LMFDB - Embedded newform 567.2.ba.a.143.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(143,567)] 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("567.143"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47978 + 1.76353i) q^{2} +(-0.573000 - 3.24965i) q^{4} +(1.41208 - 1.18487i) q^{5} +(-2.40040 + 1.11270i) q^{7} +(2.59137 + 1.49613i) q^{8} +4.24358i q^{10} +(0.0789393 - 0.0940762i) q^{11} +(0.0159063 - 0.0437022i) q^{13} +(1.58977 - 5.87972i) q^{14} +(-0.271551 + 0.0988366i) q^{16} -0.157246 q^{17} +7.59626i q^{19} +(-4.65954 - 3.90982i) q^{20} +(0.0490936 + 0.278423i) q^{22} +(-0.332628 + 0.913889i) q^{23} +(-0.278205 + 1.57778i) q^{25} +(0.0535324 + 0.0927208i) q^{26} +(4.99131 + 7.16286i) q^{28} +(3.33678 + 9.16772i) q^{29} +(-4.49600 + 0.792766i) q^{31} +(-1.81929 + 4.99845i) q^{32} +(0.232689 - 0.277308i) q^{34} +(-2.07113 + 4.41538i) q^{35} +(-4.68718 + 8.11843i) q^{37} +(-13.3962 - 11.2408i) q^{38} +(5.43192 - 0.957794i) q^{40} +(5.76925 + 2.09983i) q^{41} +(1.67890 - 9.52153i) q^{43} +(-0.350947 - 0.202619i) q^{44} +(-1.11945 - 1.93895i) q^{46} +(-0.723937 + 4.10565i) q^{47} +(4.52380 - 5.34184i) q^{49} +(-2.37078 - 2.82539i) q^{50} +(-0.151131 - 0.0266485i) q^{52} +(-0.141686 - 0.0818025i) q^{53} -0.226376i q^{55} +(-7.88504 - 0.707881i) q^{56} +(-21.1052 - 7.68168i) q^{58} +(-11.1248 - 4.04911i) q^{59} +(2.98946 + 0.527123i) q^{61} +(5.25501 - 9.10194i) q^{62} +(-6.41175 - 11.1055i) q^{64} +(-0.0293206 - 0.0805578i) q^{65} +(-7.53281 + 6.32078i) q^{67} +(0.0901020 + 0.510994i) q^{68} +(-4.72184 - 10.1863i) q^{70} +(0.863276 - 0.498413i) q^{71} +(7.95454 - 4.59256i) q^{73} +(-7.38112 - 20.2795i) q^{74} +(24.6852 - 4.35266i) q^{76} +(-0.0848069 + 0.313656i) q^{77} +(1.99133 + 1.67093i) q^{79} +(-0.266342 + 0.461318i) q^{80} +(-12.2403 + 7.06695i) q^{82} +(-6.02764 + 2.19388i) q^{83} +(-0.222043 + 0.186316i) q^{85} +(14.3071 + 17.0505i) q^{86} +(0.345310 - 0.125683i) q^{88} +10.6041 q^{89} +(0.0104460 + 0.122602i) q^{91} +(3.16041 + 0.557266i) q^{92} +(-6.16918 - 7.35214i) q^{94} +(9.00059 + 10.7265i) q^{95} +(-13.2580 - 2.33775i) q^{97} +(2.72628 + 15.8826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−1.47978	+	1.76353i	−1.04636	+	1.24700i	−0.0781303	+	0.996943i	$0.524895\pi$
$2$	−1.47978	+	1.76353i	−1.04636	+	1.24700i	−0.968230	+	0.250061i	$0.919549\pi$
$3$		0			0
$3$		0			0
$4$	−0.573000	−	3.24965i	−0.286500	−	1.62482i
$5$	1.41208	−	1.18487i	0.631499	−	0.529891i	−0.269895	−	0.962890i	$-0.586989\pi$
$5$	1.41208	−	1.18487i	0.631499	−	0.529891i	0.901394	+	0.432999i	$0.142545\pi$
$6$		0			0
$7$	−2.40040	+	1.11270i	−0.907264	+	0.420561i
$7$	−2.40040	+	1.11270i	−0.907264	+	0.420561i
$8$	2.59137	+	1.49613i	0.916186	+	0.528960i
$9$		0			0
$10$			4.24358i			1.34194i
$11$	0.0789393	−	0.0940762i	0.0238011	−	0.0283650i	−0.754013	−	0.656860i	$-0.771884\pi$
$11$	0.0789393	−	0.0940762i	0.0238011	−	0.0283650i	0.777814	+	0.628495i	$0.216329\pi$
$12$		0			0
$13$	0.0159063	−	0.0437022i	0.00441162	−	0.0121208i	−0.937467	−	0.348073i	$-0.886836\pi$
$13$	0.0159063	−	0.0437022i	0.00441162	−	0.0121208i	0.941879	+	0.335953i	$0.109058\pi$
$14$	1.58977	−	5.87972i	0.424884	−	1.57142i
$15$		0			0
$16$	−0.271551	+	0.0988366i	−0.0678878	+	0.0247091i
$17$	−0.157246			−0.0381377			−0.0190689	−	0.999818i	$-0.506070\pi$
$17$	−0.157246			−0.0381377			−0.0190689	+	0.999818i	$0.506070\pi$
$18$		0			0
$19$			7.59626i			1.74270i	0.490661	+	0.871350i	$0.336755\pi$
$19$			7.59626i			1.74270i	−0.490661	+	0.871350i	$0.663245\pi$
$20$	−4.65954	−	3.90982i	−1.04190	−	0.874261i
$21$		0			0
$22$	0.0490936	+	0.278423i	0.0104668	+	0.0593601i
$23$	−0.332628	+	0.913889i	−0.0693578	+	0.190559i	−0.969529	−	0.244978i	$-0.921219\pi$
$23$	−0.332628	+	0.913889i	−0.0693578	+	0.190559i	0.900171	+	0.435537i	$0.143441\pi$
$24$		0			0
$25$	−0.278205	+	1.57778i	−0.0556411	+	0.315556i
$26$	0.0535324	+	0.0927208i	0.0104986	+	0.0181840i
$27$		0			0
$28$	4.99131	+	7.16286i	0.943269	+	1.35365i
$29$	3.33678	+	9.16772i	0.619624	+	1.70240i	0.707906	+	0.706307i	$0.249640\pi$
$29$	3.33678	+	9.16772i	0.619624	+	1.70240i	−0.0882816	+	0.996096i	$0.528138\pi$
$30$		0			0
$31$	−4.49600	+	0.792766i	−0.807505	+	0.142385i	−0.562136	−	0.827045i	$-0.690020\pi$
$31$	−4.49600	+	0.792766i	−0.807505	+	0.142385i	−0.245369	+	0.969430i	$0.578909\pi$
$32$	−1.81929	+	4.99845i	−0.321607	+	0.883609i
$33$		0			0
$34$	0.232689	−	0.277308i	0.0399058	−	0.0475579i
$35$	−2.07113	+	4.41538i	−0.350085	+	0.746335i
$36$		0			0
$37$	−4.68718	+	8.11843i	−0.770567	+	1.33466i	0.166685	+	0.986010i	$0.446694\pi$
$37$	−4.68718	+	8.11843i	−0.770567	+	1.33466i	−0.937252	+	0.348652i	$0.886640\pi$
$38$	−13.3962	−	11.2408i	−2.17315	−	1.82349i
$39$		0			0
$40$	5.43192	−	0.957794i	0.858862	−	0.151441i
$41$	5.76925	+	2.09983i	0.901005	+	0.327939i	0.750656	−	0.660694i	$-0.229738\pi$
$41$	5.76925	+	2.09983i	0.901005	+	0.327939i	0.150350	+	0.988633i	$0.451960\pi$
$42$		0			0
$43$	1.67890	−	9.52153i	0.256030	−	1.45202i	−0.537384	−	0.843338i	$-0.680587\pi$
$43$	1.67890	−	9.52153i	0.256030	−	1.45202i	0.793414	−	0.608682i	$-0.208301\pi$
$44$	−0.350947	−	0.202619i	−0.0529072	−	0.0305460i
$45$		0			0
$46$	−1.11945	−	1.93895i	−0.165055	−	0.285883i
$47$	−0.723937	+	4.10565i	−0.105597	+	0.598871i	0.885383	+	0.464862i	$0.153896\pi$
$47$	−0.723937	+	4.10565i	−0.105597	+	0.598871i	−0.990980	+	0.134009i	$0.957215\pi$
$48$		0			0
$49$	4.52380	−	5.34184i	0.646257	−	0.763120i
$50$	−2.37078	−	2.82539i	−0.335279	−	0.399570i
$51$		0			0
$52$	−0.151131	−	0.0266485i	−0.0209581	−	0.00369548i
$53$	−0.141686	−	0.0818025i	−0.0194621	−	0.0112364i	0.490237	−	0.871589i	$-0.336910\pi$
$53$	−0.141686	−	0.0818025i	−0.0194621	−	0.0112364i	−0.509699	+	0.860353i	$0.670243\pi$
$54$		0			0
$55$		−	0.226376i		−	0.0305245i
$56$	−7.88504	−	0.707881i	−1.05368	−	0.0945946i
$57$		0			0
$58$	−21.1052	−	7.68168i	−2.77125	−	1.00865i
$59$	−11.1248	−	4.04911i	−1.44833	−	0.527150i	−0.506207	−	0.862412i	$-0.668953\pi$
$59$	−11.1248	−	4.04911i	−1.44833	−	0.527150i	−0.942125	+	0.335262i	$0.891175\pi$
$60$		0			0
$61$	2.98946	+	0.527123i	0.382762	+	0.0674912i	0.361718	−	0.932287i	$-0.382190\pi$
$61$	2.98946	+	0.527123i	0.382762	+	0.0674912i	0.0210431	+	0.999779i	$0.493301\pi$
$62$	5.25501	−	9.10194i	0.667387	−	1.15595i
$63$		0			0
$64$	−6.41175	−	11.1055i	−0.801469	−	1.38818i
$65$	−0.0293206	−	0.0805578i	−0.00363678	−	0.00999196i
$66$		0			0
$67$	−7.53281	+	6.32078i	−0.920279	+	0.772206i	−0.974047	−	0.226348i	$-0.927321\pi$
$67$	−7.53281	+	6.32078i	−0.920279	+	0.772206i	0.0537674	+	0.998553i	$0.482877\pi$
$68$	0.0901020	+	0.510994i	0.0109265	+	0.0619671i
$69$		0			0
$70$	−4.72184	−	10.1863i	−0.564367	−	1.21749i
$71$	0.863276	−	0.498413i	0.102452	−	0.0591507i	−0.447899	−	0.894084i	$-0.647827\pi$
$71$	0.863276	−	0.498413i	0.102452	−	0.0591507i	0.550351	+	0.834934i	$0.314494\pi$
$72$		0			0
$73$	7.95454	−	4.59256i	0.931009	−	0.537518i	0.0438782	−	0.999037i	$-0.486029\pi$
$73$	7.95454	−	4.59256i	0.931009	−	0.537518i	0.887130	+	0.461519i	$0.152695\pi$
$74$	−7.38112	−	20.2795i	−0.858037	−	2.35744i
$75$		0			0
$76$	24.6852	−	4.35266i	2.83158	−	0.499284i
$77$	−0.0848069	+	0.313656i	−0.00966465	+	0.0357444i
$78$		0			0
$79$	1.99133	+	1.67093i	0.224043	+	0.187994i	0.747899	−	0.663812i	$-0.231063\pi$
$79$	1.99133	+	1.67093i	0.224043	+	0.187994i	−0.523856	+	0.851807i	$0.675507\pi$
$80$	−0.266342	+	0.461318i	−0.0297780	+	0.0515769i
$81$		0			0
$82$	−12.2403	+	7.06695i	−1.35172	+	0.780414i
$83$	−6.02764	+	2.19388i	−0.661619	+	0.240810i	−0.650935	−	0.759133i	$-0.725623\pi$
