LMFDB - Embedded newform 729.2.g.d.514.4

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			514.4
Character	$\chi$	$=$	729.514
Dual form			729.2.g.d.217.4

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.0330035	+	0.566648i	0.0233370	+	0.400681i	0.989668	+	0.143378i	$0.0457966\pi$
$2$	0.0330035	+	0.566648i	0.0233370	+	0.400681i	−0.966331	+	0.257302i	$0.917166\pi$
$3$		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	$-0.200991\pi$
$5$	2.82546	+	0.669646i	1.26358	+	0.299475i	0.456399	+	0.889775i	$0.349139\pi$
$6$		0			0
$7$	1.86900	−	2.51050i	0.706414	−	0.948879i	−0.293561	−	0.955940i	$-0.594840\pi$
$7$	1.86900	−	2.51050i	0.706414	−	0.948879i	0.999975	+	0.00706140i	$0.00224773\pi$
$8$	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	$-0.0676350\pi$
$11$	2.35528	+	2.49645i	0.710144	+	0.752709i	−0.267367	+	0.963595i	$0.586153\pi$
$12$		0			0
$13$	−3.56363	+	1.78972i	−0.988373	+	0.496380i	−0.868115	−	0.496363i	$-0.834669\pi$
$13$	−3.56363	+	1.78972i	−0.988373	+	0.496380i	−0.120258	+	0.992743i	$0.538372\pi$
$14$	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	$-0.574949\pi$
$17$	0.878443	−	0.319727i	0.213054	−	0.0775452i	0.446342	+	0.894862i	$0.352726\pi$
$18$		0			0
$19$	−4.55845	−	1.65914i	−1.04578	−	0.380633i	−0.238711	−	0.971091i	$-0.576725\pi$
$19$	−4.55845	−	1.65914i	−1.04578	−	0.380633i	−0.807068	+	0.590458i	$0.798947\pi$
$20$	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	−0.998411	−	0.0563591i	$-0.982051\pi$
$23$	−3.67387	−	4.93486i	−0.766055	−	1.02899i	0.232356	−	0.972631i	$-0.425357\pi$
$24$		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	$-0.738625\pi$
$29$	−1.50363	+	0.988954i	−0.279217	+	0.183644i	0.402174	+	0.915563i	$0.368255\pi$
$30$		0			0
$31$	0.267699	−	0.620597i	0.0480802	−	0.111462i	−0.892483	−	0.451081i	$-0.851039\pi$
$31$	0.267699	−	0.620597i	0.0480802	−	0.111462i	0.940563	+	0.339618i	$0.110298\pi$
$32$	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	−0.942475	−	0.334277i	$-0.891508\pi$
$37$	−8.73079	−	7.32600i	−1.43533	−	1.20439i	−0.492858	−	0.870110i	$-0.664048\pi$
$38$	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	0.822829	+	0.568288i	$0.192394\pi$
$41$	−0.386817	+	6.64138i	−0.0604106	+	1.03721i	−0.883240	+	0.468921i	$0.844643\pi$
$42$		0			0
$43$	0.641410	−	2.14246i	0.0978141	−	0.326722i	−0.895051	−	0.445964i	$-0.852861\pi$
$43$	0.641410	−	2.14246i	0.0978141	−	0.326722i	0.992865	+	0.119242i	$0.0380463\pi$
$44$	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	$-0.203885\pi$
$47$	−1.25543	−	2.91042i	−0.183124	−	0.424529i	−0.984907	+	0.173087i	$0.944626\pi$
$48$		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	0.420498	+	0.907294i	$0.361855\pi$
$53$	−4.18963	+	7.25666i	−0.575490	+	0.996779i	−0.995988	+	0.0894851i	$0.971478\pi$
$54$		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	$-0.653059\pi$
$59$	3.45239	−	3.65932i	0.449463	−	0.476403i	0.911996	+	0.410199i	$0.134541\pi$
$60$		0			0
$61$	0.566780	+	0.0662470i	0.0725687	+	0.00848206i	0.152300	−	0.988334i	$-0.451332\pi$
$61$	0.566780	+	0.0662470i	0.0725687	+	0.00848206i	−0.0797311	+	0.996816i	$0.525406\pi$
$62$	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	1.00000		0.000954570i	$-0.000303849\pi$
$67$	11.4202	+	7.51120i	1.39520	+	0.917639i	0.395203	+	0.918594i	$0.370674\pi$
$68$	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	0.463638	+	0.886025i	$0.346544\pi$
$71$	−2.31784	+	13.1452i	−0.275078	+	1.56004i	−0.738715	+	0.674017i	$0.764567\pi$
$72$		0			0
$73$	−1.17142	−	6.64347i	−0.137105	−	0.777560i	−0.973371	−	0.229236i	$-0.926377\pi$
$73$	−1.17142	−	6.64347i	−0.137105	−	0.777560i	0.836266	−	0.548324i	$-0.184734\pi$
