LMFDB - Embedded newform 578.2.d.g.179.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [578,2,Mod(155,578)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(578, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("578.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.d (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-8,0,40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(18)] == traces)

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

Self dual:	no
Analytic conductor:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			179.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	578.179
Dual form			578.2.d.g.155.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} +(-2.61313 - 1.08239i) q^{3} -1.00000i q^{4} +(-1.08239 + 2.61313i) q^{5} +(-2.61313 + 1.08239i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(3.53553 + 3.53553i) q^{9} +(1.08239 + 2.61313i) q^{10} +(2.61313 - 1.08239i) q^{11} +(-1.08239 + 2.61313i) q^{12} +2.00000i q^{13} +(5.65685 - 5.65685i) q^{15} -1.00000 q^{16} +5.00000 q^{18} +(2.82843 - 2.82843i) q^{19} +(2.61313 + 1.08239i) q^{20} +(1.08239 - 2.61313i) q^{22} +(5.22625 - 2.16478i) q^{23} +(1.08239 + 2.61313i) q^{24} +(-2.12132 - 2.12132i) q^{25} +(1.41421 + 1.41421i) q^{26} +(-2.16478 - 5.22625i) q^{27} +(1.08239 - 2.61313i) q^{29} -8.00000i q^{30} +(-0.707107 + 0.707107i) q^{32} -8.00000 q^{33} +(3.53553 - 3.53553i) q^{36} +(7.83938 + 3.24718i) q^{37} -4.00000i q^{38} +(2.16478 - 5.22625i) q^{39} +(2.61313 - 1.08239i) q^{40} +(-2.16478 - 5.22625i) q^{41} +(2.82843 + 2.82843i) q^{43} +(-1.08239 - 2.61313i) q^{44} +(-13.0656 + 5.41196i) q^{45} +(2.16478 - 5.22625i) q^{46} +(2.61313 + 1.08239i) q^{48} +(4.94975 - 4.94975i) q^{49} -3.00000 q^{50} +2.00000 q^{52} +(-4.24264 + 4.24264i) q^{53} +(-5.22625 - 2.16478i) q^{54} +8.00000i q^{55} +(-10.4525 + 4.32957i) q^{57} +(-1.08239 - 2.61313i) q^{58} +(8.48528 + 8.48528i) q^{59} +(-5.65685 - 5.65685i) q^{60} +(3.24718 + 7.83938i) q^{61} +1.00000i q^{64} +(-5.22625 - 2.16478i) q^{65} +(-5.65685 + 5.65685i) q^{66} +4.00000 q^{67} -16.0000 q^{69} +(-5.22625 - 2.16478i) q^{71} -5.00000i q^{72} +(7.83938 - 3.24718i) q^{74} +(3.24718 + 7.83938i) q^{75} +(-2.82843 - 2.82843i) q^{76} +(-2.16478 - 5.22625i) q^{78} +(15.6788 - 6.49435i) q^{79} +(1.08239 - 2.61313i) q^{80} +1.00000i q^{81} +(-5.22625 - 2.16478i) q^{82} +(-8.48528 + 8.48528i) q^{83} +4.00000 q^{86} +(-5.65685 + 5.65685i) q^{87} +(-2.61313 - 1.08239i) q^{88} -6.00000i q^{89} +(-5.41196 + 13.0656i) q^{90} +(-2.16478 - 5.22625i) q^{92} +(4.32957 + 10.4525i) q^{95} +(2.61313 - 1.08239i) q^{96} +(-6.49435 + 15.6788i) q^{97} -7.00000i q^{98} +(13.0656 + 5.41196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{16} + 40 q^{18} - 64 q^{33} - 24 q^{50} + 16 q^{52} + 32 q^{67} - 128 q^{69} + 32 q^{86}+O(q^{100}) $ 8 * q - 8 * q^16 + 40 * q^18 - 64 * q^33 - 24 * q^50 + 16 * q^52 + 32 * q^67 - 128 * q^69 + 32 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−2.61313	−	1.08239i	−1.50869	−	0.624919i	−0.533402	−	0.845862i	$-0.679087\pi$
$3$	−2.61313	−	1.08239i	−1.50869	−	0.624919i	−0.975287	+	0.220942i	$0.929087\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.08239	+	2.61313i	−0.484061	+	1.16863i	0.473604	+	0.880738i	$0.342953\pi$
$5$	−1.08239	+	2.61313i	−0.484061	+	1.16863i	−0.957664	+	0.287887i	$0.907047\pi$
$6$	−2.61313	+	1.08239i	−1.06680	+	0.441885i
$7$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$7$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	3.53553	+	3.53553i	1.17851	+	1.17851i
$10$	1.08239	+	2.61313i	0.342282	+	0.826343i
$11$	2.61313	−	1.08239i	0.787887	−	0.326354i	0.0477934	−	0.998857i	$-0.484781\pi$
$11$	2.61313	−	1.08239i	0.787887	−	0.326354i	0.740094	+	0.672504i	$0.234781\pi$
$12$	−1.08239	+	2.61313i	−0.312460	+	0.754344i
$13$			2.00000i			0.554700i	0.960769	+	0.277350i	$0.0894562\pi$
$13$			2.00000i			0.554700i	−0.960769	+	0.277350i	$0.910544\pi$
$14$		0			0
$15$	5.65685	−	5.65685i	1.46059	−	1.46059i
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	5.00000			1.17851
$19$	2.82843	−	2.82843i	0.648886	−	0.648886i	−0.303838	−	0.952724i	$-0.598268\pi$
$19$	2.82843	−	2.82843i	0.648886	−	0.648886i	0.952724	+	0.303838i	$0.0982682\pi$
$20$	2.61313	+	1.08239i	0.584313	+	0.242030i
$21$		0			0
$22$	1.08239	−	2.61313i	0.230767	−	0.557120i
$23$	5.22625	−	2.16478i	1.08975	−	0.451389i	0.235830	−	0.971794i	$-0.424219\pi$
$23$	5.22625	−	2.16478i	1.08975	−	0.451389i	0.853919	+	0.520406i	$0.174219\pi$
$24$	1.08239	+	2.61313i	0.220942	+	0.533402i
$25$	−2.12132	−	2.12132i	−0.424264	−	0.424264i
$26$	1.41421	+	1.41421i	0.277350	+	0.277350i
$27$	−2.16478	−	5.22625i	−0.416613	−	1.00579i
$28$		0			0
$29$	1.08239	−	2.61313i	0.200995	−	0.485245i	−0.790955	−	0.611874i	$-0.790416\pi$
$29$	1.08239	−	2.61313i	0.200995	−	0.485245i	0.991950	+	0.126629i	$0.0404158\pi$
$30$		−	8.00000i		−	1.46059i
$31$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$31$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−8.00000			−1.39262
$34$		0			0
$35$		0			0
$36$	3.53553	−	3.53553i	0.589256	−	0.589256i
$37$	7.83938	+	3.24718i	1.28879	+	0.533833i	0.918623	−	0.395134i	$-0.129302\pi$
$37$	7.83938	+	3.24718i	1.28879	+	0.533833i	0.370162	+	0.928967i	$0.379302\pi$
$38$		−	4.00000i		−	0.648886i
$39$	2.16478	−	5.22625i	0.346643	−	0.836870i
$40$	2.61313	−	1.08239i	0.413171	−	0.171141i
$41$	−2.16478	−	5.22625i	−0.338083	−	0.816203i	−0.997900	−	0.0647773i	$-0.979366\pi$
$41$	−2.16478	−	5.22625i	−0.338083	−	0.816203i	0.659817	−	0.751426i	$-0.270634\pi$
$42$		0			0
$43$	2.82843	+	2.82843i	0.431331	+	0.431331i	0.889081	−	0.457750i	$-0.151344\pi$
$43$	2.82843	+	2.82843i	0.431331	+	0.431331i	−0.457750	+	0.889081i	$0.651344\pi$
$44$	−1.08239	−	2.61313i	−0.163177	−	0.393944i
$45$	−13.0656	+	5.41196i	−1.94771	+	0.806768i
$46$	2.16478	−	5.22625i	0.319180	−	0.770569i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	2.61313	+	1.08239i	0.377172	+	0.156230i
$49$	4.94975	−	4.94975i	0.707107	−	0.707107i
$50$	−3.00000			−0.424264
$51$		0			0
$52$	2.00000			0.277350
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	−0.935664	−	0.352892i	$-0.885198\pi$
$53$	−4.24264	+	4.24264i	−0.582772	+	0.582772i	0.352892	+	0.935664i	$0.385198\pi$
$54$	−5.22625	−	2.16478i	−0.711203	−	0.294590i
$55$			8.00000i			1.07872i
$56$		0			0
$57$	−10.4525	+	4.32957i	−1.38447	+	0.573465i
$58$	−1.08239	−	2.61313i	−0.142125	−	0.343120i
$59$	8.48528	+	8.48528i	1.10469	+	1.10469i	0.993837	+	0.110853i	$0.0353582\pi$
$59$	8.48528	+	8.48528i	1.10469	+	1.10469i	0.110853	+	0.993837i	$0.464642\pi$
$60$	−5.65685	−	5.65685i	−0.730297	−	0.730297i
$61$	3.24718	+	7.83938i	0.415758	+	1.00373i	0.983563	+	0.180566i	$0.0577930\pi$
$61$	3.24718	+	7.83938i	0.415758	+	1.00373i	−0.567805	+	0.823163i	$0.692207\pi$
$62$		0			0
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−5.22625	−	2.16478i	−0.648237	−	0.268508i
$66$	−5.65685	+	5.65685i	−0.696311	+	0.696311i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$		0			0
$69$	−16.0000			−1.92617
$70$		0			0
$71$	−5.22625	−	2.16478i	−0.620242	−	0.256913i	0.0503587	−	0.998731i	$-0.483964\pi$
$71$	−5.22625	−	2.16478i	−0.620242	−	0.256913i	−0.670601	+	0.741819i	$0.733964\pi$
$72$		−	5.00000i		−	0.589256i
$73$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$73$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$74$	7.83938	−	3.24718i	0.911309	−	0.377477i
$75$	3.24718	+	7.83938i	0.374952	+	0.905213i
$76$	−2.82843	−	2.82843i	−0.324443	−	0.324443i
$77$		0			0
