LMFDB - Embedded newform 504.2.bk.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(19,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("504.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bk (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.144054149089536.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 $ x^12 - 3x^11 + x^9 + 48x^8 - 189x^7 + 431x^6 - 654x^5 + 624x^4 - 340x^3 + 96x^2 - 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.5
Root			$0.609850 + 0.457915i$ of defining polynomial
Character	$\chi$	$=$	504.19
Dual form			504.2.bk.a.451.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30084 - 0.554812i) q^{2} +(1.38437 - 1.44344i) q^{4} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(1.00000 - 2.64575i) q^{8} +O(q^{10})$	\(q+(1.30084 - 0.554812i) q^{2} +(1.38437 - 1.44344i) q^{4} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(1.00000 - 2.64575i) q^{8} +(0.117294 - 0.969037i) q^{10} +(1.63090 + 2.82480i) q^{11} -5.27279 q^{13} +(3.30619 - 1.75189i) q^{14} +(-0.167055 - 3.99651i) q^{16} +(2.20393 - 1.27244i) q^{17} +(-0.484848 - 0.279927i) q^{19} +(-0.385053 - 1.32564i) q^{20} +(3.68878 + 2.76977i) q^{22} +(-2.50610 - 1.44690i) q^{23} +(2.26180 + 3.91756i) q^{25} +(-6.85905 + 2.92541i) q^{26} +(3.32885 - 4.11324i) q^{28} +0.444621i q^{29} +(-4.45228 - 7.71158i) q^{31} +(-2.43462 - 5.10613i) q^{32} +(2.16099 - 2.87800i) q^{34} +(0.776954 - 1.65261i) q^{35} +(6.00295 + 3.46580i) q^{37} +(-0.786017 - 0.0951408i) q^{38} +(-1.23637 - 1.51081i) q^{40} +9.76765i q^{41} +(6.33521 + 1.55645i) q^{44} +(-4.06279 - 0.491767i) q^{46} +(2.20094 - 3.81214i) q^{47} +(6.90116 - 1.17220i) q^{49} +(5.11575 + 3.84124i) q^{50} +(-7.29948 + 7.61097i) q^{52} +(-8.17440 + 4.71949i) q^{53} +2.25134 q^{55} +(2.04822 - 7.19756i) q^{56} +(0.246681 + 0.578380i) q^{58} +(-8.59663 + 4.96327i) q^{59} +(-5.23284 + 9.06355i) q^{61} +(-10.0702 - 7.56134i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(-1.81968 + 3.15177i) q^{65} +(-1.45058 - 2.51247i) q^{67} +(1.21435 - 4.94277i) q^{68} +(0.0938060 - 2.58084i) q^{70} +5.29150i q^{71} +(-5.28541 + 3.05153i) q^{73} +(9.73174 + 1.17795i) q^{74} +(-1.07527 + 0.312329i) q^{76} +(4.92768 + 7.08473i) q^{77} +(5.01803 + 2.89716i) q^{79} +(-2.44654 - 1.27937i) q^{80} +(5.41921 + 12.7061i) q^{82} +1.83845i q^{83} -1.75651i q^{85} +(9.10463 - 1.49016i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-13.9012 + 1.17220i) q^{91} +(-5.55787 + 1.61437i) q^{92} +(0.748048 - 6.18008i) q^{94} +(-0.334649 + 0.193210i) q^{95} +7.42325i q^{97} +(8.32695 - 5.35368i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^8	$ 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58} - 42 q^{59} - 72 q^{64} + 12 q^{65} + 30 q^{67} + 36 q^{68} + 30 q^{70} + 18 q^{73} - 12 q^{74} - 36 q^{80} + 54 q^{82} + 6 q^{88} - 18 q^{89} - 72 q^{91} - 60 q^{92} - 12 q^{94} + 6 q^{98}+O(q^{100}) $ 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	1.30084	−	0.554812i	0.919832	−	0.392311i
$2$	1.30084	−	0.554812i	0.919832	−	0.392311i
$3$		0			0
$3$		0			0
$4$	1.38437	−	1.44344i	0.692184	−	0.721721i
$5$	0.345107	−	0.597743i	0.154337	−	0.267319i	−0.778481	−	0.627669i	$-0.784009\pi$
$5$	0.345107	−	0.597743i	0.154337	−	0.267319i	0.932817	+	0.360350i	$0.117343\pi$
$6$		0			0
$7$	2.63639	−	0.222310i	0.996464	−	0.0840255i
$7$	2.63639	−	0.222310i	0.996464	−	0.0840255i
$8$	1.00000	−	2.64575i	0.353553	−	0.935414i
$9$		0			0
$10$	0.117294	−	0.969037i	0.0370916	−	0.306436i
$11$	1.63090	+	2.82480i	0.491735	+	0.851710i	0.999955	−	0.00951723i	$-0.00302947\pi$
$11$	1.63090	+	2.82480i	0.491735	+	0.851710i	−0.508220	+	0.861228i	$0.669696\pi$
$12$		0			0
$13$	−5.27279			−1.46241			−0.731204	−	0.682158i	$-0.761041\pi$
$13$	−5.27279			−1.46241			−0.731204	+	0.682158i	$0.761041\pi$
$14$	3.30619	−	1.75189i	0.883615	−	0.468213i
$15$		0			0
$16$	−0.167055	−	3.99651i	−0.0417638	−	0.999128i
$17$	2.20393	−	1.27244i	0.534531	−	0.308612i	−0.208329	−	0.978059i	$-0.566802\pi$
$17$	2.20393	−	1.27244i	0.534531	−	0.308612i	0.742860	+	0.669447i	$0.233469\pi$
$18$		0			0
$19$	−0.484848	−	0.279927i	−0.111232	−	0.0642197i	0.443352	−	0.896348i	$-0.353789\pi$
$19$	−0.484848	−	0.279927i	−0.111232	−	0.0642197i	−0.554584	+	0.832128i	$0.687123\pi$
$20$	−0.385053	−	1.32564i	−0.0861005	−	0.296422i
$21$		0			0
$22$	3.68878	+	2.76977i	0.786450	+	0.590518i
$23$	−2.50610	−	1.44690i	−0.522558	−	0.301699i	0.215423	−	0.976521i	$-0.430887\pi$
$23$	−2.50610	−	1.44690i	−0.522558	−	0.301699i	−0.737981	+	0.674822i	$0.764220\pi$
$24$		0			0
$25$	2.26180	+	3.91756i	0.452360	+	0.783511i
$26$	−6.85905	+	2.92541i	−1.34517	+	0.573720i
$27$		0			0
$28$	3.32885	−	4.11324i	0.629093	−	0.777330i
$29$			0.444621i			0.0825640i	0.999148	+	0.0412820i	$0.0131442\pi$
$29$			0.444621i			0.0825640i	−0.999148	+	0.0412820i	$0.986856\pi$
$30$		0			0
$31$	−4.45228	−	7.71158i	−0.799653	−	1.38504i	−0.919842	−	0.392289i	$-0.871683\pi$
$31$	−4.45228	−	7.71158i	−0.799653	−	1.38504i	0.120189	−	0.992751i	$-0.461650\pi$
$32$	−2.43462	−	5.10613i	−0.430385	−	0.902646i
$33$		0			0
$34$	2.16099	−	2.87800i	0.370607	−	0.493574i
$35$	0.776954	−	1.65261i	0.131329	−	0.279342i
$36$		0			0
$37$	6.00295	+	3.46580i	0.986879	+	0.569775i	0.904340	−	0.426813i	$-0.140364\pi$
$37$	6.00295	+	3.46580i	0.986879	+	0.569775i	0.0825390	+	0.996588i	$0.473697\pi$
$38$	−0.786017	−	0.0951408i	−0.127509	−	0.0154339i
$39$		0			0
$40$	−1.23637	−	1.51081i	−0.195488	−	0.238880i
$41$			9.76765i			1.52545i	0.646723	+	0.762725i	$0.276139\pi$
$41$			9.76765i			1.52545i	−0.646723	+	0.762725i	$0.723861\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	6.33521	+	1.55645i	0.955069	+	0.234644i
$45$		0			0
$46$	−4.06279	−	0.491767i	−0.599026	−	0.0725071i
$47$	2.20094	−	3.81214i	0.321040	−	0.556057i	−0.659663	−	0.751561i	$-0.729301\pi$
$47$	2.20094	−	3.81214i	0.321040	−	0.556057i	0.980703	+	0.195504i	$0.0626343\pi$
$48$		0			0
$49$	6.90116	−	1.17220i	0.985879	−	0.167457i
$50$	5.11575	+	3.84124i	0.723476	+	0.543233i
$51$		0			0
$52$	−7.29948	+	7.61097i	−1.01226	+	1.05545i
$53$	−8.17440	+	4.71949i	−1.12284	+	0.648272i	−0.942124	−	0.335263i	$-0.891175\pi$
$53$	−8.17440	+	4.71949i	−1.12284	+	0.648272i	−0.180716	+	0.983535i	$0.557841\pi$
$54$		0			0
$55$	2.25134			0.303571
$56$	2.04822	−	7.19756i	0.273704	−	0.961814i
$57$		0			0
$58$	0.246681	+	0.578380i	0.0323908	+	0.0759451i
$59$	−8.59663	+	4.96327i	−1.11919	+	0.646162i	−0.941193	−	0.337869i	$-0.890294\pi$
$59$	−8.59663	+	4.96327i	−1.11919	+	0.646162i	−0.177993	+	0.984032i	$0.556960\pi$
$60$		0			0
$61$	−5.23284	+	9.06355i	−0.669997	+	1.16047i	0.307907	+	0.951416i	$0.400371\pi$
$61$	−5.23284	+	9.06355i	−0.669997	+	1.16047i	−0.977904	+	0.209053i	$0.932962\pi$
$62$	−10.0702	−	7.56134i	−1.27891	−	0.960292i
$63$		0			0
$64$	−6.00000	−	5.29150i	−0.750000	−	0.661438i
$65$	−1.81968	+	3.15177i	−0.225703	+	0.390929i
$66$		0			0
$67$	−1.45058	−	2.51247i	−0.177216	−	0.306948i	0.763710	−	0.645560i	$-0.223376\pi$
$67$	−1.45058	−	2.51247i	−0.177216	−	0.306948i	−0.940926	+	0.338612i	$0.890043\pi$
$68$	1.21435	−	4.94277i	0.147262	−	0.599398i
$69$		0			0
$70$	0.0938060	−	2.58084i	0.0112120	−	0.308469i
$71$			5.29150i			0.627986i	0.949425	+	0.313993i	$0.101667\pi$
$71$			5.29150i			0.627986i	−0.949425	+	0.313993i	$0.898333\pi$
$72$		0			0
$73$	−5.28541	+	3.05153i	−0.618610	+	0.357155i	−0.776328	−	0.630330i	$-0.782920\pi$
$73$	−5.28541	+	3.05153i	−0.618610	+	0.357155i	0.157718	+	0.987484i	$0.449586\pi$
$74$	9.73174	+	1.17795i	1.13129	+	0.136934i
$75$		0			0
$76$	−1.07527	+	0.312329i	−0.123342	+	0.0358266i
$77$	4.92768	+	7.08473i	0.561562	+	0.807380i
