LMFDB - Embedded newform 729.2.i.a.262.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(10,729)] 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("729.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			262.22
Character	$\chi$	$=$	729.262
Dual form			729.2.i.a.64.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.03967 - 0.0791483i) q^{2} +(2.15999 - 0.167888i) q^{4} +(-1.00485 + 1.24581i) q^{5} +(2.22760 + 1.01257i) q^{7} +(0.337568 - 0.0394561i) q^{8} +(-1.95095 + 2.62057i) q^{10} +(-0.101732 + 5.24528i) q^{11} +(3.45524 - 1.10788i) q^{13} +(4.62371 + 1.88899i) q^{14} +(-3.59556 + 0.562336i) q^{16} +(1.11860 - 3.73638i) q^{17} +(6.38307 + 1.51282i) q^{19} +(-1.96130 + 2.85964i) q^{20} +(0.207655 + 10.7067i) q^{22} +(-2.65860 - 1.90025i) q^{23} +(0.516184 + 2.38297i) q^{25} +(6.95986 - 2.53318i) q^{26} +(4.98160 + 1.81315i) q^{28} +(0.186172 - 1.36302i) q^{29} +(-4.51437 + 4.42766i) q^{31} +(-7.95623 + 1.56255i) q^{32} +(1.98584 - 7.70951i) q^{34} +(-3.49987 + 1.75770i) q^{35} +(4.92352 - 3.23825i) q^{37} +(13.1391 + 2.58043i) q^{38} +(-0.290049 + 0.460194i) q^{40} +(-3.88267 - 7.37108i) q^{41} +(-3.43287 - 10.0329i) q^{43} +(0.660877 + 11.3468i) q^{44} +(-5.57305 - 3.66545i) q^{46} +(3.59597 + 3.52690i) q^{47} +(-0.665729 - 0.762841i) q^{49} +(1.24145 + 4.81961i) q^{50} +(7.27729 - 2.97310i) q^{52} +(5.38254 - 4.51648i) q^{53} +(-6.43241 - 5.39743i) q^{55} +(0.791920 + 0.253919i) q^{56} +(0.271848 - 2.79484i) q^{58} +(-6.04488 - 3.33542i) q^{59} +(-3.69728 - 0.287376i) q^{61} +(-8.85736 + 9.38825i) q^{62} +(-9.02203 + 2.13826i) q^{64} +(-2.09178 + 5.41783i) q^{65} +(0.464082 + 3.39768i) q^{67} +(1.78887 - 8.25835i) q^{68} +(-6.99945 + 3.86213i) q^{70} +(2.45599 + 5.69362i) q^{71} +(2.70227 + 3.62977i) q^{73} +(9.78604 - 6.99464i) q^{74} +(14.0413 + 2.19603i) q^{76} +(-5.53783 + 11.5814i) q^{77} +(-6.98054 - 11.0754i) q^{79} +(2.91242 - 5.04446i) q^{80} +(-8.50277 - 14.7272i) q^{82} +(-2.89733 + 5.50045i) q^{83} +(3.53082 + 5.14806i) q^{85} +(-7.79601 - 20.1922i) q^{86} +(0.172616 + 1.77465i) q^{88} +(-0.529625 + 1.22781i) q^{89} +(8.81872 + 1.03076i) q^{91} +(-6.06156 - 3.65817i) q^{92} +(7.61373 + 6.90909i) q^{94} +(-8.29869 + 6.43197i) q^{95} +(1.70401 + 2.11264i) q^{97} +(-1.41824 - 1.50325i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{80}{81}\right)$

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 $

$2$	2.03967	−	0.0791483i	1.44226	−	0.0559663i	0.694289	−	0.719696i	$-0.255719\pi$
$2$	2.03967	−	0.0791483i	1.44226	−	0.0559663i	0.747973	+	0.663730i	$0.231027\pi$
$3$		0			0
$3$		0			0
$4$	2.15999	−	0.167888i	1.07999	−	0.0839438i
$5$	−1.00485	+	1.24581i	−0.449381	+	0.557144i	−0.951498	−	0.307655i	$-0.900456\pi$
$5$	−1.00485	+	1.24581i	−0.449381	+	0.557144i	0.502117	+	0.864799i	$0.332555\pi$
$6$		0			0
$7$	2.22760	+	1.01257i	0.841955	+	0.382716i	0.787886	−	0.615822i	$-0.211176\pi$
$7$	2.22760	+	1.01257i	0.841955	+	0.382716i	0.0540695	+	0.998537i	$0.482781\pi$
$8$	0.337568	−	0.0394561i	0.119348	−	0.0139498i
$9$		0			0
$10$	−1.95095	+	2.62057i	−0.616943	+	0.828698i
$11$	−0.101732	+	5.24528i	−0.0306734	+	1.58151i	0.596489	+	0.802621i	$0.296562\pi$
$11$	−0.101732	+	5.24528i	−0.0306734	+	1.58151i	−0.627162	+	0.778889i	$0.715784\pi$
$12$		0			0
$13$	3.45524	−	1.10788i	0.958312	−	0.307270i	0.215300	−	0.976548i	$-0.430927\pi$
$13$	3.45524	−	1.10788i	0.958312	−	0.307270i	0.743012	+	0.669278i	$0.233396\pi$
$14$	4.62371	+	1.88899i	1.23574	+	0.504855i
$15$		0			0
$16$	−3.59556	+	0.562336i	−0.898891	+	0.140584i
$17$	1.11860	−	3.73638i	0.271300	−	0.906206i	−0.708412	−	0.705799i	$-0.750588\pi$
$17$	1.11860	−	3.73638i	0.271300	−	0.906206i	0.979713	−	0.200408i	$-0.0642266\pi$
$18$		0			0
$19$	6.38307	+	1.51282i	1.46438	+	0.347064i	0.884078	−	0.467339i	$-0.154787\pi$
$19$	6.38307	+	1.51282i	1.46438	+	0.347064i	0.580300	+	0.814403i	$0.302935\pi$
$20$	−1.96130	+	2.85964i	−0.438560	+	0.639435i
$21$		0			0
$22$	0.207655	+	10.7067i	0.0442723	+	2.28267i
$23$	−2.65860	−	1.90025i	−0.554356	−	0.396230i	0.269525	−	0.962993i	$-0.413133\pi$
$23$	−2.65860	−	1.90025i	−0.554356	−	0.396230i	−0.823880	+	0.566764i	$0.808195\pi$
$24$		0			0
$25$	0.516184	+	2.38297i	0.103237	+	0.476594i
$26$	6.95986	−	2.53318i	1.36494	−	0.496798i
$27$		0			0
$28$	4.98160	+	1.81315i	0.941433	+	0.342654i
$29$	0.186172	−	1.36302i	0.0345713	−	0.253106i	−0.965399	−	0.260776i	$-0.916022\pi$
$29$	0.186172	−	1.36302i	0.0345713	−	0.253106i	0.999971	+	0.00766965i	$0.00244135\pi$
$30$		0			0
$31$	−4.51437	+	4.42766i	−0.810804	+	0.795231i	−0.981775	−	0.190045i	$-0.939137\pi$
$31$	−4.51437	+	4.42766i	−0.810804	+	0.795231i	0.170971	+	0.985276i	$0.445309\pi$
$32$	−7.95623	+	1.56255i	−1.40648	+	0.276223i
$33$		0			0
$34$	1.98584	−	7.70951i	0.340569	−	1.32217i
$35$	−3.49987	+	1.75770i	−0.591586	+	0.297106i
$36$		0			0
$37$	4.92352	−	3.23825i	0.809422	−	0.532365i	−0.0760248	−	0.997106i	$-0.524223\pi$
$37$	4.92352	−	3.23825i	0.809422	−	0.532365i	0.885447	+	0.464741i	$0.153852\pi$
$38$	13.1391	+	2.58043i	2.13144	+	0.418601i
$39$		0			0
$40$	−0.290049	+	0.460194i	−0.0458608	+	0.0727631i
$41$	−3.88267	−	7.37108i	−0.606372	−	1.15117i	−0.975128	−	0.221643i	$-0.928858\pi$
$41$	−3.88267	−	7.37108i	−0.606372	−	1.15117i	0.368756	−	0.929526i	$-0.379784\pi$
$42$		0			0
$43$	−3.43287	−	10.0329i	−0.523508	−	1.53001i	−0.818498	−	0.574510i	$-0.805193\pi$
$43$	−3.43287	−	10.0329i	−0.523508	−	1.53001i	0.294989	−	0.955501i	$-0.404684\pi$
$44$	0.660877	+	11.3468i	0.0996309	+	1.71060i
$45$		0			0
$46$	−5.57305	−	3.66545i	−0.821701	−	0.540442i
$47$	3.59597	+	3.52690i	0.524526	+	0.514452i	0.913523	−	0.406787i	$-0.133351\pi$
$47$	3.59597	+	3.52690i	0.524526	+	0.514452i	−0.388997	+	0.921239i	$0.627178\pi$
$48$		0			0
$49$	−0.665729	−	0.762841i	−0.0951041	−	0.108977i
$50$	1.24145	+	4.81961i	0.175568	+	0.681596i
$51$		0			0
$52$	7.27729	−	2.97310i	1.00918	−	0.412295i
$53$	5.38254	−	4.51648i	0.739348	−	0.620387i	−0.193314	−	0.981137i	$-0.561924\pi$
$53$	5.38254	−	4.51648i	0.739348	−	0.620387i	0.932663	+	0.360750i	$0.117479\pi$
$54$		0			0
$55$	−6.43241	−	5.39743i	−0.867346	−	0.727789i
$56$	0.791920	+	0.253919i	0.105825	+	0.0339313i
$57$		0			0
$58$	0.271848	−	2.79484i	0.0356954	−	0.366980i
$59$	−6.04488	−	3.33542i	−0.786976	−	0.434235i	0.0380878	−	0.999274i	$-0.487873\pi$
$59$	−6.04488	−	3.33542i	−0.786976	−	0.434235i	−0.825064	+	0.565039i	$0.808861\pi$
$60$		0			0
$61$	−3.69728	−	0.287376i	−0.473389	−	0.0367947i	−0.161417	−	0.986886i	$-0.551607\pi$
$61$	−3.69728	−	0.287376i	−0.473389	−	0.0367947i	−0.311971	+	0.950092i	$0.600989\pi$
$62$	−8.85736	+	9.38825i	−1.12489	+	1.19231i
$63$		0			0
$64$	−9.02203	+	2.13826i	−1.12775	+	0.267283i
$65$	−2.09178	+	5.41783i	−0.259453	+	0.672000i
$66$		0			0
$67$	0.464082	+	3.39768i	0.0566966	+	0.415093i	0.997167	+	0.0752175i	$0.0239651\pi$
$67$	0.464082	+	3.39768i	0.0566966	+	0.415093i	−0.940471	+	0.339875i	$0.889615\pi$
$68$	1.78887	−	8.25835i	0.216932	−	1.00147i
$69$		0			0
$70$	−6.99945	+	3.86213i	−0.836594	+	0.461613i
$71$	2.45599	+	5.69362i	0.291472	+	0.675709i	0.999537	−	0.0304392i	$-0.00969058\pi$
$71$	2.45599	+	5.69362i	0.291472	+	0.675709i	−0.708064	+	0.706148i	$0.750431\pi$
$72$		0			0
$73$	2.70227	+	3.62977i	0.316276	+	0.424833i	0.931624	−	0.363423i	$-0.118392\pi$
$73$	2.70227	+	3.62977i	0.316276	+	0.424833i	−0.615348	+	0.788256i	$0.710984\pi$
$74$	9.78604	−	6.99464i	1.13760	−	0.813111i
$75$		0			0
$76$	14.0413	+	2.19603i	1.61065	+	0.251902i
$77$	−5.53783	+	11.5814i	−0.631094	+	1.31982i
$78$		0			0
$79$	−6.98054	−	11.0754i	−0.785372	−	1.24608i	−0.964976	−	0.262339i	$-0.915506\pi$
