LMFDB - Embedded newform 243.2.i.a.106.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(4,243)] 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("243.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.i (of order $81$, degree $54$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			106.19
Character	$\chi$	$=$	243.106
Dual form			243.2.i.a.94.19

$q$-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} +(-1.63932 - 0.559127i) q^{3} +(0.210408 + 0.190935i) q^{4} +(2.73185 + 1.95261i) q^{5} +(-1.45669 + 1.73945i) q^{6} +(-0.904700 - 0.701195i) q^{7} +(2.67376 - 1.34281i) q^{8} +(2.37475 + 1.83318i) q^{9} +(3.67497 - 2.41707i) q^{10} +(-1.27702 + 1.86194i) q^{11} +(-0.238170 - 0.430649i) q^{12} +(3.87460 - 0.760946i) q^{13} +(-1.28370 + 0.774715i) q^{14} +(-3.38662 - 4.72840i) q^{15} +(-0.324415 - 3.33528i) q^{16} +(-2.19451 - 5.08744i) q^{17} +(3.36055 - 2.03705i) q^{18} +(1.88028 + 2.52566i) q^{19} +(0.201982 + 0.932451i) q^{20} +(1.09104 + 1.65533i) q^{21} +(1.67279 + 2.43898i) q^{22} +(-7.04343 - 2.87756i) q^{23} +(-5.13395 + 0.706331i) q^{24} +(2.03165 + 5.93771i) q^{25} +(0.898168 - 5.09376i) q^{26} +(-2.86801 - 4.33296i) q^{27} +(-0.0564734 - 0.320276i) q^{28} +(0.583179 - 0.321784i) q^{29} +(-7.37591 + 1.90758i) q^{30} +(0.350612 + 0.665620i) q^{31} +(1.53607 + 0.427594i) q^{32} +(3.13451 - 2.33831i) q^{33} +(-7.25221 + 0.281419i) q^{34} +(-1.10234 - 3.68208i) q^{35} +(0.149650 + 0.839140i) q^{36} +(1.97789 + 2.09644i) q^{37} +(3.97346 - 1.10609i) q^{38} +(-6.77718 - 0.918955i) q^{39} +(9.92628 + 1.55244i) q^{40} +(-4.69930 + 5.82622i) q^{41} +(2.53756 - 0.552259i) q^{42} +(5.28700 + 5.18546i) q^{43} +(-0.624206 + 0.147940i) q^{44} +(2.90799 + 9.64493i) q^{45} +(-6.83947 + 7.24942i) q^{46} +(-3.29078 + 6.24739i) q^{47} +(-1.33302 + 5.64899i) q^{48} +(-1.41928 - 5.50999i) q^{49} +(8.21440 + 0.318756i) q^{50} +(0.752982 + 9.56697i) q^{51} +(0.960539 + 0.579688i) q^{52} +(-6.20444 - 2.25823i) q^{53} +(-6.64799 + 1.46040i) q^{54} +(-7.12427 + 2.59302i) q^{55} +(-3.36052 - 0.659985i) q^{56} +(-1.67023 - 5.19168i) q^{57} +(-0.118075 - 0.864461i) q^{58} +(-0.594668 + 0.0462212i) q^{59} +(0.190245 - 1.64152i) q^{60} +(-0.742742 + 0.674002i) q^{61} +(0.978805 - 0.114406i) q^{62} +(-0.863025 - 3.32364i) q^{63} +(5.24942 - 7.05119i) q^{64} +(12.0706 + 5.48678i) q^{65} +(-1.37854 - 4.93358i) q^{66} +(-7.73503 - 4.26801i) q^{67} +(0.509630 - 1.48945i) q^{68} +(9.93754 + 8.65542i) q^{69} +(-5.01958 - 0.390153i) q^{70} +(0.162823 + 2.79556i) q^{71} +(8.81113 + 1.71262i) q^{72} +(-4.51045 - 2.96657i) q^{73} +(3.49501 - 1.42787i) q^{74} +(-0.0105908 - 10.8698i) q^{75} +(-0.0866102 + 0.890431i) q^{76} +(2.46091 - 0.789058i) q^{77} +(-4.32044 + 7.84813i) q^{78} +(-2.87650 + 0.449876i) q^{79} +(5.62624 - 9.74493i) q^{80} +(2.27892 + 8.70669i) q^{81} +(4.90249 + 8.49136i) q^{82} +(-9.53920 - 11.8268i) q^{83} +(-0.0864970 + 0.556612i) q^{84} +(3.93872 - 18.1831i) q^{85} +(8.83103 - 4.01420i) q^{86} +(-1.13594 + 0.201438i) q^{87} +(-0.914207 + 6.69318i) q^{88} +(0.856461 - 14.7049i) q^{89} +(13.1581 + 0.996934i) q^{90} +(-4.03892 - 2.02842i) q^{91} +(-0.932569 - 1.95030i) q^{92} +(-0.202600 - 1.28720i) q^{93} +(6.08169 + 6.96885i) q^{94} +(0.205027 + 10.5712i) q^{95} +(-2.27903 - 1.55982i) q^{96} +(-1.09556 + 0.783060i) q^{97} +(-7.40281 - 0.865264i) q^{98} +(-6.44588 + 2.08065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) $ 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{50}{81}\right)$

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	−0.660001	−	0.751264i	$-0.729444\pi$
$2$	0.471802	−	1.22200i	0.333614	−	0.864082i	0.993616	−	0.112818i	$-0.0359877\pi$
$3$	−1.63932	−	0.559127i	−0.946463	−	0.322812i
$3$	−1.63932	−	0.559127i	−0.946463	−	0.322812i
$4$	0.210408	+	0.190935i	0.105204	+	0.0954676i
$5$	2.73185	+	1.95261i	1.22172	+	0.873233i	0.994916	−	0.100708i	$-0.0321108\pi$
$5$	2.73185	+	1.95261i	1.22172	+	0.873233i	0.226803	+	0.973941i	$0.427172\pi$
$6$	−1.45669	+	1.73945i	−0.594690	+	0.710127i
$7$	−0.904700	−	0.701195i	−0.341944	−	0.265027i	0.427124	−	0.904193i	$-0.359527\pi$
$7$	−0.904700	−	0.701195i	−0.341944	−	0.265027i	−0.769069	+	0.639166i	$0.779280\pi$
$8$	2.67376	−	1.34281i	0.945316	−	0.474755i
$9$	2.37475	+	1.83318i	0.791585	+	0.611059i
$10$	3.67497	−	2.41707i	1.16213	−	0.764343i
$11$	−1.27702	+	1.86194i	−0.385036	+	0.561397i	−0.967952	−	0.251136i	$-0.919196\pi$
$11$	−1.27702	+	1.86194i	−0.385036	+	0.561397i	0.582915	+	0.812533i	$0.301912\pi$
$12$	−0.238170	−	0.430649i	−0.0687537	−	0.124318i
$13$	3.87460	−	0.760946i	1.07462	−	0.211049i	0.376057	−	0.926597i	$-0.377280\pi$
$13$	3.87460	−	0.760946i	1.07462	−	0.211049i	0.698563	+	0.715548i	$0.253823\pi$
$14$	−1.28370	+	0.774715i	−0.343083	+	0.207051i
$15$	−3.38662	−	4.72840i	−0.874423	−	1.22087i
$16$	−0.324415	−	3.33528i	−0.0811038	−	0.833820i
$17$	−2.19451	−	5.08744i	−0.532247	−	1.23389i	−0.946198	−	0.323587i	$-0.895111\pi$
$17$	−2.19451	−	5.08744i	−0.532247	−	1.23389i	0.413952	−	0.910299i	$-0.364148\pi$
$18$	3.36055	−	2.03705i	0.792089	−	0.480137i
$19$	1.88028	+	2.52566i	0.431366	+	0.579425i	0.963659	−	0.267135i	$-0.0860769\pi$
$19$	1.88028	+	2.52566i	0.431366	+	0.579425i	−0.532293	+	0.846560i	$0.678670\pi$
$20$	0.201982	+	0.932451i	0.0451645	+	0.208502i
$21$	1.09104	+	1.65533i	0.238084	+	0.361222i
$22$	1.67279	+	2.43898i	0.356640	+	0.519993i
$23$	−7.04343	−	2.87756i	−1.46866	−	0.600013i	−0.504044	−	0.863678i	$-0.668155\pi$
$23$	−7.04343	−	2.87756i	−1.46866	−	0.600013i	−0.964614	+	0.263666i	$0.915068\pi$
$24$	−5.13395	+	0.706331i	−1.04796	+	0.144179i
$25$	2.03165	+	5.93771i	0.406329	+	1.18754i
$26$	0.898168	−	5.09376i	0.176145	−	0.998969i
$27$	−2.86801	−	4.33296i	−0.551949	−	0.833878i
$28$	−0.0564734	−	0.320276i	−0.0106725	−	0.0605265i
$29$	0.583179	−	0.321784i	0.108294	−	0.0597539i	−0.428041	−	0.903759i	$-0.640796\pi$
$29$	0.583179	−	0.321784i	0.108294	−	0.0597539i	0.536335	+	0.844005i	$0.319808\pi$
$30$	−7.37591	+	1.90758i	−1.34665	+	0.348274i
$31$	0.350612	+	0.665620i	0.0629717	+	0.119549i	0.914226	−	0.405204i	$-0.132800\pi$
$31$	0.350612	+	0.665620i	0.0629717	+	0.119549i	−0.851254	+	0.524753i	$0.824158\pi$
$32$	1.53607	+	0.427594i	0.271541	+	0.0755886i
$33$	3.13451	−	2.33831i	0.545648	−	0.407047i
$34$	−7.25221	+	0.281419i	−1.24374	+	0.0482629i
$35$	−1.10234	−	3.68208i	−0.186330	−	0.622386i
$36$	0.149650	+	0.839140i	0.0249416	+	0.139857i
$37$	1.97789	+	2.09644i	0.325162	+	0.344652i	0.869247	−	0.494379i	$-0.164604\pi$
$37$	1.97789	+	2.09644i	0.325162	+	0.344652i	−0.544084	+	0.839031i	$0.683123\pi$
$38$	3.97346	−	1.10609i	0.644581	−	0.179431i
$39$	−6.77718	−	0.918955i	−1.08522	−	0.147151i
$40$	9.92628	+	1.55244i	1.56948	+	0.245463i
$41$	−4.69930	+	5.82622i	−0.733908	+	0.909903i	−0.998516	−	0.0544529i	$-0.982659\pi$
$41$	−4.69930	+	5.82622i	−0.733908	+	0.909903i	0.264608	+	0.964356i	$0.414757\pi$
$42$	2.53756	−	0.552259i	0.391554	−	0.0852154i
$43$	5.28700	+	5.18546i	0.806260	+	0.790775i	0.981034	−	0.193834i	$-0.0620923\pi$
$43$	5.28700	+	5.18546i	0.806260	+	0.790775i	−0.174774	+	0.984609i	$0.555919\pi$
$44$	−0.624206	+	0.147940i	−0.0941026	+	0.0223027i
$45$	2.90799	+	9.64493i	0.433498	+	1.43778i
$46$	−6.83947	+	7.24942i	−1.00843	+	1.06887i
$47$	−3.29078	+	6.24739i	−0.480009	+	0.911275i	0.518413	+	0.855130i	$0.326523\pi$
$47$	−3.29078	+	6.24739i	−0.480009	+	0.911275i	−0.998423	+	0.0561450i	$0.982119\pi$
$48$	−1.33302	+	5.64899i	−0.192405	+	0.815361i
$49$	−1.41928	−	5.50999i	−0.202754	−	0.787141i
$50$	8.21440	+	0.318756i	1.16169	+	0.0450789i
$51$	0.752982	+	9.56697i	0.105439	+	1.33964i
$52$	0.960539	+	0.579688i	0.133203	+	0.0803883i
$53$	−6.20444	−	2.25823i	−0.852246	−	0.310192i	−0.121290	−	0.992617i	$-0.538703\pi$
$53$	−6.20444	−	2.25823i	−0.852246	−	0.310192i	−0.730956	+	0.682425i	$0.760925\pi$
$54$	−6.64799	+	1.46040i	−0.904677	+	0.198736i
$55$	−7.12427	+	2.59302i	−0.960637	+	0.349643i
$56$	−3.36052	−	0.659985i	−0.449068	−	0.0881941i
$57$	−1.67023	−	5.19168i	−0.221227	−	0.687655i
$58$	−0.118075	−	0.864461i	−0.0155040	−	0.113509i
$59$	−0.594668	+	0.0462212i	−0.0774191	+	0.00601749i	−0.116144	−	0.993232i	$-0.537053\pi$
$59$	−0.594668	+	0.0462212i	−0.0774191	+	0.00601749i	0.0387244	+	0.999250i	$0.487671\pi$
$60$	0.190245	−	1.64152i	0.0245605	−	0.211919i
$61$	−0.742742	+	0.674002i	−0.0950983	+	0.0862971i	−0.718170	−	0.695867i	$-0.755020\pi$
$61$	−0.742742	+	0.674002i	−0.0950983	+	0.0862971i	0.623072	+	0.782164i	$0.285884\pi$
$62$	0.978805	−	0.114406i	0.124308	−	0.0145296i
$63$	−0.863025	−	3.32364i	−0.108731	−	0.418740i
$64$	5.24942	−	7.05119i	0.656177	−	0.881399i
$65$	12.0706	+	5.48678i	1.49718	+	0.680551i
$66$	−1.37854	−	4.93358i	−0.169686	−	0.607282i
$67$	−7.73503	−	4.26801i	−0.944984	−	0.521420i	−0.0657637	−	0.997835i	$-0.520948\pi$
$67$	−7.73503	−	4.26801i	−0.944984	−	0.521420i	−0.879221	+	0.476415i	$0.841936\pi$
$68$	0.509630	−	1.48945i	0.0618017	−	0.180622i
$69$	9.93754	+	8.65542i	1.19634	+	1.04199i
$70$	−5.01958	−	0.390153i	−0.599955	−	0.0466322i
$71$	0.162823	+	2.79556i	0.0193235	+	0.331773i	0.994091	+	0.108550i	$0.0346207\pi$
$71$	0.162823	+	2.79556i	0.0193235	+	0.331773i	−0.974767	+	0.223223i	$0.928342\pi$
$72$	8.81113	+	1.71262i	1.03840	+	0.201835i
$73$	−4.51045	−	2.96657i	−0.527909	−	0.347211i	0.257411	−	0.966302i	$-0.417131\pi$
$73$	−4.51045	−	2.96657i	−0.527909	−	0.347211i	−0.785319	+	0.619091i	$0.787501\pi$
$74$	3.49501	−	1.42787i	0.406286	−	0.165986i
$75$	−0.0105908	−	10.8698i	−0.00122292	−	1.25513i
$76$	−0.0866102	+	0.890431i	−0.00993487	+	0.102139i
