LMFDB - Embedded newform 605.2.e.b.362.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(362,605)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			362.9
Character	$\chi$	$=$	605.362
Dual form			605.2.e.b.483.9

$q$-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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

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

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	−0.574403	−	0.818573i	$-0.694766\pi$
$2$	0.345308	−	0.345308i	0.244170	−	0.244170i	0.818573	+	0.574403i	$0.194766\pi$
$3$	−0.805651	+	0.805651i	−0.465143	+	0.465143i	−0.900337	−	0.435194i	$-0.856680\pi$
$3$	−0.805651	+	0.805651i	−0.465143	+	0.465143i	0.435194	+	0.900337i	$0.356680\pi$
$4$			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	−0.200292	−	0.979736i	$-0.564189\pi$
$7$	2.06222	−	2.06222i	0.779444	−	0.779444i	0.979736	+	0.200292i	$0.0641891\pi$
$8$	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	0.933226	−	0.359289i	$-0.116981\pi$
$13$	2.06936	+	2.06936i	0.573937	+	0.573937i	−0.359289	+	0.933226i	$0.616981\pi$
$14$		−	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	−0.995735	−	0.0922622i	$-0.970590\pi$
$17$	−3.72511	+	3.72511i	−0.903473	+	0.903473i	0.0922622	+	0.995735i	$0.470590\pi$
$18$	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	−0.892733	−	0.450586i	$-0.851215\pi$
$23$	−2.12046	+	2.12046i	−0.442147	+	0.442147i	0.450586	+	0.892733i	$0.351215\pi$
$24$	−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	0.771481	−	0.636253i	$-0.219516\pi$
$37$	0.822560	+	0.822560i	0.135228	+	0.135228i	−0.636253	+	0.771481i	$0.719516\pi$
$38$	−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	$0.0895484\pi$
$41$			3.55538i			0.555257i	−0.960689	+	0.277628i	$0.910452\pi$
$42$	1.14741	+	1.14741i	0.177049	+	0.177049i
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	0.978736	−	0.205123i	$-0.0657595\pi$
$43$	5.07292	+	5.07292i	0.773613	+	0.773613i	−0.205123	+	0.978736i	$0.565759\pi$
$44$		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	0.491270	−	0.871007i	$-0.336533\pi$
$47$	−2.60335	−	2.60335i	−0.379737	−	0.379737i	−0.871007	+	0.491270i	$0.836533\pi$
$48$	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	−0.631690	−	0.775221i	$-0.717639\pi$
$53$	1.04492	−	1.04492i	0.143531	−	0.143531i	0.775221	+	0.631690i	$0.217639\pi$
$54$	−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	$0.0333227\pi$
$59$			1.60529i			0.208991i	−0.994525	+	0.104495i	$0.966677\pi$
$60$	2.39977	+	3.79231i	0.309808	+	0.489586i
$61$		−	6.93808i		−	0.888330i	−0.895945	−	0.444165i	$-0.853500\pi$
$61$		−	6.93808i		−	0.888330i	0.895945	−	0.444165i	$-0.146500\pi$
$62$	−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	0.782840	−	0.622223i	$-0.213770\pi$
$67$	1.31471	+	1.31471i	0.160617	+	0.160617i	−0.622223	+	0.782840i	$0.713770\pi$
$68$	−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	0.965827	+	0.259186i	$0.0834542\pi$
$73$	10.4665	+	10.4665i	1.22501	+	1.22501i	0.259186	+	0.965827i	$0.416546\pi$
$74$	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	0.917171	−	0.398494i	$-0.130467\pi$
