LMFDB - Embedded newform 288.2.v.d.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(37,288)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("288.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.v (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	288.109
Dual form			288.2.v.d.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.884039 + 1.10385i) q^{2} +(-0.436951 - 1.95168i) q^{4} +(-2.14986 + 0.890503i) q^{5} +(-1.10001 + 1.10001i) q^{7} +(2.54064 + 1.24304i) q^{8} +O(q^{10})$	\(q+(-0.884039 + 1.10385i) q^{2} +(-0.436951 - 1.95168i) q^{4} +(-2.14986 + 0.890503i) q^{5} +(-1.10001 + 1.10001i) q^{7} +(2.54064 + 1.24304i) q^{8} +(0.917585 - 3.16036i) q^{10} +(-0.999449 - 2.41288i) q^{11} +(-2.03123 - 0.841362i) q^{13} +(-0.241790 - 2.18670i) q^{14} +(-3.61815 + 1.70558i) q^{16} -5.68481i q^{17} +(-6.02698 - 2.49646i) q^{19} +(2.67737 + 3.80675i) q^{20} +(3.54700 + 1.02984i) q^{22} +(-3.60241 - 3.60241i) q^{23} +(0.293385 - 0.293385i) q^{25} +(2.72442 - 1.49837i) q^{26} +(2.62753 + 1.66622i) q^{28} +(-3.82608 + 9.23698i) q^{29} +1.98933 q^{31} +(1.31588 - 5.50168i) q^{32} +(6.27515 + 5.02559i) q^{34} +(1.38531 - 3.34444i) q^{35} +(5.97179 - 2.47360i) q^{37} +(8.08378 - 4.44589i) q^{38} +(-6.56896 - 0.409916i) q^{40} +(4.33228 + 4.33228i) q^{41} +(-4.39793 - 10.6175i) q^{43} +(-4.27248 + 3.00492i) q^{44} +(7.16117 - 0.791834i) q^{46} +5.32331i q^{47} +4.57995i q^{49} +(0.0644882 + 0.583216i) q^{50} +(-0.754527 + 4.33195i) q^{52} +(-0.802971 - 1.93854i) q^{53} +(4.29736 + 4.29736i) q^{55} +(-4.16209 + 1.42738i) q^{56} +(-6.81379 - 12.3892i) q^{58} +(-5.97225 + 2.47379i) q^{59} +(-3.53897 + 8.54384i) q^{61} +(-1.75864 + 2.19591i) q^{62} +(4.90971 + 6.31623i) q^{64} +5.11610 q^{65} +(-2.25745 + 5.44997i) q^{67} +(-11.0950 + 2.48398i) q^{68} +(2.46708 + 4.48578i) q^{70} +(-2.57276 + 2.57276i) q^{71} +(8.01131 + 8.01131i) q^{73} +(-2.54883 + 8.77869i) q^{74} +(-2.23880 + 12.8536i) q^{76} +(3.75360 + 1.55479i) q^{77} -14.4931i q^{79} +(6.25970 - 6.88874i) q^{80} +(-8.61208 + 0.952266i) q^{82} +(-2.50672 - 1.03832i) q^{83} +(5.06234 + 12.2216i) q^{85} +(15.6081 + 4.53168i) q^{86} +(0.460066 - 7.37262i) q^{88} +(2.98746 - 2.98746i) q^{89} +(3.15988 - 1.30887i) q^{91} +(-5.45669 + 8.60484i) q^{92} +(-5.87611 - 4.70601i) q^{94} +15.1803 q^{95} -5.81093 q^{97} +(-5.05556 - 4.04885i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−0.884039	+	1.10385i	−0.625110	+	0.780537i
$2$	−0.884039	+	1.10385i	−0.625110	+	0.780537i
$3$		0			0
$3$		0			0
$4$	−0.436951	−	1.95168i	−0.218476	−	0.975842i
$5$	−2.14986	+	0.890503i	−0.961448	+	0.398245i	−0.807522	−	0.589837i	$-0.799192\pi$
$5$	−2.14986	+	0.890503i	−0.961448	+	0.398245i	−0.153926	+	0.988082i	$0.549192\pi$
$6$		0			0
$7$	−1.10001	+	1.10001i	−0.415765	+	0.415765i	−0.883741	−	0.467976i	$-0.844983\pi$
$7$	−1.10001	+	1.10001i	−0.415765	+	0.415765i	0.467976	+	0.883741i	$0.344983\pi$
$8$	2.54064	+	1.24304i	0.898252	+	0.439480i
$9$		0			0
$10$	0.917585	−	3.16036i	0.290166	−	0.999393i
$11$	−0.999449	−	2.41288i	−0.301345	−	0.727511i	−0.999928	−	0.0119825i	$-0.996186\pi$
$11$	−0.999449	−	2.41288i	−0.301345	−	0.727511i	0.698583	−	0.715529i	$-0.253814\pi$
$12$		0			0
$13$	−2.03123	−	0.841362i	−0.563361	−	0.233352i	0.0827824	−	0.996568i	$-0.473619\pi$
$13$	−2.03123	−	0.841362i	−0.563361	−	0.233352i	−0.646144	+	0.763216i	$0.723619\pi$
$14$	−0.241790	−	2.18670i	−0.0646212	−	0.584419i
$15$		0			0
$16$	−3.61815	+	1.70558i	−0.904537	+	0.426395i
$17$		−	5.68481i		−	1.37877i	−0.724396	−	0.689384i	$-0.757881\pi$
$17$		−	5.68481i		−	1.37877i	0.724396	−	0.689384i	$-0.242119\pi$
$18$		0			0
$19$	−6.02698	−	2.49646i	−1.38268	−	0.572726i	−0.437486	−	0.899225i	$-0.644131\pi$
$19$	−6.02698	−	2.49646i	−1.38268	−	0.572726i	−0.945197	+	0.326499i	$0.894131\pi$
$20$	2.67737	+	3.80675i	0.598677	+	0.851215i
$21$		0			0
$22$	3.54700	+	1.02984i	0.756223	+	0.219564i
$23$	−3.60241	−	3.60241i	−0.751154	−	0.751154i	0.223541	−	0.974695i	$-0.428238\pi$
$23$	−3.60241	−	3.60241i	−0.751154	−	0.751154i	−0.974695	+	0.223541i	$0.928238\pi$
$24$		0			0
$25$	0.293385	−	0.293385i	0.0586771	−	0.0586771i
$26$	2.72442	−	1.49837i	0.534302	−	0.293854i
$27$		0			0
$28$	2.62753	+	1.66622i	0.496556	+	0.314887i
$29$	−3.82608	+	9.23698i	−0.710485	+	1.71526i	−0.0117007	+	0.999932i	$0.503725\pi$
$29$	−3.82608	+	9.23698i	−0.710485	+	1.71526i	−0.698785	+	0.715332i	$0.746275\pi$
$30$		0			0
$31$	1.98933			0.357294			0.178647	−	0.983913i	$-0.442828\pi$
$31$	1.98933			0.357294			0.178647	+	0.983913i	$0.442828\pi$
$32$	1.31588	−	5.50168i	0.232618	−	0.972568i
$33$		0			0
$34$	6.27515	+	5.02559i	1.07618	+	0.861882i
$35$	1.38531	−	3.34444i	0.234160	−	0.565313i
$36$		0			0
$37$	5.97179	−	2.47360i	0.981756	−	0.406657i	0.166681	−	0.986011i	$-0.446695\pi$
$37$	5.97179	−	2.47360i	0.981756	−	0.406657i	0.815076	+	0.579354i	$0.196695\pi$
$38$	8.08378	−	4.44589i	1.31136	−	0.721218i
$39$		0			0
$40$	−6.56896	−	0.409916i	−1.03864	−	0.0648134i
$41$	4.33228	+	4.33228i	0.676589	+	0.676589i	0.959227	−	0.282638i	$-0.0912094\pi$
$41$	4.33228	+	4.33228i	0.676589	+	0.676589i	−0.282638	+	0.959227i	$0.591209\pi$
$42$		0			0
$43$	−4.39793	−	10.6175i	−0.670678	−	1.61916i	−0.780462	−	0.625204i	$-0.785016\pi$
$43$	−4.39793	−	10.6175i	−0.670678	−	1.61916i	0.109784	−	0.993955i	$-0.464984\pi$
$44$	−4.27248	+	3.00492i	−0.644100	+	0.453009i
$45$		0			0
$46$	7.16117	−	0.791834i	1.05586	−	0.116750i
$47$			5.32331i			0.776485i	0.921557	+	0.388242i	$0.126918\pi$
$47$			5.32331i			0.776485i	−0.921557	+	0.388242i	$0.873082\pi$
$48$		0			0
$49$			4.57995i			0.654278i
$50$	0.0644882	+	0.583216i	0.00912001	+	0.0824793i
$51$		0			0
$52$	−0.754527	+	4.33195i	−0.104634	+	0.600734i
$53$	−0.802971	−	1.93854i	−0.110297	−	0.266279i	0.859088	−	0.511829i	$-0.171032\pi$
$53$	−0.802971	−	1.93854i	−0.110297	−	0.266279i	−0.969384	+	0.245549i	$0.921032\pi$
$54$		0			0
$55$	4.29736	+	4.29736i	0.579455	+	0.579455i
$56$	−4.16209	+	1.42738i	−0.556183	+	0.190741i
$57$		0			0
$58$	−6.81379	−	12.3892i	−0.894695	−	1.62679i
$59$	−5.97225	+	2.47379i	−0.777521	+	0.322060i	−0.735915	−	0.677074i	$-0.763248\pi$
$59$	−5.97225	+	2.47379i	−0.777521	+	0.322060i	−0.0416066	+	0.999134i	$0.513248\pi$
$60$		0			0
$61$	−3.53897	+	8.54384i	−0.453119	+	1.09393i	0.518010	+	0.855374i	$0.326673\pi$
$61$	−3.53897	+	8.54384i	−0.453119	+	1.09393i	−0.971130	+	0.238552i	$0.923327\pi$
$62$	−1.75864	+	2.19591i	−0.223348	+	0.278881i
$63$		0			0
$64$	4.90971	+	6.31623i	0.613714	+	0.789529i
$65$	5.11610			0.634574
$66$		0			0
$67$	−2.25745	+	5.44997i	−0.275792	+	0.665820i	−0.999710	−	0.0240652i	$-0.992339\pi$
$67$	−2.25745	+	5.44997i	−0.275792	+	0.665820i	0.723919	+	0.689885i	$0.242339\pi$
$68$	−11.0950	+	2.48398i	−1.34546	+	0.301227i
$69$		0			0
$70$	2.46708	+	4.48578i	0.294872	+	0.536154i
$71$	−2.57276	+	2.57276i	−0.305330	+	0.305330i	−0.843095	−	0.537765i	$-0.819269\pi$
$71$	−2.57276	+	2.57276i	−0.305330	+	0.305330i	0.537765	+	0.843095i	$0.319269\pi$
$72$		0			0
$73$	8.01131	+	8.01131i	0.937653	+	0.937653i	0.998167	−	0.0605139i	$-0.0192740\pi$
$73$	8.01131	+	8.01131i	0.937653	+	0.937653i	−0.0605139	+	0.998167i	$0.519274\pi$
$74$	−2.54883	+	8.77869i	−0.296295	+	1.02050i
$75$		0			0
$76$	−2.23880	+	12.8536i	−0.256808	+	1.47441i
$77$	3.75360	+	1.55479i	0.427763	+	0.177185i
$78$		0			0
$79$		−	14.4931i		−	1.63060i	−0.579039	−	0.815300i	$-0.696572\pi$
$79$		−	14.4931i		−	1.63060i	0.579039	−	0.815300i	$-0.303428\pi$
$80$	6.25970	−	6.88874i	0.699856	−	0.770184i
$81$		0			0
