LMFDB - Embedded newform 117.2.f.a.94.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(61,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.61"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.f (of order $3$, degree $2$, 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.9
Character	$\chi$	$=$	117.94
Dual form			117.2.f.a.61.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.602131 - 1.04292i) q^{2} +(-1.54217 + 0.788485i) q^{3} +(0.274876 + 0.476100i) q^{4} +(1.89177 - 3.27665i) q^{5} +(-0.106261 + 2.08313i) q^{6} +0.300456 q^{7} +3.07057 q^{8} +(1.75658 - 2.43196i) q^{9} +(-2.27819 - 3.94594i) q^{10} +(-0.642309 + 1.11251i) q^{11} +(-0.799304 - 0.517492i) q^{12} +(-3.31272 + 1.42335i) q^{13} +(0.180914 - 0.313352i) q^{14} +(-0.333851 + 6.54478i) q^{15} +(1.29913 - 2.25016i) q^{16} +(-2.63848 + 4.56998i) q^{17} +(-1.47865 - 3.29634i) q^{18} +(-0.829906 + 1.43744i) q^{19} +2.08001 q^{20} +(-0.463355 + 0.236905i) q^{21} +(0.773509 + 1.33976i) q^{22} -3.34798 q^{23} +(-4.73535 + 2.42110i) q^{24} +(-4.65760 - 8.06721i) q^{25} +(-0.510251 + 4.31194i) q^{26} +(-0.791390 + 5.13553i) q^{27} +(0.0825883 + 0.143047i) q^{28} +(4.81620 - 8.34190i) q^{29} +(6.62467 + 4.28900i) q^{30} +(-3.29700 + 5.71056i) q^{31} +(1.50607 + 2.60860i) q^{32} +(0.113352 - 2.22214i) q^{33} +(3.17742 + 5.50346i) q^{34} +(0.568394 - 0.984488i) q^{35} +(1.64070 + 0.167821i) q^{36} +(1.97702 + 3.42430i) q^{37} +(0.999424 + 1.73105i) q^{38} +(3.98649 - 4.80707i) q^{39} +(5.80882 - 10.0612i) q^{40} +2.86737 q^{41} +(-0.0319268 + 0.625890i) q^{42} -0.0208439 q^{43} -0.706223 q^{44} +(-4.64561 - 10.3564i) q^{45} +(-2.01592 + 3.49168i) q^{46} +(0.954216 + 1.65275i) q^{47} +(-0.229265 + 4.49449i) q^{48} -6.90973 q^{49} -11.2180 q^{50} +(0.465627 - 9.12810i) q^{51} +(-1.58824 - 1.18594i) q^{52} -7.15248 q^{53} +(4.87944 + 3.91762i) q^{54} +(2.43021 + 4.20924i) q^{55} +0.922571 q^{56} +(0.146458 - 2.87114i) q^{57} +(-5.79997 - 10.0458i) q^{58} +(-4.36913 - 7.56755i) q^{59} +(-3.20774 + 1.64006i) q^{60} +5.13678 q^{61} +(3.97045 + 6.87702i) q^{62} +(0.527776 - 0.730696i) q^{63} +8.82395 q^{64} +(-1.60310 + 13.5472i) q^{65} +(-2.24926 - 1.45623i) q^{66} +8.31140 q^{67} -2.90103 q^{68} +(5.16316 - 2.63983i) q^{69} +(-0.684496 - 1.18558i) q^{70} +(4.64070 - 8.03792i) q^{71} +(5.39371 - 7.46750i) q^{72} -4.69504 q^{73} +4.76171 q^{74} +(13.5437 + 8.76856i) q^{75} -0.912486 q^{76} +(-0.192986 + 0.334261i) q^{77} +(-2.61301 - 7.05208i) q^{78} +(6.65302 + 11.5234i) q^{79} +(-4.91533 - 8.51360i) q^{80} +(-2.82883 - 8.54387i) q^{81} +(1.72653 - 2.99044i) q^{82} +(-6.45522 - 11.1808i) q^{83} +(-0.240156 - 0.155483i) q^{84} +(9.98281 + 17.2907i) q^{85} +(-0.0125508 + 0.0217386i) q^{86} +(-0.849940 + 16.6621i) q^{87} +(-1.97226 + 3.41605i) q^{88} +(3.19907 + 5.54096i) q^{89} +(-13.5982 - 1.39091i) q^{90} +(-0.995325 + 0.427653i) q^{91} +(-0.920281 - 1.59397i) q^{92} +(0.581838 - 11.4063i) q^{93} +2.29825 q^{94} +(3.13998 + 5.43861i) q^{95} +(-4.37946 - 2.83539i) q^{96} -3.76391 q^{97} +(-4.16056 + 7.20630i) q^{98} +(1.57731 + 3.51629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.602131	−	1.04292i	0.425771	−	0.737457i	−0.570721	−	0.821144i	$-0.693336\pi$
$2$	0.602131	−	1.04292i	0.425771	−	0.737457i	0.996492	+	0.0836870i	$0.0266696\pi$
$3$	−1.54217	+	0.788485i	−0.890373	+	0.455232i
$3$	−1.54217	+	0.788485i	−0.890373	+	0.455232i
$4$	0.274876	+	0.476100i	0.137438	+	0.238050i
$5$	1.89177	−	3.27665i	0.846026	−	1.46536i	−0.0387007	−	0.999251i	$-0.512322\pi$
$5$	1.89177	−	3.27665i	0.846026	−	1.46536i	0.884727	−	0.466110i	$-0.154345\pi$
$6$	−0.106261	+	2.08313i	−0.0433810	+	0.850436i
$7$	0.300456			0.113562			0.0567809	−	0.998387i	$-0.481916\pi$
$7$	0.300456			0.113562			0.0567809	+	0.998387i	$0.481916\pi$
$8$	3.07057			1.08561
$9$	1.75658	−	2.43196i	0.585528	−	0.810652i
$10$	−2.27819	−	3.94594i	−0.720427	−	1.24782i
$11$	−0.642309	+	1.11251i	−0.193664	+	0.335435i	−0.946462	−	0.322816i	$-0.895370\pi$
$11$	−0.642309	+	1.11251i	−0.193664	+	0.335435i	0.752798	+	0.658252i	$0.228704\pi$
$12$	−0.799304	−	0.517492i	−0.230739	−	0.149387i
$13$	−3.31272	+	1.42335i	−0.918782	+	0.394765i
$13$	−3.31272	+	1.42335i	−0.918782	+	0.394765i
$14$	0.180914	−	0.313352i	0.0483513	−	0.0837469i
$15$	−0.333851	+	6.54478i	−0.0861999	+	1.68986i
$16$	1.29913	−	2.25016i	0.324783	−	0.562541i
$17$	−2.63848	+	4.56998i	−0.639926	+	1.10838i	0.345523	+	0.938410i	$0.387702\pi$
$17$	−2.63848	+	4.56998i	−0.639926	+	1.10838i	−0.985449	+	0.169974i	$0.945632\pi$
$18$	−1.47865	−	3.29634i	−0.348520	−	0.776954i
$19$	−0.829906	+	1.43744i	−0.190393	+	0.329771i	−0.945381	−	0.325968i	$-0.894310\pi$
$19$	−0.829906	+	1.43744i	−0.190393	+	0.329771i	0.754987	+	0.655739i	$0.227643\pi$
$20$	2.08001			0.465105
$21$	−0.463355	+	0.236905i	−0.101112	+	0.0516969i
$22$	0.773509	+	1.33976i	0.164913	+	0.285637i
$23$	−3.34798			−0.698102			−0.349051	−	0.937104i	$-0.613496\pi$
$23$	−3.34798			−0.698102			−0.349051	+	0.937104i	$0.613496\pi$
$24$	−4.73535	+	2.42110i	−0.966598	+	0.494205i
$25$	−4.65760	−	8.06721i	−0.931521	−	1.61344i
$26$	−0.510251	+	4.31194i	−0.100068	+	0.845642i
$27$	−0.791390	+	5.13553i	−0.152303	+	0.988334i
$28$	0.0825883	+	0.143047i	0.0156077	+	0.0270334i
$29$	4.81620	−	8.34190i	0.894346	−	1.54905i	0.0597340	−	0.998214i	$-0.480975\pi$
$29$	4.81620	−	8.34190i	0.894346	−	1.54905i	0.834612	−	0.550838i	$-0.185692\pi$
$30$	6.62467	+	4.28900i	1.20949	+	0.783060i
$31$	−3.29700	+	5.71056i	−0.592158	+	1.02565i	0.401783	+	0.915735i	$0.368391\pi$
$31$	−3.29700	+	5.71056i	−0.592158	+	1.02565i	−0.993941	+	0.109913i	$0.964943\pi$
$32$	1.50607	+	2.60860i	0.266239	+	0.461139i
$33$	0.113352	−	2.22214i	0.0197320	−	0.386824i
$34$	3.17742	+	5.50346i	0.544924	+	0.943836i
$35$	0.568394	−	0.984488i	0.0960762	−	0.166409i
$36$	1.64070	+	0.167821i	0.273450	+	0.0279702i
$37$	1.97702	+	3.42430i	0.325020	+	0.562952i	0.981517	−	0.191378i	$-0.0612955\pi$
$37$	1.97702	+	3.42430i	0.325020	+	0.562952i	−0.656496	+	0.754329i	$0.727962\pi$
$38$	0.999424	+	1.73105i	0.162128	+	0.280814i
$39$	3.98649	−	4.80707i	0.638349	−	0.769747i
$40$	5.80882	−	10.0612i	0.918455	−	1.59081i
$41$	2.86737			0.447807			0.223904	−	0.974611i	$-0.428120\pi$
$41$	2.86737			0.447807			0.223904	+	0.974611i	$0.428120\pi$
$42$	−0.0319268	+	0.625890i	−0.00492642	+	0.0965770i
$43$	−0.0208439			−0.00317867			−0.00158933	−	0.999999i	$-0.500506\pi$
$43$	−0.0208439			−0.00317867			−0.00158933	+	0.999999i	$0.500506\pi$
$44$	−0.706223			−0.106467
$45$	−4.64561	−	10.3564i	−0.692526	−	1.54384i
$46$	−2.01592	+	3.49168i	−0.297232	+	0.514821i
$47$	0.954216	+	1.65275i	0.139187	+	0.241079i	0.927189	−	0.374594i	$-0.122218\pi$
$47$	0.954216	+	1.65275i	0.139187	+	0.241079i	−0.788002	+	0.615672i	$0.788884\pi$
$48$	−0.229265	+	4.49449i	−0.0330915	+	0.648723i
$49$	−6.90973			−0.987104
$50$	−11.2180			−1.58646
$51$	0.465627	−	9.12810i	0.0652008	−	1.27819i
$52$	−1.58824	−	1.18594i	−0.220250	−	0.164460i
$53$	−7.15248			−0.982469			−0.491235	−	0.871027i	$-0.663454\pi$
$53$	−7.15248			−0.982469			−0.491235	+	0.871027i	$0.663454\pi$
$54$	4.87944	+	3.91762i	0.664007	+	0.533121i
$55$	2.43021	+	4.20924i	0.327689	+	0.567574i
$56$	0.922571			0.123284
$57$	0.146458	−	2.87114i	0.0193988	−	0.380292i
$58$	−5.79997	−	10.0458i	−0.761573	−	1.31908i
$59$	−4.36913	−	7.56755i	−0.568812	−	0.985211i	−0.996684	−	0.0813719i	$-0.974070\pi$
$59$	−4.36913	−	7.56755i	−0.568812	−	0.985211i	0.427872	−	0.903839i	$-0.359263\pi$
$60$	−3.20774	+	1.64006i	−0.414117	+	0.211731i
$61$	5.13678			0.657697			0.328849	−	0.944383i	$-0.393339\pi$
$61$	5.13678			0.657697			0.328849	+	0.944383i	$0.393339\pi$
$62$	3.97045	+	6.87702i	0.504247	+	0.873382i
$63$	0.527776	−	0.730696i	0.0664935	−	0.0920591i
$64$	8.82395			1.10299
$65$	−1.60310	+	13.5472i	−0.198841	+	1.68033i
$66$	−2.24926	−	1.45623i	−0.276865	−	0.179250i
$67$	8.31140			1.01540			0.507700	−	0.861534i	$-0.330496\pi$
$67$	8.31140			1.01540			0.507700	+	0.861534i	$0.330496\pi$
$68$	−2.90103			−0.351801
$69$	5.16316	−	2.63983i	0.621572	−	0.317799i
$70$	−0.684496	−	1.18558i	−0.0818129	−	0.141704i
$71$	4.64070	−	8.03792i	0.550749	−	0.953926i	−0.447471	−	0.894298i	$-0.647675\pi$
$71$	4.64070	−	8.03792i	0.550749	−	0.953926i	0.998221	−	0.0596277i	$-0.0189913\pi$
$72$	5.39371	−	7.46750i	0.635655	−	0.880053i
$73$	−4.69504			−0.549512			−0.274756	−	0.961514i	$-0.588597\pi$
$73$	−4.69504			−0.549512			−0.274756	+	0.961514i	$0.588597\pi$
$74$	4.76171			0.553537
$75$	13.5437	+	8.76856i	1.56389	+	1.01251i
$76$	−0.912486			−0.104669
$77$	−0.192986	+	0.334261i	−0.0219928	+	0.0380926i
$78$	−2.61301	−	7.05208i	−0.295865	−	0.798491i
$79$	6.65302	+	11.5234i	0.748523	+	1.29648i	0.948530	+	0.316686i	$0.102570\pi$
