LMFDB - Embedded newform 552.2.n.b.91.11

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			91.11
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.409868 + 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} -3.34475 q^{5} +(0.409868 - 1.35352i) q^{6} +4.25021 q^{7} +(2.18379 - 1.79751i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.409868 + 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} -3.34475 q^{5} +(0.409868 - 1.35352i) q^{6} +4.25021 q^{7} +(2.18379 - 1.79751i) q^{8} +1.00000 q^{9} +(1.37091 - 4.52717i) q^{10} -1.35797i q^{11} +(1.66402 + 1.10953i) q^{12} +2.36562i q^{13} +(-1.74203 + 5.75273i) q^{14} +3.34475 q^{15} +(1.53790 + 3.69254i) q^{16} -1.28704i q^{17} +(-0.409868 + 1.35352i) q^{18} -1.70310i q^{19} +(5.56571 + 3.71109i) q^{20} -4.25021 q^{21} +(1.83804 + 0.556590i) q^{22} +(-1.27490 + 4.62327i) q^{23} +(-2.18379 + 1.79751i) q^{24} +6.18732 q^{25} +(-3.20191 - 0.969595i) q^{26} -1.00000 q^{27} +(-7.07242 - 4.71573i) q^{28} +7.24930i q^{29} +(-1.37091 + 4.52717i) q^{30} +9.70810i q^{31} +(-5.62825 + 0.568111i) q^{32} +1.35797i q^{33} +(1.74203 + 0.527516i) q^{34} -14.2159 q^{35} +(-1.66402 - 1.10953i) q^{36} +3.06582 q^{37} +(2.30517 + 0.698046i) q^{38} -2.36562i q^{39} +(-7.30423 + 6.01222i) q^{40} -2.62473 q^{41} +(1.74203 - 5.75273i) q^{42} +10.3795i q^{43} +(-1.50671 + 2.25969i) q^{44} -3.34475 q^{45} +(-5.73514 - 3.62053i) q^{46} -6.05402i q^{47} +(-1.53790 - 3.69254i) q^{48} +11.0643 q^{49} +(-2.53599 + 8.37464i) q^{50} +1.28704i q^{51} +(2.62473 - 3.93644i) q^{52} +11.7344 q^{53} +(0.409868 - 1.35352i) q^{54} +4.54207i q^{55} +(9.28158 - 7.63981i) q^{56} +1.70310i q^{57} +(-9.81205 - 2.97126i) q^{58} +7.81205 q^{59} +(-5.56571 - 3.71109i) q^{60} +6.82148 q^{61} +(-13.1401 - 3.97904i) q^{62} +4.25021 q^{63} +(1.53790 - 7.85079i) q^{64} -7.91241i q^{65} +(-1.83804 - 0.556590i) q^{66} -7.98334i q^{67} +(-1.42800 + 2.14165i) q^{68} +(1.27490 - 4.62327i) q^{69} +(5.82664 - 19.2414i) q^{70} +13.4634i q^{71} +(2.18379 - 1.79751i) q^{72} +6.03134 q^{73} +(-1.25658 + 4.14964i) q^{74} -6.18732 q^{75} +(-1.88963 + 2.83398i) q^{76} -5.77167i q^{77} +(3.20191 + 0.969595i) q^{78} -14.0413 q^{79} +(-5.14387 - 12.3506i) q^{80} +1.00000 q^{81} +(1.07579 - 3.55261i) q^{82} -0.0200280i q^{83} +(7.07242 + 4.71573i) q^{84} +4.30481i q^{85} +(-14.0488 - 4.25423i) q^{86} -7.24930i q^{87} +(-2.44097 - 2.96553i) q^{88} +2.91920i q^{89} +(1.37091 - 4.52717i) q^{90} +10.0544i q^{91} +(7.25109 - 6.27867i) q^{92} -9.70810i q^{93} +(8.19422 + 2.48135i) q^{94} +5.69642i q^{95} +(5.62825 - 0.568111i) q^{96} -13.4664i q^{97} +(-4.53490 + 14.9757i) q^{98} -1.35797i 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 $

$2$	−0.409868	+	1.35352i	−0.289821	+	0.957081i
$2$	−0.409868	+	1.35352i	−0.289821	+	0.957081i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.66402	−	1.10953i	−0.832008	−	0.554764i
$5$	−3.34475			−1.49582			−0.747908	−	0.663803i	$-0.768941\pi$
$5$	−3.34475			−1.49582			−0.747908	+	0.663803i	$0.768941\pi$
$6$	0.409868	−	1.35352i	0.167328	−	0.552571i
$7$	4.25021			1.60643			0.803214	−	0.595690i	$-0.203121\pi$
$7$	4.25021			1.60643			0.803214	+	0.595690i	$0.203121\pi$
$8$	2.18379	−	1.79751i	0.772087	−	0.635517i
$9$	1.00000			0.333333
$10$	1.37091	−	4.52717i	0.433518	−	1.43162i
$11$		−	1.35797i		−	0.409444i	−0.978820	−	0.204722i	$-0.934371\pi$
$11$		−	1.35797i		−	0.409444i	0.978820	−	0.204722i	$-0.0656290\pi$
$12$	1.66402	+	1.10953i	0.480360	+	0.320293i
$13$			2.36562i			0.656106i	0.944659	+	0.328053i	$0.106392\pi$
$13$			2.36562i			0.656106i	−0.944659	+	0.328053i	$0.893608\pi$
$14$	−1.74203	+	5.75273i	−0.465576	+	1.53748i
$15$	3.34475			0.863610
$16$	1.53790	+	3.69254i	0.384474	+	0.923136i
$17$		−	1.28704i		−	0.312152i	−0.987745	−	0.156076i	$-0.950115\pi$
$17$		−	1.28704i		−	0.312152i	0.987745	−	0.156076i	$-0.0498846\pi$
$18$	−0.409868	+	1.35352i	−0.0966069	+	0.319027i
$19$		−	1.70310i		−	0.390717i	−0.980732	−	0.195359i	$-0.937413\pi$
$19$		−	1.70310i		−	0.390717i	0.980732	−	0.195359i	$-0.0625871\pi$
$20$	5.56571	+	3.71109i	1.24453	+	0.829824i
$21$	−4.25021			−0.927472
$22$	1.83804	+	0.556590i	0.391871	+	0.118665i
$23$	−1.27490	+	4.62327i	−0.265834	+	0.964019i
$23$	−1.27490	+	4.62327i	−0.265834	+	0.964019i
$24$	−2.18379	+	1.79751i	−0.445765	+	0.366916i
$25$	6.18732			1.23746
$26$	−3.20191	−	0.969595i	−0.627947	−	0.190153i
$27$	−1.00000			−0.192450
$28$	−7.07242	−	4.71573i	−1.33656	−	0.891188i
$29$			7.24930i			1.34616i	0.739569	+	0.673080i	$0.235029\pi$
$29$			7.24930i			1.34616i	−0.739569	+	0.673080i	$0.764971\pi$
$30$	−1.37091	+	4.52717i	−0.250292	+	0.826544i
$31$			9.70810i			1.74363i	0.489838	+	0.871813i	$0.337056\pi$
$31$			9.70810i			1.74363i	−0.489838	+	0.871813i	$0.662944\pi$
$32$	−5.62825	+	0.568111i	−0.994944	+	0.100429i
$33$			1.35797i			0.236393i
$34$	1.74203	+	0.527516i	0.298755	+	0.0904683i
$35$	−14.2159			−2.40292
$36$	−1.66402	−	1.10953i	−0.277336	−	0.184921i
$37$	3.06582			0.504018			0.252009	−	0.967725i	$-0.418909\pi$
$37$	3.06582			0.504018			0.252009	+	0.967725i	$0.418909\pi$
$38$	2.30517	+	0.698046i	0.373948	+	0.113238i
$39$		−	2.36562i		−	0.378803i
$40$	−7.30423	+	6.01222i	−1.15490	+	0.950616i
$41$	−2.62473			−0.409913			−0.204957	−	0.978771i	$-0.565705\pi$
$41$	−2.62473			−0.409913			−0.204957	+	0.978771i	$0.565705\pi$
$42$	1.74203	−	5.75273i	0.268801	−	0.887666i
$43$			10.3795i			1.58286i	0.611261	+	0.791429i	$0.290663\pi$
$43$			10.3795i			1.58286i	−0.611261	+	0.791429i	$0.709337\pi$
$44$	−1.50671	+	2.25969i	−0.227145	+	0.340661i
$45$	−3.34475			−0.498605
$46$	−5.73514	−	3.62053i	−0.845600	−	0.533817i
$47$		−	6.05402i		−	0.883070i	−0.897244	−	0.441535i	$-0.854434\pi$
$47$		−	6.05402i		−	0.883070i	0.897244	−	0.441535i	$-0.145566\pi$
$48$	−1.53790	−	3.69254i	−0.221976	−	0.532973i
$49$	11.0643			1.58061
$50$	−2.53599	+	8.37464i	−0.358643	+	1.18435i
$51$			1.28704i			0.180221i
$52$	2.62473	−	3.93644i	0.363984	−	0.545885i
$53$	11.7344			1.61184			0.805919	−	0.592026i	$-0.201672\pi$
$53$	11.7344			1.61184			0.805919	+	0.592026i	$0.201672\pi$
$54$	0.409868	−	1.35352i	0.0557760	−	0.184190i
$55$			4.54207i			0.612453i
$56$	9.28158	−	7.63981i	1.24030	−	1.02091i
$57$			1.70310i			0.225581i
$58$	−9.81205	−	2.97126i	−1.28838	−	0.390145i
$59$	7.81205			1.01704			0.508521	−	0.861050i	$-0.330192\pi$
$59$	7.81205			1.01704			0.508521	+	0.861050i	$0.330192\pi$
$60$	−5.56571	−	3.71109i	−0.718530	−	0.479099i
$61$	6.82148			0.873401			0.436701	−	0.899607i	$-0.356147\pi$
$61$	6.82148			0.873401			0.436701	+	0.899607i	$0.356147\pi$
$62$	−13.1401	−	3.97904i	−1.66879	−	0.505339i
$63$	4.25021			0.535476
$64$	1.53790	−	7.85079i	0.192237	−	0.981349i
$65$		−	7.91241i		−	0.981414i
$66$	−1.83804	−	0.556590i	−0.226247	−	0.0685115i
$67$		−	7.98334i		−	0.975321i	−0.873033	−	0.487660i	$-0.837850\pi$
$67$		−	7.98334i		−	0.975321i	0.873033	−	0.487660i	$-0.162150\pi$
$68$	−1.42800	+	2.14165i	−0.173171	+	0.259713i
$69$	1.27490	−	4.62327i	0.153479	−	0.556577i
$70$	5.82664	−	19.2414i	0.696416	−	2.29979i
$71$			13.4634i			1.59781i	0.601457	+	0.798905i	$0.294587\pi$
$71$			13.4634i			1.59781i	−0.601457	+	0.798905i	$0.705413\pi$
$72$	2.18379	−	1.79751i	0.257362	−	0.211839i
$73$	6.03134			0.705915			0.352957	−	0.935639i	$-0.385176\pi$
$73$	6.03134			0.705915			0.352957	+	0.935639i	$0.385176\pi$
$74$	−1.25658	+	4.14964i	−0.146075	+	0.482386i
$75$	−6.18732			−0.714450
$76$	−1.88963	+	2.83398i	−0.216756	+	0.325080i
$77$		−	5.77167i		−	0.657742i
$78$	3.20191	+	0.969595i	0.362545	+	0.109785i
$79$	−14.0413			−1.57977			−0.789887	−	0.613253i	$-0.789861\pi$
$79$	−14.0413			−1.57977			−0.789887	+	0.613253i	$0.789861\pi$
