LMFDB - Embedded newform 650.2.n.e.199.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(49,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$-1.27597 - 0.609843i$ of defining polynomial
Character	$\chi$	$=$	650.199
Dual form			650.2.n.e.49.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.519785 + 0.300098i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.519785 - 0.300098i) q^{6} +(-0.719687 - 1.24653i) q^{7} -1.00000 q^{8} +(-1.31988 - 2.28610i) q^{9} +(-2.40029 - 1.38581i) q^{11} -0.600196i q^{12} +(-2.31246 - 2.76632i) q^{13} -1.43937 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.90029 + 2.25184i) q^{17} -2.63977 q^{18} +(3.75184 - 2.16612i) q^{19} -0.863906i q^{21} +(-2.40029 + 1.38581i) q^{22} +(3.84461 + 2.21969i) q^{23} +(-0.519785 - 0.300098i) q^{24} +(-3.55193 + 0.619491i) q^{26} -3.38496i q^{27} +(-0.719687 + 1.24653i) q^{28} +(3.93244 - 6.81119i) q^{29} -4.16082i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.831757 - 1.44065i) q^{33} +4.50367i q^{34} +(-1.31988 + 2.28610i) q^{36} +(0.287734 - 0.498370i) q^{37} -4.33225i q^{38} +(-0.371816 - 2.13186i) q^{39} +(3.65906 + 2.11256i) q^{41} +(-0.748164 - 0.431953i) q^{42} +(-2.26469 + 1.30752i) q^{43} +2.77162i q^{44} +(3.84461 - 2.21969i) q^{46} -12.7684 q^{47} +(-0.519785 + 0.300098i) q^{48} +(2.46410 - 4.26795i) q^{49} -2.70308 q^{51} +(-1.23947 + 3.38581i) q^{52} +9.57123i q^{53} +(-2.93146 - 1.69248i) q^{54} +(0.719687 + 1.24653i) q^{56} +2.60020 q^{57} +(-3.93244 - 6.81119i) q^{58} +(3.00000 - 1.73205i) q^{59} +(6.25184 + 10.8285i) q^{61} +(-3.60338 - 2.08041i) q^{62} +(-1.89980 + 3.29056i) q^{63} +1.00000 q^{64} -1.66351 q^{66} +(2.66449 - 4.61504i) q^{67} +(3.90029 + 2.25184i) q^{68} +(1.33225 + 2.30752i) q^{69} +(5.19615 - 3.00000i) q^{71} +(1.31988 + 2.28610i) q^{72} +1.66351 q^{73} +(-0.287734 - 0.498370i) q^{74} +(-3.75184 - 2.16612i) q^{76} +3.98940i q^{77} +(-2.03215 - 0.743926i) q^{78} -12.7288 q^{79} +(-2.94383 + 5.09886i) q^{81} +(3.65906 - 2.11256i) q^{82} +10.0469 q^{83} +(-0.748164 + 0.431953i) q^{84} +2.61504i q^{86} +(4.08805 - 2.36023i) q^{87} +(2.40029 + 1.38581i) q^{88} +(5.15906 + 2.97859i) q^{89} +(-1.78406 + 4.87345i) q^{91} -4.43937i q^{92} +(1.24865 - 2.16273i) q^{93} +(-6.38418 + 11.0577i) q^{94} +0.600196i q^{96} +(-0.793166 - 1.37380i) q^{97} +(-2.46410 - 4.26795i) q^{98} +7.31643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{6} - 8 q^{8} + 4 q^{9} - 6 q^{11} - 6 q^{13} - 4 q^{16} - 18 q^{17} + 8 q^{18} + 6 q^{19} - 6 q^{22} + 6 q^{24} + 4 q^{32} - 6 q^{33} + 4 q^{36} + 6 q^{37} + 40 q^{39}+ \cdots + 8 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^6 - 8 * q^8 + 4 * q^9 - 6 * q^11 - 6 * q^13 - 4 * q^16 - 18 * q^17 + 8 * q^18 + 6 * q^19 - 6 * q^22 + 6 * q^24 + 4 * q^32 - 6 * q^33 + 4 * q^36 + 6 * q^37 + 40 * q^39 + 12 * q^41 - 30 * q^42 + 36 * q^43 + 6 * q^48 - 8 * q^49 + 6 * q^52 - 36 * q^54 + 12 * q^57 + 24 * q^59 + 26 * q^61 + 6 * q^62 - 24 * q^63 + 8 * q^64 - 12 * q^66 - 24 * q^67 + 18 * q^68 - 12 * q^69 - 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^76 + 2 * q^78 - 20 * q^79 - 28 * q^81 + 12 * q^82 - 36 * q^83 - 30 * q^84 + 24 * q^87 + 6 * q^88 + 24 * q^89 - 66 * q^91 + 12 * q^93 + 18 * q^97 + 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.519785	+	0.300098i	0.300098	+	0.173262i	0.642487	−	0.766297i	$-0.277903\pi$
$3$	0.519785	+	0.300098i	0.300098	+	0.173262i	−0.342389	+	0.939558i	$0.611236\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.519785	−	0.300098i	0.212201	−	0.122514i
$7$	−0.719687	−	1.24653i	−0.272016	−	0.471146i	0.697362	−	0.716719i	$-0.254357\pi$
$7$	−0.719687	−	1.24653i	−0.272016	−	0.471146i	−0.969378	+	0.245574i	$0.921024\pi$
$8$	−1.00000			−0.353553
$9$	−1.31988	−	2.28610i	−0.439961	−	0.762035i
$10$		0			0
$11$	−2.40029	−	1.38581i	−0.723716	−	0.417837i	0.0924030	−	0.995722i	$-0.470545\pi$
$11$	−2.40029	−	1.38581i	−0.723716	−	0.417837i	−0.816119	+	0.577884i	$0.803879\pi$
$12$		−	0.600196i		−	0.173262i
$13$	−2.31246	−	2.76632i	−0.641362	−	0.767239i
$13$	−2.31246	−	2.76632i	−0.641362	−	0.767239i
$14$	−1.43937			−0.384689
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.90029	+	2.25184i	−0.945960	+	0.546150i	−0.891824	−	0.452383i	$-0.850574\pi$
$17$	−3.90029	+	2.25184i	−0.945960	+	0.546150i	−0.0541365	+	0.998534i	$0.517241\pi$
$18$	−2.63977			−0.622199
$19$	3.75184	−	2.16612i	0.860730	−	0.496943i	−0.00352661	−	0.999994i	$-0.501123\pi$
$19$	3.75184	−	2.16612i	0.860730	−	0.496943i	0.864257	+	0.503051i	$0.167789\pi$
$20$		0			0
$21$		−	0.863906i		−	0.188520i
$22$	−2.40029	+	1.38581i	−0.511744	+	0.295456i
$23$	3.84461	+	2.21969i	0.801657	+	0.462837i	0.844050	−	0.536264i	$-0.180165\pi$
$23$	3.84461	+	2.21969i	0.801657	+	0.462837i	−0.0423934	+	0.999101i	$0.513498\pi$
$24$	−0.519785	−	0.300098i	−0.106101	−	0.0612572i
$25$		0			0
$26$	−3.55193	+	0.619491i	−0.696591	+	0.121492i
$27$		−	3.38496i		−	0.651436i
$28$	−0.719687	+	1.24653i	−0.136008	+	0.235573i
$29$	3.93244	−	6.81119i	0.730236	−	1.26481i	−0.226546	−	0.974000i	$-0.572743\pi$
$29$	3.93244	−	6.81119i	0.730236	−	1.26481i	0.956782	−	0.290806i	$-0.0939233\pi$
$30$		0			0
$31$		−	4.16082i		−	0.747306i	−0.927569	−	0.373653i	$-0.878105\pi$
$31$		−	4.16082i		−	0.747306i	0.927569	−	0.373653i	$-0.121895\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.831757	−	1.44065i	−0.144790	−	0.250784i
$34$			4.50367i			0.772373i
$35$		0			0
$36$	−1.31988	+	2.28610i	−0.219980	+	0.381017i
$37$	0.287734	−	0.498370i	0.0473032	−	0.0819315i	−0.841404	−	0.540406i	$-0.818271\pi$
$37$	0.287734	−	0.498370i	0.0473032	−	0.0819315i	0.888708	+	0.458475i	$0.151604\pi$
$38$		−	4.33225i		−	0.702783i
$39$	−0.371816	−	2.13186i	−0.0595382	−	0.341370i
$40$		0			0
$41$	3.65906	+	2.11256i	0.571449	+	0.329926i	0.757728	−	0.652571i	$-0.226309\pi$
$41$	3.65906	+	2.11256i	0.571449	+	0.329926i	−0.186279	+	0.982497i	$0.559643\pi$
$42$	−0.748164	−	0.431953i	−0.115444	−	0.0666518i
$43$	−2.26469	+	1.30752i	−0.345362	+	0.199395i	−0.662641	−	0.748938i	$-0.730564\pi$
$43$	−2.26469	+	1.30752i	−0.345362	+	0.199395i	0.317279	+	0.948332i	$0.397231\pi$
$44$			2.77162i			0.417837i
$45$		0			0
$46$	3.84461	−	2.21969i	0.566857	−	0.327275i
$47$	−12.7684			−1.86246			−0.931228	−	0.364436i	$-0.881262\pi$
$47$	−12.7684			−1.86246			−0.931228	+	0.364436i	$0.881262\pi$
$48$	−0.519785	+	0.300098i	−0.0750245	+	0.0433154i
$49$	2.46410	−	4.26795i	0.352015	−	0.609707i
$50$		0			0
$51$	−2.70308			−0.378507
$52$	−1.23947	+	3.38581i	−0.171884	+	0.469527i
$53$			9.57123i			1.31471i	0.753581	+	0.657355i	$0.228325\pi$
$53$			9.57123i			1.31471i	−0.753581	+	0.657355i	$0.771675\pi$
$54$	−2.93146	−	1.69248i	−0.398922	−	0.230318i
$55$		0			0
$56$	0.719687	+	1.24653i	0.0961722	+	0.166575i
$57$	2.60020			0.344404
$58$	−3.93244	−	6.81119i	−0.516355	−	0.894353i
$59$	3.00000	−	1.73205i	0.390567	−	0.225494i	−0.291839	−	0.956467i	$-0.594267\pi$
$59$	3.00000	−	1.73205i	0.390567	−	0.225494i	0.682406	+	0.730974i	$0.260934\pi$
$60$		0			0
$61$	6.25184	+	10.8285i	0.800466	+	1.38645i	0.919310	+	0.393534i	$0.128748\pi$
$61$	6.25184	+	10.8285i	0.800466	+	1.38645i	−0.118845	+	0.992913i	$0.537919\pi$
$62$	−3.60338	−	2.08041i	−0.457629	−	0.264212i
$63$	−1.89980	+	3.29056i	−0.239353	+	0.414571i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.66351			−0.204764
$67$	2.66449	−	4.61504i	0.325520	−	0.563817i	−0.656098	−	0.754676i	$-0.727794\pi$
$67$	2.66449	−	4.61504i	0.325520	−	0.563817i	0.981617	+	0.190859i	$0.0611274\pi$
$68$	3.90029	+	2.25184i	0.472980	+	0.273075i
$69$	1.33225	+	2.30752i	0.160384	+	0.277793i
$70$		0			0
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$	1.31988	+	2.28610i	0.155550	+	0.269420i
$73$	1.66351			0.194700			0.0973498	−	0.995250i	$-0.468963\pi$
$73$	1.66351			0.194700			0.0973498	+	0.995250i	$0.468963\pi$
$74$	−0.287734	−	0.498370i	−0.0334484	−	0.0579343i
$75$		0			0
