LMFDB - Embedded newform 729.2.g.c.379.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,9,0,9,9,0,9,-18,0,-18,9,0,9,9,0,9,-18,0,-18,-63] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			379.7
Character	$\chi$	$=$	729.379
Dual form			729.2.g.c.352.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.579169 + 1.93456i) q^{2} +(-1.73611 + 1.14185i) q^{4} +(-1.09641 - 2.54176i) q^{5} +(0.0355426 - 0.610243i) q^{7} +(-0.120591 - 0.101188i) q^{8} +(4.28217 - 3.59317i) q^{10} +(-2.23626 - 3.00382i) q^{11} +(-2.34689 - 2.48756i) q^{13} +(1.20114 - 0.284675i) q^{14} +(-1.52016 + 3.52413i) q^{16} +(-1.31516 - 7.45862i) q^{17} +(0.132568 - 0.751830i) q^{19} +(4.80579 + 3.16082i) q^{20} +(4.51590 - 6.06590i) q^{22} +(-0.126403 - 2.17026i) q^{23} +(-1.82720 + 1.93672i) q^{25} +(3.45308 - 5.98091i) q^{26} +(0.635103 + 1.10003i) q^{28} +(-4.42027 - 1.04762i) q^{29} +(7.31490 + 3.67368i) q^{31} +(-8.01077 - 0.936325i) q^{32} +(13.6674 - 6.86404i) q^{34} +(-1.59006 + 0.578734i) q^{35} +(3.96908 + 1.44463i) q^{37} +(1.53124 - 0.178976i) q^{38} +(-0.124978 + 0.417456i) q^{40} +(-2.59329 + 8.66219i) q^{41} +(-1.74287 + 0.203712i) q^{43} +(7.31231 + 2.66146i) q^{44} +(4.12528 - 1.50148i) q^{46} +(10.5125 - 5.27956i) q^{47} +(6.58154 + 0.769271i) q^{49} +(-4.80497 - 2.41314i) q^{50} +(6.91487 + 1.63886i) q^{52} +(-2.80062 - 4.85082i) q^{53} +(-5.18313 + 8.97744i) q^{55} +(-0.0660353 + 0.0699933i) q^{56} +(-0.533395 - 9.15803i) q^{58} +(0.903619 - 1.21377i) q^{59} +(-2.52614 - 1.66147i) q^{61} +(-2.87039 + 16.2788i) q^{62} +(-1.49529 - 8.48019i) q^{64} +(-3.74962 + 8.69259i) q^{65} +(-7.44589 + 1.76471i) q^{67} +(10.7999 + 11.4472i) q^{68} +(-2.04051 - 2.74088i) q^{70} +(-5.19850 + 4.36206i) q^{71} +(0.438511 + 0.367955i) q^{73} +(-0.495949 + 8.51511i) q^{74} +(0.628329 + 1.45663i) q^{76} +(-1.91254 + 1.25790i) q^{77} +(-2.64293 - 8.82799i) q^{79} +10.6242 q^{80} -18.2595 q^{82} +(1.77486 + 5.92845i) q^{83} +(-17.5160 + 11.5205i) q^{85} +(-1.40351 - 3.25370i) q^{86} +(-0.0342772 + 0.588516i) q^{88} +(-3.52742 - 2.95986i) q^{89} +(-1.60143 + 1.34376i) q^{91} +(2.69757 + 3.62346i) q^{92} +(16.3021 + 17.2792i) q^{94} +(-2.05632 + 0.487356i) q^{95} +(-4.16552 + 9.65675i) q^{97} +(2.32362 + 13.1779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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 $

$2$	0.579169	+	1.93456i	0.409534	+	1.36794i	0.875535	+	0.483155i	$0.160509\pi$
$2$	0.579169	+	1.93456i	0.409534	+	1.36794i	−0.466001	+	0.884784i	$0.654306\pi$
$3$		0			0
$3$		0			0
$4$	−1.73611	+	1.14185i	−0.868053	+	0.570927i
$5$	−1.09641	−	2.54176i	−0.490328	−	1.13671i	−0.966340	−	0.257269i	$-0.917177\pi$
$5$	−1.09641	−	2.54176i	−0.490328	−	1.13671i	0.476012	−	0.879439i	$-0.342082\pi$
$6$		0			0
$7$	0.0355426	−	0.610243i	0.0134338	−	0.230650i	−0.984908	−	0.173081i	$-0.944628\pi$
$7$	0.0355426	−	0.610243i	0.0134338	−	0.230650i	0.998341	−	0.0575696i	$-0.0183351\pi$
$8$	−0.120591	−	0.101188i	−0.0426353	−	0.0357753i
$9$		0			0
$10$	4.28217	−	3.59317i	1.35414	−	1.13626i
$11$	−2.23626	−	3.00382i	−0.674258	−	0.905686i	0.324939	−	0.945735i	$-0.394656\pi$
$11$	−2.23626	−	3.00382i	−0.674258	−	0.905686i	−0.999198	+	0.0400487i	$0.987249\pi$
$12$		0			0
$13$	−2.34689	−	2.48756i	−0.650910	−	0.689924i	0.314915	−	0.949120i	$-0.398024\pi$
$13$	−2.34689	−	2.48756i	−0.650910	−	0.689924i	−0.965825	+	0.259196i	$0.916542\pi$
$14$	1.20114	−	0.284675i	0.321017	−	0.0760825i
$15$		0			0
$16$	−1.52016	+	3.52413i	−0.380040	+	0.881032i
$17$	−1.31516	−	7.45862i	−0.318972	−	1.80898i	−0.549030	−	0.835803i	$-0.685003\pi$
$17$	−1.31516	−	7.45862i	−0.318972	−	1.80898i	0.230058	−	0.973177i	$-0.426109\pi$
$18$		0			0
$19$	0.132568	−	0.751830i	0.0304132	−	0.172482i	−0.965818	−	0.259222i	$-0.916534\pi$
$19$	0.132568	−	0.751830i	0.0304132	−	0.172482i	0.996231	+	0.0867403i	$0.0276450\pi$
$20$	4.80579	+	3.16082i	1.07461	+	0.706781i
$21$		0			0
$22$	4.51590	−	6.06590i	0.962792	−	1.29325i
$23$	−0.126403	−	2.17026i	−0.0263569	−	0.452530i	−0.985507	−	0.169633i	$-0.945742\pi$
$23$	−0.126403	−	2.17026i	−0.0263569	−	0.452530i	0.959150	−	0.282897i	$-0.0912954\pi$
$24$		0			0
$25$	−1.82720	+	1.93672i	−0.365441	+	0.387345i
$26$	3.45308	−	5.98091i	0.677205	−	1.17295i
$27$		0			0
$28$	0.635103	+	1.10003i	0.120023	+	0.207886i
$29$	−4.42027	−	1.04762i	−0.820824	−	0.194539i	−0.201313	−	0.979527i	$-0.564521\pi$
$29$	−4.42027	−	1.04762i	−0.820824	−	0.194539i	−0.619511	+	0.784988i	$0.712669\pi$
$30$		0			0
$31$	7.31490	+	3.67368i	1.31379	+	0.659812i	0.961171	−	0.275953i	$-0.0889934\pi$
$31$	7.31490	+	3.67368i	1.31379	+	0.659812i	0.352623	+	0.935765i	$0.385290\pi$
$32$	−8.01077	−	0.936325i	−1.41612	−	0.165520i
$33$		0			0
$34$	13.6674	−	6.86404i	2.34395	−	1.17717i
$35$	−1.59006	+	0.578734i	−0.268769	+	0.0978239i
$36$		0			0
$37$	3.96908	+	1.44463i	0.652513	+	0.237495i	0.647001	−	0.762489i	$-0.276023\pi$
$37$	3.96908	+	1.44463i	0.652513	+	0.237495i	0.00551256	+	0.999985i	$0.498245\pi$
$38$	1.53124	−	0.178976i	0.248400	−	0.0290338i
$39$		0			0
$40$	−0.124978	+	0.417456i	−0.0197608	+	0.0660055i
$41$	−2.59329	+	8.66219i	−0.405004	+	1.35281i	0.475895	+	0.879502i	$0.342124\pi$
$41$	−2.59329	+	8.66219i	−0.405004	+	1.35281i	−0.880899	+	0.473304i	$0.843061\pi$
$42$		0			0
$43$	−1.74287	+	0.203712i	−0.265785	+	0.0310658i	−0.247942	−	0.968775i	$-0.579754\pi$
$43$	−1.74287	+	0.203712i	−0.265785	+	0.0310658i	−0.0178433	+	0.999841i	$0.505680\pi$
$44$	7.31231	+	2.66146i	1.10237	+	0.401231i
$45$		0			0
$46$	4.12528	−	1.50148i	0.608240	−	0.221381i
$47$	10.5125	−	5.27956i	1.53340	−	0.770103i	0.536144	−	0.844126i	$-0.319880\pi$
$47$	10.5125	−	5.27956i	1.53340	−	0.770103i	0.997256	+	0.0740235i	$0.0235840\pi$
$48$		0			0
$49$	6.58154	+	0.769271i	0.940219	+	0.109896i
$50$	−4.80497	−	2.41314i	−0.679525	−	0.341270i
$51$		0			0
$52$	6.91487	+	1.63886i	0.958920	+	0.227268i
$53$	−2.80062	−	4.85082i	−0.384695	−	0.666312i	0.607032	−	0.794678i	$-0.292360\pi$
$53$	−2.80062	−	4.85082i	−0.384695	−	0.666312i	−0.991727	+	0.128366i	$0.959027\pi$
$54$		0			0
$55$	−5.18313	+	8.97744i	−0.698893	+	1.21052i
$56$	−0.0660353	+	0.0699933i	−0.00882434	+	0.00935325i
$57$		0			0
$58$	−0.533395	−	9.15803i	−0.0700381	−	1.20251i
$59$	0.903619	−	1.21377i	0.117641	−	0.158020i	−0.739402	−	0.673264i	$-0.764892\pi$
$59$	0.903619	−	1.21377i	0.117641	−	0.158020i	0.857043	+	0.515245i	$0.172299\pi$
$60$		0			0
$61$	−2.52614	−	1.66147i	−0.323439	−	0.212729i	0.377397	−	0.926052i	$-0.376819\pi$
$61$	−2.52614	−	1.66147i	−0.323439	−	0.212729i	−0.700836	+	0.713322i	$0.747190\pi$
$62$	−2.87039	+	16.2788i	−0.364540	+	2.06741i
$63$		0			0
$64$	−1.49529	−	8.48019i	−0.186911	−	1.06002i
$65$	−3.74962	+	8.69259i	−0.465083	+	1.07818i
$66$		0			0
$67$	−7.44589	+	1.76471i	−0.909660	+	0.215593i	−0.658701	−	0.752405i	$-0.728894\pi$
$67$	−7.44589	+	1.76471i	−0.909660	+	0.215593i	−0.250958	+	0.967998i	$0.580746\pi$
$68$	10.7999	+	11.4472i	1.30968	+	1.38818i
$69$		0			0
$70$	−2.04051	−	2.74088i	−0.243887	−	0.327597i
$71$	−5.19850	+	4.36206i	−0.616948	+	0.517681i	−0.896843	−	0.442350i	$-0.854145\pi$
$71$	−5.19850	+	4.36206i	−0.616948	+	0.517681i	0.279895	+	0.960031i	$0.409701\pi$
$72$		0			0
$73$	0.438511	+	0.367955i	0.0513238	+	0.0430658i	0.668089	−	0.744082i	$-0.267113\pi$
$73$	0.438511	+	0.367955i	0.0513238	+	0.0430658i	−0.616765	+	0.787147i	$0.711557\pi$
$74$	−0.495949	+	8.51511i	−0.0576529	+	0.989861i
$75$		0			0
$76$	0.628329	+	1.45663i	0.0720742	+	0.167087i
$77$	−1.91254	+	1.25790i	−0.217955	+	0.143351i
$78$		0			0
$79$	−2.64293	−	8.82799i	−0.297353	−	0.993227i	−0.967895	−	0.251355i	$-0.919124\pi$
$79$	−2.64293	−	8.82799i	−0.297353	−	0.993227i	0.670542	−	0.741871i	$-0.266061\pi$
