LMFDB - Embedded newform 729.2.g.b.28.4

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			28.4
Character	$\chi$	$=$	729.28
Dual form			729.2.g.b.703.4

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

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

Coefficient data

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

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

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

$2$	−0.652974	+	0.429468i	−0.461722	+	0.303679i	−0.758975	−	0.651119i	$-0.774300\pi$
$2$	−0.652974	+	0.429468i	−0.461722	+	0.303679i	0.297253	+	0.954799i	$0.403929\pi$
$3$		0			0
$3$		0			0
$4$	−0.550227	+	1.27557i	−0.275114	+	0.637785i
$5$	−1.01614	+	1.07704i	−0.454430	+	0.481668i	−0.913561	−	0.406701i	$-0.866679\pi$
$5$	−1.01614	+	1.07704i	−0.454430	+	0.481668i	0.459132	+	0.888368i	$0.348161\pi$
$6$		0			0
$7$	3.77556	+	0.441300i	1.42703	+	0.166796i	0.794275	−	0.607558i	$-0.207851\pi$
$7$	3.77556	+	0.441300i	1.42703	+	0.166796i	0.632753	+	0.774354i	$0.281925\pi$
$8$	−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	−0.401849	−	0.915706i	$-0.631632\pi$
$11$	1.44963	−	4.84210i	0.437079	−	1.45995i	0.838929	−	0.544241i	$-0.183182\pi$
$12$		0			0
$13$	0.261201	−	4.48466i	0.0724443	−	1.24382i	−0.744705	−	0.667394i	$-0.767410\pi$
$13$	0.261201	−	4.48466i	0.0724443	−	1.24382i	0.817149	−	0.576426i	$-0.195553\pi$
$14$	−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	0.237800	−	0.971314i	$-0.423574\pi$
$17$	4.30582	−	1.56719i	1.04431	−	0.380099i	0.806514	+	0.591215i	$0.201352\pi$
$18$		0			0
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.774995	−	0.631967i	$-0.217752\pi$
$19$	4.19524	+	1.52694i	0.962455	+	0.350305i	0.187460	+	0.982272i	$0.439975\pi$
$20$	−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	−0.466066	−	0.884750i	$-0.654329\pi$
$23$	−3.43157	+	0.401093i	−0.715532	+	0.0836337i	−0.249466	+	0.968384i	$0.580255\pi$
$24$		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	0.393798	−	0.919197i	$-0.371161\pi$
$29$	−0.583488	−	0.293038i	−0.108351	−	0.0544159i	−0.502149	+	0.864781i	$0.667457\pi$
$30$		0			0
$31$	0.393020	+	0.527918i	0.0705886	+	0.0948169i	0.836015	−	0.548706i	$-0.184879\pi$
$31$	0.393020	+	0.527918i	0.0705886	+	0.0948169i	−0.765427	+	0.643523i	$0.777472\pi$
$32$	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	0.703590	−	0.710606i	$-0.251579\pi$
$37$	0.766165	+	0.642889i	0.125957	+	0.105690i	−0.577633	+	0.816296i	$0.696024\pi$
$38$	−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	0.504180	−	0.863598i	$-0.331795\pi$
$41$	−0.570482	−	0.375212i	−0.0890943	−	0.0585983i	−0.593274	+	0.805000i	$0.702165\pi$
$42$		0			0
$43$	8.16684	−	1.93558i	1.24543	−	0.295173i	0.445510	−	0.895277i	$-0.353022\pi$
$43$	8.16684	−	1.93558i	1.24543	−	0.295173i	0.799922	+	0.600104i	$0.204874\pi$
$44$	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	−0.999740	−	0.0228150i	$-0.992737\pi$
$47$	−4.73832	+	6.36466i	−0.691155	+	0.928382i	0.308585	+	0.951197i	$0.400145\pi$
$48$		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	−0.687624	−	0.726067i	$-0.741346\pi$
