LMFDB - Embedded newform 729.2.k.a.4.10

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			4.10
Character	$\chi$	$=$	729.4
Dual form			729.2.k.a.547.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.29202 - 0.0296337i) q^{2} +(-1.03658 - 1.38762i) q^{3} +(3.25315 + 0.0841346i) q^{4} +(3.65994 + 1.12154i) q^{5} +(2.33475 + 3.21117i) q^{6} +(-0.556114 + 1.38674i) q^{7} +(-2.87282 - 0.111478i) q^{8} +(-0.850984 + 2.87677i) q^{9} +O(q^{10})$	\(q+(-2.29202 - 0.0296337i) q^{2} +(-1.03658 - 1.38762i) q^{3} +(3.25315 + 0.0841346i) q^{4} +(3.65994 + 1.12154i) q^{5} +(2.33475 + 3.21117i) q^{6} +(-0.556114 + 1.38674i) q^{7} +(-2.87282 - 0.111478i) q^{8} +(-0.850984 + 2.87677i) q^{9} +(-8.35542 - 2.67906i) q^{10} +(-3.20888 - 1.82509i) q^{11} +(-3.25542 - 4.60135i) q^{12} +(-1.41919 - 3.17649i) q^{13} +(1.31572 - 3.16197i) q^{14} +(-2.23756 - 6.24118i) q^{15} +(0.0814789 + 0.00421731i) q^{16} +(1.56997 + 0.713639i) q^{17} +(2.03572 - 6.56841i) q^{18} +(-3.85413 - 5.61945i) q^{19} +(11.8120 + 3.95647i) q^{20} +(2.50073 - 0.665802i) q^{21} +(7.30072 + 4.27824i) q^{22} +(-1.69479 + 5.17050i) q^{23} +(2.82323 + 4.10194i) q^{24} +(7.99571 + 5.40823i) q^{25} +(3.15867 + 7.32263i) q^{26} +(4.87399 - 1.80118i) q^{27} +(-1.92580 + 4.46450i) q^{28} +(5.36459 - 3.42982i) q^{29} +(4.94358 + 14.3712i) q^{30} +(-2.84278 - 10.4739i) q^{31} +(5.55132 + 0.359348i) q^{32} +(0.793737 + 6.34456i) q^{33} +(-3.57726 - 1.68220i) q^{34} +(-3.59064 + 4.45169i) q^{35} +(-3.01042 + 9.28698i) q^{36} +(-10.1592 - 1.99520i) q^{37} +(8.66721 + 12.9941i) q^{38} +(-2.93665 + 5.26199i) q^{39} +(-10.3893 - 3.62999i) q^{40} +(2.77699 - 1.05159i) q^{41} +(-5.75147 + 1.45193i) q^{42} +(10.6392 - 4.67109i) q^{43} +(-10.2854 - 6.20727i) q^{44} +(-6.34097 + 9.57440i) q^{45} +(4.03771 - 11.8007i) q^{46} +(1.51873 - 5.59557i) q^{47} +(-0.0786077 - 0.117433i) q^{48} +(3.44666 + 3.29413i) q^{49} +(-18.1661 - 12.6327i) q^{50} +(-0.637147 - 2.91827i) q^{51} +(-4.34957 - 10.4530i) q^{52} +(3.99431 - 4.23372i) q^{53} +(-11.2247 + 3.98390i) q^{54} +(-9.69737 - 10.2786i) q^{55} +(1.75221 - 3.92187i) q^{56} +(-3.80254 + 11.1731i) q^{57} +(-12.3974 + 7.70225i) q^{58} +(12.2104 - 2.07173i) q^{59} +(-6.75402 - 20.4918i) q^{60} +(2.57877 - 4.74585i) q^{61} +(6.20532 + 24.0905i) q^{62} +(-3.51610 - 2.77991i) q^{63} +(-12.8758 - 1.00079i) q^{64} +(-1.63157 - 13.2174i) q^{65} +(-1.63125 - 14.5654i) q^{66} +(-2.61439 + 1.35560i) q^{67} +(5.04731 + 2.45366i) q^{68} +(8.93148 - 3.00793i) q^{69} +(8.36173 - 10.0970i) q^{70} +(-8.19809 - 6.35400i) q^{71} +(2.76542 - 8.16958i) q^{72} +(5.60742 - 1.79795i) q^{73} +(23.2260 + 4.87411i) q^{74} +(-0.783660 - 16.7011i) q^{75} +(-12.0653 - 18.6052i) q^{76} +(4.31543 - 3.43493i) q^{77} +(6.88680 - 11.9736i) q^{78} +(0.472814 - 2.49258i) q^{79} +(0.293478 + 0.106817i) q^{80} +(-7.55165 - 4.89618i) q^{81} +(-6.39608 + 2.32798i) q^{82} +(1.89072 + 11.5976i) q^{83} +(8.19128 - 1.95555i) q^{84} +(4.94562 + 4.37266i) q^{85} +(-24.5236 + 10.3910i) q^{86} +(-10.3201 - 3.88872i) q^{87} +(9.01505 + 5.60087i) q^{88} +(-8.64592 - 3.53225i) q^{89} +(14.8174 - 21.7568i) q^{90} +(5.19420 - 0.201559i) q^{91} +(-5.94842 + 16.6778i) q^{92} +(-11.5870 + 14.8017i) q^{93} +(-3.64678 + 12.7802i) q^{94} +(-7.80340 - 24.8894i) q^{95} +(-5.25578 - 8.07563i) q^{96} +(-0.982571 + 4.26857i) q^{97} +(-7.80220 - 7.65235i) q^{98} +(7.98107 - 7.67808i) 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 $

$2$	−2.29202	−	0.0296337i	−1.62070	−	0.0209542i	−0.802778	−	0.596278i	$-0.796646\pi$
$2$	−2.29202	−	0.0296337i	−1.62070	−	0.0209542i	−0.817926	+	0.575324i	$0.804876\pi$
$3$	−1.03658	−	1.38762i	−0.598472	−	0.801143i
$3$	−1.03658	−	1.38762i	−0.598472	−	0.801143i
$4$	3.25315	+	0.0841346i	1.62657	+	0.0420673i
$5$	3.65994	+	1.12154i	1.63677	+	0.501569i	0.969880	−	0.243584i	$-0.0783230\pi$
$5$	3.65994	+	1.12154i	1.63677	+	0.501569i	0.666894	+	0.745153i	$0.267623\pi$
$6$	2.33475	+	3.21117i	0.953159	+	1.31096i
$7$	−0.556114	+	1.38674i	−0.210191	+	0.524140i	−0.995478	−	0.0949925i	$-0.969717\pi$
$7$	−0.556114	+	1.38674i	−0.210191	+	0.524140i	0.785287	+	0.619133i	$0.212516\pi$
$8$	−2.87282	−	0.111478i	−1.01569	−	0.0394136i
$9$	−0.850984	+	2.87677i	−0.283661	+	0.958924i
$10$	−8.35542	−	2.67906i	−2.64222	−	0.847192i
$11$	−3.20888	−	1.82509i	−0.967512	−	0.550285i	−0.0730015	−	0.997332i	$-0.523258\pi$
$11$	−3.20888	−	1.82509i	−0.967512	−	0.550285i	−0.894511	+	0.447046i	$0.852476\pi$
$12$	−3.25542	−	4.60135i	−0.939758	−	1.32830i
$13$	−1.41919	−	3.17649i	−0.393611	−	0.880998i	−0.996533	−	0.0831981i	$-0.973487\pi$
$13$	−1.41919	−	3.17649i	−0.393611	−	0.880998i	0.602922	−	0.797800i	$-0.294003\pi$
$14$	1.31572	−	3.16197i	0.351641	−	0.845071i
$15$	−2.23756	−	6.24118i	−0.577735	−	1.61147i
$16$	0.0814789	+	0.00421731i	0.0203697	+	0.00105433i
$17$	1.56997	+	0.713639i	0.380774	+	0.173083i	0.595047	−	0.803691i	$-0.297133\pi$
$17$	1.56997	+	0.713639i	0.380774	+	0.173083i	−0.214273	+	0.976774i	$0.568738\pi$
$18$	2.03572	−	6.56841i	0.479825	−	1.54819i
$19$	−3.85413	−	5.61945i	−0.884197	−	1.28919i	−0.956477	−	0.291806i	$-0.905744\pi$
$19$	−3.85413	−	5.61945i	−0.884197	−	1.28919i	0.0722803	−	0.997384i	$-0.476972\pi$
$20$	11.8120	+	3.95647i	2.64124	+	0.884694i
$21$	2.50073	−	0.665802i	0.545705	−	0.145290i
$22$	7.30072	+	4.27824i	1.55652	+	0.912123i
$23$	−1.69479	+	5.17050i	−0.353388	+	1.07812i	0.605863	+	0.795569i	$0.292828\pi$
$23$	−1.69479	+	5.17050i	−0.353388	+	1.07812i	−0.959251	+	0.282554i	$0.908818\pi$
$24$	2.82323	+	4.10194i	0.576289	+	0.837305i
$25$	7.99571	+	5.40823i	1.59914	+	1.08165i
$26$	3.15867	+	7.32263i	0.619467	+	1.43609i
$27$	4.87399	−	1.80118i	0.938000	−	0.346636i
$28$	−1.92580	+	4.46450i	−0.363941	+	0.843711i
$29$	5.36459	−	3.42982i	0.996180	−	0.636902i	0.0636413	−	0.997973i	$-0.479729\pi$
$29$	5.36459	−	3.42982i	0.996180	−	0.636902i	0.932538	+	0.361071i	$0.117589\pi$
$30$	4.94358	+	14.3712i	0.902571	+	2.62381i
$31$	−2.84278	−	10.4739i	−0.510578	−	1.88116i	−0.471383	−	0.881929i	$-0.656245\pi$
$31$	−2.84278	−	10.4739i	−0.510578	−	1.88116i	−0.0391949	−	0.999232i	$-0.512479\pi$
$32$	5.55132	+	0.359348i	0.981345	+	0.0635244i
$33$	0.793737	+	6.34456i	0.138172	+	1.10445i
$34$	−3.57726	−	1.68220i	−0.613494	−	0.288495i
$35$	−3.59064	+	4.45169i	−0.606928	+	0.752473i
$36$	−3.01042	+	9.28698i	−0.501736	+	1.54783i
$37$	−10.1592	−	1.99520i	−1.67016	−	0.328010i	−0.733887	−	0.679271i	$-0.762296\pi$
$37$	−10.1592	−	1.99520i	−1.67016	−	0.328010i	−0.936277	+	0.351262i	$0.885753\pi$
$38$	8.66721	+	12.9941i	1.40601	+	2.10792i
$39$	−2.93665	+	5.26199i	−0.470241	+	0.842592i
$40$	−10.3893	−	3.62999i	−1.64269	−	0.573952i
$41$	2.77699	−	1.05159i	0.433693	−	0.164231i	−0.127642	−	0.991820i	$-0.540741\pi$
$41$	2.77699	−	1.05159i	0.433693	−	0.164231i	0.561335	+	0.827589i	$0.310288\pi$
$42$	−5.75147	+	1.45193i	−0.887471	+	0.224037i
$43$	10.6392	−	4.67109i	1.62246	−	0.712335i	0.624804	−	0.780781i	$-0.285179\pi$
$43$	10.6392	−	4.67109i	1.62246	−	0.712335i	0.997655	+	0.0684464i	$0.0218042\pi$
$44$	−10.2854	−	6.20727i	−1.55058	−	0.935781i
$45$	−6.34097	+	9.57440i	−0.945257	+	1.42727i
$46$	4.03771	−	11.8007i	0.595328	−	1.73991i
$47$	1.51873	−	5.59557i	0.221529	−	0.816198i	−0.763788	−	0.645467i	$-0.776663\pi$
$47$	1.51873	−	5.59557i	0.221529	−	0.816198i	0.985318	−	0.170731i	$-0.0546129\pi$
$48$	−0.0786077	−	0.117433i	−0.0113460	−	0.0169501i
$49$	3.44666	+	3.29413i	0.492380	+	0.470590i
