LMFDB - Embedded newform 729.2.g.b.703.5

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			703.5
Character	$\chi$	$=$	729.703
Dual form			729.2.g.b.28.5

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

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

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	0.370665	−	0.928767i	$-0.379130\pi$
$2$	−0.474230	−	0.311906i	−0.335331	−	0.220551i	−0.705996	+	0.708216i	$0.749500\pi$
$3$		0			0
$3$		0			0
$4$	−0.664551	−	1.54060i	−0.332275	−	0.770301i
$5$	1.99266	+	2.11209i	0.891144	+	0.944557i	0.998767	−	0.0496342i	$-0.0158056\pi$
$5$	1.99266	+	2.11209i	0.891144	+	0.944557i	−0.107623	+	0.994192i	$0.534324\pi$
$6$		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	$-0.919487\pi$
$11$	−0.984350	−	3.28796i	−0.296793	−	0.991357i	0.671388	−	0.741106i	$-0.265698\pi$
$12$		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	0.233289	−	0.972408i	$-0.425051\pi$
$17$	−0.878443	−	0.319727i	−0.213054	−	0.0775452i	−0.446342	+	0.894862i	$0.647274\pi$
$18$		0			0
$19$	−4.55845	+	1.65914i	−1.04578	+	0.380633i	−0.807068	−	0.590458i	$-0.798947\pi$
$19$	−4.55845	+	1.65914i	−1.04578	+	0.380633i	−0.238711	+	0.971091i	$0.576725\pi$
$20$	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	−0.548014	−	0.836469i	$-0.684616\pi$
$23$	−6.11065	−	0.714233i	−1.27416	−	0.148928i	−0.726145	+	0.687542i	$0.758690\pi$
$24$		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	−0.591814	−	0.806075i	$-0.701588\pi$
$29$	−1.60828	+	0.807706i	−0.298649	+	0.149987i	0.293165	+	0.956062i	$0.405292\pi$
$30$		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	−0.0355222	−	0.999369i	$-0.511309\pi$
$41$	5.55820	−	3.65568i	0.868045	−	0.570922i	0.903567	+	0.428447i	$0.140939\pi$
$42$		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	0.918442	−	0.395556i	$-0.129448\pi$
$47$	1.89278	+	2.54245i	0.276091	+	0.370854i	−0.642351	+	0.766411i	$0.722041\pi$
$48$		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	$0.0285221\pi$
$53$	4.18963	+	7.25666i	0.575490	+	0.996779i	−0.420498	+	0.907294i	$0.638145\pi$
$54$		0			0
$55$	4.98301	−	8.63082i	0.671909	−	1.16378i
$56$	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	$0.198793\pi$
$59$	−1.44287	+	4.81952i	−0.187846	+	0.627448i	−0.999086	+	0.0427359i	$0.986393\pi$
$60$		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	$0.235433\pi$
$71$	2.31784	+	13.1452i	0.275078	+	1.56004i	−0.463638	+	0.886025i	$0.653456\pi$
$72$		0			0
$73$	−1.17142	+	6.64347i	−0.137105	+	0.777560i	0.836266	+	0.548324i	$0.184734\pi$
$73$	−1.17142	+	6.64347i	−0.137105	+	0.777560i	−0.973371	+	0.229236i	$0.926377\pi$
$74$	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	0.371555	−	0.928411i	$-0.378825\pi$
$83$	−3.04071	−	1.99991i	−0.333761	−	0.219518i	−0.705316	+	0.708893i	$0.749195\pi$
$84$		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	$-0.699752\pi$
$89$	2.27781	−	12.9181i	0.241447	−	1.36931i	0.828601	−	0.559839i	$-0.189137\pi$
$90$		0			0
$91$	−2.16732	−	12.2915i	−0.227197	−	1.28850i
$92$	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	−0.758667	−	0.651478i	$-0.774149\pi$
$101$	2.37006	−	5.49442i	0.235830	−	0.546715i	0.994497	+	0.104763i	$0.0334084\pi$
$102$		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	−0.639755	−	0.768579i	$-0.720964\pi$
$107$	3.57628	−	6.19429i	0.345732	−	0.598825i	0.985486	+	0.169754i	$0.0542974\pi$
$108$		0			0
$109$	−5.68613	−	9.84867i	−0.544633	−	0.943332i	−0.998630	−	0.0523287i	$-0.983336\pi$
$109$	−5.68613	−	9.84867i	−0.544633	−	0.943332i	0.453997	−	0.891003i	$-0.349998\pi$
$110$	−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	0.0447643	−	0.998998i	$-0.485746\pi$
$113$	5.66711	−	1.34313i	0.533116	−	0.126351i	0.488352	+	0.872647i	$0.337598\pi$
