LMFDB - Embedded newform 324.2.p.a.83.23

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			83.23
Character	$\chi$	$=$	324.83
Dual form			324.2.p.a.203.23

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

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

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	−0.711092	−	0.703099i	$-0.751799\pi$
$5$	−0.874721	−	3.69074i	−0.391187	−	1.65055i	0.319905	−	0.947450i	$-0.396349\pi$
$6$	−2.33595	+	0.737126i	−0.953646	+	0.300930i
$7$	2.85958	−	2.12888i	1.08082	−	0.804641i	0.0991206	−	0.995075i	$-0.468397\pi$
$7$	2.85958	−	2.12888i	1.08082	−	0.804641i	0.981700	+	0.190434i	$0.0609896\pi$
$8$	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	−0.764420	−	0.644718i	$-0.776975\pi$
$11$	−0.253209	+	0.268386i	−0.0763453	+	0.0809213i	0.688075	+	0.725640i	$0.258456\pi$
$12$	0.0804759	−	3.46317i	0.0232314	−	0.999730i
$13$	1.86762	+	0.937956i	0.517986	+	0.260142i	0.688530	−	0.725208i	$-0.258256\pi$
$13$	1.86762	+	0.937956i	0.517986	+	0.260142i	−0.170544	+	0.985350i	$0.554553\pi$
$14$	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	−0.373399	−	0.927671i	$-0.621808\pi$
$17$	2.09840	−	5.76530i	0.508936	−	1.39829i	0.882336	−	0.470620i	$-0.155970\pi$
$18$	−3.42677	−	2.50144i	−0.807698	−	0.589596i
$19$	1.03264	+	2.83716i	0.236904	+	0.650888i	0.999989	+	0.00459076i	$0.00146129\pi$
$19$	1.03264	+	2.83716i	0.236904	+	0.650888i	−0.763085	+	0.646298i	$0.776316\pi$
$20$	−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	−0.213877	−	0.976861i	$-0.568609\pi$
$23$	3.75651	−	5.04586i	0.783286	−	1.05214i	0.997163	−	0.0752748i	$-0.0239834\pi$
$24$	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	0.266540	+	0.963824i	$0.414120\pi$
$29$	−3.89902	+	5.92817i	−0.724030	+	1.10083i	−0.990570	+	0.137010i	$0.956251\pi$
$30$	4.76384	+	7.97659i	0.869754	+	1.45632i
$31$	2.55754	−	1.10321i	0.459347	−	0.198143i	−0.153816	−	0.988100i	$-0.549156\pi$
$31$	2.55754	−	1.10321i	0.459347	−	0.198143i	0.613163	+	0.789957i	$0.289897\pi$
$32$	−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	−0.655790	−	0.754943i	$-0.727664\pi$
$37$	−0.159326	+	0.133690i	−0.0261930	+	0.0219785i	0.629597	+	0.776922i	$0.283220\pi$
$38$	−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	−0.834173	−	0.551502i	$-0.814055\pi$
$41$	−10.2366	+	0.596211i	−1.59868	+	0.0931125i	−0.764507	+	0.644615i	$0.777018\pi$
$42$	−5.11058	+	7.08082i	−0.788579	+	1.09259i
$43$	7.05296	−	2.11152i	1.07557	−	0.322003i	0.300434	−	0.953803i	$-0.402869\pi$
$43$	7.05296	−	2.11152i	1.07557	−	0.322003i	0.775132	+	0.631799i	$0.217683\pi$
$44$	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	0.557911	+	0.829901i	$0.311603\pi$
$47$	−2.93833	+	6.81180i	−0.428599	+	0.993604i	−0.986510	+	0.163703i	$0.947656\pi$
$48$	−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	0.00723169	−	0.999974i	$-0.497698\pi$
$53$	6.38357	−	3.68555i	0.876850	−	0.506250i	0.869619	+	0.493724i	$0.164365\pi$
$54$	−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	0.889309	−	0.457307i	$-0.151186\pi$
$59$	2.92703	+	3.10247i	0.381067	+	0.403908i	−0.508242	+	0.861214i	$0.669704\pi$
$60$	−12.8520	+	2.73229i	−1.65919	+	0.352737i
$61$	−1.15413	+	0.134898i	−0.147771	+	0.0172719i	−0.189657	−	0.981850i	$-0.560737\pi$
$61$	−1.15413	+	0.134898i	−0.147771	+	0.0172719i	0.0418860	+	0.999122i	$0.486663\pi$
$62$	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	0.993311	−	0.115466i	$-0.0368360\pi$
$67$	4.04241	+	6.14618i	0.493858	+	0.750875i	−0.499453	+	0.866341i	$0.666466\pi$
$68$	−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	0.951993	−	0.306120i	$-0.0990307\pi$
$71$	−0.398446	−	2.25970i	−0.0472869	−	0.268177i	−0.999280	+	0.0379425i	$0.987920\pi$
$72$	2.36480	+	8.14909i	0.278695	+	0.960380i
$73$	0.219535	−	1.24504i	0.0256946	−	0.145721i	−0.969261	−	0.246033i	$-0.920873\pi$
$73$	0.219535	−	1.24504i	0.0256946	−	0.145721i	0.994956	+	0.100312i	$0.0319840\pi$
$74$	−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	0.0625466	−	0.998042i	$-0.480078\pi$
