LMFDB - Embedded newform 729.2.g.c.28.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.5
Character	$\chi$	$=$	729.28
Dual form			729.2.g.c.703.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.652974 - 0.429468i) q^{2} +(-0.550227 + 1.27557i) q^{4} +(1.01614 - 1.07704i) q^{5} +(3.77556 + 0.441300i) q^{7} +(0.459961 + 2.60857i) q^{8} +O(q^{10})$	\(q+(0.652974 - 0.429468i) q^{2} +(-0.550227 + 1.27557i) q^{4} +(1.01614 - 1.07704i) q^{5} +(3.77556 + 0.441300i) q^{7} +(0.459961 + 2.60857i) q^{8} +(0.200956 - 1.13968i) q^{10} +(-1.44963 + 4.84210i) q^{11} +(0.261201 - 4.48466i) q^{13} +(2.65487 - 1.33332i) q^{14} +(-0.485993 - 0.515122i) q^{16} +(-4.30582 + 1.56719i) q^{17} +(4.19524 + 1.52694i) q^{19} +(0.814736 + 1.88877i) q^{20} +(1.13295 + 3.78433i) q^{22} +(3.43157 - 0.401093i) q^{23} +(0.163239 + 2.80270i) q^{25} +(-1.75546 - 3.04054i) q^{26} +(-2.64032 + 4.57318i) q^{28} +(0.583488 + 0.293038i) q^{29} +(0.393020 + 0.527918i) q^{31} +(-5.69339 - 1.34936i) q^{32} +(-2.13853 + 2.87254i) q^{34} +(4.31178 - 3.61801i) q^{35} +(0.766165 + 0.642889i) q^{37} +(3.39516 - 0.804667i) q^{38} +(3.27692 + 2.15526i) q^{40} +(0.570482 + 0.375212i) q^{41} +(8.16684 - 1.93558i) q^{43} +(-5.37881 - 4.51336i) q^{44} +(2.06847 - 1.73565i) q^{46} +(4.73832 - 6.36466i) q^{47} +(7.24880 + 1.71800i) q^{49} +(1.31026 + 1.75998i) q^{50} +(5.57677 + 2.80076i) q^{52} +(-2.07469 + 3.59347i) q^{53} +(3.74212 + 6.48154i) q^{55} +(0.585450 + 10.0518i) q^{56} +(0.506853 - 0.0592426i) q^{58} +(-1.51145 - 5.04858i) q^{59} +(-2.68977 - 6.23558i) q^{61} +(0.483356 + 0.175927i) q^{62} +(-2.96617 + 1.07960i) q^{64} +(-4.56474 - 4.83835i) q^{65} +(4.73732 - 2.37917i) q^{67} +(0.370118 - 6.35468i) q^{68} +(1.26166 - 4.21424i) q^{70} +(-1.06500 + 6.03991i) q^{71} +(-0.764322 - 4.33469i) q^{73} +(0.776385 + 0.0907464i) q^{74} +(-4.25606 + 4.51116i) q^{76} +(-7.60998 + 17.6419i) q^{77} +(-9.39300 + 6.17788i) q^{79} -1.04864 q^{80} +0.533651 q^{82} +(-1.35486 + 0.891108i) q^{83} +(-2.68737 + 6.23002i) q^{85} +(4.50147 - 4.77127i) q^{86} +(-13.2977 - 1.55428i) q^{88} +(-0.181087 - 1.02699i) q^{89} +(2.96526 - 16.8168i) q^{91} +(-1.37652 + 4.59790i) q^{92} +(0.360580 - 6.19091i) q^{94} +(5.90752 - 2.96687i) q^{95} +(-3.42307 - 3.62824i) q^{97} +(5.47110 - 1.99132i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.297253	−	0.954799i	$-0.596071\pi$
$2$	0.652974	−	0.429468i	0.461722	−	0.303679i	0.758975	+	0.651119i	$0.225700\pi$
$3$		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	$-0.651839\pi$
$5$	1.01614	−	1.07704i	0.454430	−	0.481668i	0.913561	+	0.406701i	$0.133321\pi$
$6$		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	$0.368368\pi$
$11$	−1.44963	+	4.84210i	−0.437079	+	1.45995i	−0.838929	+	0.544241i	$0.816818\pi$
$12$		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	−0.806514	−	0.591215i	$-0.798648\pi$
$17$	−4.30582	+	1.56719i	−1.04431	+	0.380099i	−0.237800	+	0.971314i	$0.576426\pi$
$18$		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	0.249466	−	0.968384i	$-0.419745\pi$
$23$	3.43157	−	0.401093i	0.715532	−	0.0836337i	0.466066	+	0.884750i	$0.345671\pi$
$24$		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	$-0.332543\pi$
$29$	0.583488	+	0.293038i	0.108351	+	0.0544159i	−0.393798	+	0.919197i	$0.628839\pi$
$30$		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	0.593274	−	0.805000i	$-0.297835\pi$
$41$	0.570482	+	0.375212i	0.0890943	+	0.0585983i	−0.504180	+	0.863598i	$0.668205\pi$
$42$		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	−0.308585	−	0.951197i	$-0.599855\pi$
