LMFDB - Embedded newform 324.2.p.a.203.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			203.23
Character	$\chi$	$=$	324.203
Dual form			324.2.p.a.83.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.456796 - 1.33841i) q^{2} +(1.02681 - 1.39487i) q^{3} +(-1.58267 + 1.22276i) q^{4} +(-0.874721 + 3.69074i) q^{5} +(-2.33595 - 0.737126i) q^{6} +(2.85958 + 2.12888i) q^{7} +(2.35951 + 1.55971i) q^{8} +(-0.891308 - 2.86454i) q^{9} +O(q^{10})$	\(q+(-0.456796 - 1.33841i) q^{2} +(1.02681 - 1.39487i) q^{3} +(-1.58267 + 1.22276i) q^{4} +(-0.874721 + 3.69074i) q^{5} +(-2.33595 - 0.737126i) q^{6} +(2.85958 + 2.12888i) q^{7} +(2.35951 + 1.55971i) q^{8} +(-0.891308 - 2.86454i) q^{9} +(5.33928 - 0.515181i) q^{10} +(-0.253209 - 0.268386i) q^{11} +(0.0804759 + 3.46317i) q^{12} +(1.86762 - 0.937956i) q^{13} +(1.54306 - 4.79975i) q^{14} +(4.24991 + 5.00982i) q^{15} +(1.00972 - 3.87046i) q^{16} +(2.09840 + 5.76530i) q^{17} +(-3.42677 + 2.50144i) q^{18} +(1.03264 - 2.83716i) q^{19} +(-3.12849 - 6.91081i) q^{20} +(5.90576 - 1.80277i) q^{21} +(-0.243545 + 0.461494i) q^{22} +(3.75651 + 5.04586i) q^{23} +(4.59837 - 1.68967i) q^{24} +(-8.38825 - 4.21274i) q^{25} +(-2.10849 - 2.07119i) q^{26} +(-4.91085 - 1.69809i) q^{27} +(-7.12890 + 0.127258i) q^{28} +(-3.89902 - 5.92817i) q^{29} +(4.76384 - 7.97659i) q^{30} +(2.55754 + 1.10321i) q^{31} +(-5.64149 + 0.416598i) q^{32} +(-0.634360 + 0.0776106i) q^{33} +(6.75779 - 5.44208i) q^{34} +(-10.3585 + 8.69179i) q^{35} +(4.91329 + 3.44377i) q^{36} +(-0.159326 - 0.133690i) q^{37} +(-4.26898 - 0.0860925i) q^{38} +(0.609378 - 3.56819i) q^{39} +(-7.82041 + 7.34403i) q^{40} +(-10.2366 - 0.596211i) q^{41} +(-5.11058 - 7.08082i) q^{42} +(7.05296 + 2.11152i) q^{43} +(0.728918 + 0.115154i) q^{44} +(11.3519 - 0.783915i) q^{45} +(5.03747 - 7.33267i) q^{46} +(-2.93833 - 6.81180i) q^{47} +(-4.36199 - 5.38266i) q^{48} +(1.63746 + 5.46949i) q^{49} +(-1.80664 + 13.1513i) q^{50} +(10.1965 + 2.99290i) q^{51} +(-1.80895 + 3.76814i) q^{52} +(6.38357 + 3.68555i) q^{53} +(-0.0294758 + 7.34841i) q^{54} +(1.21203 - 0.699765i) q^{55} +(3.42678 + 9.48325i) q^{56} +(-2.89713 - 4.35363i) q^{57} +(-6.15326 + 7.92645i) q^{58} +(2.92703 - 3.10247i) q^{59} +(-12.8520 - 2.73229i) q^{60} +(-1.15413 - 0.134898i) q^{61} +(0.308278 - 3.92697i) q^{62} +(3.54949 - 10.0889i) q^{63} +(3.13459 + 7.36032i) q^{64} +(1.82810 + 7.71336i) q^{65} +(0.393648 + 0.813581i) q^{66} +(4.04241 - 6.14618i) q^{67} +(-10.3707 - 6.55876i) q^{68} +(10.8955 - 0.0586662i) q^{69} +(16.3649 + 9.89349i) q^{70} +(-0.398446 + 2.25970i) q^{71} +(2.36480 - 8.14909i) q^{72} +(0.219535 + 1.24504i) q^{73} +(-0.106153 + 0.274312i) q^{74} +(-14.4894 + 7.37480i) q^{75} +(1.83483 + 5.75297i) q^{76} +(-0.152711 - 1.30652i) q^{77} +(-5.05406 + 0.814341i) q^{78} +(0.0782584 - 0.00455803i) q^{79} +(13.4016 + 7.11218i) q^{80} +(-7.41114 + 5.10637i) q^{81} +(3.87804 + 13.9730i) q^{82} +(-0.294342 - 5.05366i) q^{83} +(-7.14254 + 10.0745i) q^{84} +(-23.1137 + 2.70161i) q^{85} +(-0.395692 - 10.4043i) q^{86} +(-12.2726 - 0.648512i) q^{87} +(-0.178845 - 1.02819i) q^{88} +(-8.23009 + 1.45119i) q^{89} +(-6.23470 - 14.8354i) q^{90} +(7.33742 + 1.29379i) q^{91} +(-12.1152 - 3.39266i) q^{92} +(4.16495 - 2.43463i) q^{93} +(-7.77476 + 7.04429i) q^{94} +(9.56793 + 6.29293i) q^{95} +(-5.21166 + 8.29690i) q^{96} +(-12.4281 + 2.94552i) q^{97} +(6.57243 - 4.69003i) q^{98} +(-0.543113 + 0.964540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{53}{54}\right)$

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 $

$2$	−0.456796	−	1.33841i	−0.323004	−	0.946398i
$2$	−0.456796	−	1.33841i	−0.323004	−	0.946398i
$3$	1.02681	−	1.39487i	0.592831	−	0.805327i
$3$	1.02681	−	1.39487i	0.592831	−	0.805327i
$4$	−1.58267	+	1.22276i	−0.791337	+	0.611380i
$5$	−0.874721	+	3.69074i	−0.391187	+	1.65055i	0.319905	+	0.947450i	$0.396349\pi$
$5$	−0.874721	+	3.69074i	−0.391187	+	1.65055i	−0.711092	+	0.703099i	$0.751799\pi$
$6$	−2.33595	−	0.737126i	−0.953646	−	0.300930i
$7$	2.85958	+	2.12888i	1.08082	+	0.804641i	0.981700	−	0.190434i	$-0.0609896\pi$
$7$	2.85958	+	2.12888i	1.08082	+	0.804641i	0.0991206	+	0.995075i	$0.468397\pi$
$8$	2.35951	+	1.55971i	0.834213	+	0.551442i
$9$	−0.891308	−	2.86454i	−0.297103	−	0.954846i
$10$	5.33928	−	0.515181i	1.68843	−	0.162915i
$11$	−0.253209	−	0.268386i	−0.0763453	−	0.0809213i	0.688075	−	0.725640i	$-0.258456\pi$
$11$	−0.253209	−	0.268386i	−0.0763453	−	0.0809213i	−0.764420	+	0.644718i	$0.776975\pi$
$12$	0.0804759	+	3.46317i	0.0232314	+	0.999730i
$13$	1.86762	−	0.937956i	0.517986	−	0.260142i	−0.170544	−	0.985350i	$-0.554553\pi$
$13$	1.86762	−	0.937956i	0.517986	−	0.260142i	0.688530	+	0.725208i	$0.258256\pi$
$14$	1.54306	−	4.79975i	0.412401	−	1.28279i
$15$	4.24991	+	5.00982i	1.09732	+	1.29353i
$16$	1.00972	−	3.87046i	0.252429	−	0.967615i
$17$	2.09840	+	5.76530i	0.508936	+	1.39829i	0.882336	+	0.470620i	$0.155970\pi$
$17$	2.09840	+	5.76530i	0.508936	+	1.39829i	−0.373399	+	0.927671i	$0.621808\pi$
$18$	−3.42677	+	2.50144i	−0.807698	+	0.589596i
$19$	1.03264	−	2.83716i	0.236904	−	0.650888i	−0.763085	−	0.646298i	$-0.776316\pi$
$19$	1.03264	−	2.83716i	0.236904	−	0.650888i	0.999989	−	0.00459076i	$-0.00146129\pi$
$20$	−3.12849	−	6.91081i	−0.699551	−	1.54530i
$21$	5.90576	−	1.80277i	1.28874	−	0.393398i
$22$	−0.243545	+	0.461494i	−0.0519239	+	0.0983909i
$23$	3.75651	+	5.04586i	0.783286	+	1.05214i	0.997163	+	0.0752748i	$0.0239834\pi$
$23$	3.75651	+	5.04586i	0.783286	+	1.05214i	−0.213877	+	0.976861i	$0.568609\pi$
$24$	4.59837	−	1.68967i	0.938638	−	0.344903i
$25$	−8.38825	−	4.21274i	−1.67765	−	0.842547i
$26$	−2.10849	−	2.07119i	−0.413509	−	0.406194i
$27$	−4.91085	−	1.69809i	−0.945094	−	0.326797i
$28$	−7.12890	+	0.127258i	−1.34723	+	0.0240495i
$29$	−3.89902	−	5.92817i	−0.724030	−	1.10083i	−0.990570	−	0.137010i	$-0.956251\pi$
$29$	−3.89902	−	5.92817i	−0.724030	−	1.10083i	0.266540	−	0.963824i	$-0.414120\pi$
$30$	4.76384	−	7.97659i	0.869754	−	1.45632i
$31$	2.55754	+	1.10321i	0.459347	+	0.198143i	0.613163	−	0.789957i	$-0.289897\pi$
$31$	2.55754	+	1.10321i	0.459347	+	0.198143i	−0.153816	+	0.988100i	$0.549156\pi$
$32$	−5.64149	+	0.416598i	−0.997285	+	0.0736448i
$33$	−0.634360	+	0.0776106i	−0.110428	+	0.0135103i
$34$	6.75779	−	5.44208i	1.15895	−	0.933309i
$35$	−10.3585	+	8.69179i	−1.75090	+	1.46918i
$36$	4.91329	+	3.44377i	0.818882	+	0.573962i
$37$	−0.159326	−	0.133690i	−0.0261930	−	0.0219785i	0.629597	−	0.776922i	$-0.283220\pi$
$37$	−0.159326	−	0.133690i	−0.0261930	−	0.0219785i	−0.655790	+	0.754943i	$0.727664\pi$
$38$	−4.26898	−	0.0860925i	−0.692520	−	0.0139661i
$39$	0.609378	−	3.56819i	0.0975785	−	0.571368i
$40$	−7.82041	+	7.34403i	−1.23651	+	1.16119i
$41$	−10.2366	−	0.596211i	−1.59868	−	0.0931125i	−0.764507	−	0.644615i	$-0.777018\pi$
$41$	−10.2366	−	0.596211i	−1.59868	−	0.0931125i	−0.834173	+	0.551502i	$0.814055\pi$
$42$	−5.11058	−	7.08082i	−0.788579	−	1.09259i
$43$	7.05296	+	2.11152i	1.07557	+	0.322003i	0.775132	−	0.631799i	$-0.217683\pi$
$43$	7.05296	+	2.11152i	1.07557	+	0.322003i	0.300434	+	0.953803i	$0.402869\pi$
$44$	0.728918	+	0.115154i	0.109889	+	0.0173601i
$45$	11.3519	−	0.783915i	1.69224	−	0.116859i
$46$	5.03747	−	7.33267i	0.742734	−	1.08114i
$47$	−2.93833	−	6.81180i	−0.428599	−	0.993604i	−0.986510	−	0.163703i	$-0.947656\pi$
$47$	−2.93833	−	6.81180i	−0.428599	−	0.993604i	0.557911	−	0.829901i	$-0.311603\pi$
$48$	−4.36199	−	5.38266i	−0.629599	−	0.776920i
$49$	1.63746	+	5.46949i	0.233923	+	0.781356i
$50$	−1.80664	+	13.1513i	−0.255498	+	1.85987i
$51$	10.1965	+	2.99290i	1.42779	+	0.419090i
$52$	−1.80895	+	3.76814i	−0.250856	+	0.522546i
$53$	6.38357	+	3.68555i	0.876850	+	0.506250i	0.869619	−	0.493724i	$-0.164365\pi$
$53$	6.38357	+	3.68555i	0.876850	+	0.506250i	0.00723169	+	0.999974i	$0.497698\pi$
$54$	−0.0294758	+	7.34841i	−0.00401114	+	0.999992i
$55$	1.21203	−	0.699765i	0.163430	−	0.0943563i
$56$	3.42678	+	9.48325i	0.457922	+	1.26725i
$57$	−2.89713	−	4.35363i	−0.383734	−	0.576652i
$58$	−6.15326	+	7.92645i	−0.807963	+	1.04079i
$59$	2.92703	−	3.10247i	0.381067	−	0.403908i	−0.508242	−	0.861214i	$-0.669704\pi$
$59$	2.92703	−	3.10247i	0.381067	−	0.403908i	0.889309	+	0.457307i	$0.151186\pi$
$60$	−12.8520	−	2.73229i	−1.65919	−	0.352737i
$61$	−1.15413	−	0.134898i	−0.147771	−	0.0172719i	0.0418860	−	0.999122i	$-0.486663\pi$
$61$	−1.15413	−	0.134898i	−0.147771	−	0.0172719i	−0.189657	+	0.981850i	$0.560737\pi$
$62$	0.308278	−	3.92697i	0.0391513	−	0.498726i
$63$	3.54949	−	10.0889i	0.447193	−	1.27108i
$64$	3.13459	+	7.36032i	0.391824	+	0.920040i
$65$	1.82810	+	7.71336i	0.226748	+	0.956725i
$66$	0.393648	+	0.813581i	0.0484547	+	0.100145i
$67$	4.04241	−	6.14618i	0.493858	−	0.750875i	−0.499453	−	0.866341i	$-0.666466\pi$
$67$	4.04241	−	6.14618i	0.493858	−	0.750875i	0.993311	+	0.115466i	$0.0368360\pi$
$68$	−10.3707	−	6.55876i	−1.25763	−	0.795366i
$69$	10.8955	−	0.0586662i	1.31167	−	0.00706258i
$70$	16.3649	+	9.89349i	1.95598	+	1.18250i
$71$	−0.398446	+	2.25970i	−0.0472869	+	0.268177i	−0.999280	−	0.0379425i	$-0.987920\pi$
$71$	−0.398446	+	2.25970i	−0.0472869	+	0.268177i	0.951993	+	0.306120i	$0.0990307\pi$
$72$	2.36480	−	8.14909i	0.278695	−	0.960380i
$73$	0.219535	+	1.24504i	0.0256946	+	0.145721i	0.994956	−	0.100312i	$-0.0319840\pi$
$73$	0.219535	+	1.24504i	0.0256946	+	0.145721i	−0.969261	+	0.246033i	$0.920873\pi$
$74$	−0.106153	+	0.274312i	−0.0123400	+	0.0318882i
$75$	−14.4894	+	7.37480i	−1.67309	+	0.851568i
