	−1.00277	−	17.2170i	−0.0421870	−	0.724323i
$566$	31.5659			1.32681
$567$	−18.2020	+	14.4517i	−0.764413	+	0.606914i
$568$	14.6630			0.615246
$569$	1.19633	+	20.5401i	0.0501526	+	0.861088i	0.925771	+	0.378084i	$0.123417\pi$
$569$	1.19633	+	20.5401i	0.0501526	+	0.861088i	−0.875619	+	0.483003i	$0.839546\pi$
$570$	−6.55335	+	9.81844i	−0.274490	+	0.411249i
$571$	−2.33025	+	0.272367i	−0.0975180	+	0.0113982i	−0.164712	−	0.986342i	$-0.552669\pi$
$571$	−2.33025	+	0.272367i	−0.0975180	+	0.0113982i	0.0671940	+	0.997740i	$0.478595\pi$
$572$	−6.90829	−	1.63730i	−0.288850	−	0.0684587i
$573$	−23.1648	+	13.1659i	−0.967722	+	0.550012i
$574$	−13.7889	+	18.5218i	−0.575539	+	0.773083i
$575$	−1.04722	−	5.93909i	−0.0436721	−	0.247677i
$576$	−49.9094	+	11.1172i	−2.07956	+	0.463215i
$577$	−5.62981	+	31.9282i	−0.234372	+	1.32919i	0.609561	+	0.792739i	$0.291346\pi$
$577$	−5.62981	+	31.9282i	−0.234372	+	1.32919i	−0.843932	+	0.536449i	$0.819765\pi$
$578$	−21.6480	−	22.9455i	−0.900438	−	0.954409i
$579$	13.7450	−	26.9126i	0.571223	−	1.11845i
$580$	−54.9464	+	27.5951i	−2.28153	+	1.14583i
$581$	5.61960	+	3.69607i	0.233140	+	0.153339i
$582$	−15.9207	−	69.2614i	−0.659935	−	2.87098i
$583$	−47.9092	+	11.3547i	−1.98420	+	0.470263i
$584$	42.0213	−	15.2945i	1.73885	−	0.632891i
$585$	2.05061	−	0.211576i	0.0847822	−	0.00874758i
$586$	−40.8323	−	14.8617i	−1.68677	−	0.613932i
$587$	18.4303	+	2.15420i	0.760702	+	0.0889133i	0.487594	−	0.873070i	$-0.337874\pi$
$587$	18.4303	+	2.15420i	0.760702	+	0.0889133i	0.273107	+	0.961984i	$0.411949\pi$
$588$	0.987051	+	2.77012i	0.0407053	+	0.114238i
$589$	−9.43248	+	9.99784i	−0.388658	+	0.411954i
$590$	12.2950	+	16.5151i	0.506178	+	0.679915i
$591$	−12.7822	+	9.38217i	−0.525791	+	0.385931i
$592$	−6.49941	−	3.26413i	−0.267124	−	0.134155i
$593$	20.4339	+	35.3926i	0.839120	+	1.45340i	0.890631	+	0.454727i	$0.150263\pi$
$593$	20.4339	+	35.3926i	0.839120	+	1.45340i	−0.0515108	+	0.998672i	$0.516404\pi$
$594$	41.3293	−	29.4829i	1.69576	−	1.20970i
$595$	−5.33644	+	9.24299i	−0.218773	+	0.378926i
$596$	14.5900	−	9.59598i	0.597629	−	0.393067i
$597$	29.0179	+	27.7507i	1.18762	+	1.13576i
$598$	−1.41651	+	3.28383i	−0.0579253	+	0.134286i
$599$	−2.61997	−	8.75130i	−0.107049	−	0.357568i	0.887634	−	0.460549i	$-0.152347\pi$
$599$	−2.61997	−	8.75130i	−0.107049	−	0.357568i	−0.994683	+	0.102980i	$0.967162\pi$
$600$	8.57405	−	23.0698i	0.350034	−	0.941820i