$79$	0.0782584	+	0.00455803i	0.00880476	+	0.000512819i	−0.0537419	+	0.998555i	$0.517115\pi$
$80$	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	0.942852	+	0.333211i	$0.108132\pi$
$83$	−0.294342	+	5.05366i	−0.0323083	+	0.554711i	−0.975160	+	0.221500i	$0.928905\pi$
$84$	−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	−0.280508	−	0.959852i	$-0.590503\pi$
$89$	−8.23009	−	1.45119i	−0.872387	−	0.153825i	−0.591880	+	0.806026i	$0.701614\pi$
$90$	−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	−0.455378	−	0.890298i	$-0.650496\pi$
$97$	−12.4281	−	2.94552i	−1.26188	−	0.299072i	−0.806506	+	0.591226i	$0.798644\pi$
$98$	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	0.997137	−	0.0756184i	$-0.0240931\pi$
$101$	0.0948622	+	0.811598i	0.00943914	+	0.0807570i	−0.987698	+	0.156375i	$0.950019\pi$
$102$	−0.651993	+	15.0142i	−0.0645569	+	1.48663i
$103$	−7.31110	+	6.89767i	−0.720384	+	0.679647i	−0.956386	−	0.292105i	$-0.905644\pi$
$103$	−7.31110	+	6.89767i	−0.720384	+	0.679647i	0.236002	+	0.971753i	$0.424163\pi$
$104$	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	−0.202436	+	0.979295i	$0.564886\pi$
$107$	−9.81977	+	17.0083i	−0.949313	+	1.64426i	−0.746877	+	0.664963i	$0.768448\pi$
$108$	9.84864	+	3.31728i	0.947686	+	0.319205i
$109$	0.261103	+	0.452244i	0.0250091	+	0.0433171i	0.878259	−	0.478185i	$-0.158705\pi$
$109$	0.261103	+	0.452244i	0.0250091	+	0.0433171i	−0.853250	+	0.521502i	$0.825372\pi$
$110$	−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	0.999634	−	0.0270702i	$-0.00861778\pi$
$113$	19.3462	+	5.79188i	1.81994	+	0.544854i	0.820306	+	0.571924i	$0.193803\pi$
$114$	−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	−0.873327	−	0.487134i	$-0.838042\pi$
$127$	−2.72655	+	3.24937i	−0.241942	+	0.288335i	0.631385	+	0.775469i	$0.282487\pi$
$128$	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	0.977578	+	0.210572i	$0.0675326\pi$
$131$	5.26366	+	12.2025i	0.459888	+	1.06614i	−0.517690	+	0.855568i	$0.673208\pi$
$132$	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	−0.909400	−	0.415922i	$-0.863459\pi$
$137$	−8.19288	−	16.3134i	−0.699965	−	1.39374i	0.209435	−	0.977823i	$-0.432837\pi$
$138$	−5.05556	+	14.5559i	−0.430358	+	1.23908i
$139$	−10.0551	−	7.48577i	−0.852866	−	0.634935i	0.0793465	−	0.996847i	$-0.474717\pi$
$139$	−10.0551	−	7.48577i	−0.852866	−	0.634935i	−0.932212	+	0.361912i	$0.882124\pi$
$140$	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	−0.950172	−	0.311727i	$-0.899092\pi$
$149$	−1.62011	+	3.22591i	−0.132725	+	0.264277i	0.817447	+	0.576004i	$0.195389\pi$
$150$	16.4892	−	16.0239i	1.34634	−	1.30835i
$151$	5.22213	+	4.92682i	0.424971	+	0.400939i	0.868793	−	0.495176i	$-0.164896\pi$
$151$	5.22213	+	4.92682i	0.424971	+	0.400939i	−0.443822	+	0.896115i	$0.646378\pi$
$152$	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	0.0969799	−	0.995286i	$-0.469082\pi$
$157$	7.89799	−	1.87186i	0.630328	−	0.149390i	0.533348	+	0.845896i	$0.320934\pi$
$158$	−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	$-0.902743\pi$
$163$		−	7.68098i		−	0.601621i	0.953684	−	0.300810i	$-0.0972571\pi$
$164$	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	−0.213707	−	0.976898i	$-0.568554\pi$
$167$	0.436113	−	0.103361i	0.0337474	−	0.00799828i	0.247455	+	0.968899i	$0.420406\pi$
$168$	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	0.454822	−	0.890582i	$-0.349703\pi$
$173$	−5.36388	−	5.06056i	−0.407808	−	0.384747i	−0.862630	+	0.505835i	$0.831184\pi$
$174$	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	0.970898	−	0.239495i	$-0.0769818\pi$
$179$	20.8808	+	7.59999i	1.56070	+	0.568050i	0.589807	+	0.807545i	$0.299204\pi$
$180$	−17.0078	−	15.1213i	−1.26769	−	1.12708i
$181$	−15.8404	+	5.76543i	−1.17741	+	0.428541i	−0.855285	−	0.518158i	$-0.826618\pi$
$181$	−15.8404	+	5.76543i	−1.17741	+	0.428541i	−0.322121	+	0.946698i	$0.604396\pi$
$182$	−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	0.750259	−	0.661144i	$-0.229929\pi$
