LMFDB - Embedded newform 729.2.i.a.253.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(10,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			253.8
Character	$\chi$	$=$	729.253
Dual form			729.2.i.a.559.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.471802 - 1.22200i) q^{2} +(0.210408 - 0.190935i) q^{4} +(-2.73185 + 1.95261i) q^{5} +(-0.904700 + 0.701195i) q^{7} +(-2.67376 - 1.34281i) q^{8} +(3.67497 + 2.41707i) q^{10} +(1.27702 + 1.86194i) q^{11} +(3.87460 + 0.760946i) q^{13} +(1.28370 + 0.774715i) q^{14} +(-0.324415 + 3.33528i) q^{16} +(2.19451 - 5.08744i) q^{17} +(1.88028 - 2.52566i) q^{19} +(-0.201982 + 0.932451i) q^{20} +(1.67279 - 2.43898i) q^{22} +(7.04343 - 2.87756i) q^{23} +(2.03165 - 5.93771i) q^{25} +(-0.898168 - 5.09376i) q^{26} +(-0.0564734 + 0.320276i) q^{28} +(-0.583179 - 0.321784i) q^{29} +(0.350612 - 0.665620i) q^{31} +(-1.53607 + 0.427594i) q^{32} +(-7.25221 - 0.281419i) q^{34} +(1.10234 - 3.68208i) q^{35} +(1.97789 - 2.09644i) q^{37} +(-3.97346 - 1.10609i) q^{38} +(9.92628 - 1.55244i) q^{40} +(4.69930 + 5.82622i) q^{41} +(5.28700 - 5.18546i) q^{43} +(0.624206 + 0.147940i) q^{44} +(-6.83947 - 7.24942i) q^{46} +(3.29078 + 6.24739i) q^{47} +(-1.41928 + 5.50999i) q^{49} +(-8.21440 + 0.318756i) q^{50} +(0.960539 - 0.579688i) q^{52} +(6.20444 - 2.25823i) q^{53} +(-7.12427 - 2.59302i) q^{55} +(3.36052 - 0.659985i) q^{56} +(-0.118075 + 0.864461i) q^{58} +(0.594668 + 0.0462212i) q^{59} +(-0.742742 - 0.674002i) q^{61} +(-0.978805 - 0.114406i) q^{62} +(5.24942 + 7.05119i) q^{64} +(-12.0706 + 5.48678i) q^{65} +(-7.73503 + 4.26801i) q^{67} +(-0.509630 - 1.48945i) q^{68} +(-5.01958 + 0.390153i) q^{70} +(-0.162823 + 2.79556i) q^{71} +(-4.51045 + 2.96657i) q^{73} +(-3.49501 - 1.42787i) q^{74} +(-0.0866102 - 0.890431i) q^{76} +(-2.46091 - 0.789058i) q^{77} +(-2.87650 - 0.449876i) q^{79} +(-5.62624 - 9.74493i) q^{80} +(4.90249 - 8.49136i) q^{82} +(9.53920 - 11.8268i) q^{83} +(3.93872 + 18.1831i) q^{85} +(-8.83103 - 4.01420i) q^{86} +(-0.914207 - 6.69318i) q^{88} +(-0.856461 - 14.7049i) q^{89} +(-4.03892 + 2.02842i) q^{91} +(0.932569 - 1.95030i) q^{92} +(6.08169 - 6.96885i) q^{94} +(-0.205027 + 10.5712i) q^{95} +(-1.09556 - 0.783060i) q^{97} +(7.40281 - 0.865264i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{31}{81}\right)$

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 $

$2$	−0.471802	−	1.22200i	−0.333614	−	0.864082i	−0.993616	−	0.112818i	$-0.964012\pi$
$2$	−0.471802	−	1.22200i	−0.333614	−	0.864082i	0.660001	−	0.751264i	$-0.270556\pi$
$3$		0			0
$3$		0			0
$4$	0.210408	−	0.190935i	0.105204	−	0.0954676i
$5$	−2.73185	+	1.95261i	−1.22172	+	0.873233i	−0.994916	−	0.100708i	$-0.967889\pi$
$5$	−2.73185	+	1.95261i	−1.22172	+	0.873233i	−0.226803	+	0.973941i	$0.572828\pi$
$6$		0			0
$7$	−0.904700	+	0.701195i	−0.341944	+	0.265027i	−0.769069	−	0.639166i	$-0.779280\pi$
$7$	−0.904700	+	0.701195i	−0.341944	+	0.265027i	0.427124	+	0.904193i	$0.359527\pi$
$8$	−2.67376	−	1.34281i	−0.945316	−	0.474755i
$9$		0			0
$10$	3.67497	+	2.41707i	1.16213	+	0.764343i
$11$	1.27702	+	1.86194i	0.385036	+	0.561397i	0.967952	−	0.251136i	$-0.0808041\pi$
$11$	1.27702	+	1.86194i	0.385036	+	0.561397i	−0.582915	+	0.812533i	$0.698088\pi$
$12$		0			0
$13$	3.87460	+	0.760946i	1.07462	+	0.211049i	0.698563	−	0.715548i	$-0.253823\pi$
$13$	3.87460	+	0.760946i	1.07462	+	0.211049i	0.376057	+	0.926597i	$0.377280\pi$
$14$	1.28370	+	0.774715i	0.343083	+	0.207051i
$15$		0			0
$16$	−0.324415	+	3.33528i	−0.0811038	+	0.833820i
$17$	2.19451	−	5.08744i	0.532247	−	1.23389i	−0.413952	−	0.910299i	$-0.635852\pi$
$17$	2.19451	−	5.08744i	0.532247	−	1.23389i	0.946198	−	0.323587i	$-0.104889\pi$
$18$		0			0
$19$	1.88028	−	2.52566i	0.431366	−	0.579425i	−0.532293	−	0.846560i	$-0.678670\pi$
$19$	1.88028	−	2.52566i	0.431366	−	0.579425i	0.963659	+	0.267135i	$0.0860769\pi$
$20$	−0.201982	+	0.932451i	−0.0451645	+	0.208502i
$21$		0			0
$22$	1.67279	−	2.43898i	0.356640	−	0.519993i
$23$	7.04343	−	2.87756i	1.46866	−	0.600013i	0.504044	−	0.863678i	$-0.331845\pi$
$23$	7.04343	−	2.87756i	1.46866	−	0.600013i	0.964614	+	0.263666i	$0.0849315\pi$
$24$		0			0
$25$	2.03165	−	5.93771i	0.406329	−	1.18754i
$26$	−0.898168	−	5.09376i	−0.176145	−	0.998969i
$27$		0			0
$28$	−0.0564734	+	0.320276i	−0.0106725	+	0.0605265i
$29$	−0.583179	−	0.321784i	−0.108294	−	0.0597539i	0.428041	−	0.903759i	$-0.359204\pi$
$29$	−0.583179	−	0.321784i	−0.108294	−	0.0597539i	−0.536335	+	0.844005i	$0.680192\pi$
$30$		0			0
$31$	0.350612	−	0.665620i	0.0629717	−	0.119549i	−0.851254	−	0.524753i	$-0.824158\pi$
$31$	0.350612	−	0.665620i	0.0629717	−	0.119549i	0.914226	+	0.405204i	$0.132800\pi$
$32$	−1.53607	+	0.427594i	−0.271541	+	0.0755886i
$33$		0			0
$34$	−7.25221	−	0.281419i	−1.24374	−	0.0482629i
$35$	1.10234	−	3.68208i	0.186330	−	0.622386i
$36$		0			0
$37$	1.97789	−	2.09644i	0.325162	−	0.344652i	−0.544084	−	0.839031i	$-0.683123\pi$
$37$	1.97789	−	2.09644i	0.325162	−	0.344652i	0.869247	+	0.494379i	$0.164604\pi$
$38$	−3.97346	−	1.10609i	−0.644581	−	0.179431i
$39$		0			0
$40$	9.92628	−	1.55244i	1.56948	−	0.245463i
$41$	4.69930	+	5.82622i	0.733908	+	0.909903i	0.998516	−	0.0544529i	$-0.0173415\pi$
$41$	4.69930	+	5.82622i	0.733908	+	0.909903i	−0.264608	+	0.964356i	$0.585243\pi$
$42$		0			0
$43$	5.28700	−	5.18546i	0.806260	−	0.790775i	−0.174774	−	0.984609i	$-0.555919\pi$
$43$	5.28700	−	5.18546i	0.806260	−	0.790775i	0.981034	+	0.193834i	$0.0620923\pi$
$44$	0.624206	+	0.147940i	0.0941026	+	0.0223027i
$45$		0			0
$46$	−6.83947	−	7.24942i	−1.00843	−	1.06887i
$47$	3.29078	+	6.24739i	0.480009	+	0.911275i	0.998423	+	0.0561450i	$0.0178809\pi$
$47$	3.29078	+	6.24739i	0.480009	+	0.911275i	−0.518413	+	0.855130i	$0.673477\pi$
$48$		0			0
$49$	−1.41928	+	5.50999i	−0.202754	+	0.787141i
$50$	−8.21440	+	0.318756i	−1.16169	+	0.0450789i
$51$		0			0
$52$	0.960539	−	0.579688i	0.133203	−	0.0803883i
$53$	6.20444	−	2.25823i	0.852246	−	0.310192i	0.121290	−	0.992617i	$-0.461297\pi$
$53$	6.20444	−	2.25823i	0.852246	−	0.310192i	0.730956	+	0.682425i	$0.239075\pi$
$54$		0			0
$55$	−7.12427	−	2.59302i	−0.960637	−	0.349643i
$56$	3.36052	−	0.659985i	0.449068	−	0.0881941i
$57$		0			0
$58$	−0.118075	+	0.864461i	−0.0155040	+	0.113509i
$59$	0.594668	+	0.0462212i	0.0774191	+	0.00601749i	0.116144	−	0.993232i	$-0.462947\pi$
$59$	0.594668	+	0.0462212i	0.0774191	+	0.00601749i	−0.0387244	+	0.999250i	$0.512329\pi$
$60$		0			0
$61$	−0.742742	−	0.674002i	−0.0950983	−	0.0862971i	0.623072	−	0.782164i	$-0.285884\pi$
$61$	−0.742742	−	0.674002i	−0.0950983	−	0.0862971i	−0.718170	+	0.695867i	$0.755020\pi$
$62$	−0.978805	−	0.114406i	−0.124308	−	0.0145296i
$63$		0			0
$64$	5.24942	+	7.05119i	0.656177	+	0.881399i
$65$	−12.0706	+	5.48678i	−1.49718	+	0.680551i
$66$		0			0
$67$	−7.73503	+	4.26801i	−0.944984	+	0.521420i	−0.879221	−	0.476415i	$-0.841936\pi$
$67$	−7.73503	+	4.26801i	−0.944984	+	0.521420i	−0.0657637	+	0.997835i	$0.520948\pi$
$68$	−0.509630	−	1.48945i	−0.0618017	−	0.180622i
$69$		0			0
$70$	−5.01958	+	0.390153i	−0.599955	+	0.0466322i
$71$	−0.162823	+	2.79556i	−0.0193235	+	0.331773i	0.974767	+	0.223223i	$0.0716577\pi$
$71$	−0.162823	+	2.79556i	−0.0193235	+	0.331773i	−0.994091	+	0.108550i	$0.965379\pi$
$72$		0			0
$73$	−4.51045	+	2.96657i	−0.527909	+	0.347211i	−0.785319	−	0.619091i	$-0.787501\pi$
$73$	−4.51045	+	2.96657i	−0.527909	+	0.347211i	0.257411	+	0.966302i	$0.417131\pi$
$74$	−3.49501	−	1.42787i	−0.406286	−	0.165986i
$75$		0			0
$76$	−0.0866102	−	0.890431i	−0.00993487	−	0.102139i
$77$	−2.46091	−	0.789058i	−0.280446	−	0.0899215i
$78$		0			0
$79$	−2.87650	−	0.449876i	−0.323631	−	0.0506150i	−0.00938340	−	0.999956i	$-0.502987\pi$
