LMFDB - Embedded newform 729.2.e.g.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(82,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.e (of order $9$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			163.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	729.163
Dual form			729.2.e.g.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26604 - 0.460802i) q^{2} +(-0.141559 + 0.118782i) q^{4} +(-0.286989 - 1.62760i) q^{5} +(1.84730 + 1.55007i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-1.11334 - 1.92836i) q^{10} +(-1.03209 + 5.85327i) q^{11} +(3.03209 + 1.10359i) q^{13} +(3.05303 + 1.11121i) q^{14} +(-0.624485 + 3.54163i) q^{16} +(1.50000 + 2.59808i) q^{17} +(3.31908 - 5.74881i) q^{19} +(0.233956 + 0.196312i) q^{20} +(1.39053 + 7.88609i) q^{22} +(2.25490 - 1.89209i) q^{23} +(2.13176 - 0.775897i) q^{25} +4.34730 q^{26} -0.445622 q^{28} +(-1.21301 + 0.441500i) q^{29} +(-0.450837 + 0.378297i) q^{31} +(-0.180922 - 1.02606i) q^{32} +(3.09627 + 2.59808i) q^{34} +(1.99273 - 3.45150i) q^{35} +(-0.0209445 - 0.0362770i) q^{37} +(1.55303 - 8.80769i) q^{38} +(4.57145 + 1.66387i) q^{40} +(-4.60607 - 1.67647i) q^{41} +(-0.900330 + 5.10602i) q^{43} +(-0.549163 - 0.951178i) q^{44} +(1.98293 - 3.43453i) q^{46} +(2.86231 + 2.40176i) q^{47} +(-0.205737 - 1.16679i) q^{49} +(2.34137 - 1.96464i) q^{50} +(-0.560307 + 0.203935i) q^{52} -11.6382 q^{53} +9.82295 q^{55} +(-6.67024 + 2.42777i) q^{56} +(-1.33228 + 1.11792i) q^{58} +(1.27584 + 7.23567i) q^{59} +(8.46451 + 7.10257i) q^{61} +(-0.396459 + 0.686688i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(0.926022 - 5.25173i) q^{65} +(-1.74510 - 0.635164i) q^{67} +(-0.520945 - 0.189608i) q^{68} +(0.932419 - 5.28801i) q^{70} +(-2.75624 - 4.77396i) q^{71} +(-2.77719 + 4.81023i) q^{73} +(-0.0432332 - 0.0362770i) q^{74} +(0.213011 + 1.20805i) q^{76} +(-10.9795 + 9.21291i) q^{77} +(3.55303 - 1.29320i) q^{79} +5.94356 q^{80} -6.60401 q^{82} +(3.74510 - 1.36310i) q^{83} +(3.79813 - 3.18701i) q^{85} +(1.21301 + 6.87933i) q^{86} +(-13.4021 - 11.2457i) q^{88} +(4.07532 - 7.05866i) q^{89} +(3.89053 + 6.73859i) q^{91} +(-0.0944557 + 0.535685i) q^{92} +(4.73055 + 1.72178i) q^{94} +(-10.3093 - 3.75227i) q^{95} +(0.0452926 - 0.256867i) q^{97} +(-0.798133 - 1.38241i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29}+ \cdots + 9 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8 + 3 * q^11 + 9 * q^13 + 6 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 15 * q^23 + 18 * q^25 + 24 * q^26 - 24 * q^28 - 15 * q^29 + 9 * q^31 - 18 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 - 3 * q^38 + 27 * q^40 - 3 * q^41 + 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 + 9 * q^49 - 15 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 3 * q^56 - 36 * q^58 + 6 * q^59 + 18 * q^61 - 12 * q^62 - 12 * q^64 + 21 * q^65 - 9 * q^67 - 18 * q^70 - 9 * q^71 - 6 * q^73 + 15 * q^74 + 9 * q^76 - 3 * q^77 + 9 * q^79 + 6 * q^80 + 36 * q^82 + 21 * q^83 + 9 * q^85 + 15 * q^86 + 9 * q^88 + 6 * q^91 - 48 * q^92 - 9 * q^94 - 42 * q^95 + 36 * q^97 + 9 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.26604	−	0.460802i	0.895229	−	0.325837i	0.146889	−	0.989153i	$-0.453074\pi$
$2$	1.26604	−	0.460802i	0.895229	−	0.325837i	0.748339	+	0.663316i	$0.230852\pi$
$3$		0			0
$3$		0			0
$4$	−0.141559	+	0.118782i	−0.0707796	+	0.0593912i
$5$	−0.286989	−	1.62760i	−0.128345	−	0.727883i	−0.979264	−	0.202586i	$-0.935065\pi$
$5$	−0.286989	−	1.62760i	−0.128345	−	0.727883i	0.850919	−	0.525297i	$-0.176046\pi$
$6$		0			0
$7$	1.84730	+	1.55007i	0.698212	+	0.585870i	0.921264	−	0.388937i	$-0.127158\pi$
$7$	1.84730	+	1.55007i	0.698212	+	0.585870i	−0.223052	+	0.974807i	$0.571602\pi$
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$		0			0
$10$	−1.11334	−	1.92836i	−0.352069	−	0.609802i
$11$	−1.03209	+	5.85327i	−0.311187	+	1.76483i	0.281663	+	0.959513i	$0.409114\pi$
$11$	−1.03209	+	5.85327i	−0.311187	+	1.76483i	−0.592850	+	0.805313i	$0.701997\pi$
$12$		0			0
$13$	3.03209	+	1.10359i	0.840950	+	0.306081i	0.726345	−	0.687330i	$-0.241217\pi$
$13$	3.03209	+	1.10359i	0.840950	+	0.306081i	0.114605	+	0.993411i	$0.463440\pi$
$14$	3.05303	+	1.11121i	0.815958	+	0.296984i
$15$		0			0
$16$	−0.624485	+	3.54163i	−0.156121	+	0.885408i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	−0.180655	−	0.983547i	$-0.557822\pi$
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	0.942104	−	0.335321i	$-0.108845\pi$
$20$	0.233956	+	0.196312i	0.0523141	+	0.0438967i
$21$		0			0
$22$	1.39053	+	7.88609i	0.296462	+	1.68132i
$23$	2.25490	−	1.89209i	0.470179	−	0.394527i	−0.376681	−	0.926343i	$-0.622935\pi$
$23$	2.25490	−	1.89209i	0.470179	−	0.394527i	0.846860	+	0.531816i	$0.178490\pi$
$24$		0			0
$25$	2.13176	−	0.775897i	0.426352	−	0.155179i
$26$	4.34730			0.852575
$27$		0			0
$28$	−0.445622			−0.0842147
$29$	−1.21301	+	0.441500i	−0.225250	+	0.0819845i	−0.452180	−	0.891927i	$-0.649354\pi$
$29$	−1.21301	+	0.441500i	−0.225250	+	0.0819845i	0.226929	+	0.973911i	$0.427131\pi$
$30$		0			0
$31$	−0.450837	+	0.378297i	−0.0809727	+	0.0679442i	−0.682376	−	0.731002i	$-0.739053\pi$
$31$	−0.450837	+	0.378297i	−0.0809727	+	0.0679442i	0.601403	+	0.798946i	$0.294609\pi$
$32$	−0.180922	−	1.02606i	−0.0319828	−	0.181384i
$33$		0			0
$34$	3.09627	+	2.59808i	0.531005	+	0.445566i
$35$	1.99273	−	3.45150i	0.336832	−	0.583410i
$36$		0			0
$37$	−0.0209445	−	0.0362770i	−0.00344326	−	0.00596390i	0.864299	−	0.502979i	$-0.167763\pi$
$37$	−0.0209445	−	0.0362770i	−0.00344326	−	0.00596390i	−0.867742	+	0.497015i	$0.834429\pi$
$38$	1.55303	−	8.80769i	0.251935	−	1.42880i
$39$		0			0
$40$	4.57145	+	1.66387i	0.722810	+	0.263081i
$41$	−4.60607	−	1.67647i	−0.719347	−	0.261821i	−0.0436983	−	0.999045i	$-0.513914\pi$
$41$	−4.60607	−	1.67647i	−0.719347	−	0.261821i	−0.675648	+	0.737224i	$0.736136\pi$
$42$		0			0
$43$	−0.900330	+	5.10602i	−0.137299	+	0.778661i	0.835932	+	0.548833i	$0.184928\pi$
$43$	−0.900330	+	5.10602i	−0.137299	+	0.778661i	−0.973231	+	0.229829i	$0.926183\pi$
$44$	−0.549163	−	0.951178i	−0.0827894	−	0.143396i
$45$		0			0
$46$	1.98293	−	3.43453i	0.292366	−	0.506394i
$47$	2.86231	+	2.40176i	0.417511	+	0.350333i	0.827215	−	0.561885i	$-0.189924\pi$
