LMFDB - Embedded newform 162.2.g.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	162.31
Dual form			162.2.g.b.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.396080 + 0.918216i) q^{2} +(-1.62304 + 0.604777i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.102641 + 1.76229i) q^{5} +(-1.19817 - 1.25076i) q^{6} +(-1.24262 + 0.294506i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.26849 - 1.96315i) q^{9} +O(q^{10})$	\(q+(0.396080 + 0.918216i) q^{2} +(-1.62304 + 0.604777i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.102641 + 1.76229i) q^{5} +(-1.19817 - 1.25076i) q^{6} +(-1.24262 + 0.294506i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.26849 - 1.96315i) q^{9} +(-1.65881 + 0.603759i) q^{10} +(-4.77831 + 3.14274i) q^{11} +(0.673895 - 1.59558i) q^{12} +(-1.80009 + 0.210400i) q^{13} +(-0.762596 - 1.02434i) q^{14} +(-0.899200 - 2.92233i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(4.64536 + 3.89792i) q^{17} +(2.70110 + 1.30540i) q^{18} +(1.44222 - 1.21016i) q^{19} +(-1.21140 - 1.28401i) q^{20} +(1.83870 - 1.22950i) q^{21} +(-4.77831 - 3.14274i) q^{22} +(8.51413 + 2.01789i) q^{23} +(1.73200 - 0.0131941i) q^{24} +(1.87108 + 0.218698i) q^{25} +(-0.906172 - 1.56954i) q^{26} +(-2.49457 + 4.55819i) q^{27} +(0.638520 - 1.10595i) q^{28} +(-0.789224 + 1.06011i) q^{29} +(2.32717 - 1.98313i) q^{30} +(-0.973767 - 3.25261i) q^{31} +(0.893633 - 0.448799i) q^{32} +(5.85470 - 7.99060i) q^{33} +(-1.73920 + 5.80933i) q^{34} +(-0.391459 - 2.22008i) q^{35} +(-0.128787 + 2.99723i) q^{36} +(0.658474 - 3.73439i) q^{37} +(1.68242 + 0.844945i) q^{38} +(2.79437 - 1.43014i) q^{39} +(0.699189 - 1.62090i) q^{40} +(-0.237614 + 0.550851i) q^{41} +(1.85722 + 1.20135i) q^{42} +(0.859982 + 0.431899i) q^{43} +(0.993126 - 5.63230i) q^{44} +(3.22679 + 4.19922i) q^{45} +(1.51942 + 8.61706i) q^{46} +(-3.27215 + 10.9297i) q^{47} +(0.698125 + 1.58512i) q^{48} +(-4.79806 + 2.40968i) q^{49} +(0.540284 + 1.80467i) q^{50} +(-9.89695 - 3.51705i) q^{51} +(1.08226 - 1.45372i) q^{52} +(3.24720 - 5.62432i) q^{53} +(-5.17345 - 0.485145i) q^{54} +(-5.04796 - 8.74332i) q^{55} +(1.26841 + 0.148255i) q^{56} +(-1.60889 + 2.83636i) q^{57} +(-1.28601 - 0.304789i) q^{58} +(-3.91105 - 2.57234i) q^{59} +(2.74269 + 1.35137i) q^{60} +(6.81251 + 7.22084i) q^{61} +(2.60091 - 2.18242i) q^{62} +(-2.24070 + 3.10753i) q^{63} +(0.766044 + 0.642788i) q^{64} +(-0.186022 - 3.19387i) q^{65} +(9.65603 + 2.21097i) q^{66} +(-3.75818 - 5.04811i) q^{67} +(-6.02308 + 0.703997i) q^{68} +(-15.0391 + 1.87405i) q^{69} +(1.88346 - 1.23877i) q^{70} +(2.23180 - 0.812309i) q^{71} +(-2.80312 + 1.06889i) q^{72} +(10.7703 + 3.92007i) q^{73} +(3.68979 - 0.874496i) q^{74} +(-3.16909 + 0.776631i) q^{75} +(-0.109468 + 1.87949i) q^{76} +(5.01205 - 5.31247i) q^{77} +(2.41997 + 1.99938i) q^{78} +(-4.27156 - 9.90258i) q^{79} +1.76527 q^{80} +(1.29208 - 8.90677i) q^{81} -0.599915 q^{82} +(-2.62121 - 6.07665i) q^{83} +(-0.367488 + 2.18116i) q^{84} +(-7.34605 + 7.78636i) q^{85} +(-0.0559553 + 0.960716i) q^{86} +(0.639807 - 2.19790i) q^{87} +(5.56502 - 1.31893i) q^{88} +(-16.1151 - 5.86541i) q^{89} +(-2.57773 + 4.62612i) q^{90} +(2.17486 - 0.791584i) q^{91} +(-7.31051 + 4.80820i) q^{92} +(3.54756 + 4.69018i) q^{93} +(-11.3319 + 1.32451i) q^{94} +(1.98462 + 2.66581i) q^{95} +(-1.17897 + 1.26887i) q^{96} +(0.665093 + 11.4192i) q^{97} +(-4.11302 - 3.45123i) q^{98} +(-4.66986 + 16.5098i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	0.396080	+	0.918216i	0.280071	+	0.649277i
$2$	0.396080	+	0.918216i	0.280071	+	0.649277i
$3$	−1.62304	+	0.604777i	−0.937060	+	0.349168i
$3$	−1.62304	+	0.604777i	−0.937060	+	0.349168i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	−0.102641	+	1.76229i	−0.0459026	+	0.788118i	0.894293	+	0.447482i	$0.147679\pi$
$5$	−0.102641	+	1.76229i	−0.0459026	+	0.788118i	−0.940195	+	0.340636i	$0.889358\pi$
$6$	−1.19817	−	1.25076i	−0.489150	−	0.510620i
$7$	−1.24262	+	0.294506i	−0.469665	+	0.111313i	−0.458632	−	0.888626i	$-0.651660\pi$
$7$	−1.24262	+	0.294506i	−0.469665	+	0.111313i	−0.0110335	+	0.999939i	$0.503512\pi$
$8$	−0.939693	−	0.342020i	−0.332232	−	0.120922i
$9$	2.26849	−	1.96315i	0.756163	−	0.654383i
$10$	−1.65881	+	0.603759i	−0.524563	+	0.190925i
$11$	−4.77831	+	3.14274i	−1.44071	+	0.947573i	−0.441993	+	0.897018i	$0.645728\pi$
$11$	−4.77831	+	3.14274i	−1.44071	+	0.947573i	−0.998721	+	0.0505543i	$0.983901\pi$
$12$	0.673895	−	1.59558i	0.194537	−	0.460603i
$13$	−1.80009	+	0.210400i	−0.499255	+	0.0583546i	−0.361994	−	0.932180i	$-0.617904\pi$
$13$	−1.80009	+	0.210400i	−0.499255	+	0.0583546i	−0.137261	+	0.990535i	$0.543830\pi$
$14$	−0.762596	−	1.02434i	−0.203812	−	0.273767i
$15$	−0.899200	−	2.92233i	−0.232172	−	0.754542i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	4.64536	+	3.89792i	1.12666	+	0.945384i	0.998922	−	0.0464234i	$-0.0147823\pi$
$17$	4.64536	+	3.89792i	1.12666	+	0.945384i	0.127743	+	0.991807i	$0.459227\pi$
$18$	2.70110	+	1.30540i	0.636655	+	0.307685i
$19$	1.44222	−	1.21016i	0.330867	−	0.277630i	−0.462186	−	0.886783i	$-0.652935\pi$
$19$	1.44222	−	1.21016i	0.330867	−	0.277630i	0.793053	+	0.609153i	$0.208490\pi$
$20$	−1.21140	−	1.28401i	−0.270878	−	0.287114i
$21$	1.83870	−	1.22950i	0.401238	−	0.268299i
$22$	−4.77831	−	3.14274i	−1.01874	−	0.670035i
$23$	8.51413	+	2.01789i	1.77532	+	0.420758i	0.982128	−	0.188214i	$-0.0602698\pi$
$23$	8.51413	+	2.01789i	1.77532	+	0.420758i	0.793191	+	0.608972i	$0.208418\pi$
$24$	1.73200	−	0.0131941i	0.353543	−	0.00269322i
$25$	1.87108	+	0.218698i	0.374215	+	0.0437395i
$26$	−0.906172	−	1.56954i	−0.177715	−	0.307811i
$27$	−2.49457	+	4.55819i	−0.480080	+	0.877225i
$28$	0.638520	−	1.10595i	0.120669	−	0.209005i
$29$	−0.789224	+	1.06011i	−0.146555	+	0.196858i	−0.869339	−	0.494217i	$-0.835455\pi$
$29$	−0.789224	+	1.06011i	−0.146555	+	0.196858i	0.722784	+	0.691074i	$0.242862\pi$
$30$	2.32717	−	1.98313i	0.424882	−	0.362069i
$31$	−0.973767	−	3.25261i	−0.174894	−	0.584185i	−0.999821	−	0.0189460i	$-0.993969\pi$
$31$	−0.973767	−	3.25261i	−0.174894	−	0.584185i	0.824927	−	0.565239i	$-0.191216\pi$
$32$	0.893633	−	0.448799i	0.157973	−	0.0793372i
$33$	5.85470	−	7.99060i	1.01917	−	1.39098i
$34$	−1.73920	+	5.80933i	−0.298270	+	0.996292i
$35$	−0.391459	−	2.22008i	−0.0661687	−	0.375261i
$36$	−0.128787	+	2.99723i	−0.0214646	+	0.499539i
$37$	0.658474	−	3.73439i	0.108253	−	0.613931i	−0.881619	−	0.471962i	$-0.843546\pi$
$37$	0.658474	−	3.73439i	0.108253	−	0.613931i	0.989871	−	0.141968i	$-0.0453431\pi$
$38$	1.68242	+	0.844945i	0.272925	+	0.137068i
$39$	2.79437	−	1.43014i	0.447457	−	0.229006i
$40$	0.699189	−	1.62090i	0.110551	−	0.256287i
$41$	−0.237614	+	0.550851i	−0.0371091	+	0.0860285i	−0.935763	−	0.352631i	$-0.885287\pi$
$41$	−0.237614	+	0.550851i	−0.0371091	+	0.0860285i	0.898654	+	0.438659i	$0.144546\pi$
$42$	1.85722	+	1.20135i	0.286575	+	0.185372i
$43$	0.859982	+	0.431899i	0.131146	+	0.0658640i	0.513162	−	0.858292i	$-0.328474\pi$
$43$	0.859982	+	0.431899i	0.131146	+	0.0658640i	−0.382016	+	0.924156i	$0.624770\pi$
$44$	0.993126	−	5.63230i	0.149719	−	0.849101i
$45$	3.22679	+	4.19922i	0.481022	+	0.625983i
$46$	1.51942	+	8.61706i	0.224026	+	1.27052i
$47$	−3.27215	+	10.9297i	−0.477292	+	1.59427i	0.292694	+	0.956206i	$0.405448\pi$
$47$	−3.27215	+	10.9297i	−0.477292	+	1.59427i	−0.769986	+	0.638061i	$0.779737\pi$
$48$	0.698125	+	1.58512i	0.100766	+	0.228793i
$49$	−4.79806	+	2.40968i	−0.685438	+	0.344240i
$50$	0.540284	+	1.80467i	0.0764077	+	0.255220i