$74$	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	0.994992	−	0.0999512i	$-0.0318687\pi$
$79$	−0.0433375	−	0.744075i	−0.00487584	−	0.0837150i	−0.999868	+	0.0162362i	$0.994832\pi$
$80$	6.30319			0.704718
$81$		0			0
$82$	−3.77609			−0.417000
$83$	0.211615	+	3.63329i	0.0232277	+	0.398805i	0.989805	+	0.142429i	$0.0454914\pi$
$83$	0.211615	+	3.63329i	0.0232277	+	0.398805i	−0.966577	+	0.256376i	$0.917472\pi$
$84$		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	−0.828601	−	0.559839i	$-0.810863\pi$
$89$	−2.27781	−	12.9181i	−0.241447	−	1.36931i	0.587154	−	0.809475i	$-0.300248\pi$
$90$		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	0.439567	−	0.898210i	$-0.355132\pi$
$97$	12.1682	−	2.88392i	1.23549	−	0.292818i	0.795927	+	0.605392i	$0.206984\pi$
$98$	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	$-0.366742\pi$
$101$	5.94334	+	0.694676i	0.591384	+	0.0691229i	0.184863	+	0.982764i	$0.440816\pi$
$102$		0			0
$103$	−1.21369	+	1.28643i	−0.119588	+	0.126756i	−0.784401	−	0.620254i	$-0.787030\pi$
$103$	−1.21369	+	1.28643i	−0.119588	+	0.126756i	0.664813	+	0.747010i	$0.268511\pi$
$104$	−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	$-0.279036\pi$
$107$	−3.57628	−	6.19429i	−0.345732	−	0.598825i	−0.985486	+	0.169754i	$0.945703\pi$
$108$		0			0
$109$	−5.68613	+	9.84867i	−0.544633	+	0.943332i	0.453997	+	0.891003i	$0.349998\pi$
$109$	−5.68613	+	9.84867i	−0.544633	+	0.943332i	−0.998630	+	0.0523287i	$0.983336\pi$
$110$	−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	$-0.00426484\pi$
$113$	1.67037	+	5.57942i	0.157135	+	0.524868i	−0.842775	+	0.538266i	$0.819080\pi$
$114$		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	−0.200045	−	0.979787i	$-0.564109\pi$
$127$	8.22802	−	6.90413i	0.730119	−	0.612643i	0.930164	+	0.367144i	$0.119664\pi$
$128$	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	$-0.971671\pi$
$131$	−2.83697	+	6.57683i	−0.247867	+	0.574621i	0.748175	+	0.663501i	$0.230930\pi$
$132$		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	$-0.472021\pi$
$137$	−7.71126	−	3.87274i	−0.658817	−	0.330871i	−0.746604	+	0.665269i	$0.768317\pi$
$138$		0			0
$139$	−3.52273	−	4.73184i	−0.298794	−	0.401350i	0.627218	−	0.778843i	$-0.284193\pi$
$139$	−3.52273	−	4.73184i	−0.298794	−	0.401350i	−0.926012	+	0.377494i	$0.876786\pi$
$140$	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	$-0.839291\pi$
$149$	−12.3273	+	6.19101i	−1.00989	+	0.507187i	−0.134662	+	0.990892i	$0.542995\pi$
$150$		0			0
$151$	−4.30754	−	4.56573i	−0.350543	−	0.371553i	0.527978	−	0.849258i	$-0.322950\pi$
$151$	−4.30754	−	4.56573i	−0.350543	−	0.371553i	−0.878520	+	0.477705i	$0.841469\pi$
$152$	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	0.224162	−	0.974552i	$-0.428036\pi$
$157$	−0.161617	−	0.0383039i	−0.0128984	−	0.00305698i	−0.237060	+	0.971495i	$0.576184\pi$
$158$	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	$-0.675933\pi$
$167$	−17.7834	−	4.21475i	−1.37612	−	0.326147i	−0.851128	+	0.524959i	$0.824081\pi$
$168$		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	−0.999085	−	0.0427575i	$-0.986386\pi$
$173$	−12.9383	−	13.7138i	−0.983679	−	1.04264i	0.0154065	−	0.999881i	$-0.495096\pi$
$174$		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	$-0.485387\pi$
$179$	9.67521	−	3.52149i	0.723159	−	0.263209i	0.677266	+	0.735738i	$0.263164\pi$
$180$		0			0
$181$	0.770198	+	0.280329i	0.0572484	+	0.0208367i	0.370486	−	0.928838i	$-0.379191\pi$
$181$	0.770198	+	0.280329i	0.0572484	+	0.0208367i	−0.313237	+	0.949675i	$0.601414\pi$
$182$	−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	$-0.676374\pi$
$191$	0.639191	−	0.420402i	0.0462502	−	0.0304193i	0.572424	+	0.819958i	$0.306003\pi$
$192$		0			0
$193$	3.70520	−	8.58963i	0.266706	−	0.618295i	−0.731256	−	0.682103i	$-0.761065\pi$
