LMFDB - Embedded newform 552.2.n.b.91.5

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			91.5
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.7

$q$-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} +(-5.68172 + 3.70379i) 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} +(9.51618 + 1.20100i) 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	$-0.766910\pi$
$5$	−3.32574			−1.48731			−0.743657	+	0.668561i	$0.766910\pi$
$6$	1.07870	+	0.914558i	0.440375	+	0.373367i
$7$	−3.62001			−1.36824			−0.684118	−	0.729371i	$-0.739813\pi$
$7$	−3.62001			−1.36824			−0.684118	+	0.729371i	$0.739813\pi$
$8$	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	$0.214359\pi$
$13$			4.49735i			1.24734i	−0.781687	+	0.623671i	$0.785641\pi$
$14$	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	$0.0589246\pi$
$29$			1.98240i			0.368123i	−0.982915	+	0.184062i	$0.941075\pi$
$30$	−3.58746	−	3.04158i	−0.654977	−	0.555314i
$31$			2.69787i			0.484551i	0.970207	+	0.242276i	$0.0778939\pi$
$31$			2.69787i			0.484551i	−0.970207	+	0.242276i	$0.922106\pi$
$32$	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	$-0.169929\pi$
$37$	10.4728			1.72171			0.860855	+	0.508850i	$0.169929\pi$
$38$	−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
$46$	−5.68172	+	3.70379i	−0.837723	+	0.546095i
$47$		−	13.2124i		−	1.92723i	−0.267301	−	0.963613i	$-0.586132\pi$
$47$		−	13.2124i		−	1.92723i	0.267301	−	0.963613i	$-0.413868\pi$
$48$	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	$-0.635806\pi$
$53$	−6.02532			−0.827641			−0.413820	+	0.910359i	$0.635806\pi$
$54$	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	$-0.499330\pi$
$61$	0.0328974			0.00421208			0.00210604	+	0.999998i	$0.499330\pi$
$62$	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	$0.145938\pi$
$71$			7.45857i			0.885169i	−0.896727	+	0.442585i	$0.854062\pi$
$72$	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	$-0.422983\pi$
$79$	4.25927			0.479206			0.239603	+	0.970871i	$0.422983\pi$
$80$	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
$92$	9.51618	+	1.20100i	0.992130	+	0.125212i
$93$		−	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	$0.0347007\pi$
$101$			2.18685i			0.217600i	−0.994064	+	0.108800i	$0.965299\pi$
$102$	3.90489	−	4.60571i	0.386642	−	0.456033i
$103$	−8.61878			−0.849234			−0.424617	−	0.905373i	$-0.639591\pi$
$103$	−8.61878			−0.849234			−0.424617	+	0.905373i	$0.639591\pi$
$104$	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	$-0.379269\pi$
$109$	7.73125			0.740519			0.370260	+	0.928928i	$0.379269\pi$
$110$	−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	$-0.699599\pi$
$127$		−	18.2510i		−	1.61951i	0.586766	−	0.809756i	$-0.300401\pi$
$128$	−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	$0.687627\pi$
$138$	5.68172	−	3.70379i	0.483660	−	0.315288i
$139$	−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	$-0.104202\pi$
$149$	23.1166			1.89379			0.946895	+	0.321544i	$0.104202\pi$
$150$	6.53745	+	5.54270i	0.533781	+	0.452559i
$151$			5.42595i			0.441558i	0.975324	+	0.220779i	$0.0708599\pi$
$151$			5.42595i			0.441558i	−0.975324	+	0.220779i	$0.929140\pi$
$152$	−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	$-0.461881\pi$
$157$	2.99386			0.238936			0.119468	+	0.992838i	$0.461881\pi$
$158$	−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	$0.0177023\pi$
$167$			1.43662i			0.111169i	−0.998454	+	0.0555846i	$0.982298\pi$
$168$	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	$-0.758815\pi$
$173$		−	18.0789i		−	1.37451i	0.726415	−	0.687256i	$-0.241185\pi$
$174$	−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	$-0.496023\pi$
$181$	0.336203			0.0249898			0.0124949	+	0.999922i	$0.496023\pi$
$182$	−14.8894	+	17.5617i	−1.10368	+	1.30176i
$183$	−0.0328974			−0.00243185
$184$	−9.16667	−	9.99860i	−0.675776	−	0.737107i