$82$	−8.61208	+	0.952266i	−0.951045	+	0.105160i
$83$	−2.50672	−	1.03832i	−0.275148	−	0.113970i	0.240843	−	0.970564i	$-0.422576\pi$
$83$	−2.50672	−	1.03832i	−0.275148	−	0.113970i	−0.515991	+	0.856594i	$0.672576\pi$
$84$		0			0
$85$	5.06234	+	12.2216i	0.549088	+	1.32561i
$86$	15.6081	+	4.53168i	1.68306	+	0.488664i
$87$		0			0
$88$	0.460066	−	7.37262i	0.0490432	−	0.785924i
$89$	2.98746	−	2.98746i	0.316670	−	0.316670i	−0.530817	−	0.847487i	$-0.678115\pi$
$89$	2.98746	−	2.98746i	0.316670	−	0.316670i	0.847487	+	0.530817i	$0.178115\pi$
$90$		0			0
$91$	3.15988	−	1.30887i	0.331246	−	0.137206i
$92$	−5.45669	+	8.60484i	−0.568899	+	0.897116i
$93$		0			0
$94$	−5.87611	−	4.70601i	−0.606075	−	0.485388i
$95$	15.1803			1.55746
$96$		0			0
$97$	−5.81093			−0.590010			−0.295005	−	0.955496i	$-0.595321\pi$
$97$	−5.81093			−0.590010			−0.295005	+	0.955496i	$0.595321\pi$
$98$	−5.05556	−	4.04885i	−0.510688	−	0.408996i
$99$		0			0
$100$	−0.700791	−	0.444401i	−0.0700791	−	0.0444401i
$101$	−2.91259	+	1.20644i	−0.289814	+	0.120045i	−0.522854	−	0.852422i	$-0.675133\pi$
$101$	−2.91259	+	1.20644i	−0.289814	+	0.120045i	0.233040	+	0.972467i	$0.425133\pi$
$102$		0			0
$103$	−5.84034	+	5.84034i	−0.575466	+	0.575466i	−0.933651	−	0.358185i	$-0.883396\pi$
$103$	−5.84034	+	5.84034i	−0.575466	+	0.575466i	0.358185	+	0.933651i	$0.383396\pi$
$104$	−4.11478	−	4.66249i	−0.403487	−	0.457195i
$105$		0			0
$106$	2.84971	+	0.827391i	0.276788	+	0.0803634i
$107$	−3.26727	−	7.88789i	−0.315859	−	0.762551i	−0.999465	−	0.0327002i	$-0.989589\pi$
$107$	−3.26727	−	7.88789i	−0.315859	−	0.762551i	0.683606	−	0.729851i	$-0.260411\pi$
$108$		0			0
$109$	−12.3255	−	5.10538i	−1.18057	−	0.489006i	−0.295894	−	0.955221i	$-0.595618\pi$
$109$	−12.3255	−	5.10538i	−1.18057	−	0.489006i	−0.884672	+	0.466214i	$0.845618\pi$
$110$	−8.54265	+	0.944589i	−0.814510	+	0.0900631i
$111$		0			0
$112$	2.10385	−	5.85616i	0.198795	−	0.553355i
$113$		−	13.6962i		−	1.28843i	−0.764844	−	0.644216i	$-0.777184\pi$
$113$		−	13.6962i		−	1.28843i	0.764844	−	0.644216i	$-0.222816\pi$
$114$		0			0
$115$	10.9526	+	4.53673i	1.02134	+	0.423052i
$116$	19.6995	+	3.43120i	1.82905	+	0.318579i
$117$		0			0
$118$	2.54902	−	8.77937i	0.234657	−	0.808207i
$119$	6.25336	+	6.25336i	0.573244	+	0.573244i
$120$		0			0
$121$	2.95507	−	2.95507i	0.268643	−	0.268643i
$122$	−6.30249	−	11.4596i	−0.570601	−	1.03750i
$123$		0			0
$124$	−0.869238	−	3.88254i	−0.0780599	−	0.348662i
$125$	4.08304	−	9.85732i	0.365198	−	0.881665i
$126$		0			0
$127$	4.61080			0.409142			0.204571	−	0.978852i	$-0.434420\pi$
$127$	4.61080			0.409142			0.204571	+	0.978852i	$0.434420\pi$
$128$	−11.3125	−	0.164227i	−0.999895	−	0.0145158i
$129$		0			0
$130$	−4.52283	+	5.64738i	−0.396678	+	0.495308i
$131$	−0.640651	+	1.54667i	−0.0559740	+	0.135133i	−0.949393	−	0.314092i	$-0.898300\pi$
$131$	−0.640651	+	1.54667i	−0.0559740	+	0.135133i	0.893419	+	0.449225i	$0.148300\pi$
$132$		0			0
$133$	9.37587	−	3.88361i	0.812991	−	0.336752i
$134$	−4.02025	−	7.30987i	−0.347297	−	0.631476i
$135$		0			0
$136$	7.06644	−	14.4431i	0.605942	−	1.23848i
$137$	2.84955	+	2.84955i	0.243454	+	0.243454i	0.818277	−	0.574824i	$-0.194929\pi$
$137$	2.84955	+	2.84955i	0.243454	+	0.243454i	−0.574824	+	0.818277i	$0.694929\pi$
$138$		0			0
$139$	−0.112341	−	0.271215i	−0.00952863	−	0.0230041i	0.919044	−	0.394156i	$-0.128963\pi$
$139$	−0.112341	−	0.271215i	−0.00952863	−	0.0230041i	−0.928572	+	0.371152i	$0.878963\pi$
$140$	−7.13260	−	1.24234i	−0.602815	−	0.104997i
$141$		0			0
$142$	−0.565511	−	5.11435i	−0.0474566	−	0.429187i
$143$			5.74201i			0.480171i
$144$		0			0
$145$		−	23.2654i		−	1.93208i
$146$	−15.9256	+	1.76094i	−1.31801	+	0.145737i
$147$		0			0
$148$	−7.43706	−	10.5742i	−0.611323	−	0.869195i
$149$	5.19437	+	12.5403i	0.425539	+	1.02734i	0.980686	+	0.195590i	$0.0626621\pi$
$149$	5.19437	+	12.5403i	0.425539	+	1.02734i	−0.555147	+	0.831752i	$0.687338\pi$
$150$		0			0
$151$	−1.03696	−	1.03696i	−0.0843863	−	0.0843863i	0.663654	−	0.748040i	$-0.269005\pi$
$151$	−1.03696	−	1.03696i	−0.0843863	−	0.0843863i	−0.748040	+	0.663654i	$0.769005\pi$
$152$	−12.2092	−	13.8344i	−0.990296	−	1.12211i
$153$		0			0
$154$	−5.03458	+	2.76890i	−0.405698	+	0.223124i
$155$	−4.27678	+	1.77150i	−0.343519	+	0.142290i
$156$		0			0
$157$	0.319782	−	0.772022i	0.0255214	−	0.0616140i	−0.910605	−	0.413278i	$-0.864384\pi$
$157$	0.319782	−	0.772022i	0.0255214	−	0.0616140i	0.936126	+	0.351664i	$0.114384\pi$
$158$	15.9981	+	12.8124i	1.27274	+	1.01930i
$159$		0			0
$160$	2.07029	+	12.9997i	0.163671	+	1.02771i
$161$	7.92538			0.624607
$162$		0			0
$163$	1.96818	−	4.75161i	0.154160	−	0.372175i	−0.827865	−	0.560928i	$-0.810445\pi$
$163$	1.96818	−	4.75161i	0.154160	−	0.372175i	0.982025	+	0.188753i	$0.0604446\pi$
$164$	6.56226	−	10.3482i	0.512426	−	0.808062i
$165$		0			0
$166$	3.36218	−	1.84912i	0.260956	−	0.143520i
$167$	4.63248	−	4.63248i	0.358472	−	0.358472i	−0.504778	−	0.863249i	$-0.668426\pi$
$167$	4.63248	−	4.63248i	0.358472	−	0.358472i	0.863249	+	0.504778i	$0.168426\pi$
$168$		0			0
$169$	−5.77439	−	5.77439i	−0.444184	−	0.444184i
$170$	−17.9660	−	5.21630i	−1.37793	−	0.400072i
$171$		0			0
$172$	−18.8004	+	13.2227i	−1.43352	+	1.00822i
$173$	−12.6684	−	5.24743i	−0.963163	−	0.398955i	−0.155000	−	0.987914i	$-0.549538\pi$
$173$	−12.6684	−	5.24743i	−0.963163	−	0.398955i	−0.808163	+	0.588959i	$0.799538\pi$
$174$		0			0
$175$			0.645455i			0.0487918i
$176$	7.73152	+	7.02552i	0.582785	+	0.529569i
$177$		0			0
$178$	0.656665	+	5.93872i	0.0492191	+	0.445126i
$179$	8.55352	+	3.54299i	0.639320	+	0.264815i	0.678707	−	0.734409i	$-0.262540\pi$
$179$	8.55352	+	3.54299i	0.639320	+	0.264815i	−0.0393869	+	0.999224i	$0.512540\pi$
$180$		0			0
$181$	−0.495989	−	1.19742i	−0.0368666	−	0.0890039i	0.904374	−	0.426741i	$-0.140338\pi$
$181$	−0.495989	−	1.19742i	−0.0368666	−	0.0890039i	−0.941240	+	0.337737i	$0.890338\pi$
$182$	−1.34867	+	4.64511i	−0.0999702	+	0.344319i
$183$		0			0
$184$	−4.67449	−	13.6303i	−0.344608	−	1.00484i
$185$	−10.6358	+	10.6358i	−0.781959	+	0.781959i
$186$		0			0
$187$	−13.7168	+	5.68167i	−1.00307	+	0.415485i
$188$	10.3894	−	2.32603i	0.757727	−	0.169643i
$189$		0			0
$190$	−13.4200	+	16.7567i	−0.973586	+	1.21566i
$191$	0.646843			0.0468039			0.0234019	−	0.999726i	$-0.492550\pi$
$191$	0.646843			0.0468039			0.0234019	+	0.999726i	$0.492550\pi$
$192$		0			0
$193$	18.7195			1.34746			0.673730	−	0.738978i	$-0.264691\pi$
$193$	18.7195			1.34746			0.673730	+	0.738978i	$0.264691\pi$
$194$	5.13708	−	6.41437i	0.368821	−	0.460525i
$195$		0			0
$196$	8.93862	−	2.00121i	0.638473	−	0.142944i
$197$	0.597874	−	0.247647i	0.0425967	−	0.0176441i	−0.361283	−	0.932456i	$-0.617661\pi$
$197$	0.597874	−	0.247647i	0.0425967	−	0.0176441i	0.403880	+	0.914812i	$0.367661\pi$
$198$		0			0
$199$	−13.5447	+	13.5447i	−0.960158	+	0.960158i	−0.999236	−	0.0390782i	$-0.987558\pi$
$199$	−13.5447	+	13.5447i	−0.960158	+	0.960158i	0.0390782	+	0.999236i	$0.487558\pi$
$200$	1.11008	−	0.380698i	0.0784943	−	0.0269194i
$201$		0			0
$202$	1.24313	−	4.28159i	0.0874660	−	0.301251i
$203$	−5.95205	−	14.3695i	−0.417752	−	1.00854i
$204$		0			0
$205$	−13.1717	−	5.45591i	−0.919953	−	0.381057i
$206$	−1.28375	−	11.6099i	−0.0894430	−	0.808902i
$207$		0			0
$208$	8.78429	−	0.420252i	0.609081	−	0.0291392i
$209$			17.0375i			1.17851i
$210$		0			0
$211$	23.9743	+	9.93047i	1.65046	+	0.683642i	0.997290	−	0.0735712i	$-0.0234396\pi$
$211$	23.9743	+	9.93047i	1.65046	+	0.683642i	0.653168	+	0.757213i	$0.273440\pi$
$212$	−3.43257	+	2.41420i	−0.235750	+	0.165808i