$114$		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	−0.574994	−	0.818158i	$-0.694996\pi$
$131$	4.27722	−	5.74530i	0.373702	−	0.501969i	0.948697	+	0.316188i	$0.102403\pi$
$132$		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	$0.138687\pi$
$137$	−0.501738	+	8.61452i	−0.0428664	+	0.735988i	−0.949442	+	0.313944i	$0.898350\pi$
$138$		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	$-0.827376\pi$
$149$	−0.802085	−	13.7713i	−0.0657094	−	1.12819i	0.790807	−	0.612066i	$-0.209661\pi$
$150$		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	$-0.990734\pi$
$167$	−12.5418	−	13.2935i	−0.970513	−	1.02868i	0.0290638	−	0.999578i	$-0.490747\pi$
$168$		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	$0.161762\pi$
$173$	5.40734	+	18.0618i	0.411112	+	1.37321i	−0.462514	+	0.886612i	$0.653052\pi$
$174$		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	−0.0458930	−	0.998946i	$-0.514613\pi$
$179$	−9.67521	−	3.52149i	−0.723159	−	0.263209i	−0.677266	+	0.735738i	$0.736836\pi$
$180$		0			0
$181$	0.770198	−	0.280329i	0.0572484	−	0.0208367i	−0.313237	−	0.949675i	$-0.601414\pi$
$181$	0.770198	−	0.280329i	0.0572484	−	0.0208367i	0.370486	+	0.928838i	$0.379191\pi$
$182$	−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	−0.423893	−	0.905712i	$-0.639337\pi$
$191$	0.683675	−	0.343354i	0.0494690	−	0.0248442i	0.473362	+	0.880868i	$0.343040\pi$
$192$		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	0.611717	−	0.791077i	$-0.290479\pi$
$197$	−0.857832	−	0.719807i	−0.0611180	−	0.0512841i	−0.672835	+	0.739793i	$0.734924\pi$
$198$		0			0
$199$	5.88368	−	4.93699i	0.417083	−	0.349974i	−0.409969	−	0.912099i	$-0.634461\pi$
$199$	5.88368	−	4.93699i	0.417083	−	0.349974i	0.827052	+	0.562125i	$0.190016\pi$
$200$	−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	−0.321024	−	0.947071i	$-0.604027\pi$
$227$	9.68944	−	10.2702i	0.643111	−	0.681658i	0.964135	+	0.265414i	$0.0855085\pi$
$228$		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	0.948941	−	0.315452i	$-0.102156\pi$
$233$	−0.773336	−	4.38581i	−0.0506629	−	0.287324i	−0.999604	+	0.0281287i	$0.991045\pi$
$234$		0			0
$235$	−1.59822	+	9.06397i	−0.104257	+	0.591268i
$236$	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	$0.259464\pi$
$239$	11.5106	+	26.6846i	0.744561	+	1.72609i	0.0587876	+	0.998271i	$0.481277\pi$
$240$		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	$0.203155\pi$
$251$	−2.46091	+	13.9565i	−0.155331	+	0.880926i	−0.958483	+	0.285151i	$0.907956\pi$
$252$		0			0
$253$	3.66665	+	20.7946i	0.230521	+	1.30735i
$254$	−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	−0.0108263	−	0.999941i	$-0.503446\pi$
$257$	−13.1355	−	6.59688i	−0.819367	−	0.411502i	−0.808541	+	0.588440i	$0.799742\pi$
$258$		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	$0.298246\pi$
$263$	−6.49135	+	15.0486i	−0.400274	+	0.927939i	−0.992509	+	0.122174i	$0.961014\pi$
$264$		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	−0.985606	−	0.169057i	$-0.945928\pi$
$269$	−5.68131	+	9.84032i	−0.346396	+	0.599975i	0.639211	+	0.769032i	$0.279261\pi$
$270$		0			0
$271$	−1.38266	−	2.39483i	−0.0839903	−	0.145476i	0.820970	−	0.570971i	$-0.193433\pi$
$271$	−1.38266	−	2.39483i	−0.0839903	−	0.145476i	−0.904961	+	0.425496i	$0.860100\pi$
$272$	1.81339	−	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	−0.0930358	−	0.995663i	$-0.529657\pi$
$281$	−10.4439	−	2.47524i	−0.623028	−	0.147660i	−0.529992	+	0.848002i	$0.677805\pi$
$282$		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	$-0.576006\pi$
$293$	13.0455	−	17.5231i	0.762125	−	1.02371i	0.998643	−	0.0520843i	$-0.0165864\pi$
$294$		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	$0.260576\pi$