$191$	6.08575	+	4.00266i	0.440349	+	0.289622i	−0.309910	+	0.950766i	$0.600299\pi$
$192$	13.4853	−	3.18534i	0.973218	−	0.229882i
$193$	5.19455	+	12.0423i	0.373912	+	0.866826i	0.996446	+	0.0842331i	$0.0268440\pi$
$193$	5.19455	+	12.0423i	0.373912	+	0.866826i	−0.622534	+	0.782593i	$0.713897\pi$
$194$	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	−0.999946	−	0.0103894i	$-0.996693\pi$
$197$	−11.4542	+	13.6505i	−0.816076	+	0.972561i	0.183870	+	0.982950i	$0.441137\pi$
$198$	1.53904	−	0.286309i	0.109375	−	0.0203471i
$199$	−8.13451	−	9.69433i	−0.576640	−	0.687213i	0.396340	−	0.918104i	$-0.370280\pi$
$199$	−8.13451	−	9.69433i	−0.576640	−	0.687213i	−0.972980	+	0.230891i	$0.925836\pi$
$200$	−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	0.162041	−	0.986784i	$-0.448192\pi$
$211$	−3.55626	−	1.06468i	−0.244823	−	0.0732953i	−0.406864	+	0.913489i	$0.633378\pi$
$212$	−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	−0.979240	−	0.202705i	$-0.935027\pi$
$223$	−1.09225	−	9.34481i	−0.0731426	−	0.625775i	0.906097	−	0.423070i	$-0.139047\pi$
$224$	−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	0.0653952	−	0.997859i	$-0.479169\pi$
$227$	−4.88161	−	1.15696i	−0.324004	−	0.0767904i	−0.389399	+	0.921069i	$0.627317\pi$
$228$	9.90865	−	3.34788i	0.656216	−	0.221719i
$229$	3.99822	−	2.62967i	0.264210	−	0.173774i	−0.410491	−	0.911865i	$-0.634643\pi$
$229$	3.99822	−	2.62967i	0.264210	−	0.173774i	0.674701	+	0.738091i	$0.264272\pi$
$230$	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	0.135212	−	0.990817i	$-0.456828\pi$
$233$	9.17615	−	1.61800i	0.601149	−	0.105999i	0.465937	+	0.884818i	$0.345717\pi$
$234$	−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	−0.427816	−	0.903866i	$-0.640717\pi$
$239$	−16.2720	−	1.90192i	−1.05255	−	0.123025i	−0.624730	+	0.780841i	$0.714791\pi$
$240$	23.6815	+	11.3906i	1.52864	+	0.735262i
$241$	0.619928	−	10.6438i	0.0399331	−	0.685625i	−0.917636	−	0.397422i	$-0.869905\pi$
$241$	0.619928	−	10.6438i	0.0399331	−	0.685625i	0.957569	−	0.288203i	$-0.0930579\pi$
$242$	−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	0.653798	+	0.756669i	$0.273175\pi$
$251$	−3.47543	+	19.7101i	−0.219367	+	1.24409i	−0.873165	+	0.487424i	$0.837937\pi$
$252$	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	0.553536	−	0.832826i	$-0.313278\pi$
$257$	−6.90020	−	10.4912i	−0.430423	−	0.654426i	−0.983958	+	0.178400i	$0.942908\pi$
$258$	−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	0.266206	−	0.963916i	$-0.414230\pi$
$263$	12.1229	−	1.41697i	0.747531	−	0.0873739i	0.481325	+	0.876542i	$0.340156\pi$
$264$	−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	0.851152	−	0.524919i	$-0.175904\pi$
$269$	13.4840	+	7.78500i	0.822135	+	0.474660i	−0.0290174	+	0.999579i	$0.509238\pi$
$270$	−27.0953	+	6.53660i	−1.64897	+	0.397805i
$271$	27.8391	−	16.0729i	1.69110	−	0.976360i	0.737476	−	0.675373i	$-0.236017\pi$
$271$	27.8391	−	16.0729i	1.69110	−	0.976360i	0.953628	−	0.300987i	$-0.0973160\pi$
$272$	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	−0.705847	−	0.708365i	$-0.749433\pi$
$277$	4.88948	−	11.3351i	0.293781	−	0.681060i	0.999627	+	0.0273048i	$0.00869247\pi$
$278$	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	0.0806225	−	0.996745i	$-0.474309\pi$
$281$	11.6621	−	3.49140i	0.695702	−	0.208279i	0.615079	+	0.788465i	$0.289124\pi$
$282$	1.84261	−	18.0779i	0.109726	−	1.07652i
$283$	1.56653	−	0.0912401i	0.0931206	−	0.00542366i	−0.0115212	−	0.999934i	$-0.503667\pi$
$283$	1.56653	−	0.0912401i	0.0931206	−	0.00542366i	0.104642	+	0.994510i	$0.466630\pi$
$284$	−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	−0.351992	−	0.936003i	$-0.614496\pi$
$293$	1.49400	−	0.644447i	0.0872802	−	0.0376490i	0.439272	+	0.898354i	$0.355236\pi$
$294$	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	−0.978628	−	0.205641i	$-0.934072\pi$
$307$	−1.69558	+	4.65857i	−0.0967719	+	0.265879i	0.881856	+	0.471520i	$0.156294\pi$
$308$	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	0.938095	−	0.346377i	$-0.112588\pi$
