LMFDB - Embedded newform 495.2.n.e.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (of order $5$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	495.91
Dual form			495.2.n.e.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.596764 + 0.433574i) q^{2} +(-0.449894 + 1.38463i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.318714 - 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +O(q^{10})$	\(q+(-0.596764 + 0.433574i) q^{2} +(-0.449894 + 1.38463i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.318714 - 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +0.737640 q^{10} +(-1.93675 - 2.69240i) q^{11} +(-2.79029 + 2.02726i) q^{13} +(0.235096 + 0.723552i) q^{14} +(-0.834404 - 0.606230i) q^{16} +(1.94020 + 1.40964i) q^{17} +(-2.36979 - 7.29347i) q^{19} +(1.17784 - 0.855749i) q^{20} +(2.32313 + 0.767001i) q^{22} -2.45589 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.786174 - 2.41960i) q^{26} +(1.21480 + 0.882602i) q^{28} +(1.83998 - 5.66289i) q^{29} +(2.98382 - 2.16787i) q^{31} +5.85919 q^{32} -1.76902 q^{34} +(-0.834404 + 0.606230i) q^{35} +(1.84130 - 5.66694i) q^{37} +(4.57646 + 3.32500i) q^{38} +(-0.787747 + 2.42443i) q^{40} +(-1.21637 - 3.74360i) q^{41} -7.64941 q^{43} +(4.59931 - 1.47039i) q^{44} +(1.46558 - 1.06481i) q^{46} +(-1.80557 - 5.55697i) q^{47} +(4.80253 + 3.48924i) q^{49} +(-0.596764 - 0.433574i) q^{50} +(-1.55168 - 4.77558i) q^{52} +(-9.58526 + 6.96410i) q^{53} +(-0.0156899 + 3.31659i) q^{55} -2.62920 q^{56} +(1.35725 + 4.17718i) q^{58} +(-0.910456 + 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-0.840701 + 2.58741i) q^{62} +(-1.82774 + 1.32793i) q^{64} +3.44899 q^{65} -6.14702 q^{67} +(-2.82471 + 2.05227i) q^{68} +(0.235096 - 0.723552i) q^{70} +(1.63676 + 1.18918i) q^{71} +(-0.255207 + 0.785446i) q^{73} +(1.35822 + 4.18017i) q^{74} +11.1649 q^{76} +(-3.25824 + 1.04165i) q^{77} +(9.77146 - 7.09938i) q^{79} +(0.318714 + 0.980901i) q^{80} +(2.34901 + 1.70666i) q^{82} +(1.30253 + 0.946345i) q^{83} +(-0.741089 - 2.28084i) q^{85} +(4.56489 - 3.31659i) q^{86} +(-5.00188 + 6.81645i) q^{88} -8.16116 q^{89} +(1.09924 + 3.38312i) q^{91} +(1.10489 - 3.40050i) q^{92} +(3.48685 + 2.53335i) q^{94} +(-2.36979 + 7.29347i) q^{95} +(-1.97625 + 1.43583i) q^{97} -4.37882 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8	$ 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8 + 2 * q^10 - 3 * q^11 - 2 * q^13 + 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 + 3 * q^20 - 7 * q^22 - 10 * q^23 - 2 * q^25 - 10 * q^26 - 6 * q^28 + 9 * q^29 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 + 24 * q^37 - 4 * q^40 - 8 * q^41 - 38 * q^43 + 12 * q^44 + 3 * q^46 + q^49 + 2 * q^50 - 28 * q^52 - 13 * q^53 + 7 * q^55 - 22 * q^56 + 12 * q^58 + 27 * q^59 + 6 * q^61 + 30 * q^62 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 + 16 * q^70 + 20 * q^71 + 13 * q^73 - 20 * q^74 - 34 * q^77 + 37 * q^79 - q^80 + 28 * q^82 - 27 * q^83 - 12 * q^85 + 3 * q^86 - 36 * q^88 + 16 * q^89 + 44 * q^91 - 11 * q^92 + 17 * q^94 + 15 * q^95 + 24 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.596764	+	0.433574i	−0.421976	+	0.306583i	−0.778432	−	0.627729i	$-0.783985\pi$
$2$	−0.596764	+	0.433574i	−0.421976	+	0.306583i	0.356457	+	0.934312i	$0.383985\pi$
$3$		0			0
$3$		0			0
$4$	−0.449894	+	1.38463i	−0.224947	+	0.692315i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	0.318714	−	0.980901i	0.120463	−	0.370746i	−0.872585	−	0.488463i	$-0.837558\pi$
$7$	0.318714	−	0.980901i	0.120463	−	0.370746i	0.993047	+	0.117717i	$0.0375577\pi$
$8$	−0.787747	−	2.42443i	−0.278510	−	0.857167i
$9$		0			0
$10$	0.737640			0.233262
$11$	−1.93675	−	2.69240i	−0.583951	−	0.811789i
$11$	−1.93675	−	2.69240i	−0.583951	−	0.811789i
$12$		0			0
$13$	−2.79029	+	2.02726i	−0.773887	+	0.562262i	−0.903138	−	0.429350i	$-0.858743\pi$
$13$	−2.79029	+	2.02726i	−0.773887	+	0.562262i	0.129251	+	0.991612i	$0.458743\pi$
$14$	0.235096	+	0.723552i	0.0628321	+	0.193377i
$15$		0			0
$16$	−0.834404	−	0.606230i	−0.208601	−	0.151557i
$17$	1.94020	+	1.40964i	0.470567	+	0.341887i	0.797662	−	0.603105i	$-0.206070\pi$
$17$	1.94020	+	1.40964i	0.470567	+	0.341887i	−0.327095	+	0.944991i	$0.606070\pi$
$18$		0			0
$19$	−2.36979	−	7.29347i	−0.543668	−	1.67324i	−0.724137	−	0.689656i	$-0.757762\pi$
$19$	−2.36979	−	7.29347i	−0.543668	−	1.67324i	0.180470	−	0.983581i	$-0.442238\pi$
$20$	1.17784	−	0.855749i	0.263372	−	0.191351i
$21$		0			0
$22$	2.32313	+	0.767001i	0.495294	+	0.163525i
$23$	−2.45589			−0.512088			−0.256044	−	0.966665i	$-0.582419\pi$
$23$	−2.45589			−0.512088			−0.256044	+	0.966665i	$0.582419\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	0.786174	−	2.41960i	0.154181	−	0.474522i
$27$		0			0
$28$	1.21480	+	0.882602i	0.229575	+	0.166796i
$29$	1.83998	−	5.66289i	0.341677	−	1.05157i	−0.621663	−	0.783285i	$-0.713542\pi$
$29$	1.83998	−	5.66289i	0.341677	−	1.05157i	0.963339	−	0.268287i	$-0.0864575\pi$
$30$		0			0
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	−0.286654	−	0.958034i	$-0.592543\pi$
$31$	2.98382	−	2.16787i	0.535909	−	0.389361i	0.822564	+	0.568673i	$0.192543\pi$
$32$	5.85919			1.03577
$33$		0			0
$34$	−1.76902			−0.303384
$35$	−0.834404	+	0.606230i	−0.141040	+	0.102472i
$36$		0			0
$37$	1.84130	−	5.66694i	0.302708	−	0.931640i	−0.677814	−	0.735233i	$-0.737073\pi$
$37$	1.84130	−	5.66694i	0.302708	−	0.931640i	0.980523	−	0.196407i	$-0.0629273\pi$
$38$	4.57646	+	3.32500i	0.742401	+	0.539386i
$39$		0			0
$40$	−0.787747	+	2.42443i	−0.124554	+	0.383337i
$41$	−1.21637	−	3.74360i	−0.189965	−	0.584652i	0.810033	−	0.586384i	$-0.199449\pi$
$41$	−1.21637	−	3.74360i	−0.189965	−	0.584652i	−0.999999	+	0.00173135i	$0.999449\pi$
$42$		0			0
$43$	−7.64941			−1.16652			−0.583262	−	0.812284i	$-0.698224\pi$
$43$	−7.64941			−1.16652			−0.583262	+	0.812284i	$0.698224\pi$
$44$	4.59931	−	1.47039i	0.693372	−	0.221669i
$45$		0			0
$46$	1.46558	−	1.06481i	0.216089	−	0.156998i
$47$	−1.80557	−	5.55697i	−0.263369	−	0.810567i	−0.992065	−	0.125729i	$-0.959873\pi$
$47$	−1.80557	−	5.55697i	−0.263369	−	0.810567i	0.728695	−	0.684838i	$-0.240127\pi$
$48$		0			0
$49$	4.80253	+	3.48924i	0.686076	+	0.498463i
$50$	−0.596764	−	0.433574i	−0.0843951	−	0.0613166i
$51$		0			0
$52$	−1.55168	−	4.77558i	−0.215179	−	0.662253i
$53$	−9.58526	+	6.96410i	−1.31664	+	0.956592i	−0.316669	+	0.948536i	$0.602564\pi$
$53$	−9.58526	+	6.96410i	−1.31664	+	0.956592i	−0.999968	+	0.00805607i	$0.997436\pi$
$54$		0			0
$55$	−0.0156899	+	3.31659i	−0.00211563	+	0.447209i
$56$	−2.62920			−0.351341
$57$		0			0
$58$	1.35725	+	4.17718i	0.178215	+	0.548490i
$59$	−0.910456	+	2.80210i	−0.118531	+	0.364802i	−0.992667	−	0.120880i	$-0.961428\pi$
$59$	−0.910456	+	2.80210i	−0.118531	+	0.364802i	0.874136	+	0.485681i	$0.161428\pi$
$60$		0			0
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	0.451864	−	0.892087i	$-0.350759\pi$
$61$	−2.00666	−	1.45792i	−0.256927	−	0.186668i	−0.708791	+	0.705419i	$0.750759\pi$
$62$	−0.840701	+	2.58741i	−0.106769	+	0.328602i
$63$		0			0
$64$	−1.82774	+	1.32793i	−0.228468	+	0.165992i
$65$	3.44899			0.427794
$66$		0			0
$67$	−6.14702			−0.750978			−0.375489	−	0.926827i	$-0.622525\pi$
$67$	−6.14702			−0.750978			−0.375489	+	0.926827i	$0.622525\pi$
$68$	−2.82471	+	2.05227i	−0.342546	+	0.248874i
$69$		0			0
$70$	0.235096	−	0.723552i	0.0280994	−	0.0864810i
$71$	1.63676	+	1.18918i	0.194248	+	0.141129i	0.680658	−	0.732601i	$-0.261694\pi$
$71$	1.63676	+	1.18918i	0.194248	+	0.141129i	−0.486410	+	0.873731i	$0.661694\pi$
$72$		0			0
$73$	−0.255207	+	0.785446i	−0.0298697	+	0.0919295i	−0.964880	−	0.262691i	$-0.915390\pi$
$73$	−0.255207	+	0.785446i	−0.0298697	+	0.0919295i	0.935010	+	0.354621i	$0.115390\pi$
$74$	1.35822	+	4.18017i	0.157890	+	0.485934i
$75$		0			0
