LMFDB - Embedded newform 495.2.ba.a.289.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,2,Mod(64,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.4
Root			$-1.92464 + 0.625353i$ of defining polynomial
Character	$\chi$	$=$	495.289
Dual form			495.2.ba.a.334.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18949 + 1.63719i) q^{2} +(-0.647481 + 1.99274i) q^{4} +(1.06421 - 1.96658i) q^{5} +(-0.918552 - 0.298456i) q^{7} +(-0.183406 + 0.0595923i) q^{8} +(4.48555 - 0.596911i) q^{10} +(3.31118 - 0.189896i) q^{11} +(2.65978 + 3.66088i) q^{13} +(-0.603980 - 1.85886i) q^{14} +(3.07453 + 2.23378i) q^{16} +(-1.96126 + 2.69944i) q^{17} +(-1.01283 - 3.11717i) q^{19} +(3.22984 + 3.39403i) q^{20} +(4.24952 + 5.19517i) q^{22} +3.36643i q^{23} +(-2.73490 - 4.18573i) q^{25} +(-2.82978 + 8.70916i) q^{26} +(1.18949 - 1.63719i) q^{28} +(1.51820 - 4.67254i) q^{29} +(0.338464 - 0.245909i) q^{31} +8.07636i q^{32} -6.75241 q^{34} +(-1.56447 + 1.48879i) q^{35} +(-6.02737 - 1.95841i) q^{37} +(3.89867 - 5.36605i) q^{38} +(-0.0779900 + 0.424103i) q^{40} +(-1.78786 - 5.50247i) q^{41} -2.26205i q^{43} +(-1.76552 + 6.72129i) q^{44} +(-5.51149 + 4.00433i) q^{46} +(-4.11260 + 1.33626i) q^{47} +(-4.90846 - 3.56620i) q^{49} +(3.59970 - 9.45645i) q^{50} +(-9.01735 + 2.92991i) q^{52} +(-1.56392 - 2.15255i) q^{53} +(3.15036 - 6.71381i) q^{55} +0.186254 q^{56} +(9.45574 - 3.07235i) q^{58} +(-3.12889 + 9.62972i) q^{59} +(1.99897 + 1.45233i) q^{61} +(0.805201 + 0.261626i) q^{62} +(-7.07350 + 5.13920i) q^{64} +(10.0300 - 1.33473i) q^{65} +9.60059i q^{67} +(-4.10941 - 5.65612i) q^{68} +(-4.29836 - 0.790444i) q^{70} +(-4.41166 - 3.20526i) q^{71} +(1.36528 + 0.443607i) q^{73} +(-3.96321 - 12.1975i) q^{74} +6.86752 q^{76} +(-3.09817 - 0.813812i) q^{77} +(0.812218 - 0.590111i) q^{79} +(7.66487 - 3.66911i) q^{80} +(6.88197 - 9.47221i) q^{82} +(-4.34692 + 5.98302i) q^{83} +(3.22148 + 6.72976i) q^{85} +(3.70342 - 2.69069i) q^{86} +(-0.595976 + 0.232149i) q^{88} -12.1964 q^{89} +(-1.35054 - 4.15654i) q^{91} +(-6.70842 - 2.17970i) q^{92} +(-7.07962 - 5.14365i) q^{94} +(-7.20805 - 1.32552i) q^{95} +(-1.77467 - 2.44262i) q^{97} -12.2781i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 2 q^{5} + 6 q^{11} + 12 q^{14} + 16 q^{16} + 6 q^{19} + 8 q^{20} - 16 q^{25} - 40 q^{26} - 2 q^{29} + 8 q^{31} - 16 q^{34} - 22 q^{35} + 12 q^{40} + 52 q^{41} - 4 q^{44} - 62 q^{46} - 10 q^{49}+ \cdots - 48 q^{95}+O(q^{100}) $ 16 * q - 4 * q^4 + 2 * q^5 + 6 * q^11 + 12 * q^14 + 16 * q^16 + 6 * q^19 + 8 * q^20 - 16 * q^25 - 40 * q^26 - 2 * q^29 + 8 * q^31 - 16 * q^34 - 22 * q^35 + 12 * q^40 + 52 * q^41 - 4 * q^44 - 62 * q^46 - 10 * q^49 - 28 * q^50 - 8 * q^55 + 20 * q^56 - 2 * q^59 - 40 * q^61 - 8 * q^64 + 40 * q^65 - 34 * q^70 - 36 * q^71 - 48 * q^74 + 56 * q^76 + 38 * q^79 - 34 * q^80 + 58 * q^85 - 22 * q^86 - 24 * q^89 - 20 * q^91 + 14 * q^94 - 48 * q^95

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 $

$2$	1.18949	+	1.63719i	0.841097	+	1.15767i	0.985755	+	0.168189i	$0.0537920\pi$
$2$	1.18949	+	1.63719i	0.841097	+	1.15767i	−0.144657	+	0.989482i	$0.546208\pi$
$3$		0			0
$3$		0			0
$4$	−0.647481	+	1.99274i	−0.323741	+	0.996371i
$5$	1.06421	−	1.96658i	0.475930	−	0.879483i
$5$	1.06421	−	1.96658i	0.475930	−	0.879483i
$6$		0			0
$7$	−0.918552	−	0.298456i	−0.347180	−	0.112806i	0.130236	−	0.991483i	$-0.458427\pi$
$7$	−0.918552	−	0.298456i	−0.347180	−	0.112806i	−0.477416	+	0.878677i	$0.658427\pi$
$8$	−0.183406	+	0.0595923i	−0.0648439	+	0.0210691i
$9$		0			0
$10$	4.48555	−	0.596911i	1.41846	−	0.188760i
$11$	3.31118	−	0.189896i	0.998360	−	0.0572559i
$11$	3.31118	−	0.189896i	0.998360	−	0.0572559i
$12$		0			0
$13$	2.65978	+	3.66088i	0.737691	+	1.01534i	0.998748	+	0.0500213i	$0.0159289\pi$
$13$	2.65978	+	3.66088i	0.737691	+	1.01534i	−0.261057	+	0.965323i	$0.584071\pi$
$14$	−0.603980	−	1.85886i	−0.161420	−	0.496801i
$15$		0			0
$16$	3.07453	+	2.23378i	0.768633	+	0.558445i
$17$	−1.96126	+	2.69944i	−0.475675	+	0.654710i	−0.977667	−	0.210162i	$-0.932601\pi$
$17$	−1.96126	+	2.69944i	−0.475675	+	0.654710i	0.501992	+	0.864872i	$0.332601\pi$
$18$		0			0
$19$	−1.01283	−	3.11717i	−0.232359	−	0.715129i	−0.997461	−	0.0712189i	$-0.977311\pi$
$19$	−1.01283	−	3.11717i	−0.232359	−	0.715129i	0.765101	−	0.643910i	$-0.222689\pi$
$20$	3.22984	+	3.39403i	0.722214	+	0.758928i
$21$		0			0
$22$	4.24952	+	5.19517i	0.906001	+	1.10761i
$23$			3.36643i			0.701948i	0.936385	+	0.350974i	$0.114149\pi$
$23$			3.36643i			0.701948i	−0.936385	+	0.350974i	$0.885851\pi$
$24$		0			0
$25$	−2.73490	−	4.18573i	−0.546981	−	0.837145i
$26$	−2.82978	+	8.70916i	−0.554965	+	1.70801i
$27$		0			0
$28$	1.18949	−	1.63719i	0.224793	−	0.309401i
$29$	1.51820	−	4.67254i	0.281923	−	0.867668i	−0.705382	−	0.708828i	$-0.749224\pi$
$29$	1.51820	−	4.67254i	0.281923	−	0.867668i	0.987304	−	0.158841i	$-0.0507756\pi$
$30$		0			0
$31$	0.338464	−	0.245909i	0.0607900	−	0.0441665i	−0.556975	−	0.830529i	$-0.688038\pi$
$31$	0.338464	−	0.245909i	0.0607900	−	0.0441665i	0.617765	+	0.786363i	$0.288038\pi$
$32$			8.07636i			1.42771i
$33$		0			0
$34$	−6.75241			−1.15803
$35$	−1.56447	+	1.48879i	−0.264444	+	0.251651i
$36$		0			0
$37$	−6.02737	−	1.95841i	−0.990894	−	0.321961i	−0.231673	−	0.972794i	$-0.574420\pi$
$37$	−6.02737	−	1.95841i	−0.990894	−	0.321961i	−0.759221	+	0.650833i	$0.774420\pi$
$38$	3.89867	−	5.36605i	0.632447	−	0.870489i
$39$		0			0
$40$	−0.0779900	+	0.424103i	−0.0123313	+	0.0670565i
$41$	−1.78786	−	5.50247i	−0.279217	−	0.859341i	−0.988073	−	0.153988i	$-0.950788\pi$
$41$	−1.78786	−	5.50247i	−0.279217	−	0.859341i	0.708856	−	0.705353i	$-0.249212\pi$
$42$		0			0
$43$		−	2.26205i		−	0.344960i	−0.985013	−	0.172480i	$-0.944822\pi$
$43$		−	2.26205i		−	0.344960i	0.985013	−	0.172480i	$-0.0551780\pi$
$44$	−1.76552	+	6.72129i	−0.266161	+	1.01327i
$45$		0			0
$46$	−5.51149	+	4.00433i	−0.812625	+	0.590407i
$47$	−4.11260	+	1.33626i	−0.599884	+	0.194914i	−0.593189	−	0.805063i	$-0.702131\pi$
$47$	−4.11260	+	1.33626i	−0.599884	+	0.194914i	−0.00669531	+	0.999978i	$0.502131\pi$
$48$		0			0
$49$	−4.90846	−	3.56620i	−0.701208	−	0.509457i
$50$	3.59970	−	9.45645i	0.509075	−	1.33734i
$51$		0			0
$52$	−9.01735	+	2.92991i	−1.25048	+	0.406306i
$53$	−1.56392	−	2.15255i	−0.214821	−	0.295676i	0.687984	−	0.725726i	$-0.258496\pi$
$53$	−1.56392	−	2.15255i	−0.214821	−	0.295676i	−0.902805	+	0.430050i	$0.858496\pi$
$54$		0			0
$55$	3.15036	−	6.71381i	0.424794	−	0.905290i
$56$	0.186254			0.0248892
$57$		0			0
$58$	9.45574	−	3.07235i	1.24160	−	0.403420i
$59$	−3.12889	+	9.62972i	−0.407346	+	1.25368i	0.511574	+	0.859239i	$0.329063\pi$
$59$	−3.12889	+	9.62972i	−0.407346	+	1.25368i	−0.918920	+	0.394444i	$0.870937\pi$
$60$		0			0
$61$	1.99897	+	1.45233i	0.255941	+	0.185952i	0.708356	−	0.705856i	$-0.249437\pi$
$61$	1.99897	+	1.45233i	0.255941	+	0.185952i	−0.452414	+	0.891808i	$0.649437\pi$
$62$	0.805201	+	0.261626i	0.102261	+	0.0332265i
$63$		0			0
$64$	−7.07350	+	5.13920i	−0.884187	+	0.642400i
$65$	10.0300	−	1.33473i	1.24407	−	0.165553i
$66$		0			0
$67$			9.60059i			1.17290i	0.809986	+	0.586449i	$0.199475\pi$
$67$			9.60059i			1.17290i	−0.809986	+	0.586449i	$0.800525\pi$
$68$	−4.10941	−	5.65612i	−0.498339	−	0.685905i
$69$		0			0
$70$	−4.29836	−	0.790444i	−0.513753	−	0.0944761i
$71$	−4.41166	−	3.20526i	−0.523567	−	0.380394i	0.294379	−	0.955689i	$-0.404887\pi$
$71$	−4.41166	−	3.20526i	−0.523567	−	0.380394i	−0.817946	+	0.575295i	$0.804887\pi$
$72$		0			0
$73$	1.36528	+	0.443607i	0.159794	+	0.0519203i	0.387822	−	0.921734i	$-0.373228\pi$
$73$	1.36528	+	0.443607i	0.159794	+	0.0519203i	−0.228028	+	0.973655i	$0.573228\pi$
$74$	−3.96321	−	12.1975i	−0.460713	−	1.41793i
$75$		0			0
$76$	6.86752			0.787758
$77$	−3.09817	−	0.813812i	−0.353069	−	0.0927425i
$78$		0			0
