LMFDB - Embedded newform 729.2.e.b.568.1

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			568.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	729.568
Dual form			729.2.e.b.163.1

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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	$-0.546926\pi$
$2$	−1.26604	−	0.460802i	−0.895229	−	0.325837i	−0.748339	+	0.663316i	$0.769148\pi$
$3$		0			0
$3$		0			0
$4$	−0.141559	−	0.118782i	−0.0707796	−	0.0593912i
$5$	0.286989	−	1.62760i	0.128345	−	0.727883i	−0.850919	−	0.525297i	$-0.823954\pi$
$5$	0.286989	−	1.62760i	0.128345	−	0.727883i	0.979264	−	0.202586i	$-0.0649346\pi$
$6$		0			0
$7$	1.84730	−	1.55007i	0.698212	−	0.585870i	−0.223052	−	0.974807i	$-0.571602\pi$
$7$	1.84730	−	1.55007i	0.698212	−	0.585870i	0.921264	+	0.388937i	$0.127158\pi$
$8$	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	0.592850	+	0.805313i	$0.298003\pi$
$11$	1.03209	+	5.85327i	0.311187	+	1.76483i	−0.281663	+	0.959513i	$0.590886\pi$
$12$		0			0
$13$	3.03209	−	1.10359i	0.840950	−	0.306081i	0.114605	−	0.993411i	$-0.463440\pi$
$13$	3.03209	−	1.10359i	0.840950	−	0.306081i	0.726345	+	0.687330i	$0.241217\pi$
$14$	−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	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	3.31908	+	5.74881i	0.761449	+	1.31887i	0.942104	+	0.335321i	$0.108845\pi$
$19$	3.31908	+	5.74881i	0.761449	+	1.31887i	−0.180655	+	0.983547i	$0.557822\pi$
$20$	−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	$-0.377065\pi$
$23$	−2.25490	−	1.89209i	−0.470179	−	0.394527i	−0.846860	+	0.531816i	$0.821510\pi$
$24$		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	$-0.350646\pi$
$29$	1.21301	+	0.441500i	0.225250	+	0.0819845i	−0.226929	+	0.973911i	$0.572869\pi$
$30$		0			0
$31$	−0.450837	−	0.378297i	−0.0809727	−	0.0679442i	0.601403	−	0.798946i	$-0.294609\pi$
$31$	−0.450837	−	0.378297i	−0.0809727	−	0.0679442i	−0.682376	+	0.731002i	$0.739053\pi$
$32$	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	−0.867742	−	0.497015i	$-0.834429\pi$
$37$	−0.0209445	+	0.0362770i	−0.00344326	+	0.00596390i	0.864299	+	0.502979i	$0.167763\pi$
$38$	−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	$-0.486086\pi$
$41$	4.60607	−	1.67647i	0.719347	−	0.261821i	0.675648	+	0.737224i	$0.263864\pi$
$42$		0			0
$43$	−0.900330	−	5.10602i	−0.137299	−	0.778661i	−0.973231	−	0.229829i	$-0.926183\pi$
$43$	−0.900330	−	5.10602i	−0.137299	−	0.778661i	0.835932	−	0.548833i	$-0.184928\pi$
$44$	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	$-0.810076\pi$
$47$	−2.86231	+	2.40176i	−0.417511	+	0.350333i	0.409704	+	0.912218i	$0.365632\pi$
$48$		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	0.781821	+	0.623503i	$0.214291\pi$
$59$	−1.27584	+	7.23567i	−0.166101	+	0.942005i	−0.947922	+	0.318502i	$0.896820\pi$
$60$		0			0
$61$	8.46451	−	7.10257i	1.08377	−	0.909390i	0.0875408	−	0.996161i	$-0.472099\pi$
$61$	8.46451	−	7.10257i	1.08377	−	0.909390i	0.996228	+	0.0867707i	$0.0276547\pi$
$62$	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	−0.446411	−	0.894828i	$-0.647298\pi$
$67$	−1.74510	+	0.635164i	−0.213198	+	0.0775977i	0.233213	+	0.972426i	$0.425076\pi$
$68$	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	$-0.727260\pi$
$71$	2.75624	−	4.77396i	0.327106	−	0.566564i	0.981936	+	0.189212i	$0.0605932\pi$
$72$		0			0
$73$	−2.77719	−	4.81023i	−0.325045	−	0.562995i	0.656476	−	0.754347i	$-0.272046\pi$