$51$	−9.89695	−	3.51705i	−1.38585	−	0.492486i
$52$	1.08226	−	1.45372i	0.150082	−	0.201595i
$53$	3.24720	−	5.62432i	0.446038	−	0.772560i	−0.552086	−	0.833787i	$-0.686168\pi$
$53$	3.24720	−	5.62432i	0.446038	−	0.772560i	0.998124	+	0.0612269i	$0.0195013\pi$
$54$	−5.17345	−	0.485145i	−0.704018	−	0.0660198i
$55$	−5.04796	−	8.74332i	−0.680667	−	1.17895i
$56$	1.26841	+	0.148255i	0.169498	+	0.0198115i
$57$	−1.60889	+	2.83636i	−0.213103	+	0.375685i
$58$	−1.28601	−	0.304789i	−0.168861	−	0.0400208i
$59$	−3.91105	−	2.57234i	−0.509176	−	0.334890i	0.268788	−	0.963199i	$-0.413377\pi$
$59$	−3.91105	−	2.57234i	−0.509176	−	0.334890i	−0.777964	+	0.628309i	$0.783747\pi$
$60$	2.74269	+	1.35137i	0.354080	+	0.174461i
$61$	6.81251	+	7.22084i	0.872253	+	0.924534i	0.997715	−	0.0675643i	$-0.0215228\pi$
$61$	6.81251	+	7.22084i	0.872253	+	0.924534i	−0.125462	+	0.992098i	$0.540041\pi$
$62$	2.60091	−	2.18242i	0.330316	−	0.277168i
$63$	−2.24070	+	3.10753i	−0.282302	+	0.391512i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	−0.186022	−	3.19387i	−0.0230731	−	0.396151i
$66$	9.65603	+	2.21097i	1.18857	+	0.272152i
$67$	−3.75818	−	5.04811i	−0.459134	−	0.616724i	0.510915	−	0.859631i	$-0.329307\pi$
$67$	−3.75818	−	5.04811i	−0.459134	−	0.616724i	−0.970050	+	0.242907i	$0.921899\pi$
$68$	−6.02308	+	0.703997i	−0.730406	+	0.0853722i
$69$	−15.0391	+	1.87405i	−1.81050	+	0.225610i
$70$	1.88346	−	1.23877i	0.225116	−	0.148061i
$71$	2.23180	−	0.812309i	0.264866	−	0.0964034i	−0.206173	−	0.978515i	$-0.566101\pi$
$71$	2.23180	−	0.812309i	0.264866	−	0.0964034i	0.471040	+	0.882112i	$0.343879\pi$
$72$	−2.80312	+	1.06889i	−0.330351	+	0.125970i
$73$	10.7703	+	3.92007i	1.26057	+	0.458809i	0.883959	−	0.467564i	$-0.154868\pi$
$73$	10.7703	+	3.92007i	1.26057	+	0.458809i	0.376608	+	0.926373i	$0.377090\pi$
$74$	3.68979	−	0.874496i	0.428929	−	0.101658i
$75$	−3.16909	+	0.776631i	−0.365935	+	0.0896777i
$76$	−0.109468	+	1.87949i	−0.0125569	+	0.215593i
$77$	5.01205	−	5.31247i	0.571177	−	0.605412i
$78$	2.41997	+	1.99938i	0.274008	+	0.226385i
$79$	−4.27156	−	9.90258i	−0.480588	−	1.11413i	−0.970226	−	0.242202i	$-0.922130\pi$
$79$	−4.27156	−	9.90258i	−0.480588	−	1.11413i	0.489638	−	0.871926i	$-0.337129\pi$
$80$	1.76527			0.197363
$81$	1.29208	−	8.90677i	0.143564	−	0.989641i
$82$	−0.599915			−0.0662495
$83$	−2.62121	−	6.07665i	−0.287715	−	0.666999i	0.711653	−	0.702531i	$-0.247947\pi$
$83$	−2.62121	−	6.07665i	−0.287715	−	0.666999i	−0.999369	+	0.0355317i	$0.988688\pi$
$84$	−0.367488	+	2.18116i	−0.0400962	+	0.237984i
$85$	−7.34605	+	7.78636i	−0.796791	+	0.844549i
$86$	−0.0559553	+	0.960716i	−0.00603382	+	0.103597i
$87$	0.639807	−	2.19790i	0.0685945	−	0.235640i
$88$	5.56502	−	1.31893i	0.593233	−	0.140599i
$89$	−16.1151	−	5.86541i	−1.70819	−	0.621732i	−0.711479	−	0.702708i	$-0.751974\pi$
$89$	−16.1151	−	5.86541i	−1.70819	−	0.621732i	−0.996716	+	0.0809756i	$0.974196\pi$
$90$	−2.57773	+	4.62612i	−0.271717	+	0.487636i
$91$	2.17486	−	0.791584i	0.227987	−	0.0829806i
$92$	−7.31051	+	4.80820i	−0.762173	+	0.501289i
$93$	3.54756	+	4.69018i	0.367865	+	0.486350i
$94$	−11.3319	+	1.32451i	−1.16880	+	0.136613i
$95$	1.98462	+	2.66581i	0.203618	+	0.273506i
$96$	−1.17897	+	1.26887i	−0.120329	+	0.129503i
$97$	0.665093	+	11.4192i	0.0675300	+	1.15944i	0.846502	+	0.532386i	$0.178704\pi$
$97$	0.665093	+	11.4192i	0.0675300	+	1.15944i	−0.778972	+	0.627059i	$0.784258\pi$
$98$	−4.11302	−	3.45123i	−0.415478	−	0.348627i
$99$	−4.66986	+	16.5098i	−0.469339	+	1.65930i
$100$	−1.44309	+	1.21089i	−0.144309	+	0.121089i
$101$	−5.94861	−	6.30516i	−0.591909	−	0.627387i	0.360299	−	0.932837i	$-0.382675\pi$
$101$	−5.94861	−	6.30516i	−0.591909	−	0.627387i	−0.952208	+	0.305450i	$0.901193\pi$
$102$	−0.690569	−	10.4806i	−0.0683766	−	1.03773i
$103$	13.9250	+	9.15865i	1.37208	+	0.902428i	0.999671	−	0.0256425i	$-0.00816317\pi$
$103$	13.9250	+	9.15865i	1.37208	+	0.902428i	0.372404	+	0.928071i	$0.378534\pi$
$104$	1.76349	+	0.417955i	0.172925	+	0.0409839i
$105$	1.97800	+	3.36652i	0.193033	+	0.328538i
$106$	6.45050	+	0.753955i	0.626528	+	0.0732306i
$107$	2.84205	+	4.92258i	0.274752	+	0.475884i	0.970072	−	0.242816i	$-0.0780710\pi$
$107$	2.84205	+	4.92258i	0.274752	+	0.475884i	−0.695321	+	0.718700i	$0.744738\pi$
$108$	−1.60363	−	4.94251i	−0.154310	−	0.475593i
$109$	5.42377	−	9.39424i	0.519503	−	0.899805i	−0.480240	−	0.877137i	$-0.659450\pi$
$109$	5.42377	−	9.39424i	0.519503	−	0.899805i	0.999743	−	0.0226683i	$-0.00721617\pi$
$110$	6.02886	−	8.09817i	0.574830	−	0.772130i
$111$	1.18975	+	6.45928i	0.112926	+	0.613088i
$112$	0.366259	+	1.22339i	0.0346082	+	0.115600i
$113$	3.54439	−	1.78006i	0.333428	−	0.167454i	−0.274206	−	0.961671i	$-0.588415\pi$
$113$	3.54439	−	1.78006i	0.333428	−	0.167454i	0.607634	+	0.794217i	$0.292119\pi$
$114$	−3.24164	−	0.353884i	−0.303607	−	0.0331443i
$115$	−4.43000	+	14.7972i	−0.413099	+	1.37985i
$116$	−0.229499	−	1.30155i	−0.0213084	−	0.120846i
$117$	−3.67044	+	4.01114i	−0.339332	+	0.370830i
$118$	0.812875	−	4.61004i	0.0748312	−	0.424389i
$119$	−6.92036	−	3.47554i	−0.634389	−	0.318602i
$120$	−0.154523	+	3.05363i	−0.0141060	+	0.278757i
$121$	8.59852	−	19.9336i	0.781684	−	1.81215i
$122$	−3.93200	+	9.11539i	−0.355986	+	0.825269i
$123$	0.0525136	−	1.03775i	0.00473499	−	0.0935712i
$124$	3.03410	+	1.52378i	0.272470	+	0.136840i
$125$	−2.11014	+	11.9672i	−0.188737	+	1.07038i
$126$	−3.74088	−	0.826622i	−0.333264	−	0.0736413i
$127$	−1.14065	−	6.46893i	−0.101216	−	0.574024i	−0.992664	−	0.120902i	$-0.961421\pi$
$127$	−1.14065	−	6.46893i	−0.101216	−	0.574024i	0.891448	−	0.453122i	$-0.149690\pi$
$128$	−0.286803	+	0.957990i	−0.0253501	+	0.0846751i
$129$	−1.65698	−	0.180890i	−0.145889	−	0.0159265i
$130$	2.85898	−	1.43583i	0.250749	−	0.125931i
$131$	2.57359	+	8.59640i	0.224856	+	0.751071i	0.993743	+	0.111687i	$0.0356253\pi$
$131$	2.57359	+	8.59640i	0.224856	+	0.751071i	−0.768888	+	0.639384i	$0.779189\pi$
$132$	1.79441	+	9.74204i	0.156183	+	0.847936i
$133$	−1.43572	+	1.92851i	−0.124493	+	0.167223i
$134$	3.14672	−	5.45027i	0.271835	−	0.470832i
$135$	−7.77679	−	4.86400i	−0.669320	−	0.418627i
$136$	−3.03204	−	5.25165i	−0.259995	−	0.450325i
$137$	−8.21266	−	0.959922i	−0.701655	−	0.0820117i	−0.242218	−	0.970222i	$-0.577875\pi$
$137$	−8.21266	−	0.959922i	−0.701655	−	0.0820117i	−0.459437	+	0.888210i	$0.651949\pi$
$138$	−7.67747	−	13.0669i	−0.653550	−	1.11233i
$139$	19.5506	+	4.63357i	1.65826	+	0.393015i	0.949830	−	0.312768i	$-0.101256\pi$
$139$	19.5506	+	4.63357i	1.65826	+	0.393015i	0.708429	+	0.705782i	$0.249404\pi$
$140$	1.88346	+	1.23877i	0.159181	+	0.104695i
$141$	−1.29925	−	19.7183i	−0.109416	−	1.66058i
$142$	1.62985	+	1.72754i	0.136774	+	0.144972i
$143$	7.94015	−	6.66258i	0.663989	−	0.557153i
$144$	−2.09173	−	2.15050i	−0.174311	−	0.179209i
$145$	−1.78721	−	1.49965i	−0.148420	−	0.124539i
$146$	0.666427	+	11.4421i	0.0551539	+	0.946956i
$147$	6.33011	−	6.81275i	0.522099	−	0.561906i
$148$	2.26443	+	3.04165i	0.186135	+	0.250022i
$149$	2.64847	−	0.309562i	0.216971	−	0.0253603i	−0.00691281	−	0.999976i	$-0.502200\pi$
$149$	2.64847	−	0.309562i	0.216971	−	0.0253603i	0.223884	+	0.974616i	$0.428126\pi$
$150$	−1.96833	−	2.60230i	−0.160713	−	0.212477i
$151$	6.59462	−	4.33735i	0.536663	−	0.352969i	−0.252066	−	0.967710i	$-0.581110\pi$
$151$	6.59462	−	4.33735i	0.536663	−	0.352969i	0.788729	+	0.614741i	$0.210740\pi$
$152$	−1.76914	+	0.643914i	−0.143496	+	0.0522284i
$153$	18.1901	−	0.277154i	1.47059	−	0.0224066i
