LMFDB - Embedded newform 990.2.bh.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(73,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 14]))

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

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

chi := DirichletCharacter("990.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bh (of order $20$, degree $8$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	990.73
Dual form			990.2.bh.c.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(-2.14909 - 0.617590i) q^{5} +(-0.00697389 + 0.0136870i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.273795 + 2.21924i) q^{10} +(-2.43343 + 2.25353i) q^{11} +(-2.31203 + 0.366190i) q^{13} +(0.0146095 + 0.00474691i) q^{14} +(0.809017 - 0.587785i) q^{16} +(3.88580 + 0.615451i) q^{17} +(1.78456 - 5.49230i) q^{19} +(2.23475 - 0.0767418i) q^{20} +(2.60646 + 2.05094i) q^{22} +(4.75841 + 4.75841i) q^{23} +(4.23716 + 2.65451i) q^{25} +(0.723362 + 2.22628i) q^{26} +(0.00240304 - 0.0151722i) q^{28} +(1.28099 + 3.94247i) q^{29} +(4.70277 + 3.41676i) q^{31} +(-0.707107 - 0.707107i) q^{32} -3.93424i q^{34} +(0.0234405 - 0.0251076i) q^{35} +(-1.00521 - 0.512178i) q^{37} +(-5.70385 - 0.903401i) q^{38} +(-0.425389 - 2.19523i) q^{40} +(4.46390 + 1.45041i) q^{41} +(-5.68946 + 5.68946i) q^{43} +(1.61795 - 2.89521i) q^{44} +(3.95544 - 5.44420i) q^{46} +(0.703097 + 1.37991i) q^{47} +(4.11436 + 5.66293i) q^{49} +(1.95899 - 4.60026i) q^{50} +(2.08571 - 1.06272i) q^{52} +(-2.19559 - 13.8624i) q^{53} +(6.62142 - 3.34018i) q^{55} -0.0153613 q^{56} +(3.69354 - 1.88195i) q^{58} +(-1.86696 + 0.606613i) q^{59} +(4.84534 + 6.66904i) q^{61} +(2.63902 - 5.17937i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(5.19491 + 0.640913i) q^{65} +(3.67640 - 3.67640i) q^{67} +(-3.88580 + 0.615451i) q^{68} +(-0.0284654 - 0.0192242i) q^{70} +(5.20051 - 3.77839i) q^{71} +(4.10721 + 2.09273i) q^{73} +(-0.348623 + 1.07295i) q^{74} +5.77495i q^{76} +(-0.0138737 - 0.0490224i) q^{77} +(3.84472 + 2.79336i) q^{79} +(-2.10166 + 0.763562i) q^{80} +(0.734244 - 4.63584i) q^{82} +(-2.08413 + 13.1587i) q^{83} +(-7.97084 - 3.72249i) q^{85} +(6.50944 + 4.72938i) q^{86} +(-3.11267 - 1.14512i) q^{88} +9.48232i q^{89} +(0.0111118 - 0.0341986i) q^{91} +(-5.99594 - 3.05509i) q^{92} +(1.25293 - 0.910306i) q^{94} +(-7.22716 + 10.7013i) q^{95} +(4.39615 - 0.696283i) q^{97} +(4.94958 - 4.94958i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47}+ \cdots + 72 q^{97}+O(q^{100}) $ 48 * q + 8 * q^5 - 20 * q^7 - 12 * q^11 + 12 * q^16 + 20 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 20 * q^25 - 8 * q^26 - 20 * q^28 + 16 * q^31 + 20 * q^37 + 36 * q^38 + 20 * q^41 + 40 * q^46 - 40 * q^47 - 40 * q^50 + 40 * q^52 + 96 * q^55 + 8 * q^56 + 48 * q^58 + 80 * q^61 - 40 * q^62 - 20 * q^68 - 56 * q^70 + 56 * q^71 - 20 * q^73 + 96 * q^77 + 12 * q^80 - 80 * q^85 + 56 * q^86 - 4 * q^88 - 68 * q^91 + 12 * q^92 - 20 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$	$1$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$		0			0
$3$		0			0
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−2.14909	−	0.617590i	−0.961102	−	0.276195i
$5$	−2.14909	−	0.617590i	−0.961102	−	0.276195i
$6$		0			0
$7$	−0.00697389	+	0.0136870i	−0.00263588	+	0.00517321i	−0.892321	−	0.451402i	$-0.850924\pi$
$7$	−0.00697389	+	0.0136870i	−0.00263588	+	0.00517321i	0.889685	+	0.456575i	$0.150924\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$		0			0
$10$	−0.273795	+	2.21924i	−0.0865816	+	0.701786i
$11$	−2.43343	+	2.25353i	−0.733708	+	0.679465i
$11$	−2.43343	+	2.25353i	−0.733708	+	0.679465i
$12$		0			0
$13$	−2.31203	+	0.366190i	−0.641242	+	0.101563i	−0.468584	−	0.883419i	$-0.655236\pi$
$13$	−2.31203	+	0.366190i	−0.641242	+	0.101563i	−0.172658	+	0.984982i	$0.555236\pi$
$14$	0.0146095	+	0.00474691i	0.00390455	+	0.00126866i
$15$		0			0
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	3.88580	+	0.615451i	0.942446	+	0.149269i	0.608705	−	0.793396i	$-0.291689\pi$
$17$	3.88580	+	0.615451i	0.942446	+	0.149269i	0.333740	+	0.942665i	$0.391689\pi$
$18$		0			0
$19$	1.78456	−	5.49230i	0.409406	−	1.26002i	−0.507755	−	0.861502i	$-0.669524\pi$
$19$	1.78456	−	5.49230i	0.409406	−	1.26002i	0.917160	−	0.398519i	$-0.130476\pi$
$20$	2.23475	−	0.0767418i	0.499705	−	0.0171600i
$21$		0			0
$22$	2.60646	+	2.05094i	0.555699	+	0.437263i
$23$	4.75841	+	4.75841i	0.992196	+	0.992196i	0.999970	−	0.00777340i	$-0.00247437\pi$
$23$	4.75841	+	4.75841i	0.992196	+	0.992196i	−0.00777340	+	0.999970i	$0.502474\pi$
$24$		0			0
$25$	4.23716	+	2.65451i	0.847433	+	0.530902i
$26$	0.723362	+	2.22628i	0.141863	+	0.436609i
$27$		0			0
$28$	0.00240304	−	0.0151722i	0.000454132	−	0.00286728i
$29$	1.28099	+	3.94247i	0.237873	+	0.732099i	0.996727	+	0.0808379i	$0.0257596\pi$
$29$	1.28099	+	3.94247i	0.237873	+	0.732099i	−0.758854	+	0.651261i	$0.774240\pi$
$30$		0			0
$31$	4.70277	+	3.41676i	0.844642	+	0.613668i	0.923663	−	0.383205i	$-0.125180\pi$
$31$	4.70277	+	3.41676i	0.844642	+	0.613668i	−0.0790218	+	0.996873i	$0.525180\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$		−	3.93424i		−	0.674716i
$35$	0.0234405	−	0.0251076i	0.00396217	−	0.00424397i
$36$		0			0
$37$	−1.00521	−	0.512178i	−0.165255	−	0.0842015i	0.369407	−	0.929268i	$-0.379561\pi$
$37$	−1.00521	−	0.512178i	−0.165255	−	0.0842015i	−0.534662	+	0.845066i	$0.679561\pi$
$38$	−5.70385	−	0.903401i	−0.925287	−	0.146551i
$39$		0			0
$40$	−0.425389	−	2.19523i	−0.0672599	−	0.347097i
$41$	4.46390	+	1.45041i	0.697144	+	0.226516i	0.636086	−	0.771618i	$-0.280552\pi$
$41$	4.46390	+	1.45041i	0.697144	+	0.226516i	0.0610584	+	0.998134i	$0.480552\pi$
$42$		0			0
$43$	−5.68946	+	5.68946i	−0.867634	+	0.867634i	−0.992210	−	0.124576i	$-0.960243\pi$
$43$	−5.68946	+	5.68946i	−0.867634	+	0.867634i	0.124576	+	0.992210i	$0.460243\pi$
$44$	1.61795	−	2.89521i	0.243915	−	0.436469i
$45$		0			0
$46$	3.95544	−	5.44420i	0.583198	−	0.802704i
$47$	0.703097	+	1.37991i	0.102557	+	0.201280i	0.936583	−	0.350445i	$-0.113970\pi$
$47$	0.703097	+	1.37991i	0.102557	+	0.201280i	−0.834026	+	0.551725i	$0.813970\pi$
$48$		0			0
$49$	4.11436	+	5.66293i	0.587765	+	0.808990i
$50$	1.95899	−	4.60026i	0.277043	−	0.650574i
$51$		0			0
$52$	2.08571	−	1.06272i	0.289236	−	0.147373i
$53$	−2.19559	−	13.8624i	−0.301587	−	1.90415i	−0.413635	−	0.910443i	$-0.635741\pi$
$53$	−2.19559	−	13.8624i	−0.301587	−	1.90415i	0.112048	−	0.993703i	$-0.464259\pi$
$54$		0			0
$55$	6.62142	−	3.34018i	0.892832	−	0.450389i
$56$	−0.0153613			−0.00205274
$57$		0			0
$58$	3.69354	−	1.88195i	0.484986	−	0.247113i
$59$	−1.86696	+	0.606613i	−0.243058	+	0.0789743i	−0.428013	−	0.903773i	$-0.640786\pi$
$59$	−1.86696	+	0.606613i	−0.243058	+	0.0789743i	0.184955	+	0.982747i	$0.440786\pi$
$60$		0			0
$61$	4.84534	+	6.66904i	0.620382	+	0.853883i	0.997381	−	0.0723312i	$-0.0230439\pi$
$61$	4.84534	+	6.66904i	0.620382	+	0.853883i	−0.376999	+	0.926214i	$0.623044\pi$
$62$	2.63902	−	5.17937i	0.335156	−	0.657780i
$63$		0			0
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	5.19491	+	0.640913i	0.644350	+	0.0794955i
$66$		0			0
$67$	3.67640	−	3.67640i	0.449143	−	0.449143i	−0.445926	−	0.895070i	$-0.647126\pi$
$67$	3.67640	−	3.67640i	0.449143	−	0.449143i	0.895070	+	0.445926i	$0.147126\pi$
$68$	−3.88580	+	0.615451i	−0.471223	+	0.0746344i
$69$		0			0
$70$	−0.0284654	−	0.0192242i	−0.00340227	−	0.00229773i
$71$	5.20051	−	3.77839i	0.617187	−	0.448413i	−0.234751	−	0.972056i	$-0.575427\pi$
$71$	5.20051	−	3.77839i	0.617187	−	0.448413i	0.851938	+	0.523643i	$0.175427\pi$
$72$		0			0
$73$	4.10721	+	2.09273i	0.480713	+	0.244935i	0.677517	−	0.735508i	$-0.263056\pi$
$73$	4.10721	+	2.09273i	0.480713	+	0.244935i	−0.196804	+	0.980443i	$0.563056\pi$
$74$	−0.348623	+	1.07295i	−0.0405266	+	0.124728i
$75$		0			0
$76$			5.77495i			0.662432i
