LMFDB - Embedded newform 81.2.g.a.25.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [81,2,Mod(4,81)] 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("81.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(81, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.g (of order $27$, degree $18$, 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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	81.25
Dual form			81.2.g.a.13.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89071 + 0.949549i) q^{2} +(-0.540889 - 1.64543i) q^{3} +(1.47882 - 1.98639i) q^{4} +(-1.11651 + 3.72940i) q^{5} +(2.58508 + 2.59743i) q^{6} +(-1.32100 + 3.06243i) q^{7} +(-0.175036 + 0.992677i) q^{8} +(-2.41488 + 1.77999i) q^{9} +(-1.43025 - 8.11138i) q^{10} +(0.736337 + 0.174515i) q^{11} +(-4.06835 - 1.35887i) q^{12} +(-2.07722 + 1.36621i) q^{13} +(-0.410296 - 7.04452i) q^{14} +(6.74036 - 0.180054i) q^{15} +(0.808837 + 2.70170i) q^{16} +(-0.700932 - 0.255119i) q^{17} +(2.87564 - 5.65849i) q^{18} +(4.21736 - 1.53499i) q^{19} +(5.75694 + 7.73291i) q^{20} +(5.75353 + 0.517183i) q^{21} +(-1.55791 + 0.369231i) q^{22} +(-0.905723 - 2.09970i) q^{23} +(1.72805 - 0.248919i) q^{24} +(-8.48436 - 5.58025i) q^{25} +(2.63013 - 4.55552i) q^{26} +(4.23503 + 3.01074i) q^{27} +(4.12967 + 7.15280i) q^{28} +(-0.0269788 + 0.463208i) q^{29} +(-12.5731 + 6.74074i) q^{30} +(3.91546 + 0.457651i) q^{31} +(-5.47813 - 5.80647i) q^{32} +(-0.111124 - 1.30598i) q^{33} +(1.56751 - 0.183215i) q^{34} +(-9.94610 - 8.34577i) q^{35} +(-0.0353989 + 7.42918i) q^{36} +(-3.64375 + 3.05747i) q^{37} +(-6.51625 + 6.90682i) q^{38} +(3.37154 + 2.67895i) q^{39} +(-3.50665 - 1.76111i) q^{40} +(4.37210 + 2.19575i) q^{41} +(-11.3693 + 4.48541i) q^{42} +(-4.07702 + 4.32138i) q^{43} +(1.43556 - 1.20458i) q^{44} +(-3.94205 - 10.9934i) q^{45} +(3.70623 + 3.10990i) q^{46} +(10.6936 - 1.24990i) q^{47} +(4.00797 - 2.79221i) q^{48} +(-2.82973 - 2.99934i) q^{49} +(21.3402 + 2.49431i) q^{50} +(-0.0406530 + 1.29133i) q^{51} +(-0.357995 + 6.14654i) q^{52} +(5.75294 + 9.96438i) q^{53} +(-10.8660 - 1.67105i) q^{54} +(-1.47296 + 2.55124i) q^{55} +(-2.80878 - 1.84736i) q^{56} +(-4.80685 - 6.10911i) q^{57} +(-0.388830 - 0.901409i) q^{58} +(-4.03735 + 0.956869i) q^{59} +(9.61010 - 13.6553i) q^{60} +(0.159571 + 0.214341i) q^{61} +(-7.83755 + 2.85264i) q^{62} +(-2.26103 - 9.74676i) q^{63} +(10.5709 + 3.84748i) q^{64} +(-2.77590 - 9.27214i) q^{65} +(1.45020 + 2.36372i) q^{66} +(0.111496 + 1.91430i) q^{67} +(-1.54332 + 1.01506i) q^{68} +(-2.96502 + 2.62601i) q^{69} +(26.7299 + 6.33510i) q^{70} +(1.17278 + 6.65118i) q^{71} +(-1.34426 - 2.70876i) q^{72} +(1.37723 - 7.81064i) q^{73} +(3.98605 - 9.24071i) q^{74} +(-4.59281 + 16.9787i) q^{75} +(3.18760 - 10.6473i) q^{76} +(-1.50714 + 2.02444i) q^{77} +(-8.91839 - 1.86366i) q^{78} +(3.85762 - 1.93737i) q^{79} -10.9788 q^{80} +(2.66327 - 8.59692i) q^{81} -10.3513 q^{82} +(-2.27599 + 1.14304i) q^{83} +(9.53574 - 10.6640i) q^{84} +(1.73403 - 2.32921i) q^{85} +(3.60508 - 12.0418i) q^{86} +(0.776769 - 0.206152i) q^{87} +(-0.302122 + 0.700398i) q^{88} +(-0.935549 + 5.30576i) q^{89} +(17.8921 + 17.0421i) q^{90} +(-1.43990 - 8.16609i) q^{91} +(-5.51024 - 1.30595i) q^{92} +(-1.36479 - 6.69015i) q^{93} +(-19.0315 + 12.5172i) q^{94} +(1.01588 + 17.4421i) q^{95} +(-6.59109 + 12.1545i) q^{96} +(-2.72130 - 9.08977i) q^{97} +(8.19821 + 2.98391i) q^{98} +(-2.08880 + 0.889239i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	−1.89071	+	0.949549i	−1.33693	+	0.671433i	−0.966317	−	0.257354i	$-0.917149\pi$
$2$	−1.89071	+	0.949549i	−1.33693	+	0.671433i	−0.370615	+	0.928786i	$0.620853\pi$
$3$	−0.540889	−	1.64543i	−0.312282	−	0.949989i
$3$	−0.540889	−	1.64543i	−0.312282	−	0.949989i
$4$	1.47882	−	1.98639i	0.739408	−	0.993197i
$5$	−1.11651	+	3.72940i	−0.499317	+	1.66784i	0.221854	+	0.975080i	$0.428789\pi$
$5$	−1.11651	+	3.72940i	−0.499317	+	1.66784i	−0.721172	+	0.692756i	$0.756396\pi$
$6$	2.58508	+	2.59743i	1.05535	+	1.06040i
$7$	−1.32100	+	3.06243i	−0.499292	+	1.15749i	0.463218	+	0.886244i	$0.346695\pi$
$7$	−1.32100	+	3.06243i	−0.499292	+	1.15749i	−0.962510	+	0.271245i	$0.912565\pi$
$8$	−0.175036	+	0.992677i	−0.0618845	+	0.350964i
$9$	−2.41488	+	1.77999i	−0.804959	+	0.593330i
$10$	−1.43025	−	8.11138i	−0.452286	−	2.56504i
$11$	0.736337	+	0.174515i	0.222014	+	0.0526183i	0.340117	−	0.940383i	$-0.389533\pi$
$11$	0.736337	+	0.174515i	0.222014	+	0.0526183i	−0.118103	+	0.993001i	$0.537681\pi$
$12$	−4.06835	−	1.35887i	−1.17443	−	0.392272i
$13$	−2.07722	+	1.36621i	−0.576116	+	0.378918i	−0.803873	−	0.594800i	$-0.797231\pi$
$13$	−2.07722	+	1.36621i	−0.576116	+	0.378918i	0.227757	+	0.973718i	$0.426861\pi$
$14$	−0.410296	−	7.04452i	−0.109656	−	1.88273i
$15$	6.74036	−	0.180054i	1.74035	−	0.0464897i
$16$	0.808837	+	2.70170i	0.202209	+	0.675426i
$17$	−0.700932	−	0.255119i	−0.170001	−	0.0618753i	0.255617	−	0.966778i	$-0.417721\pi$
$17$	−0.700932	−	0.255119i	−0.170001	−	0.0618753i	−0.425619	+	0.904903i	$0.639943\pi$
$18$	2.87564	−	5.65849i	0.677795	−	1.33372i
$19$	4.21736	−	1.53499i	0.967530	−	0.352152i	0.190550	−	0.981678i	$-0.438973\pi$
$19$	4.21736	−	1.53499i	0.967530	−	0.352152i	0.776980	+	0.629526i	$0.216751\pi$
$20$	5.75694	+	7.73291i	1.28729	+	1.72913i
$21$	5.75353	+	0.517183i	1.25552	+	0.112859i
$22$	−1.55791	+	0.369231i	−0.332147	+	0.0787203i
$23$	−0.905723	−	2.09970i	−0.188856	−	0.437818i	0.797312	−	0.603568i	$-0.206255\pi$
$23$	−0.905723	−	2.09970i	−0.188856	−	0.437818i	−0.986168	+	0.165750i	$0.946996\pi$
$24$	1.72805	−	0.248919i	0.352738	−	0.0508104i
$25$	−8.48436	−	5.58025i	−1.69687	−	1.11605i
$26$	2.63013	−	4.55552i	0.515811	−	0.893410i
$27$	4.23503	+	3.01074i	0.815032	+	0.579416i
$28$	4.12967	+	7.15280i	0.780435	+	1.35175i
$29$	−0.0269788	+	0.463208i	−0.00500984	+	0.0860156i	−0.999886	−	0.0150831i	$-0.995199\pi$
$29$	−0.0269788	+	0.463208i	−0.00500984	+	0.0860156i	0.994876	+	0.101099i	$0.0322358\pi$
$30$	−12.5731	+	6.74074i	−2.29552	+	1.23068i
$31$	3.91546	+	0.457651i	0.703237	+	0.0821966i	0.460193	−	0.887819i	$-0.347780\pi$
$31$	3.91546	+	0.457651i	0.703237	+	0.0821966i	0.243044	+	0.970015i	$0.421854\pi$
$32$	−5.47813	−	5.80647i	−0.968405	−	1.02645i
$33$	−0.111124	−	1.30598i	−0.0193442	−	0.227343i
$34$	1.56751	−	0.183215i	0.268825	−	0.0314212i
$35$	−9.94610	−	8.34577i	−1.68120	−	1.41069i
$36$	−0.0353989	+	7.42918i	−0.00589982	+	1.23820i
$37$	−3.64375	+	3.05747i	−0.599029	+	0.502645i	−0.891134	−	0.453741i	$-0.850089\pi$
$37$	−3.64375	+	3.05747i	−0.599029	+	0.502645i	0.292104	+	0.956387i	$0.405645\pi$
$38$	−6.51625	+	6.90682i	−1.05708	+	1.12043i
$39$	3.37154	+	2.67895i	0.539879	+	0.428975i
$40$	−3.50665	−	1.76111i	−0.554451	−	0.278456i
$41$	4.37210	+	2.19575i	0.682807	+	0.342919i	0.756160	−	0.654387i	$-0.227073\pi$
$41$	4.37210	+	2.19575i	0.682807	+	0.342919i	−0.0733521	+	0.997306i	$0.523370\pi$
$42$	−11.3693	+	4.48541i	−1.75433	+	0.692115i
$43$	−4.07702	+	4.32138i	−0.621739	+	0.659005i	−0.959330	−	0.282288i	$-0.908907\pi$
$43$	−4.07702	+	4.32138i	−0.621739	+	0.659005i	0.337591	+	0.941293i	$0.390388\pi$
$44$	1.43556	−	1.20458i	0.216419	−	0.181597i
$45$	−3.94205	−	10.9934i	−0.587647	−	1.63880i
$46$	3.70623	+	3.10990i	0.546454	+	0.458529i
$47$	10.6936	−	1.24990i	1.55981	−	0.182316i	0.708020	−	0.706192i	$-0.249589\pi$
$47$	10.6936	−	1.24990i	1.55981	−	0.182316i	0.851795	+	0.523876i	$0.175515\pi$
$48$	4.00797	−	2.79221i	0.578501	−	0.403020i
$49$	−2.82973	−	2.99934i	−0.404247	−	0.428477i
$50$	21.3402	+	2.49431i	3.01796	+	0.352748i
$51$	−0.0406530	+	1.29133i	−0.00569256	+	0.180822i
$52$	−0.357995	+	6.14654i	−0.0496450	+	0.852372i
$53$	5.75294	+	9.96438i	0.790227	+	1.36871i	0.925826	+	0.377949i	$0.123371\pi$
$53$	5.75294	+	9.96438i	0.790227	+	1.36871i	−0.135600	+	0.990764i	$0.543296\pi$
$54$	−10.8660	−	1.67105i	−1.47868	−	0.227402i
$55$	−1.47296	+	2.55124i	−0.198614	+	0.344010i
$56$	−2.80878	−	1.84736i	−0.375339	−	0.246864i
$57$	−4.80685	−	6.10911i	−0.636683	−	0.809172i
$58$	−0.388830	−	0.901409i	−0.0510559	−	0.118361i
$59$	−4.03735	+	0.956869i	−0.525618	+	0.124574i	−0.484854	−	0.874595i	$-0.661127\pi$
$59$	−4.03735	+	0.956869i	−0.525618	+	0.124574i	−0.0407637	+	0.999169i	$0.512979\pi$
$60$	9.61010	−	13.6553i	1.24066	−	1.76289i
$61$	0.159571	+	0.214341i	0.0204310	+	0.0274436i	0.812221	−	0.583349i	$-0.198258\pi$
$61$	0.159571	+	0.214341i	0.0204310	+	0.0274436i	−0.791790	+	0.610793i	$0.790851\pi$
$62$	−7.83755	+	2.85264i	−0.995370	+	0.362285i
$63$	−2.26103	−	9.74676i	−0.284863	−	1.22798i
$64$	10.5709	+	3.84748i	1.32136	+	0.480935i
$65$	−2.77590	−	9.27214i	−0.344308	−	1.15007i
$66$	1.45020	+	2.36372i	0.178507	+	0.290953i
$67$	0.111496	+	1.91430i	0.0136213	+	0.233870i	0.998247	+	0.0591902i	$0.0188518\pi$
$67$	0.111496	+	1.91430i	0.0136213	+	0.233870i	−0.984625	+	0.174679i	$0.944111\pi$
$68$	−1.54332	+	1.01506i	−0.187155	+	0.123094i
$69$	−2.96502	+	2.62601i	−0.356946	+	0.316134i
$70$	26.7299	+	6.33510i	3.19483	+	0.757189i
$71$	1.17278	+	6.65118i	0.139184	+	0.789350i	0.971855	+	0.235582i	$0.0756996\pi$
$71$	1.17278	+	6.65118i	0.139184	+	0.789350i	−0.832671	+	0.553768i	$0.813189\pi$
$72$	−1.34426	−	2.70876i	−0.158423	−	0.319230i
$73$	1.37723	−	7.81064i	0.161192	−	0.914167i	−0.791712	−	0.610895i	$-0.790810\pi$
$73$	1.37723	−	7.81064i	0.161192	−	0.914167i	0.952904	−	0.303272i	$-0.0980791\pi$
$74$	3.98605	−	9.24071i	0.463369	−	1.07421i
