LMFDB - Embedded newform 648.2.t.a.253.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.32
Character	$\chi$	$=$	648.253
Dual form			648.2.t.a.397.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36295 + 0.377313i) q^{2} +(1.71527 + 1.02852i) q^{4} +(2.15975 - 2.57389i) q^{5} +(-1.78453 - 0.649515i) q^{7} +(1.94976 + 2.04901i) q^{8} +(3.91480 - 2.69319i) q^{10} +(3.21944 + 3.83678i) q^{11} +(-3.61424 - 0.637289i) q^{13} +(-2.18715 - 1.55858i) q^{14} +(1.88430 + 3.52837i) q^{16} +(1.74380 - 3.02034i) q^{17} +(2.73085 - 1.57666i) q^{19} +(6.35185 - 2.19358i) q^{20} +(2.94027 + 6.44408i) q^{22} +(2.93428 - 1.06799i) q^{23} +(-1.09215 - 6.19390i) q^{25} +(-4.68558 - 2.23229i) q^{26} +(-2.39291 - 2.94951i) q^{28} +(-6.61611 + 1.16660i) q^{29} +(0.842639 - 0.306695i) q^{31} +(1.23691 + 5.51997i) q^{32} +(3.51632 - 3.45862i) q^{34} +(-5.52592 + 3.19039i) q^{35} +(-6.21485 - 3.58815i) q^{37} +(4.31691 - 1.11852i) q^{38} +(9.48493 - 0.593099i) q^{40} +(0.341649 - 1.93759i) q^{41} +(5.36405 + 6.39263i) q^{43} +(1.57601 + 9.89237i) q^{44} +(4.40224 - 0.348476i) q^{46} +(-2.63733 - 0.959909i) q^{47} +(-2.59964 - 2.18135i) q^{49} +(0.848490 - 8.85407i) q^{50} +(-5.54394 - 4.81044i) q^{52} +9.52536i q^{53} +16.8287 q^{55} +(-2.14853 - 4.92292i) q^{56} +(-9.45760 - 0.906327i) q^{58} +(-6.13695 + 7.31373i) q^{59} +(-2.92540 + 8.03747i) q^{61} +(1.26420 - 0.100072i) q^{62} +(-0.396910 + 7.99015i) q^{64} +(-9.44618 + 7.92629i) q^{65} +(-13.7512 - 2.42470i) q^{67} +(6.09756 - 3.38718i) q^{68} +(-8.73534 + 2.26335i) q^{70} +(-1.50109 + 2.59997i) q^{71} +(0.472663 + 0.818676i) q^{73} +(-7.11668 - 7.23541i) q^{74} +(6.30577 + 0.104337i) q^{76} +(-3.25314 - 8.93793i) q^{77} +(-0.803209 - 4.55523i) q^{79} +(13.1513 + 2.77042i) q^{80} +(1.19673 - 2.51193i) q^{82} +(2.12803 - 0.375229i) q^{83} +(-4.00787 - 11.0115i) q^{85} +(4.89892 + 10.7368i) q^{86} +(-1.58449 + 14.0775i) q^{88} +(7.83712 + 13.5743i) q^{89} +(6.03579 + 3.48477i) q^{91} +(6.13153 + 1.18607i) q^{92} +(-3.23236 - 2.30341i) q^{94} +(1.83982 - 10.4341i) q^{95} +(1.68619 - 1.41488i) q^{97} +(-2.72012 - 3.95396i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.36295	+	0.377313i	0.963752	+	0.266801i
$2$	1.36295	+	0.377313i	0.963752	+	0.266801i
$3$		0			0
$3$		0			0
$4$	1.71527	+	1.02852i	0.857635	+	0.514259i
$5$	2.15975	−	2.57389i	0.965871	−	1.15108i	−0.0226118	−	0.999744i	$-0.507198\pi$
$5$	2.15975	−	2.57389i	0.965871	−	1.15108i	0.988482	−	0.151335i	$-0.0483574\pi$
$6$		0			0
$7$	−1.78453	−	0.649515i	−0.674489	−	0.245494i	−0.0180093	−	0.999838i	$-0.505733\pi$
$7$	−1.78453	−	0.649515i	−0.674489	−	0.245494i	−0.656479	+	0.754344i	$0.727955\pi$
$8$	1.94976	+	2.04901i	0.689343	+	0.724436i
$9$		0			0
$10$	3.91480	−	2.69319i	1.23797	−	0.851660i
$11$	3.21944	+	3.83678i	0.970699	+	1.15683i	0.987602	+	0.156977i	$0.0501747\pi$
$11$	3.21944	+	3.83678i	0.970699	+	1.15683i	−0.0169036	+	0.999857i	$0.505381\pi$
$12$		0			0
$13$	−3.61424	−	0.637289i	−1.00241	−	0.176752i	−0.351728	−	0.936102i	$-0.614406\pi$
$13$	−3.61424	−	0.637289i	−1.00241	−	0.176752i	−0.650682	+	0.759350i	$0.725517\pi$
$14$	−2.18715	−	1.55858i	−0.584542	−	0.416549i
$15$		0			0
$16$	1.88430	+	3.52837i	0.471075	+	0.882093i
$17$	1.74380	−	3.02034i	0.422932	−	0.732541i	−0.573292	−	0.819351i	$-0.694334\pi$
$17$	1.74380	−	3.02034i	0.422932	−	0.732541i	0.996225	+	0.0868103i	$0.0276674\pi$
$18$		0			0
$19$	2.73085	−	1.57666i	0.626501	−	0.361710i	−0.152895	−	0.988242i	$-0.548860\pi$
$19$	2.73085	−	1.57666i	0.626501	−	0.361710i	0.779396	+	0.626532i	$0.215526\pi$
$20$	6.35185	−	2.19358i	1.42032	−	0.490498i
$21$		0			0
$22$	2.94027	+	6.44408i	0.626869	+	1.37388i
$23$	2.93428	−	1.06799i	0.611839	−	0.222691i	−0.0174685	−	0.999847i	$-0.505561\pi$
$23$	2.93428	−	1.06799i	0.611839	−	0.222691i	0.629308	+	0.777156i	$0.283338\pi$
$24$		0			0
$25$	−1.09215	−	6.19390i	−0.218430	−	1.23878i
$26$	−4.68558	−	2.23229i	−0.918918	−	0.437789i
$27$		0			0
$28$	−2.39291	−	2.94951i	−0.452218	−	0.557406i
$29$	−6.61611	+	1.16660i	−1.22858	+	0.216632i	−0.750015	−	0.661420i	$-0.769954\pi$
$29$	−6.61611	+	1.16660i	−1.22858	+	0.216632i	−0.478565	+	0.878052i	$0.658843\pi$
$30$		0			0
$31$	0.842639	−	0.306695i	0.151342	−	0.0550841i	−0.265238	−	0.964183i	$-0.585451\pi$
$31$	0.842639	−	0.306695i	0.151342	−	0.0550841i	0.416581	+	0.909099i	$0.363228\pi$
$32$	1.23691	+	5.51997i	0.218657	+	0.975802i
$33$		0			0
$34$	3.51632	−	3.45862i	0.603044	−	0.593149i
$35$	−5.52592	+	3.19039i	−0.934052	+	0.539275i
$36$		0			0
$37$	−6.21485	−	3.58815i	−1.02172	−	0.589887i	−0.107115	−	0.994247i	$-0.534161\pi$
$37$	−6.21485	−	3.58815i	−1.02172	−	0.589887i	−0.914600	+	0.404359i	$0.867495\pi$
$38$	4.31691	−	1.11852i	0.700296	−	0.181448i
$39$		0			0
$40$	9.48493	−	0.593099i	1.49970	−	0.0937772i
$41$	0.341649	−	1.93759i	0.0533567	−	0.302601i	−0.946438	−	0.322887i	$-0.895347\pi$
$41$	0.341649	−	1.93759i	0.0533567	−	0.302601i	0.999794	+	0.0202862i	$0.00645776\pi$
$42$		0			0
$43$	5.36405	+	6.39263i	0.818010	+	0.974867i	0.999964	−	0.00844018i	$-0.00268662\pi$
$43$	5.36405	+	6.39263i	0.818010	+	0.974867i	−0.181954	+	0.983307i	$0.558242\pi$
$44$	1.57601	+	9.89237i	0.237593	+	1.49133i
$45$		0			0
$46$	4.40224	−	0.348476i	0.649075	−	0.0513800i
$47$	−2.63733	−	0.959909i	−0.384694	−	0.140017i	0.142432	−	0.989805i	$-0.454508\pi$
$47$	−2.63733	−	0.959909i	−0.384694	−	0.140017i	−0.527125	+	0.849788i	$0.676730\pi$
$48$		0			0
$49$	−2.59964	−	2.18135i	−0.371377	−	0.311622i
$50$	0.848490	−	8.85407i	0.119995	−	1.25215i
$51$		0			0
$52$	−5.54394	−	4.81044i	−0.768806	−	0.667088i
$53$			9.52536i			1.30841i	0.756318	+	0.654205i	$0.226996\pi$
$53$			9.52536i			1.30841i	−0.756318	+	0.654205i	$0.773004\pi$
$54$		0			0
$55$	16.8287			2.26918
$56$	−2.14853	−	4.92292i	−0.287109	−	0.657853i
$57$		0			0
$58$	−9.45760	−	0.906327i	−1.24184	−	0.119007i
$59$	−6.13695	+	7.31373i	−0.798963	+	0.952167i	−0.999622	−	0.0274946i	$-0.991247\pi$
$59$	−6.13695	+	7.31373i	−0.798963	+	0.952167i	0.200659	+	0.979661i	$0.435692\pi$
$60$		0			0
$61$	−2.92540	+	8.03747i	−0.374559	+	1.02909i	0.599018	+	0.800735i	$0.295558\pi$
$61$	−2.92540	+	8.03747i	−0.374559	+	1.02909i	−0.973577	+	0.228358i	$0.926664\pi$
$62$	1.26420	−	0.100072i	0.160553	−	0.0127092i
$63$		0			0
$64$	−0.396910	+	7.99015i	−0.0496138	+	0.998768i
$65$	−9.44618	+	7.92629i	−1.17165	+	0.983135i
$66$		0			0
$67$	−13.7512	−	2.42470i	−1.67997	−	0.296224i	−0.749341	−	0.662184i	$-0.769630\pi$
$67$	−13.7512	−	2.42470i	−1.67997	−	0.296224i	−0.930631	+	0.365960i	$0.880741\pi$
$68$	6.09756	−	3.38718i	0.739437	−	0.410755i
$69$		0			0
$70$	−8.73534	+	2.26335i	−1.04407	+	0.270522i
$71$	−1.50109	+	2.59997i	−0.178147	+	0.308560i	−0.941246	−	0.337722i	$-0.890344\pi$
$71$	−1.50109	+	2.59997i	−0.178147	+	0.308560i	0.763099	+	0.646282i	$0.223677\pi$
$72$		0			0
$73$	0.472663	+	0.818676i	0.0553210	+	0.0958187i	0.892360	−	0.451325i	$-0.149048\pi$
$73$	0.472663	+	0.818676i	0.0553210	+	0.0958187i	−0.837039	+	0.547144i	$0.815715\pi$
$74$	−7.11668	−	7.23541i	−0.827297	−	0.841099i
$75$		0			0
$76$	6.30577	+	0.104337i	0.723322	+	0.0119682i
$77$	−3.25314	−	8.93793i	−0.370730	−	1.01857i
$78$		0			0
$79$	−0.803209	−	4.55523i	−0.0903681	−	0.512503i	−0.996069	−	0.0885849i	$-0.971766\pi$
$79$	−0.803209	−	4.55523i	−0.0903681	−	0.512503i	0.905701	−	0.423918i	$-0.139346\pi$
$80$	13.1513	+	2.77042i	1.47036	+	0.309743i
$81$		0			0
$82$	1.19673	−	2.51193i	0.132157	−	0.277396i
$83$	2.12803	−	0.375229i	0.233582	−	0.0411868i	−0.0556319	−	0.998451i	$-0.517717\pi$
