LMFDB - Embedded newform 486.2.e.a.379.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [486,2,Mod(55,486)] 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("486.55"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(486, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			379.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	486.379
Dual form			486.2.e.a.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(-0.613341 + 3.47843i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.439693 - 0.761570i) q^{10} +(3.35844 - 1.22237i) q^{11} +(-2.83022 + 2.37484i) q^{13} +(-2.70574 + 2.27038i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.12449 + 5.41177i) q^{17} +(-2.08512 + 3.61154i) q^{19} +(0.152704 - 0.866025i) q^{20} +(3.35844 + 1.22237i) q^{22} +(-0.358441 - 2.03282i) q^{23} +(-3.23783 - 2.71686i) q^{25} -3.69459 q^{26} -3.53209 q^{28} +(-0.124485 - 0.104455i) q^{29} +(0.284463 + 1.61327i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-1.08512 + 6.15403i) q^{34} +(1.55303 - 2.68993i) q^{35} +(3.85844 + 6.68302i) q^{37} +(-3.91875 + 1.42631i) q^{38} +(0.673648 - 0.565258i) q^{40} +(5.90033 - 4.95096i) q^{41} +(10.1702 - 3.70167i) q^{43} +(1.78699 + 3.09516i) q^{44} +(1.03209 - 1.78763i) q^{46} +(1.11334 - 6.31407i) q^{47} +(-5.14543 - 1.87278i) q^{49} +(-0.733956 - 4.16247i) q^{50} +(-2.83022 - 2.37484i) q^{52} -0.716881 q^{53} -3.14290 q^{55} +(-2.70574 - 2.27038i) q^{56} +(-0.0282185 - 0.160035i) q^{58} +(-6.56418 - 2.38917i) q^{59} +(-0.220285 + 1.24930i) q^{61} +(-0.819078 + 1.41868i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(3.05303 - 1.11121i) q^{65} +(2.75490 - 2.31164i) q^{67} +(-4.78699 + 4.01676i) q^{68} +(2.91875 - 1.06234i) q^{70} +(-6.76991 - 11.7258i) q^{71} +(1.16385 - 2.01584i) q^{73} +(-1.34002 + 7.59964i) q^{74} +(-3.91875 - 1.42631i) q^{76} +(2.19207 + 12.4318i) q^{77} +(-5.07011 - 4.25433i) q^{79} +0.879385 q^{80} +7.70233 q^{82} +(3.41147 + 2.86257i) q^{83} +(-0.954241 - 5.41177i) q^{85} +(10.1702 + 3.70167i) q^{86} +(-0.620615 + 3.51968i) q^{88} +(4.62449 - 8.00984i) q^{89} +(-6.52481 - 11.3013i) q^{91} +(1.93969 - 0.705990i) q^{92} +(4.91147 - 4.12122i) q^{94} +(2.80928 - 2.35726i) q^{95} +(10.6099 - 3.86170i) q^{97} +(-2.73783 - 4.74205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 12 q^{11} + 6 q^{13} - 6 q^{14} + 6 q^{17} + 9 q^{19} + 3 q^{20} + 12 q^{22} + 6 q^{23} - 18 q^{26} - 12 q^{28} + 12 q^{29} + 9 q^{31} + 15 q^{34} - 3 q^{35}+ \cdots + 3 q^{98}+O(q^{100}) $ 6 * q - 6 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 12 * q^11 + 6 * q^13 - 6 * q^14 + 6 * q^17 + 9 * q^19 + 3 * q^20 + 12 * q^22 + 6 * q^23 - 18 * q^26 - 12 * q^28 + 12 * q^29 + 9 * q^31 + 15 * q^34 - 3 * q^35 + 15 * q^37 - 21 * q^38 + 3 * q^40 + 21 * q^41 + 18 * q^43 + 3 * q^44 - 3 * q^46 - 15 * q^49 - 9 * q^50 + 6 * q^52 + 12 * q^53 - 18 * q^55 - 6 * q^56 - 15 * q^58 - 21 * q^59 - 27 * q^61 + 12 * q^62 - 3 * q^64 + 6 * q^65 + 18 * q^67 - 21 * q^68 + 15 * q^70 - 12 * q^71 + 3 * q^73 + 12 * q^74 - 21 * q^76 + 24 * q^77 - 39 * q^79 - 6 * q^80 - 6 * q^82 - 36 * q^85 + 18 * q^86 - 15 * q^88 + 15 * q^89 - 12 * q^91 + 6 * q^92 + 9 * q^94 - 3 * q^95 + 15 * q^97 + 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	0.150565	−	0.988600i	$-0.451891\pi$
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	−0.520121	+	0.854093i	$0.674113\pi$
$6$		0			0
$7$	−0.613341	+	3.47843i	−0.231821	+	1.31472i	0.617385	+	0.786661i	$0.288192\pi$
$7$	−0.613341	+	3.47843i	−0.231821	+	1.31472i	−0.849206	+	0.528061i	$0.822919\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$		0			0
$10$	−0.439693	−	0.761570i	−0.139043	−	0.240830i
$11$	3.35844	−	1.22237i	1.01261	−	0.368559i	0.218174	−	0.975910i	$-0.429990\pi$
$11$	3.35844	−	1.22237i	1.01261	−	0.368559i	0.794434	+	0.607351i	$0.207768\pi$
$12$		0			0
$13$	−2.83022	+	2.37484i	−0.784962	+	0.658662i	−0.944493	−	0.328531i	$-0.893446\pi$
$13$	−2.83022	+	2.37484i	−0.784962	+	0.658662i	0.159531	+	0.987193i	$0.449002\pi$
$14$	−2.70574	+	2.27038i	−0.723139	+	0.606785i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.12449	+	5.41177i	0.757799	+	1.31255i	0.943971	+	0.330029i	$0.107059\pi$
$17$	3.12449	+	5.41177i	0.757799	+	1.31255i	−0.186172	+	0.982517i	$0.559608\pi$
$18$		0			0
$19$	−2.08512	+	3.61154i	−0.478360	+	0.828544i	−0.999692	−	0.0248102i	$-0.992102\pi$
$19$	−2.08512	+	3.61154i	−0.478360	+	0.828544i	0.521332	+	0.853354i	$0.325435\pi$
$20$	0.152704	−	0.866025i	0.0341456	−	0.193649i
$21$		0			0
$22$	3.35844	+	1.22237i	0.716022	+	0.260611i
$23$	−0.358441	−	2.03282i	−0.0747401	−	0.423872i	−0.999103	−	0.0423566i	$-0.986513\pi$
$23$	−0.358441	−	2.03282i	−0.0747401	−	0.423872i	0.924363	−	0.381515i	$-0.124598\pi$
$24$		0			0
$25$	−3.23783	−	2.71686i	−0.647565	−	0.543372i
$26$	−3.69459			−0.724569
$27$		0			0
$28$	−3.53209			−0.667502
$29$	−0.124485	−	0.104455i	−0.0231163	−	0.0193969i	0.631156	−	0.775656i	$-0.282581\pi$
$29$	−0.124485	−	0.104455i	−0.0231163	−	0.0193969i	−0.654273	+	0.756259i	$0.727025\pi$
$30$		0			0
$31$	0.284463	+	1.61327i	0.0510910	+	0.289752i	0.999639	−	0.0268831i	$-0.00855819\pi$
$31$	0.284463	+	1.61327i	0.0510910	+	0.289752i	−0.948548	+	0.316635i	$0.897447\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$		0			0
$34$	−1.08512	+	6.15403i	−0.186097	+	1.05541i
$35$	1.55303	−	2.68993i	0.262511	−	0.454682i
$36$		0			0
$37$	3.85844	+	6.68302i	0.634324	+	1.09868i	0.986658	+	0.162807i	$0.0520547\pi$
$37$	3.85844	+	6.68302i	0.634324	+	1.09868i	−0.352334	+	0.935874i	$0.614612\pi$
$38$	−3.91875	+	1.42631i	−0.635705	+	0.231378i
$39$		0			0
$40$	0.673648	−	0.565258i	0.106513	−	0.0893751i
$41$	5.90033	−	4.95096i	0.921477	−	0.773211i	−0.0527908	−	0.998606i	$-0.516812\pi$
$41$	5.90033	−	4.95096i	0.921477	−	0.773211i	0.974268	+	0.225395i	$0.0723672\pi$
$42$		0			0
$43$	10.1702	−	3.70167i	1.55095	−	0.564499i	0.582308	−	0.812968i	$-0.302150\pi$
$43$	10.1702	−	3.70167i	1.55095	−	0.564499i	0.968640	+	0.248469i	$0.0799276\pi$
$44$	1.78699	+	3.09516i	0.269399	+	0.466612i
$45$		0			0
$46$	1.03209	−	1.78763i	0.152173	−	0.263572i
$47$	1.11334	−	6.31407i	0.162397	−	0.921002i	−0.789310	−	0.613995i	$-0.789561\pi$
$47$	1.11334	−	6.31407i	0.162397	−	0.921002i	0.951707	−	0.307007i	$-0.0993274\pi$
$48$		0			0
$49$	−5.14543	−	1.87278i	−0.735061	−	0.267540i
$50$	−0.733956	−	4.16247i	−0.103797	−	0.588662i
$51$		0			0
$52$	−2.83022	−	2.37484i	−0.392481	−	0.329331i
$53$	−0.716881			−0.0984712			−0.0492356	−	0.998787i	$-0.515679\pi$
$53$	−0.716881			−0.0984712			−0.0492356	+	0.998787i	$0.515679\pi$
$54$		0			0
$55$	−3.14290			−0.423789
$56$	−2.70574	−	2.27038i	−0.361569	−	0.303393i
$57$		0			0
$58$	−0.0282185	−	0.160035i	−0.00370527	−	0.0210136i
$59$	−6.56418	−	2.38917i	−0.854583	−	0.311043i	−0.122676	−	0.992447i	$-0.539147\pi$
$59$	−6.56418	−	2.38917i	−0.854583	−	0.311043i	−0.731908	+	0.681404i	$0.761370\pi$
$60$		0			0
$61$	−0.220285	+	1.24930i	−0.0282046	+	0.159956i	−0.995657	−	0.0930965i	$-0.970324\pi$
$61$	−0.220285	+	1.24930i	−0.0282046	+	0.159956i	0.967452	+	0.253053i	$0.0814346\pi$
$62$	−0.819078	+	1.41868i	−0.104023	+	0.180173i
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	3.05303	−	1.11121i	0.378682	−	0.137829i
$66$		0			0
$67$	2.75490	−	2.31164i	0.336565	−	0.282411i	−0.458804	−	0.888538i	$-0.651722\pi$
$67$	2.75490	−	2.31164i	0.336565	−	0.282411i	0.795368	+	0.606126i	$0.207277\pi$
$68$	−4.78699	+	4.01676i	−0.580508	+	0.487104i
$69$		0			0
$70$	2.91875	−	1.06234i	0.348857	−	0.126974i
$71$	−6.76991	−	11.7258i	−0.803441	−	1.39160i	−0.917338	−	0.398108i	$-0.869667\pi$
$71$	−6.76991	−	11.7258i	−0.803441	−	1.39160i	0.113897	−	0.993493i	$-0.463666\pi$
$72$		0			0
$73$	1.16385	−	2.01584i	0.136218	−	0.235937i	−0.789844	−	0.613308i	$-0.789839\pi$
