LMFDB - Embedded newform 819.2.fn.e.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	819.73
Dual form			819.2.fn.e.460.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.493585 + 1.84208i) q^{2} +(-1.41759 - 0.818448i) q^{4} +(3.30509 + 0.885596i) q^{5} +(-1.12943 + 2.39257i) q^{7} +(-0.489646 + 0.489646i) q^{8} +O(q^{10})$	\(q+(-0.493585 + 1.84208i) q^{2} +(-1.41759 - 0.818448i) q^{4} +(3.30509 + 0.885596i) q^{5} +(-1.12943 + 2.39257i) q^{7} +(-0.489646 + 0.489646i) q^{8} +(-3.26268 + 5.65113i) q^{10} +(0.445825 + 1.66384i) q^{11} +(-3.57057 + 0.501030i) q^{13} +(-3.84984 - 3.26144i) q^{14} +(-2.29718 - 3.97884i) q^{16} +(1.22596 - 2.12343i) q^{17} +(5.03057 + 1.34794i) q^{19} +(-3.96046 - 3.96046i) q^{20} -3.28498 q^{22} +(-3.97172 + 2.29307i) q^{23} +(5.80922 + 3.35395i) q^{25} +(0.839440 - 6.82459i) q^{26} +(3.55926 - 2.46731i) q^{28} -0.184063 q^{29} +(0.659317 + 2.46060i) q^{31} +(7.12546 - 1.90926i) q^{32} +(3.30641 + 3.30641i) q^{34} +(-5.85172 + 6.90744i) q^{35} +(-0.210190 - 0.0563202i) q^{37} +(-4.96603 + 8.60141i) q^{38} +(-2.05195 + 1.18470i) q^{40} +(-4.63239 + 4.63239i) q^{41} +0.562412i q^{43} +(0.729768 - 2.72353i) q^{44} +(-2.26365 - 8.44806i) q^{46} +(-0.998090 + 3.72492i) q^{47} +(-4.44878 - 5.40448i) q^{49} +(-9.04560 + 9.04560i) q^{50} +(5.47168 + 2.21207i) q^{52} +(2.67755 - 4.63764i) q^{53} +5.89396i q^{55} +(-0.618491 - 1.72453i) q^{56} +(0.0908505 - 0.339059i) q^{58} +(13.9411 - 3.73550i) q^{59} +(-1.30750 + 0.754885i) q^{61} -4.85807 q^{62} +4.87935i q^{64} +(-12.2448 - 1.50613i) q^{65} +(-6.67118 + 1.78754i) q^{67} +(-3.47583 + 2.00677i) q^{68} +(-9.83576 - 14.1888i) q^{70} +(-1.70926 - 1.70926i) q^{71} +(11.7847 - 3.15770i) q^{73} +(0.207493 - 0.359389i) q^{74} +(-6.02809 - 6.02809i) q^{76} +(-4.48438 - 0.812524i) q^{77} +(-1.48398 - 2.57034i) q^{79} +(-4.06875 - 15.1848i) q^{80} +(-6.24677 - 10.8197i) q^{82} +(-0.504742 + 0.504742i) q^{83} +(5.93241 - 5.93241i) q^{85} +(-1.03601 - 0.277598i) q^{86} +(-1.03299 - 0.596396i) q^{88} +(1.92971 - 7.20177i) q^{89} +(2.83396 - 9.10871i) q^{91} +7.50704 q^{92} +(-6.36898 - 3.67713i) q^{94} +(15.4328 + 8.91011i) q^{95} +(-12.0949 + 12.0949i) q^{97} +(12.1513 - 5.52745i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.493585	+	1.84208i	−0.349017	+	1.30255i	0.538832	+	0.842414i	$0.318866\pi$
$2$	−0.493585	+	1.84208i	−0.349017	+	1.30255i	−0.887849	+	0.460136i	$0.847801\pi$
$3$		0			0
$3$		0			0
$4$	−1.41759	−	0.818448i	−0.708797	−	0.409224i
$5$	3.30509	+	0.885596i	1.47808	+	0.396051i	0.905694	−	0.423932i	$-0.139351\pi$
$5$	3.30509	+	0.885596i	1.47808	+	0.396051i	0.572388	+	0.819983i	$0.306017\pi$
$6$		0			0
$7$	−1.12943	+	2.39257i	−0.426884	+	0.904306i
$7$	−1.12943	+	2.39257i	−0.426884	+	0.904306i
$8$	−0.489646	+	0.489646i	−0.173116	+	0.173116i
$9$		0			0
$10$	−3.26268	+	5.65113i	−1.03175	+	1.78705i
$11$	0.445825	+	1.66384i	0.134421	+	0.501667i	1.00000		0.000893225i	$0.000284322\pi$
$11$	0.445825	+	1.66384i	0.134421	+	0.501667i	−0.865578	+	0.500773i	$0.833049\pi$
$12$		0			0
$13$	−3.57057	+	0.501030i	−0.990298	+	0.138961i
$13$	−3.57057	+	0.501030i	−0.990298	+	0.138961i
$14$	−3.84984	−	3.26144i	−1.02891	−	0.871656i
$15$		0			0
$16$	−2.29718	−	3.97884i	−0.574296	−	0.994709i
$17$	1.22596	−	2.12343i	0.297339	−	0.515006i	−0.678187	−	0.734889i	$-0.737234\pi$
$17$	1.22596	−	2.12343i	0.297339	−	0.515006i	0.975526	+	0.219883i	$0.0705675\pi$
$18$		0			0
$19$	5.03057	+	1.34794i	1.15409	+	0.309238i	0.784604	−	0.619997i	$-0.212866\pi$
$19$	5.03057	+	1.34794i	1.15409	+	0.309238i	0.369488	+	0.929235i	$0.379533\pi$
$20$	−3.96046	−	3.96046i	−0.885586	−	0.885586i
$21$		0			0
$22$	−3.28498			−0.700361
$23$	−3.97172	+	2.29307i	−0.828160	+	0.478139i	−0.853222	−	0.521547i	$-0.825355\pi$
$23$	−3.97172	+	2.29307i	−0.828160	+	0.478139i	0.0250620	+	0.999686i	$0.492022\pi$
$24$		0			0
$25$	5.80922	+	3.35395i	1.16184	+	0.670790i
$26$	0.839440	−	6.82459i	0.164628	−	1.33841i
$27$		0			0
$28$	3.55926	−	2.46731i	0.672638	−	0.466278i
$29$	−0.184063			−0.0341796			−0.0170898	−	0.999854i	$-0.505440\pi$
$29$	−0.184063			−0.0341796			−0.0170898	+	0.999854i	$0.505440\pi$
$30$		0			0
$31$	0.659317	+	2.46060i	0.118417	+	0.441938i	0.999520	−	0.0309869i	$-0.00986501\pi$
$31$	0.659317	+	2.46060i	0.118417	+	0.441938i	−0.881103	+	0.472924i	$0.843198\pi$
$32$	7.12546	−	1.90926i	1.25962	−	0.337513i
$33$		0			0
$34$	3.30641	+	3.30641i	0.567045	+	0.567045i
$35$	−5.85172	+	6.90744i	−0.989121	+	1.16757i
$36$		0			0
$37$	−0.210190	−	0.0563202i	−0.0345550	−	0.00925899i	0.241500	−	0.970401i	$-0.422361\pi$
$37$	−0.210190	−	0.0563202i	−0.0345550	−	0.00925899i	−0.276055	+	0.961142i	$0.589027\pi$
$38$	−4.96603	+	8.60141i	−0.805596	+	1.39533i
$39$		0			0
$40$	−2.05195	+	1.18470i	−0.324442	+	0.187317i
$41$	−4.63239	+	4.63239i	−0.723458	+	0.723458i	−0.969308	−	0.245850i	$-0.920933\pi$
$41$	−4.63239	+	4.63239i	−0.723458	+	0.723458i	0.245850	+	0.969308i	$0.420933\pi$
$42$		0			0
$43$			0.562412i			0.0857671i	0.999080	+	0.0428835i	$0.0136544\pi$
$43$			0.562412i			0.0857671i	−0.999080	+	0.0428835i	$0.986346\pi$
$44$	0.729768	−	2.72353i	0.110017	−	0.410588i
$45$		0			0
$46$	−2.26365	−	8.44806i	−0.333757	−	1.24560i
$47$	−0.998090	+	3.72492i	−0.145586	+	0.543336i	0.854142	+	0.520040i	$0.174083\pi$
$47$	−0.998090	+	3.72492i	−0.145586	+	0.543336i	−0.999729	+	0.0232964i	$0.992584\pi$
$48$		0			0
$49$	−4.44878	−	5.40448i	−0.635540	−	0.772068i
$50$	−9.04560	+	9.04560i	−1.27924	+	1.27924i
$51$		0			0
$52$	5.47168	+	2.21207i	0.758786	+	0.306759i
$53$	2.67755	−	4.63764i	0.367789	−	0.637029i	−0.621430	−	0.783469i	$-0.713448\pi$
$53$	2.67755	−	4.63764i	0.367789	−	0.637029i	0.989220	+	0.146440i	$0.0467815\pi$
$54$		0			0
$55$			5.89396i			0.794742i
$56$	−0.618491	−	1.72453i	−0.0826494	−	0.230450i
$57$		0			0
$58$	0.0908505	−	0.339059i	0.0119293	−	0.0445206i
$59$	13.9411	−	3.73550i	1.81497	−	0.486320i	0.818827	−	0.574041i	$-0.194625\pi$
$59$	13.9411	−	3.73550i	1.81497	−	0.486320i	0.996145	+	0.0877205i	$0.0279582\pi$
$60$		0			0
$61$	−1.30750	+	0.754885i	−0.167408	+	0.0966531i	−0.581363	−	0.813644i	$-0.697480\pi$
$61$	−1.30750	+	0.754885i	−0.167408	+	0.0966531i	0.413955	+	0.910297i	$0.364147\pi$
$62$	−4.85807			−0.616975
$63$		0			0
$64$			4.87935i			0.609918i
$65$	−12.2448	−	1.50613i	−1.51878	−	0.186813i
$66$		0			0
$67$	−6.67118	+	1.78754i	−0.815014	+	0.218382i	−0.642165	−	0.766566i	$-0.721964\pi$
$67$	−6.67118	+	1.78754i	−0.815014	+	0.218382i	−0.172848	+	0.984948i	$0.555297\pi$
$68$	−3.47583	+	2.00677i	−0.421506	+	0.243357i
$69$		0			0
$70$	−9.83576	−	14.1888i	−1.17560	−	1.69588i
$71$	−1.70926	−	1.70926i	−0.202852	−	0.202852i	0.598369	−	0.801221i	$-0.295816\pi$
$71$	−1.70926	−	1.70926i	−0.202852	−	0.202852i	−0.801221	+	0.598369i	$0.795816\pi$
$72$		0			0
$73$	11.7847	−	3.15770i	1.37929	−	0.369581i	0.508429	−	0.861104i	$-0.330226\pi$
$73$	11.7847	−	3.15770i	1.37929	−	0.369581i	0.870864	+	0.491523i	$0.163560\pi$
$74$	0.207493	−	0.359389i	0.0241206	−	0.0417781i
$75$		0			0
$76$	−6.02809	−	6.02809i	−0.691469	−	0.691469i
$77$	−4.48438	−	0.812524i	−0.511043	−	0.0925957i
$78$		0			0
$79$	−1.48398	−	2.57034i	−0.166961	−	0.289185i	0.770389	−	0.637574i	$-0.220062\pi$
$79$	−1.48398	−	2.57034i	−0.166961	−	0.289185i	−0.937350	+	0.348389i	$0.886729\pi$
$80$	−4.06875	−	15.1848i	−0.454900	−	1.69771i
$81$		0			0
$82$	−6.24677	−	10.8197i	−0.689840	−	1.19484i
$83$	−0.504742	+	0.504742i	−0.0554026	+	0.0554026i	−0.734265	−	0.678863i	$-0.762473\pi$