$213$		0			0
$214$	11.5954	+	3.36664i	0.792646	+	0.230139i
$215$	18.9099	+	18.9099i	1.28964	+	1.28964i
$216$		0			0
$217$	−2.18828	+	2.18828i	−0.148550	+	0.148550i
$218$	16.5317	−	9.09207i	1.11967	−	0.615793i
$219$		0			0
$220$	6.50935	−	10.2648i	0.438860	−	0.692054i
$221$	−4.78298	+	11.5471i	−0.321738	+	0.776745i
$222$		0			0
$223$	1.90075			0.127284			0.0636420	−	0.997973i	$-0.479728\pi$
$223$	1.90075			0.127284			0.0636420	+	0.997973i	$0.479728\pi$
$224$	4.60442	+	7.49940i	0.307646	+	0.501075i
$225$		0			0
$226$	15.1185	+	12.1080i	1.00567	+	0.805412i
$227$	6.11900	−	14.7726i	0.406132	−	0.980490i	−0.580013	−	0.814607i	$-0.696953\pi$
$227$	6.11900	−	14.7726i	0.406132	−	0.980490i	0.986145	−	0.165883i	$-0.0530473\pi$
$228$		0			0
$229$	−11.9674	+	4.95706i	−0.790828	+	0.327572i	−0.741277	−	0.671200i	$-0.765779\pi$
$229$	−11.9674	+	4.95706i	−0.790828	+	0.327572i	−0.0495519	+	0.998772i	$0.515779\pi$
$230$	−14.6904	+	8.07937i	−0.968657	+	0.532738i
$231$		0			0
$232$	−21.2026	+	18.7119i	−1.39202	+	1.22849i
$233$	−5.40070	−	5.40070i	−0.353811	−	0.353811i	0.507714	−	0.861526i	$-0.330491\pi$
$233$	−5.40070	−	5.40070i	−0.353811	−	0.353811i	−0.861526	+	0.507714i	$0.830491\pi$
$234$		0			0
$235$	−4.74042	−	11.4444i	−0.309231	−	0.746550i
$236$	7.43764	+	10.5750i	0.484149	+	0.688376i
$237$		0			0
$238$	−12.4309	+	1.37453i	−0.805779	+	0.0890977i
$239$		−	22.6418i		−	1.46458i	−0.680995	−	0.732288i	$-0.738453\pi$
$239$		−	22.6418i		−	1.46458i	0.680995	−	0.732288i	$-0.261547\pi$
$240$		0			0
$241$		−	20.4844i		−	1.31951i	−0.751479	−	0.659757i	$-0.770659\pi$
$241$		−	20.4844i		−	1.31951i	0.751479	−	0.659757i	$-0.229341\pi$
$242$	0.649545	+	5.87434i	0.0417544	+	0.377617i
$243$		0			0
$244$	18.2212	+	3.17372i	1.16650	+	0.203177i
$245$	−4.07846	−	9.84627i	−0.260563	−	0.629055i
$246$		0			0
$247$	10.1417	+	10.1417i	0.645303	+	0.645303i
$248$	5.05416	+	2.47281i	0.320940	+	0.157024i
$249$		0			0
$250$	7.27140	+	13.2213i	0.459884	+	0.836188i
$251$	−12.6079	+	5.22237i	−0.795804	+	0.329633i	−0.743275	−	0.668986i	$-0.766728\pi$
$251$	−12.6079	+	5.22237i	−0.795804	+	0.329633i	−0.0525298	+	0.998619i	$0.516728\pi$
$252$		0			0
$253$	−5.09176	+	12.2926i	−0.320116	+	0.772829i
$254$	−4.07613	+	5.08961i	−0.255759	+	0.319351i
$255$		0			0
$256$	10.1820	−	12.3421i	0.636374	−	0.771381i
$257$	−12.4131			−0.774307			−0.387153	−	0.922015i	$-0.626542\pi$
$257$	−12.4131			−0.774307			−0.387153	+	0.922015i	$0.626542\pi$
$258$		0			0
$259$	−3.84805	+	9.29003i	−0.239106	+	0.577254i
$260$	−2.23548	−	9.98501i	−0.138639	−	0.619244i
$261$		0			0
$262$	−1.14092	−	2.07450i	−0.0704865	−	0.128163i
$263$	−17.4830	+	17.4830i	−1.07805	+	1.07805i	−0.0813652	+	0.996684i	$0.525928\pi$
$263$	−17.4830	+	17.4830i	−1.07805	+	1.07805i	−0.996684	+	0.0813652i	$0.974072\pi$
$264$		0			0
$265$	3.45256	+	3.45256i	0.212089	+	0.212089i
$266$	−4.00172	+	13.7828i	−0.245361	+	0.845077i
$267$		0			0
$268$	11.6230	+	2.02447i	0.709989	+	0.123664i
$269$	−11.1213	−	4.60660i	−0.678079	−	0.280869i	0.0169449	−	0.999856i	$-0.494606\pi$
$269$	−11.1213	−	4.60660i	−0.678079	−	0.280869i	−0.695023	+	0.718987i	$0.744606\pi$
$270$		0			0
$271$			18.4077i			1.11819i	0.829105	+	0.559093i	$0.188850\pi$
$271$			18.4077i			1.11819i	−0.829105	+	0.559093i	$0.811150\pi$
$272$	9.69590	+	20.5685i	0.587900	+	1.24715i
$273$		0			0
$274$	−5.66459	+	0.626352i	−0.342210	+	0.0378393i
$275$	−1.00113	−	0.414681i	−0.0603703	−	0.0250062i
$276$		0			0
$277$	−4.36873	−	10.5471i	−0.262492	−	0.633711i	0.736600	−	0.676329i	$-0.236430\pi$
$277$	−4.36873	−	10.5471i	−0.262492	−	0.633711i	−0.999091	+	0.0426179i	$0.986430\pi$
$278$	0.398693	+	0.115757i	0.0239120	+	0.00694267i
$279$		0			0
$280$	7.67685	−	6.77502i	0.458779	−	0.404885i
$281$	5.71168	−	5.71168i	0.340730	−	0.340730i	−0.515912	−	0.856642i	$-0.672547\pi$
$281$	5.71168	−	5.71168i	0.340730	−	0.340730i	0.856642	+	0.515912i	$0.172547\pi$
$282$		0			0
$283$	−8.28088	+	3.43005i	−0.492247	+	0.203896i	−0.614978	−	0.788545i	$-0.710835\pi$
$283$	−8.28088	+	3.43005i	−0.492247	+	0.203896i	0.122730	+	0.992440i	$0.460835\pi$
$284$	6.14538	+	3.89705i	0.364661	+	0.231247i
$285$		0			0
$286$	−6.33830	−	5.07616i	−0.374791	−	0.300160i
$287$	−9.53112			−0.562604
$288$		0			0
$289$	−15.3170			−0.901003
$290$	25.6814	+	20.5675i	1.50806	+	1.20776i
$291$		0			0
$292$	12.1350	−	19.1361i	0.710148	−	1.11986i
$293$	17.2497	−	7.14508i	1.00774	−	0.417420i	0.183111	−	0.983092i	$-0.441383\pi$
$293$	17.2497	−	7.14508i	1.00774	−	0.417420i	0.824630	+	0.565672i	$0.191383\pi$
$294$		0			0
$295$	10.6366	−	10.6366i	0.619288	−	0.619288i
$296$	18.2470	+	1.13865i	1.06058	+	0.0661824i
$297$		0			0
$298$	−18.4346	−	5.35234i	−1.06789	−	0.310053i
$299$	4.28638	+	10.3482i	0.247888	+	0.598454i
$300$		0			0
$301$	16.5172	+	6.84164i	0.952035	+	0.394346i
$302$	2.06135	−	0.227930i	0.118617	−	0.0131159i
$303$		0			0
$304$	26.0644	−	1.24695i	1.49490	−	0.0715177i
$305$		−	21.5196i		−	1.23221i
$306$		0			0
$307$	−0.294424	−	0.121954i	−0.0168036	−	0.00696030i	0.374266	−	0.927321i	$-0.377895\pi$
$307$	−0.294424	−	0.121954i	−0.0168036	−	0.00696030i	−0.391069	+	0.920361i	$0.627895\pi$
$308$	1.39433	−	8.00522i	0.0794491	−	0.456140i
$309$		0			0
$310$	1.82538	−	6.28698i	0.103674	−	0.357077i
$311$	−9.49039	−	9.49039i	−0.538151	−	0.538151i	0.384835	−	0.922986i	$-0.374258\pi$
$311$	−9.49039	−	9.49039i	−0.538151	−	0.538151i	−0.922986	+	0.384835i	$0.874258\pi$
$312$		0			0
$313$	−23.1330	+	23.1330i	−1.30756	+	1.30756i	−0.384383	+	0.923174i	$0.625586\pi$
$313$	−23.1330	+	23.1330i	−1.30756	+	1.30756i	−0.923174	+	0.384383i	$0.874414\pi$
$314$	0.569493	+	1.03549i	0.0321384	+	0.0584359i
$315$		0			0
$316$	−28.2859	+	6.33277i	−1.59121	+	0.356246i
$317$	1.17141	−	2.82804i	0.0657931	−	0.158839i	−0.887563	−	0.460686i	$-0.847603\pi$
$317$	1.17141	−	2.82804i	0.0657931	−	0.158839i	0.953356	+	0.301848i	$0.0976034\pi$
$318$		0			0
$319$	26.1117			1.46198
$320$	−16.1798	−	9.20692i	−0.904480	−	0.514682i
$321$		0			0
$322$	−7.00634	+	8.74839i	−0.390448	+	0.487529i
$323$	−14.1919	+	34.2622i	−0.789657	+	1.90640i
$324$		0			0
$325$	−0.842776	+	0.349089i	−0.0467488	+	0.0193640i
$326$	3.50509	+	6.37317i	0.194129	+	0.352977i
$327$		0			0
$328$	5.62158	+	16.3920i	0.310400	+	0.905095i
$329$	−5.85570	−	5.85570i	−0.322835	−	0.322835i
$330$		0			0
$331$	5.82090	+	14.0529i	0.319946	+	0.772417i	0.999256	+	0.0385662i	$0.0122791\pi$
$331$	5.82090	+	14.0529i	0.319946	+	0.772417i	−0.679310	+	0.733851i	$0.737721\pi$
$332$	−0.931155	+	5.34602i	−0.0511038	+	0.293401i
$333$		0			0
$334$	1.01825	+	9.20883i	0.0557162	+	0.503885i
$335$		−	13.7270i		−	0.749984i
$336$		0			0
$337$		−	4.16517i		−	0.226891i	−0.993544	−	0.113446i	$-0.963811\pi$
$337$		−	4.16517i		−	0.226891i	0.993544	−	0.113446i	$-0.0361888\pi$
$338$	11.4788	−	1.26925i	0.624366	−	0.0690382i
$339$		0			0
$340$	21.6406	−	15.2203i	1.17363	−	0.825437i
$341$	−1.98823	−	4.80001i	−0.107669	−	0.259935i
$342$		0			0
$343$	−12.7381	−	12.7381i	−0.687792	−	0.687792i
$344$	2.02445	−	32.4421i	0.109151	−	1.74916i
$345$		0			0
$346$	16.9917	−	9.34505i	0.913481	−	0.502393i
$347$	29.5450	−	12.2380i	1.58606	−	0.656968i	0.596702	−	0.802463i	$-0.296478\pi$
$347$	29.5450	−	12.2380i	1.58606	−	0.656968i	0.989359	+	0.145495i	$0.0464775\pi$
$348$		0			0
$349$	11.3566	−	27.4173i	0.607907	−	1.46762i	−0.257365	−	0.966314i	$-0.582854\pi$
$349$	11.3566	−	27.4173i	0.607907	−	1.46762i	0.865272	−	0.501302i	$-0.167146\pi$
$350$	−0.712483	−	0.570607i	−0.0380838	−	0.0305002i