$83$	−6.02764	+	2.19388i	−0.661619	+	0.240810i	−0.0106840	+	0.999943i	$0.503401\pi$
$84$		0			0
$85$	−0.222043	+	0.186316i	−0.0240840	+	0.0202088i
$86$	14.3071	+	17.0505i	1.54277	+	1.83861i
$87$		0			0
$88$	0.345310	−	0.125683i	0.0368102	−	0.0133978i
$89$	10.6041			1.12403			0.562014	−	0.827128i	$-0.310027\pi$
$89$	10.6041			1.12403			0.562014	+	0.827128i	$0.310027\pi$
$90$		0			0
$91$	0.0104460	+	0.122602i	0.00109504	+	0.0128521i
$92$	3.16041	+	0.557266i	0.329496	+	0.0580990i
$93$		0			0
$94$	−6.16918	−	7.35214i	−0.636302	−	0.758315i
$95$	9.00059	+	10.7265i	0.923441	+	1.10051i
$96$		0			0
$97$	−13.2580	−	2.33775i	−1.34615	−	0.237363i	−0.546313	−	0.837581i	$-0.683969\pi$
$97$	−13.2580	−	2.33775i	−1.34615	−	0.237363i	−0.799836	+	0.600218i	$0.795080\pi$
$98$	2.72628	+	15.8826i	0.275396	+	1.60438i
$99$		0			0
$100$	5.28664			0.528664
$101$	13.0579	−	4.75270i	1.29931	−	0.472911i	0.402540	−	0.915403i	$-0.368128\pi$
$101$	13.0579	−	4.75270i	1.29931	−	0.472911i	0.896773	+	0.442492i	$0.145905\pi$
$102$		0			0
$103$	5.01435	+	5.97587i	0.494079	+	0.588820i	0.954250	−	0.299010i	$-0.0966564\pi$
$103$	5.01435	+	5.97587i	0.494079	+	0.588820i	−0.460171	+	0.887830i	$0.652212\pi$
$104$	0.106603	−	0.0894506i	0.0104533	−	0.00877135i
$105$		0			0
$106$	0.353925	−	0.128818i	0.0343762	−	0.0125119i
$107$	−6.46785	+	3.73421i	−0.625271	+	0.361000i	−0.778918	−	0.627126i	$-0.784231\pi$
$107$	−6.46785	+	3.73421i	−0.625271	+	0.361000i	0.153648	+	0.988126i	$0.450898\pi$
$108$		0			0
$109$	4.37239	−	7.57320i	0.418799	−	0.725381i	−0.577020	−	0.816730i	$-0.695784\pi$
$109$	4.37239	−	7.57320i	0.418799	−	0.725381i	0.995819	+	0.0913488i	$0.0291178\pi$
$110$	0.399220	+	0.334985i	0.0380641	+	0.0319396i
$111$		0			0
$112$	0.541855	−	0.539402i	0.0512005	−	0.0509687i
$113$	−16.2059	+	2.85754i	−1.52453	+	0.268815i	−0.872210	−	0.489131i	$-0.837314\pi$
$113$	−16.2059	+	2.85754i	−1.52453	+	0.268815i	−0.652317	+	0.757947i	$0.726203\pi$
$114$		0			0
$115$	0.613145	+	1.68460i	0.0571761	+	0.157090i
$116$	27.8799	−	16.0965i	2.58858	−	1.49452i
$117$		0			0
$118$	23.6030	−	13.6272i	2.17283	−	1.25449i
$119$	0.377452	−	0.174968i	0.0346010	−	0.0160392i
$120$		0			0
$121$	1.90751	+	10.8180i	0.173410	+	0.983458i
$122$	−5.35334	+	4.49198i	−0.484668	+	0.406685i
$123$		0			0
$124$	5.15242	+	14.1562i	0.462701	+	1.27126i
$125$	6.08496	+	10.5395i	0.544255	+	0.942677i
$126$		0			0
$127$	−2.14737	+	3.71936i	−0.190549	+	0.330040i	−0.945432	−	0.325819i	$-0.894360\pi$
$127$	−2.14737	+	3.71936i	−0.190549	+	0.330040i	0.754884	+	0.655859i	$0.227693\pi$
$128$	18.5960	+	3.27897i	1.64367	+	0.289823i
$129$		0			0
$130$	0.185454	+	0.0674998i	0.0162654	+	0.00592012i
$131$	−4.06526	−	1.47963i	−0.355184	−	0.129276i	0.158265	−	0.987397i	$-0.449410\pi$
$131$	−4.06526	−	1.47963i	−0.355184	−	0.129276i	−0.513448	+	0.858120i	$0.671632\pi$
$132$		0			0
$133$	−8.45235	−	18.2340i	−0.732912	−	1.58109i
$134$		−	22.6377i		−	1.95560i
$135$		0			0
$136$	−0.407482	−	0.235260i	−0.0349413	−	0.0201733i
$137$	1.72630	+	0.304394i	0.147488	+	0.0260061i	0.246905	−	0.969040i	$-0.420587\pi$
$137$	1.72630	+	0.304394i	0.147488	+	0.0260061i	−0.0994166	+	0.995046i	$0.531698\pi$
$138$		0			0
$139$	8.74606	+	10.4232i	0.741831	+	0.884080i	0.996555	−	0.0829338i	$-0.0264290\pi$
$139$	8.74606	+	10.4232i	0.741831	+	0.884080i	−0.254724	+	0.967014i	$0.581985\pi$
$140$	15.5352	+	4.20044i	1.31296	+	0.355002i
$141$		0			0
$142$	−0.398491	+	2.25995i	−0.0334406	+	0.189651i
$143$	−0.00285570	−	0.00494623i	−0.000238806	−	0.000413624i
$144$		0			0
$145$	15.5744	+	8.99186i	1.29338	+	0.746733i
$146$	−3.67184	+	20.8240i	−0.303884	+	1.72341i
$147$		0			0
$148$	29.0678	+	10.5798i	2.38936	+	0.869655i
$149$	−9.13243	+	1.61029i	−0.748158	+	0.131920i	−0.534712	−	0.845034i	$-0.679580\pi$
$149$	−9.13243	+	1.61029i	−0.748158	+	0.131920i	−0.213446	+	0.976955i	$0.568469\pi$
$150$		0			0
$151$	7.47831	+	6.27505i	0.608576	+	0.510656i	0.894189	−	0.447689i	$-0.147753\pi$
$151$	7.47831	+	6.27505i	0.608576	+	0.510656i	−0.285613	+	0.958345i	$0.592197\pi$
$152$	−11.3650	+	19.6847i	−0.921820	+	1.59664i
$153$		0			0
$154$	−0.427646	−	0.613700i	−0.0344607	−	0.0494534i
$155$	−5.40936	+	6.44663i	−0.434490	+	0.517806i
$156$		0			0
$157$	5.53496	−	15.2072i	0.441738	−	1.21366i	−0.496611	−	0.867973i	$-0.665422\pi$
$157$	5.53496	−	15.2072i	0.441738	−	1.21366i	0.938348	−	0.345691i	$-0.112356\pi$
$158$	−5.89346	+	1.03918i	−0.468859	+	0.0826725i
$159$		0			0
$160$	3.35355	+	9.21381i	0.265122	+	0.728415i
$161$	−0.218444	−	2.56381i	−0.0172158	−	0.202057i
$162$		0			0
$163$	5.65656	+	9.79745i	0.443056	+	0.767396i	0.997915	−	0.0645491i	$-0.0205609\pi$
$163$	5.65656	+	9.79745i	0.443056	+	0.767396i	−0.554858	+	0.831945i	$0.687228\pi$
$164$	3.51794	−	19.9512i	0.274705	−	1.55793i
$165$		0			0
$166$	5.05059	−	13.8764i	0.392002	−	1.07702i
$167$	−0.331914	−	1.88238i	−0.0256843	−	0.145663i	0.969269	−	0.246004i	$-0.0791176\pi$
$167$	−0.331914	−	1.88238i	−0.0256843	−	0.145663i	−0.994953	+	0.100341i	$0.968007\pi$
$168$		0			0
$169$	9.95692	+	8.35485i	0.765917	+	0.642681i
$170$		−	0.667286i		−	0.0511785i
$171$		0			0
$172$	−31.9036			−2.43263
$173$	22.9967	−	8.37010i	1.74840	−	0.636367i	0.748755	−	0.662847i	$-0.230652\pi$
$173$	22.9967	−	8.37010i	1.74840	−	0.636367i	0.999649	+	0.0264796i	$0.00842971\pi$
$174$		0			0
$175$	−1.08779	−	4.09686i	−0.0822295	−	0.309693i
$176$	−0.0121379	+	0.0333486i	−0.000914928	+	0.00251374i
$177$		0			0
$178$	−15.6916	+	18.7006i	−1.17614	+	1.40167i
$179$		−	18.4669i		−	1.38028i	−0.723676	−	0.690140i	$-0.757549\pi$
$179$		−	18.4669i		−	1.38028i	0.723676	−	0.690140i	$-0.242451\pi$
$180$		0			0
$181$	−5.58272	−	3.22319i	−0.414960	−	0.239577i	0.277958	−	0.960593i	$-0.410342\pi$
$181$	−5.58272	−	3.22319i	−0.414960	−	0.239577i	−0.692919	+	0.721016i	$0.743676\pi$
$182$	−0.231669	−	0.163001i	−0.0171725	−	0.0120824i
$183$		0			0
$184$	−2.22925	+	1.87057i	−0.164343	+	0.137900i
$185$	3.00065	+	17.0175i	0.220612	+	1.25116i
$186$		0			0
$187$	−0.0124129	+	0.0147931i	−0.000907720	+	0.00108178i
$188$	13.7567			1.00331
$189$		0			0
$190$	−32.2354			−2.33860
$191$	6.44902	−	7.68564i	0.466635	−	0.556113i	−0.480481	−	0.877005i	$-0.659538\pi$
$191$	6.44902	−	7.68564i	0.466635	−	0.556113i	0.947116	+	0.320891i	$0.103982\pi$
$192$		0			0
$193$	−4.27327	−	24.2349i	−0.307597	−	1.74447i	−0.611022	−	0.791614i	$-0.709241\pi$
$193$	−4.27327	−	24.2349i	−0.307597	−	1.74447i	0.303424	−	0.952855i	$-0.401870\pi$
$194$	23.7416	−	19.9216i	1.70455	−	1.43029i
$195$		0			0
$196$	−19.9512	−	11.6399i	−1.42509	−	0.831419i
$197$	−12.0988	−	6.98527i	−0.862007	−	0.497680i	0.00267677	−	0.999996i	$-0.499148\pi$
$197$	−12.0988	−	6.98527i	−0.862007	−	0.497680i	−0.864684	+	0.502316i	$0.832481\pi$
$198$		0			0
$199$			12.8790i			0.912968i	0.889732	+	0.456484i	$0.150892\pi$
$199$			12.8790i			0.912968i	−0.889732	+	0.456484i	$0.849108\pi$
$200$	−3.08149	+	3.67238i	−0.217894	+	0.259676i
$201$		0			0
$202$	−10.9413	+	30.0610i	−0.769827	+	2.11508i
$203$	−18.2105	−	18.2933i	−1.27813	−	1.28394i
$204$		0			0
$205$	10.6347	−	3.87070i	0.742756	−	0.270341i
$206$	−17.9587			−1.25125
$207$		0			0
$208$			0.0134395i			0.000931863i
$209$	0.714627	+	0.599643i	0.0494318	+	0.0414782i
$210$		0			0
$211$	−0.918282	−	5.20784i	−0.0632171	−	0.358522i	−0.999964	−	0.00851397i	$-0.997290\pi$
$211$	−0.918282	−	5.20784i	−0.0632171	−	0.358522i	0.936747	−	0.350008i	$-0.113821\pi$
$212$	−0.184643	+	0.507302i	−0.0126813	+	0.0348417i
$213$		0			0
$214$	2.98558	−	16.9320i	0.204090	−	1.15745i
