LMFDB - Embedded newform 216.2.t.a.13.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.18
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0971026 - 1.41088i) q^{2} +(-1.32680 + 1.11338i) q^{3} +(-1.98114 - 0.273999i) q^{4} +(-0.561427 + 0.669083i) q^{5} +(1.44200 + 1.98006i) q^{6} +(3.98166 + 1.44920i) q^{7} +(-0.578953 + 2.76854i) q^{8} +(0.520786 - 2.95445i) q^{9} +O(q^{10})$	\(q+(0.0971026 - 1.41088i) q^{2} +(-1.32680 + 1.11338i) q^{3} +(-1.98114 - 0.273999i) q^{4} +(-0.561427 + 0.669083i) q^{5} +(1.44200 + 1.98006i) q^{6} +(3.98166 + 1.44920i) q^{7} +(-0.578953 + 2.76854i) q^{8} +(0.520786 - 2.95445i) q^{9} +(0.889477 + 0.857073i) q^{10} +(2.44783 + 2.91721i) q^{11} +(2.93364 - 1.84221i) q^{12} +(0.577399 + 0.101811i) q^{13} +(2.43128 - 5.47690i) q^{14} +(-4.05053e-5 - 1.51282i) q^{15} +(3.84985 + 1.08566i) q^{16} +(-1.31879 + 2.28422i) q^{17} +(-4.11779 - 1.02165i) q^{18} +(4.73328 - 2.73276i) q^{19} +(1.29559 - 1.17172i) q^{20} +(-6.89636 + 2.51028i) q^{21} +(4.35351 - 3.17032i) q^{22} +(-1.54640 + 0.562844i) q^{23} +(-2.31427 - 4.31789i) q^{24} +(0.735770 + 4.17276i) q^{25} +(0.199710 - 0.804753i) q^{26} +(2.59844 + 4.49979i) q^{27} +(-7.49115 - 3.96205i) q^{28} +(-6.06211 + 1.06891i) q^{29} +(-2.13440 - 0.146841i) q^{30} +(-1.38232 + 0.503124i) q^{31} +(1.90557 - 5.32624i) q^{32} +(-6.49573 - 1.14519i) q^{33} +(3.09469 + 2.08246i) q^{34} +(-3.20505 + 1.85043i) q^{35} +(-1.84127 + 5.71049i) q^{36} +(-4.51882 - 2.60894i) q^{37} +(-3.39597 - 6.94343i) q^{38} +(-0.879447 + 0.507780i) q^{39} +(-1.52734 - 1.94170i) q^{40} +(1.20772 - 6.84934i) q^{41} +(2.87204 + 9.97367i) q^{42} +(4.80685 + 5.72858i) q^{43} +(-4.05019 - 6.45012i) q^{44} +(1.68439 + 2.00716i) q^{45} +(0.643943 + 2.23643i) q^{46} +(1.61813 + 0.588949i) q^{47} +(-6.31672 + 2.84587i) q^{48} +(8.39109 + 7.04096i) q^{49} +(5.95869 - 0.632894i) q^{50} +(-0.793421 - 4.49901i) q^{51} +(-1.11601 - 0.359909i) q^{52} -12.3718i q^{53} +(6.60096 - 3.22913i) q^{54} -3.32613 q^{55} +(-6.31737 + 10.1844i) q^{56} +(-3.23752 + 8.89575i) q^{57} +(0.919458 + 8.65668i) q^{58} +(1.82254 - 2.17202i) q^{59} +(-0.414431 + 2.99712i) q^{60} +(2.99099 - 8.21769i) q^{61} +(0.575619 + 1.99914i) q^{62} +(6.35520 - 11.0089i) q^{63} +(-7.32963 - 3.20571i) q^{64} +(-0.392288 + 0.329168i) q^{65} +(-2.24648 + 9.05347i) q^{66} +(-10.2425 - 1.80603i) q^{67} +(3.23859 - 4.16401i) q^{68} +(1.42510 - 2.46851i) q^{69} +(2.29952 + 4.70161i) q^{70} +(-8.21222 + 14.2240i) q^{71} +(7.87801 + 3.15231i) q^{72} +(4.34334 + 7.52289i) q^{73} +(-4.11969 + 6.12217i) q^{74} +(-5.62207 - 4.71722i) q^{75} +(-10.1261 + 4.11707i) q^{76} +(5.51879 + 15.1627i) q^{77} +(0.631018 + 1.29010i) q^{78} +(-2.60048 - 14.7480i) q^{79} +(-2.88781 + 1.96635i) q^{80} +(-8.45756 - 3.07728i) q^{81} +(-9.54630 - 2.36904i) q^{82} +(14.0767 - 2.48210i) q^{83} +(14.3505 - 3.08362i) q^{84} +(-0.787924 - 2.16480i) q^{85} +(8.54907 - 6.22560i) q^{86} +(6.85309 - 8.16764i) q^{87} +(-9.49360 + 5.08799i) q^{88} +(-4.44056 - 7.69127i) q^{89} +(2.99541 - 2.18156i) q^{90} +(2.15146 + 1.24215i) q^{91} +(3.21786 - 0.691361i) q^{92} +(1.27390 - 2.20659i) q^{93} +(0.988059 - 2.22579i) q^{94} +(-0.828949 + 4.70120i) q^{95} +(3.40181 + 9.18846i) q^{96} +(9.68946 - 8.13042i) q^{97} +(10.7487 - 11.1551i) q^{98} +(9.89356 - 5.71275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.0971026	−	1.41088i	0.0686619	−	0.997640i
$2$	0.0971026	−	1.41088i	0.0686619	−	0.997640i
$3$	−1.32680	+	1.11338i	−0.766027	+	0.642808i
$3$	−1.32680	+	1.11338i	−0.766027	+	0.642808i
$4$	−1.98114	−	0.273999i	−0.990571	−	0.137000i
$5$	−0.561427	+	0.669083i	−0.251078	+	0.299223i	−0.876831	−	0.480798i	$-0.840347\pi$
$5$	−0.561427	+	0.669083i	−0.251078	+	0.299223i	0.625754	+	0.780021i	$0.284792\pi$
$6$	1.44200	+	1.98006i	0.588694	+	0.808356i
$7$	3.98166	+	1.44920i	1.50492	+	0.547748i	0.957330	−	0.288996i	$-0.0933214\pi$
$7$	3.98166	+	1.44920i	1.50492	+	0.547748i	0.547594	+	0.836744i	$0.315544\pi$
$8$	−0.578953	+	2.76854i	−0.204691	+	0.978827i
$9$	0.520786	−	2.95445i	0.173595	−	0.984817i
$10$	0.889477	+	0.857073i	0.281277	+	0.271030i
$11$	2.44783	+	2.91721i	0.738049	+	0.879572i	0.996250	−	0.0865187i	$-0.0275742\pi$
$11$	2.44783	+	2.91721i	0.738049	+	0.879572i	−0.258201	+	0.966091i	$0.583130\pi$
$12$	2.93364	−	1.84221i	0.846869	−	0.531802i
$13$	0.577399	+	0.101811i	0.160142	+	0.0282373i	0.253144	−	0.967429i	$-0.418535\pi$
$13$	0.577399	+	0.101811i	0.160142	+	0.0282373i	−0.0930024	+	0.995666i	$0.529646\pi$
$14$	2.43128	−	5.47690i	0.649786	−	1.46376i
$15$	−4.05053e−5	−	1.51282i	−1.04584e−5	−	0.390608i
$16$	3.84985	+	1.08566i	0.962462	+	0.271416i
$17$	−1.31879	+	2.28422i	−0.319854	+	0.554004i	−0.980457	−	0.196731i	$-0.936967\pi$
$17$	−1.31879	+	2.28422i	−0.319854	+	0.554004i	0.660603	+	0.750735i	$0.270301\pi$
$18$	−4.11779	−	1.02165i	−0.970573	−	0.240805i
$19$	4.73328	−	2.73276i	1.08589	−	0.626938i	0.153410	−	0.988163i	$-0.450974\pi$
$19$	4.73328	−	2.73276i	1.08589	−	0.626938i	0.932479	+	0.361224i	$0.117641\pi$
$20$	1.29559	−	1.17172i	0.289704	−	0.262004i
$21$	−6.89636	+	2.51028i	−1.50491	+	0.547788i
$22$	4.35351	−	3.17032i	0.928172	−	0.675914i
$23$	−1.54640	+	0.562844i	−0.322447	+	0.117361i	−0.498172	−	0.867078i	$-0.665995\pi$
$23$	−1.54640	+	0.562844i	−0.322447	+	0.117361i	0.175725	+	0.984439i	$0.443773\pi$
$24$	−2.31427	−	4.31789i	−0.472399	−	0.881385i
$25$	0.735770	+	4.17276i	0.147154	+	0.834551i
$26$	0.199710	−	0.804753i	0.0391663	−	0.157825i
$27$	2.59844	+	4.49979i	0.500070	+	0.865985i
$28$	−7.49115	−	3.96205i	−1.41569	−	0.748757i
$29$	−6.06211	+	1.06891i	−1.12571	+	0.198492i	−0.705345	−	0.708865i	$-0.749208\pi$
$29$	−6.06211	+	1.06891i	−1.12571	+	0.198492i	−0.420361	+	0.907357i	$0.638097\pi$
$30$	−2.13440	−	0.146841i	−0.389687	−	0.0268094i
$31$	−1.38232	+	0.503124i	−0.248272	+	0.0903638i	−0.463159	−	0.886275i	$-0.653284\pi$
$31$	−1.38232	+	0.503124i	−0.248272	+	0.0903638i	0.214886	+	0.976639i	$0.431062\pi$
$32$	1.90557	−	5.32624i	0.336860	−	0.941555i
$33$	−6.49573	−	1.14519i	−1.13076	−	0.199353i
$34$	3.09469	+	2.08246i	0.530735	+	0.357139i
$35$	−3.20505	+	1.85043i	−0.541752	+	0.312781i
$36$	−1.84127	+	5.71049i	−0.306878	+	0.951749i
$37$	−4.51882	−	2.60894i	−0.742890	−	0.428908i	0.0802290	−	0.996776i	$-0.474435\pi$
$37$	−4.51882	−	2.60894i	−0.742890	−	0.428908i	−0.823119	+	0.567869i	$0.807768\pi$
$38$	−3.39597	−	6.94343i	−0.550900	−	1.12637i
$39$	−0.879447	+	0.507780i	−0.140824	+	0.0813099i
$40$	−1.52734	−	1.94170i	−0.241494	−	0.307010i
$41$	1.20772	−	6.84934i	0.188615	−	1.06969i	−0.732608	−	0.680651i	$-0.761697\pi$
$41$	1.20772	−	6.84934i	0.188615	−	1.06969i	0.921222	−	0.389036i	$-0.127192\pi$
$42$	2.87204	+	9.97367i	0.443165	+	1.53897i
$43$	4.80685	+	5.72858i	0.733037	+	0.873600i	0.995828	−	0.0912534i	$-0.0290873\pi$
$43$	4.80685	+	5.72858i	0.733037	+	0.873600i	−0.262791	+	0.964853i	$0.584643\pi$
$44$	−4.05019	−	6.45012i	−0.610589	−	0.972392i
$45$	1.68439	+	2.00716i	0.251094	+	0.299209i
$46$	0.643943	+	2.23643i	0.0949442	+	0.329744i
$47$	1.61813	+	0.588949i	0.236028	+	0.0859071i	0.457326	−	0.889299i	$-0.348807\pi$
$47$	1.61813	+	0.588949i	0.236028	+	0.0859071i	−0.221298	+	0.975206i	$0.571029\pi$
$48$	−6.31672	+	2.84587i	−0.911741	+	0.410767i
$49$	8.39109	+	7.04096i	1.19873	+	1.00585i
$50$	5.95869	−	0.632894i	0.842686	−	0.0895048i
$51$	−0.793421	−	4.49901i	−0.111101	−	0.629987i
$52$	−1.11601	−	0.359909i	−0.154763	−	0.0499104i
$53$		−	12.3718i		−	1.69939i	−0.527272	−	0.849697i	$-0.676785\pi$
$53$		−	12.3718i		−	1.69939i	0.527272	−	0.849697i	$-0.323215\pi$
$54$	6.60096	−	3.22913i	0.898277	−	0.439429i
$55$	−3.32613			−0.448496
$56$	−6.31737	+	10.1844i	−0.844194	+	1.36094i
$57$	−3.23752	+	8.89575i	−0.428820	+	1.17827i
$58$	0.919458	+	8.65668i	0.120731	+	1.13668i
$59$	1.82254	−	2.17202i	0.237274	−	0.282773i	−0.634247	−	0.773131i	$-0.718690\pi$
$59$	1.82254	−	2.17202i	0.237274	−	0.282773i	0.871521	+	0.490358i	$0.163134\pi$
$60$	−0.414431	+	2.99712i	−0.0535028	+	0.386926i
$61$	2.99099	−	8.21769i	0.382958	−	1.05217i	−0.587147	−	0.809480i	$-0.699749\pi$
$61$	2.99099	−	8.21769i	0.382958	−	1.05217i	0.970105	−	0.242687i	$-0.0780288\pi$
$62$	0.575619	+	1.99914i	0.0731037	+	0.253891i
$63$	6.35520	−	11.0089i	0.800679	−	1.38699i
$64$	−7.32963	−	3.20571i	−0.916203	−	0.400714i
$65$	−0.392288	+	0.329168i	−0.0486573	+	0.0408283i
$66$	−2.24648	+	9.05347i	−0.276522	+	1.11441i
$67$	−10.2425	−	1.80603i	−1.25132	−	0.220642i	−0.491560	−	0.870843i	$-0.663573\pi$
$67$	−10.2425	−	1.80603i	−1.25132	−	0.220642i	−0.759762	+	0.650202i	$0.774684\pi$
$68$	3.23859	−	4.16401i	0.392737	−	0.504961i
$69$	1.42510	−	2.46851i	0.171562	−	0.297173i
$70$	2.29952	+	4.70161i	0.274845	+	0.561949i
$71$	−8.21222	+	14.2240i	−0.974612	+	1.68808i	−0.293402	+	0.955989i	$0.594787\pi$
$71$	−8.21222	+	14.2240i	−0.974612	+	1.68808i	−0.681210	+	0.732088i	$0.738546\pi$
$72$	7.87801	+	3.15231i	0.928432	+	0.371503i
$73$	4.34334	+	7.52289i	0.508350	+	0.880488i	0.999953	+	0.00966869i	$0.00307769\pi$
$73$	4.34334	+	7.52289i	0.508350	+	0.880488i	−0.491603	+	0.870819i	$0.663589\pi$
$74$	−4.11969	+	6.12217i	−0.478904	+	0.711687i
$75$	−5.62207	−	4.71722i	−0.649180	−	0.544697i
$76$	−10.1261	+	4.11707i	−1.16154	+	0.472261i
$77$	5.51879	+	15.1627i	0.628924	+	1.72796i
$78$	0.631018	+	1.29010i	0.0714487	+	0.146075i
