LMFDB - Embedded newform 729.2.g.a.217.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,-45] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			217.5
Character	$\chi$	$=$	729.217
Dual form			729.2.g.a.514.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0330035 + 0.566648i) q^{2} +(1.66648 + 0.194783i) q^{4} +(-2.82546 + 0.669646i) q^{5} +(1.86900 + 2.51050i) q^{7} +(-0.362501 + 2.05585i) q^{8} +(-0.286203 - 1.62314i) q^{10} +(-2.35528 + 2.49645i) q^{11} +(-3.56363 - 1.78972i) q^{13} +(-1.48425 + 0.976208i) q^{14} +(2.11221 + 0.500604i) q^{16} +(-0.878443 - 0.319727i) q^{17} +(-4.55845 + 1.65914i) q^{19} +(-4.83899 + 0.565597i) q^{20} +(-1.33688 - 1.41701i) q^{22} +(3.67387 - 4.93486i) q^{23} +(3.06662 - 1.54011i) q^{25} +(1.13175 - 1.96026i) q^{26} +(2.62564 + 4.54773i) q^{28} +(1.50363 + 0.988954i) q^{29} +(0.267699 + 0.620597i) q^{31} +(-1.55082 + 5.18008i) q^{32} +(0.210164 - 0.487216i) q^{34} +(-6.96191 - 5.84174i) q^{35} +(-8.73079 + 7.32600i) q^{37} +(-0.789703 - 2.63779i) q^{38} +(-0.352457 - 6.05145i) q^{40} +(0.386817 + 6.64138i) q^{41} +(0.641410 + 2.14246i) q^{43} +(-4.41129 + 3.70151i) q^{44} +(2.67508 + 2.24466i) q^{46} +(1.25543 - 2.91042i) q^{47} +(-0.801829 + 2.67830i) q^{49} +(0.771493 + 1.78852i) q^{50} +(-5.59010 - 3.67666i) q^{52} +(4.18963 + 7.25666i) q^{53} +(4.98301 - 8.63082i) q^{55} +(-5.83871 + 2.93231i) q^{56} +(-0.610014 + 0.819391i) q^{58} +(-3.45239 - 3.65932i) q^{59} +(0.566780 - 0.0662470i) q^{61} +(-0.360495 + 0.131209i) q^{62} +(1.19553 + 0.435136i) q^{64} +(11.2674 + 2.67041i) q^{65} +(11.4202 - 7.51120i) q^{67} +(-1.40163 - 0.703923i) q^{68} +(3.53998 - 3.75216i) q^{70} +(2.31784 + 13.1452i) q^{71} +(-1.17142 + 6.64347i) q^{73} +(-3.86312 - 5.18907i) q^{74} +(-7.91971 + 1.87701i) q^{76} +(-10.6693 - 1.24707i) q^{77} +(-0.0433375 + 0.744075i) q^{79} -6.30319 q^{80} -3.77609 q^{82} +(-0.211615 + 3.63329i) q^{83} +(2.69611 + 0.315130i) q^{85} +(-1.23519 + 0.292745i) q^{86} +(-4.27853 - 5.74706i) q^{88} +(2.27781 - 12.9181i) q^{89} +(-2.16732 - 12.2915i) q^{91} +(7.08364 - 7.50822i) q^{92} +(1.60775 + 0.807443i) q^{94} +(11.7687 - 7.74037i) q^{95} +(12.1682 + 2.88392i) q^{97} +(-1.49119 - 0.542748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{14}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0330035	+	0.566648i	−0.0233370	+	0.400681i	0.966331	+	0.257302i	$0.0828336\pi$
$2$	−0.0330035	+	0.566648i	−0.0233370	+	0.400681i	−0.989668	+	0.143378i	$0.954203\pi$
$3$		0			0
$3$		0			0
$4$	1.66648	+	0.194783i	0.833238	+	0.0973916i
$5$	−2.82546	+	0.669646i	−1.26358	+	0.299475i	−0.807184	−	0.590300i	$-0.799009\pi$
$5$	−2.82546	+	0.669646i	−1.26358	+	0.299475i	−0.456399	+	0.889775i	$0.650861\pi$
$6$		0			0
$7$	1.86900	+	2.51050i	0.706414	+	0.948879i	0.999975	−	0.00706140i	$-0.00224773\pi$
$7$	1.86900	+	2.51050i	0.706414	+	0.948879i	−0.293561	+	0.955940i	$0.594840\pi$
$8$	−0.362501	+	2.05585i	−0.128164	+	0.726852i
$9$		0			0
$10$	−0.286203	−	1.62314i	−0.0905055	−	0.513282i
$11$	−2.35528	+	2.49645i	−0.710144	+	0.752709i	−0.977511	−	0.210886i	$-0.932365\pi$
$11$	−2.35528	+	2.49645i	−0.710144	+	0.752709i	0.267367	+	0.963595i	$0.413847\pi$
$12$		0			0
$13$	−3.56363	−	1.78972i	−0.988373	−	0.496380i	−0.120258	−	0.992743i	$-0.538372\pi$
$13$	−3.56363	−	1.78972i	−0.988373	−	0.496380i	−0.868115	+	0.496363i	$0.834669\pi$
$14$	−1.48425	+	0.976208i	−0.396683	+	0.260902i
$15$		0			0
$16$	2.11221	+	0.500604i	0.528053	+	0.125151i
$17$	−0.878443	−	0.319727i	−0.213054	−	0.0775452i	0.233289	−	0.972408i	$-0.425051\pi$
$17$	−0.878443	−	0.319727i	−0.213054	−	0.0775452i	−0.446342	+	0.894862i	$0.647274\pi$
$18$		0			0
$19$	−4.55845	+	1.65914i	−1.04578	+	0.380633i	−0.807068	−	0.590458i	$-0.798947\pi$
$19$	−4.55845	+	1.65914i	−1.04578	+	0.380633i	−0.238711	+	0.971091i	$0.576725\pi$
$20$	−4.83899	+	0.565597i	−1.08203	+	0.126471i
$21$		0			0
$22$	−1.33688	−	1.41701i	−0.285023	−	0.302107i
$23$	3.67387	−	4.93486i	0.766055	−	1.02899i	−0.232356	−	0.972631i	$-0.574643\pi$
$23$	3.67387	−	4.93486i	0.766055	−	1.02899i	0.998411	−	0.0563591i	$-0.0179492\pi$
$24$		0			0
$25$	3.06662	−	1.54011i	0.613324	−	0.308023i
$26$	1.13175	−	1.96026i	0.221955	−	0.384438i
$27$		0			0
$28$	2.62564	+	4.54773i	0.496198	+	0.859441i
$29$	1.50363	+	0.988954i	0.279217	+	0.183644i	0.681392	−	0.731919i	$-0.261375\pi$
$29$	1.50363	+	0.988954i	0.279217	+	0.183644i	−0.402174	+	0.915563i	$0.631745\pi$
$30$		0			0
$31$	0.267699	+	0.620597i	0.0480802	+	0.111462i	0.940563	−	0.339618i	$-0.110298\pi$
$31$	0.267699	+	0.620597i	0.0480802	+	0.111462i	−0.892483	+	0.451081i	$0.851039\pi$
$32$	−1.55082	+	5.18008i	−0.274148	+	0.915718i
$33$		0			0
$34$	0.210164	−	0.487216i	0.0360429	−	0.0835568i
$35$	−6.96191	−	5.84174i	−1.17678	−	0.987434i
$36$		0			0
$37$	−8.73079	+	7.32600i	−1.43533	+	1.20439i	−0.492858	+	0.870110i	$0.664048\pi$
$37$	−8.73079	+	7.32600i	−1.43533	+	1.20439i	−0.942475	+	0.334277i	$0.891508\pi$
$38$	−0.789703	−	2.63779i	−0.128107	−	0.427906i
$39$		0			0
$40$	−0.352457	−	6.05145i	−0.0557284	−	0.956819i
$41$	0.386817	+	6.64138i	0.0604106	+	1.03721i	0.883240	+	0.468921i	$0.155357\pi$
$41$	0.386817	+	6.64138i	0.0604106	+	1.03721i	−0.822829	+	0.568288i	$0.807606\pi$
$42$		0			0
$43$	0.641410	+	2.14246i	0.0978141	+	0.326722i	0.992865	−	0.119242i	$-0.0380463\pi$
$43$	0.641410	+	2.14246i	0.0978141	+	0.326722i	−0.895051	+	0.445964i	$0.852861\pi$
$44$	−4.41129	+	3.70151i	−0.665026	+	0.558023i
$45$		0			0
$46$	2.67508	+	2.24466i	0.394419	+	0.330957i
$47$	1.25543	−	2.91042i	0.183124	−	0.424529i	−0.801783	−	0.597616i	$-0.796115\pi$
$47$	1.25543	−	2.91042i	0.183124	−	0.424529i	0.984907	+	0.173087i	$0.0553742\pi$
$48$		0			0
$49$	−0.801829	+	2.67830i	−0.114547	+	0.382614i
$50$	0.771493	+	1.78852i	0.109106	+	0.252935i
$51$		0			0
$52$	−5.59010	−	3.67666i	−0.775207	−	0.509862i
$53$	4.18963	+	7.25666i	0.575490	+	0.996779i	0.995988	+	0.0894851i	$0.0285221\pi$
$53$	4.18963	+	7.25666i	0.575490	+	0.996779i	−0.420498	+	0.907294i	$0.638145\pi$
$54$		0			0
$55$	4.98301	−	8.63082i	0.671909	−	1.16378i
$56$	−5.83871	+	2.93231i	−0.780231	+	0.391847i
$57$		0			0
$58$	−0.610014	+	0.819391i	−0.0800987	+	0.107591i
$59$	−3.45239	−	3.65932i	−0.449463	−	0.476403i	0.462533	−	0.886602i	$-0.346941\pi$
$59$	−3.45239	−	3.65932i	−0.449463	−	0.476403i	−0.911996	+	0.410199i	$0.865459\pi$
$60$		0			0
$61$	0.566780	−	0.0662470i	0.0725687	−	0.00848206i	−0.0797311	−	0.996816i	$-0.525406\pi$
$61$	0.566780	−	0.0662470i	0.0725687	−	0.00848206i	0.152300	+	0.988334i	$0.451332\pi$
$62$	−0.360495	+	0.131209i	−0.0457829	+	0.0166636i
$63$		0			0
$64$	1.19553	+	0.435136i	0.149441	+	0.0543920i
$65$	11.2674	+	2.67041i	1.39754	+	0.331224i
$66$		0			0
$67$	11.4202	−	7.51120i	1.39520	−	0.917639i	0.395203	−	0.918594i	$-0.370674\pi$
$67$	11.4202	−	7.51120i	1.39520	−	0.917639i	1.00000		0.000954570i	$0.000303849\pi$
$68$	−1.40163	−	0.703923i	−0.169972	−	0.0853632i
$69$		0			0
$70$	3.53998	−	3.75216i	0.423108	−	0.448468i
$71$	2.31784	+	13.1452i	0.275078	+	1.56004i	0.738715	+	0.674017i	$0.235433\pi$
$71$	2.31784	+	13.1452i	0.275078	+	1.56004i	−0.463638	+	0.886025i	$0.653456\pi$
$72$		0			0
$73$	−1.17142	+	6.64347i	−0.137105	+	0.777560i	0.836266	+	0.548324i	$0.184734\pi$
$73$	−1.17142	+	6.64347i	−0.137105	+	0.777560i	−0.973371	+	0.229236i	$0.926377\pi$
$74$	−3.86312	−	5.18907i	−0.449078	−	0.603217i
$75$		0			0
$76$	−7.91971	+	1.87701i	−0.908454	+	0.215307i
$77$	−10.6693	−	1.24707i	−1.21589	−	0.142117i
$78$		0			0
$79$	−0.0433375	+	0.744075i	−0.00487584	+	0.0837150i	−0.999868	−	0.0162362i	$-0.994832\pi$
$79$	−0.0433375	+	0.744075i	−0.00487584	+	0.0837150i	0.994992	+	0.0999512i	$0.0318687\pi$
$80$	−6.30319			−0.704718
