LMFDB - Embedded newform 81.2.g.a.7.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,2,Mod(4,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("81.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	81.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:	$0.646788256372$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	81.7
Dual form			81.2.g.a.58.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.55705 + 2.09149i) q^{2} +(-1.63477 - 0.572310i) q^{3} +(-1.37629 + 4.59713i) q^{4} +(-0.270787 + 0.178099i) q^{5} +(-1.34844 - 4.31021i) q^{6} +(2.64546 - 2.80403i) q^{7} +(-6.85740 + 2.49589i) q^{8} +(2.34492 + 1.87119i) q^{9} +O(q^{10})$	\(q+(1.55705 + 2.09149i) q^{2} +(-1.63477 - 0.572310i) q^{3} +(-1.37629 + 4.59713i) q^{4} +(-0.270787 + 0.178099i) q^{5} +(-1.34844 - 4.31021i) q^{6} +(2.64546 - 2.80403i) q^{7} +(-6.85740 + 2.49589i) q^{8} +(2.34492 + 1.87119i) q^{9} +(-0.794122 - 0.289037i) q^{10} +(1.12552 - 0.565257i) q^{11} +(4.88089 - 6.72756i) q^{12} +(-1.55767 - 3.61109i) q^{13} +(9.98370 + 1.16693i) q^{14} +(0.544602 - 0.136177i) q^{15} +(-7.87890 - 5.18204i) q^{16} +(-3.68665 + 3.09347i) q^{17} +(-0.262390 + 7.81791i) q^{18} +(-3.47862 - 2.91891i) q^{19} +(-0.446064 - 1.48996i) q^{20} +(-5.92948 + 3.06990i) q^{21} +(2.93472 + 1.47387i) q^{22} +(0.385450 + 0.408553i) q^{23} +(12.6387 - 0.155637i) q^{24} +(-1.93879 + 4.49463i) q^{25} +(5.12716 - 8.88050i) q^{26} +(-2.76250 - 4.40098i) q^{27} +(9.24954 + 16.0207i) q^{28} +(2.11898 - 0.247673i) q^{29} +(1.13279 + 0.926991i) q^{30} +(3.69897 - 0.876672i) q^{31} +(-0.581095 - 9.97701i) q^{32} +(-2.16346 + 0.279917i) q^{33} +(-12.2103 - 2.89389i) q^{34} +(-0.216961 + 1.23045i) q^{35} +(-11.8294 + 8.20461i) q^{36} +(-0.248079 - 1.40693i) q^{37} +(0.688459 - 11.8204i) q^{38} +(0.479767 + 6.79475i) q^{39} +(1.41238 - 1.89715i) q^{40} +(-5.63875 + 7.57416i) q^{41} +(-15.6532 - 7.62143i) q^{42} +(0.210389 - 3.61224i) q^{43} +(1.04952 + 5.95211i) q^{44} +(-0.968232 - 0.0890637i) q^{45} +(-0.254317 + 1.44230i) q^{46} +(3.70075 + 0.877094i) q^{47} +(9.91443 + 12.9806i) q^{48} +(-0.457078 - 7.84773i) q^{49} +(-12.4192 + 2.94342i) q^{50} +(7.79724 - 2.94719i) q^{51} +(18.7444 - 2.19091i) q^{52} +(-3.57369 - 6.18982i) q^{53} +(4.90321 - 12.6303i) q^{54} +(-0.204104 + 0.353518i) q^{55} +(-11.1425 + 25.8311i) q^{56} +(4.01621 + 6.76258i) q^{57} +(3.81736 + 4.04617i) q^{58} +(5.22384 + 2.62351i) q^{59} +(-0.123507 + 2.69102i) q^{60} +(2.64794 + 8.84474i) q^{61} +(7.59304 + 6.37131i) q^{62} +(11.4503 - 1.62507i) q^{63} +(5.51392 - 4.62673i) q^{64} +(1.06493 + 0.700415i) q^{65} +(-3.95407 - 4.08900i) q^{66} +(-0.214231 - 0.0250400i) q^{67} +(-9.14717 - 21.2055i) q^{68} +(-0.396301 - 0.888485i) q^{69} +(-2.91129 + 1.46210i) q^{70} +(-11.2063 - 4.07874i) q^{71} +(-20.7503 - 6.97881i) q^{72} +(7.37938 - 2.68588i) q^{73} +(2.55629 - 2.70951i) q^{74} +(5.74179 - 6.23807i) q^{75} +(18.2062 - 11.9744i) q^{76} +(1.39252 - 4.65135i) q^{77} +(-13.4641 + 11.5832i) q^{78} +(4.98085 + 6.69044i) q^{79} +3.05642 q^{80} +(1.99732 + 8.77557i) q^{81} -24.6211 q^{82} +(0.396004 + 0.531925i) q^{83} +(-5.95205 - 31.4837i) q^{84} +(0.447353 - 1.49426i) q^{85} +(7.88253 - 5.18442i) q^{86} +(-3.60578 - 0.807824i) q^{87} +(-6.30731 + 6.68536i) q^{88} +(1.56940 - 0.571214i) q^{89} +(-1.32131 - 2.16372i) q^{90} +(-14.2463 - 5.18524i) q^{91} +(-2.40866 + 1.20967i) q^{92} +(-6.54868 - 0.683804i) q^{93} +(3.92784 + 9.10575i) q^{94} +(1.46182 + 0.170862i) q^{95} +(-4.75999 + 16.6427i) q^{96} +(13.4681 + 8.85812i) q^{97} +(15.7017 - 13.1753i) q^{98} +(3.69695 + 0.780572i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) $ 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	1.55705	+	2.09149i	1.10100	+	1.47890i	0.861327	+	0.508050i	$0.169634\pi$
$2$	1.55705	+	2.09149i	1.10100	+	1.47890i	0.239675	+	0.970853i	$0.422959\pi$
$3$	−1.63477	−	0.572310i	−0.943833	−	0.330423i
$3$	−1.63477	−	0.572310i	−0.943833	−	0.330423i
$4$	−1.37629	+	4.59713i	−0.688145	+	2.29856i
$5$	−0.270787	+	0.178099i	−0.121100	+	0.0796485i	−0.608614	−	0.793467i	$-0.708274\pi$
$5$	−0.270787	+	0.178099i	−0.121100	+	0.0796485i	0.487514	+	0.873115i	$0.337904\pi$
$6$	−1.34844	−	4.31021i	−0.550498	−	1.75963i
$7$	2.64546	−	2.80403i	0.999891	−	1.05982i	0.00168159	−	0.999999i	$-0.499465\pi$
$7$	2.64546	−	2.80403i	0.999891	−	1.05982i	0.998209	−	0.0598235i	$-0.0190538\pi$
$8$	−6.85740	+	2.49589i	−2.42446	+	0.882430i
$9$	2.34492	+	1.87119i	0.781641	+	0.623729i
$10$	−0.794122	−	0.289037i	−0.251123	−	0.0914014i
$11$	1.12552	−	0.565257i	0.339357	−	0.170431i	−0.270956	−	0.962592i	$-0.587340\pi$
$11$	1.12552	−	0.565257i	0.339357	−	0.170431i	0.610313	+	0.792160i	$0.291044\pi$
$12$	4.88089	−	6.72756i	1.40899	−	1.94208i
$13$	−1.55767	−	3.61109i	−0.432020	−	1.00154i	−0.985655	−	0.168775i	$-0.946019\pi$
$13$	−1.55767	−	3.61109i	−0.432020	−	1.00154i	0.553634	−	0.832760i	$-0.313241\pi$
$14$	9.98370	+	1.16693i	2.66826	+	0.311874i
$15$	0.544602	−	0.136177i	0.140616	−	0.0351607i
$16$	−7.87890	−	5.18204i	−1.96973	−	1.29551i
$17$	−3.68665	+	3.09347i	−0.894145	+	0.750277i	−0.969037	−	0.246915i	$-0.920583\pi$
$17$	−3.68665	+	3.09347i	−0.894145	+	0.750277i	0.0748921	+	0.997192i	$0.476139\pi$
$18$	−0.262390	+	7.81791i	−0.0618459	+	1.84270i
$19$	−3.47862	−	2.91891i	−0.798050	−	0.669644i	0.149673	−	0.988735i	$-0.452178\pi$
$19$	−3.47862	−	2.91891i	−0.798050	−	0.669644i	−0.947724	+	0.319092i	$0.896622\pi$
$20$	−0.446064	−	1.48996i	−0.0997430	−	0.333165i
$21$	−5.92948	+	3.06990i	−1.29392	+	0.669908i
$22$	2.93472	+	1.47387i	0.625684	+	0.314230i
$23$	0.385450	+	0.408553i	0.0803718	+	0.0851892i	0.766311	−	0.642469i	$-0.222090\pi$
$23$	0.385450	+	0.408553i	0.0803718	+	0.0851892i	−0.685939	+	0.727659i	$0.740609\pi$
$24$	12.6387	−	0.155637i	2.57986	−	0.0317694i
$25$	−1.93879	+	4.49463i	−0.387759	+	0.898925i
$26$	5.12716	−	8.88050i	1.00552	−	1.74161i
$27$	−2.76250	−	4.40098i	−0.531644	−	0.846968i
$28$	9.24954	+	16.0207i	1.74800	+	3.02762i
$29$	2.11898	−	0.247673i	0.393484	−	0.0459917i	0.0829493	−	0.996554i	$-0.473566\pi$
$29$	2.11898	−	0.247673i	0.393484	−	0.0459917i	0.310535	+	0.950562i	$0.399492\pi$
$30$	1.13279	+	0.926991i	0.206817	+	0.169245i
$31$	3.69897	−	0.876672i	0.664354	−	0.157455i	0.115415	−	0.993317i	$-0.463180\pi$
$31$	3.69897	−	0.876672i	0.664354	−	0.157455i	0.548939	+	0.835862i	$0.315032\pi$
$32$	−0.581095	−	9.97701i	−0.102724	−	1.76370i
$33$	−2.16346	+	0.279917i	−0.376610	+	0.0487273i
$34$	−12.2103	−	2.89389i	−2.09404	−	0.496297i
$35$	−0.216961	+	1.23045i	−0.0366732	+	0.207984i
$36$	−11.8294	+	8.20461i	−1.97156	+	1.36744i
$37$	−0.248079	−	1.40693i	−0.0407839	−	0.231297i	0.957602	−	0.288095i	$-0.0930220\pi$
$37$	−0.248079	−	1.40693i	−0.0407839	−	0.231297i	−0.998386	+	0.0567981i	$0.981911\pi$
$38$	0.688459	−	11.8204i	0.111683	−	1.91752i
$39$	0.479767	+	6.79475i	0.0768242	+	1.08803i
$40$	1.41238	−	1.89715i	0.223317	−	0.299966i
$41$	−5.63875	+	7.57416i	−0.880625	+	1.18289i	0.101533	+	0.994832i	$0.467625\pi$
$41$	−5.63875	+	7.57416i	−0.880625	+	1.18289i	−0.982159	+	0.188053i	$0.939782\pi$
$42$	−15.6532	−	7.62143i	−2.41534	−	1.17601i
$43$	0.210389	−	3.61224i	0.0320840	−	0.550861i	−0.943519	−	0.331319i	$-0.892506\pi$
$43$	0.210389	−	3.61224i	0.0320840	−	0.550861i	0.975603	−	0.219543i	$-0.0704565\pi$
$44$	1.04952	+	5.95211i	0.158221	+	0.897314i
$45$	−0.968232	−	0.0890637i	−0.144335	−	0.0132768i
$46$	−0.254317	+	1.44230i	−0.0374969	+	0.212656i
$47$	3.70075	+	0.877094i	0.539810	+	0.127937i	0.491471	−	0.870894i	$-0.336459\pi$
$47$	3.70075	+	0.877094i	0.539810	+	0.127937i	0.0483385	+	0.998831i	$0.484607\pi$
$48$	9.91443	+	12.9806i	1.43103	+	1.87359i
$49$	−0.457078	−	7.84773i	−0.0652969	−	1.12110i