$83$	2.12803	−	0.375229i	0.233582	−	0.0411868i	0.289214	+	0.957265i	$0.406606\pi$
$84$		0			0
$85$	−4.00787	−	11.0115i	−0.434715	−	1.19437i
$86$	4.89892	+	10.7368i	0.528264	+	1.15778i
$87$		0			0
$88$	−1.58449	+	14.0775i	−0.168908	+	1.50066i
$89$	7.83712	+	13.5743i	0.830733	+	1.43887i	0.897458	+	0.441101i	$0.145412\pi$
$89$	7.83712	+	13.5743i	0.830733	+	1.43887i	−0.0667245	+	0.997771i	$0.521255\pi$
$90$		0			0
$91$	6.03579	+	3.48477i	0.632723	+	0.365303i
$92$	6.13153	+	1.18607i	0.639256	+	0.123656i
$93$		0			0
$94$	−3.23236	−	2.30341i	−0.333393	−	0.237578i
$95$	1.83982	−	10.4341i	0.188761	−	1.07052i
$96$		0			0
$97$	1.68619	−	1.41488i	0.171207	−	0.143659i	−0.553158	−	0.833076i	$-0.686578\pi$
$97$	1.68619	−	1.41488i	0.171207	−	0.143659i	0.724365	+	0.689417i	$0.242133\pi$
$98$	−2.72012	−	3.95396i	−0.274774	−	0.399410i
$99$		0			0
$100$	4.49721	−	11.7475i	0.449721	−	1.17475i
$101$	6.12830	−	16.8374i	0.609789	−	1.67538i	−0.120895	−	0.992665i	$-0.538576\pi$
$101$	6.12830	−	16.8374i	0.609789	−	1.67538i	0.730684	−	0.682716i	$-0.239201\pi$
$102$		0			0
$103$	−10.6973	−	8.97613i	−1.05404	−	0.884444i	−0.0605268	−	0.998167i	$-0.519278\pi$
$103$	−10.6973	−	8.97613i	−1.05404	−	0.884444i	−0.993513	+	0.113723i	$0.963723\pi$
$104$	−5.74108	−	8.64819i	−0.562959	−	0.848025i
$105$		0			0
$106$	−3.59404	+	12.9826i	−0.349084	+	1.26098i
$107$			12.3518i			1.19409i	0.802207	+	0.597046i	$0.203659\pi$
$107$			12.3518i			1.19409i	−0.802207	+	0.597046i	$0.796341\pi$
$108$		0			0
$109$			2.18468i			0.209255i	0.994511	+	0.104627i	$0.0333650\pi$
$109$			2.18468i			0.209255i	−0.994511	+	0.104627i	$0.966635\pi$
$110$	22.9366	+	6.34968i	2.18692	+	0.605418i
$111$		0			0
$112$	−1.07086	−	7.52037i	−0.101187	−	0.710608i
$113$	−12.1210	−	10.1708i	−1.14025	−	0.956785i	−0.140805	−	0.990037i	$-0.544969\pi$
$113$	−12.1210	−	10.1708i	−1.14025	−	0.956785i	−0.999447	+	0.0332523i	$0.989413\pi$
$114$		0			0
$115$	3.58842	−	9.85911i	0.334622	−	0.919367i
$116$	−12.5483	−	4.80376i	−1.16508	−	0.446018i
$117$		0			0
$118$	−11.1239	+	7.65270i	−1.02404	+	0.704488i
$119$	−5.07361	+	4.25727i	−0.465097	+	0.390263i
$120$		0			0
$121$	−2.44596	+	13.8717i	−0.222360	+	1.26107i
$122$	−7.01982	+	9.85089i	−0.635545	+	0.891858i
$123$		0			0
$124$	1.76079	+	0.340604i	0.158124	+	0.0305871i
$125$	−3.75209	−	2.16627i	−0.335597	−	0.193757i
$126$		0			0
$127$	−5.17381	−	8.96131i	−0.459102	−	0.795187i	0.539812	−	0.841786i	$-0.318495\pi$
$127$	−5.17381	−	8.96131i	−0.459102	−	0.795187i	−0.998914	+	0.0465982i	$0.985162\pi$
$128$	−3.55576	+	10.7404i	−0.314287	+	0.949328i
$129$		0			0
$130$	−15.8654	+	7.23897i	−1.39149	+	0.634900i
$131$	−3.07414	−	8.44614i	−0.268589	−	0.737942i	−0.998518	−	0.0544195i	$-0.982669\pi$
$131$	−3.07414	−	8.44614i	−0.268589	−	0.737942i	0.729929	−	0.683523i	$-0.239553\pi$
$132$		0			0
$133$	−5.89735	+	1.03986i	−0.511365	+	0.0901675i
$134$	−17.8273	−	8.49324i	−1.54004	−	0.733704i
$135$		0			0
$136$	9.58869	−	2.31587i	0.822224	−	0.198584i
$137$	−2.92683	−	16.5989i	−0.250056	−	1.41814i	−0.808451	−	0.588563i	$-0.799694\pi$
$137$	−2.92683	−	16.5989i	−0.250056	−	1.41814i	0.558395	−	0.829575i	$-0.311417\pi$
$138$		0			0
$139$	3.76833	+	10.3534i	0.319626	+	0.878164i	0.990613	+	0.136695i	$0.0436482\pi$
$139$	3.76833	+	10.3534i	0.319626	+	0.878164i	−0.670988	+	0.741469i	$0.734130\pi$
$140$	−12.7598	−	0.211127i	−1.07840	−	0.0178435i
$141$		0			0
$142$	−3.02692	+	2.97725i	−0.254013	+	0.249845i
$143$	−9.19071	−	15.9188i	−0.768566	−	1.33120i
$144$		0			0
$145$	−11.2865	+	19.5487i	−0.937289	+	1.62343i
$146$	0.335319	+	1.29416i	0.0277512	+	0.107105i
$147$		0			0
$148$	−6.96967	−	12.5467i	−0.572903	−	1.03133i
$149$	10.6491	+	1.87772i	0.872406	+	0.153829i	0.591888	−	0.806020i	$-0.298383\pi$
$149$	10.6491	+	1.87772i	0.872406	+	0.153829i	0.280518	+	0.959849i	$0.409494\pi$
$150$		0			0
$151$	−0.489785	+	0.410979i	−0.0398582	+	0.0334450i	−0.662499	−	0.749063i	$-0.730504\pi$
$151$	−0.489785	+	0.410979i	−0.0398582	+	0.0334450i	0.622641	+	0.782508i	$0.286060\pi$
$152$	8.55509	+	2.52146i	0.693909	+	0.204517i
$153$		0			0
$154$	−1.06147	−	13.4094i	−0.0855359	−	1.08056i
$155$	1.03049	−	2.83125i	0.0827709	−	0.227411i
$156$		0			0
$157$	5.93021	−	7.06735i	0.473282	−	0.564036i	−0.475602	−	0.879661i	$-0.657770\pi$
$157$	5.93021	−	7.06735i	0.473282	−	0.564036i	0.948884	+	0.315625i	$0.102214\pi$
$158$	0.624011	−	6.51161i	0.0496437	−	0.518036i
$159$		0			0
$160$	16.8792	+	8.73810i	1.33442	+	0.690807i
$161$	−5.92998			−0.467348
$162$		0			0
$163$			8.36032i			0.654831i	0.944881	+	0.327415i	$0.106178\pi$
$163$			8.36032i			0.654831i	−0.944881	+	0.327415i	$0.893822\pi$
$164$	2.57887	−	2.97210i	0.201376	−	0.232082i
$165$		0			0
$166$	3.04198	+	0.291515i	0.236103	+	0.0226259i
$167$	4.77570	+	4.00729i	0.369555	+	0.310094i	0.808586	−	0.588379i	$-0.200234\pi$
$167$	4.77570	+	4.00729i	0.369555	+	0.310094i	−0.439030	+	0.898472i	$0.644678\pi$
$168$		0			0
$169$	0.440614	+	0.160370i	0.0338934	+	0.0123362i
$170$	−1.30774	−	16.5204i	−0.100299	−	1.26706i
$171$		0			0
$172$	2.62586	+	16.4821i	0.200220	+	1.25675i
$173$	−5.72780	−	6.82613i	−0.435477	−	0.518981i	0.503017	−	0.864276i	$-0.332223\pi$
$173$	−5.72780	−	6.82613i	−0.435477	−	0.518981i	−0.938494	+	0.345295i	$0.887779\pi$
$174$		0			0
$175$	−2.07406	+	11.7626i	−0.156784	+	0.889167i
$176$	−7.47120	+	18.5890i	−0.563163	+	1.40120i
$177$		0			0
$178$	5.55985	+	21.4581i	0.416729	+	1.60836i
$179$	12.5035	+	7.21893i	0.934559	+	0.539568i	0.888251	−	0.459359i	$-0.151921\pi$
$179$	12.5035	+	7.21893i	0.934559	+	0.539568i	0.0463085	+	0.998927i	$0.485254\pi$
$180$		0			0
$181$	−4.19806	+	2.42375i	−0.312039	+	0.180156i	−0.647839	−	0.761778i	$-0.724327\pi$
$181$	−4.19806	+	2.42375i	−0.312039	+	0.180156i	0.335799	+	0.941934i	$0.390994\pi$
$182$	6.91164	+	7.02695i	0.512325	+	0.520872i
$183$		0			0
$184$	7.90945	+	3.93006i	0.583092	+	0.289728i
$185$	−22.6580	+	8.24685i	−1.66585	+	0.606321i
$186$		0			0
$187$	17.2024	−	3.03326i	1.25797	−	0.221814i
$188$	−3.53644	−	4.35904i	−0.257922	−	0.317916i
$189$		0			0
$190$	6.44451	−	13.5270i	0.467534	−	0.981352i
$191$	4.56335	+	25.8800i	0.330192	+	1.87261i	0.470345	+	0.882483i	$0.344129\pi$
$191$	4.56335	+	25.8800i	0.330192	+	1.87261i	−0.140153	+	0.990130i	$0.544759\pi$
$192$		0			0
$193$	3.82953	−	1.39383i	0.275655	−	0.100330i	−0.200494	−	0.979695i	$-0.564255\pi$
$193$	3.82953	−	1.39383i	0.275655	−	0.100330i	0.476149	+	0.879365i	$0.342032\pi$
$194$	2.83205	−	1.29219i	0.203329	−	0.0927740i
$195$		0			0
$196$	−2.21552	−	6.41539i	−0.158251	−	0.458242i
$197$	8.91014	−	5.14427i	0.634821	−	0.366514i	−0.147796	−	0.989018i	$-0.547218\pi$
$197$	8.91014	−	5.14427i	0.634821	−	0.366514i	0.782617	+	0.622504i	$0.213884\pi$
$198$		0			0
$199$	0.690545	−	1.19606i	0.0489514	−	0.0847864i	−0.840511	−	0.541794i	$-0.817745\pi$
$199$	0.690545	−	1.19606i	0.0489514	−	0.0847864i	0.889463	+	0.457007i	$0.151079\pi$
$200$	10.5620	−	14.3144i	0.746843	−	1.01218i
$201$		0			0
$202$	14.7055	−	20.6362i	1.03468	−	1.45196i
$203$	12.5644	+	2.21544i	0.881845	+	0.155493i
$204$		0			0
$205$	−4.24927	−	5.06408i	−0.296782	−	0.353691i
$206$	−11.1931	−	16.2703i	−0.779862	−	1.13360i
$207$		0			0
$208$	−4.56173	−	13.9532i	−0.316299	−	0.967483i
$209$	14.8411	+	5.40173i	1.02658	+	0.373645i
$210$		0			0
$211$	7.42731	−	8.85152i	0.511317	−	0.609364i	−0.447188	−	0.894440i	$-0.647574\pi$
$211$	7.42731	−	8.85152i	0.511317	−	0.609364i	0.958505	+	0.285076i	$0.0920189\pi$
$212$	−9.79701	+	16.3386i	−0.672861	+	1.12214i
$213$		0			0
$214$	−4.66049	+	16.8349i	−0.318584	+	1.15081i