$81$		0			0
$82$	−3.77609			−0.417000
$83$	−0.211615	+	3.63329i	−0.0232277	+	0.398805i	0.966577	+	0.256376i	$0.0825284\pi$
$83$	−0.211615	+	3.63329i	−0.0232277	+	0.398805i	−0.989805	+	0.142429i	$0.954509\pi$
$84$		0			0
$85$	2.69611	+	0.315130i	0.292434	+	0.0341806i
$86$	−1.23519	+	0.292745i	−0.133194	+	0.0315675i
$87$		0			0
$88$	−4.27853	−	5.74706i	−0.456093	−	0.612639i
$89$	2.27781	−	12.9181i	0.241447	−	1.36931i	−0.587154	−	0.809475i	$-0.699752\pi$
$89$	2.27781	−	12.9181i	0.241447	−	1.36931i	0.828601	−	0.559839i	$-0.189137\pi$
$90$		0			0
$91$	−2.16732	−	12.2915i	−0.227197	−	1.28850i
$92$	7.08364	−	7.50822i	0.738521	−	0.782786i
$93$		0			0
$94$	1.60775	+	0.807443i	0.165827	+	0.0832814i
$95$	11.7687	−	7.74037i	1.20744	−	0.794145i
$96$		0			0
$97$	12.1682	+	2.88392i	1.23549	+	0.292818i	0.795927	−	0.605392i	$-0.206984\pi$
$97$	12.1682	+	2.88392i	1.23549	+	0.292818i	0.439567	+	0.898210i	$0.355132\pi$
$98$	−1.49119	−	0.542748i	−0.150633	−	0.0548258i
$99$		0			0
$100$	5.41044	−	1.96924i	0.541044	−	0.196924i
$101$	−5.94334	+	0.694676i	−0.591384	+	0.0691229i	−0.406521	−	0.913641i	$-0.633258\pi$
$101$	−5.94334	+	0.694676i	−0.591384	+	0.0691229i	−0.184863	+	0.982764i	$0.559184\pi$
$102$		0			0
$103$	−1.21369	−	1.28643i	−0.119588	−	0.126756i	0.664813	−	0.747010i	$-0.268511\pi$
$103$	−1.21369	−	1.28643i	−0.119588	−	0.126756i	−0.784401	+	0.620254i	$0.787030\pi$
$104$	4.97122	−	6.67750i	0.487468	−	0.654783i
$105$		0			0
$106$	−4.25024	+	2.13455i	−0.412820	+	0.207326i
$107$	3.57628	−	6.19429i	0.345732	−	0.598825i	−0.639755	−	0.768579i	$-0.720964\pi$
$107$	3.57628	−	6.19429i	0.345732	−	0.598825i	0.985486	+	0.169754i	$0.0542974\pi$
$108$		0			0
$109$	−5.68613	−	9.84867i	−0.544633	−	0.943332i	−0.998630	−	0.0523287i	$-0.983336\pi$
$109$	−5.68613	−	9.84867i	−0.544633	−	0.943332i	0.453997	−	0.891003i	$-0.349998\pi$
$110$	4.72618	+	3.10846i	0.450624	+	0.296380i
$111$		0			0
$112$	2.69095	+	6.23833i	0.254271	+	0.589467i
$113$	−1.67037	+	5.57942i	−0.157135	+	0.524868i	−0.999910	−	0.0133980i	$-0.995735\pi$
$113$	−1.67037	+	5.57942i	−0.157135	+	0.524868i	0.842775	+	0.538266i	$0.180920\pi$
$114$		0			0
$115$	−7.07575	+	16.4034i	−0.659817	+	1.52963i
$116$	2.31313	+	1.94095i	0.214769	+	0.180213i
$117$		0			0
$118$	2.18749	−	1.83552i	0.201375	−	0.168973i
$119$	−0.839132	−	2.80290i	−0.0769231	−	0.256941i
$120$		0			0
$121$	−0.0453310	−	0.778304i	−0.00412100	−	0.0707549i
$122$	0.0188330	+	0.323351i	0.00170506	+	0.0292748i
$123$		0			0
$124$	0.325233	+	1.08635i	0.0292068	+	0.0975574i
$125$	3.48865	−	2.92733i	0.312034	−	0.261828i
$126$		0			0
$127$	8.22802	+	6.90413i	0.730119	+	0.612643i	0.930164	−	0.367144i	$-0.119664\pi$
$127$	8.22802	+	6.90413i	0.730119	+	0.612643i	−0.200045	+	0.979787i	$0.564109\pi$
$128$	−4.56943	+	10.5931i	−0.403884	+	0.936308i
$129$		0			0
$130$	−1.88505	+	6.29650i	−0.165330	+	0.552239i
$131$	2.83697	+	6.57683i	0.247867	+	0.574621i	0.996042	−	0.0888807i	$-0.0283290\pi$
$131$	2.83697	+	6.57683i	0.247867	+	0.574621i	−0.748175	+	0.663501i	$0.769070\pi$
$132$		0			0
$133$	−12.6850	−	8.34305i	−1.09993	−	0.723434i
$134$	3.87930	+	6.71914i	0.335120	+	0.580446i
$135$		0			0
$136$	0.975746	−	1.69004i	0.0836695	−	0.144920i
$137$	7.71126	−	3.87274i	0.658817	−	0.330871i	−0.0877866	−	0.996139i	$-0.527979\pi$
$137$	7.71126	−	3.87274i	0.658817	−	0.330871i	0.746604	+	0.665269i	$0.231683\pi$
$138$		0			0
$139$	−3.52273	+	4.73184i	−0.298794	+	0.401350i	−0.926012	−	0.377494i	$-0.876786\pi$
$139$	−3.52273	+	4.73184i	−0.298794	+	0.401350i	0.627218	+	0.778843i	$0.284193\pi$
$140$	−10.4640	−	11.0912i	−0.884369	−	0.937376i
$141$		0			0
$142$	−7.52517	+	0.879566i	−0.631498	+	0.0738115i
$143$	12.8613	−	4.68113i	1.07552	−	0.391456i
$144$		0			0
$145$	−4.91069	−	1.78735i	−0.407811	−	0.148431i
$146$	−3.72585	−	0.883043i	−0.308354	−	0.0730811i
$147$		0			0
$148$	−15.9766	+	10.5080i	−1.31327	+	0.863752i
$149$	12.3273	+	6.19101i	1.00989	+	0.507187i	0.875232	−	0.483704i	$-0.160709\pi$
$149$	12.3273	+	6.19101i	1.00989	+	0.507187i	0.134662	+	0.990892i	$0.457005\pi$
$150$		0			0
$151$	−4.30754	+	4.56573i	−0.350543	+	0.371553i	−0.878520	−	0.477705i	$-0.841469\pi$
$151$	−4.30754	+	4.56573i	−0.350543	+	0.371553i	0.527978	+	0.849258i	$0.322950\pi$
$152$	−1.75849	−	9.97291i	−0.142633	−	0.808910i
$153$		0			0
$154$	1.05877	−	6.00461i	0.0853185	−	0.483865i
$155$	−1.17195	−	1.57421i	−0.0941335	−	0.126443i
$156$		0			0
$157$	−0.161617	+	0.0383039i	−0.0128984	+	0.00305698i	−0.237060	−	0.971495i	$-0.576184\pi$
$157$	−0.161617	+	0.0383039i	−0.0128984	+	0.00305698i	0.224162	+	0.974552i	$0.428036\pi$
$158$	−0.420199	−	0.0491142i	−0.0334292	−	0.00390731i
$159$		0			0
$160$	0.912941	−	15.6746i	0.0721744	−	1.23919i
$161$	19.2554			1.51754
$162$		0			0
$163$	16.2014			1.26899			0.634495	−	0.772927i	$-0.281208\pi$
$163$	16.2014			1.26899			0.634495	+	0.772927i	$0.281208\pi$
$164$	−0.649009	+	11.1431i	−0.0506791	+	0.870126i
$165$		0			0
$166$	−2.05181	−	0.239822i	−0.159251	−	0.0186138i
$167$	17.7834	−	4.21475i	1.37612	−	0.326147i	0.524994	−	0.851106i	$-0.324067\pi$
$167$	17.7834	−	4.21475i	1.37612	−	0.326147i	0.851128	+	0.524959i	$0.175919\pi$
$168$		0			0
$169$	1.73329	+	2.32822i	0.133330	+	0.179094i
$170$	−0.267548	+	1.51734i	−0.0205200	+	0.116375i
$171$		0			0
$172$	0.651580	+	3.69529i	0.0496825	+	0.281763i
$173$	12.9383	−	13.7138i	0.983679	−	1.04264i	−0.0154065	−	0.999881i	$-0.504904\pi$
$173$	12.9383	−	13.7138i	0.983679	−	1.04264i	0.999085	−	0.0427575i	$-0.0136143\pi$
$174$		0			0
$175$	9.59795	+	4.82027i	0.725537	+	0.364378i
$176$	−6.22459	+	4.09398i	−0.469196	+	0.308595i
$177$		0			0
$178$	7.24483	+	1.71706i	0.543023	+	0.128699i
$179$	−9.67521	−	3.52149i	−0.723159	−	0.263209i	−0.0458930	−	0.998946i	$-0.514613\pi$
$179$	−9.67521	−	3.52149i	−0.723159	−	0.263209i	−0.677266	+	0.735738i	$0.736836\pi$
$180$		0			0
$181$	0.770198	−	0.280329i	0.0572484	−	0.0208367i	−0.313237	−	0.949675i	$-0.601414\pi$
$181$	0.770198	−	0.280329i	0.0572484	−	0.0208367i	0.370486	+	0.928838i	$0.379191\pi$
$182$	7.03647	−	0.822445i	0.521578	−	0.0609637i
$183$		0			0
$184$	8.81354	+	9.34181i	0.649743	+	0.688687i
$185$	19.7626	−	26.5458i	1.45298	−	1.95169i
$186$		0			0
$187$	2.86716	−	1.43994i	0.209668	−	0.105299i
$188$	2.65905	−	4.60561i	0.193931	−	0.335899i
$189$		0			0
$190$	3.99766	+	6.92415i	0.290021	+	0.502330i
$191$	−0.639191	−	0.420402i	−0.0462502	−	0.0304193i	0.526173	−	0.850377i	$-0.323626\pi$
$191$	−0.639191	−	0.420402i	−0.0462502	−	0.0304193i	−0.572424	+	0.819958i	$0.693997\pi$
$192$		0			0
$193$	3.70520	+	8.58963i	0.266706	+	0.618295i	0.997962	−	0.0638084i	$-0.0203246\pi$
$193$	3.70520	+	8.58963i	0.266706	+	0.618295i	−0.731256	+	0.682103i	$0.761065\pi$
$194$	−2.03576	+	6.79991i	−0.146159	+	0.488205i
$195$		0			0
$196$	−1.85792	+	4.30713i	−0.132708	+	0.307652i
$197$	−0.857832	−	0.719807i	−0.0611180	−	0.0512841i	0.611717	−	0.791077i	$-0.290479\pi$
$197$	−0.857832	−	0.719807i	−0.0611180	−	0.0512841i	−0.672835	+	0.739793i	$0.734924\pi$
$198$		0			0
$199$	5.88368	−	4.93699i	0.417083	−	0.349974i	−0.409969	−	0.912099i	$-0.634461\pi$
$199$	5.88368	−	4.93699i	0.417083	−	0.349974i	0.827052	+	0.562125i	$0.190016\pi$
$200$	2.05458	+	6.86279i	0.145281	+	0.485273i
$201$		0			0
$202$	−0.197486	−	3.39071i	−0.0138951	−	0.238569i
$203$	0.327515	+	5.62322i	0.0229870	+	0.394672i
$204$		0			0
$205$	−5.54031	−	18.5059i	−0.386952	−	1.29251i
$206$	0.769010	−	0.645276i	0.0535794	−	0.0449585i
$207$		0			0
$208$	−6.63120	−	5.56424i	−0.459791	−	0.385811i
$209$	6.59446	−	15.2877i	0.456149	−	1.05747i
$210$		0			0
$211$	2.93609	−	9.80721i	0.202129	−	0.675156i	−0.795476	−	0.605985i	$-0.792779\pi$
$211$	2.93609	−	9.80721i	0.202129	−	0.675156i	0.997605	−	0.0691715i	$-0.0220356\pi$