$78$		0			0
$79$	5.01803	+	2.89716i	0.564573	+	0.325956i	0.754979	−	0.655749i	$-0.227647\pi$
$79$	5.01803	+	2.89716i	0.564573	+	0.325956i	−0.190406	+	0.981705i	$0.560980\pi$
$80$	−2.44654	−	1.27937i	−0.273531	−	0.143038i
$81$		0			0
$82$	5.41921	+	12.7061i	0.598451	+	1.40316i
$83$			1.83845i			0.201796i	0.994897	+	0.100898i	$0.0321716\pi$
$83$			1.83845i			0.201796i	−0.994897	+	0.100898i	$0.967828\pi$
$84$		0			0
$85$		−	1.75651i		−	0.190520i
$86$		0			0
$87$		0			0
$88$	9.10463	−	1.49016i	0.970557	−	0.158851i
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	0.418389	−	0.908268i	$-0.362595\pi$
$89$	−1.50000	−	0.866025i	−0.159000	−	0.0917985i	−0.577389	+	0.816469i	$0.695928\pi$
$90$		0			0
$91$	−13.9012	+	1.17220i	−1.45724	+	0.122880i
$92$	−5.55787	+	1.61437i	−0.579448	+	0.168310i
$93$		0			0
$94$	0.748048	−	6.18008i	0.0771553	−	0.637427i
$95$	−0.334649	+	0.193210i	−0.0343343	+	0.0198229i
$96$		0			0
$97$			7.42325i			0.753717i	0.926271	+	0.376859i	$0.122996\pi$
$97$			7.42325i			0.753717i	−0.926271	+	0.376859i	$0.877004\pi$
$98$	8.32695	−	5.35368i	0.841149	−	0.540804i
$99$		0			0
$100$	8.78593	+	2.15855i	0.878593	+	0.215855i
$101$	−6.30811	−	10.9260i	−0.627681	−	1.08717i	−0.988016	−	0.154352i	$-0.950671\pi$
$101$	−6.30811	−	10.9260i	−0.627681	−	1.08717i	0.360335	−	0.932823i	$-0.382662\pi$
$102$		0			0
$103$	3.19631	−	5.53618i	0.314942	−	0.545496i	−0.664483	−	0.747303i	$-0.731348\pi$
$103$	3.19631	−	5.53618i	0.314942	−	0.545496i	0.979425	+	0.201808i	$0.0646816\pi$
$104$	−5.27279	+	13.9505i	−0.517040	+	1.36796i
$105$		0			0
$106$	−8.01515	+	10.6746i	−0.778500	+	1.03680i
$107$	1.51515	−	2.62432i	0.146475	−	0.253703i	−0.783447	−	0.621458i	$-0.786540\pi$
$107$	1.51515	−	2.62432i	0.146475	−	0.253703i	0.929922	+	0.367756i	$0.119874\pi$
$108$		0			0
$109$	−7.25892	+	4.19094i	−0.695278	+	0.401419i	−0.805586	−	0.592478i	$-0.798150\pi$
$109$	−7.25892	+	4.19094i	−0.695278	+	0.401419i	0.110308	+	0.993897i	$0.464816\pi$
$110$	2.92863	−	1.24907i	0.279234	−	0.119094i
$111$		0			0
$112$	−1.32889	−	10.4992i	−0.125568	−	0.992085i
$113$	12.6260			1.18775			0.593875	−	0.804557i	$-0.297597\pi$
$113$	12.6260			1.18775			0.593875	+	0.804557i	$0.297597\pi$
$114$		0			0
$115$	−1.72974	+	0.998669i	−0.161300	+	0.0931263i
$116$	0.641785	+	0.615519i	0.0595882	+	0.0571495i
$117$		0			0
$118$	−8.42916	+	11.2259i	−0.775967	+	1.03343i
$119$	5.52755	−	3.84461i	0.506709	−	0.352434i
$120$		0			0
$121$	0.180323	−	0.312329i	0.0163930	−	0.0283935i
$122$	−1.77852	+	14.6935i	−0.161020	+	1.33028i
$123$		0			0
$124$	−17.2948	−	4.24904i	−1.55312	−	0.381575i
$125$	6.57333			0.587936
$126$		0			0
$127$		−	6.18074i		−	0.548452i	−0.961665	−	0.274226i	$-0.911578\pi$
$127$		−	6.18074i		−	0.548452i	0.961665	−	0.274226i	$-0.0884217\pi$
$128$	−10.7408	−	3.55452i	−0.949364	−	0.314178i
$129$		0			0
$130$	−0.618466	+	5.10953i	−0.0542431	+	0.448135i
$131$	1.81122	+	1.04571i	0.158247	+	0.0913642i	0.577032	−	0.816721i	$-0.304211\pi$
$131$	1.81122	+	1.04571i	0.158247	+	0.0913642i	−0.418785	+	0.908085i	$0.637544\pi$
$132$		0			0
$133$	−1.34048	−	0.630212i	−0.116235	−	0.0546463i
$134$	−3.28092	−	2.46353i	−0.283428	−	0.212816i
$135$		0			0
$136$	−1.16263	−	7.10348i	−0.0996945	−	0.609119i
$137$	−2.43543	−	4.21828i	−0.208073	−	0.360392i	0.743035	−	0.669253i	$-0.233386\pi$
$137$	−2.43543	−	4.21828i	−0.208073	−	0.360392i	−0.951107	+	0.308861i	$0.900052\pi$
$138$		0			0
$139$			1.83845i			0.155935i	0.996956	+	0.0779677i	$0.0248431\pi$
$139$			1.83845i			0.155935i	−0.996956	+	0.0779677i	$0.975157\pi$
$140$	−1.30985	−	3.40930i	−0.110703	−	0.288139i
$141$		0			0
$142$	2.93579	+	6.88340i	0.246366	+	0.577642i
$143$	−8.59940	−	14.8946i	−0.719118	−	1.24555i
$144$		0			0
$145$	0.265769	+	0.153442i	0.0220709	+	0.0127426i
$146$	−5.18244	+	6.90196i	−0.428902	+	0.571210i
$147$		0			0
$148$	13.3130	−	3.86697i	1.09432	−	0.317863i
$149$	7.68854	+	4.43898i	0.629870	+	0.363655i	0.780702	−	0.624904i	$-0.214862\pi$
$149$	7.68854	+	4.43898i	0.629870	+	0.363655i	−0.150832	+	0.988559i	$0.548195\pi$
$150$		0			0
$151$	1.69142	−	0.976544i	0.137646	−	0.0794700i	−0.429596	−	0.903021i	$-0.641344\pi$
$151$	1.69142	−	0.976544i	0.137646	−	0.0794700i	0.567242	+	0.823551i	$0.308011\pi$
$152$	−1.22547	+	1.00286i	−0.0993984	+	0.0813427i
$153$		0			0
$154$	10.3408	+	6.48216i	0.833287	+	0.522347i
$155$	−6.14605			−0.493663
$156$		0			0
$157$	0.650268	+	1.12630i	0.0518970	+	0.0898883i	0.890807	−	0.454382i	$-0.150140\pi$
$157$	0.650268	+	1.12630i	0.0518970	+	0.0898883i	−0.838910	+	0.544270i	$0.816807\pi$
$158$	8.13504	+	0.984679i	0.647189	+	0.0783368i
$159$		0			0
$160$	−3.89236	−	0.306884i	−0.307718	−	0.0242613i
$161$	−6.92873	−	3.25746i	−0.546060	−	0.256724i
$162$		0			0
$163$	4.30453	−	7.45566i	0.337156	−	0.583972i	−0.646740	−	0.762710i	$-0.723868\pi$
$163$	4.30453	−	7.45566i	0.337156	−	0.583972i	0.983897	+	0.178738i	$0.0572015\pi$
$164$	14.0990	+	13.5220i	1.10095	+	1.05589i
$165$		0			0
$166$	1.01999	+	2.39153i	0.0791669	+	0.185619i
$167$	5.27279			0.408021			0.204010	−	0.978969i	$-0.434602\pi$
$167$	5.27279			0.408021			0.204010	+	0.978969i	$0.434602\pi$
$168$		0			0
$169$	14.8023			1.13864
$170$	−0.974533	−	2.28494i	−0.0747432	−	0.175247i
$171$		0			0
$172$		0			0
$173$	−8.25429	+	14.2969i	−0.627562	+	1.08697i	0.360477	+	0.932768i	$0.382614\pi$
$173$	−8.25429	+	14.2969i	−0.627562	+	1.08697i	−0.988039	+	0.154202i	$0.950719\pi$
$174$		0			0
$175$	6.83392	+	9.82540i	0.516596	+	0.742731i
$176$	11.0169	−	6.98981i	0.830430	−	0.526877i
$177$		0			0
$178$	−2.43174	−	0.294342i	−0.182267	−	0.0220619i
$179$	−11.1242	−	19.2677i	−0.831462	−	1.44013i	−0.896879	−	0.442276i	$-0.854171\pi$
$179$	−11.1242	−	19.2677i	−0.831462	−	1.44013i	0.0654170	−	0.997858i	$-0.479162\pi$
$180$		0			0
$181$	10.0244			0.745108			0.372554	−	0.928011i	$-0.378482\pi$
$181$	10.0244			0.745108			0.372554	+	0.928011i	$0.378482\pi$
$182$	−17.4328	+	9.23737i	−1.29221	+	0.684719i
$183$		0			0
$184$	−6.33423	+	5.18362i	−0.466966	+	0.382141i
$185$	4.14332	−	2.39215i	0.304623	−	0.175874i
$186$		0			0
$187$	7.18878	+	4.15044i	0.525695	+	0.303510i
$188$	−2.45570	−	8.45433i	−0.179100	−	0.616595i
$189$		0			0
$190$	−0.328130	+	0.437002i	−0.0238050	+	0.0317035i
$191$	21.6511	+	12.5003i	1.56662	+	0.904487i	0.996559	+	0.0828820i	$0.0264125\pi$
$191$	21.6511	+	12.5003i	1.56662	+	0.904487i	0.570058	+	0.821605i	$0.306921\pi$
$192$		0			0
$193$	−5.69723	−	9.86789i	−0.410095	−	0.710306i	0.584804	−	0.811174i	$-0.301171\pi$
$193$	−5.69723	−	9.86789i	−0.410095	−	0.710306i	−0.994900	+	0.100868i	$0.967838\pi$
$194$	4.11851	+	9.65646i	0.295692	+	0.693294i
$195$		0			0
$196$	7.86174	−	11.5842i	0.561553	−	0.827441i
$197$		−	10.1384i		−	0.722330i	−0.932502	−	0.361165i	$-0.882379\pi$
$197$		−	10.1384i		−	0.722330i	0.932502	−	0.361165i	$-0.117621\pi$
$198$		0			0
$199$	−5.40309	−	9.35842i	−0.383015	−	0.663401i	0.608477	−	0.793572i	$-0.291781\pi$
$199$	−5.40309	−	9.35842i	−0.383015	−	0.663401i	−0.991492	+	0.130171i	$0.958447\pi$
$200$	12.6267	−	2.06661i	0.892841	−	0.146131i
$201$		0			0
$202$	−14.2677	−	10.7131i	−1.00387	−	0.753772i
$203$	0.0988439	+	1.17220i	0.00693748	+	0.0822720i
$204$		0			0
$205$	5.83854	+	3.37088i	0.407781	+	0.235433i
$206$	1.08635	−	8.97503i	0.0756898	−	0.625320i
$207$		0			0
$208$	0.880847	+	21.0728i	0.0610757	+	1.46113i
$209$		−	1.82613i		−	0.126316i
$210$		0			0
$211$	−15.8023			−1.08788			−0.543938	−	0.839125i	$-0.683067\pi$
$211$	−15.8023			−1.08788			−0.543938	+	0.839125i	$0.683067\pi$
$212$	−4.50405	+	18.3328i	−0.309340	+	1.25910i
$213$		0			0
$214$	0.514965	−	4.25444i	0.0352023	−	0.290828i