$53$	2.07469	−	3.59347i	0.284981	−	0.493601i	0.972605	+	0.232466i	$0.0746794\pi$
$54$		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	0.998244	+	0.0592349i	$0.0188661\pi$
$59$	1.51145	+	5.04858i	0.196773	+	0.657269i	−0.801471	+	0.598034i	$0.795949\pi$
$60$		0			0
$61$	−2.68977	−	6.23558i	−0.344389	−	0.798384i	−0.999096	−	0.0425013i	$-0.986467\pi$
$61$	−2.68977	−	6.23558i	−0.344389	−	0.798384i	0.654707	−	0.755883i	$-0.272792\pi$
$62$	−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	−0.135239	−	0.990813i	$-0.543180\pi$
$67$	4.73732	−	2.37917i	0.578756	−	0.290662i	0.713995	+	0.700151i	$0.246884\pi$
$68$	−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	−0.854079	−	0.520143i	$-0.825879\pi$
$71$	1.06500	−	6.03991i	0.126392	−	0.716805i	0.980471	−	0.196662i	$-0.0630103\pi$
$72$		0			0
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	−0.996306	−	0.0858796i	$-0.972630\pi$
$73$	−0.764322	−	4.33469i	−0.0894571	−	0.507337i	0.906848	−	0.421457i	$-0.138481\pi$
$74$	−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	−0.954052	−	0.299643i	$-0.903133\pi$
$79$	−9.39300	+	6.17788i	−1.05680	+	0.695065i	−0.102744	+	0.994708i	$0.532762\pi$
$80$	1.04864			0.117242
$81$		0			0
$82$	0.533651			0.0589319
$83$	1.35486	−	0.891108i	0.148716	−	0.0978119i	−0.472971	−	0.881078i	$-0.656818\pi$
$83$	1.35486	−	0.891108i	0.148716	−	0.0978119i	0.621686	+	0.783266i	$0.286448\pi$
$84$		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	0.992900	−	0.118952i	$-0.0379535\pi$
$89$	0.181087	+	1.02699i	0.0191952	+	0.108861i	−0.973705	+	0.227813i	$0.926842\pi$
$90$		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	0.529885	−	0.848070i	$-0.322235\pi$
$97$	−3.42307	−	3.62824i	−0.347560	−	0.368392i	−0.877445	+	0.479677i	$0.840754\pi$
$98$	−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	0.996040	+	0.0889095i	$0.0283382\pi$
$101$	3.79067	+	8.78777i	0.377186	+	0.874416i	−0.618854	+	0.785506i	$0.712403\pi$
$102$		0			0
$103$	−0.933584	−	3.11839i	−0.0919888	−	0.307264i	0.899596	−	0.436723i	$-0.143861\pi$
$103$	−0.933584	−	3.11839i	−0.0919888	−	0.307264i	−0.991585	+	0.129459i	$0.958676\pi$
$104$	−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	0.910956	+	0.412503i	$0.135345\pi$
$107$	8.40680	+	14.5610i	0.812716	+	1.40767i	−0.0982402	+	0.995163i	$0.531321\pi$
$108$		0			0
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	−0.988884	−	0.148691i	$-0.952494\pi$
$109$	−3.81772	+	6.61249i	−0.365671	+	0.633361i	0.623212	+	0.782053i	$0.285827\pi$
$110$	−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	0.661969	−	0.749531i	$-0.269721\pi$
$113$	9.74930	+	2.31063i	0.917137	+	0.217365i	0.255168	+	0.966897i	$0.417869\pi$
$114$		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	−0.501096	−	0.865392i	$-0.667070\pi$
$127$	2.97665	−	2.49770i	0.264135	−	0.221635i	0.765230	+	0.643757i	$0.222625\pi$
$128$	−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	0.984820	+	0.173577i	$0.0555325\pi$
$131$	9.94222	+	13.3547i	0.868656	+	1.16681i	−0.116165	+	0.993230i	$0.537060\pi$
$132$		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	0.939631	+	0.342190i	$0.111169\pi$