$75$	−4.59281	+	16.9787i	−0.530333	+	1.96053i
$76$	3.18760	−	10.6473i	0.365643	−	1.22133i
$77$	−1.50714	+	2.02444i	−0.171755	+	0.230707i
$78$	−8.91839	−	1.86366i	−1.00981	−	0.211018i
$79$	3.85762	−	1.93737i	0.434016	−	0.217971i	−0.218357	−	0.975869i	$-0.570070\pi$
$79$	3.85762	−	1.93737i	0.434016	−	0.217971i	0.652373	+	0.757898i	$0.273773\pi$
$80$	−10.9788			−1.22747
$81$	2.66327	−	8.59692i	0.295919	−	0.955213i
$82$	−10.3513			−1.14311
$83$	−2.27599	+	1.14304i	−0.249822	+	0.125465i	−0.569304	−	0.822127i	$-0.692787\pi$
$83$	−2.27599	+	1.14304i	−0.249822	+	0.125465i	0.319482	+	0.947592i	$0.396491\pi$
$84$	9.53574	−	10.6640i	1.04043	−	1.16353i
$85$	1.73403	−	2.32921i	0.188082	−	0.252639i
$86$	3.60508	−	12.0418i	0.388746	−	1.29850i
$87$	0.776769	−	0.206152i	0.0832784	−	0.0221019i
$88$	−0.302122	+	0.700398i	−0.0322063	+	0.0746627i
$89$	−0.935549	+	5.30576i	−0.0991680	+	0.562410i	0.894222	+	0.447623i	$0.147729\pi$
$89$	−0.935549	+	5.30576i	−0.0991680	+	0.562410i	−0.993390	+	0.114786i	$0.963382\pi$
$90$	17.8921	+	17.0421i	1.88599	+	1.79640i
$91$	−1.43990	−	8.16609i	−0.150943	−	0.856039i
$92$	−5.51024	−	1.30595i	−0.574482	−	0.136155i
$93$	−1.36479	−	6.69015i	−0.141523	−	0.693736i
$94$	−19.0315	+	12.5172i	−1.96295	+	1.29106i
$95$	1.01588	+	17.4421i	0.104227	+	1.78952i
$96$	−6.59109	+	12.1545i	−0.672700	+	1.24052i
$97$	−2.72130	−	9.08977i	−0.276306	−	0.922926i	−0.977674	−	0.210127i	$-0.932612\pi$
$97$	−2.72130	−	9.08977i	−0.276306	−	0.922926i	0.701368	−	0.712799i	$-0.252573\pi$
$98$	8.19821	+	2.98391i	0.828145	+	0.301420i
$99$	−2.08880	+	0.889239i	−0.209932	+	0.0893719i
$100$	−23.6314	+	8.60112i	−2.36314	+	0.860112i
$101$	−7.34963	−	9.87227i	−0.731315	−	0.982327i	−0.999819	−	0.0190483i	$-0.993936\pi$
$101$	−7.34963	−	9.87227i	−0.731315	−	0.982327i	0.268503	−	0.963279i	$-0.413471\pi$
$102$	−1.14931	−	2.48012i	−0.113799	−	0.245569i
$103$	16.2209	−	3.84443i	1.59830	−	0.378803i	0.667578	−	0.744539i	$-0.267331\pi$
$103$	16.2209	−	3.84443i	1.59830	−	0.378803i	0.930719	+	0.365736i	$0.119183\pi$
$104$	−0.992615	−	2.30114i	−0.0973339	−	0.225645i
$105$	−8.35264	+	20.8797i	−0.815134	+	2.03765i
$106$	−20.3388	−	13.3770i	−1.97548	−	1.29929i
$107$	1.84694	−	3.19899i	0.178550	−	0.309258i	−0.762834	−	0.646595i	$-0.776193\pi$
$107$	1.84694	−	3.19899i	0.178550	−	0.309258i	0.941384	+	0.337336i	$0.109526\pi$
$108$	12.2433	−	3.96011i	1.17812	−	0.381062i
$109$	8.66961	+	15.0162i	0.830398	+	1.43829i	0.897723	+	0.440561i	$0.145220\pi$
$109$	8.66961	+	15.0162i	0.830398	+	1.43829i	−0.0673245	+	0.997731i	$0.521446\pi$
$110$	0.362408	−	6.22231i	0.0345543	−	0.593274i
$111$	7.00172	+	4.34179i	0.664574	+	0.412104i
$112$	−9.34225	−	1.09195i	−0.882760	−	0.103180i
$113$	7.07449	+	7.49852i	0.665512	+	0.705401i	0.968896	−	0.247467i	$-0.0795982\pi$
$113$	7.07449	+	7.49852i	0.665512	+	0.705401i	−0.303385	+	0.952868i	$0.598117\pi$
$114$	14.8893	+	6.98621i	1.39451	+	0.654318i
$115$	8.84187	−	1.03347i	0.824508	−	0.0963712i
$116$	0.880217	+	0.738590i	0.0817261	+	0.0685764i
$117$	2.58439	−	6.99665i	0.238927	−	0.646840i
$118$	6.72485	−	5.64282i	0.619072	−	0.519464i
$119$	1.70722	−	1.80954i	0.156500	−	0.165881i
$120$	−1.00107	+	6.72252i	−0.0913847	+	0.613679i
$121$	−9.31822	−	4.67979i	−0.847111	−	0.425435i
$122$	−0.505229	−	0.253736i	−0.0457413	−	0.0229722i
$123$	1.24813	−	8.38164i	0.112540	−	0.755747i
$124$	6.69932	−	7.10086i	0.601617	−	0.637676i
$125$	15.3730	−	12.8995i	1.37500	−	1.15376i
$126$	13.5300	+	16.2813i	1.20535	+	1.45046i
$127$	−10.1217	−	8.49315i	−0.898159	−	0.753645i	0.0716705	−	0.997428i	$-0.477167\pi$
$127$	−10.1217	−	8.49315i	−0.898159	−	0.753645i	−0.969830	+	0.243783i	$0.921611\pi$
$128$	−7.78215	+	0.909603i	−0.687852	+	0.0803983i
$129$	9.31575	+	4.37105i	0.820206	+	0.384850i
$130$	14.0528	+	14.8951i	1.23251	+	1.30638i
$131$	−9.99331	−	1.16805i	−0.873120	−	0.102053i	−0.332282	−	0.943180i	$-0.607819\pi$
$131$	−9.99331	−	1.16805i	−0.873120	−	0.102053i	−0.540838	+	0.841127i	$0.681893\pi$
$132$	−2.75853	−	1.71057i	−0.240099	−	0.148886i
$133$	−0.870337	+	14.9431i	−0.0754678	+	1.29573i
$134$	−2.02853	−	3.51352i	−0.175238	−	0.303522i
$135$	−15.9567	+	12.4326i	−1.37333	+	1.07003i
$136$	0.375938	−	0.651145i	0.0322365	−	0.0558352i
$137$	7.91093	+	5.20310i	0.675876	+	0.444531i	0.840490	−	0.541827i	$-0.182267\pi$
$137$	7.91093	+	5.20310i	0.675876	+	0.444531i	−0.164614	+	0.986358i	$0.552638\pi$
$138$	3.11246	−	7.78045i	0.264950	−	0.662316i
$139$	−4.15897	−	9.64158i	−0.352760	−	0.817788i	−0.998527	−	0.0542545i	$-0.982722\pi$
$139$	−4.15897	−	9.64158i	−0.352760	−	0.817788i	0.645768	−	0.763534i	$-0.276537\pi$
$140$	−31.2864	+	7.41502i	−2.64419	+	0.626684i
$141$	−7.84064	−	16.9194i	−0.660301	−	1.42487i
$142$	−8.53302	−	11.4618i	−0.716075	−	0.961855i
$143$	−1.76795	+	0.643483i	−0.147844	+	0.0538107i
$144$	−6.76225	−	5.08456i	−0.563521	−	0.423714i
$145$	−1.69736	−	0.617790i	−0.140958	−	0.0513047i
$146$	4.81266	+	16.0754i	0.398298	+	1.33041i
$147$	−3.40463	+	6.27843i	−0.280809	+	0.517836i
$148$	0.684905	+	11.7594i	0.0562989	+	0.966614i
$149$	−10.3846	+	6.83006i	−0.850740	+	0.559541i	−0.898328	−	0.439326i	$-0.855217\pi$
$149$	−10.3846	+	6.83006i	−0.850740	+	0.559541i	0.0475872	+	0.998867i	$0.484847\pi$
$150$	−7.43845	−	36.4629i	−0.607347	−	2.97718i
$151$	−17.7357	−	4.20344i	−1.44331	−	0.342071i	−0.566960	−	0.823745i	$-0.691881\pi$
$151$	−17.7357	−	4.20344i	−1.44331	−	0.342071i	−0.876350	+	0.481674i	$0.840029\pi$
$152$	0.785565	+	4.45516i	0.0637177	+	0.361361i
$153$	2.14678	−	0.631572i	0.173556	−	0.0510596i
$154$	0.927258	−	5.25874i	0.0747206	−	0.423761i
$155$	−6.07840	+	14.0913i	−0.488229	+	1.13184i
$156$	10.3073	−	2.73554i	0.825247	−	0.219018i
$157$	−6.70313	+	22.3900i	−0.534968	+	1.78692i	0.0781675	+	0.996940i	$0.475093\pi$
$157$	−6.70313	+	22.3900i	−0.534968	+	1.78692i	−0.613136	+	0.789978i	$0.710092\pi$
$158$	−5.45401	+	7.32601i	−0.433898	+	0.582826i
$159$	13.2840	−	14.8557i	1.05349	−	1.17813i
$160$	27.7710	−	13.9471i	2.19549	−	1.10262i
$161$	7.62665			0.601064
$162$	3.12772	+	18.7832i	0.245737	+	1.47575i
$163$	11.7238			0.918278			0.459139	−	0.888364i	$-0.348158\pi$
$163$	11.7238			0.918278			0.459139	+	0.888364i	$0.348158\pi$
$164$	10.8272	−	5.43761i	0.845459	−	0.424606i
$165$	4.99460	+	1.04371i	0.388829	+	0.0812531i
$166$	3.21785	−	4.32232i	0.249754	−	0.335477i
$167$	6.94439	−	23.1959i	0.537373	−	1.79495i	−0.0663994	−	0.997793i	$-0.521151\pi$
$167$	6.94439	−	23.1959i	0.537373	−	1.79495i	0.603772	−	0.797157i	$-0.293664\pi$
$168$	−1.52047	+	5.62087i	−0.117307	+	0.433659i
$169$	−2.70073	+	6.26100i	−0.207748	+	0.481615i
$170$	−1.06685	+	6.05041i	−0.0818237	+	0.464045i
$171$	−7.45215	+	11.2137i	−0.569880	+	0.857532i
$172$	2.55482	+	14.4891i	0.194803	+	1.10478i
$173$	−15.0943	−	3.57742i	−1.14760	−	0.271986i	−0.387548	−	0.921849i	$-0.626678\pi$
$173$	−15.0943	−	3.57742i	−1.14760	−	0.271986i	−0.760051	+	0.649863i	$0.774826\pi$
$174$	−1.27289	+	1.12735i	−0.0964976	+	0.0854645i
$175$	28.2970	−	18.6112i	2.13905	−	1.40688i
$176$	0.124089	+	2.13052i	0.00935353	+	0.160594i
$177$	3.75822	+	6.12561i	0.282485	+	0.460429i
$178$	−3.26923	−	10.9200i	−0.245039	−	0.818489i
$179$	6.75474	+	2.45852i	0.504873	+	0.183759i	0.581884	−	0.813271i	$-0.302316\pi$
$179$	6.75474	+	2.45852i	0.504873	+	0.183759i	−0.0770114	+	0.997030i	$0.524538\pi$
$180$	−27.6668	−	8.42675i	−2.06216	−	0.628093i
$181$	7.27112	−	2.64647i	0.540458	−	0.196711i	−0.0573439	−	0.998354i	$-0.518263\pi$
$181$	7.27112	−	2.64647i	0.540458	−	0.196711i	0.597802	+	0.801644i	$0.296041\pi$
$182$	10.4765	+	14.0724i	0.776573	+	1.04312i
$183$	0.266373	−	0.378497i	0.0196909	−	0.0279793i
$184$	2.24286	−	0.531567i	0.165346	−	0.0391877i
$185$	−7.33424	−	17.0027i	−0.539224	−	1.25006i
$186$	8.93306	+	11.3532i	0.655004	+	0.832456i
$187$	−0.471600	−	0.310176i	−0.0344868	−	0.0226824i
$188$	13.3310	−	23.0900i	0.972264	−	1.68401i
$189$	−14.8146	+	8.99228i	−1.07761	+	0.654092i
$190$	−18.4828	−	32.0132i	−1.34089	−	2.32248i
$191$	0.585993	−	10.0611i	0.0424010	−	0.727996i	−0.908382	−	0.418140i	$-0.862682\pi$
$191$	0.585993	−	10.0611i	0.0424010	−	0.727996i	0.950783	−	0.309856i	$-0.100281\pi$
$192$	0.613094	−	19.4747i	0.0442463	−	1.40546i
$193$	15.8841	+	1.85659i	1.14337	+	0.133640i	0.666618	−	0.745400i	$-0.267741\pi$
$193$	15.8841	+	1.85659i	1.14337	+	0.133640i	0.476748	+	0.879040i	$0.341815\pi$
$194$	13.7764	+	14.6021i	0.989086	+	1.04837i
$195$	−13.7552	+	9.58274i	−0.985031	+	0.686234i
$196$	−10.1425	+	1.18549i	−0.724466	+	0.0846779i
$197$	8.40349	+	7.05136i	0.598724	+	0.502389i	0.891035	−	0.453934i	$-0.149980\pi$
$197$	8.40349	+	7.05136i	0.598724	+	0.502389i	−0.292311	+	0.956323i	$0.594424\pi$
$198$	3.10493	−	3.66471i	0.220658	−	0.260440i
$199$	2.68937	−	2.25665i	0.190644	−	0.159970i	−0.542470	−	0.840075i	$-0.682511\pi$
$199$	2.68937	−	2.25665i	0.190644	−	0.159970i	0.733114	+	0.680106i	$0.238066\pi$
$200$	7.02445	−	7.44548i	0.496704	−	0.526475i
$201$	3.08955	−	1.21888i	0.217920	−	0.0859735i
$202$	23.2702	+	11.6867i	1.63729	+	0.822276i
$203$	−1.38290	−	0.694520i	−0.0970607	−	0.0487457i
$204$	2.50496	+	1.99039i	0.175383	+	0.139355i
$205$	−13.0703	+	13.8537i	−0.912870	+	0.967586i
$206$	−27.0186	+	22.6713i	−1.88247	+	1.57958i
$207$	5.92466	+	3.45835i	0.411792	+	0.240372i
$208$	−5.37122	−	4.50698i	−0.372427	−	0.312503i
$209$	3.37328	−	0.394280i	0.233335	−	0.0272729i