$185$	−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	$-0.247860\pi$
$191$	19.6758			1.42369			0.711844	+	0.702337i	$0.247860\pi$
$192$	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	$-0.929674\pi$
$197$		−	6.15166i		−	0.438287i	0.975693	−	0.219144i	$-0.0703263\pi$
$198$	1.05332	−	1.24236i	0.0748560	−	0.0882906i
$199$	20.1228			1.42647			0.713233	−	0.700927i	$-0.247230\pi$
$199$	20.1228			1.42647			0.713233	+	0.700927i	$0.247230\pi$
$200$	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	$-0.916859\pi$
$223$		−	7.71252i		−	0.516468i	0.966082	−	0.258234i	$-0.0831406\pi$
$224$	−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	$-0.697316\pi$
$229$	−17.5825			−1.16189			−0.580944	+	0.813944i	$0.697316\pi$
$230$	18.8959	−	12.3178i	1.24596	−	0.812214i
$231$			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	$-0.967933\pi$
$239$		−	3.10960i		−	0.201143i	0.994930	−	0.100572i	$-0.0320672\pi$
$240$	−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	$-0.400426\pi$
$263$	9.98153			0.615488			0.307744	+	0.951469i	$0.400426\pi$
$264$	−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	$-0.847224\pi$
$269$		−	15.1464i		−	0.923490i	0.887013	−	0.461745i	$-0.152776\pi$
$270$	−3.58746	−	3.04158i	−0.218326	−	0.185105i
$271$		−	6.52820i		−	0.396560i	−0.980145	−	0.198280i	$-0.936465\pi$
$271$		−	6.52820i		−	0.396560i	0.980145	−	0.198280i	$-0.0635355\pi$
$272$	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
$276$	−9.51618	−	1.20100i	−0.572806	−	0.0722914i
$277$		−	16.8218i		−	1.01072i	−0.862908	−	0.505361i	$-0.831359\pi$
$277$		−	16.8218i		−	1.01072i	0.862908	−	0.505361i	$-0.168641\pi$
$278$	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	$-0.704363\pi$
$293$	−20.5003			−1.19764			−0.598820	+	0.800884i	$0.704363\pi$
$294$	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	$0.185785\pi$
$311$			19.4369i			1.10216i	−0.834451	+	0.551082i	$0.814215\pi$
$312$	−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	$0.0644743\pi$
$317$			7.16345i			0.402340i	−0.979556	+	0.201170i	$0.935526\pi$
$318$	−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
$322$	20.5679	−	13.4078i	1.14620	−	0.747186i
$323$	−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	$0.0600794\pi$
$349$			7.01030i			0.375253i	−0.982240	+	0.187626i	$0.939921\pi$
$350$	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	$-0.691625\pi$
$359$	−21.4596			−1.13260			−0.566298	+	0.824201i	$0.691625\pi$
$360$	−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	$-0.216889\pi$
$367$	29.7591			1.55341			0.776706	+	0.629864i	$0.216889\pi$
$368$	0.743742	+	19.1689i	0.0387702	+	0.999248i
$369$	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	$-0.360294\pi$
$373$	16.4141			0.849889			0.424945	+	0.905219i	$0.360294\pi$
$374$	−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	$-0.461538\pi$
$383$	4.71797			0.241077			0.120539	+	0.992709i	$0.461538\pi$
$384$	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	$-0.278431\pi$
$389$	25.2935			1.28243			0.641215	+	0.767361i	$0.278431\pi$
$390$	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	$-0.974234\pi$
$397$		−	3.22216i		−	0.161715i	0.996726	−	0.0808577i	$-0.0257659\pi$
$398$	−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
$414$	−5.68172	+	3.70379i	−0.279241	+	0.182032i
$415$		−	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	$-0.367837\pi$
$421$	16.5531			0.806749			0.403374	+	0.915035i	$0.367837\pi$
$422$	−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	$-0.529255\pi$
$431$	−3.81073			−0.183557			−0.0917783	+	0.995779i	$0.529255\pi$
$432$	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	$0.287652\pi$
$439$			32.9208i			1.57122i	−0.618719	+	0.785612i	$0.712348\pi$
$440$	−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
$460$	−31.6483	−	3.99419i	−1.47561	−	0.186230i
$461$		−	35.6487i		−	1.66033i	−0.557520	−	0.830163i	$-0.688247\pi$
