LMFDB - Embedded newform 729.2.e.b.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.b.568.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.748339	−	0.663316i	$-0.769148\pi$
$2$	−1.26604	+	0.460802i	−0.895229	+	0.325837i	−0.146889	+	0.989153i	$0.546926\pi$
$3$		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	$0.0649346\pi$
$5$	0.286989	+	1.62760i	0.128345	+	0.727883i	−0.850919	+	0.525297i	$0.823954\pi$
$6$		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	$-0.590886\pi$
$11$	1.03209	−	5.85327i	0.311187	−	1.76483i	0.592850	−	0.805313i	$-0.298003\pi$
$12$		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	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		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	−0.846860	−	0.531816i	$-0.821510\pi$
$23$	−2.25490	+	1.89209i	−0.470179	+	0.394527i	0.376681	+	0.926343i	$0.377065\pi$
$24$		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	−0.226929	−	0.973911i	$-0.572869\pi$
$29$	1.21301	−	0.441500i	0.225250	−	0.0819845i	0.452180	+	0.891927i	$0.350646\pi$
$30$		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	0.675648	−	0.737224i	$-0.263864\pi$
$41$	4.60607	+	1.67647i	0.719347	+	0.261821i	0.0436983	+	0.999045i	$0.486086\pi$
$42$		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	0.409704	−	0.912218i	$-0.365632\pi$
$47$	−2.86231	−	2.40176i	−0.417511	−	0.350333i	−0.827215	+	0.561885i	$0.810076\pi$
$48$		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	$-0.205198\pi$
$53$	11.6382			1.59862			0.799312	+	0.600916i	$0.205198\pi$
$54$		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	$-0.896820\pi$
$59$	−1.27584	−	7.23567i	−0.166101	−	0.942005i	0.781821	−	0.623503i	$-0.214291\pi$
$60$		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	0.981936	−	0.189212i	$-0.0605932\pi$
$71$	2.75624	+	4.77396i	0.327106	+	0.566564i	−0.654830	+	0.755776i	$0.727260\pi$
$72$		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	−0.539277	−	0.842128i	$-0.681303\pi$
$83$	−3.74510	+	1.36310i	−0.411078	+	0.149620i	0.128199	+	0.991748i	$0.459080\pi$
$84$		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	−0.997044	−	0.0768323i	$-0.975519\pi$
$89$	−4.07532	+	7.05866i	−0.431983	+	0.748217i	0.565061	+	0.825049i	$0.308853\pi$
$90$		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	0.957688	−	0.287810i	$-0.0929271\pi$
$101$	8.44743	+	7.08824i	0.840551	+	0.705306i	−0.117137	+	0.993116i	$0.537372\pi$
$102$		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	$-0.540702\pi$
$107$	−2.63816			−0.255040			−0.127520	+	0.991836i	$0.540702\pi$
$108$		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	$0.214024\pi$
$113$	2.76604	+	15.6870i	0.260208	+	1.47571i	−0.522135	+	0.852863i	$0.674864\pi$
$114$		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	$0.559299\pi$
$131$	−13.5646	+	11.3821i	−1.18515	+	0.994458i	−0.999931	+	0.0117601i	$0.996257\pi$
$132$		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	−0.179451	−	0.983767i	$-0.557432\pi$
$137$	3.69207	−	1.34380i	0.315435	−	0.114809i	0.494886	+	0.868958i	$0.335210\pi$