$193$	3.70520	−	8.58963i	0.266706	−	0.618295i	0.997962	+	0.0638084i	$0.0203246\pi$
$194$	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	$-0.709521\pi$
$197$	0.857832	−	0.719807i	0.0611180	−	0.0512841i	0.672835	+	0.739793i	$0.265076\pi$
$198$		0			0
$199$	5.88368	+	4.93699i	0.417083	+	0.349974i	0.827052	−	0.562125i	$-0.190016\pi$
$199$	5.88368	+	4.93699i	0.417083	+	0.349974i	−0.409969	+	0.912099i	$0.634461\pi$
$200$	−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	0.997605	+	0.0691715i	$0.0220356\pi$
$211$	2.93609	+	9.80721i	0.202129	+	0.675156i	−0.795476	+	0.605985i	$0.792779\pi$
$212$	−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	0.269373	−	0.963036i	$-0.413184\pi$
$223$	4.62022	+	0.540027i	0.309393	+	0.0361629i	0.0400203	+	0.999199i	$0.487258\pi$
$224$	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	$-0.418842\pi$
$227$	13.7390	−	3.25620i	0.911888	−	0.216121i	0.659676	+	0.751550i	$0.270694\pi$
$228$		0			0
$229$	4.33228	+	2.84938i	0.286285	+	0.188292i	0.684526	−	0.728988i	$-0.260009\pi$
$229$	4.33228	+	2.84938i	0.286285	+	0.188292i	−0.398242	+	0.917281i	$0.630379\pi$
$230$	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	$-0.897844\pi$
$233$	0.773336	−	4.38581i	0.0506629	−	0.287324i	0.999604	+	0.0281287i	$0.00895483\pi$
$234$		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	$-0.147943\pi$
$239$	28.8649	−	3.37382i	1.86711	−	0.218234i	0.973193	+	0.229989i	$0.0738691\pi$
$240$		0			0
$241$	−1.45269	−	24.9418i	−0.0935762	−	1.60664i	−0.639490	−	0.768800i	$-0.720854\pi$
$241$	−1.45269	−	24.9418i	−0.0935762	−	1.60664i	0.545914	−	0.837841i	$-0.316183\pi$
$242$	−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	0.958483	+	0.285151i	$0.0920438\pi$
$251$	2.46091	+	13.9565i	0.155331	+	0.880926i	−0.803152	+	0.595775i	$0.796845\pi$
$252$		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	$-0.466409\pi$
$257$	−12.2808	−	8.07720i	−0.766055	−	0.503842i	−0.871388	+	0.490595i	$0.836780\pi$
$258$		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	$-0.631579\pi$
$263$	−16.2782	−	1.90265i	−1.00376	−	0.117322i	−0.602060	+	0.798451i	$0.705653\pi$
$264$		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	$-0.0540721\pi$
$269$	5.68131	+	9.84032i	0.346396	+	0.599975i	−0.639211	+	0.769032i	$0.720739\pi$
$270$		0			0
$271$	−1.38266	+	2.39483i	−0.0839903	+	0.145476i	−0.904961	−	0.425496i	$-0.860100\pi$
$271$	−1.38266	+	2.39483i	−0.0839903	+	0.145476i	0.820970	+	0.570971i	$0.193433\pi$
$272$	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	0.984146	+	0.177362i	$0.0567564\pi$
$277$	7.28632	+	16.8916i	0.437792	+	1.01492i	−0.546353	+	0.837555i	$0.683984\pi$
$278$	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	0.815751	+	0.578403i	$0.196324\pi$
$281$	−3.07831	+	10.2823i	−0.183636	+	0.613388i	−0.999388	+	0.0349857i	$0.988861\pi$
$282$		0			0
$283$	0.831003	−	14.2678i	0.0493980	−	0.848131i	−0.879064	−	0.476704i	$-0.841832\pi$
$283$	0.831003	−	14.2678i	0.0493980	−	0.848131i	0.928462	−	0.371427i	$-0.121131\pi$
$284$	−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	0.454215	+	0.890892i	$0.349920\pi$
$293$	−8.65273	+	20.0593i	−0.505498	+	1.17188i	−0.959713	+	0.280983i	$0.909339\pi$
$294$		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	−0.986045	−	0.166478i	$-0.946760\pi$
$307$	−28.6368	+	10.4229i	−1.63439	+	0.594869i	−0.648344	+	0.761347i	$0.724538\pi$
$308$	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	$-0.369054\pi$
$311$	24.2284	−	12.1679i	1.37387	−	0.689981i	0.973990	+	0.226589i	$0.0727574\pi$
$312$		0			0
$313$	5.56294	+	5.89637i	0.314436	+	0.333282i	0.865245	−	0.501348i	$-0.167163\pi$
$313$	5.56294	+	5.89637i	0.314436	+	0.333282i	−0.550810	+	0.834631i	$0.685681\pi$