$210$	−4.03394	−	47.4087i	−0.278368	−	3.27151i
$211$	5.27290	+	5.58895i	0.363002	+	0.384759i	0.882972	−	0.469425i	$-0.155539\pi$
$211$	5.27290	+	5.58895i	0.363002	+	0.384759i	−0.519971	+	0.854184i	$0.674057\pi$
$212$	28.3007	+	3.30788i	1.94370	+	0.227186i
$213$	10.3097	−	5.52728i	0.706410	−	0.378723i
$214$	−0.454422	+	7.80212i	−0.0310636	+	0.533342i
$215$	−11.5641	−	20.0297i	−0.788667	−	1.36601i
$216$	−3.72997	+	3.67703i	−0.253792	+	0.250190i
$217$	−6.57386	+	11.3863i	−0.446262	+	0.772949i
$218$	−30.6503	−	20.1590i	−2.07590	−	1.36534i
$219$	−13.5968	+	1.95856i	−0.918786	+	0.132347i
$220$	2.88954	+	6.69870i	0.194813	+	0.451626i
$221$	1.80453	−	0.427682i	0.121386	−	0.0287690i
$222$	−17.3610	−	1.56057i	−1.16519	−	0.104739i
$223$	6.47575	+	8.69845i	0.433649	+	0.582491i	0.964205	−	0.265159i	$-0.0854243\pi$
$223$	6.47575	+	8.69845i	0.433649	+	0.582491i	−0.530556	+	0.847650i	$0.678017\pi$
$224$	25.0185	−	9.10600i	1.67162	−	0.608420i
$225$	30.4215	−	1.62644i	2.02810	−	0.108430i
$226$	−20.4960	−	7.45993i	−1.36337	−	0.496227i
$227$	3.11507	+	10.4051i	0.206754	+	0.690608i	0.996971	+	0.0777796i	$0.0247831\pi$
$227$	3.11507	+	10.4051i	0.206754	+	0.690608i	−0.790216	+	0.612828i	$0.790032\pi$
$228$	−19.2436	+	0.514049i	−1.27444	+	0.0340437i
$229$	−0.133120	−	2.28559i	−0.00879685	−	0.151036i	−0.999846	−	0.0175398i	$-0.994417\pi$
$229$	−0.133120	−	2.28559i	−0.00879685	−	0.151036i	0.991049	−	0.133496i	$-0.0426204\pi$
$230$	−15.7361	+	10.3498i	−1.03761	+	0.682444i
$231$	4.14628	+	1.38490i	0.272805	+	0.0911196i
$232$	−0.455094	−	0.107859i	−0.0298784	−	0.00708130i
$233$	3.09286	+	17.5405i	0.202620	+	1.14912i	0.901141	+	0.433526i	$0.142731\pi$
$233$	3.09286	+	17.5405i	0.202620	+	1.14912i	−0.698521	+	0.715590i	$0.746158\pi$
$234$	1.75733	+	15.6826i	0.114880	+	1.02521i
$235$	−7.27807	+	41.2760i	−0.474769	+	2.69255i
$236$	−4.06977	+	9.43480i	−0.264920	+	0.614153i
$237$	−5.27435	−	5.29954i	−0.342606	−	0.344242i
$238$	−1.50960	+	5.04240i	−0.0978526	+	0.326851i
$239$	−7.32490	+	9.83905i	−0.473808	+	0.636435i	−0.973205	−	0.229938i	$-0.926148\pi$
$239$	−7.32490	+	9.83905i	−0.473808	+	0.636435i	0.499397	+	0.866373i	$0.333555\pi$
$240$	5.93831	+	18.0648i	0.383316	+	1.16608i
$241$	15.6381	−	7.85375i	1.00734	−	0.505904i	0.132946	−	0.991123i	$-0.457556\pi$
$241$	15.6381	−	7.85375i	1.00734	−	0.505904i	0.874393	+	0.485219i	$0.161260\pi$
$242$	22.0617			1.41818
$243$	−15.5862	+	0.267746i	−0.999852	+	0.0171759i
$244$	0.661742			0.0423637
$245$	14.3451	−	7.20440i	0.916477	−	0.460272i
$246$	5.59893	+	17.0324i	0.356974	+	1.08595i
$247$	−6.66326	+	8.95031i	−0.423973	+	0.569494i
$248$	−1.13964	+	3.80668i	−0.0723675	+	0.241724i
$249$	3.11185	+	3.12672i	0.197206	+	0.198148i
$250$	−16.8172	+	38.9865i	−1.06361	+	2.46573i
$251$	3.26810	−	18.5343i	0.206281	−	1.16988i	−0.689131	−	0.724637i	$-0.742008\pi$
$251$	3.26810	−	18.5343i	0.206281	−	1.16988i	0.895412	−	0.445239i	$-0.146881\pi$
$252$	−22.7046	−	9.92237i	−1.43025	−	0.625051i
$253$	−0.300488	−	1.70415i	−0.0188915	−	0.107139i
$254$	27.2019	+	6.44697i	1.70680	+	0.404519i
$255$	−4.77048	−	1.59339i	−0.298739	−	0.0997817i
$256$	−4.94720	+	3.25382i	−0.309200	+	0.203364i
$257$	−1.00260	−	17.2139i	−0.0625403	−	1.07378i	−0.872918	−	0.487867i	$-0.837775\pi$
$257$	−1.00260	−	17.2139i	−0.0625403	−	1.07378i	0.810378	−	0.585908i	$-0.199262\pi$
$258$	−21.7639	+	0.581374i	−1.35496	+	0.0361947i
$259$	−4.54988	−	15.1977i	−0.282716	−	0.944337i
$260$	−22.5232	−	8.19776i	−1.39683	−	0.508404i
$261$	−0.759355	−	1.16661i	−0.0470029	−	0.0722115i
$262$	20.0036	−	7.28070i	1.23582	−	0.449803i
$263$	−14.6970	−	19.7415i	−0.906255	−	1.21731i	−0.975564	−	0.219716i	$-0.929487\pi$
$263$	−14.6970	−	19.7415i	−0.906255	−	1.21731i	0.0693091	−	0.997595i	$-0.477921\pi$
$264$	1.31587	+	0.118283i	0.0809862	+	0.00727984i
$265$	−43.5843	+	10.3297i	−2.67736	+	0.634547i
$266$	−12.5437	−	29.0795i	−0.769101	−	1.78298i
$267$	9.23629	−	1.33045i	0.565252	−	0.0814221i
$268$	3.96745	+	2.60943i	0.242350	+	0.159396i
$269$	−5.32448	+	9.22227i	−0.324639	+	0.562292i	−0.981439	−	0.191773i	$-0.938576\pi$
$269$	−5.32448	+	9.22227i	−0.324639	+	0.562292i	0.656800	+	0.754065i	$0.271910\pi$
$270$	18.3640	−	38.6580i	1.11760	−	2.35265i
$271$	2.35817	+	4.08447i	0.143249	+	0.248114i	0.928718	−	0.370786i	$-0.120912\pi$
$271$	2.35817	+	4.08447i	0.143249	+	0.248114i	−0.785469	+	0.618900i	$0.787578\pi$
$272$	0.122315	−	2.10006i	0.00741641	−	0.127335i
$273$	−12.6579	+	6.78621i	−0.766091	+	0.410720i
$274$	−19.8979	−	2.32573i	−1.20207	−	0.140502i
$275$	−5.27351	−	5.58959i	−0.318005	−	0.337065i
$276$	0.831577	+	9.77308i	0.0500550	+	0.588270i
$277$	6.56691	−	0.767562i	0.394567	−	0.0461183i	0.0835039	−	0.996507i	$-0.473389\pi$
$277$	6.56691	−	0.767562i	0.394567	−	0.0461183i	0.311063	+	0.950389i	$0.399315\pi$
$278$	17.0186	+	14.2803i	1.02071	+	0.856474i
$279$	−10.2700	+	5.86430i	−0.614847	+	0.351087i
$280$	10.0256	−	8.41245i	0.599142	−	0.502740i
$281$	1.69927	−	1.80112i	0.101370	−	0.107446i	−0.674702	−	0.738090i	$-0.735728\pi$
$281$	1.69927	−	1.80112i	0.101370	−	0.107446i	0.776072	+	0.630644i	$0.217209\pi$
$282$	30.8902	+	24.5446i	1.83948	+	1.46161i
$283$	0.828536	+	0.416107i	0.0492514	+	0.0247350i	0.473254	−	0.880926i	$-0.343079\pi$
$283$	0.828536	+	0.416107i	0.0492514	+	0.0247350i	−0.424003	+	0.905661i	$0.639375\pi$
$284$	14.9462	+	7.50627i	0.886894	+	0.445415i
$285$	28.1502	−	11.1058i	1.66747	−	0.657849i
$286$	2.73167	−	2.89540i	0.161527	−	0.171208i
$287$	−12.4999	+	10.4887i	−0.737845	+	0.619126i
$288$	23.5645	+	4.27092i	1.38855	+	0.251666i
$289$	−12.5965	−	10.5697i	−0.740973	−	0.621750i
$290$	3.79584	−	0.443670i	0.222900	−	0.0260532i
$291$	−13.4847	+	9.39426i	−0.790485	+	0.550701i
$292$	−13.4784	−	14.2862i	−0.788761	−	0.836038i
$293$	−2.32920	−	0.272245i	−0.136073	−	0.0159047i	0.0477835	−	0.998858i	$-0.484784\pi$
$293$	−2.32920	−	0.272245i	−0.136073	−	0.0159047i	−0.183857	+	0.982953i	$0.558858\pi$
$294$	0.475484	−	15.1035i	0.0277308	−	0.880857i
$295$	0.939186	−	16.1252i	0.0546815	−	0.938846i
$296$	−2.39729	−	4.15224i	−0.139340	−	0.241344i
$297$	2.59299	+	2.95599i	0.150460	+	0.171524i
$298$	13.1488	−	22.7744i	0.761688	−	1.31928i
$299$	4.75001	+	3.12413i	0.274700	+	0.180673i
$300$	26.9345	+	34.2315i	1.55506	+	1.97636i
$301$	−7.84818	−	18.1941i	−0.452362	−	1.04869i
$302$	37.5244	−	8.89345i	2.15929	−	0.511760i
$303$	−12.2688	+	17.4331i	−0.704823	+	1.00151i
$304$	7.55826	+	10.1525i	0.433496	+	0.582286i
$305$	−0.977524	+	0.355790i	−0.0559729	+	0.0203725i
$306$	−3.45922	+	3.23259i	−0.197750	+	0.184795i
$307$	14.3376	+	5.21846i	0.818289	+	0.297833i	0.717043	−	0.697028i	$-0.245495\pi$
$307$	14.3376	+	5.21846i	0.818289	+	0.297833i	0.101246	+	0.994861i	$0.467717\pi$
$308$	1.79256	+	5.98756i	0.102140	+	0.341173i
$309$	−15.0995	−	24.6110i	−0.858979	−	1.40007i
$310$	−1.88792	−	32.4143i	−0.107227	−	1.84101i
$311$	13.9891	−	9.20078i	0.793249	−	0.521728i	−0.0870178	−	0.996207i	$-0.527734\pi$
$311$	13.9891	−	9.20078i	0.793249	−	0.521728i	0.880267	+	0.474478i	$0.157363\pi$
$312$	−3.24947	+	2.87794i	−0.183965	+	0.162931i
$313$	31.6953	+	7.51193i	1.79153	+	0.424599i	0.985832	−	0.167734i	$-0.0536451\pi$
$313$	31.6953	+	7.51193i	1.79153	+	0.424599i	0.805693	+	0.592334i	$0.201793\pi$
$314$	−8.58676	−	48.6979i	−0.484579	−	2.74818i
$315$	38.8740	+	2.45006i	2.19030	+	0.138045i
$316$	1.85633	−	10.5278i	0.104427	−	0.592234i
$317$	8.58338	−	19.8985i	0.482091	−	1.11761i	−0.487554	−	0.873093i	$-0.662111\pi$
$317$	8.58338	−	19.8985i	0.482091	−	1.11761i	0.969645	−	0.244519i	$-0.0786300\pi$
$318$	−11.0099	+	40.7015i	−0.617407	+	2.28243i
$319$	−0.100702	+	0.336369i	−0.00563824	+	0.0188330i
$320$	−26.1512	+	35.1272i	−1.46190	+	1.96367i
$321$	−6.26271	−	1.30871i	−0.349550	−	0.0730450i
$322$	−14.4198	+	7.24188i	−0.803582	+	0.403574i
$323$	−3.34769			−0.186271
$324$	−13.1384	−	18.0036i	−0.729910	−	1.00020i
$325$	25.2476			1.40049
$326$	−22.1663	+	11.1323i	−1.22768	+	0.616562i
$327$	20.0188	−	22.3873i	1.10704	−	1.23802i
$328$	−2.94495	+	3.95575i	−0.162607	+	0.218420i
$329$	−10.2985	+	34.3994i	−0.567774	+	1.89650i
$330$	−10.4344	+	2.76926i	−0.574394	+	0.152443i
$331$	9.43153	−	21.8648i	0.518404	−	1.20180i	−0.435091	−	0.900386i	$-0.643284\pi$
$331$	9.43153	−	21.8648i	0.518404	−	1.20180i	0.953495	−	0.301409i	$-0.0974569\pi$
$332$	−1.09523	+	6.21136i	−0.0601086	+	0.340893i
$333$	3.35695	−	13.8693i	0.183960	−	0.760031i
$334$	8.89581	+	50.4507i	0.486757	+	2.76054i
$335$	−7.26368	−	1.72152i	−0.396857	−	0.0940569i
$336$	3.25639	+	15.9626i	0.177651	+	0.870834i
$337$	15.3690	−	10.1084i	0.837204	−	0.550638i	−0.0569604	−	0.998376i	$-0.518141\pi$
$337$	15.3690	−	10.1084i	0.837204	−	0.550638i	0.894164	+	0.447739i	$0.147770\pi$
$338$	−0.838832	−	14.4022i	−0.0456265	−	0.783376i
$339$	8.51177	−	15.6964i	0.462296	−	0.852513i
$340$	−2.06242	−	6.88895i	−0.111850	−	0.373606i
$341$	2.80323	+	1.02029i	0.151803	+	0.0552519i
$342$	3.44188	−	28.2780i	0.186116	−	1.52910i
$343$	−9.01506	+	3.28121i	−0.486767	+	0.177169i
$344$	−3.57611	−	4.80356i	−0.192811	−	0.258990i
$345$	−6.48296	−	13.9897i	−0.349031	−	0.753179i
$346$	31.9359	−	7.56894i	1.71688	−	0.406909i
$347$	−6.69815	−	15.5281i	−0.359576	−	0.833590i	−0.997958	−	0.0638707i	$-0.979655\pi$
$347$	−6.69815	−	15.5281i	−0.359576	−	0.833590i	0.638383	−	0.769719i	$-0.279604\pi$
$348$	0.739198	−	1.84783i	0.0396252	−	0.0990541i