$79$	0.812218	−	0.590111i	0.0913817	−	0.0663927i	−0.541156	−	0.840922i	$-0.682013\pi$
$79$	0.812218	−	0.590111i	0.0913817	−	0.0663927i	0.632538	+	0.774529i	$0.282013\pi$
$80$	7.66487	−	3.66911i	0.856958	−	0.410219i
$81$		0			0
$82$	6.88197	−	9.47221i	0.759986	−	1.04603i
$83$	−4.34692	+	5.98302i	−0.477136	+	0.656721i	−0.977951	−	0.208833i	$-0.933034\pi$
$83$	−4.34692	+	5.98302i	−0.477136	+	0.656721i	0.500815	+	0.865554i	$0.333034\pi$
$84$		0			0
$85$	3.22148	+	6.72976i	0.349418	+	0.729944i
$86$	3.70342	−	2.69069i	0.399350	−	0.290145i
$87$		0			0
$88$	−0.595976	+	0.232149i	−0.0635312	+	0.0247472i
$89$	−12.1964			−1.29282			−0.646410	−	0.762991i	$-0.723730\pi$
$89$	−12.1964			−1.29282			−0.646410	+	0.762991i	$0.723730\pi$
$90$		0			0
$91$	−1.35054	−	4.15654i	−0.141575	−	0.435723i
$92$	−6.70842	−	2.17970i	−0.699401	−	0.227249i
$93$		0			0
$94$	−7.07962	−	5.14365i	−0.730207	−	0.530527i
$95$	−7.20805	−	1.32552i	−0.739531	−	0.135995i
$96$		0			0
$97$	−1.77467	−	2.44262i	−0.180190	−	0.248010i	0.709362	−	0.704844i	$-0.248983\pi$
$97$	−1.77467	−	2.44262i	−0.180190	−	0.248010i	−0.889552	+	0.456834i	$0.848983\pi$
$98$		−	12.2781i		−	1.24027i
$99$		0			0
$100$	10.1119	−	2.73978i	1.01119	−	0.273978i
$101$	12.2940	−	8.93210i	1.22330	−	0.888777i	0.226928	−	0.973912i	$-0.427132\pi$
$101$	12.2940	−	8.93210i	1.22330	−	0.888777i	0.996369	+	0.0851342i	$0.0271319\pi$
$102$		0			0
$103$	−9.26987	−	3.01196i	−0.913387	−	0.296778i	−0.185636	−	0.982619i	$-0.559435\pi$
$103$	−9.26987	−	3.01196i	−0.913387	−	0.296778i	−0.727751	+	0.685841i	$0.759435\pi$
$104$	−0.705981	−	0.512925i	−0.0692272	−	0.0502965i
$105$		0			0
$106$	1.66387	−	5.12088i	0.161610	−	0.497384i
$107$	−7.26778	+	2.36144i	−0.702602	+	0.228289i	−0.638464	−	0.769652i	$-0.720430\pi$
$107$	−7.26778	+	2.36144i	−0.702602	+	0.228289i	−0.0641384	+	0.997941i	$0.520430\pi$
$108$		0			0
$109$	9.85576			0.944010			0.472005	−	0.881596i	$-0.343530\pi$
$109$	9.85576			0.944010			0.472005	+	0.881596i	$0.343530\pi$
$110$	14.7391	−	2.82827i	1.40532	−	0.269665i
$111$		0			0
$112$	−2.15743	−	2.96945i	−0.203858	−	0.280587i
$113$	4.77298	−	1.55084i	0.449004	−	0.145890i	−0.0757819	−	0.997124i	$-0.524145\pi$
$113$	4.77298	−	1.55084i	0.449004	−	0.145890i	0.524786	+	0.851234i	$0.324145\pi$
$114$		0			0
$115$	6.62036	+	3.58259i	0.617352	+	0.334078i
$116$	8.32816	+	6.05076i	0.773250	+	0.561799i
$117$		0			0
$118$	−19.4875	+	6.33188i	−1.79397	+	0.582896i
$119$	2.60718	−	1.89423i	0.239000	−	0.173644i
$120$		0			0
$121$	10.9279	−	1.25756i	0.993444	−	0.114324i
$122$			5.00023i			0.452700i
$123$		0			0
$124$	0.270884	+	0.833694i	0.0243261	+	0.0748679i
$125$	−11.1421	+	0.923914i	−0.996580	+	0.0826374i
$126$		0			0
$127$	−4.16764	+	5.73626i	−0.369818	+	0.509011i	−0.952851	−	0.303438i	$-0.901866\pi$
$127$	−4.16764	+	5.73626i	−0.369818	+	0.509011i	0.583033	+	0.812448i	$0.301866\pi$
$128$	−1.46559	−	0.476198i	−0.129541	−	0.0420903i
$129$		0			0
$130$	14.1158	+	14.8334i	1.23804	+	1.30097i
$131$	−7.21704			−0.630556			−0.315278	−	0.948999i	$-0.602098\pi$
$131$	−7.21704			−0.630556			−0.315278	+	0.948999i	$0.602098\pi$
$132$		0			0
$133$			3.16557i			0.274490i
$134$	−15.7180	+	11.4198i	−1.35783	+	0.986521i
$135$		0			0
$136$	0.198841	−	0.611970i	0.0170505	−	0.0524760i
$137$	4.99076	−	6.86920i	0.426390	−	0.586875i	−0.540730	−	0.841196i	$-0.681852\pi$
$137$	4.99076	−	6.86920i	0.426390	−	0.586875i	0.967120	+	0.254321i	$0.0818520\pi$
$138$		0			0
$139$	−2.39184	+	7.36133i	−0.202873	+	0.624380i	0.796921	+	0.604084i	$0.206461\pi$
$139$	−2.39184	+	7.36133i	−0.202873	+	0.624380i	−0.999794	+	0.0202958i	$0.993539\pi$
$140$	−1.95381	−	4.08156i	−0.165127	−	0.344954i
$141$		0			0
$142$		−	11.0354i		−	0.926067i
$143$	9.50222	+	11.6168i	0.794615	+	0.971442i
$144$		0			0
$145$	−7.57325	−	7.95824i	−0.628924	−	0.660896i
$146$	0.897720	+	2.76290i	0.0742958	+	0.228659i
$147$		0			0
$148$	7.80522	−	10.7430i	0.641585	−	0.883067i
$149$	13.6589	+	9.92376i	1.11898	+	0.812986i	0.984054	−	0.177870i	$-0.0569206\pi$
$149$	13.6589	+	9.92376i	1.11898	+	0.812986i	0.134925	+	0.990856i	$0.456921\pi$
$150$		0			0
$151$	−3.79555	−	11.6815i	−0.308877	−	0.950626i	−0.978202	−	0.207656i	$-0.933416\pi$
$151$	−3.79555	−	11.6815i	−0.308877	−	0.950626i	0.669325	−	0.742970i	$-0.266584\pi$
$152$	0.371519	+	0.511353i	0.0301342	+	0.0414762i
$153$		0			0
$154$	−2.35288	−	6.04033i	−0.189600	−	0.486744i
$155$	−0.123402	−	0.927318i	−0.00991190	−	0.0744840i
$156$		0			0
$157$	4.00368	−	1.30087i	0.319528	−	0.103821i	−0.144862	−	0.989452i	$-0.546274\pi$
$157$	4.00368	−	1.30087i	0.319528	−	0.103821i	0.464390	+	0.885631i	$0.346274\pi$
$158$	1.93225	+	0.627827i	0.153722	+	0.0499472i
$159$		0			0
$160$	15.8828	+	8.59496i	1.25565	+	0.679491i
$161$	1.00473	−	3.09224i	0.0791837	−	0.243702i
$162$		0			0
$163$	9.74169	+	13.4083i	0.763028	+	1.05022i	0.996956	+	0.0779643i	$0.0248420\pi$
$163$	9.74169	+	13.4083i	0.763028	+	1.05022i	−0.233928	+	0.972254i	$0.575158\pi$
$164$	12.1226			0.946617
$165$		0			0
$166$	−14.9660			−1.16159
$167$	−5.38810	−	7.41608i	−0.416944	−	0.573874i	0.547951	−	0.836510i	$-0.315408\pi$
$167$	−5.38810	−	7.41608i	−0.416944	−	0.573874i	−0.964895	+	0.262637i	$0.915408\pi$
$168$		0			0
$169$	−2.31036	+	7.11055i	−0.177720	+	0.546965i
$170$	−7.18599	+	13.2792i	−0.551141	+	1.01847i
$171$		0			0
$172$	4.50769	+	1.46464i	0.343708	+	0.111678i
$173$	−3.90853	+	1.26996i	−0.297160	+	0.0965531i	−0.453803	−	0.891102i	$-0.649933\pi$
$173$	−3.90853	+	1.26996i	−0.297160	+	0.0965531i	0.156643	+	0.987655i	$0.449933\pi$
$174$		0			0
$175$	1.26290	+	4.66106i	0.0954661	+	0.352343i
$176$	10.6045	+	6.81261i	0.799346	+	0.513520i
$177$		0			0
$178$	−14.5075	−	19.9679i	−1.08739	−	1.49666i
$179$	−5.03576	−	15.4985i	−0.376390	−	1.15841i	−0.942536	−	0.334105i	$-0.891566\pi$
$179$	−5.03576	−	15.4985i	−0.376390	−	1.15841i	0.566145	−	0.824305i	$-0.308434\pi$
$180$		0			0
$181$	4.48753	+	3.26038i	0.333555	+	0.242342i	0.741938	−	0.670469i	$-0.233907\pi$
$181$	4.48753	+	3.26038i	0.333555	+	0.242342i	−0.408382	+	0.912811i	$0.633907\pi$
$182$	5.19860	−	7.15526i	0.385346	−	0.530383i
$183$		0			0
$184$	−0.200613	−	0.617424i	−0.0147894	−	0.0455171i
$185$	−10.2658	+	9.76917i	−0.754756	+	0.718243i
$186$		0			0
$187$	−5.98147	+	9.31078i	−0.437408	+	0.680871i
$188$		−	9.06056i		−	0.660809i
$189$		0			0
$190$	−6.40378	−	13.3777i	−0.464579	−	0.970518i
$191$	−6.74155	+	20.7484i	−0.487802	+	1.50130i	0.340080	+	0.940396i	$0.389546\pi$
$191$	−6.74155	+	20.7484i	−0.487802	+	1.50130i	−0.827882	+	0.560903i	$0.810454\pi$
$192$		0			0
$193$	13.2128	−	18.1858i	0.951076	−	1.30904i	2.83481e−5	−	1.00000i	$-0.499991\pi$
$193$	13.2128	−	18.1858i	0.951076	−	1.30904i	0.951048	−	0.309044i	$-0.100009\pi$
$194$	1.88809	−	5.81094i	0.135557	−	0.417201i
$195$		0			0
$196$	10.2847	−	7.47224i	0.734619	−	0.533732i
$197$		−	25.7479i		−	1.83446i	−0.398358	−	0.917230i	$-0.630420\pi$
$197$		−	25.7479i		−	1.83446i	0.398358	−	0.917230i	$-0.369580\pi$
$198$		0			0
$199$	−16.9671			−1.20277			−0.601385	−	0.798960i	$-0.705384\pi$
$199$	−16.9671			−1.20277			−0.601385	+	0.798960i	$0.705384\pi$
$200$	0.751036	+	0.604709i	0.0531063	+	0.0427594i
$201$		0			0
$202$	29.2472	+	9.50298i	2.05782	+	0.668627i
$203$	−2.78909	+	3.83886i	−0.195756	+	0.269435i
$204$		0			0
$205$	−12.7237	−	2.33982i	−0.888664	−	0.163420i
$206$	−6.09526	−	18.7593i	−0.424677	−	1.30702i
$207$		0			0
$208$			17.1969i			1.19239i
$209$	−3.94561	−	10.1292i	−0.272924	−	0.700652i
$210$		0			0
$211$	4.71363	−	3.42465i	0.324500	−	0.235763i	−0.413593	−	0.910462i	$-0.635726\pi$
$211$	4.71363	−	3.42465i	0.324500	−	0.235763i	0.738093	+	0.674699i	$0.235726\pi$
$212$	5.30209	−	1.72275i	0.364149	−	0.118319i
$213$		0			0
$214$	−12.5111	−	9.08984i	−0.855241	−	0.621369i
