LMFDB - Embedded newform 729.2.g.c.703.4

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,-63] 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			703.4
Character	$\chi$	$=$	729.703
Dual form			729.2.g.c.28.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.474230 + 0.311906i) q^{2} +(-0.664551 - 1.54060i) q^{4} +(-1.99266 - 2.11209i) q^{5} +(-3.10865 + 0.363349i) q^{7} +(0.362501 - 2.05585i) q^{8} +(-0.286203 - 1.62314i) q^{10} +(0.984350 + 3.28796i) q^{11} +(0.231870 + 3.98106i) q^{13} +(-1.58755 - 0.797296i) q^{14} +(-1.48964 + 1.57893i) q^{16} +(0.878443 + 0.319727i) q^{17} +(-4.55845 + 1.65914i) q^{19} +(-1.92967 + 4.47349i) q^{20} +(-0.558725 + 1.86627i) q^{22} +(6.11065 + 0.714233i) q^{23} +(-0.199532 + 3.42583i) q^{25} +(-1.13175 + 1.96026i) q^{26} +(2.62564 + 4.54773i) q^{28} +(1.60828 - 0.807706i) q^{29} +(0.403603 - 0.542133i) q^{31} +(-5.26149 + 1.24700i) q^{32} +(0.316859 + 0.425615i) q^{34} +(6.96191 + 5.84174i) q^{35} +(-8.73079 + 7.32600i) q^{37} +(-2.67925 - 0.634993i) q^{38} +(-5.06448 + 3.33096i) q^{40} +(-5.55820 + 3.65568i) q^{41} +(-2.17613 - 0.515752i) q^{43} +(4.41129 - 3.70151i) q^{44} +(2.67508 + 2.24466i) q^{46} +(-1.89278 - 2.54245i) q^{47} +(2.72039 - 0.644744i) q^{49} +(-1.16316 + 1.56239i) q^{50} +(5.97913 - 3.00283i) q^{52} +(-4.18963 - 7.25666i) q^{53} +(4.98301 - 8.63082i) q^{55} +(-0.379900 + 6.52263i) q^{56} +(1.01462 + 0.118592i) q^{58} +(1.44287 - 4.81952i) q^{59} +(-0.226018 + 0.523969i) q^{61} +(0.360495 - 0.131209i) q^{62} +(1.19553 + 0.435136i) q^{64} +(7.94633 - 8.42262i) q^{65} +(-12.2150 - 6.13461i) q^{67} +(-0.0911978 - 1.56581i) q^{68} +(1.47947 + 4.94179i) q^{70} +(-2.31784 - 13.1452i) q^{71} +(-1.17142 + 6.64347i) q^{73} +(-6.42542 + 0.751024i) q^{74} +(5.58539 + 5.92017i) q^{76} +(-4.25468 - 9.86346i) q^{77} +(-0.622719 - 0.409569i) q^{79} +6.30319 q^{80} -3.77609 q^{82} +(3.04071 + 1.99991i) q^{83} +(-1.07514 - 2.49246i) q^{85} +(-0.871119 - 0.923332i) q^{86} +(7.11637 - 0.831784i) q^{88} +(-2.27781 + 12.9181i) q^{89} +(-2.16732 - 12.2915i) q^{91} +(-2.96049 - 9.88873i) q^{92} +(-0.104609 - 1.79607i) q^{94} +(12.5877 + 6.32177i) q^{95} +(-8.58165 + 9.09602i) q^{97} +(1.49119 + 0.542748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 63 q^{20} + 9 q^{22} + 36 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 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{27}\right)$

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 $

$2$	0.474230	+	0.311906i	0.335331	+	0.220551i	0.705996	−	0.708216i	$-0.250500\pi$
$2$	0.474230	+	0.311906i	0.335331	+	0.220551i	−0.370665	+	0.928767i	$0.620870\pi$
$3$		0			0
$3$		0			0
$4$	−0.664551	−	1.54060i	−0.332275	−	0.770301i
$5$	−1.99266	−	2.11209i	−0.891144	−	0.944557i	0.107623	−	0.994192i	$-0.465676\pi$
$5$	−1.99266	−	2.11209i	−0.891144	−	0.944557i	−0.998767	+	0.0496342i	$0.984194\pi$
$6$		0			0
$7$	−3.10865	+	0.363349i	−1.17496	+	0.137333i	−0.681088	−	0.732201i	$-0.738493\pi$
$7$	−3.10865	+	0.363349i	−1.17496	+	0.137333i	−0.493872	+	0.869535i	$0.664419\pi$
$8$	0.362501	−	2.05585i	0.128164	−	0.726852i
$9$		0			0
$10$	−0.286203	−	1.62314i	−0.0905055	−	0.513282i
$11$	0.984350	+	3.28796i	0.296793	+	0.991357i	0.968181	+	0.250251i	$0.0805132\pi$
$11$	0.984350	+	3.28796i	0.296793	+	0.991357i	−0.671388	+	0.741106i	$0.734302\pi$
$12$		0			0
$13$	0.231870	+	3.98106i	0.0643092	+	1.10415i	0.863920	+	0.503628i	$0.168002\pi$
$13$	0.231870	+	3.98106i	0.0643092	+	1.10415i	−0.799611	+	0.600518i	$0.794961\pi$
$14$	−1.58755	−	0.797296i	−0.424290	−	0.213086i
$15$		0			0
$16$	−1.48964	+	1.57893i	−0.372410	+	0.394732i
$17$	0.878443	+	0.319727i	0.213054	+	0.0775452i	0.446342	−	0.894862i	$-0.352726\pi$
$17$	0.878443	+	0.319727i	0.213054	+	0.0775452i	−0.233289	+	0.972408i	$0.574949\pi$
$18$		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	$0.576725\pi$
$20$	−1.92967	+	4.47349i	−0.431488	+	1.00030i
$21$		0			0
$22$	−0.558725	+	1.86627i	−0.119121	+	0.397891i
$23$	6.11065	+	0.714233i	1.27416	+	0.148928i	0.726145	−	0.687542i	$-0.241310\pi$
$23$	6.11065	+	0.714233i	1.27416	+	0.148928i	0.548014	+	0.836469i	$0.315384\pi$
$24$		0			0
$25$	−0.199532	+	3.42583i	−0.0399063	+	0.685165i
$26$	−1.13175	+	1.96026i	−0.221955	+	0.384438i
$27$		0			0
$28$	2.62564	+	4.54773i	0.496198	+	0.859441i
$29$	1.60828	−	0.807706i	0.298649	−	0.149987i	−0.293165	−	0.956062i	$-0.594708\pi$
$29$	1.60828	−	0.807706i	0.298649	−	0.149987i	0.591814	+	0.806075i	$0.298412\pi$
$30$		0			0
$31$	0.403603	−	0.542133i	0.0724892	−	0.0973699i	−0.764400	−	0.644743i	$-0.776965\pi$
$31$	0.403603	−	0.542133i	0.0724892	−	0.0973699i	0.836889	+	0.547373i	$0.184372\pi$
$32$	−5.26149	+	1.24700i	−0.930109	+	0.220440i
$33$		0			0
$34$	0.316859	+	0.425615i	0.0543409	+	0.0729924i
$35$	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	$0.891508\pi$
$38$	−2.67925	−	0.634993i	−0.434631	−	0.103009i
$39$		0			0
$40$	−5.06448	+	3.33096i	−0.800765	+	0.526672i
$41$	−5.55820	+	3.65568i	−0.868045	+	0.570922i	−0.903567	−	0.428447i	$-0.859061\pi$
$41$	−5.55820	+	3.65568i	−0.868045	+	0.570922i	0.0355222	+	0.999369i	$0.488691\pi$
$42$		0			0
$43$	−2.17613	−	0.515752i	−0.331857	−	0.0786515i	0.0613098	−	0.998119i	$-0.480472\pi$
$43$	−2.17613	−	0.515752i	−0.331857	−	0.0786515i	−0.393166	+	0.919467i	$0.628620\pi$
$44$	4.41129	−	3.70151i	0.665026	−	0.558023i
$45$		0			0
$46$	2.67508	+	2.24466i	0.394419	+	0.330957i
$47$	−1.89278	−	2.54245i	−0.276091	−	0.370854i	0.642351	−	0.766411i	$-0.277959\pi$
$47$	−1.89278	−	2.54245i	−0.276091	−	0.370854i	−0.918442	+	0.395556i	$0.870552\pi$
$48$		0			0
$49$	2.72039	−	0.644744i	0.388627	−	0.0921062i
$50$	−1.16316	+	1.56239i	−0.164496	+	0.220956i
$51$		0			0
$52$	5.97913	−	3.00283i	0.829157	−	0.416418i
$53$	−4.18963	−	7.25666i	−0.575490	−	0.996779i	−0.995988	−	0.0894851i	$-0.971478\pi$
$53$	−4.18963	−	7.25666i	−0.575490	−	0.996779i	0.420498	−	0.907294i	$-0.361855\pi$
$54$		0			0
$55$	4.98301	−	8.63082i	0.671909	−	1.16378i
$56$	−0.379900	+	6.52263i	−0.0507663	+	0.871623i
$57$		0			0
$58$	1.01462	+	0.118592i	0.133226	+	0.0155719i
$59$	1.44287	−	4.81952i	0.187846	−	0.627448i	−0.811241	−	0.584712i	$-0.801207\pi$
$59$	1.44287	−	4.81952i	0.187846	−	0.627448i	0.999086	−	0.0427359i	$-0.0136074\pi$
$60$		0			0
$61$	−0.226018	+	0.523969i	−0.0289387	+	0.0670874i	−0.932073	−	0.362272i	$-0.882001\pi$
$61$	−0.226018	+	0.523969i	−0.0289387	+	0.0670874i	0.903134	+	0.429359i	$0.141261\pi$
$62$	0.360495	−	0.131209i	0.0457829	−	0.0166636i
$63$		0			0
$64$	1.19553	+	0.435136i	0.149441	+	0.0543920i
$65$	7.94633	−	8.42262i	0.985621	−	1.04470i
$66$		0			0
$67$	−12.2150	−	6.13461i	−1.49230	−	0.749461i	−0.499173	−	0.866502i	$-0.666363\pi$
$67$	−12.2150	−	6.13461i	−1.49230	−	0.749461i	−0.993127	+	0.117041i	$0.962659\pi$
$68$	−0.0911978	−	1.56581i	−0.0110594	−	0.189882i
$69$		0			0
$70$	1.47947	+	4.94179i	0.176831	+	0.590657i
$71$	−2.31784	−	13.1452i	−0.275078	−	1.56004i	−0.738715	−	0.674017i	$-0.764567\pi$
$71$	−2.31784	−	13.1452i	−0.275078	−	1.56004i	0.463638	−	0.886025i	$-0.346544\pi$
$72$		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	$0.926377\pi$
$74$	−6.42542	+	0.751024i	−0.746940	+	0.0873048i
$75$		0			0
$76$	5.58539	+	5.92017i	0.640688	+	0.679090i