$215$		0			0
$216$		0			0
$217$	−13.4523	−	19.3410i	−0.913204	−	1.31295i
$218$	−7.11750	+	9.47907i	−0.482058	+	0.642004i
$219$		0			0
$220$	3.11668	−	3.24968i	0.210127	−	0.219094i
$221$	−11.6208	+	6.70930i	−0.781703	+	0.451316i
$222$		0			0
$223$	−14.8885			−0.997006			−0.498503	−	0.866888i	$-0.666117\pi$
$223$	−14.8885			−0.997006			−0.498503	+	0.866888i	$0.666117\pi$
$224$	−7.55378	−	12.9205i	−0.504708	−	0.863290i
$225$		0			0
$226$	16.4243	−	7.00503i	1.09253	−	0.465968i
$227$	24.3726	−	14.0715i	1.61767	−	0.933960i	0.630145	−	0.776477i	$-0.282995\pi$
$227$	24.3726	−	14.0715i	1.61767	−	0.933960i	0.987522	−	0.157483i	$-0.0503379\pi$
$228$		0			0
$229$	3.36655	−	5.83104i	0.222468	−	0.385326i	−0.733089	−	0.680133i	$-0.761922\pi$
$229$	3.36655	−	5.83104i	0.222468	−	0.385326i	0.955557	+	0.294807i	$0.0952553\pi$
$230$	−1.69605	+	2.25879i	−0.111834	+	0.148940i
$231$		0			0
$232$	1.17636	+	0.444621i	0.0772316	+	0.0291908i
$233$	8.58148	−	14.8636i	0.562191	−	0.973744i	−0.435114	−	0.900376i	$-0.643292\pi$
$233$	8.58148	−	14.8636i	0.562191	−	0.973744i	0.997305	−	0.0733685i	$-0.0233749\pi$
$234$		0			0
$235$	−1.51912	−	2.63119i	−0.0990964	−	0.171640i
$236$	−4.73670	+	19.2797i	−0.308333	+	1.25500i
$237$		0			0
$238$	5.05742	−	8.06796i	0.327824	−	0.522968i
$239$		−	11.9169i		−	0.770838i	−0.922742	−	0.385419i	$-0.874057\pi$
$239$		−	11.9169i		−	0.770838i	0.922742	−	0.385419i	$-0.125943\pi$
$240$		0			0
$241$	7.66296	−	4.42421i	0.493615	−	0.284988i	−0.232458	−	0.972606i	$-0.574677\pi$
$241$	7.66296	−	4.42421i	0.493615	−	0.284988i	0.726073	+	0.687618i	$0.241344\pi$
$242$	0.0612876	−	0.506335i	0.00393972	−	0.0325484i
$243$		0			0
$244$	5.83854	+	20.1006i	0.373774	+	1.28681i
$245$	1.68097	−	4.52965i	0.107393	−	0.289389i
$246$		0			0
$247$	2.55650	+	1.47600i	0.162666	+	0.0939155i
$248$	−24.8552	+	4.06805i	−1.57831	+	0.258321i
$249$		0			0
$250$	8.55084	−	3.64696i	0.540803	−	0.230654i
$251$		−	18.1333i		−	1.14457i	−0.820056	−	0.572283i	$-0.806058\pi$
$251$		−	18.1333i		−	1.14457i	0.820056	−	0.572283i	$-0.193942\pi$
$252$		0			0
$253$		−	9.43898i		−	0.593424i
$254$	−3.42915	−	8.04016i	−0.215164	−	0.504484i
$255$		0			0
$256$	−15.9442	+	1.33528i	−0.996512	+	0.0834547i
$257$	−8.01964	−	4.63014i	−0.500251	−	0.288820i	0.228566	−	0.973528i	$-0.426596\pi$
$257$	−8.01964	−	4.63014i	−0.500251	−	0.288820i	−0.728817	+	0.684708i	$0.759930\pi$
$258$		0			0
$259$	16.5966	+	7.80271i	1.03126	+	0.484837i
$260$	2.03030	+	6.98981i	0.125914	+	0.433490i
$261$		0			0
$262$	2.93629	+	0.355413i	0.181404	+	0.0219575i
$263$	−20.3951	+	11.7751i	−1.25762	+	0.726085i	−0.972611	−	0.232441i	$-0.925329\pi$
$263$	−20.3951	+	11.7751i	−1.25762	+	0.726085i	−0.285006	+	0.958526i	$0.591996\pi$
$264$		0			0
$265$			6.51492i			0.400208i
$266$	−2.09340	−	0.0760890i	−0.128355	−	0.00466532i
$267$		0			0
$268$	−5.63475	−	1.38436i	−0.344197	−	0.0845633i
$269$	−0.810052	−	1.40305i	−0.0493897	−	0.0855455i	0.840274	−	0.542163i	$-0.182394\pi$
$269$	−0.810052	−	1.40305i	−0.0493897	−	0.0855455i	−0.889663	+	0.456617i	$0.849061\pi$
$270$		0			0
$271$	−4.22701	+	7.32140i	−0.256773	+	0.444743i	−0.965375	−	0.260864i	$-0.915992\pi$
$271$	−4.22701	+	7.32140i	−0.256773	+	0.444743i	0.708603	+	0.705608i	$0.249326\pi$
$272$	−5.45349	−	8.59545i	−0.330666	−	0.521176i
$273$		0			0
$274$	−5.50845	−	4.13610i	−0.332778	−	0.249871i
$275$	−7.37755	+	12.7783i	−0.444883	+	0.770560i
$276$		0			0
$277$	−16.1282	+	9.31159i	−0.969047	+	0.559479i	−0.898946	−	0.438060i	$-0.855666\pi$
$277$	−16.1282	+	9.31159i	−0.969047	+	0.559479i	−0.0701013	+	0.997540i	$0.522332\pi$
$278$	1.01999	+	2.39153i	0.0611752	+	0.143434i
$279$		0			0
$280$	−3.59543	−	3.70823i	−0.214868	−	0.221609i
$281$	−12.6260			−0.753201			−0.376601	−	0.926376i	$-0.622907\pi$
$281$	−12.6260			−0.753201			−0.376601	+	0.926376i	$0.622907\pi$
$282$		0			0
$283$	21.2096	−	12.2454i	1.26078	−	0.727913i	0.287557	−	0.957764i	$-0.407157\pi$
$283$	21.2096	−	12.2454i	1.26078	−	0.727913i	0.973226	+	0.229850i	$0.0738237\pi$
$284$	7.63798	+	7.32538i	0.453231	+	0.434681i
$285$		0			0
$286$	−19.4501	−	14.6044i	−1.15011	−	0.863578i
$287$	2.17145	+	25.7514i	0.128177	+	1.52006i
$288$		0			0
$289$	−5.26180	+	9.11371i	−0.309518	+	0.536101i
$290$	0.430854	+	0.0521513i	0.0253006	+	0.00306243i
$291$		0			0
$292$	−2.91223	+	11.8536i	−0.170426	+	0.693681i
$293$	26.7727			1.56408			0.782038	−	0.623231i	$-0.214180\pi$
$293$	26.7727			1.56408			0.782038	+	0.623231i	$0.214180\pi$
$294$		0			0
$295$			6.85143i			0.398906i
$296$	15.1726	−	12.4165i	0.881890	−	0.721695i
$297$		0			0
$298$	12.4644	+	1.50871i	0.722041	+	0.0873970i
$299$	13.2141	+	7.62918i	0.764193	+	0.441207i
$300$		0			0
$301$		0			0
$302$	1.65847	−	2.20875i	0.0954344	−	0.127099i
$303$		0			0
$304$	−1.03774	+	1.98446i	−0.0595182	+	0.113817i
$305$	3.61178	+	6.25579i	0.206810	+	0.358206i
$306$		0			0
$307$		−	28.4069i		−	1.62127i	−0.585553	−	0.810634i	$-0.699122\pi$
$307$		−	28.4069i		−	1.62127i	0.585553	−	0.810634i	$-0.300878\pi$
$308$	17.0481	+	2.69504i	0.971407	+	0.153564i
$309$		0			0
$310$	−7.99503	+	3.40990i	−0.454087	+	0.193670i
$311$	−12.2816	−	21.2723i	−0.696424	−	1.20624i	−0.969698	−	0.244306i	$-0.921440\pi$
$311$	−12.2816	−	21.2723i	−0.696424	−	1.20624i	0.273274	−	0.961936i	$-0.411893\pi$
$312$		0			0
$313$	8.12245	+	4.68950i	0.459108	+	0.265066i	0.711669	−	0.702515i	$-0.247940\pi$
$313$	8.12245	+	4.68950i	0.459108	+	0.265066i	−0.252561	+	0.967581i	$0.581273\pi$
$314$	1.47078	+	1.10436i	0.0830008	+	0.0623224i
$315$		0			0
$316$	11.1287	−	3.23251i	0.626038	−	0.181843i
$317$	−10.4847	−	6.05335i	−0.588880	−	0.339990i	0.175774	−	0.984430i	$-0.443757\pi$
$317$	−10.4847	−	6.05335i	−0.588880	−	0.339990i	−0.764655	+	0.644440i	$0.777090\pi$
$318$		0			0
$319$	−1.25597	+	0.725133i	−0.0703206	+	0.0405996i
$320$	−5.23360	+	1.76032i	−0.292567	+	0.0984050i
$321$		0			0
$322$	−10.8204	−	0.393291i	−0.603000	−	0.0219173i
$323$	−1.42476			−0.0792758
$324$		0			0
$325$	−11.9260	−	20.6565i	−0.661536	−	1.14581i
$326$	1.46301	−	12.0868i	0.0810286	−	0.669427i
$327$		0			0
$328$	25.8428	+	9.76765i	1.42693	+	0.539328i
$329$	4.95506	−	10.5396i	0.273182	−	0.581066i
$330$		0			0
$331$	4.62693	−	8.01409i	0.254319	−	0.440494i	−0.710391	−	0.703807i	$-0.751482\pi$
$331$	4.62693	−	8.01409i	0.254319	−	0.440494i	0.964710	+	0.263313i	$0.0848152\pi$
$332$	2.65370	+	2.54509i	0.145641	+	0.139680i
$333$		0			0
$334$	6.85905	−	2.92541i	0.375311	−	0.160071i
$335$	−2.00242			−0.109404
$336$		0			0
$337$	−0.823644			−0.0448667			−0.0224334	−	0.999748i	$-0.507141\pi$
$337$	−0.823644			−0.0448667			−0.0224334	+	0.999748i	$0.507141\pi$
$338$	19.2554	−	8.21250i	1.04736	−	0.446701i
$339$		0			0
$340$	−2.53542	−	2.43165i	−0.137503	−	0.131875i
$341$	14.5225	−	25.1536i	0.786435	−	1.36215i
$342$		0			0
$343$	17.9336	−	4.62457i	0.968322	−	0.249703i
$344$		0			0
$345$		0			0
$346$	−2.80544	+	23.1775i	−0.150822	+	1.24603i
$347$	6.43367	+	11.1434i	0.345378	+	0.598212i	0.985422	−	0.170126i	$-0.0544175\pi$
$347$	6.43367	+	11.1434i	0.345378	+	0.598212i	−0.640045	+	0.768338i	$0.721084\pi$
$348$		0			0
$349$	30.7068			1.64370			0.821850	−	0.569704i	$-0.192942\pi$
$349$	30.7068			1.64370			0.821850	+	0.569704i	$0.192942\pi$
$350$	14.3411	+	8.98973i	0.766563	+	0.480521i
$351$		0			0
$352$	10.4532	−	15.2049i	0.557157	−	0.810426i
$353$	−11.9893	+	6.92205i	−0.638128	+	0.368423i	−0.783893	−	0.620896i	$-0.786769\pi$
$353$	−11.9893	+	6.92205i	−0.638128	+	0.368423i	0.145765	+	0.989319i	$0.453436\pi$
$354$		0			0
$355$	3.16296	+	1.82613i	0.167872	+	0.0969212i
$356$	−3.32661	+	0.966267i	−0.176310	+	0.0512121i
$357$		0			0
