LMFDB - Embedded newform 729.2.e.h.325.1

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			325.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	729.325
Dual form			729.2.e.h.406.1

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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	−0.930076	−	0.367366i	$-0.880260\pi$
$2$	−1.03209	+	0.866025i	−0.729797	+	0.612372i	0.200279	+	0.979739i	$0.435815\pi$
$3$		0			0
$3$		0			0
$4$	−0.0320889	+	0.181985i	−0.0160444	+	0.0909926i
$5$	1.55303	−	0.565258i	0.694538	−	0.252791i	0.0294608	−	0.999566i	$-0.490621\pi$
$5$	1.55303	−	0.565258i	0.694538	−	0.252791i	0.665077	+	0.746775i	$0.268399\pi$
$6$		0			0
$7$	0.418748	+	2.37484i	0.158272	+	0.897605i	0.955733	+	0.294235i	$0.0950647\pi$
$7$	0.418748	+	2.37484i	0.158272	+	0.897605i	−0.797461	+	0.603370i	$0.793824\pi$
$8$	−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	0.993846	−	0.110766i	$-0.0353306\pi$
$11$	5.58512	+	2.03282i	1.68398	+	0.612918i	0.690131	+	0.723684i	$0.257553\pi$
$12$		0			0
$13$	−2.47178	−	2.07407i	−0.685549	−	0.575244i	0.232073	−	0.972698i	$-0.425449\pi$
$13$	−2.47178	−	2.07407i	−0.685549	−	0.575244i	−0.917622	+	0.397455i	$0.869894\pi$
$14$	−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	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		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	$0.557822\pi$
$20$	0.0530334	+	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	−0.883996	−	0.467494i	$-0.845157\pi$
$23$	0.511144	−	2.89884i	0.106581	−	0.604451i	0.990577	−	0.136956i	$-0.0437320\pi$
$24$		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	−0.546341	−	0.837563i	$-0.683980\pi$
$29$	0.988856	−	0.829748i	0.183626	−	0.154080i	0.729967	+	0.683482i	$0.239535\pi$
$30$		0			0
$31$	−0.102196	+	0.579585i	−0.0183550	+	0.104097i	−0.992609	−	0.121357i	$-0.961275\pi$
$31$	−0.102196	+	0.579585i	−0.0183550	+	0.104097i	0.974254	+	0.225454i	$0.0723865\pi$
$32$	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	−0.867742	−	0.497015i	$-0.834429\pi$
$37$	−0.0209445	+	0.0362770i	−0.00344326	+	0.00596390i	0.864299	+	0.502979i	$0.167763\pi$
$38$	−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	0.887047	−	0.461679i	$-0.152753\pi$
$41$	3.75490	+	3.15074i	0.586417	+	0.492062i	−0.300630	+	0.953741i	$0.597197\pi$
$42$		0			0
$43$	4.87211	+	1.77330i	0.742990	+	0.270426i	0.685653	−	0.727929i	$-0.259517\pi$
$43$	4.87211	+	1.77330i	0.742990	+	0.270426i	0.0573371	+	0.998355i	$0.481739\pi$
$44$	−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	0.994856	+	0.101295i	$0.0322985\pi$
$47$	0.648833	+	3.67972i	0.0946421	+	0.536742i	−0.900214	+	0.435447i	$0.856590\pi$
$48$		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	−0.749792	−	0.661674i	$-0.769846\pi$
$59$	−6.90420	+	2.51292i	−0.898850	+	0.327155i	−0.149058	+	0.988828i	$0.547624\pi$
$60$		0			0
$61$	1.91875	+	10.8818i	0.245671	+	1.39327i	0.818930	+	0.573893i	$0.194567\pi$
$61$	1.91875	+	10.8818i	0.245671	+	1.39327i	−0.573260	+	0.819374i	$0.694321\pi$
$62$	−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	0.725539	−	0.688182i	$-0.241591\pi$
$67$	1.42262	+	1.19372i	0.173801	+	0.145836i	−0.551738	+	0.834017i	$0.686035\pi$
$68$	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	−0.981936	−	0.189212i	$-0.939407\pi$
$71$	−2.75624	+	4.77396i	−0.327106	+	0.566564i	0.654830	+	0.755776i	$0.272740\pi$
$72$		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	$0.938713\pi$