$215$	28.0390			1.91224
$216$		0			0
$217$	−1.70292			−0.115602
$218$	−0.824310	+	2.97762i	−0.0558293	+	0.201670i
$219$		0			0
$220$	28.8657	+	17.3086i	1.94613	+	1.16694i
$221$	−8.22733	+	9.80495i	−0.553430	+	0.659552i
$222$		0			0
$223$	2.85912	+	1.04063i	0.191461	+	0.0696860i	0.435971	−	0.899961i	$-0.356405\pi$
$223$	2.85912	+	1.04063i	0.191461	+	0.0696860i	−0.244510	+	0.969647i	$0.578627\pi$
$224$	1.37801	−	10.6539i	0.0920719	−	0.711846i
$225$		0			0
$226$	−12.6828	−	18.4357i	−0.843649	−	1.22632i
$227$	0.641654	+	0.764693i	0.0425881	+	0.0507545i	0.786918	−	0.617058i	$-0.211675\pi$
$227$	0.641654	+	0.764693i	0.0425881	+	0.0507545i	−0.744330	+	0.667812i	$0.767231\pi$
$228$		0			0
$229$	−0.846018	−	0.149176i	−0.0559064	−	0.00985781i	0.145625	−	0.989340i	$-0.453481\pi$
$229$	−0.846018	−	0.149176i	−0.0559064	−	0.00985781i	−0.201531	+	0.979482i	$0.564592\pi$
$230$	8.61082	−	12.0835i	0.567780	−	0.796764i
$231$		0			0
$232$	−15.2902	−	11.2819i	−1.00385	−	0.740694i
$233$	5.17379	−	8.96127i	0.338946	−	0.587072i	−0.645288	−	0.763939i	$-0.723263\pi$
$233$	5.17379	−	8.96127i	0.338946	−	0.587072i	0.984235	+	0.176867i	$0.0565961\pi$
$234$		0			0
$235$	−8.16668	+	4.71503i	−0.532735	+	0.307575i
$236$	−18.0488	+	6.23306i	−1.17488	+	0.405737i
$237$		0			0
$238$	−8.52141	+	3.88810i	−0.552361	+	0.252028i
$239$	11.5092	−	4.18901i	0.744469	−	0.270965i	0.0581928	−	0.998305i	$-0.481466\pi$
$239$	11.5092	−	4.18901i	0.744469	−	0.270965i	0.686277	+	0.727341i	$0.259244\pi$
$240$		0			0
$241$	−2.60278	−	14.7611i	−0.167660	−	0.950846i	−0.946279	−	0.323350i	$-0.895191\pi$
$241$	−2.60278	−	14.7611i	−0.167660	−	0.950846i	0.778620	−	0.627496i	$-0.215920\pi$
$242$	−8.56771	+	17.9836i	−0.550753	+	1.15603i
$243$		0			0
$244$	−13.2845	+	10.7776i	−0.850455	+	0.689966i
$245$	−11.2291	+	1.98000i	−0.717404	+	0.126498i
$246$		0			0
$247$	−10.8748	+	3.95809i	−0.691944	+	0.251847i
$248$	2.27136	+	1.12860i	0.144232	+	0.0716660i
$249$		0			0
$250$	−4.29655	−	4.36823i	−0.271738	−	0.276271i
$251$	−13.8356	+	7.98801i	−0.873298	+	0.504199i	−0.868443	−	0.495789i	$-0.834879\pi$
$251$	−13.8356	+	7.98801i	−0.873298	+	0.504199i	−0.00485525	+	0.999988i	$0.501545\pi$
$252$		0			0
$253$	13.5444	+	7.81986i	0.851528	+	0.491630i
$254$	−3.67043	−	14.1660i	−0.230304	−	0.888852i
$255$		0			0
$256$	−8.89882	+	13.2970i	−0.556176	+	0.831064i
$257$	1.36142	−	7.72098i	0.0849229	−	0.481622i	−0.912450	−	0.409187i	$-0.865812\pi$
$257$	1.36142	−	7.72098i	0.0849229	−	0.481622i	0.997373	−	0.0724341i	$-0.0230767\pi$
$258$		0			0
$259$	8.76002	+	10.4398i	0.544321	+	0.648697i
$260$	−24.3551	+	3.88015i	−1.51044	+	0.240637i
$261$		0			0
$262$	−1.00307	−	12.6716i	−0.0619697	−	0.782853i
$263$	19.3707	+	7.05037i	1.19445	+	0.434744i	0.861284	−	0.508124i	$-0.169661\pi$
$263$	19.3707	+	7.05037i	1.19445	+	0.434744i	0.333166	+	0.942868i	$0.391883\pi$
$264$		0			0
$265$	24.5173	+	20.5724i	1.50608	+	1.26375i
$266$	−8.43015	−	0.807866i	−0.516886	−	0.0495335i
$267$		0			0
$268$	−21.0931	−	18.3023i	−1.28847	−	1.11799i
$269$		−	15.9724i		−	0.973852i	−0.873443	−	0.486926i	$-0.838118\pi$
$269$		−	15.9724i		−	0.973852i	0.873443	−	0.486926i	$-0.161882\pi$
$270$		0			0
$271$	7.19443			0.437031			0.218515	−	0.975834i	$-0.429879\pi$
$271$	7.19443			0.437031			0.218515	+	0.975834i	$0.429879\pi$
$272$	13.9427	+	0.461526i	0.845402	+	0.0279841i
$273$		0			0
$274$	2.27385	−	23.7278i	0.137368	−	1.43345i
$275$	20.2485	−	24.1313i	1.22103	−	1.45517i
$276$		0			0
$277$	6.45750	−	17.7418i	0.387993	−	1.06600i	−0.579910	−	0.814680i	$-0.696912\pi$
$277$	6.45750	−	17.7418i	0.387993	−	1.06600i	0.967903	−	0.251322i	$-0.0808654\pi$
$278$	1.22958	+	15.5330i	0.0737450	+	0.931608i
$279$		0			0
$280$	−17.3114	−	5.10221i	−1.03455	−	0.304915i
$281$	14.1133	−	11.8425i	0.841932	−	0.706465i	−0.116066	−	0.993242i	$-0.537028\pi$
$281$	14.1133	−	11.8425i	0.841932	−	0.706465i	0.957997	+	0.286777i	$0.0925839\pi$
$282$		0			0
$283$	8.62324	+	1.52051i	0.512599	+	0.0903850i	0.423964	−	0.905679i	$-0.360638\pi$
$283$	8.62324	+	1.52051i	0.512599	+	0.0903850i	0.0886349	+	0.996064i	$0.471750\pi$
$284$	−5.24890	+	2.91575i	−0.311465	+	0.173018i
$285$		0			0
$286$	−6.52013	−	25.1643i	−0.385543	−	1.48800i
$287$	−1.86818	+	3.23578i	−0.110275	+	0.191002i
$288$		0			0
$289$	2.41836	+	4.18872i	0.142256	+	0.246395i
$290$	−22.7589	+	22.3854i	−1.33645	+	1.31452i
$291$		0			0
$292$	−0.0312789	+	1.89039i	−0.00183046	+	0.110627i
$293$	4.67724	+	12.8506i	0.273247	+	0.750741i	0.998087	+	0.0618236i	$0.0196916\pi$
$293$	4.67724	+	12.8506i	0.273247	+	0.750741i	−0.724840	+	0.688918i	$0.758086\pi$
$294$		0			0
$295$	5.57047	+	31.5917i	0.324325	+	1.83934i
$296$	−4.76528	−	19.7303i	−0.276976	−	1.14680i
$297$		0			0
$298$	13.8057	+	6.57727i	0.799742	+	0.381011i
$299$	−11.2858	+	1.98999i	−0.652675	+	0.115084i
$300$		0			0
$301$	−5.42020	−	14.8919i	−0.312415	−	0.858353i
$302$	−0.822621	+	0.375341i	−0.0473365	+	0.0215985i
$303$		0			0
$304$	10.7088	+	6.66457i	0.614191	+	0.382239i
$305$	14.3695	+	24.8886i	0.822792	+	1.42512i
$306$		0			0
$307$	−21.3532	−	12.3283i	−1.21869	−	0.703612i	−0.254053	−	0.967190i	$-0.581764\pi$
$307$	−21.3532	−	12.3283i	−1.21869	−	0.703612i	−0.964638	+	0.263578i	$0.915097\pi$
$308$	3.61281	−	18.6769i	0.205859	−	1.06421i
$309$		0			0
$310$	2.47277	−	3.47003i	0.140444	−	0.197085i
$311$	−0.221479	+	1.25607i	−0.0125589	+	0.0712250i	−0.990443	−	0.137922i	$-0.955958\pi$
$311$	−0.221479	+	1.25607i	−0.0125589	+	0.0712250i	0.977884	+	0.209147i	$0.0670688\pi$
$312$		0			0
$313$	15.3438	−	12.8749i	0.867280	−	0.727735i	−0.0962433	−	0.995358i	$-0.530683\pi$
$313$	15.3438	−	12.8749i	0.867280	−	0.727735i	0.963524	+	0.267623i	$0.0862382\pi$
$314$	10.7492	−	7.39491i	0.606612	−	0.417319i
$315$		0			0
$316$	3.30741	−	8.63956i	0.186056	−	0.486013i
$317$	−2.05364	+	5.64232i	−0.115344	+	0.316904i	−0.983909	−	0.178671i	$-0.942820\pi$
$317$	−2.05364	+	5.64232i	−0.115344	+	0.316904i	0.868565	+	0.495575i	$0.165043\pi$
$318$		0			0
$319$	−25.7762	−	21.6288i	−1.44319	−	1.21098i
$320$	19.7086	+	18.2783i	1.10174	+	1.02179i
$321$		0			0
$322$	−8.08227	−	2.23746i	−0.450407	−	0.124689i
$323$		−	10.9975i		−	0.611916i
$324$		0			0
$325$			23.0823i			1.28038i
$326$	−3.15446	+	11.3947i	−0.174709	+	0.631094i
$327$		0			0
$328$	4.63628	−	3.07778i	0.255996	−	0.169942i
$329$	4.08291	+	3.42597i	0.225098	+	0.188880i
$330$		0			0
$331$	−6.69009	+	18.3809i	−0.367721	+	1.01030i	0.608505	+	0.793550i	$0.291769\pi$
$331$	−6.69009	+	18.3809i	−0.367721	+	1.01030i	−0.976226	+	0.216755i	$0.930453\pi$
$332$	4.03608	+	1.54510i	0.221509	+	0.0847983i
$333$		0			0
$334$	4.99705	+	7.26368i	0.273426	+	0.397451i
$335$	−35.9400	+	30.1573i	−1.96361	+	1.64767i
$336$		0			0
$337$	3.82769	−	21.7079i	0.208508	−	1.18251i	−0.683316	−	0.730123i	$-0.739463\pi$
$337$	3.82769	−	21.7079i	0.208508	−	1.18251i	0.891824	−	0.452383i	$-0.149426\pi$
$338$	0.540026	+	0.384827i	0.0293735	+	0.0209318i
$339$		0			0
$340$	4.45098	−	23.0099i	0.241388	−	1.24789i
$341$	3.88955	+	2.24563i	0.210631	+	0.121608i
$342$		0			0
$343$	9.86900	+	17.0936i	0.532876	+	0.922968i
$344$	−2.63999	+	23.4551i	−0.142339	+	1.26461i
$345$		0			0
$346$	−5.23112	−	11.4648i	−0.281227	−	0.616354i
$347$	0.0110975	+	0.0304900i	0.000595743	+	0.00163679i	0.939990	−	0.341202i	$-0.110834\pi$
$347$	0.0110975	+	0.0304900i	0.000595743	+	0.00163679i	−0.939394	+	0.342838i	$0.888612\pi$
$348$		0			0
$349$	32.0493	−	5.65116i	1.71556	−	0.302500i	0.772474	−	0.635046i	$-0.219019\pi$
$349$	32.0493	−	5.65116i	1.71556	−	0.302500i	0.943087	+	0.332546i	$0.107908\pi$
