LMFDB - Embedded newform 605.2.e.b.483.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(362,605)] 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("605.362"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.9
Character	$\chi$	$=$	605.483
Dual form			605.2.e.b.362.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.345308 + 0.345308i) q^{2} +(-0.805651 - 0.805651i) q^{3} -1.76152i q^{4} +(-2.18158 + 0.490620i) q^{5} -0.556396i q^{6} +(2.06222 + 2.06222i) q^{7} +(1.29889 - 1.29889i) q^{8} -1.70185i q^{9} +(-0.922733 - 0.583903i) q^{10} +(-1.41917 + 1.41917i) q^{12} +(2.06936 - 2.06936i) q^{13} +1.42420i q^{14} +(2.15286 + 1.36232i) q^{15} -2.62602 q^{16} +(-3.72511 - 3.72511i) q^{17} +(0.587664 - 0.587664i) q^{18} -4.09936 q^{19} +(0.864239 + 3.84291i) q^{20} -3.32285i q^{21} +(-2.12046 - 2.12046i) q^{23} -2.09290 q^{24} +(4.51858 - 2.14065i) q^{25} +1.42913 q^{26} +(-3.78805 + 3.78805i) q^{27} +(3.63264 - 3.63264i) q^{28} -2.64465 q^{29} +(0.272979 + 1.21382i) q^{30} -6.74062 q^{31} +(-3.50456 - 3.50456i) q^{32} -2.57262i q^{34} +(-5.51065 - 3.48712i) q^{35} -2.99786 q^{36} +(0.822560 - 0.822560i) q^{37} +(-1.41554 - 1.41554i) q^{38} -3.33436 q^{39} +(-2.19636 + 3.47088i) q^{40} -3.55538i q^{41} +(1.14741 - 1.14741i) q^{42} +(5.07292 - 5.07292i) q^{43} +(0.834964 + 3.71273i) q^{45} -1.46443i q^{46} +(-2.60335 + 2.60335i) q^{47} +(2.11565 + 2.11565i) q^{48} +1.50546i q^{49} +(2.29949 + 0.821119i) q^{50} +6.00228i q^{51} +(-3.64523 - 3.64523i) q^{52} +(1.04492 + 1.04492i) q^{53} -2.61609 q^{54} +5.35716 q^{56} +(3.30266 + 3.30266i) q^{57} +(-0.913219 - 0.913219i) q^{58} -1.60529i q^{59} +(2.39977 - 3.79231i) q^{60} +6.93808i q^{61} +(-2.32759 - 2.32759i) q^{62} +(3.50959 - 3.50959i) q^{63} +2.83173i q^{64} +(-3.49920 + 5.52974i) q^{65} +(1.31471 - 1.31471i) q^{67} +(-6.56188 + 6.56188i) q^{68} +3.41671i q^{69} +(-0.698741 - 3.10701i) q^{70} +2.87313 q^{71} +(-2.21051 - 2.21051i) q^{72} +(10.4665 - 10.4665i) q^{73} +0.568074 q^{74} +(-5.36502 - 1.91578i) q^{75} +7.22113i q^{76} +(-1.15138 - 1.15138i) q^{78} +15.2459 q^{79} +(5.72887 - 1.28838i) q^{80} +0.998129 q^{81} +(1.22770 - 1.22770i) q^{82} +(4.72537 - 4.72537i) q^{83} -5.85328 q^{84} +(9.95425 + 6.29902i) q^{85} +3.50344 q^{86} +(2.13066 + 2.13066i) q^{87} +11.1726i q^{89} +(-0.993717 + 1.57036i) q^{90} +8.53493 q^{91} +(-3.73525 + 3.73525i) q^{92} +(5.43059 + 5.43059i) q^{93} -1.79791 q^{94} +(8.94309 - 2.01123i) q^{95} +5.64690i q^{96} +(7.11945 - 7.11945i) q^{97} +(-0.519848 + 0.519848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48}+ \cdots + 92 q^{97}+O(q^{100}) $ 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.345308	+	0.345308i	0.244170	+	0.244170i	0.818573	−	0.574403i	$-0.194766\pi$
$2$	0.345308	+	0.345308i	0.244170	+	0.244170i	−0.574403	+	0.818573i	$0.694766\pi$
$3$	−0.805651	−	0.805651i	−0.465143	−	0.465143i	0.435194	−	0.900337i	$-0.356680\pi$
$3$	−0.805651	−	0.805651i	−0.465143	−	0.465143i	−0.900337	+	0.435194i	$0.856680\pi$
$4$		−	1.76152i		−	0.880762i
$5$	−2.18158	+	0.490620i	−0.975632	+	0.219412i
$5$	−2.18158	+	0.490620i	−0.975632	+	0.219412i
$6$		−	0.556396i		−	0.227148i
$7$	2.06222	+	2.06222i	0.779444	+	0.779444i	0.979736	−	0.200292i	$-0.0641891\pi$
$7$	2.06222	+	2.06222i	0.779444	+	0.779444i	−0.200292	+	0.979736i	$0.564189\pi$
$8$	1.29889	−	1.29889i	0.459225	−	0.459225i
$9$		−	1.70185i		−	0.567285i
$10$	−0.922733	−	0.583903i	−0.291794	−	0.184646i
$11$		0			0
$11$		0			0
$12$	−1.41917	+	1.41917i	−0.409680	+	0.409680i
$13$	2.06936	−	2.06936i	0.573937	−	0.573937i	−0.359289	−	0.933226i	$-0.616981\pi$
$13$	2.06936	−	2.06936i	0.573937	−	0.573937i	0.933226	+	0.359289i	$0.116981\pi$
$14$			1.42420i			0.380633i
$15$	2.15286	+	1.36232i	0.555866	+	0.351750i
$16$	−2.62602			−0.656504
$17$	−3.72511	−	3.72511i	−0.903473	−	0.903473i	0.0922622	−	0.995735i	$-0.470590\pi$
$17$	−3.72511	−	3.72511i	−0.903473	−	0.903473i	−0.995735	+	0.0922622i	$0.970590\pi$
$18$	0.587664	−	0.587664i	0.138514	−	0.138514i
$19$	−4.09936			−0.940459			−0.470229	−	0.882544i	$-0.655829\pi$
$19$	−4.09936			−0.940459			−0.470229	+	0.882544i	$0.655829\pi$
$20$	0.864239	+	3.84291i	0.193250	+	0.859300i
$21$		−	3.32285i		−	0.725105i
$22$		0			0
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	0.450586	−	0.892733i	$-0.351215\pi$
$23$	−2.12046	−	2.12046i	−0.442147	−	0.442147i	−0.892733	+	0.450586i	$0.851215\pi$
$24$	−2.09290			−0.427210
$25$	4.51858	−	2.14065i	0.903717	−	0.428131i
$26$	1.42913			0.280276
$27$	−3.78805	+	3.78805i	−0.729011	+	0.729011i
$28$	3.63264	−	3.63264i	0.686505	−	0.686505i
$29$	−2.64465			−0.491099			−0.245549	−	0.969384i	$-0.578968\pi$
$29$	−2.64465			−0.491099			−0.245549	+	0.969384i	$0.578968\pi$
$30$	0.272979	+	1.21382i	0.0498389	+	0.221612i
$31$	−6.74062			−1.21065			−0.605326	−	0.795978i	$-0.706957\pi$
$31$	−6.74062			−1.21065			−0.605326	+	0.795978i	$0.706957\pi$
$32$	−3.50456	−	3.50456i	−0.619524	−	0.619524i
$33$		0			0
$34$		−	2.57262i		−	0.441201i
$35$	−5.51065	−	3.48712i	−0.931470	−	0.589432i
$36$	−2.99786			−0.499643
$37$	0.822560	−	0.822560i	0.135228	−	0.135228i	−0.636253	−	0.771481i	$-0.719516\pi$
$37$	0.822560	−	0.822560i	0.135228	−	0.135228i	0.771481	+	0.636253i	$0.219516\pi$
$38$	−1.41554	−	1.41554i	−0.229632	−	0.229632i
$39$	−3.33436			−0.533925
$40$	−2.19636	+	3.47088i	−0.347276	+	0.548795i
$41$		−	3.55538i		−	0.555257i	−0.960689	−	0.277628i	$-0.910452\pi$
$41$		−	3.55538i		−	0.555257i	0.960689	−	0.277628i	$-0.0895484\pi$
$42$	1.14741	−	1.14741i	0.177049	−	0.177049i
$43$	5.07292	−	5.07292i	0.773613	−	0.773613i	−0.205123	−	0.978736i	$-0.565759\pi$
$43$	5.07292	−	5.07292i	0.773613	−	0.773613i	0.978736	+	0.205123i	$0.0657595\pi$
$44$		0			0
$45$	0.834964	+	3.71273i	0.124469	+	0.553461i
$46$		−	1.46443i		−	0.215918i
$47$	−2.60335	+	2.60335i	−0.379737	+	0.379737i	−0.871007	−	0.491270i	$-0.836533\pi$
$47$	−2.60335	+	2.60335i	−0.379737	+	0.379737i	0.491270	+	0.871007i	$0.336533\pi$
$48$	2.11565	+	2.11565i	0.305368	+	0.305368i
$49$			1.50546i			0.215066i
$50$	2.29949	+	0.821119i	0.325197	+	0.116124i
$51$			6.00228i			0.840487i
$52$	−3.64523	−	3.64523i	−0.505502	−	0.505502i
$53$	1.04492	+	1.04492i	0.143531	+	0.143531i	0.775221	−	0.631690i	$-0.217639\pi$
$53$	1.04492	+	1.04492i	0.143531	+	0.143531i	−0.631690	+	0.775221i	$0.717639\pi$
$54$	−2.61609			−0.356005
$55$		0			0
$56$	5.35716			0.715881
$57$	3.30266	+	3.30266i	0.437447	+	0.437447i
$58$	−0.913219	−	0.913219i	−0.119912	−	0.119912i
$59$		−	1.60529i		−	0.208991i	−0.994525	−	0.104495i	$-0.966677\pi$
$59$		−	1.60529i		−	0.208991i	0.994525	−	0.104495i	$-0.0333227\pi$
$60$	2.39977	−	3.79231i	0.309808	−	0.489586i
$61$			6.93808i			0.888330i	0.895945	+	0.444165i	$0.146500\pi$
$61$			6.93808i			0.888330i	−0.895945	+	0.444165i	$0.853500\pi$
$62$	−2.32759	−	2.32759i	−0.295605	−	0.295605i
$63$	3.50959	−	3.50959i	0.442167	−	0.442167i
$64$			2.83173i			0.353966i
$65$	−3.49920	+	5.52974i	−0.434023	+	0.685880i
$66$		0			0
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	−0.622223	−	0.782840i	$-0.713770\pi$
$67$	1.31471	−	1.31471i	0.160617	−	0.160617i	0.782840	+	0.622223i	$0.213770\pi$
$68$	−6.56188	+	6.56188i	−0.795744	+	0.795744i
$69$			3.41671i			0.411323i
$70$	−0.698741	−	3.10701i	−0.0835155	−	0.371358i
$71$	2.87313			0.340978			0.170489	−	0.985360i	$-0.445465\pi$
$71$	2.87313			0.340978			0.170489	+	0.985360i	$0.445465\pi$
$72$	−2.21051	−	2.21051i	−0.260512	−	0.260512i
$73$	10.4665	−	10.4665i	1.22501	−	1.22501i	0.259186	−	0.965827i	$-0.416546\pi$
$73$	10.4665	−	10.4665i	1.22501	−	1.22501i	0.965827	−	0.259186i	$-0.0834542\pi$
$74$	0.568074			0.0660372
$75$	−5.36502	−	1.91578i	−0.619499	−	0.221215i
$76$			7.22113i			0.828321i
$77$		0			0
$78$	−1.15138	−	1.15138i	−0.130368	−	0.130368i
$79$	15.2459			1.71529			0.857647	−	0.514239i	$-0.171926\pi$
$79$	15.2459			1.71529			0.857647	+	0.514239i	$0.171926\pi$
$80$	5.72887	−	1.28838i	0.640507	−	0.144045i
$81$	0.998129			0.110903
$82$	1.22770	−	1.22770i	0.135577	−	0.135577i
$83$	4.72537	−	4.72537i	0.518677	−	0.518677i	−0.398494	−	0.917171i	$-0.630467\pi$