$215$	−4.44852	−	2.40730i	−0.303386	−	0.164177i
$216$		0			0
$217$	−0.384290	+	0.124863i	−0.0260873	+	0.00847628i
$218$	11.7233	+	16.1358i	0.794005	+	1.09285i
$219$		0			0
$220$	11.3391	+	10.6249i	0.764482	+	0.716332i
$221$	−15.0988			−1.01566
$222$		0			0
$223$	−18.0913	+	5.87820i	−1.21148	+	0.393634i	−0.843972	−	0.536387i	$-0.819789\pi$
$223$	−18.0913	+	5.87820i	−1.21148	+	0.393634i	−0.367508	+	0.930020i	$0.619789\pi$
$224$	2.41043	−	7.41856i	0.161054	−	0.495673i
$225$		0			0
$226$	8.21644	+	5.96959i	0.546549	+	0.397091i
$227$	27.0727	+	8.79646i	1.79688	+	0.583841i	0.999799	−	0.0200332i	$-0.00637719\pi$
$227$	27.0727	+	8.79646i	1.79688	+	0.583841i	0.797079	+	0.603874i	$0.206377\pi$
$228$		0			0
$229$	−20.5420	+	14.9247i	−1.35746	+	0.986250i	−0.358854	+	0.933394i	$0.616832\pi$
$229$	−20.5420	+	14.9247i	−1.35746	+	0.986250i	−0.998602	+	0.0528558i	$0.983168\pi$
$230$	2.00946	+	15.1003i	0.132500	+	0.995682i
$231$		0			0
$232$			0.947446i			0.0622029i
$233$	7.35755	+	10.1268i	0.482009	+	0.663429i	0.978890	−	0.204390i	$-0.0655211\pi$
$233$	7.35755	+	10.1268i	0.482009	+	0.663429i	−0.496880	+	0.867819i	$0.665521\pi$
$234$		0			0
$235$	−1.74880	+	9.50984i	−0.114079	+	0.620353i
$236$	−17.1637	−	12.4701i	−1.11726	−	0.811737i
$237$		0			0
$238$	6.20244	+	2.01529i	0.402044	+	0.130632i
$239$	6.30011	+	19.3897i	0.407520	+	1.25422i	0.918773	+	0.394787i	$0.129182\pi$
$239$	6.30011	+	19.3897i	0.407520	+	1.25422i	−0.511252	+	0.859431i	$0.670818\pi$
$240$		0			0
$241$	−22.7935			−1.46826			−0.734129	−	0.679010i	$-0.762409\pi$
$241$	−22.7935			−1.46826			−0.734129	+	0.679010i	$0.762409\pi$
$242$	15.0575	+	16.3952i	0.967932	+	1.05392i
$243$		0			0
$244$	−4.18842	+	3.04307i	−0.268136	+	0.194812i
$245$	−12.2369	+	5.85769i	−0.781785	+	0.374234i
$246$		0			0
$247$	8.71768	−	11.9989i	0.554693	−	0.763469i
$248$	−0.0474222	+	0.0652711i	−0.00301132	+	0.00414472i
$249$		0			0
$250$	−14.7661	−	17.1428i	−0.933887	−	1.08421i
$251$	13.7151	−	9.96460i	0.865689	−	0.628960i	−0.0637374	−	0.997967i	$-0.520302\pi$
$251$	13.7151	−	9.96460i	0.865689	−	0.628960i	0.929427	+	0.369007i	$0.120302\pi$
$252$		0			0
$253$	0.639272	+	11.1469i	0.0401907	+	0.700797i
$254$	−14.3487			−0.900320
$255$		0			0
$256$	4.44000	+	13.6649i	0.277500	+	0.854057i
$257$	4.50405	+	1.46346i	0.280955	+	0.0912879i	0.446105	−	0.894981i	$-0.352811\pi$
$257$	4.50405	+	1.46346i	0.280955	+	0.0912879i	−0.165150	+	0.986268i	$0.552811\pi$
$258$		0			0
$259$	4.95196	+	3.59781i	0.307700	+	0.223557i
$260$	−3.83445	+	20.8514i	−0.237803	+	1.29315i
$261$		0			0
$262$	−8.58461	−	11.8157i	−0.530359	−	0.729976i
$263$			18.1037i			1.11632i	0.829732	+	0.558162i	$0.188493\pi$
$263$			18.1037i			1.11632i	−0.829732	+	0.558162i	$0.811507\pi$
$264$		0			0
$265$	−5.89751	+	0.784807i	−0.362281	+	0.0482103i
$266$	−5.18266	+	3.76542i	−0.317769	+	0.230873i
$267$		0			0
$268$	−19.1315	−	6.21620i	−1.16864	−	0.379715i
$269$	1.85914	+	1.35074i	0.113354	+	0.0823562i	0.643018	−	0.765851i	$-0.277682\pi$
$269$	1.85914	+	1.35074i	0.113354	+	0.0823562i	−0.529664	+	0.848207i	$0.677682\pi$
$270$		0			0
$271$	0.248971	−	0.766255i	0.0151239	−	0.0465467i	−0.943210	−	0.332198i	$-0.892210\pi$
$271$	0.248971	−	0.766255i	0.0151239	−	0.0465467i	0.958334	+	0.285651i	$0.0922098\pi$
$272$	−12.0599	+	3.91850i	−0.731239	+	0.237594i
$273$		0			0
$274$	17.1827			1.03804
$275$	−9.85062	−	13.3404i	−0.594015	−	0.804454i
$276$		0			0
$277$	−6.95521	−	9.57302i	−0.417898	−	0.575187i	0.547225	−	0.836986i	$-0.315684\pi$
$277$	−6.95521	−	9.57302i	−0.417898	−	0.575187i	−0.965122	+	0.261799i	$0.915684\pi$
$278$	−14.8970	+	4.84033i	−0.893462	+	0.290304i
$279$		0			0
$280$	0.198214	−	0.366284i	0.0118455	−	0.0218897i
$281$	5.03960	+	3.66148i	0.300637	+	0.218426i	0.727869	−	0.685717i	$-0.240511\pi$
$281$	5.03960	+	3.66148i	0.300637	+	0.218426i	−0.427231	+	0.904142i	$0.640511\pi$
$282$		0			0
$283$	8.22250	−	2.67165i	0.488777	−	0.158813i	−0.0542519	−	0.998527i	$-0.517277\pi$
$283$	8.22250	−	2.67165i	0.488777	−	0.158813i	0.543029	+	0.839714i	$0.317277\pi$
$284$	9.24372	−	6.71596i	0.548514	−	0.398519i
$285$		0			0
$286$	−7.71608	+	29.3750i	−0.456261	+	1.73698i
$287$			5.58790i			0.329843i
$288$		0			0
$289$	1.81285	+	5.57937i	0.106638	+	0.328198i
$290$	4.02087	−	21.8651i	0.236114	−	1.28397i
$291$		0			0
$292$	−1.76799	+	2.43343i	−0.103464	+	0.142406i
$293$	−5.52610	−	1.79554i	−0.322838	−	0.104896i	0.143115	−	0.989706i	$-0.454288\pi$
$293$	−5.52610	−	1.79554i	−0.322838	−	0.104896i	−0.465953	+	0.884810i	$0.654288\pi$
$294$		0			0
$295$	15.6079	+	16.4013i	0.908725	+	0.954920i
$296$	1.22216			0.0710369
$297$		0			0
$298$			34.1665i			1.97921i
$299$	−12.3241	+	8.95396i	−0.712719	+	0.517821i
$300$		0			0
$301$	−0.675123	+	2.07781i	−0.0389134	+	0.119763i
$302$	14.6101	−	20.1091i	0.840717	−	1.15715i
$303$		0			0
$304$	3.84909	−	11.8463i	0.220761	−	0.679432i
$305$	4.98346	−	2.38554i	0.285352	−	0.136596i
$306$		0			0
$307$		−	18.4721i		−	1.05426i	−0.849785	−	0.527130i	$-0.823268\pi$
$307$		−	18.4721i		−	1.05426i	0.849785	−	0.527130i	$-0.176732\pi$
$308$	3.62773	−	5.64693i	0.206709	−	0.321764i
$309$		0			0
$310$	1.37141	−	1.30507i	0.0778911	−	0.0741230i
$311$	3.50158	+	10.7768i	0.198557	+	0.611094i	0.999917	+	0.0129120i	$0.00411014\pi$
$311$	3.50158	+	10.7768i	0.198557	+	0.611094i	−0.801360	+	0.598182i	$0.795890\pi$
$312$		0			0
$313$	−3.00651	+	4.13811i	−0.169938	+	0.233900i	−0.885488	−	0.464661i	$-0.846176\pi$
$313$	−3.00651	+	4.13811i	−0.169938	+	0.233900i	0.715550	+	0.698561i	$0.246176\pi$
$314$	6.89212	+	5.00742i	0.388945	+	0.282585i
$315$		0			0
$316$	0.650043	+	2.00063i	0.0365678	+	0.112544i
$317$	−6.94368	−	9.55715i	−0.389996	−	0.536783i	0.568202	−	0.822889i	$-0.307639\pi$
$317$	−6.94368	−	9.55715i	−0.389996	−	0.536783i	−0.958198	+	0.286106i	$0.907639\pi$
$318$		0			0
$319$	4.13974	−	15.7599i	0.231781	−	0.882387i
$320$	2.57896	+	19.3798i	0.144168	+	1.08337i
$321$		0			0
$322$	6.25771	−	2.03325i	0.348729	−	0.113309i
$323$	10.4010	+	3.37951i	0.578730	+	0.188041i
$324$		0			0
$325$	8.04918	−	21.1453i	0.446488	−	1.17293i
$326$	−10.3643	+	31.8981i	−0.574026	+	1.76667i
$327$		0			0
$328$	0.655810	+	0.902645i	0.0362110	+	0.0498402i
$329$	4.17645			0.230255
$330$		0			0
$331$	29.2692			1.60878			0.804391	−	0.594100i	$-0.202492\pi$
$331$	29.2692			1.60878			0.804391	+	0.594100i	$0.202492\pi$
$332$	−9.10807	−	12.5362i	−0.499870	−	0.688012i
$333$		0			0
$334$	5.73247	−	17.6427i	0.313667	−	0.965367i
$335$	18.8804	+	10.2171i	1.03154	+	0.558218i
$336$		0			0
$337$	25.3400	+	8.23348i	1.38036	+	0.448506i	0.902788	−	0.430087i	$-0.141517\pi$
$337$	25.3400	+	8.23348i	1.38036	+	0.448506i	0.477572	+	0.878593i	$0.341517\pi$
$338$	−14.3895	+	4.67543i	−0.782685	+	0.254310i
$339$		0			0
$340$	−15.4965	+	2.06219i	−0.840417	+	0.111838i
$341$	1.07402	−	0.878523i	0.0581615	−	0.0475747i
$342$		0			0
$343$	7.41820	+	10.2103i	0.400545	+	0.551303i
$344$	0.134801	+	0.414875i	0.00726798	+	0.0223686i
$345$		0			0
$346$	−6.72833	−	4.88842i	−0.361717	−	0.262803i
$347$	2.53411	−	3.48790i	0.136038	−	0.187240i	−0.735563	−	0.677457i	$-0.763082\pi$
$347$	2.53411	−	3.48790i	0.136038	−	0.187240i	0.871601	+	0.490216i	$0.163082\pi$
$348$		0			0
$349$	4.06960	+	12.5249i	0.217841	+	0.670444i	0.998940	+	0.0460373i	$0.0146593\pi$
$349$	4.06960	+	12.5249i	0.217841	+	0.670444i	−0.781099	+	0.624407i	$0.785341\pi$
$350$	−6.12885	+	7.61189i	−0.327601	+	0.406873i
$351$		0			0
$352$	1.53367	+	26.7423i	0.0817449	+	1.42537i
$353$		−	25.4904i		−	1.35672i	−0.734732	−	0.678358i	$-0.762692\pi$
$353$		−	25.4904i		−	1.35672i	0.734732	−	0.678358i	$-0.237308\pi$
$354$		0			0
$355$	−10.9983	+	5.26482i	−0.583732	+	0.279428i
$356$	7.89696	−	24.3044i	0.418538	−	1.28813i
$357$		0			0