$73$	−2.77719	−	4.81023i	−0.325045	−	0.562995i	−0.981522	+	0.191352i	$0.938713\pi$
$74$	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	0.534068	−	0.845442i	$-0.320663\pi$
$79$	3.55303	+	1.29320i	0.399747	+	0.145496i	−0.134320	+	0.990938i	$0.542885\pi$
$80$	−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	$-0.459080\pi$
$83$	−3.74510	−	1.36310i	−0.411078	−	0.149620i	−0.539277	+	0.842128i	$0.681303\pi$
$84$		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	$-0.308853\pi$
$89$	−4.07532	−	7.05866i	−0.431983	−	0.748217i	−0.997044	+	0.0768323i	$0.975519\pi$
$90$		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	0.987021	−	0.160592i	$-0.0513405\pi$
$97$	0.0452926	+	0.256867i	0.00459877	+	0.0260809i	−0.982422	+	0.186673i	$0.940229\pi$
$98$	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	$-0.537372\pi$
$101$	8.44743	−	7.08824i	0.840551	−	0.705306i	0.957688	+	0.287810i	$0.0929271\pi$
$102$		0			0
$103$	−0.678396	+	3.84737i	−0.0668443	+	0.379093i	0.932972	+	0.359948i	$0.117206\pi$
$103$	−0.678396	+	3.84737i	−0.0668443	+	0.379093i	−0.999817	+	0.0191451i	$0.993906\pi$
$104$	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	−0.522135	−	0.852863i	$-0.674864\pi$
$113$	2.76604	−	15.6870i	0.260208	−	1.47571i	0.782343	−	0.622848i	$-0.214024\pi$
$114$		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	0.775151	−	0.631776i	$-0.217674\pi$
$127$	−1.79813	−	3.11446i	−0.159559	−	0.276363i	−0.934710	+	0.355412i	$0.884340\pi$
$128$	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	−0.999931	−	0.0117601i	$-0.996257\pi$
$131$	−13.5646	−	11.3821i	−1.18515	−	0.994458i	−0.185218	−	0.982698i	$-0.559299\pi$
$132$		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	$-0.335210\pi$
$137$	3.69207	+	1.34380i	0.315435	+	0.114809i	−0.179451	+	0.983767i	$0.557432\pi$
$138$		0			0
$139$	9.16637	+	7.69150i	0.777482	+	0.652385i	0.942613	−	0.333887i	$-0.108360\pi$
$139$	9.16637	+	7.69150i	0.777482	+	0.652385i	−0.165131	+	0.986272i	$0.552805\pi$
$140$	−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	$-0.928996\pi$
$149$	−19.2875	+	7.02006i	−1.58009	+	0.575106i	−0.604866	+	0.796327i	$0.706773\pi$
$150$		0			0
$151$	2.77972	+	15.7645i	0.226210	+	1.28290i	0.860358	+	0.509689i	$0.170240\pi$
$151$	2.77972	+	15.7645i	0.226210	+	1.28290i	−0.634148	+	0.773211i	$0.718649\pi$
$152$	−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	0.321213	+	0.947007i	$0.395909\pi$
$157$	−3.81567	+	21.6398i	−0.304524	+	1.72704i	−0.625737	+	0.780034i	$0.715202\pi$
$158$	−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	$-0.891353\pi$
$167$	0.745100	−	4.22567i	0.0576576	−	0.326992i	0.999970	+	0.00774226i	$0.00246446\pi$
$168$		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	$-0.00949947\pi$
$173$	0.658633	+	3.73530i	0.0500750	+	0.283989i	−0.949480	+	0.313828i	$0.898388\pi$
$174$		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	$-0.933428\pi$
$179$	−4.13816	+	7.16750i	−0.309300	+	0.535724i	0.668909	+	0.743344i	$0.266761\pi$
$180$		0			0
$181$	−3.36097	−	5.82137i	−0.249819	−	0.432699i	0.713657	−	0.700496i	$-0.247038\pi$
$181$	−3.36097	−	5.82137i	−0.249819	−	0.432699i	−0.963475	+	0.267797i	$0.913704\pi$
$182$	−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	$-0.330820\pi$
$191$	4.71213	+	1.71508i	0.340958	+	0.124099i	−0.165866	+	0.986148i	$0.553042\pi$
$192$		0			0
$193$	−13.6853	−	11.4833i	−0.985087	−	0.826586i	−0.000237549	−	1.00000i	$-0.500076\pi$
