LMFDB - Embedded newform 729.2.e.s.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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 $ x^12 + 18x^10 + 105x^8 + 266x^6 + 306x^4 + 132*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			406.1
Root			$-1.22778i$ of defining polynomial
Character	$\chi$	$=$	729.406
Dual form			729.2.e.s.325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20913 - 1.01458i) q^{2} +(0.0853237 + 0.483895i) q^{4} +(-1.57728 - 0.574083i) q^{5} +(0.482617 - 2.73706i) q^{7} +(-1.19062 + 2.06222i) q^{8} +(1.32468 + 2.29442i) q^{10} +(3.90087 - 1.41980i) q^{11} +(5.26736 - 4.41984i) q^{13} +(-3.36051 + 2.81980i) q^{14} +(4.45535 - 1.62162i) q^{16} +(-0.488276 - 0.845718i) q^{17} +(-1.34264 + 2.32553i) q^{19} +(0.143217 - 0.812221i) q^{20} +(-6.15715 - 2.24102i) q^{22} +(0.280124 + 1.58866i) q^{23} +(-1.67198 - 1.40296i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-6.30292 - 5.28878i) q^{29} +(0.181301 + 1.02821i) q^{31} +(-2.55707 - 0.930697i) q^{32} +(-0.267660 + 1.51798i) q^{34} +(-2.33252 + 4.04005i) q^{35} +(0.654172 + 1.13306i) q^{37} +(3.98286 - 1.44964i) q^{38} +(3.06183 - 2.56918i) q^{40} +(-3.71391 + 3.11634i) q^{41} +(-9.24679 + 3.36556i) q^{43} +(1.01987 + 1.76647i) q^{44} +(1.27312 - 2.20510i) q^{46} +(2.17020 - 12.3078i) q^{47} +(-0.680721 - 0.247762i) q^{49} +(0.598226 + 3.39271i) q^{50} +(2.58817 + 2.17173i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(5.06980 + 4.25406i) q^{56} +(2.25515 + 12.7896i) q^{58} +(-8.50598 - 3.09592i) q^{59} +(-0.223267 + 1.26621i) q^{61} +(0.823982 - 1.42718i) q^{62} +(-2.59373 - 4.49247i) q^{64} +(-10.8455 + 3.94742i) q^{65} +(-3.55927 + 2.98658i) q^{67} +(0.367577 - 0.308434i) q^{68} +(6.91926 - 2.51841i) q^{70} +(-2.81187 - 4.87030i) q^{71} +(2.28072 - 3.95033i) q^{73} +(0.358600 - 2.03372i) q^{74} +(-1.23987 - 0.451276i) q^{76} +(-2.00345 - 11.3621i) q^{77} +(3.56732 + 2.99333i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(4.41578 + 3.70528i) q^{83} +(0.284635 + 1.61425i) q^{85} +(14.5952 + 5.31221i) q^{86} +(-1.71652 + 9.73490i) q^{88} +(-2.27221 + 3.93558i) q^{89} +(-9.55523 - 16.5502i) q^{91} +(-0.744844 + 0.271101i) q^{92} +(-15.1113 + 12.6799i) q^{94} +(3.45278 - 2.89722i) q^{95} +(-8.05828 + 2.93297i) q^{97} +(0.571704 + 0.990221i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots + 18 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

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 $

$2$	−1.20913	−	1.01458i	−0.854982	−	0.717415i	0.105899	−	0.994377i	$-0.466228\pi$
$2$	−1.20913	−	1.01458i	−0.854982	−	0.717415i	−0.960881	+	0.276961i	$0.910673\pi$
$3$		0			0
$3$		0			0
$4$	0.0853237	+	0.483895i	0.0426619	+	0.241948i
$5$	−1.57728	−	0.574083i	−0.705382	−	0.256738i	−0.0356747	−	0.999363i	$-0.511358\pi$
$5$	−1.57728	−	0.574083i	−0.705382	−	0.256738i	−0.669707	+	0.742626i	$0.733580\pi$
$6$		0			0
$7$	0.482617	−	2.73706i	0.182412	−	1.03451i	−0.746823	−	0.665023i	$-0.768422\pi$
$7$	0.482617	−	2.73706i	0.182412	−	1.03451i	0.929235	−	0.369488i	$-0.120467\pi$
$8$	−1.19062	+	2.06222i	−0.420948	+	0.729104i
$9$		0			0
$10$	1.32468	+	2.29442i	0.418901	+	0.725558i
$11$	3.90087	−	1.41980i	1.17616	−	0.428086i	0.321314	−	0.946973i	$-0.395875\pi$
$11$	3.90087	−	1.41980i	1.17616	−	0.428086i	0.854843	+	0.518886i	$0.173653\pi$
$12$		0			0
$13$	5.26736	−	4.41984i	1.46090	−	1.22584i	0.536792	−	0.843715i	$-0.319636\pi$
$13$	5.26736	−	4.41984i	1.46090	−	1.22584i	0.924110	−	0.382128i	$-0.124809\pi$
$14$	−3.36051	+	2.81980i	−0.898133	+	0.753623i
$15$		0			0
$16$	4.45535	−	1.62162i	1.11384	−	0.405404i
$17$	−0.488276	−	0.845718i	−0.118424	−	0.205117i	0.800719	−	0.599040i	$-0.204451\pi$
$17$	−0.488276	−	0.845718i	−0.118424	−	0.205117i	−0.919143	+	0.393923i	$0.871118\pi$
$18$		0			0
$19$	−1.34264	+	2.32553i	−0.308024	+	0.533513i	−0.977930	−	0.208933i	$-0.933001\pi$
$19$	−1.34264	+	2.32553i	−0.308024	+	0.533513i	0.669906	+	0.742446i	$0.266334\pi$
$20$	0.143217	−	0.812221i	0.0320242	−	0.181618i
$21$		0			0
$22$	−6.15715	−	2.24102i	−1.31271	−	0.477787i
$23$	0.280124	+	1.58866i	0.0584099	+	0.331259i	0.999985	−	0.00554518i	$-0.00176509\pi$
$23$	0.280124	+	1.58866i	0.0584099	+	0.331259i	−0.941575	+	0.336804i	$0.890654\pi$
$24$		0			0
$25$	−1.67198	−	1.40296i	−0.334396	−	0.280591i
$26$	−10.8532			−2.12848
$27$		0			0
$28$	1.36563			0.258079
$29$	−6.30292	−	5.28878i	−1.17042	−	0.982101i	−0.170428	−	0.985370i	$-0.554515\pi$
$29$	−6.30292	−	5.28878i	−1.17042	−	0.982101i	−0.999995	+	0.00326885i	$0.998959\pi$
$30$		0			0
$31$	0.181301	+	1.02821i	0.0325626	+	0.184672i	0.996751	−	0.0805475i	$-0.0256669\pi$
$31$	0.181301	+	1.02821i	0.0325626	+	0.184672i	−0.964188	+	0.265219i	$0.914556\pi$
$32$	−2.55707	−	0.930697i	−0.452030	−	0.164526i
$33$		0			0
$34$	−0.267660	+	1.51798i	−0.0459033	+	0.260331i
$35$	−2.33252	+	4.04005i	−0.394268	+	0.682893i
$36$		0			0
$37$	0.654172	+	1.13306i	0.107545	+	0.186274i	0.914775	−	0.403963i	$-0.132368\pi$
$37$	0.654172	+	1.13306i	0.107545	+	0.186274i	−0.807230	+	0.590237i	$0.799034\pi$
$38$	3.98286	−	1.44964i	0.646105	−	0.235163i
$39$		0			0
$40$	3.06183	−	2.56918i	0.484118	−	0.406223i
$41$	−3.71391	+	3.11634i	−0.580016	+	0.486691i	−0.884952	−	0.465682i	$-0.845809\pi$
$41$	−3.71391	+	3.11634i	−0.580016	+	0.486691i	0.304936	+	0.952373i	$0.401365\pi$
$42$		0			0
$43$	−9.24679	+	3.36556i	−1.41012	+	0.513243i	−0.931166	−	0.364596i	$-0.881207\pi$
$43$	−9.24679	+	3.36556i	−1.41012	+	0.513243i	−0.478957	+	0.877839i	$0.658985\pi$
$44$	1.01987	+	1.76647i	0.153751	+	0.266305i
$45$		0			0
$46$	1.27312	−	2.20510i	0.187711	−	0.325125i
$47$	2.17020	−	12.3078i	0.316557	−	1.79528i	−0.246798	−	0.969067i	$-0.579379\pi$
$47$	2.17020	−	12.3078i	0.316557	−	1.79528i	0.563355	−	0.826215i	$-0.309510\pi$
$48$		0			0
$49$	−0.680721	−	0.247762i	−0.0972458	−	0.0353946i
$50$	0.598226	+	3.39271i	0.0846019	+	0.479801i
$51$		0			0
$52$	2.58817	+	2.17173i	0.358914	+	0.301165i
$53$	7.34280			1.00861			0.504305	−	0.863525i	$-0.331749\pi$
$53$	7.34280			1.00861			0.504305	+	0.863525i	$0.331749\pi$
$54$		0			0
$55$	−6.96786			−0.939546
$56$	5.06980	+	4.25406i	0.677480	+	0.568473i
$57$		0			0
$58$	2.25515	+	12.7896i	0.296116	+	1.67936i
$59$	−8.50598	−	3.09592i	−1.10738	−	0.403055i	−0.277351	−	0.960769i	$-0.589456\pi$
$59$	−8.50598	−	3.09592i	−1.10738	−	0.403055i	−0.830033	+	0.557714i	$0.811679\pi$
$60$		0			0
$61$	−0.223267	+	1.26621i	−0.0285864	+	0.162121i	−0.995759	−	0.0919982i	$-0.970675\pi$
$61$	−0.223267	+	1.26621i	−0.0285864	+	0.162121i	0.967173	+	0.254120i	$0.0817857\pi$
$62$	0.823982	−	1.42718i	0.104646	−	0.181252i
$63$		0			0
$64$	−2.59373	−	4.49247i	−0.324216	−	0.561558i
$65$	−10.8455	+	3.94742i	−1.34521	+	0.489618i
$66$		0			0
$67$	−3.55927	+	2.98658i	−0.434834	+	0.364869i	−0.833772	−	0.552109i	$-0.813823\pi$
$67$	−3.55927	+	2.98658i	−0.434834	+	0.364869i	0.398938	+	0.916978i	$0.369379\pi$
$68$	0.367577	−	0.308434i	0.0445753	−	0.0374031i
$69$		0			0
$70$	6.91926	−	2.51841i	0.827010	−	0.301007i
$71$	−2.81187	−	4.87030i	−0.333707	−	0.577998i	0.649528	−	0.760337i	$-0.274966\pi$
$71$	−2.81187	−	4.87030i	−0.333707	−	0.577998i	−0.983236	+	0.182339i	$0.941633\pi$
$72$		0			0
$73$	2.28072	−	3.95033i	0.266938	−	0.462351i	−0.701131	−	0.713032i	$-0.747321\pi$
$73$	2.28072	−	3.95033i	0.266938	−	0.462351i	0.968070	+	0.250681i	$0.0806547\pi$
$74$	0.358600	−	2.03372i	0.0416864	−	0.236416i
$75$		0			0
$76$	−1.23987	−	0.451276i	−0.142223	−	0.0517649i
$77$	−2.00345	−	11.3621i	−0.228314	−	1.29484i
$78$		0			0
$79$	3.56732	+	2.99333i	0.401354	+	0.336776i	0.821017	−	0.570904i	$-0.193407\pi$
$79$	3.56732	+	2.99333i	0.401354	+	0.336776i	−0.419662	+	0.907680i	$0.637852\pi$