$358$	19.3840	−	26.6798i	1.02448	−	1.41007i
$359$	8.11915	−	24.9882i	0.428512	−	1.31883i	−0.471078	−	0.882091i	$-0.656135\pi$
$359$	8.11915	−	24.9882i	0.428512	−	1.31883i	0.899591	−	0.436734i	$-0.143865\pi$
$360$		0			0
$361$	6.68037	−	4.85358i	0.351599	−	0.255451i
$362$			11.2252i			0.589981i
$363$		0			0
$364$	9.15736			0.479976
$365$	2.32534	−	2.21285i	0.121714	−	0.115826i
$366$		0			0
$367$	−1.91993	−	0.623823i	−0.100220	−	0.0325633i	0.258478	−	0.966017i	$-0.416779\pi$
$367$	−1.91993	−	0.623823i	−0.100220	−	0.0325633i	−0.358698	+	0.933454i	$0.616779\pi$
$368$	−7.51985	+	10.3502i	−0.391999	+	0.539541i
$369$		0			0
$370$	−28.2051	−	5.18675i	−1.46631	−	0.269646i
$371$	0.794101	+	2.44399i	0.0412277	+	0.126886i
$372$		0			0
$373$		−	8.87153i		−	0.459351i	−0.973267	−	0.229675i	$-0.926234\pi$
$373$		−	8.87153i		−	0.459351i	0.973267	−	0.229675i	$-0.0737664\pi$
$374$	−22.3585	+	1.28226i	−1.15613	+	0.0663040i
$375$		0			0
$376$	0.674645	−	0.490159i	0.0347922	−	0.0252780i
$377$	21.1437	−	6.86999i	1.08895	−	0.353823i
$378$		0			0
$379$	17.0412	+	12.3812i	0.875348	+	0.635978i	0.932017	−	0.362415i	$-0.118048\pi$
$379$	17.0412	+	12.3812i	0.875348	+	0.635978i	−0.0566685	+	0.998393i	$0.518048\pi$
$380$	7.30850	−	13.5055i	0.374918	−	0.692820i
$381$		0			0
$382$	−41.9881	+	13.6428i	−2.14830	+	0.698025i
$383$	15.2704	+	21.0179i	0.780281	+	1.07396i	0.995251	+	0.0973436i	$0.0310346\pi$
$383$	15.2704	+	21.0179i	0.780281	+	1.07396i	−0.214970	+	0.976621i	$0.568965\pi$
$384$		0			0
$385$	−4.89754	+	5.22674i	−0.249602	+	0.266380i
$386$	45.4902			2.31539
$387$		0			0
$388$	6.01657	−	1.95490i	0.305445	−	0.0992451i
$389$	−0.507965	+	1.56335i	−0.0257548	+	0.0792652i	−0.963108	−	0.269116i	$-0.913269\pi$
$389$	−0.507965	+	1.56335i	−0.0257548	+	0.0792652i	0.937353	+	0.348381i	$0.113269\pi$
$390$		0			0
$391$	−9.08746	−	6.60243i	−0.459573	−	0.333899i
$392$	1.11276	+	0.361558i	0.0562029	+	0.0182614i
$393$		0			0
$394$	42.1543	−	30.6269i	2.12370	−	1.54296i
$395$	−0.296130	−	2.22530i	−0.0148999	−	0.111967i
$396$		0			0
$397$		−	16.7088i		−	0.838588i	−0.907850	−	0.419294i	$-0.862278\pi$
$397$		−	16.7088i		−	0.838588i	0.907850	−	0.419294i	$-0.137722\pi$
$398$	−20.1823	−	27.7785i	−1.01165	−	1.39241i
$399$		0			0
$400$	0.941436	−	18.9783i	0.0470718	−	0.948916i
$401$	22.4842	+	16.3357i	1.12281	+	0.815766i	0.984632	−	0.174641i	$-0.0558766\pi$
$401$	22.4842	+	16.3357i	1.12281	+	0.815766i	0.138174	+	0.990408i	$0.455877\pi$
$402$		0			0
$403$	1.80048	+	0.585013i	0.0896885	+	0.0291416i
$404$	9.83926	+	30.2821i	0.489521	+	1.50659i
$405$		0			0
$406$	−9.60255			−0.476567
$407$	−20.3296	−	5.34009i	−1.00770	−	0.264698i
$408$		0			0
$409$	31.9019	−	23.1781i	1.57745	−	1.14608i	0.657902	−	0.753104i	$-0.271444\pi$
$409$	31.9019	−	23.1781i	1.57745	−	1.14608i	0.919547	−	0.392980i	$-0.128556\pi$
$410$	−11.3040	−	23.6144i	−0.558266	−	1.16623i
$411$		0			0
$412$	12.0041	−	16.5223i	0.591401	−	0.813994i
$413$	5.74809	−	7.91157i	0.282845	−	0.389303i
$414$		0			0
$415$	7.14006	+	14.9158i	0.350492	+	0.732187i
$416$	−29.5665	+	21.4814i	−1.44962	+	1.05321i
$417$		0			0
$418$	11.8902	−	18.5083i	0.581569	−	0.905272i
$419$	14.7812			0.722111			0.361055	−	0.932544i	$-0.382417\pi$
$419$	14.7812			0.722111			0.361055	+	0.932544i	$0.382417\pi$
$420$		0			0
$421$	−3.33036	−	10.2498i	−0.162312	−	0.499545i	0.836516	−	0.547942i	$-0.184589\pi$
$421$	−3.33036	−	10.2498i	−0.162312	−	0.499545i	−0.998828	+	0.0483974i	$0.984589\pi$
$422$	11.2136	+	3.64354i	0.545872	+	0.177365i
$423$		0			0
$424$	0.415108	+	0.301594i	0.0201594	+	0.0146467i
$425$	16.6630	+	0.826581i	0.808273	+	0.0400951i
$426$		0			0
$427$	−1.40270	−	1.93065i	−0.0678813	−	0.0934306i
$428$		−	16.0118i		−	0.773960i
$429$		0			0
$430$	−1.35025	−	10.1466i	−0.0651146	−	0.489310i
$431$	26.0435	−	18.9217i	1.25447	−	0.911428i	0.256000	−	0.966677i	$-0.417595\pi$
$431$	26.0435	−	18.9217i	1.25447	−	0.911428i	0.998473	+	0.0552489i	$0.0175952\pi$
$432$		0			0
$433$	0.363904	+	0.118240i	0.0174881	+	0.00568223i	0.317748	−	0.948175i	$-0.397073\pi$
$433$	0.363904	+	0.118240i	0.0174881	+	0.00568223i	−0.300260	+	0.953857i	$0.597073\pi$
$434$	−0.661536	−	0.480634i	−0.0317547	−	0.0230712i
$435$		0			0
$436$	−6.38142	+	19.6400i	−0.305615	+	0.940585i
$437$	10.4937	−	3.40962i	0.501983	−	0.163104i
$438$		0			0
$439$	−26.5331			−1.26635			−0.633177	−	0.774007i	$-0.718249\pi$
$439$	−26.5331			−1.26635			−0.633177	+	0.774007i	$0.718249\pi$
$440$	−0.177704	+	1.41909i	−0.00847169	+	0.0676526i
$441$		0			0
$442$	−17.9599	−	24.7197i	−0.854267	−	1.17580i
$443$	−13.7913	+	4.48106i	−0.655243	+	0.212901i	−0.617725	−	0.786395i	$-0.711945\pi$
$443$	−13.7913	+	4.48106i	−0.655243	+	0.212901i	−0.0375185	+	0.999296i	$0.511945\pi$
$444$		0			0
$445$	−12.9796	+	23.9853i	−0.615292	+	1.13701i
$446$	−31.1432	−	22.6268i	−1.47467	−	1.07141i
$447$		0			0
$448$	8.03120	−	2.60950i	0.379439	−	0.123287i
$449$	−8.18240	+	5.94486i	−0.386151	+	0.280555i	−0.763876	−	0.645362i	$-0.776706\pi$
$449$	−8.18240	+	5.94486i	−0.386151	+	0.280555i	0.377725	+	0.925918i	$0.376706\pi$
$450$		0			0
$451$	−6.96483	−	17.8802i	−0.327961	−	0.841945i
$452$			10.5155i			0.494606i
$453$		0			0
$454$	17.8012	+	54.7866i	0.835454	+	2.57126i
$455$	−9.61144	−	1.76749i	−0.450591	−	0.0828610i
$456$		0			0
$457$	−22.9758	+	31.6235i	−1.07476	+	1.47928i	−0.209602	+	0.977787i	$0.567217\pi$
$457$	−22.9758	+	31.6235i	−1.07476	+	1.47928i	−0.865160	+	0.501496i	$0.832783\pi$
$458$	−48.8691	−	15.8785i	−2.28351	−	0.741956i
$459$		0			0
$460$	−11.4257	+	10.8730i	−0.532728	+	0.506957i
$461$	−39.1322			−1.82257			−0.911285	−	0.411776i	$-0.864908\pi$
$461$	−39.1322			−1.82257			−0.911285	+	0.411776i	$0.864908\pi$
$462$		0			0
$463$		−	12.9189i		−	0.600392i	−0.953878	−	0.300196i	$-0.902948\pi$
$463$		−	12.9189i		−	0.600392i	0.953878	−	0.300196i	$-0.0970521\pi$
$464$	15.1052	−	10.9745i	0.701240	−	0.509481i
$465$		0			0
$466$	−7.82780	+	24.0915i	−0.362616	+	1.11602i
$467$	−6.61206	+	9.10071i	−0.305969	+	0.421131i	−0.934119	−	0.356962i	$-0.883813\pi$
$467$	−6.61206	+	9.10071i	−0.305969	+	0.421131i	0.628150	+	0.778093i	$0.283813\pi$
$468$		0			0
$469$	2.86535	−	8.81864i	0.132310	−	0.407207i
$470$	−17.6496	+	8.44874i	−0.814117	+	0.389711i
$471$		0			0
$472$		−	1.95261i		−	0.0898762i
$473$	−0.429556	−	7.49007i	−0.0197510	−	0.344394i
$474$		0			0
$475$	−10.2776	+	12.7646i	−0.471571	+	0.585680i
$476$	2.08661	+	6.42192i	0.0956395	+	0.294348i
$477$		0			0
$478$	−24.2508	+	33.3784i	−1.10921	+	1.52669i
$479$	−16.9621	−	12.3237i	−0.775017	−	0.563083i	0.128462	−	0.991714i	$-0.458996\pi$
$479$	−16.9621	−	12.3237i	−0.775017	−	0.563083i	−0.903479	+	0.428632i	$0.858996\pi$
$480$		0			0
$481$	−8.86200	−	27.2744i	−0.404072	−	1.24361i
$482$	−27.1126	−	37.3174i	−1.23495	−	1.69976i
$483$		0			0
$484$	−4.56960	+	22.5907i	−0.207709	+	1.02685i
$485$	−6.69223	+	0.890564i	−0.303879	+	0.0404384i
$486$		0			0
$487$	21.4645	−	6.97424i	0.972649	−	0.316033i	0.220764	−	0.975327i	$-0.429145\pi$
$487$	21.4645	−	6.97424i	0.972649	−	0.316033i	0.751885	+	0.659294i	$0.229145\pi$
$488$	−0.453171	−	0.147244i	−0.0205141	−	0.00666543i
$489$		0			0
$490$	−24.1458	−	13.0665i	−1.09080	−	0.590283i
$491$	6.20389	−	19.0936i	0.279977	−	0.861682i	−0.707882	−	0.706331i	$-0.750349\pi$
$491$	6.20389	−	19.0936i	0.279977	−	0.861682i	0.987859	−	0.155351i	$-0.0496509\pi$
$492$		0			0
$493$	9.63565	+	13.2623i	0.433968	+	0.597306i
$494$	30.0141			1.35040
$495$		0			0
$496$	1.58993			0.0713898
$497$	3.09571	+	4.26088i	0.138862	+	0.191127i
$498$		0			0
$499$	−1.43750	+	4.42417i	−0.0643513	+	0.198053i	−0.978063	−	0.208311i	$-0.933203\pi$
$499$	−1.43750	+	4.42417i	−0.0643513	+	0.198053i	0.913711	+	0.406364i	$0.133203\pi$
$500$	5.37318	−	22.8016i	0.240296	−	1.01972i
$501$		0			0
