LMFDB - Embedded newform 243.2.i.a.103.18

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)

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")

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);

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			103.18
Character	$\chi$	$=$	243.103
Dual form			243.2.i.a.151.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05702 + 0.294241i) q^{2} +(1.61600 - 0.623337i) q^{3} +(-0.681624 - 0.411362i) q^{4} +(-0.410657 + 0.0159353i) q^{5} +(1.89155 - 0.183385i) q^{6} +(3.12382 + 0.488556i) q^{7} +(-2.10535 - 2.23154i) q^{8} +(2.22290 - 2.01462i) q^{9} +(-0.438760 - 0.103988i) q^{10} +(-0.0946581 - 0.693020i) q^{11} +(-1.35792 - 0.239880i) q^{12} +(-3.19607 + 4.65999i) q^{13} +(3.15818 + 1.43557i) q^{14} +(-0.653687 + 0.281729i) q^{15} +(-0.826715 - 1.56948i) q^{16} +(3.16122 - 1.58762i) q^{17} +(2.94243 - 1.47542i) q^{18} +(0.0397202 + 0.681970i) q^{19} +(0.286469 + 0.158067i) q^{20} +(5.35262 - 1.15768i) q^{21} +(0.103860 - 0.760387i) q^{22} +(-2.18314 + 5.65449i) q^{23} +(-4.79324 - 2.29382i) q^{24} +(-4.81658 + 0.374374i) q^{25} +(-4.74947 + 3.98528i) q^{26} +(2.33642 - 4.64124i) q^{27} +(-1.92829 - 1.61803i) q^{28} +(-5.86222 - 4.19007i) q^{29} +(-0.773856 + 0.105451i) q^{30} +(-3.26498 + 3.74125i) q^{31} +(0.886943 + 4.09458i) q^{32} +(-0.584952 - 1.06092i) q^{33} +(3.80861 - 0.747986i) q^{34} +(-1.29060 - 0.150850i) q^{35} +(-2.34392 + 0.458796i) q^{36} +(1.89168 + 2.54097i) q^{37} +(-0.158679 + 0.732542i) q^{38} +(-2.26011 + 9.52277i) q^{39} +(0.900136 + 0.882847i) q^{40} +(1.36657 - 5.30533i) q^{41} +(5.99845 + 0.351268i) q^{42} +(8.75275 + 7.94270i) q^{43} +(-0.220561 + 0.511318i) q^{44} +(-0.880746 + 0.862741i) q^{45} +(-3.97141 + 5.33453i) q^{46} +(-8.82629 - 10.1138i) q^{47} +(-2.31429 - 2.02096i) q^{48} +(2.85380 + 0.915034i) q^{49} +(-5.20137 - 1.02152i) q^{50} +(4.11890 - 4.53610i) q^{51} +(4.09546 - 1.86162i) q^{52} +(-0.850884 + 4.82560i) q^{53} +(3.83528 - 4.21841i) q^{54} +(0.0499155 + 0.283085i) q^{55} +(-5.48649 - 7.99950i) q^{56} +(0.489284 + 1.07730i) q^{57} +(-4.96359 - 6.15388i) q^{58} +(5.80355 - 2.37101i) q^{59} +(0.561461 + 0.0768692i) q^{60} +(-0.455597 + 0.274954i) q^{61} +(-4.55198 + 2.99388i) q^{62} +(7.92819 - 5.20730i) q^{63} +(-0.473567 + 8.13082i) q^{64} +(1.23823 - 1.96459i) q^{65} +(-0.306140 - 1.29352i) q^{66} +(0.213208 - 0.152392i) q^{67} +(-2.80785 - 0.218243i) q^{68} +(-0.00331068 + 10.4985i) q^{69} +(-1.31980 - 0.539199i) q^{70} +(-0.202999 - 0.678064i) q^{71} +(-9.17570 - 0.719014i) q^{72} +(-4.98039 + 1.18037i) q^{73} +(1.25188 + 3.24246i) q^{74} +(-7.55023 + 3.60734i) q^{75} +(0.253462 - 0.481186i) q^{76} +(0.0428845 - 2.21111i) q^{77} +(-5.19097 + 9.40073i) q^{78} +(10.6090 - 10.4053i) q^{79} +(0.364506 + 0.631343i) q^{80} +(0.882596 - 8.95662i) q^{81} +(3.00553 - 5.20573i) q^{82} +(1.62135 + 6.29445i) q^{83} +(-4.12470 - 1.41276i) q^{84} +(-1.27287 + 0.702343i) q^{85} +(6.91475 + 10.9710i) q^{86} +(-12.0852 - 3.11700i) q^{87} +(-1.34721 + 1.67028i) q^{88} +(2.51342 - 8.39540i) q^{89} +(-1.18482 + 0.652781i) q^{90} +(-12.2606 + 12.9955i) q^{91} +(3.81412 - 2.95617i) q^{92} +(-2.94415 + 8.08104i) q^{93} +(-6.35365 - 13.2875i) q^{94} +(-0.0271788 - 0.279422i) q^{95} +(3.98560 + 6.06398i) q^{96} +(9.95051 + 0.386125i) q^{97} +(2.74728 + 1.80691i) q^{98} +(-1.60659 - 1.34982i) 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 $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

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 $

$2$	1.05702	+	0.294241i	0.747425	+	0.208060i	0.620885	−	0.783902i	$-0.286773\pi$
$2$	1.05702	+	0.294241i	0.747425	+	0.208060i	0.126540	+	0.991962i	$0.459613\pi$
$3$	1.61600	−	0.623337i	0.932997	−	0.359884i
$3$	1.61600	−	0.623337i	0.932997	−	0.359884i
$4$	−0.681624	−	0.411362i	−0.340812	−	0.205681i
$5$	−0.410657	+	0.0159353i	−0.183651	+	0.00712650i	−0.130437	−	0.991457i	$-0.541638\pi$
$5$	−0.410657	+	0.0159353i	−0.183651	+	0.00712650i	−0.0532143	+	0.998583i	$0.516947\pi$
$6$	1.89155	−	0.183385i	0.772223	−	0.0748666i
$7$	3.12382	+	0.488556i	1.18069	+	0.184657i	0.714247	−	0.699894i	$-0.246769\pi$
$7$	3.12382	+	0.488556i	1.18069	+	0.184657i	0.466444	+	0.884551i	$0.345535\pi$
$8$	−2.10535	−	2.23154i	−0.744353	−	0.788968i
$9$	2.22290	−	2.01462i	0.740968	−	0.671541i
$10$	−0.438760	−	0.103988i	−0.138748	−	0.0328839i
$11$	−0.0946581	−	0.693020i	−0.0285405	−	0.208953i	0.971006	−	0.239053i	$-0.0768371\pi$
$11$	−0.0946581	−	0.693020i	−0.0285405	−	0.208953i	−0.999547	+	0.0301001i	$0.990417\pi$
$12$	−1.35792	−	0.239880i	−0.391998	−	0.0692473i
$13$	−3.19607	+	4.65999i	−0.886432	+	1.29245i	0.0691149	+	0.997609i	$0.477983\pi$
$13$	−3.19607	+	4.65999i	−0.886432	+	1.29245i	−0.955547	+	0.294840i	$0.904734\pi$
$14$	3.15818	+	1.43557i	0.844058	+	0.383672i
$15$	−0.653687	+	0.281729i	−0.168781	+	0.0727421i
$16$	−0.826715	−	1.56948i	−0.206679	−	0.392370i
$17$	3.16122	−	1.58762i	0.766707	−	0.385055i	−0.0220522	−	0.999757i	$-0.507020\pi$
$17$	3.16122	−	1.58762i	0.766707	−	0.385055i	0.788760	+	0.614702i	$0.210724\pi$
$18$	2.94243	−	1.47542i	0.693538	−	0.347760i
$19$	0.0397202	+	0.681970i	0.00911244	+	0.156455i	0.999795	+	0.0202612i	$0.00644979\pi$
$19$	0.0397202	+	0.681970i	0.00911244	+	0.156455i	−0.990682	+	0.136193i	$0.956513\pi$
$20$	0.286469	+	0.158067i	0.0640563	+	0.0353448i
$21$	5.35262	−	1.15768i	1.16804	−	0.252627i
$22$	0.103860	−	0.760387i	0.0221429	−	0.162115i
$23$	−2.18314	+	5.65449i	−0.455217	+	1.17904i	0.495397	+	0.868667i	$0.335023\pi$
$23$	−2.18314	+	5.65449i	−0.455217	+	1.17904i	−0.950614	+	0.310375i	$0.899545\pi$
$24$	−4.79324	−	2.29382i	−0.978416	−	0.468225i
$25$	−4.81658	+	0.374374i	−0.963316	+	0.0748748i
$26$	−4.74947	+	3.98528i	−0.931448	+	0.781578i
$27$	2.33642	−	4.64124i	0.449644	−	0.893208i
$28$	−1.92829	−	1.61803i	−0.364413	−	0.305779i
$29$	−5.86222	−	4.19007i	−1.08859	−	0.778076i	−0.112110	−	0.993696i	$-0.535761\pi$
$29$	−5.86222	−	4.19007i	−1.08859	−	0.778076i	−0.976477	+	0.215620i	$0.930823\pi$
$30$	−0.773856	+	0.105451i	−0.141286	+	0.0192526i
$31$	−3.26498	+	3.74125i	−0.586408	+	0.671949i	−0.967583	−	0.252554i	$-0.918729\pi$
$31$	−3.26498	+	3.74125i	−0.586408	+	0.671949i	0.381175	+	0.924503i	$0.375520\pi$
$32$	0.886943	+	4.09458i	0.156791	+	0.723827i
$33$	−0.584952	−	1.06092i	−0.101827	−	0.184682i
$34$	3.80861	−	0.747986i	0.653171	−	0.128279i
$35$	−1.29060	−	0.150850i	−0.218151	−	0.0254982i
$36$	−2.34392	+	0.458796i	−0.390654	+	0.0764661i
$37$	1.89168	+	2.54097i	0.310990	+	0.417732i	0.929948	−	0.367692i	$-0.119852\pi$
$37$	1.89168	+	2.54097i	0.310990	+	0.417732i	−0.618957	+	0.785425i	$0.712445\pi$
$38$	−0.158679	+	0.732542i	−0.0257411	+	0.118834i
$39$	−2.26011	+	9.52277i	−0.361907	+	1.52486i
$40$	0.900136	+	0.882847i	0.142324	+	0.139590i
$41$	1.36657	−	5.30533i	0.213422	−	0.828554i	−0.768591	−	0.639740i	$-0.779042\pi$
$41$	1.36657	−	5.30533i	0.213422	−	0.828554i	0.982013	−	0.188814i	$-0.0604642\pi$
$42$	5.99845	+	0.351268i	0.925581	+	0.0542018i
$43$	8.75275	+	7.94270i	1.33478	+	1.21125i	0.958617	+	0.284698i	$0.0918933\pi$
$43$	8.75275	+	7.94270i	1.33478	+	1.21125i	0.376165	+	0.926553i	$0.377242\pi$
$44$	−0.220561	+	0.511318i	−0.0332508	+	0.0770840i
$45$	−0.880746	+	0.862741i	−0.131294	+	0.128610i
$46$	−3.97141	+	5.33453i	−0.585552	+	0.786533i
$47$	−8.82629	−	10.1138i	−1.28745	−	1.47525i	−0.797264	−	0.603630i	$-0.793720\pi$
$47$	−8.82629	−	10.1138i	−1.28745	−	1.47525i	−0.490182	−	0.871620i	$-0.663070\pi$
$48$	−2.31429	−	2.02096i	−0.334038	−	0.291700i
$49$	2.85380	+	0.915034i	0.407686	+	0.130719i
$50$	−5.20137	−	1.02152i	−0.735585	−	0.144464i
$51$	4.11890	−	4.53610i	0.576761	−	0.635181i
$52$	4.09546	−	1.86162i	0.567939	−	0.258160i
$53$	−0.850884	+	4.82560i	−0.116878	+	0.662847i	0.868925	+	0.494943i	$0.164811\pi$
$53$	−0.850884	+	4.82560i	−0.116878	+	0.662847i	−0.985803	+	0.167904i	$0.946300\pi$
$54$	3.83528	−	4.21841i	0.521916	−	0.574053i
$55$	0.0499155	+	0.283085i	0.00673060	+	0.0381711i
$56$	−5.48649	−	7.99950i	−0.733163	−	1.06898i
$57$	0.489284	+	1.07730i	0.0648073	+	0.142692i
$58$	−4.96359	−	6.15388i	−0.651751	−	0.808045i
$59$	5.80355	−	2.37101i	0.755558	−	0.308679i	0.0325045	−	0.999472i	$-0.489652\pi$
$59$	5.80355	−	2.37101i	0.755558	−	0.308679i	0.723053	+	0.690792i	$0.242738\pi$
$60$	0.561461	+	0.0768692i	0.0724844	+	0.00992377i
$61$	−0.455597	+	0.274954i	−0.0583332	+	0.0352043i	−0.545566	−	0.838068i	$-0.683685\pi$
$61$	−0.455597	+	0.274954i	−0.0583332	+	0.0352043i	0.487233	+	0.873272i	$0.338006\pi$
$62$	−4.55198	+	2.99388i	−0.578102	+	0.380223i
$63$	7.92819	−	5.20730i	0.998859	−	0.656058i
$64$	−0.473567	+	8.13082i	−0.0591958	+	1.01635i
$65$	1.23823	−	1.96459i	0.153584	−	0.243677i
$66$	−0.306140	−	1.29352i	−0.0376832	−	0.159222i
$67$	0.213208	−	0.152392i	0.0260475	−	0.0186176i	−0.568394	−	0.822757i	$-0.692435\pi$
$67$	0.213208	−	0.152392i	0.0260475	−	0.0186176i	0.594441	+	0.804139i	$0.297373\pi$
$68$	−2.80785	−	0.218243i	−0.340501	−	0.0264659i
$69$	−0.00331068	+	10.4985i	−0.000398559	+	1.26387i
$70$	−1.31980	−	0.539199i	−0.157747	−	0.0644466i
$71$	−0.202999	−	0.678064i	−0.0240916	−	0.0804714i	0.945098	−	0.326786i	$-0.105966\pi$
$71$	−0.202999	−	0.678064i	−0.0240916	−	0.0804714i	−0.969190	+	0.246314i	$0.920780\pi$
$72$	−9.17570	−	0.719014i	−1.08137	−	0.0847366i
$73$	−4.98039	+	1.18037i	−0.582910	+	0.138152i	−0.511483	−	0.859294i	$-0.670904\pi$
$73$	−4.98039	+	1.18037i	−0.582910	+	0.138152i	−0.0714273	+	0.997446i	$0.522755\pi$
