LMFDB - Embedded newform 729.2.k.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(4,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(486))

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("729.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.k (of order $243$, degree $162$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$12960$
Relative dimension:	$80$ over $\Q(\zeta_{243})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{243}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48775 - 0.0321643i) q^{2} +(0.111243 + 1.72847i) q^{3} +(4.18852 + 0.108326i) q^{4} +(2.61631 + 0.801736i) q^{5} +(-0.221150 - 4.30359i) q^{6} +(0.558840 - 1.39354i) q^{7} +(-5.44433 - 0.211265i) q^{8} +(-2.97525 + 0.384562i) q^{9} +O(q^{10})$	\(q+(-2.48775 - 0.0321643i) q^{2} +(0.111243 + 1.72847i) q^{3} +(4.18852 + 0.108326i) q^{4} +(2.61631 + 0.801736i) q^{5} +(-0.221150 - 4.30359i) q^{6} +(0.558840 - 1.39354i) q^{7} +(-5.44433 - 0.211265i) q^{8} +(-2.97525 + 0.384562i) q^{9} +(-6.48293 - 2.07867i) q^{10} +(3.15263 + 1.79310i) q^{11} +(0.278706 + 7.25180i) q^{12} +(-1.89074 - 4.23194i) q^{13} +(-1.43508 + 3.44880i) q^{14} +(-1.09473 + 4.61141i) q^{15} +(5.16867 + 0.267528i) q^{16} +(7.11213 + 3.23286i) q^{17} +(7.41404 - 0.860996i) q^{18} +(3.02456 + 4.40991i) q^{19} +(10.8716 + 3.64150i) q^{20} +(2.47087 + 0.810919i) q^{21} +(-7.78527 - 4.56218i) q^{22} +(0.788145 - 2.40449i) q^{23} +(-0.240479 - 9.43388i) q^{24} +(2.06072 + 1.39386i) q^{25} +(4.56757 + 10.5888i) q^{26} +(-0.995682 - 5.09986i) q^{27} +(2.49167 - 5.77634i) q^{28} +(-3.87709 + 2.47880i) q^{29} +(2.87174 - 11.4368i) q^{30} +(-2.21573 - 8.16359i) q^{31} +(-1.97566 - 0.127888i) q^{32} +(-2.74862 + 5.64871i) q^{33} +(-17.5892 - 8.27129i) q^{34} +(2.57935 - 3.19789i) q^{35} +(-12.5036 + 1.28845i) q^{36} +(6.29290 + 1.23588i) q^{37} +(-7.38250 - 11.0680i) q^{38} +(7.10447 - 3.73887i) q^{39} +(-14.0747 - 4.91764i) q^{40} +(0.249606 - 0.0945212i) q^{41} +(-6.12081 - 2.09684i) q^{42} +(4.02908 - 1.76895i) q^{43} +(13.0106 + 7.85194i) q^{44} +(-8.09249 - 1.37923i) q^{45} +(-2.03804 + 5.95641i) q^{46} +(-0.976517 + 3.59786i) q^{47} +(0.112563 + 8.96368i) q^{48} +(3.43080 + 3.27897i) q^{49} +(-5.08173 - 3.53384i) q^{50} +(-4.79674 + 12.6528i) q^{51} +(-7.46098 - 17.9304i) q^{52} +(6.17116 - 6.54105i) q^{53} +(2.31297 + 12.7192i) q^{54} +(6.81066 + 7.21888i) q^{55} +(-3.33691 + 7.46883i) q^{56} +(-7.28597 + 5.71845i) q^{57} +(9.72496 - 6.04192i) q^{58} +(-10.3181 + 1.75067i) q^{59} +(-5.08485 + 19.1964i) q^{60} +(1.98810 - 3.65881i) q^{61} +(5.24960 + 20.3802i) q^{62} +(-1.12679 + 4.36104i) q^{63} +(-5.40923 - 0.420439i) q^{64} +(-1.55386 - 12.5879i) q^{65} +(7.01955 - 13.9641i) q^{66} +(-8.85457 + 4.59122i) q^{67} +(29.4391 + 14.3113i) q^{68} +(4.24377 + 1.09481i) q^{69} +(-6.51963 + 7.87259i) q^{70} +(7.83335 + 6.07131i) q^{71} +(16.2795 - 1.46512i) q^{72} +(5.11723 - 1.64077i) q^{73} +(-15.6154 - 3.27698i) q^{74} +(-2.18000 + 3.71697i) q^{75} +(12.1907 + 18.7987i) q^{76} +(4.26057 - 3.39126i) q^{77} +(-17.7944 + 9.07286i) q^{78} +(-2.22272 + 11.7177i) q^{79} +(13.3084 + 4.84385i) q^{80} +(8.70422 - 2.28834i) q^{81} +(-0.623997 + 0.227116i) q^{82} +(0.547989 + 3.36136i) q^{83} +(10.2614 + 3.66421i) q^{84} +(16.0156 + 14.1602i) q^{85} +(-10.0802 + 4.27111i) q^{86} +(-4.71584 - 6.42571i) q^{87} +(-16.7851 - 10.4283i) q^{88} +(-10.5517 - 4.31083i) q^{89} +(20.0877 + 3.69147i) q^{90} +(-6.95400 + 0.269847i) q^{91} +(3.56163 - 9.98587i) q^{92} +(13.8641 - 4.73798i) q^{93} +(2.54505 - 8.91915i) q^{94} +(4.37760 + 13.9626i) q^{95} +(0.00127322 - 3.42910i) q^{96} +(3.67167 - 15.9508i) q^{97} +(-8.42950 - 8.26760i) q^{98} +(-10.0694 - 4.12254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) $ 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{243}\right)$

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 $

$2$	−2.48775	−	0.0321643i	−1.75910	−	0.0227436i	−0.873402	−	0.487000i	$-0.838091\pi$
$2$	−2.48775	−	0.0321643i	−1.75910	−	0.0227436i	−0.885701	+	0.464256i	$0.846322\pi$
$3$	0.111243	+	1.72847i	0.0642263	+	0.997935i
$3$	0.111243	+	1.72847i	0.0642263	+	0.997935i
$4$	4.18852	+	0.108326i	2.09426	+	0.0541628i
$5$	2.61631	+	0.801736i	1.17005	+	0.358547i	0.816766	−	0.576969i	$-0.195765\pi$
$5$	2.61631	+	0.801736i	1.17005	+	0.358547i	0.353283	+	0.935516i	$0.385065\pi$
$6$	−0.221150	−	4.30359i	−0.0902840	−	1.75693i
$7$	0.558840	−	1.39354i	0.211222	−	0.526709i	−0.784392	−	0.620265i	$-0.787025\pi$
$7$	0.558840	−	1.39354i	0.211222	−	0.526709i	0.995614	+	0.0935559i	$0.0298234\pi$
$8$	−5.44433	−	0.211265i	−1.92486	−	0.0746933i
$9$	−2.97525	+	0.384562i	−0.991750	+	0.128187i
$10$	−6.48293	−	2.07867i	−2.05008	−	0.657332i
$11$	3.15263	+	1.79310i	0.950553	+	0.540640i	0.889221	−	0.457478i	$-0.151247\pi$
$11$	3.15263	+	1.79310i	0.950553	+	0.540640i	0.0613320	+	0.998117i	$0.480465\pi$
$12$	0.278706	+	7.25180i	0.0804556	+	2.09341i
$13$	−1.89074	−	4.23194i	−0.524397	−	1.17373i	−0.961622	−	0.274377i	$-0.911528\pi$
$13$	−1.89074	−	4.23194i	−0.524397	−	1.17373i	0.437225	−	0.899352i	$-0.355961\pi$
$14$	−1.43508	+	3.44880i	−0.383540	+	0.921732i
$15$	−1.09473	+	4.61141i	−0.282659	+	1.19066i
$16$	5.16867	+	0.267528i	1.29217	+	0.0668821i
$17$	7.11213	+	3.23286i	1.72494	+	0.784083i	0.994921	+	0.100661i	$0.0320958\pi$
$17$	7.11213	+	3.23286i	1.72494	+	0.784083i	0.730023	+	0.683422i	$0.239509\pi$
$18$	7.41404	−	0.860996i	1.74751	−	0.202939i
$19$	3.02456	+	4.40991i	0.693881	+	1.01170i	0.998249	+	0.0591493i	$0.0188388\pi$
$19$	3.02456	+	4.40991i	0.693881	+	1.01170i	−0.304368	+	0.952555i	$0.598445\pi$
$20$	10.8716	+	3.64150i	2.43097	+	0.814264i
$21$	2.47087	+	0.810919i	0.539188	+	0.176957i
$22$	−7.78527	−	4.56218i	−1.65982	−	0.972660i
$23$	0.788145	−	2.40449i	0.164340	−	0.501371i	−0.834422	−	0.551126i	$-0.814198\pi$
$23$	0.788145	−	2.40449i	0.164340	−	0.501371i	0.998761	+	0.0497558i	$0.0158443\pi$
$24$	−0.240479	−	9.43388i	−0.0490875	−	1.92568i
$25$	2.06072	+	1.39386i	0.412145	+	0.278771i
$26$	4.56757	+	10.5888i	0.895773	+	2.07664i
$27$	−0.995682	−	5.09986i	−0.191619	−	0.981469i
$28$	2.49167	−	5.77634i	0.470881	−	1.09163i
$29$	−3.87709	+	2.47880i	−0.719958	+	0.460301i	−0.846998	−	0.531596i	$-0.821592\pi$
$29$	−3.87709	+	2.47880i	−0.719958	+	0.460301i	0.127040	+	0.991898i	$0.459452\pi$
$30$	2.87174	−	11.4368i	0.524306	−	2.08807i
$31$	−2.21573	−	8.16359i	−0.397957	−	1.46622i	−0.826621	−	0.562759i	$-0.809740\pi$
$31$	−2.21573	−	8.16359i	−0.397957	−	1.46622i	0.428664	−	0.903464i	$-0.358985\pi$
$32$	−1.97566	−	0.127888i	−0.349250	−	0.0226077i
$33$	−2.74862	+	5.64871i	−0.478473	+	0.983314i
$34$	−17.5892	−	8.27129i	−3.01652	−	1.41851i
$35$	2.57935	−	3.19789i	0.435990	−	0.540543i
$36$	−12.5036	+	1.28845i	−2.08393	+	0.214742i
$37$	6.29290	+	1.23588i	1.03455	+	0.203178i	0.681034	−	0.732252i	$-0.261531\pi$
$37$	6.29290	+	1.23588i	1.03455	+	0.203178i	0.353512	+	0.935430i	$0.384987\pi$
$38$	−7.38250	−	11.0680i	−1.19760	−	1.79547i
$39$	7.10447	−	3.73887i	1.13763	−	0.598699i
$40$	−14.0747	−	4.91764i	−2.22540	−	0.777548i
$41$	0.249606	−	0.0945212i	0.0389819	−	0.0147617i	−0.334572	−	0.942370i	$-0.608592\pi$
$41$	0.249606	−	0.0945212i	0.0389819	−	0.0147617i	0.373554	+	0.927608i	$0.378139\pi$
$42$	−6.12081	−	2.09684i	−0.944462	−	0.323549i
$43$	4.02908	−	1.76895i	0.614429	−	0.269763i	−0.0714895	−	0.997441i	$-0.522775\pi$
$43$	4.02908	−	1.76895i	0.614429	−	0.269763i	0.685918	+	0.727679i	$0.259401\pi$
$44$	13.0106	+	7.85194i	1.96142	+	1.18372i
$45$	−8.09249	−	1.37923i	−1.20636	−	0.205604i
$46$	−2.03804	+	5.95641i	−0.300493	+	0.878225i
$47$	−0.976517	+	3.59786i	−0.142440	+	0.524801i	0.857507	+	0.514472i	$0.172012\pi$
$47$	−0.976517	+	3.59786i	−0.142440	+	0.524801i	−0.999947	+	0.0103290i	$0.996712\pi$
$48$	0.112563	+	8.96368i	0.0162471	+	1.29380i
