LMFDB - Embedded newform 880.2.cd.c.289.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(49,880)] 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("880.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(880, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cd (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-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:	$7.02683537787$
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	$\chi$	$=$	880.289
Dual form			880.2.cd.c.609.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.49233 - 0.809808i) q^{3} +(1.54147 - 1.61983i) q^{5} +(-0.918552 - 0.298456i) q^{7} +(3.12889 - 2.27327i) q^{9} +(3.31118 - 0.189896i) q^{11} +(-2.65978 - 3.66088i) q^{13} +(2.53011 - 5.28546i) q^{15} +(-1.96126 + 2.69944i) q^{17} +(1.01283 + 3.11717i) q^{19} -2.53103 q^{21} -3.36643i q^{23} +(-0.247725 - 4.99386i) q^{25} +(1.33628 - 1.83923i) q^{27} +(-1.51820 + 4.67254i) q^{29} +(-0.338464 + 0.245909i) q^{31} +(8.09880 - 3.15471i) q^{33} +(-1.89937 + 1.02784i) q^{35} +(6.02737 + 1.95841i) q^{37} +(-9.59368 - 6.97021i) q^{39} +(1.78786 + 5.50247i) q^{41} -2.26205i q^{43} +(1.14077 - 8.57246i) q^{45} +(4.11260 - 1.33626i) q^{47} +(-4.90846 - 3.56620i) q^{49} +(-2.70208 + 8.31615i) q^{51} +(-1.56392 - 2.15255i) q^{53} +(4.79650 - 5.65629i) q^{55} +(5.04863 + 6.94884i) q^{57} +(-3.12889 + 9.62972i) q^{59} +(1.99897 + 1.45233i) q^{61} +(-3.55252 + 1.15428i) q^{63} +(-10.0300 - 1.33473i) q^{65} +9.60059i q^{67} +(-2.72616 - 8.39026i) q^{69} +(-4.41166 - 3.20526i) q^{71} +(-1.36528 - 0.443607i) q^{73} +(-4.66148 - 12.2458i) q^{75} +(-3.09817 - 0.813812i) q^{77} +(-0.812218 + 0.590111i) q^{79} +(-1.74436 + 5.36858i) q^{81} +(4.34692 - 5.98302i) q^{83} +(1.34942 + 7.33802i) q^{85} +12.8750i q^{87} +12.1964 q^{89} +(1.35054 + 4.15654i) q^{91} +(-0.644427 + 0.886978i) q^{93} +(6.61056 + 3.16442i) q^{95} +(1.77467 + 2.44262i) q^{97} +(9.92863 - 8.12138i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{5} + 2 q^{9} + 6 q^{11} + 16 q^{15} - 6 q^{19} + 8 q^{21} - 16 q^{25} + 2 q^{29} - 8 q^{31} - 22 q^{35} - 30 q^{39} - 52 q^{41} + 12 q^{45} - 10 q^{49} + 42 q^{51} + 8 q^{55} - 2 q^{59} - 40 q^{61}+ \cdots + 72 q^{99}+O(q^{100}) $ 16 * q - 2 * q^5 + 2 * q^9 + 6 * q^11 + 16 * q^15 - 6 * q^19 + 8 * q^21 - 16 * q^25 + 2 * q^29 - 8 * q^31 - 22 * q^35 - 30 * q^39 - 52 * q^41 + 12 * q^45 - 10 * q^49 + 42 * q^51 + 8 * q^55 - 2 * q^59 - 40 * q^61 - 40 * q^65 + 26 * q^69 - 36 * q^71 + 20 * q^75 - 38 * q^79 + 68 * q^81 + 58 * q^85 + 24 * q^89 + 20 * q^91 - 48 * q^95 + 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.49233	−	0.809808i	1.43895	−	0.467543i	0.517380	−	0.855756i	$-0.326907\pi$
$3$	2.49233	−	0.809808i	1.43895	−	0.467543i	0.921570	+	0.388213i	$0.126907\pi$
$4$		0			0
$5$	1.54147	−	1.61983i	0.689367	−	0.724412i
$5$	1.54147	−	1.61983i	0.689367	−	0.724412i
$6$		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			0
$9$	3.12889	−	2.27327i	1.04296	−	0.757756i
$10$		0			0
$11$	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	$-0.984071\pi$
$13$	−2.65978	−	3.66088i	−0.737691	−	1.01534i	0.261057	−	0.965323i	$-0.415929\pi$
$14$		0			0
$15$	2.53011	−	5.28546i	0.653271	−	1.36470i
$16$		0			0
$17$	−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	$0.0226889\pi$
$19$	1.01283	+	3.11717i	0.232359	+	0.715129i	−0.765101	+	0.643910i	$0.777311\pi$
$20$		0			0
$21$	−2.53103			−0.552316
$22$		0			0
$23$		−	3.36643i		−	0.701948i	−0.936385	−	0.350974i	$-0.885851\pi$
$23$		−	3.36643i		−	0.701948i	0.936385	−	0.350974i	$-0.114149\pi$
$24$		0			0
$25$	−0.247725	−	4.99386i	−0.0495450	−	0.998772i
$26$		0			0
$27$	1.33628	−	1.83923i	0.257167	−	0.353959i
$28$		0			0
$29$	−1.51820	+	4.67254i	−0.281923	+	0.867668i	0.705382	+	0.708828i	$0.250776\pi$
$29$	−1.51820	+	4.67254i	−0.281923	+	0.867668i	−0.987304	+	0.158841i	$0.949224\pi$
$30$		0			0
$31$	−0.338464	+	0.245909i	−0.0607900	+	0.0441665i	−0.617765	−	0.786363i	$-0.711962\pi$
$31$	−0.338464	+	0.245909i	−0.0607900	+	0.0441665i	0.556975	+	0.830529i	$0.311962\pi$
$32$		0			0
$33$	8.09880	−	3.15471i	1.40982	−	0.549164i
$34$		0			0
$35$	−1.89937	+	1.02784i	−0.321052	+	0.173737i
$36$		0			0
$37$	6.02737	+	1.95841i	0.990894	+	0.321961i	0.759221	−	0.650833i	$-0.225580\pi$
$37$	6.02737	+	1.95841i	0.990894	+	0.321961i	0.231673	+	0.972794i	$0.425580\pi$
$38$		0			0
$39$	−9.59368	−	6.97021i	−1.53622	−	1.11613i
$40$		0			0
$41$	1.78786	+	5.50247i	0.279217	+	0.859341i	0.988073	+	0.153988i	$0.0492117\pi$
$41$	1.78786	+	5.50247i	0.279217	+	0.859341i	−0.708856	+	0.705353i	$0.750788\pi$
$42$		0			0
$43$		−	2.26205i		−	0.344960i	−0.985013	−	0.172480i	$-0.944822\pi$
$43$		−	2.26205i		−	0.344960i	0.985013	−	0.172480i	$-0.0551780\pi$
$44$		0			0
$45$	1.14077	−	8.57246i	0.170057	−	1.27791i
$46$		0			0
$47$	4.11260	−	1.33626i	0.599884	−	0.194914i	0.00669531	−	0.999978i	$-0.497869\pi$
$47$	4.11260	−	1.33626i	0.599884	−	0.194914i	0.593189	+	0.805063i	$0.297869\pi$
$48$		0			0
$49$	−4.90846	−	3.56620i	−0.701208	−	0.509457i
$50$		0			0
$51$	−2.70208	+	8.31615i	−0.378367	+	1.16449i
$52$		0			0
$53$	−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
$55$	4.79650	−	5.65629i	0.646760	−	0.762694i
$56$		0			0
$57$	5.04863	+	6.94884i	0.668707	+	0.920396i
$58$		0			0
$59$	−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			0
$63$	−3.55252	+	1.15428i	−0.447575	+	0.145426i
$64$		0			0
$65$	−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	$0.800525\pi$
$68$		0			0
$69$	−2.72616	−	8.39026i	−0.328191	−	1.01007i
$70$		0			0
$71$	−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	0.228028	−	0.973655i	$-0.426772\pi$
$73$	−1.36528	−	0.443607i	−0.159794	−	0.0519203i	−0.387822	+	0.921734i	$0.626772\pi$