$311$	1.57644	+	27.0664i	0.0893915	+	1.53479i	−0.593835	+	0.804587i	$0.702387\pi$
$312$		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	−0.638966	−	0.769235i	$-0.720637\pi$
$317$	−19.2878	+	2.25442i	−1.08331	+	0.126621i	−0.444345	+	0.895856i	$0.646563\pi$
$318$		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	0.794754	−	0.606931i	$-0.207600\pi$
$347$	26.6029	+	3.10943i	1.42812	+	0.166923i	0.633364	+	0.773854i	$0.281674\pi$
$348$		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	0.0780814	−	0.996947i	$-0.475121\pi$
$353$	17.3676	−	8.72232i	0.924383	−	0.464242i	0.846301	+	0.532705i	$0.178824\pi$
$354$		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	0.889308	−	0.457309i	$-0.151187\pi$
$359$	11.2428	+	9.43384i	0.593373	+	0.497899i	−0.295935	+	0.955208i	$0.595631\pi$
$360$		0			0
$361$	3.47185	−	2.91323i	0.182729	−	0.153328i
$362$	−0.452687	−	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	$0.297895\pi$
$383$	−6.74866	+	22.5421i	−0.344840	+	1.15185i	−0.937963	+	0.346735i	$0.887290\pi$
$384$		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	$0.557230\pi$
$389$	−22.6942	+	24.0545i	−1.15064	+	1.21961i	−0.971819	+	0.235730i	$0.924252\pi$
$390$		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	$0.124034\pi$
$401$	11.3452	+	26.3011i	0.566551	+	1.31341i	−0.358486	+	0.933535i	$0.616707\pi$
$402$		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	0.520927	−	0.853601i	$-0.325586\pi$
$419$	3.01535	+	1.51436i	0.147309	+	0.0739816i	−0.373617	+	0.927583i	$0.621883\pi$
$420$		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	$0.456736\pi$
$431$	−16.4068	+	28.4174i	−0.790288	+	1.36882i	−0.925789	+	0.378041i	$0.876598\pi$
$432$		0			0
$433$	6.46122	+	11.1912i	0.310507	+	0.537813i	0.978472	−	0.206379i	$-0.0661680\pi$
$433$	6.46122	+	11.1912i	0.310507	+	0.537813i	−0.667966	+	0.744192i	$0.732835\pi$
$434$	1.07298	−	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	0.927526	−	0.373759i	$-0.121931\pi$
$443$	33.4372	+	7.92477i	1.58865	+	0.376517i	0.661125	+	0.750276i	$0.270079\pi$
$444$		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	−0.267590	−	0.963533i	$-0.586227\pi$
$449$	13.4520	−	11.2876i	0.634838	−	0.532693i	0.902428	+	0.430840i	$0.141783\pi$
$450$		0			0
$451$	−17.4910	−	14.6767i	−0.823617	−	0.691097i
$452$	−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	$-0.824414\pi$
$461$	1.18266	−	20.3054i	0.0550818	−	0.945718i	0.906759	−	0.421650i	$-0.138549\pi$
$462$		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	−0.594140	−	0.804361i	$-0.702508\pi$
$467$	−11.5019	+	4.18635i	−0.532244	+	0.193721i	0.0618958	+	0.998083i	$0.480285\pi$
$468$		0			0
$469$	40.2012	+	14.6320i	1.85632	+	0.675645i
$470$	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	−0.712827	−	0.701340i	$-0.752586\pi$
$479$	−27.2416	+	3.18408i	−1.24470	+	0.145485i	−0.531873	+	0.846824i	$0.678512\pi$
$480$		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	0.719784	−	0.694198i	$-0.244241\pi$
$491$	−0.334399	−	0.354442i	−0.0150912	−	0.0159958i	−0.734875	+	0.678202i	$0.762759\pi$
$492$		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	0.110993	−	0.993821i	$-0.464597\pi$
$503$	−9.93090	−	3.61455i	−0.442797	−	0.161165i	−0.553790	+	0.832656i	$0.686819\pi$
$504$		0			0
$505$	16.3275	−	5.94271i	0.726562	−	0.264447i
$506$	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	−0.161480	−	0.986876i	$-0.551627\pi$
$509$	−12.3227	−	1.44032i	−0.546196	−	0.0638412i	−0.384716	+	0.923035i	$0.625701\pi$
$510$		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	0.890483	−	0.455016i	$-0.150366\pi$
$521$	13.6270	+	11.4344i	0.597011	+	0.500952i	−0.293472	+	0.955968i	$0.594811\pi$
$522$		0			0
$523$	−10.4002	+	8.72680i	−0.454769	+	0.381596i	−0.841202	−	0.540721i	$-0.818151\pi$