$79$	−2.87650	−	0.449876i	−0.323631	−	0.0506150i	−0.314248	+	0.949341i	$0.601752\pi$
$80$	−5.62624	−	9.74493i	−0.629032	−	1.08952i
$81$		0			0
$82$	4.90249	−	8.49136i	0.541389	−	0.937713i
$83$	9.53920	−	11.8268i	1.04706	−	1.29816i	0.0939385	−	0.995578i	$-0.470054\pi$
$83$	9.53920	−	11.8268i	1.04706	−	1.29816i	0.953125	−	0.302577i	$-0.0978470\pi$
$84$		0			0
$85$	3.93872	+	18.1831i	0.427214	+	1.97224i
$86$	−8.83103	−	4.01420i	−0.952274	−	0.432862i
$87$		0			0
$88$	−0.914207	−	6.69318i	−0.0974548	−	0.713495i
$89$	−0.856461	−	14.7049i	−0.0907846	−	1.55871i	−0.669270	−	0.743019i	$-0.733393\pi$
$89$	−0.856461	−	14.7049i	−0.0907846	−	1.55871i	0.578485	−	0.815693i	$-0.303644\pi$
$90$		0			0
$91$	−4.03892	+	2.02842i	−0.423394	+	0.212636i
$92$	0.932569	−	1.95030i	0.0972270	−	0.203333i
$93$		0			0
$94$	6.08169	−	6.96885i	0.627279	−	0.718782i
$95$	−0.205027	+	10.5712i	−0.0210354	+	1.08458i
$96$		0			0
$97$	−1.09556	−	0.783060i	−0.111237	−	0.0795077i	0.524513	−	0.851403i	$-0.324247\pi$
$97$	−1.09556	−	0.783060i	−0.111237	−	0.0795077i	−0.635750	+	0.771895i	$0.719309\pi$
$98$	7.40281	−	0.865264i	0.747796	−	0.0874049i
$99$		0			0
$100$	−0.706243	−	1.63726i	−0.0706243	−	0.163726i
$101$	18.9733	−	6.08353i	1.88791	−	0.605334i	0.903746	−	0.428068i	$-0.140806\pi$
$101$	18.9733	−	6.08353i	1.88791	−	0.605334i	0.984163	−	0.177265i	$-0.0567251\pi$
$102$		0			0
$103$	3.67806	+	7.69201i	0.362410	+	0.757916i	0.999922	−	0.0125247i	$-0.00398683\pi$
$103$	3.67806	+	7.69201i	0.362410	+	0.757916i	−0.637512	+	0.770441i	$0.720036\pi$
$104$	−9.33792	−	7.23744i	−0.915659	−	0.709689i
$105$		0			0
$106$	−5.68682	−	6.51637i	−0.552353	−	0.632926i
$107$	−15.6188	+	13.1058i	−1.50993	+	1.26698i	−0.646040	+	0.763304i	$0.723576\pi$
$107$	−15.6188	+	13.1058i	−1.50993	+	1.26698i	−0.863891	+	0.503678i	$0.831980\pi$
$108$		0			0
$109$	−15.2816	−	12.8228i	−1.46371	−	1.22820i	−0.921740	−	0.387808i	$-0.873232\pi$
$109$	−15.2816	−	12.8228i	−1.46371	−	1.22820i	−0.541974	−	0.840395i	$-0.682323\pi$
$110$	0.192577	+	9.92923i	0.0183615	+	0.946715i
$111$		0			0
$112$	−2.04518	−	3.24490i	−0.193252	−	0.306615i
$113$	10.2103	+	10.0142i	0.960504	+	0.942056i	0.998361	−	0.0572275i	$-0.0182260\pi$
$113$	10.2103	+	10.0142i	0.960504	+	0.942056i	−0.0378571	+	0.999283i	$0.512053\pi$
$114$		0			0
$115$	−13.6228	+	21.6141i	−1.27034	+	2.01553i
$116$	−0.184146	+	0.0436433i	−0.0170975	+	0.00405218i
$117$		0			0
$118$	−0.224083	−	0.748489i	−0.0206285	−	0.0689040i
$119$	1.58192	+	6.14139i	0.145014	+	0.562980i
$120$		0			0
$121$	2.12591	−	5.50624i	0.193264	−	0.500567i
$122$	−0.473202	+	1.22562i	−0.0428417	+	0.110963i
$123$		0			0
$124$	−0.0533187	−	0.206996i	−0.00478816	−	0.0185888i
$125$	1.22855	+	4.10364i	0.109885	+	0.367041i
$126$		0			0
$127$	20.8220	−	4.93491i	1.84766	−	0.437903i	0.851414	−	0.524495i	$-0.175746\pi$
$127$	20.8220	−	4.93491i	1.84766	−	0.437903i	0.996244	+	0.0865921i	$0.0275977\pi$
$128$	4.43949	−	7.04373i	0.392399	−	0.622584i
$129$		0			0
$130$	12.3998	+	12.1616i	1.08753	+	1.06664i
$131$	−10.1450	−	16.0961i	−0.886369	−	1.40632i	−0.913566	−	0.406691i	$-0.866683\pi$
$131$	−10.1450	−	16.0961i	−0.886369	−	1.40632i	0.0271964	−	0.999630i	$-0.491342\pi$
$132$		0			0
$133$	0.0698880	+	3.60341i	0.00606006	+	0.312455i
$134$	8.86489	+	7.43853i	0.765810	+	0.642591i
$135$		0			0
$136$	−12.6991	+	10.6558i	−1.08893	+	0.913725i
$137$	6.86122	+	7.86209i	0.586194	+	0.671704i	0.967537	−	0.252730i	$-0.0813284\pi$
$137$	6.86122	+	7.86209i	0.586194	+	0.671704i	−0.381343	+	0.924434i	$0.624538\pi$
$138$		0			0
$139$	0.325570	+	0.252336i	0.0276145	+	0.0214028i	0.626314	−	0.779571i	$-0.284563\pi$
$139$	0.325570	+	0.252336i	0.0276145	+	0.0214028i	−0.598700	+	0.800973i	$0.704316\pi$
$140$	−0.471097	−	0.985217i	−0.0398150	−	0.0832660i
$141$		0			0
$142$	3.49299	−	1.11998i	0.293125	−	0.0939869i
$143$	3.53111	+	8.18602i	0.295286	+	0.684550i
$144$		0			0
$145$	2.22147	−	0.259653i	0.184483	−	0.0215630i
$146$	5.75318	+	4.11213i	0.476137	+	0.340322i
$147$		0			0
$148$	0.0158797	−	0.818755i	0.00130531	−	0.0673013i
$149$	−12.7458	+	14.6050i	−1.04417	+	1.19649i	−0.0640813	+	0.997945i	$0.520412\pi$
$149$	−12.7458	+	14.6050i	−1.04417	+	1.19649i	−0.980092	+	0.198545i	$0.936378\pi$
$150$		0			0
$151$	−3.11757	+	6.51985i	−0.253704	+	0.530578i	−0.989133	−	0.147025i	$-0.953030\pi$
$151$	−3.11757	+	6.51985i	−0.253704	+	0.530578i	0.735428	+	0.677602i	$0.236981\pi$
$152$	−8.41889	+	4.22813i	−0.682862	+	0.342946i
$153$		0			0
$154$	0.196833	+	3.37950i	0.0158613	+	0.272328i
$155$	0.341877	+	2.50298i	0.0274602	+	0.201044i
$156$		0			0
$157$	16.2322	+	7.37844i	1.29547	+	0.588864i	0.938509	−	0.345255i	$-0.112208\pi$
$157$	16.2322	+	7.37844i	1.29547	+	0.588864i	0.356962	+	0.934119i	$0.383813\pi$
$158$	0.807389	+	3.72732i	0.0642324	+	0.296530i
$159$		0			0
$160$	3.36138	−	4.16746i	0.265740	−	0.329466i
$161$	−4.35446	+	7.54215i	−0.343180	+	0.594405i
$162$		0			0
$163$	−1.09406	−	1.89497i	−0.0856937	−	0.148426i	0.819993	−	0.572374i	$-0.193977\pi$
$163$	−1.09406	−	1.89497i	−0.0856937	−	0.148426i	−0.905687	+	0.423948i	$0.860644\pi$
$164$	2.10120	+	0.328622i	0.164076	+	0.0256611i
$165$		0			0
$166$	−18.9529	−	6.07699i	−1.47103	−	0.471666i
$167$	0.579933	+	5.96224i	0.0448766	+	0.461372i	0.990639	+	0.136511i	$0.0435890\pi$
$167$	0.579933	+	5.96224i	0.0448766	+	0.461372i	−0.945762	+	0.324861i	$0.894683\pi$
$168$		0			0
$169$	2.39906	+	0.980123i	0.184543	+	0.0753941i
$170$	20.3614	−	13.3919i	1.56165	−	1.02711i
$171$		0			0
$172$	0.122342	−	2.10054i	0.00932852	−	0.160165i
$173$	−3.22726	+	0.250842i	−0.245364	+	0.0190712i	−0.199585	−	0.979880i	$-0.563960\pi$
$173$	−3.22726	+	0.250842i	−0.245364	+	0.0190712i	−0.0457785	+	0.998952i	$0.514577\pi$
$174$		0			0
$175$	2.32547	+	6.79643i	0.175789	+	0.513762i
$176$	−6.62438	+	3.65518i	−0.499332	+	0.275520i
$177$		0			0
$178$	−17.5652	+	7.98437i	−1.31657	+	0.598454i
$179$	−8.55852	−	11.4961i	−0.639694	−	0.859258i	0.357516	−	0.933907i	$-0.383624\pi$
$179$	−8.55852	−	11.4961i	−0.639694	−	0.859258i	−0.997210	+	0.0746488i	$0.976216\pi$
$180$		0			0
$181$	7.11445	+	0.831560i	0.528813	+	0.0618094i	0.376310	−	0.926494i	$-0.377193\pi$
$181$	7.11445	+	0.831560i	0.528813	+	0.0618094i	0.152503	+	0.988303i	$0.451267\pi$
$182$	4.38430	+	3.97854i	0.324986	+	0.294909i
$183$		0			0
$184$	−22.6964	−	1.76411i	−1.67320	−	0.130052i
$185$	−1.30977	+	9.58918i	−0.0962958	+	0.705010i
$186$		0			0
$187$	12.2750	−	2.41072i	0.897634	−	0.176290i
$188$	1.88525	+	0.686176i	0.137496	+	0.0500445i
$189$		0			0
$190$	13.0147	−	4.73695i	0.944183	−	0.343654i
$191$	−6.80963	+	4.10963i	−0.492727	+	0.297362i	−0.741209	−	0.671274i	$-0.765747\pi$
$191$	−6.80963	+	4.10963i	−0.492727	+	0.297362i	0.248482	+	0.968637i	$0.420068\pi$
$192$		0			0
$193$	9.45850	−	0.367033i	0.680838	−	0.0264196i	0.303963	−	0.952684i	$-0.401690\pi$
$193$	9.45850	−	0.367033i	0.680838	−	0.0264196i	0.376875	+	0.926264i	$0.376999\pi$
$194$	−0.440010	+	1.70822i	−0.0315909	+	0.122643i
$195$		0			0
$196$	0.753422	+	1.43034i	0.0538159	+	0.102167i
$197$	−5.22530	−	5.53849i	−0.372287	−	0.394601i	0.513960	−	0.857814i	$-0.328178\pi$
$197$	−5.22530	−	5.53849i	−0.372287	−	0.394601i	−0.886247	+	0.463213i	$0.846697\pi$
$198$		0			0
$199$	24.8429	+	5.88788i	1.76107	+	0.417381i	0.978677	−	0.205405i	$-0.0658512\pi$
$199$	24.8429	+	5.88788i	1.76107	+	0.417381i	0.782392	+	0.622786i	$0.213999\pi$
$200$	−13.4054	+	13.1479i	−0.947902	+	0.929695i
$201$		0			0
$202$	−16.3857	−	20.3150i	−1.15289	−	1.42936i
$203$	0.753235	−	0.117804i	0.0528668	−	0.00826821i
$204$		0			0
$205$	−24.2141	−	6.74046i	−1.69119	−	0.470774i
$206$	7.66430	−	8.12368i	0.533997	−	0.566004i
$207$		0			0
$208$	−3.79495	+	12.6760i	−0.263132	+	0.878923i