$83$	4.72537	+	4.72537i	0.518677	+	0.518677i	−0.398494	+	0.917171i	$0.630467\pi$
$84$	−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	$-0.798281\pi$
$89$		−	11.1726i		−	1.18429i	0.805830	−	0.592147i	$-0.201719\pi$
$90$	−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	0.969189	−	0.246318i	$-0.0792208\pi$
$97$	7.11945	+	7.11945i	0.722871	+	0.722871i	−0.246318	+	0.969189i	$0.579221\pi$
$98$	−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	$0.0302797\pi$
$101$			1.90914i			0.189966i	−0.995479	+	0.0949830i	$0.969720\pi$
$102$	−2.07264	−	2.07264i	−0.205222	−	0.205222i
$103$	−4.36378	+	4.36378i	−0.429976	+	0.429976i	−0.888620	−	0.458644i	$-0.848335\pi$
$103$	−4.36378	+	4.36378i	−0.429976	+	0.429976i	0.458644	+	0.888620i	$0.348335\pi$
$104$			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	−0.692064	−	0.721836i	$-0.743298\pi$
$107$	0.307965	−	0.307965i	0.0297721	−	0.0297721i	0.721836	+	0.692064i	$0.243298\pi$
$108$	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	−0.460391	+	0.887716i	$0.652291\pi$
$113$	−14.3306	+	14.3306i	−1.34811	+	1.34811i	−0.887716	+	0.460391i	$0.847709\pi$
$114$		−	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	−0.346412	−	0.938083i	$-0.612600\pi$
$127$	6.66779	−	6.66779i	0.591671	−	0.591671i	0.938083	+	0.346412i	$0.112600\pi$
$128$	−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	$-0.893500\pi$
$131$		−	7.51676i		−	0.656743i	0.944549	−	0.328371i	$-0.106500\pi$
$132$		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	0.997609	−	0.0691136i	$-0.0220171\pi$
$137$	10.8678	+	10.8678i	0.928495	+	0.928495i	−0.0691136	+	0.997609i	$0.522017\pi$
$138$	−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	$-0.742323\pi$
$151$		−	17.7922i		−	1.44791i	0.689849	−	0.723953i	$-0.257677\pi$
$152$	−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	−0.970590	−	0.240741i	$-0.922610\pi$
$157$	−15.1779	−	15.1779i	−1.21133	−	1.21133i	−0.240741	−	0.970590i	$-0.577390\pi$
$158$	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	−0.356795	−	0.934183i	$-0.616130\pi$
$163$	7.37160	−	7.37160i	0.577388	−	0.577388i	0.934183	+	0.356795i	$0.116130\pi$
$164$	−6.26288			−0.489049
$165$		0			0
$166$	3.26342			0.253290
$167$	7.98527	−	7.98527i	0.617919	−	0.617919i	−0.327078	−	0.944997i	$-0.606064\pi$
$167$	7.98527	−	7.98527i	0.617919	−	0.617919i	0.944997	+	0.327078i	$0.106064\pi$
$168$	−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	0.966483	−	0.256729i	$-0.0826447\pi$
$173$	9.33537	+	9.33537i	0.709755	+	0.709755i	−0.256729	+	0.966483i	$0.582645\pi$
$174$		−	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	$0.0265195\pi$
$179$			2.22674i			0.166434i	−0.996531	+	0.0832172i	$0.973480\pi$
$180$	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	0.997820	+	0.0660005i	$0.0210239\pi$
$193$	14.7791	+	14.7791i	1.06382	+	1.06382i	0.0660005	+	0.997820i	$0.478976\pi$
$194$	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	−0.699450	−	0.714681i	$-0.746572\pi$
$197$	0.213782	−	0.213782i	0.0152313	−	0.0152313i	0.714681	+	0.699450i	$0.246572\pi$
$198$		0			0
$199$			11.0815i			0.785549i	0.919635	+	0.392775i	$0.128485\pi$
$199$			11.0815i			0.785549i	−0.919635	+	0.392775i	$0.871515\pi$