$215$	−8.91106	−	15.4344i	−0.607729	−	1.05262i
$216$		0			0
$217$	9.91006	−	6.90565i	0.672739	−	0.468786i
$218$	6.88541	+	18.9175i	0.466339	+	1.28125i
$219$		0			0
$220$	−0.735641	+	0.129713i	−0.0495969	+	0.00874527i
$221$	−0.00250120	+	0.00687200i	−0.000168249	+	0.000462260i
$222$		0			0
$223$	−5.38046	+	6.41218i	−0.360302	+	0.429392i	−0.915495	−	0.402330i	$-0.868200\pi$
$223$	−5.38046	+	6.41218i	−0.360302	+	0.429392i	0.555192	+	0.831722i	$0.312645\pi$
$224$	−1.19477	−	14.0226i	−0.0798286	−	0.936922i
$225$		0			0
$226$	18.9418	−	32.8082i	1.25999	−	2.18237i
$227$	15.4623	+	12.9744i	1.02627	+	0.861143i	0.990402	−	0.138214i	$-0.0441361\pi$
$227$	15.4623	+	12.9744i	1.02627	+	0.861143i	0.0358677	+	0.999357i	$0.488581\pi$
$228$		0			0
$229$	5.72074	−	1.00872i	0.378037	−	0.0666582i	0.0185989	−	0.999827i	$-0.494079\pi$
$229$	5.72074	−	1.00872i	0.378037	−	0.0666582i	0.359438	+	0.933169i	$0.382968\pi$
$230$	−3.87817	−	1.41154i	−0.255719	−	0.0930740i
$231$		0			0
$232$	−5.06925	+	28.7491i	−0.332813	+	1.88747i
$233$	−5.33662	−	3.08110i	−0.349614	−	0.201850i	0.314901	−	0.949124i	$-0.398029\pi$
$233$	−5.33662	−	3.08110i	−0.349614	−	0.201850i	−0.664515	+	0.747275i	$0.731362\pi$
$234$		0			0
$235$	3.84242	+	6.65527i	0.250652	+	0.434142i
$236$	−6.78365	+	38.4720i	−0.441578	+	2.50431i
$237$		0			0
$238$	−0.249985	+	0.924562i	−0.0162041	+	0.0599304i
$239$	−11.9974	−	14.2979i	−0.776046	−	0.924856i	0.222702	−	0.974887i	$-0.428512\pi$
$239$	−11.9974	−	14.2979i	−0.776046	−	0.924856i	−0.998748	+	0.0500310i	$0.984068\pi$
$240$		0			0
$241$	−12.0008	−	2.11606i	−0.773039	−	0.136308i	−0.226805	−	0.973940i	$-0.572828\pi$
$241$	−12.0008	−	2.11606i	−0.773039	−	0.136308i	−0.546234	+	0.837633i	$0.683939\pi$
$242$	−21.9006	−	12.6443i	−1.40782	−	0.812808i
$243$		0			0
$244$		−	10.0167i		−	0.641256i
$245$	0.0585478	−	12.9032i	0.00374048	−	0.824355i
$246$		0			0
$247$	0.331973	+	0.120828i	0.0211230	+	0.00768813i
$248$	−12.8368	−	4.67223i	−0.815141	−	0.296687i
$249$		0			0
$250$	−27.5910	−	4.86504i	−1.74501	−	0.307692i
$251$	−1.90241	+	3.29506i	−0.120079	+	0.207983i	−0.919799	−	0.392391i	$-0.871648\pi$
$251$	−1.90241	+	3.29506i	−0.120079	+	0.207983i	0.799720	+	0.600373i	$0.204981\pi$
$252$		0			0
$253$	0.0597177	+	0.103434i	0.00375442	+	0.00650285i
$254$	−3.38157	−	9.29078i	−0.212178	−	0.582956i
$255$		0			0
$256$	−13.6537	+	11.4568i	−0.853355	+	0.716050i
$257$	3.82957	+	21.7186i	0.238882	+	1.35477i	0.834282	+	0.551339i	$0.185883\pi$
$257$	3.82957	+	21.7186i	0.238882	+	1.35477i	−0.595399	+	0.803430i	$0.703006\pi$
$258$		0			0
$259$	2.21771	−	24.7029i	0.137802	−	1.53496i
$260$	−0.244984	+	0.141441i	−0.0151932	+	0.00877182i
$261$		0			0
$262$	8.62506	−	4.97968i	0.532858	−	0.307646i
$263$	−0.651083	−	1.78884i	−0.0401475	−	0.110304i	0.917999	−	0.396583i	$-0.129804\pi$
$263$	−0.651083	−	1.78884i	−0.0401475	−	0.110304i	−0.958146	+	0.286278i	$0.907582\pi$
$264$		0			0
$265$	−0.296997	+	0.0523686i	−0.0182444	+	0.00321698i
$266$	44.6638	+	12.0763i	2.73852	+	0.740446i
$267$		0			0
$268$	24.8566	+	20.8572i	1.51836	+	1.27405i
$269$	−6.11936	+	10.5990i	−0.373104	+	0.646235i	−0.990041	−	0.140777i	$-0.955040\pi$
$269$	−6.11936	+	10.5990i	−0.373104	+	0.646235i	0.616937	+	0.787012i	$0.288373\pi$
$270$		0			0
$271$	10.1008	−	5.83167i	0.613577	−	0.354249i	−0.160787	−	0.986989i	$-0.551403\pi$
$271$	10.1008	−	5.83167i	0.613577	−	0.354249i	0.774364	+	0.632740i	$0.218070\pi$
$272$	0.0427003	−	0.0155416i	0.00258909	−	0.000942351i
$273$		0			0
$274$	−3.09135	+	2.59395i	−0.186755	+	0.156706i
$275$	0.126470	+	0.150721i	0.00762644	+	0.00908884i
$276$		0			0
$277$	17.8050	−	6.48049i	1.06980	−	0.389375i	0.253698	−	0.967284i	$-0.418353\pi$
$277$	17.8050	−	6.48049i	1.06980	−	0.389375i	0.816102	+	0.577908i	$0.196131\pi$
$278$	−31.3238			−1.87867
$279$		0			0
$280$	−11.9730	+	8.34318i	−0.715525	+	0.498601i
$281$	−0.401346	−	0.0707682i	−0.0239423	−	0.00422168i	0.161664	−	0.986846i	$-0.448314\pi$
$281$	−0.401346	−	0.0707682i	−0.0239423	−	0.00422168i	−0.185607	+	0.982624i	$0.559425\pi$
$282$		0			0
$283$	2.99151	+	3.56515i	0.177827	+	0.211926i	0.847594	−	0.530645i	$-0.178050\pi$
$283$	2.99151	+	3.56515i	0.177827	+	0.211926i	−0.669767	+	0.742571i	$0.733606\pi$
$284$	−2.11432	−	2.51975i	−0.125462	−	0.149520i
$285$		0			0
$286$	0.0129486	+	0.00228319i	0.000765668	+	0.000135008i
$287$	−16.1850	+	1.37901i	−0.955368	+	0.0814003i
$288$		0			0
$289$	−16.9753			−0.998546
$290$	−38.9040	+	14.1599i	−2.28452	+	0.831498i
$291$		0			0
$292$	−19.4821	−	23.2179i	−1.14011	−	1.35873i
$293$	−6.35829	+	5.33524i	−0.371455	+	0.311688i	−0.809337	−	0.587345i	$-0.800173\pi$
$293$	−6.35829	+	5.33524i	−0.371455	+	0.311688i	0.437882	+	0.899033i	$0.355729\pi$
$294$		0			0
$295$	−20.5068	+	7.46387i	−1.19395	+	0.434563i
$296$	−24.2924	+	14.0252i	−1.41197	+	0.815199i
$297$		0			0
$298$	10.6742	−	18.4882i	0.618338	−	1.07099i
$299$	0.0346481	+	0.0290732i	0.00200375	+	0.00168135i
$300$		0			0
$301$	6.56457	+	24.7236i	0.378376	+	1.42504i
$302$	−22.1325	+	3.90255i	−1.27358	+	0.224567i
$303$		0			0
$304$	−0.750788	−	2.06277i	−0.0430606	−	0.118308i
$305$	4.84592	−	2.79779i	0.277477	−	0.160201i
$306$		0			0
$307$	5.10853	−	2.94941i	0.291559	−	0.168332i	−0.347086	−	0.937833i	$-0.612829\pi$
$307$	5.10853	−	2.94941i	0.291559	−	0.168332i	0.638645	+	0.769502i	$0.279495\pi$
$308$	1.06786	+	0.0958678i	0.0608472	+	0.00546257i
$309$		0			0
$310$	−3.36417	−	19.0791i	−0.191072	−	1.08362i
$311$	10.3978	−	8.72479i	0.589605	−	0.494737i	−0.298481	−	0.954416i	$-0.596480\pi$
$311$	10.3978	−	8.72479i	0.589605	−	0.494737i	0.888085	+	0.459678i	$0.152035\pi$
$312$		0			0
$313$	−1.95490	−	5.37104i	−0.110497	−	0.303589i	0.872103	−	0.489323i	$-0.162756\pi$
$313$	−1.95490	−	5.37104i	−0.110497	−	0.303589i	−0.982600	+	0.185734i	$0.940534\pi$
$314$	18.6278	+	32.2643i	1.05123	+	1.82078i
$315$		0			0
$316$	4.28889	−	7.42858i	0.241269	−	0.417890i
$317$	2.37171	+	0.418197i	0.133209	+	0.0234883i	0.239855	−	0.970809i	$-0.422900\pi$
$317$	2.37171	+	0.418197i	0.133209	+	0.0234883i	−0.106646	+	0.994297i	$0.534011\pi$
$318$		0			0
$319$	1.12587	+	0.409782i	0.0630364	+	0.0229434i
$320$	−22.2125	−	8.08467i	−1.24171	−	0.451947i
$321$		0			0
$322$	4.84461	+	3.40864i	0.269979	+	0.189956i
$323$		−	1.19448i		−	0.0664627i
$324$		0			0
$325$	0.0645273	+	0.0372549i	0.00357933	+	0.00206653i
$326$	−25.6485	−	4.52253i	−1.42054	−	0.250480i
$327$		0			0
$328$	11.8086	+	14.0730i	0.652022	+	0.777049i
$329$	−2.83062	−	10.6607i	−0.156057	−	0.587744i
$330$		0			0
$331$	1.83986	−	10.4344i	0.101128	−	0.573525i	−0.891568	−	0.452886i	$-0.850394\pi$
$331$	1.83986	−	10.4344i	0.101128	−	0.573525i	0.992696	−	0.120639i	$-0.0384944\pi$
$332$	10.5832	+	18.3306i	0.580827	+	1.00602i
$333$		0			0
$334$	3.81079	+	2.20016i	0.208517	+	0.120387i
$335$	−3.14758	+	17.8508i	−0.171971	+	0.975295i
$336$		0			0
$337$	−21.6242	−	7.87058i	−1.17795	−	0.428738i	−0.322471	−	0.946579i	$-0.604514\pi$
$337$	−21.6242	−	7.87058i	−1.17795	−	0.428738i	−0.855477	+	0.517841i	$0.826736\pi$
$338$	−29.4680	+	5.19601i	−1.60285	+	0.282626i
$339$		0			0
$340$	0.732693	+	0.614802i	0.0397359	+	0.0333423i
$341$	−0.280330	+	0.485547i	−0.0151807	+	0.0262938i
$342$		0			0
$343$	−4.91504	+	17.8562i	−0.265387	+	0.964142i
$344$	18.5961	−	22.1619i	1.00263	−	1.19489i
$345$		0			0
$346$	−19.2690	+	52.9412i	−1.03591	+	2.84614i
$347$	3.79271	−	0.668756i	0.203603	−	0.0359007i	−0.0709164	−	0.997482i	$-0.522592\pi$
$347$	3.79271	−	0.668756i	0.203603	−	0.0359007i	0.274519	+	0.961582i	$0.411481\pi$
