LMFDB - Embedded newform 729.2.e.h.406.1

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			406.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.h.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03209 - 0.866025i) q^{2} +(-0.0320889 - 0.181985i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.418748 - 2.37484i) q^{7} +(-1.47178 + 2.54920i) q^{8} +O(q^{10})$	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.0320889 - 0.181985i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.418748 - 2.37484i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-1.11334 - 1.92836i) q^{10} +(5.58512 - 2.03282i) q^{11} +(-2.47178 + 2.07407i) q^{13} +(-2.48886 + 2.08840i) q^{14} +(3.37939 - 1.23000i) q^{16} +(1.50000 + 2.59808i) q^{17} +(3.31908 - 5.74881i) q^{19} +(0.0530334 - 0.300767i) q^{20} +(-7.52481 - 2.73881i) q^{22} +(0.511144 + 2.89884i) q^{23} +(-1.73783 - 1.45821i) q^{25} +4.34730 q^{26} -0.445622 q^{28} +(0.988856 + 0.829748i) q^{29} +(-0.102196 - 0.579585i) q^{31} +(0.979055 + 0.356347i) q^{32} +(0.701867 - 3.98048i) q^{34} +(1.99273 - 3.45150i) q^{35} +(-0.0209445 - 0.0362770i) q^{37} +(-8.40420 + 3.05888i) q^{38} +(-3.72668 + 3.12706i) q^{40} +(3.75490 - 3.15074i) q^{41} +(4.87211 - 1.77330i) q^{43} +(-0.549163 - 0.951178i) q^{44} +(1.98293 - 3.43453i) q^{46} +(0.648833 - 3.67972i) q^{47} +(1.11334 + 0.405223i) q^{49} +(0.530745 + 3.01000i) q^{50} +(0.456767 + 0.383273i) q^{52} -11.6382 q^{53} +9.82295 q^{55} +(5.43763 + 4.56272i) q^{56} +(-0.302004 - 1.71275i) q^{58} +(-6.90420 - 2.51292i) q^{59} +(1.91875 - 10.8818i) q^{61} +(-0.396459 + 0.686688i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(-5.01114 + 1.82391i) q^{65} +(1.42262 - 1.19372i) q^{67} +(0.424678 - 0.356347i) q^{68} +(-5.04576 + 1.83651i) q^{70} +(-2.75624 - 4.77396i) q^{71} +(-2.77719 + 4.81023i) q^{73} +(-0.00980018 + 0.0555796i) q^{74} +(-1.15270 - 0.419550i) q^{76} +(-2.48886 - 14.1150i) q^{77} +(-2.89646 - 2.43042i) q^{79} +5.94356 q^{80} -6.60401 q^{82} +(-3.05303 - 2.56180i) q^{83} +(0.860967 + 4.88279i) q^{85} +(-6.56418 - 2.38917i) q^{86} +(-3.03802 + 17.2295i) q^{88} +(4.07532 - 7.05866i) q^{89} +(3.89053 + 6.73859i) q^{91} +(0.511144 - 0.186041i) q^{92} +(-3.85638 + 3.23589i) q^{94} +(8.40420 - 7.05196i) q^{95} +(-0.245100 + 0.0892091i) q^{97} +(-0.798133 - 1.38241i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8	$ 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8} + 12 q^{11} - 21 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} - 12 q^{20} - 18 q^{22} - 3 q^{23} + 9 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 9 q^{32} + 18 q^{34} - 6 q^{35} + 3 q^{37} - 12 q^{38} - 9 q^{40} + 24 q^{41} - 15 q^{44} - 9 q^{46} + 30 q^{47} + 3 q^{50} + 18 q^{52} - 36 q^{53} + 18 q^{55} - 24 q^{56} + 36 q^{58} - 3 q^{59} + 9 q^{61} - 12 q^{62} - 12 q^{64} - 24 q^{65} - 18 q^{67} + 27 q^{68} - 9 q^{71} - 6 q^{73} - 3 q^{74} - 9 q^{76} - 21 q^{77} - 27 q^{79} + 6 q^{80} + 36 q^{82} - 6 q^{83} - 18 q^{85} - 21 q^{86} - 36 q^{88} + 6 q^{91} - 3 q^{92} + 36 q^{94} + 12 q^{95} + 9 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8 + 12 * q^11 - 21 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 - 12 * q^20 - 18 * q^22 - 3 * q^23 + 9 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 9 * q^32 + 18 * q^34 - 6 * q^35 + 3 * q^37 - 12 * q^38 - 9 * q^40 + 24 * q^41 - 15 * q^44 - 9 * q^46 + 30 * q^47 + 3 * q^50 + 18 * q^52 - 36 * q^53 + 18 * q^55 - 24 * q^56 + 36 * q^58 - 3 * q^59 + 9 * q^61 - 12 * q^62 - 12 * q^64 - 24 * q^65 - 18 * q^67 + 27 * q^68 - 9 * q^71 - 6 * q^73 - 3 * q^74 - 9 * q^76 - 21 * q^77 - 27 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 21 * q^86 - 36 * q^88 + 6 * q^91 - 3 * q^92 + 36 * q^94 + 12 * q^95 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.03209	−	0.866025i	−0.729797	−	0.612372i	0.200279	−	0.979739i	$-0.435815\pi$
$2$	−1.03209	−	0.866025i	−0.729797	−	0.612372i	−0.930076	+	0.367366i	$0.880260\pi$
$3$		0			0
$3$		0			0
$4$	−0.0320889	−	0.181985i	−0.0160444	−	0.0909926i
$5$	1.55303	+	0.565258i	0.694538	+	0.252791i	0.665077	−	0.746775i	$-0.268399\pi$
$5$	1.55303	+	0.565258i	0.694538	+	0.252791i	0.0294608	+	0.999566i	$0.490621\pi$
$6$		0			0
$7$	0.418748	−	2.37484i	0.158272	−	0.897605i	−0.797461	−	0.603370i	$-0.793824\pi$
$7$	0.418748	−	2.37484i	0.158272	−	0.897605i	0.955733	−	0.294235i	$-0.0950647\pi$
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$		0			0
$10$	−1.11334	−	1.92836i	−0.352069	−	0.609802i
$11$	5.58512	−	2.03282i	1.68398	−	0.612918i	0.690131	−	0.723684i	$-0.257553\pi$
$11$	5.58512	−	2.03282i	1.68398	−	0.612918i	0.993846	+	0.110766i	$0.0353306\pi$
$12$		0			0
$13$	−2.47178	+	2.07407i	−0.685549	+	0.575244i	−0.917622	−	0.397455i	$-0.869894\pi$
$13$	−2.47178	+	2.07407i	−0.685549	+	0.575244i	0.232073	+	0.972698i	$0.425449\pi$
$14$	−2.48886	+	2.08840i	−0.665175	+	0.558148i
$15$		0			0
$16$	3.37939	−	1.23000i	0.844846	−	0.307499i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	−0.180655	−	0.983547i	$-0.557822\pi$
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	0.942104	−	0.335321i	$-0.108845\pi$
$20$	0.0530334	−	0.300767i	0.0118586	−	0.0672537i
$21$		0			0
$22$	−7.52481	−	2.73881i	−1.60430	−	0.583916i
$23$	0.511144	+	2.89884i	0.106581	+	0.604451i	0.990577	+	0.136956i	$0.0437320\pi$
$23$	0.511144	+	2.89884i	0.106581	+	0.604451i	−0.883996	+	0.467494i	$0.845157\pi$
$24$		0			0
$25$	−1.73783	−	1.45821i	−0.347565	−	0.291642i
$26$	4.34730			0.852575
$27$		0			0
$28$	−0.445622			−0.0842147
$29$	0.988856	+	0.829748i	0.183626	+	0.154080i	0.729967	−	0.683482i	$-0.239535\pi$
$29$	0.988856	+	0.829748i	0.183626	+	0.154080i	−0.546341	+	0.837563i	$0.683980\pi$
$30$		0			0
$31$	−0.102196	−	0.579585i	−0.0183550	−	0.104097i	0.974254	−	0.225454i	$-0.0723865\pi$
$31$	−0.102196	−	0.579585i	−0.0183550	−	0.104097i	−0.992609	+	0.121357i	$0.961275\pi$
$32$	0.979055	+	0.356347i	0.173074	+	0.0629939i
$33$		0			0
$34$	0.701867	−	3.98048i	0.120369	−	0.682647i
$35$	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	$0.834429\pi$
$38$	−8.40420	+	3.05888i	−1.36334	+	0.496216i
$39$		0			0
$40$	−3.72668	+	3.12706i	−0.589240	+	0.494431i
$41$	3.75490	−	3.15074i	0.586417	−	0.492062i	−0.300630	−	0.953741i	$-0.597197\pi$
$41$	3.75490	−	3.15074i	0.586417	−	0.492062i	0.887047	+	0.461679i	$0.152753\pi$
$42$		0			0
$43$	4.87211	−	1.77330i	0.742990	−	0.270426i	0.0573371	−	0.998355i	$-0.481739\pi$
$43$	4.87211	−	1.77330i	0.742990	−	0.270426i	0.685653	+	0.727929i	$0.259517\pi$
$44$	−0.549163	−	0.951178i	−0.0827894	−	0.143396i
$45$		0			0
$46$	1.98293	−	3.43453i	0.292366	−	0.506394i
$47$	0.648833	−	3.67972i	0.0946421	−	0.536742i	−0.900214	−	0.435447i	$-0.856590\pi$
$47$	0.648833	−	3.67972i	0.0946421	−	0.536742i	0.994856	−	0.101295i	$-0.0322985\pi$
$48$		0			0
$49$	1.11334	+	0.405223i	0.159049	+	0.0578890i
$50$	0.530745	+	3.01000i	0.0750586	+	0.425679i
$51$		0			0
$52$	0.456767	+	0.383273i	0.0633422	+	0.0531504i
$53$	−11.6382			−1.59862			−0.799312	−	0.600916i	$-0.794802\pi$
$53$	−11.6382			−1.59862			−0.799312	+	0.600916i	$0.794802\pi$
$54$		0			0
$55$	9.82295			1.32453
$56$	5.43763	+	4.56272i	0.726634	+	0.609719i
$57$		0			0
$58$	−0.302004	−	1.71275i	−0.0396550	−	0.224895i
$59$	−6.90420	−	2.51292i	−0.898850	−	0.327155i	−0.149058	−	0.988828i	$-0.547624\pi$
$59$	−6.90420	−	2.51292i	−0.898850	−	0.327155i	−0.749792	+	0.661674i	$0.769846\pi$
$60$		0			0
$61$	1.91875	−	10.8818i	0.245671	−	1.39327i	−0.573260	−	0.819374i	$-0.694321\pi$
$61$	1.91875	−	10.8818i	0.245671	−	1.39327i	0.818930	−	0.573893i	$-0.194567\pi$
$62$	−0.396459	+	0.686688i	−0.0503504	+	0.0872094i
$63$		0			0