$76$	11.1649			1.28070
$77$	−3.25824	+	1.04165i	−0.371311	+	0.118707i
$78$		0			0
$79$	9.77146	−	7.09938i	1.09937	−	0.798742i	0.118417	−	0.992964i	$-0.462218\pi$
$79$	9.77146	−	7.09938i	1.09937	−	0.798742i	0.980958	+	0.194221i	$0.0622180\pi$
$80$	0.318714	+	0.980901i	0.0356333	+	0.109668i
$81$		0			0
$82$	2.34901	+	1.70666i	0.259405	+	0.188469i
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	0.656972	−	0.753915i	$-0.271837\pi$
$83$	1.30253	+	0.946345i	0.142971	+	0.103875i	−0.514000	+	0.857790i	$0.671837\pi$
$84$		0			0
$85$	−0.741089	−	2.28084i	−0.0803824	−	0.247392i
$86$	4.56489	−	3.31659i	0.492245	−	0.357637i
$87$		0			0
$88$	−5.00188	+	6.81645i	−0.533202	+	0.726636i
$89$	−8.16116			−0.865081			−0.432541	−	0.901614i	$-0.642383\pi$
$89$	−8.16116			−0.865081			−0.432541	+	0.901614i	$0.642383\pi$
$90$		0			0
$91$	1.09924	+	3.38312i	0.115232	+	0.354647i
$92$	1.10489	−	3.40050i	0.115193	−	0.354526i
$93$		0			0
$94$	3.48685	+	2.53335i	0.359642	+	0.261295i
$95$	−2.36979	+	7.29347i	−0.243136	+	0.748294i
$96$		0			0
$97$	−1.97625	+	1.43583i	−0.200658	+	0.145787i	−0.683577	−	0.729879i	$-0.739577\pi$
$97$	−1.97625	+	1.43583i	−0.200658	+	0.145787i	0.482919	+	0.875665i	$0.339577\pi$
$98$	−4.37882			−0.442328
$99$		0			0
$100$	−1.45589			−0.145589
$101$	−6.08683	+	4.42234i	−0.605662	+	0.440039i	−0.847884	−	0.530182i	$-0.822124\pi$
$101$	−6.08683	+	4.42234i	−0.605662	+	0.440039i	0.242222	+	0.970221i	$0.422124\pi$
$102$		0			0
$103$	−2.93020	+	9.01821i	−0.288721	+	0.888591i	0.696538	+	0.717520i	$0.254723\pi$
$103$	−2.93020	+	9.01821i	−0.288721	+	0.888591i	−0.985259	+	0.171071i	$0.945277\pi$
$104$	7.11301	+	5.16791i	0.697488	+	0.506755i
$105$		0			0
$106$	2.70068	−	8.31184i	0.262313	−	0.807317i
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	0.996164	−	0.0875039i	$-0.0278890\pi$
$107$	1.43593	+	4.41935i	0.138817	+	0.427235i	−0.857347	+	0.514739i	$0.827889\pi$
$108$		0			0
$109$	−5.32826			−0.510355			−0.255178	−	0.966894i	$-0.582134\pi$
$109$	−5.32826			−0.510355			−0.255178	+	0.966894i	$0.582134\pi$
$110$	−1.42862	−	1.98602i	−0.136214	−	0.189360i
$111$		0			0
$112$	−0.860587	+	0.625253i	−0.0813179	+	0.0590809i
$113$	−0.0942195	−	0.289978i	−0.00886342	−	0.0272788i	0.946527	−	0.322625i	$-0.104565\pi$
$113$	−0.0942195	−	0.289978i	−0.00886342	−	0.0272788i	−0.955390	+	0.295346i	$0.904565\pi$
$114$		0			0
$115$	1.98685	+	1.44353i	0.185275	+	0.134610i
$116$	7.01321	+	5.09540i	0.651160	+	0.473096i
$117$		0			0
$118$	−0.671589	−	2.06694i	−0.0618248	−	0.190277i
$119$	2.00108	−	1.45387i	0.183439	−	0.133276i
$120$		0			0
$121$	−3.49802	+	10.4290i	−0.318001	+	0.948090i
$122$	1.82962			0.165646
$123$		0			0
$124$	1.65930	+	5.10680i	0.149009	+	0.458604i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	9.63536	+	7.00050i	0.855000	+	0.621194i	0.926520	−	0.376245i	$-0.122785\pi$
$127$	9.63536	+	7.00050i	0.855000	+	0.621194i	−0.0715199	+	0.997439i	$0.522785\pi$
$128$	−3.10621	+	9.55992i	−0.274552	+	0.844985i
$129$		0			0
$130$	−2.05823	+	1.49539i	−0.180519	+	0.131155i
$131$	11.1875			0.977452			0.488726	−	0.872437i	$-0.337462\pi$
$131$	11.1875			0.977452			0.488726	+	0.872437i	$0.337462\pi$
$132$		0			0
$133$	−7.90945			−0.685837
$134$	3.66832	−	2.66519i	0.316894	−	0.230237i
$135$		0			0
$136$	1.88919	−	5.81432i	0.161996	−	0.498573i
$137$	−3.46360	−	2.51645i	−0.295915	−	0.214995i	0.429914	−	0.902870i	$-0.358544\pi$
$137$	−3.46360	−	2.51645i	−0.295915	−	0.214995i	−0.725829	+	0.687875i	$0.758544\pi$
$138$		0			0
$139$	−1.83964	+	5.66183i	−0.156036	+	0.480230i	−0.998264	−	0.0588913i	$-0.981243\pi$
$139$	−1.83964	+	5.66183i	−0.156036	+	0.480230i	0.842228	+	0.539121i	$0.181243\pi$
$140$	−0.464011	−	1.42808i	−0.0392161	−	0.120695i
$141$		0			0
$142$	−1.49235			−0.125236
$143$	10.8623	+	3.58627i	0.908351	+	0.299899i
$144$		0			0
$145$	−4.81714	+	3.49986i	−0.400042	+	0.290647i
$146$	−0.188251	−	0.579377i	−0.0155798	−	0.0479495i
$147$		0			0
$148$	7.01823	+	5.09905i	0.576895	+	0.419139i
$149$	−3.06168	−	2.22444i	−0.250823	−	0.182233i	0.455269	−	0.890354i	$-0.349543\pi$
$149$	−3.06168	−	2.22444i	−0.250823	−	0.182233i	−0.706091	+	0.708121i	$0.749543\pi$
$150$		0			0
$151$	−7.52661	−	23.1645i	−0.612507	−	1.88510i	−0.433159	−	0.901317i	$-0.642601\pi$
$151$	−7.52661	−	23.1645i	−0.612507	−	1.88510i	−0.179348	−	0.983786i	$-0.557399\pi$
$152$	−15.8157	+	11.4908i	−1.28283	+	0.932028i
$153$		0			0
$154$	1.49277	−	2.03431i	0.120291	−	0.163929i
$155$	−3.68820			−0.296243
$156$		0			0
$157$	2.23484	+	6.87813i	0.178360	+	0.548935i	0.999771	−	0.0214015i	$-0.00681284\pi$
$157$	2.23484	+	6.87813i	0.178360	+	0.548935i	−0.821411	+	0.570336i	$0.806813\pi$
$158$	−2.75314	+	8.47330i	−0.219028	+	0.674100i
$159$		0			0
$160$	−4.74018	−	3.44395i	−0.374744	−	0.272268i
$161$	−0.782725	+	2.40898i	−0.0616874	+	0.189854i
$162$		0			0
$163$	−15.1198	+	10.9852i	−1.18428	+	0.860428i	−0.992648	−	0.121039i	$-0.961377\pi$
$163$	−15.1198	+	10.9852i	−1.18428	+	0.860428i	−0.191630	+	0.981467i	$0.561377\pi$
$164$	5.73074			0.447496
$165$		0			0
$166$	−1.18761			−0.0921767
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	−0.314172	−	0.949366i	$-0.601727\pi$
$167$	6.35343	−	4.61604i	0.491644	−	0.357200i	0.805816	+	0.592166i	$0.201727\pi$
$168$		0			0
$169$	−0.341302	+	1.05042i	−0.0262540	+	0.0808014i
$170$	1.43117	+	1.03980i	0.109766	+	0.0797493i
$171$		0			0
$172$	3.44142	−	10.5916i	0.262406	−	0.807603i
$173$	−3.46244	−	10.6563i	−0.263244	−	0.810183i	−0.992093	−	0.125508i	$-0.959944\pi$
$173$	−3.46244	−	10.6563i	−0.263244	−	0.810183i	0.728848	−	0.684675i	$-0.240056\pi$
$174$		0			0
$175$	1.03138			0.0779650
$176$	−0.0161823	+	3.42066i	−0.00121979	+	0.257842i
$177$		0			0
$178$	4.87028	−	3.53847i	0.365043	−	0.265219i
$179$	−0.452595	−	1.39295i	−0.0338286	−	0.104114i	0.932716	−	0.360611i	$-0.117432\pi$
$179$	−0.452595	−	1.39295i	−0.0338286	−	0.104114i	−0.966545	+	0.256497i	$0.917432\pi$
$180$		0			0
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	0.272357	−	0.962196i	$-0.412197\pi$
$181$	−7.51496	−	5.45994i	−0.558583	−	0.405834i	−0.830940	+	0.556362i	$0.812197\pi$
$182$	−2.12282	−	1.54232i	−0.157354	−	0.114324i
$183$		0			0
$184$	1.93462	+	5.95414i	0.142622	+	0.438945i
$185$	−4.82059	+	3.50236i	−0.354417	+	0.257499i
$186$		0			0
$187$	0.0376278	−	7.95389i	0.00275162	−	0.581646i
$188$	8.50666			0.620412
$189$		0			0
$190$	−1.74805	−	5.37996i	−0.126817	−	0.390303i
$191$	1.38222	−	4.25404i	0.100014	−	0.307811i	−0.888514	−	0.458850i	$-0.848262\pi$
$191$	1.38222	−	4.25404i	0.100014	−	0.307811i	0.988528	+	0.151038i	$0.0482617\pi$
$192$		0			0
$193$	18.3372	+	13.3227i	1.31994	+	0.958992i	0.999933	+	0.0115772i	$0.00368521\pi$
$193$	18.3372	+	13.3227i	1.31994	+	0.958992i	0.320007	+	0.947415i	$0.396315\pi$
$194$	0.556816	−	1.71370i	0.0399771	−	0.123037i
$195$		0			0
$196$	−6.99194	+	5.07994i	−0.499424	+	0.362853i
$197$	11.2080			0.798535			0.399267	−	0.916835i	$-0.369265\pi$
$197$	11.2080			0.798535			0.399267	+	0.916835i	$0.369265\pi$
$198$		0			0
$199$	−7.81979			−0.554330			−0.277165	−	0.960822i	$-0.589395\pi$
$199$	−7.81979			−0.554330			−0.277165	+	0.960822i	$0.589395\pi$
$200$	2.06235	−	1.49838i	0.145830	−	0.105952i
$201$		0			0
$202$	1.71499	−	5.27818i	0.120666	−	0.371372i
$203$	−4.96830	−	3.60968i	−0.348707	−	0.253350i
$204$		0			0
$205$	−1.21637	+	3.74360i	−0.0849550	+	0.261464i
$206$	−2.16143	−	6.65220i	−0.150594	−	0.463481i
$207$		0			0
$208$	3.55722			0.246649
$209$	−15.0472	+	20.5060i	−1.04084	+	1.41843i
$210$		0			0
$211$	18.4189	−	13.3821i	1.26801	−	0.921262i	0.268887	−	0.963172i	$-0.413344\pi$
$211$	18.4189	−	13.3821i	1.26801	−	0.921262i	0.999121	+	0.0419098i	$0.0133442\pi$
$212$	−5.33035	−	16.4051i	−0.366090	−	1.12671i
$213$		0			0