$80$	−5.14387	−	12.3506i	−0.575102	−	1.38084i
$81$	1.00000			0.111111
$82$	1.07579	−	3.55261i	0.118801	−	0.392320i
$83$		−	0.0200280i		−	0.00219836i	−0.999999	−	0.00109918i	$-0.999650\pi$
$83$		−	0.0200280i		−	0.00219836i	0.999999	−	0.00109918i	$-0.000349880\pi$
$84$	7.07242	+	4.71573i	0.771664	+	0.514528i
$85$			4.30481i			0.466923i
$86$	−14.0488	−	4.25423i	−1.51492	−	0.458745i
$87$		−	7.24930i		−	0.777206i
$88$	−2.44097	−	2.96553i	−0.260208	−	0.316126i
$89$			2.91920i			0.309435i	0.987959	+	0.154717i	$0.0494467\pi$
$89$			2.91920i			0.309435i	−0.987959	+	0.154717i	$0.950553\pi$
$90$	1.37091	−	4.52717i	0.144506	−	0.477206i
$91$			10.0544i			1.05399i
$92$	7.25109	−	6.27867i	0.755979	−	0.654596i
$93$		−	9.70810i		−	1.00668i
$94$	8.19422	+	2.48135i	0.845169	+	0.255932i
$95$			5.69642i			0.584441i
$96$	5.62825	−	0.568111i	0.574431	−	0.0579826i
$97$		−	13.4664i		−	1.36730i	−0.729810	−	0.683650i	$-0.760391\pi$
$97$		−	13.4664i		−	1.36730i	0.729810	−	0.683650i	$-0.239609\pi$
$98$	−4.53490	+	14.9757i	−0.458094	+	1.51277i
$99$		−	1.35797i		−	0.136481i
$100$	−10.2958	−	6.86500i	−1.02958	−	0.686500i
$101$		−	1.47763i		−	0.147030i	−0.997294	−	0.0735149i	$-0.976578\pi$
$101$		−	1.47763i		−	0.147030i	0.997294	−	0.0735149i	$-0.0234217\pi$
$102$	−1.74203	−	0.527516i	−0.172486	−	0.0522319i
$103$	−9.62302			−0.948184			−0.474092	−	0.880475i	$-0.657224\pi$
$103$	−9.62302			−0.948184			−0.474092	+	0.880475i	$0.657224\pi$
$104$	4.25224	+	5.16603i	0.416966	+	0.506571i
$105$	14.2159			1.38733
$106$	−4.80954	+	15.8826i	−0.467144	+	1.54266i
$107$			19.4666i			1.88191i	0.338529	+	0.940956i	$0.390071\pi$
$107$			19.4666i			1.88191i	−0.338529	+	0.940956i	$0.609929\pi$
$108$	1.66402	+	1.10953i	0.160120	+	0.106764i
$109$	5.61561			0.537878			0.268939	−	0.963157i	$-0.413327\pi$
$109$	5.61561			0.537878			0.268939	+	0.963157i	$0.413327\pi$
$110$	−6.14777	−	1.86165i	−0.586167	−	0.177501i
$111$	−3.06582			−0.290995
$112$	6.53638	+	15.6941i	0.617630	+	1.48295i
$113$			8.30335i			0.781113i	0.920579	+	0.390557i	$0.127717\pi$
$113$			8.30335i			0.781113i	−0.920579	+	0.390557i	$0.872283\pi$
$114$	−2.30517	−	0.698046i	−0.215899	−	0.0653780i
$115$	4.26420	−	15.4637i	0.397639	−	1.44199i
$116$	8.04330	−	12.0629i	0.746801	−	1.12002i
$117$			2.36562i			0.218702i
$118$	−3.20191	+	10.5737i	−0.294760	+	0.973391i
$119$		−	5.47018i		−	0.501451i
$120$	7.30423	−	6.01222i	0.666782	−	0.548838i
$121$	9.15591			0.832356
$122$	−2.79591	+	9.23299i	−0.253130	+	0.835916i
$123$	2.62473			0.236664
$124$	10.7714	−	16.1544i	0.967301	−	1.45071i
$125$	−3.97129			−0.355203
$126$	−1.74203	+	5.75273i	−0.155192	+	0.512494i
$127$			9.31101i			0.826218i	0.910682	+	0.413109i	$0.135557\pi$
$127$			9.31101i			0.826218i	−0.910682	+	0.413109i	$0.864443\pi$
$128$	9.99584	+	5.29936i	0.883516	+	0.468402i
$129$		−	10.3795i		−	0.913864i
$130$	10.7096	+	3.24305i	0.939292	+	0.284434i
$131$	6.40382			0.559505			0.279752	−	0.960072i	$-0.409748\pi$
$131$	6.40382			0.559505			0.279752	+	0.960072i	$0.409748\pi$
$132$	1.50671	−	2.25969i	0.131142	−	0.196680i
$133$		−	7.23852i		−	0.627659i
$134$	10.8056	+	3.27212i	0.933461	+	0.282668i
$135$	3.34475			0.287870
$136$	−2.31347	−	2.81062i	−0.198378	−	0.241009i
$137$			2.62498i			0.224267i	0.993693	+	0.112134i	$0.0357685\pi$
$137$			2.62498i			0.224267i	−0.993693	+	0.112134i	$0.964232\pi$
$138$	5.73514	+	3.62053i	0.488207	+	0.308200i
$139$	−9.34793			−0.792881			−0.396441	−	0.918060i	$-0.629755\pi$
$139$	−9.34793			−0.792881			−0.396441	+	0.918060i	$0.629755\pi$
$140$	23.6554	+	15.7729i	1.99925	+	1.33305i
$141$			6.05402i			0.509841i
$142$	−18.2229	−	5.51822i	−1.52923	−	0.463079i
$143$	3.21245			0.268639
$144$	1.53790	+	3.69254i	0.128158	+	0.307712i
$145$		−	24.2471i		−	2.01361i
$146$	−2.47206	+	8.16352i	−0.204589	+	0.675617i
$147$	−11.0643			−0.912567
$148$	−5.10158	−	3.40162i	−0.419347	−	0.279611i
$149$	−8.80052			−0.720967			−0.360483	−	0.932766i	$-0.617388\pi$
$149$	−8.80052			−0.720967			−0.360483	+	0.932766i	$0.617388\pi$
$150$	2.53599	−	8.37464i	0.207063	−	0.683787i
$151$		−	9.50018i		−	0.773114i	−0.922266	−	0.386557i	$-0.873664\pi$
$151$		−	9.50018i		−	0.773114i	0.922266	−	0.386557i	$-0.126336\pi$
$152$	−3.06134	−	3.71921i	−0.248307	−	0.301668i
$153$		−	1.28704i		−	0.104051i
$154$	7.81205	+	2.36562i	0.629513	+	0.190627i
$155$		−	32.4711i		−	2.60814i
$156$	−2.62473	+	3.93644i	−0.210146	+	0.315167i
$157$	−22.6741			−1.80959			−0.904793	−	0.425851i	$-0.859975\pi$
$157$	−22.6741			−1.80959			−0.904793	+	0.425851i	$0.859975\pi$
$158$	5.75510	−	19.0052i	0.457851	−	1.51197i
$159$	−11.7344			−0.930595
$160$	18.8251	−	1.90019i	1.48825	−	0.150223i
$161$	−5.41857	+	19.6499i	−0.427043	+	1.54863i
$162$	−0.409868	+	1.35352i	−0.0322023	+	0.106342i
$163$	−7.96419			−0.623804			−0.311902	−	0.950114i	$-0.600966\pi$
$163$	−7.96419			−0.623804			−0.311902	+	0.950114i	$0.600966\pi$
$164$	4.36758	+	2.91221i	0.341051	+	0.227405i
$165$		−	4.54207i		−	0.353600i
$166$	0.0271083	+	0.00820885i	0.00210401	+	0.000637130i
$167$		−	22.5603i		−	1.74576i	−0.487930	−	0.872882i	$-0.662248\pi$
$167$		−	22.5603i		−	1.74576i	0.487930	−	0.872882i	$-0.337752\pi$
$168$	−9.28158	+	7.63981i	−0.716089	+	0.589424i
$169$	7.40382			0.569525
$170$	−5.82664	−	1.76441i	−0.446883	−	0.135324i
$171$		−	1.70310i		−	0.130239i
$172$	11.5163	−	17.2716i	0.878113	−	1.31695i
$173$			10.1830i			0.774199i	0.922038	+	0.387100i	$0.126523\pi$
$173$			10.1830i			0.774199i	−0.922038	+	0.387100i	$0.873477\pi$
$174$	9.81205	+	2.97126i	0.743849	+	0.225251i
$175$	26.2974			1.98790
$176$	5.01437	−	2.08842i	0.377972	−	0.157421i
$177$	−7.81205			−0.587189
$178$	−3.95119	−	1.19649i	−0.296154	−	0.0896806i
$179$	12.0913			0.903746			0.451873	−	0.892082i	$-0.350756\pi$
$179$	12.0913			0.903746			0.451873	+	0.892082i	$0.350756\pi$
$180$	5.56571	+	3.71109i	0.414843	+	0.276608i
$181$	4.93435			0.366767			0.183384	−	0.983041i	$-0.441295\pi$
$181$	4.93435			0.366767			0.183384	+	0.983041i	$0.441295\pi$
$182$	−13.6088	−	4.12098i	−1.00875	−	0.305467i
$183$	−6.82148			−0.504258
$184$	5.52628	+	12.3879i	0.407403	+	0.913248i
$185$	−10.2544			−0.753918
$186$	13.1401	+	3.97904i	0.963477	+	0.291758i
$187$	−1.74776			−0.127809
$188$	−6.71711	+	10.0740i	−0.489895	+	0.734721i
$189$	−4.25021			−0.309157
$190$	−7.71021	−	2.33478i	−0.559357	−	0.169383i
$191$	18.5834			1.34465			0.672323	−	0.740258i	$-0.265297\pi$
$191$	18.5834			1.34465			0.672323	+	0.740258i	$0.265297\pi$
$192$	−1.53790	+	7.85079i	−0.110988	+	0.566582i
$193$	−0.968591			−0.0697207			−0.0348604	−	0.999392i	$-0.511099\pi$
$193$	−0.968591			−0.0697207			−0.0348604	+	0.999392i	$0.511099\pi$
$194$	18.2269	+	5.51943i	1.30862	+	0.396272i
$195$			7.91241i			0.566619i
$196$	−18.4111	−	12.2761i	−1.31508	−	0.876867i
$197$		−	13.0210i		−	0.927705i	−0.885912	−	0.463853i	$-0.846467\pi$
$197$		−	13.0210i		−	0.927705i	0.885912	−	0.463853i	$-0.153533\pi$
$198$	1.83804	+	0.556590i	0.130624	+	0.0395551i
$199$	13.8735			0.983469			0.491734	−	0.870745i	$-0.336363\pi$
$199$	13.8735			0.983469			0.491734	+	0.870745i	$0.336363\pi$
$200$	13.5118	−	11.1218i	0.955430	−	0.786429i
$201$			7.98334i			0.563102i
$202$	2.00000	+	0.605635i	0.140720	+	0.0426123i
$203$			30.8110i			2.16251i
$204$	1.42800	−	2.14165i	0.0999803	−	0.149946i
$205$	8.77904			0.613155
$206$	3.94417	−	13.0249i	0.274803	−	0.907489i
$207$	−1.27490	+	4.62327i	−0.0886113	+	0.321340i
$208$	−8.73517	+	3.63808i	−0.605675	+	0.252256i
$209$	−2.31276			−0.159977
$210$	−5.82664	+	19.2414i	−0.402076	+	1.32778i
$211$	−15.1196			−1.04088			−0.520439	−	0.853899i	$-0.674232\pi$
$211$	−15.1196			−1.04088			−0.520439	+	0.853899i	$0.674232\pi$
$212$	−19.5261	−	13.0196i	−1.34106	−	0.894189i