$77$	2.46091	−	0.789058i	0.280446	−	0.0899215i
$78$	−4.32044	+	7.84813i	−0.489194	+	0.888626i
$79$	−2.87650	+	0.449876i	−0.323631	+	0.0506150i	−0.314248	−	0.949341i	$-0.601752\pi$
$79$	−2.87650	+	0.449876i	−0.323631	+	0.0506150i	−0.00938340	+	0.999956i	$0.502987\pi$
$80$	5.62624	−	9.74493i	0.629032	−	1.08952i
$81$	2.27892	+	8.70669i	0.253213	+	0.967410i
$82$	4.90249	+	8.49136i	0.541389	+	0.937713i
$83$	−9.53920	−	11.8268i	−1.04706	−	1.29816i	−0.953125	−	0.302577i	$-0.902153\pi$
$83$	−9.53920	−	11.8268i	−1.04706	−	1.29816i	−0.0939385	−	0.995578i	$-0.529946\pi$
$84$	−0.0864970	+	0.556612i	−0.00943760	+	0.0607313i
$85$	3.93872	−	18.1831i	0.427214	−	1.97224i
$86$	8.83103	−	4.01420i	0.952274	−	0.432862i
$87$	−1.13594	+	0.201438i	−0.121785	+	0.0215964i
$88$	−0.914207	+	6.69318i	−0.0974548	+	0.713495i
$89$	0.856461	−	14.7049i	0.0907846	−	1.55871i	−0.578485	−	0.815693i	$-0.696356\pi$
$89$	0.856461	−	14.7049i	0.0907846	−	1.55871i	0.669270	−	0.743019i	$-0.266607\pi$
$90$	13.1581	+	0.996934i	1.38698	+	0.105086i
$91$	−4.03892	−	2.02842i	−0.423394	−	0.212636i
$92$	−0.932569	−	1.95030i	−0.0972270	−	0.203333i
$93$	−0.202600	−	1.28720i	−0.0210086	−	0.133477i
$94$	6.08169	+	6.96885i	0.627279	+	0.718782i
$95$	0.205027	+	10.5712i	0.0210354	+	1.08458i
$96$	−2.27903	−	1.55982i	−0.232603	−	0.159198i
$97$	−1.09556	+	0.783060i	−0.111237	+	0.0795077i	−0.635750	−	0.771895i	$-0.719309\pi$
$97$	−1.09556	+	0.783060i	−0.111237	+	0.0795077i	0.524513	+	0.851403i	$0.324247\pi$
$98$	−7.40281	−	0.865264i	−0.747796	−	0.0874049i
$99$	−6.44588	+	2.08065i	−0.647836	+	0.209113i
$100$	−0.706243	+	1.63726i	−0.0706243	+	0.163726i
$101$	−18.9733	−	6.08353i	−1.88791	−	0.605334i	−0.984163	−	0.177265i	$-0.943275\pi$
$101$	−18.9733	−	6.08353i	−1.88791	−	0.605334i	−0.903746	−	0.428068i	$-0.859194\pi$
$102$	12.0461	+	3.59357i	1.19274	+	0.355816i
$103$	3.67806	−	7.69201i	0.362410	−	0.757916i	−0.637512	−	0.770441i	$-0.720036\pi$
$103$	3.67806	−	7.69201i	0.362410	−	0.757916i	0.999922	+	0.0125247i	$0.00398683\pi$
$104$	9.33792	−	7.23744i	0.915659	−	0.709689i
$105$	−0.251655	+	6.65247i	−0.0245590	+	0.649215i
$106$	−5.68682	+	6.51637i	−0.552353	+	0.632926i
$107$	15.6188	+	13.1058i	1.50993	+	1.26698i	0.863891	+	0.503678i	$0.168020\pi$
$107$	15.6188	+	13.1058i	1.50993	+	1.26698i	0.646040	+	0.763304i	$0.276424\pi$
$108$	0.223862	−	1.45929i	0.0215411	−	0.140421i
$109$	−15.2816	+	12.8228i	−1.46371	+	1.22820i	−0.541974	+	0.840395i	$0.682323\pi$
$109$	−15.2816	+	12.8228i	−1.46371	+	1.22820i	−0.921740	+	0.387808i	$0.873232\pi$
$110$	−0.192577	+	9.92923i	−0.0183615	+	0.946715i
$111$	−2.07022	−	4.54262i	−0.196496	−	0.431167i
$112$	−2.04518	+	3.24490i	−0.193252	+	0.306615i
$113$	−10.2103	+	10.0142i	−0.960504	+	0.942056i	−0.998361	−	0.0572275i	$-0.981774\pi$
$113$	−10.2103	+	10.0142i	−0.960504	+	0.942056i	0.0378571	+	0.999283i	$0.487947\pi$
$114$	−7.13223	−	0.408433i	−0.667995	−	0.0382532i
$115$	−13.6228	−	21.6141i	−1.27034	−	2.01553i
$116$	0.184146	+	0.0436433i	0.0170975	+	0.00405218i
$117$	10.5962	+	5.29577i	0.979616	+	0.489594i
$118$	−0.224083	+	0.748489i	−0.0206285	+	0.0689040i
$119$	−1.58192	+	6.14139i	−0.145014	+	0.562980i
$120$	−15.4044	−	8.09500i	−1.40622	−	0.738969i
$121$	2.12591	+	5.50624i	0.193264	+	0.500567i
$122$	0.473202	+	1.22562i	0.0428417	+	0.110963i
$123$	10.9613	−	6.92355i	0.988344	−	0.624275i
$124$	−0.0533187	+	0.206996i	−0.00478816	+	0.0185888i
$125$	−1.22855	+	4.10364i	−0.109885	+	0.367041i
$126$	−4.46866	−	0.513486i	−0.398100	−	0.0457450i
$127$	20.8220	+	4.93491i	1.84766	+	0.437903i	0.996244	−	0.0865921i	$-0.0275977\pi$
$127$	20.8220	+	4.93491i	1.84766	+	0.437903i	0.851414	+	0.524495i	$0.175746\pi$
$128$	−4.43949	−	7.04373i	−0.392399	−	0.622584i
$129$	−5.76778	−	11.4567i	−0.507824	−	1.00871i
$130$	12.3998	−	12.1616i	1.08753	−	1.06664i
$131$	10.1450	−	16.0961i	0.886369	−	1.40632i	−0.0271964	−	0.999630i	$-0.508658\pi$
$131$	10.1450	−	16.0961i	0.886369	−	1.40632i	0.913566	−	0.406691i	$-0.133317\pi$
$132$	1.10599	+	0.106490i	0.0962643	+	0.00926874i
$133$	0.0698880	−	3.60341i	0.00606006	−	0.312455i
$134$	−8.86489	+	7.43853i	−0.765810	+	0.642591i
$135$	0.625598	−	17.4371i	0.0538429	−	1.50074i
$136$	−12.6991	−	10.6558i	−1.08893	−	0.913725i
$137$	−6.86122	+	7.86209i	−0.586194	+	0.671704i	−0.967537	−	0.252730i	$-0.918672\pi$
$137$	−6.86122	+	7.86209i	−0.586194	+	0.671704i	0.381343	+	0.924434i	$0.375462\pi$
$138$	15.2654	−	8.06000i	1.29948	−	0.686113i
$139$	0.325570	−	0.252336i	0.0276145	−	0.0214028i	−0.598700	−	0.800973i	$-0.704316\pi$
$139$	0.325570	−	0.252336i	0.0276145	−	0.0214028i	0.626314	+	0.779571i	$0.284563\pi$
$140$	0.471097	−	0.985217i	0.0398150	−	0.0832660i
$141$	8.88773	−	8.40152i	0.748482	−	0.707536i
$142$	3.49299	+	1.11998i	0.293125	+	0.0939869i
$143$	−3.53111	+	8.18602i	−0.295286	+	0.684550i
$144$	5.34375	−	8.51518i	0.445313	−	0.709598i
$145$	2.22147	+	0.259653i	0.184483	+	0.0215630i
$146$	−5.75318	+	4.11213i	−0.476137	+	0.340322i
$147$	−0.754122	+	9.82620i	−0.0621989	+	0.810451i
$148$	0.0158797	+	0.818755i	0.00130531	+	0.0673013i
$149$	12.7458	+	14.6050i	1.04417	+	1.19649i	0.980092	+	0.198545i	$0.0636216\pi$
$149$	12.7458	+	14.6050i	1.04417	+	1.19649i	0.0640813	+	0.997945i	$0.479588\pi$
$150$	−13.2878	−	5.11543i	−1.08495	−	0.417673i
$151$	−3.11757	−	6.51985i	−0.253704	−	0.530578i	0.735428	−	0.677602i	$-0.236981\pi$
$151$	−3.11757	−	6.51985i	−0.253704	−	0.530578i	−0.989133	+	0.147025i	$0.953030\pi$
$152$	8.41889	+	4.22813i	0.682862	+	0.342946i
$153$	4.11477	−	16.1044i	0.332659	−	1.30196i
$154$	0.196833	−	3.37950i	0.0158613	−	0.272328i
$155$	−0.341877	+	2.50298i	−0.0274602	+	0.201044i
$156$	−1.25051	−	1.48736i	−0.100121	−	0.119084i
$157$	16.2322	−	7.37844i	1.29547	−	0.588864i	0.356962	−	0.934119i	$-0.383813\pi$
$157$	16.2322	−	7.37844i	1.29547	−	0.588864i	0.938509	+	0.345255i	$0.112208\pi$
$158$	−0.807389	+	3.72732i	−0.0642324	+	0.296530i
$159$	8.90844	+	7.17104i	0.706485	+	0.568700i
$160$	3.36138	+	4.16746i	0.265740	+	0.329466i
$161$	4.35446	+	7.54215i	0.343180	+	0.594405i
$162$	11.7148	+	1.32300i	0.920398	+	0.103945i
$163$	−1.09406	+	1.89497i	−0.0856937	+	0.148426i	−0.905687	−	0.423948i	$-0.860644\pi$
$163$	−1.09406	+	1.89497i	−0.0856937	+	0.148426i	0.819993	+	0.572374i	$0.193977\pi$
$164$	−2.10120	+	0.328622i	−0.164076	+	0.0256611i
$165$	13.1288	−	0.267430i	1.02208	−	0.0208194i
$166$	−18.9529	+	6.07699i	−1.47103	+	0.471666i
$167$	−0.579933	+	5.96224i	−0.0448766	+	0.461372i	0.945762	+	0.324861i	$0.105317\pi$
$167$	−0.579933	+	5.96224i	−0.0448766	+	0.461372i	−0.990639	+	0.136511i	$0.956411\pi$
$168$	5.13996	+	2.96088i	0.396557	+	0.228437i
$169$	2.39906	−	0.980123i	0.184543	−	0.0753941i
$170$	−20.3614	−	13.3919i	−1.56165	−	1.02711i
$171$	−0.164769	+	9.44470i	−0.0126002	+	0.722255i
$172$	0.122342	+	2.10054i	0.00932852	+	0.160165i
$173$	3.22726	+	0.250842i	0.245364	+	0.0190712i	0.199585	−	0.979880i	$-0.436040\pi$
$173$	3.22726	+	0.250842i	0.245364	+	0.0190712i	0.0457785	+	0.998952i	$0.485423\pi$
$174$	−0.289780	+	1.48315i	−0.0219682	+	0.112437i
$175$	2.32547	−	6.79643i	0.175789	−	0.513762i
$176$	6.62438	+	3.65518i	0.499332	+	0.275520i
$177$	1.00070	+	0.256723i	0.0752169	+	0.0192965i
$178$	−17.5652	−	7.98437i	−1.31657	−	0.598454i
$179$	8.55852	−	11.4961i	0.639694	−	0.859258i	−0.357516	−	0.933907i	$-0.616376\pi$
$179$	8.55852	−	11.4961i	0.639694	−	0.859258i	0.997210	+	0.0746488i	$0.0237836\pi$
$180$	−1.22969	+	2.58461i	−0.0916557	+	0.192645i
$181$	7.11445	−	0.831560i	0.528813	−	0.0618094i	0.152503	−	0.988303i	$-0.451267\pi$
$181$	7.11445	−	0.831560i	0.528813	−	0.0618094i	0.376310	+	0.926494i	$0.377193\pi$
$182$	−4.38430	+	3.97854i	−0.324986	+	0.294909i
$183$	1.59445	−	0.689620i	0.117865	−	0.0509782i
$184$	−22.6964	+	1.76411i	−1.67320	+	0.130052i
$185$	1.30977	+	9.58918i	0.0962958	+	0.705010i
$186$	−1.66854	−	0.359728i	−0.122344	−	0.0263765i
$187$	12.2750	+	2.41072i	0.897634	+	0.176290i
$188$	−1.88525	+	0.686176i	−0.137496	+	0.0500445i
$189$	−0.443561	+	5.93106i	−0.0322643	+	0.431421i
$190$	13.0147	+	4.73695i	0.944183	+	0.343654i
$191$	6.80963	+	4.10963i	0.492727	+	0.297362i	0.741209	−	0.671274i	$-0.234253\pi$
$191$	6.80963	+	4.10963i	0.492727	+	0.297362i	−0.248482	+	0.968637i	$0.579932\pi$
$192$	−12.5480	+	8.62408i	−0.905573	+	0.622390i
$193$	9.45850	+	0.367033i	0.680838	+	0.0264196i	0.376875	−	0.926264i	$-0.376999\pi$
$193$	9.45850	+	0.367033i	0.680838	+	0.0264196i	0.303963	+	0.952684i	$0.401690\pi$
$194$	0.440010	+	1.70822i	0.0315909	+	0.122643i
$195$	−16.7199	−	15.7436i	−1.19733	−	1.12742i
$196$	0.753422	−	1.43034i	0.0538159	−	0.102167i
$197$	5.22530	−	5.53849i	0.372287	−	0.394601i	−0.513960	−	0.857814i	$-0.671822\pi$
$197$	5.22530	−	5.53849i	0.372287	−	0.394601i	0.886247	+	0.463213i	$0.153303\pi$
$198$	−0.498630	+	8.85851i	−0.0354361	+	0.629547i
$199$	24.8429	−	5.88788i	1.76107	−	0.417381i	0.782392	−	0.622786i	$-0.213999\pi$
$199$	24.8429	−	5.88788i	1.76107	−	0.417381i	0.978677	+	0.205405i	$0.0658512\pi$
$200$	13.4054	+	13.1479i	0.947902	+	0.929695i
$201$	10.2938	+	11.3215i	0.726072	+	0.798557i
$202$	−16.3857	+	20.3150i	−1.15289	+	1.42936i
$203$	−0.753235	−	0.117804i	−0.0528668	−	0.00826821i
$204$	−1.66824	+	2.15674i	−0.116800	+	0.151002i
$205$	−24.2141	+	6.74046i	−1.69119	+	0.470774i
$206$	−7.66430	−	8.12368i	−0.533997	−	0.566004i
$207$	−11.4514	−	19.7454i	−0.795924	−	1.37240i
$208$	−3.79495	−	12.6760i	−0.263132	−	0.878923i
$209$	−7.10379	+	0.275659i	−0.491379	+	0.0190678i
$210$	8.01057	+	3.44617i	0.552782	+	0.237808i
$211$	−19.6005	−	5.45617i	−1.34935	−	0.375618i	−0.483249	−	0.875483i	$-0.660544\pi$