$74$	−0.00980018	−	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	−0.791017	−	0.611794i	$-0.790448\pi$
$79$	−2.89646	+	2.43042i	−0.325877	+	0.273443i	0.465140	+	0.885237i	$0.346004\pi$
$80$	5.94356			0.664511
$81$		0			0
$82$	−6.60401			−0.729291
$83$	−3.05303	+	2.56180i	−0.335114	+	0.281194i	−0.794780	−	0.606898i	$-0.792414\pi$
$83$	−3.05303	+	2.56180i	−0.335114	+	0.281194i	0.459666	+	0.888092i	$0.347969\pi$
$84$		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	0.997044	−	0.0768323i	$-0.0244806\pi$
$89$	4.07532	+	7.05866i	0.431983	+	0.748217i	−0.565061	+	0.825049i	$0.691147\pi$
$90$		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	0.329547	−	0.944139i	$-0.393104\pi$
$97$	−0.245100	−	0.0892091i	−0.0248861	−	0.00905781i	−0.354433	+	0.935081i	$0.615326\pi$
$98$	−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	−0.918632	−	0.395115i	$-0.870705\pi$
$101$	−1.91488	−	10.8598i	−0.190537	−	1.08059i	0.728094	−	0.685477i	$-0.240406\pi$
$102$		0			0
$103$	3.67112	−	1.33618i	0.361726	−	0.131658i	−0.154762	−	0.987952i	$-0.549461\pi$
$103$	3.67112	−	1.33618i	0.361726	−	0.131658i	0.516489	+	0.856294i	$0.327239\pi$
$104$	−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	0.477533	−	0.878614i	$-0.341531\pi$
$113$	14.9684	−	5.44804i	1.40811	−	0.512509i	0.930574	+	0.366105i	$0.119309\pi$
$114$		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	0.775151	−	0.631776i	$-0.217674\pi$
$127$	−1.79813	−	3.11446i	−0.159559	−	0.276363i	−0.934710	+	0.355412i	$0.884340\pi$
$128$	−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	−0.489781	−	0.871846i	$-0.662923\pi$
$131$	3.07486	−	17.4384i	0.268651	−	1.52360i	0.758432	−	0.651752i	$-0.225966\pi$
$132$		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	−0.505097	−	0.863063i	$-0.668543\pi$
$137$	3.00980	−	2.52552i	0.257145	−	0.215770i	0.762242	+	0.647293i	$0.224099\pi$
$138$		0			0
$139$	2.07785	−	11.7841i	0.176241	−	0.999511i	−0.760461	−	0.649383i	$-0.775027\pi$
$139$	2.07785	−	11.7841i	0.176241	−	0.999511i	0.936702	−	0.350128i	$-0.113862\pi$
$140$	−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	−0.992073	−	0.125666i	$-0.959893\pi$
$149$	−15.7233	−	13.1934i	−1.28810	−	1.08085i	−0.296029	−	0.955179i	$-0.595662\pi$
$150$		0			0
$151$	−15.0424	−	5.47497i	−1.22413	−	0.445547i	−0.352546	−	0.935794i	$-0.614684\pi$
$151$	−15.0424	−	5.47497i	−1.22413	−	0.445547i	−0.871583	+	0.490248i	$0.836906\pi$
$152$	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	0.659526	−	0.751682i	$-0.270757\pi$
$157$	20.6484	−	7.51541i	1.64792	−	0.599795i	0.988398	+	0.151887i	$0.0485350\pi$
$158$	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	−0.181268	−	0.983434i	$-0.558020\pi$
$167$	4.03209	−	1.46756i	0.312012	−	0.113563i	0.493280	+	0.869871i	$0.335798\pi$
$168$		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	0.473936	−	0.880559i	$-0.342833\pi$
$173$	3.56418	+	1.29725i	0.270979	+	0.0986284i	−0.202957	+	0.979188i	$0.565055\pi$
$174$		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	−0.668909	−	0.743344i	$-0.733239\pi$
$179$	4.13816	−	7.16750i	0.309300	−	0.535724i	0.978209	+	0.207620i	$0.0665718\pi$
$180$		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	$0.913704\pi$
$182$	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	−0.493145	−	0.869947i	$-0.664153\pi$
$191$	3.84137	−	3.22329i	0.277952	−	0.233229i	0.771097	+	0.636718i	$0.219708\pi$
$192$		0			0
$193$	−3.10220	+	17.5934i	−0.223301	+	1.26640i	0.642606	+	0.766197i	$0.277853\pi$
$193$	−3.10220	+	17.5934i	−0.223301	+	1.26640i	−0.865907	+	0.500206i	$0.833258\pi$