$213$		−	13.4634i		−	0.922496i
$214$	−26.3484	−	7.97877i	−1.80114	−	0.545417i
$215$		−	34.7168i		−	2.36766i
$216$	−2.18379	+	1.79751i	−0.148588	+	0.122305i
$217$			41.2615i			2.80101i
$218$	−2.30166	+	7.60083i	−0.155888	+	0.514793i
$219$	−6.03134			−0.407560
$220$	5.03955	−	7.55808i	0.339767	−	0.509565i
$221$	3.04465			0.204805
$222$	1.25658	−	4.14964i	0.0843364	−	0.278506i
$223$			10.5610i			0.707215i	0.935394	+	0.353607i	$0.115045\pi$
$223$			10.5610i			0.707215i	−0.935394	+	0.353607i	$0.884955\pi$
$224$	−23.9213	+	2.41459i	−1.59831	+	0.161332i
$225$	6.18732			0.412488
$226$	−11.2387	−	3.40328i	−0.747589	−	0.226383i
$227$		−	3.11219i		−	0.206563i	−0.994652	−	0.103282i	$-0.967066\pi$
$227$		−	3.11219i		−	0.206563i	0.994652	−	0.103282i	$-0.0329343\pi$
$228$	1.88963	−	2.83398i	0.125144	−	0.187685i
$229$	−17.0499			−1.12669			−0.563343	−	0.826223i	$-0.690485\pi$
$229$	−17.0499			−1.12669			−0.563343	+	0.826223i	$0.690485\pi$
$230$	19.1826	+	12.1097i	1.26486	+	0.798492i
$231$			5.77167i			0.379748i
$232$	13.0307	+	15.8310i	0.855508	+	1.03935i
$233$	−14.5284			−0.951787			−0.475894	−	0.879503i	$-0.657875\pi$
$233$	−14.5284			−0.951787			−0.475894	+	0.879503i	$0.657875\pi$
$234$	−3.20191	−	0.969595i	−0.209316	−	0.0633844i
$235$			20.2492i			1.32091i
$236$	−12.9994	−	8.66768i	−0.846187	−	0.564218i
$237$	14.0413			0.912083
$238$	7.40398	+	2.24205i	0.479929	+	0.145331i
$239$		−	1.56887i		−	0.101482i	−0.998712	−	0.0507408i	$-0.983842\pi$
$239$		−	1.56887i		−	0.101482i	0.998712	−	0.0507408i	$-0.0161582\pi$
$240$	5.14387	+	12.3506i	0.332035	+	0.797229i
$241$			13.8541i			0.892423i	0.894928	+	0.446211i	$0.147227\pi$
$241$			13.8541i			0.892423i	−0.894928	+	0.446211i	$0.852773\pi$
$242$	−3.75272	+	12.3927i	−0.241234	+	0.796632i
$243$	−1.00000			−0.0641500
$244$	−11.3511	−	7.56862i	−0.726677	−	0.484531i
$245$	−37.0072			−2.36430
$246$	−1.07579	+	3.55261i	−0.0685900	+	0.226506i
$247$	4.02889			0.256352
$248$	17.4504	+	21.2005i	1.10810	+	1.34623i
$249$			0.0200280i			0.00126922i
$250$	1.62771	−	5.37520i	0.102945	−	0.339958i
$251$		−	22.7472i		−	1.43579i	−0.696151	−	0.717896i	$-0.745105\pi$
$251$		−	22.7472i		−	1.43579i	0.696151	−	0.717896i	$-0.254895\pi$
$252$	−7.07242	−	4.71573i	−0.445520	−	0.297063i
$253$	6.27827	+	1.73127i	0.394712	+	0.108844i
$254$	−12.6026	−	3.81629i	−0.790758	−	0.239455i
$255$		−	4.30481i		−	0.269578i
$256$	−11.2698	+	11.3575i	−0.704359	+	0.709843i
$257$	1.56221			0.0974479			0.0487239	−	0.998812i	$-0.484485\pi$
$257$	1.56221			0.0974479			0.0487239	+	0.998812i	$0.484485\pi$
$258$	14.0488	+	4.25423i	0.874641	+	0.264857i
$259$	13.0304			0.809669
$260$	−8.77904	+	13.1664i	−0.544453	+	0.816544i
$261$			7.24930i			0.448720i
$262$	−2.62473	+	8.66768i	−0.162156	+	0.535491i
$263$	−11.0502			−0.681385			−0.340693	−	0.940175i	$-0.610662\pi$
$263$	−11.0502			−0.681385			−0.340693	+	0.940175i	$0.610662\pi$
$264$	2.44097	+	2.96553i	0.150231	+	0.182516i
$265$	−39.2484			−2.41101
$266$	9.79746	+	2.96684i	0.600721	+	0.181909i
$267$		−	2.91920i		−	0.178652i
$268$	−8.85774	+	13.2844i	−0.541073	+	0.811474i
$269$		−	17.7522i		−	1.08237i	−0.840903	−	0.541186i	$-0.817976\pi$
$269$		−	17.7522i		−	1.08237i	0.840903	−	0.541186i	$-0.182024\pi$
$270$	−1.37091	+	4.52717i	−0.0834307	+	0.275515i
$271$		−	5.16603i		−	0.313814i	−0.987613	−	0.156907i	$-0.949848\pi$
$271$		−	5.16603i		−	0.313814i	0.987613	−	0.156907i	$-0.0501523\pi$
$272$	4.75244	−	1.97933i	0.288159	−	0.120015i
$273$		−	10.0544i		−	0.608520i
$274$	−3.55296	−	1.07590i	−0.214642	−	0.0649973i
$275$		−	8.40221i		−	0.506672i
$276$	−7.25109	+	6.27867i	−0.436465	+	0.377931i
$277$		−	23.9970i		−	1.44184i	−0.693019	−	0.720919i	$-0.743720\pi$
$277$		−	23.9970i		−	1.44184i	0.693019	−	0.720919i	$-0.256280\pi$
$278$	3.83142	−	12.6526i	0.229794	−	0.758852i
$279$			9.70810i			0.581209i
$280$	−31.0445	+	25.5532i	−1.85526	+	1.52710i
$281$		−	13.6894i		−	0.816642i	−0.912838	−	0.408321i	$-0.866114\pi$
$281$		−	13.6894i		−	0.816642i	0.912838	−	0.408321i	$-0.133886\pi$
$282$	−8.19422	−	2.48135i	−0.487959	−	0.147762i
$283$			13.2256i			0.786182i	0.919500	+	0.393091i	$0.128594\pi$
$283$			13.2256i			0.786182i	−0.919500	+	0.393091i	$0.871406\pi$
$284$	14.9380	−	22.4033i	0.886408	−	1.32939i
$285$		−	5.69642i		−	0.337427i
$286$	−1.31668	+	4.34811i	−0.0778571	+	0.257109i
$287$	−11.1556			−0.658496
$288$	−5.62825	+	0.568111i	−0.331648	+	0.0334763i
$289$	15.3435			0.902561
$290$	32.8188	+	9.93810i	1.92719	+	0.583586i
$291$			13.4664i			0.789412i
$292$	−10.0362	−	6.69194i	−0.587326	−	0.391616i
$293$	29.3779			1.71627			0.858137	−	0.513421i	$-0.171622\pi$
$293$	29.3779			1.71627			0.858137	+	0.513421i	$0.171622\pi$
$294$	4.53490	−	14.9757i	0.264481	−	0.873400i
$295$	−26.1293			−1.52131
$296$	6.69512	−	5.51085i	0.389146	−	0.320312i
$297$			1.35797i			0.0787975i
$298$	3.60706	−	11.9116i	0.208951	−	0.690023i
$299$	−10.9369	−	3.01592i	−0.632499	−	0.174415i
$300$	10.2958	+	6.86500i	0.594428	+	0.396351i
$301$			44.1150i			2.54275i
$302$	12.8587	+	3.89383i	0.739933	+	0.224064i
$303$			1.47763i			0.0848877i
$304$	6.28876	−	2.61919i	0.360685	−	0.150221i
$305$	−22.8161			−1.30645
$306$	1.74203	+	0.527516i	0.0995851	+	0.0301561i
$307$	−30.6840			−1.75123			−0.875614	−	0.483012i	$-0.839543\pi$
$307$	−30.6840			−1.75123			−0.875614	+	0.483012i	$0.839543\pi$
$308$	−6.40382	+	9.60414i	−0.364892	+	0.547247i
$309$	9.62302			0.547434
$310$	43.9502	+	13.3089i	2.49620	+	0.755894i
$311$			0.622018i			0.0352714i	0.999844	+	0.0176357i	$0.00561391\pi$
$311$			0.622018i			0.0352714i	−0.999844	+	0.0176357i	$0.994386\pi$
$312$	−4.25224	−	5.16603i	−0.240736	−	0.292469i
$313$		−	10.1923i		−	0.576101i	−0.957615	−	0.288050i	$-0.906993\pi$
$313$		−	10.1923i		−	0.576101i	0.957615	−	0.288050i	$-0.0930071\pi$
$314$	9.29338	−	30.6897i	0.524456	−	1.73192i
$315$	−14.2159			−0.800974
$316$	23.3650	+	15.5793i	1.31438	+	0.876401i
$317$			15.3301i			0.861023i	0.902585	+	0.430512i	$0.141667\pi$
$317$			15.3301i			0.861023i	−0.902585	+	0.430512i	$0.858333\pi$
$318$	4.80954	−	15.8826i	0.269706	−	0.890654i
$319$	9.84434			0.551177
$320$	−5.14387	+	26.2589i	−0.287551	+	1.46792i
$321$		−	19.4666i		−	1.08652i
$322$	−24.3755	−	15.3880i	−1.35840	−	0.857539i
$323$	−2.19195			−0.121963
$324$	−1.66402	−	1.10953i	−0.0924453	−	0.0616404i
$325$			14.6369i			0.811908i
$326$	3.26427	−	10.7797i	0.180791	−	0.597031i
$327$	−5.61561			−0.310544
$328$	−5.73185	+	4.71798i	−0.316489	+	0.260507i
$329$		−	25.7309i		−	1.41859i
$330$	6.14777	+	1.86165i	0.338424	+	0.102481i
$331$	17.6536			0.970329			0.485165	−	0.874423i	$-0.338760\pi$
$331$	17.6536			0.970329			0.485165	+	0.874423i	$0.338760\pi$
$332$	−0.0222216	+	0.0333269i	−0.00121957	+	0.00182905i
$333$	3.06582			0.168006
$334$	30.5357	+	9.24674i	1.67084	+	0.505959i
$335$			26.7023i			1.45890i
$336$	−6.53638	−	15.6941i	−0.356589	−	0.856182i
$337$		−	17.1184i		−	0.932501i	−0.884653	−	0.466251i	$-0.845604\pi$
$337$		−	17.1184i		−	0.932501i	0.884653	−	0.466251i	$-0.154396\pi$
$338$	−3.03459	+	10.0212i	−0.165060	+	0.545081i
$339$		−	8.30335i		−	0.450976i
$340$	4.77631	−	7.16328i	0.259032	−	0.388483i
$341$	13.1833			0.713917
$342$	2.30517	+	0.698046i	0.124649	+	0.0377460i
$343$	17.2741			0.932712
$344$	18.6573	+	22.6667i	1.00593	+	1.22210i
$345$	−4.26420	+	15.4637i	−0.229577	+	0.832536i
$346$	−13.7829	−	4.17369i	−0.740971	−	0.224379i
$347$	5.59562			0.300388			0.150194	−	0.988657i	$-0.452010\pi$
$347$	5.59562			0.300388			0.150194	+	0.988657i	$0.452010\pi$
$348$	−8.04330	+	12.0629i	−0.431166	+	0.646642i
$349$		−	17.1844i		−	0.919858i	−0.887956	−	0.459929i	$-0.847875\pi$
$349$		−	17.1844i		−	0.919858i	0.887956	−	0.459929i	$-0.152125\pi$
