LMFDB - Embedded newform 729.2.e.c.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.c.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	0.930076	−	0.367366i	$-0.119740\pi$
$2$	1.03209	+	0.866025i	0.729797	+	0.612372i	−0.200279	+	0.979739i	$0.564185\pi$
$3$		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	$-0.509379\pi$
$5$	−1.55303	−	0.565258i	−0.694538	−	0.252791i	−0.665077	+	0.746775i	$0.731601\pi$
$6$		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	−0.993846	−	0.110766i	$-0.964669\pi$
$11$	−5.58512	+	2.03282i	−1.68398	+	0.612918i	−0.690131	+	0.723684i	$0.742447\pi$
$12$		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	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	−0.180655	−	0.983547i	$-0.557822\pi$
$19$	3.31908	−	5.74881i	0.761449	−	1.31887i	0.942104	−	0.335321i	$-0.108845\pi$
$20$	−0.0530334	+	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	$-0.956268\pi$
$23$	−0.511144	−	2.89884i	−0.106581	−	0.604451i	0.883996	−	0.467494i	$-0.154843\pi$
$24$		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	$-0.316020\pi$
$29$	−0.988856	−	0.829748i	−0.183626	−	0.154080i	−0.729967	+	0.683482i	$0.760465\pi$
$30$		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	−0.887047	−	0.461679i	$-0.847247\pi$
$41$	−3.75490	+	3.15074i	−0.586417	+	0.492062i	0.300630	+	0.953741i	$0.402803\pi$
$42$		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	$0.143410\pi$
$47$	−0.648833	+	3.67972i	−0.0946421	+	0.536742i	−0.994856	+	0.101295i	$0.967701\pi$
$48$		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	$-0.205198\pi$
$53$	11.6382			1.59862			0.799312	+	0.600916i	$0.205198\pi$
$54$		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	$-0.230154\pi$
$59$	6.90420	+	2.51292i	0.898850	+	0.327155i	0.149058	+	0.988828i	$0.452376\pi$
$60$		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	0.981936	−	0.189212i	$-0.0605932\pi$
$71$	2.75624	+	4.77396i	0.327106	+	0.566564i	−0.654830	+	0.755776i	$0.727260\pi$
$72$		0			0
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	−0.981522	−	0.191352i	$-0.938713\pi$
$73$	−2.77719	+	4.81023i	−0.325045	+	0.562995i	0.656476	+	0.754347i	$0.272046\pi$
$74$	0.00980018	−	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	0.794780	−	0.606898i	$-0.207586\pi$
$83$	3.05303	+	2.56180i	0.335114	+	0.281194i	−0.459666	+	0.888092i	$0.652031\pi$
$84$		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	$-0.975519\pi$
$89$	−4.07532	+	7.05866i	−0.431983	+	0.748217i	0.565061	+	0.825049i	$0.308853\pi$
$90$		0			0
$91$	3.89053	+	6.73859i	0.407838	+	0.706397i
$92$	−0.511144	+	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	$-0.759594\pi$
$101$	1.91488	−	10.8598i	0.190537	−	1.08059i	0.918632	−	0.395115i	$-0.129295\pi$
$102$		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	$-0.540702\pi$
$107$	−2.63816			−0.255040			−0.127520	+	0.991836i	$0.540702\pi$
$108$		0			0
$109$	−8.95811			−0.858031			−0.429016	−	0.903297i	$-0.641140\pi$
$109$	−8.95811			−0.858031			−0.429016	+	0.903297i	$0.641140\pi$
$110$	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	$-0.658469\pi$
$113$	−14.9684	−	5.44804i	−1.40811	−	0.512509i	−0.930574	+	0.366105i	$0.880691\pi$
$114$		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	$-0.774034\pi$
$131$	−3.07486	−	17.4384i	−0.268651	−	1.52360i	0.489781	−	0.871846i	$-0.337077\pi$
$132$		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	$-0.331457\pi$