$77$	−4.25468	−	9.86346i	−0.484866	−	1.12405i
$78$		0			0
$79$	−0.622719	−	0.409569i	−0.0700614	−	0.0460801i	0.513995	−	0.857793i	$-0.328165\pi$
$79$	−0.622719	−	0.409569i	−0.0700614	−	0.0460801i	−0.584056	+	0.811713i	$0.698535\pi$
$80$	6.30319			0.704718
$81$		0			0
$82$	−3.77609			−0.417000
$83$	3.04071	+	1.99991i	0.333761	+	0.219518i	0.705316	−	0.708893i	$-0.250805\pi$
$83$	3.04071	+	1.99991i	0.333761	+	0.219518i	−0.371555	+	0.928411i	$0.621175\pi$
$84$		0			0
$85$	−1.07514	−	2.49246i	−0.116616	−	0.270345i
$86$	−0.871119	−	0.923332i	−0.0939352	−	0.0995655i
$87$		0			0
$88$	7.11637	−	0.831784i	0.758607	−	0.0886685i
$89$	−2.27781	+	12.9181i	−0.241447	+	1.36931i	0.587154	+	0.809475i	$0.300248\pi$
$89$	−2.27781	+	12.9181i	−0.241447	+	1.36931i	−0.828601	+	0.559839i	$0.810863\pi$
$90$		0			0
$91$	−2.16732	−	12.2915i	−0.227197	−	1.28850i
$92$	−2.96049	−	9.88873i	−0.308652	−	1.03097i
$93$		0			0
$94$	−0.104609	−	1.79607i	−0.0107896	−	0.185251i
$95$	12.5877	+	6.32177i	1.29147	+	0.648600i
$96$		0			0
$97$	−8.58165	+	9.09602i	−0.871335	+	0.923561i	−0.997656	−	0.0684283i	$-0.978202\pi$
$97$	−8.58165	+	9.09602i	−0.871335	+	0.923561i	0.126321	+	0.991989i	$0.459683\pi$
$98$	1.49119	+	0.542748i	0.150633	+	0.0548258i
$99$		0			0
$100$	5.41044	−	1.96924i	0.541044	−	0.196924i
$101$	−2.37006	+	5.49442i	−0.235830	+	0.546715i	−0.994497	−	0.104763i	$-0.966592\pi$
$101$	−2.37006	+	5.49442i	−0.235830	+	0.546715i	0.758667	+	0.651478i	$0.225851\pi$
$102$		0			0
$103$	−0.507240	+	1.69430i	−0.0499798	+	0.166944i	−0.979336	−	0.202240i	$-0.935178\pi$
$103$	−0.507240	+	1.69430i	−0.0499798	+	0.166944i	0.929356	+	0.369185i	$0.120363\pi$
$104$	8.26849	+	0.966448i	0.810792	+	0.0947680i
$105$		0			0
$106$	0.276545	−	4.74809i	0.0268604	−	0.461176i
$107$	−3.57628	+	6.19429i	−0.345732	+	0.598825i	−0.985486	−	0.169754i	$-0.945703\pi$
$107$	−3.57628	+	6.19429i	−0.345732	+	0.598825i	0.639755	+	0.768579i	$0.279036\pi$
$108$		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	$-0.349998\pi$
$110$	5.05509	−	2.53876i	0.481984	−	0.242062i
$111$		0			0
$112$	4.05708	−	5.44960i	0.383358	−	0.514939i
$113$	−5.66711	+	1.34313i	−0.533116	+	0.126351i	−0.488352	−	0.872647i	$-0.662402\pi$
$113$	−5.66711	+	1.34313i	−0.533116	+	0.126351i	−0.0447643	+	0.998998i	$0.514254\pi$
$114$		0			0
$115$	−10.6679	−	14.3295i	−0.994788	−	1.33623i
$116$	−2.31313	−	1.94095i	−0.214769	−	0.180213i
$117$		0			0
$118$	2.18749	−	1.83552i	0.201375	−	0.168973i
$119$	−2.84695	−	0.674739i	−0.260979	−	0.0618532i
$120$		0			0
$121$	−0.651365	+	0.428410i	−0.0592150	+	0.0389463i
$122$	−0.270614	+	0.177985i	−0.0245002	+	0.0161140i
$123$		0			0
$124$	−1.10343	−	0.261517i	−0.0990906	−	0.0234849i
$125$	−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	$0.564109\pi$
$128$	6.88920	+	9.25380i	0.608925	+	0.817928i
$129$		0			0
$130$	6.39545	−	1.51575i	0.560918	−	0.132940i
$131$	−4.27722	+	5.74530i	−0.373702	+	0.501969i	−0.948697	−	0.316188i	$-0.897597\pi$
$131$	−4.27722	+	5.74530i	−0.373702	+	0.501969i	0.574994	+	0.818158i	$0.305004\pi$
$132$		0			0
$133$	13.5678	−	6.81400i	1.17648	−	0.590848i
$134$	−3.87930	−	6.71914i	−0.335120	−	0.580446i
$135$		0			0
$136$	0.975746	−	1.69004i	0.0836695	−	0.144920i
$137$	0.501738	−	8.61452i	0.0428664	−	0.735988i	−0.906575	−	0.422044i	$-0.861313\pi$
$137$	0.501738	−	8.61452i	0.0428664	−	0.735988i	0.949442	−	0.313944i	$-0.101650\pi$
$138$		0			0
$139$	5.85926	+	0.684849i	0.496976	+	0.0580882i	0.360889	−	0.932609i	$-0.382473\pi$
$139$	5.85926	+	0.684849i	0.496976	+	0.0580882i	0.136087	+	0.990697i	$0.456547\pi$
$140$	4.37325	−	14.6077i	0.369607	−	1.23457i
$141$		0			0
$142$	3.00086	−	6.95677i	0.251826	−	0.583799i
$143$	−12.8613	+	4.68113i	−1.07552	+	0.391456i
$144$		0			0
$145$	−4.91069	−	1.78735i	−0.407811	−	0.148431i
$146$	−2.62766	+	2.78516i	−0.217467	+	0.230501i
$147$		0			0
$148$	17.0885	+	8.58217i	1.40467	+	0.705450i
$149$	0.802085	+	13.7713i	0.0657094	+	1.12819i	0.856516	+	0.516121i	$0.172624\pi$
$149$	0.802085	+	13.7713i	0.0657094	+	1.12819i	−0.790807	+	0.612066i	$0.790339\pi$
$150$		0			0
$151$	−1.80026	−	6.01330i	−0.146503	−	0.489356i	0.852965	−	0.521969i	$-0.174802\pi$
$151$	−1.80026	−	6.01330i	−0.146503	−	0.489356i	−0.999468	+	0.0326132i	$0.989617\pi$
$152$	1.75849	+	9.97291i	0.142633	+	0.808910i
$153$		0			0
$154$	1.05877	−	6.00461i	0.0853185	−	0.483865i
$155$	−1.94928	+	0.227838i	−0.156570	+	0.0183004i
$156$		0			0
$157$	0.113981	+	0.120812i	0.00909664	+	0.00964187i	0.731906	−	0.681406i	$-0.238631\pi$
$157$	0.113981	+	0.120812i	0.00909664	+	0.00964187i	−0.722809	+	0.691048i	$0.757150\pi$
$158$	−0.167565	−	0.388460i	−0.0133308	−	0.0309042i
$159$		0			0
$160$	13.1181	+	8.62793i	1.03708	+	0.682098i
$161$	−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	$0.281208\pi$
$164$	9.32566	+	6.13358i	0.728212	+	0.478952i
$165$		0			0
$166$	0.818213	+	1.89683i	0.0635056	+	0.147223i
$167$	12.5418	+	13.2935i	0.970513	+	1.02868i	0.999576	+	0.0291056i	$0.00926592\pi$
$167$	12.5418	+	13.2935i	0.970513	+	1.02868i	−0.0290638	+	0.999578i	$0.509253\pi$
$168$		0			0
$169$	−2.88294	+	0.336968i	−0.221765	+	0.0259206i
$170$	0.267548	−	1.51734i	0.0205200	−	0.116375i
$171$		0			0
$172$	0.651580	+	3.69529i	0.0496825	+	0.281763i
$173$	−5.40734	−	18.0618i	−0.411112	−	1.37321i	−0.873626	−	0.486598i	$-0.838238\pi$
$173$	−5.40734	−	18.0618i	−0.411112	−	1.37321i	0.462514	−	0.886612i	$-0.346948\pi$
$174$		0			0
$175$	−0.624497	−	10.7222i	−0.0472076	−	0.810523i
$176$	−6.65778	−	3.34366i	−0.501849	−	0.252038i
$177$		0			0
$178$	−5.10943	+	5.41568i	−0.382968	+	0.405922i
$179$	9.67521	+	3.52149i	0.723159	+	0.263209i	0.677266	−	0.735738i	$-0.263164\pi$
$179$	9.67521	+	3.52149i	0.723159	+	0.263209i	0.0458930	+	0.998946i	$0.485387\pi$
$180$		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	$0.379191\pi$
$182$	2.80597	−	6.50498i	0.207993	−	0.482181i
$183$		0			0
$184$	3.68347	−	12.3037i	0.271549	−	0.907037i
$185$	32.8707	+	3.84203i	2.41670	+	0.282472i
$186$		0			0
$187$	−0.186554	+	3.20301i	−0.0136422	+	0.234227i
$188$	−2.65905	+	4.60561i	−0.193931	+	0.335899i
$189$		0			0
$190$	3.99766	+	6.92415i	0.290021	+	0.502330i
$191$	−0.683675	+	0.343354i	−0.0494690	+	0.0248442i	−0.473362	−	0.880868i	$-0.656960\pi$
$191$	−0.683675	+	0.343354i	−0.0494690	+	0.0248442i	0.423893	+	0.905712i	$0.360663\pi$
$192$		0			0
$193$	5.58623	−	7.50362i	0.402106	−	0.540122i	−0.554241	−	0.832356i	$-0.686991\pi$
$193$	5.58623	−	7.50362i	0.402106	−	0.540122i	0.956347	+	0.292234i	$0.0943987\pi$
$194$	−6.90678	+	1.63694i	−0.495878	+	0.117525i
$195$		0			0
$196$	−2.80113	−	3.76257i	−0.200081	−	0.268755i
$197$	0.857832	+	0.719807i	0.0611180	+	0.0512841i	0.672835	−	0.739793i	$-0.265076\pi$
$197$	0.857832	+	0.719807i	0.0611180	+	0.0512841i	−0.611717	+	0.791077i	$0.709521\pi$
$198$		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	$0.190016\pi$
$200$	6.97064	+	1.65207i	0.492899	+	0.116819i
$201$		0			0
$202$	−2.83769	+	1.86638i	−0.199660	+	0.131318i
$203$	−4.70609	+	3.09524i	−0.330303	+	0.217244i
$204$		0			0
$205$	18.7967	+	4.45491i	1.31282	+	0.311144i
$206$	−0.769010	+	0.645276i	−0.0535794	+	0.0449585i
$207$		0			0
$208$	−6.63120	−	5.56424i	−0.459791	−	0.385811i
$209$	−9.94229	−	13.3548i	−0.687723	−	0.923772i
$210$		0			0