$350$	−10.7785	+	35.5940i	−0.576134	+	1.90258i
$351$		−	2.36562i		−	0.126268i
$352$	0.771479	+	7.64301i	0.0411200	+	0.407374i
$353$	−9.60017			−0.510966			−0.255483	−	0.966814i	$-0.582234\pi$
$353$	−9.60017			−0.510966			−0.255483	+	0.966814i	$0.582234\pi$
$354$	3.20191	−	10.5737i	0.170180	−	0.561988i
$355$		−	45.0316i		−	2.39003i
$356$	3.23893	−	4.85759i	0.171663	−	0.257452i
$357$			5.47018i			0.289513i
$358$	−4.95584	+	16.3658i	−0.261924	+	0.864958i
$359$	−19.4677			−1.02746			−0.513732	−	0.857951i	$-0.671737\pi$
$359$	−19.4677			−1.02746			−0.513732	+	0.857951i	$0.671737\pi$
$360$	−7.30423	+	6.01222i	−0.384967	+	0.316872i
$361$	16.0995			0.847340
$362$	−2.02243	+	6.67873i	−0.106297	+	0.351026i
$363$	−9.15591			−0.480561
$364$	11.1556	−	16.7307i	0.584714	−	0.876926i
$365$	−20.1733			−1.05592
$366$	2.79591	−	9.23299i	0.146145	−	0.482616i
$367$	−7.81885			−0.408141			−0.204070	−	0.978956i	$-0.565417\pi$
$367$	−7.81885			−0.408141			−0.204070	+	0.978956i	$0.565417\pi$
$368$	−19.0323	+	2.40251i	−0.992127	+	0.125239i
$369$	−2.62473			−0.136638
$370$	4.20295	−	13.8795i	0.218501	−	0.721561i
$371$	49.8735			2.58930
$372$	−10.7714	+	16.1544i	−0.558471	+	0.837568i
$373$	5.26079			0.272394			0.136197	−	0.990682i	$-0.456512\pi$
$373$	5.26079			0.272394			0.136197	+	0.990682i	$0.456512\pi$
$374$	0.716352	−	2.36562i	0.0370417	−	0.122323i
$375$	3.97129			0.205076
$376$	−10.8822	−	13.2207i	−0.561206	−	0.681807i
$377$	−17.1491			−0.883224
$378$	1.74203	−	5.75273i	0.0896002	−	0.295889i
$379$			12.7052i			0.652621i	0.945263	+	0.326310i	$0.105805\pi$
$379$			12.7052i			0.652621i	−0.945263	+	0.326310i	$0.894195\pi$
$380$	6.32034	−	9.47894i	0.324227	−	0.486259i
$381$		−	9.31101i		−	0.477017i
$382$	−7.61674	+	25.1529i	−0.389706	+	1.28693i
$383$	−32.8964			−1.68093			−0.840463	−	0.541869i	$-0.817717\pi$
$383$	−32.8964			−1.68093			−0.840463	+	0.541869i	$0.817717\pi$
$384$	−9.99584	−	5.29936i	−0.510098	−	0.270432i
$385$			19.3048i			0.983861i
$386$	0.396995	−	1.31100i	0.0202065	−	0.0667284i
$387$			10.3795i			0.527619i
$388$	−14.9413	+	22.4082i	−0.758529	+	1.13761i
$389$	4.95326			0.251140			0.125570	−	0.992085i	$-0.459924\pi$
$389$	4.95326			0.251140			0.125570	+	0.992085i	$0.459924\pi$
$390$	−10.7096	−	3.24305i	−0.542301	−	0.164218i
$391$	5.95033	+	1.64084i	0.300921	+	0.0829807i
$392$	24.1621	−	19.8882i	1.22037	−	1.00451i
$393$	−6.40382			−0.323030
$394$	17.6241	+	5.33688i	0.887889	+	0.268868i
$395$	46.9647			2.36305
$396$	−1.50671	+	2.25969i	−0.0757149	+	0.113554i
$397$			15.7353i			0.789733i	0.918739	+	0.394866i	$0.129209\pi$
$397$			15.7353i			0.789733i	−0.918739	+	0.394866i	$0.870791\pi$
$398$	−5.68632	+	18.7781i	−0.285030	+	0.941259i
$399$			7.23852i			0.362379i
$400$	9.51546	+	22.8470i	0.475773	+	1.14235i
$401$			23.5821i			1.17764i	0.808266	+	0.588818i	$0.200406\pi$
$401$			23.5821i			1.17764i	−0.808266	+	0.588818i	$0.799594\pi$
$402$	−10.8056	−	3.27212i	−0.538934	−	0.163199i
$403$	−22.9657			−1.14400
$404$	−1.63947	+	2.45880i	−0.0815669	+	0.122330i
$405$	−3.34475			−0.166202
$406$	−41.7033	−	12.6285i	−2.06970	−	0.626741i
$407$		−	4.16330i		−	0.206367i
$408$	2.31347	+	2.81062i	0.114534	+	0.139147i
$409$	28.8959			1.42881			0.714404	−	0.699733i	$-0.246698\pi$
$409$	28.8959			1.42881			0.714404	+	0.699733i	$0.246698\pi$
$410$	−3.59825	+	11.8826i	−0.177705	+	0.586839i
$411$		−	2.62498i		−	0.129481i
$412$	16.0129	+	10.6770i	0.788897	+	0.526018i
$413$	33.2028			1.63380
$414$	−5.73514	−	3.62053i	−0.281867	−	0.177939i
$415$			0.0669886i			0.00328834i
$416$	−1.34394	−	13.3143i	−0.0658920	−	0.652789i
$417$	9.34793			0.457770
$418$	0.947926	−	3.13036i	0.0463646	−	0.153111i
$419$		−	12.2149i		−	0.596738i	−0.954451	−	0.298369i	$-0.903557\pi$
$419$		−	12.2149i		−	0.596738i	0.954451	−	0.298369i	$-0.0964425\pi$
$420$	−23.6554	−	15.7729i	−1.15427	−	0.769639i
$421$	−24.3542			−1.18695			−0.593475	−	0.804852i	$-0.702245\pi$
$421$	−24.3542			−1.18695			−0.593475	+	0.804852i	$0.702245\pi$
$422$	6.19705	−	20.4647i	0.301668	−	0.996204i
$423$		−	6.05402i		−	0.294357i
$424$	25.6254	−	21.0926i	1.24448	−	1.02435i
$425$		−	7.96332i		−	0.386278i
$426$	18.2229	+	5.51822i	0.882904	+	0.267359i
$427$	28.9927			1.40306
$428$	21.5988	−	32.3928i	1.04402	−	1.56577i
$429$	−3.21245			−0.155099
$430$	46.9897	+	14.2293i	2.26605	+	0.686198i
$431$	−6.09907			−0.293782			−0.146891	−	0.989153i	$-0.546927\pi$
$431$	−6.09907			−0.293782			−0.146891	+	0.989153i	$0.546927\pi$
$432$	−1.53790	−	3.69254i	−0.0739921	−	0.177658i
$433$			12.5605i			0.603619i	0.953368	+	0.301809i	$0.0975906\pi$
$433$			12.5605i			0.603619i	−0.953368	+	0.301809i	$0.902409\pi$
$434$	−55.8481	−	16.9118i	−2.68079	−	0.811791i
$435$			24.2471i			1.16256i
$436$	−9.34447	−	6.23068i	−0.447519	−	0.298395i
$437$	7.87388	+	2.17127i	0.376659	+	0.103866i
$438$	2.47206	−	8.16352i	0.118119	−	0.390068i
$439$			6.97400i			0.332851i	0.986054	+	0.166426i	$0.0532225\pi$
$439$			6.97400i			0.332851i	−0.986054	+	0.166426i	$0.946777\pi$
$440$	8.16443	+	9.91894i	0.389224	+	0.472867i
$441$	11.0643			0.526871
$442$	−1.24790	+	4.12098i	−0.0593568	+	0.196015i
$443$	−20.7732			−0.986965			−0.493482	−	0.869756i	$-0.664276\pi$
$443$	−20.7732			−0.986965			−0.493482	+	0.869756i	$0.664276\pi$
$444$	5.10158	+	3.40162i	0.242110	+	0.161434i
$445$		−	9.76398i		−	0.462857i
$446$	−14.2945	−	4.32861i	−0.676862	−	0.204966i
$447$	8.80052			0.416250
$448$	6.53638	−	33.3675i	0.308815	−	1.57647i
$449$	−6.90397			−0.325819			−0.162909	−	0.986641i	$-0.552088\pi$
$449$	−6.90397			−0.325819			−0.162909	+	0.986641i	$0.552088\pi$
$450$	−2.53599	+	8.37464i	−0.119548	+	0.394784i
$451$			3.56430i			0.167836i
$452$	9.21280	−	13.8169i	0.433334	−	0.649893i
$453$			9.50018i			0.446358i
$454$	4.21240	+	1.27559i	0.197698	+	0.0598663i
$455$		−	33.6294i		−	1.57657i
$456$	3.06134	+	3.71921i	0.143360	+	0.174168i
$457$		−	36.9076i		−	1.72646i	−0.504807	−	0.863232i	$-0.668436\pi$
$457$		−	36.9076i		−	1.72646i	0.504807	−	0.863232i	$-0.331564\pi$
$458$	6.98820	−	23.0773i	0.326537	−	1.07833i
$459$			1.28704i			0.0600738i
$460$	−24.2531	+	21.0005i	−1.13080	+	0.979155i
$461$		−	7.66472i		−	0.356982i	−0.983942	−	0.178491i	$-0.942879\pi$
$461$		−	7.66472i		−	0.356982i	0.983942	−	0.178491i	$-0.0571215\pi$
$462$	−7.81205	−	2.36562i	−0.363449	−	0.110059i
$463$			20.2293i			0.940137i	0.882630	+	0.470069i	$0.155771\pi$
$463$			20.2293i			0.940137i	−0.882630	+	0.470069i	$0.844229\pi$
$464$	−26.7683	+	11.1487i	−1.24269	+	0.517564i
$465$			32.4711i			1.50581i
$466$	5.95473	−	19.6644i	0.275848	−	0.910937i
$467$			33.0233i			1.52814i	0.645136	+	0.764068i	$0.276801\pi$
$467$			33.0233i			1.52814i	−0.645136	+	0.764068i	$0.723199\pi$
$468$	2.62473	−	3.93644i	0.121328	−	0.181962i
$469$		−	33.9309i		−	1.56678i
$470$	−27.4076	−	8.29949i	−1.26422	−	0.382827i
$471$	22.6741			1.04477
$472$	17.0599	−	14.0423i	0.785245	−	0.646347i
$473$	14.0951			0.648092
$474$	−5.75510	+	19.0052i	−0.264341	+	0.872937i
$475$		−	10.5376i		−	0.483498i
$476$	−6.06932	+	9.10247i	−0.278187	+	0.417211i
$477$	11.7344			0.537279
$478$	2.12349	+	0.643030i	0.0971261	+	0.0294115i
$479$	42.3499			1.93502			0.967508	−	0.252839i	$-0.0813643\pi$
$479$	42.3499			1.93502			0.967508	+	0.252839i	$0.0813643\pi$
$480$	−18.8251	+	1.90019i	−0.859243	+	0.0867313i
$481$			7.25258i			0.330689i
$482$	−18.7518	−	5.67837i	−0.854121	−	0.258643i
$483$	5.41857	−	19.6499i	0.246554	−	0.894100i
$484$	−15.2356	−	10.1587i	−0.692526	−	0.461761i
$485$			45.0415i			2.04523i
$486$	0.409868	−	1.35352i	0.0185920	−	0.0613968i
$487$			3.10189i			0.140560i	0.997527	+	0.0702801i	$0.0223893\pi$
$487$			3.10189i			0.140560i	−0.997527	+	0.0702801i	$0.977611\pi$
$488$	14.8967	−	12.2617i	0.674342	−	0.555061i