$73$	1.16385	−	2.01584i	0.136218	−	0.235937i	0.926062	+	0.377371i	$0.123172\pi$
$74$	−1.34002	+	7.59964i	−0.155774	+	0.883441i
$75$		0			0
$76$	−3.91875	−	1.42631i	−0.449511	−	0.163609i
$77$	2.19207	+	12.4318i	0.249809	+	1.41674i
$78$		0			0
$79$	−5.07011	−	4.25433i	−0.570432	−	0.478649i	0.311357	−	0.950293i	$-0.399216\pi$
$79$	−5.07011	−	4.25433i	−0.570432	−	0.478649i	−0.881789	+	0.471644i	$0.843661\pi$
$80$	0.879385			0.0983183
$81$		0			0
$82$	7.70233			0.850580
$83$	3.41147	+	2.86257i	0.374458	+	0.314208i	0.810522	−	0.585708i	$-0.199183\pi$
$83$	3.41147	+	2.86257i	0.374458	+	0.314208i	−0.436064	+	0.899916i	$0.643628\pi$
$84$		0			0
$85$	−0.954241	−	5.41177i	−0.103502	−	0.586989i
$86$	10.1702	+	3.70167i	1.09669	+	0.399161i
$87$		0			0
$88$	−0.620615	+	3.51968i	−0.0661578	+	0.375199i
$89$	4.62449	−	8.00984i	0.490194	−	0.849042i	−0.509742	−	0.860327i	$-0.670259\pi$
$89$	4.62449	−	8.00984i	0.490194	−	0.849042i	0.999936	+	0.0112857i	$0.00359243\pi$
$90$		0			0
$91$	−6.52481	−	11.3013i	−0.683986	−	1.18470i
$92$	1.93969	−	0.705990i	0.202227	−	0.0736046i
$93$		0			0
$94$	4.91147	−	4.12122i	0.506580	−	0.425071i
$95$	2.80928	−	2.35726i	0.288226	−	0.241850i
$96$		0			0
$97$	10.6099	−	3.86170i	1.07728	−	0.392096i	0.258383	−	0.966043i	$-0.416810\pi$
$97$	10.6099	−	3.86170i	1.07728	−	0.392096i	0.818893	+	0.573946i	$0.194588\pi$
$98$	−2.73783	−	4.74205i	−0.276562	−	0.479020i
$99$		0			0
$100$	2.11334	−	3.66041i	0.211334	−	0.366041i
$101$	−1.62789	+	9.23222i	−0.161981	+	0.918640i	0.790142	+	0.612924i	$0.210007\pi$
$101$	−1.62789	+	9.23222i	−0.161981	+	0.918640i	−0.952123	+	0.305716i	$0.901104\pi$
$102$		0			0
$103$	3.03209	+	1.10359i	0.298761	+	0.108740i	0.487051	−	0.873373i	$-0.338072\pi$
$103$	3.03209	+	1.10359i	0.298761	+	0.108740i	−0.188291	+	0.982113i	$0.560295\pi$
$104$	−0.641559	−	3.63846i	−0.0629101	−	0.356781i
$105$		0			0
$106$	−0.549163	−	0.460802i	−0.0533394	−	0.0447571i
$107$	2.28312			0.220717			0.110359	−	0.993892i	$-0.464800\pi$
$107$	2.28312			0.220717			0.110359	+	0.993892i	$0.464800\pi$
$108$		0			0
$109$	10.4192			0.997980			0.498990	−	0.866608i	$-0.333704\pi$
$109$	10.4192			0.997980			0.498990	+	0.866608i	$0.333704\pi$
$110$	−2.40760	−	2.02022i	−0.229556	−	0.192620i
$111$		0			0
$112$	−0.613341	−	3.47843i	−0.0579553	−	0.328681i
$113$	10.4620	+	3.80785i	0.984180	+	0.358212i	0.783464	−	0.621437i	$-0.213451\pi$
$113$	10.4620	+	3.80785i	0.984180	+	0.358212i	0.200716	+	0.979649i	$0.435673\pi$
$114$		0			0
$115$	−0.315207	+	1.78763i	−0.0293932	+	0.166697i
$116$	0.0812519	−	0.140732i	0.00754405	−	0.0130667i
$117$		0			0
$118$	−3.49273	−	6.04958i	−0.321531	−	0.556909i
$119$	−20.7408	+	7.54904i	−1.90131	+	0.692019i
$120$		0			0
$121$	1.35844	−	1.13987i	0.123495	−	0.103624i
$122$	−0.971782	+	0.815422i	−0.0879810	+	0.0738248i
$123$		0			0
$124$	−1.53936	+	0.560282i	−0.138239	+	0.0503148i
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$		0			0
$127$	4.95336	−	8.57948i	0.439540	−	0.761305i	−0.558114	−	0.829764i	$-0.688475\pi$
$127$	4.95336	−	8.57948i	0.439540	−	0.761305i	0.997654	+	0.0684588i	$0.0218082\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$		0			0
$130$	3.05303	+	1.11121i	0.267769	+	0.0974599i
$131$	1.56805	+	8.89284i	0.137001	+	0.776971i	0.973445	+	0.228919i	$0.0735192\pi$
$131$	1.56805	+	8.89284i	0.137001	+	0.776971i	−0.836444	+	0.548052i	$0.815370\pi$
$132$		0			0
$133$	−11.2836	−	9.46805i	−0.978411	−	0.820984i
$134$	3.59627			0.310670
$135$		0			0
$136$	−6.24897			−0.535845
$137$	−1.55303	−	1.30315i	−0.132685	−	0.111336i	0.574030	−	0.818834i	$-0.305379\pi$
$137$	−1.55303	−	1.30315i	−0.132685	−	0.111336i	−0.706715	+	0.707498i	$0.749824\pi$
$138$		0			0
$139$	0.0286853	+	0.162683i	0.00243306	+	0.0137986i	0.986000	−	0.166745i	$-0.0533256\pi$
$139$	0.0286853	+	0.162683i	0.00243306	+	0.0137986i	−0.983567	+	0.180543i	$0.942214\pi$
$140$	2.91875	+	1.06234i	0.246679	+	0.0897839i
$141$		0			0
$142$	2.35117	−	13.3341i	0.197306	−	1.11898i
$143$	−6.60220	+	11.4353i	−0.552103	+	0.956271i
$144$		0			0
$145$	0.0714517	+	0.123758i	0.00593374	+	0.0102775i
$146$	2.18732	−	0.796119i	0.181024	−	0.0658873i
$147$		0			0
$148$	−5.91147	+	4.96032i	−0.485920	+	0.407735i
$149$	4.44356	−	3.72859i	0.364031	−	0.305458i	−0.442364	−	0.896836i	$-0.645860\pi$
$149$	4.44356	−	3.72859i	0.364031	−	0.305458i	0.806395	+	0.591377i	$0.201416\pi$
$150$		0			0
$151$	−13.2023	+	4.80526i	−1.07439	+	0.391046i	−0.817817	−	0.575478i	$-0.804816\pi$
$151$	−13.2023	+	4.80526i	−1.07439	+	0.391046i	−0.256574	+	0.966525i	$0.582594\pi$
$152$	−2.08512	−	3.61154i	−0.169126	−	0.292934i
$153$		0			0
$154$	−6.31180	+	10.9324i	−0.508620	+	0.880955i
$155$	0.250152	−	1.41868i	0.0200927	−	0.113951i
$156$		0			0
$157$	4.48545	+	1.63257i	0.357978	+	0.130293i	0.514747	−	0.857342i	$-0.327886\pi$
$157$	4.48545	+	1.63257i	0.357978	+	0.130293i	−0.156769	+	0.987635i	$0.550108\pi$
$158$	−1.14930	−	6.51800i	−0.0914334	−	0.518545i
$159$		0			0
$160$	0.673648	+	0.565258i	0.0532566	+	0.0446876i
$161$	7.29086			0.574600
$162$		0			0
$163$	−10.7169			−0.839411			−0.419705	−	0.907660i	$-0.637867\pi$
$163$	−10.7169			−0.839411			−0.419705	+	0.907660i	$0.637867\pi$
$164$	5.90033	+	4.95096i	0.460738	+	0.386605i
$165$		0			0
$166$	0.773318	+	4.38571i	0.0600211	+	0.340397i
$167$	−12.1211	−	4.41171i	−0.937957	−	0.341389i	−0.172599	−	0.984992i	$-0.555216\pi$
$167$	−12.1211	−	4.41171i	−0.937957	−	0.341389i	−0.765359	+	0.643604i	$0.777439\pi$
$168$		0			0
$169$	0.112874	−	0.640140i	0.00868261	−	0.0492415i
$170$	2.74763	−	4.75903i	0.210733	−	0.365001i
$171$		0			0
$172$	5.41147	+	9.37295i	0.412621	+	0.714681i
$173$	12.0963	−	4.40268i	0.919662	−	0.334730i	0.161558	−	0.986863i	$-0.448348\pi$
$173$	12.0963	−	4.40268i	0.919662	−	0.334730i	0.758104	+	0.652134i	$0.226126\pi$
$174$		0			0
$175$	11.4363	−	9.59619i	0.864502	−	0.725403i
$176$	−2.73783	+	2.29731i	−0.206371	+	0.173166i
$177$		0			0
$178$	8.69119	−	3.16333i	0.651432	−	0.237102i
$179$	−4.48158	−	7.76233i	−0.334969	−	0.580184i	0.648510	−	0.761206i	$-0.275393\pi$
$179$	−4.48158	−	7.76233i	−0.334969	−	0.580184i	−0.983479	+	0.181023i	$0.942059\pi$
$180$		0			0
$181$	0.992726	−	1.71945i	0.0737887	−	0.127806i	−0.826770	−	0.562540i	$-0.809824\pi$
$181$	0.992726	−	1.71945i	0.0737887	−	0.127806i	0.900559	+	0.434734i	$0.143158\pi$
$182$	2.26604	−	12.8514i	0.167970	−	0.952607i
$183$		0			0
$184$	1.93969	+	0.705990i	0.142996	+	0.0520463i
$185$	−1.17840	−	6.68302i	−0.0866374	−	0.491345i
$186$		0			0
$187$	17.1086	+	14.3558i	1.25110	+	1.04980i
$188$	6.41147			0.467605
$189$		0			0
$190$	3.66725			0.266050
$191$	−10.0517	−	8.43437i	−0.727315	−	0.610290i	0.202083	−	0.979368i	$-0.435229\pi$
$191$	−10.0517	−	8.43437i	−0.727315	−	0.610290i	−0.929398	+	0.369079i	$0.879673\pi$
$192$		0			0
$193$	0.999533	+	5.66863i	0.0719480	+	0.408037i	0.999417	+	0.0341376i	$0.0108684\pi$
$193$	0.999533	+	5.66863i	0.0719480	+	0.408037i	−0.927469	+	0.373900i	$0.878020\pi$
$194$	10.6099	+	3.86170i	0.761749	+	0.277254i
$195$		0			0
$196$	0.950837	−	5.39246i	0.0679169	−	0.385176i
$197$	−13.3405	+	23.1064i	−0.950471	+	1.64626i	−0.206062	+	0.978539i	$0.566065\pi$
$197$	−13.3405	+	23.1064i	−0.950471	+	1.64626i	−0.744409	+	0.667724i	$0.767269\pi$
$198$		0			0
$199$	5.32160	+	9.21729i	0.377239	+	0.653396i	0.990659	−	0.136360i	$-0.0435404\pi$
$199$	5.32160	+	9.21729i	0.377239	+	0.653396i	−0.613421	+	0.789756i	$0.710207\pi$
$200$	3.97178	−	1.44561i	0.280847	−	0.102220i
$201$		0			0
$202$	−7.18139	+	6.02590i	−0.505281	+	0.423981i
$203$	0.439693	−	0.368946i	0.0308604	−	0.0258949i
$204$		0			0
$205$	−6.36484	+	2.31661i	−0.444540	+	0.161799i
$206$	1.61334	+	2.79439i	0.112407	+	0.194694i
$207$		0			0
$208$	1.84730	−	3.19961i	0.128087	−	0.221853i
