LMFDB - Embedded newform 729.2.g.b.703.4

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			703.4
Character	$\chi$	$=$	729.703
Dual form			729.2.g.b.28.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.652974 - 0.429468i) q^{2} +(-0.550227 - 1.27557i) q^{4} +(-1.01614 - 1.07704i) q^{5} +(3.77556 - 0.441300i) q^{7} +(-0.459961 + 2.60857i) q^{8} +O(q^{10})$	\(q+(-0.652974 - 0.429468i) q^{2} +(-0.550227 - 1.27557i) q^{4} +(-1.01614 - 1.07704i) q^{5} +(3.77556 - 0.441300i) q^{7} +(-0.459961 + 2.60857i) q^{8} +(0.200956 + 1.13968i) q^{10} +(1.44963 + 4.84210i) q^{11} +(0.261201 + 4.48466i) q^{13} +(-2.65487 - 1.33332i) q^{14} +(-0.485993 + 0.515122i) q^{16} +(4.30582 + 1.56719i) q^{17} +(4.19524 - 1.52694i) q^{19} +(-0.814736 + 1.88877i) q^{20} +(1.13295 - 3.78433i) q^{22} +(-3.43157 - 0.401093i) q^{23} +(0.163239 - 2.80270i) q^{25} +(1.75546 - 3.04054i) q^{26} +(-2.64032 - 4.57318i) q^{28} +(-0.583488 + 0.293038i) q^{29} +(0.393020 - 0.527918i) q^{31} +(5.69339 - 1.34936i) q^{32} +(-2.13853 - 2.87254i) q^{34} +(-4.31178 - 3.61801i) q^{35} +(0.766165 - 0.642889i) q^{37} +(-3.39516 - 0.804667i) q^{38} +(3.27692 - 2.15526i) q^{40} +(-0.570482 + 0.375212i) q^{41} +(8.16684 + 1.93558i) q^{43} +(5.37881 - 4.51336i) q^{44} +(2.06847 + 1.73565i) q^{46} +(-4.73832 - 6.36466i) q^{47} +(7.24880 - 1.71800i) q^{49} +(-1.31026 + 1.75998i) q^{50} +(5.57677 - 2.80076i) q^{52} +(2.07469 + 3.59347i) q^{53} +(3.74212 - 6.48154i) q^{55} +(-0.585450 + 10.0518i) q^{56} +(0.506853 + 0.0592426i) q^{58} +(1.51145 - 5.04858i) q^{59} +(-2.68977 + 6.23558i) q^{61} +(-0.483356 + 0.175927i) q^{62} +(-2.96617 - 1.07960i) q^{64} +(4.56474 - 4.83835i) q^{65} +(4.73732 + 2.37917i) q^{67} +(-0.370118 - 6.35468i) q^{68} +(1.26166 + 4.21424i) q^{70} +(1.06500 + 6.03991i) q^{71} +(-0.764322 + 4.33469i) q^{73} +(-0.776385 + 0.0907464i) q^{74} +(-4.25606 - 4.51116i) q^{76} +(7.60998 + 17.6419i) q^{77} +(-9.39300 - 6.17788i) q^{79} +1.04864 q^{80} +0.533651 q^{82} +(1.35486 + 0.891108i) q^{83} +(-2.68737 - 6.23002i) q^{85} +(-4.50147 - 4.77127i) q^{86} +(-13.2977 + 1.55428i) q^{88} +(0.181087 - 1.02699i) q^{89} +(2.96526 + 16.8168i) q^{91} +(1.37652 + 4.59790i) q^{92} +(0.360580 + 6.19091i) q^{94} +(-5.90752 - 2.96687i) q^{95} +(-3.42307 + 3.62824i) q^{97} +(-5.47110 - 1.99132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.652974	−	0.429468i	−0.461722	−	0.303679i	0.297253	−	0.954799i	$-0.403929\pi$
$2$	−0.652974	−	0.429468i	−0.461722	−	0.303679i	−0.758975	+	0.651119i	$0.774300\pi$
$3$		0			0
$3$		0			0
$4$	−0.550227	−	1.27557i	−0.275114	−	0.637785i
$5$	−1.01614	−	1.07704i	−0.454430	−	0.481668i	0.459132	−	0.888368i	$-0.348161\pi$
$5$	−1.01614	−	1.07704i	−0.454430	−	0.481668i	−0.913561	+	0.406701i	$0.866679\pi$
$6$		0			0
$7$	3.77556	−	0.441300i	1.42703	−	0.166796i	0.632753	−	0.774354i	$-0.281925\pi$
$7$	3.77556	−	0.441300i	1.42703	−	0.166796i	0.794275	+	0.607558i	$0.207851\pi$
$8$	−0.459961	+	2.60857i	−0.162621	+	0.922268i
$9$		0			0
$10$	0.200956	+	1.13968i	0.0635478	+	0.360398i
$11$	1.44963	+	4.84210i	0.437079	+	1.45995i	0.838929	+	0.544241i	$0.183182\pi$
$11$	1.44963	+	4.84210i	0.437079	+	1.45995i	−0.401849	+	0.915706i	$0.631632\pi$
$12$		0			0
$13$	0.261201	+	4.48466i	0.0724443	+	1.24382i	0.817149	+	0.576426i	$0.195553\pi$
$13$	0.261201	+	4.48466i	0.0724443	+	1.24382i	−0.744705	+	0.667394i	$0.767410\pi$
$14$	−2.65487	−	1.33332i	−0.709543	−	0.356346i
$15$		0			0
$16$	−0.485993	+	0.515122i	−0.121498	+	0.128781i
$17$	4.30582	+	1.56719i	1.04431	+	0.380099i	0.806514	−	0.591215i	$-0.201352\pi$
$17$	4.30582	+	1.56719i	1.04431	+	0.380099i	0.237800	+	0.971314i	$0.423574\pi$
$18$		0			0
$19$	4.19524	−	1.52694i	0.962455	−	0.350305i	0.187460	−	0.982272i	$-0.439975\pi$
$19$	4.19524	−	1.52694i	0.962455	−	0.350305i	0.774995	+	0.631967i	$0.217752\pi$
$20$	−0.814736	+	1.88877i	−0.182181	+	0.422342i
$21$		0			0
$22$	1.13295	−	3.78433i	0.241547	−	0.806822i
$23$	−3.43157	−	0.401093i	−0.715532	−	0.0836337i	−0.249466	−	0.968384i	$-0.580255\pi$
$23$	−3.43157	−	0.401093i	−0.715532	−	0.0836337i	−0.466066	+	0.884750i	$0.654329\pi$
$24$		0			0
$25$	0.163239	−	2.80270i	0.0326477	−	0.560540i
$26$	1.75546	−	3.04054i	0.344273	−	0.596299i
$27$		0			0
$28$	−2.64032	−	4.57318i	−0.498974	−	0.864249i
$29$	−0.583488	+	0.293038i	−0.108351	+	0.0544159i	−0.502149	−	0.864781i	$-0.667457\pi$
$29$	−0.583488	+	0.293038i	−0.108351	+	0.0544159i	0.393798	+	0.919197i	$0.371161\pi$
$30$		0			0
$31$	0.393020	−	0.527918i	0.0705886	−	0.0948169i	−0.765427	−	0.643523i	$-0.777472\pi$
$31$	0.393020	−	0.527918i	0.0705886	−	0.0948169i	0.836015	+	0.548706i	$0.184879\pi$
$32$	5.69339	−	1.34936i	1.00646	−	0.238535i
$33$		0			0
$34$	−2.13853	−	2.87254i	−0.366755	−	0.492637i
$35$	−4.31178	−	3.61801i	−0.728824	−	0.611556i
$36$		0			0
$37$	0.766165	−	0.642889i	0.125957	−	0.105690i	−0.577633	−	0.816296i	$-0.696024\pi$
$37$	0.766165	−	0.642889i	0.125957	−	0.105690i	0.703590	+	0.710606i	$0.251579\pi$
$38$	−3.39516	−	0.804667i	−0.550767	−	0.130534i
$39$		0			0
$40$	3.27692	−	2.15526i	0.518126	−	0.340777i
$41$	−0.570482	+	0.375212i	−0.0890943	+	0.0585983i	−0.593274	−	0.805000i	$-0.702165\pi$
$41$	−0.570482	+	0.375212i	−0.0890943	+	0.0585983i	0.504180	+	0.863598i	$0.331795\pi$
$42$		0			0
$43$	8.16684	+	1.93558i	1.24543	+	0.295173i	0.799922	−	0.600104i	$-0.204874\pi$
$43$	8.16684	+	1.93558i	1.24543	+	0.295173i	0.445510	+	0.895277i	$0.353022\pi$
$44$	5.37881	−	4.51336i	0.810886	−	0.680414i
$45$		0			0
$46$	2.06847	+	1.73565i	0.304979	+	0.255908i
$47$	−4.73832	−	6.36466i	−0.691155	−	0.928382i	0.308585	−	0.951197i	$-0.400145\pi$
$47$	−4.73832	−	6.36466i	−0.691155	−	0.928382i	−0.999740	+	0.0228150i	$0.992737\pi$
$48$		0			0
$49$	7.24880	−	1.71800i	1.03554	−	0.245428i
$50$	−1.31026	+	1.75998i	−0.185299	+	0.248899i
$51$		0			0
$52$	5.57677	−	2.80076i	0.773359	−	0.388396i
$53$	2.07469	+	3.59347i	0.284981	+	0.493601i	0.972605	−	0.232466i	$-0.0746794\pi$
$53$	2.07469	+	3.59347i	0.284981	+	0.493601i	−0.687624	+	0.726067i	$0.741346\pi$
$54$		0			0
$55$	3.74212	−	6.48154i	0.504587	−	0.873971i
$56$	−0.585450	+	10.0518i	−0.0782340	+	1.34323i
$57$		0			0