$50$	−12.4192	+	2.94342i	−1.75635	+	0.416262i
$51$	7.79724	−	2.94719i	1.09183	−	0.412689i
$52$	18.7444	−	2.19091i	2.59939	−	0.303825i
$53$	−3.57369	−	6.18982i	−0.490884	−	0.850237i	0.509061	−	0.860731i	$-0.329993\pi$
$53$	−3.57369	−	6.18982i	−0.490884	−	0.850237i	−0.999945	+	0.0104941i	$0.996660\pi$
$54$	4.90321	−	12.6303i	0.667243	−	1.71876i
$55$	−0.204104	+	0.353518i	−0.0275214	+	0.0476684i
$56$	−11.1425	+	25.8311i	−1.48897	+	3.45183i
$57$	4.01621	+	6.76258i	0.531960	+	0.895726i
$58$	3.81736	+	4.04617i	0.501244	+	0.531288i
$59$	5.22384	+	2.62351i	0.680086	+	0.341552i	0.755081	−	0.655632i	$-0.227598\pi$
$59$	5.22384	+	2.62351i	0.680086	+	0.341552i	−0.0749947	+	0.997184i	$0.523894\pi$
$60$	−0.123507	+	2.69102i	−0.0159447	+	0.347409i
$61$	2.64794	+	8.84474i	0.339034	+	1.13245i	0.942260	+	0.334883i	$0.108697\pi$
$61$	2.64794	+	8.84474i	0.339034	+	1.13245i	−0.603225	+	0.797571i	$0.706118\pi$
$62$	7.59304	+	6.37131i	0.964317	+	0.809158i
$63$	11.4503	−	1.62507i	1.44260	−	0.204740i
$64$	5.51392	−	4.62673i	0.689240	−	0.578341i
$65$	1.06493	+	0.700415i	0.132088	+	0.0868758i
$66$	−3.95407	−	4.08900i	−0.486712	−	0.503321i
$67$	−0.214231	−	0.0250400i	−0.0261725	−	0.00305913i	0.102997	−	0.994682i	$-0.467157\pi$
$67$	−0.214231	−	0.0250400i	−0.0261725	−	0.00305913i	−0.129169	+	0.991623i	$0.541231\pi$
$68$	−9.14717	−	21.2055i	−1.10926	−	2.57155i
$69$	−0.396301	−	0.888485i	−0.0477091	−	0.106961i
$70$	−2.91129	+	1.46210i	−0.347965	+	0.174755i
$71$	−11.2063	−	4.07874i	−1.32994	−	0.484058i	−0.423308	−	0.905986i	$-0.639131\pi$
$71$	−11.2063	−	4.07874i	−1.32994	−	0.484058i	−0.906629	+	0.421928i	$0.861354\pi$
$72$	−20.7503	−	6.97881i	−2.44545	−	0.822460i
$73$	7.37938	−	2.68588i	0.863691	−	0.314358i	0.128082	−	0.991764i	$-0.459118\pi$
$73$	7.37938	−	2.68588i	0.863691	−	0.314358i	0.735610	+	0.677406i	$0.236896\pi$
$74$	2.55629	−	2.70951i	0.297163	−	0.314974i
$75$	5.74179	−	6.23807i	0.663005	−	0.720311i
$76$	18.2062	−	11.9744i	2.08839	−	1.37356i
$77$	1.39252	−	4.65135i	0.158693	−	0.530070i
$78$	−13.4641	+	11.5832i	−1.52451	+	1.31154i
$79$	4.98085	+	6.69044i	0.560389	+	0.752733i	0.988538	−	0.150975i	$-0.0482414\pi$
$79$	4.98085	+	6.69044i	0.560389	+	0.752733i	−0.428149	+	0.903708i	$0.640834\pi$
$80$	3.05642			0.341718
$81$	1.99732	+	8.77557i	0.221925	+	0.975064i
$82$	−24.6211			−2.71894
$83$	0.396004	+	0.531925i	0.0434670	+	0.0583864i	0.823325	−	0.567570i	$-0.192116\pi$
$83$	0.396004	+	0.531925i	0.0434670	+	0.0583864i	−0.779858	+	0.625956i	$0.784709\pi$
$84$	−5.95205	−	31.4837i	−0.649421	−	3.43515i
$85$	0.447353	−	1.49426i	0.0485222	−	0.162076i
$86$	7.88253	−	5.18442i	0.849995	−	0.559051i
$87$	−3.60578	−	0.807824i	−0.386580	−	0.0866078i
$88$	−6.30731	+	6.68536i	−0.672362	+	0.712662i
$89$	1.56940	−	0.571214i	0.166356	−	0.0605486i	−0.257500	−	0.966278i	$-0.582899\pi$
$89$	1.56940	−	0.571214i	0.166356	−	0.0605486i	0.423856	+	0.905730i	$0.360676\pi$
$90$	−1.32131	−	2.16372i	−0.139279	−	0.228076i
$91$	−14.2463	−	5.18524i	−1.49342	−	0.543561i
$92$	−2.40866	+	1.20967i	−0.251120	+	0.126117i
$93$	−6.54868	−	0.683804i	−0.679066	−	0.0709071i
$94$	3.92784	+	9.10575i	0.405125	+	0.939186i
$95$	1.46182	+	0.170862i	0.149980	+	0.0175301i
$96$	−4.75999	+	16.6427i	−0.485815	+	1.69858i
$97$	13.4681	+	8.85812i	1.36748	+	0.899405i	0.999537	−	0.0304429i	$-0.00969178\pi$
$97$	13.4681	+	8.85812i	1.36748	+	0.899405i	0.367943	+	0.929848i	$0.380062\pi$
$98$	15.7017	−	13.1753i	1.58611	−	1.33091i
$99$	3.69695	+	0.780572i	0.371558	+	0.0784504i
$100$	−17.9940	−	15.0988i	−1.79940	−	1.50988i
$101$	−0.991482	−	3.31178i	−0.0986562	−	0.329535i	0.894386	−	0.447297i	$-0.147613\pi$
$101$	−0.991482	−	3.31178i	−0.0986562	−	0.329535i	−0.993042	+	0.117762i	$0.962428\pi$
$102$	18.3047	+	11.7189i	1.81244	+	1.16034i
$103$	−5.55153	−	2.78808i	−0.547009	−	0.274718i	0.153758	−	0.988109i	$-0.450862\pi$
$103$	−5.55153	−	2.78808i	−0.547009	−	0.274718i	−0.700767	+	0.713390i	$0.747159\pi$
$104$	19.6944	+	20.8749i	1.93120	+	2.04695i
$105$	1.05888	−	1.88733i	0.103336	−	0.184184i
$106$	7.38148	−	17.1122i	0.716953	−	1.66208i
$107$	−0.773565	+	1.33985i	−0.0747833	+	0.129529i	−0.900992	−	0.433836i	$-0.857160\pi$
$107$	−0.773565	+	1.33985i	−0.0747833	+	0.129529i	0.826209	+	0.563364i	$0.190493\pi$
$108$	24.0338	−	6.64255i	2.31266	−	0.639180i
$109$	6.28071	+	10.8785i	0.601583	+	1.04197i	0.992581	+	0.121581i	$0.0387965\pi$
$109$	6.28071	+	10.8785i	0.601583	+	1.04197i	−0.390998	+	0.920391i	$0.627870\pi$
$110$	−1.05718	+	0.123566i	−0.100798	+	0.0117816i
$111$	−0.399647	+	2.44197i	−0.0379328	+	0.231782i
$112$	−35.3739	+	8.38377i	−3.34252	+	0.792192i
$113$	−1.13750	−	19.5301i	−0.107007	−	1.83724i	−0.444350	−	0.895853i	$-0.646565\pi$
$113$	−1.13750	−	19.5301i	−0.107007	−	1.83724i	0.337343	−	0.941382i	$-0.390472\pi$
$114$	−7.89039	+	18.9295i	−0.739003	+	1.77291i
$115$	−0.177138	−	0.0419824i	−0.0165182	−	0.00391488i
$116$	−1.77774	+	10.0821i	−0.165059	+	0.936097i
$117$	3.10440	−	11.3824i	0.287002	−	1.05230i
$118$	2.64676	+	15.0105i	0.243654	+	1.38183i
$119$	−1.07873	+	18.5211i	−0.0988873	+	1.69783i
$120$	−3.39467	+	2.29308i	−0.309889	+	0.209329i
$121$	−5.62147	+	7.55094i	−0.511043	+	0.686449i
$122$	−14.3757	+	19.3099i	−1.30151	+	1.74823i
$123$	13.5528	−	9.15487i	1.22202	−	0.825467i
$124$	−1.06068	+	18.2112i	−0.0952519	+	1.63541i
$125$	−0.556893	−	3.15830i	−0.0498100	−	0.282487i
$126$	21.2275	+	21.4177i	1.89109	+	1.90804i
$127$	0.0822160	−	0.466270i	0.00729549	−	0.0413748i	−0.980943	−	0.194297i	$-0.937757\pi$
$127$	0.0822160	−	0.466270i	0.00729549	−	0.0413748i	0.988238	+	0.152922i	$0.0488685\pi$
$128$	−1.18687	−	0.281293i	−0.104905	−	0.0248630i
$129$	−2.41126	+	5.78476i	−0.212299	+	0.509320i
$130$	0.193244	+	3.31787i	0.0169486	+	0.290996i
$131$	−6.81702	+	1.61566i	−0.595606	+	0.141161i	−0.517353	−	0.855772i	$-0.673082\pi$
$131$	−6.81702	+	1.61566i	−0.595606	+	0.141161i	−0.0782533	+	0.996934i	$0.524934\pi$
$132$	1.69074	−	10.3310i	0.147160	−	0.899194i
$133$	−17.3873	+	2.03228i	−1.50767	+	0.176221i
$134$	−0.281198	−	0.487050i	−0.0242918	−	0.0420747i
$135$	1.53186	+	0.699727i	0.131842	+	0.0602229i
$136$	17.5599	−	30.4146i	1.50575	−	2.60803i
$137$	7.86676	−	18.2372i	0.672103	−	1.55811i	−0.149947	−	0.988694i	$-0.547910\pi$
$137$	7.86676	−	18.2372i	0.672103	−	1.55811i	0.822050	−	0.569416i	$-0.192830\pi$
$138$	1.24119	−	2.21228i	0.105657	−	0.188322i
$139$	−10.6118	−	11.2479i	−0.900085	−	0.954035i	0.0990721	−	0.995080i	$-0.468413\pi$
$139$	−10.6118	−	11.2479i	−0.900085	−	0.954035i	−0.999157	+	0.0410457i	$0.986931\pi$
$140$	−5.35793	−	2.69085i	−0.452828	−	0.227419i
$141$	−5.54789	−	3.55182i	−0.467217	−	0.299117i
$142$	−8.91810	−	29.7885i	−0.748390	−	2.49980i
$143$	−3.79438	−	3.18386i	−0.317302	−	0.266248i
$144$	−8.77886	−	26.8944i	−0.731572	−	2.24120i
$145$	−0.529681	+	0.444455i	−0.0439876	+	0.0369100i
$146$	17.1076	+	11.2518i	1.41583	+	0.931207i
$147$	−3.74412	+	13.0908i	−0.308810	+	1.07971i
$148$	6.80924	+	0.795887i	0.559716	+	0.0654215i
$149$	3.42553	+	7.94126i	0.280630	+	0.650574i	0.998982	−	0.0451060i	$-0.0143626\pi$
$149$	3.42553	+	7.94126i	0.280630	+	0.650574i	−0.718352	+	0.695680i	$0.755103\pi$
$150$	21.9871	+	2.29586i	1.79524	+	0.187456i
$151$	−2.70768	+	1.35985i	−0.220348	+	0.110663i	−0.555549	−	0.831484i	$-0.687492\pi$
$151$	−2.70768	+	1.35985i	−0.220348	+	0.110663i	0.335201	+	0.942147i	$0.391196\pi$
$152$	31.1396	+	11.3339i	2.52575	+	0.919299i
$153$	−14.4334	+	0.355530i	−1.16687	+	0.0287429i
$154$	11.8965	−	4.32995i	0.958643	−	0.348918i
$155$	−0.845498	+	0.896175i	−0.0679120	+	0.0719825i
$156$	−31.8966	−	7.14600i	−2.55378	−	0.572138i
$157$	−7.77296	+	5.11236i	−0.620350	+	0.408011i	−0.820412	−	0.571773i	$-0.806256\pi$
$157$	−7.77296	+	5.11236i	−0.620350	+	0.408011i	0.200062	+	0.979783i	$0.435886\pi$