$209$	7.10379	+	0.275659i	0.491379	+	0.0190678i
$210$		0			0
$211$	−19.6005	+	5.45617i	−1.34935	+	0.375618i	−0.866103	−	0.499865i	$-0.833383\pi$
$211$	−19.6005	+	5.45617i	−1.34935	+	0.375618i	−0.483249	+	0.875483i	$0.660544\pi$
$212$	0.874289	−	1.65980i	0.0600464	−	0.113995i
$213$		0			0
$214$	23.3842	+	12.9029i	1.59851	+	0.882021i
$215$	−4.31813	+	24.4893i	−0.294494	+	1.67016i
$216$		0			0
$217$	0.149531	+	0.848034i	0.0101508	+	0.0575683i
$218$	−8.45954	+	24.7239i	−0.572952	+	1.67452i
$219$		0			0
$220$	−1.99410	+	0.814681i	−0.134443	+	0.0549258i
$221$	12.3741	−	18.0419i	0.832373	−	1.21363i
$222$		0			0
$223$	−2.61577	+	12.0757i	−0.175165	+	0.808651i	0.802194	+	0.597063i	$0.203666\pi$
$223$	−2.61577	+	12.0757i	−0.175165	+	0.808651i	−0.977359	+	0.211588i	$0.932137\pi$
$224$	1.08985	−	1.46393i	0.0728189	−	0.0978127i
$225$		0			0
$226$	7.42007	−	17.2017i	0.493576	−	1.14424i
$227$	0.342563	−	3.52185i	0.0227367	−	0.233754i	−0.977048	−	0.213018i	$-0.931671\pi$
$227$	0.342563	−	3.52185i	0.0227367	−	0.233754i	0.999785	−	0.0207358i	$-0.00660088\pi$
$228$		0			0
$229$	−16.2460	−	9.80453i	−1.07357	−	0.647902i	−0.134249	−	0.990948i	$-0.542862\pi$
$229$	−16.2460	−	9.80453i	−1.07357	−	0.647902i	−0.939319	+	0.343046i	$0.888541\pi$
$230$	32.8397	+	6.44950i	2.16538	+	0.425268i
$231$		0			0
$232$	1.12718	+	1.64347i	0.0740031	+	0.107899i
$233$	6.63043	+	4.36090i	0.434374	+	0.285692i	0.747805	−	0.663919i	$-0.231108\pi$
$233$	6.63043	+	4.36090i	0.434374	+	0.285692i	−0.313431	+	0.949611i	$0.601478\pi$
$234$		0			0
$235$	−21.1886	−	10.6413i	−1.38219	−	0.694163i
$236$	0.133948	−	0.103818i	0.00871929	−	0.00675796i
$237$		0			0
$238$	6.75841	−	4.83062i	0.438082	−	0.313122i
$239$	−10.5999	+	9.61887i	−0.685649	+	0.622193i	−0.938487	−	0.345316i	$-0.887772\pi$
$239$	−10.5999	+	9.61887i	−0.685649	+	0.622193i	0.252838	+	0.967509i	$0.418636\pi$
$240$		0			0
$241$	0.599954	+	1.55392i	0.0386464	+	0.100097i	0.950863	−	0.309611i	$-0.100199\pi$
$241$	0.599954	+	1.55392i	0.0386464	+	0.100097i	−0.912217	+	0.409707i	$0.865631\pi$
$242$	−7.73161			−0.497007
$243$		0			0
$244$	−0.284970			−0.0182433
$245$	−6.88158	−	17.8237i	−0.439648	−	1.13872i
$246$		0			0
$247$	9.20722	−	8.35511i	0.585842	−	0.531623i
$248$	−1.83125	+	1.30890i	−0.116285	+	0.0831153i
$249$		0			0
$250$	4.43501	−	3.43739i	0.280495	−	0.217400i
$251$	−3.71242	−	1.86445i	−0.234326	−	0.117683i	0.327762	−	0.944760i	$-0.393705\pi$
$251$	−3.71242	−	1.86445i	−0.234326	−	0.117683i	−0.562088	+	0.827077i	$0.690002\pi$
$252$		0			0
$253$	14.3525	+	9.43977i	0.902332	+	0.593473i
$254$	−15.8543	−	23.1162i	−0.994789	−	1.45044i
$255$		0			0
$256$	6.54978	+	1.28633i	0.409361	+	0.0803959i
$257$	−15.6094	−	9.42031i	−0.973686	−	0.587623i	−0.0618102	−	0.998088i	$-0.519687\pi$
$257$	−15.6094	−	9.42031i	−0.973686	−	0.587623i	−0.911876	+	0.410465i	$0.865366\pi$
$258$		0			0
$259$	−0.319382	+	3.28353i	−0.0198454	+	0.204029i
$260$	−1.49214	+	3.45917i	−0.0925387	+	0.214529i
$261$		0			0
$262$	−14.8829	+	19.9913i	−0.919472	+	1.23506i
$263$	1.25775	−	5.80641i	0.0775561	−	0.358039i	−0.922020	−	0.387141i	$-0.873462\pi$
$263$	1.25775	−	5.80641i	0.0775561	−	0.358039i	0.999576	+	0.0291026i	$0.00926496\pi$
$264$		0			0
$265$	−12.5401	+	18.2840i	−0.770335	+	1.12318i
$266$	4.37038	−	1.78550i	0.267965	−	0.109476i
$267$		0			0
$268$	−0.812600	+	2.37491i	−0.0496375	+	0.145071i
$269$	4.80841	+	27.2699i	0.293174	+	1.66267i	0.674532	+	0.738246i	$0.264345\pi$
$269$	4.80841	+	27.2699i	0.293174	+	1.66267i	−0.381358	+	0.924427i	$0.624543\pi$
$270$		0			0
$271$	2.58462	−	14.6581i	0.157004	−	0.890417i	−0.799926	−	0.600099i	$-0.795128\pi$
$271$	2.58462	−	14.6581i	0.157004	−	0.890417i	0.956930	−	0.290318i	$-0.0937610\pi$
$272$	16.2561	+	8.96974i	0.985671	+	0.543870i
$273$		0			0
$274$	6.37031	−	12.0937i	0.384845	−	0.730610i
$275$	13.6501	−	3.79978i	0.823134	−	0.229135i
$276$		0			0
$277$	−3.93124	−	0.152550i	−0.236206	−	0.00916585i	−0.0795992	−	0.996827i	$-0.525364\pi$
$277$	−3.93124	−	0.152550i	−0.236206	−	0.00916585i	−0.156606	+	0.987661i	$0.550055\pi$
$278$	0.154749	−	0.516898i	0.00928123	−	0.0310015i
$279$		0			0
$280$	−7.89174	+	8.36475i	−0.471622	+	0.499890i
$281$	1.59559	+	0.444162i	0.0951847	+	0.0264965i	0.315437	−	0.948946i	$-0.397849\pi$
$281$	1.59559	+	0.444162i	0.0951847	+	0.0264965i	−0.220253	+	0.975443i	$0.570688\pi$
$282$		0			0
$283$	−0.872891	+	0.136518i	−0.0518880	+	0.00811513i	−0.180410	−	0.983592i	$-0.557742\pi$
$283$	−0.872891	+	0.136518i	−0.0518880	+	0.00811513i	0.128522	+	0.991707i	$0.458977\pi$
$284$	0.499513	+	0.619298i	0.0296406	+	0.0367486i
$285$		0			0
$286$	8.33732	−	8.17718i	0.492996	−	0.483527i
$287$	−8.33678	−	1.97585i	−0.492105	−	0.116631i
$288$		0			0
$289$	−9.40010	−	9.96352i	−0.552947	−	0.586090i
$290$	−1.36539	−	2.59213i	−0.0801785	−	0.152215i
$291$		0			0
$292$	−0.382613	+	1.48540i	−0.0223907	+	0.0869262i
$293$	27.5316	−	1.06835i	1.60841	−	0.0624137i	0.781191	−	0.624292i	$-0.214613\pi$
$293$	27.5316	−	1.06835i	1.60841	−	0.0624137i	0.827220	+	0.561878i	$0.189921\pi$
$294$		0			0
$295$	−1.71479	+	1.03488i	−0.0998392	+	0.0602532i
$296$	−8.10350	+	2.94943i	−0.471006	+	0.171432i
$297$		0			0
$298$	23.8608	+	8.68461i	1.38222	+	0.503086i
$299$	29.4801	−	5.78971i	1.70488	−	0.334828i
$300$		0			0
$301$	−1.14713	+	8.39850i	−0.0661197	+	0.484082i
$302$	9.43811	+	0.733588i	0.543102	+	0.0422133i
$303$		0			0
$304$	7.81378	+	7.09062i	0.448151	+	0.406675i
$305$	3.34512	+	0.390988i	0.191541	+	0.0223879i
$306$		0			0
$307$	−11.8742	−	15.9498i	−0.677697	−	0.910305i	0.321635	−	0.946864i	$-0.395768\pi$
$307$	−11.8742	−	15.9498i	−0.677697	−	0.910305i	−0.999331	+	0.0365589i	$0.988360\pi$
$308$	−0.668454	+	0.303850i	−0.0380887	+	0.0173134i
$309$		0			0
$310$	2.89734	−	1.59868i	0.164558	−	0.0907991i
$311$	−3.13152	−	9.15222i	−0.177572	−	0.518975i	0.821083	−	0.570808i	$-0.193370\pi$
$311$	−3.13152	−	9.15222i	−0.177572	−	0.518975i	−0.998656	+	0.0518335i	$0.983493\pi$
$312$		0			0
$313$	5.92294	−	0.460367i	0.334784	−	0.0260215i	0.0909997	−	0.995851i	$-0.470994\pi$
$313$	5.92294	−	0.460367i	0.334784	−	0.0260215i	0.243785	+	0.969829i	$0.421611\pi$
$314$	1.35805	−	23.3169i	0.0766393	−	1.31585i
$315$		0			0
$316$	−0.691136	+	0.454567i	−0.0388794	+	0.0255714i
$317$	−3.68516	−	1.50555i	−0.206979	−	0.0845604i	0.272339	−	0.962201i	$-0.412203\pi$
$317$	−3.68516	−	1.50555i	−0.206979	−	0.0845604i	−0.479319	+	0.877641i	$0.659116\pi$
$318$		0			0
$319$	−0.145588	−	1.49677i	−0.00815134	−	0.0838031i
$320$	−28.1088	−	9.01273i	−1.57133	−	0.503827i
$321$		0			0
$322$	11.2709	+	1.76274i	0.628104	+	0.0982337i
$323$	−8.72284	−	15.1084i	−0.485352	−	0.840654i
$324$		0			0
$325$	12.3901	−	21.4603i	0.687279	−	1.19040i
$326$	−1.79947	+	2.23099i	−0.0996635	+	0.123563i
$327$		0			0
$328$	−4.74128	−	21.8882i	−0.261793	−	1.20857i
$329$	−7.35781	−	3.34453i	−0.405649	−	0.184390i
$330$		0			0
$331$	−2.35851	−	17.2673i	−0.129635	−	0.949099i	−0.934581	−	0.355750i	$-0.884225\pi$
$331$	−2.35851	−	17.2673i	−0.129635	−	0.949099i	0.804946	−	0.593349i	$-0.202194\pi$
$332$	−0.251018	−	4.30982i	−0.0137764	−	0.236532i
$333$		0			0
$334$	7.01222	−	3.52167i	0.383692	−	0.192697i
$335$	12.7972	−	26.7630i	0.699184	−	1.46222i
$336$		0			0
$337$	5.52218	−	6.32772i	0.300812	−	0.344693i	−0.583053	−	0.812434i	$-0.698142\pi$
$337$	5.52218	−	6.32772i	0.300812	−	0.344693i	0.883865	+	0.467741i	$0.154932\pi$
$338$	0.0658278	−	3.39407i	0.00358056	−	0.184613i
$339$		0			0
$340$	4.30054	+	3.07384i	0.233229	+	0.166702i
$341$	1.68709	−	0.197192i	0.0913608	−	0.0106785i
$342$		0			0
$343$	−5.75308	−	13.3371i	−0.310637	−	0.720138i
$344$	−21.0992	+	6.76520i	−1.13760	+	0.364755i
$345$		0			0
$346$	1.82915	+	3.82535i	0.0983360	+	0.205652i