$83$	4.72537	−	4.72537i	0.518677	−	0.518677i	0.917171	+	0.398494i	$0.130467\pi$
$84$	−5.85328			−0.638645
$85$	9.95425	+	6.29902i	1.07969	+	0.683224i
$86$	3.50344			0.377786
$87$	2.13066	+	2.13066i	0.228431	+	0.228431i
$88$		0			0
$89$			11.1726i			1.18429i	0.805830	+	0.592147i	$0.201719\pi$
$89$			11.1726i			1.18429i	−0.805830	+	0.592147i	$0.798281\pi$
$90$	−0.993717	+	1.57036i	−0.104747	+	0.165530i
$91$	8.53493			0.894704
$92$	−3.73525	+	3.73525i	−0.389427	+	0.389427i
$93$	5.43059	+	5.43059i	0.563126	+	0.563126i
$94$	−1.79791			−0.185441
$95$	8.94309	−	2.01123i	0.917542	−	0.206348i
$96$			5.64690i			0.576334i
$97$	7.11945	−	7.11945i	0.722871	−	0.722871i	−0.246318	−	0.969189i	$-0.579221\pi$
$97$	7.11945	−	7.11945i	0.722871	−	0.722871i	0.969189	+	0.246318i	$0.0792208\pi$
$98$	−0.519848	+	0.519848i	−0.0525126	+	0.0525126i
$99$		0			0
$100$	−3.77081	−	7.95960i	−0.377081	−	0.795960i
$101$		−	1.90914i		−	0.189966i	−0.995479	−	0.0949830i	$-0.969720\pi$
$101$		−	1.90914i		−	0.189966i	0.995479	−	0.0949830i	$-0.0302797\pi$
$102$	−2.07264	+	2.07264i	−0.205222	+	0.205222i
$103$	−4.36378	−	4.36378i	−0.429976	−	0.429976i	0.458644	−	0.888620i	$-0.348335\pi$
$103$	−4.36378	−	4.36378i	−0.429976	−	0.429976i	−0.888620	+	0.458644i	$0.848335\pi$
$104$		−	5.37572i		−	0.527133i
$105$	1.63026	+	7.24906i	0.159097	+	0.707436i
$106$			0.721639i			0.0700917i
$107$	0.307965	+	0.307965i	0.0297721	+	0.0297721i	0.721836	−	0.692064i	$-0.243298\pi$
$107$	0.307965	+	0.307965i	0.0297721	+	0.0297721i	−0.692064	+	0.721836i	$0.743298\pi$
$108$	6.67275	+	6.67275i	0.642085	+	0.642085i
$109$	9.46672			0.906748			0.453374	−	0.891320i	$-0.350220\pi$
$109$	9.46672			0.906748			0.453374	+	0.891320i	$0.350220\pi$
$110$		0			0
$111$	−1.32539			−0.125801
$112$	−5.41541	−	5.41541i	−0.511708	−	0.511708i
$113$	−14.3306	−	14.3306i	−1.34811	−	1.34811i	−0.887716	−	0.460391i	$-0.847709\pi$
$113$	−14.3306	−	14.3306i	−1.34811	−	1.34811i	−0.460391	−	0.887716i	$-0.652291\pi$
$114$			2.28087i			0.213623i
$115$	5.66631	+	3.58562i	0.528386	+	0.334361i
$116$			4.65861i			0.432541i
$117$	−3.52175	−	3.52175i	−0.325586	−	0.325586i
$118$	0.554319	−	0.554319i	0.0510292	−	0.0510292i
$119$		−	15.3640i		−	1.40841i
$120$	4.56582	−	1.02682i	0.416800	−	0.0937351i
$121$		0			0
$122$	−2.39578	+	2.39578i	−0.216903	+	0.216903i
$123$	−2.86439	+	2.86439i	−0.258274	+	0.258274i
$124$			11.8738i			1.06630i
$125$	−8.80741	+	6.88691i	−0.787758	+	0.615984i
$126$	2.42378			0.215928
$127$	6.66779	+	6.66779i	0.591671	+	0.591671i	0.938083	−	0.346412i	$-0.112600\pi$
$127$	6.66779	+	6.66779i	0.591671	+	0.591671i	−0.346412	+	0.938083i	$0.612600\pi$
$128$	−7.98693	+	7.98693i	−0.705952	+	0.705952i
$129$	−8.17400			−0.719681
$130$	−3.11777	+	0.701161i	−0.273446	+	0.0614959i
$131$			7.51676i			0.656743i	0.944549	+	0.328371i	$0.106500\pi$
$131$			7.51676i			0.656743i	−0.944549	+	0.328371i	$0.893500\pi$
$132$		0			0
$133$	−8.45377	−	8.45377i	−0.733035	−	0.733035i
$134$	0.907959			0.0784357
$135$	6.40545	−	10.1224i	0.551293	−	0.871200i
$136$	−9.67699			−0.829795
$137$	10.8678	−	10.8678i	0.928495	−	0.928495i	−0.0691136	−	0.997609i	$-0.522017\pi$
$137$	10.8678	−	10.8678i	0.928495	−	0.928495i	0.997609	+	0.0691136i	$0.0220171\pi$
$138$	−1.17982	+	1.17982i	−0.100433	+	0.100433i
$139$	−4.16239			−0.353049			−0.176525	−	0.984296i	$-0.556486\pi$
$139$	−4.16239			−0.353049			−0.176525	+	0.984296i	$0.556486\pi$
$140$	−6.14265	+	9.70715i	−0.519149	+	0.820404i
$141$	4.19477			0.353264
$142$	0.992116	+	0.992116i	0.0832565	+	0.0832565i
$143$		0			0
$144$			4.46910i			0.372425i
$145$	5.76951	−	1.29752i	0.479132	−	0.107753i
$146$	7.22835			0.598222
$147$	1.21288	−	1.21288i	0.100036	−	0.100036i
$148$	−1.44896	−	1.44896i	−0.119104	−	0.119104i
$149$	−17.9774			−1.47277			−0.736384	−	0.676564i	$-0.763468\pi$
$149$	−17.9774			−1.47277			−0.736384	+	0.676564i	$0.763468\pi$
$150$	−1.19105	−	2.51412i	−0.0972488	−	0.205277i
$151$			17.7922i			1.44791i	0.689849	+	0.723953i	$0.257677\pi$
$151$			17.7922i			1.44791i	−0.689849	+	0.723953i	$0.742323\pi$
$152$	−5.32460	+	5.32460i	−0.431882	+	0.431882i
$153$	−6.33960	+	6.33960i	−0.512526	+	0.512526i
$154$		0			0
$155$	14.7052	−	3.30708i	1.18115	−	0.265631i
$156$			5.87356i			0.470261i
$157$	−15.1779	+	15.1779i	−1.21133	+	1.21133i	−0.240741	+	0.970590i	$0.577390\pi$
$157$	−15.1779	+	15.1779i	−1.21133	+	1.21133i	−0.970590	+	0.240741i	$0.922610\pi$
$158$	5.26452	+	5.26452i	0.418823	+	0.418823i
$159$		−	1.68368i		−	0.133525i
$160$	9.36487	+	5.92607i	0.740358	+	0.468497i
$161$		−	8.74571i		−	0.689258i
$162$	0.344662	+	0.344662i	0.0270792	+	0.0270792i
$163$	7.37160	+	7.37160i	0.577388	+	0.577388i	0.934183	−	0.356795i	$-0.116130\pi$
$163$	7.37160	+	7.37160i	0.577388	+	0.577388i	−0.356795	+	0.934183i	$0.616130\pi$
$164$	−6.26288			−0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	7.98527	+	7.98527i	0.617919	+	0.617919i	0.944997	−	0.327078i	$-0.106064\pi$
$167$	7.98527	+	7.98527i	0.617919	+	0.617919i	−0.327078	+	0.944997i	$0.606064\pi$
$168$	−4.31600	−	4.31600i	−0.332987	−	0.332987i
$169$			4.43550i			0.341193i
$170$	1.26218	+	5.61239i	0.0968048	+	0.430450i
$171$			6.97652i			0.533508i
$172$	−8.93607	−	8.93607i	−0.681369	−	0.681369i
$173$	9.33537	−	9.33537i	0.709755	−	0.709755i	−0.256729	−	0.966483i	$-0.582645\pi$
$173$	9.33537	−	9.33537i	0.709755	−	0.709755i	0.966483	+	0.256729i	$0.0826447\pi$
$174$			1.47147i			0.111552i
$175$	13.7328	+	4.90381i	1.03810	+	0.370693i
$176$		0			0
$177$	−1.29330	+	1.29330i	−0.0972104	+	0.0972104i
$178$	−3.85799	+	3.85799i	−0.289169	+	0.289169i
$179$		−	2.22674i		−	0.166434i	−0.996531	−	0.0832172i	$-0.973480\pi$
$179$		−	2.22674i		−	0.166434i	0.996531	−	0.0832172i	$-0.0265195\pi$
$180$	6.54007	−	1.47081i	0.487468	−	0.109628i
$181$	4.33473			0.322198			0.161099	−	0.986938i	$-0.448496\pi$
$181$	4.33473			0.322198			0.161099	+	0.986938i	$0.448496\pi$
$182$	2.94718	+	2.94718i	0.218460	+	0.218460i
$183$	5.58967	−	5.58967i	0.413200	−	0.413200i
$184$	−5.50848			−0.406091
$185$	−1.39092	+	2.19805i	−0.102262	+	0.161604i
$186$			3.75045i			0.274996i
$187$		0			0
$188$	4.58586	+	4.58586i	0.334458	+	0.334458i
$189$	−15.6236			−1.13645
$190$	3.78262	+	2.39363i	0.274420	+	0.173652i
$191$	−4.07778			−0.295058			−0.147529	−	0.989058i	$-0.547132\pi$
$191$	−4.07778			−0.295058			−0.147529	+	0.989058i	$0.547132\pi$
$192$	2.28139	−	2.28139i	0.164645	−	0.164645i
$193$	14.7791	−	14.7791i	1.06382	−	1.06382i	0.0660005	−	0.997820i	$-0.478976\pi$
$193$	14.7791	−	14.7791i	1.06382	−	1.06382i	0.997820	−	0.0660005i	$-0.0210239\pi$
$194$	4.91681			0.353006
$195$	7.27418	−	1.63590i	0.520915	−	0.117149i
$196$	2.65191			0.189422
$197$	0.213782	+	0.213782i	0.0152313	+	0.0152313i	0.714681	−	0.699450i	$-0.246572\pi$
$197$	0.213782	+	0.213782i	0.0152313	+	0.0152313i	−0.699450	+	0.714681i	$0.746572\pi$
$198$		0			0
$199$		−	11.0815i		−	0.785549i	−0.919635	−	0.392775i	$-0.871515\pi$
$199$		−	11.0815i		−	0.785549i	0.919635	−	0.392775i	$-0.128485\pi$
$200$	3.08866	−	8.64959i	0.218401	−	0.611618i
$201$	−2.11839			−0.149420
$202$	0.659240	−	0.659240i	0.0463840	−	0.0463840i
$203$	−5.45383	−	5.45383i	−0.382784	−	0.382784i
$204$	10.5732			0.740269
$205$	1.74434	+	7.75634i	0.121830	+	0.541726i
$206$		−	3.01370i		−	0.209975i
$207$	−3.60872	+	3.60872i	−0.250824	+	0.250824i
$208$	−5.43417	+	5.43417i	−0.376792	+	0.376792i
$209$		0			0
$210$	−1.94022	+	3.06610i	−0.133888	+	0.211581i
$211$		−	8.85548i		−	0.609636i	−0.952411	−	0.304818i	$-0.901404\pi$
$211$		−	8.85548i		−	0.609636i	0.952411	−	0.304818i	$-0.0985957\pi$
$212$	1.84065	−	1.84065i	0.126416	−	0.126416i
$213$	−2.31474	−	2.31474i	−0.158603	−	0.158603i
$214$			0.212686i			0.0145389i
$215$	−8.57811	+	13.5559i	−0.585022	+	0.924502i
$216$			9.84049i			0.669560i
$217$	−13.9006	−	13.9006i	−0.943635	−	0.943635i
$218$	3.26894	+	3.26894i	0.221400	+	0.221400i
$219$	−16.8647			−1.13961
$220$		0			0
$221$	−15.4172			−1.03707
$222$	−0.457669	−	0.457669i	−0.0307167	−	0.0307167i
$223$	4.37149	+	4.37149i	0.292736	+	0.292736i	0.838160	−	0.545424i	$-0.183631\pi$