$137$	0.539345	+	9.26019i	0.0460793	+	0.791152i	−0.893551	+	0.448961i	$0.851794\pi$
$138$		0			0
$139$	−15.8135	+	1.84833i	−1.34128	+	0.156774i	−0.756275	−	0.654253i	$-0.772983\pi$
$139$	−15.8135	+	1.84833i	−1.34128	+	0.156774i	−0.585009	+	0.811027i	$0.698909\pi$
$140$	−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	−0.236899	−	0.971534i	$-0.576131\pi$
$149$	1.35720	−	23.3023i	0.111186	−	1.90900i	0.348085	−	0.937463i	$-0.386832\pi$
$150$		0			0
$151$	0.668852	−	2.23412i	0.0544304	−	0.181810i	−0.926452	−	0.376414i	$-0.877157\pi$
$151$	0.668852	−	2.23412i	0.0544304	−	0.181810i	0.980882	+	0.194604i	$0.0623422\pi$
$152$	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	0.0888142	−	0.996048i	$-0.471692\pi$
$157$	13.5075	−	14.3171i	1.07801	−	1.14263i	0.989199	−	0.146579i	$-0.0468263\pi$
$158$	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	−0.631076	−	0.775721i	$-0.717386\pi$
$167$	2.32646	−	2.46590i	0.180027	−	0.190817i	0.811102	+	0.584904i	$0.198868\pi$
$168$		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	0.470901	+	0.882186i	$0.343929\pi$
$173$	−5.35719	+	17.8943i	−0.407300	+	1.36048i	−0.878201	+	0.478291i	$0.841256\pi$
$174$		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	0.110927	−	0.993829i	$-0.464618\pi$
$179$	11.1678	−	4.06476i	0.834723	−	0.303814i	0.723796	+	0.690014i	$0.242396\pi$
$180$		0			0
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.828244	−	0.560367i	$-0.189340\pi$
$181$	14.8329	+	5.39873i	1.10252	+	0.401284i	0.274275	+	0.961651i	$0.411562\pi$
$182$	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	0.252486	−	0.967601i	$-0.418752\pi$
$191$	−5.15323	−	2.58805i	−0.372875	−	0.187265i	−0.625361	+	0.780336i	$0.715048\pi$
$192$		0			0
$193$	0.104955	+	0.140979i	0.00755483	+	0.0101479i	0.805885	−	0.592073i	$-0.201690\pi$
$193$	0.104955	+	0.140979i	0.00755483	+	0.0101479i	−0.798330	+	0.602221i	$0.794283\pi$
$194$	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	−0.895316	−	0.445431i	$-0.853050\pi$
$197$	−8.59155	+	7.20917i	−0.612123	+	0.513632i	0.283194	+	0.959063i	$0.408606\pi$
$198$		0			0
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.113866	−	0.993496i	$-0.536324\pi$
$199$	−15.6873	−	13.1632i	−1.11204	−	0.933114i	−0.998175	+	0.0603824i	$0.980768\pi$
$200$	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	0.270326	−	0.962769i	$-0.412869\pi$
$211$	1.15927	+	0.274753i	0.0798076	+	0.0189147i	−0.190518	+	0.981684i	$0.561017\pi$
$212$	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	−0.993387	−	0.114815i	$-0.963373\pi$
$223$	−5.90154	−	13.6813i	−0.395197	−	0.916169i	0.598190	−	0.801354i	$-0.295887\pi$
$224$	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	−0.980317	−	0.197430i	$-0.936741\pi$
$227$	−16.8807	−	17.8925i	−1.12041	−	1.18757i	−0.140095	−	0.990138i	$-0.544741\pi$
$228$		0			0
$229$	1.36456	−	0.685307i	0.0901726	−	0.0452864i	−0.403141	−	0.915138i	$-0.632082\pi$
$229$	1.36456	−	0.685307i	0.0901726	−	0.0452864i	0.493314	+	0.869851i	$0.335785\pi$
$230$	−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	0.794177	+	0.607687i	$0.207902\pi$