$158$	−6.23751	+	20.8347i	−0.496230	+	1.65752i
$159$	2.29966	+	12.1642i	0.182375	+	0.964681i
$160$	1.93425	+	2.59815i	0.152916	+	0.205402i
$161$	2.16529			0.170648
$162$	−15.2440	+	17.8414i	−1.19769	+	1.40175i
$163$	2.41567			0.189210			0.0946048	−	0.995515i	$-0.469841\pi$
$163$	2.41567			0.189210			0.0946048	+	0.995515i	$0.469841\pi$
$164$	−27.0588	−	36.3463i	−2.11294	−	2.83817i
$165$	0.535984	−	0.461109i	0.0417263	−	0.0358973i
$166$	−0.495915	+	1.65647i	−0.0384905	+	0.128567i
$167$	−0.420792	+	0.276759i	−0.0325619	+	0.0214163i	−0.565686	−	0.824621i	$-0.691388\pi$
$167$	−0.420792	+	0.276759i	−0.0325619	+	0.0214163i	0.533124	+	0.846037i	$0.321018\pi$
$168$	32.9987	−	35.8509i	2.54591	−	2.76596i
$169$	−1.69247	+	1.79391i	−0.130190	+	0.137993i
$170$	3.82178	−	1.39101i	0.293117	−	0.106686i
$171$	−2.69527	−	13.3538i	−0.206113	−	1.02119i
$172$	16.3164	+	5.93867i	1.24411	+	0.452820i
$173$	−4.77024	+	2.39570i	−0.362674	+	0.182142i	−0.620799	−	0.783970i	$-0.713192\pi$
$173$	−4.77024	+	2.39570i	−0.362674	+	0.182142i	0.258125	+	0.966112i	$0.416895\pi$
$174$	−3.92483	−	8.79925i	−0.297541	−	0.667069i
$175$	7.47405	+	17.3268i	0.564985	+	1.30978i
$176$	−11.7970	−	1.37887i	−0.889234	−	0.103937i
$177$	−7.03830	−	7.27848i	−0.529031	−	0.547084i
$178$	3.63832	+	2.39296i	0.272704	+	0.179360i
$179$	−13.8827	+	11.6490i	−1.03764	+	0.870683i	−0.991740	−	0.128263i	$-0.959060\pi$
$179$	−13.8827	+	11.6490i	−1.03764	+	0.870683i	−0.0458999	+	0.998946i	$0.514616\pi$
$180$	1.74200	−	4.32851i	0.129841	−	0.322628i
$181$	8.98433	+	7.53875i	0.667800	+	0.560351i	0.912413	−	0.409270i	$-0.134217\pi$
$181$	8.98433	+	7.53875i	0.667800	+	0.560351i	−0.244613	+	0.969621i	$0.578661\pi$
$182$	−11.3374	−	37.8697i	−0.840387	−	2.80709i
$183$	0.733168	−	15.9745i	0.0541974	−	1.18087i
$184$	−3.66289	−	1.83957i	−0.270032	−	0.135615i
$185$	0.317749	+	0.336794i	0.0233614	+	0.0247616i
$186$	−8.76647	−	14.7612i	−0.642789	−	1.08234i
$187$	−2.40079	+	5.56566i	−0.175563	+	0.407002i
$188$	−9.12542	+	15.8057i	−0.665539	+	1.15275i
$189$	−19.6485	−	3.89649i	−1.42922	−	0.283428i
$190$	1.91878	+	3.32342i	0.139203	+	0.241106i
$191$	19.7542	−	2.30893i	1.42936	−	0.167069i	0.634061	−	0.773283i	$-0.281387\pi$
$191$	19.7542	−	2.30893i	1.42936	−	0.167069i	0.795301	+	0.606214i	$0.207313\pi$
$192$	−11.6619	+	4.40795i	−0.841625	+	0.318116i
$193$	15.5278	−	3.68015i	1.11771	−	0.264903i	0.370071	−	0.929004i	$-0.379333\pi$
$193$	15.5278	−	3.68015i	1.11771	−	0.264903i	0.747643	+	0.664100i	$0.231185\pi$
$194$	2.44394	+	41.9609i	0.175465	+	3.01262i
$195$	−1.34006	−	1.75448i	−0.0959634	−	0.125641i
$196$	36.7061	+	8.69950i	2.62186	+	0.621393i
$197$	−1.15341	+	6.54129i	−0.0821768	+	0.466048i	0.915753	+	0.401741i	$0.131595\pi$
$197$	−1.15341	+	6.54129i	−0.0821768	+	0.466048i	−0.997930	+	0.0643070i	$0.979516\pi$
$198$	4.12380	+	8.94751i	0.293066	+	0.635872i
$199$	−0.983166	−	5.57581i	−0.0696948	−	0.395259i	−0.999621	−	0.0275137i	$-0.991241\pi$
$199$	−0.983166	−	5.57581i	−0.0696948	−	0.395259i	0.929927	−	0.367745i	$-0.119870\pi$
$200$	2.07699	−	35.6605i	0.146865	−	2.52158i
$201$	0.335887	+	0.163541i	0.0236917	+	0.0115353i
$202$	5.38275	−	7.23029i	0.378729	−	0.508721i
$203$	4.91119	−	6.59687i	0.344698	−	0.463009i
$204$	2.81735	+	39.9011i	0.197254	+	2.79364i
$205$	0.177948	−	3.05524i	0.0124284	−	0.213387i
$206$	−2.81279	−	15.9521i	−0.195977	−	1.11144i
$207$	0.139371	+	1.67927i	0.00968697	+	0.116718i
$208$	−6.44004	+	36.5233i	−0.446537	+	2.53244i
$209$	−5.56518	−	1.31897i	−0.384952	−	0.0912353i
$210$	5.59605	−	0.724038i	0.386164	−	0.0499634i
$211$	−0.888331	−	15.2520i	−0.0611552	−	1.04999i	−0.879693	−	0.475542i	$-0.842252\pi$
$211$	−0.888331	−	15.2520i	−0.0611552	−	1.04999i	0.818538	−	0.574453i	$-0.194785\pi$
$212$	33.3738	−	7.90974i	2.29212	−	0.543243i
$213$	15.9853	+	13.0812i	1.09529	+	0.896312i
$214$	−4.00676	+	0.468324i	−0.273897	+	0.0320139i
$215$	0.586367	+	1.01562i	0.0399899	+	0.0692645i
$216$	29.9279	+	23.2844i	2.03634	+	1.58430i
$217$	7.32727	−	12.6912i	0.497408	−	0.861535i
$218$	−12.9728	+	30.0744i	−0.878632	+	2.03690i
$219$	−13.6007	+	0.167485i	−0.919051	+	0.0113176i
$220$	−1.34426	−	1.42483i	−0.0906301	−	0.0960623i
$221$	16.9134	+	8.49422i	1.13772	+	0.571383i
$222$	−5.72962	+	2.96643i	−0.384547	+	0.199094i
$223$	−5.82713	−	19.4640i	−0.390214	−	1.30340i	−0.897266	−	0.441489i	$-0.854450\pi$
$223$	−5.82713	−	19.4640i	−0.390214	−	1.30340i	0.507053	−	0.861915i	$-0.330735\pi$
$224$	−29.5131	−	24.7644i	−1.97192	−	1.65464i
$225$	−12.9566	+	6.91171i	−0.863774	+	0.460781i
$226$	39.0757	−	32.7884i	2.59928	−	2.18105i
$227$	0.842376	+	0.554040i	0.0559105	+	0.0367729i	0.577157	−	0.816634i	$-0.304162\pi$
$227$	0.842376	+	0.554040i	0.0559105	+	0.0367729i	−0.521246	+	0.853406i	$0.674533\pi$
$228$	−36.6159	+	9.15576i	−2.42495	+	0.606355i
$229$	10.0678	+	1.17676i	0.665299	+	0.0777623i	0.442038	−	0.896996i	$-0.354256\pi$
$229$	10.0678	+	1.17676i	0.665299	+	0.0777623i	0.223261	+	0.974759i	$0.428330\pi$
$230$	−0.188007	−	0.435850i	−0.0123968	−	0.0287391i
$231$	−4.93846	+	6.80691i	−0.324927	+	0.447862i
$232$	−13.9125	+	6.98712i	−0.913400	+	0.458727i
$233$	18.4171	+	6.70328i	1.20654	+	0.439146i	0.865504	−	0.500902i	$-0.166998\pi$
$233$	18.4171	+	6.70328i	1.20654	+	0.439146i	0.341040	+	0.940049i	$0.389221\pi$
$234$	28.6399	−	11.2302i	1.87225	−	0.734142i
$235$	−1.15832	+	0.421596i	−0.0755608	+	0.0275019i
$236$	−19.2501	+	20.4039i	−1.25308	+	1.32818i
$237$	−4.31352	−	13.7879i	−0.280193	−	0.895620i
$238$	−40.4163	+	26.5822i	−2.61980	+	1.72307i
$239$	8.18779	−	27.3491i	0.529624	−	1.76907i	−0.103078	−	0.994673i	$-0.532869\pi$
$239$	8.18779	−	27.3491i	0.529624	−	1.76907i	0.632702	−	0.774395i	$-0.281946\pi$
$240$	−4.99654	−	1.74922i	−0.322525	−	0.112912i
$241$	−7.26635	−	9.76041i	−0.468067	−	0.628723i	0.503922	−	0.863749i	$-0.331890\pi$
$241$	−7.26635	−	9.76041i	−0.468067	−	0.628723i	−0.971989	+	0.235026i	$0.924482\pi$
$242$	−24.5456			−1.57785
$243$	1.75719	−	15.4891i	0.112724	−	0.993626i
$244$	−44.3047			−2.83632
$245$	1.52145	+	2.04366i	0.0972017	+	0.130564i
$246$	40.2497	+	14.0909i	2.56623	+	0.898403i
$247$	−5.12189	+	17.1083i	−0.325898	+	1.08858i
$248$	−23.1772	+	15.2439i	−1.47176	+	0.967989i
$249$	−0.342947	−	1.09621i	−0.0217334	−	0.0694695i
$250$	5.73842	−	6.08237i	0.362929	−	0.384683i
$251$	4.11036	−	1.49605i	0.259444	−	0.0944298i	−0.209024	−	0.977911i	$-0.567029\pi$
$251$	4.11036	−	1.49605i	0.259444	−	0.0944298i	0.468467	+	0.883481i	$0.344806\pi$
$252$	−8.28821	+	54.8749i	−0.522108	+	3.45679i
$253$	0.664768	+	0.241956i	0.0417936	+	0.0152116i
$254$	1.10321	−	0.554054i	0.0692216	−	0.0347644i
$255$	−1.58650	+	2.18675i	−0.0993504	+	0.136939i
$256$	−6.96159	−	16.1388i	−0.435099	−	1.00867i
$257$	−25.7692	−	3.01199i	−1.60744	−	0.187883i	−0.735511	−	0.677513i	$-0.763058\pi$
$257$	−25.7692	−	3.01199i	−1.60744	−	0.187883i	−0.871930	+	0.489630i	$0.837132\pi$
$258$	−15.8532	+	3.96407i	−0.986977	+	0.246792i
$259$	−4.60134	−	3.02635i	−0.285913	−	0.188048i
$260$	−4.68555	+	3.93164i	−0.290585	+	0.243830i
$261$	5.43227	+	3.38422i	0.336249	+	0.209478i
$262$	−13.9936	−	11.7420i	−0.864528	−	0.725425i
$263$	8.16665	+	27.2785i	0.503577	+	1.68207i	0.710491	+	0.703706i	$0.248473\pi$
$263$	8.16665	+	27.2785i	0.503577	+	1.68207i	−0.206914	+	0.978359i	$0.566342\pi$
$264$	14.1371	−	7.31926i	0.870077	−	0.450470i
$265$	2.07011	+	1.03965i	0.127166	+	0.0638651i
$266$	−31.3234	−	33.2008i	−1.92056	−	2.03567i
$267$	−2.89251	+	0.0356195i	−0.177019	+	0.00217988i
$268$	0.409956	−	0.950385i	0.0250421	−	0.0580540i
$269$	14.0246	−	24.2913i	0.855093	−	1.48106i	−0.0214661	−	0.999770i	$-0.506833\pi$
$269$	14.0246	−	24.2913i	0.855093	−	1.48106i	0.876559	−	0.481295i	$-0.159833\pi$