$50$	−18.1661	−	12.6327i	−2.56907	−	1.78654i
$51$	−0.637147	−	2.91827i	−0.0892184	−	0.408640i
$52$	−4.34957	−	10.4530i	−0.603177	−	1.44957i
$53$	3.99431	−	4.23372i	0.548661	−	0.581547i	−0.392395	−	0.919797i	$-0.628353\pi$
$53$	3.99431	−	4.23372i	0.548661	−	0.581547i	0.941056	+	0.338250i	$0.109835\pi$
$54$	−11.2247	+	3.98390i	−1.52748	+	0.542140i
$55$	−9.69737	−	10.2786i	−1.30759	−	1.38597i
$56$	1.75221	−	3.92187i	0.234149	−	0.524082i
$57$	−3.80254	+	11.1731i	−0.503659	+	1.47991i
$58$	−12.3974	+	7.70225i	−1.62786	+	1.01136i
$59$	12.2104	−	2.07173i	1.58966	−	0.269716i	0.695856	−	0.718181i	$-0.255025\pi$
$59$	12.2104	−	2.07173i	1.58966	−	0.269716i	0.893800	+	0.448465i	$0.148029\pi$
$60$	−6.75402	−	20.4918i	−0.871940	−	2.64547i
$61$	2.57877	−	4.74585i	0.330178	−	0.607644i	−0.659375	−	0.751814i	$-0.729179\pi$
$61$	2.57877	−	4.74585i	0.330178	−	0.607644i	0.989553	+	0.144171i	$0.0460514\pi$
$62$	6.20532	+	24.0905i	0.788077	+	3.05950i
$63$	−3.51610	−	2.77991i	−0.442987	−	0.350236i
$64$	−12.8758	−	1.00079i	−1.60947	−	0.125098i
$65$	−1.63157	−	13.2174i	−0.202371	−	1.63942i
$66$	−1.63125	−	14.5654i	−0.200793	−	1.79288i
$67$	−2.61439	+	1.35560i	−0.319399	+	0.165613i	−0.612505	−	0.790467i	$-0.709838\pi$
$67$	−2.61439	+	1.35560i	−0.319399	+	0.165613i	0.293106	+	0.956080i	$0.405311\pi$
$68$	5.04731	+	2.45366i	0.612076	+	0.297550i
$69$	8.93148	−	3.00793i	1.07522	−	0.362113i
$70$	8.36173	−	10.0970i	0.999418	−	1.20682i
$71$	−8.19809	−	6.35400i	−0.972934	−	0.754081i	−0.00364193	−	0.999993i	$-0.501159\pi$
$71$	−8.19809	−	6.35400i	−0.972934	−	0.754081i	−0.969292	+	0.245913i	$0.920912\pi$
$72$	2.76542	−	8.16958i	0.325908	−	0.962794i
$73$	5.60742	−	1.79795i	0.656299	−	0.210434i	0.0415253	−	0.999137i	$-0.486778\pi$
$73$	5.60742	−	1.79795i	0.656299	−	0.210434i	0.614773	+	0.788704i	$0.289247\pi$
$74$	23.2260	+	4.87411i	2.69997	+	0.566603i
$75$	−0.783660	−	16.7011i	−0.0904893	−	1.92848i
$76$	−12.0653	−	18.6052i	−1.38398	−	2.13416i
$77$	4.31543	−	3.43493i	0.491789	−	0.391447i
$78$	6.88680	−	11.9736i	0.779776	−	1.35574i
$79$	0.472814	−	2.49258i	0.0531957	−	0.280437i	−0.945825	−	0.324676i	$-0.894745\pi$
$79$	0.472814	−	2.49258i	0.0531957	−	0.280437i	0.999021	+	0.0442388i	$0.0140862\pi$
$80$	0.293478	+	0.106817i	0.0328118	+	0.0119425i
$81$	−7.55165	−	4.89618i	−0.839072	−	0.544020i
$82$	−6.39608	+	2.32798i	−0.706329	+	0.257083i
$83$	1.89072	+	11.5976i	0.207534	+	1.27301i	0.858070	+	0.513532i	$0.171663\pi$
$83$	1.89072	+	11.5976i	0.207534	+	1.27301i	−0.650537	+	0.759475i	$0.725456\pi$
$84$	8.19128	−	1.95555i	0.893742	−	0.213369i
$85$	4.94562	+	4.37266i	0.536427	+	0.474282i
$86$	−24.5236	+	10.3910i	−2.64445	+	1.12049i
$87$	−10.3201	−	3.88872i	−1.10644	−	0.416914i
$88$	9.01505	+	5.60087i	0.961008	+	0.597055i
$89$	−8.64592	−	3.53225i	−0.916465	−	0.374417i	−0.129617	−	0.991564i	$-0.541375\pi$
$89$	−8.64592	−	3.53225i	−0.916465	−	0.374417i	−0.786848	+	0.617147i	$0.788288\pi$
$90$	14.8174	−	21.7568i	1.56189	−	2.29337i
$91$	5.19420	−	0.201559i	0.544500	−	0.0211291i
$92$	−5.94842	+	16.6778i	−0.620166	+	1.73878i
$93$	−11.5870	+	14.8017i	−1.20151	+	1.53487i
$94$	−3.64678	+	12.7802i	−0.376136	+	1.31817i
$95$	−7.80340	−	24.8894i	−0.800612	−	2.55360i
$96$	−5.25578	−	8.07563i	−0.536416	−	0.824215i
$97$	−0.982571	+	4.26857i	−0.0997649	+	0.433407i	−0.999998	−	0.00200092i	$-0.999363\pi$
$97$	−0.982571	+	4.26857i	−0.0997649	+	0.433407i	0.900233	+	0.435408i	$0.143396\pi$
$98$	−7.80220	−	7.65235i	−0.788141	−	0.773004i
$99$	7.98107	−	7.67808i	0.802128	−	0.771676i
$100$	25.5562	+	18.2665i	2.55562	+	1.82665i
$101$	0.760786	−	5.07931i	0.0757010	−	0.505410i	−0.918287	−	0.395917i	$-0.870427\pi$
$101$	0.760786	−	5.07931i	0.0757010	−	0.505410i	0.993988	−	0.109493i	$-0.0349228\pi$
$102$	1.37387	+	6.70762i	0.136034	+	0.664153i
$103$	−0.395045	−	1.10760i	−0.0389249	−	0.109135i	0.920839	−	0.389942i	$-0.127505\pi$
$103$	−0.395045	−	1.10760i	−0.0389249	−	0.109135i	−0.959764	+	0.280807i	$0.909398\pi$
$104$	3.72295	+	9.28367i	0.365066	+	0.910339i
$105$	9.89926	+	0.367888i	0.966069	+	0.0359022i
$106$	−9.28051	+	9.58542i	−0.901403	+	0.931018i
$107$	0.214176	+	3.67727i	0.0207052	+	0.355495i	0.992709	+	0.120532i	$0.0384599\pi$
$107$	0.214176	+	3.67727i	0.0207052	+	0.355495i	−0.972004	+	0.234963i	$0.924503\pi$
$108$	16.0074	−	5.44942i	1.54031	−	0.524371i
$109$	0.527929	−	9.06419i	0.0505664	−	0.868192i	−0.873705	−	0.486456i	$-0.838289\pi$
$109$	0.527929	−	9.06419i	0.0505664	−	0.868192i	0.924271	−	0.381736i	$-0.124674\pi$
$110$	21.9220	+	23.8462i	2.09018	+	2.27364i
$111$	7.76230	+	16.1653i	0.736765	+	1.53435i
$112$	−0.0511599	+	0.110645i	−0.00483416	+	0.0104550i
$113$	−1.34664	+	0.989072i	−0.126681	+	0.0930441i	−0.653471	−	0.756952i	$-0.726688\pi$
$113$	−1.34664	+	0.989072i	−0.126681	+	0.0930441i	0.526789	+	0.849996i	$0.323396\pi$
$114$	9.04661	−	25.4963i	0.847293	−	2.38795i
$115$	−12.0018	+	17.0229i	−1.11917	+	1.58740i
$116$	17.7404	−	10.7064i	1.64715	−	0.994062i
$117$	10.3457	−	1.37954i	0.956463	−	0.127538i
$118$	−28.0478	+	4.38660i	−2.58201	+	0.403820i
$119$	−1.86272	+	1.78028i	−0.170755	+	0.163198i
$120$	5.73234	+	18.1792i	0.523289	+	1.65953i
$121$	1.34323	+	2.25859i	0.122112	+	0.205327i
$122$	−6.05124	+	10.8012i	−0.547853	+	0.977891i
$123$	−4.33780	−	2.76334i	−0.391126	−	0.249162i
$124$	−8.36676	−	34.3122i	−0.751358	−	3.08133i
$125$	11.1822	+	13.8637i	1.00016	+	1.24001i
$126$	7.97660	+	6.47581i	0.710612	+	0.576911i
$127$	0.144277	+	7.43888i	0.0128025	+	0.660094i	0.950167	+	0.311743i	$0.100913\pi$
$127$	0.144277	+	7.43888i	0.0128025	+	0.660094i	−0.937364	+	0.348351i	$0.886742\pi$
$128$	18.4016	+	1.66988i	1.62648	+	0.147598i
$129$	−17.5101	−	9.92116i	−1.54168	−	0.873510i
$130$	3.34791	+	30.3429i	0.293631	+	2.66125i
$131$	−0.444195	+	0.0403091i	−0.0388095	+	0.00352182i	−0.109763	−	0.993958i	$-0.535009\pi$
$131$	−0.444195	+	0.0403091i	−0.0388095	+	0.00352182i	0.0709532	+	0.997480i	$0.477396\pi$
$132$	2.04835	+	20.7066i	0.178286	+	1.80228i
$133$	9.93608	−	2.21963i	0.861567	−	0.192466i
$134$	6.03241	−	3.02959i	0.521121	−	0.261717i
$135$	19.8586	−	1.12580i	1.70916	−	0.0968937i
$136$	−4.43068	−	2.22517i	−0.379928	−	0.190807i
$137$	−11.7087	−	2.93539i	−1.00034	−	0.250787i	−0.291817	−	0.956474i	$-0.594260\pi$
$137$	−11.7087	−	2.93539i	−1.00034	−	0.250787i	−0.708524	+	0.705687i	$0.750639\pi$
$138$	−20.5603	+	6.62957i	−1.75021	+	0.564347i
$139$	4.22811	+	0.605374i	0.358623	+	0.0513472i	0.318700	−	0.947856i	$-0.396754\pi$
$139$	4.22811	+	0.605374i	0.358623	+	0.0513472i	0.0399231	+	0.999203i	$0.487289\pi$
$140$	−12.0554	+	14.1799i	−1.01887	+	1.19842i
$141$	−9.33882	+	3.69286i	−0.786471	+	0.310995i
$142$	18.6019	+	14.8064i	1.56104	+	1.24253i
$143$	−1.24338	+	12.7831i	−0.103977	+	1.06898i
$144$	−0.0814695	+	0.230807i	−0.00678913	+	0.0192340i
$145$	23.4808	−	6.53632i	1.94997	−	0.542812i
$146$	−12.9056	+	3.95476i	−1.06808	+	0.327298i
$147$	0.998244	−	8.19730i	0.0823338	−	0.676102i
$148$	−32.8816	−	7.34544i	−2.70285	−	0.603792i
$149$	4.98808	−	1.25052i	0.408640	−	0.102447i	−0.0334002	−	0.999442i	$-0.510634\pi$
$149$	4.98808	−	1.25052i	0.408640	−	0.102447i	0.442040	+	0.896995i	$0.354255\pi$
$150$	1.30125	+	38.3025i	0.106247	+	3.12739i
$151$	−7.42677	−	8.73558i	−0.604382	−	0.710891i	0.371685	−	0.928359i	$-0.378780\pi$
$151$	−7.42677	−	8.73558i	−0.604382	−	0.710891i	−0.976068	+	0.217467i	$0.930220\pi$
$152$	10.4458	+	16.5733i	0.847262	+	1.34427i
$153$	−3.38900	+	3.90915i	−0.273984	+	0.316036i