$138$		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	−0.604866	−	0.796327i	$-0.706773\pi$
$149$	−19.2875	−	7.02006i	−1.58009	−	0.575106i	−0.975224	+	0.221221i	$0.928996\pi$
$150$		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	0.999970	−	0.00774226i	$-0.00246446\pi$
$167$	0.745100	+	4.22567i	0.0576576	+	0.326992i	−0.942312	+	0.334735i	$0.891353\pi$
$168$		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	−0.949480	−	0.313828i	$-0.898388\pi$
$173$	0.658633	−	3.73530i	0.0500750	−	0.283989i	0.999555	+	0.0298390i	$0.00949947\pi$
$174$		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	0.668909	−	0.743344i	$-0.266761\pi$
$179$	−4.13816	−	7.16750i	−0.309300	−	0.535724i	−0.978209	+	0.207620i	$0.933428\pi$
$180$		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	−0.165866	−	0.986148i	$-0.553042\pi$
$191$	4.71213	−	1.71508i	0.340958	−	0.124099i	0.506824	+	0.862050i	$0.330820\pi$
$192$		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	−0.878628	−	0.477507i	$-0.841540\pi$
$197$	−0.361844	+	0.626733i	−0.0257803	+	0.0446529i	0.852847	+	0.522160i	$0.174874\pi$
$198$		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	$0.250634\pi$
$227$	−3.00980	+	17.0694i	−0.199767	+	1.13294i	−0.905464	+	0.424423i	$0.860477\pi$
$228$		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	$-0.981319\pi$
$233$	−8.39440	−	14.5395i	−0.549935	−	0.952516i	0.448343	−	0.893862i	$-0.352014\pi$
$234$		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	−0.737130	−	0.675751i	$-0.763820\pi$
$239$	−3.08647	+	2.58985i	−0.199647	+	0.167524i	0.537483	+	0.843274i	$0.319375\pi$
$240$		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	$-0.572561\pi$
$251$	11.5753	−	20.0490i	0.730628	−	1.26548i	0.956615	−	0.291354i	$-0.0941059\pi$
$252$		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	−0.0349665	−	0.999388i	$-0.511132\pi$
$257$	−11.2883	−	4.10862i	−0.704147	−	0.256289i	−0.669180	+	0.743100i	$0.733355\pi$
$258$		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	0.947803	−	0.318858i	$-0.103299\pi$
$263$	12.9474	+	10.8642i	0.798373	+	0.669914i	−0.149430	+	0.988772i	$0.547744\pi$
$264$		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	$-0.577566\pi$
$269$	−7.91447			−0.482554			−0.241277	+	0.970456i	$0.577566\pi$
$270$		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	$0.247297\pi$
$281$	−3.29860	+	18.7073i	−0.196778	+	1.11598i	−0.909864	+	0.414907i	$0.863814\pi$
$282$		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	−0.0970060	−	0.995284i	$-0.530927\pi$
$293$	14.8289	−	12.4429i	0.866312	−	0.726922i	0.963318	+	0.268361i	$0.0864822\pi$
$294$		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	0.610164	−	0.792275i	$-0.291104\pi$
$311$	10.0223	+	3.64781i	0.568312	+	0.206849i	−0.0418520	+	0.999124i	$0.513326\pi$
$312$		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	0.999279	−	0.0379748i	$-0.0120907\pi$
$317$	20.2153	+	16.9626i	1.13540	+	0.952717i	0.136125	+	0.990692i	$0.456535\pi$
$318$		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	−0.135952	−	0.990715i	$-0.543409\pi$
$347$	15.2023	−	12.7563i	0.816104	−	0.684793i	0.952056	+	0.305923i	$0.0989649\pi$