$194$	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	0.878628	−	0.477507i	$-0.158460\pi$
$197$	0.361844	+	0.626733i	0.0257803	+	0.0446529i	−0.852847	+	0.522160i	$0.825126\pi$
$198$		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	$0.0490117\pi$
$200$	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	0.186954	−	0.982369i	$-0.440139\pi$
$211$	13.9684	−	5.08407i	0.961623	−	0.350002i	0.774669	+	0.632367i	$0.217916\pi$
$212$	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	−0.979906	−	0.199458i	$-0.936082\pi$
$223$	−1.90121	−	10.7823i	−0.127314	−	0.722035i	0.852592	−	0.522577i	$-0.175029\pi$
$224$	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	−0.260743	−	0.965408i	$-0.583968\pi$
$227$	−16.2875	−	5.92815i	−1.08104	−	0.393465i	−0.820293	+	0.571943i	$0.806190\pi$
$228$		0			0
$229$	1.19665	+	1.00411i	0.0790770	+	0.0663535i	0.681469	−	0.731847i	$-0.261341\pi$
$229$	1.19665	+	1.00411i	0.0790770	+	0.0663535i	−0.602392	+	0.798200i	$0.705786\pi$
$230$	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	−0.448343	−	0.893862i	$-0.647986\pi$
$233$	8.39440	−	14.5395i	0.549935	−	0.952516i	0.998278	−	0.0586545i	$-0.0186810\pi$
$234$		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	−0.953782	−	0.300498i	$-0.902847\pi$
$239$	0.699645	−	3.96788i	0.0452563	−	0.256661i	0.999039	+	0.0438370i	$0.0139582\pi$
$240$		0			0
$241$	−2.56805	+	2.15485i	−0.165423	+	0.138806i	−0.721741	−	0.692163i	$-0.756658\pi$
$241$	−2.56805	+	2.15485i	−0.165423	+	0.138806i	0.556319	+	0.830969i	$0.312213\pi$
$242$	−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	−0.956615	−	0.291354i	$-0.905894\pi$
$251$	−11.5753	−	20.0490i	−0.730628	−	1.26548i	0.225987	−	0.974130i	$-0.427439\pi$
$252$		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	0.308953	−	0.951077i	$-0.400021\pi$
$257$	−9.20233	−	7.72167i	−0.574026	−	0.481665i	−0.882979	+	0.469412i	$0.844466\pi$
$258$		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	−0.931017	−	0.364976i	$-0.881077\pi$
$263$	−2.93494	−	16.6449i	−0.180976	−	1.02637i	0.750040	−	0.661392i	$-0.230034\pi$
$264$		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	0.736388	+	0.676560i	$0.236530\pi$
$277$	4.59034	+	26.0331i	0.275807	+	1.56418i	−0.460581	+	0.887618i	$0.652359\pi$
$278$	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	−0.250607	−	0.968089i	$-0.580630\pi$
$281$	−17.8503	−	6.49697i	−1.06486	−	0.387577i	−0.814252	+	0.580512i	$0.802852\pi$
$282$		0			0
$283$	−12.7062	−	10.6618i	−0.755305	−	0.633777i	0.181595	−	0.983373i	$-0.441874\pi$
$283$	−12.7062	−	10.6618i	−0.755305	−	0.633777i	−0.936900	+	0.349597i	$0.886319\pi$
$284$	−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	0.714067	+	0.700077i	$0.246851\pi$
$293$	−3.36143	+	19.0636i	−0.196377	+	1.11371i	−0.910444	+	0.413632i	$0.864260\pi$
$294$		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	0.400003	+	0.916514i	$0.369009\pi$
$307$	−10.4029	+	18.0183i	−0.593722	+	1.02836i	−0.993726	+	0.111844i	$0.964324\pi$
$308$	−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	0.844341	−	0.535807i	$-0.179992\pi$
$311$	8.17024	+	6.85565i	0.463292	+	0.388748i	−0.381049	+	0.924555i	$0.624437\pi$
$312$		0			0
$313$	−3.58512	−	1.30488i	−0.202643	−	0.0737561i	0.238705	−	0.971092i	$-0.423277\pi$
$313$	−3.58512	−	1.30488i	−0.202643	−	0.0737561i	−0.441348	+	0.897336i	$0.645499\pi$
$314$	−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	−0.789902	−	0.613234i	$-0.789868\pi$