$74$		0			0
$75$	−4.66148	−	12.2458i	−0.538262	−	1.41402i
$76$		0			0
$77$	−3.09817	−	0.813812i	−0.353069	−	0.0927425i
$78$		0			0
$79$	−0.812218	+	0.590111i	−0.0913817	+	0.0663927i	−0.632538	−	0.774529i	$-0.717987\pi$
$79$	−0.812218	+	0.590111i	−0.0913817	+	0.0663927i	0.541156	+	0.840922i	$0.317987\pi$
$80$		0			0
$81$	−1.74436	+	5.36858i	−0.193818	+	0.596509i
$82$		0			0
$83$	4.34692	−	5.98302i	0.477136	−	0.656721i	−0.500815	−	0.865554i	$-0.666966\pi$
$83$	4.34692	−	5.98302i	0.477136	−	0.656721i	0.977951	+	0.208833i	$0.0669664\pi$
$84$		0			0
$85$	1.34942	+	7.33802i	0.146365	+	0.795920i
$86$		0			0
$87$			12.8750i			1.38034i
$88$		0			0
$89$	12.1964			1.29282			0.646410	−	0.762991i	$-0.276270\pi$
$89$	12.1964			1.29282			0.646410	+	0.762991i	$0.276270\pi$
$90$		0			0
$91$	1.35054	+	4.15654i	0.141575	+	0.435723i
$92$		0			0
$93$	−0.644427	+	0.886978i	−0.0668240	+	0.0919754i
$94$		0			0
$95$	6.61056	+	3.16442i	0.678229	+	0.324663i
$96$		0			0
$97$	1.77467	+	2.44262i	0.180190	+	0.248010i	0.889552	−	0.456834i	$-0.151017\pi$
$97$	1.77467	+	2.44262i	0.180190	+	0.248010i	−0.709362	+	0.704844i	$0.751017\pi$
$98$		0			0
$99$	9.92863	−	8.12138i	0.997865	−	0.816229i
$100$		0			0
$101$	−12.2940	+	8.93210i	−1.22330	+	0.888777i	−0.996369	−	0.0851342i	$-0.972868\pi$
$101$	−12.2940	+	8.93210i	−1.22330	+	0.888777i	−0.226928	+	0.973912i	$0.572868\pi$
$102$		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			0
$105$	−3.90151	+	4.09985i	−0.380749	+	0.400104i
$106$		0			0
$107$	7.26778	−	2.36144i	0.702602	−	0.228289i	0.0641384	−	0.997941i	$-0.479570\pi$
$107$	7.26778	−	2.36144i	0.702602	−	0.228289i	0.638464	+	0.769652i	$0.279570\pi$
$108$		0			0
$109$	9.85576			0.944010			0.472005	−	0.881596i	$-0.343530\pi$
$109$	9.85576			0.944010			0.472005	+	0.881596i	$0.343530\pi$
$110$		0			0
$111$	16.6082			1.57638
$112$		0			0
$113$	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
$115$	−5.45305	−	5.18925i	−0.508500	−	0.483900i
$116$		0			0
$117$	−16.6443	−	5.40807i	−1.53877	−	0.499976i
$118$		0			0
$119$	2.60718	−	1.89423i	0.239000	−	0.173644i
$120$		0			0
$121$	10.9279	−	1.25756i	0.993444	−	0.114324i
$122$		0			0
$123$	8.91189	+	12.2662i	0.803558	+	1.10600i
$124$		0			0
$125$	−8.47108	−	7.29662i	−0.757677	−	0.652630i
$126$		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	$0.301866\pi$
$128$		0			0
$129$	−1.83183	−	5.63779i	−0.161284	−	0.496380i
$130$		0			0
$131$	−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
$134$		0			0
$135$	−0.919409	−	4.99967i	−0.0791301	−	0.430303i
$136$		0			0
$137$	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	$-0.793539\pi$
$139$	2.39184	−	7.36133i	0.202873	−	0.624380i	0.999794	−	0.0202958i	$-0.00646080\pi$
$140$		0			0
$141$	9.16785	−	6.66083i	0.772072	−	0.560943i
$142$		0			0
$143$	−9.50222	−	11.6168i	−0.794615	−	0.971442i
$144$		0			0
$145$	5.22847	+	9.66182i	0.434201	+	0.802370i
$146$		0			0
$147$	−15.1215	−	4.91326i	−1.24720	−	0.405239i
$148$		0			0
$149$	−13.6589	−	9.92376i	−1.11898	−	0.812986i	−0.134925	−	0.990856i	$-0.543079\pi$
$149$	−13.6589	−	9.92376i	−1.11898	−	0.812986i	−0.984054	+	0.177870i	$0.943079\pi$
$150$		0			0
$151$	3.79555	+	11.6815i	0.308877	+	0.950626i	0.978202	+	0.207656i	$0.0665835\pi$
$151$	3.79555	+	11.6815i	0.308877	+	0.950626i	−0.669325	+	0.742970i	$0.733416\pi$
$152$		0			0
$153$			12.9047i			1.04328i
$154$		0			0
$155$	−0.123402	+	0.927318i	−0.00991190	+	0.0744840i
$156$		0			0
$157$	−4.00368	+	1.30087i	−0.319528	+	0.103821i	−0.464390	−	0.885631i	$-0.653726\pi$
$157$	−4.00368	+	1.30087i	−0.319528	+	0.103821i	0.144862	+	0.989452i	$0.453726\pi$
$158$		0			0
$159$	−5.64096	−	4.09840i	−0.447357	−	0.325024i
$160$		0			0
$161$	−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	$0.575158\pi$
$164$		0			0
$165$	7.37397	−	17.9816i	0.574062	−	1.39987i
$166$		0			0
$167$	5.38810	+	7.41608i	0.416944	+	0.573874i	0.964895	−	0.262637i	$-0.0845920\pi$
$167$	5.38810	+	7.41608i	0.416944	+	0.573874i	−0.547951	+	0.836510i	$0.684592\pi$
$168$		0			0
$169$	−2.31036	+	7.11055i	−0.177720	+	0.546965i
$170$		0			0
$171$	10.2552	+	7.45085i	0.784236	+	0.569781i
$172$		0			0
$173$	−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
$176$		0			0
$177$			26.5343i			1.99444i
$178$		0			0
$179$	−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	$0.633907\pi$
$182$		0			0
$183$	6.15820	+	2.00092i	0.455227	+	0.147912i
$184$		0			0
$185$	12.4633	−	6.74451i	0.916322	−	0.495866i
$186$		0			0
$187$	−5.98147	+	9.31078i	−0.437408	+	0.680871i
$188$		0			0
$189$	−1.77637	+	1.29061i	−0.129212	+	0.0938779i
$190$		0			0
$191$	−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	$0.500009\pi$
$193$	−13.2128	+	18.1858i	−0.951076	+	1.30904i	−0.951048	+	0.309044i	$0.899991\pi$
$194$		0			0
$195$	−26.0790	+	4.79577i	−1.86755	+	0.343432i
$196$		0			0
$197$		−	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	$-0.294616\pi$
$199$	16.9671			1.20277			0.601385	+	0.798960i	$0.294616\pi$
$200$		0			0
$201$	7.77463	+	23.9279i	0.548380	+	1.68774i
$202$		0			0
$203$	2.78909	−	3.83886i	0.195756	−	0.269435i
$204$		0			0
$205$	11.6690	+	5.58587i	0.815000	+	0.390134i
$206$		0			0
$207$	−7.65279	−	10.5332i	−0.531906	−	0.732106i
$208$		0			0
$209$	3.94561	+	10.1292i	0.272924	+	0.700652i
$210$		0			0
$211$	−4.71363	+	3.42465i	−0.324500	+	0.235763i	−0.738093	−	0.674699i	$-0.764274\pi$
$211$	−4.71363	+	3.42465i	−0.324500	+	0.235763i	0.413593	+	0.910462i	$0.364274\pi$
$212$		0			0
$213$	−13.5910	−	4.41597i	−0.931238	−	0.302577i
$214$		0			0
$215$	−3.66415	−	3.48689i	−0.249893	−	0.237804i
$216$		0			0
$217$	0.384290	−	0.124863i	0.0260873	−	0.00847628i
$218$		0			0
$219$	−3.76197			−0.254211
$220$		0			0
