LMFDB - Embedded newform 552.2.n.b.91.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.8
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07870 + 0.914558i) q^{2} -1.00000 q^{3} +(0.327167 - 1.97306i) q^{4} +3.32574 q^{5} +(1.07870 - 0.914558i) q^{6} +3.62001 q^{7} +(1.45156 + 2.42754i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.07870 + 0.914558i) q^{2} -1.00000 q^{3} +(0.327167 - 1.97306i) q^{4} +3.32574 q^{5} +(1.07870 - 0.914558i) q^{6} +3.62001 q^{7} +(1.45156 + 2.42754i) q^{8} +1.00000 q^{9} +(-3.58746 + 3.04158i) q^{10} +1.15172i q^{11} +(-0.327167 + 1.97306i) q^{12} -4.49735i q^{13} +(-3.90489 + 3.31071i) q^{14} -3.32574 q^{15} +(-3.78592 - 1.29104i) q^{16} -4.26970i q^{17} +(-1.07870 + 0.914558i) q^{18} -1.61916i q^{19} +(1.08807 - 6.56187i) q^{20} -3.62001 q^{21} +(-1.05332 - 1.24236i) q^{22} +(-1.37075 + 4.59576i) q^{23} +(-1.45156 - 2.42754i) q^{24} +6.06052 q^{25} +(4.11309 + 4.85127i) q^{26} -1.00000 q^{27} +(1.18435 - 7.14250i) q^{28} -1.98240i q^{29} +(3.58746 - 3.04158i) q^{30} -2.69787i q^{31} +(5.26459 - 2.06981i) q^{32} -1.15172i q^{33} +(3.90489 + 4.60571i) q^{34} +12.0392 q^{35} +(0.327167 - 1.97306i) q^{36} -10.4728 q^{37} +(1.48082 + 1.74658i) q^{38} +4.49735i q^{39} +(4.82752 + 8.07336i) q^{40} +8.87354 q^{41} +(3.90489 - 3.31071i) q^{42} +2.83144i q^{43} +(2.27242 + 0.376806i) q^{44} +3.32574 q^{45} +(-2.72447 - 6.21106i) q^{46} +13.2124i q^{47} +(3.78592 + 1.29104i) q^{48} +6.10449 q^{49} +(-6.53745 + 5.54270i) q^{50} +4.26970i q^{51} +(-8.87354 - 1.47138i) q^{52} +6.02532 q^{53} +(1.07870 - 0.914558i) q^{54} +3.83033i q^{55} +(5.25468 + 8.78773i) q^{56} +1.61916i q^{57} +(1.81302 + 2.13841i) q^{58} -3.81302 q^{59} +(-1.08807 + 6.56187i) q^{60} -0.0328974 q^{61} +(2.46736 + 2.91018i) q^{62} +3.62001 q^{63} +(-3.78592 + 7.04747i) q^{64} -14.9570i q^{65} +(1.05332 + 1.24236i) q^{66} -9.53558i q^{67} +(-8.42437 - 1.39690i) q^{68} +(1.37075 - 4.59576i) q^{69} +(-12.9866 + 11.0106i) q^{70} -7.45857i q^{71} +(1.45156 + 2.42754i) q^{72} +9.56488 q^{73} +(11.2969 - 9.57794i) q^{74} -6.06052 q^{75} +(-3.19471 - 0.529737i) q^{76} +4.16925i q^{77} +(-4.11309 - 4.85127i) q^{78} -4.25927 q^{79} +(-12.5910 - 4.29365i) q^{80} +1.00000 q^{81} +(-9.57185 + 8.11537i) q^{82} +16.3410i q^{83} +(-1.18435 + 7.14250i) q^{84} -14.1999i q^{85} +(-2.58951 - 3.05426i) q^{86} +1.98240i q^{87} +(-2.79586 + 1.67180i) q^{88} +11.3103i q^{89} +(-3.58746 + 3.04158i) q^{90} -16.2805i q^{91} +(8.61925 + 4.20816i) q^{92} +2.69787i q^{93} +(-12.0835 - 14.2521i) q^{94} -5.38491i q^{95} +(-5.26459 + 2.06981i) q^{96} +8.75475i q^{97} +(-6.58488 + 5.58291i) q^{98} +1.15172i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.07870	+	0.914558i	−0.762753	+	0.646690i
$2$	−1.07870	+	0.914558i	−0.762753	+	0.646690i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.327167	−	1.97306i	0.163583	−	0.986530i
$5$	3.32574			1.48731			0.743657	−	0.668561i	$-0.233090\pi$
$5$	3.32574			1.48731			0.743657	+	0.668561i	$0.233090\pi$
$6$	1.07870	−	0.914558i	0.440375	−	0.373367i
$7$	3.62001			1.36824			0.684118	−	0.729371i	$-0.260187\pi$
$7$	3.62001			1.36824			0.684118	+	0.729371i	$0.260187\pi$
$8$	1.45156	+	2.42754i	0.513205	+	0.858266i
$9$	1.00000			0.333333
$10$	−3.58746	+	3.04158i	−1.13445	+	0.961832i
$11$			1.15172i			0.347258i	0.984811	+	0.173629i	$0.0555493\pi$
$11$			1.15172i			0.347258i	−0.984811	+	0.173629i	$0.944451\pi$
$12$	−0.327167	+	1.97306i	−0.0944449	+	0.569573i
$13$		−	4.49735i		−	1.24734i	−0.781687	−	0.623671i	$-0.785641\pi$
$13$		−	4.49735i		−	1.24734i	0.781687	−	0.623671i	$-0.214359\pi$
$14$	−3.90489	+	3.31071i	−1.04363	+	0.884825i
$15$	−3.32574			−0.858701
$16$	−3.78592	−	1.29104i	−0.946481	−	0.322760i
$17$		−	4.26970i		−	1.03555i	−0.855515	−	0.517777i	$-0.826760\pi$
$17$		−	4.26970i		−	1.03555i	0.855515	−	0.517777i	$-0.173240\pi$
$18$	−1.07870	+	0.914558i	−0.254251	+	0.215563i
$19$		−	1.61916i		−	0.371462i	−0.982601	−	0.185731i	$-0.940535\pi$
$19$		−	1.61916i		−	0.371462i	0.982601	−	0.185731i	$-0.0594652\pi$
$20$	1.08807	−	6.56187i	0.243300	−	1.46728i
$21$	−3.62001			−0.789951
$22$	−1.05332	−	1.24236i	−0.224568	−	0.264872i
$23$	−1.37075	+	4.59576i	−0.285822	+	0.958283i
$23$	−1.37075	+	4.59576i	−0.285822	+	0.958283i
$24$	−1.45156	−	2.42754i	−0.296299	−	0.495520i
$25$	6.06052			1.21210
$26$	4.11309	+	4.85127i	0.806643	+	0.951413i
$27$	−1.00000			−0.192450
$28$	1.18435	−	7.14250i	0.223821	−	1.34981i
$29$		−	1.98240i		−	0.368123i	−0.982915	−	0.184062i	$-0.941075\pi$
$29$		−	1.98240i		−	0.368123i	0.982915	−	0.184062i	$-0.0589246\pi$
$30$	3.58746	−	3.04158i	0.654977	−	0.555314i
$31$		−	2.69787i		−	0.484551i	−0.970207	−	0.242276i	$-0.922106\pi$
$31$		−	2.69787i		−	0.484551i	0.970207	−	0.242276i	$-0.0778939\pi$
$32$	5.26459	−	2.06981i	0.930656	−	0.365894i
$33$		−	1.15172i		−	0.200489i
$34$	3.90489	+	4.60571i	0.669683	+	0.789872i
$35$	12.0392			2.03500
$36$	0.327167	−	1.97306i	0.0545278	−	0.328843i
$37$	−10.4728			−1.72171			−0.860855	−	0.508850i	$-0.830071\pi$
$37$	−10.4728			−1.72171			−0.860855	+	0.508850i	$0.830071\pi$
$38$	1.48082	+	1.74658i	0.240221	+	0.283333i
$39$			4.49735i			0.720153i
$40$	4.82752	+	8.07336i	0.763298	+	1.27651i
$41$	8.87354			1.38581			0.692907	−	0.721027i	$-0.256330\pi$
$41$	8.87354			1.38581			0.692907	+	0.721027i	$0.256330\pi$
$42$	3.90489	−	3.31071i	0.602538	−	0.510854i
$43$			2.83144i			0.431790i	0.976417	+	0.215895i	$0.0692669\pi$
$43$			2.83144i			0.431790i	−0.976417	+	0.215895i	$0.930733\pi$
$44$	2.27242	+	0.376806i	0.342580	+	0.0568056i
$45$	3.32574			0.495771
$46$	−2.72447	−	6.21106i	−0.401701	−	0.915771i
$47$			13.2124i			1.92723i	0.267301	+	0.963613i	$0.413868\pi$
$47$			13.2124i			1.92723i	−0.267301	+	0.963613i	$0.586132\pi$
$48$	3.78592	+	1.29104i	0.546451	+	0.186345i
$49$	6.10449			0.872070
$50$	−6.53745	+	5.54270i	−0.924535	+	0.783856i
$51$			4.26970i			0.597878i
$52$	−8.87354	−	1.47138i	−1.23054	−	0.204044i
$53$	6.02532			0.827641			0.413820	−	0.910359i	$-0.364194\pi$
$53$	6.02532			0.827641			0.413820	+	0.910359i	$0.364194\pi$
$54$	1.07870	−	0.914558i	0.146792	−	0.124456i
$55$			3.83033i			0.516481i
$56$	5.25468	+	8.78773i	0.702186	+	1.17431i
$57$			1.61916i			0.214463i
$58$	1.81302	+	2.13841i	0.238062	+	0.280787i
$59$	−3.81302			−0.496413			−0.248207	−	0.968707i	$-0.579841\pi$
$59$	−3.81302			−0.496413			−0.248207	+	0.968707i	$0.579841\pi$
$60$	−1.08807	+	6.56187i	−0.140469	+	0.847134i
$61$	−0.0328974			−0.00421208			−0.00210604	−	0.999998i	$-0.500670\pi$
$61$	−0.0328974			−0.00421208			−0.00210604	+	0.999998i	$0.500670\pi$
$62$	2.46736	+	2.91018i	0.313355	+	0.369593i
$63$	3.62001			0.456079
$64$	−3.78592	+	7.04747i	−0.473240	+	0.880933i
$65$		−	14.9570i		−	1.85519i
$66$	1.05332	+	1.24236i	0.129654	+	0.152924i
$67$		−	9.53558i		−	1.16496i	−0.812846	−	0.582478i	$-0.802083\pi$
$67$		−	9.53558i		−	1.16496i	0.812846	−	0.582478i	$-0.197917\pi$
$68$	−8.42437	−	1.39690i	−1.02161	−	0.169400i
$69$	1.37075	−	4.59576i	0.165019	−	0.553265i
$70$	−12.9866	+	11.0106i	−1.55220	+	1.31601i
$71$		−	7.45857i		−	0.885169i	−0.896727	−	0.442585i	$-0.854062\pi$
$71$		−	7.45857i		−	0.885169i	0.896727	−	0.442585i	$-0.145938\pi$
$72$	1.45156	+	2.42754i	0.171068	+	0.286089i
$73$	9.56488			1.11948			0.559742	−	0.828667i	$-0.310900\pi$
$73$	9.56488			1.11948			0.559742	+	0.828667i	$0.310900\pi$
$74$	11.2969	−	9.57794i	1.31324	−	1.11341i
$75$	−6.06052			−0.699808
$76$	−3.19471	−	0.529737i	−0.366458	−	0.0607650i
$77$			4.16925i			0.475130i
$78$	−4.11309	−	4.85127i	−0.465716	−	0.549298i
$79$	−4.25927			−0.479206			−0.239603	−	0.970871i	$-0.577017\pi$
$79$	−4.25927			−0.479206			−0.239603	+	0.970871i	$0.577017\pi$
