LMFDB - Embedded newform 270.2.m.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(17,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("270.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.m (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	270.17
Dual form			270.2.m.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(1.18034 - 4.40508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.224745 - 2.22474i) q^{10} +(0.550510 - 0.317837i) q^{11} +(0.896575 + 3.34607i) q^{13} +(2.28024 - 3.94949i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.317837 - 0.317837i) q^{17} +6.44949i q^{19} +(0.358719 - 2.20711i) q^{20} +(0.614014 - 0.164525i) q^{22} +(0.965926 - 0.258819i) q^{23} +(-3.74264 + 3.31552i) q^{25} +3.46410i q^{26} +(3.22474 - 3.22474i) q^{28} +(-0.158919 - 0.275255i) q^{29} +(-0.224745 + 0.389270i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.389270 - 0.224745i) q^{34} +(-10.1459 + 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-1.66925 + 6.22973i) q^{38} +(0.917738 - 2.03906i) q^{40} +(-6.39898 - 3.69445i) q^{41} +(3.34607 + 0.896575i) q^{43} +0.635674 q^{44} +1.00000 q^{46} +(8.69333 + 2.32937i) q^{47} +(-11.9494 - 6.89898i) q^{49} +(-4.47323 + 2.23388i) q^{50} +(-0.896575 + 3.34607i) q^{52} +(3.78194 + 3.78194i) q^{53} +(-1.10102 - 0.898979i) q^{55} +(3.94949 - 2.28024i) q^{56} +(-0.0822623 - 0.307007i) q^{58} +(-4.48905 + 7.77526i) q^{59} +(0.275255 + 0.476756i) q^{61} +(-0.317837 + 0.317837i) q^{62} +1.00000i q^{64} +(6.28497 - 4.52761i) q^{65} +(6.38512 - 1.71089i) q^{67} +(0.434174 - 0.116337i) q^{68} +(-10.0655 - 1.63593i) q^{70} +6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(-3.22474 + 5.58542i) q^{76} +(-0.750311 - 2.80020i) q^{77} +(2.12132 - 1.22474i) q^{79} +(1.41421 - 1.73205i) q^{80} +(-5.22474 - 5.22474i) q^{82} +(-1.41043 + 5.26380i) q^{83} +(-0.916536 - 0.412514i) q^{85} +(3.00000 + 1.73205i) q^{86} +(0.614014 + 0.164525i) q^{88} -8.02458 q^{89} +15.7980 q^{91} +(0.965926 + 0.258819i) q^{92} +(7.79423 + 4.50000i) q^{94} +(13.4844 - 5.11376i) q^{95} +(0.695075 - 2.59405i) q^{97} +(-9.75663 - 9.75663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100}) $ 8 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 + 24 * q^11 + 4 * q^16 - 8 * q^22 + 4 * q^25 + 16 * q^28 + 8 * q^31 - 24 * q^37 - 12 * q^38 + 4 * q^40 - 12 * q^41 + 8 * q^46 - 24 * q^50 - 48 * q^55 + 12 * q^56 - 4 * q^58 + 12 * q^61 + 24 * q^65 + 4 * q^67 + 12 * q^68 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 24 * q^77 - 32 * q^82 - 12 * q^83 - 20 * q^85 + 24 * q^86 - 8 * q^88 + 48 * q^91 + 24 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$6$		0			0
$7$	1.18034	−	4.40508i	0.446126	−	1.66497i	−0.266820	−	0.963746i	$-0.585973\pi$
$7$	1.18034	−	4.40508i	0.446126	−	1.66497i	0.712946	−	0.701219i	$-0.247360\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.224745	−	2.22474i	−0.0710706	−	0.703526i
$11$	0.550510	−	0.317837i	0.165985	−	0.0958315i	−0.414706	−	0.909955i	$-0.636116\pi$
$11$	0.550510	−	0.317837i	0.165985	−	0.0958315i	0.580691	+	0.814124i	$0.302782\pi$
$12$		0			0
$13$	0.896575	+	3.34607i	0.248665	+	0.928032i	0.971506	+	0.237016i	$0.0761695\pi$
$13$	0.896575	+	3.34607i	0.248665	+	0.928032i	−0.722840	+	0.691015i	$0.757164\pi$
$14$	2.28024	−	3.94949i	0.609419	−	1.05555i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.317837	−	0.317837i	0.0770869	−	0.0770869i	−0.667512	−	0.744599i	$-0.732641\pi$
$17$	0.317837	−	0.317837i	0.0770869	−	0.0770869i	0.744599	+	0.667512i	$0.232641\pi$
$18$		0			0
$19$			6.44949i			1.47961i	0.672819	+	0.739807i	$0.265083\pi$
$19$			6.44949i			1.47961i	−0.672819	+	0.739807i	$0.734917\pi$
$20$	0.358719	−	2.20711i	0.0802121	−	0.493524i
$21$		0			0