$214$	−2.77303	−	2.01472i	−0.189560	−	0.137724i
$215$	6.18851	+	4.49621i	0.422053	+	0.306639i
$216$		0			0
$217$	−1.17548	−	3.61776i	−0.0797969	−	0.245589i
$218$	3.17971	−	2.31020i	0.215357	−	0.156466i
$219$		0			0
$220$	−4.58519	−	1.51384i	−0.309133	−	0.102063i
$221$	−8.27142			−0.556396
$222$		0			0
$223$	−4.95746	−	15.2575i	−0.331976	−	1.02172i	−0.968192	−	0.250207i	$-0.919501\pi$
$223$	−4.95746	−	15.2575i	−0.331976	−	1.02172i	0.636216	−	0.771511i	$-0.280499\pi$
$224$	1.86741	−	5.74728i	0.124771	−	0.384006i
$225$		0			0
$226$	0.181954	+	0.132197i	0.0121034	+	0.00879361i
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	−0.320809	−	0.947144i	$-0.603955\pi$
$227$	7.46468	−	22.9739i	0.495448	−	1.52483i	0.816257	−	0.577689i	$-0.196045\pi$
$228$		0			0
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	−0.109017	−	0.994040i	$-0.534770\pi$
$229$	12.1468	−	8.82517i	0.802684	−	0.583184i	0.911700	+	0.410856i	$0.134770\pi$
$230$	−1.81156			−0.119451
$231$		0			0
$232$	−15.1787			−0.996534
$233$	9.24378	−	6.71600i	0.605580	−	0.439980i	−0.242275	−	0.970208i	$-0.577894\pi$
$233$	9.24378	−	6.71600i	0.605580	−	0.439980i	0.847855	+	0.530228i	$0.177894\pi$
$234$		0			0
$235$	−1.80557	+	5.55697i	−0.117782	+	0.362497i
$236$	−3.47026	−	2.52129i	−0.225895	−	0.164122i
$237$		0			0
$238$	−0.563811	+	1.73523i	−0.0365465	+	0.112478i
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	−0.714181	−	0.699961i	$-0.753201\pi$
$239$	−8.46914	−	26.0653i	−0.547823	−	1.68603i	0.166358	−	0.986065i	$-0.446799\pi$
$240$		0			0
$241$	10.9387			0.704624			0.352312	−	0.935883i	$-0.385396\pi$
$241$	10.9387			0.704624			0.352312	+	0.935883i	$0.385396\pi$
$242$	−2.43425	−	7.74029i	−0.156480	−	0.497565i
$243$		0			0
$244$	2.92147	−	2.12257i	0.187028	−	0.135884i
$245$	−1.83440	−	5.64571i	−0.117196	−	0.360691i
$246$		0			0
$247$	21.3982	+	15.5467i	1.36154	+	0.989213i
$248$	−7.60635	−	5.52634i	−0.483004	−	0.350923i
$249$		0			0
$250$	0.227943	+	0.701538i	0.0144164	+	0.0443691i
$251$	13.9403	−	10.1282i	0.879902	−	0.639286i	−0.0533238	−	0.998577i	$-0.516982\pi$
$251$	13.9403	−	10.1282i	0.879902	−	0.639286i	0.933225	+	0.359291i	$0.116982\pi$
$252$		0			0
$253$	4.75643	+	6.61222i	0.299034	+	0.415707i
$254$	−8.78527			−0.551237
$255$		0			0
$256$	−3.68753	−	11.3491i	−0.230471	−	0.709316i
$257$	−5.71540	+	17.5902i	−0.356517	+	1.09725i	0.598608	+	0.801042i	$0.295721\pi$
$257$	−5.71540	+	17.5902i	−0.356517	+	1.09725i	−0.955125	+	0.296204i	$0.904279\pi$
$258$		0			0
$259$	−4.97186	−	3.61227i	−0.308936	−	0.224455i
$260$	−1.55168	+	4.77558i	−0.0962310	+	0.296169i
$261$		0			0
$262$	−6.67626	+	4.85059i	−0.412461	+	0.299670i
$263$	−3.69135			−0.227618			−0.113809	−	0.993503i	$-0.536305\pi$
$263$	−3.69135			−0.227618			−0.113809	+	0.993503i	$0.536305\pi$
$264$		0			0
$265$	11.8480			0.727819
$266$	4.72007	−	3.42933i	0.289406	−	0.210266i
$267$		0			0
$268$	2.76550	−	8.51135i	0.168930	−	0.519913i
$269$	−8.04575	−	5.84558i	−0.490558	−	0.356411i	0.314841	−	0.949145i	$-0.398049\pi$
$269$	−8.04575	−	5.84558i	−0.490558	−	0.356411i	−0.805399	+	0.592733i	$0.798049\pi$
$270$		0			0
$271$	0.387400	−	1.19229i	0.0235329	−	0.0724267i	−0.938600	−	0.345006i	$-0.887877\pi$
$271$	0.387400	−	1.19229i	0.0235329	−	0.0724267i	0.962133	+	0.272580i	$0.0878768\pi$
$272$	−0.764345	−	2.35241i	−0.0463452	−	0.142636i
$273$		0			0
$274$	3.15802			0.190783
$275$	1.96213	−	2.67395i	0.118321	−	0.161245i
$276$		0			0
$277$	6.54763	−	4.75713i	0.393409	−	0.285828i	−0.373442	−	0.927654i	$-0.621823\pi$
$277$	6.54763	−	4.75713i	0.393409	−	0.285828i	0.766851	+	0.641825i	$0.221823\pi$
$278$	−1.35699	−	4.17639i	−0.0813870	−	0.250483i
$279$		0			0
$280$	2.12706	+	1.54540i	0.127116	+	0.0923554i
$281$	20.5250	+	14.9123i	1.22442	+	0.889591i	0.996459	−	0.0840804i	$-0.0267953\pi$
$281$	20.5250	+	14.9123i	1.22442	+	0.889591i	0.227958	+	0.973671i	$0.426795\pi$
$282$		0			0
$283$	−6.31705	−	19.4419i	−0.375510	−	1.15570i	−0.943134	−	0.332412i	$-0.892137\pi$
$283$	−6.31705	−	19.4419i	−0.375510	−	1.15570i	0.567624	−	0.823288i	$-0.307863\pi$
$284$	−2.38294	+	1.73131i	−0.141401	+	0.102734i
$285$		0			0
$286$	−8.03714	+	2.56945i	−0.475246	+	0.151935i
$287$	−4.05977			−0.239641
$288$		0			0
$289$	−3.47600	−	10.6980i	−0.204470	−	0.629295i
$290$	1.35725	−	4.17718i	0.0797003	−	0.245292i
$291$		0			0
$292$	−0.972737	−	0.706734i	−0.0569251	−	0.0413585i
$293$	−0.787705	+	2.42431i	−0.0460182	+	0.141630i	−0.971426	−	0.237344i	$-0.923723\pi$
$293$	−0.787705	+	2.42431i	−0.0460182	+	0.141630i	0.925407	+	0.378974i	$0.123723\pi$
$294$		0			0
$295$	2.38361	−	1.73179i	0.138779	−	0.100829i
$296$	−15.1896			−0.882878
$297$		0			0
$298$	2.79156			0.161711
$299$	6.85264	−	4.97873i	0.396298	−	0.287928i
$300$		0			0
$301$	−2.43797	+	7.50331i	−0.140523	+	0.432484i
$302$	14.5352	+	10.5604i	0.836404	+	0.607683i
$303$		0			0
$304$	−2.44416	+	7.52234i	−0.140182	+	0.431436i
$305$	0.766476	+	2.35897i	0.0438883	+	0.135074i
$306$		0			0
$307$	8.99273			0.513242			0.256621	−	0.966512i	$-0.417391\pi$
$307$	8.99273			0.513242			0.256621	+	0.966512i	$0.417391\pi$
$308$	0.0235596	−	4.98010i	0.00134243	−	0.283767i
$309$		0			0
$310$	2.20098	−	1.59911i	0.125008	−	0.0908233i
$311$	6.21840	+	19.1383i	0.352613	+	1.08523i	0.957380	+	0.288830i	$0.0932662\pi$
$311$	6.21840	+	19.1383i	0.352613	+	1.08523i	−0.604767	+	0.796402i	$0.706734\pi$
$312$		0			0
$313$	−5.74792	−	4.17611i	−0.324892	−	0.236048i	0.413368	−	0.910564i	$-0.364352\pi$
$313$	−5.74792	−	4.17611i	−0.324892	−	0.236048i	−0.738260	+	0.674516i	$0.764352\pi$
$314$	−4.31585	−	3.13565i	−0.243558	−	0.176955i
$315$		0			0
$316$	5.43390	+	16.7238i	0.305681	+	0.940789i
$317$	1.85526	−	1.34793i	0.104202	−	0.0757071i	−0.534464	−	0.845191i	$-0.679487\pi$
$317$	1.85526	−	1.34793i	0.104202	−	0.0757071i	0.638666	+	0.769484i	$0.279487\pi$
$318$		0			0
$319$	−18.8103	+	6.01362i	−1.05318	+	0.336698i
$320$	2.25922			0.126294
$321$		0			0
$322$	−0.577370	−	1.77696i	−0.0321756	−	0.0990262i
$323$	5.68327	−	17.4913i	0.316226	−	0.973242i
$324$		0			0
$325$	−2.79029	−	2.02726i	−0.154777	−	0.112452i
$326$	4.26007	−	13.1111i	0.235943	−	0.726159i
$327$		0			0
$328$	−8.11793	+	5.89802i	−0.448237	+	0.325664i
$329$	−6.02629			−0.332240
$330$		0			0
$331$	15.3951			0.846192			0.423096	−	0.906085i	$-0.360943\pi$
$331$	15.3951			0.846192			0.423096	+	0.906085i	$0.360943\pi$
$332$	−1.89634	+	1.37777i	−0.104075	+	0.0756150i
$333$		0			0
$334$	−1.79010	+	5.50937i	−0.0979501	+	0.301459i
$335$	4.97304	+	3.61313i	0.271706	+	0.197406i
$336$		0			0
$337$	−6.02485	+	18.5426i	−0.328195	+	1.01008i	0.641783	+	0.766886i	$0.278195\pi$
$337$	−6.02485	+	18.5426i	−0.328195	+	1.01008i	−0.969978	+	0.243193i	$0.921805\pi$
$338$	−0.251758	−	0.774831i	−0.0136938	−	0.0421453i
$339$		0			0
$340$	3.49153			0.189355
$341$	−11.6157	−	3.83501i	−0.629024	−	0.207677i
$342$		0			0
$343$	10.7941	−	7.84234i	0.582825	−	0.423447i
$344$	6.02580	+	18.5455i	0.324889	+	0.999907i
$345$		0			0
$346$	6.68655	+	4.85806i	0.359471	+	0.261171i
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	0.539687	−	0.841866i	$-0.318543\pi$
$347$	−1.75479	−	1.27493i	−0.0942023	−	0.0684420i	−0.633889	+	0.773424i	$0.718543\pi$
$348$		0			0
$349$	−7.74150	−	23.8259i	−0.414393	−	1.27537i	−0.912793	−	0.408423i	$-0.866079\pi$
$349$	−7.74150	−	23.8259i	−0.414393	−	1.27537i	0.498400	−	0.866947i	$-0.333921\pi$
$350$	−0.615490	+	0.447180i	−0.0328993	+	0.0239028i
$351$		0			0
$352$	−11.3478	−	15.7753i	−0.604838	−	0.840825i
$353$	23.2532			1.23764			0.618821	−	0.785532i	$-0.287611\pi$
$353$	23.2532			1.23764			0.618821	+	0.785532i	$0.287611\pi$
$354$		0			0
$355$	−0.625187	−	1.92413i	−0.0331815	−	0.102122i
$356$	3.67166	−	11.3002i	0.194597	−	0.598909i
$357$		0			0
$358$	0.874037	+	0.635025i	0.0461943	+	0.0335621i