$80$	−7.95828			−0.889763
$81$		0			0
$82$	7.65237			0.845063
$83$	4.41578	+	3.70528i	0.484695	+	0.406707i	0.852121	−	0.523346i	$-0.175316\pi$
$83$	4.41578	+	3.70528i	0.484695	+	0.406707i	−0.367426	+	0.930053i	$0.619761\pi$
$84$		0			0
$85$	0.284635	+	1.61425i	0.0308730	+	0.175090i
$86$	14.5952	+	5.31221i	1.57384	+	0.572830i
$87$		0			0
$88$	−1.71652	+	9.73490i	−0.182982	+	1.03774i
$89$	−2.27221	+	3.93558i	−0.240854	+	0.417171i	−0.960958	−	0.276695i	$-0.910761\pi$
$89$	−2.27221	+	3.93558i	−0.240854	+	0.417171i	0.720104	+	0.693866i	$0.244094\pi$
$90$		0			0
$91$	−9.55523	−	16.5502i	−1.00166	−	1.73493i
$92$	−0.744844	+	0.271101i	−0.0776554	+	0.0282643i
$93$		0			0
$94$	−15.1113	+	12.6799i	−1.55861	+	1.30783i
$95$	3.45278	−	2.89722i	0.354247	−	0.297249i
$96$		0			0
$97$	−8.05828	+	2.93297i	−0.818194	+	0.297798i	−0.717004	−	0.697069i	$-0.754487\pi$
$97$	−8.05828	+	2.93297i	−0.818194	+	0.297798i	−0.101190	+	0.994867i	$0.532265\pi$
$98$	0.571704	+	0.990221i	0.0577508	+	0.100027i
$99$		0			0
$100$	0.536224	−	0.928767i	0.0536224	−	0.0928767i
$101$	−1.35545	+	7.68712i	−0.134872	+	0.764897i	0.840077	+	0.542467i	$0.182510\pi$
$101$	−1.35545	+	7.68712i	−0.134872	+	0.764897i	−0.974949	+	0.222429i	$0.928601\pi$
$102$		0			0
$103$	2.03551	+	0.740866i	0.200565	+	0.0729997i	0.440349	−	0.897826i	$-0.354855\pi$
$103$	2.03551	+	0.740866i	0.200565	+	0.0729997i	−0.239784	+	0.970826i	$0.577077\pi$
$104$	2.84324	+	16.1248i	0.278802	+	1.58117i
$105$		0			0
$106$	−8.87838	−	7.44984i	−0.862344	−	0.723593i
$107$	12.5849			1.21663			0.608317	−	0.793695i	$-0.291845\pi$
$107$	12.5849			1.21663			0.608317	+	0.793695i	$0.291845\pi$
$108$		0			0
$109$	−12.2140			−1.16989			−0.584945	−	0.811073i	$-0.698884\pi$
$109$	−12.2140			−1.16989			−0.584945	+	0.811073i	$0.698884\pi$
$110$	8.42503	+	7.06944i	0.803295	+	0.674045i
$111$		0			0
$112$	−2.28823	−	12.9772i	−0.216217	−	1.22623i
$113$	−0.423644	−	0.154194i	−0.0398531	−	0.0145053i	0.322017	−	0.946734i	$-0.395639\pi$
$113$	−0.423644	−	0.154194i	−0.0398531	−	0.0145053i	−0.361870	+	0.932229i	$0.617862\pi$
$114$		0			0
$115$	0.470190	−	2.66658i	0.0438455	−	0.248660i
$116$	2.02142	−	3.50121i	0.187685	−	0.325079i
$117$		0			0
$118$	7.14376	+	12.3734i	0.657636	+	1.13906i
$119$	−2.55043	+	0.928281i	−0.233798	+	0.0850954i
$120$		0			0
$121$	4.77448	−	4.00627i	0.434044	−	0.364206i
$122$	1.55463	−	1.30449i	0.140749	−	0.118103i
$123$		0			0
$124$	−0.482075	+	0.175461i	−0.0432916	+	0.0157569i
$125$	6.02803	+	10.4409i	0.539164	+	0.933859i
$126$		0			0
$127$	0.265534	−	0.459919i	0.0235624	−	0.0408112i	−0.854004	−	0.520267i	$-0.825833\pi$
$127$	0.265534	−	0.459919i	0.0235624	−	0.0408112i	0.877566	+	0.479456i	$0.159166\pi$
$128$	−2.36687	+	13.4232i	−0.209204	+	1.18645i
$129$		0			0
$130$	17.1185	+	6.23063i	1.50139	+	0.546462i
$131$	−1.98237	−	11.2426i	−0.173201	−	0.982271i	−0.940200	−	0.340623i	$-0.889362\pi$
$131$	−1.98237	−	11.2426i	−0.173201	−	0.982271i	0.766999	−	0.641648i	$-0.221749\pi$
$132$		0			0
$133$	5.71712	+	4.79724i	0.495738	+	0.415973i
$134$	7.33374			0.633539
$135$		0			0
$136$	2.32541			0.199402
$137$	−3.23979	−	2.71850i	−0.276794	−	0.232257i	0.493814	−	0.869568i	$-0.335603\pi$
$137$	−3.23979	−	2.71850i	−0.276794	−	0.232257i	−0.770607	+	0.637310i	$0.780047\pi$
$138$		0			0
$139$	−1.93714	−	10.9861i	−0.164306	−	0.931825i	−0.949777	−	0.312927i	$-0.898691\pi$
$139$	−1.93714	−	10.9861i	−0.164306	−	0.931825i	0.785471	−	0.618898i	$-0.212421\pi$
$140$	−2.15398	−	0.783984i	−0.182044	−	0.0662588i
$141$		0			0
$142$	−1.54139	+	8.74167i	−0.129351	+	0.733585i
$143$	14.2720	−	24.7198i	1.19348	−	2.06718i
$144$		0			0
$145$	6.90528	+	11.9603i	0.573452	+	0.993248i
$146$	−6.76560	+	2.46248i	−0.559925	+	0.203796i
$147$		0			0
$148$	−0.492465	+	0.413228i	−0.0404804	+	0.0339671i
$149$	14.9208	−	12.5200i	1.22236	−	1.02568i	0.223660	−	0.974667i	$-0.428200\pi$
$149$	14.9208	−	12.5200i	1.22236	−	1.02568i	0.998698	−	0.0510127i	$-0.0162449\pi$
$150$		0			0
$151$	1.16791	−	0.425083i	0.0950429	−	0.0345928i	−0.294061	−	0.955787i	$-0.595007\pi$
$151$	1.16791	−	0.425083i	0.0950429	−	0.0345928i	0.389104	+	0.921194i	$0.372785\pi$
$152$	−3.19716	−	5.53765i	−0.259324	−	0.449163i
$153$		0			0
$154$	−9.10535	+	15.7709i	−0.733730	+	1.27086i
$155$	0.304315	−	1.72585i	0.0244431	−	0.138624i
$156$		0			0
$157$	3.32007	+	1.20840i	0.264970	+	0.0964412i	0.471089	−	0.882086i	$-0.343861\pi$
$157$	3.32007	+	1.20840i	0.264970	+	0.0964412i	−0.206119	+	0.978527i	$0.566083\pi$
$158$	−1.27637	−	7.23865i	−0.101542	−	0.575876i
$159$		0			0
$160$	3.49892	+	2.93594i	0.276614	+	0.232107i
$161$	4.48345			0.353346
$162$		0			0
$163$	15.9509			1.24937			0.624685	−	0.780877i	$-0.285228\pi$
$163$	15.9509			1.24937			0.624685	+	0.780877i	$0.285228\pi$
$164$	−1.82487	−	1.53125i	−0.142498	−	0.119570i
$165$		0			0
$166$	−1.57994	−	8.96031i	−0.122628	−	0.695455i
$167$	13.6111	+	4.95404i	1.05326	+	0.383355i	0.809892	−	0.586579i	$-0.199526\pi$
$167$	13.6111	+	4.95404i	1.05326	+	0.383355i	0.243368	+	0.969934i	$0.421748\pi$
$168$		0			0
$169$	5.95266	−	33.7592i	0.457897	−	2.59686i
$170$	1.29362	−	2.24061i	0.0992161	−	0.171847i
$171$		0			0
$172$	−2.41755	−	4.18731i	−0.184336	−	0.319280i
$173$	11.8565	−	4.31540i	0.901431	−	0.328094i	0.150605	−	0.988594i	$-0.451878\pi$
$173$	11.8565	−	4.31540i	0.901431	−	0.328094i	0.750826	+	0.660500i	$0.229656\pi$
$174$		0			0
$175$	−4.64690	+	3.89921i	−0.351272	+	0.294753i
$176$	15.0774	−	12.6514i	1.13650	−	0.953637i
$177$		0			0
$178$	6.74035	−	2.45329i	0.505211	−	0.183882i
$179$	0.147949	+	0.256256i	0.0110582	+	0.0191534i	0.871502	−	0.490393i	$-0.163147\pi$
$179$	0.147949	+	0.256256i	0.0110582	+	0.0191534i	−0.860443	+	0.509546i	$0.829813\pi$
$180$		0			0
$181$	−0.710251	+	1.23019i	−0.0527925	+	0.0914393i	−0.891214	−	0.453583i	$-0.850146\pi$
$181$	−0.710251	+	1.23019i	−0.0527925	+	0.0914393i	0.838421	+	0.545022i	$0.183479\pi$
$182$	−5.23793	+	29.7058i	−0.388261	+	2.20194i
$183$		0			0
$184$	−3.60969	−	1.31382i	−0.266110	−	0.0968560i
$185$	−0.381343	−	2.16270i	−0.0280369	−	0.159005i
$186$		0			0
$187$	−3.10545	−	2.60578i	−0.227093	−	0.190554i
$188$	6.14087			0.447869
$189$		0			0
$190$	−7.11431			−0.516126
$191$	−15.7990	−	13.2569i	−1.14317	−	0.959236i	−0.143635	−	0.989631i	$-0.545879\pi$
$191$	−15.7990	−	13.2569i	−1.14317	−	0.959236i	−0.999538	+	0.0303946i	$0.990324\pi$
$192$		0			0
$193$	−3.63896	−	20.6376i	−0.261938	−	1.48552i	−0.777614	−	0.628741i	$-0.783570\pi$
$193$	−3.63896	−	20.6376i	−0.261938	−	1.48552i	0.515676	−	0.856784i	$-0.327541\pi$
$194$	12.7192	+	4.62942i	0.913187	+	0.332373i
$195$		0			0
$196$	0.0618092	−	0.350537i	0.00441494	−	0.0250384i
$197$	−4.79810	+	8.31056i	−0.341851	+	0.592103i	−0.984776	−	0.173826i	$-0.944387\pi$
$197$	−4.79810	+	8.31056i	−0.341851	+	0.592103i	0.642926	+	0.765929i	$0.277720\pi$
$198$		0			0
$199$	5.34583	+	9.25925i	0.378956	+	0.656371i	0.990911	−	0.134522i	$-0.0429498\pi$
$199$	5.34583	+	9.25925i	0.378956	+	0.656371i	−0.611955	+	0.790893i	$0.709616\pi$
$200$	4.88389	−	1.77759i	0.345344	−	0.125695i
$201$		0			0
$202$	9.43809	−	7.91950i	0.664062	−	0.557214i
$203$	−17.5176	+	14.6990i	−1.22949	+	1.03167i
$204$		0			0
$205$	7.64693	−	2.78325i	0.534085	−	0.194391i
$206$	−1.70953	−	2.96099i	−0.119108	−	0.206302i
$207$		0			0
$208$	16.3006	−	28.2335i	1.13025	−	1.95764i
$209$	−1.93570	+	10.9779i	−0.133895	+	0.759356i
$210$		0			0
$211$	14.1426	+	5.14749i	0.973617	+	0.354367i	0.779355	−	0.626582i	$-0.215547\pi$
$211$	14.1426	+	5.14749i	0.973617	+	0.354367i	0.194261	+	0.980950i	$0.437769\pi$
$212$	0.626515	+	3.55314i	0.0430292	+	0.244031i
$213$		0			0
$214$	−15.2168	−	12.7684i	−1.04020	−	0.872831i