$461$		−	35.6487i		−	1.66033i	0.557520	−	0.830163i	$-0.311753\pi$
$462$	3.81302	−	4.49735i	0.177398	−	0.209236i
$463$			28.5793i			1.32819i	0.747647	+	0.664096i	$0.231183\pi$
$463$			28.5793i			1.32819i	−0.747647	+	0.664096i	$0.768817\pi$
$464$	−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	$-0.302628\pi$
$479$	25.4354			1.16217			0.581086	+	0.813842i	$0.302628\pi$
$480$	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	$0.163249\pi$
$487$			21.6565i			0.981348i	−0.871343	+	0.490674i	$0.836751\pi$
$488$	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	$-0.176949\pi$
$503$	38.1013			1.69885			0.849426	+	0.527708i	$0.176949\pi$
$504$	−5.25468	+	8.78773i	−0.234062	+	0.391437i
$505$		−	7.27288i		−	0.323639i
$506$	−4.26575	−	6.54377i	−0.189636	−	0.290906i
$507$	7.22618			0.320926
$508$	36.0103	−	5.97111i	1.59770	−	0.264925i
$509$			27.4825i			1.21814i	0.793117	+	0.609070i	$0.208457\pi$
$509$			27.4825i			1.21814i	−0.793117	+	0.609070i	$0.791543\pi$
$510$	−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	$-0.590225\pi$
$541$		−	44.6625i		−	1.92019i	0.279670	−	0.960096i	$-0.409775\pi$
$542$	−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
$552$	9.16667	+	9.99860i	0.390160	+	0.425569i
$553$	−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	$-0.465029\pi$
$557$	5.17538			0.219288			0.109644	+	0.993971i	$0.465029\pi$
$558$	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
$598$	−16.6573	−	25.5527i	−0.681166	−	1.04493i
$599$		−	4.20687i		−	0.171888i	−0.996300	−	0.0859439i	$-0.972609\pi$
$599$		−	4.20687i		−	0.171888i	0.996300	−	0.0859439i	$-0.0273906\pi$
$600$	−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	$0.0108589\pi$
$607$			1.68065i			0.0682155i	−0.999418	+	0.0341078i	$0.989141\pi$
$608$	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	$-0.810583\pi$
$613$	−41.0060			−1.65622			−0.828109	+	0.560567i	$0.810583\pi$
$614$	−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	$-0.542696\pi$
$631$	−6.71856			−0.267462			−0.133731	+	0.991018i	$0.542696\pi$
$632$	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	$-0.169995\pi$
$644$	−34.4487	−	4.34762i	−1.35747	−	0.171320i
$645$			9.41661i			0.370779i
$646$	7.45739	+	6.32266i	0.293407	+	0.248762i
$647$			28.0022i			1.10088i	0.834875	+	0.550440i	$0.185540\pi$
$647$			28.0022i			1.10088i	−0.834875	+	0.550440i	$0.814460\pi$
$648$	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	$0.179097\pi$
$653$			27.2623i			1.06686i	−0.845845	+	0.533429i	$0.820903\pi$
$654$	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	$-0.423491\pi$
$661$	12.2406			0.476104			0.238052	+	0.971252i	$0.423491\pi$
$662$	−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	$-0.618425\pi$
$677$	−18.9169			−0.727037			−0.363519	+	0.931587i	$0.618425\pi$
$678$	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
$690$	−18.8959	+	12.3178i	−0.719354	+	0.468932i
$691$	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	$-0.580131\pi$
$701$	−13.1900			−0.498179			−0.249089	+	0.968481i	$0.580131\pi$
$702$	−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	$-0.633201\pi$
$709$	−21.6402			−0.812714			−0.406357	+	0.913714i	$0.633201\pi$
$710$	−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	$0.00469660\pi$
$719$			0.791248i			0.0295086i	−0.999891	+	0.0147543i	$0.995303\pi$
$720$	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	$-0.496695\pi$
$727$	0.559979			0.0207685			0.0103842	+	0.999946i	$0.496695\pi$
$728$	−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	$-0.816163\pi$
$733$	−45.3655			−1.67561			−0.837807	+	0.545966i	$0.816163\pi$
$734$	−32.1010	−	27.2164i	−1.18487	−	1.00458i
$735$	20.3019			0.748848
$736$	16.7288	−	21.3576i	0.616632	−	0.787252i
$737$	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	$-0.560697\pi$
$743$	−10.3326			−0.379065			−0.189533	+	0.981874i	$0.560697\pi$