$358$	−25.1607	−	18.8923i	−1.32979	−	0.998490i
$359$	−3.76207	−	2.17203i	−0.198554	−	0.114635i	0.397427	−	0.917634i	$-0.369903\pi$
$359$	−3.76207	−	2.17203i	−0.198554	−	0.114635i	−0.595981	+	0.802999i	$0.703237\pi$
$360$		0			0
$361$	−9.34328	−	16.1830i	−0.491752	−	0.851739i
$362$	13.0401	−	5.56166i	0.685374	−	0.292314i
$363$		0			0
$364$	−17.5523	+	21.6883i	−0.919991	+	1.13677i
$365$			4.21242i			0.220488i
$366$		0			0
$367$	2.07648	+	3.59656i	0.108391	+	0.187739i	0.915119	−	0.403185i	$-0.132097\pi$
$367$	2.07648	+	3.59656i	0.108391	+	0.187739i	−0.806727	+	0.590924i	$0.798763\pi$
$368$	−5.36388	+	10.2574i	−0.279612	+	0.534702i
$369$		0			0
$370$	4.06260	−	5.41056i	0.211205	−	0.281282i
$371$	−20.5018	+	14.2597i	−1.06440	+	0.740327i
$372$		0			0
$373$	1.52118	+	0.878255i	0.0787638	+	0.0454743i	0.538865	−	0.842392i	$-0.318853\pi$
$373$	1.52118	+	0.878255i	0.0787638	+	0.0454743i	−0.460101	+	0.887867i	$0.652187\pi$
$374$	11.6542	+	1.41064i	0.602622	+	0.0729424i
$375$		0			0
$376$	−7.88503	−	9.63527i	−0.406639	−	0.496901i
$377$		−	2.34439i		−	0.120742i
$378$		0			0
$379$	−14.9787			−0.769403			−0.384701	−	0.923041i	$-0.625696\pi$
$379$	−14.9787			−0.769403			−0.384701	+	0.923041i	$0.625696\pi$
$380$	−0.184390	+	0.750520i	−0.00945901	+	0.0385009i
$381$		0			0
$382$	35.0999	+	4.24855i	1.79587	+	0.217375i
$383$	8.26475	−	14.3150i	0.422309	−	0.731461i	−0.573856	−	0.818956i	$-0.694553\pi$
$383$	8.26475	−	14.3150i	0.422309	−	0.731461i	0.996165	+	0.0874957i	$0.0278864\pi$
$384$		0			0
$385$	5.93543	−	0.500497i	0.302497	−	0.0255077i
$386$	−12.8860	−	9.67565i	−0.655880	−	0.492478i
$387$		0			0
$388$	10.7150	+	10.2765i	0.543974	+	0.521711i
$389$	21.8776	−	12.6310i	1.10924	−	0.640418i	0.170605	−	0.985340i	$-0.445428\pi$
$389$	21.8776	−	12.6310i	1.10924	−	0.640418i	0.938631	+	0.344922i	$0.112095\pi$
$390$		0			0
$391$	−7.36435			−0.372431
$392$	3.79982	−	19.4309i	0.191920	−	0.981411i
$393$		0			0
$394$	−5.62490	−	13.1884i	−0.283378	−	0.664423i
$395$	3.46352	−	1.99966i	0.174268	−	0.100614i
$396$		0			0
$397$	−4.05677	+	7.02653i	−0.203603	+	0.352651i	−0.949687	−	0.313201i	$-0.898599\pi$
$397$	−4.05677	+	7.02653i	−0.203603	+	0.352651i	0.746083	+	0.665852i	$0.231932\pi$
$398$	−12.2207	−	9.17610i	−0.612569	−	0.459957i
$399$		0			0
$400$	15.2787	−	9.69376i	0.763935	−	0.484688i
$401$	−0.564574	+	0.977870i	−0.0281935	+	0.0488325i	−0.879778	−	0.475385i	$-0.842309\pi$
$401$	−0.564574	+	0.977870i	−0.0281935	+	0.0488325i	0.851584	+	0.524217i	$0.175642\pi$
$402$		0			0
$403$	23.4759	+	40.6615i	1.16942	+	2.02549i
$404$	−24.5038	−	6.02015i	−1.21911	−	0.299514i
$405$		0			0
$406$	0.778929	+	1.47000i	0.0386576	+	0.0729548i
$407$			22.6095i			1.12071i
$408$		0			0
$409$	−10.8567	+	6.26811i	−0.536828	+	0.309938i	−0.743793	−	0.668411i	$-0.766975\pi$
$409$	−10.8567	+	6.26811i	−0.536828	+	0.309938i	0.206964	+	0.978349i	$0.433642\pi$
$410$	9.46521	+	1.14569i	0.467454	+	0.0565814i
$411$		0			0
$412$	−3.56628	−	12.2778i	−0.175698	−	0.604884i
$413$	−21.5607	+	14.9963i	−1.06093	+	0.737917i
$414$		0			0
$415$	1.09892	+	0.634462i	0.0539439	+	0.0311445i
$416$	12.8373	+	26.9236i	0.629398	+	1.32004i
$417$		0			0
$418$	−1.01316	−	2.37551i	−0.0495554	−	0.116190i
$419$			27.3950i			1.33834i	0.743111	+	0.669168i	$0.233349\pi$
$419$			27.3950i			1.33834i	−0.743111	+	0.669168i	$0.766651\pi$
$420$		0			0
$421$		−	30.7814i		−	1.50019i	−0.661329	−	0.750096i	$-0.730007\pi$
$421$		−	30.7814i		−	1.50019i	0.661329	−	0.750096i	$-0.269993\pi$
$422$	−20.5563	+	8.76731i	−1.00066	+	0.426786i
$423$		0			0
$424$	4.31220	+	26.3469i	0.209419	+	1.27952i
$425$	9.96970	+	5.75601i	0.483601	+	0.279207i
$426$		0			0
$427$	−11.7809	+	25.0584i	−0.570119	+	1.21266i
$428$	−1.69053	−	5.82006i	−0.0817148	−	0.281323i
$429$		0			0
$430$		0			0
$431$	−13.0280	+	7.52173i	−0.627538	+	0.362309i	−0.779798	−	0.626031i	$-0.784678\pi$
$431$	−13.0280	+	7.52173i	−0.627538	+	0.362309i	0.152260	+	0.988340i	$0.451345\pi$
$432$		0			0
$433$			16.8008i			0.807396i	0.914892	+	0.403698i	$0.132275\pi$
$433$			16.8008i			0.807396i	−0.914892	+	0.403698i	$0.867725\pi$
$434$	−28.2299	−	17.6960i	−1.35508	−	0.849434i
$435$		0			0
$436$	−3.99963	+	16.2796i	−0.191547	+	0.779653i
$437$	0.810052	+	1.40305i	0.0387500	+	0.0671170i
$438$		0			0
$439$	−5.91260	+	10.2409i	−0.282193	+	0.488773i	−0.971925	−	0.235293i	$-0.924395\pi$
$439$	−5.91260	+	10.2409i	−0.282193	+	0.488773i	0.689732	+	0.724065i	$0.257729\pi$
$440$	2.25134	−	5.95649i	0.107329	−	0.283965i
$441$		0			0
$442$	−11.3945	+	15.1751i	−0.541979	+	0.721806i
$443$	9.12420	−	15.8036i	0.433504	−	0.750851i	−0.563668	−	0.826001i	$-0.690610\pi$
$443$	9.12420	−	15.8036i	0.433504	−	0.750851i	0.997172	+	0.0751504i	$0.0239437\pi$
$444$		0			0
$445$	−1.03532	+	0.597743i	−0.0490789	+	0.0283357i
$446$	−19.3675	+	8.26031i	−0.917079	+	0.391137i
$447$		0			0
$448$	−16.9947	−	12.6166i	−0.802925	−	0.596080i
$449$	3.17636			0.149902			0.0749508	−	0.997187i	$-0.476120\pi$
$449$	3.17636			0.149902			0.0749508	+	0.997187i	$0.476120\pi$
$450$		0			0
$451$	−27.5917	+	15.9301i	−1.29924	+	0.750118i
$452$	17.4790	−	18.2248i	0.822141	−	0.857225i
$453$		0			0
$454$	23.8978	−	31.8270i	1.12158	−	1.49372i
$455$	−4.09671	+	8.71385i	−0.192057	+	0.408512i
$456$		0			0
$457$	−0.714593	+	1.23771i	−0.0334273	+	0.0578977i	−0.882255	−	0.470772i	$-0.843976\pi$
$457$	−0.714593	+	1.23771i	−0.0334273	+	0.0578977i	0.848828	+	0.528669i	$0.177309\pi$
$458$	1.14421	−	9.45306i	0.0534656	−	0.441712i
$459$		0			0
$460$	−0.953081	+	3.87931i	−0.0444376	+	0.180874i
$461$	−11.4755			−0.534466			−0.267233	−	0.963632i	$-0.586109\pi$
$461$	−11.4755			−0.534466			−0.267233	+	0.963632i	$0.586109\pi$
$462$		0			0
$463$			35.6282i			1.65578i	0.560887	+	0.827892i	$0.310460\pi$
$463$			35.6282i			1.65578i	−0.560887	+	0.827892i	$0.689540\pi$
$464$	1.77693	−	0.0742762i	0.0824920	−	0.00344819i
$465$		0			0
$466$	2.91665	−	24.0962i	0.135111	−	1.11624i
$467$	21.4541	+	12.3865i	0.992777	+	0.573180i	0.906103	−	0.423057i	$-0.139043\pi$
$467$	21.4541	+	12.3865i	0.992777	+	0.573180i	0.0866736	+	0.996237i	$0.472376\pi$
$468$		0			0
$469$	−4.38285	−	6.30140i	−0.202381	−	0.290971i
$470$	−3.43595	−	2.57993i	−0.158488	−	0.119003i
$471$		0			0
$472$	4.53494	+	27.7078i	0.208738	+	1.27536i
$473$		0			0
$474$		0			0
$475$		−	2.53256i		−	0.116202i
$476$	2.10269	−	13.3010i	0.0963764	−	0.609652i
$477$		0			0
$478$	−6.61162	−	15.5019i	−0.302409	−	0.709042i
$479$	11.9318	+	20.6666i	0.545180	+	0.944279i	0.998596	+	0.0529800i	$0.0168719\pi$
$479$	11.9318	+	20.6666i	0.545180	+	0.944279i	−0.453416	+	0.891299i	$0.649795\pi$
$480$		0			0
$481$	−31.6523	−	18.2745i	−1.44322	−	0.833244i
$482$	7.51367	−	10.0067i	0.342238	−	0.455792i
$483$		0			0
$484$	−0.201195	−	0.692664i	−0.00914524	−	0.0314847i
$485$	4.43720	+	2.56182i	0.201483	+	0.116326i
$486$		0			0
$487$	−15.3829	+	8.88133i	−0.697066	+	0.402451i	−0.806254	−	0.591570i	$-0.798508\pi$
$487$	−15.3829	+	8.88133i	−0.697066	+	0.402451i	0.109188	+	0.994021i	$0.465175\pi$
$488$	18.7471	+	22.9084i	0.848639	+	1.03701i
$489$		0			0
$490$	−0.326438	−	6.82497i	−0.0147470	−	0.308321i
$491$	−24.6260			−1.11135			−0.555677	−	0.831398i	$-0.687541\pi$
$491$	−24.6260			−1.11135			−0.555677	+	0.831398i	$0.687541\pi$
$492$		0			0
$493$	0.565753	+	0.979912i	0.0254802	+	0.0441330i
$494$	4.14450	+	0.501658i	0.186470	+	0.0225706i
$495$		0			0
$496$	−30.0756	+	19.0818i	−1.35043	+	0.856800i
$497$	1.17636	+	13.9505i	0.0527668	+	0.625765i
$498$		0			0
$499$	−7.20568	+	12.4806i	−0.322571	+	0.558709i	−0.981018	−	0.193918i	$-0.937880\pi$
$499$	−7.20568	+	12.4806i	−0.322571	+	0.558709i	0.658447	+	0.752627i	$0.271214\pi$