$489$	7.96419			0.360153
$490$	15.1681	−	50.0899i	0.685225	−	2.26283i
$491$	8.49112			0.383199			0.191599	−	0.981473i	$-0.438633\pi$
$491$	8.49112			0.383199			0.191599	+	0.981473i	$0.438633\pi$
$492$	−4.36758	−	2.91221i	−0.196906	−	0.131292i
$493$	9.33012			0.420207
$494$	−1.65131	+	5.45316i	−0.0742961	+	0.245349i
$495$			4.54207i			0.204151i
$496$	−35.8476	+	14.9301i	−1.60960	+	0.670379i
$497$			57.2222i			2.56677i
$498$	−0.0271083	−	0.00820885i	−0.00121475	−	0.000367847i
$499$	34.1211			1.52747			0.763736	−	0.645529i	$-0.223363\pi$
$499$	34.1211			1.52747			0.763736	+	0.645529i	$0.223363\pi$
$500$	6.60828	+	4.40625i	0.295531	+	0.197054i
$501$			22.5603i			1.00792i
$502$	30.7887	+	9.32337i	1.37417	+	0.416122i
$503$	−27.0619			−1.20663			−0.603316	−	0.797502i	$-0.706154\pi$
$503$	−27.0619			−1.20663			−0.603316	+	0.797502i	$0.706154\pi$
$504$	9.28158	−	7.63981i	0.413434	−	0.340304i
$505$			4.94230i			0.219930i
$506$	−4.91657	+	7.78815i	−0.218568	+	0.346226i
$507$	−7.40382			−0.328815
$508$	10.3308	−	15.4937i	0.458356	−	0.687420i
$509$		−	22.9056i		−	1.01527i	−0.861571	−	0.507637i	$-0.830519\pi$
$509$		−	22.9056i		−	1.01527i	0.861571	−	0.507637i	$-0.169481\pi$
$510$	5.82664	+	1.76441i	0.258008	+	0.0781293i
$511$	25.6344			1.13400
$512$	−10.7534	−	19.9089i	−0.475240	−	0.879856i
$513$			1.70310i			0.0751935i
$514$	−0.640300	+	2.11448i	−0.0282424	+	0.0932655i
$515$	32.1865			1.41831
$516$	−11.5163	+	17.2716i	−0.506979	+	0.760342i
$517$	−8.22119			−0.361568
$518$	−5.34075	+	17.6369i	−0.234659	+	0.774919i
$519$		−	10.1830i		−	0.446984i
$520$	−14.2227	−	17.2791i	−0.623705	−	0.757737i
$521$		−	39.7228i		−	1.74029i	−0.492799	−	0.870143i	$-0.664026\pi$
$521$		−	39.7228i		−	1.74029i	0.492799	−	0.870143i	$-0.335974\pi$
$522$	−9.81205	−	2.97126i	−0.429462	−	0.130048i
$523$		−	4.07132i		−	0.178027i	−0.996030	−	0.0890133i	$-0.971629\pi$
$523$		−	4.07132i		−	0.178027i	0.996030	−	0.0890133i	$-0.0283714\pi$
$524$	−10.6561	−	7.10522i	−0.465512	−	0.310393i
$525$	−26.2974			−1.14771
$526$	4.52913	−	14.9566i	0.197480	−	0.652141i
$527$	12.4947			0.544277
$528$	−5.01437	+	2.08842i	−0.218222	+	0.0908868i
$529$	−19.7493	−	11.7884i	−0.858665	−	0.512538i
$530$	16.0867	−	53.1234i	0.698761	−	2.30753i
$531$	7.81205			0.339014
$532$	−8.03134	+	12.0450i	−0.348203	+	0.522217i
$533$		−	6.20911i		−	0.268947i
$534$	3.95119	+	1.19649i	0.170985	+	0.0517771i
$535$		−	65.1110i		−	2.81499i
$536$	−14.3502	−	17.4340i	−0.619833	−	0.753033i
$537$	−12.0913			−0.521778
$538$	24.0279	+	7.27607i	1.03592	+	0.313694i
$539$		−	15.0250i		−	0.647172i
$540$	−5.56571	−	3.71109i	−0.239510	−	0.159700i
$541$			39.1455i			1.68300i	0.540260	+	0.841498i	$0.318326\pi$
$541$			39.1455i			1.68300i	−0.540260	+	0.841498i	$0.681674\pi$
$542$	6.99231	+	2.11739i	0.300345	+	0.0909498i
$543$	−4.93435			−0.211753
$544$	0.731181	+	7.24378i	0.0313491	+	0.310574i
$545$	−18.7828			−0.804566
$546$	13.6088	+	4.12098i	0.582403	+	0.176362i
$547$	14.4989			0.619928			0.309964	−	0.950748i	$-0.399683\pi$
$547$	14.4989			0.619928			0.309964	+	0.950748i	$0.399683\pi$
$548$	2.91249	−	4.36801i	0.124415	−	0.186592i
$549$	6.82148			0.291134
$550$	11.3725	+	3.44380i	0.484926	+	0.146844i
$551$	12.3463			0.525968
$552$	−5.52628	−	12.3879i	−0.235214	−	0.527264i
$553$	−59.6786			−2.53779
$554$	32.4803	+	9.83560i	1.37996	+	0.417875i
$555$	10.2544			0.435275
$556$	15.5551	+	10.3718i	0.659684	+	0.439862i
$557$	17.8720			0.757261			0.378630	−	0.925548i	$-0.376395\pi$
$557$	17.8720			0.757261			0.378630	+	0.925548i	$0.376395\pi$
$558$	−13.1401	−	3.97904i	−0.556264	−	0.168446i
$559$	−24.5540			−1.03852
$560$	−21.8625	−	52.4927i	−0.923861	−	2.21822i
$561$	1.74776			0.0737905
$562$	18.5289	+	5.61086i	0.781593	+	0.236680i
$563$		−	12.3543i		−	0.520671i	−0.965518	−	0.260335i	$-0.916167\pi$
$563$		−	12.3543i		−	0.520671i	0.965518	−	0.260335i	$-0.0838332\pi$
$564$	6.71711	−	10.0740i	0.282841	−	0.424191i
$565$		−	27.7726i		−	1.16840i
$566$	−17.9011	−	5.42077i	−0.752440	−	0.227852i
$567$	4.25021			0.178492
$568$	24.2006	+	29.4013i	1.01544	+	1.23365i
$569$			26.1457i			1.09609i	0.836450	+	0.548043i	$0.184627\pi$
$569$			26.1457i			1.09609i	−0.836450	+	0.548043i	$0.815373\pi$
$570$	7.71021	+	2.33478i	0.322945	+	0.0977934i
$571$		−	28.1823i		−	1.17939i	−0.807626	−	0.589696i	$-0.799248\pi$
$571$		−	28.1823i		−	1.17939i	0.807626	−	0.589696i	$-0.200752\pi$
$572$	−5.34557	−	3.56430i	−0.223509	−	0.149031i
$573$	−18.5834			−0.776332
$574$	4.57234	−	15.0993i	0.190846	−	0.630234i
$575$	−7.88819	+	28.6057i	−0.328960	+	1.19294i
$576$	1.53790	−	7.85079i	0.0640790	−	0.327116i
$577$	−2.99961			−0.124875			−0.0624377	−	0.998049i	$-0.519887\pi$
$577$	−2.99961			−0.124875			−0.0624377	+	0.998049i	$0.519887\pi$
$578$	−6.28883	+	20.7677i	−0.261581	+	0.863824i
$579$	0.968591			0.0402533
$580$	−26.9028	+	40.3475i	−1.11708	+	1.67534i
$581$		−	0.0851233i		−	0.00353151i
$582$	−18.2269	−	5.51943i	−0.755531	−	0.228788i
$583$		−	15.9349i		−	0.659957i
$584$	13.1712	−	10.8414i	0.545028	−	0.448621i
$585$		−	7.91241i		−	0.327138i
$586$	−12.0411	+	39.7634i	−0.497412	+	1.64261i
$587$	16.3160			0.673432			0.336716	−	0.941606i	$-0.390684\pi$
$587$	16.3160			0.673432			0.336716	+	0.941606i	$0.390684\pi$
$588$	18.4111	+	12.2761i	0.759263	+	0.506259i
$589$	16.5338			0.681265
$590$	10.7096	−	35.3665i	0.440906	−	1.45601i
$591$			13.0210i			0.535611i
$592$	4.71492	+	11.3207i	0.193782	+	0.465277i
$593$	28.8694			1.18552			0.592762	−	0.805378i	$-0.298038\pi$
$593$	28.8694			1.18552			0.592762	+	0.805378i	$0.298038\pi$
$594$	−1.83804	−	0.556590i	−0.0754156	−	0.0228372i
$595$			18.2964i			0.750078i
$596$	14.6442	+	9.76442i	0.599850	+	0.399966i
$597$	−13.8735			−0.567806
$598$	8.56480	−	13.5672i	0.350241	−	0.554803i
$599$			12.3970i			0.506528i	0.967397	+	0.253264i	$0.0815041\pi$
$599$			12.3970i			0.506528i	−0.967397	+	0.253264i	$0.918496\pi$
$600$	−13.5118	+	11.1218i	−0.551618	+	0.454045i
$601$	3.40375			0.138842			0.0694210	−	0.997587i	$-0.477885\pi$
$601$	3.40375			0.138842			0.0694210	+	0.997587i	$0.477885\pi$
$602$	−59.7104	−	18.0814i	−2.43362	−	0.736941i
$603$		−	7.98334i		−	0.325107i
$604$	−10.5407	+	15.8085i	−0.428896	+	0.643237i
$605$	−30.6242			−1.24505
$606$	−2.00000	−	0.605635i	−0.0812444	−	0.0246022i
$607$			43.7821i			1.77706i	0.458817	+	0.888531i	$0.348273\pi$
$607$			43.7821i			1.77706i	−0.458817	+	0.888531i	$0.651727\pi$
$608$	0.967548	+	9.58546i	0.0392393	+	0.388742i
$609$		−	30.8110i		−	1.24853i
$610$	9.35161	−	30.8820i	0.378635	−	1.25038i
$611$	14.3215			0.579388
$612$	−1.42800	+	2.14165i	−0.0577236	+	0.0865711i
$613$	10.2363			0.413442			0.206721	−	0.978400i	$-0.433721\pi$
$613$	10.2363			0.413442			0.206721	+	0.978400i	$0.433721\pi$
$614$	12.5764	−	41.5313i	0.507542	−	1.67607i
$615$	−8.77904			−0.354005
$616$	−10.3746	−	12.6041i	−0.418006	−	0.507834i
$617$		−	40.8145i		−	1.64313i	−0.570114	−	0.821566i	$-0.693101\pi$
$617$		−	40.8145i		−	1.64313i	0.570114	−	0.821566i	$-0.306899\pi$
$618$	−3.94417	+	13.0249i	−0.158658	+	0.523939i
$619$			15.9260i			0.640122i	0.947397	+	0.320061i	$0.103703\pi$
$619$			15.9260i			0.640122i	−0.947397	+	0.320061i	$0.896297\pi$
$620$	−36.0276	+	54.0325i	−1.44690	+	2.17000i
$621$	1.27490	−	4.62327i	0.0511598	−	0.185526i
$622$	−0.841911	−	0.254945i	−0.0337576	−	0.0102224i
$623$			12.4072i			0.497085i
$624$	8.73517	−	3.63808i	0.349687	−	0.145640i
$625$	−17.6537			−0.706146
$626$	13.7954	+	4.17749i	0.551375	+	0.166966i
$627$	2.31276			0.0923626
$628$	37.7300	+	25.1575i	1.50559	+	1.00389i
$629$		−	3.94583i		−	0.157331i
$630$	5.82664	−	19.2414i	0.232139	−	0.766597i
$631$	−24.7354			−0.984699			−0.492349	−	0.870398i	$-0.663862\pi$