$22$	0.614014	−	0.164525i	0.130908	−	0.0350768i
$23$	0.965926	−	0.258819i	0.201409	−	0.0539675i	−0.156704	−	0.987646i	$-0.550087\pi$
$23$	0.965926	−	0.258819i	0.201409	−	0.0539675i	0.358113	+	0.933678i	$0.383420\pi$
$24$		0			0
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$			3.46410i			0.679366i
$27$		0			0
$28$	3.22474	−	3.22474i	0.609419	−	0.609419i
$29$	−0.158919	−	0.275255i	−0.0295104	−	0.0511136i	0.850893	−	0.525339i	$-0.176061\pi$
$29$	−0.158919	−	0.275255i	−0.0295104	−	0.0511136i	−0.880403	+	0.474225i	$0.842728\pi$
$30$		0			0
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	−0.885502	−	0.464635i	$-0.846186\pi$
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	0.845137	+	0.534550i	$0.179519\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$	0.389270	−	0.224745i	0.0667592	−	0.0385434i
$35$	−10.1459	+	1.02494i	−1.71497	+	0.173247i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−1.66925	+	6.22973i	−0.270788	+	1.01060i
$39$		0			0
$40$	0.917738	−	2.03906i	0.145107	−	0.322403i
$41$	−6.39898	−	3.69445i	−0.999353	−	0.576977i	−0.0912960	−	0.995824i	$-0.529101\pi$
$41$	−6.39898	−	3.69445i	−0.999353	−	0.576977i	−0.908057	+	0.418847i	$0.862434\pi$
$42$		0			0
$43$	3.34607	+	0.896575i	0.510270	+	0.136726i	0.504762	−	0.863258i	$-0.331580\pi$
$43$	3.34607	+	0.896575i	0.510270	+	0.136726i	0.00550783	+	0.999985i	$0.498247\pi$
$44$	0.635674			0.0958315
$45$		0			0
$46$	1.00000			0.147442
$47$	8.69333	+	2.32937i	1.26805	+	0.339774i	0.829285	−	0.558827i	$-0.188748\pi$
$47$	8.69333	+	2.32937i	1.26805	+	0.339774i	0.438768	+	0.898600i	$0.355415\pi$
$48$		0			0
$49$	−11.9494	−	6.89898i	−1.70705	−	0.985568i
$50$	−4.47323	+	2.23388i	−0.632611	+	0.315918i
$51$		0			0
$52$	−0.896575	+	3.34607i	−0.124333	+	0.464016i
$53$	3.78194	+	3.78194i	0.519489	+	0.519489i	0.917417	−	0.397928i	$-0.130270\pi$
$53$	3.78194	+	3.78194i	0.519489	+	0.519489i	−0.397928	+	0.917417i	$0.630270\pi$
$54$		0			0
$55$	−1.10102	−	0.898979i	−0.148462	−	0.121218i
$56$	3.94949	−	2.28024i	0.527773	−	0.304710i
$57$		0			0
$58$	−0.0822623	−	0.307007i	−0.0108016	−	0.0403120i
$59$	−4.48905	+	7.77526i	−0.584424	+	1.01225i	0.410523	+	0.911850i	$0.365346\pi$
$59$	−4.48905	+	7.77526i	−0.584424	+	1.01225i	−0.994947	+	0.100402i	$0.967987\pi$
$60$		0			0
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	0.883109	−	0.469168i	$-0.155446\pi$
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	−0.847866	+	0.530211i	$0.822113\pi$
$62$	−0.317837	+	0.317837i	−0.0403654	+	0.0403654i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	6.28497	−	4.52761i	0.779554	−	0.561580i
$66$		0			0
$67$	6.38512	−	1.71089i	0.780067	−	0.209018i	0.153253	−	0.988187i	$-0.451025\pi$
$67$	6.38512	−	1.71089i	0.780067	−	0.209018i	0.626814	+	0.779169i	$0.284358\pi$
$68$	0.434174	−	0.116337i	0.0526513	−	0.0141079i
$69$		0			0
$70$	−10.0655	−	1.63593i	−1.20305	−	0.195531i
$71$			6.29253i			0.746786i	0.927673	+	0.373393i	$0.121806\pi$
$71$			6.29253i			0.746786i	−0.927673	+	0.373393i	$0.878194\pi$
$72$		0			0
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	−0.984249	−	0.176785i	$-0.943430\pi$
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	0.176785	+	0.984249i	$0.443430\pi$
$74$	−2.12132	−	3.67423i	−0.246598	−	0.427121i
$75$		0			0
$76$	−3.22474	+	5.58542i	−0.369904	+	0.640692i
$77$	−0.750311	−	2.80020i	−0.0855059	−	0.319112i
$78$		0			0
$79$	2.12132	−	1.22474i	0.238667	−	0.137795i	−0.375897	−	0.926662i	$-0.622665\pi$
$79$	2.12132	−	1.22474i	0.238667	−	0.137795i	0.614564	+	0.788867i	$0.289332\pi$
$80$	1.41421	−	1.73205i	0.158114	−	0.193649i
$81$		0			0
$82$	−5.22474	−	5.22474i	−0.576977	−	0.576977i
$83$	−1.41043	+	5.26380i	−0.154815	+	0.577777i	0.844306	+	0.535861i	$0.180013\pi$
$83$	−1.41043	+	5.26380i	−0.154815	+	0.577777i	−0.999121	+	0.0419163i	$0.986654\pi$