$80$	−12.5910	−	4.29365i	−1.40771	−	0.480045i
$81$	1.00000			0.111111
$82$	−9.57185	+	8.11537i	−1.05703	+	0.896193i
$83$			16.3410i			1.79366i	0.442375	+	0.896830i	$0.354136\pi$
$83$			16.3410i			1.79366i	−0.442375	+	0.896830i	$0.645864\pi$
$84$	−1.18435	+	7.14250i	−0.129223	+	0.779310i
$85$		−	14.1999i		−	1.54020i
$86$	−2.58951	−	3.05426i	−0.279234	−	0.329349i
$87$			1.98240i			0.212536i
$88$	−2.79586	+	1.67180i	−0.298039	+	0.178214i
$89$			11.3103i			1.19889i	0.800417	+	0.599444i	$0.204612\pi$
$89$			11.3103i			1.19889i	−0.800417	+	0.599444i	$0.795388\pi$
$90$	−3.58746	+	3.04158i	−0.378151	+	0.320611i
$91$		−	16.2805i		−	1.70666i
$92$	8.61925	+	4.20816i	0.898619	+	0.438731i
$93$			2.69787i			0.279756i
$94$	−12.0835	−	14.2521i	−1.24632	−	1.47000i
$95$		−	5.38491i		−	0.552480i
$96$	−5.26459	+	2.06981i	−0.537315	+	0.211249i
$97$			8.75475i			0.888910i	0.895801	+	0.444455i	$0.146603\pi$
$97$			8.75475i			0.888910i	−0.895801	+	0.444455i	$0.853397\pi$
$98$	−6.58488	+	5.58291i	−0.665174	+	0.563959i
$99$			1.15172i			0.115753i
$100$	1.98280	−	11.9578i	0.198280	−	1.19578i
$101$		−	2.18685i		−	0.217600i	−0.994064	−	0.108800i	$-0.965299\pi$
$101$		−	2.18685i		−	0.217600i	0.994064	−	0.108800i	$-0.0347007\pi$
$102$	−3.90489	−	4.60571i	−0.386642	−	0.456033i
$103$	8.61878			0.849234			0.424617	−	0.905373i	$-0.360409\pi$
$103$	8.61878			0.849234			0.424617	+	0.905373i	$0.360409\pi$
$104$	10.9175	−	6.52820i	1.07055	−	0.640142i
$105$	−12.0392			−1.17491
$106$	−6.49948	+	5.51050i	−0.631285	+	0.535227i
$107$		−	13.3180i		−	1.28750i	−0.765234	−	0.643752i	$-0.777377\pi$
$107$		−	13.3180i		−	1.28750i	0.765234	−	0.643752i	$-0.222623\pi$
$108$	−0.327167	+	1.97306i	−0.0314816	+	0.189858i
$109$	−7.73125			−0.740519			−0.370260	−	0.928928i	$-0.620731\pi$
$109$	−7.73125			−0.740519			−0.370260	+	0.928928i	$0.620731\pi$
$110$	−3.50306	−	4.13176i	−0.334003	−	0.393947i
$111$	10.4728			0.994030
$112$	−13.7051	−	4.67358i	−1.29501	−	0.441611i
$113$		−	10.6668i		−	1.00344i	−0.865029	−	0.501722i	$-0.832700\pi$
$113$		−	10.6668i		−	1.00344i	0.865029	−	0.501722i	$-0.167300\pi$
$114$	−1.48082	−	1.74658i	−0.138691	−	0.163583i
$115$	−4.55876	+	15.2843i	−0.425107	+	1.42527i
$116$	−3.91140	−	0.648577i	−0.363164	−	0.0602188i
$117$		−	4.49735i		−	0.415780i
$118$	4.11309	−	3.48723i	0.378641	−	0.321026i
$119$		−	15.4564i		−	1.41688i
$120$	−4.82752	−	8.07336i	−0.440690	−	0.736994i
$121$	9.67353			0.879412
$122$	0.0354863	−	0.0300866i	0.00321278	−	0.00272391i
$123$	−8.87354			−0.800100
$124$	−5.32305	−	0.882653i	−0.478024	−	0.0792646i
$125$	3.52700			0.315465
$126$	−3.90489	+	3.31071i	−0.347875	+	0.294942i
$127$			18.2510i			1.61951i	0.586766	+	0.809756i	$0.300401\pi$
$127$			18.2510i			1.61951i	−0.586766	+	0.809756i	$0.699599\pi$
$128$	−2.36146	−	11.0645i	−0.208726	−	0.977974i
$129$		−	2.83144i		−	0.249294i
$130$	13.6791	+	16.1341i	1.19973	+	1.41505i
$131$	−8.22618			−0.718725			−0.359362	−	0.933198i	$-0.617006\pi$
$131$	−8.22618			−0.718725			−0.359362	+	0.933198i	$0.617006\pi$
$132$	−2.27242	−	0.376806i	−0.197789	−	0.0327967i
$133$		−	5.86139i		−	0.508247i
$134$	8.72084	+	10.2860i	0.753366	+	0.888574i
$135$	−3.32574			−0.286234
$136$	10.3649	−	6.19774i	0.888781	−	0.531452i
$137$			19.4590i			1.66249i	0.555903	+	0.831247i	$0.312373\pi$
$137$			19.4590i			1.66249i	−0.555903	+	0.831247i	$0.687627\pi$
$138$	2.72447	+	6.21106i	0.231922	+	0.528721i
$139$	−10.4090			−0.882879			−0.441439	−	0.897291i	$-0.645532\pi$
$139$	−10.4090			−0.882879			−0.441439	+	0.897291i	$0.645532\pi$
$140$	3.93883	−	23.7541i	0.332892	−	2.00758i
$141$		−	13.2124i		−	1.11268i
$142$	6.82130	+	8.04552i	0.572430	+	0.675165i
$143$	5.17971			0.433149
$144$	−3.78592	−	1.29104i	−0.315494	−	0.107587i
$145$		−	6.59295i		−	0.547515i
$146$	−10.3176	+	8.74763i	−0.853889	+	0.723959i
$147$	−6.10449			−0.503490
$148$	−3.42634	+	20.6634i	−0.281643	+	1.69852i
$149$	−23.1166			−1.89379			−0.946895	−	0.321544i	$-0.895798\pi$
$149$	−23.1166			−1.89379			−0.946895	+	0.321544i	$0.895798\pi$
$150$	6.53745	−	5.54270i	0.533781	−	0.452559i
$151$		−	5.42595i		−	0.441558i	−0.975324	−	0.220779i	$-0.929140\pi$
$151$		−	5.42595i		−	0.441558i	0.975324	−	0.220779i	$-0.0708599\pi$
$152$	3.93059	−	2.35032i	0.318813	−	0.190636i
$153$		−	4.26970i		−	0.345185i
$154$	−3.81302	−	4.49735i	−0.307262	−	0.362407i
$155$		−	8.97240i		−	0.720680i
$156$	8.87354	+	1.47138i	0.710452	+	0.117805i
$157$	−2.99386			−0.238936			−0.119468	−	0.992838i	$-0.538119\pi$
$157$	−2.99386			−0.238936			−0.119468	+	0.992838i	$0.538119\pi$
$158$	4.59446	−	3.89535i	0.365515	−	0.309898i
$159$	−6.02532			−0.477839
$160$	17.5086	−	6.88364i	1.38418	−	0.544200i
$161$	−4.96214	+	16.6367i	−0.391072	+	1.31116i
$162$	−1.07870	+	0.914558i	−0.0847503	+	0.0718545i
$163$	9.02632			0.706996			0.353498	−	0.935435i	$-0.384992\pi$
$163$	9.02632			0.706996			0.353498	+	0.935435i	$0.384992\pi$
$164$	2.90313	−	17.5080i	0.226696	−	1.36715i
$165$		−	3.83033i		−	0.298191i
$166$	−14.9448	−	17.6270i	−1.15994	−	1.36812i
$167$		−	1.43662i		−	0.111169i	−0.998454	−	0.0555846i	$-0.982298\pi$
$167$		−	1.43662i		−	0.111169i	0.998454	−	0.0555846i	$-0.0177023\pi$
$168$	−5.25468	−	8.78773i	−0.405407	−	0.677988i
$169$	−7.22618			−0.555860
$170$	12.9866	+	15.3174i	0.996029	+	1.17479i
$171$		−	1.61916i		−	0.123821i
$172$	5.58659	+	0.926352i	0.425973	+	0.0706336i
$173$			18.0789i			1.37451i	0.726415	+	0.687256i	$0.241185\pi$
$173$			18.0789i			1.37451i	−0.726415	+	0.687256i	$0.758815\pi$
$174$	−1.81302	−	2.13841i	−0.137445	−	0.162112i
$175$	21.9392			1.65844
$176$	1.48692	−	4.36034i	0.112081	−	0.328673i
$177$	3.81302			0.286604
$178$	−10.3439	−	12.2004i	−0.775309	−	0.914455i
$179$	−11.1479			−0.833230			−0.416615	−	0.909083i	$-0.636784\pi$
$179$	−11.1479			−0.833230			−0.416615	+	0.909083i	$0.636784\pi$
$180$	1.08807	−	6.56187i	0.0811000	−	0.489093i
$181$	−0.336203			−0.0249898			−0.0124949	−	0.999922i	$-0.503977\pi$
$181$	−0.336203			−0.0249898			−0.0124949	+	0.999922i	$0.503977\pi$
$182$	14.8894	+	17.5617i	1.10368	+	1.30176i
$183$	0.0328974			0.00243185
$184$	−13.1461	+	3.34348i	−0.969147	+	0.246485i
$185$	−34.8296			−2.56072
$186$	−2.46736	−	2.91018i	−0.180915	−	0.213385i
$187$	4.91751			0.359604
$188$	26.0688	+	4.32266i	1.90127	+	0.315262i
$189$	−3.62001			−0.263317
$190$	4.92481	+	5.80868i	0.357284	+	0.421406i
$191$	−19.6758			−1.42369			−0.711844	−	0.702337i	$-0.752140\pi$
$191$	−19.6758			−1.42369			−0.711844	+	0.702337i	$0.752140\pi$
$192$	3.78592	−	7.04747i	0.273226	−	0.508607i
$193$	−1.61302			−0.116107			−0.0580537	−	0.998313i	$-0.518489\pi$
$193$	−1.61302			−0.116107			−0.0580537	+	0.998313i	$0.518489\pi$
$194$	−8.00673	−	9.44370i	−0.574849	−	0.678018i
$195$			14.9570i			1.07109i
$196$	1.99719	−	12.0445i	0.142656	−	0.860323i
$197$			6.15166i			0.438287i	0.975693	+	0.219144i	$0.0703263\pi$
$197$			6.15166i			0.438287i	−0.975693	+	0.219144i	$0.929674\pi$
$198$	−1.05332	−	1.24236i	−0.0748560	−	0.0882906i
$199$	−20.1228			−1.42647			−0.713233	−	0.700927i	$-0.752770\pi$
$199$	−20.1228			−1.42647			−0.713233	+	0.700927i	$0.752770\pi$
$200$	8.79723	+	14.7122i	0.622058	+	1.04031i
$201$			9.53558i			0.672588i
$202$	2.00000	+	2.35894i	0.140720	+	0.165975i
$203$		−	7.17633i		−	0.503679i
$204$	8.42437	+	1.39690i	0.589824	+	0.0978029i
$205$	29.5111			2.06114
$206$	−9.29704	+	7.88238i	−0.647755	+	0.549191i
$207$	−1.37075	+	4.59576i	−0.0952739	+	0.319428i
$208$	−5.80626	+	17.0266i	−0.402591	+	1.18058i
$209$	1.86483			0.128993
$210$	12.9866	−	11.0106i	0.896163	−	0.759800i
$211$	21.4611			1.47744			0.738721	−	0.674012i	$-0.235430\pi$
$211$	21.4611			1.47744			0.738721	+	0.674012i	$0.235430\pi$
$212$	1.97128	−	11.8883i	0.135388	−	0.816492i