$233$	−2.44148	+	13.8463i	−0.159946	+	0.907101i	−0.954123	+	0.299414i	$0.903209\pi$
$234$		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	−0.322809	−	0.946464i	$-0.604627\pi$
$239$	9.07711	−	21.0431i	0.587149	−	1.36116i	0.909958	−	0.414701i	$-0.136114\pi$
$240$		0			0
$241$	5.90585	−	3.88434i	0.380429	−	0.250212i	−0.344864	−	0.938653i	$-0.612075\pi$
$241$	5.90585	−	3.88434i	0.380429	−	0.250212i	0.725293	+	0.688441i	$0.241704\pi$
$242$	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	0.984441	−	0.175714i	$-0.0562233\pi$
$251$	−0.0115419	−	0.0654574i	−0.000728518	−	0.00413163i	−0.985170	+	0.171582i	$0.945112\pi$
$252$		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	−0.897060	−	0.441909i	$-0.854301\pi$
$257$	−17.2862	+	8.68143i	−1.07828	+	0.541533i	−0.181221	+	0.983442i	$0.558005\pi$
$258$		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	−0.997142	−	0.0755547i	$-0.975927\pi$
$263$	−5.96501	−	13.8284i	−0.367818	−	0.852698i	0.629324	−	0.777143i	$-0.283332\pi$
$264$		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	0.629799	−	0.776758i	$-0.283137\pi$
$269$	−5.86823	−	10.1641i	−0.357792	−	0.619715i	−0.987592	+	0.157043i	$0.949804\pi$
$270$		0			0
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	−0.818964	−	0.573844i	$-0.805451\pi$
$271$	1.44013	−	2.49438i	0.0874817	−	0.151523i	0.906446	+	0.422322i	$0.138785\pi$
$272$	−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	−0.841485	−	0.540281i	$-0.818318\pi$
$277$	−1.37408	+	1.84571i	−0.0825603	+	0.110898i	0.758924	+	0.651179i	$0.225725\pi$
$278$	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	−0.410616	−	0.911808i	$-0.634686\pi$
$281$	−6.17447	+	1.46338i	−0.368338	+	0.0872977i	0.0422786	+	0.999106i	$0.486538\pi$
$282$		0			0
$283$	12.2665	+	8.06777i	0.729165	+	0.479579i	0.859012	−	0.511955i	$-0.171078\pi$
$283$	12.2665	+	8.06777i	0.729165	+	0.479579i	−0.129848	+	0.991534i	$0.541449\pi$
$284$	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	0.981229	+	0.192845i	$0.0617714\pi$
$293$	15.1411	+	20.3380i	0.884553	+	1.18816i	−0.0966764	+	0.995316i	$0.530821\pi$
$294$		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	0.00601852	−	0.999982i	$-0.498084\pi$
$307$	11.4486	−	4.16694i	0.653405	−	0.237820i	0.647386	+	0.762162i	$0.275862\pi$
$308$	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	0.658890	+	0.752239i	$0.271026\pi$
$311$	−1.46151	+	25.0931i	−0.0828745	+	1.42290i	−0.741764	+	0.670661i	$0.766011\pi$
$312$		0			0
$313$	−8.47873	+	28.3209i	−0.479246	+	1.60079i	0.286787	+	0.957994i	$0.407413\pi$
$313$	−8.47873	+	28.3209i	−0.479246	+	1.60079i	−0.766034	+	0.642800i	$0.777773\pi$
$314$	−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	0.234856	−	0.972030i	$-0.424538\pi$
$317$	4.25913	+	0.497821i	0.239217	+	0.0279604i	0.00436034	+	0.999990i	$0.498612\pi$
$318$		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	0.834487	−	0.551027i	$-0.185764\pi$
$331$	27.6432	+	3.23102i	1.51941	+	0.177593i	0.684918	+	0.728620i	$0.259838\pi$
$332$	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	0.636781	+	0.771045i	$0.280266\pi$
