LMFDB - Embedded newform 729.2.g.b.352.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(28,729)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("729.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([44])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,-9,0,9,-9,0,9,18,0,-18,-9,0,9,-9,0,9,18,0,-18,63] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(20)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			352.5
Character	$\chi$	$=$	729.352
Dual form			729.2.g.b.379.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0909953 - 0.303945i) q^{2} +(1.58687 + 1.04370i) q^{4} +(-0.840209 + 1.94782i) q^{5} +(0.147894 + 2.53924i) q^{7} +(0.947719 - 0.795231i) q^{8} +(0.515577 + 0.432621i) q^{10} +(1.82733 - 2.45453i) q^{11} +(-3.78737 + 4.01438i) q^{13} +(0.785249 + 0.186107i) q^{14} +(1.34911 + 3.12759i) q^{16} +(0.745021 - 4.22522i) q^{17} +(-0.0105922 - 0.0600713i) q^{19} +(-3.36625 + 2.21402i) q^{20} +(-0.579765 - 0.778760i) q^{22} +(-0.248909 + 4.27360i) q^{23} +(0.343143 + 0.363710i) q^{25} +(0.875520 + 1.51644i) q^{26} +(-2.41553 + 4.18381i) q^{28} +(-10.3910 + 2.46271i) q^{29} +(4.12278 - 2.07054i) q^{31} +(3.53097 - 0.412711i) q^{32} +(-1.21644 - 0.610921i) q^{34} +(-5.07026 - 1.84542i) q^{35} +(-3.30730 + 1.20376i) q^{37} +(-0.0192222 - 0.00224676i) q^{38} +(0.752687 + 2.51415i) q^{40} +(0.722754 + 2.41417i) q^{41} +(0.770554 + 0.0900648i) q^{43} +(5.46154 - 1.98784i) q^{44} +(1.27629 + 0.464532i) q^{46} +(4.06294 + 2.04049i) q^{47} +(0.526786 - 0.0615725i) q^{49} +(0.141773 - 0.0712008i) q^{50} +(-10.1999 + 2.41742i) q^{52} +(-0.986349 + 1.70841i) q^{53} +(3.24565 + 5.62164i) q^{55} +(2.15945 + 2.28888i) q^{56} +(-0.197001 + 3.38238i) q^{58} +(-4.30754 - 5.78603i) q^{59} +(9.75766 - 6.41771i) q^{61} +(-0.254177 - 1.44151i) q^{62} +(-0.987085 + 5.59804i) q^{64} +(-4.63712 - 10.7501i) q^{65} +(-1.18028 - 0.279730i) q^{67} +(5.59213 - 5.92731i) q^{68} +(-1.02228 + 1.37316i) q^{70} +(10.9300 + 9.17137i) q^{71} +(7.44218 - 6.24473i) q^{73} +(0.0649282 + 1.11477i) q^{74} +(0.0458881 - 0.106381i) q^{76} +(6.50290 + 4.27703i) q^{77} +(-0.462085 + 1.54347i) q^{79} -7.22552 q^{80} +0.799542 q^{82} +(0.947094 - 3.16351i) q^{83} +(7.60402 + 5.00124i) q^{85} +(0.0974916 - 0.226011i) q^{86} +(-0.220122 - 3.77936i) q^{88} +(10.7606 - 9.02919i) q^{89} +(-10.7536 - 9.02336i) q^{91} +(-4.85535 + 6.52187i) q^{92} +(0.989905 - 1.04924i) q^{94} +(0.125908 + 0.0298407i) q^{95} +(2.78173 + 6.44878i) q^{97} +(0.0292204 - 0.165717i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{16}{27}\right)$

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 $

$2$	0.0909953	−	0.303945i	0.0643434	−	0.214922i	−0.919772	−	0.392454i	$-0.871626\pi$
$2$	0.0909953	−	0.303945i	0.0643434	−	0.214922i	0.984115	+	0.177532i	$0.0568114\pi$
$3$		0			0
$3$		0			0
$4$	1.58687	+	1.04370i	0.793436	+	0.521851i
$5$	−0.840209	+	1.94782i	−0.375753	+	0.871093i	0.620468	+	0.784232i	$0.286943\pi$
$5$	−0.840209	+	1.94782i	−0.375753	+	0.871093i	−0.996220	+	0.0868610i	$0.972316\pi$
$6$		0			0
$7$	0.147894	+	2.53924i	0.0558987	+	0.959744i	0.903359	+	0.428885i	$0.141093\pi$
$7$	0.147894	+	2.53924i	0.0558987	+	0.959744i	−0.847460	+	0.530859i	$0.821870\pi$
$8$	0.947719	−	0.795231i	0.335069	−	0.281157i
$9$		0			0
$10$	0.515577	+	0.432621i	0.163040	+	0.136807i
$11$	1.82733	−	2.45453i	0.550961	−	0.740069i	−0.436191	−	0.899854i	$-0.643673\pi$
$11$	1.82733	−	2.45453i	0.550961	−	0.740069i	0.987152	+	0.159785i	$0.0510802\pi$
$12$		0			0
$13$	−3.78737	+	4.01438i	−1.05043	+	1.11339i	−0.0570649	+	0.998370i	$0.518174\pi$
$13$	−3.78737	+	4.01438i	−1.05043	+	1.11339i	−0.993363	+	0.115018i	$0.963307\pi$
$14$	0.785249	+	0.186107i	0.209867	+	0.0497393i
$15$		0			0
$16$	1.34911	+	3.12759i	0.337277	+	0.781897i
$17$	0.745021	−	4.22522i	0.180694	−	1.02477i	−0.750670	−	0.660678i	$-0.770269\pi$
$17$	0.745021	−	4.22522i	0.180694	−	1.02477i	0.931364	−	0.364090i	$-0.118620\pi$
$18$		0			0
$19$	−0.0105922	−	0.0600713i	−0.00243002	−	0.0137813i	0.983569	−	0.180535i	$-0.0577828\pi$
$19$	−0.0105922	−	0.0600713i	−0.00243002	−	0.0137813i	−0.985999	+	0.166753i	$0.946672\pi$
$20$	−3.36625	+	2.21402i	−0.752717	+	0.495070i
$21$		0			0
$22$	−0.579765	−	0.778760i	−0.123606	−	0.166032i
$23$	−0.248909	+	4.27360i	−0.0519010	+	0.891107i	0.867415	+	0.497586i	$0.165780\pi$
$23$	−0.248909	+	4.27360i	−0.0519010	+	0.891107i	−0.919316	+	0.393521i	$0.871257\pi$
$24$		0			0
$25$	0.343143	+	0.363710i	0.0686286	+	0.0727421i
$26$	0.875520	+	1.51644i	0.171704	+	0.297399i
$27$		0			0
$28$	−2.41553	+	4.18381i	−0.456491	+	0.790666i
$29$	−10.3910	+	2.46271i	−1.92956	+	0.457313i	−0.934780	+	0.355227i	$0.884404\pi$
$29$	−10.3910	+	2.46271i	−1.92956	+	0.457313i	−0.994776	+	0.102086i	$0.967448\pi$
$30$		0			0
$31$	4.12278	−	2.07054i	0.740473	−	0.371880i	−0.0382327	−	0.999269i	$-0.512173\pi$
$31$	4.12278	−	2.07054i	0.740473	−	0.371880i	0.778706	+	0.627389i	$0.215877\pi$
$32$	3.53097	−	0.412711i	0.624193	−	0.0729577i
$33$		0			0
$34$	−1.21644	−	0.610921i	−0.208618	−	0.104772i
$35$	−5.07026	−	1.84542i	−0.857030	−	0.311933i
$36$		0			0
$37$	−3.30730	+	1.20376i	−0.543716	+	0.197896i	−0.599252	−	0.800560i	$-0.704535\pi$
$37$	−3.30730	+	1.20376i	−0.543716	+	0.197896i	0.0555362	+	0.998457i	$0.482313\pi$
$38$	−0.0192222	−	0.00224676i	−0.00311826	−	0.000364472i
$39$		0			0
$40$	0.752687	+	2.51415i	0.119010	+	0.397522i
$41$	0.722754	+	2.41417i	0.112875	+	0.377030i	0.995696	−	0.0926807i	$-0.0295436\pi$
$41$	0.722754	+	2.41417i	0.112875	+	0.377030i	−0.882821	+	0.469710i	$0.844358\pi$
$42$		0			0
$43$	0.770554	+	0.0900648i	0.117508	+	0.0137348i	0.174644	−	0.984632i	$-0.444123\pi$
$43$	0.770554	+	0.0900648i	0.117508	+	0.0137348i	−0.0571354	+	0.998366i	$0.518197\pi$
$44$	5.46154	−	1.98784i	0.823359	−	0.299678i
$45$		0			0
$46$	1.27629	+	0.464532i	0.188179	+	0.0684915i
$47$	4.06294	+	2.04049i	0.592641	+	0.297635i	0.719728	−	0.694256i	$-0.244267\pi$
$47$	4.06294	+	2.04049i	0.592641	+	0.297635i	−0.127087	+	0.991892i	$0.540563\pi$
$48$		0			0
$49$	0.526786	−	0.0615725i	0.0752551	−	0.00879607i
$50$	0.141773	−	0.0712008i	0.0200497	−	0.0100693i
$51$		0			0
$52$	−10.1999	+	2.41742i	−1.41447	+	0.335236i
$53$	−0.986349	+	1.70841i	−0.135485	+	0.234668i	−0.925783	−	0.378056i	$-0.876593\pi$
$53$	−0.986349	+	1.70841i	−0.135485	+	0.234668i	0.790297	+	0.612724i	$0.209926\pi$
$54$		0			0
$55$	3.24565	+	5.62164i	0.437644	+	0.758021i
$56$	2.15945	+	2.28888i	0.288568	+	0.305864i
$57$		0			0
$58$	−0.197001	+	3.38238i	−0.0258676	+	0.444129i
$59$	−4.30754	−	5.78603i	−0.560794	−	0.753277i	0.427801	−	0.903873i	$-0.359288\pi$
$59$	−4.30754	−	5.78603i	−0.560794	−	0.753277i	−0.988595	+	0.150596i	$0.951881\pi$
$60$		0			0
$61$	9.75766	−	6.41771i	1.24934	−	0.821704i	0.259758	−	0.965674i	$-0.416357\pi$
$61$	9.75766	−	6.41771i	1.24934	−	0.821704i	0.989582	+	0.143970i	$0.0459869\pi$
$62$	−0.254177	−	1.44151i	−0.0322805	−	0.183072i
$63$		0			0
$64$	−0.987085	+	5.59804i	−0.123386	+	0.699755i
$65$	−4.63712	−	10.7501i	−0.575164	−	1.33338i
$66$		0			0
$67$	−1.18028	−	0.279730i	−0.144194	−	0.0341745i	0.157885	−	0.987457i	$-0.449532\pi$
$67$	−1.18028	−	0.279730i	−0.144194	−	0.0341745i	−0.302079	+	0.953283i	$0.597681\pi$
$68$	5.59213	−	5.92731i	0.678145	−	0.718792i
$69$		0			0
$70$	−1.02228	+	1.37316i	−0.122186	+	0.164124i
$71$	10.9300	+	9.17137i	1.29715	+	1.08844i	0.990629	+	0.136579i	$0.0436107\pi$
$71$	10.9300	+	9.17137i	1.29715	+	1.08844i	0.306525	+	0.951863i	$0.400834\pi$
$72$		0			0
$73$	7.44218	−	6.24473i	0.871042	−	0.730891i	−0.0932755	−	0.995640i	$-0.529734\pi$
$73$	7.44218	−	6.24473i	0.871042	−	0.730891i	0.964317	+	0.264750i	$0.0852893\pi$
$74$	0.0649282	+	1.11477i	0.00754775	+	0.129590i
$75$		0			0
$76$	0.0458881	−	0.106381i	0.00526373	−	0.0122027i