$154$	−9.99286	+	7.74505i	−0.805247	+	0.624114i
$155$	1.34250	−	41.5220i	0.107832	−	3.33512i
$156$	−9.99608	+	16.8710i	−0.800327	+	1.35076i
$157$	−0.696522	+	5.64256i	−0.0555885	+	0.450325i	0.938794	+	0.344479i	$0.111944\pi$
$157$	−0.696522	+	5.64256i	−0.0555885	+	0.450325i	−0.994383	+	0.105846i	$0.966245\pi$
$158$	−1.15756	+	5.69904i	−0.0920909	+	0.453391i
$159$	−10.0153	−	1.15398i	−0.794261	−	0.0915165i
$160$	19.9145	+	7.54124i	1.57438	+	0.596187i
$161$	−6.22766	−	5.22563i	−0.490808	−	0.411837i
$162$	17.1635	+	11.4459i	1.34849	+	0.899277i
$163$	−6.83374	+	5.73419i	−0.535260	+	0.449137i	−0.869913	−	0.493205i	$-0.835825\pi$
$163$	−6.83374	+	5.73419i	−0.535260	+	0.449137i	0.334653	+	0.942341i	$0.391381\pi$
$164$	9.12244	−	3.18735i	0.712343	−	0.248891i
$165$	−4.21067	+	24.1109i	−0.327800	+	1.87703i
$166$	−3.98989	−	26.6381i	−0.309676	−	2.06752i
$167$	−2.78747	+	5.46198i	−0.215701	+	0.422660i	−0.973130	−	0.230257i	$-0.926043\pi$
$167$	−2.78747	+	5.46198i	−0.215701	+	0.422660i	0.757429	+	0.652917i	$0.226455\pi$
$168$	−7.25838	+	1.63395i	−0.559996	+	0.126062i
$169$	0.597720	−	0.667297i	0.0459784	−	0.0513305i
$170$	−11.2059	−	10.1688i	−0.859452	−	0.779911i
$171$	19.4457	−	6.30538i	1.48705	−	0.482184i
$172$	35.0038	−	14.3006i	2.66902	−	1.09041i
$173$	5.26596	+	0.893472i	0.400364	+	0.0679294i	0.363976	−	0.931408i	$-0.381419\pi$
$173$	5.26596	+	0.893472i	0.400364	+	0.0679294i	0.0363877	+	0.999338i	$0.488415\pi$
$174$	23.5388	+	9.21885i	1.78447	+	0.698879i
$175$	−11.9464	+	8.08042i	−0.903060	+	0.610822i
$176$	−0.253759	−	0.162239i	−0.0191278	−	0.0122292i
$177$	−15.5319	−	14.7959i	−1.16745	−	1.11213i
$178$	19.7120	+	8.35219i	1.47747	+	0.626023i
$179$	2.13031	+	4.45516i	0.159227	+	0.332994i	0.966284	−	0.257479i	$-0.0828917\pi$
$179$	2.13031	+	4.45516i	0.159227	+	0.332994i	−0.807057	+	0.590473i	$0.798941\pi$
$180$	−21.4337	+	30.6135i	−1.59757	+	2.28179i
$181$	3.27997	+	0.913042i	0.243798	+	0.0678659i	0.387916	−	0.921695i	$-0.373195\pi$
$181$	3.27997	+	0.913042i	0.243798	+	0.0678659i	−0.144118	+	0.989561i	$0.546034\pi$
$182$	−11.9112	+	0.308053i	−0.882916	+	0.0228344i
$183$	−9.25855	+	1.34112i	−0.684412	+	0.0991381i
$184$	5.44522	−	14.6650i	0.401427	−	1.08112i
$185$	−34.9444	−	18.6963i	−2.56916	−	1.37458i
$186$	26.9962	−	33.5825i	1.97946	−	2.46239i
$187$	−3.73538	−	5.15532i	−0.273158	−	0.376994i
$188$	5.41143	−	18.0754i	0.394669	−	1.31829i
$189$	−0.212726	+	7.76063i	−0.0154735	+	0.564503i
$190$	17.1480	+	57.2783i	1.24405	+	4.15540i
$191$	−7.18261	+	9.39194i	−0.519715	+	0.679577i	−0.977850	−	0.209305i	$-0.932880\pi$
$191$	−7.18261	+	9.39194i	−0.519715	+	0.679577i	0.458135	+	0.888883i	$0.348518\pi$
$192$	11.9581	+	18.9041i	0.863004	+	1.36429i
$193$	7.64361	−	3.59440i	0.550199	−	0.258730i	−0.130306	−	0.991474i	$-0.541596\pi$
$193$	7.64361	−	3.59440i	0.550199	−	0.258730i	0.680505	+	0.732744i	$0.261761\pi$
$194$	2.37857	−	9.75453i	0.170771	−	0.700334i
$195$	−16.6495	+	15.9650i	−1.19230	+	1.14328i
$196$	10.9354	+	11.0063i	0.781097	+	0.786162i
$197$	−3.63362	+	0.713619i	−0.258885	+	0.0508433i	−0.320470	−	0.947259i	$-0.603841\pi$
$197$	−3.63362	+	0.713619i	−0.258885	+	0.0508433i	0.0615859	+	0.998102i	$0.480384\pi$
$198$	−18.5203	+	17.3618i	−1.31618	+	1.23385i
$199$	17.1169	−	9.44473i	1.21339	−	0.669519i	0.258363	−	0.966048i	$-0.416817\pi$
$199$	17.1169	−	9.44473i	1.21339	−	0.669519i	0.955024	+	0.296529i	$0.0958291\pi$
$200$	−22.3673	−	16.4282i	−1.58161	−	1.16165i
$201$	4.59110	+	2.22259i	0.323831	+	0.156769i
$202$	−1.89426	+	11.6193i	−0.133279	+	0.817533i
$203$	1.77296	+	9.34669i	0.124437	+	0.656009i
$204$	−1.82721	−	9.54718i	−0.127930	−	0.668436i
$205$	11.3430	−	0.734257i	0.792231	−	0.0512827i
$206$	0.872629	+	2.55035i	0.0607989	+	0.177692i
$207$	−13.4321	−	9.27554i	−0.933596	−	0.644694i
$208$	−0.102237	−	0.264802i	−0.00708889	−	0.0183607i
$209$	2.11140	+	25.0662i	0.146049	+	1.73387i
$210$	−22.6784	−	1.13656i	−1.56496	−	0.0784301i
$211$	−10.8402	+	16.2519i	−0.746268	+	1.11882i	0.242614	+	0.970123i	$0.421995\pi$
$211$	−10.8402	+	16.2519i	−0.746268	+	1.11882i	−0.988882	+	0.148702i	$0.952490\pi$
$212$	13.3503	−	13.4369i	0.916903	−	0.922849i
$213$	−0.318928	+	17.9623i	−0.0218526	+	1.23076i
$214$	−0.381926	−	8.43472i	−0.0261079	−	0.576586i
$215$	44.1776	−	5.16362i	3.01288	−	0.352156i
$216$	−14.2029	+	4.63110i	−0.966383	+	0.315107i
$217$	16.1055	+	1.88246i	1.09331	+	0.127790i
$218$	−1.47863	+	20.7597i	−0.100145	+	1.40602i
$219$	−8.30743	−	5.91725i	−0.561364	−	0.399851i
$220$	−30.6822	−	34.2537i	−2.06859	−	2.30939i
$221$	0.0387842	−	5.99977i	0.00260891	−	0.403588i
$222$	−17.3123	−	37.2813i	−1.16193	−	2.50216i
$223$	−4.98407	+	4.40666i	−0.333758	+	0.295092i	−0.812615	−	0.582801i	$-0.801957\pi$
$223$	−4.98407	+	4.40666i	−0.333758	+	0.295092i	0.478857	+	0.877893i	$0.341051\pi$
$224$	−3.58549	+	7.49843i	−0.239566	+	0.501010i
$225$	−22.3625	+	18.3995i	−1.49083	+	1.22664i
$226$	3.11584	−	2.22707i	0.207263	−	0.148142i
$227$	−10.0030	−	19.6007i	−0.663922	−	1.30094i	−0.940449	−	0.339935i	$-0.889595\pi$
$227$	−10.0030	−	19.6007i	−0.663922	−	1.30094i	0.276527	−	0.961006i	$-0.410817\pi$
$228$	−13.3103	+	36.0279i	−0.881495	+	2.38600i
$229$	2.89480	+	3.78522i	0.191294	+	0.250135i	0.880075	−	0.474834i	$-0.157492\pi$
$229$	2.89480	+	3.78522i	0.191294	+	0.250135i	−0.688782	+	0.724969i	$0.741854\pi$
$230$	28.0127	−	38.6612i	1.84710	−	2.54925i
$231$	−9.23969	−	2.42759i	−0.607927	−	0.159724i
$232$	−15.7938	+	9.25522i	−1.03692	+	0.607635i
$233$	4.61216	+	21.2921i	0.302152	+	1.39489i	0.835730	+	0.549140i	$0.185045\pi$
$233$	4.61216	+	21.2921i	0.302152	+	1.39489i	−0.533578	+	0.845751i	$0.679153\pi$
$234$	−23.7535	+	2.85535i	−1.55282	+	0.186660i
$235$	11.8341	−	18.7761i	0.771973	−	1.22482i
$236$	39.8965	−	5.71233i	2.59704	−	0.371841i
$237$	−3.94887	+	1.92769i	−0.256507	+	0.125217i
$238$	4.32214	−	4.02524i	0.280163	−	0.260918i
$239$	−6.35535	−	11.6961i	−0.411094	−	0.756557i	0.587519	−	0.809210i	$-0.300105\pi$
$239$	−6.35535	−	11.6961i	−0.411094	−	0.756557i	−0.998613	+	0.0526533i	$0.983232\pi$
$240$	−0.155993	−	0.517961i	−0.0100693	−	0.0334342i
$241$	−9.86769	+	16.5922i	−0.635634	+	1.06880i	0.355339	+	0.934737i	$0.384365\pi$
$241$	−9.86769	+	16.5922i	−0.635634	+	1.06880i	−0.990973	+	0.134060i	$0.957198\pi$
$242$	−3.01178	−	5.21655i	−0.193604	−	0.335333i
$243$	1.03389	+	15.5541i	0.0663238	+	0.997798i
$244$	8.78842	−	15.2220i	0.562621	−	0.974488i
$245$	8.92006	+	15.9219i	0.569882	+	1.01721i
$246$	9.86044	+	6.46219i	0.628679	+	0.412014i
$247$	−12.3804	+	20.2176i	−0.787745	+	1.28642i
$248$	6.99917	+	30.4064i	0.444448	+	1.93081i
$249$	14.1332	−	14.6455i	0.895658	−	0.928124i
$250$	−25.2189	−	32.1073i	−1.59499	−	2.03064i
$251$	−10.5484	−	20.0256i	−0.665806	−	1.26400i	−0.952078	−	0.305854i	$-0.901058\pi$
$251$	−10.5484	−	20.0256i	−0.665806	−	1.26400i	0.286272	−	0.958148i	$-0.407584\pi$
$252$	−11.2045	−	9.33930i	−0.705819	−	0.588321i
$253$	14.8750	−	13.4983i	0.935183	−	0.848633i
$254$	−0.110244	−	17.0543i	−0.00691732	−	1.07008i
$255$	0.941049	−	11.3953i	0.0589308	−	0.713600i
$256$	−16.4361	−	1.70602i	−1.02725	−	0.106626i
$257$	4.73228	−	0.615238i	0.295192	−	0.0383775i	0.0201080	−	0.999798i	$-0.493599\pi$
$257$	4.73228	−	0.615238i	0.295192	−	0.0383775i	0.275084	+	0.961420i	$0.411294\pi$
$258$	39.8395	+	23.2584i	2.48030	+	1.44800i
$259$	8.41652	−	12.9787i	0.522977	−	0.806455i
$260$	−4.19569	−	43.1355i	−0.260206	−	2.67515i
$261$	5.30164	+	18.3514i	0.328163	+	1.13593i