$523$	−10.4002	+	8.72680i	−0.454769	+	0.381596i	0.386433	+	0.922317i	$0.373707\pi$
$524$	−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	$-0.951845\pi$
$557$	−2.62356	−	14.8789i	−0.111164	−	0.630441i	0.877415	−	0.479733i	$-0.159266\pi$
$558$		0			0
$559$	1.54866	−	8.78288i	0.0655013	−	0.371476i
$560$	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	0.859335	−	0.511413i	$-0.170878\pi$
$563$	−2.42888	−	5.63077i	−0.102365	−	0.237309i	−0.961700	+	0.274104i	$0.911619\pi$
$564$		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	0.575153	−	0.818046i	$-0.304943\pi$
$569$	1.23600	+	0.812928i	0.0518157	+	0.0340797i	−0.523337	+	0.852126i	$0.675313\pi$
$570$		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	−0.834054	−	0.551683i	$-0.813986\pi$
$587$	3.38197	−	7.84028i	0.139589	−	0.323603i	0.973642	+	0.228080i	$0.0732449\pi$
$588$		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	$-0.529451\pi$
$593$	19.8740	−	34.4227i	0.816125	−	1.41357i	0.908517	−	0.417848i	$-0.137216\pi$
$594$		0			0
$595$	4.24788	+	7.35754i	0.174146	+	0.301630i
$596$	−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	0.195400	−	0.980724i	$-0.437399\pi$
$599$	19.8283	−	4.69940i	0.810164	−	0.192012i	0.614764	+	0.788711i	$0.289251\pi$
$600$		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	−0.998683	−	0.0513013i	$-0.983663\pi$
$617$	−16.4713	+	22.1249i	−0.663112	+	0.890713i	0.335572	+	0.942015i	$0.391071\pi$
$618$		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	−0.296835	−	0.954929i	$-0.595931\pi$
$641$	−9.25236	+	1.08145i	−0.365446	+	0.0427145i	−0.0686116	+	0.997643i	$0.521857\pi$
$642$		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	$-0.331128\pi$
$647$	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	−0.993896	−	0.110323i	$-0.964811\pi$
$653$	−26.7355	−	28.3380i	−1.04624	−	1.10895i	−0.0523464	−	0.998629i	$-0.516670\pi$
$654$		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	$-0.865640\pi$
$659$	−9.63166	−	32.1720i	−0.375196	−	1.25324i	0.537033	−	0.843561i	$-0.319545\pi$
$660$		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	−0.277119	−	0.960836i	$-0.589380\pi$
$677$	8.53705	−	4.28747i	0.328106	−	0.164781i	0.605225	+	0.796055i	$0.293083\pi$
$678$		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	0.00909301	−	0.999959i	$-0.497106\pi$
$683$	−25.4573	−	21.3612i	−0.974095	−	0.817363i	−0.983188	+	0.182596i	$0.941550\pi$
$684$		0			0
$685$	−19.1945	+	16.1061i	−0.733383	+	0.615381i
$686$	−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	$0.0532200\pi$
$701$	16.8694	+	29.2187i	0.637150	+	1.10358i	−0.348906	+	0.937158i	$0.613447\pi$
$702$		0			0
$703$	27.6440	−	47.8808i	1.04261	−	1.80586i
$704$	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	0.996378	−	0.0850387i	$-0.0271014\pi$
$719$	0.831346	+	4.71480i	0.0310040	+	0.175832i	−0.965374	+	0.260871i	$0.915990\pi$
$720$		0			0
$721$	0.961210	−	5.45129i	0.0357973	−	0.203017i
$722$	−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	0.178949	−	0.983858i	$-0.442730\pi$
$743$	−13.7207	−	6.89082i	−0.503365	−	0.252800i	−0.682315	+	0.731059i	$0.739027\pi$
$744$		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	−0.664704	−	0.747107i	$-0.731442\pi$
$761$	−25.4732	+	6.03726i	−0.923403	+	0.218851i	−0.258700	+	0.965958i	$0.583294\pi$
$762$		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	−0.814821	−	0.579713i	$-0.803165\pi$
$773$	−10.7154	+	8.99131i	−0.385407	+	0.323395i	0.429414	+	0.903108i	$0.358720\pi$
$774$		0			0
$775$	1.77672	+	1.49085i	0.0638217	+	0.0535528i
$776$	−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
$783$

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

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