$78$	−2.16478	−	5.22625i	−0.245114	−	0.591756i
$79$	15.6788	−	6.49435i	1.76400	−	0.730672i	0.768085	−	0.640347i	$-0.221210\pi$
$79$	15.6788	−	6.49435i	1.76400	−	0.730672i	0.995912	−	0.0903244i	$-0.0287904\pi$
$80$	1.08239	−	2.61313i	0.121015	−	0.292156i
$81$			1.00000i			0.111111i
$82$	−5.22625	−	2.16478i	−0.577143	−	0.239060i
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	−0.997792	−	0.0664117i	$-0.978845\pi$
$83$	−8.48528	+	8.48528i	−0.931381	+	0.931381i	0.0664117	+	0.997792i	$0.478845\pi$
$84$		0			0
$85$		0			0
$86$	4.00000			0.431331
$87$	−5.65685	+	5.65685i	−0.606478	+	0.606478i
$88$	−2.61313	−	1.08239i	−0.278560	−	0.115383i
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	−5.41196	+	13.0656i	−0.570471	+	1.37724i
$91$		0			0
$92$	−2.16478	−	5.22625i	−0.225694	−	0.544874i
$93$		0			0
$94$		0			0
$95$	4.32957	+	10.4525i	0.444204	+	1.07240i
$96$	2.61313	−	1.08239i	0.266701	−	0.110471i
$97$	−6.49435	+	15.6788i	−0.659402	+	1.59194i	0.139328	+	0.990246i	$0.455506\pi$
$97$	−6.49435	+	15.6788i	−0.659402	+	1.59194i	−0.798730	+	0.601690i	$0.794494\pi$
$98$		−	7.00000i		−	0.707107i
$99$	13.0656	+	5.41196i	1.31315	+	0.543923i
$100$	−2.12132	+	2.12132i	−0.212132	+	0.212132i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	1.41421	−	1.41421i	0.138675	−	0.138675i
$105$		0			0
$106$			6.00000i			0.582772i
$107$	−1.08239	+	2.61313i	−0.104639	+	0.252620i	−0.967524	−	0.252780i	$-0.918655\pi$
$107$	−1.08239	+	2.61313i	−0.104639	+	0.252620i	0.862885	+	0.505400i	$0.168655\pi$
$108$	−5.22625	+	2.16478i	−0.502896	+	0.208306i
$109$	3.24718	+	7.83938i	0.311023	+	0.750876i	0.999668	+	0.0257772i	$0.00820604\pi$
$109$	3.24718	+	7.83938i	0.311023	+	0.750876i	−0.688645	+	0.725099i	$0.741794\pi$
$110$	5.65685	+	5.65685i	0.539360	+	0.539360i
$111$	−16.9706	−	16.9706i	−1.61077	−	1.61077i
$112$		0			0
$113$	10.4525	−	4.32957i	0.983289	−	0.407292i	0.167646	−	0.985847i	$-0.446383\pi$
$113$	10.4525	−	4.32957i	0.983289	−	0.407292i	0.815643	+	0.578556i	$0.196383\pi$
$114$	−4.32957	+	10.4525i	−0.405501	+	0.978967i
$115$			16.0000i			1.49201i
$116$	−2.61313	−	1.08239i	−0.242623	−	0.100498i
$117$	−7.07107	+	7.07107i	−0.653720	+	0.653720i
$118$	12.0000			1.10469
$119$		0			0
$120$	−8.00000			−0.730297
$121$	−2.12132	+	2.12132i	−0.192847	+	0.192847i
$122$	7.83938	+	3.24718i	0.709744	+	0.293986i
$123$			16.0000i			1.44267i
$124$		0			0
$125$	−5.22625	+	2.16478i	−0.467450	+	0.193624i
$126$		0			0
$127$	−11.3137	−	11.3137i	−1.00393	−	1.00393i	−0.999992	−	0.00393704i	$-0.998747\pi$
$127$	−11.3137	−	11.3137i	−1.00393	−	1.00393i	−0.00393704	−	0.999992i	$-0.501253\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−4.32957	−	10.4525i	−0.381197	−	0.920292i
$130$	−5.22625	+	2.16478i	−0.458373	+	0.189864i
$131$	1.08239	−	2.61313i	0.0945690	−	0.228310i	−0.869515	−	0.493906i	$-0.835569\pi$
$131$	1.08239	−	2.61313i	0.0945690	−	0.228310i	0.964084	+	0.265596i	$0.0855687\pi$
$132$			8.00000i			0.696311i
$133$		0			0
$134$	2.82843	−	2.82843i	0.244339	−	0.244339i
$135$	16.0000			1.37706
$136$		0			0
$137$	−18.0000			−1.53784			−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000			−1.53784			−0.768922	+	0.639343i	$0.779207\pi$
$138$	−11.3137	+	11.3137i	−0.963087	+	0.963087i
$139$	−7.83938	−	3.24718i	−0.664927	−	0.275422i	0.0245830	−	0.999698i	$-0.492174\pi$
$139$	−7.83938	−	3.24718i	−0.664927	−	0.275422i	−0.689510	+	0.724276i	$0.742174\pi$
$140$		0			0
$141$		0			0
$142$	−5.22625	+	2.16478i	−0.438577	+	0.181665i
$143$	2.16478	+	5.22625i	0.181028	+	0.437041i
$144$	−3.53553	−	3.53553i	−0.294628	−	0.294628i
$145$	5.65685	+	5.65685i	0.469776	+	0.469776i
$146$		0			0
$147$	−18.2919	+	7.57675i	−1.50869	+	0.624919i
$148$	3.24718	−	7.83938i	0.266916	−	0.644393i
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$	7.83938	+	3.24718i	0.640083	+	0.265131i
$151$	5.65685	−	5.65685i	0.460348	−	0.460348i	−0.438421	−	0.898770i	$-0.644462\pi$
$151$	5.65685	−	5.65685i	0.460348	−	0.460348i	0.898770	+	0.438421i	$0.144462\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−5.22625	−	2.16478i	−0.418435	−	0.173321i
$157$		−	14.0000i		−	1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$		−	14.0000i		−	1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$	6.49435	−	15.6788i	0.516663	−	1.24733i
$159$	15.6788	−	6.49435i	1.24341	−	0.515036i
$160$	−1.08239	−	2.61313i	−0.0855706	−	0.206586i
$161$		0			0
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−3.24718	−	7.83938i	−0.254339	−	0.614027i	0.744207	−	0.667949i	$-0.232828\pi$
$163$	−3.24718	−	7.83938i	−0.254339	−	0.614027i	−0.998545	+	0.0539220i	$0.982828\pi$
$164$	−5.22625	+	2.16478i	−0.408102	+	0.169041i
$165$	8.65914	−	20.9050i	0.674113	−	1.62745i
$166$			12.0000i			0.931381i
$167$	−10.4525	−	4.32957i	−0.808839	−	0.335032i	−0.0603483	−	0.998177i	$-0.519221\pi$
$167$	−10.4525	−	4.32957i	−0.808839	−	0.335032i	−0.748491	+	0.663145i	$0.769221\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	20.0000			1.52944
$172$	2.82843	−	2.82843i	0.215666	−	0.215666i
$173$	2.61313	+	1.08239i	0.198672	+	0.0822928i	0.479801	−	0.877377i	$-0.340709\pi$
$173$	2.61313	+	1.08239i	0.198672	+	0.0822928i	−0.281129	+	0.959670i	$0.590709\pi$
$174$			8.00000i			0.606478i
$175$		0			0
$176$	−2.61313	+	1.08239i	−0.196972	+	0.0815884i
$177$	−12.9887	−	31.3575i	−0.976291	−	2.35697i
$178$	−4.24264	−	4.24264i	−0.317999	−	0.317999i
$179$	−8.48528	−	8.48528i	−0.634220	−	0.634220i	0.314904	−	0.949124i	$-0.398028\pi$
$179$	−8.48528	−	8.48528i	−0.634220	−	0.634220i	−0.949124	+	0.314904i	$0.898028\pi$
$180$	5.41196	+	13.0656i	0.403384	+	0.973855i
$181$	−7.83938	+	3.24718i	−0.582696	+	0.241361i	−0.654505	−	0.756058i	$-0.727123\pi$
$181$	−7.83938	+	3.24718i	−0.582696	+	0.241361i	0.0718086	+	0.997418i	$0.477123\pi$
$182$		0			0
$183$		−	24.0000i		−	1.77413i
$184$	−5.22625	−	2.16478i	−0.385284	−	0.159590i
$185$	−16.9706	+	16.9706i	−1.24770	+	1.24770i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	10.4525	+	4.32957i	0.758304	+	0.314100i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	1.08239	−	2.61313i	0.0781149	−	0.188586i
$193$	15.6788	−	6.49435i	1.12858	−	0.467474i	0.261283	−	0.965262i	$-0.415854\pi$
$193$	15.6788	−	6.49435i	1.12858	−	0.467474i	0.867298	+	0.497788i	$0.165854\pi$
$194$	6.49435	+	15.6788i	0.466267	+	1.12567i
$195$	11.3137	+	11.3137i	0.810191	+	0.810191i
$196$	−4.94975	−	4.94975i	−0.353553	−	0.353553i
$197$	−1.08239	−	2.61313i	−0.0771173	−	0.186178i	0.880619	−	0.473825i	$-0.157127\pi$
$197$	−1.08239	−	2.61313i	−0.0771173	−	0.186178i	−0.957736	+	0.287647i	$0.907127\pi$
$198$	13.0656	−	5.41196i	0.928534	−	0.384611i
$199$	6.49435	−	15.6788i	0.460372	−	1.11144i	−0.507872	−	0.861433i	$-0.669568\pi$
$199$	6.49435	−	15.6788i	0.460372	−	1.11144i	0.968245	−	0.250005i	$-0.0804323\pi$
$200$			3.00000i			0.212132i
$201$	−10.4525	−	4.32957i	−0.737263	−	0.305384i
$202$	4.24264	−	4.24264i	0.298511	−	0.298511i
$203$		0			0
$204$		0			0
$205$	16.0000			1.11749
$206$	5.65685	−	5.65685i	0.394132	−	0.394132i
$207$	26.1313	+	10.8239i	1.81625	+	0.752315i
$208$		−	2.00000i		−	0.138675i
$209$	4.32957	−	10.4525i	0.299483	−	0.723015i
$210$		0			0
$211$	−3.24718	−	7.83938i	−0.223545	−	0.539685i	0.771822	−	0.635839i	$-0.219346\pi$
$211$	−3.24718	−	7.83938i	−0.223545	−	0.539685i	−0.995366	+	0.0961541i	$0.969346\pi$
$212$	4.24264	+	4.24264i	0.291386	+	0.291386i
$213$	11.3137	+	11.3137i	0.775203	+	0.775203i
$214$	1.08239	+	2.61313i	0.0739908	+	0.178630i
$215$	−10.4525	+	4.32957i	−0.712855	+	0.295274i
$216$	−2.16478	+	5.22625i	−0.147295	+	0.355601i
$217$		0			0