$154$	6.86317	+	2.49799i	0.553050	+	0.201294i
$155$	5.83197	−	1.38220i	0.468435	−	0.111021i
$156$	−0.877363	+	3.01397i	−0.0702452	+	0.241311i
$157$	−0.512798	+	8.80441i	−0.0409258	+	0.702668i	0.913980	+	0.405759i	$0.132993\pi$
$157$	−0.512798	+	8.80441i	−0.0409258	+	0.702668i	−0.954906	+	0.296909i	$0.904044\pi$
$158$	7.40083	−	7.84442i	0.588779	−	0.624069i
$159$	−1.86886	+	11.0923i	−0.148211	+	0.879678i
$160$	0.699189	+	1.62090i	0.0552757	+	0.128143i
$161$	−11.1741			−0.880642
$162$	8.69011	−	2.34138i	0.682759	−	0.183956i
$163$	16.0528			1.25736			0.628678	−	0.777666i	$-0.283596\pi$
$163$	16.0528			1.25736			0.628678	+	0.777666i	$0.283596\pi$
$164$	−0.237614	−	0.550851i	−0.0185545	−	0.0430143i
$165$	13.4808	+	11.1378i	1.04948	+	0.867079i
$166$	4.54147	−	4.81368i	0.352487	−	0.373614i
$167$	0.830732	−	14.2631i	0.0642840	−	1.10371i	−0.799768	−	0.600310i	$-0.795044\pi$
$167$	0.830732	−	14.2631i	0.0642840	−	1.10371i	0.864052	−	0.503403i	$-0.167919\pi$
$168$	−2.14833	+	0.526479i	−0.165747	+	0.0406188i
$169$	−9.45353	+	2.24053i	−0.727194	+	0.172348i
$170$	−10.0592	−	3.66124i	−0.771504	−	0.280804i
$171$	0.895919	−	5.57653i	0.0685126	−	0.426448i
$172$	−0.904307	+	0.329141i	−0.0689528	+	0.0250968i
$173$	6.70607	−	4.41065i	0.509853	−	0.335335i	−0.268378	−	0.963314i	$-0.586488\pi$
$173$	6.70607	−	4.41065i	0.509853	−	0.335335i	0.778231	+	0.627978i	$0.216117\pi$
$174$	2.27156	−	0.283064i	0.172207	−	0.0214590i
$175$	−2.38944	+	0.279286i	−0.180625	+	0.0211120i
$176$	3.41526	+	4.58749i	0.257435	+	0.345795i
$177$	7.90347	+	1.80968i	0.594061	+	0.136024i
$178$	−0.997144	−	17.1203i	−0.0747391	−	1.28322i
$179$	14.5191	+	12.1830i	1.08521	+	0.910600i	0.996343	−	0.0854438i	$-0.0272308\pi$
$179$	14.5191	+	12.1830i	1.08521	+	0.910600i	0.0888675	+	0.996043i	$0.471675\pi$
$180$	−5.26876	−	0.534601i	−0.392710	−	0.0398468i
$181$	−9.09486	+	7.63149i	−0.676016	+	0.567244i	−0.914839	−	0.403819i	$-0.867683\pi$
$181$	−9.09486	+	7.63149i	−0.676016	+	0.567244i	0.238823	+	0.971063i	$0.423238\pi$
$182$	1.58826	+	1.68346i	0.117730	+	0.124786i
$183$	−15.4240	−	7.59963i	−1.14017	−	0.561781i
$184$	−7.31051	−	4.80820i	−0.538938	−	0.354465i
$185$	6.51348	+	1.54372i	0.478881	+	0.113497i
$186$	−2.90149	+	5.11512i	−0.212747	+	0.375058i
$187$	−34.4471	−	4.02629i	−2.51902	−	0.294431i
$188$	−5.70452	−	9.88052i	−0.416045	−	0.720611i
$189$	1.75738	−	6.39876i	0.127831	−	0.465441i
$190$	−1.66172	+	2.87818i	−0.120554	+	0.208805i
$191$	15.3416	−	20.6074i	1.11008	−	1.49110i	0.259140	−	0.965840i	$-0.416561\pi$
$191$	15.3416	−	20.6074i	1.11008	−	1.49110i	0.850942	−	0.525259i	$-0.176032\pi$
$192$	−1.63206	−	0.579981i	−0.117784	−	0.0418565i
$193$	2.38171	+	7.95546i	0.171439	+	0.572647i	0.999920	+	0.0126297i	$0.00402028\pi$
$193$	2.38171	+	7.95546i	0.171439	+	0.572647i	−0.828481	+	0.560017i	$0.810795\pi$
$194$	−10.2219	+	5.13362i	−0.733888	+	0.368572i
$195$	2.23350	+	5.07126i	0.159944	+	0.363161i
$196$	1.53989	−	5.14361i	0.109992	−	0.367400i
$197$	−1.59985	−	9.07319i	−0.113984	−	0.646438i	−0.987248	−	0.159190i	$-0.949112\pi$
$197$	−1.59985	−	9.07319i	−0.113984	−	0.646438i	0.873264	−	0.487248i	$-0.161999\pi$
$198$	−17.0092	+	2.25126i	−1.20879	+	0.159990i
$199$	−0.0235730	+	0.133689i	−0.00167105	+	0.00947699i	−0.985632	−	0.168908i	$-0.945976\pi$
$199$	−0.0235730	+	0.133689i	−0.00167105	+	0.00947699i	0.983961	+	0.178385i	$0.0570871\pi$
$200$	−1.68344	−	0.845455i	−0.119037	−	0.0597827i
$201$	9.15264	+	5.92040i	0.645577	+	0.417593i
$202$	3.43338	−	7.95946i	0.241571	−	0.560026i
$203$	0.668494	−	1.54974i	0.0469191	−	0.108771i
$204$	9.34991	−	4.78524i	0.654625	−	0.335034i
$205$	−0.946368	−	0.475284i	−0.0660972	−	0.0331953i
$206$	−2.89419	+	16.4138i	−0.201648	+	1.14360i
$207$	23.2756	−	12.1370i	1.61777	−	0.843578i
$208$	0.314710	+	1.78481i	0.0218212	+	0.123754i
$209$	−3.08812	+	10.3150i	−0.213610	+	0.713507i
$210$	−2.30774	+	3.14964i	−0.159249	+	0.217346i
$211$	−22.9784	+	11.5402i	−1.58190	+	0.794460i	−0.999826	−	0.0186757i	$-0.994055\pi$
$211$	−22.9784	+	11.5402i	−1.58190	+	0.794460i	−0.582074	+	0.813136i	$0.697759\pi$
$212$	1.86262	+	6.22158i	0.127925	+	0.427300i
$213$	−3.13103	+	2.66815i	−0.214534	+	0.182819i
$214$	−3.39431	+	4.55936i	−0.232031	+	0.311671i
$215$	−0.849399	+	1.47120i	−0.0579286	+	0.100335i
$216$	3.90312	−	3.43011i	0.265574	−	0.233389i
$217$	2.16793	+	3.75497i	0.147169	+	0.254904i
$218$	10.7742	+	1.25932i	0.729720	+	0.0852921i
$219$	−19.8513	+	0.151224i	−1.34143	+	0.0102187i
$220$	9.82378	+	2.32828i	0.662319	+	0.156973i
$221$	−9.18219	−	6.03922i	−0.617661	−	0.406242i
$222$	−5.45978	+	3.65084i	−0.366437	+	0.245028i
$223$	−2.94049	−	3.11674i	−0.196910	−	0.208712i	0.621394	−	0.783498i	$-0.286567\pi$
$223$	−2.94049	−	3.11674i	−0.196910	−	0.208712i	−0.818304	+	0.574786i	$0.805085\pi$
$224$	−0.978270	+	0.820866i	−0.0653634	+	0.0548464i
$225$	4.67385	−	3.17709i	0.311590	−	0.211806i
$226$	3.03834	+	2.54947i	0.202107	+	0.169588i
$227$	1.33212	+	22.8716i	0.0884158	+	1.51804i	0.692673	+	0.721252i	$0.256433\pi$
$227$	1.33212	+	22.8716i	0.0884158	+	1.51804i	−0.604257	+	0.796789i	$0.706530\pi$
$228$	−0.959005	−	3.11669i	−0.0635117	−	0.206408i
$229$	1.87408	+	2.51733i	0.123843	+	0.166350i	0.859721	−	0.510765i	$-0.170638\pi$
$229$	1.87408	+	2.51733i	0.123843	+	0.166350i	−0.735878	+	0.677114i	$0.763230\pi$
$230$	−15.3417	+	1.79318i	−1.01160	+	0.118239i
$231$	−4.92188	+	11.6535i	−0.323836	+	0.766744i
$232$	1.10421	−	0.726248i	0.0724947	−	0.0476805i
$233$	−16.7102	+	6.08203i	−1.09472	+	0.398447i	−0.825369	−	0.564594i	$-0.809033\pi$
$233$	−16.7102	+	6.08203i	−1.09472	+	0.398447i	−0.269355	+	0.963041i	$0.586811\pi$
$234$	−5.13688	−	1.78152i	−0.335808	−	0.116462i
$235$	−18.9255	−	6.88831i	−1.23456	−	0.449344i
$236$	4.55498	−	1.07955i	0.296504	−	0.0702727i
$237$	12.9217	+	13.4889i	0.839358	+	0.876198i
$238$	0.450278	−	7.73098i	0.0291872	−	0.501125i
$239$	−2.02296	+	2.14421i	−0.130854	+	0.138697i	−0.789487	−	0.613767i	$-0.789653\pi$
$239$	−2.02296	+	2.14421i	−0.130854	+	0.138697i	0.658633	+	0.752464i	$0.271135\pi$
$240$	−2.86510	+	1.06760i	−0.184941	+	0.0689131i
$241$	−3.76131	−	8.71971i	−0.242288	−	0.561686i	0.753069	−	0.657941i	$-0.228573\pi$
$241$	−3.76131	−	8.71971i	−0.242288	−	0.561686i	−0.995357	+	0.0962558i	$0.969313\pi$
$242$	21.7091			1.39551
$243$	3.28952	+	15.2374i	0.211023	+	0.977481i
$244$	−9.92728			−0.635529
$245$	−3.75406	−	8.70289i	−0.239838	−	0.556007i
$246$	0.973683	−	0.362815i	0.0620797	−	0.0231322i
$247$	−2.34150	+	2.48185i	−0.148986	+	0.157916i
$248$	−0.197416	+	3.38950i	−0.0125359	+	0.215233i
$249$	7.92934	+	8.27737i	0.502502	+	0.524557i
$250$	−11.8243	+	2.80240i	−0.747831	+	0.177239i
$251$	6.12939	+	2.23092i	0.386884	+	0.140814i	0.528137	−	0.849159i	$-0.322891\pi$
$251$	6.12939	+	2.23092i	0.386884	+	0.140814i	−0.141253	+	0.989974i	$0.545113\pi$
$252$	−0.722669	−	3.76234i	−0.0455239	−	0.237005i
$253$	−47.0249	+	17.1156i	−2.95643	+	1.07605i
$254$	5.48809	−	3.60957i	0.344353	−	0.226485i
$255$	7.21389	−	17.0803i	0.451751	−	1.06961i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	0.280340	+	0.376561i	0.0174871	+	0.0234892i	0.810781	−	0.585350i	$-0.199043\pi$
$257$	0.280340	+	0.376561i	0.0174871	+	0.0234892i	−0.793294	+	0.608839i	$0.791635\pi$
$258$	−0.490202	−	1.59312i	−0.0305186	−	0.0991831i
$259$	0.281569	+	4.83435i	0.0174958	+	0.300392i
$260$	2.45079	+	2.05646i	0.151992	+	0.127536i
$261$	0.290813	+	3.95422i	0.0180009	+	0.244760i
$262$	−6.87400	+	5.76797i	−0.424677	+	0.356347i