$337$	−1.56420	+	26.8562i	−0.0852071	+	1.46295i	−0.721988	+	0.691905i	$0.756772\pi$
$338$	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	−0.879769	−	0.475402i	$-0.842303\pi$
$347$	−30.2925	+	3.54069i	−1.62619	+	0.190074i	−0.746419	+	0.665476i	$0.768229\pi$
$348$		0			0
$349$	0.463724	+	7.96184i	0.0248226	+	0.426187i	0.987711	+	0.156289i	$0.0499531\pi$
$349$	0.463724	+	7.96184i	0.0248226	+	0.426187i	−0.962889	+	0.269898i	$0.913010\pi$
$350$	−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	0.884452	−	0.466631i	$-0.154532\pi$
$353$	19.5082	+	9.79737i	1.03831	+	0.521461i	0.153863	+	0.988092i	$0.450829\pi$
$354$		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	−0.221869	−	0.975076i	$-0.571216\pi$
$359$	13.2606	−	11.1269i	0.699866	−	0.587258i	0.921736	+	0.387819i	$0.126771\pi$
$360$		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	−0.787358	−	0.616496i	$-0.788552\pi$
$367$	−23.2623	+	5.51327i	−1.21428	+	0.287790i	−0.426926	+	0.904287i	$0.640403\pi$
$368$	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	−0.0703757	−	0.997521i	$-0.522420\pi$
$373$	−11.2201	−	2.65920i	−0.580952	−	0.137688i	−0.510576	+	0.859832i	$0.670568\pi$
$374$	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	−0.999282	−	0.0378763i	$-0.987941\pi$
$379$	−10.3656	−	17.9537i	−0.532443	−	0.922218i	0.466839	−	0.884342i	$-0.345393\pi$
$380$	−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	−0.992050	−	0.125845i	$-0.959836\pi$
$383$	−4.54732	−	15.1891i	−0.232357	−	0.776126i	0.759693	−	0.650282i	$-0.225349\pi$
$384$		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	−0.998677	−	0.0514160i	$-0.983627\pi$
$389$	−19.5641	−	20.7367i	−0.991938	−	1.05139i	0.00673888	−	0.999977i	$-0.497855\pi$
$390$		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	0.737117	+	0.675765i	$0.236187\pi$
$397$	5.49087	+	31.1403i	0.275579	+	1.56289i	−0.461538	+	0.887120i	$0.652702\pi$
$398$	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	0.662281	+	0.749255i	$0.269588\pi$
$401$	−6.75227	+	15.6535i	−0.337192	+	0.781700i	−0.999474	+	0.0324445i	$0.989671\pi$
$402$		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	0.508397	+	0.861123i	$0.330238\pi$
$409$	−9.44133	+	21.8875i	−0.466844	+	1.08227i	−0.975241	+	0.221143i	$0.929021\pi$
$410$	−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	−0.0708230	−	0.997489i	$-0.522563\pi$
$419$	14.0624	−	7.06241i	0.686993	−	0.345021i	0.757816	+	0.652468i	$0.226266\pi$
$420$		0			0
$421$	16.1664	+	17.1354i	0.787901	+	0.835126i	0.989529	−	0.144336i	$-0.0461046\pi$
$421$	16.1664	+	17.1354i	0.787901	+	0.835126i	−0.201628	+	0.979462i	$0.564623\pi$
$422$	−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	0.848525	−	0.529155i	$-0.177491\pi$
$431$	−0.705848	−	1.22256i	−0.0339995	−	0.0588888i	−0.882524	+	0.470267i	$0.844158\pi$
$432$		0			0
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	−0.978929	−	0.204200i	$-0.934541\pi$
$433$	−6.50524	+	11.2674i	−0.312622	+	0.541477i	0.666307	+	0.745677i	$0.267874\pi$
$434$	−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	−0.401477	−	0.915869i	$-0.631503\pi$