$218$	7.83938	+	3.24718i	0.530950	+	0.219927i
$219$		0			0
$220$	8.00000			0.539360
$221$		0			0
$222$	−24.0000			−1.61077
$223$	11.3137	−	11.3137i	0.757622	−	0.757622i	−0.218267	−	0.975889i	$-0.570040\pi$
$223$	11.3137	−	11.3137i	0.757622	−	0.757622i	0.975889	+	0.218267i	$0.0700404\pi$
$224$		0			0
$225$		−	15.0000i		−	1.00000i
$226$	4.32957	−	10.4525i	0.287999	−	0.695290i
$227$	−18.2919	+	7.57675i	−1.21407	+	0.502886i	−0.895521	−	0.445019i	$-0.853197\pi$
$227$	−18.2919	+	7.57675i	−1.21407	+	0.502886i	−0.318554	+	0.947905i	$0.603197\pi$
$228$	4.32957	+	10.4525i	0.286733	+	0.692234i
$229$	−15.5563	−	15.5563i	−1.02799	−	1.02799i	−0.999597	−	0.0283957i	$-0.990960\pi$
$229$	−15.5563	−	15.5563i	−1.02799	−	1.02799i	−0.0283957	−	0.999597i	$-0.509040\pi$
$230$	11.3137	+	11.3137i	0.746004	+	0.746004i
$231$		0			0
$232$	−2.61313	+	1.08239i	−0.171560	+	0.0710625i
$233$	−8.65914	+	20.9050i	−0.567279	+	1.36953i	0.336561	+	0.941662i	$0.390736\pi$
$233$	−8.65914	+	20.9050i	−0.567279	+	1.36953i	−0.903840	+	0.427871i	$0.859264\pi$
$234$			10.0000i			0.653720i
$235$		0			0
$236$	8.48528	−	8.48528i	0.552345	−	0.552345i
$237$	−48.0000			−3.11794
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−5.65685	+	5.65685i	−0.365148	+	0.365148i
$241$	−15.6788	−	6.49435i	−1.00996	−	0.418338i	−0.184518	−	0.982829i	$-0.559072\pi$
$241$	−15.6788	−	6.49435i	−1.00996	−	0.418338i	−0.825439	+	0.564491i	$0.809072\pi$
$242$			3.00000i			0.192847i
$243$	−5.41196	+	13.0656i	−0.347177	+	0.838161i
$244$	7.83938	−	3.24718i	0.501865	−	0.207879i
$245$	7.57675	+	18.2919i	0.484061	+	1.16863i
$246$	11.3137	+	11.3137i	0.721336	+	0.721336i
$247$	5.65685	+	5.65685i	0.359937	+	0.359937i
$248$		0			0
$249$	31.3575	−	12.9887i	1.98720	−	0.823126i
$250$	−2.16478	+	5.22625i	−0.136913	+	0.330537i
$251$		−	12.0000i		−	0.757433i	−0.925513	−	0.378717i	$-0.876365\pi$
$251$		−	12.0000i		−	0.757433i	0.925513	−	0.378717i	$-0.123635\pi$
$252$		0			0
$253$	11.3137	−	11.3137i	0.711287	−	0.711287i
$254$	−16.0000			−1.00393
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.24264	+	4.24264i	−0.264649	+	0.264649i	−0.826940	−	0.562291i	$-0.809920\pi$
$257$	−4.24264	+	4.24264i	−0.264649	+	0.264649i	0.562291	+	0.826940i	$0.309920\pi$
$258$	−10.4525	−	4.32957i	−0.650744	−	0.269547i
$259$		0			0
$260$	−2.16478	+	5.22625i	−0.134254	+	0.324118i
$261$	13.0656	−	5.41196i	0.808742	−	0.334992i
$262$	−1.08239	−	2.61313i	−0.0668704	−	0.161439i
$263$	16.9706	+	16.9706i	1.04645	+	1.04645i	0.998867	+	0.0475824i	$0.0151517\pi$
$263$	16.9706	+	16.9706i	1.04645	+	1.04645i	0.0475824	+	0.998867i	$0.484848\pi$
$264$	5.65685	+	5.65685i	0.348155	+	0.348155i
$265$	−6.49435	−	15.6788i	−0.398945	−	0.963138i
$266$		0			0
$267$	−6.49435	+	15.6788i	−0.397448	+	0.959524i
$268$		−	4.00000i		−	0.244339i
$269$	28.7444	+	11.9063i	1.75258	+	0.725941i	0.997528	+	0.0702715i	$0.0223866\pi$
$269$	28.7444	+	11.9063i	1.75258	+	0.725941i	0.755048	+	0.655669i	$0.227613\pi$
$270$	11.3137	−	11.3137i	0.688530	−	0.688530i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$		0			0
$273$		0			0
$274$	−12.7279	+	12.7279i	−0.768922	+	0.768922i
$275$	−7.83938	−	3.24718i	−0.472732	−	0.195812i
$276$			16.0000i			0.963087i
$277$	−9.74153	+	23.5181i	−0.585312	+	1.41307i	0.302628	+	0.953109i	$0.402136\pi$
$277$	−9.74153	+	23.5181i	−0.585312	+	1.41307i	−0.887940	+	0.459959i	$0.847864\pi$
$278$	−7.83938	+	3.24718i	−0.470175	+	0.194753i
$279$		0			0
$280$		0			0
$281$	−12.7279	−	12.7279i	−0.759284	−	0.759284i	0.216908	−	0.976192i	$-0.430403\pi$
$281$	−12.7279	−	12.7279i	−0.759284	−	0.759284i	−0.976192	+	0.216908i	$0.930403\pi$
$282$		0			0
$283$	−7.83938	+	3.24718i	−0.466003	+	0.193025i	−0.603315	−	0.797503i	$-0.706154\pi$
$283$	−7.83938	+	3.24718i	−0.466003	+	0.193025i	0.137312	+	0.990528i	$0.456154\pi$
$284$	−2.16478	+	5.22625i	−0.128456	+	0.310121i
$285$		−	32.0000i		−	1.89552i
$286$	5.22625	+	2.16478i	0.309035	+	0.128006i
$287$		0			0
$288$	−5.00000			−0.294628
$289$		0			0
$290$	8.00000			0.469776
$291$	33.9411	−	33.9411i	1.98966	−	1.98966i
$292$		0			0
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$	−7.57675	+	18.2919i	−0.441885	+	1.06680i
$295$	−31.3575	+	12.9887i	−1.82570	+	0.756232i
$296$	−3.24718	−	7.83938i	−0.188738	−	0.455655i
$297$	−11.3137	−	11.3137i	−0.656488	−	0.656488i
$298$	4.24264	+	4.24264i	0.245770	+	0.245770i
$299$	4.32957	+	10.4525i	0.250385	+	0.604484i
$300$	7.83938	−	3.24718i	0.452607	−	0.187476i
$301$		0			0
$302$		−	8.00000i		−	0.460348i
$303$	−15.6788	−	6.49435i	−0.900721	−	0.373091i
$304$	−2.82843	+	2.82843i	−0.162221	+	0.162221i
$305$	−24.0000			−1.37424
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	−20.9050	−	8.65914i	−1.18924	−	0.492601i
$310$		0			0
$311$	−4.32957	+	10.4525i	−0.245507	+	0.592707i	−0.997812	−	0.0661077i	$-0.978942\pi$
$311$	−4.32957	+	10.4525i	−0.245507	+	0.592707i	0.752305	+	0.658815i	$0.228942\pi$
$312$	−5.22625	+	2.16478i	−0.295878	+	0.122557i
$313$	6.49435	+	15.6788i	0.367083	+	0.886216i	0.994225	+	0.107311i	$0.0342242\pi$
$313$	6.49435	+	15.6788i	0.367083	+	0.886216i	−0.627143	+	0.778904i	$0.715776\pi$
$314$	−9.89949	−	9.89949i	−0.558661	−	0.558661i
$315$		0			0
$316$	−6.49435	−	15.6788i	−0.365336	−	0.881999i
$317$	2.61313	−	1.08239i	0.146768	−	0.0607932i	−0.308090	−	0.951357i	$-0.599690\pi$
$317$	2.61313	−	1.08239i	0.146768	−	0.0607932i	0.454858	+	0.890564i	$0.349690\pi$
$318$	6.49435	−	15.6788i	0.364185	−	0.879221i
$319$		−	8.00000i		−	0.447914i
$320$	−2.61313	−	1.08239i	−0.146078	−	0.0605076i
$321$	5.65685	−	5.65685i	0.315735	−	0.315735i
$322$		0			0
$323$		0			0
$324$	1.00000			0.0555556
$325$	4.24264	−	4.24264i	0.235339	−	0.235339i
$326$	−7.83938	−	3.24718i	−0.434183	−	0.179844i
$327$		−	24.0000i		−	1.32720i
$328$	−2.16478	+	5.22625i	−0.119530	+	0.288571i
$329$		0			0
$330$	−8.65914	−	20.9050i	−0.476670	−	1.15078i
$331$	−2.82843	−	2.82843i	−0.155464	−	0.155464i	0.625089	−	0.780553i	$-0.285063\pi$
$331$	−2.82843	−	2.82843i	−0.155464	−	0.155464i	−0.780553	+	0.625089i	$0.785063\pi$
$332$	8.48528	+	8.48528i	0.465690	+	0.465690i
$333$	16.2359	+	39.1969i	0.889721	+	2.14798i
$334$	−10.4525	+	4.32957i	−0.571936	+	0.236903i
$335$	−4.32957	+	10.4525i	−0.236550	+	0.571081i
$336$		0			0
$337$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$337$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$338$	6.36396	−	6.36396i	0.346154	−	0.346154i
$339$	−32.0000			−1.73800
$340$		0			0
$341$		0			0
$342$	14.1421	−	14.1421i	0.764719	−	0.764719i
$343$		0			0
$344$		−	4.00000i		−	0.215666i
$345$	17.3183	−	41.8100i	0.932385	−	2.25098i
$346$	2.61313	−	1.08239i	0.140483	−	0.0581898i
$347$	−5.41196	−	13.0656i	−0.290529	−	0.701400i	0.709465	−	0.704741i	$-0.248937\pi$
$347$	−5.41196	−	13.0656i	−0.290529	−	0.701400i	−0.999994	+	0.00334079i	$0.998937\pi$
$348$	5.65685	+	5.65685i	0.303239	+	0.303239i
$349$	24.0416	+	24.0416i	1.28692	+	1.28692i	0.936649	+	0.350270i	$0.113910\pi$
$349$	24.0416	+	24.0416i	1.28692	+	1.28692i	0.350270	+	0.936649i	$0.386090\pi$
$350$		0			0
$351$	10.4525	−	4.32957i	0.557913	−	0.231095i
$352$	−1.08239	+	2.61313i	−0.0576917	+	0.139280i
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$	−31.3575	−	12.9887i	−1.66663	−	0.690342i
$355$	11.3137	−	11.3137i	0.600469	−	0.600469i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	−16.9706	+	16.9706i	−0.895672	+	0.895672i	−0.995050	−	0.0993777i	$-0.968315\pi$
$359$	−16.9706	+	16.9706i	−0.895672	+	0.895672i	0.0993777	+	0.995050i	$0.468315\pi$
$360$	13.0656	+	5.41196i	0.688619	+	0.285235i
$361$			3.00000i			0.157895i