$350$	−7.26501	+	15.2492i	−0.388331	+	0.815106i
$351$		0			0
$352$	−17.1968	+	22.5170i	−0.916591	+	1.20016i
$353$	0.185474	+	1.05188i	0.00987180	+	0.0559857i	0.989346	−	0.145585i	$-0.0465065\pi$
$353$	0.185474	+	1.05188i	0.00987180	+	0.0559857i	−0.979474	+	0.201571i	$0.935395\pi$
$354$		0			0
$355$	3.45005	+	9.47895i	0.183110	+	0.503090i
$356$	−0.518628	+	31.3442i	−0.0274872	+	1.66124i
$357$		0			0
$358$	14.3179	+	14.5568i	0.756726	+	0.769350i
$359$	−5.68242	−	9.84224i	−0.299907	−	0.519453i	0.676208	−	0.736711i	$-0.263622\pi$
$359$	−5.68242	−	9.84224i	−0.299907	−	0.519453i	−0.976114	+	0.217258i	$0.930289\pi$
$360$		0			0
$361$	−4.52830	+	7.84324i	−0.238331	+	0.412802i
$362$	−6.63626	+	1.71947i	−0.348794	+	0.0903733i
$363$		0			0
$364$	6.76887	+	12.1852i	0.354785	+	0.638680i
$365$	3.12802	+	0.551554i	0.163728	+	0.0288697i
$366$		0			0
$367$	6.59453	−	5.53346i	0.344231	−	0.288844i	−0.454237	−	0.890881i	$-0.650088\pi$
$367$	6.59453	−	5.53346i	0.344231	−	0.288844i	0.798469	+	0.602036i	$0.205644\pi$
$368$	9.29733	+	8.34081i	0.484657	+	0.434795i
$369$		0			0
$370$	−33.9934	+	2.69088i	−1.76723	+	0.139892i
$371$	6.18687	−	16.9983i	0.321206	−	0.882507i
$372$		0			0
$373$	−24.5912	+	29.3067i	−1.27328	+	1.51744i	−0.530966	+	0.847393i	$0.678171\pi$
$373$	−24.5912	+	29.3067i	−1.27328	+	1.51744i	−0.742318	+	0.670048i	$0.766274\pi$
$374$	24.5906	+	2.35653i	1.27155	+	0.121853i
$375$		0			0
$376$	−3.17528	−	7.27551i	−0.163752	−	0.375206i
$377$	24.6557			1.26983
$378$		0			0
$379$		−	22.1132i		−	1.13588i	−0.823071	−	0.567939i	$-0.807741\pi$
$379$		−	22.1132i		−	1.13588i	0.823071	−	0.567939i	$-0.192259\pi$
$380$	13.8875	−	16.0050i	0.712411	−	0.821041i
$381$		0			0
$382$	−3.54525	+	36.9950i	−0.181391	+	1.89283i
$383$	1.25391	+	1.05215i	0.0640717	+	0.0537626i	0.674261	−	0.738493i	$-0.264462\pi$
$383$	1.25391	+	1.05215i	0.0640717	+	0.0537626i	−0.610189	+	0.792256i	$0.708907\pi$
$384$		0			0
$385$	−30.0312	−	10.9305i	−1.53053	−	0.557069i
$386$	5.74537	−	0.454797i	0.292432	−	0.0231485i
$387$		0			0
$388$	4.34750	−	0.692626i	0.220711	−	0.0351628i
$389$	7.37158	+	8.78511i	0.373754	+	0.445423i	0.919832	−	0.392311i	$-0.128324\pi$
$389$	7.37158	+	8.78511i	0.373754	+	0.445423i	−0.546079	+	0.837734i	$0.683880\pi$
$390$		0			0
$391$	1.89109	−	10.7249i	0.0956363	−	0.542380i
$392$	−0.599031	−	9.57980i	−0.0302557	−	0.483853i
$393$		0			0
$394$	14.0851	−	3.64948i	0.709596	−	0.183858i
$395$	−13.4594	−	7.77079i	−0.677216	−	0.390991i
$396$		0			0
$397$	2.58188	−	1.49065i	0.129581	−	0.0748137i	−0.433808	−	0.901005i	$-0.642830\pi$
$397$	2.58188	−	1.49065i	0.129581	−	0.0748137i	0.563389	+	0.826192i	$0.309497\pi$
$398$	1.39247	−	1.36962i	0.0697981	−	0.0686528i
$399$		0			0
$400$	19.7965	−	15.5247i	0.989823	−	0.776235i
$401$	8.85877	−	3.22433i	0.442386	−	0.161015i	−0.111217	−	0.993796i	$-0.535475\pi$
$401$	8.85877	−	3.22433i	0.442386	−	0.161015i	0.553603	+	0.832781i	$0.313253\pi$
$402$		0			0
$403$	−3.24096	+	0.571468i	−0.161443	+	0.0284668i
$404$	27.8292	−	22.5776i	1.38456	−	1.12328i
$405$		0			0
$406$	16.2887	+	7.76023i	0.808394	+	0.385134i
$407$	−6.24142	−	35.3969i	−0.309376	−	1.75456i
$408$		0			0
$409$	−24.0695	+	8.76058i	−1.19016	+	0.433183i	−0.859779	−	0.510665i	$-0.829399\pi$
$409$	−24.0695	+	8.76058i	−1.19016	+	0.433183i	−0.330380	+	0.943848i	$0.607177\pi$
$410$	−3.88080	−	8.50540i	−0.191659	−	0.420052i
$411$		0			0
$412$	−9.11670	−	26.3989i	−0.449148	−	1.30058i
$413$	15.7019	−	9.06552i	0.772642	−	0.446085i
$414$		0			0
$415$	3.63022	−	6.28773i	0.178201	−	0.308652i
$416$	−0.952676	−	20.7388i	−0.0467088	−	1.01680i
$417$		0			0
$418$	18.1896	+	12.9620i	0.889681	+	0.633994i
$419$	−2.41298	−	0.425474i	−0.117882	−	0.0207858i	0.114396	−	0.993435i	$-0.463507\pi$
$419$	−2.41298	−	0.425474i	−0.117882	−	0.0207858i	−0.232278	+	0.972649i	$0.574618\pi$
$420$		0			0
$421$	−8.35420	−	9.95615i	−0.407159	−	0.485233i	0.523030	−	0.852314i	$-0.324802\pi$
$421$	−8.35420	−	9.95615i	−0.407159	−	0.485233i	−0.930189	+	0.367081i	$0.880357\pi$
$422$	13.4629	−	9.26177i	0.655361	−	0.450856i
$423$		0			0
$424$	−19.5176	+	18.5721i	−0.947858	+	0.901942i
$425$	−20.6122	−	7.50223i	−0.999838	−	0.363911i
$426$		0			0
$427$	10.4409	−	12.4430i	0.505272	−	0.602160i
$428$	−12.7040	+	21.1866i	−0.614073	+	1.02409i
$429$		0			0
$430$	38.2157	+	10.5795i	1.84293	+	0.510187i
$431$	−26.6357			−1.28300			−0.641499	−	0.767124i	$-0.721687\pi$
$431$	−26.6357			−1.28300			−0.641499	+	0.767124i	$0.721687\pi$
$432$		0			0
$433$	27.8356			1.33769			0.668846	−	0.743401i	$-0.266788\pi$
$433$	27.8356			1.33769			0.668846	+	0.743401i	$0.266788\pi$
$434$	−2.32099	−	0.642533i	−0.111411	−	0.0308426i
$435$		0			0
$436$	−2.24699	+	3.74732i	−0.107611	+	0.179464i
$437$	6.32923	−	7.54288i	0.302768	−	0.360825i
$438$		0			0
$439$	15.2198	+	5.53956i	0.726402	+	0.264389i	0.678641	−	0.734470i	$-0.262569\pi$
$439$	15.2198	+	5.53956i	0.726402	+	0.264389i	0.0477612	+	0.998859i	$0.484791\pi$
$440$	32.8118	+	34.4822i	1.56424	+	1.64387i
$441$		0			0
$442$	−14.9130	+	10.2594i	−0.709338	+	0.487989i
$443$	11.8910	+	14.1711i	0.564957	+	0.673290i	0.970588	−	0.240747i	$-0.0773925\pi$
$443$	11.8910	+	14.1711i	0.564957	+	0.673290i	−0.405631	+	0.914037i	$0.632948\pi$
$444$		0			0
$445$	51.8650	+	9.14520i	2.45864	+	0.433524i
$446$	3.50419	+	2.49711i	0.165928	+	0.118242i
$447$		0			0
$448$	5.89802	−	14.0009i	0.278655	−	0.661478i
$449$	−3.76662	+	6.52398i	−0.177758	+	0.307886i	−0.941112	−	0.338094i	$-0.890218\pi$
$449$	−3.76662	+	6.52398i	−0.177758	+	0.307886i	0.763354	+	0.645980i	$0.223551\pi$
$450$		0			0
$451$	8.53403	−	4.92713i	0.401852	−	0.232009i
$452$	−10.3300	−	29.9123i	−0.485885	−	1.40696i
$453$		0			0
$454$	0.586014	+	1.28434i	0.0275030	+	0.0602772i
$455$	22.0052	−	8.00925i	1.03162	−	0.375479i
$456$		0			0
$457$	−2.46966	−	14.0062i	−0.115526	−	0.655180i	−0.986488	−	0.163831i	$-0.947615\pi$
$457$	−2.46966	−	14.0062i	−0.115526	−	0.655180i	0.870962	−	0.491350i	$-0.163496\pi$
$458$	−1.09679	−	0.522533i	−0.0512499	−	0.0244164i
$459$		0			0
$460$	16.2954	−	13.2203i	0.759776	−	0.616399i
$461$	−12.3225	+	2.17278i	−0.573914	+	0.101197i	−0.453070	−	0.891475i	$-0.649671\pi$
$461$	−12.3225	+	2.17278i	−0.573914	+	0.101197i	−0.120844	+	0.992672i	$0.538560\pi$
$462$		0			0
$463$	−5.11858	+	1.86301i	−0.237881	+	0.0865815i	−0.458210	−	0.888844i	$-0.651509\pi$
$463$	−5.11858	+	1.86301i	−0.237881	+	0.0865815i	0.220329	+	0.975426i	$0.429287\pi$
$464$	−16.5829	−	21.1459i	−0.769843	−	0.981672i
$465$		0			0
$466$	10.4328	−	10.2616i	0.483291	−	0.475361i
$467$	−6.32947	+	3.65432i	−0.292893	+	0.169102i	−0.639246	−	0.769003i	$-0.720753\pi$
$467$	−6.32947	+	3.65432i	−0.292893	+	0.169102i	0.346353	+	0.938104i	$0.387420\pi$
$468$		0			0
$469$	22.9645	+	13.2585i	1.06040	+	0.612222i
$470$	−12.9098	+	3.34496i	−0.595486	+	0.154292i
$471$		0			0
$472$	−26.9515	+	1.68529i	−1.24054	+	0.0775720i
$473$	−7.25787	+	41.1614i	−0.333717	+	1.89260i
$474$		0			0
$475$	−12.7482	−	15.1927i	−0.584926	−	0.697088i
$476$	−13.0813	+	2.08406i	−0.599580	+	0.0955226i
$477$		0			0
$478$	17.2671	−	1.36684i	0.789777	−	0.0625178i
$479$	−6.51285	−	2.37048i	−0.297580	−	0.108310i	0.188916	−	0.981993i	$-0.439503\pi$
$479$	−6.51285	−	2.37048i	−0.297580	−	0.108310i	−0.486495	+	0.873683i	$0.661725\pi$
$480$		0			0
$481$	20.1753	+	16.9291i	0.919914	+	0.771900i
$482$	2.02209	−	21.1007i	0.0921038	−	0.961111i
$483$		0			0
$484$	−18.4628	+	21.2780i	−0.839218	+	0.967184i
$485$		−	7.39586i		−	0.335829i
$486$		0			0
$487$	29.6823			1.34503			0.672517	−	0.740081i	$-0.265213\pi$