$79$	−6.98054	−	11.0754i	−0.785372	−	1.24608i	0.179604	−	0.983739i	$-0.442518\pi$
$80$	2.91242	−	5.04446i	0.325618	−	0.563988i
$81$		0			0
$82$	−8.50277	−	14.7272i	−0.938974	−	1.62635i
$83$	−2.89733	+	5.50045i	−0.318023	+	0.603753i	−0.990681	−	0.136201i	$-0.956511\pi$
$83$	−2.89733	+	5.50045i	−0.318023	+	0.603753i	0.672658	+	0.739954i	$0.265153\pi$
$84$		0			0
$85$	3.53082	+	5.14806i	0.382971	+	0.558385i
$86$	−7.79601	−	20.1922i	−0.840665	−	2.17738i
$87$		0			0
$88$	0.172616	+	1.77465i	0.0184010	+	0.189178i
$89$	−0.529625	+	1.22781i	−0.0561402	+	0.130148i	−0.943977	−	0.330010i	$-0.892948\pi$
$89$	−0.529625	+	1.22781i	−0.0561402	+	0.130148i	0.887837	+	0.460158i	$0.152207\pi$
$90$		0			0
$91$	8.81872	+	1.03076i	0.924453	+	0.108053i
$92$	−6.06156	−	3.65817i	−0.631962	−	0.381391i
$93$		0			0
$94$	7.61373	+	6.90909i	0.785296	+	0.712618i
$95$	−8.29869	+	6.43197i	−0.851428	+	0.659906i
$96$		0			0
$97$	1.70401	+	2.11264i	0.173016	+	0.214506i	0.857448	−	0.514571i	$-0.172049\pi$
$97$	1.70401	+	2.11264i	0.173016	+	0.214506i	−0.684432	+	0.729076i	$0.739950\pi$
$98$	−1.41824	−	1.50325i	−0.143264	−	0.151851i
$99$		0			0
$100$	1.51502	+	5.06053i	0.151502	+	0.506053i
$101$	−5.41927	−	11.3334i	−0.539237	−	1.12772i	−0.973869	−	0.227111i	$-0.927072\pi$
$101$	−5.41927	−	11.3334i	−0.539237	−	1.12772i	0.434632	−	0.900608i	$-0.356879\pi$
$102$		0			0
$103$	11.3647	−	6.85862i	1.11980	−	0.675800i	0.168999	−	0.985616i	$-0.445946\pi$
$103$	11.3647	−	6.85862i	1.11980	−	0.675800i	0.950797	+	0.309816i	$0.100267\pi$
$104$	1.12267	−	0.510315i	0.110087	−	0.0500405i
$105$		0			0
$106$	10.6211	−	9.63814i	1.03161	−	0.936139i
$107$	1.09985	−	6.23759i	0.106327	−	0.603010i	−0.884355	−	0.466815i	$-0.845401\pi$
$107$	1.09985	−	6.23759i	0.106327	−	0.603010i	0.990682	−	0.136195i	$-0.0434875\pi$
$108$		0			0
$109$	−2.05615	−	11.6610i	−0.196943	−	1.11692i	−0.909624	−	0.415432i	$-0.863630\pi$
$109$	−2.05615	−	11.6610i	−0.196943	−	1.11692i	0.712681	−	0.701489i	$-0.247481\pi$
$110$	−13.5472	−	10.4998i	−1.29167	−	1.00112i
$111$		0			0
$112$	−8.57889	−	2.38810i	−0.810629	−	0.225654i
$113$	−3.31997	+	9.70298i	−0.312317	+	0.912780i	0.672639	+	0.739971i	$0.265161\pi$
$113$	−3.31997	+	9.70298i	−0.312317	+	0.912780i	−0.984955	+	0.172809i	$0.944716\pi$
$114$		0			0
$115$	5.03883	−	1.40266i	0.469874	−	0.130798i
$116$	0.173295	−	2.97536i	0.0160900	−	0.276255i
$117$		0			0
$118$	−12.5935	−	6.32471i	−1.15933	−	0.582237i
$119$	6.27515	−	7.19052i	0.575242	−	0.659154i
$120$		0			0
$121$	−16.5108	−	0.640696i	−1.50098	−	0.0582450i
$122$	−7.56397	−	0.293516i	−0.684810	−	0.0265737i
$123$		0			0
$124$	−9.00763	+	10.3216i	−0.808909	+	0.926907i
$125$	−10.6389	−	5.34308i	−0.951576	−	0.477899i
$126$		0			0
$127$	−0.509772	+	8.75245i	−0.0452350	+	0.776654i	0.897068	+	0.441893i	$0.145693\pi$
$127$	−0.509772	+	8.75245i	−0.0452350	+	0.776654i	−0.942303	+	0.334761i	$0.891344\pi$
$128$	−2.61026	+	0.726616i	−0.230717	+	0.0642244i
$129$		0			0
$130$	−3.83771	+	11.2161i	−0.336590	+	0.983720i
$131$	13.7424	+	3.82545i	1.20068	+	0.334231i	0.810073	−	0.586328i	$-0.199427\pi$
$131$	13.7424	+	3.82545i	1.20068	+	0.334231i	0.390602	+	0.920559i	$0.372267\pi$
$132$		0			0
$133$	12.6871	+	9.83327i	1.10011	+	0.852652i
$134$	1.21549	+	6.89340i	0.105003	+	0.595499i
$135$		0			0
$136$	0.230181	−	1.30542i	0.0197378	−	0.111939i
$137$	12.8641	−	11.6736i	1.09906	−	0.997342i	0.0990609	−	0.995081i	$-0.468416\pi$
$137$	12.8641	−	11.6736i	1.09906	−	0.997342i	0.999997	−	0.00226085i	$-0.000719651\pi$
$138$		0			0
$139$	−19.4551	+	8.84341i	−1.65016	+	0.750088i	−0.999953	−	0.00967150i	$-0.996921\pi$
$139$	−19.4551	+	8.84341i	−1.65016	+	0.750088i	−0.650204	+	0.759760i	$0.725316\pi$
$140$	−7.26458	+	4.38420i	−0.613969	+	0.370532i
$141$		0			0
$142$	5.46004	+	11.4187i	0.458196	+	0.958236i
$143$	5.45962	+	18.2364i	0.456557	+	1.52501i
$144$		0			0
$145$	1.51099	+	1.60156i	0.125481	+	0.133002i
$146$	5.79901	+	7.18965i	0.479930	+	0.595019i
$147$		0			0
$148$	10.0911	−	7.82118i	0.829482	−	0.642897i
$149$	13.0712	+	11.8615i	1.07084	+	0.971734i	0.999669	−	0.0257302i	$-0.00819109\pi$
$149$	13.0712	+	11.8615i	1.07084	+	0.971734i	0.0711695	+	0.997464i	$0.477327\pi$
$150$		0			0
$151$	−12.7924	−	7.72023i	−1.04103	−	0.628263i	−0.110271	−	0.993902i	$-0.535172\pi$
$151$	−12.7924	−	7.72023i	−1.04103	−	0.628263i	−0.930757	+	0.365638i	$0.880851\pi$
$152$	2.21441	+	0.258828i	0.179613	+	0.0209937i
$153$		0			0
$154$	−10.3787	+	24.0605i	−0.836337	+	1.93885i
$155$	−0.979795	−	10.0732i	−0.0786990	−	0.809096i
$156$		0			0
$157$	2.49997	+	6.47508i	0.199519	+	0.516768i	0.996147	−	0.0877029i	$-0.0279526\pi$
$157$	2.49997	+	6.47508i	0.199519	+	0.516768i	−0.796628	+	0.604471i	$0.793385\pi$
$158$	−15.1146	−	22.0376i	−1.20245	−	1.75322i
$159$		0			0
$160$	6.04813	−	11.4821i	0.478147	−	0.907740i
$161$	−3.99816	−	6.92502i	−0.315099	−	0.545768i
$162$		0			0
$163$	12.2117	−	21.1512i	0.956490	−	1.65669i	0.225570	−	0.974227i	$-0.427575\pi$
$163$	12.2117	−	21.1512i	0.956490	−	1.65669i	0.730920	−	0.682463i	$-0.239091\pi$
$164$	−9.62404	−	15.2696i	−0.751512	−	1.19235i
$165$		0			0
$166$	−5.47424	+	11.4484i	−0.424883	+	0.888568i
$167$	8.99410	+	1.40665i	0.695984	+	0.108850i	0.492609	−	0.870251i	$-0.336043\pi$
$167$	8.99410	+	1.40665i	0.695984	+	0.108850i	0.203375	+	0.979101i	$0.434809\pi$
$168$		0			0
$169$	0.135133	−	0.0965874i	0.0103949	−	0.00742980i
$170$	7.60915	+	10.2209i	0.583595	+	0.783904i
$171$		0			0
$172$	−9.09937	−	21.0947i	−0.693821	−	1.60846i
$173$	3.25915	−	1.79833i	0.247789	−	0.136724i	−0.354357	−	0.935110i	$-0.615300\pi$
$173$	3.25915	−	1.79833i	0.247789	−	0.136724i	0.602146	+	0.798386i	$0.294313\pi$
$174$		0			0
$175$	−1.26307	+	5.83099i	−0.0954792	+	0.440781i
$176$	−2.58382	−	18.9169i	−0.194763	−	1.42592i
$177$		0			0
$178$	−0.983080	+	2.54624i	−0.0736850	+	0.190849i
$179$	−1.29159	+	0.306112i	−0.0965379	+	0.0228799i	−0.278601	−	0.960407i	$-0.589871\pi$
$179$	−1.29159	+	0.306112i	−0.0965379	+	0.0228799i	0.182063	+	0.983287i	$0.441723\pi$
$180$		0			0
$181$	−4.33102	+	4.59062i	−0.321922	+	0.341218i	−0.868043	−	0.496489i	$-0.834622\pi$
$181$	−4.33102	+	4.59062i	−0.321922	+	0.341218i	0.546121	+	0.837706i	$0.316104\pi$
$182$	18.0688	+	1.40442i	1.33935	+	0.104103i
$183$		0			0
$184$	−0.972434	−	0.536566i	−0.0716888	−	0.0395562i
$185$	−0.913123	+	9.38773i	−0.0671342	+	0.690200i
$186$		0			0
$187$	19.4846	+	6.24748i	1.42485	+	0.456861i
$188$	8.35938	+	7.01435i	0.609670	+	0.511574i
$189$		0			0
$190$	−16.4175	+	13.7759i	−1.19105	+	0.999409i
$191$	5.19612	−	2.12285i	0.375978	−	0.153604i	−0.182331	−	0.983237i	$-0.558364\pi$
$191$	5.19612	−	2.12285i	0.375978	−	0.153604i	0.558309	+	0.829633i	$0.311451\pi$
$192$		0			0
$193$	−1.57481	−	6.11378i	−0.113357	−	0.440080i	0.886381	−	0.462956i	$-0.153211\pi$
$193$	−1.57481	−	6.11378i	−0.113357	−	0.440080i	−0.999738	+	0.0228766i	$0.992718\pi$
$194$	3.64282	+	4.17421i	0.261539	+	0.299691i
$195$		0			0
$196$	−1.56604	−	1.53596i	−0.111860	−	0.109711i
$197$	−9.22019	−	6.06421i	−0.656911	−	0.432057i	0.176808	−	0.984245i	$-0.443423\pi$
$197$	−9.22019	−	6.06421i	−0.656911	−	0.432057i	−0.833720	+	0.552188i	$0.813793\pi$
$198$		0			0
$199$	0.760442	+	13.0563i	0.0539063	+	0.925535i	0.911524	+	0.411247i	$0.134907\pi$
$199$	0.760442	+	13.0563i	0.0539063	+	0.925535i	−0.857617	+	0.514288i	$0.828056\pi$
$200$	0.268270	+	0.784048i	0.0189695	+	0.0554406i
$201$		0			0
$202$	−11.9505	−	22.6875i	−0.840836	−	1.59629i
$203$	1.79487	−	2.84776i	0.125975	−	0.199873i
$204$		0			0
$205$	13.0845	+	2.56971i	0.913859	+	0.179476i
$206$	22.6373	−	14.8888i	1.57722	−	1.03735i
$207$		0			0
$208$	−11.8005	+	5.92646i	−0.818220	+	0.410926i