$317$	−4.58243	−	25.9883i	−0.257375	−	1.45965i	0.532526	−	0.846413i	$-0.321243\pi$
$318$		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	0.976389	−	0.216022i	$-0.0693082\pi$
$331$	−0.272908	−	1.54774i	−0.0150004	−	0.0850713i	−0.991389	+	0.130950i	$0.958197\pi$
$332$	−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	0.460043	−	0.887897i	$-0.347834\pi$
$337$	−6.14022	−	5.15225i	−0.334479	−	0.280661i	−0.794522	+	0.607236i	$0.792278\pi$
$338$	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	0.740965	+	0.671544i	$0.234368\pi$
$347$	−3.44609	+	19.5437i	−0.184996	+	1.04916i	−0.925961	+	0.377620i	$0.876743\pi$
$348$		0			0
$349$	8.49794	−	7.13062i	0.454884	−	0.381693i	−0.386360	−	0.922348i	$-0.626268\pi$
$349$	8.49794	−	7.13062i	0.454884	−	0.381693i	0.841245	+	0.540655i	$0.181823\pi$
$350$	7.37052			0.393971
$351$		0			0
$352$	6.19253			0.330063
$353$	2.19388	−	1.84088i	0.116768	−	0.0979803i	−0.582534	−	0.812806i	$-0.697939\pi$
$353$	2.19388	−	1.84088i	0.116768	−	0.0979803i	0.699302	+	0.714826i	$0.253494\pi$
$354$		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	0.943000	+	0.332793i	$0.107991\pi$
$359$	14.3944	+	24.9318i	0.759707	+	1.31585i	−0.183292	+	0.983058i	$0.558676\pi$
$360$		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	0.597236	−	0.802066i	$-0.296266\pi$
$367$	10.3293	+	3.75957i	0.539187	+	0.196248i	−0.0580485	+	0.998314i	$0.518488\pi$
$368$	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	−0.984431	−	0.175772i	$-0.943758\pi$
$373$	−31.3949	+	11.4268i	−1.62556	+	0.591657i	−0.641134	+	0.767429i	$0.721536\pi$
$374$	−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	−0.438828	−	0.898571i	$-0.644606\pi$
$383$	−3.86319	+	1.40609i	−0.197400	+	0.0718476i	0.241428	+	0.970419i	$0.422384\pi$
$384$		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	0.715457	−	0.698656i	$-0.246218\pi$
$389$	16.0633	+	5.84656i	0.814442	+	0.296433i	0.0989844	+	0.995089i	$0.468441\pi$
$390$		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	−0.997308	−	0.0733324i	$-0.976637\pi$
$397$	−11.2010	−	19.4007i	−0.562162	−	0.973692i	0.435146	−	0.900360i	$-0.356697\pi$
$398$	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	−0.853992	−	0.520287i	$-0.825825\pi$
$401$	2.53209	−	14.3602i	0.126446	−	0.717114i	0.980438	−	0.196827i	$-0.0630638\pi$
$402$		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	0.812682	+	0.582707i	$0.198007\pi$
$409$	−3.03936	+	17.2371i	−0.150287	+	0.852319i	−0.962969	+	0.269612i	$0.913105\pi$
$410$	−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	0.217551	−	0.976049i	$-0.430193\pi$
$419$	−14.4492	−	12.1244i	−0.705892	−	0.592314i	−0.923443	+	0.383735i	$0.874637\pi$
$420$		0			0
$421$	30.3837	+	11.0588i	1.48081	+	0.538971i	0.951013	−	0.309152i	$-0.100045\pi$
$421$	30.3837	+	11.0588i	1.48081	+	0.538971i	0.529799	+	0.848123i	$0.322267\pi$
$422$	−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	−0.916152	−	0.400830i	$-0.868722\pi$
$439$	−4.03003	−	22.8554i	−0.192343	−	1.09083i	0.723809	−	0.690000i	$-0.242389\pi$
$440$	−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	0.248371	−	0.968665i	$-0.420105\pi$
$443$	−3.87299	−	1.40965i	−0.184011	−	0.0669746i	−0.432382	+	0.901690i	$0.642327\pi$
$444$		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	−0.564320	−	0.825556i	$-0.690862\pi$
$449$	9.17071	−	15.8841i	0.432793	−	0.749619i	0.997113	+	0.0759373i	$0.0241949\pi$
$450$		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	−0.921024	−	0.389506i	$-0.872646\pi$