$211$	−19.6005	−	5.45617i	−1.34935	−	0.375618i	−0.866103	+	0.499865i	$0.833383\pi$
$212$	−0.874289	−	1.65980i	−0.0600464	−	0.113995i
$213$	1.29616	−	4.67387i	0.0888111	−	0.320248i
$214$	23.3842	−	12.9029i	1.59851	−	0.882021i
$215$	4.31813	+	24.4893i	0.294494	+	1.67016i
$216$	−13.4867	−	7.73408i	−0.917654	−	0.526237i
$217$	0.149531	−	0.848034i	0.0101508	−	0.0575683i
$218$	8.45954	+	24.7239i	0.572952	+	1.67452i
$219$	5.73540	+	7.38508i	0.387562	+	0.499038i
$220$	−1.99410	−	0.814681i	−0.134443	−	0.0549258i
$221$	−12.3741	−	18.0419i	−0.832373	−	1.21363i
$222$	−6.52780	+	0.386583i	−0.438117	+	0.0259458i
$223$	−2.61577	−	12.0757i	−0.175165	−	0.808651i	−0.977359	−	0.211588i	$-0.932137\pi$
$223$	−2.61577	−	12.0757i	−0.175165	−	0.808651i	0.802194	−	0.597063i	$-0.203666\pi$
$224$	−1.08985	−	1.46393i	−0.0728189	−	0.0978127i
$225$	−6.06022	+	17.8250i	−0.404014	+	1.18833i
$226$	7.42007	+	17.2017i	0.493576	+	1.14424i
$227$	−0.342563	−	3.52185i	−0.0227367	−	0.233754i	−0.999785	−	0.0207358i	$-0.993399\pi$
$227$	−0.342563	−	3.52185i	−0.0227367	−	0.233754i	0.977048	−	0.213018i	$-0.0683293\pi$
$228$	0.639846	−	1.41128i	0.0423748	−	0.0934641i
$229$	−16.2460	+	9.80453i	−1.07357	+	0.647902i	−0.939319	−	0.343046i	$-0.888541\pi$
$229$	−16.2460	+	9.80453i	−1.07357	+	0.647902i	−0.134249	+	0.990948i	$0.542862\pi$
$230$	−32.8397	+	6.44950i	−2.16538	+	0.425268i
$231$	−4.47540	−	0.0824382i	−0.294460	−	0.00542404i
$232$	1.12718	−	1.64347i	0.0740031	−	0.107899i
$233$	−6.63043	+	4.36090i	−0.434374	+	0.285692i	−0.747805	−	0.663919i	$-0.768892\pi$
$233$	−6.63043	+	4.36090i	−0.434374	+	0.285692i	0.313431	+	0.949611i	$0.398522\pi$
$234$	11.4707	−	10.4499i	0.749863	−	0.683134i
$235$	−21.1886	+	10.6413i	−1.38219	+	0.694163i
$236$	−0.133948	−	0.103818i	−0.00871929	−	0.00675796i
$237$	4.96704	+	0.870835i	0.322644	+	0.0565668i
$238$	6.75841	+	4.83062i	0.438082	+	0.313122i
$239$	10.5999	+	9.61887i	0.685649	+	0.622193i	0.938487	−	0.345316i	$-0.112228\pi$
$239$	10.5999	+	9.61887i	0.685649	+	0.622193i	−0.252838	+	0.967509i	$0.581364\pi$
$240$	−14.6719	+	12.8293i	−0.947065	+	0.828128i
$241$	0.599954	−	1.55392i	0.0386464	−	0.100097i	−0.912217	−	0.409707i	$-0.865631\pi$
$241$	0.599954	−	1.55392i	0.0386464	−	0.100097i	0.950863	+	0.309611i	$0.100199\pi$
$242$	7.73161			0.497007
$243$	1.13226	−	15.5473i	0.0726345	−	0.997359i
$244$	−0.284970			−0.0182433
$245$	6.88158	−	17.8237i	0.439648	−	1.13872i
$246$	−3.28901	−	16.6612i	−0.209700	−	1.06228i
$247$	9.20722	+	8.35511i	0.585842	+	0.531623i
$248$	1.83125	+	1.30890i	0.116285	+	0.0831153i
$249$	9.02517	+	24.7215i	0.571947	+	1.56666i
$250$	4.43501	+	3.43739i	0.280495	+	0.217400i
$251$	3.71242	−	1.86445i	0.234326	−	0.117683i	−0.327762	−	0.944760i	$-0.606295\pi$
$251$	3.71242	−	1.86445i	0.234326	−	0.117683i	0.562088	+	0.827077i	$0.309998\pi$
$252$	0.453013	−	0.864103i	0.0285371	−	0.0544334i
$253$	14.3525	−	9.43977i	0.902332	−	0.593473i
$254$	15.8543	−	23.1162i	0.994789	−	1.45044i
$255$	−16.6235	+	27.6058i	−1.04100	+	1.72874i
$256$	6.54978	−	1.28633i	0.409361	−	0.0803959i
$257$	15.6094	−	9.42031i	0.973686	−	0.587623i	0.0618102	−	0.998088i	$-0.480313\pi$
$257$	15.6094	−	9.42031i	0.973686	−	0.587623i	0.911876	+	0.410465i	$0.134634\pi$
$258$	−16.7213	+	1.64290i	−1.04103	+	0.102282i
$259$	−0.319382	−	3.28353i	−0.0198454	−	0.204029i
$260$	1.49214	+	3.45917i	0.0925387	+	0.214529i
$261$	1.97479	+	0.304911i	0.122237	+	0.0188735i
$262$	−14.8829	−	19.9913i	−0.919472	−	1.23506i
$263$	−1.25775	−	5.80641i	−0.0775561	−	0.358039i	0.922020	−	0.387141i	$-0.126538\pi$
$263$	−1.25775	−	5.80641i	−0.0775561	−	0.358039i	−0.999576	+	0.0291026i	$0.990735\pi$
$264$	5.24102	−	10.4611i	0.322562	−	0.643837i
$265$	−12.5401	−	18.2840i	−0.770335	−	1.12318i
$266$	−4.37038	−	1.78550i	−0.267965	−	0.109476i
$267$	−9.62590	+	23.6271i	−0.589095	+	1.44596i
$268$	−0.812600	−	2.37491i	−0.0496375	−	0.145071i
$269$	−4.80841	+	27.2699i	−0.293174	+	1.66267i	0.381358	+	0.924427i	$0.375457\pi$
$269$	−4.80841	+	27.2699i	−0.293174	+	1.66267i	−0.674532	+	0.738246i	$0.735655\pi$
$270$	−21.0129	−	8.99132i	−1.27880	−	0.547194i
$271$	2.58462	+	14.6581i	0.157004	+	0.890417i	0.956930	+	0.290318i	$0.0937610\pi$
$271$	2.58462	+	14.6581i	0.157004	+	0.890417i	−0.799926	+	0.600099i	$0.795128\pi$
$272$	−16.2561	+	8.96974i	−0.985671	+	0.543870i
$273$	5.48695	+	5.58351i	0.332085	+	0.337929i
$274$	6.37031	+	12.0937i	0.384845	+	0.730610i
$275$	−13.6501	−	3.79978i	−0.823134	−	0.229135i
$276$	0.438315	+	3.71860i	0.0263835	+	0.223833i
$277$	−3.93124	+	0.152550i	−0.236206	+	0.00916585i	−0.156606	−	0.987661i	$-0.550055\pi$
$277$	−3.93124	+	0.152550i	−0.236206	+	0.00916585i	−0.0795992	+	0.996827i	$0.525364\pi$
$278$	−0.154749	−	0.516898i	−0.00928123	−	0.0310015i
$279$	−0.387583	+	2.22342i	−0.0232040	+	0.133113i
$280$	−7.89174	−	8.36475i	−0.471622	−	0.499890i
$281$	−1.59559	+	0.444162i	−0.0951847	+	0.0264965i	−0.315437	−	0.948946i	$-0.602151\pi$
$281$	−1.59559	+	0.444162i	−0.0951847	+	0.0264965i	0.220253	+	0.975443i	$0.429312\pi$
$282$	−6.07339	−	14.8246i	−0.361665	−	0.882794i
$283$	−0.872891	−	0.136518i	−0.0518880	−	0.00811513i	0.128522	−	0.991707i	$-0.458977\pi$
$283$	−0.872891	−	0.136518i	−0.0518880	−	0.00811513i	−0.180410	+	0.983592i	$0.557742\pi$
$284$	−0.499513	+	0.619298i	−0.0296406	+	0.0367486i
$285$	5.57451	−	17.4442i	0.330206	−	1.03330i
$286$	8.33732	+	8.17718i	0.492996	+	0.483527i
$287$	8.33678	−	1.97585i	0.492105	−	0.116631i
$288$	2.86393	+	3.83131i	0.168759	+	0.225762i
$289$	−9.40010	+	9.96352i	−0.552947	+	0.586090i
$290$	1.36539	−	2.59213i	0.0801785	−	0.152215i
$291$	2.23381	−	0.671131i	0.130948	−	0.0393424i
$292$	−0.382613	−	1.48540i	−0.0223907	−	0.0869262i
$293$	−27.5316	−	1.06835i	−1.60841	−	0.0624137i	−0.781191	−	0.624292i	$-0.785387\pi$
$293$	−27.5316	−	1.06835i	−1.60841	−	0.0624137i	−0.827220	+	0.561878i	$0.810079\pi$
$294$	11.6518	+	5.55755i	0.679546	+	0.324123i
$295$	−1.71479	−	1.03488i	−0.0998392	−	0.0602532i
$296$	8.10350	+	2.94943i	0.471006	+	0.171432i
$297$	11.7302	+	0.193209i	0.680657	+	0.0112111i
$298$	23.8608	−	8.68461i	1.38222	−	0.503086i
$299$	−29.4801	−	5.78971i	−1.70488	−	0.334828i
$300$	2.07319	−	2.28911i	0.119696	−	0.132162i
$301$	−1.14713	−	8.39850i	−0.0661197	−	0.484082i
$302$	−9.43811	+	0.733588i	−0.543102	+	0.0422133i
$303$	27.7018	+	20.5813i	1.59143	+	1.18237i
$304$	7.81378	−	7.09062i	0.448151	−	0.406675i
$305$	−3.34512	+	0.390988i	−0.191541	+	0.0223879i
$306$	−17.7381	−	12.6263i	−1.01402	−	0.721797i
$307$	−11.8742	+	15.9498i	−0.677697	+	0.910305i	−0.999331	−	0.0365589i	$-0.988360\pi$
$307$	−11.8742	+	15.9498i	−0.677697	+	0.910305i	0.321635	+	0.946864i	$0.395768\pi$
$308$	0.668454	+	0.303850i	0.0380887	+	0.0173134i
$309$	−10.3303	+	10.5532i	−0.587672	+	0.600349i
$310$	2.89734	+	1.59868i	0.164558	+	0.0907991i
$311$	3.13152	−	9.15222i	0.177572	−	0.518975i	−0.821083	−	0.570808i	$-0.806630\pi$
$311$	3.13152	−	9.15222i	0.177572	−	0.518975i	0.998656	+	0.0518335i	$0.0165065\pi$
$312$	−19.3545	+	6.64341i	−1.09573	+	0.376109i
$313$	5.92294	+	0.460367i	0.334784	+	0.0260215i	0.243785	−	0.969829i	$-0.421611\pi$
$313$	5.92294	+	0.460367i	0.334784	+	0.0260215i	0.0909997	+	0.995851i	$0.470994\pi$
$314$	−1.35805	−	23.3169i	−0.0766393	−	1.31585i
$315$	4.13212	−	10.7648i	0.232818	−	0.606530i
$316$	−0.691136	−	0.454567i	−0.0388794	−	0.0255714i
$317$	3.68516	−	1.50555i	0.206979	−	0.0845604i	−0.272339	−	0.962201i	$-0.587797\pi$
$317$	3.68516	−	1.50555i	0.206979	−	0.0845604i	0.479319	+	0.877641i	$0.340884\pi$
$318$	12.9660	−	7.50278i	0.727097	−	0.420735i
$319$	−0.145588	+	1.49677i	−0.00815134	+	0.0838031i
$320$	28.1088	−	9.01273i	1.57133	−	0.503827i
$321$	−18.2765	−	30.2175i	−1.02010	−	1.68658i
$322$	11.2709	−	1.76274i	0.628104	−	0.0982337i
$323$	8.72284	−	15.1084i	0.485352	−	0.840654i
$324$	−1.18291	+	2.26709i	−0.0657173	+	0.125949i
$325$	12.3901	+	21.4603i	0.687279	+	1.19040i
$326$	1.79947	+	2.23099i	0.0996635	+	0.123563i
$327$	32.2211	−	12.4764i	1.78183	−	0.689944i
$328$	−4.74128	+	21.8882i	−0.261793	+	1.20857i
$329$	7.35781	−	3.34453i	0.405649	−	0.184390i
$330$	5.86739	−	16.1695i	0.322989	−	0.890104i
$331$	−2.35851	+	17.2673i	−0.129635	+	0.949099i	0.804946	+	0.593349i	$0.202194\pi$
$331$	−2.35851	+	17.2673i	−0.129635	+	0.949099i	−0.934581	+	0.355750i	$0.884225\pi$
$332$	0.251018	−	4.30982i	0.0137764	−	0.236532i
$333$	0.853853	+	8.60434i	0.0467909	+	0.471515i
$334$	7.01222	+	3.52167i	0.383692	+	0.192697i
$335$	−12.7972	−	26.7630i	−0.699184	−	1.46222i
$336$	5.16703	−	4.17593i	0.281884	−	0.227816i
$337$	5.52218	+	6.32772i	0.300812	+	0.344693i	0.883865	−	0.467741i	$-0.154932\pi$
$337$	5.52218	+	6.32772i	0.300812	+	0.344693i	−0.583053	+	0.812434i	$0.698142\pi$
$338$	−0.0658278	−	3.39407i	−0.00358056	−	0.184613i
$339$	22.3372	−	10.7076i	1.21319	−	0.581559i
$340$	4.30054	−	3.07384i	0.233229	−	0.166702i
$341$	−1.68709	−	0.197192i	−0.0913608	−	0.0106785i
$342$	11.4637	+	4.65737i	0.619884	+	0.251842i
$343$	−5.75308	+	13.3371i	−0.310637	+	0.720138i
$344$	21.0992	+	6.76520i	1.13760	+	0.364755i
$345$	10.2472	+	43.0494i	0.551691	+	2.31770i
$346$	1.82915	−	3.82535i	0.0983360	−	0.205652i
$347$	22.9044	−	17.7522i	1.22957	−	0.952990i	0.229777	−	0.973243i	$-0.426200\pi$
$347$	22.9044	−	17.7522i	1.22957	−	0.952990i	0.999795	+	0.0202528i	$0.00644709\pi$
$348$	−0.277472	−	0.174506i	−0.0148740	−	0.00935451i
$349$	13.8561	−	15.8773i	0.741700	−	0.849893i	−0.251313	−	0.967906i	$-0.580862\pi$
$349$	13.8561	−	15.8773i	0.741700	−	0.849893i	0.993012	+	0.118013i	$0.0376523\pi$
$350$	−7.20806	−	6.04828i	−0.385287	−	0.323294i