$311$	21.5229	+	10.8092i	1.22045	+	0.612933i	0.282354	+	0.959310i	$0.408885\pi$
$312$	7.00319	+	7.46874i	0.396478	+	0.422834i
$313$	−3.49585	+	3.70539i	−0.197597	+	0.209441i	−0.818594	−	0.574372i	$-0.805246\pi$
$313$	−3.49585	+	3.70539i	−0.197597	+	0.209441i	0.620997	+	0.783813i	$0.286728\pi$
$314$	−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	−0.251686	−	0.967809i	$-0.580985\pi$
$317$	10.7411	−	7.99645i	0.603280	−	0.449125i	0.854966	+	0.518683i	$0.173578\pi$
$318$	−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	−0.500064	+	0.865989i	$0.666690\pi$
$331$	−26.8006	+	19.9523i	−1.47309	+	1.09668i	−0.973028	+	0.230687i	$0.925903\pi$
$332$	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	0.907494	−	0.420065i	$-0.137993\pi$
$337$	20.4222	+	10.2564i	1.11247	+	0.558703i	0.204974	+	0.978767i	$0.434289\pi$
$338$	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	−0.859814	−	0.510607i	$-0.829421\pi$
$347$	−2.31099	+	3.10420i	−0.124060	+	0.166642i	0.735754	+	0.677249i	$0.236828\pi$
$348$	20.2165	+	13.9800i	1.08372	+	0.749409i
$349$	−11.2338	+	5.64183i	−0.601332	+	0.302000i	−0.723300	−	0.690534i	$-0.757376\pi$
$349$	−11.2338	+	5.64183i	−0.601332	+	0.302000i	0.121968	+	0.992534i	$0.461079\pi$
$350$	−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	−0.999999	−	0.00171576i	$-0.999454\pi$
$353$	−11.3170	+	17.2067i	−0.602344	+	0.915819i	0.397655	+	0.917535i	$0.369824\pi$
$354$	−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	−0.00580232	−	0.999983i	$-0.501847\pi$
$359$	−18.7882	−	15.7651i	−0.991601	−	0.832052i	−0.985799	+	0.167931i	$0.946291\pi$
$360$	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	−0.475531	−	0.879699i	$-0.657744\pi$
$367$	−7.46037	+	2.23349i	−0.389428	+	0.116587i	0.0861026	+	0.996286i	$0.472559\pi$
$368$	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	−0.859160	−	0.511707i	$-0.829013\pi$
$373$	2.70087	−	9.02152i	0.139846	−	0.467117i	0.999005	+	0.0445906i	$0.0141983\pi$
$374$	−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	0.525627	−	0.850715i	$-0.323831\pi$
$379$	1.00647	+	0.581088i	0.0516991	+	0.0298485i	−0.473928	+	0.880564i	$0.657164\pi$
$380$	−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	0.999996	−	0.00268457i	$-0.000854526\pi$
$383$	18.3800	+	19.4816i	0.939172	+	0.995464i	−0.0608246	+	0.998148i	$0.519373\pi$
$384$	−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	0.884204	+	0.467101i	$0.154702\pi$
$389$	−2.27968	+	9.61872i	−0.115584	+	0.487688i	−0.999788	+	0.0205871i	$0.993446\pi$
$390$	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	−0.855587	−	0.517659i	$-0.826803\pi$
$397$	2.49961	−	14.1760i	0.125452	−	0.711472i	0.981039	−	0.193813i	$-0.0620854\pi$
$398$	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	−0.983015	−	0.183523i	$-0.941250\pi$
$401$	0.316914	−	2.71138i	0.0158259	−	0.135400i	0.998841	+	0.0481231i	$0.0153240\pi$
$402$	−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	0.699551	−	0.714583i	$-0.253384\pi$
$409$	24.5810	+	2.87310i	1.21545	+	0.142066i	0.515900	+	0.856649i	$0.327458\pi$
$410$	−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	−0.348820	−	0.937190i	$-0.613418\pi$
$419$	7.64662	−	5.02926i	0.373562	−	0.245696i	0.722382	+	0.691494i	$0.243047\pi$
$420$	−30.9347	+	35.1737i	−1.50946	+	1.71630i
$421$	15.3360	+	3.63470i	0.747430	+	0.177144i	0.586644	−	0.809845i	$-0.300449\pi$
$421$	15.3360	+	3.63470i	0.747430	+	0.177144i	0.160786	+	0.986989i	$0.448597\pi$
$422$	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	−0.322530	−	0.946559i	$-0.604533\pi$
$431$	13.6704	−	23.6778i	0.658479	−	1.14052i	0.981009	−	0.193960i	$-0.0621332\pi$
$432$	−11.5310	−	17.2927i	−0.554784	−	0.831995i
$433$	−13.5032	−	23.3882i	−0.648922	−	1.12397i	−0.983381	−	0.181556i	$-0.941887\pi$
$433$	−13.5032	−	23.3882i	−0.648922	−	1.12397i	0.334458	−	0.942411i	$-0.391447\pi$
$434$	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	0.546673	−	0.837346i	$-0.315894\pi$