$270$	0.921720	+	4.29338i	0.0560941	+	0.261287i
$271$	5.55847	+	9.62755i	0.337653	+	0.584832i	0.983991	−	0.178219i	$-0.0570337\pi$
$271$	5.55847	+	9.62755i	0.337653	+	0.584832i	−0.646338	+	0.763051i	$0.723700\pi$
$272$	45.0773	−	5.26878i	2.73321	−	0.319466i
$273$	20.3219	+	16.6300i	1.22994	+	1.00649i
$274$	50.3918	−	11.9431i	3.04428	−	0.721508i
$275$	0.358470	+	6.15470i	0.0216166	+	0.371142i
$276$	4.62991	−	0.599035i	0.278688	−	0.0360577i
$277$	10.6239	+	2.51790i	0.638326	+	0.151286i	0.537021	−	0.843569i	$-0.319550\pi$
$277$	10.6239	+	2.51790i	0.638326	+	0.151286i	0.101306	+	0.994855i	$0.467698\pi$
$278$	7.00161	−	39.7081i	0.419929	−	2.38153i
$279$	10.3142	+	4.86573i	0.617496	+	0.291304i
$280$	−1.58327	−	8.97919i	−0.0946187	−	0.536609i
$281$	0.272736	−	4.68269i	0.0162701	−	0.279346i	−0.980354	−	0.197246i	$-0.936800\pi$
$281$	0.272736	−	4.68269i	0.0162701	−	0.279346i	0.996624	−	0.0821001i	$-0.0261627\pi$
$282$	−1.20978	−	17.1337i	−0.0720416	−	1.02030i
$283$	−19.3162	+	25.9462i	−1.14823	+	1.54234i	−0.353435	+	0.935459i	$0.614987\pi$
$283$	−19.3162	+	25.9462i	−1.14823	+	1.54234i	−0.794794	+	0.606880i	$0.792421\pi$
$284$	34.1735	−	45.9030i	2.02783	−	2.72384i
$285$	−2.29195	−	1.11594i	−0.135763	−	0.0661023i
$286$	0.750951	−	12.8933i	0.0444046	−	0.762398i
$287$	6.32103	+	35.8484i	0.373119	+	2.11606i
$288$	17.3062	−	24.4827i	1.01978	−	1.44265i
$289$	1.06984	−	6.06738i	0.0629319	−	0.356905i
$290$	−1.75431	−	0.415779i	−0.103017	−	0.0244154i
$291$	−16.9476	−	22.1889i	−0.993487	−	1.30074i
$292$	2.19114	+	37.6205i	0.128227	+	2.20157i
$293$	19.4786	−	4.61650i	1.13795	−	0.269699i	0.381894	−	0.924206i	$-0.375272\pi$
$293$	19.4786	−	4.61650i	1.13795	−	0.269699i	0.756056	+	0.654507i	$0.227124\pi$
$294$	−33.2090	+	12.5523i	−1.93679	+	0.732065i
$295$	−1.88179	+	0.219950i	−0.109562	+	0.0128060i
$296$	5.21271	+	9.02868i	0.302983	+	0.524781i
$297$	−5.59693	−	3.39186i	−0.324767	−	0.196815i
$298$	−11.2753	+	19.5294i	−0.653161	+	1.13131i
$299$	0.874916	−	2.02828i	0.0505977	−	0.117299i
$300$	20.7748	+	34.9811i	1.19944	+	2.01964i
$301$	−9.57224	−	10.1460i	−0.551735	−	0.584804i
$302$	−7.06011	−	3.54572i	−0.406264	−	0.204033i
$303$	−0.274524	+	5.98143i	−0.0157710	+	0.343624i
$304$	12.2818	+	41.0241i	0.704411	+	2.35290i
$305$	−2.29227	−	1.92344i	−0.131255	−	0.110136i
$306$	−23.2171	−	29.6336i	−1.32723	−	1.69404i
$307$	−4.16550	+	3.49527i	−0.237738	+	0.199486i	−0.753871	−	0.657023i	$-0.771816\pi$
$307$	−4.16550	+	3.49527i	−0.237738	+	0.199486i	0.516133	+	0.856509i	$0.327371\pi$
$308$	19.4663	+	12.8032i	1.10920	+	0.729530i
$309$	7.47981	+	7.73506i	0.425511	+	0.440032i
$310$	−3.19082	−	0.372954i	−0.181227	−	0.0211823i
$311$	4.35270	+	10.0907i	0.246819	+	0.572191i	0.995918	−	0.0902679i	$-0.0287723\pi$
$311$	4.35270	+	10.0907i	0.246819	+	0.572191i	−0.749099	+	0.662459i	$0.769513\pi$
$312$	−20.2489	−	45.3969i	−1.14637	−	2.57009i
$313$	22.1598	−	11.1291i	1.25255	−	0.629053i	0.306127	−	0.951991i	$-0.400967\pi$
$313$	22.1598	−	11.1291i	1.25255	−	0.629053i	0.946420	+	0.322938i	$0.104670\pi$
$314$	−22.7953	−	8.29683i	−1.28642	−	0.468217i
$315$	−2.81116	+	2.47933i	−0.158391	+	0.139695i
$316$	−37.6119	+	13.6896i	−2.11583	+	0.770100i
$317$	−16.0462	+	17.0080i	−0.901246	+	0.955265i	−0.999203	−	0.0399254i	$-0.987288\pi$
$317$	−16.0462	+	17.0080i	−0.901246	+	0.955265i	0.0979563	+	0.995191i	$0.468769\pi$
$318$	−21.8605	+	23.7499i	−1.22587	+	1.33183i
$319$	2.24495	−	1.47652i	0.125693	−	0.0826695i
$320$	−0.669080	+	2.23488i	−0.0374027	+	0.124934i
$321$	2.03141	−	1.74763i	0.113382	−	0.0975431i
$322$	3.37146	+	4.52866i	0.187884	+	0.252372i
$323$	21.8540			1.21599
$324$	−43.0913	−	2.89579i	−2.39396	−	0.160877i
$325$	19.2505			1.06783
$326$	3.76132	+	5.05233i	0.208320	+	0.279823i
$327$	−4.04162	−	21.3783i	−0.223502	−	1.18223i
$328$	19.7629	−	66.0128i	1.09123	−	3.64495i
$329$	12.2496	−	8.05668i	0.675342	−	0.444179i
$330$	1.79896	+	0.403032i	0.0990294	+	0.0221862i
$331$	10.7575	−	11.4023i	0.591288	−	0.626728i	−0.360767	−	0.932656i	$-0.617485\pi$
$331$	10.7575	−	11.4023i	0.591288	−	0.626728i	0.952055	+	0.305928i	$0.0989666\pi$
$332$	−2.99034	+	1.08840i	−0.164116	+	0.0597335i
$333$	2.05089	−	3.76333i	0.112388	−	0.206229i
$334$	−1.23403	−	0.449151i	−0.0675233	−	0.0245765i
$335$	0.0624706	−	0.0313739i	0.00341313	−	0.00171414i
$336$	62.6262	+	6.53933i	3.41654	+	0.356750i
$337$	−3.81544	−	8.84517i	−0.207840	−	0.481827i	0.782128	−	0.623118i	$-0.214134\pi$
$337$	−3.81544	−	8.84517i	−0.207840	−	0.481827i	−0.989968	+	0.141290i	$0.954875\pi$
$338$	−6.38721	−	0.746558i	−0.347418	−	0.0406074i
$339$	−9.31772	+	32.5781i	−0.506069	+	1.76940i
$340$	6.25363	+	4.11308i	0.339151	+	0.223063i
$341$	3.66771	−	3.07758i	0.198618	−	0.166660i
$342$	23.7325	−	26.4296i	1.28331	−	1.42915i
$343$	−2.54270	−	2.13358i	−0.137293	−	0.115203i
$344$	7.57303	+	25.2957i	0.408310	+	1.36385i
$345$	0.265552	+	0.170009i	0.0142968	+	0.00915299i
$346$	−12.4381	−	6.24664i	−0.668676	−	0.335822i
$347$	−14.6868	−	15.5671i	−0.788427	−	0.835683i	0.201170	−	0.979556i	$-0.435526\pi$
$347$	−14.6868	−	15.5671i	−0.788427	−	0.835683i	−0.989596	+	0.143873i	$0.954044\pi$
$348$	8.67626	−	15.4644i	0.465096	−	0.828979i
$349$	−12.2198	+	28.3286i	−0.654108	+	1.51639i	0.190882	+	0.981613i	$0.438865\pi$
$349$	−12.2198	+	28.3286i	−0.654108	+	1.51639i	−0.844991	+	0.534781i	$0.820394\pi$
$350$	−24.6012	+	42.6106i	−1.31499	+	2.27763i
$351$	−11.5892	+	16.8309i	−0.618588	+	0.898367i
$352$	−6.29361	−	10.9008i	−0.335450	−	0.581017i
$353$	−19.9661	+	2.33371i	−1.06269	+	0.124211i	−0.629429	−	0.777058i	$-0.716711\pi$
$353$	−19.9661	+	2.33371i	−1.06269	+	0.124211i	−0.433261	+	0.901268i	$0.642637\pi$
$354$	4.26384	−	26.0535i	0.226620	−	1.38473i
$355$	3.76093	−	0.891357i	0.199609	−	0.0473083i
$356$	0.465998	+	8.00088i	0.0246978	+	0.424046i
$357$	12.3633	−	29.6604i	0.654336	−	1.56979i
$358$	−45.9797	−	10.8974i	−2.43010	−	0.575945i
$359$	−2.90565	+	16.4788i	−0.153354	+	0.869715i	0.806921	+	0.590660i	$0.201132\pi$
$359$	−2.90565	+	16.4788i	−0.153354	+	0.869715i	−0.960275	+	0.279056i	$0.909979\pi$
$360$	6.86185	−	1.80585i	0.361651	−	0.0951769i
$361$	0.281455	+	1.59621i	0.0148134	+	0.0840111i
$362$	−1.77810	+	30.5288i	−0.0934550	+	1.60456i
$363$	13.5113	−	9.12680i	0.709158	−	0.479033i
$364$	43.4443	−	58.3558i	2.27710	−	3.05868i
$365$	−1.51989	+	2.04156i	−0.0795546	+	0.106860i
$366$	34.5521	−	23.3398i	1.80607	−	1.21999i
$367$	−1.41904	+	24.3640i	−0.0740733	+	1.27179i	0.732546	+	0.680718i	$0.238332\pi$
$367$	−1.41904	+	24.3640i	−0.0740733	+	1.27179i	−0.806619	+	0.591072i	$0.798705\pi$
$368$	−0.919785	−	5.21636i	−0.0479471	−	0.271922i
$369$	−27.3951	+	7.20966i	−1.42613	+	0.375320i
$370$	−0.209648	+	1.18897i	−0.0108991	+	0.0618118i
$371$	−26.8105	−	6.35420i	−1.39193	−	0.329893i
$372$	12.1564	−	29.1640i	0.630280	−	1.51208i
$373$	−0.753460	−	12.9364i	−0.0390127	−	0.669822i	−0.959960	−	0.280136i	$-0.909621\pi$
$373$	−0.753460	−	12.9364i	−0.0390127	−	0.669822i	0.920948	−	0.389686i	$-0.127416\pi$
$374$	−15.3787	+	3.64481i	−0.795212	+	0.188469i
$375$	−0.897135	+	5.48179i	−0.0463279	+	0.283079i
$376$	−27.5667	+	3.22208i	−1.42164	+	0.166166i
$377$	−4.19503	−	7.26601i	−0.216055	−	0.374219i
$378$	−22.4444	−	47.1617i	−1.15441	−	2.42573i
$379$	5.56867	−	9.64522i	0.286043	−	0.495442i	−0.686818	−	0.726829i	$-0.740993\pi$
$379$	5.56867	−	9.64522i	0.286043	−	0.495442i	0.972862	+	0.231387i	$0.0743265\pi$
$380$	−2.79737	+	6.48502i	−0.143502	+	0.332675i
$381$	−0.401255	+	0.715190i	−0.0205569	+	0.0366403i
$382$	35.5874	+	37.7204i	1.82081	+	1.92995i
$383$	−28.3677	−	14.2468i	−1.44952	−	0.727977i	−0.462209	−	0.886771i	$-0.652943\pi$
$383$	−28.3677	−	14.2468i	−1.44952	−	0.727977i	−0.987312	+	0.158795i	$0.949239\pi$