$84$		0			0
$85$	−0.916536	−	0.412514i	−0.0994123	−	0.0447434i
$86$	3.00000	+	1.73205i	0.323498	+	0.186772i
$87$		0			0
$88$	0.614014	+	0.164525i	0.0654542	+	0.0175384i
$89$	−8.02458			−0.850604			−0.425302	−	0.905052i	$-0.639832\pi$
$89$	−8.02458			−0.850604			−0.425302	+	0.905052i	$0.639832\pi$
$90$		0			0
$91$	15.7980			1.65608
$92$	0.965926	+	0.258819i	0.100705	+	0.0269838i
$93$		0			0
$94$	7.79423	+	4.50000i	0.803913	+	0.464140i
$95$	13.4844	−	5.11376i	1.38347	−	0.524660i
$96$		0			0
$97$	0.695075	−	2.59405i	0.0705741	−	0.263386i	−0.921619	−	0.388095i	$-0.873133\pi$
$97$	0.695075	−	2.59405i	0.0705741	−	0.263386i	0.992193	+	0.124709i	$0.0397998\pi$
$98$	−9.75663	−	9.75663i	−0.985568	−	0.985568i
$99$		0			0
$100$	−4.89898	+	1.00000i	−0.489898	+	0.100000i
$101$	−10.8990	+	6.29253i	−1.08449	+	0.626130i	−0.932104	−	0.362191i	$-0.882029\pi$
$101$	−10.8990	+	6.29253i	−1.08449	+	0.626130i	−0.152385	+	0.988321i	$0.548695\pi$
$102$		0			0
$103$	−2.52520	−	9.42418i	−0.248816	−	0.928592i	−0.971427	−	0.237338i	$-0.923725\pi$
$103$	−2.52520	−	9.42418i	−0.248816	−	0.928592i	0.722612	−	0.691254i	$-0.242942\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	2.67423	+	4.63191i	0.259745	+	0.449891i
$107$	13.6100	−	13.6100i	1.31573	−	1.31573i	0.398606	−	0.917122i	$-0.369494\pi$
$107$	13.6100	−	13.6100i	1.31573	−	1.31573i	0.917122	−	0.398606i	$-0.130506\pi$
$108$		0			0
$109$		−	5.65153i		−	0.541318i	−0.962675	−	0.270659i	$-0.912758\pi$
$109$		−	5.65153i		−	0.541318i	0.962675	−	0.270659i	$-0.0872417\pi$
$110$	−0.830831	−	1.15331i	−0.0792166	−	0.109964i
$111$		0			0
$112$	4.40508	−	1.18034i	0.416241	−	0.111532i
$113$	5.60040	−	1.50062i	0.526841	−	0.141167i	0.0144120	−	0.999896i	$-0.495412\pi$
$113$	5.60040	−	1.50062i	0.526841	−	0.141167i	0.512429	+	0.858729i	$0.328746\pi$
$114$		0			0
$115$	−1.30701	−	1.81431i	−0.121879	−	0.169186i
$116$		−	0.317837i		−	0.0295104i
$117$		0			0
$118$	−6.34847	+	6.34847i	−0.584424	+	0.584424i
$119$	−1.02494	−	1.77526i	−0.0939565	−	0.162737i
$120$		0			0
$121$	−5.29796	+	9.17633i	−0.481633	+	0.834212i
$122$	0.142483	+	0.531752i	0.0128998	+	0.0481426i
$123$		0			0
$124$	−0.389270	+	0.224745i	−0.0349574	+	0.0201827i
$125$	9.89949	+	5.19615i	0.885438	+	0.464758i
$126$		0			0
$127$	1.87628	+	1.87628i	0.166493	+	0.166493i	0.785436	−	0.618943i	$-0.212439\pi$
$127$	1.87628	+	1.87628i	0.166493	+	0.166493i	−0.618943	+	0.785436i	$0.712439\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$	7.24264	−	2.74666i	0.635222	−	0.240898i
$131$	3.12372	+	1.80348i	0.272921	+	0.157571i	0.630214	−	0.776421i	$-0.282967\pi$
$131$	3.12372	+	1.80348i	0.272921	+	0.157571i	−0.357293	+	0.933992i	$0.616300\pi$
$132$		0			0
$133$	28.4105	+	7.61258i	2.46351	+	0.660095i
$134$	6.61037			0.571049
$135$		0			0
$136$	0.449490			0.0385434
$137$	−21.0552	−	5.64173i	−1.79887	−	0.482005i	−0.805068	−	0.593183i	$-0.797871\pi$
$137$	−21.0552	−	5.64173i	−1.79887	−	0.482005i	−0.993801	+	0.111178i	$0.964538\pi$
$138$		0			0
$139$	−2.68556	−	1.55051i	−0.227786	−	0.131513i	0.381764	−	0.924260i	$-0.375317\pi$
$139$	−2.68556	−	1.55051i	−0.227786	−	0.131513i	−0.609550	+	0.792747i	$0.708650\pi$
$140$	−9.29908	−	4.18532i	−0.785916	−	0.353724i
$141$		0			0
$142$	−1.62863	+	6.07812i	−0.136671	+	0.510064i
$143$	1.55708	+	1.55708i	0.130209	+	0.130209i
$144$		0			0
$145$	−0.449490	+	0.550510i	−0.0373281	+	0.0457174i
$146$	−8.44949	+	4.87832i	−0.699285	+	0.403732i
$147$		0			0
$148$	−1.09808	−	4.09808i	−0.0902613	−	0.336860i
$149$	2.20881	−	3.82577i	0.180952	−	0.313419i	−0.761253	−	0.648455i	$-0.775415\pi$
$149$	2.20881	−	3.82577i	0.180952	−	0.313419i	0.942205	+	0.335036i	$0.108749\pi$
$150$		0			0
$151$	−8.79796	−	15.2385i	−0.715968	−	1.24009i	−0.962585	−	0.270980i	$-0.912652\pi$