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	−0.999043	−	0.0437429i	$-0.986072\pi$
$359$	−3.12799	+	9.62695i	−0.165089	+	0.508091i	0.833954	+	0.551834i	$0.186072\pi$
$360$		0			0
$361$	−32.2075	+	23.4001i	−1.69513	+	1.23158i
$362$	6.85194			0.360130
$363$		0			0
$364$	−5.17891			−0.271448
$365$	0.668140	−	0.485432i	0.0349721	−	0.0254087i
$366$		0			0
$367$	1.14622	−	3.52770i	0.0598322	−	0.184145i	−0.916673	−	0.399638i	$-0.869136\pi$
$367$	1.14622	−	3.52770i	0.0598322	−	0.184145i	0.976505	+	0.215493i	$0.0691359\pi$
$368$	2.04920	+	1.48883i	0.106822	+	0.0776107i
$369$		0			0
$370$	1.35822	−	4.18017i	0.0706104	−	0.217316i
$371$	3.77613	+	11.6217i	0.196047	+	0.603371i
$372$		0			0
$373$	−9.34017			−0.483616			−0.241808	−	0.970324i	$-0.577740\pi$
$373$	−9.34017			−0.483616			−0.241808	+	0.970324i	$0.577740\pi$
$374$	3.42615	+	4.76291i	0.177162	+	0.246284i
$375$		0			0
$376$	−12.0502	+	8.75496i	−0.621440	+	0.451503i
$377$	6.34609	+	19.5312i	0.326840	+	1.00591i
$378$		0			0
$379$	7.93783	+	5.76717i	0.407739	+	0.296240i	0.772686	−	0.634789i	$-0.218913\pi$
$379$	7.93783	+	5.76717i	0.407739	+	0.296240i	−0.364947	+	0.931028i	$0.618913\pi$
$380$	−9.03261	−	6.56257i	−0.463363	−	0.336653i
$381$		0			0
$382$	1.01958	+	3.13795i	0.0521663	+	0.160552i
$383$	−14.6002	+	10.6076i	−0.746034	+	0.542025i	−0.894595	−	0.446878i	$-0.852536\pi$
$383$	−14.6002	+	10.6076i	−0.746034	+	0.542025i	0.148561	+	0.988903i	$0.452536\pi$
$384$		0			0
$385$	3.24824	+	1.07243i	0.165546	+	0.0546562i
$386$	−16.7194			−0.850993
$387$		0			0
$388$	−1.09899	−	3.38235i	−0.0557929	−	0.171713i
$389$	−9.63871	+	29.6649i	−0.488702	+	1.50407i	0.337844	+	0.941202i	$0.390302\pi$
$389$	−9.63871	+	29.6649i	−0.488702	+	1.50407i	−0.826546	+	0.562869i	$0.809698\pi$
$390$		0			0
$391$	−4.76490	−	3.46191i	−0.240972	−	0.175076i
$392$	4.67626	−	14.3921i	0.236187	−	0.726909i
$393$		0			0
$394$	−6.68851	+	4.85948i	−0.336962	+	0.244817i
$395$	−12.0782			−0.607719
$396$		0			0
$397$	−10.6212			−0.533062			−0.266531	−	0.963826i	$-0.585877\pi$
$397$	−10.6212			−0.533062			−0.266531	+	0.963826i	$0.585877\pi$
$398$	4.66657	−	3.39046i	0.233914	−	0.169948i
$399$		0			0
$400$	0.318714	−	0.980901i	0.0159357	−	0.0490450i
$401$	−22.3029	−	16.2040i	−1.11375	−	0.809190i	−0.130503	−	0.991448i	$-0.541659\pi$
$401$	−22.3029	−	16.2040i	−1.11375	−	0.809190i	−0.983251	+	0.182258i	$0.941659\pi$
$402$		0			0
$403$	−3.93087	+	12.0980i	−0.195811	+	0.602643i
$404$	−3.38488	−	10.4176i	−0.168404	−	0.518295i
$405$		0			0
$406$	4.52997			0.224818
$407$	−18.8238	+	6.01792i	−0.933061	+	0.298297i
$408$		0			0
$409$	−11.6241	+	8.44540i	−0.574774	+	0.417598i	−0.836836	−	0.547453i	$-0.815598\pi$
$409$	−11.6241	+	8.44540i	−0.574774	+	0.417598i	0.262062	+	0.965051i	$0.415598\pi$
$410$	−0.897243	−	2.76143i	−0.0443117	−	0.136377i
$411$		0			0
$412$	−11.1686	−	8.11448i	−0.550238	−	0.399772i
$413$	2.45840	+	1.78613i	0.120970	+	0.0878899i
$414$		0			0
$415$	−0.497523	−	1.53122i	−0.0244224	−	0.0751645i
$416$	−16.3488	+	11.8781i	−0.801568	+	0.582373i
$417$		0			0
$418$	0.0887552	−	18.7613i	0.00434116	−	0.917647i
$419$	31.4707			1.53744			0.768722	−	0.639584i	$-0.220893\pi$
$419$	31.4707			1.53744			0.768722	+	0.639584i	$0.220893\pi$
$420$		0			0
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	0.924856	+	0.380318i	$0.124185\pi$
$421$	8.21095	+	25.2707i	0.400177	+	1.23162i	−0.524679	+	0.851300i	$0.675815\pi$
$422$	−5.18959	+	15.9719i	−0.252625	+	0.777500i
$423$		0			0
$424$	24.4348	+	17.7529i	1.18666	+	0.862156i
$425$	−0.741089	+	2.28084i	−0.0359481	+	0.110637i
$426$		0			0
$427$	−2.06963	+	1.50367i	−0.100156	+	0.0727679i
$428$	−6.76518			−0.327008
$429$		0			0
$430$	−5.64252			−0.272106
$431$	−3.12984	+	2.27397i	−0.150759	+	0.109533i	−0.660608	−	0.750731i	$-0.729701\pi$
$431$	−3.12984	+	2.27397i	−0.150759	+	0.109533i	0.509849	+	0.860264i	$0.329701\pi$
$432$		0			0
$433$	12.4036	−	38.1743i	0.596077	−	1.83454i	0.0467895	−	0.998905i	$-0.485101\pi$
$433$	12.4036	−	38.1743i	0.596077	−	1.83454i	0.549288	−	0.835633i	$-0.314899\pi$
$434$	2.27005	+	1.64929i	0.108966	+	0.0791684i
$435$		0			0
$436$	2.39715	−	7.37768i	0.114803	−	0.353327i
$437$	5.81994	+	17.9119i	0.278406	+	0.856844i
$438$		0			0
$439$	1.02336			0.0488425			0.0244212	−	0.999702i	$-0.492226\pi$
$439$	1.02336			0.0488425			0.0244212	+	0.999702i	$0.492226\pi$
$440$	8.05321	−	2.57459i	0.383922	−	0.122739i
$441$		0			0
$442$	4.93608	−	3.58627i	0.234785	−	0.170582i
$443$	4.96678	+	15.2862i	0.235979	+	0.726268i	0.996990	+	0.0775295i	$0.0247032\pi$
$443$	4.96678	+	15.2862i	0.235979	+	0.726268i	−0.761011	+	0.648739i	$0.775297\pi$
$444$		0			0
$445$	6.60252	+	4.79701i	0.312989	+	0.227400i
$446$	9.57368	+	6.95569i	0.453327	+	0.329361i
$447$		0			0
$448$	0.720043	+	2.21607i	0.0340188	+	0.104699i
$449$	28.9969	−	21.0675i	1.36845	−	0.994235i	0.370590	−	0.928797i	$-0.379156\pi$
$449$	28.9969	−	21.0675i	1.36845	−	0.994235i	0.997857	−	0.0654379i	$-0.0208444\pi$
$450$		0			0
$451$	−7.72346	+	10.5254i	−0.363684	+	0.495620i
$452$	0.443901			0.0208793
$453$		0			0
$454$	5.50625	+	16.9465i	0.258421	+	0.795338i
$455$	1.09924	−	3.38312i	0.0515332	−	0.158603i
$456$		0			0
$457$	20.3488	+	14.7842i	0.951875	+	0.691578i	0.951250	−	0.308422i	$-0.0998009\pi$
$457$	20.3488	+	14.7842i	0.951875	+	0.691578i	0.000625413		1.00000i	$0.499801\pi$
$458$	−3.42241	+	10.5331i	−0.159919	+	0.492179i
$459$		0			0
$460$	−2.89263	+	2.10162i	−0.134870	+	0.0979886i
$461$	−6.65631			−0.310015			−0.155008	−	0.987913i	$-0.549540\pi$
$461$	−6.65631			−0.310015			−0.155008	+	0.987913i	$0.549540\pi$
$462$		0			0
$463$	38.7730			1.80194			0.900968	−	0.433886i	$-0.142858\pi$
$463$	38.7730			1.80194			0.900968	+	0.433886i	$0.142858\pi$
$464$	−4.96830	+	3.60968i	−0.230648	+	0.167575i
$465$		0			0
$466$	−2.60447	+	8.01573i	−0.120650	+	0.371321i
$467$	18.2429	+	13.2542i	0.844179	+	0.613332i	0.923535	−	0.383514i	$-0.125286\pi$
$467$	18.2429	+	13.2542i	0.844179	+	0.613332i	−0.0793559	+	0.996846i	$0.525286\pi$
$468$		0			0
$469$	−1.95914	+	6.02961i	−0.0904647	+	0.278422i
$470$	−1.33186	−	4.09904i	−0.0614341	−	0.189075i
$471$		0			0
$472$	7.51071			0.345708
$473$	14.8150	+	20.5953i	0.681194	+	0.946971i
$474$		0			0
$475$	6.20420	−	4.50761i	0.284668	−	0.206823i
$476$	1.11280	+	3.42484i	0.0510051	+	0.156977i
$477$		0			0
$478$	16.3553	+	11.8828i	0.748075	+	0.543509i
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	0.557216	−	0.830368i	$-0.311870\pi$
$479$	−1.32021	−	0.959186i	−0.0603218	−	0.0438263i	−0.617538	+	0.786541i	$0.711870\pi$
$480$		0			0
$481$	6.35063	+	19.5452i	0.289564	+	0.891186i
$482$	−6.52782	+	4.74274i	−0.297334	+	0.216026i
$483$		0			0
$484$	−12.8666	−	9.53540i	−0.584844	−	0.433427i
$485$	2.44278			0.110921
$486$		0			0
$487$	0.324560	+	0.998894i	0.0147072	+	0.0452642i	0.958141	−	0.286297i	$-0.0924245\pi$
$487$	0.324560	+	0.998894i	0.0147072	+	0.0452642i	−0.943434	+	0.331562i	$0.892425\pi$
$488$	−1.95390	+	6.01349i	−0.0884490	+	0.272218i
$489$		0			0
$490$	3.54254	+	2.57381i	0.160036	+	0.116273i
$491$	4.29969	−	13.2331i	0.194042	−	0.597201i	−0.805944	−	0.591992i	$-0.798342\pi$
$491$	4.29969	−	13.2331i	0.194042	−	0.597201i	0.999986	−	0.00520928i	$-0.00165817\pi$
$492$		0			0
$493$	11.5525	−	8.39341i	0.520300	−	0.378020i
$494$	−19.5103			−0.877811
$495$		0			0
$496$	−3.80394			−0.170802
$497$	1.68812	−	1.22649i	0.0757226	−	0.0550157i
$498$		0			0
$499$	5.36679	−	16.5173i	0.240250	−	0.739415i	−0.756131	−	0.654420i	$-0.772913\pi$
$499$	5.36679	−	16.5173i	0.240250	−	0.739415i	0.996381	−	0.0849943i	$-0.0270872\pi$
$500$	1.17784	+	0.855749i	0.0526745	+	0.0382702i
$501$		0			0
$502$	−3.92772	+	12.0883i	−0.175303	+	0.539526i
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	−0.818502	−	0.574503i	$-0.805195\pi$