$631$	−24.7354			−0.984699			−0.492349	+	0.870398i	$0.663862\pi$
$632$	−30.6634	+	25.2395i	−1.21972	+	1.00397i
$633$	15.1196			0.600951
$634$	−20.7495	−	6.28332i	−0.824069	−	0.249542i
$635$		−	31.1429i		−	1.23587i
$636$	19.5261	+	13.0196i	0.774262	+	0.516260i
$637$			26.1739i			1.03705i
$638$	−4.03489	+	13.3245i	−0.159743	+	0.527521i
$639$			13.4634i			0.532604i
$640$	−33.4335	−	17.7250i	−1.32158	−	0.700642i
$641$			1.77955i			0.0702880i	0.999382	+	0.0351440i	$0.0111890\pi$
$641$			1.77955i			0.0702880i	−0.999382	+	0.0351440i	$0.988811\pi$
$642$	26.3484	+	7.97877i	1.03989	+	0.314897i
$643$			25.4338i			1.00301i	0.865154	+	0.501506i	$0.167221\pi$
$643$			25.4338i			1.00301i	−0.865154	+	0.501506i	$0.832779\pi$
$644$	30.8187	−	26.6856i	1.21443	−	1.05156i
$645$			34.7168i			1.36697i
$646$	0.898411	−	2.96684i	0.0353475	−	0.116729i
$647$		−	17.3176i		−	0.680824i	−0.940276	−	0.340412i	$-0.889434\pi$
$647$		−	17.3176i		−	0.680824i	0.940276	−	0.340412i	$-0.110566\pi$
$648$	2.18379	−	1.79751i	0.0857875	−	0.0706130i
$649$		−	10.6085i		−	0.416422i
$650$	−19.8113	−	5.99919i	−0.777061	−	0.235308i
$651$		−	41.2615i		−	1.61716i
$652$	13.2525	+	8.83649i	0.519009	+	0.346064i
$653$		−	13.6867i		−	0.535602i	−0.963474	−	0.267801i	$-0.913703\pi$
$653$		−	13.6867i		−	0.535602i	0.963474	−	0.267801i	$-0.0862970\pi$
$654$	2.30166	−	7.60083i	0.0900021	−	0.297216i
$655$	−21.4192			−0.836916
$656$	−4.03656	−	9.69191i	−0.157601	−	0.378406i
$657$	6.03134			0.235305
$658$	34.8272	+	10.5463i	1.35770	+	0.411136i
$659$			19.5992i			0.763476i	0.924271	+	0.381738i	$0.124674\pi$
$659$			19.5992i			0.763476i	−0.924271	+	0.381738i	$0.875326\pi$
$660$	−5.03955	+	7.55808i	−0.196164	+	0.294198i
$661$	−34.8466			−1.35537			−0.677687	−	0.735351i	$-0.737018\pi$
$661$	−34.8466			−1.35537			−0.677687	+	0.735351i	$0.737018\pi$
$662$	−7.23565	+	23.8944i	−0.281222	+	0.928683i
$663$	−3.04465			−0.118244
$664$	−0.0360006	−	0.0437370i	−0.00139709	−	0.00169733i
$665$			24.2110i			0.938862i
$666$	−1.25658	+	4.14964i	−0.0486916	+	0.160795i
$667$	−33.5155	−	9.24209i	−1.29772	−	0.357855i
$668$	−25.0312	+	37.5406i	−0.968487	+	1.45249i
$669$		−	10.5610i		−	0.408311i
$670$	−36.1419	−	10.9444i	−1.39629	−	0.422819i
$671$		−	9.26338i		−	0.357609i
$672$	23.9213	−	2.41459i	0.922783	−	0.0931449i
$673$	29.8650			1.15121			0.575605	−	0.817728i	$-0.304766\pi$
$673$	29.8650			1.15121			0.575605	+	0.817728i	$0.304766\pi$
$674$	23.1701	+	7.01631i	0.892479	+	0.270258i
$675$	−6.18732			−0.238150
$676$	−12.3201	−	8.21475i	−0.473849	−	0.315952i
$677$	−7.52207			−0.289097			−0.144548	−	0.989498i	$-0.546173\pi$
$677$	−7.52207			−0.289097			−0.144548	+	0.989498i	$0.546173\pi$
$678$	11.2387	+	3.40328i	0.431621	+	0.130702i
$679$		−	57.2348i		−	2.19647i
$680$	7.73796	+	9.40082i	0.296737	+	0.360505i
$681$			3.11219i			0.119259i
$682$	−5.40343	+	17.8439i	−0.206908	+	0.683277i
$683$	−17.6865			−0.676753			−0.338377	−	0.941011i	$-0.609878\pi$
$683$	−17.6865			−0.676753			−0.338377	+	0.941011i	$0.609878\pi$
$684$	−1.88963	+	2.83398i	−0.0722519	+	0.108360i
$685$		−	8.77989i		−	0.335463i
$686$	−7.08010	+	23.3807i	−0.270319	+	0.892681i
$687$	17.0499			0.650493
$688$	−38.3267	+	15.9626i	−1.46119	+	0.608568i
$689$			27.7591i			1.05754i
$690$	−19.1826	−	12.1097i	−0.730268	−	0.461010i
$691$	−12.1619			−0.462660			−0.231330	−	0.972875i	$-0.574308\pi$
$691$	−12.1619			−0.462660			−0.231330	+	0.972875i	$0.574308\pi$
$692$	11.2983	−	16.9447i	0.429498	−	0.644140i
$693$		−	5.77167i		−	0.219247i
$694$	−2.29347	+	7.57376i	−0.0870588	+	0.287496i
$695$	31.2665			1.18600
$696$	−13.0307	−	15.8310i	−0.493928	−	0.600071i
$697$			3.37812i			0.127955i
$698$	23.2593	+	7.04333i	0.880378	+	0.266594i
$699$	14.5284			0.549515
$700$	−43.7593	−	29.1777i	−1.65395	−	1.10281i
$701$	22.2613			0.840799			0.420399	−	0.907339i	$-0.361890\pi$
$701$	22.2613			0.840799			0.420399	+	0.907339i	$0.361890\pi$
$702$	3.20191	+	0.969595i	0.120848	+	0.0365950i
$703$		−	5.22139i		−	0.196929i
$704$	−10.6611	−	2.08842i	−0.401807	−	0.0787103i
$705$		−	20.2492i		−	0.762628i
$706$	3.93481	−	12.9940i	0.148088	−	0.489035i
$707$		−	6.28025i		−	0.236193i
$708$	12.9994	+	8.66768i	0.488546	+	0.325751i
$709$	45.4947			1.70859			0.854295	−	0.519788i	$-0.173989\pi$
$709$	45.4947			1.70859			0.854295	+	0.519788i	$0.173989\pi$
$710$	60.9511	+	18.4570i	2.28745	+	0.692680i
$711$	−14.0413			−0.526591
$712$	5.24730	+	6.37493i	0.196651	+	0.238910i
$713$	−44.8832	−	12.3768i	−1.68089	−	0.463515i
$714$	−7.40398	−	2.24205i	−0.277087	−	0.0839068i
$715$	−10.7448			−0.401834
$716$	−20.1201	−	13.4156i	−0.751924	−	0.501366i
$717$			1.56887i			0.0585905i
$718$	7.97918	−	26.3498i	0.297780	−	0.983366i
$719$		−	2.02839i		−	0.0756463i	−0.999284	−	0.0378232i	$-0.987958\pi$
$719$		−	2.02839i		−	0.0756463i	0.999284	−	0.0378232i	$-0.0120424\pi$
$720$	−5.14387	−	12.3506i	−0.191701	−	0.460280i
$721$	−40.8998			−1.52319
$722$	−6.59866	+	21.7909i	−0.245577	+	0.810973i
$723$		−	13.8541i		−	0.515240i
$724$	−8.21084	−	5.47480i	−0.305153	−	0.203469i
$725$			44.8537i			1.66583i
$726$	3.75272	−	12.3927i	0.139277	−	0.459936i
$727$	−43.0958			−1.59834			−0.799168	−	0.601108i	$-0.794726\pi$
$727$	−43.0958			−1.59834			−0.799168	+	0.601108i	$0.794726\pi$
$728$	18.0729	+	21.9567i	0.669827	+	0.813770i
$729$	1.00000			0.0370370
$730$	8.26839	−	27.3049i	0.306027	−	1.01060i
$731$	13.3588			0.494093
$732$	11.3511	+	7.56862i	0.419547	+	0.279744i
$733$	−13.4280			−0.495975			−0.247987	−	0.968763i	$-0.579769\pi$
$733$	−13.4280			−0.495975			−0.247987	+	0.968763i	$0.579769\pi$
$734$	3.20470	−	10.5829i	0.118288	−	0.390624i
$735$	37.0072			1.36503
$736$	4.54890	−	26.7452i	0.167675	−	0.985842i
$737$	−10.8412			−0.399339
$738$	1.07579	−	3.55261i	0.0396005	−	0.130773i
$739$	−0.341465			−0.0125610			−0.00628050	−	0.999980i	$-0.501999\pi$
$739$	−0.341465			−0.0125610			−0.00628050	+	0.999980i	$0.501999\pi$
$740$	17.0635	+	11.3775i	0.627266	+	0.418247i
$741$	−4.02889			−0.148005
$742$	−20.4416	+	67.5046i	−0.750433	+	2.47817i
$743$	10.7100			0.392913			0.196456	−	0.980513i	$-0.437057\pi$
$743$	10.7100			0.392913			0.196456	+	0.980513i	$0.437057\pi$
$744$	−17.4504	−	21.2005i	−0.639764	−	0.777247i
$745$	29.4355			1.07843
$746$	−2.15623	+	7.12057i	−0.0789453	+	0.260703i
$747$		−	0.0200280i		−	0.000732787i
$748$	2.90830	+	1.93919i	0.106338	+	0.0709038i
$749$			82.7373i			3.02316i
$750$	−1.62771	+	5.37520i	−0.0594354	+	0.196275i
$751$	13.3151			0.485874			0.242937	−	0.970042i	$-0.421889\pi$
$751$	13.3151			0.485874			0.242937	+	0.970042i	$0.421889\pi$
$752$	22.3547	−	9.31046i	0.815193	−	0.339517i
$753$			22.7472i			0.828955i
$754$	7.02888	−	23.2116i	0.255977	−	0.845317i
$755$			31.7757i			1.15644i
$756$	7.07242	+	4.71573i	0.257221	+	0.171509i
$757$	8.38541			0.304773			0.152387	−	0.988321i	$-0.451304\pi$
$757$	8.38541			0.304773			0.152387	+	0.988321i	$0.451304\pi$
$758$	−17.1967	−	5.20745i	−0.624611	−	0.189143i
$759$	−6.27827	−	1.73127i	−0.227887	−	0.0628412i
$760$	10.2394	+	12.4398i	0.371422	+	0.451239i
$761$	−53.0560			−1.92328			−0.961639	−	0.274318i	$-0.911548\pi$
$761$	−53.0560			−1.92328			−0.961639	+	0.274318i	$0.911548\pi$
$762$	12.6026	+	3.81629i	0.456544	+	0.138250i
$763$	23.8675			0.864063
$764$	−30.9230	−	20.6188i	−1.11876	−	0.745961i
$765$			4.30481i			0.155641i
$766$	13.4832	−	44.5258i	0.487167	−	1.60878i
$767$			18.4804i			0.667287i
$768$	11.2698	−	11.3575i	0.406662	−	0.409828i
$769$			39.6654i			1.43037i	0.698935	+	0.715185i	$0.253657\pi$
$769$			39.6654i			1.43037i	−0.698935	+	0.715185i	$0.746343\pi$
$770$	−26.1293	−	7.91241i	−0.941635	−	0.285143i
$771$	−1.56221			−0.0562616
$772$	1.61175	+	1.07468i	0.0580082	+	0.0386785i