$80$	10.6242			1.18782
$81$		0			0
$82$	−18.2595			−2.01642
$83$	1.77486	+	5.92845i	0.194816	+	0.650732i	0.998452	+	0.0556113i	$0.0177108\pi$
$83$	1.77486	+	5.92845i	0.194816	+	0.650732i	−0.803636	+	0.595121i	$0.797104\pi$
$84$		0			0
$85$	−17.5160	+	11.5205i	−1.89988	+	1.24957i
$86$	−1.40351	−	3.25370i	−0.151344	−	0.350855i
$87$		0			0
$88$	−0.0342772	+	0.588516i	−0.00365396	+	0.0627360i
$89$	−3.52742	−	2.95986i	−0.373906	−	0.313744i	0.436399	−	0.899753i	$-0.356254\pi$
$89$	−3.52742	−	2.95986i	−0.373906	−	0.313744i	−0.810304	+	0.586009i	$0.800698\pi$
$90$		0			0
$91$	−1.60143	+	1.34376i	−0.167875	+	0.140864i
$92$	2.69757	+	3.62346i	0.281241	+	0.377772i
$93$		0			0
$94$	16.3021	+	17.2792i	1.68143	+	1.78222i
$95$	−2.05632	+	0.487356i	−0.210974	+	0.0500017i
$96$		0			0
$97$	−4.16552	+	9.65675i	−0.422944	+	0.980495i	0.564916	+	0.825148i	$0.308909\pi$
$97$	−4.16552	+	9.65675i	−0.422944	+	0.980495i	−0.987860	+	0.155346i	$0.950351\pi$
$98$	2.32362	+	13.1779i	0.234721	+	1.33117i
$99$		0			0
$100$	0.960763	−	5.44876i	0.0960763	−	0.544876i
$101$	−2.04573	−	1.34549i	−0.203557	−	0.133882i	0.443638	−	0.896206i	$-0.353688\pi$
$101$	−2.04573	−	1.34549i	−0.203557	−	0.133882i	−0.647195	+	0.762324i	$0.724058\pi$
$102$		0			0
$103$	10.1863	−	13.6825i	1.00368	−	1.34818i	0.0670938	−	0.997747i	$-0.478627\pi$
$103$	10.1863	−	13.6825i	1.00368	−	1.34818i	0.936588	−	0.350432i	$-0.113965\pi$
$104$	0.0313031	+	0.537453i	0.00306952	+	0.0527016i
$105$		0			0
$106$	7.76217	−	8.22742i	0.753929	−	0.799118i
$107$	0.402056	−	0.696381i	0.0388682	−	0.0673217i	−0.845937	−	0.533283i	$-0.820958\pi$
$107$	0.402056	−	0.696381i	0.0388682	−	0.0673217i	0.884805	+	0.465961i	$0.154291\pi$
$108$		0			0
$109$	2.11135	+	3.65696i	0.202230	+	0.350273i	0.949247	−	0.314532i	$-0.101848\pi$
$109$	2.11135	+	3.65696i	0.202230	+	0.350273i	−0.747016	+	0.664806i	$0.768514\pi$
$110$	−20.3693	−	4.82761i	−1.94214	−	0.460295i
$111$		0			0
$112$	2.09654	+	1.05292i	0.198105	+	0.0994920i
$113$	12.2597	+	1.43296i	1.15330	+	0.134801i	0.671173	−	0.741301i	$-0.265791\pi$
$113$	12.2597	+	1.43296i	1.15330	+	0.134801i	0.482125	+	0.876102i	$0.339865\pi$
$114$		0			0
$115$	−5.37768	+	2.70077i	−0.501471	+	0.251848i
$116$	8.87030	−	3.22852i	0.823586	−	0.299761i
$117$		0			0
$118$	2.87146	+	1.04513i	0.264339	+	0.0962116i
$119$	−4.59831	+	0.537466i	−0.421527	+	0.0492694i
$120$		0			0
$121$	−0.867238	+	2.89678i	−0.0788398	+	0.263343i
$122$	1.75115	−	5.84924i	0.158541	−	0.529565i
$123$		0			0
$124$	−16.8942	+	1.97465i	−1.51715	+	0.177329i
$125$	−6.07999	−	2.21294i	−0.543811	−	0.197931i
$126$		0			0
$127$	−9.37360	+	3.41171i	−0.831772	+	0.302740i	−0.722586	−	0.691281i	$-0.757047\pi$
$127$	−9.37360	+	3.41171i	−0.831772	+	0.302740i	−0.109186	+	0.994021i	$0.534824\pi$
$128$	1.12455	−	0.564772i	0.0993973	−	0.0499192i
$129$		0			0
$130$	−18.9880	−	2.21938i	−1.66536	−	0.194652i
$131$	4.90886	+	2.46532i	0.428889	+	0.215396i	0.650130	−	0.759823i	$-0.274714\pi$
$131$	4.90886	+	2.46532i	0.428889	+	0.215396i	−0.221241	+	0.975219i	$0.571011\pi$
$132$		0			0
$133$	−0.454087	−	0.107621i	−0.0393744	−	0.00933190i
$134$	−7.72636	−	13.3824i	−0.667456	−	1.15607i
$135$		0			0
$136$	−0.596125	+	1.03252i	−0.0511173	+	0.0885378i
$137$	10.4519	−	11.0783i	0.892962	−	0.946484i	−0.105890	−	0.994378i	$-0.533769\pi$
$137$	10.4519	−	11.0783i	0.892962	−	0.946484i	0.998852	+	0.0478934i	$0.0152508\pi$
$138$		0			0
$139$	−0.931263	−	15.9892i	−0.0789887	−	1.35618i	−0.772168	−	0.635419i	$-0.780828\pi$
$139$	−0.931263	−	15.9892i	−0.0789887	−	1.35618i	0.693179	−	0.720765i	$-0.256210\pi$
$140$	2.09968	−	2.82036i	0.177455	−	0.238364i
$141$		0			0
$142$	−11.4495	−	7.53043i	−0.960818	−	0.631940i
$143$	−2.22392	+	12.6125i	−0.185973	+	1.05471i
$144$		0			0
$145$	2.18361	+	12.3839i	0.181339	+	1.02842i
$146$	−0.457858	+	1.06143i	−0.0378926	+	0.0878449i
$147$		0			0
$148$	−8.54030	+	2.02409i	−0.702009	+	0.166379i
$149$	−6.06663	−	6.43025i	−0.496997	−	0.526786i	0.429510	−	0.903062i	$-0.358686\pi$
$149$	−6.06663	−	6.43025i	−0.496997	−	0.526786i	−0.926508	+	0.376275i	$0.877205\pi$
$150$		0			0
$151$	0.589901	+	0.792374i	0.0480054	+	0.0644825i	0.825478	−	0.564435i	$-0.190906\pi$
$151$	0.589901	+	0.792374i	0.0480054	+	0.0644825i	−0.777472	+	0.628917i	$0.783498\pi$
$152$	−0.0920625	+	0.0772496i	−0.00746726	+	0.00626577i
$153$		0			0
$154$	−3.54117	−	2.97139i	−0.285355	−	0.239442i
$155$	1.31750	−	22.6205i	0.105824	−	1.81692i
$156$		0			0
$157$	7.20807	+	16.7102i	0.575267	+	1.33362i	0.918891	+	0.394511i	$0.129086\pi$
$157$	7.20807	+	16.7102i	0.575267	+	1.33362i	−0.343624	+	0.939107i	$0.611655\pi$
$158$	15.5476	−	10.2258i	1.23690	−	0.813521i
$159$		0			0
$160$	6.40315	+	21.3880i	0.506214	+	1.69087i
$161$	−1.32888			−0.104730
$162$		0			0
$163$	17.1469			1.34305			0.671524	−	0.740983i	$-0.265640\pi$
$163$	17.1469			1.34305			0.671524	+	0.740983i	$0.265640\pi$
$164$	−5.38873	−	17.9996i	−0.420789	−	1.40553i
$165$		0			0
$166$	−10.4410	+	6.86715i	−0.810379	+	0.532994i
$167$	2.33733	+	5.41854i	0.180868	+	0.419299i	0.984396	−	0.175968i	$-0.0563055\pi$
$167$	2.33733	+	5.41854i	0.180868	+	0.419299i	−0.803528	+	0.595267i	$0.797046\pi$
$168$		0			0
$169$	0.0758312	−	1.30197i	0.00583317	−	0.100152i
$170$	−32.4318	−	27.2135i	−2.48740	−	2.08718i
$171$		0			0
$172$	2.79319	−	2.34377i	0.212979	−	0.178711i
$173$	5.37008	+	7.21327i	0.408280	+	0.548415i	0.957938	−	0.286975i	$-0.0926495\pi$
$173$	5.37008	+	7.21327i	0.408280	+	0.548415i	−0.549658	+	0.835389i	$0.685242\pi$
$174$		0			0
$175$	1.11693	+	1.18388i	0.0844319	+	0.0894926i
$176$	13.9853	−	3.31458i	1.05418	−	0.249846i
$177$		0			0
$178$	3.68305	−	8.53826i	0.276056	−	0.639970i
$179$	0.223820	+	1.26935i	0.0167291	+	0.0948754i	0.992029	−	0.126009i	$-0.0402168\pi$
$179$	0.223820	+	1.26935i	0.0167291	+	0.0948754i	−0.975300	+	0.220884i	$0.929106\pi$
$180$		0			0
$181$	0.645386	−	3.66017i	0.0479712	−	0.272058i	−0.951382	−	0.308013i	$-0.900336\pi$
$181$	0.645386	−	3.66017i	0.0479712	−	0.272058i	0.999353	+	0.0359546i	$0.0114472\pi$
$182$	−3.52708	−	2.31980i	−0.261444	−	0.171955i
$183$		0			0
$184$	−0.204361	+	0.274504i	−0.0150657	+	0.0202367i
$185$	−0.679836	−	11.6723i	−0.0499826	−	0.858167i
$186$		0			0
$187$	−19.4633	+	20.6299i	−1.42330	+	1.50861i
$188$	−12.2223	+	21.1696i	−0.891400	+	1.54395i
$189$		0			0
$190$	−2.13377	−	3.69580i	−0.154800	−	0.268122i
$191$	7.09353	+	1.68120i	0.513270	+	0.121647i	0.479085	−	0.877768i	$-0.340968\pi$
$191$	7.09353	+	1.68120i	0.513270	+	0.121647i	0.0341846	+	0.999416i	$0.489117\pi$
$192$		0			0
$193$	−8.60314	−	4.32066i	−0.619267	−	0.311008i	0.111364	−	0.993780i	$-0.464478\pi$
$193$	−8.60314	−	4.32066i	−0.619267	−	0.311008i	−0.730632	+	0.682772i	$0.760774\pi$
$194$	−21.0941	−	2.46555i	−1.51447	−	0.177016i
$195$		0			0
$196$	−12.3046	+	6.17962i	−0.878902	+	0.441401i
$197$	4.63898	−	1.68845i	0.330513	−	0.120297i	−0.171433	−	0.985196i	$-0.554840\pi$
$197$	4.63898	−	1.68845i	0.330513	−	0.120297i	0.501946	+	0.864899i	$0.332617\pi$
$198$		0			0
$199$	−2.36550	−	0.860973i	−0.167686	−	0.0610327i	0.256813	−	0.966461i	$-0.417328\pi$
$199$	−2.36550	−	0.860973i	−0.167686	−	0.0610327i	−0.424499	+	0.905428i	$0.639550\pi$
$200$	0.416317	−	0.0486605i	0.0294381	−	0.00344082i
$201$		0			0
$202$	1.41812	−	4.73684i	0.0997784	−	0.333283i
$203$	−0.796414	+	2.66021i	−0.0558973	+	0.186710i
$204$		0			0
$205$	24.8605	−	2.90577i	1.73633	−	0.202948i
$206$	32.3692	+	11.7814i	2.25527	+	0.820851i
$207$		0			0
$208$	12.3341	−	4.48925i	0.855217	−	0.311273i
$209$	−2.55482	+	1.28308i	−0.176721	+	0.0887524i
$210$		0			0
$211$	−6.94056	−	0.811235i	−0.477808	−	0.0558477i	−0.126219	−	0.992002i	$-0.540284\pi$