$503$	−11.0794	−	34.0988i	−0.494005	−	1.52039i	0.324498	−	0.945887i	$-0.394805\pi$
$504$		0			0
$505$	7.52373			0.334802
$506$	−5.70536	−	1.88367i	−0.253634	−	0.0837393i
$507$		0			0
$508$	−14.0280	+	10.1919i	−0.622392	+	0.452194i
$509$	−0.660921	−	2.03410i	−0.0292948	−	0.0901601i	0.935340	−	0.353750i	$-0.115094\pi$
$509$	−0.660921	−	2.03410i	−0.0292948	−	0.0901601i	−0.964635	+	0.263590i	$0.915094\pi$
$510$		0			0
$511$	0.689106	+	0.500665i	0.0304843	+	0.0221481i
$512$	−9.14306	−	6.64282i	−0.404070	−	0.293574i
$513$		0			0
$514$	−4.21591	−	12.9752i	−0.185956	−	0.572313i
$515$	7.67135	−	5.57356i	0.338040	−	0.245601i
$516$		0			0
$517$	−11.4646	+	15.6238i	−0.504214	+	0.687132i
$518$	4.53321			0.199178
$519$		0			0
$520$	−2.71693	−	8.36185i	−0.119145	−	0.366691i
$521$	3.93540	−	12.1119i	0.172413	−	0.530633i	−0.827093	−	0.562065i	$-0.810007\pi$
$521$	3.93540	−	12.1119i	0.172413	−	0.530633i	0.999506	+	0.0314326i	$0.0100070\pi$
$522$		0			0
$523$	−19.3426	−	14.0532i	−0.845793	−	0.614504i	0.0781901	−	0.996938i	$-0.475086\pi$
$523$	−19.3426	−	14.0532i	−0.845793	−	0.614504i	−0.923983	+	0.382434i	$0.875086\pi$
$524$	−5.03317	+	15.4905i	−0.219875	+	0.676705i
$525$		0			0
$526$	2.20286	−	1.60047i	0.0960493	−	0.0697839i
$527$	8.84510			0.385299
$528$		0			0
$529$	−16.9686			−0.737766
$530$	−7.07047	+	5.13700i	−0.307122	+	0.223137i
$531$		0			0
$532$	3.55841	−	10.9517i	0.154277	−	0.474815i
$533$	10.9833	+	7.97983i	0.475739	+	0.345645i
$534$		0			0
$535$	1.43593	−	4.41935i	0.0620808	−	0.191065i
$536$	4.84229	+	14.9030i	0.209155	+	0.643713i
$537$		0			0
$538$	7.33590			0.316273
$539$	0.0931395	−	19.6881i	0.00401180	−	0.848027i
$540$		0			0
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	−0.610491	−	0.792023i	$-0.709028\pi$
$541$	−1.06726	+	0.775410i	−0.0458851	+	0.0333375i	0.564606	+	0.825360i	$0.309028\pi$
$542$	0.285762	+	0.879484i	0.0122745	+	0.0377771i
$543$		0			0
$544$	11.3680	+	8.25932i	0.487398	+	0.354116i
$545$	4.31066	+	3.13188i	0.184648	+	0.134155i
$546$		0			0
$547$	2.88044	+	8.86507i	0.123159	+	0.379043i	0.993561	−	0.113298i	$-0.0361414\pi$
$547$	2.88044	+	8.86507i	0.123159	+	0.379043i	−0.870403	+	0.492341i	$0.836141\pi$
$548$	5.04261	−	3.66367i	0.215410	−	0.156504i
$549$		0			0
$550$	−0.0115735	+	2.44645i	−0.000493497	+	0.104317i
$551$	−45.6625			−1.94529
$552$		0			0
$553$	−3.84949	−	11.8475i	−0.163697	−	0.503807i
$554$	−1.84482	+	5.67776i	−0.0783788	+	0.241225i
$555$		0			0
$556$	−7.01190	−	5.09444i	−0.297371	−	0.216052i
$557$	−12.1497	+	37.3929i	−0.514798	+	1.58439i	0.268850	+	0.963182i	$0.413356\pi$
$557$	−12.1497	+	37.3929i	−0.514798	+	1.58439i	−0.783648	+	0.621205i	$0.786644\pi$
$558$		0			0
$559$	21.3441	−	15.5074i	0.902759	−	0.655893i
$560$	1.06374			0.0449514
$561$		0			0
$562$	−18.7141			−0.789407
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	−0.192508	−	0.981295i	$-0.561662\pi$
$563$	16.1649	−	11.7445i	0.681271	−	0.494972i	0.873779	+	0.486323i	$0.161662\pi$
$564$		0			0
$565$	−0.0942195	+	0.289978i	−0.00396384	+	0.0121995i
$566$	12.1993	+	8.86330i	0.512774	+	0.372552i
$567$		0			0
$568$	1.59373	−	4.90499i	0.0668713	−	0.205809i
$569$	10.6811	+	32.8730i	0.447775	+	1.37811i	0.879412	+	0.476061i	$0.157936\pi$
$569$	10.6811	+	32.8730i	0.447775	+	1.37811i	−0.431637	+	0.902047i	$0.642064\pi$
$570$		0			0
$571$	3.15090			0.131861			0.0659306	−	0.997824i	$-0.478998\pi$
$571$	3.15090			0.131861			0.0659306	+	0.997824i	$0.478998\pi$
$572$	−9.85254	+	13.4268i	−0.411955	+	0.561404i
$573$		0			0
$574$	2.42273	−	1.76021i	0.101123	−	0.0734699i
$575$	−0.758911	−	2.33569i	−0.0316488	−	0.0974049i
$576$		0			0
$577$	−22.1044	−	16.0598i	−0.920220	−	0.668579i	0.0233590	−	0.999727i	$-0.492564\pi$
$577$	−22.1044	−	16.0598i	−0.920220	−	0.668579i	−0.943579	+	0.331148i	$0.892564\pi$
$578$	6.71273	+	4.87709i	0.279213	+	0.202860i
$579$		0			0
$580$	−2.67881	−	8.24453i	−0.111231	−	0.342335i
$581$	1.34340	−	0.976041i	0.0557338	−	0.0404930i
$582$		0			0
$583$	37.3143	+	12.3196i	1.54540	+	0.510227i
$584$	2.10530			0.0871180
$585$		0			0
$586$	−0.581043	−	1.78827i	−0.0240027	−	0.0738726i
$587$	14.2667	−	43.9082i	0.588848	−	1.81229i	0.00561158	−	0.999984i	$-0.498214\pi$
$587$	14.2667	−	43.9082i	0.588848	−	1.81229i	0.583236	−	0.812303i	$-0.301786\pi$
$588$		0			0
$589$	−22.8823	−	16.6250i	−0.942850	−	0.685020i
$590$	−0.671589	+	2.06694i	−0.0276489	+	0.0850945i
$591$		0			0
$592$	−4.97186	+	3.61227i	−0.204342	+	0.148463i
$593$	−39.4265			−1.61905			−0.809525	−	0.587085i	$-0.800275\pi$
$593$	−39.4265			−1.61905			−0.809525	+	0.587085i	$0.800275\pi$
$594$		0			0
$595$	−2.47347			−0.101402
$596$	4.45746	−	3.23853i	0.182585	−	0.132656i
$597$		0			0
$598$	−1.93075	+	5.94225i	−0.0789544	+	0.242997i
$599$	0.848455	+	0.616438i	0.0346669	+	0.0251870i	0.604984	−	0.796238i	$-0.293180\pi$
$599$	0.848455	+	0.616438i	0.0346669	+	0.0251870i	−0.570317	+	0.821425i	$0.693180\pi$
$600$		0			0
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	−0.618904	−	0.785466i	$-0.712423\pi$
$601$	8.42065	−	25.9161i	0.343485	−	1.05714i	0.962390	−	0.271673i	$-0.0875768\pi$
$602$	−1.79835	−	5.53475i	−0.0732952	−	0.225579i
$603$		0			0
$604$	35.4605			1.44287
$605$	8.95996	−	6.38115i	0.364274	−	0.259431i
$606$		0			0
$607$	−17.7350	+	12.8852i	−0.719842	+	0.522996i	−0.886334	−	0.463047i	$-0.846756\pi$
$607$	−17.7350	+	12.8852i	−0.719842	+	0.522996i	0.166492	+	0.986043i	$0.446756\pi$
$608$	−13.8851	−	42.7338i	−0.563114	−	1.73309i
$609$		0			0
$610$	−1.48019	−	1.07542i	−0.0599313	−	0.0435426i
$611$	16.3035	+	11.8452i	0.659569	+	0.479205i
$612$		0			0
$613$	3.27313	+	10.0736i	0.132200	+	0.406871i	0.995144	−	0.0984293i	$-0.0313818\pi$
$613$	3.27313	+	10.0736i	0.132200	+	0.406871i	−0.862944	+	0.505300i	$0.831382\pi$
$614$	−5.36653	+	3.89901i	−0.216576	+	0.157351i
$615$		0			0
$616$	5.09209	+	7.07884i	0.205166	+	0.285215i
$617$	−4.60402			−0.185351			−0.0926755	−	0.995696i	$-0.529542\pi$
$617$	−4.60402			−0.185351			−0.0926755	+	0.995696i	$0.529542\pi$
$618$		0			0
$619$	11.4348	+	35.1926i	0.459603	+	1.41451i	0.865645	+	0.500657i	$0.166908\pi$
$619$	11.4348	+	35.1926i	0.459603	+	1.41451i	−0.406043	+	0.913854i	$0.633092\pi$
$620$	1.65930	−	5.10680i	0.0666390	−	0.205094i
$621$		0			0
$622$	−12.0088	−	8.72489i	−0.481508	−	0.349836i
$623$	−2.60108	+	8.00529i	−0.104210	+	0.320725i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	5.24081			0.209465
$627$		0			0
$628$	−10.5291			−0.420157
$629$	11.5608	−	8.39942i	0.460960	−	0.334907i
$630$		0			0
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	0.673875	+	0.738845i	$0.264628\pi$
$631$	−7.67617	+	23.6248i	−0.305583	+	0.940489i	−0.979459	+	0.201644i	$0.935372\pi$
$632$	−24.9094	−	18.0977i	−0.990843	−	0.719890i
$633$		0			0
$634$	−0.522727	+	1.60879i	−0.0207601	+	0.0638931i
$635$	−3.68038	−	11.3270i	−0.146051	−	0.449500i
$636$		0			0
$637$	−20.4741			−0.811213
$638$	8.61798	−	11.7444i	0.341189	−	0.464965i
$639$		0			0
$640$	8.13215	−	5.90835i	0.321452	−	0.233548i
$641$	13.7294	+	42.2547i	0.542278	+	1.66896i	0.727374	+	0.686241i	$0.240740\pi$
$641$	13.7294	+	42.2547i	0.542278	+	1.66896i	−0.185096	+	0.982720i	$0.559260\pi$
$642$		0			0
$643$	−20.9220	−	15.2007i	−0.825082	−	0.599457i	0.0930818	−	0.995658i	$-0.470328\pi$
$643$	−20.9220	−	15.2007i	−0.825082	−	0.599457i	−0.918164	+	0.396201i	$0.870328\pi$
$644$	−2.98341	−	2.16757i	−0.117563	−	0.0854143i
$645$		0			0
$646$	4.19221	+	12.9023i	0.164940	+	0.507634i
$647$	15.7649	−	11.4539i	0.619782	−	0.450298i	−0.233063	−	0.972462i	$-0.574875\pi$
$647$	15.7649	−	11.4539i	0.619782	−	0.450298i	0.852845	+	0.522163i	$0.174875\pi$
$648$		0			0
$649$	9.30768	−	2.97564i	0.365358	−	0.116804i
$650$	2.54411			0.0997883