$362$	−3.24718	+	7.83938i	−0.170668	+	0.412029i
$363$	7.83938	−	3.24718i	0.411461	−	0.170433i
$364$		0			0
$365$		0			0
$366$	−16.9706	−	16.9706i	−0.887066	−	0.887066i
$367$	6.49435	+	15.6788i	0.339002	+	0.818424i	0.997812	+	0.0661146i	$0.0210603\pi$
$367$	6.49435	+	15.6788i	0.339002	+	0.818424i	−0.658810	+	0.752310i	$0.728940\pi$
$368$	−5.22625	+	2.16478i	−0.272437	+	0.112847i
$369$	10.8239	−	26.1313i	0.563471	−	1.36034i
$370$			24.0000i			1.24770i
$371$		0			0
$372$		0			0
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$	16.0000			0.826236
$376$		0			0
$377$	5.22625	+	2.16478i	0.269166	+	0.111492i
$378$		0			0
$379$	9.74153	−	23.5181i	0.500389	−	1.20805i	−0.448884	−	0.893590i	$-0.648178\pi$
$379$	9.74153	−	23.5181i	0.500389	−	1.20805i	0.949272	−	0.314455i	$-0.101822\pi$
$380$	10.4525	−	4.32957i	0.536202	−	0.222102i
$381$	17.3183	+	41.8100i	0.887242	+	2.14199i
$382$		0			0
$383$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$383$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$384$	−1.08239	−	2.61313i	−0.0552356	−	0.133351i
$385$		0			0
$386$	6.49435	−	15.6788i	0.330554	−	0.798028i
$387$			20.0000i			1.01666i
$388$	15.6788	+	6.49435i	0.795968	+	0.329701i
$389$	−4.24264	+	4.24264i	−0.215110	+	0.215110i	−0.806434	−	0.591324i	$-0.798606\pi$
$389$	−4.24264	+	4.24264i	−0.215110	+	0.215110i	0.591324	+	0.806434i	$0.298606\pi$
$390$	16.0000			0.810191
$391$		0			0
$392$	−7.00000			−0.353553
$393$	−5.65685	+	5.65685i	−0.285351	+	0.285351i
$394$	−2.61313	−	1.08239i	−0.131647	−	0.0545301i
$395$			48.0000i			2.41514i
$396$	5.41196	−	13.0656i	0.271961	−	0.656573i
$397$	7.83938	−	3.24718i	0.393447	−	0.162971i	−0.177184	−	0.984178i	$-0.556699\pi$
$397$	7.83938	−	3.24718i	0.393447	−	0.162971i	0.570631	+	0.821207i	$0.306699\pi$
$398$	−6.49435	−	15.6788i	−0.325533	−	0.785905i
$399$		0			0
$400$	2.12132	+	2.12132i	0.106066	+	0.106066i
$401$	−10.8239	−	26.1313i	−0.540521	−	1.30493i	−0.924356	−	0.381531i	$-0.875397\pi$
$401$	−10.8239	−	26.1313i	−0.540521	−	1.30493i	0.383835	−	0.923402i	$-0.374603\pi$
$402$	−10.4525	+	4.32957i	−0.521324	+	0.215939i
$403$		0			0
$404$		−	6.00000i		−	0.298511i
$405$	−2.61313	−	1.08239i	−0.129847	−	0.0537845i
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	2.00000			0.0988936			0.0494468	−	0.998777i	$-0.484254\pi$
$409$	2.00000			0.0988936			0.0494468	+	0.998777i	$0.484254\pi$
$410$	11.3137	−	11.3137i	0.558744	−	0.558744i
$411$	47.0363	+	19.4831i	2.32013	+	0.961028i
$412$		−	8.00000i		−	0.394132i
$413$		0			0
$414$	26.1313	−	10.8239i	1.28428	−	0.531967i
$415$	−12.9887	−	31.3575i	−0.637591	−	1.53928i
$416$	−1.41421	−	1.41421i	−0.0693375	−	0.0693375i
$417$	16.9706	+	16.9706i	0.831052	+	0.831052i
$418$	−4.32957	−	10.4525i	−0.211766	−	0.511249i
$419$	−13.0656	+	5.41196i	−0.638298	+	0.264392i	−0.678274	−	0.734809i	$-0.737272\pi$
$419$	−13.0656	+	5.41196i	−0.638298	+	0.264392i	0.0399763	+	0.999201i	$0.487272\pi$
$420$		0			0
$421$			26.0000i			1.26716i	0.773676	+	0.633581i	$0.218416\pi$
$421$			26.0000i			1.26716i	−0.773676	+	0.633581i	$0.781584\pi$
$422$	−7.83938	−	3.24718i	−0.381615	−	0.158070i
$423$		0			0
$424$	6.00000			0.291386
$425$		0			0
$426$	16.0000			0.775203
$427$		0			0
$428$	2.61313	+	1.08239i	0.126310	+	0.0523194i
$429$		−	16.0000i		−	0.772487i
$430$	−4.32957	+	10.4525i	−0.208790	+	0.504064i
$431$	5.22625	−	2.16478i	0.251740	−	0.104274i	−0.253245	−	0.967402i	$-0.581498\pi$
$431$	5.22625	−	2.16478i	0.251740	−	0.104274i	0.504985	+	0.863128i	$0.331498\pi$
$432$	2.16478	+	5.22625i	0.104153	+	0.251448i
$433$	9.89949	+	9.89949i	0.475739	+	0.475739i	0.903766	−	0.428027i	$-0.140791\pi$
$433$	9.89949	+	9.89949i	0.475739	+	0.475739i	−0.428027	+	0.903766i	$0.640791\pi$
$434$		0			0
$435$	−8.65914	−	20.9050i	−0.415174	−	1.00232i
$436$	7.83938	−	3.24718i	0.375438	−	0.155512i
$437$	8.65914	−	20.9050i	0.414223	−	1.00002i
$438$		0			0
$439$	15.6788	+	6.49435i	0.748306	+	0.309959i	0.724050	−	0.689747i	$-0.242278\pi$
$439$	15.6788	+	6.49435i	0.748306	+	0.309959i	0.0242559	+	0.999706i	$0.492278\pi$
$440$	5.65685	−	5.65685i	0.269680	−	0.269680i
$441$	35.0000			1.66667
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$	−16.9706	+	16.9706i	−0.805387	+	0.805387i
$445$	15.6788	+	6.49435i	0.743244	+	0.307862i
$446$		−	16.0000i		−	0.757622i
$447$	6.49435	−	15.6788i	0.307172	−	0.741580i
$448$		0			0
$449$	−2.16478	−	5.22625i	−0.102162	−	0.246642i	0.864531	−	0.502580i	$-0.167616\pi$
$449$	−2.16478	−	5.22625i	−0.102162	−	0.246642i	−0.966693	+	0.255938i	$0.917616\pi$
$450$	−10.6066	−	10.6066i	−0.500000	−	0.500000i
$451$	−11.3137	−	11.3137i	−0.532742	−	0.532742i
$452$	−4.32957	−	10.4525i	−0.203646	−	0.491644i
$453$	−20.9050	+	8.65914i	−0.982203	+	0.406842i
$454$	−7.57675	+	18.2919i	−0.355594	+	0.858481i
$455$		0			0
$456$	10.4525	+	4.32957i	0.489483	+	0.202751i
$457$	−7.07107	+	7.07107i	−0.330771	+	0.330771i	−0.852879	−	0.522108i	$-0.825146\pi$
$457$	−7.07107	+	7.07107i	−0.330771	+	0.330771i	0.522108	+	0.852879i	$0.325146\pi$
$458$	−22.0000			−1.02799
$459$		0			0
$460$	16.0000			0.746004
$461$	12.7279	−	12.7279i	0.592798	−	0.592798i	−0.345588	−	0.938386i	$-0.612320\pi$
$461$	12.7279	−	12.7279i	0.592798	−	0.592798i	0.938386	+	0.345588i	$0.112320\pi$
$462$		0			0
$463$		−	32.0000i		−	1.48717i	−0.668644	−	0.743583i	$-0.733125\pi$
$463$		−	32.0000i		−	1.48717i	0.668644	−	0.743583i	$-0.266875\pi$
$464$	−1.08239	+	2.61313i	−0.0502488	+	0.121311i
$465$		0			0
$466$	8.65914	+	20.9050i	0.401127	+	0.968406i
$467$	−25.4558	−	25.4558i	−1.17796	−	1.17796i	−0.980264	−	0.197692i	$-0.936655\pi$
$467$	−25.4558	−	25.4558i	−1.17796	−	1.17796i	−0.197692	−	0.980264i	$-0.563345\pi$
$468$	7.07107	+	7.07107i	0.326860	+	0.326860i
$469$		0			0
$470$		0			0
$471$	−15.1535	+	36.5838i	−0.698236	+	1.68569i
$472$		−	12.0000i		−	0.552345i
$473$	10.4525	+	4.32957i	0.480607	+	0.199074i
$474$	−33.9411	+	33.9411i	−1.55897	+	1.55897i
$475$	−12.0000			−0.550598
$476$		0			0
$477$	−30.0000			−1.37361
$478$		0			0
$479$	−5.22625	−	2.16478i	−0.238794	−	0.0989115i	0.260078	−	0.965588i	$-0.416252\pi$
$479$	−5.22625	−	2.16478i	−0.238794	−	0.0989115i	−0.498871	+	0.866676i	$0.666252\pi$
$480$			8.00000i			0.365148i
$481$	−6.49435	+	15.6788i	−0.296117	+	0.714890i
$482$	−15.6788	+	6.49435i	−0.714148	+	0.295810i
$483$		0			0
$484$	2.12132	+	2.12132i	0.0964237	+	0.0964237i
$485$	−33.9411	−	33.9411i	−1.54119	−	1.54119i
$486$	5.41196	+	13.0656i	0.245492	+	0.592669i
$487$	−15.6788	+	6.49435i	−0.710472	+	0.294287i	−0.708500	−	0.705711i	$-0.750628\pi$
$487$	−15.6788	+	6.49435i	−0.710472	+	0.294287i	−0.00197224	+	0.999998i	$0.500628\pi$
$488$	3.24718	−	7.83938i	0.146993	−	0.354872i
$489$			24.0000i			1.08532i
$490$	18.2919	+	7.57675i	0.826343	+	0.342282i
$491$	−8.48528	+	8.48528i	−0.382935	+	0.382935i	−0.872159	−	0.489223i	$-0.837280\pi$
$491$	−8.48528	+	8.48528i	−0.382935	+	0.382935i	0.489223	+	0.872159i	$0.337280\pi$
$492$	16.0000			0.721336
$493$		0			0
$494$	8.00000			0.359937
$495$	−28.2843	+	28.2843i	−1.27128	+	1.27128i
$496$		0			0
$497$		0			0
$498$	12.9887	−	31.3575i	0.582038	−	1.40516i
$499$	−23.5181	+	9.74153i	−1.05282	+	0.436091i	−0.840896	−	0.541196i	$-0.817972\pi$
$499$	−23.5181	+	9.74153i	−1.05282	+	0.436091i	−0.211920	+	0.977287i	$0.567972\pi$
$500$	2.16478	+	5.22625i	0.0968121	+	0.233725i
$501$	22.6274	+	22.6274i	1.01092	+	1.01092i
$502$	−8.48528	−	8.48528i	−0.378717	−	0.378717i
$503$	−10.8239	−	26.1313i	−0.482615	−	1.16514i	−0.958363	−	0.285554i	$-0.907823\pi$
$503$	−10.8239	−	26.1313i	−0.482615	−	1.16514i	0.475748	−	0.879582i	$-0.342177\pi$