$439$	12.3841	−	16.6347i	0.591061	−	0.793933i	0.992538	+	0.121936i	$0.0389103\pi$
$440$	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	−0.921386	−	0.388649i	$-0.872942\pi$
$443$	−33.0519	+	7.83344i	−1.57034	+	0.372178i	−0.648955	+	0.760826i	$0.724794\pi$
$444$		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	0.620828	−	0.783947i	$-0.286797\pi$
$449$	−0.919709	−	0.771727i	−0.0434038	−	0.0364201i	−0.664231	+	0.747527i	$0.731241\pi$
$450$		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	−0.372941	−	0.927855i	$-0.621651\pi$
$457$	−28.6438	−	14.3855i	−1.33990	−	0.672923i	−0.966959	+	0.254932i	$0.917947\pi$
$458$	−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	0.998733	−	0.0503158i	$-0.0160228\pi$
$461$	0.0195765	+	0.336115i	0.000911768	+	0.0156545i	−0.997822	+	0.0659703i	$0.978986\pi$
$462$		0			0
$463$	2.93276	−	0.342791i	0.136297	−	0.0159308i	−0.0476708	−	0.998863i	$-0.515180\pi$
$463$	2.93276	−	0.342791i	0.136297	−	0.0159308i	0.183968	+	0.982932i	$0.441106\pi$
$464$	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	0.422984	−	0.906137i	$-0.360983\pi$
$467$	3.55605	+	1.29430i	0.164554	+	0.0598929i	−0.258429	+	0.966030i	$0.583205\pi$
$468$		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	0.0439314	−	0.999035i	$-0.486012\pi$
$479$	−3.14535	−	0.367638i	−0.143715	−	0.0167978i	−0.187646	+	0.982237i	$0.560086\pi$
$480$		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	−0.334323	+	0.942459i	$0.608507\pi$
$491$	−27.8255	+	29.4933i	−1.25575	+	1.33101i	−0.921425	+	0.388556i	$0.872974\pi$
$492$		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	−0.335109	−	0.942179i	$-0.608773\pi$
$499$	2.39276	−	41.0820i	0.107114	−	1.83908i	0.442224	−	0.896905i	$-0.354190\pi$
$500$	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	−0.545858	−	0.837878i	$-0.683796\pi$
$503$	−9.54144	+	3.47280i	−0.425432	+	0.154845i	0.120426	+	0.992722i	$0.461574\pi$
$504$		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	0.435829	−	0.900029i	$-0.356455\pi$
$509$	24.0833	−	2.81493i	1.06747	−	0.124770i	0.631642	+	0.775260i	$0.282381\pi$
$510$		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	−0.529973	−	0.848014i	$-0.677798\pi$
$521$	4.86477	−	4.08202i	0.213129	−	0.178837i	0.743102	+	0.669178i	$0.233354\pi$
$522$		0			0
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	0.977862	−	0.209250i	$-0.0671024\pi$
$523$	21.5335	+	18.0688i	0.941595	+	0.790092i	−0.0362674	+	0.999342i	$0.511547\pi$
$524$	−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	0.835689	−	0.549203i	$-0.185068\pi$
$541$	−1.34390	−	2.32771i	−0.0577788	−	0.100076i	−0.893468	+	0.449127i	$0.851735\pi$
$542$	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	0.932299	+	0.361689i	$0.117800\pi$
$547$	12.9944	+	30.1244i	0.555600	+	1.28802i	−0.376699	+	0.926336i	$0.622941\pi$
$548$	−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	0.926485	+	0.376331i	$0.122815\pi$
$557$	−1.71906	+	9.74928i	−0.0728390	+	0.413090i	−0.999324	+	0.0367591i	$0.988297\pi$
$558$		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	−0.849348	−	0.527833i	$-0.823005\pi$
