LMFDB - Embedded newform 567.2.ba.a.341.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$4.52751779461$
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			341.3
Character	$\chi$	$=$	567.341
Dual form			567.2.ba.a.143.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{18}\right)$

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	−0.968230	−	0.250061i	$-0.919549\pi$
$2$	−1.47978	−	1.76353i	−1.04636	−	1.24700i	−0.0781303	−	0.996943i	$-0.524895\pi$
$3$		0			0
$3$		0			0
$4$	−0.573000	+	3.24965i	−0.286500	+	1.62482i
$5$	1.41208	+	1.18487i	0.631499	+	0.529891i	0.901394	−	0.432999i	$-0.142545\pi$
$5$	1.41208	+	1.18487i	0.631499	+	0.529891i	−0.269895	+	0.962890i	$0.586989\pi$
$6$		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	0.777814	−	0.628495i	$-0.216329\pi$
$11$	0.0789393	+	0.0940762i	0.0238011	+	0.0283650i	−0.754013	+	0.656860i	$0.771884\pi$
$12$		0			0
$13$	0.0159063	+	0.0437022i	0.00441162	+	0.0121208i	0.941879	−	0.335953i	$-0.109058\pi$
$13$	0.0159063	+	0.0437022i	0.00441162	+	0.0121208i	−0.937467	+	0.348073i	$0.886836\pi$
$14$	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	$-0.663245\pi$
$19$		−	7.59626i		−	1.74270i	0.490661	−	0.871350i	$-0.336755\pi$
$20$	−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	0.900171	−	0.435537i	$-0.143441\pi$
$23$	−0.332628	−	0.913889i	−0.0693578	−	0.190559i	−0.969529	+	0.244978i	$0.921219\pi$
$24$		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	−0.0882816	−	0.996096i	$-0.528138\pi$
$29$	3.33678	−	9.16772i	0.619624	−	1.70240i	0.707906	−	0.706307i	$-0.249640\pi$
$30$		0			0
$31$	−4.49600	−	0.792766i	−0.807505	−	0.142385i	−0.245369	−	0.969430i	$-0.578909\pi$
$31$	−4.49600	−	0.792766i	−0.807505	−	0.142385i	−0.562136	+	0.827045i	$0.690020\pi$
$32$	−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	−0.937252	−	0.348652i	$-0.886640\pi$
$37$	−4.68718	−	8.11843i	−0.770567	−	1.33466i	0.166685	−	0.986010i	$-0.446694\pi$
$38$	−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	0.150350	−	0.988633i	$-0.451960\pi$
$41$	5.76925	−	2.09983i	0.901005	−	0.327939i	0.750656	+	0.660694i	$0.229738\pi$
$42$		0			0
$43$	1.67890	+	9.52153i	0.256030	+	1.45202i	0.793414	+	0.608682i	$0.208301\pi$
$43$	1.67890	+	9.52153i	0.256030	+	1.45202i	−0.537384	+	0.843338i	$0.680587\pi$
$44$	−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	−0.990980	−	0.134009i	$-0.957215\pi$
$47$	−0.723937	−	4.10565i	−0.105597	−	0.598871i	0.885383	−	0.464862i	$-0.153896\pi$
$48$		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	−0.509699	−	0.860353i	$-0.670243\pi$
$53$	−0.141686	+	0.0818025i	−0.0194621	+	0.0112364i	0.490237	+	0.871589i	$0.336910\pi$
$54$		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	−0.942125	−	0.335262i	$-0.891175\pi$
$59$	−11.1248	+	4.04911i	−1.44833	+	0.527150i	−0.506207	+	0.862412i	$0.668953\pi$
$60$		0			0
$61$	2.98946	−	0.527123i	0.382762	−	0.0674912i	0.0210431	−	0.999779i	$-0.493301\pi$
$61$	2.98946	−	0.527123i	0.382762	−	0.0674912i	0.361718	+	0.932287i	$0.382190\pi$
$62$	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	0.0537674	−	0.998553i	$-0.482877\pi$
$67$	−7.53281	−	6.32078i	−0.920279	−	0.772206i	−0.974047	+	0.226348i	$0.927321\pi$
$68$	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	0.550351	−	0.834934i	$-0.314494\pi$
$71$	0.863276	+	0.498413i	0.102452	+	0.0591507i	−0.447899	+	0.894084i	$0.647827\pi$
$72$		0			0
$73$	7.95454	+	4.59256i	0.931009	+	0.537518i	0.887130	−	0.461519i	$-0.152695\pi$
$73$	7.95454	+	4.59256i	0.931009	+	0.537518i	0.0438782	+	0.999037i	$0.486029\pi$
$74$	−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	−0.523856	−	0.851807i	$-0.675507\pi$
$79$	1.99133	−	1.67093i	0.224043	−	0.187994i	0.747899	+	0.663812i	$0.231063\pi$