$504$		0			0
$505$	−6.49435	+	15.6788i	−0.288995	+	0.697695i
$506$		−	16.0000i		−	0.711287i
$507$	−23.5181	−	9.74153i	−1.04448	−	0.432637i
$508$	−11.3137	+	11.3137i	−0.501965	+	0.501965i
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−20.9050	−	8.65914i	−0.922979	−	0.382310i
$514$			6.00000i			0.264649i
$515$	−8.65914	+	20.9050i	−0.381567	+	0.921185i
$516$	−10.4525	+	4.32957i	−0.460146	+	0.190599i
$517$		0			0
$518$		0			0
$519$	−5.65685	−	5.65685i	−0.248308	−	0.248308i
$520$	2.16478	+	5.22625i	0.0949321	+	0.229186i
$521$	−5.22625	+	2.16478i	−0.228966	+	0.0948409i	−0.494217	−	0.869339i	$-0.664545\pi$
$521$	−5.22625	+	2.16478i	−0.228966	+	0.0948409i	0.265251	+	0.964179i	$0.414545\pi$
$522$	5.41196	−	13.0656i	0.236875	−	0.571867i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−2.61313	−	1.08239i	−0.114155	−	0.0472845i
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	8.00000			0.348155
$529$	6.36396	−	6.36396i	0.276694	−	0.276694i
$530$	−15.6788	−	6.49435i	−0.681042	−	0.282097i
$531$			60.0000i			2.60378i
$532$		0			0
$533$	10.4525	−	4.32957i	0.452748	−	0.187534i
$534$	6.49435	+	15.6788i	0.281038	+	0.678486i
$535$	−5.65685	−	5.65685i	−0.244567	−	0.244567i
$536$	−2.82843	−	2.82843i	−0.122169	−	0.122169i
$537$	12.9887	+	31.3575i	0.560504	+	1.35318i
$538$	28.7444	−	11.9063i	1.23926	−	0.513318i
$539$	7.57675	−	18.2919i	0.326354	−	0.787887i
$540$		−	16.0000i		−	0.688530i
$541$	−7.83938	−	3.24718i	−0.337041	−	0.139607i	0.207743	−	0.978184i	$-0.433388\pi$
$541$	−7.83938	−	3.24718i	−0.337041	−	0.139607i	−0.544784	+	0.838576i	$0.683388\pi$
$542$	11.3137	−	11.3137i	0.485965	−	0.485965i
$543$	24.0000			1.02994
$544$		0			0
$545$	−24.0000			−1.02805
$546$		0			0
$547$	−39.1969	−	16.2359i	−1.67594	−	0.694196i	−0.676818	−	0.736150i	$-0.736642\pi$
$547$	−39.1969	−	16.2359i	−1.67594	−	0.694196i	−0.999120	+	0.0419538i	$0.986642\pi$
$548$			18.0000i			0.768922i
$549$	−16.2359	+	39.1969i	−0.692931	+	1.67288i
$550$	−7.83938	+	3.24718i	−0.334272	+	0.138460i
$551$	−4.32957	−	10.4525i	−0.184446	−	0.445292i
$552$	11.3137	+	11.3137i	0.481543	+	0.481543i
$553$		0			0
$554$	9.74153	+	23.5181i	0.413878	+	0.999190i
$555$	62.7150	−	25.9774i	2.66210	−	1.10268i
$556$	−3.24718	+	7.83938i	−0.137711	+	0.332464i
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$		0			0
$559$	−5.65685	+	5.65685i	−0.239259	+	0.239259i
$560$		0			0
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−25.4558	+	25.4558i	−1.07284	+	1.07284i	−0.0757057	+	0.997130i	$0.524121\pi$
$563$	−25.4558	+	25.4558i	−1.07284	+	1.07284i	−0.997130	+	0.0757057i	$0.975879\pi$
$564$		0			0
$565$			32.0000i			1.34625i
$566$	−3.24718	+	7.83938i	−0.136489	+	0.329514i
$567$		0			0
$568$	2.16478	+	5.22625i	0.0908323	+	0.219289i
$569$	−4.24264	−	4.24264i	−0.177861	−	0.177861i	0.612562	−	0.790423i	$-0.290139\pi$
$569$	−4.24264	−	4.24264i	−0.177861	−	0.177861i	−0.790423	+	0.612562i	$0.790139\pi$
$570$	−22.6274	−	22.6274i	−0.947758	−	0.947758i
$571$	9.74153	+	23.5181i	0.407670	+	0.984203i	0.985749	+	0.168222i	$0.0538026\pi$
$571$	9.74153	+	23.5181i	0.407670	+	0.984203i	−0.578079	+	0.815981i	$0.696197\pi$
$572$	5.22625	−	2.16478i	0.218521	−	0.0905142i
$573$		0			0
$574$		0			0
$575$	−15.6788	−	6.49435i	−0.653849	−	0.270833i
$576$	−3.53553	+	3.53553i	−0.147314	+	0.147314i
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$		0			0
$579$	−48.0000			−1.99481
$580$	5.65685	−	5.65685i	0.234888	−	0.234888i
$581$		0			0
$582$		−	48.0000i		−	1.98966i
$583$	−6.49435	+	15.6788i	−0.268969	+	0.649348i
$584$		0			0
$585$	−10.8239	−	26.1313i	−0.447514	−	1.08039i
$586$	−4.24264	−	4.24264i	−0.175262	−	0.175262i
$587$	8.48528	+	8.48528i	0.350225	+	0.350225i	0.860193	−	0.509968i	$-0.170343\pi$
$587$	8.48528	+	8.48528i	0.350225	+	0.350225i	−0.509968	+	0.860193i	$0.670343\pi$
$588$	7.57675	+	18.2919i	0.312460	+	0.754344i
$589$		0			0
$590$	−12.9887	+	31.3575i	−0.534737	+	1.29097i
$591$			8.00000i			0.329076i
$592$	−7.83938	−	3.24718i	−0.322196	−	0.133458i
$593$	12.7279	−	12.7279i	0.522673	−	0.522673i	−0.395705	−	0.918378i	$-0.629500\pi$
$593$	12.7279	−	12.7279i	0.522673	−	0.522673i	0.918378	+	0.395705i	$0.129500\pi$
$594$	−16.0000			−0.656488
$595$		0			0
$596$	6.00000			0.245770
$597$	−33.9411	+	33.9411i	−1.38912	+	1.38912i
$598$	10.4525	+	4.32957i	0.427435	+	0.177049i
$599$		−	24.0000i		−	0.980613i	−0.871550	−	0.490307i	$-0.836885\pi$
$599$		−	24.0000i		−	0.980613i	0.871550	−	0.490307i	$-0.163115\pi$
$600$	3.24718	−	7.83938i	0.132565	−	0.320041i
$601$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$601$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$602$		0			0
$603$	14.1421	+	14.1421i	0.575912	+	0.575912i
$604$	−5.65685	−	5.65685i	−0.230174	−	0.230174i
$605$	−3.24718	−	7.83938i	−0.132017	−	0.318716i
$606$	−15.6788	+	6.49435i	−0.636906	+	0.263815i
$607$	12.9887	−	31.3575i	0.527195	−	1.27276i	−0.406158	−	0.913803i	$-0.633132\pi$
$607$	12.9887	−	31.3575i	0.527195	−	1.27276i	0.933353	−	0.358959i	$-0.116868\pi$
$608$			4.00000i			0.162221i
$609$		0			0
$610$	−16.9706	+	16.9706i	−0.687118	+	0.687118i
$611$		0			0
$612$		0			0
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$	14.1421	−	14.1421i	0.570730	−	0.570730i
$615$	−41.8100	−	17.3183i	−1.68594	−	0.698340i
$616$		0			0
$617$	−4.32957	+	10.4525i	−0.174302	+	0.420802i	−0.986754	−	0.162227i	$-0.948132\pi$
$617$	−4.32957	+	10.4525i	−0.174302	+	0.420802i	0.812452	+	0.583029i	$0.198132\pi$
$618$	−20.9050	+	8.65914i	−0.840923	+	0.348322i
$619$	3.24718	+	7.83938i	0.130515	+	0.315091i	0.975605	−	0.219533i	$-0.0704533\pi$
$619$	3.24718	+	7.83938i	0.130515	+	0.315091i	−0.845090	+	0.534624i	$0.820453\pi$
$620$		0			0
$621$	−22.6274	−	22.6274i	−0.908007	−	0.908007i
$622$	4.32957	+	10.4525i	0.173600	+	0.419107i
$623$		0			0
$624$	−2.16478	+	5.22625i	−0.0866607	+	0.209218i
$625$		−	31.0000i		−	1.24000i
$626$	15.6788	+	6.49435i	0.626649	+	0.259567i
$627$	−22.6274	+	22.6274i	−0.903652	+	0.903652i
$628$	−14.0000			−0.558661
$629$		0			0
$630$		0			0
$631$	−5.65685	+	5.65685i	−0.225196	+	0.225196i	−0.810682	−	0.585486i	$-0.800904\pi$
$631$	−5.65685	+	5.65685i	−0.225196	+	0.225196i	0.585486	+	0.810682i	$0.300904\pi$
$632$	−15.6788	−	6.49435i	−0.623667	−	0.258331i
$633$			24.0000i			0.953914i
$634$	1.08239	−	2.61313i	0.0429873	−	0.103780i
$635$	41.8100	−	17.3183i	1.65918	−	0.687255i
$636$	−6.49435	−	15.6788i	−0.257518	−	0.621703i
$637$	9.89949	+	9.89949i	0.392232	+	0.392232i
$638$	−5.65685	−	5.65685i	−0.223957	−	0.223957i
$639$	−10.8239	−	26.1313i	−0.428188	−	1.03374i
$640$	−2.61313	+	1.08239i	−0.103293	+	0.0427853i
$641$	−2.16478	+	5.22625i	−0.0855038	+	0.206425i	−0.960848	−	0.277076i	$-0.910635\pi$
$641$	−2.16478	+	5.22625i	−0.0855038	+	0.206425i	0.875344	+	0.483500i	$0.160635\pi$
$642$		−	8.00000i		−	0.315735i
$643$	−7.83938	−	3.24718i	−0.309155	−	0.128056i	0.222712	−	0.974884i	$-0.428509\pi$
$643$	−7.83938	−	3.24718i	−0.309155	−	0.128056i	−0.531866	+	0.846828i	$0.678509\pi$
$644$		0			0
$645$	32.0000			1.26000
$646$		0			0
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	31.3575	+	12.9887i	1.23089	+	0.509851i
$650$		−	6.00000i		−	0.235339i
$651$		0			0
$652$	−7.83938	+	3.24718i	−0.307014	+	0.127169i
$653$	−5.41196	−	13.0656i	−0.211786	−	0.511298i	0.781911	−	0.623390i	$-0.214245\pi$
$653$	−5.41196	−	13.0656i	−0.211786	−	0.511298i	−0.993698	+	0.112092i	$0.964245\pi$
$654$	−16.9706	−	16.9706i	−0.663602	−	0.663602i
$655$	5.65685	+	5.65685i	0.221032	+	0.221032i
$656$	2.16478	+	5.22625i	0.0845206	+	0.204051i
$657$		0			0
$658$		0			0