$77$	6.50290	+	4.27703i	0.741075	+	0.487412i
$78$		0			0
$79$	−0.462085	+	1.54347i	−0.0519886	+	0.173654i	−0.980041	−	0.198796i	$-0.936297\pi$
$79$	−0.462085	+	1.54347i	−0.0519886	+	0.173654i	0.928052	+	0.372450i	$0.121482\pi$
$80$	−7.22552			−0.807838
$81$		0			0
$82$	0.799542			0.0882947
$83$	0.947094	−	3.16351i	0.103957	−	0.347241i	−0.890147	−	0.455674i	$-0.849398\pi$
$83$	0.947094	−	3.16351i	0.103957	−	0.347241i	0.994104	+	0.108433i	$0.0345834\pi$
$84$		0			0
$85$	7.60402	+	5.00124i	0.824771	+	0.542461i
$86$	0.0974916	−	0.226011i	0.0105128	−	0.0243714i
$87$		0			0
$88$	−0.220122	−	3.77936i	−0.0234651	−	0.402881i
$89$	10.7606	−	9.02919i	1.14062	−	0.957092i	0.141159	−	0.989987i	$-0.454917\pi$
$89$	10.7606	−	9.02919i	1.14062	−	0.957092i	0.999459	+	0.0328946i	$0.0104726\pi$
$90$		0			0
$91$	−10.7536	−	9.02336i	−1.12729	−	0.945905i
$92$	−4.85535	+	6.52187i	−0.506205	+	0.679952i
$93$		0			0
$94$	0.989905	−	1.04924i	0.102101	−	0.108221i
$95$	0.125908	+	0.0298407i	0.0129179	+	0.00306160i
$96$		0			0
$97$	2.78173	+	6.44878i	0.282442	+	0.654774i	0.999090	−	0.0426612i	$-0.0135836\pi$
$97$	2.78173	+	6.44878i	0.282442	+	0.654774i	−0.716648	+	0.697436i	$0.754324\pi$
$98$	0.0292204	−	0.165717i	0.00295170	−	0.0167399i
$99$		0			0
$100$	0.164919	+	0.935301i	0.0164919	+	0.0935301i
$101$	9.06820	−	5.96425i	0.902320	−	0.593465i	−0.0113443	−	0.999936i	$-0.503611\pi$
$101$	9.06820	−	5.96425i	0.902320	−	0.593465i	0.913664	+	0.406471i	$0.133241\pi$
$102$		0			0
$103$	−7.42672	−	9.97581i	−0.731776	−	0.982946i	−0.999809	−	0.0195364i	$-0.993781\pi$
$103$	−7.42672	−	9.97581i	−0.731776	−	0.982946i	0.268033	−	0.963410i	$-0.413626\pi$
$104$	−0.397007	+	6.81634i	−0.0389297	+	0.668397i
$105$		0			0
$106$	0.429509	+	0.455253i	0.0417176	+	0.0442181i
$107$	2.48915	+	4.31134i	0.240636	+	0.416793i	0.960896	−	0.276911i	$-0.0893108\pi$
$107$	2.48915	+	4.31134i	0.240636	+	0.416793i	−0.720260	+	0.693704i	$0.755977\pi$
$108$		0			0
$109$	−0.180626	+	0.312853i	−0.0173008	+	0.0299659i	−0.874546	−	0.484942i	$-0.838841\pi$
$109$	−0.180626	+	0.312853i	−0.0173008	+	0.0299659i	0.857245	+	0.514908i	$0.172174\pi$
$110$	2.00401	−	0.474959i	0.191075	−	0.0452856i
$111$		0			0
$112$	−7.74218	+	3.88827i	−0.731567	+	0.367407i
$113$	−19.6084	+	2.29190i	−1.84461	+	0.215604i	−0.965389	−	0.260815i	$-0.916009\pi$
$113$	−19.6084	+	2.29190i	−1.84461	+	0.215604i	−0.879219	+	0.476419i	$0.841935\pi$
$114$		0			0
$115$	−8.11508	−	4.07554i	−0.756735	−	0.380047i
$116$	−19.0595	−	6.93709i	−1.76963	−	0.644092i
$117$		0			0
$118$	−2.15060	+	0.782756i	−0.197979	+	0.0720585i
$119$	10.8391	+	1.26690i	0.993614	+	0.116137i
$120$		0			0
$121$	0.469250	+	1.56740i	0.0426591	+	0.142491i
$122$	−1.06273	−	3.54978i	−0.0962154	−	0.321382i
$123$		0			0
$124$	8.70335	+	1.01728i	0.781584	+	0.0913541i
$125$	−10.9637	+	3.99045i	−0.980620	+	0.356916i
$126$		0			0
$127$	13.5556	+	4.93382i	1.20286	+	0.437806i	0.864222	−	0.503111i	$-0.167811\pi$
$127$	13.5556	+	4.93382i	1.20286	+	0.437806i	0.338639	+	0.940916i	$0.390033\pi$
$128$	7.96541	+	4.00038i	0.704050	+	0.353587i
$129$		0			0
$130$	−3.68939	+	0.431227i	−0.323581	+	0.0378211i
$131$	−2.72986	+	1.37099i	−0.238509	+	0.119784i	−0.564040	−	0.825748i	$-0.690753\pi$
$131$	−2.72986	+	1.37099i	−0.238509	+	0.119784i	0.325530	+	0.945532i	$0.394457\pi$
$132$		0			0
$133$	0.150969	−	0.0357803i	0.0130907	−	0.00310255i
$134$	−0.192422	+	0.333285i	−0.0166228	+	0.0287915i
$135$		0			0
$136$	−2.65396	−	4.59679i	−0.227575	−	0.394171i
$137$	1.78765	+	1.89480i	0.152729	+	0.161883i	0.799221	−	0.601038i	$-0.205246\pi$
$137$	1.78765	+	1.89480i	0.152729	+	0.161883i	−0.646492	+	0.762921i	$0.723764\pi$
$138$		0			0
$139$	1.10383	−	18.9519i	0.0936252	−	1.60748i	−0.545318	−	0.838229i	$-0.683591\pi$
$139$	1.10383	−	18.9519i	0.0936252	−	1.60748i	0.638943	−	0.769254i	$-0.279372\pi$
$140$	−6.11978	−	8.22030i	−0.517216	−	0.694742i
$141$		0			0
$142$	3.78218	−	2.48758i	0.317393	−	0.208753i
$143$	2.93264	+	16.6318i	0.245240	+	1.39082i
$144$		0			0
$145$	3.93367	−	22.3090i	0.326674	−	1.85266i
$146$	−1.22085	−	2.83026i	−0.101039	−	0.234234i
$147$		0			0
$148$	−6.50462	−	1.54162i	−0.534677	−	0.126721i
$149$	2.81196	−	2.98051i	0.230365	−	0.244173i	−0.601872	−	0.798592i	$-0.705578\pi$
$149$	2.81196	−	2.98051i	0.230365	−	0.244173i	0.832237	+	0.554420i	$0.187060\pi$
$150$		0			0
$151$	5.93650	−	7.97411i	0.483106	−	0.648923i	−0.492018	−	0.870585i	$-0.663741\pi$
$151$	5.93650	−	7.97411i	0.483106	−	0.648923i	0.975124	+	0.221662i	$0.0711480\pi$
$152$	−0.0578090	−	0.0485075i	−0.00468893	−	0.00393448i
$153$		0			0
$154$	1.89172	−	1.58734i	0.152439	−	0.127911i
$155$	0.569045	+	9.77013i	0.0457068	+	0.784756i
$156$		0			0
$157$	4.57455	−	10.6050i	0.365089	−	0.846371i	−0.632339	−	0.774692i	$-0.717905\pi$
$157$	4.57455	−	10.6050i	0.365089	−	0.846371i	0.997428	−	0.0716789i	$-0.0228357\pi$
$158$	0.427084	+	0.280897i	0.0339770	+	0.0223470i
$159$		0			0
$160$	−2.16286	+	7.22446i	−0.170989	+	0.571144i
$161$	−10.8885			−0.858135
$162$		0			0
$163$	−14.1333			−1.10700			−0.553502	−	0.832848i	$-0.686709\pi$
$163$	−14.1333			−1.10700			−0.553502	+	0.832848i	$0.686709\pi$
$164$	−1.37275	+	4.58532i	−0.107194	+	0.358053i
$165$		0			0
$166$	−0.875354	−	0.575730i	−0.0679407	−	0.0446853i
$167$	2.65513	−	6.15528i	0.205460	−	0.476310i	−0.784064	−	0.620681i	$-0.786856\pi$
$167$	2.65513	−	6.15528i	0.205460	−	0.476310i	0.989524	+	0.144370i	$0.0461157\pi$
$168$		0			0
$169$	−1.01518	−	17.4299i	−0.0780905	−	1.34076i
$170$	2.21203	−	1.85612i	0.169655	−	0.142358i
$171$		0			0
$172$	1.12877	+	0.947150i	0.0860679	+	0.0722195i
$173$	8.83125	−	11.8624i	0.671427	−	0.901884i	−0.327651	−	0.944799i	$-0.606257\pi$
$173$	8.83125	−	11.8624i	0.671427	−	0.901884i	0.999079	+	0.0429151i	$0.0136645\pi$
$174$		0			0
$175$	−0.872800	+	0.925114i	−0.0659775	+	0.0699321i
$176$	10.1420	+	2.40370i	0.764484	+	0.181186i
$177$		0			0
$178$	−1.76522	−	4.09224i	−0.132309	−	0.306726i
$179$	0.110050	−	0.624125i	0.00822552	−	0.0466493i	−0.980419	−	0.196924i	$-0.936905\pi$
$179$	0.110050	−	0.624125i	0.00822552	−	0.0466493i	0.988644	+	0.150275i	$0.0480159\pi$
$180$		0			0
$181$	−2.42311	−	13.7421i	−0.180108	−	1.02145i	−0.932081	−	0.362251i	$-0.882008\pi$
$181$	−2.42311	−	13.7421i	−0.180108	−	1.02145i	0.751972	−	0.659195i	$-0.229103\pi$
$182$	−3.72114	+	2.44743i	−0.275829	+	0.181416i
$183$		0			0
$184$	3.16260	+	4.24811i	0.233150	+	0.313175i
$185$	0.434113	−	7.45344i	0.0319166	−	0.547988i
$186$		0			0
$187$	−9.00954	−	9.54956i	−0.658843	−	0.698333i
$188$	4.31771	+	7.47849i	0.314901	+	0.545425i
$189$		0			0
$190$	0.0205270	−	0.0355538i	0.00148918	−	0.00257934i
$191$	−8.26432	+	1.95868i	−0.597985	+	0.141725i	−0.518451	−	0.855107i	$-0.673491\pi$
$191$	−8.26432	+	1.95868i	−0.597985	+	0.141725i	−0.0795338	+	0.996832i	$0.525343\pi$
$192$		0			0
$193$	11.8416	−	5.94705i	0.852374	−	0.428078i	0.0317154	−	0.999497i	$-0.489903\pi$
$193$	11.8416	−	5.94705i	0.852374	−	0.428078i	0.820659	+	0.571419i	$0.193607\pi$
$194$	2.21320	−	0.258686i	0.158899	−	0.0185726i
$195$		0			0
$196$	0.900206	+	0.452100i	0.0643004	+	0.0322929i
$197$	−7.09307	−	2.58167i	−0.505360	−	0.183936i	0.0767431	−	0.997051i	$-0.475548\pi$
$197$	−7.09307	−	2.58167i	−0.505360	−	0.183936i	−0.582103	+	0.813115i	$0.697770\pi$
$198$		0			0
$199$	1.98595	−	0.722827i	0.140780	−	0.0512399i	−0.270669	−	0.962672i	$-0.587245\pi$
$199$	1.98595	−	0.722827i	0.140780	−	0.0512399i	0.411449	+	0.911433i	$0.365023\pi$
$200$	0.614437	+	0.0718174i	0.0434473	+	0.00507826i
$201$		0			0
$202$	−0.987643	−	3.29896i	−0.0694903	−	0.232114i
$203$	−7.79017	−	26.0210i	−0.546763	−	1.82632i
$204$		0			0
$205$	−5.30964	−	0.620607i	−0.370841	−	0.0433451i
$206$	−3.70790	+	1.34957i	−0.258342	+	0.0940287i
$207$		0			0
$208$	−17.6649	−	6.42950i	−1.22484	−	0.445805i