$212$	5.56845	+	12.9091i	0.382443	+	0.886602i
$213$		0			0
$214$	3.39195	+	2.23092i	0.231869	+	0.152503i
$215$	−3.24697	−	5.62391i	−0.221441	−	0.383547i
$216$		0			0
$217$	−1.05768	+	1.83195i	−0.0717999	+	0.124361i
$218$	5.76839	−	2.89700i	0.390685	−	0.196209i
$219$		0			0
$220$	9.98520	−	13.4125i	0.673202	−	0.904267i
$221$	2.55822	+	2.71156i	0.172085	+	0.182399i
$222$		0			0
$223$	4.62022	−	0.540027i	0.309393	−	0.0361629i	0.0400203	−	0.999199i	$-0.487258\pi$
$223$	4.62022	−	0.540027i	0.309393	−	0.0361629i	0.269373	+	0.963036i	$0.413184\pi$
$224$	−15.9031	+	5.78824i	−1.06257	+	0.386743i
$225$		0			0
$226$	−3.10644	−	1.13065i	−0.206637	−	0.0752098i
$227$	−13.7390	−	3.25620i	−0.911888	−	0.216121i	−0.252212	−	0.967672i	$-0.581158\pi$
$227$	−13.7390	−	3.25620i	−0.911888	−	0.216121i	−0.659676	+	0.751550i	$0.729306\pi$
$228$		0			0
$229$	4.33228	−	2.84938i	0.286285	−	0.188292i	−0.398242	−	0.917281i	$-0.630379\pi$
$229$	4.33228	−	2.84938i	0.286285	−	0.188292i	0.684526	+	0.728988i	$0.260009\pi$
$230$	−9.06145	−	4.55083i	−0.597494	−	0.300073i
$231$		0			0
$232$	−2.57821	+	2.73274i	−0.169268	+	0.179413i
$233$	−0.773336	−	4.38581i	−0.0506629	−	0.287324i	0.948941	−	0.315452i	$-0.102156\pi$
$233$	−0.773336	−	4.38581i	−0.0506629	−	0.287324i	−0.999604	+	0.0281287i	$0.991045\pi$
$234$		0			0
$235$	−1.59822	+	9.06397i	−0.104257	+	0.591268i
$236$	−5.04056	−	6.77064i	−0.328112	−	0.440731i
$237$		0			0
$238$	1.61595	−	0.382987i	0.104746	−	0.0248254i
$239$	−28.8649	−	3.37382i	−1.86711	−	0.218234i	−0.893921	−	0.448224i	$-0.852057\pi$
$239$	−28.8649	−	3.37382i	−1.86711	−	0.218234i	−0.973193	+	0.229989i	$0.926131\pi$
$240$		0			0
$241$	−1.45269	+	24.9418i	−0.0935762	+	1.60664i	0.545914	+	0.837841i	$0.316183\pi$
$241$	−1.45269	+	24.9418i	−0.0935762	+	1.60664i	−0.639490	+	0.768800i	$0.720854\pi$
$242$	0.442520			0.0284463
$243$		0			0
$244$	0.957429			0.0612931
$245$	0.472025	−	8.10435i	0.0301566	−	0.517768i
$246$		0			0
$247$	19.2140	+	2.24580i	1.22256	+	0.142897i
$248$	−1.37289	+	0.325382i	−0.0871788	+	0.0206618i
$249$		0			0
$250$	1.54363	+	2.07345i	0.0976275	+	0.131136i
$251$	−2.46091	+	13.9565i	−0.155331	+	0.880926i	0.803152	+	0.595775i	$0.203155\pi$
$251$	−2.46091	+	13.9565i	−0.155331	+	0.880926i	−0.958483	+	0.285151i	$0.907956\pi$
$252$		0			0
$253$	3.66665	+	20.7946i	0.230521	+	1.30735i
$254$	−4.18376	+	4.43453i	−0.262513	+	0.278247i
$255$		0			0
$256$	−3.57791	−	1.79689i	−0.223619	−	0.112306i
$257$	12.2808	−	8.07720i	0.766055	−	0.503842i	−0.105333	−	0.994437i	$-0.533591\pi$
$257$	12.2808	−	8.07720i	0.766055	−	0.503842i	0.871388	+	0.490595i	$0.163220\pi$
$258$		0			0
$259$	−34.7097	−	8.22635i	−2.15676	−	0.511161i
$260$	18.2566	+	6.64487i	1.13223	+	0.412098i
$261$		0			0
$262$	−3.82038	+	1.39050i	−0.236024	+	0.0859056i
$263$	16.2782	−	1.90265i	1.00376	−	0.117322i	0.401696	−	0.915773i	$-0.368421\pi$
$263$	16.2782	−	1.90265i	1.00376	−	0.117322i	0.602060	+	0.798451i	$0.294347\pi$
$264$		0			0
$265$	−16.6970	−	17.6978i	−1.02569	−	1.08717i
$266$	5.14622	−	6.91257i	0.315535	−	0.423837i
$267$		0			0
$268$	20.4946	−	10.2928i	1.25191	−	0.628731i
$269$	−5.68131	+	9.84032i	−0.346396	+	0.599975i	−0.985606	−	0.169057i	$-0.945928\pi$
$269$	−5.68131	+	9.84032i	−0.346396	+	0.599975i	0.639211	+	0.769032i	$0.279261\pi$
$270$		0			0
$271$	−1.38266	−	2.39483i	−0.0839903	−	0.145476i	0.820970	−	0.570971i	$-0.193433\pi$
$271$	−1.38266	−	2.39483i	−0.0839903	−	0.145476i	−0.904961	+	0.425496i	$0.860100\pi$
$272$	−1.69540	−	1.11508i	−0.102799	−	0.0676118i
$273$		0			0
$274$	1.93998	+	4.49738i	0.117199	+	0.271697i
$275$	−3.37793	+	11.2831i	−0.203697	+	0.680395i
$276$		0			0
$277$	7.28632	−	16.8916i	0.437792	−	1.01492i	−0.546353	−	0.837555i	$-0.683984\pi$
$277$	7.28632	−	16.8916i	0.437792	−	1.01492i	0.984146	−	0.177362i	$-0.0567564\pi$
$278$	−2.56503	−	2.15231i	−0.153840	−	0.129087i
$279$		0			0
$280$	14.5334	−	12.1950i	0.868538	−	0.728790i
$281$	3.07831	+	10.2823i	0.183636	+	0.613388i	0.999388	+	0.0349857i	$0.0111386\pi$
$281$	3.07831	+	10.2823i	0.183636	+	0.613388i	−0.815751	+	0.578403i	$0.803676\pi$
$282$		0			0
$283$	0.831003	+	14.2678i	0.0493980	+	0.848131i	0.928462	+	0.371427i	$0.121131\pi$
$283$	0.831003	+	14.2678i	0.0493980	+	0.848131i	−0.879064	+	0.476704i	$0.841832\pi$
$284$	1.30218	+	22.3576i	0.0772701	+	1.32668i
$285$		0			0
$286$	2.22809	+	7.44233i	0.131750	+	0.440074i
$287$	−15.9502	+	13.3838i	−0.941512	+	0.790022i
$288$		0			0
$289$	−12.3533	−	10.3657i	−0.726666	−	0.609745i
$290$	1.17487	−	2.72365i	0.0689905	−	0.159938i
$291$		0			0
$292$	−3.24619	+	10.8430i	−0.189969	+	0.634540i
$293$	8.65273	+	20.0593i	0.505498	+	1.17188i	0.959713	+	0.280983i	$0.0906605\pi$
$293$	8.65273	+	20.0593i	0.505498	+	1.17188i	−0.454215	+	0.890892i	$0.650080\pi$
$294$		0			0
$295$	12.2050	+	8.02738i	0.710605	+	0.467372i
$296$	−11.8962	−	20.6048i	−0.691453	−	1.19763i
$297$		0			0
$298$	−3.91497	+	6.78092i	−0.226788	+	0.392808i
$299$	−21.9243	+	11.0108i	−1.26792	+	0.636772i
$300$		0			0
$301$	−4.17985	+	5.61451i	−0.240922	+	0.323615i
$302$	−2.44499	−	2.59154i	−0.140694	−	0.149127i
$303$		0			0
$304$	−10.4590	+	1.22248i	−0.599864	+	0.0701140i
$305$	−1.55705	+	0.566720i	−0.0891564	+	0.0324503i
$306$		0			0
$307$	−28.6368	−	10.4229i	−1.63439	−	0.594869i	−0.648344	−	0.761347i	$-0.724538\pi$
$307$	−28.6368	−	10.4229i	−1.63439	−	0.594869i	−0.986045	+	0.166478i	$0.946760\pi$
$308$	−17.5373	−	4.15642i	−0.999281	−	0.236834i
$309$		0			0
$310$	0.930699	−	0.612130i	0.0528602	−	0.0347667i
$311$	−24.2284	−	12.1679i	−1.37387	−	0.689981i	−0.399875	−	0.916570i	$-0.630946\pi$
$311$	−24.2284	−	12.1679i	−1.37387	−	0.689981i	−0.973990	+	0.226589i	$0.927243\pi$
$312$		0			0
$313$	5.56294	−	5.89637i	0.314436	−	0.333282i	−0.550810	−	0.834631i	$-0.685681\pi$
$313$	5.56294	−	5.89637i	0.314436	−	0.333282i	0.865245	+	0.501348i	$0.167163\pi$
$314$	−0.0163709	−	0.0928440i	−0.000923863	−	0.00523949i
$315$		0			0
$316$	−0.217154	+	1.23154i	−0.0122159	+	0.0692797i
$317$	11.5963	+	15.5765i	0.651312	+	0.874864i	0.998006	−	0.0631143i	$-0.0201033\pi$
$317$	11.5963	+	15.5765i	0.651312	+	0.874864i	−0.346694	+	0.937978i	$0.612696\pi$
$318$		0			0
$319$	−6.01035	+	1.42448i	−0.336515	+	0.0797555i
$320$	−3.66930	−	0.428879i	−0.205120	−	0.0239751i
$321$		0			0
$322$	−0.635496	+	10.9110i	−0.0354148	+	0.608048i
$323$	4.53480			0.252323
$324$		0			0
$325$	−13.6847			−0.759089
$326$	−0.534702	+	9.18047i	−0.0296144	+	0.508459i
$327$		0			0
$328$	−13.7939	−	1.61227i	−0.761640	−	0.0890229i
$329$	9.65301	−	2.28780i	0.532188	−	0.126131i
$330$		0			0
$331$	1.18638	+	1.59359i	0.0652095	+	0.0875916i	0.833531	−	0.552472i	$-0.186315\pi$
$331$	1.18638	+	1.59359i	0.0652095	+	0.0875916i	−0.768322	+	0.640064i	$0.778908\pi$
$332$	−1.06035	+	6.01357i	−0.0581945	+	0.330037i
$333$		0			0
$334$	1.80136	+	10.2160i	0.0985662	+	0.558997i
$335$	−27.2375	+	28.8701i	−1.48814	+	1.57734i
$336$		0			0
$337$	−16.4031	−	8.23796i	−0.893535	−	0.448750i	−0.0580820	−	0.998312i	$-0.518498\pi$
$337$	−16.4031	−	8.23796i	−0.893535	−	0.448750i	−0.835453	+	0.549562i	$0.814795\pi$
$338$	−1.37648	+	0.905328i	−0.0748709	+	0.0492433i
$339$		0			0
$340$	4.43161	+	1.05031i	0.240338	+	0.0569611i
$341$	−2.17980	−	0.793381i	−0.118043	−	0.0429640i
$342$		0			0
$343$	12.3650	−	4.50048i	0.667646	−	0.243003i
$344$	−4.63708	+	0.541997i	−0.250015	+	0.0292225i
$345$		0			0
$346$	7.34387	+	7.78405i	0.394809	+	0.418473i
$347$	−15.9943	+	21.4841i	−0.858618	+	1.15332i	0.128241	+	0.991743i	$0.459067\pi$
$347$	−15.9943	+	21.4841i	−0.858618	+	1.15332i	−0.986859	+	0.161582i	$0.948340\pi$
$348$		0			0
$349$	−11.7150	+	5.88351i	−0.627091	+	0.314937i	−0.733813	−	0.679352i	$-0.762261\pi$