$76$	−3.75184	−	2.16612i	−0.430365	−	0.248471i
$77$			3.98940i			0.454634i
$78$	−2.03215	−	0.743926i	−0.230096	−	0.0842330i
$79$	−12.7288			−1.43210			−0.716050	−	0.698049i	$-0.754052\pi$
$79$	−12.7288			−1.43210			−0.716050	+	0.698049i	$0.754052\pi$
$80$		0			0
$81$	−2.94383	+	5.09886i	−0.327092	+	0.566540i
$82$	3.65906	−	2.11256i	0.404076	−	0.233293i
$83$	10.0469			1.10279			0.551396	−	0.834244i	$-0.314095\pi$
$83$	10.0469			1.10279			0.551396	+	0.834244i	$0.314095\pi$
$84$	−0.748164	+	0.431953i	−0.0816314	+	0.0471299i
$85$		0			0
$86$			2.61504i			0.281987i
$87$	4.08805	−	2.36023i	0.438285	−	0.253044i
$88$	2.40029	+	1.38581i	0.255872	+	0.147728i
$89$	5.15906	+	2.97859i	0.546859	+	0.315729i	0.747854	−	0.663863i	$-0.231084\pi$
$89$	5.15906	+	2.97859i	0.546859	+	0.315729i	−0.200995	+	0.979592i	$0.564417\pi$
$90$		0			0
$91$	−1.78406	+	4.87345i	−0.187021	+	0.510876i
$92$		−	4.43937i		−	0.462837i
$93$	1.24865	−	2.16273i	0.129479	−	0.224265i
$94$	−6.38418	+	11.0577i	−0.658478	+	1.14052i
$95$		0			0
$96$			0.600196i			0.0612572i
$97$	−0.793166	−	1.37380i	−0.0805338	−	0.139489i	0.822946	−	0.568120i	$-0.192329\pi$
$97$	−0.793166	−	1.37380i	−0.0805338	−	0.139489i	−0.903479	+	0.428632i	$0.858996\pi$
$98$	−2.46410	−	4.26795i	−0.248912	−	0.431128i
$99$			7.31643i			0.735329i
$100$		0			0
$101$	6.87676	−	11.9109i	0.684263	−	1.18518i	−0.289405	−	0.957207i	$-0.593457\pi$
$101$	6.87676	−	11.9109i	0.684263	−	1.18518i	0.973668	−	0.227972i	$-0.0732093\pi$
$102$	−1.35154	+	2.34094i	−0.133823	+	0.231788i
$103$		−	5.73205i		−	0.564796i	−0.959297	−	0.282398i	$-0.908870\pi$
$103$		−	5.73205i		−	0.564796i	0.959297	−	0.282398i	$-0.0911298\pi$
$104$	2.31246	+	2.76632i	0.226756	+	0.271260i
$105$		0			0
$106$	8.28893	+	4.78561i	0.805092	+	0.464820i
$107$	4.05242	+	2.33967i	0.391762	+	0.226184i	0.682924	−	0.730490i	$-0.260708\pi$
$107$	4.05242	+	2.33967i	0.391762	+	0.226184i	−0.291161	+	0.956674i	$0.594042\pi$
$108$	−2.93146	+	1.69248i	−0.282080	+	0.162859i
$109$			2.32164i			0.222373i	0.993800	+	0.111187i	$0.0354651\pi$
$109$			2.32164i			0.222373i	−0.993800	+	0.111187i	$0.964535\pi$
$110$		0			0
$111$	0.299119	−	0.172697i	0.0283912	−	0.0163916i
$112$	1.43937			0.136008
$113$	6.69982	−	3.86814i	0.630266	−	0.363884i	−0.150589	−	0.988596i	$-0.548117\pi$
$113$	6.69982	−	3.86814i	0.630266	−	0.363884i	0.780855	+	0.624712i	$0.214784\pi$
$114$	1.30010	−	2.25184i	0.121765	−	0.210904i
$115$		0			0
$116$	−7.86488			−0.730236
$117$	−3.27191	+	8.93774i	−0.302489	+	0.826295i
$118$		−	3.46410i		−	0.318896i
$119$	5.61398	+	3.24123i	0.514633	+	0.297123i
$120$		0			0
$121$	−1.65906	−	2.87358i	−0.150824	−	0.261234i
$122$	12.5037			1.13203
$123$	1.26795	+	2.19615i	0.114327	+	0.198020i
$124$	−3.60338	+	2.08041i	−0.323593	+	0.186826i
$125$		0			0
$126$	1.89980	+	3.29056i	0.169248	+	0.293146i
$127$	13.9641	+	8.06218i	1.23911	+	0.715403i	0.968913	−	0.247401i	$-0.0795766\pi$
$127$	13.9641	+	8.06218i	1.23911	+	0.715403i	0.270201	+	0.962804i	$0.412910\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.56953			−0.138190
$130$		0			0
$131$	−19.7609			−1.72651			−0.863257	−	0.504764i	$-0.831579\pi$
$131$	−19.7609			−1.72651			−0.863257	+	0.504764i	$0.831579\pi$
$132$	−0.831757	+	1.44065i	−0.0723952	+	0.125392i
$133$	−5.40029	−	3.11786i	−0.468265	−	0.270353i
$134$	−2.66449	−	4.61504i	−0.230177	−	0.398678i
$135$		0			0
$136$	3.90029	−	2.25184i	0.334447	−	0.193093i
$137$	8.63234	+	14.9517i	0.737511	+	1.27741i	0.953613	+	0.301036i	$0.0973323\pi$
$137$	8.63234	+	14.9517i	0.737511	+	1.27741i	−0.216102	+	0.976371i	$0.569334\pi$
$138$	2.66449			0.226817
$139$	1.47328	+	2.55180i	0.124962	+	0.216441i	0.921718	−	0.387860i	$-0.126786\pi$
$139$	1.47328	+	2.55180i	0.124962	+	0.216441i	−0.796756	+	0.604301i	$0.793452\pi$
$140$		0			0
$141$	−6.63680	−	3.83176i	−0.558919	−	0.322692i
$142$		−	6.00000i		−	0.503509i
$143$	1.71699	+	9.84461i	0.143582	+	0.823248i
$144$	2.63977			0.219980
$145$		0			0
$146$	0.831757	−	1.44065i	0.0688367	−	0.119229i
$147$	2.56160	−	1.47894i	0.211278	−	0.121981i
$148$	−0.575468			−0.0473032
$149$	6.11871	−	3.53264i	0.501264	−	0.289405i	−0.227971	−	0.973668i	$-0.573209\pi$
$149$	6.11871	−	3.53264i	0.501264	−	0.289405i	0.729235	+	0.684263i	$0.239876\pi$
$150$		0			0
$151$		−	15.8327i		−	1.28844i	−0.764839	−	0.644222i	$-0.777181\pi$
$151$		−	15.8327i		−	1.28844i	0.764839	−	0.644222i	$-0.222819\pi$
$152$	−3.75184	+	2.16612i	−0.304314	+	0.175696i
$153$	10.2959	+	5.94432i	0.832371	+	0.480570i
$154$	3.45492	+	1.99470i	0.278405	+	0.160737i
$155$		0			0
$156$	−1.66033	+	1.38793i	−0.132933	+	0.111123i
$157$		−	12.6280i		−	1.00783i	−0.863754	−	0.503913i	$-0.831893\pi$
$157$		−	12.6280i		−	1.00783i	0.863754	−	0.503913i	$-0.168107\pi$
$158$	−6.36440	+	11.0235i	−0.506324	+	0.876979i
$159$	−2.87231	+	4.97498i	−0.227789	+	0.394541i
$160$		0			0
$161$		−	6.38992i		−	0.503596i
$162$	2.94383	+	5.09886i	0.231289	+	0.400604i
$163$	−9.18428	−	15.9076i	−0.719368	−	1.24598i	−0.961250	−	0.275677i	$-0.911098\pi$
$163$	−9.18428	−	15.9076i	−0.719368	−	1.24598i	0.241882	−	0.970306i	$-0.422235\pi$
$164$		−	4.22512i		−	0.329926i
$165$		0			0
$166$	5.02346	−	8.70088i	0.389896	−	0.675319i
$167$	10.8043	−	18.7135i	0.836059	−	1.44810i	−0.0571070	−	0.998368i	$-0.518188\pi$
$167$	10.8043	−	18.7135i	0.836059	−	1.44810i	0.893166	−	0.449728i	$-0.148479\pi$
$168$			0.863906i			0.0666518i
$169$	−2.30504	+	12.7940i	−0.177311	+	0.984155i
$170$		0			0
$171$	−9.90396	−	5.71806i	−0.757375	−	0.437271i
$172$	2.26469	+	1.30752i	0.172681	+	0.0996974i
$173$	−3.45492	+	1.99470i	−0.262673	+	0.151654i	−0.625553	−	0.780182i	$-0.715127\pi$
$173$	−3.45492	+	1.99470i	−0.262673	+	0.151654i	0.362880	+	0.931836i	$0.381793\pi$
$174$		−	4.72047i		−	0.357858i
$175$		0			0
$176$	2.40029	−	1.38581i	0.180929	−	0.104459i
$177$	2.07914			0.156278
$178$	5.15906	−	2.97859i	0.386688	−	0.223254i
$179$	−6.23996	+	10.8079i	−0.466397	+	0.807823i	−0.999263	−	0.0383766i	$-0.987781\pi$
$179$	−6.23996	+	10.8079i	−0.466397	+	0.807823i	0.532867	+	0.846199i	$0.321115\pi$
$180$		0			0
$181$	19.4319			1.44436			0.722180	−	0.691705i	$-0.243140\pi$
$181$	19.4319			1.44436			0.722180	+	0.691705i	$0.243140\pi$
$182$	3.32850	+	3.98177i	0.246725	+	0.295148i
$183$			7.50465i			0.554760i
$184$	−3.84461	−	2.21969i	−0.283428	−	0.163637i
$185$		0			0
$186$	−1.24865	−	2.16273i	−0.0915557	−	0.158579i
$187$	12.4825			0.912808
$188$	6.38418	+	11.0577i	0.465614	+	0.806467i
$189$	−4.21947	+	2.43611i	−0.306921	+	0.177201i
$190$		0			0
$191$	9.16074	+	15.8669i	0.662848	+	1.14809i	0.979864	+	0.199666i	$0.0639858\pi$
$191$	9.16074	+	15.8669i	0.662848	+	1.14809i	−0.317016	+	0.948420i	$0.602681\pi$
$192$	0.519785	+	0.300098i	0.0375122	+	0.0216577i
$193$	−2.37182	+	4.10811i	−0.170727	+	0.295708i	−0.938674	−	0.344805i	$-0.887945\pi$
$193$	−2.37182	+	4.10811i	−0.170727	+	0.295708i	0.767947	+	0.640513i	$0.221278\pi$
$194$	−1.58633			−0.113892
$195$		0			0
$196$	−4.92820			−0.352015
$197$	−5.40029	+	9.35358i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$197$	−5.40029	+	9.35358i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$198$	6.33621	+	3.65821i	0.450295	+	0.259978i
$199$	−5.50367	−	9.53264i	−0.390145	−	0.675751i	0.602323	−	0.798252i	$-0.294242\pi$
$199$	−5.50367	−	9.53264i	−0.390145	−	0.675751i	−0.992468	+	0.122501i	$0.960908\pi$
$200$		0			0
$201$	2.76993	−	1.59922i	0.195375	−	0.112800i
$202$	−6.87676	−	11.9109i	−0.483847	−	0.838048i
$203$	−11.3205			−0.794544
$204$	1.35154	+	2.34094i	0.0946269	+	0.163899i
$205$		0			0
$206$	−4.96410	−	2.86603i	−0.345865	−	0.199685i
$207$		−	11.7189i		−	0.814520i
$208$	3.55193	−	0.619491i	0.246282	−	0.0429540i
$209$	−12.0073			−0.830565
$210$		0			0
$211$	−13.1291	+	22.7402i	−0.903843	+	1.56550i	−0.0813811	+	0.996683i	$0.525933\pi$
$211$	−13.1291	+	22.7402i	−0.903843	+	1.56550i	−0.822462	+	0.568820i	$0.807400\pi$
$212$	8.28893	−	4.78561i	0.569286	−	0.328677i