$74$	1.25188	+	3.24246i	0.145529	+	0.376928i
$75$	−7.55023	+	3.60734i	−0.871825	+	0.416540i
$76$	0.253462	−	0.481186i	0.0290741	−	0.0551958i
$77$	0.0428845	−	2.21111i	0.00488714	−	0.251980i
$78$	−5.19097	+	9.40073i	−0.587761	+	1.06442i
$79$	10.6090	−	10.4053i	1.19361	−	1.17068i	0.212513	−	0.977158i	$-0.431835\pi$
$79$	10.6090	−	10.4053i	1.19361	−	1.17068i	0.981095	−	0.193525i	$-0.0619920\pi$
$80$	0.364506	+	0.631343i	0.0407530	+	0.0705863i
$81$	0.882596	−	8.95662i	0.0980663	−	0.995180i
$82$	3.00553	−	5.20573i	0.331906	−	0.574877i
$83$	1.62135	+	6.29445i	0.177966	+	0.690906i	0.993660	+	0.112423i	$0.0358612\pi$
$83$	1.62135	+	6.29445i	0.177966	+	0.690906i	−0.815695	+	0.578483i	$0.803645\pi$
$84$	−4.12470	−	1.41276i	−0.450041	−	0.154145i
$85$	−1.27287	+	0.702343i	−0.138063	+	0.0761797i
$86$	6.91475	+	10.9710i	0.745637	+	1.18303i
$87$	−12.0852	−	3.11700i	−1.29567	−	0.334178i
$88$	−1.34721	+	1.67028i	−0.143613	+	0.178053i
$89$	2.51342	−	8.39540i	0.266422	−	0.889910i	−0.715175	−	0.698945i	$-0.753653\pi$
$89$	2.51342	−	8.39540i	0.266422	−	0.889910i	0.981597	−	0.190965i	$-0.0611618\pi$
$90$	−1.18482	+	0.652781i	−0.124891	+	0.0688091i
$91$	−12.2606	+	12.9955i	−1.28526	+	1.36230i
$92$	3.81412	−	2.95617i	0.397650	−	0.308202i
$93$	−2.94415	+	8.08104i	−0.305294	+	0.837965i
$94$	−6.35365	−	13.2875i	−0.655329	−	1.37050i
$95$	−0.0271788	−	0.279422i	−0.00278848	−	0.0286681i
$96$	3.98560	+	6.06398i	0.406779	+	0.618902i
$97$	9.95051	+	0.386125i	1.01032	+	0.0392050i	0.538616	−	0.842551i	$-0.318947\pi$
$97$	9.95051	+	0.386125i	1.01032	+	0.0392050i	0.471705	+	0.881756i	$0.343639\pi$
$98$	2.74728	+	1.80691i	0.277517	+	0.182526i
$99$	−1.60659	−	1.34982i	−0.161468	−	0.135662i
$100$	3.43710	+	1.72618i	0.343710	+	0.172618i
$101$	−0.0587936	−	3.03139i	−0.00585019	−	0.301634i	−0.991297	−	0.131648i	$-0.957973\pi$
$101$	−0.0587936	−	3.03139i	−0.00585019	−	0.301634i	0.985446	−	0.169986i	$-0.0543724\pi$
$102$	5.68846	−	3.58279i	0.563241	−	0.354749i
$103$	−6.86258	−	5.31890i	−0.676190	−	0.524087i	0.215631	−	0.976475i	$-0.430819\pi$
$103$	−6.86258	−	5.31890i	−0.676190	−	0.524087i	−0.891821	+	0.452388i	$0.850572\pi$
$104$	17.1278	−	2.67874i	1.67952	−	0.262672i
$105$	−2.17964	+	0.560706i	−0.212711	+	0.0547193i
$106$	−2.31929	+	4.85038i	−0.225269	+	0.471111i
$107$	−6.81637	−	2.48096i	−0.658964	−	0.239843i	−0.00917483	−	0.999958i	$-0.502920\pi$
$107$	−6.81637	−	2.48096i	−0.658964	−	0.239843i	−0.649789	+	0.760115i	$0.725143\pi$
$108$	−3.50179	+	2.20247i	−0.336960	+	0.211932i
$109$	15.5615	−	5.66392i	1.49052	−	0.542505i	0.536933	−	0.843625i	$-0.319583\pi$
$109$	15.5615	−	5.66392i	1.49052	−	0.542505i	0.953586	+	0.301120i	$0.0973605\pi$
$110$	−0.0305336	+	0.313913i	−0.00291127	+	0.0299304i
$111$	4.64083	+	2.92705i	0.440488	+	0.277823i
$112$	−1.81573	−	5.30666i	−0.171570	−	0.501433i
$113$	−2.80855	+	2.54863i	−0.264206	+	0.239755i	−0.793332	−	0.608789i	$-0.791656\pi$
$113$	−2.80855	+	2.54863i	−0.264206	+	0.239755i	0.529126	+	0.848543i	$0.322520\pi$
$114$	0.200196	+	1.28270i	0.0187500	+	0.120136i
$115$	0.806417	−	2.35684i	0.0751987	−	0.219777i
$116$	2.27220	+	5.26755i	0.210968	+	0.489079i
$117$	2.28356	+	16.7976i	0.211115	+	1.55294i
$118$	6.83211	−	0.798559i	0.628946	−	0.0735133i
$119$	10.6507	−	3.41501i	0.976348	−	0.313053i
$120$	2.00493	+	0.865592i	0.183024	+	0.0790174i
$121$	10.1258	−	2.81870i	0.920524	−	0.256245i
$122$	−0.562477	+	0.156576i	−0.0509243	+	0.0141757i
$123$	−1.09864	−	9.42524i	−0.0990610	−	0.849845i
$124$	3.76450	−	1.20704i	0.338062	−	0.108395i
$125$	4.01293	−	0.469044i	0.358927	−	0.0419526i
$126$	9.91245	−	3.17141i	0.883071	−	0.282531i
$127$	−4.73994	−	10.9884i	−0.420602	−	0.975065i	−0.988397	−	0.151895i	$-0.951463\pi$
$127$	−4.73994	−	10.9884i	−0.420602	−	0.975065i	0.567795	−	0.823170i	$-0.307797\pi$
$128$	−0.180397	+	0.527231i	−0.0159450	+	0.0466011i
$129$	19.0954	+	7.37948i	1.68126	+	0.649727i
$130$	1.88689	−	1.71227i	0.165492	−	0.150176i
$131$	−2.36535	−	6.91300i	−0.206662	−	0.603992i	0.793327	−	0.608796i	$-0.208347\pi$
$131$	−2.36535	−	6.91300i	−0.206662	−	0.603992i	−0.999988	+	0.00480429i	$0.998471\pi$
$132$	−0.0377031	+	0.963772i	−0.00328164	+	0.0838856i
$133$	−0.209102	+	2.14975i	−0.0181314	+	0.186407i
$134$	0.270204	−	0.0983463i	0.0233421	−	0.00849583i
$135$	−0.885507	+	1.94319i	−0.0762123	+	0.167243i
$136$	−10.1983	−	3.71188i	−0.874497	−	0.318291i
$137$	0.308909	−	0.646029i	0.0263919	−	0.0551940i	−0.888549	−	0.458781i	$-0.848286\pi$
$137$	0.308909	−	0.646029i	0.0263919	−	0.0551940i	0.914941	+	0.403587i	$0.132237\pi$
$138$	−3.09258	+	11.0961i	−0.263258	+	0.944563i
$139$	−7.66302	+	1.19847i	−0.649969	+	0.101653i	−0.470905	−	0.882184i	$-0.656072\pi$
$139$	−7.66302	+	1.19847i	−0.649969	+	0.101653i	−0.179064	+	0.983837i	$0.557307\pi$
$140$	0.817650	+	0.633727i	0.0691041	+	0.0535597i
$141$	−20.5676	−	10.8421i	−1.73210	−	0.913074i
$142$	−0.0150594	−	0.776457i	−0.00126375	−	0.0651588i
$143$	3.53200	+	1.77384i	0.295361	+	0.148336i
$144$	−4.99962	−	1.82328i	−0.416635	−	0.151940i
$145$	2.47413	+	1.62726i	0.205465	+	0.135137i
$146$	−5.61167	−	0.217758i	−0.464425	−	0.0180218i
$147$	5.18211	−	0.300184i	0.427413	−	0.0247588i
$148$	−0.244157	−	2.51015i	−0.0200696	−	0.206333i
$149$	7.90490	+	16.5317i	0.647595	+	1.35433i	0.919913	+	0.392122i	$0.128259\pi$
$149$	7.90490	+	16.5317i	0.647595	+	1.35433i	−0.272318	+	0.962207i	$0.587790\pi$
$150$	−9.04215	+	1.59144i	−0.738289	+	0.129940i
$151$	−5.68452	+	4.40583i	−0.462600	+	0.358542i	−0.817082	−	0.576521i	$-0.804410\pi$
$151$	−5.68452	+	4.40583i	−0.462600	+	0.358542i	0.354483	+	0.935062i	$0.384657\pi$
$152$	1.43822	−	1.52442i	0.116655	−	0.123647i
$153$	3.82862	−	9.89778i	0.309525	−	0.800188i
$154$	0.695930	−	2.32457i	0.0560796	−	0.187319i
$155$	1.28117	−	1.58840i	0.102906	−	0.127583i
$156$	5.45785	−	5.56122i	0.436978	−	0.445254i
$157$	11.9310	+	18.9298i	0.952196	+	1.51076i	0.857008	+	0.515303i	$0.172321\pi$
$157$	11.9310	+	18.9298i	0.952196	+	1.51076i	0.0951880	+	0.995459i	$0.469655\pi$
$158$	14.2756	−	7.87694i	1.13571	−	0.626656i
$159$	1.63295	+	8.32855i	0.129501	+	0.660497i
$160$	−0.429477	−	1.66733i	−0.0339532	−	0.131814i
$161$	−9.58227	+	16.5970i	−0.755189	+	1.30803i
$162$	3.56833	−	9.20761i	0.280354	−	0.723419i
$163$	0.211320	+	0.366018i	0.0165519	+	0.0286687i	0.874183	−	0.485597i	$-0.161398\pi$
$163$	0.211320	+	0.366018i	0.0165519	+	0.0286687i	−0.857631	+	0.514266i	$0.828064\pi$
$164$	−3.11390	+	3.05409i	−0.243154	+	0.238484i
$165$	0.257120	+	0.426350i	0.0200168	+	0.0331913i
$166$	−0.138294	+	7.13042i	−0.0107337	+	0.553428i
$167$	−2.13649	+	4.05603i	−0.165327	+	0.313865i	−0.953396	−	0.301721i	$-0.902439\pi$
$167$	−2.13649	+	4.05603i	−0.165327	+	0.313865i	0.788069	+	0.615586i	$0.211081\pi$
$168$	−13.8525	−	9.50725i	−1.06875	−	0.733500i
$169$	−6.81831	−	17.6599i	−0.524486	−	1.35845i
$170$	−1.55211	+	0.367857i	−0.119041	+	0.0282133i
$171$	1.46221	+	1.43593i	0.111818	+	0.109808i
$172$	−2.69876	−	9.01449i	−0.205779	−	0.687348i
$173$	9.86916	+	4.03200i	0.750338	+	0.306547i	0.720918	−	0.693020i	$-0.243720\pi$
$173$	9.86916	+	4.03200i	0.750338	+	0.306547i	0.0294202	+	0.999567i	$0.490634\pi$
$174$	−11.8571	−	6.85068i	−0.898884	−	0.519349i
$175$	−15.2290	−	1.18369i	−1.15120	−	0.0894787i
$176$	−1.00943	+	0.721494i	−0.0760883	+	0.0543847i
$177$	7.90059	−	7.44911i	0.593845	−	0.559910i
$178$	5.12700	−	8.13454i	0.384285	−	0.609710i
$179$	0.627151	−	10.7678i	0.0468755	−	0.804821i	−0.890173	−	0.455622i	$-0.849417\pi$
$179$	0.627151	−	10.7678i	0.0468755	−	0.804821i	0.937049	−	0.349199i	$-0.113546\pi$
$180$	0.955236	−	0.225759i	0.0711991	−	0.0168271i
$181$	5.04938	−	3.32103i	0.375318	−	0.246850i	−0.347810	−	0.937565i	$-0.613074\pi$
$181$	5.04938	−	3.32103i	0.375318	−	0.246850i	0.723127	+	0.690715i	$0.242704\pi$
$182$	−16.7835	+	10.1289i	−1.24408	+	0.750804i
$183$	−0.564855	+	0.728316i	−0.0417553	+	0.0538386i
$184$	17.2145	−	7.03289i	1.26907	−	0.518472i
$185$	−0.817322	−	1.01332i	−0.0600907	−	0.0745008i
$186$	−5.48979	+	7.67552i	−0.402531	+	0.562797i
$187$	−1.39949	−	2.04050i	−0.102341	−	0.149216i
$188$	1.85577	+	10.5246i	0.135346	+	0.767586i
$189$	9.56605	−	13.3569i	0.695828	−	0.971573i
$190$	0.0534891	−	0.303352i	0.00388051	−	0.0220074i
$191$	19.3360	−	8.78927i	1.39910	−	0.635969i	0.434739	−	0.900557i	$-0.356841\pi$
$191$	19.3360	−	8.78927i	1.39910	−	0.635969i	0.964362	+	0.264587i	$0.0852357\pi$
$192$	4.30296	+	13.4346i	0.310539	+	0.969558i
$193$	−18.1014	−	3.55499i	−1.30297	−	0.255894i	−0.507373	−	0.861726i	$-0.669383\pi$
$193$	−18.1014	−	3.55499i	−1.30297	−	0.255894i	−0.795592	+	0.605832i	$0.792840\pi$
$194$	10.4043	+	3.33599i	0.746982	+	0.239510i
$195$	0.776380	−	3.94660i	0.0555978	−	0.282622i
$196$	−1.56881	−	1.79765i	−0.112058	−	0.128404i
$197$	−3.79295	+	5.09482i	−0.270237	+	0.362991i	−0.916438	−	0.400176i	$-0.868949\pi$
$197$	−3.79295	+	5.09482i	−0.270237	+	0.362991i	0.646202	+	0.763167i	$0.276356\pi$
$198$	−1.30102	−	1.89950i	−0.0924596	−	0.134992i
$199$	−9.59400	+	22.2414i	−0.680101	+	1.57665i	0.130762	+	0.991414i	$0.458258\pi$
$199$	−9.59400	+	22.2414i	−0.680101	+	1.57665i	−0.810862	+	0.585237i	$0.801002\pi$
$200$	10.9760	+	9.96020i	0.776121	+	0.704293i
$201$	0.249552	−	0.379165i	0.0176020	−	0.0267442i
$202$	0.829812	−	3.22153i	0.0583854	−	0.226666i
$203$	−16.2654	−	15.9530i	−1.14161	−	1.11968i
$204$	−4.67352	+	1.39755i	−0.327212	+	0.0978483i
$205$	−0.476647	+	2.20045i	−0.0332905	+	0.153686i
