LMFDB - Embedded newform 729.2.g.b.28.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
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			28.5
Character	$\chi$	$=$	729.28
Dual form			729.2.g.b.703.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

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	$-0.749500\pi$
$2$	−0.474230	+	0.311906i	−0.335331	+	0.220551i	0.370665	+	0.928767i	$0.379130\pi$
$3$		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	$-0.534324\pi$
$5$	1.99266	−	2.11209i	0.891144	−	0.944557i	0.998767	+	0.0496342i	$0.0158056\pi$
$6$		0			0
$7$	−3.10865	−	0.363349i	−1.17496	−	0.137333i	−0.493872	−	0.869535i	$-0.664419\pi$
$7$	−3.10865	−	0.363349i	−1.17496	−	0.137333i	−0.681088	+	0.732201i	$0.738493\pi$
$8$	−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	0.671388	+	0.741106i	$0.265698\pi$
$11$	−0.984350	+	3.28796i	−0.296793	+	0.991357i	−0.968181	+	0.250251i	$0.919487\pi$
$12$		0			0
$13$	0.231870	−	3.98106i	0.0643092	−	1.10415i	−0.799611	−	0.600518i	$-0.794961\pi$
$13$	0.231870	−	3.98106i	0.0643092	−	1.10415i	0.863920	−	0.503628i	$-0.168002\pi$
$14$	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	$-0.647274\pi$
$17$	−0.878443	+	0.319727i	−0.213054	+	0.0775452i	0.233289	+	0.972408i	$0.425051\pi$
$18$		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	$0.798947\pi$
$20$	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	$-0.758690\pi$
$23$	−6.11065	+	0.714233i	−1.27416	+	0.148928i	−0.548014	+	0.836469i	$0.684616\pi$
$24$		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	$-0.405292\pi$
$29$	−1.60828	−	0.807706i	−0.298649	−	0.149987i	−0.591814	+	0.806075i	$0.701588\pi$
$30$		0			0
$31$	0.403603	+	0.542133i	0.0724892	+	0.0973699i	0.836889	−	0.547373i	$-0.184372\pi$
$31$	0.403603	+	0.542133i	0.0724892	+	0.0973699i	−0.764400	+	0.644743i	$0.776965\pi$
$32$	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	−0.942475	−	0.334277i	$-0.891508\pi$
$37$	−8.73079	−	7.32600i	−1.43533	−	1.20439i	−0.492858	−	0.870110i	$-0.664048\pi$
$38$	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	$-0.140939\pi$
$41$	5.55820	+	3.65568i	0.868045	+	0.570922i	−0.0355222	+	0.999369i	$0.511309\pi$
$42$		0			0
$43$	−2.17613	+	0.515752i	−0.331857	+	0.0786515i	−0.393166	−	0.919467i	$-0.628620\pi$
$43$	−2.17613	+	0.515752i	−0.331857	+	0.0786515i	0.0613098	+	0.998119i	$0.480472\pi$
$44$	−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	$-0.722041\pi$
$47$	1.89278	−	2.54245i	0.276091	−	0.370854i	0.918442	+	0.395556i	$0.129448\pi$
$48$		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	−0.420498	−	0.907294i	$-0.638145\pi$
$53$	4.18963	−	7.25666i	0.575490	−	0.996779i	0.995988	−	0.0894851i	$-0.0285221\pi$
$54$		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	−0.999086	−	0.0427359i	$-0.986393\pi$
$59$	−1.44287	−	4.81952i	−0.187846	−	0.627448i	0.811241	−	0.584712i	$-0.198793\pi$
$60$		0			0
$61$	−0.226018	−	0.523969i	−0.0289387	−	0.0670874i	0.903134	−	0.429359i	$-0.141261\pi$
$61$	−0.226018	−	0.523969i	−0.0289387	−	0.0670874i	−0.932073	+	0.362272i	$0.882001\pi$
$62$	−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	−0.993127	−	0.117041i	$-0.962659\pi$
$67$	−12.2150	+	6.13461i	−1.49230	+	0.749461i	−0.499173	+	0.866502i	$0.666363\pi$