$79$	−2.60048	−	14.7480i	−0.292577	−	1.65928i	−0.676892	−	0.736082i	$-0.736674\pi$
$79$	−2.60048	−	14.7480i	−0.292577	−	1.65928i	0.384315	−	0.923202i	$-0.374438\pi$
$80$	−2.88781	+	1.96635i	−0.322867	+	0.219844i
$81$	−8.45756	−	3.07728i	−0.939729	−	0.341920i
$82$	−9.54630	−	2.36904i	−1.05421	−	0.261616i
$83$	14.0767	−	2.48210i	1.54512	−	0.272446i	0.664870	−	0.746959i	$-0.268487\pi$
$83$	14.0767	−	2.48210i	1.54512	−	0.272446i	0.880249	+	0.474513i	$0.157376\pi$
$84$	14.3505	−	3.08362i	1.56577	−	0.336451i
$85$	−0.787924	−	2.16480i	−0.0854624	−	0.234806i
$86$	8.54907	−	6.22560i	0.921870	−	0.671324i
$87$	6.85309	−	8.16764i	0.734729	−	0.875663i
$88$	−9.49360	+	5.08799i	−1.01202	+	0.542382i
$89$	−4.44056	−	7.69127i	−0.470698	−	0.815273i	0.528740	−	0.848784i	$-0.322665\pi$
$89$	−4.44056	−	7.69127i	−0.470698	−	0.815273i	−0.999438	+	0.0335104i	$0.989331\pi$
$90$	2.99541	−	2.18156i	0.315744	−	0.229957i
$91$	2.15146	+	1.24215i	0.225534	+	0.130212i
$92$	3.21786	−	0.691361i	0.335485	−	0.0720793i
$93$	1.27390	−	2.20659i	0.132097	−	0.228813i
$94$	0.988059	−	2.22579i	0.101910	−	0.229572i
$95$	−0.828949	+	4.70120i	−0.0850483	+	0.482333i
$96$	3.40181	+	9.18846i	0.347195	+	0.937793i
$97$	9.68946	−	8.13042i	0.983815	−	0.825519i	−0.000845433	−	1.00000i	$-0.500269\pi$
$97$	9.68946	−	8.13042i	0.983815	−	0.825519i	0.984661	+	0.174481i	$0.0558247\pi$
$98$	10.7487	−	11.1551i	1.08578	−	1.12683i
$99$	9.89356	−	5.71275i	0.994340	−	0.574153i
$100$	−0.314332	−	8.46842i	−0.0314332	−	0.846842i
$101$	0.845577	−	2.32320i	0.0841381	−	0.231167i	−0.890488	−	0.455007i	$-0.849637\pi$
$101$	0.845577	−	2.32320i	0.0841381	−	0.231167i	0.974626	+	0.223839i	$0.0718591\pi$
$102$	−6.42459	+	0.682553i	−0.636129	+	0.0675828i
$103$	−5.21096	−	4.37252i	−0.513451	−	0.430837i	0.348890	−	0.937164i	$-0.386559\pi$
$103$	−5.21096	−	4.37252i	−0.513451	−	0.430837i	−0.862342	+	0.506327i	$0.831003\pi$
$104$	−0.616155	+	1.53961i	−0.0604190	+	0.150971i
$105$	2.19222	−	6.02358i	0.213939	−	0.587841i
$106$	−17.4550	−	1.20133i	−1.69538	−	0.116684i
$107$			0.998430i			0.0965218i	0.998835	+	0.0482609i	$0.0153679\pi$
$107$			0.998430i			0.0965218i	−0.998835	+	0.0482609i	$0.984632\pi$
$108$	−3.91493	−	9.62670i	−0.376715	−	0.926329i
$109$			5.11844i			0.490257i	0.969491	+	0.245129i	$0.0788302\pi$
$109$			5.11844i			0.490257i	−0.969491	+	0.245129i	$0.921170\pi$
$110$	−0.322976	+	4.69276i	−0.0307946	+	0.447437i
$111$	8.90031	−	1.56961i	0.844780	−	0.148981i
$112$	13.7554	+	9.90196i	1.29977	+	0.935647i
$113$	1.84882	+	1.55135i	0.173922	+	0.145938i	0.725594	−	0.688123i	$-0.241565\pi$
$113$	1.84882	+	1.55135i	0.173922	+	0.145938i	−0.551671	+	0.834062i	$0.686010\pi$
$114$	12.2364	+	5.43153i	1.14605	+	0.508710i
$115$	0.491602	−	1.35067i	0.0458421	−	0.125950i
$116$	12.3028	−	0.456656i	1.14229	−	0.0423994i
$117$	0.601498	−	1.65288i	0.0556085	−	0.152809i
$118$	−2.88747	−	2.78229i	−0.265814	−	0.256130i
$119$	−8.56128	+	7.18377i	−0.784812	+	0.658535i
$120$	4.18832	+	0.875738i	0.382339	+	0.0799436i
$121$	−0.608116	+	3.44880i	−0.0552833	+	0.313527i
$122$	−11.3037	−	5.01788i	−1.02339	−	0.454298i
$123$	6.02349	+	10.4323i	0.543120	+	0.940653i
$124$	2.87643	−	0.618005i	0.258311	−	0.0554985i
$125$	−6.98704	−	4.03397i	−0.624940	−	0.360809i
$126$	−14.9151	−	10.0354i	−1.32874	−	0.894023i
$127$	−0.904394	−	1.56646i	−0.0802520	−	0.139001i	0.823106	−	0.567888i	$-0.192239\pi$
$127$	−0.904394	−	1.56646i	−0.0802520	−	0.139001i	−0.903358	+	0.428887i	$0.858906\pi$
$128$	−5.23458	+	10.0299i	−0.462676	+	0.886527i
$129$	−12.7558	−	2.24883i	−1.12308	−	0.197999i
$130$	0.426324	+	0.585432i	0.0373911	+	0.0513458i
$131$	1.85373	+	5.09309i	0.161961	+	0.444985i	0.993953	−	0.109802i	$-0.0350218\pi$
$131$	1.85373	+	5.09309i	0.161961	+	0.444985i	−0.831992	+	0.554788i	$0.812800\pi$
$132$	12.5552	+	4.04862i	1.09279	+	0.352387i
$133$	22.8066	−	4.02142i	1.97759	−	0.348702i
$134$	−3.54266	+	14.2755i	−0.306039	+	1.23322i
$135$	−4.46957	−	0.787735i	−0.384679	−	0.0677974i
$136$	−5.56043	−	4.97359i	−0.476803	−	0.426482i
$137$	−1.50776	−	8.55093i	−0.128817	−	0.730555i	−0.978968	−	0.204016i	$-0.934601\pi$
$137$	−1.50776	−	8.55093i	−0.128817	−	0.730555i	0.850151	−	0.526539i	$-0.176511\pi$
$138$	−3.34437	−	2.25034i	−0.284692	−	0.191562i
$139$	−6.99623	−	19.2220i	−0.593413	−	1.63039i	−0.764125	−	0.645068i	$-0.776829\pi$
$139$	−6.99623	−	19.2220i	−0.593413	−	1.63039i	0.170713	−	0.985321i	$-0.445393\pi$
$140$	6.85667	−	2.78779i	0.579495	−	0.235612i
$141$	−2.80265	+	1.02017i	−0.236026	+	0.0859134i
$142$	19.2709	+	12.9676i	1.61717	+	1.08822i
$143$	1.11637	+	1.93361i	0.0933557	+	0.161697i
$144$	5.21249	−	10.8088i	0.434374	−	0.900733i
$145$	2.68824	−	4.65617i	0.223246	−	0.386674i
$146$	11.0356	−	5.39743i	0.913314	−	0.446694i
$147$	−18.9725		0.000507984i	−1.56483		4.18978e-5i
$148$	8.23759	+	6.40685i	0.677125	+	0.526639i
$149$	3.88249	+	0.684589i	0.318066	+	0.0560837i	0.330402	−	0.943840i	$-0.392816\pi$
$149$	3.88249	+	0.684589i	0.318066	+	0.0560837i	−0.0123358	+	0.999924i	$0.503927\pi$
$150$	−7.20133	+	7.47398i	−0.587986	+	0.610248i
$151$	−7.15499	+	6.00375i	−0.582264	+	0.488578i	−0.885690	−	0.464277i	$-0.846314\pi$
$151$	−7.15499	+	6.00375i	−0.582264	+	0.488578i	0.303425	+	0.952855i	$0.401870\pi$
$152$	4.82541	+	14.6864i	0.391392	+	1.19123i
$153$	6.06180	+	5.08590i	0.490068	+	0.411171i
$154$	21.9286	−	6.31398i	1.76706	−	0.508795i
$155$	0.439442	−	1.20736i	0.0352968	−	0.0969771i
$156$	1.88144	−	0.765017i	0.150636	−	0.0612504i
$157$	−10.2861	+	12.2585i	−0.820918	+	0.978332i	−0.999985	−	0.00550470i	$-0.998248\pi$
$157$	−10.2861	+	12.2585i	−0.820918	+	0.978332i	0.179067	+	0.983837i	$0.442692\pi$
$158$	−21.0602	+	2.23688i	−1.67546	+	0.177957i
$159$	13.7744	+	16.4148i	1.09238	+	1.30178i
$160$	2.49386	+	4.26528i	0.197157	+	0.337200i
$161$	−6.97291			−0.549542
$162$	−5.16291	+	11.6338i	−0.405636	+	0.914035i
$163$			22.2998i			1.74666i	0.487131	+	0.873329i	$0.338043\pi$
$163$			22.2998i			1.74666i	−0.487131	+	0.873329i	$0.661957\pi$
$164$	−4.26939	+	13.2386i	−0.333383	+	1.03376i
$165$	4.41311	−	3.70324i	0.343560	−	0.288297i
$166$	−2.13505	−	20.1015i	−0.165712	−	1.56018i
$167$	10.6217	+	8.91265i	0.821931	+	0.689682i	0.953423	−	0.301635i	$-0.0975325\pi$
$167$	10.6217	+	8.91265i	0.821931	+	0.689682i	−0.131493	+	0.991317i	$0.541977\pi$
$168$	−2.95714	−	20.5462i	−0.228148	−	1.58517i
$169$	−11.8930	−	4.32869i	−0.914845	−	0.332976i
$170$	−3.13078	+	0.901455i	−0.240120	+	0.0691385i
$171$	−5.60878	−	15.4074i	−0.428914	−	1.17824i
$172$	−7.95342	−	12.6662i	−0.606442	−	0.965788i
$173$	12.4903	+	14.8854i	0.949622	+	1.13172i	0.991172	+	0.132579i	$0.0423260\pi$
$173$	12.4903	+	14.8854i	0.949622	+	1.13172i	−0.0415500	+	0.999136i	$0.513230\pi$
$174$	−10.8581	−	10.4620i	−0.823149	−	0.793120i
$175$	−3.11760	+	17.6808i	−0.235668	+	1.33654i
$176$	6.25667	+	13.8883i	0.471614	+	1.04687i
$177$	0.000131491		4.91100i	9.88345e−6		0.369133i
$178$	−11.2826	+	5.51824i	−0.845668	+	0.413609i
$179$	−9.76060	−	5.63528i	−0.729541	−	0.421201i	0.0887130	−	0.996057i	$-0.471725\pi$
$179$	−9.76060	−	5.63528i	−0.729541	−	0.421201i	−0.818254	+	0.574856i	$0.805058\pi$
$180$	−2.78705	−	4.43799i	−0.207735	−	0.330788i
$181$	−0.137847	+	0.0795857i	−0.0102461	+	0.00591556i	−0.505114	−	0.863052i	$-0.668550\pi$
$181$	−0.137847	+	0.0795857i	−0.0102461	+	0.00591556i	0.494868	+	0.868968i	$0.335216\pi$
$182$	1.96143	−	2.91483i	0.145391	−	0.216062i
$183$	5.18093	+	14.2333i	0.382986	+	1.05216i
$184$	−0.662962	−	4.60713i	−0.0488742	−	0.339642i
$185$	4.28259	−	1.55874i	0.314862	−	0.114600i
$186$	−2.98953	−	2.01158i	−0.219203	−	0.147496i
$187$	−9.89173	+	1.74418i	−0.723355	+	0.127547i
$188$	−3.04436	−	1.61016i	−0.222033	−	0.117433i
$189$	3.82497	+	21.6823i	0.278226	+	1.57715i
$190$	6.55232	+	1.62604i	0.475355	+	0.117966i
$191$	−2.57040	−	14.5775i	−0.185988	−	1.05479i	−0.924680	−	0.380745i	$-0.875668\pi$
$191$	−2.57040	−	14.5775i	−0.185988	−	1.05479i	0.738692	−	0.674043i	$-0.235444\pi$
$192$	13.2941	−	3.90730i	0.959419	−	0.281985i
$193$	−6.59993	+	2.40218i	−0.475074	+	0.172913i	−0.568449	−	0.822718i	$-0.692456\pi$
$193$	−6.59993	+	2.40218i	−0.475074	+	0.172913i	0.0933757	+	0.995631i	$0.470234\pi$
$194$	−10.5301	−	14.4601i	−0.756020	−	1.03818i
$195$	0.153998	−	0.873504i	0.0110280	−	0.0625529i
$196$	−14.6947	−	16.2483i	−1.04962	−	1.16059i
$197$	3.25342	−	1.87837i	0.231797	−	0.133828i	−0.379604	−	0.925149i	$-0.623940\pi$
$197$	3.25342	−	1.87837i	0.231797	−	0.133828i	0.611401	+	0.791321i	$0.290606\pi$
$198$	−7.09930	−	14.5133i	−0.504525	−	1.03142i
$199$	12.4769	−	21.6106i	0.884462	−	1.53193i	0.0381332	−	0.999273i	$-0.487859\pi$
$199$	12.4769	−	21.6106i	0.884462	−	1.53193i	0.846329	−	0.532661i	$-0.178808\pi$
$200$	−11.9784	−	0.378823i	−0.847002	−	0.0267868i
$201$	15.6005	−	9.00753i	1.10038	−	0.635342i
$202$	−3.19565	−	1.41859i	−0.224845	−	0.0998119i
$203$	−25.6863	−	4.52919i	−1.80283	−	0.317887i
$204$	0.339154	+	9.13058i	0.0237455	+	0.639268i
$205$	3.90473	+	4.65347i	0.272718	+	0.325013i
$206$	−6.67508	+	6.92744i	−0.465075	+	0.482658i
$207$	0.857550	+	4.86188i	0.0596038	+	0.337924i
$208$	2.11237	+	1.01882i	0.146466	+	0.0706424i
$209$	19.5583	+	7.11865i	1.35288	+	0.492407i
$210$	−8.28565	−	3.67786i	−0.571764	−	0.253796i
$211$	−4.65266	+	5.54482i	−0.320302	+	0.381721i	−0.902038	−	0.431656i	$-0.857929\pi$
$211$	−4.65266	+	5.54482i	−0.320302	+	0.381721i	0.581736	+	0.813378i	$0.302374\pi$