$563$	2.78662	−	6.46011i	0.117442	−	0.272261i	0.966790	+	0.255572i	$0.0822638\pi$
$564$		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	−0.478666	−	0.877997i	$-0.658880\pi$
$569$	3.29025	−	2.16403i	0.137935	−	0.0907209i	0.616601	+	0.787276i	$0.288509\pi$
$570$		0			0
$571$	10.1268	−	23.4765i	0.423791	−	0.982459i	−0.563871	−	0.825863i	$-0.690689\pi$
$571$	10.1268	−	23.4765i	0.423791	−	0.982459i	0.987663	−	0.156596i	$-0.0500521\pi$
$572$	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	−0.963099	−	0.269149i	$-0.913258\pi$
$577$	0.816045	−	4.62802i	0.0339724	−	0.192667i	0.997071	+	0.0764818i	$0.0243687\pi$
$578$	−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	−0.979443	−	0.201719i	$-0.935347\pi$
$587$	−11.0004	−	25.5017i	−0.454034	−	1.05257i	0.525410	−	0.850849i	$-0.323912\pi$
$588$		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	0.680533	−	0.732717i	$-0.261748\pi$
$593$	−7.16631	−	12.4124i	−0.294285	−	0.509717i	−0.974818	+	0.223000i	$0.928415\pi$
$594$		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	−0.355957	−	0.934502i	$-0.615845\pi$
$599$	−26.7617	−	6.34265i	−1.09346	−	0.259154i	−0.737499	+	0.675349i	$0.763993\pi$
$600$		0			0
$601$	11.1968	−	15.0400i	0.456729	−	0.613493i	−0.512789	−	0.858515i	$-0.671388\pi$
$601$	11.1968	−	15.0400i	0.456729	−	0.613493i	0.969518	+	0.245022i	$0.0787951\pi$
$602$	−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	0.0161458	−	0.999870i	$-0.494860\pi$
$607$	−22.0641	−	14.5118i	−0.895556	−	0.589016i	−0.911701	+	0.410853i	$0.865231\pi$
$608$	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	−0.996062	−	0.0886553i	$-0.971743\pi$
$613$	−26.7821	+	22.4728i	−1.08172	+	0.907670i	−0.0856560	+	0.996325i	$0.527299\pi$
$614$	−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	0.879731	−	0.475471i	$-0.157722\pi$
$617$	4.27053	+	5.73631i	0.171925	+	0.230935i	−0.707806	+	0.706407i	$0.750315\pi$
$618$		0			0
$619$	−16.8196	−	8.44712i	−0.676037	−	0.339518i	0.0774361	−	0.996997i	$-0.475327\pi$
$619$	−16.8196	−	8.44712i	−0.676037	−	0.339518i	−0.753473	+	0.657479i	$0.771623\pi$
$620$	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	−0.741548	−	0.670900i	$-0.765908\pi$
$631$	−22.0642	+	8.03070i	−0.878361	+	0.319697i	−0.136813	+	0.990597i	$0.543686\pi$
$632$	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	0.0301588	−	0.999545i	$-0.490399\pi$
$641$	−4.32954	−	0.506050i	−0.171006	−	0.0199878i	−0.201165	+	0.979557i	$0.564473\pi$
$642$		0			0
$643$	−13.0468	+	13.8288i	−0.514516	+	0.545355i	−0.931587	−	0.363519i	$-0.881575\pi$
$643$	−13.0468	+	13.8288i	−0.514516	+	0.545355i	0.417071	+	0.908874i	$0.363057\pi$
$644$	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	−0.641919	−	0.766772i	$-0.721862\pi$
$653$	4.11111	−	4.35752i	0.160880	−	0.170523i	0.802799	+	0.596249i	$0.203343\pi$
$654$		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	0.409587	+	0.912271i	$0.365673\pi$
$659$	−11.1391	+	37.2073i	−0.433919	+	1.44939i	−0.843506	+	0.537120i	$0.819512\pi$
$660$		0			0
$661$	−1.80224	+	30.9432i	−0.0700989	+	1.20355i	0.761496	+	0.648169i	$0.224465\pi$