$47$	4.73832	−	6.36466i	0.691155	−	0.928382i	0.999740	+	0.0228150i	$0.00726288\pi$
$48$		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	$-0.925321\pi$
$53$	−2.07469	+	3.59347i	−0.284981	+	0.493601i	0.687624	+	0.726067i	$0.258654\pi$
$54$		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	$-0.981134\pi$
$59$	−1.51145	−	5.04858i	−0.196773	−	0.657269i	0.801471	−	0.598034i	$-0.204051\pi$
$60$		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	$0.174121\pi$
$71$	−1.06500	+	6.03991i	−0.126392	+	0.716805i	−0.980471	+	0.196662i	$0.936990\pi$
$72$		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	−0.621686	−	0.783266i	$-0.713552\pi$
$83$	−1.35486	+	0.891108i	−0.148716	+	0.0978119i	0.472971	+	0.881078i	$0.343182\pi$
$84$		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	$-0.0731576\pi$
$89$	−0.181087	−	1.02699i	−0.0191952	−	0.108861i	−0.992900	+	0.118952i	$0.962046\pi$
$90$		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	$-0.971662\pi$
$101$	−3.79067	−	8.78777i	−0.377186	−	0.874416i	0.618854	−	0.785506i	$-0.287597\pi$
$102$		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	$-0.864655\pi$
$107$	−8.40680	−	14.5610i	−0.812716	−	1.40767i	0.0982402	−	0.995163i	$-0.468679\pi$
$108$		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	−0.255168	−	0.966897i	$-0.582131\pi$
$113$	−9.74930	−	2.31063i	−0.917137	−	0.217365i	−0.661969	+	0.749531i	$0.730279\pi$
$114$		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	$-0.944467\pi$
$131$	−9.94222	−	13.3547i	−0.868656	−	1.16681i	0.116165	−	0.993230i	$-0.462940\pi$
$132$		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	$-0.888831\pi$
$137$	−0.539345	−	9.26019i	−0.0460793	−	0.791152i	0.893551	−	0.448961i	$-0.148206\pi$
$138$		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	$0.423869\pi$
$149$	−1.35720	+	23.3023i	−0.111186	+	1.90900i	−0.348085	+	0.937463i	$0.613168\pi$
$150$		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	−0.811102	−	0.584904i	$-0.801132\pi$
$167$	−2.32646	+	2.46590i	−0.180027	+	0.190817i	0.631076	+	0.775721i	$0.282614\pi$
$168$		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	$-0.656071\pi$
$173$	5.35719	−	17.8943i	0.407300	−	1.36048i	0.878201	−	0.478291i	$-0.158744\pi$
$174$		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	$-0.757604\pi$
$179$	−11.1678	+	4.06476i	−0.834723	+	0.303814i	−0.110927	+	0.993829i	$0.535382\pi$
$180$		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	0.625361	−	0.780336i	$-0.284952\pi$
$191$	5.15323	+	2.58805i	0.372875	+	0.187265i	−0.252486	+	0.967601i	$0.581248\pi$
$192$		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	−0.283194	−	0.959063i	$-0.591394\pi$
$197$	8.59155	−	7.20917i	0.612123	−	0.513632i	0.895316	+	0.445431i	$0.146950\pi$
$198$		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	$0.0632594\pi$
$227$	16.8807	+	17.8925i	1.12041	+	1.18757i	0.140095	+	0.990138i	$0.455259\pi$
$228$		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	$-0.792098\pi$
$233$	2.44148	−	13.8463i	0.159946	−	0.907101i	0.954123	−	0.299414i	$-0.0967912\pi$
$234$		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	$0.395373\pi$
$239$	−9.07711	+	21.0431i	−0.587149	+	1.36116i	−0.909958	+	0.414701i	$0.863886\pi$
$240$		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	0.985170	−	0.171582i	$-0.0548878\pi$
$251$	0.0115419	+	0.0654574i	0.000728518	+	0.00413163i	−0.984441	+	0.175714i	$0.943777\pi$
$252$		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	$-0.441995\pi$
$257$	17.2862	−	8.68143i	1.07828	−	0.541533i	0.897060	+	0.441909i	$0.145699\pi$