$76$	1.83483	+	5.75297i	0.210469	+	0.659910i
$77$	−0.152711	−	1.30652i	−0.0174030	−	0.148892i
$78$	−5.05406	+	0.814341i	−0.572260	+	0.0922060i
$79$	0.0782584	−	0.00455803i	0.00880476	−	0.000512819i	−0.0537419	−	0.998555i	$-0.517115\pi$
$79$	0.0782584	−	0.00455803i	0.00880476	−	0.000512819i	0.0625466	+	0.998042i	$0.480078\pi$
$80$	13.4016	+	7.11218i	1.49835	+	0.795165i
$81$	−7.41114	+	5.10637i	−0.823460	+	0.567374i
$82$	3.87804	+	13.9730i	0.428258	+	1.54306i
$83$	−0.294342	−	5.05366i	−0.0323083	−	0.554711i	−0.975160	−	0.221500i	$-0.928905\pi$
$83$	−0.294342	−	5.05366i	−0.0323083	−	0.554711i	0.942852	−	0.333211i	$-0.108132\pi$
$84$	−7.14254	+	10.0745i	−0.779315	+	1.09922i
$85$	−23.1137	+	2.70161i	−2.50704	+	0.293031i
$86$	−0.395692	−	10.4043i	−0.0426686	−	1.12192i
$87$	−12.2726	−	0.648512i	−1.31576	−	0.0695278i
$88$	−0.178845	−	1.02819i	−0.0190649	−	0.109606i
$89$	−8.23009	+	1.45119i	−0.872387	+	0.153825i	−0.591880	−	0.806026i	$-0.701614\pi$
$89$	−8.23009	+	1.45119i	−0.872387	+	0.153825i	−0.280508	+	0.959852i	$0.590503\pi$
$90$	−6.23470	−	14.8354i	−0.657195	−	1.56379i
$91$	7.33742	+	1.29379i	0.769171	+	0.135626i
$92$	−12.1152	−	3.39266i	−1.26310	−	0.353709i
$93$	4.16495	−	2.43463i	0.431885	−	0.252459i
$94$	−7.77476	+	7.04429i	−0.801905	+	0.726563i
$95$	9.56793	+	6.29293i	0.981649	+	0.645641i
$96$	−5.21166	+	8.29690i	−0.531913	+	0.846799i
$97$	−12.4281	+	2.94552i	−1.26188	+	0.299072i	−0.806506	−	0.591226i	$-0.798644\pi$
$97$	−12.4281	+	2.94552i	−1.26188	+	0.299072i	−0.455378	+	0.890298i	$0.650496\pi$
$98$	6.57243	−	4.69003i	0.663915	−	0.473764i
$99$	−0.543113	+	0.964540i	−0.0545850	+	0.0969399i
$100$	18.4270	−	3.58942i	1.84270	−	0.358942i
$101$	0.0948622	−	0.811598i	0.00943914	−	0.0807570i	−0.987698	−	0.156375i	$-0.950019\pi$
$101$	0.0948622	−	0.811598i	0.00943914	−	0.0807570i	0.997137	+	0.0756184i	$0.0240931\pi$
$102$	−0.651993	−	15.0142i	−0.0645569	−	1.48663i
$103$	−7.31110	−	6.89767i	−0.720384	−	0.679647i	0.236002	−	0.971753i	$-0.424163\pi$
$103$	−7.31110	−	6.89767i	−0.720384	−	0.679647i	−0.956386	+	0.292105i	$0.905644\pi$
$104$	5.86963	+	0.699839i	0.575564	+	0.0686249i
$105$	1.48767	+	23.3735i	0.145182	+	2.28102i
$106$	2.01679	−	10.2274i	0.195888	−	0.993370i
$107$	−9.81977	−	17.0083i	−0.949313	−	1.64426i	−0.746877	−	0.664963i	$-0.768448\pi$
$107$	−9.81977	−	17.0083i	−0.949313	−	1.64426i	−0.202436	−	0.979295i	$-0.564886\pi$
$108$	9.84864	−	3.31728i	0.947686	−	0.319205i
$109$	0.261103	−	0.452244i	0.0250091	−	0.0433171i	−0.853250	−	0.521502i	$-0.825372\pi$
$109$	0.261103	−	0.452244i	0.0250091	−	0.0433171i	0.878259	+	0.478185i	$0.158705\pi$
$110$	−1.49022	−	1.30254i	−0.142087	−	0.124192i
$111$	−0.350078	+	0.0849634i	−0.0332279	+	0.00806437i
$112$	11.1271	−	8.91834i	1.05141	−	0.842704i
$113$	19.3462	−	5.79188i	1.81994	−	0.544854i	0.820306	−	0.571924i	$-0.193803\pi$
$113$	19.3462	−	5.79188i	1.81994	−	0.544854i	0.999634	+	0.0270702i	$0.00861778\pi$
$114$	−4.50353	+	5.86626i	−0.421795	+	0.549426i
$115$	−21.9089	+	9.45056i	−2.04301	+	0.881269i
$116$	13.4196	+	4.61480i	1.24598	+	0.428474i
$117$	−4.35144	−	4.51387i	−0.402291	−	0.417308i
$118$	−5.48943	−	2.50037i	−0.505343	−	0.230177i
$119$	−6.27309	+	20.9536i	−0.575054	+	1.92081i
$120$	2.21384	+	18.4494i	0.202095	+	1.68419i
$121$	0.631677	−	10.8455i	0.0574252	−	0.985952i
$122$	0.346652	+	1.60631i	0.0313844	+	0.145429i
$123$	−11.3427	+	13.6664i	−1.02273	+	1.23226i
$124$	−5.39671	+	1.38123i	−0.484639	+	0.124038i
$125$	10.6951	−	12.7459i	0.956598	−	1.14003i
$126$	−15.1244	−	0.142106i	−1.34739	−	0.0126598i
$127$	−2.72655	−	3.24937i	−0.241942	−	0.288335i	0.631385	−	0.775469i	$-0.282487\pi$
$127$	−2.72655	−	3.24937i	−0.241942	−	0.288335i	−0.873327	+	0.487134i	$0.838042\pi$
$128$	8.41925	−	7.55753i	0.744163	−	0.667998i
$129$	10.1874	−	7.66980i	0.896946	−	0.675288i
$130$	9.48856	−	5.97018i	0.832202	−	0.523620i
$131$	5.26366	−	12.2025i	0.459888	−	1.06614i	−0.517690	−	0.855568i	$-0.673208\pi$
$131$	5.26366	−	12.2025i	0.459888	−	1.06614i	0.977578	−	0.210572i	$-0.0675326\pi$
$132$	0.909087	−	0.898503i	0.0791259	−	0.0782046i
$133$	8.99289	−	5.91471i	0.779782	−	0.512871i
$134$	−10.0727	−	2.60284i	−0.870145	−	0.224851i
$135$	10.5628	−	16.6393i	0.909103	−	1.43209i
$136$	−4.04102	+	16.8762i	−0.346515	+	1.44712i
$137$	−8.19288	+	16.3134i	−0.699965	+	1.39374i	0.209435	+	0.977823i	$0.432837\pi$
$137$	−8.19288	+	16.3134i	−0.699965	+	1.39374i	−0.909400	+	0.415922i	$0.863459\pi$
$138$	−5.05556	−	14.5559i	−0.430358	−	1.23908i
$139$	−10.0551	+	7.48577i	−0.852866	+	0.634935i	−0.932212	−	0.361912i	$-0.882124\pi$
$139$	−10.0551	+	7.48577i	−0.852866	+	0.634935i	0.0793465	+	0.996847i	$0.474717\pi$
$140$	5.76612	−	26.4222i	0.487326	−	2.23308i
$141$	−12.5187	−	2.89588i	−1.05426	−	0.243877i
$142$	3.20641	−	0.498939i	0.269076	−	0.0418700i
$143$	−0.724633	−	0.263745i	−0.0605969	−	0.0220555i
$144$	−11.9870	+	0.557403i	−0.998921	+	0.0464502i
$145$	25.2899	−	9.20477i	2.10021	−	0.764414i
$146$	1.56610	−	0.862559i	0.129611	−	0.0713859i
$147$	9.31057	+	3.33211i	0.767923	+	0.274828i
$148$	0.415632	+	0.0167709i	0.0341647	+	0.00137856i
$149$	−1.62011	−	3.22591i	−0.132725	−	0.264277i	0.817447	−	0.576004i	$-0.195389\pi$
$149$	−1.62011	−	3.22591i	−0.132725	−	0.264277i	−0.950172	+	0.311727i	$0.899092\pi$
$150$	16.4892	+	16.0239i	1.34634	+	1.30835i
$151$	5.22213	−	4.92682i	0.424971	−	0.400939i	−0.443822	−	0.896115i	$-0.646378\pi$
$151$	5.22213	−	4.92682i	0.424971	−	0.400939i	0.868793	+	0.495176i	$0.164896\pi$
$152$	6.86168	−	5.08368i	0.556555	−	0.412341i
$153$	14.6446	−	11.1496i	1.18395	−	0.901392i
$154$	−1.67890	+	0.801203i	−0.135290	+	0.0645628i
$155$	−6.30881	+	8.47420i	−0.506735	+	0.680664i
$156$	3.39860	+	6.39241i	0.272106	+	0.511803i
$157$	7.89799	+	1.87186i	0.630328	+	0.149390i	0.533348	−	0.845896i	$-0.320934\pi$
$157$	7.89799	+	1.87186i	0.630328	+	0.149390i	0.0969799	+	0.995286i	$0.469082\pi$
$158$	−0.0418487	−	0.102660i	−0.00332930	−	0.00816716i
$159$	11.6956	−	5.11985i	0.927521	−	0.406031i
$160$	3.39718	−	21.1857i	0.268571	−	1.67488i
$161$			22.4262i			1.76743i
$162$	10.2198	+	7.58656i	0.802942	+	0.596057i
$163$			7.68098i			0.601621i	0.953684	+	0.300810i	$0.0972571\pi$
$163$			7.68098i			0.601621i	−0.953684	+	0.300810i	$0.902743\pi$
$164$	16.9302	−	11.5732i	1.32202	−	0.903718i
$165$	0.268448	−	2.40915i	0.0208986	−	0.187552i
$166$	−6.62941	+	2.70244i	−0.514542	+	0.209750i
$167$	0.436113	+	0.103361i	0.0337474	+	0.00799828i	0.247455	−	0.968899i	$-0.420406\pi$
$167$	0.436113	+	0.103361i	0.0337474	+	0.00799828i	−0.213707	+	0.976898i	$0.568554\pi$
$168$	16.7465	+	4.95763i	1.29202	+	0.382489i
$169$	−5.15480	+	6.92410i	−0.396523	+	0.532623i
$170$	14.1741	+	29.7015i	1.08711	+	2.27800i
$171$	−9.04754	−	0.429256i	−0.691883	−	0.0328260i
$172$	−13.7444	+	5.28223i	−1.04800	+	0.402766i
$173$	−5.36388	+	5.06056i	−0.407808	+	0.384747i	−0.862630	−	0.505835i	$-0.831184\pi$
$173$	−5.36388	+	5.06056i	−0.407808	+	0.384747i	0.454822	+	0.890582i	$0.349703\pi$
$174$	4.73809	+	16.7220i	0.359194	+	1.26769i
$175$	−15.0185	−	29.9042i	−1.13529	−	2.26055i
$176$	−1.29445	+	0.709041i	−0.0975725	+	0.0534460i
$177$	−1.32202	−	7.26848i	−0.0993692	−	0.546332i
$178$	5.70175	+	10.3523i	0.427364	+	0.775939i
$179$	20.8808	−	7.59999i	1.56070	−	0.568050i	0.589807	−	0.807545i	$-0.299204\pi$
$179$	20.8808	−	7.59999i	1.56070	−	0.568050i	0.970898	+	0.239495i	$0.0769818\pi$
$180$	−17.0078	+	15.1213i	−1.26769	+	1.12708i
$181$	−15.8404	−	5.76543i	−1.17741	−	0.428541i	−0.322121	−	0.946698i	$-0.604396\pi$
$181$	−15.8404	−	5.76543i	−1.17741	−	0.428541i	−0.855285	+	0.518158i	$0.826618\pi$
$182$	−1.62009	−	10.4115i	−0.120089	−	0.771749i
$183$	−1.37324	+	1.47134i	−0.101513	+	0.108764i
$184$	0.993422	+	17.7648i	0.0732360	+	1.30964i
$185$	0.632782	−	0.471088i	0.0465230	−	0.0346351i
$186$	−5.16106	−	4.46228i	−0.378427	−	0.327190i
$187$	1.01599	−	2.02301i	0.0742966	−	0.147937i
$188$	12.9796	+	7.18800i	0.946635	+	0.524239i
$189$	−10.4280	−	15.3104i	−0.758523	−	1.11367i
$190$	4.05191	−	15.6804i	0.293957	−	1.13757i
$191$	6.08575	−	4.00266i	0.440349	−	0.289622i	−0.309910	−	0.950766i	$-0.600299\pi$
$191$	6.08575	−	4.00266i	0.440349	−	0.289622i	0.750259	+	0.661144i	$0.229929\pi$
$192$	13.4853	+	3.18534i	0.973218	+	0.229882i
$193$	5.19455	−	12.0423i	0.373912	−	0.866826i	−0.622534	−	0.782593i	$-0.713897\pi$
$193$	5.19455	−	12.0423i	0.373912	−	0.866826i	0.996446	−	0.0842331i	$-0.0268440\pi$
$194$	9.61943	+	15.2884i	0.690634	+	1.09764i
$195$	12.6362	+	5.37023i	0.904900	+	0.384570i
$196$	−9.27943	−	6.65420i	−0.662817	−	0.475300i
$197$	−11.4542	−	13.6505i	−0.816076	−	0.972561i	0.183870	−	0.982950i	$-0.441137\pi$
$197$	−11.4542	−	13.6505i	−0.816076	−	0.972561i	−0.999946	+	0.0103894i	$0.996693\pi$
$198$	1.53904	+	0.286309i	0.109375	+	0.0203471i
$199$	−8.13451	+	9.69433i	−0.576640	+	0.687213i	−0.972980	−	0.230891i	$-0.925836\pi$
$199$	−8.13451	+	9.69433i	−0.576640	+	0.687213i	0.396340	+	0.918104i	$0.370280\pi$
$200$	−13.2215	−	23.0233i	−0.934902	−	1.62799i
$201$	−4.42231	−	11.9496i	−0.311925	−	0.842860i
$202$	−1.12958	+	0.243770i	−0.0794771	+	0.0171516i
$203$	1.47080	−	25.2526i	0.103230	−	1.77239i
$204$	−19.7973	+	7.73107i	−1.38609	+	0.541283i
$205$	11.1546	−	37.2589i	0.779070	−	2.60228i
$206$	−5.89221	+	12.9361i	−0.410530	+	0.901298i
$207$	11.1059	−	15.2581i	0.771910	−	1.06051i
$208$	−1.74455	−	8.17564i	−0.120963	−	0.566879i
$209$	−1.02293	+	0.441247i	−0.0707573	+	0.0305217i