$487$	29.6823			1.34503			0.672517	+	0.740081i	$0.265213\pi$
$488$	−22.1727	+	9.67692i	−1.00371	+	0.438054i
$489$		0			0
$490$	−16.0519	−	1.53826i	−0.725149	−	0.0694914i
$491$	5.65695	−	6.74169i	0.255295	−	0.304248i	−0.623140	−	0.782110i	$-0.714144\pi$
$491$	5.65695	−	6.74169i	0.255295	−	0.304248i	0.878435	+	0.477862i	$0.158588\pi$
$492$		0			0
$493$	−8.01361	+	22.0172i	−0.360915	+	0.991606i
$494$	−16.3152	+	1.29149i	−0.734055	+	0.0581069i
$495$		0			0
$496$	2.66992	+	2.39524i	0.119883	+	0.107549i
$497$	4.36747	−	3.66474i	0.195908	−	0.164386i
$498$		0			0
$499$	−14.6580	−	2.58460i	−0.656181	−	0.115702i	−0.164362	−	0.986400i	$-0.552557\pi$
$499$	−14.6580	−	2.58460i	−0.656181	−	0.115702i	−0.491819	+	0.870698i	$0.663668\pi$
$500$	−4.20780	−	7.57483i	−0.188178	−	0.338757i
$501$		0			0
$502$	−21.8713	+	5.66690i	−0.976163	+	0.252926i
$503$	5.25851	−	9.10801i	0.234465	−	0.406106i	−0.724652	−	0.689115i	$-0.757999\pi$
$503$	5.25851	−	9.10801i	0.234465	−	0.406106i	0.959117	+	0.283009i	$0.0913327\pi$
$504$		0			0
$505$	−30.1020	−	52.1381i	−1.33952	−	2.32012i
$506$	15.5098	+	15.7686i	0.689495	+	0.700998i
$507$		0			0
$508$	0.342382	−	20.6924i	0.0151907	−	0.918078i
$509$	8.68462	+	23.8608i	0.384939	+	1.05761i	0.969249	+	0.246081i	$0.0791430\pi$
$509$	8.68462	+	23.8608i	0.384939	+	1.05761i	−0.584310	+	0.811531i	$0.698635\pi$
$510$		0			0
$511$	−0.311738	−	1.76795i	−0.0137905	−	0.0782096i
$512$	−17.1458	+	14.7656i	−0.757744	+	0.652552i
$513$		0			0
$514$	4.76877	−	10.0096i	0.210341	−	0.441506i
$515$	−46.2072	+	8.14757i	−2.03613	+	0.359025i
$516$		0			0
$517$	−4.80776	−	13.2092i	−0.211445	−	0.580941i
$518$	8.00041	+	17.5342i	0.351518	+	0.770408i
$519$		0			0
$520$	−34.6588	−	3.90103i	−1.51989	−	0.171072i
$521$	5.54892	+	9.61101i	0.243103	+	0.421066i	0.961596	−	0.274467i	$-0.0885015\pi$
$521$	5.54892	+	9.61101i	0.243103	+	0.421066i	−0.718494	+	0.695533i	$0.755168\pi$
$522$		0			0
$523$	−21.2339	−	12.2594i	−0.928493	−	0.536066i	−0.0421586	−	0.999111i	$-0.513423\pi$
$523$	−21.2339	−	12.2594i	−0.928493	−	0.536066i	−0.886335	+	0.463045i	$0.846757\pi$
$524$	3.41402	−	17.6492i	0.149142	−	0.771009i
$525$		0			0
$526$	23.7412	+	16.9181i	1.03516	+	0.737666i
$527$	0.543064	−	3.07987i	0.0236563	−	0.134161i
$528$		0			0
$529$	−10.1496	+	8.51656i	−0.441289	+	0.370285i
$530$	25.6536	+	37.2899i	1.11432	+	1.61977i
$531$		0			0
$532$	−11.1851	−	4.28189i	−0.484934	−	0.185643i
$533$	−2.46961	+	6.78519i	−0.106971	+	0.293899i
$534$		0			0
$535$	31.7922	+	26.6768i	1.37450	+	1.15334i
$536$	−21.8431	−	32.9039i	−0.943480	−	1.42123i
$537$		0			0
$538$	6.02658	−	21.7695i	0.259824	−	0.938551i
$539$		−	16.9970i		−	0.732112i
$540$		0			0
$541$			10.1117i			0.434737i	0.976090	+	0.217369i	$0.0697474\pi$
$541$			10.1117i			0.434737i	−0.976090	+	0.217369i	$0.930253\pi$
$542$	9.80566	+	2.71455i	0.421189	+	0.116600i
$543$		0			0
$544$	18.8291	+	5.88981i	0.807291	+	0.252523i
$545$	5.62314	+	4.71838i	0.240869	+	0.202113i
$546$		0			0
$547$	9.82775	−	27.0015i	0.420204	−	1.15450i	−0.531386	−	0.847130i	$-0.678328\pi$
$547$	9.82775	−	27.0015i	0.420204	−	1.15450i	0.951590	−	0.307371i	$-0.0994493\pi$
$548$	12.0519	−	31.4819i	0.514834	−	1.34484i
$549$		0			0
$550$	36.7028	−	25.2497i	1.56501	−	1.07665i
$551$	−16.2283	+	13.6172i	−0.691348	+	0.580110i
$552$		0			0
$553$	−1.52534	+	8.65063i	−0.0648640	+	0.367862i
$554$	15.4955	−	21.7447i	0.658339	−	0.923845i
$555$		0			0
$556$	−4.18496	+	21.6347i	−0.177482	+	0.917514i
$557$	−10.4290	−	6.02119i	−0.441891	−	0.255126i	0.262508	−	0.964930i	$-0.415450\pi$
$557$	−10.4290	−	6.02119i	−0.441891	−	0.255126i	−0.704400	+	0.709804i	$0.748784\pi$
$558$		0			0
$559$	−15.3130	−	26.5230i	−0.647673	−	1.12180i
$560$	−21.6694	−	13.4859i	−0.915699	−	0.569881i
$561$		0			0
$562$	23.7041	−	10.8156i	0.999898	−	0.456229i
$563$	1.52700	+	4.19539i	0.0643553	+	0.176815i	0.967702	−	0.252096i	$-0.0811198\pi$
$563$	1.52700	+	4.19539i	0.0643553	+	0.176815i	−0.903347	+	0.428910i	$0.858898\pi$
$564$		0			0
$565$	−52.3569	+	9.23194i	−2.20267	+	0.388390i
$566$	11.1793	+	5.32604i	0.469903	+	0.223870i
$567$		0			0
$568$	−8.25414	+	1.99354i	−0.346336	+	0.0836473i
$569$	−5.31792	−	30.1594i	−0.222939	−	1.26435i	−0.866586	−	0.499027i	$-0.833691\pi$
$569$	−5.31792	−	30.1594i	−0.222939	−	1.26435i	0.643648	−	0.765322i	$-0.277420\pi$
$570$		0			0
$571$	4.43557	+	12.1866i	0.185623	+	0.509994i	0.997244	−	0.0741895i	$-0.0236370\pi$
$571$	4.43557	+	12.1866i	0.185623	+	0.509994i	−0.811621	+	0.584184i	$0.801415\pi$
$572$	0.608204	−	36.7578i	0.0254303	−	1.53692i
$573$		0			0
$574$	−3.76714	+	3.70532i	−0.157237	+	0.154657i
$575$	−9.81971	−	17.0082i	−0.409510	−	0.709292i
$576$		0			0
$577$	−9.34815	+	16.1915i	−0.389169	+	0.674060i	−0.992338	−	0.123553i	$-0.960571\pi$
$577$	−9.34815	+	16.1915i	−0.389169	+	0.674060i	0.603169	+	0.797613i	$0.293904\pi$
$578$	1.71564	+	6.62149i	0.0713614	+	0.275418i
$579$		0			0
$580$	−39.4655	+	21.9230i	−1.63872	+	0.910303i
$581$	−4.04125	−	0.712582i	−0.167659	−	0.0295629i
$582$		0			0
$583$	−36.5468	+	30.6664i	−1.51361	+	1.27007i
$584$	−0.755901	+	2.56471i	−0.0312794	+	0.106128i
$585$		0			0
$586$	1.52615	+	19.2795i	0.0630445	+	0.796431i
$587$	9.91990	−	27.2547i	0.409438	−	1.12492i	−0.548049	−	0.836446i	$-0.684629\pi$
$587$	9.91990	−	27.2547i	0.409438	−	1.12492i	0.957487	−	0.288475i	$-0.0931484\pi$
$588$		0			0
$589$	1.81757	−	2.16609i	0.0748916	−	0.0892523i
$590$	−4.32768	+	45.1597i	−0.178168	+	1.85920i
$591$		0			0
$592$	0.949665	−	28.6894i	0.0390310	−	1.17913i
$593$	−12.4895			−0.512883			−0.256441	−	0.966560i	$-0.582550\pi$
$593$	−12.4895			−0.512883			−0.256441	+	0.966560i	$0.582550\pi$
$594$		0			0
$595$			22.2536i			0.912308i
$596$	16.3348	+	14.1736i	0.669098	+	0.580572i
$597$		0			0
$598$	−16.1329	−	1.54602i	−0.659722	−	0.0632215i
$599$	−7.49705	−	6.29078i	−0.306321	−	0.257034i	0.476648	−	0.879094i	$-0.341852\pi$
$599$	−7.49705	−	6.29078i	−0.306321	−	0.257034i	−0.782970	+	0.622060i	$0.786296\pi$
$600$		0			0
$601$	27.8247	+	10.1274i	1.13499	+	0.413103i	0.840102	−	0.542428i	$-0.182495\pi$
$601$	27.8247	+	10.1274i	1.13499	+	0.413103i	0.294890	+	0.955531i	$0.404717\pi$
$602$	−1.76857	−	22.3420i	−0.0720814	−	0.910592i
$603$		0			0
$604$	−1.26281	+	0.201186i	−0.0513831	+	0.00818615i
$605$	30.4217	+	36.2551i	1.23682	+	1.47398i
$606$		0			0
$607$	1.41051	−	7.99939i	0.0572507	−	0.324685i	−0.942709	−	0.333615i	$-0.891731\pi$
$607$	1.41051	−	7.99939i	0.0572507	−	0.324685i	0.999960	+	0.00892998i	$0.00284254\pi$
$608$	12.0809	+	13.1240i	0.489946	+	0.532250i
$609$		0			0
$610$	10.1941	+	39.3437i	0.412745	+	1.59298i
$611$	8.92020	+	5.15008i	0.360873	+	0.208350i
$612$		0			0
$613$	10.1533	−	5.86202i	0.410088	−	0.236765i	−0.280739	−	0.959784i	$-0.590580\pi$
$613$	10.1533	−	5.86202i	0.410088	−	0.236765i	0.690828	+	0.723019i	$0.257246\pi$
$614$	−24.4517	−	24.8597i	−0.986792	−	1.00325i
$615$		0			0
$616$	11.9711	−	24.0925i	0.482330	−	0.970715i
$617$	1.24227	−	0.452149i	0.0500118	−	0.0182028i	−0.316893	−	0.948461i	$-0.602640\pi$
$617$	1.24227	−	0.452149i	0.0500118	−	0.0182028i	0.366905	+	0.930258i	$0.380417\pi$
$618$		0			0
$619$	−25.4782	+	4.49249i	−1.02405	+	0.180568i	−0.660359	−	0.750950i	$-0.729596\pi$
$619$	−25.4782	+	4.49249i	−1.02405	+	0.180568i	−0.363695	+	0.931518i	$0.618485\pi$
$620$	4.67956	−	3.79648i	0.187936	−	0.152470i
$621$		0			0
$622$	−0.775795	+	1.62839i	−0.0311065	+	0.0652925i
$623$	−5.16886	−	29.3141i	−0.207086	−	1.17444i
$624$		0			0
$625$	15.8714	−	5.77673i	0.634858	−	0.231069i
$626$	25.7707	−	11.7585i	1.03000	−	0.469965i