$79$	6.65302	+	11.5234i	0.748523	+	1.29648i	−0.200007	+	0.979794i	$0.564097\pi$
$80$	−4.91533	−	8.51360i	−0.549550	−	0.951849i
$81$	−2.82883	−	8.54387i	−0.314315	−	0.949319i
$82$	1.72653	−	2.99044i	0.190663	−	0.330239i
$83$	−6.45522	−	11.1808i	−0.708552	−	1.22725i	−0.965394	−	0.260795i	$-0.916015\pi$
$83$	−6.45522	−	11.1808i	−0.708552	−	1.22725i	0.256842	−	0.966453i	$-0.417318\pi$
$84$	−0.240156	−	0.155483i	−0.0262031	−	0.0169646i
$85$	9.98281	+	17.2907i	1.08279	+	1.87544i
$86$	−0.0125508	+	0.0217386i	−0.00135339	+	0.00234413i
$87$	−0.849940	+	16.6621i	−0.0911231	+	1.78637i
$88$	−1.97226	+	3.41605i	−0.210243	+	0.364152i
$89$	3.19907	+	5.54096i	0.339101	+	0.587340i	0.984264	−	0.176705i	$-0.0565438\pi$
$89$	3.19907	+	5.54096i	0.339101	+	0.587340i	−0.645163	+	0.764045i	$0.723210\pi$
$90$	−13.5982	−	1.39091i	−1.43337	−	0.146615i
$91$	−0.995325	+	0.427653i	−0.104338	+	0.0448302i
$92$	−0.920281	−	1.59397i	−0.0959459	−	0.166183i
$93$	0.581838	−	11.4063i	0.0603338	−	1.18278i
$94$	2.29825			0.237047
$95$	3.13998	+	5.43861i	0.322156	+	0.557990i
$96$	−4.37946	−	2.83539i	−0.446977	−	0.289385i
$97$	−3.76391			−0.382167			−0.191083	−	0.981574i	$-0.561200\pi$
$97$	−3.76391			−0.382167			−0.191083	+	0.981574i	$0.561200\pi$
$98$	−4.16056	+	7.20630i	−0.420280	+	0.727946i
$99$	1.57731	+	3.51629i	0.158526	+	0.353400i
$100$	2.56053	−	4.43497i	0.256053	−	0.443497i
$101$	2.49579	−	4.32284i	0.248341	−	0.430139i	−0.714725	−	0.699406i	$-0.753448\pi$
$101$	2.49579	−	4.32284i	0.248341	−	0.430139i	0.963066	+	0.269267i	$0.0867814\pi$
$102$	−9.23953	−	5.98193i	−0.914849	−	0.592299i
$103$	2.16757	−	3.75434i	0.213577	−	0.369926i	−0.739254	−	0.673426i	$-0.764822\pi$
$103$	2.16757	−	3.75434i	0.213577	−	0.369926i	0.952831	+	0.303500i	$0.0981553\pi$
$104$	−10.1719	+	4.37048i	−0.997440	+	0.428561i
$105$	−0.100308	+	1.96642i	−0.00978901	+	0.191903i
$106$	−4.30673	+	7.45948i	−0.418307	+	0.724529i
$107$	1.57507	+	2.72809i	0.152267	+	0.263735i	0.932061	−	0.362302i	$-0.118009\pi$
$107$	1.57507	+	2.72809i	0.152267	+	0.263735i	−0.779793	+	0.626037i	$0.784676\pi$
$108$	−2.66256	+	1.03486i	−0.256205	+	0.0995791i
$109$	14.2728			1.36708			0.683542	−	0.729911i	$-0.260439\pi$
$109$	14.2728			1.36708			0.683542	+	0.729911i	$0.260439\pi$
$110$	5.85321			0.558082
$111$	−5.74892	−	3.72201i	−0.545663	−	0.353277i
$112$	0.390332	−	0.676076i	0.0368829	−	0.0638831i
$113$	−2.63887	−	4.57066i	−0.248244	−	0.429972i	0.714794	−	0.699335i	$-0.246520\pi$
$113$	−2.63887	−	4.57066i	−0.248244	−	0.429972i	−0.963039	+	0.269363i	$0.913187\pi$
$114$	−2.90619	−	1.88155i	−0.272190	−	0.176223i
$115$	−6.33362	+	10.9702i	−0.590613	+	1.02297i
$116$	5.29544			0.491669
$117$	−2.35754	+	10.5566i	−0.217955	+	0.975959i
$118$	−10.5232			−0.968735
$119$	−0.792748	+	1.37308i	−0.0726711	+	0.125870i
$120$	−1.02511	+	20.0962i	−0.0935796	+	1.83453i
$121$	4.67488	+	8.09713i	0.424989	+	0.736102i
$122$	3.09301	−	5.35726i	0.280028	−	0.485023i
$123$	−4.42197	+	2.26087i	−0.398716	+	0.203856i
$124$	−3.62507			−0.325540
$125$	−16.3268			−1.46031
$126$	−0.444268	−	0.990404i	−0.0395786	−	0.0882322i
$127$	−5.36180	−	9.28691i	−0.475783	−	0.824080i	0.523832	−	0.851821i	$-0.324502\pi$
$127$	−5.36180	−	9.28691i	−0.475783	−	0.824080i	−0.999615	+	0.0277416i	$0.991168\pi$
$128$	2.30103	−	3.98549i	0.203384	−	0.352271i
$129$	0.0321449	−	0.0164351i	0.00283020	−	0.00144703i
$130$	13.1634	+	9.82913i	1.15451	+	0.862071i
$131$	1.67220	−	2.89633i	0.146101	−	0.253054i	−0.783682	−	0.621162i	$-0.786661\pi$
$131$	1.67220	−	2.89633i	0.146101	−	0.253054i	0.929783	+	0.368108i	$0.119994\pi$
$132$	1.08912	−	0.556846i	0.0947954	−	0.0484672i
$133$	−0.249350	+	0.431887i	−0.0216214	+	0.0374494i
$134$	5.00455	−	8.66814i	0.432327	−	0.748813i
$135$	15.3302	+	12.3084i	1.31941	+	1.05934i
$136$	−8.10165	+	14.0325i	−0.694710	+	1.20327i
$137$	−15.7557			−1.34610			−0.673051	−	0.739596i	$-0.735016\pi$
$137$	−15.7557			−1.34610			−0.673051	+	0.739596i	$0.735016\pi$
$138$	0.355761	−	6.97430i	0.0302844	−	0.593692i
$139$	−10.7754	−	18.6635i	−0.913956	−	1.58302i	−0.808422	−	0.588603i	$-0.799678\pi$
$139$	−10.7754	−	18.6635i	−0.913956	−	1.58302i	−0.105534	−	0.994416i	$-0.533655\pi$
$140$	0.624953			0.0528182
$141$	−2.77473	−	1.79644i	−0.233675	−	0.151288i
$142$	−5.58862	−	9.67977i	−0.468986	−	0.812308i
$143$	0.544298	−	4.59967i	0.0455165	−	0.384643i
$144$	−3.19027	−	7.11204i	−0.265856	−	0.592670i
$145$	−18.2223	−	31.5620i	−1.51328	−	2.62108i
$146$	−2.82703	+	4.89656i	−0.233966	+	0.405242i
$147$	10.6560	−	5.44821i	0.878890	−	0.449361i
$148$	−1.08687	+	1.88252i	−0.0893405	+	0.154742i
$149$	6.43686	+	11.1490i	0.527328	+	0.913359i	0.999493	+	0.0318483i	$0.0101393\pi$
$149$	6.43686	+	11.1490i	0.527328	+	0.913359i	−0.472165	+	0.881510i	$0.656527\pi$
$150$	17.3000	−	8.84519i	1.41254	−	0.722206i
$151$	−6.21526	−	10.7652i	−0.505791	−	0.876056i	−0.999978	−	0.00669978i	$-0.997867\pi$
$151$	−6.21526	−	10.7652i	−0.505791	−	0.876056i	0.494187	−	0.869356i	$-0.335466\pi$
$152$	−2.54828	+	4.41376i	−0.206693	+	0.358003i
$153$	6.47929	+	14.4442i	0.523820	+	1.16775i
$154$	0.232405	+	0.402538i	0.0187278	+	0.0324374i
$155$	12.4743	+	21.6062i	1.00196	+	1.73545i
$156$	3.38444	+	0.576616i	0.270972	+	0.0461663i
$157$	5.64417	−	9.77599i	0.450454	−	0.780209i	−0.547960	−	0.836504i	$-0.684596\pi$
$157$	5.64417	−	9.77599i	0.450454	−	0.780209i	0.998414	+	0.0562954i	$0.0179288\pi$
$158$	16.0240			1.27480
$159$	11.0304	−	5.63963i	0.874764	−	0.447251i
$160$	11.3966			0.900980
$161$	−1.00592			−0.0792777
$162$	−10.6139	−	2.19428i	−0.833908	−	0.172399i
$163$	−3.30893	+	5.73124i	−0.259176	+	0.448905i	−0.966021	−	0.258462i	$-0.916784\pi$
$163$	−3.30893	+	5.73124i	−0.259176	+	0.448905i	0.706846	+	0.707368i	$0.250118\pi$
$164$	0.788171	+	1.36515i	0.0615458	+	0.106601i
$165$	−7.06672	−	4.57519i	−0.550143	−	0.356178i
$166$	−15.5476			−1.20672
$167$	10.8544			0.839942			0.419971	−	0.907538i	$-0.362040\pi$
$167$	10.8544			0.839942			0.419971	+	0.907538i	$0.362040\pi$
$168$	−1.42276	+	0.727434i	−0.109769	+	0.0561227i
$169$	8.94817	−	9.43028i	0.688321	−	0.725406i
$170$	24.0438			1.84408
$171$	2.03799	+	4.54327i	0.155849	+	0.347433i
$172$	−0.00572950	−	0.00992379i	−0.000436871	−	0.000756682i
$173$	0.207102			0.0157457			0.00787286	−	0.999969i	$-0.497494\pi$
$173$	0.207102			0.0157457			0.00787286	+	0.999969i	$0.497494\pi$
$174$	16.8655	+	10.9192i	1.27857	+	0.827784i
$175$	−1.39941	−	2.42384i	−0.105785	−	0.183225i
$176$	1.66889	+	2.89060i	0.125797	+	0.217887i
$177$	12.7048	+	8.22547i	0.954955	+	0.618264i
$178$	7.70504			0.577518
$179$	−4.98833	−	8.64004i	−0.372845	−	0.645787i	0.617157	−	0.786840i	$-0.288285\pi$
$179$	−4.98833	−	8.64004i	−0.372845	−	0.645787i	−0.990002	+	0.141053i	$0.954951\pi$
$180$	3.65372	−	5.05851i	0.272332	−	0.377039i
$181$	13.9599			1.03763			0.518814	−	0.854887i	$-0.326374\pi$
$181$	13.9599			1.03763			0.518814	+	0.854887i	$0.326374\pi$
$182$	−0.153308	+	1.29555i	−0.0113639	+	0.0960325i
$183$	−7.92179	+	4.05027i	−0.585596	+	0.299405i
$184$	−10.2802			−0.757868
$185$	14.9603			1.09990
$186$	−11.5455	−	7.47490i	−0.846559	−	0.548086i
$187$	−3.38944	−	5.87069i	−0.247861	−	0.429307i
$188$	−0.524583	+	0.908605i	−0.0382592	+	0.0662668i
$189$	−0.237778	+	1.54300i	−0.0172958	+	0.112237i
$190$	7.56273			0.548658
$191$	−13.8793			−1.00427			−0.502134	−	0.864790i	$-0.667451\pi$
$191$	−13.8793			−1.00427			−0.502134	+	0.864790i	$0.667451\pi$
$192$	−13.6080	+	6.95755i	−0.982075	+	0.502118i
$193$	8.04222			0.578892			0.289446	−	0.957194i	$-0.406529\pi$
$193$	8.04222			0.578892			0.289446	+	0.957194i	$0.406529\pi$
$194$	−2.26637	+	3.92546i	−0.162716	+	0.281832i
$195$	−8.20954	−	22.1562i	−0.587897	−	1.58664i
$196$	−1.89932	−	3.28972i	−0.135666	−	0.234980i
$197$	1.50401	+	2.60502i	0.107156	+	0.185600i	0.914617	−	0.404321i	$-0.132492\pi$
$197$	1.50401	+	2.60502i	0.107156	+	0.185600i	−0.807461	+	0.589921i	$0.799159\pi$
$198$	4.61696	+	0.472254i	0.328113	+	0.0335616i
$199$	−10.4398	+	18.0823i	−0.740057	+	1.28182i	0.212411	+	0.977180i	$0.431868\pi$
$199$	−10.4398	+	18.0823i	−0.740057	+	1.28182i	−0.952469	+	0.304637i	$0.901465\pi$
$200$	−14.3015	−	24.7709i	−1.01127	−	1.75157i
$201$	−12.8176	+	6.55341i	−0.904084	+	0.462242i
$202$	−3.00559	−	5.20583i	−0.211473	−	0.366281i
$203$	1.44706	−	2.50638i	0.101563	−	0.175913i
$204$	4.47388	−	2.28741i	0.313234	−	0.160151i
$205$	5.42440	−	9.39534i	0.378857	−	0.656199i
$206$	−2.61032	−	4.52121i	−0.181870	−	0.315008i
$207$	−5.88101	+	8.14215i	−0.408758	+	0.565918i
$208$	−1.10090	+	9.30327i	−0.0763334	+	0.645066i
$209$	−1.06611	−	1.84656i	−0.0737445	−	0.127729i
$210$	1.99042	+	1.28865i	0.137352	+	0.0889256i