$500$	9.09990	−	9.48822i	0.406960	−	0.424326i
$501$		0			0
$502$	−10.0606	−	23.5886i	−0.449026	−	1.05281i
$503$	27.2938			1.21697			0.608486	−	0.793565i	$-0.291777\pi$
$503$	27.2938			1.21697			0.608486	+	0.793565i	$0.291777\pi$
$504$		0			0
$505$	−8.70789			−0.387496
$506$	−5.23686	−	12.2786i	−0.232807	−	0.545851i
$507$		0			0
$508$	−8.92155	−	8.55642i	−0.395830	−	0.379630i
$509$	−9.43037	+	16.3339i	−0.417994	+	0.723986i	−0.995738	−	0.0922319i	$-0.970600\pi$
$509$	−9.43037	+	16.3339i	−0.417994	+	0.723986i	0.577744	+	0.816218i	$0.303933\pi$
$510$		0			0
$511$	−13.2560	+	9.22004i	−0.586412	+	0.407871i
$512$	−20.0000	+	10.5830i	−0.883883	+	0.467707i
$513$		0			0
$514$	−13.0011	−	1.57368i	−0.573455	−	0.0694119i
$515$	−2.20614	−	3.82115i	−0.0972142	−	0.168380i
$516$		0			0
$517$	14.3580			0.631466
$518$	25.9186	+	0.942065i	1.13880	+	0.0413919i
$519$		0			0
$520$	6.51913	+	7.96619i	0.285883	+	0.349340i
$521$	−23.7236	+	13.6968i	−1.03935	+	0.600068i	−0.919649	−	0.392742i	$-0.871526\pi$
$521$	−23.7236	+	13.6968i	−1.03935	+	0.600068i	−0.119700	+	0.992810i	$0.538193\pi$
$522$		0			0
$523$	25.7805	+	14.8844i	1.12730	+	0.650847i	0.943255	−	0.332070i	$-0.107747\pi$
$523$	25.7805	+	14.8844i	1.12730	+	0.650847i	0.184046	+	0.982918i	$0.441080\pi$
$524$	4.01682	−	1.16675i	0.175476	−	0.0509698i
$525$		0			0
$526$	−19.9978	+	26.6330i	−0.871945	+	1.16125i
$527$	−19.6250	−	11.3305i	−0.854879	−	0.493564i
$528$		0			0
$529$	−7.31298	−	12.6664i	−0.317956	−	0.550715i
$530$	3.61456	+	8.47487i	0.157006	+	0.368125i
$531$		0			0
$532$	−2.76539	+	1.06246i	−0.119895	+	0.0460637i
$533$		−	51.5028i		−	2.23083i
$534$		0			0
$535$	−1.04578	−	1.81134i	−0.0452130	−	0.0783112i
$536$	−8.09796	+	1.32539i	−0.349779	+	0.0572483i
$537$		0			0
$538$	−1.83218	−	1.37572i	−0.0789908	−	0.0593114i
$539$	14.5663	+	17.5827i	0.627416	+	0.757339i
$540$		0			0
$541$	8.21897	+	4.74522i	0.353361	+	0.204013i	0.666165	−	0.745805i	$-0.267935\pi$
$541$	8.21897	+	4.74522i	0.353361	+	0.204013i	−0.312804	+	0.949818i	$0.601268\pi$
$542$	−1.43666	+	11.8692i	−0.0617100	+	0.509824i
$543$		0			0
$544$	−11.8630	−	8.15564i	−0.508621	−	0.349670i
$545$			5.78529i			0.247815i
$546$		0			0
$547$	10.2732			0.439252			0.219626	−	0.975584i	$-0.429516\pi$
$547$	10.2732			0.439252			0.219626	+	0.975584i	$0.429516\pi$
$548$	−9.46037	−	2.32425i	−0.404127	−	0.0992871i
$549$		0			0
$550$	−2.50746	+	20.7157i	−0.106918	+	0.883319i
$551$	0.124462	−	0.215574i	0.00530224	−	0.00918375i
$552$		0			0
$553$	13.8736	+	6.52250i	0.589965	+	0.277365i
$554$	−15.8140	+	21.0610i	−0.671871	+	0.894795i
$555$		0			0
$556$	2.65370	+	2.54509i	0.112542	+	0.107936i
$557$	−31.8011	+	18.3604i	−1.34746	+	0.777955i	−0.987889	−	0.155163i	$-0.950410\pi$
$557$	−31.8011	+	18.3604i	−1.34746	+	0.777955i	−0.359569	+	0.933119i	$0.617076\pi$
$558$		0			0
$559$		0			0
$560$	−6.73446	−	2.82903i	−0.284583	−	0.119548i
$561$		0			0
$562$	−16.4243	+	7.00503i	−0.692819	+	0.295489i
$563$	−5.48439	+	3.16641i	−0.231139	+	0.133448i	−0.611098	−	0.791555i	$-0.709272\pi$
$563$	−5.48439	+	3.16641i	−0.231139	+	0.133448i	0.379958	+	0.925004i	$0.375938\pi$
$564$		0			0
$565$	4.35731	−	7.54708i	0.183313	−	0.317508i
$566$	20.7965	−	27.6967i	0.874140	−	1.16418i
$567$		0			0
$568$	14.0000	+	5.29150i	0.587427	+	0.222027i
$569$	−19.7484	+	34.2052i	−0.827896	+	1.43396i	0.0717894	+	0.997420i	$0.477129\pi$
$569$	−19.7484	+	34.2052i	−0.827896	+	1.43396i	−0.899686	+	0.436538i	$0.856204\pi$
$570$		0			0
$571$	−6.22305	−	10.7786i	−0.260426	−	0.451072i	0.705929	−	0.708283i	$-0.250530\pi$
$571$	−6.22305	−	10.7786i	−0.260426	−	0.451072i	−0.966355	+	0.257211i	$0.917196\pi$
$572$	−33.4042	−	8.20685i	−1.39670	−	0.343146i
$573$		0			0
$574$	17.1119	+	32.2937i	0.714236	+	1.34791i
$575$		−	13.0904i		−	0.545907i
$576$		0			0
$577$	−10.8259	+	6.25035i	−0.450689	+	0.260205i	−0.708121	−	0.706091i	$-0.750457\pi$
$577$	−10.8259	+	6.25035i	−0.450689	+	0.260205i	0.257432	+	0.966296i	$0.417124\pi$
$578$	−1.78836	+	14.7748i	−0.0743862	+	0.614550i
$579$		0			0
$580$	0.589406	−	0.171203i	0.0244738	−	0.00710880i
$581$	0.408707	+	4.84688i	0.0169560	+	0.201083i
$582$		0			0
$583$	−26.6633	−	15.3940i	−1.10428	−	0.637556i
$584$	2.78819	+	17.0354i	0.115376	+	0.704930i
$585$		0			0
$586$	34.8269	−	14.8538i	1.43869	−	0.613605i
$587$		−	32.0838i		−	1.32424i	−0.749397	−	0.662121i	$-0.769657\pi$
$587$		−	32.0838i		−	1.32424i	0.749397	−	0.662121i	$-0.230343\pi$
$588$		0			0
$589$			4.98526i			0.205414i
$590$	3.80126	+	8.91262i	0.156495	+	0.366927i
$591$		0			0
$592$	12.8483	−	24.5698i	0.528062	−	1.00981i
$593$	−17.2760	−	9.97429i	−0.709439	−	0.409595i	0.101414	−	0.994844i	$-0.467663\pi$
$593$	−17.2760	−	9.97429i	−0.709439	−	0.409595i	−0.810853	+	0.585249i	$0.800997\pi$
$594$		0			0
$595$	−0.390490	−	4.63085i	−0.0160085	−	0.189846i
$596$	17.0512	−	4.95279i	0.698443	−	0.202874i
$597$		0			0
$598$	21.4222	+	2.59298i	0.876020	+	0.106035i
$599$	−9.05851	+	5.22993i	−0.370121	+	0.213689i	−0.673511	−	0.739177i	$-0.735215\pi$
$599$	−9.05851	+	5.22993i	−0.370121	+	0.213689i	0.303391	+	0.952866i	$0.401881\pi$
$600$		0			0
$601$			30.6355i			1.24965i	0.780766	+	0.624823i	$0.214829\pi$
$601$			30.6355i			1.24965i	−0.780766	+	0.624823i	$0.785171\pi$
$602$		0			0
$603$		0			0
$604$	0.931966	−	3.79337i	0.0379212	−	0.154350i
$605$	−0.124462	−	0.215574i	−0.00506008	−	0.00876432i
$606$		0			0
$607$	18.7095	−	32.4058i	0.759396	−	1.31531i	−0.183763	−	0.982971i	$-0.558828\pi$
$607$	18.7095	−	32.4058i	0.759396	−	1.31531i	0.943159	−	0.332342i	$-0.107839\pi$
$608$	−0.248923	+	3.15722i	−0.0100952	+	0.128042i
$609$		0			0
$610$	8.16914	+	6.13392i	0.330759	+	0.248355i
$611$	−11.6051	+	20.1006i	−0.469491	+	0.813183i
$612$		0			0
$613$	23.6077	−	13.6299i	0.953507	−	0.550507i	0.0593382	−	0.998238i	$-0.481101\pi$
$613$	23.6077	−	13.6299i	0.953507	−	0.550507i	0.894169	+	0.447731i	$0.147768\pi$
$614$	−15.7605	−	36.9528i	−0.636042	−	1.49130i
$615$		0			0
$616$	23.6721	−	5.95269i	0.953777	−	0.239841i
$617$	26.7810			1.07816			0.539081	−	0.842254i	$-0.318772\pi$
$617$	26.7810			1.07816			0.539081	+	0.842254i	$0.318772\pi$
$618$		0			0
$619$	31.4426	−	18.1534i	1.26379	−	0.729648i	0.289982	−	0.957032i	$-0.406351\pi$
$619$	31.4426	−	18.1534i	1.26379	−	0.729648i	0.973805	+	0.227385i	$0.0730175\pi$
$620$	−8.50839	+	8.87148i	−0.341705	+	0.356287i
$621$		0			0
$622$	−27.7785	−	20.8579i	−1.11382	−	0.836325i
$623$	−4.14712	−	1.94972i	−0.166151	−	0.0781139i
$624$		0			0
$625$	−9.04051	+	15.6586i	−0.361620	+	0.626345i
$626$	13.1678	+	1.59385i	0.526291	+	0.0637031i
$627$		0			0
$628$	2.52596	+	0.620584i	0.100797	+	0.0247640i
$629$	17.6401			0.703356
$630$		0			0
$631$			25.5683i			1.01786i	0.860809	+	0.508928i	$0.169958\pi$
$631$			25.5683i			1.01786i	−0.860809	+	0.508928i	$0.830042\pi$
$632$	12.6832	−	10.3793i	0.504511	−	0.412867i
$633$		0			0
$634$	−16.9974	−	2.05740i	−0.675053	−	0.0817096i
$635$	−3.69450	−	2.13302i	−0.146612	−	0.0846463i
$636$		0			0
$637$	−36.3883	+	6.18074i	−1.44176	+	0.244890i
$638$	−1.23150	+	1.64011i	−0.0487555	+	0.0649324i
$639$		0			0
$640$	−5.83143	+	5.19356i	−0.230507	+	0.205294i
$641$	−8.66296	−	15.0047i	−0.342166	−	0.592649i	0.642668	−	0.766144i	$-0.277827\pi$
$641$	−8.66296	−	15.0047i	−0.342166	−	0.592649i	−0.984835	+	0.173495i	$0.944494\pi$
$642$		0			0
$643$		−	19.0294i		−	0.750444i	−0.926935	−	0.375222i	$-0.877566\pi$
$643$		−	19.0294i		−	0.750444i	0.926935	−	0.375222i	$-0.122434\pi$
$644$	−14.2939	+	5.49170i	−0.563257	+	0.216403i
$645$		0			0
$646$	−1.85338	+	0.790474i	−0.0729205	+	0.0311008i