$212$	−3.38986	+	24.5102i	−0.232816	+	1.68337i
$213$	−4.94069	−	28.0157i	−0.338531	−	1.91960i
$214$	1.40866	+	0.0969501i	0.0962941	+	0.00662737i
$215$	−6.53158			−0.445450
$216$	−13.9622	+	4.58871i	−0.950009	+	0.312222i
$217$	−6.23306			−0.423128
$218$	7.22148	+	0.497013i	0.489100	+	0.0336620i
$219$	−14.1386	−	5.14558i	−0.955395	−	0.347706i
$220$	6.58954	+	0.911359i	0.444267	+	0.0614438i
$221$	−0.994030	+	1.18464i	−0.0668657	+	0.0796874i
$222$	−1.35028	−	12.7096i	−0.0906250	−	0.853015i
$223$	−7.10554	−	2.58621i	−0.475822	−	0.173185i	0.0929658	−	0.995669i	$-0.470365\pi$
$223$	−7.10554	−	2.58621i	−0.475822	−	0.173185i	−0.568788	+	0.822484i	$0.692588\pi$
$224$	15.3061	−	18.4457i	1.02268	−	1.23245i
$225$	12.7114		0.000680688i	0.847426		4.53792e-5i
$226$	2.36828	−	2.45782i	0.157536	−	0.163492i
$227$	5.52861	+	6.58874i	0.366947	+	0.437310i	0.917649	−	0.397392i	$-0.130085\pi$
$227$	5.52861	+	6.58874i	0.366947	+	0.437310i	−0.550703	+	0.834702i	$0.685640\pi$
$228$	8.85141	−	16.7367i	0.586199	−	1.10841i
$229$	−16.5497	−	2.91817i	−1.09364	−	0.192838i	−0.402399	−	0.915464i	$-0.631824\pi$
$229$	−16.5497	−	2.91817i	−1.09364	−	0.192838i	−0.691239	+	0.722626i	$0.742935\pi$
$230$	−1.85789	−	0.824742i	−0.122505	−	0.0543819i
$231$	−24.2042	−	13.9734i	−1.59252	−	0.919383i
$232$	0.550348	−	17.4020i	0.0361321	−	1.14250i
$233$	3.50156	−	6.06488i	0.229395	−	0.397323i	−0.728234	−	0.685328i	$-0.759659\pi$
$233$	3.50156	−	6.06488i	0.229395	−	0.397323i	0.957629	+	0.288005i	$0.0929920\pi$
$234$	−2.27360	−	1.00914i	−0.148630	−	0.0659694i
$235$	−1.30252	+	0.752007i	−0.0849667	+	0.0490556i
$236$	−4.20584	+	3.80370i	−0.273777	+	0.247600i
$237$	19.8704	+	16.6724i	1.29072	+	1.08299i
$238$	9.30409	+	12.7765i	0.603094	+	0.828176i
$239$	−4.71694	+	1.71683i	−0.305114	+	0.111052i	−0.490040	−	0.871700i	$-0.663018\pi$
$239$	−4.71694	+	1.71683i	−0.305114	+	0.111052i	0.184926	+	0.982752i	$0.440795\pi$
$240$	1.64225	−	5.82416i	0.106007	−	0.375948i
$241$	0.171650	+	0.973478i	0.0110570	+	0.0627072i	0.989837	−	0.142207i	$-0.0454197\pi$
$241$	0.171650	+	0.973478i	0.0110570	+	0.0627072i	−0.978780	+	0.204914i	$0.934309\pi$
$242$	4.80678	+	1.19286i	0.308991	+	0.0766802i
$243$	14.6476	−	5.33353i	0.939647	−	0.342146i
$244$	−8.17723	+	15.4609i	−0.523493	+	0.989781i
$245$	−9.42196	+	1.66135i	−0.601947	+	0.106140i
$246$	15.3036	−	7.48539i	0.975725	−	0.477251i
$247$	3.01122	−	1.09599i	0.191599	−	0.0697364i
$248$	−0.592620	−	4.11830i	−0.0376314	−	0.261512i
$249$	−15.9134	+	18.9659i	−1.00847	+	1.20192i
$250$	−6.36989	+	9.46614i	−0.402867	+	0.598691i
$251$	8.55386	−	4.93857i	0.539915	−	0.311720i	−0.205130	−	0.978735i	$-0.565762\pi$
$251$	8.55386	−	4.93857i	0.539915	−	0.311720i	0.745044	+	0.667015i	$0.232428\pi$
$252$	−15.6070	+	20.0688i	−0.983147	+	1.26422i
$253$	−5.42726	−	3.13343i	−0.341209	−	0.196997i
$254$	−2.29789	+	1.12388i	−0.144183	+	0.0705186i
$255$	3.45566	+	1.99500i	0.216402	+	0.124932i
$256$	13.6427	+	8.35928i	0.852667	+	0.522455i
$257$	0.680570	−	3.85970i	0.0424528	−	0.240762i	−0.956196	−	0.292727i	$-0.905437\pi$
$257$	0.680570	−	3.85970i	0.0424528	−	0.240762i	0.998649	+	0.0519652i	$0.0165485\pi$
$258$	−4.41145	+	17.7784i	−0.274645	+	1.10684i
$259$	−14.2115	−	16.9366i	−0.883061	−	1.05239i
$260$	0.867370	−	0.544643i	0.0537920	−	0.0337773i
$261$	0.000988893		18.4669i	6.12109e−5		1.14307i
$262$	7.36572	−	2.12084i	0.455056	−	0.131026i
$263$	20.0274	+	7.28937i	1.23494	+	0.449482i	0.875287	−	0.483604i	$-0.160673\pi$
$263$	20.0274	+	7.28937i	1.23494	+	0.449482i	0.359654	+	0.933086i	$0.382895\pi$
$264$	6.93124	−	17.3207i	0.426588	−	1.06601i
$265$	8.27774	+	6.94585i	0.508497	+	0.426680i
$266$	−3.45915	−	32.5678i	−0.212094	−	1.99686i
$267$	14.4550	+	5.26075i	0.884632	+	0.321953i
$268$	19.7970	+	6.38445i	1.20930	+	0.389992i
$269$		−	21.1749i		−	1.29105i	−0.763737	−	0.645527i	$-0.776638\pi$
$269$		−	21.1749i		−	1.29105i	0.763737	−	0.645527i	$-0.223362\pi$
$270$	−1.54540	+	6.22951i	−0.0940502	+	0.379116i
$271$	−11.7908			−0.716240			−0.358120	−	0.933676i	$-0.616582\pi$
$271$	−11.7908			−0.716240			−0.358120	+	0.933676i	$0.616582\pi$
$272$	−7.55705	+	7.36213i	−0.458213	+	0.446395i
$273$	−4.23753	+	0.747308i	−0.256467	+	0.0452291i
$274$	−12.2107	+	1.29694i	−0.737676	+	0.0783513i
$275$	−10.3718	+	12.3606i	−0.625442	+	0.745372i
$276$	−3.49970	+	4.49998i	−0.210657	+	0.270867i
$277$	2.25031	−	6.18267i	0.135208	−	0.371481i	−0.853549	−	0.521013i	$-0.825554\pi$
$277$	2.25031	−	6.18267i	0.135208	−	0.371481i	0.988757	+	0.149532i	$0.0477766\pi$
$278$	−27.7992	+	8.00431i	−1.66729	+	0.480067i
$279$	0.766561	+	4.34603i	0.0458928	+	0.260190i
$280$	−3.26743	−	9.94462i	−0.195266	−	0.594304i
$281$	3.00085	−	2.51801i	0.179016	−	0.150212i	−0.548877	−	0.835903i	$-0.684944\pi$
$281$	3.00085	−	2.51801i	0.179016	−	0.150212i	0.727893	+	0.685691i	$0.240500\pi$
$282$	1.16718	+	4.05325i	0.0695047	+	0.241368i
$283$	13.5633	+	2.39158i	0.806256	+	0.142165i	0.561561	−	0.827435i	$-0.310201\pi$
$283$	13.5633	+	2.39158i	0.806256	+	0.142165i	0.244695	+	0.969600i	$0.421312\pi$
$284$	20.1669	−	25.9296i	1.19669	−	1.53864i
$285$	−4.13436	−	7.16048i	−0.244898	−	0.424150i
$286$	2.83649	−	1.38730i	0.167725	−	0.0820330i
$287$	14.7348	−	25.5215i	0.869770	−	1.50649i
$288$	−14.7437	−	8.40374i	−0.868782	−	0.495195i
$289$	5.02157	+	8.69761i	0.295386	+	0.511624i
$290$	−6.30824	−	4.24490i	−0.370433	−	0.249269i
$291$	−3.80374	+	21.5754i	−0.222979	+	1.26477i
$292$	−6.54351	−	16.0940i	−0.382930	−	0.941830i
$293$	−1.65069	−	4.53522i	−0.0964342	−	0.264951i	0.882091	−	0.471080i	$-0.156136\pi$
$293$	−1.65069	−	4.53522i	−0.0964342	−	0.264951i	−0.978525	+	0.206129i	$0.933913\pi$
$294$	−1.84156	+	26.7679i	−0.107402	+	1.56114i
$295$	0.430037	+	2.43886i	0.0250377	+	0.141996i
$296$	9.83916	−	11.0001i	0.571889	−	0.639367i
$297$	−6.76631	+	18.5949i	−0.392621	+	1.07899i
$298$	1.34287	−	5.41124i	0.0777904	−	0.313465i
$299$	−0.950194	+	0.167545i	−0.0549512	+	0.00968937i
$300$	9.84560	+	10.8859i	0.568436	+	0.628499i
$301$	10.8373	+	29.7753i	0.624653	+	1.71622i
$302$	7.77577	+	10.6778i	0.447445	+	0.614437i
$303$	1.46469	+	4.02387i	0.0841443	+	0.231165i
$304$	21.1893	−	5.38197i	1.21529	−	0.308677i
$305$	3.81909	+	6.61485i	0.218680	+	0.378765i
$306$	7.76419	−	8.05859i	0.443849	−	0.460679i
$307$	22.1057	+	12.7627i	1.26164	+	0.728408i	0.973392	−	0.229147i	$-0.0735937\pi$
$307$	22.1057	+	12.7627i	1.26164	+	0.728408i	0.288249	+	0.957556i	$0.406927\pi$
$308$	−6.77892	−	31.5517i	−0.386265	−	1.79782i
$309$	11.7822		0.000315464i	0.670263		1.79461e-5i
$310$	−1.66076	−	0.737235i	−0.0943247	−	0.0418721i
$311$	0.262500	−	1.48871i	0.0148850	−	0.0844172i	−0.976460	−	0.215697i	$-0.930798\pi$
$311$	0.262500	−	1.48871i	0.0148850	−	0.0844172i	0.991345	+	0.131280i	$0.0419087\pi$
$312$	−0.896651	−	2.72876i	−0.0507629	−	0.154486i
$313$	−3.52016	+	2.95376i	−0.198971	+	0.166957i	−0.736830	−	0.676079i	$-0.763678\pi$
$313$	−3.52016	+	2.95376i	−0.198971	+	0.166957i	0.537858	+	0.843035i	$0.319234\pi$
$314$	16.2964	+	15.7027i	0.919658	+	0.886155i
$315$	3.79787	+	10.4328i	0.213986	+	0.587824i
$316$	1.11096	+	29.9305i	0.0624965	+	1.68372i
$317$	−2.10890	+	5.79416i	−0.118448	+	0.325433i	−0.984721	−	0.174137i	$-0.944286\pi$
$317$	−2.10890	+	5.79416i	−0.118448	+	0.325433i	0.866274	+	0.499570i	$0.166509\pi$
$318$	24.4968	−	17.8401i	1.37371	−	1.00042i
$319$	−17.9573	−	15.0679i	−1.00541	−	0.843643i
$320$	6.25993	−	3.10435i	0.349941	−	0.173539i
$321$	−1.11163	−	1.32471i	−0.0620450	−	0.0739384i
$322$	−0.677087	+	9.83791i	−0.0377326	+	0.548245i
$323$			14.4158i			0.802116i
$324$	15.9125	+	8.41389i	0.884026	+	0.467438i
$325$			2.48426i			0.137802i
$326$	31.4623	+	2.16537i	1.74254	+	0.119929i
$327$	−5.69875	−	6.79113i	−0.315141	−	0.375550i
$328$	18.2635	+	7.30908i	1.00843	+	0.403576i
$329$	5.58931	+	4.68999i	0.308149	+	0.258567i
$330$	−4.79629	−	6.58594i	−0.264027	−	0.362544i
$331$	−4.73351	+	13.0052i	−0.260177	+	0.714831i	0.738978	+	0.673730i	$0.235309\pi$
$331$	−4.73351	+	13.0052i	−0.260177	+	0.714831i	−0.999155	+	0.0411011i	$0.986913\pi$
$332$	−28.5680	+	1.06039i	−1.56788	+	0.0581965i
$333$	−10.0613	+	11.9919i	−0.551358	+	0.657155i
$334$	13.6060	−	14.1204i	0.744489	−	0.772636i
$335$	6.95881	−	5.83913i	0.380200	−	0.319026i
$336$	−29.2753	+	2.17707i	−1.59710	+	0.118769i
$337$	3.04613	−	17.2755i	0.165933	−	0.941055i	−0.782163	−	0.623073i	$-0.785884\pi$
$337$	3.04613	−	17.2755i	0.165933	−	0.941055i	0.948097	−	0.317982i	$-0.103005\pi$
$338$	−7.26208	+	16.3592i	−0.395005	+	0.889823i
$339$	−4.18024		0.000111925i	−0.227040		6.07893e-6i
$340$	0.967835	+	4.50467i	0.0524882	+	0.244300i
$341$	−4.85141	−	2.80096i	−0.262719	−	0.151681i
$342$	−22.2826	+	6.41719i	−1.20491	+	0.347002i
$343$	8.37647	+	14.5085i	0.452287	+	0.783384i
$344$	−18.6427	+	9.99137i	−1.00515	+	0.538698i
$345$	0.851542	+	2.33940i	0.0458455	+	0.125949i
$346$	22.2143	−	16.1769i	1.19425	−	0.869676i
$347$	−8.50580	−	23.3695i	−0.456615	−	1.25454i	−0.927989	−	0.372607i	$-0.878464\pi$
$347$	−8.50580	−	23.3695i	−0.456615	−	1.25454i	0.471374	−	0.881933i	$-0.343758\pi$
$348$	−15.8149	+	14.3035i	−0.847767	+	0.766749i
$349$	6.71094	−	1.18332i	0.359228	−	0.0633416i	0.00887853	−	0.999961i	$-0.497174\pi$
$349$	6.71094	−	1.18332i	0.359228	−	0.0633416i	0.350350	+	0.936619i	$0.386063\pi$
$350$	24.6426	+	6.11539i	1.31720	+	0.326881i