$211$	−18.0850			−1.24502			−0.622511	−	0.782611i	$-0.713887\pi$
$211$	−18.0850			−1.24502			−0.622511	+	0.782611i	$0.713887\pi$
$212$	−1.96605	−	3.40530i	−0.135029	−	0.233877i
$213$	−0.818968	+	16.0550i	−0.0561148	+	1.10007i
$214$	3.79358			0.259324
$215$	−0.0394320	+	0.0682982i	−0.00268924	+	0.00465790i
$216$	−2.43002	+	15.7690i	−0.165342	+	1.07295i
$217$	−0.990602	+	1.71577i	−0.0672465	+	0.116474i
$218$	8.59408	−	14.8854i	0.582064	−	1.00817i
$219$	7.24055	−	3.70197i	0.489271	−	0.250156i
$220$	−1.33601	+	2.31404i	−0.0900739	+	0.156013i
$221$	2.23587	−	18.8945i	0.150401	−	1.27098i
$222$	−7.34337	+	3.75453i	−0.492854	+	0.251988i
$223$	−11.3699	+	19.6933i	−0.761385	+	1.31876i	0.180751	+	0.983529i	$0.442147\pi$
$223$	−11.3699	+	19.6933i	−0.761385	+	1.31876i	−0.942137	+	0.335229i	$0.891186\pi$
$224$	0.452509	+	0.783769i	0.0302345	+	0.0523677i
$225$	−27.8006	−	2.84363i	−1.85337	−	0.189575i
$226$	−6.35579			−0.422781
$227$	4.91136			0.325978			0.162989	−	0.986628i	$-0.447886\pi$
$227$	4.91136			0.325978			0.162989	+	0.986628i	$0.447886\pi$
$228$	1.40721	−	0.719481i	0.0931947	−	0.0476488i
$229$	1.97040	−	3.41283i	0.130208	−	0.225526i	−0.793549	−	0.608506i	$-0.791769\pi$
$229$	1.97040	−	3.41283i	0.130208	−	0.225526i	0.923757	+	0.382980i	$0.125102\pi$
$230$	7.62734	+	13.2109i	0.502932	+	0.871103i
$231$	0.0340572	−	0.667654i	0.00224080	−	0.0439284i
$232$	14.7885	−	25.6144i	0.970912	−	1.68167i
$233$	2.49782			0.163637			0.0818187	−	0.996647i	$-0.473927\pi$
$233$	2.49782			0.163637			0.0818187	+	0.996647i	$0.473927\pi$
$234$	9.59016	+	8.81520i	0.626929	+	0.576267i
$235$	7.22064			0.471023
$236$	2.40194	−	4.16028i	0.156353	−	0.270811i
$237$	−19.3461	−	12.5252i	−1.25666	−	0.813599i
$238$	0.954676	+	1.65355i	0.0618825	+	0.107184i
$239$	−4.25640	+	7.37230i	−0.275324	+	0.476874i	−0.970217	−	0.242239i	$-0.922118\pi$
$239$	−4.25640	+	7.37230i	−0.275324	+	0.476874i	0.694893	+	0.719113i	$0.255452\pi$
$240$	14.2931	+	9.25376i	0.922617	+	0.597328i
$241$	16.2305			1.04550			0.522749	−	0.852487i	$-0.324906\pi$
$241$	16.2305			1.04550			0.522749	+	0.852487i	$0.324906\pi$
$242$	11.2596			0.723792
$243$	11.0993	+	10.9456i	0.712017	+	0.702162i
$244$	1.41198	+	2.44562i	0.0903927	+	0.156565i
$245$	−13.0716	+	22.6407i	−0.835116	+	1.44646i
$246$	−0.304690	+	5.97311i	−0.0194263	+	0.380832i
$247$	0.703269	−	5.94307i	0.0447479	−	0.378148i
$248$	−10.1237	+	17.5347i	−0.642853	+	1.11345i
$249$	18.7709	+	12.1528i	1.18956	+	0.770153i
$250$	−9.83086	+	17.0276i	−0.621758	+	1.07692i
$251$	11.7453	−	20.3434i	0.741356	−	1.28407i	−0.210522	−	0.977589i	$-0.567516\pi$
$251$	11.7453	−	20.3434i	0.741356	−	1.28407i	0.951878	−	0.306477i	$-0.0991503\pi$
$252$	0.492958	+	0.0504230i	0.0310534	+	0.00317635i
$253$	2.15044	−	3.72467i	0.135197	−	0.234168i
$254$	−12.9140			−0.810298
$255$	−29.0287	−	18.7940i	−1.81785	−	1.17692i
$256$	6.05291	+	10.4839i	0.378307	+	0.655247i
$257$	−5.73134			−0.357511			−0.178756	−	0.983894i	$-0.557207\pi$
$257$	−5.73134			−0.357511			−0.178756	+	0.983894i	$0.557207\pi$
$258$	0.00221490	−	0.0434207i	0.000137894	−	0.00270326i
$259$	0.594008	+	1.02885i	0.0369099	+	0.0639298i
$260$	−6.89050	+	2.96058i	−0.427330	+	0.183607i
$261$	−11.8271	−	26.3660i	−0.732079	−	1.63202i
$262$	−2.01376	−	3.48794i	−0.124411	−	0.215486i
$263$	0.266662	−	0.461872i	0.0164431	−	0.0284803i	−0.857687	−	0.514173i	$-0.828099\pi$
$263$	0.266662	−	0.461872i	0.0164431	−	0.0284803i	0.874130	+	0.485692i	$0.161432\pi$
$264$	0.348054	−	6.82322i	0.0214213	−	0.419940i
$265$	−13.5309	+	23.4362i	−0.831195	+	1.43967i
$266$	0.300283	+	0.520105i	0.0184115	+	0.0318897i
$267$	−9.30248	−	6.02268i	−0.569302	−	0.368582i
$268$	2.28461	+	3.95706i	0.139555	+	0.241716i
$269$	0.841875	−	1.45817i	0.0513300	−	0.0889062i	−0.839219	−	0.543794i	$-0.816987\pi$
$269$	0.841875	−	1.45817i	0.0513300	−	0.0889062i	0.890549	+	0.454888i	$0.150321\pi$
$270$	22.0674	−	8.57694i	1.34298	−	0.521976i
$271$	−2.99018	−	5.17914i	−0.181640	−	0.314610i	0.760799	−	0.648988i	$-0.224807\pi$
$271$	−2.99018	−	5.17914i	−0.181640	−	0.314610i	−0.942439	+	0.334377i	$0.891474\pi$
$272$	6.85548	+	11.8740i	0.415674	+	0.719969i
$273$	1.19776	−	1.44431i	0.0724920	−	0.0874138i
$274$	−9.48700	+	16.4320i	−0.573131	+	0.992692i
$275$	11.9665			0.721607
$276$	2.67606	+	1.73255i	0.161080	+	0.104287i
$277$	−0.482134			−0.0289686			−0.0144843	−	0.999895i	$-0.504611\pi$
$277$	−0.482134			−0.0289686			−0.0144843	+	0.999895i	$0.504611\pi$
$278$	−25.9528			−1.55654
$279$	8.09640	+	18.0492i	0.484719	+	1.08058i
$280$	1.74530	−	3.02294i	0.104301	−	0.180655i
$281$	6.37082	+	11.0346i	0.380051	+	0.658268i	0.991069	−	0.133349i	$-0.0425731\pi$
$281$	6.37082	+	11.0346i	0.380051	+	0.658268i	−0.611018	+	0.791617i	$0.709240\pi$
$282$	−3.54430	+	1.81214i	−0.211060	+	0.107911i
$283$	9.11340			0.541736			0.270868	−	0.962617i	$-0.412689\pi$
$283$	9.11340			0.541736			0.270868	+	0.962617i	$0.412689\pi$
$284$	5.10247			0.302776
$285$	−9.13066	−	5.91144i	−0.540853	−	0.350164i
$286$	−4.46935	−	3.33726i	−0.264278	−	0.197336i
$287$	0.861518			0.0508538
$288$	8.98954	+	0.919510i	0.529714	+	0.0541826i
$289$	−5.42317	−	9.39321i	−0.319010	−	0.552542i
$290$	−43.8889			−2.57724
$291$	5.80459	−	2.96778i	0.340271	−	0.173975i
$292$	−1.29055	−	2.23531i	−0.0755240	−	0.130811i
$293$	−2.05193	−	3.55405i	−0.119875	−	0.207630i	0.799843	−	0.600209i	$-0.204916\pi$
$293$	−2.05193	−	3.55405i	−0.119875	−	0.207630i	−0.919718	+	0.392580i	$0.871583\pi$
$294$	0.734236	−	14.3939i	0.0428215	−	0.839469i
$295$	−33.0616			−1.92492
$296$	6.07059	+	10.5146i	0.352846	+	0.611147i
$297$	−5.20503	−	4.17903i	−0.302026	−	0.242492i
$298$	15.5033			0.898083
$299$	11.0909	−	4.76534i	0.641404	−	0.275587i
$300$	−0.451870	+	8.85842i	−0.0260887	+	0.511441i
$301$	−0.00626268			−0.000360975
$302$	−14.9696			−0.861404
$303$	−0.440446	+	8.63445i	−0.0253029	+	0.496036i
$304$	2.15632	+	3.73485i	0.123673	+	0.214208i
$305$	9.71762	−	16.8314i	0.556429	−	0.963764i
$306$	18.9656	+	1.93993i	1.08419	+	0.110898i
$307$	21.0459			1.20115			0.600575	−	0.799568i	$-0.294938\pi$
$307$	21.0459			1.20115			0.600575	+	0.799568i	$0.294938\pi$
$308$	−0.212189			−0.0120906
$309$	−0.382522	+	7.49893i	−0.0217609	+	0.426599i
$310$	30.0447			1.70643
$311$	−13.8275	+	23.9500i	−0.784087	+	1.35808i	0.145456	+	0.989365i	$0.453535\pi$
$311$	−13.8275	+	23.9500i	−0.784087	+	1.35808i	−0.929543	+	0.368714i	$0.879798\pi$
$312$	12.2408	−	14.7604i	0.692998	−	0.835646i
$313$	−1.14415	−	1.98173i	−0.0646712	−	0.112014i	0.831877	−	0.554960i	$-0.187267\pi$
$313$	−1.14415	−	1.98173i	−0.0646712	−	0.112014i	−0.896548	+	0.442946i	$0.853933\pi$
$314$	−6.79706	−	11.7729i	−0.383580	−	0.664381i
$315$	−1.39580	−	3.11165i	−0.0786444	−	0.175321i
$316$	−3.65752	+	6.33500i	−0.205751	+	0.356372i
$317$	10.1830	+	17.6374i	0.571932	+	0.990615i	0.996368	+	0.0851568i	$0.0271391\pi$
$317$	10.1830	+	17.6374i	0.571932	+	0.990615i	−0.424436	+	0.905458i	$0.639528\pi$
$318$	0.760032	−	14.8996i	0.0426205	−	0.835527i
$319$	6.18698	+	10.7162i	0.346404	+	0.599990i
$320$	16.6929	−	28.9130i	0.933161	−	1.61628i
$321$	−4.58008	−	2.96527i	−0.255635	−	0.165505i
$322$	−0.605696	+	1.04910i	−0.0337541	+	0.0584639i
$323$	−4.37938	−	7.58531i	−0.243675	−	0.422058i
$324$	3.29016	−	3.69531i	0.182786	−	0.205295i
$325$	26.9117	+	20.0950i	1.49280	+	1.11467i
$326$	3.98482	+	6.90192i	0.220699	+	0.382262i
$327$	−22.0111	+	11.2539i	−1.21721	+	0.622340i
$328$	8.80445			0.486144
$329$	0.286700	+	0.496579i	0.0158063	+	0.0273773i
$330$	−9.02665	+	4.61517i	−0.496901	+	0.254057i
$331$	17.4437			0.958791			0.479395	−	0.877599i	$-0.340856\pi$
$331$	17.4437			0.958791			0.479395	+	0.877599i	$0.340856\pi$
$332$	3.54877	−	6.14666i	0.194764	−	0.337342i
$333$	11.8006	+	1.20704i	0.646667	+	0.0661454i
$334$	6.53580	−	11.3203i	0.357623	−	0.619421i
$335$	15.7233	−	27.2335i	0.859054	−	1.48793i
$336$	−0.0688840	+	1.35040i	−0.00375793	+	0.0736701i
$337$	12.4840	−	21.6229i	0.680048	−	1.17788i	−0.294918	−	0.955523i	$-0.595292\pi$
$337$	12.4840	−	21.6229i	0.680048	−	1.17788i	0.974966	−	0.222355i	$-0.0713743\pi$
$338$	−4.44707	−	15.0105i	−0.241889	−	0.816464i
$339$	7.67350	+	4.96803i	0.416767	+	0.269827i
$340$	−5.48808	+	9.50563i	−0.297633	+	0.515515i
$341$	−4.23538	−	7.33590i	−0.229359	−	0.397261i
$342$	5.96542	+	0.610182i	0.322573	+	0.0329949i
$343$	−4.17926			−0.225659
$344$	−0.0640028			−0.00345080
$345$	1.11773	−	21.9118i	0.0601764	−	1.17969i
$346$	0.124703	−	0.215992i	0.00670407	−	0.0116118i
$347$	5.06421	+	8.77147i	0.271861	+	0.470877i	0.969338	−	0.245730i	$-0.0790275\pi$
$347$	5.06421	+	8.77147i	0.271861	+	0.470877i	−0.697477	+	0.716607i	$0.745694\pi$
$348$	−8.16647	+	4.17537i	−0.437769	+	0.223824i