$77$	−0.0138737	−	0.0490224i	−0.00158105	−	0.00558662i
$78$		0			0
$79$	3.84472	+	2.79336i	0.432565	+	0.314277i	0.782674	−	0.622432i	$-0.213855\pi$
$79$	3.84472	+	2.79336i	0.432565	+	0.314277i	−0.350109	+	0.936709i	$0.613855\pi$
$80$	−2.10166	+	0.763562i	−0.234973	+	0.0853688i
$81$		0			0
$82$	0.734244	−	4.63584i	0.0810837	−	0.511943i
$83$	−2.08413	+	13.1587i	−0.228763	+	1.44436i	0.559405	+	0.828895i	$0.311030\pi$
$83$	−2.08413	+	13.1587i	−0.228763	+	1.44436i	−0.788168	+	0.615460i	$0.788970\pi$
$84$		0			0
$85$	−7.97084	−	3.72249i	−0.864559	−	0.403761i
$86$	6.50944	+	4.72938i	0.701931	+	0.509983i
$87$		0			0
$88$	−3.11267	−	1.14512i	−0.331811	−	0.122070i
$89$			9.48232i			1.00512i	0.864541	+	0.502562i	$0.167609\pi$
$89$			9.48232i			1.00512i	−0.864541	+	0.502562i	$0.832391\pi$
$90$		0			0
$91$	0.0111118	−	0.0341986i	0.00116483	−	0.00358499i
$92$	−5.99594	−	3.05509i	−0.625120	−	0.318515i
$93$		0			0
$94$	1.25293	−	0.910306i	0.129230	−	0.0938909i
$95$	−7.22716	+	10.7013i	−0.741491	+	1.09793i
$96$		0			0
$97$	4.39615	−	0.696283i	0.446362	−	0.0706968i	0.0707925	−	0.997491i	$-0.477447\pi$
$97$	4.39615	−	0.696283i	0.446362	−	0.0706968i	0.375569	+	0.926794i	$0.377447\pi$
$98$	4.94958	−	4.94958i	0.499983	−	0.499983i
$99$		0			0
$100$	−4.85007	−	1.21523i	−0.485007	−	0.121523i
$101$	10.2067	−	14.0483i	1.01561	−	1.39786i	0.100365	−	0.994951i	$-0.467999\pi$
$101$	10.2067	−	14.0483i	1.01561	−	1.39786i	0.915240	−	0.402910i	$-0.132001\pi$
$102$		0			0
$103$	−0.155063	+	0.304328i	−0.0152788	+	0.0299864i	−0.898520	−	0.438933i	$-0.855357\pi$
$103$	−0.155063	+	0.304328i	−0.0152788	+	0.0299864i	0.883241	+	0.468919i	$0.155357\pi$
$104$	−1.37592	−	1.89379i	−0.134920	−	0.185701i
$105$		0			0
$106$	−13.3483	+	4.33711i	−1.29650	+	0.421257i
$107$	2.04336	−	1.04115i	0.197539	−	0.100651i	−0.352423	−	0.935841i	$-0.614642\pi$
$107$	2.04336	−	1.04115i	0.197539	−	0.100651i	0.549962	+	0.835190i	$0.314642\pi$
$108$		0			0
$109$	−2.42843			−0.232602			−0.116301	−	0.993214i	$-0.537104\pi$
$109$	−2.42843			−0.232602			−0.116301	+	0.993214i	$0.537104\pi$
$110$	−4.33487	−	6.01738i	−0.413314	−	0.573735i
$111$		0			0
$112$	0.00240304	+	0.0151722i	0.000227066	+	0.00143364i
$113$	−9.70357	+	4.94421i	−0.912835	+	0.465113i	−0.846321	−	0.532673i	$-0.821188\pi$
$113$	−9.70357	+	4.94421i	−0.912835	+	0.465113i	−0.0665137	+	0.997786i	$0.521188\pi$
$114$		0			0
$115$	−7.28749	−	13.1650i	−0.679562	−	1.22764i
$116$	−2.43658	−	3.35367i	−0.226231	−	0.311380i
$117$		0			0
$118$	0.891202	+	1.74908i	0.0820418	+	0.161016i
$119$	−0.0355229	+	0.0488930i	−0.00325638	+	0.00448202i
$120$		0			0
$121$	0.843188	−	10.9676i	0.0766535	−	0.997058i
$122$	5.82895	−	5.82895i	0.527728	−	0.527728i
$123$		0			0
$124$	−5.52843	−	1.79630i	−0.496468	−	0.161312i
$125$	−7.46664	−	8.32161i	−0.667837	−	0.744308i
$126$		0			0
$127$	−17.3079	−	2.74131i	−1.53583	−	0.243252i	−0.669535	−	0.742781i	$-0.733506\pi$
$127$	−17.3079	−	2.74131i	−1.53583	−	0.243252i	−0.866297	+	0.499529i	$0.833506\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$		0			0
$130$	−0.179641	−	5.23122i	−0.0157556	−	0.458808i
$131$			3.65271i			0.319138i	0.987187	+	0.159569i	$0.0510105\pi$
$131$			3.65271i			0.319138i	−0.987187	+	0.159569i	$0.948989\pi$
$132$		0			0
$133$	0.0627280	+	0.0627280i	0.00543921	+	0.00543921i
$134$	−4.20625	−	3.05602i	−0.363364	−	0.264000i
$135$		0			0
$136$	1.21575	+	3.74168i	0.104249	+	0.320847i
$137$	−2.63360	+	16.6279i	−0.225004	+	1.42062i	0.573784	+	0.819006i	$0.305475\pi$
$137$	−2.63360	+	16.6279i	−0.225004	+	1.42062i	−0.798788	+	0.601612i	$0.794525\pi$
$138$		0			0
$139$	6.84479	+	21.0661i	0.580567	+	1.78680i	0.616386	+	0.787444i	$0.288596\pi$
$139$	6.84479	+	21.0661i	0.580567	+	1.78680i	−0.0358190	+	0.999358i	$0.511404\pi$
$140$	−0.0145345	+	0.0311223i	−0.00122839	+	0.00263031i
$141$		0			0
$142$	−4.54541	−	4.54541i	−0.381443	−	0.381443i
$143$	4.80095	−	6.10133i	0.401476	−	0.510219i
$144$		0			0
$145$	−0.318123	−	9.26385i	−0.0264186	−	0.769321i
$146$	1.42445	−	4.38402i	0.117889	−	0.362824i
$147$		0			0
$148$	1.11428	+	0.176484i	0.0915932	+	0.0145069i
$149$	−11.4310	+	8.30508i	−0.936461	+	0.680379i	−0.947566	−	0.319560i	$-0.896465\pi$
$149$	−11.4310	+	8.30508i	−0.936461	+	0.680379i	0.0111054	+	0.999938i	$0.496465\pi$
$150$		0			0
$151$	3.14883	+	1.02312i	0.256248	+	0.0832600i	0.434324	−	0.900757i	$-0.356987\pi$
$151$	3.14883	+	1.02312i	0.256248	+	0.0832600i	−0.178076	+	0.984017i	$0.556987\pi$
$152$	5.70385	−	0.903401i	0.462643	−	0.0732755i
$153$		0			0
$154$	−0.0462485	+	0.0213716i	−0.00372681	+	0.00172218i
$155$	−7.99650	−	10.2473i	−0.642295	−	0.823083i
$156$		0			0
$157$	5.84266	+	11.4669i	0.466295	+	0.915155i	0.997683	+	0.0680269i	$0.0216704\pi$
$157$	5.84266	+	11.4669i	0.466295	+	0.915155i	−0.531389	+	0.847128i	$0.678330\pi$
$158$	2.15752	−	4.23437i	0.171643	−	0.336868i
$159$		0			0
$160$	1.08293	+	1.95634i	0.0856134	+	0.154662i
$161$	−0.0983131	+	0.0319439i	−0.00774816	+	0.00251753i
$162$		0			0
$163$	−0.263165	−	1.66156i	−0.0206127	−	0.130143i	0.975236	−	0.221166i	$-0.0709864\pi$
$163$	−0.263165	−	1.66156i	−0.0206127	−	0.130143i	−0.995849	+	0.0910229i	$0.970986\pi$
$164$	−4.69362			−0.366510
$165$		0			0
$166$	13.3227			1.03404
$167$	−2.54594	−	16.0744i	−0.197011	−	1.24388i	−0.865787	−	0.500413i	$-0.833182\pi$
$167$	−2.54594	−	16.0744i	−0.197011	−	1.24388i	0.668776	−	0.743464i	$-0.266818\pi$
$168$		0			0
$169$	−7.15235	+	2.32394i	−0.550181	+	0.178764i
$170$	−2.42975	+	8.45503i	−0.186353	+	0.648471i
$171$		0			0
$172$	3.65286	−	7.16914i	0.278528	−	0.546642i
$173$	−6.86850	−	13.4802i	−0.522202	−	1.02488i	−0.990003	−	0.141046i	$-0.954954\pi$
$173$	−6.86850	−	13.4802i	−0.522202	−	1.02488i	0.467801	−	0.883834i	$-0.345046\pi$
$174$		0			0
$175$	−0.0658819	+	0.0394819i	−0.00498021	+	0.00298455i
$176$	−0.644096	+	3.25348i	−0.0485505	+	0.245240i
$177$		0			0
$178$	9.36557	−	1.48336i	0.701979	−	0.111183i
$179$	22.4795	+	7.30404i	1.68020	+	0.545930i	0.984950	−	0.172839i	$-0.0552939\pi$
$179$	22.4795	+	7.30404i	1.68020	+	0.545930i	0.695249	+	0.718769i	$0.255294\pi$
$180$		0			0
$181$	−15.4698	+	11.2395i	−1.14986	+	0.835423i	−0.988462	−	0.151466i	$-0.951601\pi$
$181$	−15.4698	+	11.2395i	−1.14986	+	0.835423i	−0.161399	+	0.986889i	$0.551601\pi$
$182$	−0.0355158	−	0.00562515i	−0.00263261	−	0.000416964i
$183$		0			0
$184$	−2.07950	+	6.40004i	−0.153303	+	0.471817i
$185$	1.84396	+	1.72152i	0.135571	+	0.126569i
$186$		0			0
$187$	−10.8428	+	7.25912i	−0.792902	+	0.530840i
$188$	−1.09510	−	1.09510i	−0.0798683	−	0.0798683i
$189$		0			0
$190$	11.7001	+	5.46413i	0.848818	+	0.396410i
$191$	3.70271	+	11.3958i	0.267919	+	0.824569i	0.991007	+	0.133813i	$0.0427222\pi$
$191$	3.70271	+	11.3958i	0.267919	+	0.824569i	−0.723088	+	0.690756i	$0.757278\pi$
$192$		0			0
$193$	2.50920	−	15.8424i	0.180616	−	1.14036i	−0.716179	−	0.697917i	$-0.754110\pi$
$193$	2.50920	−	15.8424i	0.180616	−	1.14036i	0.896795	−	0.442447i	$-0.145890\pi$
$194$	−1.37542	−	4.23311i	−0.0987494	−	0.303919i
$195$		0			0
$196$	−5.66293	−	4.11436i	−0.404495	−	0.293883i
$197$	−5.90309	−	5.90309i	−0.420578	−	0.420578i	0.464825	−	0.885403i	$-0.346117\pi$
$197$	−5.90309	−	5.90309i	−0.420578	−	0.420578i	−0.885403	+	0.464825i	$0.846117\pi$
$198$		0			0
$199$			8.46646i			0.600171i	0.953912	+	0.300086i	$0.0970153\pi$
$199$			8.46646i			0.600171i	−0.953912	+	0.300086i	$0.902985\pi$
$200$	−0.441555	+	4.98046i	−0.0312226	+	0.352172i
$201$		0			0
$202$	−15.4720	−	7.88340i	−1.08861	−	0.554674i
$203$	−0.0628942	−	0.00996146i	−0.00441431	−	0.000699158i
$204$		0			0
$205$	−8.69756	−	5.87392i	−0.607464	−	0.410252i
$206$	0.324839	+	0.105546i	0.0226326	+	0.00735377i
$207$		0			0
$208$	−1.65523	+	1.65523i	−0.114770	+	0.114770i
$209$	8.03448	+	17.3867i	0.555757	+	1.20266i
$210$		0			0
$211$	4.11272	−	5.66067i	0.283131	−	0.389697i	−0.643637	−	0.765331i	$-0.722575\pi$