$659$		−	12.0000i		−	0.467454i	−0.972302	−	0.233727i	$-0.924908\pi$
$659$		−	12.0000i		−	0.467454i	0.972302	−	0.233727i	$-0.0750921\pi$
$660$	−20.9050	−	8.65914i	−0.813726	−	0.337056i
$661$	−7.07107	+	7.07107i	−0.275033	+	0.275033i	−0.831122	−	0.556090i	$-0.812301\pi$
$661$	−7.07107	+	7.07107i	−0.275033	+	0.275033i	0.556090	+	0.831122i	$0.312301\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	12.0000			0.465690
$665$		0			0
$666$	39.1969	+	16.2359i	1.51885	+	0.629128i
$667$		−	16.0000i		−	0.619522i
$668$	−4.32957	+	10.4525i	−0.167516	+	0.404420i
$669$	−41.8100	+	17.3183i	−1.61647	+	0.669563i
$670$	4.32957	+	10.4525i	0.167266	+	0.403815i
$671$	16.9706	+	16.9706i	0.655141	+	0.655141i
$672$		0			0
$673$	−6.49435	−	15.6788i	−0.250339	−	0.604372i	0.747892	−	0.663820i	$-0.231066\pi$
$673$	−6.49435	−	15.6788i	−0.250339	−	0.604372i	−0.998231	+	0.0594483i	$0.981066\pi$
$674$		0			0
$675$	−6.49435	+	15.6788i	−0.249968	+	0.603476i
$676$		−	9.00000i		−	0.346154i
$677$	13.0656	+	5.41196i	0.502153	+	0.207999i	0.619357	−	0.785109i	$-0.287393\pi$
$677$	13.0656	+	5.41196i	0.502153	+	0.207999i	−0.117204	+	0.993108i	$0.537393\pi$
$678$	−22.6274	+	22.6274i	−0.869001	+	0.869001i
$679$		0			0
$680$		0			0
$681$	56.0000			2.14592
$682$		0			0
$683$	18.2919	+	7.57675i	0.699919	+	0.289916i	0.704126	−	0.710075i	$-0.251339\pi$
$683$	18.2919	+	7.57675i	0.699919	+	0.289916i	−0.00420661	+	0.999991i	$0.501339\pi$
$684$		−	20.0000i		−	0.764719i
$685$	19.4831	−	47.0363i	0.744409	−	1.79716i
$686$		0			0
$687$	23.8126	+	57.4888i	0.908508	+	2.19333i
$688$	−2.82843	−	2.82843i	−0.107833	−	0.107833i
$689$	−8.48528	−	8.48528i	−0.323263	−	0.323263i
$690$	−17.3183	−	41.8100i	−0.659295	−	1.59168i
$691$	−7.83938	+	3.24718i	−0.298224	+	0.123528i	−0.526778	−	0.850003i	$-0.676600\pi$
$691$	−7.83938	+	3.24718i	−0.298224	+	0.123528i	0.228554	+	0.973531i	$0.426600\pi$
$692$	1.08239	−	2.61313i	0.0411464	−	0.0993361i
$693$		0			0
$694$	−13.0656	−	5.41196i	−0.495965	−	0.205435i
$695$	16.9706	−	16.9706i	0.643730	−	0.643730i
$696$	8.00000			0.303239
$697$		0			0
$698$	34.0000			1.28692
$699$	45.2548	−	45.2548i	1.71170	−	1.71170i
$700$		0			0
$701$			30.0000i			1.13308i	0.824033	+	0.566542i	$0.191719\pi$
$701$			30.0000i			1.13308i	−0.824033	+	0.566542i	$0.808281\pi$
$702$	4.32957	−	10.4525i	0.163409	−	0.394504i
$703$	31.3575	−	12.9887i	1.18267	−	0.489878i
$704$	1.08239	+	2.61313i	0.0407942	+	0.0984859i
$705$		0			0
$706$	−4.24264	−	4.24264i	−0.159674	−	0.159674i
$707$		0			0
$708$	−31.3575	+	12.9887i	−1.17849	+	0.488145i
$709$	−3.24718	+	7.83938i	−0.121950	+	0.294414i	−0.973052	−	0.230587i	$-0.925935\pi$
$709$	−3.24718	+	7.83938i	−0.121950	+	0.294414i	0.851101	+	0.525001i	$0.175935\pi$
$710$		−	16.0000i		−	0.600469i
$711$	78.3938	+	32.4718i	2.94000	+	1.21779i
$712$	−4.24264	+	4.24264i	−0.159000	+	0.159000i
$713$		0			0
$714$		0			0
$715$	−16.0000			−0.598366
$716$	−8.48528	+	8.48528i	−0.317110	+	0.317110i
$717$		0			0
$718$			24.0000i			0.895672i
$719$	15.1535	−	36.5838i	0.565130	−	1.36434i	−0.340488	−	0.940249i	$-0.610592\pi$
$719$	15.1535	−	36.5838i	0.565130	−	1.36434i	0.905618	−	0.424095i	$-0.139408\pi$
$720$	13.0656	−	5.41196i	0.486927	−	0.201692i
$721$		0			0
$722$	2.12132	+	2.12132i	0.0789474	+	0.0789474i
$723$	33.9411	+	33.9411i	1.26228	+	1.26228i
$724$	3.24718	+	7.83938i	0.120680	+	0.291348i
$725$	−7.83938	+	3.24718i	−0.291147	+	0.120597i
$726$	3.24718	−	7.83938i	0.120514	−	0.290947i
$727$			8.00000i			0.296704i	0.988935	+	0.148352i	$0.0473968\pi$
$727$			8.00000i			0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$		0			0
$729$	30.4056	−	30.4056i	1.12613	−	1.12613i
$730$		0			0
$731$		0			0
$732$	−24.0000			−0.887066
$733$	−9.89949	+	9.89949i	−0.365646	+	0.365646i	−0.865887	−	0.500240i	$-0.833245\pi$
$733$	−9.89949	+	9.89949i	−0.365646	+	0.365646i	0.500240	+	0.865887i	$0.333245\pi$
$734$	15.6788	+	6.49435i	0.578713	+	0.239711i
$735$		−	56.0000i		−	2.06559i
$736$	−2.16478	+	5.22625i	−0.0797950	+	0.192642i
$737$	10.4525	−	4.32957i	0.385023	−	0.159482i
$738$	−10.8239	−	26.1313i	−0.398434	−	0.961905i
$739$	31.1127	+	31.1127i	1.14450	+	1.14450i	0.987617	+	0.156882i	$0.0501441\pi$
$739$	31.1127	+	31.1127i	1.14450	+	1.14450i	0.156882	+	0.987617i	$0.449856\pi$
$740$	16.9706	+	16.9706i	0.623850	+	0.623850i
$741$	−8.65914	−	20.9050i	−0.318101	−	0.767965i
$742$		0			0
$743$	4.32957	−	10.4525i	0.158836	−	0.383465i	−0.824347	−	0.566084i	$-0.808458\pi$
$743$	4.32957	−	10.4525i	0.158836	−	0.383465i	0.983184	+	0.182619i	$0.0584576\pi$
$744$		0			0
$745$	−15.6788	−	6.49435i	−0.574425	−	0.237935i
$746$	15.5563	−	15.5563i	0.569558	−	0.569558i
$747$	−60.0000			−2.19529
$748$		0			0
$749$		0			0
$750$	11.3137	−	11.3137i	0.413118	−	0.413118i
$751$	15.6788	+	6.49435i	0.572126	+	0.236982i	0.649940	−	0.759986i	$-0.274794\pi$
$751$	15.6788	+	6.49435i	0.572126	+	0.236982i	−0.0778140	+	0.996968i	$0.524794\pi$
$752$		0			0
$753$	−12.9887	+	31.3575i	−0.473335	+	1.14273i
$754$	5.22625	−	2.16478i	0.190329	−	0.0788368i
$755$	8.65914	+	20.9050i	0.315138	+	0.760811i
$756$		0			0
$757$	15.5563	+	15.5563i	0.565405	+	0.565405i	0.930838	−	0.365433i	$-0.119079\pi$
$757$	15.5563	+	15.5563i	0.565405	+	0.565405i	−0.365433	+	0.930838i	$0.619079\pi$
$758$	−9.74153	−	23.5181i	−0.353828	−	0.854217i
$759$	−41.8100	+	17.3183i	−1.51761	+	0.628614i
$760$	4.32957	−	10.4525i	0.157050	−	0.379152i
$761$			30.0000i			1.08750i	0.839248	+	0.543750i	$0.182996\pi$
$761$			30.0000i			1.08750i	−0.839248	+	0.543750i	$0.817004\pi$
$762$	41.8100	+	17.3183i	1.51462	+	0.627375i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.9706	+	16.9706i	−0.612772	+	0.612772i
$768$	−2.61313	−	1.08239i	−0.0942931	−	0.0390575i
$769$			10.0000i			0.360609i	0.983611	+	0.180305i	$0.0577084\pi$
$769$			10.0000i			0.360609i	−0.983611	+	0.180305i	$0.942292\pi$
$770$		0			0
$771$	15.6788	−	6.49435i	0.564657	−	0.233888i
$772$	−6.49435	−	15.6788i	−0.233737	−	0.564291i
$773$	−38.1838	−	38.1838i	−1.37337	−	1.37337i	−0.855390	−	0.517985i	$-0.826682\pi$
$773$	−38.1838	−	38.1838i	−1.37337	−	1.37337i	−0.517985	−	0.855390i	$-0.673318\pi$
$774$	14.1421	+	14.1421i	0.508329	+	0.508329i
$775$		0			0
$776$	15.6788	−	6.49435i	0.562835	−	0.233134i
$777$		0			0
$778$			6.00000i			0.215110i
$779$	−20.9050	−	8.65914i	−0.749000	−	0.310246i
$780$	11.3137	−	11.3137i	0.405096	−	0.405096i
$781$	−16.0000			−0.572525
$782$		0			0
$783$	−16.0000			−0.571793
$784$	−4.94975	+	4.94975i	−0.176777	+	0.176777i
$785$	36.5838	+	15.1535i	1.30573	+	0.540851i
$786$			8.00000i			0.285351i
$787$	16.2359	−	39.1969i	0.578747	−	1.39722i	−0.315192	−	0.949028i	$-0.602069\pi$
$787$	16.2359	−	39.1969i	0.578747	−	1.39722i	0.893938	−	0.448190i	$-0.147931\pi$
$788$	−2.61313	+	1.08239i	−0.0930888	+	0.0385586i
$789$	−25.9774	−	62.7150i	−0.924820	−	2.23271i
$790$	33.9411	+	33.9411i	1.20757	+	1.20757i
$791$		0			0
$792$	−5.41196	−	13.0656i	−0.192306	−	0.464267i
$793$	−15.6788	+	6.49435i	−0.556769	+	0.230621i
$794$	3.24718	−	7.83938i	0.115238	−	0.278209i
$795$			48.0000i			1.70238i
$796$	−15.6788	−	6.49435i	−0.555719	−	0.230186i
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	−0.895635	−	0.444789i	$-0.853279\pi$
$797$	−12.7279	+	12.7279i	−0.450846	+	0.450846i	0.444789	+	0.895635i	$0.353279\pi$
$798$		0			0
$799$		0			0
$800$	3.00000			0.106066
$801$	21.2132	−	21.2132i	0.749532	−	0.749532i
$802$	−26.1313	−	10.8239i	−0.922727	−	0.382206i
$803$		0			0
$804$	−4.32957	+	10.4525i	−0.152692	+	0.368631i
$805$		0			0
$806$		0			0
$807$	−62.2254	−	62.2254i	−2.19044	−	2.19044i