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	−5.01114	+	1.82391i	−0.621556	+	0.226228i
$66$		0			0
$67$	1.42262	−	1.19372i	0.173801	−	0.145836i	−0.551738	−	0.834017i	$-0.686035\pi$
$67$	1.42262	−	1.19372i	0.173801	−	0.145836i	0.725539	+	0.688182i	$0.241591\pi$
$68$	0.424678	−	0.356347i	0.0514998	−	0.0432134i
$69$		0			0
$70$	−5.04576	+	1.83651i	−0.603084	+	0.219504i
$71$	−2.75624	−	4.77396i	−0.327106	−	0.566564i	0.654830	−	0.755776i	$-0.272740\pi$
$71$	−2.75624	−	4.77396i	−0.327106	−	0.566564i	−0.981936	+	0.189212i	$0.939407\pi$
$72$		0			0
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	−0.981522	−	0.191352i	$-0.938713\pi$
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	0.656476	+	0.754347i	$0.272046\pi$
$74$	−0.00980018	+	0.0555796i	−0.00113925	+	0.00646100i
$75$		0			0
$76$	−1.15270	−	0.419550i	−0.132224	−	0.0481257i
$77$	−2.48886	−	14.1150i	−0.283631	−	1.60855i
$78$		0			0
$79$	−2.89646	−	2.43042i	−0.325877	−	0.273443i	0.465140	−	0.885237i	$-0.346004\pi$
$79$	−2.89646	−	2.43042i	−0.325877	−	0.273443i	−0.791017	+	0.611794i	$0.790448\pi$
$80$	5.94356			0.664511
$81$		0			0
$82$	−6.60401			−0.729291
$83$	−3.05303	−	2.56180i	−0.335114	−	0.281194i	0.459666	−	0.888092i	$-0.347969\pi$
$83$	−3.05303	−	2.56180i	−0.335114	−	0.281194i	−0.794780	+	0.606898i	$0.792414\pi$
$84$		0			0
$85$	0.860967	+	4.88279i	0.0933850	+	0.529613i
$86$	−6.56418	−	2.38917i	−0.707833	−	0.257630i
$87$		0			0
$88$	−3.03802	+	17.2295i	−0.323854	+	1.83667i
$89$	4.07532	−	7.05866i	0.431983	−	0.748217i	−0.565061	−	0.825049i	$-0.691147\pi$
$89$	4.07532	−	7.05866i	0.431983	−	0.748217i	0.997044	+	0.0768323i	$0.0244806\pi$
$90$		0			0
$91$	3.89053	+	6.73859i	0.407838	+	0.706397i
$92$	0.511144	−	0.186041i	0.0532905	−	0.0193961i
$93$		0			0
$94$	−3.85638	+	3.23589i	−0.397755	+	0.333756i
$95$	8.40420	−	7.05196i	0.862253	−	0.723516i
$96$		0			0
$97$	−0.245100	+	0.0892091i	−0.0248861	+	0.00905781i	−0.354433	−	0.935081i	$-0.615326\pi$
$97$	−0.245100	+	0.0892091i	−0.0248861	+	0.00905781i	0.329547	+	0.944139i	$0.393104\pi$
$98$	−0.798133	−	1.38241i	−0.0806236	−	0.139644i
$99$		0			0
$100$	−0.209607	+	0.363051i	−0.0209607	+	0.0363051i
$101$	−1.91488	+	10.8598i	−0.190537	+	1.08059i	0.728094	+	0.685477i	$0.240406\pi$
$101$	−1.91488	+	10.8598i	−0.190537	+	1.08059i	−0.918632	+	0.395115i	$0.870705\pi$
$102$		0			0
$103$	3.67112	+	1.33618i	0.361726	+	0.131658i	0.516489	−	0.856294i	$-0.327239\pi$
$103$	3.67112	+	1.33618i	0.361726	+	0.131658i	−0.154762	+	0.987952i	$0.549461\pi$
$104$	−1.64930	−	9.35365i	−0.161727	−	0.917200i
$105$		0			0
$106$	12.0116	+	10.0789i	1.16667	+	0.978953i
$107$	2.63816			0.255040			0.127520	−	0.991836i	$-0.459298\pi$
$107$	2.63816			0.255040			0.127520	+	0.991836i	$0.459298\pi$
$108$		0			0
$109$	−8.95811			−0.858031			−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95811			−0.858031			−0.429016	+	0.903297i	$0.641140\pi$
$110$	−10.1382	−	8.50692i	−0.966635	−	0.811103i
$111$		0			0
$112$	−1.50593	−	8.54055i	−0.142297	−	0.807006i
$113$	14.9684	+	5.44804i	1.40811	+	0.512509i	0.930574	−	0.366105i	$-0.119309\pi$
$113$	14.9684	+	5.44804i	1.40811	+	0.512509i	0.477533	+	0.878614i	$0.341531\pi$
$114$		0			0
$115$	−0.844770	+	4.79093i	−0.0787752	+	0.446756i
$116$	0.119271	−	0.206583i	0.0110740	−	0.0191807i
$117$		0			0
$118$	4.94949	+	8.57277i	0.455638	+	0.789188i
$119$	6.79813	−	2.47432i	0.623184	−	0.226820i
$120$		0			0
$121$	18.6348	−	15.6364i	1.69407	−	1.42149i
$122$	−11.4042	+	9.56926i	−1.03249	+	0.866360i
$123$		0			0
$124$	−0.102196	+	0.0371965i	−0.00917751	+	0.00334034i
$125$	−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	$0.217674\pi$
$128$	−1.64930	+	9.35365i	−0.145779	+	0.826753i
$129$		0			0
$130$	6.75150	+	2.45734i	0.592145	+	0.215523i
$131$	3.07486	+	17.4384i	0.268651	+	1.52360i	0.758432	+	0.651752i	$0.225966\pi$
$131$	3.07486	+	17.4384i	0.268651	+	1.52360i	−0.489781	+	0.871846i	$0.662923\pi$
$132$		0			0
$133$	−12.2626	−	10.2896i	−1.06331	−	0.892220i
$134$	−2.50206			−0.216145
$135$		0			0
$136$	−8.83069			−0.757225
$137$	3.00980	+	2.52552i	0.257145	+	0.215770i	0.762242	−	0.647293i	$-0.224099\pi$
$137$	3.00980	+	2.52552i	0.257145	+	0.215770i	−0.505097	+	0.863063i	$0.668543\pi$
$138$		0			0
$139$	2.07785	+	11.7841i	0.176241	+	0.999511i	0.936702	+	0.350128i	$0.113862\pi$
$139$	2.07785	+	11.7841i	0.176241	+	0.999511i	−0.760461	+	0.649383i	$0.775027\pi$
$140$	−0.692066	−	0.251892i	−0.0584903	−	0.0212887i
$141$		0			0
$142$	−1.28968	+	7.31412i	−0.108227	+	0.613788i
$143$	−9.58899	+	16.6086i	−0.801872	+	1.38888i
$144$		0			0
$145$	1.06670	+	1.84759i	0.0885849	+	0.153434i
$146$	7.03209	−	2.55947i	0.581980	−	0.211823i
$147$		0			0
$148$	−0.00592979	+	0.00497568i	−0.000487425	+	0.000408999i
$149$	−15.7233	+	13.1934i	−1.28810	+	1.08085i	−0.296029	+	0.955179i	$0.595662\pi$
$149$	−15.7233	+	13.1934i	−1.28810	+	1.08085i	−0.992073	+	0.125666i	$0.959893\pi$
$150$		0			0
$151$	−15.0424	+	5.47497i	−1.22413	+	0.445547i	−0.871583	−	0.490248i	$-0.836906\pi$
$151$	−15.0424	+	5.47497i	−1.22413	+	0.445547i	−0.352546	+	0.935794i	$0.614684\pi$
$152$	9.76991	+	16.9220i	0.792445	+	1.37255i
$153$		0			0
$154$	−9.65523	+	16.7233i	−0.778041	+	1.34761i
$155$	0.168900	−	0.957882i	0.0135664	−	0.0769389i
$156$		0			0
$157$	20.6484	+	7.51541i	1.64792	+	0.599795i	0.988398	−	0.151887i	$-0.0485350\pi$
$157$	20.6484	+	7.51541i	1.64792	+	0.599795i	0.659526	+	0.751682i	$0.270757\pi$
$158$	0.884600	+	5.01681i	0.0703750	+	0.399116i
$159$		0			0
$160$	1.31908	+	1.10684i	0.104282	+	0.0875032i
$161$	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	$0.203096\pi$
$164$	−0.693877	−	0.582232i	−0.0541827	−	0.0454647i
$165$		0			0
$166$	0.932419	+	5.28801i	0.0723697	+	0.410429i
$167$	4.03209	+	1.46756i	0.312012	+	0.113563i	0.493280	−	0.869871i	$-0.335798\pi$
$167$	4.03209	+	1.46756i	0.312012	+	0.113563i	−0.181268	+	0.983434i	$0.558020\pi$
$168$		0			0
$169$	−0.449493	+	2.54920i	−0.0345764	+	0.196092i
$170$	3.34002	−	5.78509i	0.256168	−	0.443696i
$171$		0			0
$172$	−0.479055	−	0.829748i	−0.0365276	−	0.0632677i
$173$	3.56418	−	1.29725i	0.270979	−	0.0986284i	−0.202957	−	0.979188i	$-0.565055\pi$
$173$	3.56418	−	1.29725i	0.270979	−	0.0986284i	0.473936	+	0.880559i	$0.342833\pi$
$174$		0			0
$175$	−4.19072	+	3.51643i	−0.316789	+	0.265817i
$176$	16.3739	−	13.7394i	1.23423	−	1.03564i
$177$		0			0
$178$	−10.3191	+	3.75584i	−0.773448	+	0.281512i
$179$	4.13816	+	7.16750i	0.309300	+	0.535724i	0.978209	−	0.207620i	$-0.0665718\pi$
$179$	4.13816	+	7.16750i	0.309300	+	0.535724i	−0.668909	+	0.743344i	$0.733239\pi$
$180$		0			0
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	−0.963475	−	0.267797i	$-0.913704\pi$
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	0.713657	+	0.700496i	$0.247038\pi$
$182$	1.82042	−	10.3241i	0.134939	−	0.765275i
$183$		0			0
$184$	−8.14203	−	2.96346i	−0.600238	−	0.218469i
$185$	−0.0120217	−	0.0681784i	−0.000883853	−	0.00501258i
$186$		0			0
$187$	13.6591	+	11.4613i	0.998852	+	0.838137i
$188$	−0.690474			−0.0503580
$189$		0			0
$190$	−14.7811			−1.07233
$191$	3.84137	+	3.22329i	0.277952	+	0.233229i	0.771097	−	0.636718i	$-0.219708\pi$
$191$	3.84137	+	3.22329i	0.277952	+	0.233229i	−0.493145	+	0.869947i	$0.664153\pi$
$192$		0			0
$193$	−3.10220	−	17.5934i	−0.223301	−	1.26640i	−0.865907	−	0.500206i	$-0.833258\pi$
$193$	−3.10220	−	17.5934i	−0.223301	−	1.26640i	0.642606	−	0.766197i	$-0.277853\pi$
$194$	0.330222	+	0.120191i	0.0237086	+	0.00862922i
$195$		0			0
$196$	0.0380187	−	0.215615i	0.00271562	−	0.0154010i
$197$	0.361844	−	0.626733i	0.0257803	−	0.0446529i	−0.852847	−	0.522160i	$-0.825126\pi$
$197$	0.361844	−	0.626733i	0.0257803	−	0.0446529i	0.878628	+	0.477507i	$0.158460\pi$