$221$	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	$0.619789\pi$
$224$		0			0
$225$	−12.1275	−	15.0621i	−0.808499	−	1.00414i
$226$		0			0
$227$	−27.0727	−	8.79646i	−1.79688	−	0.583841i	−0.797079	−	0.603874i	$-0.793623\pi$
$227$	−27.0727	−	8.79646i	−1.79688	−	0.583841i	−0.999799	+	0.0200332i	$0.993623\pi$
$228$		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	$0.983168\pi$
$230$		0			0
$231$	−8.38071	+	0.480634i	−0.551410	+	0.0316234i
$232$		0			0
$233$	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
$235$	4.17493	−	8.72154i	0.272342	−	0.568931i
$236$		0			0
$237$	−1.54644	+	2.12849i	−0.100452	+	0.138261i
$238$		0			0
$239$	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	$0.762409\pi$
$242$		0			0
$243$			21.6131i			1.38648i
$244$		0			0
$245$	−13.3429	+	2.45368i	−0.852447	+	0.156760i
$246$		0			0
$247$	8.71768	−	11.9989i	0.554693	−	0.763469i
$248$		0			0
$249$	5.98887	−	18.4318i	0.379529	−	1.16807i
$250$		0			0
$251$	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
$254$		0			0
$255$	9.30560	+	17.1960i	0.582739	+	1.07686i
$256$		0			0
$257$	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
$260$		0			0
$261$	5.87166	+	18.0711i	0.363447	+	1.11857i
$262$		0			0
$263$		−	18.1037i		−	1.11632i	−0.829732	−	0.558162i	$-0.811507\pi$
$263$		−	18.1037i		−	1.11632i	0.829732	−	0.558162i	$-0.188493\pi$
$264$		0			0
$265$	−5.89751	−	0.784807i	−0.362281	−	0.0482103i
$266$		0			0
$267$	30.3976	−	9.87677i	1.86030	−	0.604449i
$268$		0			0
$269$	−1.85914	−	1.35074i	−0.113354	−	0.0823562i	0.529664	−	0.848207i	$-0.322318\pi$
$269$	−1.85914	−	1.35074i	−0.113354	−	0.0823562i	−0.643018	+	0.765851i	$0.722318\pi$
$270$		0			0
$271$	−0.248971	+	0.766255i	−0.0151239	+	0.0465467i	−0.958334	−	0.285651i	$-0.907790\pi$
$271$	−0.248971	+	0.766255i	−0.0151239	+	0.0465467i	0.943210	+	0.332198i	$0.107790\pi$
$272$		0			0
$273$	6.73199	+	9.26579i	0.407439	+	0.560791i
$274$		0			0
$275$	−1.76858	−	16.4885i	−0.106649	−	0.994297i
$276$		0			0
$277$	6.95521	+	9.57302i	0.417898	+	0.575187i	0.965122	−	0.261799i	$-0.0843157\pi$
$277$	6.95521	+	9.57302i	0.417898	+	0.575187i	−0.547225	+	0.836986i	$0.684316\pi$
$278$		0			0
$279$	−0.500000	+	1.53884i	−0.0299342	+	0.0921280i
$280$		0			0
$281$	−5.03960	−	3.66148i	−0.300637	−	0.218426i	0.427231	−	0.904142i	$-0.359489\pi$
$281$	−5.03960	−	3.66148i	−0.300637	−	0.218426i	−0.727869	+	0.685717i	$0.759489\pi$
$282$		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	$0.317277\pi$
$284$		0			0
$285$	19.0383	+	2.53351i	1.12773	+	0.150072i
$286$		0			0
$287$		−	5.58790i		−	0.329843i
$288$		0			0
$289$	1.81285	+	5.57937i	0.106638	+	0.328198i
$290$		0			0
$291$	6.40111	+	4.65068i	0.375240	+	0.272628i
$292$		0			0
$293$	−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
$295$	10.7755	+	19.9122i	0.627372	+	1.15933i
$296$		0			0
$297$	4.07540	−	6.34377i	0.236478	−	0.368103i
$298$		0			0
$299$	−12.3241	+	8.95396i	−0.712719	+	0.517821i
$300$		0			0
$301$	−0.675123	+	2.07781i	−0.0389134	+	0.119763i
$302$		0			0
$303$	−23.4074	+	32.2176i	−1.34472	+	1.85085i
$304$		0			0
$305$	5.43389	−	0.999260i	0.311144	−	0.0572175i
$306$		0			0
$307$		−	18.4721i		−	1.05426i	−0.849785	−	0.527130i	$-0.823268\pi$
$307$		−	18.4721i		−	1.05426i	0.849785	−	0.527130i	$-0.176732\pi$
$308$		0			0
$309$	−25.5427			−1.45307
$310$		0			0
$311$	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	−0.715550	−	0.698561i	$-0.753824\pi$
$313$	3.00651	−	4.13811i	0.169938	−	0.233900i	0.885488	+	0.464661i	$0.153824\pi$
$314$		0			0
$315$	−3.60636	+	7.53378i	−0.203195	+	0.424481i
$316$		0			0
$317$	−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
$320$		0			0
$321$	16.2014	−	11.7710i	0.904274	−	0.656994i
$322$		0			0
$323$	−10.4010	−	3.37951i	−0.578730	−	0.188041i
$324$		0			0
$325$	−17.6230	+	14.1895i	−0.977549	+	0.787090i
$326$		0			0
$327$	24.5638	−	7.98127i	1.35838	−	0.441365i
$328$		0			0
$329$	−4.17645			−0.230255
$330$		0			0
$331$	−29.2692			−1.60878			−0.804391	−	0.594100i	$-0.797508\pi$
$331$	−29.2692			−1.60878			−0.804391	+	0.594100i	$0.797508\pi$
$332$		0			0
$333$	23.3110	−	7.57419i	1.27743	−	0.415063i
$334$		0			0
$335$	15.5514	+	14.7990i	0.849661	+	0.808558i
$336$		0			0
$337$	−25.3400	−	8.23348i	−1.38036	−	0.448506i	−0.477572	−	0.878593i	$-0.658483\pi$
$337$	−25.3400	−	8.23348i	−1.38036	−	0.448506i	−0.902788	+	0.430087i	$0.858483\pi$
$338$		0			0
$339$	10.6400	−	7.73040i	0.577885	−	0.419858i
$340$		0			0
$341$	−1.07402	+	0.878523i	−0.0581615	+	0.0475747i
$342$		0			0
$343$	7.41820	+	10.2103i	0.400545	+	0.551303i
$344$		0			0
$345$	−17.7931	−	8.51742i	−0.957949	−	0.458563i
$346$		0			0
$347$	−2.53411	+	3.48790i	−0.136038	+	0.187240i	−0.871601	−	0.490216i	$-0.836918\pi$
$347$	−2.53411	+	3.48790i	−0.136038	+	0.187240i	0.735563	+	0.677457i	$0.236918\pi$
$348$		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	$0.785341\pi$
$350$		0			0
$351$	−10.2874			−0.549100
$352$		0			0
$353$		−	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
$355$	−11.9924	+	2.20534i	−0.636492	+	0.117047i
$356$		0			0
$357$	4.96400	−	6.83237i	0.262723	−	0.361607i
$358$		0			0
$359$	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
$362$		0			0
$363$	26.2175	−	11.9838i	1.37606	−	0.628984i
$364$		0			0
$365$	−2.82311	+	1.52772i	−0.147769	+	0.0799646i
$366$		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	$0.616779\pi$
$368$		0			0
$369$	18.1026	+	13.1523i	0.942384	+	0.684682i
$370$		0			0
$371$	0.794101	+	2.44399i	0.0412277	+	0.126886i
$372$		0			0
$373$			8.87153i			0.459351i	0.973267	+	0.229675i	$0.0737664\pi$
$373$			8.87153i			0.459351i	−0.973267	+	0.229675i	$0.926234\pi$
$374$		0			0
$375$	−27.0216	−	11.3257i	−1.39539	−	0.584855i
$376$		0			0
$377$	21.1437	−	6.86999i	1.08895	−	0.353823i