$349$	−6.82361	−	4.48796i	−0.365259	−	0.240235i	0.353590	−	0.935400i	$-0.384961\pi$
$349$	−6.82361	−	4.48796i	−0.365259	−	0.240235i	−0.718850	+	0.695166i	$0.755331\pi$
$350$	−35.8291	+	62.0578i	−1.91514	+	3.31713i
$351$	−12.9104	−	0.468025i	−0.689104	−	0.0249813i
$352$	−3.02043	−	5.23154i	−0.160989	−	0.278842i
$353$	−1.43120	+	24.5728i	−0.0761752	+	1.30788i	0.716222	+	0.697872i	$0.245870\pi$
$353$	−1.43120	+	24.5728i	−0.0761752	+	1.30788i	−0.792397	+	0.610005i	$0.791167\pi$
$354$	−12.9223	−	8.01313i	−0.686810	−	0.425893i
$355$	−26.1143	−	3.05233i	−1.38600	−	0.162001i
$356$	9.15584	+	9.70462i	0.485258	+	0.514344i
$357$	−3.90089	−	1.83034i	−0.206457	−	0.0968720i
$358$	−15.1057	+	1.76561i	−0.798363	+	0.0933152i
$359$	−9.68682	−	8.12821i	−0.511251	−	0.428990i	0.350318	−	0.936631i	$-0.386073\pi$
$359$	−9.68682	−	8.12821i	−0.511251	−	0.428990i	−0.861569	+	0.507640i	$0.830518\pi$
$360$	11.6029	−	1.98895i	0.611526	−	0.104827i
$361$	0.875105	−	0.734300i	0.0460582	−	0.0386474i
$362$	−11.2346	+	11.9080i	−0.590478	+	0.625870i
$363$	−2.66014	+	17.8637i	−0.139621	+	0.937602i
$364$	−18.3504	−	9.21593i	−0.961824	−	0.483046i
$365$	27.5913	+	13.8569i	1.44419	+	0.725302i
$366$	−0.144231	+	0.968562i	−0.00753909	+	0.0506276i
$367$	7.20152	−	7.63317i	0.375917	−	0.398448i	−0.511600	−	0.859224i	$-0.670947\pi$
$367$	7.20152	−	7.63317i	0.375917	−	0.398448i	0.887517	+	0.460775i	$0.152429\pi$
$368$	4.94019	−	4.14531i	0.257525	−	0.216089i
$369$	−14.4665	+	2.47982i	−0.753096	+	0.129094i
$370$	30.0118	+	25.1829i	1.56024	+	1.30920i
$371$	−38.1148	+	4.45499i	−1.97882	+	0.231291i
$372$	−15.3076	−	7.18248i	−0.793660	−	0.372394i
$373$	−8.09518	−	8.58039i	−0.419152	−	0.444276i	0.483047	−	0.875594i	$-0.339530\pi$
$373$	−8.09518	−	8.58039i	−0.419152	−	0.444276i	−0.902200	+	0.431319i	$0.858048\pi$
$374$	1.18619	+	0.138645i	0.0613362	+	0.00716918i
$375$	−29.5403	−	18.3180i	−1.52545	−	0.945937i
$376$	−0.631010	+	10.8340i	−0.0325418	+	0.558722i
$377$	−0.576797	−	0.999042i	−0.0297066	−	0.0514533i
$378$	19.4716	−	31.0690i	1.00151	−	1.59802i
$379$	−9.06853	+	15.7072i	−0.465819	+	0.806823i	−0.999238	−	0.0390286i	$-0.987574\pi$
$379$	−9.06853	+	15.7072i	−0.465819	+	0.806823i	0.533419	+	0.845851i	$0.320907\pi$
$380$	36.1491	+	23.7756i	1.85441	+	1.21966i
$381$	−8.50014	+	21.2485i	−0.435475	+	1.08859i
$382$	8.44558	+	19.5791i	0.432113	+	1.00175i
$383$	15.0994	−	3.57861i	0.771541	−	0.182859i	0.174053	−	0.984736i	$-0.444314\pi$
$383$	15.0994	−	3.57861i	0.771541	−	0.182859i	0.597488	+	0.801878i	$0.296166\pi$
$384$	5.70597	+	12.3130i	0.291182	+	0.628345i
$385$	−5.86722	−	7.88104i	−0.299021	−	0.401655i
$386$	−31.7952	+	11.5725i	−1.61833	+	0.589025i
$387$	2.15348	−	17.6927i	0.109467	−	0.899369i
$388$	−22.0802	−	8.03653i	−1.12095	−	0.407993i
$389$	4.42661	+	14.7859i	0.224438	+	0.749675i	0.993832	+	0.110900i	$0.0353734\pi$
$389$	4.42661	+	14.7859i	0.224438	+	0.749675i	−0.769393	+	0.638775i	$0.779441\pi$
$390$	16.9078	−	31.1794i	0.856159	−	1.57883i
$391$	0.0991778	+	1.70282i	0.00501563	+	0.0861151i
$392$	3.47268	−	2.28402i	0.175397	−	0.115360i
$393$	3.48333	+	17.0751i	0.175711	+	0.861324i
$394$	−22.5842	−	5.35254i	−1.13777	−	0.269657i
$395$	2.91816	+	16.5497i	0.146828	+	0.832705i
$396$	−1.32257	+	5.46420i	−0.0664616	+	0.274586i
$397$	0.354695	−	2.01157i	0.0178016	−	0.100958i	−0.974612	−	0.223899i	$-0.928121\pi$
$397$	0.354695	−	2.01157i	0.0178016	−	0.100958i	0.992414	+	0.122941i	$0.0392326\pi$
$398$	−2.94201	+	6.82036i	−0.147470	+	0.341874i
$399$	25.0586	−	6.65048i	1.25450	−	0.332941i
$400$	8.21372	−	27.4357i	0.410686	−	1.37179i
$401$	8.93000	−	11.9951i	0.445943	−	0.599005i	−0.521139	−	0.853472i	$-0.674493\pi$
$401$	8.93000	−	11.9951i	0.445943	−	0.599005i	0.967081	+	0.254467i	$0.0819000\pi$
$402$	−4.68404	+	5.23823i	−0.233619	+	0.261259i
$403$	−8.75850	+	4.39868i	−0.436292	+	0.219114i
$404$	−30.4790			−1.51639
$405$	29.0877	+	19.5309i	1.44538	+	0.970499i
$406$	3.27415			0.162493
$407$	−3.21660	+	1.61544i	−0.159441	+	0.0800744i
$408$	−1.27475	−	0.266383i	−0.0631097	−	0.0131879i
$409$	6.20362	−	8.33291i	0.306749	−	0.412036i	−0.621840	−	0.783144i	$-0.713615\pi$
$409$	6.20362	−	8.33291i	0.306749	−	0.412036i	0.928590	+	0.371108i	$0.121022\pi$
$410$	11.5574	−	38.6042i	0.570777	−	1.90653i
$411$	4.28240	−	15.8312i	0.211235	−	0.780894i
$412$	16.3512	−	37.9064i	0.805567	−	1.86751i
$413$	2.40300	−	13.6281i	0.118244	−	0.670595i
$414$	−14.4857	−	0.912970i	−0.711932	−	0.0448700i
$415$	−1.72170	−	9.76427i	−0.0845151	−	0.479309i
$416$	19.3121	+	4.57705i	0.946853	+	0.224408i
$417$	−13.6150	+	12.0583i	−0.666730	+	0.590499i
$418$	−6.00350	+	3.94856i	−0.293641	+	0.193131i
$419$	−0.0308229	−	0.529208i	−0.00150580	−	0.0258535i	0.997472	−	0.0710667i	$-0.0226403\pi$
$419$	−0.0308229	−	0.529208i	−0.00150580	−	0.0258535i	−0.998977	+	0.0452132i	$0.985603\pi$
$420$	29.1234	+	47.4689i	1.42108	+	2.31625i
$421$	9.19654	+	30.7186i	0.448212	+	1.49713i	0.821929	+	0.569590i	$0.192898\pi$
$421$	9.19654	+	30.7186i	0.448212	+	1.49713i	−0.373717	+	0.927543i	$0.621917\pi$
$422$	−15.2765	−	5.56019i	−0.743649	−	0.270666i
$423$	−23.5988	+	22.0528i	−1.14741	+	1.07224i
$424$	−10.8984	+	3.96668i	−0.529272	+	0.192639i
$425$	4.52334	+	6.07590i	0.219414	+	0.294724i
$426$	−14.2442	+	20.2401i	−0.690135	+	0.980634i
$427$	−0.867198	+	0.205530i	−0.0419666	+	0.00994628i
$428$	−3.62318	−	8.39947i	−0.175133	−	0.406004i
$429$	2.01507	+	2.56099i	0.0972886	+	0.123646i
$430$	40.8835	+	26.8895i	1.97158	+	1.29673i
$431$	−2.69146	+	4.66175i	−0.129643	+	0.224549i	−0.923538	−	0.383506i	$-0.874717\pi$
$431$	−2.69146	+	4.66175i	−0.129643	+	0.224549i	0.793895	+	0.608055i	$0.208050\pi$
$432$	−4.70867	+	13.8770i	−0.226546	+	0.667657i
$433$	−16.6465	−	28.8325i	−0.799978	−	1.38560i	−0.919630	−	0.392787i	$-0.871511\pi$
$433$	−16.6465	−	28.8325i	−0.799978	−	1.38560i	0.119652	−	0.992816i	$-0.461822\pi$
$434$	1.61743	−	27.7703i	0.0776394	−	1.33302i
$435$	−0.0984446	+	3.12705i	−0.00472006	+	0.149931i
$436$	42.6489	+	4.98494i	2.04251	+	0.238735i
$437$	−7.04280	−	7.46493i	−0.336903	−	0.357096i
$438$	23.8478	−	16.6139i	1.13949	−	0.793842i
$439$	18.5556	−	2.16884i	0.885612	−	0.103513i	0.338889	−	0.940827i	$-0.389949\pi$
$439$	18.5556	−	2.16884i	0.885612	−	0.103513i	0.546723	+	0.837313i	$0.315875\pi$
$440$	−2.27474	−	1.90873i	−0.108444	−	0.0909953i
$441$	12.1722	+	2.20615i	0.579631	+	0.105055i
$442$	−3.00574	+	2.52212i	−0.142968	+	0.119965i
$443$	12.9497	−	13.7259i	0.615260	−	0.652138i	−0.342563	−	0.939495i	$-0.611295\pi$
$443$	12.9497	−	13.7259i	0.615260	−	0.652138i	0.957824	+	0.287357i	$0.0927766\pi$
$444$	18.9788	−	7.48748i	0.900692	−	0.355340i
$445$	−18.7427	−	9.41296i	−0.888491	−	0.446217i
$446$	−20.5034	−	10.2972i	−0.970862	−	0.487585i
$447$	16.8553	+	13.3928i	0.797229	+	0.633460i
$448$	−25.7468	+	27.2900i	−1.21642	+	1.28933i
$449$	−5.33643	+	4.47780i	−0.251842	+	0.211320i	−0.759965	−	0.649964i	$-0.774784\pi$
$449$	−5.33643	+	4.47780i	−0.251842	+	0.211320i	0.508123	+	0.861284i	$0.330339\pi$
$450$	−55.9738	+	31.9618i	−2.63863	+	1.50670i
$451$	2.83615	+	2.37981i	0.133549	+	0.112061i
$452$	25.3569	−	2.96379i	1.19269	−	0.139405i
$453$	2.67658	+	31.4564i	0.125757	+	1.47795i
$454$	−15.7698	−	16.7150i	−0.740113	−	0.784474i
$455$	32.0622	+	3.74754i	1.50310	+	0.175687i
$456$	6.90575	−	3.70234i	0.323391	−	0.173378i
$457$	−2.18611	+	37.5341i	−0.102262	+	1.75577i	0.424197	+	0.905570i	$0.360556\pi$
$457$	−2.18611	+	37.5341i	−0.102262	+	1.75577i	−0.526459	+	0.850201i	$0.676481\pi$
$458$	2.42197	+	4.19498i	0.113171	+	0.196018i
$459$	−2.20037	−	3.19076i	−0.102705	−	0.148932i
$460$	11.0226	−	19.0917i	0.513932	−	0.890157i
$461$	23.0904	+	15.1868i	1.07543	+	0.707320i	0.958291	−	0.285796i	$-0.0922579\pi$
$461$	23.0904	+	15.1868i	1.07543	+	0.707320i	0.117137	+	0.993116i	$0.462628\pi$
$462$	−9.15443	+	1.31866i	−0.425903	+	0.0613495i
$463$	9.73063	+	22.5581i	0.452220	+	1.04836i	0.980003	+	0.198985i	$0.0637645\pi$
$463$	9.73063	+	22.5581i	0.452220	+	1.04836i	−0.527782	+	0.849380i	$0.676976\pi$
$464$	−1.27327	+	0.301771i	−0.0591102	+	0.0140094i
$465$	26.4740	+	2.37974i	1.22770	+	0.110358i
$466$	−22.5033	−	30.2271i	−1.04244	−	1.40025i
$467$	−7.38677	+	2.68856i	−0.341819	+	0.124412i	−0.507225	−	0.861814i	$-0.669329\pi$
$467$	−7.38677	+	2.68856i	−0.341819	+	0.124412i	0.165406	+	0.986226i	$0.447107\pi$
$468$	−10.0763	−	15.4804i	−0.465775	−	0.715581i
$469$	−6.00971	−	2.18735i	−0.277503	−	0.101003i
$470$	−25.4329	−	84.9517i	−1.17313	−	3.91853i
$471$	40.4669	−	1.08098i	1.86461	−	0.0498090i
$472$	−0.243182	−	4.17527i	−0.0111933	−	0.192182i
$473$	−3.75620	+	2.47049i	−0.172710	+	0.113593i
$474$	15.0044	+	5.01163i	0.689177	+	0.230192i
$475$	−44.3473	−	10.5105i	−2.03479	−	0.482255i
$476$	−1.06981	−	6.06719i	−0.0490346	−	0.278089i
$477$	−31.6291	−	13.8226i	−1.44820	−	0.632893i
$478$	4.50659	−	25.5581i	0.206127	−	1.16900i
$479$	−7.01520	+	16.2631i	−0.320533	+	0.743079i	0.679424	+	0.733746i	$0.262230\pi$
$479$	−7.01520	+	16.2631i	−0.320533	+	0.743079i	−0.999956	+	0.00933231i	$0.997029\pi$
$480$	−37.9700	−	38.1514i	−1.73309	−	1.74136i
$481$	3.39173	−	11.3292i	0.154649	−	0.516565i
$482$	−22.1096	+	29.6983i	−1.00706	+	1.35272i
$483$	−4.12517	−	12.5491i	−0.187702	−	0.571005i
$484$	−23.0758	+	11.5891i	−1.04890	+	0.526778i
$485$	36.9377			1.67725
$486$	29.2146	−	15.3061i	1.32520	−	0.694297i
$487$	−42.1146			−1.90840			−0.954198	−	0.299175i	$-0.903289\pi$