$47$	2.86231	+	2.40176i	0.417511	+	0.350333i	−0.409704	+	0.912218i	$0.634368\pi$
$48$		0			0
$49$	−0.205737	−	1.16679i	−0.0293910	−	0.166685i
$50$	2.34137	−	1.96464i	0.331119	−	0.277842i
$51$		0			0
$52$	−0.560307	+	0.203935i	−0.0777007	+	0.0282807i
$53$	−11.6382			−1.59862			−0.799312	−	0.600916i	$-0.794802\pi$
$53$	−11.6382			−1.59862			−0.799312	+	0.600916i	$0.794802\pi$
$54$		0			0
$55$	9.82295			1.32453
$56$	−6.67024	+	2.42777i	−0.891349	+	0.324424i
$57$		0			0
$58$	−1.33228	+	1.11792i	−0.174937	+	0.146790i
$59$	1.27584	+	7.23567i	0.166101	+	0.942005i	0.947922	+	0.318502i	$0.103180\pi$
$59$	1.27584	+	7.23567i	0.166101	+	0.942005i	−0.781821	+	0.623503i	$0.785709\pi$
$60$		0			0
$61$	8.46451	+	7.10257i	1.08377	+	0.909390i	0.996228	−	0.0867707i	$-0.0276547\pi$
$61$	8.46451	+	7.10257i	1.08377	+	0.909390i	0.0875408	+	0.996161i	$0.472099\pi$
$62$	−0.396459	+	0.686688i	−0.0503504	+	0.0872094i
$63$		0			0
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	0.926022	−	5.25173i	0.114859	−	0.651397i
$66$		0			0
$67$	−1.74510	−	0.635164i	−0.213198	−	0.0775977i	0.233213	−	0.972426i	$-0.425076\pi$
$67$	−1.74510	−	0.635164i	−0.213198	−	0.0775977i	−0.446411	+	0.894828i	$0.647298\pi$
$68$	−0.520945	−	0.189608i	−0.0631738	−	0.0229934i
$69$		0			0
$70$	0.932419	−	5.28801i	0.111445	−	0.632038i
$71$	−2.75624	−	4.77396i	−0.327106	−	0.566564i	0.654830	−	0.755776i	$-0.272740\pi$
$71$	−2.75624	−	4.77396i	−0.327106	−	0.566564i	−0.981936	+	0.189212i	$0.939407\pi$
$72$		0			0
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	−0.981522	−	0.191352i	$-0.938713\pi$
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	0.656476	+	0.754347i	$0.272046\pi$
$74$	−0.0432332	−	0.0362770i	−0.00502576	−	0.00421712i
$75$		0			0
$76$	0.213011	+	1.20805i	0.0244340	+	0.138572i
$77$	−10.9795	+	9.21291i	−1.25123	+	1.04991i
$78$		0			0
$79$	3.55303	−	1.29320i	0.399747	−	0.145496i	−0.134320	−	0.990938i	$-0.542885\pi$
$79$	3.55303	−	1.29320i	0.399747	−	0.145496i	0.534068	+	0.845442i	$0.320663\pi$
$80$	5.94356			0.664511
$81$		0			0
$82$	−6.60401			−0.729291
$83$	3.74510	−	1.36310i	0.411078	−	0.149620i	−0.128199	−	0.991748i	$-0.540920\pi$
$83$	3.74510	−	1.36310i	0.411078	−	0.149620i	0.539277	+	0.842128i	$0.318697\pi$
$84$		0			0
$85$	3.79813	−	3.18701i	0.411965	−	0.345680i
$86$	1.21301	+	6.87933i	0.130802	+	0.741817i
$87$		0			0
$88$	−13.4021	−	11.2457i	−1.42867	−	1.19880i
$89$	4.07532	−	7.05866i	0.431983	−	0.748217i	−0.565061	−	0.825049i	$-0.691147\pi$
$89$	4.07532	−	7.05866i	0.431983	−	0.748217i	0.997044	+	0.0768323i	$0.0244806\pi$
$90$		0			0
$91$	3.89053	+	6.73859i	0.407838	+	0.706397i
$92$	−0.0944557	+	0.535685i	−0.00984768	+	0.0558490i
$93$		0			0
$94$	4.73055	+	1.72178i	0.487919	+	0.177588i
$95$	−10.3093	−	3.75227i	−1.05771	−	0.384975i
$96$		0			0
$97$	0.0452926	−	0.256867i	0.00459877	−	0.0260809i	−0.982422	−	0.186673i	$-0.940229\pi$
$97$	0.0452926	−	0.256867i	0.00459877	−	0.0260809i	0.987021	+	0.160592i	$0.0513405\pi$
$98$	−0.798133	−	1.38241i	−0.0806236	−	0.139644i
$99$		0			0
$100$	−0.209607	+	0.363051i	−0.0209607	+	0.0363051i
$101$	−8.44743	−	7.08824i	−0.840551	−	0.705306i	0.117137	−	0.993116i	$-0.462628\pi$
$101$	−8.44743	−	7.08824i	−0.840551	−	0.705306i	−0.957688	+	0.287810i	$0.907073\pi$
$102$		0			0
$103$	−0.678396	−	3.84737i	−0.0668443	−	0.379093i	−0.999817	−	0.0191451i	$-0.993906\pi$
$103$	−0.678396	−	3.84737i	−0.0668443	−	0.379093i	0.932972	−	0.359948i	$-0.117206\pi$
$104$	−7.27584	+	6.10516i	−0.713455	+	0.598660i
$105$		0			0
$106$	−14.7344	+	5.36289i	−1.43113	+	0.520890i
$107$	2.63816			0.255040			0.127520	−	0.991836i	$-0.459298\pi$
$107$	2.63816			0.255040			0.127520	+	0.991836i	$0.459298\pi$
$108$		0			0
$109$	−8.95811			−0.858031			−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95811			−0.858031			−0.429016	+	0.903297i	$0.641140\pi$
$110$	12.4363	−	4.52644i	1.18575	−	0.431579i
$111$		0			0
$112$	−6.64337	+	5.57445i	−0.627739	+	0.526736i
$113$	−2.76604	−	15.6870i	−0.260208	−	1.47571i	−0.782343	−	0.622848i	$-0.785976\pi$
$113$	−2.76604	−	15.6870i	−0.260208	−	1.47571i	0.522135	−	0.852863i	$-0.325136\pi$
$114$		0			0
$115$	−3.72668	−	3.12706i	−0.347515	−	0.291600i
$116$	0.119271	−	0.206583i	0.0110740	−	0.0191807i
$117$		0			0
$118$	4.94949	+	8.57277i	0.455638	+	0.789188i
$119$	−1.25624	+	7.12452i	−0.115160	+	0.653103i
$120$		0			0
$121$	−22.8589	−	8.31996i	−2.07808	−	0.756360i
$122$	13.9893	+	5.09170i	1.26653	+	0.460981i
$123$		0			0
$124$	0.0188851	−	0.107103i	0.00169594	−	0.00961813i
$125$	−6.00640	−	10.4034i	−0.537228	−	0.930507i
$126$		0			0
$127$	−1.79813	+	3.11446i	−0.159559	+	0.276363i	−0.934710	−	0.355412i	$-0.884340\pi$
$127$	−1.79813	+	3.11446i	−0.159559	+	0.276363i	0.775151	+	0.631776i	$0.217674\pi$
$128$	−7.27584	−	6.10516i	−0.643100	−	0.539625i
$129$		0			0
$130$	−1.24763	−	7.07564i	−0.109424	−	0.620575i
$131$	13.5646	−	11.3821i	1.18515	−	0.994458i	0.185218	−	0.982698i	$-0.440701\pi$
$131$	13.5646	−	11.3821i	1.18515	−	0.994458i	0.999931	−	0.0117601i	$-0.00374346\pi$
$132$		0			0
$133$	15.0424	−	5.47497i	1.30434	−	0.474740i
$134$	−2.50206			−0.216145
$135$		0			0
$136$	−8.83069			−0.757225
$137$	−3.69207	+	1.34380i	−0.315435	+	0.114809i	−0.494886	−	0.868958i	$-0.664790\pi$
$137$	−3.69207	+	1.34380i	−0.315435	+	0.114809i	0.179451	+	0.983767i	$0.442568\pi$
$138$		0			0
$139$	9.16637	−	7.69150i	0.777482	−	0.652385i	−0.165131	−	0.986272i	$-0.552805\pi$
$139$	9.16637	−	7.69150i	0.777482	−	0.652385i	0.942613	+	0.333887i	$0.108360\pi$
$140$	0.127889	+	0.725293i	0.0108086	+	0.0612984i
$141$		0			0
$142$	−5.68938	−	4.77396i	−0.477442	−	0.400621i
$143$	−9.58899	+	16.6086i	−0.801872	+	1.38888i
$144$		0			0
$145$	1.06670	+	1.84759i	0.0885849	+	0.153434i
$146$	−1.29948	+	7.36970i	−0.107546	+	0.609921i
$147$		0			0
$148$	0.00727396	+	0.00264750i	0.000597916	+	0.000217624i
$149$	19.2875	+	7.02006i	1.58009	+	0.575106i	0.975224	−	0.221221i	$-0.0710043\pi$
$149$	19.2875	+	7.02006i	1.58009	+	0.575106i	0.604866	+	0.796327i	$0.293227\pi$
$150$		0			0
$151$	2.77972	−	15.7645i	0.226210	−	1.28290i	−0.634148	−	0.773211i	$-0.718649\pi$
$151$	2.77972	−	15.7645i	0.226210	−	1.28290i	0.860358	−	0.509689i	$-0.170240\pi$