$213$	3.60117			0.246748
$214$	4.05242	−	2.33967i	0.277018	−	0.159936i
$215$		0			0
$216$			3.38496i			0.230318i
$217$	−5.18661	+	2.99449i	−0.352090	+	0.203279i
$218$	2.01060	+	1.16082i	0.136175	+	0.0786208i
$219$	0.864669	+	0.499217i	0.0584289	+	0.0337340i
$220$		0			0
$221$	15.2486	+	5.58217i	1.02573	+	0.375498i
$222$		−	0.345393i		−	0.0231813i
$223$	11.1021	−	19.2294i	0.743452	−	1.28770i	−0.207463	−	0.978243i	$-0.566521\pi$
$223$	11.1021	−	19.2294i	0.743452	−	1.28770i	0.950915	−	0.309454i	$-0.100146\pi$
$224$	0.719687	−	1.24653i	0.0480861	−	0.0832876i
$225$		0			0
$226$		−	7.73629i		−	0.514610i
$227$	−1.03957	−	1.80059i	−0.0689986	−	0.119509i	0.829462	−	0.558563i	$-0.188647\pi$
$227$	−1.03957	−	1.80059i	−0.0689986	−	0.119509i	−0.898461	+	0.439054i	$0.855314\pi$
$228$	−1.30010	−	2.25184i	−0.0861011	−	0.149131i
$229$			4.67933i			0.309219i	0.987976	+	0.154610i	$0.0494120\pi$
$229$			4.67933i			0.309219i	−0.987976	+	0.154610i	$0.950588\pi$
$230$		0			0
$231$	−1.19721	+	2.07363i	−0.0787706	+	0.136435i
$232$	−3.93244	+	6.81119i	−0.258177	+	0.447177i
$233$			0.611060i			0.0400319i	0.999800	+	0.0200160i	$0.00637170\pi$
$233$			0.611060i			0.0400319i	−0.999800	+	0.0200160i	$0.993628\pi$
$234$	6.10436	+	7.30243i	0.399054	+	0.477375i
$235$		0			0
$236$	−3.00000	−	1.73205i	−0.195283	−	0.112747i
$237$	−6.61623	−	3.81988i	−0.429770	−	0.248128i
$238$	5.61398	−	3.24123i	0.363900	−	0.210098i
$239$		−	25.6481i		−	1.65904i	−0.558479	−	0.829518i	$-0.688615\pi$
$239$		−	25.6481i		−	1.65904i	0.558479	−	0.829518i	$-0.311385\pi$
$240$		0			0
$241$	23.4633	−	13.5466i	1.51141	−	0.872610i	0.511494	−	0.859287i	$-0.329092\pi$
$241$	23.4633	−	13.5466i	1.51141	−	0.872610i	0.999911	−	0.0133234i	$-0.00424108\pi$
$242$	−3.31812			−0.213297
$243$	−11.8547	+	6.84432i	−0.760480	+	0.439063i
$244$	6.25184	−	10.8285i	0.400233	−	0.693223i
$245$		0			0
$246$	2.53590			0.161683
$247$	−14.6682	−	5.36970i	−0.933313	−	0.341666i
$248$			4.16082i			0.264212i
$249$	5.22223	+	3.01506i	0.330945	+	0.191071i
$250$		0			0
$251$	0.751836	+	1.30222i	0.0474554	+	0.0821952i	0.888777	−	0.458339i	$-0.151555\pi$
$251$	0.751836	+	1.30222i	0.0474554	+	0.0821952i	−0.841322	+	0.540534i	$0.818222\pi$
$252$	3.79961			0.239353
$253$	−6.15213	−	10.6558i	−0.386781	−	0.669924i
$254$	13.9641	−	8.06218i	0.876186	−	0.505866i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.6191	+	10.1724i	1.09905	+	0.634537i	0.935971	−	0.352076i	$-0.114524\pi$
$257$	17.6191	+	10.1724i	1.09905	+	0.634537i	0.163079	+	0.986613i	$0.447857\pi$
$258$	−0.784767	+	1.35926i	−0.0488575	+	0.0846236i
$259$	−0.828313			−0.0514689
$260$		0			0
$261$	−20.7614			−1.28510
$262$	−9.88043	+	17.1134i	−0.610415	+	1.05727i
$263$	14.8344	+	8.56466i	0.914729	+	0.528119i	0.881950	−	0.471343i	$-0.156231\pi$
$263$	14.8344	+	8.56466i	0.914729	+	0.528119i	0.0327796	+	0.999463i	$0.489564\pi$
$264$	0.831757	+	1.44065i	0.0511911	+	0.0886656i
$265$		0			0
$266$	−5.40029	+	3.11786i	−0.331113	+	0.191168i
$267$	1.78773	+	3.09645i	0.109408	+	0.189499i
$268$	−5.32899			−0.325520
$269$	9.69121	+	16.7857i	0.590883	+	1.02344i	0.994114	+	0.108342i	$0.0345540\pi$
$269$	9.69121	+	16.7857i	0.590883	+	1.02344i	−0.403230	+	0.915099i	$0.632113\pi$
$270$		0			0
$271$	−15.9098	−	9.18555i	−0.966454	−	0.557982i	−0.0683006	−	0.997665i	$-0.521758\pi$
$271$	−15.9098	−	9.18555i	−0.966454	−	0.557982i	−0.898153	+	0.439682i	$0.855091\pi$
$272$		−	4.50367i		−	0.273075i
$273$	−2.38984	+	1.99775i	−0.144640	+	0.120909i
$274$	17.2647			1.04300
$275$		0			0
$276$	1.33225	−	2.30752i	0.0801918	−	0.138896i
$277$	−23.5855	+	13.6171i	−1.41711	+	0.818171i	−0.996044	−	0.0888576i	$-0.971678\pi$
$277$	−23.5855	+	13.6171i	−1.41711	+	0.818171i	−0.421069	+	0.907028i	$0.638345\pi$
$278$	2.94657			0.176723
$279$	−9.51207	+	5.49180i	−0.569473	+	0.328785i
$280$		0			0
$281$			30.0815i			1.79451i	0.441509	+	0.897257i	$0.354443\pi$
$281$			30.0815i			1.79451i	−0.441509	+	0.897257i	$0.645557\pi$
$282$	−6.63680	+	3.83176i	−0.395216	+	0.228178i
$283$	−22.0653	−	12.7394i	−1.31164	−	0.757278i	−0.329276	−	0.944234i	$-0.606805\pi$
$283$	−22.0653	−	12.7394i	−1.31164	−	0.757278i	−0.982368	+	0.186955i	$0.940138\pi$
$284$	−5.19615	−	3.00000i	−0.308335	−	0.178017i
$285$		0			0
$286$	9.38418	+	3.43534i	0.554898	+	0.203136i
$287$		−	6.08153i		−	0.358981i
$288$	1.31988	−	2.28610i	0.0777748	−	0.134710i
$289$	1.64153	−	2.84321i	0.0965604	−	0.167247i
$290$		0			0
$291$		−	0.952110i		−	0.0558137i
$292$	−0.831757	−	1.44065i	−0.0486749	−	0.0843074i
$293$	−8.28893	−	14.3568i	−0.484244	−	0.838736i	0.515592	−	0.856834i	$-0.327572\pi$
$293$	−8.28893	−	14.3568i	−0.484244	−	0.838736i	−0.999836	+	0.0180985i	$0.994239\pi$
$294$		−	2.95789i		−	0.172507i
$295$		0			0
$296$	−0.287734	+	0.498370i	−0.0167242	+	0.0289672i
$297$	−4.69092	+	8.12490i	−0.272195	+	0.471455i
$298$		−	7.06528i		−	0.409280i
$299$	−2.75015	−	15.7684i	−0.159045	−	0.911908i
$300$		0			0
$301$	3.25973	+	1.88201i	0.187888	+	0.108477i
$302$	−13.7115	−	7.91633i	−0.789007	−	0.455534i
$303$	7.14887	−	4.12740i	0.410692	−	0.237113i
$304$			4.33225i			0.248471i
$305$		0			0
$306$	10.2959	−	5.94432i	0.588575	−	0.339814i
$307$	−16.2722			−0.928703			−0.464351	−	0.885651i	$-0.653713\pi$
$307$	−16.2722			−0.928703			−0.464351	+	0.885651i	$0.653713\pi$
$308$	3.45492	−	1.99470i	0.196862	−	0.113659i
$309$	1.72018	−	2.97943i	0.0978574	−	0.169494i
$310$		0			0
$311$	−16.1053			−0.913246			−0.456623	−	0.889660i	$-0.650941\pi$
$311$	−16.1053			−0.913246			−0.456623	+	0.889660i	$0.650941\pi$
$312$	0.371816	+	2.13186i	0.0210499	+	0.120693i
$313$		−	10.2162i		−	0.577454i	−0.957411	−	0.288727i	$-0.906768\pi$
$313$		−	10.2162i		−	0.577454i	0.957411	−	0.288727i	$-0.0932321\pi$
$314$	−10.9362	−	6.31401i	−0.617165	−	0.356320i
$315$		0			0
$316$	6.36440	+	11.0235i	0.358025	+	0.620118i
$317$	0.204368			0.0114785			0.00573923	−	0.999984i	$-0.498173\pi$
$317$	0.204368			0.0114785			0.00573923	+	0.999984i	$0.498173\pi$
$318$	2.87231	+	4.97498i	0.161071	+	0.278983i
$319$	−18.8780	+	10.8992i	−1.05697	+	0.610240i
$320$		0			0
$321$	1.40426	+	2.43225i	0.0783781	+	0.135755i
$322$	−5.53383	−	3.19496i	−0.308388	−	0.178048i
$323$	−9.75551	+	16.8970i	−0.542811	+	0.940176i
$324$	5.88766			0.327092
$325$		0			0
$326$	−18.3686			−1.01734
$327$	−0.696720	+	1.20676i	−0.0385287	+	0.0667337i
$328$	−3.65906	−	2.11256i	−0.202038	−	0.116647i
$329$	9.18922	+	15.9162i	0.506618	+	0.877488i
$330$		0			0
$331$	16.5110	−	9.53264i	0.907527	−	0.523961i	0.0278926	−	0.999611i	$-0.491120\pi$
$331$	16.5110	−	9.53264i	0.907527	−	0.523961i	0.879635	+	0.475650i	$0.157787\pi$
$332$	−5.02346	−	8.70088i	−0.275698	−	0.477523i
$333$	−1.51910			−0.0832462
$334$	−10.8043	−	18.7135i	−0.591183	−	1.02396i
$335$		0			0
$336$	0.748164	+	0.431953i	0.0408157	+	0.0235650i
$337$		−	19.8609i		−	1.08189i	−0.841057	−	0.540946i	$-0.818066\pi$
$337$		−	19.8609i		−	1.08189i	0.841057	−	0.540946i	$-0.181934\pi$
$338$	9.92742	+	8.39323i	0.539980	+	0.456532i
$339$	4.64329			0.252189
$340$		0			0
$341$	−5.76611	+	9.98719i	−0.312252	+	0.540837i
$342$	−9.90396	+	5.71806i	−0.535545	+	0.309197i
$343$	−17.1691			−0.927047
$344$	2.26469	−	1.30752i	0.122104	−	0.0704967i
$345$		0			0
$346$			3.98940i			0.214471i
$347$	−14.7661	+	8.52522i	−0.792686	+	0.457658i	−0.840907	−	0.541179i	$-0.817978\pi$
$347$	−14.7661	+	8.52522i	−0.792686	+	0.457658i	0.0482211	+	0.998837i	$0.484645\pi$
$348$	−4.08805	−	2.36023i	−0.219142	−	0.126522i
$349$	−18.3917	−	10.6185i	−0.984488	−	0.568394i	−0.0808657	−	0.996725i	$-0.525768\pi$
$349$	−18.3917	−	10.6185i	−0.984488	−	0.568394i	−0.903622	+	0.428331i	$0.859102\pi$
$350$		0			0
$351$	−9.36389	+	7.82760i	−0.499807	+	0.417806i
$352$		−	2.77162i		−	0.147728i
$353$	−8.00840	+	13.8710i	−0.426244	+	0.738276i	−0.996536	−	0.0831659i	$-0.973497\pi$
$353$	−8.00840	+	13.8710i	−0.426244	+	0.738276i	0.570292	+	0.821442i	$0.306830\pi$
$354$	1.03957	−	1.80059i	0.0552525	−	0.0957001i