$348$		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	−0.269407	−	0.963027i	$-0.586828\pi$
$353$	2.69119	−	0.979513i	0.143238	−	0.0521342i	0.412644	+	0.910892i	$0.364605\pi$
$354$		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	$0.441324\pi$
$359$	−14.3944	+	24.9318i	−0.759707	+	1.31585i	−0.943000	+	0.332793i	$0.892009\pi$
$360$		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	0.961121	−	0.276126i	$-0.0890508\pi$
$383$	−0.713888	−	4.04866i	−0.0364780	−	0.206877i	−0.997599	+	0.0692492i	$0.977940\pi$
$384$		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	$-0.801774\pi$
$389$	2.96838	−	16.8345i	0.150503	−	0.853543i	0.962783	−	0.270276i	$-0.0871149\pi$
$390$		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	−0.877577	−	0.479435i	$-0.840842\pi$
$401$	−11.1702	+	9.37295i	−0.557815	+	0.468063i	0.319762	+	0.947498i	$0.396397\pi$
$402$		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	−0.129397	−	0.991593i	$-0.541304\pi$
$419$	−17.7246	−	6.45123i	−0.865904	−	0.315163i	−0.736507	+	0.676429i	$0.763526\pi$
$420$		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	$-0.190338\pi$
$431$	34.3164			1.65297			0.826483	+	0.562962i	$0.190338\pi$
$432$		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	−0.997078	−	0.0763910i	$-0.975660\pi$
$443$	−0.715699	+	4.05893i	−0.0340039	+	0.192846i	0.963074	+	0.269237i	$0.0867714\pi$
$444$		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	0.564320	−	0.825556i	$-0.309138\pi$
$449$	−9.17071	−	15.8841i	−0.432793	−	0.749619i	−0.997113	+	0.0759373i	$0.975805\pi$
$450$		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	−0.868252	−	0.496123i	$-0.834757\pi$
$461$	−26.0758	+	9.49081i	−1.21447	+	0.442031i	−0.346218	+	0.938154i	$0.612534\pi$
$462$		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	$0.408464\pi$
$467$	−14.8819	+	25.7762i	−0.688653	+	1.19278i	−0.972274	+	0.233845i	$0.924869\pi$
$468$		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	$-0.947786\pi$
$479$	−28.8614	−	24.2176i	−1.31871	−	1.10653i	−0.332136	−	0.943231i	$-0.607769\pi$
$480$		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	0.982794	−	0.184702i	$-0.0591321\pi$
$491$	−0.0864665	−	0.490376i	−0.00390218	−	0.0221303i	−0.986697	+	0.162572i	$0.948021\pi$
$492$		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	0.585461	−	0.810701i	$-0.300914\pi$
$503$	−9.18092	−	15.9018i	−0.409357	−	0.709027i	−0.994818	+	0.101673i	$0.967580\pi$
$504$		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	−0.981487	−	0.191528i	$-0.938656\pi$
$509$	−21.7331	+	18.2362i	−0.963302	+	0.808306i	0.0181853	+	0.999835i	$0.494211\pi$
$510$		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	$-0.579782\pi$
$521$	16.3191	−	28.2655i	0.714952	−	1.23833i	0.962978	−	0.269580i	$-0.0868847\pi$
$522$		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	$-0.952621\pi$
$557$	−14.7010	−	25.4629i	−0.622901	−	1.07890i	0.366042	−	0.930598i	$-0.380713\pi$
$558$		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	−0.794657	−	0.607059i	$-0.792349\pi$
$563$	−7.94428	+	6.66604i	−0.334811	+	0.280940i	0.459845	+	0.887999i	$0.347905\pi$