$351$	−14.4095	−	14.6061i	−0.769124	−	0.779614i
$352$	−2.75775	+	2.31402i	−0.146988	+	0.123338i
$353$	0.111015	−	5.72389i	0.00590872	−	0.304652i	−0.985186	−	0.171491i	$-0.945142\pi$
$353$	0.111015	−	5.72389i	0.00590872	−	0.304652i	0.991094	−	0.133161i	$-0.0425127\pi$
$354$	0.785845	−	1.10172i	0.0417672	−	0.0585560i
$355$	−5.01383	+	7.95499i	−0.266107	+	0.422207i
$356$	2.98788	−	2.93049i	0.158357	−	0.155316i
$357$	6.02709	−	9.18322i	0.318987	−	0.486028i
$358$	−10.0103	−	15.8824i	−0.529059	−	0.839409i
$359$	10.5490	+	2.50017i	0.556758	+	0.131954i	0.499356	−	0.866397i	$-0.333570\pi$
$359$	10.5490	+	2.50017i	0.556758	+	0.131954i	0.0574020	+	0.998351i	$0.481718\pi$
$360$	20.7266	+	21.8833i	1.09239	+	1.15335i
$361$	2.60578	−	8.70391i	0.137146	−	0.458101i
$362$	2.34045	−	9.08617i	0.123011	−	0.477558i
$363$	−0.406363	−	10.2152i	−0.0213285	−	0.536156i
$364$	−0.462525	−	1.19797i	−0.0242429	−	0.0627906i
$365$	−6.52932	−	16.9114i	−0.341760	−	0.885181i
$366$	−0.0904515	−	2.27377i	−0.00472798	−	0.118852i
$367$	−4.92309	+	19.1126i	−0.256983	+	0.997670i	0.701534	+	0.712636i	$0.252499\pi$
$367$	−4.92309	+	19.1126i	−0.256983	+	0.997670i	−0.958517	+	0.285034i	$0.907995\pi$
$368$	−7.31247	+	24.4253i	−0.381189	+	1.27326i
$369$	−21.8402	+	5.22119i	−1.13696	+	0.271804i
$370$	12.3359	+	2.92366i	0.641313	+	0.151994i
$371$	4.02970	+	6.39355i	0.209211	+	0.331936i
$372$	0.203144	−	0.309521i	0.0105325	−	0.0160479i
$373$	9.03267	−	8.85918i	0.467694	−	0.458711i	−0.427742	−	0.903901i	$-0.640691\pi$
$373$	9.03267	−	8.85918i	0.467694	−	0.458711i	0.895436	+	0.445190i	$0.146864\pi$
$374$	8.73725	−	13.8626i	0.451792	−	0.716817i
$375$	4.30845	−	6.04028i	0.222487	−	0.311919i
$376$	−0.409678	+	21.1229i	−0.0211275	+	1.08933i
$377$	2.01472	−	1.69055i	0.103763	−	0.0870679i
$378$	7.03847	+	3.34032i	0.362020	+	0.171807i
$379$	−22.5864	−	18.9522i	−1.16019	−	0.973512i	−0.160278	−	0.987072i	$-0.551239\pi$
$379$	−22.5864	−	18.9522i	−1.16019	−	0.973512i	−0.999908	+	0.0135603i	$0.995683\pi$
$380$	−1.97527	+	2.26341i	−0.101329	+	0.116110i
$381$	−31.3748	−	19.7321i	−1.60738	−	1.01090i
$382$	8.23475	−	6.38241i	0.421326	−	0.326553i
$383$	6.68153	−	13.9732i	0.341410	−	0.713999i	−0.657822	−	0.753173i	$-0.728522\pi$
$383$	6.68153	−	13.9732i	0.341410	−	0.713999i	0.999232	+	0.0391746i	$0.0124729\pi$
$384$	3.33942	+	14.0292i	0.170414	+	0.715924i
$385$	8.26354	+	2.64960i	0.421149	+	0.135036i
$386$	4.91105	−	11.3851i	0.249966	−	0.579486i
$387$	3.04947	+	22.0062i	0.155014	+	1.11864i
$388$	−0.380029	−	0.0444190i	−0.0192931	−	0.00225503i
$389$	13.0775	−	9.34725i	0.663057	−	0.473924i	−0.199491	−	0.979900i	$-0.563929\pi$
$389$	13.0775	−	9.34725i	0.663057	−	0.473924i	0.862548	+	0.505975i	$0.168867\pi$
$390$	−27.1271	+	13.0038i	−1.37363	+	0.658471i
$391$	0.817458	+	42.1479i	0.0413406	+	2.13151i
$392$	−11.1937	−	12.8265i	−0.565366	−	0.647838i
$393$	−25.6306	+	20.7143i	−1.29289	+	1.04490i
$394$	−4.30272	−	8.99837i	−0.216768	−	0.453331i
$395$	−8.73659	−	4.38768i	−0.439585	−	0.220768i
$396$	−1.75354	−	0.792961i	−0.0881185	−	0.0398478i
$397$	1.18995	−	20.4306i	0.0597217	−	1.02538i	−0.826741	−	0.562582i	$-0.809808\pi$
$397$	1.18995	−	20.4306i	0.0597217	−	1.02538i	0.886463	−	0.462800i	$-0.153155\pi$
$398$	4.52596	−	33.1359i	0.226866	−	1.66095i
$399$	−2.12933	+	5.86807i	−0.106600	+	0.293771i
$400$	19.1448	−	8.70239i	0.957241	−	0.435120i
$401$	−2.92162	+	13.4877i	−0.145899	+	0.673543i	0.844529	+	0.535510i	$0.179881\pi$
$401$	−2.92162	+	13.4877i	−0.145899	+	0.673543i	−0.990428	+	0.138033i	$0.955922\pi$
$402$	18.6915	−	7.23755i	0.932247	−	0.360976i
$403$	1.86498	+	2.31221i	0.0929013	+	0.115180i
$404$	−2.83057	−	4.90269i	−0.140826	−	0.243918i
$405$	−10.7751	+	28.2352i	−0.535419	+	1.40302i
$406$	−0.499334	+	0.864871i	−0.0247815	+	0.0429228i
$407$	−6.42925	+	1.00552i	−0.318686	+	0.0498416i
$408$	14.8599	+	24.5686i	0.735675	+	1.21633i
$409$	−14.7415	+	4.72666i	−0.728918	+	0.233718i	−0.646537	−	0.762883i	$-0.723783\pi$
$409$	−14.7415	+	4.72666i	−0.728918	+	0.233718i	−0.0823814	+	0.996601i	$0.526253\pi$
$410$	−3.18744	+	32.7697i	−0.157416	+	1.61838i
$411$	15.6437	−	9.05220i	0.771645	−	0.446512i
$412$	2.24257	−	0.916190i	0.110483	−	0.0451375i
$413$	0.570406	+	0.375162i	0.0280678	+	0.0184605i
$414$	−29.5315	+	4.67762i	−1.45140	+	0.229893i
$415$	−2.96664	−	50.9352i	−0.145627	−	2.50031i
$416$	6.27702	+	0.487888i	0.307756	+	0.0239207i
$417$	−0.674802	+	0.231625i	−0.0330452	+	0.0113427i
$418$	−3.01472	+	8.81086i	−0.147455	+	0.430953i
$419$	24.4333	+	13.4817i	1.19364	+	0.658624i	0.950306	−	0.311317i	$-0.100770\pi$
$419$	24.4333	+	13.4817i	1.19364	+	0.658624i	0.243337	+	0.969942i	$0.421758\pi$
$420$	−1.32314	+	1.35168i	−0.0645627	+	0.0659554i
$421$	32.5295	+	14.7865i	1.58539	+	0.720649i	0.996180	−	0.0873284i	$-0.0278330\pi$
$421$	32.5295	+	14.7865i	1.58539	+	0.720649i	0.589213	+	0.807978i	$0.299438\pi$
$422$	−15.9150	+	21.3775i	−0.774728	+	1.04064i
$423$	−19.2674	+	8.80343i	−0.936811	+	0.428038i
$424$	−19.6215	+	2.29343i	−0.952906	+	0.111379i
$425$	25.7493	−	23.3662i	1.24902	−	1.13343i
$426$	−5.09993	−	3.78904i	−0.247092	−	0.183579i
$427$	1.14457	−	0.0889627i	0.0553894	−	0.00430520i
$428$	0.783980	+	5.73975i	0.0378951	+	0.277441i
$429$	10.3656	−	11.4452i	0.500458	−	0.552579i
$430$	31.9632	+	6.27736i	1.54140	+	0.302721i
$431$	−2.80914	+	1.02244i	−0.135311	+	0.0492493i	−0.408788	−	0.912629i	$-0.634049\pi$
$431$	−2.80914	+	1.02244i	−0.135311	+	0.0492493i	0.273477	+	0.961879i	$0.411826\pi$
$432$	−13.5212	+	10.9713i	−0.650539	+	0.527856i
$433$	23.2759	+	8.47173i	1.11857	+	0.407125i	0.834129	−	0.551569i	$-0.185971\pi$
$433$	23.2759	+	8.47173i	1.11857	+	0.407125i	0.284438	+	0.958694i	$0.408193\pi$
$434$	−0.965746	−	0.582830i	−0.0463573	−	0.0279768i
$435$	−3.49653	−	1.66774i	−0.167646	−	0.0799620i
$436$	−5.66371	−	0.219778i	−0.271242	−	0.0105254i
$437$	−5.97591	−	23.1999i	−0.285867	−	1.10980i
$438$	11.7305	−	3.52434i	0.560506	−	0.168400i
$439$	−6.22548	+	11.8188i	−0.297126	+	0.564079i	−0.987167	−	0.159691i	$-0.948950\pi$
$439$	−6.22548	+	11.8188i	−0.297126	+	0.564079i	0.690041	+	0.723770i	$0.257592\pi$
$440$	−15.5666	+	16.4997i	−0.742110	+	0.786590i
$441$	6.73034	−	15.6867i	0.320492	−	0.746984i
$442$	−27.8853	+	6.60893i	−1.32637	+	0.314355i
$443$	−1.40301	−	1.37607i	−0.0666591	−	0.0653788i	0.666124	−	0.745841i	$-0.267952\pi$
$443$	−1.40301	−	1.37607i	−0.0666591	−	0.0653788i	−0.732783	+	0.680462i	$0.761779\pi$
$444$	0.431756	−	1.35108i	0.0204902	−	0.0641195i
$445$	31.0525	−	38.4991i	1.47203	−	1.82503i
$446$	−15.9906	−	2.50089i	−0.757178	−	0.118421i
$447$	−12.7283	−	31.0688i	−0.602030	−	1.46950i
$448$	−9.69341	+	2.69834i	−0.457971	+	0.127485i
$449$	14.9917	+	15.8903i	0.707503	+	0.749909i	0.977034	−	0.213082i	$-0.0683503\pi$
$449$	14.9917	+	15.8903i	0.707503	+	0.749909i	−0.269531	+	0.962992i	$0.586869\pi$
$450$	18.9229	+	15.8154i	0.892032	+	0.745546i
$451$	−4.84698	−	16.1900i	−0.228235	−	0.762360i
$452$	−4.06039	+	0.157562i	−0.190985	+	0.00741108i
$453$	1.46528	+	12.4313i	0.0688451	+	0.584071i
$454$	−4.46532	−	1.24301i	−0.209568	−	0.0583372i
$455$	−7.07300	−	13.4278i	−0.331588	−	0.629503i
$456$	−11.4372	−	11.6385i	−0.535597	−	0.545022i
$457$	−12.5130	+	6.90437i	−0.585332	+	0.322973i	−0.747990	−	0.663710i	$-0.768981\pi$
$457$	−12.5130	+	6.90437i	−0.585332	+	0.322973i	0.162658	+	0.986683i	$0.447993\pi$
$458$	4.31620	+	24.4784i	0.201683	+	1.14380i
$459$	−15.7498	+	24.0995i	−0.735138	+	1.12487i
$460$	1.26054	−	7.14887i	0.0587729	−	0.333318i
$461$	2.27614	+	6.65228i	0.106011	+	0.309827i	0.986385	−	0.164451i	$-0.0525854\pi$
$461$	2.27614	+	6.65228i	0.106011	+	0.309827i	−0.880375	+	0.474279i	$0.842709\pi$
$462$	−2.21224	+	5.43003i	−0.102923	+	0.252628i
$463$	−26.8570	−	10.9723i	−1.24815	−	0.509926i	−0.344739	−	0.938699i	$-0.612032\pi$
$463$	−26.8570	−	10.9723i	−1.24815	−	0.509926i	−0.903412	+	0.428773i	$0.858946\pi$
$464$	−1.26243	−	1.84067i	−0.0586070	−	0.0854510i
$465$	1.95993	−	3.91204i	0.0908895	−	0.181416i
$466$	2.20076	+	10.1598i	0.101948	+	0.470646i
$467$	7.70358	+	10.3477i	0.356479	+	0.478835i	0.943799	−	0.330520i	$-0.107224\pi$
$467$	7.70358	+	10.3477i	0.356479	+	0.478835i	−0.587320	+	0.809355i	$0.699817\pi$
$468$	1.21837	+	3.13745i	0.0563193	+	0.145029i
$469$	4.00517	+	9.28503i	0.184942	+	0.428743i
$470$	3.00684	+	30.9130i	0.138695	+	1.42591i
$471$	−30.7353	+	3.01979i	−1.41621	+	0.139144i
$472$	−1.52793	+	0.922111i	−0.0703287	+	0.0424436i
$473$	−16.4066	+	3.22216i	−0.754378	+	0.148155i
$474$	3.40762	−	5.65885i	0.156517	−	0.259920i
$475$	−11.1766	+	16.2958i	−0.512815	+	0.747703i
$476$	−1.50546	+	0.990154i	−0.0690025	+	0.0453836i
$477$	−10.5943	−	16.7366i	−0.485079	−	0.766316i
$478$	16.7553	−	8.41481i	0.766368	−	0.384884i
$479$	−2.99688	−	2.32276i	−0.136931	−	0.106130i	0.541832	−	0.840487i	$-0.317731\pi$
$479$	−2.99688	−	2.32276i	−0.136931	−	0.106130i	−0.678764	+	0.734357i	$0.737484\pi$
$480$	−3.18025	−	8.71124i	−0.145158	−	0.397612i
$481$	9.25878	+	6.61778i	0.422164	+	0.301745i
$482$	−1.61583	−	1.46628i	−0.0735988	−	0.0667874i
$483$	−2.92135	−	14.7987i	−0.132926	−	0.673365i
$484$	−0.604027	+	1.56447i	−0.0274558	+	0.0711122i
$485$	−4.52192			−0.205330
$486$	−18.4645	−	8.71885i	−0.837568	−	0.395495i
$487$	−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
$489$	2.85305	−	2.49475i	0.129020	−	0.112817i
$490$	−18.5338	−	16.8185i	−0.837273	−	0.759784i
$491$	1.84337	+	1.31756i	0.0831899	+	0.0594606i	0.622327	−	0.782758i	$-0.286188\pi$
$491$	1.84337	+	1.31756i	0.0831899	+	0.0594606i	−0.539137	+	0.842218i	$0.681249\pi$
$492$	3.62829	+	0.636121i	0.163576	+	0.0286786i