$349$	−11.7150	+	5.88351i	−0.627091	+	0.314937i	0.106722	+	0.994289i	$0.465965\pi$
$350$	−3.04816	+	5.27957i	−0.162931	+	0.282205i
$351$		0			0
$352$	−9.27922	−	16.0721i	−0.494584	−	0.856645i
$353$	−16.2375	−	10.6796i	−0.864237	−	0.568418i	0.0381850	−	0.999271i	$-0.487842\pi$
$353$	−16.2375	−	10.6796i	−0.864237	−	0.568418i	−0.902422	+	0.430853i	$0.858213\pi$
$354$		0			0
$355$	−15.3516	−	35.5889i	−0.814776	−	1.88886i
$356$	6.31214	−	21.0840i	0.334543	−	1.11745i
$357$		0			0
$358$	2.31476	−	5.36622i	0.122339	−	0.283613i
$359$	11.2428	+	9.43384i	0.593373	+	0.497899i	0.889308	−	0.457309i	$-0.151187\pi$
$359$	11.2428	+	9.43384i	0.593373	+	0.497899i	−0.295935	+	0.955208i	$0.595631\pi$
$360$		0			0
$361$	3.47185	−	2.91323i	0.182729	−	0.153328i
$362$	0.133429	+	0.445683i	0.00701286	+	0.0234246i
$363$		0			0
$364$	−1.21761	−	20.9056i	−0.0638202	−	1.09575i
$365$	−1.13897	−	19.5553i	−0.0596162	−	1.02357i
$366$		0			0
$367$	3.15312	+	10.5322i	0.164592	+	0.549775i	1.00000		0.000144782i	$4.60856e-5\pi$
$367$	3.15312	+	10.5322i	0.164592	+	0.549775i	−0.835408	+	0.549630i	$0.814769\pi$
$368$	10.2304	−	8.58433i	0.533297	−	0.447489i
$369$		0			0
$370$	14.3899	+	12.0746i	0.748096	+	0.627727i
$371$	−10.3874	+	24.0807i	−0.539288	+	1.25021i
$372$		0			0
$373$	5.85601	−	19.5604i	0.303213	−	1.01280i	−0.661599	−	0.749858i	$-0.730122\pi$
$373$	5.85601	−	19.5604i	0.303213	−	1.01280i	0.964812	−	0.262943i	$-0.0846930\pi$
$374$	0.721314	+	1.67219i	0.0372983	+	0.0864671i
$375$		0			0
$376$	5.52828	+	3.63601i	0.285100	+	0.187513i
$377$	−3.58843	−	6.21535i	−0.184814	−	0.320107i
$378$		0			0
$379$	−13.0154	+	22.5433i	−0.668556	+	1.15797i	0.309753	+	0.950817i	$0.399754\pi$
$379$	−13.0154	+	22.5433i	−0.668556	+	1.15797i	−0.978308	+	0.207155i	$0.933580\pi$
$380$	21.1199	−	10.6068i	1.08343	−	0.544118i
$381$		0			0
$382$	0.259316	−	0.348321i	0.0132677	−	0.0178217i
$383$	−16.1477	−	17.1156i	−0.825109	−	0.874564i	0.168700	−	0.985667i	$-0.446043\pi$
$383$	−16.1477	−	17.1156i	−0.825109	−	0.874564i	−0.993809	+	0.111103i	$0.964562\pi$
$384$		0			0
$385$	30.9809	−	3.62115i	1.57893	−	0.184551i
$386$	−4.98958	+	1.81606i	−0.253963	+	0.0924349i
$387$		0			0
$388$	19.7163	+	7.17615i	1.00094	+	0.364314i
$389$	32.1789	+	7.62654i	1.63154	+	0.386681i	0.941478	−	0.337074i	$-0.109437\pi$
$389$	32.1789	+	7.62654i	1.63154	+	0.386681i	0.690057	+	0.723755i	$0.257585\pi$
$390$		0			0
$391$	−4.80509	+	3.16036i	−0.243004	+	0.159826i
$392$	−5.21550	−	2.61932i	−0.263423	−	0.132296i
$393$		0			0
$394$	0.436189	−	0.462333i	0.0219749	−	0.0232920i
$395$	−0.375819	−	2.13137i	−0.0189095	−	0.107241i
$396$		0			0
$397$	−0.00960087	+	0.0544493i	−0.000481854	+	0.00273273i	−0.985048	−	0.172282i	$-0.944886\pi$
$397$	−0.00960087	+	0.0544493i	−0.000481854	+	0.00273273i	0.984566	+	0.175014i	$0.0559972\pi$
$398$	2.60336	+	3.49691i	0.130494	+	0.175284i
$399$		0			0
$400$	7.24834	−	1.71789i	0.362417	−	0.0858944i
$401$	−28.4500	−	3.32533i	−1.42072	−	0.166059i	−0.629222	−	0.777225i	$-0.716626\pi$
$401$	−28.4500	−	3.32533i	−1.42072	−	0.166059i	−0.791502	+	0.611167i	$0.790701\pi$
$402$		0			0
$403$	0.156715	−	2.69069i	0.00780651	−	0.134033i
$404$	−10.0397			−0.499496
$405$		0			0
$406$	−3.19719			−0.158674
$407$	2.27445	−	39.0508i	0.112740	−	1.93568i
$408$		0			0
$409$	−31.2243	−	3.64960i	−1.54394	−	0.180461i	−0.698924	−	0.715196i	$-0.746337\pi$
$409$	−31.2243	−	3.64960i	−1.54394	−	0.180461i	−0.845020	+	0.534735i	$0.820411\pi$
$410$	10.6692	−	2.52864i	0.526914	−	0.124881i
$411$		0			0
$412$	−1.77200	−	2.38021i	−0.0873003	−	0.117265i
$413$	2.73421	−	15.5065i	0.134542	−	0.763024i
$414$		0			0
$415$	−1.83511	−	10.4074i	−0.0900818	−	0.510879i
$416$	14.7974	−	15.6844i	0.725504	−	0.768990i
$417$		0			0
$418$	8.44509	+	4.24129i	0.413063	+	0.207448i
$419$	−2.81915	+	1.85419i	−0.137725	+	0.0905829i	−0.616502	−	0.787354i	$-0.711451\pi$
$419$	−2.81915	+	1.85419i	−0.137725	+	0.0905829i	0.478777	+	0.877937i	$0.341080\pi$
$420$		0			0
$421$	24.5826	+	5.82618i	1.19808	+	0.283951i	0.780774	−	0.624814i	$-0.214825\pi$
$421$	24.5826	+	5.82618i	1.19808	+	0.283951i	0.417309	+	0.908765i	$0.362973\pi$
$422$	5.46033	+	1.98740i	0.265805	+	0.0967451i
$423$		0			0
$424$	−16.4373	+	5.98270i	−0.798267	+	0.290545i
$425$	−3.18626	+	0.372421i	−0.154557	+	0.0180651i
$426$		0			0
$427$	1.22562	+	1.29908i	0.0593120	+	0.0628671i
$428$	7.16632	−	9.62604i	0.346397	−	0.465292i
$429$		0			0
$430$	3.29394	−	1.65428i	0.158848	−	0.0797764i
$431$	−16.4068	+	28.4174i	−0.790288	+	1.36882i	0.135501	+	0.990777i	$0.456736\pi$
$431$	−16.4068	+	28.4174i	−0.790288	+	1.36882i	−0.925789	+	0.378041i	$0.876598\pi$
$432$		0			0
$433$	6.46122	+	11.1912i	0.310507	+	0.537813i	0.978472	−	0.206379i	$-0.0661680\pi$
$433$	6.46122	+	11.1912i	0.310507	+	0.537813i	−0.667966	+	0.744192i	$0.732835\pi$
$434$	−1.00316	−	0.659792i	−0.0481534	−	0.0316710i
$435$		0			0
$436$	−7.55745	−	17.5201i	−0.361936	−	0.839063i
$437$	−8.55951	+	28.5908i	−0.409457	+	1.36768i
$438$		0			0
$439$	14.6064	−	33.8614i	0.697124	−	1.61612i	−0.0875158	−	0.996163i	$-0.527893\pi$
$439$	14.6064	−	33.8614i	0.697124	−	1.61612i	0.784640	−	0.619952i	$-0.212848\pi$
$440$	15.9373	+	13.3730i	0.759781	+	0.637532i
$441$		0			0
$442$	−1.62093	+	1.36012i	−0.0770997	+	0.0646943i
$443$	−9.85556	−	32.9199i	−0.468252	−	1.56407i	−0.787448	−	0.616382i	$-0.788598\pi$
$443$	−9.85556	−	32.9199i	−0.468252	−	1.56407i	0.319196	−	0.947689i	$-0.396587\pi$
$444$		0			0
$445$	2.21469	+	38.0248i	0.104987	+	1.80255i
$446$	0.153521	+	2.63586i	0.00726945	+	0.124812i
$447$		0			0
$448$	1.14203	+	3.81464i	0.0539557	+	0.180225i
$449$	13.4520	−	11.2876i	0.634838	−	0.532693i	−0.267590	−	0.963533i	$-0.586227\pi$
$449$	13.4520	−	11.2876i	0.634838	−	0.532693i	0.902428	+	0.430840i	$0.141783\pi$
$450$		0			0
$451$	−17.4910	−	14.6767i	−0.823617	−	0.691097i
$452$	−3.87041	+	8.97261i	−0.182049	+	0.422036i
$453$		0			0
$454$	2.29855	−	7.67770i	0.107876	−	0.360332i
$455$	14.3546	+	33.2777i	0.672954	+	1.56008i
$456$		0			0
$457$	6.97539	+	4.58779i	0.326295	+	0.214608i	0.702078	−	0.712100i	$-0.252256\pi$
$457$	6.97539	+	4.58779i	0.326295	+	0.214608i	−0.375783	+	0.926708i	$0.622626\pi$
$458$	1.47162	+	2.54891i	0.0687641	+	0.119103i
$459$		0			0
$460$	−14.9867	+	25.9577i	−0.698758	+	1.21028i
$461$	−18.1763	+	9.12850i	−0.846556	+	0.425157i	−0.818539	−	0.574451i	$-0.805216\pi$
$461$	−18.1763	+	9.12850i	−0.846556	+	0.425157i	−0.0280173	+	0.999607i	$0.508919\pi$
$462$		0			0
$463$	−1.54625	+	2.07698i	−0.0718604	+	0.0965253i	−0.836600	−	0.547814i	$-0.815460\pi$
$463$	−1.54625	+	2.07698i	−0.0718604	+	0.0965253i	0.764740	+	0.644339i	$0.222868\pi$
$464$	2.68092	+	2.84160i	0.124458	+	0.131918i
$465$		0			0
$466$	2.51073	−	0.293462i	0.116307	−	0.0135944i
$467$	−11.5019	+	4.18635i	−0.532244	+	0.193721i	−0.594140	−	0.804361i	$-0.702508\pi$
$467$	−11.5019	+	4.18635i	−0.532244	+	0.193721i	0.0618958	+	0.998083i	$0.480285\pi$
$468$		0			0
$469$	40.2012	+	14.6320i	1.85632	+	0.675645i
$470$	−5.08333	−	1.20477i	−0.234477	−	0.0555720i
$471$		0			0
$472$	8.77450	−	5.77108i	0.403879	−	0.265636i
$473$	−6.85925	−	3.44484i	−0.315389	−	0.158394i
$474$		0			0
$475$	−11.4238	+	12.1085i	−0.524158	+	0.555575i
$476$	−0.852437	−	4.83441i	−0.0390714	−	0.221585i
$477$		0			0
$478$	2.86441	−	16.2449i	0.131015	−	0.743024i
$479$	16.3783	+	21.9999i	0.748343	+	1.00520i	0.999308	+	0.0372031i	$0.0118448\pi$
$479$	16.3783	+	21.9999i	0.748343	+	1.00520i	−0.250965	+	0.967996i	$0.580748\pi$
$480$		0			0
$481$	44.2248	−	10.4815i	2.01648	−	0.477914i
$482$	−14.0853	−	1.64633i	−0.641566	−	0.0749883i
$483$		0			0
$484$	0.0760574	−	1.30585i	0.00345715	−	0.0593570i
$485$	−36.3120			−1.64884
$486$		0			0