$223$	4.37149	+	4.37149i	0.292736	+	0.292736i	−0.545424	+	0.838160i	$0.683631\pi$
$224$		−	14.4543i		−	0.965768i
$225$	−3.64308	−	7.68997i	−0.242872	−	0.512665i
$226$		−	9.89693i		−	0.658334i
$227$	2.34527	+	2.34527i	0.155661	+	0.155661i	0.780641	−	0.624980i	$-0.214893\pi$
$227$	2.34527	+	2.34527i	0.155661	+	0.155661i	−0.624980	+	0.780641i	$0.714893\pi$
$228$	5.81771	−	5.81771i	0.385287	−	0.385287i
$229$		−	5.33997i		−	0.352875i	−0.984312	−	0.176438i	$-0.943543\pi$
$229$		−	5.33997i		−	0.352875i	0.984312	−	0.176438i	$-0.0564574\pi$
$230$	0.718477	+	3.19477i	0.0473750	+	0.210657i
$231$		0			0
$232$	−3.43509	+	3.43509i	−0.225525	+	0.225525i
$233$	−3.12418	+	3.12418i	−0.204672	+	0.204672i	−0.801998	−	0.597326i	$-0.796230\pi$
$233$	−3.12418	+	3.12418i	−0.204672	+	0.204672i	0.597326	+	0.801998i	$0.296230\pi$
$234$		−	2.43218i		−	0.158996i
$235$	4.40215	−	6.95666i	0.287165	−	0.453802i
$236$	−2.82775			−0.184071
$237$	−12.2828	−	12.2828i	−0.797856	−	0.797856i
$238$	5.30530	−	5.30530i	0.343892	−	0.343892i
$239$	10.4529			0.676141			0.338070	−	0.941121i	$-0.390226\pi$
$239$	10.4529			0.676141			0.338070	+	0.941121i	$0.390226\pi$
$240$	−5.65345	−	3.57748i	−0.364928	−	0.230926i
$241$		−	27.8579i		−	1.79449i	−0.441536	−	0.897243i	$-0.645566\pi$
$241$		−	27.8579i		−	1.79449i	0.441536	−	0.897243i	$-0.354434\pi$
$242$		0			0
$243$	10.5600	+	10.5600i	0.677425	+	0.677425i
$244$	12.2216			0.782408
$245$	−0.738609	−	3.28429i	−0.0471880	−	0.209825i
$246$	−1.97820			−0.126125
$247$	−8.48306	+	8.48306i	−0.539764	+	0.539764i
$248$	−8.75530	+	8.75530i	−0.555962	+	0.555962i
$249$	−7.61399			−0.482517
$250$	−5.41938	−	0.663162i	−0.342752	−	0.0419421i
$251$	−9.94627			−0.627803			−0.313901	−	0.949456i	$-0.601636\pi$
$251$	−9.94627			−0.627803			−0.313901	+	0.949456i	$0.601636\pi$
$252$	−6.18223	−	6.18223i	−0.389444	−	0.389444i
$253$		0			0
$254$			4.60489i			0.288936i
$255$	−2.94484	−	13.0945i	−0.184413	−	0.820006i
$256$	0.147554			0.00922214
$257$	2.99846	−	2.99846i	0.187039	−	0.187039i	−0.607376	−	0.794415i	$-0.707778\pi$
$257$	2.99846	−	2.99846i	0.187039	−	0.187039i	0.794415	+	0.607376i	$0.207778\pi$
$258$	−2.82255	−	2.82255i	−0.175724	−	0.175724i
$259$	3.39259			0.210805
$260$	9.74078	+	6.16393i	0.604097	+	0.382271i
$261$			4.50081i			0.278593i
$262$	−2.59560	+	2.59560i	−0.160357	+	0.160357i
$263$	16.1830	−	16.1830i	0.997884	−	0.997884i	−0.00211364	−	0.999998i	$-0.500673\pi$
$263$	16.1830	−	16.1830i	0.997884	−	0.997884i	0.999998	+	0.00211364i	$0.000672793\pi$
$264$		0			0
$265$	−2.79223	−	1.76692i	−0.171526	−	0.108541i
$266$		−	5.83831i		−	0.357970i
$267$	9.00122	−	9.00122i	0.550865	−	0.550865i
$268$	−2.31589	−	2.31589i	−0.141466	−	0.141466i
$269$			22.8715i			1.39450i	0.716829	+	0.697249i	$0.245593\pi$
$269$			22.8715i			1.39450i	−0.716829	+	0.697249i	$0.754407\pi$
$270$	5.70721	−	1.28351i	0.347330	−	0.0781117i
$271$			1.39034i			0.0844573i	0.999108	+	0.0422287i	$0.0134458\pi$
$271$			1.39034i			0.0844573i	−0.999108	+	0.0422287i	$0.986554\pi$
$272$	9.78221	+	9.78221i	0.593134	+	0.593134i
$273$	−6.87617	−	6.87617i	−0.416165	−	0.416165i
$274$	7.50545			0.453421
$275$		0			0
$276$	6.01861			0.362278
$277$	10.0804	+	10.0804i	0.605671	+	0.605671i	0.941812	−	0.336141i	$-0.109122\pi$
$277$	10.0804	+	10.0804i	0.605671	+	0.605671i	−0.336141	+	0.941812i	$0.609122\pi$
$278$	−1.43731	−	1.43731i	−0.0862040	−	0.0862040i
$279$			11.4716i			0.686784i
$280$	−11.6871	+	2.62833i	−0.698437	+	0.157073i
$281$		−	25.3767i		−	1.51385i	−0.653502	−	0.756925i	$-0.726701\pi$
$281$		−	25.3767i		−	1.51385i	0.653502	−	0.756925i	$-0.273299\pi$
$282$	1.44849	+	1.44849i	0.0862563	+	0.0862563i
$283$	−5.24017	+	5.24017i	−0.311496	+	0.311496i	−0.845489	−	0.533993i	$-0.820691\pi$
$283$	−5.24017	+	5.24017i	−0.311496	+	0.311496i	0.533993	+	0.845489i	$0.320691\pi$
$284$		−	5.06109i		−	0.300321i
$285$	−8.82536	−	5.58466i	−0.522769	−	0.330807i
$286$		0			0
$287$	7.33195	−	7.33195i	0.432791	−	0.432791i
$288$	−5.96424	+	5.96424i	−0.351446	+	0.351446i
$289$			10.7529i			0.632525i
$290$	2.44030	+	1.54422i	0.143300	+	0.0906795i
$291$	−11.4716			−0.672476
$292$	−18.4370	−	18.4370i	−1.07895	−	1.07895i
$293$	−10.3785	+	10.3785i	−0.606318	+	0.606318i	−0.941982	−	0.335664i	$-0.891039\pi$
$293$	−10.3785	+	10.3785i	−0.606318	+	0.606318i	0.335664	+	0.941982i	$0.391039\pi$
$294$	0.837632			0.0488517
$295$	0.787586	+	3.50206i	0.0458550	+	0.203898i
$296$		−	2.13682i		−	0.124200i
$297$		0			0
$298$	−6.20775	−	6.20775i	−0.359606	−	0.359606i
$299$	−8.77601			−0.507530
$300$	−3.37470	+	9.45061i	−0.194838	+	0.545631i
$301$	20.9229			1.20598
$302$	−6.14378	+	6.14378i	−0.353535	+	0.353535i
$303$	−1.53810	+	1.53810i	−0.0883613	+	0.0883613i
$304$	10.7650			0.617415
$305$	−3.40396	−	15.1360i	−0.194910	−	0.866684i
$306$	−4.37823			−0.250287
$307$	−0.874954	−	0.874954i	−0.0499363	−	0.0499363i	0.681698	−	0.731634i	$-0.261242\pi$
$307$	−0.874954	−	0.874954i	−0.0499363	−	0.0499363i	−0.731634	+	0.681698i	$0.761242\pi$
$308$		0			0
$309$			7.03137i			0.400001i
$310$	6.21979	+	3.93587i	0.353260	+	0.223542i
$311$	14.1469			0.802195			0.401097	−	0.916035i	$-0.368629\pi$
$311$	14.1469			0.802195			0.401097	+	0.916035i	$0.368629\pi$
$312$	−4.33095	+	4.33095i	−0.245192	+	0.245192i
$313$	−0.523010	−	0.523010i	−0.0295623	−	0.0295623i	0.692171	−	0.721733i	$-0.256654\pi$
$313$	−0.523010	−	0.523010i	−0.0295623	−	0.0295623i	−0.721733	+	0.692171i	$0.756654\pi$
$314$	−10.4821			−0.591540
$315$	−5.93458	+	9.37833i	−0.334376	+	0.528409i
$316$		−	26.8560i		−	1.51077i
$317$	12.0675	−	12.0675i	0.677781	−	0.677781i	−0.281717	−	0.959498i	$-0.590904\pi$
$317$	12.0675	−	12.0675i	0.677781	−	0.677781i	0.959498	+	0.281717i	$0.0909039\pi$
$318$	0.581389	−	0.581389i	0.0326027	−	0.0326027i
$319$		0			0
$320$	−1.38930	−	6.17765i	−0.0776644	−	0.345341i
$321$		−	0.496225i		−	0.0276966i
$322$	3.01997	−	3.01997i	0.168296	−	0.168296i
$323$	15.2706	+	15.2706i	0.849679	+	0.849679i
$324$		−	1.75823i		−	0.0976793i
$325$	4.92079	−	13.7804i	0.272957	−	0.764397i
$326$			5.09095i			0.281962i
$327$	−7.62687	−	7.62687i	−0.421767	−	0.421767i
$328$	−4.61803	−	4.61803i	−0.254988	−	0.254988i
$329$	−10.7373			−0.591967
$330$		0			0
$331$	−14.9189			−0.820016			−0.410008	−	0.912082i	$-0.634474\pi$
$331$	−14.9189			−0.820016			−0.410008	+	0.912082i	$0.634474\pi$
$332$	−8.32385	−	8.32385i	−0.456831	−	0.456831i
$333$	−1.39988	−	1.39988i	−0.0767128	−	0.0767128i
$334$			5.51476i			0.301754i
$335$	−2.22312	+	3.51316i	−0.121462	+	0.191945i
$336$			8.72586i			0.476035i
$337$	6.67335	+	6.67335i	0.363520	+	0.363520i	0.865107	−	0.501587i	$-0.167250\pi$
$337$	6.67335	+	6.67335i	0.363520	+	0.363520i	−0.501587	+	0.865107i	$0.667250\pi$
$338$	−1.53162	+	1.53162i	−0.0833089	+	0.0833089i
$339$			23.0909i			1.25412i
$340$	11.0959	−	17.5346i	0.601758	−	0.950950i
$341$		0			0
$342$	−2.40905	+	2.40905i	−0.130267	+	0.130267i
$343$	11.3309	−	11.3309i	0.611812	−	0.611812i
$344$		−	13.1783i		−	0.710525i
$345$	−1.67630	−	7.45382i	−0.0902492	−	0.401300i
$346$	6.44716			0.346601
$347$	13.6043	+	13.6043i	0.730319	+	0.730319i	0.970683	−	0.240364i	$-0.0772668\pi$
$347$	13.6043	+	13.6043i	0.730319	+	0.730319i	−0.240364	+	0.970683i	$0.577267\pi$
$348$	3.75321	−	3.75321i	0.201193	−	0.201193i
$349$	−14.8729			−0.796130			−0.398065	−	0.917357i	$-0.630318\pi$
$349$	−14.8729			−0.796130			−0.398065	+	0.917357i	$0.630318\pi$
$350$	3.04872	+	6.43537i	0.162961	+	0.343985i
$351$			15.6777i			0.836813i
$352$		0			0
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	0.752989	−	0.658033i	$-0.228611\pi$
$353$	1.78406	+	1.78406i	0.0949560	+	0.0949560i	−0.658033	+	0.752989i	$0.728611\pi$
$354$	−0.893175			−0.0474717
$355$	−6.26797	+	1.40962i	−0.332669	+	0.0748146i
$356$	19.6808			1.04308
$357$	−12.3780	+	12.3780i	−0.655113	+	0.655113i
$358$	0.768911	−	0.768911i	0.0406382	−	0.0406382i
$359$	8.49197			0.448189			0.224095	−	0.974567i	$-0.428058\pi$
$359$	8.49197			0.448189			0.224095	+	0.974567i	$0.428058\pi$
$360$	5.90693	+	3.73789i	0.311323	+	0.197004i