$210$	30.6038	−	12.6681i	2.11186	−	0.874179i
$211$	−3.55626	+	1.06468i	−0.244823	+	0.0732953i	−0.406864	−	0.913489i	$-0.633378\pi$
$211$	−3.55626	+	1.06468i	−0.244823	+	0.0732953i	0.162041	+	0.986784i	$0.448192\pi$
$212$	−14.6097	+	1.97254i	−1.00340	+	0.135474i
$213$	2.74285	+	2.87607i	0.187937	+	0.197065i
$214$	−18.2785	+	20.9122i	−1.24949	+	1.42953i
$215$	−13.9624	+	24.1836i	−0.952229	+	1.64931i
$216$	−8.93869	−	11.6662i	−0.608201	−	0.793783i
$217$	4.96488	+	8.59942i	0.337038	+	0.583767i
$218$	−0.724557	−	0.142879i	−0.0490732	−	0.00967700i
$219$	1.96209	+	0.972206i	0.132586	+	0.0656956i
$220$	−1.06260	+	2.58952i	−0.0716406	+	0.174585i
$221$	9.32662	+	8.79921i	0.627377	+	0.591899i
$222$	0.273630	+	0.429737i	0.0183649	+	0.0288420i
$223$	−1.09225	+	9.34481i	−0.0731426	+	0.625775i	0.906097	+	0.423070i	$0.139047\pi$
$223$	−1.09225	+	9.34481i	−0.0731426	+	0.625775i	−0.979240	+	0.202705i	$0.935027\pi$
$224$	−17.0192	−	10.8188i	−1.13714	−	0.722859i
$225$	−4.59102	+	27.7833i	−0.306068	+	1.85222i
$226$	−16.5892	−	23.2474i	−1.10350	−	1.54640i
$227$	−4.88161	+	1.15696i	−0.324004	+	0.0767904i	−0.389399	−	0.921069i	$-0.627317\pi$
$227$	−4.88161	+	1.15696i	−0.324004	+	0.0767904i	0.0653952	+	0.997859i	$0.479169\pi$
$228$	9.90865	+	3.34788i	0.656216	+	0.221719i
$229$	3.99822	+	2.62967i	0.264210	+	0.173774i	0.674701	−	0.738091i	$-0.264272\pi$
$229$	3.99822	+	2.62967i	0.264210	+	0.173774i	−0.410491	+	0.911865i	$0.634643\pi$
$230$	22.6566	+	25.0060i	1.49393	+	1.64885i
$231$	−1.97923	−	1.12854i	−0.130224	−	0.0742527i
$232$	0.0464631	−	20.0689i	0.00305045	−	1.31759i
$233$	9.17615	+	1.61800i	0.601149	+	0.105999i	0.465937	−	0.884818i	$-0.345717\pi$
$233$	9.17615	+	1.61800i	0.601149	+	0.105999i	0.135212	+	0.990817i	$0.456828\pi$
$234$	−4.05368	+	7.88592i	−0.264998	+	0.515519i
$235$	27.7108	−	4.88616i	1.80765	−	0.318738i
$236$	−0.838960	+	8.48926i	−0.0546116	+	0.552604i
$237$	0.0739990	−	0.113840i	0.00480675	−	0.00739473i
$238$	30.9100	−	1.17556i	2.00360	−	0.0762002i
$239$	−16.2720	+	1.90192i	−1.05255	+	0.123025i	−0.624730	−	0.780841i	$-0.714791\pi$
$239$	−16.2720	+	1.90192i	−1.05255	+	0.123025i	−0.427816	+	0.903866i	$0.640717\pi$
$240$	23.6815	−	11.3906i	1.52864	−	0.735262i
$241$	0.619928	+	10.6438i	0.0399331	+	0.685625i	0.957569	+	0.288203i	$0.0930579\pi$
$241$	0.619928	+	10.6438i	0.0399331	+	0.685625i	−0.917636	+	0.397422i	$0.869905\pi$
$242$	−14.8042	+	4.10873i	−0.951651	+	0.264119i
$243$	−0.487150	+	15.5808i	−0.0312507	+	0.999512i
$244$	1.99155	−	1.19772i	0.127496	−	0.0766761i
$245$	−21.6188	+	1.25915i	−1.38117	+	0.0804442i
$246$	23.4726	+	8.93834i	1.49656	+	0.569888i
$247$	−0.732544	−	6.26732i	−0.0466107	−	0.398780i
$248$	4.31384	+	6.59207i	0.273929	+	0.418597i
$249$	−7.35142	−	4.77860i	−0.465877	−	0.302831i
$250$	−21.9447	−	8.49212i	−1.38791	−	0.537089i
$251$	−3.47543	−	19.7101i	−0.219367	−	1.24409i	−0.873165	−	0.487424i	$-0.837937\pi$
$251$	−3.47543	−	19.7101i	−0.219367	−	1.24409i	0.653798	−	0.756669i	$-0.273175\pi$
$252$	6.71858	+	20.3076i	0.423231	+	1.27926i
$253$	0.403057	−	2.28585i	0.0253400	−	0.143710i
$254$	−3.10351	+	5.13354i	−0.194732	+	0.322107i
$255$	−19.9651	+	35.0146i	−1.25026	+	2.19270i
$256$	−13.9609	−	7.81614i	−0.872559	−	0.488509i
$257$	−6.90020	+	10.4912i	−0.430423	+	0.654426i	−0.983958	−	0.178400i	$-0.942908\pi$
$257$	−6.90020	+	10.4912i	−0.430423	+	0.654426i	0.553536	+	0.832826i	$0.313278\pi$
$258$	−14.9189	−	10.1313i	−0.928808	−	0.630747i
$259$	−0.170995	−	0.721484i	−0.0106251	−	0.0448308i
$260$	−12.3249	−	9.97242i	−0.764357	−	0.618463i
$261$	−13.5062	+	16.4527i	−0.836015	+	1.01840i
$262$	−18.7364	−	1.47085i	−1.15754	−	0.0908697i
$263$	12.1229	+	1.41697i	0.747531	+	0.0873739i	0.481325	−	0.876542i	$-0.340156\pi$
$263$	12.1229	+	1.41697i	0.747531	+	0.0873739i	0.266206	+	0.963916i	$0.414230\pi$
$264$	−1.61783	−	0.806297i	−0.0995706	−	0.0496242i
$265$	−19.1863	+	20.3362i	−1.17860	+	1.24925i
$266$	−12.0242	−	9.33434i	−0.737252	−	0.572325i
$267$	−6.42655	+	12.9700i	−0.393299	+	0.793749i
$268$	1.11749	+	14.6703i	0.0682615	+	0.896131i
$269$	13.4840	−	7.78500i	0.822135	−	0.474660i	−0.0290174	−	0.999579i	$-0.509238\pi$
$269$	13.4840	−	7.78500i	0.822135	−	0.474660i	0.851152	+	0.524919i	$0.175904\pi$
$270$	−27.0953	−	6.53660i	−1.64897	−	0.397805i
$271$	27.8391	+	16.0729i	1.69110	+	0.976360i	0.953628	+	0.300987i	$0.0973160\pi$
$271$	27.8391	+	16.0729i	1.69110	+	0.976360i	0.737476	+	0.675373i	$0.236017\pi$
$272$	24.4332	−	2.30045i	1.48148	−	0.139485i
$273$	9.33882	−	8.90625i	0.565211	−	0.539031i
$274$	25.5764	+	3.51354i	1.54513	+	0.212261i
$275$	0.993340	+	3.31799i	0.0599007	+	0.200082i
$276$	−17.1724	+	13.4155i	−1.03365	+	0.807517i
$277$	4.88948	+	11.3351i	0.293781	+	0.681060i	0.999627	−	0.0273048i	$-0.00869247\pi$
$277$	4.88948	+	11.3351i	0.293781	+	0.681060i	−0.705847	+	0.708365i	$0.749433\pi$
$278$	14.6122	+	10.0384i	0.876380	+	0.602064i
$279$	0.880642	−	8.30946i	0.0527227	−	0.497474i
$280$	−37.9977	+	4.35214i	−2.27079	+	0.260090i
$281$	11.6621	+	3.49140i	0.695702	+	0.208279i	0.615079	−	0.788465i	$-0.289124\pi$
$281$	11.6621	+	3.49140i	0.695702	+	0.208279i	0.0806225	+	0.996745i	$0.474309\pi$
$282$	1.84261	+	18.0779i	0.109726	+	1.07652i
$283$	1.56653	+	0.0912401i	0.0931206	+	0.00542366i	0.104642	−	0.994510i	$-0.466630\pi$
$283$	1.56653	+	0.0912401i	0.0931206	+	0.00542366i	−0.0115212	+	0.999934i	$0.503667\pi$
$284$	−2.13246	−	4.06357i	−0.126538	−	0.241129i
$285$	18.6023	−	6.88433i	1.10190	−	0.407792i
$286$	−0.0219887	+	1.09033i	−0.00130022	+	0.0644727i
$287$	−28.0030	−	23.4973i	−1.65296	−	1.38700i
$288$	6.22167	+	15.7889i	0.366615	+	0.930373i
$289$	−15.8127	+	13.2684i	−0.930157	+	0.780495i
$290$	−23.8721	−	29.6435i	−1.40182	−	1.74073i
$291$	−8.65275	+	20.3601i	−0.507233	+	1.19353i
$292$	−1.86984	−	1.70206i	−0.109424	−	0.0996056i
$293$	1.49400	+	0.644447i	0.0872802	+	0.0376490i	0.439272	−	0.898354i	$-0.355236\pi$
$293$	1.49400	+	0.644447i	0.0872802	+	0.0376490i	−0.351992	+	0.936003i	$0.614496\pi$
$294$	0.206689	−	13.9834i	0.0120543	−	0.815531i
$295$	8.89008	+	13.5167i	0.517600	+	0.786973i
$296$	−0.167413	−	0.563946i	−0.00973067	−	0.0327787i
$297$	0.787729	+	1.74797i	0.0457087	+	0.101428i
$298$	−3.57753	+	3.64196i	−0.207240	+	0.210973i
$299$	11.7485	+	5.90034i	0.679436	+	0.341226i
$300$	13.9144	−	29.3889i	0.803346	−	1.69677i
$301$	15.6733	+	21.0530i	0.903396	+	1.21347i
$302$	−8.97955	−	4.73878i	−0.516715	−	0.272686i
$303$	−1.03467	−	0.965680i	−0.0594400	−	0.0554769i
$304$	−9.93843	−	6.86152i	−0.570008	−	0.393535i
$305$	1.50741	−	4.14158i	0.0863141	−	0.237146i
$306$	−21.6123	−	14.5074i	−1.23549	−	0.829331i
$307$	−1.69558	−	4.65857i	−0.0967719	−	0.265879i	0.881856	−	0.471520i	$-0.156294\pi$
$307$	−1.69558	−	4.65857i	−0.0967719	−	0.265879i	−0.978628	+	0.205641i	$0.934072\pi$
$308$	1.83925	+	1.88107i	0.104801	+	0.107184i
$309$	−17.1285	+	3.11539i	−0.974404	+	0.177229i
$310$	14.2238	+	4.57278i	0.807856	+	0.259716i
$311$	21.5229	−	10.8092i	1.22045	−	0.612933i	0.282354	−	0.959310i	$-0.408885\pi$
$311$	21.5229	−	10.8092i	1.22045	−	0.612933i	0.938095	+	0.346377i	$0.112588\pi$
$312$	7.00319	−	7.46874i	0.396478	−	0.422834i
$313$	−3.49585	−	3.70539i	−0.197597	−	0.209441i	0.620997	−	0.783813i	$-0.286728\pi$
$313$	−3.49585	−	3.70539i	−0.197597	−	0.209441i	−0.818594	+	0.574372i	$0.805246\pi$
$314$	−1.10246	−	11.4258i	−0.0622155	−	0.644795i
$315$	34.1306	+	21.9252i	1.92304	+	1.23534i
$316$	−0.118284	+	0.102905i	−0.00665401	+	0.00578887i
$317$	10.7411	+	7.99645i	0.603280	+	0.449125i	0.854966	−	0.518683i	$-0.173578\pi$
$317$	10.7411	+	7.99645i	0.603280	+	0.449125i	−0.251686	+	0.967809i	$0.580985\pi$
$318$	−12.1950	−	13.3147i	−0.683859	−	0.746654i
$319$	−0.603770	+	2.54751i	−0.0338046	+	0.142633i
$320$	−29.9069	+	5.13073i	−1.67185	+	0.286816i
$321$	−33.8074	−	3.76712i	−1.88695	−	0.210260i
$322$	30.0154	−	10.2442i	1.67269	−	0.570887i
$323$	18.5240			1.03070
$324$	5.48556	−	17.1438i	0.304753	−	0.952431i
$325$	−19.6175			−1.08818
$326$	10.2803	−	3.50864i	0.569372	−	0.194326i
$327$	−0.362716	−	0.828574i	−0.0200582	−	0.0458202i
$328$	−23.2233	−	17.3728i	−1.28229	−	0.959255i
$329$	6.09913	−	25.7343i	0.336256	−	1.41878i
$330$	−3.34705	+	0.741196i	−0.184249	+	0.0408015i
$331$	−26.8006	−	19.9523i	−1.47309	−	1.09668i	−0.973028	−	0.230687i	$-0.925903\pi$
$331$	−26.8006	−	19.9523i	−1.47309	−	1.09668i	−0.500064	−	0.865989i	$-0.666690\pi$
$332$	6.64526	+	7.63839i	0.364706	+	0.419211i
$333$	−0.240952	+	0.575554i	−0.0132041	+	0.0315402i
$334$	−0.0608759	−	0.630912i	−0.00333098	−	0.0345219i
$335$	19.1480	+	20.2957i	1.04616	+	1.10887i
$336$	−1.01442	−	24.6783i	−0.0553411	−	1.34631i
$337$	20.4222	−	10.2564i	1.11247	−	0.558703i	0.204974	−	0.978767i	$-0.434289\pi$
$337$	20.4222	−	10.2564i	1.11247	−	0.558703i	0.907494	+	0.420065i	$0.137993\pi$
$338$	11.6220	+	3.73633i	0.632152	+	0.203229i
$339$	11.7861	−	32.9326i	0.640131	−	1.78865i
$340$	33.2781	−	32.5383i	1.80476	−	1.76464i
$341$	−0.351504	−	0.965750i	−0.0190350	−	0.0522983i
$342$	3.55836	+	12.3054i	0.192414	+	0.665399i
$343$	1.57371	−	4.32373i	0.0849723	−	0.233460i
$344$	13.3482	+	15.9827i	0.719685	+	0.861731i
$345$	−9.31404	+	40.2639i	−0.501451	+	2.16774i
$346$	9.22330	+	4.86742i	0.495848	+	0.261674i
$347$	−2.31099	−	3.10420i	−0.124060	−	0.166642i	0.735754	−	0.677249i	$-0.236828\pi$
$347$	−2.31099	−	3.10420i	−0.124060	−	0.166642i	−0.859814	+	0.510607i	$0.829421\pi$
$348$	20.2165	−	13.9800i	1.08372	−	0.749409i