$355$		0			0
$356$		−	5.95717i		−	0.315729i
$357$	1.94537	+	3.36949i	0.102960	+	0.178332i
$358$	6.23996	+	10.8079i	0.329792	+	0.571217i
$359$		−	24.2487i		−	1.27980i	−0.768459	−	0.639899i	$-0.778976\pi$
$359$		−	24.2487i		−	1.27980i	0.768459	−	0.639899i	$-0.221024\pi$
$360$		0			0
$361$	−0.115820	+	0.200606i	−0.00609580	+	0.0105582i
$362$	9.71594	−	16.8285i	0.510658	−	0.884486i
$363$		−	1.99152i		−	0.104528i
$364$	5.11256	−	0.891679i	0.267971	−	0.0467367i
$365$		0			0
$366$	6.49922	+	3.75232i	0.339720	+	0.196137i
$367$	−25.7822	−	14.8854i	−1.34582	−	0.777010i	−0.358167	−	0.933658i	$-0.616598\pi$
$367$	−25.7822	−	14.8854i	−1.34582	−	0.777010i	−0.987655	+	0.156648i	$0.949931\pi$
$368$	−3.84461	+	2.21969i	−0.200414	+	0.115709i
$369$		−	11.1533i		−	0.580619i
$370$		0			0
$371$	11.9309	−	6.88829i	0.619420	−	0.357622i
$372$	−2.49731			−0.129479
$373$	24.5828	−	14.1929i	1.27285	−	0.734880i	0.297326	−	0.954776i	$-0.403905\pi$
$373$	24.5828	−	14.1929i	1.27285	−	0.734880i	0.975523	+	0.219896i	$0.0705718\pi$
$374$	6.24123	−	10.8101i	0.322726	−	0.558979i
$375$		0			0
$376$	12.7684			0.658478
$377$	−27.9355	+	4.87223i	−1.43875	+	0.250932i
$378$			4.87223i			0.250600i
$379$	24.6070	+	14.2069i	1.26398	+	0.729759i	0.973842	−	0.227226i	$-0.0729657\pi$
$379$	24.6070	+	14.2069i	1.26398	+	0.729759i	0.290137	+	0.956985i	$0.406299\pi$
$380$		0			0
$381$	4.83888	+	8.38119i	0.247904	+	0.429382i
$382$	18.3215			0.937409
$383$	−4.69863	−	8.13827i	−0.240089	−	0.415846i	0.720651	−	0.693298i	$-0.243843\pi$
$383$	−4.69863	−	8.13827i	−0.240089	−	0.415846i	−0.960739	+	0.277452i	$0.910510\pi$
$384$	0.519785	−	0.300098i	0.0265252	−	0.0153143i
$385$		0			0
$386$	2.37182	+	4.10811i	0.120722	+	0.209097i
$387$	5.97825	+	3.45154i	0.303891	+	0.175452i
$388$	−0.793166	+	1.37380i	−0.0402669	+	0.0697443i
$389$	−11.6461			−0.590482			−0.295241	−	0.955423i	$-0.595400\pi$
$389$	−11.6461			−0.590482			−0.295241	+	0.955423i	$0.595400\pi$
$390$		0			0
$391$	−19.9935			−1.01111
$392$	−2.46410	+	4.26795i	−0.124456	+	0.215564i
$393$	−10.2714	−	5.93019i	−0.518123	−	0.299139i
$394$	5.40029	+	9.35358i	0.272063	+	0.471227i
$395$		0			0
$396$	6.33621	−	3.65821i	0.318407	−	0.183832i
$397$	0.199902	+	0.346241i	0.0100328	+	0.0173773i	0.870998	−	0.491286i	$-0.163473\pi$
$397$	0.199902	+	0.346241i	0.0100328	+	0.0173773i	−0.860965	+	0.508663i	$0.830140\pi$
$398$	−11.0073			−0.551748
$399$	−1.87133	−	3.24123i	−0.0936835	−	0.162265i
$400$		0			0
$401$	7.36793	+	4.25388i	0.367937	+	0.212428i	0.672557	−	0.740046i	$-0.265196\pi$
$401$	7.36793	+	4.25388i	0.367937	+	0.212428i	−0.304620	+	0.952474i	$0.598529\pi$
$402$		−	3.19843i		−	0.159523i
$403$	−11.5102	+	9.62174i	−0.573362	+	0.479293i
$404$	−13.7535			−0.684263
$405$		0			0
$406$	−5.66025	+	9.80385i	−0.280914	+	0.486557i
$407$	−1.38129	+	0.797489i	−0.0684681	+	0.0395301i
$408$	2.70308			0.133823
$409$	12.1357	−	7.00657i	0.600074	−	0.346453i	−0.168997	−	0.985617i	$-0.554053\pi$
$409$	12.1357	−	7.00657i	0.600074	−	0.346453i	0.769071	+	0.639164i	$0.220719\pi$
$410$		0			0
$411$			10.3622i			0.511129i
$412$	−4.96410	+	2.86603i	−0.244564	+	0.141199i
$413$	−4.31812	−	2.49307i	−0.212481	−	0.122676i
$414$	−10.1489	−	5.85945i	−0.498790	−	0.287976i
$415$		0			0
$416$	1.23947	−	3.38581i	0.0607701	−	0.166003i
$417$			1.76852i			0.0866047i
$418$	−6.00367	+	10.3987i	−0.293649	+	0.508615i
$419$	−12.0977	+	20.9539i	−0.591012	+	1.02366i	0.403084	+	0.915163i	$0.367938\pi$
$419$	−12.0977	+	20.9539i	−0.591012	+	1.02366i	−0.994096	+	0.108500i	$0.965395\pi$
$420$		0			0
$421$		−	35.6392i		−	1.73695i	−0.495735	−	0.868474i	$-0.665101\pi$
$421$		−	35.6392i		−	1.73695i	0.495735	−	0.868474i	$-0.334899\pi$
$422$	13.1291	+	22.7402i	0.639114	+	1.10698i
$423$	16.8527	+	29.1898i	0.819408	+	1.41926i
$424$		−	9.57123i		−	0.464820i
$425$		0			0
$426$	1.80059	−	3.11871i	0.0872387	−	0.151102i
$427$	8.99873	−	15.5863i	0.435479	−	0.754272i
$428$		−	4.67933i		−	0.226184i
$429$	−2.06188	+	5.63234i	−0.0995485	+	0.271932i
$430$		0			0
$431$	4.29586	+	2.48022i	0.206924	+	0.119468i	0.599881	−	0.800089i	$-0.295215\pi$
$431$	4.29586	+	2.48022i	0.206924	+	0.119468i	−0.392957	+	0.919557i	$0.628548\pi$
$432$	2.93146	+	1.69248i	0.141040	+	0.0814295i
$433$	−3.65135	+	2.10811i	−0.175472	+	0.101309i	−0.585164	−	0.810915i	$-0.698970\pi$
$433$	−3.65135	+	2.10811i	−0.175472	+	0.101309i	0.409691	+	0.912224i	$0.365636\pi$
$434$			5.98898i			0.287480i
$435$		0			0
$436$	2.01060	−	1.16082i	0.0962904	−	0.0555933i
$437$	19.2325			0.920013
$438$	0.864669	−	0.499217i	0.0413155	−	0.0238535i
$439$	7.37500	−	12.7739i	0.351989	−	0.609664i	−0.634608	−	0.772834i	$-0.718839\pi$
$439$	7.37500	−	12.7739i	0.351989	−	0.609664i	0.986598	+	0.163170i	$0.0521720\pi$
$440$		0			0
$441$	−13.0093			−0.619490
$442$	12.4586	−	10.4146i	0.592595	−	0.495370i
$443$		−	12.2374i		−	0.581417i	−0.956812	−	0.290709i	$-0.906109\pi$
$443$		−	12.2374i		−	0.581417i	0.956812	−	0.290709i	$-0.0938910\pi$
$444$	−0.299119	−	0.172697i	−0.0141956	−	0.00819582i
$445$		0			0
$446$	−11.1021	−	19.2294i	−0.525700	−	0.910539i
$447$	4.24055			0.200571
$448$	−0.719687	−	1.24653i	−0.0340020	−	0.0588932i
$449$	16.5163	−	9.53569i	0.779452	−	0.450017i	−0.0567839	−	0.998386i	$-0.518085\pi$
$449$	16.5163	−	9.53569i	0.779452	−	0.450017i	0.836236	+	0.548370i	$0.184751\pi$
$450$		0			0
$451$	−5.85521	−	10.1415i	−0.275711	−	0.477546i
$452$	−6.69982	−	3.86814i	−0.315133	−	0.181942i
$453$	4.75135	−	8.22957i	0.223238	−	0.386659i
$454$	−2.07914			−0.0975788
$455$		0			0
$456$	−2.60020			−0.121765
$457$	8.05688	−	13.9549i	0.376885	−	0.652784i	−0.613722	−	0.789522i	$-0.710329\pi$
$457$	8.05688	−	13.9549i	0.376885	−	0.652784i	0.990607	+	0.136738i	$0.0436619\pi$
$458$	4.05242	+	2.33967i	0.189357	+	0.109325i
$459$	7.62238	+	13.2023i	0.355782	+	0.616233i
$460$		0			0
$461$	4.19560	−	2.42233i	0.195408	−	0.112819i	−0.399104	−	0.916906i	$-0.630679\pi$
$461$	4.19560	−	2.42233i	0.195408	−	0.112819i	0.594512	+	0.804087i	$0.297345\pi$
$462$	1.19721	+	2.07363i	0.0556992	+	0.0964739i
$463$	8.23164			0.382557			0.191278	−	0.981536i	$-0.438737\pi$
$463$	8.23164			0.382557			0.191278	+	0.981536i	$0.438737\pi$
$464$	3.93244	+	6.81119i	0.182559	+	0.316202i
$465$		0			0
$466$	0.529194	+	0.305530i	0.0245144	+	0.0141534i
$467$			33.4873i			1.54961i	0.632203	+	0.774803i	$0.282151\pi$
$467$			33.4873i			1.54961i	−0.632203	+	0.774803i	$0.717849\pi$
$468$	9.37627	−	1.63531i	0.433418	−	0.0755923i
$469$	−7.67040			−0.354186
$470$		0			0
$471$	3.78964	−	6.56386i	0.174618	−	0.302446i
$472$	−3.00000	+	1.73205i	−0.138086	+	0.0797241i
$473$	7.24789			0.333258
$474$	−6.61623	+	3.81988i	−0.303894	+	0.175453i
$475$		0			0
$476$		−	6.48247i		−	0.297123i
$477$	21.8808	−	12.6329i	1.00185	−	0.578421i
$478$	−22.2119	−	12.8240i	−1.01595	−	0.586558i
$479$	−6.97448	−	4.02672i	−0.318672	−	0.183985i	0.332128	−	0.943234i	$-0.392233\pi$
$479$	−6.97448	−	4.02672i	−0.318672	−	0.183985i	−0.650800	+	0.759249i	$0.725567\pi$
$480$		0			0
$481$	−2.04402	+	0.356497i	−0.0931994	+	0.0162549i
$482$		−	27.0931i		−	1.23406i
$483$	1.91760	−	3.32138i	0.0872538	−	0.151128i
$484$	−1.65906	+	2.87358i	−0.0754118	+	0.130617i
$485$		0			0
$486$			13.6886i			0.620929i
$487$	0.811758	+	1.40601i	0.0367842	+	0.0637122i	0.883831	−	0.467806i	$-0.154955\pi$
$487$	0.811758	+	1.40601i	0.0367842	+	0.0637122i	−0.847047	+	0.531518i	$0.821622\pi$
$488$	−6.25184	−	10.8285i	−0.283007	−	0.490183i
$489$		−	11.0247i		−	0.498555i
$490$		0			0
$491$	5.16033	−	8.93796i	0.232883	−	0.403364i	−0.725773	−	0.687935i	$-0.758518\pi$
$491$	5.16033	−	8.93796i	0.232883	−	0.403364i	0.958655	+	0.284570i	$0.0918509\pi$
$492$	1.26795	−	2.19615i	0.0571636	−	0.0990102i
$493$			35.4209i			1.59527i
$494$	−11.9844	+	10.0182i	−0.539203	+	0.450738i
$495$		0			0
$496$	3.60338	+	2.08041i	0.161796	+	0.0934132i
$497$	−7.47921	−	4.31812i	−0.335488	−	0.193694i