$83$	−0.504742	+	0.504742i	−0.0554026	+	0.0554026i	0.678863	+	0.734265i	$0.262473\pi$
$84$		0			0
$85$	5.93241	−	5.93241i	0.643460	−	0.643460i
$86$	−1.03601	−	0.277598i	−0.111716	−	0.0299342i
$87$		0			0
$88$	−1.03299	−	0.596396i	−0.110117	−	0.0635760i
$89$	1.92971	−	7.20177i	0.204549	−	0.763386i	−0.785038	−	0.619447i	$-0.787357\pi$
$89$	1.92971	−	7.20177i	0.204549	−	0.763386i	0.989587	−	0.143938i	$-0.0459767\pi$
$90$		0			0
$91$	2.83396	−	9.10871i	0.297080	−	0.954853i
$92$	7.50704			0.782663
$93$		0			0
$94$	−6.36898	−	3.67713i	−0.656910	−	0.379267i
$95$	15.4328	+	8.91011i	1.58337	+	0.914158i
$96$		0			0
$97$	−12.0949	+	12.0949i	−1.22805	+	1.22805i	−0.263356	+	0.964699i	$0.584829\pi$
$97$	−12.0949	+	12.0949i	−1.22805	+	1.22805i	−0.964699	+	0.263356i	$0.915171\pi$
$98$	12.1513	−	5.52745i	1.22747	−	0.558357i
$99$		0			0
$100$	−5.49007	−	9.50908i	−0.549007	−	0.950908i
$101$	−4.11357	+	7.12491i	−0.409316	+	0.708955i	−0.994813	−	0.101719i	$-0.967566\pi$
$101$	−4.11357	+	7.12491i	−0.409316	+	0.708955i	0.585498	+	0.810674i	$0.300899\pi$
$102$		0			0
$103$	3.74883	+	6.49316i	0.369383	+	0.639790i	0.989469	−	0.144743i	$-0.0462357\pi$
$103$	3.74883	+	6.49316i	0.369383	+	0.639790i	−0.620086	+	0.784534i	$0.712902\pi$
$104$	1.50299	−	1.99364i	0.147380	−	0.195493i
$105$		0			0
$106$	7.22133	+	7.22133i	0.701398	+	0.701398i
$107$	−1.99457	−	3.45470i	−0.192823	−	0.333978i	0.753362	−	0.657606i	$-0.228431\pi$
$107$	−1.99457	−	3.45470i	−0.192823	−	0.333978i	−0.946185	+	0.323628i	$0.895098\pi$
$108$		0			0
$109$	11.2778	−	3.02188i	1.08022	−	0.289443i	0.325532	−	0.945531i	$-0.394456\pi$
$109$	11.2778	−	3.02188i	1.08022	−	0.289443i	0.754685	+	0.656088i	$0.227790\pi$
$110$	−10.8572	−	2.90917i	−1.03519	−	0.277378i
$111$		0			0
$112$	12.1141	−	1.00235i	1.14468	−	0.0947134i
$113$	8.36429			0.786846			0.393423	−	0.919358i	$-0.371291\pi$
$113$	8.36429			0.786846			0.393423	+	0.919358i	$0.371291\pi$
$114$		0			0
$115$	−15.1576	+	4.06147i	−1.41346	+	0.378734i
$116$	0.260926	+	0.150646i	0.0242264	+	0.0139871i
$117$		0			0
$118$			27.5244i			2.53382i
$119$	3.69581	+	5.33146i	0.338794	+	0.488734i
$120$		0			0
$121$	6.95668	−	4.01644i	0.632425	−	0.365131i
$122$	−0.745199	−	2.78112i	−0.0674671	−	0.251791i
$123$		0			0
$124$	1.07923	−	4.02775i	0.0969180	−	0.361703i
$125$	4.13226	+	4.13226i	0.369601	+	0.369601i
$126$		0			0
$127$			12.0998i			1.07368i	0.843684	+	0.536840i	$0.180382\pi$
$127$			12.0998i			1.07368i	−0.843684	+	0.536840i	$0.819618\pi$
$128$	5.26276	+	1.41015i	0.465167	+	0.124641i
$129$		0			0
$130$	8.81825	−	21.8125i	0.773412	−	1.91308i
$131$	−1.54544	+	0.892262i	−0.135026	+	0.0779573i	−0.565991	−	0.824411i	$-0.691506\pi$
$131$	−1.54544	+	0.892262i	−0.135026	+	0.0779573i	0.430965	+	0.902368i	$0.358173\pi$
$132$		0			0
$133$	−8.90671	+	10.5136i	−0.772310	+	0.911644i
$134$		−	13.1712i		−	1.13781i
$135$		0			0
$136$	0.439440	+	1.64001i	0.0376817	+	0.140630i
$137$	−5.02570	−	18.7562i	−0.429374	−	1.60245i	−0.754181	−	0.656666i	$-0.771966\pi$
$137$	−5.02570	−	18.7562i	−0.429374	−	1.60245i	0.324807	−	0.945780i	$-0.394701\pi$
$138$		0			0
$139$		−	13.5866i		−	1.15240i	−0.817310	−	0.576198i	$-0.804536\pi$
$139$		−	13.5866i		−	1.15240i	0.817310	−	0.576198i	$-0.195464\pi$
$140$	13.9487	−	5.00261i	1.17888	−	0.422798i
$141$		0			0
$142$	3.99226	−	2.30493i	0.335023	−	0.193426i
$143$	−2.42548	−	5.71748i	−0.202829	−	0.478120i
$144$		0			0
$145$	−0.608344	−	0.163005i	−0.0505202	−	0.0135368i
$146$			23.2670i			1.92559i
$147$		0			0
$148$	0.251869	+	0.251869i	0.0207035	+	0.0207035i
$149$	−0.951123	+	3.54964i	−0.0779190	+	0.290798i	−0.993879	−	0.110471i	$-0.964764\pi$
$149$	−0.951123	+	3.54964i	−0.0779190	+	0.290798i	0.915960	+	0.401269i	$0.131431\pi$
$150$		0			0
$151$	4.65978	+	17.3905i	0.379207	+	1.41522i	0.847099	+	0.531435i	$0.178347\pi$
$151$	4.65978	+	17.3905i	0.379207	+	1.41522i	−0.467892	+	0.883786i	$0.654986\pi$
$152$	−3.12321	+	1.80319i	−0.253326	+	0.146258i
$153$		0			0
$154$	3.71016	−	7.85955i	0.298973	−	0.633341i
$155$			8.71641i			0.700119i
$156$		0			0
$157$	−15.8740	−	9.16488i	−1.26689	−	0.731437i	−0.292489	−	0.956269i	$-0.594483\pi$
$157$	−15.8740	−	9.16488i	−1.26689	−	0.731437i	−0.974398	+	0.224832i	$0.927817\pi$
$158$	5.46724	−	1.46494i	0.434951	−	0.116545i
$159$		0			0
$160$	25.2411			1.99549
$161$	−1.00056	−	12.0925i	−0.0788551	−	0.953021i
$162$		0			0
$163$	12.4820	+	3.34454i	0.977665	+	0.261964i	0.712061	−	0.702118i	$-0.247762\pi$
$163$	12.4820	+	3.34454i	0.977665	+	0.261964i	0.265604	+	0.964082i	$0.414429\pi$
$164$	10.3582	−	2.77547i	0.808840	−	0.216728i
$165$		0			0
$166$	−0.680643	−	1.17891i	−0.0528282	−	0.0915011i
$167$	10.6807	+	10.6807i	0.826494	+	0.826494i	0.987030	−	0.160536i	$-0.0513221\pi$
$167$	10.6807	+	10.6807i	0.826494	+	0.826494i	−0.160536	+	0.987030i	$0.551322\pi$
$168$		0			0
$169$	12.4979	−	3.57793i	0.961380	−	0.275225i
$170$	7.99984	+	13.8561i	0.613560	+	1.06272i
$171$		0			0
$172$	0.460305	−	0.797272i	0.0350979	−	0.0607914i
$173$	−1.31009	−	2.26914i	−0.0996041	−	0.172519i	0.811917	−	0.583773i	$-0.198424\pi$
$173$	−1.31009	−	2.26914i	−0.0996041	−	0.172519i	−0.911521	+	0.411254i	$0.865091\pi$
$174$		0			0
$175$	−14.5857	+	10.1109i	−1.10257	+	0.764312i
$176$	5.59601	−	5.59601i	0.421815	−	0.421815i
$177$		0			0
$178$	12.3138	+	7.10936i	0.922957	+	0.532869i
$179$	21.9610	+	12.6792i	1.64144	+	0.947687i	0.980322	+	0.197406i	$0.0632517\pi$
$179$	21.9610	+	12.6792i	1.64144	+	0.947687i	0.661119	+	0.750281i	$0.270082\pi$
$180$		0			0
$181$	−1.00365			−0.0746008			−0.0373004	−	0.999304i	$-0.511876\pi$
$181$	−1.00365			−0.0746008			−0.0373004	+	0.999304i	$0.511876\pi$
$182$	15.3802	+	9.71631i	1.14006	+	0.720221i
$183$		0			0
$184$	0.821942	−	3.06753i	0.0605944	−	0.226141i
$185$	−0.644820	−	0.372287i	−0.0474081	−	0.0273711i
$186$		0			0
$187$	4.07960	+	1.09313i	0.298330	+	0.0799373i
$188$	4.46354	−	4.46354i	0.325537	−	0.325537i
$189$		0			0
$190$	−24.0305	+	24.0305i	−1.74336	+	1.74336i
$191$	−0.525192	−	0.909659i	−0.0380016	−	0.0658206i	0.846399	−	0.532549i	$-0.178766\pi$
$191$	−0.525192	−	0.909659i	−0.0380016	−	0.0658206i	−0.884401	+	0.466729i	$0.845433\pi$
$192$		0			0
$193$	0.511716	+	1.90975i	0.0368341	+	0.137467i	0.981894	−	0.189430i	$-0.0606639\pi$
$193$	0.511716	+	1.90975i	0.0368341	+	0.137467i	−0.945060	+	0.326896i	$0.893997\pi$
$194$	−16.3100	−	28.2497i	−1.17099	−	2.02821i
$195$		0			0
$196$	1.88327	+	11.3024i	0.134520	+	0.807317i
$197$	3.36094	+	3.36094i	0.239457	+	0.239457i	0.816625	−	0.577168i	$-0.195842\pi$
$197$	3.36094	+	3.36094i	0.239457	+	0.239457i	−0.577168	+	0.816625i	$0.695842\pi$
$198$		0			0
$199$	5.10311	−	8.83885i	0.361750	−	0.626569i	−0.626499	−	0.779422i	$-0.715513\pi$
$199$	5.10311	−	8.83885i	0.361750	−	0.626569i	0.988249	+	0.152853i	$0.0488461\pi$
$200$	−4.48671	+	1.20221i	−0.317258	+	0.0850091i
$201$		0			0
$202$	−11.0943	−	11.0943i	−0.780591	−	0.780591i
$203$	0.207886	−	0.440383i	0.0145907	−	0.0309088i
$204$		0			0
$205$	−19.4129	+	11.2080i	−1.35586	+	0.782803i
$206$	−13.8113	+	3.70073i	−0.962280	+	0.257842i
$207$		0			0
$208$	10.1958	+	13.0558i	0.706949	+	0.905254i
$209$			8.97101i			0.620538i
$210$		0			0
$211$	16.1396			1.11109			0.555547	−	0.831485i	$-0.312509\pi$
$211$	16.1396			1.11109			0.555547	+	0.831485i	$0.312509\pi$
$212$	−7.59134	+	4.38286i	−0.521375	+	0.301016i
$213$		0			0
$214$	7.34833	−	1.96898i	0.502322	−	0.134597i
$215$	−0.498070	+	1.85882i	−0.0339681	+	0.126771i
$216$		0			0
