LMFDB - Embedded newform 729.2.g.b.379.2

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			379.2
Character	$\chi$	$=$	729.379
Dual form			729.2.g.b.352.2

$q$-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	$-0.839491\pi$
$2$	−0.579169	−	1.93456i	−0.409534	−	1.36794i	0.466001	−	0.884784i	$-0.345694\pi$
$3$		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	$0.0828226\pi$
$5$	1.09641	+	2.54176i	0.490328	+	1.13671i	−0.476012	+	0.879439i	$0.657918\pi$
$6$		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	0.999198	−	0.0400487i	$-0.0127513\pi$
$11$	2.23626	+	3.00382i	0.674258	+	0.905686i	−0.324939	+	0.945735i	$0.605344\pi$
$12$		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	$0.314997\pi$
$17$	1.31516	+	7.45862i	0.318972	+	1.80898i	−0.230058	+	0.973177i	$0.573891\pi$
$18$		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	$0.0542584\pi$
$23$	0.126403	+	2.17026i	0.0263569	+	0.452530i	−0.959150	+	0.282897i	$0.908705\pi$
$24$		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	0.619511	−	0.784988i	$-0.287331\pi$
$29$	4.42027	+	1.04762i	0.820824	+	0.194539i	0.201313	+	0.979527i	$0.435479\pi$
$30$		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	$-0.657876\pi$
$41$	2.59329	−	8.66219i	0.405004	−	1.35281i	0.880899	−	0.473304i	$-0.156939\pi$
$42$		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	−0.997256	−	0.0740235i	$-0.976416\pi$
$47$	−10.5125	+	5.27956i	−1.53340	+	0.770103i	−0.536144	+	0.844126i	$0.680120\pi$
$48$		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	0.991727	−	0.128366i	$-0.0409732\pi$
$53$	2.80062	+	4.85082i	0.384695	+	0.666312i	−0.607032	+	0.794678i	$0.707640\pi$
$54$		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	−0.857043	−	0.515245i	$-0.827701\pi$
$59$	−0.903619	+	1.21377i	−0.117641	+	0.158020i	0.739402	+	0.673264i	$0.235108\pi$
$60$		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	−0.279895	−	0.960031i	$-0.590299\pi$
$71$	5.19850	−	4.36206i	0.616948	−	0.517681i	0.896843	+	0.442350i	$0.145855\pi$
$72$		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	$-0.982289\pi$
$83$	−1.77486	−	5.92845i	−0.194816	−	0.650732i	0.803636	−	0.595121i	$-0.202896\pi$
$84$		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	0.810304	−	0.586009i	$-0.199302\pi$
$89$	3.52742	+	2.95986i	0.373906	+	0.313744i	−0.436399	+	0.899753i	$0.643746\pi$
$90$		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	0.647195	−	0.762324i	$-0.275942\pi$
$101$	2.04573	+	1.34549i	0.203557	+	0.133882i	−0.443638	+	0.896206i	$0.646312\pi$
$102$		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	−0.884805	−	0.465961i	$-0.845709\pi$
$107$	−0.402056	+	0.696381i	−0.0388682	+	0.0673217i	0.845937	+	0.533283i	$0.179042\pi$
$108$		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	−0.482125	−	0.876102i	$-0.660135\pi$
$113$	−12.2597	−	1.43296i	−1.15330	−	0.134801i	−0.671173	+	0.741301i	$0.734209\pi$
$114$		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	0.221241	−	0.975219i	$-0.428989\pi$
$131$	−4.90886	−	2.46532i	−0.428889	−	0.215396i	−0.650130	+	0.759823i	$0.725286\pi$
$132$		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	−0.998852	−	0.0478934i	$-0.984749\pi$
$137$	−10.4519	+	11.0783i	−0.892962	+	0.946484i	0.105890	+	0.994378i	$0.466231\pi$
$138$		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	0.926508	−	0.376275i	$-0.122795\pi$
$149$	6.06663	+	6.43025i	0.496997	+	0.526786i	−0.429510	+	0.903062i	$0.641314\pi$
$150$		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	0.803528	−	0.595267i	$-0.202954\pi$
$167$	−2.33733	−	5.41854i	−0.180868	−	0.419299i	−0.984396	+	0.175968i	$0.943695\pi$
$168$		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	0.549658	−	0.835389i	$-0.314758\pi$
$173$	−5.37008	−	7.21327i	−0.408280	−	0.548415i	−0.957938	+	0.286975i	$0.907350\pi$
$174$		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	0.975300	−	0.220884i	$-0.0708943\pi$
$179$	−0.223820	−	1.26935i	−0.0167291	−	0.0948754i	−0.992029	+	0.126009i	$0.959783\pi$