$351$	1.04221	+	2.86273i	0.0556289	+	0.152801i
$352$	20.2023	−	7.47879i	1.07678	−	0.398621i
$353$	−5.71696	−	32.4225i	−0.304283	−	1.72568i	−0.626859	−	0.779133i	$-0.715660\pi$
$353$	−5.71696	−	32.4225i	−0.304283	−	1.72568i	0.322576	−	0.946544i	$-0.395451\pi$
$354$	6.92883	+	0.476685i	0.368263	+	0.0253355i
$355$	−4.90646	−	13.4804i	−0.260408	−	0.715465i
$356$	6.68997	+	16.4542i	0.354568	+	0.872072i
$357$	3.36086	−	19.0633i	0.177875	−	1.00894i
$358$	−8.89847	+	13.2238i	−0.470299	+	0.698899i
$359$	3.06942	+	5.31639i	0.161998	+	0.280588i	0.935585	−	0.353101i	$-0.114873\pi$
$359$	3.06942	+	5.31639i	0.161998	+	0.280588i	−0.773587	+	0.633690i	$0.781540\pi$
$360$	−6.53208	+	3.50125i	−0.344271	+	0.184532i
$361$	5.43597	−	9.41537i	0.286104	−	0.495546i
$362$	0.0989003	+	0.202212i	0.00519809	+	0.0106280i
$363$	−3.03296	−	5.25292i	−0.159189	−	0.275707i
$364$	−3.92200	−	3.05037i	−0.205569	−	0.159883i
$365$	−7.47191	−	1.31750i	−0.391097	−	0.0689610i
$366$	20.5845	−	5.92757i	1.07597	−	0.309839i
$367$	−9.94435	+	8.34430i	−0.519091	+	0.435569i	−0.864315	−	0.502952i	$-0.832247\pi$
$367$	−9.94435	+	8.34430i	−0.519091	+	0.435569i	0.345224	+	0.938520i	$0.387803\pi$
$368$	−6.56447	+	0.487993i	−0.342196	+	0.0254384i
$369$	−19.6071	−	7.13521i	−1.02070	−	0.371444i
$370$	−1.78333	−	6.19356i	−0.0927110	−	0.321988i
$371$	17.9292	−	49.2601i	0.930839	−	2.55746i
$372$	−3.12837	+	4.02252i	−0.162199	+	0.208558i
$373$	10.5636	−	12.5892i	0.546960	−	0.651842i	−0.419773	−	0.907629i	$-0.637890\pi$
$373$	10.5636	−	12.5892i	0.546960	−	0.651842i	0.966733	+	0.255787i	$0.0823347\pi$
$374$	1.50031	+	14.1254i	0.0775791	+	0.730406i
$375$	13.7617	−	2.42694i	0.710652	−	0.125327i
$376$	−2.56735	+	4.13887i	−0.132401	+	0.213446i
$377$	−3.60909			−0.185877
$378$	30.9624	−	3.29115i	1.59254	−	0.169279i
$379$			13.5072i			0.693817i	0.937899	+	0.346908i	$0.112768\pi$
$379$			13.5072i			0.693817i	−0.937899	+	0.346908i	$0.887232\pi$
$380$	2.93039	−	9.08662i	0.150326	−	0.466134i
$381$	2.94400	+	1.07144i	0.150826	+	0.0548916i
$382$	−20.8166	+	2.21101i	−1.06507	+	0.113125i
$383$	−6.99126	−	5.86636i	−0.357237	−	0.299757i	0.446451	−	0.894808i	$-0.352688\pi$
$383$	−6.99126	−	5.86636i	−0.357237	−	0.299757i	−0.803688	+	0.595051i	$0.797132\pi$
$384$	−4.22183	−	19.1357i	−0.215444	−	0.976516i
$385$	−13.2435	−	4.82025i	−0.674953	−	0.245663i
$386$	2.74831	+	9.54494i	0.139885	+	0.485825i
$387$	19.4281	−	11.2182i	0.987588	−	0.570254i
$388$	−21.4239	+	13.4526i	−1.08763	+	0.682953i
$389$	−21.2477	−	25.3220i	−1.07730	−	1.28387i	−0.956669	−	0.291177i	$-0.905953\pi$
$389$	−21.2477	−	25.3220i	−1.07730	−	1.28387i	−0.120630	−	0.992698i	$-0.538491\pi$
$390$	−1.21745	−	0.302092i	−0.0616481	−	0.0152970i
$391$	0.753725	−	4.27459i	0.0381175	−	0.216175i
$392$	−24.3512	+	19.1547i	−1.22992	+	0.967457i
$393$	−8.13005	−	4.69360i	−0.410107	−	0.236761i
$394$	−2.33422	−	4.77257i	−0.117597	−	0.240439i
$395$	11.3276	+	6.54001i	0.569955	+	0.329064i
$396$	−21.1658	+	8.60695i	−1.06362	+	0.432516i
$397$	−5.84951	+	3.37722i	−0.293578	+	0.169498i	−0.639555	−	0.768746i	$-0.720881\pi$
$397$	−5.84951	+	3.37722i	−0.293578	+	0.169498i	0.345976	+	0.938243i	$0.387548\pi$
$398$	−29.2783	−	19.7018i	−1.46759	−	0.987560i
$399$	−25.7824	+	30.7280i	−1.29074	+	1.53832i
$400$	−1.69761	+	16.8633i	−0.0848804	+	0.843164i
$401$	15.2918	−	5.56576i	0.763635	−	0.277941i	0.0693037	−	0.997596i	$-0.477922\pi$
$401$	15.2918	−	5.56576i	0.763635	−	0.277941i	0.694332	+	0.719655i	$0.255700\pi$
$402$	−11.1937	−	22.8851i	−0.558289	−	1.14140i
$403$	−0.849376	+	0.149768i	−0.0423104	+	0.00746047i
$404$	−2.31177	+	4.37091i	−0.115015	+	0.217461i
$405$	6.80726	−	3.93114i	0.338255	−	0.195340i
$406$	−8.88434	+	35.8004i	−0.440922	+	1.77674i
$407$	−3.45048	−	19.5686i	−0.171034	−	0.969981i
$408$	12.9150	+	0.408098i	0.639390	+	0.0202039i
$409$	−22.3867	+	8.14811i	−1.10695	+	0.402898i	−0.829875	−	0.557949i	$-0.811588\pi$
$409$	−22.3867	+	8.14811i	−1.10695	+	0.402898i	−0.277078	+	0.960847i	$0.589366\pi$
$410$	6.94463	−	5.05722i	0.342971	−	0.249758i
$411$	11.5209	+	9.66665i	0.568284	+	0.476821i
$412$	9.12559	+	10.0904i	0.449586	+	0.497117i
$413$	10.4044	−	6.00700i	0.511968	−	0.295585i
$414$	6.94279	−	0.737795i	0.341219	−	0.0362607i
$415$	−6.24231	+	10.8120i	−0.306423	+	0.530740i
$416$	1.64254	−	2.88136i	0.0805323	−	0.141270i
$417$	30.6839	+	17.7143i	1.50260	+	0.867471i
$418$	11.9427	−	26.9031i	0.584136	−	1.31587i
$419$	2.28983	+	0.403758i	0.111865	+	0.0197249i	0.229301	−	0.973356i	$-0.426356\pi$
$419$	2.28983	+	0.403758i	0.111865	+	0.0197249i	−0.117435	+	0.993081i	$0.537467\pi$
$420$	−5.99356	+	11.3329i	−0.292456	+	0.552989i
$421$	−14.5211	−	17.3056i	−0.707716	−	0.843423i	0.285660	−	0.958331i	$-0.407787\pi$
$421$	−14.5211	−	17.3056i	−0.707716	−	0.843423i	−0.993376	+	0.114908i	$0.963343\pi$
$422$	7.37127	+	7.10274i	0.358828	+	0.345756i
$423$	2.58272	−	4.47396i	0.125576	−	0.217531i
$424$	34.2517	+	7.16268i	1.66341	+	0.347850i
$425$	−10.5018	−	3.82235i	−0.509413	−	0.185411i
$426$	−40.0064	+	4.25031i	−1.93832	+	0.205928i
$427$	23.8182	−	28.3855i	1.15264	−	1.37367i
$428$	0.273569	−	1.97803i	0.0132235	−	0.0956118i
$429$	−3.63404	−	1.32257i	−0.175453	−	0.0638544i
$430$	−0.634233	+	9.21525i	−0.0305855	+	0.444399i
$431$	19.9187			0.959449			0.479724	−	0.877419i	$-0.340737\pi$
$431$	19.9187			0.959449			0.479724	+	0.877419i	$0.340737\pi$
$432$	5.11833	+	20.1445i	0.246256	+	0.969205i
$433$	−12.3203			−0.592077			−0.296039	−	0.955176i	$-0.595666\pi$
$433$	−12.3203			−0.592077			−0.296039	+	0.955176i	$0.595666\pi$
$434$	−0.605247	+	8.79408i	−0.0290528	+	0.422129i
$435$	1.61732	+	9.17082i	0.0775444	+	0.439707i
$436$	1.40245	−	10.1404i	0.0671651	−	0.485635i
$437$	−5.78143	+	6.89004i	−0.276563	+	0.329595i
$438$	−8.63267	+	19.4481i	−0.412485	+	0.929266i
$439$	16.4224	+	5.97728i	0.783801	+	0.285280i	0.702757	−	0.711430i	$-0.251952\pi$
$439$	16.4224	+	5.97728i	0.783801	+	0.285280i	0.0810442	+	0.996711i	$0.474175\pi$
$440$	1.92568	−	9.20854i	0.0918030	−	0.439000i
$441$	25.1721	−	21.1242i	1.19867	−	1.00592i
$442$	1.57486	+	1.51748i	0.0749082	+	0.0721794i
$443$	17.6567	+	21.0424i	0.838893	+	0.999754i	0.999918	+	0.0128036i	$0.00407562\pi$
$443$	17.6567	+	21.0424i	0.838893	+	0.999754i	−0.161025	+	0.986950i	$0.551480\pi$
$444$	−18.0628	+	0.670942i	−0.857225	+	0.0318415i
$445$	7.63915	+	1.34699i	0.362130	+	0.0638533i
$446$	−4.33878	+	9.77391i	−0.205447	+	0.462808i
$447$	−5.91349	+	3.41437i	−0.279699	+	0.161494i
$448$	−24.5383	−	23.3862i	−1.15933	−	1.10489i
$449$	−0.331257	+	0.573755i	−0.0156330	+	0.0270772i	−0.873736	−	0.486400i	$-0.838310\pi$
$449$	−0.331257	+	0.573755i	−0.0156330	+	0.0270772i	0.858103	+	0.513477i	$0.171643\pi$
$450$	1.23335	−	17.9343i	0.0581406	−	0.845429i
$451$	22.9373	−	13.2429i	1.08007	−	0.623582i
$452$	−3.23771	−	3.58001i	−0.152289	−	0.168390i
$453$	2.80879	−	15.9320i	0.131969	−	0.748548i
$454$	9.83273	−	7.16040i	0.461473	−	0.336054i
$455$	−2.03899	+	0.742131i	−0.0955892	+	0.0347916i
$456$	−22.7539	−	14.1134i	−1.06555	−	0.660921i
$457$	−2.08224	−	11.8090i	−0.0974033	−	0.552401i	−0.993984	−	0.109522i	$-0.965068\pi$
$457$	−2.08224	−	11.8090i	−0.0974033	−	0.552401i	0.896581	−	0.442880i	$-0.146043\pi$
$458$	−5.72419	+	23.0663i	−0.267474	+	1.07782i
$459$	−13.7053	+	0.00110087i	−0.639709	+	5.13841e-5i
$460$	−1.34401	+	2.54116i	−0.0626650	+	0.118482i
$461$	−3.18365	+	0.561364i	−0.148278	+	0.0261453i	−0.247294	−	0.968940i	$-0.579541\pi$
$461$	−3.18365	+	0.561364i	−0.148278	+	0.0261453i	0.0990166	+	0.995086i	$0.468430\pi$
$462$	−22.0650	+	32.7922i	−1.02656	+	1.52563i
$463$	17.9320	−	6.52670i	0.833369	−	0.303321i	0.110128	−	0.993917i	$-0.464874\pi$
$463$	17.9320	−	6.52670i	0.833369	−	0.303321i	0.723241	+	0.690596i	$0.242652\pi$
$464$	−24.4987	−	2.46626i	−1.13732	−	0.114493i
$465$	0.761191	+	2.09118i	0.0352994	+	0.0969762i
$466$	−8.21678	−	5.52918i	−0.380635	−	0.256134i
$467$	−28.3244	+	16.3531i	−1.31070	+	0.756731i	−0.982211	−	0.187778i	$-0.939871\pi$
$467$	−28.3244	+	16.3531i	−1.31070	+	0.756731i	−0.328485	+	0.944509i	$0.606538\pi$
$468$	−1.64454	+	3.10977i	−0.0760189	+	0.143749i
$469$	−38.1649	−	22.0345i	−1.76229	−	1.01746i
$470$	0.934512	+	1.91071i	0.0431058	+	0.0881344i
$471$	−0.000742110	−	27.7168i	−3.41946e−5	−	1.27712i
$472$	4.95815	+	6.30327i	0.228217	+	0.290131i
$473$	−4.94512	+	28.0452i	−0.227377	+	1.28952i
$474$	25.4521	−	26.4158i	1.16905	−	1.21332i
$475$	14.8858	+	17.7401i	0.683005	+	0.813974i
$476$	18.9295	−	11.8863i	0.867631	−	0.544807i
$477$	−36.5518	−	6.44305i	−1.67359	−	0.295007i
$478$	1.96420	+	6.82173i	0.0898405	+	0.312019i
$479$	−18.9103	−	6.88279i	−0.864035	−	0.314483i	−0.128286	−	0.991737i	$-0.540947\pi$
$479$	−18.9103	−	6.88279i	−0.864035	−	0.314483i	−0.735749	+	0.677254i	$0.763170\pi$
$480$	−8.05770	−	2.88256i	−0.367782	−	0.131570i
$481$	−2.34355	−	1.96647i	−0.106857	−	0.0896633i
$482$	1.39012	−	0.147650i	0.0633184	−	0.00672528i
$483$	9.25164	−	7.76347i	0.420964	−	0.353250i
$484$	2.14973	−	6.66594i	0.0977152	−	0.302997i
$485$			11.0477i			0.501649i
$486$	−6.10262	−	21.1839i	−0.276821	−	0.960922i
$487$	33.9829			1.53991			0.769956	−	0.638097i	$-0.220278\pi$
$487$	33.9829			1.53991			0.769956	+	0.638097i	$0.220278\pi$
$488$	21.0194	+	13.0383i	0.951501	+	0.590218i
$489$	−24.8281	−	29.5874i	−1.12277	−	1.33799i
$490$	1.42906	+	13.4545i	0.0645582	+	0.607814i