$151$	−8.79796	−	15.2385i	−0.715968	−	1.24009i	0.246617	−	0.969113i	$-0.420681\pi$
$152$	−4.56048	+	4.56048i	−0.369904	+	0.369904i
$153$		0			0
$154$		−	2.89898i		−	0.233606i
$155$	0.992072	+	0.161241i	0.0796851	+	0.0129512i
$156$		0			0
$157$	14.1363	−	3.78780i	1.12820	−	0.302300i	0.354001	−	0.935245i	$-0.384821\pi$
$157$	14.1363	−	3.78780i	1.12820	−	0.302300i	0.774196	+	0.632945i	$0.218154\pi$
$158$	2.36603	−	0.633975i	0.188231	−	0.0504363i
$159$		0			0
$160$	1.81431	−	1.30701i	0.143434	−	0.103328i
$161$		−	4.56048i		−	0.359416i
$162$		0			0
$163$	4.44949	−	4.44949i	0.348511	−	0.348511i	−0.511044	−	0.859555i	$-0.670741\pi$
$163$	4.44949	−	4.44949i	0.348511	−	0.348511i	0.859555	+	0.511044i	$0.170741\pi$
$164$	−3.69445	−	6.39898i	−0.288488	−	0.499676i
$165$		0			0
$166$	−2.72474	+	4.71940i	−0.211481	+	0.366296i
$167$	2.27708	+	8.49818i	0.176206	+	0.657609i	0.996343	+	0.0854420i	$0.0272302\pi$
$167$	2.27708	+	8.49818i	0.176206	+	0.657609i	−0.820137	+	0.572167i	$0.806103\pi$
$168$		0			0
$169$	0.866025	−	0.500000i	0.0666173	−	0.0384615i
$170$	−0.778539	−	0.635674i	−0.0597112	−	0.0487540i
$171$		0			0
$172$	2.44949	+	2.44949i	0.186772	+	0.186772i
$173$	3.33850	−	12.4595i	0.253822	−	0.947275i	−0.714921	−	0.699206i	$-0.753537\pi$
$173$	3.33850	−	12.4595i	0.253822	−	0.947275i	0.968742	−	0.248069i	$-0.0797961\pi$
$174$		0			0
$175$	10.1875	+	20.4001i	0.770105	+	1.54210i
$176$	0.550510	+	0.317837i	0.0414963	+	0.0239579i
$177$		0			0
$178$	−7.75115	−	2.07691i	−0.580973	−	0.155671i
$179$	10.6780			0.798114			0.399057	−	0.916926i	$-0.369338\pi$
$179$	10.6780			0.798114			0.399057	+	0.916926i	$0.369338\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	15.2597	+	4.08881i	1.13112	+	0.303083i
$183$		0			0
$184$	0.866025	+	0.500000i	0.0638442	+	0.0368605i
$185$	−3.89363	+	8.65099i	−0.286265	+	0.636033i
$186$		0			0
$187$	0.0739521	−	0.275993i	0.00540792	−	0.0201826i
$188$	6.36396	+	6.36396i	0.464140	+	0.464140i
$189$		0			0
$190$	14.3485	−	1.44949i	1.04095	−	0.105157i
$191$	15.1237	−	8.73169i	1.09431	−	0.631803i	0.159593	−	0.987183i	$-0.448982\pi$
$191$	15.1237	−	8.73169i	1.09431	−	0.631803i	0.934722	+	0.355380i	$0.115649\pi$
$192$		0			0
$193$	−4.48288	−	16.7303i	−0.322685	−	1.20428i	−0.916619	−	0.399762i	$-0.869093\pi$
$193$	−4.48288	−	16.7303i	−0.322685	−	1.20428i	0.593934	−	0.804513i	$-0.297574\pi$
$194$	1.34278	−	2.32577i	0.0964061	−	0.166980i
$195$		0			0
$196$	−6.89898	−	11.9494i	−0.492784	−	0.853527i
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	−0.415829	−	0.909443i	$-0.636508\pi$
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	0.909443	+	0.415829i	$0.136508\pi$
$198$		0			0
$199$			8.44949i			0.598968i	0.954101	+	0.299484i	$0.0968146\pi$
$199$			8.44949i			0.598968i	−0.954101	+	0.299484i	$0.903185\pi$
$200$	−4.99087	−	0.302023i	−0.352908	−	0.0213563i
$201$		0			0
$202$	−12.1562	+	3.25725i	−0.855310	+	0.229179i
$203$	−1.40010	+	0.375156i	−0.0982677	+	0.0263308i
$204$		0			0
$205$	−2.65054	+	16.3081i	−0.185122	+	1.13901i
$206$		−	9.75663i		−	0.679777i
$207$		0			0
$208$	−2.44949	+	2.44949i	−0.169842	+	0.169842i
$209$	2.04989	+	3.55051i	0.141794	+	0.245594i
$210$		0			0
$211$	−4.55051	+	7.88171i	−0.313270	+	0.542600i	−0.979068	−	0.203532i	$-0.934758\pi$
$211$	−4.55051	+	7.88171i	−0.313270	+	0.542600i	0.665798	+	0.746132i	$0.268091\pi$
$212$	1.38429	+	5.16622i	0.0950731	+	0.354818i
$213$		0			0
$214$	16.6688	−	9.62372i	1.13945	−	0.657864i
$215$	−0.778539	−	7.70674i	−0.0530959	−	0.525595i
$216$		0			0
$217$	1.44949	+	1.44949i	0.0983978	+	0.0983978i
$218$	1.46272	−	5.45896i	0.0990682	−	0.369727i
$219$		0			0
$220$	−0.504022	−	1.32905i	−0.0339812	−	0.0896045i
$221$	1.34847	+	0.778539i	0.0907079	+	0.0523702i
$222$		0			0