$262$	1.01930	−	0.0792262i	0.0629725	−	0.00489461i
$263$	−1.17918	−	5.80548i	−0.0727116	−	0.357981i	0.927149	−	0.374693i	$-0.122252\pi$
$263$	−1.17918	−	5.80548i	−0.0727116	−	0.357981i	−0.999860	+	0.0167124i	$0.994680\pi$
$264$	−1.57298	−	18.3153i	−0.0968102	−	1.12723i
$265$	19.3672	−	11.0154i	1.18972	−	0.676669i
$266$	−22.8395	+	4.79299i	−1.40038	+	0.293877i
$267$	4.06081	+	15.6587i	0.248517	+	0.958299i
$268$	−8.61906	+	4.19001i	−0.526493	+	0.255946i
$269$	−6.77896	+	9.10572i	−0.413320	+	0.555186i	−0.959218	−	0.282666i	$-0.908781\pi$
$269$	−6.77896	+	9.10572i	−0.413320	+	0.555186i	0.545898	+	0.837852i	$0.316189\pi$
$270$	−45.5497	+	1.99188i	−2.77206	+	0.121222i
$271$	−5.40485	−	7.25997i	−0.328321	−	0.441012i	0.607058	−	0.794657i	$-0.292349\pi$
$271$	−5.40485	−	7.25997i	−0.328321	−	0.441012i	−0.935380	+	0.353645i	$0.884942\pi$
$272$	0.124910	+	0.0647676i	0.00757377	+	0.00392711i
$273$	−5.66392	−	6.99865i	−0.342796	−	0.423578i
$274$	26.7496	+	7.07495i	1.61600	+	0.427413i
$275$	−15.7867	−	31.9472i	−0.951976	−	1.92649i
$276$	29.3085	−	9.03381i	1.76417	−	0.543771i
$277$	−3.10911	+	2.16208i	−0.186808	+	0.129907i	−0.660623	−	0.750718i	$-0.729708\pi$
$277$	−3.10911	+	2.16208i	−0.186808	+	0.129907i	0.473815	+	0.880625i	$0.342877\pi$
$278$	−9.67297	−	1.51282i	−0.580146	−	0.0907332i
$279$	32.5501	+	0.735066i	1.94872	+	0.0440072i
$280$	10.8115	−	12.3886i	0.646111	−	0.740361i
$281$	−5.02158	+	10.1620i	−0.299562	+	0.606217i	−0.993502	−	0.113816i	$-0.963692\pi$
$281$	−5.02158	+	10.1620i	−0.299562	+	0.606217i	0.693940	+	0.720033i	$0.255873\pi$
$282$	21.5142	−	8.18737i	1.28115	−	0.487551i
$283$	10.0310	−	8.64048i	0.596284	−	0.513623i	−0.301844	−	0.953357i	$-0.597602\pi$
$283$	10.0310	−	8.64048i	0.596284	−	0.513623i	0.898128	+	0.439734i	$0.144927\pi$
$284$	−26.1350	−	21.3602i	−1.55083	−	1.26750i
$285$	−26.4482	+	36.6281i	−1.56666	+	2.16966i
$286$	3.22867	−	29.2623i	0.190915	−	1.73031i
$287$	−0.0860319	+	4.43578i	−0.00507830	+	0.261836i
$288$	−5.75785	+	15.6641i	−0.339285	+	0.923016i
$289$	−9.22234	−	10.5676i	−0.542490	−	0.621625i
$290$	−54.0121	+	14.2856i	−3.17170	+	0.838877i
$291$	6.94167	−	3.06130i	0.406928	−	0.179456i
$292$	18.3930	−	5.37721i	1.07637	−	0.314678i
$293$	2.37391	−	28.1827i	0.138685	−	1.64645i	−0.492133	−	0.870520i	$-0.663783\pi$
$293$	2.37391	−	28.1827i	0.138685	−	1.64645i	0.630818	−	0.775931i	$-0.282719\pi$
$294$	−2.53091	+	18.7588i	−0.147606	+	1.09404i
$295$	47.0128	+	6.11207i	2.73719	+	0.355859i
$296$	28.9631	+	6.86439i	1.68345	+	0.398985i
$297$	−18.9273	−	3.11572i	−1.09828	−	0.180793i
$298$	−11.4698	+	2.71840i	−0.664430	+	0.157473i
$299$	18.8292	−	1.95442i	1.08892	−	0.113027i
$300$	−1.14422	−	54.3972i	−0.0660618	−	3.14062i
$301$	0.561011	+	17.3515i	0.0323361	+	1.00012i
$302$	16.7635	+	20.2422i	0.964628	+	1.16481i
$303$	−7.83677	+	4.20945i	−0.450211	+	0.241827i
$304$	−0.290331	−	0.474121i	−0.0166516	−	0.0271927i
$305$	14.7608	−	14.4773i	0.845202	−	0.828968i
$306$	7.88350	−	8.85943i	0.450670	−	0.506460i
$307$	11.9713	−	17.4545i	0.683235	−	0.996182i	−0.315645	−	0.948877i	$-0.602221\pi$
$307$	11.9713	−	17.4545i	0.683235	−	0.996182i	0.998881	−	0.0473044i	$-0.0150631\pi$
$308$	14.3278	−	10.8113i	0.816399	−	0.616029i
$309$	−1.12743	+	1.69630i	−0.0641375	+	0.0964989i
$310$	−4.30748	+	95.1294i	−0.244648	+	5.40299i
$311$	2.13428	+	29.9649i	0.121024	+	1.69915i	0.583170	+	0.812350i	$0.301812\pi$
$311$	2.13428	+	29.9649i	0.121024	+	1.69915i	−0.462145	+	0.886804i	$0.652920\pi$
$312$	9.02306	−	14.7894i	0.510830	−	0.837282i
$313$	2.08921	+	5.62663i	0.118089	+	0.318036i	0.982922	−	0.184025i	$-0.0589128\pi$
$313$	2.08921	+	5.62663i	0.118089	+	0.318036i	−0.864832	+	0.502061i	$0.832575\pi$
$314$	1.76365	−	12.9122i	0.0995287	−	0.728679i
$315$	−9.75093	−	14.1178i	−0.549403	−	0.795446i
$316$	1.74785	−	8.06896i	0.0983241	−	0.453915i
$317$	3.85415	+	11.7583i	0.216470	+	0.660412i	0.999272	+	0.0381413i	$0.0121437\pi$
$317$	3.85415	+	11.7583i	0.216470	+	0.660412i	−0.782802	+	0.622271i	$0.786210\pi$
$318$	22.9210	+	2.94173i	1.28534	+	0.164964i
$319$	−23.4740	+	1.21501i	−1.31429	+	0.0680273i
$320$	−46.0021	−	18.1036i	−2.57160	−	1.01202i
$321$	4.88064	−	4.10899i	0.272411	−	0.229342i
$322$	14.1191	+	12.1618i	0.786825	+	0.677750i
$323$	−2.04060	−	11.5728i	−0.113542	−	0.643929i
$324$	−24.1547	−	16.5634i	−1.34193	−	0.920187i
$325$	5.83176	−	33.0736i	0.323488	−	1.83459i
$326$	15.8330	−	12.9404i	0.876909	−	0.716701i
$327$	−13.1249	+	8.66324i	−0.725809	+	0.479078i
$328$	−8.09502	+	2.71146i	−0.446973	+	0.149716i
$329$	6.91504	+	5.21787i	0.381238	+	0.287670i
$330$	10.3654	−	55.1379i	0.570599	−	3.03524i
$331$	−0.688987	+	0.368629i	−0.0378701	+	0.0202617i	−0.490579	−	0.871397i	$-0.663215\pi$
$331$	−0.688987	+	0.368629i	−0.0378701	+	0.0202617i	0.452709	+	0.891658i	$0.350458\pi$
$332$	5.17504	+	37.8880i	0.284017	+	2.07937i
$333$	14.3851	−	27.5279i	0.788298	−	1.50852i
$334$	6.55079	−	12.4364i	0.358443	−	0.680487i
$335$	−11.0889	+	2.02926i	−0.605850	+	0.110870i
$336$	0.206565	−	0.0437024i	0.0112690	−	0.00238416i
$337$	4.13817	+	4.27413i	0.225420	+	0.232827i	0.821657	−	0.569982i	$-0.193050\pi$
$337$	4.13817	+	4.27413i	0.225420	+	0.232827i	−0.596237	+	0.802809i	$0.703338\pi$
$338$	−1.38976	+	1.51175i	−0.0755930	+	0.0822281i
$339$	2.76837	+	0.843371i	0.150357	+	0.0458056i
$340$	15.7209	+	14.6410i	0.852588	+	0.794021i
$341$	−9.99362	+	38.7976i	−0.541185	+	2.10101i
$342$	−44.7568	+	13.8758i	−2.42017	+	0.750318i
$343$	−16.0060	+	7.27564i	−0.864245	+	0.392847i
$344$	−31.0851	+	12.2332i	−1.67600	+	0.659568i
$345$	36.0622	−	0.991805i	1.94152	−	0.0533970i
$346$	−12.0432	−	2.20391i	−0.647447	−	0.118483i
$347$	−15.3614	+	19.5573i	−0.824644	+	1.04989i	0.173241	+	0.984880i	$0.444576\pi$
$347$	−15.3614	+	19.5573i	−0.824644	+	1.04989i	−0.997885	+	0.0650097i	$0.979292\pi$
$348$	−33.2458	−	13.5189i	−1.78216	−	0.724687i
$349$	−2.55570	−	8.95648i	−0.136804	−	0.479430i	0.862858	−	0.505447i	$-0.168672\pi$
$349$	−2.55570	−	8.95648i	−0.136804	−	0.479430i	−0.999661	+	0.0260171i	$0.991718\pi$
$350$	27.6208	−	18.1665i	1.47639	−	0.971038i
$351$	−12.6385	−	12.9260i	−0.674593	−	0.689936i
$352$	−17.1577	−	11.2848i	−0.914506	−	0.601480i
$353$	4.25260	−	13.5639i	0.226343	−	0.721935i	−0.770120	−	0.637899i	$-0.779804\pi$
$353$	4.25260	−	13.5639i	0.226343	−	0.721935i	0.996463	−	0.0840352i	$-0.0267808\pi$
$354$	35.1609	+	34.3727i	1.86878	+	1.82689i
$355$	−22.8782	−	32.4497i	−1.21425	−	1.72225i
$356$	−27.8293	−	12.2183i	−1.47495	−	0.647571i
$357$	4.40122	+	0.739333i	0.232937	+	0.0391297i
$358$	−4.75069	−	10.2745i	−0.251082	−	0.543022i
$359$	20.2669	+	11.1828i	1.06965	+	0.590206i	0.917331	−	0.398126i	$-0.130339\pi$
$359$	20.2669	+	11.1828i	1.06965	+	0.590206i	0.152315	+	0.988332i	$0.451327\pi$
$360$	19.2838	−	26.7986i	1.01635	−	1.41241i
$361$	−9.88059	+	25.5914i	−0.520031	+	1.34691i
$362$	−7.49070	−	2.18991i	−0.393703	−	0.115099i
$363$	1.74170	−	4.20512i	0.0914157	−	0.220711i
$364$	16.9145	−	0.218689i	0.886559	−	0.0114624i
$365$	22.5393	−	0.291412i	1.17976	−	0.0152532i
$366$	21.2605	−	2.79950i	1.11131	−	0.146332i
$367$	−34.8380	−	10.1849i	−1.81853	−	0.531648i	−0.819396	−	0.573228i	$-0.805691\pi$
$367$	−34.8380	−	10.1849i	−1.81853	−	0.531648i	−0.999135	+	0.0415803i	$0.986761\pi$
$368$	−0.159895	+	0.414139i	−0.00833511	+	0.0215885i
$369$	0.662023	+	8.88366i	0.0344636	+	0.462465i
$370$	79.5392	+	43.8879i	4.13505	+	2.28162i
$371$	3.64980	+	7.89353i	0.189488	+	0.409811i