$744$	−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	$-0.475766\pi$
$751$	4.16879			0.152121			0.0760606	+	0.997103i	$0.475766\pi$
$752$	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	$-0.354054\pi$
$757$	24.3555			0.885215			0.442607	+	0.896716i	$0.354054\pi$
$758$	−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	$-0.268909\pi$
$773$	36.9155			1.32776			0.663879	+	0.747840i	$0.268909\pi$
$774$	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
$782$	15.8141	+	24.2592i	0.565511	+	0.867508i
$783$		−	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	$-0.355236\pi$
$797$	24.8025			0.878549			0.439275	+	0.898353i	$0.355236\pi$
$798$	−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	$-0.998189\pi$
$821$		−	0.326099i		−	0.0113809i	0.999984	−	0.00569046i	$-0.00181134\pi$
$822$	−17.7964	+	20.9903i	−0.620720	+	0.732122i
$823$			15.8846i			0.553703i	0.960913	+	0.276852i	$0.0892910\pi$
$823$			15.8846i			0.553703i	−0.960913	+	0.276852i	$0.910709\pi$
$824$	−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	$0.911449\pi$
$828$	9.51618	+	1.20100i	0.330710	+	0.0417375i
$829$			47.1638i			1.63807i	0.573746	+	0.819033i	$0.305490\pi$
$829$			47.1638i			1.63807i	−0.573746	+	0.819033i	$0.694510\pi$
$830$	−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	$-0.653189\pi$
$839$	−26.8159			−0.925789			−0.462894	+	0.886413i	$0.653189\pi$
$840$	−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	$-0.859439\pi$
$853$		−	24.9639i		−	0.854747i	0.904075	−	0.427373i	$-0.140561\pi$
$854$	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	$-0.953339\pi$
$863$		−	8.58185i		−	0.292130i	0.989275	−	0.146065i	$-0.0466608\pi$
$864$	−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
$874$	5.99705	+	9.19963i	0.202853	+	0.311182i
$875$	12.7678			0.431630
$876$	−3.12931	−	18.8721i	−0.105730	−	0.637628i
$877$		−	34.5347i		−	1.16615i	−0.812417	−	0.583077i	$-0.801848\pi$
$877$		−	34.5347i		−	1.16615i	0.812417	−	0.583077i	$-0.198152\pi$
$878$	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	$-0.890138\pi$
$887$		−	20.1526i		−	0.676658i	0.941028	−	0.338329i	$-0.109862\pi$
$888$	−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	$-0.681597\pi$
$911$	−32.6008			−1.08011			−0.540057	+	0.841629i	$0.681597\pi$
$912$	−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	$-0.532978\pi$
$919$	−6.27025			−0.206836			−0.103418	+	0.994638i	$0.532978\pi$
$920$	30.4859	+	33.2527i	1.00509	+	1.09631i
$921$	−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	$-0.541872\pi$
$941$	−8.04712			−0.262329			−0.131164	+	0.991361i	$0.541872\pi$
$942$	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
$966$	−20.5679	+	13.4078i	−0.661761	+	0.431388i
$967$		−	43.2929i		−	1.39221i	−0.717942	−	0.696103i	$-0.754916\pi$
$967$		−	43.2929i		−	1.39221i	0.717942	−	0.696103i	$-0.245084\pi$
$968$	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	$-0.300418\pi$
$983$	36.7909			1.17345			0.586723	+	0.809788i	$0.300418\pi$
$984$	−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	$-0.941336\pi$
$991$		−	11.5379i		−	0.366512i	0.983065	−	0.183256i	$-0.0586638\pi$
$992$	−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	$0.198493\pi$
$997$			36.8768i			1.16790i	−0.811790	+	0.583949i	$0.801507\pi$
$998$	−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.91.5	✓	24
4.3	odd	2		2208.2.n.b.367.3		24
8.3	odd	2	inner	552.2.n.b.91.8	yes	24
8.5	even	2		2208.2.n.b.367.21		24
23.22	odd	2	inner	552.2.n.b.91.6	yes	24
92.91	even	2		2208.2.n.b.367.22		24
184.45	odd	2		2208.2.n.b.367.4		24
184.91	even	2	inner	552.2.n.b.91.7	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(-5.68172 + 3.70379i) 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} +(9.51618 + 1.20100i) 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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