$498$	5.22223	−	3.01506i	0.234014	−	0.135108i
$499$		−	13.9807i		−	0.625860i	−0.949776	−	0.312930i	$-0.898689\pi$
$499$		−	13.9807i		−	0.625860i	0.949776	−	0.312930i	$-0.101311\pi$
$500$		0			0
$501$	11.2318	−	6.48467i	0.501799	−	0.289714i
$502$	1.50367			0.0671121
$503$	20.5983	−	11.8924i	0.918434	−	0.530258i	0.0352988	−	0.999377i	$-0.488762\pi$
$503$	20.5983	−	11.8924i	0.918434	−	0.530258i	0.883135	+	0.469119i	$0.155428\pi$
$504$	1.89980	−	3.29056i	0.0846240	−	0.146573i
$505$		0			0
$506$	−12.3043			−0.546991
$507$	−5.03758	+	5.95839i	−0.223727	+	0.264622i
$508$		−	16.1244i		−	0.715403i
$509$	22.2023	+	12.8185i	0.984102	+	0.568171i	0.903506	−	0.428575i	$-0.140984\pi$
$509$	22.2023	+	12.8185i	0.984102	+	0.568171i	0.0805958	+	0.996747i	$0.474318\pi$
$510$		0			0
$511$	−1.19721	−	2.07363i	−0.0529614	−	0.0917319i
$512$	−1.00000			−0.0441942
$513$	−7.33225	−	12.6998i	−0.323727	−	0.560711i
$514$	17.6191	−	10.1724i	0.777146	−	0.448685i
$515$		0			0
$516$	0.784767	+	1.35926i	0.0345474	+	0.0598379i
$517$	30.6478	+	17.6945i	1.34789	+	0.778204i
$518$	−0.414157	+	0.717340i	−0.0181970	+	0.0315181i
$519$	−2.39442			−0.105103
$520$		0			0
$521$	−8.53476			−0.373915			−0.186957	−	0.982368i	$-0.559863\pi$
$521$	−8.53476			−0.373915			−0.186957	+	0.982368i	$0.559863\pi$
$522$	−10.3807	+	17.9799i	−0.454352	+	0.786961i
$523$	10.9878	+	6.34383i	0.480464	+	0.277396i	0.720610	−	0.693341i	$-0.243862\pi$
$523$	10.9878	+	6.34383i	0.480464	+	0.277396i	−0.240146	+	0.970737i	$0.577195\pi$
$524$	9.88043	+	17.1134i	0.431629	+	0.747603i
$525$		0			0
$526$	14.8344	−	8.56466i	0.646811	−	0.373437i
$527$	9.36949	+	16.2284i	0.408141	+	0.706921i
$528$	1.66351			0.0723952
$529$	−1.64598	−	2.85092i	−0.0715644	−	0.123953i
$530$		0			0
$531$	−7.91930	−	4.57221i	−0.343668	−	0.198417i
$532$			6.23572i			0.270353i
$533$	−2.61742	−	15.0073i	−0.113373	−	0.650040i
$534$	3.57547			0.154726
$535$		0			0
$536$	−2.66449	+	4.61504i	−0.115089	+	0.199339i
$537$	−6.48687	+	3.74520i	−0.279929	+	0.161617i
$538$	19.3824			0.835635
$539$	−11.8291	+	6.82955i	−0.509517	+	0.294170i
$540$		0			0
$541$			42.0507i			1.80790i	0.427636	+	0.903951i	$0.359347\pi$
$541$			42.0507i			1.80790i	−0.427636	+	0.903951i	$0.640653\pi$
$542$	−15.9098	+	9.18555i	−0.683386	+	0.394553i
$543$	10.1004	+	5.83146i	0.433449	+	0.250252i
$544$	−3.90029	−	2.25184i	−0.167224	−	0.0965467i
$545$		0			0
$546$	0.535182	+	3.06854i	0.0229037	+	0.131321i
$547$		−	24.6297i		−	1.05309i	−0.850147	−	0.526545i	$-0.823487\pi$
$547$		−	24.6297i		−	1.05309i	0.850147	−	0.526545i	$-0.176513\pi$
$548$	8.63234	−	14.9517i	0.368755	−	0.638703i
$549$	16.5034	−	28.5847i	0.704347	−	1.21996i
$550$		0			0
$551$		−	34.0726i		−	1.45154i
$552$	−1.33225	−	2.30752i	−0.0567042	−	0.0982145i
$553$	9.16074	+	15.8669i	0.389554	+	0.674728i
$554$			27.2342i			1.15707i
$555$		0			0
$556$	1.47328	−	2.55180i	0.0624811	−	0.108221i
$557$	3.95244	−	6.84583i	0.167470	−	0.290067i	−0.770059	−	0.637972i	$-0.779773\pi$
$557$	3.95244	−	6.84583i	0.167470	−	0.290067i	0.937530	+	0.347905i	$0.113107\pi$
$558$			10.9836i			0.464973i
$559$	8.85402	+	3.24126i	0.374485	+	0.137091i
$560$		0			0
$561$	6.48819	+	3.74596i	0.273932	+	0.158155i
$562$	26.0514	+	15.0408i	1.09891	+	0.634456i
$563$	−11.4931	+	6.63553i	−0.484375	+	0.279654i	−0.722238	−	0.691645i	$-0.756886\pi$
$563$	−11.4931	+	6.63553i	−0.484375	+	0.279654i	0.237863	+	0.971299i	$0.423553\pi$
$564$			7.66351i			0.322692i
$565$		0			0
$566$	−22.0653	+	12.7394i	−0.927473	+	0.535477i
$567$	8.47454			0.355897
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	−21.1323	+	36.6022i	−0.885911	+	1.53444i	−0.0412443	+	0.999149i	$0.513132\pi$
$569$	−21.1323	+	36.6022i	−0.885911	+	1.53444i	−0.844666	+	0.535293i	$0.820201\pi$
$570$		0			0
$571$	1.64965			0.0690358			0.0345179	−	0.999404i	$-0.489010\pi$
$571$	1.64965			0.0690358			0.0345179	+	0.999404i	$0.489010\pi$
$572$	7.66719	−	6.40927i	0.320581	−	0.267985i
$573$			10.9965i			0.459384i
$574$	−5.26676	−	3.04076i	−0.219830	−	0.126919i
$575$		0			0
$576$	−1.31988	−	2.28610i	−0.0549951	−	0.0952543i
$577$	28.4651			1.18502			0.592508	−	0.805564i	$-0.298138\pi$
$577$	28.4651			1.18502			0.592508	+	0.805564i	$0.298138\pi$
$578$	−1.64153	−	2.84321i	−0.0682785	−	0.118262i
$579$	−2.46567	+	1.42355i	−0.102470	+	0.0591609i
$580$		0			0
$581$	−7.23063	−	12.5238i	−0.299977	−	0.519576i
$582$	−0.824551	−	0.476055i	−0.0341788	−	0.0197331i
$583$	13.2639	−	22.9738i	0.549335	−	0.951476i
$584$	−1.66351			−0.0688367
$585$		0			0
$586$	−16.5779			−0.684825
$587$	11.0848	−	19.1994i	0.457518	−	0.792445i	−0.541311	−	0.840822i	$-0.682072\pi$
$587$	11.0848	−	19.1994i	0.457518	−	0.792445i	0.998829	+	0.0483779i	$0.0154052\pi$
$588$	−2.56160	−	1.47894i	−0.105639	−	0.0609906i
$589$	−9.01285	−	15.6107i	−0.371368	−	0.643228i
$590$		0			0
$591$	−5.61398	+	3.24123i	−0.230928	+	0.133327i
$592$	0.287734	+	0.498370i	0.0118258	+	0.0204829i
$593$	−9.68683			−0.397791			−0.198895	−	0.980021i	$-0.563735\pi$
$593$	−9.68683			−0.397791			−0.198895	+	0.980021i	$0.563735\pi$
$594$	4.69092	+	8.12490i	0.192471	+	0.333369i
$595$		0			0
$596$	−6.11871	−	3.53264i	−0.250632	−	0.144702i
$597$		−	6.60656i		−	0.270388i
$598$	−15.0309	−	5.50248i	−0.614658	−	0.225013i
$599$	−8.33012			−0.340360			−0.170180	−	0.985413i	$-0.554435\pi$
$599$	−8.33012			−0.340360			−0.170180	+	0.985413i	$0.554435\pi$
$600$		0			0
$601$	6.10117	−	10.5675i	0.248872	−	0.431059i	−0.714341	−	0.699798i	$-0.753273\pi$
$601$	6.10117	−	10.5675i	0.248872	−	0.431059i	0.963213	+	0.268739i	$0.0866068\pi$
$602$	3.25973	−	1.88201i	0.132857	−	0.0767049i
$603$	−14.0673			−0.572864
$604$	−13.7115	+	7.91633i	−0.557912	+	0.322111i
$605$		0			0
$606$		−	8.25480i		−	0.335328i
$607$	8.52075	−	4.91946i	0.345847	−	0.199675i	−0.317008	−	0.948423i	$-0.602678\pi$
$607$	8.52075	−	4.91946i	0.345847	−	0.199675i	0.662854	+	0.748748i	$0.269345\pi$
$608$	3.75184	+	2.16612i	0.152157	+	0.0878479i
$609$	−5.88423	−	3.39726i	−0.238441	−	0.137664i
$610$		0			0
$611$	29.5263	+	35.3214i	1.19451	+	1.42895i
$612$		−	11.8886i		−	0.480570i
$613$	−7.60586	+	13.1737i	−0.307198	+	0.532082i	−0.977748	−	0.209782i	$-0.932725\pi$
$613$	−7.60586	+	13.1737i	−0.307198	+	0.532082i	0.670551	+	0.741864i	$0.266058\pi$
$614$	−8.13609	+	14.0921i	−0.328346	+	0.568712i
$615$		0			0
$616$		−	3.98940i		−	0.160737i
$617$	12.2357	+	21.1929i	0.492592	+	0.853194i	0.999964	−	0.00853345i	$-0.00271631\pi$
$617$	12.2357	+	21.1929i	0.492592	+	0.853194i	−0.507372	+	0.861727i	$0.669383\pi$
$618$	−1.72018	−	2.97943i	−0.0691956	−	0.119850i
$619$			42.4157i			1.70483i	0.522864	+	0.852416i	$0.324864\pi$
$619$			42.4157i			1.70483i	−0.522864	+	0.852416i	$0.675136\pi$
$620$		0			0
$621$	7.51356	−	13.0139i	0.301509	−	0.522228i
$622$	−8.05264	+	13.9476i	−0.322881	+	0.559247i
$623$		−	8.57459i		−	0.343534i
$624$	2.03215	+	0.743926i	0.0813511	+	0.0297809i
$625$		0			0
$626$	−8.84750	−	5.10811i	−0.353617	−	0.204161i
$627$	−6.24123	−	3.60338i	−0.249251	−	0.143905i
$628$	−10.9362	+	6.31401i	−0.436402	+	0.251957i
$629$			2.59172i			0.103339i
$630$		0			0
$631$	−0.0244657	+	0.0141253i	−0.000973964	+	0.000562318i	−0.500487	−	0.865744i	$-0.666846\pi$
$631$	−0.0244657	+	0.0141253i	−0.000973964	+	0.000562318i	0.499513	+	0.866306i	$0.333512\pi$
$632$	12.7288			0.506324
$633$	−13.6486	+	7.88002i	−0.542483	+	0.313203i
$634$	0.102184	−	0.176988i	0.00405825	−	0.00702909i
$635$		0			0
$636$	5.74461			0.227789
$637$	−17.5046	+	3.05298i	−0.693559	+	0.120963i
$638$			21.7985i			0.863010i
$639$	−13.7166	−	7.91930i	−0.542621	−	0.313282i
$640$		0			0
$641$	8.10465	+	14.0377i	0.320114	+	0.554454i	0.980511	−	0.196462i	$-0.0629453\pi$
$641$	8.10465	+	14.0377i	0.320114	+	0.554454i	−0.660397	+	0.750917i	$0.729612\pi$
$642$	2.80852			0.110843
$643$	9.10586	+	15.7718i	0.359100	+	0.621979i	0.987811	−	0.155660i	$-0.0497504\pi$
$643$	9.10586	+	15.7718i	0.359100	+	0.621979i	−0.628711	+	0.777639i	$0.716417\pi$