$601$	−14.6923	−	34.0606i	−0.599311	−	1.38936i	−0.900106	−	0.435670i	$-0.856511\pi$
$601$	−14.6923	−	34.0606i	−0.599311	−	1.38936i	0.300795	−	0.953689i	$-0.402748\pi$
$602$	14.0886	−	11.8218i	0.574209	−	0.481819i
$603$	−22.9259	−	19.7723i	−0.933616	−	0.805190i
$604$	−33.9235	−	28.4652i	−1.38033	−	1.15823i
$605$	−1.24859	+	4.17057i	−0.0507623	+	0.169558i
$606$	7.40696	−	59.8531i	0.300887	−	2.43137i
$607$	1.94480	−	33.3909i	0.0789370	−	1.35530i	−0.693616	−	0.720345i	$-0.743983\pi$
$607$	1.94480	−	33.3909i	0.0789370	−	1.35530i	0.772553	−	0.634951i	$-0.218980\pi$
$608$	1.25823	−	21.6030i	0.0510281	−	0.876118i
$609$	3.63003	−	29.3331i	0.147096	−	1.18864i
$610$	10.3553	−	34.5890i	0.419273	−	1.40047i
$611$	0.0437040	+	0.0366720i	0.00176807	+	0.00148359i
$612$	−33.0464	+	11.5236i	−1.33582	+	0.465812i
$613$	35.2558	−	29.5831i	1.42397	−	1.19485i	0.474794	−	0.880097i	$-0.342522\pi$
$613$	35.2558	−	29.5831i	1.42397	−	1.19485i	0.949173	−	0.314754i	$-0.101922\pi$
$614$	26.3771	+	61.1490i	1.06449	+	2.46777i
$615$	−3.66996	+	9.87459i	−0.147987	+	0.398182i
$616$	22.6121	+	75.5297i	0.911067	+	3.04318i
$617$	16.8376	−	39.0340i	0.677858	−	1.57145i	−0.136209	−	0.990680i	$-0.543492\pi$
$617$	16.8376	−	39.0340i	0.677858	−	1.57145i	0.814067	−	0.580771i	$-0.197249\pi$
$618$	−45.8449	−	43.8429i	−1.84415	−	1.76362i
$619$	−35.1471	+	23.1166i	−1.41268	+	0.929134i	−0.412848	+	0.910800i	$0.635466\pi$
$619$	−35.1471	+	23.1166i	−1.41268	+	0.929134i	−0.999832	+	0.0183341i	$0.994164\pi$
$620$	−45.4719	+	78.7597i	−1.82620	+	3.16307i
$621$	−7.91990	−	16.6023i	−0.317815	−	0.666228i
$622$	11.0693	+	19.1725i	0.443837	+	0.768749i
$623$	7.36212	+	3.69740i	0.294957	+	0.148133i
$624$	−6.34921	+	4.66033i	−0.254172	+	0.186562i
$625$	−8.10943	−	10.8929i	−0.324377	−	0.435714i
$626$	10.1376	−	10.7452i	0.405179	−	0.429465i
$627$	2.99256	+	8.39850i	0.119511	+	0.335404i
$628$	−19.7733	−	2.31117i	−0.789042	−	0.0922258i
$629$	−1.29489	−	0.471303i	−0.0516308	−	0.0187921i
$630$	−22.0105	−	30.4166i	−0.876918	−	1.21183i
$631$	−1.25540	+	0.456928i	−0.0499766	+	0.0181900i	−0.366888	−	0.930265i	$-0.619577\pi$
$631$	−1.25540	+	0.456928i	−0.0499766	+	0.0181900i	0.316911	+	0.948455i	$0.397354\pi$
$632$	−34.4905	+	8.17439i	−1.37196	+	0.325160i
$633$	−10.0216	−	43.5981i	−0.398324	−	1.73287i
$634$	−49.2704	−	32.4057i	−1.95678	−	1.28699i
$635$	20.5241	−	10.3076i	0.814474	−	0.409044i