$384$	1.77926	+	1.13910i	0.0907977	+	0.0581296i
$385$	0.451325	+	1.50753i	0.0230017	+	0.0768309i
$386$	31.8746	+	26.7459i	1.62237	+	1.36133i
$387$	7.25252	−	8.07674i	0.368666	−	0.410564i
$388$	−59.2579	+	49.7233i	−3.00836	+	2.52432i
$389$	−5.73145	−	3.76963i	−0.290596	−	0.191128i	0.395837	−	0.918321i	$-0.370454\pi$
$389$	−5.73145	−	3.76963i	−0.290596	−	0.191128i	−0.686434	+	0.727193i	$0.740825\pi$
$390$	1.58294	−	5.53453i	0.0801553	−	0.280252i
$391$	−2.68487	−	0.313816i	−0.135780	−	0.0158704i
$392$	22.7214	+	52.6742i	1.14761	+	2.66045i
$393$	12.0689	+	1.26022i	0.608795	+	0.0635695i
$394$	−15.4769	+	7.77281i	−0.779717	+	0.391588i
$395$	−2.54031	−	0.924598i	−0.127817	−	0.0465216i
$396$	−8.67647	+	15.9211i	−0.436009	+	0.800064i
$397$	3.49386	−	1.27166i	0.175352	−	0.0638229i	−0.252852	−	0.967505i	$-0.581369\pi$
$397$	3.49386	−	1.27166i	0.175352	−	0.0638229i	0.428204	+	0.903682i	$0.359146\pi$
$398$	10.1309	−	10.7381i	0.507815	−	0.538253i
$399$	29.5872	+	6.62860i	1.48121	+	0.331845i
$400$	38.5669	−	25.3658i	1.92834	−	1.26829i
$401$	−9.50803	+	31.7590i	−0.474808	+	1.58597i	0.300107	+	0.953905i	$0.402978\pi$
$401$	−9.50803	+	31.7590i	−0.474808	+	1.58597i	−0.774916	+	0.632065i	$0.782208\pi$
$402$	0.180950	+	0.957145i	0.00902497	+	0.0477381i
$403$	−8.92751	−	11.9917i	−0.444711	−	0.597351i
$404$	16.5892			0.825346
$405$	−2.10377	−	2.02059i	−0.104537	−	0.100404i
$406$	21.4442			1.06426
$407$	−1.07449	−	1.44329i	−0.0532606	−	0.0715413i
$408$	−46.1130	+	39.6711i	−2.28293	+	1.96401i
$409$	−6.97378	+	23.2940i	−0.344831	+	1.15182i	0.593139	+	0.805100i	$0.297888\pi$
$409$	−6.97378	+	23.2940i	−0.344831	+	1.15182i	−0.937970	+	0.346716i	$0.887297\pi$
$410$	6.66707	−	4.38500i	0.329263	−	0.216560i
$411$	−23.2977	+	25.3113i	−1.14919	+	1.24852i
$412$	20.4577	−	21.6839i	1.00788	−	1.06829i
$413$	21.1759	−	7.70738i	1.04200	−	0.379255i
$414$	−3.29517	+	2.90621i	−0.161949	+	0.142832i
$415$	−0.201968	−	0.0735104i	−0.00991423	−	0.00360848i
$416$	−35.1227	+	17.6393i	−1.72203	+	0.864837i
$417$	10.9106	+	24.4610i	0.534295	+	1.19786i
$418$	−5.90667	−	13.6932i	−0.288905	−	0.669757i
$419$	−5.60280	−	0.654873i	−0.273714	−	0.0319926i	−0.0218717	−	0.999761i	$-0.506963\pi$
$419$	−5.60280	−	0.654873i	−0.273714	−	0.0319926i	−0.251843	+	0.967768i	$0.581037\pi$
$420$	7.21896	+	7.46531i	0.352249	+	0.364270i
$421$	−27.1935	−	17.8854i	−1.32533	−	0.871683i	−0.327998	−	0.944678i	$-0.606374\pi$
$421$	−27.1935	−	17.8854i	−1.32533	−	0.871683i	−0.997332	+	0.0729952i	$0.976744\pi$
$422$	30.5163	−	25.6062i	1.48551	−	1.24649i
$423$	7.03677	+	8.98151i	0.342139	+	0.436696i
$424$	39.9553	+	33.5265i	1.94040	+	1.62819i
$425$	−6.75634	−	22.5677i	−0.327730	−	1.09470i
$426$	−2.46926	+	53.8012i	−0.119636	+	2.60668i
$427$	31.8059	+	15.9735i	1.53920	+	0.773013i
$428$	−5.09483	−	5.40020i	−0.246268	−	0.261029i
$429$	4.38077	+	7.37643i	0.211505	+	0.356137i
$430$	−1.21114	+	2.80775i	−0.0584066	+	0.135402i
$431$	−0.705902	+	1.22266i	−0.0340021	+	0.0588934i	−0.882526	−	0.470264i	$-0.844159\pi$
$431$	−0.705902	+	1.22266i	−0.0340021	+	0.0588934i	0.848524	+	0.529158i	$0.177492\pi$
$432$	−1.04053	+	48.9902i	−0.0500625	+	2.35704i
$433$	−3.07047	−	5.31820i	−0.147557	−	0.255576i	0.782767	−	0.622315i	$-0.213808\pi$
$433$	−3.07047	−	5.31820i	−0.147557	−	0.255576i	−0.930324	+	0.366739i	$0.880474\pi$
$434$	37.9524	−	4.43600i	1.82177	−	0.212935i
$435$	1.12027	−	0.423438i	0.0537128	−	0.0203023i
$436$	−58.6540	+	13.9013i	−2.80902	+	0.665749i
$437$	−0.148305	−	2.54629i	−0.00709438	−	0.121806i
$438$	−21.5273	−	28.1849i	−1.02862	−	1.34673i
$439$	−12.9504	−	3.06929i	−0.618087	−	0.146489i	−0.0903681	−	0.995908i	$-0.528804\pi$
$439$	−12.9504	−	3.06929i	−0.618087	−	0.146489i	−0.527719	+	0.849419i	$0.676952\pi$
$440$	0.517279	−	2.93364i	0.0246603	−	0.139856i
$441$	13.6128	−	19.2576i	0.648226	−	0.917028i
$442$	8.56950	+	48.6000i	0.407610	+	2.31167i
$443$	0.254079	−	4.36237i	0.0120717	−	0.207263i	−0.986879	−	0.161462i	$-0.948379\pi$
$443$	0.254079	−	4.36237i	0.0120717	−	0.207263i	0.998951	−	0.0458006i	$-0.0145839\pi$
$444$	−10.6760	−	5.19809i	−0.506662	−	0.246690i
$445$	−0.323240	+	0.434186i	−0.0153230	+	0.0205824i
$446$	31.6355	−	42.4938i	1.49798	−	2.01214i
$447$	−1.05507	−	14.9426i	−0.0499032	−	0.706760i
$448$	1.61340	−	27.7010i	0.0762260	−	1.30875i
$449$	−5.92614	−	33.6088i	−0.279672	−	1.58610i	−0.723719	−	0.690095i	$-0.757569\pi$
$449$	−5.92614	−	33.6088i	−0.279672	−	1.58610i	0.444047	−	0.896003i	$-0.353542\pi$
$450$	−34.6299	−	16.3366i	−1.63247	−	0.770117i
$451$	−2.06518	+	11.7122i	−0.0972454	+	0.551506i
$452$	91.3478	+	21.6498i	4.29664	+	1.01832i
$453$	5.20468	−	0.673402i	0.244537	−	0.0316392i
$454$	0.152859	+	2.62449i	0.00717402	+	0.123173i
$455$	4.78121	−	1.13317i	0.224147	−	0.0531237i
$456$	−44.4194	−	36.3497i	−2.08013	−	1.70223i
$457$	−2.59552	+	0.303373i	−0.121413	+	0.0141912i	−0.176583	−	0.984286i	$-0.556504\pi$
$457$	−2.59552	+	0.303373i	−0.121413	+	0.0141912i	0.0551692	+	0.998477i	$0.482430\pi$
$458$	13.2149	+	22.8889i	0.617493	+	1.06953i
$459$	23.7987	+	7.67916i	1.11083	+	0.358432i
$460$	0.436791	−	0.756545i	0.0203655	−	0.0352741i
$461$	2.32730	−	5.39528i	0.108393	−	0.251283i	−0.855383	−	0.517996i	$-0.826678\pi$
$461$	2.32730	−	5.39528i	0.108393	−	0.251283i	0.963776	+	0.266713i	$0.0859375\pi$
$462$	−21.9260	+	0.270005i	−1.02009	+	0.0125618i
$463$	−17.4881	−	18.5363i	−0.812742	−	0.861456i	0.179757	−	0.983711i	$-0.442469\pi$
$463$	−17.4881	−	18.5363i	−0.812742	−	0.861456i	−0.992499	+	0.122255i	$0.960987\pi$
$464$	−17.9786	−	9.02922i	−0.834638	−	0.419171i
$465$	1.89508	−	0.981151i	0.0878823	−	0.0454998i
$466$	14.6566	+	48.9564i	0.678954	+	2.26786i
$467$	−20.6922	−	17.3628i	−0.957522	−	0.803456i	0.0230263	−	0.999735i	$-0.492670\pi$
$467$	−20.6922	−	17.3628i	−0.957522	−	0.803456i	−0.980548	+	0.196279i	$0.937114\pi$
$468$	48.0538	+	29.9368i	2.22129	+	1.38383i
$469$	−0.636953	+	0.534467i	−0.0294118	+	0.0246794i
$470$	−2.68533	−	1.76617i	−0.123865	−	0.0814675i
$471$	15.6328	−	3.90897i	0.720323	−	0.180116i
$472$	−42.3700	−	4.95234i	−1.95024	−	0.227950i
$473$	−1.80505	−	4.18457i	−0.0829961	−	0.192407i
$474$	22.1208	−	30.4901i	1.01604	−	1.40046i
$475$	19.8637	−	9.97594i	0.911411	−	0.457728i
$476$	−83.6593	−	30.4495i	−3.83452	−	1.39565i
$477$	3.20227	−	21.2017i	0.146622	−	0.970758i
$478$	69.9491	−	25.4594i	3.19940	−	1.16449i
$479$	17.8649	−	18.9357i	0.816270	−	0.865196i	−0.176614	−	0.984280i	$-0.556514\pi$
$479$	17.8649	−	18.9357i	0.816270	−	0.865196i	0.992884	+	0.119084i	$0.0379959\pi$
$480$	−1.67510	−	5.35437i	−0.0764577	−	0.244392i
$481$	−4.69411	+	3.08736i	−0.214033	+	0.140772i
$482$	9.09965	−	30.3949i	0.414478	−	1.38445i
$483$	−3.53974	−	1.23921i	−0.161064	−	0.0563862i
$484$	−26.9759	−	36.2349i	−1.22618	−	1.64704i
$485$	−5.22461			−0.237238
$486$	35.1313	−	20.4422i	1.59359	−	0.927277i
$487$	−7.41759			−0.336123			−0.168061	−	0.985777i	$-0.553751\pi$
$487$	−7.41759			−0.336123			−0.168061	+	0.985777i	$0.553751\pi$
$488$	−40.2335	−	54.0430i	−1.82129	−	2.44641i
$489$	−3.94905	−	1.38251i	−0.178582	−	0.0625193i
$490$	−1.90531	+	6.36417i	−0.0860730	+	0.287504i
$491$	14.0070	−	9.21253i	0.632126	−	0.415756i	−0.192609	−	0.981276i	$-0.561695\pi$
$491$	14.0070	−	9.21253i	0.632126	−	0.415756i	0.824735	+	0.565520i	$0.191324\pi$
$492$	23.4335	+	74.9038i	1.05646	+	3.37692i
$493$	−7.04576	+	7.46807i	−0.317325	+	0.336345i
$494$	−43.7568	+	15.9262i	−1.96871	+	0.716553i
$495$	−1.14011	+	0.447057i	−0.0512440	+	0.0200937i
$496$	−33.6868	−	12.2610i	−1.51258	−	0.550534i
$497$	−41.0826	+	20.6325i	−1.84281	+	0.925493i
$498$	1.75872	−	2.42413i	0.0788101	−	0.108628i
$499$	7.23169	+	16.7649i	0.323735	+	0.750501i	0.999905	+	0.0137564i	$0.00437895\pi$
$499$	7.23169	+	16.7649i	0.323735	+	0.750501i	−0.676171	+	0.736745i	$0.736362\pi$