$361$	−2.19521			−0.115537
$362$	1.49682	+	1.49682i	0.0786711	+	0.0786711i
$363$		0			0
$364$		−	15.0345i		−	0.788021i
$365$	−17.6985	+	27.9686i	−0.926380	+	1.46395i
$366$	3.86032			0.201782
$367$	15.0115	−	15.0115i	0.783595	−	0.783595i	−0.196841	−	0.980435i	$-0.563068\pi$
$367$	15.0115	−	15.0115i	0.783595	−	0.783595i	0.980435	+	0.196841i	$0.0630682\pi$
$368$	5.56838	+	5.56838i	0.290272	+	0.290272i
$369$	−6.05073			−0.314989
$370$	−1.23930	+	0.278708i	−0.0644281	+	0.0144894i
$371$			4.30970i			0.223748i
$372$	9.56611	−	9.56611i	0.495980	−	0.495980i
$373$	2.57445	−	2.57445i	0.133300	−	0.133300i	−0.637309	−	0.770609i	$-0.719952\pi$
$373$	2.57445	−	2.57445i	0.133300	−	0.133300i	0.770609	+	0.637309i	$0.219952\pi$
$374$		0			0
$375$	12.6441	+	1.54725i	0.652940	+	0.0798995i
$376$			6.76290i			0.348770i
$377$	−5.47273	+	5.47273i	−0.281860	+	0.281860i
$378$	−5.39494	−	5.39494i	−0.277486	−	0.277486i
$379$		−	16.5828i		−	0.851802i	−0.904770	−	0.425901i	$-0.859957\pi$
$379$		−	16.5828i		−	0.851802i	0.904770	−	0.425901i	$-0.140043\pi$
$380$	−3.54283	−	15.7535i	−0.181743	−	0.808136i
$381$		−	10.7438i		−	0.550423i
$382$	−1.40809	−	1.40809i	−0.0720442	−	0.0720442i
$383$	−8.01883	−	8.01883i	−0.409743	−	0.409743i	0.471906	−	0.881649i	$-0.343566\pi$
$383$	−8.01883	−	8.01883i	−0.409743	−	0.409743i	−0.881649	+	0.471906i	$0.843566\pi$
$384$	12.8694			0.656736
$385$		0			0
$386$	10.2067			0.519505
$387$	−8.63337	−	8.63337i	−0.438859	−	0.438859i
$388$	−12.5411	−	12.5411i	−0.636677	−	0.636677i
$389$			0.817569i			0.0414524i	0.999785	+	0.0207262i	$0.00659783\pi$
$389$			0.817569i			0.0414524i	−0.999785	+	0.0207262i	$0.993402\pi$
$390$	3.07672	+	1.94694i	0.155796	+	0.0985872i
$391$			15.7979i			0.798936i
$392$	1.95542	+	1.95542i	0.0987637	+	0.0987637i
$393$	6.05588	−	6.05588i	0.305479	−	0.305479i
$394$			0.147641i			0.00743806i
$395$	−33.2601	+	7.47992i	−1.67350	+	0.376356i
$396$		0			0
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	−0.344159	−	0.938911i	$-0.611836\pi$
$397$	11.8504	−	11.8504i	0.594752	−	0.594752i	0.938911	+	0.344159i	$0.111836\pi$
$398$	3.82654	−	3.82654i	0.191807	−	0.191807i
$399$			13.6216i			0.681932i
$400$	−11.8659	+	5.62139i	−0.593294	+	0.281070i
$401$	−28.4577			−1.42111			−0.710556	−	0.703641i	$-0.751556\pi$
$401$	−28.4577			−1.42111			−0.710556	+	0.703641i	$0.751556\pi$
$402$	−0.731498	−	0.731498i	−0.0364838	−	0.0364838i
$403$	−13.9488	+	13.9488i	−0.694838	+	0.694838i
$404$	−3.36299			−0.167315
$405$	−2.17750	+	0.489702i	−0.108201	+	0.0243335i
$406$		−	3.76651i		−	0.186929i
$407$		0			0
$408$	7.79627	+	7.79627i	0.385973	+	0.385973i
$409$	2.42266			0.119793			0.0598965	−	0.998205i	$-0.480923\pi$
$409$	2.42266			0.119793			0.0598965	+	0.998205i	$0.480923\pi$
$410$	−2.07599	+	3.28066i	−0.102526	+	0.162020i
$411$	−17.5112			−0.863765
$412$	−7.68691	+	7.68691i	−0.378707	+	0.378707i
$413$	3.31045	−	3.31045i	0.162896	−	0.162896i
$414$	−2.49224			−0.122487
$415$	−7.99041	+	12.6271i	−0.392234	+	0.619841i
$416$	−14.5044			−0.711135
$417$	3.35343	+	3.35343i	0.164218	+	0.164218i
$418$		0			0
$419$			16.4371i			0.803006i	0.915858	+	0.401503i	$0.131512\pi$
$419$			16.4371i			0.803006i	−0.915858	+	0.401503i	$0.868488\pi$
$420$	12.7694	−	2.87174i	0.623083	−	0.140126i
$421$	−12.4684			−0.607671			−0.303836	−	0.952724i	$-0.598267\pi$
$421$	−12.4684			−0.607671			−0.303836	+	0.952724i	$0.598267\pi$
$422$	3.05787	−	3.05787i	0.148855	−	0.148855i
$423$	4.43052	+	4.43052i	0.215419	+	0.215419i
$424$	2.71446			0.131826
$425$	−24.8064	−	8.85806i	−1.20329	−	0.429679i
$426$		−	1.59860i		−	0.0774523i
$427$	−14.3078	+	14.3078i	−0.692404	+	0.692404i
$428$	0.542488	−	0.542488i	0.0262222	−	0.0262222i
$429$		0			0
$430$	−7.64304	+	1.71886i	−0.368580	+	0.0828907i
$431$		−	19.8352i		−	0.955428i	−0.878515	−	0.477714i	$-0.841466\pi$
$431$		−	19.8352i		−	0.955428i	0.878515	−	0.477714i	$-0.158534\pi$
$432$	9.94749	−	9.94749i	0.478599	−	0.478599i
$433$	−20.2412	−	20.2412i	−0.972730	−	0.972730i	0.0269080	−	0.999638i	$-0.491434\pi$
$433$	−20.2412	−	20.2412i	−0.972730	−	0.972730i	−0.999638	+	0.0269080i	$0.991434\pi$
$434$		−	9.59999i		−	0.460814i
$435$	−5.69356	−	3.60287i	−0.272985	−	0.172744i
$436$		−	16.6759i		−	0.798629i
$437$	8.69256	+	8.69256i	0.415821	+	0.415821i
$438$	−5.82352	−	5.82352i	−0.278259	−	0.278259i
$439$	−3.12279			−0.149043			−0.0745214	−	0.997219i	$-0.523743\pi$
$439$	−3.12279			−0.149043			−0.0745214	+	0.997219i	$0.523743\pi$
$440$		0			0
$441$	2.56208			0.122004
$442$	−5.32368	−	5.32368i	−0.253222	−	0.253222i
$443$	22.4421	+	22.4421i	1.06626	+	1.06626i	0.997643	+	0.0686143i	$0.0218578\pi$
$443$	22.4421	+	22.4421i	1.06626	+	1.06626i	0.0686143	+	0.997643i	$0.478142\pi$
$444$			2.33471i			0.110800i
$445$	−5.48150	−	24.3739i	−0.259848	−	1.15544i
$446$			3.01902i			0.142955i
$447$	14.4835	+	14.4835i	0.685047	+	0.685047i
$448$	−5.83964	+	5.83964i	−0.275897	+	0.275897i
$449$			34.9946i			1.65150i	0.564038	+	0.825749i	$0.309247\pi$
$449$			34.9946i			1.65150i	−0.564038	+	0.825749i	$0.690753\pi$
$450$	1.39743	−	3.91340i	0.0658753	−	0.184479i
$451$		0			0
$452$	−25.2437	+	25.2437i	−1.18736	+	1.18736i
$453$	14.3343	−	14.3343i	0.673483	−	0.673483i
$454$			1.61968i			0.0760155i
$455$	−18.6196	+	4.18741i	−0.872902	+	0.196309i
$456$	8.57954			0.401774
$457$	3.60629	+	3.60629i	0.168695	+	0.168695i	0.786406	−	0.617710i	$-0.211940\pi$
$457$	3.60629	+	3.60629i	0.168695	+	0.168695i	−0.617710	+	0.786406i	$0.711940\pi$
$458$	1.84394	−	1.84394i	0.0861615	−	0.0861615i
$459$	28.2218			1.31728
$460$	6.31616	−	9.98134i	0.294493	−	0.465382i
$461$		−	12.4703i		−	0.580801i	−0.956905	−	0.290400i	$-0.906211\pi$
$461$		−	12.4703i		−	0.580801i	0.956905	−	0.290400i	$-0.0937885\pi$
$462$		0			0
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	0.0993669	−	0.995051i	$-0.468318\pi$
$463$	−19.2728	−	19.2728i	−0.895684	−	0.895684i	−0.995051	+	0.0993669i	$0.968318\pi$
$464$	6.94489			0.322409
$465$	−14.5116	−	9.18291i	−0.672960	−	0.425847i
$466$	−2.15761			−0.0999493
$467$	28.0672	−	28.0672i	1.29880	−	1.29880i	0.369611	−	0.929187i	$-0.379491\pi$
$467$	28.0672	−	28.0672i	1.29880	−	1.29880i	0.929187	−	0.369611i	$-0.120509\pi$
$468$	−6.20365	+	6.20365i	−0.286764	+	0.286764i
$469$	5.42242			0.250384
$470$	3.92229	−	0.882092i	0.180922	−	0.0406879i
$471$	24.4562			1.12688
$472$	−2.08508	−	2.08508i	−0.0959738	−	0.0959738i
$473$		0			0
$474$		−	8.48273i		−	0.389625i
$475$	−18.5233	+	8.77532i	−0.849908	+	0.402639i
$476$	−27.0640			−1.24048
$477$	1.77830	−	1.77830i	0.0814228	−	0.0814228i
$478$	3.60947	+	3.60947i	0.165093	+	0.165093i
$479$	38.2551			1.74792			0.873961	−	0.485996i	$-0.161543\pi$
$479$	38.2551			1.74792			0.873961	+	0.485996i	$0.161543\pi$
$480$	−2.77048	−	12.3192i	−0.126454	−	0.562290i
$481$		−	3.40435i		−	0.155225i
$482$	9.61957	−	9.61957i	0.438159	−	0.438159i
$483$	−7.04599	+	7.04599i	−0.320603	+	0.320603i
$484$		0			0
$485$	−12.0387	+	19.0246i	−0.546650	+	0.863863i
$486$			7.29292i			0.330813i
$487$	19.2186	−	19.2186i	0.870879	−	0.870879i	−0.121690	−	0.992568i	$-0.538831\pi$
$487$	19.2186	−	19.2186i	0.870879	−	0.870879i	0.992568	+	0.121690i	$0.0388312\pi$
$488$	9.01177	+	9.01177i	0.407944	+	0.407944i
$489$		−	11.8779i		−	0.537136i
$490$	0.879043	−	1.38914i	0.0397111	−	0.0627549i
$491$		−	3.97187i		−	0.179248i	−0.995976	−	0.0896241i	$-0.971433\pi$
$491$		−	3.97187i		−	0.179248i	0.995976	−	0.0896241i	$-0.0285666\pi$
$492$	5.04570	+	5.04570i	0.227478	+	0.227478i
$493$	9.85161	+	9.85161i	0.443694	+	0.443694i
$494$	−5.85854			−0.263588
$495$		0			0
$496$	17.7010			0.794798
$497$	5.92502	+	5.92502i	0.265773	+	0.265773i
$498$	−2.62917	−	2.62917i	−0.117816	−	0.117816i
$499$		−	6.42507i		−	0.287626i	−0.989605	−	0.143813i	$-0.954064\pi$
$499$		−	6.42507i		−	0.287626i	0.989605	−	0.143813i	$-0.0459363\pi$
$500$	12.1315	+	15.5145i	0.542536	+	0.693828i
$501$		−	12.8667i		−	0.574841i
$502$	−3.43453	−	3.43453i	−0.153291	−	0.153291i
$503$	−28.7982	+	28.7982i	−1.28405	+	1.28405i	−0.345703	+	0.938344i	$0.612360\pi$
$503$	−28.7982	+	28.7982i	−1.28405	+	1.28405i	−0.938344	+	0.345703i	$0.887640\pi$