$80$	−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	−0.0106840	−	0.999943i	$-0.503401\pi$
$83$	−6.02764	−	2.19388i	−0.661619	−	0.240810i	−0.650935	+	0.759133i	$0.725623\pi$
$84$		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	−0.799836	−	0.600218i	$-0.795080\pi$
$97$	−13.2580	+	2.33775i	−1.34615	+	0.237363i	−0.546313	+	0.837581i	$0.683969\pi$
$98$	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	0.896773	−	0.442492i	$-0.145905\pi$
$101$	13.0579	+	4.75270i	1.29931	+	0.472911i	0.402540	+	0.915403i	$0.368128\pi$
$102$		0			0
$103$	5.01435	−	5.97587i	0.494079	−	0.588820i	−0.460171	−	0.887830i	$-0.652212\pi$
$103$	5.01435	−	5.97587i	0.494079	−	0.588820i	0.954250	+	0.299010i	$0.0966564\pi$
$104$	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	0.153648	−	0.988126i	$-0.450898\pi$
$107$	−6.46785	−	3.73421i	−0.625271	−	0.361000i	−0.778918	+	0.627126i	$0.784231\pi$
$108$		0			0
$109$	4.37239	+	7.57320i	0.418799	+	0.725381i	0.995819	−	0.0913488i	$-0.0291178\pi$
$109$	4.37239	+	7.57320i	0.418799	+	0.725381i	−0.577020	+	0.816730i	$0.695784\pi$
$110$	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	−0.652317	−	0.757947i	$-0.726203\pi$
$113$	−16.2059	−	2.85754i	−1.52453	−	0.268815i	−0.872210	+	0.489131i	$0.837314\pi$
$114$		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	0.754884	−	0.655859i	$-0.227693\pi$
$127$	−2.14737	−	3.71936i	−0.190549	−	0.330040i	−0.945432	+	0.325819i	$0.894360\pi$
$128$	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	−0.513448	−	0.858120i	$-0.671632\pi$
$131$	−4.06526	+	1.47963i	−0.355184	+	0.129276i	0.158265	+	0.987397i	$0.449410\pi$
$132$		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	−0.0994166	−	0.995046i	$-0.531698\pi$
$137$	1.72630	−	0.304394i	0.147488	−	0.0260061i	0.246905	+	0.969040i	$0.420587\pi$
$138$		0			0
$139$	8.74606	−	10.4232i	0.741831	−	0.884080i	−0.254724	−	0.967014i	$-0.581985\pi$
$139$	8.74606	−	10.4232i	0.741831	−	0.884080i	0.996555	+	0.0829338i	$0.0264290\pi$
$140$	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	−0.213446	−	0.976955i	$-0.568469\pi$
$149$	−9.13243	−	1.61029i	−0.748158	−	0.131920i	−0.534712	+	0.845034i	$0.679580\pi$
$150$		0			0
$151$	7.47831	−	6.27505i	0.608576	−	0.510656i	−0.285613	−	0.958345i	$-0.592197\pi$
$151$	7.47831	−	6.27505i	0.608576	−	0.510656i	0.894189	+	0.447689i	$0.147753\pi$
$152$	−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	0.938348	+	0.345691i	$0.112356\pi$
$157$	5.53496	+	15.2072i	0.441738	+	1.21366i	−0.496611	+	0.867973i	$0.665422\pi$
$158$	−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	−0.554858	−	0.831945i	$-0.687228\pi$
$163$	5.65656	−	9.79745i	0.443056	−	0.767396i	0.997915	+	0.0645491i	$0.0205609\pi$
$164$	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	−0.994953	−	0.100341i	$-0.968007\pi$
$167$	−0.331914	+	1.88238i	−0.0256843	+	0.145663i	0.969269	+	0.246004i	$0.0791176\pi$
$168$		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	0.999649	−	0.0264796i	$-0.00842971\pi$
$173$	22.9967	+	8.37010i	1.74840	+	0.636367i	0.748755	+	0.662847i	$0.230652\pi$
$174$		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	$0.242451\pi$
$179$			18.4669i			1.38028i	−0.723676	+	0.690140i	$0.757549\pi$
$180$		0			0
$181$	−5.58272	+	3.22319i	−0.414960	+	0.239577i	−0.692919	−	0.721016i	$-0.743676\pi$
$181$	−5.58272	+	3.22319i	−0.414960	+	0.239577i	0.277958	+	0.960593i	$0.410342\pi$
$182$	−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	0.947116	−	0.320891i	$-0.103982\pi$
$191$	6.44902	+	7.68564i	0.466635	+	0.556113i	−0.480481	+	0.877005i	$0.659538\pi$
$192$		0			0
$193$	−4.27327	+	24.2349i	−0.307597	+	1.74447i	0.303424	+	0.952855i	$0.401870\pi$