$213$			7.45857i			0.511053i
$214$	12.1801	+	14.3661i	0.832616	+	0.982047i
$215$			9.41661i			0.642207i
$216$	−1.45156	−	2.42754i	−0.0987664	−	0.165173i
$217$		−	9.76632i		−	0.662981i
$218$	8.33966	−	7.07067i	0.564833	−	0.478887i
$219$	−9.56488			−0.646334
$220$	7.55746	+	1.25316i	0.509524	+	0.0844877i
$221$	−19.2024			−1.29169
$222$	−11.2969	+	9.57794i	−0.758199	+	0.642829i
$223$			7.71252i			0.516468i	0.966082	+	0.258234i	$0.0831406\pi$
$223$			7.71252i			0.516468i	−0.966082	+	0.258234i	$0.916859\pi$
$224$	19.0579	−	7.49274i	1.27336	−	0.500630i
$225$	6.06052			0.404035
$226$	9.75536	+	11.5062i	0.648917	+	0.765379i
$227$			13.2160i			0.877176i	0.898688	+	0.438588i	$0.144521\pi$
$227$			13.2160i			0.877176i	−0.898688	+	0.438588i	$0.855479\pi$
$228$	3.19471	+	0.529737i	0.211575	+	0.0350827i
$229$	17.5825			1.16189			0.580944	−	0.813944i	$-0.302684\pi$
$229$	17.5825			1.16189			0.580944	+	0.813944i	$0.302684\pi$
$230$	−9.06086	−	20.6563i	−0.597455	−	1.36204i
$231$		−	4.16925i		−	0.274317i
$232$	4.81237	−	2.87759i	0.315948	−	0.188923i
$233$	3.11752			0.204236			0.102118	−	0.994772i	$-0.467438\pi$
$233$	3.11752			0.204236			0.102118	+	0.994772i	$0.467438\pi$
$234$	4.11309	+	4.85127i	0.268881	+	0.317138i
$235$			43.9409i			2.86639i
$236$	−1.24749	+	7.52332i	−0.0812050	+	0.489726i
$237$	4.25927			0.276669
$238$	14.1358	+	16.6727i	0.916285	+	1.08073i
$239$			3.10960i			0.201143i	0.994930	+	0.100572i	$0.0320672\pi$
$239$			3.10960i			0.201143i	−0.994930	+	0.100572i	$0.967933\pi$
$240$	12.5910	+	4.29365i	0.812744	+	0.277154i
$241$		−	27.9280i		−	1.79900i	−0.436923	−	0.899499i	$-0.643932\pi$
$241$		−	27.9280i		−	1.79900i	0.436923	−	0.899499i	$-0.356068\pi$
$242$	−10.4348	+	8.84701i	−0.670774	+	0.568707i
$243$	−1.00000			−0.0641500
$244$	−0.0107629	+	0.0649085i	−0.000689026	+	0.00415534i
$245$	20.3019			1.29704
$246$	9.57185	−	8.11537i	0.610279	−	0.517417i
$247$	−7.28195			−0.463339
$248$	6.54919	−	3.91613i	0.415874	−	0.248674i
$249$		−	16.3410i		−	1.03557i
$250$	−3.80456	+	3.22565i	−0.240622	+	0.204008i
$251$		−	18.5875i		−	1.17323i	−0.809864	−	0.586617i	$-0.800459\pi$
$251$		−	18.5875i		−	1.17323i	0.809864	−	0.586617i	$-0.199541\pi$
$252$	1.18435	−	7.14250i	0.0746069	−	0.449935i
$253$	−5.29305	−	1.57873i	−0.332771	−	0.0992538i
$254$	−16.6916	−	19.6872i	−1.04732	−	1.23529i
$255$			14.1999i			0.889232i
$256$	12.6664	+	9.77555i	0.791652	+	0.610972i
$257$	−25.6119			−1.59763			−0.798814	−	0.601579i	$-0.794539\pi$
$257$	−25.6119			−1.59763			−0.798814	+	0.601579i	$0.794539\pi$
$258$	2.58951	+	3.05426i	0.161216	+	0.190150i
$259$	−37.9115			−2.35571
$260$	−29.5111	−	4.89344i	−1.83020	−	0.303478i
$261$		−	1.98240i		−	0.122708i
$262$	8.87354	−	7.52332i	0.548209	−	0.464792i
$263$	−9.98153			−0.615488			−0.307744	−	0.951469i	$-0.599574\pi$
$263$	−9.98153			−0.615488			−0.307744	+	0.951469i	$0.599574\pi$
$264$	2.79586	−	1.67180i	0.172073	−	0.102892i
$265$	20.0386			1.23096
$266$	5.36059	+	6.32266i	0.328679	+	0.387667i
$267$		−	11.3103i		−	0.692178i
$268$	−18.8143	−	3.11973i	−1.14926	−	0.190568i
$269$			15.1464i			0.923490i	0.887013	+	0.461745i	$0.152776\pi$
$269$			15.1464i			0.923490i	−0.887013	+	0.461745i	$0.847224\pi$
$270$	3.58746	−	3.04158i	0.218326	−	0.185105i
$271$			6.52820i			0.396560i	0.980145	+	0.198280i	$0.0635355\pi$
$271$			6.52820i			0.396560i	−0.980145	+	0.198280i	$0.936465\pi$
$272$	−5.51235	+	16.1648i	−0.334235	+	0.980133i
$273$			16.2805i			0.985339i
$274$	−17.7964	−	20.9903i	−1.07512	−	1.26807i
$275$			6.98004i			0.420912i
$276$	−8.61925	−	4.20816i	−0.518818	−	0.253301i
$277$			16.8218i			1.01072i	0.862908	+	0.505361i	$0.168641\pi$
$277$			16.8218i			1.01072i	−0.862908	+	0.505361i	$0.831359\pi$
$278$	11.2281	−	9.51963i	0.673418	−	0.570949i
$279$		−	2.69787i		−	0.161517i
$280$	17.4757	+	29.2257i	1.04437	+	1.74657i
$281$		−	13.1210i		−	0.782733i	−0.920235	−	0.391367i	$-0.872002\pi$
$281$		−	13.1210i		−	0.782733i	0.920235	−	0.391367i	$-0.127998\pi$
$282$	12.0835	+	14.2521i	0.719562	+	0.848703i
$283$		−	1.59861i		−	0.0950275i	−0.998871	−	0.0475137i	$-0.984870\pi$
$283$		−	1.59861i		−	0.0950275i	0.998871	−	0.0475137i	$-0.0151298\pi$
$284$	−14.7162	−	2.44020i	−0.873246	−	0.144799i
$285$			5.38491i			0.318975i
$286$	−5.58732	+	4.73714i	−0.330385	+	0.280113i
$287$	32.1223			1.89612
$288$	5.26459	−	2.06981i	0.310219	−	0.121965i
$289$	−1.23035			−0.0723735
$290$	6.02964	+	7.11179i	0.354073	+	0.417618i
$291$		−	8.75475i		−	0.513212i
$292$	3.12931	−	18.8721i	0.183129	−	1.10440i
$293$	20.5003			1.19764			0.598820	−	0.800884i	$-0.295637\pi$
$293$	20.5003			1.19764			0.598820	+	0.800884i	$0.295637\pi$
$294$	6.58488	−	5.58291i	0.384038	−	0.325602i
$295$	−12.6811			−0.738323
$296$	−15.2019	−	25.4231i	−0.883591	−	1.47768i
$297$		−	1.15172i		−	0.0668298i
$298$	24.9358	−	21.1415i	1.44449	−	1.22469i
$299$	20.6688	+	6.16476i	1.19531	+	0.356517i
$300$	−1.98280	+	11.9578i	−0.114477	+	0.690382i
$301$			10.2498i			0.590791i
$302$	4.96235	+	5.85295i	0.285551	+	0.336799i
$303$			2.18685i			0.125631i
$304$	−2.09040	+	6.13003i	−0.119893	+	0.351581i
$305$	−0.109408			−0.00626469
$306$	3.90489	+	4.60571i	0.223228	+	0.263291i
$307$	15.1609			0.865278			0.432639	−	0.901567i	$-0.357582\pi$
$307$	15.1609			0.865278			0.432639	+	0.901567i	$0.357582\pi$
$308$	8.22618	+	1.36404i	0.468730	+	0.0777234i
$309$	−8.61878			−0.490305
$310$	8.20578	+	9.67848i	0.466057	+	0.549701i
$311$		−	19.4369i		−	1.10216i	−0.834451	−	0.551082i	$-0.814215\pi$
$311$		−	19.4369i		−	1.10216i	0.834451	−	0.551082i	$-0.185785\pi$
$312$	−10.9175	+	6.52820i	−0.618083	+	0.369586i
$313$		−	31.6451i		−	1.78869i	−0.447380	−	0.894344i	$-0.647643\pi$
$313$		−	31.6451i		−	1.78869i	0.447380	−	0.894344i	$-0.352357\pi$
$314$	3.22946	−	2.73806i	0.182249	−	0.154517i
$315$	12.0392			0.678332
$316$	−1.39349	+	8.40380i	−0.0783901	+	0.472750i
$317$		−	7.16345i		−	0.402340i	−0.979556	−	0.201170i	$-0.935526\pi$
$317$		−	7.16345i		−	0.402340i	0.979556	−	0.201170i	$-0.0644743\pi$
$318$	6.49948	−	5.51050i	0.364473	−	0.309014i
$319$	2.28318			0.127834
$320$	−12.5910	+	23.4380i	−0.703857	+	1.31022i
$321$			13.3180i			0.743340i
$322$	−9.86261	−	22.4841i	−0.549622	−	1.25299i
$323$	−6.91335			−0.384669
$324$	0.327167	−	1.97306i	0.0181759	−	0.109614i
$325$		−	27.2563i		−	1.51191i
$326$	−9.73665	+	8.25510i	−0.539263	+	0.457208i
$327$	7.73125			0.427539
$328$	12.8805	+	21.5409i	0.711207	+	1.18940i
$329$			47.8290i			2.63690i
$330$	3.50306	+	4.13176i	0.192837	+	0.227446i
$331$	22.7506			1.25049			0.625243	−	0.780430i	$-0.285000\pi$
$331$	22.7506			1.25049			0.625243	+	0.780430i	$0.285000\pi$
$332$	32.2418	+	5.34624i	1.76950	+	0.293413i
$333$	−10.4728			−0.573903
$334$	1.31388	+	1.54968i	0.0718921	+	0.0847946i
$335$		−	31.7128i		−	1.73266i
$336$	13.7051	+	4.67358i	0.747674	+	0.254964i
$337$			13.8468i			0.754282i	0.926156	+	0.377141i	$0.123093\pi$
$337$			13.8468i			0.754282i	−0.926156	+	0.377141i	$0.876907\pi$
$338$	7.79485	−	6.60876i	0.423984	−	0.359469i
$339$			10.6668i			0.579338i
$340$	−28.0172	−	4.64573i	−1.51945	−	0.251950i
$341$	3.10720			0.168264
$342$	1.48082	+	1.74658i	0.0800736	+	0.0944445i
$343$	−3.24176			−0.175038
$344$	−6.87343	+	4.11001i	−0.370591	+	0.221597i
$345$	4.55876	−	15.2843i	0.245435	−	0.822879i
$346$	−16.5342	−	19.5016i	−0.888884	−	1.04841i
$347$	4.29579			0.230610			0.115305	−	0.993330i	$-0.463215\pi$
$347$	4.29579			0.230610			0.115305	+	0.993330i	$0.463215\pi$
$348$	3.91140	+	0.648577i	0.209673	+	0.0347674i
$349$		−	7.01030i		−	0.375253i	−0.982240	−	0.187626i	$-0.939921\pi$
$349$		−	7.01030i		−	0.375253i	0.982240	−	0.187626i	$-0.0600794\pi$
$350$	−23.6657	+	20.0646i	−1.26498	+	1.07250i