$49$	3.43080	+	3.27897i	0.490115	+	0.468424i
$50$	−5.08173	−	3.53384i	−0.718665	−	0.499761i
$51$	−4.79674	+	12.6528i	−0.671678	+	1.77174i
$52$	−7.46098	−	17.9304i	−1.03465	−	2.48650i
$53$	6.17116	−	6.54105i	0.847674	−	0.898482i	−0.148225	−	0.988954i	$-0.547356\pi$
$53$	6.17116	−	6.54105i	0.847674	−	0.898482i	0.995899	+	0.0904714i	$0.0288374\pi$
$54$	2.31297	+	12.7192i	0.314756	+	1.73086i
$55$	6.81066	+	7.21888i	0.918349	+	0.973393i
$56$	−3.33691	+	7.46883i	−0.445914	+	0.998064i
$57$	−7.28597	+	5.71845i	−0.965050	+	0.757427i
$58$	9.72496	−	6.04192i	1.27695	−	0.793343i
$59$	−10.3181	+	1.75067i	−1.34331	+	0.227918i	−0.794109	−	0.607775i	$-0.792062\pi$
$59$	−10.3181	+	1.75067i	−1.34331	+	0.227918i	−0.549197	+	0.835693i	$0.685066\pi$
$60$	−5.08485	+	19.1964i	−0.656451	+	2.47824i
$61$	1.98810	−	3.65881i	0.254551	−	0.468463i	−0.719592	−	0.694397i	$-0.755671\pi$
$61$	1.98810	−	3.65881i	0.254551	−	0.468463i	0.974143	+	0.225934i	$0.0725435\pi$
$62$	5.24960	+	20.3802i	0.666700	+	2.58829i
$63$	−1.12679	+	4.36104i	−0.141962	+	0.549440i
$64$	−5.40923	−	0.420439i	−0.676154	−	0.0525548i
$65$	−1.55386	−	12.5879i	−0.192733	−	1.56134i
$66$	7.01955	−	13.9641i	0.864047	−	1.71887i
$67$	−8.85457	+	4.59122i	−1.08176	+	0.560907i	−0.905893	−	0.423507i	$-0.860799\pi$
$67$	−8.85457	+	4.59122i	−1.08176	+	0.560907i	−0.175865	+	0.984414i	$0.556272\pi$
$68$	29.4391	+	14.3113i	3.57001	+	1.73550i
$69$	4.24377	+	1.09481i	0.510890	+	0.131799i
$70$	−6.51963	+	7.87259i	−0.779245	+	0.940954i
$71$	7.83335	+	6.07131i	0.929648	+	0.720532i	0.960291	−	0.278999i	$-0.0900026\pi$
$71$	7.83335	+	6.07131i	0.929648	+	0.720532i	−0.0306435	+	0.999530i	$0.509756\pi$
$72$	16.2795	−	1.46512i	1.91855	−	0.172666i
$73$	5.11723	−	1.64077i	0.598926	−	0.192038i	0.00962821	−	0.999954i	$-0.496935\pi$
$73$	5.11723	−	1.64077i	0.598926	−	0.192038i	0.589298	+	0.807916i	$0.299404\pi$
$74$	−15.6154	−	3.27698i	−1.81525	−	0.380941i
$75$	−2.18000	+	3.71697i	−0.251725	+	0.429198i
$76$	12.1907	+	18.7987i	1.39837	+	2.15635i
$77$	4.26057	−	3.39126i	0.485537	−	0.386470i
$78$	−17.7944	+	9.07286i	−2.01482	+	1.02730i
$79$	−2.22272	+	11.7177i	−0.250075	+	1.31835i	0.603494	+	0.797367i	$0.293775\pi$
$79$	−2.22272	+	11.7177i	−0.250075	+	1.31835i	−0.853570	+	0.520979i	$0.825567\pi$
$80$	13.3084	+	4.84385i	1.48792	+	0.541559i
$81$	8.70422	−	2.28834i	0.967136	−	0.254260i
$82$	−0.623997	+	0.227116i	−0.0689090	+	0.0250808i
$83$	0.547989	+	3.36136i	0.0601496	+	0.368957i	0.999651	+	0.0264120i	$0.00840818\pi$
$83$	0.547989	+	3.36136i	0.0601496	+	0.368957i	−0.939502	+	0.342545i	$0.888711\pi$
$84$	10.2614	+	3.66421i	1.11961	+	0.399798i
$85$	16.0156	+	14.1602i	1.73714	+	1.53589i
$86$	−10.0802	+	4.27111i	−1.08698	+	0.460566i
$87$	−4.71584	−	6.42571i	−0.505591	−	0.688908i
$88$	−16.7851	−	10.4283i	−1.78930	−	1.11166i
$89$	−10.5517	−	4.31083i	−1.11847	−	0.456947i	−0.257848	−	0.966185i	$-0.583013\pi$
$89$	−10.5517	−	4.31083i	−1.11847	−	0.456947i	−0.860625	+	0.509239i	$0.829927\pi$
$90$	20.0877	+	3.69147i	2.11743	+	0.389115i
$91$	−6.95400	+	0.269847i	−0.728978	+	0.0282877i
$92$	3.56163	−	9.98587i	0.371326	−	1.04110i
$93$	13.8641	−	4.73798i	1.43764	−	0.491306i
$94$	2.54505	−	8.91915i	0.262502	−	0.919940i
$95$	4.37760	+	13.9626i	0.449132	+	1.43253i
$96$	0.00127322	−	3.42910i	0.000129947	−	0.349981i
$97$	3.67167	−	15.9508i	0.372801	−	1.61956i	−0.355762	−	0.934577i	$-0.615779\pi$
$97$	3.67167	−	15.9508i	0.372801	−	1.61956i	0.728563	−	0.684978i	$-0.240188\pi$
$98$	−8.42950	−	8.26760i	−0.851508	−	0.835153i
$99$	−10.0694	−	4.12254i	−1.01201	−	0.414331i
$100$	8.48039	+	6.06142i	0.848039	+	0.606142i
$101$	−1.62088	+	10.8216i	−0.161284	+	1.07679i	0.748929	+	0.662651i	$0.230569\pi$
$101$	−1.62088	+	10.8216i	−0.161284	+	1.07679i	−0.910212	+	0.414142i	$0.864082\pi$
$102$	12.3400	−	31.3226i	1.22185	−	3.10140i
$103$	1.05782	+	2.96586i	0.104231	+	0.292235i	0.982596	−	0.185754i	$-0.0594728\pi$
$103$	1.05782	+	2.96586i	0.104231	+	0.292235i	−0.878366	+	0.477989i	$0.841366\pi$
$104$	9.39975	+	23.4395i	0.921721	+	2.29843i
$105$	5.81441	+	4.10260i	0.567429	+	0.400373i
$106$	−15.5627	+	16.0740i	−1.51158	+	1.56124i
$107$	0.699037	+	12.0020i	0.0675785	+	1.16028i	0.846229	+	0.532820i	$0.178868\pi$
$107$	0.699037	+	12.0020i	0.0675785	+	1.16028i	−0.778650	+	0.627458i	$0.784095\pi$
$108$	−3.61799	−	21.4687i	−0.348141	−	2.06583i
$109$	−0.663935	+	11.3993i	−0.0635934	+	1.09186i	0.804015	+	0.594609i	$0.202693\pi$
$109$	−0.663935	+	11.3993i	−0.0635934	+	1.09186i	−0.867608	+	0.497248i	$0.834344\pi$
$110$	−16.7110	−	18.1778i	−1.59333	−	1.73318i
$111$	−1.43615	+	11.0146i	−0.136314	+	1.04546i
$112$	3.26127	−	7.05325i	0.308161	−	0.666470i
$113$	−8.83426	+	6.48853i	−0.831057	+	0.610389i	−0.922750	−	0.385398i	$-0.874064\pi$
$113$	−8.83426	+	6.48853i	−0.831057	+	0.610389i	0.0916936	+	0.995787i	$0.470772\pi$
$114$	18.3096	−	13.9917i	1.71485	−	1.31044i
$115$	3.98980	−	5.65900i	0.372050	−	0.527705i
$116$	−16.5078	+	9.96251i	−1.53271	+	0.924996i
$117$	7.25287	+	11.8640i	0.670528	+	1.09682i
$118$	25.7252	−	4.02335i	2.36820	−	0.370379i
$119$	8.47966	−	8.10439i	0.777330	−	0.742928i
$120$	6.93431	−	24.8748i	0.633013	−	2.27074i
$121$	1.10116	+	1.85157i	0.100106	+	0.168325i
$122$	−5.06358	+	9.03825i	−0.458435	+	0.818285i
$123$	0.191144	+	0.420923i	0.0172349	+	0.0379534i
$124$	−8.39631	−	34.4334i	−0.754011	−	3.09221i
$125$	−4.31572	−	5.35065i	−0.386010	−	0.478577i
$126$	2.94343	−	10.8129i	0.262221	−	0.963292i
$127$	0.0432237	+	2.22860i	0.00383549	+	0.197757i	0.996828	+	0.0795820i	$0.0253586\pi$
$127$	0.0432237	+	2.22860i	0.00383549	+	0.197757i	−0.992993	+	0.118175i	$0.962296\pi$
$128$	17.3867	+	1.57778i	1.53678	+	0.139457i
$129$	3.50580	+	6.76738i	0.308668	+	0.595834i
$130$	3.46074	+	31.3656i	0.303527	+	2.75094i
$131$	−1.73426	+	0.157377i	−0.151523	+	0.0137501i	−0.165874	−	0.986147i	$-0.553045\pi$
$131$	−1.73426	+	0.157377i	−0.151523	+	0.0137501i	0.0143519	+	0.999897i	$0.495431\pi$
$132$	−12.1245	+	23.3620i	−1.05531	+	2.03340i
$133$	7.83564	−	1.75041i	0.679437	−	0.151780i
$134$	22.1756	−	11.1370i	1.91568	−	0.962091i
$135$	1.48373	−	14.1411i	0.127699	−	1.21707i
$136$	−38.0378	−	19.1033i	−3.26171	−	1.63809i
$137$	−16.4109	−	4.11424i	−1.40208	−	0.351503i	−0.532973	−	0.846132i	$-0.678925\pi$
$137$	−16.4109	−	4.11424i	−1.40208	−	0.351503i	−0.869104	+	0.494629i	$0.835304\pi$
$138$	−10.5222	−	2.86010i	−0.895711	−	0.243468i
$139$	0.0997342	+	0.0142798i	0.00845934	+	0.00121120i	0.145962	−	0.989290i	$-0.453372\pi$
$139$	0.0997342	+	0.0142798i	0.00845934	+	0.00121120i	−0.137502	+	0.990501i	$0.543907\pi$
$140$	11.1501	−	13.1150i	0.942353	−	1.10842i
$141$	−6.32744	−	1.28765i	−0.532866	−	0.108440i
$142$	−19.2921	−	15.3558i	−1.61896	−	1.28863i
$143$	1.62749	−	16.7320i	0.136097	−	1.39920i
$144$	−15.4810	+	1.19171i	−1.29008	+	0.0993093i
$145$	−12.1310	+	3.37690i	−1.00743	+	0.280436i
$146$	−12.7831	+	3.91724i	−1.05794	+	0.324193i
$147$	−5.28596	+	6.29482i	−0.435979	+	0.519188i
$148$	26.2241	+	5.85821i	2.15560	+	0.481542i
$149$	−11.8790	+	2.97810i	−0.973169	+	0.243975i	−0.696950	−	0.717120i	$-0.745460\pi$
$149$	−11.8790	+	2.97810i	−0.973169	+	0.243975i	−0.276219	+	0.961095i	$0.589082\pi$
$150$	5.54285	−	9.17675i	0.452572	−	0.749279i
$151$	−2.38027	−	2.79974i	−0.193703	−	0.227839i	0.656457	−	0.754364i	$-0.272055\pi$
$151$	−2.38027	−	2.79974i	−0.193703	−	0.227839i	−0.850160	+	0.526525i	$0.823495\pi$
$152$	−15.5350	−	24.6480i	−1.26006	−	1.99922i
$153$	−22.4036	−	6.88351i	−1.81122	−	0.556499i
$154$	−10.7083	+	8.29956i	−0.862900	+	0.668798i
$155$	0.748002	−	23.1349i	0.0600809	−	1.85824i
$156$	30.1622	−	14.8907i	2.41491	−	1.19221i
$157$	1.70034	−	13.7746i	0.135702	−	1.09933i	−0.758502	−	0.651671i	$-0.774068\pi$
$157$	1.70034	−	13.7746i	0.135702	−	1.09933i	0.894204	−	0.447659i	$-0.147742\pi$
$158$	5.90645	−	29.0792i	0.469892	−	2.31342i