$209$	−8.58450	+	33.3271i	−0.593802	+	2.30528i
$210$		0			0
$211$	0.804862	−	0.158070i	0.0554090	−	0.0108820i	−0.164931	−	0.986305i	$-0.552740\pi$
$211$	0.804862	−	0.158070i	0.0554090	−	0.0108820i	0.220340	+	0.975423i	$0.429283\pi$
$212$	10.8680	−	10.6592i	0.746414	−	0.732078i
$213$		0			0
$214$	1.74964	−	12.8096i	0.119603	−	0.875650i
$215$	15.9487	+	5.80485i	1.08769	+	0.395887i
$216$		0			0
$217$	−14.5395	+	5.29196i	−0.987008	+	0.359241i
$218$	−5.11680	−	23.6218i	−0.346554	−	1.59987i
$219$		0			0
$220$	−14.8001	−	10.5785i	−0.997821	−	0.713200i
$221$	−0.274427	−	14.1494i	−0.0184600	−	0.951791i
$222$		0			0
$223$	0.847689	−	1.23596i	0.0567654	−	0.0827660i	−0.795253	−	0.606277i	$-0.792662\pi$
$223$	0.847689	−	1.23596i	0.0567654	−	0.0827660i	0.852019	+	0.523511i	$0.175378\pi$
$224$	−19.3055	−	4.57549i	−1.28990	−	0.305713i
$225$		0			0
$226$	−6.00366	+	20.0536i	−0.399357	+	1.33395i
$227$	−5.49625	+	0.859597i	−0.364799	+	0.0570535i	−0.334262	−	0.942480i	$-0.608487\pi$
$227$	−5.49625	+	0.859597i	−0.364799	+	0.0570535i	−0.0305366	+	0.999534i	$0.509722\pi$
$228$		0			0
$229$	−13.6896	−	5.59283i	−0.904637	−	0.369585i	−0.122338	−	0.992488i	$-0.539039\pi$
$229$	−13.6896	−	5.59283i	−0.904637	−	0.369585i	−0.782298	+	0.622904i	$0.785953\pi$
$230$	10.1665	−	3.25976i	0.670361	−	0.214943i
$231$		0			0
$232$	0.00906633	−	0.467458i	0.000595234	−	0.0306901i
$233$	−7.85582	+	10.5522i	−0.514652	+	0.691297i	−0.981155	−	0.193222i	$-0.938106\pi$
$233$	−7.85582	+	10.5522i	−0.514652	+	0.691297i	0.466503	+	0.884519i	$0.345514\pi$
$234$		0			0
$235$	−8.00726	+	0.935914i	−0.522336	+	0.0610523i
$236$	−13.6168	−	6.18961i	−0.886381	−	0.402910i
$237$		0			0
$238$	12.2301	−	15.1629i	0.792759	−	0.982867i
$239$	11.1361	−	0.865566i	0.720334	−	0.0559888i	0.287908	−	0.957658i	$-0.407040\pi$
$239$	11.1361	−	0.865566i	0.720334	−	0.0559888i	0.432426	+	0.901669i	$0.357658\pi$
$240$		0			0
$241$	−6.42186	+	0.249197i	−0.413668	+	0.0160522i	−0.244770	−	0.969581i	$-0.578712\pi$
$241$	−6.42186	+	0.249197i	−0.413668	+	0.0160522i	−0.168898	+	0.985633i	$0.554021\pi$
$242$	−33.7273			−2.16807
$243$		0			0
$244$	−8.03433			−0.514346
$245$	1.61931	−	0.0628367i	0.103454	−	0.00401449i
$246$		0			0
$247$	23.7311	−	1.84453i	1.50997	−	0.117364i
$248$	−1.34921	+	1.67276i	−0.0856748	+	0.106220i
$249$		0			0
$250$	−22.1228	−	10.0560i	−1.39917	−	0.636000i
$251$	16.1845	−	1.89170i	1.02156	−	0.119403i	0.411213	−	0.911539i	$-0.365105\pi$
$251$	16.1845	−	1.89170i	1.02156	−	0.119403i	0.610344	+	0.792136i	$0.291031\pi$
$252$		0			0
$253$	10.2378	−	13.7518i	0.643645	−	0.864565i
$254$	−0.347023	+	17.8924i	−0.0217742	+	1.12267i
$255$		0			0
$256$	12.3919	−	3.97329i	0.774491	−	0.248331i
$257$	21.2658	+	8.68803i	1.32652	+	0.541944i	0.927097	−	0.374821i	$-0.122296\pi$
$257$	21.2658	+	8.68803i	1.32652	+	0.541944i	0.399426	+	0.916765i	$0.369209\pi$
$258$		0			0
$259$	14.2466	−	2.22813i	0.885242	−	0.138449i
$260$	−3.60862	+	12.0536i	−0.223797	+	0.747535i
$261$		0			0
$262$	28.3326	+	6.71495i	1.75039	+	0.414851i
$263$	1.71024	−	2.49358i	0.105458	−	0.153761i	−0.768355	−	0.640024i	$-0.778924\pi$
$263$	1.71024	−	2.49358i	0.105458	−	0.153761i	0.873812	+	0.486263i	$0.161640\pi$
$264$		0			0
$265$	0.218077	+	11.2440i	0.0133964	+	0.690714i
$266$	26.6558	+	19.0524i	1.63437	+	1.16818i
$267$		0			0
$268$	1.57284	+	7.26104i	0.0960765	+	0.443538i
$269$	−0.954769	+	0.347507i	−0.0582133	+	0.0211879i	−0.370963	−	0.928648i	$-0.620972\pi$
$269$	−0.954769	+	0.347507i	−0.0582133	+	0.0211879i	0.312749	+	0.949836i	$0.398750\pi$
$270$		0			0
$271$	24.4563	+	8.90135i	1.48561	+	0.540718i	0.952290	−	0.305194i	$-0.0987214\pi$
$271$	24.4563	+	8.90135i	1.48561	+	0.540718i	0.533321	+	0.845913i	$0.320944\pi$
$272$	−1.92089	+	14.0634i	−0.116471	+	0.852721i
$273$		0			0
$274$	25.3146	−	24.8284i	1.52931	−	1.49994i
$275$	−12.5518	+	2.46510i	−0.756905	+	0.148651i
$276$		0			0
$277$	−5.46341	+	21.2102i	−0.328264	+	1.27440i	0.565083	+	0.825034i	$0.308844\pi$
$277$	−5.46341	+	21.2102i	−0.328264	+	1.27440i	−0.893348	+	0.449366i	$0.851650\pi$
$278$	−38.9819	+	19.5774i	−2.33798	+	1.17418i
$279$		0			0
$280$	−1.11209	+	0.731435i	−0.0664603	+	0.0437116i
$281$	17.3873	+	3.41475i	1.03724	+	0.203707i	0.682215	−	0.731151i	$-0.261017\pi$
$281$	17.3873	+	3.41475i	1.03724	+	0.203707i	0.355022	+	0.934858i	$0.384474\pi$
$282$		0			0
$283$	−13.0610	+	20.7226i	−0.776394	+	1.23183i	0.191751	+	0.981444i	$0.438583\pi$
$283$	−13.0610	+	20.7226i	−0.776394	+	1.23183i	−0.968145	+	0.250389i	$0.919441\pi$
$284$	6.26080	+	11.8858i	0.371510	+	0.705294i
$285$		0			0
$286$	12.5792	+	36.7641i	0.743823	+	2.17390i
$287$	−1.18533	−	20.3513i	−0.0699678	−	1.20130i
$288$		0			0
$289$	1.49399	+	0.982611i	0.0878816	+	0.0578007i
$290$	3.20868	+	3.14705i	0.188420	+	0.184801i
$291$		0			0
$292$	6.44626	+	7.38659i	0.377239	+	0.432268i
$293$	−1.77558	−	6.89323i	−0.103731	−	0.402707i	0.895360	−	0.445343i	$-0.146918\pi$
$293$	−1.77558	−	6.89323i	−0.103731	−	0.402707i	−0.999091	+	0.0426362i	$0.986424\pi$
$294$		0			0
$295$	10.2295	−	4.17920i	0.595584	−	0.243323i
$296$	1.53426	−	1.28739i	0.0891768	−	0.0748282i
$297$		0			0
$298$	27.5998	+	23.1590i	1.59881	+	1.34156i
$299$	−11.2913	−	3.62042i	−0.652995	−	0.209375i
$300$		0			0
$301$	2.51198	−	25.8255i	0.144788	−	1.48855i
$302$	−26.7032	−	14.7342i	−1.53660	−	0.847858i
$303$		0			0
$304$	−23.8015	−	1.85000i	−1.36511	−	0.106105i
$305$	4.07321	−	4.31735i	0.233232	−	0.247211i
$306$		0			0
$307$	−19.6068	+	4.64690i	−1.11902	+	0.265212i	−0.748187	−	0.663488i	$-0.769075\pi$
$307$	−19.6068	+	4.64690i	−1.11902	+	0.265212i	−0.370832	+	0.928700i	$0.620927\pi$
$308$	−10.0173	+	25.9454i	−0.570787	+	1.47838i
$309$		0			0
$310$	−2.79573	−	20.4684i	−0.158787	−	1.16252i
$311$	−6.58521	+	30.4007i	−0.373413	+	1.72387i	0.274002	+	0.961729i	$0.411653\pi$
$311$	−6.58521	+	30.4007i	−0.373413	+	1.72387i	−0.647415	+	0.762138i	$0.724150\pi$
$312$		0			0
$313$	−11.9940	+	6.61803i	−0.677943	+	0.374073i	−0.784410	−	0.620243i	$-0.787034\pi$
$313$	−11.9940	+	6.61803i	−0.677943	+	0.374073i	0.106466	+	0.994316i	$0.466046\pi$
$314$	5.61159	+	13.0091i	0.316680	+	0.734148i
$315$		0			0
$316$	−16.9373	−	22.7507i	−0.952798	−	1.27983i
$317$	−3.11831	+	2.22883i	−0.175142	+	0.125184i	−0.665684	−	0.746233i	$-0.731860\pi$
$317$	−3.11831	+	2.22883i	−0.175142	+	0.125184i	0.490543	+	0.871417i	$0.336799\pi$
$318$		0			0
$319$	7.13047	+	1.11519i	0.399230	+	0.0624384i
$320$	6.40188	−	13.3884i	0.357876	−	0.748434i
$321$		0			0
$322$	−8.70302	−	13.8083i	−0.485000	−	0.769505i
$323$	12.7926	−	22.1574i	0.711798	−	1.23287i
$324$		0			0
$325$	4.42358	+	7.66187i	0.245376	+	0.425004i
$326$	23.2336	−	44.1079i	1.28679	−	2.44291i
$327$		0			0
$328$	−1.60150	−	2.33505i	−0.0884281	−	0.128931i
$329$	4.43916	+	11.4977i	0.244739	+	0.633890i
$330$		0			0
$331$	−1.31812	−	13.5514i	−0.0724503	−	0.744854i	−0.959223	−	0.282649i	$-0.908787\pi$
$331$	−1.31812	−	13.5514i	−0.0724503	−	0.744854i	0.886773	−	0.462205i	$-0.152942\pi$
$332$	−5.33475	+	12.3673i	−0.292782	+	0.678745i
$333$		0			0
$334$	18.4563	+	2.15723i	1.00988	+	0.118038i
$335$	−4.69920	−	2.83598i	−0.256745	−	0.154946i
$336$		0			0
$337$	−12.7165	−	11.5396i	−0.692712	−	0.628603i	0.247621	−	0.968857i	$-0.420351\pi$
$337$	−12.7165	−	11.5396i	−0.692712	−	0.628603i	−0.940334	+	0.340254i	$0.889487\pi$
$338$	0.267982	−	0.207702i	0.0145763	−	0.0112975i
$339$		0			0
$340$	8.49082	+	10.5270i	0.460479	+	0.570905i
$341$	−22.7650	−	24.1295i	−1.23280	−	1.30669i
$342$		0			0
$343$	−5.62308	−	18.7824i	−0.303618	−	1.01415i
$344$	−1.55469	−	3.25136i	−0.0838232	−	0.175301i
$345$		0			0
$346$	6.50525	−	3.92594i	0.349725	−	0.211060i