$314$	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	$-0.979897\pi$
$317$	−11.5963	+	15.5765i	−0.651312	+	0.874864i	0.346694	+	0.937978i	$0.387304\pi$
$318$		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	−0.768322	−	0.640064i	$-0.778908\pi$
$331$	1.18638	−	1.59359i	0.0652095	−	0.0875916i	0.833531	+	0.552472i	$0.186315\pi$
$332$	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	−0.835453	−	0.549562i	$-0.814795\pi$
$337$	−16.4031	+	8.23796i	−0.893535	+	0.448750i	−0.0580820	+	0.998312i	$0.518498\pi$
$338$	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	0.986859	+	0.161582i	$0.0516595\pi$
$347$	15.9943	+	21.4841i	0.858618	+	1.15332i	−0.128241	+	0.991743i	$0.540933\pi$
$348$		0			0
$349$	−11.7150	−	5.88351i	−0.627091	−	0.314937i	0.106722	−	0.994289i	$-0.465965\pi$
$349$	−11.7150	−	5.88351i	−0.627091	−	0.314937i	−0.733813	+	0.679352i	$0.762261\pi$
$350$	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	$-0.512158\pi$
$353$	16.2375	−	10.6796i	0.864237	−	0.568418i	0.902422	+	0.430853i	$0.141787\pi$
$354$		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	$-0.848813\pi$
$359$	−11.2428	+	9.43384i	−0.593373	+	0.497899i	0.295935	+	0.955208i	$0.404369\pi$
$360$		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	−0.835408	−	0.549630i	$-0.814769\pi$
$367$	3.15312	−	10.5322i	0.164592	−	0.549775i	1.00000		0.000144782i	$-4.60856e-5\pi$
$368$	−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	0.964812	+	0.262943i	$0.0846930\pi$
$373$	5.85601	+	19.5604i	0.303213	+	1.01280i	−0.661599	+	0.749858i	$0.730122\pi$
$374$	−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	−0.978308	−	0.207155i	$-0.933580\pi$
$379$	−13.0154	−	22.5433i	−0.668556	−	1.15797i	0.309753	−	0.950817i	$-0.399754\pi$
$380$	−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	$-0.553957\pi$
$383$	16.1477	−	17.1156i	0.825109	−	0.874564i	0.993809	+	0.111103i	$0.0354384\pi$
$384$		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	$-0.890563\pi$
$389$	−32.1789	+	7.62654i	−1.63154	+	0.386681i	−0.690057	+	0.723755i	$0.742415\pi$
$390$		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	0.984566	−	0.175014i	$-0.0559972\pi$
$397$	−0.00960087	−	0.0544493i	−0.000481854	−	0.00273273i	−0.985048	+	0.172282i	$0.944886\pi$
$398$	−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	$-0.283374\pi$
$401$	28.4500	−	3.32533i	1.42072	−	0.166059i	0.791502	+	0.611167i	$0.209299\pi$
$402$		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	−0.845020	−	0.534735i	$-0.820411\pi$
$409$	−31.2243	+	3.64960i	−1.54394	+	0.180461i	−0.698924	+	0.715196i	$0.746337\pi$
$410$	−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	$-0.288549\pi$
$419$	2.81915	+	1.85419i	0.137725	+	0.0905829i	−0.478777	+	0.877937i	$0.658920\pi$
$420$		0			0
$421$	24.5826	−	5.82618i	1.19808	−	0.283951i	0.417309	−	0.908765i	$-0.362973\pi$
$421$	24.5826	−	5.82618i	1.19808	−	0.283951i	0.780774	+	0.624814i	$0.214825\pi$
$422$	−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	0.925789	+	0.378041i	$0.123402\pi$
$431$	16.4068	+	28.4174i	0.790288	+	1.36882i	−0.135501	+	0.990777i	$0.543264\pi$
$432$		0			0
$433$	6.46122	−	11.1912i	0.310507	−	0.537813i	−0.667966	−	0.744192i	$-0.732835\pi$
$433$	6.46122	−	11.1912i	0.310507	−	0.537813i	0.978472	+	0.206379i	$0.0661680\pi$
$434$	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	0.784640	+	0.619952i	$0.212848\pi$
$439$	14.6064	+	33.8614i	0.697124	+	1.61612i	−0.0875158	+	0.996163i	$0.527893\pi$
$440$	−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	−0.319196	−	0.947689i	$-0.603413\pi$
$443$	9.85556	−	32.9199i	0.468252	−	1.56407i	0.787448	−	0.616382i	$-0.211402\pi$
$444$		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	$-0.413773\pi$