$457$	−14.9081	+	12.5094i	−0.697370	+	0.585163i	0.223654	+	0.974669i	$0.428201\pi$
$458$	−2.10464			−0.0983432
$459$		0			0
$460$	0.898986			0.0419154
$461$	−21.2572	+	17.8369i	−0.990045	+	0.830747i	−0.985574	−	0.169243i	$-0.945868\pi$
$461$	−21.2572	+	17.8369i	−0.990045	+	0.830747i	−0.00447116	+	0.999990i	$0.501423\pi$
$462$		0			0
$463$	6.71776	−	38.0983i	0.312201	−	1.77058i	−0.275304	−	0.961357i	$-0.588778\pi$
$463$	6.71776	−	38.0983i	0.312201	−	1.77058i	0.587504	−	0.809221i	$-0.300110\pi$
$464$	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	0.972274	+	0.233845i	$0.0751309\pi$
$467$	14.8819	+	25.7762i	0.688653	+	1.19278i	−0.283621	+	0.958936i	$0.591536\pi$
$468$		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	0.650794	+	0.759254i	$0.274436\pi$
$479$	6.54236	+	37.1035i	0.298928	+	1.69530i	−0.351867	+	0.936050i	$0.614453\pi$
$480$		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	−0.352557	−	0.935790i	$-0.614688\pi$
$491$	−0.467911	+	0.170306i	−0.0211165	+	0.00768579i	0.331440	+	0.943476i	$0.392465\pi$
$492$		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	0.783443	−	0.621463i	$-0.213462\pi$
$499$	6.86824	+	5.76314i	0.307465	+	0.257994i	−0.475979	+	0.879457i	$0.657906\pi$
$500$	−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	−0.585461	−	0.810701i	$-0.699086\pi$
$503$	9.18092	−	15.9018i	0.409357	−	0.709027i	0.994818	+	0.101673i	$0.0324197\pi$
$504$		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	−0.656612	−	0.754228i	$-0.728011\pi$
$509$	4.92649	−	27.9395i	0.218363	−	1.23840i	0.874975	−	0.484168i	$-0.160878\pi$
$510$		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	−0.962978	−	0.269580i	$-0.913115\pi$
$521$	−16.3191	−	28.2655i	−0.714952	−	1.23833i	0.248026	−	0.968753i	$-0.420218\pi$
$522$		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	$0.00675730\pi$
$524$	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	−0.899661	−	0.436589i	$-0.856187\pi$
$547$	−4.76130	−	27.0027i	−0.203578	−	1.15455i	0.696083	−	0.717961i	$-0.254925\pi$
$548$	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	−0.366042	−	0.930598i	$-0.619287\pi$
$557$	14.7010	−	25.4629i	0.622901	−	1.07890i	0.988943	−	0.148298i	$-0.0473794\pi$
$558$		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	−0.923057	−	0.384664i	$-0.874317\pi$
$563$	1.80082	−	10.2130i	0.0758956	−	0.430425i	0.998952	−	0.0457616i	$-0.0145715\pi$
$564$		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	0.0647903	−	0.997899i	$-0.479362\pi$
$569$	25.2558	−	21.1922i	1.05878	−	0.888422i	0.993989	+	0.109477i	$0.0349177\pi$
$570$		0			0
$571$	−0.128051	+	0.726212i	−0.00535876	+	0.0303910i	−0.987370	−	0.158432i	$-0.949356\pi$
$571$	−0.128051	+	0.726212i	−0.00535876	+	0.0303910i	0.982011	+	0.188823i	$0.0604673\pi$
$572$	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	−0.994043	−	0.108990i	$-0.965238\pi$
$577$	−9.67159	+	16.7517i	−0.402634	+	0.697382i	0.591409	+	0.806371i	$0.298572\pi$
$578$	−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	0.855442	+	0.517899i	$0.173286\pi$
$587$	5.54148	+	31.4273i	0.228721	+	1.29714i	−0.626721	+	0.779244i	$0.715603\pi$
$588$		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	−0.572791	−	0.819701i	$-0.694139\pi$
$599$	−11.8623	+	4.31753i	−0.484681	+	0.176409i	0.0881103	+	0.996111i	$0.471917\pi$
$600$		0			0
$601$	−1.54694	−	8.77314i	−0.0631011	−	0.357864i	−0.999967	−	0.00817407i	$-0.997398\pi$
$601$	−1.54694	−	8.77314i	−0.0631011	−	0.357864i	0.936866	−	0.349690i	$-0.113713\pi$