$348$		0			0
$349$	−0.721690	−	1.98283i	−0.0386312	−	0.106138i	0.918877	−	0.394543i	$-0.129097\pi$
$349$	−0.721690	−	1.98283i	−0.0386312	−	0.106138i	−0.957508	+	0.288405i	$0.906875\pi$
$350$	8.83462	+	4.14408i	0.472230	+	0.221510i
$351$		0			0
$352$	0.326622	+	0.565725i	0.0174090	+	0.0301533i
$353$	2.13381	−	12.1014i	0.113571	−	0.644094i	−0.873877	−	0.486148i	$-0.838402\pi$
$353$	2.13381	−	12.1014i	0.113571	−	0.644094i	0.987448	−	0.157946i	$-0.0504872\pi$
$354$		0			0
$355$	0.628456	−	1.72667i	0.0333550	−	0.0916421i
$356$	−6.07613	−	34.4594i	−0.322034	−	1.82635i
$357$		0			0
$358$	32.5669	+	27.3269i	1.72122	+	1.44427i
$359$			30.5874i			1.61434i	0.590319	+	0.807170i	$0.299002\pi$
$359$			30.5874i			1.61434i	−0.590319	+	0.807170i	$0.700998\pi$
$360$		0			0
$361$	−38.7031			−2.03701
$362$	13.9454	−	5.07570i	0.732952	−	0.266773i
$363$		0			0
$364$	0.392426	−	0.104197i	0.0205687	−	0.00546139i
$365$	5.79082	−	15.9102i	0.303105	−	0.832775i
$366$		0			0
$367$	8.80842	−	10.4975i	0.459796	−	0.547964i	−0.485475	−	0.874251i	$-0.661353\pi$
$367$	8.80842	−	10.4975i	0.459796	−	0.547964i	0.945271	+	0.326287i	$0.105798\pi$
$368$		−	0.281044i		−	0.0146504i
$369$		0			0
$370$	−34.4513	−	19.8904i	−1.79104	−	1.03405i
$371$	0.431124	+	0.0387043i	0.0223829	+	0.00200942i
$372$		0			0
$373$	−8.95196	+	7.51159i	−0.463515	+	0.388935i	−0.844422	−	0.535678i	$-0.820056\pi$
$373$	−8.95196	+	7.51159i	−0.463515	+	0.388935i	0.380907	+	0.924613i	$0.375612\pi$
$374$	−0.00771976	−	0.0437810i	−0.000399180	−	0.00226386i
$375$		0			0
$376$	−8.01856	+	9.55615i	−0.413526	+	0.492821i
$377$	0.453725			0.0233681
$378$		0			0
$379$	−12.7028			−0.652500			−0.326250	−	0.945283i	$-0.605785\pi$
$379$	−12.7028			−0.652500			−0.326250	+	0.945283i	$0.605785\pi$
$380$	29.7000	−	35.3950i	1.52358	−	1.81573i
$381$		0			0
$382$	4.01075	+	22.7461i	0.205208	+	1.16379i
$383$	6.13567	−	5.14843i	0.313518	−	0.263073i	−0.472426	−	0.881370i	$-0.656622\pi$
$383$	6.13567	−	5.14843i	0.313518	−	0.263073i	0.785944	+	0.618297i	$0.212177\pi$
$384$		0			0
$385$	0.251888	+	0.543391i	0.0128374	+	0.0276938i
$386$	49.0625	+	28.3263i	2.49722	+	1.44177i
$387$		0			0
$388$			44.4235i			2.25526i
$389$	8.23656	−	9.81595i	0.417610	−	0.497689i	−0.515695	−	0.856772i	$-0.672466\pi$
$389$	8.23656	−	9.81595i	0.417610	−	0.497689i	0.933305	+	0.359084i	$0.116911\pi$
$390$		0			0
$391$	0.0523045	−	0.143705i	0.00264515	−	0.00726749i
$392$	19.7149	−	7.07449i	0.995752	−	0.357316i
$393$		0			0
$394$	30.2223	−	11.0000i	1.52258	−	0.554174i
$395$	4.79175			0.241099
$396$		0			0
$397$		−	9.99710i		−	0.501740i	−0.968021	−	0.250870i	$-0.919283\pi$
$397$		−	9.99710i		−	0.501740i	0.968021	−	0.250870i	$-0.0807167\pi$
$398$	−22.7125	−	19.0581i	−1.13848	−	0.955294i
$399$		0			0
$400$	−0.0803954	−	0.455945i	−0.00401977	−	0.0227973i
$401$	12.6777	−	34.8316i	0.633092	−	1.73941i	−0.0393162	−	0.999227i	$-0.512518\pi$
$401$	12.6777	−	34.8316i	0.633092	−	1.73941i	0.672409	−	0.740180i	$-0.265260\pi$
$402$		0			0
$403$	−0.0368691	+	0.209095i	−0.00183658	+	0.0104158i
$404$	−22.9268	−	39.7104i	−1.14065	−	1.97566i
$405$		0			0
$406$	59.2083	−	5.04473i	2.93846	−	0.250366i
$407$	0.393748	+	1.08181i	0.0195174	+	0.0536236i
$408$		0			0
$409$	−2.30593	+	0.406597i	−0.114021	+	0.0201050i	−0.230367	−	0.973104i	$-0.573993\pi$
$409$	−2.30593	+	0.406597i	−0.114021	+	0.0201050i	0.116347	+	0.993209i	$0.462882\pi$
$410$	−8.91083	+	24.4823i	−0.440074	+	1.20909i
$411$		0			0
$412$	16.5462	−	19.7190i	0.815175	−	0.971488i
$413$	31.2095	−	2.65914i	1.53572	−	0.130848i
$414$		0			0
$415$	−5.91201	+	10.2399i	−0.290209	+	0.502657i
$416$	0.189505	+	0.159014i	0.00929125	+	0.00779629i
$417$		0			0
$418$	−2.11498	+	0.372927i	−0.103447	+	0.0182405i
$419$	28.6465	+	10.4265i	1.39947	+	0.509366i	0.928022	−	0.372526i	$-0.121508\pi$
$419$	28.6465	+	10.4265i	1.39947	+	0.509366i	0.471451	+	0.881892i	$0.343730\pi$
$420$		0			0
$421$	0.369085	−	2.09318i	0.0179881	−	0.102015i	−0.974492	−	0.224423i	$-0.927950\pi$
$421$	0.369085	−	2.09318i	0.0179881	−	0.102015i	0.992480	+	0.122407i	$0.0390614\pi$
$422$	10.5430	+	6.08702i	0.513227	+	0.296311i
$423$		0			0
$424$	−0.244774	−	0.423960i	−0.0118873	−	0.0205893i
$425$	0.0437466	−	0.248100i	0.00212202	−	0.0120346i
$426$		0			0
$427$	−7.76242	+	2.06107i	−0.375650	+	0.0997423i
$428$	15.8410	+	18.8785i	0.765702	+	0.912528i
$429$		0			0
$430$	40.4054	+	7.12457i	1.94852	+	0.343577i
$431$	−1.02928	−	0.594254i	−0.0495786	−	0.0286242i	0.475006	−	0.879983i	$-0.342446\pi$
$431$	−1.02928	−	0.594254i	−0.0495786	−	0.0286242i	−0.524584	+	0.851358i	$0.675779\pi$
$432$		0			0
$433$			11.1104i			0.533930i	0.963706	+	0.266965i	$0.0860208\pi$
$433$			11.1104i			0.533930i	−0.963706	+	0.266965i	$0.913979\pi$
$434$	−2.48637	+	27.6955i	−0.119350	+	1.32943i
$435$		0			0
$436$	−27.1156	−	9.86928i	−1.29860	−	0.472653i
$437$	−6.94214	−	2.52673i	−0.332087	−	0.120870i
$438$		0			0
$439$	5.47998	+	0.966269i	0.261545	+	0.0461175i	0.302883	−	0.953028i	$-0.402051\pi$
$439$	5.47998	+	0.966269i	0.261545	+	0.0461175i	−0.0413377	+	0.999145i	$0.513162\pi$
$440$	0.338686	−	0.586622i	0.0161462	−	0.0279661i
$441$		0			0
$442$	−0.00841775	−	0.0145800i	−0.000400391	−	0.000693498i
$443$	−9.30703	−	25.5708i	−0.442190	−	1.21491i	−0.938048	−	0.346504i	$-0.887369\pi$
$443$	−9.30703	−	25.5708i	−0.442190	−	1.21491i	0.495858	−	0.868403i	$-0.334854\pi$
$444$		0			0
$445$	14.9737	−	12.5644i	0.709823	−	0.595612i
$446$	−3.34619	−	18.9772i	−0.158447	−	0.898597i
$447$		0			0
$448$	27.7478	+	19.5232i	1.31096	+	0.922384i
$449$	21.3299	−	12.3148i	1.00662	−	0.581171i	0.0964182	−	0.995341i	$-0.469261\pi$
$449$	21.3299	−	12.3148i	1.00662	−	0.581171i	0.910200	+	0.414170i	$0.135928\pi$
$450$		0			0
$451$	0.652965	−	0.376989i	0.0307469	−	0.0177517i
$452$	18.5720	+	51.0262i	0.873554	+	2.40007i
$453$		0			0
$454$	−45.7616	+	8.06900i	−2.14770	+	0.378697i
$455$	0.160018	+	0.160745i	0.00750175	+	0.00753586i
$456$		0			0
$457$	−5.39560	−	4.52745i	−0.252396	−	0.211785i	0.507808	−	0.861471i	$-0.330456\pi$
$457$	−5.39560	−	4.52745i	−0.252396	−	0.211785i	−0.760203	+	0.649686i	$0.774901\pi$
$458$	−6.68651	+	11.5814i	−0.312440	+	0.541162i
$459$		0			0
$460$	5.12303	−	2.95778i	0.238863	−	0.137907i
$461$	−6.82236	+	2.48314i	−0.317749	+	0.115651i	−0.495971	−	0.868339i	$-0.665188\pi$
$461$	−6.82236	+	2.48314i	−0.317749	+	0.115651i	0.178222	+	0.983990i	$0.442966\pi$
$462$		0			0
$463$	6.25076	−	5.24501i	0.290498	−	0.243756i	−0.485878	−	0.874026i	$-0.661500\pi$
$463$	6.25076	−	5.24501i	0.290498	−	0.243756i	0.776376	+	0.630270i	$0.217056\pi$
$464$	−1.81221	−	2.15971i	−0.0841298	−	0.100262i
$465$		0			0
$466$	13.3306	−	4.85195i	0.617529	−	0.224762i
$467$	−12.7628			−0.590592			−0.295296	−	0.955406i	$-0.595418\pi$
$467$	−12.7628			−0.590592			−0.295296	+	0.955406i	$0.595418\pi$
$468$		0			0
$469$	11.0486	−	23.5541i	0.510177	−	1.08763i
$470$	−17.4227	−	3.07209i	−0.803649	−	0.141705i
$471$		0			0
$472$	−22.7706	−	27.1369i	−1.04810	−	1.24908i
$473$	−0.763218	−	0.909567i	−0.0350928	−	0.0418219i
$474$		0			0
$475$	−11.9852	−	2.11332i	−0.549920	−	0.0969657i
$476$	−0.784863	−	1.12633i	−0.0359741	−	0.0516253i
$477$		0			0
$478$	42.9683			1.96532
$479$	18.7249	−	6.81531i	0.855564	−	0.311400i	0.123257	−	0.992375i	$-0.460666\pi$
$479$	18.7249	−	6.81531i	0.855564	−	0.311400i	0.732307	+	0.680975i	$0.238444\pi$
$480$		0			0
$481$	0.280238	+	0.333974i	0.0127777	+	0.0152279i
$482$	21.4902	−	18.0325i	0.978854	−	0.821356i
$483$		0			0
$484$	34.0618	−	12.3975i	1.54826	−	0.563522i
$485$	−21.4913	+	12.4080i	−0.975869	+	0.563418i