$504$		−	9.11711i		−	0.406108i
$505$	0.936660	+	4.16493i	0.0416808	+	0.185337i
$506$		0			0
$507$	3.57347	−	3.57347i	0.158703	−	0.158703i
$508$	11.7455	−	11.7455i	0.521121	−	0.521121i
$509$		−	9.28571i		−	0.411582i	−0.978596	−	0.205791i	$-0.934023\pi$
$509$		−	9.28571i		−	0.411582i	0.978596	−	0.205791i	$-0.0659767\pi$
$510$	3.50475	−	5.53850i	0.155193	−	0.245249i
$511$	43.1684			1.90966
$512$	16.0248	+	16.0248i	0.708203	+	0.708203i
$513$	15.5286	−	15.5286i	0.685605	−	0.685605i
$514$	2.07079			0.0913386
$515$	11.6609	+	7.37899i	0.513841	+	0.325157i
$516$			14.3987i			0.633868i
$517$		0			0
$518$	1.17149	+	1.17149i	0.0514723	+	0.0514723i
$519$	−15.0421			−0.660274
$520$	2.63744	+	11.7276i	0.115659	+	0.514288i
$521$	−14.8071			−0.648710			−0.324355	−	0.945935i	$-0.605147\pi$
$521$	−14.8071			−0.648710			−0.324355	+	0.945935i	$0.605147\pi$
$522$	−1.55417	+	1.55417i	−0.0680240	+	0.0680240i
$523$	−27.4664	+	27.4664i	−1.20102	+	1.20102i	−0.227163	+	0.973857i	$0.572945\pi$
$523$	−27.4664	+	27.4664i	−1.20102	+	1.20102i	−0.973857	+	0.227163i	$0.927055\pi$
$524$	13.2410			0.578434
$525$	−7.11307	−	15.0146i	−0.310440	−	0.655290i
$526$	11.1762			0.487306
$527$	25.1096	+	25.1096i	1.09379	+	1.09379i
$528$		0			0
$529$		−	14.0073i		−	0.609011i
$530$	−0.354050	−	1.57431i	−0.0153790	−	0.0683838i
$531$	−2.73197			−0.118557
$532$	−14.8915	+	14.8915i	−0.645629	+	0.645629i
$533$	−7.35735	−	7.35735i	−0.318682	−	0.318682i
$534$	6.21639			0.269009
$535$	−0.822945	−	0.520757i	−0.0355790	−	0.0225143i
$536$		−	3.41531i		−	0.147519i
$537$	−1.79397	+	1.79397i	−0.0774157	+	0.0774157i
$538$	−7.89771	+	7.89771i	−0.340495	+	0.340495i
$539$		0			0
$540$	−17.8309	−	11.2833i	−0.767320	−	0.485558i
$541$			17.4199i			0.748942i	0.927239	+	0.374471i	$0.122176\pi$
$541$			17.4199i			0.748942i	−0.927239	+	0.374471i	$0.877824\pi$
$542$	−0.480097	+	0.480097i	−0.0206219	+	0.0206219i
$543$	−3.49228	−	3.49228i	−0.149868	−	0.149868i
$544$			26.1097i			1.11945i
$545$	−20.6524	+	4.64456i	−0.884652	+	0.198951i
$546$		−	4.74880i		−	0.203230i
$547$	27.7232	+	27.7232i	1.18536	+	1.18536i	0.978336	+	0.207025i	$0.0663781\pi$
$547$	27.7232	+	27.7232i	1.18536	+	1.18536i	0.207025	+	0.978336i	$0.433622\pi$
$548$	−19.1438	−	19.1438i	−0.817783	−	0.817783i
$549$	11.8076			0.503936
$550$		0			0
$551$	10.8414			0.461858
$552$	4.43791	+	4.43791i	0.188890	+	0.188890i
$553$	31.4402	+	31.4402i	1.33698	+	1.33698i
$554$			6.96167i			0.295773i
$555$	2.89145	−	0.650264i	0.122735	−	0.0276022i
$556$			7.33215i			0.310953i
$557$	−25.9516	−	25.9516i	−1.09961	−	1.09961i	−0.994456	−	0.105150i	$-0.966468\pi$
$557$	−25.9516	−	25.9516i	−1.09961	−	1.09961i	−0.105150	−	0.994456i	$-0.533532\pi$
$558$	−3.96122	+	3.96122i	−0.167692	+	0.167692i
$559$		−	20.9954i		−	0.888010i
$560$	14.4711	+	9.15725i	0.611514	+	0.386964i
$561$		0			0
$562$	8.76280	−	8.76280i	0.369636	−	0.369636i
$563$	−11.9367	+	11.9367i	−0.503071	+	0.503071i	−0.912391	−	0.409320i	$-0.865766\pi$
$563$	−11.9367	+	11.9367i	−0.503071	+	0.503071i	0.409320	+	0.912391i	$0.365766\pi$
$564$		−	7.38920i		−	0.311141i
$565$	38.2942	+	24.2324i	1.61105	+	1.01947i
$566$	−3.61895			−0.152116
$567$	2.05836	+	2.05836i	0.0864428	+	0.0864428i
$568$	3.73187	−	3.73187i	0.156586	−	0.156586i
$569$	−2.64882			−0.111044			−0.0555222	−	0.998457i	$-0.517682\pi$
$569$	−2.64882			−0.111044			−0.0555222	+	0.998457i	$0.517682\pi$
$570$	−1.11904	−	4.97590i	−0.0468714	−	0.208417i
$571$			29.8675i			1.24992i	0.780658	+	0.624959i	$0.214884\pi$
$571$			29.8675i			1.24992i	−0.780658	+	0.624959i	$0.785116\pi$
$572$		0			0
$573$	3.28527	+	3.28527i	0.137244	+	0.137244i
$574$	5.06357			0.211349
$575$	−14.1207	−	5.04232i	−0.588873	−	0.210279i
$576$	4.81919			0.200800
$577$	0.253778	−	0.253778i	0.0105649	−	0.0105649i	−0.701805	−	0.712370i	$-0.747622\pi$
$577$	0.253778	−	0.253778i	0.0105649	−	0.0105649i	0.712370	+	0.701805i	$0.247622\pi$
$578$	−3.71307	+	3.71307i	−0.154444	+	0.154444i
$579$	−23.8135			−0.989656
$580$	−2.28561	−	10.1631i	−0.0949047	−	0.422001i
$581$	19.4895			0.808559
$582$	−3.96123	−	3.96123i	−0.164198	−	0.164198i
$583$		0			0
$584$		−	27.1896i		−	1.12511i
$585$	9.41082	+	5.95514i	0.389089	+	0.246215i
$586$	−7.16755			−0.296089
$587$	−18.2766	+	18.2766i	−0.754355	+	0.754355i	−0.975289	−	0.220934i	$-0.929090\pi$
$587$	−18.2766	+	18.2766i	−0.754355	+	0.754355i	0.220934	+	0.975289i	$0.429090\pi$
$588$	−2.13651	−	2.13651i	−0.0881082	−	0.0881082i
$589$	27.6323			1.13857
$590$	−0.937331	+	1.48125i	−0.0385893	+	0.0609821i
$591$		−	0.344467i		−	0.0141695i
$592$	−2.16006	+	2.16006i	−0.0887778	+	0.0887778i
$593$	−9.56872	+	9.56872i	−0.392940	+	0.392940i	−0.875734	−	0.482794i	$-0.839622\pi$
$593$	−9.56872	+	9.56872i	−0.392940	+	0.392940i	0.482794	+	0.875734i	$0.339622\pi$
$594$		0			0
$595$	7.53787	+	33.5177i	0.309022	+	1.37409i
$596$			31.6677i			1.29716i
$597$	−8.92784	+	8.92784i	−0.365392	+	0.365392i
$598$	−3.03043	−	3.03043i	−0.123923	−	0.123923i
$599$			11.3229i			0.462640i	0.972878	+	0.231320i	$0.0743045\pi$
$599$			11.3229i			0.462640i	−0.972878	+	0.231320i	$0.925696\pi$
$600$	−9.45692	+	4.48016i	−0.386077	+	0.182902i
$601$			16.4892i			0.672609i	0.941753	+	0.336304i	$0.109177\pi$
$601$			16.4892i			0.672609i	−0.941753	+	0.336304i	$0.890823\pi$
$602$	7.22485	+	7.22485i	0.294463	+	0.294463i
$603$	−2.23744	−	2.23744i	−0.0911157	−	0.0911157i
$604$	31.3413			1.27526
$605$		0			0
$606$	−1.06223			−0.0431503
$607$	3.52447	+	3.52447i	0.143054	+	0.143054i	0.775007	−	0.631953i	$-0.217746\pi$
$607$	3.52447	+	3.52447i	0.143054	+	0.143054i	−0.631953	+	0.775007i	$0.717746\pi$
$608$	14.3665	+	14.3665i	0.582637	+	0.582637i
$609$			8.78777i			0.356098i
$610$	4.05116	−	6.40199i	0.164027	−	0.259209i
$611$			10.7745i			0.435890i
$612$	11.1674	+	11.1674i	0.451414	+	0.451414i
$613$	−12.9257	+	12.9257i	−0.522063	+	0.522063i	−0.918194	−	0.396131i	$-0.870352\pi$
$613$	−12.9257	+	12.9257i	−0.522063	+	0.522063i	0.396131	+	0.918194i	$0.370352\pi$
$614$		−	0.604258i		−	0.0243859i
$615$	4.84357	−	7.65423i	0.195312	−	0.308648i
$616$		0			0
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	−0.322721	−	0.946494i	$-0.604598\pi$
$617$	15.4942	−	15.4942i	0.623773	−	0.623773i	0.946494	+	0.322721i	$0.104598\pi$
$618$	−2.42799	+	2.42799i	−0.0976681	+	0.0976681i
$619$		−	49.2158i		−	1.97815i	−0.147411	−	0.989075i	$-0.547094\pi$
$619$		−	49.2158i		−	1.97815i	0.147411	−	0.989075i	$-0.452906\pi$
$620$	−5.82551	−	25.9036i	−0.233958	−	1.04031i
$621$	16.0649			0.644661
$622$	4.88503	+	4.88503i	0.195872	+	0.195872i
$623$	−23.0403	+	23.0403i	−0.923091	+	0.923091i
$624$	8.75609			0.350524
$625$	15.8352	−	19.3454i	0.633408	−	0.773818i
$626$		−	0.361199i		−	0.0144364i
$627$		0			0
$628$	26.7363	+	26.7363i	1.06689	+	1.06689i
$629$	−6.12826			−0.244350
$630$	−5.28767	+	1.18915i	−0.210666	+	0.0473771i
$631$	−9.05229			−0.360366			−0.180183	−	0.983633i	$-0.557669\pi$
$631$	−9.05229			−0.360366			−0.180183	+	0.983633i	$0.557669\pi$
$632$	19.8026	−	19.8026i	0.787706	−	0.787706i
$633$	−7.13442	+	7.13442i	−0.283568	+	0.283568i
$634$	8.33404			0.330987
$635$	−17.8177	−	11.2750i	−0.707073	−	0.447434i
$636$	−2.96584			−0.117603
$637$	3.11534	+	3.11534i	0.123434	+	0.123434i
$638$		0			0
$639$		−	4.88965i		−	0.193432i
$640$	13.5056	−	21.3427i	0.533855	−	0.843644i
$641$	−27.9282			−1.10310			−0.551549	−	0.834142i	$-0.685963\pi$
$641$	−27.9282			−1.10310			−0.551549	+	0.834142i	$0.685963\pi$
$642$	0.171351	−	0.171351i	0.00676267	−	0.00676267i
$643$	6.80902	+	6.80902i	0.268522	+	0.268522i	0.828504	−	0.559983i	$-0.189192\pi$
$643$	6.80902	+	6.80902i	0.268522	+	0.268522i	−0.559983	+	0.828504i	$0.689192\pi$
$644$	−15.4058			−0.607073
$645$	17.8322	−	4.01033i	0.702144	−	0.157907i
$646$			10.5461i			0.414932i
$647$	−21.8859	+	21.8859i	−0.860423	+	0.860423i	−0.991387	−	0.130965i	$-0.958193\pi$
$647$	−21.8859	+	21.8859i	−0.860423	+	0.860423i	0.130965	+	0.991387i	$0.458193\pi$
$648$	1.29645	−	1.29645i	0.0509296	−	0.0509296i
$649$		0			0
$650$	6.45766	−	3.05928i	0.253290	−	0.119995i