$351$		0			0
$352$	−14.5901	+	2.32357i	−0.777653	+	0.123847i
$353$	−4.26063			−0.226771			−0.113385	−	0.993551i	$-0.536169\pi$
$353$	−4.26063			−0.226771			−0.113385	+	0.993551i	$0.536169\pi$
$354$		0			0
$355$	3.24003	−	7.82213i	0.171963	−	0.415156i
$356$	−7.13595	−	4.52521i	−0.378205	−	0.239835i
$357$		0			0
$358$	−11.4726	+	6.30964i	−0.606344	+	0.333475i
$359$	−4.97012	+	4.97012i	−0.262313	+	0.262313i	−0.825993	−	0.563680i	$-0.809385\pi$
$359$	−4.97012	+	4.97012i	−0.262313	+	0.262313i	0.563680	+	0.825993i	$0.309385\pi$
$360$		0			0
$361$	16.6571	+	16.6571i	0.876691	+	0.876691i
$362$	1.76025	+	0.511074i	0.0925165	+	0.0268614i
$363$		0			0
$364$	−3.93521	−	5.59519i	−0.206261	−	0.293267i
$365$	−24.3573	−	10.0891i	−1.27492	−	0.528090i
$366$		0			0
$367$		−	15.0671i		−	0.786495i	−0.919433	−	0.393247i	$-0.871352\pi$
$367$		−	15.0671i		−	0.786495i	0.919433	−	0.393247i	$-0.128648\pi$
$368$	19.1782	+	6.88984i	0.999734	+	0.359158i
$369$		0			0
$370$	−2.33782	−	21.1427i	−0.121538	−	1.09916i
$371$	3.01570	+	1.24914i	0.156567	+	0.0648523i
$372$		0			0
$373$	−6.17375	−	14.9048i	−0.319665	−	0.771739i	−0.999272	−	0.0381624i	$-0.987850\pi$
$373$	−6.17375	−	14.9048i	−0.319665	−	0.771739i	0.679607	−	0.733577i	$-0.262150\pi$
$374$	5.85447	−	20.1640i	0.302727	−	1.04266i
$375$		0			0
$376$	−6.61708	+	13.5246i	−0.341250	+	0.697479i
$377$	15.5433	−	15.5433i	0.800520	−	0.800520i
$378$		0			0
$379$	0.511585	−	0.211905i	0.0262783	−	0.0108848i	−0.369506	−	0.929229i	$-0.620473\pi$
$379$	0.511585	−	0.211905i	0.0262783	−	0.0108848i	0.395784	+	0.918344i	$0.370473\pi$
$380$	−6.63304	−	29.6271i	−0.340268	−	1.51984i
$381$		0			0
$382$	−0.571834	+	0.714014i	−0.0292576	+	0.0365322i
$383$	−6.05003			−0.309142			−0.154571	−	0.987982i	$-0.549400\pi$
$383$	−6.05003			−0.309142			−0.154571	+	0.987982i	$0.549400\pi$
$384$		0			0
$385$	−9.45429			−0.481835
$386$	−16.5488	+	20.6635i	−0.842310	+	1.05174i
$387$		0			0
$388$	2.53909	+	11.3411i	0.128903	+	0.575757i
$389$	10.1717	−	4.21324i	0.515724	−	0.213620i	−0.109613	−	0.993974i	$-0.534961\pi$
$389$	10.1717	−	4.21324i	0.515724	−	0.213620i	0.625338	+	0.780354i	$0.284961\pi$
$390$		0			0
$391$	−20.4790	+	20.4790i	−1.03567	+	1.03567i
$392$	−5.69305	+	11.6360i	−0.287543	+	0.587707i
$393$		0			0
$394$	−0.255179	+	0.878890i	−0.0128557	+	0.0442778i
$395$	12.9061	+	31.1582i	0.649378	+	1.56774i
$396$		0			0
$397$	−22.5585	−	9.34403i	−1.13218	−	0.468963i	−0.263657	−	0.964616i	$-0.584929\pi$
$397$	−22.5585	−	9.34403i	−1.13218	−	0.468963i	−0.868521	+	0.495653i	$0.834929\pi$
$398$	−2.97722	−	26.9253i	−0.149235	−	1.34964i
$399$		0			0
$400$	−0.561119	+	1.56190i	−0.0280560	+	0.0780952i
$401$			26.6309i			1.32988i	0.746895	+	0.664942i	$0.231544\pi$
$401$			26.6309i			1.32988i	−0.746895	+	0.664942i	$0.768456\pi$
$402$		0			0
$403$	−4.04077	−	1.67374i	−0.201285	−	0.0833751i
$404$	3.62724	+	5.15731i	0.180462	+	0.256586i
$405$		0			0
$406$	21.1236	+	6.13307i	1.04835	+	0.304379i
$407$	−11.9370	−	11.9370i	−0.591695	−	0.591695i
$408$		0			0
$409$	−15.3022	+	15.3022i	−0.756647	+	0.756647i	−0.975710	−	0.219064i	$-0.929700\pi$
$409$	−15.3022	+	15.3022i	−0.756647	+	0.756647i	0.219064	+	0.975710i	$0.429700\pi$
$410$	17.6668	−	9.71632i	0.872501	−	0.479855i
$411$		0			0
$412$	13.9504	+	8.84656i	0.687289	+	0.435839i
$413$	3.84835	−	9.29075i	0.189365	−	0.457168i
$414$		0			0
$415$	6.31374			0.309929
$416$	−7.30176	+	10.0680i	−0.357998	+	0.493626i
$417$		0			0
$418$	−18.8067	−	15.0618i	−0.919867	−	0.736696i
$419$	−7.92030	+	19.1213i	−0.386932	+	0.934136i	0.603654	+	0.797246i	$0.293711\pi$
$419$	−7.92030	+	19.1213i	−0.386932	+	0.934136i	−0.990586	+	0.136890i	$0.956289\pi$
$420$		0			0
$421$	29.2323	−	12.1084i	1.42469	−	0.590128i	0.468659	−	0.883379i	$-0.344737\pi$
$421$	29.2323	−	12.1084i	1.42469	−	0.590128i	0.956035	+	0.293251i	$0.0947373\pi$
$422$	−32.1559	+	17.6850i	−1.56533	+	0.860892i
$423$		0			0
$424$	0.369623	−	5.92327i	0.0179505	−	0.287659i
$425$	−1.66784	−	1.66784i	−0.0809021	−	0.0809021i
$426$		0			0
$427$	−5.50541	−	13.2912i	−0.266425	−	0.643208i
$428$	−13.9670	+	9.82331i	−0.675123	+	0.474828i
$429$		0			0
$430$	−37.5907	+	4.15653i	−1.81278	+	0.200446i
$431$			1.99673i			0.0961789i	0.998843	+	0.0480895i	$0.0153133\pi$
$431$			1.99673i			0.0961789i	−0.998843	+	0.0480895i	$0.984687\pi$
$432$		0			0
$433$			16.8123i			0.807948i	0.914770	+	0.403974i	$0.132371\pi$
$433$			16.8123i			0.807948i	−0.914770	+	0.403974i	$0.867629\pi$
$434$	−0.481000	−	4.35005i	−0.0230887	−	0.208809i
$435$		0			0
$436$	−4.57846	+	26.2862i	−0.219269	+	1.25888i
$437$	12.7184	+	30.7049i	0.608402	+	1.46881i
$438$		0			0
$439$	−23.5940	−	23.5940i	−1.12608	−	1.12608i	−0.990808	−	0.135274i	$-0.956809\pi$
$439$	−23.5940	−	23.5940i	−1.12608	−	1.12608i	−0.135274	−	0.990808i	$-0.543191\pi$
$440$	5.57626	+	16.2598i	0.265838	+	0.775156i
$441$		0			0
$442$	−8.51792	−	15.4878i	−0.405156	−	0.736679i
$443$	21.0559	−	8.72163i	1.00039	−	0.414377i	0.178453	−	0.983948i	$-0.442891\pi$
$443$	21.0559	−	8.72163i	1.00039	−	0.414377i	0.821942	+	0.569571i	$0.192891\pi$
$444$		0			0
$445$	−3.76229	+	9.08297i	−0.178350	+	0.430574i
$446$	−1.68034	+	2.09814i	−0.0795664	+	0.0993498i
$447$		0			0
$448$	−12.3487	−	1.54719i	−0.583420	−	0.0730977i
$449$	−29.2703			−1.38135			−0.690675	−	0.723165i	$-0.742686\pi$
$449$	−29.2703			−1.38135			−0.690675	+	0.723165i	$0.742686\pi$
$450$		0			0
$451$	6.12339	−	14.7832i	0.288339	−	0.696113i
$452$	−26.7307	+	5.98458i	−1.25731	+	0.281491i
$453$		0			0
$454$	10.8972	+	19.8140i	0.511431	+	0.929915i
$455$	−5.62777	+	5.62777i	−0.263834	+	0.263834i
$456$		0			0
$457$	−13.2549	−	13.2549i	−0.620040	−	0.620040i	0.325502	−	0.945541i	$-0.394467\pi$
$457$	−13.2549	−	13.2549i	−0.620040	−	0.620040i	−0.945541	+	0.325502i	$0.894467\pi$
$458$	5.10782	−	17.5924i	0.238673	−	0.822039i
$459$		0			0
$460$	4.06850	−	23.3584i	0.189695	−	1.08909i
$461$	36.5469	+	15.1382i	1.70216	+	0.705057i	0.999976	−	0.00694059i	$-0.00220928\pi$
$461$	36.5469	+	15.1382i	1.70216	+	0.705057i	0.702182	+	0.711997i	$0.252209\pi$
$462$		0			0
$463$		−	18.4673i		−	0.858250i	−0.903245	−	0.429125i	$-0.858822\pi$
$463$		−	18.4673i		−	0.858250i	0.903245	−	0.429125i	$-0.141178\pi$
$464$	−1.91109	−	39.9464i	−0.0887201	−	1.85447i
$465$		0			0
$466$	10.7360	−	1.18711i	0.497334	−	0.0549919i
$467$	−0.983296	−	0.407295i	−0.0455015	−	0.0188474i	0.359817	−	0.933023i	$-0.382839\pi$
$467$	−0.983296	−	0.407295i	−0.0455015	−	0.0188474i	−0.405318	+	0.914176i	$0.632839\pi$
$468$		0			0
$469$	−3.51181	−	8.47826i	−0.162160	−	0.391490i
$470$	16.8236	+	4.88459i	0.776013	+	0.225309i
$471$		0			0
$472$	−18.2484	−	1.13873i	−0.839949	−	0.0524145i
$473$	−21.2234	+	21.2234i	−0.975851	+	0.975851i
$474$		0			0
$475$	−2.50065	+	1.03580i	−0.114738	+	0.0475259i
$476$	9.47217	−	14.9370i	0.434156	−	0.684636i
$477$		0			0
$478$	24.9930	+	20.0162i	1.14316	+	0.915521i
$479$	−19.1585			−0.875375			−0.437687	−	0.899127i	$-0.644202\pi$
$479$	−19.1585			−0.875375			−0.437687	+	0.899127i	$0.644202\pi$
$480$		0			0
$481$	−14.2113			−0.647978
$482$	22.6116	+	18.1090i	1.02993	+	0.824841i
$483$		0			0
$484$	−7.05859	−	4.47615i	−0.320845	−	0.203461i
$485$	12.4927	−	5.17465i	0.567264	−	0.234969i
$486$		0			0
$487$	26.4107	−	26.4107i	1.19678	−	1.19678i	0.221660	−	0.975124i	$-0.428852\pi$
$487$	26.4107	−	26.4107i	1.19678	−	1.19678i	0.975124	−	0.221660i	$-0.0711477\pi$
$488$	−19.6116	+	17.3077i	−0.887775	+	0.783485i
$489$		0			0
$490$	14.4743	+	4.20249i	0.653881	+	0.189849i