$211$	−9.96134	+	2.36088i	−0.685767	+	0.162530i	−0.558707	−	0.829365i	$-0.688702\pi$
$211$	−9.96134	+	2.36088i	−0.685767	+	0.162530i	−0.127060	+	0.991895i	$0.540554\pi$
$212$	−8.39540	+	11.2770i	−0.576598	+	0.774506i
$213$		0			0
$214$	−3.62801	+	1.82206i	−0.248006	+	0.124553i
$215$	3.24697	+	5.62391i	0.221441	+	0.383547i
$216$		0			0
$217$	−1.05768	+	1.83195i	−0.0717999	+	0.124361i
$218$	0.375325	−	6.44407i	0.0254202	−	0.436448i
$219$		0			0
$220$	−16.6081	−	1.94121i	−1.11972	−	0.130876i
$221$	−1.06917	+	3.57126i	−0.0719199	+	0.240229i
$222$		0			0
$223$	−1.84243	+	4.27124i	−0.123379	+	0.286024i	−0.968700	−	0.248234i	$-0.920150\pi$
$223$	−1.84243	+	4.27124i	−0.123379	+	0.286024i	0.845321	+	0.534258i	$0.179409\pi$
$224$	15.9031	−	5.78824i	1.06257	−	0.386743i
$225$		0			0
$226$	−3.10644	−	1.13065i	−0.206637	−	0.0752098i
$227$	−9.68944	+	10.2702i	−0.643111	+	0.681658i	−0.964135	−	0.265414i	$-0.914492\pi$
$227$	−9.68944	+	10.2702i	−0.643111	+	0.681658i	0.321024	+	0.947071i	$0.395973\pi$
$228$		0			0
$229$	−4.63378	−	2.32717i	−0.306208	−	0.153784i	0.289059	−	0.957311i	$-0.406658\pi$
$229$	−4.63378	−	2.32717i	−0.306208	−	0.153784i	−0.595268	+	0.803528i	$0.702954\pi$
$230$	−0.589589	−	10.1229i	−0.0388764	−	0.667481i
$231$		0			0
$232$	−1.07752	−	3.59916i	−0.0707425	−	0.236297i
$233$	0.773336	+	4.38581i	0.0506629	+	0.287324i	0.999604	−	0.0281287i	$-0.00895483\pi$
$233$	0.773336	+	4.38581i	0.0506629	+	0.287324i	−0.948941	+	0.315452i	$0.897844\pi$
$234$		0			0
$235$	−1.59822	+	9.06397i	−0.104257	+	0.591268i
$236$	−8.38382	+	0.979929i	−0.545740	+	0.0637879i
$237$		0			0
$238$	−1.13965	−	1.20796i	−0.0738726	−	0.0783004i
$239$	−11.5106	−	26.6846i	−0.744561	−	1.72609i	−0.685773	−	0.727815i	$-0.740536\pi$
$239$	−11.5106	−	26.6846i	−0.744561	−	1.72609i	−0.0587876	−	0.998271i	$-0.518723\pi$
$240$		0			0
$241$	−20.8739	−	13.7290i	−1.34460	−	0.884360i	−0.346055	−	0.938214i	$-0.612479\pi$
$241$	−20.8739	−	13.7290i	−1.34460	−	0.884360i	−0.998549	+	0.0538543i	$0.982849\pi$
$242$	−0.442520			−0.0284463
$243$		0			0
$244$	0.957429			0.0612931
$245$	−6.78256	−	4.46096i	−0.433322	−	0.285000i
$246$		0			0
$247$	−7.66209	−	17.7627i	−0.487527	−	1.13022i
$248$	−0.968235	−	1.02627i	−0.0614830	−	0.0651682i
$249$		0			0
$250$	−2.56747	+	0.300094i	−0.162381	+	0.0189796i
$251$	2.46091	−	13.9565i	0.155331	−	0.880926i	−0.803152	−	0.595775i	$-0.796845\pi$
$251$	2.46091	−	13.9565i	0.155331	−	0.880926i	0.958483	−	0.285151i	$-0.0920438\pi$
$252$		0			0
$253$	3.66665	+	20.7946i	0.230521	+	1.30735i
$254$	1.74853	+	5.84051i	0.109713	+	0.366466i
$255$		0			0
$256$	0.232799	+	3.99701i	0.0145499	+	0.249813i
$257$	13.1355	+	6.59688i	0.819367	+	0.411502i	0.808541	−	0.588440i	$-0.200258\pi$
$257$	13.1355	+	6.59688i	0.819367	+	0.411502i	0.0108263	+	0.999941i	$0.496554\pi$
$258$		0			0
$259$	24.4791	−	25.9463i	1.52106	−	1.61223i
$260$	−18.2566	−	6.64487i	−1.13223	−	0.412098i
$261$		0			0
$262$	−3.82038	+	1.39050i	−0.236024	+	0.0859056i
$263$	6.49135	−	15.0486i	0.400274	−	0.927939i	−0.592235	−	0.805765i	$-0.701754\pi$
$263$	6.49135	−	15.0486i	0.400274	−	0.927939i	0.992509	−	0.122174i	$-0.0389865\pi$
$264$		0			0
$265$	−6.97824	+	23.3089i	−0.428670	+	1.43186i
$266$	8.55957	+	1.00047i	0.524821	+	0.0613428i
$267$		0			0
$268$	−1.33349	+	22.8952i	−0.0814561	+	1.39855i
$269$	5.68131	−	9.84032i	0.346396	−	0.599975i	−0.639211	−	0.769032i	$-0.720739\pi$
$269$	5.68131	−	9.84032i	0.346396	−	0.599975i	0.985606	+	0.169057i	$0.0540721\pi$
$270$		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	$0.860100\pi$
$272$	−1.81339	+	0.910719i	−0.109953	+	0.0552204i
$273$		0			0
$274$	2.92486	−	3.92877i	0.176697	−	0.237345i
$275$	−11.4604	+	2.71616i	−0.691087	+	0.163791i
$276$		0			0
$277$	10.9854	+	14.7559i	0.660048	+	0.886598i	0.998520	−	0.0543783i	$-0.0173177\pi$
$277$	10.9854	+	14.7559i	0.660048	+	0.886598i	−0.338473	+	0.940976i	$0.609910\pi$
$278$	2.56503	+	2.15231i	0.153840	+	0.129087i
$279$		0			0
$280$	14.5334	−	12.1950i	0.868538	−	0.728790i
$281$	10.4439	+	2.47524i	0.623028	+	0.147660i	0.529992	−	0.848002i	$-0.322195\pi$
$281$	10.4439	+	2.47524i	0.623028	+	0.147660i	0.0930358	+	0.995663i	$0.470343\pi$
$282$		0			0
$283$	11.9407	−	7.85355i	0.709804	−	0.466845i	−0.142566	−	0.989785i	$-0.545535\pi$
$283$	11.9407	−	7.85355i	0.709804	−	0.466845i	0.852369	+	0.522940i	$0.175165\pi$
$284$	−18.7111	+	12.3065i	−1.11030	+	0.730256i
$285$		0			0
$286$	−7.55929	−	1.79158i	−0.446990	−	0.105939i
$287$	15.9502	−	13.3838i	0.941512	−	0.790022i
$288$		0			0
$289$	−12.3533	−	10.3657i	−0.726666	−	0.609745i
$290$	−1.77131	−	2.37929i	−0.104015	−	0.139717i
$291$		0			0
$292$	11.0134	−	2.61023i	0.644512	−	0.152752i
$293$	−13.0455	+	17.5231i	−0.762125	+	1.02371i	0.236518	+	0.971627i	$0.423994\pi$
$293$	−13.0455	+	17.5231i	−0.762125	+	1.02371i	−0.998643	+	0.0520843i	$0.983414\pi$
$294$		0			0
$295$	−13.0544	+	6.55618i	−0.760058	+	0.381716i
$296$	11.8962	+	20.6048i	0.691453	+	1.19763i
$297$		0			0
$298$	−3.91497	+	6.78092i	−0.226788	+	0.392808i
$299$	−1.42652	+	24.4925i	−0.0824979	+	1.41643i
$300$		0			0
$301$	6.95223	+	0.812599i	0.400720	+	0.0468374i
$302$	1.02184	−	3.41320i	0.0588006	−	0.196408i
$303$		0			0
$304$	4.17079	−	9.66898i	0.239211	−	0.554554i
$305$	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	$0.946760\pi$
$308$	−12.3682	+	13.1095i	−0.704745	+	0.746986i
$309$		0			0
$310$	−0.995470	−	0.499944i	−0.0565389	−	0.0283949i
$311$	−1.57644	−	27.0664i	−0.0893915	−	1.53479i	−0.683227	−	0.730206i	$-0.739424\pi$
$311$	−1.57644	−	27.0664i	−0.0893915	−	1.53479i	0.593835	−	0.804587i	$-0.297613\pi$
$312$		0			0
$313$	2.32494	+	7.76583i	0.131413	+	0.438950i	0.998216	−	0.0596999i	$-0.0190144\pi$
$313$	2.32494	+	7.76583i	0.131413	+	0.438950i	−0.866803	+	0.498650i	$0.833829\pi$
$314$	0.0163709	+	0.0928440i	0.000923863	+	0.00523949i
$315$		0			0
$316$	−0.217154	+	1.23154i	−0.0122159	+	0.0692797i
$317$	19.2878	−	2.25442i	1.08331	−	0.126621i	0.444345	−	0.895856i	$-0.353437\pi$
$317$	19.2878	−	2.25442i	1.08331	−	0.126621i	0.638966	+	0.769235i	$0.279363\pi$
$318$		0			0
$319$	4.23881	+	4.49288i	0.237328	+	0.251553i
$320$	−1.46323	−	3.39214i	−0.0817969	−	0.189627i
$321$		0			0
$322$	−9.13149	−	6.00587i	−0.508878	−	0.334694i
$323$	−4.53480			−0.252323
$324$		0			0
$325$	−13.6847			−0.759089
$326$	7.68317	+	5.05330i	0.425531	+	0.279876i
$327$		0			0
$328$	5.50067	+	12.7520i	0.303724	+	0.704111i
$329$	6.80780	+	7.21585i	0.375326	+	0.397823i
$330$		0			0
$331$	−1.97328	+	0.230643i	−0.108461	+	0.0126773i	−0.170150	−	0.985418i	$-0.554425\pi$
$331$	−1.97328	+	0.230643i	−0.108461	+	0.0126773i	0.0616891	+	0.998095i	$0.480351\pi$
$332$	1.06035	−	6.01357i	0.0581945	−	0.330037i
$333$		0			0
$334$	1.80136	+	10.2160i	0.0985662	+	0.558997i
$335$	11.3835	+	38.0234i	0.621945	+	2.07744i
$336$		0			0
$337$	1.06728	+	18.3245i	0.0581385	+	0.998199i	0.893661	+	0.448743i	$0.148128\pi$
$337$	1.06728	+	18.3245i	0.0581385	+	0.998199i	−0.835522	+	0.549456i	$0.814835\pi$
$338$	−1.47228	−	0.739406i	−0.0800814	−	0.0402184i
$339$		0			0
$340$	−3.12540	+	3.31273i	−0.169499	+	0.179658i
$341$	2.17980	+	0.793381i	0.118043	+	0.0429640i
$342$		0			0
$343$	12.3650	−	4.50048i	0.667646	−	0.243003i
$344$	−1.84916	+	4.28683i	−0.0996999	+	0.231130i