$500$	15.2855	+	1.78662i	0.683590	+	0.0799002i
$501$	0.846289	−	0.211613i	0.0378094	−	0.00945418i
$502$	9.52901	+	6.26733i	0.425301	+	0.279725i
$503$	−20.5047	+	17.2055i	−0.914261	+	0.767156i	−0.972925	−	0.231121i	$-0.925761\pi$
$503$	−20.5047	+	17.2055i	−0.914261	+	0.767156i	0.0586635	+	0.998278i	$0.481316\pi$
$504$	−74.4630	+	39.7223i	−3.31685	+	1.76937i
$505$	0.858307	+	0.720205i	0.0381942	+	0.0320487i
$506$	0.529032	+	1.76709i	0.0235183	+	0.0785567i
$507$	3.79347	−	1.96401i	0.168474	−	0.0872248i
$508$	2.03035	+	1.01968i	0.0900822	+	0.0452410i
$509$	20.1524	+	21.3603i	0.893241	+	0.946780i	0.998865	−	0.0476263i	$-0.0151657\pi$
$509$	20.1524	+	21.3603i	0.893241	+	0.946780i	−0.105625	+	0.994406i	$0.533684\pi$
$510$	−7.04381	+	0.0867402i	−0.311905	+	0.00384092i
$511$	11.9906	−	27.7974i	0.530433	−	1.22968i
$512$	21.6947	−	37.5763i	0.958780	−	1.66066i
$513$	−3.23635	+	23.3728i	−0.142888	+	1.03194i
$514$	−33.8245	−	58.5858i	−1.49194	−	2.58411i
$515$	1.99984	−	0.233748i	0.0881234	−	0.0103002i
$516$	−23.2747	−	19.0464i	−1.02461	−	0.838469i
$517$	4.66105	−	1.10469i	0.204993	−	0.0485841i
$518$	−0.834966	−	14.3358i	−0.0366863	−	0.629880i
$519$	9.16931	−	1.18636i	0.402488	−	0.0520754i
$520$	−9.05081	−	2.14508i	−0.396904	−	0.0940680i
$521$	−1.78086	+	10.0998i	−0.0780209	+	0.442479i	0.920625	+	0.390449i	$0.127680\pi$
$521$	−1.78086	+	10.0998i	−0.0780209	+	0.442479i	−0.998646	+	0.0520298i	$0.983431\pi$
$522$	1.38028	+	16.6309i	0.0604134	+	0.727916i
$523$	−5.81644	−	32.9867i	−0.254335	−	1.44241i	−0.797774	−	0.602957i	$-0.793989\pi$
$523$	−5.81644	−	32.9867i	−0.254335	−	1.44241i	0.543439	−	0.839449i	$-0.317122\pi$
$524$	1.95478	−	33.5623i	0.0853951	−	1.46618i
$525$	−2.30203	−	32.6027i	−0.100469	−	1.42290i
$526$	−44.3367	+	59.5545i	−1.93317	+	2.59670i
$527$	−10.9249	+	14.6746i	−0.475894	+	0.639237i
$528$	18.4962	+	9.00570i	0.804946	+	0.391923i
$529$	1.31899	−	22.6461i	0.0573473	−	0.984615i
$530$	1.04886	+	5.94840i	0.0455597	+	0.258382i
$531$	7.34042	+	15.9267i	0.318547	+	0.691160i
$532$	14.5873	−	82.7284i	0.632438	−	3.58673i
$533$	36.1343	+	8.56398i	1.56515	+	0.370947i
$534$	−4.57829	−	5.99418i	−0.198122	−	0.259394i
$535$	−0.0291558	−	0.500586i	−0.00126052	−	0.0216422i
$536$	1.53157	−	0.362988i	0.0661536	−	0.0156787i
$537$	29.3617	−	11.0981i	1.26705	−	0.478919i
$538$	72.6418	−	8.49061i	3.13181	−	0.366056i
$539$	−4.95043	−	8.57440i	−0.213230	−	0.369325i
$540$	−5.32502	+	6.07913i	−0.229152	+	0.261604i
$541$	−19.3141	+	33.4530i	−0.830377	+	1.43826i	0.0673627	+	0.997729i	$0.478542\pi$
$541$	−19.3141	+	33.4530i	−0.830377	+	1.43826i	−0.897740	+	0.440526i	$0.854792\pi$
$542$	−11.4810	+	26.6161i	−0.493153	+	1.14326i
$543$	−10.3728	−	17.4659i	−0.445139	−	0.749534i
$544$	33.0059	+	34.9842i	1.41512	+	1.49994i
$545$	−3.63819	−	1.82717i	−0.155843	−	0.0782673i
$546$	−3.13914	+	68.3967i	−0.134343	+	2.92711i
$547$	3.25227	+	10.8633i	0.139057	+	0.464482i	0.998941	−	0.0460067i	$-0.0146496\pi$
$547$	3.25227	+	10.8633i	0.139057	+	0.464482i	−0.859884	+	0.510489i	$0.829464\pi$
$548$	73.0118	+	61.2642i	3.11891	+	2.61708i
$549$	−10.3409	+	25.6950i	−0.441341	+	1.09664i
$550$	−12.3143	+	10.3329i	−0.525084	+	0.440598i
$551$	−8.09405	−	5.32354i	−0.344818	−	0.226790i
$552$	4.93516	+	5.10358i	0.210054	+	0.217223i
$553$	31.9368	+	3.73288i	1.35809	+	0.158738i
$554$	11.2758	+	26.1402i	0.479062	+	1.11059i
$555$	−0.326695	−	0.732431i	−0.0138674	−	0.0310900i
$556$	66.3130	−	33.3036i	2.81230	−	1.41239i
$557$	11.1013	+	4.04055i	0.470377	+	0.171203i	0.566323	−	0.824183i	$-0.308365\pi$
$557$	11.1013	+	4.04055i	0.470377	+	0.171203i	−0.0959459	+	0.995387i	$0.530588\pi$
$558$	5.88316	+	29.1482i	0.249054	+	1.23394i
$559$	−13.3718	+	4.86695i	−0.565568	+	0.205850i
$560$	8.08565	−	8.57028i	0.341681	−	0.362161i
$561$	7.11002	−	7.72456i	0.300185	−	0.326131i
$562$	10.2184	−	6.72078i	0.431039	−	0.283499i
$563$	−5.88403	+	19.6540i	−0.247982	+	0.828319i	0.739847	+	0.672775i	$0.234898\pi$
$563$	−5.88403	+	19.6540i	−0.247982	+	0.828319i	−0.987829	+	0.155543i	$0.950287\pi$
$564$	23.9637	−	20.6160i	1.00905	−	0.868092i
$565$	3.78631	+	5.08590i	0.159291	+	0.213966i
$566$	−84.3423			−3.54517
$567$	29.8908	+	17.6149i	1.25529	+	0.739756i
$568$	87.0259			3.65152
$569$	−9.72800	−	13.0670i	−0.407819	−	0.547796i	0.550001	−	0.835164i	$-0.314627\pi$
$569$	−9.72800	−	13.0670i	−0.407819	−	0.547796i	−0.957820	+	0.287368i	$0.907220\pi$
$570$	−1.23473	−	6.53115i	−0.0517170	−	0.273560i
$571$	−5.80130	+	19.3777i	−0.242777	+	0.810931i	0.746564	+	0.665313i	$0.231702\pi$
$571$	−5.80130	+	19.3777i	−0.242777	+	0.810931i	−0.989341	+	0.145617i	$0.953483\pi$
$572$	19.8588	−	13.0613i	0.830337	−	0.546121i
$573$	−33.6149	−	7.53095i	−1.40428	−	0.314610i
$574$	−65.1341	+	69.0382i	−2.71865	+	2.88160i
$575$	−2.58360	+	0.940353i	−0.107744	+	0.0392154i
$576$	21.5872	−	0.531747i	0.899466	−	0.0221561i
$577$	3.36027	+	1.22304i	0.139890	+	0.0509157i	0.411016	−	0.911628i	$-0.365174\pi$
$577$	3.36027	+	1.22304i	0.139890	+	0.0509157i	−0.271126	+	0.962544i	$0.587396\pi$
$578$	14.3556	−	7.20967i	0.597116	−	0.299883i
$579$	−27.4905	−	2.87052i	−1.14247	−	0.119295i
$580$	−1.31422	−	3.04671i	−0.0545701	−	0.126508i
$581$	2.53914	+	0.296783i	0.105341	+	0.0123126i
$582$	20.0194	−	69.9950i	0.829830	−	2.90139i
$583$	−7.52109	−	4.94670i	−0.311492	−	0.204871i
$584$	−43.8997	+	36.8362i	−1.81658	+	1.52429i
$585$	1.18657	+	3.63510i	0.0490586	+	0.150293i
$586$	39.9845	+	33.5510i	1.65174	+	1.38598i
$587$	2.27715	+	7.60620i	0.0939879	+	0.313941i	0.992036	−	0.125956i	$-0.0401999\pi$
$587$	2.27715	+	7.60620i	0.0939879	+	0.313941i	−0.898048	+	0.439898i	$0.855015\pi$
$588$	−55.0270	−	35.2289i	−2.26928	−	1.45282i
$589$	−15.4262	−	7.74735i	−0.635627	−	0.319224i
$590$	−3.39007	−	3.59327i	−0.139567	−	0.147933i
$591$	5.62920	−	10.0334i	0.231554	−	0.412718i
$592$	−5.33615	+	12.3706i	−0.219314	+	0.508428i
$593$	−13.0180	+	22.5478i	−0.534584	+	0.925926i	0.464599	+	0.885521i	$0.346198\pi$
$593$	−13.0180	+	22.5478i	−0.534584	+	0.925926i	−0.999183	+	0.0404055i	$0.987135\pi$
$594$	−1.62069	−	16.9872i	−0.0664979	−	0.696993i
$595$	−3.00650	−	5.20740i	−0.123254	−	0.213483i
$596$	−41.2215	+	4.81810i	−1.68850	+	0.197357i
$597$	−1.58385	+	9.67783i	−0.0648225	+	0.396087i
$598$	5.60442	−	1.32827i	0.229182	−	0.0543170i
$599$	−1.09425	−	18.7875i	−0.0447096	−	0.767635i	−0.943931	−	0.330142i	$-0.892903\pi$
$599$	−1.09425	−	18.7875i	−0.0447096	−	0.767635i	0.899222	−	0.437493i	$-0.144134\pi$
$600$	−23.8042	+	57.1079i	−0.971804	+	2.33142i
$601$	7.82024	+	1.85343i	0.318994	+	0.0756030i	0.386994	−	0.922082i	$-0.373513\pi$
$601$	7.82024	+	1.85343i	0.318994	+	0.0756030i	−0.0679995	+	0.997685i	$0.521662\pi$
$602$	6.31568	−	35.8180i	0.257408	−	1.45983i
$603$	−0.455501	−	0.459583i	−0.0185494	−	0.0187157i
$604$	−2.52485	−	14.3191i	−0.102734	−	0.582636i
$605$	0.177402	−	3.04588i	0.00721242	−	0.123833i
$606$	−12.9375	+	8.73923i	−0.525550	+	0.355007i
$607$	11.5794	−	15.5538i	0.469992	−	0.631309i	−0.502407	−	0.864631i	$-0.667552\pi$
$607$	11.5794	−	15.5538i	0.469992	−	0.631309i	0.972400	+	0.233322i	$0.0749596\pi$
$608$	−27.1006	+	36.4024i	−1.09907	+	1.47631i
$609$	−11.8041	+	7.97362i	−0.478326	+	0.323107i
$610$	0.453667	−	7.78916i	0.0183684	−	0.315374i
$611$	−2.59729	−	14.7300i	−0.105075	−	0.595910i
$612$	18.2301	−	66.8414i	0.736908	−	2.70190i
$613$	−2.54229	+	14.4180i	−0.102682	+	0.582339i	0.889439	+	0.457054i	$0.151095\pi$
$613$	−2.54229	+	14.4180i	−0.102682	+	0.582339i	−0.992121	+	0.125284i	$0.960016\pi$
$614$	−13.7962	−	3.26976i	−0.556770	−	0.131957i
$615$	−2.03945	+	4.89277i	−0.0822385	+	0.197295i
$616$	2.06017	+	35.3717i	0.0830066	+	1.42517i
$617$	−20.1538	+	4.77655i	−0.811363	+	0.192297i	−0.615298	−	0.788294i	$-0.710964\pi$