$486$		0			0
$487$	−16.5334	+	28.6367i	−0.749200	+	1.29765i	0.199007	+	0.979998i	$0.436228\pi$
$487$	−16.5334	+	28.6367i	−0.749200	+	1.29765i	−0.948207	+	0.317654i	$0.897105\pi$
$488$	6.95815	+	5.83858i	0.314981	+	0.264300i
$489$		0			0
$490$	22.6685	+	19.1971i	1.02406	+	0.867237i
$491$	−1.71158	+	0.301798i	−0.0772427	+	0.0136200i	−0.212136	−	0.977240i	$-0.568042\pi$
$491$	−1.71158	+	0.301798i	−0.0772427	+	0.0136200i	0.134893	+	0.990860i	$0.456931\pi$
$492$		0			0
$493$	−0.524695	−	1.44159i	−0.0236311	−	0.0649258i
$494$	−0.704331	+	0.406646i	−0.0316894	+	0.0182959i
$495$		0			0
$496$	1.14254	−	0.659646i	0.0513015	−	0.0296190i
$497$	−1.51762	+	2.15696i	−0.0680746	+	0.0967527i
$498$		0			0
$499$	−5.96043	−	33.8033i	−0.266825	−	1.51324i	−0.763786	−	0.645469i	$-0.776662\pi$
$499$	−5.96043	−	33.8033i	−0.266825	−	1.51324i	0.496961	−	0.867773i	$-0.334449\pi$
$500$	30.7628	−	25.8131i	1.37576	−	1.15440i
$501$		0			0
$502$	−2.99581	−	8.23091i	−0.133709	−	0.367364i
$503$	6.14413	+	10.6419i	0.273953	+	0.474501i	0.969870	−	0.243621i	$-0.0783354\pi$
$503$	6.14413	+	10.6419i	0.273953	+	0.474501i	−0.695917	+	0.718122i	$0.745002\pi$
$504$		0			0
$505$	12.8074	−	22.1831i	0.569924	−	0.987137i
$506$	−0.270778	−	0.0477455i	−0.0120376	−	0.00212255i
$507$		0			0
$508$	13.3171	+	4.84701i	0.590849	+	0.215051i
$509$	−24.5995	−	8.95349i	−1.09035	−	0.396856i	−0.266602	−	0.963807i	$-0.585901\pi$
$509$	−24.5995	−	8.95349i	−1.09035	−	0.396856i	−0.823752	+	0.566950i	$0.808123\pi$
$510$		0			0
$511$	−13.9839	+	19.8750i	−0.618612	+	0.879217i
$512$		−	3.26654i		−	0.144362i
$513$		0			0
$514$	−43.9683	−	25.3851i	−1.93936	−	1.11969i
$515$	14.1613	+	2.49702i	0.624021	+	0.110032i
$516$		0			0
$517$	0.329097	+	0.392203i	0.0144737	+	0.0172490i
$518$	40.2825	+	40.4657i	1.76991	+	1.77796i
$519$		0			0
$520$	0.0445441	−	0.252622i	0.00195339	−	0.0110782i
$521$	−7.13299	−	12.3547i	−0.312502	−	0.541269i	0.666401	−	0.745593i	$-0.267834\pi$
$521$	−7.13299	−	12.3547i	−0.312502	−	0.541269i	−0.978903	+	0.204324i	$0.934500\pi$
$522$		0			0
$523$	17.4049	+	10.0487i	0.761062	+	0.439399i	0.829677	−	0.558244i	$-0.188525\pi$
$523$	17.4049	+	10.0487i	0.761062	+	0.439399i	−0.0686150	+	0.997643i	$0.521858\pi$
$524$	−2.47889	+	14.0585i	−0.108291	+	0.614148i
$525$		0			0
$526$	4.11812	+	1.49887i	0.179559	+	0.0653540i
$527$	0.706977	−	0.124659i	0.0307964	−	0.00543024i
$528$		0			0
$529$	16.8945	+	14.1761i	0.734542	+	0.616354i
$530$	0.347136	−	0.601257i	0.0150786	−	0.0261169i
$531$		0			0
$532$	−54.4109	+	37.9153i	−2.35901	+	1.64384i
$533$	0.183535	−	0.218728i	0.00794978	−	0.00947418i
$534$		0			0
$535$	−4.70852	+	12.9366i	−0.203567	+	0.559297i
$536$	−28.9769	+	5.10942i	−1.25161	+	0.220693i
$537$		0			0
$538$	−9.63644	−	26.4759i	−0.415457	−	1.14146i
$539$	−0.145434	−	0.847262i	−0.00626430	−	0.0364942i
$540$		0			0
$541$	3.47620	+	6.02095i	0.149453	+	0.258861i	0.931026	−	0.364954i	$-0.118915\pi$
$541$	3.47620	+	6.02095i	0.149453	+	0.258861i	−0.781572	+	0.623815i	$0.785582\pi$
$542$	−4.66254	+	26.4426i	−0.200273	+	1.13581i
$543$		0			0
$544$	0.286075	−	0.785986i	0.0122654	−	0.0336989i
$545$	−2.79913	−	15.8747i	−0.119902	−	0.679996i
$546$		0			0
$547$	−10.1175	−	8.48957i	−0.432592	−	0.362988i	0.400337	−	0.916368i	$-0.368893\pi$
$547$	−10.1175	−	8.48957i	−0.432592	−	0.362988i	−0.832929	+	0.553380i	$0.813338\pi$
$548$		−	5.78429i		−	0.247093i
$549$		0			0
$550$	−0.452949			−0.0193138
$551$	−69.6404	+	25.3470i	−2.96678	+	1.07982i
$552$		0			0
$553$	−6.63923	−	1.79513i	−0.282329	−	0.0763367i
$554$	−14.9189	+	40.9894i	−0.633844	+	1.74147i
$555$		0			0
$556$	28.8601	−	34.3941i	1.22394	−	1.45863i
$557$			42.4357i			1.79806i	0.437890	+	0.899028i	$0.355726\pi$
$557$			42.4357i			1.79806i	−0.437890	+	0.899028i	$0.644274\pi$
$558$		0			0
$559$	−0.389407	−	0.224824i	−0.0164702	−	0.00950905i
$560$	0.126018	−	1.40371i	0.00532523	−	0.0593174i
$561$		0			0
$562$	0.718705	−	0.603065i	0.0303167	−	0.0254388i
$563$	5.38665	+	30.5492i	0.227020	+	1.28750i	0.858785	+	0.512336i	$0.171220\pi$
$563$	5.38665	+	30.5492i	0.227020	+	1.28750i	−0.631764	+	0.775160i	$0.717669\pi$
$564$		0			0
$565$	−19.4982	+	23.2370i	−0.820295	+	0.977589i
$566$	−10.7140			−0.450344
$567$		0			0
$568$	2.98275			0.125154
$569$	7.35768	−	8.76854i	0.308450	−	0.367596i	−0.589443	−	0.807810i	$-0.700653\pi$
$569$	7.35768	−	8.76854i	0.308450	−	0.367596i	0.897893	+	0.440213i	$0.145097\pi$
$570$		0			0
$571$	2.64153	+	14.9809i	0.110545	+	0.626931i	0.988860	+	0.148849i	$0.0475567\pi$
$571$	2.64153	+	14.9809i	0.110545	+	0.626931i	−0.878315	+	0.478082i	$0.841332\pi$
$572$	−0.0144372	+	0.0121142i	−0.000603648	+	0.000506521i
$573$		0			0
$574$	21.5182	−	30.5833i	0.898153	−	1.27652i
$575$	−1.34938	−	0.779063i	−0.0562729	−	0.0324892i
$576$		0			0
$577$		−	16.7644i		−	0.697913i	−0.937139	−	0.348956i	$-0.886536\pi$
$577$		−	16.7644i		−	0.697913i	0.937139	−	0.348956i	$-0.113464\pi$
$578$	25.1196	−	29.9364i	1.04484	−	1.24519i
$579$		0			0
$580$	20.2963	−	55.7635i	0.842756	−	2.31545i
$581$	12.0276	−	11.9731i	0.498988	−	0.496729i
$582$		0			0
$583$	−0.0188803	+	0.00687185i	−0.000781940	+	0.000284603i
$584$	27.4842			1.13730
$585$		0			0
$586$		−	19.1080i		−	0.789344i
$587$	−1.10643	−	0.928404i	−0.0456672	−	0.0383193i	0.619668	−	0.784864i	$-0.287267\pi$
$587$	−1.10643	−	0.928404i	−0.0456672	−	0.0383193i	−0.665336	+	0.746544i	$0.731712\pi$
$588$		0			0
$589$	−6.02205	−	34.1528i	−0.248134	−	1.40724i
$590$	17.1828	−	47.2092i	0.707403	−	1.94357i
$591$		0			0
$592$	0.470411	−	2.66784i	0.0193338	−	0.109647i
$593$	17.6222	+	30.5226i	0.723657	+	1.25341i	0.959524	+	0.281626i	$0.0908737\pi$
$593$	17.6222	+	30.5226i	0.723657	+	1.25341i	−0.235867	+	0.971785i	$0.575793\pi$
$594$		0			0
$595$	0.325677	−	0.694300i	0.0133515	−	0.0284635i
$596$	10.4658	+	28.7545i	0.428695	+	1.17783i
$597$		0			0
$598$	−0.102543	+	0.0180811i	−0.00419329	+	0.000739390i
$599$	14.8549	−	40.8135i	0.606955	−	1.66759i	−0.129887	−	0.991529i	$-0.541462\pi$
$599$	14.8549	−	40.8135i	0.606955	−	1.66759i	0.736842	−	0.676065i	$-0.236316\pi$
$600$		0			0
$601$	−12.1502	+	14.4801i	−0.495618	+	0.590655i	−0.954637	−	0.297772i	$-0.903757\pi$
$601$	−12.1502	+	14.4801i	−0.495618	+	0.590655i	0.459019	+	0.888427i	$0.348201\pi$
$602$	−53.3148	−	25.0085i	−2.17295	−	1.01927i
$603$		0			0
$604$	16.1066	−	27.8975i	0.655369	−	1.13513i
$605$	15.5115	+	13.0157i	0.630634	+	0.529164i
$606$		0			0
$607$	−2.09328	+	0.369101i	−0.0849635	+	0.0149814i	−0.215968	−	0.976400i	$-0.569291\pi$
$607$	−2.09328	+	0.369101i	−0.0849635	+	0.0149814i	0.131005	+	0.991382i	$0.458180\pi$
$608$	−37.9695	−	13.8198i	−1.53987	−	0.560465i
$609$		0			0
$610$	−2.23689	+	12.6860i	−0.0905691	+	0.513643i
$611$	0.167911	+	0.0969435i	0.00679295	+	0.00392191i
$612$		0			0
$613$	9.12735	+	15.8090i	0.368650	+	0.638521i	0.989355	−	0.145523i	$-0.0464866\pi$
$613$	9.12735	+	15.8090i	0.368650	+	0.638521i	−0.620704	+	0.784045i	$0.713153\pi$
$614$	−2.35811	+	13.3735i	−0.0951657	+	0.539711i
$615$		0			0
$616$	−0.689034	+	0.685915i	−0.0277620	+	0.0276363i
$617$	5.58064	+	6.65075i	0.224668	+	0.267749i	0.866590	−	0.499021i	$-0.166307\pi$
$617$	5.58064	+	6.65075i	0.224668	+	0.267749i	−0.641922	+	0.766770i	$0.721863\pi$
$618$		0			0
$619$	−38.7265	−	6.82853i	−1.55655	−	0.274462i	−0.671874	−	0.740666i	$-0.734510\pi$
$619$	−38.7265	−	6.82853i	−1.55655	−	0.274462i	−0.884677	+	0.466204i	$0.845621\pi$
$620$	24.0488	+	13.8846i	0.965824	+	0.557619i
$621$		0			0
$622$			31.2476i			1.25291i
$623$	−25.4539	+	11.7991i	−1.01979	+	0.472722i