$345$		0			0
$346$	3.06925	−	10.2520i	0.165004	−	0.551151i
$347$	−26.6029	−	3.10943i	−1.42812	−	0.166923i	−0.633364	−	0.773854i	$-0.718326\pi$
$347$	−26.6029	−	3.10943i	−1.42812	−	0.166923i	−0.794754	+	0.606931i	$0.792400\pi$
$348$		0			0
$349$	0.762246	−	13.0873i	0.0408021	−	0.700545i	−0.914440	−	0.404721i	$-0.867369\pi$
$349$	0.762246	−	13.0873i	0.0408021	−	0.700545i	0.955242	−	0.295824i	$-0.0955943\pi$
$350$	3.04816	−	5.27957i	0.162931	−	0.282205i
$351$		0			0
$352$	−9.27922	−	16.0721i	−0.494584	−	0.856645i
$353$	−17.3676	+	8.72232i	−0.924383	+	0.464242i	−0.846301	−	0.532705i	$-0.821176\pi$
$353$	−17.3676	+	8.72232i	−0.924383	+	0.464242i	−0.0780814	+	0.996947i	$0.524879\pi$
$354$		0			0
$355$	−23.1451	+	31.0893i	−1.22842	+	1.65005i
$356$	21.4153	−	5.07553i	1.13501	−	0.269003i
$357$		0			0
$358$	3.48990	+	4.68775i	0.184447	+	0.247755i
$359$	−11.2428	−	9.43384i	−0.593373	−	0.497899i	0.295935	−	0.955208i	$-0.404369\pi$
$359$	−11.2428	−	9.43384i	−0.593373	−	0.497899i	−0.889308	+	0.457309i	$0.848813\pi$
$360$		0			0
$361$	3.47185	−	2.91323i	0.182729	−	0.153328i
$362$	0.452687	+	0.107289i	0.0237927	+	0.00563898i
$363$		0			0
$364$	−17.4960	+	11.5073i	−0.917038	+	0.603146i
$365$	16.3659	−	10.7640i	0.856630	−	0.563414i
$366$		0			0
$367$	−10.6977	−	2.53540i	−0.558415	−	0.132347i	−0.0582894	−	0.998300i	$-0.518565\pi$
$367$	−10.6977	−	2.53540i	−0.558415	−	0.132347i	−0.500125	+	0.865953i	$0.666713\pi$
$368$	−10.2304	+	8.58433i	−0.533297	+	0.447489i
$369$		0			0
$370$	14.3899	+	12.0746i	0.748096	+	0.627727i
$371$	15.6608	+	21.0361i	0.813069	+	1.09214i
$372$		0			0
$373$	−19.8678	+	4.70876i	−1.02872	+	0.243810i	−0.710121	−	0.704080i	$-0.751360\pi$
$373$	−19.8678	+	4.70876i	−1.02872	+	0.243810i	−0.318596	+	0.947890i	$0.603211\pi$
$374$	−1.08751	+	1.46077i	−0.0562336	+	0.0755348i
$375$		0			0
$376$	−5.91302	+	2.96963i	−0.304941	+	0.153147i
$377$	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	$0.933580\pi$
$380$	1.37418	−	23.5938i	0.0704939	−	1.21033i
$381$		0			0
$382$	−0.431313	−	0.0504133i	−0.0220679	−	0.00257937i
$383$	6.74866	−	22.5421i	0.344840	−	1.15185i	−0.593123	−	0.805112i	$-0.702105\pi$
$383$	6.74866	−	22.5421i	0.344840	−	1.15185i	0.937963	−	0.346735i	$-0.112710\pi$
$384$		0			0
$385$	−12.3544	+	28.6408i	−0.629640	+	1.45967i
$386$	4.98958	−	1.81606i	0.253963	−	0.0924349i
$387$		0			0
$388$	19.7163	+	7.17615i	1.00094	+	0.364314i
$389$	22.6942	−	24.0545i	1.15064	−	1.21961i	0.178825	−	0.983881i	$-0.442770\pi$
$389$	22.6942	−	24.0545i	1.15064	−	1.21961i	0.971819	−	0.235730i	$-0.0757481\pi$
$390$		0			0
$391$	5.13950	+	2.58115i	0.259916	+	0.130534i
$392$	−0.339350	−	5.82642i	−0.0171398	−	0.294279i
$393$		0			0
$394$	0.182298	+	0.608917i	0.00918403	+	0.0306768i
$395$	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	$0.0559972\pi$
$398$	4.33009	−	0.506115i	0.217048	−	0.0253693i
$399$		0			0
$400$	−5.11190	−	5.41830i	−0.255595	−	0.270915i
$401$	−11.3452	−	26.3011i	−0.566551	−	1.31341i	−0.925037	−	0.379878i	$-0.875966\pi$
$401$	−11.3452	−	26.3011i	−0.566551	−	1.31341i	0.358486	−	0.933535i	$-0.383293\pi$
$402$		0			0
$403$	2.25184	+	1.48106i	0.112172	+	0.0737769i
$404$	10.0397			0.499496
$405$		0			0
$406$	−3.19719			−0.158674
$407$	−32.6817	−	21.4951i	−1.61997	−	1.06547i
$408$		0			0
$409$	12.4515	+	28.8659i	0.615688	+	1.42732i	0.885604	+	0.464441i	$0.153745\pi$
$409$	12.4515	+	28.8659i	0.615688	+	1.42732i	−0.269916	+	0.962884i	$0.586996\pi$
$410$	7.52446	+	7.97546i	0.371607	+	0.393880i
$411$		0			0
$412$	2.94733	−	0.344493i	0.145204	−	0.0169720i
$413$	−2.73421	+	15.5065i	−0.134542	+	0.763024i
$414$		0			0
$415$	−1.83511	−	10.4074i	−0.0900818	−	0.510879i
$416$	−6.18434	−	20.6571i	−0.303212	−	1.01280i
$417$		0			0
$418$	−0.549486	−	9.43431i	−0.0268762	−	0.461447i
$419$	−3.01535	−	1.51436i	−0.147309	−	0.0739816i	0.373617	−	0.927583i	$-0.378117\pi$
$419$	−3.01535	−	1.51436i	−0.147309	−	0.0739816i	−0.520927	+	0.853601i	$0.674414\pi$
$420$		0			0
$421$	−17.3369	+	18.3761i	−0.844950	+	0.895594i	−0.995668	−	0.0929825i	$-0.970360\pi$
$421$	−17.3369	+	18.3761i	−0.844950	+	0.895594i	0.150718	+	0.988577i	$0.451841\pi$
$422$	−5.46033	−	1.98740i	−0.265805	−	0.0967451i
$423$		0			0
$424$	−16.4373	+	5.98270i	−0.798267	+	0.290545i
$425$	−1.27061	+	2.94560i	−0.0616335	+	0.142882i
$426$		0			0
$427$	0.512228	−	1.71096i	0.0247885	−	0.0827992i
$428$	11.9196	+	1.39320i	0.576154	+	0.0673427i
$429$		0			0
$430$	−0.214322	+	3.67977i	−0.0103355	+	0.177454i
$431$	16.4068	−	28.4174i	0.790288	−	1.36882i	−0.135501	−	0.990777i	$-0.543264\pi$
$431$	16.4068	−	28.4174i	0.790288	−	1.36882i	0.925789	−	0.378041i	$-0.123402\pi$
$432$		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	$0.732835\pi$
$434$	−1.07298	+	0.538870i	−0.0515046	+	0.0258666i
$435$		0			0
$436$	−11.3942	+	15.3050i	−0.545681	+	0.732977i
$437$	−29.0401	+	6.88263i	−1.38918	+	0.329241i
$438$		0			0
$439$	22.0216	+	29.5802i	1.05103	+	1.41178i	0.906460	+	0.422291i	$0.138774\pi$
$439$	22.0216	+	29.5802i	1.05103	+	1.41178i	0.144574	+	0.989494i	$0.453819\pi$
$440$	−15.9373	−	13.3730i	−0.759781	−	0.637532i
$441$		0			0
$442$	−1.62093	+	1.36012i	−0.0770997	+	0.0646943i
$443$	−33.4372	−	7.92477i	−1.58865	−	0.376517i	−0.661125	−	0.750276i	$-0.729921\pi$
$443$	−33.4372	−	7.92477i	−1.58865	−	0.376517i	−0.927526	+	0.373759i	$0.878069\pi$
$444$		0			0
$445$	31.8231	−	20.9304i	1.50856	−	0.992196i
$446$	−2.20596	+	1.45088i	−0.104455	+	0.0687014i
$447$		0			0
$448$	−3.87459	−	0.918294i	−0.183057	−	0.0433853i
$449$	−13.4520	+	11.2876i	−0.634838	+	0.532693i	−0.902428	−	0.430840i	$-0.858217\pi$
$449$	−13.4520	+	11.2876i	−0.634838	+	0.532693i	0.267590	+	0.963533i	$0.413773\pi$
$450$		0			0
$451$	−17.4910	−	14.6767i	−0.823617	−	0.691097i
$452$	5.83531	+	7.83818i	0.274470	+	0.368677i
$453$		0			0
$454$	−7.79836	+	1.84824i	−0.365995	+	0.0867424i
$455$	−21.6420	+	29.0703i	−1.01459	+	1.36284i
$456$		0			0
$457$	−7.46084	+	3.74697i	−0.349003	+	0.175276i	−0.614661	−	0.788791i	$-0.710707\pi$
$457$	−7.46084	+	3.74697i	−0.349003	+	0.175276i	0.265658	+	0.964067i	$0.414411\pi$
$458$	−1.47162	−	2.54891i	−0.0687641	−	0.119103i
$459$		0			0
$460$	−14.9867	+	25.9577i	−0.698758	+	1.21028i
$461$	−1.18266	+	20.3054i	−0.0550818	+	0.945718i	0.851677	+	0.524067i	$0.175586\pi$
$461$	−1.18266	+	20.3054i	−0.0550818	+	0.945718i	−0.906759	+	0.421650i	$0.861451\pi$
$462$		0			0
$463$	2.57184	+	0.300605i	0.119524	+	0.0139703i	0.175644	−	0.984454i	$-0.443799\pi$
$463$	2.57184	+	0.300605i	0.119524	+	0.0139703i	−0.0561208	+	0.998424i	$0.517873\pi$
$464$	−1.12044	+	3.74254i	−0.0520153	+	0.173743i
$465$		0			0
$466$	−1.00122	+	2.32109i	−0.0463806	+	0.107522i
$467$	11.5019	−	4.18635i	0.532244	−	0.193721i	−0.0618958	−	0.998083i	$-0.519715\pi$
$467$	11.5019	−	4.18635i	0.532244	−	0.193721i	0.594140	+	0.804361i	$0.297492\pi$
$468$		0			0
$469$	40.2012	+	14.6320i	1.85632	+	0.675645i
$470$	−3.58503	+	3.79991i	−0.165365	+	0.175277i
$471$		0			0
$472$	−9.38515	−	4.71340i	−0.431987	−	0.216952i
$473$	−0.446302	−	7.66271i	−0.0205210	−	0.352332i
$474$		0			0
$475$	−4.77437	−	15.9475i	−0.219063	−	0.731721i
$476$	0.852437	+	4.83441i	0.0390714	+	0.221585i
$477$		0			0
$478$	2.86441	−	16.2449i	0.131015	−	0.743024i