$378$		0			0
$379$	−17.0412	−	12.3812i	−0.875348	−	0.635978i	0.0566685	−	0.998393i	$-0.481952\pi$
$379$	−17.0412	−	12.3812i	−0.875348	−	0.635978i	−0.932017	+	0.362415i	$0.881952\pi$
$380$		0			0
$381$	−5.74187	+	17.6717i	−0.294165	+	0.905346i
$382$		0			0
$383$	−15.2704	−	21.0179i	−0.780281	−	1.07396i	−0.995251	−	0.0973436i	$-0.968965\pi$
$383$	−15.2704	−	21.0179i	−0.780281	−	1.07396i	0.214970	−	0.976621i	$-0.431035\pi$
$384$		0			0
$385$	−6.09399	+	3.76405i	−0.310578	+	0.191834i
$386$		0			0
$387$	−5.14225	−	7.07771i	−0.261396	−	0.359780i
$388$		0			0
$389$	0.507965	−	1.56335i	0.0257548	−	0.0792652i	−0.937353	−	0.348381i	$-0.886731\pi$
$389$	0.507965	−	1.56335i	0.0257548	−	0.0792652i	0.963108	+	0.269116i	$0.0867315\pi$
$390$		0			0
$391$	9.08746	+	6.60243i	0.459573	+	0.333899i
$392$		0			0
$393$	−17.9873	+	5.84442i	−0.907338	+	0.294812i
$394$		0			0
$395$	−0.296130	+	2.22530i	−0.0148999	+	0.111967i
$396$		0			0
$397$			16.7088i			0.838588i	0.907850	+	0.419294i	$0.137722\pi$
$397$			16.7088i			0.838588i	−0.907850	+	0.419294i	$0.862278\pi$
$398$		0			0
$399$	−2.56351	−	7.88966i	−0.128336	−	0.394977i
$400$		0			0
$401$	−22.4842	−	16.3357i	−1.12281	−	0.815766i	−0.138174	−	0.990408i	$-0.544123\pi$
$401$	−22.4842	−	16.3357i	−1.12281	−	0.815766i	−0.984632	+	0.174641i	$0.944123\pi$
$402$		0			0
$403$	1.80048	+	0.585013i	0.0896885	+	0.0291416i
$404$		0			0
$405$	6.00733	+	11.1011i	0.298507	+	0.551618i
$406$		0			0
$407$	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	$-0.128556\pi$
$410$		0			0
$411$	6.87591	−	21.1619i	0.339164	−	1.04384i
$412$		0			0
$413$	5.74809	−	7.91157i	0.282845	−	0.389303i
$414$		0			0
$415$	−2.99084	−	16.2639i	−0.146815	−	0.798365i
$416$		0			0
$417$		−	20.2838i		−	0.993303i
$418$		0			0
$419$	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	$0.984589\pi$
$422$		0			0
$423$	9.83016	−	13.5301i	0.477959	−	0.657854i
$424$		0			0
$425$	13.9665	+	9.12553i	0.677474	+	0.442653i
$426$		0			0
$427$	−1.40270	−	1.93065i	−0.0678813	−	0.0934306i
$428$		0			0
$429$	−33.0900	−	21.2579i	−1.59760	−	1.02634i
$430$		0			0
$431$	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	0.300260	−	0.953857i	$-0.402927\pi$
$433$	−0.363904	−	0.118240i	−0.0174881	−	0.00568223i	−0.317748	+	0.948175i	$0.602927\pi$
$434$		0			0
$435$	20.8553	+	19.8464i	0.999936	+	0.951563i
$436$		0			0
$437$	10.4937	−	3.40962i	0.501983	−	0.163104i
$438$		0			0
$439$	26.5331			1.26635			0.633177	−	0.774007i	$-0.281751\pi$
$439$	26.5331			1.26635			0.633177	+	0.774007i	$0.281751\pi$
$440$		0			0
$441$	−23.4649			−1.11738
$442$		0			0
$443$	13.7913	−	4.48106i	0.655243	−	0.212901i	0.0375185	−	0.999296i	$-0.488055\pi$
$443$	13.7913	−	4.48106i	0.655243	−	0.212901i	0.617725	+	0.786395i	$0.288055\pi$
$444$		0			0
$445$	18.8005	−	19.7562i	0.891228	−	0.936534i
$446$		0			0
$447$	−42.0788	−	13.6722i	−1.99026	−	0.646675i
$448$		0			0
$449$	8.18240	−	5.94486i	0.386151	−	0.280555i	−0.377725	−	0.925918i	$-0.623294\pi$
$449$	8.18240	−	5.94486i	0.386151	−	0.280555i	0.763876	+	0.645362i	$0.223294\pi$
$450$		0			0
$451$	6.96483	+	17.8802i	0.327961	+	0.841945i
$452$		0			0
$453$	18.9195	+	26.0405i	0.888917	+	1.22349i
$454$		0			0
$455$	8.81472	+	4.21953i	0.413240	+	0.197815i
$456$		0			0
$457$	22.9758	−	31.6235i	1.07476	−	1.47928i	0.209602	−	0.977787i	$-0.432783\pi$
$457$	22.9758	−	31.6235i	1.07476	−	1.47928i	0.865160	−	0.501496i	$-0.167217\pi$
$458$		0			0
$459$	2.34410	+	7.21440i	0.109413	+	0.336739i
$460$		0			0
$461$	39.1322			1.82257			0.911285	−	0.411776i	$-0.135092\pi$
$461$	39.1322			1.82257			0.911285	+	0.411776i	$0.135092\pi$
$462$		0			0
$463$		−	12.9189i		−	0.600392i	−0.953878	−	0.300196i	$-0.902948\pi$
$463$		−	12.9189i		−	0.600392i	0.953878	−	0.300196i	$-0.0970521\pi$
$464$		0			0
$465$	0.443390	+	2.41112i	0.0205617	+	0.111813i
$466$		0			0
$467$	6.61206	−	9.10071i	0.305969	−	0.421131i	−0.628150	−	0.778093i	$-0.716187\pi$
$467$	6.61206	−	9.10071i	0.305969	−	0.421131i	0.934119	+	0.356962i	$0.116187\pi$
$468$		0			0
$469$	2.86535	−	8.81864i	0.132310	−	0.407207i
$470$		0			0
$471$	−8.92504	+	6.48442i	−0.411244	+	0.298786i
$472$		0			0
$473$	−0.429556	−	7.49007i	−0.0197510	−	0.344394i
$474$		0			0
$475$	15.3158	−	5.83014i	0.702738	−	0.267505i
$476$		0			0
$477$	−9.78665	−	3.17988i	−0.448100	−	0.145597i
$478$		0			0
$479$	−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
$482$		0			0
$483$			8.52053i			0.387697i
$484$		0			0
$485$	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			0
$489$	35.1377	+	25.5290i	1.58898	+	1.15446i
$490$		0			0
$491$	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
$494$		0			0
$495$	2.14943	−	28.6016i	0.0966098	−	1.28555i
$496$		0			0
$497$	3.09571	+	4.26088i	0.138862	+	0.191127i
$498$		0			0
$499$	1.43750	−	4.42417i	0.0643513	−	0.198053i	−0.913711	−	0.406364i	$-0.866797\pi$
$499$	1.43750	−	4.42417i	0.0643513	−	0.198053i	0.978063	+	0.208311i	$0.0667966\pi$
$500$		0			0
$501$	19.4346	+	14.1200i	0.868272	+	0.630836i
$502$		0			0
$503$	−12.3611	+	4.01636i	−0.551154	+	0.179081i	−0.571337	−	0.820716i	$-0.693575\pi$
$503$	−12.3611	+	4.01636i	−0.551154	+	0.179081i	0.0201833	+	0.999796i	$0.493575\pi$
$504$		0			0
$505$	−4.48232	+	33.6828i	−0.199460	+	1.49887i
$506$		0			0
$507$			19.5928i			0.870147i
$508$		0			0
$509$	−9.12976	−	28.0985i	−0.404669	−	1.24544i	−0.921171	−	0.389158i	$-0.872766\pi$
$509$	−9.12976	−	28.0985i	−0.404669	−	1.24544i	0.516501	−	0.856286i	$-0.327234\pi$
$510$		0			0
$511$	1.12169	+	0.814952i	0.0496205	+	0.0360514i
$512$		0			0
$513$	7.08662	+	2.30258i	0.312882	+	0.101661i
$514$		0			0
$515$	−19.1681	+	10.3728i	−0.844649	+	0.457080i
$516$		0			0
$517$	13.3638	−	5.20558i	0.587740	−	0.228941i
$518$		0			0