$449$	−13.4520	−	11.2876i	−0.634838	−	0.532693i	−0.902428	+	0.430840i	$0.858217\pi$
$450$		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	−0.375783	−	0.926708i	$-0.622626\pi$
$457$	6.97539	−	4.58779i	0.326295	−	0.214608i	0.702078	+	0.712100i	$0.252256\pi$
$458$	−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	$-0.194784\pi$
$461$	18.1763	+	9.12850i	0.846556	+	0.425157i	0.0280173	+	0.999607i	$0.491081\pi$
$462$		0			0
$463$	−1.54625	−	2.07698i	−0.0718604	−	0.0965253i	0.764740	−	0.644339i	$-0.222868\pi$
$463$	−1.54625	−	2.07698i	−0.0718604	−	0.0965253i	−0.836600	+	0.547814i	$0.815460\pi$
$464$	−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	$-0.297492\pi$
$467$	11.5019	+	4.18635i	0.532244	+	0.193721i	−0.0618958	+	0.998083i	$0.519715\pi$
$468$		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	0.250965	+	0.967996i	$0.419252\pi$
$479$	−16.3783	+	21.9999i	−0.748343	+	1.00520i	−0.999308	+	0.0372031i	$0.988155\pi$
$480$		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	$-0.429426\pi$
$491$	−0.474156	−	0.112377i	−0.0213983	−	0.00507150i	−0.241301	+	0.970450i	$0.577574\pi$
$492$		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	−0.335698	−	0.941970i	$-0.608972\pi$
$499$	4.90133	−	2.46154i	0.219414	−	0.110194i	0.555111	+	0.831776i	$0.312676\pi$
$500$	−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	$-0.535403\pi$
$503$	9.93090	−	3.61455i	0.442797	−	0.161165i	0.553790	+	0.832656i	$0.313181\pi$
$504$		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	$-0.292367\pi$
$509$	−7.40873	−	9.95165i	−0.328386	−	0.441099i	−0.935400	+	0.353592i	$0.884960\pi$
$510$		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	$-0.849634\pi$
$521$	−13.6270	+	11.4344i	−0.597011	+	0.500952i	0.293472	+	0.955968i	$0.405189\pi$
$522$		0			0
$523$	−10.4002	−	8.72680i	−0.454769	−	0.381596i	0.386433	−	0.922317i	$-0.373707\pi$
$523$	−10.4002	−	8.72680i	−0.454769	−	0.381596i	−0.841202	+	0.540721i	$0.818151\pi$
$524$	−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	0.994620	+	0.103594i	$0.0330342\pi$
$541$	13.6538	+	23.6492i	0.587025	+	1.01676i	−0.407595	+	0.913163i	$0.633632\pi$
$542$	−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	−0.157886	−	0.987457i	$-0.550468\pi$
$547$	−12.6117	−	1.47410i	−0.539239	−	0.0630281i	−0.381353	+	0.924429i	$0.624542\pi$
$548$	−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	−0.877415	−	0.479733i	$-0.840734\pi$
$557$	2.62356	−	14.8789i	0.111164	−	0.630441i	0.988578	−	0.150708i	$-0.0481553\pi$
$558$		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	$-0.578285\pi$
$563$	−6.09083	+	0.711916i	−0.256698	+	0.0300037i	−0.0132294	+	0.999912i	$0.504211\pi$
$564$		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	$-0.0283906\pi$
$569$	−0.0860178	−	1.47687i	−0.00360605	−	0.0619135i	−0.999631	+	0.0271601i	$0.991354\pi$
$570$		0			0
$571$	−8.75647	+	1.02348i	−0.366447	+	0.0428315i	−0.297324	−	0.954777i	$-0.596094\pi$
$571$	−8.75647	+	1.02348i	−0.366447	+	0.0428315i	−0.0691228	+	0.997608i	$0.522020\pi$
$572$	−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	−0.888313	−	0.459238i	$-0.848122\pi$
$577$	2.48608	−	14.0993i	0.103497	−	0.586960i	0.991810	−	0.127722i	$-0.0407665\pi$
$578$	−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	$-0.406578\pi$
$587$	8.48086	+	0.991271i	0.350043	+	0.0409141i	0.0607450	+	0.998153i	$0.480652\pi$
$588$		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	−0.908517	−	0.417848i	$-0.862784\pi$
$593$	−19.8740	−	34.4227i	−0.816125	−	1.41357i	0.0923915	−	0.995723i	$-0.470549\pi$
$594$		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	0.990426	+	0.138046i	$0.0440820\pi$