$439$	6.55305	+	2.82671i	0.312760	+	0.134911i	−0.233913	+	0.972257i	$0.575153\pi$
$440$	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	0.905518	−	0.424308i	$-0.139483\pi$
$443$	−1.77205	−	5.91905i	−0.0841926	−	0.281223i	−0.989710	+	0.143086i	$0.954298\pi$
$444$	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	0.286151	−	0.958185i	$-0.407624\pi$
$449$	−14.9846	−	17.8579i	−0.707166	−	0.842768i	−0.993317	+	0.115417i	$0.963180\pi$
$450$	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	−0.297868	−	0.954607i	$-0.596275\pi$
$457$	−27.6280	−	18.1712i	−1.29238	−	0.850014i	−0.994515	+	0.104594i	$0.966646\pi$
$458$	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	0.904232	−	0.427042i	$-0.140444\pi$
$461$	0.466380	+	0.928638i	0.0217215	+	0.0432510i	−0.882510	+	0.470293i	$0.844148\pi$
$462$	−0.606348	−	3.16453i	−0.0282098	−	0.147227i
$463$	18.2791	+	13.6083i	0.849501	+	0.632430i	0.931314	−	0.364218i	$-0.118664\pi$
$463$	18.2791	+	13.6083i	0.849501	+	0.632430i	−0.0818131	+	0.996648i	$0.526071\pi$
$464$	−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	−0.0983769	−	0.995149i	$-0.531365\pi$
$467$	10.0689	−	3.66477i	0.465932	−	0.169585i	0.564309	+	0.825564i	$0.309143\pi$
$468$	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	0.590841	−	0.806788i	$-0.298796\pi$
$479$	−7.69314	−	10.3337i	−0.351508	−	0.472158i	−0.942350	+	0.334630i	$0.891389\pi$
$480$	−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	$-0.841295\pi$
$487$		−	21.1052i		−	0.956369i	0.878259	−	0.478185i	$-0.158705\pi$
$488$	−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	−0.537161	−	0.843480i	$-0.680503\pi$
$491$	−14.1512	+	3.35389i	−0.638633	+	0.151359i	−0.101472	+	0.994838i	$0.532355\pi$
$492$	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	−0.977298	−	0.211868i	$-0.932045\pi$
$499$	−4.99823	+	9.95230i	−0.223752	+	0.445526i	0.753547	+	0.657395i	$0.228342\pi$
$500$	−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	−0.205741	−	0.978607i	$-0.565960\pi$
$503$	−22.2568	−	8.10083i	−0.992384	−	0.361198i	−0.786643	+	0.617408i	$0.788183\pi$
$504$	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	0.00618061	−	0.999981i	$-0.498033\pi$
$509$	−21.4334	−	15.9566i	−0.950018	−	0.707262i	−0.956199	+	0.292719i	$0.905440\pi$
$510$	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	−0.991455	−	0.130450i	$-0.958358\pi$
$521$	−15.7683	+	18.7919i	−0.690823	+	0.823290i	0.300632	+	0.953740i	$0.402802\pi$
$522$	28.1901	−	10.5613i	1.23385	−	0.462257i
$523$	−15.0537	−	17.9403i	−0.658253	−	0.784475i	0.328881	−	0.944371i	$-0.393329\pi$
$523$	−15.0537	−	17.9403i	−0.658253	−	0.784475i	−0.987134	+	0.159896i	$0.948884\pi$
$524$	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	0.108004	−	0.994150i	$-0.465554\pi$
$541$	21.2815	−	36.8606i	0.914962	−	1.58476i	0.806957	−	0.590610i	$-0.201113\pi$
$542$	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	−0.827061	−	0.562112i	$-0.809989\pi$
$547$	−3.55324	−	30.3999i	−0.151926	−	1.29981i	0.675135	−	0.737694i	$-0.264085\pi$
$548$	−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	−0.305138	−	0.952308i	$-0.598703\pi$
$557$	−6.28172	+	1.10764i	−0.266165	+	0.0469320i	0.0389729	+	0.999240i	$0.487591\pi$
$558$	−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	0.224062	−	0.974575i	$-0.428068\pi$
$563$	5.15676	+	0.602739i	0.217332	+	0.0254024i	−0.00673023	+	0.999977i	$0.502142\pi$
$564$	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	0.787516	−	0.616295i	$-0.211367\pi$
$569$	35.7367	+	2.08142i	1.49816	+	0.0872578i	0.710643	+	0.703552i	$0.248404\pi$
$570$	−17.7115	+	21.7527i	−0.741853	+	0.911121i
$571$	1.26983	−	10.8641i	0.0531407	−	0.454647i	−0.940304	−	0.340335i	$-0.889459\pi$
$571$	1.26983	−	10.8641i	0.0531407	−	0.454647i	0.993445	−	0.114312i	$-0.0364664\pi$
$572$	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	0.999811	+	0.0194545i	$0.00619295\pi$
$577$	1.60819	+	9.12049i	0.0669498	+	0.379691i	−0.932861	+	0.360237i	$0.882696\pi$