$372$	−38.9395	+	47.1774i	−2.01892	+	2.44603i
$373$	−9.76727	−	4.28829i	−0.505730	−	0.222039i	0.133508	−	0.991048i	$-0.457376\pi$
$373$	−9.76727	−	4.28829i	−0.505730	−	0.222039i	−0.639238	+	0.769009i	$0.720750\pi$
$374$	8.40880	+	11.9268i	0.434809	+	0.616719i
$375$	7.64632	−	29.8875i	0.394854	−	1.54339i
$376$	−4.98682	+	15.9057i	−0.257175	+	0.820276i
$377$	−18.5081	−	12.1730i	−0.953217	−	0.626941i
$378$	0.717548	−	17.7812i	0.0369067	−	0.914568i
$379$	−23.0978	+	15.1917i	−1.18646	+	0.780345i	−0.980172	−	0.198148i	$-0.936507\pi$
$379$	−23.0978	+	15.1917i	−1.18646	+	0.780345i	−0.206284	+	0.978492i	$0.566137\pi$
$380$	−23.2916	−	81.6255i	−1.19483	−	4.18730i
$381$	10.1728	−	7.91123i	0.521168	−	0.405305i
$382$	16.7410	−	21.3137i	0.856544	−	1.09050i
$383$	33.3723	+	6.10713i	1.70525	+	0.312060i	0.942392	−	0.334512i	$-0.108571\pi$
$383$	33.3723	+	6.10713i	1.70525	+	0.312060i	0.762854	+	0.646571i	$0.223798\pi$
$384$	−16.7576	−	27.2654i	−0.855159	−	1.39138i
$385$	19.6466	−	7.73168i	1.00129	−	0.394043i
$386$	−17.6258	+	8.01192i	−0.897131	+	0.407796i
$387$	4.38390	+	34.5815i	0.222846	+	1.75788i
$388$	−3.55558	+	13.8036i	−0.180507	+	0.700773i
$389$	−1.09627	−	1.02096i	−0.0555829	−	0.0517648i	0.653242	−	0.757149i	$-0.273408\pi$
$389$	−1.09627	−	1.02096i	−0.0555829	−	0.0517648i	−0.708825	+	0.705384i	$0.750775\pi$
$390$	38.6341	−	36.0987i	1.95631	−	1.82793i
$391$	−6.35064	+	6.90806i	−0.321166	+	0.349356i
$392$	−9.53440	−	9.84765i	−0.481560	−	0.497382i
$393$	0.516380	+	0.574591i	0.0260479	+	0.0289843i
$394$	8.34947	−	1.52795i	0.420640	−	0.0769771i
$395$	4.52601	−	8.59241i	0.227728	−	0.432331i
$396$	26.6096	−	24.3065i	1.33718	−	1.22145i
$397$	−2.12032	−	15.5235i	−0.106416	−	0.779101i	−0.964216	−	0.265118i	$-0.914589\pi$
$397$	−2.12032	−	15.5235i	−0.106416	−	0.779101i	0.857800	−	0.513983i	$-0.171831\pi$
$398$	−39.5123	+	21.1403i	−1.98057	+	1.05967i
$399$	−13.3796	−	11.4867i	−0.669817	−	0.575053i
$400$	0.628674	+	0.474377i	0.0314337	+	0.0237189i
$401$	−0.729222	+	0.244256i	−0.0364156	+	0.0121976i	−0.335760	−	0.941947i	$-0.608993\pi$
$401$	−0.729222	+	0.244256i	−0.0364156	+	0.0121976i	0.299345	+	0.954145i	$0.403232\pi$
$402$	−10.4570	−	5.23028i	−0.521549	−	0.260862i
$403$	−29.2356	+	23.8944i	−1.45633	+	1.19026i
$404$	2.90230	−	16.4597i	0.144395	−	0.818903i
$405$	−22.1473	−	26.3892i	−1.10051	−	1.31129i
$406$	−3.78668	−	21.4753i	−0.187930	−	1.06580i
$407$	28.9582	+	24.9438i	1.43541	+	1.23642i
$408$	1.50508	+	8.45469i	0.0745126	+	0.418569i
$409$	25.8633	+	10.1782i	1.27886	+	0.503277i	0.905474	−	0.424401i	$-0.139515\pi$
$409$	25.8633	+	10.1782i	1.27886	+	0.503277i	0.373381	+	0.927678i	$0.378198\pi$
$410$	−26.0202	+	1.34680i	−1.28505	+	0.0665135i
$411$	8.06385	+	19.2900i	0.397760	+	0.951506i
$412$	−1.19195	−	3.63643i	−0.0587233	−	0.179154i
$413$	−3.91741	+	18.0848i	−0.192763	+	0.889895i
$414$	30.5118	+	21.6578i	1.49957	+	1.06442i
$415$	−6.08734	+	44.5672i	−0.298816	+	2.18772i
$416$	−6.73690	−	18.1437i	−0.330303	−	0.889567i
$417$	−3.54276	−	6.49453i	−0.173490	−	0.318038i
$418$	−4.09656	−	57.5149i	−0.200369	−	2.81315i
$419$	0.232555	−	5.13590i	0.0113610	−	0.250905i	−0.985387	−	0.170328i	$-0.945517\pi$
$419$	0.232555	−	5.13590i	0.0113610	−	0.250905i	0.996748	−	0.0805769i	$-0.0256763\pi$
$420$	32.1728	+	2.02967i	1.56987	+	0.0990375i
$421$	−2.28874	+	1.72701i	−0.111546	+	0.0841693i	−0.656632	−	0.754211i	$-0.728020\pi$
$421$	−2.28874	+	1.72701i	−0.111546	+	0.0841693i	0.545086	+	0.838380i	$0.316497\pi$
$422$	25.3275	−	36.9284i	1.23292	−	1.79765i
$423$	14.8048	+	9.13078i	0.719833	+	0.443954i
$424$	−11.9469	+	11.7174i	−0.580193	+	0.569049i
$425$	8.69351	+	14.1968i	0.421697	+	0.688647i
$426$	1.26328	−	41.1605i	0.0612061	−	1.99423i
$427$	5.14718	+	6.21533i	0.249090	+	0.300781i
$428$	0.387363	+	11.9807i	0.0187239	+	0.579110i
$429$	19.0270	−	11.5254i	0.918630	−	0.556452i
$430$	−101.409	+	10.5260i	−4.89037	+	0.507607i
$431$	−2.14714	+	0.508881i	−0.103424	+	0.0245119i	−0.282002	−	0.959414i	$-0.590998\pi$
$431$	−2.14714	+	0.508881i	−0.103424	+	0.0245119i	0.178578	+	0.983926i	$0.442850\pi$
$432$	0.404723	−	0.126203i	0.0194723	−	0.00607193i
$433$	−26.3659	−	6.24883i	−1.26706	−	0.300300i	−0.458493	−	0.888698i	$-0.651611\pi$
$433$	−26.3659	−	6.24883i	−1.26706	−	0.300300i	−0.808571	+	0.588398i	$0.799759\pi$
$434$	−36.8583	−	4.79190i	−1.76925	−	0.230019i
$435$	−33.4097	−	25.8070i	−1.60187	−	1.23735i
$436$	2.48004	−	29.4428i	0.118773	−	1.41005i
$437$	35.5873	−	10.4040i	1.70237	−	0.497689i
$438$	18.8655	+	13.8086i	0.901426	+	0.659802i
$439$	10.7385	−	2.84021i	0.512522	−	0.135556i	0.00971166	−	0.999953i	$-0.496909\pi$
$439$	10.7385	−	2.84021i	0.512522	−	0.135556i	0.502810	+	0.864397i	$0.332300\pi$
$440$	26.7129	+	30.6096i	1.27349	+	1.45926i
$441$	−12.4095	+	7.11201i	−0.590929	+	0.338667i
$442$	−0.266690	+	13.7505i	−0.0126851	+	0.654043i
$443$	−3.97544	+	36.0305i	−0.188879	+	1.71186i	0.410890	+	0.911685i	$0.365218\pi$
$443$	−3.97544	+	36.0305i	−0.188879	+	1.71186i	−0.599769	+	0.800173i	$0.704741\pi$
$444$	23.8919	+	53.2414i	1.13386	+	2.52672i
$445$	−27.6820	−	22.6246i	−1.31225	−	1.07251i
$446$	11.5542	−	9.95246i	0.547106	−	0.471262i
$447$	−6.90582	−	5.62530i	−0.326634	−	0.266067i
$448$	8.54824	−	17.2989i	0.403866	−	0.817295i
$449$	−14.6465	+	16.7830i	−0.691209	+	0.792038i	−0.986568	−	0.163348i	$-0.947771\pi$
$449$	−14.6465	+	16.7830i	−0.691209	+	0.792038i	0.295359	+	0.955386i	$0.404561\pi$
$450$	51.8005	−	41.5094i	2.44190	−	1.95677i
$451$	−10.8303	−	1.69382i	−0.509978	−	0.0797590i
$452$	−4.46404	+	3.10430i	−0.209971	+	0.146014i
$453$	−4.42319	+	19.3607i	−0.207820	+	0.909646i
$454$	22.3462	+	45.2215i	1.04876	+	2.12235i
$455$	19.2365	+	5.08783i	0.901822	+	0.238521i
$456$	12.1696	−	31.6744i	0.569892	−	1.48329i
$457$	−30.5278	−	15.8291i	−1.42803	−	0.740456i	−0.440482	−	0.897761i	$-0.645193\pi$
$457$	−30.5278	−	15.8291i	−1.42803	−	0.740456i	−0.987550	+	0.157305i	$0.949719\pi$
$458$	−6.52277	−	8.76160i	−0.304789	−	0.409403i
$459$	8.93741	+	0.650477i	0.417162	+	0.0303616i
$460$	−40.4757	+	54.3683i	−1.88719	+	2.53494i
$461$	19.7093	−	9.58133i	0.917952	−	0.446247i	0.0829874	−	0.996551i	$-0.473554\pi$
$461$	19.7093	−	9.58133i	0.917952	−	0.446247i	0.834965	+	0.550304i	$0.185488\pi$
$462$	21.1056	+	5.83790i	0.981923	+	0.271604i
$463$	19.1967	−	4.02854i	0.892148	−	0.187222i	0.263267	−	0.964723i	$-0.415200\pi$
$463$	19.1967	−	4.02854i	0.892148	−	0.187222i	0.628882	+	0.777501i	$0.283513\pi$
$464$	0.451566	−	0.256834i	0.0209634	−	0.0119232i
$465$	−59.0084	+	41.1782i	−2.73645	+	1.90959i
$466$	−9.94020	−	48.9386i	−0.460471	−	2.26704i
$467$	−2.82212	+	0.219352i	−0.130592	+	0.0101504i	−0.142622	−	0.989777i	$-0.545553\pi$
$467$	−2.82212	+	0.219352i	−0.130592	+	0.0101504i	0.0120300	+	0.999928i	$0.496171\pi$
$468$	33.7723	−	3.61741i	1.56112	−	0.167215i
$469$	−0.425971	−	4.37936i	−0.0196695	−	0.202220i
$470$	−27.6805	+	42.6846i	−1.27680	+	1.96889i
$471$	8.55174	−	4.88248i	0.394043	−	0.224973i
$472$	−35.3092	+	4.59050i	−1.62524	+	0.211295i
$473$	−42.6650	−	4.42851i	−1.96174	−	0.203623i
$474$	9.10802	−	4.30128i	0.418345	−	0.197564i
$475$	−0.425191	−	65.7755i	−0.0195091	−	3.01799i
$476$	−6.20948	+	5.63481i	−0.284611	+	0.258271i
$477$	8.78037	+	15.0936i	0.402025	+	0.691087i
$478$	14.2200	+	26.9960i	0.650408	+	1.23477i
$479$	15.3836	+	19.5856i	0.702896	+	0.894887i	0.998167	−	0.0605268i	$-0.0192781\pi$
$479$	15.3836	+	19.5856i	0.702896	+	0.894887i	−0.295270	+	0.955414i	$0.595410\pi$