$491$	−9.74865	−	23.5353i	−0.439951	−	1.06213i	−0.975965	−	0.217926i	$-0.930071\pi$
$491$	−9.74865	−	23.5353i	−0.439951	−	1.06213i	0.536015	−	0.844209i	$-0.319929\pi$
$492$		0			0
$493$	52.5104	+	21.7505i	2.36495	+	0.979595i
$494$	−20.1606	+	2.22923i	−0.907069	+	0.100298i
$495$		0			0
$496$	−7.19768	+	3.39296i	−0.323185	+	0.152348i
$497$		−	5.66013i		−	0.253892i
$498$		0			0
$499$	12.2231	+	5.06299i	0.547183	+	0.226651i	0.639110	−	0.769115i	$-0.279303\pi$
$499$	12.2231	+	5.06299i	0.547183	+	0.226651i	−0.0919272	+	0.995766i	$0.529303\pi$
$500$	−21.0225	−	3.66163i	−0.940153	−	0.163753i
$501$		0			0
$502$	5.38119	−	18.5340i	0.240174	−	0.827212i
$503$	−21.6420	−	21.6420i	−0.964970	−	0.964970i	0.0344366	−	0.999407i	$-0.489036\pi$
$503$	−21.6420	−	21.6420i	−0.964970	−	0.964970i	−0.999407	+	0.0344366i	$0.989036\pi$
$504$		0			0
$505$	5.18734	−	5.18734i	0.230834	−	0.230834i
$506$	−9.06782	−	16.4877i	−0.403114	−	0.732966i
$507$		0			0
$508$	−2.01469	−	8.99883i	−0.0893876	−	0.399259i
$509$	−1.14400	+	2.76185i	−0.0507067	+	0.122417i	−0.947203	−	0.320634i	$-0.896104\pi$
$509$	−1.14400	+	2.76185i	−0.0507067	+	0.122417i	0.896496	+	0.443051i	$0.146104\pi$
$510$		0			0
$511$	−17.6251			−0.779688
$512$	4.62250	+	22.1502i	0.204287	+	0.978911i
$513$		0			0
$514$	10.9736	−	13.7021i	0.484027	−	0.604375i
$515$	7.35510	−	17.7568i	0.324104	−	0.782457i
$516$		0			0
$517$	12.8445	−	5.32037i	0.564901	−	0.233990i
$518$	−6.85293	−	12.4604i	−0.301100	−	0.547479i
$519$		0			0
$520$	12.9982	+	6.35951i	0.570007	+	0.278883i
$521$	16.6745	+	16.6745i	0.730525	+	0.730525i	0.970724	−	0.240199i	$-0.0772126\pi$
$521$	16.6745	+	16.6745i	0.730525	+	0.730525i	−0.240199	+	0.970724i	$0.577213\pi$
$522$		0			0
$523$	0.461277	+	1.11362i	0.0201703	+	0.0486953i	0.933644	−	0.358203i	$-0.116610\pi$
$523$	0.461277	+	1.11362i	0.0201703	+	0.0486953i	−0.913474	+	0.406898i	$0.866610\pi$
$524$	3.29854	+	0.574531i	0.144098	+	0.0250985i
$525$		0			0
$526$	−3.84289	−	34.7542i	−0.167558	−	1.51536i
$527$		−	11.3089i		−	0.492625i
$528$		0			0
$529$			2.95466i			0.128463i
$530$	−6.86328	+	0.758896i	−0.298122	+	0.0329643i
$531$		0			0
$532$	−11.6764	−	16.6018i	−0.506236	−	0.719779i
$533$	−5.15484	−	12.4449i	−0.223281	−	0.539047i
$534$		0			0
$535$	14.0484	+	14.0484i	0.607364	+	0.607364i
$536$	−12.5099	+	11.0403i	−0.540345	+	0.476869i
$537$		0			0
$538$	14.9166	−	8.20380i	0.643102	−	0.353691i
$539$	11.0509	−	4.57742i	0.475995	−	0.197164i
$540$		0			0
$541$	−4.79193	+	11.5687i	−0.206021	+	0.497379i	−0.992790	−	0.119869i	$-0.961753\pi$
$541$	−4.79193	+	11.5687i	−0.206021	+	0.497379i	0.786768	+	0.617248i	$0.211753\pi$
$542$	−20.3192	−	16.2731i	−0.872785	−	0.698988i
$543$		0			0
$544$	−31.2760	−	7.48055i	−1.34095	−	0.320726i
$545$	31.0444			1.32980
$546$		0			0
$547$	−10.4863	+	25.3162i	−0.448363	+	1.08244i	0.524573	+	0.851366i	$0.324225\pi$
$547$	−10.4863	+	25.3162i	−0.448363	+	1.08244i	−0.972935	+	0.231078i	$0.925775\pi$
$548$	4.31632	−	6.80655i	0.184384	−	0.290761i
$549$		0			0
$550$	1.34278	−	0.738497i	0.0572563	−	0.0314896i
$551$	46.1194	−	46.1194i	1.96475	−	1.96475i
$552$		0			0
$553$	15.9426	+	15.9426i	0.677947	+	0.677947i
$554$	15.5044	+	4.50160i	0.658721	+	0.191255i
$555$		0			0
$556$	−0.480238	+	0.337762i	−0.0203666	+	0.0143243i
$557$	10.9293	+	4.52708i	0.463091	+	0.191818i	0.602015	−	0.798485i	$-0.294365\pi$
$557$	10.9293	+	4.52708i	0.463091	+	0.191818i	−0.138925	+	0.990303i	$0.544365\pi$
$558$		0			0
$559$			25.2669i			1.06868i
$560$	0.691949	+	14.4634i	0.0292402	+	0.611192i
$561$		0			0
$562$	1.25547	+	11.3542i	0.0529587	+	0.478946i
$563$	33.9735	+	14.0723i	1.43181	+	0.593076i	0.957798	−	0.287442i	$-0.0928047\pi$
$563$	33.9735	+	14.0723i	1.43181	+	0.593076i	0.474014	+	0.880518i	$0.342805\pi$
$564$		0			0
$565$	12.1965	+	29.4450i	0.513112	+	1.23876i
$566$	3.53437	−	12.1731i	0.148561	−	0.511674i
$567$		0			0
$568$	−9.73449	+	3.33842i	−0.408450	+	0.140077i
$569$	3.61769	−	3.61769i	0.151661	−	0.151661i	−0.627198	−	0.778860i	$-0.715798\pi$
$569$	3.61769	−	3.61769i	0.151661	−	0.151661i	0.778860	+	0.627198i	$0.215798\pi$
$570$		0			0
$571$	−14.7686	+	6.11734i	−0.618045	+	0.256003i	−0.669664	−	0.742664i	$-0.733562\pi$
$571$	−14.7686	+	6.11734i	−0.618045	+	0.256003i	0.0516188	+	0.998667i	$0.483562\pi$
$572$	11.2066	−	2.50898i	0.468571	−	0.104906i
$573$		0			0
$574$	8.42588	−	10.5209i	0.351690	−	0.439134i
$575$	−2.11379			−0.0881510
$576$		0			0
$577$	42.0367			1.75001			0.875005	−	0.484114i	$-0.160858\pi$
$577$	42.0367			1.75001			0.875005	+	0.484114i	$0.160858\pi$
$578$	13.5409	−	16.9077i	0.563226	−	0.703266i
$579$		0			0
$580$	−45.4067	+	10.1658i	−1.88541	+	0.422113i
$581$	3.89959	−	1.61526i	0.161782	−	0.0670123i
$582$		0			0
$583$	−3.87495	+	3.87495i	−0.160484	+	0.160484i
$584$	10.3955	+	30.3122i	0.430169	+	1.25433i
$585$		0			0
$586$	−7.36238	+	25.3576i	−0.304137	+	1.04751i
$587$	8.05275	+	19.4411i	0.332372	+	0.802418i	0.998403	+	0.0564936i	$0.0179920\pi$
$587$	8.05275	+	19.4411i	0.332372	+	0.802418i	−0.666031	+	0.745925i	$0.732008\pi$
$588$		0			0
$589$	−11.9896	−	4.96626i	−0.494024	−	0.204631i
$590$	2.33800	+	21.1444i	0.0962541	+	0.870500i
$591$		0			0
$592$	−17.3879	+	19.1352i	−0.714638	+	0.786453i
$593$			24.6856i			1.01372i	0.862029	+	0.506858i	$0.169193\pi$
$593$			24.6856i			1.01372i	−0.862029	+	0.506858i	$0.830807\pi$
$594$		0			0
$595$	−19.0125	−	7.87523i	−0.779436	−	0.322853i
$596$	22.2050	−	15.6173i	0.909554	−	0.639708i
$597$		0			0
$598$	−15.2122	−	4.41674i	−0.622072	−	0.180614i
$599$	0.292862	+	0.292862i	0.0119660	+	0.0119660i	0.713064	−	0.701098i	$-0.247307\pi$
$599$	0.292862	+	0.292862i	0.0119660	+	0.0119660i	−0.701098	+	0.713064i	$0.747307\pi$
$600$		0			0
$601$	17.9233	−	17.9233i	0.731107	−	0.731107i	−0.239732	−	0.970839i	$-0.577059\pi$
$601$	17.9233	−	17.9233i	0.731107	−	0.731107i	0.970839	+	0.239732i	$0.0770595\pi$
$602$	−22.1539	+	12.1841i	−0.902928	+	0.496589i
$603$		0			0
$604$	−1.57071	+	2.47691i	−0.0639114	+	0.100784i
$605$	−3.72150	+	8.98450i	−0.151301	+	0.365272i
$606$		0			0
$607$	−30.0813			−1.22096			−0.610481	−	0.792031i	$-0.709024\pi$
$607$	−30.0813			−1.22096			−0.610481	+	0.792031i	$0.709024\pi$
$608$	−21.6655	+	29.8734i	−0.878652	+	1.21153i
$609$		0			0
$610$	23.7543	+	19.0241i	0.961782	+	0.770264i
$611$	4.47883	−	10.8129i	0.181194	−	0.437441i
$612$		0			0
$613$	−8.13147	+	3.36816i	−0.328427	+	0.136039i	−0.540803	−	0.841149i	$-0.681880\pi$
$613$	−8.13147	+	3.36816i	−0.328427	+	0.136039i	0.212377	+	0.977188i	$0.431880\pi$
$614$	0.394900	−	0.217186i	0.0159369	−	0.00876491i
$615$		0			0
$616$	7.60389	+	8.61605i	0.306369	+	0.347150i
$617$	13.3355	+	13.3355i	0.536869	+	0.536869i	0.922608	−	0.385739i	$-0.126054\pi$
$617$	13.3355	+	13.3355i	0.536869	+	0.536869i	−0.385739	+	0.922608i	$0.626054\pi$
$618$		0			0
$619$	9.84872	+	23.7769i	0.395853	+	0.955674i	0.988638	+	0.150314i	$0.0480284\pi$
$619$	9.84872	+	23.7769i	0.395853	+	0.955674i	−0.592785	+	0.805361i	$0.701972\pi$
$620$	5.32615	+	7.57287i	0.213903	+	0.304134i
$621$		0			0
$622$	18.8658	−	2.08606i	0.756450	−	0.0836432i
$623$			6.57248i			0.263321i
$624$		0			0
$625$			26.9024i			1.07610i
$626$	−5.08481	−	45.9858i	−0.203230	−	1.83796i
$627$		0			0
$628$	−1.64647	−	0.286778i	−0.0657014	−	0.0114437i
$629$	−14.0619	−	33.9485i	−0.560686	−	1.35361i
$630$		0			0
$631$	3.24320	+	3.24320i	0.129110	+	0.129110i	0.768709	−	0.639599i	$-0.220900\pi$
$631$	3.24320	+	3.24320i	0.129110	+	0.129110i	−0.639599	+	0.768709i	$0.720900\pi$
$632$	18.0155	−	36.8217i	0.716616	−	1.46469i