$602$	−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	−0.0390828	−	0.999236i	$-0.512444\pi$
$607$	−25.3746	−	21.2918i	−1.02992	−	0.864209i	−0.990842	+	0.135026i	$0.956888\pi$
$608$	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	0.630421	−	0.776254i	$-0.282882\pi$
$613$	−8.84002	−	15.3114i	−0.357045	−	0.618420i	−0.987466	+	0.157833i	$0.949549\pi$
$614$	−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	−0.752457	−	0.658642i	$-0.771131\pi$
$617$	4.46838	−	25.3414i	0.179890	−	1.02021i	0.932347	−	0.361566i	$-0.117758\pi$
$618$		0			0
$619$	21.2920	−	17.8661i	0.855799	−	0.718101i	−0.105259	−	0.994445i	$-0.533567\pi$
$619$	21.2920	−	17.8661i	0.855799	−	0.718101i	0.961059	+	0.276344i	$0.0891229\pi$
$620$	−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	0.465504	+	0.885046i	$0.345873\pi$
$631$	−13.4069	+	23.2214i	−0.533720	+	0.924430i	−0.999224	+	0.0393842i	$0.987460\pi$
$632$	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	−0.996898	−	0.0787081i	$-0.974921\pi$
$641$	−2.20368	−	12.4977i	−0.0870400	−	0.493629i	0.909858	−	0.414920i	$-0.136191\pi$
$642$		0			0
$643$	−14.5432	+	5.29330i	−0.573529	+	0.208748i	−0.612470	−	0.790494i	$-0.709824\pi$
$643$	−14.5432	+	5.29330i	−0.573529	+	0.208748i	0.0389407	+	0.999242i	$0.487602\pi$
$644$	−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	0.652786	−	0.757543i	$-0.273600\pi$
$653$	41.9029	−	15.2514i	1.63979	−	0.596834i	0.987002	+	0.160709i	$0.0513780\pi$
$654$		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	0.0708720	−	0.997485i	$-0.477422\pi$
$659$	−13.2464	−	4.82131i	−0.516008	−	0.187812i	−0.586880	+	0.809674i	$0.699644\pi$
$660$		0			0
$661$	27.6655	+	23.2141i	1.07606	+	0.902924i	0.995588	−	0.0938325i	$-0.0299118\pi$
$661$	27.6655	+	23.2141i	1.07606	+	0.902924i	0.0804751	+	0.996757i	$0.474356\pi$
$662$	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	−0.609083	−	0.793107i	$-0.708462\pi$
$673$	1.71760	−	1.44123i	0.0662085	−	0.0555555i	0.675291	+	0.737551i	$0.264018\pi$
$674$	10.7992			0.415971
$675$		0			0
$676$	0.478340			0.0183977
$677$	−26.9466	+	22.6108i	−1.03564	+	0.869005i	−0.991511	−	0.130020i	$-0.958496\pi$
$677$	−26.9466	+	22.6108i	−1.03564	+	0.869005i	−0.0441290	+	0.999026i	$0.514051\pi$
$678$		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	0.644549	−	0.764563i	$-0.277045\pi$
$683$	−8.88191	−	15.3839i	−0.339857	−	0.588649i	−0.984406	+	0.175914i	$0.943712\pi$
$684$		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	0.973886	−	0.227037i	$-0.0729039\pi$
$691$	41.3753	+	15.0594i	1.57399	+	0.572885i	0.600103	+	0.799923i	$0.295126\pi$
$692$	−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	−0.952773	−	0.303683i	$-0.901784\pi$
$709$	−4.29561	−	24.3616i	−0.161325	−	0.914919i	0.791448	−	0.611236i	$-0.209327\pi$
$710$	−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	0.0992586	+	0.995062i	$0.468353\pi$
$719$	−21.7763	+	37.7177i	−0.812119	+	1.40663i	−0.911378	+	0.411570i	$0.864980\pi$
$720$		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	−0.302607	−	0.953115i	$-0.597857\pi$
$727$	15.7324	−	13.2010i	0.583481	−	0.489599i	0.886088	+	0.463517i	$0.153413\pi$
$728$	−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	−0.906377	−	0.422470i	$-0.861163\pi$
$733$	2.43211	−	13.7932i	0.0898322	−	0.509464i	0.996209	−	0.0869932i	$-0.0277258\pi$
$734$	−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	−0.164226	−	0.986423i	$-0.552513\pi$
$739$	20.9907	−	36.3569i	0.772154	−	1.33741i	0.936380	−	0.350987i	$-0.114154\pi$