$599$	5.84437	+	19.5215i	0.238794	+	0.797629i	−0.751631	+	0.659583i	$0.770733\pi$
$600$		0			0
$601$	−5.42187	−	12.5693i	−0.221163	−	0.512713i	0.771123	−	0.636687i	$-0.219695\pi$
$601$	−5.42187	−	12.5693i	−0.221163	−	0.512713i	−0.992286	+	0.123974i	$0.960436\pi$
$602$	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	−0.988826	−	0.149074i	$-0.952371\pi$
$607$	0.261657	−	4.49247i	0.0106203	−	0.182344i	0.999446	−	0.0332701i	$-0.0105922\pi$
$608$	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	0.108971	−	0.994045i	$-0.465244\pi$
$613$	27.4040	−	22.9947i	1.10684	−	0.928746i	0.997866	+	0.0652986i	$0.0208000\pi$
$614$	−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	−0.543770	−	0.839234i	$-0.683004\pi$
$617$	10.9250	−	25.3270i	0.439825	−	1.01963i	0.983594	−	0.180394i	$-0.0577372\pi$
$618$		0			0
$619$	27.9288	−	18.3690i	1.12255	−	0.738314i	0.154233	−	0.988034i	$-0.450709\pi$
$619$	27.9288	−	18.3690i	1.12255	−	0.738314i	0.968318	+	0.249721i	$0.0803389\pi$
$620$	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	−0.129339	−	0.991600i	$-0.541286\pi$
$631$	10.2732	−	3.73914i	0.408970	−	0.148853i	0.538309	+	0.842748i	$0.319063\pi$
$632$	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	$-0.855190\pi$
$641$	−5.56274	+	7.47205i	−0.219715	+	0.295128i	0.678575	+	0.734531i	$0.262598\pi$
$642$		0			0
$643$	1.25280	+	0.296918i	0.0494055	+	0.0117093i	0.255244	−	0.966877i	$-0.417844\pi$
$643$	1.25280	+	0.296918i	0.0494055	+	0.0117093i	−0.205839	+	0.978586i	$0.565992\pi$
$644$	−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	$-0.668872\pi$
$647$	−25.7409			−1.01198			−0.505989	+	0.862540i	$0.668872\pi$
$648$		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	$-0.701855\pi$
$653$	−37.9092	−	8.98465i	−1.48350	−	0.351596i	−0.891011	+	0.453981i	$0.850003\pi$
$654$		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	$-0.0137882\pi$
$659$	23.0459	+	24.4272i	0.897742	+	0.951550i	−0.101320	+	0.994854i	$0.532307\pi$
$660$		0			0
$661$	31.6648	−	15.9027i	1.23162	−	0.618542i	0.290583	−	0.956850i	$-0.406151\pi$
$661$	31.6648	−	15.9027i	1.23162	−	0.618542i	0.941036	+	0.338308i	$0.109854\pi$
$662$	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	0.853895	−	0.520445i	$-0.174234\pi$
$673$	24.5503	+	12.3296i	0.946346	+	0.475273i	0.0924503	+	0.995717i	$0.470530\pi$
$674$	−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	$-0.626417\pi$
$677$	7.98158	−	5.24957i	0.306757	−	0.201757i	0.693549	+	0.720410i	$0.256046\pi$
$678$		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	$-0.502894\pi$
$683$	25.4573	−	21.3612i	0.974095	−	0.817363i	0.983188	+	0.182596i	$0.0584500\pi$
$684$		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	−0.923247	−	0.384208i	$-0.874475\pi$
$691$	1.55724	−	5.20154i	0.0592402	−	0.197876i	0.982487	+	0.186332i	$0.0596599\pi$
$692$	−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	0.348906	+	0.937158i	$0.386553\pi$
$701$	−16.8694	+	29.2187i	−0.637150	+	1.10358i	−0.986055	+	0.166418i	$0.946780\pi$
$702$		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	0.469685	−	0.882834i	$-0.344367\pi$
$709$	19.2544	+	2.25052i	0.723114	+	0.0845199i	0.253429	+	0.967354i	$0.418442\pi$
$710$	−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	$-0.972899\pi$
$719$	−0.831346	+	4.71480i	−0.0310040	+	0.175832i	0.965374	+	0.260871i	$0.0840097\pi$
$720$		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	0.996600	+	0.0823892i	$0.0262551\pi$
$727$	0.439589	+	7.54745i	0.0163035	+	0.279920i	−0.980297	+	0.197530i	$0.936708\pi$
$728$	−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	−0.790124	−	0.612947i	$-0.789984\pi$
$733$	−38.3799	+	4.48597i	−1.41760	+	0.165693i	−0.627471	+	0.778640i	$0.715910\pi$