$351$			4.49735i			0.240051i
$352$	2.38385	+	6.06335i	0.127060	+	0.323178i
$353$	−17.3265			−0.922197			−0.461098	−	0.887349i	$-0.652544\pi$
$353$	−17.3265			−0.922197			−0.461098	+	0.887349i	$0.652544\pi$
$354$	−4.11309	+	3.48723i	−0.218608	+	0.185344i
$355$		−	24.8052i		−	1.31653i
$356$	22.3159	+	3.70035i	1.18274	+	0.196118i
$357$			15.4564i			0.818038i
$358$	12.0251	−	10.1954i	0.635549	−	0.538842i
$359$	21.4596			1.13260			0.566298	−	0.824201i	$-0.308375\pi$
$359$	21.4596			1.13260			0.566298	+	0.824201i	$0.308375\pi$
$360$	4.82752	+	8.07336i	0.254433	+	0.425504i
$361$	16.3783			0.862016
$362$	0.362660	−	0.307477i	0.0190610	−	0.0161606i
$363$	−9.67353			−0.507729
$364$	−32.1223	−	5.32643i	−1.68367	−	0.279181i
$365$	31.8102			1.66502
$366$	−0.0354863	+	0.0300866i	−0.00185490	+	0.00157265i
$367$	−29.7591			−1.55341			−0.776706	−	0.629864i	$-0.783111\pi$
$367$	−29.7591			−1.55341			−0.776706	+	0.629864i	$0.783111\pi$
$368$	11.1229	−	15.6295i	0.579820	−	0.814745i
$369$	8.87354			0.461938
$370$	37.5705	−	31.8537i	1.95320	−	1.65600i
$371$	21.8117			1.13241
$372$	5.32305	+	0.882653i	0.275987	+	0.0457634i
$373$	−16.4141			−0.849889			−0.424945	−	0.905219i	$-0.639706\pi$
$373$	−16.4141			−0.849889			−0.424945	+	0.905219i	$0.639706\pi$
$374$	−5.30450	+	4.49735i	−0.274289	+	0.232553i
$375$	−3.52700			−0.182134
$376$	−32.0737	+	19.1786i	−1.65407	+	0.989063i
$377$	−8.91557			−0.459175
$378$	3.90489	−	3.31071i	0.200846	−	0.170285i
$379$		−	8.87510i		−	0.455883i	−0.973675	−	0.227942i	$-0.926800\pi$
$379$		−	8.87510i		−	0.455883i	0.973675	−	0.227942i	$-0.0731995\pi$
$380$	−10.6247	−	1.76176i	−0.545038	−	0.0903766i
$381$		−	18.2510i		−	0.935026i
$382$	21.2242	−	17.9946i	1.08592	−	0.920685i
$383$	−4.71797			−0.241077			−0.120539	−	0.992709i	$-0.538462\pi$
$383$	−4.71797			−0.241077			−0.120539	+	0.992709i	$0.538462\pi$
$384$	2.36146	+	11.0645i	0.120508	+	0.564634i
$385$			13.8658i			0.706668i
$386$	1.73995	−	1.47520i	0.0885612	−	0.0750855i
$387$			2.83144i			0.143930i
$388$	17.2736	+	2.86426i	0.876936	+	0.145411i
$389$	−25.2935			−1.28243			−0.641215	−	0.767361i	$-0.721569\pi$
$389$	−25.2935			−1.28243			−0.641215	+	0.767361i	$0.721569\pi$
$390$	−13.6791	−	16.1341i	−0.692666	−	0.816979i
$391$	19.6225	+	5.85270i	0.992354	+	0.295984i
$392$	8.86106	+	14.8189i	0.447551	+	0.748468i
$393$	8.22618			0.414956
$394$	−5.62605	−	6.63576i	−0.283436	−	0.334305i
$395$	−14.1652			−0.712729
$396$	2.27242	+	0.376806i	0.114193	+	0.0189352i
$397$			3.22216i			0.161715i	0.996726	+	0.0808577i	$0.0257659\pi$
$397$			3.22216i			0.161715i	−0.996726	+	0.0808577i	$0.974234\pi$
$398$	21.7064	−	18.4035i	1.08804	−	0.922482i
$399$			5.86139i			0.293437i
$400$	−22.9447	−	7.82436i	−1.14723	−	0.391218i
$401$		−	0.578635i		−	0.0288957i	−0.999896	−	0.0144478i	$-0.995401\pi$
$401$		−	0.578635i		−	0.0288957i	0.999896	−	0.0144478i	$-0.00459905\pi$
$402$	−8.72084	−	10.2860i	−0.434956	−	0.513018i
$403$	−12.1333			−0.604401
$404$	−4.31478	−	0.715464i	−0.214668	−	0.0355957i
$405$	3.32574			0.165257
$406$	6.56317	+	7.74107i	0.325725	+	0.384183i
$407$		−	12.0617i		−	0.597877i
$408$	−10.3649	+	6.19774i	−0.513138	+	0.306834i
$409$	−36.3004			−1.79494			−0.897470	−	0.441075i	$-0.854597\pi$
$409$	−36.3004			−1.79494			−0.897470	+	0.441075i	$0.854597\pi$
$410$	−31.8334	+	26.9896i	−1.57214	+	1.33292i
$411$		−	19.4590i		−	0.959842i
$412$	2.81978	−	17.0054i	0.138921	−	0.837794i
$413$	−13.8032			−0.679211
$414$	−2.72447	−	6.21106i	−0.133900	−	0.305257i
$415$			54.3459i			2.66774i
$416$	−9.30867	−	23.6767i	−0.456395	−	1.16085i
$417$	10.4090			0.509730
$418$	−2.01158	+	1.70549i	−0.0983897	+	0.0834185i
$419$		−	23.4858i		−	1.14735i	−0.819081	−	0.573677i	$-0.805516\pi$
$419$		−	23.4858i		−	1.14735i	0.819081	−	0.573677i	$-0.194484\pi$
$420$	−3.93883	+	23.7541i	−0.192195	+	1.15908i
$421$	−16.5531			−0.806749			−0.403374	−	0.915035i	$-0.632163\pi$
$421$	−16.5531			−0.806749			−0.403374	+	0.915035i	$0.632163\pi$
$422$	−23.1500	+	19.6274i	−1.12692	+	0.955447i
$423$			13.2124i			0.642409i
$424$	8.74613	+	14.6267i	0.424750	+	0.710336i
$425$		−	25.8766i		−	1.25520i
$426$	−6.82130	−	8.04552i	−0.330493	−	0.389807i
$427$	−0.119089			−0.00576312
$428$	−26.2773	−	4.35722i	−1.27016	−	0.210614i
$429$	−5.17971			−0.250079
$430$	−8.61203	−	10.1576i	−0.415309	−	0.489845i
$431$	3.81073			0.183557			0.0917783	−	0.995779i	$-0.470745\pi$
$431$	3.81073			0.183557			0.0917783	+	0.995779i	$0.470745\pi$
$432$	3.78592	+	1.29104i	0.182150	+	0.0621151i
$433$			15.8328i			0.760878i	0.924806	+	0.380439i	$0.124227\pi$
$433$			15.8328i			0.760878i	−0.924806	+	0.380439i	$0.875773\pi$
$434$	8.93186	+	10.5349i	0.428743	+	0.505690i
$435$			6.59295i			0.316108i
$436$	−2.52941	+	15.2542i	−0.121137	+	0.730544i
$437$	7.44129	+	2.21947i	0.355965	+	0.106172i
$438$	10.3176	−	8.74763i	0.492993	−	0.417978i
$439$		−	32.9208i		−	1.57122i	−0.618719	−	0.785612i	$-0.712348\pi$
$439$		−	32.9208i		−	1.57122i	0.618719	−	0.785612i	$-0.287652\pi$
$440$	−9.29828	+	5.55997i	−0.443278	+	0.265061i
$441$	6.10449			0.290690
$442$	20.7135	−	17.5617i	0.985240	−	0.835323i
$443$	10.7105			0.508870			0.254435	−	0.967090i	$-0.418110\pi$
$443$	10.7105			0.508870			0.254435	+	0.967090i	$0.418110\pi$
$444$	3.42634	−	20.6634i	0.162607	−	0.980640i
$445$			37.6150i			1.78312i
$446$	−7.05355	−	8.31946i	−0.333995	−	0.393938i
$447$	23.1166			1.09338
$448$	−13.7051	+	25.5119i	−0.647505	+	1.20532i
$449$	16.2084			0.764921			0.382460	−	0.923972i	$-0.375077\pi$
$449$	16.2084			0.764921			0.382460	+	0.923972i	$0.375077\pi$
$450$	−6.53745	+	5.54270i	−0.308178	+	0.261285i
$451$			10.2199i			0.481235i
$452$	−21.0461	−	3.48981i	−0.989927	−	0.164147i
$453$			5.42595i			0.254933i
$454$	−12.0868	−	14.2560i	−0.567261	−	0.669069i
$455$		−	54.1446i		−	2.53834i
$456$	−3.93059	+	2.35032i	−0.184067	+	0.110064i
$457$			18.7909i			0.878999i	0.898243	+	0.439500i	$0.144844\pi$
$457$			18.7909i			0.878999i	−0.898243	+	0.439500i	$0.855156\pi$
$458$	−18.9662	+	16.0803i	−0.886233	+	0.751381i
$459$			4.26970i			0.199293i
$460$	28.6653	+	13.9952i	1.33653	+	0.652530i
$461$			35.6487i			1.66033i	0.557520	+	0.830163i	$0.311753\pi$
$461$			35.6487i			1.66033i	−0.557520	+	0.830163i	$0.688247\pi$
$462$	3.81302	+	4.49735i	0.177398	+	0.209236i
$463$		−	28.5793i		−	1.32819i	−0.747647	−	0.664096i	$-0.768817\pi$
$463$		−	28.5793i		−	1.32819i	0.747647	−	0.664096i	$-0.231183\pi$
$464$	−2.55936	+	7.50523i	−0.118815	+	0.348422i
$465$			8.97240i			0.416085i
$466$	−3.36286	+	2.85116i	−0.155781	+	0.132077i
$467$		−	8.80839i		−	0.407604i	−0.979012	−	0.203802i	$-0.934670\pi$
$467$		−	8.80839i		−	0.407604i	0.979012	−	0.203802i	$-0.0653298\pi$
$468$	−8.87354	−	1.47138i	−0.410180	−	0.0680148i
$469$		−	34.5189i		−	1.59394i
$470$	−40.1865	−	47.3989i	−1.85367	−	2.18635i
$471$	2.99386			0.137950
$472$	−5.53485	−	9.25628i	−0.254762	−	0.426055i
$473$	−3.26103			−0.149942
$474$	−4.59446	+	3.89535i	−0.211030	+	0.178919i
$475$		−	9.81297i		−	0.450250i
$476$	−30.4963	−	5.05681i	−1.39780	−	0.231779i
$477$	6.02532			0.275880
$478$	−2.84391	−	3.35431i	−0.130077	−	0.153423i
$479$	−25.4354			−1.16217			−0.581086	−	0.813842i	$-0.697372\pi$
$479$	−25.4354			−1.16217			−0.581086	+	0.813842i	$0.697372\pi$
$480$	−17.5086	+	6.88364i	−0.799156	+	0.314194i
$481$			47.0997i			2.14756i
$482$	25.5417	+	30.1258i	1.16339	+	1.37219i
$483$	4.96214	−	16.6367i	0.225785	−	0.756997i
$484$	3.16486	−	19.0865i	0.143857	−	0.867566i
$485$			29.1160i			1.32209i
$486$	1.07870	−	0.914558i	0.0489306	−	0.0414852i
$487$		−	21.6565i		−	0.981348i	−0.871343	−	0.490674i	$-0.836751\pi$
$487$		−	21.6565i		−	0.981348i	0.871343	−	0.490674i	$-0.163249\pi$