$347$	−22.9044	−	17.7522i	−1.22957	−	0.952990i	−0.229777	−	0.973243i	$-0.573800\pi$
$347$	−22.9044	−	17.7522i	−1.22957	−	0.952990i	−0.999795	+	0.0202528i	$0.993553\pi$
$348$		0			0
$349$	13.8561	+	15.8773i	0.741700	+	0.849893i	0.993012	−	0.118013i	$-0.0376523\pi$
$349$	13.8561	+	15.8773i	0.741700	+	0.849893i	−0.251313	+	0.967906i	$0.580862\pi$
$350$	7.20806	−	6.04828i	0.385287	−	0.323294i
$351$		0			0
$352$	−2.75775	−	2.31402i	−0.146988	−	0.123338i
$353$	−0.111015	−	5.72389i	−0.00590872	−	0.304652i	−0.991094	−	0.133161i	$-0.957487\pi$
$353$	−0.111015	−	5.72389i	−0.00590872	−	0.304652i	0.985186	−	0.171491i	$-0.0548584\pi$
$354$		0			0
$355$	−5.01383	−	7.95499i	−0.266107	−	0.422207i
$356$	−2.98788	−	2.93049i	−0.158357	−	0.155316i
$357$		0			0
$358$	−10.0103	+	15.8824i	−0.529059	+	0.839409i
$359$	−10.5490	+	2.50017i	−0.556758	+	0.131954i	−0.499356	−	0.866397i	$-0.666430\pi$
$359$	−10.5490	+	2.50017i	−0.556758	+	0.131954i	−0.0574020	+	0.998351i	$0.518282\pi$
$360$		0			0
$361$	2.60578	+	8.70391i	0.137146	+	0.458101i
$362$	−2.34045	−	9.08617i	−0.123011	−	0.477558i
$363$		0			0
$364$	−0.462525	+	1.19797i	−0.0242429	+	0.0627906i
$365$	6.52932	−	16.9114i	0.341760	−	0.885181i
$366$		0			0
$367$	−4.92309	−	19.1126i	−0.256983	−	0.997670i	−0.958517	−	0.285034i	$-0.907995\pi$
$367$	−4.92309	−	19.1126i	−0.256983	−	0.997670i	0.701534	−	0.712636i	$-0.252499\pi$
$368$	7.31247	+	24.4253i	0.381189	+	1.27326i
$369$		0			0
$370$	12.3359	−	2.92366i	0.641313	−	0.151994i
$371$	−4.02970	+	6.39355i	−0.209211	+	0.331936i
$372$		0			0
$373$	9.03267	+	8.85918i	0.467694	+	0.458711i	0.895436	−	0.445190i	$-0.146864\pi$
$373$	9.03267	+	8.85918i	0.467694	+	0.458711i	−0.427742	+	0.903901i	$0.640691\pi$
$374$	−8.73725	−	13.8626i	−0.451792	−	0.716817i
$375$		0			0
$376$	−0.409678	−	21.1229i	−0.0211275	−	1.08933i
$377$	−2.01472	−	1.69055i	−0.103763	−	0.0870679i
$378$		0			0
$379$	−22.5864	+	18.9522i	−1.16019	+	0.973512i	−0.999908	−	0.0135603i	$-0.995683\pi$
$379$	−22.5864	+	18.9522i	−1.16019	+	0.973512i	−0.160278	+	0.987072i	$0.551239\pi$
$380$	1.97527	+	2.26341i	0.101329	+	0.116110i
$381$		0			0
$382$	8.23475	+	6.38241i	0.421326	+	0.326553i
$383$	−6.68153	−	13.9732i	−0.341410	−	0.713999i	0.657822	−	0.753173i	$-0.271478\pi$
$383$	−6.68153	−	13.9732i	−0.341410	−	0.713999i	−0.999232	+	0.0391746i	$0.987527\pi$
$384$		0			0
$385$	8.26354	−	2.64960i	0.421149	−	0.135036i
$386$	−4.91105	−	11.3851i	−0.249966	−	0.579486i
$387$		0			0
$388$	−0.380029	+	0.0444190i	−0.0192931	+	0.00225503i
$389$	−13.0775	−	9.34725i	−0.663057	−	0.473924i	0.199491	−	0.979900i	$-0.436071\pi$
$389$	−13.0775	−	9.34725i	−0.663057	−	0.473924i	−0.862548	+	0.505975i	$0.831133\pi$
$390$		0			0
$391$	0.817458	−	42.1479i	0.0413406	−	2.13151i
$392$	11.1937	−	12.8265i	0.565366	−	0.647838i
$393$		0			0
$394$	−4.30272	+	8.99837i	−0.216768	+	0.453331i
$395$	8.73659	−	4.38768i	0.439585	−	0.220768i
$396$		0			0
$397$	1.18995	+	20.4306i	0.0597217	+	1.02538i	0.886463	+	0.462800i	$0.153155\pi$
$397$	1.18995	+	20.4306i	0.0597217	+	1.02538i	−0.826741	+	0.562582i	$0.809808\pi$
$398$	−4.52596	−	33.1359i	−0.226866	−	1.66095i
$399$		0			0
$400$	19.1448	+	8.70239i	0.957241	+	0.435120i
$401$	2.92162	+	13.4877i	0.145899	+	0.673543i	0.990428	+	0.138033i	$0.0440781\pi$
$401$	2.92162	+	13.4877i	0.145899	+	0.673543i	−0.844529	+	0.535510i	$0.820119\pi$
$402$		0			0
$403$	1.86498	−	2.31221i	0.0929013	−	0.115180i
$404$	2.83057	−	4.90269i	0.140826	−	0.243918i
$405$		0			0
$406$	−0.499334	−	0.864871i	−0.0247815	−	0.0429228i
$407$	6.42925	+	1.00552i	0.318686	+	0.0498416i
$408$		0			0
$409$	−14.7415	−	4.72666i	−0.728918	−	0.233718i	−0.0823814	−	0.996601i	$-0.526253\pi$
$409$	−14.7415	−	4.72666i	−0.728918	−	0.233718i	−0.646537	+	0.762883i	$0.723783\pi$
$410$	3.18744	+	32.7697i	0.157416	+	1.61838i
$411$		0			0
$412$	2.24257	+	0.916190i	0.110483	+	0.0451375i
$413$	−0.570406	+	0.375162i	−0.0280678	+	0.0184605i
$414$		0			0
$415$	−2.96664	+	50.9352i	−0.145627	+	2.50031i
$416$	−6.27702	+	0.487888i	−0.307756	+	0.0239207i
$417$		0			0
$418$	−3.01472	−	8.81086i	−0.147455	−	0.430953i
$419$	−24.4333	+	13.4817i	−1.19364	+	0.658624i	−0.950306	−	0.311317i	$-0.899230\pi$
$419$	−24.4333	+	13.4817i	−1.19364	+	0.658624i	−0.243337	+	0.969942i	$0.578242\pi$
$420$		0			0
$421$	32.5295	−	14.7865i	1.58539	−	0.720649i	0.589213	−	0.807978i	$-0.299438\pi$
$421$	32.5295	−	14.7865i	1.58539	−	0.720649i	0.996180	+	0.0873284i	$0.0278330\pi$
$422$	15.9150	+	21.3775i	0.774728	+	1.04064i
$423$		0			0
$424$	−19.6215	−	2.29343i	−0.952906	−	0.111379i
$425$	−25.7493	−	23.3662i	−1.24902	−	1.13343i
$426$		0			0
$427$	1.14457	+	0.0889627i	0.0553894	+	0.00430520i
$428$	−0.783980	+	5.73975i	−0.0378951	+	0.277441i
$429$		0			0
$430$	31.9632	−	6.27736i	1.54140	−	0.302721i
$431$	2.80914	+	1.02244i	0.135311	+	0.0492493i	0.408788	−	0.912629i	$-0.365951\pi$
$431$	2.80914	+	1.02244i	0.135311	+	0.0492493i	−0.273477	+	0.961879i	$0.588174\pi$
$432$		0			0
$433$	23.2759	−	8.47173i	1.11857	−	0.407125i	0.284438	−	0.958694i	$-0.408193\pi$
$433$	23.2759	−	8.47173i	1.11857	−	0.407125i	0.834129	+	0.551569i	$0.185971\pi$
$434$	0.965746	−	0.582830i	0.0463573	−	0.0279768i
$435$		0			0
$436$	−5.66371	+	0.219778i	−0.271242	+	0.0105254i
$437$	5.97591	−	23.1999i	0.285867	−	1.10980i
$438$		0			0
$439$	−6.22548	−	11.8188i	−0.297126	−	0.564079i	0.690041	−	0.723770i	$-0.257592\pi$
$439$	−6.22548	−	11.8188i	−0.297126	−	0.564079i	−0.987167	+	0.159691i	$0.948950\pi$
$440$	15.5666	+	16.4997i	0.742110	+	0.786590i
$441$		0			0
$442$	−27.8853	−	6.60893i	−1.32637	−	0.314355i
$443$	1.40301	−	1.37607i	0.0666591	−	0.0653788i	−0.666124	−	0.745841i	$-0.732048\pi$
$443$	1.40301	−	1.37607i	0.0666591	−	0.0653788i	0.732783	+	0.680462i	$0.238221\pi$
$444$		0			0
$445$	31.0525	+	38.4991i	1.47203	+	1.82503i
$446$	15.9906	−	2.50089i	0.757178	−	0.118421i
$447$		0			0
$448$	−9.69341	−	2.69834i	−0.457971	−	0.127485i
$449$	−14.9917	+	15.8903i	−0.707503	+	0.749909i	−0.977034	−	0.213082i	$-0.931650\pi$
$449$	−14.9917	+	15.8903i	−0.707503	+	0.749909i	0.269531	+	0.962992i	$0.413131\pi$
$450$		0			0
$451$	−4.84698	+	16.1900i	−0.228235	+	0.762360i
$452$	4.06039	+	0.157562i	0.190985	+	0.00741108i
$453$		0			0
$454$	−4.46532	+	1.24301i	−0.209568	+	0.0583372i
$455$	7.07300	−	13.4278i	0.331588	−	0.629503i
$456$		0			0
$457$	−12.5130	−	6.90437i	−0.585332	−	0.322973i	0.162658	−	0.986683i	$-0.447993\pi$
$457$	−12.5130	−	6.90437i	−0.585332	−	0.322973i	−0.747990	+	0.663710i	$0.768981\pi$
$458$	−4.31620	+	24.4784i	−0.201683	+	1.14380i
$459$		0			0
$460$	1.26054	+	7.14887i	0.0587729	+	0.333318i
$461$	−2.27614	+	6.65228i	−0.106011	+	0.309827i	−0.986385	−	0.164451i	$-0.947415\pi$
$461$	−2.27614	+	6.65228i	−0.106011	+	0.309827i	0.880375	+	0.474279i	$0.157291\pi$
$462$		0			0
$463$	−26.8570	+	10.9723i	−1.24815	+	0.509926i	−0.903412	−	0.428773i	$-0.858946\pi$
$463$	−26.8570	+	10.9723i	−1.24815	+	0.509926i	−0.344739	+	0.938699i	$0.612032\pi$
$464$	1.26243	−	1.84067i	0.0586070	−	0.0854510i
$465$		0			0
$466$	2.20076	−	10.1598i	0.101948	−	0.470646i
$467$	−7.70358	+	10.3477i	−0.356479	+	0.478835i	−0.943799	−	0.330520i	$-0.892776\pi$
$467$	−7.70358	+	10.3477i	−0.356479	+	0.478835i	0.587320	+	0.809355i	$0.300183\pi$
$468$		0			0
$469$	4.00517	−	9.28503i	0.184942	−	0.428743i
$470$	−3.00684	+	30.9130i	−0.138695	+	1.42591i
$471$		0			0
$472$	−1.52793	−	0.922111i	−0.0703287	−	0.0424436i
$473$	16.4066	+	3.22216i	0.754378	+	0.148155i
$474$		0			0
$475$	−11.1766	−	16.2958i	−0.512815	−	0.747703i
$476$	1.50546	+	0.990154i	0.0690025	+	0.0453836i
$477$		0			0
$478$	16.7553	+	8.41481i	0.766368	+	0.384884i
$479$	2.99688	−	2.32276i	0.136931	−	0.106130i	−0.541832	−	0.840487i	$-0.682269\pi$
