LMFDB - Embedded newform 729.2.g.b.379.5

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			379.5
Character	$\chi$	$=$	729.379
Dual form			729.2.g.b.352.5

$q$-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 $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{27}\right)$

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	0.984115	−	0.177532i	$-0.0568114\pi$
$2$	0.0909953	+	0.303945i	0.0643434	+	0.214922i	−0.919772	+	0.392454i	$0.871626\pi$
$3$		0			0
$3$		0			0
$4$	1.58687	−	1.04370i	0.793436	−	0.521851i
$5$	−0.840209	−	1.94782i	−0.375753	−	0.871093i	−0.996220	−	0.0868610i	$-0.972316\pi$
$5$	−0.840209	−	1.94782i	−0.375753	−	0.871093i	0.620468	−	0.784232i	$-0.286943\pi$
$6$		0			0
$7$	0.147894	−	2.53924i	0.0558987	−	0.959744i	−0.847460	−	0.530859i	$-0.821870\pi$
$7$	0.147894	−	2.53924i	0.0558987	−	0.959744i	0.903359	−	0.428885i	$-0.141093\pi$
$8$	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	0.987152	−	0.159785i	$-0.0510802\pi$
$11$	1.82733	+	2.45453i	0.550961	+	0.740069i	−0.436191	+	0.899854i	$0.643673\pi$
$12$		0			0
$13$	−3.78737	−	4.01438i	−1.05043	−	1.11339i	−0.993363	−	0.115018i	$-0.963307\pi$
$13$	−3.78737	−	4.01438i	−1.05043	−	1.11339i	−0.0570649	−	0.998370i	$-0.518174\pi$
$14$	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	0.931364	+	0.364090i	$0.118620\pi$
$17$	0.745021	+	4.22522i	0.180694	+	1.02477i	−0.750670	+	0.660678i	$0.770269\pi$
$18$		0			0
$19$	−0.0105922	+	0.0600713i	−0.00243002	+	0.0137813i	−0.985999	−	0.166753i	$-0.946672\pi$
$19$	−0.0105922	+	0.0600713i	−0.00243002	+	0.0137813i	0.983569	+	0.180535i	$0.0577828\pi$
$20$	−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	−0.919316	−	0.393521i	$-0.871257\pi$
$23$	−0.248909	−	4.27360i	−0.0519010	−	0.891107i	0.867415	−	0.497586i	$-0.165780\pi$
$24$		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	−0.994776	−	0.102086i	$-0.967448\pi$
$29$	−10.3910	−	2.46271i	−1.92956	−	0.457313i	−0.934780	−	0.355227i	$-0.884404\pi$
$30$		0			0
$31$	4.12278	+	2.07054i	0.740473	+	0.371880i	0.778706	−	0.627389i	$-0.215877\pi$
$31$	4.12278	+	2.07054i	0.740473	+	0.371880i	−0.0382327	+	0.999269i	$0.512173\pi$
$32$	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	0.0555362	−	0.998457i	$-0.482313\pi$
$37$	−3.30730	−	1.20376i	−0.543716	−	0.197896i	−0.599252	+	0.800560i	$0.704535\pi$
$38$	−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	−0.882821	−	0.469710i	$-0.844358\pi$
$41$	0.722754	−	2.41417i	0.112875	−	0.377030i	0.995696	+	0.0926807i	$0.0295436\pi$
$42$		0			0
$43$	0.770554	−	0.0900648i	0.117508	−	0.0137348i	−0.0571354	−	0.998366i	$-0.518197\pi$
$43$	0.770554	−	0.0900648i	0.117508	−	0.0137348i	0.174644	+	0.984632i	$0.444123\pi$
$44$	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	−0.127087	−	0.991892i	$-0.540563\pi$
$47$	4.06294	−	2.04049i	0.592641	−	0.297635i	0.719728	+	0.694256i	$0.244267\pi$
$48$		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	0.790297	−	0.612724i	$-0.209926\pi$
$53$	−0.986349	−	1.70841i	−0.135485	−	0.234668i	−0.925783	+	0.378056i	$0.876593\pi$
$54$		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	−0.988595	−	0.150596i	$-0.951881\pi$
$59$	−4.30754	+	5.78603i	−0.560794	+	0.753277i	0.427801	+	0.903873i	$0.359288\pi$
$60$		0			0
$61$	9.75766	+	6.41771i	1.24934	+	0.821704i	0.989582	−	0.143970i	$-0.0459869\pi$
$61$	9.75766	+	6.41771i	1.24934	+	0.821704i	0.259758	+	0.965674i	$0.416357\pi$
$62$	−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	−0.302079	−	0.953283i	$-0.597681\pi$
$67$	−1.18028	+	0.279730i	−0.144194	+	0.0341745i	0.157885	+	0.987457i	$0.449532\pi$
$68$	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	0.306525	−	0.951863i	$-0.400834\pi$
$71$	10.9300	−	9.17137i	1.29715	−	1.08844i	0.990629	−	0.136579i	$-0.0436107\pi$
$72$		0			0
$73$	7.44218	+	6.24473i	0.871042	+	0.730891i	0.964317	−	0.264750i	$-0.0852893\pi$