$193$	−13.6853	−	11.4833i	−0.985087	−	0.826586i	−0.984849	+	0.173414i	$0.944520\pi$
$194$	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	$-0.174874\pi$
$197$	−0.361844	−	0.626733i	−0.0257803	−	0.0446529i	−0.878628	+	0.477507i	$0.841540\pi$
$198$		0			0
$199$	5.09627	−	8.82699i	0.361265	−	0.625729i	−0.626905	−	0.779096i	$-0.715678\pi$
$199$	5.09627	−	8.82699i	0.361265	−	0.625729i	0.988169	+	0.153367i	$0.0490117\pi$
$200$	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	0.757280	+	0.653091i	$0.226528\pi$
$211$	−2.58125	+	14.6390i	−0.177701	+	1.00779i	−0.934980	+	0.354700i	$0.884583\pi$
$212$	−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	−0.878861	−	0.477078i	$-0.841696\pi$
$223$	−8.38713	+	7.03763i	−0.561644	+	0.471275i	0.317217	+	0.948353i	$0.397251\pi$
$224$	−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	−0.905464	−	0.424423i	$-0.860477\pi$
$227$	−3.00980	−	17.0694i	−0.199767	−	1.13294i	0.705696	−	0.708514i	$-0.250634\pi$
$228$		0			0
$229$	−1.46791	+	0.534276i	−0.0970023	+	0.0353059i	−0.390065	−	0.920787i	$-0.627548\pi$
$229$	−1.46791	+	0.534276i	−0.0970023	+	0.0353059i	0.293063	+	0.956093i	$0.405325\pi$
$230$	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	0.448343	+	0.893862i	$0.352014\pi$
$233$	−8.39440	+	14.5395i	−0.549935	+	0.952516i	−0.998278	+	0.0586545i	$0.981319\pi$
$234$		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	$-0.319375\pi$
$239$	−3.08647	−	2.58985i	−0.199647	−	0.167524i	−0.737130	+	0.675751i	$0.763820\pi$
$240$		0			0
$241$	3.15018	+	1.14657i	0.202921	+	0.0738571i	0.441481	−	0.897271i	$-0.354453\pi$
$241$	3.15018	+	1.14657i	0.202921	+	0.0738571i	−0.238560	+	0.971128i	$0.576675\pi$
$242$	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	0.956615	+	0.291354i	$0.0941059\pi$
$251$	11.5753	+	20.0490i	0.730628	+	1.26548i	−0.225987	+	0.974130i	$0.572561\pi$
$252$		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	$-0.733355\pi$
$257$	−11.2883	+	4.10862i	−0.704147	+	0.256289i	−0.0349665	+	0.999388i	$0.511132\pi$
$258$		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	$-0.547744\pi$
$263$	12.9474	−	10.8642i	0.798373	−	0.669914i	0.947803	+	0.318858i	$0.103299\pi$
$264$		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	0.217724	−	0.976010i	$-0.430137\pi$
$277$	20.2502	−	16.9919i	1.21671	−	1.02094i	0.998990	−	0.0449336i	$-0.0143076\pi$
$278$	−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	−0.909864	−	0.414907i	$-0.863814\pi$
$281$	−3.29860	−	18.7073i	−0.196778	−	1.11598i	0.713086	−	0.701077i	$-0.247297\pi$
$282$		0			0
$283$	15.5865	−	5.67301i	0.926519	−	0.337225i	0.165690	−	0.986178i	$-0.447015\pi$
$283$	15.5865	−	5.67301i	0.926519	−	0.337225i	0.760829	+	0.648952i	$0.224793\pi$
$284$	−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	$-0.0864822\pi$
$293$	14.8289	+	12.4429i	0.866312	+	0.726922i	−0.0970060	+	0.995284i	$0.530927\pi$
$294$		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	0.400003	+	0.916514i	$0.369009\pi$
$307$	−10.4029	+	18.0183i	−0.593722	+	1.02836i	−0.993726	+	0.111844i	$0.964324\pi$
$308$	−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	$-0.513326\pi$
$311$	10.0223	−	3.64781i	0.568312	−	0.206849i	0.610164	+	0.792275i	$0.291104\pi$
$312$		0			0
$313$	0.662504	+	3.75725i	0.0374469	+	0.212372i	0.997790	−	0.0664498i	$-0.0211672\pi$
$313$	0.662504	+	3.75725i	0.0374469	+	0.212372i	−0.960343	+	0.278822i	$0.910056\pi$
$314$	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	$-0.456535\pi$