$159$	11.9925	+	9.93905i	0.951070	+	0.788218i
$160$	−5.06640	−	1.91855i	−0.400534	−	0.151675i
$161$	−2.91031	−	2.44204i	−0.229364	−	0.192460i
$162$	−21.7275	+	5.41284i	−1.70707	+	0.425273i
$163$	−2.49348	+	2.09228i	−0.195304	+	0.163880i	−0.735196	−	0.677855i	$-0.762910\pi$
$163$	−2.49348	+	2.09228i	−0.195304	+	0.163880i	0.539891	+	0.841735i	$0.318465\pi$
$164$	1.05572	−	0.368865i	0.0824378	−	0.0288035i
$165$	−11.7200	+	12.5751i	−0.912401	+	0.978970i
$166$	−1.25514	−	8.37983i	−0.0974180	−	0.650401i
$167$	−0.850600	+	1.66673i	−0.0658214	+	0.128976i	−0.921286	−	0.388886i	$-0.872860\pi$
$167$	−0.850600	+	1.66673i	−0.0658214	+	0.128976i	0.855465	+	0.517861i	$0.173272\pi$
$168$	−13.2809	−	4.93692i	−1.02464	−	0.380891i
$169$	−5.66072	+	6.31965i	−0.435440	+	0.486127i
$170$	−39.3874	−	35.7421i	−3.02087	−	2.74130i
$171$	−10.6947	−	11.9575i	−0.817845	−	0.914410i
$172$	17.0675	−	6.97284i	1.30138	−	0.531674i
$173$	12.7487	+	2.16306i	0.969264	+	0.164454i	0.630306	−	0.776347i	$-0.282930\pi$
$173$	12.7487	+	2.16306i	0.969264	+	0.164454i	0.338958	+	0.940801i	$0.389925\pi$
$174$	11.5251	+	16.1372i	0.873719	+	1.22336i
$175$	3.09401	−	2.09276i	0.233885	−	0.158198i
$176$	15.8152	+	10.1114i	1.19212	+	0.762172i
$177$	−4.17381	−	17.6399i	−0.313723	−	1.32589i
$178$	26.1112	+	11.0636i	1.95712	+	0.829254i
$179$	6.68557	+	13.9817i	0.499703	+	1.04504i	0.985296	+	0.170855i	$0.0546531\pi$
$179$	6.68557	+	13.9817i	0.499703	+	1.04504i	−0.485593	+	0.874185i	$0.661396\pi$
$180$	−33.7462	−	6.65356i	−2.51529	−	0.495927i
$181$	−22.2797	−	6.20198i	−1.65604	−	0.460990i	−0.690947	−	0.722905i	$-0.742806\pi$
$181$	−22.2797	−	6.20198i	−1.65604	−	0.460990i	−0.965091	+	0.261915i	$0.915646\pi$
$182$	17.3085	−	0.447641i	1.28299	−	0.0331813i
$183$	6.54533	+	3.02937i	0.483845	+	0.223938i
$184$	−4.79890	+	12.9243i	−0.353780	+	0.952793i
$185$	15.4733	+	8.27870i	1.13762	+	0.608662i
$186$	−34.6427	+	11.3410i	−2.54013	+	0.831560i
$187$	16.6251	+	22.9447i	1.21574	+	1.67789i
$188$	−4.47990	+	14.9639i	−0.326730	+	1.09136i
$189$	−7.66330	−	1.46248i	−0.557423	−	0.106380i
$190$	−10.4413	−	34.8762i	−0.757488	−	2.53019i
$191$	1.62908	−	2.13018i	0.117876	−	0.154134i	−0.731651	−	0.681680i	$-0.761250\pi$
$191$	1.62908	−	2.13018i	0.117876	−	0.154134i	0.849527	+	0.527546i	$0.176888\pi$
$192$	0.124978	−	9.39649i	0.00901948	−	0.678133i
$193$	−6.51760	+	3.06489i	−0.469147	+	0.220616i	−0.645573	−	0.763698i	$-0.723382\pi$
$193$	−6.51760	+	3.06489i	−0.469147	+	0.220616i	0.176427	+	0.984314i	$0.443546\pi$
$194$	−9.64722	+	39.5634i	−0.692630	+	2.84049i
$195$	21.5851	−	4.08614i	1.54574	−	0.292614i
$196$	14.0148	+	14.1057i	1.00106	+	1.00755i
$197$	19.1587	−	3.76265i	1.36500	−	0.268078i	0.544040	−	0.839059i	$-0.316894\pi$
$197$	19.1587	−	3.76265i	1.36500	−	0.268078i	0.820963	+	0.570982i	$0.193437\pi$
$198$	24.9176	+	10.5797i	1.77081	+	0.751867i
$199$	−14.3812	+	7.93522i	−1.01946	+	0.562512i	−0.902530	−	0.430628i	$-0.858292\pi$
$199$	−14.3812	+	7.93522i	−1.01946	+	0.562512i	−0.116927	+	0.993140i	$0.537304\pi$
$200$	−10.9248	−	8.02396i	−0.772499	−	0.567380i
$201$	−8.92083	−	14.7942i	−0.629227	−	1.04350i
$202$	4.38041	−	26.8694i	0.308205	−	1.89052i
$203$	1.28763	+	6.78814i	0.0903741	+	0.476434i
$204$	−21.4619	+	52.4768i	−1.50263	+	3.67411i
$205$	0.728828	−	0.0471785i	0.0509035	−	0.00329509i
$206$	−2.53621	−	7.41234i	−0.176706	−	0.516442i
$207$	−1.42025	+	7.45705i	−0.0987144	+	0.518300i
$208$	−8.64045	−	22.3793i	−0.599108	−	1.55173i
$209$	1.62790	+	19.3262i	0.112604	+	1.33682i
$210$	−14.3328	−	10.3932i	−0.989059	−	0.717202i
$211$	9.99009	−	14.9774i	0.687746	−	1.03109i	−0.309045	−	0.951047i	$-0.600009\pi$
$211$	9.99009	−	14.9774i	0.687746	−	1.03109i	0.996792	−	0.0800405i	$-0.0255050\pi$
$212$	26.5566	−	26.7288i	1.82391	−	1.83574i
$213$	−9.62269	+	14.2151i	−0.659336	+	0.974006i
$214$	−1.35299	−	29.8804i	−0.0924886	−	2.04258i
$215$	11.9595	−	1.39787i	0.815634	−	0.0953340i
$216$	4.34340	+	27.9757i	0.295531	+	1.90350i
$217$	−12.6145	−	1.47443i	−0.856331	−	0.100091i
$218$	2.01835	−	28.3373i	0.136700	−	1.91924i
$219$	3.40529	+	8.66248i	0.230108	+	0.585356i
$220$	27.7446	+	30.9742i	1.87054	+	2.08828i
$221$	0.234075	−	36.2106i	0.0157456	−	2.43579i
$222$	3.92706	−	27.3553i	0.263567	−	1.83597i
$223$	2.84055	−	2.51147i	0.190217	−	0.168181i	−0.561910	−	0.827198i	$-0.689933\pi$
$223$	2.84055	−	2.51147i	0.190217	−	0.168181i	0.752127	+	0.659018i	$0.229028\pi$
$224$	−1.28230	+	2.68169i	−0.0856769	+	0.179178i
$225$	−6.66719	−	3.35459i	−0.444479	−	0.223639i
$226$	22.1861	−	15.8577i	1.47580	−	1.05484i
$227$	0.217562	+	0.426309i	0.0144401	+	0.0282951i	0.897821	−	0.440361i	$-0.145150\pi$
$227$	0.217562	+	0.426309i	0.0144401	+	0.0282951i	−0.883380	+	0.468657i	$0.844738\pi$
$228$	−31.1369	+	23.1626i	−2.06209	+	1.53398i
$229$	12.8980	+	16.8654i	0.852326	+	1.11450i	0.992241	+	0.124333i	$0.0396792\pi$
$229$	12.8980	+	16.8654i	0.852326	+	1.11450i	−0.139915	+	0.990164i	$0.544683\pi$
$230$	−10.1076	+	13.9498i	−0.666477	+	0.919825i
$231$	6.33567	+	6.98704i	0.416856	+	0.459713i
$232$	21.6318	−	12.6763i	1.42020	−	0.832240i
$233$	−5.91311	−	27.2979i	−0.387381	−	1.78835i	−0.588195	−	0.808719i	$-0.700161\pi$
$233$	−5.91311	−	27.2979i	−0.387381	−	1.78835i	0.200815	−	0.979629i	$-0.435641\pi$
$234$	−17.6617	−	29.7478i	−1.15458	−	1.94468i
$235$	−5.43940	+	8.63020i	−0.354827	+	0.562972i
$236$	−43.4073	+	6.21500i	−2.82558	+	0.404562i
$237$	−20.5010	−	2.53839i	−1.33169	−	0.164886i
$238$	−21.3559	+	19.8889i	−1.38430	+	1.28921i
$239$	−5.62667	−	10.3550i	−0.363959	−	0.669812i	0.630354	−	0.776308i	$-0.282910\pi$
$239$	−5.62667	−	10.3550i	−0.363959	−	0.669812i	−0.994313	+	0.106495i	$0.966037\pi$
$240$	−6.89200	+	23.5420i	−0.444877	+	1.51963i
$241$	5.84391	−	9.82634i	0.376439	−	0.632970i	−0.610879	−	0.791724i	$-0.709184\pi$
$241$	5.84391	−	9.82634i	0.376439	−	0.632970i	0.987318	+	0.158754i	$0.0507476\pi$
$242$	−2.67986	−	4.64166i	−0.172268	−	0.298377i
$243$	4.92362	+	14.7905i	0.315850	+	0.948809i
$244$	8.72356	−	15.1096i	0.558469	−	0.967296i
$245$	6.34717	+	11.3294i	0.405506	+	0.723809i
$246$	−0.461980	−	1.05330i	−0.0294548	−	0.0671558i
$247$	12.9438	−	21.1378i	0.823597	−	1.34496i
$248$	10.3385	+	44.9133i	0.656494	+	2.85200i
$249$	−5.74906	+	1.32111i	−0.364332	+	0.0837222i
$250$	10.5643	+	13.4499i	0.668146	+	0.850646i
$251$	−1.06489	−	2.02164i	−0.0672151	−	0.127605i	0.848851	−	0.528633i	$-0.177295\pi$
$251$	−1.06489	−	2.02164i	−0.0672151	−	0.127605i	−0.916066	+	0.401028i	$0.868653\pi$
$252$	−5.19198	+	18.1443i	−0.327064	+	1.14298i
$253$	6.79621	−	6.16724i	0.427274	−	0.387731i
$254$	−0.0358482	−	5.54559i	−0.00224932	−	0.347961i
$255$	−22.6939	+	29.2578i	−1.42115	+	1.83220i
$256$	−32.4098	−	3.36405i	−2.02561	−	0.210253i
$257$	−18.5969	+	2.41776i	−1.16004	+	0.150816i	−0.684591	−	0.728927i	$-0.740019\pi$
$257$	−18.5969	+	2.41776i	−1.16004	+	0.150816i	−0.475450	+	0.879743i	$0.657715\pi$
$258$	−8.50387	−	16.9483i	−0.529428	−	1.05515i
$259$	5.23898	−	8.07875i	0.325534	−	0.501989i
$260$	−5.14480	−	52.8931i	−0.319067	−	3.28029i
$261$	10.5821	−	8.86603i	0.655014	−	0.548794i
$262$	4.31945	−	0.335734i	0.266857	−	0.0207417i
$263$	−0.540396	−	2.66053i	−0.0333223	−	0.164055i	0.959889	−	0.280380i	$-0.0904606\pi$
$263$	−0.540396	−	2.66053i	−0.0333223	−	0.164055i	−0.993211	+	0.116325i	$0.962889\pi$
$264$	16.1577	−	30.1727i	0.994440	−	1.85700i
$265$	21.3899	−	12.1658i	1.31397	−	0.747337i
$266$	−19.5494	+	4.10255i	−1.19865	+	0.251544i
$267$	6.27736	−	18.7178i	0.384168	−	1.14551i
$268$	−37.5849	+	18.2713i	−2.29586	+	1.11609i
$269$	12.1270	−	16.2893i	0.739394	−	0.993178i	−0.260224	−	0.965548i	$-0.583797\pi$
$269$	12.1270	−	16.2893i	0.739394	−	0.993178i	0.999618	−	0.0276300i	$-0.00879603\pi$
$270$	−4.14599	+	35.1317i	−0.252317	+	2.13805i
$271$	7.27398	+	9.77066i	0.441863	+	0.593525i	0.966139	−	0.258024i	$-0.0830712\pi$