$734$	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	0.197218	+	0.980360i	$0.436809\pi$
$739$	−8.79173	+	49.8604i	−0.323409	+	1.83414i	−0.520627	+	0.853784i	$0.674302\pi$
$740$	−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	$-0.405693\pi$
$743$	−12.8280	−	8.43710i	−0.470613	−	0.309527i	−0.762572	+	0.646904i	$0.776064\pi$
$744$		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	0.202455	−	0.979292i	$-0.435108\pi$
$751$	32.0170	−	33.9361i	1.16832	−	1.23834i	0.965863	−	0.259053i	$-0.0834106\pi$
$752$	−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	−0.739856	−	0.672765i	$-0.765107\pi$
$757$	5.85224	−	10.1364i	0.212703	−	0.368413i	0.952560	+	0.304352i	$0.0984399\pi$
$758$	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	−0.979366	−	0.202097i	$-0.935225\pi$
$761$	−7.50818	−	25.0791i	−0.272171	−	0.909116i	0.707194	−	0.707019i	$-0.249961\pi$
$762$		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	0.521977	+	0.852959i	$0.325195\pi$
$769$	−2.64810	+	45.4662i	−0.0954931	+	1.63955i	−0.617471	+	0.786594i	$0.711843\pi$
$770$	−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	$-0.196835\pi$
$773$	10.7154	+	8.99131i	0.385407	+	0.323395i	−0.429414	+	0.903108i	$0.641280\pi$
$774$		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	0.927161	−	0.374663i	$-0.122241\pi$
$787$	8.48130	+	11.3924i	0.302326	+	0.406094i	−0.624836	+	0.780756i	$0.714834\pi$
$788$	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	$-0.909327\pi$
$797$	−36.9090	+	18.5364i	−1.30738	+	0.656593i	−0.347681	+	0.937613i	$0.613031\pi$
$798$		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	$-0.362364\pi$
$809$	23.8379			0.838097			0.419048	+	0.907964i	$0.362364\pi$
$810$		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	$-0.290808\pi$
$821$	−6.16015	−	6.52938i	−0.214991	−	0.227877i	−0.825890	+	0.563832i	$0.809327\pi$
$822$		0			0
$823$	−1.16006	+	0.582603i	−0.0404371	+	0.0203083i	−0.468903	−	0.883250i	$-0.655351\pi$
$823$	−1.16006	+	0.582603i	−0.0404371	+	0.0203083i	0.428466	+	0.903558i	$0.359054\pi$
$824$	−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	$-0.426407\pi$
$827$	29.6308	−	10.7847i	1.03036	−	0.375022i	0.801219	+	0.598371i	$0.204185\pi$
$828$		0			0
$829$	−25.1437	−	9.15156i	−0.873277	−	0.317847i	−0.133783	−	0.991011i	$-0.542713\pi$
$829$	−25.1437	−	9.15156i	−0.873277	−	0.317847i	−0.739493	+	0.673164i	$0.764935\pi$
$830$	−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	$-0.706517\pi$
$839$	−3.24118	+	2.13175i	−0.111898	+	0.0735963i	0.492327	+	0.870411i	$0.336147\pi$
$840$		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	−0.939441	−	0.342711i	$-0.888655\pi$
$853$	0.986381	−	3.29474i	0.0337730	−	0.112810i	0.973214	+	0.229901i	$0.0738402\pi$
$854$	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	$-0.0490760\pi$
$857$	5.80621	+	13.4603i	0.198336	+	0.459795i	−0.789802	+	0.613362i	$0.789817\pi$
$858$		0			0
$859$	−2.73469	−	9.13449i	−0.0933063	−	0.311665i	0.898577	−	0.438816i	$-0.144602\pi$
$859$	−2.73469	−	9.13449i	−0.0933063	−	0.311665i	−0.991883	+	0.127151i	$0.959417\pi$
$860$	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	$-0.921224\pi$
$863$	−8.00876	+	13.8716i	−0.272621	+	0.472194i	0.696911	+	0.717158i	$0.254557\pi$
$864$		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	0.922764	−	0.385366i	$-0.125925\pi$
$877$	27.6716	+	18.1999i	0.934403	+	0.614567i	0.0116393	+	0.999932i	$0.496295\pi$
$878$	−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	−0.932134	−	0.362115i	$-0.882055\pi$
$881$	2.00755	−	11.3854i	0.0676360	−	0.383583i	0.999770	−	0.0214681i	$-0.00683402\pi$
$882$		0			0
$883$	−7.24692	−	41.0993i	−0.243878	−	1.38310i	−0.823084	−	0.567920i	$-0.807748\pi$