$258$		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	$0.0240727\pi$
$263$	5.96501	+	13.8284i	0.367818	+	0.852698i	−0.629324	+	0.777143i	$0.716668\pi$
$264$		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	$-0.0501962\pi$
$269$	5.86823	+	10.1641i	0.357792	+	0.619715i	−0.629799	+	0.776758i	$0.716863\pi$
$270$		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	−0.0422786	−	0.999106i	$-0.513462\pi$
$281$	6.17447	−	1.46338i	0.368338	−	0.0872977i	0.410616	+	0.911808i	$0.365314\pi$
$282$		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	$-0.938229\pi$
$293$	−15.1411	−	20.3380i	−0.884553	−	1.18816i	0.0966764	−	0.995316i	$-0.469179\pi$
$294$		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	$-0.728974\pi$
$311$	1.46151	−	25.0931i	0.0828745	−	1.42290i	0.741764	−	0.670661i	$-0.233989\pi$
$312$		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	−0.00436034	−	0.999990i	$-0.501388\pi$
$317$	−4.25913	−	0.497821i	−0.239217	−	0.0279604i	−0.234856	+	0.972030i	$0.575462\pi$
$318$		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	0.746419	−	0.665476i	$-0.231771\pi$
$347$	30.2925	−	3.54069i	1.62619	−	0.190074i	0.879769	+	0.475402i	$0.157697\pi$
$348$		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	−0.153863	−	0.988092i	$-0.549171\pi$
$353$	−19.5082	−	9.79737i	−1.03831	−	0.521461i	−0.884452	+	0.466631i	$0.845468\pi$
$354$		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	$-0.873229\pi$
$359$	−13.2606	+	11.1269i	−0.699866	+	0.587258i	0.221869	+	0.975076i	$0.428784\pi$
$360$		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	$0.0401640\pi$
$383$	4.54732	+	15.1891i	0.232357	+	0.776126i	−0.759693	+	0.650282i	$0.774651\pi$
$384$		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	$0.0163734\pi$
$389$	19.5641	+	20.7367i	0.991938	+	1.05139i	−0.00673888	+	0.999977i	$0.502145\pi$
$390$		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	$-0.730412\pi$
$401$	6.75227	−	15.6535i	0.337192	−	0.781700i	0.999474	−	0.0324445i	$-0.0103292\pi$
$402$		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	−0.757816	−	0.652468i	$-0.773734\pi$
$419$	−14.0624	+	7.06241i	−0.686993	+	0.345021i	0.0708230	+	0.997489i	$0.477437\pi$
$420$		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	0.882524	−	0.470267i	$-0.155842\pi$
$431$	0.705848	+	1.22256i	0.0339995	+	0.0588888i	−0.848525	+	0.529155i	$0.822509\pi$
$432$		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	0.648955	−	0.760826i	$-0.275206\pi$
$443$	33.0519	−	7.83344i	1.57034	−	0.372178i	0.921386	+	0.388649i	$0.127058\pi$
$444$		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	$-0.268759\pi$
$449$	0.919709	+	0.771727i	0.0434038	+	0.0364201i	−0.620828	+	0.783947i	$0.713203\pi$
$450$		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	0.997822	−	0.0659703i	$-0.0210143\pi$
$461$	−0.0195765	−	0.336115i	−0.000911768	−	0.0156545i	−0.998733	+	0.0503158i	$0.983977\pi$
$462$		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	0.258429	−	0.966030i	$-0.416795\pi$
$467$	−3.55605	−	1.29430i	−0.164554	−	0.0598929i	−0.422984	+	0.906137i	$0.639017\pi$
$468$		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	$-0.439914\pi$
$479$	3.14535	+	0.367638i	0.143715	+	0.0167978i	−0.0439314	+	0.999035i	$0.513988\pi$
$480$		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	$-0.391493\pi$
$491$	27.8255	−	29.4933i	1.25575	−	1.33101i	0.921425	−	0.388556i	$-0.127026\pi$
$492$		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	−0.120426	−	0.992722i	$-0.538426\pi$
$503$	9.54144	−	3.47280i	0.425432	−	0.154845i	0.545858	+	0.837878i	$0.316204\pi$