$263$	14.4182	+	15.2824i	0.889066	+	0.942354i	0.998667	−	0.0516212i	$-0.0164388\pi$
$263$	14.4182	+	15.2824i	0.889066	+	0.942354i	−0.109601	+	0.993976i	$0.534957\pi$
$264$	−8.23457	+	5.50628i	−0.506803	+	0.338888i
$265$	9.57837	+	6.29979i	0.588394	+	0.386993i
$266$	−2.33945	−	0.554460i	−0.143441	−	0.0339961i
$267$	29.7026	−	0.226269i	1.81777	−	0.0138474i
$268$	6.25088	+	0.730623i	0.381833	+	0.0446299i
$269$	5.04831	+	8.74393i	0.307801	+	0.533127i	0.977881	−	0.209162i	$-0.0670736\pi$
$269$	5.04831	+	8.74393i	0.307801	+	0.533127i	−0.670080	+	0.742289i	$0.733740\pi$
$270$	1.38597	−	9.06731i	0.0843477	−	0.551819i
$271$	6.92063	−	11.9869i	0.420398	−	0.728151i	−0.575580	−	0.817745i	$-0.695224\pi$
$271$	6.92063	−	11.9869i	0.420398	−	0.728151i	0.995978	+	0.0895945i	$0.0285571\pi$
$272$	3.62122	−	4.86414i	0.219569	−	0.294932i
$273$	−3.05114	+	2.60008i	−0.184664	+	0.157364i
$274$	−2.37145	−	7.92120i	−0.143265	−	0.478537i
$275$	−9.62789	+	4.83531i	−0.580584	+	0.291580i
$276$	8.95733	−	12.2251i	0.539168	−	0.735865i
$277$	4.63998	−	15.4986i	0.278789	−	0.931221i	−0.697833	−	0.716260i	$-0.745852\pi$
$277$	4.63998	−	15.4986i	0.278789	−	0.931221i	0.976623	−	0.214961i	$-0.0689624\pi$
$278$	3.48897	+	19.7869i	0.209254	+	1.18674i
$279$	−8.59434	−	5.46685i	−0.514529	−	0.327292i
$280$	−0.391459	+	2.22008i	−0.0233942	+	0.132675i
$281$	−22.1299	−	11.1141i	−1.32016	−	0.663010i	−0.357549	−	0.933894i	$-0.616388\pi$
$281$	−22.1299	−	11.1141i	−1.32016	−	0.663010i	−0.962612	+	0.270885i	$0.912684\pi$
$282$	17.5910	−	9.00300i	1.04753	−	0.536121i
$283$	11.6043	−	26.9017i	0.689801	−	1.59914i	−0.106551	−	0.994307i	$-0.533981\pi$
$283$	11.6043	−	26.9017i	0.689801	−	1.59914i	0.796353	−	0.604832i	$-0.206760\pi$
$284$	−0.940703	+	2.18079i	−0.0558204	+	0.129406i
$285$	−4.83333	−	3.12645i	−0.286302	−	0.185195i
$286$	9.26262	+	4.65186i	0.547710	+	0.275070i
$287$	0.133034	−	0.754476i	0.00785278	−	0.0445353i
$288$	1.14614	−	2.77243i	0.0675367	−	0.163367i
$289$	3.43356	+	19.4727i	0.201974	+	1.14545i
$290$	0.669123	−	2.23503i	0.0392923	−	0.131245i
$291$	−7.98555	−	18.1315i	−0.468121	−	1.06289i
$292$	−10.2424	+	5.14391i	−0.599390	+	0.301025i
$293$	−2.63754	−	8.80998i	−0.154087	−	0.514685i	0.845735	−	0.533604i	$-0.179163\pi$
$293$	−2.63754	−	8.80998i	−0.154087	−	0.514685i	−0.999821	+	0.0189191i	$0.993977\pi$
$294$	8.76281	+	3.11401i	0.511057	+	0.181613i
$295$	4.93463	−	6.62836i	0.287305	−	0.385918i
$296$	−1.89600	+	3.28397i	−0.110203	+	0.190877i
$297$	−2.40541	−	29.6202i	−0.139576	−	1.71874i
$298$	1.33325	+	2.30926i	0.0772331	+	0.133772i
$299$	−15.7508	−	1.84100i	−0.910891	−	0.106468i
$300$	1.60986	−	2.83807i	0.0929452	−	0.163856i
$301$	−1.19583	−	0.283416i	−0.0689262	−	0.0163358i
$302$	6.59462	+	4.33735i	0.379478	+	0.249587i
$303$	13.4680	+	6.63591i	0.773718	+	0.381223i
$304$	−1.29197	−	1.36941i	−0.0740997	−	0.0785411i
$305$	−13.4244	+	11.2644i	−0.768681	+	0.645000i
$306$	7.45923	+	16.5927i	0.426416	+	0.948542i
$307$	−5.57659	−	4.67931i	−0.318273	−	0.267062i	0.469629	−	0.882864i	$-0.344388\pi$
$307$	−5.57659	−	4.67931i	−0.318273	−	0.267062i	−0.787901	+	0.615802i	$0.788832\pi$
$308$	0.424668	+	7.29127i	0.0241977	+	0.415459i
$309$	−28.1398	−	6.44325i	−1.60082	−	0.366544i
$310$	3.57909	+	4.80755i	0.203278	+	0.273050i
$311$	2.62115	−	0.306368i	0.148632	−	0.0173725i	−0.0414517	−	0.999141i	$-0.513198\pi$
$311$	2.62115	−	0.306368i	0.148632	−	0.0173725i	0.190083	+	0.981768i	$0.439124\pi$
$312$	−3.11498	+	0.388164i	−0.176351	+	0.0219755i
$313$	4.54399	−	2.98863i	0.256841	−	0.168927i	−0.414558	−	0.910023i	$-0.636064\pi$
$313$	4.54399	−	2.98863i	0.256841	−	0.168927i	0.671399	+	0.741096i	$0.265694\pi$
$314$	−8.28746	+	3.01639i	−0.467688	+	0.170225i
$315$	−5.24636	−	4.26772i	−0.295599	−	0.240459i
$316$	10.1342	+	3.68855i	0.570093	+	0.207497i
$317$	29.6920	−	7.03713i	1.66767	−	0.395244i	0.714967	−	0.699158i	$-0.246441\pi$
$317$	29.6920	−	7.03713i	1.66767	−	0.395244i	0.952700	+	0.303913i	$0.0982933\pi$
$318$	−10.9254	+	2.67742i	−0.612664	+	0.150142i
$319$	0.439497	−	7.54587i	0.0246071	−	0.422487i
$320$	−1.21140	+	1.28401i	−0.0677195	+	0.0717785i
$321$	−7.58982	−	6.27072i	−0.423623	−	0.349997i
$322$	−4.42583	−	10.2602i	−0.246642	−	0.571780i
$323$	11.4167			0.635244
$324$	5.59187	+	7.05202i	0.310659	+	0.391779i
$325$	−3.41412			−0.189381
$326$	6.35820	+	14.7400i	0.352148	+	0.816372i
$327$	−3.12154	+	18.5274i	−0.172622	+	1.02457i
$328$	0.411686	−	0.436362i	0.0227316	−	0.0240941i
$329$	0.847159	−	14.5452i	0.0467054	−	0.801900i
$330$	−4.88747	+	16.7897i	−0.269046	+	0.924245i
$331$	28.5318	−	6.76216i	1.56825	−	0.371682i	0.647572	−	0.762004i	$-0.275785\pi$
$331$	28.5318	−	6.76216i	1.56825	−	0.371682i	0.920678	+	0.390322i	$0.127636\pi$
$332$	6.21878	+	2.26345i	0.341300	+	0.124223i
$333$	−5.83744	−	9.76411i	−0.319889	−	0.535070i
$334$	13.4257	−	4.88654i	0.734619	−	0.267380i
$335$	9.28195	−	6.10483i	0.507127	−	0.333543i
$336$	−1.33433	−	1.76410i	−0.0727937	−	0.0962397i
$337$	−33.6001	+	3.92729i	−1.83032	+	0.213933i	−0.960277	−	0.279049i	$-0.909981\pi$
$337$	−33.6001	+	3.92729i	−1.83032	+	0.213933i	−0.870039	+	0.492983i	$0.835907\pi$
$338$	−5.80164	−	7.79295i	−0.315568	−	0.423881i
$339$	−4.67613	+	5.03266i	−0.253972	+	0.273337i
$340$	−0.622426	−	10.6866i	−0.0337558	−	0.579565i
$341$	14.8751	+	12.4817i	0.805530	+	0.675920i
$342$	5.47531	−	1.38610i	0.296071	−	0.0749519i
$343$	12.1004	−	10.1534i	0.653359	−	0.548233i
$344$	−0.660400	−	0.699984i	−0.0356064	−	0.0377406i
$345$	−1.75898	−	26.6956i	−0.0947004	−	1.43724i
$346$	6.70607	+	4.41065i	0.360520	+	0.237118i
$347$	−11.6926	−	2.77120i	−0.627692	−	0.148766i	−0.0955551	−	0.995424i	$-0.530463\pi$
$347$	−11.6926	−	2.77120i	−0.627692	−	0.148766i	−0.532137	+	0.846658i	$0.678611\pi$
$348$	1.15963	+	1.97367i	0.0621630	+	0.105800i
$349$	6.52156	+	0.762261i	0.349091	+	0.0408029i	0.288832	−	0.957380i	$-0.406733\pi$
$349$	6.52156	+	0.762261i	0.349091	+	0.0408029i	0.0602593	+	0.998183i	$0.480807\pi$
$350$	−1.20285	−	2.08340i	−0.0642952	−	0.111363i
$351$	3.53140	−	8.73002i	0.188492	−	0.465974i
$352$	−2.85959	+	4.95296i	−0.152417	+	0.263994i
$353$	4.39144	−	5.89873i	0.233733	−	0.313958i	−0.669746	−	0.742590i	$-0.733597\pi$
$353$	4.39144	−	5.89873i	0.233733	−	0.313958i	0.903479	+	0.428632i	$0.141004\pi$
$354$	1.46872	+	7.97387i	0.0780619	+	0.423806i
$355$	1.20245	+	4.01645i	0.0638192	+	0.213171i
$356$	15.3252	−	7.69660i	0.812233	−	0.407919i
$357$	13.3339	+	1.45564i	0.705706	+	0.0770406i
$358$	−5.43589	+	18.1571i	−0.287296	+	0.959634i
$359$	−2.01556	−	11.4308i	−0.106377	−	0.603296i	−0.990661	−	0.136346i	$-0.956464\pi$
$359$	−2.01556	−	11.4308i	−0.106377	−	0.603296i	0.884284	−	0.466950i	$-0.154647\pi$
$360$	−1.59597	−	5.04961i	−0.0841151	−	0.266138i
$361$	−2.68382	+	15.2207i	−0.141254	+	0.801090i
$362$	−10.6097	−	5.32837i	−0.557631	−	0.280053i
$363$	−1.90031	+	37.5532i	−0.0997402	+	1.97103i
$364$	−0.916702	+	2.12515i	−0.0480482	+	0.111388i
$365$	−8.01375	+	18.5780i	−0.419459	+	0.972415i
$366$	0.868986	−	17.1726i	0.0454226	−	0.897625i
$367$	−14.5052	−	7.28479i	−0.757166	−	0.380263i	0.0279521	−	0.999609i	$-0.491101\pi$
$367$	−14.5052	−	7.28479i	−0.757166	−	0.380263i	−0.785118	+	0.619346i	$0.787398\pi$
$368$	1.51942	−	8.61706i	0.0792052	−	0.449195i
$369$	0.542379	+	1.71607i	0.0282351	+	0.0893351i
$370$	1.16239	+	6.59222i	0.0604296	+	0.342713i
$371$	−2.37864	+	7.94520i	−0.123493	+	0.412494i
$372$	−5.84600	−	0.638198i	−0.303101	−	0.0330890i