$627$		0			0
$628$	17.4408	−	6.02308i	0.695964	−	0.240347i
$629$	−21.6749	+	12.5140i	−0.864233	+	0.498965i
$630$		0			0
$631$	−6.70635	+	11.6157i	−0.266976	+	0.462415i	−0.968079	−	0.250644i	$-0.919358\pi$
$631$	−6.70635	+	11.6157i	−0.266976	+	0.462415i	0.701104	+	0.713059i	$0.252691\pi$
$632$	7.76766	−	10.5274i	0.308981	−	0.418756i
$633$		0			0
$634$	−4.92793	+	6.91534i	−0.195713	+	0.274643i
$635$	−34.2396	−	6.03736i	−1.35876	−	0.239585i
$636$		0			0
$637$	8.00557	+	9.54067i	0.317192	+	0.378015i
$638$	−26.9708	−	39.2046i	−1.06779	−	1.55213i
$639$		0			0
$640$	19.9651	+	32.3488i	0.789191	+	1.27870i
$641$	30.4904	+	11.0976i	1.20430	+	0.438328i	0.864722	−	0.502251i	$-0.167495\pi$
$641$	30.4904	+	11.0976i	1.20430	+	0.438328i	0.339575	+	0.940579i	$0.389717\pi$
$642$		0			0
$643$	−17.3052	+	20.6235i	−0.682449	+	0.813312i	−0.990420	−	0.138084i	$-0.955906\pi$
$643$	−17.3052	+	20.6235i	−0.682449	+	0.813312i	0.307971	+	0.951396i	$0.400350\pi$
$644$	−10.1715	−	6.09909i	−0.400814	−	0.240338i
$645$		0			0
$646$	4.14949	−	14.9890i	0.163260	−	0.589735i
$647$	−25.1491			−0.988713			−0.494356	−	0.869259i	$-0.664596\pi$
$647$	−25.1491			−0.988713			−0.494356	+	0.869259i	$0.664596\pi$
$648$		0			0
$649$	−47.8188			−1.87705
$650$	−8.70925	+	31.4600i	−0.341605	+	1.23396i
$651$		0			0
$652$	−8.59874	+	14.3402i	−0.336753	+	0.561606i
$653$	−13.3995	+	15.9689i	−0.524363	+	0.624912i	−0.961607	−	0.274431i	$-0.911510\pi$
$653$	−13.3995	+	15.9689i	−0.524363	+	0.624912i	0.437243	+	0.899343i	$0.355955\pi$
$654$		0			0
$655$	−28.3788	−	10.3291i	−1.10885	−	0.403589i
$656$	7.48031	−	2.44554i	0.292057	−	0.0954821i
$657$		0			0
$658$	4.27214	+	6.20996i	0.166546	+	0.242090i
$659$	18.1622	+	21.6448i	0.707497	+	0.843162i	0.993353	−	0.115110i	$-0.0367222\pi$
$659$	18.1622	+	21.6448i	0.707497	+	0.843162i	−0.285856	+	0.958273i	$0.592278\pi$
$660$		0			0
$661$	37.0880	+	6.53962i	1.44256	+	0.254362i	0.839510	−	0.543344i	$-0.182842\pi$
$661$	37.0880	+	6.53962i	1.44256	+	0.254362i	0.603046	+	0.797706i	$0.293953\pi$
$662$	−16.0536	+	22.5280i	−0.623941	+	0.875575i
$663$		0			0
$664$	4.91799	+	3.62876i	0.190855	+	0.140823i
$665$	−10.0603	+	17.4250i	−0.390123	+	0.675712i
$666$		0			0
$667$	−18.1676	+	10.4891i	−0.703452	+	0.406138i
$668$	4.07005	+	11.7855i	0.157475	+	0.455994i
$669$		0			0
$670$	−60.3632	+	27.5422i	−2.33203	+	1.06405i
$671$	−40.2562	+	14.6521i	−1.55407	+	0.565636i
$672$		0			0
$673$	0.887037	+	5.03064i	0.0341928	+	0.193917i	0.997120	−	0.0758462i	$-0.0241658\pi$
$673$	0.887037	+	5.03064i	0.0341928	+	0.193917i	−0.962927	+	0.269763i	$0.913055\pi$
$674$	13.4076	−	28.1426i	0.516443	−	1.08401i
$675$		0			0
$676$	0.590828	+	0.728258i	0.0227242	+	0.0280099i
$677$	−29.3482	+	5.17487i	−1.12794	+	0.198887i	−0.706325	−	0.707888i	$-0.749648\pi$
$677$	−29.3482	+	5.17487i	−1.12794	+	0.198887i	−0.421617	+	0.906774i	$0.638537\pi$
$678$		0			0
$679$	−3.92804	+	1.42969i	−0.150744	+	0.0548665i
$680$	14.7484	−	29.6820i	0.565576	−	1.13825i
$681$		0			0
$682$	4.45396	+	4.52827i	0.170551	+	0.173396i
$683$	41.0964	−	23.7270i	1.57251	−	0.907889i	0.576650	−	0.816991i	$-0.304360\pi$
$683$	41.0964	−	23.7270i	1.57251	−	0.907889i	0.995860	−	0.0908981i	$-0.0289738\pi$
$684$		0			0
$685$	−49.0450	−	28.3161i	−1.87391	−	1.08190i
$686$	7.00132	+	27.0215i	0.267312	+	1.03168i
$687$		0			0
$688$	−12.4481	+	30.9720i	−0.474579	+	1.18080i
$689$	6.07041	−	34.4270i	0.231264	−	1.31156i
$690$		0			0
$691$	−19.5742	−	23.3276i	−0.744637	−	0.887424i	0.252136	−	0.967692i	$-0.418867\pi$
$691$	−19.5742	−	23.3276i	−0.744637	−	0.887424i	−0.996773	+	0.0802677i	$0.974422\pi$
$692$	−2.80393	−	17.5998i	−0.106589	−	0.669044i
$693$		0			0
$694$	0.00362101	+	0.0457436i	0.000137452	+	0.00173640i
$695$	34.7872	+	12.6615i	1.31955	+	0.480278i
$696$		0			0
$697$	−5.25642	−	4.41066i	−0.199101	−	0.167066i
$698$	45.8139	+	4.39037i	1.73408	+	0.166178i
$699$		0			0
$700$	−15.6556	+	18.0428i	−0.591726	+	0.681953i
$701$			22.9653i			0.867386i	0.901061	+	0.433693i	$0.142790\pi$
$701$			22.9653i			0.867386i	−0.901061	+	0.433693i	$0.857210\pi$
$702$		0			0
$703$	−22.6291			−0.853473
$704$	−31.9343	+	24.2010i	−1.20357	+	0.912108i
$705$		0			0
$706$	−0.144094	+	1.50364i	−0.00542307	+	0.0565901i
$707$	−21.8723	+	26.0664i	−0.822591	+	0.980326i
$708$		0			0
$709$	12.4178	−	34.1176i	0.466361	−	1.28132i	−0.454264	−	0.890867i	$-0.650098\pi$
$709$	12.4178	−	34.1176i	0.466361	−	1.28132i	0.920625	−	0.390448i	$-0.127680\pi$
$710$	1.12572	+	14.2211i	0.0422477	+	0.533708i
$711$		0			0
$712$	−12.5334	+	42.5249i	−0.469710	+	1.59369i
$713$	2.14499	−	1.79986i	0.0803305	−	0.0674053i
$714$		0			0
$715$	−60.8229	−	10.7247i	−2.27465	−	0.401082i
$716$	14.0222	+	25.2425i	0.524033	+	0.943358i
$717$		0			0
$718$	−4.03125	−	15.5585i	−0.150445	−	0.580639i
$719$	−13.7419	+	23.8016i	−0.512485	+	0.887651i	0.487410	+	0.873173i	$0.337942\pi$
$719$	−13.7419	+	23.8016i	−0.512485	+	0.887651i	−0.999895	+	0.0144775i	$0.995392\pi$
$720$		0			0
$721$	13.2596	+	22.9662i	0.493812	+	0.855308i
$722$	−9.13120	+	8.98136i	−0.339828	+	0.334252i
$723$		0			0
$724$	−9.69367	−	0.160394i	−0.360263	−	0.00596099i
$725$	14.4516	+	39.7054i	0.536719	+	1.47462i
$726$		0			0
$727$	−0.612001	−	3.47083i	−0.0226979	−	0.128726i	0.971353	−	0.237640i	$-0.0763738\pi$
$727$	−0.612001	−	3.47083i	−0.0226979	−	0.128726i	−0.994051	+	0.108914i	$0.965263\pi$
$728$	4.62799	+	19.1619i	0.171525	+	0.710186i
$729$		0			0
$730$	4.05523	+	1.93198i	0.150091	+	0.0715059i
$731$	28.6617	−	5.05384i	1.06009	−	0.186923i
$732$		0			0
$733$	−4.83027	−	13.2711i	−0.178410	−	0.490178i	0.817963	−	0.575271i	$-0.195103\pi$
$733$	−4.83027	−	13.2711i	−0.178410	−	0.490178i	−0.996373	+	0.0850933i	$0.972881\pi$
$734$	11.0759	−	5.05364i	0.408818	−	0.186533i
$735$		0			0
$736$	9.52471	+	14.8761i	0.351085	+	0.548341i
$737$	−34.9680	−	60.5664i	−1.28806	−	2.23099i
$738$		0			0
$739$	2.52352	+	1.45695i	0.0928291	+	0.0535949i	0.545696	−	0.837983i	$-0.316265\pi$
$739$	2.52352	+	1.45695i	0.0928291	+	0.0535949i	−0.452867	+	0.891578i	$0.649599\pi$
$740$	−47.3467	−	9.15863i	−1.74050	−	0.336678i
$741$		0			0
$742$	14.8461	−	20.8334i	0.545017	−	0.764820i
$743$	−0.918280	+	5.20783i	−0.0336884	+	0.191057i	−0.997008	−	0.0773010i	$-0.975370\pi$
$743$	−0.918280	+	5.20783i	−0.0336884	+	0.191057i	0.963319	+	0.268358i	$0.0864809\pi$
$744$		0			0
$745$	27.8324	−	23.3542i	1.01970	−	0.855631i
$746$	−44.5744	+	30.6649i	−1.63198	+	1.12272i
$747$		0			0
$748$	32.6266	+	12.4902i	1.19295	+	0.456686i
$749$	8.02267	−	22.0421i	0.293142	−	0.805401i
$750$		0			0
$751$	−27.0071	−	22.6616i	−0.985502	−	0.826935i	−0.000591865	−	1.00000i	$-0.500188\pi$
$751$	−27.0071	−	22.6616i	−0.985502	−	0.826935i	−0.984910	+	0.173065i	$0.944633\pi$
$752$	−1.58260	−	11.1142i	−0.0577116	−	0.405294i
$753$		0			0
$754$	33.6045	+	9.30291i	1.22380	+	0.338792i
$755$			2.14827i			0.0781834i
$756$		0			0
$757$		−	38.9874i		−	1.41702i	−0.705700	−	0.708511i	$-0.749367\pi$
$757$		−	38.9874i		−	1.41702i	0.705700	−	0.708511i	$-0.250633\pi$
$758$	8.34359	−	30.1392i	0.303053	−	1.09470i
$759$		0			0
$760$	24.9668	−	16.5742i	0.905642	−	0.601208i
$761$	−31.7399	−	26.6329i	−1.15057	−	0.965443i	−0.150837	−	0.988559i	$-0.548197\pi$
$761$	−31.7399	−	26.6329i	−1.15057	−	0.965443i	−0.999733	+	0.0231155i	$0.992641\pi$
$762$		0			0
$763$	1.41899	−	3.89863i	0.0513708	−	0.141140i
$764$	−18.7907	+	49.0847i	−0.679824	+	1.77582i
$765$		0			0
$766$	1.31202	+	1.90715i	0.0474054	+	0.0689081i
$767$	26.8414	−	22.5226i	0.969186	−	0.813244i
$768$		0			0