$198$		0			0
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	0.988169	−	0.153367i	$-0.0490117\pi$
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	−0.626905	+	0.779096i	$0.715678\pi$
$200$	6.27497	−	2.28390i	0.443707	−	0.161496i
$201$		0			0
$202$	11.3812	−	9.54996i	0.800778	−	0.671933i
$203$	2.38460	−	2.00092i	0.167366	−	0.140437i
$204$		0			0
$205$	7.61246	−	2.77071i	0.531678	−	0.193515i
$206$	−2.63176	−	4.55834i	−0.183363	−	0.317595i
$207$		0			0
$208$	−5.80200	+	10.0494i	−0.402297	+	0.696798i
$209$	6.85117	−	38.8549i	0.473905	−	2.68765i
$210$		0			0
$211$	13.9684	+	5.08407i	0.961623	+	0.350002i	0.774669	−	0.632367i	$-0.217916\pi$
$211$	13.9684	+	5.08407i	0.961623	+	0.350002i	0.186954	+	0.982369i	$0.440139\pi$
$212$	0.373455	+	2.11797i	0.0256490	+	0.145463i
$213$		0			0
$214$	−2.72281	−	2.28471i	−0.186128	−	0.156180i
$215$	8.56893			0.584396
$216$		0			0
$217$	−1.41921			−0.0963426
$218$	9.24557	+	7.75795i	0.626189	+	0.525435i
$219$		0			0
$220$	−0.315207	−	1.78763i	−0.0212513	−	0.120522i
$221$	−9.09627	−	3.31077i	−0.611881	−	0.222707i
$222$		0			0
$223$	−1.90121	+	10.7823i	−0.127314	+	0.722035i	0.852592	+	0.522577i	$0.175029\pi$
$223$	−1.90121	+	10.7823i	−0.127314	+	0.722035i	−0.979906	+	0.199458i	$0.936082\pi$
$224$	1.25624	−	2.17588i	0.0839364	−	0.145382i
$225$		0			0
$226$	−10.7306	−	18.5859i	−0.713786	−	1.23631i
$227$	−16.2875	+	5.92815i	−1.08104	+	0.393465i	−0.820293	−	0.571943i	$-0.806190\pi$
$227$	−16.2875	+	5.92815i	−1.08104	+	0.393465i	−0.260743	+	0.965408i	$0.583968\pi$
$228$		0			0
$229$	1.19665	−	1.00411i	0.0790770	−	0.0663535i	−0.602392	−	0.798200i	$-0.705786\pi$
$229$	1.19665	−	1.00411i	0.0790770	−	0.0663535i	0.681469	+	0.731847i	$0.261341\pi$
$230$	5.02094	−	4.21307i	0.331071	−	0.277802i
$231$		0			0
$232$	−3.57057	+	1.29958i	−0.234420	+	0.0853218i
$233$	8.39440	+	14.5395i	0.549935	+	0.952516i	0.998278	+	0.0586545i	$0.0186810\pi$
$233$	8.39440	+	14.5395i	0.549935	+	0.952516i	−0.448343	+	0.893862i	$0.647986\pi$
$234$		0			0
$235$	3.08765	−	5.34796i	0.201416	−	0.348863i
$236$	−0.235767	+	1.33710i	−0.0153471	+	0.0870377i
$237$		0			0
$238$	−9.15910	−	3.33364i	−0.593696	−	0.216088i
$239$	0.699645	+	3.96788i	0.0452563	+	0.256661i	0.999039	−	0.0438370i	$-0.0139582\pi$
$239$	0.699645	+	3.96788i	0.0452563	+	0.256661i	−0.953782	+	0.300498i	$0.902847\pi$
$240$		0			0
$241$	−2.56805	−	2.15485i	−0.165423	−	0.138806i	0.556319	−	0.830969i	$-0.312213\pi$
$241$	−2.56805	−	2.15485i	−0.165423	−	0.138806i	−0.721741	+	0.692163i	$0.756658\pi$
$242$	−32.7743			−2.10681
$243$		0			0
$244$	−2.04189			−0.130719
$245$	1.50000	+	1.25865i	0.0958315	+	0.0804122i
$246$		0			0
$247$	3.71941	+	21.0938i	0.236660	+	1.34217i
$248$	1.62789	+	0.592503i	0.103371	+	0.0376240i
$249$		0			0
$250$	−2.81046	+	15.9389i	−0.177749	+	1.00807i
$251$	−11.5753	+	20.0490i	−0.730628	+	1.26548i	0.225987	+	0.974130i	$0.427439\pi$
$251$	−11.5753	+	20.0490i	−0.730628	+	1.26548i	−0.956615	+	0.291354i	$0.905894\pi$
$252$		0			0
$253$	8.74763	+	15.1513i	0.549959	+	0.952556i
$254$	4.55303	−	1.65717i	0.285683	−	0.103980i
$255$		0			0
$256$	−3.36753	+	2.82569i	−0.210470	+	0.176606i
$257$	−9.20233	+	7.72167i	−0.574026	+	0.481665i	−0.882979	−	0.469412i	$-0.844466\pi$
$257$	−9.20233	+	7.72167i	−0.574026	+	0.481665i	0.308953	+	0.951077i	$0.400021\pi$
$258$		0			0
$259$	−0.0949225	+	0.0345490i	−0.00589820	+	0.00214677i
$260$	0.492726	+	0.853427i	0.0305576	+	0.0529273i
$261$		0			0
$262$	11.9285	−	20.6609i	0.736948	−	1.27643i
$263$	−2.93494	+	16.6449i	−0.180976	+	1.02637i	0.750040	+	0.661392i	$0.230034\pi$
$263$	−2.93494	+	16.6449i	−0.180976	+	1.02637i	−0.931017	+	0.364976i	$0.881077\pi$
$264$		0			0
$265$	−18.0744	−	6.57856i	−1.11030	−	0.404118i
$266$	3.74510	+	21.2395i	0.229627	+	1.30228i
$267$		0			0
$268$	−0.262889	−	0.220590i	−0.0160585	−	0.0134747i
$269$	7.91447			0.482554			0.241277	−	0.970456i	$-0.422434\pi$
$269$	7.91447			0.482554			0.241277	+	0.970456i	$0.422434\pi$
$270$		0			0
$271$	−17.2344			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$271$	−17.2344			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$272$	8.26470	+	6.93491i	0.501121	+	0.420490i
$273$		0			0
$274$	−0.919215	−	5.21313i	−0.0555318	−	0.314937i
$275$	−12.6702	−	4.61159i	−0.764044	−	0.278089i
$276$		0			0
$277$	4.59034	−	26.0331i	0.275807	−	1.56418i	−0.460581	−	0.887618i	$-0.652359\pi$
$277$	4.59034	−	26.0331i	0.275807	−	1.56418i	0.736388	−	0.676560i	$-0.236530\pi$
$278$	8.06077	−	13.9617i	0.483453	−	0.837365i
$279$		0			0
$280$	5.86571	+	10.1597i	0.350543	+	0.607159i
$281$	−17.8503	+	6.49697i	−1.06486	+	0.387577i	−0.814252	−	0.580512i	$-0.802852\pi$
$281$	−17.8503	+	6.49697i	−1.06486	+	0.387577i	−0.250607	+	0.968089i	$0.580630\pi$
$282$		0			0
$283$	−12.7062	+	10.6618i	−0.755305	+	0.633777i	−0.936900	−	0.349597i	$-0.886319\pi$
$283$	−12.7062	+	10.6618i	−0.755305	+	0.633777i	0.181595	+	0.983373i	$0.441874\pi$
$284$	−0.780344	+	0.654786i	−0.0463049	+	0.0388544i
$285$		0			0
$286$	24.2802	−	8.83726i	1.43572	−	0.522558i
$287$	−5.91013	−	10.2366i	−0.348864	−	0.604250i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	0.499123	−	2.83067i	0.0293095	−	0.166222i
$291$		0			0
$292$	0.964508	+	0.351052i	0.0564435	+	0.0205438i
$293$	−3.36143	−	19.0636i	−0.196377	−	1.11371i	−0.910444	−	0.413632i	$-0.864260\pi$
$293$	−3.36143	−	19.0636i	−0.196377	−	1.11371i	0.714067	−	0.700077i	$-0.246851\pi$
$294$		0			0
$295$	−9.30200	−	7.80531i	−0.541584	−	0.454443i
$296$	0.123303			0.00716685
$297$		0			0
$298$	27.6536			1.60193
$299$	−7.27584	−	6.10516i	−0.420773	−	0.353070i
$300$		0			0
$301$	−2.17112	−	12.3130i	−0.125141	−	0.709712i
$302$	20.2665	+	7.37641i	1.16621	+	0.424465i
$303$		0			0
$304$	4.14543	−	23.5099i	0.237757	−	1.34839i
$305$	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	$-0.369009\pi$
$308$	−2.48886	+	0.905869i	−0.141816	+	0.0516167i
$309$		0			0
$310$	−1.00387	+	0.842347i	−0.0570160	+	0.0478421i
$311$	8.17024	−	6.85565i	0.463292	−	0.388748i	−0.381049	−	0.924555i	$-0.624437\pi$
$311$	8.17024	−	6.85565i	0.463292	−	0.388748i	0.844341	+	0.535807i	$0.179992\pi$
$312$		0			0
$313$	−3.58512	+	1.30488i	−0.202643	+	0.0737561i	−0.441348	−	0.897336i	$-0.645499\pi$
$313$	−3.58512	+	1.30488i	−0.202643	+	0.0737561i	0.238705	+	0.971092i	$0.423277\pi$
$314$	−14.8025	−	25.6386i	−0.835352	−	1.44687i
$315$		0			0
$316$	−0.349356	+	0.605102i	−0.0196528	+	0.0340396i
$317$	−4.58243	+	25.9883i	−0.257375	+	1.45965i	0.532526	+	0.846413i	$0.321243\pi$
$317$	−4.58243	+	25.9883i	−0.257375	+	1.45965i	−0.789902	+	0.613234i	$0.789868\pi$
$318$		0			0
$319$	7.20961	+	2.62408i	0.403661	+	0.146920i
$320$	−2.46703	−	13.9912i	−0.137911	−	0.782134i
$321$		0			0
$322$	−7.32610	−	6.14733i	−0.408268	−	0.342577i
$323$	19.9145			1.10807
$324$		0			0
$325$	7.31996			0.406038
$326$	−21.1689	−	17.7628i	−1.17244	−	0.983791i
$327$		0			0
$328$	2.50546	+	14.2092i	0.138341	+	0.784571i
$329$	−8.46703	−	3.08175i	−0.466803	−	0.169902i
$330$		0			0
$331$	−0.272908	+	1.54774i	−0.0150004	+	0.0850713i	−0.991389	−	0.130950i	$-0.958197\pi$
$331$	−0.272908	+	1.54774i	−0.0150004	+	0.0850713i	0.976389	+	0.216022i	$0.0693082\pi$
$332$	−0.368241	+	0.637812i	−0.0202098	+	0.0350045i
$333$		0			0
$334$	−2.89053	−	5.00654i	−0.158163	−	0.273946i
$335$	2.88413	−	1.04974i	0.157577	−	0.0573533i
$336$		0			0
$337$	−6.14022	+	5.15225i	−0.334479	+	0.280661i	−0.794522	−	0.607236i	$-0.792278\pi$
$337$	−6.14022	+	5.15225i	−0.334479	+	0.280661i	0.460043	+	0.887897i	$0.347834\pi$
$338$	2.67159	−	2.24173i	0.145315	−	0.121934i
$339$		0			0
$340$	0.860967	−	0.313366i	0.0466925	−	0.0169947i