$651$			22.3981i			0.877850i
$652$	12.9853	−	12.9853i	0.508542	−	0.508542i
$653$	−4.32070	−	4.32070i	−0.169082	−	0.169082i	0.617494	−	0.786576i	$-0.288148\pi$
$653$	−4.32070	−	4.32070i	−0.169082	−	0.169082i	−0.786576	+	0.617494i	$0.788148\pi$
$654$		−	5.26724i		−	0.205965i
$655$	−3.68787	−	16.3984i	−0.144097	−	0.640739i
$656$			9.33648i			0.364528i
$657$	−17.8125	−	17.8125i	−0.694931	−	0.694931i
$658$	−3.70768	−	3.70768i	−0.144541	−	0.144541i
$659$	12.0647			0.469975			0.234988	−	0.971998i	$-0.424495\pi$
$659$	12.0647			0.469975			0.234988	+	0.971998i	$0.424495\pi$
$660$		0			0
$661$	−29.6228			−1.15219			−0.576097	−	0.817382i	$-0.695425\pi$
$661$	−29.6228			−1.15219			−0.576097	+	0.817382i	$0.695425\pi$
$662$	−5.15162	−	5.15162i	−0.200223	−	0.200223i
$663$	12.4209	+	12.4209i	0.482387	+	0.482387i
$664$		−	12.2754i		−	0.476379i
$665$	22.5902	+	14.2950i	0.876009	+	0.554336i
$666$		−	0.966779i		−	0.0374619i
$667$	5.60788	+	5.60788i	0.217138	+	0.217138i
$668$	14.0663	−	14.0663i	0.544240	−	0.544240i
$669$		−	7.04378i		−	0.272328i
$670$	−1.98079	+	0.445463i	−0.0765244	+	0.0172097i
$671$		0			0
$672$	−11.6451	+	11.6451i	−0.449220	+	0.449220i
$673$	3.56085	−	3.56085i	0.137261	−	0.137261i	−0.635138	−	0.772399i	$-0.719057\pi$
$673$	3.56085	−	3.56085i	0.137261	−	0.137261i	0.772399	+	0.635138i	$0.219057\pi$
$674$			4.60872i			0.177521i
$675$	−9.00773	+	25.2255i	−0.346708	+	0.970931i
$676$	7.81325			0.300510
$677$	25.7430	+	25.7430i	0.989383	+	0.989383i	0.999944	−	0.0105611i	$-0.00336178\pi$
$677$	25.7430	+	25.7430i	0.989383	+	0.989383i	−0.0105611	+	0.999944i	$0.503362\pi$
$678$	−7.97347	+	7.97347i	−0.306219	+	0.306219i
$679$	29.3637			1.12687
$680$	21.1111	−	4.74772i	0.809575	−	0.182067i
$681$		−	3.77894i		−	0.144809i
$682$		0			0
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	0.535567	−	0.844492i	$-0.320098\pi$
$683$	−8.07353	−	8.07353i	−0.308925	−	0.308925i	−0.844492	+	0.535567i	$0.820098\pi$
$684$	12.2893			0.469894
$685$	−18.3769	+	29.0408i	−0.702147	+	1.10959i
$686$	7.82532			0.298772
$687$	−4.30215	+	4.30215i	−0.164137	+	0.164137i
$688$	−13.3216	+	13.3216i	−0.507880	+	0.507880i
$689$	4.32463			0.164755
$690$	1.99502	−	3.15271i	0.0759493	−	0.120022i
$691$	−11.8796			−0.451920			−0.225960	−	0.974137i	$-0.572552\pi$
$691$	−11.8796			−0.451920			−0.225960	+	0.974137i	$0.572552\pi$
$692$	−16.4445	−	16.4445i	−0.625125	−	0.625125i
$693$		0			0
$694$			9.39538i			0.356644i
$695$	9.08059	−	2.04215i	0.344446	−	0.0774632i
$696$	5.53497			0.209803
$697$	−13.2442	+	13.2442i	−0.501659	+	0.501659i
$698$	−5.13574	−	5.13574i	−0.194391	−	0.194391i
$699$	5.03399			0.190403
$700$	8.63817	−	24.1906i	0.326492	−	0.914320i
$701$		−	26.5468i		−	1.00266i	−0.865256	−	0.501330i	$-0.832844\pi$
$701$		−	26.5468i		−	1.00266i	0.865256	−	0.501330i	$-0.167156\pi$
$702$	−5.41363	+	5.41363i	−0.204324	+	0.204324i
$703$	−3.37197	+	3.37197i	−0.127176	+	0.127176i
$704$		0			0
$705$	−9.15124	+	2.05804i	−0.344655	+	0.0775102i
$706$			1.23210i			0.0463708i
$707$	3.93705	−	3.93705i	0.148068	−	0.148068i
$708$	2.27818	+	2.27818i	0.0856193	+	0.0856193i
$709$		−	17.8609i		−	0.670781i	−0.942079	−	0.335390i	$-0.891132\pi$
$709$		−	17.8609i		−	0.670781i	0.942079	−	0.335390i	$-0.108868\pi$
$710$	−2.65113	−	1.67763i	−0.0994952	−	0.0629603i
$711$		−	25.9462i		−	0.973060i
$712$	14.5119	+	14.5119i	0.543858	+	0.543858i
$713$	14.2933	+	14.2933i	0.535286	+	0.535286i
$714$	−8.54844			−0.319917
$715$		0			0
$716$	−3.92246			−0.146589
$717$	−8.42137	−	8.42137i	−0.314502	−	0.314502i
$718$	2.93235	+	2.93235i	0.109434	+	0.109434i
$719$		−	32.7646i		−	1.22191i	−0.791665	−	0.610956i	$-0.790785\pi$
$719$		−	32.7646i		−	1.22191i	0.791665	−	0.610956i	$-0.209215\pi$
$720$	−2.19263	−	9.74970i	−0.0817144	−	0.363350i
$721$		−	17.9981i		−	0.670285i
$722$	−0.758024	−	0.758024i	−0.0282107	−	0.0282107i
$723$	−22.4438	+	22.4438i	−0.834692	+	0.834692i
$724$		−	7.63574i		−	0.283780i
$725$	−11.9501	+	5.66127i	−0.443814	+	0.210254i
$726$		0			0
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	−0.688987	−	0.724773i	$-0.741944\pi$
$727$	0.964903	−	0.964903i	0.0357863	−	0.0357863i	0.724773	+	0.688987i	$0.241944\pi$
$728$	11.0859	−	11.0859i	0.410871	−	0.410871i
$729$		−	20.0097i		−	0.741102i
$730$	−15.7692	+	3.54637i	−0.583645	+	0.131257i
$731$	−37.7944			−1.39788
$732$	−9.84634	−	9.84634i	−0.363931	−	0.363931i
$733$	−8.33913	+	8.33913i	−0.308013	+	0.308013i	−0.844138	−	0.536125i	$-0.819887\pi$
$733$	−8.33913	+	8.33913i	−0.308013	+	0.308013i	0.536125	+	0.844138i	$0.319887\pi$
$734$	10.3672			0.382660
$735$	−2.05093	+	3.24105i	−0.0756495	+	0.119548i
$736$			14.8626i			0.547842i
$737$		0			0
$738$	−2.08937	−	2.08937i	−0.0769107	−	0.0769107i
$739$	−43.0948			−1.58527			−0.792635	−	0.609697i	$-0.791291\pi$
$739$	−43.0948			−1.58527			−0.792635	+	0.609697i	$0.791291\pi$
$740$	3.87191	+	2.45013i	0.142334	+	0.0900687i
$741$	13.6688			0.502135
$742$	−1.48817	+	1.48817i	−0.0546326	+	0.0546326i
$743$	26.8092	−	26.8092i	0.983534	−	0.983534i	−0.0163324	−	0.999867i	$-0.505199\pi$
$743$	26.8092	−	26.8092i	0.983534	−	0.983534i	0.999867	+	0.0163324i	$0.00519900\pi$
$744$	14.1074			0.517203
$745$	39.2192	−	8.82008i	1.43688	−	0.323143i
$746$	1.77796			0.0650958
$747$	−8.04189	−	8.04189i	−0.294237	−	0.294237i
$748$		0			0
$749$			1.27018i			0.0464114i
$750$	3.83185	+	4.90040i	0.139919	+	0.178937i
$751$	34.9112			1.27393			0.636963	−	0.770894i	$-0.280190\pi$
$751$	34.9112			1.27393			0.636963	+	0.770894i	$0.280190\pi$
$752$	6.83643	−	6.83643i	0.249299	−	0.249299i
$753$	8.01322	+	8.01322i	0.292018	+	0.292018i
$754$	−3.77956			−0.137643
$755$	−8.72919	−	38.8150i	−0.317688	−	1.41262i
$756$			27.5213i			1.00094i
$757$	−24.3781	+	24.3781i	−0.886036	+	0.886036i	−0.994140	−	0.108104i	$-0.965522\pi$
$757$	−24.3781	+	24.3781i	−0.886036	+	0.886036i	0.108104	+	0.994140i	$0.465522\pi$
$758$	5.72618	−	5.72618i	0.207984	−	0.207984i
$759$		0			0
$760$	9.00370	−	14.2284i	0.326598	−	0.516119i
$761$		−	13.9146i		−	0.504403i	−0.967675	−	0.252201i	$-0.918845\pi$
$761$		−	13.9146i		−	0.504403i	0.967675	−	0.252201i	$-0.0811546\pi$
$762$	3.70993	−	3.70993i	0.134397	−	0.134397i
$763$	19.5224	+	19.5224i	0.706759	+	0.706759i
$764$			7.18311i			0.259876i
$765$	10.7200	−	16.9407i	0.387583	−	0.612491i
$766$		−	5.53793i		−	0.200094i
$767$	−3.32192	−	3.32192i	−0.119947	−	0.119947i
$768$	−0.118877	−	0.118877i	−0.00428961	−	0.00428961i
$769$	−13.3273			−0.480596			−0.240298	−	0.970699i	$-0.577245\pi$
$769$	−13.3273			−0.480596			−0.240298	+	0.970699i	$0.577245\pi$
$770$		0			0
$771$	−4.83143			−0.174000
$772$	−26.0337	−	26.0337i	−0.936973	−	0.936973i
$773$	8.83857	+	8.83857i	0.317901	+	0.317901i	0.847961	−	0.530059i	$-0.177830\pi$
$773$	8.83857	+	8.83857i	0.317901	+	0.317901i	−0.530059	+	0.847961i	$0.677830\pi$
$774$		−	5.96235i		−	0.214312i
$775$	−30.4581	+	14.4293i	−1.09409	+	0.518317i
$776$		−	18.4947i		−	0.663921i
$777$	−2.73324	−	2.73324i	−0.0980546	−	0.0980546i
$778$	−0.282313	+	0.282313i	−0.0101214	+	0.0101214i
$779$			14.5748i			0.522196i
$780$	−2.88168	−	12.8136i	−0.103181	−	0.458802i
$781$		0			0
$782$	−5.45516	+	5.45516i	−0.195076	+	0.195076i
$783$	10.0181	−	10.0181i	0.358016	−	0.358016i
$784$		−	3.95337i		−	0.141192i
$785$	25.6653	−	40.5584i	0.916033	−	1.44759i
$786$	4.18229			0.149177
$787$	4.44966	+	4.44966i	0.158613	+	0.158613i	0.781952	−	0.623339i	$-0.214224\pi$
$787$	4.44966	+	4.44966i	0.158613	+	0.158613i	−0.623339	+	0.781952i	$0.714224\pi$
$788$	0.376582	−	0.376582i	0.0134152	−	0.0134152i
$789$	−26.0756			−0.928317
$790$	−14.0679	−	8.90210i	−0.500512	−	0.316722i
$791$		−	59.1055i		−	2.10155i
$792$		0			0
$793$	14.3574	+	14.3574i	0.509846	+	0.509846i
$794$	8.18405			0.290441
$795$	0.826047	+	3.67308i	0.0292969	+	0.130271i
$796$	−19.5204			−0.691882
$797$	1.25057	−	1.25057i	0.0442976	−	0.0442976i	−0.684611	−	0.728909i	$-0.740028\pi$
$797$	1.25057	−	1.25057i	0.0442976	−	0.0442976i	0.728909	+	0.684611i	$0.240028\pi$
$798$	−4.70364	+	4.70364i	−0.166507	+	0.166507i
$799$	19.3955			0.686164