$180$		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	−0.0341846	−	0.999416i	$-0.510883\pi$
$191$	−7.09353	−	1.68120i	−0.513270	−	0.121647i	−0.479085	+	0.877768i	$0.659032\pi$
$192$		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	−0.501946	−	0.864899i	$-0.667383\pi$
$197$	−4.63898	+	1.68845i	−0.330513	+	0.120297i	0.171433	+	0.985196i	$0.445160\pi$
$198$		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	−0.909962	−	0.414693i	$-0.863889\pi$
$227$	0.242999	−	0.563336i	0.0161284	−	0.0373899i	0.926090	+	0.377303i	$0.123148\pi$
$228$		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	−0.910180	−	0.414213i	$-0.864057\pi$
$233$	−10.0792	+	8.45747i	−0.660311	+	0.554067i	0.249869	+	0.968280i	$0.419613\pi$
$234$		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	−0.771028	−	0.636802i	$-0.780257\pi$
$239$	−7.60142	+	4.99953i	−0.491695	+	0.323393i	0.279333	+	0.960194i	$0.409887\pi$
$240$		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	0.410908	−	0.911677i	$-0.365212\pi$
$251$	−6.58379	−	5.52445i	−0.415565	−	0.348700i	−0.826473	+	0.562976i	$0.809656\pi$
$252$		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	0.507219	−	0.861817i	$-0.330674\pi$
$257$	21.5984	−	5.11891i	1.34727	−	0.319309i	0.840050	+	0.542509i	$0.182525\pi$
$258$		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	0.677786	−	0.735259i	$-0.262940\pi$
$263$	4.39677	+	2.89180i	0.271117	+	0.178316i	−0.406669	+	0.913575i	$0.633310\pi$
$264$		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	−0.755331	−	0.655343i	$-0.772524\pi$
$269$	3.11423	−	5.39401i	0.189878	−	0.328878i	0.945209	+	0.326465i	$0.105857\pi$
$270$		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	−0.146315	−	0.989238i	$-0.546741\pi$
$281$	−1.01503	+	0.118640i	−0.0605517	+	0.00707747i	0.0857631	+	0.996316i	$0.472667\pi$
$282$		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	−0.317375	−	0.948300i	$-0.602801\pi$
$293$	−21.6970	−	10.8966i	−1.26755	−	0.636588i	−0.950177	+	0.311712i	$0.899098\pi$
$294$		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	0.762380	−	0.647130i	$-0.224031\pi$
$311$	1.27003	+	1.34616i	0.0720170	+	0.0763335i	−0.690363	+	0.723463i	$0.742549\pi$
$312$		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	$-0.720442\pi$
$317$	1.51393	−	25.9932i	0.0850310	−	1.45993i	0.723524	−	0.690299i	$-0.242521\pi$
$318$		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	$-0.779470\pi$
$347$	−1.47816	−	25.3791i	−0.0793520	−	1.36242i	0.690099	−	0.723715i	$-0.257567\pi$
$348$		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	−0.594051	−	0.804428i	$-0.702472\pi$
$353$	−27.9183	−	6.61675i	−1.48594	−	0.352174i	−0.891890	+	0.452253i	$0.850620\pi$
$354$		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	−0.802740	−	0.596329i	$-0.796625\pi$
$359$	−19.5984	+	7.13322i	−1.03436	+	0.376477i	−0.231622	+	0.972806i	$0.574403\pi$
$360$		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	−0.992968	−	0.118387i	$-0.962228\pi$
$383$	−11.6398	+	15.6350i	−0.594768	+	0.798912i	0.398199	+	0.917299i	$0.369635\pi$
$384$		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	−0.801454	−	0.598057i	$-0.795940\pi$
$389$	3.62013	−	8.39242i	0.183548	−	0.425512i	0.985002	+	0.172545i	$0.0551989\pi$
$390$		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	−0.621378	−	0.783511i	$-0.713427\pi$
$401$	−2.96491	+	1.95005i	−0.148061	+	0.0973809i	0.473317	+	0.880892i	$0.343056\pi$
$402$		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	0.137653	−	0.990480i	$-0.456044\pi$
$419$	14.4349	−	3.42114i	0.705192	−	0.167134i	0.567538	+	0.823347i	$0.307896\pi$
$420$		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	−0.849979	−	0.526817i	$-0.823385\pi$
$431$	0.648713	−	1.12360i	0.0312474	−	0.0541221i	0.881226	+	0.472695i	$0.156719\pi$
$432$		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	0.102424	−	0.994741i	$-0.467340\pi$
$443$	9.08183	−	1.06151i	0.431491	−	0.0504340i	0.329066	+	0.944307i	$0.393266\pi$
$444$		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	0.602443	−	0.798162i	$-0.294194\pi$