$317$	20.2153	−	16.9626i	1.13540	−	0.952717i	0.999279	+	0.0379748i	$0.0120907\pi$
$318$		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	−0.675275	−	0.737566i	$-0.735975\pi$
$331$	−1.20393	+	1.01021i	−0.0661738	+	0.0555264i	0.609101	+	0.793093i	$0.291530\pi$
$332$	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	−0.128620	−	0.991694i	$-0.541055\pi$
$337$	7.53209	−	2.74146i	0.410299	−	0.149337i	0.538920	+	0.842357i	$0.318833\pi$
$338$	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	$-0.0989649\pi$
$347$	15.2023	+	12.7563i	0.816104	+	0.684793i	−0.135952	+	0.990715i	$0.543409\pi$
$348$		0			0
$349$	−10.4243	−	3.79412i	−0.557998	−	0.203095i	0.0475984	−	0.998867i	$-0.484843\pi$
$349$	−10.4243	−	3.79412i	−0.557998	−	0.203095i	−0.605597	+	0.795772i	$0.707065\pi$
$350$	−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	$-0.364605\pi$
$353$	2.69119	+	0.979513i	0.143238	+	0.0521342i	−0.269407	+	0.963027i	$0.586828\pi$
$354$		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	−0.943000	−	0.332793i	$-0.892009\pi$
$359$	−14.3944	−	24.9318i	−0.759707	−	1.31585i	0.183292	−	0.983058i	$-0.441324\pi$
$360$		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	−0.993227	−	0.116189i	$-0.962932\pi$
$367$	−1.90879	−	10.8253i	−0.0996378	−	0.565074i	0.893589	−	0.448885i	$-0.148179\pi$
$368$	−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	−0.344046	−	0.938953i	$-0.611798\pi$
$373$	5.80154	−	32.9022i	0.300392	−	1.70361i	0.644439	−	0.764656i	$-0.277091\pi$
$374$	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	$-0.977940\pi$
$383$	−0.713888	+	4.04866i	−0.0364780	+	0.206877i	0.961121	+	0.276126i	$0.0890508\pi$
$384$		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	0.962783	+	0.270276i	$0.0871149\pi$
$389$	2.96838	+	16.8345i	0.150503	+	0.853543i	−0.812280	+	0.583267i	$0.801774\pi$
$390$		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	−0.997308	−	0.0733324i	$-0.976637\pi$
$397$	−11.2010	−	19.4007i	−0.562162	−	0.973692i	0.435146	−	0.900360i	$-0.356697\pi$
$398$	−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	$-0.396397\pi$
$401$	−11.1702	−	9.37295i	−0.557815	−	0.468063i	−0.877577	+	0.479435i	$0.840842\pi$
$402$		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	0.247994	−	0.968762i	$-0.420229\pi$
$409$	−13.4081	−	11.2507i	−0.662986	−	0.556312i	−0.910980	+	0.412450i	$0.864673\pi$
$410$	−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	$-0.763526\pi$
$419$	−17.7246	+	6.45123i	−0.865904	+	0.315163i	−0.129397	+	0.991593i	$0.541304\pi$
$420$		0			0
$421$	−5.61468	−	31.8425i	−0.273643	−	1.55191i	−0.743240	−	0.669025i	$-0.766712\pi$
$421$	−5.61468	−	31.8425i	−0.273643	−	1.55191i	0.469597	−	0.882881i	$-0.344399\pi$
$422$	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	−0.959462	−	0.281837i	$-0.909056\pi$
$439$	−17.7784	+	14.9178i	−0.848515	+	0.711989i	0.110947	+	0.993826i	$0.464612\pi$
$440$	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	$-0.0867714\pi$
$443$	−0.715699	−	4.05893i	−0.0340039	−	0.192846i	−0.997078	+	0.0763910i	$0.975660\pi$
$444$		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	$-0.975805\pi$
$449$	−9.17071	+	15.8841i	−0.432793	+	0.749619i	0.564320	+	0.825556i	$0.309138\pi$
$450$		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	0.732261	−	0.681024i	$-0.238465\pi$
$457$	18.2875	+	6.65609i	0.855451	+	0.311359i	0.123190	+	0.992383i	$0.460687\pi$