$564$		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	0.402185	−	0.915559i	$-0.368251\pi$
$569$	30.9809	−	11.2761i	1.29879	−	0.472719i	0.896601	+	0.442839i	$0.146029\pi$
$570$		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	−0.0207926	−	0.999784i	$-0.506619\pi$
$587$	−24.4461	−	20.5127i	−1.00900	−	0.846650i	−0.988205	+	0.153134i	$0.951063\pi$
$588$		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	$-0.274586\pi$
$593$	31.6783			1.30087			0.650436	+	0.759561i	$0.274586\pi$
$594$		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	$-0.972527\pi$
$599$	−2.19207	−	12.4318i	−0.0895654	−	0.507951i	0.906712	−	0.421750i	$-0.138584\pi$
$600$		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	−0.946629	−	0.322326i	$-0.895535\pi$
$617$	−19.7121	+	16.5404i	−0.793581	+	0.665893i	0.153048	+	0.988219i	$0.451091\pi$
$618$		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	0.814261	−	0.580500i	$-0.197143\pi$
$641$	9.72147	+	8.15728i	0.383975	+	0.322193i	−0.430286	+	0.902693i	$0.641587\pi$
$642$		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	$-0.429659\pi$
$647$	11.1506			0.438377			0.219189	+	0.975683i	$0.429659\pi$
$648$		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	$0.281955\pi$
$653$	7.74335	+	43.9147i	0.303021	+	1.71851i	−0.329658	+	0.944100i	$0.606934\pi$
$654$		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	$0.144088\pi$
$659$	−2.44784	+	13.8824i	−0.0953545	+	0.540782i	−0.994638	+	0.103416i	$0.967023\pi$
$660$		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	−0.887246	−	0.461296i	$-0.847385\pi$
$677$	−33.0548	+	12.0310i	−1.27040	+	0.462388i	−0.383155	+	0.923684i	$0.625162\pi$
$678$		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	−0.644549	−	0.764563i	$-0.722955\pi$
$683$	8.88191	−	15.3839i	0.339857	−	0.588649i	0.984406	+	0.175914i	$0.0562880\pi$
$684$		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	$-0.692488\pi$
$701$	−30.1052			−1.13706			−0.568530	+	0.822663i	$0.692488\pi$
$702$		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	$0.135020\pi$
$719$	21.7763	+	37.7177i	0.812119	+	1.40663i	−0.0992586	+	0.995062i	$0.531647\pi$
$720$		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	−0.186282	−	0.982496i	$-0.559644\pi$
$743$	−26.1819	−	9.52942i	−0.960519	−	0.349600i	−0.774237	+	0.632896i	$0.781866\pi$
$744$		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	$-0.748052\pi$
$761$	−7.88144	−	44.6979i	−0.285702	−	1.62030i	0.417064	−	0.908877i	$-0.363059\pi$
$762$		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	$0.228952\pi$
$773$	26.3214	+	45.5899i	0.946713	+	1.63976i	0.194430	+	0.980916i	$0.437714\pi$
$774$		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
$781$	30.7879	−	11.2059i	1.10168	−	0.400978i
$782$	−11.8976			−0.425456
$783$		0			0
$784$	4.26083			0.152172
$785$	34.1257	−	12.4207i	1.21800	−	0.443315i
$786$		0			0
$787$	−15.9049	+	13.3458i	−0.566949	+	0.475727i	−0.880632	−	0.473801i	$-0.842882\pi$
$787$	−15.9049	+	13.3458i	−0.566949	+	0.475727i	0.313683	+	0.949528i	$0.398437\pi$