$217$	−6.63182	−	1.20162i	−0.450197	−	0.0815711i
$218$			22.2662i			1.50806i
$219$		0			0
$220$	4.82390	−	8.35524i	0.325227	−	0.563310i
$221$	−3.31348	+	8.19608i	−0.222889	+	0.551328i
$222$		0			0
$223$	−0.0939482	+	0.0939482i	−0.00629124	+	0.00629124i	−0.710245	−	0.703954i	$-0.751416\pi$
$223$	−0.0939482	+	0.0939482i	−0.00629124	+	0.00629124i	0.703954	+	0.710245i	$0.251416\pi$
$224$	−3.47967	+	19.2045i	−0.232495	+	1.28316i
$225$		0			0
$226$	−4.12848	+	15.4077i	−0.274623	+	1.02491i
$227$	6.86181	+	25.6086i	0.455434	+	1.69970i	0.686808	+	0.726839i	$0.259011\pi$
$227$	6.86181	+	25.6086i	0.455434	+	1.69970i	−0.231374	+	0.972865i	$0.574322\pi$
$228$		0			0
$229$	4.55909	−	17.0148i	0.301273	−	1.12437i	−0.634833	−	0.772650i	$-0.718931\pi$
$229$	4.55909	−	17.0148i	0.301273	−	1.12437i	0.936106	−	0.351718i	$-0.114402\pi$
$230$		−	29.9263i		−	1.97328i
$231$		0			0
$232$	0.0901255	−	0.0901255i	0.00591703	−	0.00591703i
$233$	4.40536	−	2.54344i	0.288605	−	0.166626i	−0.348708	−	0.937232i	$-0.613379\pi$
$233$	4.40536	−	2.54344i	0.288605	−	0.166626i	0.637313	+	0.770605i	$0.280046\pi$
$234$		0			0
$235$	−6.59756	+	11.4273i	−0.430377	+	0.745435i
$236$	−22.8201	−	6.11462i	−1.48546	−	0.398028i
$237$		0			0
$238$	−11.6452	+	4.17646i	−0.754845	+	0.270720i
$239$	13.0182	+	13.0182i	0.842079	+	0.842079i	0.989129	−	0.147050i	$-0.0469780\pi$
$239$	13.0182	+	13.0182i	0.842079	+	0.842079i	−0.147050	+	0.989129i	$0.546978\pi$
$240$		0			0
$241$	−2.63382	+	0.705731i	−0.169659	+	0.0454601i	−0.342649	−	0.939464i	$-0.611324\pi$
$241$	−2.63382	+	0.705731i	−0.169659	+	0.0454601i	0.172989	+	0.984924i	$0.444657\pi$
$242$	3.96490	+	14.7972i	0.254874	+	0.951202i
$243$		0			0
$244$	2.47133			0.158211
$245$	−9.91743	−	21.8021i	−0.633601	−	1.39289i
$246$		0			0
$247$	−18.6374	−	2.29244i	−1.18587	−	0.145864i
$248$	−1.52766	−	0.881993i	−0.0970063	−	0.0560066i
$249$		0			0
$250$	−9.65160	+	5.57235i	−0.610421	+	0.352426i
$251$	21.4230			1.35221			0.676105	−	0.736805i	$-0.263666\pi$
$251$	21.4230			1.35221			0.676105	+	0.736805i	$0.263666\pi$
$252$		0			0
$253$	−5.58599	−	5.58599i	−0.351188	−	0.351188i
$254$	−22.2888	−	5.97226i	−1.39852	−	0.374733i
$255$		0			0
$256$	−10.0746	+	17.4497i	−0.629662	+	1.09061i
$257$	−4.80460	−	8.32182i	−0.299703	−	0.519101i	0.676365	−	0.736567i	$-0.263554\pi$
$257$	−4.80460	−	8.32182i	−0.299703	−	0.519101i	−0.976068	+	0.217466i	$0.930221\pi$
$258$		0			0
$259$	0.372145	−	0.439284i	0.0231240	−	0.0272958i
$260$	16.1254	+	12.1568i	1.00006	+	0.753932i
$261$		0			0
$262$	−0.880814	−	3.28724i	−0.0544168	−	0.203086i
$263$	−3.93499	+	6.81560i	−0.242642	+	0.420268i	−0.961466	−	0.274924i	$-0.911347\pi$
$263$	−3.93499	+	6.81560i	−0.242642	+	0.420268i	0.718824	+	0.695192i	$0.244681\pi$
$264$		0			0
$265$	12.9566	−	12.9566i	0.795918	−	0.795918i
$266$	−14.9707	−	21.5962i	−0.917912	−	1.32415i
$267$		0			0
$268$	10.9200	+	2.92601i	0.667046	+	0.178734i
$269$	3.44131	+	1.98684i	0.209820	+	0.121140i	0.601228	−	0.799078i	$-0.294678\pi$
$269$	3.44131	+	1.98684i	0.209820	+	0.121140i	−0.391408	+	0.920217i	$0.628012\pi$
$270$		0			0
$271$	4.42472	−	16.5133i	0.268782	−	1.00311i	−0.691112	−	0.722748i	$-0.742879\pi$
$271$	4.42472	−	16.5133i	0.268782	−	1.00311i	0.959894	−	0.280362i	$-0.0904544\pi$
$272$	−11.2650			−0.683042
$273$		0			0
$274$	37.0310			2.23712
$275$	−2.99055	+	11.1609i	−0.180337	+	0.673026i
$276$		0			0
$277$	21.7301	+	12.5459i	1.30564	+	0.753811i	0.981365	−	0.192153i	$-0.0615470\pi$
$277$	21.7301	+	12.5459i	1.30564	+	0.753811i	0.324273	+	0.945963i	$0.394880\pi$
$278$	25.0276	+	6.70611i	1.50105	+	0.402206i
$279$		0			0
$280$	−0.516930	−	6.24747i	−0.0308925	−	0.373358i
$281$	2.15639	−	2.15639i	0.128639	−	0.128639i	−0.639856	−	0.768495i	$-0.721006\pi$
$281$	2.15639	−	2.15639i	0.128639	−	0.128639i	0.768495	+	0.639856i	$0.221006\pi$
$282$		0			0
$283$	−5.67952	+	9.83723i	−0.337613	+	0.584762i	−0.983983	−	0.178261i	$-0.942953\pi$
$283$	−5.67952	+	9.83723i	−0.337613	+	0.584762i	0.646370	+	0.763024i	$0.276286\pi$
$284$	1.02410	+	3.82198i	0.0607689	+	0.226793i
$285$		0			0
$286$	11.7293	−	1.64588i	0.693566	−	0.0973226i
$287$	−5.85136	−	16.3153i	−0.345395	−	0.963060i
$288$		0			0
$289$	5.49404	+	9.51596i	0.323179	+	0.559762i
$290$	0.600538	−	1.04016i	0.0352648	−	0.0610805i
$291$		0			0
$292$	−19.2903	−	5.16882i	−1.12888	−	0.302482i
$293$	−10.2833	−	10.2833i	−0.600758	−	0.600758i	0.339756	−	0.940514i	$-0.389656\pi$
$293$	−10.2833	−	10.2833i	−0.600758	−	0.600758i	−0.940514	+	0.339756i	$0.889656\pi$
$294$		0			0
$295$	49.3846			2.87528
$296$	0.130496	−	0.0753417i	0.00758490	−	0.00437915i
$297$		0			0
$298$	−6.06927	−	3.50410i	−0.351583	−	0.202987i
$299$	13.0324	−	10.1775i	0.753683	−	0.588581i
$300$		0			0
$301$	−1.34561	−	0.635205i	−0.0775597	−	0.0366126i
$302$	−34.3348			−1.97575
$303$		0			0
$304$	−6.19292	−	23.1123i	−0.355188	−	1.32558i
$305$	−4.98992	+	1.33705i	−0.285722	+	0.0765590i
$306$		0			0
$307$	−7.01794	−	7.01794i	−0.400535	−	0.400535i	0.477886	−	0.878422i	$-0.341403\pi$
$307$	−7.01794	−	7.01794i	−0.400535	−	0.400535i	−0.878422	+	0.477886i	$0.841403\pi$
$308$	5.69202	+	4.82206i	0.324333	+	0.274762i
$309$		0			0
$310$	−16.0563	−	4.30229i	−0.911939	−	0.244353i
$311$	1.26356	−	2.18855i	0.0716498	−	0.124101i	−0.827975	−	0.560766i	$-0.810507\pi$
$311$	1.26356	−	2.18855i	0.0716498	−	0.124101i	0.899625	+	0.436664i	$0.143840\pi$
$312$		0			0
$313$	−2.98609	+	1.72402i	−0.168784	+	0.0974473i	−0.582012	−	0.813180i	$-0.697734\pi$
$313$	−2.98609	+	1.72402i	−0.168784	+	0.0974473i	0.413229	+	0.910627i	$0.364401\pi$
$314$	24.7177	−	24.7177i	1.39490	−	1.39490i
$315$		0			0
$316$			4.85825i			0.273298i
$317$	8.19402	−	30.5805i	0.460222	−	1.71757i	−0.212041	−	0.977261i	$-0.568011\pi$
$317$	8.19402	−	30.5805i	0.460222	−	1.71757i	0.672264	−	0.740312i	$-0.265322\pi$
$318$		0			0
$319$	−0.0820597	−	0.306251i	−0.00459446	−	0.0171468i
$320$	−4.32113	+	16.1267i	−0.241559	+	0.901509i
$321$		0			0
$322$	22.7692	+	4.12555i	1.26888	+	0.229908i
$323$	9.02953	−	9.02953i	0.502416	−	0.502416i
$324$		0			0
$325$	−22.4226	−	9.06493i	−1.24378	−	0.502832i
$326$	−12.3218	+	21.3420i	−0.682443	+	1.18203i
$327$		0			0
$328$		−	4.53646i		−	0.250484i
$329$	−7.78487	−	6.59504i	−0.429194	−	0.363596i
$330$		0			0
$331$	8.44029	−	31.4996i	0.463920	−	1.73137i	−0.196525	−	0.980499i	$-0.562966\pi$
$331$	8.44029	−	31.4996i	0.463920	−	1.73137i	0.660445	−	0.750874i	$-0.270368\pi$
$332$	1.12862	−	0.302414i	0.0619412	−	0.0165971i
$333$		0			0
$334$	−24.9465	+	14.4029i	−1.36501	+	0.788089i
$335$	−23.6319			−1.29115
$336$		0			0
$337$		−	8.54695i		−	0.465582i	−0.972527	−	0.232791i	$-0.925214\pi$
$337$		−	8.54695i		−	0.465582i	0.972527	−	0.232791i	$-0.0747858\pi$
$338$	0.422045	+	24.7882i	0.0229562	+	1.34830i
$339$		0			0
$340$	−13.2651	+	3.55437i	−0.719401	+	0.192763i
$341$	−3.80011	+	2.19400i	−0.205788	+	0.118812i
$342$		0			0
$343$	17.9552	−	4.54003i	0.969488	−	0.245139i
$344$	−0.275383	−	0.275383i	−0.0148476	−	0.0148476i
$345$		0			0
$346$	4.82658	−	1.29328i	0.259478	−	0.0695270i
$347$	1.36789	−	2.36925i	0.0734321	−	0.127188i	−0.826971	−	0.562244i	$-0.809938\pi$
$347$	1.36789	−	2.36925i	0.0734321	−	0.127188i	0.900403	+	0.435056i	$0.143271\pi$
$348$		0			0
$349$	−8.57575	−	8.57575i	−0.459049	−	0.459049i	0.439294	−	0.898343i	$-0.355229\pi$
$349$	−8.57575	−	8.57575i	−0.459049	−	0.459049i	−0.898343	+	0.439294i	$0.855229\pi$
$350$	−11.4259	−	31.8586i	−0.610738	−	1.70291i
$351$		0			0
$352$	6.35341	+	11.0044i	0.338638	+	0.586538i