$636$	−54.3088	+	106.336i	−2.15348	+	4.21651i
$637$	0.0860451	+	0.0912025i	0.00340923	+	0.00361357i
$638$	−11.2112	+	63.5818i	−0.443855	+	2.51723i
$639$	−1.58083	+	5.03132i	−0.0625365	+	0.199036i
$640$	−4.64087	−	26.3197i	−0.183446	−	1.04038i
$641$	−5.74977	+	7.72328i	−0.227102	+	0.305051i	−0.901039	−	0.433738i	$-0.857195\pi$
$641$	−5.74977	+	7.72328i	−0.227102	+	0.305051i	0.673937	+	0.738789i	$0.264602\pi$
$642$	−9.26622	+	5.26652i	−0.365709	+	0.207853i
$643$	−17.8664	−	4.23442i	−0.704583	−	0.166989i	−0.137321	−	0.990527i	$-0.543849\pi$
$643$	−17.8664	−	4.23442i	−0.704583	−	0.166989i	−0.567262	+	0.823537i	$0.691997\pi$
$644$	46.5335	−	5.43898i	1.83368	−	0.214326i
$645$	4.65802	−	6.97878i	0.183409	−	0.274789i
$646$	−0.496842	−	8.53044i	−0.0195480	−	0.335626i
$647$	−24.2705			−0.954170			−0.477085	−	0.878857i	$-0.658307\pi$
$647$	−24.2705			−0.954170			−0.477085	+	0.878857i	$0.658307\pi$
$648$	6.39278	−	74.7965i	0.251132	−	2.93828i
$649$	15.5506			0.610413
$650$	−0.100069	−	1.71811i	−0.00392501	−	0.0673898i
$651$	−19.3552	−	39.1989i	−0.758590	−	1.53633i
$652$	121.340	−	14.1826i	4.75204	−	0.555433i
$653$	41.4115	+	9.81470i	1.62056	+	0.384079i	0.937967	−	0.346724i	$-0.112706\pi$
$653$	41.4115	+	9.81470i	1.62056	+	0.384079i	0.682589	+	0.730802i	$0.260854\pi$
$654$	36.8876	+	21.6314i	1.44242	+	0.845854i
$655$	−16.1317	+	21.6687i	−0.630319	+	0.846665i
$656$	−6.98888	−	39.6359i	−0.272870	−	1.54752i
$657$	0.717667	+	16.0677i	0.0279988	+	0.626859i
$658$	0.180430	−	1.02327i	0.00703388	−	0.0398911i
$659$	−1.29417	−	1.37174i	−0.0504138	−	0.0534355i	0.701676	−	0.712496i	$-0.252435\pi$
$659$	−1.29417	−	1.37174i	−0.0504138	−	0.0534355i	−0.752090	+	0.659061i	$0.770954\pi$
$660$	32.0813	+	49.5042i	1.24876	+	1.92695i
$661$	37.6179	−	18.8924i	1.46317	−	0.734829i	0.473848	−	0.880607i	$-0.342865\pi$
$661$	37.6179	−	18.8924i	1.46317	−	0.734829i	0.989317	+	0.145778i	$0.0465684\pi$
$662$	6.38513	+	4.19956i	0.248165	+	0.163221i
$663$	−1.09232	+	1.01666i	−0.0424223	+	0.0394839i
$664$	−21.1396	+	5.01018i	−0.820376	+	0.194433i
$665$	6.19596	−	2.25514i	0.240269	−	0.0874507i
$666$	3.37401	−	3.48058i	0.130740	−	0.134870i
$667$	21.9822	+	8.00086i	0.851154	+	0.309795i
$668$	−65.0950	−	7.60852i	−2.51860	−	0.294382i
$669$	6.94939	+	1.27394i	0.268679	+	0.0492534i
$670$	33.5616	−	35.5732i	1.29660	−	1.37431i
$671$	−16.2845	−	21.8738i	−0.628655	−	0.844430i
$672$	63.0110	+	27.6878i	2.43070	+	1.06808i