$349$	−11.2338	−	5.64183i	−0.601332	−	0.302000i	0.121968	−	0.992534i	$-0.461079\pi$
$349$	−11.2338	−	5.64183i	−0.601332	−	0.302000i	−0.723300	+	0.690534i	$0.757376\pi$
$350$	−33.1637	+	33.7610i	−1.77268	+	1.80460i
$351$	−10.7644	+	1.43478i	−0.574559	+	0.0765827i
$352$	1.54028	+	1.40861i	0.0820974	+	0.0750791i
$353$	−11.3170	−	17.2067i	−0.602344	−	0.915819i	0.397655	−	0.917535i	$-0.369824\pi$
$353$	−11.3170	−	17.2067i	−0.602344	−	0.915819i	−0.999999	+	0.00171576i	$0.999454\pi$
$354$	−9.12430	+	5.08962i	−0.484951	+	0.270510i
$355$	−7.99143	−	3.44717i	−0.424141	−	0.182957i
$356$	11.2511	−	12.3602i	0.596307	−	0.655088i
$357$	22.7862	+	30.2656i	1.20597	+	1.60182i
$358$	−19.7102	−	24.4754i	−1.04171	−	1.29356i
$359$	−18.7882	+	15.7651i	−0.991601	+	0.832052i	−0.985799	−	0.167931i	$-0.946291\pi$
$359$	−18.7882	+	15.7651i	−0.991601	+	0.832052i	−0.00580232	+	0.999983i	$0.501847\pi$
$360$	28.0076	+	15.8561i	1.47613	+	0.835687i
$361$	7.57173	+	6.35344i	0.398512	+	0.334392i
$362$	−0.480671	+	23.8345i	−0.0252635	+	1.25271i
$363$	−14.4794	−	12.0174i	−0.759970	−	0.630749i
$364$	−13.1947	+	6.92426i	−0.691592	+	0.362930i
$365$	−4.78717	−	0.278821i	−0.250572	−	0.0145941i
$366$	2.59654	+	1.16585i	0.135723	+	0.0609399i
$367$	−7.46037	−	2.23349i	−0.389428	−	0.116587i	0.0861026	−	0.996286i	$-0.472559\pi$
$367$	−7.46037	−	2.23349i	−0.389428	−	0.116587i	−0.475531	+	0.879699i	$0.657744\pi$
$368$	23.3228	−	9.44452i	1.21579	−	0.492330i
$369$	7.41605	+	29.8544i	0.386064	+	1.55416i
$370$	−0.919561	−	0.631729i	−0.0478057	−	0.0328420i
$371$	10.4082	+	24.1290i	0.540368	+	1.25271i
$372$	−3.61479	+	8.94596i	−0.187418	+	0.463826i
$373$	2.70087	+	9.02152i	0.139846	+	0.467117i	0.999005	−	0.0445906i	$-0.0141983\pi$
$373$	2.70087	+	9.02152i	0.139846	+	0.467117i	−0.859160	+	0.511707i	$0.829013\pi$
$374$	−3.17171	−	0.435710i	−0.164005	−	0.0225301i
$375$	−6.79699	−	28.0059i	−0.350995	−	1.44622i
$376$	3.69145	−	20.6555i	0.190372	−	1.06522i
$377$	−12.8423	−	7.41449i	−0.661411	−	0.381866i
$378$	−15.7282	+	20.9506i	−0.808970	+	1.07758i
$379$	1.00647	−	0.581088i	0.0516991	−	0.0298485i	−0.473928	−	0.880564i	$-0.657164\pi$
$379$	1.00647	−	0.581088i	0.0516991	−	0.0298485i	0.525627	+	0.850715i	$0.323831\pi$
$380$	−22.8377	+	1.73963i	−1.17155	+	0.0892409i
$381$	−7.33210	+	0.466672i	−0.375635	+	0.0239083i
$382$	−8.13714	−	6.31682i	−0.416332	−	0.323196i
$383$	18.3800	−	19.4816i	0.939172	−	0.995464i	−0.0608246	−	0.998148i	$-0.519373\pi$
$383$	18.3800	−	19.4816i	0.939172	−	0.995464i	0.999996	+	0.00268457i	$0.000854526\pi$
$384$	−1.89675	−	19.5039i	−0.0967933	−	0.995305i
$385$	4.95561	+	0.579228i	0.252561	+	0.0295202i
$386$	−18.4904	−	1.45154i	−0.941137	−	0.0738817i
$387$	−0.237842	−	22.0855i	−0.0120902	−	1.12267i
$388$	16.0680	−	19.8584i	0.815729	−	1.00816i
$389$	−2.27968	−	9.61872i	−0.115584	−	0.487688i	−0.999788	−	0.0205871i	$-0.993446\pi$
$389$	−2.27968	−	9.61872i	−0.115584	−	0.487688i	0.884204	−	0.467101i	$-0.154702\pi$
$390$	1.41537	−	19.3655i	0.0716703	−	0.980613i
$391$	−21.2083	+	32.2456i	−1.07255	+	1.63073i
$392$	−4.66723	+	15.4593i	−0.235731	+	0.780812i
$393$	−11.6161	−	19.8718i	−0.585955	−	1.00240i
$394$	−13.0378	+	21.5659i	−0.656834	+	1.08647i
$395$	−0.0516318	+	0.292818i	−0.00259788	+	0.0147333i
$396$	−0.319829	−	2.19065i	−0.0160720	−	0.110084i
$397$	2.49961	+	14.1760i	0.125452	+	0.711472i	0.981039	+	0.193813i	$0.0620854\pi$
$397$	2.49961	+	14.1760i	0.125452	+	0.711472i	−0.855587	+	0.517659i	$0.826803\pi$
$398$	16.6908	+	6.45896i	0.836633	+	0.323758i
$399$	0.983776	−	18.6172i	0.0492504	−	0.932025i
$400$	−24.7750	+	28.2127i	−1.23875	+	1.41064i
$401$	0.316914	+	2.71138i	0.0158259	+	0.135400i	0.998841	−	0.0481231i	$-0.0153240\pi$
$401$	0.316914	+	2.71138i	0.0158259	+	0.135400i	−0.983015	+	0.183523i	$0.941250\pi$
$402$	−13.9733	+	11.3774i	−0.696927	+	0.567452i
$403$	5.81129	−	0.338469i	0.289481	−	0.0168603i
$404$	0.842253	+	1.40049i	0.0419037	+	0.0696769i
$405$	−12.3636	−	31.8192i	−0.614352	−	1.58111i
$406$	−34.4702	+	9.56678i	−1.71073	+	0.474792i
$407$	0.00446216	+	0.0766123i	0.000221181	+	0.00379753i
$408$	19.3907	+	22.9654i	0.959982	+	1.13696i
$409$	24.5810	−	2.87310i	1.21545	−	0.142066i	0.515900	−	0.856649i	$-0.327458\pi$
$409$	24.5810	−	2.87310i	1.21545	−	0.142066i	0.699551	+	0.714583i	$0.253384\pi$
$410$	−54.9630	+	2.09034i	−2.71443	+	0.103234i
$411$	14.3424	+	28.1788i	0.707459	+	1.38996i
$412$	20.0053	+	1.97704i	0.985589	+	0.0974019i
$413$	14.9749	−	2.64048i	0.736866	−	0.129929i
$414$	−25.4946	−	7.89434i	−1.25299	−	0.387986i
$415$	18.9092	+	3.33420i	0.928217	+	0.163670i
$416$	−10.1454	+	6.06952i	−0.497421	+	0.297583i
$417$	0.116907	+	21.7121i	0.00572496	+	1.06324i
$418$	1.05784	+	1.16753i	0.0517405	+	0.0571059i
$419$	7.64662	+	5.02926i	0.373562	+	0.245696i	0.722382	−	0.691494i	$-0.243047\pi$
$419$	7.64662	+	5.02926i	0.373562	+	0.245696i	−0.348820	+	0.937190i	$0.613418\pi$
$420$	−30.9347	−	35.1737i	−1.50946	−	1.71630i
$421$	15.3360	−	3.63470i	0.747430	−	0.177144i	0.160786	−	0.986989i	$-0.448597\pi$
$421$	15.3360	−	3.63470i	0.747430	−	0.177144i	0.586644	+	0.809845i	$0.300449\pi$
$422$	3.04946	+	4.27339i	0.148445	+	0.208026i
$423$	−16.8937	+	14.4884i	−0.821400	+	0.704448i
$424$	9.31369	+	18.6526i	0.452313	+	0.905852i
$425$	6.68581	−	57.2008i	0.324310	−	2.77465i
$426$	2.59643	−	4.98483i	0.125798	−	0.241516i
$427$	−3.01313	−	2.84275i	−0.145816	−	0.137570i
$428$	36.3386	+	14.9114i	1.75649	+	0.720772i
$429$	−1.11195	+	0.739950i	−0.0536855	+	0.0357251i
$430$	38.7456	+	7.64044i	1.86848	+	0.368455i
$431$	13.6704	+	23.6778i	0.658479	+	1.14052i	0.981009	+	0.193960i	$0.0621332\pi$
$431$	13.6704	+	23.6778i	0.658479	+	1.14052i	−0.322530	+	0.946559i	$0.604533\pi$
$432$	−11.5310	+	17.2927i	−0.554784	+	0.831995i
$433$	−13.5032	+	23.3882i	−0.648922	+	1.12397i	0.334458	+	0.942411i	$0.391447\pi$
$433$	−13.5032	+	23.3882i	−0.648922	+	1.12397i	−0.983381	+	0.181556i	$0.941887\pi$
$434$	9.24160	−	10.5732i	0.443611	−	0.507531i
$435$	13.1286	−	44.7276i	0.629467	−	2.14453i
$436$	0.139744	+	1.03502i	0.00669254	+	0.0495685i
$437$	18.1950	−	5.44723i	0.870386	−	0.260577i
$438$	0.404933	−	3.07018i	0.0193484	−	0.146699i
$439$	6.55305	−	2.82671i	0.312760	−	0.134911i	−0.233913	−	0.972257i	$-0.575153\pi$
$439$	6.55305	−	2.82671i	0.312760	−	0.134911i	0.546673	+	0.837346i	$0.315894\pi$
$440$	3.95123	+	0.239313i	0.188367	+	0.0114088i
$441$	14.2081	−	9.56556i	0.676575	−	0.455503i
$442$	7.51658	−	16.5023i	0.357527	−	0.784933i
$443$	−1.77205	+	5.91905i	−0.0841926	+	0.281223i	−0.989710	−	0.143086i	$-0.954298\pi$
$443$	−1.77205	+	5.91905i	−0.0841926	+	0.281223i	0.905518	+	0.424308i	$0.139483\pi$
$444$	0.450170	−	0.562531i	0.0213641	−	0.0266965i
$445$	1.84308	−	31.6445i	0.0873704	−	1.50009i
$446$	13.0061	−	2.80679i	0.615857	−	0.132906i
$447$	−6.16327	−	1.05257i	−0.291513	−	0.0497847i
$448$	−6.70562	+	27.7206i	−0.316811	+	1.30968i
$449$	−14.9846	+	17.8579i	−0.707166	+	0.842768i	−0.993317	−	0.115417i	$-0.963180\pi$
$449$	−14.9846	+	17.8579i	−0.707166	+	0.842768i	0.286151	+	0.958185i	$0.407624\pi$
$450$	39.2826	−	6.54664i	1.85180	−	0.308611i
$451$	2.43197	+	2.89831i	0.114517	+	0.136476i
$452$	−23.5367	+	32.8224i	−1.10707	+	1.54384i
$453$	−1.51011	−	12.3431i	−0.0709513	−	0.579929i
$454$	3.77839	+	6.00509i	0.177329	+	0.281833i
$455$	−11.1932	+	25.9488i	−0.524746	+	1.21650i
$456$	−0.0453971	−	14.7911i	−0.00212591	−	0.692658i
$457$	−27.6280	+	18.1712i	−1.29238	+	0.850014i	−0.994515	−	0.104594i	$-0.966646\pi$
$457$	−27.6280	+	18.1712i	−1.29238	+	0.850014i	−0.297868	+	0.954607i	$0.596275\pi$
$458$	1.69320	−	6.55248i	0.0791182	−	0.306177i
$459$	−0.514939	−	31.8758i	−0.0240353	−	1.48784i
$460$	23.1188	−	41.7464i	1.07792	−	1.94644i
$461$	0.466380	−	0.928638i	0.0217215	−	0.0432510i	−0.882510	−	0.470293i	$-0.844148\pi$
$461$	0.466380	−	0.928638i	0.0217215	−	0.0432510i	0.904232	+	0.427042i	$0.140444\pi$
$462$	−0.606348	+	3.16453i	−0.0282098	+	0.147227i
$463$	18.2791	−	13.6083i	0.849501	−	0.632430i	−0.0818131	−	0.996648i	$-0.526071\pi$
$463$	18.2791	−	13.6083i	0.849501	−	0.632430i	0.931314	+	0.364218i	$0.118664\pi$
$464$	−26.8817	+	9.10523i	−1.24795	+	0.422700i
$465$	5.34241	+	17.5014i	0.247748	+	0.811606i
$466$	−2.02608	−	13.0205i	−0.0938564	−	0.603164i
$467$	10.0689	+	3.66477i	0.465932	+	0.169585i	0.564309	−	0.825564i	$-0.309143\pi$
$467$	10.0689	+	3.66477i	0.465932	+	0.169585i	−0.0983769	+	0.995149i	$0.531365\pi$
$468$	12.4063	+	1.82322i	0.573481	+	0.0842785i
$469$	24.6441	−	8.96971i	1.13796	−	0.414183i
$470$	−19.1979	−	34.8564i	−0.885532	−	1.60781i
$471$	10.7208	−	9.09459i	0.493986	−	0.419057i
$472$	11.7453	−	2.75499i	0.540623	−	0.126809i
$473$	−1.21917	−	2.42757i	−0.0560575	−	0.111620i
$474$	−0.186167	−	0.0470390i	−0.00855095	−	0.00216057i
$475$	−20.6142	+	19.4485i	−0.945846	+	0.892360i
$476$	−15.6929	−	40.8332i	−0.719285	−	1.87159i
$477$	4.86768	−	21.5709i	0.222876	−	0.987665i
$478$	9.97851	+	20.9097i	0.456407	+	0.956389i
$479$	−7.69314	+	10.3337i	−0.351508	+	0.472158i	−0.942350	−	0.334630i	$-0.891389\pi$
$479$	−7.69314	+	10.3337i	−0.351508	+	0.472158i	0.590841	+	0.806788i	$0.298796\pi$
$480$	−26.0629	−	26.4924i	−1.18961	−	1.20921i
$481$	−0.422957	−	0.100243i	−0.0192852	−	0.00457067i
$482$	13.9625	−	5.69175i	0.635975	−	0.259252i
$483$	31.2816	+	23.0275i	1.42336	+	1.04779i
$484$	12.2617	+	17.9372i	0.557349	+	0.815329i
$485$		−	48.4454i		−	2.19979i
$486$	21.0761	−	6.46526i	0.956030	−	0.293270i