$487$	−6.02417			−0.272981			−0.136491	−	0.990641i	$-0.543582\pi$
$487$	−6.02417			−0.272981			−0.136491	+	0.990641i	$0.543582\pi$
$488$	−0.0692646	+	1.18923i	−0.00313546	+	0.0538338i
$489$		0			0
$490$	4.57674	+	0.534944i	0.206756	+	0.0241663i
$491$	0.474156	−	0.112377i	0.0213983	−	0.00507150i	−0.219903	−	0.975522i	$-0.570574\pi$
$491$	0.474156	−	0.112377i	0.0213983	−	0.00507150i	0.241301	+	0.970450i	$0.422426\pi$
$492$		0			0
$493$	−1.00466	−	1.34949i	−0.0452475	−	0.0607780i
$494$	−1.90671	+	10.8135i	−0.0857867	+	0.486521i
$495$		0			0
$496$	0.254765	+	1.44484i	0.0114393	+	0.0648754i
$497$	−28.6688	+	30.3872i	−1.28597	+	1.36305i
$498$		0			0
$499$	4.90133	+	2.46154i	0.219414	+	0.110194i	0.555111	−	0.831776i	$-0.312676\pi$
$499$	4.90133	+	2.46154i	0.219414	+	0.110194i	−0.335698	+	0.941970i	$0.608972\pi$
$500$	6.38395	−	4.19879i	0.285499	−	0.187776i
$501$		0			0
$502$	−7.82720	−	1.85508i	−0.349345	−	0.0827963i
$503$	−9.93090	−	3.61455i	−0.442797	−	0.161165i	0.110993	−	0.993821i	$-0.464597\pi$
$503$	−9.93090	−	3.61455i	−0.442797	−	0.161165i	−0.553790	+	0.832656i	$0.686819\pi$
$504$		0			0
$505$	16.3275	−	5.94271i	0.726562	−	0.264447i
$506$	−11.9042	+	1.39141i	−0.529208	+	0.0618556i
$507$		0			0
$508$	12.3670	+	13.1082i	0.548697	+	0.581584i
$509$	7.40873	−	9.95165i	0.328386	−	0.441099i	−0.607013	−	0.794692i	$-0.707633\pi$
$509$	7.40873	−	9.95165i	0.328386	−	0.441099i	0.935400	+	0.353592i	$0.115040\pi$
$510$		0			0
$511$	−18.8678	+	9.47577i	−0.834663	+	0.419183i
$512$	−10.4003	+	18.0139i	−0.459634	+	0.796110i
$513$		0			0
$514$	4.17162	+	7.22546i	0.184002	+	0.318701i
$515$	4.29067	+	2.82202i	0.189069	+	0.124353i
$516$		0			0
$517$	4.30883	+	9.98899i	0.189502	+	0.439315i
$518$	5.80699	−	19.3967i	0.255144	−	0.852242i
$519$		0			0
$520$	−9.57440	+	22.1959i	−0.419865	+	0.973357i
$521$	13.6270	+	11.4344i	0.597011	+	0.500952i	0.890483	−	0.455016i	$-0.150366\pi$
$521$	13.6270	+	11.4344i	0.597011	+	0.500952i	−0.293472	+	0.955968i	$0.594811\pi$
$522$		0			0
$523$	−10.4002	+	8.72680i	−0.454769	+	0.381596i	−0.841202	−	0.540721i	$-0.818151\pi$
$523$	−10.4002	+	8.72680i	−0.454769	+	0.381596i	0.386433	+	0.922317i	$0.373707\pi$
$524$	3.44668	+	11.5127i	0.150569	+	0.502936i
$525$		0			0
$526$	0.540894	+	9.28679i	0.0235841	+	0.404923i
$527$	−0.0367370	−	0.630749i	−0.00160029	−	0.0274759i
$528$		0			0
$529$	−4.25908	−	14.2263i	−0.185177	−	0.618536i
$530$	10.5795	−	8.87724i	0.459543	−	0.385603i
$531$		0			0
$532$	−19.5141	−	16.3743i	−0.846045	−	0.709916i
$533$	10.5078	−	24.3597i	0.455142	−	1.05514i
$534$		0			0
$535$	−5.95664	+	19.8966i	−0.257528	+	0.860203i
$536$	11.3020	+	26.2011i	0.488173	+	1.13171i
$537$		0			0
$538$	−5.38849	−	3.54407i	−0.232314	−	0.152796i
$539$	−4.79771	−	8.30987i	−0.206652	−	0.357931i
$540$		0			0
$541$	13.6538	−	23.6492i	0.587025	−	1.01676i	−0.407595	−	0.913163i	$-0.633632\pi$
$541$	13.6538	−	23.6492i	0.587025	−	1.01676i	0.994620	−	0.103594i	$-0.0330342\pi$
$542$	1.40266	−	0.704441i	0.0602493	−	0.0302583i
$543$		0			0
$544$	3.01851	−	4.05457i	0.129418	−	0.173838i
$545$	22.6611	+	24.0193i	0.970693	+	1.02887i
$546$		0			0
$547$	−12.6117	+	1.47410i	−0.539239	+	0.0630281i	−0.381353	−	0.924429i	$-0.624542\pi$
$547$	−12.6117	+	1.47410i	−0.539239	+	0.0630281i	−0.157886	+	0.987457i	$0.550468\pi$
$548$	13.6050	−	4.95181i	0.581176	−	0.211531i
$549$		0			0
$550$	−6.28204	−	2.28648i	−0.267867	−	0.0974957i
$551$	−8.49504	−	2.01336i	−0.361901	−	0.0857720i
$552$		0			0
$553$	−1.94900	+	1.28188i	−0.0828798	+	0.0545109i
$554$	9.33111	+	4.68626i	0.396441	+	0.199100i
$555$		0			0
$556$	−6.79222	+	7.19934i	−0.288054	+	0.305320i
$557$	−2.62356	−	14.8789i	−0.111164	−	0.630441i	−0.988578	−	0.150708i	$-0.951845\pi$
$557$	−2.62356	−	14.8789i	−0.111164	−	0.630441i	0.877415	−	0.479733i	$-0.159266\pi$
$558$		0			0
$559$	1.54866	−	8.78288i	0.0655013	−	0.371476i
$560$	−11.7806	−	15.8242i	−0.497823	−	0.668692i
$561$		0			0
$562$	−5.92802	+	1.40497i	−0.250058	+	0.0592649i
$563$	6.09083	+	0.711916i	0.256698	+	0.0300037i	0.243469	−	0.969909i	$-0.421715\pi$
$563$	6.09083	+	0.711916i	0.256698	+	0.0300037i	0.0132294	+	0.999912i	$0.495789\pi$
$564$		0			0
$565$	0.983321	−	16.8830i	0.0413686	−	0.710272i
$566$	−8.11223			−0.340982
$567$		0			0
$568$	−27.8646			−1.16917
$569$	0.0860178	−	1.47687i	0.00360605	−	0.0619135i	−0.996025	−	0.0890736i	$-0.971609\pi$
$569$	0.0860178	−	1.47687i	0.00360605	−	0.0619135i	0.999631	+	0.0271601i	$0.00864639\pi$
$570$		0			0
$571$	−8.75647	−	1.02348i	−0.366447	−	0.0428315i	−0.0691228	−	0.997608i	$-0.522020\pi$
$571$	−8.75647	−	1.02348i	−0.366447	−	0.0428315i	−0.297324	+	0.954777i	$0.596094\pi$
$572$	22.3449	−	5.29583i	0.934286	−	0.221430i
$573$		0			0
$574$	−7.05750	−	9.47987i	−0.294574	−	0.395682i
$575$	3.66611	−	20.7915i	0.152887	−	0.867066i
$576$		0			0
$577$	2.48608	+	14.0993i	0.103497	+	0.586960i	0.991810	+	0.127722i	$0.0407665\pi$
$577$	2.48608	+	14.0993i	0.103497	+	0.586960i	−0.888313	+	0.459238i	$0.848122\pi$
$578$	6.28139	−	6.65788i	0.261271	−	0.276931i
$579$		0			0
$580$	−7.83541	−	3.93509i	−0.325348	−	0.163396i
$581$	−9.51686	+	6.25934i	−0.394826	+	0.259681i
$582$		0			0
$583$	−27.9837	−	6.63225i	−1.15897	−	0.274680i
$584$	−13.2333	−	4.81654i	−0.547599	−	0.199310i
$585$		0			0
$586$	−11.6521	+	4.24102i	−0.481344	+	0.175195i
$587$	−8.48086	+	0.991271i	−0.350043	+	0.0409141i	−0.289298	−	0.957239i	$-0.593422\pi$
$587$	−8.48086	+	0.991271i	−0.350043	+	0.0409141i	−0.0607450	+	0.998153i	$0.519348\pi$
$588$		0			0
$589$	−2.24995	−	2.38481i	−0.0927076	−	0.0982643i
$590$	−4.95151	+	6.65103i	−0.203850	+	0.273818i
$591$		0			0
$592$	−22.1087	+	11.1034i	−0.908662	+	0.456347i
$593$	19.8740	−	34.4227i	0.816125	−	1.41357i	−0.0923915	−	0.995723i	$-0.529451\pi$
$593$	19.8740	−	34.4227i	0.816125	−	1.41357i	0.908517	−	0.417848i	$-0.137216\pi$
$594$		0			0
$595$	4.24788	+	7.35754i	0.174146	+	0.301630i
$596$	19.3373	+	12.7183i	0.792086	+	0.520963i
$597$		0			0
$598$	−5.51568	−	12.7868i	−0.225553	−	0.522890i
$599$	−5.84437	+	19.5215i	−0.238794	+	0.797629i	0.751631	+	0.659583i	$0.229267\pi$
$599$	−5.84437	+	19.5215i	−0.238794	+	0.797629i	−0.990426	+	0.138046i	$0.955918\pi$
$600$		0			0
$601$	−5.42187	+	12.5693i	−0.221163	+	0.512713i	−0.992286	−	0.123974i	$-0.960436\pi$
$601$	−5.42187	+	12.5693i	−0.221163	+	0.512713i	0.771123	+	0.636687i	$0.219695\pi$
$602$	−3.04350	−	2.55380i	−0.124044	−	0.104085i
$603$		0			0
$604$	−8.06774	+	6.76964i	−0.328272	+	0.275453i
$605$	0.649269	+	2.16871i	0.0263965	+	0.0881705i
$606$		0			0
$607$	0.261657	+	4.49247i	0.0106203	+	0.182344i	0.999446	+	0.0332701i	$0.0105922\pi$
$607$	0.261657	+	4.49247i	0.0106203	+	0.182344i	−0.988826	+	0.149074i	$0.952371\pi$
$608$	−1.52517	−	26.1861i	−0.0618538	−	1.06199i
$609$		0			0
$610$	−0.269742	−	0.901003i	−0.0109216	−	0.0364805i
$611$	−9.68275	+	8.12479i	−0.391722	+	0.328694i
$612$		0			0
$613$	27.4040	+	22.9947i	1.10684	+	0.928746i	0.997866	−	0.0652986i	$-0.0208000\pi$
$613$	27.4040	+	22.9947i	1.10684	+	0.928746i	0.108971	+	0.994045i	$0.465244\pi$
$614$	6.85126	−	15.8830i	0.276494	−	0.640986i
$615$		0			0
$616$	6.43143	−	21.4825i	0.259130	−	0.865554i
$617$	−10.9250	−	25.3270i	−0.439825	−	1.01963i	−0.983594	−	0.180394i	$-0.942263\pi$
$617$	−10.9250	−	25.3270i	−0.439825	−	1.01963i	0.543770	−	0.839234i	$-0.316996\pi$
$618$		0			0
$619$	27.9288	+	18.3690i	1.12255	+	0.738314i	0.968318	−	0.249721i	$-0.0803389\pi$
$619$	27.9288	+	18.3690i	1.12255	+	0.738314i	0.154233	+	0.988034i	$0.450709\pi$
$620$	−1.64640	−	2.85165i	−0.0661211	−	0.114525i
$621$		0			0
$622$	7.69456	−	13.3274i	0.308524	−	0.534379i
$623$	36.6880	−	18.4254i	1.46988	−	0.738199i
$624$		0			0
$625$	−18.1429	+	24.3702i	−0.725716	+	0.974806i