$519$	−8.71293	+	6.33032i	−0.382455	+	0.277870i
$520$		0			0
$521$	−9.71896	+	29.9119i	−0.425796	+	1.31046i	0.476435	+	0.879210i	$0.341929\pi$
$521$	−9.71896	+	29.9119i	−0.425796	+	1.31046i	−0.902230	+	0.431254i	$0.858071\pi$
$522$		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	$0.136811\pi$
$524$		0			0
$525$	0.626999	+	12.6396i	0.0273645	+	0.551638i
$526$		0			0
$527$		−	1.39595i		−	0.0608088i
$528$		0			0
$529$	11.6672			0.507269
$530$		0			0
$531$	12.1010	+	37.2431i	0.525140	+	1.61621i
$532$		0			0
$533$	15.3885	−	21.1805i	0.666552	−	0.917430i
$534$		0			0
$535$	7.37793	−	15.4127i	0.318976	−	0.666349i
$536$		0			0
$537$	−25.1016	−	34.5494i	−1.08321	−	1.49092i
$538$		0			0
$539$	−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	$0.241160\pi$
$542$		0			0
$543$	13.8247	+	4.49192i	0.593275	+	0.192767i
$544$		0			0
$545$	15.1924	−	15.9647i	0.650770	−	0.683852i
$546$		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	$0.658332\pi$
$548$		0			0
$549$	9.55608			0.407844
$550$		0			0
$551$	−16.1028			−0.686002
$552$		0			0
$553$	0.922187	−	0.299637i	0.0392154	−	0.0127418i
$554$		0			0
$555$	25.6010	−	26.9025i	1.08670	−	1.14195i
$556$		0			0
$557$	−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
$560$		0			0
$561$	−7.36788	+	28.0494i	−0.311072	+	1.18425i
$562$		0			0
$563$	−5.45619	−	7.50980i	−0.229951	−	0.316500i	0.678413	−	0.734681i	$-0.262668\pi$
$563$	−5.45619	−	7.50980i	−0.229951	−	0.316500i	−0.908364	+	0.418180i	$0.862668\pi$
$564$		0			0
$565$	4.84532	−	10.1220i	0.203844	−	0.425836i
$566$		0			0
$567$	3.20457	−	4.41071i	0.134579	−	0.185232i
$568$		0			0
$569$	−9.55701	−	29.4135i	−0.400651	−	1.23308i	−0.924473	−	0.381248i	$-0.875494\pi$
$569$	−9.55701	−	29.4135i	−0.400651	−	1.23308i	0.523822	−	0.851828i	$-0.324506\pi$
$570$		0			0
$571$	2.63736			0.110370			0.0551851	−	0.998476i	$-0.482425\pi$
$571$	2.63736			0.110370			0.0551851	+	0.998476i	$0.482425\pi$
$572$		0			0
$573$			57.1712i			2.38836i
$574$		0			0
$575$	−16.8115	+	0.833947i	−0.701086	+	0.0347780i
$576$		0			0
$577$	−21.5309	+	29.6347i	−0.896342	+	1.23371i	0.0752785	+	0.997163i	$0.476015\pi$
$577$	−21.5309	+	29.6347i	−0.896342	+	1.23371i	−0.971620	+	0.236546i	$0.923985\pi$
$578$		0			0
$579$	−18.2036	+	56.0249i	−0.756516	+	2.32832i
$580$		0			0
$581$	−5.77854	+	4.19835i	−0.239734	+	0.174177i
$582$		0			0
$583$	−5.58719	−	6.83051i	−0.231398	−	0.282891i
$584$		0			0
$585$	−34.4169	+	18.6247i	−1.42297	+	0.770035i
$586$		0			0
$587$	−13.0793	−	4.24973i	−0.539842	−	0.175405i	0.0263892	−	0.999652i	$-0.491599\pi$
$587$	−13.0793	−	4.24973i	−0.539842	−	0.175405i	−0.566231	+	0.824246i	$0.691599\pi$
$588$		0			0
$589$	−1.10935	−	0.805989i	−0.0457099	−	0.0332102i
$590$		0			0
$591$	−20.8508	−	64.1723i	−0.857689	−	2.63970i
$592$		0			0
$593$		−	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
$596$		0			0
$597$	42.2878	−	13.7401i	1.73072	−	0.562346i
$598$		0			0
$599$	−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	$-0.162359\pi$
$602$		0			0
$603$	21.8247	+	30.0391i	0.888771	+	1.22329i
$604$		0			0
$605$	14.8080	−	19.6399i	0.602030	−	0.798473i
$606$		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	$0.502343\pi$
$608$		0			0
$609$	3.84261	−	11.8263i	0.155710	−	0.479227i
$610$		0			0
$611$	−15.8305	−	11.5015i	−0.640434	−	0.465303i
$612$		0			0
$613$	−3.62818	+	1.17887i	−0.146541	+	0.0476139i	−0.381369	−	0.924423i	$-0.624547\pi$
$613$	−3.62818	+	1.17887i	−0.146541	+	0.0476139i	0.234828	+	0.972037i	$0.424547\pi$
$614$		0			0
$615$	33.6066	+	4.47217i	1.35515	+	0.180335i
$616$		0			0
$617$			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	$0.0607236\pi$
$619$	7.43830	+	22.8927i	0.298971	+	0.920137i	−0.682888	+	0.730523i	$0.739276\pi$
$620$		0			0
$621$	−6.19162	−	4.49848i	−0.248461	−	0.180518i
$622$		0			0
$623$	−11.2031	−	3.64010i	−0.448841	−	0.145837i
$624$		0			0
$625$	−24.8773	+	2.47421i	−0.995091	+	0.0989682i
$626$		0			0
$627$	18.0365	+	22.0502i	0.720308	+	0.880599i
$628$		0			0
$629$	−17.1078	+	12.4296i	−0.682135	+	0.495600i
$630$		0			0
$631$	−5.90889	+	18.1857i	−0.235229	+	0.723961i	0.761862	+	0.647740i	$0.224286\pi$
$631$	−5.90889	+	18.1857i	−0.235229	+	0.723961i	−0.997091	+	0.0762213i	$0.975714\pi$
$632$		0			0
$633$	−8.97463	+	12.3525i	−0.356710	+	0.490969i
$634$		0			0
$635$	2.86749	+	15.5932i	0.113793	+	0.618796i
$636$		0			0
$637$			27.4546i			1.08779i
$638$		0			0
$639$	−21.0900			−0.834307
$640$		0			0
$641$	3.70172	+	11.3927i	0.146209	+	0.449985i	0.997165	−	0.0752526i	$-0.0239763\pi$
$641$	3.70172	+	11.3927i	0.146209	+	0.449985i	−0.850955	+	0.525238i	$0.823976\pi$
$642$		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	$0.0305478\pi$
$644$		0			0
$645$	−11.9560	−	5.72324i	−0.470767	−	0.225352i
$646$		0			0
$647$	−5.46774	−	7.52570i	−0.214959	−	0.295866i	0.687897	−	0.725808i	$-0.258534\pi$
$647$	−5.46774	−	7.52570i	−0.214959	−	0.295866i	−0.902856	+	0.429942i	$0.858534\pi$
$648$		0			0
$649$	−8.53167	+	32.4800i	−0.334897	+	1.27495i
$650$		0			0
$651$	0.856664	−	0.622403i	0.0335753	−	0.0243939i
$652$		0			0
$653$	−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
$655$	−11.1249	+	11.6904i	−0.434685	+	0.456782i
$656$		0			0
$657$	−5.28025	+	1.71566i	−0.206002	+	0.0669342i
$658$		0			0
$659$	−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	$0.529891\pi$
$662$		0			0
$663$	37.6313	−	12.2272i	1.46148	−	0.474864i
$664$		0			0
$665$	−5.12770	−	4.87964i	−0.198844	−	0.189224i
$666$		0			0
$667$	15.7297	+	5.11091i	0.609058	+	0.197895i
$668$		0			0
$669$	−40.3292	+	29.3009i	−1.55922	+	1.13284i
$670$		0			0
$671$	6.89474	+	4.42935i	0.266168	+	0.170993i
$672$		0			0
$673$	−19.3464	−	26.6280i	−0.745749	−	1.02644i	−0.998267	−	0.0588431i	$-0.981259\pi$