$373$	21.0756	−	10.5846i	1.09125	−	0.548047i	0.190194	−	0.981747i	$-0.439088\pi$
$373$	21.0756	−	10.5846i	1.09125	−	0.548047i	0.901058	+	0.433699i	$0.142792\pi$
$374$	−9.94680	−	33.2246i	−0.514337	−	1.71800i
$375$	−3.81266	−	20.6993i	−0.196885	−	1.06891i
$376$	6.81301	−	9.15146i	0.351354	−	0.471950i
$377$	1.19763	−	2.07435i	0.0616809	−	0.106834i
$378$	6.57150	−	0.920763i	0.338002	−	0.0473589i
$379$	6.29421	+	10.9019i	0.323312	+	0.559993i	0.981169	−	0.193150i	$-0.0618703\pi$
$379$	6.29421	+	10.9019i	0.323312	+	0.559993i	−0.657857	+	0.753143i	$0.728537\pi$
$380$	−3.30097	−	0.385828i	−0.169336	−	0.0197926i
$381$	5.76357	+	9.80946i	0.295277	+	0.502554i
$382$	24.9986	+	5.92477i	1.27904	+	0.303137i
$383$	−26.0098	−	17.1069i	−1.32904	−	0.874122i	−0.331445	−	0.943474i	$-0.607536\pi$
$383$	−26.0098	−	17.1069i	−1.32904	−	0.874122i	−0.997592	+	0.0693529i	$0.977907\pi$
$384$	−0.113879	−	1.72830i	−0.00581134	−	0.0881971i
$385$	8.84764	+	9.37795i	0.450917	+	0.477945i
$386$	−6.36149	+	5.33792i	−0.323791	+	0.271693i
$387$	2.79874	−	0.708516i	0.142268	−	0.0360159i
$388$	−8.76245	−	7.35257i	−0.444846	−	0.373270i
$389$	−1.71787	−	29.4946i	−0.0870993	−	1.49544i	−0.705015	−	0.709192i	$-0.749060\pi$
$389$	−1.71787	−	29.4946i	−0.0870993	−	1.49544i	0.617916	−	0.786244i	$-0.287977\pi$
$390$	−3.77187	+	4.05946i	−0.190996	+	0.205559i
$391$	31.6856	+	42.5612i	1.60241	+	2.15241i
$392$	5.33286	−	0.623322i	0.269350	−	0.0314825i
$393$	−9.37594	−	12.3958i	−0.472954	−	0.625286i
$394$	7.69748	−	5.06271i	0.387794	−	0.255056i
$395$	17.8896	−	6.51129i	0.900124	−	0.327618i
$396$	−8.80415	−	14.7265i	−0.442425	−	0.740032i
$397$	11.5130	+	4.19038i	0.577820	+	0.210309i	0.614364	−	0.789023i	$-0.289413\pi$
$397$	11.5130	+	4.19038i	0.577820	+	0.210309i	−0.0365442	+	0.999332i	$0.511635\pi$
$398$	−0.132093	+	0.0313065i	−0.00662120	+	0.00156925i
$399$	1.16391	−	3.99833i	0.0582684	−	0.200167i
$400$	0.109534	−	1.88063i	0.00547670	−	0.0940314i
$401$	−19.0425	+	20.1839i	−0.950937	+	1.00793i	0.0490209	+	0.998798i	$0.484390\pi$
$401$	−19.0425	+	20.1839i	−0.950937	+	1.00793i	−0.999958	+	0.00913701i	$0.997092\pi$
$402$	−1.81103	+	10.7490i	−0.0903260	+	0.536114i
$403$	2.43722	+	5.65011i	0.121406	+	0.281452i
$404$	8.66840			0.431269
$405$	15.5636	+	3.19122i	0.773364	+	0.158573i
$406$	1.68778			0.0837630
$407$	8.58985	+	19.9135i	0.425783	+	0.987076i
$408$	8.09719	+	6.68990i	0.400871	+	0.331200i
$409$	0.114220	−	0.121066i	0.00564782	−	0.00598634i	−0.724544	−	0.689229i	$-0.757949\pi$
$409$	0.114220	−	0.121066i	0.00564782	−	0.00598634i	0.730191	+	0.683243i	$0.239431\pi$
$410$	0.0615761	−	1.05722i	0.00304103	−	0.0522124i
$411$	13.9100	−	3.40884i	0.686128	−	0.168146i
$412$	−16.2177	+	3.84367i	−0.798989	+	0.189364i
$413$	5.61751	+	2.04461i	0.276420	+	0.100609i
$414$	20.3634	+	16.5648i	1.00080	+	0.814118i
$415$	10.9778	−	3.99561i	0.538881	−	0.196137i
$416$	−1.51419	+	0.995900i	−0.0742394	+	0.0488280i
$417$	−34.5336	+	4.30330i	−1.69112	+	0.210733i
$418$	−10.6946	+	1.25002i	−0.523089	+	0.0611404i
$419$	−3.93942	−	5.29156i	−0.192453	−	0.258510i	0.695414	−	0.718609i	$-0.255221\pi$
$419$	−3.93942	−	5.29156i	−0.192453	−	0.258510i	−0.887867	+	0.460100i	$0.847814\pi$
$420$	−3.80610	−	0.871495i	−0.185719	−	0.0425246i
$421$	−1.56373	−	26.8482i	−0.0762116	−	1.30850i	−0.792144	−	0.610334i	$-0.791035\pi$
$421$	−1.56373	−	26.8482i	−0.0762116	−	1.30850i	0.715933	−	0.698169i	$-0.246002\pi$
$422$	−19.6977	−	16.5283i	−0.958868	−	0.804586i
$423$	14.0339	+	31.2177i	0.682351	+	1.51786i
$424$	−4.97501	+	4.17453i	−0.241608	+	0.202733i
$425$	7.83936	+	8.30923i	0.380265	+	0.403057i
$426$	−3.69007	−	1.81816i	−0.178785	−	0.0880901i
$427$	−10.5919	−	6.96642i	−0.512579	−	0.337129i
$428$	−5.53089	−	1.31085i	−0.267346	−	0.0633621i
$429$	−8.85777	+	15.6156i	−0.427657	+	0.753930i
$430$	−1.68731	−	0.197218i	−0.0813694	−	0.00951072i
$431$	9.37590	+	16.2395i	0.451621	+	0.782231i	0.998487	−	0.0549892i	$-0.0175124\pi$
$431$	9.37590	+	16.2395i	0.451621	+	0.782231i	−0.546866	+	0.837220i	$0.684179\pi$
$432$	4.69553	+	2.22531i	0.225914	+	0.107065i
$433$	−12.3539	+	21.3977i	−0.593692	+	1.02831i	0.400038	+	0.916499i	$0.368997\pi$
$433$	−12.3539	+	21.3977i	−0.593692	+	1.02831i	−0.993730	+	0.111807i	$0.964336\pi$
$434$	−2.58920	+	3.47790i	−0.124285	+	0.166944i
$435$	3.80766	+	1.35312i	0.182563	+	0.0648770i
$436$	3.11111	+	10.3918i	0.148995	+	0.497678i
$437$	14.7212	−	7.39326i	0.704210	−	0.353668i
$438$	−8.00157	−	18.1679i	−0.382330	−	0.868097i
$439$	3.17608	−	10.6088i	0.151586	−	0.506333i	−0.848139	−	0.529773i	$-0.822277\pi$
$439$	3.17608	−	10.6088i	0.151586	−	0.506333i	0.999725	+	0.0234408i	$0.00746214\pi$
$440$	1.75314	+	9.94254i	0.0835776	+	0.473992i
$441$	−6.15379	+	14.8856i	−0.293038	+	0.708840i
$442$	1.90843	−	10.8232i	0.0907748	−	0.514809i
$443$	10.6152	+	5.33117i	0.504345	+	0.253291i	0.682732	−	0.730669i	$-0.260792\pi$
$443$	10.6152	+	5.33117i	0.504345	+	0.253291i	−0.178387	+	0.983960i	$0.557088\pi$
$444$	−5.51477	−	3.56724i	−0.261719	−	0.169294i
$445$	11.9906	−	27.7973i	0.568409	−	1.31772i
$446$	1.69717	−	3.93448i	0.0803633	−	0.186303i
$447$	−4.11134	+	2.10416i	−0.194460	+	0.0995236i
$448$	−1.14120	−	0.573135i	−0.0539169	−	0.0270781i
$449$	−0.524278	+	2.97333i	−0.0247422	+	0.140320i	−0.994677	−	0.103047i	$-0.967141\pi$
$449$	−0.524278	+	2.97333i	−0.0247422	+	0.140320i	0.969934	+	0.243367i	$0.0782519\pi$
$450$	4.76848	+	3.03322i	0.224788	+	0.142988i
$451$	−0.595791	−	3.37890i	−0.0280547	−	0.159106i
$452$	−1.13754	+	3.79964i	−0.0535053	+	0.178720i
$453$	−8.08018	+	11.0280i	−0.379640	+	0.518139i
$454$	−20.4734	+	10.2821i	−0.960866	+	0.482565i
$455$	1.17177	+	3.91397i	0.0549333	+	0.183490i
$456$	2.48195	−	2.11503i	0.116228	−	0.0990454i
$457$	0.109969	−	0.147714i	0.00514413	−	0.00690977i	−0.799544	−	0.600608i	$-0.794925\pi$
$457$	0.109969	−	0.147714i	0.00514413	−	0.00690977i	0.804688	+	0.593698i	$0.202333\pi$
$458$	−1.56916	+	2.71787i	−0.0733222	+	0.126998i
$459$	−29.3556	+	11.4508i	−1.37020	+	0.534478i
$460$	−7.72306	−	13.3767i	−0.360089	−	0.623693i
$461$	−14.7018	−	1.71839i	−0.684731	−	0.0800336i	−0.233388	−	0.972384i	$-0.574981\pi$
$461$	−14.7018	−	1.71839i	−0.684731	−	0.0800336i	−0.451344	+	0.892350i	$0.649055\pi$
$462$	−12.6499	+	0.0963645i	−0.588526	+	0.00448328i
$463$	11.8315	+	2.80412i	0.549856	+	0.130318i	0.496147	−	0.868238i	$-0.334748\pi$
$463$	11.8315	+	2.80412i	0.549856	+	0.130318i	0.0537088	+	0.998557i	$0.482896\pi$
$464$	1.10421	+	0.726248i	0.0512615	+	0.0337152i
$465$	−8.62957	+	5.77041i	−0.400187	+	0.267596i
$466$	−12.2032	−	12.9346i	−0.565303	−	0.599186i
$467$	−24.6438	+	20.6786i	−1.14038	+	0.956893i	−0.999451	−	0.0331269i	$-0.989453\pi$
$467$	−24.6438	+	20.6786i	−1.14038	+	0.956893i	−0.140929	+	0.990020i	$0.545009\pi$
$468$	−0.398790	−	5.42239i	−0.0184341	−	0.250650i
$469$	6.15667	+	5.16606i	0.284289	+	0.238547i
$470$	−1.17104	−	20.1060i	−0.0540161	−	0.927420i
$471$	−4.49242	−	14.6000i	−0.207000	−	0.672732i
$472$	2.79539	+	3.75487i	0.128668	+	0.172832i
$473$	−5.46661	+	0.638955i	−0.251355	+	0.0293792i
$474$	−7.26768	+	17.2076i	−0.333816	+	0.790373i
$475$	2.96316	−	1.94890i	0.135959	−	0.0894216i
$476$	7.27705	−	2.64863i	0.333543	−	0.121400i
$477$	−3.67515	−	19.1335i	−0.168273	−	0.876061i
$478$	−2.77010	−	1.00823i	−0.126701	−	0.0461156i
$479$	10.1219	−	2.39894i	0.462483	−	0.109610i	0.00723231	−	0.999974i	$-0.497698\pi$
$479$	10.1219	−	2.39894i	0.462483	−	0.109610i	0.455250	+	0.890363i	$0.349550\pi$