$200$	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	$0.0985957\pi$
$211$			8.85548i			0.609636i	−0.952411	+	0.304818i	$0.901404\pi$
$212$	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	−0.545424	−	0.838160i	$-0.683631\pi$
$223$	4.37149	−	4.37149i	0.292736	−	0.292736i	0.838160	+	0.545424i	$0.183631\pi$
$224$			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	−0.624980	−	0.780641i	$-0.714893\pi$
$227$	2.34527	−	2.34527i	0.155661	−	0.155661i	0.780641	+	0.624980i	$0.214893\pi$
$228$	5.81771	+	5.81771i	0.385287	+	0.385287i
$229$			5.33997i			0.352875i	0.984312	+	0.176438i	$0.0564574\pi$
$229$			5.33997i			0.352875i	−0.984312	+	0.176438i	$0.943543\pi$
$230$	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	0.597326	−	0.801998i	$-0.296230\pi$
$233$	−3.12418	−	3.12418i	−0.204672	−	0.204672i	−0.801998	+	0.597326i	$0.796230\pi$
$234$			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	$0.354434\pi$
$241$			27.8579i			1.79449i	−0.441536	+	0.897243i	$0.645566\pi$
$242$		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	0.794415	−	0.607376i	$-0.207778\pi$
$257$	2.99846	+	2.99846i	0.187039	+	0.187039i	−0.607376	+	0.794415i	$0.707778\pi$
$258$	−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	0.999998	−	0.00211364i	$-0.000672793\pi$
$263$	16.1830	+	16.1830i	0.997884	+	0.997884i	−0.00211364	+	0.999998i	$0.500673\pi$
$264$		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	$-0.754407\pi$
$269$		−	22.8715i		−	1.39450i	0.716829	−	0.697249i	$-0.245593\pi$
$270$	5.70721	+	1.28351i	0.347330	+	0.0781117i
$271$		−	1.39034i		−	0.0844573i	−0.999108	−	0.0422287i	$-0.986554\pi$
$271$		−	1.39034i		−	0.0844573i	0.999108	−	0.0422287i	$-0.0134458\pi$
$272$	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	−0.336141	−	0.941812i	$-0.609122\pi$
$277$	10.0804	−	10.0804i	0.605671	−	0.605671i	0.941812	+	0.336141i	$0.109122\pi$
$278$	−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	$0.273299\pi$
$281$			25.3767i			1.51385i	−0.653502	+	0.756925i	$0.726701\pi$
$282$	1.44849	−	1.44849i	0.0862563	−	0.0862563i
$283$	−5.24017	−	5.24017i	−0.311496	−	0.311496i	0.533993	−	0.845489i	$-0.320691\pi$
$283$	−5.24017	−	5.24017i	−0.311496	−	0.311496i	−0.845489	+	0.533993i	$0.820691\pi$
$284$			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	0.335664	−	0.941982i	$-0.391039\pi$
$293$	−10.3785	−	10.3785i	−0.606318	−	0.606318i	−0.941982	+	0.335664i	$0.891039\pi$
$294$	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	−0.731634	−	0.681698i	$-0.761242\pi$
$307$	−0.874954	+	0.874954i	−0.0499363	+	0.0499363i	0.681698	+	0.731634i	$0.261242\pi$
$308$		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	−0.721733	−	0.692171i	$-0.756654\pi$
$313$	−0.523010	+	0.523010i	−0.0295623	+	0.0295623i	0.692171	+	0.721733i	$0.256654\pi$
$314$	−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	0.959498	−	0.281717i	$-0.0909039\pi$
$317$	12.0675	+	12.0675i	0.677781	+	0.677781i	−0.281717	+	0.959498i	$0.590904\pi$
$318$	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	−0.501587	−	0.865107i	$-0.667250\pi$
$337$	6.67335	−	6.67335i	0.363520	−	0.363520i	0.865107	+	0.501587i	$0.167250\pi$