$480$	−10.1787	−	35.4509i	−0.464590	−	1.61810i
$481$	8.08008	+	35.1022i	0.368420	+	1.60052i
$482$	23.1086	−	37.7373i	1.05257	−	1.71888i
$483$	−0.795693	+	14.0584i	−0.0362053	+	0.639681i
$484$	4.17970	+	7.46056i	0.189986	+	0.339116i
$485$	−8.38353	+	14.5207i	−0.380676	+	0.659351i
$486$	−1.90876	−	35.6810i	−0.0865831	−	1.61852i
$487$	6.50615	+	11.2690i	0.294822	+	0.510646i	0.974943	−	0.222453i	$-0.0714064\pi$
$487$	6.50615	+	11.2690i	0.294822	+	0.510646i	−0.680122	+	0.733099i	$0.738073\pi$
$488$	−7.93740	+	13.3465i	−0.359309	+	0.604167i
$489$	15.0406	+	3.53867i	0.680161	+	0.160024i
$490$	−19.9731	−	36.7576i	−0.902294	−	1.66054i
$491$	23.4685	−	21.8563i	1.05912	−	0.986363i	0.0591871	−	0.998247i	$-0.481149\pi$
$491$	23.4685	−	21.8563i	1.05912	−	0.986363i	0.999929	+	0.0118840i	$0.00378289\pi$
$492$	−13.8790	−	9.35453i	−0.625715	−	0.421735i
$493$	10.8699	−	1.55634i	0.489556	−	0.0700939i
$494$	28.9752	−	45.9723i	1.30366	−	2.06839i
$495$	37.8215	−	19.1502i	1.69995	−	0.860737i
$496$	−0.187455	−	0.865387i	−0.00841696	−	0.0388570i
$497$	13.3704	−	7.83510i	0.599746	−	0.351452i
$498$	−32.8277	+	33.1491i	−1.47104	+	1.48545i
$499$	19.3354	−	26.6853i	0.865569	−	1.19460i	−0.113998	−	0.993481i	$-0.536366\pi$
$499$	19.3354	−	26.6853i	0.865569	−	1.19460i	0.979567	−	0.201118i	$-0.0644574\pi$
$500$	35.2109	+	46.0415i	1.57468	+	2.05904i
$501$	10.4686	−	1.79386i	0.467702	−	0.0801436i
$502$	23.5836	+	46.2116i	1.05259	+	2.06252i
$503$	1.97233	−	1.40973i	0.0879417	−	0.0628569i	−0.536671	−	0.843791i	$-0.680318\pi$
$503$	1.97233	−	1.40973i	0.0879417	−	0.0628569i	0.624613	+	0.780934i	$0.285257\pi$
$504$	9.79122	+	8.37815i	0.436136	+	0.373192i
$505$	8.48109	−	17.7367i	0.377403	−	0.789272i
$506$	−34.4938	+	30.4977i	−1.53344	+	1.35579i
$507$	−1.54554	−	0.137699i	−0.0686399	−	0.00611542i
$508$	−0.156513	+	24.2119i	−0.00694412	+	1.07423i
$509$	11.8874	+	13.2711i	0.526898	+	0.588231i	0.947796	−	0.318877i	$-0.103306\pi$
$509$	11.8874	+	13.2711i	0.526898	+	0.588231i	−0.420898	+	0.907108i	$0.638285\pi$
$510$	−2.49459	+	26.0903i	−0.110462	+	1.15530i
$511$	−0.625074	+	8.77592i	−0.0276517	+	0.388224i
$512$	0.916755	+	0.107153i	0.0405152	+	0.00473555i
$513$	−28.9066	−	20.4472i	−1.27626	−	0.902766i
$514$	−10.8647	+	1.26990i	−0.479222	+	0.0560130i
$515$	−0.203617	−	4.49681i	−0.00897242	−	0.198153i
$516$	−56.1283	−	33.7482i	−2.47091	−	1.48568i
$517$	−15.0858	+	15.1837i	−0.663474	+	0.667777i
$518$	−19.6755	+	29.4980i	−0.864490	+	1.29607i
$519$	−4.21882	−	8.23332i	−0.185185	−	0.361403i
$520$	3.21374	+	38.1531i	0.140932	+	1.67312i
$521$	−6.80648	−	17.6292i	−0.298197	−	0.772351i	−0.998299	−	0.0583070i	$-0.981430\pi$
$521$	−6.80648	−	17.6292i	−0.298197	−	0.772351i	0.700101	−	0.714044i	$-0.253138\pi$
$522$	−11.6076	−	42.2190i	−0.508053	−	1.84788i
$523$	5.40670	+	15.8017i	0.236418	+	0.690959i	0.999027	+	0.0440987i	$0.0140416\pi$
$523$	5.40670	+	15.8017i	0.236418	+	0.690959i	−0.762609	+	0.646860i	$0.776082\pi$
$524$	−1.44842	+	0.0937595i	−0.0632747	+	0.00409590i
$525$	23.5960	+	8.20099i	1.02981	+	0.357921i
$526$	2.53068	+	13.3412i	0.110343	+	0.581705i
$527$	3.01148	−	18.4724i	0.131182	−	0.804669i
$528$	0.0379158	+	0.520295i	0.00165007	+	0.0226429i
$529$	−5.32450	−	3.91070i	−0.231500	−	0.170030i
$530$	−44.7165	+	24.6735i	−1.94236	+	1.07175i
$531$	−4.43096	+	36.8895i	−0.192287	+	1.60087i
$532$	32.5103	−	6.38481i	1.40950	−	0.276817i
$533$	−7.28144	−	7.32866i	−0.315394	−	0.317440i
$534$	−8.84343	−	36.0105i	−0.382693	−	1.55833i
$535$	−3.34034	+	13.6988i	−0.144415	+	0.592250i
$536$	7.66179	−	3.60295i	0.330939	−	0.155624i
$537$	3.97383	−	7.57421i	0.171484	−	0.326851i
$538$	15.8074	−	20.6696i	0.681503	−	0.891131i
$539$	−5.04783	−	16.8609i	−0.217425	−	0.726251i
$540$	64.6977	−	1.99161i	2.78415	−	0.0857054i
$541$	−7.12516	+	23.7997i	−0.306334	+	1.02323i	0.656768	+	0.754093i	$0.271923\pi$
$541$	−7.12516	+	23.7997i	−0.306334	+	1.02323i	−0.963102	+	0.269136i	$0.913262\pi$
$542$	12.1729	+	16.8002i	0.522870	+	0.721629i
$543$	−2.13301	−	5.49780i	−0.0915362	−	0.235933i
$544$	8.45897	+	4.52581i	0.362675	+	0.194042i
$545$	12.0981	−	32.5823i	0.518224	−	1.39567i
$546$	12.7744	+	16.2089i	0.546695	+	0.693677i
$547$	20.5914	−	0.532545i	0.880425	−	0.0227700i	0.417000	−	0.908906i	$-0.363081\pi$
$547$	20.5914	−	0.532545i	0.880425	−	0.0227700i	0.463425	+	0.886136i	$0.346621\pi$
$548$	−37.8432	−	10.5344i	−1.61658	−	0.450006i
$549$	11.4582	+	11.4572i	0.489026	+	0.488981i
$550$	35.2368	+	73.6916i	1.50250	+	3.14222i
$551$	−39.9495	−	16.9271i	−1.70191	−	0.721119i
$552$	−25.9938	+	7.64557i	−1.10637	+	0.325417i
$553$	3.19363	+	2.04183i	0.135807	+	0.0868276i
$554$	7.19022	−	4.86340i	0.305483	−	0.206626i
$555$	10.2794	+	67.8699i	0.436337	+	2.88092i
$556$	13.7037	+	2.32510i	0.581168	+	0.0986063i
$557$	40.5789	−	16.5783i	1.71939	−	0.702446i	0.719416	−	0.694579i	$-0.244410\pi$
$557$	40.5789	−	16.5783i	1.71939	−	0.702446i	0.999969	−	0.00786664i	$-0.00250405\pi$
$558$	−74.5837	−	2.64937i	−3.15738	−	0.112157i
$559$	−29.9366	−	27.1660i	−1.26618	−	1.14900i
$560$	−0.311335	+	0.347576i	−0.0131563	+	0.0146878i
$561$	−3.28158	+	10.5272i	−0.138549	+	0.444459i
$562$	11.8107	−	23.1428i	0.498204	−	0.976221i
$563$	6.11747	+	40.8426i	0.257821	+	1.72131i	0.616074	+	0.787688i	$0.288722\pi$
$563$	6.11747	+	40.8426i	0.257821	+	1.72131i	−0.358254	+	0.933624i	$0.616628\pi$
$564$	−30.6913	+	11.2277i	−1.29234	+	0.472772i
$565$	−6.03791	+	2.10963i	−0.254017	+	0.0887527i
$566$	−23.2474	+	19.5069i	−0.977162	+	0.819936i
$567$	10.9893	−	7.74937i	0.461508	−	0.325443i
$568$	22.8433	+	19.1678i	0.958482	+	0.804262i
$569$	−19.1675	−	7.25839i	−0.803545	−	0.304288i	−0.0819799	−	0.996634i	$-0.526124\pi$
$569$	−19.1675	−	7.25839i	−0.803545	−	0.304288i	−0.721565	+	0.692346i	$0.756577\pi$
$570$	61.7052	−	83.1687i	2.58455	−	3.48355i
$571$	−1.21440	+	5.97886i	−0.0508211	+	0.250208i	−0.997382	−	0.0723189i	$-0.976960\pi$
$571$	−1.21440	+	5.97886i	−0.0508211	+	0.250208i	0.946560	+	0.322526i	$0.104532\pi$
$572$	−5.12041	+	41.4807i	−0.214095	+	1.73439i
$573$	20.4778	+	0.231192i	0.855474	+	0.00965819i
$574$	0.328636	−	10.1644i	0.0137170	−	0.424252i
$575$	−41.5143	+	32.1760i	−1.73127	+	1.34183i
$576$	13.8361	−	36.1891i	0.576505	−	1.50788i
$577$	0.487438	+	0.773373i	0.0202923	+	0.0321959i	0.855979	−	0.517010i	$-0.172955\pi$
$577$	0.487438	+	0.773373i	0.0202923	+	0.0321959i	−0.835687	+	0.549206i	$0.814930\pi$
$578$	20.8246	+	24.4945i	0.866190	+	1.01884i
$579$	−12.9109	−	6.88054i	−0.536559	−	0.285945i
$580$	76.9364	−	19.2881i	3.19461	−	0.800894i
$581$	−17.1344	−	3.82767i	−0.710856	−	0.158799i
$582$	−16.0012	+	6.81085i	−0.663270	+	0.282319i
$583$	−20.5442	+	6.29551i	−0.850853	+	0.260733i
$584$	−16.3095	+	4.54007i	−0.674893	+	0.187869i
$585$	39.4119	+	6.55416i	1.62948	+	0.270981i
$586$	−6.27620	+	64.5250i	−0.259267	+	2.66550i
$587$	8.77420	+	6.98395i	0.362150	+	0.288258i	0.786935	−	0.617036i	$-0.211667\pi$
$587$	8.77420	+	6.98395i	0.362150	+	0.288258i	−0.424785	+	0.905294i	$0.639650\pi$
$588$	3.93711	−	26.5831i	0.162364	−	1.09627i
$589$	−47.9009	+	56.3424i	−1.97372	+	2.32155i
$590$	−107.573	−	15.4022i	−4.42872	−	0.634097i
$591$	4.75678	+	4.30236i	0.195668	+	0.176975i
$592$	−0.819347	−	0.205412i	−0.0336750	−	0.00844237i
$593$	30.4533	+	15.2942i	1.25057	+	0.628058i	0.945917	−	0.324407i	$-0.105165\pi$
$593$	30.4533	+	15.2942i	1.25057	+	0.628058i	0.304648	+	0.952465i	$0.401461\pi$
$594$	43.2895	+	7.70219i	1.77619	+	0.316025i