$223$	−24.7575	−	6.63374i	−1.65788	−	0.444228i	−0.696078	−	0.717966i	$-0.745073\pi$
$223$	−24.7575	−	6.63374i	−1.65788	−	0.444228i	−0.961804	+	0.273738i	$0.911740\pi$
$224$	4.56048			0.304710
$225$		0			0
$226$	5.79796			0.385674
$227$	−24.0506	−	6.44433i	−1.59629	−	0.427725i	−0.652372	−	0.757899i	$-0.726226\pi$
$227$	−24.0506	−	6.44433i	−1.59629	−	0.427725i	−0.943920	+	0.330174i	$0.892893\pi$
$228$		0			0
$229$	1.43027	+	0.825765i	0.0945147	+	0.0545681i	0.546512	−	0.837451i	$-0.315955\pi$
$229$	1.43027	+	0.825765i	0.0945147	+	0.0545681i	−0.451998	+	0.892019i	$0.649288\pi$
$230$	−0.792893	−	2.09077i	−0.0522818	−	0.137861i
$231$		0			0
$232$	0.0822623	−	0.307007i	0.00540079	−	0.0201560i
$233$	−14.4600	−	14.4600i	−0.947304	−	0.947304i	0.0513751	−	0.998679i	$-0.483640\pi$
$233$	−14.4600	−	14.4600i	−0.947304	−	0.947304i	−0.998679	+	0.0513751i	$0.983640\pi$
$234$		0			0
$235$	−2.02270	−	20.0227i	−0.131947	−	1.30614i
$236$	−7.77526	+	4.48905i	−0.506126	+	0.292212i
$237$		0			0
$238$	−0.530550	−	1.98004i	−0.0343905	−	0.128347i
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	0.449485	+	0.893288i	$0.351607\pi$
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	−0.998353	+	0.0573782i	$0.981726\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$	−7.49245	+	7.49245i	−0.481633	+	0.481633i
$243$		0			0
$244$			0.550510i			0.0352428i
$245$	−4.94960	+	30.4536i	−0.316218	+	1.94561i
$246$		0			0
$247$	−21.5804	+	5.78245i	−1.37313	+	0.367929i
$248$	−0.434174	+	0.116337i	−0.0275701	+	0.00738738i
$249$		0			0
$250$	8.21731	+	7.58128i	0.519709	+	0.479482i
$251$			2.68556i			0.169511i	0.996402	+	0.0847556i	$0.0270110\pi$
$251$			2.68556i			0.169511i	−0.996402	+	0.0847556i	$0.972989\pi$
$252$		0			0
$253$	0.449490	−	0.449490i	0.0282592	−	0.0282592i
$254$	1.32673	+	2.29796i	0.0832463	+	0.144187i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.67050	+	17.4305i	0.291337	+	1.08729i	0.944083	+	0.329709i	$0.106951\pi$
$257$	4.67050	+	17.4305i	0.291337	+	1.08729i	−0.652745	+	0.757578i	$0.726383\pi$
$258$		0			0
$259$	−16.7563	+	9.67423i	−1.04118	+	0.601128i
$260$	7.70674	−	0.778539i	0.477952	−	0.0482829i
$261$		0			0
$262$	2.55051	+	2.55051i	0.157571	+	0.157571i
$263$	−4.32149	+	16.1280i	−0.266474	+	0.994495i	0.694868	+	0.719138i	$0.255463\pi$
$263$	−4.32149	+	16.1280i	−0.266474	+	0.994495i	−0.961342	+	0.275358i	$0.911204\pi$
$264$		0			0
$265$	4.90849	−	10.9058i	0.301526	−	0.669940i
$266$	25.4722	+	14.7064i	1.56180	+	0.901706i
$267$		0			0
$268$	6.38512	+	1.71089i	0.390033	+	0.104509i
$269$	−15.0956			−0.920398			−0.460199	−	0.887816i	$-0.652222\pi$
$269$	−15.0956			−0.920398			−0.460199	+	0.887816i	$0.652222\pi$
$270$		0			0
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	0.434174	+	0.116337i	0.0263257	+	0.00705394i
$273$		0			0
$274$	−18.8776	−	10.8990i	−1.14044	−	0.658431i
$275$	−1.00657	+	3.01478i	−0.0606983	+	0.181798i
$276$		0			0
$277$	−7.28353	+	27.1825i	−0.437625	+	1.63324i	0.297080	+	0.954852i	$0.403987\pi$
$277$	−7.28353	+	27.1825i	−0.437625	+	1.63324i	−0.734705	+	0.678386i	$0.762680\pi$
$278$	−2.19275	−	2.19275i	−0.131513	−	0.131513i
$279$		0			0
$280$	−7.89898	−	6.44949i	−0.472054	−	0.385431i
$281$	14.8485	−	8.57277i	0.885785	−	0.511408i	0.0132238	−	0.999913i	$-0.495791\pi$
$281$	14.8485	−	8.57277i	0.885785	−	0.511408i	0.872562	+	0.488504i	$0.162457\pi$
$282$		0			0
$283$	6.26772	+	23.3914i	0.372577	+	1.39048i	0.856853	+	0.515561i	$0.172417\pi$
$283$	6.26772	+	23.3914i	0.372577	+	1.39048i	−0.484275	+	0.874916i	$0.660917\pi$
$284$	−3.14626	+	5.44949i	−0.186696	+	0.323368i
$285$		0			0
$286$	1.10102	+	1.90702i	0.0651047	+	0.112765i
$287$	−23.8273	+	23.8273i	−1.40648	+	1.40648i
$288$		0			0
$289$			16.7980i			0.988115i
$290$	−0.576656	+	0.415416i	−0.0338624	+	0.0243940i