$487$			21.1052i			0.956369i	0.878259	+	0.478185i	$0.158705\pi$
$487$			21.1052i			0.956369i	−0.878259	+	0.478185i	$0.841295\pi$
$488$	−2.51277	−	2.11840i	−0.113748	−	0.0958953i
$489$	10.7139	+	7.88693i	0.484501	+	0.356659i
$490$	11.5606	+	28.3596i	0.522256	+	1.28115i
$491$	−14.1512	−	3.35389i	−0.638633	−	0.151359i	−0.101472	−	0.994838i	$-0.532355\pi$
$491$	−14.1512	−	3.35389i	−0.638633	−	0.151359i	−0.537161	+	0.843480i	$0.680503\pi$
$492$	1.24098	−	35.4989i	0.0559479	−	1.60041i
$493$	25.9960	−	34.9187i	1.17080	−	1.57266i
$494$	−8.05360	+	3.84333i	−0.362349	+	0.172920i
$495$	−3.08479	−	2.84819i	−0.138651	−	0.128017i
$496$	6.85234	−	8.78491i	0.307679	−	0.394454i
$497$	−5.95002	+	5.61355i	−0.266895	+	0.251802i
$498$	−3.03762	+	12.0220i	−0.136119	+	0.538721i
$499$	−4.99823	−	9.95230i	−0.223752	−	0.445526i	0.753547	−	0.657395i	$-0.228342\pi$
$499$	−4.99823	−	9.95230i	−0.223752	−	0.445526i	−0.977298	+	0.211868i	$0.932045\pi$
$500$	−1.34166	+	33.2502i	−0.0600008	+	1.48699i
$501$	0.591981	−	0.502187i	0.0264477	−	0.0224361i
$502$	−24.7927	+	13.6551i	−1.10655	+	0.609455i
$503$	−22.2568	+	8.10083i	−0.992384	+	0.361198i	−0.786643	−	0.617408i	$-0.788183\pi$
$503$	−22.2568	+	8.10083i	−0.992384	+	0.361198i	−0.205741	+	0.978607i	$0.565960\pi$
$504$	24.1108	−	18.2686i	1.07398	−	0.813749i
$505$	2.91242	+	1.06003i	0.129601	+	0.0471709i
$506$	−3.24352	+	0.504713i	−0.144192	+	0.0224372i
$507$	4.36518	+	14.3000i	0.193864	+	0.635086i
$508$	8.28844	+	1.80879i	0.367740	+	0.0802520i
$509$	−21.4334	+	15.9566i	−0.950018	+	0.707262i	−0.956199	−	0.292719i	$-0.905440\pi$
$509$	−21.4334	+	15.9566i	−0.950018	+	0.707262i	0.00618061	+	0.999981i	$0.498033\pi$
$510$	55.9839	+	10.7269i	2.47901	+	0.474996i
$511$	−2.02277	+	4.02767i	−0.0894822	+	0.178174i
$512$	−4.08389	+	22.2558i	−0.180484	+	0.983578i
$513$	−9.88889	+	12.1793i	−0.436605	+	0.537731i
$514$	17.1936	+	4.44292i	0.758375	+	0.195969i
$515$	31.8527	−	20.9498i	1.40360	−	0.923159i
$516$	−6.74494	+	24.5955i	−0.296929	+	1.08276i
$517$	−1.08418	+	2.51341i	−0.0476822	+	0.110540i
$518$	−0.887530	+	0.558432i	−0.0389959	+	0.0245361i
$519$	1.55110	+	12.6782i	0.0680859	+	0.556509i
$520$	−7.71721	+	21.0511i	−0.338422	+	0.923151i
$521$	−15.7683	−	18.7919i	−0.690823	−	0.823290i	0.300632	−	0.953740i	$-0.402802\pi$
$521$	−15.7683	−	18.7919i	−0.690823	−	0.823290i	−0.991455	+	0.130450i	$0.958358\pi$
$522$	28.1901	+	10.5613i	1.23385	+	0.462257i
$523$	−15.0537	+	17.9403i	−0.658253	+	0.784475i	−0.987134	−	0.159896i	$-0.948884\pi$
$523$	−15.0537	+	17.9403i	−0.658253	+	0.784475i	0.328881	+	0.944371i	$0.393329\pi$
$524$	6.59011	+	25.7488i	0.287890	+	1.12484i
$525$	−57.1336	−	9.75730i	−2.49352	−	0.425844i
$526$	−3.64122	−	16.8727i	−0.158765	−	0.735684i
$527$	−0.993629	+	17.0600i	−0.0432832	+	0.743143i
$528$	−0.340136	+	2.53363i	−0.0148025	+	0.110262i
$529$	−4.75293	+	15.8759i	−0.206649	+	0.690256i
$530$	35.9824	+	16.3895i	1.56298	+	0.711916i
$531$	−11.4960	−	5.61933i	−0.498885	−	0.243858i
$532$	−7.00054	+	20.3572i	−0.303512	+	0.882597i
$533$	−19.6773	+	8.48794i	−0.852317	+	0.367654i
$534$	20.2947	+	2.67672i	0.878240	+	0.115833i
$535$	71.3629	−	21.3646i	3.08529	−	0.923674i
$536$	19.1244	−	8.19699i	0.826047	−	0.354056i
$537$	10.8397	−	36.9297i	0.467768	−	1.59363i
$538$	−16.5790	−	14.4910i	−0.714769	−	0.624750i
$539$	1.05331	−	1.82439i	0.0453694	−	0.0785822i
$540$	3.62838	+	39.2504i	0.156141	+	1.68907i
$541$	21.2815	+	36.8606i	0.914962	+	1.58476i	0.806957	+	0.590610i	$0.201113\pi$
$541$	21.2815	+	36.8606i	0.914962	+	1.58476i	0.108004	+	0.994150i	$0.465554\pi$
$542$	8.79533	−	44.6021i	0.377792	−	1.91583i
$543$	−24.3071	+	16.1752i	−1.04312	+	0.694145i
$544$	−14.2399	−	31.6507i	−0.610531	−	1.35701i
$545$	1.44072	+	1.35925i	0.0617137	+	0.0582239i
$546$	−16.1861	−	8.43082i	−0.692703	−	0.360806i
$547$	−3.55324	+	30.3999i	−0.151926	+	1.29981i	0.675135	+	0.737694i	$0.264085\pi$
$547$	−3.55324	+	30.3999i	−0.151926	+	1.29981i	−0.827061	+	0.562112i	$0.809989\pi$
$548$	−6.98066	−	35.8367i	−0.298199	−	1.53087i
$549$	0.642261	+	3.42627i	0.0274110	+	0.146230i
$550$	3.98707	−	2.84514i	0.170009	−	0.121317i
$551$	−20.8454	+	4.94046i	−0.888046	+	0.210471i
$552$	25.7997	+	16.8555i	1.09811	+	0.717417i
$553$	0.233490	+	0.153569i	0.00992900	+	0.00653041i
$554$	12.9375	−	11.7220i	0.549661	−	0.498018i
$555$	−0.00735709	−	1.36637i	−0.000312291	−	0.0579990i
$556$	6.76071	−	24.1426i	0.286718	−	1.02387i
$557$	−6.28172	−	1.10764i	−0.266165	−	0.0469320i	0.0389729	−	0.999240i	$-0.487591\pi$
$557$	−6.28172	−	1.10764i	−0.266165	−	0.0469320i	−0.305138	+	0.952308i	$0.598703\pi$
$558$	−11.5237	+	2.61707i	−0.487838	+	0.110789i
$559$	15.1528	−	2.67184i	0.640894	−	0.113007i
$560$	23.1821	+	48.8683i	0.979623	+	2.06506i
$561$	−1.77859	−	3.49442i	−0.0750921	−	0.147535i
$562$	−0.654278	−	17.2035i	−0.0275991	−	0.725686i
$563$	5.15676	−	0.602739i	0.217332	−	0.0254024i	−0.00673023	−	0.999977i	$-0.502142\pi$
$563$	5.15676	−	0.602739i	0.217332	−	0.0254024i	0.224062	+	0.974575i	$0.428068\pi$
$564$	23.3539	−	10.7241i	0.983379	−	0.451566i
$565$	4.45376	+	76.4681i	0.187371	+	3.21704i
$566$	−0.593469	−	2.13834i	−0.0249454	−	0.0898810i
$567$	−32.0636	−	1.17534i	−1.34655	−	0.0493597i
$568$	−4.46462	+	4.71033i	−0.187331	+	0.197641i
$569$	35.7367	−	2.08142i	1.49816	−	0.0872578i	0.710643	−	0.703552i	$-0.248404\pi$
$569$	35.7367	−	2.08142i	1.49816	−	0.0872578i	0.787516	+	0.616295i	$0.211367\pi$
$570$	−17.7115	−	21.7527i	−0.741853	−	0.911121i
$571$	1.26983	+	10.8641i	0.0531407	+	0.454647i	0.993445	+	0.114312i	$0.0364664\pi$
$571$	1.26983	+	10.8641i	0.0531407	+	0.454647i	−0.940304	+	0.340335i	$0.889459\pi$
$572$	1.46935	−	0.468630i	0.0614368	−	0.0195944i
$573$	0.665750	−	12.5988i	0.0278121	−	0.526322i
$574$	−18.6573	+	48.2129i	−0.778742	+	2.01237i
$575$	−10.2536	−	58.1511i	−0.427605	−	2.42507i
$576$	18.2900	−	15.5395i	0.762084	−	0.647478i
$577$	1.60819	−	9.12049i	0.0669498	−	0.379691i	−0.932861	−	0.360237i	$-0.882696\pi$
$577$	1.60819	−	9.12049i	0.0669498	−	0.379691i	0.999811	−	0.0194545i	$-0.00619295\pi$
$578$	24.9817	+	15.1029i	1.03910	+	0.628196i
$579$	−11.4636	−	19.6109i	−0.476411	−	0.815003i
$580$	−28.7705	+	45.4916i	−1.19463	+	1.88894i
$581$	9.91694	−	15.0780i	0.411424	−	0.625540i
$582$	31.2026	+	2.28052i	1.29339	+	0.0945304i
$583$	−0.627225	−	2.64647i	−0.0259770	−	0.109606i
$584$	−1.42392	+	3.28011i	−0.0589221	+	0.135732i
$585$	20.4658	−	12.1116i	0.846157	−	0.500755i
$586$	0.180082	−	2.29396i	0.00743911	−	0.0947626i
$587$	−18.4325	−	2.15446i	−0.760793	−	0.0889239i	−0.273155	−	0.961970i	$-0.588067\pi$
$587$	−18.4325	−	2.15446i	−0.760793	−	0.0889239i	−0.487638	+	0.873046i	$0.662141\pi$
$588$	−18.8100	+	6.11095i	−0.775710	+	0.252011i
$589$	5.77101	−	6.11691i	0.237790	−	0.252043i
$590$	14.0299	−	18.0729i	0.577603	−	0.744051i
$591$	−30.8020	+	1.96048i	−1.26702	+	0.0806433i
$592$	−0.678317	+	0.481675i	−0.0278787	+	0.0197967i
$593$	−5.66767	+	3.27223i	−0.232743	+	0.134374i	−0.611837	−	0.790984i	$-0.709569\pi$
$593$	−5.66767	+	3.27223i	−0.232743	+	0.134374i	0.379094	+	0.925358i	$0.376236\pi$
$594$	1.97967	−	1.85277i	0.0812269	−	0.0760201i
$595$	−71.8470	−	41.4809i	−2.94544	−	1.70055i
$596$	6.50863	+	3.12456i	0.266604	+	0.127987i
$597$	5.16968	+	21.3008i	0.211581	+	0.871785i
$598$	2.53038	−	18.4196i	0.103475	−	0.753234i
$599$	0.528274	+	1.76456i	0.0215847	+	0.0720979i	0.968103	−	0.250551i	$-0.0806118\pi$
$599$	0.528274	+	1.76456i	0.0215847	+	0.0720979i	−0.946519	+	0.322649i	$0.895427\pi$
$600$	−45.6904	−	5.19835i	−1.86530	−	0.212222i
$601$	4.82735	+	11.1910i	0.196912	+	0.456492i	0.987851	−	0.155402i	$-0.0496672\pi$
$601$	4.82735	+	11.1910i	0.196912	+	0.456492i	−0.790940	+	0.611894i	$0.790408\pi$
$602$	21.0179	−	30.5942i	0.856627	−	1.24693i
$603$	−21.2090	−	6.10148i	−0.863697	−	0.248471i
$604$	−2.24061	+	14.1830i	−0.0911690	+	0.577096i
$605$	39.4753	+	11.8181i	1.60490	+	0.480475i
$606$	−0.819843	+	1.82592i	−0.0333038	+	0.0741731i
$607$	35.1472	+	2.04709i	1.42658	+	0.0830890i	0.753972	−	0.656907i	$-0.228136\pi$
$607$	35.1472	+	2.04709i	1.42658	+	0.0830890i	0.672611	+	0.739996i	$0.265173\pi$
$608$	−4.64368	+	16.4360i	−0.188326	+	0.666568i
$609$	−33.7139	−	27.9813i	−1.36615	−	1.13386i
$610$	−6.23170	−	0.125675i	−0.252314	−	0.00508842i
$611$	−11.8769	−	9.96587i	−0.480486	−	0.403176i
$612$	−9.54435	+	35.5530i	−0.385807	+	1.43715i
$613$	27.2490	−	22.8647i	1.10058	−	0.923495i	0.103115	−	0.994669i	$-0.467119\pi$
$613$	27.2490	−	22.8647i	1.10058	−	0.923495i	0.997464	+	0.0711743i	$0.0226747\pi$
$614$	−5.46053	+	4.39740i	−0.220369	+	0.177464i
$615$	−40.5176	−	53.8171i	−1.63383	−	2.17012i
$616$	1.67748	−	3.32094i	0.0675875	−	0.133804i
$617$	−40.8912	−	17.6387i	−1.64622	−	0.710108i	−0.647564	−	0.762011i	$-0.724212\pi$
$617$	−40.8912	−	17.6387i	−1.64622	−	0.710108i	−0.998652	+	0.0519027i	$0.983471\pi$
$618$	11.9939	+	21.5018i	0.482465	+	0.864928i
$619$	18.2520	+	27.7508i	0.733609	+	1.11540i	0.988907	+	0.148536i	$0.0474561\pi$
$619$	18.2520	+	27.7508i	0.733609	+	1.11540i	−0.255298	+	0.966862i	$0.582174\pi$
$620$	−0.377121	−	21.1260i	−0.0151455	−	0.848442i
$621$	−9.87934	−	31.1584i	−0.396444	−	1.25034i
$622$	−24.2987	−	23.8688i	−0.974288	−	0.957051i
$623$	−26.6240	−	13.3711i	−1.06667	−	0.535701i
$624$	−13.1953	−	5.96144i	−0.528233	−	0.238649i
$625$	9.65991	+	12.9755i	0.386396	+	0.519020i
$626$	−3.36243	+	6.37149i	−0.134390	+	0.254656i
$627$	−0.434873	+	1.87992i	−0.0173671	+	0.0750769i