$578$	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	−0.487638	−	0.873046i	$-0.662141\pi$
$587$	−18.4325	+	2.15446i	−0.760793	+	0.0889239i	−0.273155	+	0.961970i	$0.588067\pi$
$588$	−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	0.379094	−	0.925358i	$-0.376236\pi$
$593$	−5.66767	−	3.27223i	−0.232743	−	0.134374i	−0.611837	+	0.790984i	$0.709569\pi$
$594$	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	−0.946519	−	0.322649i	$-0.895427\pi$
$599$	0.528274	−	1.76456i	0.0215847	−	0.0720979i	0.968103	+	0.250551i	$0.0806118\pi$
$600$	−45.6904	+	5.19835i	−1.86530	+	0.212222i
$601$	4.82735	−	11.1910i	0.196912	−	0.456492i	−0.790940	−	0.611894i	$-0.790408\pi$
$601$	4.82735	−	11.1910i	0.196912	−	0.456492i	0.987851	+	0.155402i	$0.0496672\pi$
$602$	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	0.672611	−	0.739996i	$-0.265173\pi$
$607$	35.1472	−	2.04709i	1.42658	−	0.0830890i	0.753972	+	0.656907i	$0.228136\pi$
$608$	−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	0.997464	−	0.0711743i	$-0.0226747\pi$
$613$	27.2490	+	22.8647i	1.10058	+	0.923495i	0.103115	+	0.994669i	$0.467119\pi$
$614$	−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	−0.998652	−	0.0519027i	$-0.983471\pi$
$617$	−40.8912	+	17.6387i	−1.64622	+	0.710108i	−0.647564	+	0.762011i	$0.724212\pi$
$618$	11.9939	−	21.5018i	0.482465	−	0.864928i
$619$	18.2520	−	27.7508i	0.733609	−	1.11540i	−0.255298	−	0.966862i	$-0.582174\pi$
$619$	18.2520	−	27.7508i	0.733609	−	1.11540i	0.988907	−	0.148536i	$-0.0474561\pi$
$620$	−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	0.392863	+	0.919597i	$0.371485\pi$
$631$	−12.5396	+	34.4522i	−0.499193	+	1.37152i	−0.892056	+	0.451925i	$0.850738\pi$
$632$	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	−0.719879	−	0.694100i	$-0.755803\pi$
$641$	−6.61816	+	4.92704i	−0.261402	+	0.194606i	0.458477	+	0.888706i	$0.348395\pi$
$642$	10.4012	−	46.9690i	0.410501	−	1.85372i
$643$	−0.0807862	−	0.340864i	−0.00318590	−	0.0134424i	0.971429	−	0.237332i	$-0.0762728\pi$
$643$	−0.0807862	−	0.340864i	−0.00318590	−	0.0134424i	−0.974615	+	0.223889i	$0.928125\pi$
$644$	−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	−0.743029	−	0.669260i	$-0.766611\pi$
$653$	−9.69506	−	40.9067i	−0.379397	−	1.60080i	0.363631	−	0.931543i	$-0.381537\pi$
$654$	−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	−0.231408	+	0.972857i	$0.574333\pi$
$659$	−30.5270	+	32.3568i	−1.18916	+	1.26044i	−0.957756	+	0.287583i	$0.907148\pi$
$660$	2.52094	−	4.14114i	0.0981275	−	0.161194i
$661$	−0.0414178	−	0.0208008i	−0.00161097	−	0.000809058i	0.447994	−	0.894037i	$-0.352139\pi$
$661$	−0.0414178	−	0.0208008i	−0.00161097	−	0.000809058i	−0.449604	+	0.893228i	$0.648435\pi$
$662$	−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	−0.873971	−	0.485978i	$-0.838463\pi$
$673$	−26.0993	+	13.1076i	−1.00606	+	0.505260i	−0.132085	+	0.991238i	$0.542167\pi$
$674$	−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	0.00976724	−	0.999952i	$-0.496891\pi$
$677$	24.0436	−	36.5565i	0.924071	−	1.40498i	0.914304	−	0.405029i	$-0.132739\pi$
$678$	−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	0.0387764	−	0.999248i	$-0.487654\pi$
$683$	−24.5285	−	20.5819i	−0.938557	−	0.787543i	−0.977334	+	0.211705i	$0.932098\pi$
$684$	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	−0.856080	−	0.516843i	$-0.827107\pi$
$691$	−33.8395	+	10.1309i	−1.28732	+	0.385397i	−0.431235	+	0.902240i	$0.641922\pi$
$692$	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	−0.932205	−	0.361932i	$-0.882117\pi$
$701$	−28.7233	+	16.5834i	−1.08487	+	0.626347i	−0.152660	+	0.988279i	$0.548784\pi$
$702$	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	0.198907	−	0.980018i	$-0.436261\pi$
$709$	16.4678	−	1.92481i	0.618460	−	0.0722877i	0.419553	+	0.907731i	$0.362187\pi$
$710$	−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	−0.990662	−	0.136340i	$-0.956466\pi$
$719$	−2.85237	−	16.1766i	−0.106375	−	0.603284i	0.884287	−	0.466944i	$-0.154645\pi$