$491$	5.93394	−	7.07180i	0.267795	−	0.319146i	−0.615342	−	0.788260i	$-0.710982\pi$
$491$	5.93394	−	7.07180i	0.267795	−	0.319146i	0.883138	+	0.469114i	$0.155427\pi$
$492$	−9.07494	−	22.3184i	−0.409130	−	1.00619i
$493$	5.55304	−	15.2569i	0.250096	−	0.687134i
$494$	−1.25391	−	4.35488i	−0.0564163	−	0.195935i
$495$	−1.73221	+	9.82690i	−0.0778568	+	0.441686i
$496$	−5.86796	+	0.436215i	−0.263479	+	0.0195866i
$497$	−53.3117	+	44.7339i	−2.39136	+	2.00659i
$498$	25.2133	+	24.2935i	1.12984	+	1.08862i
$499$	−10.4788	−	1.84769i	−0.469095	−	0.0827141i	−0.0658962	−	0.997826i	$-0.520991\pi$
$499$	−10.4788	−	1.84769i	−0.469095	−	0.0827141i	−0.403199	+	0.915112i	$0.632102\pi$
$500$	12.7370	+	9.90631i	0.569617	+	0.443024i
$501$	−24.0160		0.000643021i	−1.07295		2.87281e-5i
$502$	−6.13711	−	12.5480i	−0.273913	−	0.560044i
$503$	4.86659	−	8.42917i	0.216990	−	0.375838i	−0.736896	−	0.676006i	$-0.763709\pi$
$503$	4.86659	−	8.42917i	0.216990	−	0.375838i	0.953886	+	0.300168i	$0.0970427\pi$
$504$	26.7992	+	23.9682i	1.19373	+	1.06763i
$505$	1.07969	+	1.87007i	0.0480454	+	0.0832170i
$506$	−4.94788	+	7.35293i	−0.219960	+	0.326878i
$507$	20.5990	−	7.49806i	0.914836	−	0.333001i
$508$	1.36253	+	3.35118i	0.0604523	+	0.148684i
$509$	10.0766	+	27.6853i	0.446639	+	1.22713i	0.935050	+	0.354516i	$0.115354\pi$
$509$	10.0766	+	27.6853i	0.446639	+	1.22713i	−0.488411	+	0.872614i	$0.662423\pi$
$510$	3.15025	−	4.68178i	0.139496	−	0.207313i
$511$	6.39149	+	36.2480i	0.282743	+	1.60352i
$512$	13.1186	−	18.4364i	0.579768	−	0.814782i
$513$	24.5960	+	14.1979i	1.08594	+	0.626851i
$514$	−5.37948	−	1.33499i	−0.237279	−	0.0588837i
$515$	5.85115	−	1.03172i	0.257833	−	0.0454628i
$516$	24.6548	+	7.95033i	1.08537	+	0.349994i
$517$	2.24281	+	6.16206i	0.0986386	+	0.271007i
$518$	−25.2755	+	18.4061i	−1.11054	+	0.808717i
$519$	−33.1452	−	5.84348i	−1.45491	−	0.256500i
$520$	−0.684200	−	1.27664i	−0.0300041	−	0.0559842i
$521$	15.4542	+	26.7675i	0.677063	+	1.17271i	0.975861	+	0.218391i	$0.0700807\pi$
$521$	15.4542	+	26.7675i	0.677063	+	1.17271i	−0.298799	+	0.954316i	$0.596586\pi$
$522$	26.0546	+	1.79179i	1.14038	+	0.0784244i
$523$	−15.5320	−	8.96741i	−0.679167	−	0.392117i	0.120374	−	0.992729i	$-0.461591\pi$
$523$	−15.5320	−	8.96741i	−0.679167	−	0.392117i	−0.799541	+	0.600611i	$0.794924\pi$
$524$	−2.27701	−	10.5981i	−0.0994714	−	0.462978i
$525$	−15.5489	−	26.9299i	−0.678611	−	1.17532i
$526$	12.2291	−	27.5483i	0.533214	−	1.20116i
$527$	0.673753	−	3.82104i	0.0293491	−	0.166447i
$528$	−23.7643	−	11.4610i	−1.03421	−	0.498776i
$529$	−15.5445	+	13.0434i	−0.675846	+	0.567102i
$530$	10.6035	−	11.0044i	0.460587	−	0.478001i
$531$	−5.46797	−	6.51576i	−0.237290	−	0.282760i
$532$	−46.2850	+	1.71801i	−2.00671	+	0.0744852i
$533$	1.39468	−	3.83185i	0.0604102	−	0.165976i
$534$	8.82589	−	19.8834i	0.381934	−	0.860438i
$535$	−0.668032	−	0.560545i	−0.0288815	−	0.0242345i
$536$	10.9300	−	27.3112i	0.472104	−	1.17966i
$537$	19.2245	−	3.39034i	0.829600	−	0.146304i
$538$	−29.8751	−	2.05613i	−1.28801	−	0.0886462i
$539$			41.7136i			1.79673i
$540$	8.63901	+	2.78527i	0.371764	+	0.119859i
$541$			18.2082i			0.782833i	0.920214	+	0.391416i	$0.128015\pi$
$541$			18.2082i			0.782833i	−0.920214	+	0.391416i	$0.871985\pi$
$542$	−1.14492	+	16.6353i	−0.0491784	+	0.714549i
$543$	0.0942856	−	0.259069i	0.00404618	−	0.0111177i
$544$	9.65324	+	11.3769i	0.413879	+	0.487782i
$545$	−3.42466	−	2.87363i	−0.146696	−	0.123093i
$546$	0.642884	+	6.05120i	0.0275129	+	0.258967i
$547$	−4.37809	+	12.0287i	−0.187194	+	0.514311i	−0.997418	−	0.0718089i	$-0.977123\pi$
$547$	−4.37809	+	12.0287i	−0.187194	+	0.514311i	0.810225	+	0.586119i	$0.199345\pi$
$548$	0.644137	+	17.3537i	0.0275162	+	0.741315i
$549$	−22.7211	−	13.1164i	−0.969713	−	0.559795i
$550$	16.4321	+	15.8335i	0.700669	+	0.675144i
$551$	−25.7726	+	21.6258i	−1.09795	+	0.921289i
$552$	6.00909	+	5.37461i	0.255764	+	0.228758i
$553$	11.0187	−	62.4903i	0.468564	−	2.65736i
$554$	−8.50447	−	3.77526i	−0.361320	−	0.160395i
$555$	−3.94667	+	6.83626i	−0.167527	+	0.290183i
$556$	8.59372	+	39.9985i	0.364455	+	1.69631i
$557$	11.6436	+	6.72245i	0.493356	+	0.284839i	0.725966	−	0.687731i	$-0.241393\pi$
$557$	11.6436	+	6.72245i	0.493356	+	0.284839i	−0.232609	+	0.972570i	$0.574726\pi$
$558$	6.20614	−	0.659513i	0.262727	−	0.0279194i
$559$	2.19224	+	3.79707i	0.0927218	+	0.160599i
$560$	−14.3479	+	3.64429i	−0.606309	+	0.153999i
$561$	11.1824	−	13.3274i	0.472121	−	0.562683i
$562$	−3.26122	−	4.47834i	−0.137566	−	0.188907i
$563$	−4.03319	−	11.0811i	−0.169979	−	0.467012i	0.825229	−	0.564798i	$-0.191046\pi$
$563$	−4.03319	−	11.0811i	−0.169979	−	0.467012i	−0.995207	+	0.0977862i	$0.968824\pi$
$564$	5.83197	−	1.25317i	0.245570	−	0.0527679i
$565$	−2.07596	+	0.366047i	−0.0873361	+	0.0153997i
$566$	4.69126	−	18.9039i	0.197188	−	0.794592i
$567$	−29.2155	−	24.5094i	−1.22694	−	1.02930i
$568$	−34.6252	−	30.9709i	−1.45284	−	1.29951i
$569$	7.06201	+	40.0506i	0.296055	+	1.67901i	0.662884	+	0.748722i	$0.269332\pi$
$569$	7.06201	+	40.0506i	0.296055	+	1.67901i	−0.366829	+	0.930288i	$0.619557\pi$
$570$	−10.5040	+	5.13777i	−0.439964	+	0.215197i
$571$	1.60281	+	4.40368i	0.0670755	+	0.184288i	0.968702	−	0.248228i	$-0.0798481\pi$
$571$	1.60281	+	4.40368i	0.0670755	+	0.184288i	−0.901626	+	0.432516i	$0.857626\pi$
$572$	−1.68188	−	4.13665i	−0.0703231	−	0.172962i
$573$	19.6406	+	16.4795i	0.820498	+	0.688442i
$574$	−34.5769	−	23.2672i	−1.44321	−	0.971156i
$575$	−3.48640	−	6.03863i	−0.145393	−	0.251828i
$576$	−13.2883	+	19.9855i	−0.553678	+	0.832731i
$577$	−12.3616	+	21.4109i	−0.514620	+	0.891348i	0.485236	+	0.874383i	$0.338734\pi$
$577$	−12.3616	+	21.4109i	−0.514620	+	0.891348i	−0.999856	+	0.0169645i	$0.994600\pi$
$578$	12.7589	−	6.24025i	0.530698	−	0.259560i
$579$	6.08225	−	10.5354i	0.252770	−	0.437837i
$580$	−6.60158	+	8.48796i	−0.274116	+	0.352443i
$581$	59.6457	+	10.5171i	2.47452	+	0.436325i
$582$	30.0709	+	7.46163i	1.24648	+	0.309294i
$583$	36.0911	−	30.2840i	1.49474	−	1.25424i
$584$	−23.3420	+	7.66932i	−0.965900	+	0.317359i
$585$	0.768214	+	1.33042i	0.0317617	+	0.0550061i
$586$	−6.55893	+	1.88853i	−0.270947	+	0.0780146i
$587$	−0.150984	+	0.414824i	−0.00623177	+	0.0171216i	−0.942770	−	0.333445i	$-0.891789\pi$
$587$	−0.150984	+	0.414824i	−0.00623177	+	0.0171216i	0.936538	+	0.350567i	$0.114011\pi$
$588$	37.5874	+	5.19745i	1.55008	+	0.214339i
$589$	−5.16800	+	6.15899i	−0.212944	+	0.253777i
$590$	3.48268	−	0.369909i	0.143380	−	0.0152289i
$591$	−2.22531	+	6.11450i	−0.0915370	+	0.251517i
$592$	−14.5644	−	14.9500i	−0.598591	−	0.614440i
$593$	−11.8140			−0.485142			−0.242571	−	0.970134i	$-0.577991\pi$
$593$	−11.8140			−0.485142			−0.242571	+	0.970134i	$0.577991\pi$
$594$	25.5781	+	11.3520i	1.04948	+	0.465780i
$595$		−	9.76137i		−	0.400177i
$596$	−7.50420	−	2.42007i	−0.307384	−	0.0991299i
$597$	7.50641	+	42.5643i	0.307217	+	1.74204i
$598$	0.144119	+	1.35688i	0.00589345	+	0.0554868i
$599$	−15.7110	−	13.1831i	−0.641935	−	0.538647i	0.262677	−	0.964884i	$-0.415395\pi$
$599$	−15.7110	−	13.1831i	−0.641935	−	0.538647i	−0.904612	+	0.426236i	$0.859839\pi$
$600$	16.3147	−	12.8339i	0.666046	−	0.523940i
$601$	22.7666	+	8.28638i	0.928671	+	0.338008i	0.761682	−	0.647950i	$-0.224374\pi$
$601$	22.7666	+	8.28638i	0.928671	+	0.338008i	0.166988	+	0.985959i	$0.446596\pi$
$602$	43.0616	−	12.3989i	1.75506	−	0.505340i
$603$	−10.6700	+	29.3204i	−0.434516	+	1.19402i
$604$	15.8201	−	9.93381i	0.643709	−	0.404201i
$605$	−1.96612	−	2.34313i	−0.0799341	−	0.0952617i
$606$	5.81940	−	1.67577i	0.236397	−	0.0680734i
$607$	−8.02152	+	45.4923i	−0.325583	+	1.84647i	0.179961	+	0.983674i	$0.442403\pi$
$607$	−8.02152	+	45.4923i	−0.325583	+	1.84647i	−0.505544	+	0.862801i	$0.668708\pi$
$608$	−5.53576	−	30.4180i	−0.224505	−	1.23361i
$609$	39.1233	−	22.5892i	1.58535	−	0.915361i
$610$	9.70358	−	4.74594i	0.392887	−	0.192157i
$611$	0.874343	+	0.504802i	0.0353721	+	0.0204221i
$612$	−10.6158	−	11.7368i	−0.429116	−	0.474433i
$613$	−24.2293	+	13.9888i	−0.978610	+	0.565001i	−0.901850	−	0.432049i	$-0.857791\pi$
$613$	−24.2293	+	13.9888i	−0.978610	+	0.565001i	−0.0767600	+	0.997050i	$0.524458\pi$
$614$	20.1532	−	29.9491i	0.813316	−	1.20865i
$615$	−10.3619	−	1.82679i	−0.417830	−	0.0736632i
$616$	−45.1738	+	6.50047i	−1.82010	+	0.261911i
$617$	−24.1813	+	8.80127i	−0.973502	+	0.354326i	−0.779310	−	0.626638i	$-0.784430\pi$
$617$	−24.1813	+	8.80127i	−0.973502	+	0.354326i	−0.194191	+	0.980964i	$0.562208\pi$
$618$	1.14363	−	16.6232i	0.0460036	−	0.668683i
$619$	−20.9215	+	3.68902i	−0.840905	+	0.148274i	−0.577479	−	0.816405i	$-0.695964\pi$
$619$	−20.9215	+	3.68902i	−0.840905	+	0.148274i	−0.263426	+	0.964680i	$0.584852\pi$
$620$	−1.20141	+	2.27154i	−0.0482498	+	0.0912271i
$621$	−6.55090	−	5.49596i	−0.262879	−	0.220545i
$622$	−2.07490	−	0.514913i	−0.0831959	−	0.0206461i
$623$	−6.53455	−	37.0593i	−0.261801	−	1.48475i
$624$	−3.93701	+	1.00009i	−0.157607	+	0.0400358i
$625$	−13.2862	+	4.83579i	−0.531449	+	0.193431i
$626$	3.82558	+	5.25333i	0.152901	+	0.209965i
$627$	−33.8757	+	12.3308i	−1.35286	+	0.492443i
$628$	23.7370	−	21.4674i	0.947209	−	0.856642i
$629$	11.9188	−	6.88132i	0.475234	−	0.274376i
$630$	15.0882	−	4.34527i	0.601129	−	0.173120i
$631$	4.14510	−	7.17952i	0.165014	−	0.285812i	−0.771646	−	0.636052i	$-0.780567\pi$
$631$	4.14510	−	7.17952i	0.165014	−	0.285812i	0.936660	+	0.350240i	$0.113900\pi$