$338$	−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	−0.240364	−	0.970683i	$-0.577267\pi$
$347$	13.6043	−	13.6043i	0.730319	−	0.730319i	0.970683	+	0.240364i	$0.0772668\pi$
$348$	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	−0.658033	−	0.752989i	$-0.728611\pi$
$353$	1.78406	−	1.78406i	0.0949560	−	0.0949560i	0.752989	+	0.658033i	$0.228611\pi$
$354$	−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	0.980435	−	0.196841i	$-0.0630682\pi$
$367$	15.0115	+	15.0115i	0.783595	+	0.783595i	−0.196841	+	0.980435i	$0.563068\pi$
$368$	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	0.770609	−	0.637309i	$-0.219952\pi$
$373$	2.57445	+	2.57445i	0.133300	+	0.133300i	−0.637309	+	0.770609i	$0.719952\pi$
$374$		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	$0.140043\pi$
$379$			16.5828i			0.851802i	−0.904770	+	0.425901i	$0.859957\pi$
$380$	−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	−0.881649	−	0.471906i	$-0.843566\pi$
$383$	−8.01883	+	8.01883i	−0.409743	+	0.409743i	0.471906	+	0.881649i	$0.343566\pi$
$384$	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	$-0.993402\pi$
$389$		−	0.817569i		−	0.0414524i	0.999785	−	0.0207262i	$-0.00659783\pi$
$390$	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	0.938911	−	0.344159i	$-0.111836\pi$
$397$	11.8504	+	11.8504i	0.594752	+	0.594752i	−0.344159	+	0.938911i	$0.611836\pi$
$398$	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	$-0.868488\pi$
$419$		−	16.4371i		−	0.803006i	0.915858	−	0.401503i	$-0.131512\pi$
$420$	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	$0.158534\pi$
$431$			19.8352i			0.955428i	−0.878515	+	0.477714i	$0.841466\pi$
$432$	9.94749	+	9.94749i	0.478599	+	0.478599i
$433$	−20.2412	+	20.2412i	−0.972730	+	0.972730i	−0.999638	−	0.0269080i	$-0.991434\pi$
$433$	−20.2412	+	20.2412i	−0.972730	+	0.972730i	0.0269080	+	0.999638i	$0.491434\pi$
$434$			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	0.0686143	−	0.997643i	$-0.478142\pi$
$443$	22.4421	−	22.4421i	1.06626	−	1.06626i	0.997643	−	0.0686143i	$-0.0218578\pi$
$444$		−	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	$-0.690753\pi$
$449$		−	34.9946i		−	1.65150i	0.564038	−	0.825749i	$-0.309247\pi$
$450$	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	−0.617710	−	0.786406i	$-0.711940\pi$
$457$	3.60629	−	3.60629i	0.168695	−	0.168695i	0.786406	+	0.617710i	$0.211940\pi$
$458$	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	$0.0937885\pi$
$461$			12.4703i			0.580801i	−0.956905	+	0.290400i	$0.906211\pi$
$462$		0			0
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	−0.995051	−	0.0993669i	$-0.968318\pi$
$463$	−19.2728	+	19.2728i	−0.895684	+	0.895684i	0.0993669	+	0.995051i	$0.468318\pi$
$464$	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	0.929187	+	0.369611i	$0.120509\pi$
$467$	28.0672	+	28.0672i	1.29880	+	1.29880i	0.369611	+	0.929187i	$0.379491\pi$
$468$	−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	0.992568	−	0.121690i	$-0.0388312\pi$
$487$	19.2186	+	19.2186i	0.870879	+	0.870879i	−0.121690	+	0.992568i	$0.538831\pi$
$488$	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	$0.0285666\pi$