$458$	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	$-0.612534\pi$
$461$	−26.0758	−	9.49081i	−1.21447	−	0.442031i	−0.868252	+	0.496123i	$0.834757\pi$
$462$		0			0
$463$	29.6352	+	24.8669i	1.37727	+	1.15566i	0.970212	+	0.242259i	$0.0778883\pi$
$463$	29.6352	+	24.8669i	1.37727	+	1.15566i	0.407054	+	0.913404i	$0.366556\pi$
$464$	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	−0.972274	−	0.233845i	$-0.924869\pi$
$467$	−14.8819	−	25.7762i	−0.688653	−	1.19278i	0.283621	−	0.958936i	$-0.408464\pi$
$468$		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	−0.332136	+	0.943231i	$0.607769\pi$
$479$	−28.8614	+	24.2176i	−1.31871	+	1.10653i	−0.986577	+	0.163300i	$0.947786\pi$
$480$		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	$-0.948021\pi$
$491$	−0.0864665	+	0.490376i	−0.00390218	+	0.0221303i	0.982794	+	0.184702i	$0.0591321\pi$
$492$		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	−0.523643	−	0.851938i	$-0.675427\pi$
$499$	−8.42514	+	3.06650i	−0.377161	+	0.137275i	0.146482	+	0.989213i	$0.453205\pi$
$500$	−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	$-0.967580\pi$
$503$	−9.18092	+	15.9018i	−0.409357	+	0.709027i	0.585461	+	0.810701i	$0.300914\pi$
$504$		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	$-0.494211\pi$
$509$	−21.7331	−	18.2362i	−0.963302	−	0.808306i	−0.981487	+	0.191528i	$0.938656\pi$
$510$		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	0.962978	+	0.269580i	$0.0868847\pi$
$521$	16.3191	+	28.2655i	0.714952	+	1.23833i	−0.248026	+	0.968753i	$0.579782\pi$
$522$		0			0
$523$	11.0116	−	19.0727i	0.481504	−	0.833990i	−0.518271	−	0.855217i	$-0.673424\pi$
$523$	11.0116	−	19.0727i	0.481504	−	0.833990i	0.999775	+	0.0212271i	$0.00675730\pi$
$524$	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	−0.969814	−	0.243845i	$-0.921591\pi$
$547$	−21.0043	+	17.6247i	−0.898081	+	0.753579i	0.0717337	+	0.997424i	$0.477147\pi$
$548$	−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	0.366042	+	0.930598i	$0.380713\pi$
$557$	−14.7010	+	25.4629i	−0.622901	+	1.07890i	−0.988943	+	0.148298i	$0.952621\pi$
$558$		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	$-0.347905\pi$
$563$	−7.94428	−	6.66604i	−0.334811	−	0.280940i	−0.794657	+	0.607059i	$0.792349\pi$
$564$		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	$-0.146029\pi$
$569$	30.9809	+	11.2761i	1.29879	+	0.472719i	0.402185	+	0.915559i	$0.368251\pi$
$570$		0			0
$571$	−0.564893	−	0.474002i	−0.0236400	−	0.0198363i	0.630891	−	0.775871i	$-0.282689\pi$
$571$	−0.564893	−	0.474002i	−0.0236400	−	0.0198363i	−0.654531	+	0.756035i	$0.727134\pi$
$572$	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	−0.994043	−	0.108990i	$-0.965238\pi$
$577$	−9.67159	+	16.7517i	−0.402634	+	0.697382i	0.591409	+	0.806371i	$0.298572\pi$
$578$	−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	$-0.951063\pi$
$587$	−24.4461	+	20.5127i	−1.00900	+	0.846650i	−0.0207926	+	0.999784i	$0.506619\pi$
$588$		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	0.906712	+	0.421750i	$0.138584\pi$
$599$	−2.19207	+	12.4318i	−0.0895654	+	0.507951i	−0.996278	+	0.0862011i	$0.972527\pi$
$600$		0			0
$601$	−6.82429	+	5.72626i	−0.278369	+	0.233579i	−0.771273	−	0.636504i	$-0.780380\pi$
$601$	−6.82429	+	5.72626i	−0.278369	+	0.233579i	0.492904	+	0.870084i	$0.335935\pi$
$602$	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	0.378485	−	0.925608i	$-0.376445\pi$
$607$	31.1266	−	11.3292i	1.26339	−	0.459836i	0.884905	+	0.465771i	$0.154223\pi$