$271$	7.27398	+	9.77066i	0.441863	+	0.593525i	−0.524276	+	0.851549i	$0.675664\pi$
$272$	35.8954	+	18.6123i	2.17648	+	1.12854i
$273$	−1.24001	−	11.9898i	−0.0750488	−	0.725656i
$274$	40.6938	+	10.7630i	2.45840	+	0.650219i
$275$	3.99737	+	8.08939i	0.241051	+	0.487809i
$276$	17.6565	+	5.04533i	1.06280	+	0.303693i
$277$	10.4055	−	7.23602i	0.625207	−	0.434770i	−0.215317	−	0.976544i	$-0.569078\pi$
$277$	10.4055	−	7.23602i	0.625207	−	0.434770i	0.840524	+	0.541774i	$0.182247\pi$
$278$	−0.247654	−	0.0387324i	−0.0148533	−	0.00232301i
$279$	9.73176	+	23.4366i	0.582625	+	1.40311i
$280$	−14.7184	+	16.8654i	−0.879594	+	1.00790i
$281$	7.40619	−	14.9877i	0.441816	−	0.894093i	−0.556195	−	0.831052i	$-0.687739\pi$
$281$	7.40619	−	14.9877i	0.441816	−	0.894093i	0.998011	−	0.0630407i	$-0.0200798\pi$
$282$	15.6996	+	3.40686i	0.934900	+	0.202876i
$283$	6.66617	−	5.74206i	0.396263	−	0.341330i	−0.431796	−	0.901971i	$-0.642120\pi$
$283$	6.66617	−	5.74206i	0.396263	−	0.341330i	0.828059	+	0.560641i	$0.189445\pi$
$284$	32.1525	+	26.2783i	1.90790	+	1.55933i
$285$	−23.6470	+	9.11981i	−1.40073	+	0.540211i
$286$	−4.58695	+	41.5727i	−0.271232	+	2.45824i
$287$	0.00777077	−	0.400659i	0.000458694	−	0.0236501i
$288$	5.92726	−	0.379264i	0.349267	−	0.0223483i
$289$	28.9531	+	33.1766i	1.70312	+	1.95156i
$290$	30.2875	−	8.01069i	1.77854	−	0.470404i
$291$	27.9789	+	4.57197i	1.64015	+	0.268013i
$292$	21.6114	−	6.31809i	1.26471	−	0.369738i
$293$	−0.371089	+	4.40552i	−0.0216792	+	0.257373i	0.977287	+	0.211919i	$0.0679714\pi$
$293$	−0.371089	+	4.40552i	−0.0216792	+	0.257373i	−0.998966	+	0.0454540i	$0.985527\pi$
$294$	13.3526	−	15.4899i	0.778740	−	0.903389i
$295$	−28.3990	−	3.69212i	−1.65345	−	0.214963i
$296$	−33.9995	−	8.05803i	−1.97618	−	0.468363i
$297$	6.00555	−	17.8633i	0.348477	−	1.03654i
$298$	29.6478	−	7.02667i	1.71745	−	0.407044i
$299$	−11.6658	+	1.21088i	−0.674652	+	0.0700271i
$300$	−9.53363	+	15.3324i	−0.550424	+	0.885219i
$301$	−0.213497	−	6.60325i	−0.0123058	−	0.380605i
$302$	5.83145	+	7.04160i	0.335562	+	0.405198i
$303$	−18.8852	−	1.59782i	−1.08493	−	0.0917922i
$304$	14.4532	+	23.6026i	0.828947	+	1.35370i
$305$	8.13490	−	7.97865i	0.465803	−	0.456856i
$306$	55.5131	+	17.8450i	3.17347	+	1.02013i
$307$	−5.26906	+	7.68248i	−0.300721	+	0.438462i	−0.945362	−	0.326024i	$-0.894291\pi$
$307$	−5.26906	+	7.68248i	−0.300721	+	0.438462i	0.644640	+	0.764486i	$0.277007\pi$
$308$	18.2129	−	13.7428i	1.03777	−	0.783071i
$309$	−5.00874	+	2.15836i	−0.284937	+	0.122785i
$310$	−2.60496	+	57.5297i	−0.147952	+	3.26747i
$311$	−1.10131	−	15.4621i	−0.0624495	−	0.876778i	−0.927198	−	0.374572i	$-0.877790\pi$
$311$	−1.10131	−	15.4621i	−0.0624495	−	0.876778i	0.864748	−	0.502206i	$-0.167478\pi$
$312$	−39.4689	+	18.8547i	−2.23449	+	1.06744i
$313$	−5.86553	−	15.7969i	−0.331539	−	0.892896i	−0.990099	−	0.140368i	$-0.955172\pi$
$313$	−5.86553	−	15.7969i	−0.331539	−	0.892896i	0.658560	−	0.752528i	$-0.271166\pi$
$314$	−4.67307	+	34.2129i	−0.263717	+	1.93075i
$315$	−6.44442	+	10.5065i	−0.363102	+	0.591971i
$316$	−10.5792	+	48.8391i	−0.595128	+	2.74741i
$317$	−8.83894	−	26.9660i	−0.496444	−	1.51456i	−0.822251	−	0.569125i	$-0.807282\pi$
$317$	−8.83894	−	26.9660i	−0.496444	−	1.51456i	0.325807	−	0.945436i	$-0.394364\pi$
$318$	−29.5147	−	25.1116i	−1.65510	−	1.40819i
$319$	−16.6678	+	0.862717i	−0.933216	+	0.0483029i
$320$	−13.8151	−	5.43677i	−0.772290	−	0.303925i
$321$	−20.6674	+	2.54341i	−1.15354	+	0.141959i
$322$	7.16156	+	6.16878i	0.399098	+	0.343773i
$323$	7.25442	+	41.1418i	0.403647	+	2.28919i
$324$	36.7057	−	8.64185i	2.03921	−	0.480103i
$325$	2.00242	−	11.3563i	0.111074	−	0.629933i
$326$	6.27044	−	5.12485i	0.347287	−	0.283839i
$327$	−19.7773	+	0.120502i	−1.09369	+	0.00666379i
$328$	−1.37891	+	0.461871i	−0.0761374	+	0.0255026i
$329$	4.46805	+	3.37144i	0.246331	+	0.185874i
$330$	29.5609	−	30.9067i	1.62727	−	1.70136i
$331$	−10.9396	+	5.85301i	−0.601294	+	0.321711i	−0.744129	−	0.668036i	$-0.767135\pi$
$331$	−10.9396	+	5.85301i	−0.601294	+	0.321711i	0.142835	+	0.989746i	$0.454378\pi$
$332$	1.93114	+	14.1385i	0.105985	+	0.775949i
$333$	−19.1982	−	1.25706i	−1.05206	−	0.0688863i
$334$	2.16969	−	4.11905i	0.118720	−	0.225384i
$335$	−26.8472	+	4.91304i	−1.46682	+	0.268428i
$336$	12.5542	+	4.85240i	0.684886	+	0.264720i
$337$	−2.34328	−	2.42027i	−0.127647	−	0.131840i	0.651587	−	0.758574i	$-0.274103\pi$
$337$	−2.34328	−	2.42027i	−0.127647	−	0.131840i	−0.779234	+	0.626733i	$0.784392\pi$
$338$	14.2857	−	15.5396i	0.777040	−	0.845244i
$339$	−12.1980	−	14.5480i	−0.662505	−	0.790138i
$340$	65.5479	+	61.0452i	3.55483	+	3.31064i
$341$	7.65275	−	29.7098i	0.414419	−	1.60887i
$342$	26.2211	+	30.0911i	1.41788	+	1.62714i
$343$	16.0545	−	7.29767i	0.866862	−	0.394037i
$344$	−22.3093	+	8.77955i	−1.20284	+	0.473362i
$345$	10.2253	+	6.26674i	0.550511	+	0.337390i
$346$	−31.6459	−	5.79120i	−1.70129	−	0.311337i
$347$	−16.7803	+	21.3637i	−0.900812	+	1.14686i	0.0877642	+	0.996141i	$0.472028\pi$
$347$	−16.7803	+	21.3637i	−0.900812	+	1.14686i	−0.988576	+	0.150721i	$0.951841\pi$
$348$	−19.0563	−	27.4251i	−1.02153	−	1.47014i
$349$	−1.07918	−	3.78199i	−0.0577671	−	0.202445i	0.927391	−	0.374093i	$-0.122046\pi$
$349$	−1.07918	−	3.78199i	−0.0577671	−	0.202445i	−0.985158	+	0.171647i	$0.945091\pi$
$350$	−7.76443	+	5.10674i	−0.415026	+	0.272967i
$351$	−19.6997	+	13.8562i	−1.05149	+	0.739588i
$352$	−5.99920	−	3.94574i	−0.319758	−	0.210308i
$353$	−2.79119	+	8.90266i	−0.148560	+	0.473841i	−0.998601	−	0.0528756i	$-0.983161\pi$
$353$	−2.79119	+	8.90266i	−0.148560	+	0.473841i	0.850041	+	0.526716i	$0.176577\pi$
$354$	9.81601	+	44.0178i	0.521715	+	2.33952i
$355$	15.6269	+	22.1647i	0.829389	+	1.17638i
$356$	−43.7289	−	19.1990i	−2.31762	−	1.01754i
$357$	14.9515	+	13.7553i	0.791320	+	0.728009i
$358$	−16.1823	−	34.9979i	−0.855261	−	1.84970i
$359$	−14.7369	−	8.13147i	−0.777783	−	0.429163i	0.0439507	−	0.999034i	$-0.486006\pi$
$359$	−14.7369	−	8.13147i	−0.777783	−	0.429163i	−0.821734	+	0.569871i	$0.806993\pi$
$360$	43.7668	+	9.21864i	2.30671	+	0.485865i
$361$	−3.45602	+	8.95131i	−0.181896	+	0.471121i
$362$	55.2268	+	16.1456i	2.90266	+	0.848593i
$363$	−3.07789	+	2.10931i	−0.161548	+	0.110710i
$364$	−29.1562	+	0.376963i	−1.52820	+	0.0197582i
$365$	14.7037	−	0.190106i	0.769628	−	0.00995058i
$366$	−16.1857	−	7.74683i	−0.846039	−	0.404933i
$367$	−4.49014	−	1.31269i	−0.234383	−	0.0685220i	0.161314	−	0.986903i	$-0.448427\pi$
$367$	−4.49014	−	1.31269i	−0.234383	−	0.0685220i	−0.395697	+	0.918381i	$0.629497\pi$
$368$	4.71693	−	12.2172i	0.245887	−	0.636864i
$369$	−0.706291	+	0.377213i	−0.0367681	+	0.0196369i
$370$	−38.2274	−	21.0930i	−1.98735	−	1.09657i
$371$	−5.66653	−	12.2552i	−0.294192	−	0.636257i
$372$	58.5832	−	18.3433i	3.03740	−	0.951055i
$373$	−6.36238	−	2.79338i	−0.329432	−	0.144636i	0.230733	−	0.973017i	$-0.425888\pi$
$373$	−6.36238	−	2.79338i	−0.329432	−	0.144636i	−0.560165	+	0.828381i	$0.689262\pi$
$374$	−40.6209	−	57.6155i	−2.10046	−	2.97922i
$375$	8.76838	−	8.05484i	0.452797	−	0.415950i
$376$	6.07658	−	19.3816i	0.313376	−	0.999530i
$377$	17.8207	+	11.7209i	0.917813	+	0.603655i
$378$	19.0173	+	3.88478i	0.978145	+	0.199811i
$379$	16.8267	−	11.0671i	0.864332	−	0.568480i	−0.0381190	−	0.999273i	$-0.512137\pi$
$379$	16.8267	−	11.0671i	0.864332	−	0.568480i	0.902451	+	0.430793i	$0.141766\pi$
$380$	16.8231	+	58.9568i	0.863009	+	3.02442i
$381$	−3.84728	+	0.322628i	−0.197102	+	0.0165287i
$382$	−4.12125	+	5.24694i	−0.210862	+	0.268457i
$383$	24.2650	+	4.44049i	1.23988	+	0.226899i	0.759703	−	0.650271i	$-0.225345\pi$
$383$	24.2650	+	4.44049i	1.23988	+	0.226899i	0.480181	+	0.877169i	$0.340571\pi$
$384$	−0.793001	+	30.2279i	−0.0404676	+	1.54256i
$385$	13.8659	−	5.45674i	0.706670	−	0.278101i
$386$	16.3127	−	7.41504i	0.830295	−	0.377415i
$387$	−11.3072	+	6.81251i	−0.574779	+	0.346299i
$388$	17.1067	−	66.4124i	0.868462	−	3.37158i