$211$	4.11272	−	5.66067i	0.283131	−	0.389697i	0.926768	+	0.375635i	$0.122575\pi$
$212$	6.37184	+	12.5054i	0.437620	+	0.858877i
$213$		0			0
$214$	−1.34798	−	1.85533i	−0.0921460	−	0.126828i
$215$	15.7409	−	8.71340i	1.07352	−	0.594249i
$216$		0			0
$217$	−0.0795619	+	0.0405388i	−0.00540101	+	0.00275195i
$218$	0.379891	+	2.39853i	0.0257294	+	0.162449i
$219$		0			0
$220$	−5.26518	+	5.22283i	−0.354978	+	0.352123i
$221$	−9.20946			−0.619496
$222$		0			0
$223$	−16.6612	+	8.48928i	−1.11571	+	0.568484i	−0.911854	−	0.410516i	$-0.865349\pi$
$223$	−16.6612	+	8.48928i	−1.11571	+	0.568484i	−0.203860	+	0.979000i	$0.565349\pi$
$224$	0.0146095	−	0.00474691i	0.000976137	−	0.000317166i
$225$		0			0
$226$	6.40132	+	8.81066i	0.425809	+	0.586076i
$227$	4.59950	−	9.02703i	0.305280	−	0.599145i	−0.686496	−	0.727134i	$-0.740852\pi$
$227$	4.59950	−	9.02703i	0.305280	−	0.599145i	0.991776	+	0.127989i	$0.0408521\pi$
$228$		0			0
$229$	6.38012	−	8.78149i	0.421610	−	0.580297i	−0.544392	−	0.838831i	$-0.683239\pi$
$229$	6.38012	−	8.78149i	0.421610	−	0.580297i	0.966002	+	0.258534i	$0.0832395\pi$
$230$	−11.8629	+	9.25723i	−0.782215	+	0.610404i
$231$		0			0
$232$	−2.93121	+	2.93121i	−0.192444	+	0.192444i
$233$	4.69333	−	0.743350i	0.307470	−	0.0486985i	−0.000792791	−	1.00000i	$-0.500252\pi$
$233$	4.69333	−	0.743350i	0.307470	−	0.0486985i	0.308263	+	0.951301i	$0.400252\pi$
$234$		0			0
$235$	−0.658802	−	3.39977i	−0.0429755	−	0.221776i
$236$	1.58813	−	1.15385i	0.103379	−	0.0751091i
$237$		0			0
$238$	0.0538481	+	0.0274370i	0.00349045	+	0.00177847i
$239$	−4.17166	+	12.8391i	−0.269842	+	0.830490i	0.720696	+	0.693252i	$0.243823\pi$
$239$	−4.17166	+	12.8391i	−0.269842	+	0.830490i	−0.990538	+	0.137238i	$0.956177\pi$
$240$		0			0
$241$		−	21.5441i		−	1.38778i	−0.720081	−	0.693890i	$-0.755895\pi$
$241$		−	21.5441i		−	1.38778i	0.720081	−	0.693890i	$-0.244105\pi$
$242$	−10.9645	+	0.882909i	−0.704825	+	0.0567555i
$243$		0			0
$244$	−6.66904	−	4.84534i	−0.426941	−	0.310191i
$245$	−5.34475	−	14.7111i	−0.341464	−	0.939859i
$246$		0			0
$247$	−2.11473	+	13.3519i	−0.134557	+	0.849558i
$248$	−0.909344	+	5.74137i	−0.0577434	+	0.364577i
$249$		0			0
$250$	−7.05112	+	8.67650i	−0.445952	+	0.548750i
$251$	15.8467	+	11.5133i	1.00023	+	0.726713i	0.962138	−	0.272561i	$-0.0878707\pi$
$251$	15.8467	+	11.5133i	1.00023	+	0.726713i	0.0380961	+	0.999274i	$0.487871\pi$
$252$		0			0
$253$	−22.3025	−	0.856041i	−1.40215	−	0.0538188i
$254$			17.5237i			1.09953i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−17.5999	−	8.96760i	−1.09785	−	0.559384i	−0.191323	−	0.981527i	$-0.561278\pi$
$257$	−17.5999	−	8.96760i	−1.09785	−	0.559384i	−0.906529	+	0.422143i	$0.861278\pi$
$258$		0			0
$259$	0.0140204	−	0.0101864i	0.000871185	−	0.000632953i
$260$	−5.13871	+	0.995772i	−0.318689	+	0.0617551i
$261$		0			0
$262$	3.60774	−	0.571409i	0.222887	−	0.0353018i
$263$	−20.0880	+	20.0880i	−1.23868	+	1.23868i	−0.278140	+	0.960541i	$0.589718\pi$
$263$	−20.0880	+	20.0880i	−1.23868	+	1.23868i	−0.960541	+	0.278140i	$0.910282\pi$
$264$		0			0
$265$	−3.84276	+	31.1475i	−0.236059	+	1.91337i
$266$	0.0521429	−	0.0717686i	0.00319709	−	0.00440041i
$267$		0			0
$268$	−2.36039	+	4.63253i	−0.144184	+	0.282977i
$269$	5.50591	+	7.57823i	0.335701	+	0.462053i	0.943180	−	0.332283i	$-0.107819\pi$
$269$	5.50591	+	7.57823i	0.335701	+	0.462053i	−0.607479	+	0.794336i	$0.707819\pi$
$270$		0			0
$271$	5.85356	−	1.90194i	0.355578	−	0.115534i	−0.125780	−	0.992058i	$-0.540143\pi$
$271$	5.85356	−	1.90194i	0.355578	−	0.115534i	0.481359	+	0.876524i	$0.340143\pi$
$272$	3.50543	−	1.78611i	0.212548	−	0.108299i
$273$		0			0
$274$	16.8352			1.01705
$275$	−16.2929	+	3.08901i	−0.982498	+	0.186274i
$276$		0			0
$277$	−4.66256	−	29.4382i	−0.280146	−	1.76877i	−0.579834	−	0.814734i	$-0.696883\pi$
$277$	−4.66256	−	29.4382i	−0.280146	−	1.76877i	0.299688	−	0.954037i	$-0.403117\pi$
$278$	19.7360	−	10.0560i	1.18368	−	0.603117i
$279$		0			0
$280$	0.0330128	+	0.00948700i	0.00197289	+	0.000566957i
$281$	−3.35941	−	4.62383i	−0.200406	−	0.275835i	0.696972	−	0.717099i	$-0.254530\pi$
$281$	−3.35941	−	4.62383i	−0.200406	−	0.275835i	−0.897377	+	0.441264i	$0.854530\pi$
$282$		0			0
$283$	−1.97387	−	3.87395i	−0.117335	−	0.230282i	0.824868	−	0.565325i	$-0.191249\pi$
$283$	−1.97387	−	3.87395i	−0.117335	−	0.230282i	−0.942203	+	0.335043i	$0.891249\pi$
$284$	−3.77839	+	5.20051i	−0.224206	+	0.308594i
$285$		0			0
$286$	−6.77725	−	3.78738i	−0.400747	−	0.223953i
$287$	−0.0509826	+	0.0509826i	−0.00300941	+	0.00300941i
$288$		0			0
$289$	−1.44728	−	0.470250i	−0.0851341	−	0.0276618i
$290$	−9.10003	+	1.76339i	−0.534372	+	0.103550i
$291$		0			0
$292$	−4.55288	−	0.721105i	−0.266437	−	0.0421995i
$293$	−12.1120	−	6.17139i	−0.707593	−	0.360537i	0.0628696	−	0.998022i	$-0.479975\pi$
$293$	−12.1120	−	6.17139i	−0.707593	−	0.360537i	−0.770463	+	0.637485i	$0.779975\pi$
$294$		0			0
$295$	4.38691	−	0.150647i	0.255416	−	0.00877103i
$296$		−	1.12817i		−	0.0655735i
$297$		0			0
$298$	9.99102	+	9.99102i	0.578765	+	0.578765i
$299$	−12.7441	−	9.25910i	−0.737008	−	0.535468i
$300$		0			0
$301$	−0.0381941	−	0.117549i	−0.00220147	−	0.00677544i
$302$	0.517934	−	3.27011i	0.0298038	−	0.188174i
$303$		0			0
$304$	−1.78456	−	5.49230i	−0.102351	−	0.315005i
$305$	−6.29433	−	17.3248i	−0.360412	−	0.992014i
$306$		0			0
$307$	16.8816	+	16.8816i	0.963484	+	0.963484i	0.999356	−	0.0358726i	$-0.0114211\pi$
$307$	16.8816	+	16.8816i	0.963484	+	0.963484i	−0.0358726	+	0.999356i	$0.511421\pi$
$308$	0.0283434	+	0.0423358i	0.00161501	+	0.00241231i
$309$		0			0
$310$	−8.87021	+	9.50108i	−0.503794	+	0.539625i
$311$	−8.96103	+	27.5792i	−0.508133	+	1.56387i	0.287305	+	0.957839i	$0.407241\pi$
$311$	−8.96103	+	27.5792i	−0.508133	+	1.56387i	−0.795439	+	0.606034i	$0.792759\pi$
$312$		0			0
$313$	17.0901	+	2.70681i	0.965990	+	0.152998i	0.619449	−	0.785037i	$-0.287356\pi$
$313$	17.0901	+	2.70681i	0.965990	+	0.152998i	0.346541	+	0.938035i	$0.387356\pi$
$314$	10.4117	−	7.56454i	0.587566	−	0.426891i
$315$		0			0
$316$	−4.51974	−	1.46855i	−0.254255	−	0.0826126i
$317$	20.4927	−	3.24572i	1.15098	−	0.182298i	0.448355	−	0.893855i	$-0.352010\pi$
$317$	20.4927	−	3.24572i	1.15098	−	0.182298i	0.702628	+	0.711558i	$0.252010\pi$
$318$		0			0
$319$	−12.0017	−	6.70700i	−0.671965	−	0.375520i
$320$	1.76284	−	1.37564i	0.0985460	−	0.0769006i
$321$		0			0
$322$	0.0469301	+	0.0921056i	0.00261531	+	0.00513284i
$323$	10.3147	−	20.2437i	0.573924	−	1.12639i
$324$		0			0
$325$	−10.7685	−	4.58571i	−0.597329	−	0.254369i
$326$	−1.59994	+	0.519851i	−0.0886122	+	0.0287919i
$327$		0			0
$328$	0.734244	+	4.63584i	0.0405419	+	0.255971i
$329$	−0.0237901			−0.00131159
$330$		0			0
$331$	27.7235			1.52382			0.761912	−	0.647681i	$-0.224261\pi$
$331$	27.7235			1.52382			0.761912	+	0.647681i	$0.224261\pi$
$332$	−2.08413	−	13.1587i	−0.114382	−	0.722178i
$333$		0			0
$334$	−15.4782	+	5.02919i	−0.846932	+	0.275185i
$335$	−10.1714	+	5.63039i	−0.555723	+	0.307621i
$336$		0			0
$337$	3.19123	−	6.26314i	0.173837	−	0.341175i	−0.787606	−	0.616180i	$-0.788680\pi$
$337$	3.19123	−	6.26314i	0.173837	−	0.341175i	0.961443	+	0.275005i	$0.0886795\pi$
$338$	3.41420	+	6.70075i	0.185708	+	0.364473i
$339$		0			0
$340$	8.73103	+	1.07718i	0.473507	+	0.0584180i
$341$	−19.1436	+	2.28338i	−1.03669	+	0.123652i
$342$		0			0
$343$	−0.212407	+	0.0336420i	−0.0114689	+	0.00181650i
$344$	−7.65230	−	2.48638i	−0.412585	−	0.134057i
$345$		0			0
$346$	−12.2398	+	8.89270i	−0.658013	+	0.478075i
$347$	21.4415	+	3.39601i	1.15104	+	0.182307i	0.702654	−	0.711532i	$-0.251998\pi$
$347$	21.4415	+	3.39601i	1.15104	+	0.182307i	0.448388	+	0.893839i	$0.351998\pi$
$348$		0			0
$349$	−3.67193	+	11.3010i	−0.196554	+	0.604930i	0.803401	+	0.595438i	$0.203021\pi$
$349$	−3.67193	+	11.3010i	−0.196554	+	0.604930i	−0.999955	+	0.00949216i	$0.996979\pi$