$58$	0.506853	+	0.0592426i	0.0665530	+	0.00777893i
$59$	1.51145	−	5.04858i	0.196773	−	0.657269i	−0.801471	−	0.598034i	$-0.795949\pi$
$59$	1.51145	−	5.04858i	0.196773	−	0.657269i	0.998244	−	0.0592349i	$-0.0188661\pi$
$60$		0			0
$61$	−2.68977	+	6.23558i	−0.344389	+	0.798384i	0.654707	+	0.755883i	$0.272792\pi$
$61$	−2.68977	+	6.23558i	−0.344389	+	0.798384i	−0.999096	+	0.0425013i	$0.986467\pi$
$62$	−0.483356	+	0.175927i	−0.0613862	+	0.0223428i
$63$		0			0
$64$	−2.96617	−	1.07960i	−0.370771	−	0.134950i
$65$	4.56474	−	4.83835i	0.566187	−	0.600123i
$66$		0			0
$67$	4.73732	+	2.37917i	0.578756	+	0.290662i	0.713995	−	0.700151i	$-0.246884\pi$
$67$	4.73732	+	2.37917i	0.578756	+	0.290662i	−0.135239	+	0.990813i	$0.543180\pi$
$68$	−0.370118	−	6.35468i	−0.0448834	−	0.770618i
$69$		0			0
$70$	1.26166	+	4.21424i	0.150797	+	0.503698i
$71$	1.06500	+	6.03991i	0.126392	+	0.716805i	0.980471	+	0.196662i	$0.0630103\pi$
$71$	1.06500	+	6.03991i	0.126392	+	0.716805i	−0.854079	+	0.520143i	$0.825879\pi$
$72$		0			0
$73$	−0.764322	+	4.33469i	−0.0894571	+	0.507337i	0.906848	+	0.421457i	$0.138481\pi$
$73$	−0.764322	+	4.33469i	−0.0894571	+	0.507337i	−0.996306	+	0.0858796i	$0.972630\pi$
$74$	−0.776385	+	0.0907464i	−0.0902530	+	0.0105491i
$75$		0			0
$76$	−4.25606	−	4.51116i	−0.488204	−	0.517466i
$77$	7.60998	+	17.6419i	0.867237	+	2.01048i
$78$		0			0
$79$	−9.39300	−	6.17788i	−1.05680	−	0.695065i	−0.102744	−	0.994708i	$-0.532762\pi$
$79$	−9.39300	−	6.17788i	−1.05680	−	0.695065i	−0.954052	+	0.299643i	$0.903133\pi$
$80$	1.04864			0.117242
$81$		0			0
$82$	0.533651			0.0589319
$83$	1.35486	+	0.891108i	0.148716	+	0.0978119i	0.621686	−	0.783266i	$-0.286448\pi$
$83$	1.35486	+	0.891108i	0.148716	+	0.0978119i	−0.472971	+	0.881078i	$0.656818\pi$
$84$		0			0
$85$	−2.68737	−	6.23002i	−0.291486	−	0.675741i
$86$	−4.50147	−	4.77127i	−0.485406	−	0.514500i
$87$		0			0
$88$	−13.2977	+	1.55428i	−1.41754	+	0.165687i
$89$	0.181087	−	1.02699i	0.0191952	−	0.108861i	−0.973705	−	0.227813i	$-0.926842\pi$
$89$	0.181087	−	1.02699i	0.0191952	−	0.108861i	0.992900	+	0.118952i	$0.0379535\pi$
$90$		0			0
$91$	2.96526	+	16.8168i	0.310844	+	1.76288i
$92$	1.37652	+	4.59790i	0.143512	+	0.479364i
$93$		0			0
$94$	0.360580	+	6.19091i	0.0371909	+	0.638544i
$95$	−5.90752	−	2.96687i	−0.606099	−	0.304394i
$96$		0			0
$97$	−3.42307	+	3.62824i	−0.347560	+	0.368392i	−0.877445	−	0.479677i	$-0.840754\pi$
$97$	−3.42307	+	3.62824i	−0.347560	+	0.368392i	0.529885	+	0.848070i	$0.322235\pi$
$98$	−5.47110	−	1.99132i	−0.552664	−	0.201153i
$99$		0			0
$100$	−3.66486	+	1.33390i	−0.366486	+	0.133390i
$101$	3.79067	−	8.78777i	0.377186	−	0.874416i	−0.618854	−	0.785506i	$-0.712403\pi$
$101$	3.79067	−	8.78777i	0.377186	−	0.874416i	0.996040	−	0.0889095i	$-0.0283382\pi$
$102$		0			0
$103$	−0.933584	+	3.11839i	−0.0919888	+	0.307264i	−0.991585	−	0.129459i	$-0.958676\pi$
$103$	−0.933584	+	3.11839i	−0.0919888	+	0.307264i	0.899596	+	0.436723i	$0.143861\pi$
$104$	−11.8187	−	1.38140i	−1.15892	−	0.135458i
$105$		0			0
$106$	0.188560	−	3.23746i	0.0183146	−	0.314450i
$107$	8.40680	−	14.5610i	0.812716	−	1.40767i	−0.0982402	−	0.995163i	$-0.531321\pi$
$107$	8.40680	−	14.5610i	0.812716	−	1.40767i	0.910956	−	0.412503i	$-0.135345\pi$
$108$		0			0
$109$	−3.81772	−	6.61249i	−0.365671	−	0.633361i	0.623212	−	0.782053i	$-0.285827\pi$
$109$	−3.81772	−	6.61249i	−0.365671	−	0.633361i	−0.988884	+	0.148691i	$0.952494\pi$
$110$	−5.22712	+	2.62516i	−0.498386	+	0.250299i
$111$		0			0
$112$	−1.60757	+	2.15934i	−0.151901	+	0.204039i
$113$	9.74930	−	2.31063i	0.917137	−	0.217365i	0.255168	−	0.966897i	$-0.417869\pi$
$113$	9.74930	−	2.31063i	0.917137	−	0.217365i	0.661969	+	0.749531i	$0.269721\pi$
$114$		0			0
$115$	3.05495	+	4.10351i	0.284875	+	0.382654i
$116$	0.694842	+	0.583042i	0.0645144	+	0.0541340i
$117$		0			0
$118$	−3.15514	+	2.64747i	−0.290454	+	0.243720i
$119$	16.9485	+	4.01686i	1.55366	+	0.368225i
$120$		0			0
$121$	−12.1541	+	7.99389i	−1.10492	+	0.726717i
$122$	4.43432	−	2.91650i	0.401465	−	0.264048i
$123$		0			0
$124$	−0.889647	−	0.210850i	−0.0798927	−	0.0189349i
$125$	−8.85601	+	7.43107i	−0.792105	+	0.664655i
$126$		0			0
$127$	2.97665	+	2.49770i	0.264135	+	0.221635i	0.765230	−	0.643757i	$-0.222625\pi$
$127$	2.97665	+	2.49770i	0.264135	+	0.221635i	−0.501096	+	0.865392i	$0.667070\pi$
$128$	−5.51490	−	7.40779i	−0.487453	−	0.654763i
$129$		0			0
$130$	−5.05857	+	1.19890i	−0.443666	+	0.105151i
$131$	9.94222	−	13.3547i	0.868656	−	1.16681i	−0.116165	−	0.993230i	$-0.537060\pi$
$131$	9.94222	−	13.3547i	0.868656	−	1.16681i	0.984820	−	0.173577i	$-0.0555325\pi$
$132$		0			0
$133$	15.1656	−	7.61643i	1.31502	−	0.660428i
$134$	−2.07157	−	3.58807i	−0.178956	−	0.309962i
$135$		0			0
$136$	−6.06863	+	10.5112i	−0.520380	+	0.901325i
$137$	0.539345	−	9.26019i	0.0460793	−	0.791152i	−0.893551	−	0.448961i	$-0.851794\pi$
$137$	0.539345	−	9.26019i	0.0460793	−	0.791152i	0.939631	−	0.342190i	$-0.111169\pi$
$138$		0			0
$139$	−15.8135	−	1.84833i	−1.34128	−	0.156774i	−0.585009	−	0.811027i	$-0.698909\pi$
$139$	−15.8135	−	1.84833i	−1.34128	−	0.156774i	−0.756275	+	0.654253i	$0.772983\pi$
$140$	−2.24257	+	7.49071i	−0.189532	+	0.633080i
$141$		0			0
$142$	1.89853	−	4.40128i	0.159321	−	0.369348i
$143$	−21.3365	+	7.76585i	−1.78425	+	0.649413i
$144$		0			0
$145$	0.908517	+	0.330673i	0.0754483	+	0.0274609i
$146$	2.36069	−	2.50218i	0.195372	−	0.207082i
$147$		0			0
$148$	−1.24161	−	0.623562i	−0.102060	−	0.0512565i
$149$	1.35720	+	23.3023i	0.111186	+	1.90900i	0.348085	+	0.937463i	$0.386832\pi$
$149$	1.35720	+	23.3023i	0.111186	+	1.90900i	−0.236899	+	0.971534i	$0.576131\pi$
$150$		0			0
$151$	0.668852	+	2.23412i	0.0544304	+	0.181810i	0.980882	−	0.194604i	$-0.0623422\pi$
$151$	0.668852	+	2.23412i	0.0544304	+	0.181810i	−0.926452	+	0.376414i	$0.877157\pi$
$152$	2.05349	+	11.6459i	0.166560	+	0.944608i
$153$		0			0
$154$	2.60751	−	14.7879i	0.210119	−	1.19165i
$155$	−0.967952	+	0.113137i	−0.0777478	+	0.00908741i
$156$		0			0
$157$	13.5075	+	14.3171i	1.07801	+	1.14263i	0.989199	+	0.146579i	$0.0468263\pi$
$157$	13.5075	+	14.3171i	1.07801	+	1.14263i	0.0888142	+	0.996048i	$0.471692\pi$
$158$	3.48019	+	8.06798i	0.276869	+	0.641854i
$159$		0			0