$673$	9.62352	+	4.83311i	0.370960	+	0.186303i	0.624505	−	0.781020i	$-0.285301\pi$
$673$	9.62352	+	4.83311i	0.370960	+	0.186303i	−0.253546	+	0.967323i	$0.581597\pi$
$674$	−21.5748	−	37.3687i	−0.831031	−	1.43939i
$675$	6.99156	+	5.42917i	0.269105	+	0.208969i
$676$	32.9446	−	57.0616i	1.26710	−	2.19468i
$677$	8.76356	−	5.76388i	0.336811	−	0.221524i	−0.369825	−	0.929102i	$-0.620582\pi$
$677$	8.76356	−	5.76388i	0.336811	−	0.221524i	0.706636	+	0.707577i	$0.250212\pi$
$678$	−42.1550	+	12.3100i	−1.61895	+	0.472762i
$679$	−15.7227	+	36.4493i	−0.603381	+	1.39879i
$680$	−9.88699	−	33.0249i	−0.379149	−	1.26645i
$681$	36.3528	−	6.15648i	1.39304	−	0.235917i
$682$	37.8231	+	87.6837i	1.44832	+	3.35758i
$683$	−18.5237	+	15.5432i	−0.708789	+	0.594745i	−0.924259	−	0.381766i	$-0.875316\pi$
$683$	−18.5237	+	15.5432i	−0.708789	+	0.594745i	0.215470	+	0.976510i	$0.430872\pi$
$684$	20.2154	+	7.66940i	0.772957	+	0.293247i
$685$	−22.5977	−	18.9617i	−0.863413	−	0.724490i
$686$	14.4935	−	48.4117i	0.553365	−	1.84837i
$687$	16.7546	+	12.6505i	0.639227	+	0.482648i
$688$	−1.86390	+	32.0019i	−0.0710604	+	1.22006i
$689$	−0.296019	+	5.08244i	−0.0112774	+	0.193626i
$690$	27.3641	−	11.5846i	1.04173	−	0.441018i
$691$	2.45603	−	8.20373i	0.0934320	−	0.312084i	−0.898480	−	0.439015i	$-0.855327\pi$
$691$	2.45603	−	8.20373i	0.0934320	−	0.312084i	0.991912	+	0.126931i	$0.0405126\pi$
$692$	−20.0163	−	16.7957i	−0.760907	−	0.638476i
$693$	−28.3543	−	0.383998i	−1.07709	−	0.0145869i
$694$	−30.1399	+	25.2904i	−1.14410	+	0.960011i
$695$	−11.8710	−	27.5200i	−0.450291	−	1.04389i
$696$	60.8688	+	73.5463i	2.30723	+	2.78776i
$697$	−2.18703	−	7.30519i	−0.0828397	−	0.276704i
$698$	2.61529	−	6.06293i	0.0989903	−	0.229485i
$699$	−9.90526	+	40.5675i	−0.374652	+	1.53440i
$700$	−18.8366	+	12.3890i	−0.711957	+	0.468261i
$701$	−1.21019	+	2.09612i	−0.0457084	+	0.0791693i	−0.887974	−	0.459893i	$-0.847888\pi$
$701$	−1.21019	+	2.09612i	−0.0457084	+	0.0791693i	0.842266	+	0.539062i	$0.181221\pi$
$702$	−1.69483	−	4.96826i	−0.0639674	−	0.187515i
$703$	0.425656	+	0.737258i	0.0160539	+	0.0278062i
$704$	−55.7510	−	27.9992i	−2.10119	−	1.05526i
$705$	−0.0518430	−	0.471192i	−0.00195252	−	0.0177461i
$706$	−24.9690	−	33.5392i	−0.939720	−	1.26226i
$707$	−23.1172	+	24.5028i	−0.869413	+	0.921524i
$708$	24.4354	−	28.7238i	0.918340	−	1.07951i
$709$	−49.4393	−	5.77862i	−1.85673	−	0.217021i	−0.887098	−	0.461582i	$-0.847282\pi$