$651$		0			0
$652$	−8.40814	−	25.8776i	−0.329288	−	1.01344i
$653$	5.16979	−	15.9110i	0.202310	−	0.622645i	−0.797504	−	0.603314i	$-0.793847\pi$
$653$	5.16979	−	15.9110i	0.202310	−	0.622645i	0.999813	−	0.0193305i	$-0.00615349\pi$
$654$		0			0
$655$	−9.05084	−	6.57582i	−0.353646	−	0.256939i
$656$	−1.25454	+	3.86108i	−0.0489815	+	0.150750i
$657$		0			0
$658$	3.59627	−	2.61284i	0.140197	−	0.101859i
$659$	1.66127			0.0647137			0.0323569	−	0.999476i	$-0.489699\pi$
$659$	1.66127			0.0647137			0.0323569	+	0.999476i	$0.489699\pi$
$660$		0			0
$661$	−44.0130			−1.71191			−0.855953	−	0.517053i	$-0.827029\pi$
$661$	−44.0130			−1.71191			−0.855953	+	0.517053i	$0.827029\pi$
$662$	−9.18724	+	6.67492i	−0.357072	+	0.259428i
$663$		0			0
$664$	1.26829	−	3.90338i	0.0492190	−	0.151481i
$665$	6.39888	+	4.64906i	0.248138	+	0.180283i
$666$		0			0
$667$	−4.51879	+	13.9074i	−0.174968	+	0.538497i
$668$	3.53314	+	10.8739i	0.136701	+	0.420723i
$669$		0			0
$670$	−4.53429			−0.175175
$671$	−0.0389168	+	8.22636i	−0.00150237	+	0.317575i
$672$		0			0
$673$	31.2239	−	22.6855i	1.20359	−	0.874462i	0.208961	−	0.977924i	$-0.432992\pi$
$673$	31.2239	−	22.6855i	1.20359	−	0.874462i	0.994633	+	0.103462i	$0.0329920\pi$
$674$	−4.44417	−	13.6778i	−0.171183	−	0.526848i
$675$		0			0
$676$	−1.30089	−	0.945154i	−0.0500343	−	0.0363521i
$677$	−31.2271	−	22.6878i	−1.20016	−	0.871964i	−0.205855	−	0.978582i	$-0.565998\pi$
$677$	−31.2271	−	22.6878i	−1.20016	−	0.871964i	−0.994300	+	0.106619i	$0.965998\pi$
$678$		0			0
$679$	0.778549	+	2.39613i	0.0298780	+	0.0919549i
$680$	−4.94595	+	3.59344i	−0.189669	+	0.137802i
$681$		0			0
$682$	8.59457	−	2.74766i	0.329103	−	0.105213i
$683$	0.748158			0.0286275			0.0143137	−	0.999898i	$-0.495444\pi$
$683$	0.748158			0.0286275			0.0143137	+	0.999898i	$0.495444\pi$
$684$		0			0
$685$	1.32298	+	4.07170i	0.0505484	+	0.155572i
$686$	−3.04126	+	9.36005i	−0.116116	+	0.357368i
$687$		0			0
$688$	6.38270	+	4.63730i	0.243338	+	0.176796i
$689$	12.6276	−	38.8637i	0.481073	−	1.48059i
$690$		0			0
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	−0.665234	−	0.746635i	$-0.731668\pi$
$691$	−4.22456	+	3.06932i	−0.160710	+	0.116763i	0.504524	+	0.863398i	$0.331668\pi$
$692$	16.3128			0.620118
$693$		0			0
$694$	1.59998			0.0607342
$695$	4.81624	−	3.49920i	0.182690	−	0.132732i
$696$		0			0
$697$	2.91712	−	8.97796i	0.110494	−	0.340065i
$698$	14.9501	+	10.8619i	0.565871	+	0.411129i
$699$		0			0
$700$	−0.464011	+	1.42808i	−0.0175380	+	0.0539764i
$701$	4.37506	+	13.4650i	0.165244	+	0.508568i	0.999054	−	0.0434831i	$-0.0138455\pi$
$701$	4.37506	+	13.4650i	0.165244	+	0.508568i	−0.833811	+	0.552051i	$0.813845\pi$
$702$		0			0
$703$	−45.6952			−1.72343
$704$	7.11520	+	2.34914i	0.268164	+	0.0885366i
$705$		0			0
$706$	−13.8766	+	10.0820i	−0.522255	+	0.379440i
$707$	2.39792	+	7.38004i	0.0901830	+	0.277555i
$708$		0			0
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	0.817744	−	0.575583i	$-0.195225\pi$
$709$	13.9267	+	10.1183i	0.523028	+	0.380002i	−0.294715	+	0.955585i	$0.595225\pi$
$710$	1.20734	+	0.877184i	0.0453107	+	0.0329201i
$711$		0			0
$712$	6.42893	+	19.7862i	0.240934	+	0.741519i
$713$	−7.32792	+	5.32404i	−0.274433	+	0.199387i
$714$		0			0
$715$	−6.67982	−	9.28605i	−0.249811	−	0.347279i
$716$	2.13233			0.0796891
$717$		0			0
$718$	−2.30733	−	7.10123i	−0.0861087	−	0.265015i
$719$	8.20624	−	25.2562i	0.306041	−	0.941897i	−0.673246	−	0.739419i	$-0.735100\pi$
$719$	8.20624	−	25.2562i	0.306041	−	0.941897i	0.979287	−	0.202478i	$-0.0648996\pi$
$720$		0			0
$721$	7.91208	+	5.74846i	0.294661	+	0.214084i
$722$	9.07457	−	27.9286i	0.337720	−	1.03940i
$723$		0			0
$724$	10.9409	−	7.94905i	0.406617	−	0.295424i
$725$	5.95431			0.221138
$726$		0			0
$727$	44.1917			1.63898			0.819490	−	0.573094i	$-0.194257\pi$
$727$	44.1917			1.63898			0.819490	+	0.573094i	$0.194257\pi$
$728$	7.33622	−	5.33007i	0.271898	−	0.197546i
$729$		0			0
$730$	−0.188251	+	0.579377i	−0.00696748	+	0.0214437i
$731$	−14.8414	−	10.7829i	−0.548928	−	0.398819i
$732$		0			0
$733$	7.71320	−	23.7388i	0.284894	−	0.876812i	−0.701537	−	0.712633i	$-0.747502\pi$
$733$	7.71320	−	23.7388i	0.284894	−	0.876812i	0.986431	−	0.164179i	$-0.0524975\pi$
$734$	0.845498	+	2.60218i	0.0312079	+	0.0960480i
$735$		0			0
$736$	−14.3895			−0.530404
$737$	11.9052	+	16.5502i	0.438534	+	0.609635i
$738$		0			0
$739$	−17.1789	+	12.4812i	−0.631934	+	0.459127i	−0.857070	−	0.515200i	$-0.827718\pi$
$739$	−17.1789	+	12.4812i	−0.631934	+	0.459127i	0.225135	+	0.974327i	$0.427718\pi$
$740$	−2.68073	−	8.25043i	−0.0985455	−	0.303292i
$741$		0			0
$742$	−7.29234	−	5.29820i	−0.267710	−	0.194503i
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	0.0311852	−	0.999514i	$-0.490072\pi$
$743$	−24.7986	−	18.0172i	−0.909772	−	0.660988i	−0.940957	+	0.338526i	$0.890072\pi$
$744$		0			0
$745$	1.16946	+	3.59922i	0.0428456	+	0.131865i
$746$	5.57387	−	4.04965i	0.204074	−	0.148268i
$747$		0			0
$748$	10.9963	+	3.63051i	0.402064	+	0.132744i
$749$	4.79259			0.175118
$750$		0			0
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	−0.963300	−	0.268427i	$-0.913496\pi$
$751$	−9.36548	−	28.8240i	−0.341751	−	1.05180i	0.621549	−	0.783375i	$-0.286504\pi$
$752$	−1.86223	+	5.73134i	−0.0679084	+	0.209001i
$753$		0			0
$754$	−12.2554	−	8.90404i	−0.446314	−	0.324266i
$755$	−7.52661	+	23.1645i	−0.273922	+	0.843044i
$756$		0			0
$757$	28.2099	−	20.4957i	1.02531	−	0.744929i	0.0579427	−	0.998320i	$-0.481546\pi$
$757$	28.2099	−	20.4957i	1.02531	−	0.744929i	0.967364	+	0.253391i	$0.0815459\pi$
$758$	−7.23750			−0.262878
$759$		0			0
$760$	19.5493			0.709129
$761$	−2.17603	+	1.58098i	−0.0788809	+	0.0573104i	−0.626527	−	0.779400i	$-0.715524\pi$
$761$	−2.17603	+	1.58098i	−0.0788809	+	0.0573104i	0.547646	+	0.836710i	$0.315524\pi$
$762$		0			0
$763$	−1.69819	+	5.22650i	−0.0614787	+	0.189212i
$764$	5.26842	+	3.82773i	0.190605	+	0.138482i
$765$		0			0
$766$	4.11365	−	12.6605i	0.148632	−	0.457443i
$767$	−3.14015	−	9.66440i	−0.113384	−	0.348961i
$768$		0			0
$769$	−32.5735			−1.17463			−0.587315	−	0.809359i	$-0.699815\pi$
$769$	−32.5735			−1.17463			−0.587315	+	0.809359i	$0.699815\pi$
$770$	−2.40341	+	0.768365i	−0.0866129	+	0.0276899i
$771$		0			0
$772$	−26.6969	+	19.3964i	−0.960841	+	0.698092i
$773$	−12.8748	−	39.6246i	−0.463074	−	1.42520i	−0.861388	−	0.507947i	$-0.830405\pi$
$773$	−12.8748	−	39.6246i	−0.463074	−	1.42520i	0.398314	−	0.917249i	$-0.369595\pi$
$774$		0			0
$775$	2.98382	+	2.16787i	0.107182	+	0.0778722i
$776$	5.03787	+	3.66022i	0.180849	+	0.131394i
$777$		0			0
$778$	−7.10990	−	21.8820i	−0.254902	−	0.784509i
$779$	−24.4213	+	17.7431i	−0.874984	+	0.635713i
$780$		0			0
$781$	0.0317431	−	6.70994i	0.00113586	−	0.240101i
$782$	4.34451			0.155359
$783$		0			0
$784$	−1.89197	−	5.82288i	−0.0675703	−	0.207960i
$785$	2.23484	−	6.87813i	0.0797649	−	0.245491i
$786$		0			0
$787$	29.0605	+	21.1137i	1.03589	+	0.752622i	0.969480	−	0.245170i	$-0.0788439\pi$
$787$	29.0605	+	21.1137i	1.03589	+	0.752622i	0.0664148	+	0.997792i	$0.478844\pi$
$788$	−5.04239	+	15.5189i	−0.179628	+	0.552838i
$789$		0			0
$790$	7.20782	−	5.23679i	0.256443	−	0.186317i
$791$	−0.314468			−0.0111812
$792$		0			0
$793$	8.55476			0.303789
$794$	6.33833	−	4.60507i	0.224939	−	0.163428i
$795$		0			0
$796$	3.51808	−	10.8275i	0.124695	−	0.383771i
$797$	−25.6618	−	18.6444i	−0.908987	−	0.660418i	0.0317713	−	0.999495i	$-0.489885\pi$
$797$	−25.6618	−	18.6444i	−0.908987	−	0.660418i	−0.940759	+	0.339077i	$0.889885\pi$
$798$		0			0
$799$	4.33014	−	13.3268i	0.153189	−	0.471468i
$800$	1.81059	+	5.57242i	0.0640140	+	0.197015i
$801$		0			0
$802$	20.3352			0.718061
$803$	2.60900	−	0.834092i	0.0920698	−	0.0294345i
$804$		0			0
$805$	2.04920	−	1.48883i	0.0722249	−	0.0524744i
$806$	−2.89957	−	8.92396i	−0.102133	−	0.314333i