$211$	−6.94056	−	0.811235i	−0.477808	−	0.0558477i	−0.351589	+	0.936155i	$0.614358\pi$
$212$	10.4011	+	5.22364i	0.714351	+	0.358761i
$213$		0			0
$214$	1.58005	+	0.374478i	0.108010	+	0.0255988i
$215$	2.42868	+	4.20659i	0.165634	+	0.286887i
$216$		0			0
$217$	2.50183	−	4.33330i	0.169835	−	0.294163i
$218$	−5.85178	+	6.20253i	−0.396333	+	0.420088i
$219$		0			0
$220$	−1.25247	−	21.5042i	−0.0844418	−	1.44981i
$221$	−15.4672	+	20.7761i	−1.04044	+	1.39755i
$222$		0			0
$223$	15.0373	+	9.89018i	1.00697	+	0.662295i	0.942007	−	0.335592i	$-0.108936\pi$
$223$	15.0373	+	9.89018i	1.00697	+	0.662295i	0.0649637	+	0.997888i	$0.479307\pi$
$224$	−0.856110	+	4.85524i	−0.0572012	+	0.324404i
$225$		0			0
$226$	4.32831	+	24.5471i	0.287915	+	1.63285i
$227$	−0.242999	+	0.563336i	−0.0161284	+	0.0373899i	−0.926090	−	0.377303i	$-0.876852\pi$
$227$	−0.242999	+	0.563336i	−0.0161284	+	0.0373899i	0.909962	+	0.414693i	$0.136111\pi$
$228$		0			0
$229$	−4.86058	+	1.15198i	−0.321196	+	0.0761249i	−0.388051	−	0.921638i	$-0.626852\pi$
$229$	−4.86058	+	1.15198i	−0.321196	+	0.0761249i	0.0668550	+	0.997763i	$0.478704\pi$
$230$	−8.33938	−	8.83923i	−0.549883	−	0.582842i
$231$		0			0
$232$	0.427038	+	0.573612i	0.0280364	+	0.0376595i
$233$	10.0792	−	8.45747i	0.660311	−	0.554067i	−0.249869	−	0.968280i	$-0.580387\pi$
$233$	10.0792	−	8.45747i	0.660311	−	0.554067i	0.910180	+	0.414213i	$0.135943\pi$
$234$		0			0
$235$	−24.9453	−	20.9316i	−1.62725	−	1.36543i
$236$	−0.182828	+	3.13904i	−0.0119011	+	0.204334i
$237$		0			0
$238$	−3.70296	−	8.58442i	−0.240027	−	0.556446i
$239$	7.60142	−	4.99953i	0.491695	−	0.323393i	−0.279333	−	0.960194i	$-0.590113\pi$
$239$	7.60142	−	4.99953i	0.491695	−	0.323393i	0.771028	+	0.636802i	$0.219743\pi$
$240$		0			0
$241$	4.08698	+	13.6515i	0.263265	+	0.879368i	0.982763	+	0.184872i	$0.0591872\pi$
$241$	4.08698	+	13.6515i	0.263265	+	0.879368i	−0.719497	+	0.694496i	$0.755628\pi$
$242$	−6.10626			−0.392526
$243$		0			0
$244$	6.28280			0.402215
$245$	−5.26074	−	17.5721i	−0.336096	−	1.12264i
$246$		0			0
$247$	−2.18134	+	1.43469i	−0.138795	+	0.0912872i
$248$	−0.510379	−	1.18319i	−0.0324091	−	0.0751327i
$249$		0			0
$250$	0.759713	−	13.0438i	0.0480484	−	0.824960i
$251$	6.58379	+	5.52445i	0.415565	+	0.348700i	0.826473	−	0.562976i	$-0.190344\pi$
$251$	6.58379	+	5.52445i	0.415565	+	0.348700i	−0.410908	+	0.911677i	$0.634788\pi$
$252$		0			0
$253$	−6.23640	+	5.23296i	−0.392079	+	0.328993i
$254$	−12.0291	−	16.1578i	−0.754770	−	1.01383i
$255$		0			0
$256$	−10.0746	−	10.6784i	−0.629661	−	0.667401i
$257$	−21.5984	+	5.11891i	−1.34727	+	0.319309i	−0.840050	−	0.542509i	$-0.817475\pi$
$257$	−21.5984	+	5.11891i	−1.34727	+	0.319309i	−0.507219	+	0.861817i	$0.669326\pi$
$258$		0			0
$259$	1.02265	−	2.37076i	0.0635441	−	0.147312i
$260$	−3.41594	−	19.3728i	−0.211848	−	1.20145i
$261$		0			0
$262$	−1.92625	+	10.9243i	−0.119004	+	0.674906i
$263$	−4.39677	−	2.89180i	−0.271117	−	0.178316i	0.406669	−	0.913575i	$-0.366690\pi$
$263$	−4.39677	−	2.89180i	−0.271117	−	0.178316i	−0.677786	+	0.735259i	$0.737060\pi$
$264$		0			0
$265$	−9.25898	+	12.4370i	−0.568775	+	0.763997i
$266$	−0.0547947	−	0.940789i	−0.00335968	−	0.0576835i
$267$		0			0
$268$	10.9118	−	11.5658i	0.666545	−	0.706496i
$269$	−3.11423	+	5.39401i	−0.189878	+	0.328878i	−0.945209	−	0.326465i	$-0.894143\pi$
$269$	−3.11423	+	5.39401i	−0.189878	+	0.328878i	0.755331	+	0.655343i	$0.227476\pi$
$270$		0			0
$271$	−3.65935	−	6.33818i	−0.222290	−	0.385017i	0.733213	−	0.679999i	$-0.238020\pi$
$271$	−3.65935	−	6.33818i	−0.222290	−	0.385017i	−0.955503	+	0.294982i	$0.904686\pi$
$272$	28.2844	+	6.70351i	1.71499	+	0.406460i
$273$		0			0
$274$	27.4850	+	13.8035i	1.66043	+	0.833900i
$275$	9.90368	+	1.15757i	0.597214	+	0.0698043i
$276$		0			0
$277$	−16.6496	+	8.36174i	−1.00038	+	0.502409i	−0.872099	−	0.489330i	$-0.837242\pi$
$277$	−16.6496	+	8.36174i	−1.00038	+	0.502409i	−0.128279	+	0.991738i	$0.540945\pi$
$278$	30.3926	−	11.0620i	1.82283	−	0.663456i
$279$		0			0
$280$	0.250307	+	0.0911045i	0.0149587	+	0.00544453i
$281$	1.01503	−	0.118640i	0.0605517	−	0.00707747i	−0.0857631	−	0.996316i	$-0.527333\pi$
$281$	1.01503	−	0.118640i	0.0605517	−	0.00707747i	0.146315	+	0.989238i	$0.453259\pi$
$282$		0			0
$283$	3.14431	−	10.5027i	0.186910	−	0.624322i	−0.812249	−	0.583311i	$-0.801757\pi$
$283$	3.14431	−	10.5027i	0.186910	−	0.624322i	0.999159	−	0.0410113i	$-0.0130580\pi$
$284$	4.04430	−	13.5089i	0.239985	−	0.801607i
$285$		0			0
$286$	−25.6876	+	3.00245i	−1.51894	+	0.177538i
$287$	5.19387	+	1.89041i	0.306584	+	0.111588i
$288$		0			0
$289$	−37.9265	+	13.8041i	−2.23097	+	0.812008i
$290$	−22.6927	+	11.3967i	−1.33256	+	0.669236i
$291$		0			0
$292$	−1.18145	−	0.138092i	−0.0691393	−	0.00808122i
$293$	21.6970	+	10.8966i	1.26755	+	0.636588i	0.950177	−	0.311712i	$-0.100902\pi$
$293$	21.6970	+	10.8966i	1.26755	+	0.636588i	0.317375	+	0.948300i	$0.397199\pi$
$294$		0			0
$295$	−4.07584	−	0.965992i	−0.237305	−	0.0562422i
$296$	−0.332457	−	0.575832i	−0.0193237	−	0.0334696i
$297$		0			0
$298$	8.92609	−	15.4604i	0.517075	−	0.895599i
$299$	−5.10199	+	5.40779i	−0.295056	+	0.312741i
$300$		0			0
$301$	0.0623678	+	1.07081i	0.00359482	+	0.0617207i
$302$	−1.19124	+	1.60012i	−0.0685483	+	0.0920763i
$303$		0			0
$304$	2.44802	+	1.61009i	0.140404	+	0.0923449i
$305$	−1.45337	+	8.24247i	−0.0832198	+	0.471963i
$306$		0			0
$307$	−4.31169	−	24.4528i	−0.246081	−	1.39560i	−0.817968	−	0.575264i	$-0.804899\pi$
$307$	−4.31169	−	24.4528i	−0.246081	−	1.39560i	0.571887	−	0.820333i	$-0.306212\pi$
$308$	1.88404	−	4.36769i	0.107353	−	0.248872i
$309$		0			0
$310$	44.5238	−	10.5523i	2.52878	−	0.599332i
$311$	−1.27003	−	1.34616i	−0.0720170	−	0.0763335i	0.690363	−	0.723463i	$-0.257451\pi$
$311$	−1.27003	−	1.34616i	−0.0720170	−	0.0763335i	−0.762380	+	0.647130i	$0.775969\pi$
$312$		0			0
$313$	−4.15117	−	5.57599i	−0.234638	−	0.315173i	0.669172	−	0.743108i	$-0.266649\pi$
$313$	−4.15117	−	5.57599i	−0.234638	−	0.315173i	−0.903810	+	0.427934i	$0.859242\pi$
$314$	−28.1521	+	23.6225i	−1.58872	+	1.33309i
$315$		0			0
$316$	14.6687	+	12.3085i	0.825178	+	0.692406i
$317$	−1.51393	+	25.9932i	−0.0850310	+	1.45993i	0.638493	+	0.769627i	$0.279558\pi$
$317$	−1.51393	+	25.9932i	−0.0850310	+	1.45993i	−0.723524	+	0.690299i	$0.757479\pi$
$318$		0			0
$319$	6.73802	+	15.6205i	0.377256	+	0.874579i
$320$	−19.9151	+	13.0984i	−1.11329	+	0.732222i
$321$		0			0
$322$	−0.769645	−	2.57079i	−0.0428906	−	0.143265i
$323$	−5.78196			−0.321717
$324$		0			0
$325$	9.10595			0.505107
$326$	9.93094	+	33.1717i	0.550024	+	1.83721i
$327$		0			0
$328$	1.18923	−	0.782172i	0.0656645	−	0.0431882i
$329$	−2.84817	−	6.60281i	−0.157025	−	0.364025i
$330$		0			0
$331$	1.51383	−	25.9914i	0.0832075	−	1.42862i	−0.655807	−	0.754928i	$-0.727672\pi$
$331$	1.51383	−	25.9914i	0.0832075	−	1.42862i	0.739015	−	0.673689i	$-0.235291\pi$
$332$	−9.85078	−	8.26579i	−0.540632	−	0.453644i
$333$		0			0
$334$	−9.12878	+	7.65996i	−0.499505	+	0.419134i
$335$	12.6492	+	16.9908i	0.691098	+	0.928306i
$336$		0			0
$337$	10.3150	+	10.9332i	0.561892	+	0.595571i	0.944570	−	0.328311i	$-0.106479\pi$
$337$	10.3150	+	10.9332i	0.561892	+	0.595571i	−0.382677	+	0.923882i	$0.624998\pi$
$338$	2.56266	−	0.607362i	0.139390	−	0.0330361i
$339$		0			0
$340$	17.2550	−	40.0015i	0.935782	−	2.16939i
$341$	−5.32295	−	30.1880i	−0.288254	−	1.63477i
$342$		0			0
$343$	1.44640	−	8.20293i	0.0780981	−	0.442917i
$344$	0.230787	+	0.151791i	0.0124432	+	0.00818403i
$345$		0			0
$346$	−10.8443	+	14.5664i	−0.582994	+	0.783097i
$347$	1.47816	+	25.3791i	0.0793520	+	1.36242i	0.769451	+	0.638706i	$0.220530\pi$
$347$	1.47816	+	25.3791i	0.0793520	+	1.36242i	−0.690099	+	0.723715i	$0.742433\pi$
$348$		0			0
$349$	20.0832	−	21.2870i	1.07503	−	1.13947i	0.0853248	−	0.996353i	$-0.472807\pi$