$740$	−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	0.160985	−	0.986957i	$-0.448533\pi$
$743$	−21.3436	−	17.9094i	−0.783022	−	0.657034i	−0.944008	+	0.329923i	$0.892977\pi$
$744$		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	0.817692	−	0.575656i	$-0.195253\pi$
$751$	49.7144	−	18.0946i	1.81410	−	0.660280i	0.996413	−	0.0846236i	$-0.0269688\pi$
$752$	−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	−0.967492	−	0.252904i	$-0.918614\pi$
$761$	−42.6502	+	15.5234i	−1.54607	+	0.562723i	−0.578578	+	0.815627i	$0.696392\pi$
$762$		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	0.710716	−	0.703479i	$-0.248371\pi$
$769$	3.91946	+	3.28882i	0.141339	+	0.118598i	−0.569377	+	0.822077i	$0.692815\pi$
$770$	−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	−0.194430	+	0.980916i	$0.562286\pi$
$773$	−26.3214	+	45.5899i	−0.946713	+	1.63976i	−0.752284	+	0.658839i	$0.771048\pi$
$774$		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	0.850640	+	0.525749i	$0.176215\pi$
$787$	−3.60535	+	20.4470i	−0.128517	+	0.728856i	−0.979157	+	0.203107i	$0.934896\pi$
$788$	−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	0.997767	+	0.0667847i	$0.0212741\pi$
$797$	34.9163	+	29.2982i	1.23680	+	1.03780i	0.239031	+	0.971012i	$0.423170\pi$
$798$		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	0.368809	−	0.929505i	$-0.379766\pi$
$821$	1.54323	+	0.561691i	0.0538592	+	0.0196031i	−0.314950	+	0.949108i	$0.601988\pi$
$822$		0			0
$823$	8.59421	+	7.21140i	0.299575	+	0.251373i	0.780167	−	0.625571i	$-0.215134\pi$
$823$	8.59421	+	7.21140i	0.299575	+	0.251373i	−0.480592	+	0.876944i	$0.659578\pi$
$824$	−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	−0.937414	−	0.348218i	$-0.886787\pi$
$827$	−4.80659	+	8.32526i	−0.167141	+	0.289498i	0.770272	+	0.637715i	$0.220120\pi$
$828$		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	$-0.364257\pi$
$830$	−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	−0.112794	−	0.993618i	$-0.535980\pi$
$839$	24.5089	−	20.5654i	0.846142	−	0.709997i	0.958936	+	0.283621i	$0.0915357\pi$
$840$		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	−0.294192	−	0.955746i	$-0.595050\pi$
$853$	−33.1168	−	12.0535i	−1.13390	−	0.412705i	−0.839706	+	0.543041i	$0.817273\pi$
$854$	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	0.980683	+	0.195603i	$0.0626665\pi$
$857$	3.68984	+	20.9262i	0.126043	+	0.714824i	−0.854640	+	0.519220i	$0.826222\pi$
$858$		0			0
$859$	−48.7122	+	17.7298i	−1.66204	+	0.604933i	−0.990681	−	0.136201i	$-0.956511\pi$
$859$	−48.7122	+	17.7298i	−1.66204	+	0.604933i	−0.671357	+	0.741134i	$0.734288\pi$
$860$	−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	0.657329	−	0.753604i	$-0.271686\pi$
$877$	0.868241	+	0.728541i	0.0293184	+	0.0246011i	−0.628011	+	0.778205i	$0.716131\pi$
$878$	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	0.480421	+	0.877038i	$0.340484\pi$
$881$	−15.4145	+	26.6986i	−0.519327	+	0.899500i	−0.999748	+	0.0224621i	$0.992849\pi$
$882$		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	$0.783127\pi$
$884$	−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	−0.915753	−	0.401741i	$-0.868405\pi$
$887$	2.44743	−	13.8801i	0.0821768	−	0.466048i	0.997930	−	0.0643068i	$-0.0204836\pi$
$888$		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	0.474741	−	0.880126i	$-0.342542\pi$
$907$	8.21213	+	2.98897i	0.272679	+	0.0992472i	−0.202061	+	0.979373i	$0.564764\pi$