$628$	−14.7888	+	6.69480i	−0.590136	+	0.267152i
$629$	0.436436	−	1.19910i	0.0174018	−	0.0478111i
$630$	13.7541	−	55.6960i	0.547977	−	2.21898i
$631$	−12.5396	−	34.4522i	−0.499193	−	1.37152i	−0.892056	−	0.451925i	$-0.850738\pi$
$631$	−12.5396	−	34.4522i	−0.499193	−	1.37152i	0.392863	−	0.919597i	$-0.371485\pi$
$632$	0.191761	+	0.111306i	0.00762784	+	0.00442751i
$633$	−2.16654	+	6.05374i	−0.0861122	+	0.240615i
$634$	5.79602	−	18.0287i	0.230190	−	0.716012i
$635$	14.3776	−	7.22068i	0.570556	−	0.286544i
$636$	−12.2500	+	22.4040i	−0.485743	+	0.888375i
$637$	8.18830	+	8.67909i	0.324432	+	0.343878i
$638$	3.68541	−	0.355600i	0.145907	−	0.0140783i
$639$	6.82813	−	0.872726i	0.270117	−	0.0345245i
$640$	20.5284	+	37.6840i	0.811455	+	1.48959i
$641$	−6.61816	−	4.92704i	−0.261402	−	0.194606i	0.458477	−	0.888706i	$-0.348395\pi$
$641$	−6.61816	−	4.92704i	−0.261402	−	0.194606i	−0.719879	+	0.694100i	$0.755803\pi$
$642$	10.4012	+	46.9690i	0.410501	+	1.85372i
$643$	−0.0807862	+	0.340864i	−0.00318590	+	0.0134424i	−0.974615	−	0.223889i	$-0.928125\pi$
$643$	−0.0807862	+	0.340864i	−0.00318590	+	0.0134424i	0.971429	+	0.237332i	$0.0762728\pi$
$644$	−27.4219	−	35.4934i	−1.08057	−	1.39864i
$645$	19.3961	+	44.3078i	0.763722	+	1.74462i
$646$	−8.46167	−	24.7926i	−0.332920	−	0.975453i
$647$	1.81191			0.0712337			0.0356168	−	0.999366i	$-0.488660\pi$
$647$	1.81191			0.0712337			0.0356168	+	0.999366i	$0.488660\pi$
$648$	−25.4511	+	0.489290i	−0.999815	+	0.0192211i
$649$	−1.57381			−0.0617774
$650$	8.96118	+	26.2562i	0.351487	+	1.02985i
$651$	17.0931	+	1.90466i	0.669930	+	0.0746494i
$652$	−9.39199	−	12.1565i	−0.367819	−	0.476085i
$653$	−9.69506	+	40.9067i	−0.379397	+	1.60080i	0.363631	+	0.931543i	$0.381537\pi$
$653$	−9.69506	+	40.9067i	−0.379397	+	1.60080i	−0.743029	+	0.669260i	$0.766611\pi$
$654$	−0.943283	+	0.863951i	−0.0368853	+	0.0337832i
$655$	40.4321	+	30.1006i	1.57981	+	1.17613i
$656$	−12.6436	+	39.0182i	−0.493651	+	1.52340i
$657$	3.37080	−	1.73858i	0.131508	−	0.0678286i
$658$	−37.2290	+	3.59218i	−1.45134	+	0.140038i
$659$	−30.5270	−	32.3568i	−1.18916	−	1.26044i	−0.957756	−	0.287583i	$-0.907148\pi$
$659$	−30.5270	−	32.3568i	−1.18916	−	1.26044i	−0.231408	−	0.972857i	$-0.574333\pi$
$660$	2.52094	+	4.14114i	0.0981275	+	0.161194i
$661$	−0.0414178	+	0.0208008i	−0.00161097	+	0.000809058i	−0.449604	−	0.893228i	$-0.648435\pi$
$661$	−0.0414178	+	0.0208008i	−0.00161097	+	0.000809058i	0.447994	+	0.894037i	$0.352139\pi$
$662$	−14.4619	+	44.9842i	−0.562078	+	1.74836i
$663$	21.8504	−	3.97425i	0.848601	−	0.154347i
$664$	7.18776	−	12.3833i	0.278939	−	0.480564i
$665$	13.9634	+	38.3641i	0.541477	+	1.48770i
$666$	0.880392	+	0.0595816i	0.0341145	+	0.00230874i
$667$	15.2661	−	41.9432i	0.591104	−	1.62405i
$668$	−0.816610	+	0.369675i	−0.0315956	+	0.0143031i
$669$	11.9132	+	11.1189i	0.460592	+	0.429882i
$670$	18.4172	−	34.8988i	0.711517	−	1.34826i
$671$	0.256030	+	0.343908i	0.00988393	+	0.0132764i
$672$	−32.5663	+	12.6307i	−1.25627	+	0.487239i
$673$	−26.0993	−	13.1076i	−1.00606	−	0.505260i	−0.132085	−	0.991238i	$-0.542167\pi$
$673$	−26.0993	−	13.1076i	−1.00606	−	0.505260i	−0.873971	+	0.485978i	$0.838463\pi$
$674$	−23.0561	−	22.6482i	−0.888086	−	0.872375i
$675$	34.0399	+	34.9321i	1.31020	+	1.34454i
$676$	−0.308138	−	17.2617i	−0.0118515	−	0.663911i
$677$	24.0436	+	36.5565i	0.924071	+	1.40498i	0.914304	+	0.405029i	$0.132739\pi$
$677$	24.0436	+	36.5565i	0.924071	+	1.40498i	0.00976724	+	0.999952i	$0.496891\pi$
$678$	−49.4611	−	0.731083i	−1.89954	−	0.0280771i
$679$	−41.8099	−	18.0350i	−1.60452	−	0.692121i
$680$	−58.7509	−	29.6763i	−2.25299	−	1.13803i
$681$	−3.39870	+	7.99719i	−0.130238	+	0.306453i
$682$	−1.13200	+	0.911607i	−0.0433466	+	0.0349072i
$683$	−24.5285	+	20.5819i	−0.938557	+	0.787543i	−0.977334	−	0.211705i	$-0.932098\pi$
$683$	−24.5285	+	20.5819i	−0.938557	+	0.787543i	0.0387764	+	0.999248i	$0.487654\pi$
$684$	14.8442	−	10.3836i	0.567582	−	0.397027i
$685$	−53.0419	−	44.5074i	−2.02663	−	1.70054i
$686$	−6.50578	−	0.131202i	−0.248392	−	0.00500932i
$687$	7.77347	−	2.87681i	0.296577	−	0.109757i
$688$	15.2940	−	25.1662i	0.583079	−	0.959451i
$689$	15.3790	+	0.895725i	0.585893	+	0.0341244i
$690$	58.1442	−	5.92641i	2.21351	−	0.225615i
$691$	−33.8395	−	10.1309i	−1.28732	−	0.385397i	−0.431235	−	0.902240i	$-0.641922\pi$
$691$	−33.8395	−	10.1309i	−1.28732	−	0.385397i	−0.856080	+	0.516843i	$0.827107\pi$
$692$	2.30143	−	14.5680i	0.0874872	−	0.553791i
$693$	−3.60647	+	1.60196i	−0.136998	+	0.0608534i
$694$	−3.09903	+	4.51103i	−0.117638	+	0.171236i
$695$	−18.8326	−	43.6589i	−0.714361	−	1.65607i
$696$	−27.9458	−	20.6719i	−1.05928	−	0.783565i
$697$	−18.0430	−	60.2679i	−0.683428	−	2.28281i
$698$	−2.41951	+	17.6126i	−0.0915799	+	0.666646i
$699$	11.6791	−	11.1381i	0.441744	−	0.421282i
$700$	60.3351	+	28.9647i	2.28045	+	1.09476i
$701$	−28.7233	−	16.5834i	−1.08487	−	0.626347i	−0.152660	−	0.988279i	$-0.548784\pi$
$701$	−28.7233	−	16.5834i	−1.08487	−	0.626347i	−0.932205	+	0.361932i	$0.882117\pi$
$702$	6.83744	+	13.7517i	0.258062	+	0.519025i
$703$	−0.543827	+	0.313978i	−0.0205108	+	0.0118419i
$704$	1.18170	−	2.70498i	0.0445369	−	0.101948i
$705$	21.6383	−	43.6701i	0.814945	−	1.64471i
$706$	−17.8600	+	23.0067i	−0.672170	+	0.865870i
$707$	1.99906	−	2.11888i	0.0751824	−	0.0796887i
$708$	10.9799	+	9.88713i	0.412651	+	0.371581i
$709$	16.4678	+	1.92481i	0.618460	+	0.0722877i	0.419553	−	0.907731i	$-0.362187\pi$
$709$	16.4678	+	1.92481i	0.618460	+	0.0722877i	0.198907	+	0.980018i	$0.436261\pi$
$710$	−0.963262	+	12.2705i	−0.0361506	+	0.460502i
$711$	−0.0828090	−	0.220112i	−0.00310558	−	0.00825483i
$712$	−21.6824	−	9.41248i	−0.812583	−	0.352748i
$713$	4.04074	+	17.0492i	0.151327	+	0.638498i
$714$	30.0990	−	44.3224i	1.12643	−	1.65872i
$715$	1.60727	−	2.44373i	0.0601083	−	0.0913902i
$716$	−23.7545	+	37.5605i	−0.887749	+	1.40370i
$717$	−14.0553	+	24.6501i	−0.524906	+	0.920576i
$718$	29.6826	+	17.9448i	1.10774	+	0.669693i
$719$	−2.85237	+	16.1766i	−0.106375	+	0.603284i	0.884287	+	0.466944i	$0.154645\pi$
$719$	−2.85237	+	16.1766i	−0.106375	+	0.603284i	−0.990662	+	0.136340i	$0.956466\pi$
$720$	8.42810	−	44.7286i	0.314097	−	1.66694i
$721$	−6.22238	−	35.2889i	−0.231734	−	1.31423i
$722$	5.04476	−	13.0363i	0.187746	−	0.485161i
$723$	15.4832	+	10.0644i	0.575826	+	0.374300i
$724$	32.1199	−	10.2442i	1.19373	−	0.380722i
$725$	7.73212	+	66.1526i	0.287164	+	2.45684i
$726$	−9.47004	+	24.8688i	−0.351466	+	0.922969i
$727$	−31.9318	+	1.85982i	−1.18429	+	0.0689768i	−0.638955	−	0.769244i	$-0.720633\pi$
$727$	−31.9318	+	1.85982i	−1.18429	+	0.0689768i	−0.545331	+	0.838221i	$0.683596\pi$
$728$	15.2948	+	14.4970i	0.566863	+	0.537294i
$729$	21.2330	+	16.6781i	0.786407	+	0.617708i
$730$	1.81358	+	6.53455i	0.0671237	+	0.241854i
$731$	2.62638	+	45.0932i	0.0971402	+	1.66783i
$732$	0.374295	−	4.00778i	0.0138343	−	0.148132i
$733$	19.3169	−	2.25782i	0.713485	−	0.0833944i	0.248396	−	0.968659i	$-0.420097\pi$
$733$	19.3169	−	2.25782i	0.713485	−	0.0833944i	0.465089	+	0.885264i	$0.346022\pi$
$734$	0.418549	+	11.0053i	0.0154489	+	0.406212i
$735$	−20.4421	+	31.4482i	−0.754018	+	1.15999i
$736$	−23.2944	−	26.9013i	−0.858643	−	0.991593i
$737$	−2.67312	+	0.471343i	−0.0984656	+	0.0173621i
$738$	36.5697	−	23.5631i	1.34615	−	0.867369i
$739$	−14.5280	−	2.56167i	−0.534420	−	0.0942326i	−0.100076	−	0.994980i	$-0.531909\pi$
$739$	−14.5280	−	2.56167i	−0.534420	−	0.0942326i	−0.434344	+	0.900747i	$0.643020\pi$
$740$	−0.425459	+	1.51932i	−0.0156402	+	0.0558513i
$741$	−9.49426	−	5.41356i	−0.348780	−	0.198872i
$742$	27.5400	−	24.9525i	1.01103	−	0.916035i
$743$	−1.61301	−	1.06090i	−0.0591758	−	0.0389205i	0.519576	−	0.854424i	$-0.326090\pi$
$743$	−1.61301	−	1.06090i	−0.0591758	−	0.0389205i	−0.578752	+	0.815503i	$0.696460\pi$
$744$	13.6246	+	0.751590i	0.499501	+	0.0275546i
$745$	13.3231	−	3.15764i	0.488122	−	0.115687i
$746$	10.8407	−	7.73586i	0.396908	−	0.283230i
$747$	−14.2140	+	5.34752i	−0.520065	+	0.195656i
$748$	0.865666	+	4.44407i	0.0316519	+	0.162491i
$749$	8.12828	−	69.5418i	0.297001	−	2.54100i
$750$	−34.3785	+	21.8901i	−1.25533	+	0.799315i
$751$	18.4272	+	17.3851i	0.672417	+	0.634393i	0.944743	−	0.327812i	$-0.106311\pi$
$751$	18.4272	+	17.3851i	0.672417	+	0.634393i	−0.272326	+	0.962205i	$0.587793\pi$
$752$	−29.3317	+	4.49468i	−1.06962	+	0.163904i
$753$	−31.0617	−	15.3909i	−1.13195	−	0.560875i
$754$	−4.05732	+	20.5751i	−0.147759	+	0.749302i
$755$	13.6157	+	23.5831i	0.495526	+	0.858277i
$756$	35.2251	+	11.4806i	1.28112	+	0.417544i
$757$	−9.88889	+	17.1281i	−0.359418	+	0.622530i	−0.987864	−	0.155324i	$-0.950358\pi$
$757$	−9.88889	+	17.1281i	−0.359418	+	0.622530i	0.628446	+	0.777853i	$0.283691\pi$
$758$	−1.23749	−	1.08164i	−0.0449476	−	0.0392868i
$759$	−2.77459	−	2.90935i	−0.100711	−	0.105603i
$760$	12.7605	+	29.7715i	0.462871	+	1.07992i
$761$	9.77015	−	2.92499i	0.354168	−	0.106031i	−0.104777	−	0.994496i	$-0.533413\pi$
$761$	9.77015	−	2.92499i	0.354168	−	0.106031i	0.458944	+	0.888465i	$0.348228\pi$
$762$	3.97387	+	9.60017i	0.143958	+	0.347778i
$763$	1.70942	−	0.737371i	0.0618851	−	0.0266946i
$764$	−4.73747	+	13.7763i	−0.171396	+	0.498410i
$765$	28.3403	+	63.8022i	1.02465	+	2.30677i
$766$	−34.4702	−	15.7008i	−1.24546	−	0.567291i
$767$	2.55661	−	8.53968i	0.0923140	−	0.308350i
$768$	−25.2378	+	11.4479i	−0.910689	+	0.413092i
$769$	−2.97182	+	51.0242i	−0.107167	+	1.83998i	0.334024	+	0.942565i	$0.391593\pi$
$769$	−2.97182	+	51.0242i	−0.107167	+	1.83998i	−0.441190	+	0.897413i	$0.645444\pi$