$353$	−2.83977	−	10.5982i	−0.151146	−	0.564083i	−0.999405	−	0.0345014i	$-0.989016\pi$
$353$	−2.83977	−	10.5982i	−0.151146	−	0.564083i	0.848259	−	0.529581i	$-0.177651\pi$
$354$		0			0
$355$	−4.13555	−	7.16298i	−0.219492	−	0.380171i
$356$	−8.62981	+	8.62981i	−0.457379	+	0.457379i
$357$		0			0
$358$	−34.1957	+	34.1957i	−1.80730	+	1.80730i
$359$	−1.03433	−	0.277147i	−0.0545897	−	0.0146273i	0.231421	−	0.972854i	$-0.425663\pi$
$359$	−1.03433	−	0.277147i	−0.0545897	−	0.0146273i	−0.286011	+	0.958226i	$0.592329\pi$
$360$		0			0
$361$	7.03523	+	4.06179i	0.370275	+	0.213779i
$362$	0.495387	−	1.84881i	0.0260370	−	0.0971712i
$363$		0			0
$364$	−11.4724	+	10.5930i	−0.601317	+	0.555224i
$365$	41.7459			2.18508
$366$		0			0
$367$	6.72705	+	3.88386i	0.351149	+	0.202736i	0.665191	−	0.746673i	$-0.268350\pi$
$367$	6.72705	+	3.88386i	0.351149	+	0.202736i	−0.314042	+	0.949409i	$0.601683\pi$
$368$	18.2475	+	10.5352i	0.951218	+	0.549186i
$369$		0			0
$370$	1.00406	−	1.00406i	0.0521984	−	0.0521984i
$371$	8.07179	+	11.6441i	0.419066	+	0.604532i
$372$		0			0
$373$	8.89119	+	15.4000i	0.460368	+	0.797382i	0.998979	−	0.0451732i	$-0.0143840\pi$
$373$	8.89119	+	15.4000i	0.460368	+	0.797382i	−0.538611	+	0.842555i	$0.681051\pi$
$374$	−4.02726	+	6.97542i	−0.208245	+	0.360690i
$375$		0			0
$376$	−1.33518	−	2.31260i	−0.0688568	−	0.119263i
$377$	0.657209	−	0.0922209i	0.0338480	−	0.00474962i
$378$		0			0
$379$	−25.3241	−	25.3241i	−1.30081	−	1.30081i	−0.927846	−	0.372964i	$-0.878341\pi$
$379$	−25.3241	−	25.3241i	−1.30081	−	1.30081i	−0.372964	−	0.927846i	$-0.621659\pi$
$380$	−14.5849	−	25.2618i	−0.748191	−	1.29590i
$381$		0			0
$382$	1.93489	−	0.518453i	0.0989978	−	0.0265264i
$383$	−20.0607	−	5.37524i	−1.02505	−	0.274662i	−0.293147	−	0.956068i	$-0.594702\pi$
$383$	−20.0607	−	5.37524i	−1.02505	−	0.274662i	−0.731906	+	0.681405i	$0.761369\pi$
$384$		0			0
$385$	−14.1017	−	6.65682i	−0.718690	−	0.339263i
$386$	−3.77049			−0.191913
$387$		0			0
$388$	27.0448	−	7.24662i	1.37299	−	0.367892i
$389$	6.90083	+	3.98420i	0.349886	+	0.202007i	0.664635	−	0.747168i	$-0.268587\pi$
$389$	6.90083	+	3.98420i	0.349886	+	0.202007i	−0.314749	+	0.949175i	$0.601920\pi$
$390$		0			0
$391$			11.2449i			0.568677i
$392$	4.82461	+	0.467955i	0.243679	+	0.0236353i
$393$		0			0
$394$	−7.85005	+	4.53223i	−0.395480	+	0.228330i
$395$	−2.62842	−	9.80941i	−0.132250	−	0.493565i
$396$		0			0
$397$	7.95249	−	29.6791i	0.399124	−	1.48955i	−0.415516	−	0.909586i	$-0.636399\pi$
$397$	7.95249	−	29.6791i	0.399124	−	1.48955i	0.814641	−	0.579966i	$-0.196934\pi$
$398$	13.7631	+	13.7631i	0.689880	+	0.689880i
$399$		0			0
$400$		−	30.8186i		−	1.54093i
$401$	21.7664	+	5.83228i	1.08696	+	0.291250i	0.757444	−	0.652900i	$-0.226448\pi$
$401$	21.7664	+	5.83228i	1.08696	+	0.291250i	0.329516	+	0.944150i	$0.393115\pi$
$402$		0			0
$403$	−3.58697	−	8.45542i	−0.178680	−	0.421195i
$404$	11.6627	−	6.73348i	0.580243	−	0.335003i
$405$		0			0
$406$	0.708612	+	0.600309i	0.0351678	+	0.0297928i
$407$		−	0.374831i		−	0.0185797i
$408$		0			0
$409$	10.2133	+	38.1167i	0.505016	+	1.88475i	0.464510	+	0.885568i	$0.346230\pi$
$409$	10.2133	+	38.1167i	0.505016	+	1.88475i	0.0405065	+	0.999179i	$0.487103\pi$
$410$	−11.0642	−	41.2923i	−0.546423	−	2.03928i
$411$		0			0
$412$		−	12.2729i		−	0.604642i
$413$	−6.80801	+	37.5739i	−0.335001	+	1.84889i
$414$		0			0
$415$	−2.11521	+	1.22122i	−0.103832	+	0.0599473i
$416$	−24.4854	+	10.3872i	−1.20049	+	0.509276i
$417$		0			0
$418$	−16.5253	−	4.42795i	−0.808281	−	0.216578i
$419$		−	6.86945i		−	0.335595i	−0.985821	−	0.167797i	$-0.946335\pi$
$419$		−	6.86945i		−	0.335595i	0.985821	−	0.167797i	$-0.0536654\pi$
$420$		0			0
$421$	−16.8752	−	16.8752i	−0.822445	−	0.822445i	0.164013	−	0.986458i	$-0.447556\pi$
$421$	−16.8752	−	16.8752i	−0.822445	−	0.822445i	−0.986458	+	0.164013i	$0.947556\pi$
$422$	−7.96624	+	29.7304i	−0.387790	+	1.44725i
$423$		0			0
$424$	0.959754	+	3.58185i	0.0466098	+	0.173950i
$425$	14.2437	−	8.22363i	0.690923	−	0.398904i
$426$		0			0
$427$	−0.329386	−	3.98087i	−0.0159401	−	0.192648i
$428$			6.52981i			0.315630i
$429$		0			0
$430$	−3.17827	−	1.83497i	−0.153270	−	0.0884903i
$431$	−34.3384	+	9.20095i	−1.65402	+	0.443194i	−0.960735	−	0.277467i	$-0.910505\pi$
$431$	−34.3384	+	9.20095i	−1.65402	+	0.443194i	−0.693288	+	0.720661i	$0.743839\pi$
$432$		0			0
$433$	6.53945			0.314266			0.157133	−	0.987577i	$-0.449775\pi$
$433$	6.53945			0.314266			0.157133	+	0.987577i	$0.449775\pi$
$434$	5.48684	−	11.6233i	0.263377	−	0.557934i
$435$		0			0
$436$	−18.4606	−	4.94650i	−0.884101	−	0.236894i
$437$	−23.0709	+	6.18184i	−1.10363	+	0.295717i
$438$		0			0
$439$	−12.2931	−	21.2923i	−0.586719	−	1.01623i	−0.994659	−	0.103218i	$-0.967086\pi$
$439$	−12.2931	−	21.2923i	−0.586719	−	1.01623i	0.407940	−	0.913009i	$-0.366247\pi$
$440$	−2.88595	−	2.88595i	−0.137582	−	0.137582i
$441$		0			0
$442$	−13.4624	−	10.1492i	−0.640340	−	0.482746i
$443$	−7.79952	−	13.5092i	−0.370566	−	0.641840i	0.619086	−	0.785323i	$-0.287503\pi$
$443$	−7.79952	−	13.5092i	−0.370566	−	0.641840i	−0.989653	+	0.143483i	$0.954170\pi$
$444$		0			0
$445$	12.7557	−	22.0935i	0.604679	−	1.04733i
$446$	−0.126689	−	0.219432i	−0.00599890	−	0.0103904i
$447$		0			0
$448$	−11.6742	−	5.51088i	−0.551553	−	0.260365i
$449$	−28.6271	+	28.6271i	−1.35100	+	1.35100i	−0.466445	+	0.884550i	$0.654465\pi$
$449$	−28.6271	+	28.6271i	−1.35100	+	1.35100i	−0.884550	+	0.466445i	$0.845535\pi$
$450$		0			0
$451$	−9.77279	−	5.64232i	−0.460183	−	0.265686i
$452$	−11.8572	−	6.84573i	−0.557714	−	0.321996i
$453$		0			0
$454$	−50.5601			−2.37290
$455$	17.4331	−	27.5954i	0.817278	−	1.29369i
$456$		0			0
$457$	−3.38248	+	12.6236i	−0.158226	+	0.590507i	0.840582	+	0.541685i	$0.182213\pi$
$457$	−3.38248	+	12.6236i	−0.158226	+	0.590507i	−0.998808	+	0.0488218i	$0.984453\pi$
$458$	29.0923	+	16.7965i	1.35939	+	0.784847i
$459$		0			0
$460$	24.8114	+	6.64821i	1.15684	+	0.309974i
$461$	−3.55813	+	3.55813i	−0.165719	+	0.165719i	−0.785095	−	0.619376i	$-0.787386\pi$
$461$	−3.55813	+	3.55813i	−0.165719	+	0.165719i	0.619376	+	0.785095i	$0.287386\pi$
$462$		0			0
$463$	−11.6246	+	11.6246i	−0.540241	+	0.540241i	−0.923600	−	0.383359i	$-0.874767\pi$
$463$	−11.6246	+	11.6246i	−0.540241	+	0.540241i	0.383359	+	0.923600i	$0.374767\pi$
$464$	0.422825	+	0.732355i	0.0196292	+	0.0339987i
$465$		0			0
$466$	2.51080	+	9.37044i	0.116311	+	0.434077i
$467$	−2.86541	−	4.96304i	−0.132595	−	0.229662i	0.792081	−	0.610416i	$-0.208998\pi$
$467$	−2.86541	−	4.96304i	−0.132595	−	0.229662i	−0.924676	+	0.380754i	$0.875664\pi$
$468$		0			0
$469$	3.25782	−	17.9801i	0.150432	−	0.830246i
$470$	−17.7936	−	17.7936i	−0.820757	−	0.820757i
$471$		0			0
$472$	−4.99711	+	8.65525i	−0.230011	+	0.398390i
$473$	−0.935764	+	0.250737i	−0.0430265	+	0.0115289i
$474$		0			0
$475$	24.7028	+	24.7028i	1.13344	+	1.13344i
$476$	−0.875634	−	10.5827i	−0.0401346	−	0.485055i
$477$		0			0
$478$	−30.4062	+	17.5550i	−1.39075	+	0.802949i
$479$	−19.5560	+	5.24001i	−0.893536	+	0.239422i	−0.676238	−	0.736683i	$-0.736391\pi$
$479$	−19.5560	+	5.24001i	−0.893536	+	0.239422i	−0.217298	+	0.976105i	$0.569724\pi$
$480$		0			0
$481$	0.778716	+	0.0957839i	0.0355064	+	0.00436737i
$482$		−	5.20006i		−	0.236856i
$483$		0			0
$484$	−13.1490			−0.597681
$485$	−50.6861	+	29.2636i	−2.30154	+	1.32879i
$486$		0			0
$487$	1.53006	−	0.409978i	0.0693336	−	0.0185779i	−0.223986	−	0.974592i	$-0.571907\pi$
$487$	1.53006	−	0.409978i	0.0693336	−	0.0185779i	0.293319	+	0.956015i	$0.405240\pi$
$488$	0.270585	−	1.00984i	0.0122488	−	0.0457132i