$480$	−2.11509	−	2.20793i	−0.0965403	−	0.100778i
$481$	−0.399595	+	6.86079i	−0.0182200	+	0.312825i
$482$	6.51679	−	6.90740i	0.296832	−	0.314623i
$483$	18.1359	−	6.75784i	0.825214	−	0.307492i
$484$	8.59852	+	19.9336i	0.390842	+	0.906074i
$485$	−20.1922			−0.916879
$486$	−12.6883	+	9.05573i	−0.575555	+	0.410776i
$487$	4.60462			0.208655			0.104328	−	0.994543i	$-0.466731\pi$
$487$	4.60462			0.208655			0.104328	+	0.994543i	$0.466731\pi$
$488$	−3.93200	−	9.11539i	−0.177993	−	0.412634i
$489$	−26.0543	+	9.70840i	−1.17822	+	0.439029i
$490$	6.50423	−	6.89408i	0.293831	−	0.311443i
$491$	0.935137	−	16.0557i	0.0422022	−	0.724583i	−0.909148	−	0.416472i	$-0.863266\pi$
$491$	0.935137	−	16.0557i	0.0422022	−	0.724583i	0.951351	−	0.308111i	$-0.0996967\pi$
$492$	0.718798	+	0.750348i	0.0324059	+	0.0338283i
$493$	−7.79845	+	1.84827i	−0.351225	+	0.0832418i
$494$	−3.20629	−	1.16699i	−0.144258	−	0.0525056i
$495$	−28.6157	−	9.92422i	−1.28618	−	0.446061i
$496$	−3.19048	+	1.16124i	−0.143257	+	0.0521413i
$497$	−2.53405	+	1.66667i	−0.113667	+	0.0747603i
$498$	−4.45976	+	10.5593i	−0.199847	+	0.473176i
$499$	2.02618	−	0.236826i	0.0907042	−	0.0106018i	−0.0706197	−	0.997503i	$-0.522498\pi$
$499$	2.02618	−	0.236826i	0.0907042	−	0.0106018i	0.161324	+	0.986902i	$0.448424\pi$
$500$	−7.25656	−	9.74724i	−0.324523	−	0.435910i
$501$	7.27770	+	23.6520i	0.325144	+	1.05669i
$502$	0.379265	+	6.51173i	0.0169274	+	0.290633i
$503$	−27.0044	−	22.6594i	−1.20407	−	1.01033i	−0.999504	−	0.0314791i	$-0.989978\pi$
$503$	−27.0044	−	22.6594i	−1.20407	−	1.01033i	−0.204563	−	0.978853i	$-0.565577\pi$
$504$	3.16841	−	2.15376i	0.141132	−	0.0959359i
$505$	11.7221	−	9.83598i	0.521625	−	0.437696i
$506$	−34.3415	−	36.3998i	−1.52666	−	1.61817i
$507$	13.9884	−	9.35373i	0.621246	−	0.415414i
$508$	5.48809	+	3.60957i	0.243494	+	0.160149i
$509$	32.6264	+	7.73261i	1.44614	+	0.342742i	0.877394	−	0.479770i	$-0.159280\pi$
$509$	32.6264	+	7.73261i	1.44614	+	0.342742i	0.568747	+	0.822512i	$0.307428\pi$
$510$	18.5406	−	0.141239i	0.820994	−	0.00625417i
$511$	−14.5378	−	1.69923i	−0.643116	−	0.0751695i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	1.91845	+	9.59274i	0.0847017	+	0.423530i
$514$	−0.234728	+	0.406561i	−0.0103534	+	0.0179326i
$515$	−17.5694	+	23.5998i	−0.774202	+	1.03993i
$516$	1.26867	−	1.08111i	0.0558499	−	0.0475933i
$517$	−18.7140	−	62.5092i	−0.823042	−	2.74915i
$518$	−4.32745	+	2.17333i	−0.190137	+	0.0954906i
$519$	−8.21672	+	11.2143i	−0.360674	+	0.492254i
$520$	−0.917564	+	3.06488i	−0.0402379	+	0.134404i
$521$	−1.80418	−	10.2320i	−0.0790425	−	0.448273i	−0.998484	−	0.0550453i	$-0.982470\pi$
$521$	−1.80418	−	10.2320i	−0.0790425	−	0.448273i	0.919441	−	0.393227i	$-0.128641\pi$
$522$	−3.51564	+	1.83321i	−0.153875	+	0.0802376i
$523$	−4.47445	+	25.3759i	−0.195654	+	1.10961i	0.715830	+	0.698274i	$0.246048\pi$
$523$	−4.47445	+	25.3759i	−0.195654	+	1.10961i	−0.911484	+	0.411335i	$0.865063\pi$
$524$	−8.01890	−	4.02724i	−0.350307	−	0.175931i
$525$	3.70924	−	1.89837i	0.161885	−	0.0828517i
$526$	−8.32180	+	19.2921i	−0.362848	+	0.841176i
$527$	8.15490	−	18.9052i	0.355233	−	0.823523i
$528$	−8.31750	−	5.38019i	−0.361973	−	0.234143i
$529$	47.8650	+	24.0387i	2.08109	+	1.04516i
$530$	−1.99077	+	11.2902i	−0.0864736	+	0.490416i
$531$	−13.9221	+	1.84266i	−0.604166	+	0.0799647i
$532$	−0.417495	−	2.36773i	−0.0181007	−	0.102654i
$533$	0.311827	−	1.04158i	0.0135067	−	0.0451157i
$534$	11.9724	+	27.1838i	0.518095	+	1.17636i
$535$	−8.96671	+	4.50325i	−0.387665	+	0.194693i
$536$	1.80498	+	6.02904i	0.0779631	+	0.260415i
$537$	−30.9331	−	10.9926i	−1.33486	−	0.474365i
$538$	−6.02928	+	8.09873i	−0.259941	+	0.349161i
$539$	15.3536	−	26.5933i	0.661328	−	1.14545i
$540$	8.87470	−	2.31875i	0.381906	−	0.0997833i
$541$	8.11527	+	14.0561i	0.348903	+	0.604317i	0.986055	−	0.166421i	$-0.0532211\pi$
$541$	8.11527	+	14.0561i	0.348903	+	0.604317i	−0.637152	+	0.770738i	$0.719888\pi$
$542$	13.7477	+	1.60687i	0.590513	+	0.0690210i
$543$	10.1459	−	17.8866i	0.435403	−	0.767585i
$544$	5.90063	+	1.39847i	0.252987	+	0.0599591i
$545$	15.9986	+	10.5225i	0.685306	+	0.450733i
$546$	−3.59593	−	1.77177i	−0.153891	−	0.0758248i
$547$	−6.29681	−	6.67423i	−0.269232	−	0.285370i	0.578625	−	0.815593i	$-0.303589\pi$
$547$	−6.29681	−	6.67423i	−0.269232	−	0.285370i	−0.847858	+	0.530224i	$0.822108\pi$
$548$	6.33409	−	5.31493i	0.270579	−	0.227043i
$549$	29.6297	+	3.00641i	1.26457	+	0.128310i
$550$	−8.25327	−	6.92532i	−0.351921	−	0.295297i
$551$	0.144676	+	2.48400i	0.00616343	+	0.105822i
$552$	14.7731	+	3.38264i	0.628785	+	0.143975i
$553$	8.22428	+	11.0471i	0.349732	+	0.469771i
$554$	16.0689	−	1.87818i	0.682701	−	0.0797963i
$555$	−11.5052	+	1.43369i	−0.488369	+	0.0608567i
$556$	−16.7868	+	11.0408i	−0.711917	+	0.468235i
$557$	10.1478	−	3.69351i	0.429977	−	0.156499i	−0.117960	−	0.993018i	$-0.537635\pi$
$557$	10.1478	−	3.69351i	0.429977	−	0.156499i	0.547937	+	0.836519i	$0.315413\pi$
$558$	1.61571	−	10.0568i	0.0683984	−	0.425737i
$559$	−1.63892	−	0.596517i	−0.0693188	−	0.0252300i
$560$	−2.19356	+	0.519883i	−0.0926947	+	0.0219691i
$561$	58.3439	−	14.2980i	2.46328	−	0.603663i
$562$	1.43990	−	24.7221i	0.0607385	−	1.04284i
$563$	0.887457	−	0.940649i	0.0374018	−	0.0396436i	−0.708403	−	0.705809i	$-0.750584\pi$
$563$	0.887457	−	0.940649i	0.0374018	−	0.0396436i	0.745804	+	0.666165i	$0.232065\pi$
$564$	15.2342	+	12.5865i	0.641474	+	0.529986i
$565$	2.77317	+	6.42893i	0.116668	+	0.270467i
$566$	29.2978			1.23148
$567$	1.01753	+	11.4482i	0.0427324	+	0.480781i
$568$	−2.37503			−0.0996542
$569$	0.174206	+	0.403854i	0.00730307	+	0.0169304i	0.921829	−	0.387598i	$-0.126695\pi$
$569$	0.174206	+	0.403854i	0.00730307	+	0.0169304i	−0.914526	+	0.404528i	$0.867436\pi$
$570$	0.956371	−	5.67637i	0.0400580	−	0.237757i
$571$	−12.4916	+	13.2403i	−0.522758	+	0.554091i	−0.933925	−	0.357469i	$-0.883640\pi$
$571$	−12.4916	+	13.2403i	−0.522758	+	0.554091i	0.411167	+	0.911560i	$0.365121\pi$
$572$	−0.602679	+	10.3476i	−0.0251993	+	0.432655i
$573$	−12.4371	+	42.7248i	−0.519569	+	1.78485i
$574$	0.745464	−	0.176678i	0.0311151	−	0.00737441i
$575$	15.4893	+	5.63764i	0.645948	+	0.235106i
$576$	2.99965	−	0.0457042i	0.124985	−	0.00190434i
$577$	9.46838	−	3.44621i	0.394174	−	0.143467i	−0.137326	−	0.990526i	$-0.543851\pi$
$577$	9.46838	−	3.44621i	0.394174	−	0.143467i	0.531500	+	0.847058i	$0.321629\pi$
$578$	−16.5202	+	10.8655i	−0.687149	+	0.451945i
$579$	−8.67688	−	11.4716i	−0.360599	−	0.476743i
$580$	2.31726	−	0.270849i	0.0962192	−	0.0112464i
$581$	5.04677	+	6.77899i	0.209375	+	0.281240i
$582$	13.4858	−	14.5140i	0.559003	−	0.601625i
$583$	2.15966	+	37.0799i	0.0894439	+	1.53569i
$584$	−8.78002	−	7.36731i	−0.363320	−	0.304862i
$585$	−6.69203	−	6.88007i	−0.276682	−	0.284456i
$586$	7.04479	−	5.91128i	0.291018	−	0.244193i
$587$	−16.3396	−	17.3190i	−0.674408	−	0.714831i	0.296299	−	0.955095i	$-0.404247\pi$
$587$	−16.3396	−	17.3190i	−0.674408	−	0.714831i	−0.970707	+	0.240264i	$0.922766\pi$
$588$	0.611433	+	9.27955i	0.0252151	+	0.382682i
$589$	−5.34057	−	3.51255i	−0.220054	−	0.144732i
$590$	8.04078	+	1.90570i	0.331034	+	0.0784564i
$591$	8.08387	+	13.7586i	0.332526	+	0.565952i
$592$	−3.76636	−	0.440225i	−0.154797	−	0.0180931i
$593$	−6.64959	−	11.5174i	−0.273066	−	0.472964i	0.696579	−	0.717480i	$-0.254704\pi$
$593$	−6.64959	−	11.5174i	−0.273066	−	0.472964i	−0.969645	+	0.244515i	$0.921371\pi$
$594$	26.2451	−	13.9407i	1.07685	−	0.571993i
$595$	6.83520	−	11.8389i	0.280216	−	0.485348i