$152$	9.76991	+	16.9220i	0.792445	+	1.37255i
$153$		0			0
$154$	−9.65523	+	16.7233i	−0.778041	+	1.34761i
$155$	0.745100	+	0.625213i	0.0598479	+	0.0502183i
$156$		0			0
$157$	−3.81567	−	21.6398i	−0.304524	−	1.72704i	−0.625737	−	0.780034i	$-0.715202\pi$
$157$	−3.81567	−	21.6398i	−0.304524	−	1.72704i	0.321213	−	0.947007i	$-0.395909\pi$
$158$	3.90239	−	3.27449i	0.310457	−	0.260505i
$159$		0			0
$160$	−1.61809	+	0.588936i	−0.127921	+	0.0465595i
$161$	7.09833			0.559426
$162$		0			0
$163$	20.5107			1.60652			0.803262	−	0.595625i	$-0.203096\pi$
$163$	20.5107			1.60652			0.803262	+	0.595625i	$0.203096\pi$
$164$	0.851167	−	0.309799i	0.0664650	−	0.0241913i
$165$		0			0
$166$	4.11334	−	3.45150i	0.319257	−	0.267889i
$167$	−0.745100	−	4.22567i	−0.0576576	−	0.326992i	0.942312	−	0.334735i	$-0.108647\pi$
$167$	−0.745100	−	4.22567i	−0.0576576	−	0.326992i	−0.999970	+	0.00774226i	$0.997536\pi$
$168$		0			0
$169$	−1.98293	−	1.66387i	−0.152533	−	0.127990i
$170$	3.34002	−	5.78509i	0.256168	−	0.443696i
$171$		0			0
$172$	−0.479055	−	0.829748i	−0.0365276	−	0.0632677i
$173$	−0.658633	+	3.73530i	−0.0500750	+	0.283989i	−0.999555	−	0.0298390i	$-0.990501\pi$
$173$	−0.658633	+	3.73530i	−0.0500750	+	0.283989i	0.949480	+	0.313828i	$0.101612\pi$
$174$		0			0
$175$	5.14068	+	1.87106i	0.388599	+	0.141438i
$176$	−20.0856	−	7.31056i	−1.51401	−	0.551054i
$177$		0			0
$178$	1.90689	−	10.8145i	0.142927	−	0.810581i
$179$	4.13816	+	7.16750i	0.309300	+	0.535724i	0.978209	−	0.207620i	$-0.0665718\pi$
$179$	4.13816	+	7.16750i	0.309300	+	0.535724i	−0.668909	+	0.743344i	$0.733239\pi$
$180$		0			0
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	−0.963475	−	0.267797i	$-0.913704\pi$
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	0.713657	+	0.700496i	$0.247038\pi$
$182$	8.03074	+	6.73859i	0.595278	+	0.499498i
$183$		0			0
$184$	1.50459	+	8.53293i	0.110920	+	0.629056i
$185$	−0.0530334	+	0.0445003i	−0.00389909	+	0.00327173i
$186$		0			0
$187$	−16.7554	+	6.09845i	−1.22527	+	0.445963i
$188$	−0.690474			−0.0503580
$189$		0			0
$190$	−14.7811			−1.07233
$191$	−4.71213	+	1.71508i	−0.340958	+	0.124099i	−0.506824	−	0.862050i	$-0.669180\pi$
$191$	−4.71213	+	1.71508i	−0.340958	+	0.124099i	0.165866	+	0.986148i	$0.446958\pi$
$192$		0			0
$193$	−13.6853	+	11.4833i	−0.985087	+	0.826586i	−0.984849	−	0.173414i	$-0.944520\pi$
$193$	−13.6853	+	11.4833i	−0.985087	+	0.826586i	−0.000237549		1.00000i	$0.500076\pi$
$194$	−0.0610226	−	0.346076i	−0.00438117	−	0.0248468i
$195$		0			0
$196$	0.167718	+	0.140732i	0.0119799	+	0.0100523i
$197$	0.361844	−	0.626733i	0.0257803	−	0.0446529i	−0.852847	−	0.522160i	$-0.825126\pi$
$197$	0.361844	−	0.626733i	0.0257803	−	0.0446529i	0.878628	+	0.477507i	$0.158460\pi$
$198$		0			0
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	0.988169	−	0.153367i	$-0.0490117\pi$
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	−0.626905	+	0.779096i	$0.715678\pi$
$200$	−1.15957	+	6.57623i	−0.0819938	+	0.465010i
$201$		0			0
$202$	−13.9611	−	5.08143i	−0.982300	−	0.357528i
$203$	−2.92514	−	1.06467i	−0.205305	−	0.0747249i
$204$		0			0
$205$	−1.40673	+	7.97794i	−0.0982500	+	0.557204i
$206$	−2.63176	−	4.55834i	−0.183363	−	0.317595i
$207$		0			0
$208$	−5.80200	+	10.0494i	−0.402297	+	0.696798i
$209$	30.2237	+	25.3607i	2.09062	+	1.75424i
$210$		0			0
$211$	−2.58125	−	14.6390i	−0.177701	−	1.00779i	−0.934980	−	0.354700i	$-0.884583\pi$
$211$	−2.58125	−	14.6390i	−0.177701	−	1.00779i	0.757280	−	0.653091i	$-0.226528\pi$
$212$	1.64749	−	1.38241i	0.113150	−	0.0949441i
$213$		0			0
$214$	3.34002	−	1.21567i	0.228319	−	0.0831014i
$215$	8.56893			0.584396
$216$		0			0
$217$	−1.41921			−0.0963426
$218$	−11.3414	+	4.12792i	−0.768134	+	0.279578i
$219$		0			0
$220$	−1.39053	+	1.16679i	−0.0937495	+	0.0786652i
$221$	1.68092	+	9.53298i	0.113071	+	0.641258i
$222$		0			0
$223$	−8.38713	−	7.03763i	−0.561644	−	0.471275i	0.317217	−	0.948353i	$-0.397251\pi$
$223$	−8.38713	−	7.03763i	−0.561644	−	0.471275i	−0.878861	+	0.477078i	$0.841696\pi$
$224$	1.25624	−	2.17588i	0.0839364	−	0.145382i
$225$		0			0
$226$	−10.7306	−	18.5859i	−0.713786	−	1.23631i
$227$	3.00980	−	17.0694i	0.199767	−	1.13294i	−0.705696	−	0.708514i	$-0.749366\pi$
$227$	3.00980	−	17.0694i	0.199767	−	1.13294i	0.905464	−	0.424423i	$-0.139523\pi$
$228$		0			0
$229$	−1.46791	−	0.534276i	−0.0970023	−	0.0353059i	0.293063	−	0.956093i	$-0.405325\pi$
$229$	−1.46791	−	0.534276i	−0.0970023	−	0.0353059i	−0.390065	+	0.920787i	$0.627548\pi$
$230$	−6.15910	−	2.24173i	−0.406119	−	0.147815i
$231$		0			0
$232$	0.659815	−	3.74200i	0.0433190	−	0.245674i
$233$	8.39440	+	14.5395i	0.549935	+	0.952516i	0.998278	+	0.0586545i	$0.0186810\pi$
$233$	8.39440	+	14.5395i	0.549935	+	0.952516i	−0.448343	+	0.893862i	$0.647986\pi$
$234$		0			0
$235$	3.08765	−	5.34796i	0.201416	−	0.348863i
$236$	−1.04008	−	0.872729i	−0.0677033	−	0.0568098i
$237$		0			0
$238$	1.69253	+	9.59883i	0.109711	+	0.622200i
$239$	3.08647	−	2.58985i	0.199647	−	0.167524i	−0.537483	−	0.843274i	$-0.680625\pi$
$239$	3.08647	−	2.58985i	0.199647	−	0.167524i	0.737130	+	0.675751i	$0.236180\pi$
$240$		0			0
$241$	3.15018	−	1.14657i	0.202921	−	0.0738571i	−0.238560	−	0.971128i	$-0.576675\pi$
$241$	3.15018	−	1.14657i	0.202921	−	0.0738571i	0.441481	+	0.897271i	$0.354453\pi$
$242$	−32.7743			−2.10681
$243$		0			0
$244$	−2.04189			−0.130719
$245$	−1.84002	+	0.669713i	−0.117555	+	0.0427864i
$246$		0			0
$247$	16.4081	−	13.7680i	1.04402	−	0.876037i
$248$	−0.300822	−	1.70604i	−0.0191022	−	0.108334i
$249$		0			0
$250$	−12.3983	−	10.4034i	−0.784135	−	0.657968i
$251$	−11.5753	+	20.0490i	−0.730628	+	1.26548i	0.225987	+	0.974130i	$0.427439\pi$
$251$	−11.5753	+	20.0490i	−0.730628	+	1.26548i	−0.956615	+	0.291354i	$0.905894\pi$
$252$		0			0
$253$	8.74763	+	15.1513i	0.549959	+	0.952556i
$254$	−0.841367	+	4.77163i	−0.0527920	+	0.299399i
$255$		0			0
$256$	4.13088	+	1.50352i	0.258180	+	0.0939699i
$257$	11.2883	+	4.10862i	0.704147	+	0.256289i	0.669180	−	0.743100i	$-0.266645\pi$
$257$	11.2883	+	4.10862i	0.704147	+	0.256289i	0.0349665	+	0.999388i	$0.488868\pi$
$258$		0			0
$259$	0.0175410	−	0.0994798i	0.00108994	−	0.00618137i
$260$	0.492726	+	0.853427i	0.0305576	+	0.0529273i
$261$		0			0