$647$	−1.28545	−	2.22647i	−0.0505364	−	0.0875317i	0.839651	−	0.543127i	$-0.182760\pi$
$647$	−1.28545	−	2.22647i	−0.0505364	−	0.0875317i	−0.890187	+	0.455595i	$0.849426\pi$
$648$		0			0
$649$	−28.0405	−	16.1892i	−1.10069	−	0.635482i
$650$	−26.9743	−	20.2540i	−1.05802	−	0.794429i
$651$		0			0
$652$	−4.80277	−	16.5347i	−0.188091	−	0.647549i
$653$	37.8296	+	21.8410i	1.48039	+	0.854702i	0.999753	−	0.0222184i	$-0.00707291\pi$
$653$	37.8296	+	21.8410i	1.48039	+	0.854702i	0.480635	+	0.876921i	$0.340406\pi$
$654$		0			0
$655$	1.25013	−	0.721764i	0.0488467	−	0.0282017i
$656$	39.0365	−	1.63174i	1.52412	−	0.0637086i
$657$		0			0
$658$	0.598252	−	16.4594i	0.0233223	−	0.641656i
$659$	25.4496			0.991376			0.495688	−	0.868501i	$-0.334916\pi$
$659$	25.4496			0.991376			0.495688	+	0.868501i	$0.334916\pi$
$660$		0			0
$661$	11.9660	+	20.7256i	0.465422	+	0.806134i	0.999220	−	0.0394776i	$-0.0125694\pi$
$661$	11.9660	+	20.7256i	0.465422	+	0.806134i	−0.533799	+	0.845612i	$0.679236\pi$
$662$	1.57259	−	12.9921i	0.0611204	−	0.504953i
$663$		0			0
$664$	4.86408	+	1.83845i	0.188763	+	0.0713457i
$665$	−0.839315	+	0.583773i	−0.0325472	+	0.0226378i
$666$		0			0
$667$	0.643321	−	1.11426i	0.0249095	−	0.0431445i
$668$	7.29948	−	7.61097i	0.282425	−	0.294477i
$669$		0			0
$670$	−2.60483	+	1.11097i	−0.100633	+	0.0429204i
$671$	−34.1370			−1.31784
$672$		0			0
$673$	42.7810			1.64909			0.824543	−	0.565800i	$-0.191432\pi$
$673$	42.7810			1.64909			0.824543	+	0.565800i	$0.191432\pi$
$674$	−1.07143	+	0.456967i	−0.0412699	+	0.0176017i
$675$		0			0
$676$	20.4918	−	21.3663i	0.788147	−	0.821781i
$677$	0.685590	−	1.18748i	0.0263494	−	0.0456385i	−0.852550	−	0.522646i	$-0.824945\pi$
$677$	0.685590	−	1.18748i	0.0263494	−	0.0456385i	0.878899	+	0.477007i	$0.158278\pi$
$678$		0			0
$679$	1.65027	+	19.5706i	0.0633314	+	0.751052i
$680$	−4.64729	−	1.75651i	−0.178215	−	0.0673591i
$681$		0			0
$682$	4.93585	−	40.7781i	0.189003	−	1.56147i
$683$	22.9399	+	39.7331i	0.877771	+	1.52034i	0.853781	+	0.520632i	$0.174304\pi$
$683$	22.9399	+	39.7331i	0.877771	+	1.52034i	0.0239904	+	0.999712i	$0.492363\pi$
$684$		0			0
$685$	−3.36193			−0.128453
$686$	20.7629	−	15.9656i	0.792733	−	0.609569i
$687$		0			0
$688$		0			0
$689$	43.1019	−	24.8849i	1.64205	−	0.948039i
$690$		0			0
$691$	8.57530	+	4.95095i	0.326220	+	0.188343i	0.654162	−	0.756355i	$-0.273022\pi$
$691$	8.57530	+	4.95095i	0.326220	+	0.188343i	−0.327942	+	0.944698i	$0.606355\pi$
$692$	9.20972	+	31.7067i	0.350101	+	1.20531i
$693$		0			0
$694$	14.5517	+	10.9264i	0.552375	+	0.414759i
$695$	1.09892	+	0.634462i	0.0416844	+	0.0240665i
$696$		0			0
$697$	12.4287	+	21.5272i	0.470772	+	0.815400i
$698$	39.9447	−	17.0365i	1.51193	−	0.644842i
$699$		0			0
$700$	23.6431	+	3.73760i	0.893624	+	0.141268i
$701$			22.9445i			0.866602i	0.901249	+	0.433301i	$0.142651\pi$
$701$			22.9445i			0.866602i	−0.901249	+	0.433301i	$0.857349\pi$
$702$		0			0
$703$	−1.94035	−	3.36078i	−0.0731816	−	0.126754i
$704$	5.16205	−	25.5787i	0.194552	−	0.964035i
$705$		0			0
$706$	−11.7558	+	15.6563i	−0.442434	+	0.589233i
$707$	−19.0596	−	27.4028i	−0.716811	−	1.03059i
$708$		0			0
$709$	−17.4404	−	10.0692i	−0.654986	−	0.378157i	0.135378	−	0.990794i	$-0.456775\pi$
$709$	−17.4404	−	10.0692i	−0.654986	−	0.378157i	−0.790364	+	0.612637i	$0.790109\pi$
$710$	5.12766	+	0.620661i	0.192438	+	0.0232930i
$711$		0			0
$712$	−3.79129	+	3.10260i	−0.142085	+	0.116275i
$713$			25.7680i			0.965018i
$714$		0			0
$715$	−11.8709			−0.443945
$716$	−43.2118	−	10.6164i	−1.61490	−	0.396753i
$717$		0			0
$718$	−6.09891	−	0.738223i	−0.227609	−	0.0275502i
$719$	−3.19631	+	5.53618i	−0.119202	+	0.206465i	−0.919452	−	0.393203i	$-0.871367\pi$
$719$	−3.19631	+	5.53618i	−0.119202	+	0.206465i	0.800249	+	0.599667i	$0.204700\pi$
$720$		0			0
$721$	7.19599	−	15.3061i	0.267993	−	0.570030i
$722$	−21.1327	−	15.8678i	−0.786476	−	0.590537i
$723$		0			0
$724$	13.8774	−	14.4696i	0.515751	−	0.537760i
$725$	−1.74183	+	1.00564i	−0.0646898	+	0.0373487i
$726$		0			0
$727$	27.2938			1.01227			0.506136	−	0.862454i	$-0.331073\pi$
$727$	27.2938			1.01227			0.506136	+	0.862454i	$0.331073\pi$
$728$	−10.7998	+	37.9512i	−0.400268	+	1.40656i
$729$		0			0
$730$	2.33710	+	5.47968i	0.0865000	+	0.202812i
$731$		0			0
$732$		0			0
$733$	5.90214	−	10.2228i	0.218001	−	0.377588i	−0.736196	−	0.676768i	$-0.763380\pi$
$733$	5.90214	−	10.2228i	0.218001	−	0.377588i	0.954197	+	0.299180i	$0.0967132\pi$
$734$	4.69658	+	3.52650i	0.173354	+	0.130165i
$735$		0			0
$736$	−1.28664	+	16.3191i	−0.0474262	+	0.601531i
$737$	4.73150	−	8.19520i	0.174287	−	0.301874i
$738$		0			0
$739$	−5.17141	−	8.95715i	−0.190233	−	0.329494i	0.755094	−	0.655616i	$-0.227591\pi$
$739$	−5.17141	−	8.95715i	−0.190233	−	0.329494i	−0.945328	+	0.326122i	$0.894258\pi$
$740$	2.28295	−	9.29226i	0.0839229	−	0.341590i
$741$		0			0
$742$	−18.7580	+	29.9242i	−0.688629	+	1.09855i
$743$		−	7.06999i		−	0.259373i	−0.991555	−	0.129686i	$-0.958603\pi$
$743$		−	7.06999i		−	0.259373i	0.991555	−	0.129686i	$-0.0413970\pi$
$744$		0			0
$745$	5.30674	−	3.06385i	0.194424	−	0.112251i
$746$	2.46608	+	0.298498i	0.0902896	+	0.0109288i
$747$		0			0
$748$	15.9428	−	4.63085i	0.582928	−	0.169321i
$749$	3.41112	−	7.25558i	0.124640	−	0.265113i
$750$		0			0
$751$	−24.1630	−	13.9505i	−0.881721	−	0.509062i	−0.0104954	−	0.999945i	$-0.503341\pi$
$751$	−24.1630	−	13.9505i	−0.881721	−	0.509062i	−0.871225	+	0.490883i	$0.836674\pi$
$752$	−15.6029	−	8.15923i	−0.568980	−	0.297537i
$753$		0			0
$754$	−1.30070	−	3.04968i	−0.0473686	−	0.111063i
$755$		−	1.34805i		−	0.0490605i
$756$		0			0
$757$		−	18.9429i		−	0.688492i	−0.938880	−	0.344246i	$-0.888135\pi$
$757$		−	18.9429i		−	0.688492i	0.938880	−	0.344246i	$-0.111865\pi$
$758$	−19.4848	+	8.31035i	−0.707721	+	0.301845i
$759$		0			0
$760$	0.176536	+	1.07861i	0.00640363	+	0.0391252i
$761$	−10.8780	−	6.28042i	−0.394328	−	0.227665i	0.289706	−	0.957116i	$-0.406442\pi$
$761$	−10.8780	−	6.28042i	−0.394328	−	0.227665i	−0.684034	+	0.729451i	$0.739776\pi$
$762$		0			0
$763$	−18.2057	+	12.6627i	−0.659090	+	0.458420i
$764$	48.0164	−	13.9472i	1.73717	−	0.504590i
$765$		0			0
$766$	2.80900	−	23.2069i	0.101493	−	0.838498i
$767$	45.3282	−	26.1703i	1.63671	−	0.944953i
$768$		0			0
$769$		−	32.9798i		−	1.18928i	−0.803991	−	0.594642i	$-0.797294\pi$
$769$		−	32.9798i		−	1.18928i	0.803991	−	0.594642i	$-0.202706\pi$
$770$	7.44336	−	3.94411i	0.268240	−	0.142136i
$771$		0			0
$772$	−22.1308	−	5.43716i	−0.796505	−	0.195688i
$773$	−19.3656	−	33.5422i	−0.696533	−	1.20643i	−0.969661	−	0.244453i	$-0.921392\pi$
$773$	−19.3656	−	33.5422i	−0.696533	−	1.20643i	0.273128	−	0.961978i	$-0.411942\pi$
$774$		0			0
$775$	20.1404	−	34.8841i	0.723463	−	1.25307i
$776$	19.6401	+	7.42325i	0.705038	+	0.266479i
$777$		0			0
$778$	21.4514	−	28.5689i	0.769068	−	1.02424i
$779$	2.73423	−	4.73583i	0.0979640	−	0.169679i
$780$		0			0
$781$	−14.9475	+	8.62992i	−0.534862	+	0.308803i
$782$	−9.57984	+	4.08583i	−0.342574	+	0.146109i
$783$		0			0
$784$	−5.83757	−	27.3847i	−0.208485	−	0.978026i
$785$	0.897649			0.0320384
$786$		0			0
$787$	25.8406	−	14.9191i	0.921118	−	0.531808i	0.0371266	−	0.999311i	$-0.488180\pi$
$787$	25.8406	−	14.9191i	0.921118	−	0.531808i	0.883992	+	0.467503i	$0.154846\pi$
$788$	−14.6342	−	14.0352i	−0.521321	−	0.499985i
$789$		0			0
$790$	3.39604	−	4.52284i	0.120826	−	0.160915i
$791$	33.2870	−	2.80688i	1.18355	−	0.0998012i
$792$		0			0
$793$	27.5917	−	47.7902i	0.979809	−	1.69708i
$794$	−1.37880	+	11.3911i	−0.0489319	+	0.404256i
$795$		0			0
$796$	−20.9882	−	5.15644i	−0.743907	−	0.182765i
$797$	−0.929890			−0.0329384			−0.0164692	−	0.999864i	$-0.505243\pi$
$797$	−0.929890			−0.0329384			−0.0164692	+	0.999864i	$0.505243\pi$