$291$		0			0
$292$	−9.42418	+	2.52520i	−0.551508	+	0.147776i
$293$	−21.2942	+	5.70577i	−1.24402	+	0.333335i	−0.820024	−	0.572329i	$-0.806040\pi$
$293$	−21.2942	+	5.70577i	−1.24402	+	0.333335i	−0.423998	+	0.905663i	$0.639374\pi$
$294$		0			0
$295$	19.8156	+	3.22062i	1.15371	+	0.187512i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	3.12372	−	3.12372i	0.180952	−	0.180952i
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$		0			0
$301$	7.89898	−	13.6814i	0.455290	−	0.788585i
$302$	−4.55416	−	16.9964i	−0.262062	−	0.978030i
$303$		0			0
$304$	−5.58542	+	3.22474i	−0.320346	+	0.184952i
$305$	0.778539	−	0.953512i	0.0445790	−	0.0545979i
$306$		0			0
$307$	−6.67423	−	6.67423i	−0.380919	−	0.380919i	0.490514	−	0.871433i	$-0.336809\pi$
$307$	−6.67423	−	6.67423i	−0.380919	−	0.380919i	−0.871433	+	0.490514i	$0.836809\pi$
$308$	0.750311	−	2.80020i	0.0427529	−	0.159556i
$309$		0			0
$310$	0.916536	+	0.412514i	0.0520557	+	0.0234292i
$311$	−23.8207	−	13.7529i	−1.35075	−	0.779853i	−0.362392	−	0.932026i	$-0.618040\pi$
$311$	−23.8207	−	13.7529i	−1.35075	−	0.779853i	−0.988354	+	0.152172i	$0.951373\pi$
$312$		0			0
$313$	−11.5422	−	3.09273i	−0.652405	−	0.174811i	−0.0825888	−	0.996584i	$-0.526319\pi$
$313$	−11.5422	−	3.09273i	−0.652405	−	0.174811i	−0.569816	+	0.821772i	$0.692985\pi$
$314$	14.6349			0.825898
$315$		0			0
$316$	2.44949			0.137795
$317$	10.5276	+	2.82086i	0.591289	+	0.158435i	0.542042	−	0.840351i	$-0.317651\pi$
$317$	10.5276	+	2.82086i	0.591289	+	0.158435i	0.0492469	+	0.998787i	$0.484318\pi$
$318$		0			0
$319$	−0.174973	−	0.101021i	−0.00979659	−	0.00565606i
$320$	2.09077	−	0.792893i	0.116878	−	0.0443241i
$321$		0			0
$322$	1.18034	−	4.40508i	0.0657777	−	0.245486i
$323$	2.04989	+	2.04989i	0.114059	+	0.114059i
$324$		0			0
$325$	−14.4495	−	9.55051i	−0.801513	−	0.529767i
$326$	5.44949	−	3.14626i	0.301819	−	0.174255i
$327$		0			0
$328$	−1.91239	−	7.13713i	−0.105594	−	0.394082i
$329$	20.5222	−	35.5454i	1.13142	−	1.95968i
$330$		0			0
$331$	−0.224745	−	0.389270i	−0.0123531	−	0.0213962i	0.859783	−	0.510660i	$-0.170599\pi$
$331$	−0.224745	−	0.389270i	−0.0123531	−	0.0213962i	−0.872136	+	0.489264i	$0.837266\pi$
$332$	−3.85337	+	3.85337i	−0.211481	+	0.211481i
$333$		0			0
$334$			8.79796i			0.481403i
$335$	−8.63980	−	11.9933i	−0.472042	−	0.655263i
$336$		0			0
$337$	3.00804	−	0.806003i	0.163859	−	0.0439058i	−0.175957	−	0.984398i	$-0.556302\pi$
$337$	3.00804	−	0.806003i	0.163859	−	0.0439058i	0.339816	+	0.940492i	$0.389635\pi$
$338$	0.965926	−	0.258819i	0.0525394	−	0.0140779i
$339$		0			0
$340$	−0.587486	−	0.815515i	−0.0318609	−	0.0442275i
$341$			0.285729i			0.0154731i
$342$		0			0
$343$	−21.9217	+	21.9217i	−1.18366	+	1.18366i
$344$	1.73205	+	3.00000i	0.0933859	+	0.161749i
$345$		0			0
$346$	6.44949	−	11.1708i	0.346727	−	0.600548i
$347$	−6.15937	−	22.9871i	−0.330652	−	1.23401i	−0.908507	−	0.417870i	$-0.862777\pi$
$347$	−6.15937	−	22.9871i	−0.330652	−	1.23401i	0.577855	−	0.816140i	$-0.303890\pi$
$348$		0			0
$349$	25.1541	−	14.5227i	1.34647	−	0.777383i	0.358719	−	0.933446i	$-0.383214\pi$
$349$	25.1541	−	14.5227i	1.34647	−	0.777383i	0.987747	+	0.156063i	$0.0498803\pi$
$350$	4.56048	+	22.3417i	0.243768	+	1.19421i
$351$		0			0
$352$	0.449490	+	0.449490i	0.0239579	+	0.0239579i
$353$	8.87564	−	33.1244i	0.472403	−	1.76303i	−0.158694	−	0.987328i	$-0.550728\pi$
$353$	8.87564	−	33.1244i	0.472403	−	1.76303i	0.631097	−	0.775704i	$-0.282605\pi$
$354$		0			0
$355$	13.1562	−	4.98930i	0.698260	−	0.264805i
$356$	−6.94949	−	4.01229i	−0.368322	−	0.212651i
$357$		0			0
$358$	10.3142	+	2.76368i	0.545122	+	0.146065i
$359$	3.32124			0.175288			0.0876441	−	0.996152i	$-0.472066\pi$
$359$	3.32124			0.175288			0.0876441	+	0.996152i	$0.472066\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$	−14.9231	−	3.99862i	−0.784339	−	0.210163i