$350$	0.0493021	+	0.0588945i	0.00263531	+	0.00314804i
$351$		0			0
$352$	3.31418	+	0.127209i	0.176647	+	0.00678026i
$353$	−0.766521	−	0.766521i	−0.0407978	−	0.0407978i	0.686414	−	0.727211i	$-0.259184\pi$
$353$	−0.766521	−	0.766521i	−0.0407978	−	0.0407978i	−0.727211	+	0.686414i	$0.759184\pi$
$354$		0			0
$355$	−13.5099	+	4.90832i	−0.717029	+	0.260506i
$356$	−2.93020	−	9.01822i	−0.155300	−	0.477965i
$357$		0			0
$358$	3.69755	−	23.3454i	0.195421	−	1.23384i
$359$	−2.56417	−	7.89171i	−0.135332	−	0.416508i	0.860310	−	0.509772i	$-0.170270\pi$
$359$	−2.56417	−	7.89171i	−0.135332	−	0.416508i	−0.995641	+	0.0932633i	$0.970270\pi$
$360$		0			0
$361$	−11.6094	−	8.43474i	−0.611022	−	0.443934i
$362$	13.5211	+	13.5211i	0.710653	+	0.710653i
$363$		0			0
$364$			0.0359585i			0.00188474i
$365$	−7.53431	−	7.03403i	−0.394364	−	0.368178i
$366$		0			0
$367$	13.4231	+	6.83943i	0.700683	+	0.357016i	0.767765	−	0.640732i	$-0.221369\pi$
$367$	13.4231	+	6.83943i	0.700683	+	0.357016i	−0.0670822	+	0.997747i	$0.521369\pi$
$368$	6.64655	+	1.05271i	0.346476	+	0.0548763i
$369$		0			0
$370$	1.41187	−	2.09056i	0.0733995	−	0.108683i
$371$	0.205047	+	0.0666237i	0.0106455	+	0.00345893i
$372$		0			0
$373$	−5.33739	+	5.33739i	−0.276360	+	0.276360i	−0.831654	−	0.555294i	$-0.812606\pi$
$373$	−5.33739	+	5.33739i	−0.276360	+	0.276360i	0.555294	+	0.831654i	$0.312606\pi$
$374$	8.86593	+	9.57371i	0.458447	+	0.495045i
$375$		0			0
$376$	−0.910306	+	1.25293i	−0.0469454	+	0.0646149i
$377$	−4.40537	−	8.64603i	−0.226888	−	0.445293i
$378$		0			0
$379$	5.86042	+	8.06617i	0.301029	+	0.414331i	0.932557	−	0.361022i	$-0.117572\pi$
$379$	5.86042	+	8.06617i	0.301029	+	0.414331i	−0.631528	+	0.775353i	$0.717572\pi$
$380$	3.56655	−	12.4109i	0.182960	−	0.636665i
$381$		0			0
$382$	10.6762	−	5.43982i	0.546244	−	0.278325i
$383$	3.72711	+	23.5321i	0.190447	+	1.20243i	0.878848	+	0.477103i	$0.158313\pi$
$383$	3.72711	+	23.5321i	0.190447	+	1.20243i	−0.688401	+	0.725330i	$0.741687\pi$
$384$		0			0
$385$	−0.000459977		0.113922i	−2.34426e−5		0.00580598i
$386$	−16.0399			−0.816410
$387$		0			0
$388$	−3.96583	+	2.02069i	−0.201334	+	0.102585i
$389$	4.97947	−	1.61793i	0.252469	−	0.0820322i	−0.180048	−	0.983658i	$-0.557625\pi$
$389$	4.97947	−	1.61793i	0.252469	−	0.0820322i	0.432517	+	0.901626i	$0.357625\pi$
$390$		0			0
$391$	15.5617	+	21.4188i	0.786987	+	1.08319i
$392$	−3.17783	+	6.23684i	−0.160504	+	0.315008i
$393$		0			0
$394$	−4.90697	+	6.75386i	−0.247209	+	0.340255i
$395$	−6.53750	−	8.37763i	−0.328938	−	0.421524i
$396$		0			0
$397$	1.68624	−	1.68624i	0.0846300	−	0.0846300i	−0.663525	−	0.748155i	$-0.730940\pi$
$397$	1.68624	−	1.68624i	0.0846300	−	0.0846300i	0.748155	+	0.663525i	$0.230940\pi$
$398$	8.36222	−	1.32445i	0.419160	−	0.0663885i
$399$		0			0
$400$	4.98822	−	0.342998i	0.249411	−	0.0171499i
$401$	12.7078	−	9.23274i	0.634596	−	0.461061i	−0.223393	−	0.974728i	$-0.571713\pi$
$401$	12.7078	−	9.23274i	0.634596	−	0.461061i	0.857989	+	0.513667i	$0.171713\pi$
$402$		0			0
$403$	−12.1241	−	6.17755i	−0.603945	−	0.307725i
$404$	−5.36598	+	16.5148i	−0.266968	+	0.821642i
$405$		0			0
$406$			0.0636782i			0.00316030i
$407$	3.60031	−	1.01891i	0.178461	−	0.0505056i
$408$		0			0
$409$	1.39836	+	1.01597i	0.0691444	+	0.0502363i	0.621820	−	0.783160i	$-0.286393\pi$
$409$	1.39836	+	1.01597i	0.0691444	+	0.0502363i	−0.552676	+	0.833396i	$0.686393\pi$
$410$	−4.44100	+	9.50936i	−0.219326	+	0.469634i
$411$		0			0
$412$	0.0534311	−	0.337350i	0.00263236	−	0.0166201i
$413$	0.00471727	−	0.0297837i	0.000232122	−	0.00146556i
$414$		0			0
$415$	12.6057	−	26.9921i	0.618788	−	1.32499i
$416$	1.89379	+	1.37592i	0.0928506	+	0.0674599i
$417$		0			0
$418$	15.9158	−	10.6554i	0.778466	−	0.521175i
$419$			16.7994i			0.820703i	0.911927	+	0.410351i	$0.134594\pi$
$419$			16.7994i			0.820703i	−0.911927	+	0.410351i	$0.865406\pi$
$420$		0			0
$421$	3.47207	−	10.6859i	0.169219	−	0.520801i	−0.830104	−	0.557609i	$-0.811719\pi$
$421$	3.47207	−	10.6859i	0.169219	−	0.520801i	0.999322	+	0.0368077i	$0.0117189\pi$
$422$	−6.23435	−	3.17656i	−0.303483	−	0.154632i
$423$		0			0
$424$	11.3547	−	8.24968i	0.551433	−	0.400640i
$425$	14.8311	+	12.9227i	0.719412	+	0.626842i
$426$		0			0
$427$	−0.125070	+	0.0198092i	−0.00605257	+	0.000958633i
$428$	−1.62162	+	1.62162i	−0.0783840	+	0.0783840i
$429$		0			0
$430$	−11.0685	−	14.1840i	−0.533772	−	0.684015i
$431$	22.5280	−	31.0071i	1.08513	−	1.49356i	0.231392	−	0.972861i	$-0.425672\pi$
$431$	22.5280	−	31.0071i	1.08513	−	1.49356i	0.853741	−	0.520697i	$-0.174328\pi$
$432$		0			0
$433$	8.91179	−	17.4904i	0.428273	−	0.840533i	−0.571528	−	0.820583i	$-0.693649\pi$
$433$	8.91179	−	17.4904i	0.428273	−	0.840533i	0.999801	−	0.0199507i	$-0.00635091\pi$
$434$	0.0524859	+	0.0722407i	0.00251940	+	0.00346766i
$435$		0			0
$436$	2.30958	−	0.750427i	0.110609	−	0.0359389i
$437$	34.6263	−	17.6430i	1.65640	−	0.843977i
$438$		0			0
$439$	1.05214			0.0502158			0.0251079	−	0.999685i	$-0.492007\pi$
$439$	1.05214			0.0502158			0.0251079	+	0.999685i	$0.492007\pi$
$440$	5.98218	+	4.38332i	0.285189	+	0.208967i
$441$		0			0
$442$	1.44068	+	9.09608i	0.0685260	+	0.432656i
$443$	0.280755	−	0.143052i	0.0133391	−	0.00679659i	−0.447308	−	0.894380i	$-0.647617\pi$
$443$	0.280755	−	0.143052i	0.0133391	−	0.00679659i	0.460647	+	0.887583i	$0.347617\pi$
$444$		0			0
$445$	5.85619	−	20.3783i	0.277610	−	0.966026i
$446$	10.9911	+	15.1280i	0.520446	+	0.716332i
$447$		0			0
$448$	−0.00697389	−	0.0136870i	−0.000329485	−	0.000646652i
$449$	19.7505	−	27.1842i	0.932084	−	1.28290i	−0.0269576	−	0.999637i	$-0.508582\pi$
$449$	19.7505	−	27.1842i	0.932084	−	1.28290i	0.959041	−	0.283266i	$-0.0914181\pi$
$450$		0			0
$451$	−14.1311	+	6.53007i	−0.665410	+	0.307489i
$452$	7.70080	−	7.70080i	0.362215	−	0.362215i
$453$		0			0
$454$	−9.63541	−	3.13074i	−0.452212	−	0.146933i
$455$	−0.0450010	+	0.0666333i	−0.00210968	+	0.00312382i
$456$		0			0
$457$	29.5629	+	4.68231i	1.38290	+	0.219029i	0.803154	−	0.595771i	$-0.203153\pi$
$457$	29.5629	+	4.68231i	1.38290	+	0.219029i	0.579742	+	0.814800i	$0.303153\pi$
$458$	−9.67144	−	4.92785i	−0.451917	−	0.230263i
$459$		0			0
$460$	10.9990	+	10.2687i	0.512832	+	0.478780i
$461$		−	27.6150i		−	1.28616i	−0.765800	−	0.643079i	$-0.777657\pi$
$461$		−	27.6150i		−	1.28616i	0.765800	−	0.643079i	$-0.222343\pi$
$462$		0			0
$463$	−26.6620	−	26.6620i	−1.23909	−	1.23909i	−0.960373	−	0.278717i	$-0.910091\pi$
$463$	−26.6620	−	26.6620i	−1.23909	−	1.23909i	−0.278717	−	0.960373i	$-0.589909\pi$
$464$	3.35367	+	2.43658i	0.155690	+	0.113115i
$465$		0			0
$466$	−1.46840	−	4.51926i	−0.0680221	−	0.209351i
$467$	−4.66728	+	29.4680i	−0.215976	+	1.36362i	0.606620	+	0.794992i	$0.292525\pi$
$467$	−4.66728	+	29.4680i	−0.215976	+	1.36362i	−0.822596	+	0.568626i	$0.807475\pi$
$468$		0			0
$469$	0.0246802	+	0.0759577i	0.00113962	+	0.00350740i
$470$	−3.25485	+	1.18253i	−0.150135	+	0.0545461i
$471$		0			0
$472$	−1.38808	−	1.38808i	−0.0638916	−	0.0638916i
$473$	1.02354	−	26.6663i	0.0470623	−	1.22612i
$474$		0			0
$475$	22.1408	−	18.5347i	1.01589	−	0.850429i
$476$	0.0186755	−	0.0574772i	0.000855989	−	0.00263446i
$477$		0			0
$478$	13.3336	+	2.11183i	0.609864	+	0.0965929i
$479$	5.27658	−	3.83366i	0.241093	−	0.175165i	−0.460677	−	0.887568i	$-0.652393\pi$
$479$	5.27658	−	3.83366i	0.241093	−	0.175165i	0.701770	+	0.712403i	$0.252393\pi$
$480$		0			0
$481$	2.51162	+	0.816075i	0.114520	+	0.0372098i
$482$	−21.2789	+	3.37025i	−0.969227	+	0.153510i
$483$		0			0
$484$	2.58727	+	10.6914i	0.117603	+	0.485973i
$485$	−9.87774	−	1.21865i	−0.448525	−	0.0553360i
$486$		0			0
$487$	3.88945	+	7.63347i	0.176248	+	0.345906i	0.962183	−	0.272403i	$-0.0878183\pi$
$487$	3.88945	+	7.63347i	0.176248	+	0.345906i	−0.785936	+	0.618308i	$0.787818\pi$
$488$	−3.74242	+	7.34491i	−0.169411	+	0.332488i
$489$		0			0
$490$	−13.6939	+	7.58028i	−0.618627	+	0.342442i