$487$	−42.1146			−1.90840			−0.954198	+	0.299175i	$0.903289\pi$
$488$	−0.240702	+	0.120885i	−0.0108961	+	0.00547221i
$489$	−6.34127	−	19.2907i	−0.286762	−	0.872354i
$490$	−20.2815	+	27.2428i	−0.916226	+	1.23071i
$491$	2.08723	−	6.97182i	0.0941952	−	0.314634i	−0.897887	−	0.440227i	$-0.854898\pi$
$491$	2.08723	−	6.97182i	0.0941952	−	0.314634i	0.992082	+	0.125593i	$0.0400833\pi$
$492$	−14.8035	−	14.8742i	−0.667393	−	0.670581i
$493$	0.137083	−	0.317795i	0.00617392	−	0.0143128i
$494$	4.09952	−	23.2495i	0.184446	−	1.04604i
$495$	−0.984165	−	8.78280i	−0.0442349	−	0.394757i
$496$	1.93053	+	10.9486i	0.0866833	+	0.491606i
$497$	−21.9180	−	5.19467i	−0.983158	−	0.233013i
$498$	−8.85258	−	2.95685i	−0.396694	−	0.132500i
$499$	−13.4764	+	8.86359i	−0.603288	+	0.396789i	−0.814089	−	0.580740i	$-0.802763\pi$
$499$	−13.4764	+	8.86359i	−0.603288	+	0.396789i	0.210801	+	0.977529i	$0.432393\pi$
$500$	−2.88961	−	49.6128i	−0.129228	−	2.21875i
$501$	−41.9233	+	1.11989i	−1.87300	+	0.0500329i
$502$	11.4202	+	38.1462i	0.509710	+	1.70255i
$503$	34.7114	+	12.6339i	1.54771	+	0.563319i	0.967878	−	0.251421i	$-0.0808977\pi$
$503$	34.7114	+	12.6339i	1.54771	+	0.563319i	0.579827	+	0.814739i	$0.303120\pi$
$504$	10.0711	−	0.538441i	0.448605	−	0.0239840i
$505$	45.0235	−	16.3872i	2.00352	−	0.729221i
$506$	2.18631	+	2.93672i	0.0971933	+	0.130553i
$507$	11.7628	+	1.05736i	0.522405	+	0.0469589i
$508$	−31.8389	+	7.54597i	−1.41262	+	0.334798i
$509$	4.62698	+	10.7265i	0.205087	+	0.475445i	0.989453	−	0.144853i	$-0.0462709\pi$
$509$	4.62698	+	10.7265i	0.205087	+	0.475445i	−0.784366	+	0.620298i	$0.787012\pi$
$510$	10.5326	−	1.51717i	0.466390	−	0.0671815i
$511$	22.1002	+	14.5355i	0.977656	+	0.643015i
$512$	14.0992	−	24.4205i	0.623101	−	1.07924i
$513$	22.4821	+	6.19662i	0.992610	+	0.273588i
$514$	18.2411	+	31.5945i	0.804580	+	1.39357i
$515$	−3.77339	+	64.7866i	−0.166276	+	2.85484i
$516$	22.4589	−	12.0408i	0.988699	−	0.530065i
$517$	8.09218	+	0.945840i	0.355894	+	0.0415980i
$518$	23.0334	+	24.4140i	1.01203	+	1.07269i
$519$	2.27796	+	26.7716i	0.0999912	+	1.17514i
$520$	9.69012	−	1.13261i	0.424940	−	0.0496683i
$521$	−0.659940	−	0.553755i	−0.0289125	−	0.0242605i	0.628217	−	0.778038i	$-0.283785\pi$
$521$	−0.659940	−	0.553755i	−0.0289125	−	0.0242605i	−0.657129	+	0.753778i	$0.728229\pi$
$522$	2.54348	+	1.48468i	0.111325	+	0.0649827i
$523$	−6.06895	+	5.09246i	−0.265377	+	0.222678i	−0.765760	−	0.643126i	$-0.777637\pi$
$523$	−6.06895	+	5.09246i	−0.265377	+	0.222678i	0.500383	+	0.865804i	$0.333192\pi$
$524$	−17.0985	+	18.1233i	−0.746951	+	0.791721i
$525$	−45.9290	−	36.4941i	−2.00451	−	1.59273i
$526$	46.5332	+	23.3699i	2.02894	+	1.01897i
$527$	−2.62772	−	1.31969i	−0.114465	−	0.0574866i
$528$	3.43850	−	1.35655i	0.149642	−	0.0590364i
$529$	12.1951	−	12.9261i	0.530224	−	0.562004i
$530$	72.5967	−	60.9158i	3.15340	−	2.64601i
$531$	8.04648	−	9.49715i	0.349188	−	0.412141i
$532$	28.3958	+	23.8269i	1.23112	+	1.03303i
$533$	−12.0817	+	1.41214i	−0.523314	+	0.0611667i
$534$	−16.1998	+	11.2858i	−0.701034	+	0.488385i
$535$	9.86818	+	10.4597i	0.426639	+	0.452211i
$536$	−1.91980	−	0.224393i	−0.0829228	−	0.00969228i
$537$	0.391765	−	12.4442i	0.0169059	−	0.537009i
$538$	1.31004	−	22.4925i	0.0564797	−	0.969720i
$539$	−1.56020	−	2.70235i	−0.0672028	−	0.116399i
$540$	1.09905	+	50.0817i	0.0472956	+	2.15518i
$541$	6.01461	−	10.4176i	0.258588	−	0.447888i	−0.707276	−	0.706938i	$-0.750076\pi$
$541$	6.01461	−	10.4176i	0.258588	−	0.447888i	0.965864	+	0.259050i	$0.0834094\pi$
$542$	−8.33703	−	5.48335i	−0.358106	−	0.235530i
$543$	−8.28745	−	10.5327i	−0.355649	−	0.452000i
$544$	2.35846	+	5.46752i	0.101118	+	0.234418i
$545$	−65.6811	+	15.5667i	−2.81347	+	0.666804i
$546$	17.4886	−	24.8500i	0.748441	−	1.06348i
$547$	−3.81051	−	5.11840i	−0.162926	−	0.218847i	0.713162	−	0.701000i	$-0.247263\pi$
$547$	−3.81051	−	5.11840i	−0.162926	−	0.218847i	−0.876087	+	0.482152i	$0.839855\pi$
$548$	22.0342	−	8.01980i	0.941255	−	0.342589i
$549$	−0.766869	−	0.233573i	−0.0327292	−	0.00996864i
$550$	15.2783	+	5.56083i	0.651467	+	0.237115i
$551$	0.597243	+	1.99493i	0.0254434	+	0.0849868i
$552$	−2.08779	−	3.40295i	−0.0888624	−	0.144839i
$553$	0.837130	+	14.3730i	0.0355984	+	0.611201i
$554$	−11.6873	+	7.68684i	−0.496545	+	0.326583i
$555$	−24.0097	+	21.2645i	−1.01916	+	0.902630i
$556$	−25.3023	−	5.99677i	−1.07306	−	0.254320i
$557$	−6.99671	−	39.6803i	−0.296460	−	1.68131i	−0.661207	−	0.750203i	$-0.729956\pi$
$557$	−6.99671	−	39.6803i	−0.296460	−	1.68131i	0.364747	−	0.931107i	$-0.381156\pi$
$558$	13.8491	−	20.8395i	0.586278	−	0.882208i
$559$	2.56494	−	14.5465i	0.108485	−	0.615251i
$560$	14.5030	−	33.6218i	0.612864	−	1.42078i
$561$	−0.255290	+	0.943756i	−0.0107784	+	0.0398454i
$562$	−1.50257	+	5.01892i	−0.0633820	+	0.211711i
$563$	−0.946894	+	1.27190i	−0.0399068	+	0.0536042i	−0.821629	−	0.570023i	$-0.806934\pi$
$563$	−0.946894	+	1.27190i	−0.0399068	+	0.0536042i	0.781722	+	0.623627i	$0.214342\pi$
$564$	−45.2035	−	9.44612i	−1.90341	−	0.397753i
$565$	−35.8637	+	18.0114i	−1.50880	+	0.757745i
$566$	−1.96163			−0.0824536
$567$	22.8093	+	19.5126i	0.957899	+	0.819454i
$568$	−6.80775			−0.285647
$569$	9.86944	−	4.95662i	0.413748	−	0.207792i	−0.229733	−	0.973254i	$-0.573785\pi$
$569$	9.86944	−	4.95662i	0.413748	−	0.207792i	0.643482	+	0.765461i	$0.277489\pi$
$570$	−42.6783	+	47.7278i	−1.78760	+	1.99910i
$571$	4.72230	−	6.34315i	0.197622	−	0.265452i	−0.692255	−	0.721653i	$-0.743383\pi$
$571$	4.72230	−	6.34315i	0.197622	−	0.265452i	0.889877	+	0.456201i	$0.150790\pi$
$572$	−1.33627	+	4.46345i	−0.0558722	+	0.186626i
$573$	−16.8718	+	4.47773i	−0.704830	+	0.187060i
$574$	13.6742	−	31.7002i	0.570748	−	1.32314i
$575$	−4.03238	+	22.8688i	−0.168162	+	0.953695i
$576$	−32.3758	+	9.52483i	−1.34899	+	0.396868i
$577$	−8.01656	−	45.4642i	−0.333734	−	1.89270i	−0.439392	−	0.898295i	$-0.644806\pi$
$577$	−8.01656	−	45.4642i	−0.333734	−	1.89270i	0.105658	−	0.994402i	$-0.466305\pi$
$578$	33.8529	+	8.02328i	1.40809	+	0.333724i
$579$	−5.53667	−	27.1405i	−0.230096	−	1.12792i
$580$	−3.73726	+	2.45804i	−0.155181	+	0.102064i
$581$	−0.493904	−	8.48001i	−0.0204906	−	0.351810i
$582$	16.5752	−	30.5662i	0.687066	−	1.26701i
$583$	2.49717	+	8.34111i	0.103422	+	0.345454i
$584$	7.51238	+	2.73428i	0.310865	+	0.113145i
$585$	23.2078	+	17.4500i	0.959523	+	0.721470i
$586$	4.66235	−	1.69696i	0.192600	−	0.0701007i
$587$	21.9518	+	29.4864i	0.906049	+	1.21703i	0.975622	+	0.219458i	$0.0704288\pi$
$587$	21.9518	+	29.4864i	0.906049	+	1.21703i	−0.0695732	+	0.997577i	$0.522164\pi$
$588$	7.43662	+	16.0476i	0.306681	+	0.661791i
$589$	17.2154	−	4.08013i	0.709348	−	0.168119i
$590$	13.5360	+	31.3799i	0.557266	+	1.29189i
$591$	7.05717	−	17.6414i	0.290293	−	0.725668i
$592$	−11.2076	−	7.37135i	−0.460629	−	0.302960i
$593$	−7.17407	+	12.4258i	−0.294604	+	0.510268i	−0.974893	−	0.222676i	$-0.928521\pi$
$593$	−7.17407	+	12.4258i	−0.294604	+	0.510268i	0.680289	+	0.732944i	$0.261854\pi$
$594$	−7.70945	−	3.12675i	−0.316322	−	0.128292i
$595$	4.84238	+	8.38725i	0.198518	+	0.343844i
$596$	−1.78972	+	30.7283i	−0.0733099	+	1.25868i
$597$	−5.16781	−	3.20457i	−0.211504	−	0.131154i
$598$	−11.9474	−	1.39645i	−0.488565	−	0.0571051i
$599$	8.93203	+	9.46739i	0.364953	+	0.386827i	0.883664	−	0.468122i	$-0.155069\pi$
$599$	8.93203	+	9.46739i	0.364953	+	0.386827i	−0.518711	+	0.854950i	$0.673588\pi$
$600$	−16.0505	−	7.53106i	−0.655258	−	0.307454i
$601$	6.25526	−	0.731135i	0.255157	−	0.0298236i	0.0124474	−	0.999923i	$-0.496038\pi$
$601$	6.25526	−	0.731135i	0.255157	−	0.0298236i	0.242710	+	0.970099i	$0.421964\pi$
$602$	32.1148	+	26.9476i	1.30890	+	1.09830i
$603$	−3.67669	−	4.42435i	−0.149726	−	0.180174i
$604$	−34.5775	+	29.0140i	−1.40694	+	1.18056i
$605$	27.8566	−	29.5263i	1.13253	−	1.20042i
$606$	6.64311	−	44.6107i	0.269858	−	1.81219i
$607$	11.7509	+	5.90153i	0.476955	+	0.239536i	0.671001	−	0.741457i	$-0.265865\pi$
$607$	11.7509	+	5.90153i	0.476955	+	0.239536i	−0.194046	+	0.980992i	$0.562161\pi$
$608$	−32.0162	−	16.0791i	−1.29843	−	0.652094i
$609$	−0.394787	+	2.65113i	−0.0159976	+	0.107429i
$610$	1.51037	−	1.60090i	0.0611532	−	0.0648186i
$611$	−20.5052	+	17.2059i	−0.829552	+	0.696076i
$612$	1.92013	−	5.19832i	0.0776168	−	0.210130i
$613$	−28.3321	−	23.7734i	−1.14432	−	0.960200i	−0.144750	−	0.989468i	$-0.546238\pi$
$613$	−28.3321	−	23.7734i	−1.14432	−	0.960200i	−0.999572	+	0.0292684i	$0.990682\pi$
$614$	−32.0634	+	3.74767i	−1.29397	+	0.151244i
$615$	29.8649	+	14.0130i	1.20427	+	0.565057i
$616$	−1.74581	−	1.85046i	−0.0703409	−	0.0745570i
$617$	−32.2582	−	3.77044i	−1.29867	−	0.151792i	−0.561484	−	0.827487i	$-0.689769\pi$
$617$	−32.2582	−	3.77044i	−1.29867	−	0.151792i	−0.737181	+	0.675695i	$0.763844\pi$
$618$	51.9181	+	32.1945i	2.08845	+	1.29505i
$619$	2.49564	−	42.8485i	0.100308	−	1.72223i	−0.454924	−	0.890530i	$-0.650333\pi$
$619$	2.49564	−	42.8485i	0.100308	−	1.72223i	0.555232	−	0.831696i	$-0.312629\pi$
$620$	19.0021	+	32.9126i	0.763142	+	1.32180i
$621$	2.48589	−	11.6192i	0.0997551	−	0.466262i
$622$	−17.7127	+	30.6793i	−0.710215	+	1.23013i
$623$	−15.0127	−	9.87398i	−0.601470	−	0.395593i
$624$	−4.51070	+	11.2757i	−0.180572	+	0.451391i
$625$	10.8323	+	25.1120i	0.433290	+	1.00448i
$626$	−67.0595	+	15.8934i	−2.68024	+	0.635228i
$627$	−2.47333	−	5.33723i	−0.0987753	−	0.213149i
$628$	34.5627	+	46.4258i	1.37920	+	1.85259i
$629$	3.33404	−	1.21349i	0.132937	−	0.0483851i