$209$	−0.166802	−	0.0837713i	−0.0115380	−	0.00579458i
$210$		0			0
$211$	−0.652038	+	0.0762123i	−0.0448882	+	0.00524667i	−0.138507	−	0.990361i	$-0.544230\pi$
$211$	−0.652038	+	0.0762123i	−0.0448882	+	0.00524667i	0.0936192	+	0.995608i	$0.470156\pi$
$212$	−3.34828	+	1.68157i	−0.229961	+	0.115491i
$213$		0			0
$214$	1.53691	−	0.364255i	0.105061	−	0.0249000i
$215$	−0.822857	+	1.42523i	−0.0561184	+	0.0971998i
$216$		0			0
$217$	5.86733	+	10.1625i	0.398301	+	0.689877i
$218$	0.0786542	+	0.0833686i	0.00532714	+	0.00564643i
$219$		0			0
$220$	−0.716878	+	12.3083i	−0.0483319	+	0.829827i
$221$	14.1400	+	18.9933i	0.951158	+	1.27763i
$222$		0			0
$223$	−18.8077	+	12.3700i	−1.25945	+	0.828356i	−0.990860	−	0.134897i	$-0.956930\pi$
$223$	−18.8077	+	12.3700i	−1.25945	+	0.828356i	−0.268595	+	0.963253i	$0.586559\pi$
$224$	1.57018	+	8.90495i	0.104912	+	0.594987i
$225$		0			0
$226$	−1.08766	+	6.16845i	−0.0723503	+	0.410319i
$227$	5.31087	+	12.3120i	0.352495	+	0.817175i	0.998547	+	0.0538820i	$0.0171595\pi$
$227$	5.31087	+	12.3120i	0.352495	+	0.817175i	−0.646052	+	0.763293i	$0.723581\pi$
$228$		0			0
$229$	6.05564	+	1.43521i	0.400168	+	0.0948415i	0.425772	−	0.904831i	$-0.360003\pi$
$229$	6.05564	+	1.43521i	0.400168	+	0.0948415i	−0.0256038	+	0.999672i	$0.508151\pi$
$230$	−1.97718	+	2.09569i	−0.130371	+	0.138185i
$231$		0			0
$232$	−7.88931	+	10.5972i	−0.517958	+	0.695739i
$233$	9.49107	+	7.96396i	0.621781	+	0.521736i	0.898363	−	0.439254i	$-0.144757\pi$
$233$	9.49107	+	7.96396i	0.621781	+	0.521736i	−0.276582	+	0.960990i	$0.589202\pi$
$234$		0			0
$235$	−7.38822	+	6.19946i	−0.481955	+	0.404408i
$236$	−0.796623	−	13.6775i	−0.0518557	−	0.890329i
$237$		0			0
$238$	1.37137	−	3.17920i	0.0888929	−	0.206077i
$239$	−8.21456	−	5.40280i	−0.531356	−	0.349478i	0.255308	−	0.966860i	$-0.417823\pi$
$239$	−8.21456	−	5.40280i	−0.531356	−	0.349478i	−0.786664	+	0.617382i	$0.788193\pi$
$240$		0			0
$241$	4.97235	−	16.6088i	0.320297	−	1.06987i	−0.634577	−	0.772859i	$-0.718826\pi$
$241$	4.97235	−	16.6088i	0.320297	−	1.06987i	0.954875	−	0.297009i	$-0.0959890\pi$
$242$	0.519105			0.0333693
$243$		0			0
$244$	22.1823			1.42008
$245$	−0.322678	+	1.07782i	−0.0206151	+	0.0688594i
$246$		0			0
$247$	0.281266	+	0.184991i	0.0178965	+	0.0117707i
$248$	2.26068	−	5.24085i	0.143553	−	0.332794i
$249$		0			0
$250$	0.215237	+	3.69547i	0.0136128	+	0.233722i
$251$	19.1764	−	16.0909i	1.21040	−	1.01565i	0.211132	−	0.977458i	$-0.432285\pi$
$251$	19.1764	−	16.0909i	1.21040	−	1.01565i	0.999270	−	0.0381908i	$-0.0121595\pi$
$252$		0			0
$253$	10.0348	+	8.42023i	0.630885	+	0.529375i
$254$	2.73310	−	3.67120i	0.171490	−	0.230351i
$255$		0			0
$256$	−5.86103	+	6.21233i	−0.366314	+	0.388270i
$257$	−2.34548	−	0.555890i	−0.146307	−	0.0346755i	0.156810	−	0.987629i	$-0.449879\pi$
$257$	−2.34548	−	0.555890i	−0.146307	−	0.0346755i	−0.303117	+	0.952953i	$0.598027\pi$
$258$		0			0
$259$	−3.54576	−	8.22000i	−0.220323	−	0.510766i
$260$	3.86134	−	21.8987i	0.239470	−	1.35810i
$261$		0			0
$262$	0.168301	+	0.954483i	0.0103977	+	0.0589682i
$263$	−3.27743	+	2.15560i	−0.202095	+	0.132920i	−0.646523	−	0.762895i	$-0.723777\pi$
$263$	−3.27743	+	2.15560i	−0.202095	+	0.132920i	0.444428	+	0.895815i	$0.353407\pi$
$264$		0			0
$265$	−2.49894	−	3.35665i	−0.153508	−	0.206198i
$266$	0.00286221	−	0.0491422i	0.000175493	−	0.00301310i
$267$		0			0
$268$	−1.58099	−	1.67575i	−0.0965745	−	0.102363i
$269$	5.54513	+	9.60445i	0.338093	+	0.585594i	0.984074	−	0.177760i	$-0.0568849\pi$
$269$	5.54513	+	9.60445i	0.338093	+	0.585594i	−0.645981	+	0.763353i	$0.723552\pi$
$270$		0			0
$271$	−0.397309	+	0.688159i	−0.0241348	+	0.0418027i	−0.877841	−	0.478953i	$-0.841016\pi$
$271$	−0.397309	+	0.688159i	−0.0241348	+	0.0418027i	0.853706	+	0.520756i	$0.174350\pi$
$272$	14.2199	−	3.37017i	0.862206	−	0.204347i
$273$		0			0
$274$	0.738582	−	0.370930i	0.0446194	−	0.0224087i
$275$	1.51977	−	0.177636i	0.0916458	−	0.0107119i
$276$		0			0
$277$	26.0832	+	13.0995i	1.56719	+	0.787070i	0.999349	−	0.0360708i	$-0.0114842\pi$
$277$	26.0832	+	13.0995i	1.56719	+	0.787070i	0.567837	+	0.823141i	$0.307780\pi$
$278$	−5.65991	−	2.06004i	−0.339459	−	0.123553i
$279$		0			0
$280$	−6.27272	+	2.28308i	−0.374867	+	0.136440i
$281$	−27.4024	−	3.20288i	−1.63469	−	0.191068i	−0.751384	−	0.659865i	$-0.770613\pi$
$281$	−27.4024	−	3.20288i	−1.63469	−	0.191068i	−0.883306	+	0.468798i	$0.844687\pi$
$282$		0			0
$283$	1.46517	+	4.89400i	0.0870951	+	0.290918i	0.990430	−	0.138019i	$-0.0440735\pi$
$283$	1.46517	+	4.89400i	0.0870951	+	0.290918i	−0.903334	+	0.428937i	$0.858888\pi$
$284$	7.77236	+	25.9615i	0.461205	+	1.54053i
$285$		0			0
$286$	5.32202	+	0.622055i	0.314698	+	0.0367829i
$287$	−6.02327	+	2.19229i	−0.355542	+	0.129407i
$288$		0			0
$289$	−1.32268	−	0.481415i	−0.0778046	−	0.0283185i
$290$	−6.42277	−	3.22563i	−0.377158	−	0.189416i
$291$		0			0
$292$	18.3274	−	2.14217i	1.07253	−	0.125361i
$293$	2.09418	−	1.05174i	0.122344	−	0.0614432i	−0.386575	−	0.922258i	$-0.626342\pi$
$293$	2.09418	−	1.05174i	0.122344	−	0.0614432i	0.508918	+	0.860815i	$0.330046\pi$
$294$		0			0
$295$	14.8894	−	3.52885i	0.866895	−	0.205458i
$296$	−2.17712	+	3.77089i	−0.126543	+	0.219178i
$297$		0			0
$298$	−0.650036	−	1.12590i	−0.0376556	−	0.0652214i
$299$	−16.2131	−	17.1849i	−0.937630	−	0.993829i
$300$		0			0
$301$	−0.114736	+	1.96994i	−0.00661328	+	0.113546i
$302$	−1.88350	−	2.52998i	−0.108383	−	0.145584i
$303$		0			0
$304$	0.173588	−	0.114171i	0.00995597	−	0.00654814i
$305$	4.30210	+	24.3984i	0.246337	+	1.39705i
$306$		0			0
$307$	−2.80743	+	15.9217i	−0.160228	+	0.908700i	0.793620	+	0.608413i	$0.208194\pi$
$307$	−2.80743	+	15.9217i	−0.160228	+	0.908700i	−0.953849	+	0.300287i	$0.902918\pi$
$308$	5.85534	+	13.5742i	0.333639	+	0.773462i
$309$		0			0
$310$	3.02137	+	0.716077i	0.171602	+	0.0406705i
$311$	−14.5476	+	15.4196i	−0.824919	+	0.874363i	−0.993790	−	0.111276i	$-0.964506\pi$
$311$	−14.5476	+	15.4196i	−0.824919	+	0.874363i	0.168871	+	0.985638i	$0.445988\pi$
$312$		0			0
$313$	−3.23147	+	4.34062i	−0.182654	+	0.245346i	−0.884014	−	0.467461i	$-0.845169\pi$
$313$	−3.23147	+	4.34062i	−0.182654	+	0.245346i	0.701360	+	0.712807i	$0.252576\pi$
$314$	−2.80708	−	2.35542i	−0.158413	−	0.132924i
$315$		0			0
$316$	−2.34420	+	1.96701i	−0.131871	+	0.110653i
$317$	0.507449	+	8.71256i	0.0285012	+	0.489346i	0.982111	+	0.188302i	$0.0602983\pi$
$317$	0.507449	+	8.71256i	0.0285012	+	0.489346i	−0.953610	+	0.301045i	$0.902665\pi$
$318$		0			0
$319$	−12.9430	+	30.0052i	−0.724667	+	1.67997i
$320$	−10.0746	−	6.62619i	−0.563189	−	0.370415i
$321$		0			0
$322$	−0.990803	+	3.30951i	−0.0552153	+	0.184432i
$323$	−0.261706			−0.0145617
$324$		0			0
$325$	−2.75968			−0.153080
$326$	−1.28606	+	4.29574i	−0.0712283	+	0.237919i
$327$		0			0
$328$	2.60479	+	1.71320i	0.143825	+	0.0945954i
$329$	−4.58040	+	10.6186i	−0.252526	+	0.585421i
$330$		0			0
$331$	1.14258	+	19.6173i	0.0628019	+	1.07827i	0.871612	+	0.490196i	$0.163075\pi$
$331$	1.14258	+	19.6173i	0.0628019	+	1.07827i	−0.808810	+	0.588070i	$0.799888\pi$
$332$	4.80468	−	4.03161i	0.263691	−	0.221263i
$333$		0			0
$334$	−1.62927	−	1.36712i	−0.0891495	−	0.0748053i
$335$	1.53654	−	2.06394i	0.0839504	−	0.112765i
$336$		0			0
$337$	5.04080	−	5.34293i	0.274590	−	0.291048i	−0.575373	−	0.817891i	$-0.695143\pi$
$337$	5.04080	−	5.34293i	0.274590	−	0.291048i	0.849962	+	0.526843i	$0.176625\pi$
$338$	−5.39012	−	1.27748i	−0.293184	−	0.0694858i
$339$		0			0
$340$	6.84680	+	15.8727i	0.371320	+	0.860816i
$341$	2.45148	−	13.9030i	0.132755	−	0.752892i
$342$		0			0
$343$	3.32603	+	18.8629i	0.179589	+	1.01850i
$344$	0.801891	−	0.527412i	0.0432351	−	0.0284361i
$345$		0			0
$346$	−2.80193	−	3.76364i	−0.150633	−	0.202335i
$347$	1.05931	−	18.1877i	0.0568668	−	0.976365i	−0.842369	−	0.538901i	$-0.818840\pi$