$720$	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	−0.545331	−	0.838221i	$-0.683596\pi$
$727$	−31.9318	−	1.85982i	−1.18429	−	0.0689768i	−0.638955	+	0.769244i	$0.720633\pi$
$728$	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	0.465089	−	0.885264i	$-0.346022\pi$
$733$	19.3169	+	2.25782i	0.713485	+	0.0833944i	0.248396	+	0.968659i	$0.420097\pi$
$734$	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	−0.434344	−	0.900747i	$-0.643020\pi$
$739$	−14.5280	+	2.56167i	−0.534420	+	0.0942326i	−0.100076	+	0.994980i	$0.531909\pi$
$740$	−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	−0.578752	−	0.815503i	$-0.696460\pi$
$743$	−1.61301	+	1.06090i	−0.0591758	+	0.0389205i	0.519576	+	0.854424i	$0.326090\pi$
$744$	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	−0.272326	−	0.962205i	$-0.587793\pi$
$751$	18.4272	−	17.3851i	0.672417	−	0.634393i	0.944743	+	0.327812i	$0.106311\pi$
$752$	−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	0.628446	−	0.777853i	$-0.283691\pi$
$757$	−9.88889	−	17.1281i	−0.359418	−	0.622530i	−0.987864	+	0.155324i	$0.950358\pi$
$758$	−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	0.458944	−	0.888465i	$-0.348228\pi$
$761$	9.77015	+	2.92499i	0.354168	+	0.106031i	−0.104777	+	0.994496i	$0.533413\pi$
$762$	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	−0.441190	−	0.897413i	$-0.645444\pi$
$769$	−2.97182	−	51.0242i	−0.107167	−	1.83998i	0.334024	−	0.942565i	$-0.391593\pi$
$770$	−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	−0.998204	−	0.0599139i	$-0.980917\pi$
$773$	−24.5742	−	29.2863i	−0.883871	−	1.05336i	0.114333	−	0.993443i	$-0.463527\pi$
$774$	−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	0.109849	−	0.993948i	$-0.464963\pi$
$787$	−22.7469	−	16.9344i	−0.810838	−	0.603647i	−0.920687	+	0.390302i	$0.872371\pi$
$788$	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	−0.975371	−	0.220569i	$-0.929209\pi$
$797$	−6.09784	+	12.1418i	−0.215997	+	0.430085i	0.759375	+	0.650654i	$0.225505\pi$
$798$	−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	$0.0907793\pi$
$809$			16.0043i			0.562683i	−0.959608	+	0.281341i	$0.909221\pi$
$810$	−36.9395	−	31.0824i	−1.29792	−	1.09213i
$811$		−	14.6868i		−	0.515725i	−0.966182	−	0.257862i	$-0.916982\pi$
$811$		−	14.6868i		−	0.515725i	0.966182	−	0.257862i	$-0.0830181\pi$
$812$	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	0.550412	−	0.834893i	$-0.314471\pi$
$821$	−7.19381	−	6.78701i	−0.251066	−	0.236868i	−0.801477	+	0.598025i	$0.795952\pi$
$822$	31.1631	+	32.0680i	1.08694	+	1.11850i
$823$	−2.12742	+	4.23604i	−0.0741571	+	0.147659i	−0.927656	−	0.373435i	$-0.878180\pi$
$823$	−2.12742	+	4.23604i	−0.0741571	+	0.147659i	0.853499	+	0.521094i	$0.174476\pi$
$824$	−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	0.874624	−	0.484801i	$-0.161108\pi$
$827$	35.4582	+	12.9057i	1.23300	+	0.448776i	0.358377	+	0.933577i	$0.383330\pi$
$828$	1.08000	−	37.7284i	0.0375326	−	1.31115i
$829$	−24.4864	+	8.91232i	−0.850448	+	0.309538i	−0.730223	−	0.683209i	$-0.760584\pi$
$829$	−24.4864	+	8.91232i	−0.850448	+	0.309538i	−0.120225	+	0.992747i	$0.538362\pi$
$830$	−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	0.247475	−	0.968894i	$-0.420399\pi$
$839$	−15.7619	−	10.3667i	−0.544160	−	0.357900i	−0.791635	+	0.610995i	$0.790770\pi$
$840$	−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	0.980399	−	0.197024i	$-0.0631276\pi$
$853$	1.54855	+	5.17251i	0.0530213	+	0.177104i	−0.927377	+	0.374127i	$0.877942\pi$
$854$	−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	0.855204	−	0.518291i	$-0.173432\pi$
$857$	31.1800	+	13.4498i	1.06509	+	0.459435i	0.209885	+	0.977726i	$0.432691\pi$
$858$	1.49829	−	1.15024i	0.0511508	−	0.0392685i
$859$	−31.5742	−	9.45269i	−1.07730	−	0.322522i	−0.301476	−	0.953474i	$-0.597479\pi$
$859$	−31.5742	−	9.45269i	−1.07730	−	0.322522i	−0.775822	+	0.630952i	$0.782664\pi$
$860$	−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	0.996196	+	0.0871400i	$0.0277727\pi$