$491$			3.97187i			0.179248i	−0.995976	+	0.0896241i	$0.971433\pi$
$492$	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	$0.0459363\pi$
$499$			6.42507i			0.287626i	−0.989605	+	0.143813i	$0.954064\pi$
$500$	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	−0.938344	−	0.345703i	$-0.887640\pi$
$503$	−28.7982	−	28.7982i	−1.28405	−	1.28405i	−0.345703	−	0.938344i	$-0.612360\pi$
$504$			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	$0.0659767\pi$
$509$			9.28571i			0.411582i	−0.978596	+	0.205791i	$0.934023\pi$
$510$	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	−0.973857	−	0.227163i	$-0.927055\pi$
$523$	−27.4664	−	27.4664i	−1.20102	−	1.20102i	−0.227163	−	0.973857i	$-0.572945\pi$
$524$	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	$-0.877824\pi$
$541$		−	17.4199i		−	0.748942i	0.927239	−	0.374471i	$-0.122176\pi$
$542$	−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	0.207025	−	0.978336i	$-0.433622\pi$
$547$	27.7232	−	27.7232i	1.18536	−	1.18536i	0.978336	−	0.207025i	$-0.0663781\pi$
$548$	−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	−0.105150	+	0.994456i	$0.533532\pi$
$557$	−25.9516	+	25.9516i	−1.09961	+	1.09961i	−0.994456	+	0.105150i	$0.966468\pi$
$558$	−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	0.409320	−	0.912391i	$-0.365766\pi$
$563$	−11.9367	−	11.9367i	−0.503071	−	0.503071i	−0.912391	+	0.409320i	$0.865766\pi$
$564$			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	$-0.785116\pi$
$571$		−	29.8675i		−	1.24992i	0.780658	−	0.624959i	$-0.214884\pi$
$572$		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	0.712370	−	0.701805i	$-0.247622\pi$
$577$	0.253778	+	0.253778i	0.0105649	+	0.0105649i	−0.701805	+	0.712370i	$0.747622\pi$
$578$	−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	0.220934	−	0.975289i	$-0.429090\pi$
$587$	−18.2766	−	18.2766i	−0.754355	−	0.754355i	−0.975289	+	0.220934i	$0.929090\pi$
$588$	−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	0.482794	−	0.875734i	$-0.339622\pi$
$593$	−9.56872	−	9.56872i	−0.392940	−	0.392940i	−0.875734	+	0.482794i	$0.839622\pi$
$594$		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	$-0.925696\pi$
$599$		−	11.3229i		−	0.462640i	0.972878	−	0.231320i	$-0.0743045\pi$
$600$	−9.45692	−	4.48016i	−0.386077	−	0.182902i
$601$		−	16.4892i		−	0.672609i	−0.941753	−	0.336304i	$-0.890823\pi$
$601$		−	16.4892i		−	0.672609i	0.941753	−	0.336304i	$-0.109177\pi$
$602$	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	−0.631953	−	0.775007i	$-0.717746\pi$
$607$	3.52447	−	3.52447i	0.143054	−	0.143054i	0.775007	+	0.631953i	$0.217746\pi$
$608$	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	0.396131	−	0.918194i	$-0.370352\pi$
$613$	−12.9257	−	12.9257i	−0.522063	−	0.522063i	−0.918194	+	0.396131i	$0.870352\pi$
$614$			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	0.946494	−	0.322721i	$-0.104598\pi$
$617$	15.4942	+	15.4942i	0.623773	+	0.623773i	−0.322721	+	0.946494i	$0.604598\pi$
$618$	−2.42799	−	2.42799i	−0.0976681	−	0.0976681i
$619$			49.2158i			1.97815i	0.147411	+	0.989075i	$0.452906\pi$
$619$			49.2158i			1.97815i	−0.147411	+	0.989075i	$0.547094\pi$