$363$		0			0
$364$	13.6814	+	7.89898i	0.717102	+	0.414019i
$365$	19.8943	+	8.95403i	1.04132	+	0.468675i
$366$		0			0
$367$	−1.06110	+	3.96008i	−0.0553890	+	0.206714i	−0.988075	−	0.153976i	$-0.950792\pi$
$367$	−1.06110	+	3.96008i	−0.0553890	+	0.206714i	0.932686	+	0.360690i	$0.117459\pi$
$368$	0.707107	+	0.707107i	0.0368605	+	0.0368605i
$369$		0			0
$370$	−6.00000	+	7.34847i	−0.311925	+	0.382029i
$371$	21.1237	−	12.1958i	1.09669	−	0.633174i
$372$		0			0
$373$	−0.127549	−	0.476018i	−0.00660422	−	0.0246473i	0.962545	−	0.271122i	$-0.0873946\pi$
$373$	−0.127549	−	0.476018i	−0.00660422	−	0.0246473i	−0.969149	+	0.246474i	$0.920728\pi$
$374$	0.142865	−	0.247449i	0.00738735	−	0.0127953i
$375$		0			0
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	0.778539	−	0.778539i	0.0400968	−	0.0400968i
$378$		0			0
$379$		−	21.3485i		−	1.09660i	−0.836283	−	0.548299i	$-0.815276\pi$
$379$		−	21.3485i		−	1.09660i	0.836283	−	0.548299i	$-0.184724\pi$
$380$	14.2347	+	2.31356i	0.730225	+	0.118683i
$381$		0			0
$382$	16.8683	−	4.51985i	0.863058	−	0.231256i
$383$	7.92256	−	2.12284i	0.404824	−	0.108472i	−0.0506606	−	0.998716i	$-0.516133\pi$
$383$	7.92256	−	2.12284i	0.404824	−	0.108472i	0.455485	+	0.890244i	$0.349466\pi$
$384$		0			0
$385$	−5.25966	+	3.78899i	−0.268057	+	0.193105i
$386$		−	17.3205i		−	0.881591i
$387$		0			0
$388$	1.89898	−	1.89898i	0.0964061	−	0.0964061i
$389$	18.4008	+	31.8712i	0.932959	+	1.61593i	0.778233	+	0.627975i	$0.216116\pi$
$389$	18.4008	+	31.8712i	0.932959	+	1.61593i	0.154726	+	0.987957i	$0.450551\pi$
$390$		0			0
$391$	0.224745	−	0.389270i	0.0113658	−	0.0196862i
$392$	−3.57117	−	13.3278i	−0.180372	−	0.673156i
$393$		0			0
$394$	8.48528	−	4.89898i	0.427482	−	0.246807i
$395$	−4.24264	−	3.46410i	−0.213470	−	0.174298i
$396$		0			0
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	0.920428	−	0.390913i	$-0.127841\pi$
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	−0.390913	+	0.920428i	$0.627841\pi$
$398$	−2.18689	+	8.16158i	−0.109619	+	0.409103i
$399$		0			0
$400$	−4.74264	−	1.58346i	−0.237132	−	0.0791732i
$401$	−7.65153	−	4.41761i	−0.382099	−	0.220605i	0.296632	−	0.954992i	$-0.404137\pi$
$401$	−7.65153	−	4.41761i	−0.382099	−	0.220605i	−0.678731	+	0.734387i	$0.737470\pi$
$402$		0			0
$403$	−1.50402	−	0.403001i	−0.0749207	−	0.0200749i
$404$	−12.5851			−0.626130
$405$		0			0
$406$	−1.44949			−0.0719370
$407$	−2.60504	−	0.698019i	−0.129127	−	0.0345995i
$408$		0			0
$409$	25.0273	+	14.4495i	1.23752	+	0.714481i	0.968586	−	0.248678i	$-0.0799961\pi$
$409$	25.0273	+	14.4495i	1.23752	+	0.714481i	0.268932	+	0.963159i	$0.413329\pi$
$410$	−6.78108	+	15.0664i	−0.334893	+	0.744077i
$411$		0			0
$412$	2.52520	−	9.42418i	0.124408	−	0.464296i
$413$	28.9521	+	28.9521i	1.42464	+	1.42464i
$414$		0			0
$415$	12.1237	−	1.22474i	0.595130	−	0.0601204i
$416$	−3.00000	+	1.73205i	−0.147087	+	0.0849208i
$417$		0			0
$418$	1.06110	+	3.96008i	0.0519001	+	0.193694i
$419$	2.51059	−	4.34847i	0.122650	−	0.212437i	−0.798162	−	0.602443i	$-0.794194\pi$
$419$	2.51059	−	4.34847i	0.122650	−	0.212437i	0.920812	+	0.390007i	$0.127527\pi$
$420$		0			0
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	0.921461	−	0.388471i	$-0.126997\pi$
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	−0.797157	+	0.603773i	$0.793663\pi$
$422$	−6.43539	+	6.43539i	−0.313270	+	0.313270i
$423$		0			0
$424$			5.34847i			0.259745i
$425$	−0.135756	+	2.24334i	−0.00658515	+	0.108818i
$426$		0			0
$427$	2.42504	−	0.649788i	0.117356	−	0.0314455i
$428$	18.5916	−	4.98161i	0.898659	−	0.240795i
$429$		0			0
$430$	1.24264	−	7.64564i	0.0599255	−	0.368706i
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$		0			0