$73$	7.44218	+	6.24473i	0.871042	+	0.730891i	−0.0932755	+	0.995640i	$0.529734\pi$
$74$	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	0.928052	−	0.372450i	$-0.121482\pi$
$79$	−0.462085	−	1.54347i	−0.0519886	−	0.173654i	−0.980041	+	0.198796i	$0.936297\pi$
$80$	−7.22552			−0.807838
$81$		0			0
$82$	0.799542			0.0882947
$83$	0.947094	+	3.16351i	0.103957	+	0.347241i	0.994104	−	0.108433i	$-0.0345834\pi$
$83$	0.947094	+	3.16351i	0.103957	+	0.347241i	−0.890147	+	0.455674i	$0.849398\pi$
$84$		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	0.999459	−	0.0328946i	$-0.0104726\pi$
$89$	10.7606	+	9.02919i	1.14062	+	0.957092i	0.141159	+	0.989987i	$0.454917\pi$
$90$		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	−0.716648	−	0.697436i	$-0.754324\pi$
$97$	2.78173	−	6.44878i	0.282442	−	0.654774i	0.999090	+	0.0426612i	$0.0135836\pi$
$98$	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	0.913664	−	0.406471i	$-0.133241\pi$
$101$	9.06820	+	5.96425i	0.902320	+	0.593465i	−0.0113443	+	0.999936i	$0.503611\pi$
$102$		0			0
$103$	−7.42672	+	9.97581i	−0.731776	+	0.982946i	0.268033	+	0.963410i	$0.413626\pi$
$103$	−7.42672	+	9.97581i	−0.731776	+	0.982946i	−0.999809	+	0.0195364i	$0.993781\pi$
$104$	−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	−0.720260	−	0.693704i	$-0.755977\pi$
$107$	2.48915	−	4.31134i	0.240636	−	0.416793i	0.960896	+	0.276911i	$0.0893108\pi$
$108$		0			0
$109$	−0.180626	−	0.312853i	−0.0173008	−	0.0299659i	0.857245	−	0.514908i	$-0.172174\pi$
$109$	−0.180626	−	0.312853i	−0.0173008	−	0.0299659i	−0.874546	+	0.484942i	$0.838841\pi$
$110$	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	−0.879219	−	0.476419i	$-0.841935\pi$
$113$	−19.6084	−	2.29190i	−1.84461	−	0.215604i	−0.965389	+	0.260815i	$0.916009\pi$
$114$		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	0.338639	−	0.940916i	$-0.390033\pi$
$127$	13.5556	−	4.93382i	1.20286	−	0.437806i	0.864222	+	0.503111i	$0.167811\pi$
$128$	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	0.325530	−	0.945532i	$-0.394457\pi$
$131$	−2.72986	−	1.37099i	−0.238509	−	0.119784i	−0.564040	+	0.825748i	$0.690753\pi$
$132$		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	−0.646492	−	0.762921i	$-0.723764\pi$
$137$	1.78765	−	1.89480i	0.152729	−	0.161883i	0.799221	+	0.601038i	$0.205246\pi$
$138$		0			0
$139$	1.10383	+	18.9519i	0.0936252	+	1.60748i	0.638943	+	0.769254i	$0.279372\pi$
$139$	1.10383	+	18.9519i	0.0936252	+	1.60748i	−0.545318	+	0.838229i	$0.683591\pi$
$140$	−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	0.832237	−	0.554420i	$-0.187060\pi$
$149$	2.81196	+	2.98051i	0.230365	+	0.244173i	−0.601872	+	0.798592i	$0.705578\pi$
$150$		0			0
$151$	5.93650	+	7.97411i	0.483106	+	0.648923i	0.975124	−	0.221662i	$-0.0711480\pi$
$151$	5.93650	+	7.97411i	0.483106	+	0.648923i	−0.492018	+	0.870585i	$0.663741\pi$
$152$	−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	0.997428	+	0.0716789i	$0.0228357\pi$
$157$	4.57455	+	10.6050i	0.365089	+	0.846371i	−0.632339	+	0.774692i	$0.717905\pi$
$158$	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	0.989524	−	0.144370i	$-0.0461157\pi$
$167$	2.65513	+	6.15528i	0.205460	+	0.476310i	−0.784064	+	0.620681i	$0.786856\pi$
$168$		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	0.999079	−	0.0429151i	$-0.0136645\pi$
$173$	8.83125	+	11.8624i	0.671427	+	0.901884i	−0.327651	+	0.944799i	$0.606257\pi$
$174$		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	0.988644	−	0.150275i	$-0.0480159\pi$
$179$	0.110050	+	0.624125i	0.00822552	+	0.0466493i	−0.980419	+	0.196924i	$0.936905\pi$
$180$		0			0
$181$	−2.42311	+	13.7421i	−0.180108	+	1.02145i	0.751972	+	0.659195i	$0.229103\pi$
$181$	−2.42311	+	13.7421i	−0.180108	+	1.02145i	−0.932081	+	0.362251i	$0.882008\pi$
$182$	−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	−0.0795338	−	0.996832i	$-0.525343\pi$