$620$	−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	−0.559983	−	0.828504i	$-0.689192\pi$
$643$	6.80902	−	6.80902i	0.268522	−	0.268522i	0.828504	+	0.559983i	$0.189192\pi$
$644$	−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	0.130965	−	0.991387i	$-0.458193\pi$
$647$	−21.8859	−	21.8859i	−0.860423	−	0.860423i	−0.991387	+	0.130965i	$0.958193\pi$
$648$	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	−0.786576	−	0.617494i	$-0.788148\pi$
$653$	−4.32070	+	4.32070i	−0.169082	+	0.169082i	0.617494	+	0.786576i	$0.288148\pi$
$654$			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	0.772399	−	0.635138i	$-0.219057\pi$
$673$	3.56085	+	3.56085i	0.137261	+	0.137261i	−0.635138	+	0.772399i	$0.719057\pi$
$674$		−	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	−0.0105611	−	0.999944i	$-0.503362\pi$
$677$	25.7430	−	25.7430i	0.989383	−	0.989383i	0.999944	+	0.0105611i	$0.00336178\pi$
$678$	−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	−0.844492	−	0.535567i	$-0.820098\pi$
$683$	−8.07353	+	8.07353i	−0.308925	+	0.308925i	0.535567	+	0.844492i	$0.320098\pi$
$684$	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	$0.167156\pi$
$701$			26.5468i			1.00266i	−0.865256	+	0.501330i	$0.832844\pi$
$702$	−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	$0.108868\pi$
$709$			17.8609i			0.670781i	−0.942079	+	0.335390i	$0.891132\pi$
$710$	−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	$0.209215\pi$
$719$			32.7646i			1.22191i	−0.791665	+	0.610956i	$0.790785\pi$
$720$	−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	0.724773	−	0.688987i	$-0.241944\pi$
$727$	0.964903	+	0.964903i	0.0357863	+	0.0357863i	−0.688987	+	0.724773i	$0.741944\pi$
$728$	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	0.536125	−	0.844138i	$-0.319887\pi$
$733$	−8.33913	−	8.33913i	−0.308013	−	0.308013i	−0.844138	+	0.536125i	$0.819887\pi$
$734$	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	0.999867	−	0.0163324i	$-0.00519900\pi$
$743$	26.8092	+	26.8092i	0.983534	+	0.983534i	−0.0163324	+	0.999867i	$0.505199\pi$
$744$	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	0.108104	−	0.994140i	$-0.465522\pi$
$757$	−24.3781	−	24.3781i	−0.886036	−	0.886036i	−0.994140	+	0.108104i	$0.965522\pi$
$758$	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	$0.0811546\pi$
$761$			13.9146i			0.504403i	−0.967675	+	0.252201i	$0.918845\pi$
$762$	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	−0.530059	−	0.847961i	$-0.677830\pi$
$773$	8.83857	−	8.83857i	0.317901	−	0.317901i	0.847961	+	0.530059i	$0.177830\pi$
$774$			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	−0.623339	−	0.781952i	$-0.714224\pi$
$787$	4.44966	−	4.44966i	0.158613	−	0.158613i	0.781952	+	0.623339i	$0.214224\pi$
$788$	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	0.728909	−	0.684611i	$-0.240028\pi$
$797$	1.25057	+	1.25057i	0.0442976	+	0.0442976i	−0.684611	+	0.728909i	$0.740028\pi$
$798$	−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	$0.0735525\pi$
$811$			13.0441i			0.458042i	−0.973421	+	0.229021i	$0.926448\pi$
$812$	−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	$-0.849822\pi$