$709$	−49.4393	−	5.77862i	−1.85673	−	0.217021i	−0.969634	+	0.244561i	$0.921356\pi$
$710$	−8.00572	−	2.91384i	−0.300449	−	0.109355i
$711$	0.913554	−	12.7160i	0.0342610	−	0.476887i
$712$	−25.0051	+	9.10110i	−0.937104	+	0.341078i
$713$	33.6675	−	7.97934i	1.26086	−	0.298829i
$714$	25.9823	+	7.97069i	0.972364	+	0.298295i
$715$	2.10144	+	1.38214i	0.0785895	+	0.0516892i
$716$	−5.40188	+	2.71293i	−0.201878	+	0.101387i
$717$	−41.0621	+	2.11272i	−1.53349	+	0.0789011i
$718$	−0.431766	−	0.457646i	−0.0161134	−	0.0170792i
$719$	−9.09244	+	51.5658i	−0.339091	+	1.92308i	0.0432647	+	0.999064i	$0.486224\pi$
$719$	−9.09244	+	51.5658i	−0.339091	+	1.92308i	−0.382355	+	0.924015i	$0.624887\pi$
$720$	64.8895	+	8.47670i	2.41829	+	0.315908i
$721$	6.15275	+	34.8940i	0.229140	+	1.29952i
$722$	27.1329	−	36.4458i	1.00978	−	1.35637i
$723$	0.148647	−	21.9531i	0.00552825	−	0.816446i
$724$	57.1170	+	13.5370i	2.12274	+	0.503098i
$725$	−11.1812	+	1.30690i	−0.415260	+	0.0485369i
$726$	11.0623	+	0.719493i	0.410560	+	0.0267029i
$727$	2.04674	+	35.1411i	0.0759093	+	1.30331i	0.794237	+	0.607608i	$0.207871\pi$
$727$	2.04674	+	35.1411i	0.0759093	+	1.30331i	−0.718328	+	0.695705i	$0.755092\pi$
$728$	8.15228			0.302143
$729$	24.9757	+	10.2574i	0.925026	+	0.379903i
$730$	−25.9821			−0.961642
$731$	0.353147	+	6.06329i	0.0130616	+	0.224259i
$732$	−65.9923	−	4.29215i	−2.43915	−	0.158642i
$733$	−23.6318	+	2.76216i	−0.872860	+	0.102023i	−0.540715	−	0.841206i	$-0.681846\pi$
$733$	−23.6318	+	2.76216i	−0.872860	+	0.102023i	−0.332145	+	0.943228i	$0.607772\pi$
$734$	25.0236	+	5.93071i	0.923639	+	0.218906i
$735$	0.00705413	−	1.04180i	0.000260196	−	0.0384273i
$736$	−32.5289	+	43.6938i	−1.19903	+	1.61058i
$737$	−6.41419	−	36.3767i	−0.236270	−	1.33995i
$738$	26.5991	+	3.47472i	0.979127	+	0.127906i
$739$	−7.56827	+	42.9218i	−0.278403	+	1.57890i	0.449536	+	0.893262i	$0.351589\pi$
$739$	−7.56827	+	42.9218i	−0.278403	+	1.57890i	−0.727939	+	0.685642i	$0.759522\pi$
$740$	3.86537	+	4.09705i	0.142094	+	0.150611i
$741$	0.920672	−	0.0473704i	0.0338217	−	0.00174019i
$742$	82.8585	−	41.6131i	3.04183	−	1.52767i
$743$	−8.49641	−	5.58817i	−0.311703	−	0.205010i	0.384012	−	0.923328i	$-0.374542\pi$
$743$	−8.49641	−	5.58817i	−0.311703	−	0.205010i	−0.695715	+	0.718318i	$0.744912\pi$
$744$	134.995	+	41.4129i	4.94916	+	1.51827i
$745$	−6.01987	+	1.42674i	−0.220551	+	0.0522716i