$215$	16.5169			1.12644
$216$		0			0
$217$	2.90176			0.196984
$218$	14.7683	+	12.3921i	1.00023	+	0.839296i
$219$		0			0
$220$	−0.594524	−	3.37171i	−0.0400828	−	0.227321i
$221$	−6.30986	−	2.29660i	−0.424447	−	0.154486i
$222$		0			0
$223$	−2.13381	+	12.1014i	−0.142890	+	0.810371i	0.826147	+	0.563455i	$0.190528\pi$
$223$	−2.13381	+	12.1014i	−0.142890	+	0.810371i	−0.969037	+	0.246916i	$0.920583\pi$
$224$	−3.78146	+	6.54968i	−0.252659	+	0.437619i
$225$		0			0
$226$	0.355798	+	0.616261i	0.0236674	+	0.0409931i
$227$	3.52625	−	1.28345i	0.234046	−	0.0851856i	−0.222335	−	0.974970i	$-0.571368\pi$
$227$	3.52625	−	1.28345i	0.234046	−	0.0851856i	0.456380	+	0.889785i	$0.349146\pi$
$228$		0			0
$229$	−14.2503	+	11.9574i	−0.941685	+	0.790168i	−0.977878	−	0.209177i	$-0.932921\pi$
$229$	−14.2503	+	11.9574i	−0.941685	+	0.790168i	0.0361925	+	0.999345i	$0.488477\pi$
$230$	−3.27398	+	2.74719i	−0.215880	+	0.181145i
$231$		0			0
$232$	18.4110	−	6.70106i	1.20874	−	0.439946i
$233$	0.272892	+	0.472663i	0.0178777	+	0.0309652i	0.874826	−	0.484438i	$-0.160976\pi$
$233$	0.272892	+	0.472663i	0.0178777	+	0.0309652i	−0.856948	+	0.515403i	$0.827642\pi$
$234$		0			0
$235$	−10.4887	+	18.1670i	−0.684210	+	1.18509i
$236$	0.772340	−	4.38016i	0.0502750	−	0.285124i
$237$		0			0
$238$	4.02561	+	1.46520i	0.260942	+	0.0949750i
$239$	3.48942	+	19.7895i	0.225712	+	1.28007i	0.861320	+	0.508062i	$0.169638\pi$
$239$	3.48942	+	19.7895i	0.225712	+	1.28007i	−0.635609	+	0.772011i	$0.719251\pi$
$240$		0			0
$241$	11.7138	+	9.82906i	0.754553	+	0.633145i	0.936703	−	0.350125i	$-0.113861\pi$
$241$	11.7138	+	9.82906i	0.754553	+	0.633145i	−0.182150	+	0.983271i	$0.558305\pi$
$242$	−9.83763			−0.632387
$243$		0			0
$244$	−0.631762			−0.0404444
$245$	0.931452	+	0.781581i	0.0595083	+	0.0499334i
$246$		0			0
$247$	3.20627	+	18.1837i	0.204010	+	1.15700i
$248$	−2.33625	−	0.850325i	−0.148352	−	0.0539957i
$249$		0			0
$250$	3.30441	−	18.7403i	0.208989	−	1.18524i
$251$	6.37816	−	11.0473i	0.402586	−	0.697299i	−0.591451	−	0.806341i	$-0.701445\pi$
$251$	6.37816	−	11.0473i	0.402586	−	0.697299i	0.994037	+	0.109042i	$0.0347782\pi$
$252$		0			0
$253$	3.34831	+	5.79945i	0.210507	+	0.364608i
$254$	−0.787689	+	0.286695i	−0.0494240	+	0.0179889i
$255$		0			0
$256$	8.53308	−	7.16010i	0.533317	−	0.447506i
$257$	10.0388	−	8.42354i	0.626202	−	0.525446i	−0.273544	−	0.961860i	$-0.588196\pi$
$257$	10.0388	−	8.42354i	0.626202	−	0.525446i	0.899746	+	0.436413i	$0.143751\pi$
$258$		0			0
$259$	3.41697	−	1.24367i	0.212320	−	0.0772781i
$260$	−2.83551	−	4.91125i	−0.175851	−	0.304583i
$261$		0			0
$262$	−9.00956	+	15.6050i	−0.556613	+	0.964081i
$263$	1.65212	−	9.36963i	0.101874	−	0.577756i	−0.890549	−	0.454888i	$-0.849679\pi$
$263$	1.65212	−	9.36963i	0.101874	−	0.577756i	0.992423	−	0.122869i	$-0.0392094\pi$
$264$		0			0
$265$	−11.5817	−	4.21538i	−0.711455	−	0.258949i
$266$	−2.04556	−	11.6009i	−0.125421	−	0.711299i
$267$		0			0
$268$	−1.74888	−	1.46749i	−0.106830	−	0.0896411i
$269$	−22.1408			−1.34995			−0.674973	−	0.737842i	$-0.735845\pi$
$269$	−22.1408			−1.34995			−0.674973	+	0.737842i	$0.735845\pi$
$270$		0			0
$271$	27.9627			1.69861			0.849307	−	0.527899i	$-0.177020\pi$
$271$	27.9627			1.69861			0.849307	+	0.527899i	$0.177020\pi$
$272$	−3.54687	−	2.97618i	−0.215060	−	0.180457i
$273$		0			0
$274$	1.15918	+	6.57404i	0.0700286	+	0.397152i
$275$	−8.51409	−	3.09888i	−0.513419	−	0.186869i
$276$		0			0
$277$	−3.27912	+	18.5968i	−0.197023	+	1.11737i	0.712485	+	0.701687i	$0.247570\pi$
$277$	−3.27912	+	18.5968i	−0.197023	+	1.11737i	−0.909508	+	0.415686i	$0.863542\pi$
$278$	−8.80397	+	15.2489i	−0.528027	+	0.914569i
$279$		0			0
$280$	−5.55431	−	9.62034i	−0.331933	−	0.574925i
$281$	−18.7955	+	6.84100i	−1.12125	+	0.408100i	−0.835106	−	0.550088i	$-0.814594\pi$
$281$	−18.7955	+	6.84100i	−1.12125	+	0.408100i	−0.286139	+	0.958188i	$0.592372\pi$
$282$		0			0
$283$	12.8274	−	10.7635i	0.762512	−	0.639824i	−0.176267	−	0.984342i	$-0.556402\pi$
$283$	12.8274	−	10.7635i	0.762512	−	0.639824i	0.938780	+	0.344519i	$0.111958\pi$
$284$	2.11679	−	1.77620i	0.125609	−	0.105398i
$285$		0			0
$286$	−42.3369	+	15.4094i	−2.50343	+	0.911175i
$287$	6.73722	+	11.6692i	0.397685	+	0.688811i
$288$		0			0
$289$	8.02317	−	13.8965i	0.471951	−	0.817444i
$290$	3.78529	−	21.4675i	0.222280	−	1.26061i
$291$		0			0
$292$	2.10614	+	0.766573i	0.123253	+	0.0448603i
$293$	−3.39864	−	19.2747i	−0.198551	−	1.12604i	−0.907271	−	0.420548i	$-0.861838\pi$
$293$	−3.39864	−	19.2747i	−0.198551	−	1.12604i	0.708720	−	0.705490i	$-0.249273\pi$
$294$		0			0
$295$	11.6390	+	9.76628i	0.677649	+	0.568615i
$296$	−3.11549			−0.181084
$297$		0			0
$298$	−30.7437			−1.78093
$299$	8.49714	+	7.12995i	0.491402	+	0.412335i
$300$		0			0
$301$	4.74906	+	26.9333i	0.273731	+	1.55241i
$302$	−1.84343	−	0.670953i	−0.106077	−	0.0386090i
$303$		0			0
$304$	−2.21084	+	12.5383i	−0.126800	+	0.719121i
$305$	1.07906	−	1.86899i	0.0617870	−	0.107018i
$306$		0			0
$307$	−7.44973	−	12.9033i	−0.425179	−	0.736431i	0.571258	−	0.820770i	$-0.306455\pi$
$307$	−7.44973	−	12.9033i	−0.425179	−	0.736431i	−0.996437	+	0.0843392i	$0.973122\pi$
$308$	5.32714	−	1.93892i	0.303542	−	0.110480i
$309$		0			0
$310$	−2.11897	+	1.77803i	−0.120349	+	0.100985i
$311$	−3.51795	+	2.95191i	−0.199485	+	0.167388i	−0.737058	−	0.675829i	$-0.763786\pi$
$311$	−3.51795	+	2.95191i	−0.199485	+	0.167388i	0.537573	+	0.843217i	$0.319341\pi$
$312$		0			0
$313$	−11.1529	+	4.05933i	−0.630400	+	0.229447i	−0.637405	−	0.770529i	$-0.719992\pi$
$313$	−11.1529	+	4.05933i	−0.630400	+	0.229447i	0.00700533	+	0.999975i	$0.497770\pi$
$314$	−2.78836	−	4.82958i	−0.157356	−	0.272549i
$315$		0			0
$316$	−1.14408	+	1.98161i	−0.0643597	+	0.111474i
$317$	2.52091	−	14.2968i	0.141588	−	0.802988i	−0.828455	−	0.560056i	$-0.810780\pi$
$317$	2.52091	−	14.2968i	0.141588	−	0.802988i	0.970043	−	0.242932i	$-0.0781092\pi$
$318$		0			0
$319$	−32.0959	−	11.6820i	−1.79703	−	0.654064i
$320$	1.51199	+	8.57490i	0.0845226	+	0.479351i
$321$		0			0
$322$	−5.42107	−	4.54882i	−0.302104	−	0.253496i
$323$	2.62232			0.145910
$324$		0			0
$325$	−15.0077			−0.832480
$326$	−19.2867	−	16.1834i	−1.06819	−	0.896317i
$327$		0			0
$328$	−2.00471	−	11.3693i	−0.110692	−	0.627764i
$329$	−32.6399	−	11.8799i	−1.79949	−	0.654963i
$330$		0			0
$331$	−1.40754	+	7.98256i	−0.0773654	+	0.438761i	0.921379	+	0.388665i	$0.127064\pi$
$331$	−1.40754	+	7.98256i	−0.0773654	+	0.438761i	−0.998744	+	0.0500957i	$0.984047\pi$
$332$	−1.41620	+	2.45292i	−0.0777238	+	0.134622i
$333$		0			0
$334$	−11.4313	−	19.7996i	−0.625494	−	1.08339i
$335$	7.32852	−	2.66736i	0.400400	−	0.145734i
$336$		0			0
$337$	−14.4077	+	12.0895i	−0.784839	+	0.658558i	−0.944462	−	0.328620i	$-0.893417\pi$
$337$	−14.4077	+	12.0895i	−0.784839	+	0.658558i	0.159623	+	0.987178i	$0.448972\pi$
$338$	−41.4489	+	34.7798i	−2.25452	+	1.89177i
$339$		0			0
$340$	−0.756840	+	0.275467i	−0.0410454	+	0.0149393i
$341$	2.16708	+	3.75350i	0.117354	+	0.203263i
$342$		0			0
$343$	8.72082	−	15.1049i	0.470880	−	0.815588i
$344$	4.06892	−	23.0760i	0.219382	−	1.24417i
$345$		0			0
$346$	−18.7143	−	6.81145i	−1.00609	−	0.366186i
$347$	3.05927	+	17.3500i	0.164230	+	0.931396i	0.949855	+	0.312692i	$0.101231\pi$
$347$	3.05927	+	17.3500i	0.164230	+	0.931396i	−0.785624	+	0.618704i	$0.787658\pi$
$348$		0			0
$349$	−13.0146	−	10.9205i	−0.696653	−	0.584561i	0.224166	−	0.974551i	$-0.428034\pi$
$349$	−13.0146	−	10.9205i	−0.696653	−	0.584561i	−0.920819	+	0.389990i	$0.872479\pi$
$350$	9.57475			0.511792
$351$		0			0
$352$	−11.2962			−0.602090
$353$	11.6099	+	9.74183i	0.617931	+	0.518505i	0.897152	−	0.441721i	$-0.145632\pi$