$908$	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	0.984793	+	0.173730i	$0.0555820\pi$
$911$	3.58600	+	20.3372i	0.118809	+	0.673802i	−0.865984	+	0.500072i	$0.833307\pi$
$912$		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	−0.106301	−	0.994334i	$-0.533901\pi$
$929$	−25.2028	−	9.17307i	−0.826877	−	0.300959i	−0.720577	+	0.693375i	$0.756123\pi$
$930$		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	0.849805	−	0.527097i	$-0.176719\pi$
$937$	−0.966567	−	1.67414i	−0.0315764	−	0.0546919i	−0.881382	+	0.472405i	$0.843386\pi$
$938$	−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	0.932361	+	0.361528i	$0.117745\pi$
$941$	−2.06821	+	11.7294i	−0.0674217	+	0.382368i	−0.999783	+	0.0208393i	$0.993366\pi$
$942$		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	−0.638848	−	0.769333i	$-0.720589\pi$
$947$	0.241945	−	0.203016i	0.00786215	−	0.00659713i	0.646710	+	0.762736i	$0.276144\pi$
$948$		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	0.891154	−	0.453701i	$-0.149897\pi$
$953$	1.62567	+	2.81574i	0.0526605	+	0.0912107i	−0.838494	+	0.544912i	$0.816563\pi$
$954$		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	−0.502372	−	0.864651i	$-0.667539\pi$
$967$	−10.3062	+	3.75114i	−0.331424	+	0.120629i	0.170948	+	0.985280i	$0.445317\pi$
$968$	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	−0.958237	−	0.285974i	$-0.907683\pi$
$977$	−47.1502	+	17.1613i	−1.50847	+	0.549038i	−0.550232	+	0.835012i	$0.685461\pi$
$978$		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	0.112287	−	0.993676i	$-0.464183\pi$
$983$	−13.8084	−	5.02585i	−0.440420	−	0.160300i	−0.552706	+	0.833376i	$0.686405\pi$
$984$		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	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	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	−0.998243	−	0.0592450i	$-0.981131\pi$
$997$	−35.1509	+	29.4951i	−1.11324	+	0.934121i	−0.114998	+	0.993366i	$0.536686\pi$
$998$	−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.325.1		6
3.2	odd	2		729.2.e.c.325.1		6
9.2	odd	6		729.2.e.b.568.1		6
9.4	even	3		729.2.e.a.82.1		6
9.5	odd	6		729.2.e.i.82.1		6
9.7	even	3		729.2.e.g.568.1		6
27.2	odd	18		729.2.e.b.163.1		6
27.4	even	9		243.2.a.e.1.2	✓	3
27.5	odd	18		243.2.c.e.82.2		6
27.7	even	9		729.2.e.a.649.1		6
27.11	odd	18		729.2.e.c.406.1		6
27.13	even	9		243.2.c.f.163.2		6
27.14	odd	18		243.2.c.e.163.2		6
27.16	even	9	inner	729.2.e.h.406.1		6
27.20	odd	18		729.2.e.i.649.1		6
27.22	even	9		243.2.c.f.82.2		6
27.23	odd	18		243.2.a.f.1.2	yes	3
27.25	even	9		729.2.e.g.163.1		6
108.23	even	18		3888.2.a.bk.1.2		3
108.31	odd	18		3888.2.a.bd.1.2		3
135.4	even	18		6075.2.a.bv.1.2		3
135.104	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	27.4	even	9
243.2.a.f.1.2	yes	3	27.23	odd	18
243.2.c.e.82.2		6	27.5	odd	18
243.2.c.e.163.2		6	27.14	odd	18
243.2.c.f.82.2		6	27.22	even	9
243.2.c.f.163.2		6	27.13	even	9
729.2.e.a.82.1		6	9.4	even	3
729.2.e.a.649.1		6	27.7	even	9
729.2.e.b.163.1		6	27.2	odd	18
729.2.e.b.568.1		6	9.2	odd	6
729.2.e.c.325.1		6	3.2	odd	2
729.2.e.c.406.1		6	27.11	odd	18
729.2.e.g.163.1		6	27.25	even	9
729.2.e.g.568.1		6	9.7	even	3
729.2.e.h.325.1		6	1.1	even	1	trivial
729.2.e.h.406.1		6	27.16	even	9	inner
729.2.e.i.82.1		6	9.5	odd	6
729.2.e.i.649.1		6	27.20	odd	18
3888.2.a.bd.1.2		3	108.31	odd	18
3888.2.a.bk.1.2		3	108.23	even	18
6075.2.a.bq.1.2		3	135.104	odd	18
6075.2.a.bv.1.2		3	135.4	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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