$389$	10.5779	+	9.85125i	0.536320	+	0.499478i	0.902279	−	0.431152i	$-0.141893\pi$
$389$	10.5779	+	9.85125i	0.536320	+	0.499478i	−0.365959	+	0.930631i	$0.619259\pi$
$390$	−53.8296	+	9.47101i	−2.72577	+	0.479583i
$391$	13.3788	−	14.5531i	0.676593	−	0.735980i
$392$	−17.9857	−	18.5766i	−0.908414	−	0.938259i
$393$	−0.464947	−	2.98011i	−0.0234535	−	0.150327i
$394$	−47.7831	+	8.74430i	−2.40728	+	0.440531i
$395$	−15.2098	+	28.8751i	−0.765289	+	1.45287i
$396$	−41.7294	−	18.3581i	−2.09698	−	0.922529i
$397$	−4.90272	−	35.8943i	−0.246061	−	1.80148i	−0.535766	−	0.844367i	$-0.679977\pi$
$397$	−4.90272	−	35.8943i	−0.246061	−	1.80148i	0.289705	−	0.957116i	$-0.406443\pi$
$398$	36.0320	−	19.2782i	1.80612	−	0.966331i
$399$	3.89720	+	13.3490i	0.195104	+	0.668285i
$400$	10.2783	+	7.75568i	0.513916	+	0.387784i
$401$	−11.2872	+	3.78069i	−0.563655	+	0.188799i	−0.585086	−	0.810971i	$-0.698939\pi$
$401$	−11.2872	+	3.78069i	−0.563655	+	0.188799i	0.0214308	+	0.999770i	$0.493178\pi$
$402$	21.7169	+	37.0910i	1.08314	+	1.84993i
$403$	−30.3584	+	24.8121i	−1.51226	+	1.23598i
$404$	−7.96135	+	45.1511i	−0.396092	+	2.24635i
$405$	24.6076	+	0.991490i	1.22276	+	0.0492676i
$406$	−2.98497	−	16.9286i	−0.148142	−	0.840152i
$407$	17.6231	+	15.1801i	0.873545	+	0.752448i
$408$	28.7881	−	67.8724i	1.42522	−	3.36018i
$409$	5.48829	+	2.15984i	0.271378	+	0.106797i	0.497975	−	0.867191i	$-0.334077\pi$
$409$	5.48829	+	2.15984i	0.271378	+	0.106797i	−0.226597	+	0.973989i	$0.572760\pi$
$410$	−1.81466	+	0.0939259i	−0.0896195	+	0.00463867i
$411$	5.28576	−	28.8235i	0.260727	−	1.42176i
$412$	4.10944	+	12.5372i	0.202458	+	0.617662i
$413$	−3.32655	+	15.3571i	−0.163689	+	0.755673i
$414$	3.77308	−	18.5056i	0.185437	−	0.909499i
$415$	−1.26121	+	9.23369i	−0.0619104	+	0.453264i
$416$	3.19424	+	8.60267i	0.156611	+	0.421781i
$417$	−0.0135875	+	0.173977i	−0.000665383	+	0.00851967i
$418$	−3.42818	−	48.1309i	−0.167678	−	2.35416i
$419$	−0.390376	+	8.62134i	−0.0190711	+	0.421180i	0.966992	+	0.254807i	$0.0820121\pi$
$419$	−0.390376	+	8.62134i	−0.0190711	+	0.421180i	−0.986063	+	0.166373i	$0.946795\pi$
$420$	23.9094	+	17.8137i	1.16666	+	0.869218i
$421$	23.6030	−	17.8101i	1.15034	−	0.868011i	0.157509	−	0.987518i	$-0.449654\pi$
$421$	23.6030	−	17.8101i	1.15034	−	0.868011i	0.992833	+	0.119506i	$0.0381311\pi$
$422$	−25.3346	+	36.9387i	−1.23327	+	1.79815i
$423$	1.52178	−	11.0801i	0.0739916	−	0.538731i
$424$	−34.9797	+	34.3079i	−1.69876	+	1.66614i
$425$	10.1500	+	16.5753i	0.492347	+	0.804020i
$426$	24.3960	−	35.0542i	1.18199	−	1.69838i
$427$	−3.98767	−	4.81520i	−0.192977	−	0.233024i
$428$	1.62781	+	50.3464i	0.0786830	+	2.43358i
$429$	29.1019	+	0.951745i	1.40505	+	0.0459507i
$430$	−29.7973	+	3.09288i	−1.43695	+	0.149152i
$431$	21.7773	−	5.16132i	1.04898	−	0.248612i	0.330242	−	0.943896i	$-0.392870\pi$
$431$	21.7773	−	5.16132i	1.04898	−	0.248612i	0.718735	+	0.695284i	$0.244722\pi$
$432$	−3.78200	−	26.6259i	−0.181961	−	1.28104i
$433$	−31.8098	−	7.53906i	−1.52868	−	0.362304i	−0.621625	−	0.783315i	$-0.713527\pi$
$433$	−31.8098	−	7.53906i	−1.52868	−	0.362304i	−0.907056	+	0.421011i	$0.861675\pi$
$434$	31.3344	+	4.07374i	1.50410	+	0.195546i
$435$	−7.18638	−	20.5925i	−0.344561	−	0.987335i
$436$	−4.01574	+	47.6744i	−0.192319	+	2.28319i
$437$	12.9874	−	3.79687i	0.621271	−	0.181629i
$438$	−8.19288	−	21.6596i	−0.391471	−	1.03493i
$439$	−9.10215	+	2.40741i	−0.434422	+	0.114899i	−0.466369	−	0.884590i	$-0.654438\pi$
$439$	−9.10215	+	2.40741i	−0.434422	+	0.114899i	0.0319472	+	0.999490i	$0.489829\pi$
$440$	−35.5543	−	40.7408i	−1.69499	−	1.94224i
$441$	−11.4685	−	8.43640i	−0.546117	−	0.401733i
$442$	−1.74701	+	90.0752i	−0.0830967	+	4.28444i
$443$	2.44453	−	22.1554i	0.116143	−	1.05263i	−0.785115	−	0.619350i	$-0.787396\pi$
$443$	2.44453	−	22.1554i	0.116143	−	1.05263i	0.901258	−	0.433283i	$-0.142645\pi$
$444$	−7.20852	+	45.9793i	−0.342101	+	2.18208i
$445$	−24.1503	−	19.7381i	−1.14483	−	0.935676i
$446$	−7.14735	+	6.15654i	−0.338437	+	0.291521i
$447$	−6.46903	−	20.2013i	−0.305974	−	0.955490i
$448$	−3.60880	+	7.30303i	−0.170500	+	0.345036i
$449$	−16.4564	+	18.8570i	−0.776626	+	0.889915i	−0.996325	−	0.0856528i	$-0.972702\pi$
$449$	−16.4564	+	18.8570i	−0.776626	+	0.889915i	0.219699	+	0.975568i	$0.429493\pi$
$450$	16.4784	+	8.55982i	0.776799	+	0.403514i
$451$	0.956401	+	0.149578i	0.0450352	+	0.00704337i
$452$	−37.7053	+	26.2203i	−1.77351	+	1.23330i
$453$	4.57448	−	4.42568i	0.214928	−	0.207937i
$454$	−0.527529	−	1.06755i	−0.0247581	−	0.0501024i
$455$	−18.4102	−	4.86927i	−0.863082	−	0.228275i
$456$	40.8753	−	29.5938i	1.91416	−	1.38586i
$457$	−28.7820	−	14.9239i	−1.34636	−	0.698109i	−0.373098	−	0.927792i	$-0.621704\pi$
$457$	−28.7820	−	14.9239i	−1.34636	−	0.698109i	−0.973266	+	0.229682i	$0.926231\pi$
$458$	−31.5446	−	42.3717i	−1.47398	−	1.97990i
$459$	9.40572	−	39.4898i	0.439021	−	1.84323i
$460$	17.3244	−	23.2706i	0.807752	−	1.08500i
$461$	17.4419	−	8.47911i	0.812352	−	0.394911i	0.0160958	−	0.999870i	$-0.494876\pi$
$461$	17.4419	−	8.47911i	0.812352	−	0.394911i	0.796257	+	0.604959i	$0.206810\pi$
$462$	−15.5368	−	17.5858i	−0.722838	−	0.818164i
$463$	16.5754	−	3.47843i	0.770323	−	0.161657i	0.196353	−	0.980533i	$-0.437090\pi$
$463$	16.5754	−	3.47843i	0.770323	−	0.161657i	0.573969	+	0.818877i	$0.305403\pi$
$464$	−20.7026	+	11.7749i	−0.961093	+	0.546635i
$465$	40.0713	−	1.28070i	1.85826	−	0.0593910i
$466$	13.8323	+	68.1006i	0.640769	+	3.15470i
$467$	15.1979	−	1.18127i	0.703275	−	0.0546629i	0.279125	−	0.960255i	$-0.409956\pi$
$467$	15.1979	−	1.18127i	0.703275	−	0.0546629i	0.424150	+	0.905592i	$0.360573\pi$
$468$	29.0936	+	50.4781i	1.34485	+	2.33335i
$469$	1.44977	+	14.9050i	0.0669443	+	0.688247i
$470$	13.8094	−	21.2948i	0.636982	−	0.982256i
$471$	23.9981	+	1.40667i	1.10578	+	0.0648161i
$472$	56.5451	−	7.35136i	2.60270	−	0.338374i
$473$	15.8741	+	1.64769i	0.729892	+	0.0757608i
$474$	50.9198	+	6.97428i	2.33882	+	0.320339i
$475$	0.0859969	+	13.3034i	0.00394581	+	0.610402i
$476$	36.3952	−	33.0268i	1.66817	−	1.51378i
$477$	−15.8453	+	21.8345i	−0.725507	+	0.999731i
$478$	13.6647	+	25.9417i	0.625007	+	1.18655i
$479$	8.05058	+	10.2495i	0.367840	+	0.468313i	0.934667	−	0.355524i	$-0.115698\pi$
$479$	8.05058	+	10.2495i	0.367840	+	0.468313i	−0.566827	+	0.823837i	$0.691829\pi$
$480$	2.75256	−	8.97057i	0.125637	−	0.409449i
$481$	−6.66805	−	28.9679i	−0.304037	−	1.32082i
$482$	−14.8542	+	24.2575i	−0.676591	+	1.10490i
$483$	3.89725	−	5.30205i	0.177331	−	0.241252i
$484$	4.41167	+	7.87462i	0.200531	+	0.357937i
$485$	22.3945	−	38.7884i	1.01688	−	1.76129i
$486$	−11.7730	−	36.9533i	−0.534034	−	1.67624i
$487$	−18.0518	−	31.2666i	−0.818003	−	1.41682i	−0.907151	−	0.420804i	$-0.861748\pi$
$487$	−18.0518	−	31.2666i	−0.818003	−	1.41682i	0.0891484	−	0.996018i	$-0.471585\pi$
$488$	−11.5969	+	19.4998i	−0.524965	+	0.882712i
$489$	−3.89383	−	4.07716i	−0.176085	−	0.184376i
$490$	−15.4258	−	28.3888i	−0.696865	−	1.28248i
$491$	−31.6417	+	29.4681i	−1.42797	+	1.32988i	−0.564544	+	0.825403i	$0.690948\pi$
$491$	−31.6417	+	29.4681i	−1.42797	+	1.32988i	−0.863426	+	0.504475i	$0.831686\pi$
$492$	0.755016	+	1.78375i	0.0340387	+	0.0804177i
$493$	−35.5880	+	5.09544i	−1.60280	+	0.229487i
$494$	−32.8809	+	52.1691i	−1.47938	+	2.34720i
$495$	−23.0395	−	18.8588i	−1.03555	−	0.847642i
$496$	−9.26840	−	42.7877i	−0.416163	−	1.92122i
$497$	12.8382	−	7.52321i	0.575872	−	0.337462i
$498$	14.3447	−	3.10168i	0.642801	−	0.138990i
$499$	23.1730	−	31.9818i	1.03737	−	1.43170i	0.140140	−	0.990132i	$-0.455245\pi$
$499$	23.1730	−	31.9818i	1.03737	−	1.43170i	0.897227	−	0.441570i	$-0.145578\pi$
$500$	−17.4969	−	22.8788i	−0.782484	−	1.02317i
$501$	−2.97553	−	1.28483i	−0.132937	−	0.0574019i
$502$	2.58414	+	5.06357i	0.115336	+	0.225998i
$503$	−32.1944	+	23.0112i	−1.43548	+	1.02602i	−0.443958	+	0.896048i	$0.646426\pi$