$479$	2.99688	−	2.32276i	0.136931	−	0.106130i	0.678764	+	0.734357i	$0.262516\pi$
$480$		0			0
$481$	9.25878	−	6.61778i	0.422164	−	0.301745i
$482$	1.61583	−	1.46628i	0.0735988	−	0.0667874i
$483$		0			0
$484$	−0.604027	−	1.56447i	−0.0274558	−	0.0711122i
$485$	4.52192			0.205330
$486$		0			0
$487$	−20.6259			−0.934649			−0.467324	−	0.884086i	$-0.654782\pi$
$487$	−20.6259			−0.934649			−0.467324	+	0.884086i	$0.654782\pi$
$488$	1.08085	+	2.79948i	0.0489279	+	0.126726i
$489$		0			0
$490$	−18.5338	+	16.8185i	−0.837273	+	0.759784i
$491$	−1.84337	+	1.31756i	−0.0831899	+	0.0594606i	−0.622327	−	0.782758i	$-0.713812\pi$
$491$	−1.84337	+	1.31756i	−0.0831899	+	0.0594606i	0.539137	+	0.842218i	$0.318751\pi$
$492$		0			0
$493$	−2.91685	+	2.26073i	−0.131368	+	0.101818i
$494$	−14.5539	−	7.30924i	−0.654811	−	0.328858i
$495$		0			0
$496$	2.10628	+	1.38533i	0.0945750	+	0.0622029i
$497$	−1.81293	−	2.64332i	−0.0813211	−	0.118569i
$498$		0			0
$499$	2.73096	+	0.536344i	0.122255	+	0.0240100i	0.253465	−	0.967344i	$-0.418430\pi$
$499$	2.73096	+	0.536344i	0.122255	+	0.0240100i	−0.131211	+	0.991355i	$0.541886\pi$
$500$	1.04203	+	0.628867i	0.0466009	+	0.0281238i
$501$		0			0
$502$	−0.526823	+	5.41621i	−0.0235133	+	0.241737i
$503$	4.48569	−	10.3990i	0.200007	−	0.463668i	−0.788464	−	0.615081i	$-0.789123\pi$
$503$	4.48569	−	10.3990i	0.200007	−	0.463668i	0.988471	+	0.151413i	$0.0483824\pi$
$504$		0			0
$505$	−39.9533	+	53.6666i	−1.77790	+	2.38813i
$506$	4.76385	−	21.9924i	0.211779	−	0.977680i
$507$		0			0
$508$	3.43888	−	5.01401i	0.152576	−	0.222461i
$509$	−1.59411	+	0.651267i	−0.0706578	+	0.0288669i	−0.413253	−	0.910616i	$-0.635608\pi$
$509$	−1.59411	+	0.651267i	−0.0706578	+	0.0288669i	0.342595	+	0.939483i	$0.388694\pi$
$510$		0			0
$511$	2.00046	−	5.84657i	0.0884952	−	0.258637i
$512$	−4.40991	−	25.0098i	−0.194892	−	1.10529i
$513$		0			0
$514$	−4.14706	+	23.5191i	−0.182919	+	1.03738i
$515$	−25.0674	−	13.8316i	−1.10460	−	0.609493i
$516$		0			0
$517$	−7.42989	+	14.1053i	−0.326766	+	0.620350i
$518$	4.16315	−	1.15889i	0.182918	−	0.0509188i
$519$		0			0
$520$	39.6417	+	1.53828i	1.73840	+	0.0674579i
$521$	−8.50756	+	28.4172i	−0.372723	+	1.24498i	0.541821	+	0.840494i	$0.317735\pi$
$521$	−8.50756	+	28.4172i	−0.372723	+	1.24498i	−0.914544	+	0.404487i	$0.867450\pi$
$522$		0			0
$523$	8.45997	−	8.96704i	0.369928	−	0.392101i	−0.515490	−	0.856895i	$-0.672390\pi$
$523$	8.45997	−	8.96704i	0.369928	−	0.392101i	0.885419	+	0.464794i	$0.153872\pi$
$524$	−5.20789	−	1.44972i	−0.227508	−	0.0633311i
$525$		0			0
$526$	−7.68883	+	1.20251i	−0.335249	+	0.0524320i
$527$	−2.61688	−	3.24443i	−0.113993	−	0.141329i
$528$		0			0
$529$	24.9092	−	24.4308i	1.08301	−	1.06221i
$530$	28.2594	+	6.69761i	1.22751	+	0.290926i
$531$		0			0
$532$	0.702722	+	0.744842i	0.0304669	+	0.0322930i
$533$	13.7745	+	26.1502i	0.596639	+	1.13269i
$534$		0			0
$535$	17.0779	−	66.3004i	0.738342	−	2.86642i
$536$	26.4127	−	1.02493i	1.14086	−	0.0442704i
$537$		0			0
$538$	31.0551	−	18.7418i	1.33888	−	0.808018i
$539$	−12.0717	+	4.39375i	−0.519966	+	0.189252i
$540$		0			0
$541$	8.81849	+	3.20967i	0.379136	+	0.137994i	0.524556	−	0.851376i	$-0.324231\pi$
$541$	8.81849	+	3.20967i	0.379136	+	0.137994i	−0.145420	+	0.989370i	$0.546453\pi$
$542$	−19.1316	+	3.75732i	−0.821772	+	0.161391i
$543$		0			0
$544$	−1.19556	+	8.75301i	−0.0512590	+	0.375282i
$545$	66.7850	+	5.19094i	2.86076	+	0.222356i
$546$		0			0
$547$	−17.9621	−	16.2997i	−0.768002	−	0.696925i	0.190602	−	0.981667i	$-0.438956\pi$
$547$	−17.9621	−	16.2997i	−0.768002	−	0.696925i	−0.958604	+	0.284743i	$0.908092\pi$
$548$	2.94481	+	0.344199i	0.125796	+	0.0147034i
$549$		0			0
$550$	−11.0835	−	14.8877i	−0.472601	−	0.634813i
$551$	−1.90926	+	0.867864i	−0.0813371	+	0.0369722i
$552$		0			0
$553$	2.91782	−	1.60998i	0.124078	−	0.0684635i
$554$	1.66835	+	4.87594i	0.0708815	+	0.207159i
$555$		0			0
$556$	0.116682	−	0.00906927i	0.00494843	−	0.000384623i
$557$	−0.916202	+	15.7306i	−0.0388207	+	0.666526i	0.921629	+	0.388073i	$0.126859\pi$
$557$	−0.916202	+	15.7306i	−0.0388207	+	0.666526i	−0.960450	+	0.278454i	$0.910178\pi$
$558$		0			0
$559$	24.4309	−	16.0684i	1.03332	−	0.679622i
$560$	11.9232	+	4.87114i	0.503845	+	0.205843i
$561$		0			0
$562$	−0.210036	−	2.15936i	−0.00885983	−	0.0910870i
$563$	13.0165	+	4.17358i	0.548581	+	0.175896i	0.566676	−	0.823941i	$-0.308229\pi$
$563$	13.0165	+	4.17358i	0.548581	+	0.175896i	−0.0180946	+	0.999836i	$0.505760\pi$
$564$		0			0
$565$	−47.4468	−	7.42054i	−1.99610	−	0.312184i
$566$	0.578656	+	1.00226i	0.0243227	+	0.0421282i
$567$		0			0
$568$	4.18926	−	7.25602i	0.175778	−	0.304456i
$569$	−17.8902	+	22.1804i	−0.749997	+	0.929850i	−0.999255	−	0.0385870i	$-0.987714\pi$
$569$	−17.8902	+	22.1804i	−0.749997	+	0.929850i	0.249259	+	0.968437i	$0.419813\pi$
$570$		0			0
$571$	2.45851	+	11.3497i	0.102885	+	0.474972i	0.999484	+	0.0321272i	$0.0102282\pi$
$571$	2.45851	+	11.3497i	0.102885	+	0.474972i	−0.896598	+	0.442844i	$0.853969\pi$
$572$	2.30597	+	1.04819i	0.0964176	+	0.0438272i
$573$		0			0
$574$	1.51882	+	11.1197i	0.0633943	+	0.464129i
$575$	−2.77635	−	47.6681i	−0.115782	−	1.98790i
$576$		0			0
$577$	25.7878	−	12.9511i	1.07356	−	0.539163i	0.177968	−	0.984036i	$-0.443048\pi$
$577$	25.7878	−	12.9511i	1.07356	−	0.539163i	0.895593	+	0.444874i	$0.146751\pi$
$578$	−7.74041	+	16.1877i	−0.321959	+	0.673320i
$579$		0			0
$580$	0.417839	−	0.478791i	0.0173498	−	0.0198807i
$581$	−0.337250	+	17.3885i	−0.0139915	+	0.721397i
$582$		0			0
$583$	12.1279	+	8.66850i	0.502286	+	0.359013i
$584$	16.0434	−	1.87520i	0.663880	−	0.0775965i
$585$		0			0
$586$	−14.2950	−	33.1394i	−0.590519	−	1.36898i
$587$	−12.7643	+	4.09272i	−0.526841	+	0.168925i	−0.556831	−	0.830626i	$-0.687983\pi$
$587$	−12.7643	+	4.09272i	−0.526841	+	0.168925i	0.0299908	+	0.999550i	$0.490452\pi$
$588$		0			0
$589$	−1.02188	−	2.13708i	−0.0421058	−	0.0880568i
$590$	2.07367	+	1.60721i	0.0853715	+	0.0661679i
$591$		0			0
$592$	6.35054	+	7.27691i	0.261006	+	0.299079i
$593$	15.3902	−	12.9139i	0.632000	−	0.530311i	−0.269549	−	0.962987i	$-0.586875\pi$
$593$	15.3902	−	12.9139i	0.632000	−	0.530311i	0.901550	+	0.432675i	$0.142430\pi$
$594$		0			0
$595$	−16.3133	−	13.6885i	−0.668779	−	0.561173i
$596$	0.106801	+	5.50663i	0.00437474	+	0.225560i
$597$		0			0
$598$	−20.9838	−	33.2931i	−0.858091	−	1.36145i
$599$	11.3279	+	11.1103i	0.462846	+	0.453956i	0.893832	−	0.448402i	$-0.148007\pi$
$599$	11.3279	+	11.1103i	0.462846	+	0.453956i	−0.430985	+	0.902359i	$0.641834\pi$
$600$		0			0
$601$	−15.7816	+	25.0393i	−0.643746	+	1.02137i	0.352584	+	0.935780i	$0.385303\pi$
$601$	−15.7816	+	25.0393i	−0.643746	+	1.02137i	−0.996330	+	0.0855930i	$0.972722\pi$
$602$	10.8042	−	2.56063i	0.440345	−	0.104364i
$603$		0			0
$604$	0.588906	+	1.96708i	0.0239623	+	0.0800395i
$605$	4.94387	+	19.1933i	0.200997	+	0.780317i
$606$		0			0
$607$	4.92873	−	12.7657i	0.200051	−	0.518145i	−0.796163	−	0.605083i	$-0.793140\pi$
$607$	4.92873	−	12.7657i	0.200051	−	0.518145i	0.996214	+	0.0869374i	$0.0277080\pi$
$608$	−1.80828	+	4.68357i	−0.0733356	+	0.189944i
$609$		0			0
$610$	−1.10045	−	4.27219i	−0.0445558	−	0.172976i
$611$	7.99652	+	26.7102i	0.323504	+	1.08058i
$612$		0			0
$613$	28.1886	−	6.68083i	1.13853	−	0.269836i	0.382232	−	0.924066i	$-0.375155\pi$
$613$	28.1886	−	6.68083i	1.13853	−	0.269836i	0.756296	+	0.654230i	$0.227007\pi$
$614$	−13.8884	+	22.0354i	−0.560489	+	0.889277i
$615$		0			0
$616$	5.52031	+	5.41428i	0.222420	+	0.218148i
$617$	20.9510	+	33.2411i	0.843457	+	1.33824i	0.939391	+	0.342849i	$0.111392\pi$
$617$	20.9510	+	33.2411i	0.843457	+	1.33824i	−0.0959332	+	0.995388i	$0.530584\pi$
$618$		0			0