$347$	7.07154	−	3.21441i	0.379620	−	0.172559i	−0.214906	−	0.976635i	$-0.568945\pi$
$347$	7.07154	−	3.21441i	0.379620	−	0.172559i	0.594526	+	0.804076i	$0.297340\pi$
$348$		0			0
$349$	−0.216277	+	0.196261i	−0.0115771	+	0.0105056i	−0.677776	−	0.735269i	$-0.737056\pi$
$349$	−0.216277	+	0.196261i	−0.0115771	+	0.0105056i	0.666199	+	0.745774i	$0.267920\pi$
$350$	−2.11473	+	11.9932i	−0.113037	+	0.641065i
$351$		0			0
$352$	−7.38662	−	41.8916i	−0.393708	−	2.23283i
$353$	−23.6090	−	18.2984i	−1.25658	−	0.973924i	−0.999973	−	0.00740871i	$-0.997642\pi$
$353$	−23.6090	−	18.2984i	−1.25658	−	0.973924i	−0.256609	−	0.966515i	$-0.582605\pi$
$354$		0			0
$355$	−9.56108	−	2.66151i	−0.507449	−	0.141258i
$356$	−0.937851	+	2.74097i	−0.0497060	+	0.145271i
$357$		0			0
$358$	−2.61018	+	0.726594i	−0.137952	+	0.0384017i
$359$	−1.00011	+	17.1712i	−0.0527839	+	0.906264i	0.863153	+	0.504942i	$0.168486\pi$
$359$	−1.00011	+	17.1712i	−0.0527839	+	0.906264i	−0.915937	+	0.401322i	$0.868551\pi$
$360$		0			0
$361$	21.4760	+	10.7857i	1.13032	+	0.567666i
$362$	−8.47050	+	9.70612i	−0.445200	+	0.510142i
$363$		0			0
$364$	19.2214	+	0.745877i	1.00747	+	0.0390946i
$365$	−7.23738	−	0.280843i	−0.378822	−	0.0147000i
$366$		0			0
$367$	8.81529	−	10.1012i	0.460155	−	0.527279i	−0.475727	−	0.879593i	$-0.657815\pi$
$367$	8.81529	−	10.1012i	0.460155	−	0.527279i	0.935882	+	0.352314i	$0.114605\pi$
$368$	10.6277	+	5.33745i	0.554009	+	0.278234i
$369$		0			0
$370$	−1.11944	+	19.2201i	−0.0581971	+	0.999206i
$371$	16.5634	−	4.61074i	0.859930	−	0.239378i
$372$		0			0
$373$	1.45916	−	4.26455i	0.0755524	−	0.220810i	−0.901908	−	0.431927i	$-0.857834\pi$
$373$	1.45916	−	4.26455i	0.0755524	−	0.220810i	0.977461	+	0.211117i	$0.0677102\pi$
$374$	40.2365	+	11.2006i	2.08058	+	0.579169i
$375$		0			0
$376$	1.35304	+	1.04869i	0.0697779	+	0.0540819i
$377$	−0.866792	−	4.91582i	−0.0446420	−	0.253178i
$378$		0			0
$379$	−0.140699	+	0.797946i	−0.00722724	+	0.0409877i	−0.988208	−	0.153117i	$-0.951069\pi$
$379$	−0.140699	+	0.797946i	−0.00722724	+	0.0409877i	0.980981	+	0.194104i	$0.0621801\pi$
$380$	−16.8452	+	15.2862i	−0.864142	+	0.784167i
$381$		0			0
$382$	10.4303	−	4.74117i	0.533662	−	0.242579i
$383$	−27.1156	+	16.3643i	−1.38554	+	0.836179i	−0.996382	−	0.0849914i	$-0.972914\pi$
$383$	−27.1156	+	16.3643i	−1.38554	+	0.836179i	−0.389160	+	0.921170i	$0.627235\pi$
$384$		0			0
$385$	−8.86358	−	18.5366i	−0.451730	−	0.944713i
$386$	−3.69598	−	12.3454i	−0.188120	−	0.628366i
$387$		0			0
$388$	4.03532	+	4.27719i	0.204862	+	0.217142i
$389$	−15.5698	−	19.3036i	−0.789421	−	0.978729i	−0.999999	−	0.00115183i	$-0.999633\pi$
$389$	−15.5698	−	19.3036i	−0.789421	−	0.978729i	0.210578	−	0.977577i	$-0.432465\pi$
$390$		0			0
$391$	−10.0740	+	7.80792i	−0.509463	+	0.394863i
$392$	−0.254828	−	0.231244i	−0.0128707	−	0.0116796i
$393$		0			0
$394$	−19.2861	−	11.6392i	−0.971618	−	0.586375i
$395$	20.8122	+	2.43260i	1.04718	+	0.122397i
$396$		0			0
$397$	−14.1362	+	32.7713i	−0.709475	+	1.64475i	0.0537021	+	0.998557i	$0.482898\pi$
$397$	−14.1362	+	32.7713i	−0.709475	+	1.64475i	−0.763177	+	0.646190i	$0.776361\pi$
$398$	2.58443	+	26.5703i	0.129546	+	1.33185i
$399$		0			0
$400$	−3.19600	−	8.27785i	−0.159800	−	0.413892i
$401$	−21.9235	−	31.9652i	−1.09481	−	1.59627i	−0.754942	−	0.655791i	$-0.772335\pi$
$401$	−21.9235	−	31.9652i	−1.09481	−	1.59627i	−0.339863	−	0.940475i	$-0.610381\pi$
$402$		0			0
$403$	−10.6929	+	20.3000i	−0.532652	+	1.01122i
$404$	−13.6083	−	23.5703i	−0.677038	−	1.17266i
$405$		0			0
$406$	3.43554	−	5.95053i	0.170503	−	0.295320i
$407$	16.4846	+	26.1547i	0.817113	+	1.29644i
$408$		0			0
$409$	3.04884	−	6.37612i	0.150756	−	0.315279i	−0.812910	−	0.582389i	$-0.802118\pi$
$409$	3.04884	−	6.37612i	0.150756	−	0.315279i	0.963666	+	0.267110i	$0.0860687\pi$
$410$	26.8913	+	4.20573i	1.32807	+	0.207706i
$411$		0			0
$412$	23.3961	−	16.7225i	1.15264	−	0.823860i
$413$	−10.0882	−	13.5509i	−0.496410	−	0.666795i
$414$		0			0
$415$	−3.94116	−	9.13663i	−0.193464	−	0.448500i
$416$	−25.7596	+	14.2135i	−1.26297	+	0.696876i
$417$		0			0
$418$	−14.8717	+	68.6556i	−0.727400	+	3.35805i
$419$	5.10858	+	37.4014i	0.249570	+	1.82718i	0.508244	+	0.861213i	$0.330295\pi$
$419$	5.10858	+	37.4014i	0.249570	+	1.82718i	−0.258673	+	0.965965i	$0.583285\pi$
$420$		0			0
$421$	3.88589	−	10.0647i	0.189386	−	0.490523i	−0.805373	−	0.592769i	$-0.798035\pi$
$421$	3.88589	−	10.0647i	0.189386	−	0.490523i	0.994759	+	0.102245i	$0.0326027\pi$
$422$	1.62914	−	0.386113i	0.0793052	−	0.0187957i
$423$		0			0
$424$	1.63877	−	1.73699i	0.0795857	−	0.0843559i
$425$	9.48110	+	0.736929i	0.459901	+	0.0357463i
$426$		0			0
$427$	−7.94509	−	4.38392i	−0.384490	−	0.212153i
$428$	1.32846	−	13.6578i	0.0642136	−	0.660173i
$429$		0			0
$430$	32.9894	+	10.5776i	1.59089	+	0.510099i
$431$	23.7275	+	19.9098i	1.14292	+	0.959020i	0.999530	−	0.0306467i	$-0.00975669\pi$
$431$	23.7275	+	19.9098i	1.14292	+	0.959020i	0.143385	+	0.989667i	$0.454201\pi$
$432$		0			0
$433$	7.89284	−	6.62288i	0.379305	−	0.318275i	−0.433124	−	0.901334i	$-0.642589\pi$
$433$	7.89284	−	6.62288i	0.379305	−	0.318275i	0.812430	+	0.583059i	$0.198144\pi$
$434$	−29.2369	+	11.9446i	−1.40342	+	0.573360i
$435$		0			0
$436$	−6.39899	−	24.8424i	−0.306456	−	1.18974i
$437$	−14.0953	−	16.1514i	−0.674269	−	0.772627i
$438$		0			0
$439$	25.2633	+	24.7781i	1.20575	+	1.18259i	0.977940	+	0.208888i	$0.0669843\pi$
$439$	25.2633	+	24.7781i	1.20575	+	1.18259i	0.227812	+	0.973705i	$0.426843\pi$
$440$	−2.38434	−	1.56820i	−0.113669	−	0.0747611i
$441$		0			0
$442$	−1.67964	−	28.8383i	−0.0798924	−	1.37170i
$443$	−11.8151	−	34.5309i	−0.561351	−	1.64061i	−0.752158	−	0.658983i	$-0.770987\pi$
$443$	−11.8151	−	34.5309i	−0.561351	−	1.64061i	0.190807	−	0.981628i	$-0.438890\pi$
$444$		0			0
$445$	−0.997430	−	1.89357i	−0.0472827	−	0.0897640i
$446$	1.63118	−	2.58804i	0.0772385	−	0.122547i
$447$		0			0
$448$	−22.2627	−	4.37224i	−1.05181	−	0.206569i
$449$	13.4390	−	8.83897i	0.634226	−	0.417137i	−0.191276	−	0.981536i	$-0.561263\pi$
$449$	13.4390	−	8.83897i	0.634226	−	0.417137i	0.825502	+	0.564399i	$0.190892\pi$
$450$		0			0
$451$	39.0583	−	19.6158i	1.83918	−	0.923673i
$452$	−5.54209	+	21.5157i	−0.260678	+	1.01201i
$453$		0			0
$454$	−11.1425	+	2.18831i	−0.522942	+	0.102702i
$455$	−10.1456	+	9.95072i	−0.475632	+	0.466497i
$456$		0			0
$457$	−3.98603	+	29.1829i	−0.186459	+	1.36512i	0.624961	+	0.780656i	$0.285115\pi$
$457$	−3.98603	+	29.1829i	−0.186459	+	1.36512i	−0.811420	+	0.584463i	$0.801305\pi$
$458$	−28.3650	−	10.3240i	−1.32541	−	0.482409i
$459$		0			0
$460$	10.6483	−	3.87568i	0.496481	−	0.180704i
$461$	3.35349	+	15.4814i	0.156187	+	0.721042i	0.986502	+	0.163747i	$0.0523581\pi$
$461$	3.35349	+	15.4814i	0.156187	+	0.721042i	−0.830315	+	0.557295i	$0.811839\pi$
$462$		0			0
$463$	8.13784	+	5.81658i	0.378197	+	0.270319i	0.754665	−	0.656111i	$-0.227800\pi$
$463$	8.13784	+	5.81658i	0.378197	+	0.270319i	−0.376467	+	0.926430i	$0.622861\pi$
$464$	0.0970818	+	5.00551i	0.00450691	+	0.232375i
$465$		0			0
$466$	−15.1881	+	22.1447i	−0.703573	+	1.02583i
$467$	−2.33942	−	0.554454i	−0.108256	−	0.0256571i	0.176131	−	0.984367i	$-0.443642\pi$
$467$	−2.33942	−	0.554454i	−0.108256	−	0.0256571i	−0.284387	+	0.958710i	$0.591790\pi$
$468$		0			0
$469$	−2.40660	+	8.03860i	−0.111126	+	0.371188i
$470$	−16.2581	+	2.54271i	−0.749928	+	0.117287i
$471$		0			0
$472$	−2.17216	−	0.887425i	−0.0999818	−	0.0408471i
$473$	52.9748	−	16.9857i	2.43578	−	0.781003i
$474$		0			0
$475$	−0.310156	+	15.9916i	−0.0142309	+	0.733743i
$476$	12.3471	−	16.5850i	0.565926	−	0.760171i
$477$		0			0
$478$	22.6454	−	2.64687i	1.03578	−	0.121065i
$479$	8.37802	+	3.80828i	0.382802	+	0.174005i	0.595962	−	0.803012i	$-0.296771\pi$