$479$	27.2416	−	3.18408i	1.24470	−	0.145485i	0.531873	−	0.846824i	$-0.321488\pi$
$479$	27.2416	−	3.18408i	1.24470	−	0.145485i	0.712827	+	0.701340i	$0.247414\pi$
$480$		0			0
$481$	−31.1896	−	33.0591i	−1.42212	−	1.50736i
$482$	−5.61687	−	13.0214i	−0.255841	−	0.593107i
$483$		0			0
$484$	1.09287	+	0.718795i	0.0496761	+	0.0326725i
$485$	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	$0.543582\pi$
$488$	0.995268	+	0.654598i	0.0450537	+	0.0296323i
$489$		0			0
$490$	−1.82509	−	4.23104i	−0.0824493	−	0.191139i
$491$	0.334399	+	0.354442i	0.0150912	+	0.0159958i	0.734875	−	0.678202i	$-0.237241\pi$
$491$	0.334399	+	0.354442i	0.0150912	+	0.0159958i	−0.719784	+	0.694198i	$0.755759\pi$
$492$		0			0
$493$	1.67102	−	0.195315i	0.0752591	−	0.00879652i
$494$	1.90671	−	10.8135i	0.0857867	−	0.486521i
$495$		0			0
$496$	0.254765	+	1.44484i	0.0114393	+	0.0648754i
$497$	11.9817	+	40.0215i	0.537451	+	1.79521i
$498$		0			0
$499$	−0.318908	−	5.47545i	−0.0142763	−	0.245115i	−0.997895	−	0.0648523i	$-0.979342\pi$
$499$	−0.318908	−	5.47545i	−0.0142763	−	0.245115i	0.983619	−	0.180262i	$-0.0576947\pi$
$500$	6.82823	+	3.42927i	0.305368	+	0.153361i
$501$		0			0
$502$	5.52014	−	5.85101i	0.246376	−	0.261143i
$503$	9.93090	+	3.61455i	0.442797	+	0.161165i	0.553790	−	0.832656i	$-0.313181\pi$
$503$	9.93090	+	3.61455i	0.442797	+	0.161165i	−0.110993	+	0.993821i	$0.535403\pi$
$504$		0			0
$505$	16.3275	−	5.94271i	0.726562	−	0.264447i
$506$	−4.74713	+	11.0051i	−0.211036	+	0.489236i
$507$		0			0
$508$	5.16858	−	17.2643i	0.229319	−	0.765977i
$509$	12.3227	+	1.44032i	0.546196	+	0.0638412i	0.384716	−	0.923035i	$-0.374299\pi$
$509$	12.3227	+	1.44032i	0.546196	+	0.0638412i	0.161480	+	0.986876i	$0.448373\pi$
$510$		0			0
$511$	1.22765	−	21.0779i	0.0543079	−	0.932431i
$512$	10.4003	−	18.0139i	0.459634	−	0.796110i
$513$		0			0
$514$	4.17162	+	7.22546i	0.184002	+	0.318701i
$515$	4.58927	−	2.30482i	0.202228	−	0.101562i
$516$		0			0
$517$	6.49630	−	8.72605i	0.285707	−	0.383771i
$518$	19.7015	−	4.66935i	0.865635	−	0.205159i
$519$		0			0
$520$	−14.4351	−	19.3896i	−0.633019	−	0.850292i
$521$	−13.6270	−	11.4344i	−0.597011	−	0.500952i	0.293472	−	0.955968i	$-0.405189\pi$
$521$	−13.6270	−	11.4344i	−0.597011	−	0.500952i	−0.890483	+	0.455016i	$0.849634\pi$
$522$		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	$0.373707\pi$
$524$	11.6937	+	2.77145i	0.510840	+	0.121071i
$525$		0			0
$526$	7.77215	−	5.11182i	0.338882	−	0.222886i
$527$	0.527877	−	0.347190i	0.0229947	−	0.0151238i
$528$		0			0
$529$	14.4499	+	3.42469i	0.628256	+	0.148899i
$530$	−10.5795	+	8.87724i	−0.459543	+	0.385603i
$531$		0			0
$532$	−19.5141	−	16.3743i	−0.846045	−	0.709916i
$533$	−15.8423	−	21.2799i	−0.686205	−	0.921733i
$534$		0			0
$535$	20.2092	−	4.78968i	0.873722	−	0.207076i
$536$	−17.0398	+	22.8884i	−0.736006	+	0.988627i
$537$		0			0
$538$	5.76350	−	2.89454i	0.248482	−	0.124792i
$539$	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	$-0.0330342\pi$
$542$	0.0912649	−	1.56696i	0.00392016	−	0.0673066i
$543$		0			0
$544$	−5.02062	−	0.586826i	−0.215257	−	0.0251600i
$545$	−9.47081	+	31.6347i	−0.405685	+	1.35508i
$546$		0			0
$547$	5.02926	−	11.6591i	0.215036	−	0.498509i	−0.776220	−	0.630462i	$-0.782865\pi$
$547$	5.02926	−	11.6591i	0.215036	−	0.498509i	0.991256	+	0.131953i	$0.0421247\pi$
$548$	−13.6050	+	4.95181i	−0.581176	+	0.211531i
$549$		0			0
$550$	−6.28204	−	2.28648i	−0.267867	−	0.0974957i
$551$	−5.99114	+	6.35024i	−0.255231	+	0.270529i
$552$		0			0
$553$	2.08464	+	1.04694i	0.0886477	+	0.0445206i
$554$	0.607135	+	10.4241i	0.0257947	+	0.442878i
$555$		0			0
$556$	−2.83870	−	9.48191i	−0.120388	−	0.402122i
$557$	2.62356	+	14.8789i	0.111164	+	0.630441i	0.988578	+	0.150708i	$0.0481553\pi$
$557$	2.62356	+	14.8789i	0.111164	+	0.630441i	−0.877415	+	0.479733i	$0.840734\pi$
$558$		0			0
$559$	1.54866	−	8.78288i	0.0655013	−	0.371476i
$560$	−19.5944	+	2.29026i	−0.828016	+	0.0967812i
$561$		0			0
$562$	4.18075	+	4.43133i	0.176354	+	0.186924i
$563$	2.42888	+	5.63077i	0.102365	+	0.237309i	0.961700	−	0.274104i	$-0.0883814\pi$
$563$	2.42888	+	5.63077i	0.102365	+	0.237309i	−0.859335	+	0.511413i	$0.829122\pi$
$564$		0			0
$565$	14.1294	+	9.29307i	0.594429	+	0.390962i
$566$	8.11223			0.340982
$567$		0			0
$568$	−27.8646			−1.16917
$569$	−1.23600	−	0.812928i	−0.0518157	−	0.0340797i	0.523337	−	0.852126i	$-0.324687\pi$
$569$	−1.23600	−	0.812928i	−0.0518157	−	0.0340797i	−0.575153	+	0.818046i	$0.695057\pi$
$570$		0			0
$571$	3.49187	+	8.09506i	0.146130	+	0.338768i	0.975523	−	0.219898i	$-0.0705726\pi$
$571$	3.49187	+	8.09506i	0.146130	+	0.338768i	−0.829393	+	0.558666i	$0.811313\pi$
$572$	15.7588	+	16.7033i	0.658907	+	0.698400i
$573$		0			0
$574$	11.7386	−	1.37204i	0.489958	−	0.0572679i
$575$	−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	$0.848122\pi$
$578$	−2.62520	−	8.76878i	−0.109194	−	0.364733i
$579$		0			0
$580$	0.509816	+	8.75321i	0.0211690	+	0.363457i
$581$	−10.1792	−	5.11218i	−0.422304	−	0.212089i
$582$		0			0
$583$	19.7355	−	20.9184i	0.817362	−	0.866353i
$584$	13.2333	+	4.81654i	0.547599	+	0.199310i
$585$		0			0
$586$	−11.6521	+	4.24102i	−0.481344	+	0.175195i
$587$	−3.38197	+	7.84028i	−0.139589	+	0.323603i	−0.973642	−	0.228080i	$-0.926755\pi$
$587$	−3.38197	+	7.84028i	−0.139589	+	0.323603i	0.834054	+	0.551683i	$0.186014\pi$
$588$		0			0
$589$	−0.940329	+	3.14092i	−0.0387456	+	0.129419i
$590$	−8.23571	−	0.962617i	−0.339059	−	0.0396303i
$591$		0			0
$592$	1.43852	−	24.6984i	0.0591227	−	1.01510i
$593$	−19.8740	+	34.4227i	−0.816125	+	1.41357i	0.0923915	+	0.995723i	$0.470549\pi$
$593$	−19.8740	+	34.4227i	−0.816125	+	1.41357i	−0.908517	+	0.417848i	$0.862784\pi$
$594$		0			0
$595$	4.24788	+	7.35754i	0.174146	+	0.301630i
$596$	20.6830	−	10.3874i	0.847210	−	0.425485i
$597$		0			0
$598$	−8.31584	+	11.1701i	−0.340060	+	0.456780i
$599$	−19.8283	+	4.69940i	−0.810164	+	0.192012i	−0.614764	−	0.788711i	$-0.710749\pi$
$599$	−19.8283	+	4.69940i	−0.810164	+	0.192012i	−0.195400	+	0.980724i	$0.562601\pi$
$600$		0			0
$601$	−8.17441	−	10.9801i	−0.333441	−	0.447889i	0.603507	−	0.797358i	$-0.293770\pi$
$601$	−8.17441	−	10.9801i	−0.333441	−	0.447889i	−0.936948	+	0.349469i	$0.886362\pi$
$602$	3.04350	+	2.55380i	0.124044	+	0.104085i
$603$		0			0
$604$	−8.06774	+	6.76964i	−0.328272	+	0.275453i
$605$	2.20279	+	0.522071i	0.0895562	+	0.0212252i
$606$		0			0
$607$	3.75977	−	2.47284i	0.152604	−	0.100369i	−0.470910	−	0.882181i	$-0.656075\pi$
$607$	3.75977	−	2.47284i	0.152604	−	0.100369i	0.623515	+	0.781812i	$0.285704\pi$
$608$	21.9153	−	14.4139i	0.888782	−	0.584561i
$609$		0			0
$610$	0.915162	+	0.216897i	0.0370538	+	0.00878192i
$611$	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	$0.465244\pi$
$614$	−10.3295	−	13.8749i	−0.416863	−	0.559944i
$615$		0			0
$616$	−21.8201	+	5.17146i	−0.879157	+	0.208364i
$617$	16.4713	−	22.1249i	0.663112	−	0.890713i	−0.335572	−	0.942015i	$-0.608929\pi$
$617$	16.4713	−	22.1249i	0.663112	−	0.890713i	0.998683	+	0.0513013i	$0.0163369\pi$
$618$		0			0
$619$	−29.8724	+	15.0025i	−1.20067	+	0.603001i	−0.932780	−	0.360447i	$-0.882624\pi$
$619$	−29.8724	+	15.0025i	−1.20067	+	0.603001i	−0.267894	+	0.963448i	$0.586328\pi$
$620$	1.64640	+	2.85165i	0.0661211	+	0.114525i
$621$		0			0
$622$	7.69456	−	13.3274i	0.308524	−	0.534379i