$619$	0.572024	+	29.4934i	0.0229916	+	1.18544i	0.816671	+	0.577103i	$0.195817\pi$
$619$	0.572024	+	29.4934i	0.0229916	+	1.18544i	−0.793679	+	0.608336i	$0.791837\pi$
$620$	0.549841	+	0.461371i	0.0220821	+	0.0185291i
$621$		0			0
$622$	−9.70653	+	8.14474i	−0.389196	+	0.326574i
$623$	11.0858	+	12.7029i	0.444144	+	0.508933i
$624$		0			0
$625$	13.4322	+	10.4107i	0.537288	+	0.416429i
$626$	−3.35702	−	7.02061i	−0.134173	−	0.280600i
$627$		0			0
$628$	4.82419	−	1.54682i	0.192506	−	0.0617247i
$629$	−6.32501	−	14.6630i	−0.252195	−	0.584653i
$630$		0			0
$631$	14.0896	−	1.64684i	0.560899	−	0.0655597i	0.169081	−	0.985602i	$-0.445920\pi$
$631$	14.0896	−	1.64684i	0.560899	−	0.0655597i	0.391818	+	0.920043i	$0.371846\pi$
$632$	7.08696	+	5.06545i	0.281904	+	0.201493i
$633$		0			0
$634$	−0.101117	+	5.21358i	−0.00401588	+	0.207058i
$635$	−47.2467	+	54.1387i	−1.87493	+	2.14843i
$636$		0			0
$637$	−9.69195	+	20.2690i	−0.384009	+	0.803087i
$638$	−1.76036	+	0.884087i	−0.0696934	+	0.0350013i
$639$		0			0
$640$	1.62563	+	27.9110i	0.0642587	+	1.10328i
$641$	−3.32437	−	24.3387i	−0.131305	−	0.961320i	−0.932054	−	0.362320i	$-0.881985\pi$
$641$	−3.32437	−	24.3387i	−0.131305	−	0.961320i	0.800749	−	0.599000i	$-0.204435\pi$
$642$		0			0
$643$	−9.86610	−	4.48469i	−0.389081	−	0.176859i	0.209711	−	0.977763i	$-0.432748\pi$
$643$	−9.86610	−	4.48469i	−0.389081	−	0.176859i	−0.598792	+	0.800904i	$0.704353\pi$
$644$	0.523848	+	2.41835i	0.0206425	+	0.0952964i
$645$		0			0
$646$	−14.3470	+	17.7874i	−0.564474	+	0.699838i
$647$	2.31697	−	4.01310i	0.0910894	−	0.157771i	−0.816880	−	0.576807i	$-0.804298\pi$
$647$	2.31697	−	4.01310i	0.0910894	−	0.157771i	0.907970	+	0.419036i	$0.137632\pi$
$648$		0			0
$649$	0.673342	+	1.16626i	0.0264310	+	0.0457798i
$650$	−32.0701	−	5.01567i	−1.25789	−	0.196731i
$651$		0			0
$652$	−0.592017	−	0.189823i	−0.0231852	−	0.00743403i
$653$	−1.39800	−	14.3727i	−0.0547081	−	0.562448i	−0.982100	−	0.188358i	$-0.939683\pi$
$653$	−1.39800	−	14.3727i	−0.0547081	−	0.562448i	0.927392	−	0.374090i	$-0.122045\pi$
$654$		0			0
$655$	59.1438	+	24.1629i	2.31094	+	0.944123i
$656$	−20.9566	+	13.7834i	−0.818218	+	0.538150i
$657$		0			0
$658$	−0.615584	+	10.5692i	−0.0239980	+	0.412029i
$659$	−20.1953	+	1.56971i	−0.786698	+	0.0611470i	−0.464555	−	0.885544i	$-0.653786\pi$
$659$	−20.1953	+	1.56971i	−0.786698	+	0.0611470i	−0.322143	+	0.946691i	$0.604403\pi$
$660$		0			0
$661$	10.4400	+	30.5120i	0.406068	+	1.18678i	0.939977	+	0.341237i	$0.110846\pi$
$661$	10.4400	+	30.5120i	0.406068	+	1.18678i	−0.533909	+	0.845542i	$0.679278\pi$
$662$	−19.9879	+	11.0289i	−0.776852	+	0.428649i
$663$		0			0
$664$	−41.3866	+	18.8125i	−1.60611	+	0.730067i
$665$	−7.22696	−	9.70749i	−0.280249	−	0.376440i
$666$		0			0
$667$	−5.03353	−	0.588336i	−0.194899	−	0.0227805i
$668$	1.26042	+	1.14377i	0.0487673	+	0.0442539i
$669$		0			0
$670$	−38.7421	−	3.01127i	−1.49674	−	0.116336i
$671$	0.306456	−	2.24366i	0.0118306	−	0.0866154i
$672$		0			0
$673$	−25.2799	+	4.96482i	−0.974470	+	0.191380i	−0.654512	−	0.756052i	$-0.727126\pi$
$673$	−25.2799	+	4.96482i	−0.974470	+	0.191380i	−0.319958	+	0.947432i	$0.603669\pi$
$674$	−10.3378	−	3.76266i	−0.398198	−	0.144932i
$675$		0			0
$676$	0.691922	−	0.251839i	0.0266124	−	0.00968611i
$677$	13.3615	−	8.06373i	0.513525	−	0.309914i	−0.236154	−	0.971716i	$-0.575887\pi$
$677$	13.3615	−	8.06373i	0.513525	−	0.309914i	0.749679	+	0.661802i	$0.230208\pi$
$678$		0			0
$679$	1.54023	−	0.0597681i	0.0591087	−	0.00229369i
$680$	13.8853	−	53.9062i	0.532479	−	2.06721i
$681$		0			0
$682$	−1.03694	−	1.96858i	−0.0397064	−	0.0753807i
$683$	0.109120	+	0.115661i	0.00417537	+	0.00442563i	0.729458	−	0.684026i	$-0.239772\pi$
$683$	0.109120	+	0.115661i	0.00417537	+	0.00442563i	−0.725283	+	0.688451i	$0.758291\pi$
$684$		0			0
$685$	−34.0954	−	8.08076i	−1.30272	−	0.308750i
$686$	−13.5836	+	13.3227i	−0.518626	+	0.508664i
$687$		0			0
$688$	15.5798	+	19.3159i	0.593973	+	0.736411i
$689$	25.7581	−	4.02849i	0.981306	−	0.153473i
$690$		0			0
$691$	−18.8668	−	5.25193i	−0.717726	−	0.199793i	−0.109991	−	0.993933i	$-0.535082\pi$
$691$	−18.8668	−	5.25193i	−0.717726	−	0.199793i	−0.607735	+	0.794140i	$0.707922\pi$
$692$	−0.631147	+	0.668977i	−0.0239926	+	0.0254307i
$693$		0			0
$694$	−10.8869	+	36.3646i	−0.413259	+	1.38038i
$695$	−1.38212	−	0.0536326i	−0.0524268	−	0.00203440i
$696$		0			0
$697$	39.9532	−	11.1217i	1.51334	−	0.421266i
$698$	12.8647	−	24.4230i	0.486936	−	0.924426i
$699$		0			0
$700$	1.78697	+	0.986011i	0.0675413	+	0.0372677i
$701$	3.63706	−	20.6268i	0.137370	−	0.779064i	−0.835810	−	0.549019i	$-0.815001\pi$
$701$	3.63706	−	20.6268i	0.137370	−	0.779064i	0.973180	−	0.230045i	$-0.0738874\pi$
$702$		0			0
$703$	−1.57590	−	8.93735i	−0.0594360	−	0.337078i
$704$	−6.42530	+	18.7786i	−0.242162	+	0.707746i
$705$		0			0
$706$	−6.94220	+	2.83620i	−0.261273	+	0.106742i
$707$	−12.8994	+	18.8077i	−0.485130	+	0.707337i
$708$		0			0
$709$	−8.62768	+	39.8298i	−0.324019	+	1.49584i	0.467114	+	0.884197i	$0.345294\pi$
$709$	−8.62768	+	39.8298i	−0.324019	+	1.49584i	−0.791134	+	0.611643i	$0.790509\pi$
$710$	−7.35544	+	9.88007i	−0.276045	+	0.370792i
$711$		0			0
$712$	−17.4559	+	40.4673i	−0.654187	+	1.51658i
$713$	0.554150	−	5.69716i	0.0207531	−	0.213360i
$714$		0			0
$715$	−25.6305	−	15.4681i	−0.958528	−	0.578474i
$716$	−3.99579	−	0.784748i	−0.149330	−	0.0293274i
$717$		0			0
$718$	8.03226	+	11.7113i	0.299761	+	0.437063i
$719$	−14.6635	−	9.64436i	−0.546857	−	0.359674i	0.245820	−	0.969316i	$-0.420943\pi$
$719$	−14.6635	−	9.64436i	−0.546857	−	0.359674i	−0.792677	+	0.609642i	$0.791313\pi$
$720$		0			0
$721$	−8.72114	−	4.37992i	−0.324792	−	0.163117i
$722$	9.40674	−	7.29078i	0.350083	−	0.271335i
$723$		0			0
$724$	1.65571	−	1.18343i	0.0615341	−	0.0439819i
$725$	−3.09548	+	2.80899i	−0.114963	+	0.104323i
$726$		0			0
$727$	−14.6458	−	37.9335i	−0.543182	−	1.40688i	−0.884328	−	0.466866i	$-0.845383\pi$
$727$	−14.6458	−	37.9335i	−0.543182	−	1.40688i	0.341146	−	0.940010i	$-0.389185\pi$
$728$	13.5229			0.501191
$729$		0			0
$730$	−23.7462			−0.878886
$731$	−14.7783	−	38.2769i	−0.546597	−	1.41572i
$732$		0			0
$733$	−19.5116	+	17.7059i	−0.720678	+	0.653981i	−0.947427	−	0.319973i	$-0.896326\pi$
$733$	−19.5116	+	17.7059i	−0.720678	+	0.653981i	0.226748	+	0.973953i	$0.427191\pi$
$734$	−21.0328	+	15.0334i	−0.776336	+	0.554892i
$735$		0			0
$736$	−9.58876	+	7.43185i	−0.353446	+	0.273942i
$737$	−17.8246	−	8.95184i	−0.656577	−	0.329745i
$738$		0			0
$739$	15.8444	+	10.4210i	0.582846	+	0.383344i	0.806420	−	0.591343i	$-0.201402\pi$
$739$	15.8444	+	10.4210i	0.582846	+	0.383344i	−0.223574	+	0.974687i	$0.571772\pi$
$740$	1.55533	+	2.26772i	0.0571749	+	0.0833631i
$741$		0			0
$742$	9.71411	+	1.90779i	0.356616	+	0.0700372i
$743$	39.3478	+	23.7465i	1.44353	+	0.871176i	0.999689	−	0.0249280i	$-0.00793566\pi$
$743$	39.3478	+	23.7465i	1.44353	+	0.871176i	0.443843	+	0.896104i	$0.353615\pi$
$744$		0			0
$745$	6.30160	−	64.7861i	0.230873	−	2.37358i
$746$	6.56426	−	15.2177i	0.240335	−	0.557158i
$747$		0			0
$748$	2.12246	−	2.85096i	0.0776048	−	0.104241i
$749$	4.94066	−	22.8086i	0.180528	−	0.833410i
$750$		0			0
$751$	−12.9756	+	18.9189i	−0.473486	+	0.690360i	−0.985702	−	0.168497i	$-0.946109\pi$
$751$	−12.9756	+	18.9189i	−0.473486	+	0.690360i	0.512216	+	0.858857i	$0.328825\pi$
$752$	−21.9044	+	8.94891i	−0.798770	+	0.326333i
$753$		0			0
$754$	−1.11530	+	3.25959i	−0.0406169	+	0.118707i
$755$	−4.21397	−	23.8986i	−0.153362	−	0.869760i
$756$		0			0
$757$	−2.95169	+	16.7399i	−0.107281	+	0.608420i	0.883004	+	0.469366i	$0.155517\pi$
$757$	−2.95169	+	16.7399i	−0.107281	+	0.608420i	−0.990285	+	0.139054i	$0.955594\pi$
$758$	33.8159	+	18.6588i	1.22825	+	0.677719i
$759$		0			0