$347$	1.05931	−	18.1877i	0.0568668	−	0.976365i	0.899236	−	0.437464i	$-0.144123\pi$
$348$		0			0
$349$	11.0555	+	11.7182i	0.591788	+	0.627258i	0.952178	−	0.305543i	$-0.0988380\pi$
$349$	11.0555	+	11.7182i	0.591788	+	0.627258i	−0.360390	+	0.932802i	$0.617357\pi$
$350$	0.201764	+	0.349465i	0.0107847	+	0.0186797i
$351$		0			0
$352$	5.43923	−	9.42103i	0.289912	−	0.502142i
$353$	16.7207	−	3.96288i	0.889953	−	0.210923i	0.239887	−	0.970801i	$-0.422890\pi$
$353$	16.7207	−	3.96288i	0.889953	−	0.210923i	0.650066	+	0.759878i	$0.274741\pi$
$354$		0			0
$355$	−27.0477	+	13.5839i	−1.43554	+	0.720957i
$356$	26.4994	−	3.09734i	1.40447	−	0.164159i
$357$		0			0
$358$	−0.179686	−	0.0902416i	−0.00949669	−	0.00476942i
$359$	−26.7193	−	9.72505i	−1.41019	−	0.513268i	−0.479007	−	0.877811i	$-0.659003\pi$
$359$	−26.7193	−	9.72505i	−1.41019	−	0.513268i	−0.931187	+	0.364543i	$0.881225\pi$
$360$		0			0
$361$	17.8507	−	6.49711i	0.939509	−	0.341953i
$362$	−4.39735	−	0.513977i	−0.231120	−	0.0270140i
$363$		0			0
$364$	−7.64692	−	25.5425i	−0.400808	−	1.33879i
$365$	5.91065	+	19.7429i	0.309377	+	1.03339i
$366$		0			0
$367$	−10.3069	−	1.20471i	−0.538017	−	0.0628851i	−0.157254	−	0.987558i	$-0.550264\pi$
$367$	−10.3069	−	1.20471i	−0.538017	−	0.0628851i	−0.380762	+	0.924673i	$0.624338\pi$
$368$	−13.7018	+	4.98706i	−0.714258	+	0.259969i
$369$		0			0
$370$	−2.22594	−	0.810174i	−0.115721	−	0.0421190i
$371$	−4.48394	−	2.25192i	−0.232794	−	0.116914i
$372$		0			0
$373$	−14.7918	+	1.72891i	−0.765890	+	0.0895198i	−0.490063	−	0.871687i	$-0.663026\pi$
$373$	−14.7918	+	1.72891i	−0.765890	+	0.0895198i	−0.275828	+	0.961207i	$0.588952\pi$
$374$	−3.72237	+	1.86944i	−0.192479	+	0.0966667i
$375$		0			0
$376$	5.47318	−	1.29717i	0.282258	−	0.0668963i
$377$	29.4683	−	51.0405i	1.51769	−	2.62872i
$378$		0			0
$379$	−5.81217	−	10.0670i	−0.298551	−	0.517106i	0.677253	−	0.735750i	$-0.263170\pi$
$379$	−5.81217	−	10.0670i	−0.298551	−	0.517106i	−0.975805	+	0.218644i	$0.929837\pi$
$380$	0.168655	+	0.178764i	0.00865182	+	0.00917040i
$381$		0			0
$382$	−0.156682	+	2.69013i	−0.00801657	+	0.137639i
$383$	17.0286	+	22.8733i	0.870119	+	1.16877i	0.984508	+	0.175337i	$0.0561015\pi$
$383$	17.0286	+	22.8733i	0.870119	+	1.16877i	−0.114389	+	0.993436i	$0.536491\pi$
$384$		0			0
$385$	−13.7947	+	9.07291i	−0.703042	+	0.462398i
$386$	−0.730054	−	4.14034i	−0.0371588	−	0.210738i
$387$		0			0
$388$	−2.31635	+	13.1367i	−0.117595	+	0.666915i
$389$	−1.21611	−	2.81926i	−0.0616592	−	0.142942i	0.884601	−	0.466349i	$-0.154431\pi$
$389$	−1.21611	−	2.81926i	−0.0616592	−	0.142942i	−0.946260	+	0.323407i	$0.895172\pi$
$390$		0			0
$391$	17.8715	+	4.23561i	0.903798	+	0.214204i
$392$	0.450281	−	0.477270i	0.0227426	−	0.0241058i
$393$		0			0
$394$	−1.43012	+	1.92099i	−0.0720485	+	0.0967779i
$395$	−2.61816	−	2.19690i	−0.131734	−	0.110538i
$396$		0			0
$397$	−8.05095	+	6.75555i	−0.404065	+	0.339051i	−0.822063	−	0.569397i	$-0.807177\pi$
$397$	−8.05095	+	6.75555i	−0.404065	+	0.339051i	0.417997	+	0.908448i	$0.362732\pi$
$398$	−0.0389878	−	0.669395i	−0.00195428	−	0.0335537i
$399$		0			0
$400$	−0.674598	+	1.56389i	−0.0337299	+	0.0781947i
$401$	22.1390	+	14.5610i	1.10557	+	0.727143i	0.964822	−	0.262903i	$-0.0846799\pi$
$401$	22.1390	+	14.5610i	1.10557	+	0.727143i	0.140745	+	0.990046i	$0.455050\pi$
$402$		0			0
$403$	−7.30258	+	24.3923i	−0.363767	+	1.21507i
$404$	20.6150			1.02563
$405$		0			0
$406$	−8.61783			−0.427696
$407$	−3.08886	+	10.3175i	−0.153109	+	0.511421i
$408$		0			0
$409$	−22.0172	−	14.4809i	−1.08868	−	0.716036i	−0.127466	−	0.991843i	$-0.540684\pi$
$409$	−22.0172	−	14.4809i	−1.08868	−	0.716036i	−0.961213	+	0.275807i	$0.911055\pi$
$410$	−0.671783	+	1.55737i	−0.0331770	+	0.0769129i
$411$		0			0
$412$	−1.37347	−	23.5816i	−0.0676662	−	1.16178i
$413$	14.0551	−	11.7936i	0.691605	−	0.580326i
$414$		0			0
$415$	5.36621	+	4.50278i	0.263417	+	0.221033i
$416$	−11.7163	+	15.7377i	−0.574439	+	0.771606i
$417$		0			0
$418$	−0.0406401	+	0.0430760i	−0.00198777	+	0.00210692i
$419$	−7.62045	−	1.80608i	−0.372284	−	0.0882328i	0.0402151	−	0.999191i	$-0.487196\pi$
$419$	−7.62045	−	1.80608i	−0.372284	−	0.0882328i	−0.412499	+	0.910958i	$0.635344\pi$
$420$		0			0
$421$	−12.6159	−	29.2469i	−0.614860	−	1.42541i	−0.886373	−	0.462971i	$-0.846783\pi$
$421$	−12.6159	−	29.2469i	−0.614860	−	1.42541i	0.271513	−	0.962435i	$-0.412476\pi$
$422$	−0.0361680	+	0.205119i	−0.00176063	+	0.00998504i
$423$		0			0
$424$	0.423796	+	2.40347i	0.0205813	+	0.116723i
$425$	1.79241	−	1.17888i	0.0869445	−	0.0571843i
$426$		0			0
$427$	17.7392	+	23.8279i	0.858461	+	1.15311i
$428$	−0.549788	+	9.43949i	−0.0265750	+	0.456275i
$429$		0			0
$430$	0.358316	+	0.379793i	0.0172795	+	0.0183152i
$431$	−16.6567	−	28.8502i	−0.802324	−	1.38967i	−0.918083	−	0.396389i	$-0.870263\pi$
$431$	−16.6567	−	28.8502i	−0.802324	−	1.38967i	0.115759	−	0.993277i	$-0.463070\pi$
$432$		0			0
$433$	2.75793	−	4.77688i	0.132538	−	0.229562i	−0.792116	−	0.610370i	$-0.791021\pi$
$433$	2.75793	−	4.77688i	0.132538	−	0.229562i	0.924654	+	0.380808i	$0.124354\pi$
$434$	3.62275	−	0.858608i	0.173898	−	0.0412145i
$435$		0			0
$436$	−0.613156	+	0.307939i	−0.0293649	+	0.0147476i
$437$	0.259357	−	0.0303145i	0.0124067	−	0.00145014i
$438$		0			0
$439$	−2.95797	−	1.48555i	−0.141176	−	0.0709013i	0.376809	−	0.926291i	$-0.377021\pi$
$439$	−2.95797	−	1.48555i	−0.141176	−	0.0709013i	−0.517985	+	0.855390i	$0.673318\pi$
$440$	7.54647	+	2.74669i	0.359764	+	0.130943i
$441$		0			0
$442$	7.05960	−	2.56948i	0.335791	−	0.122218i
$443$	17.0697	+	1.99516i	0.811004	+	0.0947928i	0.511479	−	0.859296i	$-0.329098\pi$
$443$	17.0697	+	1.99516i	0.811004	+	0.0947928i	0.299525	+	0.954088i	$0.403172\pi$
$444$		0			0
$445$	8.54614	+	28.5461i	0.405126	+	1.35321i
$446$	2.04840	+	6.84212i	0.0969944	+	0.323984i
$447$		0			0
$448$	−14.3608	−	1.67853i	−0.678482	−	0.0793032i
$449$	−16.5392	+	6.01977i	−0.780532	+	0.284090i	−0.701394	−	0.712773i	$-0.747439\pi$
$449$	−16.5392	+	6.01977i	−0.780532	+	0.284090i	−0.0791375	+	0.996864i	$0.525217\pi$
$450$		0			0
$451$	7.24636	+	2.63746i	0.341218	+	0.124193i
$452$	−33.5082	−	16.8284i	−1.57609	−	0.791543i
$453$		0			0
$454$	4.22544	−	0.493883i	0.198310	−	0.0231791i
$455$	26.6112	−	13.3646i	1.24755	−	0.626544i
$456$		0			0
$457$	17.3927	−	4.12215i	0.813597	−	0.192826i	0.197304	−	0.980342i	$-0.436782\pi$
$457$	17.3927	−	4.12215i	0.813597	−	0.192826i	0.616294	+	0.787516i	$0.288633\pi$
$458$	0.987261	−	1.70999i	0.0461317	−	0.0799024i
$459$		0			0
$460$	−8.62394	−	14.9371i	−0.402093	−	0.696446i
$461$	−3.44987	−	3.65664i	−0.160676	−	0.170307i	0.642034	−	0.766676i	$-0.278091\pi$
$461$	−3.44987	−	3.65664i	−0.160676	−	0.170307i	−0.802710	+	0.596369i	$0.796609\pi$
$462$		0			0
$463$	−1.00039	+	17.1761i	−0.0464922	+	0.798240i	0.891807	+	0.452416i	$0.149438\pi$
$463$	−1.00039	+	17.1761i	−0.0464922	+	0.798240i	−0.938299	+	0.345824i	$0.887599\pi$
$464$	−21.7209	−	29.1762i	−1.00837	−	1.35447i
$465$		0			0
$466$	3.28425	−	2.16009i	0.152140	−	0.100064i
$467$	6.50441	+	36.8883i	0.300988	+	1.70699i	0.641812	+	0.766862i	$0.278183\pi$
$467$	6.50441	+	36.8883i	0.300988	+	1.70699i	−0.340824	+	0.940127i	$0.610706\pi$
$468$		0			0
$469$	0.535748	−	3.03838i	0.0247385	−	0.140299i
$470$	1.21200	+	2.80974i	0.0559055	+	0.129604i
$471$		0			0
$472$	−8.68357	−	2.05804i	−0.399694	−	0.0947292i
$473$	1.62912	−	1.72677i	0.0749072	−	0.0793970i
$474$		0			0
$475$	0.0182139	−	0.0244655i	0.000835712	−	0.00112256i
$476$	15.8779	+	13.3232i	0.727764	+	0.610666i
$477$		0			0
$478$	−2.38964	+	2.00515i	−0.109300	+	0.0917134i
$479$	−0.199015	−	3.41695i	−0.00909321	−	0.156124i	−0.999798	−	0.0200954i	$-0.993603\pi$
$479$	−0.199015	−	3.41695i	−0.00909321	−	0.156124i	0.990705	−	0.136029i	$-0.0434340\pi$
$480$		0			0
$481$	7.69362	−	17.8358i	0.350799	−	0.813244i