$137$	−3.00980	−	2.52552i	−0.257145	−	0.215770i	−0.762242	+	0.647293i	$0.775901\pi$
$138$		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	$-0.404338\pi$
$149$	15.7233	−	13.1934i	1.28810	−	1.08085i	0.992073	−	0.125666i	$-0.0401068\pi$
$150$		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	0.181268	−	0.983434i	$-0.441980\pi$
$167$	−4.03209	−	1.46756i	−0.312012	−	0.113563i	−0.493280	+	0.869871i	$0.664202\pi$
$168$		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	$-0.657167\pi$
$173$	−3.56418	+	1.29725i	−0.270979	+	0.0986284i	0.202957	+	0.979188i	$0.434945\pi$
$174$		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	$-0.266761\pi$
$179$	−4.13816	−	7.16750i	−0.309300	−	0.535724i	−0.978209	+	0.207620i	$0.933428\pi$
$180$		0			0
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	−0.963475	−	0.267797i	$-0.913704\pi$
$181$	−3.36097	+	5.82137i	−0.249819	+	0.432699i	0.713657	+	0.700496i	$0.247038\pi$
$182$	−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	$-0.335847\pi$
$191$	−3.84137	−	3.22329i	−0.277952	−	0.233229i	−0.771097	+	0.636718i	$0.780292\pi$
$192$		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	−0.878628	−	0.477507i	$-0.841540\pi$
$197$	−0.361844	+	0.626733i	−0.0257803	+	0.0446529i	0.852847	+	0.522160i	$0.174874\pi$
$198$		0			0
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	0.988169	−	0.153367i	$-0.0490117\pi$
$199$	5.09627	+	8.82699i	0.361265	+	0.625729i	−0.626905	+	0.779096i	$0.715678\pi$
$200$	−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	0.260743	−	0.965408i	$-0.416032\pi$
$227$	16.2875	−	5.92815i	1.08104	−	0.393465i	0.820293	+	0.571943i	$0.193810\pi$
$228$		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	$-0.981319\pi$
$233$	−8.39440	−	14.5395i	−0.549935	−	0.952516i	0.448343	−	0.893862i	$-0.352014\pi$
$234$		0			0
$235$	3.08765	−	5.34796i	0.201416	−	0.348863i
$236$	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	$-0.0971529\pi$
$239$	−0.699645	−	3.96788i	−0.0452563	−	0.256661i	−0.999039	+	0.0438370i	$0.986042\pi$
$240$		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	$-0.572561\pi$
$251$	11.5753	−	20.0490i	0.730628	−	1.26548i	0.956615	−	0.291354i	$-0.0941059\pi$
$252$		0			0
$253$	8.74763	+	15.1513i	0.549959	+	0.952556i
$254$	−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	$-0.599979\pi$
$257$	9.20233	−	7.72167i	0.574026	−	0.481665i	0.882979	+	0.469412i	$0.155534\pi$
$258$		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	$-0.769966\pi$
$263$	2.93494	−	16.6449i	0.180976	−	1.02637i	0.931017	−	0.364976i	$-0.118923\pi$
$264$		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	$-0.577566\pi$
$269$	−7.91447			−0.482554			−0.241277	+	0.970456i	$0.577566\pi$
$270$		0			0
$271$	−17.2344			−1.04692			−0.523458	−	0.852051i	$-0.675358\pi$
$271$	−17.2344			−1.04692			−0.523458	+	0.852051i	$0.675358\pi$
$272$	−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	0.250607	−	0.968089i	$-0.419370\pi$
$281$	17.8503	−	6.49697i	1.06486	−	0.387577i	0.814252	+	0.580512i	$0.197148\pi$
$282$		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	$0.135740\pi$
$293$	3.36143	+	19.0636i	0.196377	+	1.11371i	−0.714067	+	0.700077i	$0.753149\pi$
$294$		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	−0.844341	−	0.535807i	$-0.820008\pi$
$311$	−8.17024	+	6.85565i	−0.463292	+	0.388748i	0.381049	+	0.924555i	$0.375563\pi$
$312$		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	$-0.678757\pi$