$349$	−11.2845	+	19.5453i	−0.604044	+	1.04623i	0.388158	+	0.921593i	$0.373111\pi$
$349$	−11.2845	+	19.5453i	−0.604044	+	1.04623i	−0.992202	+	0.124642i	$0.960222\pi$
$350$	−3.37050			−0.180161
$351$	−4.68799	−	18.1390i	−0.250226	−	0.968187i
$352$	−3.86946			−0.206243
$353$	−12.4509	+	21.5655i	−0.662693	+	1.14782i	0.317212	+	0.948355i	$0.397253\pi$
$353$	−12.4509	+	21.5655i	−0.662693	+	1.14782i	−0.979905	+	0.199463i	$0.936080\pi$
$354$	16.2285	−	8.29735i	0.862535	−	0.440999i
$355$	−17.5583	−	30.4118i	−0.931897	−	1.61409i
$356$	−1.75870	+	3.04616i	−0.0932109	+	0.161446i
$357$	0.139900	−	2.74259i	0.00740431	−	0.145153i
$358$	−12.0145			−0.634987
$359$	−35.7532			−1.88698			−0.943492	−	0.331395i	$-0.892481\pi$
$359$	−35.7532			−1.88698			−0.943492	+	0.331395i	$0.892481\pi$
$360$	−14.2647	−	31.8001i	−0.751814	−	1.67601i
$361$	8.12251	+	14.0686i	0.427501	+	0.740453i
$362$	8.40567	−	14.5590i	0.441792	−	0.765206i
$363$	−13.5939	−	8.80108i	−0.713496	−	0.461937i
$364$	−0.477197	−	0.356323i	−0.0250119	−	0.0186764i
$365$	−8.88194	+	15.3840i	−0.464902	+	0.805234i
$366$	−0.545840	+	10.7006i	−0.0285315	+	0.559330i
$367$	6.69188	−	11.5907i	0.349313	−	0.605028i	−0.636814	−	0.771017i	$-0.719748\pi$
$367$	6.69188	−	11.5907i	0.349313	−	0.605028i	0.986128	+	0.165989i	$0.0530815\pi$
$368$	−4.34947	+	7.53351i	−0.226732	+	0.392711i
$369$	5.03677	−	6.97331i	0.262204	−	0.363016i
$370$	9.00806	−	15.6024i	0.468307	−	0.811131i
$371$	−2.14901			−0.111571
$372$	5.59047	−	2.85831i	0.289852	−	0.148196i
$373$	−3.57470	−	6.19157i	−0.185091	−	0.320587i	0.758516	−	0.651654i	$-0.225925\pi$
$373$	−3.57470	−	6.19157i	−0.185091	−	0.320587i	−0.943607	+	0.331067i	$0.892591\pi$
$374$	−8.16356			−0.422127
$375$	25.1787	−	12.8734i	1.30022	−	0.664781i
$376$	2.92999	+	5.07489i	0.151103	+	0.261717i
$377$	−4.08129	+	34.4895i	−0.210197	+	1.77630i
$378$	1.46606	+	1.17707i	0.0754058	+	0.0605421i
$379$	13.7475	+	23.8114i	0.706162	+	1.22311i	0.966271	+	0.257529i	$0.0829082\pi$
$379$	13.7475	+	23.8114i	0.706162	+	1.22311i	−0.260109	+	0.965579i	$0.583758\pi$
$380$	−1.72622	+	2.98989i	−0.0885530	+	0.153378i
$381$	15.5914	+	10.0943i	0.798771	+	0.517147i
$382$	−8.35713	+	14.4750i	−0.427588	+	0.740604i
$383$	5.66249	+	9.80773i	0.289340	+	0.501151i	0.973652	−	0.228037i	$-0.0732309\pi$
$383$	5.66249	+	9.80773i	0.289340	+	0.501151i	−0.684312	+	0.729189i	$0.739898\pi$
$384$	−0.406074	+	7.96064i	−0.0207224	+	0.406239i
$385$	0.730170	+	1.26469i	0.0372129	+	0.0644547i
$386$	4.84247	−	8.38741i	0.246475	−	0.426908i
$387$	−0.0366141	+	0.0506915i	−0.00186120	+	0.00257680i
$388$	−1.03461	−	1.79200i	−0.0525243	−	0.0909748i
$389$	−7.75413	−	13.4306i	−0.393150	−	0.680956i	0.599713	−	0.800215i	$-0.295281\pi$
$389$	−7.75413	−	13.4306i	−0.393150	−	0.680956i	−0.992863	+	0.119259i	$0.961948\pi$
$390$	−28.0504	−	4.77903i	−1.42039	−	0.241995i
$391$	8.83359	−	15.3002i	0.446734	−	0.773766i
$392$	−21.2168			−1.07161
$393$	−0.295101	+	5.78514i	−0.0148859	+	0.291822i
$394$	3.62244			0.182496
$395$	50.3440			2.53308
$396$	−1.24054	+	1.71750i	−0.0623394	+	0.0863078i
$397$	−5.84662	+	10.1266i	−0.293434	+	0.508242i	−0.974619	−	0.223869i	$-0.928131\pi$
$397$	−5.84662	+	10.1266i	−0.293434	+	0.508242i	0.681186	+	0.732111i	$0.261465\pi$
$398$	12.5722	+	21.7758i	0.630190	+	1.09152i
$399$	0.0440041	−	0.862653i	0.00220296	−	0.0431866i
$400$	−24.2034			−1.21017
$401$	0.715696			0.0357402			0.0178701	−	0.999840i	$-0.494311\pi$
$401$	0.715696			0.0357402			0.0178701	+	0.999840i	$0.494311\pi$
$402$	−0.883179	+	17.3138i	−0.0440490	+	0.863532i
$403$	2.79390	−	23.6102i	0.139174	−	1.17611i
$404$	2.74414			0.136526
$405$	−33.3467	−	6.89398i	−1.65701	−	0.342565i
$406$	−1.74264	−	3.01833i	−0.0864855	−	0.149797i
$407$	−5.07944			−0.251778
$408$	1.42974	−	28.0285i	0.0707827	−	1.38762i
$409$	1.74702	+	3.02593i	0.0863846	+	0.149623i	0.905980	−	0.423320i	$-0.139135\pi$
$409$	1.74702	+	3.02593i	0.0863846	+	0.149623i	−0.819596	+	0.572942i	$0.805802\pi$
$410$	−6.53240	−	11.3145i	−0.322612	−	0.558781i
$411$	24.2980	−	12.4231i	1.19853	−	0.612788i
$412$	2.38325			0.117415
$413$	−1.31273	−	2.27372i	−0.0645953	−	0.111882i
$414$	4.95048	+	11.0361i	0.243303	+	0.542393i
$415$	−48.8472			−2.39782
$416$	−8.70213	−	6.49787i	−0.426657	−	0.318585i
$417$	31.3334	+	20.2861i	1.53440	+	0.993415i
$418$	−2.56776			−0.125593
$419$	−18.2792			−0.893000			−0.446500	−	0.894784i	$-0.647330\pi$
$419$	−18.2792			−0.893000			−0.446500	+	0.894784i	$0.647330\pi$
$420$	−0.963784	+	0.492766i	−0.0470278	+	0.0240445i
$421$	−1.70275	−	2.94926i	−0.0829871	−	0.143738i	0.821545	−	0.570144i	$-0.193113\pi$
$421$	−1.70275	−	2.94926i	−0.0829871	−	0.143738i	−0.904532	+	0.426406i	$0.859779\pi$
$422$	−10.8895	+	18.8612i	−0.530094	+	0.918150i
$423$	5.69558	+	0.582582i	0.276929	+	0.0283261i
$424$	−21.9622			−1.06658
$425$	49.1560			2.38442
$426$	16.2510	+	10.5213i	0.787361	+	0.509759i
$427$	1.54338			0.0746892
$428$	−0.865896	+	1.49978i	−0.0418547	+	0.0724944i
$429$	2.78737	+	7.52264i	0.134575	+	0.363197i
$430$	0.0474864	+	0.0822489i	0.00229000	+	0.00396639i
$431$	−7.51196	−	13.0111i	−0.361839	−	0.626723i	0.626425	−	0.779482i	$-0.284518\pi$
$431$	−7.51196	−	13.0111i	−0.361839	−	0.626723i	−0.988263	+	0.152759i	$0.951184\pi$
$432$	10.5277	+	8.45250i	0.506513	+	0.406671i
$433$	1.01128	−	1.75159i	0.0485991	−	0.0841762i	−0.840703	−	0.541497i	$-0.817858\pi$
$433$	1.01128	−	1.75159i	0.0485991	−	0.0841762i	0.889302	+	0.457321i	$0.151191\pi$
$434$	1.19294	+	2.06624i	0.0572632	+	0.0991827i
$435$	52.9880	+	34.3059i	2.54058	+	1.64484i
$436$	3.92325	+	6.79526i	0.187889	+	0.325434i
$437$	2.77851	−	4.81252i	0.132914	−	0.230214i
$438$	0.498900	−	9.78039i	0.0238384	−	0.467325i
$439$	−6.58663	+	11.4084i	−0.314363	+	0.544492i	−0.979302	−	0.202405i	$-0.935124\pi$
$439$	−6.58663	+	11.4084i	−0.314363	+	0.544492i	0.664939	+	0.746898i	$0.268457\pi$
$440$	7.46212	+	12.9248i	0.355743	+	0.616164i
$441$	−12.1375	+	16.8042i	−0.577977	+	0.800198i
$442$	−18.3592	−	13.7088i	−0.873259	−	0.652062i
$443$	−5.48308	−	9.49698i	−0.260509	−	0.451215i	0.705868	−	0.708343i	$-0.250557\pi$
$443$	−5.48308	−	9.49698i	−0.260509	−	0.451215i	−0.966377	+	0.257128i	$0.917224\pi$
$444$	0.191806	−	3.76015i	0.00910272	−	0.178449i
$445$	24.2077			1.14755
$446$	13.6923	+	23.7158i	0.648351	+	1.12298i
$447$	−18.7175	−	12.1182i	−0.885308	−	0.573173i
$448$	2.65121			0.125258
$449$	−18.1471	+	31.4318i	−0.856416	+	1.48336i	0.0189089	+	0.999821i	$0.493981\pi$
$449$	−18.1471	+	31.4318i	−0.856416	+	1.48336i	−0.875325	+	0.483535i	$0.839353\pi$
$450$	−19.7053	+	27.2816i	−0.928915	+	1.28607i
$451$	−1.84174	+	3.18998i	−0.0867240	+	0.150210i
$452$	1.45073	−	2.51274i	0.0682365	−	0.118189i
$453$	18.0732	+	11.7011i	0.849151	+	0.549764i
$454$	2.95728	−	5.12216i	0.138792	−	0.240395i
$455$	−0.481662	+	4.07035i	−0.0225807	+	0.190821i
$456$	0.449709	−	8.81605i	0.0210595	−	0.412849i
$457$	16.9893	−	29.4263i	0.794726	−	1.37651i	−0.128286	−	0.991737i	$-0.540948\pi$
$457$	16.9893	−	29.4263i	0.794726	−	1.37651i	0.923013	−	0.384769i	$-0.125719\pi$
$458$	−2.37288	−	4.10994i	−0.110877	−	0.192045i
$459$	−21.3812	−	17.1667i	−0.997991	−	0.801271i
$460$	−6.96385			−0.324691
$461$	−11.5299			−0.537003			−0.268502	−	0.963279i	$-0.586528\pi$
$461$	−11.5299			−0.537003			−0.268502	+	0.963279i	$0.586528\pi$
$462$	−0.675804	−	0.437534i	−0.0314412	−	0.0203559i
$463$	−15.1765	+	26.2864i	−0.705310	+	1.22163i	0.261270	+	0.965266i	$0.415859\pi$
$463$	−15.1765	+	26.2864i	−0.705310	+	1.22163i	−0.966580	+	0.256366i	$0.917475\pi$
$464$	−12.5138	−	21.6745i	−0.580937	−	1.00621i
$465$	−36.2737	−	23.4846i	−1.68215	−	1.08907i
$466$	1.50401	−	2.60503i	0.0696721	−	0.120676i
$467$	−1.64762			−0.0762426			−0.0381213	−	0.999273i	$-0.512137\pi$
$467$	−1.64762			−0.0762426			−0.0381213	+	0.999273i	$0.512137\pi$
$468$	−5.67403	+	1.77934i	−0.262282	+	0.0822498i
$469$	2.49721			0.115310
$470$	4.34777	−	7.53056i	0.200548	−	0.347359i
$471$	−0.996056	+	19.5266i	−0.0458958	+	0.899738i
$472$	−13.4157	−	23.2367i	−0.617508	−	1.06956i
$473$	0.0133883	−	0.0231891i	0.000615592	−	0.00106624i
$474$	−24.7117	+	12.6347i	−1.13505	+	0.580329i
$475$	15.4615			0.709422
$476$	−0.871631			−0.0399511
$477$	−12.5639	+	17.3945i	−0.575263	+	0.796441i
$478$	5.12582	+	8.87818i	0.234450	+	0.406079i
$479$	5.29372	−	9.16900i	0.241876	−	0.418942i	−0.719372	−	0.694625i	$-0.755570\pi$
$479$	5.29372	−	9.16900i	0.241876	−	0.418942i	0.961249	+	0.275682i	$0.0889038\pi$
$480$	−17.5755	+	8.98604i	−0.802208	+	0.410155i
$481$	−11.4233	−	8.52976i	−0.520857	−	0.388923i
$482$	9.77289	−	16.9271i	0.445143	−	0.771010i
$483$	1.55130	−	0.793154i	0.0705867	−	0.0360897i
$484$	−2.57003	+	4.45142i	−0.116819	+	0.202337i
$485$	−7.12045	+	12.3330i	−0.323323	+	0.560012i