$488$	−0.0477527	−	0.0798598i	−0.00216166	−	0.00361508i
$489$	−9.02632			−0.408184
$490$	−21.8996	+	18.5673i	−0.989322	+	0.838785i
$491$	−22.4744			−1.01425			−0.507127	−	0.861871i	$-0.669292\pi$
$491$	−22.4744			−1.01425			−0.507127	+	0.861871i	$0.669292\pi$
$492$	−2.90313	+	17.5080i	−0.130883	+	0.789323i
$493$	−8.46427			−0.381212
$494$	7.85501	−	6.65977i	0.353413	−	0.299637i
$495$			3.83033i			0.172160i
$496$	−3.48305	+	10.2139i	−0.156394	+	0.458619i
$497$		−	27.0001i		−	1.21112i
$498$	14.9448	+	17.6270i	0.669693	+	0.789884i
$499$	3.69851			0.165568			0.0827841	−	0.996568i	$-0.473619\pi$
$499$	3.69851			0.165568			0.0827841	+	0.996568i	$0.473619\pi$
$500$	1.15392	−	6.95899i	0.0516048	−	0.311215i
$501$			1.43662i			0.0641836i
$502$	16.9994	+	20.0503i	0.758719	+	0.894888i
$503$	−38.1013			−1.69885			−0.849426	−	0.527708i	$-0.823051\pi$
$503$	−38.1013			−1.69885			−0.849426	+	0.527708i	$0.823051\pi$
$504$	5.25468	+	8.78773i	0.234062	+	0.391437i
$505$		−	7.27288i		−	0.323639i
$506$	7.15342	−	3.13783i	0.318008	−	0.139494i
$507$	7.22618			0.320926
$508$	36.0103	+	5.97111i	1.59770	+	0.264925i
$509$		−	27.4825i		−	1.21814i	−0.793117	−	0.609070i	$-0.791543\pi$
$509$		−	27.4825i		−	1.21814i	0.793117	−	0.609070i	$-0.208457\pi$
$510$	−12.9866	−	15.3174i	−0.575058	−	0.678264i
$511$	34.6250			1.53172
$512$	−22.6035	+	1.03936i	−0.998944	+	0.0459336i
$513$			1.61916i			0.0714878i
$514$	27.6274	−	23.4236i	1.21859	−	1.03317i
$515$	28.6638			1.26308
$516$	−5.58659	−	0.926352i	−0.245936	−	0.0407804i
$517$	−15.2170			−0.669244
$518$	40.8949	−	34.6723i	1.79682	−	1.52341i
$519$		−	18.0789i		−	0.793575i
$520$	36.3088	−	21.7111i	1.59224	−	0.952093i
$521$			9.99306i			0.437804i	0.975747	+	0.218902i	$0.0702475\pi$
$521$			9.99306i			0.437804i	−0.975747	+	0.218902i	$0.929753\pi$
$522$	1.81302	+	2.13841i	0.0793539	+	0.0935957i
$523$			14.1931i			0.620622i	0.950635	+	0.310311i	$0.100433\pi$
$523$			14.1931i			0.620622i	−0.950635	+	0.310311i	$0.899567\pi$
$524$	−2.69133	+	16.2307i	−0.117571	+	0.709043i
$525$	−21.9392			−0.957503
$526$	10.7670	−	9.12869i	0.469465	−	0.398030i
$527$	−11.5191			−0.501779
$528$	−1.48692	+	4.36034i	−0.0647099	+	0.189759i
$529$	−19.2421	−	12.5993i	−0.836612	−	0.547796i
$530$	−21.6155	+	18.3265i	−0.938919	+	0.796051i
$531$	−3.81302			−0.165471
$532$	−11.5649	−	1.91765i	−0.501401	−	0.0831408i
$533$		−	39.9074i		−	1.72858i
$534$	10.3439	+	12.2004i	0.447625	+	0.527961i
$535$		−	44.2923i		−	1.91492i
$536$	23.1480	−	13.8415i	0.999843	−	0.597862i
$537$	11.1479			0.481066
$538$	−13.8522	−	16.3383i	−0.597212	−	0.704394i
$539$			7.03068i			0.302833i
$540$	−1.08807	+	6.56187i	−0.0468231	+	0.282378i
$541$			44.6625i			1.92019i	0.279670	+	0.960096i	$0.409775\pi$
$541$			44.6625i			1.92019i	−0.279670	+	0.960096i	$0.590225\pi$
$542$	−5.97041	−	7.04193i	−0.256451	−	0.302477i
$543$	0.336203			0.0144278
$544$	−8.83747	−	22.4782i	−0.378903	−	0.963746i
$545$	−25.7121			−1.10138
$546$	−14.8894	−	17.5617i	−0.637209	−	0.751570i
$547$	−31.4942			−1.34659			−0.673297	−	0.739372i	$-0.735122\pi$
$547$	−31.4942			−1.34659			−0.673297	+	0.739372i	$0.735122\pi$
$548$	38.3938	+	6.36634i	1.64010	+	0.271956i
$549$	−0.0328974			−0.00140403
$550$	−6.38365	−	7.52934i	−0.272200	−	0.321052i
$551$	−3.20984			−0.136744
$552$	13.1461	−	3.34348i	0.559537	−	0.142308i
$553$	−15.4186			−0.655666
$554$	−15.3845	−	18.1456i	−0.653624	−	0.770931i
$555$	34.8296			1.47843
$556$	−3.40548	+	20.5376i	−0.144424	+	0.870986i
$557$	−5.17538			−0.219288			−0.109644	−	0.993971i	$-0.534971\pi$
$557$	−5.17538			−0.219288			−0.109644	+	0.993971i	$0.534971\pi$
$558$	2.46736	+	2.91018i	0.104452	+	0.123198i
$559$	12.7340			0.538589
$560$	−45.5795	−	15.5431i	−1.92609	−	0.656815i
$561$	−4.91751			−0.207618
$562$	11.9999	+	14.1536i	0.506186	+	0.597032i
$563$			15.9334i			0.671512i	0.941949	+	0.335756i	$0.108992\pi$
$563$			15.9334i			0.671512i	−0.941949	+	0.335756i	$0.891008\pi$
$564$	−26.0688	−	4.32266i	−1.09770	−	0.182017i
$565$		−	35.4748i		−	1.49244i
$566$	1.46202	+	1.72441i	0.0614533	+	0.0724825i
$567$	3.62001			0.152026
$568$	18.1060	−	10.8266i	0.759711	−	0.454274i
$569$		−	5.57622i		−	0.233767i	−0.993146	−	0.116884i	$-0.962710\pi$
$569$		−	5.57622i		−	0.233767i	0.993146	−	0.116884i	$-0.0372905\pi$
$570$	−4.92481	−	5.80868i	−0.206278	−	0.243299i
$571$		−	7.53008i		−	0.315124i	−0.987509	−	0.157562i	$-0.949637\pi$
$571$		−	7.53008i		−	0.315124i	0.987509	−	0.157562i	$-0.0503634\pi$
$572$	1.69463	−	10.2199i	0.0708559	−	0.427314i
$573$	19.6758			0.821967
$574$	−34.6502	+	29.3777i	−1.44627	+	1.22620i
$575$	−8.30747	+	27.8527i	−0.346446	+	1.16154i
$576$	−3.78592	+	7.04747i	−0.157747	+	0.293644i
$577$	35.5460			1.47980			0.739899	−	0.672718i	$-0.234873\pi$
$577$	35.5460			1.47980			0.739899	+	0.672718i	$0.234873\pi$
$578$	1.32717	−	1.12523i	0.0552031	−	0.0468032i
$579$	1.61302			0.0670346
$580$	−13.0083	−	2.15699i	−0.540140	−	0.0895643i
$581$			59.1547i			2.45415i
$582$	8.00673	+	9.44370i	0.331889	+	0.391454i
$583$			6.93950i			0.287405i
$584$	13.8840	+	23.2191i	0.574525	+	0.960815i
$585$		−	14.9570i		−	0.618396i
$586$	−22.1136	+	18.7487i	−0.913503	+	0.774502i
$587$	2.09161			0.0863299			0.0431650	−	0.999068i	$-0.486256\pi$
$587$	2.09161			0.0863299			0.0431650	+	0.999068i	$0.486256\pi$
$588$	−1.99719	+	12.0445i	−0.0823626	+	0.496708i
$589$	−4.36829			−0.179992
$590$	13.6791	−	11.5976i	0.563158	−	0.477466i
$591$		−	6.15166i		−	0.253045i
$592$	39.6490	+	13.5207i	1.62957	+	0.555698i
$593$	11.8893			0.488234			0.244117	−	0.969746i	$-0.421502\pi$
$593$	11.8893			0.488234			0.244117	+	0.969746i	$0.421502\pi$
$594$	1.05332	+	1.24236i	0.0432182	+	0.0509746i
$595$		−	51.4038i		−	2.10735i
$596$	−7.56300	+	45.6105i	−0.309792	+	1.86828i
$597$	20.1228			0.823571
$598$	−27.9333	+	12.2529i	−1.14228	+	0.501058i
$599$			4.20687i			0.171888i	0.996300	+	0.0859439i	$0.0273906\pi$
$599$			4.20687i			0.171888i	−0.996300	+	0.0859439i	$0.972609\pi$
$600$	−8.79723	−	14.7122i	−0.359145	−	0.600622i
$601$	−7.04829			−0.287506			−0.143753	−	0.989614i	$-0.545917\pi$
$601$	−7.04829			−0.287506			−0.143753	+	0.989614i	$0.545917\pi$
$602$	−9.37407	−	11.0564i	−0.382058	−	0.450627i
$603$		−	9.53558i		−	0.388319i
$604$	−10.7057	−	1.77519i	−0.435610	−	0.0722315i
$605$	32.1716			1.30796
$606$	−2.00000	−	2.35894i	−0.0812444	−	0.0958255i
$607$		−	1.68065i		−	0.0682155i	−0.999418	−	0.0341078i	$-0.989141\pi$
$607$		−	1.68065i		−	0.0682155i	0.999418	−	0.0341078i	$-0.0108589\pi$
$608$	−3.35136	−	8.52423i	−0.135916	−	0.345703i
$609$			7.17633i			0.290799i
$610$	0.118018	−	0.100060i	0.00477841	−	0.00405131i
$611$	59.4208			2.40391
$612$	−8.42437	−	1.39690i	−0.340535	−	0.0564665i
$613$	41.0060			1.65622			0.828109	−	0.560567i	$-0.189417\pi$
$613$	41.0060			1.65622			0.828109	+	0.560567i	$0.189417\pi$
$614$	−16.3540	+	13.8655i	−0.659993	+	0.559567i
$615$	−29.5111			−1.19000
$616$	−10.1210	+	6.05194i	−0.407788	+	0.243839i
$617$			34.3764i			1.38394i	0.721925	+	0.691971i	$0.243257\pi$
$617$			34.3764i			1.38394i	−0.721925	+	0.691971i	$0.756743\pi$
$618$	9.29704	−	7.88238i	0.373982	−	0.317076i
$619$			46.2916i			1.86062i	0.366779	+	0.930308i	$0.380460\pi$
$619$			46.2916i			1.86062i	−0.366779	+	0.930308i	$0.619540\pi$
$620$	−17.7031	−	2.93547i	−0.710972	−	0.117891i
$621$	1.37075	−	4.59576i	0.0550064	−	0.184422i
$622$	17.7761	+	20.9664i	0.712758	+	0.840678i
$623$			40.9434i			1.64036i
$624$	5.80626	−	17.0266i	0.232436	−	0.681611i
$625$	−18.5727			−0.742908
$626$	28.9413	+	34.1354i	1.15673	+	1.36433i
$627$	−1.86483			−0.0744741
$628$	−0.979490	+	5.90705i	−0.0390859	+	0.235717i
$629$			44.7155i			1.78292i
$630$	−12.9866	+	11.0106i	−0.517400	+	0.438671i