$193$	−4.27327	+	24.2349i	−0.307597	+	1.74447i	−0.611022	+	0.791614i	$0.709241\pi$
$194$	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	−0.864684	−	0.502316i	$-0.832481\pi$
$197$	−12.0988	+	6.98527i	−0.862007	+	0.497680i	0.00267677	+	0.999996i	$0.499148\pi$
$198$		0			0
$199$		−	12.8790i		−	0.912968i	−0.889732	−	0.456484i	$-0.849108\pi$
$199$		−	12.8790i		−	0.912968i	0.889732	−	0.456484i	$-0.150892\pi$
$200$	−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	0.936747	+	0.350008i	$0.113821\pi$
$211$	−0.918282	+	5.20784i	−0.0632171	+	0.358522i	−0.999964	+	0.00851397i	$0.997290\pi$
$212$	−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	0.555192	−	0.831722i	$-0.312645\pi$
$223$	−5.38046	−	6.41218i	−0.360302	−	0.429392i	−0.915495	+	0.402330i	$0.868200\pi$
$224$	−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	0.0358677	−	0.999357i	$-0.488581\pi$
$227$	15.4623	−	12.9744i	1.02627	−	0.861143i	0.990402	+	0.138214i	$0.0441361\pi$
$228$		0			0
$229$	5.72074	+	1.00872i	0.378037	+	0.0666582i	0.359438	−	0.933169i	$-0.382968\pi$
$229$	5.72074	+	1.00872i	0.378037	+	0.0666582i	0.0185989	+	0.999827i	$0.494079\pi$
$230$	−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	−0.664515	−	0.747275i	$-0.731362\pi$
$233$	−5.33662	+	3.08110i	−0.349614	+	0.201850i	0.314901	+	0.949124i	$0.398029\pi$
$234$		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	−0.998748	−	0.0500310i	$-0.984068\pi$
$239$	−11.9974	+	14.2979i	−0.776046	+	0.924856i	0.222702	+	0.974887i	$0.428512\pi$
$240$		0			0
$241$	−12.0008	+	2.11606i	−0.773039	+	0.136308i	−0.546234	−	0.837633i	$-0.683939\pi$
$241$	−12.0008	+	2.11606i	−0.773039	+	0.136308i	−0.226805	+	0.973940i	$0.572828\pi$
$242$	−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	0.799720	−	0.600373i	$-0.204981\pi$
$251$	−1.90241	−	3.29506i	−0.120079	−	0.207983i	−0.919799	+	0.392391i	$0.871648\pi$
$252$		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	−0.595399	−	0.803430i	$-0.703006\pi$
$257$	3.82957	−	21.7186i	0.238882	−	1.35477i	0.834282	−	0.551339i	$-0.185883\pi$
$258$		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	−0.958146	−	0.286278i	$-0.907582\pi$
$263$	−0.651083	+	1.78884i	−0.0401475	+	0.110304i	0.917999	+	0.396583i	$0.129804\pi$
$264$		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	0.616937	−	0.787012i	$-0.288373\pi$
$269$	−6.11936	−	10.5990i	−0.373104	−	0.646235i	−0.990041	+	0.140777i	$0.955040\pi$
$270$		0			0
$271$	10.1008	+	5.83167i	0.613577	+	0.354249i	0.774364	−	0.632740i	$-0.218070\pi$
$271$	10.1008	+	5.83167i	0.613577	+	0.354249i	−0.160787	+	0.986989i	$0.551403\pi$
$272$	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	0.816102	−	0.577908i	$-0.196131\pi$
$277$	17.8050	+	6.48049i	1.06980	+	0.389375i	0.253698	+	0.967284i	$0.418353\pi$
$278$	−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	−0.185607	−	0.982624i	$-0.559425\pi$
$281$	−0.401346	+	0.0707682i	−0.0239423	+	0.00422168i	0.161664	+	0.986846i	$0.448314\pi$
$282$		0			0
$283$	2.99151	−	3.56515i	0.177827	−	0.211926i	−0.669767	−	0.742571i	$-0.733606\pi$
$283$	2.99151	−	3.56515i	0.177827	−	0.211926i	0.847594	+	0.530645i	$0.178050\pi$
$284$	−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	0.437882	−	0.899033i	$-0.355729\pi$
$293$	−6.35829	−	5.33524i	−0.371455	−	0.311688i	−0.809337	+	0.587345i	$0.800173\pi$
$294$		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	0.638645	−	0.769502i	$-0.279495\pi$
$307$	5.10853	+	2.94941i	0.291559	+	0.168332i	−0.347086	+	0.937833i	$0.612829\pi$
$308$	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	0.888085	−	0.459678i	$-0.152035\pi$
$311$	10.3978	+	8.72479i	0.589605	+	0.494737i	−0.298481	+	0.954416i	$0.596480\pi$