$661$	−1.80224	+	30.9432i	−0.0700989	+	1.20355i	−0.831595	+	0.555382i	$0.812572\pi$
$662$	−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	0.710562	+	0.703635i	$0.248441\pi$
$673$	2.24379	+	38.5243i	0.0864916	+	1.48500i	−0.624070	+	0.781368i	$0.714522\pi$
$674$	−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	0.378983	−	0.925404i	$-0.376274\pi$
$677$	−3.56442	−	1.79012i	−0.136992	−	0.0688000i	−0.515975	+	0.856604i	$0.672570\pi$
$678$		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	−0.236551	+	0.971619i	$0.576017\pi$
$683$	−32.2624	+	27.0713i	−1.23449	+	1.03586i	−0.997935	+	0.0642370i	$0.979539\pi$
$684$		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	−0.385802	−	0.922582i	$-0.626075\pi$
$691$	−8.32013	+	1.97191i	−0.316513	+	0.0750149i	0.0692889	+	0.997597i	$0.477927\pi$
$692$	−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	−0.857578	−	0.514355i	$-0.828032\pi$
$701$	0.440975	−	0.763791i	0.0166554	−	0.0288480i	0.874233	+	0.485507i	$0.161365\pi$
$702$		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	−0.900803	−	0.434227i	$-0.857022\pi$
$709$	−15.9358	−	36.9432i	−0.598480	−	1.38743i	0.302324	−	0.953205i	$-0.402238\pi$
$710$	−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	−0.907186	−	0.420730i	$-0.861774\pi$
$719$	2.39151	−	13.5629i	0.0891883	−	0.505812i	0.996374	−	0.0850815i	$-0.0271151\pi$
$720$		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	−0.341147	−	0.940010i	$-0.610815\pi$
$727$	10.4310	−	6.86056i	0.386864	−	0.254444i	0.728011	+	0.685566i	$0.240445\pi$
$728$	−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	0.600587	+	0.799559i	$0.294933\pi$
$733$	−10.6438	+	24.6752i	−0.393139	+	0.911398i	−0.993726	+	0.111839i	$0.964326\pi$
$734$	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	0.802365	+	0.596833i	$0.203575\pi$
$739$	−4.23374	+	24.0107i	−0.155740	+	0.883248i	−0.958106	+	0.286415i	$0.907536\pi$
$740$	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	0.254743	−	0.967009i	$-0.418009\pi$
$743$	32.2333	−	16.1882i	1.18253	−	0.593887i	0.927782	+	0.373122i	$0.121713\pi$
$744$		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	0.969345	−	0.245705i	$-0.0790194\pi$
$751$	0.670091	+	2.23826i	0.0244520	+	0.0816753i	−0.944893	+	0.327380i	$0.893834\pi$
$752$	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	−0.680823	−	0.732448i	$-0.738378\pi$
$757$	8.08646	−	14.0062i	0.293907	−	0.509063i	0.974730	+	0.223386i	$0.0717109\pi$
$758$	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	0.931234	−	0.364421i	$-0.118733\pi$
$761$	44.1342	+	10.4600i	1.59986	+	0.379175i	0.668630	+	0.743595i	$0.266881\pi$
$762$		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	0.241839	−	0.970316i	$-0.422250\pi$
$769$	−15.3444	−	10.0922i	−0.553334	−	0.363934i	−0.795173	+	0.606383i	$0.792620\pi$
$770$	−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	0.138915	−	0.990304i	$-0.455639\pi$
$773$	−22.5821	−	18.9486i	−0.812222	−	0.681536i	−0.951137	+	0.308769i	$0.900083\pi$
$774$		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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