$626$	3.15757	+	3.34683i	0.126202	+	0.133766i
$627$		0			0
$628$	−0.276791	+	0.0323523i	−0.0110452	+	0.00129100i
$629$	10.0118	−	3.64400i	0.399197	−	0.145296i
$630$		0			0
$631$	10.2732	+	3.73914i	0.408970	+	0.148853i	0.538309	−	0.842748i	$-0.319063\pi$
$631$	10.2732	+	3.73914i	0.408970	+	0.148853i	−0.129339	+	0.991600i	$0.541286\pi$
$632$	−1.51400	−	0.358823i	−0.0602235	−	0.0142732i
$633$		0			0
$634$	−9.20911	+	6.05693i	−0.365741	+	0.240551i
$635$	−27.8712	−	13.9975i	−1.10604	−	0.555472i
$636$		0			0
$637$	7.65083	−	8.10941i	0.303137	−	0.321306i
$638$	−0.608816	−	3.45277i	−0.0241032	−	0.136696i
$639$		0			0
$640$	5.81708	−	32.9903i	0.229940	−	1.30406i
$641$	5.56274	+	7.47205i	0.219715	+	0.295128i	0.898290	−	0.439402i	$-0.144810\pi$
$641$	5.56274	+	7.47205i	0.219715	+	0.295128i	−0.678575	+	0.734531i	$0.737402\pi$
$642$		0			0
$643$	1.25280	−	0.296918i	0.0494055	−	0.0117093i	−0.205839	−	0.978586i	$-0.565992\pi$
$643$	1.25280	−	0.296918i	0.0494055	−	0.0117093i	0.255244	+	0.966877i	$0.417844\pi$
$644$	32.0887	+	3.75063i	1.26447	+	0.147795i
$645$		0			0
$646$	−0.149664	+	2.56964i	−0.00588847	+	0.101101i
$647$	25.7409			1.01198			0.505989	−	0.862540i	$-0.331128\pi$
$647$	25.7409			1.01198			0.505989	+	0.862540i	$0.331128\pi$
$648$		0			0
$649$	17.2667			0.677776
$650$	0.451642	−	7.75439i	0.0177149	−	0.304152i
$651$		0			0
$652$	26.9992	+	3.15575i	1.05737	+	0.123589i
$653$	37.9092	−	8.98465i	1.48350	−	0.351596i	0.592490	−	0.805578i	$-0.298145\pi$
$653$	37.9092	−	8.98465i	1.48350	−	0.351596i	0.891011	+	0.453981i	$0.149997\pi$
$654$		0			0
$655$	−12.4199	−	16.6828i	−0.485285	−	0.651851i
$656$	−2.50766	+	14.2217i	−0.0979077	+	0.555262i
$657$		0			0
$658$	0.977797	+	5.54536i	0.0381185	+	0.216181i
$659$	−23.0459	+	24.4272i	−0.897742	+	0.951550i	−0.999062	−	0.0433034i	$-0.986212\pi$
$659$	−23.0459	+	24.4272i	−0.897742	+	0.951550i	0.101320	+	0.994854i	$0.467693\pi$
$660$		0			0
$661$	31.6648	+	15.9027i	1.23162	+	0.618542i	0.941036	−	0.338308i	$-0.109854\pi$
$661$	31.6648	+	15.9027i	1.23162	+	0.618542i	0.290583	+	0.956850i	$0.406151\pi$
$662$	−0.942159	+	0.619668i	−0.0366180	+	0.0240841i
$663$		0			0
$664$	−7.39277	−	1.75212i	−0.286895	−	0.0679954i
$665$	41.4278	+	15.0785i	1.60650	+	0.584718i
$666$		0			0
$667$	10.4045	−	3.78693i	0.402864	−	0.146630i
$668$	30.4566	−	3.55987i	1.17840	−	0.137735i
$669$		0			0
$670$	−15.4602	−	16.3869i	−0.597281	−	0.633081i
$671$	−1.16954	+	1.57097i	−0.0451497	+	0.0606466i
$672$		0			0
$673$	24.5503	−	12.3296i	0.946346	−	0.475273i	0.0924503	−	0.995717i	$-0.470530\pi$
$673$	24.5503	−	12.3296i	0.946346	−	0.475273i	0.853895	+	0.520445i	$0.174234\pi$
$674$	5.20938	−	9.02292i	0.200658	−	0.347550i
$675$		0			0
$676$	2.43499	+	4.21753i	0.0936536	+	0.162213i
$677$	−7.98158	−	5.24957i	−0.306757	−	0.201757i	0.386791	−	0.922167i	$-0.373583\pi$
$677$	−7.98158	−	5.24957i	−0.306757	−	0.201757i	−0.693549	+	0.720410i	$0.743954\pi$
$678$		0			0
$679$	15.5023	+	35.9383i	0.594923	+	1.37919i
$680$	−1.62520	+	5.42854i	−0.0623236	+	0.208175i
$681$		0			0
$682$	0.521509	−	1.20899i	0.0199696	−	0.0462948i
$683$	−25.4573	−	21.3612i	−0.974095	−	0.817363i	0.00909301	−	0.999959i	$-0.497106\pi$
$683$	−25.4573	−	21.3612i	−0.974095	−	0.817363i	−0.983188	+	0.182596i	$0.941550\pi$
$684$		0			0
$685$	−19.1945	+	16.1061i	−0.733383	+	0.615381i
$686$	2.14210	+	7.15512i	0.0817859	+	0.273184i
$687$		0			0
$688$	0.282272	+	4.84642i	0.0107615	+	0.184768i
$689$	−1.94290	−	33.3583i	−0.0740187	−	1.27085i
$690$		0			0
$691$	1.55724	+	5.20154i	0.0592402	+	0.197876i	0.982487	−	0.186332i	$-0.0596599\pi$
$691$	1.55724	+	5.20154i	0.0592402	+	0.197876i	−0.923247	+	0.384208i	$0.874475\pi$
$692$	24.2325	−	20.3335i	0.921183	−	0.772964i
$693$		0			0
$694$	−11.6460	−	9.77218i	−0.442077	−	0.370947i
$695$	6.78466	−	15.7286i	0.257357	−	0.596620i
$696$		0			0
$697$	1.78363	−	5.95775i	0.0675599	−	0.225666i
$698$	−2.94724	−	6.83247i	−0.111555	−	0.258613i
$699$		0			0
$700$	15.0559	+	9.90239i	0.569058	+	0.374275i
$701$	16.8694	+	29.2187i	0.637150	+	1.10358i	0.986055	+	0.166418i	$0.0532200\pi$
$701$	16.8694	+	29.2187i	0.637150	+	1.10358i	−0.348906	+	0.937158i	$0.613447\pi$
$702$		0			0
$703$	27.6440	−	47.8808i	1.04261	−	1.80586i
$704$	−3.90210	+	1.95971i	−0.147066	+	0.0738593i
$705$		0			0
$706$	6.58747	−	8.84850i	0.247923	−	0.333018i
$707$	−12.8521	−	13.6224i	−0.483351	−	0.512323i
$708$		0			0
$709$	19.2544	−	2.25052i	0.723114	−	0.0845199i	0.253429	−	0.967354i	$-0.418442\pi$
$709$	19.2544	−	2.25052i	0.723114	−	0.0845199i	0.469685	+	0.882834i	$0.344367\pi$
$710$	20.6730	−	7.52437i	0.775846	−	0.282385i
$711$		0			0
$712$	25.7319	+	9.36564i	0.964343	+	0.350992i
$713$	4.04605	+	0.958932i	0.151526	+	0.0359123i
$714$		0			0
$715$	−33.2044	+	21.8389i	−1.24177	+	0.816727i
$716$	−15.4376	−	7.75305i	−0.576930	−	0.289745i
$717$		0			0
$718$	−5.71672	+	6.05937i	−0.213346	+	0.226134i
$719$	0.831346	+	4.71480i	0.0310040	+	0.175832i	0.996378	−	0.0850387i	$-0.0271014\pi$
$719$	0.831346	+	4.71480i	0.0310040	+	0.175832i	−0.965374	+	0.260871i	$0.915990\pi$
$720$		0			0
$721$	0.961210	−	5.45129i	0.0357973	−	0.203017i
$722$	1.53619	+	2.06346i	0.0571711	+	0.0767941i
$723$		0			0
$724$	1.33812	−	0.317140i	0.0497308	−	0.0117864i
$725$	6.13417	+	0.716981i	0.227817	+	0.0266280i
$726$		0			0
$727$	0.439589	−	7.54745i	0.0163035	−	0.279920i	−0.980297	−	0.197530i	$-0.936708\pi$
$727$	0.439589	−	7.54745i	0.0163035	−	0.279920i	0.996600	−	0.0823892i	$-0.0262551\pi$
$728$	26.0550			0.965664
$729$		0			0
$730$	11.1186			0.411516
$731$	0.121560	−	2.08710i	0.00449606	−	0.0771943i
$732$		0			0
$733$	−38.3799	−	4.48597i	−1.41760	−	0.165693i	−0.627471	−	0.778640i	$-0.715910\pi$
$733$	−38.3799	−	4.48597i	−1.41760	−	0.165693i	−0.790124	+	0.612947i	$0.789984\pi$
$734$	−6.07210	+	1.43911i	−0.224125	+	0.0531186i
$735$		0			0
$736$	19.8655	+	26.6840i	0.732252	+	0.983586i
$737$	−8.14649	+	46.2010i	−0.300080	+	1.70184i
$738$		0			0
$739$	−8.79173	−	49.8604i	−0.323409	−	1.83414i	−0.520627	−	0.853784i	$-0.674302\pi$
$739$	−8.79173	−	49.8604i	−0.323409	−	1.83414i	0.197218	−	0.980360i	$-0.436809\pi$
$740$	38.1046	−	40.3886i	1.40075	−	1.48471i
$741$		0			0
$742$	−13.3025	−	6.68076i	−0.488349	−	0.245258i
$743$	12.8280	−	8.43710i	0.470613	−	0.309527i	−0.291958	−	0.956431i	$-0.594307\pi$
$743$	12.8280	−	8.43710i	0.470613	−	0.309527i	0.762572	+	0.646904i	$0.223936\pi$
$744$		0			0
$745$	−38.9761	−	9.23750i	−1.42797	−	0.338436i
$746$	10.8906	+	3.96386i	0.398733	+	0.145127i
$747$		0			0
$748$	5.05853	−	1.84116i	0.184958	−	0.0673193i
$749$	22.2348	−	2.59888i	0.812442	−	0.0949609i
$750$		0			0
$751$	32.0170	+	33.9361i	1.16832	+	1.23834i	0.965863	+	0.259053i	$0.0834106\pi$
$751$	32.0170	+	33.9361i	1.16832	+	1.23834i	0.202455	+	0.979292i	$0.435108\pi$
$752$	4.10871	−	5.51896i	0.149829	−	0.201256i
$753$		0			0
$754$	3.64035	−	1.82825i	0.132574	−	0.0665810i
$755$	9.11335	−	15.7848i	0.331669	−	0.574467i
$756$		0			0
$757$	5.85224	+	10.1364i	0.212703	+	0.368413i	0.952560	−	0.304352i	$-0.0984399\pi$
$757$	5.85224	+	10.1364i	0.212703	+	0.368413i	−0.739856	+	0.672765i	$0.765107\pi$
$758$	−12.3446	−	8.11915i	−0.448375	−	0.294901i
$759$		0			0
$760$	11.6469	+	27.0005i	0.422476	+	0.979409i
$761$	7.50818	−	25.0791i	0.272171	−	0.909116i	−0.707194	−	0.707019i	$-0.750039\pi$
$761$	7.50818	−	25.0791i	0.272171	−	0.909116i	0.979366	−	0.202097i	$-0.0647755\pi$
$762$		0			0
$763$	14.0977	−	32.6822i	0.510371	−	1.18317i
$764$	−0.983309	−	0.825094i	−0.0355749	−	0.0298509i
$765$		0			0
$766$	10.2314	−	8.58519i	0.369676	−	0.310195i
$767$	5.75388	+	19.2193i	0.207761	+	0.693969i
$768$		0			0
$769$	−2.64810	−	45.4662i	−0.0954931	−	1.63955i	−0.617471	−	0.786594i	$-0.711843\pi$