$317$	4.58243	−	25.9883i	0.257375	−	1.45965i	0.789902	−	0.613234i	$-0.210132\pi$
$318$		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	$0.123257\pi$
$347$	3.44609	+	19.5437i	0.184996	+	1.04916i	−0.740965	+	0.671544i	$0.765632\pi$
$348$		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	0.582534	−	0.812806i	$-0.302061\pi$
$353$	−2.19388	−	1.84088i	−0.116768	−	0.0979803i	−0.699302	+	0.714826i	$0.746506\pi$
$354$		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	$0.441324\pi$
$359$	−14.3944	+	24.9318i	−0.759707	+	1.31585i	−0.943000	+	0.332793i	$0.892009\pi$
$360$		0			0
$361$	−12.5326	−	21.7070i	−0.659608	−	1.14247i
$362$	−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	0.438828	−	0.898571i	$-0.355394\pi$
$383$	3.86319	+	1.40609i	0.197400	+	0.0718476i	−0.241428	+	0.970419i	$0.577616\pi$
$384$		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	$-0.753782\pi$
$389$	−16.0633	+	5.84656i	−0.814442	+	0.296433i	−0.0989844	+	0.995089i	$0.531559\pi$
$390$		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	$-0.936936\pi$
$401$	−2.53209	−	14.3602i	−0.126446	−	0.717114i	0.853992	−	0.520287i	$-0.174175\pi$
$402$		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	−0.217551	−	0.976049i	$-0.569807\pi$
$419$	14.4492	−	12.1244i	0.705892	−	0.592314i	0.923443	+	0.383735i	$0.125363\pi$
$420$		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	$-0.190338\pi$
$431$	34.3164			1.65297			0.826483	+	0.562962i	$0.190338\pi$
$432$		0			0
$433$	−25.0669			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$433$	−25.0669			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$434$	−1.46476	−	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	−0.248371	−	0.968665i	$-0.579895\pi$
$443$	3.87299	−	1.40965i	0.184011	−	0.0669746i	0.432382	+	0.901690i	$0.357673\pi$
$444$		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	$-0.309138\pi$
$449$	−9.17071	−	15.8841i	−0.432793	−	0.749619i	−0.997113	+	0.0759373i	$0.975805\pi$
$450$		0			0
$451$	14.5667	−	25.2303i	0.685919	−	1.18805i
$452$	−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	0.985574	−	0.169243i	$-0.0541323\pi$
$461$	21.2572	+	17.8369i	0.990045	+	0.830747i	0.00447116	+	0.999990i	$0.498577\pi$
$462$		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	$0.408464\pi$
$467$	−14.8819	+	25.7762i	−0.688653	+	1.19278i	−0.972274	+	0.233845i	$0.924869\pi$
$468$		0			0
$469$	−2.23917	−	3.87836i	−0.103395	−	0.179086i
$470$	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	$0.385547\pi$
$479$	−6.54236	+	37.1035i	−0.298928	+	1.69530i	−0.650794	+	0.759254i	$0.725564\pi$
$480$		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	$-0.385312\pi$
$491$	0.467911	+	0.170306i	0.0211165	+	0.00768579i	−0.331440	+	0.943476i	$0.607535\pi$
$492$		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	0.585461	−	0.810701i	$-0.300914\pi$
$503$	−9.18092	−	15.9018i	−0.409357	−	0.709027i	−0.994818	+	0.101673i	$0.967580\pi$
$504$		0			0
$505$	−9.11246	+	15.7832i	−0.405499	+	0.702345i
$506$	−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	$-0.839122\pi$
$509$	−4.92649	−	27.9395i	−0.218363	−	1.23840i	0.656612	−	0.754228i	$-0.271989\pi$
$510$		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	$-0.579782\pi$
$521$	16.3191	−	28.2655i	0.714952	−	1.23833i	0.962978	−	0.269580i	$-0.0868847\pi$
$522$		0			0
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	0.999775	−	0.0212271i	$-0.00675730\pi$