$631$	6.71856			0.267462			0.133731	−	0.991018i	$-0.457304\pi$
$631$	6.71856			0.267462			0.133731	+	0.991018i	$0.457304\pi$
$632$	−6.18261	−	10.3396i	−0.245931	−	0.411286i
$633$	−21.4611			−0.853001
$634$	6.55139	+	7.72718i	0.260189	+	0.306886i
$635$			60.6979i			2.40872i
$636$	−1.97128	+	11.8883i	−0.0781664	+	0.471402i
$637$		−	27.4540i		−	1.08777i
$638$	−2.46286	+	2.08810i	−0.0975054	+	0.0826687i
$639$		−	7.45857i		−	0.295056i
$640$	−7.85359	−	36.7977i	−0.310440	−	1.45456i
$641$		−	13.6941i		−	0.540884i	−0.962736	−	0.270442i	$-0.912830\pi$
$641$		−	13.6941i		−	0.540884i	0.962736	−	0.270442i	$-0.0871698\pi$
$642$	−12.1801	−	14.3661i	−0.480711	−	0.566985i
$643$		−	25.8152i		−	1.01805i	−0.860751	−	0.509027i	$-0.830005\pi$
$643$		−	25.8152i		−	1.01805i	0.860751	−	0.509027i	$-0.169995\pi$
$644$	31.2018	+	15.2336i	1.22952	+	0.600287i
$645$		−	9.41661i		−	0.370779i
$646$	7.45739	−	6.32266i	0.293407	−	0.248762i
$647$		−	28.0022i		−	1.10088i	−0.834875	−	0.550440i	$-0.814460\pi$
$647$		−	28.0022i		−	1.10088i	0.834875	−	0.550440i	$-0.185540\pi$
$648$	1.45156	+	2.42754i	0.0570228	+	0.0953629i
$649$		−	4.39155i		−	0.172383i
$650$	24.9275	+	29.4012i	0.977735	+	1.15321i
$651$			9.76632i			0.382772i
$652$	2.95311	−	17.8095i	0.115653	−	0.697473i
$653$		−	27.2623i		−	1.06686i	−0.845845	−	0.533429i	$-0.820903\pi$
$653$		−	27.2623i		−	1.06686i	0.845845	−	0.533429i	$-0.179097\pi$
$654$	−8.33966	+	7.07067i	−0.326106	+	0.276485i
$655$	−27.3581			−1.06897
$656$	−33.5946	−	11.4561i	−1.31165	−	0.447285i
$657$	9.56488			0.373161
$658$	−43.7424	−	51.5930i	−1.70526	−	2.01130i
$659$		−	18.8859i		−	0.735691i	−0.929887	−	0.367845i	$-0.880096\pi$
$659$		−	18.8859i		−	0.735691i	0.929887	−	0.367845i	$-0.119904\pi$
$660$	−7.55746	−	1.25316i	−0.294174	−	0.0487790i
$661$	−12.2406			−0.476104			−0.238052	−	0.971252i	$-0.576509\pi$
$661$	−12.2406			−0.476104			−0.238052	+	0.971252i	$0.576509\pi$
$662$	−24.5410	+	20.8067i	−0.953812	+	0.808677i
$663$	19.2024			0.745758
$664$	−39.6685	+	23.7200i	−1.53944	+	0.920516i
$665$		−	19.4934i		−	0.755923i
$666$	11.2969	−	9.57794i	0.437746	−	0.371138i
$667$	9.11066	+	2.71739i	0.352766	+	0.105218i
$668$	−2.83454	−	0.470015i	−0.109672	−	0.0181854i
$669$		−	7.71252i		−	0.298183i
$670$	29.0032	+	34.2085i	1.12049	+	1.32159i
$671$		−	0.0378887i		−	0.00146268i
$672$	−19.0579	+	7.49274i	−0.735173	+	0.289039i
$673$	−4.75005			−0.183101			−0.0915506	−	0.995800i	$-0.529182\pi$
$673$	−4.75005			−0.183101			−0.0915506	+	0.995800i	$0.529182\pi$
$674$	−12.6637	−	14.9365i	−0.487787	−	0.575331i
$675$	−6.06052			−0.233269
$676$	−2.36417	+	14.2577i	−0.0909295	+	0.548372i
$677$	18.9169			0.727037			0.363519	−	0.931587i	$-0.381575\pi$
$677$	18.9169			0.727037			0.363519	+	0.931587i	$0.381575\pi$
$678$	−9.75536	−	11.5062i	−0.374653	−	0.441892i
$679$			31.6923i			1.21624i
$680$	34.4709	−	20.6121i	1.32190	−	0.790436i
$681$		−	13.2160i		−	0.506438i
$682$	−3.35172	+	2.84171i	−0.128344	+	0.108815i
$683$	41.2202			1.57725			0.788623	−	0.614877i	$-0.210794\pi$
$683$	41.2202			1.57725			0.788623	+	0.614877i	$0.210794\pi$
$684$	−3.19471	−	0.529737i	−0.122153	−	0.0202550i
$685$			64.7155i			2.47265i
$686$	3.49687	−	2.96477i	0.133511	−	0.113196i
$687$	−17.5825			−0.670816
$688$	3.65549	−	10.7196i	0.139364	−	0.408681i
$689$		−	27.0980i		−	1.03235i
$690$	9.06086	+	20.6563i	0.344941	+	0.786374i
$691$	27.3937			1.04211			0.521053	−	0.853525i	$-0.325540\pi$
$691$	27.3937			1.04211			0.521053	+	0.853525i	$0.325540\pi$
$692$	35.6707	+	5.91481i	1.35600	+	0.224847i
$693$			4.16925i			0.158377i
$694$	−4.63384	+	3.92875i	−0.175898	+	0.149133i
$695$	−34.6175			−1.31312
$696$	−4.81237	+	2.87759i	−0.182412	+	0.109075i
$697$		−	37.8874i		−	1.43509i
$698$	6.41133	+	7.56198i	0.242672	+	0.286225i
$699$	−3.11752			−0.117916
$700$	7.17776	−	43.2872i	0.271294	−	1.63610i
$701$	13.1900			0.498179			0.249089	−	0.968481i	$-0.419869\pi$
$701$	13.1900			0.498179			0.249089	+	0.968481i	$0.419869\pi$
$702$	−4.11309	−	4.85127i	−0.155239	−	0.183099i
$703$			16.9571i			0.639549i
$704$	−8.11673	−	4.36034i	−0.305911	−	0.164336i
$705$		−	43.9409i		−	1.65491i
$706$	18.6900	−	15.8461i	0.703408	−	0.596376i
$707$		−	7.91642i		−	0.297728i
$708$	1.24749	−	7.52332i	0.0468837	−	0.282744i
$709$	21.6402			0.812714			0.406357	−	0.913714i	$-0.366799\pi$
$709$	21.6402			0.812714			0.406357	+	0.913714i	$0.366799\pi$
$710$	22.6858	+	26.7573i	0.851384	+	1.00418i
$711$	−4.25927			−0.159735
$712$	−27.4562	+	16.4176i	−1.02896	+	0.615276i
$713$	12.3988	+	3.69811i	0.464337	+	0.138495i
$714$	−14.1358	−	16.6727i	−0.529017	−	0.623961i
$715$	17.2263			0.644228
$716$	−3.64721	+	21.9954i	−0.136303	+	0.822006i
$717$		−	3.10960i		−	0.116130i
$718$	−23.1484	+	19.6261i	−0.863890	+	0.732438i
$719$		−	0.791248i		−	0.0295086i	−0.999891	−	0.0147543i	$-0.995303\pi$
$719$		−	0.791248i		−	0.0295086i	0.999891	−	0.0147543i	$-0.00469660\pi$
$720$	−12.5910	−	4.29365i	−0.469238	−	0.160015i
$721$	31.2001			1.16195
$722$	−17.6672	+	14.9789i	−0.657505	+	0.557458i
$723$			27.9280i			1.03865i
$724$	−0.109994	+	0.663348i	−0.00408791	+	0.0246531i
$725$		−	12.0144i		−	0.446203i
$726$	10.4348	−	8.84701i	0.387272	−	0.328343i
$727$	−0.559979			−0.0207685			−0.0103842	−	0.999946i	$-0.503305\pi$
$727$	−0.559979			−0.0207685			−0.0103842	+	0.999946i	$0.503305\pi$
$728$	39.5215	−	23.6321i	1.46477	−	0.875866i
$729$	1.00000			0.0370370
$730$	−34.3136	+	29.0923i	−1.27000	+	1.07676i
$731$	12.0894			0.447142
$732$	0.0107629	−	0.0649085i	0.000397809	−	0.00239909i
$733$	45.3655			1.67561			0.837807	−	0.545966i	$-0.183837\pi$
$733$	45.3655			1.67561			0.837807	+	0.545966i	$0.183837\pi$
$734$	32.1010	−	27.2164i	1.18487	−	1.00458i
$735$	−20.3019			−0.748848
$736$	2.29591	+	27.0320i	0.0846283	+	0.996413i
$737$	10.9824			0.404540
$738$	−9.57185	+	8.11537i	−0.352345	+	0.298731i
$739$	−21.3679			−0.786032			−0.393016	−	0.919532i	$-0.628568\pi$
$739$	−21.3679			−0.786032			−0.393016	+	0.919532i	$0.628568\pi$
$740$	−11.3951	+	68.7209i	−0.418892	+	2.52623i
$741$	7.28195			0.267509
$742$	−23.5282	+	19.9481i	−0.863747	+	0.732317i
$743$	10.3326			0.379065			0.189533	−	0.981874i	$-0.439303\pi$
$743$	10.3326			0.379065			0.189533	+	0.981874i	$0.439303\pi$
$744$	−6.54919	+	3.91613i	−0.240105	+	0.143572i
$745$	−76.8798			−2.81666
$746$	17.7058	−	15.0116i	0.648255	−	0.549615i
$747$			16.3410i			0.597887i
$748$	1.60885	−	9.70255i	0.0588253	−	0.354760i
$749$		−	48.2115i		−	1.76161i
$750$	3.80456	−	3.22565i	0.138923	−	0.117784i
$751$	−4.16879			−0.152121			−0.0760606	−	0.997103i	$-0.524234\pi$
$751$	−4.16879			−0.152121			−0.0760606	+	0.997103i	$0.524234\pi$
$752$	17.0577	−	50.0211i	0.622031	−	1.82408i
$753$			18.5875i			0.677367i
$754$	9.61718	−	8.15381i	0.350237	−	0.296944i
$755$		−	18.0453i		−	0.656735i
$756$	−1.18435	+	7.14250i	−0.0430743	+	0.259770i
$757$	−24.3555			−0.885215			−0.442607	−	0.896716i	$-0.645946\pi$
$757$	−24.3555			−0.885215			−0.442607	+	0.896716i	$0.645946\pi$
$758$	8.11679	+	9.57352i	0.294815	+	0.347726i
$759$	5.29305	+	1.57873i	0.192125	+	0.0573042i
$760$	13.0721	−	7.81654i	0.474175	−	0.283536i
$761$	31.3131			1.13510			0.567549	−	0.823340i	$-0.307892\pi$
$761$	31.3131			1.13510			0.567549	+	0.823340i	$0.307892\pi$
$762$	16.6916	+	19.6872i	0.604672	+	0.713194i
$763$	−27.9872			−1.01321
$764$	−6.43726	+	38.8214i	−0.232892	+	1.40451i
$765$		−	14.1999i		−	0.513398i
$766$	5.08925	−	4.31486i	0.183882	−	0.155902i
$767$			17.1485i			0.619197i
$768$	−12.6664	−	9.77555i	−0.457061	−	0.352745i
$769$			9.27949i			0.334627i	0.985904	+	0.167314i	$0.0535092\pi$
$769$			9.27949i			0.334627i	−0.985904	+	0.167314i	$0.946491\pi$
$770$	−12.6811	−	14.9570i	−0.456995	−	0.539013i
$771$	25.6119			0.922391