$644$	−5.53383	+	3.19496i	−0.218064	+	0.125899i
$645$		0			0
$646$	9.75551	+	16.8970i	0.383825	+	0.664805i
$647$	6.16852	+	3.56139i	0.242509	+	0.140013i	0.616330	−	0.787488i	$-0.288619\pi$
$647$	6.16852	+	3.56139i	0.242509	+	0.140013i	−0.373820	+	0.927501i	$0.621952\pi$
$648$	2.94383	−	5.09886i	0.115644	−	0.200302i
$649$	−9.60117			−0.376879
$650$		0			0
$651$	−3.59456			−0.140882
$652$	−9.18428	+	15.9076i	−0.359684	+	0.622991i
$653$	13.9178	+	8.03546i	0.544647	+	0.314452i	0.746960	−	0.664869i	$-0.231513\pi$
$653$	13.9178	+	8.03546i	0.544647	+	0.314452i	−0.202313	+	0.979321i	$0.564846\pi$
$654$	0.696720	+	1.20676i	0.0272439	+	0.0471879i
$655$		0			0
$656$	−3.65906	+	2.11256i	−0.142862	+	0.0824816i
$657$	−2.19564	−	3.80297i	−0.0856602	−	0.148368i
$658$	18.3784			0.716466
$659$	22.5988	+	39.1423i	0.880326	+	1.52477i	0.850979	+	0.525200i	$0.176010\pi$
$659$	22.5988	+	39.1423i	0.880326	+	1.52477i	0.0293473	+	0.999569i	$0.490657\pi$
$660$		0			0
$661$	−7.63354	−	4.40723i	−0.296910	−	0.171421i	0.344144	−	0.938917i	$-0.388169\pi$
$661$	−7.63354	−	4.40723i	−0.296910	−	0.171421i	−0.641054	+	0.767496i	$0.721503\pi$
$662$		−	19.0653i		−	0.740993i
$663$	6.25078	+	7.47759i	0.242760	+	0.290406i
$664$	−10.0469			−0.389896
$665$		0			0
$666$	−0.759550	+	1.31558i	−0.0294320	+	0.0509777i
$667$	30.2374	−	17.4576i	1.17080	−	0.675960i
$668$	−21.6085			−0.836059
$669$	11.5414	−	6.66344i	0.446217	−	0.257623i
$670$		0			0
$671$		−	34.6554i		−	1.33786i
$672$	0.748164	−	0.431953i	0.0288611	−	0.0166629i
$673$	35.8879	+	20.7199i	1.38338	+	0.798693i	0.992558	−	0.121775i	$-0.0388586\pi$
$673$	35.8879	+	20.7199i	1.38338	+	0.798693i	0.390819	+	0.920468i	$0.372192\pi$
$674$	−17.2001	−	9.93045i	−0.662521	−	0.382507i
$675$		0			0
$676$	12.2325	−	4.40078i	0.470479	−	0.169261i
$677$			18.8510i			0.724504i	0.932080	+	0.362252i	$0.117992\pi$
$677$			18.8510i			0.724504i	−0.932080	+	0.362252i	$0.882008\pi$
$678$	2.32164	−	4.02121i	0.0891622	−	0.154433i
$679$	−1.14166	+	1.97742i	−0.0438130	+	0.0758863i
$680$		0			0
$681$		−	1.24789i		−	0.0478193i
$682$	5.76611	+	9.98719i	0.220796	+	0.382429i
$683$	11.3332	+	19.6297i	0.433654	+	0.751110i	0.997185	−	0.0749846i	$-0.0238908\pi$
$683$	11.3332	+	19.6297i	0.433654	+	0.751110i	−0.563531	+	0.826095i	$0.690557\pi$
$684$			11.4361i			0.437271i
$685$		0			0
$686$	−8.58457	+	14.8689i	−0.327760	+	0.567698i
$687$	−1.40426	+	2.43225i	−0.0535758	+	0.0927960i
$688$		−	2.61504i		−	0.0996974i
$689$	26.4771	−	22.1331i	1.00870	−	0.843204i
$690$		0			0
$691$	27.5736	+	15.9196i	1.04895	+	0.605612i	0.922355	−	0.386343i	$-0.126262\pi$
$691$	27.5736	+	15.9196i	1.04895	+	0.605612i	0.126595	+	0.991954i	$0.459595\pi$
$692$	3.45492	+	1.99470i	0.131336	+	0.0758271i
$693$	9.12018	−	5.26554i	0.346447	−	0.200021i
$694$			17.0504i			0.647226i
$695$		0			0
$696$	−4.08805	+	2.36023i	−0.154957	+	0.0894645i
$697$	−19.0285			−0.720758
$698$	−18.3917	+	10.6185i	−0.696138	+	0.401915i
$699$	−0.183378	+	0.317620i	−0.00693599	+	0.0120135i
$700$		0			0
$701$	0.611060			0.0230794			0.0115397	−	0.999933i	$-0.496327\pi$
$701$	0.611060			0.0230794			0.0115397	+	0.999933i	$0.496327\pi$
$702$	2.09695	+	12.0232i	0.0791444	+	0.453785i
$703$		−	2.49307i		−	0.0940279i
$704$	−2.40029	−	1.38581i	−0.0904645	−	0.0522297i
$705$		0			0
$706$	8.00840	+	13.8710i	0.301400	+	0.522040i
$707$	−19.7965			−0.744522
$708$	−1.03957	−	1.80059i	−0.0390694	−	0.0676702i
$709$	−11.2274	+	6.48212i	−0.421653	+	0.243441i	−0.695784	−	0.718251i	$-0.744943\pi$
$709$	−11.2274	+	6.48212i	−0.421653	+	0.243441i	0.274131	+	0.961692i	$0.411610\pi$
$710$		0			0
$711$	16.8005	+	29.0993i	0.630068	+	1.09131i
$712$	−5.15906	−	2.97859i	−0.193344	−	0.111627i
$713$	9.23572	−	15.9967i	0.345881	−	0.599083i
$714$	3.89075			0.145608
$715$		0			0
$716$	12.4799			0.466397
$717$	7.69694	−	13.3315i	0.287447	−	0.497873i
$718$	−21.0000	−	12.1244i	−0.783713	−	0.452477i
$719$	−17.8616	−	30.9372i	−0.666126	−	1.15376i	−0.978979	−	0.203963i	$-0.934618\pi$
$719$	−17.8616	−	30.9372i	−0.666126	−	1.15376i	0.312853	−	0.949802i	$-0.398715\pi$
$720$		0			0
$721$	−7.14520	+	4.12528i	−0.266101	+	0.153634i
$722$	0.115820	+	0.200606i	0.00431038	+	0.00746580i
$723$	16.2612			0.604759
$724$	−9.71594	−	16.8285i	−0.361090	−	0.625426i
$725$		0			0
$726$	−1.72471	−	0.995761i	−0.0640099	−	0.0369562i
$727$			51.7313i			1.91861i	0.282375	+	0.959304i	$0.408878\pi$
$727$			51.7313i			1.91861i	−0.282375	+	0.959304i	$0.591122\pi$
$728$	1.78406	−	4.87345i	0.0661218	−	0.180622i
$729$	9.44711			0.349893
$730$		0			0
$731$	5.88863	−	10.1994i	0.217799	−	0.377239i
$732$	6.49922	−	3.75232i	0.240218	−	0.138690i
$733$	−26.4319			−0.976284			−0.488142	−	0.872764i	$-0.662325\pi$
$733$	−26.4319			−0.976284			−0.488142	+	0.872764i	$0.662325\pi$
$734$	−25.7822	+	14.8854i	−0.951639	+	0.549429i
$735$		0			0
$736$			4.43937i			0.163637i
$737$	−12.7911	+	7.38496i	−0.471167	+	0.272029i
$738$	−9.65906	−	5.57666i	−0.355555	−	0.205280i
$739$	23.7380	+	13.7051i	0.873215	+	0.504151i	0.868415	−	0.495837i	$-0.165139\pi$
$739$	23.7380	+	13.7051i	0.873215	+	0.504151i	0.00480000	+	0.999988i	$0.498472\pi$
$740$		0			0
$741$	−6.01285	−	7.19297i	−0.220888	−	0.264240i
$742$		−	13.7766i		−	0.505754i
$743$	21.0909	−	36.5306i	0.773751	−	1.34018i	−0.161742	−	0.986833i	$-0.551711\pi$
$743$	21.0909	−	36.5306i	0.773751	−	1.34018i	0.935494	−	0.353344i	$-0.114955\pi$
$744$	−1.24865	+	2.16273i	−0.0457779	+	0.0792896i
$745$		0			0
$746$		−	28.3858i		−	1.03928i
$747$	−13.2607	−	22.9683i	−0.485185	−	0.840365i
$748$	−6.24123	−	10.8101i	−0.228202	−	0.395258i
$749$		−	6.73531i		−	0.246103i
$750$		0			0
$751$	9.66351	−	16.7377i	0.352627	−	0.610767i	−0.634082	−	0.773266i	$-0.718622\pi$
$751$	9.66351	−	16.7377i	0.352627	−	0.610767i	0.986709	+	0.162498i	$0.0519552\pi$
$752$	6.38418	−	11.0577i	0.232807	−	0.403234i
$753$			0.902497i			0.0328888i
$754$	−9.74830	+	26.6290i	−0.355012	+	0.969771i
$755$		0			0
$756$	4.21947	+	2.43611i	0.153461	+	0.0886006i
$757$	−17.5825	−	10.1513i	−0.639048	−	0.368955i	0.145200	−	0.989402i	$-0.453618\pi$
$757$	−17.5825	−	10.1513i	−0.639048	−	0.368955i	−0.784248	+	0.620448i	$0.786951\pi$
$758$	24.6070	−	14.2069i	0.893768	−	0.516017i
$759$		−	7.38496i		−	0.268057i
$760$		0			0
$761$	−38.3386	+	22.1348i	−1.38977	+	0.802386i	−0.993289	−	0.115656i	$-0.963103\pi$
$761$	−38.3386	+	22.1348i	−1.38977	+	0.802386i	−0.396484	+	0.918042i	$0.629770\pi$
$762$	9.67777			0.350589
$763$	2.89401	−	1.67086i	0.104770	−	0.0604891i
$764$	9.16074	−	15.8669i	0.331424	−	0.574043i
$765$		0			0
$766$	−9.39726			−0.339537
$767$	−11.7288	−	4.29366i	−0.423502	−	0.155035i
$768$		−	0.600196i		−	0.0216577i
$769$	−3.23903	−	1.87005i	−0.116802	−	0.0674359i	0.440461	−	0.897772i	$-0.354815\pi$
$769$	−3.23903	−	1.87005i	−0.116802	−	0.0674359i	−0.557263	+	0.830336i	$0.688148\pi$
$770$		0			0
$771$	6.10543	+	10.5749i	0.219882	+	0.380846i
$772$	4.74363			0.170727
$773$	2.24045	+	3.88057i	0.0805834	+	0.139575i	0.903501	−	0.428587i	$-0.140988\pi$
$773$	2.24045	+	3.88057i	0.0805834	+	0.139575i	−0.822917	+	0.568161i	$0.807655\pi$
$774$	5.97825	−	3.45154i	0.214884	−	0.124063i
$775$		0			0
$776$	0.793166	+	1.37380i	0.0284730	+	0.0493167i
$777$	−0.430545	−	0.248575i	−0.0154457	−	0.00891758i
$778$	−5.82306	+	10.0858i	−0.208767	+	0.361595i
$779$	18.3043			0.655818
$780$		0			0
$781$	−16.6297			−0.595058
$782$	−9.99674	+	17.3149i	−0.357483	+	0.619178i
$783$	−23.0556	−	13.3112i	−0.823941	−	0.475702i
$784$	2.46410	+	4.26795i	0.0880036	+	0.152427i
$785$		0			0
$786$	−10.2714	+	5.93019i	−0.366368	+	0.211523i
$787$	16.0482	+	27.7963i	0.572056	+	0.990830i	0.996355	+	0.0853077i	$0.0271873\pi$
$787$	16.0482	+	27.7963i	0.572056	+	0.990830i	−0.424299	+	0.905522i	$0.639479\pi$
$788$	10.8006			0.384755
$789$	5.14047	+	8.90355i	0.183006	+	0.316975i
$790$		0			0
$791$	−9.64355	−	5.56771i	−0.342885	−	0.197965i
$792$		−	7.31643i		−	0.259978i