$633$		0			0
$634$	2.08615	+	3.79316i	0.0828514	+	0.150645i
$635$	−9.91260	+	4.10593i	−0.393369	+	0.162939i
$636$		0			0
$637$	3.85340	−	9.30292i	0.152677	−	0.368595i
$638$	−23.0838	+	28.8233i	−0.913895	+	1.14113i
$639$		0			0
$640$	24.4666	−	9.72076i	0.967128	−	0.384247i
$641$	−27.4171			−1.08291			−0.541455	−	0.840729i	$-0.682126\pi$
$641$	−27.4171			−1.08291			−0.541455	+	0.840729i	$0.682126\pi$
$642$		0			0
$643$	−0.821316	+	1.98283i	−0.0323896	+	0.0781953i	−0.939247	−	0.343243i	$-0.888475\pi$
$643$	−0.821316	+	1.98283i	−0.0323896	+	0.0781953i	0.906857	+	0.421438i	$0.138475\pi$
$644$	−3.46300	−	15.4678i	−0.136461	−	0.609518i
$645$		0			0
$646$	−25.2740	−	45.9548i	−0.994393	−	1.80807i
$647$	−13.6349	+	13.6349i	−0.536044	+	0.536044i	−0.922365	−	0.386321i	$-0.873746\pi$
$647$	−13.6349	+	13.6349i	−0.536044	+	0.536044i	0.386321	+	0.922365i	$0.373746\pi$
$648$		0			0
$649$	11.9379	+	11.9379i	0.468604	+	0.468604i
$650$	0.359706	−	1.23890i	0.0141088	−	0.0485938i
$651$		0			0
$652$	−10.1336	−	1.76505i	−0.396864	−	0.0691246i
$653$	12.3455	+	5.11368i	0.483118	+	0.200114i	0.610930	−	0.791684i	$-0.290796\pi$
$653$	12.3455	+	5.11368i	0.483118	+	0.200114i	−0.127813	+	0.991798i	$0.540796\pi$
$654$		0			0
$655$		−	3.89563i		−	0.152215i
$656$	−23.0639	−	8.28578i	−0.900494	−	0.323505i
$657$		0			0
$658$	11.6405	−	1.28712i	0.453792	−	0.0501773i
$659$	−26.7406	−	11.0763i	−1.04166	−	0.431472i	−0.204755	−	0.978813i	$-0.565640\pi$
$659$	−26.7406	−	11.0763i	−1.04166	−	0.431472i	−0.836909	+	0.547342i	$0.815640\pi$
$660$		0			0
$661$	5.00939	+	12.0937i	0.194843	+	0.470392i	0.990862	−	0.134879i	$-0.0430646\pi$
$661$	5.00939	+	12.0937i	0.194843	+	0.470392i	−0.796019	+	0.605271i	$0.793065\pi$
$662$	−20.6581	−	5.99793i	−0.802901	−	0.233116i
$663$		0			0
$664$	−5.07801	−	5.75394i	−0.197065	−	0.223296i
$665$	−16.6985	+	16.6985i	−0.647539	+	0.647539i
$666$		0			0
$667$	47.0584	−	19.4922i	1.82211	−	0.754743i
$668$	−11.0653	−	7.01697i	−0.428129	−	0.271495i
$669$		0			0
$670$	15.1525	+	12.1352i	0.585390	+	0.468823i
$671$	24.1523			0.932389
$672$		0			0
$673$	−25.2282			−0.972477			−0.486239	−	0.873826i	$-0.661631\pi$
$673$	−25.2282			−0.972477			−0.486239	+	0.873826i	$0.661631\pi$
$674$	4.59771	+	3.68217i	0.177097	+	0.141832i
$675$		0			0
$676$	−8.74667	+	13.7929i	−0.336410	+	0.530497i
$677$	−10.3092	+	4.27021i	−0.396214	+	0.164117i	−0.571889	−	0.820331i	$-0.693789\pi$
$677$	−10.3092	+	4.27021i	−0.396214	+	0.164117i	0.175675	+	0.984448i	$0.443789\pi$
$678$		0			0
$679$	6.39209	−	6.39209i	0.245306	−	0.245306i
$680$	−2.33029	+	37.3433i	−0.0893627	+	1.43205i
$681$		0			0
$682$	7.05614	+	2.04870i	0.270194	+	0.0784486i
$683$	4.79116	+	11.5669i	0.183329	+	0.442595i	0.988649	−	0.150246i	$-0.0480065\pi$
$683$	4.79116	+	11.5669i	0.183329	+	0.442595i	−0.805320	+	0.592840i	$0.798006\pi$
$684$		0			0
$685$	−8.66369	−	3.58862i	−0.331023	−	0.137114i
$686$	25.3218	−	2.79992i	0.966792	−	0.106901i
$687$		0			0
$688$	34.0214	+	30.9148i	1.29705	+	1.17862i
$689$			4.61321i			0.175749i
$690$		0			0
$691$	5.63700	+	2.33492i	0.214441	+	0.0888245i	0.487318	−	0.873224i	$-0.337975\pi$
$691$	5.63700	+	2.33492i	0.214441	+	0.0888245i	−0.272877	+	0.962049i	$0.587975\pi$
$692$	−4.70586	+	27.0176i	−0.178890	+	1.02706i
$693$		0			0
$694$	−12.6101	+	43.4320i	−0.478674	+	1.64866i
$695$	0.483035	+	0.483035i	0.0183226	+	0.0183226i
$696$		0			0
$697$	24.6282	−	24.6282i	0.932860	−	0.932860i
$698$	20.2248	+	36.7740i	0.765520	+	1.39192i
$699$		0			0
$700$	1.25972	−	0.282032i	0.0476131	−	0.0106598i
$701$	9.95368	−	24.0303i	0.375945	−	0.907612i	−0.616772	−	0.787142i	$-0.711560\pi$
$701$	9.95368	−	24.0303i	0.375945	−	0.907612i	0.992717	−	0.120470i	$-0.0384402\pi$
$702$		0			0
$703$	−42.1671			−1.59036
$704$	10.3333	−	18.1593i	0.389451	−	0.684404i
$705$		0			0
$706$	3.76656	−	4.70308i	0.141756	−	0.177003i
$707$	1.87679	−	4.53098i	0.0705840	−	0.170405i
$708$		0			0
$709$	−36.9193	+	15.2925i	−1.38653	+	0.574322i	−0.946221	−	0.323522i	$-0.895133\pi$
$709$	−36.9193	+	15.2925i	−1.38653	+	0.574322i	−0.440314	+	0.897844i	$0.645133\pi$
$710$	5.77011	+	10.4916i	0.216548	+	0.393741i
$711$		0			0
$712$	11.3036	−	3.87653i	0.423620	−	0.145279i
$713$	−7.16636	−	7.16636i	−0.268382	−	0.268382i
$714$		0			0
$715$	−5.11328	−	12.3445i	−0.191226	−	0.461660i
$716$	3.17732	−	18.2419i	0.118742	−	0.681732i
$717$		0			0
$718$	−1.09247	−	9.88002i	−0.0407705	−	0.368719i
$719$			38.7035i			1.44340i	0.692208	+	0.721698i	$0.256638\pi$
$719$			38.7035i			1.44340i	−0.692208	+	0.721698i	$0.743362\pi$
$720$		0			0
$721$		−	12.8489i		−	0.478518i
$722$	−33.1124	+	3.66135i	−1.23232	+	0.136261i
$723$		0			0
$724$	−2.12027	+	1.49123i	−0.0787993	+	0.0554212i
$725$	1.58748	+	3.83251i	0.0589575	+	0.142336i
$726$		0			0
$727$	−8.44191	−	8.44191i	−0.313093	−	0.313093i	0.533014	−	0.846107i	$-0.321059\pi$
$727$	−8.44191	−	8.44191i	−0.313093	−	0.313093i	−0.846107	+	0.533014i	$0.821059\pi$
$728$	9.65510	+	0.602497i	0.357842	+	0.0223300i
$729$		0			0
$730$	32.6697	−	17.9676i	1.20916	−	0.665009i
$731$	−60.3587	+	25.0014i	−2.23245	+	0.924709i
$732$		0			0
$733$	8.42070	−	20.3294i	0.311026	−	0.750883i	−0.688642	−	0.725102i	$-0.741793\pi$
$733$	8.42070	−	20.3294i	0.311026	−	0.750883i	0.999668	−	0.0257810i	$-0.00820726\pi$
$734$	16.6317	+	13.3199i	0.613888	+	0.491646i
$735$		0			0
$736$	−24.5596	+	15.0789i	−0.905280	+	0.555817i
$737$	15.4064			0.567500
$738$		0			0
$739$	6.97881	−	16.8483i	0.256720	−	0.619776i	−0.741998	−	0.670402i	$-0.766122\pi$
$739$	6.97881	−	16.8483i	0.256720	−	0.619776i	0.998718	+	0.0506261i	$0.0161217\pi$
$740$	25.4050	+	16.1104i	0.933908	+	0.592230i
$741$		0			0
$742$	−4.04486	+	2.22457i	−0.148491	+	0.0816667i
$743$	−12.3355	+	12.3355i	−0.452546	+	0.452546i	−0.896199	−	0.443653i	$-0.853682\pi$
$743$	−12.3355	+	12.3355i	−0.452546	+	0.452546i	0.443653	+	0.896199i	$0.353682\pi$
$744$		0			0
$745$	−22.3344	−	22.3344i	−0.818267	−	0.818267i
$746$	21.9104	+	6.36151i	0.802196	+	0.232911i
$747$		0			0
$748$	17.0824	+	24.2882i	0.624594	+	0.888065i
$749$	12.2708	+	5.08274i	0.448366	+	0.185719i
$750$		0			0
$751$		−	17.5511i		−	0.640449i	−0.947342	−	0.320224i	$-0.896242\pi$
$751$		−	17.5511i		−	0.640449i	0.947342	−	0.320224i	$-0.103758\pi$
$752$	−9.07934	−	19.2605i	−0.331089	−	0.702359i
$753$		0			0
$754$	3.41652	+	30.8983i	0.124422	+	1.12525i
$755$	3.15273	+	1.30590i	0.114740	+	0.0475267i
$756$		0			0
$757$	2.89105	+	6.97962i	0.105077	+	0.253679i	0.967670	−	0.252220i	$-0.0811608\pi$
$757$	2.89105	+	6.97962i	0.105077	+	0.253679i	−0.862593	+	0.505899i	$0.831161\pi$
$758$	−0.218350	+	0.752043i	−0.00793083	+	0.0273154i
$759$		0			0
$760$	38.5676	+	18.8697i	1.39900	+	0.684475i
$761$	−22.3535	+	22.3535i	−0.810314	+	0.810314i	−0.984681	−	0.174367i	$-0.944212\pi$
$761$	−22.3535	+	22.3535i	−0.810314	+	0.810314i	0.174367	+	0.984681i	$0.444212\pi$
$762$		0			0
$763$	19.1741	−	7.94219i	0.694150	−	0.287527i
$764$	−0.282638	−	1.26243i	−0.0102255	−	0.0456732i
$765$		0			0
$766$	5.34846	−	6.67830i	0.193248	−	0.241297i
$767$	14.2124			0.513179
$768$		0			0
$769$	−3.22764			−0.116392			−0.0581958	−	0.998305i	$-0.518535\pi$
$769$	−3.22764			−0.116392			−0.0581958	+	0.998305i	$0.518535\pi$
$770$	8.35795	−	10.4361i	0.301200	−	0.376090i
$771$		0			0
$772$	−8.17951	−	36.5346i	−0.294387	−	1.31491i
$773$	−6.48169	+	2.68480i	−0.233130	+	0.0965656i	−0.496190	−	0.868214i	$-0.665268\pi$
$773$	−6.48169	+	2.68480i	−0.233130	+	0.0965656i	0.263060	+	0.964779i	$0.415268\pi$
$774$		0			0