$68$	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	−0.463638	−	0.886025i	$-0.653456\pi$
$71$	2.31784	−	13.1452i	0.275078	−	1.56004i	0.738715	−	0.674017i	$-0.235433\pi$
$72$		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	$-0.184734\pi$
$74$	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	−0.584056	−	0.811713i	$-0.698535\pi$
$79$	−0.622719	+	0.409569i	−0.0700614	+	0.0460801i	0.513995	+	0.857793i	$0.328165\pi$
$80$	−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	$-0.749195\pi$
$83$	−3.04071	+	1.99991i	−0.333761	+	0.219518i	0.371555	+	0.928411i	$0.378825\pi$
$84$		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	0.828601	+	0.559839i	$0.189137\pi$
$89$	2.27781	+	12.9181i	0.241447	+	1.36931i	−0.587154	+	0.809475i	$0.699752\pi$
$90$		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	0.126321	−	0.991989i	$-0.459683\pi$
$97$	−8.58165	−	9.09602i	−0.871335	−	0.923561i	−0.997656	+	0.0684283i	$0.978202\pi$
$98$	−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	$-0.0334084\pi$
$101$	2.37006	+	5.49442i	0.235830	+	0.546715i	−0.758667	+	0.651478i	$0.774149\pi$
$102$		0			0
$103$	−0.507240	−	1.69430i	−0.0499798	−	0.166944i	0.929356	−	0.369185i	$-0.120363\pi$
$103$	−0.507240	−	1.69430i	−0.0499798	−	0.166944i	−0.979336	+	0.202240i	$0.935178\pi$
$104$	−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	$-0.0542974\pi$
$107$	3.57628	+	6.19429i	0.345732	+	0.598825i	−0.639755	+	0.768579i	$0.720964\pi$
$108$		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	$0.983336\pi$
$110$	−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	$-0.337598\pi$
$113$	5.66711	+	1.34313i	0.533116	+	0.126351i	0.0447643	+	0.998998i	$0.485746\pi$
$114$		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	−0.200045	−	0.979787i	$-0.564109\pi$
$127$	8.22802	−	6.90413i	0.730119	−	0.612643i	0.930164	+	0.367144i	$0.119664\pi$
$128$	−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	$-0.102403\pi$
$131$	4.27722	+	5.74530i	0.373702	+	0.501969i	−0.574994	+	0.818158i	$0.694996\pi$
$132$		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	−0.949442	−	0.313944i	$-0.898350\pi$
$137$	−0.501738	−	8.61452i	−0.0428664	−	0.735988i	0.906575	−	0.422044i	$-0.138687\pi$
$138$		0			0
$139$	5.85926	−	0.684849i	0.496976	−	0.0580882i	0.136087	−	0.990697i	$-0.456547\pi$
$139$	5.85926	−	0.684849i	0.496976	−	0.0580882i	0.360889	+	0.932609i	$0.382473\pi$
$140$	−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	0.790807	+	0.612066i	$0.209661\pi$
$149$	−0.802085	+	13.7713i	−0.0657094	+	1.12819i	−0.856516	+	0.516121i	$0.827376\pi$
$150$		0			0
$151$	−1.80026	+	6.01330i	−0.146503	+	0.489356i	−0.999468	−	0.0326132i	$-0.989617\pi$
$151$	−1.80026	+	6.01330i	−0.146503	+	0.489356i	0.852965	+	0.521969i	$0.174802\pi$
$152$	−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	−0.722809	−	0.691048i	$-0.757150\pi$
$157$	0.113981	−	0.120812i	0.00909664	−	0.00964187i	0.731906	+	0.681406i	$0.238631\pi$
$158$	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	0.0290638	+	0.999578i	$0.490747\pi$
$167$	−12.5418	+	13.2935i	−0.970513	+	1.02868i	−0.999576	+	0.0291056i	$0.990734\pi$
$168$		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	−0.462514	−	0.886612i	$-0.653052\pi$
$173$	5.40734	−	18.0618i	0.411112	−	1.37321i	0.873626	−	0.486598i	$-0.161762\pi$