$486$	18.0986	−	4.98495i	0.820970	−	0.226122i
$487$	13.3185	−	23.0683i	0.603517	−	1.04532i	−0.388767	−	0.921336i	$-0.627099\pi$
$487$	13.3185	−	23.0683i	0.603517	−	1.04532i	0.992284	−	0.123986i	$-0.0395679\pi$
$488$	15.7728			0.714003
$489$	0.583945	−	11.4476i	0.0264069	−	0.517678i
$490$	15.7417	+	27.2654i	0.711136	+	1.23172i
$491$	23.3513			1.05383			0.526915	−	0.849918i	$-0.323349\pi$
$491$	23.3513			1.05383			0.526915	+	0.849918i	$0.323349\pi$
$492$	−2.29190	−	1.48384i	−0.103327	−	0.0668966i
$493$	25.4149	+	44.0199i	1.14463	+	1.98256i
$494$	−5.77469	−	4.31196i	−0.259816	−	0.194004i
$495$	14.5056	+	1.48372i	0.651976	+	0.0666884i
$496$	8.56647	+	14.8376i	0.384646	+	0.666226i
$497$	1.39433	−	2.41504i	0.0625440	−	0.108329i
$498$	23.9770	−	12.2590i	1.07443	−	0.549339i
$499$	−0.396185	+	0.686212i	−0.0177357	+	0.0307191i	−0.874757	−	0.484562i	$-0.838979\pi$
$499$	−0.396185	+	0.686212i	−0.0177357	+	0.0307191i	0.857021	+	0.515281i	$0.172312\pi$
$500$	−4.48785	−	7.77318i	−0.200703	−	0.347627i
$501$	−16.7394	+	8.55856i	−0.747862	+	0.382368i
$502$	−14.1444	−	24.4988i	−0.631296	−	1.09344i
$503$	11.9019	−	20.6147i	0.530681	−	0.919166i	−0.468678	−	0.883369i	$-0.655270\pi$
$503$	11.9019	−	20.6147i	0.530681	−	0.919166i	0.999359	−	0.0357971i	$-0.0113970\pi$
$504$	1.62057	−	2.24365i	0.0721861	−	0.0999403i
$505$	−9.44294	−	16.3557i	−0.420206	−	0.727817i
$506$	−2.58969	−	4.48548i	−0.115126	−	0.199404i
$507$	−6.36398	+	21.5986i	−0.282634	+	0.959228i
$508$	2.94766	−	5.10550i	0.130781	−	0.226520i
$509$	24.2029			1.07278			0.536388	−	0.843971i	$-0.319788\pi$
$509$	24.2029			1.07278			0.536388	+	0.843971i	$0.319788\pi$
$510$	−37.0797	+	18.9582i	−1.64192	+	0.839484i
$511$	−1.41065			−0.0624036
$512$	23.7827			1.05106
$513$	−6.72523	−	5.39958i	−0.296926	−	0.238397i
$514$	−3.45102	+	5.97734i	−0.152218	+	0.263649i
$515$	−8.20109	−	14.2047i	−0.361383	−	0.625934i
$516$	0.0166606	+	0.0107866i	0.000733444	+	0.000474852i
$517$	−2.45161			−0.107822
$518$	1.43068			0.0628606
$519$	−0.319387	+	0.163297i	−0.0140196	+	0.00716795i
$520$	−4.92244	+	41.5978i	−0.215863	+	1.82418i
$521$	−10.2515			−0.449125			−0.224563	−	0.974460i	$-0.572095\pi$
$521$	−10.2515			−0.449125			−0.224563	+	0.974460i	$0.572095\pi$
$522$	−34.6192	−	3.54108i	−1.51524	−	0.154989i
$523$	−13.3127	−	23.0583i	−0.582124	−	1.00827i	−0.995227	−	0.0975847i	$-0.968888\pi$
$523$	−13.3127	−	23.0583i	−0.582124	−	1.00827i	0.413103	−	0.910684i	$-0.364445\pi$
$524$	1.83859			0.0803192
$525$	4.06928	+	2.63457i	0.177598	+	0.114982i
$526$	−0.321131	−	0.556215i	−0.0140020	−	0.0242521i
$527$	−17.3981	−	30.1344i	−0.757874	−	1.31268i
$528$	−4.85291	−	3.14191i	−0.211196	−	0.136734i
$529$	−11.7910			−0.512653
$530$	16.2947	+	28.2233i	0.707797	+	1.22594i
$531$	−26.0787	−	2.66750i	−1.13172	−	0.115760i
$532$	−0.274162			−0.0118864
$533$	−9.49877	+	4.08125i	−0.411437	+	0.176779i
$534$	−11.8825	+	6.07531i	−0.514206	+	0.262904i
$535$	11.9187			0.515289
$536$	25.5207			1.10233
$537$	14.5054	+	9.39120i	0.625954	+	0.405260i
$538$	−1.01384	−	1.75602i	−0.0437096	−	0.0757073i
$539$	4.43818	−	7.68716i	0.191166	−	0.331109i
$540$	−1.64610	+	10.6820i	−0.0708370	+	0.459679i
$541$	−11.7447			−0.504943			−0.252471	−	0.967604i	$-0.581243\pi$
$541$	−11.7447			−0.504943			−0.252471	+	0.967604i	$0.581243\pi$
$542$	−7.20192			−0.309349
$543$	−21.5285	+	11.0071i	−0.923876	+	0.472362i
$544$	−15.8950			−0.681492
$545$	27.0008	−	46.7668i	1.15659	−	2.00327i
$546$	−0.785094	−	2.11884i	−0.0335989	−	0.0906780i
$547$	0.492671	+	0.853331i	0.0210651	+	0.0364858i	0.876366	−	0.481646i	$-0.159961\pi$
$547$	0.492671	+	0.853331i	0.0210651	+	0.0364858i	−0.855301	+	0.518132i	$0.826628\pi$
$548$	−4.33087	−	7.50129i	−0.185006	−	0.320439i
$549$	9.02318	−	12.4924i	0.385100	−	0.533164i
$550$	7.20540	−	12.4801i	0.307239	−	0.532154i
$551$	7.99398	+	13.8460i	0.340555	+	0.589859i
$552$	15.8539	−	8.10579i	0.674785	−	0.345006i
$553$	1.99894	+	3.46227i	0.0850036	+	0.147231i
$554$	−0.290308	+	0.502828i	−0.0123340	+	0.0213631i
$555$	−23.0713	+	11.7960i	−0.979324	+	0.500711i
$556$	5.92380	−	10.2603i	0.251225	−	0.435134i
$557$	12.1835	+	21.1025i	0.516233	+	0.894141i	0.999822	+	0.0188462i	$0.00599930\pi$
$557$	12.1835	+	21.1025i	0.516233	+	0.894141i	−0.483590	+	0.875295i	$0.660667\pi$
$558$	23.6990	+	2.42409i	1.00326	+	0.102620i
$559$	0.0690500	−	0.0296681i	0.00292050	−	0.00125483i
$560$	−1.47684	−	2.55796i	−0.0624079	−	0.108094i
$561$	9.85605	+	6.38108i	0.416123	+	0.269409i
$562$	15.3443			0.647259
$563$	−16.9796	−	29.4095i	−0.715603	−	1.23946i	−0.962726	−	0.270477i	$-0.912819\pi$
$563$	−16.9796	−	29.4095i	−0.715603	−	1.23946i	0.247123	−	0.968984i	$-0.420515\pi$
$564$	0.0925759	−	1.81485i	0.00389815	−	0.0764190i
$565$	−19.9686			−0.840085
$566$	5.48746	−	9.50456i	0.230655	−	0.399507i
$567$	−0.849939	−	2.56706i	−0.0356941	−	0.107806i
$568$	14.2496	−	24.6810i	0.597899	−	1.03559i
$569$	12.0308	−	20.8379i	0.504356	−	0.873571i	−0.495631	−	0.868533i	$-0.665063\pi$
$569$	12.0308	−	20.8379i	0.504356	−	0.873571i	0.999987	−	0.00503776i	$-0.00160358\pi$
$570$	−11.6630	+	5.96310i	−0.488510	+	0.249767i
$571$	−2.33817	+	4.04984i	−0.0978495	+	0.169480i	−0.910794	−	0.412860i	$-0.864530\pi$
$571$	−2.33817	+	4.04984i	−0.0978495	+	0.169480i	0.812945	+	0.582341i	$0.197863\pi$
$572$	2.33952	−	1.00520i	0.0978200	−	0.0420295i
$573$	21.4042	−	10.9436i	0.894172	−	0.457175i
$574$	0.518746	−	0.898495i	0.0216521	−	0.0375025i
$575$	15.5936	+	27.0089i	0.650297	+	1.12635i
$576$	15.5000	−	21.4595i	0.645833	−	0.894144i
$577$	−24.2913			−1.01126			−0.505630	−	0.862750i	$-0.668740\pi$
$577$	−24.2913			−1.01126			−0.505630	+	0.862750i	$0.668740\pi$
$578$	−13.0618			−0.543301
$579$	−12.4025	+	6.34117i	−0.515430	+	0.263530i
$580$	10.0178	−	17.3513i	0.415965	−	0.720473i
$581$	−1.93951	−	3.35933i	−0.0804644	−	0.139368i
$582$	0.399957	−	7.84073i	0.0165788	−	0.325009i
$583$	4.59411	−	7.95723i	0.190269	−	0.329555i
$584$	−14.4164			−0.596557
$585$	30.1303	+	27.6955i	1.24574	+	1.14507i
$586$	−4.94212			−0.204157
$587$	8.51672	−	14.7514i	0.351522	−	0.608855i	−0.634994	−	0.772517i	$-0.718997\pi$
$587$	8.51672	−	14.7514i	0.351522	−	0.608855i	0.986516	+	0.163662i	$0.0523307\pi$
$588$	5.52297	+	3.57573i	0.227764	+	0.147460i
$589$	−5.47239	−	9.47846i	−0.225486	−	0.390553i
$590$	−19.9074	+	34.4806i	−0.819575	+	1.41955i
$591$	−4.37346	−	2.83150i	−0.179900	−	0.116472i
$592$	10.2737			0.422245
$593$	16.1029			0.661266			0.330633	−	0.943759i	$-0.392738\pi$
$593$	16.1029			0.661266			0.330633	+	0.943759i	$0.392738\pi$
$594$	−7.49251	+	2.91211i	−0.307421	+	0.119485i
$595$	2.99940	+	5.19511i	0.122963	+	0.212979i
$596$	−3.53868	+	6.12917i	−0.144950	+	0.251061i
$597$	1.84236	−	36.1175i	0.0754030	−	1.47819i
$598$	1.70831	−	14.4363i	0.0698580	−	0.590345i
$599$	−10.4601	+	18.1175i	−0.427390	+	0.740261i	−0.996640	−	0.0819032i	$-0.973900\pi$
$599$	−10.4601	+	18.1175i	−0.427390	+	0.740261i	0.569250	+	0.822164i	$0.307234\pi$
$600$	41.5869	+	26.9245i	1.69778	+	1.09919i
$601$	−1.19984	+	2.07818i	−0.0489425	+	0.0847709i	−0.889459	−	0.457015i	$-0.848918\pi$
$601$	−1.19984	+	2.07818i	−0.0489425	+	0.0847709i	0.840516	+	0.541786i	$0.182252\pi$
$602$	−0.00377096	+	0.00653149i	−0.000153693	+	0.000266204i
$603$	14.5997	−	20.2130i	0.594544	−	0.823136i
$604$	3.41686	−	5.91817i	0.139030	−	0.240807i
$605$	35.3752			1.43821
$606$	8.73985	+	5.65842i	0.355032	+	0.229858i
$607$	20.9512	+	36.2885i	0.850382	+	1.47291i	0.880864	+	0.473370i	$0.156963\pi$
$607$	20.9512	+	36.2885i	0.850382	+	1.47291i	−0.0304814	+	0.999535i	$0.509704\pi$
$608$	−4.99960			−0.202760
$609$	−0.255370	+	5.00624i	−0.0103481	+	0.202863i
$610$	−11.7026	−	20.2694i	−0.473823	−	0.820685i
$611$	−5.51349	−	4.11692i	−0.223052	−	0.166553i
$612$	−5.09589	+	7.05517i	−0.205989	+	0.285188i
$613$	−6.47866	−	11.2214i	−0.261671	−	0.453227i	0.705015	−	0.709192i	$-0.250940\pi$
$613$	−6.47866	−	11.2214i	−0.261671	−	0.453227i	−0.966686	+	0.255965i	$0.917607\pi$
$614$	12.6724	−	21.9492i	0.511415	−	0.885797i
$615$	−0.957273	+	18.7663i	−0.0386010	+	0.756730i
$616$	−0.592576	+	1.02637i	−0.0238756	+	0.0413537i
$617$	7.28332	+	12.6151i	0.293216	+	0.507864i	0.974568	−	0.224091i	$-0.0719413\pi$
$617$	7.28332	+	12.6151i	0.293216	+	0.507864i	−0.681353	+	0.731955i	$0.738608\pi$
$618$	7.59047	+	4.91428i	0.305333	+	0.197681i
$619$	4.73531	+	8.20179i	0.190328	+	0.329658i	0.945359	−	0.326031i	$-0.105711\pi$
$619$	4.73531	+	8.20179i	0.190328	+	0.329658i	−0.755031	+	0.655689i	$0.772378\pi$
$620$	−6.85780	+	11.8781i	−0.275416	+	0.477034i
$621$	2.64956	−	17.1937i	0.106323	−	0.689958i
$622$	16.6520	+	28.8420i	0.667683	+	1.15646i
$623$	0.961181	+	1.66481i	0.0385089	+	0.0666994i
$624$	−5.63772	−	15.2153i	−0.225689	−	0.609099i