$160$	−7.23857	−	4.76088i	−0.572259	−	0.376381i
$161$	−13.1331			−1.03503
$162$		0			0
$163$	−17.6622			−1.38341			−0.691707	−	0.722179i	$-0.743141\pi$
$163$	−17.6622			−1.38341			−0.691707	+	0.722179i	$0.743141\pi$
$164$	0.792504	+	0.521238i	0.0618842	+	0.0407018i
$165$		0			0
$166$	−0.501989	−	1.16374i	−0.0389619	−	0.0903238i
$167$	2.32646	+	2.46590i	0.180027	+	0.190817i	0.811102	−	0.584904i	$-0.198868\pi$
$167$	2.32646	+	2.46590i	0.180027	+	0.190817i	−0.631076	+	0.775721i	$0.717386\pi$
$168$		0			0
$169$	−7.13182	+	0.833590i	−0.548601	+	0.0641223i
$170$	−0.920811	+	5.22218i	−0.0706230	+	0.400523i
$171$		0			0
$172$	−2.02465	−	11.4824i	−0.154378	−	0.875524i
$173$	−5.35719	−	17.8943i	−0.407300	−	1.36048i	−0.878201	−	0.478291i	$-0.841256\pi$
$173$	−5.35719	−	17.8943i	−0.407300	−	1.36048i	0.470901	−	0.882186i	$-0.343929\pi$
$174$		0			0
$175$	−0.620513	−	10.6538i	−0.0469064	−	0.805351i
$176$	−3.19878	−	1.60649i	−0.241117	−	0.121094i
$177$		0			0
$178$	−0.559306	+	0.592829i	−0.0419217	+	0.0444344i
$179$	11.1678	+	4.06476i	0.834723	+	0.303814i	0.723796	−	0.690014i	$-0.242396\pi$
$179$	11.1678	+	4.06476i	0.834723	+	0.303814i	0.110927	+	0.993829i	$0.464618\pi$
$180$		0			0
$181$	14.8329	−	5.39873i	1.10252	−	0.401284i	0.274275	−	0.961651i	$-0.411562\pi$
$181$	14.8329	−	5.39873i	1.10252	−	0.401284i	0.828244	+	0.560367i	$0.189340\pi$
$182$	5.28604	−	12.2544i	0.391828	−	0.908358i
$183$		0			0
$184$	2.62467	−	8.76699i	0.193493	−	0.646311i
$185$	−1.47095	−	0.171929i	−0.108146	−	0.0126405i
$186$		0			0
$187$	−1.34665	+	23.1210i	−0.0984765	+	1.69078i
$188$	−5.51142	+	9.54607i	−0.401962	+	0.696219i
$189$		0			0
$190$	2.58328	+	4.47437i	0.187411	+	0.324605i
$191$	−5.15323	+	2.58805i	−0.372875	+	0.187265i	−0.625361	−	0.780336i	$-0.715048\pi$
$191$	−5.15323	+	2.58805i	−0.372875	+	0.187265i	0.252486	+	0.967601i	$0.418752\pi$
$192$		0			0
$193$	0.104955	−	0.140979i	0.00755483	−	0.0101479i	−0.798330	−	0.602221i	$-0.794283\pi$
$193$	0.104955	−	0.140979i	0.00755483	−	0.0101479i	0.805885	+	0.592073i	$0.201690\pi$
$194$	3.79339	−	0.899050i	0.272349	−	0.0645480i
$195$		0			0
$196$	−6.17991	−	8.30106i	−0.441422	−	0.592933i
$197$	−8.59155	−	7.20917i	−0.612123	−	0.513632i	0.283194	−	0.959063i	$-0.408606\pi$
$197$	−8.59155	−	7.20917i	−0.612123	−	0.513632i	−0.895316	+	0.445431i	$0.853050\pi$
$198$		0			0
$199$	−15.6873	+	13.1632i	−1.11204	+	0.933114i	−0.998175	−	0.0603824i	$-0.980768\pi$
$199$	−15.6873	+	13.1632i	−1.11204	+	0.933114i	−0.113866	+	0.993496i	$0.536324\pi$
$200$	7.23595	+	1.71495i	0.511659	+	0.121265i
$201$		0			0
$202$	−6.24927	+	4.11021i	−0.439697	+	0.289193i
$203$	−2.07367	+	1.36388i	−0.145543	+	0.0957254i
$204$		0			0
$205$	0.983806	+	0.233166i	0.0687120	+	0.0162850i
$206$	1.94885	−	1.63528i	0.135783	−	0.113935i
$207$		0			0
$208$	−2.43709	−	2.04496i	−0.168982	−	0.141792i
$209$	13.4752	+	18.1003i	0.932096	+	1.25202i
$210$		0			0
$211$	1.15927	−	0.274753i	0.0798076	−	0.0189147i	−0.190518	−	0.981684i	$-0.561017\pi$
$211$	1.15927	−	0.274753i	0.0798076	−	0.0189147i	0.270326	+	0.962769i	$0.412869\pi$
$212$	3.44217	−	4.62364i	0.236409	−	0.317553i
$213$		0			0
$214$	−11.7429	+	5.89751i	−0.802728	+	0.403145i
$215$	−6.21393	−	10.7628i	−0.423786	−	0.734019i
$216$		0			0
$217$	1.25090	−	2.16663i	0.0849168	−	0.147080i
$218$	−0.346977	+	5.95737i	−0.0235003	+	0.403484i
$219$		0			0
$220$	−10.3267	−	1.20702i	−0.696224	−	0.0813769i
$221$	−5.90362	+	19.7195i	−0.397120	+	1.32647i
$222$		0			0
$223$	−5.90154	+	13.6813i	−0.395197	+	0.916169i	0.598190	+	0.801354i	$0.295887\pi$
$223$	−5.90154	+	13.6813i	−0.395197	+	0.916169i	−0.993387	+	0.114815i	$0.963373\pi$
$224$	20.9003	−	7.60707i	1.39646	−	0.508269i
$225$		0			0
$226$	−7.35838	−	2.67823i	−0.489472	−	0.178153i
$227$	−16.8807	+	17.8925i	−1.12041	+	1.18757i	−0.140095	+	0.990138i	$0.544741\pi$
$227$	−16.8807	+	17.8925i	−1.12041	+	1.18757i	−0.980317	+	0.197430i	$0.936741\pi$
$228$		0			0
$229$	1.36456	+	0.685307i	0.0901726	+	0.0452864i	0.493314	−	0.869851i	$-0.335785\pi$
$229$	1.36456	+	0.685307i	0.0901726	+	0.0452864i	−0.403141	+	0.915138i	$0.632082\pi$
$230$	−0.232477	−	3.99148i	−0.0153291	−	0.263191i
$231$		0			0
$232$	−0.496029	−	1.65685i	−0.0325659	−	0.108778i
$233$	−2.44148	−	13.8463i	−0.159946	−	0.907101i	−0.954123	−	0.299414i	$-0.903209\pi$
$233$	−2.44148	−	13.8463i	−0.159946	−	0.907101i	0.794177	−	0.607687i	$-0.207902\pi$
$234$		0			0
$235$	−2.04023	+	11.5707i	−0.133090	+	0.754791i
$236$	−7.27145	+	0.849911i	−0.473331	+	0.0553245i
$237$		0			0
$238$	−9.34179	−	9.90172i	−0.605539	−	0.641833i
$239$	9.07711	+	21.0431i	0.587149	+	1.36116i	0.909958	+	0.414701i	$0.136114\pi$
$239$	9.07711	+	21.0431i	0.587149	+	1.36116i	−0.322809	+	0.946464i	$0.604627\pi$
$240$		0			0
$241$	5.90585	+	3.88434i	0.380429	+	0.250212i	0.725293	−	0.688441i	$-0.241704\pi$
$241$	5.90585	+	3.88434i	0.380429	+	0.250212i	−0.344864	+	0.938653i	$0.612075\pi$
$242$	11.3694			0.730855
$243$		0			0
$244$	9.43390			0.603943
$245$	−9.21612	−	6.06153i	−0.588796	−	0.387257i
$246$		0			0
$247$	7.94362	+	18.4154i	0.505441	+	1.17174i
$248$	1.19634	+	1.26804i	0.0759674	+	0.0805207i
$249$		0			0
$250$	8.97414	−	1.04893i	0.567575	−	0.0663400i
$251$	−0.0115419	+	0.0654574i	−0.000728518	+	0.00413163i	−0.985170	−	0.171582i	$-0.945112\pi$
$251$	−0.0115419	+	0.0654574i	−0.000728518	+	0.00413163i	0.984441	+	0.175714i	$0.0562233\pi$
$252$		0			0
$253$	−3.03237	−	17.1974i	−0.190644	−	1.08119i
$254$	−0.870990	−	2.90931i	−0.0546508	−	0.182546i
$255$		0			0
$256$	0.786748	+	13.5079i	0.0491718	+	0.844246i
$257$	−17.2862	−	8.68143i	−1.07828	−	0.541533i	−0.181221	−	0.983442i	$-0.558005\pi$
$257$	−17.2862	−	8.68143i	−1.07828	−	0.541533i	−0.897060	+	0.441909i	$0.854301\pi$
$258$		0			0
$259$	2.60900	−	2.76537i	0.162115	−	0.171832i
$260$	−8.68330	−	3.16046i	−0.538515	−	0.196003i
$261$		0			0
$262$	−12.2274	+	4.45042i	−0.755413	+	0.274948i
$263$	−5.96501	+	13.8284i	−0.367818	+	0.852698i	0.629324	+	0.777143i	$0.283332\pi$
$263$	−5.96501	+	13.8284i	−0.367818	+	0.852698i	−0.997142	+	0.0755547i	$0.975927\pi$
$264$		0			0
$265$	1.76215	−	5.88599i	0.108248	−	0.361573i
$266$	−13.1737	−	1.53979i	−0.807732	−	0.0944104i