$191$	−8.26432	−	1.95868i	−0.597985	−	0.141725i	−0.518451	+	0.855107i	$0.673491\pi$
$192$		0			0
$193$	11.8416	+	5.94705i	0.852374	+	0.428078i	0.820659	−	0.571419i	$-0.193607\pi$
$193$	11.8416	+	5.94705i	0.852374	+	0.428078i	0.0317154	+	0.999497i	$0.489903\pi$
$194$	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	−0.582103	−	0.813115i	$-0.697770\pi$
$197$	−7.09307	+	2.58167i	−0.505360	+	0.183936i	0.0767431	+	0.997051i	$0.475548\pi$
$198$		0			0
$199$	1.98595	+	0.722827i	0.140780	+	0.0512399i	0.411449	−	0.911433i	$-0.365023\pi$
$199$	1.98595	+	0.722827i	0.140780	+	0.0512399i	−0.270669	+	0.962672i	$0.587245\pi$
$200$	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	0.0936192	−	0.995608i	$-0.470156\pi$
$211$	−0.652038	−	0.0762123i	−0.0448882	−	0.00524667i	−0.138507	+	0.990361i	$0.544230\pi$
$212$	−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	−0.268595	−	0.963253i	$-0.586559\pi$
$223$	−18.8077	−	12.3700i	−1.25945	−	0.828356i	−0.990860	+	0.134897i	$0.956930\pi$
$224$	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	−0.646052	−	0.763293i	$-0.723581\pi$
$227$	5.31087	−	12.3120i	0.352495	−	0.817175i	0.998547	−	0.0538820i	$-0.0171595\pi$
$228$		0			0
$229$	6.05564	−	1.43521i	0.400168	−	0.0948415i	−0.0256038	−	0.999672i	$-0.508151\pi$
$229$	6.05564	−	1.43521i	0.400168	−	0.0948415i	0.425772	+	0.904831i	$0.360003\pi$
$230$	−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	−0.276582	−	0.960990i	$-0.589202\pi$
$233$	9.49107	−	7.96396i	0.621781	−	0.521736i	0.898363	+	0.439254i	$0.144757\pi$
$234$		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	−0.786664	−	0.617382i	$-0.788193\pi$
$239$	−8.21456	+	5.40280i	−0.531356	+	0.349478i	0.255308	+	0.966860i	$0.417823\pi$
$240$		0			0
$241$	4.97235	+	16.6088i	0.320297	+	1.06987i	0.954875	+	0.297009i	$0.0959890\pi$
$241$	4.97235	+	16.6088i	0.320297	+	1.06987i	−0.634577	+	0.772859i	$0.718826\pi$
$242$	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	0.999270	+	0.0381908i	$0.0121595\pi$
$251$	19.1764	+	16.0909i	1.21040	+	1.01565i	0.211132	+	0.977458i	$0.432285\pi$
$252$		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	−0.303117	−	0.952953i	$-0.598027\pi$
$257$	−2.34548	+	0.555890i	−0.146307	+	0.0346755i	0.156810	+	0.987629i	$0.449879\pi$
$258$		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	0.444428	−	0.895815i	$-0.353407\pi$
$263$	−3.27743	−	2.15560i	−0.202095	−	0.132920i	−0.646523	+	0.762895i	$0.723777\pi$
$264$		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	−0.645981	−	0.763353i	$-0.723552\pi$
$269$	5.54513	−	9.60445i	0.338093	−	0.585594i	0.984074	+	0.177760i	$0.0568849\pi$
$270$		0			0
$271$	−0.397309	−	0.688159i	−0.0241348	−	0.0418027i	0.853706	−	0.520756i	$-0.174350\pi$
$271$	−0.397309	−	0.688159i	−0.0241348	−	0.0418027i	−0.877841	+	0.478953i	$0.841016\pi$
$272$	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	0.567837	−	0.823141i	$-0.307780\pi$
$277$	26.0832	−	13.0995i	1.56719	−	0.787070i	0.999349	+	0.0360708i	$0.0114842\pi$
$278$	−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	−0.883306	−	0.468798i	$-0.844687\pi$
$281$	−27.4024	+	3.20288i	−1.63469	+	0.191068i	−0.751384	+	0.659865i	$0.770613\pi$
$282$		0			0
$283$	1.46517	−	4.89400i	0.0870951	−	0.290918i	−0.903334	−	0.428937i	$-0.858888\pi$
$283$	1.46517	−	4.89400i	0.0870951	−	0.290918i	0.990430	+	0.138019i	$0.0440735\pi$
$284$	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	0.508918	−	0.860815i	$-0.330046\pi$
$293$	2.09418	+	1.05174i	0.122344	+	0.0614432i	−0.386575	+	0.922258i	$0.626342\pi$
$294$		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	−0.953849	−	0.300287i	$-0.902918\pi$
$307$	−2.80743	−	15.9217i	−0.160228	−	0.908700i	0.793620	−	0.608413i	$-0.208194\pi$
$308$	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	0.168871	−	0.985638i	$-0.445988\pi$