$630$	−75.8258	+	32.2804i	−3.02097	+	1.28608i
$631$	13.0635	+	4.75472i	0.520049	+	0.189282i	0.588690	−	0.808359i	$-0.299644\pi$
$631$	13.0635	+	4.75472i	0.520049	+	0.189282i	−0.0686408	+	0.997641i	$0.521866\pi$
$632$	1.24796	+	4.16848i	0.0496412	+	0.165813i
$633$	6.34417	−	11.6992i	0.252158	−	0.465001i
$634$	2.66595	+	45.7726i	0.105878	+	1.81786i
$635$	42.9753	−	28.2653i	1.70542	−	1.12167i
$636$	−9.86467	−	48.3561i	−0.391159	−	1.91744i
$637$	9.97568	+	2.36428i	0.395251	+	0.0936761i
$638$	−0.129000	−	0.731597i	−0.00510717	−	0.0289642i
$639$	−14.6712	−	13.9743i	−0.580382	−	0.552813i
$640$	5.29656	−	30.0383i	0.209365	−	1.18737i
$641$	−1.03758	+	2.40538i	−0.0409819	+	0.0950068i	−0.937477	−	0.348046i	$-0.886845\pi$
$641$	−1.03758	+	2.40538i	−0.0409819	+	0.0950068i	0.896496	+	0.443053i	$0.146105\pi$
$642$	13.0836	−	3.47236i	0.516370	−	0.137043i
$643$	0.0293991	−	0.0981997i	0.00115939	−	0.00387262i	−0.957408	−	0.288739i	$-0.906764\pi$
$643$	0.0293991	−	0.0981997i	0.00115939	−	0.00387262i	0.958567	+	0.284866i	$0.0919492\pi$
$644$	11.2784	−	15.1495i	0.444432	−	0.596975i
$645$	−26.7025	+	29.8618i	−1.05141	+	1.17581i
$646$	6.32951	−	3.17880i	0.249031	−	0.125068i
$647$	−25.1564			−0.988998			−0.494499	−	0.869178i	$-0.664649\pi$
$647$	−25.1564			−0.988998			−0.494499	+	0.869178i	$0.664649\pi$
$648$	8.06779	+	4.14854i	0.316933	+	0.162970i
$649$	−3.13983			−0.123249
$650$	−47.7359	+	23.9739i	−1.87236	+	0.940332i
$651$	22.2910	+	4.65812i	0.873653	+	0.182566i
$652$	17.3373	−	23.2881i	0.678982	−	0.912031i
$653$	2.13941	−	7.14613i	0.0837217	−	0.279650i	−0.905870	−	0.423557i	$-0.860781\pi$
$653$	2.13941	−	7.14613i	0.0837217	−	0.279650i	0.989591	+	0.143907i	$0.0459666\pi$
$654$	−16.5919	+	61.3368i	−0.648793	+	2.39846i
$655$	15.5137	−	35.9649i	0.606172	−	1.40526i
$656$	−2.39595	+	13.5881i	−0.0935463	+	0.530527i
$657$	10.5770	+	21.3132i	0.412649	+	0.831507i
$658$	−13.1924	−	74.8181i	−0.514295	−	2.91671i
$659$	15.8217	+	3.74981i	0.616325	+	0.146072i	0.526908	−	0.849922i	$-0.323351\pi$
$659$	15.8217	+	3.74981i	0.616325	+	0.146072i	0.0894175	+	0.995994i	$0.471499\pi$
$660$	9.45933	−	8.37779i	0.368204	−	0.326105i
$661$	−15.7657	+	10.3693i	−0.613214	+	0.403318i	−0.817776	−	0.575536i	$-0.804793\pi$
$661$	−15.7657	+	10.3693i	−0.613214	+	0.403318i	0.204562	+	0.978854i	$0.434423\pi$
$662$	2.92938	+	50.2956i	0.113854	+	1.95479i
$663$	−1.67977	−	2.73790i	−0.0652370	−	0.106331i
$664$	−0.736294	−	2.45939i	−0.0285737	−	0.0954429i
$665$	−54.7570	−	19.9299i	−2.12339	−	0.772849i
$666$	6.82253	+	29.4103i	0.264368	+	1.13963i
$667$	0.997034	−	0.362891i	0.0386053	−	0.0140512i
$668$	−35.8067	−	48.0967i	−1.38540	−	1.86092i
$669$	10.8100	−	15.3603i	0.417939	−	0.593863i
$670$	15.3682	−	3.64233i	0.593725	−	0.140715i
$671$	0.0800923	+	0.185675i	0.00309193	+	0.00716789i
$672$	−28.5155	−	36.2409i	−1.10001	−	1.39802i
$673$	6.83522	+	4.49560i	0.263478	+	0.173293i	0.674374	−	0.738390i	$-0.264414\pi$
$673$	6.83522	+	4.49560i	0.263478	+	0.173293i	−0.410896	+	0.911682i	$0.634784\pi$
$674$	−19.4599	+	33.7056i	−0.749569	+	1.29829i
$675$	−19.1308	−	49.1767i	−0.736347	−	1.89281i
$676$	8.44293	+	14.6236i	0.324728	+	0.562445i
$677$	1.34268	−	23.0529i	0.0516033	−	0.885995i	−0.868834	−	0.495104i	$-0.835130\pi$
$677$	1.34268	−	23.0529i	0.0516033	−	0.885995i	0.920437	−	0.390891i	$-0.127833\pi$
$678$	−1.18874	+	37.7597i	−0.0456532	+	1.45015i
$679$	31.4316	+	3.67383i	1.20623	+	0.140989i
$680$	2.00864	+	2.12903i	0.0770277	+	0.0816446i
$681$	15.4359	−	10.7536i	0.591504	−	0.412079i
$682$	−6.26891	+	0.732730i	−0.240049	+	0.0280577i
$683$	−14.3566	−	12.0466i	−0.549340	−	0.460951i	0.325378	−	0.945584i	$-0.394509\pi$
$683$	−14.3566	−	12.0466i	−0.549340	−	0.460951i	−0.874717	+	0.484633i	$0.838953\pi$
$684$	11.2545	+	31.3859i	0.430325	+	1.20007i
$685$	−28.2370	+	23.6937i	−1.07888	+	0.905289i
$686$	13.9292	−	14.7641i	0.531818	−	0.563694i
$687$	−3.68877	+	1.45529i	−0.140736	+	0.0555228i
$688$	−14.9727	−	7.51959i	−0.570830	−	0.286682i
$689$	−25.5635	−	12.8385i	−0.973892	−	0.489107i
$690$	25.5413	+	20.2945i	0.972340	+	0.772599i
$691$	4.56302	−	4.83652i	0.173586	−	0.183990i	−0.634740	−	0.772726i	$-0.718893\pi$
$691$	4.56302	−	4.83652i	0.173586	−	0.183990i	0.808325	+	0.588736i	$0.200374\pi$
$692$	−29.4279	+	24.6929i	−1.11868	+	0.938684i
$693$	0.0360770	−	7.57149i	0.00137045	−	0.287617i
$694$	27.4089	+	22.9988i	1.04043	+	0.873023i
$695$	40.6008	−	4.74555i	1.54008	−	0.180009i
$696$	0.0686804	+	0.807164i	0.00260332	+	0.0305955i
$697$	−2.50437	−	2.65448i	−0.0948598	−	0.100546i
$698$	17.1630	+	2.00607i	0.649629	+	0.0759307i
$699$	27.1888	−	14.5766i	1.02837	−	0.551336i
$700$	4.87681	−	83.7316i	0.184326	−	3.16476i
$701$	12.1477	+	21.0405i	0.458813	+	0.794687i	0.998899	−	0.0469230i	$-0.0149415\pi$
$701$	12.1477	+	21.0405i	0.458813	+	0.794687i	−0.540086	+	0.841610i	$0.681608\pi$
$702$	24.8541	−	11.3741i	0.938059	−	0.429289i
$703$	−10.6738	+	18.4876i	−0.402571	+	0.697274i
$704$	7.11227	+	4.67782i	0.268054	+	0.176302i
$705$	71.8534	−	10.3502i	2.70615	−	0.389810i
$706$	−20.6271	−	47.8190i	−0.776311	−	1.79969i
$707$	39.9420	−	9.46643i	1.50217	−	0.356022i
$708$	17.7256	+	1.59335i	0.666168	+	0.0598818i
$709$	17.8682	+	24.0012i	0.671054	+	0.901382i	0.999062	−	0.0432925i	$-0.0137847\pi$
$709$	17.8682	+	24.0012i	0.671054	+	0.901382i	−0.328008	+	0.944675i	$0.606377\pi$
$710$	52.2729	−	19.0258i	1.96177	−	0.714024i
$711$	−5.86719	+	11.5450i	−0.220037	+	0.432973i
$712$	−5.10315	−	1.85740i	−0.191249	−	0.0696089i
$713$	−2.58539	−	8.63580i	−0.0968236	−	0.323413i
$714$	9.11345	−	0.243445i	0.341062	−	0.00911071i
$715$	−0.425867	−	7.31185i	−0.0159265	−	0.273448i
$716$	14.8726	−	9.78188i	0.555816	−	0.365566i
$717$	20.1514	+	6.73078i	0.752569	+	0.251365i
$718$	26.0331	+	6.16995i	0.971546	+	0.230261i
$719$	−2.12889	−	12.0735i	−0.0793943	−	0.450267i	−0.998426	−	0.0560838i	$-0.982139\pi$
$719$	−2.12889	−	12.0735i	−0.0793943	−	0.450267i	0.919032	−	0.394183i	$-0.128973\pi$
$720$	26.5125	−	19.5421i	0.988061	−	0.728292i
$721$	−9.65461	+	54.7540i	−0.359556	+	2.03915i
$722$	−0.957314	+	2.21930i	−0.0356275	+	0.0825939i
$723$	−21.3813	−	21.4834i	−0.795178	−	0.798976i
$724$	5.49571	−	18.3570i	0.204247	−	0.682231i
$725$	2.81372	−	3.77948i	0.104499	−	0.140366i
$726$	−11.9329	−	36.3010i	−0.442873	−	1.34726i
$727$	−43.8058	+	22.0001i	−1.62467	+	0.815938i	−0.625298	+	0.780386i	$0.715023\pi$
$727$	−43.8058	+	22.0001i	−1.62467	+	0.815938i	−0.999368	+	0.0355521i	$0.988681\pi$
$728$	8.35832			0.309780
$729$	8.87094	+	25.5011i	0.328553	+	0.944485i
$730$	−65.3249			−2.41778
$731$	3.96018	−	1.98888i	0.146472	−	0.0735612i
$732$	−0.357929	−	1.08885i	−0.0132294	−	0.0402450i
$733$	−12.0622	+	16.2024i	−0.445528	+	0.598448i	−0.966986	−	0.254829i	$-0.917981\pi$
$733$	−12.0622	+	16.2024i	−0.445528	+	0.598448i	0.521458	+	0.853277i	$0.325388\pi$
$734$	−6.36791	+	21.2703i	−0.235044	+	0.785101i
$735$	−19.6135	−	19.7071i	−0.723453	−	0.726908i
$736$	−7.23020	+	16.7615i	−0.266509	+	0.617837i
$737$	−0.251977	+	1.42903i	−0.00928168	+	0.0526390i
$738$	24.9972	−	18.4253i	0.920161	−	0.678244i
$739$	0.349401	+	1.98155i	0.0128529	+	0.0728925i	0.990560	−	0.137083i	$-0.0437727\pi$
$739$	0.349401	+	1.98155i	0.0128529	+	0.0728925i	−0.977707	+	0.209975i	$0.932662\pi$
$740$	−44.6200	−	10.5751i	−1.64027	−	0.388750i
$741$	18.3312	+	6.12280i	0.673413	+	0.224927i
$742$	67.8338	−	44.6150i	2.49026	−	1.63787i
$743$	−1.25430	−	21.5356i	−0.0460160	−	0.790064i	−0.939834	−	0.341633i	$-0.889020\pi$
$743$	−1.25430	−	21.5356i	−0.0460160	−	0.790064i	0.893818	−	0.448431i	$-0.148017\pi$
$744$	6.88004	−	0.183785i	0.252235	−	0.00673789i
$745$	−13.8775	−	46.3541i	−0.508433	−	1.69828i
$746$	23.4531	+	8.53624i	0.858680	+	0.312534i
$747$	3.46163	−	6.81154i	0.126654	−	0.249221i
$748$	−1.31354	+	0.478091i	−0.0480279	+	0.0174807i
$749$	7.35687	+	9.88200i	0.268814	+	0.361080i
$750$	73.2458	+	6.58405i	2.67456	+	0.240416i
$751$	−14.0873	+	3.33875i	−0.514053	+	0.121833i	−0.479451	−	0.877568i	$-0.659164\pi$
$751$	−14.0873	+	3.33875i	−0.514053	+	0.121833i	−0.0346015	+	0.999401i	$0.511016\pi$
$752$	12.0262	+	27.8798i	0.438550	+	1.01667i
$753$	−32.2646	+	4.64758i	−1.17579	+	0.169367i
$754$	2.03919	+	1.34120i	0.0742631	+	0.0488436i
$755$	35.4783	−	61.4503i	1.29119	−	2.23640i
$756$	−4.04592	+	42.7257i	−0.147149	+	1.55392i
$757$	−5.26451	−	9.11840i	−0.191342	−	0.331414i	0.754353	−	0.656469i	$-0.227951\pi$
$757$	−5.26451	−	9.11840i	−0.191342	−	0.331414i	−0.945695	+	0.325055i	$0.894617\pi$
$758$	2.23123	−	38.3087i	0.0810418	−	1.39143i
$759$	−2.64153	+	1.41619i	−0.0958814	+	0.0514044i
$760$	−17.4921	−	2.04454i	−0.634506	−	0.0741632i
$761$	29.0111	+	30.7500i	1.05165	+	1.11469i	0.993203	+	0.116395i	$0.0371338\pi$
$761$	29.0111	+	30.7500i	1.05165	+	1.11469i	0.0584483	+	0.998290i	$0.481385\pi$
$762$	−4.10518	−	48.2459i	−0.148715	−	1.74777i
$763$	−57.4387	+	6.71362i	−2.07942	+	0.243049i
$764$	−19.1188	−	16.0425i	−0.691693	−	0.580399i
$765$	−0.0415082	+	8.71133i	−0.00150073	+	0.314959i
$766$	−25.1504	+	21.1037i	−0.908721	+	0.762507i
$767$	7.07916	−	7.50347i	0.255614	−	0.270935i
$768$	8.02983	+	6.38031i	0.289751	+	0.230230i
$769$	−8.05989	−	4.04783i	−0.290647	−	0.145968i	0.297501	−	0.954721i	$-0.403847\pi$
$769$	−8.05989	−	4.04783i	−0.290647	−	0.145968i	−0.588149	+	0.808753i	$0.700143\pi$
$770$	18.5766	+	9.32953i	0.669455	+	0.336213i
$771$	−27.7820	+	10.9605i	−1.00054	+	0.394734i