$482$	−4.59571	−	3.02265i	−0.209329	−	0.137678i
$483$		0			0
$484$	−0.891264	+	2.97703i	−0.0405120	+	0.135319i
$485$	−14.8983			−0.676498
$486$		0			0
$487$	−5.43342			−0.246212			−0.123106	−	0.992394i	$-0.539285\pi$
$487$	−5.43342			−0.246212			−0.123106	+	0.992394i	$0.539285\pi$
$488$	4.14396	−	13.8418i	0.187588	−	0.626588i
$489$		0			0
$490$	0.298236	+	0.196153i	0.0134729	+	0.00886129i
$491$	−1.57397	+	3.64886i	−0.0710321	+	0.164671i	−0.950033	−	0.312149i	$-0.898951\pi$
$491$	−1.57397	+	3.64886i	−0.0710321	+	0.164671i	0.879001	+	0.476820i	$0.158211\pi$
$492$		0			0
$493$	2.66399	+	45.7390i	0.119980	+	2.05998i
$494$	0.0818212	−	0.0686561i	0.00368131	−	0.00308898i
$495$		0			0
$496$	12.0379	+	10.1010i	0.540516	+	0.453547i
$497$	−21.6719	+	29.1104i	−0.972116	+	1.30578i
$498$		0			0
$499$	14.7243	−	15.6069i	0.659151	−	0.698659i	−0.308423	−	0.951249i	$-0.599801\pi$
$499$	14.7243	−	15.6069i	0.659151	−	0.698659i	0.967573	+	0.252591i	$0.0812826\pi$
$500$	−21.5628	−	5.11047i	−0.964317	−	0.228547i
$501$		0			0
$502$	−3.14579	−	7.29277i	−0.140404	−	0.325492i
$503$	−4.28340	+	24.2924i	−0.190987	+	1.08314i	0.727031	+	0.686605i	$0.240900\pi$
$503$	−4.28340	+	24.2924i	−0.190987	+	1.08314i	−0.918018	+	0.396538i	$0.870211\pi$
$504$		0			0
$505$	3.99812	+	22.6745i	0.177914	+	1.00900i
$506$	3.47241	−	2.28384i	0.154368	−	0.101529i
$507$		0			0
$508$	16.3615	+	21.9773i	0.725924	+	0.975086i
$509$	−0.427185	+	7.33448i	−0.0189346	+	0.325095i	0.975519	+	0.219916i	$0.0705785\pi$
$509$	−0.427185	+	7.33448i	−0.0189346	+	0.325095i	−0.994453	+	0.105179i	$0.966459\pi$
$510$		0			0
$511$	16.9576	+	17.9740i	0.750158	+	0.795121i
$512$	10.2684	+	17.7854i	0.453804	+	0.786011i
$513$		0			0
$514$	−0.382388	+	0.662316i	−0.0168664	+	0.0292135i
$515$	25.6711	−	6.08417i	1.13120	−	0.268100i
$516$		0			0
$517$	12.4328	−	6.24397i	0.546793	−	0.274610i
$518$	−2.82108	+	0.329737i	−0.123951	+	0.0144878i
$519$		0			0
$520$	−12.9435	−	6.50045i	−0.567608	−	0.285064i
$521$	25.5909	+	9.31432i	1.12116	+	0.408068i	0.835074	−	0.550137i	$-0.185425\pi$
$521$	25.5909	+	9.31432i	1.12116	+	0.408068i	0.286082	+	0.958205i	$0.407647\pi$
$522$		0			0
$523$	−14.3006	+	5.20499i	−0.625321	+	0.227598i	−0.635193	−	0.772353i	$-0.719080\pi$
$523$	−14.3006	+	5.20499i	−0.625321	+	0.227598i	0.00987267	+	0.999951i	$0.496857\pi$
$524$	−5.76285	−	0.673581i	−0.251751	−	0.0294255i
$525$		0			0
$526$	0.356954	+	1.19231i	0.0155639	+	0.0519872i
$527$	−5.67693	−	18.9623i	−0.247291	−	0.826009i
$528$		0			0
$529$	4.64281	+	0.542667i	0.201861	+	0.0235942i
$530$	−1.24763	+	0.454101i	−0.0541936	+	0.0197249i
$531$		0			0
$532$	0.276913	+	0.100788i	0.0120057	+	0.00436972i
$533$	−12.4287	−	6.24194i	−0.538348	−	0.270368i
$534$		0			0
$535$	−10.4891	+	1.22600i	−0.453485	+	0.0530048i
$536$	−1.34102	+	0.673486i	−0.0579233	+	0.0290902i
$537$		0			0
$538$	3.42381	−	0.811458i	0.147611	−	0.0349844i
$539$	0.811481	−	1.40553i	0.0349530	−	0.0605403i
$540$		0			0
$541$	−8.31159	−	14.3961i	−0.357343	−	0.618937i	0.630173	−	0.776455i	$-0.282984\pi$
$541$	−8.31159	−	14.3961i	−0.357343	−	0.618937i	−0.987516	+	0.157518i	$0.949651\pi$
$542$	0.173009	+	0.183379i	0.00743139	+	0.00787682i
$543$		0			0
$544$	0.886848	−	15.2266i	0.0380233	−	0.652835i
$545$	−0.457619	−	0.614690i	−0.0196023	−	0.0263304i
$546$		0			0
$547$	−9.42672	+	6.20005i	−0.403057	+	0.265095i	−0.734812	−	0.678271i	$-0.762730\pi$
$547$	−9.42672	+	6.20005i	−0.403057	+	0.265095i	0.331755	+	0.943366i	$0.392359\pi$
$548$	0.859166	+	4.87257i	0.0367018	+	0.208146i
$549$		0			0
$550$	0.0843006	−	0.478093i	0.00359459	−	0.0203859i
$551$	0.258001	+	0.598114i	0.0109912	+	0.0254805i
$552$		0			0
$553$	−3.98759	−	0.945076i	−0.169570	−	0.0401887i
$554$	6.35497	−	6.73587i	0.269997	−	0.286180i
$555$		0			0
$556$	21.5318	−	28.9223i	0.913153	−	1.22658i
$557$	−22.3339	−	18.7404i	−0.946318	−	0.794055i	0.0323557	−	0.999476i	$-0.489699\pi$
$557$	−22.3339	−	18.7404i	−0.946318	−	0.794055i	−0.978674	+	0.205421i	$0.934144\pi$
$558$		0			0
$559$	−3.27993	+	2.75219i	−0.138726	+	0.116405i
$560$	−1.06861	−	18.3474i	−0.0451571	−	0.775317i
$561$		0			0
$562$	−3.46699	+	8.03739i	−0.146246	+	0.339037i
$563$	−17.9346	−	11.7958i	−0.755853	−	0.497133i	0.112150	−	0.993691i	$-0.464226\pi$
$563$	−17.9346	−	11.7958i	−0.755853	−	0.497133i	−0.868003	+	0.496559i	$0.834597\pi$
$564$		0			0
$565$	12.0110	−	40.1195i	0.505306	−	1.68784i
$566$	1.62083			0.0681286
$567$		0			0
$568$	17.6519			0.740659
$569$	−0.768966	+	2.56852i	−0.0322367	+	0.107678i	−0.972594	−	0.232511i	$-0.925306\pi$
$569$	−0.768966	+	2.56852i	−0.0322367	+	0.107678i	0.940357	+	0.340189i	$0.110491\pi$
$570$		0			0
$571$	2.37346	+	1.56105i	0.0993261	+	0.0653278i	0.598200	−	0.801347i	$-0.295883\pi$
$571$	2.37346	+	1.56105i	0.0993261	+	0.0653278i	−0.498874	+	0.866674i	$0.666253\pi$
$572$	−12.7050	+	29.4534i	−0.531221	+	1.23151i
$573$		0			0
$574$	0.118248	+	2.03023i	0.00493556	+	0.0847403i
$575$	−1.63976	+	1.37592i	−0.0683828	+	0.0573800i
$576$		0			0
$577$	4.53692	+	3.80692i	0.188874	+	0.158484i	0.732322	−	0.680959i	$-0.238437\pi$
$577$	4.53692	+	3.80692i	0.188874	+	0.158484i	−0.543447	+	0.839443i	$0.682881\pi$
$578$	−0.266681	+	0.358215i	−0.0110925	+	0.0148998i
$579$		0			0
$580$	29.5262	−	31.2959i	1.22601	−	1.29949i
$581$	8.17300	+	1.93704i	0.339073	+	0.0803618i
$582$		0			0
$583$	2.39095	+	5.54285i	0.0990231	+	0.229561i
$584$	2.08710	−	11.8365i	0.0863646	−	0.489798i
$585$		0			0
$586$	−0.129110	−	0.732221i	−0.00533350	−	0.0302478i
$587$	−9.41411	+	6.19176i	−0.388562	+	0.255561i	−0.728727	−	0.684805i	$-0.759888\pi$
$587$	−9.41411	+	6.19176i	−0.388562	+	0.255561i	0.340165	+	0.940366i	$0.389517\pi$
$588$		0			0
$589$	−0.168049	−	0.225729i	−0.00692435	−	0.00930101i
$590$	0.282287	−	4.84668i	0.0116216	−	0.199535i
$591$		0			0
$592$	−8.22676	−	8.71985i	−0.338118	−	0.358384i
$593$	−4.74627	−	8.22078i	−0.194906	−	0.337587i	0.751964	−	0.659205i	$-0.229107\pi$
$593$	−4.74627	−	8.22078i	−0.194906	−	0.337587i	−0.946870	+	0.321617i	$0.895774\pi$
$594$		0			0
$595$	−11.5748	+	20.0481i	−0.474519	+	0.821892i
$596$	7.57299	−	1.79483i	0.310202	−	0.0735191i
$597$		0			0
$598$	−6.69860	+	3.36416i	−0.273926	+	0.137571i
$599$	24.7821	−	2.89661i	1.01257	−	0.118352i	0.406405	−	0.913693i	$-0.366782\pi$
$599$	24.7821	−	2.89661i	1.01257	−	0.118352i	0.606163	+	0.795341i	$0.292708\pi$
$600$		0			0
$601$	−10.2652	−	5.15539i	−0.418728	−	0.210293i	0.226945	−	0.973908i	$-0.427126\pi$
$601$	−10.2652	−	5.15539i	−0.418728	−	0.210293i	−0.645672	+	0.763615i	$0.723423\pi$
$602$	0.588315	+	0.214129i	0.0239779	+	0.00872725i
$603$		0			0
$604$	17.7431	−	6.45795i	0.721955	−	0.262770i
$605$	−3.44729	−	0.402931i	−0.140152	−	0.0163815i
$606$		0			0
$607$	−11.4303	−	38.1799i	−0.463942	−	1.54967i	−0.795328	−	0.606180i	$-0.792701\pi$
$607$	−11.4303	−	38.1799i	−0.463942	−	1.54967i	0.331386	−	0.943495i	$-0.392484\pi$
$608$	−0.0621928	−	0.207738i	−0.00252225	−	0.00842490i
$609$		0			0
$610$	7.80726	+	0.912537i	0.316107	+	0.0369476i
$611$	−23.5792	+	8.58211i	−0.953911	+	0.347195i
$612$		0			0
$613$	−16.9065	−	6.15347i	−0.682848	−	0.248536i	−0.0227782	−	0.999741i	$-0.507251\pi$
$613$	−16.9065	−	6.15347i	−0.682848	−	0.248536i	−0.660070	+	0.751204i	$0.729473\pi$
$614$	4.58387	+	2.30211i	0.184990	+	0.0929054i
$615$		0			0
$616$	9.56415	−	1.11789i	0.385351	−	0.0450410i
$617$	−16.3959	+	8.23431i	−0.660072	+	0.331501i	−0.747106	−	0.664704i	$-0.768557\pi$
$617$	−16.3959	+	8.23431i	−0.660072	+	0.331501i	0.0870339	+	0.996205i	$0.472261\pi$
$618$		0			0
$619$	−43.7258	+	10.3632i	−1.75749	+	0.416532i	−0.977784	−	0.209617i	$-0.932778\pi$
$619$	−43.7258	+	10.3632i	−1.75749	+	0.416532i	−0.779703	+	0.626149i	$0.784630\pi$
$620$	−9.29411	+	16.0979i	−0.373260	+	0.646506i
$621$		0			0
$622$	3.36294	+	5.82478i	0.134842	+	0.233553i