$769$	8.75977	−	49.6791i	0.315886	−	1.79148i	−0.251325	−	0.967903i	$-0.580866\pi$
$769$	8.75977	−	49.6791i	0.315886	−	1.79148i	0.567210	−	0.823573i	$-0.308023\pi$
$770$	−36.8069	−	26.2289i	−1.32643	−	0.945224i
$771$		0			0
$772$	8.00225	+	1.54794i	0.288007	+	0.0557115i
$773$	26.2565	+	15.1592i	0.944379	+	0.545238i	0.891330	−	0.453354i	$-0.149773\pi$
$773$	26.2565	+	15.1592i	0.944379	+	0.545238i	0.0530488	+	0.998592i	$0.483106\pi$
$774$		0			0
$775$	−2.81993	−	4.88427i	−0.101295	−	0.175448i
$776$	6.18677	+	0.696353i	0.222092	+	0.0249976i
$777$		0			0
$778$	6.73237	+	14.7551i	0.241367	+	0.528995i
$779$	−2.12192	−	5.82994i	−0.0760258	−	0.208879i
$780$		0			0
$781$	−14.8082	+	2.61109i	−0.529879	+	0.0934320i
$782$	6.62409	−	13.9040i	0.236877	−	0.497204i
$783$		0			0
$784$	2.79813	−	13.2828i	0.0999333	−	0.474386i
$785$	−5.38281	−	30.5275i	−0.192121	−	1.08957i
$786$		0			0
$787$	9.23473	+	25.3722i	0.329182	+	0.904421i	0.988319	+	0.152398i	$0.0486996\pi$
$787$	9.23473	+	25.3722i	0.329182	+	0.904421i	−0.659137	+	0.752023i	$0.729078\pi$
$788$	20.5743	+	0.340427i	0.732928	+	0.0121272i
$789$		0			0
$790$	−15.4125	−	15.6696i	−0.548351	−	0.557500i
$791$	15.0243	+	26.0228i	0.534202	+	0.925265i
$792$		0			0
$793$	15.6953	−	27.1851i	0.557356	−	0.965370i
$794$	4.08142	−	1.05751i	0.144844	−	0.0375295i
$795$		0			0
$796$	2.41464	−	1.34133i	0.0855846	−	0.0475420i
$797$	−52.0759	−	9.18239i	−1.84462	−	0.325257i	−0.861437	−	0.507864i	$-0.830435\pi$
$797$	−52.0759	−	9.18239i	−1.84462	−	0.325257i	−0.983186	+	0.182608i	$0.941546\pi$
$798$		0			0
$799$	−7.49821	+	6.29175i	−0.265268	+	0.222586i
$800$	32.8393	−	13.6899i	1.16104	−	0.484012i
$801$		0			0
$802$	13.2906	−	1.05207i	0.469309	−	0.0371499i
$803$	−1.61937	+	4.44918i	−0.0571463	+	0.157008i
$804$		0			0
$805$	−12.8073	+	15.2631i	−0.451398	+	0.537955i
$806$	−4.63288	−	0.443972i	−0.163186	−	0.0156382i
$807$		0			0
$808$	46.4487	−	20.2718i	1.63406	−	0.713159i
$809$	18.3017			0.643453			0.321727	−	0.946833i	$-0.395737\pi$
$809$	18.3017			0.643453			0.321727	+	0.946833i	$0.395737\pi$
$810$		0			0
$811$		−	34.2759i		−	1.20359i	−0.798650	−	0.601795i	$-0.794452\pi$
$811$		−	34.2759i		−	1.20359i	0.798650	−	0.601795i	$-0.205548\pi$
$812$	19.2727	+	16.7227i	0.676338	+	0.586853i
$813$		0			0
$814$	4.84895	−	50.5992i	0.169955	−	1.77350i
$815$	21.5186	+	18.0562i	0.753762	+	0.632482i
$816$		0			0
$817$	24.7274	+	9.00005i	0.865103	+	0.314872i
$818$	−36.1110	+	2.85850i	−1.26259	+	0.0999453i
$819$		0			0
$820$	−2.08014	−	13.0567i	−0.0726418	−	0.455960i
$821$	−16.1380	−	19.2325i	−0.563221	−	0.671220i	0.407004	−	0.913426i	$-0.366573\pi$
$821$	−16.1380	−	19.2325i	−0.563221	−	0.671220i	−0.970225	+	0.242206i	$0.922129\pi$
$822$		0			0
$823$	−5.65012	+	32.0434i	−0.196951	+	1.11696i	0.712662	+	0.701507i	$0.247489\pi$
$823$	−5.65012	+	32.0434i	−0.196951	+	1.11696i	−0.909613	+	0.415456i	$0.863622\pi$
$824$	−2.46497	−	39.4202i	−0.0858714	−	1.37327i
$825$		0			0
$826$	24.8215	−	6.43131i	0.863651	−	0.223774i
$827$	−39.6695	−	22.9032i	−1.37944	−	0.796423i	−0.387352	−	0.921932i	$-0.626610\pi$
$827$	−39.6695	−	22.9032i	−1.37944	−	0.796423i	−0.992092	+	0.125509i	$0.959944\pi$
$828$		0			0
$829$	−17.0001	+	9.81500i	−0.590437	+	0.340889i	−0.765270	−	0.643709i	$-0.777395\pi$
$829$	−17.0001	+	9.81500i	−0.590437	+	0.340889i	0.174833	+	0.984598i	$0.444061\pi$
$830$	7.32025	−	7.20013i	0.254090	−	0.249920i
$831$		0			0
$832$	6.52656	−	28.6254i	0.226268	−	0.992407i
$833$	−11.1217	+	4.04796i	−0.385343	+	0.140253i
$834$		0			0
$835$	20.6287	−	3.63739i	0.713885	−	0.125877i
$836$	19.9008	+	24.5298i	0.688282	+	0.848380i
$837$		0			0
$838$	−3.12824	−	1.49035i	−0.108063	−	0.0514833i
$839$	8.40287	+	47.6550i	0.290099	+	1.64523i	0.686480	+	0.727149i	$0.259155\pi$
$839$	8.40287	+	47.6550i	0.290099	+	1.64523i	−0.396381	+	0.918086i	$0.629734\pi$
$840$		0			0
$841$	15.1609	−	5.51810i	0.522788	−	0.190279i
$842$	−7.62978	−	16.7219i	−0.262940	−	0.576275i
$843$		0			0
$844$	21.8438	−	7.54363i	0.751894	−	0.259662i
$845$	1.36439	−	0.787733i	0.0469366	−	0.0270989i
$846$		0			0
$847$	13.3748	−	23.1658i	0.459563	−	0.795987i
$848$	−33.6090	+	17.9486i	−1.15414	+	0.616359i
$849$		0			0
$850$	−25.2627	−	18.0024i	−0.866504	−	0.617478i
$851$	−22.0682	−	3.89122i	−0.756488	−	0.133389i
$852$		0			0
$853$	30.1220	+	35.8980i	1.03136	+	1.22912i	0.972995	+	0.230828i	$0.0741434\pi$
$853$	30.1220	+	35.8980i	1.03136	+	1.22912i	0.0583624	+	0.998295i	$0.481412\pi$
$854$	18.9254	−	13.0197i	0.647613	−	0.445525i
$855$		0			0
$856$	−25.3090	+	24.0830i	−0.865043	+	0.823138i
$857$	5.93538	+	2.16030i	0.202749	+	0.0737946i	0.441399	−	0.897311i	$-0.354483\pi$
$857$	5.93538	+	2.16030i	0.202749	+	0.0737946i	−0.238650	+	0.971106i	$0.576705\pi$
$858$		0			0
$859$	19.3877	−	23.1054i	0.661501	−	0.788346i	−0.326100	−	0.945335i	$-0.605734\pi$
$859$	19.3877	−	23.1054i	0.661501	−	0.788346i	0.987600	+	0.156990i	$0.0501789\pi$
$860$	48.0944	+	28.8386i	1.64001	+	0.983388i
$861$		0			0
$862$	−36.3032	−	10.0500i	−1.23649	−	0.342304i
$863$	−48.6885			−1.65737			−0.828687	−	0.559712i	$-0.810912\pi$
$863$	−48.6885			−1.65737			−0.828687	+	0.559712i	$0.810912\pi$
$864$		0			0
$865$	−29.9404			−1.01800
$866$	37.9385	+	10.5027i	1.28920	+	0.356897i
$867$		0			0
$868$	−2.92096	−	1.75148i	−0.0991439	−	0.0594491i
$869$	14.8915	−	17.7470i	0.505161	−	0.602027i
$870$		0			0
$871$	48.1548	+	17.5269i	1.63166	+	0.593877i
$872$	−4.47645	+	4.25960i	−0.151592	+	0.144248i
$873$		0			0
$874$	11.4724	−	7.89247i	0.388061	−	0.266967i
$875$	5.28869	+	6.30281i	0.178790	+	0.213074i
$876$		0			0
$877$	34.7601	+	6.12915i	1.17377	+	0.206967i	0.726328	−	0.687348i	$-0.241225\pi$
$877$	34.7601	+	6.12915i	1.17377	+	0.206967i	0.447438	+	0.894315i	$0.352336\pi$
$878$	18.6537	+	13.2928i	0.629533	+	0.448610i
$879$		0			0
$880$	31.7103	+	59.3778i	1.06895	+	2.00163i
$881$	−7.22906	+	12.5211i	−0.243553	+	0.421847i	−0.961724	−	0.274020i	$-0.911646\pi$
$881$	−7.22906	+	12.5211i	−0.243553	+	0.421847i	0.718171	+	0.695867i	$0.244980\pi$
$882$		0			0
$883$	30.6193	−	17.6781i	1.03042	−	0.594915i	0.113317	−	0.993559i	$-0.463852\pi$
$883$	30.6193	−	17.6781i	1.03042	−	0.594915i	0.917106	+	0.398644i	$0.130519\pi$
$884$	−24.1967	+	8.35618i	−0.813822	+	0.281049i
$885$		0			0
$886$	10.8599	+	23.8011i	0.364844	+	0.799615i
$887$	33.6657	−	12.2533i	1.13038	−	0.411426i	0.291952	−	0.956433i	$-0.405695\pi$
$887$	33.6657	−	12.2533i	1.13038	−	0.411426i	0.838432	+	0.545007i	$0.183473\pi$
$888$		0			0
$889$	3.41231	+	19.3522i	0.114445	+	0.649051i
$890$	67.2389	+	32.0338i	2.25385	+	1.07378i
$891$		0			0
$892$	3.83385	+	4.72562i	0.128367	+	0.158225i
$893$	−8.71560	+	1.53680i	−0.291656	+	0.0514269i
$894$		0			0
$895$	45.5853	−	16.5917i	1.52375	−	0.554599i
$896$	13.3214	−	16.8571i	0.445037	−	0.563155i
$897$		0			0
$898$	−7.59530	+	7.47067i	−0.253458	+	0.249299i
$899$	−5.21720	+	3.01215i	−0.174003	+	0.100461i
$900$		0			0
$901$	28.7699	+	16.6103i	0.958463	+	0.553369i
$902$	13.4905	−	3.49543i	0.449186	−	0.116385i
$903$		0			0
$904$	−2.79304	−	44.6667i	−0.0928951	−	1.48559i
$905$	−2.82829	+	16.0401i	−0.0940157	+	0.533189i
$906$		0			0
$907$	−5.65021	−	6.73365i	−0.187612	−	0.223587i	0.664037	−	0.747700i	$-0.268842\pi$
$907$	−5.65021	−	6.73365i	−0.187612	−	0.223587i	−0.851649	+	0.524112i	$0.824397\pi$
$908$	0.314109	+	1.97161i	0.0104241	+	0.0654301i
$909$		0			0
$910$	33.0140	−	2.61335i	1.09441	−	0.0866318i
$911$	−13.4129	−	4.88190i	−0.444389	−	0.161744i	0.110127	−	0.993918i	$-0.464874\pi$
$911$	−13.4129	−	4.88190i	−0.444389	−	0.161744i	−0.554516	+	0.832173i	$0.687097\pi$