$772$	27.1777	−	28.8066i	0.978145	−	1.03677i
$773$	0.551231	−	0.462537i	0.0198264	−	0.0166363i	−0.632821	−	0.774298i	$-0.718103\pi$
$773$	0.551231	−	0.462537i	0.0198264	−	0.0166363i	0.652647	+	0.757662i	$0.273658\pi$
$774$	12.7285	+	35.4965i	0.457515	+	1.27590i
$775$	−30.6663	−	25.7321i	−1.10157	−	0.924325i
$776$	9.49953	−	1.11034i	0.341013	−	0.0398587i
$777$	−22.5457	+	15.7068i	−0.808823	+	0.563477i
$778$	−22.4094	−	23.7526i	−0.803415	−	0.851570i
$779$	21.8092	+	2.54913i	0.781396	+	0.0913321i
$780$	−1.30631	+	41.4944i	−0.0467734	+	1.48574i
$781$	−0.297168	+	5.10218i	−0.0106335	+	0.182570i
$782$	−1.80442	−	3.12535i	−0.0645261	−	0.111762i
$783$	−1.50885	+	1.88047i	−0.0539220	+	0.0672026i
$784$	5.81453	−	10.0711i	0.207662	−	0.359681i
$785$	−76.0171	−	49.9972i	−2.71317	−	1.78448i
$786$	−22.7996	−	28.9764i	−0.813234	−	1.03355i
$787$	6.11050	+	14.1657i	0.217816	+	0.504953i	0.991731	−	0.128336i	$-0.0409636\pi$
$787$	6.11050	+	14.1657i	0.217816	+	0.504953i	−0.773915	+	0.633289i	$0.781704\pi$
$788$	26.4340	−	6.26497i	0.941672	−	0.223180i
$789$	−24.5338	+	34.8608i	−0.873425	+	1.24108i
$790$	−21.2321	−	28.5197i	−0.755405	−	1.01469i
$791$	−32.3091	+	11.7595i	−1.14878	+	0.418121i
$792$	−0.517113	−	2.22915i	−0.0183748	−	0.0792094i
$793$	−0.624297	−	0.227226i	−0.0221695	−	0.00806902i
$794$	1.23946	+	4.14010i	0.0439869	+	0.146927i
$795$	40.5710	+	66.1277i	1.43891	+	2.34531i
$796$	−0.505513	−	8.67932i	−0.0179174	−	0.307630i
$797$	−11.6388	+	7.65494i	−0.412266	+	0.271152i	−0.738655	−	0.674084i	$-0.764539\pi$
$797$	−11.6388	+	7.65494i	−0.412266	+	0.271152i	0.326389	+	0.945236i	$0.394168\pi$
$798$	−41.0635	+	36.3685i	−1.45363	+	1.28743i
$799$	−7.81433	−	1.85203i	−0.276451	−	0.0655201i
$800$	14.0768	+	79.8335i	0.497690	+	2.82254i
$801$	−7.18497	−	14.4780i	−0.253868	−	0.511557i
$802$	−5.49411	+	31.1586i	−0.194004	+	1.10025i
$803$	2.37718	−	5.51092i	0.0838888	−	0.194476i
$804$	2.14769	−	7.93957i	0.0757431	−	0.280007i
$805$	−8.51521	+	28.4428i	−0.300122	+	1.00248i
$806$	12.3830	−	16.6333i	0.436173	−	0.585881i
$807$	18.0546	+	3.77283i	0.635550	+	0.132810i
$808$	11.0864	−	5.56781i	0.390019	−	0.195875i
$809$	−40.8781			−1.43720			−0.718599	−	0.695424i	$-0.755216\pi$
$809$	−40.8781			−1.43720			−0.718599	+	0.695424i	$0.755216\pi$
$810$	−73.5420	−	9.30704i	−2.58400	−	0.327016i
$811$	51.1039			1.79450			0.897250	−	0.441524i	$-0.145562\pi$
$811$	51.1039			1.79450			0.897250	+	0.441524i	$0.145562\pi$
$812$	−3.42465	+	1.71992i	−0.120182	+	0.0603575i
$813$	5.44521	−	6.08945i	0.190972	−	0.213566i
$814$	4.54772	−	6.10865i	0.159398	−	0.214108i
$815$	−13.0897	+	43.7226i	−0.458512	+	1.53154i
$816$	−3.52166	+	0.934640i	−0.123283	+	0.0327189i
$817$	−10.5610	+	24.4830i	−0.369481	+	0.856553i
$818$	−3.81673	+	21.6457i	−0.133449	+	0.756825i
$819$	18.0127	+	17.1571i	0.629416	+	0.599518i
$820$	8.19037	+	46.4499i	0.286020	+	1.62210i
$821$	−47.2620	−	11.2013i	−1.64946	−	0.390928i	−0.702345	−	0.711836i	$-0.747864\pi$
$821$	−47.2620	−	11.2013i	−1.64946	−	0.390928i	−0.947110	+	0.320908i	$0.896012\pi$
$822$	6.93571	+	33.9985i	0.241911	+	1.18583i
$823$	−22.5809	+	14.8517i	−0.787119	+	0.517696i	−0.878284	−	0.478139i	$-0.841311\pi$
$823$	−22.5809	+	14.8517i	−0.787119	+	0.517696i	0.0911649	+	0.995836i	$0.470941\pi$
$824$	0.977036	+	16.7751i	0.0340367	+	0.584387i
$825$	−6.34490	+	11.7005i	−0.220901	+	0.407360i
$826$	8.39718	+	28.0485i	0.292175	+	0.975934i
$827$	−14.9793	−	5.45201i	−0.520880	−	0.189585i	0.0681816	−	0.997673i	$-0.478280\pi$
$827$	−14.9793	−	5.45201i	−0.520880	−	0.189585i	−0.589062	+	0.808088i	$0.700503\pi$
$828$	15.6311	−	6.65445i	0.543219	−	0.231258i
$829$	1.59698	−	0.581253i	0.0554654	−	0.0201877i	−0.314138	−	0.949377i	$-0.601716\pi$
$829$	1.59698	−	0.581253i	0.0554654	−	0.0201877i	0.369604	+	0.929189i	$0.379493\pi$
$830$	12.5269	+	16.8265i	0.434815	+	0.584058i
$831$	−4.81494	−	10.3902i	−0.167028	−	0.360433i
$832$	−27.2144	+	6.44994i	−0.943490	+	0.223611i
$833$	1.21826	+	2.82425i	0.0422103	+	0.0978545i
$834$	14.2920	−	35.7269i	0.494892	−	1.23712i
$835$	78.7531	+	51.7967i	2.72536	+	1.79250i
$836$	4.20527	−	7.28373i	0.145442	−	0.251913i
$837$	15.2042	+	13.7266i	0.525534	+	0.474460i
$838$	0.560786	+	0.971310i	0.0193720	+	0.0335534i
$839$	2.69510	−	46.2731i	0.0930453	−	1.59753i	−0.552307	−	0.833641i	$-0.686253\pi$
$839$	2.69510	−	46.2731i	0.0930453	−	1.59753i	0.645353	−	0.763885i	$-0.276710\pi$
$840$	−19.2648	−	11.9462i	−0.664699	−	0.412182i
$841$	28.5901	+	3.34170i	0.985865	+	0.115231i
$842$	−46.5568	−	49.3473i	−1.60445	−	1.70062i
$843$	−3.88273	−	1.82182i	−0.133728	−	0.0627468i
$844$	18.8995	−	2.20904i	0.650548	−	0.0760382i
$845$	−20.3343	−	17.0625i	−0.699523	−	0.586969i
$846$	23.6783	−	64.1036i	0.814077	−	2.20393i
$847$	26.6409	−	22.3544i	0.915393	−	0.768106i
$848$	−22.2676	+	23.6023i	−0.764673	+	0.810506i
$849$	0.236528	−	1.58837i	0.00811762	−	0.0545126i
$850$	−14.3217	−	7.19262i	−0.491229	−	0.246705i
$851$	9.72001	+	4.88157i	0.333198	+	0.167338i
$852$	4.26680	−	28.6530i	0.146178	−	0.981635i
$853$	16.6035	−	17.5986i	0.568492	−	0.602566i	−0.377797	−	0.925888i	$-0.623318\pi$
$853$	16.6035	−	17.5986i	0.568492	−	0.602566i	0.946289	+	0.323322i	$0.104800\pi$
$854$	1.44446	−	1.21204i	0.0494283	−	0.0414753i
$855$	−33.4999	−	40.3122i	−1.14567	−	1.37865i
$856$	2.85228	+	2.39335i	0.0974891	+	0.0818031i
$857$	12.7419	−	1.48931i	0.435254	−	0.0508739i	0.104355	−	0.994540i	$-0.466722\pi$
$857$	12.7419	−	1.48931i	0.435254	−	0.0508739i	0.330899	+	0.943666i	$0.392648\pi$
$858$	−6.24170	−	2.92868i	−0.213088	−	0.0999834i
$859$	−14.0817	−	14.9257i	−0.480461	−	0.509259i	0.441118	−	0.897449i	$-0.354582\pi$
$859$	−14.0817	−	14.9257i	−0.480461	−	0.509259i	−0.921579	+	0.388190i	$0.873100\pi$
$860$	−56.8880	−	6.64926i	−1.93987	−	0.226738i
$861$	24.0194	+	14.8945i	0.818579	+	0.507603i
$862$	0.662209	−	11.3697i	0.0225549	−	0.387253i
$863$	18.5110	+	32.0620i	0.630121	+	1.09140i	0.987527	+	0.157453i	$0.0503282\pi$
$863$	18.5110	+	32.0620i	0.630121	+	1.09140i	−0.357405	+	0.933949i	$0.616338\pi$
$864$	−5.71826	−	41.0838i	−0.194539	−	1.39770i
$865$	30.1945	−	52.2984i	1.02664	−	1.77820i
$866$	58.8515	+	38.7072i	1.99986	+	1.31533i
$867$	−10.5785	+	26.4438i	−0.359263	+	0.898078i
$868$	12.8961	+	29.8965i	0.437721	+	1.01475i
$869$	3.17861	−	0.753344i	0.107827	−	0.0255555i
$870$	−2.78316	−	6.00581i	−0.0943579	−	0.203616i
$871$	−2.84694	−	3.82410i	−0.0964648	−	0.129575i
$872$	−16.4237	+	5.97775i	−0.556178	+	0.202432i
$873$	22.7513	+	17.1068i	0.770015	+	0.578978i
$874$	20.4042	+	7.42652i	0.690182	+	0.251206i
$875$	19.1959	+	64.1189i	0.648941	+	2.16762i
$876$	−16.2167	+	29.9049i	−0.547911	+	1.01039i
$877$	−2.52161	−	43.2944i	−0.0851488	−	1.46195i	−0.722498	−	0.691373i	$-0.757006\pi$
$877$	−2.52161	−	43.2944i	−0.0851488	−	1.46195i	0.637349	−	0.770575i	$-0.280031\pi$
$878$	−33.0239	+	21.7201i	−1.11450	+	0.733019i
$879$	0.811880	+	3.97979i	0.0273840	+	0.134235i
$880$	−8.08409	−	1.91596i	−0.272515	−	0.0645872i
$881$	1.78531	+	10.1250i	0.0601486	+	0.341120i	1.00000		0.000464198i	$-0.000147759\pi$
$881$	1.78531	+	10.1250i	0.0601486	+	0.341120i	−0.939851	+	0.341584i	$0.889037\pi$
$882$	−25.1090	+	7.38697i	−0.845464	+	0.248732i
$883$	1.36337	−	7.73205i	0.0458810	−	0.260204i	−0.953236	−	0.302228i	$-0.902269\pi$
$883$	1.36337	−	7.73205i	0.0458810	−	0.260204i	0.999117	+	0.0420240i	$0.0133806\pi$
$884$	1.81903	−	4.21698i	0.0611805	−	0.141832i
$885$	−27.0409	+	7.17658i	−0.908970	+	0.241238i
$886$	−11.4507	+	38.2481i	−0.384695	+	1.28497i
$887$	−20.8967	+	28.0692i	−0.701643	+	0.942471i	−0.999928	−	0.0120063i	$-0.996178\pi$
$887$	−20.8967	+	28.0692i	−0.701643	+	0.942471i	0.298284	+	0.954477i	$0.403586\pi$
$888$	−5.53554	+	6.19048i	−0.185761	+	0.207739i
$889$	39.3805	−	19.7776i	1.32078	−	0.663321i
$890$	44.3751			1.48746
$891$	3.46136	−	5.86545i	0.115960	−	0.196500i
$892$	26.8550			0.899172
$893$	43.1800	−	21.6858i	1.44496	−	0.725688i
$894$	−44.5856	−	9.31700i	−1.49117	−	0.311607i
$895$	−16.7105	+	22.4461i	−0.558571	+	0.750292i
$896$	7.49465	−	25.0339i	0.250379	−	0.836323i
$897$	2.57131	−	9.50562i	0.0858535	−	0.317383i
$898$	5.83774	−	13.5334i	0.194808	−	0.451616i
$899$	−0.317622	+	1.80133i	−0.0105933	+	0.0600776i
$900$	41.7570	−	62.8343i	1.39190	−	2.09448i
$901$	−1.49032	−	8.45204i	−0.0496498	−	0.281578i
$902$	−7.62207	−	1.80646i	−0.253787	−	0.0601487i
$903$	−25.6922	+	22.7546i	−0.854982	+	0.757227i
$904$	−8.68189	+	5.71017i	−0.288755	+	0.189917i
$905$	1.75148	+	30.0717i	0.0582210	+	0.999616i
$906$	−34.9301	−	56.9334i	−1.16047	−	1.89149i
$907$	14.4087	+	48.1283i	0.478432	+	1.59807i	0.767689	+	0.640822i	$0.221407\pi$
$907$	14.4087	+	48.1283i	0.478432	+	1.59807i	−0.289257	+	0.957251i	$0.593408\pi$
$908$	25.2752	+	9.19941i	0.838786	+	0.305293i
$909$	35.3210	+	10.7581i	1.17152	+	0.356822i
$910$	−64.1788	+	23.3592i	−2.12751	+	0.774349i
$911$	−14.7268	−	19.7816i	−0.487922	−	0.655393i	0.488170	−	0.872748i	$-0.337664\pi$
$911$	−14.7268	−	19.7816i	−0.487922	−	0.655393i	−0.976093	+	0.217355i	$0.930257\pi$
$912$	12.6171	−	17.9280i	0.417793	−	0.593654i
$913$	−1.87537	+	0.444471i	−0.0620657	+	0.0147098i
$914$	−31.5072	−	73.0418i	−1.04216	−	2.41601i
$915$	1.11416	+	1.41601i	0.0368330	+	0.0468117i
$916$	−4.73694	−	3.11554i	−0.156513	−	0.102940i
$917$	16.7783	−	29.0608i	0.554067	−	0.959672i
$918$	7.19005	+	3.94343i	0.237307	+	0.130152i