$821$		−	26.0450i		−	0.908977i	0.890753	−	0.454489i	$-0.150178\pi$
$822$	−6.04677	+	6.04677i	−0.210905	+	0.210905i
$823$	−3.55266	+	3.55266i	−0.123838	+	0.123838i	−0.766310	−	0.642472i	$-0.777909\pi$
$823$	−3.55266	+	3.55266i	−0.123838	+	0.123838i	0.642472	+	0.766310i	$0.277909\pi$
$824$	−11.3361			−0.394912
$825$		0			0
$826$	2.28625			0.0795488
$827$	−8.60606	+	8.60606i	−0.299262	+	0.299262i	−0.840725	−	0.541463i	$-0.817871\pi$
$827$	−8.60606	+	8.60606i	−0.299262	+	0.299262i	0.541463	+	0.840725i	$0.317871\pi$
$828$	6.35685	−	6.35685i	0.220916	−	0.220916i
$829$		−	11.0116i		−	0.382449i	−0.981546	−	0.191224i	$-0.938754\pi$
$829$		−	11.0116i		−	0.382449i	0.981546	−	0.191224i	$-0.0612458\pi$
$830$	−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	$-0.948724\pi$
$839$		−	9.29162i		−	0.320782i	0.987054	−	0.160391i	$-0.0512756\pi$
$840$	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	0.299335	−	0.954148i	$-0.403235\pi$
$853$	−19.1246	−	19.1246i	−0.654813	−	0.654813i	−0.954148	+	0.299335i	$0.903235\pi$
$854$	−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	0.142591	−	0.989782i	$-0.454457\pi$
$857$	33.1497	−	33.1497i	1.13237	−	1.13237i	0.989782	−	0.142591i	$-0.0455432\pi$
$858$		0			0
$859$		−	47.2517i		−	1.61221i	−0.591775	−	0.806103i	$-0.701573\pi$
$859$		−	47.2517i		−	1.61221i	0.591775	−	0.806103i	$-0.298427\pi$
$860$	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	−0.869130	−	0.494583i	$-0.835321\pi$
$863$	−11.0030	+	11.0030i	−0.374547	+	0.374547i	0.494583	+	0.869130i	$0.335321\pi$
$864$	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	−0.963454	−	0.267875i	$-0.913679\pi$
$877$	−20.5990	+	20.5990i	−0.695579	+	0.695579i	0.267875	+	0.963454i	$0.413679\pi$
$878$	−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	−0.0921598	+	0.995744i	$0.529377\pi$
$883$	−32.3274	+	32.3274i	−1.08790	+	1.08790i	−0.995744	+	0.0921598i	$0.970623\pi$
$884$		−	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	−0.167713	−	0.985836i	$-0.553638\pi$
$887$	24.3658	−	24.3658i	0.818123	−	0.818123i	0.985836	+	0.167713i	$0.0536381\pi$
$888$	−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	0.0915526	−	0.995800i	$-0.470817\pi$
$907$	−27.2327	−	27.2327i	−0.904248	−	0.904248i	−0.995800	+	0.0915526i	$0.970817\pi$
$908$	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	$-0.875175\pi$
$929$		−	23.2970i		−	0.764350i	0.924090	−	0.382175i	$-0.124825\pi$
$930$	−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	−0.793881	−	0.608074i	$-0.791942\pi$
$937$	−5.68763	+	5.68763i	−0.185807	+	0.185807i	0.608074	+	0.793881i	$0.291942\pi$
$938$	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	$0.285078\pi$
$941$			47.8899i			1.56117i	−0.625051	+	0.780584i	$0.714922\pi$
$942$	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	0.842970	−	0.537960i	$-0.180805\pi$
$947$	9.38618	+	9.38618i	0.305010	+	0.305010i	−0.537960	+	0.842970i	$0.680805\pi$
$948$	−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	0.967761	+	0.251869i	$0.0810453\pi$
$953$	37.6508	+	37.6508i	1.21963	+	1.21963i	0.251869	+	0.967761i	$0.418955\pi$