$489$		0			0
$490$	45.0564	−	7.50754i	2.03544	−	0.339156i
$491$		−	22.7308i		−	1.02583i	−0.858440	−	0.512913i	$-0.828566\pi$
$491$		−	22.7308i		−	1.02583i	0.858440	−	0.512913i	$-0.171434\pi$
$492$		0			0
$493$	−0.225654	+	0.390843i	−0.0101629	+	0.0176027i
$494$	13.4220	−	33.2001i	0.603883	−	1.49374i
$495$		0			0
$496$	8.27577	−	8.27577i	0.371593	−	0.371593i
$497$	6.02001	−	2.15904i	0.270035	−	0.0968460i
$498$		0			0
$499$	−1.52547	+	5.69314i	−0.0682895	+	0.254860i	−0.991628	−	0.129127i	$-0.958783\pi$
$499$	−1.52547	+	5.69314i	−0.0682895	+	0.254860i	0.923339	+	0.383987i	$0.125449\pi$
$500$	−2.47583	−	9.23991i	−0.110722	−	0.413221i
$501$		0			0
$502$	−10.5741	+	39.4630i	−0.471945	+	1.76132i
$503$			11.3499i			0.506069i	0.967457	+	0.253035i	$0.0814286\pi$
$503$			11.3499i			0.506069i	−0.967457	+	0.253035i	$0.918571\pi$
$504$		0			0
$505$	−19.9055	+	19.9055i	−0.885784	+	0.885784i
$506$	13.0470	−	7.53270i	0.580011	−	0.334870i
$507$		0			0
$508$	9.90302	−	17.1525i	0.439376	−	0.761021i
$509$	−28.6462	−	7.67573i	−1.26972	−	0.340221i	−0.439797	−	0.898097i	$-0.644950\pi$
$509$	−28.6462	−	7.67573i	−1.26972	−	0.340221i	−0.829924	+	0.557876i	$0.811616\pi$
$510$		0			0
$511$	−5.75496	+	31.7621i	−0.254585	+	1.40507i
$512$	−19.4659	−	19.4659i	−0.860279	−	0.860279i
$513$		0			0
$514$	17.7010	−	4.74296i	0.780756	−	0.209203i
$515$	6.63990	+	24.7804i	0.292589	+	1.09196i
$516$		0			0
$517$	−6.64265			−0.292143
$518$	0.625513	+	0.902346i	0.0274835	+	0.0396468i
$519$		0			0
$520$	6.73307	−	5.25813i	0.295265	−	0.230584i
$521$	−35.0486	−	20.2353i	−1.53551	−	0.886524i	−0.999094	−	0.0425681i	$-0.986446\pi$
$521$	−35.0486	−	20.2353i	−1.53551	−	0.886524i	−0.536412	−	0.843956i	$-0.680221\pi$
$522$		0			0
$523$	−29.2572	+	16.8917i	−1.27933	+	0.738621i	−0.976725	−	0.214495i	$-0.931189\pi$
$523$	−29.2572	+	16.8917i	−1.27933	+	0.738621i	−0.302604	+	0.953116i	$0.597856\pi$
$524$	2.92108			0.127608
$525$		0			0
$526$	−10.6127	−	10.6127i	−0.462734	−	0.462734i
$527$	6.03321	+	1.61659i	0.262811	+	0.0704199i
$528$		0			0
$529$	−0.983639	+	1.70371i	−0.0427669	+	0.0740744i
$530$	17.4720	+	30.2623i	0.758934	+	1.31451i
$531$		0			0
$532$	21.2309	−	7.61432i	0.920477	−	0.330122i
$533$	14.2193	−	18.8612i	0.615906	−	0.816971i
$534$		0			0
$535$	−3.53277	−	13.1845i	−0.152735	−	0.570015i
$536$	2.39125	−	4.14177i	0.103286	−	0.178897i
$537$		0			0
$538$	−5.35850	+	5.35850i	−0.231021	+	0.231021i
$539$	7.00881	−	9.81150i	0.301891	−	0.422611i
$540$		0			0
$541$	15.5379	+	4.16337i	0.668026	+	0.178997i	0.576866	−	0.816839i	$-0.304276\pi$
$541$	15.5379	+	4.16337i	0.668026	+	0.178997i	0.0911607	+	0.995836i	$0.470942\pi$
$542$	28.2348	+	16.3014i	1.21279	+	0.700205i
$543$		0			0
$544$	4.68136	−	17.4711i	0.200712	−	0.749066i
$545$	39.9503			1.71128
$546$		0			0
$547$	4.19513			0.179371			0.0896853	−	0.995970i	$-0.471414\pi$
$547$	4.19513			0.179371			0.0896853	+	0.995970i	$0.471414\pi$
$548$	−8.22654	+	30.7019i	−0.351420	+	1.31152i
$549$		0			0
$550$	−19.0832	−	11.0177i	−0.813709	−	0.469795i
$551$	−0.925940	−	0.248105i	−0.0394464	−	0.0105696i
$552$		0			0
$553$	7.82576	−	0.647522i	0.332785	−	0.0275354i
$554$	−33.8363	+	33.8363i	−1.43757	+	1.43757i
$555$		0			0
$556$	−11.1199	+	19.2602i	−0.471588	+	0.816814i
$557$	−8.80155	−	32.8478i	−0.372934	−	1.39181i	−0.856340	−	0.516412i	$-0.827267\pi$
$557$	−8.80155	−	32.8478i	−0.372934	−	1.39181i	0.483407	−	0.875396i	$-0.339399\pi$
$558$		0			0
$559$	−0.281785	−	2.00813i	−0.0119183	−	0.0849349i
$560$	40.9260	+	7.41538i	1.72944	+	0.313357i
$561$		0			0
$562$	2.90789	+	5.03661i	0.122662	+	0.212457i
$563$	−14.8890	+	25.7886i	−0.627498	+	1.08686i	0.360554	+	0.932738i	$0.382588\pi$
$563$	−14.8890	+	25.7886i	−0.627498	+	1.08686i	−0.988052	+	0.154120i	$0.950746\pi$
$564$		0			0
$565$	27.6447	+	7.40738i	1.16302	+	0.311631i
$566$	−15.3177	−	15.3177i	−0.643849	−	0.643849i
$567$		0			0
$568$	1.67386			0.0702338
$569$	10.9152	−	6.30190i	0.457589	−	0.264189i	−0.253441	−	0.967351i	$-0.581562\pi$
$569$	10.9152	−	6.30190i	0.457589	−	0.264189i	0.711030	+	0.703162i	$0.248229\pi$
$570$		0			0
$571$	4.31551	+	2.49156i	0.180598	+	0.104269i	0.587574	−	0.809171i	$-0.300083\pi$
$571$	4.31551	+	2.49156i	0.180598	+	0.104269i	−0.406975	+	0.913439i	$0.633417\pi$
$572$	−1.24112	+	10.0902i	−0.0518937	+	0.421892i
$573$		0			0
$574$	32.9422	−	2.72571i	1.37498	−	0.113769i
$575$	−30.7634			−1.28292
$576$		0			0
$577$	0.150997	+	0.563527i	0.00628607	+	0.0234599i	0.968998	−	0.247070i	$-0.0794678\pi$
$577$	0.150997	+	0.563527i	0.00628607	+	0.0234599i	−0.962712	+	0.270530i	$0.912801\pi$
$578$	−20.2410	+	5.42355i	−0.841913	+	0.225590i
$579$		0			0
$580$	0.728973	+	0.728973i	0.0302689	+	0.0302689i
$581$	−0.637559	−	1.77770i	−0.0264504	−	0.0737514i
$582$		0			0
$583$	8.91001	+	2.38743i	0.369015	+	0.0988773i
$584$	−4.22417	+	7.31648i	−0.174797	+	0.302758i
$585$		0			0
$586$	24.0184	−	13.8670i	0.992191	−	0.572842i
$587$	−2.10756	+	2.10756i	−0.0869883	+	0.0869883i	−0.749262	−	0.662274i	$-0.769592\pi$
$587$	−2.10756	+	2.10756i	−0.0869883	+	0.0869883i	0.662274	+	0.749262i	$0.269592\pi$
$588$		0			0
$589$			13.2670i			0.546656i
$590$	−24.3755	+	90.9706i	−1.00352	+	3.74520i
$591$		0			0
$592$	0.258756	+	0.965689i	0.0106348	+	0.0396896i
$593$	−0.363170	+	1.35537i	−0.0149136	+	0.0556584i	−0.972982	−	0.230882i	$-0.925839\pi$
$593$	−0.363170	+	1.35537i	−0.0149136	+	0.0556584i	0.958068	+	0.286541i	$0.0925054\pi$
$594$		0			0
$595$	7.49346	+	20.8939i	0.307202	+	0.856568i
$596$	4.25350	−	4.25350i	0.174230	−	0.174230i
$597$		0			0
$598$	12.3153	+	29.0302i	0.503608	+	1.18713i
$599$	23.1607	−	40.1154i	0.946319	−	1.63907i	0.193230	−	0.981153i	$-0.438104\pi$
$599$	23.1607	−	40.1154i	0.946319	−	1.63907i	0.753089	−	0.657919i	$-0.228563\pi$
$600$		0			0
$601$			41.2270i			1.68169i	0.541279	+	0.840843i	$0.317940\pi$
$601$			41.2270i			1.68169i	−0.541279	+	0.840843i	$0.682060\pi$
$602$	1.83427	−	2.16520i	0.0747594	−	0.0882469i
$603$		0			0
$604$	7.62757	−	28.4665i	0.310361	−	1.15828i
$605$	26.5494	−	7.11389i	1.07939	−	0.289221i
$606$		0			0
$607$	−7.17511	+	4.14255i	−0.291229	+	0.168141i	−0.638496	−	0.769625i	$-0.720443\pi$
$607$	−7.17511	+	4.14255i	−0.291229	+	0.168141i	0.347267	+	0.937766i	$0.387110\pi$
$608$	38.4187			1.55808
$609$		0			0
$610$		−	9.85180i		−	0.398888i
$611$	1.69745	−	13.8002i	0.0686716	−	0.558295i
$612$		0			0
$613$	−17.2066	+	4.61049i	−0.694967	+	0.186216i	−0.588975	−	0.808151i	$-0.700468\pi$
$613$	−17.2066	+	4.61049i	−0.694967	+	0.186216i	−0.105992	+	0.994367i	$0.533802\pi$
$614$	16.3916	−	9.46369i	0.661511	−	0.381923i
$615$		0			0
$616$	2.59361	−	1.79791i	0.104499	−	0.0724398i
$617$	1.41807	+	1.41807i	0.0570895	+	0.0570895i	0.735075	−	0.677986i	$-0.237147\pi$
$617$	1.41807	+	1.41807i	0.0570895	+	0.0570895i	−0.677986	+	0.735075i	$0.737147\pi$
$618$		0			0
$619$	9.84753	−	2.63864i	0.395806	−	0.106056i	−0.0554256	−	0.998463i	$-0.517652\pi$
$619$	9.84753	−	2.63864i	0.395806	−	0.106056i	0.451231	+	0.892407i	$0.350985\pi$
$620$	7.13392	−	12.3563i	0.286505	−	0.496242i
$621$		0			0
$622$	3.40781	+	3.40781i	0.136641	+	0.136641i
$623$	15.0513	+	12.7508i	0.603016	+	0.510852i
$624$		0			0
$625$	−6.77177	−	11.7291i	−0.270871	−	0.469162i
$626$	−1.70190	−	6.35157i	−0.0680215	−	0.253860i
$627$		0			0
$628$	15.0020	+	25.9841i	0.598643	+	1.03688i
$629$	−0.377276	+	0.377276i	−0.0150430	+	0.0150430i
$630$		0			0
$631$	−4.32633	+	4.32633i	−0.172228	+	0.172228i	−0.787958	−	0.615729i	$-0.788861\pi$