$503$	−32.1944	+	23.0112i	−1.43548	+	1.02602i	−0.991518	+	0.129969i	$0.958512\pi$
$504$	7.05592	−	23.5049i	0.314296	−	1.04699i
$505$	−12.9168	+	27.0132i	−0.574791	+	1.20207i
$506$	−17.1056	+	15.1239i	−0.760438	+	0.672341i
$507$	−11.5531	−	9.08139i	−0.513090	−	0.403319i
$508$	−0.0603713	+	9.33923i	−0.00267855	+	0.414361i
$509$	0.0139096	+	0.0155288i	0.000616534	+	0.000688301i	0.745181	−	0.666863i	$-0.232363\pi$
$509$	0.0139096	+	0.0155288i	0.000616534	+	0.000688301i	−0.744564	+	0.667551i	$0.767343\pi$
$510$	57.3978	−	72.0561i	2.54162	−	3.19070i
$511$	0.573228	−	8.04800i	0.0253581	−	0.356023i
$512$	45.8390	+	5.35781i	2.02582	+	0.236784i
$513$	19.4785	−	19.8157i	0.859995	−	0.874885i
$514$	46.3421	−	5.41662i	2.04406	−	0.238917i
$515$	0.389759	+	8.60771i	0.0171748	+	0.379301i
$516$	13.9510	+	28.7251i	0.614159	+	1.26455i
$517$	−9.52991	+	9.59171i	−0.419125	+	0.421843i
$518$	−13.2931	+	19.9294i	−0.584066	+	0.875647i
$519$	−2.32059	+	22.2764i	−0.101863	+	0.977825i
$520$	5.80036	+	68.8611i	0.254363	+	3.01976i
$521$	−2.63608	−	6.82761i	−0.115489	−	0.299123i	0.863072	−	0.505080i	$-0.168537\pi$
$521$	−2.63608	−	6.82761i	−0.115489	−	0.299123i	−0.978561	+	0.205957i	$0.933969\pi$
$522$	−26.6107	+	21.7161i	−1.16472	+	0.950487i
$523$	4.24256	+	12.3993i	0.185514	+	0.542185i	0.999237	−	0.0390682i	$-0.0124390\pi$
$523$	4.24256	+	12.3993i	0.185514	+	0.542185i	−0.813722	+	0.581254i	$0.802562\pi$
$524$	−7.28101	+	0.471314i	−0.318072	+	0.0205895i
$525$	3.96147	+	5.11511i	0.172893	+	0.223242i
$526$	1.25879	+	6.63611i	0.0548861	+	0.289348i
$527$	10.6332	−	65.2236i	0.463188	−	2.84119i
$528$	−15.7179	+	28.4610i	−0.684034	+	1.23861i
$529$	13.3768	+	9.82493i	0.581602	+	0.427171i
$530$	−53.6039	+	29.5774i	−2.32840	+	1.28476i
$531$	30.0258	−	9.17664i	1.30301	−	0.398232i
$532$	33.0094	−	6.48283i	1.43114	−	0.281066i
$533$	−0.871948	−	0.877603i	−0.0377683	−	0.0380132i
$534$	−16.2185	+	46.3633i	−0.701844	+	2.00634i
$535$	−7.79354	+	31.9614i	−0.336944	+	1.38181i
$536$	49.1771	−	23.1255i	2.12413	−	0.998868i
$537$	−23.4233	+	13.1112i	−1.01079	+	0.565790i
$538$	−30.6927	+	40.1337i	−1.32326	+	1.73029i
$539$	4.93652	+	16.4891i	0.212631	+	0.710238i
$540$	7.74648	−	59.0695i	0.333355	−	2.54195i
$541$	9.77214	−	32.6412i	0.420137	−	1.40336i	−0.442152	−	0.896940i	$-0.645785\pi$
$541$	9.77214	−	32.6412i	0.420137	−	1.40336i	0.862289	−	0.506416i	$-0.169030\pi$
$542$	−17.7816	−	24.5409i	−0.763784	−	1.05412i
$543$	8.24150	−	39.1999i	0.353677	−	1.68223i
$544$	−13.6377	−	7.29658i	−0.584711	−	0.312838i
$545$	−10.8763	+	29.2918i	−0.465890	+	1.25472i
$546$	2.69919	+	29.8675i	0.115515	+	1.27821i
$547$	−29.1031	+	0.752679i	−1.24436	+	0.0321822i	−0.642416	−	0.766356i	$-0.722068\pi$
$547$	−29.1031	+	0.752679i	−1.24436	+	0.0321822i	−0.601944	+	0.798538i	$0.705607\pi$
$548$	−68.2917	−	19.0103i	−2.91728	−	0.812080i
$549$	−4.50807	+	11.6504i	−0.192400	+	0.497228i
$550$	−9.68427	−	20.2529i	−0.412939	−	0.863588i
$551$	−22.6578	−	9.60038i	−0.965255	−	0.408990i
$552$	−22.8732	−	6.85704i	−0.973548	−	0.291855i
$553$	15.0870	+	9.64578i	0.641564	+	0.410180i
$554$	−26.1191	+	17.6667i	−1.10969	+	0.750586i
$555$	−12.5882	+	27.6662i	−0.534340	+	1.17436i
$556$	0.416192	+	0.0706150i	0.0176505	+	0.00299474i
$557$	−27.4825	+	11.2278i	−1.16447	+	0.475738i	−0.876264	−	0.481831i	$-0.839972\pi$
$557$	−27.4825	+	11.2278i	−1.16447	+	0.475738i	−0.288205	+	0.957569i	$0.593058\pi$
$558$	−23.4563	−	58.6174i	−0.992986	−	2.48147i
$559$	−15.1040	−	13.7062i	−0.638833	−	0.579710i
$560$	14.1873	−	15.8388i	0.599525	−	0.669312i
$561$	−37.8100	+	31.2884i	−1.59634	+	1.32100i
$562$	−18.9068	+	37.0475i	−0.797535	+	1.56275i
$563$	−4.05462	−	27.0702i	−0.170882	−	1.14087i	−0.893314	−	0.449433i	$-0.851626\pi$
$563$	−4.05462	−	27.0702i	−0.170882	−	1.14087i	0.722432	−	0.691442i	$-0.243024\pi$
$564$	−26.3631	−	6.07876i	−1.11009	−	0.255962i
$565$	−28.3152	+	9.89325i	−1.19123	+	0.416212i
$566$	−16.7684	+	14.0704i	−0.704830	+	0.591423i
$567$	1.67538	−	13.4085i	0.0703593	−	0.563105i
$568$	−41.3647	−	34.7091i	−1.73562	−	1.45636i
$569$	12.1893	+	4.61585i	0.511001	+	0.193507i	0.596168	−	0.802860i	$-0.296689\pi$
$569$	12.1893	+	4.61585i	0.511001	+	0.193507i	−0.0851661	+	0.996367i	$0.527142\pi$
$570$	59.1211	−	21.9272i	2.47631	−	0.918429i
$571$	−3.51546	+	17.3077i	−0.147118	+	0.724304i	0.837059	+	0.547113i	$0.184273\pi$
$571$	−3.51546	+	17.3077i	−0.147118	+	0.724304i	−0.984176	+	0.177191i	$0.943299\pi$
$572$	8.62926	−	69.9061i	0.360807	−	2.92292i
$573$	3.86318	+	2.57885i	0.161387	+	0.107733i
$574$	−0.0322186	+	0.996488i	−0.00134478	+	0.0415926i
$575$	4.97566	−	3.85643i	0.207499	−	0.160824i
$576$	16.2555	−	0.829275i	0.677313	−	0.0345531i
$577$	4.02035	+	6.37872i	0.167369	+	0.265550i	0.919187	−	0.393822i	$-0.128847\pi$
$577$	4.02035	+	6.37872i	0.167369	+	0.265550i	−0.751817	+	0.659371i	$0.770823\pi$
$578$	−70.9609	−	83.4662i	−2.95159	−	3.47174i
$579$	−6.02262	−	10.9246i	−0.250292	−	0.454009i
$580$	−51.1768	+	12.8301i	−2.12500	+	0.532741i
$581$	4.99043	+	1.11482i	0.207038	+	0.0462503i
$582$	−69.4575	−	12.2738i	−2.87911	−	0.508766i
$583$	31.1841	−	9.55599i	1.29151	−	0.395769i
$584$	−28.2065	+	7.85182i	−1.16719	+	0.324910i
$585$	9.46398	+	36.8547i	0.391287	+	1.52375i
$586$	1.06488	−	10.9479i	0.0439896	−	0.452253i
$587$	1.65572	+	1.31790i	0.0683390	+	0.0543954i	0.656343	−	0.754463i	$-0.272102\pi$
$587$	1.65572	+	1.31790i	0.0683390	+	0.0543954i	−0.588004	+	0.808858i	$0.700086\pi$
$588$	−22.8223	+	25.7934i	−0.941174	+	1.06370i
$589$	29.2991	−	34.4624i	1.20725	−	1.42000i
$590$	70.5307	+	10.0985i	2.90370	+	0.415748i
$591$	8.63493	+	32.6968i	0.355193	+	1.34497i
$592$	32.1953	+	8.07141i	1.32322	+	0.331733i
$593$	−17.5324	−	8.80508i	−0.719968	−	0.361581i	0.0507904	−	0.998709i	$-0.483826\pi$
$593$	−17.5324	−	8.80508i	−0.719968	−	0.361581i	−0.770758	+	0.637128i	$0.780122\pi$
$594$	−15.5148	+	44.2463i	−0.636582	+	1.81545i
$595$	28.6830	−	14.4051i	1.17589	−	0.590553i
$596$	−50.0782	+	11.1870i	−2.05128	+	0.458238i
$597$	−15.3156	−	23.9748i	−0.626827	−	0.981224i
$598$	29.0606	−	2.63714i	1.18838	−	0.107841i
$599$	−0.113249	−	1.02640i	−0.00462721	−	0.0419376i	0.991433	−	0.130614i	$-0.0416950\pi$
$599$	−0.113249	−	1.02640i	−0.00462721	−	0.0419376i	−0.996060	+	0.0886768i	$0.971736\pi$
$600$	12.6539	−	19.7758i	0.516594	−	0.807344i
$601$	−15.9322	−	1.44579i	−0.649888	−	0.0589750i	−0.239515	−	0.970893i	$-0.576988\pi$
$601$	−15.9322	−	1.44579i	−0.649888	−	0.0589750i	−0.410373	+	0.911918i	$0.634602\pi$
$602$	0.318739	+	16.4341i	0.0129908	+	0.669803i
$603$	24.5789	−	17.0652i	1.00093	−	0.694947i
$604$	−9.66651	−	11.9846i	−0.393325	−	0.487646i
$605$	1.39651	+	5.72712i	0.0567764	+	0.232841i
$606$	46.9303	+	4.58240i	1.90641	+	0.186147i
$607$	−8.61138	+	15.3709i	−0.349525	+	0.623886i	−0.989504	−	0.144507i	$-0.953840\pi$
$607$	−8.61138	+	15.3709i	−0.349525	+	0.623886i	0.639978	+	0.768393i	$0.278943\pi$
$608$	−5.41152	−	9.09929i	−0.219466	−	0.369025i
$609$	−11.5899	+	2.98078i	−0.469646	+	0.120787i
$610$	−20.4942	+	19.5872i	−0.829786	+	0.793063i
$611$	17.0723	−	2.67005i	0.690669	−	0.108019i
$612$	−93.0922	−	31.2586i	−3.76303	−	1.26355i
$613$	19.0637	−	11.5050i	0.769976	−	0.464683i	−0.0765263	−	0.997068i	$-0.524383\pi$
$613$	19.0637	−	11.5050i	0.769976	−	0.464683i	0.846503	+	0.532384i	$0.178704\pi$
$614$	13.3552	−	18.9426i	0.538972	−	0.764461i
$615$	0.162624	+	1.25451i	0.00655763	+	0.0505868i
$616$	−23.9124	+	17.5630i	−0.963458	+	0.707634i
$617$	−1.90277	+	4.11519i	−0.0766028	+	0.165671i	−0.942183	−	0.335100i	$-0.891230\pi$
$617$	−1.90277	+	4.11519i	−0.0766028	+	0.165671i	0.865580	+	0.500771i	$0.166950\pi$
$618$	12.5299	−	5.20834i	0.504027	−	0.209510i
$619$	14.5058	+	15.7790i	0.583035	+	0.634211i	0.955906	−	0.293673i	$-0.0948775\pi$
$619$	14.5058	+	15.7790i	0.583035	+	0.634211i	−0.372871	+	0.927883i	$0.621627\pi$
$620$	5.63912	−	96.8200i	0.226473	−	3.88838i