$491$	24.6223	−	8.00027i	1.11119	−	0.361047i	0.304790	−	0.952419i	$-0.401414\pi$
$491$	24.6223	−	8.00027i	1.11119	−	0.361047i	0.806399	+	0.591372i	$0.201414\pi$
$492$		0			0
$493$	2.55126	+	16.1081i	0.114903	+	0.725470i
$494$	13.5183			0.608217
$495$		0			0
$496$	5.81294			0.261009
$497$	0.0154472	+	0.0975297i	0.000692901	+	0.00437480i
$498$		0			0
$499$	15.9071	−	5.16853i	0.712099	−	0.231375i	0.0695049	−	0.997582i	$-0.477858\pi$
$499$	15.9071	−	5.16853i	0.712099	−	0.231375i	0.642594	+	0.766207i	$0.277858\pi$
$500$	9.67272	+	5.60700i	0.432577	+	0.250753i
$501$		0			0
$502$	8.89258	−	17.4527i	0.396895	−	0.778951i
$503$	−6.24553	−	12.2575i	−0.278475	−	0.546537i	0.708829	−	0.705380i	$-0.249224\pi$
$503$	−6.24553	−	12.2575i	−0.278475	−	0.546537i	−0.987304	+	0.158843i	$0.949224\pi$
$504$		0			0
$505$	−30.6112	+	23.8875i	−1.36218	+	1.06298i
$506$	2.64338	+	22.1618i	0.117512	+	0.985213i
$507$		0			0
$508$	17.3079	−	2.74131i	0.767916	−	0.121626i
$509$	−32.6519	−	10.6092i	−1.44727	−	0.470246i	−0.523113	−	0.852263i	$-0.675229\pi$
$509$	−32.6519	−	10.6092i	−1.44727	−	0.470246i	−0.924155	+	0.382017i	$0.875229\pi$
$510$		0			0
$511$	−0.0572865	+	0.0416211i	−0.00253421	+	0.00184121i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$		0			0
$514$	−6.10397	+	18.7861i	−0.269234	+	0.828618i
$515$	0.521194	−	0.558263i	0.0229666	−	0.0246000i
$516$		0			0
$517$	−4.82060	−	1.77346i	−0.212010	−	0.0779965i
$518$	−0.0122543	−	0.0122543i	−0.000538422	−	0.000538422i
$519$		0			0
$520$	1.78738	+	4.91967i	0.0783819	+	0.215742i
$521$	−1.49330	−	4.59591i	−0.0654227	−	0.201351i	0.913002	−	0.407956i	$-0.133758\pi$
$521$	−1.49330	−	4.59591i	−0.0654227	−	0.201351i	−0.978424	+	0.206606i	$0.933758\pi$
$522$		0			0
$523$	−2.62342	+	16.5636i	−0.114714	+	0.724276i	0.861547	+	0.507678i	$0.169496\pi$
$523$	−2.62342	+	16.5636i	−0.114714	+	0.724276i	−0.976261	+	0.216598i	$0.930504\pi$
$524$	−1.12875	−	3.47393i	−0.0493096	−	0.151759i
$525$		0			0
$526$	22.9832	+	16.6982i	1.00211	+	0.728078i
$527$	16.1712	+	16.1712i	0.704427	+	0.704427i
$528$		0			0
$529$			22.2849i			0.968907i
$530$	31.3651	−	1.07709i	1.36241	−	0.0467856i
$531$		0			0
$532$	−0.0790419	−	0.0402739i	−0.00342690	−	0.00174609i
$533$	−10.8518	−	1.71876i	−0.470044	−	0.0744476i
$534$		0			0
$535$	−5.03437	+	0.975553i	−0.217655	+	0.0421768i
$536$	4.94474	+	1.60664i	0.213580	+	0.0693964i
$537$		0			0
$538$	6.62361	−	6.62361i	0.285564	−	0.285564i
$539$	−22.7736	−	4.50852i	−0.980928	−	0.194196i
$540$		0			0
$541$	6.42200	−	8.83913i	0.276103	−	0.380024i	−0.648335	−	0.761355i	$-0.724534\pi$
$541$	6.42200	−	8.83913i	0.276103	−	0.380024i	0.924438	+	0.381331i	$0.124534\pi$
$542$	−2.79422	−	5.48397i	−0.120022	−	0.235556i
$543$		0			0
$544$	−2.31249	−	3.18287i	−0.0991471	−	0.136464i
$545$	5.21892	+	1.49978i	0.223554	+	0.0642433i
$546$		0			0
$547$	31.3306	−	15.9637i	1.33960	−	0.682559i	0.370407	−	0.928870i	$-0.379218\pi$
$547$	31.3306	−	15.9637i	1.33960	−	0.682559i	0.969191	+	0.246310i	$0.0792182\pi$
$548$	−2.63360	−	16.6279i	−0.112502	−	0.710309i
$549$		0			0
$550$	5.59975	+	15.6091i	0.238774	+	0.665573i
$551$	23.9392			1.01985
$552$		0			0
$553$	−0.0650454	+	0.0331423i	−0.00276601	+	0.00140935i
$554$	−28.3464	+	9.21031i	−1.20432	+	0.391308i
$555$		0			0
$556$	−13.0196	−	17.9199i	−0.552152	−	0.759972i
$557$	1.38133	−	2.71100i	0.0585286	−	0.114869i	−0.859889	−	0.510481i	$-0.829467\pi$
$557$	1.38133	−	2.71100i	0.0585286	−	0.114869i	0.918418	+	0.395612i	$0.129467\pi$
$558$		0			0
$559$	11.0708	−	15.2376i	0.468244	−	0.644483i
$560$	0.00420585	−	0.0340905i	0.000177730	−	0.00144059i
$561$		0			0
$562$	−4.04138	+	4.04138i	−0.170475	+	0.170475i
$563$	−36.3351	+	5.75492i	−1.53134	+	0.242541i	−0.864490	−	0.502649i	$-0.832359\pi$
$563$	−36.3351	+	5.75492i	−1.53134	+	0.242541i	−0.666852	+	0.745190i	$0.732359\pi$
$564$		0			0
$565$	23.9073	−	4.63273i	1.00579	−	0.194900i
$566$	−3.51747	+	2.55559i	−0.147850	+	0.107419i
$567$		0			0
$568$	5.72756	+	2.91834i	0.240323	+	0.122451i
$569$	5.11991	−	15.7575i	0.214638	−	0.660587i	−0.784541	−	0.620077i	$-0.787102\pi$
$569$	5.11991	−	15.7575i	0.214638	−	0.660587i	0.999179	−	0.0405107i	$-0.0128985\pi$
$570$		0			0
$571$			10.4437i			0.437057i	0.975831	+	0.218529i	$0.0701257\pi$
$571$			10.4437i			0.437057i	−0.975831	+	0.218529i	$0.929874\pi$
$572$	−2.68056	+	7.28629i	−0.112080	+	0.304655i
$573$		0			0
$574$	0.0583303	+	0.0423795i	0.00243466	+	0.00176888i
$575$	7.53091	+	32.7934i	0.314061	+	1.36758i
$576$		0			0
$577$	−0.310767	+	1.96210i	−0.0129374	+	0.0816834i	−0.993312	−	0.115459i	$-0.963166\pi$
$577$	−0.310767	+	1.96210i	−0.0129374	+	0.0816834i	0.980375	+	0.197142i	$0.0631661\pi$
$578$	−0.238056	+	1.50302i	−0.00990181	+	0.0625176i
$579$		0			0
$580$	3.16524	+	8.71214i	0.131429	+	0.361752i
$581$	−0.165569	−	0.120293i	−0.00686896	−	0.00499059i
$582$		0			0
$583$	36.5822	+	28.7854i	1.51508	+	1.19217i
$584$			4.60963i			0.190748i
$585$		0			0
$586$	−4.20067	+	12.9283i	−0.173528	+	0.534065i
$587$	−12.4878	−	6.36284i	−0.515426	−	0.262623i	0.176873	−	0.984234i	$-0.443402\pi$
$587$	−12.4878	−	6.36284i	−0.515426	−	0.262623i	−0.692299	+	0.721611i	$0.743402\pi$
$588$		0			0
$589$	27.1582	−	19.7316i	1.11904	−	0.813027i
$590$	−0.835057	−	4.30933i	−0.0343787	−	0.177412i
$591$		0			0
$592$	−1.11428	+	0.176484i	−0.0457966	+	0.00725347i
$593$	24.8101	−	24.8101i	1.01883	−	1.01883i	0.0190108	−	0.999819i	$-0.493948\pi$
$593$	24.8101	−	24.8101i	1.01883	−	1.01883i	0.999819	−	0.0190108i	$-0.00605170\pi$
$594$		0			0
$595$	0.106538	−	0.0831369i	0.00436762	−	0.00340828i
$596$	8.30508	−	11.4310i	0.340189	−	0.468230i
$597$		0			0
$598$	−7.15150	+	14.0356i	−0.292446	+	0.573958i
$599$	−6.95362	−	9.57083i	−0.284117	−	0.391054i	0.642975	−	0.765887i	$-0.277700\pi$
$599$	−6.95362	−	9.57083i	−0.284117	−	0.391054i	−0.927092	+	0.374833i	$0.877700\pi$
$600$		0			0
$601$	−18.9484	+	6.15671i	−0.772922	+	0.251138i	−0.668815	−	0.743429i	$-0.733198\pi$
$601$	−18.9484	+	6.15671i	−0.772922	+	0.251138i	−0.104107	+	0.994566i	$0.533198\pi$
$602$	−0.110127	+	0.0561127i	−0.00448846	+	0.00228698i
$603$		0			0
$604$	−3.31087			−0.134717
$605$	−8.58559	+	23.0497i	−0.349054	+	0.937103i
$606$		0			0
$607$	−3.67280	−	23.1891i	−0.149074	−	0.941218i	−0.942901	−	0.333074i	$-0.891914\pi$
$607$	−3.67280	−	23.1891i	−0.149074	−	0.941218i	0.793827	−	0.608144i	$-0.208086\pi$
$608$	−5.14552	+	2.62177i	−0.208678	+	0.106327i
$609$		0			0
$610$	−16.1268	+	8.92703i	−0.652957	+	0.361445i
$611$	−2.13089	−	2.93292i	−0.0862065	−	0.118653i
$612$		0			0
$613$	−11.3849	−	22.3442i	−0.459833	−	0.902473i	−0.998212	−	0.0597703i	$-0.980963\pi$
$613$	−11.3849	−	22.3442i	−0.459833	−	0.902473i	0.538379	−	0.842703i	$-0.319037\pi$
$614$	14.0329	−	19.3146i	0.566322	−	0.779475i
$615$		0			0
$616$	0.0373807	−	0.0346172i	0.00150611	−	0.00139477i
$617$	−25.6695	+	25.6695i	−1.03341	+	1.03341i	−0.0339923	+	0.999422i	$0.510822\pi$
$617$	−25.6695	+	25.6695i	−1.03341	+	1.03341i	−0.999422	+	0.0339923i	$0.989178\pi$
$618$		0			0
$619$	−15.3896	−	5.00040i	−0.618562	−	0.200983i	−0.0170601	−	0.999854i	$-0.505431\pi$
$619$	−15.3896	−	5.00040i	−0.618562	−	0.200983i	−0.601502	+	0.798872i	$0.705431\pi$
$620$	10.7717	+	7.27471i	0.432603	+	0.292159i
$621$		0			0
$622$	28.6415	+	4.53636i	1.14842	+	0.181892i
$623$	−0.129785	−	0.0661287i	−0.00519972	−	0.00264939i
$624$		0			0
$625$	10.9071	+	22.4952i	0.436285	+	0.899808i
$626$		−	17.3031i		−	0.691573i
$627$		0			0
$628$	−9.10015	−	9.10015i	−0.363136	−	0.363136i
$629$	−3.59081	−	2.60888i	−0.143175	−	0.104023i
$630$		0			0
$631$	−4.71355	−	14.5068i	−0.187644	−	0.577508i	0.812340	−	0.583184i	$-0.198193\pi$
$631$	−4.71355	−	14.5068i	−0.187644	−	0.577508i	−0.999984	+	0.00567610i	$0.998193\pi$
$632$	−0.743430	+	4.69383i	−0.0295720	+	0.186711i
$633$		0			0
$634$	−6.41152	−	19.7326i	−0.254634	−	0.783683i