$353$	11.6099	+	9.74183i	0.617931	+	0.518505i	−0.279222	+	0.960227i	$0.590076\pi$
$354$		0			0
$355$	1.63915	+	9.29607i	0.0869970	+	0.493384i
$356$	−2.09828	−	0.763712i	−0.111209	−	0.0404767i
$357$		0			0
$358$	0.0811020	−	0.459952i	0.00428637	−	0.0243092i
$359$	1.22548	−	2.12259i	0.0646783	−	0.112026i	−0.831873	−	0.554966i	$-0.812731\pi$
$359$	1.22548	−	2.12259i	0.0646783	−	0.112026i	0.896551	+	0.442940i	$0.146065\pi$
$360$		0			0
$361$	5.89461	+	10.2098i	0.310243	+	0.537356i
$362$	2.10691	−	0.766852i	0.110737	−	0.0403049i
$363$		0			0
$364$	7.19325	−	6.03585i	0.377029	−	0.316365i
$365$	−5.86516	+	4.92145i	−0.306996	+	0.257600i
$366$		0			0
$367$	1.23432	−	0.449255i	0.0644309	−	0.0234509i	−0.309604	−	0.950866i	$-0.600196\pi$
$367$	1.23432	−	0.449255i	0.0644309	−	0.0234509i	0.374035	+	0.927415i	$0.377974\pi$
$368$	3.82425	+	6.62379i	0.199353	+	0.345289i
$369$		0			0
$370$	−1.73314	+	3.00189i	−0.0901017	+	0.156061i
$371$	3.54376	−	20.0977i	0.183983	−	1.04342i
$372$		0			0
$373$	9.04564	+	3.29234i	0.468366	+	0.170471i	0.565412	−	0.824809i	$-0.308717\pi$
$373$	9.04564	+	3.29234i	0.468366	+	0.170471i	−0.0970463	+	0.995280i	$0.530939\pi$
$374$	1.11112	+	6.30145i	0.0574544	+	0.325840i
$375$		0			0
$376$	22.7975	+	19.1294i	1.17569	+	0.986524i
$377$	−56.5753			−2.91377
$378$		0			0
$379$	−8.56311			−0.439857			−0.219929	−	0.975516i	$-0.570582\pi$
$379$	−8.56311			−0.439857			−0.219929	+	0.975516i	$0.570582\pi$
$380$	1.69656	+	1.42358i	0.0870314	+	0.0730281i
$381$		0			0
$382$	5.65279	+	32.0586i	0.289222	+	1.64026i
$383$	31.6062	+	11.5037i	1.61500	+	0.587813i	0.982420	−	0.186681i	$-0.0597732\pi$
$383$	31.6062	+	11.5037i	1.61500	+	0.587813i	0.632581	+	0.774494i	$0.281995\pi$
$384$		0			0
$385$	−3.36281	+	19.0714i	−0.171385	+	0.971970i
$386$	−16.5385	+	28.6455i	−0.841786	+	1.45802i
$387$		0			0
$388$	−2.10681	−	3.64911i	−0.106957	−	0.185255i
$389$	−14.0521	+	5.11456i	−0.712472	+	0.259319i	−0.672727	−	0.739891i	$-0.734877\pi$
$389$	−14.0521	+	5.11456i	−0.712472	+	0.259319i	−0.0397455	+	0.999210i	$0.512655\pi$
$390$		0			0
$391$	1.20678	−	1.01261i	0.0610296	−	0.0512099i
$392$	1.32142	−	1.10880i	0.0667418	−	0.0560030i
$393$		0			0
$394$	14.2332	−	5.18048i	0.717060	−	0.260989i
$395$	−3.90824	−	6.76927i	−0.196645	−	0.340599i
$396$		0			0
$397$	8.38938	−	14.5308i	0.421051	−	0.729282i	−0.574991	−	0.818159i	$-0.694995\pi$
$397$	8.38938	−	14.5308i	0.421051	−	0.729282i	0.996043	+	0.0888774i	$0.0283279\pi$
$398$	2.93045	−	16.6194i	0.146890	−	0.833055i
$399$		0			0
$400$	−9.72430	−	3.53936i	−0.486215	−	0.176968i
$401$	−2.27936	−	12.9269i	−0.113826	−	0.645537i	−0.987325	−	0.158712i	$-0.949266\pi$
$401$	−2.27936	−	12.9269i	−0.113826	−	0.645537i	0.873499	−	0.486825i	$-0.161845\pi$
$402$		0			0
$403$	5.49948	+	4.61462i	0.273949	+	0.229870i
$404$	−3.83541			−0.190819
$405$		0			0
$406$	36.0943			1.79133
$407$	4.16056	+	3.49113i	0.206231	+	0.173049i
$408$		0			0
$409$	4.41943	+	25.0639i	0.218527	+	1.23933i	0.874680	+	0.484700i	$0.161071\pi$
$409$	4.41943	+	25.0639i	0.218527	+	1.23933i	−0.656153	+	0.754628i	$0.727818\pi$
$410$	−12.0699	−	4.39310i	−0.596092	−	0.216960i
$411$		0			0
$412$	−0.184824	+	1.04819i	−0.00910561	+	0.0516405i
$413$	−12.5789	+	21.7872i	−0.618965	+	1.07208i
$414$		0			0
$415$	−4.83779	−	8.37929i	−0.237478	−	0.411323i
$416$	−17.5825	+	6.39952i	−0.862054	+	0.313762i
$417$		0			0
$418$	13.4784	−	11.3097i	0.659251	−	0.553178i
$419$	9.70582	−	8.14415i	0.474160	−	0.397868i	−0.374149	−	0.927369i	$-0.622065\pi$
$419$	9.70582	−	8.14415i	0.474160	−	0.397868i	0.848309	+	0.529501i	$0.177621\pi$
$420$		0			0
$421$	16.6112	−	6.04597i	0.809579	−	0.294663i	0.0961292	−	0.995369i	$-0.469354\pi$
$421$	16.6112	−	6.04597i	0.809579	−	0.294663i	0.713450	+	0.700706i	$0.247132\pi$
$422$	−11.8777	−	20.5727i	−0.578196	−	1.00147i
$423$		0			0
$424$	−8.74249	+	15.1424i	−0.424573	+	0.735382i
$425$	−0.370119	+	2.09905i	−0.0179534	+	0.101819i
$426$		0			0
$427$	3.35793	+	1.22219i	0.162502	+	0.0591458i
$428$	1.07380	+	6.08979i	0.0519038	+	0.294361i
$429$		0			0
$430$	−19.9710	−	16.7577i	−0.963089	−	0.808128i
$431$	−15.6974			−0.756117			−0.378059	−	0.925782i	$-0.623408\pi$
$431$	−15.6974			−0.756117			−0.378059	+	0.925782i	$0.623408\pi$
$432$		0			0
$433$	−12.6258			−0.606759			−0.303380	−	0.952870i	$-0.598115\pi$
$433$	−12.6258			−0.606759			−0.303380	+	0.952870i	$0.598115\pi$
$434$	−3.50860	−	2.94407i	−0.168418	−	0.141320i
$435$		0			0
$436$	−1.04214	−	5.91029i	−0.0499097	−	0.283052i
$437$	−4.07059	−	1.48157i	−0.194723	−	0.0708732i
$438$		0			0
$439$	4.67755	−	26.5277i	0.223247	−	1.26610i	−0.642761	−	0.766067i	$-0.722211\pi$
$439$	4.67755	−	26.5277i	0.223247	−	1.26610i	0.866008	−	0.500030i	$-0.166678\pi$
$440$	8.29608	−	14.3692i	0.395500	−	0.685027i
$441$		0			0
$442$	5.29934	+	9.17873i	0.252064	+	0.436588i
$443$	32.6335	−	11.8776i	1.55047	−	0.564324i	0.581940	−	0.813232i	$-0.302294\pi$
$443$	32.6335	−	11.8776i	1.55047	−	0.564324i	0.968527	+	0.248908i	$0.0800718\pi$
$444$		0			0
$445$	5.84327	−	4.90308i	0.276997	−	0.232428i
$446$	14.8579	−	12.4673i	0.703542	−	0.590342i
$447$		0			0
$448$	−13.5479	+	4.93104i	−0.640079	+	0.232970i
$449$	−10.3731	−	17.9667i	−0.489535	−	0.847900i	0.510392	−	0.859942i	$-0.329500\pi$
$449$	−10.3731	−	17.9667i	−0.489535	−	0.847900i	−0.999927	+	0.0120419i	$0.996167\pi$
$450$		0			0
$451$	−10.0629	+	17.4295i	−0.473844	+	0.820722i
$452$	0.0384668	−	0.218156i	0.00180932	−	0.0102612i
$453$		0			0
$454$	−5.56585	−	2.02580i	−0.261218	−	0.0950757i
$455$	5.57012	+	31.5897i	0.261131	+	1.48095i
$456$		0			0
$457$	−5.52144	−	4.63304i	−0.258282	−	0.216725i	0.504447	−	0.863443i	$-0.331697\pi$
$457$	−5.52144	−	4.63304i	−0.258282	−	0.216725i	−0.762729	+	0.646718i	$0.776141\pi$
$458$	29.3621			1.37200
$459$		0			0
$460$	1.33046			0.0620332
$461$	−17.7162	−	14.8656i	−0.825125	−	0.692362i	0.129041	−	0.991639i	$-0.458810\pi$
$461$	−17.7162	−	14.8656i	−0.825125	−	0.692362i	−0.954166	+	0.299277i	$0.903254\pi$
$462$		0			0
$463$	0.864046	+	4.90025i	0.0401556	+	0.227734i	0.998281	−	0.0586166i	$-0.0186690\pi$
$463$	0.864046	+	4.90025i	0.0401556	+	0.227734i	−0.958125	+	0.286350i	$0.907558\pi$
$464$	−36.6581	−	13.3424i	−1.70181	−	0.619408i
$465$		0			0
$466$	0.149592	−	0.848380i	0.00692973	−	0.0393004i
$467$	−6.24068	+	10.8092i	−0.288784	+	0.500189i	−0.973520	−	0.228602i	$-0.926584\pi$
$467$	−6.24068	+	10.8092i	−0.288784	+	0.500189i	0.684735	+	0.728792i	$0.259918\pi$
$468$		0			0
$469$	6.45669	+	11.1833i	0.298142	+	0.516397i
$470$	31.1141	−	11.3246i	1.43519	−	0.522365i
$471$		0			0
$472$	16.5119	−	13.8551i	0.760021	−	0.637733i
$473$	−31.2921	+	26.2572i	−1.43881	+	1.20731i
$474$		0			0
$475$	5.50749	−	2.00456i	0.252701	−	0.0919756i
$476$	−0.666803	−	1.15494i	−0.0305628	−	0.0529364i
$477$		0			0
$478$	15.8588	−	27.4683i	0.725365	−	1.25637i
$479$	−4.94398	+	28.0387i	−0.225896	+	1.28112i	0.635068	+	0.772456i	$0.280972\pi$
$479$	−4.94398	+	28.0387i	−0.225896	+	1.28112i	−0.860964	+	0.508666i	$0.830139\pi$
$480$		0			0
$481$	8.45370	+	3.07689i	0.385455	+	0.140294i
$482$	−4.19115	−	23.7692i	−0.190902	−	1.08266i
$483$		0			0
$484$	2.34599	+	1.96852i	0.106636	+	0.0894781i
$485$	14.3939			0.653595
$486$		0			0
$487$	29.6841			1.34511			0.672557	−	0.740045i	$-0.265196\pi$
$487$	29.6841			1.34511			0.672557	+	0.740045i	$0.265196\pi$
$488$	−2.34537	−	1.96800i	−0.106170	−	0.0890872i
$489$		0			0
$490$	−0.333269	−	1.89006i	−0.0150556	−	0.0853843i
$491$	11.6568	+	4.24274i	0.526066	+	0.191472i	0.591381	−	0.806392i	$-0.298583\pi$
$491$	11.6568	+	4.24274i	0.526066	+	0.191472i	−0.0653150	+	0.997865i	$0.520805\pi$
$492$		0			0
$493$	−1.39525	+	7.91287i	−0.0628390	+	0.356378i
$494$	14.5720	−	25.2394i	0.655623	−	1.13557i