$775$	0.583639	−	0.583639i	0.0209649	−	0.0209649i
$776$	−14.7635	−	7.22320i	−0.529978	−	0.259298i
$777$		0			0
$778$	−4.34138	+	14.9526i	−0.155646	+	0.536078i
$779$	−15.2952	−	36.9259i	−0.548008	−	1.32301i
$780$		0			0
$781$	8.77910	+	3.63642i	0.314141	+	0.130121i
$782$	−4.50143	−	40.7099i	−0.160971	−	1.45578i
$783$		0			0
$784$	−7.81147	−	16.5709i	−0.278981	−	0.591819i
$785$			1.94451i			0.0694025i
$786$		0			0
$787$	−44.8838	−	18.5915i	−1.59994	−	0.662715i	−0.608530	−	0.793531i	$-0.708240\pi$
$787$	−44.8838	−	18.5915i	−1.59994	−	0.662715i	−0.991407	+	0.130816i	$0.958240\pi$
$788$	−0.744571	−	1.05865i	−0.0265242	−	0.0377129i
$789$		0			0
$790$	−45.8033	−	13.2986i	−1.62961	−	0.473144i
$791$	15.0660	+	15.0660i	0.535685	+	0.535685i
$792$		0			0
$793$	14.3769	−	14.3769i	0.510540	−	0.510540i
$794$	30.2569	−	16.6406i	1.07378	−	0.590553i
$795$		0			0
$796$	32.3533	+	20.5166i	1.14673	+	0.727192i
$797$	9.68913	−	23.3916i	0.343207	−	0.828574i	−0.654181	−	0.756338i	$-0.726986\pi$
$797$	9.68913	−	23.3916i	0.343207	−	0.828574i	0.997388	−	0.0722361i	$-0.0230135\pi$
$798$		0			0
$799$	30.2620			1.07059
$800$	−1.22805	−	2.00017i	−0.0434182	−	0.0707168i
$801$		0			0
$802$	−29.3964	−	23.5428i	−1.03802	−	0.831324i
$803$	11.3235	−	27.3373i	0.399596	−	0.964711i
$804$		0			0
$805$	−17.0385	+	7.05757i	−0.600528	+	0.248747i
$806$	5.41976	−	2.98074i	0.190903	−	0.104992i
$807$		0			0
$808$	−8.89949	−	0.555346i	−0.313083	−	0.0195370i
$809$	−21.6097	−	21.6097i	−0.759757	−	0.759757i	0.216521	−	0.976278i	$-0.430529\pi$
$809$	−21.6097	−	21.6097i	−0.759757	−	0.759757i	−0.976278	+	0.216521i	$0.930529\pi$
$810$		0			0
$811$	0.140101	+	0.338233i	0.00491960	+	0.0118770i	0.926320	−	0.376737i	$-0.122954\pi$
$811$	0.140101	+	0.338233i	0.00491960	+	0.0118770i	−0.921401	+	0.388614i	$0.872954\pi$
$812$	−25.4440	+	17.8953i	−0.892910	+	0.628002i
$813$		0			0
$814$	23.7294	−	2.62384i	0.831714	−	0.0919654i
$815$			11.9680i			0.419220i
$816$		0			0
$817$			74.9709i			2.62290i
$818$	−3.36354	−	30.4191i	−0.117603	−	1.06358i
$819$		0			0
$820$	−4.89281	+	28.0910i	−0.170864	+	0.980981i
$821$	−1.08174	−	2.61154i	−0.0377528	−	0.0911434i	0.903878	−	0.427789i	$-0.140707\pi$
$821$	−1.08174	−	2.61154i	−0.0377528	−	0.0911434i	−0.941631	+	0.336646i	$0.890707\pi$
$822$		0			0
$823$	−21.0047	−	21.0047i	−0.732179	−	0.732179i	0.238872	−	0.971051i	$-0.423222\pi$
$823$	−21.0047	−	21.0047i	−0.732179	−	0.732179i	−0.971051	+	0.238872i	$0.923222\pi$
$824$	−22.0980	+	7.57844i	−0.769819	+	0.264007i
$825$		0			0
$826$	6.85346	+	12.4614i	0.238462	+	0.433586i
$827$	−19.4976	+	8.07616i	−0.677997	+	0.280835i	−0.694989	−	0.719020i	$-0.744591\pi$
$827$	−19.4976	+	8.07616i	−0.677997	+	0.280835i	0.0169924	+	0.999856i	$0.494591\pi$
$828$		0			0
$829$	−8.42223	+	20.3331i	−0.292516	+	0.706196i	−1.00000		0.000533349i	$-0.999830\pi$
$829$	−8.42223	+	20.3331i	−0.292516	+	0.706196i	0.707484	+	0.706730i	$0.249830\pi$
$830$	−5.58159	+	6.96939i	−0.193740	+	0.241911i
$831$		0			0
$832$	−4.65851	−	16.9605i	−0.161505	−	0.588001i
$833$	26.0361			0.902098
$834$		0			0
$835$	−5.83396	+	14.0844i	−0.201893	+	0.487412i
$836$	33.2518	−	7.44454i	1.15004	−	0.257475i
$837$		0			0
$838$	−14.1051	−	25.6468i	−0.487253	−	0.885952i
$839$	8.19553	−	8.19553i	0.282941	−	0.282941i	−0.551340	−	0.834281i	$-0.685883\pi$
$839$	8.19553	−	8.19553i	0.282941	−	0.282941i	0.834281	+	0.551340i	$0.185883\pi$
$840$		0			0
$841$	−50.1768	−	50.1768i	−1.73023	−	1.73023i
$842$	−12.4767	+	42.9722i	−0.429974	+	1.48092i
$843$		0			0
$844$	8.90557	−	51.1294i	0.306542	−	1.75995i
$845$	17.5563	+	7.27204i	0.603954	+	0.250166i
$846$		0			0
$847$			6.50123i			0.223385i
$848$	6.21161	+	5.64440i	0.213308	+	0.193830i
$849$		0			0
$850$	3.31547	−	0.366603i	0.113720	−	0.0125744i
$851$	−30.4237	−	12.6019i	−1.04291	−	0.431988i
$852$		0			0
$853$	3.85955	+	9.31778i	0.132148	+	0.319035i	0.976078	−	0.217419i	$-0.0697637\pi$
$853$	3.85955	+	9.31778i	0.132148	+	0.319035i	−0.843930	+	0.536453i	$0.819764\pi$
$854$	19.5385	+	5.67284i	0.668593	+	0.194121i
$855$		0			0
$856$	1.50399	−	24.1016i	0.0514053	−	0.823777i
$857$	16.3295	−	16.3295i	0.557806	−	0.557806i	−0.370876	−	0.928682i	$-0.620943\pi$
$857$	16.3295	−	16.3295i	0.557806	−	0.557806i	0.928682	+	0.370876i	$0.120943\pi$
$858$		0			0
$859$	18.7583	−	7.76993i	0.640024	−	0.265107i	−0.0389814	−	0.999240i	$-0.512411\pi$
$859$	18.7583	−	7.76993i	0.640024	−	0.265107i	0.679005	+	0.734133i	$0.262411\pi$
$860$	28.6435	−	45.1688i	0.976734	−	1.54024i
$861$		0			0
$862$	−2.20408	−	1.76518i	−0.0750712	−	0.0601224i
$863$	−25.9774			−0.884280			−0.442140	−	0.896946i	$-0.645780\pi$
$863$	−25.9774			−0.884280			−0.442140	+	0.896946i	$0.645780\pi$
$864$		0			0
$865$	31.9082			1.08491
$866$	−18.5582	−	14.8627i	−0.630633	−	0.505056i
$867$		0			0
$868$	5.22701	+	3.31466i	0.177416	+	0.112507i
$869$	−34.9701	+	14.4851i	−1.18628	+	0.491373i
$870$		0			0
$871$	9.17080	−	9.17080i	0.310741	−	0.310741i
$872$	−24.9684	−	28.2920i	−0.845537	−	0.958087i
$873$		0			0
$874$	−45.1370	−	13.1052i	−1.52678	−	0.443289i
$875$	6.35178	+	15.3346i	0.214729	+	0.518403i
$876$		0			0
$877$	−10.3735	−	4.29686i	−0.350289	−	0.145095i	0.200599	−	0.979673i	$-0.435711\pi$
$877$	−10.3735	−	4.29686i	−0.350289	−	0.145095i	−0.550889	+	0.834579i	$0.685711\pi$
$878$	46.9022	−	5.18614i	1.58287	−	0.175024i
$879$		0			0
$880$	−22.8780	−	8.21898i	−0.771216	−	0.277062i
$881$		−	23.3514i		−	0.786727i	−0.919383	−	0.393364i	$-0.871311\pi$
$881$		−	23.3514i		−	0.786727i	0.919383	−	0.393364i	$-0.128689\pi$
$882$		0			0
$883$	−16.9363	−	7.01525i	−0.569953	−	0.236082i	0.0790470	−	0.996871i	$-0.474812\pi$
$883$	−16.9363	−	7.01525i	−0.569953	−	0.236082i	−0.649000	+	0.760789i	$0.724812\pi$
$884$	24.6263	+	4.28934i	0.828273	+	0.144266i
$885$		0			0
$886$	−8.98687	+	30.9527i	−0.301920	+	1.03988i
$887$	−31.0507	−	31.0507i	−1.04258	−	1.04258i	−0.999052	−	0.0435268i	$-0.986141\pi$
$887$	−31.0507	−	31.0507i	−1.04258	−	1.04258i	−0.0435268	−	0.999052i	$-0.513859\pi$
$888$		0			0
$889$	−5.07194	+	5.07194i	−0.170107	+	0.170107i
$890$	−6.70019	−	12.1827i	−0.224591	−	0.408365i
$891$		0			0
$892$	−0.830536	−	3.70967i	−0.0278084	−	0.124209i
$893$	13.2894	−	32.0835i	0.444713	−	1.07363i
$894$		0			0
$895$	−21.5440			−0.720135
$896$	12.6246	−	12.2632i	0.421757	−	0.409686i
$897$		0			0
$898$	25.8761	−	32.3099i	0.863495	−	1.07819i
$899$	−7.61132	+	18.3754i	−0.253852	+	0.612853i
$900$		0			0
$901$	−11.0202	+	4.56474i	−0.367138	+	0.152073i
$902$	10.9050	+	19.8282i	0.363098	+	0.660207i
$903$		0			0
$904$	17.0249	−	34.7972i	0.566241	−	1.15734i
$905$	2.13262	+	2.13262i	0.0708907	+	0.0708907i
$906$		0			0
$907$	13.3144	+	32.1439i	0.442098	+	1.06732i	0.975211	+	0.221276i	$0.0710220\pi$
$907$	13.3144	+	32.1439i	0.442098	+	1.06732i	−0.533113	+	0.846044i	$0.678978\pi$
$908$	−31.5051	−	5.48747i	−1.04553	−	0.182108i
$909$		0			0
$910$	−1.23702	−	11.1874i	−0.0410069	−	0.370857i
$911$		−	30.1527i		−	0.999003i	−0.866313	−	0.499501i	$-0.833517\pi$
$911$		−	30.1527i		−	0.999003i	0.866313	−	0.499501i	$-0.166483\pi$
$912$		0			0
$913$			7.08617i			0.234518i
$914$	26.3493	−	2.91353i	0.871557	−	0.0963709i
$915$		0			0
$916$	14.9038	+	21.1906i	0.492435	+	0.700158i
$917$	−0.996630	−	2.40608i	−0.0329116	−	0.0794557i
$918$		0			0
$919$	40.8534	+	40.8534i	1.34763	+	1.34763i	0.888230	+	0.459399i	$0.151935\pi$
$919$	40.8534	+	40.8534i	1.34763	+	1.34763i	0.459399	+	0.888230i	$0.348065\pi$
$920$	22.1874	+	25.1407i	0.731496	+	0.828866i
$921$		0			0
$922$	−49.0191	+	26.9594i	−1.61436	+	0.887859i