$632$	42.3361	+	1.33890i	1.68404	+	0.0532585i
$633$	−0.000335676	−	12.5370i	−1.33419e−5	−	0.498302i
$634$	7.97007	+	3.53803i	0.316532	+	0.140513i
$635$	1.55584	+	0.274337i	0.0617416	+	0.0108867i
$636$	−22.7915	−	36.2943i	−0.903740	−	1.43916i
$637$	4.12816	+	4.91975i	0.163564	+	0.194928i
$638$	−23.0027	+	23.8724i	−0.910685	+	0.945115i
$639$	37.7473	+	31.6703i	1.49326	+	1.25286i
$640$	−3.77200	−	9.13343i	−0.149101	−	0.361031i
$641$	46.3924	+	16.8854i	1.83239	+	0.666935i	0.992202	+	0.124637i	$0.0397766\pi$
$641$	46.3924	+	16.8854i	1.83239	+	0.666935i	0.840186	+	0.542298i	$0.182446\pi$
$642$	−1.97695	+	1.43974i	−0.0780240	+	0.0568219i
$643$	−3.89927	+	4.64697i	−0.153772	+	0.183259i	−0.837431	−	0.546543i	$-0.815943\pi$
$643$	−3.89927	+	4.64697i	−0.153772	+	0.183259i	0.683658	+	0.729802i	$0.260388\pi$
$644$	13.8143	+	1.91057i	0.544361	+	0.0752871i
$645$	8.66609	−	7.27211i	0.341227	−	0.286339i
$646$	20.3389	+	1.39981i	0.800223	+	0.0550748i
$647$	5.00360			0.196712			0.0983558	−	0.995151i	$-0.468642\pi$
$647$	5.00360			0.196712			0.0983558	+	0.995151i	$0.468642\pi$
$648$	13.4161	−	21.6335i	0.527034	−	0.849844i
$649$	10.7975			0.423839
$650$	3.50498	+	0.241228i	0.137477	+	0.00946173i
$651$	8.27002	−	6.93975i	0.324128	−	0.271990i
$652$	6.11014	−	44.1791i	0.239292	−	1.73019i
$653$	−11.4781	+	13.6791i	−0.449175	+	0.535305i	−0.942352	−	0.334623i	$-0.891391\pi$
$653$	−11.4781	+	13.6791i	−0.449175	+	0.535305i	0.493177	+	0.869929i	$0.335835\pi$
$654$	−10.1348	+	7.38079i	−0.396302	+	0.288612i
$655$	−4.44843	−	1.61910i	−0.173815	−	0.0632634i
$656$	12.0856	−	25.0578i	0.471865	−	0.978341i
$657$	24.4880	−	8.91438i	0.955367	−	0.347783i
$658$	7.15973	−	7.43042i	0.279115	−	0.289668i
$659$	5.97809	+	7.12441i	0.232873	+	0.277528i	0.869808	−	0.493390i	$-0.164242\pi$
$659$	5.97809	+	7.12441i	0.232873	+	0.277528i	−0.636935	+	0.770918i	$0.719798\pi$
$660$	−9.75768	+	6.12745i	−0.379817	+	0.238511i
$661$	39.7470	+	7.00847i	1.54598	+	0.272598i	0.880583	−	0.473892i	$-0.157151\pi$
$661$	39.7470	+	7.00847i	1.54598	+	0.272598i	0.665397	+	0.746490i	$0.268262\pi$
$662$	17.8891	+	7.94123i	0.695280	+	0.308645i
$663$	−7.17163e−5	−	2.67850i	−2.78523e−6	−	0.104025i
$664$	−1.27795	+	40.4089i	−0.0495941	+	1.56817i
$665$	−10.1136	+	17.5173i	−0.392188	+	0.679290i
$666$	15.9422	+	15.3598i	0.617746	+	0.595178i
$667$	8.77282	−	5.06499i	0.339685	−	0.196117i
$668$	−18.6010	−	20.5676i	−0.719695	−	0.795783i
$669$	12.3070	−	4.47977i	0.475818	−	0.173198i
$670$	−7.56257	−	10.3850i	−0.292168	−	0.401208i
$671$	31.2942	−	11.3902i	1.20810	−	0.439712i
$672$	0.228871	+	41.5152i	0.00882889	+	1.60148i
$673$	−4.00887	−	22.7354i	−0.154530	−	0.876385i	−0.959214	−	0.282681i	$-0.908776\pi$
$673$	−4.00887	−	22.7354i	−0.154530	−	0.876385i	0.804683	−	0.593704i	$-0.202335\pi$
$674$	−24.0778	−	5.97521i	−0.927441	−	0.230156i
$675$	−16.8647	+	14.1535i	−0.649122	+	0.544767i
$676$	22.3756	+	11.8344i	0.860601	+	0.455170i
$677$	−44.7493	+	7.89052i	−1.71986	+	0.303257i	−0.944560	−	0.328339i	$-0.893511\pi$
$677$	−44.7493	+	7.89052i	−1.71986	+	0.303257i	−0.775297	+	0.631597i	$0.782400\pi$
$678$	−0.405754	+	5.89782i	−0.0155829	+	0.226504i
$679$	50.3627	−	18.3305i	1.93274	−	0.703461i
$680$	6.44952	−	0.928079i	0.247328	−	0.0355902i
$681$	−14.6711	−	2.58650i	−0.562197	−	0.0991150i
$682$	−4.42290	+	6.57276i	−0.169362	+	0.251684i
$683$	−4.33907	+	2.50516i	−0.166030	+	0.0958573i	−0.580712	−	0.814109i	$-0.697226\pi$
$683$	−4.33907	+	2.50516i	−0.166030	+	0.0958573i	0.414683	+	0.909966i	$0.363893\pi$
$684$	6.89017	+	32.0611i	0.263452	+	1.22589i
$685$	6.56777	+	3.79191i	0.250942	+	0.144881i
$686$	21.2830	−	10.4093i	0.812590	−	0.397431i
$687$	25.2072	−	14.5543i	0.961714	−	0.555280i
$688$	12.2863	+	27.2728i	0.468412	+	1.03976i
$689$	1.25958	−	7.14345i	0.0479863	−	0.272144i
$690$	3.38329	−	0.974259i	0.128800	−	0.0370894i
$691$	−5.18542	−	6.17974i	−0.197263	−	0.235088i	0.658341	−	0.752720i	$-0.271258\pi$
$691$	−5.18542	−	6.17974i	−0.197263	−	0.235088i	−0.855604	+	0.517631i	$0.826814\pi$
$692$	−20.6665	−	32.9124i	−0.785624	−	1.25114i
$693$	47.6717	−	8.40844i	1.81090	−	0.319410i
$694$	−33.7974	+	9.73139i	−1.28293	+	0.369398i
$695$	16.7890	+	6.11069i	0.636842	+	0.231792i
$696$	18.6448	+	23.7017i	0.706730	+	0.898412i
$697$	14.0527	+	11.7916i	0.532282	+	0.446638i
$698$	−1.01787	−	9.58321i	−0.0385269	−	0.362730i
$699$	2.10663	+	11.9454i	0.0796801	+	0.451817i
$700$	11.0209	−	34.1739i	0.416552	−	1.29165i
$701$			2.75919i			0.104213i	0.998642	+	0.0521066i	$0.0165936\pi$
$701$			2.75919i			0.104213i	−0.998642	+	0.0521066i	$0.983406\pi$
$702$	4.14015	−	1.19245i	0.156260	−	0.0450060i
$703$	−28.5185			−1.07560
$704$	−8.58996	−	29.2291i	−0.323746	−	1.10161i
$705$	0.890907	−	2.44795i	0.0335535	−	0.0921952i
$706$	−46.2993	+	4.91762i	−1.74250	+	0.185077i
$707$	6.73360	−	8.02479i	0.253243	−	0.301803i
$708$	1.34535	−	9.72943i	0.0505614	−	0.365654i
$709$	−3.37681	+	9.27771i	−0.126819	+	0.348432i	−0.986811	−	0.161875i	$-0.948246\pi$
$709$	−3.37681	+	9.27771i	−0.126819	+	0.348432i	0.859993	+	0.510307i	$0.170468\pi$
$710$	−19.4956	+	5.61343i	−0.731656	+	0.210668i
$711$	−44.9267	+	0.00240580i	−1.68488	+	9.02245e-5i
$712$	23.8645	−	7.84098i	0.894359	−	0.293853i
$713$	1.85444	−	1.55606i	0.0694495	−	0.0582750i
$714$	−26.5697	−	6.59285i	−0.994345	−	0.246731i
$715$	−1.92051	−	0.338637i	−0.0718229	−	0.0126643i
$716$	17.7931	+	13.8387i	0.664958	+	0.517176i
$717$	4.34695	−	7.52961i	0.162340	−	0.281198i
$718$	7.79882	−	3.81434i	0.291049	−	0.142350i
$719$	−14.8854	+	25.7823i	−0.555131	+	0.961516i	0.442762	+	0.896639i	$0.353999\pi$
$719$	−14.8854	+	25.7823i	−0.555131	+	0.961516i	−0.997893	+	0.0648765i	$0.979335\pi$
$720$	4.30554	+	9.55593i	0.160458	+	0.356129i
$721$	−14.4116	−	24.9616i	−0.536716	−	0.929619i
$722$	−12.7561	−	8.58373i	−0.474732	−	0.319453i
$723$	−1.31159	−	1.10050i	−0.0487787	−	0.0409279i
$724$	0.294900	−	0.119901i	0.0109599	−	0.00445608i
$725$	−8.92063	−	24.5092i	−0.331304	−	0.910250i
$726$	−7.70573	+	3.76906i	−0.285987	+	0.139883i
$727$	4.02552	+	22.8299i	0.149298	+	0.846713i	0.963815	+	0.266573i	$0.0858912\pi$
$727$	4.02552	+	22.8299i	0.149298	+	0.846713i	−0.814516	+	0.580140i	$0.802998\pi$
$728$	−4.68453	+	5.23726i	−0.173620	+	0.194106i
$729$	−13.4962	+	23.3849i	−0.499861	+	0.866106i
$730$	−2.58437	+	10.4140i	−0.0956518	+	0.385439i
$731$	−19.4246	+	3.42507i	−0.718443	+	0.126681i
$732$	−6.36425	−	29.6178i	−0.235229	−	1.09471i
$733$	4.25415	+	11.6882i	0.157131	+	0.431713i	0.993130	−	0.117018i	$-0.0373335\pi$
$733$	4.25415	+	11.6882i	0.157131	+	0.431713i	−0.835999	+	0.548731i	$0.815111\pi$
$734$	10.8071	+	14.8405i	0.398899	+	0.547773i
$735$	10.6513	−	12.6945i	0.392881	−	0.468242i
$736$	0.0510709	+	9.30903i	0.00188250	+	0.343135i
$737$	−19.8034	−	34.3004i	−0.729466	−	1.26347i
$738$	−11.9708	+	26.9703i	−0.440651	+	0.992791i
$739$	2.84663	+	1.64350i	0.104715	+	0.0604572i	0.551443	−	0.834213i	$-0.314077\pi$
$739$	2.84663	+	1.64350i	0.104715	+	0.0604572i	−0.446728	+	0.894670i	$0.647411\pi$
$740$	−8.91151	+	1.91465i	−0.327594	+	0.0703839i
$741$	−2.77503	+	4.80678i	−0.101943	+	0.176582i
$742$	−67.7590	−	30.0792i	−2.48751	−	1.10424i
$743$	−4.23528	+	24.0195i	−0.155377	+	0.881189i	0.803063	+	0.595895i	$0.203202\pi$
$743$	−4.23528	+	24.0195i	−0.155377	+	0.881189i	−0.958440	+	0.285294i	$0.907909\pi$
$744$	5.37151	+	4.80435i	0.196929	+	0.176136i
$745$	−2.63778	+	2.21336i	−0.0966409	+	0.0810914i
$746$	−16.7360	−	16.1263i	−0.612748	−	0.590426i
$747$	−0.00229629	−	42.8816i	−8.40167e−5	−	1.56895i
$748$	20.0748	−	0.745139i	0.734009	−	0.0272450i
$749$	−1.44693	+	3.97540i	−0.0528696	+	0.145258i
$750$	−2.08782	−	19.6517i	−0.0762363	−	0.717580i
$751$	−23.7598	−	19.9368i	−0.867006	−	0.727504i	0.0964598	−	0.995337i	$-0.469248\pi$
$751$	−23.7598	−	19.9368i	−0.867006	−	0.727504i	−0.963465	+	0.267833i	$0.913693\pi$
$752$	5.59014	+	4.02411i	0.203851	+	0.146744i
$753$	−5.85075	+	16.0762i	−0.213213	+	0.585848i
$754$	−0.350452	+	5.09197i	−0.0127627	+	0.185439i
$755$		−	8.15794i		−	0.296898i
$756$	−1.63687	−	44.0037i	−0.0595325	−	1.60040i
$757$		−	29.0100i		−	1.05439i	−0.849746	−	0.527193i	$-0.823244\pi$
$757$		−	29.0100i		−	1.05439i	0.849746	−	0.527193i	$-0.176756\pi$
$758$	19.0569	+	1.31158i	0.692179	+	0.0476388i
$759$	10.6896	−	1.88515i	0.388007	−	0.0684268i
$760$	−12.5355	−	5.01675i	−0.454712	−	0.181977i
$761$	−7.72321	−	6.48054i	−0.279966	−	0.234920i	0.491981	−	0.870606i	$-0.336273\pi$
$761$	−7.72321	−	6.48054i	−0.279966	−	0.234920i	−0.771948	+	0.635686i	$0.780717\pi$
$762$	1.79754	−	4.04958i	0.0651180	−	0.146701i
$763$	−7.41766	+	20.3799i	−0.268537	+	0.737800i
$764$	1.09811	+	29.5843i	0.0397283	+	1.07032i
$765$	−6.80615	+	1.20048i	−0.246077	+	0.0434036i
$766$	−8.95558	+	9.29416i	−0.323578	+	0.335812i
$767$	1.27347	−	1.06857i	0.0459823	−	0.0385837i
$768$	−27.4081	+	4.09835i	−0.989004	+	0.147886i
$769$	−1.90561	+	10.8072i	−0.0687180	+	0.389719i	0.930978	+	0.365075i	$0.118957\pi$
$769$	−1.90561	+	10.8072i	−0.0687180	+	0.389719i	−0.999696	+	0.0246446i	$0.992155\pi$
$770$	−8.08675	+	18.2169i	−0.291426	+	0.656492i
$771$	3.39432	+	5.87878i	0.122244	+	0.211719i
$772$	13.7336	−	2.95068i	0.494283	−	0.106197i
$773$	17.8236	+	10.2904i	0.641070	+	0.370122i	0.785026	−	0.619462i	$-0.212649\pi$
$773$	17.8236	+	10.2904i	0.641070	+	0.370122i	−0.143957	+	0.989584i	$0.545983\pi$