$174$		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	$-0.736836\pi$
$179$	−9.67521	+	3.52149i	−0.723159	+	0.263209i	−0.0458930	+	0.998946i	$0.514613\pi$
$180$		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	$0.601414\pi$
$182$	−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	$-0.343040\pi$
$191$	0.683675	+	0.343354i	0.0494690	+	0.0248442i	−0.423893	+	0.905712i	$0.639337\pi$
$192$		0			0
$193$	5.58623	+	7.50362i	0.402106	+	0.540122i	0.956347	−	0.292234i	$-0.0943987\pi$
$193$	5.58623	+	7.50362i	0.402106	+	0.540122i	−0.554241	+	0.832356i	$0.686991\pi$
$194$	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	$-0.734924\pi$
$197$	−0.857832	+	0.719807i	−0.0611180	+	0.0512841i	0.611717	+	0.791077i	$0.290479\pi$
$198$		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	$0.634461\pi$
$200$	−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	−0.127060	−	0.991895i	$-0.540554\pi$
$211$	−9.96134	−	2.36088i	−0.685767	−	0.162530i	−0.558707	+	0.829365i	$0.688702\pi$
$212$	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	0.845321	−	0.534258i	$-0.179409\pi$
$223$	−1.84243	−	4.27124i	−0.123379	−	0.286024i	−0.968700	+	0.248234i	$0.920150\pi$
$224$	−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	$-0.0855085\pi$
$227$	9.68944	+	10.2702i	0.643111	+	0.681658i	−0.321024	+	0.947071i	$0.604027\pi$
$228$		0			0
$229$	−4.63378	+	2.32717i	−0.306208	+	0.153784i	−0.595268	−	0.803528i	$-0.702954\pi$
$229$	−4.63378	+	2.32717i	−0.306208	+	0.153784i	0.289059	+	0.957311i	$0.406658\pi$
$230$	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	$-0.991045\pi$
$233$	−0.773336	+	4.38581i	−0.0506629	+	0.287324i	0.948941	+	0.315452i	$0.102156\pi$
$234$		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	0.0587876	−	0.998271i	$-0.481277\pi$
$239$	11.5106	−	26.6846i	0.744561	−	1.72609i	0.685773	−	0.727815i	$-0.259464\pi$
$240$		0			0
$241$	−20.8739	+	13.7290i	−1.34460	+	0.884360i	−0.998549	−	0.0538543i	$-0.982849\pi$
$241$	−20.8739	+	13.7290i	−1.34460	+	0.884360i	−0.346055	+	0.938214i	$0.612479\pi$
$242$	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	−0.958483	−	0.285151i	$-0.907956\pi$
$251$	−2.46091	−	13.9565i	−0.155331	−	0.880926i	0.803152	−	0.595775i	$-0.203155\pi$
$252$		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	$-0.799742\pi$
$257$	−13.1355	+	6.59688i	−0.819367	+	0.411502i	−0.0108263	+	0.999941i	$0.503446\pi$
$258$		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	−0.992509	−	0.122174i	$-0.961014\pi$
$263$	−6.49135	−	15.0486i	−0.400274	−	0.927939i	0.592235	−	0.805765i	$-0.298246\pi$
$264$		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	$-0.279261\pi$
$269$	−5.68131	−	9.84032i	−0.346396	−	0.599975i	−0.985606	+	0.169057i	$0.945928\pi$
$270$		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	$0.193433\pi$
$272$	1.81339	+	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	−0.338473	−	0.940976i	$-0.609910\pi$
$277$	10.9854	−	14.7559i	0.660048	−	0.886598i	0.998520	+	0.0543783i	$0.0173177\pi$
$278$	−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	$-0.677805\pi$
$281$	−10.4439	+	2.47524i	−0.623028	+	0.147660i	−0.0930358	+	0.995663i	$0.529657\pi$
$282$		0			0
$283$	11.9407	+	7.85355i	0.709804	+	0.466845i	0.852369	−	0.522940i	$-0.175165\pi$