$631$	−4.32633	+	4.32633i	−0.172228	+	0.172228i	0.615729	+	0.787958i	$0.288861\pi$
$632$	1.98518	+	0.531928i	0.0789663	+	0.0211589i
$633$		0			0
$634$	52.2874	+	30.1881i	2.07660	+	1.19892i
$635$	−10.7155	+	39.9908i	−0.425232	+	1.58699i
$636$		0			0
$637$	18.5925	+	17.0681i	0.736661	+	0.676263i
$638$	0.604643			0.0239380
$639$		0			0
$640$	16.1451	+	9.32137i	0.638190	+	0.368459i
$641$	25.2944	+	14.6037i	0.999068	+	0.576812i	0.907972	−	0.419030i	$-0.137630\pi$
$641$	25.2944	+	14.6037i	0.999068	+	0.576812i	0.0910953	+	0.995842i	$0.470963\pi$
$642$		0			0
$643$	14.6743	−	14.6743i	0.578699	−	0.578699i	−0.355846	−	0.934545i	$-0.615807\pi$
$643$	14.6743	−	14.6743i	0.578699	−	0.578699i	0.934545	+	0.355846i	$0.115807\pi$
$644$	−8.47867	+	17.9611i	−0.334107	+	0.707767i
$645$		0			0
$646$	12.1763	+	21.0900i	0.479070	+	0.829774i
$647$	4.85993	−	8.41764i	0.191064	−	0.330932i	−0.754539	−	0.656255i	$-0.772140\pi$
$647$	4.85993	−	8.41764i	0.191064	−	0.330932i	0.945603	+	0.325323i	$0.105473\pi$
$648$		0			0
$649$	12.4305	+	21.5303i	0.487941	+	0.845139i
$650$	27.7658	−	36.8301i	1.08907	−	1.44459i
$651$		0			0
$652$	−14.9570	−	14.9570i	−0.585763	−	0.585763i
$653$	7.16248	+	12.4058i	0.280289	+	0.485475i	0.971456	−	0.237220i	$-0.0762363\pi$
$653$	7.16248	+	12.4058i	0.280289	+	0.485475i	−0.691167	+	0.722695i	$0.742903\pi$
$654$		0			0
$655$	−5.89801	+	1.58037i	−0.230454	+	0.0617501i
$656$	29.0730	+	7.79008i	1.13511	+	0.304151i
$657$		0			0
$658$	15.9911	−	11.0852i	0.623398	−	0.432145i
$659$	19.4182			0.756424			0.378212	−	0.925719i	$-0.376539\pi$
$659$	19.4182			0.756424			0.378212	+	0.925719i	$0.376539\pi$
$660$		0			0
$661$	−24.3914	+	6.53565i	−0.948715	+	0.254207i	−0.699817	−	0.714322i	$-0.746735\pi$
$661$	−24.3914	+	6.53565i	−0.948715	+	0.254207i	−0.248898	+	0.968530i	$0.580068\pi$
$662$	53.8588	+	31.0954i	2.09328	+	1.20856i
$663$		0			0
$664$		−	0.494289i		−	0.0191821i
$665$	−38.7483	+	26.8606i	−1.50259	+	1.04161i
$666$		0			0
$667$	0.731045	−	0.422069i	0.0283062	−	0.0163426i
$668$	−6.39927	−	23.8824i	−0.247595	−	0.924038i
$669$		0			0
$670$	11.6643	−	43.5319i	0.450632	−	1.68178i
$671$	−1.83892	−	1.83892i	−0.0709908	−	0.0709908i
$672$		0			0
$673$		−	39.3180i		−	1.51560i	−0.652488	−	0.757799i	$-0.726275\pi$
$673$		−	39.3180i		−	1.51560i	0.652488	−	0.757799i	$-0.273725\pi$
$674$	15.7442	+	4.21864i	0.606443	+	0.162496i
$675$		0			0
$676$	−20.6453	−	5.15687i	−0.794051	−	0.198341i
$677$	−12.1361	+	7.00677i	−0.466428	+	0.269292i	−0.714743	−	0.699387i	$-0.753456\pi$
$677$	−12.1361	+	7.00677i	−0.466428	+	0.269292i	0.248315	+	0.968679i	$0.420123\pi$
$678$		0			0
$679$	−15.2776	−	42.5984i	−0.586300	−	1.63477i
$680$			5.80956i			0.222786i
$681$		0			0
$682$	−2.16584	−	8.08304i	−0.0829345	−	0.309516i
$683$	1.54598	+	5.76967i	0.0591552	+	0.220770i	0.989175	−	0.146738i	$-0.0468775\pi$
$683$	1.54598	+	5.76967i	0.0591552	+	0.220770i	−0.930020	+	0.367509i	$0.880211\pi$
$684$		0			0
$685$		−	66.4415i		−	2.53860i
$686$	−0.499281	+	35.3158i	−0.0190626	+	1.34836i
$687$		0			0
$688$	2.23775	−	1.29196i	0.0853133	−	0.0492556i
$689$	−7.23676	+	17.9006i	−0.275699	+	0.681957i
$690$		0			0
$691$	−24.0220	−	6.43667i	−0.913839	−	0.244862i	−0.228889	−	0.973453i	$-0.573509\pi$
$691$	−24.0220	−	6.43667i	−0.913839	−	0.244862i	−0.684950	+	0.728590i	$0.740176\pi$
$692$			4.28895i			0.163041i
$693$		0			0
$694$	3.68919	+	3.68919i	0.140040	+	0.140040i
$695$	12.0322	−	44.9048i	0.456407	−	1.70334i
$696$		0			0
$697$	4.15741	+	15.5157i	0.157473	+	0.587698i
$698$	20.0301	−	11.5644i	0.758150	−	0.437718i
$699$		0			0
$700$	28.9518	−	2.39554i	1.09427	−	0.0905428i
$701$		−	50.8136i		−	1.91920i	−0.281364	−	0.959601i	$-0.590787\pi$
$701$		−	50.8136i		−	1.91920i	0.281364	−	0.959601i	$-0.409213\pi$
$702$		0			0
$703$	−0.981460	−	0.566646i	−0.0370165	−	0.0213715i
$704$	−8.11845	+	2.17533i	−0.305976	+	0.0819859i
$705$		0			0
$706$	20.9243			0.787498
$707$	−12.4009	−	17.8891i	−0.466382	−	0.672788i
$708$		0			0
$709$	−15.8032	−	4.23445i	−0.593501	−	0.159028i	−0.0504483	−	0.998727i	$-0.516065\pi$
$709$	−15.8032	−	4.23445i	−0.593501	−	0.159028i	−0.543053	+	0.839699i	$0.682732\pi$
$710$	15.2360	−	4.08248i	0.571798	−	0.153213i
$711$		0			0
$712$	2.58144	+	4.47119i	0.0967436	+	0.167565i
$713$	−8.26096	−	8.26096i	−0.309376	−	0.309376i
$714$		0			0
$715$	−2.95305	−	21.0448i	−0.110438	−	0.787031i
$716$	−20.7545	−	35.9478i	−0.775632	−	1.34343i
$717$		0			0
$718$	1.02106	−	1.76852i	0.0381055	−	0.0660007i
$719$	−13.2682	−	22.9812i	−0.494821	−	0.857055i	0.505161	−	0.863025i	$-0.331433\pi$
$719$	−13.2682	−	22.9812i	−0.494821	−	0.857055i	−0.999982	+	0.00597015i	$0.998100\pi$
$720$		0			0
$721$	−19.7694	+	1.63576i	−0.736250	+	0.0609190i
$722$	−10.9546	+	10.9546i	−0.407690	+	0.407690i
$723$		0			0
$724$	1.42277	+	0.821436i	0.0528768	+	0.0305284i
$725$	−1.06926	−	0.617337i	−0.0397113	−	0.0229273i
$726$		0			0
$727$	−30.2407			−1.12157			−0.560783	−	0.827963i	$-0.689500\pi$
$727$	−30.2407			−1.12157			−0.560783	+	0.827963i	$0.689500\pi$
$728$	3.07241	+	5.84768i	0.113871	+	0.216729i
$729$		0			0
$730$	−20.6051	+	76.8994i	−0.762630	+	2.84618i
$731$	1.19424	+	0.689495i	0.0441706	+	0.0255019i
$732$		0			0
$733$	12.8860	+	3.45279i	0.475955	+	0.127532i	0.488818	−	0.872386i	$-0.337428\pi$
$733$	12.8860	+	3.45279i	0.475955	+	0.127532i	−0.0128637	+	0.999917i	$0.504095\pi$
$734$	−10.4748	+	10.4748i	−0.386631	+	0.386631i
$735$		0			0
$736$	−23.9223	+	23.9223i	−0.881786	+	0.881786i
$737$	−5.94835	−	10.3028i	−0.219110	−	0.379510i
$738$		0			0
$739$	−2.27661	−	8.49643i	−0.0837466	−	0.312546i	0.911327	−	0.411683i	$-0.135059\pi$
$739$	−2.27661	−	8.49643i	−0.0837466	−	0.312546i	−0.995074	+	0.0991361i	$0.968392\pi$
$740$	0.609395	+	1.05550i	0.0224018	+	0.0388011i
$741$		0			0
$742$	−25.4335	+	9.12155i	−0.933694	+	0.334863i
$743$	7.57023	+	7.57023i	0.277725	+	0.277725i	0.832200	−	0.554475i	$-0.187081\pi$
$743$	7.57023	+	7.57023i	0.277725	+	0.277725i	−0.554475	+	0.832200i	$0.687081\pi$
$744$		0			0
$745$	−6.28710	+	10.8896i	−0.230341	+	0.398963i
$746$	−32.7566	+	8.77711i	−1.19931	+	0.321353i
$747$		0			0
$748$	−4.88855	−	4.88855i	−0.178743	−	0.178743i
$749$	10.5183	−	0.870311i	0.384332	−	0.0318005i
$750$		0			0
$751$	31.9329	−	18.4365i	1.16525	−	0.672756i	0.212692	−	0.977119i	$-0.431777\pi$
$751$	31.9329	−	18.4365i	1.16525	−	0.672756i	0.952556	+	0.304363i	$0.0984435\pi$
$752$	17.1137	−	4.58559i	0.624071	−	0.167219i
$753$		0			0
$754$	−0.154510	+	1.25615i	−0.00562690	+	0.0457463i
$755$			61.6040i			2.24200i
$756$		0			0
$757$	4.46764			0.162379			0.0811896	−	0.996699i	$-0.474128\pi$
$757$	4.46764			0.162379			0.0811896	+	0.996699i	$0.474128\pi$
$758$	59.1486	−	34.1495i	2.14837	−	1.24036i
$759$		0			0
$760$	−11.9194	+	3.19379i	−0.432362	+	0.115851i
$761$	11.5822	−	43.2252i	0.419853	−	1.56691i	−0.355059	−	0.934844i	$-0.615539\pi$
$761$	11.5822	−	43.2252i	0.419853	−	1.56691i	0.774912	−	0.632069i	$-0.217794\pi$
$762$		0			0
$763$	−5.50743	+	30.3959i	−0.199382	+	1.10041i
$764$			1.71937i			0.0622046i
$765$		0			0
$766$	19.8033	−	34.3003i	0.715522	−	1.23932i
$767$	−47.9059	+	20.3227i	−1.72978	+	0.733812i
$768$		0			0
$769$	19.6232	−	19.6232i	0.707631	−	0.707631i	−0.258406	−	0.966036i	$-0.583197\pi$
$769$	19.6232	−	19.6232i	0.707631	−	0.707631i	0.966036	+	0.258406i	$0.0831971\pi$
$770$	19.2228	−	22.6908i	0.692741	−	0.817721i
$771$		0			0
$772$	0.837625	−	3.12606i	0.0301468	−	0.112509i
$773$	2.70681	+	10.1019i	0.0973571	+	0.363342i	0.997366	−	0.0725293i	$-0.0231071\pi$