$262$	11.9285	−	20.6609i	0.736948	−	1.27643i
$263$	−12.9474	−	10.8642i	−0.798373	−	0.669914i	0.149430	−	0.988772i	$-0.452256\pi$
$263$	−12.9474	−	10.8642i	−0.798373	−	0.669914i	−0.947803	+	0.318858i	$0.896701\pi$
$264$		0			0
$265$	3.34002	+	18.9422i	0.205176	+	1.16361i
$266$	16.5214	−	13.8631i	1.01299	−	0.850002i
$267$		0			0
$268$	0.322481	−	0.117374i	0.0196987	−	0.00716974i
$269$	7.91447			0.482554			0.241277	−	0.970456i	$-0.422434\pi$
$269$	7.91447			0.482554			0.241277	+	0.970456i	$0.422434\pi$
$270$		0			0
$271$	−17.2344			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$271$	−17.2344			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$272$	−10.1382	+	3.68999i	−0.614716	+	0.223738i
$273$		0			0
$274$	−4.05509	+	3.40263i	−0.244977	+	0.205560i
$275$	2.34137	+	13.2785i	0.141190	+	0.800727i
$276$		0			0
$277$	20.2502	+	16.9919i	1.21671	+	1.02094i	0.998990	+	0.0449336i	$0.0143076\pi$
$277$	20.2502	+	16.9919i	1.21671	+	1.02094i	0.217724	+	0.976010i	$0.430137\pi$
$278$	8.06077	−	13.9617i	0.483453	−	0.837365i
$279$		0			0
$280$	5.86571	+	10.1597i	0.350543	+	0.607159i
$281$	3.29860	−	18.7073i	0.196778	−	1.11598i	−0.713086	−	0.701077i	$-0.752703\pi$
$281$	3.29860	−	18.7073i	0.196778	−	1.11598i	0.909864	−	0.414907i	$-0.136186\pi$
$282$		0			0
$283$	15.5865	+	5.67301i	0.926519	+	0.337225i	0.760829	−	0.648952i	$-0.224793\pi$
$283$	15.5865	+	5.67301i	0.926519	+	0.337225i	0.165690	+	0.986178i	$0.447015\pi$
$284$	0.957234	+	0.348405i	0.0568014	+	0.0206740i
$285$		0			0
$286$	−4.48680	+	25.4459i	−0.265310	+	1.50465i
$287$	−5.91013	−	10.2366i	−0.348864	−	0.604250i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	2.20187	+	1.84759i	0.129298	+	0.108494i
$291$		0			0
$292$	−0.178234	−	1.01081i	−0.0104303	−	0.0591534i
$293$	−14.8289	+	12.4429i	−0.866312	+	0.726922i	−0.963318	−	0.268361i	$-0.913518\pi$
$293$	−14.8289	+	12.4429i	−0.866312	+	0.726922i	0.0970060	+	0.995284i	$0.469073\pi$
$294$		0			0
$295$	11.4106	−	4.15312i	0.664351	−	0.241804i
$296$	0.123303			0.00716685
$297$		0			0
$298$	27.6536			1.60193
$299$	8.92514	−	3.24849i	0.516154	−	0.187865i
$300$		0			0
$301$	−9.57785	+	8.03677i	−0.552058	+	0.463232i
$302$	−3.74510	−	21.2395i	−0.215506	−	1.22220i
$303$		0			0
$304$	18.2875	+	15.3450i	1.04886	+	0.880096i
$305$	9.13088	−	15.8152i	0.522833	−	0.905573i
$306$		0			0
$307$	−10.4029	−	18.0183i	−0.593722	−	1.02836i	−0.993726	−	0.111844i	$-0.964324\pi$
$307$	−10.4029	−	18.0183i	−0.593722	−	1.02836i	0.400003	−	0.916514i	$-0.369009\pi$
$308$	0.459922	−	2.60835i	0.0262065	−	0.148624i
$309$		0			0
$310$	1.23143	+	0.448204i	0.0699405	+	0.0254563i
$311$	−10.0223	−	3.64781i	−0.568312	−	0.206849i	0.0418520	−	0.999124i	$-0.486674\pi$
$311$	−10.0223	−	3.64781i	−0.568312	−	0.206849i	−0.610164	+	0.792275i	$0.708896\pi$
$312$		0			0
$313$	0.662504	−	3.75725i	0.0374469	−	0.212372i	−0.960343	−	0.278822i	$-0.910056\pi$
$313$	0.662504	−	3.75725i	0.0374469	−	0.212372i	0.997790	+	0.0664498i	$0.0211672\pi$
$314$	−14.8025	−	25.6386i	−0.835352	−	1.44687i
$315$		0			0
$316$	−0.349356	+	0.605102i	−0.0196528	+	0.0340396i
$317$	−20.2153	−	16.9626i	−1.13540	−	0.952717i	−0.136125	−	0.990692i	$-0.543465\pi$
$317$	−20.2153	−	16.9626i	−1.13540	−	0.952717i	−0.999279	+	0.0379748i	$0.987909\pi$
$318$		0			0
$319$	−1.33228	−	7.55574i	−0.0745934	−	0.423040i
$320$	−10.8833	+	9.13214i	−0.608392	+	0.510502i
$321$		0			0
$322$	8.98680	−	3.27093i	0.500815	−	0.182282i
$323$	19.9145			1.10807
$324$		0			0
$325$	7.31996			0.406038
$326$	25.9675	−	9.45140i	1.43821	−	0.523464i
$327$		0			0
$328$	11.0528	−	9.27439i	0.610288	−	0.512092i
$329$	1.56464	+	8.87354i	0.0862616	+	0.489214i
$330$		0			0
$331$	−1.20393	−	1.01021i	−0.0661738	−	0.0555264i	0.609101	−	0.793093i	$-0.291530\pi$
$331$	−1.20393	−	1.01021i	−0.0661738	−	0.0555264i	−0.675275	+	0.737566i	$0.735975\pi$
$332$	−0.368241	+	0.637812i	−0.0202098	+	0.0350045i
$333$		0			0
$334$	−2.89053	−	5.00654i	−0.158163	−	0.273946i
$335$	−0.532966	+	3.02260i	−0.0291191	+	0.165142i
$336$		0			0
$337$	7.53209	+	2.74146i	0.410299	+	0.149337i	0.538920	−	0.842357i	$-0.318833\pi$
$337$	7.53209	+	2.74146i	0.410299	+	0.149337i	−0.128620	+	0.991694i	$0.541055\pi$
$338$	−3.27719	−	1.19280i	−0.178256	−	0.0648797i
$339$		0			0
$340$	−0.159100	+	0.902302i	−0.00862842	+	0.0489342i
$341$	−1.74897	−	3.02931i	−0.0947121	−	0.164046i
$342$		0			0
$343$	9.86871	−	17.0931i	0.532860	−	0.922941i
$344$	−11.6912	−	9.81007i	−0.630347	−	0.528924i
$345$		0			0
$346$	0.887374	+	5.03255i	0.0477055	+	0.270552i
$347$	−15.2023	+	12.7563i	−0.816104	+	0.684793i	−0.952056	−	0.305923i	$-0.901035\pi$
$347$	−15.2023	+	12.7563i	−0.816104	+	0.684793i	0.135952	+	0.990715i	$0.456591\pi$
$348$		0			0
$349$	−10.4243	+	3.79412i	−0.557998	+	0.203095i	−0.605597	−	0.795772i	$-0.707065\pi$
$349$	−10.4243	+	3.79412i	−0.557998	+	0.203095i	0.0475984	+	0.998867i	$0.484843\pi$
$350$	7.37052			0.393971
$351$		0			0
$352$	6.19253			0.330063
$353$	−2.69119	+	0.979513i	−0.143238	+	0.0521342i	−0.412644	−	0.910892i	$-0.635395\pi$
$353$	−2.69119	+	0.979513i	−0.143238	+	0.0521342i	0.269407	+	0.963027i	$0.413172\pi$
$354$		0			0
$355$	−6.97906	+	5.85612i	−0.370410	+	0.310811i
$356$	0.261545	+	1.48330i	0.0138619	+	0.0786145i
$357$		0			0
$358$	8.54189	+	7.16750i	0.451453	+	0.378814i
$359$	14.3944	−	24.9318i	0.759707	−	1.31585i	−0.183292	−	0.983058i	$-0.558676\pi$
$359$	14.3944	−	24.9318i	0.759707	−	1.31585i	0.943000	−	0.332793i	$-0.107991\pi$
$360$		0			0
$361$	−12.5326	−	21.7070i	−0.659608	−	1.14247i
$362$	−1.57263	+	8.91885i	−0.0826558	+	0.468764i
$363$		0			0
$364$	−1.35117	−	0.491784i	−0.0708204	−	0.0257765i
$365$	8.62613	+	3.13966i	0.451512	+	0.164337i
$366$		0			0
$367$	−1.90879	+	10.8253i	−0.0996378	+	0.565074i	0.893589	+	0.448885i	$0.148179\pi$
$367$	−1.90879	+	10.8253i	−0.0996378	+	0.565074i	−0.993227	+	0.116189i	$0.962932\pi$
$368$	5.29292	+	9.16760i	0.275912	+	0.477894i
$369$		0			0
$370$	−0.0466368	+	0.0807773i	−0.00242453	+	0.00419941i
$371$	−21.4991	−	18.0399i	−1.11618	−	0.936585i
$372$		0			0
$373$	5.80154	+	32.9022i	0.300392	+	1.70361i	0.644439	+	0.764656i	$0.277091\pi$
$373$	5.80154	+	32.9022i	0.300392	+	1.70361i	−0.344046	+	0.938953i	$0.611798\pi$