$788$	−0.0232224	−	0.131701i	−0.000827262	−	0.00469164i
$789$		0			0
$790$	−6.44949	−	5.41177i	−0.229463	−	0.192542i
$791$	−19.2062	+	33.2661i	−0.682894	+	1.18281i
$792$		0			0
$793$	17.8268	+	30.8770i	0.633049	+	1.09647i
$794$	5.24107	−	29.7236i	0.185999	−	1.05485i
$795$		0			0
$796$	−1.76991	−	0.644196i	−0.0627330	−	0.0228329i
$797$	42.8312	+	15.5893i	1.51716	+	0.552200i	0.960436	−	0.278499i	$-0.0898370\pi$
$797$	42.8312	+	15.5893i	1.51716	+	0.552200i	0.556721	+	0.830700i	$0.312059\pi$
$798$		0			0
$799$	−1.94650	+	11.0391i	−0.0688622	+	0.390537i
$800$	1.18180	+	2.04694i	0.0417829	+	0.0723701i
$801$		0			0
$802$	9.82295	−	17.0138i	0.346860	−	0.600780i
$803$	25.2893	+	21.2202i	0.892439	+	0.748845i
$804$		0			0
$805$	−2.03714	−	11.5532i	−0.0717998	−	0.407197i
$806$	1.95992	−	1.64457i	0.0690353	−	0.0579275i
$807$		0			0
$808$	30.5021	−	11.1019i	1.07306	−	0.390562i
$809$	−4.21120			−0.148058			−0.0740290	−	0.997256i	$-0.523586\pi$
$809$	−4.21120			−0.148058			−0.0740290	+	0.997256i	$0.523586\pi$
$810$		0			0
$811$	11.3618			0.398968			0.199484	−	0.979901i	$-0.436073\pi$
$811$	11.3618			0.398968			0.199484	+	0.979901i	$0.436073\pi$
$812$	−0.540545	+	0.196742i	−0.0189694	+	0.00690430i
$813$		0			0
$814$	0.256959	−	0.215615i	0.00900643	−	0.00755729i
$815$	5.88635	+	33.3832i	0.206190	+	1.16936i
$816$		0			0
$817$	26.3653	+	22.1231i	0.922405	+	0.773990i
$818$	11.7909	−	20.4224i	0.412258	−	0.714051i
$819$		0			0
$820$	−0.748503	−	1.29645i	−0.0261389	−	0.0452739i
$821$	0.285178	−	1.61732i	0.00995278	−	0.0564450i	−0.979427	−	0.201799i	$-0.935321\pi$
$821$	0.285178	−	1.61732i	0.00995278	−	0.0564450i	0.989380	+	0.145354i	$0.0464322\pi$
$822$		0			0
$823$	−10.5424	−	3.83710i	−0.367483	−	0.133753i	0.151676	−	0.988430i	$-0.451533\pi$
$823$	−10.5424	−	3.83710i	−0.367483	−	0.133753i	−0.519160	+	0.854677i	$0.673755\pi$
$824$	−10.8062	−	3.93313i	−0.376451	−	0.137017i
$825$		0			0
$826$	−4.14518	+	23.5085i	−0.144229	+	0.817965i
$827$	4.80659	+	8.32526i	0.167141	+	0.289498i	0.937414	−	0.348218i	$-0.113213\pi$
$827$	4.80659	+	8.32526i	0.167141	+	0.289498i	−0.770272	+	0.637715i	$0.779880\pi$
$828$		0			0
$829$	−16.7469	+	29.0065i	−0.581644	+	1.00744i	0.413640	+	0.910440i	$0.364257\pi$
$829$	−16.7469	+	29.0065i	−0.581644	+	1.00744i	−0.995285	+	0.0969971i	$0.969076\pi$
$830$	6.79813	+	5.70431i	0.235967	+	0.198000i
$831$		0			0
$832$	−4.81655	−	27.3160i	−0.166984	−	0.947013i
$833$	−2.72281	+	2.28471i	−0.0943398	+	0.0791605i
$834$		0			0
$835$	−6.66385	+	2.42544i	−0.230612	+	0.0839359i
$836$	7.29086			0.252160
$837$		0			0
$838$	25.4129			0.877874
$839$	30.0646	−	10.9426i	1.03795	−	0.377782i	0.233845	−	0.972274i	$-0.424869\pi$
$839$	30.0646	−	10.9426i	1.03795	−	0.377782i	0.804101	+	0.594492i	$0.202647\pi$
$840$		0			0
$841$	−20.9388	+	17.5698i	−0.722028	+	0.605854i
$842$	−7.56464	−	42.9012i	−0.260695	−	1.47847i
$843$		0			0
$844$	2.10426	+	1.76568i	0.0724315	+	0.0607772i
$845$	2.13903	−	3.70491i	0.0735850	−	0.127453i
$846$		0			0
$847$	−29.3307	−	50.8022i	−1.00781	−	1.74559i
$848$	−7.26786	+	41.2181i	−0.249579	+	1.41543i
$849$		0			0
$850$	8.61633	+	3.13609i	0.295538	+	0.107567i