$625$	−7.59854	+	13.1611i	−0.303941	+	0.526442i
$626$	−2.75571			−0.110141
$627$	3.10011	+	2.00710i	0.123807	+	0.0801558i
$628$	6.20580			0.247638
$629$	−20.8654			−0.831956
$630$	−4.08566	−	0.417908i	−0.162776	−	0.0166499i
$631$	24.2342	−	41.9749i	0.964749	−	1.67099i	0.254461	−	0.967083i	$-0.418102\pi$
$631$	24.2342	−	41.9749i	0.964749	−	1.67099i	0.710288	−	0.703911i	$-0.248565\pi$
$632$	20.4286	+	35.3833i	0.812605	+	1.40747i
$633$	27.8901	−	14.2597i	1.10853	−	0.566774i
$634$	24.5259			0.974048
$635$	−40.5732			−1.61010
$636$	5.71701	+	3.70135i	0.226694	+	0.146768i
$637$	22.8900	−	9.83493i	0.906933	−	0.389674i
$638$	14.9015			0.589956
$639$	−11.3961	−	25.4053i	−0.450823	−	1.00502i
$640$	−8.70603	−	15.0793i	−0.344136	−	0.596061i
$641$	−0.768707			−0.0303621			−0.0151811	−	0.999885i	$-0.504832\pi$
$641$	−0.768707			−0.0303621			−0.0151811	+	0.999885i	$0.504832\pi$
$642$	−5.85035	+	2.99118i	−0.230895	+	0.118053i
$643$	0.142264	+	0.246408i	0.00561034	+	0.00971740i	0.868817	−	0.495133i	$-0.164881\pi$
$643$	0.142264	+	0.246408i	0.00561034	+	0.00971740i	−0.863207	+	0.504851i	$0.831547\pi$
$644$	−0.276504	−	0.478919i	−0.0108958	−	0.0188721i
$645$	0.00695877	−	0.136419i	0.000274001	−	0.00537149i
$646$	−10.5478			−0.414999
$647$	14.6716	+	25.4119i	0.576798	+	0.999044i	0.995844	+	0.0910787i	$0.0290315\pi$
$647$	14.6716	+	25.4119i	0.576798	+	0.999044i	−0.419045	+	0.907965i	$0.637635\pi$
$648$	−8.68612	−	26.2346i	−0.341223	−	1.03059i
$649$	11.2253			0.440633
$650$	37.1619	−	15.9670i	1.45761	−	0.626278i
$651$	0.174817	−	3.42709i	0.00685161	−	0.134318i
$652$	−3.63819			−0.142483
$653$	−49.6340			−1.94233			−0.971164	−	0.238413i	$-0.923373\pi$
$653$	−49.6340			−1.94233			−0.971164	+	0.238413i	$0.923373\pi$
$654$	−1.51664	+	29.7321i	−0.0593054	+	1.16262i
$655$	−6.32683	−	10.9584i	−0.247210	−	0.428180i
$656$	3.72509	−	6.45205i	0.145440	−	0.251910i
$657$	−8.24722	+	11.4181i	−0.321755	+	0.445464i
$658$	0.690524			0.0269194
$659$	−42.8101			−1.66765			−0.833823	−	0.552032i	$-0.813852\pi$
$659$	−42.8101			−1.66765			−0.833823	+	0.552032i	$0.813852\pi$
$660$	0.235773	−	4.62207i	0.00917746	−	0.179914i
$661$	−35.3171			−1.37367			−0.686837	−	0.726811i	$-0.741001\pi$
$661$	−35.3171			−1.37367			−0.686837	+	0.726811i	$0.741001\pi$
$662$	10.5034	−	18.1924i	0.408225	−	0.707067i
$663$	11.4500	+	30.9016i	0.444680	+	1.20012i
$664$	−19.8212	−	34.3313i	−0.769212	−	1.33231i
$665$	0.943427	+	1.63406i	0.0365845	+	0.0633663i
$666$	8.36433	−	11.5803i	0.324111	−	0.448726i
$667$	−16.1246	+	27.9285i	−0.624345	+	1.08140i
$668$	2.98363	+	5.16780i	0.115440	+	0.199948i
$669$	2.00651	−	39.3354i	0.0775760	−	1.52079i
$670$	−18.9349	−	32.7963i	−0.731521	−	1.26703i
$671$	−3.29940	+	5.71473i	−0.127372	+	0.220615i
$672$	−1.31584	−	0.851909i	−0.0507595	−	0.0328631i
$673$	−17.3693	+	30.0845i	−0.669537	+	1.15967i	0.308497	+	0.951225i	$0.400174\pi$
$673$	−17.3693	+	30.0845i	−0.669537	+	1.15967i	−0.978034	+	0.208446i	$0.933159\pi$
$674$	−15.0340	−	26.0397i	−0.579089	−	1.00301i
$675$	45.1154	−	17.5350i	1.73649	−	0.674921i
$676$	6.94940	+	1.66806i	0.267285	+	0.0641562i
$677$	9.05262	+	15.6796i	0.347920	+	0.602616i	0.985880	−	0.167454i	$-0.0535546\pi$
$677$	9.05262	+	15.6796i	0.347920	+	0.602616i	−0.637959	+	0.770070i	$0.720221\pi$
$678$	9.80172	−	5.01145i	0.376433	−	0.192463i
$679$	−1.13089			−0.0433995
$680$	30.6529	+	53.0924i	1.17549	+	2.03600i
$681$	−7.57415	+	3.87253i	−0.290242	+	0.148396i
$682$	−10.2010			−0.390617
$683$	−11.6147	+	20.1173i	−0.444426	+	0.769768i	−0.998012	−	0.0630237i	$-0.979926\pi$
$683$	−11.6147	+	20.1173i	−0.444426	+	0.769768i	0.553586	+	0.832792i	$0.313259\pi$
$684$	−1.60286	+	2.21913i	−0.0612868	+	0.0848504i
$685$	−29.8062	+	51.6259i	−1.13884	+	1.97252i
$686$	−2.51646	+	4.35864i	−0.0960790	+	0.166414i
$687$	−0.347726	+	6.81680i	−0.0132666	+	0.260077i
$688$	−0.0270790	+	0.0469023i	−0.00103238	+	0.00178813i
$689$	23.6941	−	10.1805i	0.902675	−	0.387845i
$690$	−22.1793	−	14.3595i	−0.844351	−	0.546656i
$691$	2.25475	−	3.90535i	0.0857748	−	0.148566i	−0.819946	−	0.572440i	$-0.805997\pi$
$691$	2.25475	−	3.90535i	0.0857748	−	0.148566i	0.905721	+	0.423874i	$0.139330\pi$
$692$	0.0569276	+	0.0986015i	0.00216406	+	0.00374827i
$693$	0.473913	+	1.05649i	0.0180025	+	0.0401328i
$694$	12.1973			0.463002
$695$	−81.5383			−3.09292
$696$	−2.60980	+	51.1623i	−0.0989242	+	1.93930i
$697$	−7.56549	+	13.1038i	−0.286564	+	0.496343i
$698$	13.5895	+	23.5376i	0.514369	+	0.890913i
$699$	−3.85206	+	1.96949i	−0.145698	+	0.0744930i
$700$	0.769327	−	1.33251i	0.0290778	−	0.0503643i
$701$	−12.6104			−0.476288			−0.238144	−	0.971230i	$-0.576539\pi$
$701$	−12.6104			−0.476288			−0.238144	+	0.971230i	$0.576539\pi$
$702$	−21.7403	−	6.03284i	−0.820536	−	0.227695i
$703$	−6.56297			−0.247527
$704$	−5.66770	+	9.81675i	−0.213610	+	0.369983i
$705$	−11.1355	+	5.69337i	−0.419386	+	0.214425i
$706$	14.9941	+	25.9706i	0.564311	+	0.977415i
$707$	0.749876	−	1.29882i	0.0282020	−	0.0488473i
$708$	−0.423883	+	8.30976i	−0.0159305	+	0.312300i
$709$	−50.2539			−1.88732			−0.943662	−	0.330910i	$-0.892644\pi$
$709$	−50.2539			−1.88732			−0.943662	+	0.330910i	$0.892644\pi$
$710$	−42.2896			−1.58710
$711$	39.7109	+	4.06190i	1.48928	+	0.152333i
$712$	9.82298	+	17.0139i	0.368132	+	0.637623i
$713$	11.0383	−	19.1189i	0.413387	−	0.716007i
$714$	−2.77607	−	1.79731i	−0.103892	−	0.0672625i
$715$	−14.0418	−	10.4850i	−0.525133	−	0.392117i
$716$	2.74235	−	4.74989i	0.102486	−	0.177512i
$717$	0.751149	−	14.7255i	0.0280522	−	0.549932i
$718$	−21.5281	+	37.2878i	−0.803423	+	1.39157i
$719$	21.5058	−	37.2492i	0.802031	−	1.38916i	−0.116246	−	0.993221i	$-0.537086\pi$
$719$	21.5058	−	37.2492i	0.802031	−	1.38916i	0.918277	−	0.395939i	$-0.129581\pi$
$720$	−29.3389	−	3.00098i	−1.09340	−	0.111840i
$721$	0.651259	−	1.12801i	0.0242542	−	0.0420094i
$722$	19.5633			0.728070
$723$	−25.0302	+	12.7975i	−0.930883	+	0.475944i
$724$	3.83724	+	6.64629i	0.142610	+	0.247007i
$725$	−89.7278			−3.33241
$726$	−17.3642	+	8.87799i	−0.644444	+	0.329493i
$727$	6.80760	+	11.7911i	0.252480	+	0.437308i	0.964208	−	0.265147i	$-0.0854205\pi$
$727$	6.80760	+	11.7911i	0.252480	+	0.437308i	−0.711728	+	0.702455i	$0.752087\pi$
$728$	−3.05622	+	1.31314i	−0.113271	+	0.0486681i
$729$	−25.7474	−	8.12842i	−0.953607	−	0.301053i
$730$	10.6962	+	18.5263i	0.395884	+	0.685690i
$731$	0.0549963	−	0.0952565i	0.00203411	−	0.00352319i
$732$	−4.10585	−	2.65824i	−0.151757	−	0.0982514i
$733$	23.0761	−	39.9690i	0.852336	−	1.47629i	−0.0267594	−	0.999642i	$-0.508519\pi$
$733$	23.0761	−	39.9690i	0.852336	−	1.47629i	0.879095	−	0.476647i	$-0.158148\pi$
$734$	−8.05878	−	13.9582i	−0.297455	−	0.515207i
$735$	2.30682	−	45.2227i	0.0850883	−	1.66806i
$736$	−5.04231	−	8.73353i	−0.185862	−	0.321922i
$737$	−5.33849	+	9.24654i	−0.196646	+	0.340601i
$738$	−4.23982	−	9.45180i	−0.156070	−	0.347926i
$739$	−0.339921	−	0.588761i	−0.0125042	−	0.0216579i	0.859706	−	0.510790i	$-0.170647\pi$
$739$	−0.339921	−	0.588761i	−0.0125042	−	0.0216579i	−0.872210	+	0.489132i	$0.837314\pi$
$740$	4.11223	+	7.12260i	0.151169	+	0.261832i
$741$	3.60146	+	9.71974i	0.132303	+	0.357064i
$742$	−1.29398	+	2.24125i	−0.0475036	+	0.0822787i
$743$	26.5298			0.973284			0.486642	−	0.873601i	$-0.338222\pi$
$743$	26.5298			0.973284			0.486642	+	0.873601i	$0.338222\pi$
$744$	1.78657	−	35.0238i	0.0654990	−	1.28404i
$745$	48.7083			1.78453
$746$	−8.60976			−0.315226
$747$	−38.5303	−	3.94113i	−1.40975	−	0.144199i
$748$	1.86336	−	3.22743i	0.0681310	−	0.118006i
$749$	0.473238	+	0.819672i	0.0172917	+	0.0299502i
$750$	1.73490	−	34.0109i	0.0633497	−	1.24190i
$751$	32.0132			1.16818			0.584088	−	0.811690i	$-0.301452\pi$
$751$	32.0132			1.16818			0.584088	+	0.811690i	$0.301452\pi$
$752$	4.95862			0.180822
$753$	−2.07275	+	40.6340i	−0.0755353	+	1.48079i
$754$	33.5123	+	25.0236i	1.22045	+	0.911308i
$755$	−47.0315			−1.71165
$756$	−0.799983	+	0.310929i	−0.0290951	+	0.0113084i
$757$	10.5610	+	18.2922i	0.383846	+	0.664840i	0.991608	−	0.129278i	$-0.0412661\pi$
$757$	10.5610	+	18.2922i	0.383846	+	0.664840i	−0.607763	+	0.794119i	$0.707933\pi$
$758$	33.1112			1.20265
$759$	−0.379499	+	7.43967i	−0.0137750	+	0.270043i
$760$	9.64154	+	16.6996i	0.349736	+	0.605760i
$761$	12.2230	+	21.1708i	0.443083	+	0.767442i	0.997916	−	0.0645194i	$-0.0205514\pi$
$761$	12.2230	+	21.1708i	0.443083	+	0.767442i	−0.554834	+	0.831961i	$0.687218\pi$
$762$	19.9156	−	10.1825i	0.721467	−	0.368873i
$763$	4.28834			0.155248
$764$	−3.81508	−	6.60791i	−0.138025	−	0.239066i
$765$	59.5860	+	6.09485i	2.15434	+	0.220360i
$766$	13.6383			0.492770
$767$	25.2449	+	18.8504i	0.911541	+	0.680647i
$768$	−17.6011	−	11.3954i	−0.635123	−	0.411197i