$374$	−18.4029	+	15.4418i	−0.951589	+	0.798478i
$375$		0			0
$376$	−10.3353	+	3.76173i	−0.533001	+	0.193997i
$377$	−4.16519			−0.214518
$378$		0			0
$379$	20.9394			1.07559			0.537794	−	0.843077i	$-0.319258\pi$
$379$	20.9394			1.07559			0.537794	+	0.843077i	$0.319258\pi$
$380$	1.90508	−	0.693392i	0.0977284	−	0.0355702i
$381$		0			0
$382$	−5.17546	+	4.34273i	−0.264800	+	0.222193i
$383$	0.713888	+	4.04866i	0.0364780	+	0.206877i	0.997599	−	0.0692492i	$-0.0220604\pi$
$383$	0.713888	+	4.04866i	0.0364780	+	0.206877i	−0.961121	+	0.276126i	$0.910949\pi$
$384$		0			0
$385$	18.1459	+	15.2262i	0.924801	+	0.776000i
$386$	−12.0346	+	20.8446i	−0.612546	+	1.06096i
$387$		0			0
$388$	0.0240997	+	0.0417419i	0.00122348	+	0.00211912i
$389$	−2.96838	+	16.8345i	−0.150503	+	0.853543i	0.812280	+	0.583267i	$0.198226\pi$
$389$	−2.96838	+	16.8345i	−0.150503	+	0.853543i	−0.962783	+	0.270276i	$0.912885\pi$
$390$		0			0
$391$	8.29813	+	3.02027i	0.419655	+	0.152742i
$392$	3.27719	+	1.19280i	0.165523	+	0.0602455i
$393$		0			0
$394$	0.169311	−	0.960210i	0.00852976	−	0.0483747i
$395$	−3.12449	−	5.41177i	−0.157210	−	0.272296i
$396$		0			0
$397$	−11.2010	+	19.4007i	−0.562162	+	0.973692i	0.435146	+	0.900360i	$0.356697\pi$
$397$	−11.2010	+	19.4007i	−0.562162	+	0.973692i	−0.997308	+	0.0733324i	$0.976637\pi$
$398$	10.5196	+	8.82699i	0.527300	+	0.442457i
$399$		0			0
$400$	1.41669	+	8.03444i	0.0708344	+	0.401722i
$401$	11.1702	−	9.37295i	0.557815	−	0.468063i	−0.319762	−	0.947498i	$-0.603603\pi$
$401$	11.1702	−	9.37295i	0.557815	−	0.468063i	0.877577	+	0.479435i	$0.159158\pi$
$402$		0			0
$403$	−1.78446	+	0.649491i	−0.0888904	+	0.0323535i
$404$	2.03777			0.101383
$405$		0			0
$406$	−4.19396			−0.208143
$407$	0.233956	−	0.0851529i	0.0115967	−	0.00422087i
$408$		0			0
$409$	−13.4081	+	11.2507i	−0.662986	+	0.556312i	−0.910980	−	0.412450i	$-0.864673\pi$
$409$	−13.4081	+	11.2507i	−0.662986	+	0.556312i	0.247994	+	0.968762i	$0.420229\pi$
$410$	1.89528	+	10.7487i	0.0936011	+	0.530838i
$411$		0			0
$412$	0.553033	+	0.464050i	0.0272460	+	0.0228621i
$413$	−8.85891	+	15.3441i	−0.435918	+	0.755033i
$414$		0			0
$415$	−3.29339	−	5.70431i	−0.161666	−	0.280014i
$416$	0.583778	−	3.31077i	0.0286221	−	0.162324i
$417$		0			0
$418$	49.9509	+	18.1806i	2.44318	+	0.889244i
$419$	17.7246	+	6.45123i	0.865904	+	0.315163i	0.736507	−	0.676429i	$-0.236474\pi$
$419$	17.7246	+	6.45123i	0.865904	+	0.315163i	0.129397	+	0.991593i	$0.458696\pi$
$420$		0			0
$421$	−5.61468	+	31.8425i	−0.273643	+	1.55191i	0.469597	+	0.882881i	$0.344399\pi$
$421$	−5.61468	+	31.8425i	−0.273643	+	1.55191i	−0.743240	+	0.669025i	$0.766712\pi$
$422$	−10.0137	−	17.3442i	−0.487458	−	0.844302i
$423$		0			0
$424$	17.1288	−	29.6680i	0.831849	−	1.44080i
$425$	5.21348	+	4.37463i	0.252891	+	0.212201i
$426$		0			0
$427$	4.62701	+	26.2411i	0.223917	+	1.26990i
$428$	−0.373455	+	0.313366i	−0.0180517	+	0.0151471i
$429$		0			0
$430$	10.8486	−	3.94858i	0.523168	−	0.190418i
$431$	−34.3164			−1.65297			−0.826483	−	0.562962i	$-0.809662\pi$
$431$	−34.3164			−1.65297			−0.826483	+	0.562962i	$0.809662\pi$
$432$		0			0
$433$	−25.0669			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$433$	−25.0669			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$434$	−1.79679	+	0.653978i	−0.0862486	+	0.0313919i
$435$		0			0
$436$	1.26810	−	1.06407i	0.0607312	−	0.0509595i
$437$	−3.39306	−	19.2430i	−0.162312	−	0.920516i
$438$		0			0
$439$	−17.7784	−	14.9178i	−0.848515	−	0.711989i	0.110947	−	0.993826i	$-0.464612\pi$
$439$	−17.7784	−	14.9178i	−0.848515	−	0.711989i	−0.959462	+	0.281837i	$0.909056\pi$
$440$	−14.4572	+	25.0407i	−0.689222	+	1.19377i
$441$		0			0
$442$	6.52094	+	11.2946i	0.310170	+	0.537230i
$443$	0.715699	−	4.05893i	0.0340039	−	0.192846i	−0.963074	−	0.269237i	$-0.913229\pi$
$443$	0.715699	−	4.05893i	0.0340039	−	0.192846i	0.997078	+	0.0763910i	$0.0243397\pi$
$444$		0			0
$445$	−12.6582	−	4.60722i	−0.600057	−	0.218403i
$446$	−13.8614	−	5.04515i	−0.656358	−	0.238895i
$447$		0			0
$448$	3.59967	−	20.4147i	0.170068	−	0.964506i
$449$	9.17071	+	15.8841i	0.432793	+	0.749619i	0.997113	−	0.0759373i	$-0.0241949\pi$
$449$	9.17071	+	15.8841i	0.432793	+	0.749619i	−0.564320	+	0.825556i	$0.690862\pi$
$450$		0			0
$451$	14.5667	−	25.2303i	0.685919	−	1.18805i
$452$	2.25490	+	1.89209i	0.106062	+	0.0889962i
$453$		0			0
$454$	−4.05509	−	22.9976i	−0.190315	−	1.07933i
$455$	9.85117	−	8.26611i	0.461830	−	0.387521i
$456$		0			0
$457$	18.2875	−	6.65609i	0.855451	−	0.311359i	0.123190	−	0.992383i	$-0.460687\pi$
$457$	18.2875	−	6.65609i	0.855451	−	0.311359i	0.732261	+	0.681024i	$0.238465\pi$
$458$	−2.10464			−0.0983432
$459$		0			0
$460$	0.898986			0.0419154
$461$	26.0758	−	9.49081i	1.21447	−	0.442031i	0.346218	−	0.938154i	$-0.387466\pi$
$461$	26.0758	−	9.49081i	1.21447	−	0.442031i	0.868252	+	0.496123i	$0.165243\pi$
$462$		0			0
$463$	29.6352	−	24.8669i	1.37727	−	1.15566i	0.407054	−	0.913404i	$-0.366556\pi$
$463$	29.6352	−	24.8669i	1.37727	−	1.15566i	0.970212	−	0.242259i	$-0.0778883\pi$
$464$	−0.806123	−	4.57175i	−0.0374233	−	0.212238i
$465$		0			0
$466$	17.3275	+	14.5395i	0.802683	+	0.673531i
$467$	14.8819	−	25.7762i	0.688653	−	1.19278i	−0.283621	−	0.958936i	$-0.591536\pi$
$467$	14.8819	−	25.7762i	0.688653	−	1.19278i	0.972274	−	0.233845i	$-0.0751309\pi$
$468$		0			0
$469$	−2.23917	−	3.87836i	−0.103395	−	0.179086i
$470$	1.44475	−	8.19356i	0.0666411	−	0.377941i
$471$		0			0
$472$	−20.3229	−	7.39695i	−0.935440	−	0.340472i
$473$	−28.9577	−	10.5397i	−1.33148	−	0.484618i
$474$		0			0
$475$	2.61499	−	14.8303i	0.119984	−	0.680463i
$476$	−0.668434	−	1.15776i	−0.0306376	−	0.0530659i
$477$		0			0
$478$	2.71419	−	4.70112i	0.124144	−	0.215024i
$479$	28.8614	+	24.2176i	1.31871	+	1.10653i	0.986577	+	0.163300i	$0.0522138\pi$
$479$	28.8614	+	24.2176i	1.31871	+	1.10653i	0.332136	+	0.943231i	$0.392231\pi$
$480$		0			0
$481$	−0.0234708	−	0.133109i	−0.00107017	−	0.00606926i
$482$	3.45992	−	2.90322i	0.157595	−	0.132238i
$483$		0			0
$484$	4.22416	−	1.53747i	0.192007	−	0.0698849i
$485$	−0.431074			−0.0195741
$486$		0			0
$487$	−0.763823			−0.0346121			−0.0173061	−	0.999850i	$-0.505509\pi$
$487$	−0.763823			−0.0346121			−0.0173061	+	0.999850i	$0.505509\pi$