$954$	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	−0.283994	+	0.958826i	$0.591660\pi$
$967$	−38.6475	+	38.6475i	−1.24282	+	1.24282i	−0.958826	+	0.283994i	$0.908340\pi$
$968$		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	0.960541	+	0.278137i	$0.0897169\pi$
$977$	38.7174	+	38.7174i	1.23868	+	1.23868i	0.278137	+	0.960541i	$0.410283\pi$
$978$	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	−0.536375	−	0.843980i	$-0.680207\pi$
$983$	9.64430	−	9.64430i	0.307606	−	0.307606i	0.843980	+	0.536375i	$0.180207\pi$
$984$		−	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	−0.427529	−	0.904002i	$-0.640616\pi$
$997$	15.0448	−	15.0448i	0.476473	−	0.476473i	0.904002	+	0.427529i	$0.140616\pi$
$998$	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.362.9		32
5.3	odd	4	inner	605.2.e.b.483.8		32
11.2	odd	10		55.2.l.a.7.3	✓	32
11.3	even	5		605.2.m.d.112.2		32
11.4	even	5		605.2.m.c.457.3		32
11.5	even	5		55.2.l.a.52.2	yes	32
11.6	odd	10		605.2.m.e.602.3		32
11.7	odd	10		605.2.m.d.457.2		32
11.8	odd	10		605.2.m.c.112.3		32
11.9	even	5		605.2.m.e.282.2		32
11.10	odd	2	inner	605.2.e.b.362.8		32
33.2	even	10		495.2.bj.a.172.2		32
33.5	odd	10		495.2.bj.a.217.3		32
44.27	odd	10		880.2.cm.a.657.3		32
44.35	even	10		880.2.cm.a.337.2		32
55.2	even	20		275.2.bm.b.18.3		32
55.3	odd	20		605.2.m.d.233.2		32
55.8	even	20		605.2.m.c.233.3		32
55.13	even	20		55.2.l.a.18.2	yes	32
55.18	even	20		605.2.m.d.578.2		32
55.24	odd	10		275.2.bm.b.7.2		32
55.27	odd	20		275.2.bm.b.118.2		32
55.28	even	20		605.2.m.e.118.2		32
55.38	odd	20		55.2.l.a.8.3	yes	32
55.43	even	4	inner	605.2.e.b.483.9		32
55.48	odd	20		605.2.m.c.578.3		32
55.49	even	10		275.2.bm.b.107.3		32
55.53	odd	20		605.2.m.e.403.3		32
165.38	even	20		495.2.bj.a.118.2		32
165.68	odd	20		495.2.bj.a.73.3		32
220.123	odd	20		880.2.cm.a.513.3		32
220.203	even	20		880.2.cm.a.833.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.7.3	✓	32	11.2	odd	10
55.2.l.a.8.3	yes	32	55.38	odd	20
55.2.l.a.18.2	yes	32	55.13	even	20
55.2.l.a.52.2	yes	32	11.5	even	5
275.2.bm.b.7.2		32	55.24	odd	10
275.2.bm.b.18.3		32	55.2	even	20
275.2.bm.b.107.3		32	55.49	even	10
275.2.bm.b.118.2		32	55.27	odd	20
495.2.bj.a.73.3		32	165.68	odd	20
495.2.bj.a.118.2		32	165.38	even	20
495.2.bj.a.172.2		32	33.2	even	10
495.2.bj.a.217.3		32	33.5	odd	10
605.2.e.b.362.8		32	11.10	odd	2	inner
605.2.e.b.362.9		32	1.1	even	1	trivial
605.2.e.b.483.8		32	5.3	odd	4	inner
605.2.e.b.483.9		32	55.43	even	4	inner
605.2.m.c.112.3		32	11.8	odd	10
605.2.m.c.233.3		32	55.8	even	20
605.2.m.c.457.3		32	11.4	even	5
605.2.m.c.578.3		32	55.48	odd	20
605.2.m.d.112.2		32	11.3	even	5
605.2.m.d.233.2		32	55.3	odd	20
605.2.m.d.457.2		32	11.7	odd	10
605.2.m.d.578.2		32	55.18	even	20
605.2.m.e.118.2		32	55.28	even	20
605.2.m.e.282.2		32	11.9	even	5
605.2.m.e.403.3		32	55.53	odd	20
605.2.m.e.602.3		32	11.6	odd	10
880.2.cm.a.337.2		32	44.35	even	10
880.2.cm.a.513.3		32	220.123	odd	20
880.2.cm.a.657.3		32	44.27	odd	10
880.2.cm.a.833.2		32	220.203	even	20

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 $\F_{q}$

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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