$311$	−14.5476	−	15.4196i	−0.824919	−	0.874363i	−0.993790	+	0.111276i	$0.964506\pi$
$312$		0			0
$313$	−3.23147	−	4.34062i	−0.182654	−	0.245346i	0.701360	−	0.712807i	$-0.252576\pi$
$313$	−3.23147	−	4.34062i	−0.182654	−	0.245346i	−0.884014	+	0.467461i	$0.845169\pi$
$314$	−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	−0.953610	−	0.301045i	$-0.902665\pi$
$317$	0.507449	−	8.71256i	0.0285012	−	0.489346i	0.982111	−	0.188302i	$-0.0602983\pi$
$318$		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	−0.808810	−	0.588070i	$-0.799888\pi$
$331$	1.14258	−	19.6173i	0.0628019	−	1.07827i	0.871612	−	0.490196i	$-0.163075\pi$
$332$	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	0.849962	−	0.526843i	$-0.176625\pi$
$337$	5.04080	+	5.34293i	0.274590	+	0.291048i	−0.575373	+	0.817891i	$0.695143\pi$
$338$	−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	0.899236	+	0.437464i	$0.144123\pi$
$347$	1.05931	+	18.1877i	0.0568668	+	0.976365i	−0.842369	+	0.538901i	$0.818840\pi$
$348$		0			0
$349$	11.0555	−	11.7182i	0.591788	−	0.627258i	−0.360390	−	0.932802i	$-0.617357\pi$
$349$	11.0555	−	11.7182i	0.591788	−	0.627258i	0.952178	+	0.305543i	$0.0988380\pi$
$350$	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	0.650066	−	0.759878i	$-0.274741\pi$
$353$	16.7207	+	3.96288i	0.889953	+	0.210923i	0.239887	+	0.970801i	$0.422890\pi$
$354$		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	−0.931187	−	0.364543i	$-0.881225\pi$
$359$	−26.7193	+	9.72505i	−1.41019	+	0.513268i	−0.479007	+	0.877811i	$0.659003\pi$
$360$		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	−0.380762	−	0.924673i	$-0.624338\pi$
$367$	−10.3069	+	1.20471i	−0.538017	+	0.0628851i	−0.157254	+	0.987558i	$0.550264\pi$
$368$	−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	−0.275828	−	0.961207i	$-0.588952\pi$
$373$	−14.7918	−	1.72891i	−0.765890	−	0.0895198i	−0.490063	+	0.871687i	$0.663026\pi$
$374$	−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	−0.975805	−	0.218644i	$-0.929837\pi$
$379$	−5.81217	+	10.0670i	−0.298551	+	0.517106i	0.677253	+	0.735750i	$0.263170\pi$
$380$	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	−0.114389	−	0.993436i	$-0.536491\pi$
$383$	17.0286	−	22.8733i	0.870119	−	1.16877i	0.984508	−	0.175337i	$-0.0561015\pi$
$384$		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	−0.946260	−	0.323407i	$-0.895172\pi$
$389$	−1.21611	+	2.81926i	−0.0616592	+	0.142942i	0.884601	+	0.466349i	$0.154431\pi$
$390$		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	0.417997	−	0.908448i	$-0.362732\pi$
$397$	−8.05095	−	6.75555i	−0.404065	−	0.339051i	−0.822063	+	0.569397i	$0.807177\pi$
$398$	−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	0.140745	−	0.990046i	$-0.455050\pi$
$401$	22.1390	−	14.5610i	1.10557	−	0.727143i	0.964822	+	0.262903i	$0.0846799\pi$
$402$		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	−0.961213	−	0.275807i	$-0.911055\pi$
$409$	−22.0172	+	14.4809i	−1.08868	+	0.716036i	−0.127466	+	0.991843i	$0.540684\pi$
$410$	−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	−0.412499	−	0.910958i	$-0.635344\pi$
$419$	−7.62045	+	1.80608i	−0.372284	+	0.0882328i	0.0402151	+	0.999191i	$0.487196\pi$
$420$		0			0
$421$	−12.6159	+	29.2469i	−0.614860	+	1.42541i	0.271513	+	0.962435i	$0.412476\pi$
$421$	−12.6159	+	29.2469i	−0.614860	+	1.42541i	−0.886373	+	0.462971i	$0.846783\pi$
$422$	−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	0.115759	+	0.993277i	$0.463070\pi$
$431$	−16.6567	+	28.8502i	−0.802324	+	1.38967i	−0.918083	+	0.396389i	$0.870263\pi$
$432$		0			0
$433$	2.75793	+	4.77688i	0.132538	+	0.229562i	0.924654	−	0.380808i	$-0.124354\pi$
$433$	2.75793	+	4.77688i	0.132538	+	0.229562i	−0.792116	+	0.610370i	$0.791021\pi$
$434$	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	−0.517985	−	0.855390i	$-0.673318\pi$