$623$	24.5187	+	25.9883i	0.982322	+	1.04120i
$624$		0			0
$625$	1.29371	−	22.2122i	0.0517484	−	0.888487i
$626$	1.02526	+	1.37717i	0.0409778	+	0.0550427i
$627$		0			0
$628$	18.3277	−	12.0543i	0.731354	−	0.481019i
$629$	2.62214	+	14.8709i	0.104552	+	0.592941i
$630$		0			0
$631$	5.90645	−	33.4972i	0.235132	−	1.33350i	−0.607203	−	0.794547i	$-0.707708\pi$
$631$	5.90645	−	33.4972i	0.235132	−	1.33350i	0.842335	−	0.538954i	$-0.181180\pi$
$632$	0.789489	+	1.83024i	0.0314042	+	0.0728031i
$633$		0			0
$634$	2.69432	+	0.638565i	0.107005	+	0.0253607i
$635$	−20.9997	+	22.2584i	−0.833348	+	0.883297i
$636$		0			0
$637$	−1.74796	+	2.34792i	−0.0692567	+	0.0930279i
$638$	7.94218	+	6.66428i	0.314434	+	0.263841i
$639$		0			0
$640$	−14.4847	+	12.1541i	−0.572556	+	0.480432i
$641$	−0.0182934	−	0.314085i	−0.000722545	−	0.0124056i	0.997928	−	0.0643465i	$-0.0204963\pi$
$641$	−0.0182934	−	0.314085i	−0.000722545	−	0.0124056i	−0.998650	+	0.0519409i	$0.983459\pi$
$642$		0			0
$643$	−13.1236	+	30.4240i	−0.517546	+	1.19981i	0.436380	+	0.899762i	$0.356260\pi$
$643$	−13.1236	+	30.4240i	−0.517546	+	1.19981i	−0.953926	+	0.300043i	$0.902999\pi$
$644$	−17.2787	−	11.3644i	−0.680876	−	0.447819i
$645$		0			0
$646$	−0.0238140	+	0.0795444i	−0.000936950	+	0.00312963i
$647$	−14.0510			−0.552403			−0.276201	−	0.961100i	$-0.589076\pi$
$647$	−14.0510			−0.552403			−0.276201	+	0.961100i	$0.589076\pi$
$648$		0			0
$649$	−22.0733			−0.866453
$650$	−0.251118	+	0.838793i	−0.00984966	+	0.0329002i
$651$		0			0
$652$	−22.4277	−	14.7509i	−0.878337	−	0.577691i
$653$	17.7892	−	41.2399i	0.696144	−	1.61384i	−0.0901041	−	0.995932i	$-0.528720\pi$
$653$	17.7892	−	41.2399i	0.696144	−	1.61384i	0.786248	−	0.617911i	$-0.212021\pi$
$654$		0			0
$655$	−0.376789	−	6.46921i	−0.0147223	−	0.252773i
$656$	−6.57544	+	5.51745i	−0.256728	+	0.215420i
$657$		0			0
$658$	2.81067	+	2.35843i	0.109571	+	0.0919413i
$659$	20.0167	−	26.8871i	0.779741	−	1.04737i	−0.217709	−	0.976014i	$-0.569858\pi$
$659$	20.0167	−	26.8871i	0.779741	−	1.04737i	0.997451	−	0.0713607i	$-0.0227341\pi$
$660$		0			0
$661$	−11.1359	+	11.8033i	−0.433134	+	0.459096i	−0.906770	−	0.421625i	$-0.861460\pi$
$661$	−11.1359	+	11.8033i	−0.433134	+	0.459096i	0.473636	+	0.880721i	$0.342941\pi$
$662$	6.06657	+	1.43780i	0.235784	+	0.0558818i
$663$		0			0
$664$	−1.61814	−	3.75128i	−0.0627962	−	0.145578i
$665$	−0.0571518	+	0.324124i	−0.00221625	+	0.0125690i
$666$		0			0
$667$	−7.93821	−	45.0198i	−0.307369	−	1.74317i
$668$	10.6376	−	6.99649i	0.411583	−	0.270702i
$669$		0			0
$670$	−0.487506	−	0.654834i	−0.0188340	−	0.0252985i
$671$	2.07799	−	35.6778i	0.0802200	−	1.37732i
$672$		0			0
$673$	−1.34992	−	1.43083i	−0.0520355	−	0.0551545i	0.700833	−	0.713325i	$-0.252812\pi$
$673$	−1.34992	−	1.43083i	−0.0520355	−	0.0551545i	−0.752868	+	0.658171i	$0.771330\pi$
$674$	−1.16527	−	2.01831i	−0.0448846	−	0.0777424i
$675$		0			0
$676$	16.5807	−	28.7186i	0.637719	−	1.10456i
$677$	−19.9663	+	4.73209i	−0.767366	+	0.181869i	−0.595613	−	0.803271i	$-0.703091\pi$
$677$	−19.9663	+	4.73209i	−0.767366	+	0.181869i	−0.171752	+	0.985140i	$0.554943\pi$
$678$		0			0
$679$	−15.9636	+	8.01723i	−0.612627	+	0.307673i
$680$	11.1836	−	1.30718i	0.428872	−	0.0501279i
$681$		0			0
$682$	−4.00270	−	2.01023i	−0.153271	−	0.0769756i
$683$	−20.1405	−	7.33055i	−0.770656	−	0.280496i	−0.0733852	−	0.997304i	$-0.523380\pi$
$683$	−20.1405	−	7.33055i	−0.770656	−	0.280496i	−0.697271	+	0.716808i	$0.745602\pi$
$684$		0			0
$685$	−5.19273	+	1.89000i	−0.198404	+	0.0722131i
$686$	6.03593	+	0.705500i	0.230453	+	0.0269361i
$687$		0			0
$688$	0.757876	+	2.53148i	0.0288937	+	0.0965118i
$689$	−3.12252	−	10.4300i	−0.118959	−	0.397350i
$690$		0			0
$691$	−27.5730	−	3.22282i	−1.04893	−	0.122602i	−0.425875	−	0.904782i	$-0.640034\pi$
$691$	−27.5730	−	3.22282i	−1.04893	−	0.122602i	−0.623052	+	0.782180i	$0.714108\pi$
$692$	26.3949	−	9.60696i	1.00338	−	0.365202i
$693$		0			0
$694$	−5.43167	−	1.97696i	−0.206183	−	0.0750446i
$695$	35.9876	+	18.0737i	1.36509	+	0.685573i
$696$		0			0
$697$	10.7389	−	1.25519i	0.406763	−	0.0475438i
$698$	4.56768	−	2.29397i	0.172889	−	0.0868282i
$699$		0			0
$700$	−2.35057	+	0.557095i	−0.0888431	+	0.0210562i
$701$	0.354873	−	0.614659i	0.0134034	−	0.0232153i	−0.859246	−	0.511563i	$-0.829067\pi$
$701$	0.354873	−	0.614659i	0.0134034	−	0.0232153i	0.872649	+	0.488347i	$0.162400\pi$
$702$		0			0
$703$	0.107343	+	0.185923i	0.00404851	+	0.00701223i
$704$	11.9368	+	12.6523i	0.449886	+	0.476852i
$705$		0			0
$706$	0.317006	−	5.44278i	0.0119307	−	0.204842i
$707$	16.4858	+	22.1443i	0.620013	+	0.832822i
$708$		0			0
$709$	16.8691	−	11.0950i	0.633533	−	0.416681i	−0.191716	−	0.981450i	$-0.561405\pi$
$709$	16.8691	−	11.0950i	0.633533	−	0.416681i	0.825249	+	0.564769i	$0.191035\pi$
$710$	1.66754	+	9.45710i	0.0625817	+	0.354919i
$711$		0			0
$712$	3.01771	−	17.1143i	0.113093	−	0.641385i
$713$	7.82245	+	18.1345i	0.292953	+	0.679141i
$714$		0			0
$715$	−34.8599	−	8.26195i	−1.30369	−	0.308979i
$716$	0.826036	−	0.875547i	0.0308704	−	0.0327207i
$717$		0			0
$718$	−5.38722	+	7.23629i	−0.201049	+	0.270056i
$719$	−12.8502	−	10.7826i	−0.479231	−	0.402123i	0.370917	−	0.928666i	$-0.379043\pi$
$719$	−12.8502	−	10.7826i	−0.479231	−	0.402123i	−0.850148	+	0.526543i	$0.823488\pi$
$720$		0			0
$721$	24.2326	−	20.3336i	0.902471	−	0.757263i
$722$	−0.350441	−	6.01683i	−0.0130421	−	0.223923i
$723$		0			0
$724$	10.4975	−	24.3360i	0.390138	−	0.904442i
$725$	−4.46130	−	2.93424i	−0.165689	−	0.108975i
$726$		0			0
$727$	6.36767	−	21.2695i	0.236164	−	0.788842i	−0.754945	−	0.655788i	$-0.772337\pi$
$727$	6.36767	−	21.2695i	0.236164	−	0.788842i	0.991109	−	0.133054i	$-0.0424783\pi$
$728$	−17.3671			−0.643666
$729$		0			0
$730$	6.53862			0.242005
$731$	0.954622	−	3.18866i	0.0353080	−	0.117937i
$732$		0			0
$733$	−3.25396	−	2.14016i	−0.120188	−	0.0790488i	0.487992	−	0.872848i	$-0.337730\pi$
$733$	−3.25396	−	2.14016i	−0.120188	−	0.0790488i	−0.608180	+	0.793799i	$0.708100\pi$
$734$	−1.30405	+	3.02312i	−0.0481332	+	0.111585i
$735$		0			0
$736$	0.884871	+	15.1927i	0.0326168	+	0.560009i
$737$	−2.84336	+	2.38586i	−0.104737	+	0.0878844i
$738$		0			0
$739$	−15.2233	−	12.7738i	−0.559997	−	0.469894i	0.318312	−	0.947986i	$-0.396884\pi$
$739$	−15.2233	−	12.7738i	−0.559997	−	0.469894i	−0.878310	+	0.478092i	$0.841328\pi$
$740$	8.46805	−	11.3746i	0.311292	−	0.418138i
$741$		0			0
$742$	−1.09248	+	1.15796i	−0.0401061	+	0.0425100i
$743$	−6.05085	−	1.43408i	−0.221984	−	0.0526112i	0.118119	−	0.992999i	$-0.462314\pi$
$743$	−6.05085	−	1.43408i	−0.221984	−	0.0526112i	−0.340103	+	0.940388i	$0.610462\pi$
$744$		0			0
$745$	3.44286	+	7.98145i	0.126137	+	0.292418i
$746$	−0.820489	+	4.65322i	−0.0300402	+	0.170367i
$747$		0			0
$748$	−4.33010	−	24.5572i	−0.158324	−	0.897901i
$749$	−10.5794	+	6.95819i	−0.386563	+	0.254247i
$750$		0			0
$751$	−9.62286	−	12.9257i	−0.351143	−	0.471667i	0.591099	−	0.806599i	$-0.298694\pi$
$751$	−9.62286	−	12.9257i	−0.351143	−	0.471667i	−0.942242	+	0.334932i	$0.891287\pi$
$752$	−0.900444	+	15.4600i	−0.0328358	+	0.563769i
$753$		0			0
$754$	−12.8321	−	13.6012i	−0.467316	−	0.495326i
$755$	10.5442	+	18.2632i	0.383744	+	0.664665i
$756$		0			0
$757$	17.7618	−	30.7643i	0.645563	−	1.11815i	−0.338608	−	0.940928i	$-0.609956\pi$
$757$	17.7618	−	30.7643i	0.645563	−	1.11815i	0.984171	−	0.177221i	$-0.0567106\pi$
$758$	−3.58869	+	0.850536i	−0.130347	+	0.0308929i
$759$		0			0
$760$	0.143056	−	0.0718453i	0.00518917	−	0.00260610i
$761$	−20.2160	+	2.36292i	−0.732831	+	0.0856556i	−0.474320	−	0.880353i	$-0.657306\pi$
$761$	−20.2160	+	2.36292i	−0.732831	+	0.0856556i	−0.258511	+	0.966008i	$0.583232\pi$
$762$		0			0
$763$	−0.821124	−	0.412384i	−0.0297267	−	0.0149293i
$764$	−15.1587	−	5.51732i	−0.548423	−	0.199610i
$765$		0			0
$766$	8.50177	−	3.09439i	0.307181	−	0.111805i