$495$		0			0
$496$	2.47512	+	4.28702i	0.111136	+	0.192493i
$497$	−14.6873	+	5.34576i	−0.658817	+	0.239790i
$498$		0			0
$499$	−1.74645	+	1.46544i	−0.0781816	+	0.0656022i	−0.681041	−	0.732245i	$-0.738472\pi$
$499$	−1.74645	+	1.46544i	−0.0781816	+	0.0656022i	0.602859	+	0.797847i	$0.294028\pi$
$500$	−4.53795	+	3.80779i	−0.202943	+	0.170290i
$501$		0			0
$502$	−18.9204	+	6.88645i	−0.844457	+	0.307357i
$503$	20.6406	+	35.7506i	0.920320	+	1.59404i	0.798920	+	0.601437i	$0.205405\pi$
$503$	20.6406	+	35.7506i	0.920320	+	1.59404i	0.121399	+	0.992604i	$0.461262\pi$
$504$		0			0
$505$	6.55097	−	11.3466i	0.291514	−	0.504917i
$506$	1.83546	−	10.4094i	0.0815961	−	0.462754i
$507$		0			0
$508$	0.245209	+	0.0892487i	0.0108794	+	0.00395977i
$509$	−2.85202	−	16.1746i	−0.126414	−	0.716928i	−0.980458	−	0.196728i	$-0.936968\pi$
$509$	−2.85202	−	16.1746i	−0.126414	−	0.716928i	0.854044	−	0.520200i	$-0.174143\pi$
$510$		0			0
$511$	−9.71156	−	8.14896i	−0.429614	−	0.360489i
$512$	9.67844			0.427731
$513$		0			0
$514$	−20.6845			−0.912355
$515$	−2.78526	−	2.33711i	−0.122733	−	0.102985i
$516$		0			0
$517$	−9.00899	−	51.0925i	−0.396215	−	2.24705i
$518$	−5.39335	−	1.96302i	−0.236970	−	0.0862501i
$519$		0			0
$520$	4.77239	−	27.0656i	0.209283	−	1.18690i
$521$	−4.64836	+	8.05119i	−0.203648	+	0.352729i	−0.949701	−	0.313157i	$-0.898613\pi$
$521$	−4.64836	+	8.05119i	−0.203648	+	0.352729i	0.746053	+	0.665887i	$0.231947\pi$
$522$		0			0
$523$	11.3736	+	19.6996i	0.497331	+	0.861402i	0.999995	−	0.00307938i	$-0.000980199\pi$
$523$	11.3736	+	19.6996i	0.497331	+	0.861402i	−0.502664	+	0.864482i	$0.667647\pi$
$524$	5.27110	−	1.91852i	0.230269	−	0.0838110i
$525$		0			0
$526$	−11.5039	+	9.65288i	−0.501592	+	0.420886i
$527$	0.781049	−	0.655378i	0.0340230	−	0.0285487i
$528$		0			0
$529$	19.1676	−	6.97642i	0.833372	−	0.303323i
$530$	9.72687	+	16.8474i	0.422508	+	0.731806i
$531$		0			0
$532$	−1.83355	+	3.17581i	−0.0794946	+	0.137689i
$533$	−5.78878	+	32.8298i	−0.250740	+	1.42202i
$534$		0			0
$535$	−19.8500	−	7.22481i	−0.858191	−	0.312356i
$536$	−1.92124	−	10.8959i	−0.0829849	−	0.470631i
$537$		0			0
$538$	26.7710	+	22.4636i	1.15418	+	0.968473i
$539$	−3.00718			−0.129528
$540$		0			0
$541$	2.38959			0.102737			0.0513683	−	0.998680i	$-0.483642\pi$
$541$	2.38959			0.102737			0.0513683	+	0.998680i	$0.483642\pi$
$542$	−33.8105	−	28.3704i	−1.45229	−	1.21861i
$543$		0			0
$544$	0.461447	+	2.61700i	0.0197844	+	0.112203i
$545$	19.2649	+	7.01185i	0.825218	+	0.300355i
$546$		0			0
$547$	5.15158	−	29.2161i	0.220266	−	1.24919i	−0.651266	−	0.758850i	$-0.725762\pi$
$547$	5.15158	−	29.2161i	0.220266	−	1.24919i	0.871531	−	0.490340i	$-0.163127\pi$
$548$	1.03904	−	1.79967i	0.0443856	−	0.0768781i
$549$		0			0
$550$	7.15057	+	12.3852i	0.304901	+	0.528105i
$551$	20.7618	−	7.55667i	0.884482	−	0.321925i
$552$		0			0
$553$	9.91458	−	8.31932i	0.421611	−	0.353773i
$554$	22.8328	−	19.1590i	0.970072	−	0.813987i
$555$		0			0
$556$	5.15081	−	1.87474i	0.218443	−	0.0795068i
$557$	4.20706	+	7.28685i	0.178259	+	0.308754i	0.941284	−	0.337615i	$-0.109620\pi$
$557$	4.20706	+	7.28685i	0.178259	+	0.308754i	−0.763025	+	0.646369i	$0.776287\pi$
$558$		0			0
$559$	−33.8309	+	58.5969i	−1.43090	+	2.47838i
$560$	−3.84080	+	21.7823i	−0.162304	+	0.920470i
$561$		0			0
$562$	29.6669	+	10.7979i	1.25142	+	0.455480i
$563$	4.72783	+	26.8129i	0.199254	+	1.13003i	0.906228	+	0.422788i	$0.138949\pi$
$563$	4.72783	+	26.8129i	0.199254	+	1.13003i	−0.706974	+	0.707240i	$0.749940\pi$
$564$		0			0
$565$	0.579686	+	0.486415i	0.0243876	+	0.0204636i
$566$	−26.4304			−1.11095
$567$		0			0
$568$	13.3915			0.561894
$569$	16.8141	+	14.1087i	0.704886	+	0.591469i	0.923159	−	0.384418i	$-0.125598\pi$
$569$	16.8141	+	14.1087i	0.704886	+	0.591469i	−0.218273	+	0.975888i	$0.570042\pi$
$570$		0			0
$571$	−7.78872	−	44.1720i	−0.325948	−	1.84854i	−0.502929	−	0.864328i	$-0.667744\pi$
$571$	−7.78872	−	44.1720i	−0.325948	−	1.84854i	0.176981	−	0.984214i	$-0.443367\pi$
$572$	13.1795	+	4.79696i	0.551064	+	0.200571i
$573$		0			0
$574$	3.69317	−	20.9450i	0.154150	−	0.874227i
$575$	1.76046	−	3.04921i	0.0734163	−	0.127161i
$576$		0			0
$577$	−6.00955	−	10.4088i	−0.250181	−	0.433326i	0.713395	−	0.700762i	$-0.247157\pi$
$577$	−6.00955	−	10.4088i	−0.250181	−	0.433326i	−0.963575	+	0.267437i	$0.913823\pi$
$578$	−23.8002	+	8.66256i	−0.989957	+	0.360315i
$579$		0			0
$580$	−5.19834	+	4.36193i	−0.215849	+	0.181119i
$581$	12.2727	−	10.2980i	0.509157	−	0.427234i
$582$		0			0
$583$	28.6433	−	10.4253i	1.18628	−	0.431772i
$584$	5.43095	+	9.40669i	0.224734	+	0.389252i
$585$		0			0
$586$	−15.4463	+	26.7537i	−0.638079	+	1.10519i
$587$	2.95721	−	16.7711i	0.122057	−	0.692219i	−0.860956	−	0.508680i	$-0.830134\pi$
$587$	2.95721	−	16.7711i	0.122057	−	0.692219i	0.983012	−	0.183539i	$-0.0587554\pi$
$588$		0			0
$589$	−2.63455	−	0.958897i	−0.108555	−	0.0395107i
$590$	−4.16438	−	23.6174i	−0.171445	−	0.972312i
$591$		0			0
$592$	4.75195	+	3.98736i	0.195304	+	0.163880i
$593$	14.9284			0.613037			0.306519	−	0.951865i	$-0.400836\pi$
$593$	14.9284			0.613037			0.306519	+	0.951865i	$0.400836\pi$
$594$		0			0
$595$	4.55566			0.186764
$596$	7.33147	+	6.15184i	0.300309	+	0.251989i
$597$		0			0
$598$	−3.04024	−	17.2420i	−0.124324	−	0.705079i
$599$	12.7186	+	4.62917i	0.519666	+	0.189143i	0.588518	−	0.808484i	$-0.299712\pi$
$599$	12.7186	+	4.62917i	0.519666	+	0.189143i	−0.0688523	+	0.997627i	$0.521934\pi$
$600$		0			0
$601$	−7.86926	+	44.6288i	−0.320994	+	1.82045i	0.215456	+	0.976514i	$0.430876\pi$
$601$	−7.86926	+	44.6288i	−0.320994	+	1.82045i	−0.536449	+	0.843933i	$0.680235\pi$
$602$	21.5837	−	37.3841i	0.879686	−	1.52366i
$603$		0			0
$604$	0.305346	+	0.528874i	0.0124243	+	0.0215196i
$605$	−9.83063	+	3.57806i	−0.399672	+	0.145469i
$606$		0			0
$607$	18.7197	−	15.7077i	0.759808	−	0.637554i	−0.178269	−	0.983982i	$-0.557050\pi$
$607$	18.7197	−	15.7077i	0.759808	−	0.637554i	0.938077	+	0.346427i	$0.112605\pi$
$608$	5.59760	−	4.69694i	0.227013	−	0.190486i
$609$		0			0
$610$	−3.20097	+	1.16506i	−0.129603	+	0.0471718i
$611$	−42.9674	−	74.4217i	−1.73827	−	3.01078i
$612$		0			0
$613$	12.5998	−	21.8235i	0.508901	−	0.881443i	−0.491046	−	0.871134i	$-0.663385\pi$
$613$	12.5998	−	21.8235i	0.508901	−	0.881443i	0.999947	−	0.0103088i	$-0.00328145\pi$
$614$	−4.08375	+	23.1601i	−0.164807	+	0.934665i
$615$		0			0
$616$	25.8166	+	9.39646i	1.04018	+	0.378594i
$617$	−0.701860	−	3.98045i	−0.0282558	−	0.160247i	0.967415	−	0.253196i	$-0.0814817\pi$
$617$	−0.701860	−	3.98045i	−0.0282558	−	0.160247i	−0.995671	+	0.0929492i	$0.970371\pi$
$618$		0			0
$619$	−34.2958	−	28.7776i	−1.37846	−	1.15667i	−0.969776	−	0.243995i	$-0.921542\pi$
$619$	−34.2958	−	28.7776i	−1.37846	−	1.15667i	−0.408688	−	0.912674i	$-0.634014\pi$
$620$	0.861097			0.0345825
$621$		0			0
$622$	7.24860			0.290642
$623$	9.67531	+	8.11855i	0.387633	+	0.325263i
$624$		0			0
$625$	−1.61895	−	9.18150i	−0.0647579	−	0.367260i
$626$	17.6038	+	6.40726i	0.703590	+	0.256086i
$627$		0			0
$628$	−0.301461	+	1.70967i	−0.0120296	+	0.0682232i
$629$	0.638833	−	1.10649i	0.0254719	−	0.0441187i
$630$		0			0
$631$	−15.7058	−	27.2033i	−0.625238	−	1.08294i	−0.988495	−	0.151255i	$-0.951668\pi$
$631$	−15.7058	−	27.2033i	−0.625238	−	1.08294i	0.363256	−	0.931689i	$-0.381665\pi$
$632$	−10.4202	+	3.79265i	−0.414495	+	0.150864i
$633$		0			0
$634$	−17.5533	+	14.7290i	−0.697132	+	0.584963i
$635$	−0.682854	+	0.572983i	−0.0270982	+	0.0227381i
$636$		0			0
$637$	−4.68067	+	1.70362i	−0.185455	+	0.0675000i
$638$	26.9558	+	46.6888i	1.06719	+	1.84843i
$639$		0			0
$640$	11.4392	−	19.8133i	0.452176	−	0.783191i
$641$	−8.44635	+	47.9016i	−0.333611	+	1.89200i	0.106926	+	0.994267i	$0.465899\pi$