$209$	−2.58812	+	14.6779i	−0.179024	+	1.01529i
$210$		0			0
$211$	5.01842	+	1.82655i	0.345482	+	0.125745i	0.508933	−	0.860806i	$-0.330040\pi$
$211$	5.01842	+	1.82655i	0.345482	+	0.125745i	−0.163451	+	0.986552i	$0.552262\pi$
$212$	−0.124485	−	0.705990i	−0.00854968	−	0.0484876i
$213$		0			0
$214$	1.74897	+	1.46756i	0.119557	+	0.100320i
$215$	−9.51754			−0.649091
$216$		0			0
$217$	−5.78611			−0.392787
$218$	7.98158	+	6.69734i	0.540581	+	0.453601i
$219$		0			0
$220$	−0.545759	−	3.09516i	−0.0367951	−	0.208675i
$221$	−21.6951	−	7.89636i	−1.45937	−	0.531166i
$222$		0			0
$223$	−3.30793	+	18.7602i	−0.221516	+	1.25628i	0.647720	+	0.761879i	$0.275723\pi$
$223$	−3.30793	+	18.7602i	−0.221516	+	1.25628i	−0.869235	+	0.494399i	$0.835388\pi$
$224$	1.76604	−	3.05888i	0.117999	−	0.204380i
$225$		0			0
$226$	5.56670	+	9.64181i	0.370292	+	0.641364i
$227$	−3.25237	+	1.18377i	−0.215868	+	0.0785694i	−0.447690	−	0.894189i	$-0.647753\pi$
$227$	−3.25237	+	1.18377i	−0.215868	+	0.0785694i	0.231823	+	0.972758i	$0.425531\pi$
$228$		0			0
$229$	−22.1689	+	18.6019i	−1.46496	+	1.22925i	−0.544299	+	0.838891i	$0.683204\pi$
$229$	−22.1689	+	18.6019i	−1.46496	+	1.22925i	−0.920663	+	0.390358i	$0.872351\pi$
$230$	−1.39053	+	1.16679i	−0.0916888	+	0.0769360i
$231$		0			0
$232$	0.152704	−	0.0555796i	0.0100255	−	0.00364898i
$233$	−3.33022	−	5.76811i	−0.218170	−	0.377882i	0.736078	−	0.676896i	$-0.236675\pi$
$233$	−3.33022	−	5.76811i	−0.218170	−	0.377882i	−0.954249	+	0.299015i	$0.903342\pi$
$234$		0			0
$235$	−2.81908	+	4.88279i	−0.183896	+	0.318518i
$236$	1.21301	−	6.87933i	0.0789603	−	0.447806i
$237$		0			0
$238$	−20.7408	−	7.54904i	−1.34443	−	0.489332i
$239$	−1.35251	−	7.67047i	−0.0874867	−	0.496161i	−0.996792	−	0.0800325i	$-0.974498\pi$
$239$	−1.35251	−	7.67047i	−0.0874867	−	0.496161i	0.909306	−	0.416129i	$-0.136614\pi$
$240$		0			0
$241$	16.7724	+	14.0737i	1.08041	+	0.906570i	0.995955	−	0.0898576i	$-0.0286412\pi$
$241$	16.7724	+	14.0737i	1.08041	+	0.906570i	0.0844533	+	0.996427i	$0.473086\pi$
$242$	1.77332			0.113993
$243$		0			0
$244$	−1.26857			−0.0812119
$245$	3.68866	+	3.09516i	0.235660	+	0.197742i
$246$		0			0
$247$	−2.67546	−	15.1733i	−0.170235	−	0.965453i
$248$	−1.53936	−	0.560282i	−0.0977496	−	0.0355780i
$249$		0			0
$250$	−1.40895	+	7.99054i	−0.0891097	+	0.505366i
$251$	8.04236	−	13.9298i	0.507629	−	0.879239i	−0.492332	−	0.870407i	$-0.663855\pi$
$251$	8.04236	−	13.9298i	0.507629	−	0.879239i	0.999961	−	0.00883173i	$-0.00281126\pi$
$252$		0			0
$253$	−3.68866	−	6.38895i	−0.231904	−	0.401670i
$254$	9.30928	−	3.38830i	0.584116	−	0.212601i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−19.8136	+	16.6256i	−1.23594	+	1.03708i	−0.238109	+	0.971238i	$0.576528\pi$
$257$	−19.8136	+	16.6256i	−1.23594	+	1.03708i	−0.997830	+	0.0658378i	$0.979028\pi$
$258$		0			0
$259$	−25.6129	+	9.32234i	−1.59151	+	0.579262i
$260$	1.62449	+	2.81369i	0.100746	+	0.174498i
$261$		0			0
$262$	−4.51501	+	7.82023i	−0.278939	+	0.483136i
$263$	5.46926	−	31.0177i	0.337249	−	1.91263i	−0.0665468	−	0.997783i	$-0.521198\pi$
$263$	5.46926	−	31.0177i	0.337249	−	1.91263i	0.403795	−	0.914849i	$-0.367691\pi$
$264$		0			0
$265$	0.592396	+	0.215615i	0.0363906	+	0.0132451i
$266$	−2.55778	−	14.5059i	−0.156828	−	0.889414i
$267$		0			0
$268$	2.75490	+	2.31164i	0.168282	+	0.141206i
$269$	4.60906			0.281019			0.140510	−	0.990079i	$-0.455126\pi$
$269$	4.60906			0.281019			0.140510	+	0.990079i	$0.455126\pi$
$270$		0			0
$271$	−1.31820			−0.0800750			−0.0400375	−	0.999198i	$-0.512748\pi$
$271$	−1.31820			−0.0800750			−0.0400375	+	0.999198i	$0.512748\pi$
$272$	−4.78699	−	4.01676i	−0.290254	−	0.243552i
$273$		0			0
$274$	−0.352044	−	1.99654i	−0.0212678	−	0.120615i
$275$	−14.1951	−	5.16658i	−0.855994	−	0.311556i
$276$		0			0
$277$	5.35204	−	30.3530i	0.321573	−	1.82373i	−0.211163	−	0.977451i	$-0.567725\pi$
$277$	5.35204	−	30.3530i	0.321573	−	1.82373i	0.532736	−	0.846281i	$-0.321164\pi$
$278$	−0.0825961	+	0.143061i	−0.00495378	+	0.00858021i
$279$		0			0
$280$	1.55303	+	2.68993i	0.0928115	+	0.160754i
$281$	20.1386	−	7.32986i	1.20137	−	0.437263i	0.337667	−	0.941265i	$-0.390362\pi$
$281$	20.1386	−	7.32986i	1.20137	−	0.437263i	0.863702	+	0.504003i	$0.168140\pi$
$282$		0			0
$283$	−1.35844	+	1.13987i	−0.0807509	+	0.0677581i	−0.682270	−	0.731101i	$-0.739007\pi$
$283$	−1.35844	+	1.13987i	−0.0807509	+	0.0677581i	0.601519	+	0.798859i	$0.294563\pi$
$284$	10.3721	−	8.70323i	0.615472	−	0.516442i
$285$		0			0
$286$	−12.4081	+	4.51617i	−0.733705	+	0.267047i
$287$	13.6027	+	23.5605i	0.802940	+	1.39073i
$288$		0			0
$289$	−11.0248	+	19.0955i	−0.648519	+	1.12327i
$290$	−0.0248149	+	0.140732i	−0.00145718	+	0.00826409i
$291$		0			0
$292$	2.18732	+	0.796119i	0.128003	+	0.0465893i
$293$	5.37598	+	30.4887i	0.314068	+	1.78117i	0.577397	+	0.816463i	$0.304068\pi$
$293$	5.37598	+	30.4887i	0.314068	+	1.78117i	−0.263329	+	0.964706i	$0.584821\pi$
$294$		0			0
$295$	4.70574	+	3.94858i	0.273979	+	0.229895i
$296$	−7.71688			−0.448535
$297$		0			0
$298$	5.80066			0.336023
$299$	5.84208	+	4.90209i	0.337856	+	0.283495i
$300$		0			0
$301$	6.63816	+	37.6469i	0.382617	+	2.16993i
$302$	−13.2023	−	4.80526i	−0.759709	−	0.276511i
$303$		0			0
$304$	0.724155	−	4.10689i	0.0415332	−	0.235546i
$305$	0.557781	−	0.966105i	0.0319385	−	0.0553190i
$306$		0			0
$307$	−4.26857	−	7.39338i	−0.243620	−	0.421963i	0.718123	−	0.695917i	$-0.245002\pi$
$307$	−4.26857	−	7.39338i	−0.243620	−	0.421963i	−0.961743	+	0.273954i	$0.911668\pi$
$308$	−11.8623	+	4.31753i	−0.675918	+	0.246014i
$309$		0			0
$310$	1.10354	−	0.925981i	0.0626769	−	0.0525922i
$311$	13.7986	−	11.5784i	0.782447	−	0.656551i	−0.161417	−	0.986886i	$-0.551606\pi$
$311$	13.7986	−	11.5784i	0.782447	−	0.656551i	0.943864	+	0.330335i	$0.107162\pi$
$312$		0			0
$313$	−16.1677	+	5.88457i	−0.913853	+	0.332615i	−0.755790	−	0.654814i	$-0.772747\pi$
$313$	−16.1677	+	5.88457i	−0.913853	+	0.332615i	−0.158063	+	0.987429i	$0.550525\pi$
$314$	2.38666	+	4.13381i	0.134687	+	0.233285i
$315$		0			0
$316$	3.30928	−	5.73184i	0.186161	−	0.322441i
$317$	−4.32588	+	24.5333i	−0.242966	+	1.37793i	0.582204	+	0.813043i	$0.302191\pi$
$317$	−4.32588	+	24.5333i	−0.242966	+	1.37793i	−0.825170	+	0.564885i	$0.808920\pi$
$318$		0			0
$319$	−0.545759	−	0.198640i	−0.0305567	−	0.0111217i
$320$	0.152704	+	0.866025i	0.00853639	+	0.0484123i
$321$		0			0
$322$	5.58512	+	4.68647i	0.311247	+	0.261167i
$323$	−26.0597			−1.45000
$324$		0			0
$325$	15.6159			0.866212
$326$	−8.20961	−	6.88868i	−0.454688	−	0.381529i
$327$		0			0
$328$	1.33750	+	7.58532i	0.0738509	+	0.418829i
$329$	21.2802	+	7.74535i	1.17321	+	0.427015i
$330$		0			0
$331$	1.53849	−	8.72518i	0.0845628	−	0.479580i	−0.912887	−	0.408212i	$-0.866152\pi$
$331$	1.53849	−	8.72518i	0.0845628	−	0.479580i	0.997450	−	0.0713678i	$-0.0227364\pi$
$332$	−2.22668	+	3.85673i	−0.122205	+	0.211665i
$333$		0			0
$334$	−6.44949	−	11.1708i	−0.352901	−	0.611242i
$335$	−2.97178	+	1.08164i	−0.162366	+	0.0590963i
$336$		0			0
$337$	16.1420	−	13.5448i	0.879312	−	0.737831i	−0.0867254	−	0.996232i	$-0.527640\pi$
$337$	16.1420	−	13.5448i	0.879312	−	0.737831i	0.966038	+	0.258402i	$0.0831958\pi$
$338$	0.497941	−	0.417822i	0.0270844	−	0.0227265i
$339$		0			0
$340$	5.16385	−	1.87949i	0.280049	−	0.101929i
$341$	2.92737	+	5.07035i	0.158526	+	0.274575i
$342$		0			0
$343$	−2.69207	+	4.66280i	−0.145358	+	0.251767i
$344$	−1.87939	+	10.6585i	−0.101330	+	0.574669i
$345$		0			0
$346$	12.0963	+	4.40268i	0.650299	+	0.236690i
$347$	−3.83915	−	21.7729i	−0.206096	−	1.16883i	−0.895706	−	0.444648i	$-0.853329\pi$
$347$	−3.83915	−	21.7729i	−0.206096	−	1.16883i	0.689609	−	0.724181i	$-0.257782\pi$
$348$		0			0
$349$	1.68479	+	1.41371i	0.0901849	+	0.0756741i	0.686765	−	0.726879i	$-0.259030\pi$