$617$	−20.1538	+	4.77655i	−0.811363	+	0.192297i	−0.196065	+	0.980591i	$0.562816\pi$
$618$	−4.53131	+	27.6878i	−0.182276	+	1.11377i
$619$	25.7358	−	3.00809i	1.03441	−	0.120905i	0.418094	−	0.908404i	$-0.362698\pi$
$619$	25.7358	−	3.00809i	1.03441	−	0.120905i	0.616316	+	0.787499i	$0.288624\pi$
$620$	−2.95618	−	5.12026i	−0.118723	−	0.205635i
$621$	0.733226	−	2.82498i	0.0294233	−	0.113363i
$622$	−14.3271	+	24.8154i	−0.574466	+	0.995005i
$623$	2.55008	−	5.91176i	0.102167	−	0.236850i
$624$	31.4306	−	56.0214i	1.25823	−	2.24265i
$625$	−16.0823	−	17.0463i	−0.643293	−	0.681851i
$626$	57.7803	+	29.0184i	2.30937	+	1.15981i
$627$	8.34291	+	5.34122i	0.333184	+	0.213308i
$628$	−12.8043	−	42.7694i	−0.510948	−	1.70668i
$629$	5.26686	+	4.41942i	0.210004	+	0.176214i
$630$	−9.56261	−	2.01904i	−0.380983	−	0.0804405i
$631$	−13.6194	+	11.4280i	−0.542180	+	0.454943i	−0.872283	−	0.489002i	$-0.837361\pi$
$631$	−13.6194	+	11.4280i	−0.542180	+	0.454943i	0.330102	+	0.943945i	$0.392917\pi$
$632$	−50.8543	−	33.4474i	−2.02287	−	1.33046i
$633$	−7.27669	+	25.4419i	−0.289222	+	1.01123i
$634$	−60.5568	−	7.07808i	−2.40502	−	0.281106i
$635$	0.0607794	+	0.140902i	0.00241196	+	0.00559154i
$636$	−59.0852	−	6.16959i	−2.34288	−	0.244640i
$637$	−27.6269	+	13.8747i	−1.09462	+	0.549737i
$638$	6.58363	+	2.39625i	0.260648	+	0.0948683i
$639$	−18.6457	−	30.5333i	−0.737613	−	1.20788i
$640$	0.371486	−	0.135210i	0.0146843	−	0.00534464i
$641$	3.24563	−	3.44017i	0.128195	−	0.135878i	−0.660096	−	0.751181i	$-0.729485\pi$
$641$	3.24563	−	3.44017i	0.128195	−	0.135878i	0.788291	+	0.615302i	$0.210966\pi$
$642$	6.81815	+	1.52751i	0.269091	+	0.0602861i
$643$	7.04365	−	4.63268i	0.277774	−	0.182695i	−0.402976	−	0.915211i	$-0.632024\pi$
$643$	7.04365	−	4.63268i	0.277774	−	0.182695i	0.680750	+	0.732515i	$0.261654\pi$
$644$	−2.98006	+	9.95409i	−0.117431	+	0.392246i
$645$	−0.377325	−	1.99588i	−0.0148572	−	0.0785878i
$646$	34.0279	+	45.7074i	1.33881	+	1.79833i
$647$	23.1964			0.911943			0.455971	−	0.889994i	$-0.349292\pi$
$647$	23.1964			0.911943			0.455971	+	0.889994i	$0.349292\pi$
$648$	−35.5993	−	55.1925i	−1.39847	−	2.16817i
$649$	7.36248			0.289003
$650$	29.9740	+	40.2621i	1.17568	+	1.57921i
$651$	−19.2417	+	16.5537i	−0.754141	+	0.648790i
$652$	−3.32466	+	11.1051i	−0.130204	+	0.434910i
$653$	−30.1768	+	19.8476i	−1.18091	+	0.776697i	−0.979230	−	0.202755i	$-0.935011\pi$
$653$	−30.1768	+	19.8476i	−1.18091	+	0.776697i	−0.201680	+	0.979451i	$0.564640\pi$
$654$	38.4195	−	41.7402i	1.50232	−	1.63217i
$655$	1.55821	−	1.65161i	0.0608844	−	0.0645337i
$656$	83.6768	−	30.4559i	3.26703	−	1.18910i
$657$	22.3299	+	7.51003i	0.871171	+	0.292994i
$658$	35.9237	+	13.0752i	1.40045	+	0.509722i
$659$	27.0962	−	13.6082i	1.05552	−	0.530100i	0.165586	−	0.986195i	$-0.447049\pi$
$659$	27.0962	−	13.6082i	1.05552	−	0.530100i	0.889931	+	0.456095i	$0.150752\pi$
$660$	1.38211	+	3.09861i	0.0537985	+	0.120613i
$661$	−5.10606	−	11.8372i	−0.198603	−	0.460413i	0.789589	−	0.613636i	$-0.210294\pi$
$661$	−5.10606	−	11.8372i	−0.198603	−	0.460413i	−0.988192	+	0.153224i	$0.951035\pi$
$662$	40.5978	+	4.74521i	1.57788	+	0.184428i
$663$	−22.7881	−	23.5658i	−0.885017	−	0.915219i
$664$	−4.04318	−	2.65924i	−0.156906	−	0.103199i
$665$	4.34629	−	3.64697i	0.168542	−	0.141424i
$666$	11.0643	−	1.57029i	0.428733	−	0.0608477i
$667$	0.917946	+	0.770248i	0.0355430	+	0.0298241i
$668$	−0.693166	−	2.31534i	−0.0268194	−	0.0895830i
$669$	−1.61343	+	35.1540i	−0.0623788	+	1.35913i
$670$	0.162888	+	0.0818055i	0.00629292	+	0.00316042i
$671$	7.97986	+	8.45815i	0.308059	+	0.326523i
$672$	34.0741	+	57.3746i	1.31444	+	2.21327i
$673$	2.55712	−	5.92808i	0.0985698	−	0.228511i	−0.861795	−	0.507257i	$-0.830660\pi$
$673$	2.55712	−	5.92808i	0.0985698	−	0.228511i	0.960365	+	0.278746i	$0.0899188\pi$
$674$	12.5587	−	21.7523i	0.483744	−	0.837869i
$675$	25.1367	−	3.88383i	0.967510	−	0.149489i
$676$	−5.91752	−	10.2494i	−0.227597	−	0.394209i
$677$	−17.4366	+	2.03804i	−0.670142	+	0.0783284i	−0.444358	−	0.895849i	$-0.646568\pi$
$677$	−17.4366	+	2.03804i	−0.670142	+	0.0783284i	−0.225784	+	0.974177i	$0.572494\pi$
$678$	−82.6448	+	31.2380i	−3.17396	+	1.19969i
$679$	60.4678	−	14.3311i	2.32054	−	0.549978i
$680$	0.661837	+	11.3633i	0.0253803	+	0.435763i
$681$	−1.06001	−	1.38783i	−0.0406195	−	0.0531816i
$682$	12.1475	+	2.87902i	0.465153	+	0.110243i
$683$	3.16828	−	17.9682i	0.121231	−	0.687535i	−0.862244	−	0.506492i	$-0.830942\pi$
$683$	3.16828	−	17.9682i	0.121231	−	0.687535i	0.983475	−	0.181042i	$-0.0579471\pi$
$684$	65.0984	+	5.98814i	2.48910	+	0.228962i
$685$	1.11782	+	6.33946i	0.0427097	+	0.242218i
$686$	0.503230	−	8.64012i	0.0192134	−	0.329881i
$687$	−15.7850	−	7.68563i	−0.602237	−	0.293225i
$688$	−20.3764	+	27.3702i	−0.776843	+	1.04348i
$689$	−16.7853	+	22.5466i	−0.639470	+	0.858957i
$690$	0.0579067	+	0.820111i	0.00220447	+	0.0312211i
$691$	2.37017	−	40.6942i	0.0901653	−	1.54808i	−0.585379	−	0.810760i	$-0.699054\pi$
$691$	2.37017	−	40.6942i	0.0901653	−	1.54808i	0.675544	−	0.737319i	$-0.263909\pi$
$692$	−4.44812	−	25.2266i	−0.169092	−	0.958970i
$693$	11.9689	−	8.30138i	0.454661	−	0.315343i
$694$	9.69020	−	54.9559i	0.367835	−	2.08610i
$695$	4.87679	+	1.15582i	0.184987	+	0.0438428i
$696$	26.7425	−	3.46005i	1.01367	−	0.131153i
$697$	−2.64231	−	45.3666i	−0.100084	−	1.71838i
$698$	−78.2756	+	18.5517i	−2.96277	+	0.702191i
$699$	−26.2713	−	21.4986i	−0.993672	−	0.813151i
$700$	−89.9399	+	10.5125i	−3.39941	+	0.397334i
$701$	21.5739	+	37.3671i	0.814834	+	1.41133i	0.909447	+	0.415820i	$0.136505\pi$
$701$	21.5739	+	37.3671i	0.814834	+	1.41133i	−0.0946129	+	0.995514i	$0.530161\pi$
$702$	−53.2466	+	1.96789i	−2.00967	+	0.0742734i
$703$	−3.24372	+	5.61828i	−0.122339	+	0.211897i
$704$	3.59073	−	8.32425i	0.135331	−	0.313732i
$705$	2.13487	−	0.0262897i	0.0804040	−	0.000990126i
$706$	−35.9692	−	38.1252i	−1.35372	−	1.43486i
$707$	−11.9093	−	5.98105i	−0.447893	−	0.224941i
$708$	43.1468	−	22.3386i	1.62156	−	0.839537i
$709$	2.70162	+	9.02404i	0.101461	+	0.338905i	0.993614	−	0.112828i	$-0.0359911\pi$
$709$	2.70162	+	9.02404i	0.101461	+	0.338905i	−0.892153	+	0.451733i	$0.850806\pi$
$710$	7.72023	+	6.47804i	0.289735	+	0.243116i
$711$	−0.839358	+	25.0086i	−0.0314784	+	0.937898i
$712$	−9.33630	+	7.83409i	−0.349893	+	0.293595i
$713$	1.78393	+	1.17331i	0.0668088	+	0.0439409i
$714$	81.2845	−	20.3251i	3.04200	−	0.760647i
$715$	1.59451	+	0.186372i	0.0596314	+	0.00696991i
$716$	−34.4451	−	79.8528i	−1.28727	−	2.98424i
$717$	−29.0373	+	40.0235i	−1.08442	+	1.49470i
$718$	−38.9893	+	19.5812i	−1.45507	+	0.730763i
$719$	20.4128	+	7.42965i	0.761268	+	0.277079i	0.693339	−	0.720611i	$-0.256139\pi$
$719$	20.4128	+	7.42965i	0.761268	+	0.277079i	0.0679289	+	0.997690i	$0.478361\pi$
$720$	7.16707	+	5.71913i	0.267101	+	0.213140i
$721$	−22.5042	+	8.19087i	−0.838101	+	0.305044i
$722$	−2.90021	+	3.07405i	−0.107935	+	0.114404i
$723$	6.29281	+	20.1146i	0.234032	+	0.748070i
$724$	−47.0216	+	30.9266i	−1.74755	+	1.14938i
$725$	−2.99506	+	10.0042i	−0.111234	+	0.371546i
$726$	40.1263	+	14.0477i	1.48923	+	0.521359i
$727$	13.4477	+	18.0635i	0.498749	+	0.669937i	0.978208	−	0.207628i	$-0.0665743\pi$
$727$	13.4477	+	18.0635i	0.498749	+	0.669937i	−0.479459	+	0.877565i	$0.659167\pi$
$728$	110.635			4.10039
$729$	−11.7372	+	24.3154i	−0.434710	+	0.900571i
$730$	−6.63645			−0.245626
$731$	10.3987	+	13.9679i	0.384611	+	0.516622i
$732$	72.4279	+	25.3561i	2.67701	+	0.937187i
$733$	−7.81755	+	26.1124i	−0.288748	+	0.964485i	0.683386	+	0.730058i	$0.260507\pi$
$733$	−7.81755	+	26.1124i	−0.288748	+	0.964485i	−0.972134	+	0.234428i	$0.924678\pi$
$734$	−53.1664	+	34.9681i	−1.96241	+	1.29070i
$735$	−1.31760	−	4.21164i	−0.0486006	−	0.155349i
$736$	3.85216	−	4.08305i	0.141992	−	0.150503i