$439$	−2.95797	+	1.48555i	−0.141176	+	0.0709013i	0.376809	+	0.926291i	$0.377021\pi$
$440$	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	0.299525	−	0.954088i	$-0.403172\pi$
$443$	17.0697	−	1.99516i	0.811004	−	0.0947928i	0.511479	+	0.859296i	$0.329098\pi$
$444$		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	−0.0791375	−	0.996864i	$-0.525217\pi$
$449$	−16.5392	−	6.01977i	−0.780532	−	0.284090i	−0.701394	+	0.712773i	$0.747439\pi$
$450$		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	0.616294	−	0.787516i	$-0.288633\pi$
$457$	17.3927	+	4.12215i	0.813597	+	0.192826i	0.197304	+	0.980342i	$0.436782\pi$
$458$	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	−0.802710	−	0.596369i	$-0.796609\pi$
$461$	−3.44987	+	3.65664i	−0.160676	+	0.170307i	0.642034	+	0.766676i	$0.278091\pi$
$462$		0			0
$463$	−1.00039	−	17.1761i	−0.0464922	−	0.798240i	−0.938299	−	0.345824i	$-0.887599\pi$
$463$	−1.00039	−	17.1761i	−0.0464922	−	0.798240i	0.891807	−	0.452416i	$-0.149438\pi$
$464$	−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	−0.340824	−	0.940127i	$-0.610706\pi$
$467$	6.50441	−	36.8883i	0.300988	−	1.70699i	0.641812	−	0.766862i	$-0.278183\pi$
$468$		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	0.990705	+	0.136029i	$0.0434340\pi$
$479$	−0.199015	+	3.41695i	−0.00909321	+	0.156124i	−0.999798	+	0.0200954i	$0.993603\pi$
$480$		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	0.879001	−	0.476820i	$-0.158211\pi$
$491$	−1.57397	−	3.64886i	−0.0710321	−	0.164671i	−0.950033	+	0.312149i	$0.898951\pi$
$492$		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	0.967573	−	0.252591i	$-0.0812826\pi$
$499$	14.7243	+	15.6069i	0.659151	+	0.698659i	−0.308423	+	0.951249i	$0.599801\pi$
$500$	−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	−0.918018	−	0.396538i	$-0.870211\pi$
$503$	−4.28340	−	24.2924i	−0.190987	−	1.08314i	0.727031	−	0.686605i	$-0.240900\pi$
$504$		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	−0.994453	−	0.105179i	$-0.966459\pi$
$509$	−0.427185	−	7.33448i	−0.0189346	−	0.325095i	0.975519	−	0.219916i	$-0.0705785\pi$
$510$		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	0.286082	−	0.958205i	$-0.407647\pi$
$521$	25.5909	−	9.31432i	1.12116	−	0.408068i	0.835074	+	0.550137i	$0.185425\pi$
$522$		0			0
$523$	−14.3006	−	5.20499i	−0.625321	−	0.227598i	0.00987267	−	0.999951i	$-0.496857\pi$
$523$	−14.3006	−	5.20499i	−0.625321	−	0.227598i	−0.635193	+	0.772353i	$0.719080\pi$
$524$	−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	−0.987516	−	0.157518i	$-0.949651\pi$
$541$	−8.31159	+	14.3961i	−0.357343	+	0.618937i	0.630173	+	0.776455i	$0.282984\pi$
$542$	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	0.331755	−	0.943366i	$-0.392359\pi$
$547$	−9.42672	−	6.20005i	−0.403057	−	0.265095i	−0.734812	+	0.678271i	$0.762730\pi$
$548$	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	−0.978674	−	0.205421i	$-0.934144\pi$
$557$	−22.3339	+	18.7404i	−0.946318	+	0.794055i	0.0323557	+	0.999476i	$0.489699\pi$
$558$		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	−0.868003	−	0.496559i	$-0.834597\pi$
$563$	−17.9346	+	11.7958i	−0.755853	+	0.497133i	0.112150	+	0.993691i	$0.464226\pi$
$564$		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	0.940357	−	0.340189i	$-0.110491\pi$
$569$	−0.768966	−	2.56852i	−0.0322367	−	0.107678i	−0.972594	+	0.232511i	$0.925306\pi$
$570$		0			0
$571$	2.37346	−	1.56105i	0.0993261	−	0.0653278i	−0.498874	−	0.866674i	$-0.666253\pi$
$571$	2.37346	−	1.56105i	0.0993261	−	0.0653278i	0.598200	+	0.801347i	$0.295883\pi$
$572$	−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	−0.543447	−	0.839443i	$-0.682881\pi$
$577$	4.53692	−	3.80692i	0.188874	−	0.158484i	0.732322	+	0.680959i	$0.238437\pi$
$578$	−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	0.340165	−	0.940366i	$-0.389517\pi$
$587$	−9.41411	−	6.19176i	−0.388562	−	0.255561i	−0.728727	+	0.684805i	$0.759888\pi$