$206$	−5.68883	−	7.64143i	−0.396360	−	0.532404i
$207$	6.53873	+	16.9676i	0.454473	+	1.17933i
$208$	9.95601	+	1.16369i	0.690325	+	0.0806874i
$209$	0.468859	−	0.0920808i	0.0324316	−	0.00636936i
$210$	−2.46890	−	0.0486632i	−0.170370	−	0.00335808i
$211$	−3.32177	−	15.3350i	−0.228680	−	1.05570i	−0.936869	−	0.349681i	$-0.886290\pi$
$211$	−3.32177	−	15.3350i	−0.228680	−	1.05570i	0.708189	−	0.706023i	$-0.249513\pi$
$212$	2.56505	−	2.93922i	0.176168	−	0.201867i
$213$	−0.750708	−	0.969214i	−0.0514377	−	0.0664094i
$214$	−6.47503	−	4.62807i	−0.442624	−	0.316369i
$215$	−3.72095	−	3.12224i	−0.253766	−	0.212935i
$216$	−15.2761	+	4.55762i	−1.03941	+	0.310107i
$217$	−12.0270	+	10.0919i	−0.816447	+	0.685080i
$218$	18.1153	−	1.40803i	1.22692	−	0.0953641i
$219$	−7.31253	+	5.01194i	−0.494135	+	0.338675i
$220$	0.0824268	−	0.213491i	0.00555721	−	0.0143935i
$221$	−2.70518	+	19.8054i	−0.181970	+	1.33226i
$222$	4.04419	+	4.45947i	0.271428	+	0.299300i
$223$	−20.4049	−	11.2590i	−1.36642	−	0.753957i	−0.381074	−	0.924545i	$-0.624446\pi$
$223$	−20.4049	−	11.2590i	−1.36642	−	0.753957i	−0.985342	+	0.170588i	$0.945433\pi$
$224$	0.770213	+	13.2240i	0.0514620	+	0.883568i
$225$	−9.95257	+	10.5358i	−0.663505	+	0.702386i
$226$	−3.71860	+	1.86755i	−0.247358	+	0.124228i
$227$	5.09617	+	9.67483i	0.338244	+	0.642141i	0.993572	−	0.113204i	$-0.0361113\pi$
$227$	5.09617	+	9.67483i	0.338244	+	0.642141i	−0.655327	+	0.755345i	$0.727469\pi$
$228$	0.109654	−	0.935588i	0.00726199	−	0.0619609i
$229$	−8.74216	−	3.97380i	−0.577698	−	0.262596i	0.103579	−	0.994621i	$-0.466970\pi$
$229$	−8.74216	−	3.97380i	−0.577698	−	0.262596i	−0.681278	+	0.732025i	$0.738575\pi$
$230$	1.54588	−	2.25394i	0.101932	−	0.148621i
$231$	−1.30897	−	3.59989i	−0.0861236	−	0.236855i
$232$	2.99173	+	21.9033i	0.196417	+	1.43802i
$233$	6.40584	+	1.51821i	0.419661	+	0.0994614i	0.435020	−	0.900421i	$-0.356741\pi$
$233$	6.40584	+	1.51821i	0.419661	+	0.0994614i	−0.0153598	+	0.999882i	$0.504889\pi$
$234$	−2.52878	+	18.4273i	−0.165312	+	1.20463i
$235$	3.78574	+	4.01265i	0.246955	+	0.261757i
$236$	−4.93118	−	0.771223i	−0.320993	−	0.0502023i
$237$	10.6582	−	23.4279i	0.692324	−	1.52180i
$238$	12.2628	−	0.475853i	0.794880	−	0.0308450i
$239$	−22.7908	−	13.7543i	−1.47422	−	0.889694i	−0.999957	−	0.00930879i	$-0.997037\pi$
$239$	−22.7908	−	13.7543i	−1.47422	−	0.889694i	−0.474259	−	0.880385i	$-0.657284\pi$
$240$	0.982581	+	0.793040i	0.0634253	+	0.0511905i
$241$	−17.9612	−	4.99984i	−1.15698	−	0.322068i	−0.364051	−	0.931379i	$-0.618607\pi$
$241$	−17.9612	−	4.99984i	−1.15698	−	0.322068i	−0.792931	+	0.609311i	$0.791446\pi$
$242$	11.5325			0.741337
$243$	−4.15671	−	15.0240i	−0.266653	−	0.963793i
$244$	0.423651			0.0271215
$245$	−1.18651	−	0.330289i	−0.0758036	−	0.0211014i
$246$	1.61201	−	10.2859i	0.102778	−	0.655806i
$247$	−3.30492	−	1.99453i	−0.210287	−	0.126909i
$248$	15.2227	−	0.590709i	0.966641	−	0.0375101i
$249$	6.54365	+	9.16118i	0.414687	+	0.580566i
$250$	4.37975	+	0.684981i	0.277000	+	0.0433220i
$251$	−3.87408	−	4.10629i	−0.244530	−	0.259187i	0.593471	−	0.804855i	$-0.297757\pi$
$251$	−3.87408	−	4.10629i	−0.244530	−	0.259187i	−0.838001	+	0.545669i	$0.816276\pi$
$252$	−7.54613	+	0.288058i	−0.475362	+	0.0181459i
$253$	4.12532	+	0.977720i	0.259357	+	0.0614687i
$254$	−1.77696	−	13.0096i	−0.111496	−	0.816298i
$255$	−1.61917	+	1.92841i	−0.101396	+	0.120762i
$256$	8.86747	−	12.9291i	0.554217	−	0.808068i
$257$	0.574784	+	0.261271i	0.0358540	+	0.0162976i	0.431657	−	0.902038i	$-0.357929\pi$
$257$	0.574784	+	0.261271i	0.0358540	+	0.0162976i	−0.395803	+	0.918335i	$0.629534\pi$
$258$	18.0129	+	13.4189i	1.12143	+	0.835425i
$259$	4.66786	+	8.86170i	0.290046	+	0.550640i
$260$	−1.65216	+	0.829748i	−0.102463	+	0.0514588i
$261$	−21.4726	+	2.49606i	−1.32912	+	0.154502i
$262$	−0.466131	−	8.00316i	−0.0287977	−	0.494437i
$263$	−8.20269	−	4.52605i	−0.505800	−	0.279088i	0.209621	−	0.977783i	$-0.432777\pi$
$263$	−8.20269	−	4.52605i	−0.505800	−	0.279088i	−0.715420	+	0.698694i	$0.753765\pi$
$264$	−1.13595	+	3.53894i	−0.0699127	+	0.217807i
$265$	0.272523	−	1.99522i	0.0167410	−	0.122566i
$266$	−0.853570	+	2.21080i	−0.0523357	+	0.135553i
$267$	−1.17148	−	15.1337i	−0.0716934	−	0.926165i
$268$	−0.208016	+	0.0161683i	−0.0127066	+	0.000987633i
$269$	−20.2337	+	16.9781i	−1.23367	+	1.03517i	−0.235679	+	0.971831i	$0.575731\pi$
$269$	−20.2337	+	16.9781i	−1.23367	+	1.03517i	−0.997992	+	0.0633421i	$0.979824\pi$
$270$	−1.50776	+	1.79343i	−0.0917595	+	0.109145i
$271$	6.32458	+	5.30696i	0.384191	+	0.322375i	0.814345	−	0.580381i	$-0.197096\pi$
$271$	6.32458	+	5.30696i	0.384191	+	0.322375i	−0.430154	+	0.902756i	$0.641541\pi$
$272$	−5.10517	−	3.64895i	−0.309546	−	0.221250i
$273$	−11.7126	+	28.6432i	−0.708877	+	1.73356i
$274$	0.516611	−	0.591970i	0.0312096	−	0.0357622i
$275$	0.715377	+	3.30255i	0.0431389	+	0.199151i
$276$	4.32093	−	7.15465i	0.260090	−	0.430659i
$277$	12.4856	−	2.45209i	0.750187	−	0.147332i	0.197017	−	0.980400i	$-0.436875\pi$
$277$	12.4856	−	2.45209i	0.750187	−	0.147332i	0.553170	+	0.833068i	$0.313418\pi$
$278$	−8.45260	−	0.987967i	−0.506953	−	0.0592543i
$279$	0.279475	+	14.8941i	0.0167317	+	0.891689i
$280$	2.38054	+	3.19762i	0.142264	+	0.191094i
$281$	−3.18475	+	14.7024i	−0.189986	+	0.877074i	0.778429	+	0.627732i	$0.216017\pi$
$281$	−3.18475	+	14.7024i	−0.189986	+	0.877074i	−0.968416	+	0.249342i	$0.919786\pi$
$282$	−18.5501	−	17.5122i	−1.10464	−	1.04283i
$283$	−8.50577	−	8.34240i	−0.505616	−	0.495904i	0.402039	−	0.915623i	$-0.368302\pi$
$283$	−8.50577	−	8.34240i	−0.505616	−	0.495904i	−0.907654	+	0.419718i	$0.862129\pi$
$284$	−0.140561	+	0.545691i	−0.00834075	+	0.0323808i
$285$	−0.218095	−	0.434605i	−0.0129188	−	0.0257438i
$286$	3.21145	+	2.91424i	0.189897	+	0.172323i
$287$	6.86085	−	15.9052i	0.404983	−	0.938857i
$288$	10.2206	+	7.31501i	0.602256	+	0.431041i
$289$	−2.67896	+	3.59846i	−0.157586	+	0.211674i
$290$	2.13639	+	2.44804i	0.125453	+	0.143754i
$291$	16.3207	−	5.57854i	0.956736	−	0.327020i
$292$	3.88031	+	1.24417i	0.227078	+	0.0728096i
$293$	−4.51050	−	0.885833i	−0.263506	−	0.0517509i	0.0592142	−	0.998245i	$-0.481141\pi$
$293$	−4.51050	−	0.885833i	−0.263506	−	0.0517509i	−0.322720	+	0.946494i	$0.604597\pi$
$294$	5.56591	+	1.20749i	0.324611	+	0.0704223i
$295$	−2.34548	+	1.06615i	−0.136559	+	0.0620738i
$296$	1.68762	−	9.57098i	0.0980911	−	0.556302i
$297$	−3.43763	−	1.17985i	−0.199472	−	0.0684621i
$298$	3.49132	+	19.8003i	0.202247	+	1.14700i
$299$	−19.3724	−	28.2456i	−1.12033	−	1.63349i
$300$	6.63034	+	0.647029i	0.382803	+	0.0373562i
$301$	23.4615	+	29.0877i	1.35230	+	1.67659i
$302$	−7.30502	+	2.98443i	−0.420357	+	0.171735i
$303$	−1.98458	−	4.86207i	−0.114011	−	0.279318i
$304$	1.03750	−	0.626135i	0.0595047	−	0.0359113i
$305$	0.182712	−	0.120172i	0.0104621	−	0.00688102i
$306$	6.95925	−	9.33560i	0.397834	−	0.533681i
$307$	0.414900	−	7.12356i	0.0236796	−	0.406563i	−0.965553	−	0.260208i	$-0.916209\pi$
$307$	0.414900	−	7.12356i	0.0236796	−	0.406563i	0.989232	−	0.146355i	$-0.0467541\pi$
$308$	−0.938799	+	1.48951i	−0.0534930	+	0.0848725i
$309$	−14.4054	−	4.31764i	−0.819494	−	0.245622i
$310$	1.82159	−	1.30199i	0.103459	−	0.0739483i
$311$	−14.4106	−	1.12008i	−0.817152	−	0.0635140i	−0.337889	−	0.941186i	$-0.609713\pi$
$311$	−14.4106	−	1.12008i	−0.817152	−	0.0635140i	−0.479262	+	0.877672i	$0.659096\pi$
$312$	26.0088	−	15.0052i	1.47246	−	0.849504i
$313$	3.86078	+	1.57730i	0.218224	+	0.0891544i	0.484676	−	0.874694i	$-0.338938\pi$
$313$	3.86078	+	1.57730i	0.218224	+	0.0891544i	−0.266452	+	0.963848i	$0.585851\pi$
$314$	7.04134	+	23.5197i	0.397366	+	1.32730i
$315$	−3.17279	+	2.26475i	−0.178766	+	0.127604i
$316$	−11.5117	+	2.72832i	−0.647583	+	0.153480i
$317$	7.57152	+	19.6107i	0.425259	+	1.10145i	0.965607	+	0.260007i	$0.0837248\pi$
$317$	7.57152	+	19.6107i	0.425259	+	1.10145i	−0.540348	+	0.841442i	$0.681707\pi$
$318$	−0.724548	+	9.28391i	−0.0406306	+	0.520616i
$319$	−2.34889	+	4.45926i	−0.131513	+	0.249671i
$320$	0.0649057	−	3.34652i	0.00362834	−	0.187076i
$321$	−12.5617	+	0.239672i	−0.701127	+	0.0133772i
$322$	−15.0122	+	14.7238i	−0.836595	+	0.820526i
$323$	1.20827	+	2.09279i	0.0672302	+	0.116446i
$324$	−4.28601	+	5.74198i	−0.238112	+	0.318999i
$325$	13.6496	−	23.6417i	0.757142	−	1.31141i
$326$	0.115672	+	0.449067i	0.00640648	+	0.0248715i
$327$	21.6168	−	18.8529i	1.19541	−	1.04257i
$328$	−14.7162	+	8.12003i	−0.812564	+	0.448354i
$329$	−22.6305	−	35.9058i	−1.24766	−	1.97955i
$330$	0.146331	+	0.526316i	0.00805527	+	0.0289727i
$331$	1.63496	−	2.02703i	0.0898655	−	0.111416i	−0.731436	−	0.681910i	$-0.761150\pi$
$331$	1.63496	−	2.02703i	0.0898655	−	0.111416i	0.821302	+	0.570494i	$0.193248\pi$
$332$	1.48415	−	4.95741i	0.0814533	−	0.272073i
$333$	9.32411	+	1.83730i	0.510958	+	0.100684i
$334$	−3.45176	+	3.65865i	−0.188872	+	0.200193i
$335$	−0.0851267	+	0.0659782i	−0.00465097	+	0.00360477i
$336$	−6.24205	−	7.44375i	−0.340532	−	0.406090i
$337$	9.53274	+	19.9360i	0.519281	+	1.08598i	0.980103	+	0.198492i	$0.0636042\pi$
$337$	9.53274	+	19.9360i	0.519281	+	1.08598i	−0.460821	+	0.887493i	$0.652445\pi$
$338$	−2.01082	−	20.6730i	−0.109374	−	1.12447i
$339$	−2.94997	+	5.86925i	−0.160220	+	0.318774i
$340$	1.15654	+	0.0448790i	0.0627221	+	0.00243390i
$341$	2.90182	+	1.90856i	0.157142	+	0.103354i
$342$	1.12307	+	1.94805i	0.0607285	+	0.105338i
$343$	−11.3106	−	5.68042i	−0.610717	−	0.306714i
$344$	−0.703151	−	36.2543i	−0.0379114	−	1.95470i
$345$	−0.165937	−	4.31132i	−0.00893376	−	0.232114i