$773$	−28.5395			−1.02650			−0.513248	−	0.858240i	$-0.671558\pi$
$773$	−28.5395			−1.02650			−0.513248	+	0.858240i	$0.671558\pi$
$774$	−14.0488	−	4.25423i	−0.504974	−	0.152915i
$775$			60.0671i			2.15768i
$776$	−24.2059	−	29.4077i	−0.868943	−	1.05568i
$777$	−13.0304			−0.467463
$778$	−2.03018	+	6.70432i	−0.0727856	+	0.240361i
$779$			4.47016i			0.160160i
$780$	8.77904	−	13.1664i	0.314340	−	0.471432i
$781$	18.2829			0.654214
$782$	−4.65975	+	7.38134i	−0.166632	+	0.263956i
$783$		−	7.24930i		−	0.259069i
$784$	17.0157	+	40.8554i	0.607704	+	1.45912i
$785$	75.8389			2.70681
$786$	2.62473	−	8.66768i	0.0936209	−	0.309166i
$787$		−	6.16750i		−	0.219848i	−0.993940	−	0.109924i	$-0.964939\pi$
$787$		−	6.16750i		−	0.219848i	0.993940	−	0.109924i	$-0.0350607\pi$
$788$	−14.4471	+	21.6671i	−0.514657	+	0.771858i
$789$	11.0502			0.393398
$790$	−19.2493	+	63.5675i	−0.684861	+	2.26163i
$791$			35.2910i			1.25480i
$792$	−2.44097	−	2.96553i	−0.0867362	−	0.105375i
$793$			16.1371i			0.573044i
$794$	−21.2980	−	6.44941i	−0.755838	−	0.228881i
$795$	39.2484			1.39200
$796$	−23.0858	−	15.3931i	−0.818254	−	0.545593i
$797$	3.67557			0.130195			0.0650977	−	0.997879i	$-0.479264\pi$
$797$	3.67557			0.130195			0.0650977	+	0.997879i	$0.479264\pi$
$798$	−9.79746	−	2.96684i	−0.346826	−	0.105025i
$799$	−7.79176			−0.275652
$800$	−34.8238	+	3.51509i	−1.23121	+	0.124277i
$801$			2.91920i			0.103145i
$802$	−31.9188	−	9.66558i	−1.12709	−	0.341303i
$803$		−	8.19039i		−	0.289032i
$804$	8.85774	−	13.2844i	0.312388	−	0.468505i
$805$	18.1237	−	65.7238i	0.638778	−	2.31646i
$806$	9.41292	−	31.0845i	0.331556	−	1.09490i
$807$			17.7522i			0.624907i
$808$	−2.65606	−	3.22684i	−0.0934400	−	0.113520i
$809$	43.7199			1.53711			0.768556	−	0.639783i	$-0.220976\pi$
$809$	43.7199			1.53711			0.768556	+	0.639783i	$0.220976\pi$
$810$	1.37091	−	4.52717i	0.0481687	−	0.159069i
$811$	−1.77417			−0.0622995			−0.0311498	−	0.999515i	$-0.509917\pi$
$811$	−1.77417			−0.0622995			−0.0311498	+	0.999515i	$0.509917\pi$
$812$	34.1857	−	51.2701i	1.19968	−	1.79923i
$813$			5.16603i			0.181181i
$814$	5.63510	+	1.70641i	0.197510	+	0.0598095i
$815$	26.6382			0.933095
$816$	−4.75244	+	1.97933i	−0.166369	+	0.0692904i
$817$	17.6773			0.618450
$818$	−11.8435	+	39.1110i	−0.414098	+	1.36748i
$819$			10.0544i			0.351329i
$820$	−14.6085	−	9.74059i	−0.510149	−	0.340156i
$821$			18.0724i			0.630730i	0.948971	+	0.315365i	$0.102127\pi$
$821$			18.0724i			0.630730i	−0.948971	+	0.315365i	$0.897873\pi$
$822$	3.55296	+	1.07590i	0.123924	+	0.0375262i
$823$		−	27.3675i		−	0.953971i	−0.878911	−	0.476985i	$-0.841729\pi$
$823$		−	27.3675i		−	0.953971i	0.878911	−	0.476985i	$-0.158271\pi$
$824$	−21.0147	+	17.2975i	−0.732081	+	0.602587i
$825$			8.40221i			0.292527i
$826$	−13.6088	+	44.9406i	−0.473511	+	1.56368i
$827$		−	30.2311i		−	1.05124i	−0.850720	−	0.525619i	$-0.823834\pi$
$827$		−	30.2311i		−	1.05124i	0.850720	−	0.525619i	$-0.176166\pi$
$828$	7.25109	−	6.27867i	0.251993	−	0.218199i
$829$		−	28.8709i		−	1.00273i	−0.865237	−	0.501363i	$-0.832832\pi$
$829$		−	28.8709i		−	1.00273i	0.865237	−	0.501363i	$-0.167168\pi$
$830$	−0.0906702	−	0.0274565i	−0.00314721	−	0.000953030i
$831$			23.9970i			0.832446i
$832$	18.5720	+	3.63808i	0.643869	+	0.126128i
$833$		−	14.2402i		−	0.493392i
$834$	−3.83142	+	12.6526i	−0.132671	+	0.438123i
$835$			75.4583i			2.61134i
$836$	3.84846	+	2.56607i	0.133102	+	0.0887493i
$837$		−	9.70810i		−	0.335561i
$838$	16.5331	+	5.00651i	0.571126	+	0.172947i
$839$	53.7723			1.85643			0.928213	−	0.372048i	$-0.121344\pi$
$839$	53.7723			1.85643			0.928213	+	0.372048i	$0.121344\pi$
$840$	31.0445	−	25.5532i	1.07114	−	0.881669i
$841$	−23.5523			−0.812149
$842$	9.98202	−	32.9638i	0.344003	−	1.13601i
$843$			13.6894i			0.471489i
$844$	25.1593	+	16.7756i	0.866018	+	0.577441i
$845$	−24.7639			−0.851904
$846$	8.19422	+	2.48135i	0.281723	+	0.0853107i
$847$	38.9146			1.33712
$848$	18.0462	+	43.3296i	0.619709	+	1.48794i
$849$		−	13.2256i		−	0.453902i
$850$	10.7785	+	3.26391i	0.369699	+	0.111951i
$851$	−3.90860	+	14.1741i	−0.133985	+	0.485883i
$852$	−14.9380	+	22.4033i	−0.511768	+	0.767524i
$853$		−	30.6100i		−	1.04807i	−0.851698	−	0.524033i	$-0.824427\pi$
$853$		−	30.6100i		−	1.04807i	0.851698	−	0.524033i	$-0.175573\pi$
$854$	−11.8832	+	39.2421i	−0.406635	+	1.34284i
$855$			5.69642i			0.194814i
$856$	34.9915	+	42.5111i	1.19599	+	1.45300i
$857$	−1.65741			−0.0566162			−0.0283081	−	0.999599i	$-0.509012\pi$
$857$	−1.65741			−0.0566162			−0.0283081	+	0.999599i	$0.509012\pi$
$858$	1.31668	−	4.34811i	0.0449508	−	0.148442i
$859$	1.69125			0.0577049			0.0288524	−	0.999584i	$-0.490815\pi$
$859$	1.69125			0.0577049			0.0288524	+	0.999584i	$0.490815\pi$
$860$	−38.5192	+	57.7692i	−1.31349	+	1.96991i
$861$	11.1556			0.380183
$862$	2.49982	−	8.25519i	0.0851441	−	0.281173i
$863$			31.6977i			1.07900i	0.841985	+	0.539501i	$0.181387\pi$
$863$			31.6977i			1.07900i	−0.841985	+	0.539501i	$0.818613\pi$
$864$	5.62825	−	0.568111i	0.191477	−	0.0193275i
$865$		−	34.0596i		−	1.15806i
$866$	−17.0008	−	5.14815i	−0.577712	−	0.174941i
$867$	−15.3435			−0.521094
$868$	45.7807	−	68.6597i	1.55390	−	2.33046i
$869$			19.0677i			0.646829i
$870$	−32.8188	−	9.93810i	−1.11266	−	0.336933i
$871$	18.8856			0.639914
$872$	12.2633	−	10.0941i	0.415289	−	0.341831i
$873$		−	13.4664i		−	0.455767i
$874$	−6.16610	+	9.76749i	−0.208572	+	0.330390i
$875$	−16.8788			−0.570608
$876$	10.0362	+	6.69194i	0.339093	+	0.226100i
$877$		−	8.42097i		−	0.284356i	−0.989841	−	0.142178i	$-0.954589\pi$
$877$		−	8.42097i		−	0.284356i	0.989841	−	0.142178i	$-0.0454106\pi$
$878$	−9.43943	−	2.85842i	−0.318565	−	0.0964671i
$879$	−29.3779			−0.990891
$880$	−16.7718	+	6.98523i	−0.565377	+	0.235472i
$881$			0.409682i			0.0138025i	0.999976	+	0.00690126i	$0.00219676\pi$
$881$			0.409682i			0.0138025i	−0.999976	+	0.00690126i	$0.997803\pi$
$882$	−4.53490	+	14.9757i	−0.152698	+	0.504258i
$883$	5.67751			0.191063			0.0955317	−	0.995426i	$-0.469545\pi$
$883$	5.67751			0.191063			0.0955317	+	0.995426i	$0.469545\pi$
$884$	−5.06634	−	3.37812i	−0.170399	−	0.113618i
$885$	26.1293			0.878327
$886$	8.51428	−	28.1169i	0.286043	−	0.944605i
$887$		−	11.9861i		−	0.402454i	−0.979545	−	0.201227i	$-0.935507\pi$
$887$		−	11.9861i		−	0.402454i	0.979545	−	0.201227i	$-0.0644929\pi$
$888$	−6.69512	+	5.51085i	−0.224673	+	0.184932i
$889$			39.5737i			1.32726i
$890$	13.2157	+	4.00195i	0.442992	+	0.134146i
$891$		−	1.35797i		−	0.0454938i
$892$	11.7177	−	17.5736i	0.392337	−	0.588408i
$893$	−10.3106			−0.345031
$894$	−3.60706	+	11.9116i	−0.120638	+	0.398385i
$895$	−40.4423			−1.35184
$896$	42.4844	+	22.5234i	1.41930	+	0.752454i
$897$	10.9369	+	3.01592i	0.365173	+	0.100699i
$898$	2.82972	−	9.34464i	0.0944290	−	0.311835i
$899$	−70.3769			−2.34720
$900$	−10.2958	−	6.86500i	−0.343193	−	0.228833i
$901$		−	15.1026i		−	0.503139i
$902$	−4.82434	−	1.46090i	−0.160633	−	0.0486425i
$903$		−	44.1150i		−	1.46806i
$904$	14.9254	+	18.1328i	0.496411	+	0.603088i
$905$	−16.5041			−0.548616
$906$	−12.8587	−	3.89383i	−0.427200	−	0.129364i
$907$		−	37.0908i		−	1.23158i	−0.787910	−	0.615790i	$-0.788837\pi$
$907$		−	37.0908i		−	1.23158i	0.787910	−	0.615790i	$-0.211163\pi$
$908$	−3.45306	+	5.17873i	−0.114594	+	0.171862i
$909$		−	1.47763i		−	0.0490100i
$910$	45.5180	+	13.7836i	1.50891	+	0.456923i
$911$	−27.3370			−0.905717			−0.452858	−	0.891582i	$-0.649596\pi$
$911$	−27.3370			−0.905717			−0.452858	+	0.891582i	$0.649596\pi$
$912$	−6.28876	+	2.61919i	−0.208242	+	0.0867299i
$913$	−0.0271975			−0.000900105
$914$	49.9551	+	15.1273i	1.65237	+	0.500365i
$915$	22.8161			0.754277
$916$	28.3712	+	18.9173i	0.937412	+	0.625045i
$917$	27.2176			0.898804
$918$	−1.74203	−	0.527516i	−0.0574955	−	0.0174106i