$349$	20.0832	−	21.2870i	1.07503	−	1.13947i	0.989706	−	0.143113i	$-0.0457113\pi$
$350$	−1.64339	+	2.84643i	−0.0878427	+	0.152148i
$351$		0			0
$352$	15.1016	+	26.1568i	0.804920	+	1.39416i
$353$	27.9183	+	6.61675i	1.48594	+	0.352174i	0.891890	−	0.452253i	$-0.149380\pi$
$353$	27.9183	+	6.61675i	1.48594	+	0.352174i	0.594051	+	0.804428i	$0.297528\pi$
$354$		0			0
$355$	16.7869	+	8.43072i	0.890958	+	0.447456i
$356$	9.50370	+	1.11082i	0.503695	+	0.0588735i
$357$		0			0
$358$	−2.32599	+	1.16816i	−0.122933	+	0.0617391i
$359$	19.5984	−	7.13322i	1.03436	−	0.376477i	0.231622	−	0.972806i	$-0.425597\pi$
$359$	19.5984	−	7.13322i	1.03436	−	0.376477i	0.802740	+	0.596329i	$0.203375\pi$
$360$		0			0
$361$	17.3065	+	6.29905i	0.910868	+	0.331529i
$362$	7.45460	−	0.871318i	0.391805	−	0.0457954i
$363$		0			0
$364$	1.24587	−	4.16151i	0.0653015	−	0.218122i
$365$	0.454464	−	1.51802i	0.0237877	−	0.0794566i
$366$		0			0
$367$	34.3330	−	4.01296i	1.79217	−	0.209475i	0.846009	−	0.533169i	$-0.178999\pi$
$367$	34.3330	−	4.01296i	1.79217	−	0.209475i	0.946162	+	0.323694i	$0.104925\pi$
$368$	7.84042	+	2.85368i	0.408710	+	0.148758i
$369$		0			0
$370$	22.1871	−	8.07544i	1.15345	−	0.419822i
$371$	−3.05972	+	1.53665i	−0.158853	+	0.0797790i
$372$		0			0
$373$	9.30608	+	1.08773i	0.481851	+	0.0563203i	0.353551	−	0.935415i	$-0.384974\pi$
$373$	9.30608	+	1.08773i	0.481851	+	0.0563203i	0.128300	+	0.991735i	$0.459048\pi$
$374$	−51.1823	−	25.7047i	−2.64657	−	1.32916i
$375$		0			0
$376$	−1.80194	−	0.427067i	−0.0929277	−	0.0220243i
$377$	7.76787	+	13.4543i	0.400065	+	0.692934i
$378$		0			0
$379$	0.963771	−	1.66930i	0.0495056	−	0.0857462i	−0.840211	−	0.542260i	$-0.817569\pi$
$379$	0.963771	−	1.66930i	0.0495056	−	0.0857462i	0.889716	+	0.456514i	$0.150902\pi$
$380$	3.01349	−	3.19411i	0.154589	−	0.163855i
$381$		0			0
$382$	0.855977	+	14.6966i	0.0437956	+	0.751941i
$383$	11.6398	−	15.6350i	0.594768	−	0.798912i	−0.398199	−	0.917299i	$-0.630365\pi$
$383$	11.6398	−	15.6350i	0.594768	−	0.798912i	0.992968	+	0.118387i	$0.0377722\pi$
$384$		0			0
$385$	5.29420	+	3.48205i	0.269817	+	0.177462i
$386$	3.37590	−	19.1457i	0.171829	−	0.974489i
$387$		0			0
$388$	−3.79483	−	21.5216i	−0.192653	−	1.09259i
$389$	−3.62013	+	8.39242i	−0.183548	+	0.425512i	−0.985002	−	0.172545i	$-0.944801\pi$
$389$	−3.62013	+	8.39242i	−0.183548	+	0.425512i	0.801454	+	0.598057i	$0.204060\pi$
$390$		0			0
$391$	−16.0209	+	3.79702i	−0.810211	+	0.192024i
$392$	−0.715833	−	0.758738i	−0.0361550	−	0.0383221i
$393$		0			0
$394$	5.95315	+	7.99647i	0.299916	+	0.402857i
$395$	−19.5409	+	16.3967i	−0.983208	+	0.825009i
$396$		0			0
$397$	25.5466	+	21.4361i	1.28215	+	1.07585i	0.992944	+	0.118581i	$0.0378344\pi$
$397$	25.5466	+	21.4361i	1.28215	+	1.07585i	0.289202	+	0.957268i	$0.406610\pi$
$398$	0.295577	−	5.07485i	0.0148159	−	0.254379i
$399$		0			0
$400$	−4.04762	−	9.38343i	−0.202381	−	0.469172i
$401$	2.96491	−	1.95005i	0.148061	−	0.0973809i	−0.473317	−	0.880892i	$-0.656944\pi$
$401$	2.96491	−	1.95005i	0.148061	−	0.0973809i	0.621378	+	0.783511i	$0.286573\pi$
$402$		0			0
$403$	−8.02876	−	26.8179i	−0.399941	−	1.33590i
$404$	5.08795			0.253135
$405$		0			0
$406$	−5.60758			−0.278300
$407$	−4.53651	−	15.1530i	−0.224866	−	0.751106i
$408$		0			0
$409$	26.7647	−	17.6034i	1.32343	−	0.870435i	0.326237	−	0.945288i	$-0.394219\pi$
$409$	26.7647	−	17.6034i	1.32343	−	0.870435i	0.997195	+	0.0748535i	$0.0238489\pi$
$410$	20.0198	+	46.4111i	0.988707	+	2.29208i
$411$		0			0
$412$	−2.06097	+	35.3855i	−0.101537	+	1.74332i
$413$	−0.708579	−	0.594568i	−0.0348669	−	0.0292568i
$414$		0			0
$415$	13.1227	−	11.0113i	0.644168	−	0.540522i
$416$	16.4712	+	22.1247i	0.807568	+	1.08475i
$417$		0			0
$418$	−3.96186	−	4.19933i	−0.193781	−	0.205396i
$419$	−14.4349	+	3.42114i	−0.705192	+	0.167134i	−0.567538	−	0.823347i	$-0.692104\pi$
$419$	−14.4349	+	3.42114i	−0.705192	+	0.167134i	−0.137653	+	0.990480i	$0.543956\pi$
$420$		0			0
$421$	−6.17082	+	14.3056i	−0.300747	+	0.697210i	−0.999841	−	0.0178193i	$-0.994328\pi$
$421$	−6.17082	+	14.3056i	−0.300747	+	0.697210i	0.699094	+	0.715030i	$0.253587\pi$
$422$	−2.45037	−	13.8968i	−0.119282	−	0.676484i
$423$		0			0
$424$	−0.153114	+	0.868355i	−0.00743589	+	0.0421710i
$425$	16.8483	+	11.0813i	0.817264	+	0.537523i
$426$		0			0
$427$	−1.10369	+	1.48251i	−0.0534111	+	0.0717435i
$428$	0.0971546	+	1.66808i	0.00469614	+	0.0806297i
$429$		0			0
$430$	−6.73129	+	7.13475i	−0.324611	+	0.344068i
$431$	−0.648713	+	1.12360i	−0.0312474	+	0.0541221i	−0.881226	−	0.472695i	$-0.843281\pi$
$431$	−0.648713	+	1.12360i	−0.0312474	+	0.0541221i	0.849979	+	0.526817i	$0.176615\pi$
$432$		0			0
$433$	−8.76506	−	15.1815i	−0.421222	−	0.729577i	0.574838	−	0.818268i	$-0.305065\pi$
$433$	−8.76506	−	15.1815i	−0.421222	−	0.729577i	−0.996059	+	0.0886901i	$0.971732\pi$
$434$	9.83200	+	2.33023i	0.471951	+	0.111854i
$435$		0			0
$436$	−7.84124	−	3.93802i	−0.375527	−	0.188597i
$437$	−1.64842	−	0.192673i	−0.0788548	−	0.00921680i
$438$		0			0
$439$	19.4081	−	9.74712i	0.926298	−	0.465205i	0.0793304	−	0.996848i	$-0.474722\pi$
$439$	19.4081	−	9.74712i	0.926298	−	0.465205i	0.846968	+	0.531644i	$0.178426\pi$
$440$	1.53345	−	0.558129i	0.0731042	−	0.0266077i
$441$		0			0
$442$	−49.1506	−	17.8894i	−2.33786	−	0.850910i
$443$	−9.08183	+	1.06151i	−0.431491	+	0.0504340i	−0.329066	−	0.944307i	$-0.606734\pi$
$443$	−9.08183	+	1.06151i	−0.431491	+	0.0504340i	−0.102424	+	0.994741i	$0.532660\pi$
$444$		0			0
$445$	−3.65575	+	12.2110i	−0.173299	+	0.578859i
$446$	−10.4240	+	34.8186i	−0.493591	+	1.64871i
$447$		0			0
$448$	−5.22812	+	0.611080i	−0.247006	+	0.0288708i
$449$	−11.6732	−	4.24870i	−0.550893	−	0.200509i	0.0515501	−	0.998670i	$-0.483584\pi$
$449$	−11.6732	−	4.24870i	−0.550893	−	0.200509i	−0.602443	+	0.798162i	$0.705806\pi$
$450$		0			0
$451$	31.8189	−	11.5811i	1.49829	−	0.545335i
$452$	−22.9204	+	11.5111i	−1.07809	+	0.541435i
$453$		0			0
$454$	−1.23054	−	0.143830i	−0.0577523	−	0.00675027i
$455$	5.17132	+	2.59714i	0.242435	+	0.121756i
$456$		0			0
$457$	−18.1910	−	4.31134i	−0.850938	−	0.201676i	−0.218067	−	0.975934i	$-0.569975\pi$
$457$	−18.1910	−	4.31134i	−0.850938	−	0.201676i	−0.632870	+	0.774258i	$0.718123\pi$
$458$	−5.04367	−	8.73589i	−0.235675	−	0.408201i
$459$		0			0
$460$	6.25233	−	10.8293i	0.291516	−	0.504921i
$461$	−28.1921	+	29.8819i	−1.31304	+	1.39174i	−0.444768	+	0.895646i	$0.646714\pi$
$461$	−28.1921	+	29.8819i	−1.31304	+	1.39174i	−0.868270	+	0.496093i	$0.834768\pi$
$462$		0			0
$463$	0.240127	+	4.12282i	0.0111597	+	0.191604i	0.999281	+	0.0379254i	$0.0120749\pi$
$463$	0.240127	+	4.12282i	0.0111597	+	0.191604i	−0.988121	+	0.153678i	$0.950888\pi$
$464$	10.4115	−	13.9851i	0.483341	−	0.649240i
$465$		0			0
$466$	22.1990	+	14.6005i	1.02835	+	0.676357i
$467$	−4.38922	+	24.8925i	−0.203109	+	1.15189i	0.697279	+	0.716799i	$0.254394\pi$
$467$	−4.38922	+	24.8925i	−0.203109	+	1.15189i	−0.900388	+	0.435087i	$0.856717\pi$
$468$		0			0
$469$	0.812254	+	4.60652i	0.0375064	+	0.212710i
$470$	26.0458	−	60.3810i	1.20140	−	2.78517i
$471$		0			0
$472$	−0.231787	+	0.0549346i	−0.0106689	+	0.00252857i
$473$	4.50942	+	4.77971i	0.207344	+	0.219771i
$474$		0			0
$475$	1.21386	+	1.63049i	0.0556956	+	0.0748122i
$476$	7.36945	−	6.18370i	0.337778	−	0.283430i
$477$		0			0
$478$	14.0744	+	11.8098i	0.643748	+	0.540168i
$479$	1.20953	−	20.7669i	0.0552650	−	0.948863i	−0.850737	−	0.525591i	$-0.823844\pi$
$479$	1.20953	−	20.7669i	0.0552650	−	0.948863i	0.906002	−	0.423272i	$-0.139119\pi$
$480$		0			0
$481$	−5.72140	−	13.2637i	−0.260873	−	0.604773i
$482$	−24.0425	+	15.8130i	−1.09511	+	0.720263i
$483$		0			0
$484$	−1.80208	−	6.01937i	−0.0819128	−	0.273608i
$485$	29.1122			1.32192