$863$	16.8495	+	29.1842i	0.573563	+	0.993441i	−0.422633	+	0.906301i	$0.638894\pi$
$864$	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	−0.468031	+	0.883712i	$0.655037\pi$
$877$	−43.3803	+	28.5317i	−1.46485	+	0.963445i	−0.996816	+	0.0797337i	$0.974593\pi$
$878$	−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	0.324659	−	0.945831i	$-0.394751\pi$
$881$	28.2935	−	4.98890i	0.953232	−	0.168080i	0.628573	+	0.777751i	$0.283639\pi$
$882$	−19.2928	+	14.6467i	−0.649623	+	0.493180i
$883$	−25.5035	−	4.49695i	−0.858260	−	0.151334i	−0.272835	−	0.962061i	$-0.587961\pi$
$883$	−25.5035	−	4.49695i	−0.858260	−	0.151334i	−0.585425	+	0.810727i	$0.699072\pi$
$884$	−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	0.284883	−	0.958562i	$-0.408045\pi$
$887$	10.1567	+	1.18715i	0.341028	+	0.0398604i	0.0561446	+	0.998423i	$0.482119\pi$
$888$	−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	0.462639	+	0.886547i	$0.346903\pi$
$907$	−10.5008	+	44.3062i	−0.348672	+	1.47116i	−0.811311	+	0.584615i	$0.801246\pi$
$908$	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	0.706267	−	0.707945i	$-0.250378\pi$
$911$	46.9874	−	5.49204i	1.55676	−	0.181959i	0.850493	+	0.525986i	$0.176304\pi$
$912$	−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	0.0274862	−	0.999622i	$-0.491250\pi$
$919$	27.4935	−	15.8734i	0.906928	−	0.523615i	0.879441	+	0.476007i	$0.157916\pi$
$920$	−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	−0.937312	−	0.348491i	$-0.886694\pi$
$929$	−46.6009	+	13.9514i	−1.52893	+	0.457730i	−0.591614	+	0.806221i	$0.701509\pi$
$930$	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	0.900659	−	0.434527i	$-0.143084\pi$
$937$	19.2580	+	16.1594i	0.629132	+	0.527904i	−0.271527	+	0.962431i	$0.587529\pi$
$938$	−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	0.257078	−	0.966391i	$-0.417240\pi$
$941$	34.8606	−	15.0374i	1.13642	−	0.490205i	0.879345	+	0.476186i	$0.157981\pi$
$942$	−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	−0.529078	−	0.848573i	$-0.677462\pi$
$947$	−5.05797	+	2.54021i	−0.164362	+	0.0825457i	0.364716	+	0.931119i	$0.381166\pi$
$948$	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	−0.979917	−	0.199404i	$-0.936099\pi$
$953$	−11.0342	−	30.3161i	−0.357432	−	0.982035i	0.622486	−	0.782631i	$-0.286123\pi$
$954$	−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	0.967346	+	0.253458i	$0.0815681\pi$
$967$	6.73696	+	28.4255i	0.216646	+	0.914101i	−0.750700	+	0.660643i	$0.770284\pi$
$968$	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	0.999361	−	0.0357446i	$-0.0113803\pi$
$977$	2.82117	+	11.9035i	0.0902572	+	0.380825i	−0.909104	+	0.416570i	$0.863232\pi$
$978$	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	−0.162747	−	0.986668i	$-0.552035\pi$
$983$	26.0766	−	27.6396i	0.831715	−	0.881566i	0.994461	+	0.105102i	$0.0335168\pi$
$984$	−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	−0.850690	−	0.525668i	$-0.823816\pi$
$991$	−16.9022	−	46.4384i	−0.536916	−	1.47517i	0.313774	−	0.949498i	$-0.398407\pi$
$992$	−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	−0.301140	−	0.953580i	$-0.597367\pi$
$997$	8.96485	−	4.50232i	0.283920	−	0.142590i	0.585060	+	0.810990i	$0.301071\pi$
$998$	−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.83.23	✓	936
3.2	odd	2		972.2.p.a.251.30		936
4.3	odd	2	inner	324.2.p.a.83.24	yes	936
12.11	even	2		972.2.p.a.251.29		936
81.40	even	27		972.2.p.a.395.29		936
81.41	odd	54	inner	324.2.p.a.203.24	yes	936
324.203	even	54	inner	324.2.p.a.203.23	yes	936
324.283	odd	54		972.2.p.a.395.30		936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.83.23	✓	936	1.1	even	1	trivial
324.2.p.a.83.24	yes	936	4.3	odd	2	inner
324.2.p.a.203.23	yes	936	324.203	even	54	inner
324.2.p.a.203.24	yes	936	81.41	odd	54	inner
972.2.p.a.251.29		936	12.11	even	2
972.2.p.a.251.30		936	3.2	odd	2
972.2.p.a.395.29		936	81.40	even	27
972.2.p.a.395.30		936	324.283	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

L-functions

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