$267$		0			0
$268$	0.428198	−	7.35188i	0.0261564	−	0.449087i
$269$	−5.86823	+	10.1641i	−0.357792	+	0.619715i	−0.987592	−	0.157043i	$-0.949804\pi$
$269$	−5.86823	+	10.1641i	−0.357792	+	0.619715i	0.629799	+	0.776758i	$0.283137\pi$
$270$		0			0
$271$	1.44013	+	2.49438i	0.0874817	+	0.151523i	0.906446	−	0.422322i	$-0.138785\pi$
$271$	1.44013	+	2.49438i	0.0874817	+	0.151523i	−0.818964	+	0.573844i	$0.805451\pi$
$272$	−2.89989	+	1.45638i	−0.175832	+	0.0883060i
$273$		0			0
$274$	−4.32913	+	5.81503i	−0.261532	+	0.351299i
$275$	13.8076	−	3.27246i	0.832628	−	0.197337i
$276$		0			0
$277$	−1.37408	−	1.84571i	−0.0825603	−	0.110898i	0.758924	−	0.651179i	$-0.225725\pi$
$277$	−1.37408	−	1.84571i	−0.0825603	−	0.110898i	−0.841485	+	0.540281i	$0.818318\pi$
$278$	9.53200	+	7.99830i	0.571692	+	0.479706i
$279$		0			0
$280$	11.4211	−	9.58343i	0.682540	−	0.572719i
$281$	−6.17447	−	1.46338i	−0.368338	−	0.0872977i	0.0422786	−	0.999106i	$-0.486538\pi$
$281$	−6.17447	−	1.46338i	−0.368338	−	0.0872977i	−0.410616	+	0.911808i	$0.634686\pi$
$282$		0			0
$283$	12.2665	−	8.06777i	0.729165	−	0.479579i	−0.129848	−	0.991534i	$-0.541449\pi$
$283$	12.2665	−	8.06777i	0.729165	−	0.479579i	0.859012	+	0.511955i	$0.171078\pi$
$284$	7.11834	−	4.68180i	0.422396	−	0.277814i
$285$		0			0
$286$	17.2674	+	4.09244i	1.02104	+	0.241991i
$287$	−1.98831	+	1.66839i	−0.117366	+	0.0984819i
$288$		0			0
$289$	3.06122	+	2.56867i	0.180072	+	0.151098i
$290$	−0.451224	−	0.606100i	−0.0264968	−	0.0355914i
$291$		0			0
$292$	5.94975	−	1.41012i	0.348183	−	0.0825208i
$293$	15.1411	−	20.3380i	0.884553	−	1.18816i	−0.0966764	−	0.995316i	$-0.530821\pi$
$293$	15.1411	−	20.3380i	0.884553	−	1.18816i	0.981229	−	0.192845i	$-0.0617714\pi$
$294$		0			0
$295$	−6.97336	+	3.50215i	−0.406005	+	0.203903i
$296$	1.32461	+	2.29430i	0.0769916	+	0.133353i
$297$		0			0
$298$	9.12136	−	15.7987i	0.528386	−	0.915191i
$299$	0.902433	−	15.4942i	0.0521891	−	0.896051i
$300$		0			0
$301$	31.6886	+	3.70386i	1.82650	+	0.213487i
$302$	0.522740	−	1.74607i	0.0300803	−	0.100475i
$303$		0			0
$304$	−1.25230	+	2.90315i	−0.0718241	+	0.166507i
$305$	9.44914	−	3.43921i	0.541056	−	0.196928i
$306$		0			0
$307$	11.4486	+	4.16694i	0.653405	+	0.237820i	0.647386	−	0.762162i	$-0.275862\pi$
$307$	11.4486	+	4.16694i	0.653405	+	0.237820i	0.00601852	+	0.999982i	$0.498084\pi$
$308$	18.3163	−	19.4141i	1.04367	−	1.10622i
$309$		0			0
$310$	0.680636	+	0.341828i	0.0386575	+	0.0194145i
$311$	−1.46151	−	25.0931i	−0.0828745	−	1.42290i	−0.741764	−	0.670661i	$-0.766011\pi$
$311$	−1.46151	−	25.0931i	−0.0828745	−	1.42290i	0.658890	−	0.752239i	$-0.271026\pi$
$312$		0			0
$313$	−8.47873	−	28.3209i	−0.479246	−	1.60079i	−0.766034	−	0.642800i	$-0.777773\pi$
$313$	−8.47873	−	28.3209i	−0.479246	−	1.60079i	0.286787	−	0.957994i	$-0.407413\pi$
$314$	−2.67130	−	15.1497i	−0.150750	−	0.854947i
$315$		0			0
$316$	−2.71203	+	15.3807i	−0.152563	+	0.865230i
$317$	4.25913	−	0.497821i	0.239217	−	0.0279604i	0.00436034	−	0.999990i	$-0.498612\pi$
$317$	4.25913	−	0.497821i	0.239217	−	0.0279604i	0.234856	+	0.972030i	$0.424538\pi$
$318$		0			0
$319$	−2.26476	−	2.40051i	−0.126802	−	0.134403i
$320$	1.85126	+	4.29170i	0.103489	+	0.239913i
$321$		0			0
$322$	8.57557	+	5.64024i	0.477898	+	0.314318i
$323$	20.4570			1.13826
$324$		0			0
$325$	12.6118			0.699576
$326$	11.5330	+	7.58536i	0.638752	+	0.420114i
$327$		0			0
$328$	−0.716366	−	1.66072i	−0.0395547	−	0.0916981i
$329$	−20.6985	−	21.9392i	−1.14115	−	1.20954i
$330$		0			0
$331$	27.6432	−	3.23102i	1.51941	−	0.177593i	0.684918	−	0.728620i	$-0.259838\pi$
$331$	27.6432	−	3.23102i	1.51941	−	0.177593i	0.834487	+	0.551027i	$0.185764\pi$
$332$	0.391188	−	2.21854i	0.0214692	−	0.121758i
$333$		0			0
$334$	−0.460091	−	2.60930i	−0.0251750	−	0.142775i
$335$	−2.25130	−	7.51986i	−0.123002	−	0.410854i
$336$		0			0
$337$	−1.56420	−	26.8562i	−0.0852071	−	1.46295i	−0.721988	−	0.691905i	$-0.756772\pi$
$337$	−1.56420	−	26.8562i	−0.0852071	−	1.46295i	0.636781	−	0.771045i	$-0.280266\pi$
$338$	5.01489	+	2.51857i	0.272774	+	0.136992i
$339$		0			0
$340$	−6.46816	+	6.85585i	−0.350785	+	0.371811i
$341$	3.12596	+	1.13776i	0.169280	+	0.0616130i
$342$		0			0
$343$	1.60598	−	0.584529i	0.0867148	−	0.0315616i
$344$	−8.80551	+	20.4135i	−0.474761	+	1.10062i
$345$		0			0
$346$	−4.18690	+	13.9852i	−0.225089	+	0.751851i
$347$	−30.2925	−	3.54069i	−1.62619	−	0.190074i	−0.746419	−	0.665476i	$-0.768229\pi$
$347$	−30.2925	−	3.54069i	−1.62619	−	0.190074i	−0.879769	+	0.475402i	$0.842303\pi$
$348$		0			0
$349$	0.463724	−	7.96184i	0.0248226	−	0.426187i	−0.962889	−	0.269898i	$-0.913010\pi$
$349$	0.463724	−	7.96184i	0.0248226	−	0.426187i	0.987711	−	0.156289i	$-0.0499531\pi$
$350$	−4.17028	+	7.22314i	−0.222911	+	0.386093i
$351$		0			0
$352$	14.7870	+	25.6119i	0.788151	+	1.36512i
$353$	19.5082	−	9.79737i	1.03831	−	0.521461i	0.153863	−	0.988092i	$-0.450829\pi$
$353$	19.5082	−	9.79737i	1.03831	−	0.521461i	0.884452	+	0.466631i	$0.154532\pi$
$354$		0			0
$355$	5.42305	−	7.28442i	0.287826	−	0.386617i
$356$	−1.40964	+	0.334091i	−0.0747109	+	0.0177068i
$357$		0			0
$358$	−5.54662	−	7.45040i	−0.293148	−	0.393766i
$359$	13.2606	+	11.1269i	0.699866	+	0.587258i	0.921736	−	0.387819i	$-0.126771\pi$
$359$	13.2606	+	11.1269i	0.699866	+	0.587258i	−0.221869	+	0.975076i	$0.571216\pi$
$360$		0			0
$361$	0.713665	−	0.598836i	0.0375613	−	0.0315177i
$362$	−12.0041	−	2.84502i	−0.630920	−	0.149531i
$363$		0			0
$364$	19.8195	−	13.0355i	1.03882	−	0.683244i
$365$	5.44529	−	3.58142i	0.285020	−	0.187460i
$366$		0			0
$367$	−23.2623	−	5.51327i	−1.21428	−	0.287790i	−0.426926	−	0.904287i	$-0.640403\pi$
$367$	−23.2623	−	5.51327i	−1.21428	−	0.287790i	−0.787358	+	0.616496i	$0.788552\pi$
$368$	1.87433	−	1.57275i	0.0977062	−	0.0819853i
$369$		0			0
$370$	0.886651	+	0.743989i	0.0460948	+	0.0386781i
$371$	9.41892	+	12.6518i	0.489006	+	0.656849i
$372$		0			0
$373$	−11.2201	+	2.65920i	−0.580952	+	0.137688i	−0.510576	−	0.859832i	$-0.670568\pi$
$373$	−11.2201	+	2.65920i	−0.580952	+	0.137688i	−0.0703757	+	0.997521i	$0.522420\pi$
$374$	10.8091	−	14.5191i	0.558923	−	0.750764i
$375$		0			0
$376$	18.7821	−	9.43272i	0.968613	−	0.486456i