$486$		0			0
$487$	−6.60060			−0.299102			−0.149551	−	0.988754i	$-0.547783\pi$
$487$	−6.60060			−0.299102			−0.149551	+	0.988754i	$0.547783\pi$
$488$	0.136509	+	0.455973i	0.00617949	+	0.0206409i
$489$		0			0
$490$	30.9474	−	20.3544i	1.39806	−	0.919518i
$491$	−14.4749	−	33.5565i	−0.653241	−	1.51438i	−0.846026	−	0.533142i	$-0.821011\pi$
$491$	−14.4749	−	33.5565i	−0.653241	−	1.51438i	0.192785	−	0.981241i	$-0.438248\pi$
$492$		0			0
$493$	−2.00048	+	34.3469i	−0.0900971	+	1.54691i
$494$	−4.03886	−	3.38900i	−0.181717	−	0.152479i
$495$		0			0
$496$	−24.0663	+	20.1941i	−1.08061	+	0.906740i
$497$	2.47715	+	3.32739i	0.111115	+	0.149254i
$498$		0			0
$499$	−24.9750	−	26.4720i	−1.11804	−	1.18505i	−0.980903	−	0.194496i	$-0.937693\pi$
$499$	−24.9750	−	26.4720i	−1.11804	−	1.18505i	−0.137132	−	0.990553i	$-0.543788\pi$
$500$	13.0824	−	3.10058i	0.585061	−	0.138662i
$501$		0			0
$502$	−6.87426	+	15.9363i	−0.306813	+	0.711273i
$503$	1.38230	+	7.83939i	0.0616335	+	0.349541i	0.999992	+	0.00387871i	$0.00123464\pi$
$503$	1.38230	+	7.83939i	0.0616335	+	0.349541i	−0.938359	+	0.345662i	$0.887654\pi$
$504$		0			0
$505$	−1.17697	+	6.67494i	−0.0523746	+	0.297031i
$506$	−13.7354	−	9.03391i	−0.610613	−	0.401606i
$507$		0			0
$508$	12.3779	−	16.6264i	0.549180	−	0.737676i
$509$	0.0970326	+	1.66599i	0.00430090	+	0.0738435i	0.999776	−	0.0211833i	$-0.00674336\pi$
$509$	0.0970326	+	1.66599i	0.00430090	+	0.0738435i	−0.995475	+	0.0950268i	$0.969706\pi$
$510$		0			0
$511$	0.240128	−	0.254520i	0.0106226	−	0.0112593i
$512$	16.0816	−	27.8541i	0.710711	−	1.23099i
$513$		0			0
$514$	−22.4119	−	38.8186i	−0.988548	−	1.71221i
$515$	−45.9459	−	10.8894i	−2.02462	−	0.479843i
$516$		0			0
$517$	−39.3675	−	19.7711i	−1.73138	−	0.869532i
$518$	5.17866	+	0.605299i	0.227537	+	0.0265953i
$519$		0			0
$520$	1.33175	−	0.668832i	0.0584013	−	0.0293302i
$521$	32.9725	−	12.0010i	1.44455	−	0.525773i	0.503486	−	0.864003i	$-0.332050\pi$
$521$	32.9725	−	12.0010i	1.44455	−	0.525773i	0.941063	+	0.338230i	$0.109828\pi$
$522$		0			0
$523$	11.3086	+	4.11600i	0.494491	+	0.179980i	0.577214	−	0.816593i	$-0.304140\pi$
$523$	11.3086	+	4.11600i	0.494491	+	0.179980i	−0.0827236	+	0.996573i	$0.526362\pi$
$524$	−11.3373	+	1.32514i	−0.495274	+	0.0578892i
$525$		0			0
$526$	3.04789	−	10.1807i	0.132894	−	0.443898i
$527$	17.7803	−	59.3905i	0.774524	−	2.58709i
$528$		0			0
$529$	18.1504	−	2.12148i	0.789149	−	0.0922383i
$530$	−29.4226	−	10.7089i	−1.27803	−	0.465167i
$531$		0			0
$532$	0.911231	−	0.331661i	0.0395069	−	0.0143793i
$533$	27.6338	−	13.8782i	1.19695	−	0.601133i
$534$		0			0
$535$	−2.21085	−	0.258411i	−0.0955832	−	0.0111721i
$536$	1.07647	+	0.540625i	0.0464966	+	0.0233515i
$537$		0			0
$538$	−12.2387	−	2.90062i	−0.527647	−	0.125055i
$539$	−12.4073	−	21.4900i	−0.534420	−	0.925642i
$540$		0			0
$541$	−9.81306	+	16.9967i	−0.421896	+	0.730746i	−0.996125	−	0.0879490i	$-0.971969\pi$
$541$	−9.81306	+	16.9967i	−0.421896	+	0.730746i	0.574229	+	0.818695i	$0.305302\pi$
$542$	10.1422	−	10.7501i	0.435645	−	0.461757i
$543$		0			0
$544$	3.55172	+	60.9807i	0.152279	+	2.61452i
$545$	6.98021	−	9.37604i	0.298999	−	0.401626i
$546$		0			0
$547$	−7.28872	−	4.79386i	−0.311643	−	0.204971i	0.384046	−	0.923314i	$-0.374530\pi$
$547$	−7.28872	−	4.79386i	−0.311643	−	0.204971i	−0.695689	+	0.718343i	$0.744901\pi$
$548$	−5.49569	+	31.1676i	−0.234764	+	1.33141i
$549$		0			0
$550$	3.49651	+	19.8297i	0.149092	+	0.845540i
$551$	−1.37362	+	3.18441i	−0.0585183	+	0.135661i
$552$		0			0
$553$	−5.48116	+	1.29906i	−0.233083	+	0.0552416i
$554$	−25.8192	−	27.3668i	−1.09695	−	1.16270i
$555$		0			0
$556$	19.8741	+	26.6955i	0.842849	+	1.13214i
$557$	15.1698	−	12.7290i	0.642765	−	0.539344i	−0.262101	−	0.965041i	$-0.584415\pi$
$557$	15.1698	−	12.7290i	0.642765	−	0.539344i	0.904866	+	0.425696i	$0.139971\pi$
$558$		0			0
$559$	4.59706	+	3.85739i	0.194435	+	0.163150i
$560$	0.377611	−	6.48333i	0.0159570	−	0.273971i
$561$		0			0
$562$	0.817391	+	1.89492i	0.0344795	+	0.0799326i
$563$	−28.3702	+	18.6594i	−1.19566	+	0.786400i	−0.981699	−	0.190442i	$-0.939008\pi$
$563$	−28.3702	+	18.6594i	−1.19566	+	0.786400i	−0.213964	+	0.976841i	$0.568638\pi$
$564$		0			0
$565$	−9.79942	−	32.7323i	−0.412265	−	1.37706i
$566$	22.1392			0.930581
$567$		0			0
$568$	1.06828			0.0448240
$569$	5.51785	+	18.4309i	0.231320	+	0.772664i	0.992297	+	0.123884i	$0.0395352\pi$
$569$	5.51785	+	18.4309i	0.231320	+	0.772664i	−0.760976	+	0.648780i	$0.775280\pi$
$570$		0			0
$571$	2.07779	−	1.36658i	0.0869528	−	0.0571898i	−0.505288	−	0.862951i	$-0.668614\pi$
$571$	2.07779	−	1.36658i	0.0869528	−	0.0571898i	0.592241	+	0.805761i	$0.298243\pi$
$572$	−10.5406	−	24.4360i	−0.440726	−	1.02172i
$573$		0			0
$574$	−0.648989	+	11.1427i	−0.0270883	+	0.465088i
$575$	4.43416	+	3.72070i	0.184917	+	0.155164i
$576$		0			0
$577$	19.5278	−	16.3857i	0.812951	−	0.682147i	−0.138359	−	0.990382i	$-0.544183\pi$
$577$	19.5278	−	16.3857i	0.812951	−	0.682147i	0.951310	+	0.308235i	$0.0997383\pi$
$578$	−48.6708	−	65.3762i	−2.02444	−	2.71929i
$579$		0			0
$580$	−17.9316	−	19.0063i	−0.744568	−	0.789196i
$581$	3.68088	−	0.872385i	0.152709	−	0.0361926i
$582$		0			0
$583$	−8.30808	+	19.2603i	−0.344085	+	0.797680i
$584$	−0.0156480	−	0.0887440i	−0.000647517	−	0.00367225i
$585$		0			0
$586$	−8.51396	+	48.2851i	−0.351709	+	1.99464i
$587$	−0.748080	−	0.492020i	−0.0308765	−	0.0203078i	0.533977	−	0.845499i	$-0.320697\pi$
$587$	−0.748080	−	0.492020i	−0.0308765	−	0.0203078i	−0.564853	+	0.825191i	$0.691067\pi$
$588$		0			0
$589$	3.73170	−	5.01255i	0.153762	−	0.206538i
$590$	−0.491832	−	8.44443i	−0.0202484	−	0.347652i
$591$		0			0
$592$	−11.1247	+	11.7915i	−0.457222	+	0.484627i
$593$	−16.2145	+	28.0843i	−0.665848	+	1.15328i	0.313207	+	0.949685i	$0.398597\pi$
$593$	−16.2145	+	28.0843i	−0.665848	+	1.15328i	−0.979055	+	0.203597i	$0.934737\pi$
$594$		0			0
$595$	6.40773	+	11.0985i	0.262691	+	0.454994i
$596$	17.8747	+	4.23638i	0.732177	+	0.173529i
$597$		0			0
$598$	−13.4166	−	6.73807i	−0.548646	−	0.275540i
$599$	41.8092	+	4.88680i	1.70828	+	0.199669i	0.913390	−	0.407086i	$-0.133455\pi$
$599$	41.8092	+	4.88680i	1.70828	+	0.199669i	0.794889	+	0.606755i	$0.207529\pi$
$600$		0			0
$601$	−27.6486	+	13.8857i	−1.12781	+	0.566408i	−0.912067	−	0.410042i	$-0.865514\pi$
$601$	−27.6486	+	13.8857i	−1.12781	+	0.566408i	−0.215744	+	0.976450i	$0.569218\pi$
$602$	−2.03543	+	0.740836i	−0.0829580	+	0.0301942i
$603$		0			0
$604$	−1.92891	−	0.702064i	−0.0784861	−	0.0285666i
$605$	8.31375	−	0.971737i	0.338002	−	0.0395067i
$606$		0			0
$607$	4.29468	−	14.3452i	0.174316	−	0.582255i	−0.825524	−	0.564367i	$-0.809120\pi$
$607$	4.29468	−	14.3452i	0.174316	−	0.582255i	0.999840	−	0.0178885i	$-0.00569440\pi$
$608$	−1.76593	+	5.89861i	−0.0716179	+	0.239220i
$609$		0			0
$610$	−16.7873	+	1.96215i	−0.679698	+	0.0794453i
$611$	−37.8048	−	13.7598i	−1.52942	−	0.556663i
$612$		0			0
$613$	17.2467	−	6.27730i	0.696589	−	0.253538i	0.0306353	−	0.999531i	$-0.490247\pi$
$613$	17.2467	−	6.27730i	0.696589	−	0.253538i	0.665954	+	0.745993i	$0.268025\pi$
$614$	44.8082	−	22.5035i	1.80831	−	0.908169i
$615$		0			0
$616$	0.357920	+	0.0418348i	0.0144210	+	0.00168557i
$617$	−29.2891	−	14.7095i	−1.17913	−	0.592184i	−0.252299	−	0.967649i	$-0.581187\pi$
$617$	−29.2891	−	14.7095i	−1.17913	−	0.592184i	−0.926836	+	0.375466i	$0.877483\pi$
$618$		0			0
$619$	−5.84054	−	1.38423i	−0.234751	−	0.0556370i	0.111556	−	0.993758i	$-0.464416\pi$
$619$	−5.84054	−	1.38423i	−0.234751	−	0.0556370i	−0.346307	+	0.938121i	$0.612565\pi$
$620$	23.5420	+	40.7760i	0.945471	+	1.63760i
$621$		0			0
$622$	1.86865	−	3.23661i	0.0749262	−	0.129776i
$623$	−1.93161	+	2.04738i	−0.0773882	+	0.0820267i
$624$		0			0
$625$	1.81549	+	31.1707i	0.0726195	+	1.24683i