$504$		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	$-0.717619\pi$
$509$	−24.0833	+	2.81493i	−1.06747	+	0.124770i	−0.435829	+	0.900029i	$0.643545\pi$
$510$		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	$-0.766646\pi$
$521$	−4.86477	+	4.08202i	−0.213129	+	0.178837i	0.529973	+	0.848014i	$0.322202\pi$
$522$		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	$-0.877185\pi$
$557$	1.71906	−	9.74928i	0.0728390	−	0.413090i	0.999324	−	0.0367591i	$-0.0117034\pi$
$558$		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	$-0.917736\pi$
$563$	−2.78662	+	6.46011i	−0.117442	+	0.272261i	0.849348	+	0.527833i	$0.176995\pi$
$564$		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	$-0.711491\pi$
$569$	−3.29025	+	2.16403i	−0.137935	+	0.0907209i	0.478666	+	0.877997i	$0.341120\pi$
$570$		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	$0.0646528\pi$
$587$	11.0004	+	25.5017i	0.454034	+	1.05257i	−0.525410	+	0.850849i	$0.676088\pi$
$588$		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	$-0.0715851\pi$
$593$	7.16631	+	12.4124i	0.294285	+	0.509717i	−0.680533	+	0.732717i	$0.738252\pi$
$594$		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	$-0.236007\pi$
$599$	26.7617	+	6.34265i	1.09346	+	0.259154i	0.355957	+	0.934502i	$0.384155\pi$
$600$		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	0.707806	−	0.706407i	$-0.249685\pi$
$617$	−4.27053	−	5.73631i	−0.171925	−	0.230935i	−0.879731	+	0.475471i	$0.842278\pi$
$618$		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	0.201165	−	0.979557i	$-0.435527\pi$
$641$	4.32954	+	0.506050i	0.171006	+	0.0199878i	−0.0301588	+	0.999545i	$0.509601\pi$
$642$		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	$-0.632889\pi$
$647$	−20.6268			−0.810924			−0.405462	+	0.914112i	$0.632889\pi$
$648$		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	$-0.796657\pi$
$653$	−4.11111	+	4.35752i	−0.160880	+	0.170523i	0.641919	+	0.766772i	$0.278138\pi$
$654$		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	$-0.634327\pi$
$659$	11.1391	−	37.2073i	0.433919	−	1.44939i	0.843506	−	0.537120i	$-0.180488\pi$
$660$		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	0.515975	−	0.856604i	$-0.327430\pi$
$677$	3.56442	+	1.79012i	0.136992	+	0.0688000i	−0.378983	+	0.925404i	$0.623726\pi$
$678$		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	$-0.423983\pi$
$683$	32.2624	−	27.0713i	1.23449	−	1.03586i	0.997935	−	0.0642370i	$-0.0204614\pi$
$684$		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	−0.874233	−	0.485507i	$-0.838635\pi$
$701$	−0.440975	+	0.763791i	−0.0166554	+	0.0288480i	0.857578	+	0.514355i	$0.171968\pi$
$702$		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	$0.138226\pi$
$719$	−2.39151	+	13.5629i	−0.0891883	+	0.505812i	−0.996374	+	0.0850815i	$0.972885\pi$
$720$		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	−0.927782	−	0.373122i	$-0.878287\pi$
$743$	−32.2333	+	16.1882i	−1.18253	+	0.593887i	−0.254743	+	0.967009i	$0.581991\pi$
$744$		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	−0.668630	−	0.743595i	$-0.733119\pi$
$761$	−44.1342	−	10.4600i	−1.59986	−	0.379175i	−0.931234	+	0.364421i	$0.881267\pi$
$762$		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	0.951137	−	0.308769i	$-0.0999169\pi$
$773$	22.5821	+	18.9486i	0.812222	+	0.681536i	−0.138915	+	0.990304i	$0.544361\pi$
$774$		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

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

L-functions

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