$770$	−1.48846	−	6.89722i	−0.0536404	−	0.248559i
$771$	7.54867	+	20.3974i	0.271859	+	0.734595i
$772$	6.50359	+	25.4108i	0.234069	+	0.914554i
$773$	−24.5742	+	29.2863i	−0.883871	+	1.05336i	0.114333	+	0.993443i	$0.463527\pi$
$773$	−24.5742	+	29.2863i	−0.883871	+	1.05336i	−0.998204	+	0.0599139i	$0.980917\pi$
$774$	−29.4507	+	10.4069i	−1.05858	+	0.374068i
$775$	−16.8057	−	20.0283i	−0.603679	−	0.719437i
$776$	−33.9185	−	12.4343i	−1.21760	−	0.446366i
$777$	−1.18195	−	0.502314i	−0.0424024	−	0.0180204i
$778$	−11.8324	+	7.44493i	−0.424213	+	0.266914i
$779$	−12.2622	+	28.4270i	−0.439340	+	1.01850i
$780$	−26.5656	+	6.95176i	−0.951199	+	0.248913i
$781$	0.707361	−	0.465239i	0.0253114	−	0.0166476i
$782$	52.8457	+	13.6557i	1.88976	+	0.488326i
$783$	9.08097	+	35.7333i	0.324527	+	1.27700i
$784$	22.8228	−	0.815080i	0.815101	−	0.0291100i
$785$	−13.8171	+	27.5121i	−0.493152	+	0.981947i
$786$	−21.2904	+	24.6245i	−0.759404	+	0.878326i
$787$	−22.7469	+	16.9344i	−0.810838	+	0.603647i	−0.920687	−	0.390302i	$-0.872371\pi$
$787$	−22.7469	+	16.9344i	−0.810838	+	0.603647i	0.109849	+	0.993948i	$0.464963\pi$
$788$	34.8196	+	7.59867i	1.24040	+	0.270692i
$789$	14.4245	−	15.4549i	0.513524	−	0.550209i
$790$	0.415496	−	0.0646539i	0.0147827	−	0.00230028i
$791$	67.6523	+	24.6234i	2.40544	+	0.875509i
$792$	−2.78589	+	1.42874i	−0.0989922	+	0.0507682i
$793$	−2.28200	+	0.830581i	−0.0810362	+	0.0294948i
$794$	17.8314	−	9.82103i	0.632814	−	0.348535i
$795$	8.66565	+	47.6438i	0.307339	+	1.68975i
$796$	1.02044	−	25.2895i	0.0361686	−	0.896363i
$797$	−6.09784	−	12.1418i	−0.215997	−	0.430085i	0.759375	−	0.650654i	$-0.225505\pi$
$797$	−6.09784	−	12.1418i	−0.215997	−	0.430085i	−0.975371	+	0.220569i	$0.929209\pi$
$798$	−25.3668	+	7.18757i	−0.897975	+	0.254437i
$799$	33.1063	−	31.2342i	1.17122	−	1.10499i
$800$	49.0773	+	20.2716i	1.73514	+	0.716709i
$801$	11.4925	+	22.2819i	0.406068	+	0.787293i
$802$	3.48416	−	1.66271i	0.123030	−	0.0587122i
$803$	0.278564	−	0.374176i	0.00983031	−	0.0132044i
$804$	21.6106	+	13.5049i	0.762146	+	0.476281i
$805$	−82.7693	−	19.6167i	−2.91723	−	0.691397i
$806$	−3.10758	−	7.62326i	−0.109460	−	0.268518i
$807$	2.98653	−	26.8021i	0.105131	−	0.943480i
$808$	1.48969	−	1.76702i	0.0524071	−	0.0621634i
$809$		−	16.0043i		−	0.562683i	−0.959608	−	0.281341i	$-0.909221\pi$
$809$		−	16.0043i		−	0.562683i	0.959608	−	0.281341i	$-0.0907793\pi$
$810$	−36.9395	+	31.0824i	−1.29792	+	1.09213i
$811$			14.6868i			0.515725i	0.966182	+	0.257862i	$0.0830181\pi$
$811$			14.6868i			0.515725i	−0.966182	+	0.257862i	$0.916982\pi$
$812$	28.5501	+	41.7652i	1.00191	+	1.46567i
$813$	51.0051	−	22.3280i	1.78883	−	0.783076i
$814$	0.100500	−	0.0409684i	0.00352253	−	0.00143594i
$815$	−28.3485	−	6.71871i	−0.993004	−	0.235346i
$816$	21.8795	−	36.4431i	0.765935	−	1.27577i
$817$	13.2739	−	17.8299i	0.464394	−	0.623789i
$818$	−15.0739	−	31.5869i	−0.527046	−	1.10441i
$819$	−2.83381	−	22.1715i	−0.0990213	−	0.774734i
$820$	27.9046	+	72.6081i	0.974472	+	2.53559i
$821$	−7.19381	+	6.78701i	−0.251066	+	0.236868i	−0.801477	−	0.598025i	$-0.795952\pi$
$821$	−7.19381	+	6.78701i	−0.251066	+	0.236868i	0.550412	+	0.834893i	$0.314471\pi$
$822$	31.1631	−	32.0680i	1.08694	−	1.11850i
$823$	−2.12742	−	4.23604i	−0.0741571	−	0.147659i	0.853499	−	0.521094i	$-0.174476\pi$
$823$	−2.12742	−	4.23604i	−0.0741571	−	0.147659i	−0.927656	+	0.373435i	$0.878180\pi$
$824$	−6.49224	−	27.6783i	−0.226168	−	0.964221i
$825$	5.64813	+	2.02138i	0.196643	+	0.0703753i
$826$	−10.3745	−	18.8363i	−0.360975	−	0.655400i
$827$	35.4582	−	12.9057i	1.23300	−	0.448776i	0.358377	−	0.933577i	$-0.383330\pi$
$827$	35.4582	−	12.9057i	1.23300	−	0.448776i	0.874624	+	0.484801i	$0.161108\pi$
$828$	1.08000	+	37.7284i	0.0375326	+	1.31115i
$829$	−24.4864	−	8.91232i	−0.850448	−	0.309538i	−0.120225	−	0.992747i	$-0.538362\pi$
$829$	−24.4864	−	8.91232i	−0.850448	−	0.309538i	−0.730223	+	0.683209i	$0.760584\pi$
$830$	−4.17513	−	26.8313i	−0.144921	−	0.931328i
$831$	20.8315	+	4.81885i	0.722638	+	0.167164i
$832$	12.7579	+	10.8062i	0.442301	+	0.374638i
$833$	−28.0972	+	20.9176i	−0.973511	+	0.724752i
$834$	29.0062	−	10.0745i	1.00440	−	0.348850i
$835$	−0.762954	+	1.51917i	−0.0264031	+	0.0525729i
$836$	1.07942	−	1.94914i	0.0373325	−	0.0674125i
$837$	−10.6863	−	9.76065i	−0.369374	−	0.337377i
$838$	3.23826	−	12.5317i	0.111864	−	0.432899i
$839$	−15.7619	+	10.3667i	−0.544160	+	0.357900i	−0.791635	−	0.610995i	$-0.790770\pi$
$839$	−15.7619	+	10.3667i	−0.544160	+	0.357900i	0.247475	+	0.968894i	$0.420399\pi$
$840$	−32.9458	+	57.4705i	−1.13674	+	1.98292i
$841$	−8.45457	+	19.5999i	−0.291537	+	0.675858i
$842$	−11.8701	−	18.8655i	−0.409072	−	0.650148i
$843$	16.8448	−	12.6820i	0.580167	−	0.436793i
$844$	4.32657	−	6.03349i	0.148927	−	0.207681i
$845$	−21.0460	−	25.0817i	−0.724005	−	0.862836i
$846$	27.1083	+	15.9925i	0.932003	+	0.549832i
$847$	24.8950	−	29.6688i	0.855404	−	1.01943i
$848$	20.7104	−	20.9860i	0.711198	−	0.720662i
$849$	1.73580	−	2.09142i	0.0595726	−	0.0717772i
$850$	−79.6121	+	17.1808i	−2.73067	+	0.589295i
$851$	0.0760743	−	1.30615i	0.00260779	−	0.0447741i
$852$	−7.85778	−	1.19803i	−0.269203	−	0.0410440i
$853$	1.54855	−	5.17251i	0.0530213	−	0.177104i	−0.927377	−	0.374127i	$-0.877942\pi$
$853$	1.54855	−	5.17251i	0.0530213	−	0.177104i	0.980399	+	0.197024i	$0.0631276\pi$
$854$	−2.42837	+	5.33136i	−0.0830970	+	0.182435i
$855$	9.49834	−	33.0166i	0.324836	−	1.12914i
$856$	3.35827	−	55.4474i	0.114783	−	1.89515i
$857$	31.1800	−	13.4498i	1.06509	−	0.459435i	0.209885	−	0.977726i	$-0.432691\pi$
$857$	31.1800	−	13.4498i	1.06509	−	0.459435i	0.855204	+	0.518291i	$0.173432\pi$
$858$	1.49829	+	1.15024i	0.0511508	+	0.0392685i
$859$	−31.5742	+	9.45269i	−1.07730	+	0.322522i	−0.775822	−	0.630952i	$-0.782664\pi$
$859$	−31.5742	+	9.45269i	−1.07730	+	0.322522i	−0.301476	+	0.953474i	$0.597479\pi$
$860$	−7.47279	−	55.3475i	−0.254820	−	1.88733i
$861$	−61.5295	+	14.9331i	−2.09692	+	0.508919i
$862$	25.4460	−	29.1125i	0.866694	−	0.991575i
$863$	16.8495	−	29.1842i	0.573563	−	0.993441i	−0.422633	−	0.906301i	$-0.638894\pi$
$863$	16.8495	−	29.1842i	0.573563	−	0.993441i	0.996196	−	0.0871400i	$-0.0277727\pi$
$864$	28.4120	+	7.53390i	0.966595	+	0.256308i
$865$	−13.9853	−	24.2233i	−0.475515	−	0.823616i
$866$	37.4712	+	7.38914i	1.27332	+	0.251093i
$867$	2.27100	+	35.6808i	0.0771272	+	1.21178i
$868$	−18.3728	−	7.53923i	−0.623614	−	0.255898i
$869$	−0.0210390	−	0.0198493i	−0.000713700	−	0.000673342i
$870$	−65.8609	+	2.86001i	−2.23289	+	0.0969634i
$871$	1.78485	−	15.2704i	0.0604773	−	0.517416i
$872$	1.32145	−	0.659828i	0.0447498	−	0.0223446i
$873$	19.5148	+	32.9754i	0.660477	+	1.11605i
$874$	−15.6020	−	21.8641i	−0.527747	−	0.739564i
$875$	57.7180	−	13.6794i	1.95123	−	0.462449i
$876$	−4.29413	+	0.860482i	−0.145085	+	0.0290730i
$877$	−43.3803	−	28.5317i	−1.46485	−	0.963445i	−0.996816	−	0.0797337i	$-0.974593\pi$
$877$	−43.3803	−	28.5317i	−1.46485	−	0.963445i	−0.468031	−	0.883712i	$-0.655037\pi$
$878$	−6.77670	−	7.47942i	−0.228702	−	0.252418i
$879$	2.43297	−	1.42220i	0.0820622	−	0.0479696i
$880$	−1.48461	−	5.39767i	−0.0500461	−	0.181956i
$881$	28.2935	+	4.98890i	0.953232	+	0.168080i	0.628573	−	0.777751i	$-0.283639\pi$
$881$	28.2935	+	4.98890i	0.953232	+	0.168080i	0.324659	+	0.945831i	$0.394751\pi$
$882$	−19.2928	−	14.6467i	−0.649623	−	0.493180i
$883$	−25.5035	+	4.49695i	−0.858260	+	0.151334i	−0.585425	−	0.810727i	$-0.699072\pi$
$883$	−25.5035	+	4.49695i	−0.858260	+	0.151334i	−0.272835	+	0.962061i	$0.587961\pi$
$884$	−25.5203	−	2.52207i	−0.858342	−	0.0848265i
$885$	27.9825	+	1.47866i	0.940620	+	0.0497046i
$886$	8.73158	−	0.332077i	0.293343	−	0.0111563i
$887$	10.1567	−	1.18715i	0.341028	−	0.0398604i	0.0561446	−	0.998423i	$-0.482119\pi$
$887$	10.1567	−	1.18715i	0.341028	−	0.0398604i	0.284883	+	0.958562i	$0.408045\pi$
$888$	−0.958532	−	0.345549i	−0.0321662	−	0.0115959i
$889$	−0.879262	−	15.0963i	−0.0294895	−	0.506315i
$890$	−43.1951	+	11.9883i	−1.44790	+	0.401848i
$891$	3.24704	+	0.696066i	0.108780	+	0.0233191i
$892$	−9.69778	−	16.1254i	−0.324706	−	0.539917i
$893$	−22.3604	+	1.30234i	−0.748262	+	0.0435813i
$894$	1.40660	+	8.72978i	0.0470436	+	0.291968i
$895$	9.78470	+	83.7134i	0.327066	+	2.79823i
$896$	40.1646	−	3.68781i	1.34181	−	0.123201i
$897$	20.2938	−	10.3291i	0.677589	−	0.344879i
$898$	30.7461	+	11.8981i	1.02601	+	0.397043i
$899$	−3.43185	−	19.4630i	−0.114459	−	0.649127i
$900$	−26.7062	−	49.5856i	−0.890207	−	1.65285i
$901$	−7.85307	+	44.5369i	−0.261624	+	1.48374i
$902$	2.76821	−	4.57891i	0.0921712	−	0.152461i
$903$	45.4597	−	0.244774i	1.51280	−	0.00814557i
$904$	54.6813	+	16.5086i	1.81867	+	0.549066i
$905$	35.1346	−	53.4196i	1.16791	−	1.77573i
$906$	−15.8303	+	7.65943i	−0.525926	+	0.254467i
$907$	−10.5008	−	44.3062i	−0.348672	−	1.47116i	−0.811311	−	0.584615i	$-0.801246\pi$
$907$	−10.5008	−	44.3062i	−0.348672	−	1.47116i	0.462639	−	0.886547i	$-0.346903\pi$
$908$	6.31131	−	7.80014i	0.209448	−	0.258857i
$909$	−2.40940	+	0.451648i	−0.0799149	+	0.0149802i
$910$	39.8431	+	3.12779i	1.32079	+	0.103685i
$911$	46.9874	+	5.49204i	1.55676	+	0.181959i	0.850493	−	0.525986i	$-0.176304\pi$
$911$	46.9874	+	5.49204i	1.55676	+	0.181959i	0.706267	+	0.707945i	$0.250378\pi$
$912$	−19.7758	+	6.81729i	−0.654843	+	0.225743i
$913$	−1.28180	+	1.35863i	−0.0424214	+	0.0449640i
$914$	36.9409	+	28.6770i	1.22190	+	0.948551i
$915$	−4.22912	−	6.35526i	−0.139810	−	0.210099i
$916$	−9.54335	+	0.726951i	−0.315321	+	0.0240191i