$800$	−23.3377	−	8.33359i	−0.825111	−	0.294637i
$801$	19.0141			0.671832
$802$	−9.82669	−	9.82669i	−0.346992	−	0.346992i
$803$		0			0
$804$			3.73160i			0.131603i
$805$	4.29082	+	19.0795i	0.151231	+	0.672463i
$806$	−9.63325			−0.339317
$807$	18.4264	−	18.4264i	0.648641	−	0.648641i
$808$	−2.47975	−	2.47975i	−0.0872372	−	0.0872372i
$809$	−18.4537			−0.648799			−0.324399	−	0.945920i	$-0.605162\pi$
$809$	−18.4537			−0.648799			−0.324399	+	0.945920i	$0.605162\pi$
$810$	−0.921006	−	0.582810i	−0.0323609	−	0.0204779i
$811$		−	13.0441i		−	0.458042i	−0.973421	−	0.229021i	$-0.926448\pi$
$811$		−	13.0441i		−	0.458042i	0.973421	−	0.229021i	$-0.0735525\pi$
$812$	−9.60706	+	9.60706i	−0.337142	+	0.337142i
$813$	1.12013	−	1.12013i	0.0392847	−	0.0392847i
$814$		0			0
$815$	−19.6984	−	12.4651i	−0.690004	−	0.436633i
$816$		−	15.7621i		−	0.551783i
$817$	−20.7958	+	20.7958i	−0.727551	+	0.727551i
$818$	0.836566	+	0.836566i	0.0292498	+	0.0292498i
$819$		−	14.5252i		−	0.507552i
$820$	13.6630	−	3.07270i	0.477132	−	0.107303i
$821$			26.0450i			0.908977i	0.890753	+	0.454489i	$0.150178\pi$
$821$			26.0450i			0.908977i	−0.890753	+	0.454489i	$0.849822\pi$
$822$	−6.04677	−	6.04677i	−0.210905	−	0.210905i
$823$	−3.55266	−	3.55266i	−0.123838	−	0.123838i	0.642472	−	0.766310i	$-0.277909\pi$
$823$	−3.55266	−	3.55266i	−0.123838	−	0.123838i	−0.766310	+	0.642472i	$0.777909\pi$
$824$	−11.3361			−0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−8.60606	−	8.60606i	−0.299262	−	0.299262i	0.541463	−	0.840725i	$-0.317871\pi$
$827$	−8.60606	−	8.60606i	−0.299262	−	0.299262i	−0.840725	+	0.541463i	$0.817871\pi$
$828$	6.35685	+	6.35685i	0.220916	+	0.220916i
$829$			11.0116i			0.382449i	0.981546	+	0.191224i	$0.0612458\pi$
$829$			11.0116i			0.382449i	−0.981546	+	0.191224i	$0.938754\pi$
$830$	−7.11941	+	1.60110i	−0.247118	+	0.0555749i
$831$		−	16.2425i		−	0.563446i
$832$	5.85987	+	5.85987i	0.203154	+	0.203154i
$833$	5.60801	−	5.60801i	0.194306	−	0.194306i
$834$			2.31594i			0.0801943i
$835$	−21.3382	−	13.5028i	−0.738440	−	0.467283i
$836$		0			0
$837$	25.5338	−	25.5338i	0.882578	−	0.882578i
$838$	−5.67587	+	5.67587i	−0.196070	+	0.196070i
$839$			9.29162i			0.320782i	0.987054	+	0.160391i	$0.0512756\pi$
$839$			9.29162i			0.320782i	−0.987054	+	0.160391i	$0.948724\pi$
$840$	11.5332	+	7.29819i	0.397934	+	0.251811i
$841$	−22.0058			−0.758822
$842$	−4.30543	−	4.30543i	−0.148375	−	0.148375i
$843$	−20.4448	+	20.4448i	−0.704156	+	0.704156i
$844$	−15.5991			−0.536945
$845$	−2.17615	−	9.67641i	−0.0748617	−	0.332879i
$846$			3.05979i			0.105198i
$847$		0			0
$848$	−2.74398	−	2.74398i	−0.0942286	−	0.0942286i
$849$	8.44349			0.289780
$850$	−5.50710	−	11.6246i	−0.188892	−	0.398721i
$851$	−3.48842			−0.119582
$852$	−4.07747	+	4.07747i	−0.139692	+	0.139692i
$853$	−19.1246	+	19.1246i	−0.654813	+	0.654813i	−0.954148	−	0.299335i	$-0.903235\pi$
$853$	−19.1246	+	19.1246i	−0.654813	+	0.654813i	0.299335	+	0.954148i	$0.403235\pi$
$854$	−9.88121			−0.338128
$855$	−3.42282	−	15.2198i	−0.117058	−	0.520508i
$856$	0.800023			0.0273442
$857$	33.1497	+	33.1497i	1.13237	+	1.13237i	0.989782	+	0.142591i	$0.0455432\pi$
$857$	33.1497	+	33.1497i	1.13237	+	1.13237i	0.142591	+	0.989782i	$0.454457\pi$
$858$		0			0
$859$			47.2517i			1.61221i	0.591775	+	0.806103i	$0.298427\pi$
$859$			47.2517i			1.61221i	−0.591775	+	0.806103i	$0.701573\pi$
$860$	23.8790	+	15.1105i	0.814266	+	0.515265i
$861$	−11.8140			−0.402619
$862$	6.84926	−	6.84926i	0.233287	−	0.233287i
$863$	−11.0030	−	11.0030i	−0.374547	−	0.374547i	0.494583	−	0.869130i	$-0.335321\pi$
$863$	−11.0030	−	11.0030i	−0.374547	−	0.374547i	−0.869130	+	0.494583i	$0.835321\pi$
$864$	26.5509			0.903279
$865$	−15.7857	+	24.9460i	−0.536731	+	0.848188i
$866$		−	13.9789i		−	0.475023i
$867$	8.66310	−	8.66310i	0.294214	−	0.294214i
$868$	−24.4863	+	24.4863i	−0.831118	+	0.831118i
$869$		0			0
$870$	−0.721933	−	3.21013i	−0.0244758	−	0.108834i
$871$		−	5.44121i		−	0.184368i
$872$	12.2962	−	12.2962i	0.416401	−	0.416401i
$873$	−12.1163	−	12.1163i	−0.410074	−	0.410074i
$874$			6.00322i			0.203062i
$875$	−32.3651	−	3.96047i	−1.09414	−	0.133888i
$876$			29.7076i			1.00373i
$877$	−20.5990	−	20.5990i	−0.695579	−	0.695579i	0.267875	−	0.963454i	$-0.413679\pi$
$877$	−20.5990	−	20.5990i	−0.695579	−	0.695579i	−0.963454	+	0.267875i	$0.913679\pi$
$878$	−1.07833	−	1.07833i	−0.0363918	−	0.0363918i
$879$	16.7229			0.564048
$880$		0			0
$881$	4.18815			0.141102			0.0705512	−	0.997508i	$-0.477524\pi$
$881$	4.18815			0.141102			0.0705512	+	0.997508i	$0.477524\pi$
$882$	0.884706	+	0.884706i	0.0297896	+	0.0297896i
$883$	−32.3274	−	32.3274i	−1.08790	−	1.08790i	−0.995744	−	0.0921598i	$-0.970623\pi$
$883$	−32.3274	−	32.3274i	−1.08790	−	1.08790i	−0.0921598	−	0.995744i	$-0.529377\pi$
$884$			27.1578i			0.913414i
$885$	2.18692	−	3.45596i	0.0735125	−	0.116171i
$886$			15.4989i			0.520696i
$887$	24.3658	+	24.3658i	0.818123	+	0.818123i	0.985836	−	0.167713i	$-0.0536381\pi$
$887$	24.3658	+	24.3658i	0.818123	+	0.818123i	−0.167713	+	0.985836i	$0.553638\pi$
$888$	−1.72153	+	1.72153i	−0.0577709	+	0.0577709i
$889$			27.5008i			0.922349i
$890$	6.52371	−	10.3093i	0.218675	−	0.345569i
$891$		0			0
$892$	7.70048	−	7.70048i	0.257831	−	0.257831i
$893$	10.6721	−	10.6721i	0.357127	−	0.357127i
$894$			10.0026i			0.334536i
$895$	1.09248	+	4.85781i	0.0365177	+	0.162379i
$896$	−32.9415			−1.10050
$897$	7.07040	+	7.07040i	0.236074	+	0.236074i
$898$	−12.0839	+	12.0839i	−0.403246	+	0.403246i
$899$	17.8266			0.594550
$900$	−13.5461	+	6.41737i	−0.451536	+	0.213912i
$901$		−	7.78489i		−	0.259352i
$902$		0			0
$903$	−16.8566	−	16.8566i	−0.560951	−	0.560951i
$904$	−37.2276			−1.23817
$905$	−9.45657	+	2.12671i	−0.314347	+	0.0706941i
$906$	9.89948			0.328888
$907$	−27.2327	+	27.2327i	−0.904248	+	0.904248i	−0.995800	−	0.0915526i	$-0.970817\pi$
$907$	−27.2327	+	27.2327i	−0.904248	+	0.904248i	0.0915526	+	0.995800i	$0.470817\pi$
$908$	4.13125	−	4.13125i	0.137100	−	0.137100i
$909$	−3.24907			−0.107765
$910$	−7.87546	−	4.98357i	−0.261069	−	0.165204i
$911$	−36.8694			−1.22154			−0.610769	−	0.791809i	$-0.709139\pi$
$911$	−36.8694			−1.22154			−0.610769	+	0.791809i	$0.709139\pi$
$912$	−8.67283	−	8.67283i	−0.287186	−	0.287186i
$913$		0			0
$914$			2.49056i			0.0823805i
$915$	−9.45191	+	14.9367i	−0.312470	+	0.493792i
$916$	−9.40649			−0.310799
$917$	−15.5012	+	15.5012i	−0.511894	+	0.511894i
$918$	9.74523	+	9.74523i	0.321641	+	0.321641i
$919$	−30.4040			−1.00294			−0.501468	−	0.865176i	$-0.667206\pi$
$919$	−30.4040			−1.00294			−0.501468	+	0.865176i	$0.667206\pi$
$920$	12.0172	−	2.70257i	0.396195	−	0.0891011i
$921$			1.40981i			0.0464550i
$922$	4.30611	−	4.30611i	0.141814	−	0.141814i
$923$	5.94554	−	5.94554i	0.195700	−	0.195700i
$924$		0			0
$925$	1.95599	−	5.47762i	0.0643126	−	0.180103i
$926$		−	13.3101i		−	0.437398i
$927$	−7.42653	+	7.42653i	−0.243919	+	0.243919i
$928$	9.26832	+	9.26832i	0.304247	+	0.304247i
$929$			23.2970i			0.764350i	0.924090	+	0.382175i	$0.124825\pi$
$929$			23.2970i			0.764350i	−0.924090	+	0.382175i	$0.875175\pi$
$930$	−1.84005	−	8.18191i	−0.0603375	−	0.268295i
$931$		−	6.17144i		−	0.202261i
$932$	5.50332	+	5.50332i	0.180267	+	0.180267i
$933$	−11.3974	−	11.3974i	−0.373135	−	0.373135i
$934$	19.3837			0.634254
$935$		0			0
$936$	−9.14869			−0.299034
$937$	−5.68763	−	5.68763i	−0.185807	−	0.185807i	0.608074	−	0.793881i	$-0.291942\pi$
$937$	−5.68763	−	5.68763i	−0.185807	−	0.185807i	−0.793881	+	0.608074i	$0.791942\pi$
$938$	1.87241	+	1.87241i	0.0611363	+	0.0611363i
$939$			0.842727i			0.0275013i
$940$	−12.2543	−	7.75450i	−0.399692	−	0.252924i
$941$		−	47.8899i		−	1.56117i	−0.625051	−	0.780584i	$-0.714922\pi$
$941$		−	47.8899i		−	1.56117i	0.625051	−	0.780584i	$-0.285078\pi$
$942$	8.44493	+	8.44493i	0.275151	+	0.275151i
$943$	−7.53905	+	7.53905i	−0.245505	+	0.245505i
$944$			4.21551i			0.137203i
$945$	34.0840	−	7.66523i	1.10875	−	0.249350i
$946$		0			0
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	−0.537960	−	0.842970i	$-0.680805\pi$
$947$	9.38618	−	9.38618i	0.305010	−	0.305010i	0.842970	+	0.537960i	$0.180805\pi$