$488$	−30.5638	+	11.1243i	−1.38356	+	0.503573i
$489$		0			0
$490$	−2.02094	+	1.69577i	−0.0912970	+	0.0766073i
$491$	0.0864665	+	0.490376i	0.00390218	+	0.0221303i	0.986697	−	0.162572i	$-0.0519790\pi$
$491$	0.0864665	+	0.490376i	0.00390218	+	0.0221303i	−0.982794	+	0.184702i	$0.940868\pi$
$492$		0			0
$493$	−2.96657	−	2.48925i	−0.133607	−	0.112110i
$494$	14.4290	−	24.9918i	0.649192	−	1.12443i
$495$		0			0
$496$	−1.05825	−	1.83294i	−0.0475167	−	0.0823014i
$497$	2.30834	−	13.0913i	0.103543	−	0.587224i
$498$		0			0
$499$	−8.42514	−	3.06650i	−0.377161	−	0.137275i	0.146482	−	0.989213i	$-0.453205\pi$
$499$	−8.42514	−	3.06650i	−0.377161	−	0.137275i	−0.523643	+	0.851938i	$0.675427\pi$
$500$	2.08600	+	0.759242i	0.0932887	+	0.0339543i
$501$		0			0
$502$	−5.41622	+	30.7169i	−0.241738	+	1.37096i
$503$	9.18092	+	15.9018i	0.409357	+	0.709027i	0.994818	−	0.101673i	$-0.0324197\pi$
$503$	9.18092	+	15.9018i	0.409357	+	0.709027i	−0.585461	+	0.810701i	$0.699086\pi$
$504$		0			0
$505$	−9.11246	+	15.7832i	−0.405499	+	0.702345i
$506$	18.0567	+	15.1513i	0.802716	+	0.673559i
$507$		0			0
$508$	−0.115400	−	0.654467i	−0.00512006	−	0.0290373i
$509$	21.7331	−	18.2362i	0.963302	−	0.808306i	−0.0181853	−	0.999835i	$-0.505789\pi$
$509$	21.7331	−	18.2362i	0.963302	−	0.808306i	0.981487	+	0.191528i	$0.0613444\pi$
$510$		0			0
$511$	−12.5865	+	4.58110i	−0.556792	+	0.202656i
$512$	24.9186			1.10126
$513$		0			0
$514$	16.1848			0.713881
$515$	−6.06728	+	2.20831i	−0.267356	+	0.0973097i
$516$		0			0
$517$	−17.0123	+	14.2750i	−0.748201	+	0.627815i
$518$	−0.0236329	−	0.134029i	−0.00103837	−	0.00588888i
$519$		0			0
$520$	12.0248	+	10.0900i	0.527323	+	0.442477i
$521$	−16.3191	+	28.2655i	−0.714952	+	1.23833i	0.248026	+	0.968753i	$0.420218\pi$
$521$	−16.3191	+	28.2655i	−0.714952	+	1.23833i	−0.962978	+	0.269580i	$0.913115\pi$
$522$		0			0
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	0.999775	−	0.0212271i	$-0.00675730\pi$
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	−0.518271	+	0.855217i	$0.673424\pi$
$524$	−0.568210	+	3.22248i	−0.0248224	+	0.140775i
$525$		0			0
$526$	−21.3983	−	7.78833i	−0.933009	−	0.339587i
$527$	−1.65910	−	0.603863i	−0.0722715	−	0.0263047i
$528$		0			0
$529$	−2.48932	+	14.1176i	−0.108231	+	0.613811i
$530$	12.9572	+	22.4426i	0.562826	+	0.974844i
$531$		0			0
$532$	−1.47906	+	2.56180i	−0.0641252	+	0.111068i
$533$	−12.1159	−	10.1664i	−0.524796	−	0.440357i
$534$		0			0
$535$	−0.757122	−	4.29385i	−0.0327332	−	0.185639i
$536$	4.18757	−	3.51379i	0.180875	−	0.151772i
$537$		0			0
$538$	10.0201	−	3.64701i	0.431996	−	0.157234i
$539$	7.04189			0.303316
$540$		0			0
$541$	−15.7870			−0.678738			−0.339369	−	0.940653i	$-0.610214\pi$
$541$	−15.7870			−0.678738			−0.339369	+	0.940653i	$0.610214\pi$
$542$	−21.8195	+	7.94166i	−0.937230	+	0.341124i
$543$		0			0
$544$	2.39440	−	2.00914i	0.102659	−	0.0861412i
$545$	2.57088	+	14.5802i	0.110124	+	0.624546i
$546$		0			0
$547$	−21.0043	−	17.6247i	−0.898081	−	0.753579i	0.0717337	−	0.997424i	$-0.477147\pi$
$547$	−21.0043	−	17.6247i	−0.898081	−	0.753579i	−0.969814	+	0.243845i	$0.921591\pi$
$548$	0.363026	−	0.628780i	0.0155077	−	0.0268602i
$549$		0			0
$550$	9.08306	+	15.7323i	0.387303	+	0.670829i
$551$	−1.48798	+	8.43874i	−0.0633900	+	0.359503i
$552$		0			0
$553$	8.56805	+	3.11851i	0.364350	+	0.132613i
$554$	33.4675	+	12.1812i	1.42190	+	0.517528i
$555$		0			0
$556$	−0.383971	+	2.17761i	−0.0162840	+	0.0923511i
$557$	14.7010	+	25.4629i	0.622901	+	1.07890i	0.988943	+	0.148298i	$0.0473794\pi$
$557$	14.7010	+	25.4629i	0.622901	+	1.07890i	−0.366042	+	0.930598i	$0.619287\pi$
$558$		0			0
$559$	−8.36484	+	14.4883i	−0.353795	+	0.612791i
$560$	10.9795	+	9.21291i	0.463969	+	0.389317i
$561$		0			0
$562$	−4.44419	−	25.2043i	−0.187467	−	1.06318i
$563$	7.94428	−	6.66604i	0.334811	−	0.280940i	−0.459845	−	0.887999i	$-0.652095\pi$
$563$	7.94428	−	6.66604i	0.334811	−	0.280940i	0.794657	+	0.607059i	$0.207651\pi$
$564$		0			0
$565$	−24.7383	+	9.00400i	−1.04075	+	0.378801i
$566$	22.3473			0.939327
$567$		0			0
$568$	16.2264			0.680843
$569$	−30.9809	+	11.2761i	−1.29879	+	0.472719i	−0.896601	−	0.442839i	$-0.853971\pi$
$569$	−30.9809	+	11.2761i	−1.29879	+	0.472719i	−0.402185	+	0.915559i	$0.631749\pi$
$570$		0			0
$571$	−0.564893	+	0.474002i	−0.0236400	+	0.0198363i	−0.654531	−	0.756035i	$-0.727134\pi$
$571$	−0.564893	+	0.474002i	−0.0236400	+	0.0198363i	0.630891	+	0.775871i	$0.282689\pi$
$572$	−0.615400	−	3.49011i	−0.0257312	−	0.145929i
$573$		0			0
$574$	−12.1996	−	10.2366i	−0.509200	−	0.427269i
$575$	3.33884	−	5.78304i	0.139239	−	0.241169i
$576$		0			0
$577$	−9.67159	−	16.7517i	−0.402634	−	0.697382i	0.591409	−	0.806371i	$-0.298572\pi$
$577$	−9.67159	−	16.7517i	−0.402634	−	0.697382i	−0.994043	+	0.108990i	$0.965238\pi$
$578$	1.87164	−	10.6146i	0.0778501	−	0.441510i
$579$		0			0
$580$	−0.370462	−	0.134837i	−0.0153826	−	0.00559881i
$581$	9.03121	+	3.28709i	0.374678	+	0.136372i
$582$		0			0
$583$	12.0116	−	68.1212i	0.497470	−	2.82129i
$584$	−8.17483	−	14.1592i	−0.338277	−	0.585913i
$585$		0			0
$586$	−13.0403	+	22.5865i	−0.538690	+	0.933038i
$587$	24.4461	+	20.5127i	1.00900	+	0.846650i	0.988205	−	0.153134i	$-0.0489366\pi$
$587$	24.4461	+	20.5127i	1.00900	+	0.846650i	0.0207926	+	0.999784i	$0.493381\pi$
$588$		0			0
$589$	0.678396	+	3.84737i	0.0279528	+	0.158528i
$590$	12.5326	−	10.5161i	0.515957	−	0.432939i
$591$		0			0
$592$	0.141559	−	0.0515234i	0.00581805	−	0.00211760i
$593$	−31.6783			−1.30087			−0.650436	−	0.759561i	$-0.725414\pi$
$593$	−31.6783			−1.30087			−0.650436	+	0.759561i	$0.725414\pi$
$594$		0			0
$595$	11.9564			0.490163
$596$	−3.56418	+	1.29725i	−0.145994	+	0.0531376i
$597$		0			0
$598$	9.80272	−	8.22546i	0.400863	−	0.336364i
$599$	2.19207	+	12.4318i	0.0895654	+	0.507951i	0.996278	+	0.0862011i	$0.0274728\pi$
$599$	2.19207	+	12.4318i	0.0895654	+	0.507951i	−0.906712	+	0.421750i	$0.861416\pi$
$600$		0			0
$601$	−6.82429	−	5.72626i	−0.278369	−	0.233579i	0.492904	−	0.870084i	$-0.335935\pi$
$601$	−6.82429	−	5.72626i	−0.278369	−	0.233579i	−0.771273	+	0.636504i	$0.780380\pi$
$602$	−8.42262	+	14.5884i	−0.343280	+	0.594579i
$603$		0			0
$604$	1.47906	+	2.56180i	0.0601819	+	0.104238i
$605$	−6.98128	+	39.5928i	−0.283829	+	1.60968i