$624$		0			0
$625$	13.5528	+	4.93282i	0.542113	+	0.197313i
$626$	12.3648	+	4.50042i	0.494197	+	0.179873i
$627$		0			0
$628$	−52.5895	−	9.27294i	−2.09855	−	0.370031i
$629$	0.737040	−	1.27659i	0.0293877	−	0.0509010i
$630$		0			0
$631$	5.26401	+	9.11753i	0.209557	+	0.362963i	0.951575	−	0.307417i	$-0.0994645\pi$
$631$	5.26401	+	9.11753i	0.209557	+	0.362963i	−0.742018	+	0.670380i	$0.766131\pi$
$632$	2.66036	+	7.30927i	0.105823	+	0.290747i
$633$		0			0
$634$	−4.24711	+	3.56375i	−0.168674	+	0.141535i
$635$	1.37471	+	7.79638i	0.0545538	+	0.309390i
$636$		0			0
$637$	−0.161493	−	0.282669i	−0.00639860	−	0.0111998i
$638$	−2.38869	+	1.37911i	−0.0945693	+	0.0545996i
$639$		0			0
$640$	30.1441	−	17.4037i	1.19155	−	0.687941i
$641$	−4.22019	−	11.5949i	−0.166688	−	0.457970i	0.828022	−	0.560695i	$-0.189466\pi$
$641$	−4.22019	−	11.5949i	−0.166688	−	0.457970i	−0.994710	+	0.102725i	$0.967244\pi$
$642$		0			0
$643$	22.7208	−	4.00630i	0.896023	−	0.157993i	0.293372	−	0.955998i	$-0.405222\pi$
$643$	22.7208	−	4.00630i	0.896023	−	0.157993i	0.602650	+	0.798005i	$0.294111\pi$
$644$	−8.20631	+	2.17893i	−0.323374	+	0.0858620i
$645$		0			0
$646$	2.10650	+	1.76757i	0.0828792	+	0.0695439i
$647$	19.2253	−	33.2993i	0.755826	−	1.30913i	−0.189137	−	0.981951i	$-0.560569\pi$
$647$	19.2253	−	33.2993i	0.755826	−	1.30913i	0.944963	−	0.327178i	$-0.106098\pi$
$648$		0			0
$649$	−1.25911	+	0.726949i	−0.0494245	+	0.0285352i
$650$	−0.161186	+	0.0586669i	−0.00632224	+	0.00230111i
$651$		0			0
$652$	28.5970	−	23.9958i	1.11995	−	0.939747i
$653$	−9.10813	−	10.8547i	−0.356429	−	0.424775i	0.557799	−	0.829976i	$-0.311646\pi$
$653$	−9.10813	−	10.8547i	−0.356429	−	0.424775i	−0.914228	+	0.405201i	$0.867202\pi$
$654$		0			0
$655$	−7.49363	+	2.72746i	−0.292801	+	0.106571i
$656$	−1.77419			−0.0692704
$657$		0			0
$658$	22.9892	+	10.7836i	0.896212	+	0.420388i
$659$	−39.3185	−	6.93292i	−1.53163	−	0.270068i	−0.656640	−	0.754204i	$-0.728023\pi$
$659$	−39.3185	−	6.93292i	−1.53163	−	0.270068i	−0.874993	+	0.484136i	$0.839134\pi$
$660$		0			0
$661$	15.7489	+	18.7688i	0.612562	+	0.730023i	0.979772	−	0.200115i	$-0.0641315\pi$
$661$	15.7489	+	18.7688i	0.612562	+	0.730023i	−0.367210	+	0.930138i	$0.619687\pi$
$662$	15.6787	+	18.6852i	0.609372	+	0.726221i
$663$		0			0
$664$	−18.9021	−	3.33296i	−0.733545	−	0.129344i
$665$	−33.5403	−	15.7329i	−1.30064	−	0.610094i
$666$		0			0
$667$	−9.48818			−0.367384
$668$	−5.92687	+	2.15721i	−0.229318	+	0.0834648i
$669$		0			0
$670$	−26.8228	−	31.9661i	−1.03625	−	1.23496i
$671$	0.285576	−	0.239627i	0.0110245	−	0.00925068i
$672$		0			0
$673$	−12.2850	+	4.47136i	−0.473551	+	0.172358i	−0.567760	−	0.823194i	$-0.692190\pi$
$673$	−12.2850	+	4.47136i	−0.473551	+	0.172358i	0.0942095	+	0.995552i	$0.469968\pi$
$674$	45.8791	−	26.4883i	1.76720	−	1.02029i
$675$		0			0
$676$	21.4450	−	37.1438i	0.824807	−	1.42861i
$677$	20.8680	+	17.5103i	0.802021	+	0.672976i	0.948689	−	0.316210i	$-0.102410\pi$
$677$	20.8680	+	17.5103i	0.802021	+	0.672976i	−0.146668	+	0.989186i	$0.546855\pi$
$678$		0			0
$679$	34.4257	−	9.14069i	1.32114	−	0.350788i
$680$	−0.854147	+	0.150609i	−0.0327551	+	0.00577560i
$681$		0			0
$682$	−0.441449	−	1.21287i	−0.0169040	−	0.0464433i
$683$	−40.3439	+	23.2926i	−1.54372	+	0.891265i	−0.545117	+	0.838360i	$0.683515\pi$
$683$	−40.3439	+	23.2926i	−1.54372	+	0.891265i	−0.998600	+	0.0529057i	$0.983152\pi$
$684$		0			0
$685$	2.79834	−	1.61562i	0.106919	−	0.0617297i
$686$	−24.2167	−	35.0910i	−0.924598	−	1.33978i
$687$		0			0
$688$	0.485167	+	2.75152i	0.0184968	+	0.104901i
$689$	−0.00582865	+	0.00489082i	−0.000222054	+	0.000186325i
$690$		0			0
$691$	−3.08293	−	8.47029i	−0.117280	−	0.322225i	0.867138	−	0.498068i	$-0.165957\pi$
$691$	−3.08293	−	8.47029i	−0.117280	−	0.322225i	−0.984418	+	0.175843i	$0.943735\pi$
$692$	−40.3770	−	69.9350i	−1.53490	−	2.65853i
$693$		0			0
$694$	−4.43299	+	7.67816i	−0.168274	+	0.291459i
$695$	24.7002	+	4.35531i	0.936932	+	0.165206i
$696$		0			0
$697$	−0.907191	−	0.330190i	−0.0343623	−	0.0125069i
$698$	4.56471	+	1.66142i	0.172777	+	0.0628857i
$699$		0			0
$700$	−12.6900	+	5.88245i	−0.479638	+	0.222336i
$701$			28.1670i			1.06385i	0.846790	+	0.531927i	$0.178532\pi$
$701$			28.1670i			1.06385i	−0.846790	+	0.531927i	$0.821468\pi$
$702$		0			0
$703$	−61.6697	−	35.6050i	−2.32592	−	1.34287i
$704$	−1.55090	−	0.273465i	−0.0584517	−	0.0103066i
$705$		0			0
$706$	18.1837	+	21.6704i	0.684351	+	0.815578i
$707$	−26.0559	+	25.9379i	−0.979932	+	0.975495i
$708$		0			0
$709$	−6.18586	+	35.0818i	−0.232315	+	1.31752i	0.615880	+	0.787840i	$0.288800\pi$
$709$	−6.18586	+	35.0818i	−0.232315	+	1.31752i	−0.848195	+	0.529684i	$0.822311\pi$
$710$	2.11506	+	3.66339i	0.0793767	+	0.137484i
$711$		0			0
$712$	27.4790	+	15.8650i	1.02982	+	0.594566i
$713$	0.770997	−	4.37254i	0.0288741	−	0.163753i
$714$		0			0
$715$	−0.00989312	−	0.00360080i	−0.000369982	−	0.000134662i
$716$	−60.0109	+	10.5815i	−2.24271	+	0.395451i
$717$		0			0
$718$	−53.9418	−	45.2625i	−2.01309	−	1.68918i
$719$	−4.56902	+	7.91377i	−0.170396	+	0.295134i	−0.938558	−	0.345121i	$-0.887838\pi$
$719$	−4.56902	+	7.91377i	−0.170396	+	0.295134i	0.768163	+	0.640255i	$0.221171\pi$
$720$		0			0
$721$	−18.6858	−	8.76499i	−0.695895	−	0.326425i
$722$	57.2720	−	68.2541i	2.13144	−	2.54016i
$723$		0			0
$724$	−7.27531	+	19.9888i	−0.270385	+	0.742876i
$725$	−15.3930	+	2.71419i	−0.571680	+	0.100803i
$726$		0			0
$727$	−3.56316	−	9.78970i	−0.132150	−	0.363080i	0.855915	−	0.517117i	$-0.172995\pi$
$727$	−3.56316	−	9.78970i	−0.132150	−	0.363080i	−0.988065	+	0.154037i	$0.950772\pi$
$728$	−0.156358	+	0.333334i	−0.00579501	+	0.0123542i
$729$		0			0
$730$	19.4889	+	33.7558i	0.721317	+	1.24936i
$731$	−0.264001	+	1.49722i	−0.00976442	+	0.0553768i
$732$		0			0
$733$	9.50030	−	26.1019i	0.350902	−	0.964094i	−0.631180	−	0.775637i	$-0.717429\pi$
$733$	9.50030	−	26.1019i	0.350902	−	0.964094i	0.982081	−	0.188458i	$-0.0603488\pi$
$734$	5.47810	+	31.0678i	0.202200	+	1.14673i
$735$		0			0
$736$	−3.96288	−	3.32525i	−0.146074	−	0.122570i
$737$			1.20762i			0.0444831i
$738$		0			0
$739$	−35.6793			−1.31248			−0.656242	−	0.754551i	$-0.727855\pi$
$739$	−35.6793			−1.31248			−0.656242	+	0.754551i	$0.727855\pi$
$740$	53.5816	−	19.5021i	1.96970	−	0.716912i
$741$		0			0
$742$	−0.706224	+	0.703027i	−0.0259263	+	0.0258089i
$743$	−2.30236	+	6.32568i	−0.0844653	+	0.232067i	−0.974734	−	0.223369i	$-0.928294\pi$
$743$	−2.30236	+	6.32568i	−0.0844653	+	0.232067i	0.890269	+	0.455436i	$0.150517\pi$
$744$		0			0
$745$	−10.9877	+	13.0946i	−0.402558	+	0.479750i
$746$		−	26.9025i		−	0.984972i
$747$		0			0
$748$	0.0551849	+	0.0318610i	0.00201776	+	0.00116495i
$749$	11.3703	−	16.1604i	0.415463	−	0.590487i
$750$		0			0
$751$	−36.6592	+	30.7607i	−1.33771	+	1.12247i	−0.355504	+	0.934675i	$0.615691\pi$
$751$	−36.6592	+	30.7607i	−1.33771	+	1.12247i	−0.982208	+	0.187799i	$0.939865\pi$
$752$	−0.209203	−	1.18645i	−0.00762883	−	0.0432653i
$753$		0			0
$754$	−0.671413	+	0.800158i	−0.0244514	+	0.0291401i
$755$	17.9951			0.654907
$756$		0			0
$757$	35.1225			1.27655			0.638274	−	0.769809i	$-0.279649\pi$
$757$	35.1225			1.27655			0.638274	+	0.769809i	$0.279649\pi$
$758$	18.7974	−	22.4018i	0.682751	−	0.813671i
$759$		0			0
$760$	7.27565	+	41.2623i	0.263916	+	1.49674i
$761$	26.2041	−	21.9878i	0.949897	−	0.797059i	−0.0293828	−	0.999568i	$-0.509354\pi$
$761$	26.2041	−	21.9878i	0.949897	−	0.797059i	0.979280	+	0.202510i	$0.0649097\pi$
$762$		0			0
$763$	−2.06877	+	23.0438i	−0.0748943	+	0.834243i
$764$	−28.6709	−	16.5532i	−1.03728	−	0.598872i
$765$		0			0