$635$	35.5033	+	16.5805i	1.40891	+	0.657978i
$636$		0			0
$637$	−11.5862	−	11.5862i	−0.459063	−	0.459063i
$638$	−4.74694	+	12.9031i	−0.187933	+	0.510840i
$639$		0			0
$640$	−1.63447	−	1.52594i	−0.0646082	−	0.0603182i
$641$	−3.02959	+	9.32412i	−0.119662	+	0.368280i	−0.992891	−	0.119029i	$-0.962022\pi$
$641$	−3.02959	+	9.32412i	−0.119662	+	0.368280i	0.873229	+	0.487310i	$0.162022\pi$
$642$		0			0
$643$	4.86380	+	0.770351i	0.191810	+	0.0303797i	0.251600	−	0.967831i	$-0.419043\pi$
$643$	4.86380	+	0.770351i	0.191810	+	0.0303797i	−0.0597904	+	0.998211i	$0.519043\pi$
$644$	0.0836301	−	0.0607608i	0.00329549	−	0.00239431i
$645$		0			0
$646$	−21.6080	−	7.02088i	−0.850157	−	0.276233i
$647$	8.21829	−	1.30165i	0.323094	−	0.0511731i	0.00721944	−	0.999974i	$-0.497702\pi$
$647$	8.21829	−	1.30165i	0.323094	−	0.0511731i	0.315875	+	0.948801i	$0.397702\pi$
$648$		0			0
$649$	3.17611	−	5.68342i	0.124673	−	0.223094i
$650$	−2.84468	+	11.3533i	−0.111578	+	0.445313i
$651$		0			0
$652$	0.763736	+	1.49892i	0.0299102	+	0.0587021i
$653$	−10.2557	+	20.1279i	−0.401335	+	0.787665i	−0.999910	−	0.0134022i	$-0.995734\pi$
$653$	−10.2557	+	20.1279i	−0.401335	+	0.787665i	0.598575	+	0.801067i	$0.295734\pi$
$654$		0			0
$655$	2.25588	−	7.84999i	0.0881444	−	0.306725i
$656$	4.46390	−	1.45041i	0.174286	−	0.0566290i
$657$		0			0
$658$	0.00372160	+	0.0234972i	0.000145083	+	0.000916018i
$659$	25.7362			1.00254			0.501270	−	0.865291i	$-0.332866\pi$
$659$	25.7362			1.00254			0.501270	+	0.865291i	$0.332866\pi$
$660$		0			0
$661$	−14.3297			−0.557360			−0.278680	−	0.960384i	$-0.589897\pi$
$661$	−14.3297			−0.557360			−0.278680	+	0.960384i	$0.589897\pi$
$662$	−4.33692	−	27.3822i	−0.168559	−	1.06424i
$663$		0			0
$664$	−12.6707	+	4.11695i	−0.491717	+	0.159769i
$665$	−0.0960679	−	0.173548i	−0.00372535	−	0.00672991i
$666$		0			0
$667$	−12.6644	+	24.8553i	−0.490369	+	0.962403i
$668$	7.38860	+	14.5009i	0.285874	+	0.561058i
$669$		0			0
$670$	7.15223	+	9.16539i	0.276315	+	0.354090i
$671$	−26.8197	−	5.30953i	−1.03536	−	0.204972i
$672$		0			0
$673$	−36.8427	+	5.83531i	−1.42018	+	0.224935i	−0.818824	−	0.574045i	$-0.805373\pi$
$673$	−36.8427	+	5.83531i	−1.42018	+	0.224935i	−0.601358	+	0.798980i	$0.705373\pi$
$674$	−6.68524	−	2.17217i	−0.257506	−	0.0836688i
$675$		0			0
$676$	6.08415	−	4.42039i	0.234006	−	0.170015i
$677$	10.9011	+	1.72656i	0.418963	+	0.0663572i	0.362357	−	0.932039i	$-0.381972\pi$
$677$	10.9011	+	1.72656i	0.418963	+	0.0663572i	0.0566060	+	0.998397i	$0.481972\pi$
$678$		0			0
$679$	−0.0211283	+	0.0650261i	−0.000810828	+	0.00249547i
$680$	−0.301921	−	8.79204i	−0.0115781	−	0.337160i
$681$		0			0
$682$	5.24999	+	18.5507i	0.201033	+	0.710345i
$683$	4.64732	+	4.64732i	0.177825	+	0.177825i	0.790407	−	0.612582i	$-0.209869\pi$
$683$	4.64732	+	4.64732i	0.177825	+	0.177825i	−0.612582	+	0.790407i	$0.709869\pi$
$684$		0			0
$685$	15.9291	−	34.1084i	0.608619	−	1.30321i
$686$	0.0664556	+	0.204529i	0.00253729	+	0.00780896i
$687$		0			0
$688$	−1.25869	+	7.94705i	−0.0479871	+	0.302978i
$689$	10.1525	+	31.2463i	0.386780	+	1.19039i
$690$		0			0
$691$	−1.72951	−	1.25656i	−0.0657935	−	0.0478018i	0.554402	−	0.832249i	$-0.312947\pi$
$691$	−1.72951	−	1.25656i	−0.0657935	−	0.0478018i	−0.620196	+	0.784447i	$0.712947\pi$
$692$	10.6979	+	10.6979i	0.406674	+	0.406674i
$693$		0			0
$694$		−	21.7088i		−	0.824055i
$695$	−1.69985	−	49.5002i	−0.0644789	−	1.87765i
$696$		0			0
$697$	16.4532	+	8.38331i	0.623209	+	0.317541i
$698$	11.7363	+	1.85885i	0.444226	+	0.0703585i
$699$		0			0
$700$	0.0504568	−	0.0579082i	0.00190709	−	0.00218872i
$701$	−16.0121	−	5.20265i	−0.604769	−	0.196501i	−0.00940286	−	0.999956i	$-0.502993\pi$
$701$	−16.0121	−	5.20265i	−0.604769	−	0.196501i	−0.595366	+	0.803454i	$0.702993\pi$
$702$		0			0
$703$	−4.60688	+	4.60688i	−0.173752	+	0.173752i
$704$	−0.392810	−	3.29328i	−0.0148046	−	0.124120i
$705$		0			0
$706$	−0.637174	+	0.876995i	−0.0239804	+	0.0330061i
$707$	0.121099	+	0.237671i	0.00455441	+	0.00893854i
$708$		0			0
$709$	10.9910	+	15.1277i	0.412774	+	0.568134i	0.963892	−	0.266293i	$-0.0857988\pi$
$709$	10.9910	+	15.1277i	0.412774	+	0.568134i	−0.551118	+	0.834427i	$0.685799\pi$
$710$	6.96130	+	12.5757i	0.261253	+	0.471958i
$711$		0			0
$712$	−8.44881	+	4.30488i	−0.316632	+	0.161332i
$713$	6.11934	+	38.6360i	0.229171	+	1.44693i
$714$		0			0
$715$	−14.0858	+	10.1473i	−0.526779	+	0.379487i
$716$	−23.6364			−0.883333
$717$		0			0
$718$	−7.39342	+	3.76714i	−0.275920	+	0.140588i
$719$	−16.7305	+	5.43605i	−0.623941	+	0.202731i	−0.603889	−	0.797068i	$-0.706383\pi$
$719$	−16.7305	+	5.43605i	−0.623941	+	0.202731i	−0.0200516	+	0.999799i	$0.506383\pi$
$720$		0			0
$721$	−0.00308396	−	0.00424470i	−0.000114853	−	0.000158081i
$722$	−6.51478	+	12.7860i	−0.242455	+	0.475845i
$723$		0			0
$724$	11.2395	−	15.4698i	0.417712	−	0.574931i
$725$	−5.03759	+	20.1053i	−0.187091	+	0.746692i
$726$		0			0
$727$	−3.51865	+	3.51865i	−0.130500	+	0.130500i	−0.769340	−	0.638840i	$-0.779415\pi$
$727$	−3.51865	+	3.51865i	−0.130500	+	0.130500i	0.638840	+	0.769340i	$0.279415\pi$
$728$	0.0355158	−	0.00562515i	0.00131630	−	0.000208482i
$729$		0			0
$730$	−5.76881	+	8.54192i	−0.213513	+	0.316151i
$731$	−25.6097	+	18.6065i	−0.947209	+	0.688187i
$732$		0			0
$733$	−8.32881	−	4.24374i	−0.307631	−	0.156746i	0.293359	−	0.956002i	$-0.405227\pi$
$733$	−8.32881	−	4.24374i	−0.307631	−	0.156746i	−0.600990	+	0.799256i	$0.705227\pi$
$734$	4.65539	−	14.3278i	0.171833	−	0.528849i
$735$		0			0
$736$		−	6.72940i		−	0.248049i
$737$	−0.661386	+	17.2311i	−0.0243625	+	0.634717i
$738$		0			0
$739$	−22.0128	−	15.9932i	−0.809754	−	0.588321i	0.104005	−	0.994577i	$-0.466834\pi$
$739$	−22.0128	−	15.9932i	−0.809754	−	0.588321i	−0.913759	+	0.406256i	$0.866834\pi$
$740$	−2.28569	−	1.06745i	−0.0840236	−	0.0392402i
$741$		0			0
$742$	0.0337271	−	0.212945i	0.00123816	−	0.00781744i
$743$	3.73190	−	23.5623i	0.136910	−	0.864417i	−0.819646	−	0.572870i	$-0.805830\pi$
$743$	3.73190	−	23.5623i	0.136910	−	0.864417i	0.956557	−	0.291547i	$-0.0941700\pi$
$744$		0			0
$745$	29.6953	−	10.7887i	1.08795	−	0.395267i
$746$	6.10663	+	4.43673i	0.223580	+	0.162440i
$747$		0			0
$748$	8.06890	−	10.2544i	0.295028	−	0.374939i
$749$			0.0352284i			0.00128722i
$750$		0			0
$751$	5.95219	−	18.3190i	0.217199	−	0.668469i	−0.781792	−	0.623540i	$-0.785694\pi$
$751$	5.95219	−	18.3190i	0.217199	−	0.668469i	0.998990	−	0.0449289i	$-0.0143061\pi$
$752$	1.37991	+	0.703097i	0.0503200	+	0.0256393i
$753$		0			0
$754$	−7.85043	+	5.70367i	−0.285896	+	0.207715i
$755$	−6.13524	−	4.14345i	−0.223284	−	0.150796i
$756$		0			0
$757$	−10.6845	+	1.69226i	−0.388336	+	0.0615063i	−0.347550	−	0.937662i	$-0.612986\pi$
$757$	−10.6845	+	1.69226i	−0.388336	+	0.0615063i	−0.0407860	+	0.999168i	$0.512986\pi$
$758$	7.05009	−	7.05009i	0.256071	−	0.256071i
$759$		0			0
$760$	−12.8160	−	1.58115i	−0.464886	−	0.0573544i
$761$	−13.9786	+	19.2399i	−0.506723	+	0.697444i	−0.983362	−	0.181655i	$-0.941855\pi$
$761$	−13.9786	+	19.2399i	−0.506723	+	0.697444i	0.476640	+	0.879099i	$0.341855\pi$
$762$		0			0
$763$	0.0169356	−	0.0332380i	0.000613111	−	0.00120330i
$764$	−7.04298	−	9.69383i	−0.254806	−	0.350710i
$765$		0			0
$766$	22.6593	−	7.36246i	0.818714	−	0.266016i
$767$	4.09434	−	2.08617i	0.147838	−	0.0753273i
$768$		0			0
$769$	5.84739			0.210862			0.105431	−	0.994427i	$-0.466378\pi$
$769$	5.84739			0.210862			0.105431	+	0.994427i	$0.466378\pi$
$770$	0.112591	−	0.0173670i	0.00405750	−	0.000625862i
$771$		0			0
$772$	2.50920	+	15.8424i	0.0903080	+	0.570182i
$773$	8.04258	−	4.09790i	0.289272	−	0.147391i	−0.303333	−	0.952885i	$-0.598100\pi$
$773$	8.04258	−	4.09790i	0.289272	−	0.147391i	0.592605	+	0.805493i	$0.298100\pi$
$774$		0			0
$775$	10.8566	+	26.9609i	0.389979	+	0.968465i
$776$	2.61620	+	3.60090i	0.0939163	+	0.129265i
$777$		0			0
$778$	−2.37697	−	4.66507i	−0.0852185	−	0.167251i