$341$	−1.74897	−	3.02931i	−0.0947121	−	0.164046i
$342$		0			0
$343$	9.86871	−	17.0931i	0.532860	−	0.922941i
$344$	−2.65018	+	15.0299i	−0.142888	+	0.810358i
$345$		0			0
$346$	−4.80200	−	1.74779i	−0.258157	−	0.0939616i
$347$	−3.44609	−	19.5437i	−0.184996	−	1.04916i	−0.925961	−	0.377620i	$-0.876743\pi$
$347$	−3.44609	−	19.5437i	−0.184996	−	1.04916i	0.740965	−	0.671544i	$-0.234368\pi$
$348$		0			0
$349$	8.49794	+	7.13062i	0.454884	+	0.381693i	0.841245	−	0.540655i	$-0.181823\pi$
$349$	8.49794	+	7.13062i	0.454884	+	0.381693i	−0.386360	+	0.922348i	$0.626268\pi$
$350$	7.37052			0.393971
$351$		0			0
$352$	6.19253			0.330063
$353$	2.19388	+	1.84088i	0.116768	+	0.0979803i	0.699302	−	0.714826i	$-0.253494\pi$
$353$	2.19388	+	1.84088i	0.116768	+	0.0979803i	−0.582534	+	0.812806i	$0.697939\pi$
$354$		0			0
$355$	−1.58202	−	8.97210i	−0.0839651	−	0.476190i
$356$	−1.41534	−	0.515143i	−0.0750131	−	0.0273025i
$357$		0			0
$358$	1.93629	−	10.9812i	0.102336	−	0.580377i
$359$	14.3944	−	24.9318i	0.759707	−	1.31585i	−0.183292	−	0.983058i	$-0.558676\pi$
$359$	14.3944	−	24.9318i	0.759707	−	1.31585i	0.943000	−	0.332793i	$-0.107991\pi$
$360$		0			0
$361$	−12.5326	−	21.7070i	−0.659608	−	1.14247i
$362$	8.51027	−	3.09748i	0.447290	−	0.162800i
$363$		0			0
$364$	1.10148	−	0.924252i	0.0577333	−	0.0484440i
$365$	−7.03209	+	5.90062i	−0.368076	+	0.308853i
$366$		0			0
$367$	10.3293	−	3.75957i	0.539187	−	0.196248i	−0.0580485	−	0.998314i	$-0.518488\pi$
$367$	10.3293	−	3.75957i	0.539187	−	0.196248i	0.597236	+	0.802066i	$0.296266\pi$
$368$	5.29292	+	9.16760i	0.275912	+	0.477894i
$369$		0			0
$370$	−0.0466368	+	0.0807773i	−0.00242453	+	0.00419941i
$371$	−4.87346	+	27.6387i	−0.253017	+	1.43493i
$372$		0			0
$373$	−31.3949	−	11.4268i	−1.62556	−	0.591657i	−0.641134	−	0.767429i	$-0.721536\pi$
$373$	−31.3949	−	11.4268i	−1.62556	−	0.591657i	−0.984431	+	0.175772i	$0.943758\pi$
$374$	−4.17159	−	23.6583i	−0.215708	−	1.22334i
$375$		0			0
$376$	8.42539	+	7.06974i	0.434506	+	0.364594i
$377$	−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	$0.319258\pi$
$380$	−1.55303	−	1.30315i	−0.0796689	−	0.0668502i
$381$		0			0
$382$	−1.17318	−	6.65344i	−0.0600252	−	0.340420i
$383$	−3.86319	−	1.40609i	−0.197400	−	0.0718476i	0.241428	−	0.970419i	$-0.422384\pi$
$383$	−3.86319	−	1.40609i	−0.197400	−	0.0718476i	−0.438828	+	0.898571i	$0.644606\pi$
$384$		0			0
$385$	4.11334	−	23.3279i	0.209635	−	1.18890i
$386$	−12.0346	+	20.8446i	−0.612546	+	1.06096i
$387$		0			0
$388$	0.0240997	+	0.0417419i	0.00122348	+	0.00211912i
$389$	16.0633	−	5.84656i	0.814442	−	0.296433i	0.0989844	−	0.995089i	$-0.468441\pi$
$389$	16.0633	−	5.84656i	0.814442	−	0.296433i	0.715457	+	0.698656i	$0.246218\pi$
$390$		0			0
$391$	−6.76470	+	5.67626i	−0.342106	+	0.287061i
$392$	−2.67159	+	2.24173i	−0.134936	+	0.113224i
$393$		0			0
$394$	−0.916222	+	0.333477i	−0.0461586	+	0.0168004i
$395$	−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	$0.976637\pi$
$398$	2.38460	−	13.5237i	0.119529	−	0.677884i
$399$		0			0
$400$	−7.66637	−	2.79033i	−0.383319	−	0.139517i
$401$	2.53209	+	14.3602i	0.126446	+	0.717114i	0.980438	+	0.196827i	$0.0630638\pi$
$401$	2.53209	+	14.3602i	0.126446	+	0.717114i	−0.853992	+	0.520287i	$0.825825\pi$
$402$		0			0
$403$	1.45471	+	1.22064i	0.0724641	+	0.0608046i
$404$	2.03777			0.101383
$405$		0			0
$406$	−4.19396			−0.208143
$407$	−0.190722	−	0.160035i	−0.00945375	−	0.00793264i
$408$		0			0
$409$	−3.03936	−	17.2371i	−0.150287	−	0.852319i	−0.962969	−	0.269612i	$-0.913105\pi$
$409$	−3.03936	−	17.2371i	−0.150287	−	0.852319i	0.812682	−	0.582707i	$-0.198007\pi$
$410$	−10.2562	−	3.73297i	−0.506520	−	0.184358i
$411$		0			0
$412$	0.125362	−	0.710966i	0.00617617	−	0.0350268i
$413$	−8.85891	+	15.3441i	−0.435918	+	0.755033i
$414$		0			0
$415$	−3.29339	−	5.70431i	−0.161666	−	0.280014i
$416$	−3.15910	+	1.14982i	−0.154888	+	0.0563745i
$417$		0			0
$418$	−40.7203	+	34.1684i	−1.99170	+	1.67123i
$419$	−14.4492	+	12.1244i	−0.705892	+	0.592314i	−0.923443	−	0.383735i	$-0.874637\pi$
$419$	−14.4492	+	12.1244i	−0.705892	+	0.592314i	0.217551	+	0.976049i	$0.430193\pi$
$420$		0			0
$421$	30.3837	−	11.0588i	1.48081	−	0.538971i	0.529799	−	0.848123i	$-0.322267\pi$
$421$	30.3837	−	11.0588i	1.48081	−	0.538971i	0.951013	+	0.309152i	$0.100045\pi$
$422$	−10.0137	−	17.3442i	−0.487458	−	0.844302i
$423$		0			0
$424$	17.1288	−	29.6680i	0.831849	−	1.44080i
$425$	1.18180	−	6.70232i	0.0573257	−	0.325110i
$426$		0			0
$427$	−25.0390	−	9.11343i	−1.21172	−	0.441030i
$428$	−0.0846555	−	0.480105i	−0.00409198	−	0.0232068i
$429$		0			0
$430$	−8.84389	−	7.42091i	−0.426490	−	0.357868i
$431$	−34.3164			−1.65297			−0.826483	−	0.562962i	$-0.809662\pi$
$431$	−34.3164			−1.65297			−0.826483	+	0.562962i	$0.809662\pi$
$432$		0			0
$433$	−25.0669			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$433$	−25.0669			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$434$	1.46476	+	1.22908i	0.0703105	+	0.0589975i
$435$		0			0
$436$	0.287456	+	1.63024i	0.0137666	+	0.0780745i
$437$	18.3614	+	6.68302i	0.878346	+	0.319692i
$438$		0			0
$439$	−4.03003	+	22.8554i	−0.192343	+	1.09083i	0.723809	+	0.690000i	$0.242389\pi$
$439$	−4.03003	+	22.8554i	−0.192343	+	1.09083i	−0.916152	+	0.400830i	$0.868722\pi$
$440$	−14.4572	+	25.0407i	−0.689222	+	1.19377i
$441$		0			0
$442$	6.52094	+	11.2946i	0.310170	+	0.537230i
$443$	−3.87299	+	1.40965i	−0.184011	+	0.0669746i	−0.432382	−	0.901690i	$-0.642327\pi$
$443$	−3.87299	+	1.40965i	−0.184011	+	0.0669746i	0.248371	+	0.968665i	$0.420105\pi$
$444$		0			0
$445$	10.3191	−	8.65873i	0.489171	−	0.410463i
$446$	11.2999	−	9.48178i	0.535068	−	0.448975i
$447$		0			0
$448$	−19.4795	+	7.08997i	−0.920321	+	0.334969i
$449$	9.17071	+	15.8841i	0.432793	+	0.749619i	0.997113	−	0.0759373i	$-0.0241949\pi$
$449$	9.17071	+	15.8841i	0.432793	+	0.749619i	−0.564320	+	0.825556i	$0.690862\pi$
$450$		0			0
$451$	14.5667	−	25.2303i	0.685919	−	1.18805i
$452$	0.511144	−	2.89884i	0.0240422	−	0.136350i
$453$		0			0
$454$	21.9440	+	7.98697i	1.02988	+	0.374847i
$455$	2.23308	+	12.6644i	0.104688	+	0.593717i
$456$		0			0
$457$	−14.9081	−	12.5094i	−0.697370	−	0.585163i	0.223654	−	0.974669i	$-0.428201\pi$
$457$	−14.9081	−	12.5094i	−0.697370	−	0.585163i	−0.921024	+	0.389506i	$0.872646\pi$
$458$	−2.10464			−0.0983432
$459$		0			0
$460$	0.898986			0.0419154
$461$	−21.2572	−	17.8369i	−0.990045	−	0.830747i	−0.00447116	−	0.999990i	$-0.501423\pi$
$461$	−21.2572	−	17.8369i	−0.990045	−	0.830747i	−0.985574	+	0.169243i	$0.945868\pi$
$462$		0			0
$463$	6.71776	+	38.0983i	0.312201	+	1.77058i	0.587504	+	0.809221i	$0.300110\pi$
$463$	6.71776	+	38.0983i	0.312201	+	1.77058i	−0.275304	+	0.961357i	$0.588778\pi$
$464$	4.36231	+	1.58775i	0.202515	+	0.0737095i
$465$		0			0
$466$	3.92783	−	22.2758i	0.181953	−	1.03191i
$467$	14.8819	−	25.7762i	0.688653	−	1.19278i	−0.283621	−	0.958936i	$-0.591536\pi$
$467$	14.8819	−	25.7762i	0.688653	−	1.19278i	0.972274	−	0.233845i	$-0.0751309\pi$
$468$		0			0
$469$	−2.23917	−	3.87836i	−0.103395	−	0.179086i
$470$	−7.81820	+	2.84559i	−0.360627	+	0.131257i
$471$		0			0
$472$	16.5674	−	13.9017i	0.762577	−	0.639878i
$473$	23.6065	−	19.8082i	1.08543	−	0.910784i
$474$		0			0
$475$	−14.1509	+	5.15052i	−0.649290	+	0.236322i
$476$	−0.668434	−	1.15776i	−0.0306376	−	0.0530659i
$477$		0			0
$478$	2.71419	−	4.70112i	0.124144	−	0.215024i
$479$	6.54236	−	37.1035i	0.298928	−	1.69530i	−0.351867	−	0.936050i	$-0.614453\pi$
$479$	6.54236	−	37.1035i	0.298928	−	1.69530i	0.650794	−	0.759254i	$-0.274436\pi$
$480$		0			0
$481$	0.127011	+	0.0462284i	0.00579122	+	0.00210783i
$482$	0.784301	+	4.44799i	0.0357239	+	0.202600i
$483$		0			0
$484$	−3.44356	−	2.88949i	−0.156526	−	0.131341i