$798$		0			0
$799$		−	11.2022i		−	0.396306i
$800$	14.4969	−	21.0868i	0.512544	−	0.745532i
$801$		0			0
$802$	−0.191886	+	1.58528i	−0.00677571	+	0.0559783i
$803$	−17.2400	−	9.95349i	−0.608385	−	0.351251i
$804$		0			0
$805$	−4.33828	+	3.01743i	−0.152904	+	0.106350i
$806$	53.0979	+	39.8694i	1.87029	+	1.40434i
$807$		0			0
$808$	−35.2155	+	5.76372i	−1.23888	+	0.202767i
$809$	−8.69326	−	15.0572i	−0.305639	−	0.529382i	0.671765	−	0.740765i	$-0.265537\pi$
$809$	−8.69326	−	15.0572i	−0.305639	−	0.529382i	−0.977403	+	0.211383i	$0.932203\pi$
$810$		0			0
$811$			19.0294i			0.668211i	0.942536	+	0.334105i	$0.108434\pi$
$811$			19.0294i			0.668211i	−0.942536	+	0.334105i	$0.891566\pi$
$812$	1.82883	+	1.48007i	0.0641795	+	0.0519404i
$813$		0			0
$814$	12.5440	+	29.4114i	0.439669	+	1.03087i
$815$	−2.97104	−	5.14600i	−0.104071	−	0.180256i
$816$		0			0
$817$		0			0
$818$	−10.6452	+	14.1772i	−0.372200	+	0.495695i
$819$		0			0
$820$	12.9484	−	3.76106i	0.452177	−	0.131342i
$821$	−38.6560	−	22.3180i	−1.34910	−	0.778905i	−0.360981	−	0.932573i	$-0.617558\pi$
$821$	−38.6560	−	22.3180i	−1.34910	−	0.778905i	−0.988122	+	0.153668i	$0.950891\pi$
$822$		0			0
$823$	−0.764272	+	0.441253i	−0.0266408	+	0.0153811i	−0.513261	−	0.858232i	$-0.671563\pi$
$823$	−0.764272	+	0.441253i	−0.0266408	+	0.0153811i	0.486620	+	0.873614i	$0.338229\pi$
$824$	−11.4510	−	13.9928i	−0.398916	−	0.487463i
$825$		0			0
$826$	−19.7269	+	31.4699i	−0.686388	+	1.09498i
$827$	−18.3527			−0.638186			−0.319093	−	0.947723i	$-0.603378\pi$
$827$	−18.3527			−0.638186			−0.319093	+	0.947723i	$0.603378\pi$
$828$		0			0
$829$	18.2550	+	31.6186i	0.634024	+	1.09816i	0.986721	+	0.162424i	$0.0519311\pi$
$829$	18.2550	+	31.6186i	0.634024	+	1.09816i	−0.352698	+	0.935737i	$0.614736\pi$
$830$	1.78153	+	0.215639i	0.0618377	+	0.00748494i
$831$		0			0
$832$	31.6367	+	27.9010i	1.09681	+	0.967292i
$833$	13.7181	−	11.3647i	0.475304	−	0.393765i
$834$		0			0
$835$	1.81968	−	3.15177i	0.0629725	−	0.109072i
$836$	−2.63592	−	2.52804i	−0.0911653	−	0.0874341i
$837$		0			0
$838$	15.1991	+	35.6366i	0.525044	+	1.23104i
$839$	−31.6367			−1.09222			−0.546111	−	0.837713i	$-0.683892\pi$
$839$	−31.6367			−1.09222			−0.546111	+	0.837713i	$0.683892\pi$
$840$		0			0
$841$	28.8023			0.993183
$842$	−17.0779	−	40.0416i	−0.588542	−	1.37993i
$843$		0			0
$844$	−21.8762	+	22.8097i	−0.753010	+	0.785144i
$845$	5.10838	−	8.84798i	0.175734	−	0.304380i
$846$		0			0
$847$	0.405969	−	0.863509i	0.0139493	−	0.0296705i
$848$	20.2271	+	31.8807i	0.694601	+	1.09479i
$849$		0			0
$850$	16.1625	+	1.95633i	0.554368	+	0.0671017i
$851$	−10.0293	−	17.3713i	−0.343801	−	0.595481i
$852$		0			0
$853$	26.3639			0.902684			0.451342	−	0.892351i	$-0.350945\pi$
$853$	26.3639			0.902684			0.451342	+	0.892351i	$0.350945\pi$
$854$	−1.42238	+	39.1332i	−0.0486727	+	1.33911i
$855$		0			0
$856$	−5.42815	−	6.63303i	−0.185530	−	0.226712i
$857$	22.5909	−	13.0429i	0.771691	−	0.445536i	−0.0617866	−	0.998089i	$-0.519680\pi$
$857$	22.5909	−	13.0429i	0.771691	−	0.445536i	0.833477	+	0.552553i	$0.186347\pi$
$858$		0			0
$859$	6.13760	+	3.54355i	0.209412	+	0.120904i	0.601038	−	0.799220i	$-0.294754\pi$
$859$	6.13760	+	3.54355i	0.209412	+	0.120904i	−0.391626	+	0.920124i	$0.628087\pi$
$860$		0			0
$861$		0			0
$862$	−12.7742	+	17.0127i	−0.435092	+	0.579454i
$863$	13.4014	+	7.73731i	0.456189	+	0.263381i	0.710441	−	0.703757i	$-0.248496\pi$
$863$	13.4014	+	7.73731i	0.456189	+	0.263381i	−0.254251	+	0.967138i	$0.581829\pi$
$864$		0			0
$865$	5.69723	+	9.86789i	0.193712	+	0.335518i
$866$	9.32130	+	21.8552i	0.316751	+	0.742669i
$867$		0			0
$868$	−46.5406	−	7.35733i	−1.57969	−	0.249724i
$869$			18.8999i			0.641137i
$870$		0			0
$871$	7.64859	+	13.2478i	0.259163	+	0.448883i
$872$	3.82926	+	23.3962i	0.129675	+	0.792296i
$873$		0			0
$874$	1.83218	+	1.37572i	0.0619743	+	0.0465343i
$875$	17.3299	−	1.46132i	0.585857	−	0.0494016i
$876$		0			0
$877$	−40.0954	−	23.1491i	−1.35392	−	0.781689i	−0.365128	−	0.930957i	$-0.618975\pi$
$877$	−40.0954	−	23.1491i	−1.35392	−	0.781689i	−0.988797	+	0.149268i	$0.952308\pi$
$878$	−2.00956	+	16.6022i	−0.0678192	+	0.560296i
$879$		0			0
$880$	−0.376098	−	8.99751i	−0.0126783	−	0.303306i
$881$			37.7381i			1.27143i	0.771925	+	0.635714i	$0.219294\pi$
$881$			37.7381i			1.27143i	−0.771925	+	0.635714i	$0.780706\pi$
$882$		0			0
$883$	−37.0542			−1.24697			−0.623487	−	0.781834i	$-0.714285\pi$
$883$	−37.0542			−1.24697			−0.623487	+	0.781834i	$0.714285\pi$
$884$	−6.40303	+	26.0622i	−0.215357	+	0.876565i
$885$		0			0
$886$	3.10111	−	25.6201i	0.104184	−	0.860725i
$887$	21.7519	−	37.6754i	0.730357	−	1.26502i	−0.226374	−	0.974040i	$-0.572687\pi$
$887$	21.7519	−	37.6754i	0.730357	−	1.26502i	0.956731	−	0.290975i	$-0.0939795\pi$
$888$		0			0
$889$	−1.37404	−	16.2949i	−0.0460840	−	0.546513i
$890$	−1.01515	+	1.35198i	−0.0340280	+	0.0453183i
$891$		0			0
$892$	−20.6111	+	21.4907i	−0.690111	+	0.719561i
$893$	−2.13424	+	1.23221i	−0.0714197	+	0.0412342i
$894$		0			0
$895$	−15.3562			−0.513300
$896$	−29.1073	−	6.98333i	−0.972406	−	0.233297i
$897$		0			0
$898$	4.13193	−	1.76228i	0.137884	−	0.0588081i
$899$	3.42873	−	1.97958i	0.114354	−	0.0660226i
$900$		0			0
$901$	−12.0105	+	20.8028i	−0.400129	+	0.693043i
$902$	−27.0542	+	36.0307i	−0.900805	+	1.19969i
$903$		0			0
$904$	12.6260	−	33.4051i	0.419933	−	1.11104i
$905$	3.45949	−	5.99201i	0.114997	−	0.199181i
$906$		0			0
$907$	−26.6304	−	46.1253i	−0.884249	−	1.53156i	−0.846572	−	0.532275i	$-0.821337\pi$
$907$	−26.6304	−	46.1253i	−0.884249	−	1.53156i	−0.0376777	−	0.999290i	$-0.511996\pi$
$908$	13.4292	−	54.6606i	0.445663	−	1.81398i
$909$		0			0
$910$	−0.494619	+	13.6082i	−0.0163965	+	0.451108i
$911$			46.2112i			1.53105i	0.643408	+	0.765523i	$0.277520\pi$
$911$			46.2112i			1.53105i	−0.643408	+	0.765523i	$0.722480\pi$
$912$		0			0
$913$	−5.19326	+	2.99833i	−0.171872	+	0.0992303i
$914$	−0.242874	+	2.00653i	−0.00803355	+	0.0663701i
$915$		0			0
$916$	−3.75623	−	12.9317i	−0.124109	−	0.427277i
$917$	5.00757	+	2.35425i	0.165365	+	0.0777443i
$918$		0			0
$919$	12.7256	+	7.34713i	0.419779	+	0.242359i	0.694983	−	0.719026i	$-0.255412\pi$
$919$	12.7256	+	7.34713i	0.419779	+	0.242359i	−0.275204	+	0.961386i	$0.588745\pi$
$920$	0.912484	+	5.57514i	0.0300837	+	0.183807i
$921$		0			0
$922$	−14.9277	+	6.36673i	−0.491619	+	0.209677i
$923$		−	27.9010i		−	0.918372i
$924$		0			0
$925$			31.3559i			1.03097i
$926$	19.7670	+	46.3466i	0.649583	+	1.52304i
$927$		0			0
$928$	2.27029	−	1.08248i	0.0745260	−	0.0355343i
$929$	−10.5507	−	6.09146i	−0.346158	−	0.199854i	0.316834	−	0.948481i	$-0.397380\pi$
$929$	−10.5507	−	6.09146i	−0.346158	−	0.199854i	−0.662992	+	0.748627i	$0.730714\pi$
$930$		0			0
$931$	−3.67414	−	1.36348i	−0.120415	−	0.0446864i
$932$	−9.57478	−	32.9635i	−0.313632	−	1.07976i
$933$		0			0
$934$	34.7805	+	4.20989i	1.13805	+	0.137752i
$935$	4.96179	−	2.86469i	0.162268	−	0.0936855i
$936$		0			0
$937$			30.7049i			1.00309i	0.865133	+	0.501543i	$0.167234\pi$
$937$			30.7049i			1.00309i	−0.865133	+	0.501543i	$0.832766\pi$
$938$	−9.19747	−	5.76545i	−0.300308	−	0.188249i
$939$		0			0
$940$	−5.90099	−	1.44977i	−0.192469	−	0.0472864i
$941$	20.8705	+	36.1488i	0.680359	+	1.17842i	0.974871	+	0.222769i	$0.0715096\pi$
$941$	20.8705	+	36.1488i	0.680359	+	1.17842i	−0.294512	+	0.955648i	$0.595157\pi$
$942$		0			0
$943$	14.1328	−	24.4787i	0.460227	−	0.797136i
$944$	21.2719	+	33.5274i	0.692340	+	1.09122i
$945$		0			0
$946$		0			0
$947$	24.1540	−	41.8360i	0.784901	−	1.35949i	−0.144157	−	0.989555i	$-0.546047\pi$
$947$	24.1540	−	41.8360i	0.784901	−	1.35949i	0.929058	−	0.369934i	$-0.120620\pi$