$283$	11.9407	+	7.85355i	0.709804	+	0.466845i	−0.142566	+	0.989785i	$0.545535\pi$
$284$	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	0.998643	+	0.0520843i	$0.0165864\pi$
$293$	13.0455	+	17.5231i	0.762125	+	1.02371i	−0.236518	+	0.971627i	$0.576006\pi$
$294$		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	−0.986045	−	0.166478i	$-0.946760\pi$
$307$	−28.6368	+	10.4229i	−1.63439	+	0.594869i	−0.648344	+	0.761347i	$0.724538\pi$
$308$	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	−0.593835	−	0.804587i	$-0.702387\pi$
$311$	1.57644	−	27.0664i	0.0893915	−	1.53479i	0.683227	−	0.730206i	$-0.260576\pi$
$312$		0			0
$313$	2.32494	−	7.76583i	0.131413	−	0.438950i	−0.866803	−	0.498650i	$-0.833829\pi$
$313$	2.32494	−	7.76583i	0.131413	−	0.438950i	0.998216	+	0.0596999i	$0.0190144\pi$
$314$	−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	$-0.646563\pi$
$317$	−19.2878	−	2.25442i	−1.08331	−	0.126621i	−0.638966	+	0.769235i	$0.720637\pi$
$318$		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	0.0616891	−	0.998095i	$-0.480351\pi$
$331$	−1.97328	−	0.230643i	−0.108461	−	0.0126773i	−0.170150	+	0.985418i	$0.554425\pi$
$332$	−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	−0.835522	−	0.549456i	$-0.814835\pi$
$337$	1.06728	−	18.3245i	0.0581385	−	0.998199i	0.893661	−	0.448743i	$-0.148128\pi$
$338$	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	$-0.281674\pi$
$347$	26.6029	−	3.10943i	1.42812	−	0.166923i	0.794754	+	0.606931i	$0.207600\pi$
$348$		0			0
$349$	0.762246	+	13.0873i	0.0408021	+	0.700545i	0.955242	+	0.295824i	$0.0955943\pi$
$349$	0.762246	+	13.0873i	0.0408021	+	0.700545i	−0.914440	+	0.404721i	$0.867369\pi$
$350$	−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	$-0.178824\pi$
$353$	17.3676	+	8.72232i	0.924383	+	0.464242i	0.0780814	+	0.996947i	$0.475121\pi$
$354$		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	$-0.595631\pi$
$359$	11.2428	−	9.43384i	0.593373	−	0.497899i	0.889308	+	0.457309i	$0.151187\pi$
$360$		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	−0.500125	−	0.865953i	$-0.666713\pi$
$367$	−10.6977	+	2.53540i	−0.558415	+	0.132347i	−0.0582894	+	0.998300i	$0.518565\pi$
$368$	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	−0.318596	−	0.947890i	$-0.603211\pi$
$373$	−19.8678	−	4.70876i	−1.02872	−	0.243810i	−0.710121	+	0.704080i	$0.751360\pi$
$374$	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	−0.978308	−	0.207155i	$-0.933580\pi$
$379$	−13.0154	−	22.5433i	−0.668556	−	1.15797i	0.309753	−	0.950817i	$-0.399754\pi$
$380$	−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	−0.937963	−	0.346735i	$-0.887290\pi$
$383$	−6.74866	−	22.5421i	−0.344840	−	1.15185i	0.593123	−	0.805112i	$-0.297895\pi$
$384$		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	−0.971819	−	0.235730i	$-0.924252\pi$
$389$	−22.6942	−	24.0545i	−1.15064	−	1.21961i	−0.178825	−	0.983881i	$-0.557230\pi$
$390$		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	0.984566	−	0.175014i	$-0.0559972\pi$
$397$	−0.00960087	−	0.0544493i	−0.000481854	−	0.00273273i	−0.985048	+	0.172282i	$0.944886\pi$
$398$	−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	−0.358486	−	0.933535i	$-0.616707\pi$
$401$	11.3452	−	26.3011i	0.566551	−	1.31341i	0.925037	−	0.379878i	$-0.124034\pi$