$596$	−1.59232	+	2.13886i	−0.0652241	+	0.0876112i
$597$	−0.0425924	−	0.231239i	−0.00174319	−	0.00946398i
$598$	−4.54813	−	15.1918i	−0.185987	−	0.621239i
$599$	−30.0827	+	15.1081i	−1.22915	+	0.617301i	−0.940389	−	0.340102i	$-0.889539\pi$
$599$	−30.0827	+	15.1081i	−1.22915	+	0.617301i	−0.288758	+	0.957402i	$0.593242\pi$
$600$	3.24359	+	0.354097i	0.132419	+	0.0144560i
$601$	7.67744	−	25.6444i	0.313169	−	1.04606i	−0.646026	−	0.763315i	$-0.723570\pi$
$601$	7.67744	−	25.6444i	0.313169	−	1.04606i	0.959196	−	0.282743i	$-0.0912444\pi$
$602$	−0.213405	−	1.21028i	−0.00869775	−	0.0493274i
$603$	−18.4356	−	4.07371i	−0.750755	−	0.165894i
$604$	−1.37063	+	7.77323i	−0.0557701	+	0.316288i
$605$	34.2462	+	17.1991i	1.39230	+	0.699242i
$606$	−0.758789	+	14.9949i	−0.0308237	+	0.609127i
$607$	−1.28662	+	2.98271i	−0.0522222	+	0.121065i	−0.942330	−	0.334686i	$-0.891370\pi$
$607$	−1.28662	+	2.98271i	−0.0522222	+	0.121065i	0.890108	+	0.455750i	$0.150629\pi$
$608$	0.745691	−	1.72871i	0.0302418	−	0.0701083i
$609$	−0.147740	+	2.91958i	−0.00598672	+	0.118307i
$610$	−15.6603	−	7.86491i	−0.634068	−	0.318441i
$611$	3.59054	−	20.3630i	0.145258	−	0.823798i
$612$	−12.2812	+	13.4212i	−0.496440	+	0.542521i
$613$	−7.05628	−	40.0181i	−0.285000	−	1.61632i	−0.705284	−	0.708925i	$-0.749181\pi$
$613$	−7.05628	−	40.0181i	−0.285000	−	1.61632i	0.420284	−	0.907393i	$-0.361931\pi$
$614$	2.08785	−	6.97389i	0.0842586	−	0.281443i
$615$	1.82343	+	0.199061i	0.0735278	+	0.00802690i
$616$	−6.52676	+	3.27786i	−0.262971	+	0.132069i
$617$	11.9220	+	39.8221i	0.479960	+	1.60318i	0.764573	+	0.644537i	$0.222950\pi$
$617$	11.9220	+	39.8221i	0.479960	+	1.60318i	−0.284613	+	0.958642i	$0.591865\pi$
$618$	−5.22930	−	28.3904i	−0.210353	−	1.14203i
$619$	−2.81095	+	3.77577i	−0.112982	+	0.151761i	−0.855017	−	0.518600i	$-0.826453\pi$
$619$	−2.81095	+	3.77577i	−0.112982	+	0.151761i	0.742035	+	0.670361i	$0.233861\pi$
$620$	−2.99676	+	5.19055i	−0.120353	+	0.208457i
$621$	−30.4370	+	33.7753i	−1.22139	+	1.35536i
$622$	1.31950	+	2.28543i	0.0529069	+	0.0916375i
$623$	21.7523	+	2.54248i	0.871486	+	0.101862i
$624$	−1.59020	−	2.70648i	−0.0636589	−	0.108346i
$625$	−11.7078	−	2.77481i	−0.468314	−	0.110992i
$626$	4.54399	+	2.98863i	0.181614	+	0.119450i
$627$	−1.22618	−	18.6093i	−0.0489687	−	0.743185i
$628$	−6.05219	−	6.41495i	−0.241509	−	0.255984i
$629$	17.6152	−	14.7809i	0.702364	−	0.589354i
$630$	1.84071	−	6.50765i	0.0733358	−	0.259271i
$631$	−9.99020	−	8.38278i	−0.397704	−	0.333713i	0.421902	−	0.906642i	$-0.361363\pi$
$631$	−9.99020	−	8.38278i	−0.397704	−	0.333713i	−0.819605	+	0.572929i	$0.805807\pi$
$632$	0.627068	+	10.7663i	0.0249434	+	0.428262i
$633$	30.3155	−	32.6270i	1.20493	−	1.29681i
$634$	18.2220	+	24.4764i	0.723688	+	0.972081i
$635$	11.5172	−	1.34616i	0.457045	−	0.0534209i
$636$	−6.78576	−	8.97137i	−0.269073	−	0.355738i
$637$	8.12995	−	5.34715i	0.322120	−	0.211862i
$638$	7.10281	−	2.58521i	0.281203	−	0.102350i
$639$	3.46813	−	6.22408i	0.137197	−	0.246221i
$640$	−1.65881	−	0.603759i	−0.0655703	−	0.0238657i
$641$	20.1164	−	4.76768i	0.794551	−	0.188312i	0.186756	−	0.982406i	$-0.440203\pi$
$641$	20.1164	−	4.76768i	0.794551	−	0.188312i	0.607794	+	0.794094i	$0.292054\pi$
$642$	2.75170	−	9.45280i	0.108601	−	0.373072i
$643$	0.602517	−	10.3448i	0.0237609	−	0.407959i	−0.965366	−	0.260898i	$-0.915981\pi$
$643$	0.602517	−	10.3448i	0.0237609	−	0.407959i	0.989127	−	0.147062i	$-0.0469816\pi$
$644$	7.66813	−	8.12774i	0.302166	−	0.320278i
$645$	0.488855	−	2.90151i	0.0192486	−	0.114247i
$646$	4.52193	+	10.4830i	0.177913	+	0.412449i
$647$	−38.2038			−1.50195			−0.750973	−	0.660333i	$-0.770415\pi$
$647$	−38.2038			−1.50195			−0.750973	+	0.660333i	$0.770415\pi$
$648$	−4.26045	+	7.92771i	−0.167366	+	0.311430i
$649$	26.7724			1.05091
$650$	−1.35226	−	3.13490i	−0.0530402	−	0.122961i
$651$	−5.78955	−	4.78333i	−0.226910	−	0.187473i
$652$	−11.0161	+	11.6764i	−0.431425	+	0.457284i
$653$	−1.63240	+	28.0272i	−0.0638806	+	1.09679i	0.802256	+	0.596981i	$0.203633\pi$
$653$	−1.63240	+	28.0272i	−0.0638806	+	1.09679i	−0.866136	+	0.499808i	$0.833404\pi$
$654$	−18.2485	+	4.47206i	−0.713573	+	0.174871i
$655$	−15.4135	+	3.65306i	−0.602254	+	0.142737i
$656$	0.563735	+	0.205183i	0.0220102	+	0.00801105i
$657$	32.1280	−	12.2511i	1.25343	−	0.477960i
$658$	13.6911	−	4.98317i	0.533736	−	0.194264i
$659$	4.31823	−	2.84015i	0.168214	−	0.110636i	−0.462610	−	0.886562i	$-0.653087\pi$
$659$	4.31823	−	2.84015i	0.168214	−	0.110636i	0.630825	+	0.775925i	$0.282717\pi$
$660$	−17.3524	+	2.16232i	−0.675443	+	0.0841683i
$661$	−37.3013	+	4.35990i	−1.45085	+	0.169581i	−0.804725	−	0.593648i	$-0.797687\pi$
$661$	−37.3013	+	4.35990i	−1.45085	+	0.169581i	−0.646129	+	0.763228i	$0.723613\pi$
$662$	17.5100	+	23.5200i	0.680546	+	0.914131i
$663$	18.5554	+	4.24869i	0.720632	+	0.165005i
$664$	0.384796	+	6.60669i	0.0149330	+	0.256389i
$665$	−3.25122	−	2.72810i	−0.126077	−	0.105791i
$666$	6.65348	−	9.22740i	0.257817	−	0.357554i
$667$	−8.85874	+	7.43337i	−0.343012	+	0.287821i
$668$	9.80453	+	10.3922i	0.379349	+	0.402086i
$669$	6.65745	+	3.28023i	0.257392	+	0.126821i
$670$	9.28195	+	6.10483i	0.358593	+	0.235850i
$671$	−55.2456	−	13.0934i	−2.13273	−	0.505466i
$672$	1.09133	−	1.92393i	0.0420988	−	0.0742172i
$673$	29.2094	+	3.41408i	1.12594	+	0.131603i	0.658613	−	0.752482i	$-0.271144\pi$
$673$	29.2094	+	3.41408i	1.12594	+	0.131603i	0.467325	+	0.884085i	$0.345218\pi$
$674$	−16.9144	−	29.2967i	−0.651520	−	1.12847i
$675$	−5.66440	+	7.98318i	−0.218023	+	0.307273i
$676$	4.85770	−	8.41379i	0.186835	−	0.323607i
$677$	−18.6310	+	25.0258i	−0.716048	+	0.961819i	0.283948	+	0.958840i	$0.408356\pi$
$677$	−18.6310	+	25.0258i	−0.716048	+	0.961819i	−0.999996	+	0.00297909i	$0.999052\pi$
$678$	−6.47319	−	2.30036i	−0.248601	−	0.0883448i
$679$	−4.18948	−	13.9938i	−0.160777	−	0.537034i
$680$	9.56612	−	4.80429i	0.366844	−	0.184236i
$681$	−15.9943	−	36.3158i	−0.612903	−	1.39162i
$682$	−5.56915	+	18.6023i	−0.213254	+	0.712317i
$683$	−3.96194	−	22.4693i	−0.151599	−	0.859763i	−0.961829	−	0.273651i	$-0.911769\pi$
$683$	−3.96194	−	22.4693i	−0.151599	−	0.859763i	0.810230	−	0.586112i	$-0.199342\pi$
$684$	3.44140	+	4.47851i	0.131585	+	0.171240i
$685$	2.53462	−	14.3745i	0.0968427	−	0.549222i
$686$	14.1158	+	7.08920i	0.538942	+	0.270667i
$687$	−4.56412	−	2.95231i	−0.174132	−	0.112638i
$688$	0.381165	−	0.883640i	0.0145318	−	0.0336884i
$689$	−4.66190	+	10.8075i	−0.177604	+	0.411733i
$690$	23.8156	−	12.1887i	0.906644	−	0.464016i
$691$	−8.44467	−	4.24108i	−0.321251	−	0.161338i	0.280864	−	0.959747i	$-0.409379\pi$
$691$	−8.44467	−	4.24108i	−0.321251	−	0.161338i	−0.602115	+	0.798409i	$0.705675\pi$
$692$	−1.39379	+	7.90459i	−0.0529840	+	0.300487i
$693$	0.940615	−	21.8907i	0.0357310	−	0.831558i
$694$	−2.08665	−	11.8340i	−0.0792080	−	0.449211i
$695$	−10.1724	+	33.9781i	−0.385860	+	1.28886i
$696$	−1.35295	+	1.84653i	−0.0512834	+	0.0699924i
$697$	−3.25097	+	1.63270i	−0.123139	+	0.0618430i
$698$	1.88314	+	6.29012i	0.0712778	+	0.238084i
$699$	23.4430	−	19.9773i	0.886697	−	0.755612i
$700$	1.43659	−	1.92967i	0.0542980	−	0.0729348i
$701$	−6.49526	+	11.2501i	−0.245323	+	0.424911i	−0.962222	−	0.272265i	$-0.912227\pi$
$701$	−6.49526	+	11.2501i	−0.245323	+	0.424911i	0.716900	+	0.697176i	$0.245561\pi$
$702$	9.41476	−	0.215193i	0.355337	−	0.00812193i
$703$	−3.56956	−	6.18266i	−0.134629	−	0.233184i
$704$	−5.68051	−	0.663957i	−0.214092	−	0.0250238i
$705$	34.8826	−	0.265729i	1.31375	−	0.0100079i