$760$	14.7433	−	27.9894i	0.534794	−	1.01528i
$761$	−35.5440	+	9.89435i	−1.28847	+	0.358670i	−0.843622	−	0.536937i	$-0.819581\pi$
$761$	−35.5440	+	9.89435i	−1.28847	+	0.358670i	−0.444847	+	0.895607i	$0.646742\pi$
$762$		0			0
$763$	22.8166	+	0.885387i	0.826016	+	0.0320532i
$764$	−0.648128	+	2.16490i	−0.0234484	+	0.0783232i
$765$		0			0
$766$	−13.9229	+	14.7574i	−0.503054	+	0.533206i
$767$	2.26893	+	0.631599i	0.0819262	+	0.0228057i
$768$		0			0
$769$	1.06884	−	0.167164i	0.0385434	−	0.00602807i	−0.135218	−	0.990816i	$-0.543173\pi$
$769$	1.06884	−	0.167164i	0.0385434	−	0.00602807i	0.173761	+	0.984788i	$0.444408\pi$
$770$	−7.13656	−	8.84794i	−0.257184	−	0.318858i
$771$		0			0
$772$	1.92007	−	1.88319i	0.0691047	−	0.0677774i
$773$	49.6186	+	11.7598i	1.78466	+	0.422972i	0.984293	−	0.176542i	$-0.0564913\pi$
$773$	49.6186	+	11.7598i	1.78466	+	0.422972i	0.800364	+	0.599514i	$0.204639\pi$
$774$		0			0
$775$	−3.23994	−	3.43414i	−0.116382	−	0.123358i
$776$	1.87776	+	3.56485i	0.0674078	+	0.127970i
$777$		0			0
$778$	−5.25231	+	20.3907i	−0.188305	+	0.731043i
$779$	23.5510	−	0.913888i	0.843804	−	0.0327434i
$780$		0			0
$781$	−5.41311	+	3.26683i	−0.193696	+	0.116896i
$782$	−51.8903	+	18.8865i	−1.85559	+	0.675381i
$783$		0			0
$784$	−17.9169	−	6.52122i	−0.639889	−	0.232901i
$785$	−58.7511	+	11.5383i	−2.09692	+	0.411821i
$786$		0			0
$787$	2.14872	−	15.7314i	0.0765936	−	0.560764i	−0.912004	−	0.410182i	$-0.865465\pi$
$787$	2.14872	−	15.7314i	0.0765936	−	0.560764i	0.988597	−	0.150583i	$-0.0481149\pi$
$788$	−2.15694	−	0.167651i	−0.0768378	−	0.00597231i
$789$		0			0
$790$	−9.48367	−	8.60597i	−0.337414	−	0.306187i
$791$	−16.2592	−	1.90042i	−0.578109	−	0.0675713i
$792$		0			0
$793$	−2.36495	−	3.17667i	−0.0839817	−	0.112807i
$794$	24.4047	−	11.0933i	0.866091	−	0.393686i
$795$		0			0
$796$	6.35136	−	3.50453i	0.225118	−	0.124215i
$797$	−13.6154	−	39.7926i	−0.482283	−	1.40953i	−0.872415	−	0.488767i	$-0.837447\pi$
$797$	−13.6154	−	39.7926i	−0.482283	−	1.40953i	0.390131	−	0.920759i	$-0.372430\pi$
$798$		0			0
$799$	39.0049	−	3.03170i	1.37989	−	0.107254i
$800$	−0.581819	+	9.98944i	−0.0205704	+	0.353180i
$801$		0			0
$802$	15.1035	−	9.93372i	0.533323	−	0.350772i
$803$	−11.2835	−	4.60983i	−0.398187	−	0.162677i
$804$		0			0
$805$	−2.83113	−	29.1066i	−0.0997842	−	1.02587i
$806$	−3.70542	−	1.18809i	−0.130518	−	0.0418489i
$807$		0			0
$808$	−58.8989	−	9.21162i	−2.07206	−	0.324064i
$809$	2.96128	+	5.12908i	0.104113	+	0.180329i	0.913375	−	0.407118i	$-0.133466\pi$
$809$	2.96128	+	5.12908i	0.104113	+	0.180329i	−0.809262	+	0.587447i	$0.800133\pi$
$810$		0			0
$811$	18.5633	−	32.1526i	0.651846	−	1.12903i	−0.330828	−	0.943691i	$-0.607328\pi$
$811$	18.5633	−	32.1526i	0.651846	−	1.12903i	0.982675	−	0.185340i	$-0.0593386\pi$
$812$	0.135994	−	0.168606i	0.00477245	−	0.00591691i
$813$		0			0
$814$	−1.80459	−	8.33092i	−0.0632509	−	0.291999i
$815$	6.68896	+	3.04050i	0.234304	+	0.106504i
$816$		0			0
$817$	−3.15563	−	23.1033i	−0.110401	−	0.808281i
$818$	1.17908	+	20.2441i	0.0412257	+	0.707817i
$819$		0			0
$820$	−6.38184	+	3.20508i	−0.222863	+	0.111926i
$821$	8.08078	−	16.8995i	0.282021	−	0.589797i	−0.711598	−	0.702587i	$-0.752028\pi$
$821$	8.08078	−	16.8995i	0.282021	−	0.589797i	0.993619	+	0.112790i	$0.0359787\pi$
$822$		0			0
$823$	−22.9456	+	26.2928i	−0.799834	+	0.916508i	−0.997971	−	0.0636663i	$-0.979721\pi$
$823$	−22.9456	+	26.2928i	−0.799834	+	0.916508i	0.198137	+	0.980174i	$0.436511\pi$
$824$	0.494678	−	25.5055i	0.0172329	−	0.888526i
$825$		0			0
$826$	0.727565	+	0.520032i	0.0253152	+	0.0180942i
$827$	−9.81756	+	1.14751i	−0.341390	+	0.0399028i	−0.285061	−	0.958509i	$-0.592014\pi$
$827$	−9.81756	+	1.14751i	−0.341390	+	0.0399028i	−0.0563293	+	0.998412i	$0.517940\pi$
$828$		0			0
$829$	−1.44409	−	3.34778i	−0.0501554	−	0.116273i	0.891296	−	0.453422i	$-0.149797\pi$
$829$	−1.44409	−	3.34778i	−0.0501554	−	0.116273i	−0.941451	+	0.337148i	$0.890538\pi$
$830$	63.6423	−	20.4061i	2.20906	−	0.708306i
$831$		0			0
$832$	14.9738	+	31.3151i	0.519123	+	1.08565i
$833$	24.9171	+	19.3122i	0.863327	+	0.669129i
$834$		0			0
$835$	−13.2262	−	15.1555i	−0.457711	−	0.524479i
$836$	1.54733	−	1.29836i	0.0535155	−	0.0449048i
$837$		0			0
$838$	28.0023	+	23.4967i	0.967322	+	0.811679i
$839$	0.471572	+	24.3141i	0.0162805	+	0.839416i	0.915592	+	0.402108i	$0.131722\pi$
$839$	0.471572	+	24.3141i	0.0162805	+	0.839416i	−0.899312	+	0.437308i	$0.855932\pi$
$840$		0			0
$841$	−15.2264	−	24.1583i	−0.525047	−	0.833045i
$842$	−33.4165	−	32.7747i	−1.15161	−	1.12949i
$843$		0			0
$844$	−3.08233	+	4.89045i	−0.106098	+	0.168336i
$845$	−8.46766	+	2.00687i	−0.291296	+	0.0690385i
$846$		0			0
$847$	1.93764	+	6.47217i	0.0665781	+	0.222386i
$848$	5.51902	+	21.4261i	0.189524	+	0.735777i
$849$		0			0
$850$	−16.4049	+	42.4898i	−0.562684	+	1.45739i
$851$	7.89849	−	20.4576i	0.270757	−	0.701277i
$852$		0			0
$853$	2.60468	+	10.1120i	0.0891825	+	0.346228i	0.997382	−	0.0723092i	$-0.0230368\pi$
$853$	2.60468	+	10.1120i	0.0891825	+	0.346228i	−0.908200	+	0.418537i	$0.862543\pi$
$854$	−0.431296	−	1.44063i	−0.0147586	−	0.0492973i
$855$		0			0
$856$	59.3596	−	14.0685i	2.02887	−	0.480850i
$857$	−13.4859	+	21.3968i	−0.460668	+	0.730899i	−0.993315	−	0.115438i	$-0.963173\pi$
$857$	−13.4859	+	21.3968i	−0.460668	+	0.730899i	0.532647	+	0.846338i	$0.321197\pi$
$858$		0			0
$859$	−39.1221	−	38.3707i	−1.33483	−	1.30919i	−0.916029	−	0.401111i	$-0.868624\pi$
$859$	−39.1221	−	38.3707i	−1.33483	−	1.30919i	−0.418799	−	0.908079i	$-0.637549\pi$
$860$	3.76731	+	5.97724i	0.128464	+	0.203822i
$861$		0			0
$862$	−0.0759342	−	3.91515i	−0.00258633	−	0.133350i
$863$	24.1377	+	20.2540i	0.821658	+	0.689453i	0.953360	−	0.301836i	$-0.0975996\pi$
$863$	24.1377	+	20.2540i	0.821658	+	0.689453i	−0.131701	+	0.991289i	$0.542044\pi$
$864$		0			0
$865$	8.32658	−	6.98683i	0.283112	−	0.237559i
$866$	−21.3340	−	24.4461i	−0.724960	−	0.830711i
$867$		0			0
$868$	0.193382	+	0.149882i	0.00656382	+	0.00508734i
$869$	−2.83571	−	5.93038i	−0.0961947	−	0.201174i
$870$		0			0
$871$	−33.2179	+	10.6509i	−1.12554	+	0.360891i
$872$	23.6407	+	54.8054i	0.800577	+	1.85595i
$873$		0			0
$874$	−31.1697	+	3.64321i	−1.05433	+	0.123233i
$875$	−3.98893	−	2.85111i	−0.134850	−	0.0963852i
$876$		0			0
$877$	−0.423694	+	21.8456i	−0.0143071	+	0.737673i	0.922138	+	0.386860i	$0.126440\pi$
$877$	−0.423694	+	21.8456i	−0.0143071	+	0.737673i	−0.936446	+	0.350813i	$0.885905\pi$
$878$	−11.5053	+	13.1836i	−0.388286	+	0.444926i
$879$		0			0
$880$	10.9597	−	22.9202i	0.369451	−	0.772640i
$881$	15.8215	−	7.94586i	0.533040	−	0.267703i	−0.161854	−	0.986815i	$-0.551747\pi$
$881$	15.8215	−	7.94586i	0.533040	−	0.267703i	0.694894	+	0.719112i	$0.255451\pi$
$882$		0			0
$883$	−0.243031	−	4.17269i	−0.00817866	−	0.140422i	−0.999925	−	0.0122102i	$-0.996113\pi$
$883$	−0.243031	−	4.17269i	−0.00817866	−	0.140422i	0.991747	−	0.128212i	$-0.0409238\pi$
$884$	−0.841219	−	6.15882i	−0.0282933	−	0.207143i
$885$		0			0
$886$	−2.34349	−	1.06525i	−0.0787311	−	0.0357877i
$887$	−5.29557	−	24.4471i	−0.177808	−	0.820853i	−0.975883	−	0.218294i	$-0.929951\pi$
$887$	−5.29557	−	24.4471i	−0.177808	−	0.820853i	0.798075	−	0.602558i	$-0.205852\pi$
$888$		0			0
$889$	−15.3774	+	19.0649i	−0.515740	+	0.639417i
$890$	32.3952	−	56.1101i	1.08589	−	1.88081i
$891$		0			0
$892$	1.75530	+	3.04027i	0.0587719	+	0.101796i
$893$	21.9663	+	3.43547i	0.735076	+	0.114964i
$894$		0			0
$895$	45.8279	+	14.6941i	1.53186	+	0.491171i
$896$	0.922625	+	9.48542i	0.0308227	+	0.316885i
$897$		0			0
$898$	26.4910	+	10.8228i	0.884016	+	0.361160i
$899$	−0.418655	+	0.275354i	−0.0139629	+	0.00918357i
$900$		0			0
$901$	2.12707	−	36.5204i	0.0708631	−	1.21667i
$902$	22.0710	−	1.71549i	0.734884	−	0.0571197i