$485$	−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	$0.505509\pi$
$488$	24.9158	+	20.9068i	1.12789	+	0.946409i
$489$		0			0
$490$	−0.458111	−	2.59808i	−0.0206953	−	0.117369i
$491$	−0.467911	−	0.170306i	−0.0211165	−	0.00768579i	0.331440	−	0.943476i	$-0.392465\pi$
$491$	−0.467911	−	0.170306i	−0.0211165	−	0.00768579i	−0.352557	+	0.935790i	$0.614688\pi$
$492$		0			0
$493$	−0.672466	+	3.81374i	−0.0302864	+	0.171762i
$494$	14.4290	−	24.9918i	0.649192	−	1.12443i
$495$		0			0
$496$	−1.05825	−	1.83294i	−0.0475167	−	0.0823014i
$497$	−12.4915	+	4.54655i	−0.560322	+	0.203941i
$498$		0			0
$499$	6.86824	−	5.76314i	0.307465	−	0.257994i	−0.475979	−	0.879457i	$-0.657906\pi$
$499$	6.86824	−	5.76314i	0.307465	−	0.257994i	0.783443	+	0.621463i	$0.213462\pi$
$500$	−1.70052	+	1.42691i	−0.0760497	+	0.0638133i
$501$		0			0
$502$	29.3097	−	10.6679i	1.30816	−	0.476131i
$503$	9.18092	+	15.9018i	0.409357	+	0.709027i	0.994818	−	0.101673i	$-0.0324197\pi$
$503$	9.18092	+	15.9018i	0.409357	+	0.709027i	−0.585461	+	0.810701i	$0.699086\pi$
$504$		0			0
$505$	−9.11246	+	15.7832i	−0.405499	+	0.702345i
$506$	4.09311	−	23.2132i	0.181961	−	1.03195i
$507$		0			0
$508$	0.624485	+	0.227294i	0.0277070	+	0.0100845i
$509$	4.92649	+	27.9395i	0.218363	+	1.23840i	0.874975	+	0.484168i	$0.160878\pi$
$509$	4.92649	+	27.9395i	0.218363	+	1.23840i	−0.656612	+	0.754228i	$0.728011\pi$
$510$		0			0
$511$	10.2606	+	8.60965i	0.453901	+	0.380868i
$512$	24.9186			1.10126
$513$		0			0
$514$	16.1848			0.713881
$515$	4.94609	+	4.15026i	0.217951	+	0.182882i
$516$		0			0
$517$	−3.85638	−	21.8706i	−0.169603	−	0.961869i
$518$	0.127889	+	0.0465477i	0.00561911	+	0.00204519i
$519$		0			0
$520$	2.72580	−	15.4588i	0.119534	−	0.677913i
$521$	−16.3191	+	28.2655i	−0.714952	+	1.23833i	0.248026	+	0.968753i	$0.420218\pi$
$521$	−16.3191	+	28.2655i	−0.714952	+	1.23833i	−0.962978	+	0.269580i	$0.913115\pi$
$522$		0			0
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	0.999775	−	0.0212271i	$-0.00675730\pi$
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	−0.518271	+	0.855217i	$0.673424\pi$
$524$	3.07486	−	1.11916i	0.134326	−	0.0488905i
$525$		0			0
$526$	17.4440	−	14.6373i	0.760596	−	0.638216i
$527$	1.35251	−	1.13489i	0.0589163	−	0.0494366i
$528$		0			0
$529$	13.4709	−	4.90301i	0.585691	−	0.213174i
$530$	12.9572	+	22.4426i	0.562826	+	0.974844i
$531$		0			0
$532$	−1.47906	+	2.56180i	−0.0641252	+	0.111068i
$533$	−2.74644	+	15.5759i	−0.118962	+	0.674665i
$534$		0			0
$535$	4.09714	+	1.49124i	0.177135	+	0.0644719i
$536$	0.949244	+	5.38343i	0.0410011	+	0.232529i
$537$		0			0
$538$	−8.16843	−	6.85413i	−0.352166	−	0.295503i
$539$	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	$0.610214\pi$
$542$	17.7875	+	14.9254i	0.764037	+	0.641103i
$543$		0			0
$544$	0.542766	+	3.07818i	0.0232709	+	0.131976i
$545$	−13.9122	−	5.06364i	−0.595935	−	0.216903i
$546$		0			0
$547$	−4.76130	+	27.0027i	−0.203578	+	1.15455i	0.696083	+	0.717961i	$0.254925\pi$
$547$	−4.76130	+	27.0027i	−0.203578	+	1.15455i	−0.899661	+	0.436589i	$0.856187\pi$
$548$	0.363026	−	0.628780i	0.0155077	−	0.0268602i
$549$		0			0
$550$	9.08306	+	15.7323i	0.387303	+	0.670829i
$551$	8.05216	−	2.93075i	0.343033	−	0.124854i
$552$		0			0
$553$	−6.98474	+	5.86089i	−0.297021	+	0.249230i
$554$	−27.2830	+	22.8931i	−1.15914	+	0.972635i
$555$		0			0
$556$	2.07785	−	0.756275i	0.0881204	−	0.0320732i
$557$	14.7010	+	25.4629i	0.622901	+	1.07890i	0.988943	+	0.148298i	$0.0473794\pi$
$557$	14.7010	+	25.4629i	0.622901	+	1.07890i	−0.366042	+	0.930598i	$0.619287\pi$
$558$		0			0
$559$	−8.36484	+	14.4883i	−0.353795	+	0.612791i
$560$	2.48886	−	14.1150i	0.105173	−	0.596468i
$561$		0			0
$562$	24.0496	+	8.75335i	1.01447	+	0.369238i
$563$	1.80082	+	10.2130i	0.0758956	+	0.430425i	0.998952	+	0.0457616i	$0.0145715\pi$
$563$	1.80082	+	10.2130i	0.0758956	+	0.430425i	−0.923057	+	0.384664i	$0.874317\pi$
$564$		0			0
$565$	20.1668	+	16.9220i	0.848425	+	0.711913i
$566$	22.3473			0.939327
$567$		0			0
$568$	16.2264			0.680843
$569$	25.2558	+	21.1922i	1.05878	+	0.888422i	0.993989	−	0.109477i	$-0.0349177\pi$
$569$	25.2558	+	21.1922i	1.05878	+	0.888422i	0.0647903	+	0.997899i	$0.479362\pi$
$570$		0			0
$571$	−0.128051	−	0.726212i	−0.00535876	−	0.0303910i	0.982011	−	0.188823i	$-0.0604673\pi$
$571$	−0.128051	−	0.726212i	−0.00535876	−	0.0303910i	−0.987370	+	0.158432i	$0.949356\pi$
$572$	3.33022	+	1.21210i	0.139244	+	0.0506805i
$573$		0			0
$574$	−2.76542	+	15.6835i	−0.115426	+	0.654615i
$575$	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	$0.965238\pi$
$578$	−10.1284	+	3.68642i	−0.421284	+	0.153335i
$579$		0			0
$580$	0.302004	−	0.253411i	0.0125400	−	0.0105223i
$581$	−7.36231	+	6.17771i	−0.305440	+	0.256295i
$582$		0			0
$583$	−65.0005	+	23.6583i	−2.69205	+	0.979825i
$584$	−8.17483	−	14.1592i	−0.338277	−	0.585913i
$585$		0			0
$586$	−13.0403	+	22.5865i	−0.538690	+	0.933038i
$587$	5.54148	−	31.4273i	0.228721	−	1.29714i	−0.626721	−	0.779244i	$-0.715603\pi$
$587$	5.54148	−	31.4273i	0.228721	−	1.29714i	0.855442	−	0.517899i	$-0.173286\pi$
$588$		0			0
$589$	−3.67112	−	1.33618i	−0.151266	−	0.0550563i
$590$	2.84090	+	16.1115i	0.116958	+	0.663302i
$591$		0			0
$592$	−0.115400	−	0.0968323i	−0.00474292	−	0.00397978i
$593$	−31.6783			−1.30087			−0.650436	−	0.759561i	$-0.725414\pi$
$593$	−31.6783			−1.30087			−0.650436	+	0.759561i	$0.725414\pi$
$594$		0			0
$595$	11.9564			0.490163
$596$	2.90554	+	2.43804i	0.119016	+	0.0998661i
$597$		0			0
$598$	2.22210	+	12.6021i	0.0908683	+	0.515340i
$599$	−11.8623	−	4.31753i	−0.484681	−	0.176409i	0.0881103	−	0.996111i	$-0.471917\pi$
$599$	−11.8623	−	4.31753i	−0.484681	−	0.176409i	−0.572791	+	0.819701i	$0.694139\pi$
$600$		0			0
$601$	−1.54694	+	8.77314i	−0.0631011	+	0.357864i	0.936866	+	0.349690i	$0.113713\pi$
$601$	−1.54694	+	8.77314i	−0.0631011	+	0.357864i	−0.999967	+	0.00817407i	$0.997398\pi$
$602$	−8.42262	+	14.5884i	−0.343280	+	0.594579i
$603$		0			0
$604$	1.47906	+	2.56180i	0.0601819	+	0.104238i
$605$	37.7790	−	13.7504i	1.53593	−	0.559035i
$606$		0			0
$607$	−25.3746	+	21.2918i	−1.02992	+	0.864209i	−0.990842	−	0.135026i	$-0.956888\pi$
$607$	−25.3746	+	21.2918i	−1.02992	+	0.864209i	−0.0390828	+	0.999236i	$0.512444\pi$
$608$	5.29813	−	4.44566i	0.214868	−	0.180295i
$609$		0			0
$610$	−23.1202	+	8.41507i	−0.936110	+	0.340716i
$611$	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	$0.282882\pi$
$614$	−4.86761	+	27.6056i	−0.196441	+	1.11407i
$615$		0			0
$616$	39.6450	+	14.4296i	1.59734	+	0.581385i
$617$	4.46838	+	25.3414i	0.179890	+	1.02021i	0.932347	+	0.361566i	$0.117758\pi$
$617$	4.46838	+	25.3414i	0.179890	+	1.02021i	−0.752457	+	0.658642i	$0.771131\pi$
$618$		0			0
$619$	21.2920	+	17.8661i	0.855799	+	0.718101i	0.961059	−	0.276344i	$-0.0891229\pi$
$619$	21.2920	+	17.8661i	0.855799	+	0.718101i	−0.105259	+	0.994445i	$0.533567\pi$
$620$	−0.179740			−0.00721854
$621$		0			0
$622$	−14.3696			−0.576168
$623$	−15.0567	−	12.6340i	−0.603232	−	0.506172i
$624$		0			0
$625$	−1.47787	−	8.38144i	−0.0591149	−	0.335257i
$626$	4.83022	+	1.75806i	0.193055	+	0.0702661i
$627$		0			0
$628$	0.705108	−	3.99887i	0.0281369	−	0.159572i
$629$	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	$-0.345873\pi$
$632$	10.4586	−	3.80661i	0.416020	−	0.151419i
$633$		0			0
$634$	27.2360	−	22.8537i	1.08168	−	0.907637i
$635$	−4.55303	+	3.82045i	−0.180682	+	0.151610i
$636$		0			0
$637$	−3.59240	+	1.30753i	−0.142336	+	0.0518060i
$638$	−5.16843	−	8.95199i	−0.204620	−	0.354413i
$639$		0			0
$640$	−7.84864	+	13.5942i	−0.310245	+	0.537360i
$641$	−2.20368	+	12.4977i	−0.0870400	+	0.493629i	0.909858	+	0.414920i	$0.136191\pi$
$641$	−2.20368	+	12.4977i	−0.0870400	+	0.493629i	−0.996898	+	0.0787081i	$0.974921\pi$