$449$	11.6732	+	4.24870i	0.550893	+	0.200509i	−0.0515501	+	0.998670i	$0.516416\pi$
$450$		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	$-0.353286\pi$
$461$	28.1921	−	29.8819i	1.31304	−	1.39174i	0.868270	−	0.496093i	$-0.165232\pi$
$462$		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	$-0.745606\pi$
$467$	4.38922	−	24.8925i	0.203109	−	1.15189i	0.900388	−	0.435087i	$-0.143283\pi$
$468$		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	$0.176156\pi$
$479$	−1.20953	+	20.7669i	−0.0552650	+	0.948863i	−0.906002	+	0.423272i	$0.860881\pi$
$480$		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	$0.178989\pi$
$491$	14.4749	+	33.5565i	0.653241	+	1.51438i	−0.192785	+	0.981241i	$0.561752\pi$
$492$		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	$-0.998765\pi$
$503$	−1.38230	−	7.83939i	−0.0616335	−	0.349541i	0.938359	−	0.345662i	$-0.112346\pi$
$504$		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	0.995475	−	0.0950268i	$-0.0302937\pi$
$509$	−0.0970326	−	1.66599i	−0.00430090	−	0.0738435i	−0.999776	+	0.0211833i	$0.993257\pi$
$510$		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	−0.941063	−	0.338230i	$-0.890172\pi$
$521$	−32.9725	+	12.0010i	−1.44455	+	0.525773i	−0.503486	+	0.864003i	$0.667950\pi$
$522$		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	−0.904866	−	0.425696i	$-0.860029\pi$
$557$	−15.1698	+	12.7290i	−0.642765	+	0.539344i	0.262101	+	0.965041i	$0.415585\pi$
$558$		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	0.213964	−	0.976841i	$-0.431362\pi$
$563$	28.3702	−	18.6594i	1.19566	−	0.786400i	0.981699	+	0.190442i	$0.0609920\pi$
$564$		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	$-0.960465\pi$
$569$	−5.51785	−	18.4309i	−0.231320	−	0.772664i	0.760976	−	0.648780i	$-0.224720\pi$
$570$		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	0.564853	−	0.825191i	$-0.308933\pi$
$587$	0.748080	+	0.492020i	0.0308765	+	0.0203078i	−0.533977	+	0.845499i	$0.679303\pi$
$588$		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	$-0.601403\pi$
$593$	16.2145	−	28.0843i	0.665848	−	1.15328i	0.979055	−	0.203597i	$-0.0652634\pi$
$594$		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	−0.794889	−	0.606755i	$-0.792471\pi$
$599$	−41.8092	−	4.88680i	−1.70828	−	0.199669i	−0.913390	+	0.407086i	$0.866545\pi$
$600$		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	0.926836	−	0.375466i	$-0.122517\pi$
$617$	29.2891	+	14.7095i	1.17913	+	0.592184i	0.252299	+	0.967649i	$0.418813\pi$
$618$		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	$-0.916181\pi$
$641$	0.599772	−	10.2977i	0.0236896	−	0.406734i	0.989219	−	0.146441i	$-0.0467820\pi$
$642$		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	$-0.540783\pi$
$647$	−6.50021			−0.255550			−0.127775	+	0.991803i	$0.540783\pi$
$648$		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	0.893585	−	0.448895i	$-0.148182\pi$
$653$	−1.17917	−	2.73362i	−0.0461444	−	0.106975i	−0.939729	+	0.341920i	$0.888923\pi$
$654$		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	0.998166	−	0.0605394i	$-0.0192821\pi$
$659$	16.7861	+	22.5476i	0.653893	+	0.878330i	−0.344273	+	0.938869i	$0.611875\pi$
$660$		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	0.428546	−	0.903520i	$-0.359026\pi$
$677$	10.5640	+	2.50372i	0.406009	+	0.0962259i	−0.0225368	+	0.999746i	$0.507174\pi$
$678$		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	0.342380	−	0.939562i	$-0.388767\pi$
$683$	31.5858	−	11.4963i	1.20860	−	0.439893i	0.866217	+	0.499668i	$0.166545\pi$
$684$		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	0.826990	−	0.562216i	$-0.190051\pi$
$701$	−1.94332	−	3.36593i	−0.0733982	−	0.127129i	−0.900389	+	0.435087i	$0.856718\pi$
$702$		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	−0.974770	−	0.223210i	$-0.928346\pi$
$719$	−24.7821	+	20.7947i	−0.924218	+	0.775511i	0.0505523	+	0.998721i	$0.483902\pi$
$720$		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	0.330807	−	0.943698i	$-0.392679\pi$
$743$	28.6198	−	6.78302i	1.04996	−	0.248845i	0.719151	+	0.694854i	$0.244531\pi$