$608$	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	0.630421	−	0.776254i	$-0.282882\pi$
$613$	−8.84002	−	15.3114i	−0.357045	−	0.618420i	−0.987466	+	0.157833i	$0.949549\pi$
$614$	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	$-0.451091\pi$
$617$	−19.7121	−	16.5404i	−0.793581	−	0.665893i	−0.946629	+	0.322326i	$0.895535\pi$
$618$		0			0
$619$	−26.1186	−	9.50638i	−1.04979	−	0.382094i	−0.241209	−	0.970473i	$-0.577544\pi$
$619$	−26.1186	−	9.50638i	−1.04979	−	0.382094i	−0.808585	+	0.588380i	$0.799766\pi$
$620$	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	0.465504	+	0.885046i	$0.345873\pi$
$631$	−13.4069	+	23.2214i	−0.533720	+	0.924430i	−0.999224	+	0.0393842i	$0.987460\pi$
$632$	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	$-0.641587\pi$
$641$	9.72147	−	8.15728i	0.383975	−	0.322193i	0.814261	+	0.580500i	$0.197143\pi$
$642$		0			0
$643$	2.68748	−	15.2415i	0.105984	−	0.601065i	−0.884839	−	0.465897i	$-0.845732\pi$
$643$	2.68748	−	15.2415i	0.105984	−	0.601065i	0.990823	−	0.135167i	$-0.0431572\pi$
$644$	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	−0.329658	−	0.944100i	$-0.606934\pi$
$653$	7.74335	−	43.9147i	0.303021	−	1.71851i	0.632679	−	0.774414i	$-0.281955\pi$
$654$		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	−0.994638	−	0.103416i	$-0.967023\pi$
$659$	−2.44784	−	13.8824i	−0.0953545	−	0.540782i	0.899284	−	0.437366i	$-0.144088\pi$
$660$		0			0
$661$	−33.9368	+	12.3520i	−1.31999	+	0.480436i	−0.903454	−	0.428685i	$-0.858977\pi$
$661$	−33.9368	+	12.3520i	−1.31999	+	0.480436i	−0.416533	+	0.909121i	$0.636755\pi$
$662$	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	0.301092	−	0.953595i	$-0.402649\pi$
$673$	−2.10694	−	0.766865i	−0.0812167	−	0.0295605i	−0.382309	+	0.924035i	$0.624871\pi$
$674$	−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	$-0.625162\pi$
$677$	−33.0548	−	12.0310i	−1.27040	−	0.462388i	−0.887246	+	0.461296i	$0.847385\pi$
$678$		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	$-0.0562880\pi$
$683$	8.88191	+	15.3839i	0.339857	+	0.588649i	−0.644549	+	0.764563i	$0.722955\pi$
$684$		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	−0.683563	−	0.729891i	$-0.739571\pi$
$691$	−7.64584	−	43.3617i	−0.290861	−	1.64956i	0.392702	−	0.919666i	$-0.371541\pi$
$692$	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	−0.925070	−	0.379796i	$-0.875994\pi$
$709$	−18.9500	+	15.9009i	−0.711681	+	0.597171i	0.213390	+	0.976967i	$0.431550\pi$
$710$	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	−0.0992586	−	0.995062i	$-0.531647\pi$
$719$	21.7763	−	37.7177i	0.812119	−	1.40663i	0.911378	−	0.411570i	$-0.135020\pi$
$720$		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	−0.0416269	−	0.999133i	$-0.513254\pi$
$727$	−19.2986	−	7.02412i	−0.715745	−	0.260510i	−0.674119	+	0.738623i	$0.735476\pi$
$728$	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	0.819058	−	0.573710i	$-0.194496\pi$
$733$	10.7292	+	9.00287i	0.396292	+	0.332529i	−0.422766	+	0.906239i	$0.638941\pi$
$734$	−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	−0.164226	−	0.986423i	$-0.552513\pi$
$739$	20.9907	−	36.3569i	0.772154	−	1.33741i	0.936380	−	0.350987i	$-0.114154\pi$
$740$	−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	$-0.781866\pi$
$743$	−26.1819	+	9.52942i	−0.960519	+	0.349600i	−0.186282	+	0.982496i	$0.559644\pi$
$744$		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	0.0896873	+	0.995970i	$0.471413\pi$