$312$		0			0
$313$	−1.95490	+	5.37104i	−0.110497	+	0.303589i	−0.982600	−	0.185734i	$-0.940534\pi$
$313$	−1.95490	+	5.37104i	−0.110497	+	0.303589i	0.872103	+	0.489323i	$0.162756\pi$
$314$	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	−0.106646	−	0.994297i	$-0.534011\pi$
$317$	2.37171	−	0.418197i	0.133209	−	0.0234883i	0.239855	+	0.970809i	$0.422900\pi$
$318$		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	0.992696	+	0.120639i	$0.0384944\pi$
$331$	1.83986	+	10.4344i	0.101128	+	0.573525i	−0.891568	+	0.452886i	$0.850394\pi$
$332$	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	−0.855477	−	0.517841i	$-0.826736\pi$
$337$	−21.6242	+	7.87058i	−1.17795	+	0.428738i	−0.322471	+	0.946579i	$0.604514\pi$
$338$	−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	0.274519	−	0.961582i	$-0.411481\pi$
$347$	3.79271	+	0.668756i	0.203603	+	0.0359007i	−0.0709164	+	0.997482i	$0.522592\pi$
$348$		0			0
$349$	−0.721690	+	1.98283i	−0.0386312	+	0.106138i	−0.957508	−	0.288405i	$-0.906875\pi$
$349$	−0.721690	+	1.98283i	−0.0386312	+	0.106138i	0.918877	+	0.394543i	$0.129097\pi$
$350$	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	0.987448	+	0.157946i	$0.0504872\pi$
$353$	2.13381	+	12.1014i	0.113571	+	0.644094i	−0.873877	+	0.486148i	$0.838402\pi$
$354$		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	$-0.700998\pi$
$359$		−	30.5874i		−	1.61434i	0.590319	−	0.807170i	$-0.299002\pi$
$360$		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	0.945271	−	0.326287i	$-0.105798\pi$
$367$	8.80842	+	10.4975i	0.459796	+	0.547964i	−0.485475	+	0.874251i	$0.661353\pi$
$368$			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	0.380907	−	0.924613i	$-0.375612\pi$
$373$	−8.95196	−	7.51159i	−0.463515	−	0.388935i	−0.844422	+	0.535678i	$0.820056\pi$
$374$	−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	0.785944	−	0.618297i	$-0.212177\pi$
$383$	6.13567	+	5.14843i	0.313518	+	0.263073i	−0.472426	+	0.881370i	$0.656622\pi$
$384$		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	0.933305	−	0.359084i	$-0.116911\pi$
$389$	8.23656	+	9.81595i	0.417610	+	0.497689i	−0.515695	+	0.856772i	$0.672466\pi$
$390$		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	$0.0807167\pi$
$397$			9.99710i			0.501740i	−0.968021	+	0.250870i	$0.919283\pi$
$398$	−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	0.672409	+	0.740180i	$0.265260\pi$
$401$	12.6777	+	34.8316i	0.633092	+	1.73941i	−0.0393162	+	0.999227i	$0.512518\pi$
$402$		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	0.116347	−	0.993209i	$-0.462882\pi$
$409$	−2.30593	−	0.406597i	−0.114021	−	0.0201050i	−0.230367	+	0.973104i	$0.573993\pi$
$410$	−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	0.471451	−	0.881892i	$-0.343730\pi$
$419$	28.6465	−	10.4265i	1.39947	−	0.509366i	0.928022	+	0.372526i	$0.121508\pi$
$420$		0			0
$421$	0.369085	+	2.09318i	0.0179881	+	0.102015i	0.992480	−	0.122407i	$-0.0390614\pi$
$421$	0.369085	+	2.09318i	0.0179881	+	0.102015i	−0.974492	+	0.224423i	$0.927950\pi$
$422$	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	−0.524584	−	0.851358i	$-0.675779\pi$
$431$	−1.02928	+	0.594254i	−0.0495786	+	0.0286242i	0.475006	+	0.879983i	$0.342446\pi$
$432$		0			0
$433$		−	11.1104i		−	0.533930i	−0.963706	−	0.266965i	$-0.913979\pi$
$433$		−	11.1104i		−	0.533930i	0.963706	−	0.266965i	$-0.0860208\pi$
$434$	−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	−0.0413377	−	0.999145i	$-0.513162\pi$
$439$	5.47998	−	0.966269i	0.261545	−	0.0461175i	0.302883	+	0.953028i	$0.402051\pi$
$440$	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	0.495858	+	0.868403i	$0.334854\pi$
$443$	−9.30703	+	25.5708i	−0.442190	+	1.21491i	−0.938048	+	0.346504i	$0.887369\pi$