$349$	1.68479	+	1.41371i	0.0901849	+	0.0756741i	−0.596581	+	0.802553i	$0.703474\pi$
$350$	14.9290			0.797989
$351$		0			0
$352$	−3.57398			−0.190494
$353$	−3.64543	−	3.05888i	−0.194027	−	0.162808i	0.540599	−	0.841280i	$-0.318198\pi$
$353$	−3.64543	−	3.05888i	−0.194027	−	0.162808i	−0.734626	+	0.678473i	$0.762642\pi$
$354$		0			0
$355$	2.06758	+	11.7258i	0.109736	+	0.622343i
$356$	8.69119	+	3.16333i	0.460632	+	0.167656i
$357$		0			0
$358$	1.55644	−	8.82699i	0.0822603	−	0.466521i
$359$	−1.30288	+	2.25666i	−0.0687634	+	0.119102i	−0.898357	−	0.439266i	$-0.855239\pi$
$359$	−1.30288	+	2.25666i	−0.0687634	+	0.119102i	0.829594	+	0.558367i	$0.188572\pi$
$360$		0			0
$361$	0.804530	+	1.39349i	0.0423437	+	0.0733414i
$362$	1.86571	−	0.679065i	0.0980598	−	0.0356908i
$363$		0			0
$364$	9.99660	−	8.38814i	0.523964	−	0.439658i
$365$	−1.56805	+	1.31575i	−0.0820754	+	0.0688694i
$366$		0			0
$367$	13.3760	−	4.86846i	0.698221	−	0.254132i	0.0315696	−	0.999502i	$-0.489949\pi$
$367$	13.3760	−	4.86846i	0.698221	−	0.254132i	0.666651	+	0.745370i	$0.267727\pi$
$368$	1.03209	+	1.78763i	0.0538014	+	0.0931867i
$369$		0			0
$370$	3.39306	−	5.87695i	0.176397	−	0.305528i
$371$	0.439693	−	2.49362i	0.0228277	−	0.129462i
$372$		0			0
$373$	2.16890	+	0.789415i	0.112301	+	0.0408744i	0.397560	−	0.917576i	$-0.369857\pi$
$373$	2.16890	+	0.789415i	0.112301	+	0.0408744i	−0.285258	+	0.958451i	$0.592079\pi$
$374$	3.87820	+	21.9944i	0.200537	+	1.13730i
$375$		0			0
$376$	4.91147	+	4.12122i	0.253290	+	0.212535i
$377$	0.600385			0.0309214
$378$		0			0
$379$	−6.02734			−0.309604			−0.154802	−	0.987946i	$-0.549474\pi$
$379$	−6.02734			−0.309604			−0.154802	+	0.987946i	$0.549474\pi$
$380$	2.80928	+	2.35726i	0.144113	+	0.120925i
$381$		0			0
$382$	−2.27853	−	12.9222i	−0.116580	−	0.661157i
$383$	19.9957	+	7.27785i	1.02173	+	0.371881i	0.797928	−	0.602753i	$-0.205930\pi$
$383$	19.9957	+	7.27785i	1.02173	+	0.371881i	0.223806	+	0.974634i	$0.428152\pi$
$384$		0			0
$385$	1.92767	−	10.9324i	0.0982432	−	0.557165i
$386$	−2.87804	+	4.98491i	−0.146488	+	0.253725i
$387$		0			0
$388$	5.64543	+	9.77817i	0.286603	+	0.496411i
$389$	−19.4119	+	7.06537i	−0.984224	+	0.358228i	−0.783481	−	0.621415i	$-0.786558\pi$
$389$	−19.4119	+	7.06537i	−0.984224	+	0.358228i	−0.200743	+	0.979644i	$0.564336\pi$
$390$		0			0
$391$	9.88120	−	8.29131i	0.499714	−	0.419309i
$392$	4.19459	−	3.51968i	0.211859	−	0.177771i
$393$		0			0
$394$	−25.0719	+	9.12543i	−1.26311	+	0.459733i
$395$	2.91013	+	5.04049i	0.146425	+	0.253615i
$396$		0			0
$397$	12.2638	−	21.2416i	0.615504	−	1.06608i	−0.374792	−	0.927109i	$-0.622286\pi$
$397$	12.2638	−	21.2416i	0.615504	−	1.06608i	0.990296	−	0.138975i	$-0.0443807\pi$
$398$	−1.84817	+	10.4815i	−0.0926406	+	0.525391i
$399$		0			0
$400$	3.97178	+	1.44561i	0.198589	+	0.0722805i
$401$	−2.53967	−	14.4032i	−0.126825	−	0.719260i	−0.980207	−	0.197974i	$-0.936564\pi$
$401$	−2.53967	−	14.4032i	−0.126825	−	0.719260i	0.853382	−	0.521286i	$-0.174547\pi$
$402$		0			0
$403$	−4.63634	−	3.89036i	−0.230953	−	0.193792i
$404$	−9.37464			−0.466406
$405$		0			0
$406$	0.573978			0.0284860
$407$	21.1275	+	17.7281i	1.04725	+	0.878747i
$408$		0			0
$409$	−6.27332	−	35.5778i	−0.310196	−	1.75921i	−0.597979	−	0.801511i	$-0.704030\pi$
$409$	−6.27332	−	35.5778i	−0.310196	−	1.75921i	0.287784	−	0.957695i	$-0.407082\pi$
$410$	−6.36484	−	2.31661i	−0.314337	−	0.114409i
$411$		0			0
$412$	−0.560307	+	3.17766i	−0.0276044	+	0.156552i
$413$	12.3366	−	21.3677i	0.607045	−	1.05143i
$414$		0			0
$415$	−1.95811	−	3.39155i	−0.0961199	−	0.166485i
$416$	3.47178	−	1.26363i	0.170218	−	0.0619543i
$417$		0			0
$418$	−11.4174	+	9.58034i	−0.558443	+	0.468590i
$419$	−15.1009	+	12.6711i	−0.737725	+	0.619025i	−0.932226	−	0.361878i	$-0.882136\pi$
$419$	−15.1009	+	12.6711i	−0.737725	+	0.619025i	0.194501	+	0.980902i	$0.437691\pi$
$420$		0			0
$421$	−3.22668	+	1.17442i	−0.157259	+	0.0572375i	−0.419450	−	0.907778i	$-0.637777\pi$
$421$	−3.22668	+	1.17442i	−0.157259	+	0.0572375i	0.262191	+	0.965016i	$0.415555\pi$
$422$	2.67024	+	4.62500i	0.129985	+	0.225141i
$423$		0			0
$424$	0.358441	−	0.620838i	0.0174074	−	0.0301505i
$425$	4.58647	−	26.0111i	0.222476	−	1.26173i
$426$		0			0
$427$	−4.21048	−	1.53249i	−0.203760	−	0.0741624i
$428$	0.396459	+	2.24843i	0.0191636	+	0.108682i
$429$		0			0
$430$	−7.29086	−	6.11776i	−0.351596	−	0.295024i
$431$	28.7151			1.38316			0.691579	−	0.722300i	$-0.256915\pi$
$431$	28.7151			1.38316			0.691579	+	0.722300i	$0.256915\pi$
$432$		0			0
$433$	−14.1179			−0.678464			−0.339232	−	0.940703i	$-0.610167\pi$
$433$	−14.1179			−0.678464			−0.339232	+	0.940703i	$0.610167\pi$
$434$	−4.43242	−	3.71924i	−0.212763	−	0.178529i
$435$		0			0
$436$	1.80928	+	10.2609i	0.0866487	+	0.491409i
$437$	8.08899	+	2.94415i	0.386949	+	0.140838i
$438$		0			0
$439$	2.69506	−	15.2844i	0.128628	−	0.729487i	−0.850458	−	0.526042i	$-0.823675\pi$
$439$	2.69506	−	15.2844i	0.128628	−	0.729487i	0.979087	−	0.203444i	$-0.0652136\pi$
$440$	1.57145	−	2.72183i	0.0749160	−	0.129758i
$441$		0			0
$442$	−11.5437	−	19.9943i	−0.549078	−	0.951031i
$443$	−33.5984	+	12.2288i	−1.59631	+	0.581008i	−0.978667	−	0.205452i	$-0.934133\pi$
$443$	−33.5984	+	12.2288i	−1.59631	+	0.581008i	−0.617640	+	0.786461i	$0.711911\pi$
$444$		0			0
$445$	−6.23055	+	5.22805i	−0.295356	+	0.247834i
$446$	−14.5929	+	12.2449i	−0.690992	+	0.579811i
$447$		0			0
$448$	3.31908	−	1.20805i	0.156812	−	0.0570748i
$449$	−12.8564	−	22.2679i	−0.606730	−	1.05089i	−0.991775	−	0.127990i	$-0.959148\pi$
$449$	−12.8564	−	22.2679i	−0.606730	−	1.05089i	0.385045	−	0.922898i	$-0.374186\pi$
$450$		0			0
$451$	13.7640	−	23.8399i	0.648121	−	1.12258i
$452$	−1.93330	+	10.9643i	−0.0909346	+	0.515716i
$453$		0			0
$454$	−3.25237	−	1.18377i	−0.152641	−	0.0555570i
$455$	1.99273	+	11.3013i	0.0934204	+	0.529814i
$456$		0			0
$457$	1.55690	+	1.30640i	0.0728289	+	0.0611107i	0.678475	−	0.734623i	$-0.262641\pi$
$457$	1.55690	+	1.30640i	0.0728289	+	0.0611107i	−0.605647	+	0.795734i	$0.707085\pi$
$458$	−28.9394			−1.35225
$459$		0			0
$460$	−1.81521			−0.0846345
$461$	−16.5266	−	13.8675i	−0.769722	−	0.645873i	0.170916	−	0.985286i	$-0.445327\pi$
$461$	−16.5266	−	13.8675i	−0.769722	−	0.645873i	−0.940638	+	0.339412i	$0.889772\pi$
$462$		0			0
$463$	−3.75103	−	21.2731i	−0.174325	−	0.988647i	−0.938920	−	0.344136i	$-0.888172\pi$
$463$	−3.75103	−	21.2731i	−0.174325	−	0.988647i	0.764595	−	0.644511i	$-0.222939\pi$
$464$	0.152704	+	0.0555796i	0.00708909	+	0.00258022i
$465$		0			0
$466$	1.15657	−	6.55926i	0.0535773	−	0.303852i
$467$	12.2622	−	21.2387i	0.567426	−	0.982810i	−0.429394	−	0.903117i	$-0.641273\pi$
$467$	12.2622	−	21.2387i	0.567426	−	0.982810i	0.996819	−	0.0796928i	$-0.0253939\pi$
$468$		0			0
$469$	6.35117	+	11.0005i	0.293270	+	0.507958i
$470$	−5.29813	+	1.92836i	−0.244385	+	0.0889487i
$471$		0			0
$472$	5.35117	−	4.49016i	0.246307	−	0.206676i
$473$	29.6313	−	24.8637i	1.36245	−	1.14323i
$474$		0			0
$475$	16.5633	−	6.02855i	0.759976	−	0.276609i
$476$	−11.0360	−	19.1148i	−0.505832	−	0.876127i
$477$		0			0
$478$	3.89440	−	6.74530i	0.178126	−	0.308523i
$479$	−2.48767	+	14.1083i	−0.113665	+	0.644625i	0.873738	+	0.486397i	$0.161689\pi$
$479$	−2.48767	+	14.1083i	−0.113665	+	0.644625i	−0.987403	+	0.158228i	$0.949422\pi$
$480$		0			0
$481$	−26.7913	−	9.75125i	−1.22158	−	0.444619i
$482$	3.80200	+	21.5622i	0.173177	+	0.982133i
$483$		0			0
$484$	1.35844	+	1.13987i	0.0617473	+	0.0518121i
$485$	−9.92902			−0.450853
$486$		0			0
$487$	32.3114			1.46417			0.732084	−	0.681214i	$-0.238548\pi$
$487$	32.3114			1.46417			0.732084	+	0.681214i	$0.238548\pi$
$488$	−0.971782	−	0.815422i	−0.0439905	−	0.0369124i
$489$		0			0
$490$	0.836152	+	4.74205i	0.0377735	+	0.214224i
$491$	30.4923	+	11.0983i	1.37610	+	0.500859i	0.920993	−	0.389578i	$-0.127379\pi$