$346$	9.24550	+	7.16581i	0.497041	+	0.385236i
$347$	14.6642	−	2.29344i	0.787214	−	0.123118i	0.251880	−	0.967758i	$-0.418951\pi$
$347$	14.6642	−	2.29344i	0.787214	−	0.123118i	0.535334	+	0.844640i	$0.320186\pi$
$348$	6.95532	+	7.09600i	0.372844	+	0.380386i
$349$	3.02645	−	6.32929i	0.162002	−	0.338799i	−0.805119	−	0.593113i	$-0.797899\pi$
$349$	3.02645	−	6.32929i	0.162002	−	0.338799i	0.967122	+	0.254313i	$0.0818495\pi$
$350$	−15.7491	−	5.73219i	−0.841822	−	0.306398i
$351$	14.1608	+	25.7215i	0.755846	+	1.37291i
$352$	2.75367	−	1.00225i	0.146771	−	0.0534203i
$353$	−2.20260	+	22.6447i	−0.117233	+	1.20526i	0.733512	+	0.679677i	$0.237880\pi$
$353$	−2.20260	+	22.6447i	−0.117233	+	1.20526i	−0.850744	+	0.525579i	$0.823849\pi$
$354$	10.5429	−	5.54917i	0.560349	−	0.294935i
$355$	0.0941681	+	0.275217i	0.00499792	+	0.0146070i
$356$	−5.16675	+	4.68858i	−0.273837	+	0.248494i
$357$	15.0828	−	12.1576i	0.798267	−	0.643449i
$358$	3.83123	−	11.1972i	0.202487	−	0.591790i
$359$	−10.2496	−	23.7611i	−0.540951	−	1.25407i	−0.941259	−	0.337685i	$-0.890356\pi$
$359$	−10.2496	−	23.7611i	−0.540951	−	1.25407i	0.400308	−	0.916381i	$-0.368903\pi$
$360$	3.77952	+	0.149050i	0.199198	+	0.00785562i
$361$	18.4080	−	2.15159i	0.968843	−	0.113242i
$362$	6.31447	−	2.02465i	0.331881	−	0.106413i
$363$	14.6062	−	10.8668i	0.766628	−	0.570358i
$364$	13.7030	−	3.81448i	0.718231	−	0.199933i
$365$	2.02642	−	0.564092i	0.106068	−	0.0295259i
$366$	−0.811363	+	0.603639i	−0.0424106	+	0.0315527i
$367$	−14.0231	+	4.49631i	−0.731998	+	0.234706i	−0.647872	−	0.761749i	$-0.724341\pi$
$367$	−14.0231	+	4.49631i	−0.731998	+	0.234706i	−0.0841261	+	0.996455i	$0.526810\pi$
$368$	10.6794	−	1.24825i	0.556705	−	0.0650694i
$369$	−7.65050	−	14.5464i	−0.398269	−	0.757253i
$370$	−0.565764	−	1.31159i	−0.0294127	−	0.0681862i
$371$	−5.01558	+	14.6586i	−0.260396	+	0.761036i
$372$	5.33104	−	4.29712i	0.276401	−	0.222795i
$373$	11.4991	−	10.4348i	0.595399	−	0.540296i	−0.317617	−	0.948219i	$-0.602883\pi$
$373$	11.4991	−	10.4348i	0.595399	−	0.540296i	0.913016	+	0.407923i	$0.133747\pi$
$374$	−0.878885	−	2.56864i	−0.0454460	−	0.132821i
$375$	6.19252	−	3.25938i	0.319780	−	0.168314i
$376$	−3.98694	+	40.9893i	−0.205611	+	2.11386i
$377$	38.2618	−	13.9261i	1.97058	−	0.717233i
$378$	14.0416	−	11.3038i	0.722224	−	0.581404i
$379$	34.3209	+	12.4918i	1.76295	+	0.641660i	0.999989	−	0.00478940i	$-0.00152452\pi$
$379$	34.3209	+	12.4918i	1.76295	+	0.641660i	0.762957	+	0.646449i	$0.223747\pi$
$380$	−0.0964181	+	0.201641i	−0.00494614	+	0.0103440i
$381$	−14.5092	−	14.8027i	−0.743330	−	0.758365i
$382$	23.0246	−	3.60099i	1.17804	−	0.184242i
$383$	25.0553	+	19.4193i	1.28026	+	0.992280i	0.999471	+	0.0325116i	$0.0103506\pi$
$383$	25.0553	+	19.4193i	1.28026	+	0.992280i	0.280793	+	0.959768i	$0.409402\pi$
$384$	0.0371206	+	0.964453i	0.00189430	+	0.0492170i
$385$	0.0176240	+	0.908691i	0.000898204	+	0.0463112i
$386$	−18.0875	−	9.08387i	−0.920628	−	0.462357i
$387$	35.4581	+	0.0223633i	1.80243	+	0.00113679i
$388$	−6.62366	−	4.35645i	−0.336266	−	0.221165i
$389$	29.5310	+	1.14594i	1.49728	+	0.0581013i	0.774323	−	0.632790i	$-0.218091\pi$
$389$	29.5310	+	1.14594i	1.49728	+	0.0581013i	0.722958	+	0.690892i	$0.242782\pi$
$390$	1.98190	−	3.94319i	0.100357	−	0.199671i
$391$	2.07580	+	21.3411i	0.104978	+	1.07926i
$392$	−3.96631	−	8.29484i	−0.200329	−	0.418952i
$393$	−8.13153	−	9.69699i	−0.410182	−	0.489149i
$394$	−5.50833	+	4.26928i	−0.277506	+	0.215083i
$395$	−4.19086	+	4.44205i	−0.210865	+	0.223504i
$396$	0.539826	+	1.58096i	0.0271273	+	0.0794460i
$397$	0.0255025	−	0.0851843i	0.00127993	−	0.00427528i	−0.957347	−	0.288940i	$-0.906697\pi$
$397$	0.0255025	−	0.0851843i	0.00127993	−	0.00427528i	0.958627	+	0.284665i	$0.0918823\pi$
$398$	−16.6854	+	20.6866i	−0.836362	+	1.03693i
$399$	1.00211	+	3.60434i	0.0501683	+	0.180443i
$400$	4.56951	+	7.25003i	0.228476	+	0.362501i
$401$	14.1175	−	7.78969i	0.704993	−	0.388999i	−0.0897342	−	0.995966i	$-0.528602\pi$
$401$	14.1175	−	7.78969i	0.704993	−	0.388999i	0.794727	+	0.606967i	$0.207614\pi$
$402$	0.375347	−	0.327356i	0.0187206	−	0.0163270i
$403$	−6.99908	−	27.1721i	−0.348649	−	1.35354i
$404$	−1.20692	+	2.09045i	−0.0600466	+	0.104004i
$405$	−0.219717	+	3.69216i	−0.0109178	+	0.183465i
$406$	−12.4988	−	21.6486i	−0.620306	−	1.07440i
$407$	1.58188	−	1.55150i	0.0784108	−	0.0769048i
$408$	−18.7942	+	0.358584i	−0.930451	+	0.0177526i
$409$	−0.119689	+	6.17114i	−0.00591824	+	0.305143i	0.985143	+	0.171736i	$0.0549375\pi$
$409$	−0.119689	+	6.17114i	−0.00591824	+	0.305143i	−0.991061	+	0.133407i	$0.957408\pi$
$410$	−1.15129	+	2.18566i	−0.0568580	+	0.107942i
$411$	0.0965035	−	1.23654i	0.00476017	−	0.0609938i
$412$	2.48970	+	6.44849i	0.122659	+	0.317695i
$413$	19.2876	−	4.57124i	0.949080	−	0.224936i
$414$	1.91900	+	19.8590i	0.0943137	+	0.976017i
$415$	−0.766121	−	2.55902i	−0.0376074	−	0.125617i
$416$	−21.9155	−	8.95345i	−1.07449	−	0.438979i
$417$	−11.6364	+	6.71338i	−0.569836	+	0.328755i
$418$	0.522686	+	0.0406264i	0.0255654	+	0.00198710i
$419$	−30.1632	+	21.5594i	−1.47357	+	1.05324i	−0.490203	+	0.871608i	$0.663078\pi$
$419$	−30.1632	+	21.5594i	−1.47357	+	1.05324i	−0.983366	+	0.181636i	$0.941861\pi$
$420$	1.71635	+	0.514430i	0.0837492	+	0.0251016i
$421$	8.64599	−	13.7178i	0.421380	−	0.668564i	−0.566451	−	0.824095i	$-0.691684\pi$
$421$	8.64599	−	13.7178i	0.421380	−	0.668564i	0.987831	+	0.155531i	$0.0497088\pi$
$422$	1.00102	−	17.1868i	0.0487287	−	0.836639i
$423$	−39.9955	−	4.70037i	−1.94465	−	0.228540i
$424$	12.5599	−	8.26079i	0.609964	−	0.401180i
$425$	−14.6319	+	8.83039i	−0.709750	+	0.428337i
$426$	−0.508330	−	1.24537i	−0.0246287	−	0.0603382i
$427$	−1.55753	+	0.636321i	−0.0753742	+	0.0307938i
$428$	3.62563	+	4.49508i	0.175251	+	0.217278i
$429$	6.81341	+	0.664894i	0.328954	+	0.0321014i
$430$	−3.01442	−	4.39513i	−0.145368	−	0.211952i
$431$	2.84749	+	16.1489i	0.137159	+	0.777865i	0.973332	+	0.229400i	$0.0736765\pi$
$431$	2.84749	+	16.1489i	0.137159	+	0.777865i	−0.836174	+	0.548465i	$0.815212\pi$
$432$	−9.21589	+	0.170020i	−0.443400	+	0.00818011i
$433$	5.53025	−	31.3636i	0.265767	−	1.50724i	−0.501076	−	0.865403i	$-0.667062\pi$
$433$	5.53025	−	31.3636i	0.265767	−	1.50724i	0.766843	−	0.641835i	$-0.221827\pi$
$434$	−15.6822	+	7.12844i	−0.752770	+	0.342176i
$435$	5.01252	+	1.08744i	0.240332	+	0.0521386i
$436$	−12.9370	−	2.54074i	−0.619570	−	0.121680i
$437$	−3.94290	−	1.26424i	−0.188615	−	0.0604768i
$438$	−9.20419	+	3.14606i	−0.439793	+	0.150325i
$439$	25.3952	+	29.0996i	1.21205	+	1.38885i	0.898323	+	0.439335i	$0.144786\pi$
$439$	25.3952	+	29.0996i	1.21205	+	1.38885i	0.313722	+	0.949515i	$0.398424\pi$
$440$	0.526625	−	0.707381i	0.0251059	−	0.0337230i
$441$	8.18717	−	3.71530i	0.389865	−	0.176919i
$442$	−8.68698	+	20.1387i	−0.413198	+	0.957900i
$443$	18.7455	+	17.0106i	0.890626	+	0.808200i	0.982247	−	0.187594i	$-0.0600690\pi$
$443$	18.7455	+	17.0106i	0.890626	+	0.808200i	−0.0916208	+	0.995794i	$0.529205\pi$
$444$	−1.95922	−	3.90421i	−0.0929807	−	0.185285i
$445$	−0.898368	+	3.48768i	−0.0425867	+	0.165332i
$446$	−18.2555	−	17.9049i	−0.864425	−	0.847822i
$447$	23.0791	+	21.7878i	1.09161	+	1.03053i
$448$	−5.45170	+	25.1678i	−0.257568	+	1.18907i
$449$	−1.14479	−	1.53772i	−0.0540259	−	0.0725694i	0.774289	−	0.632832i	$-0.218108\pi$
$449$	−1.14479	−	1.53772i	−0.0540259	−	0.0725694i	−0.828315	+	0.560263i	$0.810700\pi$
$450$	−13.6201	+	8.20806i	−0.642058	+	0.386932i
$451$	−3.80606	−	0.444864i	−0.179220	−	0.0209478i
$452$	2.96278	−	0.581872i	0.139358	−	0.0273690i
$453$	−6.43986	+	10.6632i	−0.302571	+	0.501000i
$454$	2.54001	+	11.7260i	0.119208	+	0.550327i
$455$	4.82781	−	5.53206i	0.226331	−	0.259347i
$456$	1.37393	−	3.35996i	0.0643402	−	0.157344i
$457$	4.44810	+	3.17931i	0.208074	+	0.148722i	0.680755	−	0.732512i	$-0.261652\pi$
$457$	4.44810	+	3.17931i	0.208074	+	0.148722i	−0.472681	+	0.881234i	$0.656714\pi$
$458$	−8.07137	−	6.77268i	−0.377150	−	0.316467i
$459$	0.0173896	−	18.3813i	0.000811677	−	0.857967i
$460$	−1.51919	+	1.27475i	−0.0708325	+	0.0594355i
$461$	−34.0114	+	2.64357i	−1.58407	+	0.123124i	−0.839100	−	0.543977i	$-0.816918\pi$
$461$	−34.0114	+	2.64357i	−1.58407	+	0.123124i	−0.744968	+	0.667100i	$0.767535\pi$
$462$	−0.324366	−	4.19030i	−0.0150909	−	0.194950i
$463$	−4.51419	+	11.6921i	−0.209792	+	0.543376i	−0.997341	−	0.0728766i	$-0.976782\pi$
$463$	−4.51419	+	11.6921i	−0.209792	+	0.543376i	0.787549	+	0.616253i	$0.211350\pi$
$464$	−1.72984	+	12.6646i	−0.0803056	+	0.587941i
$465$	1.08026	−	3.36545i	0.0500958	−	0.156069i
$466$	6.32437	+	3.48964i	0.292971	+	0.161654i
$467$	−2.44029	−	41.8981i	−0.112923	−	1.93881i	−0.294934	−	0.955518i	$-0.595298\pi$
$467$	−2.44029	−	41.8981i	−0.112923	−	1.93881i	0.182011	−	0.983296i	$-0.441739\pi$
$468$	5.35337	−	12.3890i	0.247459	−	0.572682i
$469$	0.740473	−	0.371880i	0.0341919	−	0.0171718i
$470$	2.82091	+	5.35537i	0.130119	+	0.247025i
$471$	31.0801	+	23.1535i	1.43209	+	1.06686i
$472$	−17.5095	−	7.95904i	−0.805940	−	0.366345i
$473$	4.67593	−	6.81767i	0.215000	−	0.313477i
$474$	18.1594	−	21.6276i	0.834087	−	0.993389i
$475$	−0.446627	−	3.26989i	−0.0204927	−	0.150033i
$476$	−8.66457	−	2.05354i	−0.397140	−	0.0941239i
$477$	7.83033	+	12.4411i	0.358526	+	0.569637i
$478$	−20.0432	−	21.2446i	−0.916756	−	0.971705i
$479$	24.7585	+	3.87216i	1.13124	+	0.176923i	0.692313	−	0.721597i	$-0.256592\pi$
$479$	24.7585	+	3.87216i	1.13124	+	0.176923i	0.438932	+	0.898520i	$0.355357\pi$
$480$	−1.73334	−	2.42670i	−0.0791160	−	0.110763i