$766$			18.4390i			0.666227i
$767$	−0.353910	+	0.421774i	−0.0127790	+	0.0152294i
$768$		0			0
$769$	−3.20130	+	8.79549i	−0.115442	+	0.317174i	−0.983935	−	0.178528i	$-0.942867\pi$
$769$	−3.20130	+	8.79549i	−0.115442	+	0.317174i	0.868493	+	0.495701i	$0.165089\pi$
$770$	−1.33102	−	0.359885i	−0.0479668	−	0.0129694i
$771$		0			0
$772$	−76.3064	+	27.7733i	−2.74633	+	0.999582i
$773$	−20.1128			−0.723406			−0.361703	−	0.932293i	$-0.617805\pi$
$773$	−20.1128			−0.723406			−0.361703	+	0.932293i	$0.617805\pi$
$774$		0			0
$775$		−	7.31425i		−	0.262736i
$776$	−30.8589	−	25.8936i	−1.10777	−	0.929528i
$777$		0			0
$778$	5.12245	+	29.0509i	0.183649	+	1.04152i
$779$	−15.9509	+	43.8247i	−0.571500	+	1.57018i
$780$		0			0
$781$	0.0212576	−	0.120558i	0.000760658	−	0.00431391i
$782$	0.176030	+	0.304892i	0.00629481	+	0.0109029i
$783$		0			0
$784$	−0.700474	+	1.89770i	−0.0250169	+	0.0677750i
$785$	−10.2028	−	28.0319i	−0.364153	−	1.00050i
$786$		0			0
$787$	47.3837	−	8.35503i	1.68905	−	0.297825i	0.755200	−	0.655495i	$-0.227540\pi$
$787$	47.3837	−	8.35503i	1.68905	−	0.297825i	0.933848	+	0.357670i	$0.116429\pi$
$788$	−15.7670	+	43.3195i	−0.561677	+	1.54319i
$789$		0			0
$790$	−7.09073	+	8.45040i	−0.252277	+	0.300652i
$791$	35.7211	−	24.8916i	1.27010	−	0.885043i
$792$		0			0
$793$	0.0705878	−	0.122262i	0.00250665	−	0.00434164i
$794$	17.6302	+	14.7935i	0.625672	+	0.525001i
$795$		0			0
$796$	41.8522	−	7.37968i	1.48341	−	0.261566i
$797$	30.7365	+	11.1872i	1.08874	+	0.396270i	0.823155	−	0.567817i	$-0.192212\pi$
$797$	30.7365	+	11.1872i	1.08874	+	0.396270i	0.265588	+	0.964087i	$0.414434\pi$
$798$		0			0
$799$	0.113836	−	0.645597i	0.00402724	−	0.0228396i
$800$	−7.38032	−	4.26103i	−0.260934	−	0.150650i
$801$		0			0
$802$	42.6664	+	73.9004i	1.50660	+	2.60952i
$803$	0.195876	−	1.11087i	0.00691230	−	0.0392016i
$804$		0			0
$805$	−3.34625	−	3.36147i	−0.117940	−	0.118476i
$806$	−0.314187	−	0.374434i	−0.0110668	−	0.0131889i
$807$		0			0
$808$	40.9485	+	7.22032i	1.44056	+	0.254010i
$809$	2.72104	+	1.57099i	0.0956666	+	0.0552332i	0.547070	−	0.837087i	$-0.315743\pi$
$809$	2.72104	+	1.57099i	0.0956666	+	0.0552332i	−0.451403	+	0.892320i	$0.649076\pi$
$810$		0			0
$811$			36.4973i			1.28159i	0.767711	+	0.640797i	$0.221396\pi$
$811$			36.4973i			1.28159i	−0.767711	+	0.640797i	$0.778604\pi$
$812$	−49.0122	+	69.6598i	−1.71999	+	2.44458i
$813$		0			0
$814$	−2.49047	−	0.906458i	−0.0872910	−	0.0317713i
$815$	19.5962	+	7.13244i	0.686426	+	0.249839i
$816$		0			0
$817$	72.3280	+	12.7534i	2.53044	+	0.446184i
$818$	2.69521	−	4.66825i	0.0942360	−	0.163221i
$819$		0			0
$820$	−18.6721	−	32.3409i	−0.652056	−	1.12939i
$821$	15.7386	+	43.2415i	0.549282	+	1.50914i	0.834683	+	0.550731i	$0.185651\pi$
$821$	15.7386	+	43.2415i	0.549282	+	1.50914i	−0.285401	+	0.958408i	$0.592127\pi$
$822$		0			0
$823$	32.5272	−	27.2935i	1.13383	−	0.951393i	0.134607	−	0.990899i	$-0.457023\pi$
$823$	32.5272	−	27.2935i	1.13383	−	0.951393i	0.999219	+	0.0395062i	$0.0125785\pi$
$824$	4.05336	+	22.9878i	0.141206	+	0.800817i
$825$		0			0
$826$	−41.4936	+	58.9738i	−1.44375	+	2.05196i
$827$	9.94149	−	5.73972i	0.345699	−	0.199590i	−0.317090	−	0.948395i	$-0.602706\pi$
$827$	9.94149	−	5.73972i	0.345699	−	0.199590i	0.662789	+	0.748806i	$0.269372\pi$
$828$		0			0
$829$	32.3724	−	18.6902i	1.12434	−	0.649137i	0.181834	−	0.983329i	$-0.441797\pi$
$829$	32.3724	−	18.6902i	1.12434	−	0.649137i	0.942505	+	0.334192i	$0.108463\pi$
$830$	−9.30992	−	25.5788i	−0.323152	−	0.887853i
$831$		0			0
$832$	−0.587321	+	0.103561i	−0.0203617	+	0.00359032i
$833$	−0.711349	+	0.839983i	−0.0246468	+	0.0291037i
$834$		0			0
$835$	−2.69906	−	2.26478i	−0.0934050	−	0.0783761i
$836$	1.53915	−	2.66588i	0.0532325	−	0.0922014i
$837$		0			0
$838$	−60.7778	+	35.0901i	−2.09954	+	1.21217i
$839$	14.8437	−	5.40267i	0.512462	−	0.186521i	−0.0728286	−	0.997344i	$-0.523203\pi$
$839$	14.8437	−	5.40267i	0.512462	−	0.186521i	0.585291	+	0.810824i	$0.300980\pi$
$840$		0			0
$841$	−50.6977	+	42.5404i	−1.74820	+	1.46691i
$842$	3.14523	+	3.74833i	0.108392	+	0.129176i
$843$		0			0
$844$	−16.3975	+	5.96818i	−0.564424	+	0.205433i
$845$	23.9594			0.824227
$846$		0			0
$847$	−16.6160	−	23.8451i	−0.570933	−	0.819326i
$848$	0.0465601	+	0.00820980i	0.00159888	+	0.000281926i
$849$		0			0
$850$	0.372796	+	0.444281i	0.0127868	+	0.0152387i
$851$	−5.86026	−	6.98398i	−0.200887	−	0.239408i
$852$		0			0
$853$	30.8230	+	5.43493i	1.05536	+	0.186089i	0.674297	−	0.738460i	$-0.264447\pi$
$853$	30.8230	+	5.43493i	1.05536	+	0.186089i	0.381064	+	0.924549i	$0.375558\pi$
$854$	7.85190	−	16.7392i	0.268686	−	0.572803i
$855$		0			0
$856$	−22.3474			−0.763819
$857$	25.0495	−	9.11726i	0.855673	−	0.311440i	0.123322	−	0.992367i	$-0.460645\pi$
$857$	25.0495	−	9.11726i	0.855673	−	0.311440i	0.732351	+	0.680927i	$0.238423\pi$
$858$		0			0
$859$	18.2968	+	21.8052i	0.624278	+	0.743985i	0.981800	−	0.189920i	$-0.0608228\pi$
$859$	18.2968	+	21.8052i	0.624278	+	0.743985i	−0.357522	+	0.933905i	$0.616378\pi$
$860$	−45.0503	+	37.8017i	−1.53620	+	1.28903i
$861$		0			0
$862$	2.57109	−	0.935799i	0.0875716	−	0.0318734i
$863$	2.69995	−	1.55882i	0.0919074	−	0.0530628i	−0.453342	−	0.891337i	$-0.649768\pi$
$863$	2.69995	−	1.55882i	0.0919074	−	0.0530628i	0.545249	+	0.838274i	$0.316435\pi$
$864$		0			0
$865$	22.5555	−	39.0673i	0.766911	−	1.32833i
$866$	−19.5935	−	16.4409i	−0.665813	−	0.558683i
$867$		0			0
$868$	−28.1194	−	28.2473i	−0.954434	−	0.958775i
$869$	0.314389	−	0.0554353i	0.0106649	−	0.00188051i
$870$		0			0
$871$	0.156413	+	0.429741i	0.00529985	+	0.0145612i
$872$	22.6609	−	13.0833i	0.767396	−	0.443056i
$873$		0			0
$874$	14.7288	−	8.50367i	0.498208	−	0.287641i
$875$	−26.3335	−	18.5281i	−0.890236	−	0.626365i
$876$		0			0
$877$	1.13187	+	6.41916i	0.0382206	+	0.216760i	0.997936	−	0.0642135i	$-0.0204539\pi$
$877$	1.13187	+	6.41916i	0.0382206	+	0.216760i	−0.959716	+	0.280973i	$0.909343\pi$
$878$	−9.81320	+	8.23425i	−0.331179	+	0.277892i
$879$		0			0
$880$	0.0223742	+	0.0614726i	0.000754234	+	0.00207224i
$881$	0.192986	+	0.334261i	0.00650186	+	0.0112615i	0.869258	−	0.494359i	$-0.164597\pi$
$881$	0.192986	+	0.334261i	0.00650186	+	0.0112615i	−0.862756	+	0.505620i	$0.831264\pi$
$882$		0			0
$883$	6.61385	−	11.4555i	0.222574	−	0.385509i	−0.733015	−	0.680212i	$-0.761888\pi$
$883$	6.61385	−	11.4555i	0.222574	−	0.385509i	0.955589	+	0.294704i	$0.0952209\pi$
$884$	0.0237648	+	0.00419037i	0.000799295	+	0.000140937i
$885$		0			0
$886$	58.8673	+	21.4259i	1.97768	+	0.719818i
$887$	22.2545	+	8.09998i	0.747233	+	0.271971i	0.687441	−	0.726240i	$-0.258734\pi$
$887$	22.2545	+	8.09998i	0.747233	+	0.271971i	0.0597923	+	0.998211i	$0.480956\pi$
$888$		0			0
$889$	1.01601	−	11.3173i	0.0340760	−	0.379571i
$890$			44.9992i			1.50838i
$891$		0			0
$892$	23.9203	+	13.8104i	0.800912	+	0.462407i
$893$	−31.1876	−	5.49922i	−1.04365	−	0.184024i
$894$		0			0
$895$	−21.8809	−	26.0767i	−0.731398	−	0.871647i
$896$	−48.2862	+	12.8209i	−1.61313	+	0.428316i
$897$		0			0
$898$	−9.84592	+	55.8390i	−0.328563	+	1.86337i
$899$	−22.2700	−	38.5728i	−0.742746	−	1.28647i
$900$		0			0
$901$	0.0222796	+	0.0128631i	0.000742240	+	0.000428532i
$902$	−0.301410	+	1.70938i	−0.0100359	+	0.0569162i
$903$		0			0
$904$	−46.2708	−	16.8412i	−1.53894	−	0.560129i
$905$	−11.7023	+	2.06343i	−0.388997	+	0.0685907i
$906$		0			0
$907$	9.64234	+	8.09089i	0.320169	+	0.268653i	0.788680	−	0.614804i	$-0.210765\pi$
$907$	9.64234	+	8.09089i	0.320169	+	0.268653i	−0.468511	+	0.883458i	$0.655209\pi$
$908$	33.3024	−	57.6814i	1.10518	−	1.91423i
$909$		0			0