$444$		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	0.910200	−	0.414170i	$-0.135928\pi$
$449$	21.3299	+	12.3148i	1.00662	+	0.581171i	0.0964182	+	0.995341i	$0.469261\pi$
$450$		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	−0.760203	−	0.649686i	$-0.774901\pi$
$457$	−5.39560	+	4.52745i	−0.252396	+	0.211785i	0.507808	+	0.861471i	$0.330456\pi$
$458$	−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	0.178222	−	0.983990i	$-0.442966\pi$
$461$	−6.82236	−	2.48314i	−0.317749	−	0.115651i	−0.495971	+	0.868339i	$0.665188\pi$
$462$		0			0
$463$	6.25076	+	5.24501i	0.290498	+	0.243756i	0.776376	−	0.630270i	$-0.217056\pi$
$463$	6.25076	+	5.24501i	0.290498	+	0.243756i	−0.485878	+	0.874026i	$0.661500\pi$
$464$	−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	0.732307	−	0.680975i	$-0.238444\pi$
$479$	18.7249	+	6.81531i	0.855564	+	0.311400i	0.123257	+	0.992375i	$0.460666\pi$
$480$		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	−0.948207	−	0.317654i	$-0.897105\pi$
$487$	−16.5334	−	28.6367i	−0.749200	−	1.29765i	0.199007	−	0.979998i	$-0.436228\pi$
$488$	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	0.134893	−	0.990860i	$-0.456931\pi$
$491$	−1.71158	−	0.301798i	−0.0772427	−	0.0136200i	−0.212136	+	0.977240i	$0.568042\pi$
$492$		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	0.496961	+	0.867773i	$0.334449\pi$
$499$	−5.96043	+	33.8033i	−0.266825	+	1.51324i	−0.763786	+	0.645469i	$0.776662\pi$
$500$	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	−0.695917	−	0.718122i	$-0.745002\pi$
$503$	6.14413	−	10.6419i	0.273953	−	0.474501i	0.969870	+	0.243621i	$0.0783354\pi$
$504$		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	−0.823752	−	0.566950i	$-0.808123\pi$
$509$	−24.5995	+	8.95349i	−1.09035	+	0.396856i	−0.266602	+	0.963807i	$0.585901\pi$
$510$		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	−0.978903	−	0.204324i	$-0.934500\pi$
$521$	−7.13299	+	12.3547i	−0.312502	+	0.541269i	0.666401	+	0.745593i	$0.267834\pi$
$522$		0			0
$523$	17.4049	−	10.0487i	0.761062	−	0.439399i	−0.0686150	−	0.997643i	$-0.521858\pi$
$523$	17.4049	−	10.0487i	0.761062	−	0.439399i	0.829677	+	0.558244i	$0.188525\pi$
$524$	−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	−0.781572	−	0.623815i	$-0.785582\pi$
$541$	3.47620	−	6.02095i	0.149453	−	0.258861i	0.931026	+	0.364954i	$0.118915\pi$
$542$	−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	−0.832929	−	0.553380i	$-0.813338\pi$
$547$	−10.1175	+	8.48957i	−0.432592	+	0.362988i	0.400337	+	0.916368i	$0.368893\pi$
$548$			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	$-0.644274\pi$
$557$		−	42.4357i		−	1.79806i	0.437890	−	0.899028i	$-0.355726\pi$
$558$		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	−0.631764	−	0.775160i	$-0.717669\pi$
$563$	5.38665	−	30.5492i	0.227020	−	1.28750i	0.858785	−	0.512336i	$-0.171220\pi$
$564$		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	0.897893	−	0.440213i	$-0.145097\pi$
$569$	7.35768	+	8.76854i	0.308450	+	0.367596i	−0.589443	+	0.807810i	$0.700653\pi$
$570$		0			0
$571$	2.64153	−	14.9809i	0.110545	−	0.626931i	−0.878315	−	0.478082i	$-0.841332\pi$
$571$	2.64153	−	14.9809i	0.110545	−	0.626931i	0.988860	−	0.148849i	$-0.0475567\pi$
$572$	−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	$0.113464\pi$
$577$			16.7644i			0.697913i	−0.937139	+	0.348956i	$0.886536\pi$
$578$	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	−0.665336	−	0.746544i	$-0.731712\pi$
$587$	−1.10643	+	0.928404i	−0.0456672	+	0.0383193i	0.619668	+	0.784864i	$0.287267\pi$
$588$		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	−0.235867	−	0.971785i	$-0.575793\pi$