$481$	−17.8868	+	0.694091i	−0.815570	+	0.0316478i
$482$	−17.5142	−	10.5698i	−0.797748	−	0.481443i
$483$	−5.13943	+	32.7937i	−0.233852	+	1.49216i
$484$	−8.06147	−	2.24406i	−0.366430	−	0.102003i
$485$	−4.09239			−0.185826
$486$	0.0269683	−	17.1038i	0.00122331	−	0.775842i
$487$	15.3758			0.696745			0.348373	−	0.937356i	$-0.386734\pi$
$487$	15.3758			0.696745			0.348373	+	0.937356i	$0.386734\pi$
$488$	1.57276	+	0.437808i	0.0711956	+	0.0198186i
$489$	0.569646	+	0.459760i	0.0257603	+	0.0207911i
$490$	−1.15698	−	0.698242i	−0.0522671	−	0.0315434i
$491$	−41.7269	+	1.61920i	−1.88311	+	0.0730733i	−0.954540	−	0.298083i	$-0.903653\pi$
$491$	−41.7269	+	1.61920i	−1.88311	+	0.0730733i	−0.928570	+	0.371156i	$0.878961\pi$
$492$	−3.12833	+	6.87641i	−0.141036	+	0.310012i
$493$	−25.1840	−	3.93870i	−1.13423	−	0.177390i
$494$	−2.90649	−	3.08070i	−0.130769	−	0.138607i
$495$	0.681266	+	0.528709i	0.0306206	+	0.0237637i
$496$	8.57104	+	2.03137i	0.384851	+	0.0912113i
$497$	−0.302859	−	2.21732i	−0.0135851	−	0.0994605i
$498$	4.22117	+	11.6089i	0.189155	+	0.520209i
$499$	−17.8565	+	26.0354i	−0.799366	+	1.16550i	0.183831	+	0.982958i	$0.441150\pi$
$499$	−17.8565	+	26.0354i	−0.799366	+	1.16550i	−0.983197	+	0.182546i	$0.941566\pi$
$500$	−2.92825	−	1.33106i	−0.130956	−	0.0595266i
$501$	−0.924296	+	7.88629i	−0.0412945	+	0.352334i
$502$	−2.88674	−	5.48034i	−0.128841	−	0.244599i
$503$	−5.59953	+	2.81219i	−0.249671	+	0.125389i	−0.569234	−	0.822176i	$-0.692760\pi$
$503$	−5.59953	+	2.81219i	−0.249671	+	0.125389i	0.319563	+	0.947565i	$0.396464\pi$
$504$	−28.3119	−	6.72891i	−1.26111	−	0.299729i
$505$	0.0724502	+	1.24392i	0.00322399	+	0.0553538i
$506$	4.07286	+	2.24731i	0.181061	+	0.0999050i
$507$	−22.0264	−	24.2882i	−0.978228	−	1.07868i
$508$	−1.28936	+	9.43980i	−0.0572062	+	0.418823i
$509$	−10.7198	+	27.7651i	−0.475148	+	1.23066i	0.463595	+	0.886047i	$0.346559\pi$
$509$	−10.7198	+	27.7651i	−0.475148	+	1.23066i	−0.938743	+	0.344617i	$0.888009\pi$
$510$	−2.27891	+	1.56194i	−0.100912	+	0.0691640i
$511$	−16.1345	+	1.25407i	−0.713747	+	0.0554768i
$512$	14.0311	−	11.7735i	0.620093	−	0.520319i
$513$	3.25799	+	1.40902i	0.143844	+	0.0622096i
$514$	0.530680	+	0.445293i	0.0234073	+	0.0196411i
$515$	2.90292	+	2.07488i	0.127918	+	0.0914303i
$516$	−9.98025	−	12.8852i	−0.439356	−	0.567238i
$517$	−6.17359	+	7.07415i	−0.271514	+	0.311121i
$518$	2.32653	+	10.7405i	0.102222	+	0.471909i
$519$	18.4618	+	0.363891i	0.810385	+	0.0159730i
$520$	−6.99096	+	1.37298i	−0.306574	+	0.0602092i
$521$	11.1647	+	1.30497i	0.489135	+	0.0571717i	0.357086	−	0.934072i	$-0.383770\pi$
$521$	11.1647	+	1.30497i	0.489135	+	0.0571717i	0.132049	+	0.991243i	$0.457844\pi$
$522$	−23.4313	−	3.67973i	−1.02556	−	0.161058i
$523$	−7.90314	−	10.6158i	−0.345580	−	0.464195i	0.595020	−	0.803711i	$-0.297144\pi$
$523$	−7.90314	−	10.6158i	−0.345580	−	0.464195i	−0.940600	+	0.339516i	$0.889737\pi$
$524$	−1.23147	+	5.68508i	−0.0537969	+	0.248354i
$525$	−25.3479	+	7.57995i	−1.10627	+	0.330816i
$526$	−7.33865	−	7.19769i	−0.319980	−	0.313834i
$527$	−4.38161	+	17.0105i	−0.190866	+	0.740988i
$528$	−1.18150	+	1.79515i	−0.0514181	+	0.0781237i
$529$	−10.1746	−	9.23294i	−0.442373	−	0.401432i
$530$	0.875139	−	2.02880i	0.0380136	−	0.0881255i
$531$	8.12404	−	16.9625i	0.352553	−	0.736109i
$532$	1.02686	−	1.37931i	0.0445198	−	0.0598005i
$533$	20.3552	+	23.3244i	0.881680	+	1.01029i
$534$	3.21467	−	16.3413i	0.139112	−	0.707155i
$535$	2.83872	+	0.910200i	0.122729	+	0.0393514i
$536$	−0.788945	−	0.154944i	−0.0340772	−	0.00669255i
$537$	−5.69847	−	17.7916i	−0.245907	−	0.767765i
$538$	−26.3831	+	11.9926i	−1.13745	+	0.517037i
$539$	0.364002	−	2.06436i	0.0156787	−	0.0889181i
$540$	1.40294	−	0.960260i	0.0603728	−	0.0413230i
$541$	−1.60174	−	9.08394i	−0.0688643	−	0.390549i	−0.999686	−	0.0250743i	$-0.992018\pi$
$541$	−1.60174	−	9.08394i	−0.0688643	−	0.390549i	0.930821	−	0.365475i	$-0.119093\pi$
$542$	5.12368	+	7.47050i	0.220081	+	0.320886i
$543$	6.08968	−	8.51425i	0.261333	−	0.365381i
$544$	9.30447	+	11.5357i	0.398926	+	0.494590i
$545$	−6.30017	+	2.57390i	−0.269870	+	0.110254i
$546$	−20.8084	+	26.8301i	−0.890518	+	1.14822i
$547$	−4.25840	+	2.56995i	−0.182076	+	0.109883i	−0.604808	−	0.796371i	$-0.706750\pi$
$547$	−4.25840	+	2.56995i	−0.182076	+	0.109883i	0.422732	+	0.906255i	$0.361071\pi$
$548$	−0.476312	+	0.313275i	−0.0203470	+	0.0133824i
$549$	−0.458819	+	1.52905i	−0.0195819	+	0.0652583i
$550$	−0.215579	+	3.70135i	−0.00919232	+	0.157826i
$551$	2.62465	−	4.16429i	0.111814	−	0.177405i
$552$	23.4347	−	22.0956i	0.997449	−	0.940450i
$553$	38.2242	−	27.3210i	1.62546	−	1.16181i
$554$	13.9190	+	1.08187i	0.591362	+	0.0459643i
$555$	−1.95243	−	1.12806i	−0.0828761	−	0.0478834i
$556$	5.71631	+	2.33537i	0.242425	+	0.0990417i
$557$	10.2423	+	34.2115i	0.433979	+	1.44959i	0.843421	+	0.537253i	$0.180538\pi$
$557$	10.2423	+	34.2115i	0.433979	+	1.44959i	−0.409442	+	0.912336i	$0.634277\pi$
$558$	−4.08706	+	15.8256i	−0.173019	+	0.669952i
$559$	−64.9874	+	15.4023i	−2.74867	+	0.651448i
$560$	0.830204	+	2.15028i	0.0350825	+	0.0908660i
$561$	−3.53349	−	2.42510i	−0.149184	−	0.102388i
$562$	−7.69240	+	14.6037i	−0.324484	+	0.616018i
$563$	−0.316098	+	16.2980i	−0.0133220	+	0.686877i	0.932314	+	0.361650i	$0.117786\pi$
$563$	−0.316098	+	16.2980i	−0.0133220	+	0.686877i	−0.945636	+	0.325227i	$0.894559\pi$
$564$	9.55930	+	15.8510i	0.402519	+	0.667447i
$565$	1.11274	−	1.09137i	0.0468132	−	0.0459141i
$566$	−6.53608	−	11.3208i	−0.274732	−	0.475850i
$567$	7.13288	−	27.5476i	0.299553	−	1.15689i
$568$	−1.08574	+	1.88056i	−0.0455568	+	0.0789066i
$569$	−3.76341	−	14.6104i	−0.157770	−	0.612501i	−0.997574	−	0.0696117i	$-0.977824\pi$
$569$	−3.76341	−	14.6104i	−0.157770	−	0.612501i	0.839804	−	0.542890i	$-0.182670\pi$
$570$	−0.102652	−	0.523558i	−0.00429962	−	0.0219294i
$571$	2.93461	−	1.61925i	0.122809	−	0.0677634i	−0.420518	−	0.907284i	$-0.638152\pi$
$571$	2.93461	−	1.61925i	0.122809	−	0.0677634i	0.543328	+	0.839521i	$0.317164\pi$
$572$	−1.67781	−	2.66202i	−0.0701526	−	0.111305i
$573$	25.7682	−	26.2563i	1.07648	−	1.09687i
$574$	11.9320	−	14.7934i	0.498033	−	0.617464i
$575$	8.39840	−	28.0526i	0.350237	−	1.16987i
$576$	15.3278	+	19.0281i	0.638660	+	0.792837i
$577$	26.5657	−	28.1580i	1.10594	−	1.17223i	0.122227	−	0.992502i	$-0.460996\pi$
$577$	26.5657	−	28.1580i	1.10594	−	1.17223i	0.983716	−	0.179729i	$-0.0575221\pi$
$578$	−3.89052	+	3.01538i	−0.161824	+	0.125423i
$579$	−31.4678	+	5.53838i	−1.30776	+	0.230167i
$580$	−1.01703	−	2.12694i	−0.0422300	−	0.0883165i
$581$	1.98959	+	20.4548i	0.0825423	+	0.848609i
$582$	18.8927	−	1.09440i	0.783128	−	0.0453642i
$583$	3.42478	+	0.132897i	0.141840	+	0.00550403i
$584$	13.1195	+	8.62883i	0.542889	+	0.357064i
$585$	−1.20543	−	6.86165i	−0.0498385	−	0.283694i
$586$	−4.50703	−	2.26352i	−0.186184	−	0.0935050i
$587$	0.338750	+	17.4659i	0.0139817	+	0.720893i	0.939569	+	0.342359i	$0.111226\pi$
$587$	0.338750	+	17.4659i	0.0139817	+	0.720893i	−0.925587	+	0.378534i	$0.876428\pi$
$588$	−3.65574	−	1.92711i	−0.150760	−	0.0794728i
$589$	−2.68111	−	2.07802i	−0.110473	−	0.0856231i
$590$	−2.79292	+	0.436805i	−0.114983	+	0.0179830i
$591$	−2.95362	+	10.5975i	−0.121496	+	0.435923i
$592$	2.42412	−	5.06961i	0.0996306	−	0.208360i
$593$	37.5890	+	13.6813i	1.54360	+	0.561823i	0.966904	−	0.255139i	$-0.0821213\pi$
$593$	37.5890	+	13.6813i	1.54360	+	0.561823i	0.576691	+	0.816962i	$0.304344\pi$
$594$	−3.28648	−	2.25862i	−0.134846	−	0.0926724i
$595$	−4.31936	+	1.57212i	−0.177076	+	0.0644506i
$596$	1.41235	−	14.5202i	0.0578519	−	0.594770i
$597$	−1.64002	+	41.9224i	−0.0671215	+	1.71577i
$598$	−12.1659	−	35.5563i	−0.497502	−	1.45400i
$599$	17.7637	−	16.1197i	0.725807	−	0.658635i	−0.222882	−	0.974845i	$-0.571546\pi$
$599$	17.7637	−	16.1197i	0.725807	−	0.658635i	0.948689	+	0.316211i	$0.102411\pi$
$600$	23.9458	+	9.25392i	0.977582	+	0.377790i
$601$	5.54132	−	16.1951i	0.226035	−	0.660613i	−0.773602	−	0.633672i	$-0.781547\pi$
$601$	5.54132	−	16.1951i	0.226035	−	0.660613i	0.999637	−	0.0269411i	$-0.00857664\pi$
$602$	16.2405	+	37.6496i	0.661912	+	1.53448i
$603$	0.166928	−	0.768285i	0.00679785	−	0.0312870i
$604$	5.68710	−	0.664726i	0.231405	−	0.0270473i
$605$	−4.11329	+	1.31887i	−0.167229	+	0.0536199i
$606$	−0.667121	−	5.72324i	−0.0271000	−	0.232491i
$607$	41.5062	−	11.5540i	1.68468	−	0.468964i	0.712208	−	0.701968i	$-0.247695\pi$
$607$	41.5062	−	11.5540i	1.68468	−	0.468964i	0.972476	+	0.233004i	$0.0748557\pi$
$608$	−2.75715	+	0.767506i	−0.111817	+	0.0311265i
$609$	−36.2290	−	15.6412i	−1.46807	−	0.633814i
$610$	0.228490	−	0.0732623i	0.00925128	−	0.00296630i
$611$	75.3397	−	8.80595i	3.04792	−	0.356251i
$612$	−6.68125	+	5.17162i	−0.270074	+	0.209050i
$613$	−0.352329	−	0.816790i	−0.0142304	−	0.0329899i	0.910953	−	0.412511i	$-0.135348\pi$
$613$	−0.352329	−	0.816790i	−0.0142304	−	0.0329899i	−0.925183	+	0.379521i	$0.876089\pi$
$614$	2.53460	−	7.40765i	0.102288	−	0.298948i
$615$	0.601358	+	3.85303i	0.0242491	+	0.155369i
$616$	−5.02447	+	4.55946i	−0.202442	+	0.183706i
$617$	−1.39562	−	4.07886i	−0.0561856	−	0.164209i	0.914486	−	0.404617i	$-0.132595\pi$
$617$	−1.39562	−	4.07886i	−0.0561856	−	0.164209i	−0.970672	+	0.240408i	$0.922719\pi$
$618$	−13.9563	−	8.80248i	−0.561406	−	0.354088i
$619$	1.27700	−	13.1288i	0.0513272	−	0.527689i	−0.934031	−	0.357192i	$-0.883734\pi$
$619$	1.27700	−	13.1288i	0.0513272	−	0.527689i	0.985358	−	0.170497i	$-0.0545374\pi$
$620$	−1.52668	+	0.555667i	−0.0613130	+	0.0223161i
$621$	21.1431	+	23.3438i	0.848443	+	0.936753i