$948$	−21.6365	+	21.6365i	−0.702721	+	0.702721i
$949$		−	43.3180i		−	1.40616i
$950$	−9.42645	−	3.36607i	−0.305834	−	0.109210i
$951$	−19.4444			−0.630529
$952$	−19.9560	−	19.9560i	−0.646779	−	0.646779i
$953$	37.6508	−	37.6508i	1.21963	−	1.21963i	0.251869	−	0.967761i	$-0.418955\pi$
$953$	37.6508	−	37.6508i	1.21963	−	1.21963i	0.967761	−	0.251869i	$-0.0810453\pi$
$954$	1.22812			0.0397620
$955$	8.89601	−	2.00064i	0.287868	−	0.0647392i
$956$		−	18.4130i		−	0.595519i
$957$		0			0
$958$	13.2098	+	13.2098i	0.426790	+	0.426790i
$959$	44.8233			1.44742
$960$	−3.85773	+	6.09632i	−0.124508	+	0.196758i
$961$	14.4360			0.465677
$962$	1.17555	−	1.17555i	0.0379012	−	0.0379012i
$963$	0.524112	−	0.524112i	0.0168893	−	0.0168893i
$964$	−49.0724			−1.58052
$965$	−24.9908	+	39.4926i	−0.804482	+	1.27131i
$966$	−4.86607			−0.156563
$967$	−38.6475	−	38.6475i	−1.24282	−	1.24282i	−0.958826	−	0.283994i	$-0.908340\pi$
$967$	−38.6475	−	38.6475i	−1.24282	−	1.24282i	−0.283994	−	0.958826i	$-0.591660\pi$
$968$		0			0
$969$		−	24.6055i		−	0.790443i
$970$	−10.7264	+	2.41229i	−0.344405	+	0.0774538i
$971$	8.26997			0.265396			0.132698	−	0.991157i	$-0.457636\pi$
$971$	8.26997			0.265396			0.132698	+	0.991157i	$0.457636\pi$
$972$	18.6017	−	18.6017i	0.596650	−	0.596650i
$973$	−8.58374	−	8.58374i	−0.275182	−	0.275182i
$974$	13.2727			0.425285
$975$	−15.0666	+	7.13771i	−0.482517	+	0.228590i
$976$		−	18.2195i		−	0.583193i
$977$	38.7174	−	38.7174i	1.23868	−	1.23868i	0.278137	−	0.960541i	$-0.410283\pi$
$977$	38.7174	−	38.7174i	1.23868	−	1.23868i	0.960541	−	0.278137i	$-0.0897169\pi$
$978$	4.10153	−	4.10153i	0.131152	−	0.131152i
$979$		0			0
$980$	−5.78535	+	1.30108i	−0.184806	+	0.0415614i
$981$		−	16.1110i		−	0.514384i
$982$	1.37152	−	1.37152i	0.0437670	−	0.0437670i
$983$	9.64430	+	9.64430i	0.307606	+	0.307606i	0.843980	−	0.536375i	$-0.180207\pi$
$983$	9.64430	+	9.64430i	0.307606	+	0.307606i	−0.536375	+	0.843980i	$0.680207\pi$
$984$			7.44103i			0.237211i
$985$	−0.571268	−	0.361497i	−0.0182021	−	0.0115182i
$986$			6.80369i			0.216673i
$987$	8.65053	+	8.65053i	0.275349	+	0.275349i
$988$	14.9431	+	14.9431i	0.475404	+	0.475404i
$989$	−21.5139			−0.684102
$990$		0			0
$991$	6.43457			0.204401			0.102200	−	0.994764i	$-0.467412\pi$
$991$	6.43457			0.204401			0.102200	+	0.994764i	$0.467412\pi$
$992$	23.6229	+	23.6229i	0.750027	+	0.750027i
$993$	12.0194	+	12.0194i	0.381425	+	0.381425i
$994$			4.09191i			0.129788i
$995$	5.43682	+	24.1753i	0.172359	+	0.766407i
$996$			13.4122i			0.424983i
$997$	15.0448	+	15.0448i	0.476473	+	0.476473i	0.904002	−	0.427529i	$-0.140616\pi$
$997$	15.0448	+	15.0448i	0.476473	+	0.476473i	−0.427529	+	0.904002i	$0.640616\pi$
$998$	2.21863	−	2.21863i	0.0702295	−	0.0702295i
$999$			6.23180i			0.197165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.e.b.483.9		32
5.2	odd	4	inner	605.2.e.b.362.8		32
11.2	odd	10		605.2.m.e.403.3		32
11.3	even	5		605.2.m.c.233.3		32
11.4	even	5		605.2.m.d.578.2		32
11.5	even	5		605.2.m.e.118.2		32
11.6	odd	10		55.2.l.a.8.3	yes	32
11.7	odd	10		605.2.m.c.578.3		32
11.8	odd	10		605.2.m.d.233.2		32
11.9	even	5		55.2.l.a.18.2	yes	32
11.10	odd	2	inner	605.2.e.b.483.8		32
33.17	even	10		495.2.bj.a.118.2		32
33.20	odd	10		495.2.bj.a.73.3		32
44.31	odd	10		880.2.cm.a.513.3		32
44.39	even	10		880.2.cm.a.833.2		32
55.2	even	20		605.2.m.e.282.2		32
55.7	even	20		605.2.m.c.457.3		32
55.9	even	10		275.2.bm.b.18.3		32
55.17	even	20		55.2.l.a.52.2	yes	32
55.27	odd	20		605.2.m.e.602.3		32
55.28	even	20		275.2.bm.b.107.3		32
55.32	even	4	inner	605.2.e.b.362.9		32
55.37	odd	20		605.2.m.d.457.2		32
55.39	odd	10		275.2.bm.b.118.2		32
55.42	odd	20		55.2.l.a.7.3	✓	32
55.47	odd	20		605.2.m.c.112.3		32
55.52	even	20		605.2.m.d.112.2		32
55.53	odd	20		275.2.bm.b.7.2		32
165.17	odd	20		495.2.bj.a.217.3		32
165.152	even	20		495.2.bj.a.172.2		32
220.127	odd	20		880.2.cm.a.657.3		32
220.207	even	20		880.2.cm.a.337.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	55.42	odd	20
55.2.l.a.8.3	yes	32	11.6	odd	10
55.2.l.a.18.2	yes	32	11.9	even	5
55.2.l.a.52.2	yes	32	55.17	even	20
275.2.bm.b.7.2		32	55.53	odd	20
275.2.bm.b.18.3		32	55.9	even	10
275.2.bm.b.107.3		32	55.28	even	20
275.2.bm.b.118.2		32	55.39	odd	10
495.2.bj.a.73.3		32	33.20	odd	10
495.2.bj.a.118.2		32	33.17	even	10
495.2.bj.a.172.2		32	165.152	even	20
495.2.bj.a.217.3		32	165.17	odd	20
605.2.e.b.362.8		32	5.2	odd	4	inner
605.2.e.b.362.9		32	55.32	even	4	inner
605.2.e.b.483.8		32	11.10	odd	2	inner
605.2.e.b.483.9		32	1.1	even	1	trivial
605.2.m.c.112.3		32	55.47	odd	20
605.2.m.c.233.3		32	11.3	even	5
605.2.m.c.457.3		32	55.7	even	20
605.2.m.c.578.3		32	11.7	odd	10
605.2.m.d.112.2		32	55.52	even	20
605.2.m.d.233.2		32	11.8	odd	10
605.2.m.d.457.2		32	55.37	odd	20
605.2.m.d.578.2		32	11.4	even	5
605.2.m.e.118.2		32	11.5	even	5
605.2.m.e.282.2		32	55.2	even	20
605.2.m.e.403.3		32	11.2	odd	10
605.2.m.e.602.3		32	55.27	odd	20
880.2.cm.a.337.2		32	220.207	even	20
880.2.cm.a.513.3		32	44.31	odd	10
880.2.cm.a.657.3		32	220.127	odd	20
880.2.cm.a.833.2		32	44.39	even	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.345308 + 0.345308i) q^{2} +(-0.805651 - 0.805651i) q^{3} -1.76152i q^{4} +(-2.18158 + 0.490620i) q^{5} -0.556396i q^{6} +(2.06222 + 2.06222i) q^{7} +(1.29889 - 1.29889i) q^{8} -1.70185i q^{9} +(-0.922733 - 0.583903i) q^{10} +(-1.41917 + 1.41917i) q^{12} +(2.06936 - 2.06936i) q^{13} +1.42420i q^{14} +(2.15286 + 1.36232i) q^{15} -2.62602 q^{16} +(-3.72511 - 3.72511i) q^{17} +(0.587664 - 0.587664i) q^{18} -4.09936 q^{19} +(0.864239 + 3.84291i) q^{20} -3.32285i q^{21} +(-2.12046 - 2.12046i) q^{23} -2.09290 q^{24} +(4.51858 - 2.14065i) q^{25} +1.42913 q^{26} +(-3.78805 + 3.78805i) q^{27} +(3.63264 - 3.63264i) q^{28} -2.64465 q^{29} +(0.272979 + 1.21382i) q^{30} -6.74062 q^{31} +(-3.50456 - 3.50456i) q^{32} -2.57262i q^{34} +(-5.51065 - 3.48712i) q^{35} -2.99786 q^{36} +(0.822560 - 0.822560i) q^{37} +(-1.41554 - 1.41554i) q^{38} -3.33436 q^{39} +(-2.19636 + 3.47088i) q^{40} -3.55538i q^{41} +(1.14741 - 1.14741i) q^{42} +(5.07292 - 5.07292i) q^{43} +(0.834964 + 3.71273i) q^{45} -1.46443i q^{46} +(-2.60335 + 2.60335i) q^{47} +(2.11565 + 2.11565i) q^{48} +1.50546i q^{49} +(2.29949 + 0.821119i) q^{50} +6.00228i q^{51} +(-3.64523 - 3.64523i) q^{52} +(1.04492 + 1.04492i) q^{53} -2.61609 q^{54} +5.35716 q^{56} +(3.30266 + 3.30266i) q^{57} +(-0.913219 - 0.913219i) q^{58} -1.60529i q^{59} +(2.39977 - 3.79231i) q^{60} +6.93808i q^{61} +(-2.32759 - 2.32759i) q^{62} +(3.50959 - 3.50959i) q^{63} +2.83173i q^{64} +(-3.49920 + 5.52974i) q^{65} +(1.31471 - 1.31471i) q^{67} +(-6.56188 + 6.56188i) q^{68} +3.41671i q^{69} +(-0.698741 - 3.10701i) q^{70} +2.87313 q^{71} +(-2.21051 - 2.21051i) q^{72} +(10.4665 - 10.4665i) q^{73} +0.568074 q^{74} +(-5.36502 - 1.91578i) q^{75} +7.22113i q^{76} +(-1.15138 - 1.15138i) q^{78} +15.2459 q^{79} +(5.72887 - 1.28838i) q^{80} +0.998129 q^{81} +(1.22770 - 1.22770i) q^{82} +(4.72537 - 4.72537i) q^{83} -5.85328 q^{84} +(9.95425 + 6.29902i) q^{85} +3.50344 q^{86} +(2.13066 + 2.13066i) q^{87} +11.1726i q^{89} +(-0.993717 + 1.57036i) q^{90} +8.53493 q^{91} +(-3.73525 + 3.73525i) q^{92} +(5.43059 + 5.43059i) q^{93} -1.79791 q^{94} +(8.94309 - 2.01123i) q^{95} +5.64690i q^{96} +(7.11945 - 7.11945i) q^{97} +(-0.519848 + 0.519848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} + 8 q^{5} + 12 q^{12} - 36 q^{15} - 8 q^{16} - 64 q^{20} - 24 q^{23} + 16 q^{25} - 16 q^{27} - 8 q^{31} + 24 q^{36} + 32 q^{37} - 40 q^{38} + 60 q^{42} - 28 q^{45} - 28 q^{47} + 56 q^{48}+ \cdots + 92 q^{97}+O(q^{100}) \) 32 * q - 4 * q^3 + 8 * q^5 + 12 * q^12 - 36 * q^15 - 8 * q^16 - 64 * q^20 - 24 * q^23 + 16 * q^25 - 16 * q^27 - 8 * q^31 + 24 * q^36 + 32 * q^37 - 40 * q^38 + 60 * q^42 - 28 * q^45 - 28 * q^47 + 56 * q^48 + 116 * q^53 - 80 * q^56 - 80 * q^58 + 104 * q^60 - 8 * q^67 - 80 * q^70 + 24 * q^71 - 76 * q^75 + 60 * q^78 + 8 * q^80 + 8 * q^81 - 20 * q^82 - 40 * q^86 + 80 * q^91 + 52 * q^92 + 32 * q^93 + 92 * q^97

Introduction

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