$673$	−19.3464	−	26.6280i	−0.745749	−	1.02644i	0.252518	−	0.967592i	$-0.418741\pi$
$674$		0			0
$675$	−9.51587	−	6.21756i	−0.366266	−	0.239314i
$676$		0			0
$677$	−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			0
$681$	−74.5977			−2.85859
$682$		0			0
$683$		−	19.3586i		−	0.740737i	−0.928885	−	0.370368i	$-0.879231\pi$
$683$		−	19.3586i		−	0.740737i	0.928885	−	0.370368i	$-0.120769\pi$
$684$		0			0
$685$	−3.43383	−	18.6729i	−0.131200	−	0.713454i
$686$		0			0
$687$	−39.1115	+	53.8324i	−1.49220	+	2.05383i
$688$		0			0
$689$	−3.72054	+	11.4506i	−0.141741	+	0.436234i
$690$		0			0
$691$	−7.39559	+	5.37321i	−0.281342	+	0.204407i	−0.719502	−	0.694490i	$-0.755630\pi$
$691$	−7.39559	+	5.37321i	−0.281342	+	0.204407i	0.438161	+	0.898897i	$0.355630\pi$
$692$		0			0
$693$	−11.5438	+	4.49665i	−0.438514	+	0.170814i
$694$		0			0
$695$	−8.23717	−	15.2217i	−0.312454	−	0.577391i
$696$		0			0
$697$	−18.3600	−	5.96554i	−0.695436	−	0.225961i
$698$		0			0
$699$	26.5383	+	19.2812i	1.00377	+	0.729281i
$700$		0			0
$701$	−4.72594	−	14.5450i	−0.178496	−	0.549355i	0.821279	−	0.570526i	$-0.193261\pi$
$701$	−4.72594	−	14.5450i	−0.178496	−	0.549355i	−0.999776	+	0.0211707i	$0.993261\pi$
$702$		0			0
$703$			20.7719i			0.783428i
$704$		0			0
$705$	3.34254	−	25.1179i	0.125887	−	0.945994i
$706$		0			0
$707$	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	$0.401729\pi$
$710$		0			0
$711$	−1.19986	+	3.69278i	−0.0449982	+	0.138490i
$712$		0			0
$713$	0.827834	+	1.13942i	0.0310026	+	0.0426714i
$714$		0			0
$715$	−33.4646	−	2.51489i	−1.25151	−	0.0940516i
$716$		0			0
$717$	31.4039	+	43.2238i	1.17280	+	1.61422i
$718$		0			0
$719$	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
$722$		0			0
$723$	−56.8090	+	18.4584i	−2.11275	+	0.686473i
$724$		0			0
$725$	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			0
$729$	12.2694	+	37.7614i	0.454423	+	1.39857i
$730$		0			0
$731$	6.10627	+	4.43647i	0.225849	+	0.164089i
$732$		0			0
$733$	45.6788	+	14.8419i	1.68718	+	0.548199i	0.986284	−	0.165060i	$-0.0527817\pi$
$733$	45.6788	+	14.8419i	1.68718	+	0.548199i	0.700901	+	0.713259i	$0.252782\pi$
$734$		0			0
$735$	−31.2680	+	16.9206i	−1.15334	+	0.624125i
$736$		0			0
$737$	1.82312	+	31.7893i	0.0671554	+	1.17097i
$738$		0			0
$739$	27.5934	−	20.0478i	1.01504	−	0.737470i	0.0497805	−	0.998760i	$-0.484148\pi$
$739$	27.5934	−	20.0478i	1.01504	−	0.737470i	0.965260	+	0.261290i	$0.0841478\pi$
$740$		0			0
$741$	12.0106	−	36.9648i	0.441220	−	1.35794i
$742$		0			0
$743$	−15.5411	+	21.3906i	−0.570149	+	0.784743i	−0.992572	−	0.121656i	$-0.961180\pi$
$743$	−15.5411	+	21.3906i	−0.570149	+	0.784743i	0.422423	+	0.906399i	$0.361180\pi$
$744$		0			0
$745$	−37.1296	+	6.82792i	−1.36032	+	0.250156i
$746$		0			0
$747$		−	28.6019i		−	1.04649i
$748$		0			0
$749$	−7.38062			−0.269682
$750$		0			0
$751$	−14.1963	−	43.6918i	−0.518032	−	1.59434i	−0.777697	−	0.628639i	$-0.783612\pi$
$751$	−14.1963	−	43.6918i	−0.518032	−	1.59434i	0.259666	−	0.965699i	$-0.416388\pi$
$752$		0			0
$753$	26.1132	−	35.9417i	0.951617	−	1.30979i
$754$		0			0
$755$	24.7728	+	11.8585i	0.901575	+	0.431577i
$756$		0			0
$757$	18.1365	+	24.9628i	0.659183	+	0.907288i	0.999454	−	0.0330398i	$-0.0105188\pi$
$757$	18.1365	+	24.9628i	0.659183	+	0.907288i	−0.340271	+	0.940327i	$0.610519\pi$
$758$		0			0
$759$	−10.6201	−	27.2640i	−0.385485	−	0.989620i
$760$		0			0
$761$	11.4860	−	8.34507i	0.416367	−	0.302508i	−0.359807	−	0.933027i	$-0.617158\pi$
$761$	11.4860	−	8.34507i	0.416367	−	0.302508i	0.776175	+	0.630518i	$0.217158\pi$
$762$		0			0
$763$	−9.05303	−	2.94151i	−0.327742	−	0.106490i
$764$		0			0
$765$	20.9035	+	19.8923i	0.755767	+	0.719206i
$766$		0			0
$767$	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	$0.317936\pi$
$770$		0			0
$771$	12.4107			0.446961
$772$		0			0
$773$	−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
$775$	1.31188	+	1.62933i	0.0471241	+	0.0585271i
$776$		0			0
$777$	−15.2555	−	4.95680i	−0.547287	−	0.177824i
$778$		0			0
$779$	−15.3414	+	11.1461i	−0.549661	+	0.399352i
$780$		0			0
$781$	−15.2165	−	9.77544i	−0.544488	−	0.349793i
$782$		0			0
$783$	6.56512	+	9.03612i	0.234618	+	0.322925i
$784$		0			0
$785$	−4.06436	+	8.49055i	−0.145063	+	0.303041i
$786$		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	$0.382702\pi$
$788$		0			0
$789$	−14.6605	−	45.1205i	−0.521929	−	1.60633i
$790$		0			0
$791$	−4.84709			−0.172343
$792$		0			0
$793$		−	11.1809i		−	0.397044i
$794$		0			0
$795$	−15.3341	+	2.81985i	−0.543845	+	0.100010i
$796$		0			0
$797$	−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
$800$		0			0
$801$	38.1613	−	27.7258i	1.34836	−	0.979642i
$802$		0			0
$803$	−4.60494	−	1.20960i	−0.162505	−	0.0426859i
$804$		0			0
$805$	3.46015	+	6.39409i	0.121954	+	0.225362i
$806$		0			0
$807$	−5.72743	−	1.86095i	−0.201615	−	0.0655087i
$808$		0			0
$809$	8.89072	+	6.45948i	0.312581	+	0.227103i	0.733003	−	0.680225i	$-0.238118\pi$
$809$	8.89072	+	6.45948i	0.312581	+	0.227103i	−0.420422	+	0.907329i	$0.638118\pi$
$810$		0			0
$811$	−12.5951	−	38.7638i	−0.442275	−	1.36118i	−0.885445	−	0.464744i	$-0.846146\pi$
$811$	−12.5951	−	38.7638i	−0.442275	−	1.36118i	0.443171	−	0.896437i	$-0.353854\pi$
$812$		0			0
$813$			2.11138i			0.0740494i
$814$		0			0
$815$	36.7358	+	4.88858i	1.28680	+	0.171240i
$816$		0			0
$817$	7.05121	−	2.29108i	0.246691	−	0.0801547i
$818$		0			0
$819$	13.6746	+	9.93519i	0.477830	+	0.347164i
$820$		0			0
$821$	4.66851	−	14.3682i	0.162932	−	0.501454i	−0.835946	−	0.548812i	$-0.815080\pi$
$821$	4.66851	−	14.3682i	0.162932	−	0.501454i	0.998878	+	0.0473584i	$0.0150803\pi$
$822$		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	$-0.418982\pi$
$824$		0			0
$825$	−17.7604	−	39.6627i	−0.618339	−	1.38088i