$402$		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	−0.269916	−	0.962884i	$-0.586996\pi$
$409$	12.4515	−	28.8659i	0.615688	−	1.42732i	0.885604	−	0.464441i	$-0.153745\pi$
$410$	−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	$-0.621883\pi$
$419$	3.01535	−	1.51436i	0.147309	−	0.0739816i	0.520927	+	0.853601i	$0.325586\pi$
$420$		0			0
$421$	−17.3369	−	18.3761i	−0.844950	−	0.895594i	0.150718	−	0.988577i	$-0.451841\pi$
$421$	−17.3369	−	18.3761i	−0.844950	−	0.895594i	−0.995668	+	0.0929825i	$0.970360\pi$
$422$	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	−0.925789	−	0.378041i	$-0.876598\pi$
$431$	−16.4068	−	28.4174i	−0.790288	−	1.36882i	0.135501	−	0.990777i	$-0.456736\pi$
$432$		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	$0.0661680\pi$
$434$	1.07298	+	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	0.144574	−	0.989494i	$-0.453819\pi$
$439$	22.0216	−	29.5802i	1.05103	−	1.41178i	0.906460	−	0.422291i	$-0.138774\pi$
$440$	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	$-0.270079\pi$
$443$	33.4372	−	7.92477i	1.58865	−	0.376517i	0.927526	+	0.373759i	$0.121931\pi$
$444$		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	$-0.141783\pi$
$449$	13.4520	+	11.2876i	0.634838	+	0.532693i	−0.267590	+	0.963533i	$0.586227\pi$
$450$		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	0.265658	−	0.964067i	$-0.414411\pi$
$457$	−7.46084	−	3.74697i	−0.349003	−	0.175276i	−0.614661	+	0.788791i	$0.710707\pi$
$458$	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	0.906759	+	0.421650i	$0.138549\pi$
$461$	1.18266	+	20.3054i	0.0550818	+	0.945718i	−0.851677	+	0.524067i	$0.824414\pi$
$462$		0			0
$463$	2.57184	−	0.300605i	0.119524	−	0.0139703i	−0.0561208	−	0.998424i	$-0.517873\pi$
$463$	2.57184	−	0.300605i	0.119524	−	0.0139703i	0.175644	+	0.984454i	$0.443799\pi$
$464$	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	$-0.480285\pi$
$467$	−11.5019	−	4.18635i	−0.532244	−	0.193721i	−0.594140	+	0.804361i	$0.702508\pi$
$468$		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	$-0.678512\pi$
$479$	−27.2416	−	3.18408i	−1.24470	−	0.145485i	−0.712827	+	0.701340i	$0.752586\pi$
$480$		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	$-0.762759\pi$
$491$	−0.334399	+	0.354442i	−0.0150912	+	0.0159958i	0.719784	+	0.694198i	$0.244241\pi$
$492$		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	0.983619	+	0.180262i	$0.0576947\pi$
$499$	−0.318908	+	5.47545i	−0.0142763	+	0.245115i	−0.997895	+	0.0648523i	$0.979342\pi$
$500$	−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	$-0.686819\pi$
$503$	−9.93090	+	3.61455i	−0.442797	+	0.161165i	0.110993	+	0.993821i	$0.464597\pi$
$504$		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	$-0.625701\pi$
$509$	−12.3227	+	1.44032i	−0.546196	+	0.0638412i	−0.161480	+	0.986876i	$0.551627\pi$
$510$		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	$-0.594811\pi$
$521$	13.6270	−	11.4344i	0.597011	−	0.500952i	0.890483	+	0.455016i	$0.150366\pi$
$522$		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	$0.818151\pi$
$524$	−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	0.994620	+	0.103594i	$0.0330342\pi$
$541$	13.6538	+	23.6492i	0.587025	+	1.01676i	−0.407595	+	0.913163i	$0.633632\pi$