$851$	0.115867	+	0.0421721i	0.00397187	+	0.00144564i
$852$		0			0
$853$	6.11974	−	34.7068i	0.209536	−	1.18834i	−0.680605	−	0.732651i	$-0.738283\pi$
$853$	6.11974	−	34.7068i	0.209536	−	1.18834i	0.890141	−	0.455686i	$-0.150606\pi$
$854$	−17.9500	−	31.0902i	−0.614235	−	1.06389i
$855$		0			0
$856$	−3.88279	+	6.72519i	−0.132711	+	0.229862i
$857$	−16.2777	−	13.6586i	−0.556034	−	0.466568i	0.320944	−	0.947098i	$-0.396000\pi$
$857$	−16.2777	−	13.6586i	−0.556034	−	0.466568i	−0.876978	+	0.480530i	$0.840444\pi$
$858$		0			0
$859$	9.00165	+	51.0509i	0.307132	+	1.74183i	0.613294	+	0.789854i	$0.289844\pi$
$859$	9.00165	+	51.0509i	0.307132	+	1.74183i	−0.306162	+	0.951979i	$0.599045\pi$
$860$	1.21301	−	1.01784i	0.0413633	−	0.0347080i
$861$		0			0
$862$	−43.4461	+	15.8131i	−1.47978	+	0.538596i
$863$	−22.6783			−0.771978			−0.385989	−	0.922503i	$-0.626140\pi$
$863$	−22.6783			−0.771978			−0.385989	+	0.922503i	$0.626140\pi$
$864$		0			0
$865$	6.26857			0.213138
$866$	31.7358	−	11.5509i	1.07843	−	0.392515i
$867$		0			0
$868$	0.200903	−	0.168578i	0.00681909	−	0.00572190i
$869$	−3.90239	−	22.1315i	−0.132379	−	0.750761i
$870$		0			0
$871$	−4.59034	−	3.85175i	−0.155538	−	0.130512i
$872$	−13.1844	+	22.8360i	−0.446480	+	0.773325i
$873$		0			0
$874$	−13.1630	−	22.7989i	−0.445244	−	0.771185i
$875$	−5.03033	+	28.5284i	−0.170056	+	0.964437i
$876$		0			0
$877$	−1.06506	−	0.387648i	−0.0359644	−	0.0130900i	0.323975	−	0.946066i	$-0.394981\pi$
$877$	−1.06506	−	0.387648i	−0.0359644	−	0.0130900i	−0.359940	+	0.932976i	$0.617203\pi$
$878$	29.3824	+	10.6943i	0.991607	+	0.360916i
$879$		0			0
$880$	−6.13429	+	34.7893i	−0.206787	+	1.17275i
$881$	15.4145	+	26.6986i	0.519327	+	0.899500i	0.999748	+	0.0224621i	$0.00715051\pi$
$881$	15.4145	+	26.6986i	0.519327	+	0.899500i	−0.480421	+	0.877038i	$0.659516\pi$
$882$		0			0
$883$	4.66756	−	8.08444i	0.157076	−	0.272063i	−0.776737	−	0.629825i	$-0.783127\pi$
$883$	4.66756	−	8.08444i	0.157076	−	0.272063i	0.933813	+	0.357762i	$0.116460\pi$
$884$	1.37030	+	1.14982i	0.0460882	+	0.0386726i
$885$		0			0
$886$	−0.964259	−	5.46859i	−0.0323949	−	0.183721i
$887$	−10.7968	+	9.05958i	−0.362521	+	0.304191i	−0.805794	−	0.592195i	$-0.798261\pi$
$887$	−10.7968	+	9.05958i	−0.362521	+	0.304191i	0.443274	+	0.896386i	$0.353817\pi$
$888$		0			0
$889$	−8.14930	+	2.96610i	−0.273319	+	0.0994799i
$890$	18.1489			0.608352
$891$		0			0
$892$	2.02322			0.0677425
$893$	−23.3075	+	8.48324i	−0.779957	+	0.283881i
$894$		0			0
$895$	10.4782	−	8.79224i	0.350247	−	0.293892i
$896$	3.97724	+	22.5561i	0.132870	+	0.753546i
$897$		0			0
$898$	18.9300	+	15.8841i	0.631702	+	0.530061i
$899$	−0.379852	+	0.657923i	−0.0126688	+	0.0219430i
$900$		0			0
$901$	−17.4572	−	30.2368i	−0.581585	−	1.00733i
$902$	−6.81592	+	38.6550i	−0.226945	+	1.28707i
$903$		0			0
$904$	44.0604	+	16.0367i	1.46543	+	0.533371i
$905$	−10.4394	−	3.79963i	−0.347017	−	0.126304i
$906$		0			0
$907$	−1.51754	+	8.60640i	−0.0503891	+	0.285771i	−0.999582	−	0.0289253i	$-0.990792\pi$
$907$	−1.51754	+	8.60640i	−0.0503891	+	0.285771i	0.949192	+	0.314696i	$0.101903\pi$
$908$	−1.60148	−	2.77385i	−0.0531470	−	0.0920533i