$491$	30.4923	+	11.0983i	1.37610	+	0.500859i	0.455106	+	0.890437i	$0.349601\pi$
$492$		0			0
$493$	0.176337	−	1.00005i	0.00794180	−	0.0450402i
$494$	7.70368	−	13.3432i	0.346605	−	0.600337i
$495$		0			0
$496$	−0.819078	−	1.41868i	−0.0367777	−	0.0637008i
$497$	44.9397	−	16.3567i	2.01582	−	0.733700i
$498$		0			0
$499$	−19.0214	+	15.9609i	−0.851515	+	0.714506i	−0.960123	−	0.279579i	$-0.909805\pi$
$499$	−19.0214	+	15.9609i	−0.851515	+	0.714506i	0.108608	+	0.994085i	$0.465361\pi$
$500$	−6.21554	+	5.21546i	−0.277967	+	0.233242i
$501$		0			0
$502$	15.1147	−	5.50130i	0.674601	−	0.245535i
$503$	−7.46198	−	12.9245i	−0.332713	−	0.576276i	0.650330	−	0.759652i	$-0.274631\pi$
$503$	−7.46198	−	12.9245i	−0.332713	−	0.576276i	−0.983043	+	0.183376i	$0.941297\pi$
$504$		0			0
$505$	4.12196	−	7.13944i	0.183425	−	0.317701i
$506$	1.28106	−	7.26525i	0.0569500	−	0.322980i
$507$		0			0
$508$	9.30928	+	3.38830i	0.413032	+	0.150332i
$509$	−2.67200	−	15.1537i	−0.118434	−	0.671674i	−0.984992	−	0.172598i	$-0.944784\pi$
$509$	−2.67200	−	15.1537i	−0.118434	−	0.671674i	0.866558	−	0.499076i	$-0.166327\pi$
$510$		0			0
$511$	6.29813	+	5.28476i	0.278613	+	0.233784i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−25.8648			−1.14085
$515$	−2.17365	−	1.82391i	−0.0957824	−	0.0803710i
$516$		0			0
$517$	−3.97906	−	22.5663i	−0.174999	−	0.992467i
$518$	−25.6129	−	9.32234i	−1.12537	−	0.409600i
$519$		0			0
$520$	−0.564178	+	3.19961i	−0.0247408	+	0.140312i
$521$	6.69207	−	11.5910i	0.293185	−	0.507811i	−0.681376	−	0.731933i	$-0.738618\pi$
$521$	6.69207	−	11.5910i	0.293185	−	0.507811i	0.974561	+	0.224122i	$0.0719516\pi$
$522$		0			0
$523$	12.4402	+	21.5470i	0.543970	+	0.942184i	0.998671	+	0.0515397i	$0.0164129\pi$
$523$	12.4402	+	21.5470i	0.543970	+	0.942184i	−0.454701	+	0.890644i	$0.650254\pi$
$524$	−8.48545	+	3.08845i	−0.370689	+	0.134920i
$525$		0			0
$526$	24.1275	−	20.2454i	1.05201	−	0.882740i
$527$	−7.84183	+	6.58008i	−0.341596	+	0.286633i
$528$		0			0
$529$	17.6091	−	6.40917i	0.765611	−	0.278660i
$530$	0.315207	+	0.545955i	0.0136917	+	0.0237148i
$531$		0			0
$532$	7.36484	−	12.7563i	0.319306	−	0.553055i
$533$	−4.94150	+	28.0247i	−0.214040	+	1.21388i
$534$		0			0
$535$	−1.88666	−	0.686688i	−0.0815674	−	0.0296881i
$536$	0.624485	+	3.54163i	0.0269737	+	0.152975i
$537$		0			0
$538$	3.53074	+	2.96265i	0.152221	+	0.127729i
$539$	−19.5699			−0.842934
$540$		0			0
$541$	−9.09421			−0.390991			−0.195495	−	0.980705i	$-0.562631\pi$
$541$	−9.09421			−0.390991			−0.195495	+	0.980705i	$0.562631\pi$
$542$	−1.00980	−	0.847323i	−0.0433746	−	0.0363956i
$543$		0			0
$544$	−1.08512	−	6.15403i	−0.0465242	−	0.263852i
$545$	−8.60994	−	3.13376i	−0.368809	−	0.134236i
$546$		0			0
$547$	3.85663	−	21.8720i	0.164898	−	0.935181i	−0.784272	−	0.620417i	$-0.786964\pi$
$547$	3.85663	−	21.8720i	0.164898	−	0.935181i	0.949170	−	0.314764i	$-0.101925\pi$
$548$	1.01367	−	1.75573i	0.0433019	−	0.0750010i
$549$		0			0
$550$	−7.55303	−	13.0822i	−0.322062	−	0.557828i
$551$	0.636812	−	0.231780i	0.0271291	−	0.00987418i
$552$		0			0
$553$	17.9081	−	15.0267i	0.761529	−	0.638998i
$554$	23.6104	−	19.8115i	1.00311	−	0.841709i
$555$		0			0
$556$	−0.155230	+	0.0564991i	−0.00658321	+	0.00239609i
$557$	−1.35369	−	2.34466i	−0.0573578	−	0.0993466i	0.835921	−	0.548850i	$-0.184934\pi$
$557$	−1.35369	−	2.34466i	−0.0573578	−	0.0993466i	−0.893279	+	0.449504i	$0.851601\pi$
$558$		0			0
$559$	−19.9932	+	34.6292i	−0.845622	+	1.46466i
$560$	−0.539363	+	3.05888i	−0.0227922	+	0.129261i
$561$		0			0
$562$	20.1386	+	7.32986i	0.849497	+	0.309191i
$563$	−1.22122	−	6.92588i	−0.0514682	−	0.291891i	0.948199	−	0.317676i	$-0.102902\pi$
$563$	−1.22122	−	6.92588i	−0.0514682	−	0.291891i	−0.999668	+	0.0257853i	$0.991791\pi$
$564$		0			0
$565$	−7.50000	−	6.29325i	−0.315527	−	0.264759i
$566$	−1.77332			−0.0745381
$567$		0			0
$568$	13.5398			0.568119
$569$	−19.1682	−	16.0840i	−0.803572	−	0.674277i	0.145492	−	0.989359i	$-0.453523\pi$
$569$	−19.1682	−	16.0840i	−0.803572	−	0.674277i	−0.949064	+	0.315082i	$0.897968\pi$
$570$		0			0
$571$	1.18866	+	6.74124i	0.0497440	+	0.282112i	0.999526	−	0.0308016i	$-0.00980601\pi$
$571$	1.18866	+	6.74124i	0.0497440	+	0.282112i	−0.949782	+	0.312914i	$0.898695\pi$
$572$	−12.4081	−	4.51617i	−0.518807	−	0.188830i
$573$		0			0
$574$	−4.72416	+	26.7920i	−0.197182	+	1.11828i
$575$	−4.36231	+	7.55574i	−0.181921	+	0.315096i
$576$		0			0
$577$	−2.10014	−	3.63754i	−0.0874298	−	0.151433i	0.818994	−	0.573802i	$-0.194532\pi$
$577$	−2.10014	−	3.63754i	−0.0874298	−	0.151433i	−0.906424	+	0.422369i	$0.861199\pi$
$578$	−20.7199	+	7.54142i	−0.861833	+	0.313682i
$579$		0			0
$580$	−0.109470	+	0.0918566i	−0.00454551	+	0.00381414i
$581$	−12.0496	+	10.1108i	−0.499903	+	0.419468i
$582$		0			0
$583$	−2.40760	+	0.876296i	−0.0997128	+	0.0362925i
$584$	1.16385	+	2.01584i	0.0481604	+	0.0834162i
$585$		0			0
$586$	−15.4795	+	26.8113i	−0.639453	+	1.10757i
$587$	6.34746	−	35.9982i	0.261988	−	1.48581i	−0.515490	−	0.856895i	$-0.672390\pi$
$587$	6.34746	−	35.9982i	0.261988	−	1.48581i	0.777478	−	0.628910i	$-0.216499\pi$
$588$		0			0
$589$	−6.41952	−	2.33651i	−0.264512	−	0.0962744i
$590$	1.06670	+	6.04958i	0.0439155	+	0.249057i
$591$		0			0
$592$	−5.91147	−	4.96032i	−0.242960	−	0.203868i
$593$	45.0660			1.85064			0.925320	−	0.379186i	$-0.123796\pi$
$593$	45.0660			1.85064			0.925320	+	0.379186i	$0.123796\pi$
$594$		0			0
$595$	19.4097			0.795721
$596$	4.44356	+	3.72859i	0.182015	+	0.152729i
$597$		0			0
$598$	1.32429	+	7.51044i	0.0541543	+	0.307125i
$599$	15.2760	+	5.56001i	0.624161	+	0.227176i	0.634688	−	0.772769i	$-0.281129\pi$
$599$	15.2760	+	5.56001i	0.624161	+	0.227176i	−0.0105271	+	0.999945i	$0.503351\pi$
$600$		0			0
$601$	−7.20796	+	40.8784i	−0.294019	+	1.66746i	0.377145	+	0.926154i	$0.376906\pi$
$601$	−7.20796	+	40.8784i	−0.294019	+	1.66746i	−0.671164	+	0.741309i	$0.734205\pi$
$602$	−19.1138	+	33.1061i	−0.779021	+	1.34930i
$603$		0			0
$604$	−7.02481	−	12.1673i	−0.285836	−	0.495082i
$605$	−1.46538	+	0.533356i	−0.0595764	+	0.0216840i
$606$		0			0
$607$	−32.4051	+	27.1911i	−1.31528	+	1.10365i	−0.328002	+	0.944677i	$0.606375\pi$
$607$	−32.4051	+	27.1911i	−1.31528	+	1.10365i	−0.987282	+	0.158977i	$0.949180\pi$
$608$	3.19459	−	2.68058i	0.129558	−	0.108712i
$609$		0			0
$610$	1.04829	−	0.381545i	0.0424438	−	0.0154483i
$611$	11.8439	+	20.5142i	0.479153	+	0.829917i
$612$		0			0
$613$	−9.50686	+	16.4664i	−0.383979	+	0.665070i	−0.991627	−	0.129136i	$-0.958780\pi$
$613$	−9.50686	+	16.4664i	−0.383979	+	0.665070i	0.607648	+	0.794206i	$0.292113\pi$
$614$	1.48246	−	8.40744i	0.0598272	−	0.339297i
$615$		0			0
$616$	−11.8623	−	4.31753i	−0.477946	−	0.173958i
$617$	−6.42246	−	36.4236i	−0.258558	−	1.46636i	−0.786771	−	0.617245i	$-0.788249\pi$
$617$	−6.42246	−	36.4236i	−0.258558	−	1.46636i	0.528213	−	0.849112i	$-0.322862\pi$
$618$		0			0
$619$	−23.3653	−	19.6058i	−0.939131	−	0.788024i	0.0383030	−	0.999266i	$-0.487805\pi$
$619$	−23.3653	−	19.6058i	−0.939131	−	0.788024i	−0.977434	+	0.211242i	$0.932249\pi$
$620$	1.44057			0.0578547
$621$		0			0
$622$	18.0128			0.722247
$623$	25.0253	+	20.9987i	1.00262	+	0.841295i
$624$		0			0
$625$	2.43077	+	13.7856i	0.0972308	+	0.551423i
$626$	−16.1677	−	5.88457i	−0.646192	−	0.235195i
$627$		0			0
$628$	−0.828878	+	4.70080i	−0.0330758	+	0.187582i
$629$	−24.1113	+	41.7620i	−0.961380	+	1.66516i
$630$		0			0
$631$	−6.86349	−	11.8879i	−0.273231	−	0.473251i	0.696456	−	0.717599i	$-0.254759\pi$
$631$	−6.86349	−	11.8879i	−0.273231	−	0.473251i	−0.969687	+	0.244349i	$0.921426\pi$
$632$	6.21941	−	2.26368i	0.247395	−	0.0900443i
$633$		0			0
$634$	−19.0835	+	16.0130i	−0.757904	+	0.635957i
$635$	−6.67365	+	5.59986i	−0.264836	+	0.222223i
$636$		0			0
$637$	19.0103	−	6.91917i	0.753214	−	0.274148i