$769$	−2.64810	−	45.4662i	−0.0954931	−	1.63955i	0.521977	−	0.852959i	$-0.325195\pi$
$770$	1.02944	+	17.6748i	0.0370984	+	0.636954i
$771$		0			0
$772$	4.50152	+	15.0361i	0.162013	+	0.541162i
$773$	−10.7154	+	8.99131i	−0.385407	+	0.323395i	−0.814821	−	0.579713i	$-0.803165\pi$
$773$	−10.7154	+	8.99131i	−0.385407	+	0.323395i	0.429414	+	0.903108i	$0.358720\pi$
$774$		0			0
$775$	1.77672	+	1.49085i	0.0638217	+	0.0535528i
$776$	−10.3399	+	23.9706i	−0.371180	+	0.860493i
$777$		0			0
$778$	−5.38358	+	17.9824i	−0.193011	+	0.644701i
$779$	−12.7823	−	29.6326i	−0.457972	−	1.06170i
$780$		0			0
$781$	−38.2754	−	25.1741i	−1.36960	−	0.900801i
$782$	−1.63223	−	2.82710i	−0.0583683	−	0.101097i
$783$		0			0
$784$	−3.03440	+	5.25573i	−0.108371	+	0.187705i
$785$	0.430991	−	0.216452i	0.0153827	−	0.00772550i
$786$		0			0
$787$	8.48130	−	11.3924i	0.302326	−	0.406094i	−0.624836	−	0.780756i	$-0.714834\pi$
$787$	8.48130	−	11.3924i	0.302326	−	0.406094i	0.927161	+	0.374663i	$0.122241\pi$
$788$	−1.28935	−	1.36663i	−0.0459312	−	0.0486843i
$789$		0			0
$790$	1.22014	−	0.142614i	0.0434107	−	0.00507398i
$791$	−17.1290	+	6.23446i	−0.609039	+	0.221672i
$792$		0			0
$793$	−2.13836	−	0.778298i	−0.0759353	−	0.0276382i
$794$	−0.0305367	−	0.00723733i	−0.00108371	−	0.000256843i
$795$		0			0
$796$	10.7667	−	7.08134i	0.381614	−	0.250991i
$797$	36.9090	+	18.5364i	1.30738	+	0.656593i	0.959702	−	0.281020i	$-0.0906728\pi$
$797$	36.9090	+	18.5364i	1.30738	+	0.656593i	0.347681	+	0.937613i	$0.386969\pi$
$798$		0			0
$799$	−2.03337	+	2.15524i	−0.0719353	+	0.0762470i
$800$	3.22216	+	18.2738i	0.113921	+	0.646075i
$801$		0			0
$802$	2.82324	−	16.0114i	0.0996920	−	0.565381i
$803$	−13.8261	−	18.5717i	−0.487912	−	0.655379i
$804$		0			0
$805$	−54.4053	+	12.8943i	−1.91754	+	0.454464i
$806$	1.51950	+	0.177604i	0.0535221	+	0.00625583i
$807$		0			0
$808$	0.726319	−	12.4704i	0.0255518	−	0.438708i
$809$	−23.8379			−0.838097			−0.419048	−	0.907964i	$-0.637636\pi$
$809$	−23.8379			−0.838097			−0.419048	+	0.907964i	$0.637636\pi$
$810$		0			0
$811$	−3.33188			−0.116998			−0.0584991	−	0.998287i	$-0.518631\pi$
$811$	−3.33188			−0.116998			−0.0584991	+	0.998287i	$0.518631\pi$
$812$	−0.549511	+	9.43475i	−0.0192841	+	0.331095i
$813$		0			0
$814$	22.0530	+	2.57762i	0.772957	+	0.0903457i
$815$	−45.7763	+	10.8492i	−1.60347	+	0.380030i
$816$		0			0
$817$	−6.47847	−	8.70210i	−0.226653	−	0.304448i
$818$	3.09855	−	17.5727i	0.108338	−	0.614417i
$819$		0			0
$820$	−5.62815	−	31.9188i	−0.196543	−	1.11465i
$821$	6.16015	−	6.52938i	0.214991	−	0.227877i	−0.610899	−	0.791709i	$-0.709192\pi$
$821$	6.16015	−	6.52938i	0.214991	−	0.227877i	0.825890	+	0.563832i	$0.190673\pi$
$822$		0			0
$823$	−1.16006	−	0.582603i	−0.0404371	−	0.0203083i	0.428466	−	0.903558i	$-0.359054\pi$
$823$	−1.16006	−	0.582603i	−0.0404371	−	0.0203083i	−0.468903	+	0.883250i	$0.655351\pi$
$824$	3.08467	−	2.02882i	0.107460	−	0.0706772i
$825$		0			0
$826$	8.69648	+	2.06110i	0.302589	+	0.0717150i
$827$	−29.6308	−	10.7847i	−1.03036	−	0.375022i	−0.229144	−	0.973392i	$-0.573593\pi$
$827$	−29.6308	−	10.7847i	−1.03036	−	0.375022i	−0.801219	+	0.598371i	$0.795815\pi$
$828$		0			0
$829$	−25.1437	+	9.15156i	−0.873277	+	0.317847i	−0.739493	−	0.673164i	$-0.764935\pi$
$829$	−25.1437	+	9.15156i	−0.873277	+	0.317847i	−0.133783	+	0.991011i	$0.542713\pi$
$830$	5.95790	−	0.696378i	0.206802	−	0.0241716i
$831$		0			0
$832$	−3.48164	−	3.69033i	−0.120704	−	0.127939i
$833$	1.56068	−	2.09636i	0.0540745	−	0.0726347i
$834$		0			0
$835$	−47.4239	+	23.8172i	−1.64117	+	0.824227i
$836$	13.9673	−	24.1921i	0.483069	−	0.836700i
$837$		0			0
$838$	−0.957629	−	1.65866i	−0.0330807	−	0.0572975i
$839$	3.24118	+	2.13175i	0.111898	+	0.0735963i	0.604224	−	0.796814i	$-0.293483\pi$
$839$	3.24118	+	2.13175i	0.111898	+	0.0735963i	−0.492327	+	0.870411i	$0.663853\pi$
$840$		0			0
$841$	−10.2034	−	23.6542i	−0.351843	−	0.815663i
$842$	−4.11270	+	13.7374i	−0.141733	+	0.473422i
$843$		0			0
$844$	6.80320	−	15.7716i	0.234176	−	0.542880i
$845$	−6.45643	−	5.41758i	−0.222108	−	0.186371i
$846$		0			0
$847$	1.86921	−	1.56845i	0.0642267	−	0.0538926i
$848$	5.21669	+	17.4250i	0.179142	+	0.598375i
$849$		0			0
$850$	−0.105874	−	1.81778i	−0.00363144	−	0.0623494i
$851$	4.07704	+	70.0000i	0.139759	+	2.39957i
$852$		0			0
$853$	0.986381	+	3.29474i	0.0337730	+	0.112810i	0.973214	−	0.229901i	$-0.0738402\pi$
$853$	0.986381	+	3.29474i	0.0337730	+	0.112810i	−0.939441	+	0.342711i	$0.888655\pi$
$854$	−0.776573	+	0.651622i	−0.0265738	+	0.0222980i
$855$		0			0
$856$	11.4381	+	9.59772i	0.390947	+	0.328043i
$857$	−5.80621	+	13.4603i	−0.198336	+	0.459795i	−0.988138	−	0.153567i	$-0.950924\pi$
$857$	−5.80621	+	13.4603i	−0.198336	+	0.459795i	0.789802	+	0.613362i	$0.210183\pi$
$858$		0			0
$859$	−2.73469	+	9.13449i	−0.0933063	+	0.311665i	−0.991883	−	0.127151i	$-0.959417\pi$
$859$	−2.73469	+	9.13449i	−0.0933063	+	0.311665i	0.898577	+	0.438816i	$0.144602\pi$
$860$	−4.31555	−	10.0046i	−0.147159	−	0.341153i
$861$		0			0
$862$	−15.5612	−	10.2348i	−0.530016	−	0.348597i
$863$	8.00876	+	13.8716i	0.272621	+	0.472194i	0.969532	−	0.244964i	$-0.0787760\pi$
$863$	8.00876	+	13.8716i	0.272621	+	0.472194i	−0.696911	+	0.717158i	$0.745443\pi$
$864$		0			0
$865$	−27.3732	+	47.4117i	−0.930716	+	1.61205i
$866$	−6.55469	+	3.29189i	−0.222738	+	0.111863i
$867$		0			0
$868$	−2.11943	+	2.84689i	−0.0719381	+	0.0966296i
$869$	−1.75548	−	1.86070i	−0.0595505	−	0.0631198i
$870$		0			0
$871$	−54.1404	+	6.32811i	−1.83448	+	0.214420i
$872$	22.3086	−	8.11966i	0.755464	−	0.274967i
$873$		0			0
$874$	−15.9184	−	5.79383i	−0.538448	−	0.195979i
$875$	13.8693	+	3.28709i	0.468869	+	0.111124i
$876$		0			0
$877$	27.6716	−	18.1999i	0.934403	−	0.614567i	0.0116393	−	0.999932i	$-0.496295\pi$
$877$	27.6716	−	18.1999i	0.934403	−	0.614567i	0.922764	+	0.385366i	$0.125925\pi$
$878$	18.7054	+	9.39421i	0.631277	+	0.317039i
$879$		0			0
$880$	14.8458	−	15.7356i	0.500452	−	0.530448i
$881$	−2.00755	−	11.3854i	−0.0676360	−	0.383583i	−0.999770	−	0.0214681i	$-0.993166\pi$
$881$	−2.00755	−	11.3854i	−0.0676360	−	0.383583i	0.932134	−	0.362115i	$-0.117945\pi$
$882$		0			0
$883$	−7.24692	+	41.0993i	−0.243878	+	1.38310i	0.579206	+	0.815182i	$0.303363\pi$
$883$	−7.24692	+	41.0993i	−0.243878	+	1.38310i	−0.823084	+	0.567920i	$0.807748\pi$
$884$	3.73505	+	5.01704i	0.125623	+	0.168741i
$885$		0			0
$886$	18.9792	−	4.49816i	0.637620	−	0.151119i
$887$	23.9390	+	2.79807i	0.803793	+	0.0939499i	0.508061	−	0.861321i	$-0.330362\pi$
$887$	23.9390	+	2.79807i	0.803793	+	0.0939499i	0.295732	+	0.955271i	$0.404436\pi$
$888$		0			0
$889$	−1.95466	+	33.5602i	−0.0655572	+	1.12557i
$890$	−21.6198			−0.724697
$891$		0			0
$892$	7.80468			0.261320
$893$	−0.894032	+	15.3499i	−0.0299176	+	0.513666i
$894$		0			0
$895$	29.6951	+	3.47085i	0.992596	+	0.116018i
$896$	−35.1342	+	8.32697i	−1.17375	+	0.278184i
$897$		0			0
$898$	5.95211	+	7.99507i	0.198624	+	0.266799i
$899$	−0.211221	+	1.19789i	−0.00704460	+	0.0399519i
$900$		0			0
$901$	−1.36020	−	7.71410i	−0.0453149	−	0.256994i
$902$	8.89376	−	9.42683i	0.296130	−	0.313879i
$903$		0			0
$904$	−10.8649	−	5.45657i	−0.361362	−	0.181483i
$905$	−1.98844	+	1.30782i	−0.0660980	+	0.0434733i
$906$		0			0
$907$	22.4691	+	5.32526i	0.746073	+	0.176822i	0.586032	−	0.810288i	$-0.300689\pi$
$907$	22.4691	+	5.32526i	0.746073	+	0.176822i	0.160041	+	0.987110i	$0.448837\pi$
$908$	−22.2614	−	8.10250i	−0.738771	−	0.268891i
$909$		0			0
$910$	−19.3305	+	7.03572i	−0.640799	+	0.233232i
$911$	−22.7444	+	2.65844i	−0.753555	+	0.0880779i	−0.484193	−	0.874961i	$-0.660887\pi$
$911$	−22.7444	+	2.65844i	−0.753555	+	0.0880779i	−0.269362	+	0.963039i	$0.586813\pi$
$912$		0			0
$913$	−8.57191	−	9.08570i	−0.283689	−	0.300693i