$595$	−8.81409	+	4.42660i	−0.361343	+	0.181473i
$596$	16.3322	−	3.64846i	0.668993	−	0.149447i
$597$	−30.8489	−	13.9616i	−1.26256	−	0.571409i
$598$	−43.2149	+	3.92160i	−1.76719	+	0.160366i
$599$	2.17318	+	19.6961i	0.0887936	+	0.804759i	0.953277	+	0.302098i	$0.0976869\pi$
$599$	2.17318	+	19.6961i	0.0887936	+	0.804759i	−0.864483	+	0.502662i	$0.832354\pi$
$600$	0.389500	+	48.0666i	0.0159013	+	1.96231i
$601$	17.5502	+	1.59262i	0.715887	+	0.0649642i	0.442280	−	0.896877i	$-0.354170\pi$
$601$	17.5502	+	1.59262i	0.715887	+	0.0649642i	0.273608	+	0.961841i	$0.411783\pi$
$602$	−0.771660	−	39.7866i	−0.0314505	−	1.62158i
$603$	−1.67495	−	8.67461i	−0.0682093	−	0.353257i
$604$	−23.4254	−	29.0430i	−0.953168	−	1.18174i
$605$	2.38302	+	9.77280i	0.0968836	+	0.397321i
$606$	18.0868	−	9.41591i	0.734725	−	0.382495i
$607$	18.3210	−	32.7020i	0.743625	−	1.32733i	−0.194454	−	0.980912i	$-0.562294\pi$
$607$	18.3210	−	32.7020i	0.743625	−	1.32733i	0.938079	−	0.346422i	$-0.112604\pi$
$608$	−19.3762	−	32.5804i	−0.785807	−	1.32131i
$609$	11.1318	−	12.1488i	0.451085	−	0.492296i
$610$	−34.2611	+	32.7449i	−1.38719	+	1.32580i
$611$	−19.9296	+	3.11693i	−0.806265	+	0.126098i
$612$	−11.3538	+	12.4319i	−0.458951	+	0.502531i
$613$	−9.12963	+	5.50976i	−0.368742	+	0.222537i	−0.688948	−	0.724811i	$-0.741927\pi$
$613$	−9.12963	+	5.50976i	−0.368742	+	0.222537i	0.320206	+	0.947348i	$0.396248\pi$
$614$	−27.9556	+	39.6514i	−1.12820	+	1.60020i
$615$	−12.7769	−	14.9787i	−0.515213	−	0.603999i
$616$	−12.7804	+	9.38685i	−0.514936	+	0.378207i
$617$	−7.66119	+	16.5691i	−0.308428	+	0.667046i	−0.998385	−	0.0568040i	$-0.981909\pi$
$617$	−7.66119	+	16.5691i	−0.308428	+	0.667046i	0.689958	+	0.723850i	$0.257629\pi$
$618$	2.63437	−	3.85454i	0.105970	−	0.155052i
$619$	3.40741	+	3.70649i	0.136955	+	0.148976i	0.800884	−	0.598819i	$-0.204363\pi$
$619$	3.40741	+	3.70649i	0.136955	+	0.148976i	−0.663929	+	0.747796i	$0.731112\pi$
$620$	7.86077	−	134.964i	0.315696	−	5.42029i
$621$	1.05259	+	28.2536i	0.0422389	+	1.13378i
$622$	−4.00385	−	68.7435i	−0.160540	−	2.75636i
$623$	9.70644	−	10.0253i	0.388880	−	0.401657i
$624$	−0.261467	+	0.416356i	−0.0104670	+	0.0166676i
$625$	7.41267	+	18.4845i	0.296507	+	0.739379i
$626$	−4.62178	−	12.9583i	−0.184723	−	0.517916i
$627$	32.5938	−	28.9131i	1.30167	−	1.15468i
$628$	−2.74062	+	18.2975i	−0.109363	+	0.730149i
$629$	−14.5258	−	10.3824i	−0.579182	−	0.413974i
$630$	21.9310	+	32.6472i	0.873751	+	1.30069i
$631$	26.0345	+	25.5345i	1.03642	+	1.01651i	0.999852	+	0.0171798i	$0.00546876\pi$
$631$	26.0345	+	25.5345i	1.03642	+	1.01651i	0.0365650	+	0.999331i	$0.488358\pi$
$632$	−1.63618	+	7.10802i	−0.0650837	+	0.282742i
$633$	33.7882	−	1.80439i	1.34296	−	0.0717182i
$634$	−8.48534	−	27.0645i	−0.336996	−	1.07487i
$635$	−7.81498	+	27.3876i	−0.310128	+	1.08685i
$636$	−32.4840	−	4.59670i	−1.28808	−	0.182271i
$637$	5.57229	−	15.6232i	0.220782	−	0.619016i
$638$	53.8390	−	2.08920i	2.13151	−	0.0827122i
$639$	25.2555	−	18.1769i	0.999090	−	0.719067i
$640$	65.4757	+	26.7498i	2.58815	+	1.05738i
$641$	−5.29833	−	3.29175i	−0.209272	−	0.130016i	0.419070	−	0.907954i	$-0.362356\pi$
$641$	−5.29833	−	3.29175i	−0.209272	−	0.130016i	−0.628341	+	0.777938i	$0.716266\pi$
$642$	−11.3083	+	9.27327i	−0.446303	+	0.365987i
$643$	−10.2276	+	4.33356i	−0.403338	+	0.170899i	−0.582332	−	0.812951i	$-0.697860\pi$
$643$	−10.2276	+	4.33356i	−0.403338	+	0.170899i	0.178994	+	0.983850i	$0.442716\pi$
$644$	−19.8199	−	17.5237i	−0.781012	−	0.690531i
$645$	−52.9589	−	55.9492i	−2.08526	−	2.20300i
$646$	4.33416	+	26.5856i	0.170525	+	1.04600i
$647$	−7.59891	+	2.76578i	−0.298744	+	0.108734i	−0.487044	−	0.873378i	$-0.661925\pi$
$647$	−7.59891	+	2.76578i	−0.298744	+	0.108734i	0.188299	+	0.982112i	$0.439702\pi$
$648$	21.1487	+	14.9077i	0.830799	+	0.585629i
$649$	−42.9627	−	15.6371i	−1.68643	−	0.613811i
$650$	−14.3466	+	75.6325i	−0.562720	+	2.96655i
$651$	−14.0825	−	24.2996i	−0.551938	−	0.952377i
$652$	−22.7136	+	18.0792i	−0.889535	+	0.708037i
$653$	11.9677	+	18.4548i	0.468334	+	0.722193i	0.991510	−	0.130032i	$-0.0415081\pi$
$653$	11.9677	+	18.4548i	0.468334	+	0.722193i	−0.523176	+	0.852225i	$0.675253\pi$
$654$	30.3393	−	19.4674i	1.18636	−	0.761235i
$655$	−1.67093	−	0.350655i	−0.0652888	−	0.0137012i
$656$	0.230701	−	0.0739713i	0.00900736	−	0.00288809i
$657$	0.400459	+	17.6613i	0.0156234	+	0.689033i
$658$	−15.6948	−	12.1644i	−0.611846	−	0.474217i
$659$	−5.15359	+	6.22307i	−0.200755	+	0.242416i	−0.860964	−	0.508666i	$-0.830139\pi$
$659$	−5.15359	+	6.22307i	−0.200755	+	0.242416i	0.660208	+	0.751083i	$0.270468\pi$
$660$	−15.7265	+	78.0822i	−0.612153	+	3.03934i
$661$	27.0052	+	13.1281i	1.05038	+	0.510625i	0.880109	−	0.474772i	$-0.157470\pi$
$661$	27.0052	+	13.1281i	1.05038	+	0.510625i	0.170272	+	0.985397i	$0.445536\pi$
$662$	1.59010	−	0.824488i	0.0618008	−	0.0320447i
$663$	−8.36561	+	6.16546i	−0.324894	+	0.239446i
$664$	−4.13881	−	33.5287i	−0.160617	−	1.30117i
$665$	38.8548	+	3.02004i	1.50673	+	0.117112i
$666$	−33.7867	+	62.6682i	−1.30921	+	2.42834i
$667$	8.64203	+	33.5504i	0.334621	+	1.29908i
$668$	−9.52758	+	17.5341i	−0.368633	+	0.678415i
$669$	11.2812	+	2.34812i	0.436156	+	0.0907836i
$670$	25.4761	−	4.32251i	0.984227	−	0.166993i
$671$	−16.9366	+	10.5223i	−0.653829	+	0.406210i
$672$	14.1216	−	2.79745i	0.544754	−	0.107914i
$673$	14.6481	−	32.7860i	0.564643	−	1.26381i	−0.376693	−	0.926338i	$-0.622939\pi$
$673$	14.6481	−	32.7860i	0.564643	−	1.26381i	0.941336	−	0.337471i	$-0.109571\pi$
$674$	−9.35811	−	9.91902i	−0.360461	−	0.382066i
$675$	48.7122	+	11.9580i	1.87493	+	0.460263i
$676$	2.00061	−	2.12053i	0.0769467	−	0.0815588i
$677$	12.8011	+	30.7639i	0.491987	+	1.18235i	0.955161	+	0.296087i	$0.0956818\pi$
$677$	12.8011	+	30.7639i	0.491987	+	1.18235i	−0.463174	+	0.886268i	$0.653289\pi$
$678$	−6.32016	−	2.01506i	−0.242724	−	0.0773879i
$679$	−5.37299	−	3.73639i	−0.206196	−	0.143389i
$680$	−13.7204	−	13.1132i	−0.526153	−	0.502868i
$681$	−16.8293	+	34.1981i	−0.644901	+	1.31047i
$682$	24.0553	−	88.6288i	0.921125	−	3.39377i
$683$	−9.64272	+	28.1819i	−0.368968	+	1.07835i	0.593003	+	0.805200i	$0.297942\pi$
$683$	−9.64272	+	28.1819i	−0.368968	+	1.07835i	−0.961971	+	0.273151i	$0.911934\pi$
$684$	63.7903	−	18.8763i	2.43908	−	0.721753i
$685$	−39.5609	−	23.8751i	−1.51155	−	0.912222i
$686$	36.9018	−	16.2016i	1.40892	−	0.618580i
$687$	2.25175	−	7.94059i	0.0859098	−	0.302952i
$688$	0.886568	−	0.335727i	0.0338001	−	0.0127995i
$689$	−19.1170	−	6.67943i	−0.728301	−	0.254466i
$690$	−82.6847	+	1.20458i	−3.14775	+	0.0458576i
$691$	−11.4798	−	17.2108i	−0.436710	−	0.654728i	0.546446	−	0.837494i	$-0.315980\pi$
$691$	−11.4798	−	17.2108i	−0.436710	−	0.654728i	−0.983156	+	0.182767i	$0.941495\pi$
$692$	17.0558	+	3.34965i	0.648364	+	0.127335i
$693$	6.20915	+	15.3376i	0.235866	+	0.582627i
$694$	35.7882	−	44.3705i	1.35850	−	1.68428i
$695$	14.7956	+	6.95763i	0.561231	+	0.263918i
$696$	29.2144	+	12.3221i	1.10737	+	0.467066i
$697$	5.11025	+	0.330797i	0.193565	+	0.0125298i
$698$	5.59231	+	20.6042i	0.211672	+	0.779880i
$699$	24.7645	−	28.4710i	0.936678	−	1.07687i
$700$	−39.5432	+	25.2817i	−1.49459	+	0.955558i
$701$	4.96992	−	11.5216i	0.187711	−	0.435164i	−0.798209	−	0.602381i	$-0.794219\pi$
$701$	4.96992	−	11.5216i	0.187711	−	0.435164i	0.985920	+	0.167217i	$0.0534781\pi$
$702$	28.5847	+	30.0011i	1.07886	+	1.13232i
$703$	27.9429	+	64.7790i	1.05389	+	2.44319i
$704$	39.4903	+	26.7109i	1.48835	+	1.00670i
$705$	−38.3212	+	3.04175i	−1.44326	+	0.114559i