$807$		0			0
$808$	15.5166	+	11.2734i	0.545870	+	0.396598i
$809$	−6.88936	−	5.00541i	−0.242217	−	0.175981i	0.460053	−	0.887891i	$-0.347830\pi$
$809$	−6.88936	−	5.00541i	−0.242217	−	0.175981i	−0.702270	+	0.711910i	$0.747830\pi$
$810$		0			0
$811$	2.79052	+	8.58832i	0.0979882	+	0.301577i	0.988021	−	0.154320i	$-0.0493186\pi$
$811$	2.79052	+	8.58832i	0.0979882	+	0.301577i	−0.890033	+	0.455897i	$0.849319\pi$
$812$	7.23329	−	5.25529i	0.253839	−	0.184425i
$813$		0			0
$814$	8.62415	−	11.7528i	0.302276	−	0.411935i
$815$	18.6892			0.654653
$816$		0			0
$817$	18.1275	+	55.7908i	0.634202	+	1.95187i
$818$	3.27513	−	10.0798i	0.114512	−	0.352432i
$819$		0			0
$820$	−4.63627	−	3.36845i	−0.161906	−	0.117631i
$821$	16.7866	−	51.6638i	0.585856	−	1.80308i	−0.00994979	−	0.999950i	$-0.503167\pi$
$821$	16.7866	−	51.6638i	0.585856	−	1.80308i	0.595806	−	0.803129i	$-0.296833\pi$
$822$		0			0
$823$	−14.4486	+	10.4975i	−0.503646	+	0.365920i	−0.810408	−	0.585866i	$-0.800755\pi$
$823$	−14.4486	+	10.4975i	−0.503646	+	0.365920i	0.306762	+	0.951786i	$0.400755\pi$
$824$	24.1723			0.842083
$825$		0			0
$826$	−2.24151			−0.0779920
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.478474	+	0.878102i	$0.658810\pi$
$827$	−42.0280	+	30.5351i	−1.46146	+	1.06181i	−0.982981	+	0.183708i	$0.941190\pi$
$828$		0			0
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	0.787431	+	0.616402i	$0.211410\pi$
$829$	−6.10185	+	18.7796i	−0.211926	+	0.652241i	−0.999358	+	0.0358392i	$0.988590\pi$
$830$	0.960800	+	0.698062i	0.0333498	+	0.0242301i
$831$		0			0
$832$	2.40786	−	7.41064i	0.0834776	−	0.256918i
$833$	4.39930	+	13.5396i	0.152427	+	0.469121i
$834$		0			0
$835$	−7.85328			−0.271774
$836$	−21.6236	−	30.0604i	−0.747869	−	1.03966i
$837$		0			0
$838$	−18.7806	+	13.6449i	−0.648763	+	0.471354i
$839$	1.27207	+	3.91502i	0.0439166	+	0.135162i	0.970611	−	0.240655i	$-0.0773623\pi$
$839$	1.27207	+	3.91502i	0.0439166	+	0.135162i	−0.926694	+	0.375817i	$0.877362\pi$
$840$		0			0
$841$	−5.22128	−	3.79348i	−0.180044	−	0.130810i
$842$	−15.8567	−	11.5206i	−0.546458	−	0.397025i
$843$		0			0
$844$	10.2427	+	31.5239i	0.352569	+	1.08510i
$845$	0.893540	−	0.649194i	0.0307387	−	0.0223330i
$846$		0			0
$847$	9.11494	+	6.75507i	0.313193	+	0.232107i
$848$	12.2198			0.419630
$849$		0			0
$850$	−0.546657	−	1.68244i	−0.0187502	−	0.0577072i
$851$	−4.52203	+	13.9174i	−0.155013	+	0.477081i
$852$		0			0
$853$	−4.45190	−	3.23449i	−0.152430	−	0.110747i	0.508956	−	0.860792i	$-0.330032\pi$
$853$	−4.45190	−	3.23449i	−0.152430	−	0.110747i	−0.661386	+	0.750046i	$0.730032\pi$
$854$	0.583125	−	1.79468i	0.0199541	−	0.0614125i
$855$		0			0
$856$	9.58327	−	6.96265i	0.327549	−	0.237979i
$857$	26.9281			0.919847			0.459924	−	0.887959i	$-0.347877\pi$
$857$	26.9281			0.919847			0.459924	+	0.887959i	$0.347877\pi$
$858$		0			0
$859$	19.1519			0.653456			0.326728	−	0.945118i	$-0.394054\pi$
$859$	19.1519			0.653456			0.326728	+	0.945118i	$0.394054\pi$
$860$	−9.00976	+	6.54598i	−0.307230	+	0.223216i
$861$		0			0
$862$	0.881845	−	2.71404i	0.0300358	−	0.0924405i
$863$	4.01394	+	2.91630i	0.136636	+	0.0992720i	0.654004	−	0.756491i	$-0.273088\pi$
$863$	4.01394	+	2.91630i	0.136636	+	0.0992720i	−0.517368	+	0.855763i	$0.673088\pi$
$864$		0			0
$865$	−3.46244	+	10.6563i	−0.117726	+	0.362325i
$866$	9.14937	+	28.1589i	0.310908	+	0.956877i
$867$		0			0
$868$	5.53810			0.187975
$869$	−38.0392	−	12.5589i	−1.29039	−	0.426033i
$870$		0			0
$871$	17.1520	−	12.4616i	0.581172	−	0.422246i
$872$	4.19732	+	12.9180i	0.142139	+	0.437460i
$873$		0			0
$874$	−11.2393	−	8.16581i	−0.380174	−	0.276213i
$875$	−0.834404	−	0.606230i	−0.0282080	−	0.0204943i
$876$		0			0
$877$	−8.40691	−	25.8738i	−0.283881	−	0.873696i	−0.986732	−	0.162359i	$-0.948090\pi$
$877$	−8.40691	−	25.8738i	−0.283881	−	0.873696i	0.702851	−	0.711338i	$-0.251910\pi$
$878$	−0.610706	+	0.443704i	−0.0206103	+	0.0149743i
$879$		0			0
$880$	2.02371	−	2.75786i	0.0682191	−	0.0929675i
$881$	−10.3570			−0.348935			−0.174467	−	0.984663i	$-0.555820\pi$
$881$	−10.3570			−0.348935			−0.174467	+	0.984663i	$0.555820\pi$
$882$		0			0
$883$	2.28515	+	7.03296i	0.0769014	+	0.236678i	0.982116	−	0.188276i	$-0.0602901\pi$
$883$	2.28515	+	7.03296i	0.0769014	+	0.236678i	−0.905215	+	0.424954i	$0.860290\pi$
$884$	3.72126	−	11.4529i	0.125159	−	0.385201i
$885$		0			0
$886$	−9.59168	−	6.96877i	−0.322239	−	0.234120i
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	−0.812605	−	0.582815i	$-0.801951\pi$
$887$	5.58054	−	17.1752i	0.187376	−	0.576685i	0.999981	+	0.00612989i	$0.00195122\pi$
$888$		0			0
$889$	9.93772	−	7.22018i	0.333300	−	0.242157i
$890$	−6.02000			−0.201791
$891$		0			0
$892$	23.3563			0.782027
$893$	−36.2507	+	26.3377i	−1.21309	+	0.881358i
$894$		0			0
$895$	−0.452595	+	1.39295i	−0.0151286	+	0.0465610i
$896$	8.38734	+	6.09376i	0.280201	+	0.203578i
$897$		0			0
$898$	−8.16997	+	25.1446i	−0.272635	+	0.839085i
$899$	−6.78623	−	20.8859i	−0.226334	−	0.696583i
$900$		0			0
$901$	−28.4141			−0.946612
$902$	0.0455564	−	9.62985i	0.00151686	−	0.320639i
$903$		0			0
$904$	−0.628811	+	0.456858i	−0.0209139	+	0.0151949i
$905$	2.87046	+	8.83437i	0.0954173	+	0.293664i
$906$		0			0
$907$	−21.2748	−	15.4570i	−0.706417	−	0.513242i	0.175599	−	0.984462i	$-0.443814\pi$
$907$	−21.2748	−	15.4570i	−0.706417	−	0.513242i	−0.882016	+	0.471220i	$0.843814\pi$
$908$	28.4521	+	20.6716i	0.944215	+	0.686013i
$909$		0			0
$910$	0.810844	+	2.49552i	0.0268792	+	0.0827258i
$911$	23.1774	−	16.8394i	0.767902	−	0.557913i	−0.133422	−	0.991059i	$-0.542597\pi$
$911$	23.1774	−	16.8394i	0.767902	−	0.557913i	0.901324	+	0.433146i	$0.142597\pi$
$912$		0			0
$913$	0.0252611	−	5.33976i	0.000836020	−	0.176720i
$914$	−18.5535			−0.613694
$915$		0			0
$916$	6.75483	+	20.7892i	0.223186	+	0.686896i
$917$	3.56560	−	10.9738i	0.117746	−	0.362386i
$918$		0			0
$919$	−31.4358	−	22.8394i	−1.03697	−	0.753404i	−0.0672794	−	0.997734i	$-0.521432\pi$
$919$	−31.4358	−	22.8394i	−1.03697	−	0.753404i	−0.969692	+	0.244330i	$0.921432\pi$
$920$	1.93462	−	5.95414i	0.0637824	−	0.196302i
$921$		0			0
$922$	3.97224	−	2.88600i	0.130819	−	0.0950455i
$923$	−6.97781			−0.229677
$924$		0			0
$925$	5.95858			0.195917
$926$	−23.1383	+	16.8110i	−0.760373	+	0.552443i
$927$		0			0
$928$	10.7808	−	33.1799i	0.353898	−	1.08919i
$929$	6.00397	+	4.36214i	0.196984	+	0.143117i	0.681905	−	0.731441i	$-0.261152\pi$
$929$	6.00397	+	4.36214i	0.196984	+	0.143117i	−0.484921	+	0.874558i	$0.661152\pi$
$930$		0			0
$931$	14.0677	−	43.2959i	0.461050	−	1.41897i
$932$	5.14046	+	15.8207i	0.168381	+	0.518224i
$933$		0			0
$934$	−16.6334			−0.544260
$935$	−4.70562	+	6.41272i	−0.153890	+	0.209718i
$936$		0			0
$937$	12.0834	−	8.77914i	0.394749	−	0.286802i	−0.372650	−	0.927972i	$-0.621551\pi$
$937$	12.0834	−	8.77914i	0.394749	−	0.286802i	0.767399	+	0.641170i	$0.221551\pi$
$938$	−1.44514	−	4.44768i	−0.0471855	−	0.145222i
$939$		0			0
$940$	−6.88203	−	5.00009i	−0.224467	−	0.163085i
$941$	−42.3447	−	30.7652i	−1.38040	−	1.00292i	−0.996843	−	0.0793986i	$-0.974700\pi$
$941$	−42.3447	−	30.7652i	−1.38040	−	1.00292i	−0.383554	−	0.923518i	$-0.625300\pi$
$942$		0			0
$943$	2.98727	+	9.19386i	0.0972788	+	0.299393i
$944$	2.45840	−	1.78613i	0.0800142	−	0.0581337i
$945$		0			0
$946$	−17.7706	−	5.86711i	−0.577773	−	0.190756i
$947$	3.69553			0.120088			0.0600442	−	0.998196i	$-0.480876\pi$
$947$	3.69553			0.120088			0.0600442	+	0.998196i	$0.480876\pi$
$948$		0			0
$949$	−0.880206	−	2.70899i	−0.0285727	−	0.0879377i
$950$	−1.74805	+	5.37996i	−0.0567144	+	0.174549i
$951$		0			0
$952$	−5.10116	−	3.70621i	−0.165329	−	0.120119i
$953$	−13.3349	+	41.0406i	−0.431959	+	1.32943i	0.464211	+	0.885724i	$0.346338\pi$
$953$	−13.3349	+	41.0406i	−0.431959	+	1.32943i	−0.896171	+	0.443709i	$0.853662\pi$