$377$	−1.46658	−	2.54020i	−0.0755329	−	0.130827i
$378$		0			0
$379$	−10.3656	+	17.9537i	−0.532443	+	0.922218i	0.466839	+	0.884342i	$0.345393\pi$
$379$	−10.3656	+	17.9537i	−0.532443	+	0.922218i	−0.999282	+	0.0378763i	$0.987941\pi$
$380$	−0.533970	+	9.16791i	−0.0273921	+	0.470304i
$381$		0			0
$382$	4.47641	+	0.523217i	0.229033	+	0.0267701i
$383$	−4.54732	+	15.1891i	−0.232357	+	0.776126i	0.759693	+	0.650282i	$0.225349\pi$
$383$	−4.54732	+	15.1891i	−0.232357	+	0.776126i	−0.992050	+	0.125845i	$0.959836\pi$
$384$		0			0
$385$	11.2683	−	26.1228i	0.574285	−	1.33134i
$386$	−0.129079	+	0.0469808i	−0.00656994	+	0.00239126i
$387$		0			0
$388$	6.51155	+	2.37001i	0.330574	+	0.120319i
$389$	−19.5641	+	20.7367i	−0.991938	+	1.05139i	0.00673888	+	0.999977i	$0.497855\pi$
$389$	−19.5641	+	20.7367i	−0.991938	+	1.05139i	−0.998677	+	0.0514160i	$0.983627\pi$
$390$		0			0
$391$	−14.1471	−	7.10495i	−0.715451	−	0.359313i
$392$	1.14735	+	19.6992i	0.0579498	+	0.994959i
$393$		0			0
$394$	2.51395	+	8.39719i	0.126651	+	0.423044i
$395$	2.89074	+	16.3942i	0.145449	+	0.824882i
$396$		0			0
$397$	5.49087	−	31.1403i	0.275579	−	1.56289i	−0.461538	−	0.887120i	$-0.652702\pi$
$397$	5.49087	−	31.1403i	0.275579	−	1.56289i	0.737117	−	0.675765i	$-0.236187\pi$
$398$	15.8965	−	1.85804i	0.796822	−	0.0931351i
$399$		0			0
$400$	1.36440	+	1.44618i	0.0682200	+	0.0723090i
$401$	−6.75227	−	15.6535i	−0.337192	−	0.781700i	−0.999474	−	0.0324445i	$-0.989671\pi$
$401$	−6.75227	−	15.6535i	−0.337192	−	0.781700i	0.662281	−	0.749255i	$-0.269588\pi$
$402$		0			0
$403$	2.47019	+	1.62467i	0.123049	+	0.0809305i
$404$	−13.2952			−0.661458
$405$		0			0
$406$	1.93980			0.0962705
$407$	4.22358	+	2.77790i	0.209355	+	0.137695i
$408$		0			0
$409$	−9.44133	−	21.8875i	−0.466844	−	1.08227i	−0.975241	−	0.221143i	$-0.929021\pi$
$409$	−9.44133	−	21.8875i	−0.466844	−	1.08227i	0.508397	−	0.861123i	$-0.330238\pi$
$410$	−0.542262	−	0.574764i	−0.0267804	−	0.0283856i
$411$		0			0
$412$	4.49141	−	0.524970i	0.221276	−	0.0258634i
$413$	3.47862	−	19.7282i	0.171172	−	0.970762i
$414$		0			0
$415$	−0.416966	−	2.36473i	−0.0204681	−	0.116080i
$416$	7.53853	+	25.1804i	0.369607	+	1.23457i
$417$		0			0
$418$	−1.02544	−	17.6061i	−0.0501560	−	0.861145i
$419$	14.0624	+	7.06241i	0.686993	+	0.345021i	0.757816	−	0.652468i	$-0.226266\pi$
$419$	14.0624	+	7.06241i	0.686993	+	0.345021i	−0.0708230	+	0.997489i	$0.522563\pi$
$420$		0			0
$421$	16.1664	−	17.1354i	0.787901	−	0.835126i	−0.201628	−	0.979462i	$-0.564623\pi$
$421$	16.1664	−	17.1354i	0.787901	−	0.835126i	0.989529	+	0.144336i	$0.0461046\pi$
$422$	−0.874971	−	0.318464i	−0.0425929	−	0.0155026i
$423$		0			0
$424$	−10.3281	+	3.75912i	−0.501577	+	0.182559i
$425$	5.09524	−	11.8121i	0.247155	−	0.572970i
$426$		0			0
$427$	−7.40361	+	24.7298i	−0.358286	+	1.19676i
$428$	−23.1992	−	2.71160i	−1.12138	−	0.131070i
$429$		0			0
$430$	−0.564759	+	9.69653i	−0.0272351	+	0.467608i
$431$	−0.705848	+	1.22256i	−0.0339995	+	0.0588888i	−0.882524	−	0.470267i	$-0.844158\pi$
$431$	−0.705848	+	1.22256i	−0.0339995	+	0.0588888i	0.848525	+	0.529155i	$0.177491\pi$
$432$		0			0
$433$	−6.50524	−	11.2674i	−0.312622	−	0.541477i	0.666307	−	0.745677i	$-0.267874\pi$
$433$	−6.50524	−	11.2674i	−0.312622	−	0.541477i	−0.978929	+	0.204200i	$0.934541\pi$
$434$	−1.74730	+	0.877528i	−0.0838732	+	0.0421227i
$435$		0			0
$436$	−6.33408	+	8.50814i	−0.303347	+	0.407466i
$437$	−15.0087	+	3.55713i	−0.717964	+	0.170161i
$438$		0			0
$439$	12.3841	+	16.6347i	0.591061	+	0.793933i	0.992538	−	0.121936i	$-0.0389103\pi$
$439$	12.3841	+	16.6347i	0.591061	+	0.793933i	−0.401477	+	0.915869i	$0.631503\pi$
$440$	15.1863	+	12.7428i	0.723979	+	0.607490i
$441$		0			0
$442$	12.3238	−	10.3409i	0.586182	−	0.491865i
$443$	−33.0519	−	7.83344i	−1.57034	−	0.372178i	−0.648955	−	0.760826i	$-0.724794\pi$
$443$	−33.0519	−	7.83344i	−1.57034	−	0.372178i	−0.921386	+	0.388649i	$0.872942\pi$
$444$		0			0
$445$	−1.29012	+	0.848528i	−0.0611578	+	0.0402241i
$446$	9.72924	−	6.39902i	0.460693	−	0.303002i
$447$		0			0
$448$	−11.6754	−	2.76711i	−0.551609	−	0.130734i
$449$	−0.919709	+	0.771727i	−0.0434038	+	0.0364201i	−0.664231	−	0.747527i	$-0.731241\pi$
$449$	−0.919709	+	0.771727i	−0.0434038	+	0.0364201i	0.620828	+	0.783947i	$0.286797\pi$
$450$		0			0
$451$	−2.64380	−	2.21841i	−0.124492	−	0.104461i
$452$	−8.31170	−	11.1645i	−0.390949	−	0.525136i
$453$		0			0
$454$	18.7069	−	4.43362i	0.877959	−	0.208080i
$455$	15.0993	−	20.2819i	0.707866	−	0.950830i
$456$		0			0
$457$	−28.6438	+	14.3855i	−1.33990	+	0.672923i	−0.966959	−	0.254932i	$-0.917947\pi$
$457$	−28.6438	+	14.3855i	−1.33990	+	0.672923i	−0.372941	+	0.927855i	$0.621651\pi$
$458$	−0.596704	−	1.03352i	−0.0278821	−	0.0482933i
$459$		0			0
$460$	3.55340	−	6.15466i	0.165678	−	0.286963i
$461$	0.0195765	−	0.336115i	0.000911768	−	0.0156545i	−0.997822	−	0.0659703i	$-0.978986\pi$
$461$	0.0195765	−	0.336115i	0.000911768	−	0.0156545i	0.998733	+	0.0503158i	$0.0160228\pi$
$462$		0			0
$463$	2.93276	+	0.342791i	0.136297	+	0.0159308i	0.183968	−	0.982932i	$-0.441106\pi$
$463$	2.93276	+	0.342791i	0.136297	+	0.0159308i	−0.0476708	+	0.998863i	$0.515180\pi$
$464$	0.132620	−	0.442982i	0.00615673	−	0.0205649i
$465$		0			0
$466$	−4.35232	+	10.0898i	−0.201617	+	0.467401i
$467$	3.55605	−	1.29430i	0.164554	−	0.0598929i	−0.258429	−	0.966030i	$-0.583205\pi$
$467$	3.55605	−	1.29430i	0.164554	−	0.0598929i	0.422984	+	0.906137i	$0.360983\pi$
$468$		0			0
$469$	18.9360	+	6.89213i	0.874382	+	0.318249i
$470$	6.30147	−	6.67917i	0.290665	−	0.308087i
$471$		0			0
$472$	12.4744	+	6.26486i	0.574179	+	0.288363i
$473$	2.46664	+	42.3505i	0.113416	+	1.94728i
$474$		0			0
$475$	−3.59474	−	12.0073i	−0.164938	−	0.550931i
$476$	−4.20172	−	23.8292i	−0.192586	−	1.09221i
$477$		0			0
$478$	3.11022	−	17.6389i	0.142258	−	0.806785i
$479$	−3.14535	+	0.367638i	−0.143715	+	0.0167978i	−0.187646	−	0.982237i	$-0.560086\pi$
$479$	−3.14535	+	0.367638i	−0.143715	+	0.0167978i	0.0439314	+	0.999035i	$0.486012\pi$
$480$		0			0
$481$	3.08326	+	3.26806i	0.140584	+	0.149011i
$482$	−2.18817	−	5.07274i	−0.0996683	−	0.231057i
$483$		0			0
$484$	16.8843	+	11.1050i	0.767468	+	0.504771i
$485$	7.38607			0.335384
$486$		0			0