$774$	−13.9410	−	28.5000i	−0.501099	−	1.02441i
$775$	−3.11649	−	5.39791i	−0.111947	−	0.193899i
$776$	16.8996	+	31.5328i	0.606662	+	1.13196i
$777$	37.7126	+	6.64872i	1.35293	+	0.238521i
$778$	−37.7894	+	27.5190i	−1.35481	+	0.986603i
$779$	−13.0011	−	35.7203i	−0.465814	−	1.27981i
$780$	−0.544432	+	1.68834i	−0.0194938	+	0.0604523i
$781$	−61.5965	+	10.8611i	−2.20410	+	0.388642i
$782$	−5.95773	−	1.47849i	−0.213048	−	0.0528706i
$783$	−20.5619	−	24.5007i	−0.734823	−	0.875585i
$784$	24.6603	+	36.2165i	0.880725	+	1.29345i
$785$	−2.42705	−	13.7645i	−0.0866250	−	0.491275i
$786$	−7.41154	+	11.0147i	−0.264361	+	0.392883i
$787$	−2.41642	−	6.63907i	−0.0861362	−	0.236657i	0.889145	−	0.457626i	$-0.151300\pi$
$787$	−2.41642	−	6.63907i	−0.0861362	−	0.236657i	−0.975281	+	0.220969i	$0.929078\pi$
$788$	−6.96017	+	2.82987i	−0.247946	+	0.100810i
$789$	−34.6881	+	12.6265i	−1.23493	+	0.449515i
$790$	10.3271	−	15.3468i	0.367421	−	0.546016i
$791$	5.11315	+	8.85624i	0.181803	+	0.314892i
$792$	10.0881	+	30.6981i	0.358464	+	1.09081i
$793$	2.56365	−	4.44037i	0.0910379	−	0.157682i
$794$	4.19683	+	8.58087i	0.148940	+	0.304524i
$795$	−18.7162		0.000501122i	−0.663796		1.77730e-5i
$796$	−30.6397	+	39.3950i	−1.08600	+	1.39632i
$797$	−10.1647	−	1.79231i	−0.360051	−	0.0634868i	−0.00930356	−	0.999957i	$-0.502961\pi$
$797$	−10.1647	−	1.79231i	−0.360051	−	0.0634868i	−0.350748	+	0.936470i	$0.614073\pi$
$798$	40.8498	+	39.3596i	1.44607	+	1.39331i
$799$	−3.47926	+	2.91945i	−0.123087	+	0.103283i
$800$	23.6272	+	4.03258i	0.835346	+	0.142573i
$801$	−25.0361	+	9.11390i	−0.884606	+	0.322024i
$802$	−6.36772	−	22.1153i	−0.224852	−	0.780917i
$803$	−11.3141	+	31.0852i	−0.399266	+	1.09697i
$804$	−33.3749	+	13.5707i	−1.17704	+	0.478600i
$805$	3.91478	−	4.66545i	0.137978	−	0.164436i
$806$	0.128827	+	1.21291i	0.00453775	+	0.0427228i
$807$	23.5756	+	28.0948i	0.829900	+	0.988983i
$808$	5.94233	+	3.68604i	0.209051	+	0.129674i
$809$	29.0766			1.02228			0.511139	−	0.859498i	$-0.329224\pi$
$809$	29.0766			1.02228			0.511139	+	0.859498i	$0.329224\pi$
$810$	−4.88535	−	9.98592i	−0.171654	−	0.350869i
$811$		−	52.2233i		−	1.83381i	−0.399108	−	0.916904i	$-0.630680\pi$
$811$		−	52.2233i		−	1.83381i	0.399108	−	0.916904i	$-0.369320\pi$
$812$	49.6473	+	16.0110i	1.74228	+	0.561876i
$813$	15.6440	−	13.1276i	0.548659	−	0.460405i
$814$	−27.9440	+	2.96803i	−0.979435	+	0.104029i
$815$	−14.9204	−	12.5197i	−0.522640	−	0.438547i
$816$	1.82986	−	18.1819i	0.0640579	−	0.636494i
$817$	38.4070	+	13.9790i	1.34369	+	0.489063i
$818$	9.32216	+	32.3761i	0.325942	+	1.13200i
$819$	4.79031	−	5.70949i	0.167387	−	0.199506i
$820$	−6.46077	−	10.2891i	−0.225620	−	0.359310i
$821$	25.4058	+	30.2775i	0.886670	+	1.05669i	0.998019	+	0.0629110i	$0.0200384\pi$
$821$	25.4058	+	30.2775i	0.886670	+	1.05669i	−0.111349	+	0.993781i	$0.535517\pi$
$822$	14.7572	−	15.3159i	0.514715	−	0.534203i
$823$	−5.55309	+	31.4931i	−0.193569	+	1.09778i	0.720874	+	0.693066i	$0.243741\pi$
$823$	−5.55309	+	31.4931i	−0.193569	+	1.09778i	−0.914443	+	0.404716i	$0.867371\pi$
$824$	15.1224	−	11.8953i	0.526814	−	0.414392i
$825$	−0.000748293	−	27.9477i	−2.60522e−5	−	0.973014i
$826$	−7.46483	−	15.2626i	−0.259735	−	0.531055i
$827$	22.4521	+	12.9627i	0.780737	+	0.450759i	0.836691	−	0.547675i	$-0.184487\pi$
$827$	22.4521	+	12.9627i	0.780737	+	0.450759i	−0.0559543	+	0.998433i	$0.517820\pi$
$828$	−0.366775	−	9.86705i	−0.0127463	−	0.342904i
$829$	43.7303	−	25.2477i	1.51882	−	0.876889i	0.519061	−	0.854737i	$-0.326282\pi$
$829$	43.7303	−	25.2477i	1.51882	−	0.876889i	0.999755	−	0.0221517i	$-0.00705169\pi$
$830$	14.6482	+	9.85700i	0.508448	+	0.342141i
$831$	3.89794	+	10.7086i	0.135218	+	0.371477i
$832$	−3.90575	−	2.59721i	−0.135407	−	0.0900421i
$833$	−27.1492	+	9.88150i	−0.940664	+	0.342374i
$834$	27.9721	−	41.5711i	0.968595	−	1.43949i
$835$	−11.9266	+	2.10298i	−0.412737	+	0.0727767i
$836$	−36.7973	−	19.4620i	−1.27266	−	0.673108i
$837$	−5.85583	−	4.91283i	−0.202407	−	0.169812i
$838$	0.792000	−	3.19145i	0.0273592	−	0.110247i
$839$	7.04629	+	39.9615i	0.243265	+	1.37962i	0.824488	+	0.565879i	$0.191463\pi$
$839$	7.04629	+	39.9615i	0.243265	+	1.37962i	−0.581223	+	0.813744i	$0.697426\pi$
$840$	15.4073	+	9.55662i	0.531603	+	0.329735i
$841$	8.35553	−	3.04117i	0.288122	−	0.104868i
$842$	−25.8261	+	18.8071i	−0.890026	+	0.648135i
$843$	−1.17803	+	6.68197i	−0.0405734	+	0.230139i
$844$	10.7369	−	9.71026i	0.369578	−	0.334241i
$845$	9.57329	−	5.52714i	0.329331	−	0.190139i
$846$	−6.06141	−	4.07833i	−0.208395	−	0.140216i
$847$	−7.41933	+	12.8507i	−0.254931	+	0.441554i
$848$	13.4316	−	47.6295i	0.461242	−	1.63560i
$849$	−20.6585	+	11.9279i	−0.708999	+	0.409366i
$850$	−6.41261	+	14.4456i	−0.219951	+	0.495480i
$851$	8.45634	+	1.49108i	0.289880	+	0.0511136i
$852$	2.11194	+	56.8568i	0.0723538	+	1.94788i
$853$	26.9773	+	32.1503i	0.923685	+	1.10081i	0.994648	+	0.103326i	$0.0329486\pi$
$853$	26.9773	+	32.1503i	0.923685	+	1.10081i	−0.0709621	+	0.997479i	$0.522607\pi$
$854$	−37.7355	−	36.3609i	−1.29128	−	1.24424i
$855$	13.4578	+	4.89741i	0.460246	+	0.167488i
$856$	−2.76419	−	0.578044i	−0.0944782	−	0.0197571i
$857$	−19.0448	−	6.93174i	−0.650558	−	0.236784i	−0.00440329	−	0.999990i	$-0.501402\pi$
$857$	−19.0448	−	6.93174i	−0.650558	−	0.236784i	−0.646154	+	0.763207i	$0.723624\pi$
$858$	−2.21886	+	4.99875i	−0.0757506	+	0.170655i
$859$	−10.3219	+	12.3011i	−0.352177	+	0.419708i	−0.912828	−	0.408344i	$-0.866106\pi$
$859$	−10.3219	+	12.3011i	−0.352177	+	0.419708i	0.560651	+	0.828052i	$0.310551\pi$
$860$	12.9400	+	1.78965i	0.441250	+	0.0610265i
$861$	8.86487	+	50.2673i	0.302114	+	1.71310i
$862$	1.93415	−	28.1028i	0.0658776	−	0.957184i
$863$	−15.4584			−0.526210			−0.263105	−	0.964767i	$-0.584747\pi$
$863$	−15.4584			−0.526210			−0.263105	+	0.964767i	$0.584747\pi$
$864$	28.9185	−	5.26525i	0.983826	−	0.179127i
$865$	−16.9720			−0.577064
$866$	−1.19634	+	17.3825i	−0.0406531	+	0.590680i
$867$	−16.3463	−	5.94908i	−0.555150	−	0.202041i
$868$	12.3486	+	1.70786i	0.419138	+	0.0579684i
$869$	36.6576	−	43.6869i	1.24352	−	1.48198i
$870$	13.0959	−	1.39132i	0.443994	−	0.0471703i
$871$	−5.73015	−	2.08560i	−0.194159	−	0.0706680i
$872$	−14.1706	−	2.96333i	−0.479877	−	0.100351i
$873$	−18.9748	−	32.8612i	−0.642199	−	1.11218i
$874$	9.15960	+	8.82592i	0.309828	+	0.298541i
$875$	−21.9740	−	26.1875i	−0.742855	−	0.885300i
$876$	26.6006	+	14.0681i	0.898751	+	0.475317i
$877$	−18.6305	−	3.28506i	−0.629107	−	0.110929i	−0.150002	−	0.988686i	$-0.547928\pi$
$877$	−18.6305	−	3.28506i	−0.629107	−	0.110929i	−0.479106	+	0.877757i	$0.659039\pi$
$878$	10.0279	−	22.5896i	0.338424	−	0.762363i
$879$	7.23954	+	4.17949i	0.244184	+	0.140971i
$880$	−12.8051	−	3.61106i	−0.431660	−	0.121729i
$881$	−0.358235	+	0.620481i	−0.0120692	+	0.0209045i	−0.871997	−	0.489511i	$-0.837175\pi$
$881$	−0.358235	+	0.620481i	−0.0120692	+	0.0209045i	0.859928	+	0.510416i	$0.170509\pi$
$882$	−27.3594	−	37.5660i	−0.921238	−	1.26491i
$883$	2.30843	−	1.33277i	0.0776849	−	0.0448514i	−0.460654	−	0.887580i	$-0.652385\pi$
$883$	2.30843	−	1.33277i	0.0776849	−	0.0448514i	0.538339	+	0.842728i	$0.319052\pi$
$884$	2.29390	−	2.07457i	0.0771523	−	0.0697755i
$885$	−3.28594	−	2.75708i	−0.110456	−	0.0926782i
$886$	31.4027	−	22.8681i	1.05499	−	0.768268i
$887$	−48.5222	+	17.6606i	−1.62922	+	0.592987i	−0.985106	−	0.171946i	$-0.944995\pi$
$887$	−48.5222	+	17.6606i	−1.62922	+	0.592987i	−0.644111	+	0.764932i	$0.722772\pi$
$888$	−0.807332	+	25.5496i	−0.0270923	+	0.857388i
$889$	−1.33087	−	7.54774i	−0.0446360	−	0.253143i
$890$	2.64221	−	10.6471i	0.0885672	−	0.356891i
$891$	−11.7256	−	32.2052i	−0.392823	−	1.07891i
$892$	13.3685	+	7.07055i	0.447609	+	0.236740i
$893$	9.26850	−	1.63429i	0.310159	−	0.0546893i
$894$	4.24303	+	8.67475i	0.141908	+	0.290127i
$895$	9.25033	−	3.36685i	0.309205	−	0.112541i
$896$	−35.3777	+	32.3497i	−1.18189	+	1.08073i
$897$	1.07418	−	1.28022i	0.0358657	−	0.0427454i
$898$	0.777331	+	0.523076i	0.0259399	+	0.0174553i
$899$	7.84200	−	4.52758i	0.261545	−	0.151003i
$900$	−25.1832	−	3.48156i	−0.839442	−	0.116052i
$901$	28.2598	+	16.3158i	0.941471	+	0.543559i
$902$	−16.4568	−	33.6476i	−0.547950	−	1.12034i
$903$	−47.5301	−	27.4398i	−1.58170	−	0.913140i
$904$	−5.36534	+	4.22038i	−0.178449	+	0.140368i
$905$	0.0241413	−	0.136912i	0.000802485	−	0.00455112i
$906$	−22.2053	−	5.50989i	−0.737721	−	0.183054i
$907$	−21.1838	−	25.2459i	−0.703398	−	0.838277i	0.289508	−	0.957175i	$-0.406508\pi$
$907$	−21.1838	−	25.2459i	−0.703398	−	0.838277i	−0.992906	+	0.118898i	$0.962064\pi$
$908$	−9.14765	−	14.5681i	−0.303575	−	0.483458i
$909$	−6.42343	−	3.70811i	−0.213052	−	0.122990i
$910$	0.849063	+	2.94882i	0.0281462	+	0.0977525i
$911$	42.9325	+	15.6262i	1.42242	+	0.517718i	0.934748	−	0.355311i	$-0.115625\pi$
$911$	42.9325	+	15.6262i	1.42242	+	0.517718i	0.487670	+	0.873028i	$0.337847\pi$
$912$	−22.1217	+	30.7324i	−0.732524	+	1.01765i
$913$	41.6982	+	34.9890i	1.38001	+	1.15797i
$914$	−16.8632	+	1.79111i	−0.557786	+	0.0592445i
$915$	−12.4320	−	4.52449i	−0.410989	−	0.149575i
$916$	31.9878	+	10.3159i	1.05691	+	0.340848i
$917$			22.9654i			0.758383i
$918$	−1.32927	+	19.3366i	−0.0438724	+	0.638203i
$919$	15.4250			0.508825			0.254412	−	0.967096i	$-0.418118\pi$
$919$	15.4250			0.508825			0.254412	+	0.967096i	$0.418118\pi$
$920$	3.45476	+	2.14299i	0.113900	+	0.0706523i
$921$	−43.5396	+	7.67840i	−1.43468	+	0.253012i