$767$	39.5416	+	4.62175i	1.42776	+	0.166882i
$768$		0			0
$769$	5.34047	+	17.8384i	0.192582	+	0.643270i	0.998674	+	0.0514792i	$0.0163936\pi$
$769$	5.34047	+	17.8384i	0.192582	+	0.643270i	−0.806092	+	0.591791i	$0.798421\pi$
$770$	1.50242	+	5.01843i	0.0541434	+	0.180852i
$771$		0			0
$772$	24.9980	+	2.92185i	0.899698	+	0.105160i
$773$	−3.69733	+	1.34572i	−0.132984	+	0.0484021i	−0.407655	−	0.913136i	$-0.633653\pi$
$773$	−3.69733	+	1.34572i	−0.132984	+	0.0484021i	0.274671	+	0.961538i	$0.411431\pi$
$774$		0			0
$775$	2.16778	+	0.789007i	0.0778689	+	0.0283420i
$776$	7.76457	+	3.89951i	0.278732	+	0.139984i
$777$		0			0
$778$	−0.967561	+	0.113092i	−0.0346888	+	0.00405453i
$779$	0.137367	−	0.0689881i	0.00492167	−	0.00247176i
$780$		0			0
$781$	42.4842	−	10.0689i	1.52020	−	0.360295i
$782$	2.91361	−	5.04653i	0.104191	−	0.180463i
$783$		0			0
$784$	0.903265	+	1.56450i	0.0322595	+	0.0558750i
$785$	16.8131	+	17.8208i	0.600085	+	0.636052i
$786$		0			0
$787$	−0.428922	+	7.36431i	−0.0152894	+	0.262509i	0.981997	+	0.188895i	$0.0604905\pi$
$787$	−0.428922	+	7.36431i	−0.0152894	+	0.262509i	−0.997287	+	0.0736146i	$0.976547\pi$
$788$	−8.56131	−	11.4998i	−0.304984	−	0.409664i
$789$		0			0
$790$	−0.905978	+	0.595871i	−0.0322333	+	0.0212001i
$791$	−8.71966	−	49.4517i	−0.310035	−	1.75830i
$792$		0			0
$793$	−11.1927	+	63.4772i	−0.397466	+	2.25414i
$794$	1.32072	+	3.06177i	0.0468706	+	0.108658i
$795$		0			0
$796$	3.90587	+	0.925708i	0.138440	+	0.0328108i
$797$	10.2575	−	10.8723i	0.363340	−	0.385118i	−0.519752	−	0.854317i	$-0.673976\pi$
$797$	10.2575	−	10.8723i	0.363340	−	0.385118i	0.883093	+	0.469199i	$0.155457\pi$
$798$		0			0
$799$	11.6485	−	15.6466i	0.412094	−	0.553538i
$800$	1.36173	+	1.14263i	0.0481446	+	0.0403981i
$801$		0			0
$802$	6.44030	−	5.40405i	0.227415	−	0.190824i
$803$	−1.72856	−	29.6783i	−0.0609996	−	1.04732i
$804$		0			0
$805$	9.14863	−	21.2089i	0.322447	−	0.747516i
$806$	6.74943	+	4.43917i	0.237739	+	0.156363i
$807$		0			0
$808$	3.85115	−	12.8637i	0.135483	−	0.452545i
$809$	28.6228			1.00633			0.503163	−	0.864192i	$-0.332170\pi$
$809$	28.6228			1.00633			0.503163	+	0.864192i	$0.332170\pi$
$810$		0			0
$811$	15.2720			0.536273			0.268136	−	0.963381i	$-0.413592\pi$
$811$	15.2720			0.536273			0.268136	+	0.963381i	$0.413592\pi$
$812$	14.7962	−	49.4226i	0.519244	−	1.73439i
$813$		0			0
$814$	2.85489	+	1.87769i	0.100064	+	0.0658131i
$815$	11.8749	−	27.5291i	0.415960	−	0.964303i
$816$		0			0
$817$	−0.00275154	−	0.0472422i	−9.62643e−5	−	0.00165279i
$818$	−6.40487	+	5.37433i	−0.223941	+	0.187909i
$819$		0			0
$820$	−7.77799	−	6.52651i	−0.271619	−	0.227915i
$821$	1.85868	−	2.49663i	0.0648682	−	0.0871331i	−0.768505	−	0.639844i	$-0.778999\pi$
$821$	1.85868	−	2.49663i	0.0648682	−	0.0871331i	0.833373	+	0.552711i	$0.186406\pi$
$822$		0			0
$823$	−26.4373	+	28.0219i	−0.921546	+	0.976781i	−0.999797	−	0.0201524i	$-0.993585\pi$
$823$	−26.4373	+	28.0219i	−0.921546	+	0.976781i	0.0782513	+	0.996934i	$0.475066\pi$
$824$	−14.9715	−	3.54831i	−0.521558	−	0.123611i
$825$		0			0
$826$	−2.30567	−	5.34514i	−0.0802245	−	0.185981i
$827$	1.37656	−	7.80687i	0.0478677	−	0.271471i	−0.951475	−	0.307727i	$-0.900432\pi$
$827$	1.37656	−	7.80687i	0.0478677	−	0.271471i	0.999343	+	0.0362552i	$0.0115429\pi$
$828$		0			0
$829$	5.51283	+	31.2648i	0.191469	+	1.08587i	0.917359	+	0.398061i	$0.130317\pi$
$829$	5.51283	+	31.2648i	0.191469	+	1.08587i	−0.725890	+	0.687811i	$0.758572\pi$
$830$	1.85690	−	1.22130i	0.0644540	−	0.0423920i
$831$		0			0
$832$	−18.7342	−	25.1644i	−0.649492	−	0.872419i
$833$	0.132309	−	2.27166i	0.00458424	−	0.0787084i
$834$		0			0
$835$	9.75854	+	10.3435i	0.337708	+	0.357950i
$836$	−0.177262	−	0.307026i	−0.00613073	−	0.0106187i
$837$		0			0
$838$	−1.24238	+	2.15186i	−0.0429172	+	0.0743347i
$839$	−44.0468	+	10.4393i	−1.52067	+	0.360404i	−0.904246	−	0.427013i	$-0.859566\pi$
$839$	−44.0468	+	10.4393i	−1.52067	+	0.360404i	−0.616420	+	0.787417i	$0.711418\pi$
$840$		0			0
$841$	75.9921	−	38.1647i	2.62042	−	1.31602i
$842$	−10.0374	+	1.17321i	−0.345913	+	0.0404314i
$843$		0			0
$844$	−1.11424	−	0.559595i	−0.0383539	−	0.0192620i
$845$	34.8033	+	12.6674i	1.19727	+	0.435771i
$846$		0			0
$847$	−3.91062	+	1.42335i	−0.134370	+	0.0489069i
$848$	−6.67388	−	0.780065i	−0.229182	−	0.0267875i
$849$		0			0
$850$	−0.195216	−	0.652067i	−0.00669585	−	0.0223657i
$851$	−4.32116	−	14.4337i	−0.148127	−	0.494780i
$852$		0			0
$853$	−46.3159	−	5.41356i	−1.58583	−	0.185357i	−0.722997	−	0.690851i	$-0.757236\pi$
$853$	−46.3159	−	5.41356i	−1.58583	−	0.185357i	−0.862830	+	0.505494i	$0.831310\pi$
$854$	8.85657	−	3.22353i	0.303066	−	0.110307i
$855$		0			0
$856$	5.78753	+	2.10649i	0.197814	+	0.0719983i
$857$	6.10059	+	3.06383i	0.208392	+	0.104659i	0.549934	−	0.835208i	$-0.314653\pi$
$857$	6.10059	+	3.06383i	0.208392	+	0.104659i	−0.341542	+	0.939867i	$0.610949\pi$
$858$		0			0
$859$	−10.9129	+	1.27554i	−0.372344	+	0.0435207i	−0.300207	−	0.953874i	$-0.597056\pi$
$859$	−10.9129	+	1.27554i	−0.372344	+	0.0435207i	−0.0721365	+	0.997395i	$0.522982\pi$
$860$	−2.79328	+	1.40284i	−0.0952502	+	0.0478365i
$861$		0			0
$862$	−10.2846	+	2.43749i	−0.350294	+	0.0830212i
$863$	−27.8142	+	48.1756i	−0.946807	+	1.63992i	−0.194715	+	0.980860i	$0.562378\pi$
$863$	−27.8142	+	48.1756i	−0.946807	+	1.63992i	−0.752092	+	0.659058i	$0.770955\pi$
$864$		0			0
$865$	15.6858	+	27.1686i	0.533334	+	0.923761i
$866$	−1.20095	−	1.27293i	−0.0408100	−	0.0432561i
$867$		0			0
$868$	−1.29594	+	22.2504i	−0.0439870	+	0.755227i
$869$	2.94412	+	3.95464i	0.0998723	+	0.134152i
$870$		0			0
$871$	5.59309	−	3.67863i	0.189515	−	0.124646i
$872$	0.0776079	+	0.440136i	0.00262814	+	0.0149049i
$873$		0			0
$874$	0.0143863	−	0.0815889i	0.000486625	−	0.00275979i
$875$	−11.7542	−	27.2492i	−0.397364	−	0.921193i
$876$		0			0
$877$	24.0085	+	5.69012i	0.810710	+	0.192142i	0.615007	−	0.788522i	$-0.289153\pi$
$877$	24.0085	+	5.69012i	0.810710	+	0.192142i	0.195703	+	0.980663i	$0.437301\pi$
$878$	−0.720687	+	0.763883i	−0.0243220	+	0.0257798i
$879$		0			0
$880$	−13.2034	+	17.7353i	−0.445087	+	0.597856i
$881$	13.2241	+	11.0964i	0.445532	+	0.373846i	0.837775	−	0.546016i	$-0.183856\pi$
$881$	13.2241	+	11.0964i	0.445532	+	0.373846i	−0.392243	+	0.919862i	$0.628301\pi$
$882$		0			0
$883$	−24.0818	+	20.2071i	−0.810419	+	0.680022i	−0.950708	−	0.310089i	$-0.899641\pi$
$883$	−24.0818	+	20.2071i	−0.810419	+	0.680022i	0.140289	+	0.990111i	$0.455197\pi$
$884$	2.61500	+	44.8979i	0.0879521	+	1.51008i
$885$		0			0
$886$	2.15968	−	5.00670i	0.0725558	−	0.168203i
$887$	36.9492	+	24.3019i	1.24063	+	0.815977i	0.988427	−	0.151696i	$-0.0484735\pi$
$887$	36.9492	+	24.3019i	1.24063	+	0.815977i	0.252206	+	0.967674i	$0.418844\pi$
$888$		0			0
$889$	−10.5234	+	35.1505i	−0.352943	+	1.17891i
$890$	9.45412			0.316903
$891$		0			0
$892$	−42.7560			−1.43158
$893$	0.0795392	−	0.265679i	0.00266168	−	0.00889062i
$894$		0			0
$895$	1.12322	+	0.738753i	0.0375451	+	0.0246938i
$896$	−8.97990	+	20.8178i	−0.299998	+	0.695472i
$897$		0			0
$898$	0.324694	+	5.57478i	0.0108352	+	0.186033i
$899$	−37.7406	+	31.6681i	−1.25872	+	1.05619i
$900$		0			0
$901$	6.48355	+	5.44034i	0.215998	+	0.181244i
$902$	1.46103	−	1.96250i	0.0486469	−	0.0653442i
$903$		0			0
$904$	−16.7607	+	17.7653i	−0.557453	+	0.590866i
$905$	28.8032	+	6.82648i	0.957450	+	0.226920i
$906$		0			0
$907$	5.85457	+	13.5724i	0.194398	+	0.450665i	0.987337	−	0.158636i	$-0.0507096\pi$
$907$	5.85457	+	13.5724i	0.194398	+	0.450665i	−0.792939	+	0.609301i	$0.791450\pi$
$908$	−4.42237	+	25.0805i	−0.146762	+	0.832327i
$909$		0			0
$910$	−1.64063	−	9.30447i	−0.0543863	−	0.308440i
$911$	−32.3790	+	21.2960i	−1.07276	+	0.705567i	−0.957693	−	0.287790i	$-0.907079\pi$
$911$	−32.3790	+	21.2960i	−1.07276	+	0.705567i	−0.115069	+	0.993357i	$0.536709\pi$