$606$		0			0
$607$	31.1266	+	11.3292i	1.26339	+	0.459836i	0.884905	−	0.465771i	$-0.154223\pi$
$607$	31.1266	+	11.3292i	1.26339	+	0.459836i	0.378485	+	0.925608i	$0.376445\pi$
$608$	−6.49912	−	2.36549i	−0.263574	−	0.0959332i
$609$		0			0
$610$	4.27244	−	24.2302i	0.172986	−	0.981053i
$611$	6.02822	+	10.4412i	0.243876	+	0.422405i
$612$		0			0
$613$	−8.84002	+	15.3114i	−0.357045	+	0.618420i	−0.987466	−	0.157833i	$-0.949549\pi$
$613$	−8.84002	+	15.3114i	−0.357045	+	0.618420i	0.630421	+	0.776254i	$0.282882\pi$
$614$	−21.4733	−	18.0183i	−0.866594	−	0.727158i
$615$		0			0
$616$	−7.32610	−	41.5484i	−0.295177	−	1.67403i
$617$	19.7121	−	16.5404i	0.793581	−	0.665893i	−0.153048	−	0.988219i	$-0.548909\pi$
$617$	19.7121	−	16.5404i	0.793581	−	0.665893i	0.946629	+	0.322326i	$0.104465\pi$
$618$		0			0
$619$	−26.1186	+	9.50638i	−1.04979	+	0.382094i	−0.808585	−	0.588380i	$-0.799766\pi$
$619$	−26.1186	+	9.50638i	−1.04979	+	0.382094i	−0.241209	+	0.970473i	$0.577544\pi$
$620$	−0.179740			−0.00721854
$621$		0			0
$622$	−14.3696			−0.576168
$623$	18.4697	−	6.72243i	0.739974	−	0.269328i
$624$		0			0
$625$	−6.51960	+	5.47059i	−0.260784	+	0.218824i
$626$	−0.892589	−	5.06212i	−0.0356750	−	0.202323i
$627$		0			0
$628$	3.11057	+	2.61007i	0.124125	+	0.104153i
$629$	0.0628336	−	0.108831i	0.00250534	−	0.00433938i
$630$		0			0
$631$	−13.4069	−	23.2214i	−0.533720	−	0.924430i	−0.999224	−	0.0393842i	$-0.987460\pi$
$631$	−13.4069	−	23.2214i	−0.533720	−	0.924430i	0.465504	−	0.885046i	$-0.345873\pi$
$632$	−1.93267	+	10.9607i	−0.0768774	+	0.435993i
$633$		0			0
$634$	−33.4099	−	12.1602i	−1.32688	−	0.482943i
$635$	5.58512	+	2.03282i	0.221639	+	0.0806699i
$636$		0			0
$637$	0.663848	−	3.76487i	0.0263026	−	0.149170i
$638$	−5.16843	−	8.95199i	−0.204620	−	0.354413i
$639$		0			0
$640$	−7.84864	+	13.5942i	−0.310245	+	0.537360i
$641$	−9.72147	−	8.15728i	−0.383975	−	0.322193i	0.430286	−	0.902693i	$-0.358413\pi$
$641$	−9.72147	−	8.15728i	−0.383975	−	0.322193i	−0.814261	+	0.580500i	$0.802857\pi$
$642$		0			0
$643$	2.68748	+	15.2415i	0.105984	+	0.601065i	0.990823	+	0.135167i	$0.0431572\pi$
$643$	2.68748	+	15.2415i	0.105984	+	0.601065i	−0.884839	+	0.465897i	$0.845732\pi$
$644$	−1.00483	+	0.843156i	−0.0395960	+	0.0332250i
$645$		0			0
$646$	25.2126	−	9.17664i	0.991976	−	0.361050i
$647$	−11.1506			−0.438377			−0.219189	−	0.975683i	$-0.570341\pi$
$647$	−11.1506			−0.438377			−0.219189	+	0.975683i	$0.570341\pi$
$648$		0			0
$649$	−43.6691			−1.71416
$650$	9.26739	−	3.37305i	0.363497	−	0.132302i
$651$		0			0
$652$	−2.90348	+	2.43631i	−0.113709	+	0.0954134i
$653$	−7.74335	−	43.9147i	−0.303021	−	1.71851i	−0.632679	−	0.774414i	$-0.718045\pi$
$653$	−7.74335	−	43.9147i	−0.303021	−	1.71851i	0.329658	−	0.944100i	$-0.393066\pi$
$654$		0			0
$655$	−22.4183	−	18.8112i	−0.875957	−	0.735015i
$656$	8.81386	−	15.2661i	0.344124	−	0.596039i
$657$		0			0
$658$	6.06986	+	10.5133i	0.236628	+	0.409851i
$659$	2.44784	−	13.8824i	0.0953545	−	0.540782i	−0.899284	−	0.437366i	$-0.855912\pi$
$659$	2.44784	−	13.8824i	0.0953545	−	0.540782i	0.994638	−	0.103416i	$-0.0329774\pi$
$660$		0			0
$661$	−33.9368	−	12.3520i	−1.31999	−	0.480436i	−0.416533	−	0.909121i	$-0.636755\pi$
$661$	−33.9368	−	12.3520i	−1.31999	−	0.480436i	−0.903454	+	0.428685i	$0.858977\pi$
$662$	−1.98973	−	0.724204i	−0.0773332	−	0.0281470i
$663$		0			0
$664$	−2.03714	+	11.5532i	−0.0790564	+	0.448351i
$665$	−13.2280	−	22.9116i	−0.512961	−	0.888474i
$666$		0			0
$667$	−1.89986	+	3.29066i	−0.0735630	+	0.127415i
$668$	0.607411	+	0.509678i	0.0235014	+	0.0197200i
$669$		0			0
$670$	0.718063	+	4.07234i	0.0277412	+	0.157328i
$671$	−50.3093	+	42.2145i	−1.94217	+	1.62967i
$672$		0			0
$673$	−2.10694	+	0.766865i	−0.0812167	+	0.0295605i	−0.382309	−	0.924035i	$-0.624871\pi$
$673$	−2.10694	+	0.766865i	−0.0812167	+	0.0295605i	0.301092	+	0.953595i	$0.402649\pi$
$674$	10.7992			0.415971
$675$		0			0
$676$	0.478340			0.0183977
$677$	33.0548	−	12.0310i	1.27040	−	0.462388i	0.383155	−	0.923684i	$-0.374838\pi$
$677$	33.0548	−	12.0310i	1.27040	−	0.462388i	0.887246	+	0.461296i	$0.152615\pi$
$678$		0			0
$679$	0.481830	−	0.404303i	0.0184909	−	0.0155157i
$680$	2.53431	+	14.3728i	0.0971864	+	0.551171i
$681$		0			0
$682$	−3.61019	−	3.02931i	−0.138241	−	0.115998i
$683$	−8.88191	+	15.3839i	−0.339857	+	0.588649i	−0.984406	−	0.175914i	$-0.943712\pi$
$683$	−8.88191	+	15.3839i	−0.339857	+	0.588649i	0.644549	+	0.764563i	$0.277045\pi$
$684$		0			0
$685$	3.24675	+	5.62353i	0.124052	+	0.214864i
$686$	4.61768	−	26.1882i	0.176304	−	0.999868i
$687$		0			0
$688$	−17.5214	−	6.37727i	−0.667998	−	0.243131i
$689$	−35.2879	−	12.8438i	−1.34436	−	0.489308i
$690$		0			0
$691$	−7.64584	+	43.3617i	−0.290861	+	1.64956i	0.392702	+	0.919666i	$0.371541\pi$
$691$	−7.64584	+	43.3617i	−0.290861	+	1.64956i	−0.683563	+	0.729891i	$0.739571\pi$
$692$	−0.350452	−	0.607000i	−0.0133222	−	0.0230747i
$693$		0			0
$694$	−13.3687	+	23.1553i	−0.507469	+	0.878962i
$695$	−15.1493	−	12.7118i	−0.574646	−	0.482185i
$696$		0			0
$697$	−2.55350	−	14.4816i	−0.0967207	−	0.548530i
$698$	−11.4492	+	9.60706i	−0.433360	+	0.363632i
$699$		0			0
$700$	−0.949960	+	0.345757i	−0.0359051	+	0.0130684i
$701$	30.1052			1.13706			0.568530	−	0.822663i	$-0.307512\pi$
$701$	30.1052			1.13706			0.568530	+	0.822663i	$0.307512\pi$
$702$		0			0
$703$	−0.278066			−0.0104875
$704$	48.0112	−	17.4746i	1.80949	−	0.658601i
$705$		0			0
$706$	−2.95580	+	2.48021i	−0.111243	+	0.0933441i
$707$	−4.61768	−	26.1882i	−0.173666	−	0.984907i
$708$		0			0
$709$	−18.9500	−	15.9009i	−0.711681	−	0.597171i	0.213390	−	0.976967i	$-0.431550\pi$
$709$	−18.9500	−	15.9009i	−0.711681	−	0.597171i	−0.925070	+	0.379796i	$0.875994\pi$
$710$	−6.13728	+	10.6301i	−0.230328	+	0.398940i
$711$		0			0
$712$	11.9960	+	20.7776i	0.449568	+	0.778674i
$713$	−0.300822	+	1.70604i	−0.0112659	+	0.0638919i
$714$		0			0
$715$	29.7841	+	10.8405i	1.11386	+	0.405412i
$716$	−1.43717	−	0.523086i	−0.0537094	−	0.0195486i
$717$		0			0
$718$	6.73530	−	38.1978i	0.251359	−	1.42553i
$719$	−21.7763	−	37.7177i	−0.812119	−	1.40663i	−0.911378	−	0.411570i	$-0.864980\pi$
$719$	−21.7763	−	37.7177i	−0.812119	−	1.40663i	0.0992586	−	0.995062i	$-0.468353\pi$
$720$		0			0