$493$	−2.91685	−	2.26073i	−0.131368	−	0.101818i
$494$	14.5539	−	7.30924i	0.654811	−	0.328858i
$495$	−21.6719	−	6.90226i	−0.974078	−	0.310234i
$496$	2.10628	−	1.38533i	0.0945750	−	0.0622029i
$497$	1.81293	−	2.64332i	0.0813211	−	0.118569i
$498$	34.4677	+	0.634905i	1.54453	+	0.0284508i
$499$	2.73096	−	0.536344i	0.122255	−	0.0240100i	−0.131211	−	0.991355i	$-0.541886\pi$
$499$	2.73096	−	0.536344i	0.122255	−	0.0240100i	0.253465	+	0.967344i	$0.418430\pi$
$500$	−1.04203	+	0.628867i	−0.0466009	+	0.0281238i
$501$	4.28434	−	9.44977i	0.191410	−	0.422185i
$502$	−0.526823	−	5.41621i	−0.0235133	−	0.241737i
$503$	−4.48569	−	10.3990i	−0.200007	−	0.463668i	0.788464	−	0.615081i	$-0.210877\pi$
$503$	−4.48569	−	10.3990i	−0.200007	−	0.463668i	−0.988471	+	0.151413i	$0.951618\pi$
$504$	−6.77054	−	7.72773i	−0.301584	−	0.344220i
$505$	−39.9533	−	53.6666i	−1.77790	−	2.38813i
$506$	−4.76385	−	21.9924i	−0.211779	−	0.977680i
$507$	−4.48084	+	0.265360i	−0.199001	+	0.0117851i
$508$	3.43888	+	5.01401i	0.152576	+	0.222461i
$509$	1.59411	+	0.651267i	0.0706578	+	0.0288669i	0.413253	−	0.910616i	$-0.364392\pi$
$509$	1.59411	+	0.651267i	0.0706578	+	0.0288669i	−0.342595	+	0.939483i	$0.611306\pi$
$510$	25.8912	+	33.3383i	1.14648	+	1.47625i
$511$	2.00046	+	5.84657i	0.0884952	+	0.258637i
$512$	4.40991	−	25.0098i	0.194892	−	1.10529i
$513$	5.55089	−	15.3908i	0.245078	−	0.679520i
$514$	−4.14706	−	23.5191i	−0.182919	−	1.03738i
$515$	25.0674	−	13.8316i	1.10460	−	0.609493i
$516$	0.973908	−	3.51186i	0.0428739	−	0.154601i
$517$	−7.42989	−	14.1053i	−0.326766	−	0.620350i
$518$	−4.16315	−	1.15889i	−0.182918	−	0.0509188i
$519$	−5.15027	−	2.21566i	−0.226072	−	0.0972566i
$520$	39.6417	−	1.53828i	1.73840	−	0.0674579i
$521$	8.50756	+	28.4172i	0.372723	+	1.24498i	0.914544	+	0.404487i	$0.132550\pi$
$521$	8.50756	+	28.4172i	0.372723	+	1.24498i	−0.541821	+	0.840494i	$0.682265\pi$
$522$	1.30431	−	2.26934i	0.0570882	−	0.0993261i
$523$	8.45997	+	8.96704i	0.369928	+	0.392101i	0.885419	−	0.464794i	$-0.153872\pi$
$523$	8.45997	+	8.96704i	0.369928	+	0.392101i	−0.515490	+	0.856895i	$0.672390\pi$
$524$	5.20789	−	1.44972i	0.227508	−	0.0633311i
$525$	−7.61225	+	9.84131i	−0.332226	+	0.429510i
$526$	−7.68883	−	1.20251i	−0.335249	−	0.0524320i
$527$	2.61688	−	3.24443i	0.113993	−	0.141329i
$528$	−8.81579	−	9.69589i	−0.383658	−	0.421959i
$529$	24.9092	+	24.4308i	1.08301	+	1.06221i
$530$	−28.2594	+	6.69761i	−1.22751	+	0.290926i
$531$	−1.49692	−	0.980367i	−0.0649609	−	0.0425443i
$532$	0.702722	−	0.744842i	0.0304669	−	0.0322930i
$533$	−13.7745	+	26.1502i	−0.596639	+	1.13269i
$534$	24.3308	+	22.9101i	1.05290	+	0.991419i
$535$	17.0779	+	66.3004i	0.738342	+	2.86642i
$536$	−26.4127	−	1.02493i	−1.14086	−	0.0442704i
$537$	−20.4579	+	14.0605i	−0.882826	+	0.606755i
$538$	31.0551	+	18.7418i	1.33888	+	0.808018i
$539$	12.0717	+	4.39375i	0.519966	+	0.189252i
$540$	3.46098	−	3.54946i	0.148937	−	0.152744i
$541$	8.81849	−	3.20967i	0.379136	−	0.137994i	−0.145420	−	0.989370i	$-0.546453\pi$
$541$	8.81849	−	3.20967i	0.379136	−	0.137994i	0.524556	+	0.851376i	$0.324231\pi$
$542$	19.1316	+	3.75732i	0.821772	+	0.161391i
$543$	−12.1278	−	2.61468i	−0.520455	−	0.112207i
$544$	−1.19556	−	8.75301i	−0.0512590	−	0.375282i
$545$	−66.7850	+	5.19094i	−2.86076	+	0.222356i
$546$	9.41178	−	4.07073i	0.402787	−	0.174211i
$547$	−17.9621	+	16.2997i	−0.768002	+	0.696925i	−0.958604	−	0.284743i	$-0.908092\pi$
$547$	−17.9621	+	16.2997i	−0.768002	+	0.696925i	0.190602	+	0.981667i	$0.438956\pi$
$548$	−2.94481	+	0.344199i	−0.125796	+	0.0147034i
$549$	−2.99939	+	0.239012i	−0.128011	+	0.0102008i
$550$	−11.0835	+	14.8877i	−0.472601	+	0.634813i
$551$	1.90926	+	0.867864i	0.0813371	+	0.0369722i
$552$	38.1931	+	9.79825i	1.62561	+	0.417041i
$553$	2.91782	+	1.60998i	0.124078	+	0.0684635i
$554$	−1.66835	+	4.87594i	−0.0708815	+	0.207159i
$555$	3.21444	−	16.4521i	0.136445	−	0.698352i
$556$	0.116682	+	0.00906927i	0.00494843	+	0.000384623i
$557$	0.916202	+	15.7306i	0.0388207	+	0.666526i	0.960450	+	0.278454i	$0.0898220\pi$
$557$	0.916202	+	15.7306i	0.0388207	+	0.666526i	−0.921629	+	0.388073i	$0.873141\pi$
$558$	2.53415	+	1.52264i	0.107279	+	0.0644584i
$559$	24.4309	+	16.0684i	1.03332	+	0.679622i
$560$	−11.9232	+	4.87114i	−0.503845	+	0.205843i
$561$	−18.7747	−	10.8152i	−0.792669	−	0.456619i
$562$	−0.210036	+	2.15936i	−0.00885983	+	0.0910870i
$563$	−13.0165	+	4.17358i	−0.548581	+	0.175896i	−0.566676	−	0.823941i	$-0.691771\pi$
$563$	−13.0165	+	4.17358i	−0.548581	+	0.175896i	0.0180946	+	0.999836i	$0.494240\pi$
$564$	3.47420	−	0.0707683i	0.146290	−	0.00297989i
$565$	−47.4468	+	7.42054i	−1.99610	+	0.312184i
$566$	−0.578656	+	1.00226i	−0.0243227	+	0.0421282i
$567$	4.04335	−	9.47491i	0.169805	−	0.397909i
$568$	4.18926	+	7.25602i	0.175778	+	0.304456i
$569$	17.8902	+	22.1804i	0.749997	+	0.929850i	0.999255	−	0.0385870i	$-0.0122857\pi$
$569$	17.8902	+	22.1804i	0.749997	+	0.929850i	−0.249259	+	0.968437i	$0.580187\pi$
$570$	−18.6867	−	15.0422i	−0.782698	−	0.630050i
$571$	2.45851	−	11.3497i	0.102885	−	0.474972i	−0.896598	−	0.442844i	$-0.853969\pi$
$571$	2.45851	−	11.3497i	0.102885	−	0.474972i	0.999484	−	0.0321272i	$-0.0102282\pi$
$572$	−2.30597	+	1.04819i	−0.0964176	+	0.0438272i
$573$	−8.86537	−	10.5445i	−0.370356	−	0.440501i
$574$	1.51882	−	11.1197i	0.0633943	−	0.464129i
$575$	2.77635	−	47.6681i	0.115782	−	1.98790i
$576$	25.3922	−	7.12174i	1.05801	−	0.296739i
$577$	25.7878	+	12.9511i	1.07356	+	0.539163i	0.895593	−	0.444874i	$-0.146751\pi$
$577$	25.7878	+	12.9511i	1.07356	+	0.539163i	0.177968	+	0.984036i	$0.443048\pi$
$578$	7.74041	+	16.1877i	0.321959	+	0.673320i
$579$	−15.3003	−	5.89018i	−0.635859	−	0.244788i
$580$	0.417839	+	0.478791i	0.0173498	+	0.0198807i
$581$	0.337250	+	17.3885i	0.0139915	+	0.721397i
$582$	0.233795	−	3.04635i	0.00969112	−	0.126275i
$583$	12.1279	−	8.66850i	0.502286	−	0.359013i
$584$	−16.0434	−	1.87520i	−0.663880	−	0.0775965i
$585$	18.6066	+	35.1574i	0.769287	+	1.45358i
$586$	−14.2950	+	33.1394i	−0.590519	+	1.36898i
$587$	12.7643	+	4.09272i	0.526841	+	0.168925i	0.556831	−	0.830626i	$-0.312017\pi$
$587$	12.7643	+	4.09272i	0.526841	+	0.168925i	−0.0299908	+	0.999550i	$0.509548\pi$
$588$	−2.03484	+	1.92353i	−0.0839155	+	0.0793248i
$589$	−1.02188	+	2.13708i	−0.0421058	+	0.0880568i
$590$	−2.07367	+	1.60721i	−0.0853715	+	0.0661679i
$591$	−11.6627	+	6.15777i	−0.479738	+	0.253297i
$592$	6.35054	−	7.27691i	0.261006	−	0.299079i
$593$	−15.3902	−	12.9139i	−0.632000	−	0.530311i	0.269549	−	0.962987i	$-0.413125\pi$
$593$	−15.3902	−	12.9139i	−0.632000	−	0.530311i	−0.901550	+	0.432675i	$0.857570\pi$
$594$	5.77044	−	14.2431i	0.236764	−	0.584403i
$595$	−16.3133	+	13.6885i	−0.668779	+	0.561173i
$596$	−0.106801	+	5.50663i	−0.00437474	+	0.225560i
$597$	−44.0177	−	4.23821i	−1.80152	−	0.173458i
$598$	−20.9838	+	33.2931i	−0.858091	+	1.36145i
$599$	−11.3279	+	11.1103i	−0.462846	+	0.453956i	−0.893832	−	0.448402i	$-0.851993\pi$
$599$	−11.3279	+	11.1103i	−0.462846	+	0.453956i	0.430985	+	0.902359i	$0.358166\pi$
$600$	−14.6244	−	29.0489i	−0.597037	−	1.18592i
$601$	−15.7816	−	25.0393i	−0.643746	−	1.02137i	−0.996330	−	0.0855930i	$-0.972722\pi$
$601$	−15.7816	−	25.0393i	−0.643746	−	1.02137i	0.352584	−	0.935780i	$-0.385303\pi$
$602$	−10.8042	−	2.56063i	−0.440345	−	0.104364i
$603$	−10.5448	−	24.3152i	−0.429417	−	0.990190i
$604$	0.588906	−	1.96708i	0.0239623	−	0.0800395i
$605$	−4.94387	+	19.1933i	−0.200997	+	0.780317i
$606$	38.2201	−	24.1412i	1.55258	−	0.980671i
$607$	4.92873	+	12.7657i	0.200051	+	0.518145i	0.996214	−	0.0869374i	$-0.0277080\pi$
$607$	4.92873	+	12.7657i	0.200051	+	0.518145i	−0.796163	+	0.605083i	$0.793140\pi$
$608$	1.80828	+	4.68357i	0.0733356	+	0.189944i
$609$	1.16893	+	0.614272i	0.0473674	+	0.0248916i
$610$	−1.10045	+	4.27219i	−0.0445558	+	0.172976i
$611$	−7.99652	+	26.7102i	−0.323504	+	1.08058i
$612$	3.94067	−	2.60283i	0.159292	−	0.105213i
$613$	28.1886	+	6.68083i	1.13853	+	0.269836i	0.756296	−	0.654230i	$-0.227007\pi$
$613$	28.1886	+	6.68083i	1.13853	+	0.269836i	0.382232	+	0.924066i	$0.375155\pi$
$614$	13.8884	+	22.0354i	0.560489	+	0.889277i
$615$	43.4635	+	2.48897i	1.75262	+	0.100365i
$616$	5.52031	−	5.41428i	0.222420	−	0.218148i
$617$	−20.9510	+	33.2411i	−0.843457	+	1.33824i	0.0959332	+	0.995388i	$0.469416\pi$
$617$	−20.9510	+	33.2411i	−0.843457	+	1.33824i	−0.939391	+	0.342849i	$0.888608\pi$
$618$	8.02209	+	17.6026i	0.322696	+	0.708082i
$619$	0.572024	−	29.4934i	0.0229916	−	1.18544i	−0.793679	−	0.608336i	$-0.791837\pi$
$619$	0.572024	−	29.4934i	0.0229916	−	1.18544i	0.816671	−	0.577103i	$-0.195817\pi$
$620$	−0.549841	+	0.461371i	−0.0220821	+	0.0185291i
$621$	7.73230	+	38.7718i	0.310286	+	1.55586i
$622$	−9.70653	−	8.14474i	−0.389196	−	0.326574i
$623$	−11.0858	+	12.7029i	−0.444144	+	0.508933i
$624$	−0.866351	+	22.9019i	−0.0346818	+	0.916810i
$625$	13.4322	−	10.4107i	0.537288	−	0.416429i
$626$	3.35702	−	7.02061i	0.134173	−	0.280600i
$627$	11.7995	+	3.52002i	0.471228	+	0.140576i
$628$	4.82419	+	1.54682i	0.192506	+	0.0617247i
$629$	6.32501	−	14.6630i	0.252195	−	0.584653i
$630$	−11.2051	−	10.1283i	−0.446420	−	0.403521i
$631$	14.0896	+	1.64684i	0.560899	+	0.0655597i	0.391818	−	0.920043i	$-0.371846\pi$
$631$	14.0896	+	1.64684i	0.560899	+	0.0655597i	0.169081	+	0.985602i	$0.445920\pi$
$632$	−7.08696	+	5.06545i	−0.281904	+	0.201493i
$633$	29.0808	+	19.9036i	1.15586	+	0.791096i
$634$	−0.101117	−	5.21358i	−0.00401588	−	0.207058i
$635$	47.2467	+	54.1387i	1.87493	+	2.14843i
$636$	0.505205	+	3.20978i	0.0200327	+	0.127276i
$637$	−9.69195	−	20.2690i	−0.384009	−	0.803087i
$638$	1.76036	+	0.884087i	0.0696934	+	0.0350013i