$542$	−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	0.991256	−	0.131953i	$-0.0421247\pi$
$547$	5.02926	+	11.6591i	0.215036	+	0.498509i	−0.776220	+	0.630462i	$0.782865\pi$
$548$	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	0.877415	+	0.479733i	$0.159266\pi$
$557$	−2.62356	+	14.8789i	−0.111164	+	0.630441i	−0.988578	+	0.150708i	$0.951845\pi$
$558$		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	$-0.911619\pi$
$563$	−2.42888	+	5.63077i	−0.102365	+	0.237309i	0.859335	+	0.511413i	$0.170878\pi$
$564$		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	$-0.675313\pi$
$569$	1.23600	−	0.812928i	0.0518157	−	0.0340797i	0.575153	+	0.818046i	$0.304943\pi$
$570$		0			0
$571$	3.49187	−	8.09506i	0.146130	−	0.338768i	−0.829393	−	0.558666i	$-0.811313\pi$
$571$	3.49187	−	8.09506i	0.146130	−	0.338768i	0.975523	+	0.219898i	$0.0705726\pi$
$572$	−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	−0.888313	−	0.459238i	$-0.848122\pi$
$577$	2.48608	−	14.0993i	0.103497	−	0.586960i	0.991810	−	0.127722i	$-0.0407665\pi$
$578$	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	$-0.0732449\pi$
$587$	3.38197	+	7.84028i	0.139589	+	0.323603i	−0.834054	+	0.551683i	$0.813986\pi$
$588$		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	0.908517	+	0.417848i	$0.137216\pi$
$593$	19.8740	+	34.4227i	0.816125	+	1.41357i	−0.0923915	+	0.995723i	$0.529451\pi$
$594$		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	$-0.289251\pi$
$599$	19.8283	+	4.69940i	0.810164	+	0.192012i	0.195400	+	0.980724i	$0.437399\pi$
$600$		0			0
$601$	−8.17441	+	10.9801i	−0.333441	+	0.447889i	−0.936948	−	0.349469i	$-0.886362\pi$
$601$	−8.17441	+	10.9801i	−0.333441	+	0.447889i	0.603507	+	0.797358i	$0.293770\pi$
$602$	−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	0.623515	−	0.781812i	$-0.285704\pi$
$607$	3.75977	+	2.47284i	0.152604	+	0.100369i	−0.470910	+	0.882181i	$0.656075\pi$
$608$	−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	0.108971	−	0.994045i	$-0.465244\pi$
$613$	27.4040	−	22.9947i	1.10684	−	0.928746i	0.997866	+	0.0652986i	$0.0208000\pi$
$614$	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	$-0.391071\pi$
$617$	−16.4713	−	22.1249i	−0.663112	−	0.890713i	−0.998683	+	0.0513013i	$0.983663\pi$
$618$		0			0
$619$	−29.8724	−	15.0025i	−1.20067	−	0.603001i	−0.267894	−	0.963448i	$-0.586328\pi$
$619$	−29.8724	−	15.0025i	−1.20067	−	0.603001i	−0.932780	+	0.360447i	$0.882624\pi$
$620$	−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	−0.129339	−	0.991600i	$-0.541286\pi$
$631$	10.2732	−	3.73914i	0.408970	−	0.148853i	0.538309	+	0.842748i	$0.319063\pi$
$632$	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	$-0.521857\pi$
$641$	−9.25236	−	1.08145i	−0.365446	−	0.0427145i	−0.296835	+	0.954929i	$0.595931\pi$
$642$		0			0
$643$	−0.883538	+	0.936495i	−0.0348433	+	0.0369318i	−0.744561	−	0.667555i	$-0.767341\pi$
$643$	−0.883538	+	0.936495i	−0.0348433	+	0.0369318i	0.709718	+	0.704486i	$0.248823\pi$
$644$	−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	$-0.331128\pi$
$647$	25.7409			1.01198			0.505989	+	0.862540i	$0.331128\pi$
$648$		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	−0.0523464	+	0.998629i	$0.516670\pi$
$653$	−26.7355	+	28.3380i	−1.04624	+	1.10895i	−0.993896	+	0.110323i	$0.964811\pi$