$744$		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	0.603634	−	0.797261i	$-0.293719\pi$
$761$	27.7831	+	3.24738i	1.00714	+	0.117717i	0.403502	+	0.914979i	$0.367793\pi$
$762$		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	−0.539851	−	0.841761i	$-0.681519\pi$
$773$	−41.5507	−	15.1232i	−1.49447	−	0.543944i	−0.954623	+	0.297816i	$0.903742\pi$
$774$		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	0.517084	−	0.855935i	$-0.327018\pi$
$797$	−10.3741	−	10.9959i	−0.367469	−	0.389494i	−0.884552	+	0.466441i	$0.845536\pi$
$798$		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	$-0.161753\pi$
$809$	49.6978			1.74728			0.873641	+	0.486571i	$0.161753\pi$
$810$		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	$0.00869851\pi$
$821$	21.1777	+	28.4466i	0.739106	+	0.992792i	−0.260520	+	0.965468i	$0.583894\pi$
$822$		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	0.941909	−	0.335869i	$-0.109030\pi$
$827$	−1.66995	−	9.47075i	−0.0580698	−	0.329330i	−0.999979	+	0.00653851i	$0.997919\pi$
$828$		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	0.833764	−	0.552121i	$-0.186181\pi$
$839$	38.5546	+	9.13760i	1.33105	+	0.315465i	0.497288	+	0.867586i	$0.334329\pi$
$840$		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	−0.0774344	−	0.996997i	$-0.524673\pi$
$857$	19.7908	−	9.93930i	0.676040	−	0.339520i	0.753474	+	0.657477i	$0.228377\pi$
$858$		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	0.630465	−	0.776218i	$-0.282864\pi$
$863$	−10.4873	−	18.1645i	−0.356992	−	0.618328i	−0.987457	+	0.157890i	$0.949531\pi$
$864$		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	0.00173943	−	0.999998i	$-0.499446\pi$
$881$	29.2913	−	24.5783i	0.986848	−	0.828064i	0.985108	+	0.171935i	$0.0550019\pi$
$882$		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	−0.727156	−	0.686472i	$-0.759158\pi$
$887$	−11.4615	+	7.53832i	−0.384838	+	0.253112i	0.342318	+	0.939584i	$0.388788\pi$
$888$		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	0.539592	−	0.841926i	$-0.318578\pi$
$911$	−0.596300	−	0.392193i	−0.0197563	−	0.0129939i	−0.559349	+	0.828932i	$0.688949\pi$
$912$		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	0.131261	−	0.991348i	$-0.458097\pi$
$929$	14.8620	−	1.73711i	0.487605	−	0.0569928i	0.356344	+	0.934355i	$0.384023\pi$
$930$		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	0.754099	−	0.656761i	$-0.228074\pi$
$941$	20.7862	+	10.4392i	0.677612	+	0.340310i	−0.0764865	+	0.997071i	$0.524370\pi$
$942$		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	−0.904989	−	0.425435i	$-0.860121\pi$
$947$	−13.1603	+	13.9491i	−0.427653	+	0.453286i	0.477336	+	0.878721i	$0.341603\pi$
$948$		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	$0.222883\pi$
$953$	−5.37991	+	30.5110i	−0.174272	+	0.988348i	−0.938980	+	0.343971i	$0.888228\pi$
$954$		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	$-0.482655\pi$
$971$	3.39436			0.108930			0.0544651	+	0.998516i	$0.482655\pi$
$972$		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	$0.197976\pi$
$977$	21.2170	+	49.1866i	0.678793	+	1.57362i	−0.133945	+	0.990989i	$0.542765\pi$
$978$		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	0.453878	−	0.891064i	$-0.350040\pi$
$983$	−16.6147	−	22.3174i	−0.529925	−	0.711813i	−0.983803	+	0.179250i	$0.942633\pi$
$984$		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.b.379.2		144
3.2	odd	2		729.2.g.c.379.7		144
9.2	odd	6		729.2.g.d.622.7		144
9.4	even	3		243.2.g.a.208.7		144
9.5	odd	6		81.2.g.a.16.2	✓	144
9.7	even	3		729.2.g.a.622.2		144
81.5	odd	54		729.2.g.d.109.7		144
81.7	even	27		6561.2.a.d.1.59		72
81.22	even	27		243.2.g.a.118.7		144
81.32	odd	54		729.2.g.c.352.7		144
81.49	even	27	inner	729.2.g.b.352.2		144
81.59	odd	54		81.2.g.a.76.2	yes	144
81.74	odd	54		6561.2.a.c.1.14		72
81.76	even	27		729.2.g.a.109.2		144

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

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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