$623$	2.38713	−	40.9855i	0.0956384	−	1.64205i
$624$		0			0
$625$	30.1766	+	3.52714i	1.20707	+	0.141086i
$626$	−1.31965	+	4.40795i	−0.0527439	+	0.176177i
$627$		0			0
$628$	0.110378	−	0.255885i	0.00440455	−	0.0102109i
$629$	−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	$0.541286\pi$
$632$	−1.06775	+	1.13175i	−0.0424727	+	0.0450185i
$633$		0			0
$634$	9.85001	+	4.94686i	0.391194	+	0.196465i
$635$	−1.81346	−	31.1359i	−0.0719650	−	1.23559i
$636$		0			0
$637$	3.19754	+	10.6805i	0.126691	+	0.423177i
$638$	0.608816	+	3.45277i	0.0241032	+	0.136696i
$639$		0			0
$640$	5.81708	−	32.9903i	0.229940	−	1.30406i
$641$	9.25236	−	1.08145i	0.365446	−	0.0427145i	0.0686116	−	0.997643i	$-0.478143\pi$
$641$	9.25236	−	1.08145i	0.365446	−	0.0427145i	0.296835	+	0.954929i	$0.404069\pi$
$642$		0			0
$643$	−0.883538	−	0.936495i	−0.0348433	−	0.0369318i	0.709718	−	0.704486i	$-0.248823\pi$
$643$	−0.883538	−	0.936495i	−0.0348433	−	0.0369318i	−0.744561	+	0.667555i	$0.767341\pi$
$644$	12.7962	+	29.6649i	0.504241	+	1.16896i
$645$		0			0
$646$	−2.15054	−	1.41443i	−0.0846118	−	0.0556501i
$647$	−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
$650$	−6.48968	−	4.26833i	−0.254546	−	0.167418i
$651$		0			0
$652$	−10.7666	−	24.9599i	−0.421654	−	0.977504i
$653$	26.7355	+	28.3380i	1.04624	+	1.10895i	0.993896	+	0.110323i	$0.0351885\pi$
$653$	26.7355	+	28.3380i	1.04624	+	1.10895i	0.0523464	+	0.998629i	$0.483330\pi$
$654$		0			0
$655$	20.6577	−	2.41453i	0.807162	−	0.0943437i
$656$	2.50766	−	14.2217i	0.0979077	−	0.555262i
$657$		0			0
$658$	0.977797	+	5.54536i	0.0381185	+	0.216181i
$659$	9.63166	+	32.1720i	0.375196	+	1.25324i	0.912229	+	0.409681i	$0.134360\pi$
$659$	9.63166	+	32.1720i	0.375196	+	1.25324i	−0.537033	+	0.843561i	$0.680455\pi$
$660$		0			0
$661$	−2.06029	−	35.3739i	−0.0801361	−	1.37588i	−0.763501	−	0.645807i	$-0.776521\pi$
$661$	−2.06029	−	35.3739i	−0.0801361	−	1.37588i	0.683365	−	0.730077i	$-0.260516\pi$
$662$	−1.00773	−	0.506100i	−0.0391664	−	0.0196701i
$663$		0			0
$664$	5.21376	−	5.52627i	0.202333	−	0.214461i
$665$	−41.4278	−	15.0785i	−1.60650	−	0.584718i
$666$		0			0
$667$	10.4045	−	3.78693i	0.402864	−	0.146630i
$668$	12.1454	−	28.1561i	0.469918	−	1.08939i
$669$		0			0
$670$	−6.46135	+	21.5824i	−0.249624	+	0.833801i
$671$	−1.94527	−	0.227369i	−0.0750963	−	0.00877750i
$672$		0			0
$673$	−1.59738	+	27.4260i	−0.0615746	+	1.05720i	0.816091	+	0.577923i	$0.196137\pi$
$673$	−1.59738	+	27.4260i	−0.0615746	+	1.05720i	−0.877666	+	0.479273i	$0.840900\pi$
$674$	−5.20938	+	9.02292i	−0.200658	+	0.347550i
$675$		0			0
$676$	2.43499	+	4.21753i	0.0936536	+	0.162213i
$677$	−8.53705	+	4.28747i	−0.328106	+	0.164781i	−0.605225	−	0.796055i	$-0.706917\pi$
$677$	−8.53705	+	4.28747i	−0.328106	+	0.164781i	0.277119	+	0.960836i	$0.410620\pi$
$678$		0			0
$679$	23.3724	−	31.3945i	0.896948	−	1.20481i
$680$	−5.51386	+	1.30681i	−0.211447	+	0.0501138i
$681$		0			0
$682$	0.786265	+	1.05614i	0.0301076	+	0.0404416i
$683$	25.4573	+	21.3612i	0.974095	+	0.817363i	0.983188	−	0.182596i	$-0.0584500\pi$
$683$	25.4573	+	21.3612i	0.974095	+	0.817363i	−0.00909301	+	0.999959i	$0.502894\pi$
$684$		0			0
$685$	−19.1945	+	16.1061i	−0.733383	+	0.615381i
$686$	7.26757	+	1.72245i	0.277477	+	0.0657633i
$687$		0			0
$688$	4.05599	−	2.66767i	0.154633	−	0.101704i
$689$	27.9177	−	18.3618i	1.06358	−	0.699528i
$690$		0			0
$691$	−5.28329	−	1.25216i	−0.200986	−	0.0476345i	0.128890	−	0.991659i	$-0.458859\pi$
$691$	−5.28329	−	1.25216i	−0.200986	−	0.0476345i	−0.329876	+	0.944024i	$0.607007\pi$
$692$	−24.2325	+	20.3335i	−0.921183	+	0.772964i
$693$		0			0
$694$	−11.6460	−	9.77218i	−0.442077	−	0.370947i
$695$	−10.2290	−	13.7400i	−0.388010	−	0.521187i
$696$		0			0
$697$	−6.05138	+	1.43420i	−0.229212	+	0.0543243i
$698$	4.44347	−	5.96862i	0.168188	−	0.225916i
$699$		0			0
$700$	−16.1036	+	8.08755i	−0.608661	+	0.305681i
$701$	−16.8694	−	29.2187i	−0.637150	−	1.10358i	−0.986055	−	0.166418i	$-0.946780\pi$
$701$	−16.8694	−	29.2187i	−0.637150	−	1.10358i	0.348906	−	0.937158i	$-0.386553\pi$
$702$		0			0
$703$	27.6440	−	47.8808i	1.04261	−	1.80586i
$704$	−0.253893	+	4.35917i	−0.00956894	+	0.164292i
$705$		0			0
$706$	−10.9568	−	1.28066i	−0.412363	−	0.0481983i
$707$	5.37130	−	17.9414i	0.202009	−	0.674756i
$708$		0			0
$709$	−7.67820	+	17.8001i	−0.288361	+	0.668495i	−0.999399	−	0.0346578i	$-0.988966\pi$
$709$	−7.67820	+	17.8001i	−0.288361	+	0.668495i	0.711039	+	0.703153i	$0.248225\pi$
$710$	−20.6730	+	7.52437i	−0.775846	+	0.282385i
$711$		0			0
$712$	25.7319	+	9.36564i	0.964343	+	0.350992i
$713$	2.85349	−	3.02452i	0.106864	−	0.113269i
$714$		0			0
$715$	35.5152	+	17.8364i	1.32819	+	0.667044i
$716$	−1.00446	−	17.2459i	−0.0375383	−	0.644508i
$717$		0			0
$718$	−2.38921	−	7.98051i	−0.0891644	−	0.297830i
$719$	−0.831346	−	4.71480i	−0.0310040	−	0.175832i	0.965374	−	0.260871i	$-0.0840097\pi$
$719$	−0.831346	−	4.71480i	−0.0310040	−	0.175832i	−0.996378	+	0.0850387i	$0.972899\pi$
$720$		0			0
$721$	0.961210	−	5.45129i	0.0357973	−	0.203017i
$722$	2.55511	−	0.298649i	0.0950912	−	0.0111146i
$723$		0			0
$724$	−0.943712	−	1.00028i	−0.0350728	−	0.0371750i
$725$	2.44616	+	5.67083i	0.0908481	+	0.210610i
$726$		0			0
$727$	6.31649	+	4.15442i	0.234266	+	0.154079i	0.661215	−	0.750197i	$-0.270041\pi$
$727$	6.31649	+	4.15442i	0.234266	+	0.154079i	−0.426949	+	0.904276i	$0.640412\pi$
$728$	−26.0550			−0.965664
$729$		0			0
$730$	11.1186			0.411516
$731$	−1.74670	−	1.14883i	−0.0646042	−	0.0424909i
$732$		0			0
$733$	15.3050	+	35.4810i	0.565303	+	1.31052i	0.925890	+	0.377794i	$0.123317\pi$
$733$	15.3050	+	35.4810i	0.565303	+	1.31052i	−0.360587	+	0.932726i	$0.617423\pi$
$734$	−4.28236	−	4.53903i	−0.158065	−	0.167539i
$735$		0			0
$736$	−33.0418	+	3.86203i	−1.21794	+	0.142356i
$737$	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	$-0.436809\pi$
$740$	−15.9252	−	53.1939i	−0.585422	−	1.95545i
$741$		0			0
$742$	0.865535	+	14.8607i	0.0317748	+	0.545552i
$743$	13.7207	+	6.89082i	0.503365	+	0.252800i	0.682315	−	0.731059i	$-0.260973\pi$
$743$	13.7207	+	6.89082i	0.503365	+	0.252800i	−0.178949	+	0.983858i	$0.557270\pi$
$744$		0			0
$745$	27.4880	−	29.1355i	1.00708	−	1.06744i
$746$	−10.8906	−	3.96386i	−0.398733	−	0.145127i
$747$		0			0
$748$	5.05853	−	1.84116i	0.184958	−	0.0673193i
$749$	8.86671	−	20.5554i	0.323983	−	0.751076i
$750$		0			0
$751$	13.3810	−	44.6956i	0.488279	−	1.63097i	−0.258585	−	0.965989i	$-0.583256\pi$
$751$	13.3810	−	44.6956i	0.488279	−	1.63097i	0.746864	−	0.664977i	$-0.231559\pi$
$752$	6.83391	+	0.798770i	0.249207	+	0.0291281i
$753$		0			0
$754$	−0.236862	+	4.06676i	−0.00862599	+	0.148103i
$755$	−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	$0.765107\pi$
$758$	−13.2037	+	6.63113i	−0.479579	+	0.240854i
$759$		0			0
$760$	17.5596	−	23.5867i	0.636955	−	0.855580i
$761$	25.4732	−	6.03726i	0.923403	−	0.218851i	0.258700	−	0.965958i	$-0.416706\pi$
$761$	25.4732	−	6.03726i	0.923403	−	0.218851i	0.664704	+	0.747107i	$0.268558\pi$
$762$		0			0
$763$	21.2547	+	28.5501i	0.769473	+	1.03358i
$764$	0.983309	+	0.825094i	0.0355749	+	0.0298509i
$765$		0			0
$766$	10.2314	−	8.58519i	0.369676	−	0.310195i
$767$	19.5213	+	4.62664i	0.704875	+	0.167058i
$768$		0			0
$769$	−38.0508	+	25.0264i	−1.37215	+	0.902476i	−0.999673	−	0.0255660i	$-0.991861\pi$