$622$	−14.9027	−	5.42415i	−0.597545	−	0.217488i
$623$	11.9531	−	24.9977i	0.478890	−	1.00151i
$624$	16.8143	−	4.32542i	0.673109	−	0.173155i
$625$	22.2250	−	3.47592i	0.888999	−	0.139037i
$626$	3.61681	+	2.80324i	0.144557	+	0.112040i
$627$	0.700278	−	0.441059i	0.0279664	−	0.0176142i
$628$	−0.345443	−	17.8110i	−0.0137847	−	0.710734i
$629$	10.0141	+	5.02927i	0.399289	+	0.200530i
$630$	−4.02007	+	1.46032i	−0.160164	+	0.0581804i
$631$	−6.82033	−	4.48580i	−0.271513	−	0.178577i	0.406450	−	0.913673i	$-0.366767\pi$
$631$	−6.82033	−	4.48580i	−0.271513	−	0.178577i	−0.677963	+	0.735096i	$0.737137\pi$
$632$	−45.5555	−	1.76776i	−1.81210	−	0.0703177i
$633$	−14.9268	−	22.7108i	−0.593289	−	0.902671i
$634$	2.23295	+	22.9568i	0.0886819	+	0.911729i
$635$	2.12159	+	4.43693i	0.0841928	+	0.176074i
$636$	2.31300	−	6.34867i	0.0917162	−	0.251741i
$637$	−13.3850	+	10.3742i	−0.530334	+	0.411039i
$638$	−3.79492	+	4.02238i	−0.150242	+	0.159248i
$639$	−1.81729	−	1.09830i	−0.0718909	−	0.0434482i
$640$	0.0656797	−	0.219386i	0.00259622	−	0.00867197i
$641$	−20.6123	+	25.5553i	−0.814138	+	1.00937i	0.185505	+	0.982643i	$0.440608\pi$
$641$	−20.6123	+	25.5553i	−0.814138	+	1.00937i	−0.999643	+	0.0267289i	$0.991491\pi$
$642$	−13.3485	−	3.44284i	−0.526823	−	0.135878i
$643$	2.20536	+	3.49904i	0.0869708	+	0.137989i	0.886654	−	0.462434i	$-0.153024\pi$
$643$	2.20536	+	3.49904i	0.0869708	+	0.137989i	−0.799683	+	0.600423i	$0.794999\pi$
$644$	13.3589	−	7.37112i	0.526413	−	0.290463i
$645$	−7.95925	−	2.72614i	−0.313395	−	0.107342i
$646$	0.661382	+	2.56764i	0.0260217	+	0.101023i
$647$	−7.46302	+	12.9263i	−0.293401	+	0.508186i	−0.974612	−	0.223902i	$-0.928121\pi$
$647$	−7.46302	+	12.9263i	−0.293401	+	0.508186i	0.681210	+	0.732088i	$0.261454\pi$
$648$	−21.8452	+	16.8873i	−0.858161	+	0.663394i
$649$	−2.19251	−	3.79754i	−0.0860636	−	0.149066i
$650$	21.3842	−	20.9735i	0.838758	−	0.822648i
$651$	−13.1450	+	23.8053i	−0.515194	+	0.933004i
$652$	0.00652477	−	0.336416i	0.000255530	−	0.0131751i
$653$	18.4261	−	34.9812i	0.721070	−	1.36892i	−0.200106	−	0.979774i	$-0.564129\pi$
$653$	18.4261	−	34.9812i	0.721070	−	1.36892i	0.921177	−	0.389144i	$-0.127229\pi$
$654$	28.3967	−	13.5673i	1.11040	−	0.530525i
$655$	1.08151	+	2.80118i	0.0422580	+	0.109451i
$656$	−9.45638	+	2.24120i	−0.369209	+	0.0875043i
$657$	−8.69291	+	12.6574i	−0.339143	+	0.493814i
$658$	−13.3559	−	44.6119i	−0.520669	−	1.73915i
$659$	8.03509	+	3.28269i	0.313003	+	0.127876i	0.529257	−	0.848461i	$-0.322471\pi$
$659$	8.03509	+	3.28269i	0.313003	+	0.127876i	−0.216255	+	0.976337i	$0.569384\pi$
$660$	0.000124998	−	0.396380i	4.86554e−6	−	0.0154291i
$661$	−35.9663	−	2.79553i	−1.39893	−	0.108733i	−0.644244	−	0.764820i	$-0.722828\pi$
$661$	−35.9663	−	2.79553i	−1.39893	−	0.108733i	−0.754685	+	0.656087i	$0.772210\pi$
$662$	2.32462	−	1.66154i	0.0903489	−	0.0645775i
$663$	7.97387	+	33.6917i	0.309679	+	1.30848i
$664$	10.6328	−	16.8701i	0.412633	−	0.654687i
$665$	0.0516119	−	0.886142i	0.00200142	−	0.0343631i
$666$	9.31515	+	4.68560i	0.360955	+	0.181563i
$667$	36.4908	−	24.0003i	1.41293	−	0.929297i
$668$	3.12478	−	1.88581i	0.120901	−	0.0729644i
$669$	−39.9925	−	5.47534i	−1.54620	−	0.211689i
$670$	−0.109394	+	0.0446924i	−0.00422626	+	0.00172662i
$671$	0.233675	+	0.289711i	0.00902091	+	0.0111842i
$672$	9.48769	+	20.8899i	0.365996	+	0.805847i
$673$	16.2157	+	23.6431i	0.625071	+	0.911376i	0.999876	−	0.0157277i	$-0.00500650\pi$
$673$	16.2157	+	23.6431i	0.625071	+	0.911376i	−0.374805	+	0.927104i	$0.622290\pi$
$674$	4.21028	+	23.8777i	0.162174	+	0.919733i
$675$	−9.51600	+	23.2296i	−0.366271	+	0.894108i
$676$	−2.61708	+	14.8422i	−0.100657	+	0.570853i
$677$	−15.1831	+	6.90157i	−0.583534	+	0.265249i	−0.683749	−	0.729717i	$-0.739652\pi$
$677$	−15.1831	+	6.90157i	−0.583534	+	0.265249i	0.100215	+	0.994966i	$0.468047\pi$
$678$	−4.84514	+	5.33590i	−0.186077	+	0.204924i
$679$	30.8949	+	6.06756i	1.18564	+	0.232852i
$680$	4.24715	+	1.36179i	0.162871	+	0.0522224i
$681$	14.2661	+	12.4579i	0.546677	+	0.477387i
$682$	2.50570	+	2.87122i	0.0959483	+	0.109945i
$683$	−11.2985	+	15.1765i	−0.432324	+	0.580712i	−0.963889	−	0.266306i	$-0.914197\pi$
$683$	−11.2985	+	15.1765i	−0.432324	+	0.580712i	0.531565	+	0.847018i	$0.321604\pi$
$684$	−0.405986	−	1.58026i	−0.0155233	−	0.0604228i
$685$	−0.116561	+	0.270219i	−0.00445356	+	0.0103245i
$686$	−10.2841	−	9.33236i	−0.392650	−	0.356311i
$687$	−16.6043	−	0.972346i	−0.633495	−	0.0370973i
$688$	5.22988	−	20.3036i	0.199387	−	0.774069i
$689$	−19.7678	−	19.3881i	−0.753092	−	0.738628i
$690$	1.09317	−	4.60597i	0.0416163	−	0.175346i
$691$	−3.20564	+	14.7989i	−0.121948	+	0.562976i	0.874946	+	0.484221i	$0.160897\pi$
$691$	−3.20564	+	14.7989i	−0.121948	+	0.562976i	−0.996894	+	0.0787552i	$0.974905\pi$
$692$	−5.06844	−	6.80810i	−0.192673	−	0.258805i
$693$	−4.35923	−	5.00148i	−0.165593	−	0.189991i
$694$	16.1751	+	1.89060i	0.613999	+	0.0717662i
$695$	3.12777	−	0.614275i	0.118643	−	0.0233008i
$696$	18.4878	+	33.5309i	0.700778	+	1.27099i
$697$	−4.10286	−	18.9409i	−0.155407	−	0.717437i
$698$	5.06136	−	5.79967i	0.191575	−	0.219521i
$699$	11.2982	−	1.53957i	0.427337	−	0.0582317i
$700$	9.89353	+	7.07147i	0.373940	+	0.267276i
$701$	−36.1095	−	30.2994i	−1.36384	−	1.14439i	−0.974777	−	0.223181i	$-0.928356\pi$
$701$	−36.1095	−	30.2994i	−1.36384	−	1.14439i	−0.389059	−	0.921213i	$-0.627200\pi$
$702$	7.39989	+	31.3547i	0.279291	+	1.18341i
$703$	−1.65772	+	1.39100i	−0.0625223	+	0.0524624i
$704$	5.67965	−	0.441457i	0.214060	−	0.0166380i
$705$	8.61898	+	4.12465i	0.324610	+	0.155343i
$706$	−8.99119	+	23.2878i	−0.338388	+	0.876447i
$707$	1.29734	−	9.49821i	0.0487915	−	0.357217i
$708$	−8.44951	+	1.82749i	−0.317552	+	0.0686813i
$709$	23.2482	+	12.8278i	0.873105	+	0.481759i	0.855330	−	0.518083i	$-0.173354\pi$
$709$	23.2482	+	12.8278i	0.873105	+	0.481759i	0.0177744	+	0.999842i	$0.494342\pi$
$710$	0.0185573	+	0.318617i	0.000696444	+	0.0119575i
$711$	2.62017	−	44.5031i	0.0982641	−	1.66900i
$712$	−24.0263	+	12.0665i	−0.900423	+	0.452210i
$713$	−14.0269	−	26.6295i	−0.525313	−	0.997282i
$714$	19.5201	−	8.41284i	0.730521	−	0.314843i
$715$	−1.47871	−	0.672154i	−0.0553005	−	0.0251371i
$716$	−4.85693	+	7.08158i	−0.181512	+	0.264651i
$717$	−45.4035	−	8.02063i	−1.69563	−	0.299536i
$718$	−3.84246	−	28.1318i	−0.143399	−	1.04987i
$719$	−38.3859	−	9.09763i	−1.43155	−	0.339284i	−0.559555	−	0.828793i	$-0.689028\pi$
$719$	−38.3859	−	9.09763i	−1.43155	−	0.339284i	−0.871998	+	0.489509i	$0.837176\pi$
$720$	2.08218	+	0.669073i	0.0775983	+	0.0249349i
$721$	−18.8389	−	19.9680i	−0.701596	−	0.743648i
$722$	20.0907	+	3.14213i	0.747699	+	0.116938i
$723$	−32.1418	+	3.11613i	−1.19537	+	0.115890i
$724$	−4.80793	+	0.186569i	−0.178685	+	0.00693380i
$725$	29.8045	+	17.9871i	1.10691	+	0.668025i
$726$	18.6365	−	7.18863i	0.691665	−	0.266795i
$727$	−8.53090	−	2.37474i	−0.316394	−	0.0880742i	0.106335	−	0.994330i	$-0.466088\pi$
$727$	−8.53090	−	2.37474i	−0.316394	−	0.0880742i	−0.422729	+	0.906256i	$0.638928\pi$
$728$	54.8128			2.03150
$729$	−16.0823	−	21.6878i	−0.595640	−	0.803252i
$730$	2.30794			0.0854207
$731$	40.2793	+	11.2125i	1.48979	+	0.414710i
$732$	0.684620	−	0.264077i	0.0253043	−	0.00976058i
$733$	0.525762	+	0.317299i	0.0194195	+	0.0117197i	0.526376	−	0.850252i	$-0.323550\pi$
$733$	0.525762	+	0.317299i	0.0194195	+	0.0117197i	−0.506956	+	0.861972i	$0.669229\pi$
$734$	−16.1456	+	0.626524i	−0.595946	+	0.0231254i
$735$	−2.12329	+	0.205851i	−0.0783186	+	0.00759294i
$736$	−25.0891	−	3.92386i	−0.924796	−	0.144635i
$737$	−0.125792	−	0.133332i	−0.00463362	−	0.00491135i
$738$	−3.80658	−	17.6269i	−0.140122	−	0.648854i
$739$	10.7200	+	2.54068i	0.394341	+	0.0934605i	0.423002	−	0.906129i	$-0.360976\pi$
$739$	10.7200	+	2.54068i	0.394341	+	0.0934605i	−0.0286612	+	0.999589i	$0.509124\pi$
$740$	0.140265	+	1.02692i	0.00515623	+	0.0377503i
$741$	−6.58401	−	1.16308i	−0.241870	−	0.0427268i
$742$	−9.61472	+	14.0186i	−0.352967	+	0.514639i
$743$	18.3025	+	8.31950i	0.671453	+	0.305213i	0.720370	−	0.693590i	$-0.243972\pi$
$743$	18.3025	+	8.31950i	0.671453	+	0.305213i	−0.0489167	+	0.998803i	$0.515577\pi$
$744$	24.2316	−	10.4434i	0.888374	−	0.382875i
$745$	−3.50964	−	6.66288i	−0.128583	−	0.244109i
$746$	15.2251	−	7.64633i	0.557430	−	0.279952i
$747$	16.2850	+	10.7256i	0.595838	+	0.392428i
$748$	0.114539	+	1.96655i	0.00418795	+	0.0719043i
$749$	−20.0810	−	11.0802i	−0.733744	−	0.404863i
$750$	7.50465	−	1.62313i	0.274031	−	0.0592684i
$751$	−0.789753	+	5.78202i	−0.0288185	+	0.210989i	−0.999577	−	0.0290676i	$-0.990746\pi$
$751$	−0.789753	+	5.78202i	−0.0288185	+	0.210989i	0.970759	+	0.240056i	$0.0771659\pi$
$752$	−8.57659	+	22.2139i	−0.312756	+	0.810059i
$753$	−8.82011	−	4.22090i	−0.321423	−	0.153818i
$754$	44.5410	−	3.46200i	1.62209	−	0.126079i
$755$	2.26418	−	1.89987i	0.0824018	−	0.0691433i
$756$	−12.0150	+	5.16928i	−0.436981	+	0.188005i
$757$	12.6779	+	10.6380i	0.460785	+	0.386645i	0.843420	−	0.537255i	$-0.180539\pi$
$757$	12.6779	+	10.6380i	0.460785	+	0.386645i	−0.382635	+	0.923900i	$0.624983\pi$
$758$	32.6022	+	23.3027i	1.18417	+	0.846391i
$759$	7.27597	−	0.991471i	0.264101	−	0.0359881i
$760$	−0.566321	+	0.648932i	−0.0205426	+	0.0235392i
$761$	−1.57061	−	7.25076i	−0.0569347	−	0.262840i	0.939990	−	0.341201i	$-0.110834\pi$
$761$	−1.57061	−	7.25076i	−0.0569347	−	0.262840i	−0.996925	+	0.0783613i	$0.975031\pi$
$762$	−10.9810	−	19.9159i	−0.397798	−	0.721478i
$763$	51.3783	−	10.0904i	1.86002	−	0.365296i
$764$	−16.7954	−	1.96310i	−0.607637	−	0.0710226i