$909$		0			0
$910$	8.66297	−	15.0047i	0.287175	−	0.497401i
$911$	−15.8195	−	13.2742i	−0.524125	−	0.439793i	0.341942	−	0.939721i	$-0.388915\pi$
$911$	−15.8195	−	13.2742i	−0.524125	−	0.439793i	−0.866067	+	0.499928i	$0.833360\pi$
$912$		0			0
$913$	4.11334	+	23.3279i	0.136132	+	0.772041i
$914$	−20.0856	+	16.8538i	−0.664372	+	0.557475i
$915$		0			0
$916$	0.271259	−	0.0987302i	0.00896265	−	0.00326214i
$917$	−42.7009			−1.41011
$918$		0			0
$919$	−2.36009			−0.0778522			−0.0389261	−	0.999242i	$-0.512394\pi$
$919$	−2.36009			−0.0778522			−0.0389261	+	0.999242i	$0.512394\pi$
$920$	−13.4564	+	4.89771i	−0.443643	+	0.161473i
$921$		0			0
$922$	28.6397	−	24.0316i	0.943199	−	0.791438i
$923$	3.08869	+	17.5168i	0.101665	+	0.576573i
$924$		0			0
$925$	−0.0727959	−	0.0610830i	−0.00239351	−	0.00200840i
$926$	−26.0608	+	45.1386i	−0.856410	+	1.48335i
$927$		0			0
$928$	0.672466	+	1.16475i	0.0220748	+	0.0382346i
$929$	−4.65729	+	26.4128i	−0.152801	+	0.866576i	0.807968	+	0.589226i	$0.200567\pi$
$929$	−4.65729	+	26.4128i	−0.152801	+	0.866576i	−0.960769	+	0.277350i	$0.910544\pi$
$930$		0			0
$931$	−7.39053	−	2.68993i	−0.242215	−	0.0881590i
$932$	2.91534	+	1.06110i	0.0954953	+	0.0347574i
$933$		0			0
$934$	6.96341	−	39.4915i	0.227850	−	1.29220i
$935$	−14.7344	−	25.5208i	−0.481867	−	0.834618i
$936$		0			0
$937$	−0.966567	+	1.67414i	−0.0315764	+	0.0546919i	−0.881382	−	0.472405i	$-0.843386\pi$
$937$	−0.966567	+	1.67414i	−0.0315764	+	0.0546919i	0.849805	+	0.527097i	$0.176719\pi$
$938$	4.62205	+	3.87836i	0.150915	+	0.126633i
$939$		0			0
$940$	0.198158	+	1.12381i	0.00646321	+	0.0366547i
$941$	9.12386	−	7.65582i	0.297429	−	0.249573i	−0.481844	−	0.876257i	$-0.660033\pi$
$941$	9.12386	−	7.65582i	0.297429	−	0.249573i	0.779273	+	0.626684i	$0.215588\pi$
$942$		0			0
$943$	−13.5582	+	4.93480i	−0.441517	+	0.160699i
$944$	26.4228			0.859990
$945$		0			0
$946$	−41.5185			−1.34988
$947$	0.296789	−	0.108022i	0.00964435	−	0.00351026i	−0.337193	−	0.941435i	$-0.609478\pi$
$947$	0.296789	−	0.108022i	0.00964435	−	0.00351026i	0.346838	+	0.937925i	$0.387255\pi$
$948$		0			0
$949$	−13.7292	+	11.5202i	−0.445669	+	0.373961i
$950$	3.52317	+	19.9809i	0.114307	+	0.648265i
$951$		0			0
$952$	−16.3129	−	13.6881i	−0.528704	−	0.443635i
$953$	−1.62567	+	2.81574i	−0.0526605	+	0.0912107i	−0.891154	−	0.453701i	$-0.850103\pi$
$953$	−1.62567	+	2.81574i	−0.0526605	+	0.0912107i	0.838494	+	0.544912i	$0.183437\pi$
$954$		0			0
$955$	4.14378	+	7.17724i	0.134090	+	0.232250i
$956$	0.129289	−	0.733235i	0.00418151	−	0.0237145i
$957$		0			0
$958$	47.6994	+	17.3612i	1.54110	+	0.560914i
$959$	8.90332	+	3.24054i	0.287503	+	0.104643i
$960$		0			0
$961$	−5.32295	+	30.1879i	−0.171708	+	0.973805i
$962$	0.0910521	+	0.157707i	0.00293564	+	0.00508467i
$963$		0			0
$964$	−0.309745	+	0.536493i	−0.00997620	+	0.0172793i
$965$	−22.6177	−	18.9785i	−0.728089	−	0.610939i
$966$		0			0
$967$	1.90450	+	10.8010i	0.0612447	+	0.347336i	0.999996	+	0.00274134i	$0.000872598\pi$
$967$	1.90450	+	10.8010i	0.0612447	+	0.347336i	−0.938751	+	0.344595i	$0.888016\pi$
$968$	−54.8526	+	46.0268i	−1.76303	+	1.47936i