$479$	8.37802	+	3.80828i	0.382802	+	0.174005i	−0.213161	+	0.977017i	$0.568376\pi$
$480$		0			0
$481$	13.4244	−	16.6436i	0.612099	−	0.758884i
$482$	−13.0787	+	1.01656i	−0.595719	+	0.0463030i
$483$		0			0
$484$	−35.7708	+	1.38807i	−1.62594	+	0.0630940i
$485$	−4.34422			−0.197261
$486$		0			0
$487$	−13.1955			−0.597943			−0.298972	−	0.954262i	$-0.596644\pi$
$487$	−13.1955			−0.597943			−0.298972	+	0.954262i	$0.596644\pi$
$488$	−1.25942	+	0.0488714i	−0.0570114	+	0.00221230i
$489$		0			0
$490$	3.29788	−	0.256332i	0.148983	−	0.0115799i
$491$	8.07499	−	10.0114i	0.364419	−	0.451809i	−0.562652	−	0.826694i	$-0.690219\pi$
$491$	8.07499	−	10.0114i	0.364419	−	0.451809i	0.927071	+	0.374885i	$0.122318\pi$
$492$		0			0
$493$	−4.88451	−	2.22028i	−0.219987	−	0.0999965i
$494$	48.2575	−	5.64049i	2.17121	−	0.253778i
$495$		0			0
$496$	13.7419	−	18.4585i	0.617027	−	0.828812i
$497$	−0.294222	+	15.1700i	−0.0131977	+	0.680468i
$498$		0			0
$499$	−33.7089	+	10.8083i	−1.50902	+	0.483847i	−0.940780	−	0.339018i	$-0.889905\pi$
$499$	−33.7089	+	10.8083i	−1.50902	+	0.483847i	−0.568237	+	0.822865i	$0.692374\pi$
$500$	−23.8770	−	9.75484i	−1.06781	−	0.436250i
$501$		0			0
$502$	32.8613	−	5.13941i	1.46667	−	0.229383i
$503$	−4.33940	+	14.4946i	−0.193484	+	0.646282i	0.805103	+	0.593135i	$0.202110\pi$
$503$	−4.33940	+	14.4946i	−0.193484	+	0.646282i	−0.998587	+	0.0531463i	$0.983075\pi$
$504$		0			0
$505$	19.5649	+	4.63696i	0.870625	+	0.206342i
$506$	19.7933	−	28.8593i	0.879918	−	1.28295i
$507$		0			0
$508$	0.368326	+	18.9908i	0.0163418	+	0.842579i
$509$	−24.9514	−	17.8342i	−1.10595	−	0.790488i	−0.126461	−	0.991972i	$-0.540362\pi$
$509$	−24.9514	−	17.8342i	−1.10595	−	0.790488i	−0.979492	+	0.201484i	$0.935424\pi$
$510$		0			0
$511$	2.34418	+	10.8219i	0.103700	+	0.478734i
$512$	30.0530	−	10.9384i	1.32817	−	0.483413i
$513$		0			0
$514$	44.0627	+	16.0375i	1.94352	+	0.707385i
$515$	−2.87519	+	21.0501i	−0.126696	+	0.927580i
$516$		0			0
$517$	−18.8654	+	18.5031i	−0.829700	+	0.813764i
$518$	28.8820	−	5.67224i	1.26900	−	0.249224i
$519$		0			0
$520$	−0.492350	+	1.91142i	−0.0215910	+	0.0838214i
$521$	4.81344	−	2.41740i	0.210881	−	0.105908i	−0.340224	−	0.940344i	$-0.610503\pi$
$521$	4.81344	−	2.41740i	0.210881	−	0.105908i	0.551105	+	0.834436i	$0.314207\pi$
$522$		0			0
$523$	15.9736	−	10.5060i	0.698477	−	0.459396i	−0.149960	−	0.988692i	$-0.547914\pi$
$523$	15.9736	−	10.5060i	0.698477	−	0.459396i	0.848437	+	0.529296i	$0.177544\pi$
$524$	30.3256	+	5.95575i	1.32478	+	0.260178i
$525$		0			0
$526$	3.29095	−	5.22144i	0.143492	−	0.227666i
$527$	11.4937	+	21.8202i	0.500672	+	0.950502i
$528$		0			0
$529$	−3.98870	−	11.6574i	−0.173422	−	0.506844i
$530$	1.33475	+	22.9168i	0.0579778	+	0.995440i
$531$		0			0
$532$	29.0549	+	19.1097i	1.25969	+	0.828512i
$533$	−21.5818	−	21.1673i	−0.934814	−	0.916859i
$534$		0			0
$535$	6.66568	+	7.63803i	0.288183	+	0.330221i
$536$	0.290718	+	1.12864i	0.0125571	+	0.0487497i
$537$		0			0
$538$	−1.91991	+	0.784368i	−0.0827730	+	0.0338165i
$539$	4.06904	−	3.41433i	0.175266	−	0.147065i
$540$		0			0
$541$	−20.6854	−	17.3571i	−0.889334	−	0.746240i	0.0787424	−	0.996895i	$-0.474910\pi$
$541$	−20.6854	−	17.3571i	−0.889334	−	0.746240i	−0.968076	+	0.250655i	$0.919354\pi$
$542$	50.5871	+	16.2201i	2.17290	+	0.696713i
$543$		0			0
$544$	−3.06154	+	31.4754i	−0.131263	+	1.34950i
$545$	16.5935	+	9.15592i	0.710789	+	0.392197i
$546$		0			0
$547$	7.63133	+	0.593154i	0.326292	+	0.0253614i	0.239594	−	0.970873i	$-0.422986\pi$
$547$	7.63133	+	0.593154i	0.326292	+	0.0253614i	0.0866983	+	0.996235i	$0.472368\pi$
$548$	25.8266	−	27.3746i	1.10326	−	1.16938i
$549$		0			0
$550$	−25.4065	+	6.02144i	−1.08334	+	0.256755i
$551$	3.25035	−	8.41861i	0.138469	−	0.358645i
$552$		0			0
$553$	−4.33528	−	31.7399i	−0.184355	−	1.34972i
$554$	−9.46477	+	43.6942i	−0.402120	+	1.85639i
$555$		0			0
$556$	−40.5380	+	22.3679i	−1.71919	+	0.948611i
$557$	7.59294	+	17.6024i	0.321723	+	0.745838i	0.999940	+	0.0109759i	$0.00349380\pi$
$557$	7.59294	+	17.6024i	0.321723	+	0.745838i	−0.678217	+	0.734862i	$0.737247\pi$
$558$		0			0
$559$	−22.9767	−	30.8631i	−0.971811	−	1.30537i
$560$	11.5956	−	8.28803i	0.490003	−	0.350233i
$561$		0			0
$562$	35.7345	+	5.58877i	1.50737	+	0.235748i
$563$	−14.7531	+	30.8536i	−0.621771	+	1.30032i	0.314571	+	0.949234i	$0.398139\pi$
$563$	−14.7531	+	30.8536i	−0.621771	+	1.30032i	−0.936342	+	0.351090i	$0.885811\pi$
$564$		0			0
$565$	−8.75204	−	13.8861i	−0.368201	−	0.584191i
$566$	−24.9999	+	43.3010i	−1.05082	+	1.82008i
$567$		0			0
$568$	1.05371	+	1.82508i	0.0442128	+	0.0765787i
$569$	−12.7703	+	24.2438i	−0.535359	+	1.01635i	0.456585	+	0.889680i	$0.349072\pi$
$569$	−12.7703	+	24.2438i	−0.535359	+	1.01635i	−0.991944	+	0.126675i	$0.959570\pi$
$570$		0			0
$571$	12.1745	+	17.7509i	0.509489	+	0.742853i	0.991040	−	0.133565i	$-0.0426425\pi$
$571$	12.1745	+	17.7509i	0.509489	+	0.742853i	−0.481551	+	0.876418i	$0.659926\pi$
$572$	14.8544	+	38.4738i	0.621093	+	1.60867i
$573$		0			0
$574$	−4.02845	−	41.4161i	−0.168144	−	1.72867i
$575$	3.15592	−	7.31623i	0.131611	−	0.305108i
$576$		0			0
$577$	−31.5497	−	3.68763i	−1.31343	−	0.153518i	−0.569620	−	0.821908i	$-0.692910\pi$
$577$	−31.5497	−	3.68763i	−1.31343	−	0.153518i	−0.743811	+	0.668390i	$0.766984\pi$
$578$	3.12501	+	1.88595i	0.129983	+	0.0784453i
$579$		0			0
$580$	3.53261	+	3.20567i	0.146684	+	0.133108i
$581$	−12.0237	+	9.31907i	−0.498827	+	0.386620i
$582$		0			0
$583$	23.1426	+	28.6924i	0.958470	+	1.18832i
$584$	1.05542	+	1.11868i	0.0436734	+	0.0462911i
$585$		0			0
$586$	−4.16718	−	13.9193i	−0.172145	−	0.575003i
$587$	9.32074	+	19.4927i	0.384708	+	0.804549i	0.999870	+	0.0161475i	$0.00514013\pi$
$587$	9.32074	+	19.4927i	0.384708	+	0.804549i	−0.615162	+	0.788401i	$0.710909\pi$
$588$		0			0
$589$	−35.5138	+	21.4327i	−1.46332	+	0.883118i
$590$	20.5340	−	9.33383i	0.845370	−	0.384268i
$591$		0			0
$592$	−15.8818	+	14.4120i	−0.652740	+	0.592330i
$593$	7.80646	−	44.2726i	0.320573	−	1.81806i	−0.218542	−	0.975827i	$-0.570130\pi$
$593$	7.80646	−	44.2726i	0.320573	−	1.81806i	0.539115	−	0.842232i	$-0.318759\pi$
$594$		0			0
$595$	2.65249	+	15.0430i	0.108742	+	0.616704i
$596$	30.2251	+	23.4263i	1.23807	+	0.959577i
$597$		0			0
$598$	−23.3171	−	6.49077i	−0.953508	−	0.265427i
$599$	1.78999	−	5.23143i	0.0731369	−	0.213751i	−0.903524	−	0.428537i	$-0.859029\pi$
$599$	1.78999	−	5.23143i	0.0731369	−	0.213751i	0.976661	+	0.214787i	$0.0689056\pi$
$600$		0			0
$601$	−23.2331	+	6.46737i	−0.947697	+	0.263809i	−0.707339	−	0.706875i	$-0.750104\pi$
$601$	−23.2331	+	6.46737i	−0.947697	+	0.263809i	−0.240358	+	0.970684i	$0.577265\pi$
$602$	3.07957	−	52.8741i	0.125514	−	2.15499i
$603$		0			0
$604$	−28.9275	−	14.5279i	−1.17704	−	0.591133i
$605$	17.3890	−	19.9256i	0.706964	−	0.810091i
$606$		0			0
$607$	13.0250	+	0.505431i	0.528670	+	0.0205148i	0.301729	−	0.953394i	$-0.402436\pi$
$607$	13.0250	+	0.505431i	0.528670	+	0.0205148i	0.226941	+	0.973908i	$0.427128\pi$
$608$	−53.1491	−	2.06243i	−2.15548	−	0.0836424i
$609$		0			0
$610$	7.96629	−	9.12835i	0.322546	−	0.369596i
$611$	16.3323	+	8.20241i	0.660736	+	0.331834i
$612$		0			0
$613$	0.894026	−	15.3498i	0.0361094	−	0.619974i	−0.930906	−	0.365258i	$-0.880981\pi$
$613$	0.894026	−	15.3498i	0.0361094	−	0.619974i	0.967016	−	0.254716i	$-0.0819821\pi$
$614$	−39.6235	+	11.0300i	−1.59908	+	0.445133i
$615$		0			0
$616$	−1.41244	+	4.12801i	−0.0569088	+	0.166322i
$617$	−0.771362	−	0.214723i	−0.0310538	−	0.00864443i	0.252611	−	0.967568i	$-0.418711\pi$
$617$	−0.771362	−	0.214723i	−0.0310538	−	0.00864443i	−0.283665	+	0.958924i	$0.591550\pi$
$618$		0			0
$619$	−26.5280	−	20.5608i	−1.06625	−	0.826406i	−0.0808614	−	0.996725i	$-0.525767\pi$