$779$	15.9322	−	21.9288i	0.570829	−	0.785679i
$780$		0			0
$781$	−4.14037	+	20.9140i	−0.148154	+	0.748361i
$782$	18.7207	−	18.7207i	0.669451	−	0.669451i
$783$		0			0
$784$	6.65717	+	2.16305i	0.237756	+	0.0772516i
$785$	−5.47457	−	28.2517i	−0.195396	−	1.00835i
$786$		0			0
$787$	−46.5577	−	7.37402i	−1.65960	−	0.262855i	−0.744957	−	0.667112i	$-0.767530\pi$
$787$	−46.5577	−	7.37402i	−1.65960	−	0.262855i	−0.914646	+	0.404257i	$0.867530\pi$
$788$	7.43833	+	3.79002i	0.264979	+	0.135014i
$789$		0			0
$790$	−7.25180	+	7.76757i	−0.258007	+	0.276358i
$791$		−	0.167293i		−	0.00594827i
$792$		0			0
$793$	−13.6447	−	13.6447i	−0.484537	−	0.484537i
$794$	−1.92927	−	1.40169i	−0.0684671	−	0.0497443i
$795$		0			0
$796$	−2.61628	−	8.05208i	−0.0927316	−	0.285398i
$797$	−0.195418	+	1.23382i	−0.00692208	+	0.0437043i	−0.990908	−	0.134544i	$-0.957043\pi$
$797$	−0.195418	+	1.23382i	−0.00692208	+	0.0437043i	0.983986	+	0.178248i	$0.0570430\pi$
$798$		0			0
$799$	1.88283	+	5.79476i	0.0666098	+	0.205004i
$800$	−1.11910	−	4.87315i	−0.0395663	−	0.172292i
$801$		0			0
$802$	−11.1070	−	11.1070i	−0.392202	−	0.392202i
$803$	−14.7107	+	4.16322i	−0.519128	+	0.146917i
$804$		0			0
$805$	0.231012	−	0.00793300i	0.00814209	−	0.000279601i
$806$	−4.20486	+	12.9412i	−0.148110	+	0.455835i
$807$		0			0
$808$	17.1509	+	2.71643i	0.603366	+	0.0955638i
$809$	16.9646	−	12.3255i	0.596442	−	0.433341i	−0.248172	−	0.968716i	$-0.579830\pi$
$809$	16.9646	−	12.3255i	0.596442	−	0.433341i	0.844614	+	0.535375i	$0.179830\pi$
$810$		0			0
$811$	2.18611	+	0.710312i	0.0767649	+	0.0249424i	0.347148	−	0.937810i	$-0.387150\pi$
$811$	2.18611	+	0.710312i	0.0767649	+	0.0249424i	−0.270383	+	0.962753i	$0.587150\pi$
$812$	0.0628942	−	0.00996146i	0.00220715	−	0.000349579i
$813$		0			0
$814$	−1.56958	−	3.39659i	−0.0550138	−	0.119050i
$815$	−0.460598	+	3.73337i	−0.0161340	+	0.130774i
$816$		0			0
$817$	21.0951	+	41.4014i	0.738023	+	1.44845i
$818$	0.784707	−	1.54007i	0.0274366	−	0.0538474i
$819$		0			0
$820$	10.0870	+	2.89874i	0.352254	+	0.101228i
$821$	−28.7277	+	9.33418i	−1.00260	+	0.325765i	−0.763905	−	0.645329i	$-0.776720\pi$
$821$	−28.7277	+	9.33418i	−1.00260	+	0.325765i	−0.238697	+	0.971094i	$0.576720\pi$
$822$		0			0
$823$	0.511401	+	3.22886i	0.0178263	+	0.112551i	0.994997	−	0.0999048i	$-0.0318538\pi$
$823$	0.511401	+	3.22886i	0.0178263	+	0.112551i	−0.977171	+	0.212456i	$0.931854\pi$
$824$	−0.341556			−0.0118987
$825$		0			0
$826$	−0.0301549			−0.00104922
$827$	1.84276	+	11.6347i	0.0640791	+	0.404579i	0.998790	+	0.0491714i	$0.0156580\pi$
$827$	1.84276	+	11.6347i	0.0640791	+	0.404579i	−0.934711	+	0.355408i	$0.884342\pi$
$828$		0			0
$829$	−19.4970	+	6.33497i	−0.677160	+	0.220023i	−0.627351	−	0.778736i	$-0.715861\pi$
$829$	−19.4970	+	6.33497i	−0.677160	+	0.220023i	−0.0498083	+	0.998759i	$0.515861\pi$
$830$	−28.6317	−	8.22798i	−0.993821	−	0.285597i
$831$		0			0
$832$	1.06272	−	2.08571i	0.0368433	−	0.0723091i
$833$	12.5023	+	24.5372i	0.433180	+	0.850164i
$834$		0			0
$835$	−4.45596	+	36.1177i	−0.154205	+	1.24990i
$836$	−13.0140	−	14.0529i	−0.450100	−	0.486031i
$837$		0			0
$838$	16.5925	−	2.62800i	0.573180	−	0.0907828i
$839$	15.2019	+	4.93940i	0.524828	+	0.170527i	0.559435	−	0.828874i	$-0.311018\pi$
$839$	15.2019	+	4.93940i	0.524828	+	0.170527i	−0.0346074	+	0.999401i	$0.511018\pi$
$840$		0			0
$841$	9.55933	−	6.94526i	0.329632	−	0.239492i
$842$	−11.0975	−	1.75768i	−0.382446	−	0.0605736i
$843$		0			0
$844$	−2.16218	+	6.65452i	−0.0744254	+	0.229058i
$845$	16.8063	−	0.577131i	0.578153	−	0.0198539i
$846$		0			0
$847$	0.144234	+	0.0880279i	0.00495594	+	0.00302467i
$848$	−9.92438	−	9.92438i	−0.340804	−	0.340804i
$849$		0			0
$850$	10.4435	−	16.6700i	0.358209	−	0.571777i
$851$	−2.34603	−	7.22033i	−0.0804208	−	0.247510i
$852$		0			0
$853$	−6.04382	+	38.1592i	−0.206936	+	1.30655i	0.637317	+	0.770601i	$0.280044\pi$
$853$	−6.04382	+	38.1592i	−0.206936	+	1.30655i	−0.844254	+	0.535944i	$0.819956\pi$
$854$	0.0391306	+	0.120432i	0.00133902	+	0.00412108i
$855$		0			0
$856$	1.85533	+	1.34798i	0.0634140	+	0.0460730i
$857$	−26.7350	−	26.7350i	−0.913251	−	0.913251i	0.0832758	−	0.996527i	$-0.473462\pi$
$857$	−26.7350	−	26.7350i	−0.913251	−	0.913251i	−0.996527	+	0.0832758i	$0.973462\pi$
$858$		0			0
$859$			35.7867i			1.22103i	0.792005	+	0.610514i	$0.209037\pi$
$859$			35.7867i			1.22103i	−0.792005	+	0.610514i	$0.790963\pi$
$860$	−12.2779	+	13.1511i	−0.418673	+	0.448450i
$861$		0			0
$862$	−34.1495	−	17.4000i	−1.16314	−	0.592647i
$863$	38.2576	+	6.05941i	1.30230	+	0.206265i	0.768776	−	0.639518i	$-0.220866\pi$
$863$	38.2576	+	6.05941i	1.30230	+	0.206265i	0.533528	+	0.845782i	$0.320866\pi$
$864$		0			0
$865$	6.43578	+	33.2120i	0.218823	+	1.12924i
$866$	−18.6691	−	6.06597i	−0.634403	−	0.206130i
$867$		0			0
$868$	0.0631407	−	0.0631407i	0.00214313	−	0.00214313i
$869$	−15.6508	+	1.86677i	−0.530917	+	0.0633257i
$870$		0			0
$871$	−7.15368	+	9.84619i	−0.242393	+	0.333626i
$872$	−1.10249	−	2.16375i	−0.0373349	−	0.0732738i
$873$		0			0
$874$	−22.8425	−	31.4400i	−0.772659	−	1.06347i
$875$	0.165970	−	0.0441622i	0.00561080	−	0.00149295i
$876$		0			0
$877$	−9.96725	+	5.07857i	−0.336570	+	0.171491i	−0.614105	−	0.789225i	$-0.710483\pi$
$877$	−9.96725	+	5.07857i	−0.336570	+	0.171491i	0.277534	+	0.960716i	$0.410483\pi$
$878$	−0.164590	−	1.03918i	−0.00555466	−	0.0350707i
$879$		0			0
$880$	3.39354	−	6.59423i	0.114396	−	0.222292i
$881$	2.54074			0.0855998			0.0427999	−	0.999084i	$-0.486372\pi$
$881$	2.54074			0.0855998			0.0427999	+	0.999084i	$0.486372\pi$
$882$		0			0
$883$	13.9170	−	7.09109i	0.468346	−	0.238634i	−0.203858	−	0.979001i	$-0.565348\pi$
$883$	13.9170	−	7.09109i	0.468346	−	0.238634i	0.672203	+	0.740366i	$0.265348\pi$
$884$	8.75872	−	2.84588i	0.294588	−	0.0957173i
$885$		0			0
$886$	−0.185210	−	0.254920i	−0.00622226	−	0.00856421i
$887$	1.38930	−	2.72665i	0.0466480	−	0.0915519i	−0.866506	−	0.499167i	$-0.833639\pi$
$887$	1.38930	−	2.72665i	0.0466480	−	0.0915519i	0.913154	+	0.407615i	$0.133639\pi$
$888$		0			0
$889$	0.158224	−	0.217777i	0.00530667	−	0.00730400i
$890$	−21.0436	−	2.59621i	−0.705382	−	0.0870252i
$891$		0			0
$892$	13.2224	−	13.2224i	0.442718	−	0.442718i
$893$	8.83358	−	1.39910i	0.295604	−	0.0468191i
$894$		0			0
$895$	−43.7996	−	29.5802i	−1.46406	−	0.988756i
$896$	−0.0124276	+	0.00902916i	−0.000415176	+	0.000301643i
$897$		0			0
$898$	−29.9392	−	15.2548i	−0.999084	−	0.509059i
$899$	−7.44630	+	22.9173i	−0.248348	+	0.764336i
$900$		0			0
$901$		−	55.2178i		−	1.83957i
$902$	8.66027	+	12.9356i	0.288356	+	0.430710i
$903$		0			0
$904$	−8.81066	−	6.40132i	−0.293038	−	0.212905i
$905$	40.1874	−	14.6006i	1.33587	−	0.485341i
$906$		0			0
$907$	−8.26589	+	52.1888i	−0.274464	+	1.73290i	0.336892	+	0.941543i	$0.390624\pi$
$907$	−8.26589	+	52.1888i	−0.274464	+	1.73290i	−0.611356	+	0.791356i	$0.709376\pi$
$908$	−1.58488	+	10.0065i	−0.0525961	+	0.332079i
$909$		0			0
$910$	0.0728526	+	0.0340232i	0.00241504	+	0.00112786i
$911$	−9.97151	−	7.24473i	−0.330371	−	0.240029i	0.410217	−	0.911988i	$-0.365453\pi$
$911$	−9.97151	−	7.24473i	−0.330371	−	0.240029i	−0.740588	+	0.671959i	$0.765453\pi$
$912$		0			0
$913$	−24.5820	−	36.7175i	−0.813544	−	1.21517i
$914$		−	29.9314i		−	0.990044i
$915$		0			0
$916$	−3.35423	+	10.3233i	−0.110827	+	0.341090i
$917$	−0.0499947	−	0.0254736i	−0.00165097	−	0.000841212i
$918$		0			0
$919$	0.0894366	−	0.0649795i	0.00295024	−	0.00214348i	−0.586309	−	0.810087i	$-0.699420\pi$
$919$	0.0894366	−	0.0649795i	0.00295024	−	0.00214348i	0.589259	+	0.807944i	$0.299420\pi$
$920$	8.42163	−	12.4700i	0.277653	−	0.411123i
$921$		0			0
$922$	−27.2750	+	4.31993i	−0.898254	+	0.142269i
$923$	−10.6401	+	10.6401i	−0.350224	+	0.350224i
$924$		0			0
$925$	−2.89964	−	4.83851i	−0.0953396	−	0.159089i
$926$	−22.1629	+	30.5047i	−0.728319	+	1.00245i
$927$		0			0
$928$	1.88195	−	3.69354i	0.0617782	−	0.121247i