$912$		0			0
$913$	−6.03429	−	8.10546i	−0.199706	−	0.268251i
$914$	0.329747	−	5.66154i	0.0109071	−	0.187267i
$915$		0			0
$916$	8.11159	+	8.59779i	0.268015	+	0.284079i
$917$	−3.88500	−	6.72903i	−0.128294	−	0.222212i
$918$		0			0
$919$	−20.8939	+	36.1894i	−0.689228	+	1.19378i	0.282860	+	0.959161i	$0.408717\pi$
$919$	−20.8939	+	36.1894i	−0.689228	+	1.19378i	−0.972088	+	0.234616i	$0.924617\pi$
$920$	−10.9318	+	2.59089i	−0.360411	+	0.0854190i
$921$		0			0
$922$	−1.42534	+	0.715834i	−0.0469412	+	0.0235747i
$923$	−78.2134	+	9.14184i	−2.57443	+	0.300907i
$924$		0			0
$925$	−1.57269	−	0.789837i	−0.0517099	−	0.0259697i
$926$	5.12956	+	1.86701i	0.168568	+	0.0613536i
$927$		0			0
$928$	−35.6738	+	12.9842i	−1.17105	+	0.426227i
$929$	−26.4446	−	3.09093i	−0.867619	−	0.101410i	−0.329375	−	0.944199i	$-0.606838\pi$
$929$	−26.4446	−	3.09093i	−0.867619	−	0.101410i	−0.538244	+	0.842789i	$0.680912\pi$
$930$		0			0
$931$	−0.00927856	−	0.0309925i	−0.000304092	−	0.00101574i
$932$	6.74912	+	22.5436i	0.221075	+	0.738442i
$933$		0			0
$934$	11.8039	+	1.37968i	0.386236	+	0.0451445i
$935$	26.1707	−	9.52537i	0.855875	−	0.311513i
$936$		0			0
$937$	10.5874	+	3.85350i	0.345875	+	0.125888i	0.509116	−	0.860698i	$-0.329972\pi$
$937$	10.5874	+	3.85350i	0.345875	+	0.125888i	−0.163241	+	0.986586i	$0.552195\pi$
$938$	−0.874751	−	0.439316i	−0.0285616	−	0.0143442i
$939$		0			0
$940$	−18.1946	+	2.12664i	−0.593441	+	0.0693633i
$941$	−15.8260	+	7.94813i	−0.515914	+	0.259102i	−0.687651	−	0.726041i	$-0.741358\pi$
$941$	−15.8260	+	7.94813i	−0.515914	+	0.259102i	0.171737	+	0.985143i	$0.445062\pi$
$942$		0			0
$943$	−10.4971	+	2.48785i	−0.341832	+	0.0810156i
$944$	12.2850	−	21.2782i	0.399842	−	0.692546i
$945$		0			0
$946$	−0.376601	−	0.652293i	−0.0122444	−	0.0212079i
$947$	−40.7779	−	43.2221i	−1.32510	−	1.40453i	−0.852018	−	0.523513i	$-0.824621\pi$
$947$	−40.7779	−	43.2221i	−1.32510	−	1.40453i	−0.473086	−	0.881016i	$-0.656860\pi$
$948$		0			0
$949$	−3.11759	+	53.5269i	−0.101201	+	1.73756i
$950$	−0.00577881	−	0.00776229i	−0.000187489	−	0.000251842i
$951$		0			0
$952$	11.2799	−	7.41888i	0.365582	−	0.240447i
$953$	−9.46496	−	53.6784i	−0.306600	−	1.73881i	−0.615876	−	0.787843i	$-0.711198\pi$
$953$	−9.46496	−	53.6784i	−0.306600	−	1.73881i	0.309277	−	0.950972i	$-0.399913\pi$
$954$		0			0
$955$	3.12859	−	17.7431i	0.101239	−	0.574155i
$956$	−7.39654	−	17.1471i	−0.239221	−	0.554577i
$957$		0			0
$958$	−1.05668	−	0.250437i	−0.0341396	−	0.00809124i
$959$	−4.54696	+	4.81950i	−0.146829	+	0.155630i
$960$		0			0
$961$	−5.80173	+	7.79308i	−0.187153	+	0.251390i
$962$	−4.72103	−	3.96142i	−0.152212	−	0.127721i
$963$		0			0
$964$	25.2252	−	21.1664i	0.812448	−	0.681725i
$965$	1.63443	+	28.0620i	0.0526141	+	0.903349i
$966$		0			0
$967$	11.2247	−	26.0218i	0.360962	−	0.836804i	−0.636869	−	0.770972i	$-0.719771\pi$
$967$	11.2247	−	26.0218i	0.360962	−	0.836804i	0.997831	−	0.0658319i	$-0.0209701\pi$
$968$	1.69117	+	1.11230i	0.0543561	+	0.0357506i
$969$		0			0
$970$	−1.35568	+	4.52828i	−0.0435282	+	0.145394i
$971$	34.6038			1.11049			0.555244	−	0.831687i	$-0.312625\pi$
$971$	34.6038			1.11049			0.555244	+	0.831687i	$0.312625\pi$
$972$		0			0
$973$	48.2868			1.54801
$974$	−0.494416	+	1.65146i	−0.0158421	+	0.0529163i
$975$		0			0
$976$	33.2361	+	21.8597i	1.06386	+	0.699713i
$977$	5.25612	−	12.1851i	0.168158	−	0.389835i	−0.813210	−	0.581970i	$-0.802282\pi$
$977$	5.25612	−	12.1851i	0.168158	−	0.389835i	0.981368	+	0.192135i	$0.0615413\pi$
$978$		0			0
$979$	−2.49931	−	42.9115i	−0.0798782	−	1.37146i
$980$	−1.63697	+	1.37358i	−0.0522912	+	0.0438775i
$981$		0			0
$982$	0.965832	+	0.810430i	0.0308209	+	0.0258618i
$983$	−21.4988	+	28.8779i	−0.685706	+	0.921063i	−0.999597	−	0.0283960i	$-0.990960\pi$
$983$	−21.4988	+	28.8779i	−0.685706	+	0.921063i	0.313891	+	0.949459i	$0.398367\pi$
$984$		0			0
$985$	10.9883	−	11.6469i	0.350116	−	0.371101i
$986$	14.1446	+	3.35232i	0.450455	+	0.106760i
$987$		0			0
$988$	0.253257	+	0.587116i	0.00805718	+	0.0186786i
$989$	−0.576698	+	3.27062i	−0.0183379	+	0.104000i
$990$		0			0
$991$	9.06181	+	51.3921i	0.287858	+	1.63252i	0.694895	+	0.719111i	$0.255451\pi$
$991$	9.06181	+	51.3921i	0.287858	+	1.63252i	−0.407037	+	0.913412i	$0.633438\pi$
$992$	13.7029	−	9.01252i	0.435066	−	0.286148i
$993$		0			0
$994$	6.87592	+	9.23597i	0.218091	+	0.292947i
$995$	−0.260674	+	4.47561i	−0.00826394	+	0.141886i
$996$		0			0
$997$	−12.3868	−	13.1292i	−0.392293	−	0.415806i	0.500882	−	0.865516i	$-0.333009\pi$
$997$	−12.3868	−	13.1292i	−0.392293	−	0.415806i	−0.893175	+	0.449709i	$0.851528\pi$
$998$	−3.40379	−	5.89554i	−0.107745	−	0.186620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.b.352.5		144
3.2	odd	2		729.2.g.c.352.4		144
9.2	odd	6		81.2.g.a.76.5	yes	144
9.4	even	3		729.2.g.a.109.5		144
9.5	odd	6		729.2.g.d.109.4		144
9.7	even	3		243.2.g.a.118.4		144
81.11	odd	54		81.2.g.a.16.5	✓	144
81.16	even	27		729.2.g.a.622.5		144
81.23	odd	54		6561.2.a.c.1.42		72
81.38	odd	54		729.2.g.c.379.4		144
81.43	even	27	inner	729.2.g.b.379.5		144
81.58	even	27		6561.2.a.d.1.31		72
81.65	odd	54		729.2.g.d.622.4		144
81.70	even	27		243.2.g.a.208.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.5	✓	144	81.11	odd	54
81.2.g.a.76.5	yes	144	9.2	odd	6
243.2.g.a.118.4		144	9.7	even	3
243.2.g.a.208.4		144	81.70	even	27
729.2.g.a.109.5		144	9.4	even	3
729.2.g.a.622.5		144	81.16	even	27
729.2.g.b.352.5		144	1.1	even	1	trivial
729.2.g.b.379.5		144	81.43	even	27	inner
729.2.g.c.352.4		144	3.2	odd	2
729.2.g.c.379.4		144	81.38	odd	54
729.2.g.d.109.4		144	9.5	odd	6
729.2.g.d.622.4		144	81.65	odd	54
6561.2.a.c.1.42		72	81.23	odd	54
6561.2.a.d.1.31		72	81.58	even	27

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0909953 - 0.303945i) q^{2} +(1.58687 + 1.04370i) q^{4} +(-0.840209 + 1.94782i) q^{5} +(0.147894 + 2.53924i) q^{7} +(0.947719 - 0.795231i) q^{8} +(0.515577 + 0.432621i) q^{10} +(1.82733 - 2.45453i) q^{11} +(-3.78737 + 4.01438i) q^{13} +(0.785249 + 0.186107i) q^{14} +(1.34911 + 3.12759i) q^{16} +(0.745021 - 4.22522i) q^{17} +(-0.0105922 - 0.0600713i) q^{19} +(-3.36625 + 2.21402i) q^{20} +(-0.579765 - 0.778760i) q^{22} +(-0.248909 + 4.27360i) q^{23} +(0.343143 + 0.363710i) q^{25} +(0.875520 + 1.51644i) q^{26} +(-2.41553 + 4.18381i) q^{28} +(-10.3910 + 2.46271i) q^{29} +(4.12278 - 2.07054i) q^{31} +(3.53097 - 0.412711i) q^{32} +(-1.21644 - 0.610921i) q^{34} +(-5.07026 - 1.84542i) q^{35} +(-3.30730 + 1.20376i) q^{37} +(-0.0192222 - 0.00224676i) q^{38} +(0.752687 + 2.51415i) q^{40} +(0.722754 + 2.41417i) q^{41} +(0.770554 + 0.0900648i) q^{43} +(5.46154 - 1.98784i) q^{44} +(1.27629 + 0.464532i) q^{46} +(4.06294 + 2.04049i) q^{47} +(0.526786 - 0.0615725i) q^{49} +(0.141773 - 0.0712008i) q^{50} +(-10.1999 + 2.41742i) q^{52} +(-0.986349 + 1.70841i) q^{53} +(3.24565 + 5.62164i) q^{55} +(2.15945 + 2.28888i) q^{56} +(-0.197001 + 3.38238i) q^{58} +(-4.30754 - 5.78603i) q^{59} +(9.75766 - 6.41771i) q^{61} +(-0.254177 - 1.44151i) q^{62} +(-0.987085 + 5.59804i) q^{64} +(-4.63712 - 10.7501i) q^{65} +(-1.18028 - 0.279730i) q^{67} +(5.59213 - 5.92731i) q^{68} +(-1.02228 + 1.37316i) q^{70} +(10.9300 + 9.17137i) q^{71} +(7.44218 - 6.24473i) q^{73} +(0.0649282 + 1.11477i) q^{74} +(0.0458881 - 0.106381i) q^{76} +(6.50290 + 4.27703i) q^{77} +(-0.462085 + 1.54347i) q^{79} -7.22552 q^{80} +0.799542 q^{82} +(0.947094 - 3.16351i) q^{83} +(7.60402 + 5.00124i) q^{85} +(0.0974916 - 0.226011i) q^{86} +(-0.220122 - 3.77936i) q^{88} +(10.7606 - 9.02919i) q^{89} +(-10.7536 - 9.02336i) q^{91} +(-4.85535 + 6.52187i) q^{92} +(0.989905 - 1.04924i) q^{94} +(0.125908 + 0.0298407i) q^{95} +(2.78173 + 6.44878i) q^{97} +(0.0292204 - 0.165717i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

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