$772$	−0.527725	+	3.18257i	−0.0189932	+	0.114543i
$773$	−36.9155			−1.32776			−0.663879	−	0.747840i	$-0.731091\pi$
$773$	−36.9155			−1.32776			−0.663879	+	0.747840i	$0.731091\pi$
$774$	−2.58951	−	3.05426i	−0.0930781	−	0.109783i
$775$		−	16.3505i		−	0.587327i
$776$	−21.2525	+	12.7081i	−0.762921	+	0.456193i
$777$	37.9115			1.36007
$778$	27.2839	−	23.1323i	0.978177	−	0.829335i
$779$		−	14.3677i		−	0.514777i
$780$	29.5111	+	4.89344i	1.05667	+	0.175213i
$781$	8.59021			0.307382
$782$	−26.5194	+	11.6327i	−0.948331	+	0.415983i
$783$			1.98240i			0.0708453i
$784$	−23.1111	−	7.88113i	−0.825398	−	0.281469i
$785$	−9.95677			−0.355373
$786$	−8.87354	+	7.52332i	−0.316509	+	0.268348i
$787$			17.0360i			0.607266i	0.952789	+	0.303633i	$0.0981997\pi$
$787$			17.0360i			0.607266i	−0.952789	+	0.303633i	$0.901800\pi$
$788$	12.1376	+	2.01262i	0.432383	+	0.0716965i
$789$	9.98153			0.355352
$790$	15.2799	−	12.9549i	0.543636	−	0.460915i
$791$		−	38.6138i		−	1.37295i
$792$	−2.79586	+	1.67180i	−0.0993464	+	0.0594048i
$793$			0.147951i			0.00525390i
$794$	−2.94685	−	3.47572i	−0.104580	−	0.123349i
$795$	−20.0386			−0.710696
$796$	−6.58351	+	39.7034i	−0.233346	+	1.40725i
$797$	−24.8025			−0.878549			−0.439275	−	0.898353i	$-0.644764\pi$
$797$	−24.8025			−0.878549			−0.439275	+	0.898353i	$0.644764\pi$
$798$	−5.36059	−	6.32266i	−0.189763	−	0.223820i
$799$	56.4130			1.99575
$800$	31.9061	−	12.5441i	1.12805	−	0.443502i
$801$			11.3103i			0.399629i
$802$	0.529195	+	0.624171i	0.0186865	+	0.0220402i
$803$			11.0161i			0.388749i
$804$	18.8143	+	3.11973i	0.663528	+	0.110024i
$805$	−16.5028	+	55.3293i	−0.581646	+	1.95010i
$806$	13.0881	−	11.0966i	0.461008	−	0.390860i
$807$		−	15.1464i		−	0.533177i
$808$	5.30867	−	3.17435i	0.186758	−	0.111673i
$809$	6.25681			0.219978			0.109989	−	0.993933i	$-0.464918\pi$
$809$	6.25681			0.219978			0.109989	+	0.993933i	$0.464918\pi$
$810$	−3.58746	+	3.04158i	−0.126050	+	0.106870i
$811$	−10.7589			−0.377797			−0.188899	−	0.981997i	$-0.560492\pi$
$811$	−10.7589			−0.377797			−0.188899	+	0.981997i	$0.560492\pi$
$812$	−14.1593	−	2.34786i	−0.496895	−	0.0823936i
$813$		−	6.52820i		−	0.228954i
$814$	11.0311	+	13.0109i	0.386641	+	0.456032i
$815$	30.0192			1.05153
$816$	5.51235	−	16.1648i	0.192971	−	0.565880i
$817$	4.58456			0.160393
$818$	39.1571	−	33.1988i	1.36910	−	1.16077i
$819$		−	16.2805i		−	0.568886i
$820$	9.65504	−	58.2271i	0.337169	−	2.03338i
$821$			0.326099i			0.0113809i	0.999984	+	0.00569046i	$0.00181134\pi$
$821$			0.326099i			0.0113809i	−0.999984	+	0.00569046i	$0.998189\pi$
$822$	17.7964	+	20.9903i	0.620720	+	0.732122i
$823$		−	15.8846i		−	0.553703i	−0.960913	−	0.276852i	$-0.910709\pi$
$823$		−	15.8846i		−	0.553703i	0.960913	−	0.276852i	$-0.0892910\pi$
$824$	12.5107	+	20.9225i	0.435831	+	0.728868i
$825$		−	6.98004i		−	0.243014i
$826$	14.8894	−	12.6238i	0.518070	−	0.439239i
$827$			15.7947i			0.549236i	0.961553	+	0.274618i	$0.0885515\pi$
$827$			15.7947i			0.549236i	−0.961553	+	0.274618i	$0.911449\pi$
$828$	8.61925	+	4.20816i	0.299540	+	0.146244i
$829$		−	47.1638i		−	1.63807i	−0.573746	−	0.819033i	$-0.694510\pi$
$829$		−	47.1638i		−	1.63807i	0.573746	−	0.819033i	$-0.305490\pi$
$830$	−49.7025	−	58.6227i	−1.72520	−	2.03482i
$831$		−	16.8218i		−	0.583540i
$832$	31.6949	+	17.0266i	1.09882	+	0.590292i
$833$		−	26.0644i		−	0.903076i
$834$	−11.2281	+	9.51963i	−0.388798	+	0.329638i
$835$		−	4.77783i		−	0.165344i
$836$	0.610110	−	3.67942i	0.0211011	−	0.127255i
$837$			2.69787i			0.0932520i
$838$	21.4791	+	25.3340i	0.741983	+	0.875148i
$839$	26.8159			0.925789			0.462894	−	0.886413i	$-0.346811\pi$
$839$	26.8159			0.925789			0.462894	+	0.886413i	$0.346811\pi$
$840$	−17.4757	−	29.2257i	−0.602968	−	1.00838i
$841$	25.0701			0.864485
$842$	17.8557	−	15.1388i	0.615350	−	0.521716i
$843$			13.1210i			0.451911i
$844$	7.02135	−	42.3440i	0.241685	−	1.45754i
$845$	−24.0324			−0.826739
$846$	−12.0835	−	14.2521i	−0.415439	−	0.489999i
$847$	35.0183			1.20324
$848$	−22.8114	−	7.77891i	−0.783346	−	0.267129i
$849$			1.59861i			0.0548641i
$850$	23.6657	+	27.9130i	0.811725	+	0.957407i
$851$	14.3556	−	48.1303i	0.492102	−	1.64989i
$852$	14.7162	+	2.44020i	0.504169	+	0.0835997i
$853$			24.9639i			0.854747i	0.904075	+	0.427373i	$0.140561\pi$
$853$			24.9639i			0.854747i	−0.904075	+	0.427373i	$0.859439\pi$
$854$	0.128461	−	0.108914i	0.00439584	−	0.00372695i
$855$		−	5.38491i		−	0.184160i
$856$	32.3301	−	19.3320i	1.10502	−	0.660754i
$857$	51.2287			1.74994			0.874970	−	0.484177i	$-0.160881\pi$
$857$	51.2287			1.74994			0.874970	+	0.484177i	$0.160881\pi$
$858$	5.58732	−	4.73714i	0.190748	−	0.161723i
$859$	−15.0418			−0.513220			−0.256610	−	0.966515i	$-0.582606\pi$
$859$	−15.0418			−0.513220			−0.256610	+	0.966515i	$0.582606\pi$
$860$	18.5795	+	3.08080i	0.633556	+	0.105054i
$861$	−32.1223			−1.09473
$862$	−4.11062	+	3.48514i	−0.140008	+	0.118704i
$863$			8.58185i			0.292130i	0.989275	+	0.146065i	$0.0466608\pi$
$863$			8.58185i			0.292130i	−0.989275	+	0.146065i	$0.953339\pi$
$864$	−5.26459	+	2.06981i	−0.179105	+	0.0704164i
$865$			60.1256i			2.04433i
$866$	−14.4800	−	17.0788i	−0.492052	−	0.580361i
$867$	1.23035			0.0417848
$868$	−19.2695	−	3.19521i	−0.654050	−	0.108453i
$869$		−	4.90550i		−	0.166408i
$870$	−6.02964	−	7.11179i	−0.204424	−	0.241112i
$871$	−42.8849			−1.45310
$872$	−11.2224	−	18.7679i	−0.380038	−	0.635562i
$873$			8.75475i			0.296303i
$874$	−10.0567	+	4.41136i	−0.340174	+	0.149216i
$875$	12.7678			0.431630
$876$	−3.12931	+	18.8721i	−0.105730	+	0.637628i
$877$			34.5347i			1.16615i	0.812417	+	0.583077i	$0.198152\pi$
$877$			34.5347i			1.16615i	−0.812417	+	0.583077i	$0.801848\pi$
$878$	30.1080	+	35.5115i	1.01610	+	1.19846i
$879$	−20.5003			−0.691457
$880$	4.94510	−	14.5013i	0.166699	−	0.488840i
$881$			20.7769i			0.699992i	0.936751	+	0.349996i	$0.113817\pi$
$881$			20.7769i			0.699992i	−0.936751	+	0.349996i	$0.886183\pi$
$882$	−6.58488	+	5.58291i	−0.221725	+	0.187986i
$883$	−20.2020			−0.679850			−0.339925	−	0.940453i	$-0.610402\pi$
$883$	−20.2020			−0.679850			−0.339925	+	0.940453i	$0.610402\pi$
$884$	−6.28237	+	37.8874i	−0.211299	+	1.27429i
$885$	12.6811			0.426271
$886$	−11.5533	+	9.79535i	−0.388142	+	0.329081i
$887$			20.1526i			0.676658i	0.941028	+	0.338329i	$0.109862\pi$
$887$			20.1526i			0.676658i	−0.941028	+	0.338329i	$0.890138\pi$
$888$	15.2019	+	25.4231i	0.510141	+	0.853142i
$889$			66.0688i			2.21588i
$890$	−34.4011	−	40.5752i	−1.15313	−	1.36008i
$891$			1.15172i			0.0385842i
$892$	15.2173	+	2.52328i	0.509511	+	0.0844856i
$893$	21.3930			0.715891
$894$	−24.9358	+	21.1415i	−0.833978	+	0.707078i
$895$	−37.0748			−1.23928
$896$	−8.54851	−	40.0537i	−0.285586	−	1.33810i
$897$	−20.6688	−	6.16476i	−0.690110	−	0.205835i
$898$	−17.4839	+	14.8235i	−0.583445	+	0.494667i
$899$	−5.34826			−0.178375
$900$	1.98280	−	11.9578i	0.0660933	−	0.398592i
$901$		−	25.7263i		−	0.857067i
$902$	−9.34666	−	11.0241i	−0.311210	−	0.367063i
$903$		−	10.2498i		−	0.341093i
$904$	25.8940	−	15.4835i	0.861221	−	0.514973i
$905$	−1.11812			−0.0371676
$906$	−4.96235	−	5.85295i	−0.164863	−	0.194451i
$907$		−	11.1639i		−	0.370691i	−0.982673	−	0.185346i	$-0.940660\pi$
$907$		−	11.1639i		−	0.370691i	0.982673	−	0.185346i	$-0.0593405\pi$
$908$	26.0759	+	4.32383i	0.865360	+	0.143491i
$909$		−	2.18685i		−	0.0725332i
$910$	49.5183	+	58.4055i	1.64152	+	1.93612i
$911$	32.6008			1.08011			0.540057	−	0.841629i	$-0.318403\pi$
$911$	32.6008			1.08011			0.540057	+	0.841629i	$0.318403\pi$
$912$	2.09040	−	6.13003i	0.0692202	−	0.202986i
$913$	−18.8203			−0.622862
$914$	−17.1853	−	20.2696i	−0.568440	−	0.670459i
$915$	0.109408			0.00361692
$916$	5.75243	−	34.6914i	0.190065	−	1.14624i
$917$	−29.7789			−0.983385