$502$	32.6280	+	10.6015i	1.45626	+	0.473167i
$503$	12.3611	−	4.01636i	0.551154	−	0.179081i	−0.0201833	−	0.999796i	$-0.506425\pi$
$503$	12.3611	−	4.01636i	0.551154	−	0.179081i	0.571337	+	0.820716i	$0.306425\pi$
$504$		0			0
$505$	−4.48232	−	33.6828i	−0.199460	−	1.49887i
$506$	−17.4892	+	14.3057i	−0.777488	+	0.635966i
$507$		0			0
$508$	−8.73242	−	12.0191i	−0.387439	−	0.533263i
$509$	9.12976	+	28.0985i	0.404669	+	1.24544i	0.921171	+	0.389158i	$0.127234\pi$
$509$	9.12976	+	28.0985i	0.404669	+	1.24544i	−0.516501	+	0.856286i	$0.672766\pi$
$510$		0			0
$511$	−1.12169	−	0.814952i	−0.0496205	−	0.0360514i
$512$	−18.9023	+	26.0168i	−0.835373	+	1.14979i
$513$		0			0
$514$	2.96157	+	9.11478i	0.130629	+	0.402036i
$515$	−15.7884	+	15.0246i	−0.695720	+	0.662063i
$516$		0			0
$517$	−13.3638	+	5.20558i	−0.587740	+	0.228941i
$518$			12.3869i			0.544248i
$519$		0			0
$520$	−1.76003	+	0.842510i	−0.0771822	+	0.0369465i
$521$	9.71896	−	29.9119i	0.425796	−	1.31046i	−0.476435	−	0.879210i	$-0.658071\pi$
$521$	9.71896	−	29.9119i	0.425796	−	1.31046i	0.902230	−	0.431254i	$-0.141929\pi$
$522$		0			0
$523$	5.30194	−	7.29750i	0.231838	−	0.319097i	−0.677210	−	0.735790i	$-0.736811\pi$
$523$	5.30194	−	7.29750i	0.231838	−	0.319097i	0.909047	+	0.416693i	$0.136811\pi$
$524$	4.67290	−	14.3817i	0.204137	−	0.628268i
$525$		0			0
$526$	−29.6393	+	21.5342i	−1.29234	+	0.938937i
$527$			1.39595i			0.0608088i
$528$		0			0
$529$	11.6672			0.507269
$530$	−8.29992	−	8.72185i	−0.360526	−	0.378853i
$531$		0			0
$532$	−6.30817	−	2.04965i	−0.273494	−	0.0888636i
$533$	15.3885	−	21.1805i	0.666552	−	0.917430i
$534$		0			0
$535$	−3.09048	+	16.8058i	−0.133613	+	0.726577i
$536$	−0.572121	−	1.76081i	−0.0247119	−	0.0760553i
$537$		0			0
$538$			4.65046i			0.200496i
$539$	−16.9300	−	10.8763i	−0.729227	−	0.468473i
$540$		0			0
$541$	6.91720	−	5.02564i	0.297394	−	0.216069i	−0.429075	−	0.903269i	$-0.641160\pi$
$541$	6.91720	−	5.02564i	0.297394	−	0.216069i	0.726468	+	0.687200i	$0.241160\pi$
$542$	1.55066	−	0.503839i	0.0666064	−	0.0216417i
$543$		0			0
$544$	−21.8016	−	15.8398i	−0.934737	−	0.679126i
$545$	10.4886	−	19.3822i	0.449283	−	0.830241i
$546$		0			0
$547$	−32.2693	+	10.4849i	−1.37974	+	0.448304i	−0.902583	−	0.430516i	$-0.858332\pi$
$547$	−32.2693	+	10.4849i	−1.37974	+	0.448304i	−0.477154	+	0.878820i	$0.658332\pi$
$548$	10.4571	+	14.3930i	0.446706	+	0.614838i
$549$		0			0
$550$	10.1235	−	31.9956i	0.431669	−	1.36430i
$551$	−16.1028			−0.686002
$552$		0			0
$553$	−0.922187	+	0.299637i	−0.0392154	+	0.0127418i
$554$	7.39974	−	22.7740i	0.314385	−	0.967577i
$555$		0			0
$556$	−13.1206	−	9.53265i	−0.556436	−	0.404274i
$557$	−21.8178	−	7.08904i	−0.924451	−	0.300372i	−0.192160	−	0.981364i	$-0.561549\pi$
$557$	−21.8178	−	7.08904i	−0.924451	−	0.300372i	−0.732291	+	0.680991i	$0.761549\pi$
$558$		0			0
$559$	8.28110	−	6.01657i	0.350253	−	0.254474i
$560$	−8.13565	+	1.08265i	−0.343794	+	0.0457501i
$561$		0			0
$562$			12.6061i			0.531757i
$563$	5.45619	+	7.50980i	0.229951	+	0.316500i	0.908364	−	0.418180i	$-0.137332\pi$
$563$	5.45619	+	7.50980i	0.229951	+	0.316500i	−0.678413	+	0.734681i	$0.737332\pi$
$564$		0			0
$565$	2.02962	−	11.0369i	0.0853867	−	0.464325i
$566$	14.1546	+	10.2839i	0.594962	+	0.432266i
$567$		0			0
$568$	1.00013	+	0.324963i	0.0419647	+	0.0136352i
$569$	9.55701	+	29.4135i	0.400651	+	1.23308i	0.924473	+	0.381248i	$0.124506\pi$
$569$	9.55701	+	29.4135i	0.400651	+	1.23308i	−0.523822	+	0.851828i	$0.675494\pi$
$570$		0			0
$571$	−2.63736			−0.110370			−0.0551851	−	0.998476i	$-0.517575\pi$
$571$	−2.63736			−0.110370			−0.0551851	+	0.998476i	$0.517575\pi$
$572$	−29.3017	+	11.4138i	−1.22517	+	0.477237i
$573$		0			0
$574$	−9.14848	+	6.64676i	−0.381850	+	0.277430i
$575$	14.0909	−	9.20685i	0.587633	−	0.383952i
$576$		0			0
$577$	21.5309	−	29.6347i	0.896342	−	1.23371i	−0.0752785	−	0.997163i	$-0.523985\pi$
$577$	21.5309	−	29.6347i	0.896342	−	1.23371i	0.971620	−	0.236546i	$-0.0760154\pi$
$578$	−6.97814	+	9.60459i	−0.290252	+	0.399498i
$579$		0			0
$580$	20.7623	−	9.93873i	0.862106	−	0.412683i
$581$	5.77854	−	4.19835i	0.239734	−	0.174177i
$582$		0			0
$583$	−5.58719	−	6.83051i	−0.231398	−	0.282891i
$584$	−0.276837			−0.0114556
$585$		0			0
$586$	−3.63360	−	11.1831i	−0.150103	−	0.461968i
$587$	13.0793	+	4.24973i	0.539842	+	0.175405i	0.566231	−	0.824246i	$-0.308401\pi$
$587$	13.0793	+	4.24973i	0.539842	+	0.175405i	−0.0263892	+	0.999652i	$0.508401\pi$
$588$		0			0
$589$	−1.10935	−	0.805989i	−0.0457099	−	0.0332102i
$590$	−8.28669	+	45.0623i	−0.341158	+	1.85518i
$591$		0			0
$592$	−14.1567	−	19.4850i	−0.581837	−	0.800829i
$593$		−	20.1550i		−	0.827668i	−0.910352	−	0.413834i	$-0.864189\pi$
$593$		−	20.1550i		−	0.827668i	0.910352	−	0.413834i	$-0.135811\pi$
$594$		0			0
$595$	−0.950563	−	7.14310i	−0.0389693	−	0.292839i
$596$	−28.6194	+	20.7932i	−1.17230	+	0.851722i
$597$		0			0
$598$	−29.3187	−	9.52624i	−1.19893	−	0.389557i
$599$	−3.49753	−	2.54110i	−0.142905	−	0.103827i	0.514036	−	0.857769i	$-0.328150\pi$
$599$	−3.49753	−	2.54110i	−0.142905	−	0.103827i	−0.656941	+	0.753942i	$0.728150\pi$
$600$		0			0
$601$	11.1214	−	34.2281i	0.453650	−	1.39619i	−0.419063	−	0.907957i	$-0.637641\pi$
$601$	11.1214	−	34.2281i	0.453650	−	1.39619i	0.872713	−	0.488234i	$-0.162359\pi$
$602$	−4.20484	+	1.36623i	−0.171376	+	0.0556836i
$603$		0			0
$604$	25.7358			1.04717
$605$	9.15648	−	22.8289i	0.372264	−	0.928127i
$606$		0			0
$607$	23.3056	+	32.0774i	0.945945	+	1.30198i	0.953305	+	0.302009i	$0.0976572\pi$
$607$	23.3056	+	32.0774i	0.945945	+	1.30198i	−0.00736018	+	0.999973i	$0.502343\pi$
$608$	25.1754	−	8.17999i	1.02100	−	0.331742i
$609$		0			0
$610$	9.83338	+	5.32131i	0.398142	+	0.215454i
$611$	−15.8305	−	11.5015i	−0.640434	−	0.465303i
$612$		0			0
$613$	3.62818	−	1.17887i	0.146541	−	0.0476139i	−0.234828	−	0.972037i	$-0.575453\pi$
$613$	3.62818	−	1.17887i	0.146541	−	0.0476139i	0.381369	+	0.924423i	$0.375453\pi$
$614$	30.2424	−	21.9724i	1.22049	−	0.886735i
$615$		0			0
$616$	0.616721	−	0.0353690i	0.0248484	−	0.00142506i
$617$			28.4055i			1.14356i	0.820407	+	0.571781i	$0.193747\pi$
$617$			28.4055i			1.14356i	−0.820407	+	0.571781i	$0.806253\pi$
$618$		0			0
$619$	−7.43830	−	22.8927i	−0.298971	−	0.920137i	−0.981859	−	0.189614i	$-0.939276\pi$
$619$	−7.43830	−	22.8927i	−0.298971	−	0.920137i	0.682888	−	0.730523i	$-0.260724\pi$
$620$	1.92781	+	0.354512i	0.0774226	+	0.0142376i
$621$		0			0
$622$	−13.4786	+	18.5516i	−0.540441	+	0.743853i
$623$	11.2031	+	3.64010i	0.448841	+	0.145837i
$624$		0			0
$625$	−10.0406	+	22.8951i	−0.401624	+	0.915805i
$626$	−10.3511			−0.413714
$627$		0			0
$628$			8.82059i			0.351980i
$629$	17.1078	−	12.4296i	0.682135	−	0.495600i
$630$		0			0
$631$	5.90889	−	18.1857i	0.235229	−	0.723961i	−0.761862	−	0.647740i	$-0.775714\pi$
$631$	5.90889	−	18.1857i	0.235229	−	0.723961i	0.997091	−	0.0762213i	$-0.0242855\pi$
$632$	−0.113800	+	0.156632i	−0.00452672	+	0.00623049i
$633$		0			0
$634$	7.38747	−	22.7363i	0.293394	−	0.902974i
$635$	6.84558	+	14.3006i	0.271659	+	0.567502i
$636$		0			0
$637$		−	27.4546i		−	1.08779i
$638$	30.7263	−	11.9687i	1.21646	−	0.473847i
$639$		0			0
$640$	−2.49618	+	2.37542i	−0.0986700	+	0.0938968i
$641$	−3.70172	−	11.3927i	−0.146209	−	0.449985i	0.850955	−	0.525238i	$-0.176024\pi$
$641$	−3.70172	−	11.3927i	−0.146209	−	0.449985i	−0.997165	+	0.0752526i	$0.976024\pi$
$642$		0			0
$643$	15.1301	−	20.8248i	0.596672	−	0.821248i	−0.398727	−	0.917070i	$-0.630548\pi$
$643$	15.1301	−	20.8248i	0.596672	−	0.821248i	0.995399	+	0.0958216i	$0.0305478\pi$
$644$	5.51149	+	4.00433i	0.217183	+	0.157793i
$645$		0			0
$646$	6.83905	+	21.0484i	0.269079	+	0.828139i
$647$	5.46774	+	7.52570i	0.214959	+	0.295866i	0.902856	−	0.429942i	$-0.141466\pi$