$765$	−1.41452	+	4.12560i	−0.0511422	+	0.149161i
$766$	20.7699	+	27.8989i	0.750448	+	1.00803i
$767$	−7.49969	+	34.6224i	−0.270798	+	1.25014i
$768$	6.27065	−	26.4208i	0.226273	−	0.953379i
$769$	−32.7538	−	32.1247i	−1.18113	−	1.15845i	−0.984019	−	0.178066i	$-0.943016\pi$
$769$	−32.7538	−	32.1247i	−1.18113	−	1.15845i	−0.197114	−	0.980381i	$-0.563157\pi$
$770$	−0.248745	+	0.965689i	−0.00896416	+	0.0348010i
$771$	1.09171	+	0.0639303i	0.0393170	+	0.00230239i
$772$	10.8759	+	9.86939i	0.391434	+	0.355207i
$773$	1.38789	−	3.21748i	0.0499188	−	0.115725i	−0.891432	−	0.453155i	$-0.850298\pi$
$773$	1.38789	−	3.21748i	0.0499188	−	0.115725i	0.941351	+	0.337430i	$0.109558\pi$
$774$	37.4732	+	10.4569i	1.34695	+	0.375864i
$775$	14.3254	−	19.2424i	0.514584	−	0.691206i
$776$	−20.0876	−	23.0179i	−0.721104	−	0.826294i
$777$	13.0671	+	11.4109i	0.468779	+	0.409362i
$778$	30.8776	+	9.90051i	1.10702	+	0.354951i
$779$	3.67236	+	0.721227i	0.131576	+	0.0258406i
$780$	−2.15268	+	2.37073i	−0.0770784	+	0.0848856i
$781$	−0.450696	+	0.204867i	−0.0161272	+	0.00733070i
$782$	−4.08526	+	23.1687i	−0.146089	+	0.828510i
$783$	−33.1437	+	17.4182i	−1.18446	+	0.622477i
$784$	−0.923152	−	5.23546i	−0.0329697	−	0.186981i
$785$	−5.20119	−	7.58352i	−0.185638	−	0.270667i
$786$	−5.74193	−	12.6425i	−0.204808	−	0.450944i
$787$	−1.29851	−	1.60990i	−0.0462870	−	0.0573869i	0.754692	−	0.656079i	$-0.227786\pi$
$787$	−1.29851	−	1.60990i	−0.0462870	−	0.0573869i	−0.800979	+	0.598692i	$0.795687\pi$
$788$	4.68118	−	1.91247i	0.166760	−	0.0681291i
$789$	−16.0768	−	2.20106i	−0.572349	−	0.0783598i
$790$	−5.73684	+	3.46220i	−0.204108	+	0.123180i
$791$	−10.0185	+	6.58930i	−0.356219	+	0.234289i
$792$	0.370263	+	6.42700i	0.0131567	+	0.228373i
$793$	0.174838	−	3.00185i	0.00620868	−	0.106599i
$794$	0.0520214	−	0.0825375i	0.00184617	−	0.00292915i
$795$	−0.803299	−	3.39415i	−0.0284901	−	0.120378i
$796$	15.6888	−	11.2137i	0.556074	−	0.397457i
$797$	32.9667	+	2.56237i	1.16774	+	0.0907640i	0.646684	−	0.762758i	$-0.276155\pi$
$797$	32.9667	+	2.56237i	1.16774	+	0.0907640i	0.521057	+	0.853522i	$0.325538\pi$
$798$	−0.00129442	+	4.10471i	−4.58219e−5	+	0.145305i
$799$	−43.9587	−	17.9591i	−1.55515	−	0.635348i
$800$	−5.80494	−	19.3898i	−0.205235	−	0.685534i
$801$	−11.3265	−	23.7257i	−0.400201	−	0.838308i
$802$	17.2145	−	4.07990i	0.607864	−	0.144066i
$803$	1.28946	+	3.33977i	0.0455039	+	0.117858i
$804$	−0.326075	+	0.155792i	−0.0114998	+	0.00549435i
$805$	3.67055	−	6.96836i	0.129370	−	0.245602i
$806$	0.596994	−	30.7808i	0.0210282	−	1.08421i
$807$	−22.1146	+	40.0490i	−0.778470	+	1.40979i
$808$	−6.64087	+	6.51332i	−0.233625	+	0.229138i
$809$	−19.5314	−	33.8295i	−0.686689	−	1.18938i	−0.972903	−	0.231215i	$-0.925730\pi$
$809$	−19.5314	−	33.8295i	−0.686689	−	1.18938i	0.286214	−	0.958166i	$-0.407603\pi$
$810$	−1.31863	+	3.83803i	−0.0463319	+	0.134855i
$811$	−12.1210	+	20.9942i	−0.425627	+	0.737207i	−0.996479	−	0.0838456i	$-0.973280\pi$
$811$	−12.1210	+	20.9942i	−0.425627	+	0.737207i	0.570852	+	0.821053i	$0.306613\pi$
$812$	4.52444	+	17.5649i	0.158777	+	0.616408i
$813$	13.5285	+	4.63369i	0.474467	+	0.162511i
$814$	2.12859	−	1.17451i	0.0746070	−	0.0411664i
$815$	−0.0926127	−	0.146940i	−0.00324408	−	0.00514709i
$816$	−10.5245	−	2.71447i	−0.368430	−	0.0950254i
$817$	−5.06902	+	6.28460i	−0.177343	+	0.219870i
$818$	−1.94232	+	6.48779i	−0.0679115	+	0.226840i
$819$	−1.07315	+	53.5882i	−0.0374990	+	1.87252i
$820$	1.23007	−	1.30380i	0.0429561	−	0.0455308i
$821$	−13.2498	+	10.2694i	−0.462422	+	0.358404i	−0.817015	−	0.576617i	$-0.804373\pi$
$821$	−13.2498	+	10.2694i	−0.462422	+	0.358404i	0.354593	+	0.935021i	$0.384620\pi$
$822$	0.465846	−	1.27865i	0.0162482	−	0.0445979i
$823$	−13.4686	−	28.1673i	−0.469487	−	0.981849i	−0.991645	−	0.129000i	$-0.958823\pi$
$823$	−13.4686	−	28.1673i	−0.469487	−	0.981849i	0.522157	−	0.852849i	$-0.325127\pi$
$824$	2.57879	+	26.5123i	0.0898363	+	0.923598i
$825$	3.21465	+	4.89099i	0.111920	+	0.170282i
$826$	21.7324	+	0.843315i	0.756166	+	0.0293427i
$827$	−18.2704	−	12.0166i	−0.635324	−	0.417859i	0.190579	−	0.981672i	$-0.438964\pi$
$827$	−18.2704	−	12.0166i	−0.635324	−	0.417859i	−0.825903	+	0.563813i	$0.809334\pi$
$828$	2.52287	−	14.2553i	0.0876756	−	0.495406i
$829$	29.5641	+	14.8477i	1.02681	+	0.515681i	0.880743	−	0.473594i	$-0.157044\pi$
$829$	29.5641	+	14.8477i	1.02681	+	0.515681i	0.146062	+	0.989275i	$0.453340\pi$
$830$	−0.0568342	−	2.93036i	−0.00197274	−	0.101714i
$831$	18.6482	−	11.7453i	0.646900	−	0.407440i
$832$	−36.3760	−	28.1935i	−1.26111	−	0.977435i
$833$	10.4742	−	1.63814i	0.362910	−	0.0567581i
$834$	−14.2752	+	3.67226i	−0.494310	+	0.127160i
$835$	0.812730	−	1.69968i	0.0281257	−	0.0588199i
$836$	−0.357464	−	0.130106i	−0.0123631	−	0.00449982i
$837$	9.73570	+	23.8947i	0.336515	+	0.825922i
$838$	−38.2267	+	13.9134i	−1.32052	+	0.480630i
$839$	−1.68055	+	17.2775i	−0.0580189	+	0.596487i	0.920558	+	0.390606i	$0.127734\pi$
$839$	−1.68055	+	17.2775i	−0.0580189	+	0.596487i	−0.978577	+	0.205881i	$0.933994\pi$
$840$	5.84014	+	3.68347i	0.201504	+	0.127092i
$841$	7.42073	+	21.6879i	0.255887	+	0.747859i
$842$	13.1753	−	11.9560i	0.454051	−	0.412029i
$843$	4.01802	+	25.7443i	0.138388	+	0.886680i
$844$	−4.04404	+	11.8191i	−0.139202	+	0.406832i
$845$	3.08140	+	7.14349i	0.106003	+	0.245744i
$846$	−40.8929	−	16.7367i	−1.40593	−	0.575420i
$847$	33.0081	−	3.85809i	1.13417	−	0.132566i
$848$	8.27712	−	2.65395i	0.284238	−	0.0911371i
$849$	−18.9454	−	8.17935i	−0.650206	−	0.280715i
$850$	−18.0644	+	5.02858i	−0.619605	+	0.172479i
$851$	−18.4977	+	5.14918i	−0.634092	+	0.176512i
$852$	0.113003	+	0.969452i	0.00387141	+	0.0332129i
$853$	−15.7543	+	5.05143i	−0.539418	+	0.172958i	−0.562532	−	0.826775i	$-0.690173\pi$
$853$	−15.7543	+	5.05143i	−0.539418	+	0.172958i	0.0231140	+	0.999733i	$0.492642\pi$
$854$	−1.83357	+	0.214314i	−0.0627435	+	0.00733366i
$855$	−0.623346	−	0.566374i	−0.0213180	−	0.0193696i
$856$	8.81449	+	20.4343i	0.301273	+	0.698430i
$857$	11.4234	−	33.3862i	0.390216	−	1.14045i	−0.559902	−	0.828559i	$-0.689161\pi$
$857$	11.4234	−	33.3862i	0.390216	−	1.14045i	0.950118	−	0.311891i	$-0.100962\pi$
$858$	7.00626	+	2.70759i	0.239190	+	0.0924356i
$859$	−19.9832	+	18.1338i	−0.681817	+	0.618716i	−0.937475	−	0.348051i	$-0.886843\pi$
$859$	−19.9832	+	18.1338i	−0.681817	+	0.618716i	0.255659	+	0.966767i	$0.417708\pi$
$860$	1.25191	+	3.65885i	0.0426899	+	0.124766i
$861$	1.17281	−	29.9795i	0.0399692	−	1.02170i
$862$	−1.74183	+	17.9075i	−0.0593268	+	0.609933i
$863$	17.4072	−	6.33570i	0.592548	−	0.215670i	−0.0283017	−	0.999599i	$-0.509010\pi$
$863$	17.4072	−	6.33570i	0.592548	−	0.215670i	0.620850	+	0.783930i	$0.286788\pi$
$864$	21.0762	+	5.45015i	0.717028	+	0.185418i
$865$	−4.11709	−	1.49850i	−0.139985	−	0.0509504i
$866$	15.0740	−	31.5247i	0.512237	−	1.07125i
$867$	−2.08614	+	7.48500i	−0.0708489	+	0.254204i
$868$	12.3493	−	1.93140i	0.419163	−	0.0655559i
$869$	−8.21528	−	6.36732i	−0.278684	−	0.215997i
$870$	4.97836	+	2.62433i	0.168782	+	0.0889732i
$871$	0.0287162	+	1.48060i	0.000973012	+	0.0501683i
$872$	−45.4016	−	22.8015i	−1.53749	−	0.772158i
$873$	22.8969	−	19.1882i	0.774943	−	0.649422i
$874$	−3.79573	−	2.49649i	−0.128392	−	0.0844450i
$875$	12.7648	+	0.495332i	0.431529	+	0.0167453i
$876$	7.04611	−	0.408160i	0.238066	−	0.0137904i
$877$	−0.176311	−	1.81264i	−0.00595361	−	0.0612084i	0.991855	−	0.127369i	$-0.0406533\pi$
$877$	−0.176311	−	1.81264i	−0.00595361	−	0.0612084i	−0.997809	+	0.0661609i	$0.978925\pi$
$878$	18.2808	+	38.2311i	0.616949	+	1.29024i
$879$	−7.84113	+	1.38005i	−0.264475	+	0.0465480i
$880$	0.403030	−	0.312372i	0.0135861	−	0.0105301i
$881$	−19.3989	+	20.5616i	−0.653565	+	0.692738i	−0.966392	−	0.257072i	$-0.917242\pi$
$881$	−19.3989	+	20.5616i	−0.653565	+	0.692738i	0.312827	+	0.949810i	$0.398724\pi$
$882$	9.74718	−	1.51813i	0.328205	−	0.0511182i
$883$	−1.45673	+	4.86583i	−0.0490230	+	0.163748i	−0.978996	−	0.203880i	$-0.934645\pi$
$883$	−1.45673	+	4.86583i	−0.0490230	+	0.163748i	0.929973	+	0.367628i	$0.119830\pi$
$884$	9.99110	−	12.3870i	0.336037	−	0.416621i
$885$	−3.12572	+	3.18493i	−0.105070	+	0.107060i
$886$	14.8091	+	23.4963i	0.497522	+	0.789372i
$887$	3.62105	−	1.99801i	0.121583	−	0.0670867i	−0.421155	−	0.906989i	$-0.638375\pi$
$887$	3.62105	−	1.99801i	0.121583	−	0.0670867i	0.542738	+	0.839902i	$0.317388\pi$
$888$	−3.23875	−	16.5187i	−0.108685	−	0.554330i
$889$	−9.43825	−	36.6415i	−0.316549	−	1.22892i
$890$	−1.97581	+	3.42220i	−0.0662293	+	0.114713i
$891$	−6.29066	+	0.236160i	−0.210745	+	0.00791165i
$892$	9.27698	+	16.0682i	0.310616	+	0.538003i
$893$	6.54673	−	6.42098i	0.219078	−	0.214870i
$894$	17.9842	+	29.8209i	0.601481	+	0.997361i
$895$	−0.0859556	+	4.43185i	−0.00287318	+	0.148140i
$896$	−0.821109	+	1.55884i	−0.0274313	+	0.0520771i
$897$	−48.9122	−	33.5693i	−1.63313	−	1.12085i
$898$	−0.757602	−	1.96224i	−0.0252815	−	0.0654808i
$899$	34.8162	−	8.25158i	1.16118	−	0.275206i
$900$	11.1179	−	3.08733i	0.370598	−	0.102911i
$901$	4.97140	+	16.6056i	0.165621	+	0.553214i
$902$	−3.89218	−	1.59013i	−0.129595	−	0.0529455i
$903$	56.0453	+	32.3813i	1.86507	+	1.07758i
$904$	11.6003	+	0.901650i	0.385822	+	0.0299884i
$905$	−2.02064	+	1.44427i	−0.0671684	+	0.0480091i
$906$	−9.94460	+	9.37632i	−0.330387	+	0.311507i
$907$	9.41231	−	14.9336i	0.312531	−	0.495864i	−0.652575	−	0.757724i	$-0.726311\pi$
$907$	9.41231	−	14.9336i	0.312531	−	0.495864i	0.965106	+	0.261860i	$0.0843360\pi$
$908$	0.506191	−	8.69096i	0.0167985	−	0.288420i