$793$	15.4979	−	42.3351i	0.550348	−	1.50336i
$794$	0.399804			0.0141885
$795$		0			0
$796$	−5.50367	+	9.53264i	−0.195072	+	0.337875i
$797$	19.2402	−	11.1083i	0.681522	−	0.393477i	−0.118906	−	0.992905i	$-0.537939\pi$
$797$	19.2402	−	11.1083i	0.681522	−	0.393477i	0.800428	+	0.599429i	$0.204605\pi$
$798$	−3.74265			−0.132488
$799$	49.8004	−	28.7522i	1.76181	−	1.01718i
$800$		0			0
$801$		−	15.7255i		−	0.555634i
$802$	7.36793	−	4.25388i	0.260171	−	0.150210i
$803$	−3.99292	−	2.30532i	−0.140907	−	0.0813528i
$804$	−2.76993	−	1.59922i	−0.0976877	−	0.0564000i
$805$		0			0
$806$	2.57759	+	14.7790i	0.0907918	+	0.520567i
$807$			11.6332i			0.409510i
$808$	−6.87676	+	11.9109i	−0.241924	+	0.419024i
$809$	−5.27410	+	9.13501i	−0.185427	+	0.321170i	−0.943720	−	0.330744i	$-0.892700\pi$
$809$	−5.27410	+	9.13501i	−0.185427	+	0.321170i	0.758293	+	0.651914i	$0.226034\pi$
$810$		0			0
$811$			41.6434i			1.46230i	0.682218	+	0.731149i	$0.261016\pi$
$811$			41.6434i			1.46230i	−0.682218	+	0.731149i	$0.738984\pi$
$812$	5.66025	+	9.80385i	0.198636	+	0.344048i
$813$	−5.51313	−	9.54902i	−0.193354	−	0.334899i
$814$			1.59498i			0.0559040i
$815$		0			0
$816$	1.35154	−	2.34094i	0.0473134	−	0.0819493i
$817$	−5.66449	+	9.81119i	−0.198176	+	0.343250i
$818$		−	14.0131i		−	0.489958i
$819$	13.4960	−	2.35382i	0.471587	−	0.0822493i
$820$		0			0
$821$	20.1160	+	11.6140i	0.702053	+	0.405331i	0.808112	−	0.589029i	$-0.200490\pi$
$821$	20.1160	+	11.6140i	0.702053	+	0.405331i	−0.106058	+	0.994360i	$0.533823\pi$
$822$	8.97392	+	5.18110i	0.313001	+	0.180711i
$823$	0.865033	−	0.499427i	0.0301531	−	0.0174089i	−0.484848	−	0.874599i	$-0.661125\pi$
$823$	0.865033	−	0.499427i	0.0301531	−	0.0174089i	0.515001	+	0.857190i	$0.327792\pi$
$824$			5.73205i			0.199685i
$825$		0			0
$826$	−4.31812	+	2.49307i	−0.150247	+	0.0867449i
$827$	−29.8030			−1.03635			−0.518175	−	0.855274i	$-0.673389\pi$
$827$	−29.8030			−1.03635			−0.518175	+	0.855274i	$0.673389\pi$
$828$	−10.1489	+	5.85945i	−0.352698	+	0.203630i
$829$	−11.8508	+	20.5261i	−0.411594	+	0.712902i	−0.995064	−	0.0992329i	$-0.968361\pi$
$829$	−11.8508	+	20.5261i	−0.411594	+	0.712902i	0.583470	+	0.812134i	$0.301694\pi$
$830$		0			0
$831$	−16.3458			−0.567030
$832$	−2.31246	−	2.76632i	−0.0801702	−	0.0959049i
$833$			22.1950i			0.769011i
$834$	1.53158	+	0.884259i	0.0530343	+	0.0306194i
$835$		0			0
$836$	6.00367	+	10.3987i	0.207641	+	0.359645i
$837$	−14.0842			−0.486822
$838$	12.0977	+	20.9539i	0.417909	+	0.723839i
$839$	21.2991	−	12.2971i	0.735327	−	0.424541i	−0.0850406	−	0.996377i	$-0.527102\pi$
$839$	21.2991	−	12.2971i	0.735327	−	0.424541i	0.820368	+	0.571836i	$0.193769\pi$
$840$		0			0
$841$	−16.4282	−	28.4545i	−0.566490	−	0.981189i
$842$	−30.8644	−	17.8196i	−1.06366	−	0.614104i
$843$	−9.02740	+	15.6359i	−0.310920	+	0.538530i
$844$	26.2582			0.903843
$845$		0			0
$846$	33.7055			1.15882
$847$	−2.38801	+	4.13615i	−0.0820529	+	0.142120i
$848$	−8.28893	−	4.78561i	−0.284643	−	0.164339i
$849$	−7.64613	−	13.2435i	−0.262414	−	0.454515i
$850$		0			0
$851$	2.21245	−	1.27736i	0.0758418	−	0.0437873i
$852$	−1.80059	−	3.11871i	−0.0616871	−	0.106845i
$853$	41.7449			1.42932			0.714659	−	0.699473i	$-0.246582\pi$
$853$	41.7449			1.42932			0.714659	+	0.699473i	$0.246582\pi$
$854$	−8.99873	−	15.5863i	−0.307930	−	0.533351i
$855$		0			0
$856$	−4.05242	−	2.33967i	−0.138509	−	0.0799682i
$857$		−	18.7543i		−	0.640636i	−0.947310	−	0.320318i	$-0.896210\pi$
$857$		−	18.7543i		−	0.640636i	0.947310	−	0.320318i	$-0.103790\pi$
$858$	3.84681	+	4.60181i	0.131328	+	0.157103i
$859$	−13.8357			−0.472066			−0.236033	−	0.971745i	$-0.575847\pi$
$859$	−13.8357			−0.472066			−0.236033	+	0.971745i	$0.575847\pi$
$860$		0			0
$861$	1.82505	−	3.16108i	0.0621976	−	0.107729i
$862$	4.29586	−	2.48022i	0.146318	−	0.0844765i
$863$	8.00891			0.272626			0.136313	−	0.990666i	$-0.456475\pi$
$863$	8.00891			0.272626			0.136313	+	0.990666i	$0.456475\pi$
$864$	2.93146	−	1.69248i	0.0997304	−	0.0575794i
$865$		0			0
$866$			4.21621i			0.143273i
$867$	1.70648	−	0.985237i	0.0579551	−	0.0334604i
$868$	5.18661	+	2.99449i	0.176045	+	0.101640i
$869$	30.5528	+	17.6397i	1.03643	+	0.598385i
$870$		0			0
$871$	−18.9282	+	3.30126i	−0.641358	+	0.111859i
$872$		−	2.32164i		−	0.0786208i
$873$	−2.09377	+	3.62652i	−0.0708635	+	0.122739i
$874$	9.61623	−	16.6558i	0.325274	−	0.563391i
$875$		0			0
$876$		−	0.998434i		−	0.0337340i
$877$	−18.7658	−	32.5033i	−0.633677	−	1.09756i	−0.986794	−	0.161981i	$-0.948212\pi$
$877$	−18.7658	−	32.5033i	−0.633677	−	1.09756i	0.353117	−	0.935579i	$-0.385122\pi$
$878$	−7.37500	−	12.7739i	−0.248894	−	0.431097i
$879$		−	9.94996i		−	0.335604i
$880$		0			0
$881$	6.05808	−	10.4929i	0.204102	−	0.353515i	−0.745744	−	0.666232i	$-0.767906\pi$
$881$	6.05808	−	10.4929i	0.204102	−	0.353515i	0.949846	+	0.312717i	$0.101239\pi$
$882$	−6.50465	+	11.2664i	−0.219023	+	0.379359i
$883$			44.4026i			1.49427i	0.664675	+	0.747133i	$0.268570\pi$
$883$			44.4026i			1.49427i	−0.664675	+	0.747133i	$0.731430\pi$
$884$	−2.78998	−	15.9967i	−0.0938373	−	0.538029i
$885$		0			0
$886$	−10.5979	−	6.11871i	−0.356044	−	0.205562i
$887$	−5.64153	−	3.25714i	−0.189424	−	0.109364i	0.402289	−	0.915513i	$-0.368215\pi$
$887$	−5.64153	−	3.25714i	−0.189424	−	0.109364i	−0.591713	+	0.806149i	$0.701548\pi$
$888$	−0.299119	+	0.172697i	−0.0100378	+	0.00579532i
$889$		−	23.2090i		−	0.778404i
$890$		0			0
$891$	14.1321	−	8.15917i	0.473443	−	0.273343i
$892$	−22.2042			−0.743452
$893$	−47.9048	+	27.6578i	−1.60307	+	0.925534i
$894$	2.12027	−	3.67242i	0.0709126	−	0.122824i
$895$		0			0
$896$	−1.43937			−0.0480861
$897$	3.30256	−	9.02147i	0.110269	−	0.301218i
$898$		−	19.0714i		−	0.636420i
$899$	−28.3401	−	16.3622i	−0.945197	−	0.545710i
$900$		0			0
$901$	−21.5528	−	37.3306i	−0.718029	−	1.24366i
$902$	−11.7104			−0.389915
$903$	1.12957	+	1.95648i	0.0375898	+	0.0651075i
$904$	−6.69982	+	3.86814i	−0.222833	+	0.128653i
$905$		0			0
$906$	−4.75135	−	8.22957i	−0.157853	−	0.273409i
$907$	5.14216	+	2.96883i	0.170743	+	0.0985784i	0.582936	−	0.812518i	$-0.301904\pi$
$907$	5.14216	+	2.96883i	0.170743	+	0.0985784i	−0.412193	+	0.911096i	$0.635237\pi$
$908$	−1.03957	+	1.80059i	−0.0344993	+	0.0597546i
$909$	−36.3061			−1.20420
$910$		0			0
$911$	48.7860			1.61635			0.808177	−	0.588940i	$-0.200455\pi$
$911$	48.7860			1.61635			0.808177	+	0.588940i	$0.200455\pi$
$912$	−1.30010	+	2.25184i	−0.0430505	+	0.0745657i
$913$	−24.1155	−	13.9231i	−0.798108	−	0.460788i
$914$	−8.05688	−	13.9549i	−0.266498	−	0.461588i
$915$		0			0
$916$	4.05242	−	2.33967i	0.133896	−	0.0773048i
$917$	14.2216	+	24.6326i	0.469640	+	0.813440i
$918$	15.2448			0.503152
$919$	−14.8564	−	25.7321i	−0.490068	−	0.848822i	0.509867	−	0.860253i	$-0.329695\pi$
$919$	−14.8564	−	25.7321i	−0.490068	−	0.848822i	−0.999935	+	0.0114312i	$0.996361\pi$
$920$		0			0
$921$	−8.45803	−	4.88325i	−0.278702	−	0.160909i
$922$		−	4.84466i		−	0.159550i
$923$	−20.3149	−	7.43683i	−0.668672	−	0.244786i
$924$	2.39442			0.0787706
$925$		0			0
$926$	4.11582	−	7.12881i	0.135254	−	0.234267i
$927$	−13.1041	+	7.56563i	−0.430394	+	0.248488i
$928$	7.86488			0.258177
$929$	−15.6012	+	9.00734i	−0.511858	+	0.295521i	−0.733597	−	0.679585i	$-0.762160\pi$
$929$	−15.6012	+	9.00734i	−0.511858	+	0.295521i	0.221739	+	0.975106i	$0.428827\pi$
$930$		0			0
$931$		−	21.3502i		−	0.699724i
$932$	0.529194	−	0.305530i	0.0173343	−	0.0100080i
$933$	−8.37128	−	4.83316i	−0.274063	−	0.158231i
$934$	29.0008	+	16.7436i	0.948936	+	0.547868i
$935$		0			0
$936$	3.27191	−	8.93774i	0.106946	−	0.292139i
$937$		−	28.9796i		−	0.946723i	−0.880868	−	0.473361i	$-0.843040\pi$
$937$		−	28.9796i		−	0.946723i	0.880868	−	0.473361i	$-0.156960\pi$
$938$	−3.83520	+	6.64276i	−0.125224	+	0.216894i
$939$	3.06586	−	5.31023i	0.100051	−	0.173293i
$940$		0			0
$941$			4.61504i			0.150446i	0.997167	+	0.0752230i	$0.0239669\pi$
$941$			4.61504i			0.150446i	−0.997167	+	0.0752230i	$0.976033\pi$