$917$	41.0296	−	23.6884i	1.35492	−	0.782261i
$918$	−42.4277	+	15.2500i	−1.40032	+	0.503324i
$919$	27.4935	+	15.8734i	0.906928	+	0.523615i	0.879441	−	0.476007i	$-0.157916\pi$
$919$	27.4935	+	15.8734i	0.906928	+	0.523615i	0.0274862	+	0.999622i	$0.491250\pi$
$920$	−66.4344	−	11.8728i	−2.19028	−	0.391435i
$921$	−8.23913	−	2.41837i	−0.271488	−	0.0796881i
$922$	−1.45594	−	0.200008i	−0.0479487	−	0.00658691i
$923$	1.37535	+	4.59400i	0.0452703	+	0.151213i
$924$	4.51241	−	0.634005i	0.148448	−	0.0208572i
$925$	0.773263	+	1.79263i	0.0254247	+	0.0589412i
$926$	−26.5632	−	18.2487i	−0.872922	−	0.599688i
$927$	−13.2422	+	27.0909i	−0.434930	+	0.889781i
$928$	24.4660	+	31.8194i	0.803135	+	1.04452i
$929$	−46.6009	−	13.9514i	−1.52893	−	0.457730i	−0.591614	−	0.806221i	$-0.701509\pi$
$929$	−46.6009	−	13.9514i	−1.52893	−	0.457730i	−0.937312	+	0.348491i	$0.886694\pi$
$930$	20.9836	−	15.1449i	0.688079	−	0.496620i
$931$	17.2087	+	1.00229i	0.563992	+	0.0328488i
$932$	−16.5013	+	8.65945i	−0.540518	+	0.283650i
$933$	7.02259	−	41.1206i	0.229909	−	1.34623i
$934$	0.305536	−	15.1503i	0.00999746	−	0.495733i
$935$	6.57767	+	5.51932i	0.215113	+	0.180501i
$936$	−3.22693	−	17.4375i	−0.105476	−	0.569963i
$937$	19.2580	−	16.1594i	0.629132	−	0.527904i	−0.271527	−	0.962431i	$-0.587529\pi$
$937$	19.2580	−	16.1594i	0.629132	−	0.527904i	0.900659	+	0.434527i	$0.143084\pi$
$938$	−23.2624	−	28.8865i	−0.759546	−	0.943178i
$939$	−8.75811	+	1.07151i	−0.285810	+	0.0349673i
$940$	−37.8826	+	41.6169i	−1.23559	+	1.35739i
$941$	34.8606	+	15.0374i	1.13642	+	0.490205i	0.879345	−	0.476186i	$-0.157981\pi$
$941$	34.8606	+	15.0374i	1.13642	+	0.490205i	0.257078	+	0.966391i	$0.417240\pi$
$942$	−17.0695	−	10.1944i	−0.556154	−	0.332151i
$943$	−35.4453	−	53.8919i	−1.15426	−	1.75496i
$944$	−9.05253	−	14.4616i	−0.294635	−	0.470684i
$945$	65.6284	−	25.0945i	2.13489	−	0.816325i
$946$	−2.69216	+	2.74065i	−0.0875298	+	0.0891062i
$947$	−5.05797	−	2.54021i	−0.164362	−	0.0825457i	0.364716	−	0.931119i	$-0.381166\pi$
$947$	−5.05797	−	2.54021i	−0.164362	−	0.0825457i	−0.529078	+	0.848573i	$0.677462\pi$
$948$	0.0220831	+	0.270655i	0.000717227	+	0.00879047i
$949$	1.57781	+	2.11936i	0.0512178	+	0.0687974i
$950$	35.4466	+	18.7063i	1.15004	+	0.606911i
$951$	22.1831	−	6.77154i	0.719336	−	0.219582i
$952$	−47.4830	+	39.6560i	−1.53893	+	1.28526i
$953$	−11.0342	+	30.3161i	−0.357432	+	0.982035i	0.622486	+	0.782631i	$0.286123\pi$
$953$	−11.0342	+	30.3161i	−0.357432	+	0.982035i	−0.979917	+	0.199404i	$0.936099\pi$
$954$	−31.0942	+	3.33857i	−1.00671	+	0.108090i
$955$	9.44944	+	25.9621i	0.305777	+	0.840114i
$956$	23.4276	−	22.9068i	0.757704	−	0.740859i
$957$	2.93347	+	3.45799i	0.0948258	+	0.111781i
$958$	17.3449	+	5.57618i	0.560388	+	0.180158i
$959$	−58.1574	+	29.2077i	−1.87800	+	0.943167i
$960$	−23.5521	+	46.9845i	−0.760142	+	1.51642i
$961$	−15.9496	−	16.9056i	−0.514502	−	0.545341i
$962$	0.0590395	+	0.611879i	0.00190351	+	0.0197278i
$963$	−39.9686	+	43.2888i	−1.28797	+	1.39496i
$964$	−13.9959	−	16.0876i	−0.450778	−	0.518146i
$965$	39.9013	+	29.7054i	1.28447	+	0.956251i
$966$	16.5309	−	52.3864i	0.531874	−	1.68551i
$967$	6.73696	−	28.4255i	0.216646	−	0.914101i	−0.750700	−	0.660643i	$-0.770284\pi$
$967$	6.73696	−	28.4255i	0.216646	−	0.914101i	0.967346	−	0.253458i	$-0.0815681\pi$
$968$	18.4063	−	24.6048i	0.591600	−	0.790828i
$969$	19.0206	−	25.8385i	0.611031	−	0.830051i
$970$	−64.8398	+	22.1297i	−2.08188	+	0.710542i
$971$	23.4277			0.751829			0.375915	−	0.926654i	$-0.377329\pi$
$971$	23.4277			0.751829			0.375915	+	0.926654i	$0.377329\pi$
$972$	−18.2806	−	25.2551i	−0.586351	−	0.810057i
$973$	−44.6898			−1.43269
$974$	28.2474	−	9.64079i	0.905106	−	0.308911i
$975$	−20.1435	+	27.3638i	−0.645108	+	0.876342i
$976$	−1.68746	+	4.33079i	−0.0540142	+	0.138625i
$977$	2.82117	−	11.9035i	0.0902572	−	0.380825i	−0.909104	−	0.416570i	$-0.863232\pi$
$977$	2.82117	−	11.9035i	0.0902572	−	0.380825i	0.999361	+	0.0357446i	$0.0113803\pi$
$978$	5.66185	−	17.9424i	0.181046	−	0.573733i
$979$	2.47341	+	1.84138i	0.0790504	+	0.0588509i
$980$	32.6758	−	28.4274i	1.04379	−	0.908080i
$981$	−1.52819	−	0.344850i	−0.0487914	−	0.0110102i
$982$	1.97533	+	20.4721i	0.0630352	+	0.653290i
$983$	26.0766	+	27.6396i	0.831715	+	0.881566i	0.994461	−	0.105102i	$-0.0335168\pi$
$983$	26.0766	+	27.6396i	0.831715	+	0.881566i	−0.162747	+	0.986668i	$0.552035\pi$
$984$	−48.0789	+	14.5548i	−1.53270	+	0.463990i
$985$	60.3998	−	30.3339i	1.92450	−	0.966519i
$986$	−58.6104	−	18.8426i	−1.86653	−	0.600069i
$987$	−29.6332	−	34.9318i	−0.943235	−	1.11189i
$988$	8.82280	+	9.02339i	0.280691	+	0.287072i
$989$	15.8400	+	43.5202i	0.503684	+	1.38386i
$990$	−2.40292	+	5.42976i	−0.0763699	+	0.172569i
$991$	−16.9022	+	46.4384i	−0.536916	+	1.47517i	0.313774	+	0.949498i	$0.398407\pi$
$991$	−16.9022	+	46.4384i	−0.536916	+	1.47517i	−0.850690	+	0.525668i	$0.823816\pi$
$992$	−14.8879	−	5.15831i	−0.472692	−	0.163776i
$993$	−55.3499	+	16.8959i	−1.75648	+	0.536177i
$994$	10.2312	+	5.39931i	0.324513	+	0.171256i
$995$	−28.6638	−	38.5022i	−0.908704	−	1.22060i
$996$	17.4780	−	1.42605i	0.553811	−	0.0451863i
$997$	8.96485	+	4.50232i	0.283920	+	0.142590i	0.585060	−	0.810990i	$-0.301071\pi$
$997$	8.96485	+	4.50232i	0.283920	+	0.142590i	−0.301140	+	0.953580i	$0.597367\pi$
$998$	−11.0371	+	11.2359i	−0.349372	+	0.355665i
$999$	0.555408	+	0.927083i	0.0175723	+	0.0293316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.203.23	yes	936
3.2	odd	2		972.2.p.a.395.30		936
4.3	odd	2	inner	324.2.p.a.203.24	yes	936
12.11	even	2		972.2.p.a.395.29		936
81.2	odd	54	inner	324.2.p.a.83.24	yes	936
81.79	even	27		972.2.p.a.251.29		936
324.79	odd	54		972.2.p.a.251.30		936
324.83	even	54	inner	324.2.p.a.83.23	✓	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.83.23	✓	936	324.83	even	54	inner
324.2.p.a.83.24	yes	936	81.2	odd	54	inner
324.2.p.a.203.23	yes	936	1.1	even	1	trivial
324.2.p.a.203.24	yes	936	4.3	odd	2	inner
972.2.p.a.251.29		936	81.79	even	27
972.2.p.a.251.30		936	324.79	odd	54
972.2.p.a.395.29		936	12.11	even	2
972.2.p.a.395.30		936	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.456796 - 1.33841i) q^{2} +(1.02681 - 1.39487i) q^{3} +(-1.58267 + 1.22276i) q^{4} +(-0.874721 + 3.69074i) q^{5} +(-2.33595 - 0.737126i) q^{6} +(2.85958 + 2.12888i) q^{7} +(2.35951 + 1.55971i) q^{8} +(-0.891308 - 2.86454i) q^{9} +O(q^{10})\)	\(q+(-0.456796 - 1.33841i) q^{2} +(1.02681 - 1.39487i) q^{3} +(-1.58267 + 1.22276i) q^{4} +(-0.874721 + 3.69074i) q^{5} +(-2.33595 - 0.737126i) q^{6} +(2.85958 + 2.12888i) q^{7} +(2.35951 + 1.55971i) q^{8} +(-0.891308 - 2.86454i) q^{9} +(5.33928 - 0.515181i) q^{10} +(-0.253209 - 0.268386i) q^{11} +(0.0804759 + 3.46317i) q^{12} +(1.86762 - 0.937956i) q^{13} +(1.54306 - 4.79975i) q^{14} +(4.24991 + 5.00982i) q^{15} +(1.00972 - 3.87046i) q^{16} +(2.09840 + 5.76530i) q^{17} +(-3.42677 + 2.50144i) q^{18} +(1.03264 - 2.83716i) q^{19} +(-3.12849 - 6.91081i) q^{20} +(5.90576 - 1.80277i) q^{21} +(-0.243545 + 0.461494i) q^{22} +(3.75651 + 5.04586i) q^{23} +(4.59837 - 1.68967i) q^{24} +(-8.38825 - 4.21274i) q^{25} +(-2.10849 - 2.07119i) q^{26} +(-4.91085 - 1.69809i) q^{27} +(-7.12890 + 0.127258i) q^{28} +(-3.89902 - 5.92817i) q^{29} +(4.76384 - 7.97659i) q^{30} +(2.55754 + 1.10321i) q^{31} +(-5.64149 + 0.416598i) q^{32} +(-0.634360 + 0.0776106i) q^{33} +(6.75779 - 5.44208i) q^{34} +(-10.3585 + 8.69179i) q^{35} +(4.91329 + 3.44377i) q^{36} +(-0.159326 - 0.133690i) q^{37} +(-4.26898 - 0.0860925i) q^{38} +(0.609378 - 3.56819i) q^{39} +(-7.82041 + 7.34403i) q^{40} +(-10.2366 - 0.596211i) q^{41} +(-5.11058 - 7.08082i) q^{42} +(7.05296 + 2.11152i) q^{43} +(0.728918 + 0.115154i) q^{44} +(11.3519 - 0.783915i) q^{45} +(5.03747 - 7.33267i) q^{46} +(-2.93833 - 6.81180i) q^{47} +(-4.36199 - 5.38266i) q^{48} +(1.63746 + 5.46949i) q^{49} +(-1.80664 + 13.1513i) q^{50} +(10.1965 + 2.99290i) q^{51} +(-1.80895 + 3.76814i) q^{52} +(6.38357 + 3.68555i) q^{53} +(-0.0294758 + 7.34841i) q^{54} +(1.21203 - 0.699765i) q^{55} +(3.42678 + 9.48325i) q^{56} +(-2.89713 - 4.35363i) q^{57} +(-6.15326 + 7.92645i) q^{58} +(2.92703 - 3.10247i) q^{59} +(-12.8520 - 2.73229i) q^{60} +(-1.15413 - 0.134898i) q^{61} +(0.308278 - 3.92697i) q^{62} +(3.54949 - 10.0889i) q^{63} +(3.13459 + 7.36032i) q^{64} +(1.82810 + 7.71336i) q^{65} +(0.393648 + 0.813581i) q^{66} +(4.04241 - 6.14618i) q^{67} +(-10.3707 - 6.55876i) q^{68} +(10.8955 - 0.0586662i) q^{69} +(16.3649 + 9.89349i) q^{70} +(-0.398446 + 2.25970i) q^{71} +(2.36480 - 8.14909i) q^{72} +(0.219535 + 1.24504i) q^{73} +(-0.106153 + 0.274312i) q^{74} +(-14.4894 + 7.37480i) q^{75} +(1.83483 + 5.75297i) q^{76} +(-0.152711 - 1.30652i) q^{77} +(-5.05406 + 0.814341i) q^{78} +(0.0782584 - 0.00455803i) q^{79} +(13.4016 + 7.11218i) q^{80} +(-7.41114 + 5.10637i) q^{81} +(3.87804 + 13.9730i) q^{82} +(-0.294342 - 5.05366i) q^{83} +(-7.14254 + 10.0745i) q^{84} +(-23.1137 + 2.70161i) q^{85} +(-0.395692 - 10.4043i) q^{86} +(-12.2726 - 0.648512i) q^{87} +(-0.178845 - 1.02819i) q^{88} +(-8.23009 + 1.45119i) q^{89} +(-6.23470 - 14.8354i) q^{90} +(7.33742 + 1.29379i) q^{91} +(-12.1152 - 3.39266i) q^{92} +(4.16495 - 2.43463i) q^{93} +(-7.77476 + 7.04429i) q^{94} +(9.56793 + 6.29293i) q^{95} +(-5.21166 + 8.29690i) q^{96} +(-12.4281 + 2.94552i) q^{97} +(6.57243 - 4.69003i) q^{98} +(-0.543113 + 0.964540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

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