$642$		0			0
$643$	−14.5432	−	5.29330i	−0.573529	−	0.208748i	0.0389407	−	0.999242i	$-0.487602\pi$
$643$	−14.5432	−	5.29330i	−0.573529	−	0.208748i	−0.612470	+	0.790494i	$0.709824\pi$
$644$	−0.227777	−	1.29179i	−0.00897569	−	0.0509036i
$645$		0			0
$646$	−20.5535	−	17.2464i	−0.808667	−	0.678552i
$647$	−11.1506			−0.438377			−0.219189	−	0.975683i	$-0.570341\pi$
$647$	−11.1506			−0.438377			−0.219189	+	0.975683i	$0.570341\pi$
$648$		0			0
$649$	−43.6691			−1.71416
$650$	−7.55484	−	6.33927i	−0.296325	−	0.248647i
$651$		0			0
$652$	−0.658167	−	3.73265i	−0.0257758	−	0.146182i
$653$	41.9029	+	15.2514i	1.63979	+	0.596834i	0.987002	−	0.160709i	$-0.0513780\pi$
$653$	41.9029	+	15.2514i	1.63979	+	0.596834i	0.652786	+	0.757543i	$0.273600\pi$
$654$		0			0
$655$	−5.08182	+	28.8205i	−0.198563	+	1.12611i
$656$	8.81386	−	15.2661i	0.344124	−	0.596039i
$657$		0			0
$658$	6.06986	+	10.5133i	0.236628	+	0.409851i
$659$	−13.2464	+	4.82131i	−0.516008	+	0.187812i	−0.586880	−	0.809674i	$-0.699644\pi$
$659$	−13.2464	+	4.82131i	−0.516008	+	0.187812i	0.0708720	+	0.997485i	$0.477422\pi$
$660$		0			0
$661$	27.6655	−	23.2141i	1.07606	−	0.902924i	0.0804751	−	0.996757i	$-0.474356\pi$
$661$	27.6655	−	23.2141i	1.07606	−	0.902924i	0.995588	+	0.0938325i	$0.0299118\pi$
$662$	1.62205	−	1.36106i	0.0630426	−	0.0528990i
$663$		0			0
$664$	11.0239	−	4.01239i	0.427812	−	0.155711i
$665$	−13.2280	−	22.9116i	−0.512961	−	0.888474i
$666$		0			0
$667$	−1.89986	+	3.29066i	−0.0735630	+	0.127415i
$668$	0.137689	−	0.780873i	0.00532734	−	0.0302129i
$669$		0			0
$670$	−3.88578	−	1.41431i	−0.150121	−	0.0546395i
$671$	−11.4042	−	64.6764i	−0.440254	−	2.49681i
$672$		0			0
$673$	1.71760	+	1.44123i	0.0662085	+	0.0555555i	0.675291	−	0.737551i	$-0.264018\pi$
$673$	1.71760	+	1.44123i	0.0662085	+	0.0555555i	−0.609083	+	0.793107i	$0.708462\pi$
$674$	10.7992			0.415971
$675$		0			0
$676$	0.478340			0.0183977
$677$	−26.9466	−	22.6108i	−1.03564	−	0.869005i	−0.0441290	−	0.999026i	$-0.514051\pi$
$677$	−26.9466	−	22.6108i	−1.03564	−	0.869005i	−0.991511	+	0.130020i	$0.958496\pi$
$678$		0			0
$679$	0.109222	+	0.619429i	0.00419156	+	0.0237715i
$680$	−13.7144	−	4.99162i	−0.525922	−	0.191420i
$681$		0			0
$682$	−0.818363	+	4.64117i	−0.0313367	+	0.177719i
$683$	−8.88191	+	15.3839i	−0.339857	+	0.588649i	−0.984406	−	0.175914i	$-0.943712\pi$
$683$	−8.88191	+	15.3839i	−0.339857	+	0.588649i	0.644549	+	0.764563i	$0.277045\pi$
$684$		0			0
$685$	3.24675	+	5.62353i	0.124052	+	0.214864i
$686$	−24.9884	+	9.09505i	−0.954063	+	0.347251i
$687$		0			0
$688$	14.2836	−	11.9854i	0.544557	−	0.456937i
$689$	28.7670	−	24.1384i	1.09593	−	0.919598i
$690$		0			0
$691$	41.3753	−	15.0594i	1.57399	−	0.572885i	0.600103	−	0.799923i	$-0.295126\pi$
$691$	41.3753	−	15.0594i	1.57399	−	0.572885i	0.973886	+	0.227037i	$0.0729039\pi$
$692$	−0.350452	−	0.607000i	−0.0133222	−	0.0230747i
$693$		0			0
$694$	−13.3687	+	23.1553i	−0.507469	+	0.878962i
$695$	−3.43407	+	19.4756i	−0.130262	+	0.738750i
$696$		0			0
$697$	13.8182	+	5.02941i	0.523402	+	0.190503i
$698$	−2.59533	−	14.7189i	−0.0982348	−	0.557117i
$699$		0			0
$700$	0.774414	+	0.649811i	0.0292701	+	0.0245605i
$701$	30.1052			1.13706			0.568530	−	0.822663i	$-0.307512\pi$
$701$	30.1052			1.13706			0.568530	+	0.822663i	$0.307512\pi$
$702$		0			0
$703$	−0.278066			−0.0104875
$704$	−39.1391	−	32.8416i	−1.47511	−	1.23776i
$705$		0			0
$706$	−0.670026	−	3.79991i	−0.0252168	−	0.143011i
$707$	24.9884	+	9.09505i	0.939787	+	0.342055i
$708$		0			0
$709$	−4.29561	+	24.3616i	−0.161325	+	0.914919i	0.791448	+	0.611236i	$0.209327\pi$
$709$	−4.29561	+	24.3616i	−0.161325	+	0.914919i	−0.952773	+	0.303683i	$0.901784\pi$
$710$	−6.13728	+	10.6301i	−0.230328	+	0.398940i
$711$		0			0
$712$	11.9960	+	20.7776i	0.449568	+	0.778674i
$713$	1.62789	−	0.592503i	0.0609649	−	0.0221894i
$714$		0			0
$715$	−24.2802	+	20.3735i	−0.908027	+	0.761925i
$716$	1.17159	−	0.983080i	0.0437843	−	0.0367394i
$717$		0			0
$718$	−36.4479	+	13.2660i	−1.36022	+	0.495081i
$719$	−21.7763	−	37.7177i	−0.812119	−	1.40663i	−0.911378	−	0.411570i	$-0.864980\pi$
$719$	−21.7763	−	37.7177i	−0.812119	−	1.40663i	0.0992586	−	0.995062i	$-0.468353\pi$
$720$		0			0
$721$	4.71048	−	8.15880i	0.175428	−	0.303850i
$722$	−5.86412	+	33.2571i	−0.218240	+	1.23770i
$723$		0			0
$724$	1.16725	+	0.424845i	0.0433806	+	0.0157892i
$725$	−0.508512	−	2.88392i	−0.0188857	−	0.107106i
$726$		0			0
$727$	15.7324	+	13.2010i	0.583481	+	0.489599i	0.886088	−	0.463517i	$-0.153413\pi$
$727$	15.7324	+	13.2010i	0.583481	+	0.489599i	−0.302607	+	0.953115i	$0.597857\pi$
$728$	−22.9040			−0.848880
$729$		0			0
$730$	12.3678			0.457754
$731$	11.9153	+	9.99816i	0.440705	+	0.369795i
$732$		0			0
$733$	2.43211	+	13.7932i	0.0898322	+	0.509464i	0.996209	+	0.0869932i	$0.0277258\pi$
$733$	2.43211	+	13.7932i	0.0898322	+	0.509464i	−0.906377	+	0.422470i	$0.861163\pi$
$734$	−13.9167	−	5.06526i	−0.513674	−	0.186962i
$735$		0			0
$736$	−0.532556	+	3.02027i	−0.0196303	+	0.111329i
$737$	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	$0.552513\pi$
$740$	−0.0120217	+	0.00437554i	−0.000441926	+	0.000160848i
$741$		0			0
$742$	28.9657	−	24.3051i	1.06336	−	0.892268i
$743$	−21.3436	+	17.9094i	−0.783022	+	0.657034i	−0.944008	−	0.329923i	$-0.892977\pi$
$743$	−21.3436	+	17.9094i	−0.783022	+	0.657034i	0.160985	+	0.986957i	$0.448533\pi$
$744$		0			0
$745$	−31.8764	+	11.6021i	−1.16786	+	0.425067i
$746$	22.5064	+	38.9822i	0.824018	+	1.42724i
$747$		0			0
$748$	1.64749	−	2.85353i	0.0602382	−	0.104336i
$749$	1.10472	−	6.26519i	0.0403657	−	0.228925i
$750$		0			0
$751$	49.7144	+	18.0946i	1.81410	+	0.660280i	0.996413	+	0.0846236i	$0.0269688\pi$
$751$	49.7144	+	18.0946i	1.81410	+	0.660280i	0.817692	+	0.575656i	$0.195253\pi$
$752$	−2.33338	−	13.2332i	−0.0850895	−	0.482567i
$753$		0			0
$754$	4.29885	+	3.60716i	0.156555	+	0.131365i
$755$	−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	$0.771836\pi$
$758$	−21.6114	−	18.1341i	−0.784960	−	0.658660i
$759$		0			0
$760$	5.60772	+	31.8029i	0.203413	+	1.15361i
$761$	−42.6502	−	15.5234i	−1.54607	−	0.562723i	−0.578578	−	0.815627i	$-0.696392\pi$
$761$	−42.6502	−	15.5234i	−1.54607	−	0.562723i	−0.967492	+	0.252904i	$0.918614\pi$
$762$		0			0
$763$	−3.75119	+	21.2741i	−0.135802	+	0.770173i
$764$	0.463326	−	0.802503i	0.0167625	−	0.0290336i
$765$		0			0
$766$	2.76945	+	4.79682i	0.100064	+	0.173316i
$767$	22.2777	−	8.10840i	0.804400	−	0.292777i
$768$		0			0
$769$	3.91946	−	3.28882i	0.141339	−	0.118598i	−0.569377	−	0.822077i	$-0.692815\pi$
$769$	3.91946	−	3.28882i	0.141339	−	0.118598i	0.710716	+	0.703479i	$0.248371\pi$
$770$	−24.4479	+	20.5142i	−0.881041	+	0.739281i
$771$		0			0
$772$	−3.10220	+	1.12911i	−0.111650	+	0.0406375i
$773$	−26.3214	−	45.5899i	−0.946713	−	1.63976i	−0.752284	−	0.658839i	$-0.771048\pi$
$773$	−26.3214	−	45.5899i	−0.946713	−	1.63976i	−0.194430	−	0.980916i	$-0.562286\pi$
$774$		0			0
$775$	−0.667556	+	1.15624i	−0.0239793	+	0.0415334i
$776$	0.133322	−	0.756105i	0.00478597	−	0.0271426i
$777$		0			0
$778$	−21.6420	−	7.87705i	−0.775904	−	0.282406i
$779$	−5.65018	−	32.0437i	−0.202439	−	1.14809i
$780$		0			0
$781$	−25.0985	−	21.0602i	−0.898097	−	0.753592i
$782$	11.8976			0.425456
$783$		0			0
$784$	4.26083			0.152172
$785$	27.8195	+	23.3434i	0.992922	+	0.833161i
$786$		0			0
$787$	−3.60535	−	20.4470i	−0.128517	−	0.728856i	−0.979157	−	0.203107i	$-0.934896\pi$
$787$	−3.60535	−	20.4470i	−0.128517	−	0.728856i	0.850640	−	0.525749i	$-0.176215\pi$
$788$	−0.125667	−	0.0457391i	−0.00447671	−	0.00162939i
$789$		0			0
$790$	−1.46198	+	8.29131i	−0.0520150	+	0.294992i
$791$	19.2062	−	33.2661i	0.682894	−	1.18281i
$792$		0			0