$626$	8.38285	−	11.2601i	0.335046	−	0.450045i
$627$		0			0
$628$	−31.5946	−	20.7801i	−1.26076	−	0.829215i
$629$	5.55497	−	31.5038i	0.221491	−	1.25614i
$630$		0			0
$631$	−4.24361	−	24.0667i	−0.168935	−	0.958080i	−0.944914	−	0.327320i	$-0.893854\pi$
$631$	−4.24361	−	24.0667i	−0.168935	−	0.958080i	0.775978	−	0.630760i	$-0.217257\pi$
$632$	−0.574572	+	1.33201i	−0.0228553	+	0.0529844i
$633$		0			0
$634$	−51.1623	+	12.1257i	−2.03191	+	0.481572i
$635$	18.9490	+	20.0848i	0.751968	+	0.797040i
$636$		0			0
$637$	−13.5325	−	18.1773i	−0.536178	−	0.720212i
$638$	−26.3163	+	22.0820i	−1.04187	+	0.874234i
$639$		0			0
$640$	−2.66848	−	2.23912i	−0.105481	−	0.0885089i
$641$	−0.599772	+	10.2977i	−0.0236896	+	0.406734i	0.965530	+	0.260293i	$0.0838190\pi$
$641$	−0.599772	+	10.2977i	−0.0236896	+	0.406734i	−0.989219	+	0.146441i	$0.953218\pi$
$642$		0			0
$643$	−17.1529	−	39.7650i	−0.676446	−	1.56818i	−0.816057	−	0.577971i	$-0.803845\pi$
$643$	−17.1529	−	39.7650i	−0.676446	−	1.56818i	0.139612	−	0.990206i	$-0.455415\pi$
$644$	2.30707	−	1.51739i	0.0909114	−	0.0597934i
$645$		0			0
$646$	−3.34873	−	11.1855i	−0.131754	−	0.440089i
$647$	6.50021			0.255550			0.127775	−	0.991803i	$-0.459217\pi$
$647$	6.50021			0.255550			0.127775	+	0.991803i	$0.459217\pi$
$648$		0			0
$649$	−5.66668			−0.222437
$650$	5.27389	+	17.6160i	0.206859	+	0.690956i
$651$		0			0
$652$	−29.7688	+	19.5792i	−1.16584	+	0.766782i
$653$	1.17917	+	2.73362i	0.0461444	+	0.106975i	0.939729	−	0.341920i	$-0.111077\pi$
$653$	1.17917	+	2.73362i	0.0461444	+	0.106975i	−0.893585	+	0.448895i	$0.851818\pi$
$654$		0			0
$655$	0.884140	−	15.1801i	0.0345462	−	0.593136i
$656$	−26.5844	−	22.3070i	−1.03795	−	0.870941i
$657$		0			0
$658$	11.1240	−	9.33410i	0.433657	−	0.363881i
$659$	−16.7861	−	22.5476i	−0.653893	−	0.878330i	0.344273	−	0.938869i	$-0.388125\pi$
$659$	−16.7861	−	22.5476i	−0.653893	−	0.878330i	−0.998166	+	0.0605394i	$0.980718\pi$
$660$		0			0
$661$	2.23073	+	2.36443i	0.0867653	+	0.0919658i	0.769301	−	0.638886i	$-0.220604\pi$
$661$	2.23073	+	2.36443i	0.0867653	+	0.0919658i	−0.682536	+	0.730852i	$0.739123\pi$
$662$	51.1587	−	12.1248i	1.98834	−	0.471245i
$663$		0			0
$664$	0.385855	−	0.894513i	0.0149741	−	0.0347138i
$665$	0.224319	+	1.27217i	0.00869871	+	0.0493328i
$666$		0			0
$667$	−1.71488	+	9.72556i	−0.0664004	+	0.376575i
$668$	−10.2450	−	6.73827i	−0.396393	−	0.260711i
$669$		0			0
$670$	−25.5437	+	34.3111i	−0.986838	+	1.32555i
$671$	0.658357	+	11.3036i	0.0254156	+	0.436369i
$672$		0			0
$673$	−9.53489	+	10.1064i	−0.367543	+	0.389573i	−0.884579	−	0.466391i	$-0.845554\pi$
$673$	−9.53489	+	10.1064i	−0.367543	+	0.389573i	0.517036	+	0.855964i	$0.327035\pi$
$674$	−15.1769	+	26.2871i	−0.584591	+	1.01254i
$675$		0			0
$676$	1.35501	+	2.34695i	0.0521158	+	0.0902672i
$677$	−10.5640	−	2.50372i	−0.406009	−	0.0962259i	0.0225368	−	0.999746i	$-0.492826\pi$
$677$	−10.5640	−	2.50372i	−0.406009	−	0.0962259i	−0.428546	+	0.903520i	$0.640974\pi$
$678$		0			0
$679$	5.74491	+	2.88520i	0.220470	+	0.110724i
$680$	3.27801	+	0.383144i	0.125706	+	0.0146929i
$681$		0			0
$682$	55.3175	−	27.7815i	2.11822	−	1.06381i
$683$	−31.5858	+	11.4963i	−1.20860	+	0.439893i	−0.866217	−	0.499668i	$-0.833455\pi$
$683$	−31.5858	+	11.4963i	−1.20860	+	0.439893i	−0.342380	+	0.939562i	$0.611233\pi$
$684$		0			0
$685$	−39.6178	−	14.4197i	−1.51372	−	0.550949i
$686$	16.7068	−	1.95274i	0.637867	−	0.0745560i
$687$		0			0
$688$	1.93153	−	6.45176i	0.0736389	−	0.245971i
$689$	−5.49394	+	18.3511i	−0.209303	+	0.699119i
$690$		0			0
$691$	0.444637	−	0.0519706i	0.0169148	−	0.00197706i	−0.107631	−	0.994191i	$-0.534327\pi$
$691$	0.444637	−	0.0519706i	0.0169148	−	0.00197706i	0.124546	+	0.992214i	$0.460253\pi$
$692$	−17.5595	−	6.39115i	−0.667513	−	0.242955i
$693$		0			0
$694$	−48.2412	+	17.5584i	−1.83121	+	0.666507i
$695$	−39.6195	+	19.8977i	−1.50285	+	0.754762i
$696$		0			0
$697$	68.0185	+	7.95022i	2.57638	+	0.301136i
$698$	52.8125	+	26.5234i	1.99898	+	1.00393i
$699$		0			0
$700$	−3.29092	−	0.779962i	−0.124385	−	0.0294798i
$701$	1.94332	+	3.36593i	0.0733982	+	0.127129i	0.900389	−	0.435087i	$-0.143282\pi$
$701$	1.94332	+	3.36593i	0.0733982	+	0.127129i	−0.826990	+	0.562216i	$0.809949\pi$
$702$		0			0
$703$	1.61229	−	2.79256i	0.0608086	−	0.105324i
$704$	−22.1291	+	23.4555i	−0.834022	+	0.884012i
$705$		0			0
$706$	3.36890	+	57.8418i	0.126790	+	2.17690i
$707$	−0.893789	+	1.20057i	−0.0336144	+	0.0451520i
$708$		0			0
$709$	12.3151	+	8.09975i	0.462502	+	0.304193i	0.759292	−	0.650750i	$-0.225546\pi$
$709$	12.3151	+	8.09975i	0.462502	+	0.304193i	−0.296789	+	0.954943i	$0.595916\pi$
$710$	−6.58725	+	37.3581i	−0.247215	+	1.40203i
$711$		0			0
$712$	0.125874	+	0.713864i	0.00471731	+	0.0267532i
$713$	7.04821	−	16.3396i	0.263958	−	0.611922i
$714$		0			0
$715$	34.4961	−	8.17573i	1.29008	−	0.305755i
$716$	−1.83798	−	1.94815i	−0.0686887	−	0.0728057i
$717$		0			0
$718$	25.1504	+	33.7829i	0.938605	+	1.26076i
$719$	24.7821	−	20.7947i	0.924218	−	0.775511i	−0.0505523	−	0.998721i	$-0.516098\pi$
$719$	24.7821	−	20.7947i	0.924218	−	0.775511i	0.974770	+	0.223210i	$0.0716537\pi$
$720$		0			0
$721$	−7.98762	−	6.70241i	−0.297474	−	0.249611i
$722$	−2.16250	+	37.1286i	−0.0804798	+	1.38178i
$723$		0			0
$724$	3.05892	+	7.09138i	0.113684	+	0.263549i
$725$	10.1057	−	6.64663i	0.375316	−	0.246849i
$726$		0			0
$727$	2.64725	+	8.84244i	0.0981811	+	0.327948i	0.992942	−	0.118597i	$-0.0378396\pi$
$727$	2.64725	+	8.84244i	0.0981811	+	0.327948i	−0.894761	+	0.446545i	$0.852654\pi$
$728$	0.329090			0.0121969
$729$		0			0
$730$	3.19990			0.118434
$731$	3.81155	+	12.7315i	0.140975	+	0.470890i
$732$		0			0
$733$	44.2756	−	29.1205i	1.63535	−	1.07559i	0.704820	−	0.709386i	$-0.251028\pi$
$733$	44.2756	−	29.1205i	1.63535	−	1.07559i	0.930535	−	0.366204i	$-0.119343\pi$
$734$	27.6479	+	64.0951i	1.02050	+	2.36579i
$735$		0			0
$736$	−1.01948	+	17.5038i	−0.0375786	+	0.645199i
$737$	21.9518	+	18.4198i	0.808606	+	0.678501i
$738$		0			0
$739$	2.18316	−	1.83188i	0.0803087	−	0.0673870i	−0.601750	−	0.798685i	$-0.705529\pi$
$739$	2.18316	−	1.83188i	0.0803087	−	0.0673870i	0.682058	+	0.731298i	$0.261085\pi$
$740$	14.5084	+	19.4881i	0.533339	+	0.716398i
$741$		0			0
$742$	−4.74484	−	5.02924i	−0.174189	−	0.184629i
$743$	−28.6198	+	6.78302i	−1.04996	+	0.248845i	−0.719151	−	0.694854i	$-0.755469\pi$
$743$	−28.6198	+	6.78302i	−1.04996	+	0.248845i	−0.330807	+	0.943698i	$0.607321\pi$
$744$		0			0
$745$	−9.69263	+	22.4700i	−0.355110	+	0.823239i
$746$	3.28553	+	18.6331i	0.120292	+	0.682208i
$747$		0			0
$748$	10.2340	−	58.0400i	0.374193	−	2.12215i
$749$	−0.410672	−	0.270103i	−0.0150056	−	0.00986935i
$750$		0			0
$751$	−16.3799	+	22.0021i	−0.597712	+	0.802866i	−0.993300	−	0.115561i	$-0.963133\pi$
$751$	−16.3799	+	22.0021i	−0.597712	+	0.802866i	0.395588	+	0.918428i	$0.370541\pi$
$752$	2.62521	+	45.0730i	0.0957314	+	1.64364i
$753$		0			0
$754$	−21.5293	+	22.8197i	−0.784051	+	0.831045i
$755$	1.36725	−	2.36815i	0.0497593	−	0.0861857i
$756$		0			0
$757$	14.2323	+	24.6511i	0.517282	+	0.895959i	0.999799	+	0.0200719i	$0.00638952\pi$
$757$	14.2323	+	24.6511i	0.517282	+	0.895959i	−0.482516	+	0.875887i	$0.660277\pi$
$758$	3.78754	+	0.897664i	0.137570	+	0.0326046i
$759$		0			0
$760$	0.297288	+	0.149303i	0.0107838	+	0.00541580i
$761$	−27.7831	−	3.24738i	−1.00714	−	0.117717i	−0.403502	−	0.914979i	$-0.632207\pi$
$761$	−27.7831	−	3.24738i	−1.00714	−	0.117717i	−0.603634	+	0.797261i	$0.706281\pi$
$762$		0			0
$763$	2.30668	−	1.15846i	0.0835074	−	0.0419390i
$764$	−14.2348	+	5.18104i	−0.514997	+	0.187444i
$765$		0			0
$766$	36.9883	+	13.4626i	1.33644	+	0.486425i
$767$	−5.14002	+	0.600782i	−0.185595	+	0.0216930i
$768$		0			0