$914$	−2.82987	+	3.80118i	−0.0936039	+	0.125732i
$915$		0			0
$916$	7.77464	−	3.90457i	0.256881	−	0.129011i
$917$	−11.2088	+	19.4143i	−0.370148	+	0.641116i
$918$		0			0
$919$	−9.84136	−	17.0457i	−0.324636	−	0.562287i	0.656802	−	0.754063i	$-0.271909\pi$
$919$	−9.84136	−	17.0457i	−0.324636	−	0.562287i	−0.981439	+	0.191776i	$0.938575\pi$
$920$	−31.1580	−	20.4929i	−1.02725	−	0.675632i
$921$		0			0
$922$	−4.57276	−	10.6009i	−0.150596	−	0.349121i
$923$	15.2662	−	50.9928i	0.502494	−	1.67845i
$924$		0			0
$925$	−15.4911	+	35.9125i	−0.509345	+	1.18079i
$926$	−1.12588	−	0.944728i	−0.0369988	−	0.0310457i
$927$		0			0
$928$	−7.45472	+	6.25525i	−0.244713	+	0.205339i
$929$	−8.29364	−	27.7027i	−0.272105	−	0.908895i	−0.979392	−	0.201968i	$-0.935266\pi$
$929$	−8.29364	−	27.7027i	−0.272105	−	0.908895i	0.707287	−	0.706927i	$-0.249919\pi$
$930$		0			0
$931$	−0.788570	−	13.5392i	−0.0258443	−	0.443730i
$932$	−0.434465	−	7.45947i	−0.0142314	−	0.244343i
$933$		0			0
$934$	−1.99258	−	6.65569i	−0.0651993	−	0.217781i
$935$	−7.13679	+	5.98848i	−0.233398	+	0.195844i
$936$		0			0
$937$	14.9990	+	12.5856i	0.489995	+	0.411155i	0.854025	−	0.520233i	$-0.174155\pi$
$937$	14.9990	+	12.5856i	0.489995	+	0.411155i	−0.364029	+	0.931388i	$0.618599\pi$
$938$	−9.61800	+	22.2970i	−0.314039	+	0.728024i
$939$		0			0
$940$	−4.42891	+	14.7936i	−0.144455	+	0.482513i
$941$	3.99887	+	9.27041i	0.130359	+	0.302207i	0.970877	−	0.239577i	$-0.0770086\pi$
$941$	3.99887	+	9.27041i	0.130359	+	0.302207i	−0.840518	+	0.541783i	$0.817749\pi$
$942$		0			0
$943$	34.1954	+	22.4907i	1.11356	+	0.732397i
$944$	−5.46032	−	9.45755i	−0.177718	−	0.307817i
$945$		0			0
$946$	2.17839	−	3.77309i	0.0708257	−	0.122674i
$947$	−18.7726	+	9.42795i	−0.610027	+	0.306367i	−0.726861	−	0.686784i	$-0.759022\pi$
$947$	−18.7726	+	9.42795i	−0.610027	+	0.306367i	0.116834	+	0.993151i	$0.462725\pi$
$948$		0			0
$949$	16.0645	−	21.5784i	0.521476	−	0.700463i
$950$	−6.48422	−	6.87287i	−0.210376	−	0.222985i
$951$		0			0
$952$	6.06651	−	0.709074i	0.196617	−	0.0229812i
$953$	−6.34571	+	2.30965i	−0.205558	+	0.0748169i	−0.442747	−	0.896647i	$-0.645996\pi$
$953$	−6.34571	+	2.30965i	−0.205558	+	0.0748169i	0.237189	+	0.971463i	$0.423774\pi$
$954$		0			0
$955$	2.08753	+	0.759798i	0.0675508	+	0.0245865i
$956$	−47.4455	−	11.2448i	−1.53450	−	0.363682i
$957$		0			0
$958$	−13.0067	+	8.55465i	−0.420228	+	0.276388i
$959$	24.1348	+	12.1210i	0.779354	+	0.391406i
$960$		0			0
$961$	20.9600	−	22.2163i	0.676129	−	0.716655i
$962$	4.47973	+	25.4058i	0.144432	+	0.819117i
$963$		0			0
$964$	−7.27912	+	41.2819i	−0.234445	+	1.32960i
$965$	−16.2209	−	21.7885i	−0.522169	−	0.701395i
$966$		0			0
$967$	11.4754	−	2.71973i	0.369025	−	0.0874605i	−0.0419193	−	0.999121i	$-0.513347\pi$
$967$	11.4754	−	2.71973i	0.369025	−	0.0874605i	0.410944	+	0.911660i	$0.365199\pi$
$968$	1.61651	+	0.188942i	0.0519565	+	0.00607284i
$969$		0			0
$970$	1.19842	−	20.5761i	0.0384790	−	0.660659i
$971$	−24.4687			−0.785239			−0.392620	−	0.919701i	$-0.628431\pi$
$971$	−24.4687			−0.785239			−0.392620	+	0.919701i	$0.628431\pi$
$972$		0			0
$973$	−18.4632			−0.591905
$974$	0.198819	−	3.41358i	0.00637056	−	0.109378i
$975$		0			0
$976$	1.23032	+	0.143804i	0.0393817	+	0.00460306i
$977$	−37.8679	+	8.97486i	−1.21150	+	0.287131i	−0.786230	−	0.617935i	$-0.787970\pi$
$977$	−37.8679	+	8.97486i	−1.21150	+	0.287131i	−0.425272	+	0.905066i	$0.639821\pi$
$978$		0			0
$979$	26.8845	+	36.1122i	0.859233	+	1.15415i
$980$	2.36521	−	13.4138i	0.0755538	−	0.428487i
$981$		0			0
$982$	0.0480294	+	0.272388i	0.00153268	+	0.00869226i
$983$	12.8443	−	13.6142i	0.409670	−	0.434225i	−0.489380	−	0.872071i	$-0.662777\pi$
$983$	12.8443	−	13.6142i	0.409670	−	0.434225i	0.899050	+	0.437846i	$0.144258\pi$
$984$		0			0
$985$	2.90578	+	1.45934i	0.0925860	+	0.0464984i
$986$	0.797843	−	0.524750i	0.0254085	−	0.0167114i
$987$		0			0
$988$	31.5823	+	7.48513i	1.00477	+	0.238134i
$989$	12.9292	+	4.70584i	0.411125	+	0.149637i
$990$		0			0
$991$	−2.15353	+	0.783819i	−0.0684090	+	0.0248988i	−0.375998	−	0.926620i	$-0.622700\pi$
$991$	−2.15353	+	0.783819i	−0.0684090	+	0.0248988i	0.307589	+	0.951519i	$0.400478\pi$
$992$	−3.62990	+	0.424274i	−0.115249	+	0.0134707i
$993$		0			0
$994$	−16.2727	−	17.2480i	−0.516138	−	0.547074i
$995$	−13.3180	+	17.8892i	−0.422211	+	0.567127i
$996$		0			0
$997$	27.9526	−	14.0383i	0.885267	−	0.444598i	0.0527567	−	0.998607i	$-0.483199\pi$
$997$	27.9526	−	14.0383i	0.885267	−	0.444598i	0.832510	+	0.554010i	$0.186903\pi$
$998$	−1.55659	+	2.69609i	−0.0492729	+	0.0853432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.217.5		144
3.2	odd	2		729.2.g.d.217.4		144
9.2	odd	6		81.2.g.a.25.5	yes	144
9.4	even	3		729.2.g.b.703.5		144
9.5	odd	6		729.2.g.c.703.4		144
9.7	even	3		243.2.g.a.73.4		144
81.11	odd	54		6561.2.a.c.1.32		72
81.13	even	27		729.2.g.b.28.5		144
81.14	odd	54		81.2.g.a.13.5	✓	144
81.40	even	27	inner	729.2.g.a.514.5		144
81.41	odd	54		729.2.g.d.514.4		144
81.67	even	27		243.2.g.a.10.4		144
81.68	odd	54		729.2.g.c.28.4		144
81.70	even	27		6561.2.a.d.1.41		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.5	✓	144	81.14	odd	54
81.2.g.a.25.5	yes	144	9.2	odd	6
243.2.g.a.10.4		144	81.67	even	27
243.2.g.a.73.4		144	9.7	even	3
729.2.g.a.217.5		144	1.1	even	1	trivial
729.2.g.a.514.5		144	81.40	even	27	inner
729.2.g.b.28.5		144	81.13	even	27
729.2.g.b.703.5		144	9.4	even	3
729.2.g.c.28.4		144	81.68	odd	54
729.2.g.c.703.4		144	9.5	odd	6
729.2.g.d.217.4		144	3.2	odd	2
729.2.g.d.514.4		144	81.41	odd	54
6561.2.a.c.1.32		72	81.11	odd	54
6561.2.a.d.1.41		72	81.70	even	27

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0330035 + 0.566648i) q^{2} +(1.66648 + 0.194783i) q^{4} +(-2.82546 + 0.669646i) q^{5} +(1.86900 + 2.51050i) q^{7} +(-0.362501 + 2.05585i) q^{8} +(-0.286203 - 1.62314i) q^{10} +(-2.35528 + 2.49645i) q^{11} +(-3.56363 - 1.78972i) q^{13} +(-1.48425 + 0.976208i) q^{14} +(2.11221 + 0.500604i) q^{16} +(-0.878443 - 0.319727i) q^{17} +(-4.55845 + 1.65914i) q^{19} +(-4.83899 + 0.565597i) q^{20} +(-1.33688 - 1.41701i) q^{22} +(3.67387 - 4.93486i) q^{23} +(3.06662 - 1.54011i) q^{25} +(1.13175 - 1.96026i) q^{26} +(2.62564 + 4.54773i) q^{28} +(1.50363 + 0.988954i) q^{29} +(0.267699 + 0.620597i) q^{31} +(-1.55082 + 5.18008i) q^{32} +(0.210164 - 0.487216i) q^{34} +(-6.96191 - 5.84174i) q^{35} +(-8.73079 + 7.32600i) q^{37} +(-0.789703 - 2.63779i) q^{38} +(-0.352457 - 6.05145i) q^{40} +(0.386817 + 6.64138i) q^{41} +(0.641410 + 2.14246i) q^{43} +(-4.41129 + 3.70151i) q^{44} +(2.67508 + 2.24466i) q^{46} +(1.25543 - 2.91042i) q^{47} +(-0.801829 + 2.67830i) q^{49} +(0.771493 + 1.78852i) q^{50} +(-5.59010 - 3.67666i) q^{52} +(4.18963 + 7.25666i) q^{53} +(4.98301 - 8.63082i) q^{55} +(-5.83871 + 2.93231i) q^{56} +(-0.610014 + 0.819391i) q^{58} +(-3.45239 - 3.65932i) q^{59} +(0.566780 - 0.0662470i) q^{61} +(-0.360495 + 0.131209i) q^{62} +(1.19553 + 0.435136i) q^{64} +(11.2674 + 2.67041i) q^{65} +(11.4202 - 7.51120i) q^{67} +(-1.40163 - 0.703923i) q^{68} +(3.53998 - 3.75216i) q^{70} +(2.31784 + 13.1452i) q^{71} +(-1.17142 + 6.64347i) q^{73} +(-3.86312 - 5.18907i) q^{74} +(-7.91971 + 1.87701i) q^{76} +(-10.6693 - 1.24707i) q^{77} +(-0.0433375 + 0.744075i) q^{79} -6.30319 q^{80} -3.77609 q^{82} +(-0.211615 + 3.63329i) q^{83} +(2.69611 + 0.315130i) q^{85} +(-1.23519 + 0.292745i) q^{86} +(-4.27853 - 5.74706i) q^{88} +(2.27781 - 12.9181i) q^{89} +(-2.16732 - 12.2915i) q^{91} +(7.08364 - 7.50822i) q^{92} +(1.60775 + 0.807443i) q^{94} +(11.7687 - 7.74037i) q^{95} +(12.1682 + 2.88392i) q^{97} +(-1.49119 - 0.542748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

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