$793$	17.8268	+	30.8770i	0.633049	+	1.09647i
$794$	28.3619	−	10.3229i	1.00653	−	0.366346i
$795$		0			0
$796$	1.44285	−	1.21069i	0.0511404	−	0.0429119i
$797$	34.9163	−	29.2982i	1.23680	−	1.03780i	0.239031	−	0.971012i	$-0.423170\pi$
$797$	34.9163	−	29.2982i	1.23680	−	1.03780i	0.997767	−	0.0667847i	$-0.0212741\pi$
$798$		0			0
$799$	10.5334	−	3.83386i	0.372646	−	0.135632i
$800$	−1.18180	−	2.04694i	−0.0417829	−	0.0723701i
$801$		0			0
$802$	9.82295	−	17.0138i	0.346860	−	0.600780i
$803$	−5.73261	+	32.5113i	−0.202299	+	1.14730i
$804$		0			0
$805$	11.0239	+	4.01239i	0.388543	+	0.141418i
$806$	−0.444278	−	2.51963i	−0.0156490	−	0.0887501i
$807$		0			0
$808$	−24.8656	−	20.8647i	−0.874767	−	0.734017i
$809$	4.21120			0.148058			0.0740290	−	0.997256i	$-0.476414\pi$
$809$	4.21120			0.148058			0.0740290	+	0.997256i	$0.476414\pi$
$810$		0			0
$811$	11.3618			0.398968			0.199484	−	0.979901i	$-0.436073\pi$
$811$	11.3618			0.398968			0.199484	+	0.979901i	$0.436073\pi$
$812$	−0.440656	−	0.369754i	−0.0154640	−	0.0129758i
$813$		0			0
$814$	0.0582480	+	0.330341i	0.00204159	+	0.0115784i
$815$	31.8539	+	11.5939i	1.11579	+	0.406115i
$816$		0			0
$817$	5.97653	−	33.8946i	0.209092	−	1.18582i
$818$	−11.7909	+	20.4224i	−0.412258	+	0.714051i
$819$		0			0
$820$	−0.748503	−	1.29645i	−0.0261389	−	0.0452739i
$821$	1.54323	−	0.561691i	0.0538592	−	0.0196031i	−0.314950	−	0.949108i	$-0.601988\pi$
$821$	1.54323	−	0.561691i	0.0538592	−	0.0196031i	0.368809	+	0.929505i	$0.379766\pi$
$822$		0			0
$823$	8.59421	−	7.21140i	0.299575	−	0.251373i	−0.480592	−	0.876944i	$-0.659578\pi$
$823$	8.59421	−	7.21140i	0.299575	−	0.251373i	0.780167	+	0.625571i	$0.215134\pi$
$824$	−8.80928	+	7.39186i	−0.306886	+	0.257508i
$825$		0			0
$826$	22.4315	−	8.16441i	0.780493	−	0.284076i
$827$	−4.80659	−	8.32526i	−0.167141	−	0.289498i	0.770272	−	0.637715i	$-0.220120\pi$
$827$	−4.80659	−	8.32526i	−0.167141	−	0.289498i	−0.937414	+	0.348218i	$0.886787\pi$
$828$		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	$0.969076\pi$
$830$	−1.54101	+	8.73951i	−0.0534893	+	0.303353i
$831$		0			0
$832$	26.0646	+	9.48675i	0.903629	+	0.328894i
$833$	0.617211	+	3.50038i	0.0213851	+	0.121281i
$834$		0			0
$835$	5.43242	+	4.55834i	0.187997	+	0.157748i
$836$	−7.29086			−0.252160
$837$		0			0
$838$	25.4129			0.877874
$839$	24.5089	+	20.5654i	0.846142	+	0.709997i	0.958936	−	0.283621i	$-0.0915357\pi$
$839$	24.5089	+	20.5654i	0.846142	+	0.709997i	−0.112794	+	0.993618i	$0.535980\pi$
$840$		0			0
$841$	−4.74644	−	26.9184i	−0.163670	−	0.928221i
$842$	−40.9359	−	14.8994i	−1.41074	−	0.513469i
$843$		0			0
$844$	0.476996	−	2.70518i	0.0164189	−	0.0931161i
$845$	−2.13903	+	3.70491i	−0.0735850	+	0.127453i
$846$		0			0
$847$	−29.3307	−	50.8022i	−1.00781	−	1.74559i
$848$	−39.3298	+	14.3149i	−1.35059	+	0.491575i
$849$		0			0
$850$	−7.02410	+	5.89392i	−0.240925	+	0.202160i
$851$	0.0944557	−	0.0792577i	0.00323790	−	0.00271692i
$852$		0			0
$853$	−33.1168	+	12.0535i	−1.13390	+	0.412705i	−0.839706	−	0.543041i	$-0.817273\pi$
$853$	−33.1168	+	12.0535i	−1.13390	+	0.412705i	−0.294192	+	0.955746i	$0.595050\pi$
$854$	17.9500	+	31.0902i	0.614235	+	1.06389i
$855$		0			0
$856$	−3.88279	+	6.72519i	−0.132711	+	0.229862i
$857$	3.68984	−	20.9262i	0.126043	−	0.714824i	−0.854640	−	0.519220i	$-0.826222\pi$
$857$	3.68984	−	20.9262i	0.126043	−	0.714824i	0.980683	−	0.195603i	$-0.0626665\pi$
$858$		0			0
$859$	−48.7122	−	17.7298i	−1.66204	−	0.604933i	−0.671357	−	0.741134i	$-0.734288\pi$
$859$	−48.7122	−	17.7298i	−1.66204	−	0.604933i	−0.990681	+	0.136201i	$0.956511\pi$
$860$	−0.274967	−	1.55942i	−0.00937631	−	0.0531757i
$861$		0			0
$862$	35.4176	+	29.7189i	1.20633	+	1.01223i
$863$	22.6783			0.771978			0.385989	−	0.922503i	$-0.373860\pi$
$863$	22.6783			0.771978			0.385989	+	0.922503i	$0.373860\pi$
$864$		0			0
$865$	6.26857			0.213138
$866$	25.8712	+	21.7085i	0.879140	+	0.737686i
$867$		0			0
$868$	0.0455410	+	0.258276i	0.00154576	+	0.00876646i
$869$	−21.1177	−	7.68621i	−0.716368	−	0.260737i
$870$		0			0
$871$	−1.04054	+	5.90122i	−0.0352575	+	0.199955i
$872$	13.1844	−	22.8360i	0.446480	−	0.773325i
$873$		0			0
$874$	−13.1630	−	22.7989i	−0.445244	−	0.771185i
$875$	−27.2215	+	9.90782i	−0.920255	+	0.334946i
$876$		0			0
$877$	0.868241	−	0.728541i	0.0293184	−	0.0246011i	−0.628011	−	0.778205i	$-0.716131\pi$
$877$	0.868241	−	0.728541i	0.0293184	−	0.0246011i	0.657329	+	0.753604i	$0.271686\pi$
$878$	23.9527	−	20.0987i	0.808366	−	0.678299i
$879$		0			0
$880$	33.1955	−	12.0822i	1.11902	−	0.407290i
$881$	−15.4145	−	26.6986i	−0.519327	−	0.899500i	−0.999748	−	0.0224621i	$-0.992849\pi$
$881$	−15.4145	−	26.6986i	−0.519327	−	0.899500i	0.480421	−	0.877038i	$-0.340484\pi$
$882$		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	$0.116460\pi$
$884$	−0.310622	+	1.76162i	−0.0104473	+	0.0592498i
$885$		0			0
$886$	5.21806	+	1.89922i	0.175304	+	0.0638055i
$887$	2.44743	+	13.8801i	0.0821768	+	0.466048i	0.997930	+	0.0643068i	$0.0204836\pi$
$887$	2.44743	+	13.8801i	0.0821768	+	0.466048i	−0.915753	+	0.401741i	$0.868405\pi$
$888$		0			0
$889$	6.64337	+	5.57445i	0.222811	+	0.186961i
$890$	−18.1489			−0.608352
$891$		0			0
$892$	2.02322			0.0677425
$893$	−19.0005	−	15.9433i	−0.635826	−	0.533522i
$894$		0			0
$895$	2.37521	+	13.4705i	0.0793945	+	0.450269i
$896$	21.5228	+	7.83364i	0.719025	+	0.261704i
$897$		0			0
$898$	4.29108	−	24.3359i	0.143195	−	0.812100i
$899$	0.379852	−	0.657923i	0.0126688	−	0.0219430i
$900$		0			0
$901$	−17.4572	−	30.2368i	−0.581585	−	1.00733i
$902$	−36.8842	+	13.4247i	−1.22811	+	0.446995i
$903$		0			0
$904$	−35.9183	+	30.1391i	−1.19463	+	1.00241i
$905$	−8.51027	+	7.14096i	−0.282891	+	0.237374i
$906$		0			0
$907$	8.21213	−	2.98897i	0.272679	−	0.0992472i	−0.202061	−	0.979373i	$-0.564764\pi$
$907$	8.21213	−	2.98897i	0.272679	−	0.0992472i	0.474741	+	0.880126i	$0.342542\pi$
$908$	1.60148	+	2.77385i	0.0531470	+	0.0920533i
$909$		0			0
$910$	8.66297	−	15.0047i	0.287175	−	0.497401i
$911$	3.58600	−	20.3372i	0.118809	−	0.673802i	−0.865984	−	0.500072i	$-0.833307\pi$
$911$	3.58600	−	20.3372i	0.118809	−	0.673802i	0.984793	−	0.173730i	$-0.0555820\pi$
$912$		0			0
$913$	−22.2592	−	8.10170i	−0.736673	−	0.268127i
$914$	4.55303	+	25.8215i	0.150601	+	0.854100i
$915$		0			0
$916$	−0.221132	−	0.185552i	−0.00730642	−	0.00613081i
$917$	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	$0.512394\pi$
$920$	−10.9697	−	9.20469i	−0.361661	−	0.303470i
$921$		0			0
$922$	6.49210	+	36.8185i	0.213806	+	1.21255i
$923$	16.7144	+	6.08353i	0.550160	+	0.200242i
$924$		0			0
$925$	−0.0165015	+	0.0935846i	−0.000542566	+	0.00307704i
$926$	26.0608	−	45.1386i	0.856410	−	1.48335i
$927$		0			0
$928$	0.672466	+	1.16475i	0.0220748	+	0.0382346i
$929$	−25.2028	+	9.17307i	−0.826877	+	0.300959i	−0.720577	−	0.693375i	$-0.756123\pi$
$929$	−25.2028	+	9.17307i	−0.826877	+	0.300959i	−0.106301	+	0.994334i	$0.533901\pi$
$930$		0			0
$931$	6.02481	−	5.05542i	0.197455	−	0.165685i
$932$	2.37661	−	1.99421i	0.0778485	−	0.0653226i
$933$		0			0
$934$	−37.6823	+	13.7152i	−1.23300	+	0.448776i
$935$	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	$0.176719\pi$
$938$	−1.04773	+	5.94199i	−0.0342097	+	0.194013i
$939$		0			0
$940$	−1.07233	−	0.390296i	−0.0349755	−	0.0127300i
$941$	−2.06821	−	11.7294i	−0.0674217	−	0.382368i	−0.999783	−	0.0208393i	$-0.993366\pi$
$941$	−2.06821	−	11.7294i	−0.0674217	−	0.382368i	0.932361	−	0.361528i	$-0.117745\pi$
$942$		0			0
$943$	11.0528	+	9.27439i	0.359928	+	0.302016i
$944$	−26.4228			−0.859990
$945$		0			0
$946$	−41.5185			−1.34988
$947$	0.241945	+	0.203016i	0.00786215	+	0.00659713i	0.646710	−	0.762736i	$-0.276144\pi$