$969$		0			0
$970$	−0.545759	+	0.198640i	−0.0175233	+	0.00637795i
$971$	23.3868			0.750519			0.375259	−	0.926920i	$-0.377554\pi$
$971$	23.3868			0.750519			0.375259	+	0.926920i	$0.377554\pi$
$972$		0			0
$973$	28.8553			0.925060
$974$	0.967034	−	0.351972i	0.0309858	−	0.0112779i
$975$		0			0
$976$	−30.4406	+	25.5427i	−0.974381	+	0.817602i
$977$	−8.71301	−	49.4139i	−0.278754	−	1.58089i	−0.726779	−	0.686871i	$-0.758984\pi$
$977$	−8.71301	−	49.4139i	−0.278754	−	1.58089i	0.448025	−	0.894021i	$-0.352127\pi$
$978$		0			0
$979$	37.1102	+	31.1391i	1.18605	+	0.995211i
$980$	−0.180922	+	0.313366i	−0.00577935	+	0.0100101i
$981$		0			0
$982$	0.335437	+	0.580994i	0.0107042	+	0.0185402i
$983$	−2.55169	+	14.4713i	−0.0813862	+	0.461564i	0.916692	+	0.399595i	$0.130849\pi$
$983$	−2.55169	+	14.4713i	−0.0813862	+	0.461564i	−0.998078	+	0.0619694i	$0.980262\pi$
$984$		0			0
$985$	−1.12391	−	0.409071i	−0.0358108	−	0.0130341i
$986$	4.90286	+	1.78449i	0.156139	+	0.0568299i
$987$		0			0
$988$	−0.687319	+	3.89798i	−0.0218665	+	0.124011i
$989$	−7.63088	−	13.2171i	−0.242648	−	0.420279i
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	−0.469722	−	0.394144i	−0.0149137	−	0.0125141i
$993$		0			0
$994$	−3.11002	−	17.6378i	−0.0986440	−	0.559438i
$995$	−12.9042	+	10.8279i	−0.409091	+	0.343268i
$996$		0			0
$997$	43.1190	−	15.6940i	1.36559	−	0.497035i	0.447814	−	0.894127i	$-0.352203\pi$
$997$	43.1190	−	15.6940i	1.36559	−	0.497035i	0.917779	+	0.397091i	$0.129980\pi$
$998$	12.0797			0.382375
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.b.163.1		6
3.2	odd	2		729.2.e.g.163.1		6
9.2	odd	6		729.2.e.h.406.1		6
9.4	even	3		729.2.e.i.649.1		6
9.5	odd	6		729.2.e.a.649.1		6
9.7	even	3		729.2.e.c.406.1		6
27.2	odd	18		243.2.a.e.1.2	✓	3
27.4	even	9	inner	729.2.e.b.568.1		6
27.5	odd	18		729.2.e.a.82.1		6
27.7	even	9		243.2.c.e.163.2		6
27.11	odd	18		243.2.c.f.82.2		6
27.13	even	9		729.2.e.c.325.1		6
27.14	odd	18		729.2.e.h.325.1		6
27.16	even	9		243.2.c.e.82.2		6
27.20	odd	18		243.2.c.f.163.2		6
27.22	even	9		729.2.e.i.82.1		6
27.23	odd	18		729.2.e.g.568.1		6
27.25	even	9		243.2.a.f.1.2	yes	3
108.79	odd	18		3888.2.a.bk.1.2		3
108.83	even	18		3888.2.a.bd.1.2		3
135.29	odd	18		6075.2.a.bv.1.2		3
135.79	even	18		6075.2.a.bq.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.a.e.1.2	✓	3	27.2	odd	18
243.2.a.f.1.2	yes	3	27.25	even	9
243.2.c.e.82.2		6	27.16	even	9
243.2.c.e.163.2		6	27.7	even	9
243.2.c.f.82.2		6	27.11	odd	18
243.2.c.f.163.2		6	27.20	odd	18
729.2.e.a.82.1		6	27.5	odd	18
729.2.e.a.649.1		6	9.5	odd	6
729.2.e.b.163.1		6	1.1	even	1	trivial
729.2.e.b.568.1		6	27.4	even	9	inner
729.2.e.c.325.1		6	27.13	even	9
729.2.e.c.406.1		6	9.7	even	3
729.2.e.g.163.1		6	3.2	odd	2
729.2.e.g.568.1		6	27.23	odd	18
729.2.e.h.325.1		6	27.14	odd	18
729.2.e.h.406.1		6	9.2	odd	6
729.2.e.i.82.1		6	27.22	even	9
729.2.e.i.649.1		6	9.4	even	3
3888.2.a.bd.1.2		3	108.83	even	18
3888.2.a.bk.1.2		3	108.79	odd	18
6075.2.a.bq.1.2		3	135.79	even	18
6075.2.a.bv.1.2		3	135.29	odd	18

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)

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