$588$		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	−0.946870	−	0.321617i	$-0.895774\pi$
$593$	−4.74627	+	8.22078i	−0.194906	+	0.337587i	0.751964	+	0.659205i	$0.229107\pi$
$594$		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	0.606163	−	0.795341i	$-0.292708\pi$
$599$	24.7821	+	2.89661i	1.01257	+	0.118352i	0.406405	+	0.913693i	$0.366782\pi$
$600$		0			0
$601$	−10.2652	+	5.15539i	−0.418728	+	0.210293i	−0.645672	−	0.763615i	$-0.723423\pi$
$601$	−10.2652	+	5.15539i	−0.418728	+	0.210293i	0.226945	+	0.973908i	$0.427126\pi$
$602$	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	0.331386	+	0.943495i	$0.392484\pi$
$607$	−11.4303	+	38.1799i	−0.463942	+	1.54967i	−0.795328	+	0.606180i	$0.792701\pi$
$608$	−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	−0.660070	−	0.751204i	$-0.729473\pi$
$613$	−16.9065	+	6.15347i	−0.682848	+	0.248536i	−0.0227782	+	0.999741i	$0.507251\pi$
$614$	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	0.0870339	−	0.996205i	$-0.472261\pi$
$617$	−16.3959	−	8.23431i	−0.660072	−	0.331501i	−0.747106	+	0.664704i	$0.768557\pi$
$618$		0			0
$619$	−43.7258	−	10.3632i	−1.75749	−	0.416532i	−0.779703	−	0.626149i	$-0.784630\pi$
$619$	−43.7258	−	10.3632i	−1.75749	−	0.416532i	−0.977784	+	0.209617i	$0.932778\pi$
$620$	−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	0.842335	+	0.538954i	$0.181180\pi$
$631$	5.90645	+	33.4972i	0.235132	+	1.33350i	−0.607203	+	0.794547i	$0.707708\pi$
$632$	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	−0.998650	−	0.0519409i	$-0.983459\pi$
$641$	−0.0182934	+	0.314085i	−0.000722545	+	0.0124056i	0.997928	+	0.0643465i	$0.0204963\pi$
$642$		0			0
$643$	−13.1236	−	30.4240i	−0.517546	−	1.19981i	−0.953926	−	0.300043i	$-0.902999\pi$
$643$	−13.1236	−	30.4240i	−0.517546	−	1.19981i	0.436380	−	0.899762i	$-0.356260\pi$
$644$	−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	0.786248	+	0.617911i	$0.212021\pi$
$653$	17.7892	+	41.2399i	0.696144	+	1.61384i	−0.0901041	+	0.995932i	$0.528720\pi$
$654$		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	0.997451	+	0.0713607i	$0.0227341\pi$
$659$	20.0167	+	26.8871i	0.779741	+	1.04737i	−0.217709	+	0.976014i	$0.569858\pi$
$660$		0			0
$661$	−11.1359	−	11.8033i	−0.433134	−	0.459096i	0.473636	−	0.880721i	$-0.342941\pi$
$661$	−11.1359	−	11.8033i	−0.433134	−	0.459096i	−0.906770	+	0.421625i	$0.861460\pi$
$662$	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	−0.752868	−	0.658171i	$-0.771330\pi$
$673$	−1.34992	+	1.43083i	−0.0520355	+	0.0551545i	0.700833	+	0.713325i	$0.252812\pi$
$674$	−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	−0.171752	−	0.985140i	$-0.554943\pi$
$677$	−19.9663	−	4.73209i	−0.767366	−	0.181869i	−0.595613	+	0.803271i	$0.703091\pi$
$678$		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	−0.697271	−	0.716808i	$-0.745602\pi$
$683$	−20.1405	+	7.33055i	−0.770656	+	0.280496i	−0.0733852	+	0.997304i	$0.523380\pi$
$684$		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	−0.623052	−	0.782180i	$-0.714108\pi$
$691$	−27.5730	+	3.22282i	−1.04893	+	0.122602i	−0.425875	+	0.904782i	$0.640034\pi$
$692$	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	0.872649	−	0.488347i	$-0.162400\pi$
$701$	0.354873	+	0.614659i	0.0134034	+	0.0232153i	−0.859246	+	0.511563i	$0.829067\pi$
$702$		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	0.825249	−	0.564769i	$-0.191035\pi$
$709$	16.8691	+	11.0950i	0.633533	+	0.416681i	−0.191716	+	0.981450i	$0.561405\pi$
$710$	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	−0.850148	−	0.526543i	$-0.823488\pi$
$719$	−12.8502	+	10.7826i	−0.479231	+	0.402123i	0.370917	+	0.928666i	$0.379043\pi$
$720$		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	0.991109	+	0.133054i	$0.0424783\pi$
$727$	6.36767	+	21.2695i	0.236164	+	0.788842i	−0.754945	+	0.655788i	$0.772337\pi$