$641$	−8.44635	+	47.9016i	−0.333611	+	1.89200i	−0.440537	+	0.897734i	$0.645212\pi$
$642$		0			0
$643$	26.3418	+	9.58763i	1.03882	+	0.378099i	0.804432	−	0.594044i	$-0.202470\pi$
$643$	26.3418	+	9.58763i	1.03882	+	0.378099i	0.234387	+	0.972143i	$0.424692\pi$
$644$	0.382545	+	2.16952i	0.0150744	+	0.0854911i
$645$		0			0
$646$	−3.17072	−	2.66055i	−0.124750	−	0.104678i
$647$	37.5519			1.47632			0.738159	−	0.674627i	$-0.235696\pi$
$647$	37.5519			1.47632			0.738159	+	0.674627i	$0.235696\pi$
$648$		0			0
$649$	−37.5763			−1.47500
$650$	18.1463	+	15.2265i	0.711756	+	0.597234i
$651$		0			0
$652$	1.36099	+	7.71855i	0.0533004	+	0.302282i
$653$	−4.80391	−	1.74848i	−0.187992	−	0.0684234i	0.246309	−	0.969191i	$-0.420782\pi$
$653$	−4.80391	−	1.74848i	−0.187992	−	0.0684234i	−0.434301	+	0.900768i	$0.643004\pi$
$654$		0			0
$655$	−3.32743	+	18.8708i	−0.130013	+	0.737343i
$656$	−11.4933	+	19.9069i	−0.448737	+	0.777236i
$657$		0			0
$658$	27.4126	+	47.4801i	1.06866	+	1.85097i
$659$	32.8948	−	11.9727i	1.28140	−	0.466391i	0.390505	−	0.920601i	$-0.372301\pi$
$659$	32.8948	−	11.9727i	1.28140	−	0.466391i	0.890895	+	0.454210i	$0.150078\pi$
$660$		0			0
$661$	1.02149	−	0.857133i	0.0397314	−	0.0333386i	−0.622706	−	0.782456i	$-0.713967\pi$
$661$	1.02149	−	0.857133i	0.0397314	−	0.0333386i	0.662437	+	0.749118i	$0.269522\pi$
$662$	9.80083	−	8.22387i	0.380920	−	0.319630i
$663$		0			0
$664$	−12.8986	+	4.69471i	−0.500563	+	0.182190i
$665$	−6.26350	−	10.8487i	−0.242888	−	0.420694i
$666$		0			0
$667$	6.63648	−	11.4947i	0.256966	−	0.445077i
$668$	−1.23588	+	7.00905i	−0.0478178	+	0.271188i
$669$		0			0
$670$	−11.5674	−	4.21018i	−0.446886	−	0.162653i
$671$	0.926830	+	5.25631i	0.0357799	+	0.202918i
$672$		0			0
$673$	−2.74208	−	2.30088i	−0.105699	−	0.0886923i	0.588406	−	0.808565i	$-0.299756\pi$
$673$	−2.74208	−	2.30088i	−0.105699	−	0.0886923i	−0.694106	+	0.719873i	$0.744200\pi$
$674$	29.6866			1.14348
$675$		0			0
$676$	16.8438			0.647839
$677$	28.2968	+	23.7439i	1.08754	+	0.912551i	0.996525	−	0.0832991i	$-0.0265457\pi$
$677$	28.2968	+	23.7439i	1.08754	+	0.912551i	0.0910111	+	0.995850i	$0.470990\pi$
$678$		0			0
$679$	4.13866	+	23.4715i	0.158827	+	0.900753i
$680$	−3.66782	−	1.33498i	−0.140654	−	0.0511940i
$681$		0			0
$682$	1.18794	−	6.73713i	0.0454885	−	0.257978i
$683$	19.0083	−	32.9233i	0.727332	−	1.25978i	−0.230675	−	0.973031i	$-0.574093\pi$
$683$	19.0083	−	32.9233i	0.727332	−	1.25978i	0.958007	−	0.286745i	$-0.0925733\pi$
$684$		0			0
$685$	3.54941	+	6.14775i	0.135616	+	0.234894i
$686$	−25.8697	+	9.41580i	−0.987710	+	0.359497i
$687$		0			0
$688$	−35.7401	+	29.9895i	−1.36258	+	1.14334i
$689$	38.6771	−	32.4540i	1.47348	−	1.23640i
$690$		0			0
$691$	−0.517267	+	0.188270i	−0.0196778	+	0.00716212i	−0.351840	−	0.936060i	$-0.614444\pi$
$691$	−0.517267	+	0.188270i	−0.0196778	+	0.00716212i	0.332163	+	0.943222i	$0.392222\pi$
$692$	3.09984	+	5.36908i	0.117838	+	0.204102i
$693$		0			0
$694$	13.9039	−	24.0822i	0.527784	−	0.914148i
$695$	−3.25150	+	18.4402i	−0.123336	+	0.699476i
$696$		0			0
$697$	4.44896	+	1.61929i	0.168516	+	0.0613350i
$698$	4.65654	+	26.4086i	0.176253	+	0.999579i
$699$		0			0
$700$	−2.28330	−	1.91592i	−0.0863006	−	0.0724148i
$701$	−19.0242			−0.718534			−0.359267	−	0.933235i	$-0.616973\pi$
$701$	−19.0242			−0.718534			−0.359267	+	0.933235i	$0.616973\pi$
$702$		0			0
$703$	−3.51328			−0.132506
$704$	−16.4962	−	13.8420i	−0.621724	−	0.521689i
$705$		0			0
$706$	−4.15395	−	23.5582i	−0.156336	−	0.886626i
$707$	20.3859	+	7.41987i	0.766692	+	0.279053i
$708$		0			0
$709$	2.11100	−	11.9721i	0.0792804	−	0.449621i	−0.919165	−	0.393874i	$-0.871135\pi$
$709$	2.11100	−	11.9721i	0.0792804	−	0.449621i	0.998445	−	0.0557476i	$-0.0177542\pi$
$710$	7.44966	−	12.9032i	0.279581	−	0.484248i
$711$		0			0
$712$	−5.41068	−	9.37158i	−0.202774	−	0.351215i
$713$	−1.58269	+	0.576051i	−0.0592721	+	0.0215733i
$714$		0			0
$715$	−36.7022	+	30.7968i	−1.37258	+	1.15173i
$716$	−0.111377	+	0.0934566i	−0.00416236	+	0.00349264i
$717$		0			0
$718$	−3.63530	+	1.32314i	−0.135668	+	0.0493791i
$719$	4.88834	+	8.46685i	0.182304	+	0.315760i	0.942665	−	0.333741i	$-0.108311\pi$
$719$	4.88834	+	8.46685i	0.182304	+	0.315760i	−0.760361	+	0.649501i	$0.774978\pi$
$720$		0			0
$721$	3.01017	−	5.21376i	0.112104	−	0.194171i
$722$	3.23127	−	18.3255i	0.120256	−	0.682003i
$723$		0			0
$724$	−0.655884	−	0.238722i	−0.0243757	−	0.00887205i
$725$	3.11842	+	17.6854i	0.115815	+	0.656821i
$726$		0			0
$727$	3.32075	+	2.78644i	0.123160	+	0.103343i	0.702287	−	0.711894i	$-0.252162\pi$
$727$	3.32075	+	2.78644i	0.123160	+	0.103343i	−0.579128	+	0.815237i	$0.696607\pi$
$728$	45.5067			1.68659
$729$		0			0
$730$	12.0849			0.447283
$731$	7.36129	+	6.17686i	0.272267	+	0.228459i
$732$		0			0
$733$	5.06943	+	28.7501i	0.187244	+	1.06191i	0.923039	+	0.384707i	$0.125697\pi$
$733$	5.06943	+	28.7501i	0.187244	+	1.06191i	−0.735795	+	0.677204i	$0.763191\pi$
$734$	−1.94825	−	0.709106i	−0.0719113	−	0.0261736i
$735$		0			0
$736$	0.762267	−	4.32303i	0.0280975	−	0.159349i
$737$	−9.64391	+	16.7037i	−0.355238	+	0.615290i
$738$		0			0
$739$	−20.7777	−	35.9880i	−0.764319	−	1.32384i	−0.940606	−	0.339501i	$-0.889742\pi$
$739$	−20.7777	−	35.9880i	−0.764319	−	1.32384i	0.176287	−	0.984339i	$-0.443591\pi$
$740$	1.01398	−	0.369060i	0.0372748	−	0.0135669i
$741$		0			0
$742$	−24.6755	+	20.7052i	−0.905867	+	0.760112i
$743$	−16.3760	+	13.7411i	−0.600777	+	0.504112i	−0.891695	−	0.452636i	$-0.850484\pi$
$743$	−16.3760	+	13.7411i	−0.600777	+	0.504112i	0.290918	+	0.956748i	$0.406039\pi$
$744$		0			0
$745$	−30.7218	+	11.1818i	−1.12556	+	0.409670i
$746$	−7.59699	−	13.1584i	−0.278146	−	0.481763i
$747$		0			0
$748$	0.995957	−	1.72505i	0.0364158	−	0.0630740i
$749$	6.07371	−	34.4457i	0.221929	−	1.25862i
$750$		0			0
$751$	37.5573	+	13.6697i	1.37048	+	0.498816i	0.919280	−	0.393605i	$-0.128772\pi$
$751$	37.5573	+	13.6697i	1.37048	+	0.498816i	0.451205	+	0.892420i	$0.350994\pi$
$752$	−10.2896	−	58.3549i	−0.375221	−	2.12799i
$753$		0			0
$754$	68.4067	+	57.4000i	2.49123	+	2.09039i
$755$	−2.08615			−0.0759228
$756$		0			0
$757$	6.68348			0.242915			0.121458	−	0.992597i	$-0.461243\pi$
$757$	6.68348			0.242915			0.121458	+	0.992597i	$0.461243\pi$
$758$	10.3539	+	8.68795i	0.376070	+	0.315561i
$759$		0			0
$760$	1.86375	+	10.5699i	0.0676054	+	0.383410i
$761$	39.4906	+	14.3734i	1.43153	+	0.521035i	0.937370	−	0.348334i	$-0.113253\pi$
$761$	39.4906	+	14.3734i	1.43153	+	0.521035i	0.494163	+	0.869369i	$0.335475\pi$
$762$		0			0
$763$	−5.89469	+	33.4304i	−0.213402	+	1.21026i
$764$	5.06692	−	8.77617i	0.183315	−	0.317511i
$765$		0			0
$766$	−26.5445	−	45.9764i	−0.959092	−	1.66120i
$767$	−58.4875	+	21.2877i	−2.11186	+	0.768655i
$768$		0			0
$769$	1.84864	−	1.55120i	0.0666638	−	0.0559375i	−0.608847	−	0.793288i	$-0.708368\pi$
$769$	1.84864	−	1.55120i	0.0666638	−	0.0559375i	0.675511	+	0.737350i	$0.263923\pi$
$770$	23.4155	−	19.6480i	0.843837	−	0.708064i
$771$		0			0
$772$	9.67593	−	3.52175i	0.348244	−	0.126751i
$773$	0.698900	+	1.21053i	0.0251377	+	0.0435398i	0.878321	−	0.478072i	$-0.158664\pi$
$773$	0.698900	+	1.21053i	0.0251377	+	0.0435398i	−0.853183	+	0.521612i	$0.825331\pi$
$774$		0			0
$775$	1.13940	−	1.97350i	0.0409284	−	0.0708901i
$776$	3.54593	−	20.1100i	0.127292	−	0.721907i
$777$		0			0
$778$	22.1800	+	8.07285i	0.795190	+	0.289426i
$779$	−2.26068	−	12.8210i	−0.0809973	−	0.459358i
$780$		0			0
$781$	−17.8836	−	15.0061i	−0.639925	−	0.536961i
$782$	−2.48653			−0.0889181
$783$		0			0
$784$	−3.43462			−0.122665
$785$	−4.54295	−	3.81199i	−0.162145	−	0.136056i
$786$		0			0
$787$	−6.88542	−	39.0491i	−0.245439	−	1.39195i	−0.819472	−	0.573119i	$-0.805733\pi$