$948$		0			0
$949$	27.8688	−	16.0901i	0.904661	−	0.522306i
$950$	−1.40510	−	3.29446i	−0.0455873	−	0.106886i
$951$		0			0
$952$	−4.64432	−	18.4691i	−0.150523	−	0.598588i
$953$	26.2732			0.851074			0.425537	−	0.904941i	$-0.360085\pi$
$953$	26.2732			0.851074			0.425537	+	0.904941i	$0.360085\pi$
$954$		0			0
$955$	14.9439	−	8.62785i	0.483573	−	0.279191i
$956$	−17.2013	−	16.4973i	−0.556330	−	0.533561i
$957$		0			0
$958$	26.9875	+	20.2639i	0.871925	+	0.654698i
$959$	−7.35851	−	10.5796i	−0.237619	−	0.341634i
$960$		0			0
$961$	−24.1456	+	41.8214i	−0.778890	+	1.34908i
$962$	−51.3134	−	6.21107i	−1.65441	−	0.200253i
$963$		0			0
$964$	4.22225	−	17.1858i	0.135990	−	0.553517i
$965$	−7.86462			−0.253171
$966$		0			0
$967$			3.51302i			0.112971i	0.998403	+	0.0564855i	$0.0179895\pi$
$967$			3.51302i			0.112971i	−0.998403	+	0.0564855i	$0.982011\pi$
$968$	−0.646021	−	0.789419i	−0.0207639	−	0.0253729i
$969$		0			0
$970$	7.19341	+	0.870703i	0.230966	+	0.0279566i
$971$	−37.4934	−	21.6468i	−1.20322	−	0.694679i	−0.241950	−	0.970289i	$-0.577787\pi$
$971$	−37.4934	−	21.6468i	−1.20322	−	0.694679i	−0.961270	+	0.275610i	$0.911120\pi$
$972$		0			0
$973$	0.408707	+	4.84688i	0.0131025	+	0.155384i
$974$	−15.0832	+	20.0878i	−0.483298	+	0.643655i
$975$		0			0
$976$	37.0967	+	19.3990i	1.18744	+	0.620947i
$977$	−11.4106	−	19.7637i	−0.365057	−	0.632297i	0.623728	−	0.781641i	$-0.285617\pi$
$977$	−11.4106	−	19.7637i	−0.365057	−	0.632297i	−0.988785	+	0.149344i	$0.952284\pi$
$978$		0			0
$979$		−	5.64961i		−	0.180562i
$980$	−4.21122	−	8.69708i	−0.134522	−	0.277818i
$981$		0			0
$982$	−32.0344	+	13.6628i	−1.02226	+	0.435997i
$983$	26.9239	+	46.6335i	0.858738	+	1.48738i	0.873133	+	0.487481i	$0.162084\pi$
$983$	26.9239	+	46.6335i	0.858738	+	1.48738i	−0.0143953	+	0.999896i	$0.504582\pi$
$984$		0			0
$985$	−6.06015	−	3.49883i	−0.193092	−	0.111482i
$986$	1.27962	+	0.960822i	0.0407514	+	0.0305988i
$987$		0			0
$988$	5.66966	−	1.64684i	0.180376	−	0.0523931i
$989$		0			0
$990$		0			0
$991$	33.3611	−	19.2610i	1.05975	−	0.611846i	0.134386	−	0.990929i	$-0.457094\pi$
$991$	33.3611	−	19.2610i	1.05975	−	0.611846i	0.925363	+	0.379083i	$0.123760\pi$
$992$	−28.5367	+	41.5087i	−0.906041	+	1.31790i
$993$		0			0
$994$	9.27015	+	17.4947i	0.294031	+	0.554898i
$995$	−7.45857			−0.236453
$996$		0			0
$997$	10.0643	+	17.4320i	0.318741	+	0.552075i	0.980226	−	0.197883i	$-0.0634067\pi$
$997$	10.0643	+	17.4320i	0.318741	+	0.552075i	−0.661485	+	0.749959i	$0.730073\pi$
$998$	−2.44904	+	20.2331i	−0.0775232	+	0.640466i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bk.a.19.5		12
3.2	odd	2		56.2.m.a.19.2	yes	12
4.3	odd	2		2016.2.bs.a.271.4		12
7.3	odd	6	inner	504.2.bk.a.451.4		12
8.3	odd	2	inner	504.2.bk.a.19.3		12
8.5	even	2		2016.2.bs.a.271.3		12
12.11	even	2		224.2.q.a.47.1		12
21.2	odd	6		392.2.e.e.195.12		12
21.5	even	6		392.2.e.e.195.11		12
21.11	odd	6		392.2.m.g.227.3		12
21.17	even	6		56.2.m.a.3.3	yes	12
21.20	even	2		392.2.m.g.19.2		12
24.5	odd	2		224.2.q.a.47.2		12
24.11	even	2		56.2.m.a.19.4	yes	12
28.3	even	6		2016.2.bs.a.1711.3		12
56.3	even	6	inner	504.2.bk.a.451.6		12
56.45	odd	6		2016.2.bs.a.1711.4		12
84.11	even	6		1568.2.q.g.815.5		12
84.23	even	6		1568.2.e.e.783.4		12
84.47	odd	6		1568.2.e.e.783.9		12
84.59	odd	6		224.2.q.a.143.2		12
84.83	odd	2		1568.2.q.g.1391.6		12
168.5	even	6		1568.2.e.e.783.10		12
168.11	even	6		392.2.m.g.227.1		12
168.53	odd	6		1568.2.q.g.815.6		12
168.59	odd	6		56.2.m.a.3.1	✓	12
168.83	odd	2		392.2.m.g.19.4		12
168.101	even	6		224.2.q.a.143.1		12
168.107	even	6		392.2.e.e.195.10		12
168.125	even	2		1568.2.q.g.1391.5		12
168.131	odd	6		392.2.e.e.195.9		12
168.149	odd	6		1568.2.e.e.783.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.m.a.3.1	✓	12	168.59	odd	6
56.2.m.a.3.3	yes	12	21.17	even	6
56.2.m.a.19.2	yes	12	3.2	odd	2
56.2.m.a.19.4	yes	12	24.11	even	2
224.2.q.a.47.1		12	12.11	even	2
224.2.q.a.47.2		12	24.5	odd	2
224.2.q.a.143.1		12	168.101	even	6
224.2.q.a.143.2		12	84.59	odd	6
392.2.e.e.195.9		12	168.131	odd	6
392.2.e.e.195.10		12	168.107	even	6
392.2.e.e.195.11		12	21.5	even	6
392.2.e.e.195.12		12	21.2	odd	6
392.2.m.g.19.2		12	21.20	even	2
392.2.m.g.19.4		12	168.83	odd	2
392.2.m.g.227.1		12	168.11	even	6
392.2.m.g.227.3		12	21.11	odd	6
504.2.bk.a.19.3		12	8.3	odd	2	inner
504.2.bk.a.19.5		12	1.1	even	1	trivial
504.2.bk.a.451.4		12	7.3	odd	6	inner
504.2.bk.a.451.6		12	56.3	even	6	inner
1568.2.e.e.783.3		12	168.149	odd	6
1568.2.e.e.783.4		12	84.23	even	6
1568.2.e.e.783.9		12	84.47	odd	6
1568.2.e.e.783.10		12	168.5	even	6
1568.2.q.g.815.5		12	84.11	even	6
1568.2.q.g.815.6		12	168.53	odd	6
1568.2.q.g.1391.5		12	168.125	even	2
1568.2.q.g.1391.6		12	84.83	odd	2
2016.2.bs.a.271.3		12	8.5	even	2
2016.2.bs.a.271.4		12	4.3	odd	2
2016.2.bs.a.1711.3		12	28.3	even	6
2016.2.bs.a.1711.4		12	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30084 - 0.554812i) q^{2} +(1.38437 - 1.44344i) q^{4} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(1.00000 - 2.64575i) q^{8} +O(q^{10})\)	\(q+(1.30084 - 0.554812i) q^{2} +(1.38437 - 1.44344i) q^{4} +(0.345107 - 0.597743i) q^{5} +(2.63639 - 0.222310i) q^{7} +(1.00000 - 2.64575i) q^{8} +(0.117294 - 0.969037i) q^{10} +(1.63090 + 2.82480i) q^{11} -5.27279 q^{13} +(3.30619 - 1.75189i) q^{14} +(-0.167055 - 3.99651i) q^{16} +(2.20393 - 1.27244i) q^{17} +(-0.484848 - 0.279927i) q^{19} +(-0.385053 - 1.32564i) q^{20} +(3.68878 + 2.76977i) q^{22} +(-2.50610 - 1.44690i) q^{23} +(2.26180 + 3.91756i) q^{25} +(-6.85905 + 2.92541i) q^{26} +(3.32885 - 4.11324i) q^{28} +0.444621i q^{29} +(-4.45228 - 7.71158i) q^{31} +(-2.43462 - 5.10613i) q^{32} +(2.16099 - 2.87800i) q^{34} +(0.776954 - 1.65261i) q^{35} +(6.00295 + 3.46580i) q^{37} +(-0.786017 - 0.0951408i) q^{38} +(-1.23637 - 1.51081i) q^{40} +9.76765i q^{41} +(6.33521 + 1.55645i) q^{44} +(-4.06279 - 0.491767i) q^{46} +(2.20094 - 3.81214i) q^{47} +(6.90116 - 1.17220i) q^{49} +(5.11575 + 3.84124i) q^{50} +(-7.29948 + 7.61097i) q^{52} +(-8.17440 + 4.71949i) q^{53} +2.25134 q^{55} +(2.04822 - 7.19756i) q^{56} +(0.246681 + 0.578380i) q^{58} +(-8.59663 + 4.96327i) q^{59} +(-5.23284 + 9.06355i) q^{61} +(-10.0702 - 7.56134i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(-1.81968 + 3.15177i) q^{65} +(-1.45058 - 2.51247i) q^{67} +(1.21435 - 4.94277i) q^{68} +(0.0938060 - 2.58084i) q^{70} +5.29150i q^{71} +(-5.28541 + 3.05153i) q^{73} +(9.73174 + 1.17795i) q^{74} +(-1.07527 + 0.312329i) q^{76} +(4.92768 + 7.08473i) q^{77} +(5.01803 + 2.89716i) q^{79} +(-2.44654 - 1.27937i) q^{80} +(5.41921 + 12.7061i) q^{82} +1.83845i q^{83} -1.75651i q^{85} +(9.10463 - 1.49016i) q^{88} +(-1.50000 - 0.866025i) q^{89} +(-13.9012 + 1.17220i) q^{91} +(-5.55787 + 1.61437i) q^{92} +(0.748048 - 6.18008i) q^{94} +(-0.334649 + 0.193210i) q^{95} +7.42325i q^{97} +(8.32695 - 5.35368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^8	\( 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58} - 42 q^{59} - 72 q^{64} + 12 q^{65} + 30 q^{67} + 36 q^{68} + 30 q^{70} + 18 q^{73} - 12 q^{74} - 36 q^{80} + 54 q^{82} + 6 q^{88} - 18 q^{89} - 72 q^{91} - 60 q^{92} - 12 q^{94} + 6 q^{98}+O(q^{100}) \) 12 * q + 12 * q^8 + 6 * q^10 + 6 * q^11 - 6 * q^14 + 6 * q^17 - 6 * q^19 + 24 * q^22 - 6 * q^26 + 6 * q^28 - 18 * q^35 + 24 * q^38 + 42 * q^40 - 6 * q^44 - 18 * q^46 - 12 * q^49 + 48 * q^50 - 24 * q^52 + 18 * q^58 - 42 * q^59 - 72 * q^64 + 12 * q^65 + 30 * q^67 + 36 * q^68 + 30 * q^70 + 18 * q^73 - 12 * q^74 - 36 * q^80 + 54 * q^82 + 6 * q^88 - 18 * q^89 - 72 * q^91 - 60 * q^92 - 12 * q^94 + 6 * q^98

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