$619$	−26.5280	−	20.5608i	−1.06625	−	0.826406i	−0.985389	+	0.170319i	$0.945520\pi$
$620$	−3.80750	−	21.5934i	−0.152913	−	0.867213i
$621$		0			0
$622$	−11.0255	+	62.5285i	−0.442081	+	2.50717i
$623$	−2.42304	+	2.19879i	−0.0970770	+	0.0880927i
$624$		0			0
$625$	6.24858	−	2.84033i	0.249943	−	0.113613i
$626$	−23.9400	+	14.4479i	−0.956837	+	0.577454i
$627$		0			0
$628$	6.48699	+	13.5664i	0.258859	+	0.541358i
$629$	−6.59190	−	22.0185i	−0.262836	−	0.877934i
$630$		0			0
$631$	14.1697	+	15.0190i	0.564088	+	0.597899i	0.945144	−	0.326653i	$-0.105921\pi$
$631$	14.1697	+	15.0190i	0.564088	+	0.597899i	−0.381056	+	0.924552i	$0.624439\pi$
$632$	−2.79340	−	3.46327i	−0.111115	−	0.137762i
$633$		0			0
$634$	−6.18390	+	4.79288i	−0.245594	+	0.190350i
$635$	−10.3917	−	9.42994i	−0.412381	−	0.374216i
$636$		0			0
$637$	−3.14539	−	1.89825i	−0.124625	−	0.0752115i
$638$	14.6320	+	1.71024i	0.579288	+	0.0677091i
$639$		0			0
$640$	1.71768	−	3.98203i	0.0678973	−	0.157404i
$641$	−1.89924	−	19.5259i	−0.0750155	−	0.771227i	−0.955075	−	0.296364i	$-0.904226\pi$
$641$	−1.89924	−	19.5259i	−0.0750155	−	0.771227i	0.880060	−	0.474863i	$-0.157502\pi$
$642$		0			0
$643$	1.32545	+	3.43301i	0.0522707	+	0.135385i	0.956560	−	0.291536i	$-0.0941663\pi$
$643$	1.32545	+	3.43301i	0.0522707	+	0.135385i	−0.904289	+	0.426921i	$0.859598\pi$
$644$	−9.79861	−	14.2867i	−0.386119	−	0.562976i
$645$		0			0
$646$	24.3389	−	46.2062i	0.957599	−	1.81796i
$647$	−18.9601	−	32.8398i	−0.745397	−	1.29107i	−0.950009	−	0.312222i	$-0.898927\pi$
$647$	−18.9601	−	32.8398i	−0.745397	−	1.29107i	0.204612	−	0.978843i	$-0.434407\pi$
$648$		0			0
$649$	18.1102	−	31.3677i	0.710886	−	1.23129i
$650$	9.62906	+	15.2775i	0.377683	+	0.599235i
$651$		0			0
$652$	22.8260	−	47.7365i	0.893935	−	1.86951i
$653$	−16.5394	−	2.58672i	−0.647237	−	0.101226i	−0.177624	−	0.984098i	$-0.556841\pi$
$653$	−16.5394	−	2.58672i	−0.647237	−	0.101226i	−0.469613	+	0.882872i	$0.655607\pi$
$654$		0			0
$655$	−18.5747	+	13.2764i	−0.725775	+	0.518753i
$656$	18.1054	+	24.3198i	0.706898	+	0.949529i
$657$		0			0
$658$	9.96443	+	23.1002i	0.388454	+	0.900538i
$659$	−38.4720	+	21.2280i	−1.49866	+	0.826924i	−0.999222	−	0.0394284i	$-0.987446\pi$
$659$	−38.4720	+	21.2280i	−1.49866	+	0.826924i	−0.499434	+	0.866352i	$0.666459\pi$
$660$		0			0
$661$	0.165067	−	0.762033i	0.00642035	−	0.0296396i	−0.974011	−	0.226499i	$-0.927272\pi$
$661$	0.165067	−	0.762033i	0.00642035	−	0.0296396i	0.980432	+	0.196860i	$0.0630744\pi$
$662$	−3.76109	−	27.5361i	−0.146179	−	1.07022i
$663$		0			0
$664$	−0.761021	+	1.97109i	−0.0295333	+	0.0764933i
$665$	−24.9990	+	5.92487i	−0.969420	+	0.229757i
$666$		0			0
$667$	−3.08503	+	3.26995i	−0.119453	+	0.126613i
$668$	19.6633	+	1.52835i	0.760796	+	0.0591337i
$669$		0			0
$670$	−9.80927	−	5.41253i	−0.378965	−	0.209104i
$671$	1.88350	−	19.3640i	0.0727115	−	0.747540i
$672$		0			0
$673$	−23.3369	−	7.48268i	−0.899571	−	0.288436i	−0.180667	−	0.983544i	$-0.557825\pi$
$673$	−23.3369	−	7.48268i	−0.899571	−	0.288436i	−0.718905	+	0.695108i	$0.755356\pi$
$674$	−26.8508	−	22.5305i	−1.03425	−	0.867841i
$675$		0			0
$676$	0.275670	−	0.231315i	0.0106027	−	0.00889673i
$677$	−24.7397	+	10.1073i	−0.950825	+	0.388455i	−0.799929	−	0.600095i	$-0.795129\pi$
$677$	−24.7397	+	10.1073i	−0.950825	+	0.388455i	−0.150896	+	0.988550i	$0.548216\pi$
$678$		0			0
$679$	1.65666	+	6.43155i	0.0635768	+	0.246820i
$680$	1.39501	+	1.59851i	0.0534963	+	0.0613000i
$681$		0			0
$682$	−48.3429	−	47.4144i	−1.85114	−	1.81559i
$683$	−22.4069	−	14.7372i	−0.857376	−	0.563905i	0.0429720	−	0.999076i	$-0.486317\pi$
$683$	−22.4069	−	14.7372i	−0.857376	−	0.563905i	−0.900348	+	0.435171i	$0.856688\pi$
$684$		0			0
$685$	1.61663	+	27.7565i	0.0617683	+	1.06052i
$686$	−12.9558	−	37.8648i	−0.494655	−	1.44568i
$687$		0			0
$688$	17.9850	+	34.1437i	0.685672	+	1.30172i
$689$	13.5943	−	21.5688i	0.517900	−	0.821704i
$690$		0			0
$691$	14.2610	+	2.80076i	0.542513	+	0.106546i	0.456459	−	0.889745i	$-0.349118\pi$
$691$	14.2610	+	2.80076i	0.542513	+	0.106546i	0.0860537	+	0.996291i	$0.472574\pi$
$692$	6.73782	−	4.43153i	0.256133	−	0.168462i
$693$		0			0
$694$	14.1692	−	7.11602i	0.537854	−	0.270121i
$695$	8.53210	−	33.1236i	0.323641	−	1.25645i
$696$		0			0
$697$	−31.8843	+	6.26188i	−1.20771	+	0.237186i
$698$	−0.425599	+	0.417425i	−0.0161092	+	0.0157998i
$699$		0			0
$700$	−1.74927	+	12.8069i	−0.0661162	+	0.484056i
$701$	−1.50780	−	0.548796i	−0.0569490	−	0.0207277i	0.313389	−	0.949625i	$-0.398536\pi$
$701$	−1.50780	−	0.548796i	−0.0569490	−	0.0207277i	−0.370338	+	0.928897i	$0.620758\pi$
$702$		0			0
$703$	36.3261	−	13.2216i	1.37006	−	0.498663i
$704$	−10.2979	−	47.5406i	−0.388118	−	1.79175i
$705$		0			0
$706$	−49.6028	−	35.4540i	−1.86683	−	1.33433i
$707$	−0.596081	−	30.7338i	−0.0224179	−	1.15586i
$708$		0			0
$709$	−11.9898	+	17.4815i	−0.450285	+	0.656532i	−0.981668	−	0.190600i	$-0.938957\pi$
$709$	−11.9898	+	17.4815i	−0.450285	+	0.656532i	0.531382	+	0.847132i	$0.321673\pi$
$710$	−19.7121	−	4.67185i	−0.739781	−	0.175331i
$711$		0			0
$712$	−0.130340	+	0.435366i	−0.00488470	+	0.0163160i
$713$	20.4155	−	3.19293i	0.764568	−	0.119576i
$714$		0			0
$715$	−28.2052	−	11.5231i	−1.05482	−	0.430940i
$716$	−2.73842	+	0.878040i	−0.102340	+	0.0328139i
$717$		0			0
$718$	−0.680817	+	35.1028i	−0.0254079	+	1.31002i
$719$	7.53586	−	10.1224i	0.281040	−	0.377502i	−0.639079	−	0.769141i	$-0.720684\pi$
$719$	7.53586	−	10.1224i	0.281040	−	0.377502i	0.920119	+	0.391639i	$0.128092\pi$
$720$		0			0
$721$	32.2609	−	3.77075i	1.20146	−	0.140430i
$722$	44.6575	+	20.2993i	1.66198	+	0.755463i
$723$		0			0
$724$	−8.58425	+	10.6428i	−0.319031	+	0.395537i
$725$	3.34413	−	0.259927i	0.124198	−	0.00965343i
$726$		0			0
$727$	17.8680	−	0.693362i	0.662689	−	0.0257154i	0.294763	−	0.955570i	$-0.404759\pi$
$727$	17.8680	−	0.693362i	0.662689	−	0.0257154i	0.367926	+	0.929855i	$0.380068\pi$
$728$	3.01759			0.111839
$729$		0			0
$730$	−14.7841			−0.547183
$731$	−41.3270	+	1.60367i	−1.52853	+	0.0593141i
$732$		0			0
$733$	30.9720	−	2.40733i	1.14398	−	0.0889169i	0.508517	−	0.861052i	$-0.330194\pi$
$733$	30.9720	−	2.40733i	1.14398	−	0.0889169i	0.635459	+	0.772135i	$0.280811\pi$
$734$	17.1808	−	21.3008i	0.634154	−	0.786227i
$735$		0			0
$736$	24.1216	+	10.9646i	0.889136	+	0.404162i
$737$	−17.8690	+	2.08858i	−0.658212	+	0.0769340i
$738$		0			0
$739$	−1.52810	+	2.05259i	−0.0562120	+	0.0755058i	−0.829340	−	0.558744i	$-0.811283\pi$
$739$	−1.52810	+	2.05259i	−0.0562120	+	0.0755058i	0.773128	+	0.634250i	$0.218691\pi$
$740$	−0.396253	+	20.4307i	−0.0145665	+	0.751047i
$741$		0			0
$742$	33.4189	−	10.7153i	1.22685	−	0.393373i
$743$	−20.7192	−	8.46474i	−0.760115	−	0.310541i	−0.0352009	−	0.999380i	$-0.511207\pi$
$743$	−20.7192	−	8.46474i	−0.760115	−	0.310541i	−0.724914	+	0.688839i	$0.758121\pi$
$744$		0			0
$745$	−27.9118	+	4.36533i	−1.02261	+	0.159933i
$746$	2.63866	−	8.81375i	0.0966084	−	0.322694i
$747$		0			0
$748$	43.1353	+	10.2233i	1.57718	+	0.373799i
$749$	8.76604	−	12.7812i	0.320304	−	0.467015i
$750$		0			0
$751$	−1.00564	−	51.8507i	−0.0366965	−	1.89206i	−0.341846	−	0.939756i	$-0.611052\pi$
$751$	−1.00564	−	51.8507i	−0.0366965	−	1.89206i	0.305149	−	0.952304i	$-0.401294\pi$
$752$	−14.9128	−	10.6591i	−0.543815	−	0.388696i
$753$		0			0
$754$	−2.15704	−	9.95803i	−0.0785549	−	0.362650i
$755$	22.4723	−	8.17925i	0.817851	−	0.297673i
$756$		0			0
$757$	−9.59834	−	3.49351i	−0.348858	−	0.126974i	0.161647	−	0.986849i	$-0.448319\pi$
$757$	−9.59834	−	3.49351i	−0.348858	−	0.126974i	−0.510505	+	0.859875i	$0.670542\pi$
$758$	−0.223824	+	1.63868i	−0.00812964	+	0.0595195i
$759$		0			0
$760$	−2.54759	+	2.49866i	−0.0924109	+	0.0906360i