$721$	4.71048	−	8.15880i	0.175428	−	0.303850i
$722$	−25.8694	−	21.7070i	−0.962760	−	0.807852i
$723$		0			0
$724$	−0.215699	−	1.22329i	−0.00801640	−	0.0454633i
$725$	−2.24329	+	1.88234i	−0.0833137	+	0.0699085i
$726$		0			0
$727$	−19.2986	+	7.02412i	−0.715745	+	0.260510i	−0.674119	−	0.738623i	$-0.735476\pi$
$727$	−19.2986	+	7.02412i	−0.715745	+	0.260510i	−0.0416269	+	0.999133i	$0.513254\pi$
$728$	−22.9040			−0.848880
$729$		0			0
$730$	12.3678			0.457754
$731$	−14.6163	+	5.31991i	−0.540605	+	0.196764i
$732$		0			0
$733$	10.7292	−	9.00287i	0.396292	−	0.332529i	−0.422766	−	0.906239i	$-0.638941\pi$
$733$	10.7292	−	9.00287i	0.396292	−	0.332529i	0.819058	+	0.573710i	$0.194496\pi$
$734$	2.57170	+	14.5848i	0.0949232	+	0.538336i
$735$		0			0
$736$	−2.34936	−	1.97134i	−0.0865984	−	0.0726647i
$737$	5.51889	−	9.55899i	0.203291	−	0.352110i
$738$		0			0
$739$	20.9907	+	36.3569i	0.772154	+	1.33741i	0.936380	+	0.350987i	$0.114154\pi$
$739$	20.9907	+	36.3569i	0.772154	+	1.33741i	−0.164226	+	0.986423i	$0.552513\pi$
$740$	0.00222152	−	0.0125989i	8.16647e−5	−	0.000463144i
$741$		0			0
$742$	−35.5317	−	12.9325i	−1.30441	−	0.474766i
$743$	26.1819	+	9.52942i	0.960519	+	0.349600i	0.774237	−	0.632896i	$-0.218134\pi$
$743$	26.1819	+	9.52942i	0.960519	+	0.349600i	0.186282	+	0.982496i	$0.440356\pi$
$744$		0			0
$745$	5.89053	−	33.4069i	0.215812	−	1.22393i
$746$	22.5064	+	38.9822i	0.824018	+	1.42724i
$747$		0			0
$748$	1.64749	−	2.85353i	0.0602382	−	0.104336i
$749$	4.87346	+	4.08931i	0.178072	+	0.149420i
$750$		0			0
$751$	−9.18685	−	52.1012i	−0.335233	−	1.90120i	−0.424920	−	0.905231i	$-0.639698\pi$
$751$	−9.18685	−	52.1012i	−0.335233	−	1.90120i	0.0896873	−	0.995970i	$-0.471413\pi$
$752$	−10.2936	+	8.63738i	−0.375370	+	0.314973i
$753$		0			0
$754$	−5.27332	+	1.91933i	−0.192043	+	0.0698979i
$755$	−26.4561			−0.962834
$756$		0			0
$757$	−41.4858			−1.50783			−0.753913	−	0.656975i	$-0.771836\pi$
$757$	−41.4858			−1.50783			−0.753913	+	0.656975i	$0.771836\pi$
$758$	26.5103	−	9.64895i	0.962896	−	0.350466i
$759$		0			0
$760$	24.7383	−	20.7579i	0.897352	−	0.752968i
$761$	7.88144	+	44.6979i	0.285702	+	1.62030i	0.702767	+	0.711420i	$0.251948\pi$
$761$	7.88144	+	44.6979i	0.285702	+	1.62030i	−0.417064	+	0.908877i	$0.636941\pi$
$762$		0			0
$763$	−16.5483	−	13.8857i	−0.599088	−	0.502695i
$764$	0.463326	−	0.802503i	0.0167625	−	0.0290336i
$765$		0			0
$766$	2.76945	+	4.79682i	0.100064	+	0.173316i
$767$	−4.11674	+	23.3472i	−0.148647	+	0.843019i
$768$		0			0
$769$	−4.80793	−	1.74994i	−0.173379	−	0.0631046i	0.253872	−	0.967238i	$-0.418296\pi$
$769$	−4.80793	−	1.74994i	−0.173379	−	0.0631046i	−0.427251	+	0.904133i	$0.640518\pi$
$770$	29.9898	+	10.9154i	1.08076	+	0.393363i
$771$		0			0
$772$	0.573263	−	3.25113i	0.0206322	−	0.117011i
$773$	−26.3214	−	45.5899i	−0.946713	−	1.63976i	−0.752284	−	0.658839i	$-0.771048\pi$
$773$	−26.3214	−	45.5899i	−0.946713	−	1.63976i	−0.194430	−	0.980916i	$-0.562286\pi$
$774$		0			0
$775$	−0.667556	+	1.15624i	−0.0239793	+	0.0415334i
$776$	0.588145	+	0.493513i	0.0211132	+	0.0177161i
$777$		0			0
$778$	3.99928	+	22.6811i	0.143381	+	0.813156i
$779$	−24.9256	+	20.9151i	−0.893053	+	0.749360i
$780$		0			0

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26604 - 0.460802i) q^{2} +(-0.141559 + 0.118782i) q^{4} +(-0.286989 - 1.62760i) q^{5} +(1.84730 + 1.55007i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-1.11334 - 1.92836i) q^{10} +(-1.03209 + 5.85327i) q^{11} +(3.03209 + 1.10359i) q^{13} +(3.05303 + 1.11121i) q^{14} +(-0.624485 + 3.54163i) q^{16} +(1.50000 + 2.59808i) q^{17} +(3.31908 - 5.74881i) q^{19} +(0.233956 + 0.196312i) q^{20} +(1.39053 + 7.88609i) q^{22} +(2.25490 - 1.89209i) q^{23} +(2.13176 - 0.775897i) q^{25} +4.34730 q^{26} -0.445622 q^{28} +(-1.21301 + 0.441500i) q^{29} +(-0.450837 + 0.378297i) q^{31} +(-0.180922 - 1.02606i) q^{32} +(3.09627 + 2.59808i) q^{34} +(1.99273 - 3.45150i) q^{35} +(-0.0209445 - 0.0362770i) q^{37} +(1.55303 - 8.80769i) q^{38} +(4.57145 + 1.66387i) q^{40} +(-4.60607 - 1.67647i) q^{41} +(-0.900330 + 5.10602i) q^{43} +(-0.549163 - 0.951178i) q^{44} +(1.98293 - 3.43453i) q^{46} +(2.86231 + 2.40176i) q^{47} +(-0.205737 - 1.16679i) q^{49} +(2.34137 - 1.96464i) q^{50} +(-0.560307 + 0.203935i) q^{52} -11.6382 q^{53} +9.82295 q^{55} +(-6.67024 + 2.42777i) q^{56} +(-1.33228 + 1.11792i) q^{58} +(1.27584 + 7.23567i) q^{59} +(8.46451 + 7.10257i) q^{61} +(-0.396459 + 0.686688i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(0.926022 - 5.25173i) q^{65} +(-1.74510 - 0.635164i) q^{67} +(-0.520945 - 0.189608i) q^{68} +(0.932419 - 5.28801i) q^{70} +(-2.75624 - 4.77396i) q^{71} +(-2.77719 + 4.81023i) q^{73} +(-0.0432332 - 0.0362770i) q^{74} +(0.213011 + 1.20805i) q^{76} +(-10.9795 + 9.21291i) q^{77} +(3.55303 - 1.29320i) q^{79} +5.94356 q^{80} -6.60401 q^{82} +(3.74510 - 1.36310i) q^{83} +(3.79813 - 3.18701i) q^{85} +(1.21301 + 6.87933i) q^{86} +(-13.4021 - 11.2457i) q^{88} +(4.07532 - 7.05866i) q^{89} +(3.89053 + 6.73859i) q^{91} +(-0.0944557 + 0.535685i) q^{92} +(4.73055 + 1.72178i) q^{94} +(-10.3093 - 3.75227i) q^{95} +(0.0452926 - 0.256867i) q^{97} +(-0.798133 - 1.38241i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 9 q^{4} + 6 q^{5} + 9 q^{7} + 6 q^{8} + 3 q^{11} + 9 q^{13} + 6 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 15 q^{23} + 18 q^{25} + 24 q^{26} - 24 q^{28} - 15 q^{29}+ \cdots + 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 9 * q^4 + 6 * q^5 + 9 * q^7 + 6 * q^8 + 3 * q^11 + 9 * q^13 + 6 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 15 * q^23 + 18 * q^25 + 24 * q^26 - 24 * q^28 - 15 * q^29 + 9 * q^31 - 18 * q^32 - 9 * q^34 - 6 * q^35 + 3 * q^37 - 3 * q^38 + 27 * q^40 - 3 * q^41 + 9 * q^43 - 15 * q^44 - 9 * q^46 - 15 * q^47 + 9 * q^49 - 15 * q^50 - 9 * q^52 - 36 * q^53 + 18 * q^55 + 3 * q^56 - 36 * q^58 + 6 * q^59 + 18 * q^61 - 12 * q^62 - 12 * q^64 + 21 * q^65 - 9 * q^67 - 18 * q^70 - 9 * q^71 - 6 * q^73 + 15 * q^74 + 9 * q^76 - 3 * q^77 + 9 * q^79 + 6 * q^80 + 36 * q^82 + 21 * q^83 + 9 * q^85 + 15 * q^86 + 9 * q^88 + 6 * q^91 - 48 * q^92 - 9 * q^94 - 42 * q^95 + 36 * q^97 + 9 * q^98

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