$769$	−13.4693	+	44.9907i	−0.485717	+	1.62241i	0.266742	+	0.963768i	$0.414053\pi$
$769$	−13.4693	+	44.9907i	−0.485717	+	1.62241i	−0.752459	+	0.658640i	$0.771132\pi$
$770$	−3.66999	+	12.2586i	−0.132257	+	0.441770i
$771$		0			0
$772$	19.8695	−	2.32241i	0.715120	−	0.0835855i
$773$	41.5507	+	15.1232i	1.49447	+	0.543944i	0.954623	−	0.297816i	$-0.0962583\pi$
$773$	41.5507	+	15.1232i	1.49447	+	0.543944i	0.539851	+	0.841761i	$0.318481\pi$
$774$		0			0
$775$	−20.4807	+	7.45437i	−0.735689	+	0.267769i
$776$	1.47947	−	0.743018i	0.0531099	−	0.0266728i
$777$		0			0
$778$	−18.3323	−	2.14274i	−0.657244	−	0.0768209i
$779$	6.16870	+	3.09804i	0.221017	+	0.110999i
$780$		0			0
$781$	24.7280	+	5.86065i	0.884839	+	0.209711i
$782$	−16.6244	−	28.7942i	−0.594486	−	1.02968i
$783$		0			0
$784$	−12.7160	+	22.0247i	−0.454143	+	0.786598i
$785$	34.5702	−	36.6423i	1.23386	−	1.30782i
$786$		0			0
$787$	−2.12128	−	36.4210i	−0.0756155	−	1.29827i	−0.796256	−	0.604959i	$-0.793189\pi$
$787$	−2.12128	−	36.4210i	−0.0756155	−	1.29827i	0.720641	−	0.693308i	$-0.243848\pi$
$788$	−6.12579	+	8.22836i	−0.218222	+	0.293123i
$789$		0			0
$790$	−43.0379	−	28.3065i	−1.53122	−	1.00710i
$791$	1.31019	−	7.43049i	0.0465852	−	0.264198i
$792$		0			0
$793$	1.79557	+	10.1832i	0.0637627	+	0.361616i
$794$	−26.6737	+	61.8365i	−0.946613	+	2.19450i
$795$		0			0
$796$	5.08987	−	1.20632i	0.180406	−	0.0427569i
$797$	10.3741	+	10.9959i	0.367469	+	0.389494i	0.884552	−	0.466441i	$-0.154464\pi$
$797$	10.3741	+	10.9959i	0.367469	+	0.389494i	−0.517084	+	0.855935i	$0.672982\pi$
$798$		0			0
$799$	−53.2037	−	71.4650i	−1.88221	−	2.52825i
$800$	16.4507	−	13.8038i	0.581621	−	0.488038i
$801$		0			0
$802$	5.48967	+	4.60638i	0.193847	+	0.162657i
$803$	0.124644	−	2.14005i	0.00439859	−	0.0755208i
$804$		0			0
$805$	1.45699	+	3.37768i	0.0513522	+	0.119048i
$806$	47.2309	−	31.0642i	1.66364	−	1.09419i
$807$		0			0
$808$	0.110548	+	0.369257i	0.00388908	+	0.0129904i
$809$	−49.6978			−1.74728			−0.873641	−	0.486571i	$-0.838247\pi$
$809$	−49.6978			−1.74728			−0.873641	+	0.486571i	$0.838247\pi$
$810$		0			0
$811$	−8.76133			−0.307652			−0.153826	−	0.988098i	$-0.549159\pi$
$811$	−8.76133			−0.307652			−0.153826	+	0.988098i	$0.549159\pi$
$812$	−1.65491	−	5.52779i	−0.0580760	−	0.193987i
$813$		0			0
$814$	26.6869	−	17.5523i	0.935377	−	0.615207i
$815$	−18.7999	−	43.5832i	−0.658533	−	1.52665i
$816$		0			0
$817$	−0.0778915	+	1.33735i	−0.00272508	+	0.0467878i
$818$	49.5562	+	41.5826i	1.73269	+	1.45390i
$819$		0			0
$820$	−39.8424	+	33.4317i	−1.39136	+	1.16749i
$821$	−21.1777	−	28.4466i	−0.739106	−	0.992792i	−0.999627	−	0.0273238i	$-0.991301\pi$
$821$	−21.1777	−	28.4466i	−0.739106	−	0.992792i	0.260520	−	0.965468i	$-0.416106\pi$
$822$		0			0
$823$	1.28955	+	1.36684i	0.0449508	+	0.0476451i	0.749459	−	0.662051i	$-0.230314\pi$
$823$	1.28955	+	1.36684i	0.0449508	+	0.0476451i	−0.704508	+	0.709696i	$0.748832\pi$
$824$	−2.61288	+	0.619263i	−0.0910238	+	0.0215730i
$825$		0			0
$826$	0.739840	−	1.71514i	0.0257423	−	0.0596774i
$827$	1.66995	+	9.47075i	0.0580698	+	0.329330i	0.999979	−	0.00653851i	$-0.00208129\pi$
$827$	1.66995	+	9.47075i	0.0580698	+	0.329330i	−0.941909	+	0.335869i	$0.890970\pi$
$828$		0			0
$829$	−1.31856	+	7.47791i	−0.0457954	+	0.259719i	−0.999106	−	0.0422726i	$-0.986540\pi$
$829$	−1.31856	+	7.47791i	−0.0457954	+	0.259719i	0.953311	+	0.301991i	$0.0976513\pi$
$830$	28.9022	+	19.0093i	1.00321	+	0.659821i
$831$		0			0
$832$	−17.5857	+	23.6217i	−0.609673	+	0.818934i
$833$	−2.91804	−	50.1008i	−0.101104	−	1.73589i
$834$		0			0
$835$	11.2099	−	11.8818i	0.387936	−	0.411188i
$836$	2.97035	−	5.14479i	0.102732	−	0.177936i
$837$		0			0
$838$	−14.9786	−	25.9438i	−0.517429	−	0.896213i
$839$	−38.5546	−	9.13760i	−1.33105	−	0.315465i	−0.497288	−	0.867586i	$-0.665671\pi$
$839$	−38.5546	−	9.13760i	−1.33105	−	0.315465i	−0.833764	+	0.552121i	$0.813819\pi$
$840$		0			0
$841$	−7.47404	−	3.75360i	−0.257725	−	0.129435i
$842$	−31.2489	−	3.65247i	−1.07691	−	0.125873i
$843$		0			0
$844$	12.9759	−	6.51672i	0.446647	−	0.224315i
$845$	−3.39243	+	1.23475i	−0.116703	+	0.0424765i
$846$		0			0
$847$	1.73692	+	0.632185i	0.0596811	+	0.0217221i
$848$	21.3523	−	2.49573i	0.733242	−	0.0857036i
$849$		0			0
$850$	−11.6794	+	39.0120i	−0.400601	+	1.33810i
$851$	2.63351	−	8.79654i	0.0902756	−	0.301542i
$852$		0			0
$853$	−3.42041	+	0.399789i	−0.117113	+	0.0136885i	−0.174447	−	0.984667i	$-0.555814\pi$
$853$	−3.42041	+	0.399789i	−0.117113	+	0.0136885i	0.0573346	+	0.998355i	$0.481740\pi$
$854$	−3.50722	−	1.27652i	−0.120015	−	0.0436817i
$855$		0			0
$856$	−0.118950	+	0.0432941i	−0.00406561	+	0.00147976i
$857$	−19.7908	+	9.93930i	−0.676040	+	0.339520i	−0.753474	−	0.657477i	$-0.771623\pi$
$857$	−19.7908	+	9.93930i	−0.676040	+	0.339520i	0.0774344	+	0.996997i	$0.475327\pi$
$858$		0			0
$859$	−35.3818	−	4.13554i	−1.20721	−	0.141103i	−0.511409	−	0.859337i	$-0.670876\pi$
$859$	−35.3818	−	4.13554i	−1.20721	−	0.141103i	−0.695801	+	0.718235i	$0.744950\pi$
$860$	−9.01976	−	4.52989i	−0.307571	−	0.154468i
$861$		0			0
$862$	−2.54939	−	0.604217i	−0.0868327	−	0.0205797i
$863$	10.4873	+	18.1645i	0.356992	+	0.618328i	0.987457	−	0.157890i	$-0.0504691\pi$
$863$	10.4873	+	18.1645i	0.356992	+	0.618328i	−0.630465	+	0.776218i	$0.717136\pi$
$864$		0			0
$865$	12.4466	−	21.5581i	0.423196	−	0.732998i
$866$	24.2931	−	25.7492i	0.825513	−	0.874993i
$867$		0			0
$868$	0.604553	+	10.3798i	0.0205199	+	0.352313i
$869$	−20.6074	+	27.6806i	−0.699059	+	0.938999i
$870$		0			0
$871$	21.8645	+	14.3805i	0.740849	+	0.487264i
$872$	0.115431	−	0.654639i	0.00390897	−	0.0221689i
$873$		0			0
$874$	−0.581978	−	3.30056i	−0.0196857	−	0.111643i
$875$	−1.56653	+	3.63162i	−0.0529583	+	0.122771i
$876$		0			0
$877$	41.0756	−	9.73510i	1.38702	−	0.328731i	0.531748	−	0.846903i	$-0.321535\pi$
$877$	41.0756	−	9.73510i	1.38702	−	0.328731i	0.855277	+	0.518172i	$0.173387\pi$
$878$	30.0969	+	31.9009i	1.01572	+	1.07660i
$879$		0			0
$880$	−23.7585	−	31.9131i	−0.800897	−	1.07579i
$881$	−29.2913	+	24.5783i	−0.986848	+	0.828064i	−0.985108	−	0.171935i	$-0.944998\pi$
$881$	−29.2913	+	24.5783i	−0.986848	+	0.828064i	−0.00173943	+	0.999998i	$0.500554\pi$
$882$		0			0
$883$	−22.0694	−	18.5184i	−0.742693	−	0.623194i	0.190866	−	0.981616i	$-0.438870\pi$
$883$	−22.0694	−	18.5184i	−0.742693	−	0.623194i	−0.933560	+	0.358422i	$0.883315\pi$
$884$	3.12946	−	53.7307i	0.105255	−	1.80716i
$885$		0			0
$886$	−7.31347	−	16.9545i	−0.245701	−	0.569599i
$887$	11.4615	−	7.53832i	0.384838	−	0.253112i	−0.342318	−	0.939584i	$-0.611212\pi$
$887$	11.4615	−	7.53832i	0.384838	−	0.253112i	0.727156	+	0.686472i	$0.240842\pi$
$888$		0			0
$889$	1.74881	+	5.84144i	0.0586532	+	0.195915i
$890$	−25.7403			−0.862816
$891$		0			0
$892$	−37.3995			−1.25223
$893$	−2.57571	−	8.60349i	−0.0861930	−	0.287905i
$894$		0			0
$895$	2.98097	−	1.96061i	0.0996428	−	0.0655361i
$896$	−0.304678	−	0.706324i	−0.0101786	−	0.0235966i
$897$		0			0
$898$	1.45860	−	25.0432i	0.0486742	−	0.835704i
$899$	−28.4852	−	23.9019i	−0.950035	−	0.797174i
$900$		0			0
$901$	−32.4972	+	27.2684i	−1.08264	+	0.908441i
$902$	40.8329	+	54.8482i	1.35959	+	1.82624i
$903$		0			0
$904$	−1.33341	−	1.41334i	−0.0443487	−	0.0470069i
$905$	−10.0109	+	2.37262i	−0.332772	+	0.0788685i
$906$		0			0
$907$	22.4724	−	52.0969i	0.746184	−	1.72985i	0.0648290	−	0.997896i	$-0.479350\pi$
$907$	22.4724	−	52.0969i	0.746184	−	1.72985i	0.681355	−	0.731953i	$-0.261391\pi$
$908$	−0.221375	−	1.25548i	−0.00734659	−	0.0416646i
$909$		0			0
$910$	−2.02924	+	11.5084i	−0.0672687	+	0.381500i
$911$	0.596300	+	0.392193i	0.0197563	+	0.0129939i	0.559349	−	0.828932i	$-0.311051\pi$
$911$	0.596300	+	0.392193i	0.0197563	+	0.0129939i	−0.539592	+	0.841926i	$0.681422\pi$
$912$		0			0