$523$	11.0116	+	19.0727i	0.481504	+	0.833990i	−0.518271	+	0.855217i	$0.673424\pi$
$524$	−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	$-0.952621\pi$
$557$	−14.7010	−	25.4629i	−0.622901	−	1.07890i	0.366042	−	0.930598i	$-0.380713\pi$
$558$		0			0
$559$	−8.36484	+	14.4883i	−0.353795	+	0.612791i
$560$	−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	$-0.985429\pi$
$563$	−1.80082	−	10.2130i	−0.0758956	−	0.430425i	0.923057	−	0.384664i	$-0.125683\pi$
$564$		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	$-0.520638\pi$
$569$	−25.2558	−	21.1922i	−1.05878	−	0.888422i	−0.993989	+	0.109477i	$0.965082\pi$
$570$		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	$0.284397\pi$
$587$	−5.54148	+	31.4273i	−0.228721	+	1.29714i	−0.855442	+	0.517899i	$0.826714\pi$
$588$		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	$-0.274586\pi$
$593$	31.6783			1.30087			0.650436	+	0.759561i	$0.274586\pi$
$594$		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	$-0.305861\pi$
$599$	11.8623	+	4.31753i	0.484681	+	0.176409i	−0.0881103	+	0.996111i	$0.528083\pi$
$600$		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	$-0.882242\pi$
$617$	−4.46838	−	25.3414i	−0.179890	−	1.02021i	0.752457	−	0.658642i	$-0.228869\pi$
$618$		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	$-0.863809\pi$
$641$	2.20368	−	12.4977i	0.0870400	−	0.493629i	0.996898	−	0.0787081i	$-0.0250795\pi$
$642$		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	$-0.429659\pi$
$647$	11.1506			0.438377			0.219189	+	0.975683i	$0.429659\pi$
$648$		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	$-0.726400\pi$
$653$	−41.9029	−	15.2514i	−1.63979	−	0.596834i	−0.987002	+	0.160709i	$0.948622\pi$
$654$		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	$-0.522578\pi$
$659$	13.2464	−	4.82131i	0.516008	−	0.187812i	0.586880	+	0.809674i	$0.300356\pi$
$660$		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	0.991511	−	0.130020i	$-0.0415043\pi$
$677$	26.9466	+	22.6108i	1.03564	+	0.869005i	0.0441290	+	0.999026i	$0.485949\pi$
$678$		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	$-0.722955\pi$
$683$	8.88191	−	15.3839i	0.339857	−	0.588649i	0.984406	+	0.175914i	$0.0562880\pi$
$684$		0			0
$685$	3.24675	+	5.62353i	0.124052	+	0.214864i
$686$	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	$-0.692488\pi$
$701$	−30.1052			−1.13706			−0.568530	+	0.822663i	$0.692488\pi$
$702$		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	$0.135020\pi$
$719$	21.7763	+	37.7177i	0.812119	+	1.40663i	−0.0992586	+	0.995062i	$0.531647\pi$
$720$		0			0
$721$	4.71048	−	8.15880i	0.175428	−	0.303850i
$722$	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	−0.160985	−	0.986957i	$-0.551467\pi$
$743$	21.3436	−	17.9094i	0.783022	−	0.657034i	0.944008	+	0.329923i	$0.107023\pi$
$744$		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	0.967492	−	0.252904i	$-0.0813855\pi$
$761$	42.6502	+	15.5234i	1.54607	+	0.562723i	0.578578	+	0.815627i	$0.303608\pi$
$762$		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	$0.228952\pi$
$773$	26.3214	+	45.5899i	0.946713	+	1.63976i	0.194430	+	0.980916i	$0.437714\pi$
$774$		0			0
$775$	−0.667556	+	1.15624i	−0.0239793	+	0.0415334i
$776$	−0.133322	+	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
\

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

L-functions

Modular forms

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