$919$	−4.12738	−	7.14883i	−0.136150	−	0.235818i	0.789886	−	0.613253i	$-0.210139\pi$
$919$	−4.12738	−	7.14883i	−0.136150	−	0.235818i	−0.926036	+	0.377435i	$0.876806\pi$
$920$	−0.521745	+	8.95801i	−0.0172014	+	0.295337i
$921$	0.831559	−	26.4141i	0.0274008	−	0.870374i
$922$	−58.0779	−	6.78833i	−1.91269	−	0.223562i
$923$	−11.5230	−	12.2137i	−0.379285	−	0.402018i
$924$	8.88254	−	6.18813i	0.292214	−	0.203575i
$925$	47.9764	−	5.60763i	1.57745	−	0.184378i
$926$	−39.8178	−	33.4111i	−1.30849	−	1.09796i
$927$	−32.3286	+	38.1570i	−1.06181	+	1.25324i
$928$	2.83740	−	2.38086i	0.0931422	−	0.0781556i
$929$	6.73053	−	7.13394i	0.220821	−	0.234057i	−0.607487	−	0.794330i	$-0.707822\pi$
$929$	6.73053	−	7.13394i	0.220821	−	0.234057i	0.828308	+	0.560273i	$0.189304\pi$
$930$	−52.3143	+	20.6390i	−1.71545	+	0.676779i
$931$	−16.5380	−	8.30568i	−0.542010	−	0.272208i
$932$	39.4161	+	19.7955i	1.29112	+	0.648424i
$933$	−22.7058	−	18.0415i	−0.743354	−	0.590652i
$934$	11.4133	−	12.0974i	0.373455	−	0.395839i
$935$	1.68332	−	1.41247i	0.0550503	−	0.0461927i
$936$	6.49305	+	3.79013i	0.212232	+	0.123884i
$937$	33.8490	+	28.4027i	1.10580	+	0.927875i	0.997801	−	0.0662763i	$-0.0211119\pi$
$937$	33.8490	+	28.4027i	1.10580	+	0.927875i	0.107997	+	0.994151i	$0.465556\pi$
$938$	13.4396	−	1.57086i	0.438819	−	0.0512905i
$939$	−4.78330	−	56.2155i	−0.156097	−	1.83452i
$940$	71.2275	+	75.4967i	2.32318	+	2.46243i
$941$	10.5684	+	1.23526i	0.344519	+	0.0402684i	0.286593	−	0.958052i	$-0.407477\pi$
$941$	10.5684	+	1.23526i	0.344519	+	0.0402684i	0.0579256	+	0.998321i	$0.481551\pi$
$942$	−75.4846	+	40.4691i	−2.45942	+	1.31855i
$943$	0.650512	−	11.1689i	0.0211836	−	0.363708i
$944$	−5.85073	−	10.1338i	−0.190425	−	0.329826i
$945$	−16.9951	−	65.2896i	−0.552851	−	2.12387i
$946$	4.75603	−	8.23768i	0.154632	−	0.267830i
$947$	9.18551	+	6.04140i	0.298489	+	0.196319i	0.689915	−	0.723890i	$-0.257648\pi$
$947$	9.18551	+	6.04140i	0.298489	+	0.196319i	−0.391426	+	0.920209i	$0.628018\pi$
$948$	−18.3268	+	2.63990i	−0.595226	+	0.0857398i
$949$	7.81015	+	18.1060i	0.253528	+	0.587745i
$950$	93.8280	−	22.2376i	3.04418	−	0.721485i
$951$	−37.3843	−	3.36046i	−1.21227	−	0.108971i
$952$	1.49747	+	2.01145i	0.0485332	+	0.0651914i
$953$	39.7723	−	14.4759i	1.28835	−	0.468921i	0.395165	−	0.918610i	$-0.370687\pi$
$953$	39.7723	−	14.4759i	1.28835	−	0.468921i	0.893185	+	0.449689i	$0.148465\pi$
$954$	72.9267	−	3.89893i	2.36109	−	0.126233i
$955$	36.8676	+	13.4187i	1.19301	+	0.434219i
$956$	8.71206	+	29.1003i	0.281768	+	0.941171i
$957$	0.607940	−	0.0162398i	0.0196519	−	0.000524957i
$958$	−2.17888	−	37.4100i	−0.0703965	−	1.20866i
$959$	−26.3845	+	17.3533i	−0.851999	+	0.560369i
$960$	71.9442	+	24.0301i	2.32199	+	0.775568i
$961$	−15.0430	−	3.56526i	−0.485259	−	0.115008i
$962$	4.34483	+	24.6407i	0.140083	+	0.794449i
$963$	1.23404	+	11.0127i	0.0397664	+	0.354880i
$964$	7.52523	−	42.6777i	0.242371	−	1.37456i
$965$	−24.6587	+	57.1654i	−0.793793	+	1.84022i
$966$	19.7155	+	19.8097i	0.634336	+	0.637366i
$967$	2.38375	−	7.96226i	0.0766561	−	0.256049i	−0.911068	−	0.412255i	$-0.864741\pi$
$967$	2.38375	−	7.96226i	0.0766561	−	0.256049i	0.987724	+	0.156206i	$0.0499264\pi$
$968$	6.27654	−	8.43085i	0.201736	−	0.270978i
$969$	1.81073	+	5.50839i	0.0581690	+	0.176955i
$970$	−69.8384	+	35.0742i	−2.24238	+	1.12616i
$971$	−17.9539			−0.576169			−0.288084	−	0.957605i	$-0.593018\pi$
$971$	−17.9539			−0.576169			−0.288084	+	0.957605i	$0.593018\pi$
$972$	−22.5172	+	31.3562i	−0.722240	+	1.00575i
$973$	35.0207			1.12271
$974$	79.6265	−	39.9899i	2.55140	−	1.28136i
$975$	−13.6562	−	41.5432i	−0.437347	−	1.33045i
$976$	−0.450019	+	0.604480i	−0.0144048	+	0.0193489i
$977$	7.00093	−	23.3847i	0.223979	−	0.748144i	−0.769948	−	0.638107i	$-0.779718\pi$
$977$	7.00093	−	23.3847i	0.223979	−	0.748144i	0.993927	−	0.110037i	$-0.0350969\pi$
$978$	30.3069	+	30.4517i	0.969109	+	0.973737i
$979$	−1.61482	+	3.74356i	−0.0516097	+	0.119645i
$980$	6.90304	−	39.1491i	0.220509	−	1.25057i
$981$	−47.6648	−	20.8305i	−1.52182	−	0.665067i
$982$	2.67375	+	15.1636i	0.0853228	+	0.483890i
$983$	45.3567	+	10.7497i	1.44665	+	0.342863i	0.877583	−	0.479425i	$-0.159155\pi$
$983$	45.3567	+	10.7497i	1.44665	+	0.342863i	0.569071	+	0.822288i	$0.307303\pi$
$984$	8.10179	+	2.70608i	0.258276	+	0.0862667i
$985$	−35.6799	+	23.4670i	−1.13686	+	0.747722i
$986$	0.0425773	+	0.731025i	0.00135594	+	0.0232806i
$987$	62.1721	−	1.66079i	1.97896	−	0.0528635i
$988$	7.92511	+	26.4717i	0.252131	+	0.842177i
$989$	12.7663	+	4.64654i	0.405944	+	0.147751i
$990$	10.2005	+	15.6712i	0.324192	+	0.498063i
$991$	−55.3339	+	20.1399i	−1.75774	+	0.639765i	−0.999919	−	0.0126995i	$-0.995958\pi$
$991$	−55.3339	+	20.1399i	−1.75774	+	0.639765i	−0.757820	+	0.652464i	$0.773735\pi$
$992$	−18.7920	−	25.2421i	−0.596648	−	0.801437i
$993$	−41.0783	−	3.69252i	−1.30358	−	0.117179i
$994$	46.3732	−	10.9906i	1.47087	−	0.348602i
$995$	5.41324	+	12.5493i	0.171611	+	0.397839i
$996$	10.8128	−	1.55753i	0.342615	−	0.0493523i
$997$	−50.3721	−	33.1302i	−1.59530	−	1.04925i	−0.961147	−	0.276038i	$-0.910978\pi$
$997$	−50.3721	−	33.1302i	−1.59530	−	1.04925i	−0.634154	−	0.773207i	$-0.718651\pi$
$998$	17.0636	−	29.5550i	0.540138	−	0.935547i
$999$	−24.6366	+	1.97810i	−0.779469	+	0.0625844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.2.g.a.25.2	yes	144
3.2	odd	2		243.2.g.a.73.7		144
9.2	odd	6		729.2.g.b.703.2		144
9.4	even	3		729.2.g.d.217.7		144
9.5	odd	6		729.2.g.a.217.2		144
9.7	even	3		729.2.g.c.703.7		144
81.13	even	27	inner	81.2.g.a.13.2	✓	144
81.14	odd	54		729.2.g.a.514.2		144
81.16	even	27		6561.2.a.c.1.12		72
81.40	even	27		729.2.g.c.28.7		144
81.41	odd	54		729.2.g.b.28.2		144
81.65	odd	54		6561.2.a.d.1.61		72
81.67	even	27		729.2.g.d.514.7		144
81.68	odd	54		243.2.g.a.10.7		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.2	✓	144	81.13	even	27	inner
81.2.g.a.25.2	yes	144	1.1	even	1	trivial
243.2.g.a.10.7		144	81.68	odd	54
243.2.g.a.73.7		144	3.2	odd	2
729.2.g.a.217.2		144	9.5	odd	6
729.2.g.a.514.2		144	81.14	odd	54
729.2.g.b.28.2		144	81.41	odd	54
729.2.g.b.703.2		144	9.2	odd	6
729.2.g.c.28.7		144	81.40	even	27
729.2.g.c.703.7		144	9.7	even	3
729.2.g.d.217.7		144	9.4	even	3
729.2.g.d.514.7		144	81.67	even	27
6561.2.a.c.1.12		72	81.16	even	27
6561.2.a.d.1.61		72	81.65	odd	54

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.89071 + 0.949549i) q^{2} +(-0.540889 - 1.64543i) q^{3} +(1.47882 - 1.98639i) q^{4} +(-1.11651 + 3.72940i) q^{5} +(2.58508 + 2.59743i) q^{6} +(-1.32100 + 3.06243i) q^{7} +(-0.175036 + 0.992677i) q^{8} +(-2.41488 + 1.77999i) q^{9} +(-1.43025 - 8.11138i) q^{10} +(0.736337 + 0.174515i) q^{11} +(-4.06835 - 1.35887i) q^{12} +(-2.07722 + 1.36621i) q^{13} +(-0.410296 - 7.04452i) q^{14} +(6.74036 - 0.180054i) q^{15} +(0.808837 + 2.70170i) q^{16} +(-0.700932 - 0.255119i) q^{17} +(2.87564 - 5.65849i) q^{18} +(4.21736 - 1.53499i) q^{19} +(5.75694 + 7.73291i) q^{20} +(5.75353 + 0.517183i) q^{21} +(-1.55791 + 0.369231i) q^{22} +(-0.905723 - 2.09970i) q^{23} +(1.72805 - 0.248919i) q^{24} +(-8.48436 - 5.58025i) q^{25} +(2.63013 - 4.55552i) q^{26} +(4.23503 + 3.01074i) q^{27} +(4.12967 + 7.15280i) q^{28} +(-0.0269788 + 0.463208i) q^{29} +(-12.5731 + 6.74074i) q^{30} +(3.91546 + 0.457651i) q^{31} +(-5.47813 - 5.80647i) q^{32} +(-0.111124 - 1.30598i) q^{33} +(1.56751 - 0.183215i) q^{34} +(-9.94610 - 8.34577i) q^{35} +(-0.0353989 + 7.42918i) q^{36} +(-3.64375 + 3.05747i) q^{37} +(-6.51625 + 6.90682i) q^{38} +(3.37154 + 2.67895i) q^{39} +(-3.50665 - 1.76111i) q^{40} +(4.37210 + 2.19575i) q^{41} +(-11.3693 + 4.48541i) q^{42} +(-4.07702 + 4.32138i) q^{43} +(1.43556 - 1.20458i) q^{44} +(-3.94205 - 10.9934i) q^{45} +(3.70623 + 3.10990i) q^{46} +(10.6936 - 1.24990i) q^{47} +(4.00797 - 2.79221i) q^{48} +(-2.82973 - 2.99934i) q^{49} +(21.3402 + 2.49431i) q^{50} +(-0.0406530 + 1.29133i) q^{51} +(-0.357995 + 6.14654i) q^{52} +(5.75294 + 9.96438i) q^{53} +(-10.8660 - 1.67105i) q^{54} +(-1.47296 + 2.55124i) q^{55} +(-2.80878 - 1.84736i) q^{56} +(-4.80685 - 6.10911i) q^{57} +(-0.388830 - 0.901409i) q^{58} +(-4.03735 + 0.956869i) q^{59} +(9.61010 - 13.6553i) q^{60} +(0.159571 + 0.214341i) q^{61} +(-7.83755 + 2.85264i) q^{62} +(-2.26103 - 9.74676i) q^{63} +(10.5709 + 3.84748i) q^{64} +(-2.77590 - 9.27214i) q^{65} +(1.45020 + 2.36372i) q^{66} +(0.111496 + 1.91430i) q^{67} +(-1.54332 + 1.01506i) q^{68} +(-2.96502 + 2.62601i) q^{69} +(26.7299 + 6.33510i) q^{70} +(1.17278 + 6.65118i) q^{71} +(-1.34426 - 2.70876i) q^{72} +(1.37723 - 7.81064i) q^{73} +(3.98605 - 9.24071i) q^{74} +(-4.59281 + 16.9787i) q^{75} +(3.18760 - 10.6473i) q^{76} +(-1.50714 + 2.02444i) q^{77} +(-8.91839 - 1.86366i) q^{78} +(3.85762 - 1.93737i) q^{79} -10.9788 q^{80} +(2.66327 - 8.59692i) q^{81} -10.3513 q^{82} +(-2.27599 + 1.14304i) q^{83} +(9.53574 - 10.6640i) q^{84} +(1.73403 - 2.32921i) q^{85} +(3.60508 - 12.0418i) q^{86} +(0.776769 - 0.206152i) q^{87} +(-0.302122 + 0.700398i) q^{88} +(-0.935549 + 5.30576i) q^{89} +(17.8921 + 17.0421i) q^{90} +(-1.43990 - 8.16609i) q^{91} +(-5.51024 - 1.30595i) q^{92} +(-1.36479 - 6.69015i) q^{93} +(-19.0315 + 12.5172i) q^{94} +(1.01588 + 17.4421i) q^{95} +(-6.59109 + 12.1545i) q^{96} +(-2.72130 - 9.08977i) q^{97} +(8.19821 + 2.98391i) q^{98} +(-2.08880 + 0.889239i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19}+ \cdots + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more