$910$	−0.520270	+	0.0443286i	−0.0172468	+	0.00146948i
$911$	−12.9220	+	15.3999i	−0.428125	+	0.510220i	−0.936380	−	0.350987i	$-0.885846\pi$
$911$	−12.9220	+	15.3999i	−0.428125	+	0.510220i	0.508255	+	0.861207i	$0.330291\pi$
$912$		0			0
$913$	−0.269425	+	0.740240i	−0.00891668	+	0.0244984i
$914$	15.9686	−	2.81569i	0.528193	−	0.0931347i
$915$		0			0
$916$	−6.55597	−	18.0124i	−0.216615	−	0.595146i
$917$	11.4046	−	0.971709i	0.376614	−	0.0320886i
$918$		0			0
$919$	−4.76251	−	8.24891i	−0.157101	−	0.272106i	0.776721	−	0.629845i	$-0.216881\pi$
$919$	−4.76251	−	8.24891i	−0.157101	−	0.272106i	−0.933822	+	0.357738i	$0.883548\pi$
$920$	−0.931494	+	5.28276i	−0.0307104	+	0.174168i
$921$		0			0
$922$	5.71649	−	15.7059i	0.188263	−	0.517247i
$923$	−0.00805021	−	0.0456550i	−0.000264976	−	0.00150275i
$924$		0			0
$925$	−11.5051	−	9.65393i	−0.378286	−	0.317419i
$926$			18.7849i			0.617309i
$927$		0			0
$928$	−51.8949			−1.70353
$929$	45.8614	−	16.6922i	1.50467	−	0.547653i	0.547402	−	0.836870i	$-0.315617\pi$
$929$	45.8614	−	16.6922i	1.50467	−	0.547653i	0.957264	+	0.289217i	$0.0933948\pi$
$930$		0			0
$931$	40.5780	+	34.3639i	1.32989	+	1.12623i
$932$	−6.95460	+	19.1076i	−0.227805	+	0.625890i
$933$		0			0
$934$	18.8861	−	22.5076i	0.617972	−	0.736471i
$935$			0.0355966i			0.00116413i
$936$		0			0
$937$	−14.6214	−	8.44169i	−0.477661	−	0.275778i	0.241780	−	0.970331i	$-0.422269\pi$
$937$	−14.6214	−	8.44169i	−0.477661	−	0.275778i	−0.719441	+	0.694553i	$0.755602\pi$
$938$	25.1889	+	54.3394i	0.822448	+	1.77424i
$939$		0			0
$940$	19.4256	−	16.3000i	0.633592	−	0.531647i
$941$	−1.58531	−	8.99075i	−0.0516797	−	0.293090i	0.948004	−	0.318260i	$-0.103098\pi$
$941$	−1.58531	−	8.99075i	−0.0516797	−	0.293090i	−0.999683	+	0.0251698i	$0.991987\pi$
$942$		0			0
$943$	−3.83803	+	4.57399i	−0.124984	+	0.148950i
$944$	3.42117			0.111349
$945$		0			0
$946$	2.73344			0.0888718
$947$	−25.8747	+	30.8363i	−0.840815	+	1.00204i	0.159076	+	0.987266i	$0.449148\pi$
$947$	−25.8747	+	30.8363i	−0.840815	+	1.00204i	−0.999891	+	0.0147774i	$0.995296\pi$
$948$		0			0
$949$	−0.0741775	−	0.420682i	−0.00240790	−	0.0136559i
$950$	21.4624	−	18.0091i	0.696331	−	0.584291i
$951$		0			0
$952$	1.23989	+	0.111311i	0.0401851	+	0.00360762i
$953$	15.4047	+	8.89392i	0.499008	+	0.288102i	0.728304	−	0.685254i	$-0.240309\pi$
$953$	15.4047	+	8.89392i	0.499008	+	0.288102i	−0.229296	+	0.973357i	$0.573642\pi$
$954$		0			0
$955$		−	18.4940i		−	0.598451i
$956$	−39.5887	+	47.1800i	−1.28039	+	1.52591i
$957$		0			0
$958$	−15.6897	+	43.1071i	−0.506911	+	1.39273i
$959$	−4.48251	+	1.19019i	−0.144748	+	0.0384333i
$960$		0			0
$961$	−9.54495	+	3.47408i	−0.307902	+	0.112067i
$962$	−1.00366			−0.0323594
$963$		0			0
$964$			40.2108i			1.29510i
$965$	−34.7495	−	29.1583i	−1.11863	−	0.938639i
$966$		0			0
$967$	−2.19010	−	12.4206i	−0.0704287	−	0.399421i	−0.999560	−	0.0296704i	$-0.990554\pi$
$967$	−2.19010	−	12.4206i	−0.0704287	−	0.399421i	0.929131	−	0.369751i	$-0.120557\pi$
$968$	−11.2421	+	30.8874i	−0.361334	+	0.992757i
$969$		0			0
$970$	9.92044	−	56.2616i	0.318526	−	1.80645i
$971$	9.58786	+	16.6067i	0.307689	+	0.532933i	0.977856	−	0.209277i	$-0.0671110\pi$
$971$	9.58786	+	16.6067i	0.307689	+	0.532933i	−0.670167	+	0.742210i	$0.733778\pi$
$972$		0			0
$973$	−32.5918	−	15.2879i	−1.04485	−	0.490109i
$974$	−26.0359	−	71.5330i	−0.834244	−	2.29207i
$975$		0			0
$976$	−0.863892	+	0.152327i	−0.0276525	+	0.00487588i
$977$	−8.45265	+	23.2235i	−0.270424	+	0.742985i	0.727931	+	0.685651i	$0.240482\pi$
$977$	−8.45265	+	23.2235i	−0.270424	+	0.742985i	−0.998355	+	0.0573341i	$0.981740\pi$
$978$		0			0
$979$	0.837076	−	0.997588i	0.0267531	−	0.0318831i
$980$	−41.9644	+	7.20328i	−1.34050	+	0.230100i
$981$		0			0
$982$	2.00053	−	3.46502i	0.0638395	−	0.110573i
$983$	−13.0228	−	10.9274i	−0.415363	−	0.348531i	0.411033	−	0.911620i	$-0.365168\pi$
$983$	−13.0228	−	10.9274i	−0.415363	−	0.348531i	−0.826396	+	0.563090i	$0.809613\pi$
$984$		0			0
$985$	−25.3611	+	4.47185i	−0.808073	+	0.142485i
$986$	3.31871	+	1.20791i	0.105689	+	0.0384678i
$987$		0			0
$988$	0.202429	−	1.14803i	0.00644012	−	0.0365237i
$989$	8.14317	+	4.70146i	0.258938	+	0.149498i
$990$		0			0
$991$	1.42204	+	2.46304i	0.0451725	+	0.0782411i	0.887728	−	0.460369i	$-0.152283\pi$
$991$	1.42204	+	2.46304i	0.0451725	+	0.0782411i	−0.842555	+	0.538610i	$0.818950\pi$
$992$	4.21691	−	23.9153i	0.133887	−	0.759311i
$993$		0			0
$994$	−1.55811	−	5.86818i	−0.0494204	−	0.186127i
$995$	15.2600	+	18.1861i	0.483774	+	0.576539i
$996$		0			0
$997$	34.6537	+	6.11039i	1.09750	+	0.193518i	0.692940	−	0.720995i	$-0.256315\pi$
$997$	34.6537	+	6.11039i	1.09750	+	0.193518i	0.404555	+	0.914513i	$0.367426\pi$
$998$	68.4332	+	39.5099i	2.16621	+	1.25066i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.3		132
3.2	odd	2		189.2.ba.a.101.20	✓	132
7.5	odd	6		567.2.bd.a.467.20		132
21.5	even	6		189.2.bd.a.47.3	yes	132
27.4	even	9		189.2.bd.a.185.3	yes	132
27.23	odd	18		567.2.bd.a.17.20		132
189.131	even	18	inner	567.2.ba.a.341.3		132
189.166	odd	18		189.2.ba.a.131.20	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.20	✓	132	3.2	odd	2
189.2.ba.a.131.20	yes	132	189.166	odd	18
189.2.bd.a.47.3	yes	132	21.5	even	6
189.2.bd.a.185.3	yes	132	27.4	even	9
567.2.ba.a.143.3		132	1.1	even	1	trivial
567.2.ba.a.341.3		132	189.131	even	18	inner
567.2.bd.a.17.20		132	27.23	odd	18
567.2.bd.a.467.20		132	7.5	odd	6

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.47978 + 1.76353i) q^{2} +(-0.573000 - 3.24965i) q^{4} +(1.41208 - 1.18487i) q^{5} +(-2.40040 + 1.11270i) q^{7} +(2.59137 + 1.49613i) q^{8} +4.24358i q^{10} +(0.0789393 - 0.0940762i) q^{11} +(0.0159063 - 0.0437022i) q^{13} +(1.58977 - 5.87972i) q^{14} +(-0.271551 + 0.0988366i) q^{16} -0.157246 q^{17} +7.59626i q^{19} +(-4.65954 - 3.90982i) q^{20} +(0.0490936 + 0.278423i) q^{22} +(-0.332628 + 0.913889i) q^{23} +(-0.278205 + 1.57778i) q^{25} +(0.0535324 + 0.0927208i) q^{26} +(4.99131 + 7.16286i) q^{28} +(3.33678 + 9.16772i) q^{29} +(-4.49600 + 0.792766i) q^{31} +(-1.81929 + 4.99845i) q^{32} +(0.232689 - 0.277308i) q^{34} +(-2.07113 + 4.41538i) q^{35} +(-4.68718 + 8.11843i) q^{37} +(-13.3962 - 11.2408i) q^{38} +(5.43192 - 0.957794i) q^{40} +(5.76925 + 2.09983i) q^{41} +(1.67890 - 9.52153i) q^{43} +(-0.350947 - 0.202619i) q^{44} +(-1.11945 - 1.93895i) q^{46} +(-0.723937 + 4.10565i) q^{47} +(4.52380 - 5.34184i) q^{49} +(-2.37078 - 2.82539i) q^{50} +(-0.151131 - 0.0266485i) q^{52} +(-0.141686 - 0.0818025i) q^{53} -0.226376i q^{55} +(-7.88504 - 0.707881i) q^{56} +(-21.1052 - 7.68168i) q^{58} +(-11.1248 - 4.04911i) q^{59} +(2.98946 + 0.527123i) q^{61} +(5.25501 - 9.10194i) q^{62} +(-6.41175 - 11.1055i) q^{64} +(-0.0293206 - 0.0805578i) q^{65} +(-7.53281 + 6.32078i) q^{67} +(0.0901020 + 0.510994i) q^{68} +(-4.72184 - 10.1863i) q^{70} +(0.863276 - 0.498413i) q^{71} +(7.95454 - 4.59256i) q^{73} +(-7.38112 - 20.2795i) q^{74} +(24.6852 - 4.35266i) q^{76} +(-0.0848069 + 0.313656i) q^{77} +(1.99133 + 1.67093i) q^{79} +(-0.266342 + 0.461318i) q^{80} +(-12.2403 + 7.06695i) q^{82} +(-6.02764 + 2.19388i) q^{83} +(-0.222043 + 0.186316i) q^{85} +(14.3071 + 17.0505i) q^{86} +(0.345310 - 0.125683i) q^{88} +10.6041 q^{89} +(0.0104460 + 0.122602i) q^{91} +(3.16041 + 0.557266i) q^{92} +(-6.16918 - 7.35214i) q^{94} +(9.00059 + 10.7265i) q^{95} +(-13.2580 - 2.33775i) q^{97} +(2.72628 + 15.8826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34}+ \cdots - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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