$593$	17.6222	−	30.5226i	0.723657	−	1.25341i	0.959524	−	0.281626i	$-0.0908737\pi$
$594$		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	0.736842	+	0.676065i	$0.236316\pi$
$599$	14.8549	+	40.8135i	0.606955	+	1.66759i	−0.129887	+	0.991529i	$0.541462\pi$
$600$		0			0
$601$	−12.1502	−	14.4801i	−0.495618	−	0.590655i	0.459019	−	0.888427i	$-0.348201\pi$
$601$	−12.1502	−	14.4801i	−0.495618	−	0.590655i	−0.954637	+	0.297772i	$0.903757\pi$
$602$	−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	0.131005	−	0.991382i	$-0.458180\pi$
$607$	−2.09328	−	0.369101i	−0.0849635	−	0.0149814i	−0.215968	+	0.976400i	$0.569291\pi$
$608$	−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	−0.620704	−	0.784045i	$-0.713153\pi$
$613$	9.12735	−	15.8090i	0.368650	−	0.638521i	0.989355	+	0.145523i	$0.0464866\pi$
$614$	−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	−0.641922	−	0.766770i	$-0.721863\pi$
$617$	5.58064	−	6.65075i	0.224668	−	0.267749i	0.866590	+	0.499021i	$0.166307\pi$
$618$		0			0
$619$	−38.7265	+	6.82853i	−1.55655	+	0.274462i	−0.884677	−	0.466204i	$-0.845621\pi$
$619$	−38.7265	+	6.82853i	−1.55655	+	0.274462i	−0.671874	+	0.740666i	$0.734510\pi$
$620$	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	−0.742018	−	0.670380i	$-0.766131\pi$
$631$	5.26401	−	9.11753i	0.209557	−	0.362963i	0.951575	+	0.307417i	$0.0994645\pi$
$632$	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	−0.994710	−	0.102725i	$-0.967244\pi$
$641$	−4.22019	+	11.5949i	−0.166688	+	0.457970i	0.828022	+	0.560695i	$0.189466\pi$
$642$		0			0
$643$	22.7208	+	4.00630i	0.896023	+	0.157993i	0.602650	−	0.798005i	$-0.294111\pi$
$643$	22.7208	+	4.00630i	0.896023	+	0.157993i	0.293372	+	0.955998i	$0.405222\pi$
$644$	−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	0.944963	+	0.327178i	$0.106098\pi$
$647$	19.2253	+	33.2993i	0.755826	+	1.30913i	−0.189137	+	0.981951i	$0.560569\pi$
$648$		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	−0.914228	−	0.405201i	$-0.867202\pi$
$653$	−9.10813	+	10.8547i	−0.356429	+	0.424775i	0.557799	+	0.829976i	$0.311646\pi$
$654$		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	−0.874993	−	0.484136i	$-0.839134\pi$
$659$	−39.3185	+	6.93292i	−1.53163	+	0.270068i	−0.656640	+	0.754204i	$0.728023\pi$
$660$		0			0
$661$	15.7489	−	18.7688i	0.612562	−	0.730023i	−0.367210	−	0.930138i	$-0.619687\pi$
$661$	15.7489	−	18.7688i	0.612562	−	0.730023i	0.979772	+	0.200115i	$0.0641315\pi$
$662$	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	0.0942095	−	0.995552i	$-0.469968\pi$
$673$	−12.2850	−	4.47136i	−0.473551	−	0.172358i	−0.567760	+	0.823194i	$0.692190\pi$
$674$	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	−0.146668	−	0.989186i	$-0.546855\pi$
$677$	20.8680	−	17.5103i	0.802021	−	0.672976i	0.948689	+	0.316210i	$0.102410\pi$
$678$		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	−0.998600	−	0.0529057i	$-0.983152\pi$
$683$	−40.3439	−	23.2926i	−1.54372	−	0.891265i	−0.545117	−	0.838360i	$-0.683515\pi$
$684$		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	−0.984418	−	0.175843i	$-0.943735\pi$
$691$	−3.08293	+	8.47029i	−0.117280	+	0.322225i	0.867138	+	0.498068i	$0.165957\pi$
$692$	−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	$-0.821468\pi$
$701$		−	28.1670i		−	1.06385i	0.846790	−	0.531927i	$-0.178532\pi$
$702$		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	−0.848195	−	0.529684i	$-0.822311\pi$
$709$	−6.18586	−	35.0818i	−0.232315	−	1.31752i	0.615880	−	0.787840i	$-0.288800\pi$
$710$	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	0.768163	−	0.640255i	$-0.221171\pi$
$719$	−4.56902	−	7.91377i	−0.170396	−	0.295134i	−0.938558	+	0.345121i	$0.887838\pi$
$720$		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	−0.988065	−	0.154037i	$-0.950772\pi$