$638$	−0.290393	−	0.502975i	−0.0114968	−	0.0199130i
$639$		0			0
$640$	−0.439693	+	0.761570i	−0.0173804	+	0.0301037i
$641$	−0.741696	+	4.20637i	−0.0292952	+	0.166142i	−0.995946	−	0.0899585i	$-0.971327\pi$
$641$	−0.741696	+	4.20637i	−0.0292952	+	0.166142i	0.966650	+	0.256100i	$0.0824377\pi$
$642$		0			0
$643$	19.8123	+	7.21108i	0.781320	+	0.284377i	0.701723	−	0.712450i	$-0.252414\pi$
$643$	19.8123	+	7.21108i	0.781320	+	0.284377i	0.0795968	+	0.996827i	$0.474637\pi$
$644$	1.26604	+	7.18009i	0.0498891	+	0.282935i
$645$		0			0
$646$	−19.9629	−	16.7509i	−0.785430	−	0.659054i
$647$	27.4023			1.07730			0.538648	−	0.842531i	$-0.318935\pi$
$647$	27.4023			1.07730			0.538648	+	0.842531i	$0.318935\pi$
$648$		0			0
$649$	−24.9659			−0.979995
$650$	11.9624	+	10.0377i	0.469206	+	0.393710i
$651$		0			0
$652$	−1.86097	−	10.5541i	−0.0728811	−	0.413329i
$653$	4.43494	+	1.61419i	0.173553	+	0.0631681i	0.427335	−	0.904093i	$-0.359452\pi$
$653$	4.43494	+	1.61419i	0.173553	+	0.0631681i	−0.253782	+	0.967261i	$0.581675\pi$
$654$		0			0
$655$	1.37892	−	7.82023i	0.0538788	−	0.305562i
$656$	−3.85117	+	6.67042i	−0.150363	+	0.260436i
$657$		0			0
$658$	11.3229	+	19.6119i	0.441414	+	0.764552i
$659$	19.7618	−	7.19269i	0.769809	−	0.280188i	0.0728925	−	0.997340i	$-0.476777\pi$
$659$	19.7618	−	7.19269i	0.769809	−	0.280188i	0.696917	+	0.717152i	$0.254555\pi$
$660$		0			0
$661$	19.4186	−	16.2941i	0.755295	−	0.633768i	−0.181602	−	0.983372i	$-0.558128\pi$
$661$	19.4186	−	16.2941i	0.755295	−	0.633768i	0.936898	+	0.349604i	$0.113684\pi$
$662$	6.78699	−	5.69496i	0.263784	−	0.221341i
$663$		0			0
$664$	−4.18479	+	1.52314i	−0.162401	+	0.0591093i
$665$	6.47653	+	11.2177i	0.251149	+	0.435003i
$666$		0			0
$667$	−0.167718	+	0.290497i	−0.00649408	+	0.0112481i
$668$	2.23989	−	12.7030i	0.0866638	−	0.491495i
$669$		0			0
$670$	−2.97178	−	1.08164i	−0.114810	−	0.0417874i
$671$	0.787294	+	4.46496i	0.0303931	+	0.172368i
$672$		0			0
$673$	10.9003	+	9.14646i	0.420177	+	0.352570i	0.828230	−	0.560388i	$-0.189348\pi$
$673$	10.9003	+	9.14646i	0.420177	+	0.352570i	−0.408054	+	0.912958i	$0.633792\pi$
$674$	21.0719			0.811660
$675$		0			0
$676$	0.650015			0.0250006
$677$	−35.6393	−	29.9050i	−1.36973	−	1.14934i	−0.972841	−	0.231475i	$-0.925645\pi$
$677$	−35.6393	−	29.9050i	−1.36973	−	1.14934i	−0.396890	−	0.917866i	$-0.629911\pi$
$678$		0			0
$679$	6.92514	+	39.2744i	0.265763	+	1.50721i
$680$	5.16385	+	1.87949i	0.198025	+	0.0720750i
$681$		0			0
$682$	−1.01666	+	5.76579i	−0.0389301	+	0.220783i
$683$	−5.10101	+	8.83522i	−0.195185	+	0.338070i	−0.946961	−	0.321348i	$-0.895864\pi$
$683$	−5.10101	+	8.83522i	−0.195185	+	0.338070i	0.751776	+	0.659418i	$0.229197\pi$
$684$		0			0
$685$	0.891407	+	1.54396i	0.0340589	+	0.0589918i
$686$	−5.05943	+	1.84148i	−0.193170	+	0.0703081i
$687$		0			0
$688$	−8.29086	+	6.95686i	−0.316086	+	0.265228i
$689$	2.02893	−	1.70248i	0.0772962	−	0.0648592i
$690$		0			0
$691$	0.331100	−	0.120510i	0.0125956	−	0.00458443i	−0.335715	−	0.941964i	$-0.608978\pi$
$691$	0.331100	−	0.120510i	0.0125956	−	0.00458443i	0.348310	+	0.937379i	$0.386756\pi$
$692$	6.43629	+	11.1480i	0.244671	+	0.423783i
$693$		0			0
$694$	11.0544	−	19.1467i	0.419618	−	0.726800i
$695$	0.0252254	−	0.143061i	0.000956856	−	0.00542660i
$696$		0			0
$697$	45.2290	+	16.4620i	1.71317	+	0.623543i
$698$	0.381911	+	2.16593i	0.0144556	+	0.0819816i
$699$		0			0
$700$	11.4363	+	9.59619i	0.432251	+	0.362702i
$701$	−39.9358			−1.50836			−0.754178	−	0.656671i	$-0.771964\pi$
$701$	−39.9358			−1.50836			−0.754178	+	0.656671i	$0.771964\pi$
$702$		0			0
$703$	−32.1813			−1.21374
$704$	−2.73783	−	2.29731i	−0.103186	−	0.0865831i
$705$		0			0
$706$	−0.826352	−	4.68647i	−0.0311002	−	0.176378i
$707$	−31.1152	−	11.3250i	−1.17021	−	0.425920i
$708$		0			0
$709$	−8.55199	+	48.5008i	−0.321177	+	1.82148i	0.214105	+	0.976811i	$0.431317\pi$
$709$	−8.55199	+	48.5008i	−0.321177	+	1.82148i	−0.535281	+	0.844674i	$0.679794\pi$
$710$	−5.95336	+	10.3115i	−0.223426	+	0.386985i
$711$		0			0
$712$	4.62449	+	8.00984i	0.173310	+	0.300182i
$713$	3.17752	−	1.15652i	0.118999	−	0.0433121i
$714$		0			0
$715$	8.89512	−	7.46389i	0.332658	−	0.279134i
$716$	6.86618	−	5.76141i	0.256601	−	0.215314i
$717$		0			0
$718$	−2.44862	+	0.891223i	−0.0913815	+	0.0332602i
$719$	−25.8050	−	44.6956i	−0.962364	−	1.66686i	−0.716536	−	0.697550i	$-0.754274\pi$
$719$	−25.8050	−	44.6956i	−0.962364	−	1.66686i	−0.245828	−	0.969314i	$-0.579060\pi$
$720$		0			0
$721$	−5.69846	+	9.87003i	−0.212222	+	0.367579i
$722$	−0.279410	+	1.58461i	−0.0103986	+	0.0589733i
$723$		0			0
$724$	1.86571	+	0.679065i	0.0693387	+	0.0252372i
$725$	0.119271	+	0.676417i	0.00442960	+	0.0251215i
$726$		0			0
$727$	−21.1721	−	17.7655i	−0.785228	−	0.658885i	0.159331	−	0.987225i	$-0.449066\pi$
$727$	−21.1721	−	17.7655i	−0.785228	−	0.658885i	−0.944559	+	0.328341i	$0.893511\pi$
$728$	13.0496			0.483651
$729$		0			0
$730$	−2.04694			−0.0757607
$731$	51.8093	+	43.4732i	1.91624	+	1.60791i
$732$		0			0
$733$	4.78746	+	27.1510i	0.176829	+	1.00285i	0.936012	+	0.351968i	$0.114488\pi$
$733$	4.78746	+	27.1510i	0.176829	+	1.00285i	−0.759183	+	0.650877i	$0.774401\pi$
$734$	13.3760	+	4.86846i	0.493716	+	0.179698i
$735$		0			0
$736$	−0.358441	+	2.03282i	−0.0132123	+	0.0749307i
$737$	6.42649	−	11.1310i	0.236723	−	0.410016i
$738$		0			0
$739$	2.01320	+	3.48697i	0.0740569	+	0.128270i	0.900676	−	0.434492i	$-0.143072\pi$
$739$	2.01320	+	3.48697i	0.0740569	+	0.128270i	−0.826619	+	0.562762i	$0.809739\pi$
$740$	6.37686	−	2.32099i	0.234418	−	0.0853212i
$741$		0			0
$742$	1.93969	−	1.62760i	0.0712084	−	0.0597509i
$743$	−22.2770	+	18.6926i	−0.817265	+	0.685767i	−0.952330	−	0.305070i	$-0.901320\pi$
$743$	−22.2770	+	18.6926i	−0.817265	+	0.685767i	0.135065	+	0.990837i	$0.456876\pi$
$744$		0			0
$745$	−4.79339	+	1.74465i	−0.175616	+	0.0639190i
$746$	1.15405	+	1.99887i	0.0422527	+	0.0731838i
$747$		0			0
$748$	−11.1668	+	19.3415i	−0.408300	+	0.707197i
$749$	−1.40033	+	7.94166i	−0.0511669	+	0.290182i
$750$		0			0
$751$	−38.2679	−	13.9284i	−1.39641	−	0.508253i	−0.469302	−	0.883038i	$-0.655494\pi$
$751$	−38.2679	−	13.9284i	−1.39641	−	0.508253i	−0.927112	+	0.374785i	$0.877717\pi$
$752$	1.11334	+	6.31407i	0.0405994	+	0.230250i
$753$		0			0
$754$	0.459922	+	0.385920i	0.0167494	+	0.0140544i
$755$	12.3550			0.449646
$756$		0			0
$757$	32.9486			1.19754			0.598769	−	0.800922i	$-0.295657\pi$
$757$	32.9486			1.19754			0.598769	+	0.800922i	$0.295657\pi$
$758$	−4.61721	−	3.87430i	−0.167705	−	0.140721i
$759$		0			0
$760$	0.636812	+	3.61154i	0.0230996	+	0.131004i
$761$	−0.948615	−	0.345268i	−0.0343873	−	0.0125159i	0.324769	−	0.945793i	$-0.394713\pi$
$761$	−0.948615	−	0.345268i	−0.0343873	−	0.0125159i	−0.359157	+	0.933277i	$0.616936\pi$
$762$		0			0
$763$	−6.39053	+	36.2425i	−0.231353	+	1.31207i
$764$	6.56077	−	11.3636i	0.237360	−	0.411120i
$765$		0			0
$766$	10.6395	+	18.4282i	0.384421	+	0.665836i
$767$	24.2520	−	8.82699i	0.875688	−	0.318724i
$768$		0			0
$769$	−23.7704	+	19.9457i	−0.857182	+	0.719261i	−0.961359	−	0.275298i	$-0.911224\pi$
$769$	−23.7704	+	19.9457i	−0.857182	+	0.719261i	0.104177	+	0.994559i	$0.466779\pi$
$770$	8.50387	−	7.13559i	0.306458	−	0.257149i
$771$		0			0
$772$	−5.40895	+	1.96870i	−0.194672	+	0.0708549i
$773$	8.32295	+	14.4158i	0.299356	+	0.518499i	0.975989	−	0.217821i	$-0.0698950\pi$
$773$	8.32295	+	14.4158i	0.299356	+	0.518499i	−0.676633	+	0.736320i	$0.736562\pi$
$774$		0			0
$775$	3.46198	−	5.99633i	0.124358	−	0.215394i
$776$	−1.96064	+	11.1193i	−0.0703828	+	0.399161i
$777$		0			0
$778$	−19.4119	−	7.06537i	−0.695952	−	0.253306i
$779$	5.57769	+	31.6326i	0.199841	+	1.13336i
$780$		0			0
$781$	−37.0697	−	31.1052i	−1.32646	−	1.11303i
$782$	12.8990			0.461267
$783$		0			0
$784$	5.47565			0.195559