$639$	−4.73810	+	6.93726i	−0.187436	+	0.274434i
$640$	1.62563	−	27.9110i	0.0642587	−	1.10328i
$641$	3.32437	−	24.3387i	0.131305	−	0.961320i	−0.800749	−	0.599000i	$-0.795565\pi$
$641$	3.32437	−	24.3387i	0.131305	−	0.961320i	0.932054	−	0.362320i	$-0.118015\pi$
$642$	−45.5486	+	8.07721i	−1.79766	+	0.318782i
$643$	−9.86610	+	4.48469i	−0.389081	+	0.176859i	−0.598792	−	0.800904i	$-0.704353\pi$
$643$	−9.86610	+	4.48469i	−0.389081	+	0.176859i	0.209711	+	0.977763i	$0.432748\pi$
$644$	−0.523848	+	2.41835i	−0.0206425	+	0.0952964i
$645$	6.61383	−	42.5603i	0.260419	−	1.67581i
$646$	−14.3470	−	17.7874i	−0.564474	−	0.699838i
$647$	−2.31697	−	4.01310i	−0.0910894	−	0.157771i	0.816880	−	0.576807i	$-0.195702\pi$
$647$	−2.31697	−	4.01310i	−0.0910894	−	0.157771i	−0.907970	+	0.419036i	$0.862368\pi$
$648$	17.7847	+	20.2194i	0.698650	+	0.794294i
$649$	0.673342	−	1.16626i	0.0264310	−	0.0457798i
$650$	32.0701	−	5.01567i	1.25789	−	0.196731i
$651$	−0.719288	+	1.30659i	−0.0281911	+	0.0512094i
$652$	−0.592017	+	0.189823i	−0.0231852	+	0.00743403i
$653$	1.39800	−	14.3727i	0.0547081	−	0.562448i	−0.927392	−	0.374090i	$-0.877955\pi$
$653$	1.39800	−	14.3727i	0.0547081	−	0.562448i	0.982100	−	0.188358i	$-0.0603166\pi$
$654$	−0.0440989	−	45.2604i	−0.00172440	−	1.76982i
$655$	59.1438	−	24.1629i	2.31094	−	0.944123i
$656$	20.9566	+	13.7834i	0.818218	+	0.538150i
$657$	−5.27297	−	15.3133i	−0.205718	−	0.597430i
$658$	−0.615584	−	10.5692i	−0.0239980	−	0.412029i
$659$	20.1953	+	1.56971i	0.786698	+	0.0611470i	0.464555	−	0.885544i	$-0.346214\pi$
$659$	20.1953	+	1.56971i	0.786698	+	0.0611470i	0.322143	+	0.946691i	$0.395597\pi$
$660$	2.81347	+	2.45048i	0.109514	+	0.0953849i
$661$	10.4400	−	30.5120i	0.406068	−	1.18678i	−0.533909	−	0.845542i	$-0.679278\pi$
$661$	10.4400	−	30.5120i	0.406068	−	1.18678i	0.939977	−	0.341237i	$-0.110846\pi$
$662$	19.9879	+	11.0289i	0.776852	+	0.428649i
$663$	10.1974	+	36.4952i	0.396036	+	1.41735i
$664$	−41.3866	−	18.8125i	−1.60611	−	0.730067i
$665$	7.22696	−	9.70749i	0.280249	−	0.376440i
$666$	10.9173	+	3.01613i	0.423038	+	0.116873i
$667$	−5.03353	+	0.588336i	−0.194899	+	0.0227805i
$668$	−1.26042	+	1.14377i	−0.0487673	+	0.0442539i
$669$	−2.46378	+	21.2586i	−0.0952551	+	0.821903i
$670$	−38.7421	+	3.01127i	−1.49674	+	0.116336i
$671$	−0.306456	−	2.24366i	−0.0118306	−	0.0866154i
$672$	0.968100	+	3.00921i	0.0373453	+	0.116083i
$673$	−25.2799	−	4.96482i	−0.974470	−	0.191380i	−0.319958	−	0.947432i	$-0.603669\pi$
$673$	−25.2799	−	4.96482i	−0.974470	−	0.191380i	−0.654512	+	0.756052i	$0.727126\pi$
$674$	10.3378	−	3.76266i	0.398198	−	0.144932i
$675$	19.9011	−	25.8325i	0.765993	−	0.994292i
$676$	0.691922	+	0.251839i	0.0266124	+	0.00968611i
$677$	−13.3615	−	8.06373i	−0.513525	−	0.309914i	0.236154	−	0.971716i	$-0.424113\pi$
$677$	−13.3615	−	8.06373i	−0.513525	−	0.309914i	−0.749679	+	0.661802i	$0.769792\pi$
$678$	−2.54598	−	32.3478i	−0.0977779	−	1.24231i
$679$	1.54023	+	0.0597681i	0.0591087	+	0.00229369i
$680$	−13.8853	−	53.9062i	−0.532479	−	2.06721i
$681$	−1.40759	+	5.96499i	−0.0539390	+	0.228579i
$682$	−1.03694	+	1.96858i	−0.0397064	+	0.0753807i
$683$	−0.109120	+	0.115661i	−0.00417537	+	0.00442563i	−0.729458	−	0.684026i	$-0.760228\pi$
$683$	−0.109120	+	0.115661i	−0.00417537	+	0.00442563i	0.725283	+	0.688451i	$0.241709\pi$
$684$	−1.83800	+	1.95578i	−0.0702775	+	0.0747812i
$685$	−34.0954	+	8.08076i	−1.30272	+	0.308750i
$686$	13.5836	+	13.3227i	0.518626	+	0.508664i
$687$	32.1145	−	6.98920i	1.22524	−	0.266654i
$688$	15.5798	−	19.3159i	0.593973	−	0.736411i
$689$	−25.7581	−	4.02849i	−0.981306	−	0.153473i
$690$	57.4409	+	7.78872i	2.18674	+	0.296512i
$691$	−18.8668	+	5.25193i	−0.717726	+	0.199793i	−0.607735	−	0.794140i	$-0.707922\pi$
$691$	−18.8668	+	5.25193i	−0.717726	+	0.199793i	−0.109991	+	0.993933i	$0.535082\pi$
$692$	0.631147	+	0.668977i	0.0239926	+	0.0254307i
$693$	7.29053	+	2.63746i	0.276944	+	0.100189i
$694$	−10.8869	−	36.3646i	−0.413259	−	1.38038i
$695$	1.38212	−	0.0536326i	0.0524268	−	0.00203440i
$696$	−2.76672	+	2.06394i	−0.104872	+	0.0782335i
$697$	39.9532	+	11.1217i	1.51334	+	0.421266i
$698$	−12.8647	−	24.4230i	−0.486936	−	0.924426i
$699$	13.3077	−	3.44167i	0.503343	−	0.130176i
$700$	1.78697	−	0.986011i	0.0675413	−	0.0372677i
$701$	−3.63706	−	20.6268i	−0.137370	−	0.779064i	−0.973180	−	0.230045i	$-0.926113\pi$
$701$	−3.63706	−	20.6268i	−0.137370	−	0.779064i	0.835810	−	0.549019i	$-0.184999\pi$
$702$	−24.6470	+	10.7172i	−0.930241	+	0.404496i
$703$	−1.57590	+	8.93735i	−0.0594360	+	0.337078i
$704$	6.42530	+	18.7786i	0.242162	+	0.707746i
$705$	40.6848	−	5.59743i	1.53228	−	0.210812i
$706$	−6.94220	−	2.83620i	−0.261273	−	0.106742i
$707$	12.8994	+	18.8077i	0.485130	+	0.707337i
$708$	0.161537	+	0.245085i	0.00607093	+	0.00921085i
$709$	−8.62768	−	39.8298i	−0.324019	−	1.49584i	−0.791134	−	0.611643i	$-0.790509\pi$
$709$	−8.62768	−	39.8298i	−0.324019	−	1.49584i	0.467114	−	0.884197i	$-0.345294\pi$
$710$	7.35544	+	9.88007i	0.276045	+	0.370792i
$711$	−7.65568	−	4.20479i	−0.287110	−	0.157692i
$712$	−17.4559	−	40.4673i	−0.654187	−	1.51658i
$713$	−0.554150	−	5.69716i	−0.0207531	−	0.213360i
$714$	−8.37828	−	11.6977i	−0.313549	−	0.437777i
$715$	−25.6305	+	15.4681i	−0.958528	+	0.578474i
$716$	3.99579	−	0.784748i	0.149330	−	0.0293274i
$717$	−11.9984	−	21.6951i	−0.448090	−	0.810218i
$718$	8.03226	−	11.7113i	0.299761	−	0.437063i
$719$	14.6635	−	9.64436i	0.546857	−	0.359674i	−0.245820	−	0.969316i	$-0.579057\pi$
$719$	14.6635	−	9.64436i	0.546857	−	0.359674i	0.792677	+	0.609642i	$0.208687\pi$
$720$	31.2251	−	12.8279i	1.16369	−	0.478069i
$721$	−8.72114	+	4.37992i	−0.324792	+	0.163117i
$722$	−9.40674	−	7.29078i	−0.350083	−	0.271335i
$723$	−1.85235	+	2.21192i	−0.0688898	+	0.0822623i
$724$	1.65571	+	1.18343i	0.0615341	+	0.0439819i
$725$	3.09548	+	2.80899i	0.114963	+	0.104323i
$726$	−12.6746	−	4.32295i	−0.470399	−	0.160440i
$727$	−14.6458	+	37.9335i	−0.543182	+	1.40688i	0.341146	+	0.940010i	$0.389185\pi$
$727$	−14.6458	+	37.9335i	−0.543182	+	1.40688i	−0.884328	+	0.466866i	$0.845383\pi$
$728$	−13.5229			−0.501191
$729$	−10.5490	+	24.8539i	−0.390705	+	0.920516i
$730$	−23.7462			−0.878886
$731$	14.7783	−	38.2769i	0.546597	−	1.41572i
$732$	0.467157	+	0.159334i	0.0172666	+	0.00588916i
$733$	−19.5116	−	17.7059i	−0.720678	−	0.653981i	0.226748	−	0.973953i	$-0.427191\pi$
$733$	−19.5116	−	17.7059i	−0.720678	−	0.653981i	−0.947427	+	0.319973i	$0.896326\pi$
$734$	21.0328	+	15.0334i	0.776336	+	0.554892i
$735$	−21.2469	+	25.3712i	−0.783702	+	0.935830i
$736$	−9.58876	−	7.43185i	−0.353446	−	0.273942i
$737$	17.8246	−	8.95184i	0.656577	−	0.329745i
$738$	−3.92396	+	29.1520i	−0.144443	+	1.07310i
$739$	15.8444	−	10.4210i	0.582846	−	0.383344i	−0.223574	−	0.974687i	$-0.571772\pi$
$739$	15.8444	−	10.4210i	0.582846	−	0.383344i	0.806420	+	0.591343i	$0.201402\pi$
$740$	−1.55533	+	2.26772i	−0.0571749	+	0.0833631i
$741$	−10.4220	−	18.8447i	−0.382863	−	0.692278i
$742$	9.71411	−	1.90779i	0.356616	−	0.0700372i
$743$	−39.3478	+	23.7465i	−1.44353	+	0.871176i	−0.999689	−	0.0249280i	$-0.992064\pi$
$743$	−39.3478	+	23.7465i	−1.44353	+	0.871176i	−0.443843	+	0.896104i	$0.646385\pi$
$744$	−2.27017	−	3.16961i	−0.0832285	−	0.116204i
$745$	6.30160	+	64.7861i	0.230873	+	2.37358i
$746$	−6.56426	−	15.2177i	−0.240335	−	0.557158i
$747$	−0.972725	−	45.5727i	−0.0355901	−	1.66742i
$748$	2.12246	+	2.85096i	0.0776048	+	0.104241i
$749$	−4.94066	−	22.8086i	−0.180528	−	0.833410i
$750$	−5.34847	−	8.11472i	−0.195299	−	0.296308i
$751$	−12.9756	−	18.9189i	−0.473486	−	0.690360i	0.512216	−	0.858857i	$-0.328825\pi$
$751$	−12.9756	−	18.9189i	−0.473486	−	0.690360i	−0.985702	+	0.168497i	$0.946109\pi$
$752$	21.9044	+	8.94891i	0.798770	+	0.326333i
$753$	−7.12831	+	0.980717i	−0.259770	+	0.0357393i
$754$	−1.11530	−	3.25959i	−0.0406169	−	0.118707i
$755$	4.21397	−	23.8986i	0.153362	−	0.869760i
$756$	−1.22578	+	1.16325i	−0.0445811	+	0.0423071i
$757$	−2.95169	−	16.7399i	−0.107281	−	0.608420i	−0.990285	−	0.139054i	$-0.955594\pi$
$757$	−2.95169	−	16.7399i	−0.107281	−	0.608420i	0.883004	−	0.469366i	$-0.155517\pi$
$758$	−33.8159	+	18.6588i	−1.22825	+	0.677719i
$759$	−28.8063	+	7.44997i	−1.04560	+	0.270417i
$760$	14.7433	+	27.9894i	0.534794	+	1.01528i
$761$	35.5440	+	9.89435i	1.28847	+	0.358670i	0.843622	−	0.536937i	$-0.180419\pi$
$761$	35.5440	+	9.89435i	1.28847	+	0.358670i	0.444847	+	0.895607i	$0.353258\pi$
$762$	−38.9152	+	29.0303i	−1.40975	+	1.05166i
$763$	22.8166	−	0.885387i	0.826016	−	0.0320532i
$764$	0.648128	+	2.16490i	0.0234484	+	0.0783232i
$765$	42.6864	−	35.9601i	1.54333	−	1.30014i
$766$	−13.9229	−	14.7574i	−0.503054	−	0.533206i
$767$	−2.26893	+	0.631599i	−0.0819262	+	0.0228057i
$768$	−11.4564	−	1.55344i	−0.413398	−	0.0560549i
$769$	1.06884	+	0.167164i	0.0385434	+	0.00602807i	0.173761	−	0.984788i	$-0.444408\pi$
$769$	1.06884	+	0.167164i	0.0385434	+	0.00602807i	−0.135218	+	0.990816i	$0.543173\pi$
$770$	7.13656	−	8.84794i	0.257184	−	0.318858i
$771$	−30.8560	+	6.71530i	−1.11125	+	0.241846i
$772$	1.92007	+	1.88319i	0.0691047	+	0.0677774i
$773$	−49.6186	+	11.7598i	−1.78466	+	0.422972i	−0.984293	−	0.176542i	$-0.943509\pi$
$773$	−49.6186	+	11.7598i	−1.78466	+	0.422972i	−0.800364	+	0.599514i	$0.795361\pi$
$774$	28.3303	+	6.65611i	1.01831	+	0.239249i
$775$	−3.23994	+	3.43414i	−0.116382	+	0.123358i
$776$	−1.87776	+	3.56485i	−0.0674078	+	0.127970i
$777$	−1.31234	+	5.56134i	−0.0470799	+	0.199512i
$778$	−5.25231	−	20.3907i	−0.188305	−	0.731043i
$779$	−23.5510	−	0.913888i	−0.843804	−	0.0327434i
$780$	−0.511985	−	6.50500i	−0.0183320	−	0.232916i
$781$	−5.41311	−	3.26683i	−0.193696	−	0.116896i