$769$	−8.72140			−0.314502			−0.157251	−	0.987559i	$-0.550263\pi$
$769$	−8.72140			−0.314502			−0.157251	+	0.987559i	$0.550263\pi$
$770$	1.75863			0.0633767
$771$	8.83870	−	4.51907i	0.318318	−	0.162750i
$772$	2.21062	+	3.82890i	0.0795619	+	0.137805i
$773$	−0.571592	+	0.990027i	−0.0205587	+	0.0356088i	−0.876122	−	0.482090i	$-0.839878\pi$
$773$	−0.571592	+	0.990027i	−0.0205587	+	0.0356088i	0.855563	+	0.517699i	$0.173211\pi$
$774$	0.0308208	+	0.0687086i	0.00110783	+	0.00246968i
$775$	61.4244			2.20643
$776$	−11.5573			−0.414884
$777$	−1.72730	−	1.11830i	−0.0619664	−	0.0401188i
$778$	−18.6760			−0.669568
$779$	−2.37964	+	4.12166i	−0.0852596	+	0.147674i
$780$	8.29195	−	9.99877i	0.296899	−	0.358013i
$781$	5.96153	+	10.3257i	0.213320	+	0.369481i
$782$	−10.6380	−	18.4255i	−0.380413	−	0.658894i
$783$	39.0286	+	31.3355i	1.39477	+	1.11984i
$784$	−8.97665	+	15.5480i	−0.320595	+	0.555286i
$785$	−21.3550	−	36.9879i	−0.762192	−	1.32015i
$786$	5.85576	+	3.79118i	0.208868	+	0.135227i
$787$	−7.29553	−	12.6362i	−0.260058	−	0.450433i	0.706199	−	0.708013i	$-0.250408\pi$
$787$	−7.29553	−	12.6362i	−0.260058	−	0.450433i	−0.966257	+	0.257580i	$0.917075\pi$
$788$	−0.826834	+	1.43212i	−0.0294547	+	0.0510171i
$789$	−0.0470592	+	0.922545i	−0.00167535	+	0.0328435i
$790$	30.3137	−	52.5048i	1.07851	−	1.86804i
$791$	−0.792866	−	1.37328i	−0.0281911	−	0.0488283i
$792$	4.84325	+	10.7970i	0.172097	+	0.383655i
$793$	−17.0167	+	7.31142i	−0.604281	+	0.259636i
$794$	7.04087	+	12.1951i	0.249871	+	0.432789i
$795$	2.38786	−	46.8115i	0.0846888	−	1.66023i
$796$	−11.4786			−0.406849
$797$	9.89726	+	17.1426i	0.350579	+	0.607221i	0.986351	−	0.164656i	$-0.0526515\pi$
$797$	9.89726	+	17.1426i	0.350579	+	0.607221i	−0.635772	+	0.771877i	$0.719318\pi$
$798$	−0.873183	−	0.565323i	−0.0309103	−	0.0200122i
$799$	−10.0707			−0.356277
$800$	14.0294	−	24.2996i	0.496014	−	0.859121i
$801$	19.0948	+	1.95314i	0.674682	+	0.0690109i
$802$	0.430943	−	0.746415i	0.0152171	−	0.0263568i
$803$	3.01567	−	5.22329i	0.106421	−	0.184326i
$804$	−6.64333	−	4.30108i	−0.234292	−	0.151687i
$805$	−1.90297	+	3.29605i	−0.0670710	+	0.116170i
$806$	−22.9413	−	17.1303i	−0.808074	−	0.603388i
$807$	−0.148570	+	2.91255i	−0.00522991	+	0.102527i
$808$	7.66351	−	13.2736i	0.269601	−	0.466963i
$809$	13.6595	+	23.6589i	0.480241	+	0.831802i	0.999743	−	0.0226673i	$-0.00721584\pi$
$809$	13.6595	+	23.6589i	0.480241	+	0.831802i	−0.519502	+	0.854469i	$0.673883\pi$
$810$	−27.2690	+	30.6270i	−0.958135	+	1.07612i
$811$	38.3231			1.34571			0.672854	−	0.739776i	$-0.265068\pi$
$811$	38.3231			1.34571			0.672854	+	0.739776i	$0.265068\pi$
$812$	1.59105			0.0558348
$813$	8.69504	+	5.62941i	0.304948	+	0.197432i
$814$	−3.05849	+	5.29746i	−0.107200	+	0.185676i
$815$	12.5195	+	21.6844i	0.438539	+	0.759572i
$816$	−19.9348	−	12.9064i	−0.697858	−	0.451813i
$817$	0.0172985	−	0.0299619i	0.000605198	−	0.00104823i
$818$	4.20774			0.147120
$819$	−0.708339	+	3.17180i	−0.0247514	+	0.110832i
$820$	5.96416			0.208278
$821$	−27.2978	+	47.2812i	−0.952700	+	1.65013i	−0.213156	+	0.977018i	$0.568374\pi$
$821$	−27.2978	+	47.2812i	−0.952700	+	1.65013i	−0.739545	+	0.673107i	$0.764959\pi$
$822$	1.67422	−	32.8213i	0.0583952	−	1.14477i
$823$	26.4160	+	45.7538i	0.920804	+	1.59488i	0.798174	+	0.602426i	$0.205799\pi$
$823$	26.4160	+	45.7538i	0.920804	+	1.59488i	0.122629	+	0.992453i	$0.460867\pi$
$824$	6.65567	−	11.5280i	0.231861	−	0.401596i
$825$	−18.4544	+	9.43540i	−0.642499	+	0.328498i
$826$	−3.16174			−0.110011
$827$	20.8919			0.726482			0.363241	−	0.931695i	$-0.381670\pi$
$827$	20.8919			0.726482			0.363241	+	0.931695i	$0.381670\pi$
$828$	−5.49303	−	0.561863i	−0.190896	−	0.0195261i
$829$	−7.33261	−	12.7005i	−0.254672	−	0.441105i	0.710134	−	0.704066i	$-0.248634\pi$
$829$	−7.33261	−	12.7005i	−0.254672	−	0.441105i	−0.964806	+	0.262961i	$0.915301\pi$
$830$	−29.4124	+	50.9438i	−1.02092	+	1.76829i
$831$	0.743534	−	0.380156i	0.0257929	−	0.0131875i
$832$	−29.2312	+	12.5595i	−1.01341	+	0.435423i
$833$	18.2312	−	31.5773i	0.631673	−	1.09409i
$834$	40.0236	−	20.4634i	1.38590	−	0.708589i
$835$	20.5341	−	35.5662i	0.710613	−	1.23082i
$836$	0.586098	−	1.01515i	0.0202706	−	0.0351098i
$837$	−26.7176	−	21.4511i	−0.923495	−	0.741459i
$838$	−11.0065	+	19.0638i	−0.380213	+	0.658549i
$839$	4.51106			0.155739			0.0778696	−	0.996964i	$-0.475188\pi$
$839$	4.51106			0.155739			0.0778696	+	0.996964i	$0.475188\pi$
$840$	−0.308001	+	6.03803i	−0.0106271	+	0.208332i
$841$	−31.8916	−	55.2378i	−1.09971	−	1.90475i
$842$	−4.10112			−0.141334
$843$	−18.5255	−	11.9939i	−0.638052	−	0.413092i
$844$	−4.97114	−	8.61026i	−0.171114	−	0.296377i
$845$	−13.9718	−	47.1599i	−0.480644	−	1.62235i
$846$	4.03707	−	5.58925i	0.138797	−	0.192163i
$847$	1.40460	+	2.43283i	0.0482625	+	0.0835930i
$848$	−9.29203	+	16.0943i	−0.319090	+	0.552679i
$849$	−14.0544	+	7.18578i	−0.482347	+	0.246615i
$850$	29.5984	−	51.2659i	1.01522	−	1.75841i
$851$	−6.61903	−	11.4645i	−0.226898	−	0.392998i
$852$	−7.86889	+	4.02322i	−0.269584	+	0.137833i
$853$	11.4853	+	19.8932i	0.393250	+	0.681129i	0.992876	−	0.119151i	$-0.0380174\pi$
$853$	11.4853	+	19.8932i	0.393250	+	0.681129i	−0.599626	+	0.800280i	$0.704684\pi$
$854$	0.929315	−	1.60962i	0.0318005	−	0.0550801i
$855$	18.7421	+	1.91707i	0.640967	+	0.0655623i
$856$	4.83635	+	8.37680i	0.165303	+	0.286313i
$857$	−20.3594	−	35.2635i	−0.695463	−	1.20458i	−0.970024	−	0.243008i	$-0.921866\pi$
$857$	−20.3594	−	35.2635i	−0.695463	−	1.20458i	0.274561	−	0.961570i	$-0.411467\pi$
$858$	9.52389	+	1.62261i	0.325140	+	0.0553951i
$859$	−26.7637	+	46.3561i	−0.913167	+	1.58165i	−0.103603	+	0.994619i	$0.533037\pi$
$859$	−26.7637	+	46.3561i	−0.913167	+	1.58165i	−0.809563	+	0.587033i	$0.800296\pi$
$860$	−0.0433557			−0.00147842
$861$	−1.32861	+	0.679294i	−0.0452788	+	0.0231503i
$862$	−18.0927			−0.616241
$863$	26.8211			0.913000			0.456500	−	0.889724i	$-0.349103\pi$
$863$	26.8211			0.913000			0.456500	+	0.889724i	$0.349103\pi$
$864$	−14.5884	+	5.67007i	−0.496308	+	0.192900i
$865$	0.391791	−	0.678601i	0.0133213	−	0.0230731i
$866$	−1.21785	−	2.10938i	−0.0413842	−	0.0716796i
$867$	15.7699	+	10.2099i	0.535573	+	0.346745i
$868$	−1.08917			−0.0369689
$869$	−17.0932			−0.579847
$870$	67.6841	−	34.6057i	2.29471	−	1.17324i
$871$	−27.5333	+	11.8300i	−0.932930	+	0.400844i
$872$	43.8255			1.48412
$873$	−6.61162	+	9.15366i	−0.223769	+	0.309804i
$874$	−3.34605	−	5.79553i	−0.113182	−	0.196037i
$875$	−4.90548			−0.165836
$876$	3.75276	+	2.42964i	0.126794	+	0.0820900i
$877$	12.3170	+	21.3337i	0.415917	+	0.720390i	0.995524	−	0.0945065i	$-0.0301273\pi$
$877$	12.3170	+	21.3337i	0.415917	+	0.720390i	−0.579607	+	0.814896i	$0.696794\pi$
$878$	7.93203	+	13.7387i	0.267693	+	0.463658i
$879$	5.96674	+	3.86303i	0.201253	+	0.130297i
$880$	12.6286			0.425712
$881$	−14.7520	−	25.5512i	−0.497008	−	0.860843i	0.502986	−	0.864294i	$-0.332235\pi$
$881$	−14.7520	−	25.5512i	−0.497008	−	0.860843i	−0.999994	+	0.00345150i	$0.998901\pi$
$882$	10.2170	+	22.7768i	0.344026	+	0.766934i
$883$	−29.2625			−0.984761			−0.492380	−	0.870380i	$-0.663873\pi$
$883$	−29.2625			−0.984761			−0.492380	+	0.870380i	$0.663873\pi$
$884$	9.61027	−	4.12916i	0.323228	−	0.138879i
$885$	50.9866	−	26.0686i	1.71390	−	0.876285i
$886$	−13.2061			−0.443669
$887$	8.26501			0.277512			0.138756	−	0.990327i	$-0.455690\pi$
$887$	8.26501			0.277512			0.138756	+	0.990327i	$0.455690\pi$
$888$	−17.6525	−	11.4287i	−0.592378	−	0.383522i
$889$	−1.61098	−	2.79031i	−0.0540307	−	0.0935839i
$890$	14.5762	−	25.2467i	0.488595	−	0.846271i
$891$	11.3221	+	2.34070i	0.379306	+	0.0784163i
$892$	−12.5013			−0.418574
$893$	−3.16764			−0.106001
$894$	−23.9088	+	12.2241i	−0.799629	+	0.408836i
$895$	−37.7472			−1.26175
$896$	0.691357	−	1.19747i	0.0230966	−	0.0400045i
$897$	−13.3467	+	16.0940i	−0.445633	+	0.537362i
$898$	21.8539	+	37.8521i	0.729274	+	1.26314i
$899$	31.7580	+	55.0064i	1.05919	+	1.83457i
$900$	−6.28787	−	14.0175i	−0.209596	−	0.467250i
$901$	18.8717	−	32.6867i	0.628708	−	1.08895i
$902$	2.21793	+	3.84157i	0.0738491	+	0.127910i
$903$	0.00965813	−	0.00493803i	0.000321402	−	0.000164327i
$904$	−8.10285	−	14.0345i	−0.269497	−	0.466782i
$905$	26.4089	−	45.7415i	0.877861	−	1.52050i
$906$	23.0857	−	11.8033i	0.766971	−	0.392139i
$907$	−9.21731	+	15.9648i	−0.306056	+	0.530104i	−0.977496	−	0.210955i	$-0.932343\pi$
$907$	−9.21731	+	15.9648i	−0.306056	+	0.530104i	0.671440	+	0.741059i	$0.265676\pi$
$908$	1.35002	+	2.33830i	0.0448019	+	0.0775991i
$909$	−6.12889	−	13.6631i	−0.203283	−	0.453176i
$910$	3.95503	+	2.95322i	0.131108	+	0.0978983i
$911$	−23.0212	−	39.8739i	−0.762726	−	1.32108i	−0.941441	−	0.337179i	$-0.890527\pi$
$911$	−23.0212	−	39.8739i	−0.762726	−	1.32108i	0.178715	−	0.983901i	$-0.442806\pi$