$728$	−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	−0.608180	−	0.793799i	$-0.708100\pi$
$733$	−3.25396	+	2.14016i	−0.120188	+	0.0790488i	0.487992	+	0.872848i	$0.337730\pi$
$734$	−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	−0.878310	−	0.478092i	$-0.841328\pi$
$739$	−15.2233	+	12.7738i	−0.559997	+	0.469894i	0.318312	+	0.947986i	$0.396884\pi$
$740$	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	−0.340103	−	0.940388i	$-0.610462\pi$
$743$	−6.05085	+	1.43408i	−0.221984	+	0.0526112i	0.118119	+	0.992999i	$0.462314\pi$
$744$		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	−0.942242	−	0.334932i	$-0.891287\pi$
$751$	−9.62286	+	12.9257i	−0.351143	+	0.471667i	0.591099	+	0.806599i	$0.298694\pi$
$752$	−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	0.984171	+	0.177221i	$0.0567106\pi$
$757$	17.7618	+	30.7643i	0.645563	+	1.11815i	−0.338608	+	0.940928i	$0.609956\pi$
$758$	−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	−0.258511	−	0.966008i	$-0.583232\pi$
$761$	−20.2160	−	2.36292i	−0.732831	−	0.0856556i	−0.474320	+	0.880353i	$0.657306\pi$
$762$		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	−0.806092	−	0.591791i	$-0.798421\pi$
$769$	5.34047	−	17.8384i	0.192582	−	0.643270i	0.998674	−	0.0514792i	$-0.0163936\pi$
$770$	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	0.274671	−	0.961538i	$-0.411431\pi$
$773$	−3.69733	−	1.34572i	−0.132984	−	0.0484021i	−0.407655	+	0.913136i	$0.633653\pi$
$774$		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	−0.997287	−	0.0736146i	$-0.976547\pi$
$787$	−0.428922	−	7.36431i	−0.0152894	−	0.262509i	0.981997	−	0.188895i	$-0.0604905\pi$
$788$	−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	0.883093	−	0.469199i	$-0.155457\pi$
$797$	10.2575	+	10.8723i	0.363340	+	0.385118i	−0.519752	+	0.854317i	$0.673976\pi$
$798$		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	0.833373	−	0.552711i	$-0.186406\pi$
$821$	1.85868	+	2.49663i	0.0648682	+	0.0871331i	−0.768505	+	0.639844i	$0.778999\pi$
$822$		0			0
$823$	−26.4373	−	28.0219i	−0.921546	−	0.976781i	0.0782513	−	0.996934i	$-0.475066\pi$
$823$	−26.4373	−	28.0219i	−0.921546	−	0.976781i	−0.999797	+	0.0201524i	$0.993585\pi$
$824$	−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	0.999343	−	0.0362552i	$-0.0115429\pi$
$827$	1.37656	+	7.80687i	0.0478677	+	0.271471i	−0.951475	+	0.307727i	$0.900432\pi$
$828$		0			0
$829$	5.51283	−	31.2648i	0.191469	−	1.08587i	−0.725890	−	0.687811i	$-0.758572\pi$
$829$	5.51283	−	31.2648i	0.191469	−	1.08587i	0.917359	−	0.398061i	$-0.130317\pi$
$830$	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	−0.616420	−	0.787417i	$-0.711418\pi$
$839$	−44.0468	−	10.4393i	−1.52067	−	0.360404i	−0.904246	+	0.427013i	$0.859566\pi$
$840$		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	−0.862830	−	0.505494i	$-0.831310\pi$
$853$	−46.3159	+	5.41356i	−1.58583	+	0.185357i	−0.722997	+	0.690851i	$0.757236\pi$
$854$	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	−0.341542	−	0.939867i	$-0.610949\pi$
$857$	6.10059	−	3.06383i	0.208392	−	0.104659i	0.549934	+	0.835208i	$0.314653\pi$
$858$		0			0
$859$	−10.9129	−	1.27554i	−0.372344	−	0.0435207i	−0.0721365	−	0.997395i	$-0.522982\pi$
$859$	−10.9129	−	1.27554i	−0.372344	−	0.0435207i	−0.300207	+	0.953874i	$0.597056\pi$
$860$	−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	−0.752092	−	0.659058i	$-0.770955\pi$
$863$	−27.8142	−	48.1756i	−0.946807	−	1.63992i	−0.194715	−	0.980860i	$-0.562378\pi$
$864$		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	0.195703	−	0.980663i	$-0.437301\pi$
$877$	24.0085	−	5.69012i	0.810710	−	0.192142i	0.615007	+	0.788522i	$0.289153\pi$
$878$	−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	−0.392243	−	0.919862i	$-0.628301\pi$
$881$	13.2241	−	11.0964i	0.445532	−	0.373846i	0.837775	+	0.546016i	$0.183856\pi$
$882$		0			0