$769$	−38.0508	+	25.0264i	−1.37215	+	0.902476i	−0.372475	+	0.928042i	$0.621491\pi$
$770$	−14.7921	+	9.72890i	−0.533069	+	0.350605i
$771$		0			0
$772$	−15.2724	−	3.61963i	−0.549667	−	0.130273i
$773$	10.7154	−	8.99131i	0.385407	−	0.323395i	−0.429414	−	0.903108i	$-0.641280\pi$
$773$	10.7154	−	8.99131i	0.385407	−	0.323395i	0.814821	+	0.579713i	$0.196835\pi$
$774$		0			0
$775$	1.77672	+	1.49085i	0.0638217	+	0.0535528i
$776$	15.5892	+	20.9399i	0.559618	+	0.751698i
$777$		0			0
$778$	18.2650	−	4.32889i	0.654833	−	0.155198i
$779$	19.2715	−	25.8861i	0.690472	−	0.927465i
$780$		0			0
$781$	40.9391	−	20.5604i	1.46492	−	0.735709i
$782$	1.63223	+	2.82710i	0.0583683	+	0.101097i
$783$		0			0
$784$	−3.03440	+	5.25573i	−0.108371	+	0.187705i
$785$	0.0280427	−	0.481475i	0.00100089	−	0.0171846i
$786$		0			0
$787$	−14.1067	−	1.64884i	−0.502850	−	0.0587748i	−0.139113	−	0.990276i	$-0.544425\pi$
$787$	−14.1067	−	1.64884i	−0.502850	−	0.0587748i	−0.363737	+	0.931502i	$0.618499\pi$
$788$	0.538863	−	1.79993i	0.0191962	−	0.0641197i
$789$		0			0
$790$	−0.486563	+	1.12798i	−0.0173112	+	0.0401318i
$791$	17.1290	−	6.23446i	0.609039	−	0.221672i
$792$		0			0
$793$	−2.13836	−	0.778298i	−0.0759353	−	0.0276382i
$794$	−0.0215361	+	0.0228269i	−0.000764286	+	0.000810096i
$795$		0			0
$796$	−11.5159	−	5.78353i	−0.408172	−	0.204992i
$797$	2.40151	+	41.2323i	0.0850658	+	1.46052i	0.723222	+	0.690616i	$0.242661\pi$
$797$	2.40151	+	41.2323i	0.0850658	+	1.46052i	−0.638156	+	0.769907i	$0.720302\pi$
$798$		0			0
$799$	−0.849812	−	2.83857i	−0.0300642	−	0.100421i
$800$	−3.22216	−	18.2738i	−0.113921	−	0.646075i
$801$		0			0
$802$	2.82324	−	16.0114i	0.0996920	−	0.565381i
$803$	−22.9966	+	2.68791i	−0.811531	+	0.0948544i
$804$		0			0
$805$	38.3695	+	40.6693i	1.35235	+	1.43340i
$806$	0.605940	+	1.40473i	0.0213433	+	0.0494794i
$807$		0			0
$808$	10.4365	+	6.86422i	0.367156	+	0.241482i
$809$	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	$0.518631\pi$
$812$	7.89598	+	5.19326i	0.277094	+	0.182248i
$813$		0			0
$814$	−8.79420	−	20.3873i	−0.308237	−	0.714573i
$815$	−32.2838	−	34.2188i	−1.13085	−	1.19863i
$816$		0			0
$817$	10.7755	−	1.25947i	0.376986	−	0.0440634i
$818$	−3.09855	+	17.5727i	−0.108338	+	0.614417i
$819$		0			0
$820$	−5.62815	−	31.9188i	−0.196543	−	1.11465i
$821$	−2.57453	−	8.59953i	−0.0898518	−	0.300126i	0.901237	−	0.433326i	$-0.142660\pi$
$821$	−2.57453	−	8.59953i	−0.0898518	−	0.300126i	−0.991089	+	0.133200i	$0.957475\pi$
$822$		0			0
$823$	0.0754800	+	1.29594i	0.00263107	+	0.0451737i	0.999368	−	0.0355431i	$-0.0113161\pi$
$823$	0.0754800	+	1.29594i	0.00263107	+	0.0451737i	−0.996737	+	0.0807168i	$0.974279\pi$
$824$	3.29934	+	1.65699i	0.114938	+	0.0577241i
$825$		0			0
$826$	−6.13321	+	6.50082i	−0.213402	+	0.226192i
$827$	29.6308	+	10.7847i	1.03036	+	0.375022i	0.801219	−	0.598371i	$-0.204185\pi$
$827$	29.6308	+	10.7847i	1.03036	+	0.375022i	0.229144	+	0.973392i	$0.426407\pi$
$828$		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	$0.542713\pi$
$830$	2.37587	−	5.50788i	0.0824676	−	0.191181i
$831$		0			0
$832$	−1.45509	+	4.86035i	−0.0504463	+	0.168502i
$833$	2.59585	+	0.303411i	0.0899407	+	0.0105126i
$834$		0			0
$835$	3.08567	−	52.9789i	0.106784	−	1.83341i
$836$	−13.9673	+	24.1921i	−0.483069	+	0.836700i
$837$		0			0
$838$	−0.957629	−	1.65866i	−0.0330807	−	0.0572975i
$839$	3.46674	−	1.74106i	0.119685	−	0.0601082i	−0.387949	−	0.921681i	$-0.626816\pi$
$839$	3.46674	−	1.74106i	0.119685	−	0.0601082i	0.507634	+	0.861573i	$0.330520\pi$
$840$		0			0
$841$	−15.3834	+	20.6635i	−0.530463	+	0.712536i
$842$	−13.9533	+	3.30699i	−0.480862	+	0.113966i
$843$		0			0
$844$	10.2570	+	13.7775i	0.353060	+	0.474242i
$845$	6.45643	+	5.41758i	0.222108	+	0.186371i
$846$		0			0
$847$	1.86921	−	1.56845i	0.0642267	−	0.0538926i
$848$	17.6988	+	4.19469i	0.607779	+	0.144046i
$849$		0			0
$850$	−1.52131	+	1.00058i	−0.0521804	+	0.0343196i
$851$	−58.5833	+	38.5308i	−2.00821	+	1.32082i
$852$		0			0
$853$	−3.34652	−	0.793140i	−0.114583	−	0.0271566i	0.172924	−	0.984935i	$-0.444678\pi$
$853$	−3.34652	−	0.793140i	−0.114583	−	0.0271566i	−0.287507	+	0.957778i	$0.592827\pi$
$854$	0.776573	−	0.651622i	0.0265738	−	0.0222980i
$855$		0			0
$856$	11.4381	+	9.59772i	0.390947	+	0.328043i
$857$	8.75386	+	11.7585i	0.299026	+	0.401662i	0.926088	−	0.377308i	$-0.123150\pi$
$857$	8.75386	+	11.7585i	0.299026	+	0.401662i	−0.627062	+	0.778969i	$0.715743\pi$
$858$		0			0
$859$	9.27804	−	2.19894i	0.316563	−	0.0750268i	−0.0692629	−	0.997598i	$-0.522065\pi$
$859$	9.27804	−	2.19894i	0.316563	−	0.0750268i	0.385826	+	0.922572i	$0.373917\pi$
$860$	6.50643	−	8.73966i	0.221868	−	0.298020i
$861$		0			0
$862$	16.6441	−	8.35900i	0.566902	−	0.284709i
$863$	−8.00876	−	13.8716i	−0.272621	−	0.472194i	0.696911	−	0.717158i	$-0.254557\pi$
$863$	−8.00876	−	13.8716i	−0.272621	−	0.472194i	−0.969532	+	0.244964i	$0.921224\pi$
$864$		0			0
$865$	−27.3732	+	47.4117i	−0.930716	+	1.61205i
$866$	−0.426486	+	7.32248i	−0.0144926	+	0.248828i
$867$		0			0
$868$	3.52519	+	0.412036i	0.119653	+	0.0139854i
$869$	0.733672	−	2.45064i	0.0248881	−	0.0831321i
$870$		0			0
$871$	21.5899	−	50.0510i	0.731546	−	1.69591i
$872$	−22.3086	+	8.11966i	−0.755464	+	0.274967i
$873$		0			0
$874$	−15.9184	−	5.79383i	−0.538448	−	0.195979i
$875$	9.78136	−	10.3676i	0.330670	−	0.350490i
$876$		0			0
$877$	−29.5974	−	14.8644i	−0.999432	−	0.501934i	−0.127646	−	0.991820i	$-0.540742\pi$
$877$	−29.5974	−	14.8644i	−0.999432	−	0.501934i	−0.871786	+	0.489886i	$0.837038\pi$
$878$	1.21708	+	20.8965i	0.0410745	+	0.705222i
$879$		0			0
$880$	6.20455	+	20.7246i	0.209155	+	0.698628i
$881$	2.00755	+	11.3854i	0.0676360	+	0.383583i	0.999770	+	0.0214681i	$0.00683402\pi$
$881$	2.00755	+	11.3854i	0.0676360	+	0.383583i	−0.932134	+	0.362115i	$0.882055\pi$
$882$		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	$0.807748\pi$
$884$	6.21241	−	0.726127i	0.208946	−	0.0244223i
$885$		0			0
$886$	−13.3851	−	14.1874i	−0.449683	−	0.476636i
$887$	9.54630	+	22.1308i	0.320533	+	0.743080i	0.999956	+	0.00933326i	$0.00297091\pi$
$887$	9.54630	+	22.1308i	0.320533	+	0.743080i	−0.679423	+	0.733747i	$0.737770\pi$
$888$		0			0
$889$	−28.0867	−	18.4729i	−0.941997	−	0.619561i
$890$	21.6198			0.724697
$891$		0			0
$892$	7.80468			0.261320
$893$	12.8464	+	8.44922i	0.429889	+	0.282743i
$894$		0			0
$895$	−11.8417	−	27.4521i	−0.395824	−	0.917622i
$896$	−24.7785	−	26.2637i	−0.827791	−	0.877407i
$897$		0			0
$898$	−9.89998	+	1.15714i	−0.330367	+	0.0386143i
$899$	0.211221	−	1.19789i	0.00704460	−	0.0399519i
$900$		0			0
$901$	−1.36020	−	7.71410i	−0.0453149	−	0.256994i
$902$	−3.71700	−	12.4156i	−0.123762	−	0.413396i
$903$		0			0
$904$	0.706934	+	12.1376i	0.0235123	+	0.403690i
$905$	−2.12682	−	1.06813i	−0.0706980	−	0.0355059i
$906$		0			0
$907$	−15.8463	+	16.7961i	−0.526169	+	0.557707i	−0.934883	−	0.354956i	$-0.884496\pi$
$907$	−15.8463	+	16.7961i	−0.526169	+	0.557707i	0.408714	+	0.912663i	$0.365977\pi$
$908$	22.2614	+	8.10250i	0.738771	+	0.268891i
$909$		0			0
$910$	−19.3305	+	7.03572i	−0.640799	+	0.233232i
$911$	−9.06991	+	21.0264i	−0.300500	+	0.696637i	−0.999835	−	0.0181571i	$-0.994220\pi$
$911$	−9.06991	+	21.0264i	−0.300500	+	0.696637i	0.699335	+	0.714794i	$0.253479\pi$
$912$		0			0