$883$	−7.24692	−	41.0993i	−0.243878	−	1.38310i	0.579206	−	0.815182i	$-0.303363\pi$
$884$	−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	$-0.669638\pi$
$887$	−23.9390	+	2.79807i	−0.803793	+	0.0939499i	−0.295732	+	0.955271i	$0.595564\pi$
$888$		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	0.160041	−	0.987110i	$-0.448837\pi$
$907$	22.4691	−	5.32526i	0.746073	−	0.176822i	0.586032	+	0.810288i	$0.300689\pi$
$908$	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	$-0.339113\pi$
$911$	22.7444	+	2.65844i	0.753555	+	0.0880779i	0.269362	+	0.963039i	$0.413187\pi$
$912$		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	−0.981439	−	0.191776i	$-0.938575\pi$
$919$	−9.84136	+	17.0457i	−0.324636	+	0.562287i	0.656802	+	0.754063i	$0.271909\pi$
$920$	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	−0.707287	−	0.706927i	$-0.750081\pi$
$929$	8.29364	−	27.7027i	0.272105	−	0.908895i	0.979392	−	0.201968i	$-0.0647339\pi$
$930$		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	−0.364029	−	0.931388i	$-0.618599\pi$
$937$	14.9990	−	12.5856i	0.489995	−	0.411155i	0.854025	+	0.520233i	$0.174155\pi$
$938$	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	$-0.922991\pi$
$941$	−3.99887	+	9.27041i	−0.130359	+	0.302207i	0.840518	+	0.541783i	$0.182251\pi$
$942$		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	$-0.240978\pi$
$947$	18.7726	+	9.42795i	0.610027	+	0.306367i	−0.116834	+	0.993151i	$0.537275\pi$
$948$		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	$-0.354004\pi$
$953$	6.34571	+	2.30965i	0.205558	+	0.0748169i	−0.237189	+	0.971463i	$0.576226\pi$
$954$		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	0.410944	−	0.911660i	$-0.365199\pi$
$967$	11.4754	+	2.71973i	0.369025	+	0.0874605i	−0.0419193	+	0.999121i	$0.513347\pi$
$968$	−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	$-0.371569\pi$
$971$	24.4687			0.785239			0.392620	+	0.919701i	$0.371569\pi$
$972$		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	$-0.212030\pi$
$977$	37.8679	+	8.97486i	1.21150	+	0.287131i	0.425272	+	0.905066i	$0.360179\pi$
$978$		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	$-0.337223\pi$
$983$	−12.8443	−	13.6142i	−0.409670	−	0.434225i	−0.899050	+	0.437846i	$0.855742\pi$
$984$		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	0.307589	−	0.951519i	$-0.400478\pi$
$991$	−2.15353	−	0.783819i	−0.0684090	−	0.0248988i	−0.375998	+	0.926620i	$0.622700\pi$
$992$	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	0.832510	−	0.554010i	$-0.186903\pi$
$997$	27.9526	+	14.0383i	0.885267	+	0.444598i	0.0527567	+	0.998607i	$0.483199\pi$
$998$	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.d.514.4		144
3.2	odd	2		729.2.g.a.514.5		144
9.2	odd	6		729.2.g.b.28.5		144
9.4	even	3		81.2.g.a.13.5	✓	144
9.5	odd	6		243.2.g.a.10.4		144
9.7	even	3		729.2.g.c.28.4		144
81.2	odd	54		729.2.g.a.217.5		144
81.22	even	27		6561.2.a.c.1.32		72
81.25	even	27		729.2.g.c.703.4		144
81.29	odd	54		243.2.g.a.73.4		144
81.52	even	27		81.2.g.a.25.5	yes	144
81.56	odd	54		729.2.g.b.703.5		144
81.59	odd	54		6561.2.a.d.1.41		72
81.79	even	27	inner	729.2.g.d.217.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.5	✓	144	9.4	even	3
81.2.g.a.25.5	yes	144	81.52	even	27
243.2.g.a.10.4		144	9.5	odd	6
243.2.g.a.73.4		144	81.29	odd	54
729.2.g.a.217.5		144	81.2	odd	54
729.2.g.a.514.5		144	3.2	odd	2
729.2.g.b.28.5		144	9.2	odd	6
729.2.g.b.703.5		144	81.56	odd	54
729.2.g.c.28.4		144	9.7	even	3
729.2.g.c.703.4		144	81.25	even	27
729.2.g.d.217.4		144	81.79	even	27	inner
729.2.g.d.514.4		144	1.1	even	1	trivial
6561.2.a.c.1.32		72	81.22	even	27
6561.2.a.d.1.41		72	81.59	odd	54

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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