$785$	−3.21554	−	2.69816i	−0.114767	−	0.0963013i
$786$		0			0
$787$	−0.357563	−	2.02784i	−0.0127458	−	0.0722848i	0.977771	−	0.209674i	$-0.0672401\pi$
$787$	−0.357563	−	2.02784i	−0.0127458	−	0.0722848i	−0.990517	+	0.137389i	$0.956129\pi$
$788$	−25.0719	−	9.12543i	−0.893150	−	0.325080i
$789$		0			0
$790$	−1.01068	+	5.73184i	−0.0359583	+	0.203930i
$791$	−19.6621	+	34.0557i	−0.699104	+	1.21088i
$792$		0			0
$793$	−2.34343	−	4.05893i	−0.0832175	−	0.144137i
$794$	23.0484	−	8.38895i	0.817959	−	0.297713i
$795$		0			0
$796$	−8.15317	+	6.84132i	−0.288981	+	0.242484i
$797$	−39.4975	+	33.1424i	−1.39907	+	1.17396i	−0.437566	+	0.899186i	$0.644159\pi$
$797$	−39.4975	+	33.1424i	−1.39907	+	1.17396i	−0.961508	+	0.274777i	$0.911396\pi$
$798$		0			0
$799$	37.6489	−	13.7031i	1.33192	−	0.484780i
$800$	2.11334	+	3.66041i	0.0747179	+	0.129415i
$801$		0			0
$802$	7.31268	−	12.6659i	0.258220	−	0.447250i
$803$	1.44460	−	8.19275i	0.0509789	−	0.289116i
$804$		0			0
$805$	−6.02481	−	2.19285i	−0.212347	−	0.0772879i
$806$	−1.05097	−	5.96037i	−0.0370190	−	0.209945i
$807$		0			0
$808$	−7.18139	−	6.02590i	−0.252640	−	0.211990i
$809$	−25.9709			−0.913088			−0.456544	−	0.889701i	$-0.650913\pi$
$809$	−25.9709			−0.913088			−0.456544	+	0.889701i	$0.650913\pi$
$810$		0			0
$811$	−14.4442			−0.507204			−0.253602	−	0.967309i	$-0.581615\pi$
$811$	−14.4442			−0.507204			−0.253602	+	0.967309i	$0.581615\pi$
$812$	0.439693	+	0.368946i	0.0154302	+	0.0129475i
$813$		0			0
$814$	4.78921	+	27.1610i	0.167862	+	0.951991i
$815$	8.85591	+	3.22329i	0.310209	+	0.112907i
$816$		0			0
$817$	−7.83750	+	44.4486i	−0.274199	+	1.55506i
$818$	18.0633	−	31.2866i	0.631568	−	1.09391i
$819$		0			0
$820$	−3.38666	−	5.86587i	−0.118267	−	0.204845i
$821$	−6.28136	+	2.28623i	−0.219221	+	0.0797900i	−0.449296	−	0.893383i	$-0.648325\pi$
$821$	−6.28136	+	2.28623i	−0.219221	+	0.0797900i	0.230075	+	0.973173i	$0.426103\pi$
$822$		0			0
$823$	−5.92649	+	4.97291i	−0.206584	+	0.173345i	−0.740210	−	0.672376i	$-0.765274\pi$
$823$	−5.92649	+	4.97291i	−0.206584	+	0.173345i	0.533625	+	0.845721i	$0.320829\pi$
$824$	−2.47178	+	2.07407i	−0.0861086	+	0.0722537i
$825$		0			0
$826$	23.1853	−	8.43874i	0.806718	−	0.293621i
$827$	23.4038	+	40.5366i	0.813830	+	1.40959i	0.910165	+	0.414245i	$0.135954\pi$
$827$	23.4038	+	40.5366i	0.813830	+	1.40959i	−0.0963358	+	0.995349i	$0.530712\pi$
$828$		0			0
$829$	22.6648	−	39.2566i	0.787180	−	1.36344i	−0.140507	−	0.990080i	$-0.544873\pi$
$829$	22.6648	−	39.2566i	0.787180	−	1.36344i	0.927688	−	0.373357i	$-0.121793\pi$
$830$	0.680045	−	3.85673i	0.0236047	−	0.133869i
$831$		0			0
$832$	3.47178	+	1.26363i	0.120362	+	0.0438083i
$833$	−5.94175	−	33.6974i	−0.205870	−	1.16754i
$834$		0			0
$835$	8.68938	+	7.29125i	0.300708	+	0.252324i
$836$	−14.9044			−0.515478
$837$		0			0
$838$	−19.7128			−0.680966
$839$	−8.02553	−	6.73422i	−0.277072	−	0.232491i	0.493653	−	0.869659i	$-0.335661\pi$
$839$	−8.02553	−	6.73422i	−0.277072	−	0.232491i	−0.770725	+	0.637168i	$0.780106\pi$
$840$		0			0
$841$	−5.03121	−	28.5334i	−0.173490	−	0.983911i
$842$	−3.22668	−	1.17442i	−0.111199	−	0.0404731i
$843$		0			0
$844$	−0.927366	+	5.25936i	−0.0319213	+	0.181034i
$845$	−0.285807	+	0.495032i	−0.00983206	+	0.0170296i
$846$		0			0
$847$	3.13176	+	5.42437i	0.107609	+	0.186383i
$848$	0.673648	−	0.245188i	0.0231332	−	0.00841979i
$849$		0			0
$850$	20.2331	−	16.9776i	0.693989	−	0.582326i
$851$	12.2023	−	10.2390i	0.418291	−	0.350987i
$852$		0			0
$853$	−33.7254	+	12.2750i	−1.15474	+	0.420289i	−0.847214	−	0.531252i	$-0.821722\pi$
$853$	−33.7254	+	12.2750i	−1.15474	+	0.420289i	−0.307522	+	0.951541i	$0.599500\pi$
$854$	−2.24035	−	3.88040i	−0.0766633	−	0.132785i
$855$		0			0
$856$	−1.14156	+	1.97724i	−0.0390177	+	0.0675806i
$857$	2.87329	−	16.2953i	0.0981498	−	0.556635i	−0.895587	−	0.444887i	$-0.853244\pi$
$857$	2.87329	−	16.2953i	0.0981498	−	0.556635i	0.993737	−	0.111748i	$-0.0356451\pi$
$858$		0			0
$859$	−13.2934	−	4.83840i	−0.453564	−	0.165084i	0.105128	−	0.994459i	$-0.466475\pi$
$859$	−13.2934	−	4.83840i	−0.453564	−	0.165084i	−0.558693	+	0.829375i	$0.688697\pi$
$860$	−1.65270	−	9.37295i	−0.0563567	−	0.319615i
$861$		0			0
$862$	21.9971	+	18.4577i	0.749223	+	0.628673i
$863$	32.8939			1.11972			0.559861	−	0.828586i	$-0.310854\pi$
$863$	32.8939			1.11972			0.559861	+	0.828586i	$0.310854\pi$
$864$		0			0
$865$	−11.3200			−0.384890
$866$	−10.8150	−	9.07483i	−0.367507	−	0.308375i
$867$		0			0
$868$	−1.00475	−	5.69821i	−0.0341034	−	0.193410i
$869$	−22.2280	−	8.09034i	−0.754034	−	0.274446i
$870$		0			0
$871$	−2.30722	+	13.0849i	−0.0781771	+	0.443364i
$872$	−5.20961	+	9.02330i	−0.176420	+	0.305568i
$873$		0			0
$874$	4.30406	+	7.45486i	0.145587	+	0.252164i
$875$	−26.9304	+	9.80185i	−0.910412	+	0.331363i
$876$		0			0
$877$	18.3353	−	15.3851i	0.619138	−	0.519519i	−0.278394	−	0.960467i	$-0.589802\pi$
$877$	18.3353	−	15.3851i	0.619138	−	0.519519i	0.897533	+	0.440948i	$0.145358\pi$
$878$	11.8892	−	9.97621i	0.401241	−	0.336681i
$879$		0			0
$880$	2.95336	−	1.07494i	0.0995579	−	0.0362361i
$881$	−9.34183	−	16.1805i	−0.314734	−	0.545136i	0.664647	−	0.747158i	$-0.268582\pi$
$881$	−9.34183	−	16.1805i	−0.314734	−	0.545136i	−0.979381	+	0.202022i	$0.935249\pi$
$882$		0			0
$883$	2.99407	−	5.18588i	0.100758	−	0.174519i	−0.811239	−	0.584715i	$-0.801206\pi$
$883$	2.99407	−	5.18588i	0.100758	−	0.174519i	0.911997	+	0.410196i	$0.134540\pi$
$884$	4.00908	−	22.7367i	0.134840	−	0.764716i
$885$		0			0
$886$	−33.5984	−	12.2288i	−1.12876	−	0.410835i
$887$	−1.36050	−	7.71578i	−0.0456811	−	0.259071i	0.953411	−	0.301675i	$-0.0975457\pi$
$887$	−1.36050	−	7.71578i	−0.0456811	−	0.259071i	−0.999092	+	0.0426042i	$0.986435\pi$
$888$		0			0
$889$	26.8050	+	22.4921i	0.899011	+	0.754360i
$890$	−8.13341			−0.272632
$891$		0			0
$892$	−19.0496			−0.637829
$893$	20.4820	+	17.1865i	0.685406	+	0.575124i
$894$		0			0
$895$	1.36871	+	7.76233i	0.0457509	+	0.259466i
$896$	3.31908	+	1.20805i	0.110883	+	0.0403580i
$897$		0			0
$898$	4.46497	−	25.3221i	0.148998	−	0.845010i
$899$	0.133103	−	0.230542i	0.00443924	−	0.00768899i
$900$		0			0
$901$	−2.23989	−	3.87960i	−0.0746214	−	0.129248i
$902$	25.8678	−	9.41512i	0.861305	−	0.313489i
$903$		0			0
$904$	−8.52869	+	7.15642i	−0.283660	+	0.238019i
$905$	−1.33750	+	1.12229i	−0.0444599	+	0.0373063i
$906$		0			0
$907$	10.1928	−	3.70989i	0.338448	−	0.123185i	−0.167205	−	0.985922i	$-0.553474\pi$
$907$	10.1928	−	3.70989i	0.338448	−	0.123185i	0.505652	+	0.862737i	$0.331252\pi$
$908$	−1.73055	−	2.99740i	−0.0574304	−	0.0994723i
$909$		0			0
$910$	−5.73783	+	9.93821i	−0.190207	+	0.329448i
$911$	−5.25553	+	29.8056i	−0.174123	+	0.987503i	0.765027	+	0.643998i	$0.222725\pi$
$911$	−5.25553	+	29.8056i	−0.174123	+	0.987503i	−0.939151	+	0.343505i	$0.888386\pi$
$912$		0			0
$913$	14.9564	+	5.44367i	0.494983	+	0.180159i
$914$	0.352921	+	2.00152i	0.0116736	+	0.0662043i
$915$		0			0
$916$	−22.1689	−	18.6019i	−0.732481	−	0.614625i
$917$	−31.8949			−1.05326
$918$		0			0
$919$	16.3492			0.539309			0.269655	−	0.962957i	$-0.413090\pi$
$919$	16.3492			0.539309			0.269655	+	0.962957i	$0.413090\pi$
$920$	−1.39053	−	1.16679i	−0.0458444	−	0.0384680i
$921$		0			0
$922$	−3.74628	−	21.2462i	−0.123377	−	0.699707i
$923$	47.0073	+	17.1093i	1.54727	+	0.563158i
$924$		0			0
$925$	5.66385	−	32.1213i	0.186226	−	1.05614i
$926$	10.8007	−	18.7073i	0.354932	−	0.614760i
$927$		0			0
$928$	0.0812519	+	0.140732i	0.00266722	+	0.00461977i
$929$	−37.4270	+	13.6223i	−1.22794	+	0.446933i	−0.872891	−	0.487915i	$-0.837758\pi$
$929$	−37.4270	+	13.6223i	−1.22794	+	0.446933i	−0.355048	+	0.934848i	$0.615535\pi$
$930$		0			0
$931$	17.4925	−	14.6779i	0.573293	−	0.481050i
$932$	5.10220	−	4.28125i	0.167128	−	0.140237i
$933$		0			0
$934$	23.0453	−	8.38782i	0.754067	−	0.274458i