$647$	5.46774	+	7.52570i	0.214959	+	0.295866i	−0.687897	+	0.725808i	$0.741466\pi$
$648$		0			0
$649$	−8.53167	+	32.4800i	−0.334897	+	1.27495i
$650$	44.1933	−	11.9740i	1.73341	−	0.469661i
$651$		0			0
$652$	−33.0268	+	10.7311i	−1.29343	+	0.420261i
$653$	−35.6177	−	11.5729i	−1.39383	−	0.452882i	−0.486637	−	0.873604i	$-0.661777\pi$
$653$	−35.6177	−	11.5729i	−1.39383	−	0.452882i	−0.907189	+	0.420723i	$0.861777\pi$
$654$		0			0
$655$	−7.68047	+	14.1929i	−0.300101	+	0.554563i
$656$	6.79446	−	20.9112i	0.265279	−	0.816445i
$657$		0			0
$658$	4.96785	+	6.83766i	0.193667	+	0.266560i
$659$	−4.93753			−0.192339			−0.0961693	−	0.995365i	$-0.530659\pi$
$659$	−4.93753			−0.192339			−0.0961693	+	0.995365i	$0.530659\pi$
$660$		0			0
$661$	−4.82155			−0.187537			−0.0937683	−	0.995594i	$-0.529891\pi$
$661$	−4.82155			−0.187537			−0.0937683	+	0.995594i	$0.529891\pi$
$662$	34.8155	+	47.9194i	1.35314	+	1.86244i
$663$		0			0
$664$	0.440710	−	1.35637i	0.0171029	−	0.0526372i
$665$	6.22536	+	3.36884i	0.241409	+	0.130638i
$666$		0			0
$667$	15.7297	+	5.11091i	0.609058	+	0.197895i
$668$	18.2670	−	5.93532i	0.706773	−	0.229645i
$669$		0			0
$670$	5.73070	+	43.0639i	0.221396	+	1.66370i
$671$	6.89474	+	4.42935i	0.266168	+	0.170993i
$672$		0			0
$673$	19.3464	+	26.6280i	0.745749	+	1.02644i	0.998267	+	0.0588431i	$0.0187412\pi$
$673$	19.3464	+	26.6280i	0.745749	+	1.02644i	−0.252518	+	0.967592i	$0.581259\pi$
$674$	16.6619	+	51.2802i	0.641794	+	1.97524i
$675$		0			0
$676$	−12.6736	−	9.20789i	−0.487445	−	0.354150i
$677$	−10.0761	+	13.8686i	−0.387258	+	0.533014i	−0.957489	−	0.288470i	$-0.906854\pi$
$677$	−10.0761	+	13.8686i	−0.387258	+	0.533014i	0.570231	+	0.821484i	$0.306854\pi$
$678$		0			0
$679$	0.901110	+	2.77333i	0.0345814	+	0.106431i
$680$	−0.991882	−	1.04230i	−0.0380369	−	0.0399705i
$681$		0			0
$682$	2.71585	+	0.713386i	0.103995	+	0.0273170i
$683$			19.3586i			0.740737i	0.928885	+	0.370368i	$0.120769\pi$
$683$			19.3586i			0.740737i	−0.928885	+	0.370368i	$0.879231\pi$
$684$		0			0
$685$	−8.19762	−	17.1250i	−0.313215	−	0.654314i
$686$	−7.89232	+	24.2901i	−0.301330	+	0.927399i
$687$		0			0
$688$	5.05292	−	6.95475i	0.192641	−	0.265148i
$689$	3.72054	−	11.4506i	0.141741	−	0.436234i
$690$		0			0
$691$	7.39559	−	5.37321i	0.281342	−	0.204407i	−0.438161	−	0.898897i	$-0.644370\pi$
$691$	7.39559	−	5.37321i	0.281342	−	0.204407i	0.719502	+	0.694490i	$0.244370\pi$
$692$		−	8.61097i		−	0.327340i
$693$		0			0
$694$	8.72467			0.331184
$695$	11.9312	+	12.5378i	0.452578	+	0.475585i
$696$		0			0
$697$	18.3600	+	5.96554i	0.695436	+	0.225961i
$698$	−15.6650	+	21.5610i	−0.592929	+	0.816096i
$699$		0			0
$700$	−10.1060	−	0.501317i	−0.381971	−	0.0189480i
$701$	4.72594	+	14.5450i	0.178496	+	0.549355i	0.999776	−	0.0211707i	$-0.00673934\pi$
$701$	4.72594	+	14.5450i	0.178496	+	0.549355i	−0.821279	+	0.570526i	$0.806739\pi$
$702$		0			0
$703$			20.7719i			0.783428i
$704$	−22.4457	+	18.3601i	−0.845956	+	0.691971i
$705$		0			0
$706$	41.7327	−	30.3206i	1.57063	−	1.14113i
$707$	−13.9585	+	4.53539i	−0.524964	+	0.170571i
$708$		0			0
$709$	34.7172	+	25.2235i	1.30383	+	0.947290i	0.999985	−	0.00543044i	$-0.00172857\pi$
$709$	34.7172	+	25.2235i	1.30383	+	0.947290i	0.303848	+	0.952721i	$0.401729\pi$
$710$	−21.7020	−	11.7440i	−0.814460	−	0.440743i
$711$		0			0
$712$	2.23690	−	0.726814i	0.0838315	−	0.0272385i
$713$	0.827834	+	1.13942i	0.0310026	+	0.0426714i
$714$		0			0
$715$	32.9577	−	6.32421i	1.23255	−	0.236512i
$716$	34.1450			1.27606
$717$		0			0
$718$	50.5682	−	16.4306i	1.88719	−	0.613184i
$719$	1.48738	−	4.57768i	0.0554699	−	0.170719i	−0.919483	−	0.393129i	$-0.871393\pi$
$719$	1.48738	−	4.57768i	0.0554699	−	0.170719i	0.974953	+	0.222411i	$0.0713925\pi$
$720$		0			0
$721$	7.61592	+	5.53329i	0.283632	+	0.206071i
$722$	15.8925	+	5.16378i	0.591457	+	0.192176i
$723$		0			0
$724$	−9.40269	+	6.83146i	−0.349448	+	0.253889i
$725$	−23.7101	+	6.42417i	−0.880571	+	0.238588i
$726$		0			0
$727$			21.8922i			0.811937i	0.913887	+	0.405969i	$0.133066\pi$
$727$			21.8922i			0.811937i	−0.913887	+	0.405969i	$0.866934\pi$
$728$	0.495395	+	0.681853i	0.0183606	+	0.0252712i
$729$		0			0
$730$	6.38884	+	1.17487i	0.236461	+	0.0434839i
$731$	6.10627	+	4.43647i	0.225849	+	0.164089i
$732$		0			0
$733$	−45.6788	−	14.8419i	−1.68718	−	0.548199i	−0.700901	−	0.713259i	$-0.747218\pi$
$733$	−45.6788	−	14.8419i	−1.68718	−	0.548199i	−0.986284	+	0.165060i	$0.947218\pi$
$734$	−1.26242	−	3.88533i	−0.0465968	−	0.143410i
$735$		0			0
$736$	−27.1885			−1.00218
$737$	1.82312	+	31.7893i	0.0671554	+	1.17097i
$738$		0			0
$739$	−27.5934	+	20.0478i	−1.01504	+	0.737470i	−0.965260	−	0.261290i	$-0.915852\pi$
$739$	−27.5934	+	20.0478i	−1.01504	+	0.737470i	−0.0497805	+	0.998760i	$0.515852\pi$
$740$	−12.8205	−	26.7824i	−0.471292	−	0.984542i
$741$		0			0
$742$	−3.05671	+	4.20720i	−0.112215	+	0.154451i
$743$	15.5411	−	21.3906i	0.570149	−	0.784743i	−0.422423	−	0.906399i	$-0.638820\pi$
$743$	15.5411	−	21.3906i	0.570149	−	0.784743i	0.992572	+	0.121656i	$0.0388203\pi$
$744$		0			0
$745$	34.0519	−	16.3003i	1.24756	−	0.597199i
$746$	14.5244	−	10.5526i	0.531777	−	0.386359i
$747$		0			0
$748$	−14.6811	−	17.9481i	−0.536794	−	0.656247i
$749$	7.38062			0.269682
$750$		0			0
$751$	14.1963	+	43.6918i	0.518032	+	1.59434i	0.777697	+	0.628639i	$0.216388\pi$
$751$	14.1963	+	43.6918i	0.518032	+	1.59434i	−0.259666	+	0.965699i	$0.583612\pi$
$752$	−15.6292	−	5.07825i	−0.569939	−	0.185185i
$753$		0			0
$754$	36.3977	+	26.4445i	1.32553	+	0.963052i
$755$	−27.0119	−	4.96733i	−0.983064	−	0.180780i
$756$		0			0
$757$	−18.1365	−	24.9628i	−0.659183	−	0.907288i	0.340271	−	0.940327i	$-0.389481\pi$
$757$	−18.1365	−	24.9628i	−0.659183	−	0.907288i	−0.999454	+	0.0330398i	$0.989481\pi$
$758$			42.6271i			1.54828i
$759$		0			0
$760$	1.40099	−	0.186436i	0.0508194	−	0.00676275i
$761$	−11.4860	+	8.34507i	−0.416367	+	0.302508i	−0.776175	−	0.630518i	$-0.782842\pi$
$761$	−11.4860	+	8.34507i	−0.416367	+	0.302508i	0.359807	+	0.933027i	$0.382842\pi$
$762$		0			0
$763$	−9.05303	−	2.94151i	−0.327742	−	0.106490i
$764$	−36.9811	−	26.8684i	−1.33793	−	0.972063i
$765$		0			0
$766$	−16.2464	+	50.0012i	−0.587005	+	1.80662i
$767$	−43.5754	+	14.1585i	−1.57342	+	0.511234i
$768$		0			0
$769$	30.0208			1.08258			0.541290	−	0.840836i	$-0.317936\pi$
$769$	30.0208			1.08258			0.541290	+	0.840836i	$0.317936\pi$
$770$	−14.3828	−	1.80106i	−0.518319	−	0.0649057i
$771$		0			0
$772$	27.6846	+	38.1046i	0.996392	+	1.37142i
$773$	−28.9401	+	9.40320i	−1.04090	+	0.338209i	−0.779092	−	0.626910i	$-0.784319\pi$
$773$	−28.9401	+	9.40320i	−1.04090	+	0.338209i	−0.261810	+	0.965119i	$0.584319\pi$
$774$		0			0
$775$	−1.95497	−	0.744183i	−0.0702248	−	0.0267318i
$776$	0.471046	+	0.342235i	0.0169096	+	0.0122855i
$777$		0			0
$778$	−3.16373	+	1.02796i	−0.113425	+	0.0368541i
$779$	−15.3414	+	11.1461i	−0.549661	+	0.399352i
$780$		0			0
$781$	−15.2165	−	9.77544i	−0.544488	−	0.349793i
$782$		−	22.7315i		−	0.812876i
$783$		0			0
$784$	−7.12510	−	21.9288i	−0.254468	−	0.783172i
$785$	1.70249	−	9.25797i	0.0607643	−	0.330431i
$786$		0			0
$787$	−17.9067	+	24.6465i	−0.638306	+	0.878553i	−0.998524	−	0.0543151i	$-0.982702\pi$
$787$	−17.9067	+	24.6465i	−0.638306	+	0.878553i	0.360218	+	0.932868i	$0.382702\pi$
$788$	51.3089	+	16.6713i	1.82780	+	0.593890i
$789$		0			0
$790$	3.29100	−	3.13180i	0.117089	−	0.111424i
$791$	−4.84709			−0.172343
$792$		0			0
$793$			11.1809i			0.397044i
$794$	27.3555	−	19.8749i	0.970810	−	0.705334i
$795$		0			0
$796$	10.9859	−	33.8112i	0.389385	−	1.19840i
$797$	−19.4235	+	26.7341i	−0.688014	+	0.946970i	−0.999995	−	0.00311796i	$-0.999008\pi$
$797$	−19.4235	+	26.7341i	−0.688014	+	0.946970i	0.311981	+	0.950088i	$0.399008\pi$
$798$		0			0
$799$	4.45870	−	13.7225i	0.157737	−	0.485466i
$800$	33.8054	−	22.0881i	1.19520	−	0.780931i