$727$	−3.56316	+	9.78970i	−0.132150	+	0.363080i	0.855915	+	0.517117i	$0.172995\pi$
$728$	−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	0.982081	+	0.188458i	$0.0603488\pi$
$733$	9.50030	+	26.1019i	0.350902	+	0.964094i	−0.631180	+	0.775637i	$0.717429\pi$
$734$	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	0.890269	−	0.455436i	$-0.150517\pi$
$743$	−2.30236	−	6.32568i	−0.0844653	−	0.232067i	−0.974734	+	0.223369i	$0.928294\pi$
$744$		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	−0.982208	−	0.187799i	$-0.939865\pi$
$751$	−36.6592	−	30.7607i	−1.33771	−	1.12247i	−0.355504	−	0.934675i	$-0.615691\pi$
$752$	−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	0.979280	−	0.202510i	$-0.0649097\pi$
$761$	26.2041	+	21.9878i	0.949897	+	0.797059i	−0.0293828	+	0.999568i	$0.509354\pi$
$762$		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	0.868493	−	0.495701i	$-0.165089\pi$
$769$	−3.20130	−	8.79549i	−0.115442	−	0.317174i	−0.983935	+	0.178528i	$0.942867\pi$
$770$	−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	0.933848	−	0.357670i	$-0.116429\pi$
$787$	47.3837	+	8.35503i	1.68905	+	0.297825i	0.755200	+	0.655495i	$0.227540\pi$
$788$	−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	0.265588	−	0.964087i	$-0.414434\pi$
$797$	30.7365	−	11.1872i	1.08874	−	0.396270i	0.823155	+	0.567817i	$0.192212\pi$
$798$		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	−0.451403	−	0.892320i	$-0.649076\pi$
$809$	2.72104	−	1.57099i	0.0956666	−	0.0552332i	0.547070	+	0.837087i	$0.315743\pi$
$810$		0			0
$811$		−	36.4973i		−	1.28159i	−0.767711	−	0.640797i	$-0.778604\pi$
$811$		−	36.4973i		−	1.28159i	0.767711	−	0.640797i	$-0.221396\pi$
$812$	−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	−0.285401	−	0.958408i	$-0.592127\pi$
$821$	15.7386	−	43.2415i	0.549282	−	1.50914i	0.834683	−	0.550731i	$-0.185651\pi$
$822$		0			0
$823$	32.5272	+	27.2935i	1.13383	+	0.951393i	0.999219	−	0.0395062i	$-0.0125785\pi$
$823$	32.5272	+	27.2935i	1.13383	+	0.951393i	0.134607	+	0.990899i	$0.457023\pi$
$824$	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	0.662789	−	0.748806i	$-0.269372\pi$
$827$	9.94149	+	5.73972i	0.345699	+	0.199590i	−0.317090	+	0.948395i	$0.602706\pi$
$828$		0			0
$829$	32.3724	+	18.6902i	1.12434	+	0.649137i	0.942505	−	0.334192i	$-0.108463\pi$
$829$	32.3724	+	18.6902i	1.12434	+	0.649137i	0.181834	+	0.983329i	$0.441797\pi$
$830$	−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	0.585291	−	0.810824i	$-0.300980\pi$
$839$	14.8437	+	5.40267i	0.512462	+	0.186521i	−0.0728286	+	0.997344i	$0.523203\pi$
$840$		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	0.381064	−	0.924549i	$-0.375558\pi$
$853$	30.8230	−	5.43493i	1.05536	−	0.186089i	0.674297	+	0.738460i	$0.264447\pi$
$854$	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	0.732351	−	0.680927i	$-0.238423\pi$
$857$	25.0495	+	9.11726i	0.855673	+	0.311440i	0.123322	+	0.992367i	$0.460645\pi$
$858$		0			0
$859$	18.2968	−	21.8052i	0.624278	−	0.743985i	−0.357522	−	0.933905i	$-0.616378\pi$
$859$	18.2968	−	21.8052i	0.624278	−	0.743985i	0.981800	+	0.189920i	$0.0608228\pi$
$860$	−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	0.545249	−	0.838274i	$-0.316435\pi$
$863$	2.69995	+	1.55882i	0.0919074	+	0.0530628i	−0.453342	+	0.891337i	$0.649768\pi$
$864$		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	−0.959716	−	0.280973i	$-0.909343\pi$
$877$	1.13187	−	6.41916i	0.0382206	−	0.216760i	0.997936	+	0.0642135i	$0.0204539\pi$
$878$	−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	−0.862756	−	0.505620i	$-0.831264\pi$
$881$	0.192986	−	0.334261i	0.00650186	−	0.0112615i	0.869258	+	0.494359i	$0.164597\pi$