$935$	−9.81996	−	17.0087i	−0.321147	−	0.556243i
$936$		0			0
$937$	−24.4124	+	42.2835i	−0.797519	+	1.38134i	0.123709	+	0.992319i	$0.460521\pi$
$937$	−24.4124	+	42.2835i	−0.797519	+	1.38134i	−0.921228	+	0.389024i	$0.872812\pi$
$938$	−2.20574	+	12.5094i	−0.0720199	+	0.408445i
$939$		0			0
$940$	−5.29813	−	1.92836i	−0.172806	−	0.0628963i
$941$	−2.19443	−	12.4452i	−0.0715364	−	0.405703i	−0.999458	−	0.0329271i	$-0.989517\pi$
$941$	−2.19443	−	12.4452i	−0.0715364	−	0.405703i	0.927921	−	0.372776i	$-0.121594\pi$
$942$		0			0
$943$	−12.1793	−	10.2197i	−0.396614	−	0.332798i
$944$	6.98545			0.227357
$945$		0			0
$946$	38.6810			1.25763
$947$	−29.1272	−	24.4406i	−0.946508	−	0.794214i	0.0321982	−	0.999482i	$-0.489749\pi$
$947$	−29.1272	−	24.4406i	−0.946508	−	0.794214i	−0.978706	+	0.205267i	$0.934194\pi$
$948$		0			0
$949$	1.49335	+	8.46924i	0.0484764	+	0.274923i
$950$	16.5633	+	6.02855i	0.537384	+	0.195592i
$951$		0			0
$952$	3.83275	−	21.7366i	0.124220	−	0.704487i
$953$	7.95353	−	13.7759i	0.257640	−	0.446245i	−0.707969	−	0.706243i	$-0.750388\pi$
$953$	7.95353	−	13.7759i	0.257640	−	0.446245i	0.965609	+	0.259998i	$0.0837218\pi$
$954$		0			0
$955$	5.76945	+	9.99298i	0.186695	+	0.323365i
$956$	7.31908	−	2.66393i	0.236716	−	0.0861575i
$957$		0			0
$958$	−10.9743	+	9.20854i	−0.354564	+	0.297514i
$959$	5.48545	−	4.60284i	0.177134	−	0.148633i
$960$		0			0
$961$	26.6088	−	9.68479i	0.858347	−	0.312413i
$962$	−14.2554	−	24.6910i	−0.459611	−	0.796070i
$963$		0			0
$964$	−10.9474	+	18.9615i	−0.352593	+	0.610709i
$965$	0.878975	−	4.98491i	0.0282952	−	0.160470i
$966$		0			0
$967$	55.5715	+	20.2264i	1.78706	+	0.650436i	0.999411	+	0.0343109i	$0.0109236\pi$
$967$	55.5715	+	20.2264i	1.78706	+	0.650436i	0.787648	+	0.616125i	$0.211299\pi$
$968$	0.307934	+	1.74638i	0.00989736	+	0.0561307i
$969$		0			0
$970$	−7.60607	−	6.38225i	−0.244216	−	0.204922i
$971$	9.68004			0.310647			0.155324	−	0.987864i	$-0.450358\pi$
$971$	9.68004			0.310647			0.155324	+	0.987864i	$0.450358\pi$
$972$		0			0
$973$	−0.583473			−0.0187053
$974$	24.7520	+	20.7694i	0.793104	+	0.665493i
$975$		0			0
$976$	−0.220285	−	1.24930i	−0.00705115	−	0.0399891i
$977$	3.25015	+	1.18296i	0.103982	+	0.0378462i	0.393487	−	0.919330i	$-0.371269\pi$
$977$	3.25015	+	1.18296i	0.103982	+	0.0378462i	−0.289505	+	0.957176i	$0.593491\pi$
$978$		0			0
$979$	5.74005	−	32.5534i	0.183453	−	1.04041i
$980$	−2.40760	+	4.17009i	−0.0769081	+	0.133209i
$981$		0			0
$982$	16.2246	+	28.1019i	0.517748	+	0.896767i
$983$	−39.5788	+	14.4055i	−1.26237	+	0.459464i	−0.884563	−	0.466421i	$-0.845543\pi$
$983$	−39.5788	+	14.4055i	−1.26237	+	0.459464i	−0.377804	+	0.925885i	$0.623321\pi$
$984$		0			0
$985$	17.9736	−	15.0816i	0.572686	−	0.480541i
$986$	0.777904	−	0.652739i	0.0247735	−	0.0207874i
$987$		0			0
$988$	14.4782	−	5.26963i	0.460612	−	0.167649i
$989$	−11.1702	−	19.3474i	−0.355193	−	0.615213i
$990$		0			0
$991$	9.26786	−	16.0524i	0.294403	−	0.509921i	−0.680443	−	0.732801i	$-0.738213\pi$
$991$	9.26786	−	16.0524i	0.294403	−	0.509921i	0.974846	+	0.222880i	$0.0715458\pi$
$992$	0.284463	−	1.61327i	0.00903170	−	0.0512213i
$993$		0			0
$994$	44.9397	+	16.3567i	1.42540	+	0.518804i
$995$	−1.62526	−	9.21729i	−0.0515241	−	0.292208i
$996$		0			0
$997$	−8.42056	−	7.06569i	−0.266682	−	0.223773i	0.499634	−	0.866237i	$-0.333468\pi$
$997$	−8.42056	−	7.06569i	−0.266682	−	0.223773i	−0.766316	+	0.642464i	$0.777912\pi$
$998$	−24.8307			−0.786002
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.e.a.379.1		6
3.2	odd	2		486.2.e.d.379.1		6
9.2	odd	6		54.2.e.a.25.1	yes	6
9.4	even	3		486.2.e.c.55.1		6
9.5	odd	6		486.2.e.b.55.1		6
9.7	even	3		162.2.e.a.73.1		6
27.2	odd	18		1458.2.c.d.973.3		6
27.4	even	9		162.2.e.a.91.1		6
27.5	odd	18		486.2.e.d.109.1		6
27.7	even	9		1458.2.a.d.1.3		3
27.11	odd	18		1458.2.c.d.487.3		6
27.13	even	9		486.2.e.c.433.1		6
27.14	odd	18		486.2.e.b.433.1		6
27.16	even	9		1458.2.c.a.487.1		6
27.20	odd	18		1458.2.a.a.1.1		3
27.22	even	9	inner	486.2.e.a.109.1		6
27.23	odd	18		54.2.e.a.13.1	✓	6
27.25	even	9		1458.2.c.a.973.1		6
36.11	even	6		432.2.u.a.241.1		6
108.23	even	18		432.2.u.a.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.a.13.1	✓	6	27.23	odd	18
54.2.e.a.25.1	yes	6	9.2	odd	6
162.2.e.a.73.1		6	9.7	even	3
162.2.e.a.91.1		6	27.4	even	9
432.2.u.a.241.1		6	36.11	even	6
432.2.u.a.337.1		6	108.23	even	18
486.2.e.a.109.1		6	27.22	even	9	inner
486.2.e.a.379.1		6	1.1	even	1	trivial
486.2.e.b.55.1		6	9.5	odd	6
486.2.e.b.433.1		6	27.14	odd	18
486.2.e.c.55.1		6	9.4	even	3
486.2.e.c.433.1		6	27.13	even	9
486.2.e.d.109.1		6	27.5	odd	18
486.2.e.d.379.1		6	3.2	odd	2
1458.2.a.a.1.1		3	27.20	odd	18
1458.2.a.d.1.3		3	27.7	even	9
1458.2.c.a.487.1		6	27.16	even	9
1458.2.c.a.973.1		6	27.25	even	9
1458.2.c.d.487.3		6	27.11	odd	18
1458.2.c.d.973.3		6	27.2	odd	18

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.173648 + 0.984808i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(-0.613341 + 3.47843i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.439693 - 0.761570i) q^{10} +(3.35844 - 1.22237i) q^{11} +(-2.83022 + 2.37484i) q^{13} +(-2.70574 + 2.27038i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(3.12449 + 5.41177i) q^{17} +(-2.08512 + 3.61154i) q^{19} +(0.152704 - 0.866025i) q^{20} +(3.35844 + 1.22237i) q^{22} +(-0.358441 - 2.03282i) q^{23} +(-3.23783 - 2.71686i) q^{25} -3.69459 q^{26} -3.53209 q^{28} +(-0.124485 - 0.104455i) q^{29} +(0.284463 + 1.61327i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(-1.08512 + 6.15403i) q^{34} +(1.55303 - 2.68993i) q^{35} +(3.85844 + 6.68302i) q^{37} +(-3.91875 + 1.42631i) q^{38} +(0.673648 - 0.565258i) q^{40} +(5.90033 - 4.95096i) q^{41} +(10.1702 - 3.70167i) q^{43} +(1.78699 + 3.09516i) q^{44} +(1.03209 - 1.78763i) q^{46} +(1.11334 - 6.31407i) q^{47} +(-5.14543 - 1.87278i) q^{49} +(-0.733956 - 4.16247i) q^{50} +(-2.83022 - 2.37484i) q^{52} -0.716881 q^{53} -3.14290 q^{55} +(-2.70574 - 2.27038i) q^{56} +(-0.0282185 - 0.160035i) q^{58} +(-6.56418 - 2.38917i) q^{59} +(-0.220285 + 1.24930i) q^{61} +(-0.819078 + 1.41868i) q^{62} +(-0.500000 - 0.866025i) q^{64} +(3.05303 - 1.11121i) q^{65} +(2.75490 - 2.31164i) q^{67} +(-4.78699 + 4.01676i) q^{68} +(2.91875 - 1.06234i) q^{70} +(-6.76991 - 11.7258i) q^{71} +(1.16385 - 2.01584i) q^{73} +(-1.34002 + 7.59964i) q^{74} +(-3.91875 - 1.42631i) q^{76} +(2.19207 + 12.4318i) q^{77} +(-5.07011 - 4.25433i) q^{79} +0.879385 q^{80} +7.70233 q^{82} +(3.41147 + 2.86257i) q^{83} +(-0.954241 - 5.41177i) q^{85} +(10.1702 + 3.70167i) q^{86} +(-0.620615 + 3.51968i) q^{88} +(4.62449 - 8.00984i) q^{89} +(-6.52481 - 11.3013i) q^{91} +(1.93969 - 0.705990i) q^{92} +(4.91147 - 4.12122i) q^{94} +(2.80928 - 2.35726i) q^{95} +(10.6099 - 3.86170i) q^{97} +(-2.73783 - 4.74205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 12 q^{11} + 6 q^{13} - 6 q^{14} + 6 q^{17} + 9 q^{19} + 3 q^{20} + 12 q^{22} + 6 q^{23} - 18 q^{26} - 12 q^{28} + 12 q^{29} + 9 q^{31} + 15 q^{34} - 3 q^{35}+ \cdots + 3 q^{98}+O(q^{100}) \) 6 * q - 6 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 12 * q^11 + 6 * q^13 - 6 * q^14 + 6 * q^17 + 9 * q^19 + 3 * q^20 + 12 * q^22 + 6 * q^23 - 18 * q^26 - 12 * q^28 + 12 * q^29 + 9 * q^31 + 15 * q^34 - 3 * q^35 + 15 * q^37 - 21 * q^38 + 3 * q^40 + 21 * q^41 + 18 * q^43 + 3 * q^44 - 3 * q^46 - 15 * q^49 - 9 * q^50 + 6 * q^52 + 12 * q^53 - 18 * q^55 - 6 * q^56 - 15 * q^58 - 21 * q^59 - 27 * q^61 + 12 * q^62 - 3 * q^64 + 6 * q^65 + 18 * q^67 - 21 * q^68 + 15 * q^70 - 12 * q^71 + 3 * q^73 + 12 * q^74 - 21 * q^76 + 24 * q^77 - 39 * q^79 - 6 * q^80 - 6 * q^82 - 36 * q^85 + 18 * q^86 - 15 * q^88 + 15 * q^89 - 12 * q^91 + 6 * q^92 + 9 * q^94 - 3 * q^95 + 15 * q^97 + 3 * q^98

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