$913$	13.8390	−	18.5889i	0.458003	−	0.615204i
$914$	−2.19510	−	37.6885i	−0.0726076	−	1.24662i
$915$		0			0
$916$	7.12309	−	7.55004i	0.235354	−	0.249460i
$917$	1.67892	−	2.90797i	0.0554428	−	0.0960297i
$918$		0			0
$919$	28.6606	+	49.6416i	0.945425	+	1.63752i	0.754898	+	0.655842i	$0.227686\pi$
$919$	28.6606	+	49.6416i	0.945425	+	1.63752i	0.190527	+	0.981682i	$0.438980\pi$
$920$	0.921785	+	0.218467i	0.0303903	+	0.00720264i
$921$		0			0
$922$	−74.1363	−	37.2326i	−2.44155	−	1.22619i
$923$	23.0512	+	2.69429i	0.758738	+	0.0886837i
$924$		0			0
$925$	−10.0502	+	5.04739i	−0.330448	+	0.165957i
$926$	−7.83677	+	2.85235i	−0.257532	+	0.0937341i
$927$		0			0
$928$	34.4289	+	12.5311i	1.13018	+	0.411353i
$929$	−14.8620	+	1.73711i	−0.487605	+	0.0569928i	−0.356344	−	0.934355i	$-0.615977\pi$
$929$	−14.8620	+	1.73711i	−0.487605	+	0.0569928i	−0.131261	+	0.991348i	$0.541903\pi$
$930$		0			0
$931$	1.45086	−	4.84621i	0.0475501	−	0.158828i
$932$	−7.84139	+	26.1921i	−0.256853	+	0.857949i
$933$		0			0
$934$	−50.6981	+	5.92575i	−1.65889	+	0.193897i
$935$	73.7759	+	26.8522i	2.41273	+	0.878162i
$936$		0			0
$937$	23.1819	−	8.43751i	0.757319	−	0.275641i	0.0656366	−	0.997844i	$-0.479092\pi$
$937$	23.1819	−	8.43751i	0.757319	−	0.275641i	0.691682	+	0.722202i	$0.256870\pi$
$938$	−8.44116	+	4.23931i	−0.275614	+	0.138418i
$939$		0			0
$940$	67.2084	+	7.85554i	2.19210	+	0.256219i
$941$	−20.7862	−	10.4392i	−0.677612	−	0.340310i	0.0764865	−	0.997071i	$-0.475630\pi$
$941$	−20.7862	−	10.4392i	−0.677612	−	0.340310i	−0.754099	+	0.656761i	$0.771926\pi$
$942$		0			0
$943$	19.1270	+	4.53318i	0.622860	+	0.147621i
$944$	2.90384	+	5.02959i	0.0945119	+	0.163699i
$945$		0			0
$946$	−6.63491	+	11.4920i	−0.215720	+	0.373637i
$947$	13.1603	−	13.9491i	0.427653	−	0.453286i	−0.477336	−	0.878721i	$-0.658397\pi$
$947$	13.1603	−	13.9491i	0.427653	−	0.453286i	0.904989	+	0.425435i	$0.139879\pi$
$948$		0			0
$949$	−0.113829	−	1.95437i	−0.00369505	−	0.0634415i
$950$	−2.45126	+	3.29261i	−0.0795293	+	0.106826i
$951$		0			0
$952$	0.608900	+	0.400480i	0.0197346	+	0.0129796i
$953$	5.37991	−	30.5110i	0.174272	−	0.988348i	−0.764708	−	0.644377i	$-0.777117\pi$
$953$	5.37991	−	30.5110i	0.174272	−	0.988348i	0.938980	−	0.343971i	$-0.111772\pi$
$954$		0			0
$955$	−3.50420	−	19.8733i	−0.113393	−	0.643085i
$956$	−7.48812	+	17.3594i	−0.242183	+	0.561444i
$957$		0			0
$958$	40.8753	−	9.68762i	1.32062	−	0.312993i
$959$	−6.38898	−	6.77192i	−0.206311	−	0.218677i
$960$		0			0
$961$	21.4999	+	28.8794i	0.693545	+	0.931593i
$962$	22.3457	−	18.7503i	0.720456	−	0.604534i
$963$		0			0
$964$	−22.6834	−	19.0336i	−0.730583	−	0.613032i
$965$	−1.54952	+	26.6043i	−0.0498809	+	0.856422i
$966$		0			0
$967$	7.86525	+	18.2337i	0.252929	+	0.586356i	0.996618	−	0.0821696i	$-0.0261849\pi$
$967$	7.86525	+	18.2337i	0.252929	+	0.586356i	−0.743689	+	0.668526i	$0.766926\pi$
$968$	0.397700	−	0.261571i	0.0127826	−	0.00840722i
$969$		0			0
$970$	16.8609	+	56.3193i	0.541370	+	1.80830i
$971$	−3.39436			−0.108930			−0.0544651	−	0.998516i	$-0.517345\pi$
$971$	−3.39436			−0.108930			−0.0544651	+	0.998516i	$0.517345\pi$
$972$		0			0
$973$	−9.79039			−0.313865
$974$	−3.82286	−	12.7693i	−0.122492	−	0.409153i
$975$		0			0
$976$	9.69536	−	6.37674i	0.310341	−	0.204115i
$977$	−21.2170	−	49.1866i	−0.678793	−	1.57362i	−0.812738	−	0.582630i	$-0.802024\pi$
$977$	−21.2170	−	49.1866i	−0.678793	−	1.57362i	0.133945	−	0.990989i	$-0.457235\pi$
$978$		0			0
$979$	−1.00265	+	17.2148i	−0.0320447	+	0.550186i
$980$	29.1980	+	24.5000i	0.932694	+	0.782624i
$981$		0			0
$982$	56.5336	−	47.4373i	1.80406	−	1.51379i
$983$	16.6147	+	22.3174i	0.529925	+	0.711813i	0.983803	−	0.179250i	$-0.0573672\pi$
$983$	16.6147	+	22.3174i	0.529925	+	0.711813i	−0.453878	+	0.891064i	$0.649960\pi$
$984$		0			0
$985$	−9.37783	−	9.93992i	−0.298802	−	0.316712i
$986$	−67.6047	+	16.0226i	−2.15297	+	0.510264i
$987$		0			0
$988$	2.14883	−	4.98155i	0.0683634	−	0.158484i
$989$	0.662412	+	3.75672i	0.0210635	+	0.119457i
$990$		0			0
$991$	2.53438	−	14.3732i	0.0805071	−	0.456579i	−0.917729	−	0.397207i	$-0.869979\pi$
$991$	2.53438	−	14.3732i	0.0805071	−	0.456579i	0.998236	−	0.0593711i	$-0.0189095\pi$
$992$	−55.1582	−	36.2781i	−1.75128	−	1.15183i
$993$		0			0
$994$	−5.00234	+	6.71931i	−0.158665	+	0.213123i
$995$	0.405170	+	6.95651i	0.0128448	+	0.220536i
$996$		0			0
$997$	1.67236	−	1.77260i	0.0529641	−	0.0561386i	−0.700350	−	0.713800i	$-0.746973\pi$
$997$	1.67236	−	1.77260i	0.0529641	−	0.0561386i	0.753314	+	0.657661i	$0.228454\pi$
$998$	36.7468	−	63.6474i	1.16320	−	2.01472i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.379.7		144
3.2	odd	2		729.2.g.b.379.2		144
9.2	odd	6		729.2.g.a.622.2		144
9.4	even	3		81.2.g.a.16.2	✓	144
9.5	odd	6		243.2.g.a.208.7		144
9.7	even	3		729.2.g.d.622.7		144
81.5	odd	54		729.2.g.a.109.2		144
81.7	even	27		6561.2.a.c.1.14		72
81.22	even	27		81.2.g.a.76.2	yes	144
81.32	odd	54		729.2.g.b.352.2		144
81.49	even	27	inner	729.2.g.c.352.7		144
81.59	odd	54		243.2.g.a.118.7		144
81.74	odd	54		6561.2.a.d.1.59		72
81.76	even	27		729.2.g.d.109.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.2	✓	144	9.4	even	3
81.2.g.a.76.2	yes	144	81.22	even	27
243.2.g.a.118.7		144	81.59	odd	54
243.2.g.a.208.7		144	9.5	odd	6
729.2.g.a.109.2		144	81.5	odd	54
729.2.g.a.622.2		144	9.2	odd	6
729.2.g.b.352.2		144	81.32	odd	54
729.2.g.b.379.2		144	3.2	odd	2
729.2.g.c.352.7		144	81.49	even	27	inner
729.2.g.c.379.7		144	1.1	even	1	trivial
729.2.g.d.109.7		144	81.76	even	27
729.2.g.d.622.7		144	9.7	even	3
6561.2.a.c.1.14		72	81.7	even	27
6561.2.a.d.1.59		72	81.74	odd	54

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.579169 + 1.93456i) q^{2} +(-1.73611 + 1.14185i) q^{4} +(-1.09641 - 2.54176i) q^{5} +(0.0355426 - 0.610243i) q^{7} +(-0.120591 - 0.101188i) q^{8} +(4.28217 - 3.59317i) q^{10} +(-2.23626 - 3.00382i) q^{11} +(-2.34689 - 2.48756i) q^{13} +(1.20114 - 0.284675i) q^{14} +(-1.52016 + 3.52413i) q^{16} +(-1.31516 - 7.45862i) q^{17} +(0.132568 - 0.751830i) q^{19} +(4.80579 + 3.16082i) q^{20} +(4.51590 - 6.06590i) q^{22} +(-0.126403 - 2.17026i) q^{23} +(-1.82720 + 1.93672i) q^{25} +(3.45308 - 5.98091i) q^{26} +(0.635103 + 1.10003i) q^{28} +(-4.42027 - 1.04762i) q^{29} +(7.31490 + 3.67368i) q^{31} +(-8.01077 - 0.936325i) q^{32} +(13.6674 - 6.86404i) q^{34} +(-1.59006 + 0.578734i) q^{35} +(3.96908 + 1.44463i) q^{37} +(1.53124 - 0.178976i) q^{38} +(-0.124978 + 0.417456i) q^{40} +(-2.59329 + 8.66219i) q^{41} +(-1.74287 + 0.203712i) q^{43} +(7.31231 + 2.66146i) q^{44} +(4.12528 - 1.50148i) q^{46} +(10.5125 - 5.27956i) q^{47} +(6.58154 + 0.769271i) q^{49} +(-4.80497 - 2.41314i) q^{50} +(6.91487 + 1.63886i) q^{52} +(-2.80062 - 4.85082i) q^{53} +(-5.18313 + 8.97744i) q^{55} +(-0.0660353 + 0.0699933i) q^{56} +(-0.533395 - 9.15803i) q^{58} +(0.903619 - 1.21377i) q^{59} +(-2.52614 - 1.66147i) q^{61} +(-2.87039 + 16.2788i) q^{62} +(-1.49529 - 8.48019i) q^{64} +(-3.74962 + 8.69259i) q^{65} +(-7.44589 + 1.76471i) q^{67} +(10.7999 + 11.4472i) q^{68} +(-2.04051 - 2.74088i) q^{70} +(-5.19850 + 4.36206i) q^{71} +(0.438511 + 0.367955i) q^{73} +(-0.495949 + 8.51511i) q^{74} +(0.628329 + 1.45663i) q^{76} +(-1.91254 + 1.25790i) q^{77} +(-2.64293 - 8.82799i) q^{79} +10.6242 q^{80} -18.2595 q^{82} +(1.77486 + 5.92845i) q^{83} +(-17.5160 + 11.5205i) q^{85} +(-1.40351 - 3.25370i) q^{86} +(-0.0342772 + 0.588516i) q^{88} +(-3.52742 - 2.95986i) q^{89} +(-1.60143 + 1.34376i) q^{91} +(2.69757 + 3.62346i) q^{92} +(16.3021 + 17.2792i) q^{94} +(-2.05632 + 0.487356i) q^{95} +(-4.16552 + 9.65675i) q^{97} +(2.32362 + 13.1779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

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