$751$	−9.18685	+	52.1012i	−0.335233	+	1.90120i	−0.424920	+	0.905231i	$0.639698\pi$
$752$	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	0.417064	+	0.908877i	$0.363059\pi$
$761$	−7.88144	+	44.6979i	−0.285702	+	1.62030i	−0.702767	+	0.711420i	$0.748052\pi$
$762$		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	−0.427251	−	0.904133i	$-0.640518\pi$
$769$	−4.80793	+	1.74994i	−0.173379	+	0.0631046i	0.253872	+	0.967238i	$0.418296\pi$
$770$	−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	0.194430	−	0.980916i	$-0.437714\pi$
$773$	26.3214	−	45.5899i	0.946713	−	1.63976i	0.752284	−	0.658839i	$-0.228952\pi$
$774$		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	0.313683	−	0.949528i	$-0.398437\pi$
$787$	−15.9049	−	13.3458i	−0.566949	−	0.475727i	−0.880632	+	0.473801i	$0.842882\pi$
$788$	−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	0.556721	−	0.830700i	$-0.312059\pi$
$797$	42.8312	−	15.5893i	1.51716	−	0.552200i	0.960436	+	0.278499i	$0.0898370\pi$
$798$		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	0.989380	−	0.145354i	$-0.0464322\pi$
$821$	0.285178	+	1.61732i	0.00995278	+	0.0564450i	−0.979427	+	0.201799i	$0.935321\pi$
$822$		0			0
$823$	−10.5424	+	3.83710i	−0.367483	+	0.133753i	−0.519160	−	0.854677i	$-0.673755\pi$
$823$	−10.5424	+	3.83710i	−0.367483	+	0.133753i	0.151676	+	0.988430i	$0.451533\pi$
$824$	−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	−0.770272	−	0.637715i	$-0.779880\pi$
$827$	4.80659	−	8.32526i	0.167141	−	0.289498i	0.937414	+	0.348218i	$0.113213\pi$
$828$		0			0
$829$	−16.7469	−	29.0065i	−0.581644	−	1.00744i	−0.995285	−	0.0969971i	$-0.969076\pi$
$829$	−16.7469	−	29.0065i	−0.581644	−	1.00744i	0.413640	−	0.910440i	$-0.364257\pi$
$830$	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	0.804101	−	0.594492i	$-0.202647\pi$
$839$	30.0646	+	10.9426i	1.03795	+	0.377782i	0.233845	+	0.972274i	$0.424869\pi$
$840$		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	0.890141	+	0.455686i	$0.150606\pi$
$853$	6.11974	+	34.7068i	0.209536	+	1.18834i	−0.680605	+	0.732651i	$0.738283\pi$
$854$	−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	−0.876978	−	0.480530i	$-0.840444\pi$
$857$	−16.2777	+	13.6586i	−0.556034	+	0.466568i	0.320944	+	0.947098i	$0.396000\pi$
$858$		0			0
$859$	9.00165	−	51.0509i	0.307132	−	1.74183i	−0.306162	−	0.951979i	$-0.599045\pi$
$859$	9.00165	−	51.0509i	0.307132	−	1.74183i	0.613294	−	0.789854i	$-0.289844\pi$
$860$	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	−0.359940	−	0.932976i	$-0.617203\pi$
$877$	−1.06506	+	0.387648i	−0.0359644	+	0.0130900i	0.323975	+	0.946066i	$0.394981\pi$
$878$	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	−0.480421	−	0.877038i	$-0.659516\pi$
$881$	15.4145	−	26.6986i	0.519327	−	0.899500i	0.999748	−	0.0224621i	$-0.00715051\pi$
$882$		0			0
$883$	4.66756	+	8.08444i	0.157076	+	0.272063i	0.933813	−	0.357762i	$-0.116460\pi$
$883$	4.66756	+	8.08444i	0.157076	+	0.272063i	−0.776737	+	0.629825i	$0.783127\pi$
$884$	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	0.443274	−	0.896386i	$-0.353817\pi$
$887$	−10.7968	−	9.05958i	−0.362521	−	0.304191i	−0.805794	+	0.592195i	$0.798261\pi$
$888$		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	0.949192	−	0.314696i	$-0.101903\pi$
$907$	−1.51754	−	8.60640i	−0.0503891	−	0.285771i	−0.999582	+	0.0289253i	$0.990792\pi$
$908$	−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	−0.866067	−	0.499928i	$-0.833360\pi$