$737$	−0.255275	+	0.0929125i	−0.00940318	+	0.00342248i
$738$	−57.7345	−	46.0706i	−2.12524	−	1.69588i
$739$	−29.4451	−	10.7172i	−1.08316	−	0.394237i	−0.262075	−	0.965048i	$-0.584407\pi$
$739$	−29.4451	−	10.7172i	−1.08316	−	0.394237i	−0.821082	+	0.570811i	$0.806629\pi$
$740$	−1.98560	+	0.997207i	−0.0729922	+	0.0366580i
$741$	18.1643	−	25.0368i	0.667284	−	0.919749i
$742$	−28.4556	−	65.9675i	−1.04464	−	2.42174i
$743$	43.2335	+	5.05328i	1.58608	+	0.185387i	0.862939	−	0.505309i	$-0.168621\pi$
$743$	43.2335	+	5.05328i	1.58608	+	0.185387i	0.723146	+	0.690695i	$0.242695\pi$
$744$	46.6136	−	11.6557i	1.70894	−	0.427317i
$745$	−2.34192	−	1.54031i	−0.0858014	−	0.0564325i
$746$	25.8831	−	21.7185i	0.947648	−	0.795171i
$747$	−0.0667334	+	1.98832i	−0.00244165	+	0.0727488i
$748$	−22.2819	−	18.6967i	−0.814706	−	0.683620i
$749$	1.71055	+	5.71363i	0.0625020	+	0.208771i
$750$	−12.8620	+	6.65910i	−0.469653	+	0.243156i
$751$	45.8151	+	23.0092i	1.67182	+	0.839617i	0.994594	+	0.103838i	$0.0331124\pi$
$751$	45.8151	+	23.0092i	1.67182	+	0.839617i	0.677221	+	0.735779i	$0.263184\pi$
$752$	−24.6127	−	26.0880i	−0.897533	−	0.951330i
$753$	−7.57568	+	0.0932899i	−0.276073	+	0.00339967i
$754$	8.66487	−	20.0874i	0.315556	−	0.731541i
$755$	0.491017	−	0.850466i	0.0178699	−	0.0309516i
$756$	44.9547	−	84.9641i	1.63499	−	3.09012i
$757$	−6.51051	−	11.2765i	−0.236629	−	0.409853i	0.723116	−	0.690727i	$-0.242709\pi$
$757$	−6.51051	−	11.2765i	−0.236629	−	0.409853i	−0.959745	+	0.280874i	$0.909376\pi$
$758$	28.8436	−	3.37133i	1.04764	−	0.122452i
$759$	−0.948267	−	0.775995i	−0.0344199	−	0.0281668i
$760$	−10.4507	+	2.47687i	−0.379088	+	0.0898456i
$761$	1.37835	+	23.6653i	0.0499651	+	0.857868i	0.926445	+	0.376430i	$0.122848\pi$
$761$	1.37835	+	23.6653i	0.0499651	+	0.857868i	−0.876480	+	0.481438i	$0.840115\pi$
$762$	−2.12058	+	0.274369i	−0.0768206	+	0.00993935i
$763$	47.1190	+	11.1674i	1.70582	+	0.404288i
$764$	−16.5730	+	93.9902i	−0.599591	+	3.40045i
$765$	3.84505	−	2.66685i	0.139018	−	0.0964201i
$766$	−14.3730	−	81.5136i	−0.519319	−	2.94520i
$767$	1.33670	−	22.9503i	0.0482655	−	0.828687i
$768$

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.55705 + 2.09149i) q^{2} +(-1.63477 - 0.572310i) q^{3} +(-1.37629 + 4.59713i) q^{4} +(-0.270787 + 0.178099i) q^{5} +(-1.34844 - 4.31021i) q^{6} +(2.64546 - 2.80403i) q^{7} +(-6.85740 + 2.49589i) q^{8} +(2.34492 + 1.87119i) q^{9} +O(q^{10})\)	\(q+(1.55705 + 2.09149i) q^{2} +(-1.63477 - 0.572310i) q^{3} +(-1.37629 + 4.59713i) q^{4} +(-0.270787 + 0.178099i) q^{5} +(-1.34844 - 4.31021i) q^{6} +(2.64546 - 2.80403i) q^{7} +(-6.85740 + 2.49589i) q^{8} +(2.34492 + 1.87119i) q^{9} +(-0.794122 - 0.289037i) q^{10} +(1.12552 - 0.565257i) q^{11} +(4.88089 - 6.72756i) q^{12} +(-1.55767 - 3.61109i) q^{13} +(9.98370 + 1.16693i) q^{14} +(0.544602 - 0.136177i) q^{15} +(-7.87890 - 5.18204i) q^{16} +(-3.68665 + 3.09347i) q^{17} +(-0.262390 + 7.81791i) q^{18} +(-3.47862 - 2.91891i) q^{19} +(-0.446064 - 1.48996i) q^{20} +(-5.92948 + 3.06990i) q^{21} +(2.93472 + 1.47387i) q^{22} +(0.385450 + 0.408553i) q^{23} +(12.6387 - 0.155637i) q^{24} +(-1.93879 + 4.49463i) q^{25} +(5.12716 - 8.88050i) q^{26} +(-2.76250 - 4.40098i) q^{27} +(9.24954 + 16.0207i) q^{28} +(2.11898 - 0.247673i) q^{29} +(1.13279 + 0.926991i) q^{30} +(3.69897 - 0.876672i) q^{31} +(-0.581095 - 9.97701i) q^{32} +(-2.16346 + 0.279917i) q^{33} +(-12.2103 - 2.89389i) q^{34} +(-0.216961 + 1.23045i) q^{35} +(-11.8294 + 8.20461i) q^{36} +(-0.248079 - 1.40693i) q^{37} +(0.688459 - 11.8204i) q^{38} +(0.479767 + 6.79475i) q^{39} +(1.41238 - 1.89715i) q^{40} +(-5.63875 + 7.57416i) q^{41} +(-15.6532 - 7.62143i) q^{42} +(0.210389 - 3.61224i) q^{43} +(1.04952 + 5.95211i) q^{44} +(-0.968232 - 0.0890637i) q^{45} +(-0.254317 + 1.44230i) q^{46} +(3.70075 + 0.877094i) q^{47} +(9.91443 + 12.9806i) q^{48} +(-0.457078 - 7.84773i) q^{49} +(-12.4192 + 2.94342i) q^{50} +(7.79724 - 2.94719i) q^{51} +(18.7444 - 2.19091i) q^{52} +(-3.57369 - 6.18982i) q^{53} +(4.90321 - 12.6303i) q^{54} +(-0.204104 + 0.353518i) q^{55} +(-11.1425 + 25.8311i) q^{56} +(4.01621 + 6.76258i) q^{57} +(3.81736 + 4.04617i) q^{58} +(5.22384 + 2.62351i) q^{59} +(-0.123507 + 2.69102i) q^{60} +(2.64794 + 8.84474i) q^{61} +(7.59304 + 6.37131i) q^{62} +(11.4503 - 1.62507i) q^{63} +(5.51392 - 4.62673i) q^{64} +(1.06493 + 0.700415i) q^{65} +(-3.95407 - 4.08900i) q^{66} +(-0.214231 - 0.0250400i) q^{67} +(-9.14717 - 21.2055i) q^{68} +(-0.396301 - 0.888485i) q^{69} +(-2.91129 + 1.46210i) q^{70} +(-11.2063 - 4.07874i) q^{71} +(-20.7503 - 6.97881i) q^{72} +(7.37938 - 2.68588i) q^{73} +(2.55629 - 2.70951i) q^{74} +(5.74179 - 6.23807i) q^{75} +(18.2062 - 11.9744i) q^{76} +(1.39252 - 4.65135i) q^{77} +(-13.4641 + 11.5832i) q^{78} +(4.98085 + 6.69044i) q^{79} +3.05642 q^{80} +(1.99732 + 8.77557i) q^{81} -24.6211 q^{82} +(0.396004 + 0.531925i) q^{83} +(-5.95205 - 31.4837i) q^{84} +(0.447353 - 1.49426i) q^{85} +(7.88253 - 5.18442i) q^{86} +(-3.60578 - 0.807824i) q^{87} +(-6.30731 + 6.68536i) q^{88} +(1.56940 - 0.571214i) q^{89} +(-1.32131 - 2.16372i) q^{90} +(-14.2463 - 5.18524i) q^{91} +(-2.40866 + 1.20967i) q^{92} +(-6.54868 - 0.683804i) q^{93} +(3.92784 + 9.10575i) q^{94} +(1.46182 + 0.170862i) q^{95} +(-4.75999 + 16.6427i) q^{96} +(13.4681 + 8.85812i) q^{97} +(15.7017 - 13.1753i) q^{98} +(3.69695 + 0.780572i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9}+O(q^{10}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9	\( 144 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 18 q^{5} - 18 q^{6} - 18 q^{7} - 18 q^{8} - 18 q^{9} - 18 q^{10} - 18 q^{11} - 18 q^{12} - 18 q^{13} - 18 q^{14} - 18 q^{15} - 18 q^{16} - 18 q^{17} - 9 q^{18} - 18 q^{19} + 18 q^{20} + 9 q^{21} - 18 q^{22} + 9 q^{23} + 36 q^{24} - 18 q^{25} + 45 q^{26} + 9 q^{27} - 9 q^{28} + 9 q^{29} + 36 q^{30} - 18 q^{31} + 36 q^{32} + 9 q^{33} - 18 q^{34} + 9 q^{35} + 18 q^{36} - 18 q^{37} - 9 q^{38} - 18 q^{39} - 18 q^{40} + 27 q^{42} - 18 q^{43} + 54 q^{44} + 36 q^{45} - 18 q^{46} + 36 q^{47} + 81 q^{48} - 18 q^{49} + 99 q^{50} + 45 q^{51} + 45 q^{53} + 108 q^{54} - 9 q^{55} + 126 q^{56} + 36 q^{57} - 18 q^{58} + 45 q^{59} + 99 q^{60} - 18 q^{61} + 81 q^{62} + 36 q^{63} - 18 q^{64} - 18 q^{66} + 9 q^{67} - 99 q^{68} - 72 q^{69} + 36 q^{70} - 90 q^{71} - 234 q^{72} - 18 q^{73} - 162 q^{74} - 108 q^{75} + 63 q^{76} - 162 q^{77} - 135 q^{78} + 36 q^{79} - 288 q^{80} - 90 q^{81} - 36 q^{82} - 90 q^{83} - 243 q^{84} + 36 q^{85} - 162 q^{86} - 162 q^{87} + 63 q^{88} - 81 q^{89} - 99 q^{90} - 18 q^{91} - 144 q^{92} + 36 q^{94} + 18 q^{95} - 27 q^{96} + 9 q^{97} + 81 q^{98} + 54 q^{99}+O(q^{100}) \) 144 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 - 9 * q^18 - 18 * q^19 + 18 * q^20 + 9 * q^21 - 18 * q^22 + 9 * q^23 + 36 * q^24 - 18 * q^25 + 45 * q^26 + 9 * q^27 - 9 * q^28 + 9 * q^29 + 36 * q^30 - 18 * q^31 + 36 * q^32 + 9 * q^33 - 18 * q^34 + 9 * q^35 + 18 * q^36 - 18 * q^37 - 9 * q^38 - 18 * q^39 - 18 * q^40 + 27 * q^42 - 18 * q^43 + 54 * q^44 + 36 * q^45 - 18 * q^46 + 36 * q^47 + 81 * q^48 - 18 * q^49 + 99 * q^50 + 45 * q^51 + 45 * q^53 + 108 * q^54 - 9 * q^55 + 126 * q^56 + 36 * q^57 - 18 * q^58 + 45 * q^59 + 99 * q^60 - 18 * q^61 + 81 * q^62 + 36 * q^63 - 18 * q^64 - 18 * q^66 + 9 * q^67 - 99 * q^68 - 72 * q^69 + 36 * q^70 - 90 * q^71 - 234 * q^72 - 18 * q^73 - 162 * q^74 - 108 * q^75 + 63 * q^76 - 162 * q^77 - 135 * q^78 + 36 * q^79 - 288 * q^80 - 90 * q^81 - 36 * q^82 - 90 * q^83 - 243 * q^84 + 36 * q^85 - 162 * q^86 - 162 * q^87 + 63 * q^88 - 81 * q^89 - 99 * q^90 - 18 * q^91 - 144 * q^92 + 36 * q^94 + 18 * q^95 - 27 * q^96 + 9 * q^97 + 81 * q^98 + 54 * q^99

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