$942$	−3.78964	−	6.56386i	−0.123473	−	0.213862i
$943$	9.37844	+	16.2439i	0.305404	+	0.528975i
$944$			3.46410i			0.112747i
$945$		0			0
$946$	3.62395	−	6.27686i	0.117825	−	0.204078i
$947$	5.30031	−	9.18041i	0.172237	−	0.298323i	−0.766965	−	0.641689i	$-0.778234\pi$
$947$	5.30031	−	9.18041i	0.172237	−	0.298323i	0.939202	+	0.343366i	$0.111567\pi$
$948$			7.63977i			0.248128i
$949$	−3.84681	−	4.60181i	−0.124873	−	0.149381i
$950$		0			0
$951$	0.106227	+	0.0613304i	0.00344466	+	0.00198878i
$952$	−5.61398	−	3.24123i	−0.181950	−	0.105049i
$953$	−24.8905	+	14.3705i	−0.806283	+	0.465508i	−0.845663	−	0.533717i	$-0.820795\pi$
$953$	−24.8905	+	14.3705i	−0.806283	+	0.465508i	0.0393806	+	0.999224i	$0.487462\pi$
$954$		−	25.2658i		−	0.818010i
$955$		0			0
$956$	−22.2119	+	12.8240i	−0.718384	+	0.414759i
$957$	−13.0833			−0.422925
$958$	−6.97448	+	4.02672i	−0.225335	+	0.130097i
$959$	12.4252	−	21.5210i	0.401230	−	0.694950i
$960$		0			0
$961$	13.6876			0.441534
$962$	−0.713276	+	1.94842i	−0.0229969	+	0.0628197i
$963$		−	12.3523i		−	0.398049i
$964$	−23.4633	−	13.5466i	−0.755703	−	0.436305i
$965$		0			0
$966$	−1.91760	−	3.32138i	−0.0616978	−	0.106864i
$967$	−8.08648			−0.260044			−0.130022	−	0.991511i	$-0.541505\pi$
$967$	−8.08648			−0.260044			−0.130022	+	0.991511i	$0.541505\pi$
$968$	1.65906	+	2.87358i	0.0533242	+	0.0923603i
$969$	−10.1415	+	5.85521i	−0.325793	+	0.188097i
$970$		0			0
$971$	−0.302790	−	0.524448i	−0.00971701	−	0.0168304i	0.861126	−	0.508392i	$-0.169760\pi$
$971$	−0.302790	−	0.524448i	−0.00971701	−	0.0168304i	−0.870843	+	0.491561i	$0.836426\pi$
$972$	11.8547	+	6.84432i	0.380240	+	0.219532i
$973$	2.12061	−	3.67300i	0.0679835	−	0.117751i
$974$	1.62352			0.0520208
$975$		0			0
$976$	−12.5037			−0.400233
$977$	24.5216	−	42.4727i	0.784516	−	1.35882i	−0.144772	−	0.989465i	$-0.546245\pi$
$977$	24.5216	−	42.4727i	0.784516	−	1.35882i	0.929288	−	0.369356i	$-0.120422\pi$
$978$	−9.54769	−	5.51236i	−0.305302	−	0.176266i
$979$	−8.25551	−	14.2990i	−0.263847	−	0.456997i
$980$		0			0
$981$	5.30752	−	3.06430i	0.169456	−	0.0978355i
$982$	−5.16033	−	8.93796i	−0.164673	−	0.285222i
$983$	−30.7684			−0.981358			−0.490679	−	0.871340i	$-0.663251\pi$
$983$	−30.7684			−0.981358			−0.490679	+	0.871340i	$0.663251\pi$
$984$	−1.26795	−	2.19615i	−0.0404207	−	0.0700108i
$985$		0			0
$986$	30.6754	+	17.7104i	0.976902	+	0.564015i
$987$			11.0307i			0.351110i
$988$	2.68379	+	15.3879i	0.0853827	+	0.489553i
$989$	−11.6091			−0.369149
$990$		0			0
$991$	−7.74435	+	13.4136i	−0.246007	+	0.426097i	−0.962414	−	0.271585i	$-0.912452\pi$
$991$	−7.74435	+	13.4136i	−0.246007	+	0.426097i	0.716407	+	0.697683i	$0.245785\pi$
$992$	3.60338	−	2.08041i	0.114407	−	0.0660531i
$993$	11.4429			0.363129
$994$	−7.47921	+	4.31812i	−0.237226	+	0.136962i
$995$		0			0
$996$		−	6.03011i		−	0.191071i
$997$	6.77423	−	3.91111i	0.214542	−	0.123866i	−0.388878	−	0.921289i	$-0.627137\pi$
$997$	6.77423	−	3.91111i	0.214542	−	0.123866i	0.603421	+	0.797423i	$0.293804\pi$
$998$	−12.1076	−	6.99033i	−0.383260	−	0.221275i
$999$	−1.68696	−	0.973969i	−0.0533731	−	0.0308150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.n.e.199.3		8
5.2	odd	4		130.2.l.b.121.4	yes	8
5.3	odd	4		650.2.m.c.251.1		8
5.4	even	2		650.2.n.d.199.2		8
13.10	even	6		650.2.n.d.49.2		8
15.2	even	4		1170.2.bs.g.901.2		8
20.7	even	4		1040.2.da.d.641.2		8
65.2	even	12		1690.2.e.t.991.3		8
65.7	even	12		1690.2.a.u.1.2		4
65.12	odd	4		1690.2.l.j.1161.2		8
65.17	odd	12		1690.2.d.k.1351.6		8
65.22	odd	12		1690.2.d.k.1351.2		8
65.23	odd	12		650.2.m.c.101.1		8
65.32	even	12		1690.2.a.t.1.2		4
65.33	even	12		8450.2.a.ci.1.3		4
65.37	even	12		1690.2.e.s.991.3		8
65.42	odd	12		1690.2.l.j.361.2		8
65.47	even	4		1690.2.e.s.191.3		8
65.49	even	6	inner	650.2.n.e.49.3		8
65.57	even	4		1690.2.e.t.191.3		8
65.58	even	12		8450.2.a.cm.1.3		4
65.62	odd	12		130.2.l.b.101.4	✓	8
195.62	even	12		1170.2.bs.g.361.2		8
260.127	even	12		1040.2.da.d.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.4	✓	8	65.62	odd	12
130.2.l.b.121.4	yes	8	5.2	odd	4
650.2.m.c.101.1		8	65.23	odd	12
650.2.m.c.251.1		8	5.3	odd	4
650.2.n.d.49.2		8	13.10	even	6
650.2.n.d.199.2		8	5.4	even	2
650.2.n.e.49.3		8	65.49	even	6	inner
650.2.n.e.199.3		8	1.1	even	1	trivial
1040.2.da.d.641.2		8	20.7	even	4
1040.2.da.d.881.2		8	260.127	even	12
1170.2.bs.g.361.2		8	195.62	even	12
1170.2.bs.g.901.2		8	15.2	even	4
1690.2.a.t.1.2		4	65.32	even	12
1690.2.a.u.1.2		4	65.7	even	12
1690.2.d.k.1351.2		8	65.22	odd	12
1690.2.d.k.1351.6		8	65.17	odd	12
1690.2.e.s.191.3		8	65.47	even	4
1690.2.e.s.991.3		8	65.37	even	12
1690.2.e.t.191.3		8	65.57	even	4
1690.2.e.t.991.3		8	65.2	even	12
1690.2.l.j.361.2		8	65.42	odd	12
1690.2.l.j.1161.2		8	65.12	odd	4
8450.2.a.ci.1.3		4	65.33	even	12
8450.2.a.cm.1.3		4	65.58	even	12

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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.519785 + 0.300098i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.519785 - 0.300098i) q^{6} +(-0.719687 - 1.24653i) q^{7} -1.00000 q^{8} +(-1.31988 - 2.28610i) q^{9} +(-2.40029 - 1.38581i) q^{11} -0.600196i q^{12} +(-2.31246 - 2.76632i) q^{13} -1.43937 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.90029 + 2.25184i) q^{17} -2.63977 q^{18} +(3.75184 - 2.16612i) q^{19} -0.863906i q^{21} +(-2.40029 + 1.38581i) q^{22} +(3.84461 + 2.21969i) q^{23} +(-0.519785 - 0.300098i) q^{24} +(-3.55193 + 0.619491i) q^{26} -3.38496i q^{27} +(-0.719687 + 1.24653i) q^{28} +(3.93244 - 6.81119i) q^{29} -4.16082i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.831757 - 1.44065i) q^{33} +4.50367i q^{34} +(-1.31988 + 2.28610i) q^{36} +(0.287734 - 0.498370i) q^{37} -4.33225i q^{38} +(-0.371816 - 2.13186i) q^{39} +(3.65906 + 2.11256i) q^{41} +(-0.748164 - 0.431953i) q^{42} +(-2.26469 + 1.30752i) q^{43} +2.77162i q^{44} +(3.84461 - 2.21969i) q^{46} -12.7684 q^{47} +(-0.519785 + 0.300098i) q^{48} +(2.46410 - 4.26795i) q^{49} -2.70308 q^{51} +(-1.23947 + 3.38581i) q^{52} +9.57123i q^{53} +(-2.93146 - 1.69248i) q^{54} +(0.719687 + 1.24653i) q^{56} +2.60020 q^{57} +(-3.93244 - 6.81119i) q^{58} +(3.00000 - 1.73205i) q^{59} +(6.25184 + 10.8285i) q^{61} +(-3.60338 - 2.08041i) q^{62} +(-1.89980 + 3.29056i) q^{63} +1.00000 q^{64} -1.66351 q^{66} +(2.66449 - 4.61504i) q^{67} +(3.90029 + 2.25184i) q^{68} +(1.33225 + 2.30752i) q^{69} +(5.19615 - 3.00000i) q^{71} +(1.31988 + 2.28610i) q^{72} +1.66351 q^{73} +(-0.287734 - 0.498370i) q^{74} +(-3.75184 - 2.16612i) q^{76} +3.98940i q^{77} +(-2.03215 - 0.743926i) q^{78} -12.7288 q^{79} +(-2.94383 + 5.09886i) q^{81} +(3.65906 - 2.11256i) q^{82} +10.0469 q^{83} +(-0.748164 + 0.431953i) q^{84} +2.61504i q^{86} +(4.08805 - 2.36023i) q^{87} +(2.40029 + 1.38581i) q^{88} +(5.15906 + 2.97859i) q^{89} +(-1.78406 + 4.87345i) q^{91} -4.43937i q^{92} +(1.24865 - 2.16273i) q^{93} +(-6.38418 + 11.0577i) q^{94} +0.600196i q^{96} +(-0.793166 - 1.37380i) q^{97} +(-2.46410 - 4.26795i) q^{98} +7.31643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{6} - 8 q^{8} + 4 q^{9} - 6 q^{11} - 6 q^{13} - 4 q^{16} - 18 q^{17} + 8 q^{18} + 6 q^{19} - 6 q^{22} + 6 q^{24} + 4 q^{32} - 6 q^{33} + 4 q^{36} + 6 q^{37} + 40 q^{39}+ \cdots + 8 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^6 - 8 * q^8 + 4 * q^9 - 6 * q^11 - 6 * q^13 - 4 * q^16 - 18 * q^17 + 8 * q^18 + 6 * q^19 - 6 * q^22 + 6 * q^24 + 4 * q^32 - 6 * q^33 + 4 * q^36 + 6 * q^37 + 40 * q^39 + 12 * q^41 - 30 * q^42 + 36 * q^43 + 6 * q^48 - 8 * q^49 + 6 * q^52 - 36 * q^54 + 12 * q^57 + 24 * q^59 + 26 * q^61 + 6 * q^62 - 24 * q^63 + 8 * q^64 - 12 * q^66 - 24 * q^67 + 18 * q^68 - 12 * q^69 - 4 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^76 + 2 * q^78 - 20 * q^79 - 28 * q^81 + 12 * q^82 - 36 * q^83 - 30 * q^84 + 24 * q^87 + 6 * q^88 + 24 * q^89 - 66 * q^91 + 12 * q^93 + 18 * q^97 + 8 * q^98

Introduction

L-functions

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