$706$	7.15567	+	1.69592i	0.269307	+	0.0638270i
$707$	9.24876	+	6.08300i	0.347835	+	0.228775i
$708$	−6.74001	+	4.50690i	−0.253305	+	0.169380i
$709$	−4.29279	−	4.55009i	−0.161219	−	0.170882i	0.641728	−	0.766932i	$-0.278218\pi$
$709$	−4.29279	−	4.55009i	−0.161219	−	0.170882i	−0.802948	+	0.596050i	$0.796736\pi$
$710$	−3.21170	+	2.69494i	−0.120533	+	0.101139i
$711$	−29.1302	−	14.0782i	−1.09247	−	0.527973i
$712$	13.1371	+	11.0234i	0.492335	+	0.413118i
$713$	−1.72739	−	29.6581i	−0.0646911	−	1.11070i
$714$	3.94470	+	12.8200i	0.147627	+	0.479775i
$715$	10.9264	+	14.6767i	0.408623	+	0.548876i
$716$	−18.8252	+	2.20035i	−0.703531	+	0.0822310i
$717$	1.98656	−	4.70357i	0.0741895	−	0.175658i
$718$	9.69764	−	6.37824i	0.361913	−	0.238034i
$719$	−12.5735	+	4.57640i	−0.468914	+	0.170671i	−0.565660	−	0.824638i	$-0.691379\pi$
$719$	−12.5735	+	4.57640i	−0.468914	+	0.170671i	0.0967463	+	0.995309i	$0.469156\pi$
$720$	4.00450	−	3.46549i	0.149239	−	0.129151i
$721$	−20.0008	−	7.27969i	−0.744868	−	0.271110i
$722$	−15.0389	+	3.56429i	−0.559690	+	0.132649i
$723$	11.3782	+	11.8776i	0.423161	+	0.441734i
$724$	0.690324	−	11.8524i	0.0256557	−	0.440491i
$725$	−1.70854	+	1.81095i	−0.0634537	+	0.0672570i
$726$	−35.2346	+	13.1292i	−1.30768	+	0.487269i
$727$	−0.647191	−	1.50036i	−0.0240030	−	0.0556452i	0.905793	−	0.423720i	$-0.139276\pi$
$727$	−0.647191	−	1.50036i	−0.0240030	−	0.0556452i	−0.929796	+	0.368075i	$0.880017\pi$
$728$	−2.31444			−0.0857787
$729$	−14.5543	−	22.7415i	−0.539047	−	0.842276i
$730$	−20.2327			−0.748845
$731$	2.31142	+	5.35846i	0.0854908	+	0.198190i
$732$	16.1123	−	6.00380i	0.595529	−	0.221907i
$733$	−21.8323	+	23.1409i	−0.806394	+	0.854727i	−0.991782	−	0.127938i	$-0.959164\pi$
$733$	−21.8323	+	23.1409i	−0.806394	+	0.854727i	0.185389	+	0.982665i	$0.440646\pi$
$734$	0.943792	−	16.2043i	0.0348360	−	0.598111i
$735$	11.3563	+	11.8547i	0.418883	+	0.437268i
$736$	8.51413	−	2.01789i	0.313835	−	0.0743803i
$737$	33.8226	+	12.3104i	1.24587	+	0.453461i
$738$	−1.36090	+	1.17772i	−0.0500954	+	0.0433526i
$739$	16.4196	−	5.97624i	0.604004	−	0.219840i	−0.0218734	−	0.999761i	$-0.506963\pi$
$739$	16.4196	−	5.97624i	0.604004	−	0.219840i	0.625878	+	0.779921i	$0.284741\pi$
$740$	−5.59269	+	3.67837i	−0.205591	+	0.135219i
$741$	2.29937	−	5.44421i	0.0844696	−	0.199998i
$742$	−8.23754	+	0.962831i	−0.302410	+	0.0353466i
$743$	29.5153	+	39.6459i	1.08281	+	1.45447i	0.879833	+	0.475282i	$0.157654\pi$
$743$	29.5153	+	39.6459i	1.08281	+	1.45447i	0.202976	+	0.979184i	$0.434939\pi$
$744$	−1.72948	−	5.62067i	−0.0634058	−	0.206064i
$745$	0.273693	+	4.69913i	0.0100273	+	0.172163i
$746$	18.0665	+	15.1596i	0.661462	+	0.555033i
$747$	−17.8756	−	8.63898i	−0.654033	−	0.316084i
$748$	26.5677	−	22.2929i	0.971410	−	0.815110i
$749$	−4.98132	−	5.27989i	−0.182013	−	0.192923i
$750$	17.4964	−	11.6994i	0.638876	−	0.427203i
$751$	0.520103	+	0.342077i	0.0189788	+	0.0124826i	0.558963	−	0.829193i	$-0.311199\pi$
$751$	0.520103	+	0.342077i	0.0189788	+	0.0124826i	−0.539984	+	0.841675i	$0.681570\pi$
$752$	11.1015	+	2.63111i	0.404830	+	0.0959466i
$753$	−11.2974	+	0.0860617i	−0.411701	+	0.00313626i
$754$	2.37906	+	0.278072i	0.0866401	+	0.0101268i
$755$	6.96677	+	12.0668i	0.253547	+	0.439156i
$756$	3.44830	+	5.66936i	0.125413	+	0.206193i
$757$	−11.7600	+	20.3689i	−0.427425	+	0.740322i	−0.996643	−	0.0818644i	$-0.973913\pi$
$757$	−11.7600	+	20.3689i	−0.427425	+	0.740322i	0.569218	+	0.822186i	$0.307246\pi$
$758$	−7.51729	+	10.0975i	−0.273040	+	0.366757i
$759$	65.9719	−	56.2189i	2.39463	−	2.04062i
$760$	−0.953174	−	3.18382i	−0.0345752	−	0.115489i
$761$	19.8334	−	9.96071i	0.718960	−	0.361075i	−0.0514054	−	0.998678i	$-0.516370\pi$
$761$	19.8334	−	9.96071i	0.718960	−	0.361075i	0.770366	+	0.637603i	$0.220074\pi$
$762$	−6.72437	+	9.17753i	−0.243598	+	0.332467i
$763$	−3.97301	+	13.2708i	−0.143833	+	0.480435i
$764$	4.46121	+	25.3008i	0.161401	+	0.915349i
$765$	−1.37864	+	32.0847i	−0.0498447	+	1.16002i
$766$	5.40588	−	30.6583i	0.195323	−	1.10773i
$767$	7.58147	+	3.80756i	0.273751	+	0.137483i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.396080 + 0.918216i) q^{2} +(-1.62304 + 0.604777i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.102641 + 1.76229i) q^{5} +(-1.19817 - 1.25076i) q^{6} +(-1.24262 + 0.294506i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.26849 - 1.96315i) q^{9} +O(q^{10})\)	\(q+(0.396080 + 0.918216i) q^{2} +(-1.62304 + 0.604777i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.102641 + 1.76229i) q^{5} +(-1.19817 - 1.25076i) q^{6} +(-1.24262 + 0.294506i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.26849 - 1.96315i) q^{9} +(-1.65881 + 0.603759i) q^{10} +(-4.77831 + 3.14274i) q^{11} +(0.673895 - 1.59558i) q^{12} +(-1.80009 + 0.210400i) q^{13} +(-0.762596 - 1.02434i) q^{14} +(-0.899200 - 2.92233i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(4.64536 + 3.89792i) q^{17} +(2.70110 + 1.30540i) q^{18} +(1.44222 - 1.21016i) q^{19} +(-1.21140 - 1.28401i) q^{20} +(1.83870 - 1.22950i) q^{21} +(-4.77831 - 3.14274i) q^{22} +(8.51413 + 2.01789i) q^{23} +(1.73200 - 0.0131941i) q^{24} +(1.87108 + 0.218698i) q^{25} +(-0.906172 - 1.56954i) q^{26} +(-2.49457 + 4.55819i) q^{27} +(0.638520 - 1.10595i) q^{28} +(-0.789224 + 1.06011i) q^{29} +(2.32717 - 1.98313i) q^{30} +(-0.973767 - 3.25261i) q^{31} +(0.893633 - 0.448799i) q^{32} +(5.85470 - 7.99060i) q^{33} +(-1.73920 + 5.80933i) q^{34} +(-0.391459 - 2.22008i) q^{35} +(-0.128787 + 2.99723i) q^{36} +(0.658474 - 3.73439i) q^{37} +(1.68242 + 0.844945i) q^{38} +(2.79437 - 1.43014i) q^{39} +(0.699189 - 1.62090i) q^{40} +(-0.237614 + 0.550851i) q^{41} +(1.85722 + 1.20135i) q^{42} +(0.859982 + 0.431899i) q^{43} +(0.993126 - 5.63230i) q^{44} +(3.22679 + 4.19922i) q^{45} +(1.51942 + 8.61706i) q^{46} +(-3.27215 + 10.9297i) q^{47} +(0.698125 + 1.58512i) q^{48} +(-4.79806 + 2.40968i) q^{49} +(0.540284 + 1.80467i) q^{50} +(-9.89695 - 3.51705i) q^{51} +(1.08226 - 1.45372i) q^{52} +(3.24720 - 5.62432i) q^{53} +(-5.17345 - 0.485145i) q^{54} +(-5.04796 - 8.74332i) q^{55} +(1.26841 + 0.148255i) q^{56} +(-1.60889 + 2.83636i) q^{57} +(-1.28601 - 0.304789i) q^{58} +(-3.91105 - 2.57234i) q^{59} +(2.74269 + 1.35137i) q^{60} +(6.81251 + 7.22084i) q^{61} +(2.60091 - 2.18242i) q^{62} +(-2.24070 + 3.10753i) q^{63} +(0.766044 + 0.642788i) q^{64} +(-0.186022 - 3.19387i) q^{65} +(9.65603 + 2.21097i) q^{66} +(-3.75818 - 5.04811i) q^{67} +(-6.02308 + 0.703997i) q^{68} +(-15.0391 + 1.87405i) q^{69} +(1.88346 - 1.23877i) q^{70} +(2.23180 - 0.812309i) q^{71} +(-2.80312 + 1.06889i) q^{72} +(10.7703 + 3.92007i) q^{73} +(3.68979 - 0.874496i) q^{74} +(-3.16909 + 0.776631i) q^{75} +(-0.109468 + 1.87949i) q^{76} +(5.01205 - 5.31247i) q^{77} +(2.41997 + 1.99938i) q^{78} +(-4.27156 - 9.90258i) q^{79} +1.76527 q^{80} +(1.29208 - 8.90677i) q^{81} -0.599915 q^{82} +(-2.62121 - 6.07665i) q^{83} +(-0.367488 + 2.18116i) q^{84} +(-7.34605 + 7.78636i) q^{85} +(-0.0559553 + 0.960716i) q^{86} +(0.639807 - 2.19790i) q^{87} +(5.56502 - 1.31893i) q^{88} +(-16.1151 - 5.86541i) q^{89} +(-2.57773 + 4.62612i) q^{90} +(2.17486 - 0.791584i) q^{91} +(-7.31051 + 4.80820i) q^{92} +(3.54756 + 4.69018i) q^{93} +(-11.3319 + 1.32451i) q^{94} +(1.98462 + 2.66581i) q^{95} +(-1.17897 + 1.26887i) q^{96} +(0.665093 + 11.4192i) q^{97} +(-4.11302 - 3.45123i) q^{98} +(-4.66986 + 16.5098i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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