$487$	1.22501			0.0555106			0.0277553	−	0.999615i	$-0.491164\pi$
$487$	1.22501			0.0555106			0.0277553	+	0.999615i	$0.491164\pi$
$488$	−15.0287	−	9.88456i	−0.680319	−	0.447453i
$489$		0			0
$490$	3.41465	+	7.91605i	0.154258	+	0.357610i
$491$	−27.8255	−	29.4933i	−1.25575	−	1.33101i	−0.921425	−	0.388556i	$-0.872974\pi$
$491$	−27.8255	−	29.4933i	−1.25575	−	1.33101i	−0.334323	−	0.942459i	$-0.608507\pi$
$492$		0			0
$493$	−2.97164	+	0.347335i	−0.133836	+	0.0156432i
$494$	2.72183	−	15.4363i	0.122461	−	0.694512i
$495$		0			0
$496$	0.0809373	+	0.459018i	0.00363419	+	0.0206105i
$497$	6.68638	+	22.3341i	0.299925	+	1.00182i
$498$		0			0
$499$	2.39276	+	41.0820i	0.107114	+	1.83908i	0.442224	+	0.896905i	$0.354190\pi$
$499$	2.39276	+	41.0820i	0.107114	+	1.83908i	−0.335109	+	0.942179i	$0.608773\pi$
$500$	14.3517	+	7.20768i	0.641826	+	0.322337i
$501$		0			0
$502$	0.0356484	−	0.0377851i	0.00159106	−	0.00168643i
$503$	−9.54144	−	3.47280i	−0.425432	−	0.154845i	0.120426	−	0.992722i	$-0.461574\pi$
$503$	−9.54144	−	3.47280i	−0.425432	−	0.154845i	−0.545858	+	0.837878i	$0.683796\pi$
$504$		0			0
$505$	−13.3166	+	4.84686i	−0.592582	+	0.215682i
$506$	−5.40568	+	12.5318i	−0.240312	+	0.557105i
$507$		0			0
$508$	1.54816	−	5.17123i	0.0686887	−	0.229436i
$509$	24.0833	+	2.81493i	1.06747	+	0.124770i	0.631642	−	0.775260i	$-0.282381\pi$
$509$	24.0833	+	2.81493i	1.06747	+	0.124770i	0.435829	+	0.900029i	$0.356455\pi$
$510$		0			0
$511$	−0.972849	+	16.7032i	−0.0430363	+	0.738904i
$512$	−3.94773	+	6.83768i	−0.174467	+	0.302186i
$513$		0			0
$514$	7.55901	+	13.0926i	0.333414	+	0.577490i
$515$	4.30728	−	2.16320i	0.189802	−	0.0953219i
$516$		0			0
$517$	23.9495	−	32.1698i	1.05330	−	1.41483i
$518$	−2.89124	+	0.685237i	−0.127034	+	0.0301076i
$519$		0			0
$520$	10.5215	+	14.1329i	0.461400	+	0.619768i
$521$	4.86477	+	4.08202i	0.213129	+	0.178837i	0.743102	−	0.669178i	$-0.233354\pi$
$521$	4.86477	+	4.08202i	0.213129	+	0.178837i	−0.529973	+	0.848014i	$0.677798\pi$
$522$		0			0
$523$	21.5335	−	18.0688i	0.941595	−	0.790092i	−0.0362674	−	0.999342i	$-0.511547\pi$
$523$	21.5335	−	18.0688i	0.941595	−	0.790092i	0.977862	+	0.209250i	$0.0671024\pi$
$524$	−22.5054	−	5.33387i	−0.983151	−	0.233011i
$525$		0			0
$526$	9.83386	−	6.46783i	0.428777	−	0.282011i
$527$	2.51962	−	1.65718i	0.109756	−	0.0721879i
$528$		0			0
$529$	−10.7652	−	2.55141i	−0.468054	−	0.110931i
$530$	−3.67848	+	3.08661i	−0.159783	+	0.134074i
$531$		0			0
$532$	−18.0598	−	15.1540i	−0.782991	−	0.657008i
$533$	−1.83171	−	2.46041i	−0.0793400	−	0.106572i
$534$		0			0
$535$	−24.2253	+	5.74149i	−1.04735	+	0.248226i
$536$	−8.38522	+	11.2633i	−0.362186	+	0.486501i
$537$		0			0
$538$	8.19694	−	4.11666i	0.353395	−	0.177482i
$539$	18.8268	+	32.6089i	0.810926	+	1.40457i
$540$		0			0
$541$	−1.34390	+	2.32771i	−0.0577788	+	0.100076i	−0.893468	−	0.449127i	$-0.851735\pi$
$541$	−1.34390	+	2.32771i	−0.0577788	+	0.100076i	0.835689	+	0.549203i	$0.185068\pi$
$542$	0.130888	−	2.24725i	0.00562211	−	0.0965279i
$543$		0			0
$544$	26.6294	+	3.11253i	1.14173	+	0.133449i
$545$	−3.24260	+	10.8310i	−0.138898	+	0.463950i
$546$		0			0
$547$	12.9944	−	30.1244i	0.555600	−	1.28802i	−0.376699	−	0.926336i	$-0.622941\pi$
$547$	12.9944	−	30.1244i	0.555600	−	1.28802i	0.932299	−	0.361689i	$-0.117800\pi$
$548$	−12.1088	+	4.40724i	−0.517262	+	0.188268i
$549$		0			0
$550$	−10.4214	−	3.79308i	−0.444370	−	0.161737i
$551$	−2.00042	+	2.12032i	−0.0852207	+	0.0903287i
$552$		0			0
$553$	−38.1901	−	19.1798i	−1.62401	−	0.815608i
$554$	0.104565	+	1.79532i	0.00444256	+	0.0762758i
$555$		0			0
$556$	6.34334	+	21.1882i	0.269018	+	0.898581i
$557$	−1.71906	−	9.74928i	−0.0728390	−	0.413090i	−0.999324	−	0.0367591i	$-0.988297\pi$
$557$	−1.71906	−	9.74928i	−0.0728390	−	0.413090i	0.926485	−	0.376331i	$-0.122815\pi$
$558$		0			0
$559$	−6.54721	+	37.1311i	−0.276917	+	1.57048i
$560$	3.95921	−	0.462766i	0.167307	−	0.0195554i
$561$		0			0
$562$	3.40329	+	3.60728i	0.143559	+	0.152164i
$563$	2.78662	+	6.46011i	0.117442	+	0.272261i	0.966790	−	0.255572i	$-0.0822638\pi$
$563$	2.78662	+	6.46011i	0.117442	+	0.272261i	−0.849348	+	0.527833i	$0.823005\pi$
$564$		0			0
$565$	−12.3953	−	8.15249i	−0.521472	−	0.342978i
$566$	−11.4745			−0.482310
$567$		0			0
$568$	−16.2454			−0.681640
$569$	3.29025	+	2.16403i	0.137935	+	0.0907209i	0.616601	−	0.787276i	$-0.288509\pi$
$569$	3.29025	+	2.16403i	0.137935	+	0.0907209i	−0.478666	+	0.877997i	$0.658880\pi$
$570$		0			0
$571$	10.1268	+	23.4765i	0.423791	+	0.982459i	0.987663	+	0.156596i	$0.0500521\pi$
$571$	10.1268	+	23.4765i	0.423791	+	0.982459i	−0.563871	+	0.825863i	$0.690689\pi$
$572$	21.6458	+	22.9432i	0.905057	+	0.959304i
$573$		0			0
$574$	2.01483	−	0.235500i	0.0840975	−	0.00982958i
$575$	−1.68431	+	9.55219i	−0.0702405	+	0.398354i
$576$		0			0
$577$	0.816045	+	4.62802i	0.0339724	+	0.192667i	0.997071	−	0.0764818i	$-0.0243687\pi$
$577$	0.816045	+	4.62802i	0.0339724	+	0.192667i	−0.963099	+	0.269149i	$0.913258\pi$
$578$	−0.895737	−	2.99197i	−0.0372577	−	0.124450i
$579$		0			0
$580$	−0.0780940	−	1.34082i	−0.00324268	−	0.0556746i
$581$	5.50862	+	2.76653i	0.228536	+	0.114775i
$582$		0			0
$583$	−14.3924	+	15.2551i	−0.596073	+	0.631800i
$584$	−10.9558	−	3.98757i	−0.453353	−	0.165007i
$585$		0			0
$586$	−18.6213	+	6.77759i	−0.769238	+	0.279980i
$587$	−11.0004	+	25.5017i	−0.454034	+	1.05257i	0.525410	+	0.850849i	$0.323912\pi$
$587$	−11.0004	+	25.5017i	−0.454034	+	1.05257i	−0.979443	+	0.201719i	$0.935347\pi$
$588$		0			0
$589$	0.842715	−	2.81486i	0.0347235	−	0.115984i
$590$	6.05748	+	0.708018i	0.249383	+	0.0291487i
$591$		0			0
$592$	−0.0411844	+	0.707108i	−0.00169267	+	0.0290620i
$593$	−7.16631	+	12.4124i	−0.294285	+	0.509717i	−0.974818	−	0.223000i	$-0.928415\pi$
$593$	−7.16631	+	12.4124i	−0.294285	+	0.509717i	0.680533	+	0.732717i	$0.261748\pi$
$594$		0			0
$595$	−12.8956	−	22.3359i	−0.528669	−	0.915682i
$596$	28.9769	−	14.5528i	1.18694	−	0.596104i
$597$		0			0
$598$	−7.24351	+	9.72973i	−0.296209	+	0.397878i
$599$	−26.7617	+	6.34265i	−1.09346	+	0.259154i	−0.737499	−	0.675349i	$-0.763993\pi$
$599$	−26.7617	+	6.34265i	−1.09346	+	0.259154i	−0.355957	+	0.934502i	$0.615845\pi$
$600$		0			0