$746$	−0.151015	+	0.0549648i	−0.00552904	+	0.00201240i
$747$	0.559928	−	7.79378i	0.0204867	−	0.285159i
$748$	−40.1258	−	14.6046i	−1.46714	−	0.533997i
$749$	5.91307	+	0.691139i	0.216059	+	0.0252537i
$750$	−36.4607	+	42.8594i	−1.33136	+	1.56501i
$751$	11.4749	−	12.1627i	0.418724	−	0.443822i	−0.483334	−	0.875436i	$-0.660574\pi$
$751$	11.4749	−	12.1627i	0.418724	−	0.443822i	0.902058	+	0.431614i	$0.142056\pi$
$752$	1.08149	+	1.45270i	0.0394380	+	0.0529744i
$753$	−2.56967	−	23.3553i	−0.0936439	−	0.851114i
$754$	5.96571	+	2.99609i	0.217258	+	0.109111i
$755$	7.84433	+	13.5868i	0.285485	+	0.494474i
$756$	−45.2640	+	51.7705i	−1.64623	+	1.88287i
$757$	20.3289	−	35.2107i	0.738867	−	1.27975i	−0.214139	−	0.976803i	$-0.568695\pi$
$757$	20.3289	−	35.2107i	0.738867	−	1.27975i	0.953006	−	0.302951i	$-0.0979720\pi$
$758$	5.51347	−	3.62627i	0.200258	−	0.131712i
$759$	5.32352	−	21.8028i	0.193232	−	0.791390i
$760$	−8.43536	+	19.5554i	−0.305983	+	0.709348i
$761$	−3.90514	−	13.0441i	−0.141561	−	0.472847i	0.857577	−	0.514356i	$-0.171969\pi$
$761$	−3.90514	−	13.0441i	−0.141561	−	0.472847i	−0.999138	+	0.0415084i	$0.986784\pi$
$762$	−37.2881	−	45.0543i	−1.35081	−	1.63215i
$763$	−9.46052	−	21.9320i	−0.342494	−	0.793990i
$764$	−60.3933	+	50.6760i	−2.18495	+	1.83339i
$765$	12.3977	+	0.167901i	0.448241	+	0.00607047i
$766$	56.4147	+	47.3375i	2.03835	+	1.71037i
$767$	0.461161	−	1.54038i	0.0166515	−	0.0556200i
$768$	−8.29850	+

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)

\(f(q)\)	\(=\)	\(q+(0.155203 + 2.66473i) q^{2} +(-1.72840 - 0.112415i) q^{3} +(-5.09021 + 0.594960i) q^{4} +(1.76667 + 0.418708i) q^{5} +(0.0313040 - 4.62316i) q^{6} +(-1.54209 + 2.07139i) q^{7} +(-1.44840 - 8.21430i) q^{8} +(2.97473 + 0.388597i) q^{9} +O(q^{10})\)	\(q+(0.155203 + 2.66473i) q^{2} +(-1.72840 - 0.112415i) q^{3} +(-5.09021 + 0.594960i) q^{4} +(1.76667 + 0.418708i) q^{5} +(0.0313040 - 4.62316i) q^{6} +(-1.54209 + 2.07139i) q^{7} +(-1.44840 - 8.21430i) q^{8} +(2.97473 + 0.388597i) q^{9} +(-0.841551 + 4.77267i) q^{10} +(2.51185 + 2.66241i) q^{11} +(8.86480 - 0.456111i) q^{12} +(0.338219 - 0.169860i) q^{13} +(-5.75903 - 3.78777i) q^{14} +(-3.00644 - 0.922295i) q^{15} +(11.6906 - 2.77073i) q^{16} +(2.13907 - 0.778557i) q^{17} +(-0.573820 + 7.98715i) q^{18} +(-1.32149 - 0.480985i) q^{19} +(-9.24183 - 1.08021i) q^{20} +(2.89821 - 3.40683i) q^{21} +(-6.70474 + 7.10661i) q^{22} +(2.11397 + 2.83955i) q^{23} +(1.58001 + 14.3604i) q^{24} +(-1.52236 - 0.764560i) q^{25} +(0.505123 + 0.874898i) q^{26} +(-5.09783 - 1.00606i) q^{27} +(6.61718 - 11.4613i) q^{28} +(5.52098 - 3.63121i) q^{29} +(1.99106 - 8.15448i) q^{30} +(3.87125 - 8.97457i) q^{31} +(4.41321 + 14.7411i) q^{32} +(-4.04218 - 4.88407i) q^{33} +(2.40663 + 5.57920i) q^{34} +(-3.59167 + 3.01377i) q^{35} +(-15.3732 - 0.208197i) q^{36} +(-0.463728 - 0.389114i) q^{37} +(1.07659 - 3.59607i) q^{38} +(-0.603672 + 0.255565i) q^{39} +(0.880547 - 15.1184i) q^{40} +(0.194779 - 3.34423i) q^{41} +(9.52810 + 7.19419i) q^{42} +(-0.765225 + 2.55603i) q^{43} +(-14.3699 - 12.0578i) q^{44} +(5.09264 + 1.93206i) q^{45} +(-7.23854 + 6.07386i) q^{46} +(0.0597051 + 0.138412i) q^{47} +(-20.5176 + 3.47473i) q^{48} +(0.0950155 + 0.317374i) q^{49} +(1.80107 - 4.17535i) q^{50} +(-3.78469 + 1.10519i) q^{51} +(-1.62055 + 1.06585i) q^{52} +(-6.72572 + 11.6493i) q^{53} +(1.88967 - 13.7405i) q^{54} +(3.32284 + 5.75532i) q^{55} +(19.2486 + 9.66701i) q^{56} +(2.23000 + 0.979890i) q^{57} +(10.5331 + 14.1483i) q^{58} +(2.91546 - 3.09020i) q^{59} +(15.8521 + 2.90596i) q^{60} +(-7.39981 - 0.864914i) q^{61} +(24.5156 + 8.92296i) q^{62} +(-5.39224 + 5.56257i) q^{63} +(-16.0163 + 5.82946i) q^{64} +(0.668642 - 0.158471i) q^{65} +(12.3874 - 11.5293i) q^{66} +(-8.43131 - 5.54536i) q^{67} +(-10.4251 + 5.23568i) q^{68} +(-3.33457 - 5.14552i) q^{69} +(-8.58832 - 9.10309i) q^{70} +(-0.305263 + 1.73123i) q^{71} +(-1.11655 - 24.9981i) q^{72} +(0.930968 + 5.27978i) q^{73} +(0.964911 - 1.29610i) q^{74} +(2.54530 + 1.49260i) q^{75} +(7.01285 + 1.66208i) q^{76} +(-9.38839 + 1.09735i) q^{77} +(-0.774702 - 1.56896i) q^{78} +(-0.247092 - 4.24240i) q^{79} +21.8136 q^{80} +(8.69798 + 2.31194i) q^{81} +8.94171 q^{82} +(-0.151445 - 2.60022i) q^{83} +(-12.7256 + 19.0658i) q^{84} +(4.10501 - 0.479807i) q^{85} +(-6.92989 - 1.64241i) q^{86} +(-9.95066 + 5.65553i) q^{87} +(18.2316 - 24.4893i) q^{88} +(-0.553979 - 3.14177i) q^{89} +(-4.35803 + 13.8704i) q^{90} +(-0.169719 + 0.962523i) q^{91} +(-12.4500 - 13.1962i) q^{92} +(-7.69995 + 15.0765i) q^{93} +(-0.359564 + 0.180580i) q^{94} +(-2.13325 - 1.40306i) q^{95} +(-5.97065 - 25.9747i) q^{96} +(14.9574 - 3.54497i) q^{97} +(-0.830968 + 0.302448i) q^{98} +(6.43746 + 8.89603i) 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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