$903$		0			0
$904$	−13.8527	−	40.4860i	−0.460733	−	1.34654i
$905$	−21.0593	+	11.6200i	−0.700035	+	0.386263i
$906$		0			0
$907$	−14.1664	+	6.43940i	−0.470386	+	0.213817i	−0.634955	−	0.772549i	$-0.718982\pi$
$907$	−14.1664	+	6.43940i	−0.470386	+	0.213817i	0.164569	+	0.986366i	$0.447377\pi$
$908$	−0.600368	−	0.806434i	−0.0199239	−	0.0267625i
$909$		0			0
$910$	−19.7457	−	2.30795i	−0.654565	−	0.0765077i
$911$	8.41010	+	7.63176i	0.278639	+	0.252852i	0.799328	−	0.600895i	$-0.205189\pi$
$911$	8.41010	+	7.63176i	0.278639	+	0.252852i	−0.520689	+	0.853747i	$0.674325\pi$
$912$		0			0
$913$	34.2025	+	2.65843i	1.13194	+	0.0879812i
$914$	−2.53347	+	18.5483i	−0.0837998	+	0.613523i
$915$		0			0
$916$	−5.29033	+	1.03899i	−0.174797	+	0.0343291i
$917$	20.4646	+	7.44852i	0.675802	+	0.245972i
$918$		0			0
$919$	17.5344	−	6.38200i	0.578407	−	0.210523i	−0.0362160	−	0.999344i	$-0.511530\pi$
$919$	17.5344	−	6.38200i	0.578407	−	0.210523i	0.614623	+	0.788821i	$0.289308\pi$
$920$	65.4478	−	39.4980i	2.15775	−	1.30221i
$921$		0			0
$922$	9.20295	−	0.357116i	0.303083	−	0.0117610i
$923$	−2.75815	+	10.7078i	−0.0907856	+	0.352451i
$924$		0			0
$925$	−8.42967	−	16.0033i	−0.277166	−	0.526186i
$926$	26.0793	+	27.6424i	0.857019	+	0.908387i
$927$		0			0
$928$	1.03339	+	0.244919i	0.0339228	+	0.00803986i
$929$	37.0099	−	36.2991i	1.21426	−	1.19093i	0.238721	−	0.971088i	$-0.423272\pi$
$929$	37.0099	−	36.2991i	1.21426	−	1.19093i	0.975535	−	0.219845i	$-0.0705552\pi$
$930$		0			0
$931$	11.2477	+	13.9449i	0.368628	+	0.457027i
$932$	2.22775	−	0.348413i	0.0729722	−	0.0114126i
$933$		0			0
$934$	16.2794	+	4.53169i	0.532679	+	0.148281i
$935$	−28.8261	+	30.5539i	−0.942715	+	0.999220i
$936$		0			0
$937$	9.55335	−	31.9104i	0.312094	−	1.04247i	−0.647731	−	0.761869i	$-0.724282\pi$
$937$	9.55335	−	31.9104i	0.312094	−	1.04247i	0.959825	−	0.280599i	$-0.0905330\pi$
$938$	−13.2359	−	0.513614i	−0.432168	−	0.0167701i
$939$		0			0
$940$	−6.49006	+	1.80663i	−0.211682	+	0.0589258i
$941$	0.957261	−	1.81731i	0.0312058	−	0.0592428i	−0.868663	−	0.495404i	$-0.835020\pi$
$941$	0.957261	−	1.81731i	0.0312058	−	0.0592428i	0.899869	+	0.436161i	$0.143662\pi$
$942$		0			0
$943$	49.8645	+	27.5141i	1.62381	+	0.895982i
$944$	−0.347080	+	1.96839i	−0.0112965	+	0.0640656i
$945$		0			0
$946$	−3.80321	−	21.5691i	−0.123653	−	0.701271i
$947$	4.00747	−	11.7123i	0.130225	−	0.380598i	−0.861701	−	0.507417i	$-0.830600\pi$
$947$	4.00747	−	11.7123i	0.130225	−	0.380598i	0.991926	+	0.126819i	$0.0404768\pi$
$948$		0			0
$949$	−19.7336	+	8.06206i	−0.640580	+	0.261706i
$950$	−14.6403	+	21.3461i	−0.474995	+	0.692559i
$951$		0			0
$952$	4.01706	−	18.5448i	0.130194	−	0.601040i
$953$	−20.5559	+	27.6114i	−0.665871	+	0.894420i	−0.998822	−	0.0485239i	$-0.984548\pi$
$953$	−20.5559	+	27.6114i	−0.665871	+	0.894420i	0.332951	+	0.942944i	$0.391956\pi$
$954$		0			0
$955$	10.5784	−	24.5234i	0.342308	−	0.793559i
$956$	−0.393718	+	4.04778i	−0.0127338	+	0.130914i
$957$		0			0
$958$	−4.25234	−	2.56630i	−0.137387	−	0.0829134i
$959$	−11.7202	−	2.30177i	−0.378465	−	0.0743282i
$960$		0			0
$961$	17.2137	+	25.0982i	0.555280	+	0.809619i
$962$	−12.4552	−	8.19193i	−0.401572	−	0.264118i
$963$		0			0
$964$	0.422933	+	0.212405i	0.0136218	+	0.00684110i
$965$	−25.1225	+	19.4714i	−0.808722	+	0.626807i
$966$		0			0
$967$	10.8069	−	7.72430i	0.347526	−	0.248397i	−0.394311	−	0.918977i	$-0.629017\pi$
$967$	10.8069	−	7.72430i	0.347526	−	0.248397i	0.741837	+	0.670580i	$0.233955\pi$
$968$	−13.0780	+	11.8676i	−0.420343	+	0.381441i
$969$		0			0
$970$	−2.13345	−	5.52577i	−0.0685009	−	0.177422i
$971$	−47.5882			−1.52718			−0.763589	−	0.645702i	$-0.776565\pi$
$971$	−47.5882			−1.52718			−0.763589	+	0.645702i	$0.776565\pi$
$972$		0			0
$973$	−0.471480			−0.0151149
$974$	9.73133	+	25.2048i	0.311812	+	0.807614i
$975$		0			0
$976$	2.48894	−	2.25859i	0.0796691	−	0.0722958i
$977$	36.3951	−	26.0137i	1.16438	−	0.832251i	0.176024	−	0.984386i	$-0.443676\pi$
$977$	36.3951	−	26.0137i	1.16438	−	0.832251i	0.988360	+	0.152135i	$0.0486147\pi$
$978$		0			0
$979$	26.2859	−	20.3731i	0.840101	−	0.651127i
$980$	−4.85112	−	2.43633i	−0.154963	−	0.0778256i
$981$		0			0
$982$	2.47976	+	1.63096i	0.0791322	+	0.0520460i
$983$	−10.1601	−	14.8137i	−0.324055	−	0.472484i	0.628085	−	0.778145i	$-0.283839\pi$
$983$	−10.1601	−	14.8137i	−0.324055	−	0.472484i	−0.952141	+	0.305660i	$0.901123\pi$
$984$		0			0
$985$	25.0892	+	4.92736i	0.799409	+	0.156999i
$986$	4.13878	+	2.49777i	0.131806	+	0.0795451i
$987$		0			0
$988$	0.341990	−	3.51597i	0.0108802	−	0.111858i
$989$	22.3172	−	51.7371i	0.709646	−	1.64514i
$990$		0			0
$991$	6.79565	−	9.12814i	0.215871	−	0.289965i	−0.680976	−	0.732306i	$-0.738444\pi$
$991$	6.79565	−	9.12814i	0.215871	−	0.289965i	0.896847	+	0.442341i	$0.145852\pi$
$992$	−0.253948	+	1.17236i	−0.00806287	+	0.0372224i
$993$		0			0
$994$	−2.37478	+	3.46252i	−0.0753235	+	0.109824i
$995$	−79.3639	+	32.4237i	−2.51600	+	1.02790i
$996$		0			0
$997$	0.563783	−	1.64772i	0.0178552	−	0.0521837i	−0.936861	−	0.349703i	$-0.886283\pi$
$997$	0.563783	−	1.64772i	0.0178552	−	0.0521837i	0.954716	+	0.297519i	$0.0961591\pi$
$998$	−0.633063	−	3.59028i	−0.0200392	−	0.113648i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.253.8		1404
3.2	odd	2		243.2.i.a.94.19	✓	1404
243.106	even	81	inner	729.2.i.a.559.8		1404
243.137	odd	162		243.2.i.a.106.19	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.94.19	✓	1404	3.2	odd	2
243.2.i.a.106.19	yes	1404	243.137	odd	162
729.2.i.a.253.8		1404	1.1	even	1	trivial
729.2.i.a.559.8		1404	243.106	even	81	inner

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.471802 - 1.22200i) q^{2} +(0.210408 - 0.190935i) q^{4} +(-2.73185 + 1.95261i) q^{5} +(-0.904700 + 0.701195i) q^{7} +(-2.67376 - 1.34281i) q^{8} +(3.67497 + 2.41707i) q^{10} +(1.27702 + 1.86194i) q^{11} +(3.87460 + 0.760946i) q^{13} +(1.28370 + 0.774715i) q^{14} +(-0.324415 + 3.33528i) q^{16} +(2.19451 - 5.08744i) q^{17} +(1.88028 - 2.52566i) q^{19} +(-0.201982 + 0.932451i) q^{20} +(1.67279 - 2.43898i) q^{22} +(7.04343 - 2.87756i) q^{23} +(2.03165 - 5.93771i) q^{25} +(-0.898168 - 5.09376i) q^{26} +(-0.0564734 + 0.320276i) q^{28} +(-0.583179 - 0.321784i) q^{29} +(0.350612 - 0.665620i) q^{31} +(-1.53607 + 0.427594i) q^{32} +(-7.25221 - 0.281419i) q^{34} +(1.10234 - 3.68208i) q^{35} +(1.97789 - 2.09644i) q^{37} +(-3.97346 - 1.10609i) q^{38} +(9.92628 - 1.55244i) q^{40} +(4.69930 + 5.82622i) q^{41} +(5.28700 - 5.18546i) q^{43} +(0.624206 + 0.147940i) q^{44} +(-6.83947 - 7.24942i) q^{46} +(3.29078 + 6.24739i) q^{47} +(-1.41928 + 5.50999i) q^{49} +(-8.21440 + 0.318756i) q^{50} +(0.960539 - 0.579688i) q^{52} +(6.20444 - 2.25823i) q^{53} +(-7.12427 - 2.59302i) q^{55} +(3.36052 - 0.659985i) q^{56} +(-0.118075 + 0.864461i) q^{58} +(0.594668 + 0.0462212i) q^{59} +(-0.742742 - 0.674002i) q^{61} +(-0.978805 - 0.114406i) q^{62} +(5.24942 + 7.05119i) q^{64} +(-12.0706 + 5.48678i) q^{65} +(-7.73503 + 4.26801i) q^{67} +(-0.509630 - 1.48945i) q^{68} +(-5.01958 + 0.390153i) q^{70} +(-0.162823 + 2.79556i) q^{71} +(-4.51045 + 2.96657i) q^{73} +(-3.49501 - 1.42787i) q^{74} +(-0.0866102 - 0.890431i) q^{76} +(-2.46091 - 0.789058i) q^{77} +(-2.87650 - 0.449876i) q^{79} +(-5.62624 - 9.74493i) q^{80} +(4.90249 - 8.49136i) q^{82} +(9.53920 - 11.8268i) q^{83} +(3.93872 + 18.1831i) q^{85} +(-8.83103 - 4.01420i) q^{86} +(-0.914207 - 6.69318i) q^{88} +(-0.856461 - 14.7049i) q^{89} +(-4.03892 + 2.02842i) q^{91} +(0.932569 - 1.95030i) q^{92} +(6.08169 - 6.96885i) q^{94} +(-0.205027 + 10.5712i) q^{95} +(-1.09556 - 0.783060i) q^{97} +(7.40281 - 0.865264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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