$883$	−24.0818	−	20.2071i	−0.810419	−	0.680022i	0.140289	−	0.990111i	$-0.455197\pi$
$883$	−24.0818	−	20.2071i	−0.810419	−	0.680022i	−0.950708	+	0.310089i	$0.899641\pi$
$884$	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	0.252206	−	0.967674i	$-0.418844\pi$
$887$	36.9492	−	24.3019i	1.24063	−	0.815977i	0.988427	+	0.151696i	$0.0484735\pi$
$888$		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	−0.792939	−	0.609301i	$-0.791450\pi$
$907$	5.85457	−	13.5724i	0.194398	−	0.450665i	0.987337	+	0.158636i	$0.0507096\pi$
$908$	−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	−0.115069	−	0.993357i	$-0.536709\pi$
$911$	−32.3790	−	21.2960i	−1.07276	−	0.705567i	−0.957693	+	0.287790i	$0.907079\pi$
$912$		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	−0.972088	−	0.234616i	$-0.924617\pi$
$919$	−20.8939	−	36.1894i	−0.689228	−	1.19378i	0.282860	−	0.959161i	$-0.408717\pi$
$920$	−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	−0.538244	−	0.842789i	$-0.680912\pi$
$929$	−26.4446	+	3.09093i	−0.867619	+	0.101410i	−0.329375	+	0.944199i	$0.606838\pi$
$930$		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	−0.163241	−	0.986586i	$-0.552195\pi$
$937$	10.5874	−	3.85350i	0.345875	−	0.125888i	0.509116	+	0.860698i	$0.329972\pi$
$938$	−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	0.171737	−	0.985143i	$-0.445062\pi$
$941$	−15.8260	−	7.94813i	−0.515914	−	0.259102i	−0.687651	+	0.726041i	$0.741358\pi$
$942$		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	−0.473086	+	0.881016i	$0.656860\pi$
$947$	−40.7779	+	43.2221i	−1.32510	+	1.40453i	−0.852018	+	0.523513i	$0.824621\pi$
$948$		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	0.309277	+	0.950972i	$0.399913\pi$
$953$	−9.46496	+	53.6784i	−0.306600	+	1.73881i	−0.615876	+	0.787843i	$0.711198\pi$
$954$		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	0.997831	+	0.0658319i	$0.0209701\pi$
$967$	11.2247	+	26.0218i	0.360962	+	0.836804i	−0.636869	+	0.770972i	$0.719771\pi$
$968$	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	0.981368	−	0.192135i	$-0.0615413\pi$
$977$	5.25612	+	12.1851i	0.168158	+	0.389835i	−0.813210	+	0.581970i	$0.802282\pi$
$978$		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	0.313891	−	0.949459i	$-0.398367\pi$
$983$	−21.4988	−	28.8779i	−0.685706	−	0.921063i	−0.999597	+	0.0283960i	$0.990960\pi$
$984$		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	−0.407037	−	0.913412i	$-0.633438\pi$
$991$	9.06181	−	51.3921i	0.287858	−	1.63252i	0.694895	−	0.719111i	$-0.255451\pi$
$992$	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	−0.893175	−	0.449709i	$-0.851528\pi$
$997$	−12.3868	+	13.1292i	−0.392293	+	0.415806i	0.500882	+	0.865516i	$0.333009\pi$
$998$	−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.379.5		144
3.2	odd	2		729.2.g.c.379.4		144
9.2	odd	6		729.2.g.d.622.4		144
9.4	even	3		243.2.g.a.208.4		144
9.5	odd	6		81.2.g.a.16.5	✓	144
9.7	even	3		729.2.g.a.622.5		144
81.5	odd	54		729.2.g.d.109.4		144
81.7	even	27		6561.2.a.d.1.31		72
81.22	even	27		243.2.g.a.118.4		144
81.32	odd	54		729.2.g.c.352.4		144
81.49	even	27	inner	729.2.g.b.352.5		144
81.59	odd	54		81.2.g.a.76.5	yes	144
81.74	odd	54		6561.2.a.c.1.42		72
81.76	even	27		729.2.g.a.109.5		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.16.5	✓	144	9.5	odd	6
81.2.g.a.76.5	yes	144	81.59	odd	54
243.2.g.a.118.4		144	81.22	even	27
243.2.g.a.208.4		144	9.4	even	3
729.2.g.a.109.5		144	81.76	even	27
729.2.g.a.622.5		144	9.7	even	3
729.2.g.b.352.5		144	81.49	even	27	inner
729.2.g.b.379.5		144	1.1	even	1	trivial
729.2.g.c.352.4		144	81.32	odd	54
729.2.g.c.379.4		144	3.2	odd	2
729.2.g.d.109.4		144	81.5	odd	54
729.2.g.d.622.4		144	9.2	odd	6
6561.2.a.c.1.42		72	81.74	odd	54
6561.2.a.d.1.31		72	81.7	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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