$954$		0			0
$955$	−3.61870	+	2.62914i	−0.117098	+	0.0850770i
$956$	39.9011			1.29049
$957$		0			0
$958$	1.20373			0.0388907
$959$	−3.57229	+	2.59542i	−0.115355	+	0.0838104i
$960$		0			0
$961$	−5.37602	+	16.5457i	−0.173420	+	0.533732i
$962$	−12.2641	−	8.91041i	−0.395411	−	0.287283i
$963$		0			0
$964$	−4.92126	+	15.1461i	−0.158503	+	0.487822i
$965$	−7.00418	−	21.5567i	−0.225473	−	0.693933i
$966$		0			0
$967$	−29.2144			−0.939471			−0.469736	−	0.882807i	$-0.655651\pi$
$967$	−29.2144			−0.939471			−0.469736	+	0.882807i	$0.655651\pi$
$968$	28.0400	+	0.265306i	0.901238	+	0.00852725i
$969$		0			0
$970$	−1.45776	+	1.05913i	−0.0468060	+	0.0340065i
$971$	8.15948	+	25.1123i	0.261850	+	0.805892i	0.992402	+	0.123035i	$0.0392628\pi$
$971$	8.15948	+	25.1123i	0.261850	+	0.805892i	−0.730552	+	0.682857i	$0.760737\pi$
$972$		0			0
$973$	4.96737	+	3.60901i	0.159247	+	0.115699i
$974$	−0.626780	−	0.455382i	−0.0200833	−	0.0145914i
$975$		0			0
$976$	0.790528	+	2.43300i	0.0253042	+	0.0778783i
$977$	−12.8176	+	9.31251i	−0.410070	+	0.297934i	−0.773630	−	0.633637i	$-0.781561\pi$
$977$	−12.8176	+	9.31251i	−0.410070	+	0.297934i	0.363560	+	0.931571i	$0.381561\pi$
$978$		0			0
$979$	15.8061	+	21.9731i	0.505166	+	0.702263i
$980$	8.64252			0.276075
$981$		0			0
$982$	3.17163	+	9.76126i	0.101211	+	0.311494i
$983$	−10.8477	+	33.3858i	−0.345988	+	1.06484i	0.615064	+	0.788477i	$0.289130\pi$
$983$	−10.8477	+	33.3858i	−0.345988	+	1.06484i	−0.961053	+	0.276365i	$0.910870\pi$
$984$		0			0
$985$	−9.06744	−	6.58788i	−0.288913	−	0.209907i
$986$	−3.25497	+	10.0178i	−0.103659	+	0.319031i
$987$		0			0
$988$	−31.1534	+	22.6342i	−0.991120	+	0.720091i
$989$	18.7861			0.597363
$990$		0			0
$991$	18.9700			0.602600			0.301300	−	0.953529i	$-0.402579\pi$
$991$	18.9700			0.602600			0.301300	+	0.953529i	$0.402579\pi$
$992$	17.4828	−	12.7020i	0.555078	−	0.403288i
$993$		0			0
$994$	−0.475634	+	1.46385i	−0.0150862	+	0.0464306i
$995$	6.32635	+	4.59636i	0.200559	+	0.145714i
$996$		0			0
$997$	9.31213	−	28.6598i	0.294918	−	0.907665i	−0.688331	−	0.725397i	$-0.741656\pi$
$997$	9.31213	−	28.6598i	0.294918	−	0.907665i	0.983249	−	0.182268i	$-0.0583438\pi$
$998$	3.95876	+	12.1838i	0.125312	+	0.385672i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.e.91.1		8
3.2	odd	2		55.2.g.b.36.2	yes	8
11.2	odd	10		5445.2.a.bi.1.2		4
11.4	even	5	inner	495.2.n.e.136.1		8
11.9	even	5		5445.2.a.bp.1.3		4
12.11	even	2		880.2.bo.h.641.2		8
15.2	even	4		275.2.z.a.124.3		16
15.8	even	4		275.2.z.a.124.2		16
15.14	odd	2		275.2.h.a.201.1		8
33.2	even	10		605.2.a.k.1.3		4
33.5	odd	10		605.2.g.m.251.1		8
33.8	even	10		605.2.g.e.511.2		8
33.14	odd	10		605.2.g.m.511.1		8
33.17	even	10		605.2.g.e.251.2		8
33.20	odd	10		605.2.a.j.1.2		4
33.26	odd	10		55.2.g.b.26.2	✓	8
33.29	even	10		605.2.g.k.81.1		8
33.32	even	2		605.2.g.k.366.1		8
132.35	odd	10		9680.2.a.cm.1.4		4
132.59	even	10		880.2.bo.h.81.2		8
132.119	even	10		9680.2.a.cn.1.4		4
165.59	odd	10		275.2.h.a.26.1		8
165.92	even	20		275.2.z.a.224.2		16
165.119	odd	10		3025.2.a.bd.1.3		4
165.134	even	10		3025.2.a.w.1.2		4
165.158	even	20		275.2.z.a.224.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.2	✓	8	33.26	odd	10
55.2.g.b.36.2	yes	8	3.2	odd	2
275.2.h.a.26.1		8	165.59	odd	10
275.2.h.a.201.1		8	15.14	odd	2
275.2.z.a.124.2		16	15.8	even	4
275.2.z.a.124.3		16	15.2	even	4
275.2.z.a.224.2		16	165.92	even	20
275.2.z.a.224.3		16	165.158	even	20
495.2.n.e.91.1		8	1.1	even	1	trivial
495.2.n.e.136.1		8	11.4	even	5	inner
605.2.a.j.1.2		4	33.20	odd	10
605.2.a.k.1.3		4	33.2	even	10
605.2.g.e.251.2		8	33.17	even	10
605.2.g.e.511.2		8	33.8	even	10
605.2.g.k.81.1		8	33.29	even	10
605.2.g.k.366.1		8	33.32	even	2
605.2.g.m.251.1		8	33.5	odd	10
605.2.g.m.511.1		8	33.14	odd	10
880.2.bo.h.81.2		8	132.59	even	10
880.2.bo.h.641.2		8	12.11	even	2
3025.2.a.w.1.2		4	165.134	even	10
3025.2.a.bd.1.3		4	165.119	odd	10
5445.2.a.bi.1.2		4	11.2	odd	10
5445.2.a.bp.1.3		4	11.9	even	5
9680.2.a.cm.1.4		4	132.35	odd	10
9680.2.a.cn.1.4		4	132.119	even	10

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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.596764 + 0.433574i) q^{2} +(-0.449894 + 1.38463i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.318714 - 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +O(q^{10})\)	\(q+(-0.596764 + 0.433574i) q^{2} +(-0.449894 + 1.38463i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.318714 - 0.980901i) q^{7} +(-0.787747 - 2.42443i) q^{8} +0.737640 q^{10} +(-1.93675 - 2.69240i) q^{11} +(-2.79029 + 2.02726i) q^{13} +(0.235096 + 0.723552i) q^{14} +(-0.834404 - 0.606230i) q^{16} +(1.94020 + 1.40964i) q^{17} +(-2.36979 - 7.29347i) q^{19} +(1.17784 - 0.855749i) q^{20} +(2.32313 + 0.767001i) q^{22} -2.45589 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.786174 - 2.41960i) q^{26} +(1.21480 + 0.882602i) q^{28} +(1.83998 - 5.66289i) q^{29} +(2.98382 - 2.16787i) q^{31} +5.85919 q^{32} -1.76902 q^{34} +(-0.834404 + 0.606230i) q^{35} +(1.84130 - 5.66694i) q^{37} +(4.57646 + 3.32500i) q^{38} +(-0.787747 + 2.42443i) q^{40} +(-1.21637 - 3.74360i) q^{41} -7.64941 q^{43} +(4.59931 - 1.47039i) q^{44} +(1.46558 - 1.06481i) q^{46} +(-1.80557 - 5.55697i) q^{47} +(4.80253 + 3.48924i) q^{49} +(-0.596764 - 0.433574i) q^{50} +(-1.55168 - 4.77558i) q^{52} +(-9.58526 + 6.96410i) q^{53} +(-0.0156899 + 3.31659i) q^{55} -2.62920 q^{56} +(1.35725 + 4.17718i) q^{58} +(-0.910456 + 2.80210i) q^{59} +(-2.00666 - 1.45792i) q^{61} +(-0.840701 + 2.58741i) q^{62} +(-1.82774 + 1.32793i) q^{64} +3.44899 q^{65} -6.14702 q^{67} +(-2.82471 + 2.05227i) q^{68} +(0.235096 - 0.723552i) q^{70} +(1.63676 + 1.18918i) q^{71} +(-0.255207 + 0.785446i) q^{73} +(1.35822 + 4.18017i) q^{74} +11.1649 q^{76} +(-3.25824 + 1.04165i) q^{77} +(9.77146 - 7.09938i) q^{79} +(0.318714 + 0.980901i) q^{80} +(2.34901 + 1.70666i) q^{82} +(1.30253 + 0.946345i) q^{83} +(-0.741089 - 2.28084i) q^{85} +(4.56489 - 3.31659i) q^{86} +(-5.00188 + 6.81645i) q^{88} -8.16116 q^{89} +(1.09924 + 3.38312i) q^{91} +(1.10489 - 3.40050i) q^{92} +(3.48685 + 2.53335i) q^{94} +(-2.36979 + 7.29347i) q^{95} +(-1.97625 + 1.43583i) q^{97} -4.37882 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8	\( 8 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - q^{7} - 4 q^{8} + 2 q^{10} - 3 q^{11} - 2 q^{13} + 16 q^{14} + 4 q^{16} + 13 q^{17} + 15 q^{19} + 3 q^{20} - 7 q^{22} - 10 q^{23} - 2 q^{25} - 10 q^{26} - 6 q^{28} + 9 q^{29} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} + 24 q^{37} - 4 q^{40} - 8 q^{41} - 38 q^{43} + 12 q^{44} + 3 q^{46} + q^{49} + 2 q^{50} - 28 q^{52} - 13 q^{53} + 7 q^{55} - 22 q^{56} + 12 q^{58} + 27 q^{59} + 6 q^{61} + 30 q^{62} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} + 16 q^{70} + 20 q^{71} + 13 q^{73} - 20 q^{74} - 34 q^{77} + 37 q^{79} - q^{80} + 28 q^{82} - 27 q^{83} - 12 q^{85} + 3 q^{86} - 36 q^{88} + 16 q^{89} + 44 q^{91} - 11 q^{92} + 17 q^{94} + 15 q^{95} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - q^7 - 4 * q^8 + 2 * q^10 - 3 * q^11 - 2 * q^13 + 16 * q^14 + 4 * q^16 + 13 * q^17 + 15 * q^19 + 3 * q^20 - 7 * q^22 - 10 * q^23 - 2 * q^25 - 10 * q^26 - 6 * q^28 + 9 * q^29 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 + 24 * q^37 - 4 * q^40 - 8 * q^41 - 38 * q^43 + 12 * q^44 + 3 * q^46 + q^49 + 2 * q^50 - 28 * q^52 - 13 * q^53 + 7 * q^55 - 22 * q^56 + 12 * q^58 + 27 * q^59 + 6 * q^61 + 30 * q^62 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 + 16 * q^70 + 20 * q^71 + 13 * q^73 - 20 * q^74 - 34 * q^77 + 37 * q^79 - q^80 + 28 * q^82 - 27 * q^83 - 12 * q^85 + 3 * q^86 - 36 * q^88 + 16 * q^89 + 44 * q^91 - 11 * q^92 + 17 * q^94 + 15 * q^95 + 24 * q^97 - 16 * q^98

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