$761$	26.9581	−	5.29440i	0.977231	−	0.191922i	0.321494	−	0.946912i	$-0.395815\pi$
$761$	26.9581	−	5.29440i	0.977231	−	0.191922i	0.655737	+	0.754990i	$0.272358\pi$
$762$		0			0
$763$	7.22729	−	28.0581i	0.261646	−	1.01577i
$764$	10.8672	−	5.45769i	0.393160	−	0.197452i
$765$		0			0
$766$	−54.0115	+	35.5239i	−1.95152	+	1.28353i
$767$	−24.5818	−	4.82770i	−0.887596	−	0.174318i
$768$		0			0
$769$	−6.93460	+	11.0025i	−0.250068	+	0.396760i	−0.947432	−	0.319957i	$-0.896331\pi$
$769$	−6.93460	+	11.0025i	−0.250068	+	0.396760i	0.697364	+	0.716717i	$0.254356\pi$
$770$	−19.5459	−	37.1069i	−0.704385	−	1.33724i
$771$		0			0
$772$	−4.42800	−	12.9413i	−0.159367	−	0.465768i
$773$	2.86580	+	49.2038i	0.103076	+	1.76974i	0.513734	+	0.857949i	$0.328262\pi$
$773$	2.86580	+	49.2038i	0.103076	+	1.76974i	−0.410659	+	0.911789i	$0.634701\pi$
$774$		0			0
$775$	−12.8812	−	8.47211i	−0.462707	−	0.304327i
$776$	0.658575	+	0.645926i	0.0236415	+	0.0231874i
$777$		0			0
$778$	−33.2851	−	38.1405i	−1.19333	−	1.36740i
$779$	−13.6323	−	52.9239i	−0.488428	−	1.89620i
$780$		0			0
$781$	−30.1145	+	12.3031i	−1.07758	+	0.440240i
$782$	−19.9296	+	16.7229i	−0.712680	+	0.598009i
$783$		0			0
$784$	2.82264	+	2.36848i	0.100809	+	0.0845885i
$785$	−10.5788	−	3.39196i	−0.377574	−	0.121064i
$786$		0			0
$787$	3.61485	−	37.1640i	0.128856	−	1.32475i	−0.678462	−	0.734635i	$-0.737353\pi$
$787$	3.61485	−	37.1640i	0.128856	−	1.32475i	0.807318	−	0.590117i	$-0.200918\pi$
$788$	−20.9336	−	11.5507i	−0.745729	−	0.411476i
$789$		0			0
$790$	42.6425	+	3.31444i	1.51715	+	0.117922i
$791$	−17.2205	+	18.2527i	−0.612291	+	0.648991i
$792$		0			0
$793$	−13.0934	+	3.10319i	−0.464960	+	0.110198i
$794$	−26.2393	+	67.9615i	−0.931198	+	2.41186i
$795$		0			0
$796$	3.83453	+	28.0738i	0.135911	+	0.995048i
$797$	−0.695772	+	3.21204i	−0.0246455	+	0.113776i	−0.988000	−	0.154457i	$-0.950637\pi$
$797$	−0.695772	+	3.21204i	−0.0246455	+	0.113776i	0.963354	+	0.268233i	$0.0864397\pi$
$798$		0			0
$799$	17.2003	−	9.49074i	0.608504	−	0.335758i
$800$	−7.83039	−	18.1529i	−0.276846	−	0.641802i
$801$		0			0
$802$	−47.2466	−	63.4631i	−1.66833	−	2.24096i
$803$	−19.3141	+	13.8049i	−0.681579	+	0.487163i
$804$		0			0
$805$	12.6448	+	1.97761i	0.445671	+	0.0697017i
$806$	−20.2033	+	42.2516i	−0.711630	+	1.48825i
$807$		0			0
$808$	−2.27654	−	3.61198i	−0.0800886	−	0.127069i
$809$	−9.21655	+	15.9635i	−0.324037	+	0.561248i	−0.981317	−	0.192398i	$-0.938373\pi$
$809$	−9.21655	+	15.9635i	−0.324037	+	0.561248i	0.657280	+	0.753646i	$0.271707\pi$
$810$		0			0
$811$	−18.3254	−	31.7406i	−0.643493	−	1.11456i	−0.984647	−	0.174556i	$-0.944151\pi$
$811$	−18.3254	−	31.7406i	−0.643493	−	1.11456i	0.341154	−	0.940007i	$-0.389182\pi$
$812$	3.39880	−	6.45245i	0.119274	−	0.226437i
$813$		0			0
$814$	35.6933	+	52.0421i	1.25105	+	1.82407i
$815$	14.0796	+	36.4671i	0.493187	+	1.27739i
$816$		0			0
$817$	−6.73427	−	69.2344i	−0.235602	−	2.42220i
$818$	5.71397	−	13.2465i	0.199784	−	0.463152i
$819$		0			0
$820$	28.6937	+	3.35382i	1.00203	+	0.117120i
$821$	−25.7964	−	15.5682i	−0.900302	−	0.543335i	−0.0106339	−	0.999943i	$-0.503385\pi$
$821$	−25.7964	−	15.5682i	−0.900302	−	0.543335i	−0.889668	+	0.456609i	$0.849064\pi$
$822$		0			0
$823$	26.6631	+	24.1955i	0.929417	+	0.843401i	0.987932	−	0.154885i	$-0.0495008\pi$
$823$	26.6631	+	24.1955i	0.929417	+	0.843401i	−0.0585152	+	0.998287i	$0.518637\pi$
$824$	3.56574	−	2.76366i	0.124218	−	0.0962766i
$825$		0			0
$826$	−21.6492	−	26.8408i	−0.753271	−	0.933910i
$827$	−18.0111	−	19.0907i	−0.626308	−	0.663848i	0.334070	−	0.942548i	$-0.391578\pi$
$827$	−18.0111	−	19.0907i	−0.626308	−	0.663848i	−0.960378	+	0.278701i	$0.910096\pi$
$828$		0			0
$829$	0.870287	+	2.90696i	0.0302263	+	0.100963i	0.971772	−	0.235923i	$-0.0758114\pi$
$829$	0.870287	+	2.90696i	0.0302263	+	0.100963i	−0.941545	+	0.336886i	$0.890626\pi$
$830$	−8.76180	−	18.3237i	−0.304127	−	0.636027i
$831$		0			0
$832$	−28.8044	+	17.3835i	−0.998613	+	0.602666i
$833$	−3.59495	+	1.63411i	−0.124558	+	0.0566184i
$834$		0			0
$835$	−10.7901	+	9.79150i	−0.373407	+	0.338849i
$836$	−12.9472	+	73.4273i	−0.447789	+	2.53954i
$837$		0			0
$838$	13.3801	+	75.8821i	0.462206	+	2.62130i
$839$	9.92541	+	7.69278i	0.342663	+	0.265584i	0.769367	−	0.638808i	$-0.220572\pi$
$839$	9.92541	+	7.69278i	0.342663	+	0.265584i	−0.426703	+	0.904392i	$0.640325\pi$
$840$		0			0
$841$	26.1146	+	7.26949i	0.900503	+	0.250672i
$842$	7.12931	−	20.8362i	0.245692	−	0.718062i
$843$		0			0
$844$	1.71195	−	0.476555i	0.0589279	−	0.0164037i
$845$	−0.0154581	+	0.265406i	−0.000531776	+	0.00913025i
$846$		0			0
$847$	−36.1308	−	18.1456i	−1.24147	−	0.623490i
$848$	−16.8135	+	19.2661i	−0.577377	+	0.661600i
$849$		0			0
$850$	19.3966	+	0.752676i	0.665298	+	0.0258166i
$851$	−19.2431	−	0.746722i	−0.659647	−	0.0255973i
$852$		0			0
$853$	3.99726	−	4.58036i	0.136864	−	0.156828i	−0.680912	−	0.732365i	$-0.738417\pi$
$853$	3.99726	−	4.58036i	0.136864	−	0.156828i	0.817776	+	0.575536i	$0.195207\pi$
$854$	−16.5523	−	8.31289i	−0.566409	−	0.284461i
$855$		0			0
$856$	0.125165	−	2.14901i	0.00427806	−	0.0734515i
$857$	−8.59182	+	2.39170i	−0.293491	+	0.0816988i	−0.411789	−	0.911279i	$-0.635096\pi$
$857$	−8.59182	+	2.39170i	−0.293491	+	0.0816988i	0.118298	+	0.992978i	$0.462256\pi$
$858$		0			0
$859$	9.65732	−	28.2246i	0.329504	−	0.963010i	−0.649711	−	0.760182i	$-0.725110\pi$
$859$	9.65732	−	28.2246i	0.329504	−	0.963010i	0.979214	−	0.202829i	$-0.0650135\pi$
$860$	35.4235	+	9.86081i	1.20793	+	0.336251i
$861$		0			0
$862$	49.9721	+	38.7313i	1.70206	+	1.31919i
$863$	2.79073	+	15.8270i	0.0949975	+	0.538758i	0.994748	+	0.102353i	$0.0326372\pi$
$863$	2.79073	+	15.8270i	0.0949975	+	0.538758i	−0.899751	+	0.436404i	$0.856252\pi$
$864$		0			0
$865$	−1.03457	+	5.86734i	−0.0351764	+	0.199495i
$866$	15.5746	−	14.1332i	0.529245	−	0.480264i
$867$		0			0
$868$	−30.5168	+	13.8716i	−1.03581	+	0.470832i
$869$	58.8036	−	35.4881i	1.99477	−	1.20385i
$870$		0			0
$871$	5.36773	+	11.2257i	0.181879	+	0.380367i
$872$	−1.15419	−	3.85525i	−0.0390857	−	0.130555i
$873$		0			0
$874$	−30.0280	−	31.8279i	−1.01571	−	1.07659i
$875$	−18.2891	−	22.6749i	−0.618285	−	0.766553i
$876$		0			0
$877$	34.1702	−	26.4839i	1.15385	−	0.894299i	0.158191	−	0.987408i	$-0.449434\pi$
$877$	34.1702	−	26.4839i	1.15385	−	0.894299i	0.995656	+	0.0931093i	$0.0296806\pi$
$878$	53.4898	+	48.5394i	1.80519	+	1.63813i
$879$		0			0
$880$	26.1633	+	15.7896i	0.881964	+	0.532268i
$881$	−9.82711	−	1.14862i	−0.331084	−	0.0386981i	−0.0510728	−	0.998695i	$-0.516264\pi$
$881$	−9.82711	−	1.14862i	−0.331084	−	0.0386981i	−0.280011	+	0.959997i	$0.590338\pi$
$882$		0			0
$883$	−11.7141	+	27.1563i	−0.394211	+	0.913883i	0.599340	+	0.800495i	$0.295430\pi$
$883$	−11.7141	+	27.1563i	−0.394211	+	0.913883i	−0.993551	+	0.113389i	$0.963830\pi$
$884$	−2.96827	−	30.5164i	−0.0998336	−	1.02638i
$885$		0			0
$886$	−26.8319	−	69.4963i	−0.901434	−	2.33477i
$887$	6.87193	+	10.0195i	0.230737	+	0.336423i	0.922706	−	0.385505i	$-0.125973\pi$
$887$	6.87193	+	10.0195i	0.230737	+	0.336423i	−0.691969	+	0.721927i	$0.743257\pi$
$888$		0			0
$889$	−9.99804	+	18.9808i	−0.335323	+	0.636596i
$890$	−2.18430	−	3.78331i	−0.0732178	−	0.126817i
$891$		0			0
$892$	1.62349	−	2.81198i	0.0543586	−	0.0941519i
$893$	17.6178	+	27.9525i	0.589557	+	0.935396i
$894$		0			0
$895$	0.916489	−	1.91667i	0.0306348	−	0.0640673i
$896$	−6.55038	−	1.02446i	−0.218833	−	0.0342248i
$897$		0			0
$898$	26.7115	−	19.0922i	0.891374	−	0.637116i
$899$	5.19454	+	6.97747i	0.173248	+	0.232712i
$900$		0			0
$901$	−10.8544	−	25.1634i	−0.361613	−	0.838313i
$902$	78.1134	−	43.1011i	2.60089	−	1.43511i
$903$		0			0