$882$		0			0
$883$	6.61385	+	11.4555i	0.222574	+	0.385509i	0.955589	−	0.294704i	$-0.0952209\pi$
$883$	6.61385	+	11.4555i	0.222574	+	0.385509i	−0.733015	+	0.680212i	$0.761888\pi$
$884$	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	0.0597923	−	0.998211i	$-0.480956\pi$
$887$	22.2545	−	8.09998i	0.747233	−	0.271971i	0.687441	+	0.726240i	$0.258734\pi$
$888$		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	−0.468511	−	0.883458i	$-0.655209\pi$
$907$	9.64234	−	8.09089i	0.320169	−	0.268653i	0.788680	+	0.614804i	$0.210765\pi$
$908$	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	0.508255	−	0.861207i	$-0.330291\pi$
$911$	−12.9220	−	15.3999i	−0.428125	−	0.510220i	−0.936380	+	0.350987i	$0.885846\pi$
$912$		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	−0.933822	−	0.357738i	$-0.883548\pi$
$919$	−4.76251	+	8.24891i	−0.157101	+	0.272106i	0.776721	+	0.629845i	$0.216881\pi$
$920$	−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	0.957264	−	0.289217i	$-0.0933948\pi$
$929$	45.8614	+	16.6922i	1.50467	+	0.547653i	0.547402	+	0.836870i	$0.315617\pi$
$930$		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	−0.719441	−	0.694553i	$-0.755602\pi$
$937$	−14.6214	+	8.44169i	−0.477661	+	0.275778i	0.241780	+	0.970331i	$0.422269\pi$
$938$	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	−0.999683	−	0.0251698i	$-0.991987\pi$
$941$	−1.58531	+	8.99075i	−0.0516797	+	0.293090i	0.948004	+	0.318260i	$0.103098\pi$
$942$		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	−0.999891	−	0.0147774i	$-0.995296\pi$
$947$	−25.8747	−	30.8363i	−0.840815	−	1.00204i	0.159076	−	0.987266i	$-0.449148\pi$
$948$		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	−0.229296	−	0.973357i	$-0.573642\pi$
$953$	15.4047	−	8.89392i	0.499008	−	0.288102i	0.728304	+	0.685254i	$0.240309\pi$
$954$		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	0.929131	+	0.369751i	$0.120557\pi$
$967$	−2.19010	+	12.4206i	−0.0704287	+	0.399421i	−0.999560	+	0.0296704i	$0.990554\pi$
$968$	−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	−0.670167	−	0.742210i	$-0.733778\pi$
$971$	9.58786	−	16.6067i	0.307689	−	0.532933i	0.977856	+	0.209277i	$0.0671110\pi$
$972$		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	−0.998355	−	0.0573341i	$-0.981740\pi$
$977$	−8.45265	−	23.2235i	−0.270424	−	0.742985i	0.727931	−	0.685651i	$-0.240482\pi$
$978$		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	−0.826396	−	0.563090i	$-0.809613\pi$
$983$	−13.0228	+	10.9274i	−0.415363	+	0.348531i	0.411033	+	0.911620i	$0.365168\pi$
$984$		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	−0.842555	−	0.538610i	$-0.818950\pi$
$991$	1.42204	−	2.46304i	0.0451725	−	0.0782411i	0.887728	+	0.460369i	$0.152283\pi$
$992$	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	0.404555	−	0.914513i	$-0.367426\pi$
$997$	34.6537	−	6.11039i	1.09750	−	0.193518i	0.692940	+	0.720995i	$0.256315\pi$
$998$	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.341.3		132
3.2	odd	2		189.2.ba.a.131.20	yes	132
7.3	odd	6		567.2.bd.a.17.20		132
21.17	even	6		189.2.bd.a.185.3	yes	132
27.7	even	9		189.2.bd.a.47.3	yes	132
27.20	odd	18		567.2.bd.a.467.20		132
189.101	even	18	inner	567.2.ba.a.143.3		132
189.115	odd	18		189.2.ba.a.101.20	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.20	✓	132	189.115	odd	18
189.2.ba.a.131.20	yes	132	3.2	odd	2
189.2.bd.a.47.3	yes	132	27.7	even	9
189.2.bd.a.185.3	yes	132	21.17	even	6
567.2.ba.a.143.3		132	189.101	even	18	inner
567.2.ba.a.341.3		132	1.1	even	1	trivial
567.2.bd.a.17.20		132	7.3	odd	6
567.2.bd.a.467.20		132	27.20	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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