$773$	2.70681	+	10.1019i	0.0973571	+	0.363342i	−0.900009	+	0.435871i	$0.856440\pi$
$774$		0			0
$775$	−4.42263	+	16.5055i	−0.158866	+	0.592895i
$776$		−	11.8445i		−	0.425192i
$777$		0			0
$778$	−10.7454	+	10.7454i	−0.385240	+	0.385240i
$779$	−29.5477	+	17.0594i	−1.05866	+	0.611216i
$780$		0			0
$781$	2.08191	−	3.60597i	0.0744964	−	0.129032i
$782$	−20.7140	−	5.55029i	−0.740730	−	0.198478i
$783$		0			0
$784$	−11.2839	+	30.1160i	−0.402996	+	1.07557i
$785$	−44.3488	−	44.3488i	−1.58287	−	1.58287i
$786$		0			0
$787$	6.41695	−	1.71942i	0.228740	−	0.0612906i	−0.142629	−	0.989776i	$-0.545555\pi$
$787$	6.41695	−	1.71942i	0.228740	−	0.0612906i	0.371368	+	0.928486i	$0.378889\pi$
$788$	−2.01369	−	7.51521i	−0.0717349	−	0.267718i
$789$		0			0
$790$	19.3671			0.689050
$791$	−9.44687	+	20.0121i	−0.335892	+	0.711550i
$792$		0			0
$793$	4.29029	−	3.35046i	0.152353	−	0.118978i
$794$	50.7462	+	29.2983i	1.80091	+	1.03976i
$795$		0			0
$796$	−14.4683	+	8.35326i	−0.512814	+	0.296073i
$797$	−21.9115			−0.776146			−0.388073	−	0.921629i	$-0.626859\pi$
$797$	−21.9115			−0.776146			−0.388073	+	0.921629i	$0.626859\pi$
$798$		0			0
$799$	6.68598	+	6.68598i	0.236533	+	0.236533i
$800$	47.7969	+	12.8071i	1.68988	+	0.452801i
$801$		0			0
$802$	−21.4871	+	37.2167i	−0.758735	+	1.31417i
$803$	10.5078	+	18.2001i	0.370812	+	0.642266i
$804$		0			0
$805$	7.40211	−	40.8528i	0.260890	−	1.43987i
$806$	17.3461	−	2.43404i	0.610989	−	0.0857353i
$807$		0			0
$808$	−1.47449	−	5.50288i	−0.0518724	−	0.193591i
$809$	−11.2486	+	19.4832i	−0.395480	+	0.684992i	−0.993162	−	0.116741i	$-0.962755\pi$
$809$	−11.2486	+	19.4832i	−0.395480	+	0.684992i	0.597682	+	0.801733i	$0.296088\pi$
$810$		0			0
$811$	−12.3587	+	12.3587i	−0.433973	+	0.433973i	−0.889978	−	0.456004i	$-0.849280\pi$
$811$	−12.3587	+	12.3587i	−0.433973	+	0.433973i	0.456004	+	0.889978i	$0.349280\pi$
$812$	−0.655128	+	0.454140i	−0.0229905	+	0.0159372i
$813$		0			0
$814$	0.690471	+	0.185011i	0.0242010	+	0.00648463i
$815$	38.2922	+	22.1080i	1.34132	+	0.774410i
$816$		0			0
$817$	−0.758097	+	2.82926i	−0.0265224	+	0.0989831i
$818$	−75.2552			−2.63124
$819$		0			0
$820$	36.6928			1.28137
$821$	6.52308	−	24.3445i	0.227657	−	0.849628i	−0.753665	−	0.657258i	$-0.771716\pi$
$821$	6.52308	−	24.3445i	0.227657	−	0.849628i	0.981323	−	0.192370i	$-0.0616173\pi$
$822$		0			0
$823$	−35.2081	−	20.3274i	−1.22728	−	0.708568i	−0.260817	−	0.965388i	$-0.583992\pi$
$823$	−35.2081	−	20.3274i	−1.22728	−	0.708568i	−0.966459	+	0.256820i	$0.917325\pi$
$824$	−5.01495	−	1.34375i	−0.174704	−	0.0468118i
$825$		0			0
$826$	−65.8540	−	31.0869i	−2.29135	−	1.08165i
$827$	21.0284	−	21.0284i	0.731228	−	0.731228i	−0.239635	−	0.970863i	$-0.577028\pi$
$827$	21.0284	−	21.0284i	0.731228	−	0.731228i	0.970863	+	0.239635i	$0.0770277\pi$
$828$		0			0
$829$	−8.91208	+	15.4362i	−0.309530	+	0.536121i	−0.978260	−	0.207385i	$-0.933505\pi$
$829$	−8.91208	+	15.4362i	−0.309530	+	0.536121i	0.668730	+	0.743505i	$0.266838\pi$
$830$	−1.20555	−	4.49918i	−0.0418453	−	0.156169i
$831$		0			0
$832$	−2.44470	−	17.4221i	−0.0847547	−	0.604001i
$833$	−16.9300	+	2.82097i	−0.586591	+	0.0977409i
$834$		0			0
$835$	25.8418	+	44.7593i	0.894292	+	1.54896i
$836$	7.34230	−	12.7172i	0.253939	−	0.439835i
$837$		0			0
$838$	12.6541	+	3.39066i	0.437129	+	0.117128i
$839$	19.0512	+	19.0512i	0.657721	+	0.657721i	0.954840	−	0.297119i	$-0.0960258\pi$
$839$	19.0512	+	19.0512i	0.657721	+	0.657721i	−0.297119	+	0.954840i	$0.596026\pi$
$840$		0			0
$841$	−28.9661			−0.998832
$842$	39.4147	−	22.7561i	1.35832	−	0.784228i
$843$		0			0
$844$	−22.8793	−	13.2094i	−0.787539	−	0.454686i
$845$	44.4754	−	0.757238i	1.53000	−	0.0260498i
$846$		0			0
$847$	1.75253	+	21.1806i	0.0602177	+	0.727775i
$848$	−24.6032			−0.844879
$849$		0			0
$850$	8.11811	+	30.2972i	0.278449	+	1.03919i
$851$	0.963962	−	0.258293i	0.0330442	−	0.00885416i
$852$		0			0
$853$	9.31374	+	9.31374i	0.318896	+	0.318896i	0.848343	−	0.529447i	$-0.177600\pi$
$853$	9.31374	+	9.31374i	0.318896	+	0.318896i	−0.529447	+	0.848343i	$0.677600\pi$
$854$	7.49567	+	1.35814i	0.256497	+	0.0464746i
$855$		0			0
$856$	2.66821	+	0.714946i	0.0911977	+	0.0244363i
$857$	17.9524	−	31.0945i	0.613242	−	1.06217i	−0.377448	−	0.926031i	$-0.623198\pi$
$857$	17.9524	−	31.0945i	0.613242	−	1.06217i	0.990690	−	0.136136i	$-0.0434683\pi$
$858$		0			0
$859$	−17.6264	+	10.1766i	−0.601406	+	0.347222i	−0.769594	−	0.638533i	$-0.779542\pi$
$859$	−17.6264	+	10.1766i	−0.601406	+	0.347222i	0.168189	+	0.985755i	$0.446208\pi$
$860$	2.22741	−	2.22741i	0.0759541	−	0.0759541i
$861$		0			0
$862$		−	67.7957i		−	2.30913i
$863$	2.11076	−	7.87746i	0.0718511	−	0.268152i	−0.920650	−	0.390390i	$-0.872340\pi$
$863$	2.11076	−	7.87746i	0.0718511	−	0.268152i	0.992501	+	0.122238i	$0.0390070\pi$
$864$		0			0
$865$	−2.32042	−	8.65991i	−0.0788965	−	0.294446i
$866$	−3.22777	+	12.0462i	−0.109684	+	0.409347i
$867$		0			0
$868$	8.41776	+	7.13120i	0.285717	+	0.242049i
$869$	3.61503	−	3.61503i	0.122632	−	0.122632i
$870$		0			0
$871$	22.9243	−	9.72498i	0.776760	−	0.329518i
$872$	−4.04248	+	7.00178i	−0.136896	+	0.237110i
$873$		0			0
$874$		−	45.5498i		−	1.54075i
$875$	−14.5538	+	5.21963i	−0.492009	+	0.176456i
$876$		0			0
$877$	−11.5533	+	43.1175i	−0.390127	+	1.45597i	0.439797	+	0.898097i	$0.355051\pi$
$877$	−11.5533	+	43.1175i	−0.390127	+	1.45597i	−0.829924	+	0.557877i	$0.811616\pi$
$878$	45.2899	−	12.1354i	1.52846	−	0.409550i
$879$		0			0
$880$	23.4511	−	13.5395i	0.790537	−	0.456417i
$881$	−0.616060			−0.0207556			−0.0103778	−	0.999946i	$-0.503303\pi$
$881$	−0.616060			−0.0207556			−0.0103778	+	0.999946i	$0.503303\pi$
$882$		0			0
$883$			16.5050i			0.555437i	0.960662	+	0.277719i	$0.0895783\pi$
$883$			16.5050i			0.555437i	−0.960662	+	0.277719i	$0.910422\pi$
$884$	11.4052	−	8.90680i	0.383599	−	0.299568i
$885$		0			0
$886$	28.7347	−	7.69945i	0.965362	−	0.258668i
$887$	−16.0290	+	9.25435i	−0.538201	+	0.310731i	−0.744350	−	0.667790i	$-0.767240\pi$
$887$	−16.0290	+	9.25435i	−0.538201	+	0.310731i	0.206148	+	0.978521i	$0.433907\pi$
$888$		0			0
$889$	−28.9495	−	13.6658i	−0.970936	−	0.458337i
$890$	34.4021	+	34.4021i	1.15316	+	1.15316i
$891$		0			0
$892$	0.210072	−	0.0562886i	0.00703373	−	0.00188468i
$893$	−10.0419	+	17.3931i	−0.336040	+	0.582039i
$894$		0			0
$895$	61.3544	+	61.3544i	2.05085	+	2.05085i
$896$	−9.31781	+	10.9989i	−0.311286	+	0.367446i
$897$		0			0
$898$	−38.6036	−	66.8633i	−1.28822	−	2.23126i
$899$	−0.121356	−	0.452905i	−0.00404744	−	0.0151052i
$900$		0			0
$901$	−6.56513	−	11.3711i	−0.218716	−	0.378828i
$902$	15.2173	−	15.2173i	0.506681	−	0.506681i
$903$		0			0
$904$	−4.09554	+	4.09554i	−0.136216	+	0.136216i
$905$	−3.31716	−	0.888830i	−0.110266	−	0.0295457i
$906$		0			0
$907$	23.9675	+	13.8377i	0.795829	+	0.459472i	0.842010	−	0.539461i	$-0.181372\pi$
$907$	23.9675	+	13.8377i	0.795829	+	0.459472i	−0.0461819	+	0.998933i	$0.514705\pi$
$908$	11.2321	−	41.9186i	0.372749	−	1.39112i
$909$		0			0
$910$	42.2283	+	45.7339i	1.39985	+	1.51607i
$911$	−23.1900			−0.768320			−0.384160	−	0.923267i	$-0.625509\pi$
$911$	−23.1900			−0.768320			−0.384160	+	0.923267i	$0.625509\pi$
$912$		0			0
$913$	−1.06484	−	0.614783i	−0.0352409	−	0.0203464i
$914$	−21.5842	−	12.4616i	−0.713940	−	0.412194i
$915$		0			0
$916$	−20.3886	+	20.3886i	−0.673659	+	0.673659i
$917$	−0.389330	−	4.70533i	−0.0128568	−	0.155384i
$918$		0			0
$919$	−11.1083	−	19.2401i	−0.366428	−	0.634672i	0.622576	−	0.782559i	$-0.286086\pi$