$904$	−0.737875	+	3.40641i	−0.0245414	+	0.113295i
$905$	−1.36704	−	10.0085i	−0.0454420	−	0.332694i
$906$		0			0
$907$	6.41638	−	16.6188i	0.213052	−	0.551819i	−0.784623	−	0.619974i	$-0.787143\pi$
$907$	6.41638	−	16.6188i	0.213052	−	0.551819i	0.997675	+	0.0681546i	$0.0217111\pi$
$908$	−11.7275	+	2.77947i	−0.389191	+	0.0922400i
$909$		0			0
$910$	−19.9060	+	21.0992i	−0.659878	+	0.699430i
$911$	21.0214	+	1.63392i	0.696472	+	0.0541341i	0.420847	−	0.907131i	$-0.361733\pi$
$911$	21.0214	+	1.63392i	0.696472	+	0.0541341i	0.275624	+	0.961265i	$0.411115\pi$
$912$		0			0
$913$	−28.5566	−	15.7569i	−0.945086	−	0.521476i
$914$	−5.82039	+	59.8389i	−0.192522	+	1.97929i
$915$		0			0
$916$	−30.5084	−	9.78213i	−1.00803	−	0.323211i
$917$	26.7390	+	22.4367i	0.883000	+	0.740925i
$918$		0			0
$919$	−43.3283	+	36.3568i	−1.42927	+	1.19930i	−0.483126	+	0.875551i	$0.660499\pi$
$919$	−43.3283	+	36.3568i	−1.42927	+	1.19930i	−0.946143	+	0.323749i	$0.895057\pi$
$920$	1.64561	−	0.672304i	0.0542540	−	0.0221652i
$921$		0			0
$922$	8.06532	+	31.3115i	0.265617	+	1.03119i
$923$	14.7939	+	16.9519i	0.486947	+	0.557979i
$924$		0			0
$925$	10.2581	+	10.0611i	0.337284	+	0.330806i
$926$	17.0588	+	11.2198i	0.560588	+	0.368705i
$927$		0			0
$928$	0.648563	+	11.1354i	0.0212901	+	0.365537i
$929$	4.42562	+	12.9344i	0.145200	+	0.424363i	0.994650	−	0.103307i	$-0.0329424\pi$
$929$	4.42562	+	12.9344i	0.145200	+	0.424363i	−0.849450	+	0.527670i	$0.823066\pi$
$930$		0			0
$931$	−3.09536	−	5.87639i	−0.101446	−	0.192591i
$932$	−15.1969	+	24.1115i	−0.497791	+	0.789799i
$933$		0			0
$934$	−4.81553	−	0.945739i	−0.157569	−	0.0309455i
$935$	−27.3622	+	17.9964i	−0.894839	+	0.588545i
$936$		0			0
$937$	−4.68517	+	2.35298i	−0.153058	+	0.0768685i	−0.523679	−	0.851915i	$-0.675441\pi$
$937$	−4.68517	+	2.35298i	−0.153058	+	0.0768685i	0.370622	+	0.928784i	$0.379145\pi$
$938$	−4.27242	+	16.5865i	−0.139499	+	0.541570i
$939$		0			0
$940$	−17.1385	+	3.36588i	−0.558995	+	0.109783i
$941$	1.33767	−	1.31197i	0.0436067	−	0.0427691i	−0.678087	−	0.734981i	$-0.737191\pi$
$941$	1.33767	−	1.31197i	0.0436067	−	0.0427691i	0.721694	+	0.692212i	$0.243364\pi$
$942$		0			0
$943$	−3.68443	+	26.9748i	−0.119981	+	0.878419i
$944$	23.6104	+	8.59347i	0.768452	+	0.279694i
$945$		0			0
$946$	106.707	−	38.8380i	3.46933	−	1.26273i
$947$	−6.42874	−	29.6784i	−0.208906	−	0.964418i	−0.954545	−	0.298067i	$-0.903658\pi$
$947$	−6.42874	−	29.6784i	−0.208906	−	0.964418i	0.745639	−	0.666350i	$-0.232144\pi$
$948$		0			0
$949$	13.3583	+	9.54797i	0.433630	+	0.309940i
$950$	0.633091	+	32.6420i	0.0205402	+	1.05905i
$951$		0			0
$952$	1.83458	−	2.67488i	0.0594591	−	0.0866935i
$953$	1.69751	+	0.402316i	0.0549876	+	0.0130323i	0.258018	−	0.966140i	$-0.416931\pi$
$953$	1.69751	+	0.402316i	0.0549876	+	0.0130323i	−0.203030	+	0.979173i	$0.565079\pi$
$954$		0			0
$955$	−2.57663	+	8.60653i	−0.0833776	+	0.278501i
$956$	23.9085	−	3.73922i	0.773257	−	0.120935i
$957$		0			0
$958$	17.3898	+	7.10451i	0.561839	+	0.229536i
$959$	40.4766	−	12.9783i	1.30706	−	0.419091i
$960$		0			0
$961$	0.174205	−	8.98197i	0.00561952	−	0.289741i
$962$	26.0639	−	35.0099i	0.840335	−	1.12877i
$963$		0			0
$964$	−13.8293	+	1.61641i	−0.445412	+	0.0520612i
$965$	9.19907	+	4.18149i	0.296129	+	0.134607i
$966$		0			0
$967$	−15.6603	+	19.4157i	−0.503600	+	0.624366i	−0.964817	−	0.262921i	$-0.915314\pi$
$967$	−15.6603	+	19.4157i	−0.503600	+	0.624366i	0.461217	+	0.887287i	$0.347413\pi$
$968$	−5.59881	+	0.435174i	−0.179953	+	0.0139870i
$969$		0			0
$970$	−8.86075	+	0.343838i	−0.284502	+	0.0110400i
$971$	−14.3218			−0.459608			−0.229804	−	0.973237i	$-0.573809\pi$
$971$	−14.3218			−0.459608			−0.229804	+	0.973237i	$0.573809\pi$
$972$		0			0
$973$	−52.2928			−1.67643
$974$	−26.9143	+	1.04440i	−0.862391	+	0.0334647i
$975$		0			0
$976$	13.4554	−	1.04584i	0.430697	−	0.0334764i
$977$	−14.0672	+	17.4405i	−0.450048	+	0.557972i	−0.951673	−	0.307113i	$-0.900637\pi$
$977$	−14.0672	+	17.4405i	−0.450048	+	0.557972i	0.501625	+	0.865085i	$0.332736\pi$
$978$		0			0
$979$	−6.38632	−	2.90294i	−0.204108	−	0.0927783i
$980$	3.48714	−	0.407589i	0.111393	−	0.0130199i
$981$		0			0
$982$	15.6779	−	21.0591i	0.500302	−	0.672022i
$983$	0.353053	−	18.2033i	0.0112606	−	0.580595i	−0.951110	−	0.308854i	$-0.900055\pi$
$983$	0.353053	−	18.2033i	0.0112606	−	0.580595i	0.962370	−	0.271742i	$-0.0875996\pi$
$984$		0			0
$985$	16.8197	−	5.39303i	0.535921	−	0.171836i
$986$	−10.1385	−	4.14204i	−0.322876	−	0.131909i
$987$		0			0
$988$	50.9492	−	7.96831i	1.62091	−	0.253506i
$989$	−9.93849	+	33.1969i	−0.316026	+	1.05560i
$990$		0			0
$991$	39.3482	+	9.32570i	1.24994	+	0.296241i	0.801728	−	0.597689i	$-0.203914\pi$
$991$	39.3482	+	9.32570i	1.24994	+	0.296241i	0.448209	+	0.893929i	$0.352062\pi$
$992$	28.9989	−	42.2814i	0.920716	−	1.34244i
$993$		0			0
$994$	0.600566	+	30.9650i	0.0190488	+	0.982151i
$995$	−17.0298	−	12.1722i	−0.539881	−	0.385884i
$996$		0			0
$997$	7.51178	+	34.6782i	0.237900	+	1.09827i	0.927425	+	0.374009i	$0.122017\pi$
$997$	7.51178	+	34.6782i	0.237900	+	1.09827i	−0.689525	+	0.724262i	$0.742181\pi$
$998$	−67.8994	+	24.7134i	−2.14932	+	0.782288i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.262.22		1404
3.2	odd	2		243.2.i.a.61.5	yes	1404
243.4	even	81	inner	729.2.i.a.64.22		1404
243.239	odd	162		243.2.i.a.4.5	✓	1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.4.5	✓	1404	243.239	odd	162
243.2.i.a.61.5	yes	1404	3.2	odd	2
729.2.i.a.64.22		1404	243.4	even	81	inner
729.2.i.a.262.22		1404	1.1	even	1	trivial

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.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.03967 - 0.0791483i) q^{2} +(2.15999 - 0.167888i) q^{4} +(-1.00485 + 1.24581i) q^{5} +(2.22760 + 1.01257i) q^{7} +(0.337568 - 0.0394561i) q^{8} +(-1.95095 + 2.62057i) q^{10} +(-0.101732 + 5.24528i) q^{11} +(3.45524 - 1.10788i) q^{13} +(4.62371 + 1.88899i) q^{14} +(-3.59556 + 0.562336i) q^{16} +(1.11860 - 3.73638i) q^{17} +(6.38307 + 1.51282i) q^{19} +(-1.96130 + 2.85964i) q^{20} +(0.207655 + 10.7067i) q^{22} +(-2.65860 - 1.90025i) q^{23} +(0.516184 + 2.38297i) q^{25} +(6.95986 - 2.53318i) q^{26} +(4.98160 + 1.81315i) q^{28} +(0.186172 - 1.36302i) q^{29} +(-4.51437 + 4.42766i) q^{31} +(-7.95623 + 1.56255i) q^{32} +(1.98584 - 7.70951i) q^{34} +(-3.49987 + 1.75770i) q^{35} +(4.92352 - 3.23825i) q^{37} +(13.1391 + 2.58043i) q^{38} +(-0.290049 + 0.460194i) q^{40} +(-3.88267 - 7.37108i) q^{41} +(-3.43287 - 10.0329i) q^{43} +(0.660877 + 11.3468i) q^{44} +(-5.57305 - 3.66545i) q^{46} +(3.59597 + 3.52690i) q^{47} +(-0.665729 - 0.762841i) q^{49} +(1.24145 + 4.81961i) q^{50} +(7.27729 - 2.97310i) q^{52} +(5.38254 - 4.51648i) q^{53} +(-6.43241 - 5.39743i) q^{55} +(0.791920 + 0.253919i) q^{56} +(0.271848 - 2.79484i) q^{58} +(-6.04488 - 3.33542i) q^{59} +(-3.69728 - 0.287376i) q^{61} +(-8.85736 + 9.38825i) q^{62} +(-9.02203 + 2.13826i) q^{64} +(-2.09178 + 5.41783i) q^{65} +(0.464082 + 3.39768i) q^{67} +(1.78887 - 8.25835i) q^{68} +(-6.99945 + 3.86213i) q^{70} +(2.45599 + 5.69362i) q^{71} +(2.70227 + 3.62977i) q^{73} +(9.78604 - 6.99464i) q^{74} +(14.0413 + 2.19603i) q^{76} +(-5.53783 + 11.5814i) q^{77} +(-6.98054 - 11.0754i) q^{79} +(2.91242 - 5.04446i) q^{80} +(-8.50277 - 14.7272i) q^{82} +(-2.89733 + 5.50045i) q^{83} +(3.53082 + 5.14806i) q^{85} +(-7.79601 - 20.1922i) q^{86} +(0.172616 + 1.77465i) q^{88} +(-0.529625 + 1.22781i) q^{89} +(8.81872 + 1.03076i) q^{91} +(-6.06156 - 3.65817i) q^{92} +(7.61373 + 6.90909i) q^{94} +(-8.29869 + 6.43197i) q^{95} +(1.70401 + 2.11264i) q^{97} +(-1.41824 - 1.50325i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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