$621$	−13.0473	−	1.62533i	−0.523570	−	0.0652221i
$622$	2.24245	+	38.5013i	0.0899140	+	1.54376i
$623$	−11.9040	+	12.2951i	−0.476924	+	0.492593i
$624$	37.7209	−	17.4244i	1.51005	−	0.697532i
$625$	−11.6314	−	29.0045i	−0.465258	−	1.16018i
$626$	14.0839	+	39.4874i	0.562904	+	1.57824i
$627$	−33.2237	+	4.96368i	−1.32683	+	0.198230i
$628$	8.61406	−	57.5109i	0.343738	−	2.29493i
$629$	40.7605	+	29.1338i	1.62523	+	1.16164i
$630$	16.3700	−	25.9301i	0.652198	−	1.03308i
$631$	15.8128	+	15.5091i	0.629497	+	0.617406i	0.943244	−	0.332100i	$-0.107757\pi$
$631$	15.8128	+	15.5091i	0.629497	+	0.617406i	−0.313747	+	0.949507i	$0.601584\pi$
$632$	14.5767	−	63.3255i	0.579831	−	2.51895i
$633$	26.9994	+	15.6015i	1.07313	+	0.620103i
$634$	21.1217	+	67.3689i	0.838850	+	2.67556i
$635$	−1.67366	+	5.86537i	−0.0664173	+	0.232760i
$636$	49.1543	+	42.9290i	1.94910	+	1.70225i
$637$	7.38965	−	20.7186i	0.292788	−	0.820902i
$638$	41.4929	−	1.61012i	1.64272	−	0.0637451i
$639$	−25.6410	−	15.0512i	−1.01434	−	0.595418i
$640$	44.2239	+	18.0675i	1.74810	+	0.714179i
$641$	−5.62184	−	3.49273i	−0.222049	−	0.137955i	0.412173	−	0.911106i	$-0.364770\pi$
$641$	−5.62184	−	3.49273i	−0.222049	−	0.137955i	−0.634222	+	0.773151i	$0.718679\pi$
$642$	51.4971	−	5.66261i	2.03243	−	0.223485i
$643$	−44.9260	+	19.0357i	−1.77171	+	0.750695i	−0.779458	+	0.626455i	$0.784505\pi$
$643$	−44.9260	+	19.0357i	−1.77171	+	0.750695i	−0.992252	+	0.124240i	$0.960351\pi$
$644$	−11.9253	−	10.5438i	−0.469924	−	0.415483i
$645$	3.74660	+	20.5163i	0.147522	+	0.807827i
$646$	−16.7239	−	102.584i	−0.657991	−	4.03611i
$647$	−17.6475	+	6.42316i	−0.693795	+	0.252521i	−0.664759	−	0.747058i	$-0.731466\pi$
$647$	−17.6475	+	6.42316i	−0.693795	+	0.252521i	−0.0290355	+	0.999578i	$0.509244\pi$
$648$	−47.8721	+	10.6196i	−1.88059	+	0.417176i
$649$	−35.6683	−	12.9822i	−1.40010	−	0.509596i
$650$	−5.34678	+	28.1871i	−0.209718	+	1.10559i
$651$	1.14523	−	21.9679i	0.0448851	−	0.860991i
$652$	−10.6706	+	8.49343i	−0.417894	+	0.332628i
$653$	21.5578	+	33.2432i	0.843624	+	1.30091i	0.951783	+	0.306773i	$0.0992492\pi$
$653$	21.5578	+	33.2432i	0.843624	+	1.30091i	−0.108159	+	0.994134i	$0.534496\pi$
$654$	49.2048	+	0.336344i	1.92406	+	0.0131521i
$655$	−4.66352	−	0.978666i	−0.182219	−	0.0382396i
$656$	1.31542	−	0.421772i	0.0513585	−	0.0164674i
$657$	−14.5941	+	6.84960i	−0.569368	+	0.267228i
$658$	−11.0069	−	8.53101i	−0.429095	−	0.332573i
$659$	14.3471	−	17.3244i	0.558883	−	0.674863i	−0.412890	−	0.910781i	$-0.635480\pi$
$659$	14.3471	−	17.3244i	0.558883	−	0.674863i	0.971773	+	0.235918i	$0.0758097\pi$
$660$	−50.4517	+	51.4015i	−1.96383	+	2.00080i
$661$	−12.1853	−	5.92368i	−0.473953	−	0.230404i	0.184781	−	0.982780i	$-0.440842\pi$
$661$	−12.1853	−	5.92368i	−0.473953	−	0.230404i	−0.658735	+	0.752375i	$0.728908\pi$
$662$	27.4032	−	14.2090i	1.06506	−	0.552247i
$663$	62.6151	−	3.62359i	2.43177	−	0.140729i
$664$	−2.27330	−	18.4161i	−0.0882210	−	0.714683i
$665$	21.9038	+	1.70250i	0.849394	+	0.0660201i
$666$	47.7199	+	3.74474i	1.84911	+	0.145106i
$667$	2.90453	+	11.2761i	0.112464	+	0.436612i
$668$	−3.74330	+	6.88900i	−0.144833	+	0.266543i
$669$	4.65701	+	4.63044i	0.180050	+	0.179023i
$670$	66.9472	−	11.3589i	2.58639	−	0.438832i
$671$	12.8284	−	7.97001i	0.495234	−	0.307679i
$672$	−4.77788	−	1.91809i	−0.184311	−	0.0739921i
$673$	14.1057	−	31.5721i	0.543736	−	1.21701i	−0.408810	−	0.912620i	$-0.634056\pi$
$673$	14.1057	−	31.5721i	0.543736	−	1.21701i	0.952546	−	0.304395i	$-0.0984542\pi$
$674$	5.75165	+	6.09639i	0.221545	+	0.234824i
$675$	5.05665	−	11.8972i	0.194630	−	0.457925i
$676$	−24.3946	+	25.8568i	−0.938254	+	0.994492i
$677$	1.70544	+	4.09855i	0.0655454	+	0.157520i	0.952667	−	0.304016i	$-0.0983275\pi$
$677$	1.70544	+	4.09855i	0.0655454	+	0.157520i	−0.887122	+	0.461536i	$0.847299\pi$
$678$	29.8776	+	36.5840i	1.14744	+	1.40500i
$679$	−20.1762	−	14.0305i	−0.774291	−	0.538443i
$680$	−84.2027	−	80.4763i	−3.22903	−	3.08613i
$681$	−0.712662	+	0.423475i	−0.0273093	+	0.0162276i
$682$	−19.9937	+	73.6643i	−0.765598	+	2.82075i
$683$	4.21089	−	12.3068i	0.161125	−	0.470906i	−0.835821	−	0.549003i	$-0.815008\pi$
$683$	4.21089	−	12.3068i	0.161125	−	0.470906i	0.996946	+	0.0780965i	$0.0248842\pi$
$684$	−43.4997	−	51.2426i	−1.66325	−	1.95931i
$685$	−39.6375	−	23.9213i	−1.51447	−	0.913987i
$686$	−40.1743	+	17.6384i	−1.53386	+	0.673436i
$687$	−27.7166	+	24.1701i	−1.05745	+	0.922146i
$688$	21.2982	−	8.06524i	0.811988	−	0.307485i
$689$	−39.3494	−	13.7486i	−1.49909	−	0.523778i
$690$	−25.2363	−	15.9189i	−0.960731	−	0.606024i
$691$	−0.762640	−	1.14337i	−0.0290122	−	0.0434959i	0.817128	−	0.576456i	$-0.195565\pi$
$691$	−0.762640	−	1.14337i	−0.0290122	−	0.0434959i	−0.846140	+	0.532961i	$0.821079\pi$
$692$	53.1638	+	10.4410i	2.02098	+	0.396908i
$693$	−11.3721	+	11.7283i	−0.431991	+	0.445522i
$694$	42.4322	−	52.6077i	1.61071	−	1.99696i
$695$	0.249487	+	0.117321i	0.00946357	+	0.00445023i
$696$	24.3171	+	35.9800i	0.921736	+	1.36382i
$697$	2.08080	+	0.134695i	0.0788161	+	0.00510192i
$698$	2.56308	+	9.44335i	0.0970139	+	0.357436i
$699$	46.5260	−	13.2574i	1.75978	−	0.501440i
$700$	13.1860	−	8.43041i	0.498385	−	0.318640i
$701$	−5.92472	+	13.7350i	−0.223773	+	0.518765i	−0.992705	−	0.120566i	$-0.961529\pi$
$701$	−5.92472	+	13.7350i	−0.223773	+	0.518765i	0.768932	+	0.639331i	$0.220788\pi$
$702$	49.4536	−	33.8371i	1.86651	−	1.27710i
$703$	13.5831	+	31.4892i	0.512296	+	1.18764i
$704$	−16.2994	−	11.0248i	−0.614307	−	0.415512i
$705$	−15.5222	−	8.44182i	−0.584599	−	0.317937i
$706$	7.23012	−	22.0578i	0.272109	−	0.830156i
$707$	14.1746	+	8.30633i	0.533090	+	0.312392i
$708$	−15.5712	−	74.3371i	−0.585203	−	2.79376i
$709$	10.5920	+	3.54783i	0.397790	+	0.133242i	0.509440	−	0.860506i	$-0.329852\pi$
$709$	10.5920	+	3.54783i	0.397790	+	0.133242i	−0.111651	+	0.993748i	$0.535614\pi$
$710$	−38.1628	−	55.6428i	−1.43223	−	2.08824i
$711$	2.10695	−	35.7179i	0.0790167	−	1.33953i
$712$	56.5359	+	25.6987i	2.11877	+	0.963101i
$713$	−21.3756	−	1.10639i	−0.800521	−	0.0414347i
$714$	−36.7532	−	34.7007i	−1.37545	−	1.29864i
$715$	17.6727	−	42.4713i	0.660920	−	1.58834i
$716$	26.4881	+	59.2868i	0.989906	+	2.21565i
$717$	17.2725	−	10.8775i	0.645054	−	0.406227i
$718$	36.4001	+	20.7031i	1.35844	+	0.772631i
$719$	−48.8498	−	15.6630i	−1.82179	−	0.584133i	−0.999895	−	0.0144924i	$-0.995387\pi$
$719$	−48.8498	−	15.6630i	−1.82179	−	0.584133i	−0.821894	−	0.569641i	$-0.807082\pi$
$720$	−41.4585	−	9.29376i	−1.54507	−	0.346358i
$721$	4.72421	+	0.183321i	0.175939	+	0.00682722i
$722$	8.88561	−	22.1574i	0.330688	−	0.824614i
$723$	17.6347	+	9.00794i	0.655841	+	0.335009i
$724$	−92.6472	−	28.3906i	−3.44321	−	1.05513i
$725$	−11.4447	−	0.295989i	−0.425046	−	0.0109927i
$726$	7.72487	−	5.14842i	0.286697	−	0.191076i
$727$	20.8176	+	0.269153i	0.772083	+	0.00998232i	0.397967	−	0.917400i	$-0.369716\pi$
$727$	20.8176	+	0.269153i	0.772083	+	0.00998232i	0.374116	+	0.927382i	$0.377946\pi$
$728$	37.9169			1.40529
$729$	−25.0172	+	10.1557i	−0.926564	+	0.376137i
$730$	−36.5853			−1.35408
$731$	34.3741	+	0.444426i	1.27137	+	0.0164377i
$732$	27.0871	+	13.3976i	1.00117	+	0.495190i
$733$	6.90895	+	0.178683i	0.255188	+	0.00659980i	0.153236	−	0.988190i	$-0.451030\pi$
$733$	6.90895	+	0.178683i	0.255188	+	0.00659980i	0.101952	+	0.994789i	$0.467491\pi$
$734$	11.1281	+	3.41007i	0.410746	+	0.125868i
$735$	−18.8765	+	12.2312i	−0.696270	+	0.451156i
$736$	−1.86461	+	4.64965i	−0.0687305	+	0.171389i
$737$	−36.1477	−	1.40269i	−1.33152	−	0.0516689i
$738$	1.76921	−	0.915694i	0.0651254	−	0.0337072i
$739$	−24.8271	−	7.96050i	−0.913281	−	0.292832i	−0.188711	−	0.982033i	$-0.560431\pi$
$739$	−24.8271	−	7.96050i	−0.913281	−	0.292832i	−0.724570	+	0.689201i	$0.757962\pi$
$740$	63.9135	+	36.3516i	2.34951	+	1.33631i
$741$	37.9760	+	20.0217i	1.39508	+	0.735514i
$742$	13.7027	+	30.6700i	0.503042	+	1.12593i