$913$	−3.58249	+	11.9663i	−0.118563	+	0.396028i
$914$	−4.70685	−	0.550152i	−0.155689	−	0.0181974i
$915$		0			0
$916$	−0.505863	+	8.68533i	−0.0167142	+	0.286971i
$917$	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	$0.938575\pi$
$920$	−33.3264	+	16.7371i	−1.09874	+	0.551807i
$921$		0			0
$922$	−6.89423	+	9.26056i	−0.227049	+	0.304980i
$923$	51.7941	−	12.2754i	1.70482	−	0.404051i
$924$		0			0
$925$	−23.3555	−	31.3719i	−0.767926	−	1.03150i
$926$	1.12588	+	0.944728i	0.0369988	+	0.0310457i
$927$		0			0
$928$	−7.45472	+	6.25525i	−0.244713	+	0.205339i
$929$	−28.1380	−	6.66884i	−0.923179	−	0.218797i	−0.258573	−	0.965992i	$-0.583252\pi$
$929$	−28.1380	−	6.66884i	−0.923179	−	0.218797i	−0.664606	+	0.747194i	$0.731401\pi$
$930$		0			0
$931$	−11.3310	+	7.45253i	−0.371359	+	0.244247i
$932$	6.24286	−	4.10599i	0.204492	−	0.134496i
$933$		0			0
$934$	6.76029	+	1.60222i	0.221203	+	0.0524262i
$935$	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	$0.618599\pi$
$938$	14.5008	+	19.4779i	0.473468	+	0.635977i
$939$		0			0
$940$	15.0261	−	3.56124i	0.490096	−	0.116155i
$941$	−6.02898	+	8.09833i	−0.196539	+	0.263998i	−0.889457	−	0.457018i	$-0.848917\pi$
$941$	−6.02898	+	8.09833i	−0.196539	+	0.263998i	0.692918	+	0.721016i	$0.256325\pi$
$942$		0			0
$943$	−36.5752	+	18.3688i	−1.19105	+	0.598169i
$944$	5.46032	+	9.45755i	0.177718	+	0.307817i
$945$		0			0
$946$	2.17839	−	3.77309i	0.0708257	−	0.122674i
$947$	−1.22145	+	20.9715i	−0.0396918	+	0.681483i	0.918511	+	0.395394i	$0.129392\pi$
$947$	−1.22145	+	20.9715i	−0.0396918	+	0.681483i	−0.958203	+	0.286088i	$0.907645\pi$
$948$		0			0
$949$	−26.7197	−	3.12308i	−0.867357	−	0.101379i
$950$	2.70997	−	9.05193i	0.0879231	−	0.293683i
$951$		0			0
$952$	−2.41918	+	5.60829i	−0.0784061	+	0.181766i
$953$	6.34571	−	2.30965i	0.205558	−	0.0748169i	−0.237189	−	0.971463i	$-0.576226\pi$
$953$	6.34571	−	2.30965i	0.205558	−	0.0748169i	0.442747	+	0.896647i	$0.354004\pi$
$954$		0			0
$955$	2.08753	+	0.759798i	0.0675508	+	0.0245865i
$956$	−33.4610	+	35.4666i	−1.08221	+	1.14707i
$957$		0			0
$958$	13.9119	+	6.98682i	0.449473	+	0.225734i
$959$	1.57035	+	26.9619i	0.0507092	+	0.870644i
$960$		0			0
$961$	8.75989	+	29.2601i	0.282577	+	0.943873i
$962$	−4.47973	−	25.4058i	−0.144432	−	0.819117i
$963$		0			0
$964$	−7.27912	+	41.2819i	−0.234445	+	1.32960i
$965$	−26.9798	+	3.15349i	−0.868511	+	0.101514i
$966$		0			0
$967$	−8.09307	−	8.57815i	−0.260256	−	0.275855i	0.584049	−	0.811718i	$-0.301468\pi$
$967$	−8.09307	−	8.57815i	−0.260256	−	0.275855i	−0.844305	+	0.535864i	$0.819986\pi$
$968$	0.644624	+	1.49441i	0.0207190	+	0.0480320i
$969$		0			0
$970$	17.2202	+	11.3259i	0.552908	+	0.363653i
$971$	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
$974$	−2.85684	−	1.87897i	−0.0915391	−	0.0602062i
$975$		0			0
$976$	−0.490623	−	1.13739i	−0.0157045	−	0.0364071i
$977$	−26.7064	−	28.3071i	−0.854413	−	0.905625i	0.142032	−	0.989862i	$-0.454636\pi$
$977$	−26.7064	−	28.3071i	−0.854413	−	0.905625i	−0.996446	+	0.0842367i	$0.973155\pi$
$978$		0			0
$979$	−44.7163	+	5.22659i	−1.42914	+	0.167042i
$980$	−2.36521	+	13.4138i	−0.0755538	+	0.428487i
$981$		0			0
$982$	0.0480294	+	0.272388i	0.00153268	+	0.00869226i
$983$	−5.36807	−	17.9306i	−0.171215	−	0.571897i	−0.999925	−	0.0122197i	$-0.996110\pi$
$983$	−5.36807	−	17.9306i	−0.171215	−	0.571897i	0.828711	−	0.559677i	$-0.189075\pi$
$984$		0			0
$985$	−0.189067	−	3.24615i	−0.00602417	−	0.103431i
$986$	0.853368	+	0.428578i	0.0271768	+	0.0136487i
$987$		0			0
$988$	−22.2734	+	23.6085i	−0.708613	+	0.751085i
$989$	−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	$0.400478\pi$
$992$	−1.44752	+	3.35572i	−0.0459587	+	0.106544i
$993$		0			0
$994$	−6.80089	+	22.7165i	−0.215711	+	0.720525i
$995$	−22.1516	−	2.58915i	−0.702252	−	0.0820815i
$996$		0			0
$997$	−1.81875	+	31.2268i	−0.0576005	+	0.988963i	0.838441	+	0.544992i	$0.183467\pi$
$997$	−1.81875	+	31.2268i	−0.0576005	+	0.988963i	−0.896042	+	0.443970i	$0.853570\pi$
$998$	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.c.703.4		144
3.2	odd	2		729.2.g.b.703.5		144
9.2	odd	6		729.2.g.a.217.5		144
9.4	even	3		81.2.g.a.25.5	yes	144
9.5	odd	6		243.2.g.a.73.4		144
9.7	even	3		729.2.g.d.217.4		144
81.13	even	27		729.2.g.d.514.4		144
81.14	odd	54		729.2.g.b.28.5		144
81.38	odd	54		6561.2.a.d.1.41		72
81.40	even	27		81.2.g.a.13.5	✓	144
81.41	odd	54		243.2.g.a.10.4		144
81.43	even	27		6561.2.a.c.1.32		72
81.67	even	27	inner	729.2.g.c.28.4		144
81.68	odd	54		729.2.g.a.514.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.5	✓	144	81.40	even	27
81.2.g.a.25.5	yes	144	9.4	even	3
243.2.g.a.10.4		144	81.41	odd	54
243.2.g.a.73.4		144	9.5	odd	6
729.2.g.a.217.5		144	9.2	odd	6
729.2.g.a.514.5		144	81.68	odd	54
729.2.g.b.28.5		144	81.14	odd	54
729.2.g.b.703.5		144	3.2	odd	2
729.2.g.c.28.4		144	81.67	even	27	inner
729.2.g.c.703.4		144	1.1	even	1	trivial
729.2.g.d.217.4		144	9.7	even	3
729.2.g.d.514.4		144	81.13	even	27
6561.2.a.c.1.32		72	81.43	even	27
6561.2.a.d.1.41		72	81.38	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)

\(f(q)\)	\(=\)	\(q+(0.474230 + 0.311906i) q^{2} +(-0.664551 - 1.54060i) q^{4} +(-1.99266 - 2.11209i) q^{5} +(-3.10865 + 0.363349i) q^{7} +(0.362501 - 2.05585i) q^{8} +(-0.286203 - 1.62314i) q^{10} +(0.984350 + 3.28796i) q^{11} +(0.231870 + 3.98106i) q^{13} +(-1.58755 - 0.797296i) q^{14} +(-1.48964 + 1.57893i) q^{16} +(0.878443 + 0.319727i) q^{17} +(-4.55845 + 1.65914i) q^{19} +(-1.92967 + 4.47349i) q^{20} +(-0.558725 + 1.86627i) q^{22} +(6.11065 + 0.714233i) q^{23} +(-0.199532 + 3.42583i) q^{25} +(-1.13175 + 1.96026i) q^{26} +(2.62564 + 4.54773i) q^{28} +(1.60828 - 0.807706i) q^{29} +(0.403603 - 0.542133i) q^{31} +(-5.26149 + 1.24700i) q^{32} +(0.316859 + 0.425615i) q^{34} +(6.96191 + 5.84174i) q^{35} +(-8.73079 + 7.32600i) q^{37} +(-2.67925 - 0.634993i) q^{38} +(-5.06448 + 3.33096i) q^{40} +(-5.55820 + 3.65568i) q^{41} +(-2.17613 - 0.515752i) q^{43} +(4.41129 - 3.70151i) q^{44} +(2.67508 + 2.24466i) q^{46} +(-1.89278 - 2.54245i) q^{47} +(2.72039 - 0.644744i) q^{49} +(-1.16316 + 1.56239i) q^{50} +(5.97913 - 3.00283i) q^{52} +(-4.18963 - 7.25666i) q^{53} +(4.98301 - 8.63082i) q^{55} +(-0.379900 + 6.52263i) q^{56} +(1.01462 + 0.118592i) q^{58} +(1.44287 - 4.81952i) q^{59} +(-0.226018 + 0.523969i) q^{61} +(0.360495 - 0.131209i) q^{62} +(1.19553 + 0.435136i) q^{64} +(7.94633 - 8.42262i) q^{65} +(-12.2150 - 6.13461i) q^{67} +(-0.0911978 - 1.56581i) q^{68} +(1.47947 + 4.94179i) q^{70} +(-2.31784 - 13.1452i) q^{71} +(-1.17142 + 6.64347i) q^{73} +(-6.42542 + 0.751024i) q^{74} +(5.58539 + 5.92017i) q^{76} +(-4.25468 - 9.86346i) q^{77} +(-0.622719 - 0.409569i) q^{79} +6.30319 q^{80} -3.77609 q^{82} +(3.04071 + 1.99991i) q^{83} +(-1.07514 - 2.49246i) q^{85} +(-0.871119 - 0.923332i) q^{86} +(7.11637 - 0.831784i) q^{88} +(-2.27781 + 12.9181i) q^{89} +(-2.16732 - 12.2915i) q^{91} +(-2.96049 - 9.88873i) q^{92} +(-0.104609 - 1.79607i) q^{94} +(12.5877 + 6.32177i) q^{95} +(-8.58165 + 9.09602i) q^{97} +(1.49119 + 0.542748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 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 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

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