$808$	−4.24264	−	4.24264i	−0.149256	−	0.149256i
$809$	15.1535	+	36.5838i	0.532768	+	1.28622i	0.929683	+	0.368361i	$0.120081\pi$
$809$	15.1535	+	36.5838i	0.532768	+	1.28622i	−0.396914	+	0.917856i	$0.629919\pi$
$810$	−2.61313	+	1.08239i	−0.0918159	+	0.0380314i
$811$	16.2359	−	39.1969i	0.570119	−	1.37639i	−0.331335	−	0.943513i	$-0.607499\pi$
$811$	16.2359	−	39.1969i	0.570119	−	1.37639i	0.901454	−	0.432876i	$-0.142501\pi$
$812$		0			0
$813$	−41.8100	−	17.3183i	−1.46634	−	0.607378i
$814$	16.9706	−	16.9706i	0.594818	−	0.594818i
$815$	24.0000			0.840683
$816$		0			0
$817$	16.0000			0.559769
$818$	1.41421	−	1.41421i	0.0494468	−	0.0494468i
$819$		0			0
$820$		−	16.0000i		−	0.558744i
$821$	18.4007	−	44.4231i	0.642188	−	1.55038i	−0.181534	−	0.983385i	$-0.558106\pi$
$821$	18.4007	−	44.4231i	0.642188	−	1.55038i	0.823722	−	0.566994i	$-0.191894\pi$
$822$	47.0363	−	19.4831i	1.64058	−	0.679550i
$823$	6.49435	+	15.6788i	0.226379	+	0.546527i	0.995731	−	0.0922973i	$-0.0294210\pi$
$823$	6.49435	+	15.6788i	0.226379	+	0.546527i	−0.769353	+	0.638824i	$0.779421\pi$
$824$	−5.65685	−	5.65685i	−0.197066	−	0.197066i
$825$	16.9706	+	16.9706i	0.590839	+	0.590839i
$826$		0			0
$827$	33.9706	−	14.0711i	1.18127	−	0.489300i	0.296371	−	0.955073i	$-0.404224\pi$
$827$	33.9706	−	14.0711i	1.18127	−	0.489300i	0.884904	+	0.465773i	$0.154224\pi$
$828$	10.8239	−	26.1313i	0.376157	−	0.908124i
$829$		−	34.0000i		−	1.18087i	−0.807086	−	0.590434i	$-0.798956\pi$
$829$		−	34.0000i		−	1.18087i	0.807086	−	0.590434i	$-0.201044\pi$
$830$	−31.3575	−	12.9887i	−1.08844	−	0.450845i
$831$	50.9117	−	50.9117i	1.76611	−	1.76611i
$832$	−2.00000			−0.0693375
$833$		0			0
$834$	24.0000			0.831052
$835$	22.6274	−	22.6274i	0.783054	−	0.783054i
$836$	−10.4525	−	4.32957i	−0.361507	−	0.149741i
$837$		0			0
$838$	−5.41196	+	13.0656i	−0.186953	+	0.451345i
$839$	−41.8100	+	17.3183i	−1.44344	+	0.597893i	−0.960630	−	0.277831i	$-0.910385\pi$
$839$	−41.8100	+	17.3183i	−1.44344	+	0.597893i	−0.482812	+	0.875724i	$0.660385\pi$
$840$		0			0
$841$	14.8492	+	14.8492i	0.512043	+	0.512043i
$842$	18.3848	+	18.3848i	0.633581	+	0.633581i
$843$	19.4831	+	47.0363i	0.671032	+	1.62002i
$844$	−7.83938	+	3.24718i	−0.269843	+	0.111772i
$845$	−9.74153	+	23.5181i	−0.335119	+	0.809048i
$846$		0			0
$847$		0			0
$848$	4.24264	−	4.24264i	0.145693	−	0.145693i
$849$	24.0000			0.823678
$850$		0			0
$851$	48.0000			1.64542
$852$	11.3137	−	11.3137i	0.387601	−	0.387601i
$853$	23.5181	+	9.74153i	0.805246	+	0.333544i	0.747055	−	0.664762i	$-0.231467\pi$
$853$	23.5181	+	9.74153i	0.805246	+	0.333544i	0.0581902	+	0.998306i	$0.481467\pi$
$854$		0			0
$855$	−21.6478	+	52.2625i	−0.740341	+	1.78734i
$856$	2.61313	−	1.08239i	0.0893148	−	0.0369954i
$857$	10.8239	+	26.1313i	0.369738	+	0.892627i	0.993793	+	0.111246i	$0.0354842\pi$
$857$	10.8239	+	26.1313i	0.369738	+	0.892627i	−0.624055	+	0.781381i	$0.714516\pi$
$858$	−11.3137	−	11.3137i	−0.386244	−	0.386244i
$859$	2.82843	+	2.82843i	0.0965047	+	0.0965047i	0.753711	−	0.657206i	$-0.228262\pi$
$859$	2.82843	+	2.82843i	0.0965047	+	0.0965047i	−0.657206	+	0.753711i	$0.728262\pi$
$860$	4.32957	+	10.4525i	0.147637	+	0.356427i
$861$		0			0
$862$	2.16478	−	5.22625i	0.0737328	−	0.178007i
$863$		−	48.0000i		−	1.63394i	−0.576681	−	0.816970i	$-0.695652\pi$
$863$		−	48.0000i		−	1.63394i	0.576681	−	0.816970i	$-0.304348\pi$
$864$	5.22625	+	2.16478i	0.177801	+	0.0736475i
$865$	−5.65685	+	5.65685i	−0.192339	+	0.192339i
$866$	14.0000			0.475739
$867$		0			0
$868$		0			0
$869$	33.9411	−	33.9411i	1.15137	−	1.15137i
$870$	−20.9050	−	8.65914i	−0.708746	−	0.293572i
$871$			8.00000i			0.271070i
$872$	3.24718	−	7.83938i	0.109963	−	0.265475i
$873$	−78.3938	+	32.4718i	−2.65323	+	1.09900i
$874$	−8.65914	−	20.9050i	−0.292900	−	0.707122i
$875$		0			0
$876$		0			0
$877$	−3.24718	−	7.83938i	−0.109649	−	0.264717i	0.859525	−	0.511094i	$-0.170760\pi$
$877$	−3.24718	−	7.83938i	−0.109649	−	0.264717i	−0.969174	+	0.246377i	$0.920760\pi$
$878$	15.6788	−	6.49435i	0.529132	−	0.219174i
$879$	−6.49435	+	15.6788i	−0.219049	+	0.528831i
$880$		−	8.00000i		−	0.269680i
$881$	−41.8100	−	17.3183i	−1.40862	−	0.583468i	−0.456642	−	0.889650i	$-0.650948\pi$
$881$	−41.8100	−	17.3183i	−1.40862	−	0.583468i	−0.951973	+	0.306183i	$0.900948\pi$
$882$	24.7487	−	24.7487i	0.833333	−	0.833333i
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$	96.0000			3.22700
$886$	−8.48528	+	8.48528i	−0.285069	+	0.285069i
$887$	−36.5838	−	15.1535i	−1.22836	−	0.508804i	−0.328303	−	0.944572i	$-0.606477\pi$
$887$	−36.5838	−	15.1535i	−1.22836	−	0.508804i	−0.900059	+	0.435768i	$0.856477\pi$
$888$			24.0000i			0.805387i
$889$		0			0
$890$	15.6788	−	6.49435i	0.525553	−	0.217691i
$891$	1.08239	+	2.61313i	0.0362615	+	0.0875430i
$892$	−11.3137	−	11.3137i	−0.378811	−	0.378811i
$893$		0			0
$894$	−6.49435	−	15.6788i	−0.217204	−	0.524376i
$895$	31.3575	−	12.9887i	1.04817	−	0.434165i
$896$		0			0
$897$		−	32.0000i		−	1.06845i
$898$	−5.22625	−	2.16478i	−0.174402	−	0.0722398i
$899$		0			0
$900$	−15.0000			−0.500000
$901$		0			0
$902$	−16.0000			−0.532742
$903$		0			0
$904$	−10.4525	−	4.32957i	−0.347645	−	0.143999i
$905$		−	24.0000i		−	0.797787i
$906$	−8.65914	+	20.9050i	−0.287681	+	0.694522i
$907$	39.1969	−	16.2359i	1.30151	−	0.539104i	0.379115	−	0.925349i	$-0.376228\pi$
$907$	39.1969	−	16.2359i	1.30151	−	0.539104i	0.922396	+	0.386246i	$0.126228\pi$
$908$	7.57675	+	18.2919i	0.251443	+	0.607037i
$909$	21.2132	+	21.2132i	0.703598	+	0.703598i
$910$		0			0
$911$	21.6478	+	52.2625i	0.717225	+	1.73153i	0.681104	+	0.732187i	$0.261500\pi$
$911$	21.6478	+	52.2625i	0.717225	+	1.73153i	0.0361215	+	0.999347i	$0.488500\pi$
$912$	10.4525	−	4.32957i	0.346117	−	0.143366i
$913$	−12.9887	+	31.3575i	−0.429863	+	1.03778i
$914$			10.0000i			0.330771i
$915$	62.7150	+	25.9774i	2.07329	+	0.858787i
$916$	−15.5563	+	15.5563i	−0.513996	+	0.513996i
$917$		0			0
$918$		0			0
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$	11.3137	−	11.3137i	0.373002	−	0.373002i
$921$	−52.2625	−	21.6478i	−1.72211	−	0.713321i
$922$		−	18.0000i		−	0.592798i
$923$	4.32957	−	10.4525i	0.142509	−	0.344048i
$924$		0			0
$925$	−9.74153	−	23.5181i	−0.320300	−	0.773271i
$926$	−22.6274	−	22.6274i	−0.743583	−	0.743583i
$927$	28.2843	+	28.2843i	0.928977	+	0.928977i
$928$	1.08239	+	2.61313i	0.0355313	+	0.0857801i
$929$	−5.22625	+	2.16478i	−0.171468	+	0.0710243i	−0.466766	−	0.884381i	$-0.654581\pi$
$929$	−5.22625	+	2.16478i	−0.171468	+	0.0710243i	0.295298	+	0.955405i	$0.404581\pi$
$930$		0			0
$931$		−	28.0000i		−	0.917663i
$932$	20.9050	+	8.65914i	0.684766	+	0.283639i
$933$	22.6274	−	22.6274i	0.740788	−	0.740788i
$934$	−36.0000			−1.17796
$935$		0			0
$936$	10.0000			0.326860
$937$	−1.41421	+	1.41421i	−0.0462003	+	0.0462003i	−0.729830	−	0.683629i	$-0.760401\pi$
$937$	−1.41421	+	1.41421i	−0.0462003	+	0.0462003i	0.683629	+	0.729830i	$0.260401\pi$
$938$		0			0
$939$		−	48.0000i		−	1.56642i
$940$		0			0
$941$	−33.9706	+	14.0711i	−1.10741	+	0.458705i	−0.860045	−	0.510217i	$-0.829565\pi$
$941$	−33.9706	+	14.0711i	−1.10741	+	0.458705i	−0.247366	+	0.968922i	$0.579565\pi$
$942$	15.1535	+	36.5838i	0.493727	+	1.19196i
$943$	−22.6274	−	22.6274i	−0.736850	−	0.736850i
$944$	−8.48528	−	8.48528i	−0.276172	−	0.276172i
$945$		0			0
$946$	10.4525	−	4.32957i	0.339840	−	0.140766i
$947$	1.08239	−	2.61313i	0.0351730	−	0.0849152i	−0.905317	−	0.424737i	$-0.860367\pi$
$947$	1.08239	−	2.61313i	0.0351730	−	0.0849152i	0.940490	+	0.339822i	$0.110367\pi$
$948$			48.0000i			1.55897i
$949$		0			0
$950$	−8.48528	+	8.48528i	−0.275299	+	0.275299i
$951$	−8.00000			−0.259418