$743$	0.136790	−	0.328737i	0.00501835	−	0.0120602i	−0.920731	−	0.390198i	$-0.872407\pi$
$743$	0.136790	−	0.328737i	0.00501835	−	0.0120602i	0.925749	+	0.378138i	$0.123435\pi$
$744$	−76.4815	+	22.8661i	−2.80395	+	0.838312i
$745$	−33.4669	−	1.73223i	−1.22613	−	0.0634641i
$746$	15.7381	+	7.15386i	0.576214	+	0.261922i
$747$	−2.92306	−	9.79014i	−0.106949	−	0.358202i
$748$	67.1489	+	97.9055i	2.45521	+	3.57978i
$749$	17.1159	+	5.73307i	0.625403	+	0.209482i
$750$	−22.0726	+	19.7564i	−0.805977	+	0.721401i
$751$	−14.1150	−	8.27142i	−0.515064	−	0.301828i	0.225007	−	0.974357i	$-0.427760\pi$
$751$	−14.1150	−	8.27142i	−0.515064	−	0.301828i	−0.740071	+	0.672529i	$0.765208\pi$
$752$	−6.00983	+	18.3349i	−0.219156	+	0.668605i
$753$	3.37589	−	2.06552i	0.123024	−	0.0752719i
$754$	−43.9564	−	29.7317i	−1.60080	−	1.08277i
$755$	−3.98287	−	9.23332i	−0.144951	−	0.336035i
$756$	−31.9395	−	6.95578i	−1.16163	−	0.252979i
$757$	−10.4549	+	24.2371i	−0.379989	+	0.880913i	0.615685	+	0.787993i	$0.288880\pi$
$757$	−10.4549	+	24.2371i	−0.379989	+	0.880913i	−0.995674	+	0.0929206i	$0.970380\pi$
$758$	−42.2166	+	26.9910i	−1.53338	+	0.980356i
$759$	11.4159	+	11.0610i	0.414373	+	0.401490i
$760$	−20.8833	−	76.9418i	−0.757515	−	2.79097i
$761$	41.3713	+	2.67805i	1.49971	+	0.0970791i	0.792476	−	0.609903i	$-0.208792\pi$
$761$	41.3713	+	2.67805i	1.49971	+	0.0970791i	0.707231	+	0.706982i	$0.249944\pi$
$762$	9.58143	−	0.678872i	0.347099	−	0.0245929i
$763$	15.5144	+	7.29562i	0.561659	+	0.264119i
$764$	7.05418	−	8.74581i	0.255211	−	0.316412i
$765$	−53.0960	−	35.9711i	−1.91969	−	1.30054i
$766$	−60.2224	−	11.8273i	−2.17592	−	0.427337i
$767$	26.9176	+	40.3556i	0.971939	+	1.45716i
$768$	2.20930	−	56.3937i	0.0797213

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.k (of order \(243\), degree \(162\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48775 - 0.0321643i) q^{2} +(0.111243 + 1.72847i) q^{3} +(4.18852 + 0.108326i) q^{4} +(2.61631 + 0.801736i) q^{5} +(-0.221150 - 4.30359i) q^{6} +(0.558840 - 1.39354i) q^{7} +(-5.44433 - 0.211265i) q^{8} +(-2.97525 + 0.384562i) q^{9} +O(q^{10})\)	\(q+(-2.48775 - 0.0321643i) q^{2} +(0.111243 + 1.72847i) q^{3} +(4.18852 + 0.108326i) q^{4} +(2.61631 + 0.801736i) q^{5} +(-0.221150 - 4.30359i) q^{6} +(0.558840 - 1.39354i) q^{7} +(-5.44433 - 0.211265i) q^{8} +(-2.97525 + 0.384562i) q^{9} +(-6.48293 - 2.07867i) q^{10} +(3.15263 + 1.79310i) q^{11} +(0.278706 + 7.25180i) q^{12} +(-1.89074 - 4.23194i) q^{13} +(-1.43508 + 3.44880i) q^{14} +(-1.09473 + 4.61141i) q^{15} +(5.16867 + 0.267528i) q^{16} +(7.11213 + 3.23286i) q^{17} +(7.41404 - 0.860996i) q^{18} +(3.02456 + 4.40991i) q^{19} +(10.8716 + 3.64150i) q^{20} +(2.47087 + 0.810919i) q^{21} +(-7.78527 - 4.56218i) q^{22} +(0.788145 - 2.40449i) q^{23} +(-0.240479 - 9.43388i) q^{24} +(2.06072 + 1.39386i) q^{25} +(4.56757 + 10.5888i) q^{26} +(-0.995682 - 5.09986i) q^{27} +(2.49167 - 5.77634i) q^{28} +(-3.87709 + 2.47880i) q^{29} +(2.87174 - 11.4368i) q^{30} +(-2.21573 - 8.16359i) q^{31} +(-1.97566 - 0.127888i) q^{32} +(-2.74862 + 5.64871i) q^{33} +(-17.5892 - 8.27129i) q^{34} +(2.57935 - 3.19789i) q^{35} +(-12.5036 + 1.28845i) q^{36} +(6.29290 + 1.23588i) q^{37} +(-7.38250 - 11.0680i) q^{38} +(7.10447 - 3.73887i) q^{39} +(-14.0747 - 4.91764i) q^{40} +(0.249606 - 0.0945212i) q^{41} +(-6.12081 - 2.09684i) q^{42} +(4.02908 - 1.76895i) q^{43} +(13.0106 + 7.85194i) q^{44} +(-8.09249 - 1.37923i) q^{45} +(-2.03804 + 5.95641i) q^{46} +(-0.976517 + 3.59786i) q^{47} +(0.112563 + 8.96368i) q^{48} +(3.43080 + 3.27897i) q^{49} +(-5.08173 - 3.53384i) q^{50} +(-4.79674 + 12.6528i) q^{51} +(-7.46098 - 17.9304i) q^{52} +(6.17116 - 6.54105i) q^{53} +(2.31297 + 12.7192i) q^{54} +(6.81066 + 7.21888i) q^{55} +(-3.33691 + 7.46883i) q^{56} +(-7.28597 + 5.71845i) q^{57} +(9.72496 - 6.04192i) q^{58} +(-10.3181 + 1.75067i) q^{59} +(-5.08485 + 19.1964i) q^{60} +(1.98810 - 3.65881i) q^{61} +(5.24960 + 20.3802i) q^{62} +(-1.12679 + 4.36104i) q^{63} +(-5.40923 - 0.420439i) q^{64} +(-1.55386 - 12.5879i) q^{65} +(7.01955 - 13.9641i) q^{66} +(-8.85457 + 4.59122i) q^{67} +(29.4391 + 14.3113i) q^{68} +(4.24377 + 1.09481i) q^{69} +(-6.51963 + 7.87259i) q^{70} +(7.83335 + 6.07131i) q^{71} +(16.2795 - 1.46512i) q^{72} +(5.11723 - 1.64077i) q^{73} +(-15.6154 - 3.27698i) q^{74} +(-2.18000 + 3.71697i) q^{75} +(12.1907 + 18.7987i) q^{76} +(4.26057 - 3.39126i) q^{77} +(-17.7944 + 9.07286i) q^{78} +(-2.22272 + 11.7177i) q^{79} +(13.3084 + 4.84385i) q^{80} +(8.70422 - 2.28834i) q^{81} +(-0.623997 + 0.227116i) q^{82} +(0.547989 + 3.36136i) q^{83} +(10.2614 + 3.66421i) q^{84} +(16.0156 + 14.1602i) q^{85} +(-10.0802 + 4.27111i) q^{86} +(-4.71584 - 6.42571i) q^{87} +(-16.7851 - 10.4283i) q^{88} +(-10.5517 - 4.31083i) q^{89} +(20.0877 + 3.69147i) q^{90} +(-6.95400 + 0.269847i) q^{91} +(3.56163 - 9.98587i) q^{92} +(13.8641 - 4.73798i) q^{93} +(2.54505 - 8.91915i) q^{94} +(4.37760 + 13.9626i) q^{95} +(0.00127322 - 3.42910i) q^{96} +(3.67167 - 15.9508i) q^{97} +(-8.42950 - 8.26760i) q^{98} +(-10.0694 - 4.12254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9}+O(q^{10}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9	\( 12960 q - 162 q^{2} - 162 q^{3} - 162 q^{4} - 162 q^{5} - 162 q^{6} - 162 q^{7} - 162 q^{8} - 162 q^{9} - 162 q^{10} - 162 q^{11} - 162 q^{12} - 162 q^{13} - 162 q^{14} - 162 q^{15} - 162 q^{16} - 162 q^{17} - 162 q^{18} - 162 q^{19} - 162 q^{20} - 162 q^{21} - 162 q^{22} - 162 q^{23} - 162 q^{24} - 162 q^{25} - 162 q^{26} - 162 q^{27} - 162 q^{28} - 162 q^{29} - 162 q^{30} - 162 q^{31} - 162 q^{32} - 162 q^{33} - 162 q^{34} - 162 q^{35} - 162 q^{36} - 162 q^{37} - 162 q^{38} - 162 q^{39} - 162 q^{40} - 162 q^{41} - 162 q^{42} - 162 q^{43} - 162 q^{44} - 162 q^{45} - 162 q^{46} - 162 q^{47} - 162 q^{48} - 162 q^{49} - 162 q^{50} - 162 q^{51} - 162 q^{52} - 162 q^{53} - 162 q^{54} - 162 q^{55} - 162 q^{56} - 162 q^{57} - 162 q^{58} - 162 q^{59} - 162 q^{60} - 162 q^{61} - 162 q^{62} - 162 q^{63} - 162 q^{64} - 162 q^{65} - 162 q^{66} - 162 q^{67} - 162 q^{68} - 162 q^{69} - 162 q^{70} - 162 q^{71} - 162 q^{72} - 162 q^{73} - 162 q^{74} - 162 q^{75} - 162 q^{76} - 162 q^{77} - 162 q^{78} - 162 q^{79} - 162 q^{80} - 162 q^{81} - 162 q^{82} - 162 q^{83} - 162 q^{84} - 162 q^{85} - 162 q^{86} - 162 q^{87} - 162 q^{88} - 162 q^{89} - 162 q^{90} - 162 q^{91} - 162 q^{92} - 162 q^{93} - 162 q^{94} - 162 q^{95} - 162 q^{96} - 162 q^{97} - 162 q^{98} - 162 q^{99}+O(q^{100}) \) 12960 * q - 162 * q^2 - 162 * q^3 - 162 * q^4 - 162 * q^5 - 162 * q^6 - 162 * q^7 - 162 * q^8 - 162 * q^9 - 162 * q^10 - 162 * q^11 - 162 * q^12 - 162 * q^13 - 162 * q^14 - 162 * q^15 - 162 * q^16 - 162 * q^17 - 162 * q^18 - 162 * q^19 - 162 * q^20 - 162 * q^21 - 162 * q^22 - 162 * q^23 - 162 * q^24 - 162 * q^25 - 162 * q^26 - 162 * q^27 - 162 * q^28 - 162 * q^29 - 162 * q^30 - 162 * q^31 - 162 * q^32 - 162 * q^33 - 162 * q^34 - 162 * q^35 - 162 * q^36 - 162 * q^37 - 162 * q^38 - 162 * q^39 - 162 * q^40 - 162 * q^41 - 162 * q^42 - 162 * q^43 - 162 * q^44 - 162 * q^45 - 162 * q^46 - 162 * q^47 - 162 * q^48 - 162 * q^49 - 162 * q^50 - 162 * q^51 - 162 * q^52 - 162 * q^53 - 162 * q^54 - 162 * q^55 - 162 * q^56 - 162 * q^57 - 162 * q^58 - 162 * q^59 - 162 * q^60 - 162 * q^61 - 162 * q^62 - 162 * q^63 - 162 * q^64 - 162 * q^65 - 162 * q^66 - 162 * q^67 - 162 * q^68 - 162 * q^69 - 162 * q^70 - 162 * q^71 - 162 * q^72 - 162 * q^73 - 162 * q^74 - 162 * q^75 - 162 * q^76 - 162 * q^77 - 162 * q^78 - 162 * q^79 - 162 * q^80 - 162 * q^81 - 162 * q^82 - 162 * q^83 - 162 * q^84 - 162 * q^85 - 162 * q^86 - 162 * q^87 - 162 * q^88 - 162 * q^89 - 162 * q^90 - 162 * q^91 - 162 * q^92 - 162 * q^93 - 162 * q^94 - 162 * q^95 - 162 * q^96 - 162 * q^97 - 162 * q^98 - 162 * q^99

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