$826$		0			0
$827$	2.23560	+	3.07703i	0.0777393	+	0.106999i	0.846116	−	0.532999i	$-0.178935\pi$
$827$	2.23560	+	3.07703i	0.0777393	+	0.106999i	−0.768376	+	0.639998i	$0.778935\pi$
$828$		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	$-0.0572601\pi$
$830$		0			0
$831$	25.0870	+	18.2268i	0.870259	+	0.632280i
$832$		0			0
$833$	19.2535	−	6.25584i	0.667094	−	0.216752i
$834$		0			0
$835$	20.3184	+	2.70386i	0.703148	+	0.0935710i
$836$		0			0
$837$			0.951115i			0.0328754i
$838$		0			0
$839$	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
$842$		0			0
$843$	−15.5255	−	5.04453i	−0.534725	−	0.173743i
$844$		0			0
$845$	7.95655	+	14.7031i	0.273714	+	0.505802i
$846$		0			0
$847$	−10.4132	−	2.10635i	−0.357800	−	0.0723750i
$848$		0			0
$849$	18.3297	−	13.3173i	0.629073	−	0.457048i
$850$		0			0
$851$	6.59285	−	20.2907i	0.226000	−	0.695556i
$852$		0			0
$853$	−4.90400	+	6.74977i	−0.167910	+	0.231108i	−0.884677	−	0.466205i	$-0.845621\pi$
$853$	−4.90400	+	6.74977i	−0.167910	+	0.231108i	0.716767	+	0.697313i	$0.245621\pi$
$854$		0			0
$855$	27.8773	−	5.12646i	0.953382	−	0.175321i
$856$		0			0
$857$		−	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	$-0.448689\pi$
$859$	9.40807			0.320999			0.160500	+	0.987036i	$0.448689\pi$
$860$		0			0
$861$	−4.52513	−	13.9269i	−0.154216	−	0.474628i
$862$		0			0
$863$	−6.06951	+	8.35396i	−0.206608	+	0.284372i	−0.899728	−	0.436450i	$-0.856236\pi$
$863$	−6.06951	+	8.35396i	−0.206608	+	0.284372i	0.693120	+	0.720822i	$0.256236\pi$
$864$		0			0
$865$	−3.96777	+	8.28877i	−0.134908	+	0.281827i
$866$		0			0
$867$	9.03644	+	12.4376i	0.306893	+	0.422403i
$868$		0			0
$869$	−2.57734	+	2.10820i	−0.0874304	+	0.0715159i
$870$		0			0
$871$	35.1466	−	25.5355i	1.19090	−	0.865237i
$872$		0			0
$873$	11.1055	+	3.60838i	0.375863	+	0.122125i
$874$		0			0
$875$	5.60342	+	9.23057i	0.189430	+	0.312050i
$876$		0			0
$877$	−28.3445	+	9.20969i	−0.957126	+	0.310989i	−0.745608	−	0.666385i	$-0.767841\pi$
$877$	−28.3445	+	9.20969i	−0.957126	+	0.310989i	−0.211518	+	0.977374i	$0.567841\pi$
$878$		0			0
$879$	−15.2269			−0.513591
$880$		0			0
$881$	30.1175			1.01469			0.507343	−	0.861744i	$-0.330628\pi$
$881$	30.1175			1.01469			0.507343	+	0.861744i	$0.330628\pi$
$882$		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	$0.721837\pi$
$884$		0			0
$885$	42.9811	+	40.9019i	1.44480	+	1.37490i
$886$		0			0
$887$	−39.3789	−	12.7950i	−1.32221	−	0.429613i	−0.438959	−	0.898507i	$-0.644653\pi$
$887$	−39.3789	−	12.7950i	−1.32221	−	0.429613i	−0.883255	+	0.468893i	$0.844653\pi$
$888$		0			0
$889$	5.54021	−	4.02520i	0.185813	−	0.135001i
$890$		0			0
$891$	−4.75642	+	18.1076i	−0.159346	+	0.606628i
$892$		0			0
$893$	8.33074	+	11.4663i	0.278777	+	0.383704i
$894$		0			0
$895$	−32.8674	−	15.7334i	−1.09864	−	0.525909i
$896$		0			0
$897$	−23.4647	+	32.2964i	−0.783464	+	1.07835i
$898$		0			0
$899$	−0.635162	−	1.95483i	−0.0211838	−	0.0651971i
$900$		0			0
$901$	8.87793			0.295767
$902$		0			0
$903$			5.72532i			0.190527i
$904$		0			0
$905$	12.1987	−	2.24327i	0.405498	−	0.0745687i
$906$		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	$0.175496\pi$
$908$		0			0
$909$	−18.1614	+	55.8951i	−0.602376	+	1.85392i
$910$		0			0
$911$	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
$914$		0			0
$915$	12.7339	−	6.89090i	0.420968	−	0.227806i
$916$		0			0
$917$	6.62923	+	2.15397i	0.218916	+	0.0711303i
$918$		0			0
$919$	18.9477	+	13.7663i	0.625027	+	0.454109i	0.854674	−	0.519165i	$-0.173757\pi$
$919$	18.9477	+	13.7663i	0.625027	+	0.454109i	−0.229647	+	0.973274i	$0.573757\pi$
$920$		0			0
$921$	−14.9589	−	46.0387i	−0.492912	−	1.51703i
$922$		0			0
$923$			24.6758i			0.812215i
$924$		0			0
$925$	8.28691	−	30.5850i	0.272472	−	1.00563i
$926$		0			0
$927$	−35.8514	+	11.6488i	−1.17751	+	0.382597i
$928$		0			0
$929$	−14.6355	−	10.6333i	−0.480175	−	0.348868i	0.321218	−	0.947005i	$-0.395908\pi$
$929$	−14.6355	−	10.6333i	−0.480175	−	0.348868i	−0.801394	+	0.598137i	$0.795908\pi$
$930$		0			0
$931$	6.14504	−	18.9125i	0.201395	−	0.619831i
$932$		0			0
$933$	17.4542	+	24.0237i	0.571426	+	0.786500i
$934$		0			0
$935$	5.86164	+	24.0413i	0.191696	+	0.786235i
$936$		0			0
$937$	−6.47128	−	8.90696i	−0.211408	−	0.290978i	0.690124	−	0.723691i	$-0.257556\pi$
$937$	−6.47128	−	8.90696i	−0.211408	−	0.290978i	−0.901531	+	0.432714i	$0.857556\pi$
$938$		0			0
$939$	4.14216	−	12.7483i	0.135174	−	0.416023i
$940$		0			0
$941$	−27.3293	−	19.8559i	−0.890908	−	0.647283i	0.0452063	−	0.998978i	$-0.485605\pi$
$941$	−27.3293	−	19.8559i	−0.890908	−	0.647283i	−0.936115	+	0.351695i	$0.885605\pi$
$942$		0			0
$943$	18.5237	−	6.01870i	0.603213	−	0.195996i
$944$		0			0
$945$	−0.647654	+	4.86686i	−0.0210682	+	0.158319i
$946$		0			0
$947$			46.9853i			1.52682i	0.645915	+	0.763409i	$0.276476\pi$
$947$			46.9853i			1.52682i	−0.645915	+	0.763409i	$0.723524\pi$
$948$		0			0
$949$	2.00736	+	6.17803i	0.0651618	+	0.200547i
$950$		0			0
$951$	−25.0454	−	18.1966i	−0.812154	−	0.590064i
$952$		0			0
$953$	−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
$955$	23.2170	+	42.9032i	0.751284	+	1.38832i
$956$		0			0
$957$	2.44491	+	42.6314i	0.0790328	+	1.37808i
$958$		0			0
$959$	−6.63443	+	4.82019i	−0.214237	+	0.155652i
$960$		0			0
$961$	−9.52544	+	29.3163i	−0.307272	+	0.945687i
$962$		0			0
$963$	17.3719	−	23.9103i	0.559800	−	0.770499i
$964$		0			0
$965$	9.09089	+	49.4354i	0.292646	+	1.59138i
$966$		0			0
$967$		−	54.1642i		−	1.74180i	−0.491458	−	0.870901i	$-0.663536\pi$
$967$		−	54.1642i		−	1.74180i	0.491458	−	0.870901i	$-0.336464\pi$
$968$		0			0
$969$	−28.6596			−0.920680
$970$		0			0
$971$	−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
$974$		0			0
$975$	−32.4317	+	49.6362i	−1.03864	+	1.58963i