$923$	7.39048	−	3.06124i	0.243261	−	0.100762i
$924$		0			0
$925$	1.02632	−	2.47775i	0.0337452	−	0.0814681i
$926$	20.3851	+	16.3258i	0.669895	+	0.536500i
$927$		0			0
$928$	45.7842	+	33.2047i	1.50294	+	1.09000i
$929$	−17.8445			−0.585459			−0.292730	−	0.956195i	$-0.594564\pi$
$929$	−17.8445			−0.585459			−0.292730	+	0.956195i	$0.594564\pi$
$930$		0			0
$931$	11.4336	−	27.6032i	0.374722	−	0.904660i
$932$	−8.18062	+	12.9003i	−0.267965	+	0.422563i
$933$		0			0
$934$	1.31886	−	0.725343i	0.0431545	−	0.0237340i
$935$	24.4296	−	24.4296i	0.798935	−	0.798935i
$936$		0			0
$937$	−23.4570	−	23.4570i	−0.766305	−	0.766305i	0.211149	−	0.977454i	$-0.432280\pi$
$937$	−23.4570	−	23.4570i	−0.766305	−	0.766305i	−0.977454	+	0.211149i	$0.932280\pi$
$938$	12.4633	+	3.61861i	0.406940	+	0.118152i
$939$		0			0
$940$	−20.2645	+	14.2524i	−0.660956	+	0.464864i
$941$	−52.6462	−	21.8068i	−1.71622	−	0.710880i	−0.999914	−	0.0130904i	$-0.995833\pi$
$941$	−52.6462	−	21.8068i	−1.71622	−	0.710880i	−0.716303	−	0.697790i	$-0.754167\pi$
$942$		0			0
$943$		−	31.2133i		−	1.01644i
$944$	17.3893	−	19.1367i	0.565972	−	0.622847i
$945$		0			0
$946$	−4.66504	−	42.1896i	−0.151674	−	1.37170i
$947$	16.8510	+	6.97991i	0.547583	+	0.226817i	0.639285	−	0.768970i	$-0.279231\pi$
$947$	16.8510	+	6.97991i	0.547583	+	0.226817i	−0.0917013	+	0.995787i	$0.529231\pi$
$948$		0			0
$949$	−9.53239	−	23.0132i	−0.309434	−	0.747041i
$950$	1.06730	−	3.67602i	0.0346279	−	0.119266i
$951$		0			0
$952$	8.11437	+	23.6607i	0.262988	+	0.766847i
$953$	12.6109	−	12.6109i	0.408508	−	0.408508i	−0.472710	−	0.881218i	$-0.656724\pi$
$953$	12.6109	−	12.6109i	0.408508	−	0.408508i	0.881218	+	0.472710i	$0.156724\pi$
$954$		0			0
$955$	−1.39062	+	0.576015i	−0.0449995	+	0.0186394i
$956$	−44.1896	+	9.89335i	−1.42920	+	0.319974i
$957$		0			0
$958$	16.9369	−	21.1480i	0.547205	−	0.683262i
$959$	−6.26909			−0.202439
$960$		0			0
$961$	−27.0426			−0.872341
$962$	12.5633	−	15.6870i	0.405057	−	0.505771i
$963$		0			0
$964$	−39.9790	+	8.95067i	−1.28764	+	0.288282i
$965$	−40.2444	+	16.6698i	−1.29551	+	0.536619i
$966$		0			0
$967$	25.3370	−	25.3370i	0.814782	−	0.814782i	−0.170564	−	0.985347i	$-0.554559\pi$
$967$	25.3370	−	25.3370i	0.814782	−	0.814782i	0.985347	+	0.170564i	$0.0545591\pi$
$968$	11.1810	−	3.83451i	0.359372	−	0.123246i
$969$		0			0
$970$	−5.33202	+	18.3646i	−0.171201	+	0.589652i
$971$	5.11357	+	12.3453i	0.164102	+	0.396178i	0.984445	−	0.175695i	$-0.0562171\pi$
$971$	5.11357	+	12.3453i	0.164102	+	0.396178i	−0.820342	+	0.571873i	$0.806217\pi$
$972$		0			0
$973$	0.421916	+	0.174763i	0.0135260	+	0.00560265i
$974$	5.80526	+	52.5015i	0.186013	+	1.68226i
$975$		0			0
$976$	−1.76768	−	36.9489i	−0.0565821	−	1.18270i
$977$		−	56.2505i		−	1.79961i	−0.436291	−	0.899806i	$-0.643708\pi$
$977$		−	56.2505i		−	1.79961i	0.436291	−	0.899806i	$-0.356292\pi$
$978$		0			0
$979$	−10.1942	−	4.22258i	−0.325808	−	0.134954i
$980$	−17.4347	+	12.2622i	−0.556932	+	0.391702i
$981$		0			0
$982$	34.5976	+	10.0451i	1.10405	+	0.320553i
$983$	36.5021	+	36.5021i	1.16424	+	1.16424i	0.983538	+	0.180699i	$0.0578360\pi$
$983$	36.5021	+	36.5021i	1.16424	+	1.16424i	0.180699	+	0.983538i	$0.442164\pi$
$984$		0			0
$985$	−1.06482	+	1.06482i	−0.0339279	+	0.0339279i
$986$	−70.4305	+	38.7351i	−2.24296	+	1.23358i
$987$		0			0
$988$	15.3620	−	24.2249i	0.488732	−	0.770698i
$989$	−22.4056	+	54.0918i	−0.712455	+	1.72002i
$990$		0			0
$991$	−18.2602			−0.580054			−0.290027	−	0.957018i	$-0.593664\pi$
$991$	−18.2602			−0.580054			−0.290027	+	0.957018i	$0.593664\pi$
$992$	2.61772	−	10.9446i	0.0831128	−	0.347492i
$993$		0			0
$994$	6.24791	+	5.00377i	0.198172	+	0.158710i
$995$	17.0577	−	41.1808i	0.540764	−	1.30552i
$996$		0			0
$997$	26.7726	−	11.0896i	0.847898	−	0.351211i	0.0839354	−	0.996471i	$-0.473251\pi$
$997$	26.7726	−	11.0896i	0.847898	−	0.351211i	0.763963	+	0.645260i	$0.223251\pi$
$998$	−16.3945	+	9.01659i	−0.518959	+	0.285415i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.v.d.109.3		32
3.2	odd	2		96.2.n.a.13.6	✓	32
4.3	odd	2		1152.2.v.c.145.2		32
12.11	even	2		384.2.n.a.145.8		32
24.5	odd	2		768.2.n.a.289.5		32
24.11	even	2		768.2.n.b.289.1		32
32.5	even	8	inner	288.2.v.d.37.3		32
32.27	odd	8		1152.2.v.c.1009.2		32
96.5	odd	8		96.2.n.a.37.6	yes	32
96.11	even	8		768.2.n.b.481.1		32
96.53	odd	8		768.2.n.a.481.5		32
96.59	even	8		384.2.n.a.241.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.6	✓	32	3.2	odd	2
96.2.n.a.37.6	yes	32	96.5	odd	8
288.2.v.d.37.3		32	32.5	even	8	inner
288.2.v.d.109.3		32	1.1	even	1	trivial
384.2.n.a.145.8		32	12.11	even	2
384.2.n.a.241.8		32	96.59	even	8
768.2.n.a.289.5		32	24.5	odd	2
768.2.n.a.481.5		32	96.53	odd	8
768.2.n.b.289.1		32	24.11	even	2
768.2.n.b.481.1		32	96.11	even	8
1152.2.v.c.145.2		32	4.3	odd	2
1152.2.v.c.1009.2		32	32.27	odd	8

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.884039 + 1.10385i) q^{2} +(-0.436951 - 1.95168i) q^{4} +(-2.14986 + 0.890503i) q^{5} +(-1.10001 + 1.10001i) q^{7} +(2.54064 + 1.24304i) q^{8} +O(q^{10})\)	\(q+(-0.884039 + 1.10385i) q^{2} +(-0.436951 - 1.95168i) q^{4} +(-2.14986 + 0.890503i) q^{5} +(-1.10001 + 1.10001i) q^{7} +(2.54064 + 1.24304i) q^{8} +(0.917585 - 3.16036i) q^{10} +(-0.999449 - 2.41288i) q^{11} +(-2.03123 - 0.841362i) q^{13} +(-0.241790 - 2.18670i) q^{14} +(-3.61815 + 1.70558i) q^{16} -5.68481i q^{17} +(-6.02698 - 2.49646i) q^{19} +(2.67737 + 3.80675i) q^{20} +(3.54700 + 1.02984i) q^{22} +(-3.60241 - 3.60241i) q^{23} +(0.293385 - 0.293385i) q^{25} +(2.72442 - 1.49837i) q^{26} +(2.62753 + 1.66622i) q^{28} +(-3.82608 + 9.23698i) q^{29} +1.98933 q^{31} +(1.31588 - 5.50168i) q^{32} +(6.27515 + 5.02559i) q^{34} +(1.38531 - 3.34444i) q^{35} +(5.97179 - 2.47360i) q^{37} +(8.08378 - 4.44589i) q^{38} +(-6.56896 - 0.409916i) q^{40} +(4.33228 + 4.33228i) q^{41} +(-4.39793 - 10.6175i) q^{43} +(-4.27248 + 3.00492i) q^{44} +(7.16117 - 0.791834i) q^{46} +5.32331i q^{47} +4.57995i q^{49} +(0.0644882 + 0.583216i) q^{50} +(-0.754527 + 4.33195i) q^{52} +(-0.802971 - 1.93854i) q^{53} +(4.29736 + 4.29736i) q^{55} +(-4.16209 + 1.42738i) q^{56} +(-6.81379 - 12.3892i) q^{58} +(-5.97225 + 2.47379i) q^{59} +(-3.53897 + 8.54384i) q^{61} +(-1.75864 + 2.19591i) q^{62} +(4.90971 + 6.31623i) q^{64} +5.11610 q^{65} +(-2.25745 + 5.44997i) q^{67} +(-11.0950 + 2.48398i) q^{68} +(2.46708 + 4.48578i) q^{70} +(-2.57276 + 2.57276i) q^{71} +(8.01131 + 8.01131i) q^{73} +(-2.54883 + 8.77869i) q^{74} +(-2.23880 + 12.8536i) q^{76} +(3.75360 + 1.55479i) q^{77} -14.4931i q^{79} +(6.25970 - 6.88874i) q^{80} +(-8.61208 + 0.952266i) q^{82} +(-2.50672 - 1.03832i) q^{83} +(5.06234 + 12.2216i) q^{85} +(15.6081 + 4.53168i) q^{86} +(0.460066 - 7.37262i) q^{88} +(2.98746 - 2.98746i) q^{89} +(3.15988 - 1.30887i) q^{91} +(-5.45669 + 8.60484i) q^{92} +(-5.87611 - 4.70601i) q^{94} +15.1803 q^{95} -5.81093 q^{97} +(-5.05556 - 4.04885i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 + 32 * q^14 - 8 * q^16 + 32 * q^20 - 8 * q^22 + 16 * q^23 - 40 * q^26 + 40 * q^28 - 48 * q^31 - 40 * q^32 + 40 * q^34 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 16 * q^43 - 8 * q^44 - 32 * q^46 - 24 * q^50 - 8 * q^52 + 32 * q^53 + 32 * q^55 - 56 * q^56 - 32 * q^58 - 64 * q^59 - 32 * q^61 - 48 * q^62 + 24 * q^64 + 16 * q^67 + 8 * q^68 - 24 * q^70 - 64 * q^71 + 32 * q^74 - 56 * q^76 + 32 * q^77 + 56 * q^80 - 40 * q^82 + 64 * q^86 - 48 * q^88 - 48 * q^91 + 80 * q^92 - 32 * q^94 + 80 * q^98

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