$601$	11.1968	+	15.0400i	0.456729	+	0.613493i	0.969518	−	0.245022i	$-0.0787951\pi$
$601$	11.1968	+	15.0400i	0.456729	+	0.613493i	−0.512789	+	0.858515i	$0.671388\pi$
$602$	−19.1011	−	16.0277i	−0.778503	−	0.653242i
$603$		0			0
$604$	2.48176	−	2.08244i	0.100981	−	0.0847333i
$605$	20.9600	+	4.96761i	0.852144	+	0.201962i
$606$		0			0
$607$	−22.0641	+	14.5118i	−0.895556	+	0.589016i	−0.911701	−	0.410853i	$-0.865231\pi$
$607$	−22.0641	+	14.5118i	−0.895556	+	0.589016i	0.0161458	+	0.999870i	$0.494860\pi$
$608$	21.8248	−	14.3544i	0.885111	−	0.582146i
$609$		0			0
$610$	−7.64707	−	1.81239i	−0.309621	−	0.0733815i
$611$	27.3057	−	22.9122i	1.10467	−	0.926928i
$612$		0			0
$613$	−26.7821	−	22.4728i	−1.08172	−	0.907670i	−0.0856560	−	0.996325i	$-0.527299\pi$
$613$	−26.7821	−	22.4728i	−1.08172	−	0.907670i	−0.996062	+	0.0886553i	$0.971743\pi$
$614$	−5.68606	−	7.63770i	−0.229471	−	0.308232i
$615$		0			0
$616$	−49.5204	+	11.7365i	−1.99523	+	0.472879i
$617$	4.27053	−	5.73631i	0.171925	−	0.230935i	−0.707806	−	0.706407i	$-0.750315\pi$
$617$	4.27053	−	5.73631i	0.171925	−	0.230935i	0.879731	+	0.475471i	$0.157722\pi$
$618$		0			0
$619$	−16.8196	+	8.44712i	−0.676037	+	0.339518i	−0.753473	−	0.657479i	$-0.771623\pi$
$619$	−16.8196	+	8.44712i	−0.676037	+	0.339518i	0.0774361	+	0.996997i	$0.475327\pi$
$620$	0.676908	+	1.17244i	0.0271853	+	0.0470863i
$621$		0			0
$622$	−9.82235	+	17.0128i	−0.393841	+	0.682152i
$623$	0.230492	−	3.95739i	0.00923446	−	0.158550i
$624$		0			0
$625$	3.06015	+	0.357680i	0.122406	+	0.0143072i
$626$	−6.62654	+	22.1342i	−0.264850	+	0.884660i
$627$		0			0
$628$	10.8303	−	25.1074i	0.432174	−	1.00189i
$629$	4.30649	−	1.56744i	0.171711	−	0.0624978i
$630$		0			0
$631$	−22.0642	−	8.03070i	−0.878361	−	0.319697i	−0.136813	−	0.990597i	$-0.543686\pi$
$631$	−22.0642	−	8.03070i	−0.878361	−	0.319697i	−0.741548	+	0.670900i	$0.765908\pi$
$632$	20.4358	−	21.6607i	0.812893	−	0.861616i
$633$		0			0
$634$	−2.99490	−	1.50410i	−0.118943	−	0.0597353i
$635$	−0.334549	−	5.74398i	−0.0132762	−	0.227943i
$636$		0			0
$637$	9.59802	+	32.0596i	0.380287	+	1.27025i
$638$	0.447890	+	2.54011i	0.0177321	+	0.100564i
$639$		0			0
$640$	−2.37461	+	13.4671i	−0.0938648	+	0.532334i
$641$	−4.32954	+	0.506050i	−0.171006	+	0.0199878i	−0.201165	−	0.979557i	$-0.564473\pi$
$641$	−4.32954	+	0.506050i	−0.171006	+	0.0199878i	0.0301588	+	0.999545i	$0.490399\pi$
$642$		0			0
$643$	−13.0468	−	13.8288i	−0.514516	−	0.545355i	0.417071	−	0.908874i	$-0.363057\pi$
$643$	−13.0468	−	13.8288i	−0.514516	−	0.545355i	−0.931587	+	0.363519i	$0.881575\pi$
$644$	7.22619	+	16.7522i	0.284752	+	0.660129i
$645$		0			0
$646$	−13.3579	−	8.78560i	−0.525558	−	0.345665i
$647$	20.6268			0.810924			0.405462	−	0.914112i	$-0.367111\pi$
$647$	20.6268			0.810924			0.405462	+	0.914112i	$0.367111\pi$
$648$		0			0
$649$	26.6367			1.04558
$650$	−8.23516	−	5.41635i	−0.323010	−	0.212447i
$651$		0			0
$652$	9.71824	+	22.5294i	0.380596	+	0.882320i
$653$	4.11111	+	4.35752i	0.160880	+	0.170523i	0.802799	−	0.596249i	$-0.203343\pi$
$653$	4.11111	+	4.35752i	0.160880	+	0.170523i	−0.641919	+	0.766772i	$0.721862\pi$
$654$		0			0
$655$	−24.4862	+	2.86203i	−0.956756	+	0.111829i
$656$	0.0839701	−	0.476218i	0.00327848	−	0.0185932i
$657$		0			0
$658$	4.09344	+	23.2150i	0.159579	+	0.905016i
$659$	−11.1391	−	37.2073i	−0.433919	−	1.44939i	−0.843506	−	0.537120i	$-0.819512\pi$
$659$	−11.1391	−	37.2073i	−0.433919	−	1.44939i	0.409587	−	0.912271i	$-0.365673\pi$
$660$		0			0
$661$	−1.80224	−	30.9432i	−0.0700989	−	1.20355i	−0.831595	−	0.555382i	$-0.812572\pi$
$661$	−1.80224	−	30.9432i	−0.0700989	−	1.20355i	0.761496	−	0.648169i	$-0.224465\pi$
$662$	−19.4379	−	9.76207i	−0.755474	−	0.379414i
$663$		0			0
$664$	−2.94770	+	3.12438i	−0.114393	+	0.121249i
$665$	−23.6135	−	8.59460i	−0.915691	−	0.333284i
$666$		0			0
$667$	2.11981	−	0.771549i	0.0820795	−	0.0298745i
$668$	1.86535	−	4.32436i	0.0721725	−	0.167315i
$669$		0			0
$670$	−1.75950	+	5.87713i	−0.0679753	+	0.227053i
$671$	−34.0924	−	3.98483i	−1.31612	−	0.153833i
$672$		0			0
$673$	2.24379	−	38.5243i	0.0864916	−	1.48500i	−0.624070	−	0.781368i	$-0.714522\pi$
$673$	2.24379	−	38.5243i	0.0864916	−	1.48500i	0.710562	−	0.703635i	$-0.248441\pi$
$674$	−10.5125	+	18.2082i	−0.404926	+	0.701352i
$675$		0			0
$676$	4.98742	+	8.63847i	0.191824	+	0.332249i
$677$	−3.56442	+	1.79012i	−0.136992	+	0.0688000i	−0.515975	−	0.856604i	$-0.672570\pi$
$677$	−3.56442	+	1.79012i	−0.136992	+	0.0688000i	0.378983	+	0.925404i	$0.376274\pi$
$678$		0			0
$679$	−11.3229	+	15.2093i	−0.434532	+	0.583677i
$680$	17.4875	−	4.14462i	0.670615	−	0.158939i
$681$		0			0
$682$	−1.55254	−	2.08543i	−0.0594499	−	0.0798551i
$683$	−32.2624	−	27.0713i	−1.23449	−	1.03586i	−0.997935	−	0.0642370i	$-0.979539\pi$
$683$	−32.2624	−	27.0713i	−1.23449	−	1.03586i	−0.236551	−	0.971619i	$-0.576017\pi$
$684$		0			0
$685$	−10.5217	+	8.82872i	−0.402012	+	0.337328i
$686$	−1.29970	−	0.308034i	−0.0496227	−	0.0117608i
$687$		0			0
$688$	−4.96609	+	3.26625i	−0.189330	+	0.124524i
$689$	−15.5736	+	10.2429i	−0.593306	+	0.390224i
$690$		0			0
$691$	−8.32013	−	1.97191i	−0.316513	−	0.0750149i	0.0692889	−	0.997597i	$-0.477927\pi$
$691$	−8.32013	−	1.97191i	−0.316513	−	0.0750149i	−0.385802	+	0.922582i	$0.626075\pi$
$692$	−19.8777	+	16.6794i	−0.755638	+	0.634056i
$693$		0			0
$694$	18.2596	+	15.3216i	0.693125	+	0.581601i
$695$	14.0779	+	18.9100i	0.534007	+	0.717296i
$696$		0			0
$697$	−3.04442	+	0.721541i	−0.115316	+	0.0273303i
$698$	−3.72215	+	4.99972i	−0.140885	+	0.189242i
$699$		0			0
$700$	−13.2482	+	6.65352i	−0.500737	+	0.251479i
$701$	0.440975	+	0.763791i	0.0166554	+	0.0288480i	0.874233	−	0.485507i	$-0.161365\pi$
$701$	0.440975	+	0.763791i	0.0166554	+	0.0288480i	−0.857578	+	0.514355i	$0.828032\pi$
$702$		0			0
$703$	2.23259	−	3.86697i	0.0842039	−	0.145845i
$704$	0.927670	−	15.9275i	0.0349629	−	0.600290i
$705$		0			0
$706$	−16.9460	−	1.98070i	−0.637770	−	0.0745446i
$707$	10.4339	−	34.8516i	0.392406	−	1.31073i
$708$		0			0
$709$	−15.9358	+	36.9432i	−0.598480	+	1.38743i	0.302324	+	0.953205i	$0.402238\pi$
$709$	−15.9358	+	36.9432i	−0.598480	+	1.38743i	−0.900803	+	0.434227i	$0.857022\pi$
$710$	−6.66953	+	2.42751i	−0.250303	+	0.0911028i