$912$	−6.27028	−	4.05955i	−0.207630	−	0.134425i
$913$	16.5850			0.548883
$914$	−20.4596	−	35.4370i	−0.676743	−	1.17215i
$915$	−1.71492	+	33.6191i	−0.0566935	+	1.11141i
$916$	2.16646			0.0715820
$917$	0.502422	−	0.870220i	0.0165914	−	0.0287372i
$918$	−30.7778	+	11.9624i	−1.01582	+	0.394817i
$919$	16.5071	−	28.5912i	0.544520	−	0.943136i	−0.454117	−	0.890942i	$-0.650045\pi$
$919$	16.5071	−	28.5912i	0.544520	−	0.943136i	0.998637	−	0.0521939i	$-0.0166214\pi$
$920$	−19.4478	+	33.6846i	−0.641176	+	1.11055i
$921$	−32.4563	+	16.5943i	−1.06947	+	0.546802i
$922$	−6.94254	+	12.0248i	−0.228640	+	0.396017i
$923$	−3.93257	+	33.2327i	−0.129442	+	1.09387i
$924$	0.327232	−	0.167308i	0.0107651	−	0.00550402i
$925$	18.4164	−	31.8981i	0.605527	−	1.04880i
$926$	18.2764	+	31.6557i	0.600601	+	1.04027i
$927$	−5.32288	−	11.8662i	−0.174826	−	0.389739i
$928$	29.0142			0.952438
$929$	34.4070			1.12886			0.564429	−	0.825482i	$-0.309096\pi$
$929$	34.4070			1.12886			0.564429	+	0.825482i	$0.309096\pi$
$930$	−46.3341	+	23.6898i	−1.51936	+	0.776820i
$931$	5.73442	−	9.93231i	0.187938	−	0.325518i
$932$	0.686591	+	1.18921i	0.0224900	+	0.0389539i
$933$	2.44021	−	47.8377i	0.0798891	−	1.56614i
$934$	−0.992081	+	1.71833i	−0.0324619	+	0.0562256i
$935$	−25.6482			−0.838786
$936$	−7.23901	+	32.4148i	−0.236614	+	1.05951i
$937$	−3.49544			−0.114191			−0.0570956	−	0.998369i	$-0.518184\pi$
$937$	−3.49544			−0.114191			−0.0570956	+	0.998369i	$0.518184\pi$
$938$	1.50365	−	2.60439i	0.0490958	−	0.0850365i
$939$	3.32704	+	2.15402i	0.108574	+	0.0702937i
$940$	1.98478	+	3.43775i	0.0647365	+	0.112127i
$941$	−11.7060	+	20.2754i	−0.381605	+	0.660959i	−0.991292	−	0.131684i	$-0.957962\pi$
$941$	−11.7060	+	20.2754i	−0.381605	+	0.660959i	0.609687	+	0.792642i	$0.291295\pi$
$942$	19.7649	+	12.7964i	0.643977	+	0.416928i
$943$	−9.59989			−0.312615
$944$	−22.7043			−0.738963
$945$	4.60605	+	3.69812i	0.149835	+	0.120300i
$946$	−0.0161230	−	0.0279258i	−0.000524203	−	0.000907946i
$947$	20.3033	−	35.1664i	0.659769	−	1.14275i	−0.320906	−	0.947111i	$-0.603987\pi$
$947$	20.3033	−	35.1664i	0.659769	−	1.14275i	0.980675	−	0.195643i	$-0.0626792\pi$
$948$	0.645461	−	12.6536i	0.0209636	−	0.410968i
$949$	15.5533	−	6.68266i	0.504882	−	0.216928i
$950$	9.30984	−	16.1251i	0.302051	−	0.523168i
$951$	−29.6107	−	19.1708i	−0.960192	−	0.621655i
$952$	−2.43419	+	4.21614i	−0.0788925	+	0.136646i
$953$	24.9334	−	43.1859i	0.807672	−	1.39893i	−0.106801	−	0.994280i	$-0.534061\pi$
$953$	24.9334	−	43.1859i	0.807672	−	1.39893i	0.914473	−	0.404648i	$-0.132606\pi$
$954$	10.5760	+	23.5770i	0.342411	+	0.763333i
$955$	−26.2564	+	45.4774i	−0.849637	+	1.47161i
$956$	−4.67993			−0.151360
$957$	−17.9909	−	11.6478i	−0.581564	−	0.376521i
$958$	−6.37503	−	11.0419i	−0.205968	−	0.356747i
$959$	−4.73390			−0.152866
$960$	−2.94588	+	57.7508i	−0.0950780	+	1.86390i
$961$	−6.24036	−	10.8086i	−0.201302	−	0.348665i
$962$	−15.7742	+	6.77756i	−0.508580	+	0.218517i
$963$	9.40134	+	0.961631i	0.302954	+	0.0309881i
$964$	4.46138	+	7.72734i	0.143691	+	0.248881i
$965$	15.2141	−	26.3515i	0.489758	−	0.848285i
$966$	0.106890	−	2.09547i	0.00343914	−	0.0674206i
$967$	5.80396	−	10.0528i	0.186643	−	0.323275i	−0.757486	−	0.652851i	$-0.773573\pi$
$967$	5.80396	−	10.0528i	0.186643	−	0.323275i	0.944129	+	0.329576i	$0.106906\pi$
$968$	14.3545	+	24.8628i	0.461372	+	0.799120i
$969$	12.7347	+	8.24477i	0.409096	+	0.264860i
$970$	8.57489	+	14.8522i	0.275323	+	0.476874i
$971$	7.04458	−	12.2016i	0.226071	−	0.391567i	−0.730569	−	0.682839i	$-0.760745\pi$
$971$	7.04458	−	12.2016i	0.226071	−	0.391567i	0.956640	+	0.291272i	$0.0940785\pi$
$972$	−2.16029	+	8.29305i	−0.0692912	+	0.266000i
$973$	−3.23753	−	5.60756i	−0.103790	−	0.179770i
$974$	−16.0389	−	27.7802i	−0.513920	−	0.890136i
$975$	−57.3471	−	9.77040i	−1.83658	−	0.312903i
$976$	6.67336	−	11.5586i	0.213609	−	0.369982i
$977$	−13.3499			−0.427101			−0.213550	−	0.976932i	$-0.568503\pi$
$977$	−13.3499			−0.427101			−0.213550	+	0.976932i	$0.568503\pi$
$978$	−11.5873	−	7.50196i	−0.370522	−	0.239886i
$979$	−8.21918			−0.262686
$980$	−14.3723			−0.459107
$981$	25.0713	−	34.7108i	0.800465	−	1.10823i
$982$	14.0606	−	24.3536i	0.448690	−	0.777154i
$983$	−8.77579	−	15.2001i	−0.279904	−	0.484808i	0.691456	−	0.722418i	$-0.256969\pi$
$983$	−8.77579	−	15.2001i	−0.279904	−	0.484808i	−0.971361	+	0.237610i	$0.923636\pi$
$984$	−13.5780	+	6.94218i	−0.432850	+	0.221308i
$985$	11.3810			0.362628
$986$	61.2124			1.94940
$987$	−0.833686	−	0.539751i	−0.0265365	−	0.0171805i
$988$	3.02281	−	1.29878i	0.0961683	−	0.0413198i
$989$	0.0697851			0.00221904
$990$	10.2817	−	14.2348i	0.326772	−	0.452410i
$991$	12.8289	+	22.2202i	0.407522	+	0.705849i	0.994611	−	0.103673i	$-0.0330596\pi$
$991$	12.8289	+	22.2202i	0.407522	+	0.705849i	−0.587089	+	0.809522i	$0.699726\pi$
$992$	−19.8621			−0.630622
$993$	−26.9011	+	13.7541i	−0.853681	+	0.436472i
$994$	−1.67913	−	2.90834i	−0.0532589	−	0.0922471i
$995$	39.4994	+	68.4150i	1.25222	+	2.16890i
$996$	−0.626271	+	12.2774i	−0.0198441	+	0.389023i
$997$	18.2294			0.577330			0.288665	−	0.957430i	$-0.406789\pi$
$997$	18.2294			0.577330			0.288665	+	0.957430i	$0.406789\pi$
$998$	0.477110	+	0.826379i	0.0151027	+	0.0261586i
$999$	−19.1502	+	7.44310i	−0.605886	+	0.235489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.f.a.94.9	yes	24
3.2	odd	2		351.2.f.a.172.4		24
9.2	odd	6		351.2.h.a.289.9		24
9.7	even	3		117.2.h.a.16.4	yes	24
13.9	even	3		117.2.h.a.22.4	yes	24
39.35	odd	6		351.2.h.a.334.9		24
117.61	even	3	inner	117.2.f.a.61.9	✓	24
117.74	odd	6		351.2.f.a.100.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.9	✓	24	117.61	even	3	inner
117.2.f.a.94.9	yes	24	1.1	even	1	trivial
117.2.h.a.16.4	yes	24	9.7	even	3
117.2.h.a.22.4	yes	24	13.9	even	3
351.2.f.a.100.4		24	117.74	odd	6
351.2.f.a.172.4		24	3.2	odd	2
351.2.h.a.289.9		24	9.2	odd	6
351.2.h.a.334.9		24	39.35	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.602131 - 1.04292i) q^{2} +(-1.54217 + 0.788485i) q^{3} +(0.274876 + 0.476100i) q^{4} +(1.89177 - 3.27665i) q^{5} +(-0.106261 + 2.08313i) q^{6} +0.300456 q^{7} +3.07057 q^{8} +(1.75658 - 2.43196i) q^{9} +(-2.27819 - 3.94594i) q^{10} +(-0.642309 + 1.11251i) q^{11} +(-0.799304 - 0.517492i) q^{12} +(-3.31272 + 1.42335i) q^{13} +(0.180914 - 0.313352i) q^{14} +(-0.333851 + 6.54478i) q^{15} +(1.29913 - 2.25016i) q^{16} +(-2.63848 + 4.56998i) q^{17} +(-1.47865 - 3.29634i) q^{18} +(-0.829906 + 1.43744i) q^{19} +2.08001 q^{20} +(-0.463355 + 0.236905i) q^{21} +(0.773509 + 1.33976i) q^{22} -3.34798 q^{23} +(-4.73535 + 2.42110i) q^{24} +(-4.65760 - 8.06721i) q^{25} +(-0.510251 + 4.31194i) q^{26} +(-0.791390 + 5.13553i) q^{27} +(0.0825883 + 0.143047i) q^{28} +(4.81620 - 8.34190i) q^{29} +(6.62467 + 4.28900i) q^{30} +(-3.29700 + 5.71056i) q^{31} +(1.50607 + 2.60860i) q^{32} +(0.113352 - 2.22214i) q^{33} +(3.17742 + 5.50346i) q^{34} +(0.568394 - 0.984488i) q^{35} +(1.64070 + 0.167821i) q^{36} +(1.97702 + 3.42430i) q^{37} +(0.999424 + 1.73105i) q^{38} +(3.98649 - 4.80707i) q^{39} +(5.80882 - 10.0612i) q^{40} +2.86737 q^{41} +(-0.0319268 + 0.625890i) q^{42} -0.0208439 q^{43} -0.706223 q^{44} +(-4.64561 - 10.3564i) q^{45} +(-2.01592 + 3.49168i) q^{46} +(0.954216 + 1.65275i) q^{47} +(-0.229265 + 4.49449i) q^{48} -6.90973 q^{49} -11.2180 q^{50} +(0.465627 - 9.12810i) q^{51} +(-1.58824 - 1.18594i) q^{52} -7.15248 q^{53} +(4.87944 + 3.91762i) q^{54} +(2.43021 + 4.20924i) q^{55} +0.922571 q^{56} +(0.146458 - 2.87114i) q^{57} +(-5.79997 - 10.0458i) q^{58} +(-4.36913 - 7.56755i) q^{59} +(-3.20774 + 1.64006i) q^{60} +5.13678 q^{61} +(3.97045 + 6.87702i) q^{62} +(0.527776 - 0.730696i) q^{63} +8.82395 q^{64} +(-1.60310 + 13.5472i) q^{65} +(-2.24926 - 1.45623i) q^{66} +8.31140 q^{67} -2.90103 q^{68} +(5.16316 - 2.63983i) q^{69} +(-0.684496 - 1.18558i) q^{70} +(4.64070 - 8.03792i) q^{71} +(5.39371 - 7.46750i) q^{72} -4.69504 q^{73} +4.76171 q^{74} +(13.5437 + 8.76856i) q^{75} -0.912486 q^{76} +(-0.192986 + 0.334261i) q^{77} +(-2.61301 - 7.05208i) q^{78} +(6.65302 + 11.5234i) q^{79} +(-4.91533 - 8.51360i) q^{80} +(-2.82883 - 8.54387i) q^{81} +(1.72653 - 2.99044i) q^{82} +(-6.45522 - 11.1808i) q^{83} +(-0.240156 - 0.155483i) q^{84} +(9.98281 + 17.2907i) q^{85} +(-0.0125508 + 0.0217386i) q^{86} +(-0.849940 + 16.6621i) q^{87} +(-1.97226 + 3.41605i) q^{88} +(3.19907 + 5.54096i) q^{89} +(-13.5982 - 1.39091i) q^{90} +(-0.995325 + 0.427653i) q^{91} +(-0.920281 - 1.59397i) q^{92} +(0.581838 - 11.4063i) q^{93} +2.29825 q^{94} +(3.13998 + 5.43861i) q^{95} +(-4.37946 - 2.83539i) q^{96} -3.76391 q^{97} +(-4.16056 + 7.20630i) q^{98} +(1.57731 + 3.51629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

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