$801$		0			0
$802$			56.2421i			1.98598i
$803$	4.60494	+	1.20960i	0.162505	+	0.0426859i
$804$		0			0
$805$	−5.01190	−	5.26668i	−0.176646	−	0.185626i
$806$	1.18388	+	3.64361i	0.0417004	+	0.128341i
$807$		0			0
$808$	−1.72251	+	2.37083i	−0.0605977	+	0.0834056i
$809$	−8.89072	−	6.45948i	−0.312581	−	0.227103i	0.420422	−	0.907329i	$-0.361882\pi$
$809$	−8.89072	−	6.45948i	−0.312581	−	0.227103i	−0.733003	+	0.680225i	$0.761882\pi$
$810$		0			0
$811$	12.5951	+	38.7638i	0.442275	+	1.36118i	0.885445	+	0.464744i	$0.153854\pi$
$811$	12.5951	+	38.7638i	0.442275	+	1.36118i	−0.443171	+	0.896437i	$0.646146\pi$
$812$	−5.84397	−	8.04353i	−0.205083	−	0.282273i
$813$		0			0
$814$	−15.4392	−	39.6355i	−0.541142	−	1.38923i
$815$	36.7358	−	4.88858i	1.28680	−	0.171240i
$816$		0			0
$817$	−7.05121	+	2.29108i	−0.246691	+	0.0801547i
$818$	75.8941	+	24.6595i	2.65358	+	0.862199i
$819$		0			0
$820$	12.9010	−	23.8401i	0.450524	−	0.832534i
$821$	−4.66851	+	14.3682i	−0.162932	+	0.501454i	−0.998878	−	0.0473584i	$-0.984920\pi$
$821$	−4.66851	+	14.3682i	−0.162932	+	0.501454i	0.835946	+	0.548812i	$0.184920\pi$
$822$		0			0
$823$	−21.4138	−	29.4735i	−0.746437	−	1.02738i	−0.998222	−	0.0595989i	$-0.981018\pi$
$823$	−21.4138	−	29.4735i	−0.746437	−	1.02738i	0.251786	−	0.967783i	$-0.418982\pi$
$824$	1.87964			0.0654805
$825$		0			0
$826$	19.7901			0.688585
$827$	−2.23560	−	3.07703i	−0.0777393	−	0.106999i	0.768376	−	0.639998i	$-0.221065\pi$
$827$	−2.23560	−	3.07703i	−0.0777393	−	0.106999i	−0.846116	+	0.532999i	$0.821065\pi$
$828$		0			0
$829$	8.43810	−	25.9698i	0.293067	−	0.901969i	−0.690796	−	0.723049i	$-0.742740\pi$
$829$	8.43810	−	25.9698i	0.293067	−	0.901969i	0.983864	−	0.178919i	$-0.0572601\pi$
$830$	−15.9270	+	29.4318i	−0.552834	+	1.02159i
$831$		0			0
$832$	−37.6279	−	12.2261i	−1.30451	−	0.423862i
$833$	19.2535	−	6.25584i	0.667094	−	0.216752i
$834$		0			0
$835$	−20.3184	+	2.70386i	−0.703148	+	0.0935710i
$836$	22.7396	−	1.30412i	0.786466	−	0.0451038i
$837$		0			0
$838$	17.5821	+	24.1998i	0.607365	+	0.835967i
$839$	8.75291	+	26.9387i	0.302184	+	0.930026i	0.980713	+	0.195453i	$0.0626177\pi$
$839$	8.75291	+	26.9387i	0.302184	+	0.930026i	−0.678529	+	0.734573i	$0.737382\pi$
$840$		0			0
$841$	3.93381	+	2.85808i	0.135649	+	0.0985546i
$842$	12.8195	−	17.6445i	0.441788	−	0.608070i
$843$		0			0
$844$	3.77247	+	11.6105i	0.129854	+	0.399649i
$845$	11.5248	+	12.1106i	0.396464	+	0.416619i
$846$		0			0
$847$	−10.4132	−	2.10635i	−0.357800	−	0.0723750i
$848$		−	10.1115i		−	0.347232i
$849$		0			0
$850$	18.4672	+	28.2637i	0.633419	+	0.969438i
$851$	6.59285	−	20.2907i	0.226000	−	0.695556i
$852$		0			0
$853$	4.90400	−	6.74977i	0.167910	−	0.231108i	−0.716767	−	0.697313i	$-0.754379\pi$
$853$	4.90400	−	6.74977i	0.167910	−	0.231108i	0.884677	+	0.466205i	$0.154379\pi$
$854$	1.49235	−	4.59298i	0.0510671	−	0.157168i
$855$		0			0
$856$	1.19223	−	0.866207i	0.0407497	−	0.0296064i
$857$		−	8.59547i		−	0.293616i	−0.989165	−	0.146808i	$-0.953100\pi$
$857$		−	8.59547i		−	0.293616i	0.989165	−	0.146808i	$-0.0468999\pi$
$858$		0			0
$859$	−9.40807			−0.320999			−0.160500	−	0.987036i	$-0.551311\pi$
$859$	−9.40807			−0.320999			−0.160500	+	0.987036i	$0.551311\pi$
$860$	7.67747	−	7.30606i	0.261800	−	0.249135i
$861$		0			0
$862$	61.9571	+	20.1311i	2.11027	+	0.685667i
$863$	6.06951	−	8.35396i	0.206608	−	0.284372i	−0.693120	−	0.720822i	$-0.743764\pi$
$863$	6.06951	−	8.35396i	0.206608	−	0.284372i	0.899728	+	0.436450i	$0.143764\pi$
$864$		0			0
$865$	−1.66203	+	9.03795i	−0.0565106	+	0.307300i
$866$	0.239279	+	0.736426i	0.00813104	+	0.0250248i
$867$		0			0
$868$		−	0.846638i		−	0.0287368i
$869$	2.57734	−	2.10820i	0.0874304	−	0.0715159i
$870$		0			0
$871$	−35.1466	+	25.5355i	−1.19090	+	0.865237i
$872$	−1.80761	+	0.587328i	−0.0612133	+	0.0198894i
$873$		0			0
$874$	18.0644	+	13.1246i	0.611038	+	0.443945i
$875$	10.5103	+	2.47676i	0.355315	+	0.0837298i
$876$		0			0
$877$	28.3445	−	9.20969i	0.957126	−	0.310989i	0.211518	−	0.977374i	$-0.432159\pi$
$877$	28.3445	−	9.20969i	0.957126	−	0.310989i	0.745608	+	0.666385i	$0.232159\pi$
$878$	−31.5608	−	43.4398i	−1.06513	−	1.46602i
$879$		0			0
$880$	24.6830	−	13.6046i	0.832065	−	0.458612i
$881$	−30.1175			−1.01469			−0.507343	−	0.861744i	$-0.669372\pi$
$881$	−30.1175			−1.01469			−0.507343	+	0.861744i	$0.669372\pi$
$882$		0			0
$883$	−47.8970	+	15.5627i	−1.61186	+	0.523726i	−0.970002	−	0.243096i	$-0.921837\pi$
$883$	−47.8970	+	15.5627i	−1.61186	+	0.523726i	−0.641860	+	0.766822i	$0.721837\pi$
$884$	9.77622	−	30.0881i	0.328810	−	1.01197i
$885$		0			0
$886$	−23.7410	−	17.2488i	−0.797593	−	0.579485i
$887$	39.3789	+	12.7950i	1.32221	+	0.429613i	0.883255	−	0.468893i	$-0.155347\pi$
$887$	39.3789	+	12.7950i	1.32221	+	0.429613i	0.438959	+	0.898507i	$0.355347\pi$
$888$		0			0
$889$	5.54021	−	4.02520i	0.185813	−	0.135001i
$890$	−54.7077	+	7.28019i	−1.83381	+	0.244033i
$891$		0			0
$892$		−	39.8572i		−	1.33452i
$893$	8.33074	+	11.4663i	0.278777	+	0.383704i
$894$		0			0
$895$	−35.8382	−	6.59043i	−1.19794	−	0.220294i
$896$	1.20409	+	0.874825i	0.0402259	+	0.0292258i
$897$		0			0
$898$	−19.4658	−	6.32481i	−0.649581	−	0.211062i
$899$	−0.635162	−	1.95483i	−0.0211838	−	0.0651971i
$900$		0			0
$901$	8.87793			0.295767
$902$	20.9887	−	32.6711i	0.698848	−	1.08783i
$903$		0			0
$904$	−0.782977	+	0.568866i	−0.0260414	+	0.0189202i
$905$	11.1875	−	5.35536i	0.371885	−	0.178018i
$906$		0			0
$907$	2.72271	−	3.74749i	0.0904062	−	0.124433i	−0.761418	−	0.648261i	$-0.775496\pi$
$907$	2.72271	−	3.74749i	0.0904062	−	0.124433i	0.851824	+	0.523828i	$0.175496\pi$
$908$	−35.0582	+	48.2534i	−1.16345	+	1.60135i
$909$		0			0
$910$	−8.53900	−	17.8382i	−0.283065	−	0.591330i
$911$	5.64577	−	4.10189i	0.187053	−	0.135902i	−0.490318	−	0.871544i	$-0.663119\pi$
$911$	5.64577	−	4.10189i	0.187053	−	0.135902i	0.677371	+	0.735642i	$0.263119\pi$
$912$		0			0
$913$	−13.2573	+	20.6363i	−0.438752	+	0.682963i
$914$	−79.1032			−2.61650
$915$		0			0
$916$	−16.4404	−	50.5984i	−0.543207	−	1.67182i
$917$	6.62923	+	2.15397i	0.218916	+	0.0711303i
$918$		0			0
$919$	−18.9477	−	13.7663i	−0.625027	−	0.454109i	0.229647	−	0.973274i	$-0.426243\pi$
$919$	−18.9477	−	13.7663i	−0.625027	−	0.454109i	−0.854674	+	0.519165i	$0.826243\pi$
$920$	−1.42771	−	0.262548i	−0.0470702	−	0.00865594i
$921$		0			0
$922$	−46.5474	−	64.0671i	−1.53296	−	2.10994i
$923$		−	24.6758i		−	0.812215i
$924$		0			0
$925$	8.28691	+	30.5850i	0.272472	+	1.00563i
$926$	21.1507	−	15.3669i	0.695057	−	0.504988i
$927$		0			0
$928$	37.7371	+	12.2615i	1.23878	+	0.402504i
$929$	14.6355	+	10.6333i	0.480175	+	0.348868i	0.801394	−	0.598137i	$-0.204092\pi$
$929$	14.6355	+	10.6333i	0.480175	+	0.348868i	−0.321218	+	0.947005i	$0.604092\pi$
$930$		0			0
$931$	−6.14504	+	18.9125i	−0.201395	+	0.619831i
$932$	−24.9440	+	8.10480i	−0.817068	+	0.265481i
$933$		0			0
$934$	−22.7646			−0.744881
$935$	11.9449	+	21.6717i	0.390639	+	0.708741i
$936$		0			0
$937$	6.47128	+	8.90696i	0.211408	+	0.290978i	0.901531	−	0.432714i	$-0.142444\pi$
$937$	6.47128	+	8.90696i	0.211408	+	0.290978i	−0.690124	+	0.723691i	$0.742444\pi$
$938$	17.8461	−	5.79856i	0.582697	−	0.189330i
$939$		0			0
$940$	−17.8183	−	9.64236i	−0.581170	−	0.314499i
$941$	27.3293	+	19.8559i	0.890908	+	0.647283i	0.936115	−	0.351695i	$-0.114395\pi$
$941$	27.3293	+	19.8559i	0.890908	+	0.647283i	−0.0452063	+	0.998978i	$0.514395\pi$
$942$		0			0
$943$	18.5237	−	6.01870i	0.603213	−	0.195996i
$944$	−31.1305	+	22.6177i	−1.01321	+	0.736142i
$945$		0			0
$946$	11.7517	−	9.61264i	0.382082	−	0.312534i
$947$		−	46.9853i		−	1.52682i	−0.645915	−	0.763409i	$-0.723524\pi$
$947$		−	46.9853i		−	1.52682i	0.645915	−	0.763409i	$-0.276476\pi$
$948$		0			0
$949$	2.00736	+	6.17803i	0.0651618	+	0.200547i
$950$	−33.1233	−	1.64311i	−1.07466	−	0.0533096i