$909$	−6.23779	−	6.62003i	−0.206894	−	0.219572i
$910$	6.73085	−	4.42695i	0.223125	−	0.146752i
$911$	6.00982	−	3.62694i	0.199114	−	0.120166i	−0.413637	−	0.910442i	$-0.635742\pi$
$911$	6.00982	−	3.62694i	0.199114	−	0.120166i	0.612751	+	0.790276i	$0.290063\pi$
$912$	1.28631	−	1.65855i	0.0425939	−	0.0549199i
$913$	4.20871	−	1.71945i	0.139288	−	0.0569053i
$914$	3.76624	+	4.66941i	0.124576	+	0.154450i
$915$	0.220355	−	0.308089i	0.00728473	−	0.0101851i
$916$	4.32419	+	6.30483i	0.142875	+	0.208317i
$917$	−4.01154	−	22.7506i	−0.132473	−	0.751289i
$918$	5.42692	−	19.4243i	0.179115	−	0.641097i
$919$	0.498376	−	2.82643i	0.0164399	−	0.0932354i	−0.975484	−	0.220071i	$-0.929371\pi$
$919$	0.498376	−	2.82643i	0.0164399	−	0.0932354i	0.991924	+	0.126836i	$0.0404821\pi$
$920$	−6.95717	+	3.16242i	−0.229371	+	0.104262i
$921$	−3.76990	−	11.7703i	−0.124222	−	0.387844i
$922$	−36.7285	−	7.21324i	−1.20959	−	0.237556i
$923$	3.80857	+	1.22117i	0.125361	+	0.0401953i
$924$	−0.588634	+	2.99223i	−0.0193646	+	0.0984370i
$925$	−10.0627	−	11.5306i	−0.330860	−	0.379123i
$926$	−8.21187	+	11.0305i	−0.269859	+	0.362483i
$927$	−25.9704	+	2.00210i	−0.852981	+	0.0657577i
$928$	11.9571	−	27.7197i	0.392512	−	0.909944i
$929$	−1.30814	−	1.18708i	−0.0429188	−	0.0389468i	0.650266	−	0.759706i	$-0.274657\pi$
$929$	−1.30814	−	1.18708i	−0.0429188	−	0.0389468i	−0.693185	+	0.720760i	$0.743793\pi$
$930$	2.13211	−	3.23949i	0.0699146	−	0.106227i
$931$	−0.510672	+	1.98255i	−0.0167366	+	0.0649755i
$932$	−3.74184	−	3.66997i	−0.122568	−	0.120214i
$933$	−23.9857	+	7.17262i	−0.785258	+	0.234821i
$934$	9.74872	−	45.0051i	0.318988	−	1.47261i
$935$	0.607225	+	0.815645i	0.0198584	+	0.0266744i
$936$	32.6768	−	40.4606i	1.06807	−	1.32250i
$937$	−38.8781	−	4.54419i	−1.27009	−	0.148452i	−0.545781	−	0.837928i	$-0.683767\pi$
$937$	−38.8781	−	4.54419i	−1.27009	−	0.148452i	−0.724309	+	0.689475i	$0.757841\pi$
$938$	0.892116	−	0.175206i	0.0291286	−	0.00572068i
$939$	7.22220	+	0.142353i	0.235688	+	0.00464551i
$940$	−0.929799	−	4.29243i	−0.0303267	−	0.140004i
$941$	−15.9035	+	18.2234i	−0.518441	+	0.594067i	−0.951634	−	0.307234i	$-0.900597\pi$
$941$	−15.9035	+	18.2234i	−0.518441	+	0.594067i	0.433193	+	0.901301i	$0.357387\pi$
$942$	26.0395	+	33.6187i	0.848413	+	1.09536i
$943$	27.0155	+	19.3095i	0.879747	+	0.628805i
$944$	−8.51914	−	7.14840i	−0.277274	−	0.232661i
$945$	−3.71552	+	5.63754i	−0.120866	+	0.183389i
$946$	6.94858	−	5.83055i	0.225918	−	0.189568i
$947$	−40.9367	+	3.18185i	−1.33026	+	0.103396i	−0.722858	−	0.690996i	$-0.757172\pi$
$947$	−40.9367	+	3.18185i	−1.33026	+	0.103396i	−0.607405	+	0.794393i	$0.707789\pi$
$948$	−16.9022	+	11.5846i	−0.548959	+	0.376251i
$949$	10.4172	−	26.9811i	0.338155	−	0.875844i
$950$	0.490043	−	3.58775i	0.0158991	−	0.116402i
$951$	24.4597	+	26.9713i	0.793159	+	0.874605i
$952$	−30.0442	−	16.5777i	−0.973737	−	0.537285i
$953$	2.62090	+	44.9991i	0.0848993	+	1.45767i	0.724668	+	0.689098i	$0.241993\pi$
$953$	2.62090	+	44.9991i	0.0848993	+	1.45767i	−0.639769	+	0.768567i	$0.720970\pi$
$954$	4.61613	+	15.4544i	0.149453	+	0.500356i
$955$	−7.80038	+	3.91750i	−0.252414	+	0.126767i
$956$	9.87676	+	18.7506i	0.319437	+	0.606437i
$957$	−1.01619	+	8.67031i	−0.0328486	+	0.280271i
$958$	25.0308	+	11.3779i	0.808710	+	0.367604i
$959$	1.28060	−	1.86715i	0.0413526	−	0.0602936i
$960$	−1.98112	−	5.44844i	−0.0639405	−	0.175847i
$961$	0.858394	+	6.28456i	0.0276901	+	0.202728i
$962$	−19.1109	−	4.52938i	−0.616162	−	0.146033i
$963$	−20.1503	+	8.21749i	−0.649335	+	0.264805i
$964$	10.1860	+	10.7966i	0.328070	+	0.347734i
$965$	7.49010	+	1.17143i	0.241115	+	0.0377097i
$966$	−15.0817	+	33.1513i	−0.485247	+	1.06663i
$967$	−56.9864	+	2.21133i	−1.83256	+	0.0711116i	−0.931749	−	0.363104i	$-0.881717\pi$
$967$	−56.9864	+	2.21133i	−1.83256	+	0.0711116i	−0.900809	+	0.434215i	$0.857026\pi$
$968$	−27.6083	−	16.6617i	−0.887365	−	0.535527i
$969$	3.25708	+	2.62879i	0.104633	+	0.0844488i
$970$	−4.32574	−	1.20415i	−0.138891	−	0.0386630i
$971$	7.87948			0.252865			0.126432	−	0.991975i	$-0.459647\pi$
$971$	7.87948			0.252865			0.126432	+	0.991975i	$0.459647\pi$
$972$	−3.34700	+	11.9507i	−0.107355	+	0.383318i
$973$	−24.5234			−0.786184
$974$	16.2525	+	4.52420i	0.520765	+	0.144965i
$975$	7.32092	−	46.7133i	0.234457	−	1.49602i
$976$	0.808184	+	0.487742i	0.0258693	+	0.0156122i
$977$	8.15246	−	0.316353i	0.260820	−	0.0101210i	0.0919665	−	0.995762i	$-0.470685\pi$
$977$	8.15246	−	0.316353i	0.260820	−	0.0101210i	0.168854	+	0.985641i	$0.445993\pi$
$978$	0.466846	+	0.653588i	0.0149281	+	0.0208995i
$979$	−6.05609	−	0.947156i	−0.193554	−	0.0302712i
$980$	0.672888	+	0.713219i	0.0214946	+	0.0227830i
$981$	23.1810	−	43.9408i	0.740113	−	1.40292i
$982$	−44.5826	−	10.5663i	−1.42269	−	0.337183i
$983$	−7.62564	−	55.8296i	−0.243220	−	1.78069i	−0.556322	−	0.830967i	$-0.687788\pi$
$983$	−7.62564	−	55.8296i	−0.243220	−	1.78069i	0.313102	−	0.949720i	$-0.398632\pi$
$984$	−18.7198	+	22.2951i	−0.596765	+	0.710741i
$985$	1.47641	−	2.15266i	0.0470425	−	0.0685896i
$986$	−25.4610	−	11.5735i	−0.810844	−	0.368574i
$987$	−58.9523	−	43.9173i	−1.87647	−	1.39790i
$988$	1.43224	+	2.71904i	0.0455656	+	0.0865041i
$989$	−64.0204	+	32.1523i	−2.03573	+	1.02238i
$990$	0.564543	+	0.759312i	0.0179423	+	0.0241325i
$991$	0.706550	+	12.1310i	0.0224443	+	0.385354i	0.990760	+	0.135625i	$0.0433044\pi$
$991$	0.706550	+	12.1310i	0.0224443	+	0.385354i	−0.968316	+	0.249729i	$0.919659\pi$
$992$	−18.2147	−	10.0505i	−0.578318	−	0.319102i
$993$	1.37857	−	4.29481i	0.0437476	−	0.136292i
$994$	0.332300	−	2.43287i	0.0105399	−	0.0771658i
$995$	3.58542	−	9.28646i	0.113665	−	0.294401i
$996$	−0.691748	−	8.93629i	−0.0219189	−	0.283157i
$997$	16.0391	−	1.24666i	0.507965	−	0.0394821i	0.179047	−	0.983841i	$-0.442699\pi$
$997$	16.0391	−	1.24666i	0.507965	−	0.0394821i	0.328918	+	0.944358i	$0.393316\pi$
$998$	−26.5353	+	22.2658i	−0.839961	+	0.704811i
$999$	16.2130	−	2.84298i	0.512957	−	0.0899479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.i.a.103.18	✓	1404
3.2	odd	2		729.2.i.a.685.9		1404
243.92	odd	162		729.2.i.a.613.9		1404
243.151	even	81	inner	243.2.i.a.151.18	yes	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.103.18	✓	1404	1.1	even	1	trivial
243.2.i.a.151.18	yes	1404	243.151	even	81	inner
729.2.i.a.613.9		1404	243.92	odd	162
729.2.i.a.685.9		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+(1.05702 + 0.294241i) q^{2} +(1.61600 - 0.623337i) q^{3} +(-0.681624 - 0.411362i) q^{4} +(-0.410657 + 0.0159353i) q^{5} +(1.89155 - 0.183385i) q^{6} +(3.12382 + 0.488556i) q^{7} +(-2.10535 - 2.23154i) q^{8} +(2.22290 - 2.01462i) q^{9} +(-0.438760 - 0.103988i) q^{10} +(-0.0946581 - 0.693020i) q^{11} +(-1.35792 - 0.239880i) q^{12} +(-3.19607 + 4.65999i) q^{13} +(3.15818 + 1.43557i) q^{14} +(-0.653687 + 0.281729i) q^{15} +(-0.826715 - 1.56948i) q^{16} +(3.16122 - 1.58762i) q^{17} +(2.94243 - 1.47542i) q^{18} +(0.0397202 + 0.681970i) q^{19} +(0.286469 + 0.158067i) q^{20} +(5.35262 - 1.15768i) q^{21} +(0.103860 - 0.760387i) q^{22} +(-2.18314 + 5.65449i) q^{23} +(-4.79324 - 2.29382i) q^{24} +(-4.81658 + 0.374374i) q^{25} +(-4.74947 + 3.98528i) q^{26} +(2.33642 - 4.64124i) q^{27} +(-1.92829 - 1.61803i) q^{28} +(-5.86222 - 4.19007i) q^{29} +(-0.773856 + 0.105451i) q^{30} +(-3.26498 + 3.74125i) q^{31} +(0.886943 + 4.09458i) q^{32} +(-0.584952 - 1.06092i) q^{33} +(3.80861 - 0.747986i) q^{34} +(-1.29060 - 0.150850i) q^{35} +(-2.34392 + 0.458796i) q^{36} +(1.89168 + 2.54097i) q^{37} +(-0.158679 + 0.732542i) q^{38} +(-2.26011 + 9.52277i) q^{39} +(0.900136 + 0.882847i) q^{40} +(1.36657 - 5.30533i) q^{41} +(5.99845 + 0.351268i) q^{42} +(8.75275 + 7.94270i) q^{43} +(-0.220561 + 0.511318i) q^{44} +(-0.880746 + 0.862741i) q^{45} +(-3.97141 + 5.33453i) q^{46} +(-8.82629 - 10.1138i) q^{47} +(-2.31429 - 2.02096i) q^{48} +(2.85380 + 0.915034i) q^{49} +(-5.20137 - 1.02152i) q^{50} +(4.11890 - 4.53610i) q^{51} +(4.09546 - 1.86162i) q^{52} +(-0.850884 + 4.82560i) q^{53} +(3.83528 - 4.21841i) q^{54} +(0.0499155 + 0.283085i) q^{55} +(-5.48649 - 7.99950i) q^{56} +(0.489284 + 1.07730i) q^{57} +(-4.96359 - 6.15388i) q^{58} +(5.80355 - 2.37101i) q^{59} +(0.561461 + 0.0768692i) q^{60} +(-0.455597 + 0.274954i) q^{61} +(-4.55198 + 2.99388i) q^{62} +(7.92819 - 5.20730i) q^{63} +(-0.473567 + 8.13082i) q^{64} +(1.23823 - 1.96459i) q^{65} +(-0.306140 - 1.29352i) q^{66} +(0.213208 - 0.152392i) q^{67} +(-2.80785 - 0.218243i) q^{68} +(-0.00331068 + 10.4985i) q^{69} +(-1.31980 - 0.539199i) q^{70} +(-0.202999 - 0.678064i) q^{71} +(-9.17570 - 0.719014i) q^{72} +(-4.98039 + 1.18037i) q^{73} +(1.25188 + 3.24246i) q^{74} +(-7.55023 + 3.60734i) q^{75} +(0.253462 - 0.481186i) q^{76} +(0.0428845 - 2.21111i) q^{77} +(-5.19097 + 9.40073i) q^{78} +(10.6090 - 10.4053i) q^{79} +(0.364506 + 0.631343i) q^{80} +(0.882596 - 8.95662i) q^{81} +(3.00553 - 5.20573i) q^{82} +(1.62135 + 6.29445i) q^{83} +(-4.12470 - 1.41276i) q^{84} +(-1.27287 + 0.702343i) q^{85} +(6.91475 + 10.9710i) q^{86} +(-12.0852 - 3.11700i) q^{87} +(-1.34721 + 1.67028i) q^{88} +(2.51342 - 8.39540i) q^{89} +(-1.18482 + 0.652781i) q^{90} +(-12.2606 + 12.9955i) q^{91} +(3.81412 - 2.95617i) q^{92} +(-2.94415 + 8.08104i) q^{93} +(-6.35365 - 13.2875i) q^{94} +(-0.0271788 - 0.279422i) q^{95} +(3.98560 + 6.06398i) q^{96} +(9.95051 + 0.386125i) q^{97} +(2.74728 + 1.80691i) q^{98} +(-1.60659 - 1.34982i) 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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