$976$		0			0
$977$	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
$980$		0			0
$981$	30.8376	−	22.4048i	0.984567	−	0.715330i
$982$		0			0
$983$	48.9924	+	15.9186i	1.56261	+	0.507724i	0.957504	−	0.288419i	$-0.0931295\pi$
$983$	48.9924	+	15.9186i	1.56261	+	0.507724i	0.605109	+	0.796143i	$0.293129\pi$
$984$		0			0
$985$	−41.7073	−	39.6896i	−1.32890	−	1.26462i
$986$		0			0
$987$	−10.4091	+	3.38213i	−0.331326	+	0.107654i
$988$		0			0
$989$	−7.61503			−0.242144
$990$		0			0
$991$	22.3382			0.709596			0.354798	−	0.934943i	$-0.384550\pi$
$991$	22.3382			0.709596			0.354798	+	0.934943i	$0.384550\pi$
$992$		0			0
$993$	−72.9487	+	23.7025i	−2.31496	+	0.752175i
$994$		0			0
$995$	26.1544	−	27.4840i	0.829150	−	0.871300i
$996$		0			0
$997$	0.175514	+	0.0570278i	0.00555857	+	0.00180609i	0.311795	−	0.950149i	$-0.399070\pi$
$997$	0.175514	+	0.0570278i	0.00555857	+	0.00180609i	−0.306236	+	0.951955i	$0.599070\pi$
$998$		0			0
$999$	11.6562	−	8.46873i	0.368786	−	0.267939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cd.c.289.4		16
4.3	odd	2		55.2.j.a.14.4	yes	16
5.4	even	2	inner	880.2.cd.c.289.1		16
11.4	even	5	inner	880.2.cd.c.609.1		16
12.11	even	2		495.2.ba.a.289.1		16
20.3	even	4		275.2.h.d.201.4		16
20.7	even	4		275.2.h.d.201.1		16
20.19	odd	2		55.2.j.a.14.1	yes	16
44.3	odd	10		605.2.j.h.269.4		16
44.7	even	10		605.2.j.d.444.4		16
44.15	odd	10		55.2.j.a.4.1	✓	16
44.19	even	10		605.2.j.g.269.1		16
44.27	odd	10		605.2.j.h.9.1		16
44.31	odd	10		605.2.b.g.364.1		8
44.35	even	10		605.2.b.f.364.8		8
44.39	even	10		605.2.j.g.9.4		16
44.43	even	2		605.2.j.d.124.1		16
55.4	even	10	inner	880.2.cd.c.609.4		16
60.59	even	2		495.2.ba.a.289.4		16
132.59	even	10		495.2.ba.a.334.4		16
220.19	even	10		605.2.j.g.269.4		16
220.39	even	10		605.2.j.g.9.1		16
220.59	odd	10		55.2.j.a.4.4	yes	16
220.79	even	10		605.2.b.f.364.1		8
220.103	even	20		275.2.h.d.26.4		16
220.119	odd	10		605.2.b.g.364.8		8
220.123	odd	20		3025.2.a.bk.1.8		8
220.139	even	10		605.2.j.d.444.1		16
220.147	even	20		275.2.h.d.26.1		16
220.159	odd	10		605.2.j.h.9.4		16
220.163	even	20		3025.2.a.bl.1.1		8
220.167	odd	20		3025.2.a.bk.1.1		8
220.179	odd	10		605.2.j.h.269.1		16
220.207	even	20		3025.2.a.bl.1.8		8
220.219	even	2		605.2.j.d.124.4		16
660.59	even	10		495.2.ba.a.334.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.4.1	✓	16	44.15	odd	10
55.2.j.a.4.4	yes	16	220.59	odd	10
55.2.j.a.14.1	yes	16	20.19	odd	2
55.2.j.a.14.4	yes	16	4.3	odd	2
275.2.h.d.26.1		16	220.147	even	20
275.2.h.d.26.4		16	220.103	even	20
275.2.h.d.201.1		16	20.7	even	4
275.2.h.d.201.4		16	20.3	even	4
495.2.ba.a.289.1		16	12.11	even	2
495.2.ba.a.289.4		16	60.59	even	2
495.2.ba.a.334.1		16	660.59	even	10
495.2.ba.a.334.4		16	132.59	even	10
605.2.b.f.364.1		8	220.79	even	10
605.2.b.f.364.8		8	44.35	even	10
605.2.b.g.364.1		8	44.31	odd	10
605.2.b.g.364.8		8	220.119	odd	10
605.2.j.d.124.1		16	44.43	even	2
605.2.j.d.124.4		16	220.219	even	2
605.2.j.d.444.1		16	220.139	even	10
605.2.j.d.444.4		16	44.7	even	10
605.2.j.g.9.1		16	220.39	even	10
605.2.j.g.9.4		16	44.39	even	10
605.2.j.g.269.1		16	44.19	even	10
605.2.j.g.269.4		16	220.19	even	10
605.2.j.h.9.1		16	44.27	odd	10
605.2.j.h.9.4		16	220.159	odd	10
605.2.j.h.269.1		16	220.179	odd	10
605.2.j.h.269.4		16	44.3	odd	10
880.2.cd.c.289.1		16	5.4	even	2	inner
880.2.cd.c.289.4		16	1.1	even	1	trivial
880.2.cd.c.609.1		16	11.4	even	5	inner
880.2.cd.c.609.4		16	55.4	even	10	inner
3025.2.a.bk.1.1		8	220.167	odd	20
3025.2.a.bk.1.8		8	220.123	odd	20
3025.2.a.bl.1.1		8	220.163	even	20
3025.2.a.bl.1.8		8	220.207	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.49233 - 0.809808i) q^{3} +(1.54147 - 1.61983i) q^{5} +(-0.918552 - 0.298456i) q^{7} +(3.12889 - 2.27327i) q^{9} +(3.31118 - 0.189896i) q^{11} +(-2.65978 - 3.66088i) q^{13} +(2.53011 - 5.28546i) q^{15} +(-1.96126 + 2.69944i) q^{17} +(1.01283 + 3.11717i) q^{19} -2.53103 q^{21} -3.36643i q^{23} +(-0.247725 - 4.99386i) q^{25} +(1.33628 - 1.83923i) q^{27} +(-1.51820 + 4.67254i) q^{29} +(-0.338464 + 0.245909i) q^{31} +(8.09880 - 3.15471i) q^{33} +(-1.89937 + 1.02784i) q^{35} +(6.02737 + 1.95841i) q^{37} +(-9.59368 - 6.97021i) q^{39} +(1.78786 + 5.50247i) q^{41} -2.26205i q^{43} +(1.14077 - 8.57246i) q^{45} +(4.11260 - 1.33626i) q^{47} +(-4.90846 - 3.56620i) q^{49} +(-2.70208 + 8.31615i) q^{51} +(-1.56392 - 2.15255i) q^{53} +(4.79650 - 5.65629i) q^{55} +(5.04863 + 6.94884i) q^{57} +(-3.12889 + 9.62972i) q^{59} +(1.99897 + 1.45233i) q^{61} +(-3.55252 + 1.15428i) q^{63} +(-10.0300 - 1.33473i) q^{65} +9.60059i q^{67} +(-2.72616 - 8.39026i) q^{69} +(-4.41166 - 3.20526i) q^{71} +(-1.36528 - 0.443607i) q^{73} +(-4.66148 - 12.2458i) q^{75} +(-3.09817 - 0.813812i) q^{77} +(-0.812218 + 0.590111i) q^{79} +(-1.74436 + 5.36858i) q^{81} +(4.34692 - 5.98302i) q^{83} +(1.34942 + 7.33802i) q^{85} +12.8750i q^{87} +12.1964 q^{89} +(1.35054 + 4.15654i) q^{91} +(-0.644427 + 0.886978i) q^{93} +(6.61056 + 3.16442i) q^{95} +(1.77467 + 2.44262i) q^{97} +(9.92863 - 8.12138i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{5} + 2 q^{9} + 6 q^{11} + 16 q^{15} - 6 q^{19} + 8 q^{21} - 16 q^{25} + 2 q^{29} - 8 q^{31} - 22 q^{35} - 30 q^{39} - 52 q^{41} + 12 q^{45} - 10 q^{49} + 42 q^{51} + 8 q^{55} - 2 q^{59} - 40 q^{61}+ \cdots + 72 q^{99}+O(q^{100}) \) 16 * q - 2 * q^5 + 2 * q^9 + 6 * q^11 + 16 * q^15 - 6 * q^19 + 8 * q^21 - 16 * q^25 + 2 * q^29 - 8 * q^31 - 22 * q^35 - 30 * q^39 - 52 * q^41 + 12 * q^45 - 10 * q^49 + 42 * q^51 + 8 * q^55 - 2 * q^59 - 40 * q^61 - 40 * q^65 + 26 * q^69 - 36 * q^71 + 20 * q^75 - 38 * q^79 + 68 * q^81 + 58 * q^85 + 24 * q^89 + 20 * q^91 - 48 * q^95 + 72 * q^99

Introduction

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