$911$	−15.8195	+	13.2742i	−0.524125	+	0.439793i	0.341942	+	0.939721i	$0.388915\pi$
$912$		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	−0.960769	−	0.277350i	$-0.910544\pi$
$929$	−4.65729	−	26.4128i	−0.152801	−	0.866576i	0.807968	−	0.589226i	$-0.200567\pi$
$930$		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	0.849805	−	0.527097i	$-0.176719\pi$
$937$	−0.966567	−	1.67414i	−0.0315764	−	0.0546919i	−0.881382	+	0.472405i	$0.843386\pi$
$938$	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	0.779273	−	0.626684i	$-0.215588\pi$
$941$	9.12386	+	7.65582i	0.297429	+	0.249573i	−0.481844	+	0.876257i	$0.660033\pi$
$942$		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	0.346838	−	0.937925i	$-0.387255\pi$
$947$	0.296789	+	0.108022i	0.00964435	+	0.00351026i	−0.337193	+	0.941435i	$0.609478\pi$
$948$		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	0.838494	−	0.544912i	$-0.183437\pi$
$953$	−1.62567	−	2.81574i	−0.0526605	−	0.0912107i	−0.891154	+	0.453701i	$0.850103\pi$
$954$		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	−0.938751	−	0.344595i	$-0.888016\pi$
$967$	1.90450	−	10.8010i	0.0612447	−	0.347336i	0.999996	−	0.00274134i	$-0.000872598\pi$
$968$	−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	0.448025	+	0.894021i	$0.352127\pi$
$977$	−8.71301	+	49.4139i	−0.278754	+	1.58089i	−0.726779	+	0.686871i	$0.758984\pi$
$978$		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	−0.998078	−	0.0619694i	$-0.980262\pi$
$983$	−2.55169	−	14.4713i	−0.0813862	−	0.461564i	0.916692	−	0.399595i	$-0.130849\pi$
$984$		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	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	−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	0.917779	−	0.397091i	$-0.129980\pi$
$997$	43.1190	+	15.6940i	1.36559	+	0.497035i	0.447814	+	0.894127i	$0.352203\pi$
$998$	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.568.1		6
3.2	odd	2		729.2.e.g.568.1		6
9.2	odd	6		729.2.e.a.82.1		6
9.4	even	3		729.2.e.c.325.1		6
9.5	odd	6		729.2.e.h.325.1		6
9.7	even	3		729.2.e.i.82.1		6
27.2	odd	18		729.2.e.h.406.1		6
27.4	even	9		243.2.c.e.82.2		6
27.5	odd	18		243.2.c.f.163.2		6
27.7	even	9	inner	729.2.e.b.163.1		6
27.11	odd	18		729.2.e.a.649.1		6
27.13	even	9		243.2.a.f.1.2	yes	3
27.14	odd	18		243.2.a.e.1.2	✓	3
27.16	even	9		729.2.e.i.649.1		6
27.20	odd	18		729.2.e.g.163.1		6
27.22	even	9		243.2.c.e.163.2		6
27.23	odd	18		243.2.c.f.82.2		6
27.25	even	9		729.2.e.c.406.1		6
108.67	odd	18		3888.2.a.bk.1.2		3
108.95	even	18		3888.2.a.bd.1.2		3
135.14	odd	18		6075.2.a.bv.1.2		3
135.94	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	27.14	odd	18
243.2.a.f.1.2	yes	3	27.13	even	9
243.2.c.e.82.2		6	27.4	even	9
243.2.c.e.163.2		6	27.22	even	9
243.2.c.f.82.2		6	27.23	odd	18
243.2.c.f.163.2		6	27.5	odd	18
729.2.e.a.82.1		6	9.2	odd	6
729.2.e.a.649.1		6	27.11	odd	18
729.2.e.b.163.1		6	27.7	even	9	inner
729.2.e.b.568.1		6	1.1	even	1	trivial
729.2.e.c.325.1		6	9.4	even	3
729.2.e.c.406.1		6	27.25	even	9
729.2.e.g.163.1		6	27.20	odd	18
729.2.e.g.568.1		6	3.2	odd	2
729.2.e.h.325.1		6	9.5	odd	6
729.2.e.h.406.1		6	27.2	odd	18
729.2.e.i.82.1		6	9.7	even	3
729.2.e.i.649.1		6	27.16	even	9
3888.2.a.bd.1.2		3	108.95	even	18
3888.2.a.bk.1.2		3	108.67	odd	18
6075.2.a.bq.1.2		3	135.94	even	18
6075.2.a.bv.1.2		3	135.14	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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