$919$	−11.1083	−	19.2401i	−0.366428	−	0.634672i	−0.989004	+	0.147887i	$0.952753\pi$
$920$	5.43318	−	9.41055i	0.179127	−	0.310257i
$921$		0			0
$922$	−4.79814	−	8.31062i	−0.158018	−	0.273696i
$923$	6.95942	+	5.24664i	0.229072	+	0.172695i
$924$		0			0
$925$	−1.03214	−	1.03214i	−0.0339367	−	0.0339367i
$926$	−15.6757	−	27.1512i	−0.515137	−	0.892243i
$927$		0			0
$928$	−1.31153	+	0.351424i	−0.0430531	+	0.0115361i
$929$	−19.2602	−	5.16075i	−0.631907	−	0.169319i	−0.0713719	−	0.997450i	$-0.522738\pi$
$929$	−19.2602	−	5.16075i	−0.631907	−	0.169319i	−0.560535	+	0.828131i	$0.689404\pi$
$930$		0			0
$931$	−15.0950	−	33.1843i	−0.494718	−	1.08757i
$932$	−8.32668			−0.272750
$933$		0			0
$934$	10.5567	−	2.82865i	0.345424	−	0.0925561i
$935$	12.5154	+	7.22576i	0.409297	+	0.236308i
$936$		0			0
$937$		−	32.0817i		−	1.04806i	−0.851699	−	0.524031i	$-0.824428\pi$
$937$		−	32.0817i		−	1.04806i	0.851699	−	0.524031i	$-0.175572\pi$
$938$	31.5129	+	14.8759i	1.02893	+	0.485715i
$939$		0			0
$940$	18.7053	−	10.7995i	0.610100	−	0.352241i
$941$	2.07717	+	7.75209i	0.0677137	+	0.252711i	0.991483	−	0.130240i	$-0.0415747\pi$
$941$	2.07717	+	7.75209i	0.0677137	+	0.252711i	−0.923769	+	0.382950i	$0.874908\pi$
$942$		0			0
$943$	7.77614	−	29.0209i	0.253226	−	0.945052i
$944$	−46.8881	−	46.8881i	−1.52608	−	1.52608i
$945$		0			0
$946$		−	1.84751i		−	0.0600679i
$947$	16.0044	+	4.28837i	0.520074	+	0.139353i	0.509301	−	0.860589i	$-0.329904\pi$
$947$	16.0044	+	4.28837i	0.520074	+	0.139353i	0.0107733	+	0.999942i	$0.496571\pi$
$948$		0			0
$949$	−40.4959	+	17.1793i	−1.31455	+	0.557662i
$950$	−57.6974	+	33.3116i	−1.87195	+	1.08077i
$951$		0			0
$952$	−4.42016	−	0.800888i	−0.143258	−	0.0259569i
$953$			37.7682i			1.22343i	0.791077	+	0.611717i	$0.209521\pi$
$953$			37.7682i			1.22343i	−0.791077	+	0.611717i	$0.790479\pi$
$954$		0			0
$955$	−0.930216	−	3.47161i	−0.0301011	−	0.112339i
$956$	−7.79981	−	29.1093i	−0.252264	−	0.941461i
$957$		0			0
$958$		−	38.6101i		−	1.24744i
$959$	50.5516	+	9.15943i	1.63240	+	0.295773i
$960$		0			0
$961$	21.2269	−	12.2554i	0.684739	−	0.395334i
$962$	−0.560804	+	1.38718i	−0.0180811	+	0.0447246i
$963$		0			0
$964$	4.31129	+	1.15521i	0.138857	+	0.0372067i
$965$			6.76507i			0.217775i
$966$		0			0
$967$	−33.4886	−	33.4886i	−1.07692	−	1.07692i	−0.996784	−	0.0801380i	$-0.974464\pi$
$967$	−33.4886	−	33.4886i	−1.07692	−	1.07692i	−0.0801380	−	0.996784i	$-0.525536\pi$
$968$	−1.43968	+	5.37294i	−0.0462729	+	0.172693i
$969$		0			0
$970$	−28.8882	−	107.812i	−0.927543	−	3.46164i
$971$	−51.9221	+	29.9772i	−1.66626	+	0.962015i	−0.696631	+	0.717430i	$0.745318\pi$
$971$	−51.9221	+	29.9772i	−1.66626	+	0.962015i	−0.969628	+	0.244585i	$0.921348\pi$
$972$		0			0
$973$	32.5068	+	15.3451i	1.04212	+	0.491940i
$974$			3.02085i			0.0967944i
$975$		0			0
$976$	6.00712	+	3.46821i	0.192283	+	0.111015i
$977$	29.0823	−	7.79257i	0.930424	−	0.249306i	0.238389	−	0.971170i	$-0.423381\pi$
$977$	29.0823	−	7.79257i	0.930424	−	0.249306i	0.692035	+	0.721864i	$0.256714\pi$
$978$		0			0
$979$	12.8429			0.410461
$980$	−3.78501	+	39.0234i	−0.120908	+	1.24656i
$981$		0			0
$982$	41.8720	+	11.2196i	1.33619	+	0.358031i
$983$	15.2428	−	4.08428i	0.486168	−	0.130268i	−0.00740505	−	0.999973i	$-0.502357\pi$
$983$	15.2428	−	4.08428i	0.486168	−	0.130268i	0.493573	+	0.869704i	$0.335690\pi$
$984$		0			0
$985$	8.13178	+	14.0847i	0.259100	+	0.448775i
$986$	−0.608587	−	0.608587i	−0.0193814	−	0.0193814i
$987$		0			0
$988$	24.5440	+	18.5035i	0.780847	+	0.588673i
$989$	−1.28965	−	2.23374i	−0.0410085	−	0.0710289i
$990$		0			0
$991$	−15.1135	+	26.1773i	−0.480096	+	0.831550i	−0.999739	−	0.0228331i	$-0.992731\pi$
$991$	−15.1135	+	26.1773i	−0.480096	+	0.831550i	0.519644	+	0.854383i	$0.326065\pi$
$992$	9.39588	+	16.2741i	0.298319	+	0.516704i
$993$		0			0
$994$	1.00574	+	12.1550i	0.0319000	+	0.385534i
$995$	24.6939	−	24.6939i	0.782849	−	0.782849i
$996$		0			0
$997$	−40.0442	−	23.1195i	−1.26821	−	0.732203i	−0.293563	−	0.955940i	$-0.594841\pi$
$997$	−40.0442	−	23.1195i	−1.26821	−	0.732203i	−0.974650	+	0.223737i	$0.928174\pi$
$998$	−9.73428	−	5.62009i	−0.308133	−	0.177901i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.73.2		32
3.2	odd	2		91.2.bb.a.73.7	yes	32
7.5	odd	6	inner	819.2.fn.e.775.7		32
13.5	odd	4	inner	819.2.fn.e.577.7		32
21.2	odd	6		637.2.bc.b.411.2		32
21.5	even	6		91.2.bb.a.47.2	yes	32
21.11	odd	6		637.2.i.a.489.13		32
21.17	even	6		637.2.i.a.489.14		32
21.20	even	2		637.2.bc.b.619.7		32
39.5	even	4		91.2.bb.a.31.2	yes	32
91.5	even	12	inner	819.2.fn.e.460.2		32
273.5	odd	12		91.2.bb.a.5.7	✓	32
273.44	even	12		637.2.bc.b.460.7		32
273.83	odd	4		637.2.bc.b.31.2		32
273.122	odd	12		637.2.i.a.538.14		32
273.200	even	12		637.2.i.a.538.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.7	✓	32	273.5	odd	12
91.2.bb.a.31.2	yes	32	39.5	even	4
91.2.bb.a.47.2	yes	32	21.5	even	6
91.2.bb.a.73.7	yes	32	3.2	odd	2
637.2.i.a.489.13		32	21.11	odd	6
637.2.i.a.489.14		32	21.17	even	6
637.2.i.a.538.13		32	273.200	even	12
637.2.i.a.538.14		32	273.122	odd	12
637.2.bc.b.31.2		32	273.83	odd	4
637.2.bc.b.411.2		32	21.2	odd	6
637.2.bc.b.460.7		32	273.44	even	12
637.2.bc.b.619.7		32	21.20	even	2
819.2.fn.e.73.2		32	1.1	even	1	trivial
819.2.fn.e.460.2		32	91.5	even	12	inner
819.2.fn.e.577.7		32	13.5	odd	4	inner
819.2.fn.e.775.7		32	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.493585 + 1.84208i) q^{2} +(-1.41759 - 0.818448i) q^{4} +(3.30509 + 0.885596i) q^{5} +(-1.12943 + 2.39257i) q^{7} +(-0.489646 + 0.489646i) q^{8} +O(q^{10})\)	\(q+(-0.493585 + 1.84208i) q^{2} +(-1.41759 - 0.818448i) q^{4} +(3.30509 + 0.885596i) q^{5} +(-1.12943 + 2.39257i) q^{7} +(-0.489646 + 0.489646i) q^{8} +(-3.26268 + 5.65113i) q^{10} +(0.445825 + 1.66384i) q^{11} +(-3.57057 + 0.501030i) q^{13} +(-3.84984 - 3.26144i) q^{14} +(-2.29718 - 3.97884i) q^{16} +(1.22596 - 2.12343i) q^{17} +(5.03057 + 1.34794i) q^{19} +(-3.96046 - 3.96046i) q^{20} -3.28498 q^{22} +(-3.97172 + 2.29307i) q^{23} +(5.80922 + 3.35395i) q^{25} +(0.839440 - 6.82459i) q^{26} +(3.55926 - 2.46731i) q^{28} -0.184063 q^{29} +(0.659317 + 2.46060i) q^{31} +(7.12546 - 1.90926i) q^{32} +(3.30641 + 3.30641i) q^{34} +(-5.85172 + 6.90744i) q^{35} +(-0.210190 - 0.0563202i) q^{37} +(-4.96603 + 8.60141i) q^{38} +(-2.05195 + 1.18470i) q^{40} +(-4.63239 + 4.63239i) q^{41} +0.562412i q^{43} +(0.729768 - 2.72353i) q^{44} +(-2.26365 - 8.44806i) q^{46} +(-0.998090 + 3.72492i) q^{47} +(-4.44878 - 5.40448i) q^{49} +(-9.04560 + 9.04560i) q^{50} +(5.47168 + 2.21207i) q^{52} +(2.67755 - 4.63764i) q^{53} +5.89396i q^{55} +(-0.618491 - 1.72453i) q^{56} +(0.0908505 - 0.339059i) q^{58} +(13.9411 - 3.73550i) q^{59} +(-1.30750 + 0.754885i) q^{61} -4.85807 q^{62} +4.87935i q^{64} +(-12.2448 - 1.50613i) q^{65} +(-6.67118 + 1.78754i) q^{67} +(-3.47583 + 2.00677i) q^{68} +(-9.83576 - 14.1888i) q^{70} +(-1.70926 - 1.70926i) q^{71} +(11.7847 - 3.15770i) q^{73} +(0.207493 - 0.359389i) q^{74} +(-6.02809 - 6.02809i) q^{76} +(-4.48438 - 0.812524i) q^{77} +(-1.48398 - 2.57034i) q^{79} +(-4.06875 - 15.1848i) q^{80} +(-6.24677 - 10.8197i) q^{82} +(-0.504742 + 0.504742i) q^{83} +(5.93241 - 5.93241i) q^{85} +(-1.03601 - 0.277598i) q^{86} +(-1.03299 - 0.596396i) q^{88} +(1.92971 - 7.20177i) q^{89} +(2.83396 - 9.10871i) q^{91} +7.50704 q^{92} +(-6.36898 - 3.67713i) q^{94} +(15.4328 + 8.91011i) q^{95} +(-12.0949 + 12.0949i) q^{97} +(12.1513 - 5.52745i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

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