$919$	−25.0423			−0.826069			−0.413035	−	0.910715i	$-0.635531\pi$
$919$	−25.0423			−0.826069			−0.413035	+	0.910715i	$0.635531\pi$
$920$	−18.4840	−	41.4344i	−0.609400	−	1.36605i
$921$	30.6840			1.01107
$922$	10.3743	+	3.14153i	0.341660	+	0.103461i
$923$	−31.8493			−1.04833
$924$	6.40382	−	9.60414i	0.210670	−	0.315953i
$925$	18.9692			0.623704
$926$	−27.3808	−	8.29137i	−0.899787	−	0.272471i
$927$	−9.62302			−0.316061
$928$	−4.11841	−	40.8009i	−0.135193	−	1.33935i
$929$	45.5702			1.49511			0.747555	−	0.664200i	$-0.231228\pi$
$929$	45.5702			1.49511			0.747555	+	0.664200i	$0.231228\pi$
$930$	−43.9502	−	13.3089i	−1.44118	−	0.436416i
$931$		−	18.8435i		−	0.617572i
$932$	24.1755	+	16.1197i	0.791894	+	0.528017i
$933$		−	0.622018i		−	0.0203639i
$934$	−44.6976	−	13.5352i	−1.46255	−	0.442885i
$935$	5.84582			0.191179
$936$	4.25224	+	5.16603i	0.138989	+	0.168857i
$937$		−	18.4326i		−	0.602166i	−0.953598	−	0.301083i	$-0.902652\pi$
$937$		−	18.4326i		−	0.602166i	0.953598	−	0.301083i	$-0.0973481\pi$
$938$	45.9260	+	13.9072i	1.49954	+	0.454086i
$939$			10.1923i			0.332612i
$940$	22.4670	−	33.6949i	0.732793	−	1.09901i
$941$	7.16226			0.233483			0.116741	−	0.993162i	$-0.462755\pi$
$941$	7.16226			0.233483			0.116741	+	0.993162i	$0.462755\pi$
$942$	−9.29338	+	30.6897i	−0.302795	+	0.999925i
$943$	3.34625	−	12.1348i	0.108969	−	0.395164i
$944$	12.0141	+	28.8463i	0.391026	+	0.938868i
$945$	14.2159			0.462442
$946$	−5.77712	+	19.0779i	−0.187830	+	0.620276i
$947$	5.24153			0.170327			0.0851634	−	0.996367i	$-0.472859\pi$
$947$	5.24153			0.170327			0.0851634	+	0.996367i	$0.472859\pi$
$948$	−23.3650	−	15.5793i	−0.758860	−	0.505991i
$949$			14.2679i			0.463155i
$950$	14.2628	+	4.31903i	0.462747	+	0.140128i
$951$		−	15.3301i		−	0.497112i
$952$	−9.83272	−	11.9457i	−0.318680	−	0.387164i
$953$		−	47.7506i		−	1.54679i	−0.633923	−	0.773397i	$-0.718556\pi$
$953$		−	47.7506i		−	1.54679i	0.633923	−	0.773397i	$-0.281444\pi$
$954$	−4.80954	+	15.8826i	−0.155715	+	0.514220i
$955$	−62.1567			−2.01134
$956$	−1.74070	+	2.61062i	−0.0562984	+	0.0844335i
$957$	−9.84434			−0.318222
$958$	−17.3579	+	57.3213i	−0.560808	+	1.85197i
$959$			11.1567i			0.360269i
$960$	5.14387	−	26.2589i	0.166018	−	0.847502i
$961$	−63.2472			−2.04023
$962$	−9.81649	−	2.97261i	−0.316496	−	0.0958406i
$963$			19.4666i			0.627304i
$964$	15.3715	−	23.0535i	0.495084	−	0.742503i
$965$	3.23969			0.104289
$966$	24.3755	+	15.3880i	0.784270	+	0.495101i
$967$			20.1259i			0.647205i	0.946193	+	0.323603i	$0.104894\pi$
$967$			20.1259i			0.647205i	−0.946193	+	0.323603i	$0.895106\pi$
$968$	19.9946	−	16.4579i	0.642651	−	0.528976i
$969$	2.19195			0.0704156
$970$	−60.9645	−	18.4611i	−1.95745	−	0.592750i
$971$			1.26842i			0.0407055i	0.999793	+	0.0203528i	$0.00647893\pi$
$971$			1.26842i			0.0407055i	−0.999793	+	0.0203528i	$0.993521\pi$
$972$	1.66402	+	1.10953i	0.0533733	+	0.0355881i
$973$	−39.7307			−1.27371
$974$	−4.19846	−	1.27137i	−0.134527	−	0.0407373i
$975$		−	14.6369i		−	0.468755i
$976$	10.4907	+	25.1886i	0.335800	+	0.806268i
$977$			1.39122i			0.0445091i	0.999752	+	0.0222546i	$0.00708443\pi$
$977$			1.39122i			0.0445091i	−0.999752	+	0.0222546i	$0.992916\pi$
$978$	−3.26427	+	10.7797i	−0.104380	+	0.344696i
$979$	3.96419			0.126696
$980$	61.5806	+	41.0605i	1.96712	+	1.31163i
$981$	5.61561			0.179293
$982$	−3.48024	+	11.4929i	−0.111059	+	0.366752i
$983$	−50.0347			−1.59586			−0.797929	−	0.602752i	$-0.794071\pi$
$983$	−50.0347			−1.59586			−0.797929	+	0.602752i	$0.794071\pi$
$984$	5.73185	−	4.71798i	0.182725	−	0.150404i
$985$			43.5518i			1.38768i
$986$	−3.82412	+	12.6285i	−0.121785	+	0.402173i
$987$			25.7309i			0.819023i
$988$	−6.70413	−	4.47016i	−0.213287	−	0.142215i
$989$	−47.9872	−	13.2328i	−1.52591	−	0.420778i
$990$	−6.14777	−	1.86165i	−0.195389	−	0.0591672i
$991$			43.7351i			1.38929i	0.719352	+	0.694646i	$0.244439\pi$
$991$			43.7351i			1.38929i	−0.719352	+	0.694646i	$0.755561\pi$
$992$	−5.51528	−	54.6397i	−0.175110	−	1.73481i
$993$	−17.6536			−0.560220
$994$	−77.4513	−	23.4536i	−2.45661	−	0.743903i
$995$	−46.4034			−1.47109
$996$	0.0222216	−	0.0333269i	0.000704120	−	0.00105600i
$997$			46.9693i			1.48753i	0.668440	+	0.743766i	$0.266962\pi$
$997$			46.9693i			1.48753i	−0.668440	+	0.743766i	$0.733038\pi$
$998$	−13.9852	+	46.1835i	−0.442693	+	1.46191i
$999$	−3.06582			−0.0969983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.b.91.11	yes	24
4.3	odd	2		2208.2.n.b.367.2		24
8.3	odd	2	inner	552.2.n.b.91.10	yes	24
8.5	even	2		2208.2.n.b.367.24		24
23.22	odd	2	inner	552.2.n.b.91.12	yes	24
92.91	even	2		2208.2.n.b.367.23		24
184.45	odd	2		2208.2.n.b.367.1		24
184.91	even	2	inner	552.2.n.b.91.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.9	✓	24	184.91	even	2	inner
552.2.n.b.91.10	yes	24	8.3	odd	2	inner
552.2.n.b.91.11	yes	24	1.1	even	1	trivial
552.2.n.b.91.12	yes	24	23.22	odd	2	inner
2208.2.n.b.367.1		24	184.45	odd	2
2208.2.n.b.367.2		24	4.3	odd	2
2208.2.n.b.367.23		24	92.91	even	2
2208.2.n.b.367.24		24	8.5	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)

\(f(q)\)	\(=\)	\(q+(-0.409868 + 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} -3.34475 q^{5} +(0.409868 - 1.35352i) q^{6} +4.25021 q^{7} +(2.18379 - 1.79751i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.409868 + 1.35352i) q^{2} -1.00000 q^{3} +(-1.66402 - 1.10953i) q^{4} -3.34475 q^{5} +(0.409868 - 1.35352i) q^{6} +4.25021 q^{7} +(2.18379 - 1.79751i) q^{8} +1.00000 q^{9} +(1.37091 - 4.52717i) q^{10} -1.35797i q^{11} +(1.66402 + 1.10953i) q^{12} +2.36562i q^{13} +(-1.74203 + 5.75273i) q^{14} +3.34475 q^{15} +(1.53790 + 3.69254i) q^{16} -1.28704i q^{17} +(-0.409868 + 1.35352i) q^{18} -1.70310i q^{19} +(5.56571 + 3.71109i) q^{20} -4.25021 q^{21} +(1.83804 + 0.556590i) q^{22} +(-1.27490 + 4.62327i) q^{23} +(-2.18379 + 1.79751i) q^{24} +6.18732 q^{25} +(-3.20191 - 0.969595i) q^{26} -1.00000 q^{27} +(-7.07242 - 4.71573i) q^{28} +7.24930i q^{29} +(-1.37091 + 4.52717i) q^{30} +9.70810i q^{31} +(-5.62825 + 0.568111i) q^{32} +1.35797i q^{33} +(1.74203 + 0.527516i) q^{34} -14.2159 q^{35} +(-1.66402 - 1.10953i) q^{36} +3.06582 q^{37} +(2.30517 + 0.698046i) q^{38} -2.36562i q^{39} +(-7.30423 + 6.01222i) q^{40} -2.62473 q^{41} +(1.74203 - 5.75273i) q^{42} +10.3795i q^{43} +(-1.50671 + 2.25969i) q^{44} -3.34475 q^{45} +(-5.73514 - 3.62053i) q^{46} -6.05402i q^{47} +(-1.53790 - 3.69254i) q^{48} +11.0643 q^{49} +(-2.53599 + 8.37464i) q^{50} +1.28704i q^{51} +(2.62473 - 3.93644i) q^{52} +11.7344 q^{53} +(0.409868 - 1.35352i) q^{54} +4.54207i q^{55} +(9.28158 - 7.63981i) q^{56} +1.70310i q^{57} +(-9.81205 - 2.97126i) q^{58} +7.81205 q^{59} +(-5.56571 - 3.71109i) q^{60} +6.82148 q^{61} +(-13.1401 - 3.97904i) q^{62} +4.25021 q^{63} +(1.53790 - 7.85079i) q^{64} -7.91241i q^{65} +(-1.83804 - 0.556590i) q^{66} -7.98334i q^{67} +(-1.42800 + 2.14165i) q^{68} +(1.27490 - 4.62327i) q^{69} +(5.82664 - 19.2414i) q^{70} +13.4634i q^{71} +(2.18379 - 1.79751i) q^{72} +6.03134 q^{73} +(-1.25658 + 4.14964i) q^{74} -6.18732 q^{75} +(-1.88963 + 2.83398i) q^{76} -5.77167i q^{77} +(3.20191 + 0.969595i) q^{78} -14.0413 q^{79} +(-5.14387 - 12.3506i) q^{80} +1.00000 q^{81} +(1.07579 - 3.55261i) q^{82} -0.0200280i q^{83} +(7.07242 + 4.71573i) q^{84} +4.30481i q^{85} +(-14.0488 - 4.25423i) q^{86} -7.24930i q^{87} +(-2.44097 - 2.96553i) q^{88} +2.91920i q^{89} +(1.37091 - 4.52717i) q^{90} +10.0544i q^{91} +(7.25109 - 6.27867i) q^{92} -9.70810i q^{93} +(8.19422 + 2.48135i) q^{94} +5.69642i q^{95} +(5.62825 - 0.568111i) q^{96} -13.4664i q^{97} +(-4.53490 + 14.9757i) q^{98} -1.35797i 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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