$922$	0.482874	+	4.54625i	0.0159026	+	0.149723i
$923$	−6.18989	+	7.37683i	−0.203743	+	0.242811i
$924$	44.1232	+	34.3152i	1.45155	+	1.12889i
$925$	7.56168	−	20.7755i	0.248626	−	0.683096i
$926$	−7.46712	−	25.9335i	−0.245385	−	0.852228i
$927$	−15.6322	+	13.1184i	−0.513428	+	0.430864i
$928$	−5.85847	+	34.3251i	−0.192314	+	1.12678i
$929$	10.4860	−	8.79880i	0.344034	−	0.288679i	−0.454355	−	0.890821i	$-0.650130\pi$
$929$	10.4860	−	8.79880i	0.344034	−	0.288679i	0.798389	+	0.602142i	$0.205686\pi$
$930$	3.02431	−	0.870887i	0.0991711	−	0.0285575i
$931$	58.9586	+	10.3960i	1.93229	+	0.340715i
$932$	−8.59886	+	11.0560i	−0.281665	+	0.362150i
$933$	1.30921	+	2.26748i	0.0428617	+	0.0742341i
$934$	20.3218	+	41.5501i	0.664950	+	1.35956i
$935$	4.38649	−	7.59762i	0.143453	−	0.248469i
$936$	4.22782	+	2.62221i	0.138190	+	0.0857096i
$937$	−5.37859	−	9.31599i	−0.175711	−	0.304340i	0.764696	−	0.644391i	$-0.222889\pi$
$937$	−5.37859	−	9.31599i	−0.175711	−	0.304340i	−0.940407	+	0.340051i	$0.889556\pi$
$938$	−34.7938	+	51.7063i	−1.13606	+	1.68827i
$939$	1.38189	−	7.83831i	0.0450963	−	0.255794i
$940$	2.78652	−	1.13295i	0.0908862	−	0.0369526i
$941$	−8.33193	−	22.8918i	−0.271613	−	0.746251i	−0.998245	−	0.0592236i	$-0.981137\pi$
$941$	−8.33193	−	22.8918i	−0.271613	−	0.746251i	0.726632	−	0.687027i	$-0.241085\pi$
$942$	−39.1050	−	2.69032i	−1.27411	−	0.0876555i
$943$	1.98748	+	11.2716i	0.0647214	+	0.367053i
$944$	9.37458	−	6.38328i	0.305117	−	0.207758i
$945$	−16.6547	−	9.61380i	−0.541777	−	0.312737i
$946$	39.0881	+	9.70021i	1.27086	+	0.315381i
$947$	−47.9694	+	8.45830i	−1.55880	+	0.274858i	−0.885544	−	0.464556i	$-0.846214\pi$
$947$	−47.9694	+	8.45830i	−1.55880	+	0.274858i	−0.673252	+	0.739413i	$0.735103\pi$
$948$	−34.7979	−	38.4748i	−1.13018	−	1.24960i
$949$	1.74193	+	4.78591i	0.0565455	+	0.155357i
$950$	26.4746	−	19.2793i	0.858949	−	0.625504i
$951$	−3.65300	−	10.0357i	−0.118457	−	0.325429i
$952$	−14.9320	−	27.8613i	−0.483948	−	0.902991i
$953$	−19.7860	−	34.2704i	−0.640931	−	1.11013i	−0.985225	−	0.171264i	$-0.945215\pi$
$953$	−19.7860	−	34.2704i	−0.640931	−	1.11013i	0.344294	−	0.938862i	$-0.388118\pi$
$954$	−12.6396	+	50.9444i	−0.409223	+	1.64939i
$955$	11.1966	+	6.46437i	0.362314	+	0.209182i
$956$	9.81534	−	2.10884i	0.317451	−	0.0682047i
$957$	40.6020	−	0.00108711i	1.31248	−	3.51412e-5i
$958$	−11.5470	+	26.0118i	−0.373067	+	0.840402i
$959$	6.38866	−	36.2319i	0.206301	−	1.16999i
$960$	−4.84936	+	11.0885i	−0.156512	+	0.357880i
$961$	−22.0897	+	18.5355i	−0.712571	+	0.597918i
$962$	−3.00201	+	3.11551i	−0.0967887	+	0.100448i
$963$	2.94981	+	0.519969i	0.0950564	+	0.0167558i
$964$	−0.0733316	−	1.97563i	−0.00236185	−	0.0636308i
$965$	2.09812	−	5.76455i	0.0675410	−	0.185567i
$966$	−10.0549	−	13.8068i	−0.323512	−	0.444226i
$967$	−0.298329	−	0.250328i	−0.00959362	−	0.00805001i	0.637978	−	0.770054i	$-0.279771\pi$
$967$	−0.298329	−	0.250328i	−0.00959362	−	0.00805001i	−0.647572	+	0.762004i	$0.724215\pi$
$968$	−9.19607	−	3.68029i	−0.295573	−	0.118289i
$969$	−16.0502	−	19.1268i	−0.515607	−	0.614443i
$970$	15.5869	+	1.07276i	0.500466	+	0.0344442i
$971$		−	57.2060i		−	1.83583i	−0.396781	−	0.917913i	$-0.629873\pi$
$971$		−	57.2060i		−	1.83583i	0.396781	−	0.917913i	$-0.370127\pi$
$972$	−30.4804	+	6.55303i	−0.977661	+	0.210189i
$973$		−	86.6744i		−	2.77865i
$974$	3.29983	−	47.9457i	0.105733	−	1.53628i
$975$	−2.76591	−	3.29611i	−0.0885801	−	0.105560i
$976$	20.4365	−	28.3896i	0.654157	−	0.908730i
$977$	−18.7900	−	15.7667i	−0.601147	−	0.504422i	0.290667	−	0.956824i	$-0.406123\pi$
$977$	−18.7900	−	15.7667i	−0.601147	−	0.504422i	−0.891814	+	0.452402i	$0.850567\pi$
$978$	−44.1550	+	32.1564i	−1.41192	+	1.02825i
$979$	11.5673	−	31.7810i	0.369694	−	1.01572i
$980$	19.1215	−	0.709751i	0.610813	−	0.0226722i
$981$	15.1222	+	2.66561i	0.482814	+	0.0851064i
$982$	−9.40123	−	9.05875i	−0.300005	−	0.289076i
$983$	−1.86959	+	1.56877i	−0.0596306	+	0.0500360i	−0.672116	−	0.740446i	$-0.734614\pi$
$983$	−1.86959	+	1.56877i	−0.0596306	+	0.0500360i	0.612485	+	0.790482i	$0.290170\pi$
$984$	−32.3697	+	10.6364i	−1.03191	+	0.339077i
$985$	−0.569779	+	3.23137i	−0.0181547	+	0.102960i
$986$	−20.9863	−	9.31614i	−0.668341	−	0.296686i
$987$	−12.6376		0.000338369i	−0.402260		1.07704e-5i
$988$	−6.26596	+	1.34625i	−0.199347	+	0.0428299i
$989$	−10.6576	−	6.15317i	−0.338892	−	0.195659i
$990$	13.6963	+	3.39814i	0.435298	+	0.108000i
$991$	−4.60390	−	7.97419i	−0.146248	−	0.253309i	0.783590	−	0.621278i	$-0.213386\pi$
$991$	−4.60390	−	7.97419i	−0.146248	−	0.253309i	−0.929838	+	0.367970i	$0.880053\pi$
$992$	0.0456522	+	8.32132i	0.00144946	+	0.264202i
$993$	−8.19928	−	22.5255i	−0.260196	−	0.714824i
$994$	57.9372	+	79.5600i	1.83766	+	2.52349i
$995$	7.45441	+	20.4808i	0.236321	+	0.649286i
$996$	36.7234	−	33.2139i	1.16363	−	1.05242i
$997$	55.4811	−	9.78282i	1.75710	−	0.309825i	0.800093	−	0.599876i	$-0.204783\pi$
$997$	55.4811	−	9.78282i	1.75710	−	0.309825i	0.957011	+	0.290051i	$0.0936723\pi$
$998$	−3.62438	+	14.6049i	−0.114728	+	0.462309i
$999$	−0.00217783	−	27.1129i	−6.89034e−5	−	0.857816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.18	yes	204
3.2	odd	2		648.2.t.a.253.17		204
4.3	odd	2		864.2.bf.a.337.27		204
8.3	odd	2		864.2.bf.a.337.8		204
8.5	even	2	inner	216.2.t.a.13.13	✓	204
24.5	odd	2		648.2.t.a.253.22		204
27.2	odd	18		648.2.t.a.397.22		204
27.25	even	9	inner	216.2.t.a.133.13	yes	204
108.79	odd	18		864.2.bf.a.241.8		204
216.29	odd	18		648.2.t.a.397.17		204
216.133	even	18	inner	216.2.t.a.133.18	yes	204
216.187	odd	18		864.2.bf.a.241.27		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.13	✓	204	8.5	even	2	inner
216.2.t.a.13.18	yes	204	1.1	even	1	trivial
216.2.t.a.133.13	yes	204	27.25	even	9	inner
216.2.t.a.133.18	yes	204	216.133	even	18	inner
648.2.t.a.253.17		204	3.2	odd	2
648.2.t.a.253.22		204	24.5	odd	2
648.2.t.a.397.17		204	216.29	odd	18
648.2.t.a.397.22		204	27.2	odd	18
864.2.bf.a.241.8		204	108.79	odd	18
864.2.bf.a.241.27		204	216.187	odd	18
864.2.bf.a.337.8		204	8.3	odd	2
864.2.bf.a.337.27		204	4.3	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0971026 - 1.41088i) q^{2} +(-1.32680 + 1.11338i) q^{3} +(-1.98114 - 0.273999i) q^{4} +(-0.561427 + 0.669083i) q^{5} +(1.44200 + 1.98006i) q^{6} +(3.98166 + 1.44920i) q^{7} +(-0.578953 + 2.76854i) q^{8} +(0.520786 - 2.95445i) q^{9} +O(q^{10})\)	\(q+(0.0971026 - 1.41088i) q^{2} +(-1.32680 + 1.11338i) q^{3} +(-1.98114 - 0.273999i) q^{4} +(-0.561427 + 0.669083i) q^{5} +(1.44200 + 1.98006i) q^{6} +(3.98166 + 1.44920i) q^{7} +(-0.578953 + 2.76854i) q^{8} +(0.520786 - 2.95445i) q^{9} +(0.889477 + 0.857073i) q^{10} +(2.44783 + 2.91721i) q^{11} +(2.93364 - 1.84221i) q^{12} +(0.577399 + 0.101811i) q^{13} +(2.43128 - 5.47690i) q^{14} +(-4.05053e-5 - 1.51282i) q^{15} +(3.84985 + 1.08566i) q^{16} +(-1.31879 + 2.28422i) q^{17} +(-4.11779 - 1.02165i) q^{18} +(4.73328 - 2.73276i) q^{19} +(1.29559 - 1.17172i) q^{20} +(-6.89636 + 2.51028i) q^{21} +(4.35351 - 3.17032i) q^{22} +(-1.54640 + 0.562844i) q^{23} +(-2.31427 - 4.31789i) q^{24} +(0.735770 + 4.17276i) q^{25} +(0.199710 - 0.804753i) q^{26} +(2.59844 + 4.49979i) q^{27} +(-7.49115 - 3.96205i) q^{28} +(-6.06211 + 1.06891i) q^{29} +(-2.13440 - 0.146841i) q^{30} +(-1.38232 + 0.503124i) q^{31} +(1.90557 - 5.32624i) q^{32} +(-6.49573 - 1.14519i) q^{33} +(3.09469 + 2.08246i) q^{34} +(-3.20505 + 1.85043i) q^{35} +(-1.84127 + 5.71049i) q^{36} +(-4.51882 - 2.60894i) q^{37} +(-3.39597 - 6.94343i) q^{38} +(-0.879447 + 0.507780i) q^{39} +(-1.52734 - 1.94170i) q^{40} +(1.20772 - 6.84934i) q^{41} +(2.87204 + 9.97367i) q^{42} +(4.80685 + 5.72858i) q^{43} +(-4.05019 - 6.45012i) q^{44} +(1.68439 + 2.00716i) q^{45} +(0.643943 + 2.23643i) q^{46} +(1.61813 + 0.588949i) q^{47} +(-6.31672 + 2.84587i) q^{48} +(8.39109 + 7.04096i) q^{49} +(5.95869 - 0.632894i) q^{50} +(-0.793421 - 4.49901i) q^{51} +(-1.11601 - 0.359909i) q^{52} -12.3718i q^{53} +(6.60096 - 3.22913i) q^{54} -3.32613 q^{55} +(-6.31737 + 10.1844i) q^{56} +(-3.23752 + 8.89575i) q^{57} +(0.919458 + 8.65668i) q^{58} +(1.82254 - 2.17202i) q^{59} +(-0.414431 + 2.99712i) q^{60} +(2.99099 - 8.21769i) q^{61} +(0.575619 + 1.99914i) q^{62} +(6.35520 - 11.0089i) q^{63} +(-7.32963 - 3.20571i) q^{64} +(-0.392288 + 0.329168i) q^{65} +(-2.24648 + 9.05347i) q^{66} +(-10.2425 - 1.80603i) q^{67} +(3.23859 - 4.16401i) q^{68} +(1.42510 - 2.46851i) q^{69} +(2.29952 + 4.70161i) q^{70} +(-8.21222 + 14.2240i) q^{71} +(7.87801 + 3.15231i) q^{72} +(4.34334 + 7.52289i) q^{73} +(-4.11969 + 6.12217i) q^{74} +(-5.62207 - 4.71722i) q^{75} +(-10.1261 + 4.11707i) q^{76} +(5.51879 + 15.1627i) q^{77} +(0.631018 + 1.29010i) q^{78} +(-2.60048 - 14.7480i) q^{79} +(-2.88781 + 1.96635i) q^{80} +(-8.45756 - 3.07728i) q^{81} +(-9.54630 - 2.36904i) q^{82} +(14.0767 - 2.48210i) q^{83} +(14.3505 - 3.08362i) q^{84} +(-0.787924 - 2.16480i) q^{85} +(8.54907 - 6.22560i) q^{86} +(6.85309 - 8.16764i) q^{87} +(-9.49360 + 5.08799i) q^{88} +(-4.44056 - 7.69127i) q^{89} +(2.99541 - 2.18156i) q^{90} +(2.15146 + 1.24215i) q^{91} +(3.21786 - 0.691361i) q^{92} +(1.27390 - 2.20659i) q^{93} +(0.988059 - 2.22579i) q^{94} +(-0.828949 + 4.70120i) q^{95} +(3.40181 + 9.18846i) q^{96} +(9.68946 - 8.13042i) q^{97} +(10.7487 - 11.1551i) q^{98} +(9.89356 - 5.71275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

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