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−21.2132	+	21.2132i	−0.686803	+	0.686803i
$955$		0			0
$956$		0			0
$957$	−8.65914	+	20.9050i	−0.279910	+	0.675763i
$958$	−5.22625	+	2.16478i	−0.168853	+	0.0699410i
$959$		0			0
$960$	5.65685	+	5.65685i	0.182574	+	0.182574i
$961$	−21.9203	−	21.9203i	−0.707107	−	0.707107i
$962$	6.49435	+	15.6788i	0.209386	+	0.505503i
$963$	−13.0656	+	5.41196i	−0.421034	+	0.174398i
$964$	−6.49435	+	15.6788i	−0.209169	+	0.504979i
$965$			48.0000i			1.54517i
$966$		0			0
$967$	5.65685	−	5.65685i	0.181912	−	0.181912i	−0.610276	−	0.792189i	$-0.708942\pi$
$967$	5.65685	−	5.65685i	0.181912	−	0.181912i	0.792189	+	0.610276i	$0.208942\pi$
$968$	3.00000			0.0964237
$969$		0			0
$970$	−48.0000			−1.54119
$971$	−8.48528	+	8.48528i	−0.272306	+	0.272306i	−0.830028	−	0.557722i	$-0.811675\pi$
$971$	−8.48528	+	8.48528i	−0.272306	+	0.272306i	0.557722	+	0.830028i	$0.311675\pi$
$972$	13.0656	+	5.41196i	0.419080	+	0.173589i
$973$		0			0
$974$	−6.49435	+	15.6788i	−0.208092	+	0.502380i
$975$	−15.6788	+	6.49435i	−0.502122	+	0.207986i
$976$	−3.24718	−	7.83938i	−0.103940	−	0.250932i
$977$	12.7279	+	12.7279i	0.407202	+	0.407202i	0.880762	−	0.473560i	$-0.157031\pi$
$977$	12.7279	+	12.7279i	0.407202	+	0.407202i	−0.473560	+	0.880762i	$0.657031\pi$
$978$	16.9706	+	16.9706i	0.542659	+	0.542659i
$979$	−6.49435	−	15.6788i	−0.207560	−	0.501095i
$980$	18.2919	−	7.57675i	0.584313	−	0.242030i
$981$	−16.2359	+	39.1969i	−0.518372	+	1.25146i
$982$			12.0000i			0.382935i
$983$	5.22625	+	2.16478i	0.166692	+	0.0690459i	0.464469	−	0.885589i	$-0.346245\pi$
$983$	5.22625	+	2.16478i	0.166692	+	0.0690459i	−0.297777	+	0.954635i	$0.596245\pi$
$984$	11.3137	−	11.3137i	0.360668	−	0.360668i
$985$	8.00000			0.254901
$986$		0			0
$987$		0			0
$988$	5.65685	−	5.65685i	0.179969	−	0.179969i
$989$	20.9050	+	8.65914i	0.664741	+	0.275345i
$990$			40.0000i			1.27128i
$991$	−19.4831	+	47.0363i	−0.618900	+	1.49416i	0.234083	+	0.972217i	$0.424791\pi$
$991$	−19.4831	+	47.0363i	−0.618900	+	1.49416i	−0.852982	+	0.521940i	$0.825209\pi$
$992$		0			0
$993$	4.32957	+	10.4525i	0.137395	+	0.331700i
$994$		0			0
$995$	33.9411	+	33.9411i	1.07601	+	1.07601i
$996$	−12.9887	−	31.3575i	−0.411563	−	0.993601i
$997$	54.8756	−	22.7302i	1.73793	−	0.719874i	0.738995	−	0.673711i	$-0.235301\pi$
$997$	54.8756	−	22.7302i	1.73793	−	0.719874i	0.998934	−	0.0461631i	$-0.0146994\pi$
$998$	−9.74153	+	23.5181i	−0.308363	+	0.744454i
$999$		−	48.0000i		−	1.51865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.g.179.1		8
17.2	even	8	inner	578.2.d.g.155.1		8
17.3	odd	16		578.2.c.a.251.1		2
17.4	even	4	inner	578.2.d.g.399.1		8
17.5	odd	16		578.2.c.d.327.1		2
17.6	odd	16		578.2.a.d.1.1		2
17.7	odd	16		34.2.b.a.33.2	yes	2
17.8	even	8	inner	578.2.d.g.423.2		8
17.9	even	8	inner	578.2.d.g.423.1		8
17.10	odd	16		34.2.b.a.33.1	✓	2
17.11	odd	16		578.2.a.d.1.2		2
17.12	odd	16		578.2.c.a.327.1		2
17.13	even	4	inner	578.2.d.g.399.2		8
17.14	odd	16		578.2.c.d.251.1		2
17.15	even	8	inner	578.2.d.g.155.2		8
17.16	even	2	inner	578.2.d.g.179.2		8
51.11	even	16		5202.2.a.u.1.2		2
51.23	even	16		5202.2.a.u.1.1		2
51.41	even	16		306.2.b.d.271.2		2
51.44	even	16		306.2.b.d.271.1		2
68.7	even	16		272.2.b.a.33.1		2
68.11	even	16		4624.2.a.s.1.1		2
68.23	even	16		4624.2.a.s.1.2		2
68.27	even	16		272.2.b.a.33.2		2
85.7	even	16		850.2.d.i.849.2		4
85.24	odd	16		850.2.b.f.101.1		2
85.27	even	16		850.2.d.i.849.1		4
85.44	odd	16		850.2.b.f.101.2		2
85.58	even	16		850.2.d.i.849.3		4
85.78	even	16		850.2.d.i.849.4		4
119.27	even	16		1666.2.b.c.883.2		2
119.41	even	16		1666.2.b.c.883.1		2
136.27	even	16		1088.2.b.a.577.1		2
136.61	odd	16		1088.2.b.b.577.2		2
136.75	even	16		1088.2.b.a.577.2		2
136.109	odd	16		1088.2.b.b.577.1		2
204.95	odd	16		2448.2.c.n.577.1		2
204.143	odd	16		2448.2.c.n.577.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.b.a.33.1	✓	2	17.10	odd	16
34.2.b.a.33.2	yes	2	17.7	odd	16
272.2.b.a.33.1		2	68.7	even	16
272.2.b.a.33.2		2	68.27	even	16
306.2.b.d.271.1		2	51.44	even	16
306.2.b.d.271.2		2	51.41	even	16
578.2.a.d.1.1		2	17.6	odd	16
578.2.a.d.1.2		2	17.11	odd	16
578.2.c.a.251.1		2	17.3	odd	16
578.2.c.a.327.1		2	17.12	odd	16
578.2.c.d.251.1		2	17.14	odd	16
578.2.c.d.327.1		2	17.5	odd	16
578.2.d.g.155.1		8	17.2	even	8	inner
578.2.d.g.155.2		8	17.15	even	8	inner
578.2.d.g.179.1		8	1.1	even	1	trivial
578.2.d.g.179.2		8	17.16	even	2	inner
578.2.d.g.399.1		8	17.4	even	4	inner
578.2.d.g.399.2		8	17.13	even	4	inner
578.2.d.g.423.1		8	17.9	even	8	inner
578.2.d.g.423.2		8	17.8	even	8	inner
850.2.b.f.101.1		2	85.24	odd	16
850.2.b.f.101.2		2	85.44	odd	16
850.2.d.i.849.1		4	85.27	even	16
850.2.d.i.849.2		4	85.7	even	16
850.2.d.i.849.3		4	85.58	even	16
850.2.d.i.849.4		4	85.78	even	16
1088.2.b.a.577.1		2	136.27	even	16
1088.2.b.a.577.2		2	136.75	even	16
1088.2.b.b.577.1		2	136.109	odd	16
1088.2.b.b.577.2		2	136.61	odd	16
1666.2.b.c.883.1		2	119.41	even	16
1666.2.b.c.883.2		2	119.27	even	16
2448.2.c.n.577.1		2	204.95	odd	16
2448.2.c.n.577.2		2	204.143	odd	16
4624.2.a.s.1.1		2	68.11	even	16
4624.2.a.s.1.2		2	68.23	even	16
5202.2.a.u.1.1		2	51.23	even	16
5202.2.a.u.1.2		2	51.11	even	16

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:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-2.61313 - 1.08239i) q^{3} -1.00000i q^{4} +(-1.08239 + 2.61313i) q^{5} +(-2.61313 + 1.08239i) q^{6} +(-0.707107 - 0.707107i) q^{8} +(3.53553 + 3.53553i) q^{9} +(1.08239 + 2.61313i) q^{10} +(2.61313 - 1.08239i) q^{11} +(-1.08239 + 2.61313i) q^{12} +2.00000i q^{13} +(5.65685 - 5.65685i) q^{15} -1.00000 q^{16} +5.00000 q^{18} +(2.82843 - 2.82843i) q^{19} +(2.61313 + 1.08239i) q^{20} +(1.08239 - 2.61313i) q^{22} +(5.22625 - 2.16478i) q^{23} +(1.08239 + 2.61313i) q^{24} +(-2.12132 - 2.12132i) q^{25} +(1.41421 + 1.41421i) q^{26} +(-2.16478 - 5.22625i) q^{27} +(1.08239 - 2.61313i) q^{29} -8.00000i q^{30} +(-0.707107 + 0.707107i) q^{32} -8.00000 q^{33} +(3.53553 - 3.53553i) q^{36} +(7.83938 + 3.24718i) q^{37} -4.00000i q^{38} +(2.16478 - 5.22625i) q^{39} +(2.61313 - 1.08239i) q^{40} +(-2.16478 - 5.22625i) q^{41} +(2.82843 + 2.82843i) q^{43} +(-1.08239 - 2.61313i) q^{44} +(-13.0656 + 5.41196i) q^{45} +(2.16478 - 5.22625i) q^{46} +(2.61313 + 1.08239i) q^{48} +(4.94975 - 4.94975i) q^{49} -3.00000 q^{50} +2.00000 q^{52} +(-4.24264 + 4.24264i) q^{53} +(-5.22625 - 2.16478i) q^{54} +8.00000i q^{55} +(-10.4525 + 4.32957i) q^{57} +(-1.08239 - 2.61313i) q^{58} +(8.48528 + 8.48528i) q^{59} +(-5.65685 - 5.65685i) q^{60} +(3.24718 + 7.83938i) q^{61} +1.00000i q^{64} +(-5.22625 - 2.16478i) q^{65} +(-5.65685 + 5.65685i) q^{66} +4.00000 q^{67} -16.0000 q^{69} +(-5.22625 - 2.16478i) q^{71} -5.00000i q^{72} +(7.83938 - 3.24718i) q^{74} +(3.24718 + 7.83938i) q^{75} +(-2.82843 - 2.82843i) q^{76} +(-2.16478 - 5.22625i) q^{78} +(15.6788 - 6.49435i) q^{79} +(1.08239 - 2.61313i) q^{80} +1.00000i q^{81} +(-5.22625 - 2.16478i) q^{82} +(-8.48528 + 8.48528i) q^{83} +4.00000 q^{86} +(-5.65685 + 5.65685i) q^{87} +(-2.61313 - 1.08239i) q^{88} -6.00000i q^{89} +(-5.41196 + 13.0656i) q^{90} +(-2.16478 - 5.22625i) q^{92} +(4.32957 + 10.4525i) q^{95} +(2.61313 - 1.08239i) q^{96} +(-6.49435 + 15.6788i) q^{97} -7.00000i q^{98} +(13.0656 + 5.41196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{16} + 40 q^{18} - 64 q^{33} - 24 q^{50} + 16 q^{52} + 32 q^{67} - 128 q^{69} + 32 q^{86}+O(q^{100}) \) 8 * q - 8 * q^16 + 40 * q^18 - 64 * q^33 - 24 * q^50 + 16 * q^52 + 32 * q^67 - 128 * q^69 + 32 * q^86

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