$787$	−6.88542	−	39.0491i	−0.245439	−	1.39195i	0.574033	−	0.818832i	$-0.305378\pi$
$788$	−4.43083	−	1.61269i	−0.157842	−	0.0574497i
$789$		0			0
$790$	−2.14239	+	12.1501i	−0.0762230	+	0.432282i
$791$	−0.626496	+	1.08512i	−0.0222756	+	0.0385825i
$792$		0			0
$793$	4.42041	+	7.65637i	0.156973	+	0.271886i
$794$	−24.8865	+	9.05795i	−0.883190	+	0.321455i
$795$		0			0
$796$	−4.02438	+	3.37686i	−0.142640	+	0.119689i
$797$	2.52325	−	2.11726i	0.0893781	−	0.0749971i	−0.597004	−	0.802238i	$-0.703642\pi$
$797$	2.52325	−	2.11726i	0.0893781	−	0.0749971i	0.686382	+	0.727241i	$0.259198\pi$
$798$		0			0
$799$	−11.4686	+	4.17423i	−0.405730	+	0.147674i
$800$	2.96964	+	5.14356i	0.104993	+	0.181852i
$801$		0			0
$802$	−10.3593	+	17.9428i	−0.365800	+	0.633583i
$803$	3.28813	−	18.6479i	0.116035	−	0.658070i
$804$		0			0
$805$	−7.07167	−	2.57388i	−0.249244	−	0.0907172i
$806$	−1.96769	−	11.1593i	−0.0693089	−	0.393070i
$807$		0			0
$808$	−14.2387	−	11.9477i	−0.500915	−	0.420318i
$809$	6.54436			0.230087			0.115044	−	0.993360i	$-0.463299\pi$
$809$	6.54436			0.230087			0.115044	+	0.993360i	$0.463299\pi$
$810$		0			0
$811$	−44.7516			−1.57144			−0.785721	−	0.618581i	$-0.787708\pi$
$811$	−44.7516			−1.57144			−0.785721	+	0.618581i	$0.787708\pi$
$812$	−8.60744	−	7.22250i	−0.302062	−	0.253460i
$813$		0			0
$814$	−1.48863	−	8.44244i	−0.0521764	−	0.295907i
$815$	−25.1590	−	9.15714i	−0.881282	−	0.320760i
$816$		0			0
$817$	4.58845	−	26.0224i	0.160530	−	0.910409i
$818$	20.0856	−	34.7893i	0.702276	−	1.21638i
$819$		0			0
$820$	1.99927	+	3.46283i	0.0698174	+	0.120927i
$821$	−46.6876	+	16.9929i	−1.62941	+	0.593057i	−0.985142	−	0.171743i	$-0.945060\pi$
$821$	−46.6876	+	16.9929i	−1.62941	+	0.593057i	−0.644268	+	0.764800i	$0.722838\pi$
$822$		0			0
$823$	8.13586	−	6.82680i	0.283598	−	0.237967i	−0.489880	−	0.871790i	$-0.662959\pi$
$823$	8.13586	−	6.82680i	0.283598	−	0.237967i	0.773479	+	0.633822i	$0.218515\pi$
$824$	−3.95135	+	3.31558i	−0.137652	+	0.115504i
$825$		0			0
$826$	37.3143	−	13.5813i	1.29833	−	0.472554i
$827$	−8.20039	−	14.2035i	−0.285156	−	0.493904i	0.687491	−	0.726193i	$-0.258712\pi$
$827$	−8.20039	−	14.2035i	−0.285156	−	0.493904i	−0.972647	+	0.232289i	$0.925379\pi$
$828$		0			0
$829$	1.47823	−	2.56036i	0.0513409	−	0.0889251i	−0.839213	−	0.543803i	$-0.816984\pi$
$829$	1.47823	−	2.56036i	0.0513409	−	0.0889251i	0.890554	+	0.454878i	$0.150317\pi$
$830$	−2.65195	+	15.0400i	−0.0920505	+	0.522044i
$831$		0			0
$832$	−33.5181	−	12.1996i	−1.16203	−	0.422944i
$833$	0.122842	+	0.696674i	0.00425624	+	0.0241383i
$834$		0			0
$835$	−18.6245	−	15.6278i	−0.644528	−	0.540823i
$836$	−5.47730			−0.189436
$837$		0			0
$838$	−19.9985			−0.690835
$839$	24.8554	+	20.8562i	0.858104	+	0.720035i	0.961559	−	0.274599i	$-0.0885452\pi$
$839$	24.8554	+	20.8562i	0.858104	+	0.720035i	−0.103455	+	0.994634i	$0.532990\pi$
$840$		0			0
$841$	6.71983	+	38.1100i	0.231718	+	1.31414i
$842$	−26.2191	−	9.54299i	−0.903572	−	0.328873i
$843$		0			0
$844$	−1.28414	+	7.28274i	−0.0442020	+	0.250682i
$845$	−28.7696	+	49.8304i	−0.989705	+	1.71422i
$846$		0			0
$847$	−8.66114	−	15.0015i	−0.297600	−	0.515459i
$848$	32.7147	−	11.9072i	1.12343	−	0.408895i
$849$		0			0
$850$	2.57717	−	2.16251i	0.0883964	−	0.0741734i
$851$	−1.61680	+	1.35666i	−0.0554232	+	0.0465056i
$852$		0			0
$853$	−26.6244	+	9.69049i	−0.911602	+	0.331796i	−0.754892	−	0.655849i	$-0.772311\pi$
$853$	−26.6244	+	9.69049i	−0.911602	+	0.331796i	−0.156710	+	0.987645i	$0.550089\pi$
$854$	−2.82017	−	4.88467i	−0.0965041	−	0.167150i
$855$		0			0
$856$	−14.9839	+	25.9529i	−0.512140	+	0.887052i
$857$	−2.43168	+	13.7907i	−0.0830644	+	0.471082i	0.914693	+	0.404149i	$0.132432\pi$
$857$	−2.43168	+	13.7907i	−0.0830644	+	0.471082i	−0.997757	+	0.0669326i	$0.978679\pi$
$858$		0			0
$859$	2.02952	+	0.738685i	0.0692464	+	0.0252036i	0.376411	−	0.926453i	$-0.377158\pi$
$859$	2.02952	+	0.738685i	0.0692464	+	0.0252036i	−0.307165	+	0.951656i	$0.599380\pi$
$860$	1.40928	+	7.99244i	0.0480562	+	0.272540i
$861$		0			0
$862$	18.9802	+	15.9262i	0.646467	+	0.542450i
$863$	14.9487			0.508859			0.254430	−	0.967091i	$-0.418112\pi$
$863$	14.9487			0.508859			0.254430	+	0.967091i	$0.418112\pi$
$864$		0			0
$865$	−21.1784			−0.720087
$866$	15.2663	+	12.8099i	0.518769	+	0.435299i
$867$		0			0
$868$	0.247589	+	1.40415i	0.00840373	+	0.0476599i
$869$	18.1656	+	6.61173i	0.616225	+	0.224288i
$870$		0			0
$871$	−5.54774	+	31.4628i	−0.187978	+	1.06608i
$872$	14.5423	−	25.1879i	0.492463	−	0.852971i
$873$		0			0
$874$	3.41869	+	5.92134i	0.115639	+	0.200292i
$875$	31.4865	−	11.4601i	1.06444	−	0.387424i
$876$		0			0
$877$	−1.44559	+	1.21299i	−0.0488140	+	0.0409598i	−0.666868	−	0.745176i	$-0.732366\pi$
$877$	−1.44559	+	1.21299i	−0.0488140	+	0.0409598i	0.618054	+	0.786135i	$0.287921\pi$
$878$	−32.5702	+	27.3296i	−1.09919	+	0.922330i
$879$		0			0
$880$	−31.0443	+	11.2992i	−1.04650	+	0.380895i
$881$	23.4129	+	40.5523i	0.788800	+	1.36624i	0.926702	+	0.375796i	$0.122631\pi$
$881$	23.4129	+	40.5523i	0.788800	+	1.36624i	−0.137902	+	0.990446i	$0.544036\pi$
$882$		0			0
$883$	15.0317	−	26.0357i	0.505858	−	0.876172i	−0.494119	−	0.869394i	$-0.664509\pi$
$883$	15.0317	−	26.0357i	0.505858	−	0.876172i	0.999977	−	0.00677750i	$-0.00215736\pi$
$884$	0.572933	−	3.24926i	0.0192698	−	0.109285i
$885$		0			0
$886$	−51.5089	−	18.7477i	−1.73048	−	0.629842i
$887$	5.19449	+	29.4594i	0.174414	+	0.989150i	0.938818	+	0.344413i	$0.111922\pi$
$887$	5.19449	+	29.4594i	0.174414	+	0.989150i	−0.764404	+	0.644737i	$0.776967\pi$
$888$		0			0
$889$	−1.13067	−	0.948748i	−0.0379216	−	0.0318200i
$890$	−12.0398			−0.403576
$891$		0			0
$892$	−6.03788			−0.202163
$893$	25.7084	+	21.5719i	0.860299	+	0.721877i
$894$		0			0
$895$	−0.0862455	−	0.489122i	−0.00288287	−	0.0163496i
$896$	35.5977	+	12.9565i	1.18924	+	0.432847i
$897$		0			0
$898$	−5.68624	+	32.2483i	−0.189752	+	1.07614i
$899$	4.29524	−	7.43957i	0.143254	−	0.248123i
$900$		0			0
$901$	−3.58531	−	6.20994i	−0.119444	−	0.206883i
$902$	29.8509	−	10.8648i	0.993927	−	0.361760i
$903$		0			0
$904$	0.822382	−	0.690060i	0.0273520	−	0.0229511i
$905$	1.82650	−	1.53261i	0.0607148	−	0.0509458i
$906$		0			0
$907$	−25.1511	+	9.15425i	−0.835129	+	0.303962i	−0.723962	−	0.689840i	$-0.757681\pi$
$907$	−25.1511	+	9.15425i	−0.835129	+	0.303962i	−0.111167	+	0.993802i	$0.535459\pi$
$908$	0.921928	+	1.59683i	0.0305953	+	0.0529926i
$909$		0			0
$910$	25.3153	−	43.8474i	0.839194	−	1.45353i
$911$	−0.0766027	+	0.434435i	−0.00253796	+	0.0143935i	−0.986050	−	0.166447i	$-0.946771\pi$
$911$	−0.0766027	+	0.434435i	−0.00253796	+	0.0143935i	0.983512	+	0.180840i	$0.0578817\pi$
$912$		0			0
$913$	22.4862	+	8.18429i	0.744183	+	0.270861i
$914$	1.97555	+	11.2039i	0.0653453	+	0.370591i
$915$		0			0
$916$	−7.00202	−	5.87539i	−0.231353	−	0.194128i
$917$	−31.7284			−1.04776
$918$		0			0
$919$	49.0749			1.61883			0.809416	−	0.587236i	$-0.199784\pi$
$919$	49.0749			1.61883			0.809416	+	0.587236i	$0.199784\pi$
$920$	4.93925	+	4.14452i	0.162842	+	0.136641i
$921$		0			0
$922$	6.33877	+	35.9489i	0.208756	+	1.18391i
$923$	−36.3370	−	13.2256i	−1.19605	−	0.435326i
$924$		0			0
$925$	0.495871	−	2.81223i	0.0163041	−	0.0924654i
$926$	3.92694	−	6.80167i	0.129047	−	0.223517i
$927$		0			0
$928$	11.1948	+	19.3899i	0.367486	+	0.636504i
$929$	30.4754	−	11.0921i	0.999865	−	0.363921i	0.210333	−	0.977630i	$-0.432545\pi$
$929$	30.4754	−	11.0921i	0.999865	−	0.363921i	0.789533	+	0.613709i	$0.210323\pi$
$930$		0			0
$931$	1.49014	−	1.25038i	0.0488375	−	0.0409795i
$932$	−0.205435	+	0.172380i	−0.00672924	+	0.00564651i
$933$		0			0
$934$	18.5125	−	6.73802i	0.605749	−	0.220475i
$935$	3.40224	+	5.89284i	0.111265	+	0.192717i
$936$		0			0