$706$	−10.1490	+	30.9628i	−0.381963	+	1.16530i
$707$	6.62061	+	3.87969i	0.248994	+	0.145911i
$708$	−49.2827	−	49.4399i	−1.85216	−	1.85807i
$709$	7.85570	+	2.63130i	0.295027	+	0.0988207i	0.461258	−	0.887266i	$-0.347398\pi$
$709$	7.85570	+	2.63130i	0.295027	+	0.0988207i	−0.166231	+	0.986087i	$0.553160\pi$
$710$	51.4757	+	75.0534i	1.93185	+	2.81671i
$711$	6.76824	+	3.48133i	0.253829	+	0.130560i
$712$	24.4444	+	11.1113i	0.916092	+	0.416415i
$713$	58.9730	+	3.05242i	2.20855	+	0.114314i
$714$	−10.0658	−	1.82499i	−0.376702	−	0.0682986i
$715$	−18.8875	+	45.3908i	−0.706352	+	1.69752i
$716$	6.55538	+	14.6725i	0.244986	+	0.548339i
$717$	−9.64187	+	20.9428i	−0.360082	+	0.782123i
$718$	−46.1208	−	26.2318i	−1.72121	−	0.978962i
$719$	−27.0285	−	8.66633i	−1.00799	−	0.323200i	−0.244941	−	0.969538i	$-0.578769\pi$
$719$	−27.0285	−	8.66633i	−1.00799	−	0.323200i	−0.763051	+	0.646338i	$0.776300\pi$
$720$	−0.557034	+	0.753369i	−0.0207594	+	0.0280764i
$721$	1.75565	+	0.0681273i	0.0653839	+	0.00253719i
$722$	23.4049	−	58.3631i	0.871039	−	2.17205i
$723$	33.2524	−	3.50660i	1.23667	−	0.130412i
$724$	10.5934	+	3.24622i	0.393701	+	0.120645i
$725$	61.4430	+	1.58907i	2.28194	+	0.0590166i
$726$	−4.11663	+	9.58660i	−0.152783	+	0.355792i
$727$	39.2480	+	0.507440i	1.45563	+	0.0188199i	0.736678	−	0.676244i	$-0.236393\pi$
$727$	39.2480	+	0.507440i	1.45563	+	0.0188199i	0.718948	+	0.695064i	$0.244624\pi$
$728$	−14.9445			−0.553879
$729$	20.5115	−	17.5578i	0.759686	−	0.650290i
$730$	−51.6691			−1.91236
$731$	20.0367	+	0.259056i	0.741083	+	0.00958152i
$732$	−30.2323	+	3.58389i	−1.11742	+	0.132464i
$733$	2.77260	+	0.0717063i	0.102408	+	0.00264853i	0.0770240	−	0.997029i	$-0.475458\pi$
$733$	2.77260	+	0.0717063i	0.102408	+	0.00264853i	0.0253842	+	0.999678i	$0.491919\pi$
$734$	79.5477	+	24.3764i	2.93616	+	0.899750i
$735$	12.8471	−	28.8820i	0.473874	−	1.06533i
$736$	−11.2663	+	28.0941i	−0.415283	+	1.03556i
$737$	10.8634	+	0.421548i	0.400157	+	0.0155279i
$738$	−1.25412	−	20.3812i	−0.0461646	−	0.750241i
$739$	5.48893	+	1.75995i	0.201913	+	0.0647409i	0.404562	−	0.914511i	$-0.367424\pi$
$739$	5.48893	+	1.75995i	0.201913	+	0.0647409i	−0.202648	+	0.979252i	$0.564955\pi$
$740$	−112.106	−	63.7620i	−4.12111	−	2.34394i
$741$	40.8877	−	3.77799i	1.50205	−	0.138788i
$742$	−8.13150	−	18.2003i	−0.298517	−	0.668153i
$743$	−1.79053	+	4.30305i	−0.0656883	+	0.157863i	−0.952724	−	0.303838i	$-0.901732\pi$
$743$	−1.79053	+	4.30305i	−0.0656883	+	0.157863i	0.887036	+	0.461701i	$0.152761\pi$
$744$	34.9373	−	41.2310i	1.28086	−	1.51160i
$745$	19.6586	+	1.01752i	0.720235	+	0.0372791i
$746$	22.2597	+	10.1183i	0.814986	+	0.370457i
$747$	−34.9728	−	4.43024i	−1.27959	−	0.162094i
$748$	−11.7180	−	17.0853i	−0.428453	−	0.624700i
$749$	−5.21853	−	1.74797i	−0.190681	−	0.0638695i
$750$	−18.4112	+	68.2762i	−0.672282	+	2.49310i
$751$	37.3310	+	21.8760i	1.36223	+	0.798267i	0.991454	−	0.130456i	$-0.0416441\pi$
$751$	37.3310	+	21.8760i	1.36223	+	0.798267i	0.370773	+	0.928723i	$0.379093\pi$
$752$	0.147343	−	0.449516i	0.00537303	−	0.0163922i
$753$	−16.8536	+	35.3953i	−0.614180	+	1.28988i
$754$	42.0603	+	28.4492i	1.53175	+	1.03606i
$755$	−17.3842	−	40.3011i	−0.632676	−	1.46671i
$756$	−1.34497	+	25.2286i	−0.0489159	+	0.917556i
$757$	18.9080	−	43.8337i	0.687224	−	1.59316i	−0.113092	−	0.993585i	$-0.536075\pi$
$757$	18.9080	−	43.8337i	0.687224	−	1.59316i	0.800316	−	0.599579i	$-0.204665\pi$
$758$	53.3909	−	34.1352i	1.93925	−	1.23985i
$759$	−34.1498	−	6.64868i	−1.23956	−	0.241332i
$760$	19.6431	+	72.3726i	0.712531	+	2.62523i
$761$	−26.3135	−	1.70333i	−0.953863	−	0.0617455i	−0.420190	−	0.907436i	$-0.638037\pi$
$761$	−26.3135	−	1.70333i	−0.953863	−	0.0617455i	−0.533673	+	0.845691i	$0.679189\pi$
$762$	−23.5507	+	17.8312i	−0.853151	+	0.645958i
$763$	12.2761	+	5.77283i	0.444426	+	0.208990i
$764$	−24.1563	+	29.9491i	−0.873944	+	1.08352i
$765$	−16.7878	+	10.5063i	−0.606964	+	0.379858i
$766$	−76.3090	−	14.9866i	−2.75716	−	0.541488i
$767$	−23.9096	−	35.8459i	−0.863326	−	1.29432i
$768$	14.6701	+	24.5754i

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)

\(f(q)\)	\(=\)	\(q+(-2.29202 - 0.0296337i) q^{2} +(-1.03658 - 1.38762i) q^{3} +(3.25315 + 0.0841346i) q^{4} +(3.65994 + 1.12154i) q^{5} +(2.33475 + 3.21117i) q^{6} +(-0.556114 + 1.38674i) q^{7} +(-2.87282 - 0.111478i) q^{8} +(-0.850984 + 2.87677i) q^{9} +O(q^{10})\)	\(q+(-2.29202 - 0.0296337i) q^{2} +(-1.03658 - 1.38762i) q^{3} +(3.25315 + 0.0841346i) q^{4} +(3.65994 + 1.12154i) q^{5} +(2.33475 + 3.21117i) q^{6} +(-0.556114 + 1.38674i) q^{7} +(-2.87282 - 0.111478i) q^{8} +(-0.850984 + 2.87677i) q^{9} +(-8.35542 - 2.67906i) q^{10} +(-3.20888 - 1.82509i) q^{11} +(-3.25542 - 4.60135i) q^{12} +(-1.41919 - 3.17649i) q^{13} +(1.31572 - 3.16197i) q^{14} +(-2.23756 - 6.24118i) q^{15} +(0.0814789 + 0.00421731i) q^{16} +(1.56997 + 0.713639i) q^{17} +(2.03572 - 6.56841i) q^{18} +(-3.85413 - 5.61945i) q^{19} +(11.8120 + 3.95647i) q^{20} +(2.50073 - 0.665802i) q^{21} +(7.30072 + 4.27824i) q^{22} +(-1.69479 + 5.17050i) q^{23} +(2.82323 + 4.10194i) q^{24} +(7.99571 + 5.40823i) q^{25} +(3.15867 + 7.32263i) q^{26} +(4.87399 - 1.80118i) q^{27} +(-1.92580 + 4.46450i) q^{28} +(5.36459 - 3.42982i) q^{29} +(4.94358 + 14.3712i) q^{30} +(-2.84278 - 10.4739i) q^{31} +(5.55132 + 0.359348i) q^{32} +(0.793737 + 6.34456i) q^{33} +(-3.57726 - 1.68220i) q^{34} +(-3.59064 + 4.45169i) q^{35} +(-3.01042 + 9.28698i) q^{36} +(-10.1592 - 1.99520i) q^{37} +(8.66721 + 12.9941i) q^{38} +(-2.93665 + 5.26199i) q^{39} +(-10.3893 - 3.62999i) q^{40} +(2.77699 - 1.05159i) q^{41} +(-5.75147 + 1.45193i) q^{42} +(10.6392 - 4.67109i) q^{43} +(-10.2854 - 6.20727i) q^{44} +(-6.34097 + 9.57440i) q^{45} +(4.03771 - 11.8007i) q^{46} +(1.51873 - 5.59557i) q^{47} +(-0.0786077 - 0.117433i) q^{48} +(3.44666 + 3.29413i) q^{49} +(-18.1661 - 12.6327i) q^{50} +(-0.637147 - 2.91827i) q^{51} +(-4.34957 - 10.4530i) q^{52} +(3.99431 - 4.23372i) q^{53} +(-11.2247 + 3.98390i) q^{54} +(-9.69737 - 10.2786i) q^{55} +(1.75221 - 3.92187i) q^{56} +(-3.80254 + 11.1731i) q^{57} +(-12.3974 + 7.70225i) q^{58} +(12.2104 - 2.07173i) q^{59} +(-6.75402 - 20.4918i) q^{60} +(2.57877 - 4.74585i) q^{61} +(6.20532 + 24.0905i) q^{62} +(-3.51610 - 2.77991i) q^{63} +(-12.8758 - 1.00079i) q^{64} +(-1.63157 - 13.2174i) q^{65} +(-1.63125 - 14.5654i) q^{66} +(-2.61439 + 1.35560i) q^{67} +(5.04731 + 2.45366i) q^{68} +(8.93148 - 3.00793i) q^{69} +(8.36173 - 10.0970i) q^{70} +(-8.19809 - 6.35400i) q^{71} +(2.76542 - 8.16958i) q^{72} +(5.60742 - 1.79795i) q^{73} +(23.2260 + 4.87411i) q^{74} +(-0.783660 - 16.7011i) q^{75} +(-12.0653 - 18.6052i) q^{76} +(4.31543 - 3.43493i) q^{77} +(6.88680 - 11.9736i) q^{78} +(0.472814 - 2.49258i) q^{79} +(0.293478 + 0.106817i) q^{80} +(-7.55165 - 4.89618i) q^{81} +(-6.39608 + 2.32798i) q^{82} +(1.89072 + 11.5976i) q^{83} +(8.19128 - 1.95555i) q^{84} +(4.94562 + 4.37266i) q^{85} +(-24.5236 + 10.3910i) q^{86} +(-10.3201 - 3.88872i) q^{87} +(9.01505 + 5.60087i) q^{88} +(-8.64592 - 3.53225i) q^{89} +(14.8174 - 21.7568i) q^{90} +(5.19420 - 0.201559i) q^{91} +(-5.94842 + 16.6778i) q^{92} +(-11.5870 + 14.8017i) q^{93} +(-3.64678 + 12.7802i) q^{94} +(-7.80340 - 24.8894i) q^{95} +(-5.25578 - 8.07563i) q^{96} +(-0.982571 + 4.26857i) q^{97} +(-7.80220 - 7.65235i) q^{98} +(7.98107 - 7.67808i) 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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