$711$		0			0
$712$	2.59569	+	0.944754i	0.0972777	+	0.0354062i
$713$	−1.56042	+	1.65395i	−0.0584382	+	0.0619409i
$714$		0			0
$715$	30.0449	+	15.0891i	1.12362	+	0.564301i
$716$	−0.959961	−	16.4819i	−0.0358754	−	0.615957i
$717$		0			0
$718$	−3.88015	−	12.9606i	−0.144806	−	0.483685i
$719$	2.39151	+	13.5629i	0.0891883	+	0.505812i	0.996374	+	0.0850815i	$0.0271151\pi$
$719$	2.39151	+	13.5629i	0.0891883	+	0.505812i	−0.907186	+	0.420730i	$0.861774\pi$
$720$		0			0
$721$	−2.14866	+	12.1857i	−0.0800203	+	0.453817i
$722$	−0.723185	+	0.0845282i	−0.0269142	+	0.00314581i
$723$		0			0
$724$	−15.0479	−	15.9499i	−0.559251	−	0.592772i
$725$	0.726051	+	1.68318i	0.0269649	+	0.0625116i
$726$		0			0
$727$	10.4310	+	6.86056i	0.386864	+	0.254444i	0.728011	−	0.685566i	$-0.240445\pi$
$727$	10.4310	+	6.86056i	0.386864	+	0.254444i	−0.341147	+	0.940010i	$0.610815\pi$
$728$	−45.2317			−1.67640
$729$		0			0
$730$	−5.09374			−0.188528
$731$	32.1315	+	21.1332i	1.18843	+	0.781641i
$732$		0			0
$733$	−10.6438	−	24.6752i	−0.393139	−	0.911398i	−0.993726	−	0.111839i	$-0.964326\pi$
$733$	−10.6438	−	24.6752i	−0.393139	−	0.911398i	0.600587	−	0.799559i	$-0.294933\pi$
$734$	12.8219	+	13.5904i	0.473266	+	0.501632i
$735$		0			0
$736$	−20.0785	+	2.34684i	−0.740103	+	0.0865056i
$737$	−4.65283	+	26.3875i	−0.171389	+	0.971996i
$738$		0			0
$739$	−4.23374	−	24.0107i	−0.155740	−	0.883248i	−0.958106	−	0.286415i	$-0.907536\pi$
$739$	−4.23374	−	24.0107i	−0.155740	−	0.883248i	0.802365	−	0.596833i	$-0.203575\pi$
$740$	0.590047	+	1.97089i	0.0216906	+	0.0724515i
$741$		0			0
$742$	−0.716768	−	12.3064i	−0.0263134	−	0.451783i
$743$	32.2333	+	16.1882i	1.18253	+	0.593887i	0.927782	−	0.373122i	$-0.121713\pi$
$743$	32.2333	+	16.1882i	1.18253	+	0.593887i	0.254743	+	0.967009i	$0.418009\pi$
$744$		0			0
$745$	23.7184	−	25.1401i	0.868975	−	0.921060i
$746$	8.46844	+	3.08226i	0.310052	+	0.112850i
$747$		0			0
$748$	30.2335	−	11.0041i	1.10544	−	0.402349i
$749$	25.3146	−	58.6859i	0.924976	−	2.14434i
$750$		0			0
$751$	0.670091	−	2.23826i	0.0244520	−	0.0816753i	−0.944893	−	0.327380i	$-0.893834\pi$
$751$	0.670091	−	2.23826i	0.0244520	−	0.0816753i	0.969345	+	0.245705i	$0.0790194\pi$
$752$	5.58137	+	0.652369i	0.203532	+	0.0237894i
$753$		0			0
$754$	−0.133292	+	2.28853i	−0.00485421	+	0.0833435i
$755$	1.72660	−	2.99055i	0.0628372	−	0.108837i
$756$		0			0
$757$	8.08646	+	14.0062i	0.293907	+	0.509063i	0.974730	−	0.223386i	$-0.0717109\pi$
$757$	8.08646	+	14.0062i	0.293907	+	0.509063i	−0.680823	+	0.732448i	$0.738378\pi$
$758$	14.4790	−	7.27161i	0.525899	−	0.264117i
$759$		0			0
$760$	10.4565	−	14.0455i	0.379297	−	0.509485i
$761$	44.1342	−	10.4600i	1.59986	−	0.379175i	0.668630	−	0.743595i	$-0.266881\pi$
$761$	44.1342	−	10.4600i	1.59986	−	0.379175i	0.931234	+	0.364421i	$0.118733\pi$
$762$		0			0
$763$	−17.3321	−	23.2811i	−0.627465	−	0.842832i
$764$	6.13669	+	5.14929i	0.222018	+	0.186295i
$765$		0			0
$766$	9.49250	−	7.96515i	0.342978	−	0.287793i
$767$	23.0359	+	5.45962i	0.831779	+	0.197135i
$768$		0			0
$769$	−15.3444	+	10.0922i	−0.553334	+	0.363934i	−0.795173	−	0.606383i	$-0.792620\pi$
$769$	−15.3444	+	10.0922i	−0.553334	+	0.363934i	0.241839	+	0.970316i	$0.422250\pi$
$770$	−18.5768	+	12.2182i	−0.669462	+	0.440312i
$771$		0			0
$772$	−0.237578	−	0.0563069i	−0.00855061	−	0.00202653i
$773$	−22.5821	+	18.9486i	−0.812222	+	0.681536i	−0.951137	−	0.308769i	$-0.900083\pi$
$773$	−22.5821	+	18.9486i	−0.812222	+	0.681536i	0.138915	+	0.990304i	$0.455639\pi$
$774$		0			0
$775$	−1.41544	−	1.18769i	−0.0508441	−	0.0426633i
$776$	−7.89004	−	10.5982i	−0.283236	−	0.380452i
$777$		0			0
$778$	21.6806	−	5.13839i	0.777286	−	0.184220i
$779$	−1.82038	+	2.44520i	−0.0652220	+	0.0876083i
$780$		0			0
$781$	−27.7020	+	13.9125i	−0.991255	+	0.497827i
$782$	6.18635	+	10.7151i	0.221224	+	0.383170i
$783$

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)

\(f(q)\)	\(=\)	\(q+(-0.652974 - 0.429468i) q^{2} +(-0.550227 - 1.27557i) q^{4} +(-1.01614 - 1.07704i) q^{5} +(3.77556 - 0.441300i) q^{7} +(-0.459961 + 2.60857i) q^{8} +O(q^{10})\)	\(q+(-0.652974 - 0.429468i) q^{2} +(-0.550227 - 1.27557i) q^{4} +(-1.01614 - 1.07704i) q^{5} +(3.77556 - 0.441300i) q^{7} +(-0.459961 + 2.60857i) q^{8} +(0.200956 + 1.13968i) q^{10} +(1.44963 + 4.84210i) q^{11} +(0.261201 + 4.48466i) q^{13} +(-2.65487 - 1.33332i) q^{14} +(-0.485993 + 0.515122i) q^{16} +(4.30582 + 1.56719i) q^{17} +(4.19524 - 1.52694i) q^{19} +(-0.814736 + 1.88877i) q^{20} +(1.13295 - 3.78433i) q^{22} +(-3.43157 - 0.401093i) q^{23} +(0.163239 - 2.80270i) q^{25} +(1.75546 - 3.04054i) q^{26} +(-2.64032 - 4.57318i) q^{28} +(-0.583488 + 0.293038i) q^{29} +(0.393020 - 0.527918i) q^{31} +(5.69339 - 1.34936i) q^{32} +(-2.13853 - 2.87254i) q^{34} +(-4.31178 - 3.61801i) q^{35} +(0.766165 - 0.642889i) q^{37} +(-3.39516 - 0.804667i) q^{38} +(3.27692 - 2.15526i) q^{40} +(-0.570482 + 0.375212i) q^{41} +(8.16684 + 1.93558i) q^{43} +(5.37881 - 4.51336i) q^{44} +(2.06847 + 1.73565i) q^{46} +(-4.73832 - 6.36466i) q^{47} +(7.24880 - 1.71800i) q^{49} +(-1.31026 + 1.75998i) q^{50} +(5.57677 - 2.80076i) q^{52} +(2.07469 + 3.59347i) q^{53} +(3.74212 - 6.48154i) q^{55} +(-0.585450 + 10.0518i) q^{56} +(0.506853 + 0.0592426i) q^{58} +(1.51145 - 5.04858i) q^{59} +(-2.68977 + 6.23558i) q^{61} +(-0.483356 + 0.175927i) q^{62} +(-2.96617 - 1.07960i) q^{64} +(4.56474 - 4.83835i) q^{65} +(4.73732 + 2.37917i) q^{67} +(-0.370118 - 6.35468i) q^{68} +(1.26166 + 4.21424i) q^{70} +(1.06500 + 6.03991i) q^{71} +(-0.764322 + 4.33469i) q^{73} +(-0.776385 + 0.0907464i) q^{74} +(-4.25606 - 4.51116i) q^{76} +(7.60998 + 17.6419i) q^{77} +(-9.39300 - 6.17788i) q^{79} +1.04864 q^{80} +0.533651 q^{82} +(1.35486 + 0.891108i) q^{83} +(-2.68737 - 6.23002i) q^{85} +(-4.50147 - 4.77127i) q^{86} +(-13.2977 + 1.55428i) q^{88} +(0.181087 - 1.02699i) q^{89} +(2.96526 + 16.8168i) q^{91} +(1.37652 + 4.59790i) q^{92} +(0.360580 + 6.19091i) q^{94} +(-5.90752 - 2.96687i) q^{95} +(-3.42307 + 3.62824i) q^{97} +(-5.47110 - 1.99132i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 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

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