$782$	51.8903	+	18.8865i	1.85559	+	0.675381i
$783$	−3.06684	−	1.60401i	−0.109600	−	0.0573226i
$784$	−17.9169	+	6.52122i	−0.639889	+	0.232901i
$785$	58.7511	+	11.5383i	2.09692	+	0.411821i
$786$	13.2203	+	41.0936i	0.471552	+	1.46576i
$787$	2.14872	+	15.7314i	0.0765936	+	0.560764i	0.988597	+	0.150583i	$0.0481149\pi$
$787$	2.14872	+	15.7314i	0.0765936	+	0.560764i	−0.912004	+	0.410182i	$0.865465\pi$
$788$	2.15694	−	0.167651i	0.0768378	−	0.00597231i
$789$	−1.18467	+	10.2218i	−0.0421752	+	0.363907i
$790$	−9.48367	+	8.60597i	−0.337414	+	0.306187i
$791$	16.2592	−	1.90042i	0.578109	−	0.0675713i
$792$	−14.4408	+	14.2188i	−0.513132	+	0.505242i
$793$	−2.36495	+	3.17667i	−0.0839817	+	0.112807i
$794$	−24.4047	−	11.0933i	−0.866091	−	0.393686i
$795$	10.3343	+	36.9849i	0.366519	+	1.31172i
$796$	6.35136	+	3.50453i	0.225118	+	0.124215i
$797$	13.6154	−	39.7926i	0.482283	−	1.40953i	−0.390131	−	0.920759i	$-0.627570\pi$
$797$	13.6154	−	39.7926i	0.482283	−	1.40953i	0.872415	−	0.488767i	$-0.162553\pi$
$798$	6.16614	+	5.37060i	0.218279	+	0.190117i
$799$	39.0049	+	3.03170i	1.37989	+	0.107254i
$800$	0.581819	+	9.98944i	0.0205704	+	0.353180i
$801$	28.9905	−	33.3504i	1.02433	−	1.17838i
$802$	15.1035	+	9.93372i	0.533323	+	0.350772i
$803$	11.2835	−	4.60983i	0.398187	−	0.162677i
$804$	0.00423602	+	4.34760i	0.000149393	+	0.153328i
$805$	−2.83113	+	29.1066i	−0.0997842	+	1.02587i
$806$	3.70542	−	1.18809i	0.130518	−	0.0418489i
$807$	23.1298	−	42.0156i	0.814209	−	1.47902i
$808$	−58.8989	+	9.21162i	−2.07206	+	0.324064i
$809$	−2.96128	+	5.12908i	−0.104113	+	0.180329i	−0.913375	−	0.407118i	$-0.866534\pi$
$809$	−2.96128	+	5.12908i	−0.104113	+	0.180329i	0.809262	+	0.587447i	$0.199867\pi$
$810$	29.4196	+	26.4885i	1.03370	+	0.930713i
$811$	18.5633	+	32.1526i	0.651846	+	1.12903i	0.982675	+	0.185340i	$0.0593386\pi$
$811$	18.5633	+	32.1526i	0.651846	+	1.12903i	−0.330828	+	0.943691i	$0.607328\pi$
$812$	−0.135994	−	0.168606i	−0.00477245	−	0.00591691i
$813$	3.95871	−	25.4745i	0.138838	−	0.893429i
$814$	−1.80459	+	8.33092i	−0.0632509	+	0.291999i
$815$	−6.68896	+	3.04050i	−0.234304	+	0.106504i
$816$	31.6642	−	5.61507i	1.10847	−	0.196567i
$817$	−3.15563	+	23.1033i	−0.110401	+	0.808281i
$818$	−1.17908	+	20.2441i	−0.0412257	+	0.707817i
$819$	−5.87299	−	12.2211i	−0.205219	−	0.427038i
$820$	−6.38184	−	3.20508i	−0.222863	−	0.111926i
$821$	−8.08078	−	16.8995i	−0.282021	−	0.589797i	0.711598	−	0.702587i	$-0.247972\pi$
$821$	−8.08078	−	16.8995i	−0.282021	−	0.589797i	−0.993619	+	0.112790i	$0.964021\pi$
$822$	−3.68106	−	23.3873i	−0.128392	−	0.815727i
$823$	−22.9456	−	26.2928i	−0.799834	−	0.916508i	0.198137	−	0.980174i	$-0.436511\pi$
$823$	−22.9456	−	26.2928i	−0.799834	−	0.916508i	−0.997971	+	0.0636663i	$0.979721\pi$
$824$	−0.494678	−	25.5055i	−0.0172329	−	0.888526i
$825$	20.2524	+	13.8612i	0.705099	+	0.482585i
$826$	0.727565	−	0.520032i	0.0253152	−	0.0180942i
$827$	9.81756	+	1.14751i	0.341390	+	0.0399028i	0.285061	−	0.958509i	$-0.407986\pi$
$827$	9.81756	+	1.14751i	0.341390	+	0.0399028i	0.0563293	+	0.998412i	$0.482060\pi$
$828$	1.36063	−	6.34105i	0.0472851	−	0.220367i
$829$	−1.44409	+	3.34778i	−0.0501554	+	0.116273i	−0.941451	−	0.337148i	$-0.890538\pi$
$829$	−1.44409	+	3.34778i	−0.0501554	+	0.116273i	0.891296	+	0.453422i	$0.149797\pi$
$830$	−63.6423	−	20.4061i	−2.20906	−	0.708306i
$831$	6.52987	+	1.94798i	0.226519	+	0.0675748i
$832$	14.9738	−	31.3151i	0.519123	−	1.08565i
$833$	−24.9171	+	19.3122i	−0.863327	+	0.669129i
$834$	−0.0353278	+	0.933886i	−0.00122330	+	0.0323378i
$835$	−13.2262	+	15.1555i	−0.457711	+	0.524479i
$836$	−1.54733	−	1.29836i	−0.0535155	−	0.0449048i
$837$	1.87855	−	3.42819i	0.0649320	−	0.118496i
$838$	28.0023	−	23.4967i	0.967322	−	0.811679i
$839$	−0.471572	+	24.3141i	−0.0162805	+	0.839416i	0.899312	+	0.437308i	$0.144068\pi$
$839$	−0.471572	+	24.3141i	−0.0162805	+	0.839416i	−0.915592	+	0.402108i	$0.868278\pi$
$840$	8.26014	+	18.1250i	0.285002	+	0.625372i
$841$	−15.2264	+	24.1583i	−0.525047	+	0.833045i
$842$	33.4165	−	32.7747i	1.15161	−	1.12949i
$843$	2.86402	+	0.164010i	0.0986421	+	0.00564882i
$844$	−3.08233	−	4.89045i	−0.106098	−	0.168336i
$845$	8.46766	+	2.00687i	0.291296	+	0.0690385i
$846$	1.66740	+	27.6981i	0.0573263	+	0.952281i
$847$	1.93764	−	6.47217i	0.0665781	−	0.222386i
$848$	−5.51902	+	21.4261i	−0.189524	+	0.735777i
$849$	1.35462	+	0.711853i	0.0464904	+	0.0244307i
$850$	−16.4049	−	42.4898i	−0.562684	−	1.45739i
$851$	−7.89849	−	20.4576i	−0.270757	−	0.701277i
$852$	1.16513	−	0.735939i	0.0399166	−	0.0252129i
$853$	2.60468	−	10.1120i	0.0891825	−	0.346228i	−0.908200	−	0.418537i	$-0.862543\pi$
$853$	2.60468	−	10.1120i	0.0891825	−	0.346228i	0.997382	+	0.0723092i	$0.0230368\pi$
$854$	0.431296	−	1.44063i	0.0147586	−	0.0492973i
$855$	−18.8919	+	25.4798i	−0.646090	+	0.871390i
$856$	59.3596	+	14.0685i	2.02887	+	0.480850i
$857$	13.4859	+	21.3968i	0.460668	+	0.730899i	0.993315	−	0.115438i	$-0.0368272\pi$
$857$	13.4859	+	21.3968i	0.460668	+	0.730899i	−0.532647	+	0.846338i	$0.678803\pi$
$858$	−9.09547	−	18.0667i	−0.310514	−	0.616785i
$859$	−39.1221	+	38.3707i	−1.33483	+	1.30919i	−0.418799	+	0.908079i	$0.637549\pi$
$859$	−39.1221	+	38.3707i	−1.33483	+	1.30919i	−0.916029	+	0.401111i	$0.868624\pi$
$860$	−3.76731	+	5.97724i	−0.128464	+	0.203822i
$861$	−14.7714	−	1.42226i	−0.503409	−	0.0484703i
$862$	−0.0759342	+	3.91515i	−0.00258633	+	0.133350i
$863$	−24.1377	+	20.2540i	−0.821658	+	0.689453i	−0.953360	−	0.301836i	$-0.902400\pi$
$863$	−24.1377	+	20.2540i	−0.821658	+	0.689453i	0.131701	+	0.991289i	$0.457956\pi$
$864$	−2.55271	−	7.88206i	−0.0868450	−	0.268153i
$865$	8.32658	+	6.98683i	0.283112	+	0.237559i
$866$	21.3340	−	24.4461i	0.724960	−	0.830711i
$867$	20.9807	−	11.0776i	0.712541	−	0.376214i
$868$	0.193382	−	0.149882i	0.00656382	−	0.00508734i
$869$	2.83571	−	5.93038i	0.0961947	−	0.201174i
$870$	−3.68764	+	3.48591i	−0.125023	+	0.118183i
$871$	−33.2179	−	10.6509i	−1.12554	−	0.360891i
$872$	−23.6407	+	54.8054i	−0.800577	+	1.85595i
$873$	−4.03718	−	0.148783i	−0.136638	−	0.00503553i
$874$	−31.1697	−	3.64321i	−1.05433	−	0.123233i
$875$	3.98893	−	2.85111i	0.134850	−	0.0963852i
$876$	−0.203298	+	2.64897i	−0.00686880	+	0.0895004i
$877$	−0.423694	−	21.8456i	−0.0143071	−	0.737673i	−0.936446	−	0.350813i	$-0.885905\pi$
$877$	−0.423694	−	21.8456i	−0.0143071	−	0.737673i	0.922138	−	0.386860i	$-0.126440\pi$
$878$	11.5053	+	13.1836i	0.388286	+	0.444926i
$879$	44.5358	+	17.1450i	1.50215	+	0.578286i
$880$	10.9597	+	22.9202i	0.369451	+	0.772640i
$881$	−15.8215	−	7.94586i	−0.533040	−	0.267703i	0.161854	−	0.986815i	$-0.448253\pi$
$881$	−15.8215	−	7.94586i	−0.533040	−	0.267703i	−0.694894	+	0.719112i	$0.744549\pi$
$882$	−15.9937	−	15.6254i	−0.538535	−	0.526136i
$883$	−0.243031	+	4.17269i	−0.00817866	+	0.140422i	0.991747	+	0.128212i	$0.0409238\pi$
$883$	−0.243031	+	4.17269i	−0.00817866	+	0.140422i	−0.999925	+	0.0122102i	$0.996113\pi$
$884$	0.841219	−	6.15882i	0.0282933	−	0.207143i
$885$	2.23247	+	2.65529i	0.0750436	+	0.0892567i
$886$	−2.34349	+	1.06525i	−0.0787311	+	0.0357877i
$887$	5.29557	−	24.4471i	0.177808	−	0.820853i	−0.798075	−	0.602558i	$-0.794148\pi$
$887$	5.29557	−	24.4471i	0.177808	−	0.820853i	0.975883	−	0.218294i	$-0.0700493\pi$
$888$	−11.6351	−	9.36595i	−0.390450	−	0.314301i
$889$	−15.3774	−	19.0649i	−0.515740	−	0.639417i
$890$	−32.3952	−	56.1101i	−1.08589	−	1.88081i
$891$	−19.1216	−	6.87542i	−0.640598	−	0.230335i
$892$	1.75530	−	3.04027i	0.0587719	−	0.101796i
$893$	−21.9663	+	3.43547i	−0.735076	+	0.114964i
$894$	−43.9713	+	0.895681i	−1.47062	+	0.0299561i
$895$	45.8279	−	14.6941i	1.53186	−	0.491171i
$896$	−0.922625	+	9.48542i	−0.0308227	+	0.316885i
$897$	45.0903	+	25.9743i	1.50552	+	0.867258i
$898$	26.4910	−	10.8228i	0.884016	−	0.361160i
$899$	0.418655	+	0.275354i	0.0139629	+	0.00918357i
$900$	−4.67854	+	2.59341i	−0.155951	+	0.0864471i
$901$	2.12707	+	36.5204i	0.0708631	+	1.21667i
$902$	−22.0710	−	1.71549i	−0.734884	−	0.0571197i
$903$	−2.81531	+	14.4092i	−0.0936875	+	0.479510i
$904$	−13.8527	+	40.4860i	−0.460733	+	1.34654i
$905$	21.0593	+	11.6200i	0.700035	+	0.386263i
$906$	15.8823	+	4.07451i	0.527653	+	0.135367i
$907$	−14.1664	−	6.43940i	−0.470386	−	0.213817i	0.164569	−	0.986366i	$-0.447377\pi$
$907$	−14.1664	−	6.43940i	−0.470386	−	0.213817i	−0.634955	+	0.772549i	$0.718982\pi$
$908$	0.600368	−	0.806434i	0.0199239	−	0.0267625i
$909$	−33.9046	−	49.2282i	−1.12455	−	1.63280i
$910$	−19.7457	+	2.30795i	−0.654565	+	0.0765077i
$911$	−8.41010	+	7.63176i	−0.278639	+	0.252852i	−0.799328	−	0.600895i	$-0.794811\pi$
$911$	−8.41010	+	7.63176i	−0.278639	+	0.252852i	0.520689	+	0.853747i	$0.325675\pi$
$912$	−16.7739	+	7.25493i	−0.555438	+	0.240235i
$913$	34.2025	−	2.65843i	1.13194	−	0.0879812i
$914$	2.53347	+	18.5483i	0.0837998	+	0.613523i
$915$	5.70234	+	1.22939i	0.188514	+	0.0406424i
$916$	−5.29033	−	1.03899i	−0.174797	−	0.0343291i
$917$	−20.4646	+	7.44852i	−0.675802	+	0.245972i
$918$	22.0188	+	30.6164i	0.726728	+	1.01049i
$919$	17.5344	+	6.38200i	0.578407	+	0.210523i	0.614623	−	0.788821i	$-0.289308\pi$
$919$	17.5344	+	6.38200i	0.578407	+	0.210523i	−0.0362160	+	0.999344i	$0.511530\pi$
$920$	−65.4478	−	39.4980i	−2.15775	−	1.30221i
$921$	28.3836	−	19.5077i	0.935272	−	0.642801i
$922$	9.20295	+	0.357116i	0.303083	+	0.0117610i
$923$	2.75815	+	10.7078i	0.0907856	+	0.352451i
$924$	−0.925921	−	0.871858i	−0.0304606	−	0.0286820i
$925$	−8.42967	+	16.0033i	−0.277166	+	0.526186i
$926$	−26.0793	+	27.6424i	−0.857019	+	0.908387i
$927$	22.8353	−	11.5241i	0.750010	−	0.378501i
$928$	1.03339	−	0.244919i	0.0339228	−	0.00803986i