$654$		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	0.537033	+	0.843561i	$0.319545\pi$
$659$	−9.63166	+	32.1720i	−0.375196	+	1.25324i	−0.912229	+	0.409681i	$0.865640\pi$
$660$		0			0
$661$	−2.06029	+	35.3739i	−0.0801361	+	1.37588i	0.683365	+	0.730077i	$0.260516\pi$
$661$	−2.06029	+	35.3739i	−0.0801361	+	1.37588i	−0.763501	+	0.645807i	$0.776521\pi$
$662$	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	−0.877666	−	0.479273i	$-0.840900\pi$
$673$	−1.59738	−	27.4260i	−0.0615746	−	1.05720i	0.816091	−	0.577923i	$-0.196137\pi$
$674$	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	$-0.293083\pi$
$677$	8.53705	+	4.28747i	0.328106	+	0.164781i	−0.277119	+	0.960836i	$0.589380\pi$
$678$		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	$-0.941550\pi$
$683$	−25.4573	+	21.3612i	−0.974095	+	0.817363i	0.00909301	+	0.999959i	$0.497106\pi$
$684$		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	−0.329876	−	0.944024i	$-0.607007\pi$
$691$	−5.28329	+	1.25216i	−0.200986	+	0.0476345i	0.128890	+	0.991659i	$0.458859\pi$
$692$	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	−0.348906	−	0.937158i	$-0.613447\pi$
$701$	16.8694	−	29.2187i	0.637150	−	1.10358i	0.986055	−	0.166418i	$-0.0532200\pi$
$702$		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	0.711039	−	0.703153i	$-0.248225\pi$
$709$	−7.67820	−	17.8001i	−0.288361	−	0.668495i	−0.999399	+	0.0346578i	$0.988966\pi$
$710$	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	$-0.915990\pi$
$719$	0.831346	−	4.71480i	0.0310040	−	0.175832i	0.996378	+	0.0850387i	$0.0271014\pi$
$720$		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	−0.426949	−	0.904276i	$-0.640412\pi$
$727$	6.31649	−	4.15442i	0.234266	−	0.154079i	0.661215	+	0.750197i	$0.270041\pi$
$728$	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	−0.360587	−	0.932726i	$-0.617423\pi$
$733$	15.3050	−	35.4810i	0.565303	−	1.31052i	0.925890	−	0.377794i	$-0.123317\pi$
$734$	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	0.197218	+	0.980360i	$0.436809\pi$
$739$	−8.79173	+	49.8604i	−0.323409	+	1.83414i	−0.520627	+	0.853784i	$0.674302\pi$
$740$	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	$-0.739027\pi$
$743$	−13.7207	+	6.89082i	−0.503365	+	0.252800i	0.178949	+	0.983858i	$0.442730\pi$
$744$		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	0.746864	+	0.664977i	$0.231559\pi$
$751$	13.3810	+	44.6956i	0.488279	+	1.63097i	−0.258585	+	0.965989i	$0.583256\pi$
$752$	−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	−0.739856	−	0.672765i	$-0.765107\pi$
$757$	5.85224	−	10.1364i	0.212703	−	0.368413i	0.952560	+	0.304352i	$0.0984399\pi$
$758$	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	$-0.583294\pi$
$761$	−25.4732	−	6.03726i	−0.923403	−	0.218851i	−0.664704	+	0.747107i	$0.731442\pi$
$762$		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	−0.372475	−	0.928042i	$-0.621491\pi$
$769$	−38.0508	−	25.0264i	−1.37215	−	0.902476i	−0.999673	+	0.0255660i	$0.991861\pi$
$770$	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	$-0.358720\pi$
$773$	−10.7154	−	8.99131i	−0.385407	−	0.323395i	−0.814821	+	0.579713i	$0.803165\pi$
$774$		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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more