$912$		0			0
$913$	8.29075	+	6.95676i	0.274384	+	0.230235i
$914$	1.91868	−	20.0215i	0.0634642	−	0.662254i
$915$		0			0
$916$	−1.29772	−	1.12602i	−0.0428778	−	0.0372048i
$917$			17.0691i			0.563671i
$918$		0			0
$919$	−54.9336			−1.81209			−0.906046	−	0.423179i	$-0.860914\pi$
$919$	−54.9336			−1.81209			−0.906046	+	0.423179i	$0.860914\pi$
$920$	27.1980	−	11.8701i	0.896691	−	0.391346i
$921$		0			0
$922$	−17.6147	−	1.68803i	−0.580110	−	0.0555923i
$923$	7.08225	−	8.44030i	0.233115	−	0.277816i
$924$		0			0
$925$	−15.4371	+	42.4130i	−0.507567	+	1.39453i
$926$	−7.67931	+	0.607885i	−0.252358	+	0.0199764i
$927$		0			0
$928$	−14.6231	−	35.0777i	−0.480027	−	1.15148i
$929$	−20.0336	+	16.8102i	−0.657282	+	0.551525i	−0.909271	−	0.416205i	$-0.863360\pi$
$929$	−20.0336	+	16.8102i	−0.657282	+	0.551525i	0.251989	+	0.967730i	$0.418915\pi$
$930$		0			0
$931$	−10.5385	−	1.85822i	−0.345385	−	0.0609006i
$932$	18.0913	−	10.0497i	0.592599	−	0.329187i
$933$		0			0
$934$	−10.0056	+	2.59247i	−0.327392	+	0.0848281i
$935$	29.3458	−	50.8283i	0.959709	−	1.66226i
$936$		0			0
$937$	30.0604	+	52.0662i	0.982031	+	1.70093i	0.654451	+	0.756105i	$0.272900\pi$
$937$	30.0604	+	52.0662i	0.982031	+	1.70093i	0.327580	+	0.944823i	$0.393767\pi$
$938$	26.2968	+	26.7355i	0.858621	+	0.872946i
$939$		0			0
$940$	−18.8575	−	0.312021i	−0.615065	−	0.0101770i
$941$	−19.3533	−	53.1728i	−0.630900	−	1.73338i	−0.678585	−	0.734522i	$-0.737406\pi$
$941$	−19.3533	−	53.1728i	−0.630900	−	1.73338i	0.0476846	−	0.998862i	$-0.484816\pi$
$942$		0			0
$943$	−1.06683	−	6.05031i	−0.0347408	−	0.197025i
$944$	−37.3694	−	7.87217i	−1.21627	−	0.256217i
$945$		0			0
$946$	−25.4229	+	53.3625i	−0.826568	+	1.73496i
$947$	45.6408	−	8.04770i	1.48313	−	0.261515i	0.627299	−	0.778778i	$-0.284160\pi$
$947$	45.6408	−	8.04770i	1.48313	−	0.261515i	0.855826	+	0.517263i	$0.173049\pi$
$948$		0			0
$949$	−1.18659	−	3.26012i	−0.0385182	−	0.105828i
$950$	−11.6427	−	25.5169i	−0.377740	−	0.827879i
$951$		0			0
$952$	−18.6155	−	2.09527i	−0.603332	−	0.0679082i
$953$	2.93376	+	5.08142i	0.0950338	+	0.164603i	0.909623	−	0.415435i	$-0.136371\pi$
$953$	2.93376	+	5.08142i	0.0950338	+	0.164603i	−0.814589	+	0.580039i	$0.803037\pi$
$954$		0			0
$955$	76.4681	+	44.1489i	2.47445	+	1.42862i
$956$	24.0499	+	4.65215i	0.777829	+	0.150461i
$957$		0			0
$958$	−7.98228	−	5.68824i	−0.257896	−	0.183779i
$959$	−5.55822	+	31.5222i	−0.179484	+	1.01791i
$960$		0			0
$961$	−23.1314	+	19.4095i	−0.746174	+	0.626114i
$962$	21.1104	+	30.6859i	0.680626	+	0.989353i
$963$		0			0
$964$	10.7176	−	27.9963i	0.345190	−	0.901699i
$965$	4.68325	−	12.8671i	0.150759	−	0.414207i
$966$		0			0
$967$	−17.2553	−	14.4789i	−0.554893	−	0.465610i	0.321701	−	0.946841i	$-0.395745\pi$
$967$	−17.2553	−	14.4789i	−0.554893	−	0.465610i	−0.876594	+	0.481231i	$0.840190\pi$
$968$	−33.1924	+	22.0347i	−1.06684	+	0.708221i
$969$		0			0
$970$	2.79056	−	10.0802i	0.0895994	−	0.323656i
$971$			21.9521i			0.704475i	0.935911	+	0.352238i	$0.114579\pi$
$971$			21.9521i			0.704475i	−0.935911	+	0.352238i	$0.885421\pi$
$972$		0			0
$973$		−	20.9235i		−	0.670778i
$974$	40.4556	+	11.1995i	1.29628	+	0.358856i
$975$		0			0
$976$	−33.8715	+	4.82311i	−1.08420	+	0.154384i
$977$	36.9729	+	31.0239i	1.18287	+	0.992543i	0.999956	+	0.00941403i	$0.00299662\pi$
$977$	36.9729	+	31.0239i	1.18287	+	0.992543i	0.182911	+	0.983129i	$0.441448\pi$
$978$		0			0
$979$	−26.8504	+	73.7710i	−0.858144	+	2.35773i
$980$	−21.2975	−	8.15314i	−0.680323	−	0.260443i
$981$		0			0
$982$	10.2539	−	7.05415i	0.327214	−	0.225107i
$983$	35.0417	−	29.4034i	1.11766	−	0.937824i	0.119172	−	0.992874i	$-0.461976\pi$
$983$	35.0417	−	29.4034i	1.11766	−	0.937824i	0.998484	+	0.0550493i	$0.0175316\pi$
$984$		0			0
$985$	6.00289	−	34.0441i	0.191268	−	1.08474i
$986$	−19.2295	+	26.9847i	−0.612393	+	0.859369i
$987$		0			0
$988$	−22.7241	−	4.39569i	−0.722950	−	0.139846i
$989$	22.5669	+	13.0290i	0.717585	+	0.414298i
$990$		0			0
$991$	6.44420	+	11.1617i	0.204707	+	0.354562i	0.950039	−	0.312130i	$-0.101043\pi$
$991$	6.44420	+	11.1617i	0.204707	+	0.354562i	−0.745333	+	0.666693i	$0.767709\pi$
$992$	2.73522	+	4.27199i	0.0868432	+	0.135636i
$993$		0			0
$994$	7.33540	−	3.34696i	0.232665	−	0.106159i
$995$	−1.58712	−	4.36058i	−0.0503151	−	0.138240i
$996$		0			0
$997$	4.83400	−	0.852365i	0.153094	−	0.0269947i	−0.0965756	−	0.995326i	$-0.530789\pi$
$997$	4.83400	−	0.852365i	0.153094	−	0.0269947i	0.249670	+	0.968331i	$0.419678\pi$
$998$	−19.0029	−	9.05332i	−0.601526	−	0.286578i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.253.32		204
3.2	odd	2		216.2.t.a.13.3	✓	204
8.5	even	2	inner	648.2.t.a.253.6		204
12.11	even	2		864.2.bf.a.337.15		204
24.5	odd	2		216.2.t.a.13.29	yes	204
24.11	even	2		864.2.bf.a.337.20		204
27.2	odd	18		216.2.t.a.133.29	yes	204
27.25	even	9	inner	648.2.t.a.397.6		204
108.83	even	18		864.2.bf.a.241.20		204
216.29	odd	18		216.2.t.a.133.3	yes	204
216.83	even	18		864.2.bf.a.241.15		204
216.133	even	18	inner	648.2.t.a.397.32		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.3	✓	204	3.2	odd	2
216.2.t.a.13.29	yes	204	24.5	odd	2
216.2.t.a.133.3	yes	204	216.29	odd	18
216.2.t.a.133.29	yes	204	27.2	odd	18
648.2.t.a.253.6		204	8.5	even	2	inner
648.2.t.a.253.32		204	1.1	even	1	trivial
648.2.t.a.397.6		204	27.25	even	9	inner
648.2.t.a.397.32		204	216.133	even	18	inner
864.2.bf.a.241.15		204	216.83	even	18
864.2.bf.a.241.20		204	108.83	even	18
864.2.bf.a.337.15		204	12.11	even	2
864.2.bf.a.337.20		204	24.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36295 + 0.377313i) q^{2} +(1.71527 + 1.02852i) q^{4} +(2.15975 - 2.57389i) q^{5} +(-1.78453 - 0.649515i) q^{7} +(1.94976 + 2.04901i) q^{8} +(3.91480 - 2.69319i) q^{10} +(3.21944 + 3.83678i) q^{11} +(-3.61424 - 0.637289i) q^{13} +(-2.18715 - 1.55858i) q^{14} +(1.88430 + 3.52837i) q^{16} +(1.74380 - 3.02034i) q^{17} +(2.73085 - 1.57666i) q^{19} +(6.35185 - 2.19358i) q^{20} +(2.94027 + 6.44408i) q^{22} +(2.93428 - 1.06799i) q^{23} +(-1.09215 - 6.19390i) q^{25} +(-4.68558 - 2.23229i) q^{26} +(-2.39291 - 2.94951i) q^{28} +(-6.61611 + 1.16660i) q^{29} +(0.842639 - 0.306695i) q^{31} +(1.23691 + 5.51997i) q^{32} +(3.51632 - 3.45862i) q^{34} +(-5.52592 + 3.19039i) q^{35} +(-6.21485 - 3.58815i) q^{37} +(4.31691 - 1.11852i) q^{38} +(9.48493 - 0.593099i) q^{40} +(0.341649 - 1.93759i) q^{41} +(5.36405 + 6.39263i) q^{43} +(1.57601 + 9.89237i) q^{44} +(4.40224 - 0.348476i) q^{46} +(-2.63733 - 0.959909i) q^{47} +(-2.59964 - 2.18135i) q^{49} +(0.848490 - 8.85407i) q^{50} +(-5.54394 - 4.81044i) q^{52} +9.52536i q^{53} +16.8287 q^{55} +(-2.14853 - 4.92292i) q^{56} +(-9.45760 - 0.906327i) q^{58} +(-6.13695 + 7.31373i) q^{59} +(-2.92540 + 8.03747i) q^{61} +(1.26420 - 0.100072i) q^{62} +(-0.396910 + 7.99015i) q^{64} +(-9.44618 + 7.92629i) q^{65} +(-13.7512 - 2.42470i) q^{67} +(6.09756 - 3.38718i) q^{68} +(-8.73534 + 2.26335i) q^{70} +(-1.50109 + 2.59997i) q^{71} +(0.472663 + 0.818676i) q^{73} +(-7.11668 - 7.23541i) q^{74} +(6.30577 + 0.104337i) q^{76} +(-3.25314 - 8.93793i) q^{77} +(-0.803209 - 4.55523i) q^{79} +(13.1513 + 2.77042i) q^{80} +(1.19673 - 2.51193i) q^{82} +(2.12803 - 0.375229i) q^{83} +(-4.00787 - 11.0115i) q^{85} +(4.89892 + 10.7368i) q^{86} +(-1.58449 + 14.0775i) q^{88} +(7.83712 + 13.5743i) q^{89} +(6.03579 + 3.48477i) q^{91} +(6.13153 + 1.18607i) q^{92} +(-3.23236 - 2.30341i) q^{94} +(1.83982 - 10.4341i) q^{95} +(1.68619 - 1.41488i) q^{97} +(-2.72012 - 3.95396i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

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