$929$	−37.0099	−	36.2991i	−1.21426	−	1.19093i	−0.975535	−	0.219845i	$-0.929445\pi$
$929$	−37.0099	−	36.2991i	−1.21426	−	1.19093i	−0.238721	−	0.971088i	$-0.576728\pi$
$930$	−3.85580	−	4.24073i	−0.126437	−	0.139059i
$931$	11.2477	−	13.9449i	0.368628	−	0.457027i
$932$	−2.22775	−	0.348413i	−0.0729722	−	0.0114126i
$933$	−10.2508	+	13.2525i	−0.335597	+	0.433868i
$934$	16.2794	−	4.53169i	0.532679	−	0.148281i
$935$	28.8261	+	30.5539i	0.942715	+	0.999220i
$936$	35.4428	−	0.0690665i	1.15848	−	0.00225751i
$937$	9.55335	+	31.9104i	0.312094	+	1.04247i	0.959825	+	0.280599i	$0.0905330\pi$
$937$	9.55335	+	31.9104i	0.312094	+	1.04247i	−0.647731	+	0.761869i	$0.724282\pi$
$938$	13.2359	−	0.513614i	0.432168	−	0.0167701i
$939$	−9.45220	−	4.06636i	−0.308461	−	0.132701i
$940$	−6.49006	−	1.80663i	−0.211682	−	0.0589258i
$941$	−0.957261	−	1.81731i	−0.0312058	−	0.0592428i	0.868663	−	0.495404i	$-0.164980\pi$
$941$	−0.957261	−	1.81731i	−0.0312058	−	0.0592428i	−0.899869	+	0.436161i	$0.856338\pi$
$942$	−10.8108	+	38.9832i	−0.352235	+	1.27014i
$943$	49.8645	−	27.5141i	1.62381	−	0.895982i
$944$	0.347080	+	1.96839i	0.0112965	+	0.0640656i
$945$	−12.7928	+	15.3367i	−0.416149	+	0.498901i
$946$	−3.80321	+	21.5691i	−0.123653	+	0.701271i
$947$	−4.00747	−	11.7123i	−0.130225	−	0.380598i	0.861701	−	0.507417i	$-0.169400\pi$
$947$	−4.00747	−	11.7123i	−0.130225	−	0.380598i	−0.991926	+	0.126819i	$0.959523\pi$
$948$	0.878834	+	1.13161i	0.0285432	+	0.0367531i
$949$	−19.7336	−	8.06206i	−0.640580	−	0.261706i
$950$	14.6403	+	21.3461i	0.474995	+	0.692559i
$951$	−6.88297	+	0.407617i	−0.223195	+	0.0132179i
$952$	4.01706	+	18.5448i	0.130194	+	0.601040i
$953$	20.5559	+	27.6114i	0.665871	+	0.894420i	0.998822	−	0.0485239i	$-0.0154517\pi$
$953$	20.5559	+	27.6114i	0.665871	+	0.894420i	−0.332951	+	0.942944i	$0.608044\pi$
$954$	−25.4505	+	5.04984i	−0.823989	+	0.163494i
$955$	10.5784	+	24.5234i	0.342308	+	0.793559i
$956$	0.393718	+	4.04778i	0.0127338	+	0.130914i
$957$	1.07555	−	2.37229i	0.0347676	−	0.0766852i
$958$	−4.25234	+	2.56630i	−0.137387	+	0.0829134i
$959$	11.7202	−	2.30177i	0.378465	−	0.0743282i
$960$	−51.1187	−	0.941621i	−1.64985	−	0.0303907i
$961$	17.2137	−	25.0982i	0.555280	−	0.809619i
$962$	12.4552	−	8.19193i	0.401572	−	0.264118i
$963$	13.0657	+	59.7551i	0.421037	+	1.92558i
$964$	0.422933	−	0.212405i	0.0136218	−	0.00684110i
$965$	25.1225	+	19.4714i	0.808722	+	0.626807i
$966$	−19.4623	−	3.41218i	−0.626189	−	0.109785i
$967$	10.8069	+	7.72430i	0.347526	+	0.248397i	0.741837	−	0.670580i	$-0.233955\pi$
$967$	10.8069	+	7.72430i	0.347526	+	0.248397i	−0.394311	+	0.918977i	$0.629017\pi$
$968$	13.0780	+	11.8676i	0.420343	+	0.381441i
$969$	−22.7471	+	19.8904i	−0.730741	+	0.638970i
$970$	−2.13345	+	5.52577i	−0.0685009	+	0.177422i
$971$	47.5882			1.52718			0.763589	−	0.645702i	$-0.223435\pi$
$971$	47.5882			1.52718			0.763589	+	0.645702i	$0.223435\pi$
$972$	3.20676	−	3.05509i	0.102857	−	0.0979920i
$973$	−0.471480			−0.0151149
$974$	−9.73133	+	25.2048i	−0.311812	+	0.807614i
$975$	−8.31235	−	42.1079i	−0.266208	−	1.34853i
$976$	2.48894	+	2.25859i	0.0796691	+	0.0722958i
$977$	−36.3951	−	26.0137i	−1.16438	−	0.832251i	−0.176024	−	0.984386i	$-0.556324\pi$
$977$	−36.3951	−	26.0137i	−1.16438	−	0.832251i	−0.988360	+	0.152135i	$0.951385\pi$
$978$	−1.70251	−	4.66345i	−0.0544401	−	0.149121i
$979$	26.2859	+	20.3731i	0.840101	+	0.651127i
$980$	4.85112	−	2.43633i	0.154963	−	0.0778256i
$981$	−59.7966	+	2.43709i	−1.90916	+	0.0778103i
$982$	2.47976	−	1.63096i	0.0791322	−	0.0520460i
$983$	10.1601	−	14.8137i	0.324055	−	0.472484i	−0.628085	−	0.778145i	$-0.716161\pi$
$983$	10.1601	−	14.8137i	0.324055	−	0.472484i	0.952141	+	0.305660i	$0.0988771\pi$
$984$	20.0107	−	33.2308i	0.637919	−	1.05936i
$985$	25.0892	−	4.92736i	0.799409	−	0.156999i
$986$	−4.13878	+	2.49777i	−0.131806	+	0.0795451i
$987$	−13.9318	+	1.36882i	−0.443455	+	0.0435701i
$988$	0.341990	+	3.51597i	0.0108802	+	0.111858i
$989$	−22.3172	−	51.7371i	−0.709646	−	1.64514i
$990$	−18.6594	+	23.2265i	−0.593034	+	0.738185i
$991$	6.79565	+	9.12814i	0.215871	+	0.289965i	0.896847	−	0.442341i	$-0.145852\pi$
$991$	6.79565	+	9.12814i	0.215871	+	0.289965i	−0.680976	+	0.732306i	$0.738444\pi$
$992$	0.253948	+	1.17236i	0.00806287	+	0.0372224i
$993$	13.5210	−	26.9880i	0.429076	−	0.856439i
$994$	−2.37478	−	3.46252i	−0.0753235	−	0.109824i
$995$	79.3639	+	32.4237i	2.51600	+	1.02790i
$996$	−2.82123	+	6.92483i	−0.0893942	+	0.219422i
$997$	0.563783	+	1.64772i	0.0178552	+	0.0521837i	0.954716	−	0.297519i	$-0.0961591\pi$
$997$	0.563783	+	1.64772i	0.0178552	+	0.0521837i	−0.936861	+	0.349703i	$0.886283\pi$
$998$	0.633063	−	3.59028i	0.0200392	−	0.113648i
$999$	3.41117	−	14.5827i	0.107925	−	0.461376i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.94.19	✓	1404	243.94	even	81	inner
243.2.i.a.106.19	yes	1404	1.1	even	1	trivial
729.2.i.a.253.8		1404	243.149	odd	162
729.2.i.a.559.8		1404	3.2	odd	2

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.i (of order \(81\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(0.471802 - 1.22200i) q^{2} +(-1.63932 - 0.559127i) q^{3} +(0.210408 + 0.190935i) q^{4} +(2.73185 + 1.95261i) q^{5} +(-1.45669 + 1.73945i) q^{6} +(-0.904700 - 0.701195i) q^{7} +(2.67376 - 1.34281i) q^{8} +(2.37475 + 1.83318i) q^{9} +(3.67497 - 2.41707i) q^{10} +(-1.27702 + 1.86194i) q^{11} +(-0.238170 - 0.430649i) q^{12} +(3.87460 - 0.760946i) q^{13} +(-1.28370 + 0.774715i) q^{14} +(-3.38662 - 4.72840i) q^{15} +(-0.324415 - 3.33528i) q^{16} +(-2.19451 - 5.08744i) q^{17} +(3.36055 - 2.03705i) q^{18} +(1.88028 + 2.52566i) q^{19} +(0.201982 + 0.932451i) q^{20} +(1.09104 + 1.65533i) q^{21} +(1.67279 + 2.43898i) q^{22} +(-7.04343 - 2.87756i) q^{23} +(-5.13395 + 0.706331i) q^{24} +(2.03165 + 5.93771i) q^{25} +(0.898168 - 5.09376i) q^{26} +(-2.86801 - 4.33296i) q^{27} +(-0.0564734 - 0.320276i) q^{28} +(0.583179 - 0.321784i) q^{29} +(-7.37591 + 1.90758i) q^{30} +(0.350612 + 0.665620i) q^{31} +(1.53607 + 0.427594i) q^{32} +(3.13451 - 2.33831i) q^{33} +(-7.25221 + 0.281419i) q^{34} +(-1.10234 - 3.68208i) q^{35} +(0.149650 + 0.839140i) q^{36} +(1.97789 + 2.09644i) q^{37} +(3.97346 - 1.10609i) q^{38} +(-6.77718 - 0.918955i) q^{39} +(9.92628 + 1.55244i) q^{40} +(-4.69930 + 5.82622i) q^{41} +(2.53756 - 0.552259i) q^{42} +(5.28700 + 5.18546i) q^{43} +(-0.624206 + 0.147940i) q^{44} +(2.90799 + 9.64493i) q^{45} +(-6.83947 + 7.24942i) q^{46} +(-3.29078 + 6.24739i) q^{47} +(-1.33302 + 5.64899i) q^{48} +(-1.41928 - 5.50999i) q^{49} +(8.21440 + 0.318756i) q^{50} +(0.752982 + 9.56697i) q^{51} +(0.960539 + 0.579688i) q^{52} +(-6.20444 - 2.25823i) q^{53} +(-6.64799 + 1.46040i) q^{54} +(-7.12427 + 2.59302i) q^{55} +(-3.36052 - 0.659985i) q^{56} +(-1.67023 - 5.19168i) q^{57} +(-0.118075 - 0.864461i) q^{58} +(-0.594668 + 0.0462212i) q^{59} +(0.190245 - 1.64152i) q^{60} +(-0.742742 + 0.674002i) q^{61} +(0.978805 - 0.114406i) q^{62} +(-0.863025 - 3.32364i) q^{63} +(5.24942 - 7.05119i) q^{64} +(12.0706 + 5.48678i) q^{65} +(-1.37854 - 4.93358i) q^{66} +(-7.73503 - 4.26801i) q^{67} +(0.509630 - 1.48945i) q^{68} +(9.93754 + 8.65542i) q^{69} +(-5.01958 - 0.390153i) q^{70} +(0.162823 + 2.79556i) q^{71} +(8.81113 + 1.71262i) q^{72} +(-4.51045 - 2.96657i) q^{73} +(3.49501 - 1.42787i) q^{74} +(-0.0105908 - 10.8698i) q^{75} +(-0.0866102 + 0.890431i) q^{76} +(2.46091 - 0.789058i) q^{77} +(-4.32044 + 7.84813i) q^{78} +(-2.87650 + 0.449876i) q^{79} +(5.62624 - 9.74493i) q^{80} +(2.27892 + 8.70669i) q^{81} +(4.90249 + 8.49136i) q^{82} +(-9.53920 - 11.8268i) q^{83} +(-0.0864970 + 0.556612i) q^{84} +(3.93872 - 18.1831i) q^{85} +(8.83103 - 4.01420i) q^{86} +(-1.13594 + 0.201438i) q^{87} +(-0.914207 + 6.69318i) q^{88} +(0.856461 - 14.7049i) q^{89} +(13.1581 + 0.996934i) q^{90} +(-4.03892 - 2.02842i) q^{91} +(-0.932569 - 1.95030i) q^{92} +(-0.202600 - 1.28720i) q^{93} +(6.08169 + 6.96885i) q^{94} +(0.205027 + 10.5712i) q^{95} +(-2.27903 - 1.55982i) q^{96} +(-1.09556 + 0.783060i) q^{97} +(-7.40281 - 0.865264i) q^{98} +(-6.44588 + 2.08065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q - 54 q^{2} - 54 q^{3} - 54 q^{4} - 54 q^{5} - 54 q^{6} - 54 q^{7} - 54 q^{8} - 54 q^{9} - 54 q^{10} - 54 q^{11} - 54 q^{12} - 54 q^{13} - 54 q^{14} - 54 q^{15} - 54 q^{16} - 54 q^{17} - 54 q^{18}+ \cdots + 54 q^{98}+O(q^{100}) \) 1404 * q - 54 * q^2 - 54 * q^3 - 54 * q^4 - 54 * q^5 - 54 * q^6 - 54 * q^7 - 54 * q^8 - 54 * q^9 - 54 * q^10 - 54 * q^11 - 54 * q^12 - 54 * q^13 - 54 * q^14 - 54 * q^15 - 54 * q^16 - 54 * q^17 - 54 * q^18 - 54 * q^19 - 54 * q^20 - 54 * q^21 - 54 * q^22 - 54 * q^23 - 54 * q^24 - 54 * q^25 - 54 * q^26 - 54 * q^27 - 54 * q^28 - 54 * q^29 - 54 * q^30 - 54 * q^31 - 54 * q^32 - 54 * q^33 - 54 * q^34 - 54 * q^35 - 54 * q^36 - 54 * q^37 - 54 * q^38 - 54 * q^39 - 54 * q^40 - 54 * q^41 - 54 * q^42 - 54 * q^43 - 54 * q^44 - 54 * q^45 - 54 * q^46 - 54 * q^47 - 54 * q^48 - 54 * q^49 - 54 * q^50 - 54 * q^51 - 54 * q^52 - 54 * q^53 - 54 * q^54 - 54 * q^55 - 54 * q^56 - 54 * q^57 - 54 * q^58 - 54 * q^59 - 54 * q^60 - 54 * q^61 - 54 * q^62 - 54 * q^63 - 54 * q^64 + 54 * q^66 - 54 * q^67 + 135 * q^68 + 54 * q^69 - 54 * q^70 + 54 * q^71 + 270 * q^72 - 54 * q^73 + 162 * q^74 + 81 * q^75 - 54 * q^76 + 162 * q^77 + 162 * q^78 - 54 * q^79 + 351 * q^80 + 54 * q^81 - 27 * q^82 + 54 * q^83 + 324 * q^84 - 54 * q^85 + 162 * q^86 + 162 * q^87 - 54 * q^88 + 81 * q^89 + 162 * q^90 - 54 * q^91 + 270 * q^92 + 54 * q^93 - 54 * q^94 + 54 * q^95 + 135 * q^96 - 54 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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