$918$	−3.90489	−	4.60571i	−0.128881	−	0.152011i
$919$	6.27025			0.206836			0.103418	−	0.994638i	$-0.467022\pi$
$919$	6.27025			0.206836			0.103418	+	0.994638i	$0.467022\pi$
$920$	−43.7206	+	11.1195i	−1.44143	+	0.366600i
$921$	−15.1609			−0.499569
$922$	−32.6028	−	38.4541i	−1.07372	−	1.26642i
$923$	−33.5438			−1.10411
$924$	−8.22618	−	1.36404i	−0.270621	−	0.0448736i
$925$	−63.4703			−2.08689
$926$	26.1374	+	30.8283i	0.858929	+	1.01308i
$927$	8.61878			0.283078
$928$	−4.10320	−	10.4365i	−0.134694	−	0.342596i
$929$	4.58873			0.150551			0.0752757	−	0.997163i	$-0.476016\pi$
$929$	4.58873			0.150551			0.0752757	+	0.997163i	$0.476016\pi$
$930$	−8.20578	−	9.67848i	−0.269078	−	0.317370i
$931$		−	9.88417i		−	0.323941i
$932$	1.01995	−	6.15106i	0.0334096	−	0.201485i
$933$			19.4369i			0.636334i
$934$	8.05578	+	9.50157i	0.263593	+	0.310901i
$935$	16.3544			0.534845
$936$	10.9175	−	6.52820i	0.356850	−	0.213381i
$937$		−	51.8489i		−	1.69383i	−0.531727	−	0.846916i	$-0.678457\pi$
$937$		−	51.8489i		−	1.69383i	0.531727	−	0.846916i	$-0.321543\pi$
$938$	31.5696	+	37.2354i	1.03078	+	1.21578i
$939$			31.6451i			1.03270i
$940$	86.6981	+	14.3760i	2.82778	+	0.468894i
$941$	8.04712			0.262329			0.131164	−	0.991361i	$-0.458128\pi$
$941$	8.04712			0.262329			0.131164	+	0.991361i	$0.458128\pi$
$942$	−3.22946	+	2.73806i	−0.105221	+	0.0892107i
$943$	−12.1634	+	40.7807i	−0.396096	+	1.32800i
$944$	14.4358	+	4.92276i	0.469846	+	0.160222i
$945$	−12.0392			−0.391635
$946$	3.51766	−	2.98240i	0.114369	−	0.0969662i
$947$	5.62850			0.182902			0.0914508	−	0.995810i	$-0.470850\pi$
$947$	5.62850			0.182902			0.0914508	+	0.995810i	$0.470850\pi$
$948$	1.39349	−	8.40380i	0.0452585	−	0.272943i
$949$		−	43.0166i		−	1.39638i
$950$	8.97453	+	10.5852i	0.291172	+	0.343429i
$951$			7.16345i			0.232291i
$952$	37.5210	−	22.4359i	1.21606	−	0.727152i
$953$			15.9663i			0.517200i	0.965984	+	0.258600i	$0.0832612\pi$
$953$			15.9663i			0.517200i	−0.965984	+	0.258600i	$0.916739\pi$
$954$	−6.49948	+	5.51050i	−0.210428	+	0.178409i
$955$	−65.4364			−2.11747
$956$	6.13542	+	1.01736i	0.198434	+	0.0329037i
$957$	−2.28318			−0.0738048
$958$	27.4370	−	23.2621i	0.886450	−	0.751565i
$959$			70.4418i			2.27469i
$960$	12.5910	−	23.4380i	0.406372	−	0.756459i
$961$	23.7215			0.765210
$962$	−43.0754	−	50.8062i	−1.38881	−	1.63806i
$963$		−	13.3180i		−	0.429168i
$964$	−55.1035	−	9.13710i	−1.77476	−	0.294286i
$965$	−5.36446			−0.172688
$966$	9.86261	+	22.4841i	0.317324	+	0.723415i
$967$			43.2929i			1.39221i	0.717942	+	0.696103i	$0.245084\pi$
$967$			43.2929i			1.39221i	−0.717942	+	0.696103i	$0.754916\pi$
$968$	14.0418	+	23.4829i	0.451319	+	0.754769i
$969$	6.91335			0.222089
$970$	−26.6283	−	31.4073i	−0.854982	−	1.00843i
$971$		−	48.8957i		−	1.56914i	−0.620042	−	0.784568i	$-0.712885\pi$
$971$		−	48.8957i		−	1.56914i	0.620042	−	0.784568i	$-0.287115\pi$
$972$	−0.327167	+	1.97306i	−0.0104939	+	0.0632859i
$973$	−37.6807			−1.20799
$974$	19.8061	+	23.3607i	0.634628	+	0.748526i
$975$			27.2563i			0.872900i
$976$	0.124547	+	0.0424718i	0.00398665	+	0.00135949i
$977$			38.7998i			1.24131i	0.784082	+	0.620657i	$0.213134\pi$
$977$			38.7998i			1.24131i	−0.784082	+	0.620657i	$0.786866\pi$
$978$	9.73665	−	8.25510i	0.311344	−	0.263969i
$979$	−13.0263			−0.416323
$980$	6.64211	−	40.0569i	0.212175	−	1.27957i
$981$	−7.73125			−0.246840
$982$	24.2430	−	20.5541i	0.773625	−	0.655908i
$983$	−36.7909			−1.17345			−0.586723	−	0.809788i	$-0.699582\pi$
$983$	−36.7909			−1.17345			−0.586723	+	0.809788i	$0.699582\pi$
$984$	−12.8805	−	21.5409i	−0.410616	−	0.686699i
$985$			20.4588i			0.651871i
$986$	9.13037	−	7.74107i	0.290770	−	0.246526i
$987$		−	47.8290i		−	1.52242i
$988$	−2.38241	+	14.3677i	−0.0757946	+	0.457098i
$989$	−13.0126	−	3.88120i	−0.413777	−	0.123415i
$990$	−3.50306	−	4.13176i	−0.111334	−	0.131316i
$991$			11.5379i			0.366512i	0.983065	+	0.183256i	$0.0586638\pi$
$991$			11.5379i			0.366512i	−0.983065	+	0.183256i	$0.941336\pi$
$992$	−5.58408	−	14.2032i	−0.177295	−	0.450951i
$993$	−22.7506			−0.721968
$994$	24.6932	+	29.1249i	0.783220	+	0.923786i
$995$	−66.9231			−2.12160
$996$	−32.2418	−	5.34624i	−1.02162	−	0.169402i
$997$		−	36.8768i		−	1.16790i	−0.811790	−	0.583949i	$-0.801507\pi$
$997$		−	36.8768i		−	1.16790i	0.811790	−	0.583949i	$-0.198493\pi$
$998$	−3.98957	+	3.38250i	−0.126288	+	0.107071i
$999$	10.4728			0.331343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.b.91.8	yes	24
4.3	odd	2		2208.2.n.b.367.21		24
8.3	odd	2	inner	552.2.n.b.91.5	✓	24
8.5	even	2		2208.2.n.b.367.3		24
23.22	odd	2	inner	552.2.n.b.91.7	yes	24
92.91	even	2		2208.2.n.b.367.4		24
184.45	odd	2		2208.2.n.b.367.22		24
184.91	even	2	inner	552.2.n.b.91.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.5	✓	24	8.3	odd	2	inner
552.2.n.b.91.6	yes	24	184.91	even	2	inner
552.2.n.b.91.7	yes	24	23.22	odd	2	inner
552.2.n.b.91.8	yes	24	1.1	even	1	trivial
2208.2.n.b.367.3		24	8.5	even	2
2208.2.n.b.367.4		24	92.91	even	2
2208.2.n.b.367.21		24	4.3	odd	2
2208.2.n.b.367.22		24	184.45	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07870 + 0.914558i) q^{2} -1.00000 q^{3} +(0.327167 - 1.97306i) q^{4} +3.32574 q^{5} +(1.07870 - 0.914558i) q^{6} +3.62001 q^{7} +(1.45156 + 2.42754i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.07870 + 0.914558i) q^{2} -1.00000 q^{3} +(0.327167 - 1.97306i) q^{4} +3.32574 q^{5} +(1.07870 - 0.914558i) q^{6} +3.62001 q^{7} +(1.45156 + 2.42754i) q^{8} +1.00000 q^{9} +(-3.58746 + 3.04158i) q^{10} +1.15172i q^{11} +(-0.327167 + 1.97306i) q^{12} -4.49735i q^{13} +(-3.90489 + 3.31071i) q^{14} -3.32574 q^{15} +(-3.78592 - 1.29104i) q^{16} -4.26970i q^{17} +(-1.07870 + 0.914558i) q^{18} -1.61916i q^{19} +(1.08807 - 6.56187i) q^{20} -3.62001 q^{21} +(-1.05332 - 1.24236i) q^{22} +(-1.37075 + 4.59576i) q^{23} +(-1.45156 - 2.42754i) q^{24} +6.06052 q^{25} +(4.11309 + 4.85127i) q^{26} -1.00000 q^{27} +(1.18435 - 7.14250i) q^{28} -1.98240i q^{29} +(3.58746 - 3.04158i) q^{30} -2.69787i q^{31} +(5.26459 - 2.06981i) q^{32} -1.15172i q^{33} +(3.90489 + 4.60571i) q^{34} +12.0392 q^{35} +(0.327167 - 1.97306i) q^{36} -10.4728 q^{37} +(1.48082 + 1.74658i) q^{38} +4.49735i q^{39} +(4.82752 + 8.07336i) q^{40} +8.87354 q^{41} +(3.90489 - 3.31071i) q^{42} +2.83144i q^{43} +(2.27242 + 0.376806i) q^{44} +3.32574 q^{45} +(-2.72447 - 6.21106i) q^{46} +13.2124i q^{47} +(3.78592 + 1.29104i) q^{48} +6.10449 q^{49} +(-6.53745 + 5.54270i) q^{50} +4.26970i q^{51} +(-8.87354 - 1.47138i) q^{52} +6.02532 q^{53} +(1.07870 - 0.914558i) q^{54} +3.83033i q^{55} +(5.25468 + 8.78773i) q^{56} +1.61916i q^{57} +(1.81302 + 2.13841i) q^{58} -3.81302 q^{59} +(-1.08807 + 6.56187i) q^{60} -0.0328974 q^{61} +(2.46736 + 2.91018i) q^{62} +3.62001 q^{63} +(-3.78592 + 7.04747i) q^{64} -14.9570i q^{65} +(1.05332 + 1.24236i) q^{66} -9.53558i q^{67} +(-8.42437 - 1.39690i) q^{68} +(1.37075 - 4.59576i) q^{69} +(-12.9866 + 11.0106i) q^{70} -7.45857i q^{71} +(1.45156 + 2.42754i) q^{72} +9.56488 q^{73} +(11.2969 - 9.57794i) q^{74} -6.06052 q^{75} +(-3.19471 - 0.529737i) q^{76} +4.16925i q^{77} +(-4.11309 - 4.85127i) q^{78} -4.25927 q^{79} +(-12.5910 - 4.29365i) q^{80} +1.00000 q^{81} +(-9.57185 + 8.11537i) q^{82} +16.3410i q^{83} +(-1.18435 + 7.14250i) q^{84} -14.1999i q^{85} +(-2.58951 - 3.05426i) q^{86} +1.98240i q^{87} +(-2.79586 + 1.67180i) q^{88} +11.3103i q^{89} +(-3.58746 + 3.04158i) q^{90} -16.2805i q^{91} +(8.61925 + 4.20816i) q^{92} +2.69787i q^{93} +(-12.0835 - 14.2521i) q^{94} -5.38491i q^{95} +(-5.26459 + 2.06981i) q^{96} +8.75475i q^{97} +(-6.58488 + 5.58291i) q^{98} +1.15172i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

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