$947$	0.241945	+	0.203016i	0.00786215	+	0.00659713i	−0.638848	+	0.769333i	$0.720589\pi$
$948$		0			0
$949$	−3.11216	−	17.6499i	−0.101025	−	0.572941i
$950$	19.0655	+	6.93928i	0.618567	+	0.225140i
$951$		0			0
$952$	−3.69783	+	20.9715i	−0.119847	+	0.679689i
$953$	1.62567	−	2.81574i	0.0526605	−	0.0912107i	−0.838494	−	0.544912i	$-0.816563\pi$
$953$	1.62567	−	2.81574i	0.0526605	−	0.0912107i	0.891154	+	0.453701i	$0.149897\pi$
$954$		0			0
$955$	4.14378	+	7.17724i	0.134090	+	0.232250i
$956$	0.699645	−	0.254650i	0.0226281	−	0.00823597i
$957$		0			0
$958$	−38.8849	+	32.6283i	−1.25631	+	1.05417i
$959$	7.25806	−	6.09023i	0.234375	−	0.196664i
$960$		0			0
$961$	28.8050	−	10.4842i	0.929193	−	0.338199i
$962$	−0.0910521	−	0.157707i	−0.00293564	−	0.00508467i
$963$		0			0
$964$	−0.309745	+	0.536493i	−0.00997620	+	0.0172793i
$965$	5.12701	−	29.0767i	0.165044	−	0.936013i
$966$		0			0
$967$	−10.3062	−	3.75114i	−0.331424	−	0.120629i	0.170948	−	0.985280i	$-0.445317\pi$
$967$	−10.3062	−	3.75114i	−0.331424	−	0.120629i	−0.502372	+	0.864651i	$0.667539\pi$
$968$	12.4341	+	70.5171i	0.399646	+	2.26651i
$969$		0			0
$970$	0.444907	+	0.373321i	0.0142851	+	0.0119866i
$971$	−23.3868			−0.750519			−0.375259	−	0.926920i	$-0.622446\pi$
$971$	−23.3868			−0.750519			−0.375259	+	0.926920i	$0.622446\pi$
$972$		0			0
$973$	28.8553			0.925060
$974$	0.788333	+	0.661490i	0.0252598	+	0.0211955i
$975$		0			0
$976$	−6.90033	−	39.1337i	−0.220874	−	1.25264i
$977$	−47.1502	−	17.1613i	−1.50847	−	0.549038i	−0.550232	−	0.835012i	$-0.685461\pi$
$977$	−47.1502	−	17.1613i	−1.50847	−	0.549038i	−0.958237	+	0.285974i	$0.907683\pi$
$978$		0			0
$979$	8.41219	−	47.7079i	0.268855	−	1.52475i
$980$	0.180922	−	0.313366i	0.00577935	−	0.0100101i
$981$		0			0
$982$	0.335437	+	0.580994i	0.0107042	+	0.0185402i
$983$	−13.8084	+	5.02585i	−0.440420	+	0.160300i	−0.552706	−	0.833376i	$-0.686405\pi$
$983$	−13.8084	+	5.02585i	−0.440420	+	0.160300i	0.112287	+	0.993676i	$0.464183\pi$
$984$		0			0
$985$	0.916222	−	0.768801i	0.0291933	−	0.0244961i
$986$	3.99684	−	3.35375i	0.127285	−	0.106805i
$987$		0			0
$988$	3.71941	−	1.35375i	0.118330	−	0.0430686i
$989$	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	$0.176780\pi$
$992$	0.106477	−	0.603863i	0.00338066	−	0.0191727i
$993$		0			0
$994$	16.8298	+	6.12555i	0.533809	+	0.194291i
$995$	2.92514	+	16.5893i	0.0927333	+	0.525917i
$996$		0			0
$997$	−35.1509	−	29.4951i	−1.11324	−	0.934121i	−0.114998	−	0.993366i	$-0.536686\pi$
$997$	−35.1509	−	29.4951i	−1.11324	−	0.934121i	−0.998243	+	0.0592450i	$0.981131\pi$
$998$	−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.h.406.1		6
3.2	odd	2		729.2.e.c.406.1		6
9.2	odd	6		729.2.e.i.649.1		6
9.4	even	3		729.2.e.g.163.1		6
9.5	odd	6		729.2.e.b.163.1		6
9.7	even	3		729.2.e.a.649.1		6
27.2	odd	18		243.2.c.e.82.2		6
27.4	even	9		729.2.e.a.82.1		6
27.5	odd	18		729.2.e.c.325.1		6
27.7	even	9		243.2.a.e.1.2	✓	3
27.11	odd	18		243.2.c.e.163.2		6
27.13	even	9		729.2.e.g.568.1		6
27.14	odd	18		729.2.e.b.568.1		6
27.16	even	9		243.2.c.f.163.2		6
27.20	odd	18		243.2.a.f.1.2	yes	3
27.22	even	9	inner	729.2.e.h.325.1		6
27.23	odd	18		729.2.e.i.82.1		6
27.25	even	9		243.2.c.f.82.2		6
108.7	odd	18		3888.2.a.bd.1.2		3
108.47	even	18		3888.2.a.bk.1.2		3
135.34	even	18		6075.2.a.bv.1.2		3
135.74	odd	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	27.7	even	9
243.2.a.f.1.2	yes	3	27.20	odd	18
243.2.c.e.82.2		6	27.2	odd	18
243.2.c.e.163.2		6	27.11	odd	18
243.2.c.f.82.2		6	27.25	even	9
243.2.c.f.163.2		6	27.16	even	9
729.2.e.a.82.1		6	27.4	even	9
729.2.e.a.649.1		6	9.7	even	3
729.2.e.b.163.1		6	9.5	odd	6
729.2.e.b.568.1		6	27.14	odd	18
729.2.e.c.325.1		6	27.5	odd	18
729.2.e.c.406.1		6	3.2	odd	2
729.2.e.g.163.1		6	9.4	even	3
729.2.e.g.568.1		6	27.13	even	9
729.2.e.h.325.1		6	27.22	even	9	inner
729.2.e.h.406.1		6	1.1	even	1	trivial
729.2.e.i.82.1		6	27.23	odd	18
729.2.e.i.649.1		6	9.2	odd	6
3888.2.a.bd.1.2		3	108.7	odd	18
3888.2.a.bk.1.2		3	108.47	even	18
6075.2.a.bq.1.2		3	135.74	odd	18
6075.2.a.bv.1.2		3	135.34	even	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)

\(f(q)\)	\(=\)	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.0320889 - 0.181985i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.418748 - 2.37484i) q^{7} +(-1.47178 + 2.54920i) q^{8} +O(q^{10})\)	\(q+(-1.03209 - 0.866025i) q^{2} +(-0.0320889 - 0.181985i) q^{4} +(1.55303 + 0.565258i) q^{5} +(0.418748 - 2.37484i) q^{7} +(-1.47178 + 2.54920i) q^{8} +(-1.11334 - 1.92836i) q^{10} +(5.58512 - 2.03282i) q^{11} +(-2.47178 + 2.07407i) q^{13} +(-2.48886 + 2.08840i) q^{14} +(3.37939 - 1.23000i) q^{16} +(1.50000 + 2.59808i) q^{17} +(3.31908 - 5.74881i) q^{19} +(0.0530334 - 0.300767i) q^{20} +(-7.52481 - 2.73881i) q^{22} +(0.511144 + 2.89884i) q^{23} +(-1.73783 - 1.45821i) q^{25} +4.34730 q^{26} -0.445622 q^{28} +(0.988856 + 0.829748i) q^{29} +(-0.102196 - 0.579585i) q^{31} +(0.979055 + 0.356347i) q^{32} +(0.701867 - 3.98048i) q^{34} +(1.99273 - 3.45150i) q^{35} +(-0.0209445 - 0.0362770i) q^{37} +(-8.40420 + 3.05888i) q^{38} +(-3.72668 + 3.12706i) q^{40} +(3.75490 - 3.15074i) q^{41} +(4.87211 - 1.77330i) q^{43} +(-0.549163 - 0.951178i) q^{44} +(1.98293 - 3.43453i) q^{46} +(0.648833 - 3.67972i) q^{47} +(1.11334 + 0.405223i) q^{49} +(0.530745 + 3.01000i) q^{50} +(0.456767 + 0.383273i) q^{52} -11.6382 q^{53} +9.82295 q^{55} +(5.43763 + 4.56272i) q^{56} +(-0.302004 - 1.71275i) q^{58} +(-6.90420 - 2.51292i) q^{59} +(1.91875 - 10.8818i) q^{61} +(-0.396459 + 0.686688i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(-5.01114 + 1.82391i) q^{65} +(1.42262 - 1.19372i) q^{67} +(0.424678 - 0.356347i) q^{68} +(-5.04576 + 1.83651i) q^{70} +(-2.75624 - 4.77396i) q^{71} +(-2.77719 + 4.81023i) q^{73} +(-0.00980018 + 0.0555796i) q^{74} +(-1.15270 - 0.419550i) q^{76} +(-2.48886 - 14.1150i) q^{77} +(-2.89646 - 2.43042i) q^{79} +5.94356 q^{80} -6.60401 q^{82} +(-3.05303 - 2.56180i) q^{83} +(0.860967 + 4.88279i) q^{85} +(-6.56418 - 2.38917i) q^{86} +(-3.03802 + 17.2295i) q^{88} +(4.07532 - 7.05866i) q^{89} +(3.89053 + 6.73859i) q^{91} +(0.511144 - 0.186041i) q^{92} +(-3.85638 + 3.23589i) q^{94} +(8.40420 - 7.05196i) q^{95} +(-0.245100 + 0.0892091i) q^{97} +(-0.798133 - 1.38241i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8	\( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{8} + 12 q^{11} - 21 q^{14} + 9 q^{16} + 9 q^{17} + 3 q^{19} - 12 q^{20} - 18 q^{22} - 3 q^{23} + 9 q^{25} + 24 q^{26} - 24 q^{28} + 12 q^{29} + 9 q^{32} + 18 q^{34} - 6 q^{35} + 3 q^{37} - 12 q^{38} - 9 q^{40} + 24 q^{41} - 15 q^{44} - 9 q^{46} + 30 q^{47} + 3 q^{50} + 18 q^{52} - 36 q^{53} + 18 q^{55} - 24 q^{56} + 36 q^{58} - 3 q^{59} + 9 q^{61} - 12 q^{62} - 12 q^{64} - 24 q^{65} - 18 q^{67} + 27 q^{68} - 9 q^{71} - 6 q^{73} - 3 q^{74} - 9 q^{76} - 21 q^{77} - 27 q^{79} + 6 q^{80} + 36 q^{82} - 6 q^{83} - 18 q^{85} - 21 q^{86} - 36 q^{88} + 6 q^{91} - 3 q^{92} + 36 q^{94} + 12 q^{95} + 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 9 * q^4 - 3 * q^5 + 6 * q^8 + 12 * q^11 - 21 * q^14 + 9 * q^16 + 9 * q^17 + 3 * q^19 - 12 * q^20 - 18 * q^22 - 3 * q^23 + 9 * q^25 + 24 * q^26 - 24 * q^28 + 12 * q^29 + 9 * q^32 + 18 * q^34 - 6 * q^35 + 3 * q^37 - 12 * q^38 - 9 * q^40 + 24 * q^41 - 15 * q^44 - 9 * q^46 + 30 * q^47 + 3 * q^50 + 18 * q^52 - 36 * q^53 + 18 * q^55 - 24 * q^56 + 36 * q^58 - 3 * q^59 + 9 * q^61 - 12 * q^62 - 12 * q^64 - 24 * q^65 - 18 * q^67 + 27 * q^68 - 9 * q^71 - 6 * q^73 - 3 * q^74 - 9 * q^76 - 21 * q^77 - 27 * q^79 + 6 * q^80 + 36 * q^82 - 6 * q^83 - 18 * q^85 - 21 * q^86 - 36 * q^88 + 6 * q^91 - 3 * q^92 + 36 * q^94 + 12 * q^95 + 9 * q^98

Introduction

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