$929$	6.25774	+	8.61305i	0.205310	+	0.282585i	0.899238	−	0.437459i	$-0.144122\pi$
$929$	6.25774	+	8.61305i	0.205310	+	0.282585i	−0.693928	+	0.720044i	$0.744122\pi$
$930$		0			0
$931$	38.4448	−	12.4915i	1.25998	−	0.409392i
$932$	−4.23391	+	2.15729i	−0.138686	+	0.0706643i
$933$		0			0
$934$	29.8354			0.976243
$935$	27.7852	−	8.90411i	0.908675	−	0.291195i
$936$		0			0
$937$	4.09535	+	25.8570i	0.133789	+	0.844712i	0.959724	+	0.280946i	$0.0906482\pi$
$937$	4.09535	+	25.8570i	0.133789	+	0.844712i	−0.825934	+	0.563766i	$0.809352\pi$
$938$	0.0711617	−	0.0362587i	0.00232351	−	0.00118389i
$939$		0			0
$940$	1.67714	+	3.02979i	0.0547024	+	0.0988208i
$941$	19.4803	+	26.8123i	0.635038	+	0.874055i	0.998339	−	0.0576167i	$-0.0183501\pi$
$941$	19.4803	+	26.8123i	0.635038	+	0.874055i	−0.363300	+	0.931672i	$0.618350\pi$
$942$		0			0
$943$	14.3394	+	28.1427i	0.466956	+	0.916452i
$944$	−1.15385	+	1.58813i	−0.0375545	+	0.0516894i
$945$		0			0
$946$	−26.4981	+	3.16059i	−0.861528	+	0.102760i
$947$	−31.2894	+	31.2894i	−1.01677	+	1.01677i	−0.0169134	+	0.999857i	$0.505384\pi$
$947$	−31.2894	+	31.2894i	−1.01677	+	1.01677i	−0.999857	+	0.0169134i	$0.994616\pi$
$948$		0			0
$949$	−10.2623	−	3.33443i	−0.333129	−	0.108240i
$950$	−21.7701	−	18.9688i	−0.706314	−	0.615429i
$951$		0			0
$952$	−0.0596910	−	0.00945413i	−0.00193460	−	0.000306410i
$953$	17.3932	+	8.86229i	0.563421	+	0.287078i	0.712412	−	0.701761i	$-0.247603\pi$
$953$	17.3932	+	8.86229i	0.563421	+	0.287078i	−0.148991	+	0.988839i	$0.547603\pi$
$954$		0			0
$955$	−0.919538	−	26.7773i	−0.0297556	−	0.866493i
$956$		−	13.4998i		−	0.436614i
$957$		0			0
$958$	−4.61190	−	4.61190i	−0.149004	−	0.149004i
$959$	−0.209220	−	0.152007i	−0.00675608	−	0.00490858i
$960$		0			0
$961$	0.862234	+	2.65368i	0.0278140	+	0.0856027i
$962$	0.413124	−	2.60836i	0.0133196	−	0.0840969i
$963$		0			0
$964$	6.65750	+	20.4897i	0.214424	+	0.659929i
$965$	−15.1766	+	32.4972i	−0.488553	+	1.04612i
$966$		0			0
$967$	−25.7251	−	25.7251i	−0.827262	−	0.827262i	0.159875	−	0.987137i	$-0.448891\pi$
$967$	−25.7251	−	25.7251i	−0.827262	−	0.827262i	−0.987137	+	0.159875i	$0.948891\pi$
$968$	10.1550	−	4.22792i	0.326395	−	0.135890i
$969$		0			0
$970$	0.341574	+	9.94677i	0.0109673	+	0.319372i
$971$	12.5009	−	38.4738i	0.401173	−	1.23468i	−0.522876	−	0.852409i	$-0.675141\pi$
$971$	12.5009	−	38.4738i	0.401173	−	1.23468i	0.924049	−	0.382274i	$-0.124859\pi$
$972$		0			0
$973$	−0.336067	−	0.0532278i	−0.0107738	−	0.00170640i
$974$	6.93105	−	5.03570i	0.222085	−	0.161354i
$975$		0			0
$976$	7.83992	+	2.54735i	0.250950	+	0.0815385i
$977$	−37.1310	+	5.88097i	−1.18792	+	0.188149i	−0.718949	−	0.695063i	$-0.755377\pi$
$977$	−37.1310	+	5.88097i	−1.18792	+	0.188149i	−0.468975	+	0.883211i	$0.655377\pi$
$978$		0			0
$979$	−21.3687	−	23.0746i	−0.682947	−	0.737467i
$980$	9.62915	+	12.3395i	0.307592	+	0.394171i
$981$		0			0
$982$	−11.7536	−	23.0676i	−0.375071	−	0.736118i
$983$	−6.95538	+	13.6507i	−0.221842	+	0.435390i	−0.974924	−	0.222537i	$-0.928566\pi$
$983$	−6.95538	+	13.6507i	−0.221842	+	0.435390i	0.753082	+	0.657927i	$0.228566\pi$
$984$		0			0
$985$	9.04058	+	16.3320i	0.288057	+	0.520379i
$986$	15.5106	−	5.03971i	0.493959	−	0.160497i
$987$		0			0
$988$	−2.11473	−	13.3519i	−0.0672784	−	0.424779i
$989$	−54.1455			−1.72173
$990$		0			0
$991$	−42.6744			−1.35560			−0.677798	−	0.735248i	$-0.737066\pi$
$991$	−42.6744			−1.35560			−0.677798	+	0.735248i	$0.737066\pi$
$992$	−0.909344	−	5.74137i	−0.0288717	−	0.182289i
$993$		0			0
$994$	0.0939125	−	0.0305140i	0.00297872	−	0.000967846i
$995$	5.22880	−	18.1952i	0.165764	−	0.576826i
$996$		0			0
$997$	7.94283	−	15.5887i	0.251552	−	0.493698i	−0.730354	−	0.683069i	$-0.760645\pi$
$997$	7.94283	−	15.5887i	0.251552	−	0.493698i	0.981906	+	0.189371i	$0.0606448\pi$
$998$	−7.59331	−	14.9027i	−0.240362	−	0.471737i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bh.c.73.1		48
3.2	odd	2		110.2.k.a.73.5	yes	48
5.2	odd	4	inner	990.2.bh.c.667.5		48
11.8	odd	10	inner	990.2.bh.c.613.5		48
12.11	even	2		880.2.cm.c.513.4		48
15.2	even	4		110.2.k.a.7.2	✓	48
15.8	even	4		550.2.bh.b.7.5		48
15.14	odd	2		550.2.bh.b.293.2		48
33.8	even	10		110.2.k.a.63.2	yes	48
55.52	even	20	inner	990.2.bh.c.217.1		48
60.47	odd	4		880.2.cm.c.337.3		48
132.107	odd	10		880.2.cm.c.833.3		48
165.8	odd	20		550.2.bh.b.107.2		48
165.74	even	10		550.2.bh.b.393.5		48
165.107	odd	20		110.2.k.a.107.5	yes	48
660.107	even	20		880.2.cm.c.657.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.2	✓	48	15.2	even	4
110.2.k.a.63.2	yes	48	33.8	even	10
110.2.k.a.73.5	yes	48	3.2	odd	2
110.2.k.a.107.5	yes	48	165.107	odd	20
550.2.bh.b.7.5		48	15.8	even	4
550.2.bh.b.107.2		48	165.8	odd	20
550.2.bh.b.293.2		48	15.14	odd	2
550.2.bh.b.393.5		48	165.74	even	10
880.2.cm.c.337.3		48	60.47	odd	4
880.2.cm.c.513.4		48	12.11	even	2
880.2.cm.c.657.4		48	660.107	even	20
880.2.cm.c.833.3		48	132.107	odd	10
990.2.bh.c.73.1		48	1.1	even	1	trivial
990.2.bh.c.217.1		48	55.52	even	20	inner
990.2.bh.c.613.5		48	11.8	odd	10	inner
990.2.bh.c.667.5		48	5.2	odd	4	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-0.951057 + 0.309017i) q^{4} +(-2.14909 - 0.617590i) q^{5} +(-0.00697389 + 0.0136870i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.273795 + 2.21924i) q^{10} +(-2.43343 + 2.25353i) q^{11} +(-2.31203 + 0.366190i) q^{13} +(0.0146095 + 0.00474691i) q^{14} +(0.809017 - 0.587785i) q^{16} +(3.88580 + 0.615451i) q^{17} +(1.78456 - 5.49230i) q^{19} +(2.23475 - 0.0767418i) q^{20} +(2.60646 + 2.05094i) q^{22} +(4.75841 + 4.75841i) q^{23} +(4.23716 + 2.65451i) q^{25} +(0.723362 + 2.22628i) q^{26} +(0.00240304 - 0.0151722i) q^{28} +(1.28099 + 3.94247i) q^{29} +(4.70277 + 3.41676i) q^{31} +(-0.707107 - 0.707107i) q^{32} -3.93424i q^{34} +(0.0234405 - 0.0251076i) q^{35} +(-1.00521 - 0.512178i) q^{37} +(-5.70385 - 0.903401i) q^{38} +(-0.425389 - 2.19523i) q^{40} +(4.46390 + 1.45041i) q^{41} +(-5.68946 + 5.68946i) q^{43} +(1.61795 - 2.89521i) q^{44} +(3.95544 - 5.44420i) q^{46} +(0.703097 + 1.37991i) q^{47} +(4.11436 + 5.66293i) q^{49} +(1.95899 - 4.60026i) q^{50} +(2.08571 - 1.06272i) q^{52} +(-2.19559 - 13.8624i) q^{53} +(6.62142 - 3.34018i) q^{55} -0.0153613 q^{56} +(3.69354 - 1.88195i) q^{58} +(-1.86696 + 0.606613i) q^{59} +(4.84534 + 6.66904i) q^{61} +(2.63902 - 5.17937i) q^{62} +(-0.587785 + 0.809017i) q^{64} +(5.19491 + 0.640913i) q^{65} +(3.67640 - 3.67640i) q^{67} +(-3.88580 + 0.615451i) q^{68} +(-0.0284654 - 0.0192242i) q^{70} +(5.20051 - 3.77839i) q^{71} +(4.10721 + 2.09273i) q^{73} +(-0.348623 + 1.07295i) q^{74} +5.77495i q^{76} +(-0.0138737 - 0.0490224i) q^{77} +(3.84472 + 2.79336i) q^{79} +(-2.10166 + 0.763562i) q^{80} +(0.734244 - 4.63584i) q^{82} +(-2.08413 + 13.1587i) q^{83} +(-7.97084 - 3.72249i) q^{85} +(6.50944 + 4.72938i) q^{86} +(-3.11267 - 1.14512i) q^{88} +9.48232i q^{89} +(0.0111118 - 0.0341986i) q^{91} +(-5.99594 - 3.05509i) q^{92} +(1.25293 - 0.910306i) q^{94} +(-7.22716 + 10.7013i) q^{95} +(4.39615 - 0.696283i) q^{97} +(4.94958 - 4.94958i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{5} - 20 q^{7} - 12 q^{11} + 12 q^{16} + 20 q^{17} + 4 q^{20} - 4 q^{22} + 8 q^{23} - 20 q^{25} - 8 q^{26} - 20 q^{28} + 16 q^{31} + 20 q^{37} + 36 q^{38} + 20 q^{41} + 40 q^{46} - 40 q^{47}+ \cdots + 72 q^{97}+O(q^{100}) \) 48 * q + 8 * q^5 - 20 * q^7 - 12 * q^11 + 12 * q^16 + 20 * q^17 + 4 * q^20 - 4 * q^22 + 8 * q^23 - 20 * q^25 - 8 * q^26 - 20 * q^28 + 16 * q^31 + 20 * q^37 + 36 * q^38 + 20 * q^41 + 40 * q^46 - 40 * q^47 - 40 * q^50 + 40 * q^52 + 96 * q^55 + 8 * q^56 + 48 * q^58 + 80 * q^61 - 40 * q^62 - 20 * q^68 - 56 * q^70 + 56 * q^71 - 20 * q^73 + 96 * q^77 + 12 * q^80 - 80 * q^85 + 56 * q^86 - 4 * q^88 - 68 * q^91 + 12 * q^92 - 20 * q^95 + 72 * q^97

Introduction

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