$937$	−24.3079	+	42.1025i	−0.794103	+	1.37543i	0.129303	+	0.991605i	$0.458726\pi$
$937$	−24.3079	+	42.1025i	−0.794103	+	1.37543i	−0.923407	+	0.383822i	$0.874607\pi$
$938$	3.53939	−	20.0729i	0.115565	−	0.655402i
$939$		0			0
$940$	−9.68588	−	3.52537i	−0.315918	−	0.114985i
$941$	0.123366	+	0.699641i	0.00402160	+	0.0228076i	0.986753	−	0.162233i	$-0.0518695\pi$
$941$	0.123366	+	0.699641i	0.00402160	+	0.0228076i	−0.982731	+	0.185040i	$0.940758\pi$
$942$		0			0
$943$	−5.99117	−	5.02719i	−0.195099	−	0.163708i
$944$	−42.9175			−1.39685
$945$		0			0
$946$	64.4762			2.09630
$947$	−19.9997	−	16.7817i	−0.649902	−	0.545333i	0.257139	−	0.966374i	$-0.417220\pi$
$947$	−19.9997	−	16.7817i	−0.649902	−	0.545333i	−0.907041	+	0.421042i	$0.861665\pi$
$948$		0			0
$949$	−5.44642	−	30.8882i	−0.176798	−	1.00267i
$950$	−8.69304	−	3.16401i	−0.282039	−	0.102654i
$951$		0			0
$952$	1.12228	−	6.36477i	0.0363733	−	0.206284i
$953$	−25.5027	+	44.1720i	−0.826114	+	1.43087i	0.0749515	+	0.997187i	$0.476120\pi$
$953$	−25.5027	+	44.1720i	−0.826114	+	1.43087i	−0.901065	+	0.433684i	$0.857214\pi$
$954$		0			0
$955$	17.3088	+	29.9798i	0.560101	+	0.970123i
$956$	−9.27829	+	3.37702i	−0.300081	+	0.109221i
$957$		0			0
$958$	34.4254	−	28.8863i	1.11223	−	0.933275i
$959$	−9.00428	+	7.55549i	−0.290763	+	0.243979i
$960$		0			0
$961$	28.1061	−	10.2298i	0.906649	−	0.329993i
$962$	−7.09985	−	12.2973i	−0.228908	−	0.396481i
$963$		0			0
$964$	−3.75677	+	6.50691i	−0.120997	+	0.209573i
$965$	−6.10802	+	34.6403i	−0.196624	+	1.11511i
$966$		0			0
$967$	−9.40146	−	3.42185i	−0.302330	−	0.110039i	0.186401	−	0.982474i	$-0.440318\pi$
$967$	−9.40146	−	3.42185i	−0.302330	−	0.110039i	−0.488731	+	0.872435i	$0.662540\pi$
$968$	2.57719	+	14.6160i	0.0828340	+	0.469775i
$969$		0			0
$970$	−17.4041	−	14.6038i	−0.558812	−	0.468899i
$971$	−44.6269			−1.43215			−0.716073	−	0.698025i	$-0.754062\pi$
$971$	−44.6269			−1.43215			−0.716073	+	0.698025i	$0.754062\pi$
$972$		0			0
$973$	−31.0044			−0.993954
$974$	−35.8918	−	30.1168i	−1.15005	−	0.965006i
$975$		0			0
$976$	1.05857	+	6.00346i	0.0338840	+	0.192166i
$977$	−36.7285	−	13.3681i	−1.17505	−	0.427683i	−0.320598	−	0.947215i	$-0.603884\pi$
$977$	−36.7285	−	13.3681i	−1.17505	−	0.427683i	−0.854451	+	0.519533i	$0.826106\pi$
$978$		0			0
$979$	−3.27585	+	18.5783i	−0.104697	+	0.593765i
$980$	−0.298728	+	0.517412i	−0.00954252	+	0.0165281i
$981$		0			0
$982$	−9.79001	−	16.9568i	−0.312412	−	0.541113i
$983$	6.38482	−	2.32389i	0.203644	−	0.0741204i	−0.238184	−	0.971220i	$-0.576552\pi$
$983$	6.38482	−	2.32389i	0.203644	−	0.0741204i	0.441828	+	0.897100i	$0.354330\pi$
$984$		0			0
$985$	12.3389	−	10.3536i	0.393151	−	0.329892i
$986$	9.71527	−	8.15208i	0.309397	−	0.259615i
$987$		0			0
$988$	−8.52541	+	3.10300i	−0.271229	+	0.0987194i
$989$	−7.93698	−	13.7473i	−0.252381	−	0.437137i
$990$		0			0
$991$	−8.60230	+	14.8996i	−0.273261	+	0.473302i	−0.969695	−	0.244319i	$-0.921436\pi$
$991$	−8.60230	+	14.8996i	−0.273261	+	0.473302i	0.696434	+	0.717621i	$0.254769\pi$
$992$	0.493351	−	2.79793i	0.0156639	−	0.0888345i
$993$		0			0
$994$	23.1826	+	8.43776i	0.735306	+	0.267630i
$995$	−3.11630	−	17.6734i	−0.0987933	−	0.560284i
$996$		0			0
$997$	5.61793	+	4.71400i	0.177922	+	0.149294i	0.727399	−	0.686214i	$-0.240729\pi$
$997$	5.61793	+	4.71400i	0.177922	+	0.149294i	−0.549478	+	0.835508i	$0.685173\pi$
$998$	3.59848			0.113908
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.e.s.406.1		12
3.2	odd	2		729.2.e.l.406.2		12
9.2	odd	6		729.2.e.k.649.2		12
9.4	even	3		729.2.e.j.163.2		12
9.5	odd	6		729.2.e.u.163.1		12
9.7	even	3		729.2.e.t.649.1		12
27.2	odd	18		729.2.c.a.244.3		12
27.4	even	9		729.2.e.t.82.1		12
27.5	odd	18		729.2.e.l.325.2		12
27.7	even	9		729.2.a.b.1.3	✓	6
27.11	odd	18		729.2.c.a.487.3		12
27.13	even	9		729.2.e.j.568.2		12
27.14	odd	18		729.2.e.u.568.1		12
27.16	even	9		729.2.c.d.487.4		12
27.20	odd	18		729.2.a.e.1.4	yes	6
27.22	even	9	inner	729.2.e.s.325.1		12
27.23	odd	18		729.2.e.k.82.2		12
27.25	even	9		729.2.c.d.244.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
729.2.a.b.1.3	✓	6	27.7	even	9
729.2.a.e.1.4	yes	6	27.20	odd	18
729.2.c.a.244.3		12	27.2	odd	18
729.2.c.a.487.3		12	27.11	odd	18
729.2.c.d.244.4		12	27.25	even	9
729.2.c.d.487.4		12	27.16	even	9
729.2.e.j.163.2		12	9.4	even	3
729.2.e.j.568.2		12	27.13	even	9
729.2.e.k.82.2		12	27.23	odd	18
729.2.e.k.649.2		12	9.2	odd	6
729.2.e.l.325.2		12	27.5	odd	18
729.2.e.l.406.2		12	3.2	odd	2
729.2.e.s.325.1		12	27.22	even	9	inner
729.2.e.s.406.1		12	1.1	even	1	trivial
729.2.e.t.82.1		12	27.4	even	9
729.2.e.t.649.1		12	9.7	even	3
729.2.e.u.163.1		12	9.5	odd	6
729.2.e.u.568.1		12	27.14	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20913 - 1.01458i) q^{2} +(0.0853237 + 0.483895i) q^{4} +(-1.57728 - 0.574083i) q^{5} +(0.482617 - 2.73706i) q^{7} +(-1.19062 + 2.06222i) q^{8} +(1.32468 + 2.29442i) q^{10} +(3.90087 - 1.41980i) q^{11} +(5.26736 - 4.41984i) q^{13} +(-3.36051 + 2.81980i) q^{14} +(4.45535 - 1.62162i) q^{16} +(-0.488276 - 0.845718i) q^{17} +(-1.34264 + 2.32553i) q^{19} +(0.143217 - 0.812221i) q^{20} +(-6.15715 - 2.24102i) q^{22} +(0.280124 + 1.58866i) q^{23} +(-1.67198 - 1.40296i) q^{25} -10.8532 q^{26} +1.36563 q^{28} +(-6.30292 - 5.28878i) q^{29} +(0.181301 + 1.02821i) q^{31} +(-2.55707 - 0.930697i) q^{32} +(-0.267660 + 1.51798i) q^{34} +(-2.33252 + 4.04005i) q^{35} +(0.654172 + 1.13306i) q^{37} +(3.98286 - 1.44964i) q^{38} +(3.06183 - 2.56918i) q^{40} +(-3.71391 + 3.11634i) q^{41} +(-9.24679 + 3.36556i) q^{43} +(1.01987 + 1.76647i) q^{44} +(1.27312 - 2.20510i) q^{46} +(2.17020 - 12.3078i) q^{47} +(-0.680721 - 0.247762i) q^{49} +(0.598226 + 3.39271i) q^{50} +(2.58817 + 2.17173i) q^{52} +7.34280 q^{53} -6.96786 q^{55} +(5.06980 + 4.25406i) q^{56} +(2.25515 + 12.7896i) q^{58} +(-8.50598 - 3.09592i) q^{59} +(-0.223267 + 1.26621i) q^{61} +(0.823982 - 1.42718i) q^{62} +(-2.59373 - 4.49247i) q^{64} +(-10.8455 + 3.94742i) q^{65} +(-3.55927 + 2.98658i) q^{67} +(0.367577 - 0.308434i) q^{68} +(6.91926 - 2.51841i) q^{70} +(-2.81187 - 4.87030i) q^{71} +(2.28072 - 3.95033i) q^{73} +(0.358600 - 2.03372i) q^{74} +(-1.23987 - 0.451276i) q^{76} +(-2.00345 - 11.3621i) q^{77} +(3.56732 + 2.99333i) q^{79} -7.95828 q^{80} +7.65237 q^{82} +(4.41578 + 3.70528i) q^{83} +(0.284635 + 1.61425i) q^{85} +(14.5952 + 5.31221i) q^{86} +(-1.71652 + 9.73490i) q^{88} +(-2.27221 + 3.93558i) q^{89} +(-9.55523 - 16.5502i) q^{91} +(-0.744844 + 0.271101i) q^{92} +(-15.1113 + 12.6799i) q^{94} +(3.45278 - 2.89722i) q^{95} +(-8.05828 + 2.93297i) q^{97} +(0.571704 + 0.990221i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 12 q^{5} - 3 q^{7} + 6 q^{8} - 6 q^{10} + 3 q^{11} + 6 q^{13} + 6 q^{14} + 27 q^{16} - 9 q^{17} - 12 q^{19} - 39 q^{20} - 39 q^{22} - 21 q^{23} + 6 q^{25} - 48 q^{26} + 6 q^{28}+ \cdots + 18 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 12 * q^5 - 3 * q^7 + 6 * q^8 - 6 * q^10 + 3 * q^11 + 6 * q^13 + 6 * q^14 + 27 * q^16 - 9 * q^17 - 12 * q^19 - 39 * q^20 - 39 * q^22 - 21 * q^23 + 6 * q^25 - 48 * q^26 + 6 * q^28 - 6 * q^29 + 6 * q^31 - 27 * q^32 - 18 * q^34 + 30 * q^35 - 3 * q^37 - 3 * q^38 + 33 * q^40 + 15 * q^41 - 30 * q^43 - 33 * q^44 + 3 * q^46 + 21 * q^47 - 3 * q^49 - 6 * q^50 + 18 * q^53 + 30 * q^55 - 15 * q^56 - 3 * q^58 - 30 * q^59 - 30 * q^61 - 30 * q^62 - 6 * q^64 + 12 * q^65 - 39 * q^67 - 18 * q^68 + 51 * q^70 - 12 * q^73 - 57 * q^74 + 57 * q^76 + 24 * q^77 + 15 * q^79 + 42 * q^80 - 42 * q^82 + 21 * q^83 + 54 * q^85 + 60 * q^86 + 12 * q^88 - 9 * q^89 - 18 * q^91 + 15 * q^92 + 33 * q^94 - 42 * q^95 - 12 * q^97 + 18 * q^98

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