$951$		0			0
$952$	−0.365292	+	0.502781i	−0.0118392	+	0.0162952i
$953$	−40.4110	−	13.1303i	−1.30904	−	0.425333i	−0.430323	−	0.902675i	$-0.641600\pi$
$953$	−40.4110	−	13.1303i	−1.30904	−	0.425333i	−0.878718	+	0.477341i	$0.841600\pi$
$954$		0			0
$955$	33.6290	+	35.3385i	1.08821	+	1.14353i
$956$	−42.7180			−1.38160
$957$		0			0
$958$		−	42.4291i		−	1.37082i
$959$	−6.63443	+	4.82019i	−0.214237	+	0.155652i
$960$		0			0
$961$	−9.52544	+	29.3163i	−0.307272	+	0.945687i
$962$	34.1123	−	46.9515i	1.09982	−	1.51378i
$963$		0			0
$964$	14.7584	−	45.4216i	0.475335	−	1.46293i
$965$	−21.7027	−	45.3376i	−0.698636	−	1.45947i
$966$		0			0
$967$		−	54.1642i		−	1.74180i	−0.491458	−	0.870901i	$-0.663536\pi$
$967$		−	54.1642i		−	1.74180i	0.491458	−	0.870901i	$-0.336464\pi$
$968$	−1.92930	+	0.881863i	−0.0620101	+	0.0283442i
$969$		0			0
$970$	−9.41838	−	9.89717i	−0.302406	−	0.317779i
$971$	−1.61878	−	4.98209i	−0.0519491	−	0.159883i	0.921716	−	0.387865i	$-0.126787\pi$
$971$	−1.61878	−	4.98209i	−0.0519491	−	0.159883i	−0.973665	+	0.227982i	$0.926787\pi$
$972$		0			0
$973$	4.39406	−	6.04791i	0.140867	−	0.193887i
$974$	36.9500	+	26.8457i	1.18395	+	0.860193i
$975$		0			0
$976$	2.90169	+	8.93049i	0.0928809	+	0.285858i
$977$	4.57381	+	6.29530i	0.146329	+	0.201405i	0.875890	−	0.482512i	$-0.160275\pi$
$977$	4.57381	+	6.29530i	0.146329	+	0.201405i	−0.729561	+	0.683916i	$0.760275\pi$
$978$		0			0
$979$	−40.3846	+	2.31606i	−1.29070	+	0.0740216i
$980$	−3.74973	−	28.1777i	−0.119781	−	0.900104i
$981$		0			0
$982$	38.6394	−	12.5547i	1.23303	−	0.400637i
$983$	−48.9924	−	15.9186i	−1.56261	−	0.507724i	−0.605109	−	0.796143i	$-0.706871\pi$
$983$	−48.9924	−	15.9186i	−1.56261	−	0.507724i	−0.957504	+	0.288419i	$0.906871\pi$
$984$		0			0
$985$	−50.6354	−	27.4012i	−1.61338	−	0.873075i
$986$	−10.2515	+	31.5509i	−0.326474	+	1.00478i
$987$		0			0
$988$	18.2661	+	25.1411i	0.581122	+	0.799846i
$989$	7.61503			0.242144
$990$		0			0
$991$	−22.3382			−0.709596			−0.354798	−	0.934943i	$-0.615450\pi$
$991$	−22.3382			−0.709596			−0.354798	+	0.934943i	$0.615450\pi$
$992$	1.98605	+	2.73356i	0.0630571	+	0.0867906i
$993$		0			0
$994$	−3.29357	+	10.1366i	−0.104466	+	0.321512i
$995$	−18.0566	+	33.3673i	−0.572434	+	1.05781i
$996$		0			0
$997$	−0.175514	−	0.0570278i	−0.00555857	−	0.00180609i	0.306236	−	0.951955i	$-0.400930\pi$
$997$	−0.175514	−	0.0570278i	−0.00555857	−	0.00180609i	−0.311795	+	0.950149i	$0.600930\pi$
$998$	−8.95311	+	2.90904i	−0.283406	+	0.0920841i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.ba.a.289.4		16
3.2	odd	2		55.2.j.a.14.1	yes	16
5.4	even	2	inner	495.2.ba.a.289.1		16
11.4	even	5	inner	495.2.ba.a.334.1		16
12.11	even	2		880.2.cd.c.289.1		16
15.2	even	4		275.2.h.d.201.4		16
15.8	even	4		275.2.h.d.201.1		16
15.14	odd	2		55.2.j.a.14.4	yes	16
33.2	even	10		605.2.b.f.364.1		8
33.5	odd	10		605.2.j.h.9.4		16
33.8	even	10		605.2.j.g.269.4		16
33.14	odd	10		605.2.j.h.269.1		16
33.17	even	10		605.2.j.g.9.1		16
33.20	odd	10		605.2.b.g.364.8		8
33.26	odd	10		55.2.j.a.4.4	yes	16
33.29	even	10		605.2.j.d.444.1		16
33.32	even	2		605.2.j.d.124.4		16
55.4	even	10	inner	495.2.ba.a.334.4		16
60.59	even	2		880.2.cd.c.289.4		16
132.59	even	10		880.2.cd.c.609.4		16
165.2	odd	20		3025.2.a.bk.1.8		8
165.14	odd	10		605.2.j.h.269.4		16
165.29	even	10		605.2.j.d.444.4		16
165.53	even	20		3025.2.a.bl.1.8		8
165.59	odd	10		55.2.j.a.4.1	✓	16
165.68	odd	20		3025.2.a.bk.1.1		8
165.74	even	10		605.2.j.g.269.1		16
165.92	even	20		275.2.h.d.26.4		16
165.104	odd	10		605.2.j.h.9.1		16
165.119	odd	10		605.2.b.g.364.1		8
165.134	even	10		605.2.b.f.364.8		8
165.149	even	10		605.2.j.g.9.4		16
165.152	even	20		3025.2.a.bl.1.1		8
165.158	even	20		275.2.h.d.26.1		16
165.164	even	2		605.2.j.d.124.1		16
660.59	even	10		880.2.cd.c.609.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	165.59	odd	10
55.2.j.a.4.4	yes	16	33.26	odd	10
55.2.j.a.14.1	yes	16	3.2	odd	2
55.2.j.a.14.4	yes	16	15.14	odd	2
275.2.h.d.26.1		16	165.158	even	20
275.2.h.d.26.4		16	165.92	even	20
275.2.h.d.201.1		16	15.8	even	4
275.2.h.d.201.4		16	15.2	even	4
495.2.ba.a.289.1		16	5.4	even	2	inner
495.2.ba.a.289.4		16	1.1	even	1	trivial
495.2.ba.a.334.1		16	11.4	even	5	inner
495.2.ba.a.334.4		16	55.4	even	10	inner
605.2.b.f.364.1		8	33.2	even	10
605.2.b.f.364.8		8	165.134	even	10
605.2.b.g.364.1		8	165.119	odd	10
605.2.b.g.364.8		8	33.20	odd	10
605.2.j.d.124.1		16	165.164	even	2
605.2.j.d.124.4		16	33.32	even	2
605.2.j.d.444.1		16	33.29	even	10
605.2.j.d.444.4		16	165.29	even	10
605.2.j.g.9.1		16	33.17	even	10
605.2.j.g.9.4		16	165.149	even	10
605.2.j.g.269.1		16	165.74	even	10
605.2.j.g.269.4		16	33.8	even	10
605.2.j.h.9.1		16	165.104	odd	10
605.2.j.h.9.4		16	33.5	odd	10
605.2.j.h.269.1		16	33.14	odd	10
605.2.j.h.269.4		16	165.14	odd	10
880.2.cd.c.289.1		16	12.11	even	2
880.2.cd.c.289.4		16	60.59	even	2
880.2.cd.c.609.1		16	660.59	even	10
880.2.cd.c.609.4		16	132.59	even	10
3025.2.a.bk.1.1		8	165.68	odd	20
3025.2.a.bk.1.8		8	165.2	odd	20
3025.2.a.bl.1.1		8	165.152	even	20
3025.2.a.bl.1.8		8	165.53	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18949 + 1.63719i) q^{2} +(-0.647481 + 1.99274i) q^{4} +(1.06421 - 1.96658i) q^{5} +(-0.918552 - 0.298456i) q^{7} +(-0.183406 + 0.0595923i) q^{8} +(4.48555 - 0.596911i) q^{10} +(3.31118 - 0.189896i) q^{11} +(2.65978 + 3.66088i) q^{13} +(-0.603980 - 1.85886i) q^{14} +(3.07453 + 2.23378i) q^{16} +(-1.96126 + 2.69944i) q^{17} +(-1.01283 - 3.11717i) q^{19} +(3.22984 + 3.39403i) q^{20} +(4.24952 + 5.19517i) q^{22} +3.36643i q^{23} +(-2.73490 - 4.18573i) q^{25} +(-2.82978 + 8.70916i) q^{26} +(1.18949 - 1.63719i) q^{28} +(1.51820 - 4.67254i) q^{29} +(0.338464 - 0.245909i) q^{31} +8.07636i q^{32} -6.75241 q^{34} +(-1.56447 + 1.48879i) q^{35} +(-6.02737 - 1.95841i) q^{37} +(3.89867 - 5.36605i) q^{38} +(-0.0779900 + 0.424103i) q^{40} +(-1.78786 - 5.50247i) q^{41} -2.26205i q^{43} +(-1.76552 + 6.72129i) q^{44} +(-5.51149 + 4.00433i) q^{46} +(-4.11260 + 1.33626i) q^{47} +(-4.90846 - 3.56620i) q^{49} +(3.59970 - 9.45645i) q^{50} +(-9.01735 + 2.92991i) q^{52} +(-1.56392 - 2.15255i) q^{53} +(3.15036 - 6.71381i) q^{55} +0.186254 q^{56} +(9.45574 - 3.07235i) q^{58} +(-3.12889 + 9.62972i) q^{59} +(1.99897 + 1.45233i) q^{61} +(0.805201 + 0.261626i) q^{62} +(-7.07350 + 5.13920i) q^{64} +(10.0300 - 1.33473i) q^{65} +9.60059i q^{67} +(-4.10941 - 5.65612i) q^{68} +(-4.29836 - 0.790444i) q^{70} +(-4.41166 - 3.20526i) q^{71} +(1.36528 + 0.443607i) q^{73} +(-3.96321 - 12.1975i) q^{74} +6.86752 q^{76} +(-3.09817 - 0.813812i) q^{77} +(0.812218 - 0.590111i) q^{79} +(7.66487 - 3.66911i) q^{80} +(6.88197 - 9.47221i) q^{82} +(-4.34692 + 5.98302i) q^{83} +(3.22148 + 6.72976i) q^{85} +(3.70342 - 2.69069i) q^{86} +(-0.595976 + 0.232149i) q^{88} -12.1964 q^{89} +(-1.35054 - 4.15654i) q^{91} +(-6.70842 - 2.17970i) q^{92} +(-7.07962 - 5.14365i) q^{94} +(-7.20805 - 1.32552i) q^{95} +(-1.77467 - 2.44262i) q^{97} -12.2781i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 2 q^{5} + 6 q^{11} + 12 q^{14} + 16 q^{16} + 6 q^{19} + 8 q^{20} - 16 q^{25} - 40 q^{26} - 2 q^{29} + 8 q^{31} - 16 q^{34} - 22 q^{35} + 12 q^{40} + 52 q^{41} - 4 q^{44} - 62 q^{46} - 10 q^{49}+ \cdots - 48 q^{95}+O(q^{100}) \) 16 * q - 4 * q^4 + 2 * q^5 + 6 * q^11 + 12 * q^14 + 16 * q^16 + 6 * q^19 + 8 * q^20 - 16 * q^25 - 40 * q^26 - 2 * q^29 + 8 * q^31 - 16 * q^34 - 22 * q^35 + 12 * q^40 + 52 * q^41 - 4 * q^44 - 62 * q^46 - 10 * q^49 - 28 * q^50 - 8 * q^55 + 20 * q^56 - 2 * q^59 - 40 * q^61 - 8 * q^64 + 40 * q^65 - 34 * q^70 - 36 * q^71 - 48 * q^74 + 56 * q^76 + 38 * q^79 - 34 * q^80 + 58 * q^85 - 22 * q^86 - 24 * q^89 - 20 * q^91 + 14 * q^94 - 48 * q^95

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