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	−0.305766	−	0.952107i	$-0.598912\pi$
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	0.952107	+	0.305766i	$0.0989124\pi$
$434$	1.02494	+	1.77526i	0.0491989	+	0.0852150i
$435$		0			0
$436$	2.82577	−	4.89437i	0.135330	−	0.234398i
$437$	1.66925	+	6.22973i	0.0798511	+	0.298008i
$438$		0			0
$439$	25.8058	−	14.8990i	1.23164	−	0.711089i	0.264271	−	0.964449i	$-0.414869\pi$
$439$	25.8058	−	14.8990i	1.23164	−	0.711089i	0.967372	+	0.253359i	$0.0815354\pi$
$440$	−0.142865	−	1.41421i	−0.00681080	−	0.0674200i
$441$		0			0
$442$	1.10102	+	1.10102i	0.0523702	+	0.0523702i
$443$	1.41043	−	5.26380i	0.0670116	−	0.250091i	−0.924292	−	0.381687i	$-0.875343\pi$
$443$	1.41043	−	5.26380i	0.0670116	−	0.250091i	0.991303	+	0.131596i	$0.0420101\pi$
$444$		0			0
$445$	6.36263	+	16.7776i	0.301618	+	0.795332i
$446$	−22.1969	−	12.8154i	−1.05106	−	0.606827i
$447$		0			0
$448$	4.40508	+	1.18034i	0.208121	+	0.0557658i
$449$	0.921404			0.0434837			0.0217419	−	0.999764i	$-0.493079\pi$
$449$	0.921404			0.0434837			0.0217419	+	0.999764i	$0.493079\pi$
$450$		0			0
$451$	−4.69694			−0.221170
$452$	5.60040	+	1.50062i	0.263421	+	0.0705833i
$453$		0			0
$454$	−21.5631	−	12.4495i	−1.01201	−	0.584284i
$455$	−12.5261	−	33.0299i	−0.587232	−	1.54847i
$456$		0			0
$457$	−3.78780	+	14.1363i	−0.177186	+	0.661267i	0.818983	+	0.573818i	$0.194538\pi$
$457$	−3.78780	+	14.1363i	−0.177186	+	0.661267i	−0.996169	+	0.0874492i	$0.972128\pi$
$458$	1.16781	+	1.16781i	0.0545681	+	0.0545681i
$459$		0			0
$460$	−0.224745	−	2.22474i	−0.0104788	−	0.103729i
$461$	−28.6237	+	16.5259i	−1.33314	+	0.769689i	−0.985780	−	0.168043i	$-0.946255\pi$
$461$	−28.6237	+	16.5259i	−1.33314	+	0.769689i	−0.347360	+	0.937732i	$0.612922\pi$
$462$		0			0
$463$	−3.16668	−	11.8182i	−0.147168	−	0.549239i	−0.999649	−	0.0264810i	$-0.991570\pi$
$463$	−3.16668	−	11.8182i	−0.147168	−	0.549239i	0.852481	−	0.522758i	$-0.175097\pi$
$464$	0.158919	−	0.275255i	0.00737761	−	0.0127784i
$465$		0			0
$466$	−10.2247	−	17.7098i	−0.473652	−	0.820390i
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	−0.638630	−	0.769514i	$-0.720499\pi$
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	0.769514	+	0.638630i	$0.220499\pi$
$468$		0			0
$469$		−	30.1464i		−	1.39203i
$470$	3.22848	−	19.8640i	0.148918	−	0.916256i
$471$		0			0
$472$	−8.67217	+	2.32370i	−0.399169	+	0.106957i
$473$	2.12701	−	0.569930i	0.0977999	−	0.0262054i
$474$		0			0
$475$	−21.3834	−	24.1381i	−0.981137	−	1.10753i
$476$		−	2.04989i		−	0.0939565i
$477$		0			0
$478$	−12.0000	+	12.0000i	−0.548867	+	0.548867i
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	0.773879	−	0.633333i	$-0.218314\pi$
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	−0.935422	+	0.353533i	$0.884980\pi$
$480$		0			0
$481$	7.34847	−	12.7279i	0.335061	−	0.580343i
$482$	−4.91756	−	18.3526i	−0.223989	−	0.835938i
$483$		0			0
$484$	−9.17633	+	5.29796i	−0.417106	+	0.240816i
$485$	−5.97469	+	0.603566i	−0.271297	+	0.0274065i
$486$		0			0
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	0.380861	−	0.924632i	$-0.375628\pi$
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	−0.924632	+	0.380861i	$0.875628\pi$
$488$	−0.142483	+	0.531752i	−0.00644988	+	0.0240713i
$489$		0			0
$490$	−12.6629	+	28.1348i	−0.572052	+	1.27100i
$491$	24.2474	+	13.9993i	1.09427	+	0.631778i	0.934711	−	0.355410i	$-0.115659\pi$
$491$	24.2474	+	13.9993i	1.09427	+	0.631778i	0.159561	+	0.987188i	$0.448992\pi$
$492$		0			0
$493$	−0.137997	−	0.0369761i	−0.00621505	−	0.00166532i
$494$	−22.3417			−1.00520
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	27.7191	+	7.42731i	1.24337	+	0.333161i
$498$		0			0
$499$	−0.778539	−	0.449490i	−0.0348522	−	0.0201219i	0.482473	−	0.875911i	$-0.339739\pi$
$499$	−0.778539	−	0.449490i	−0.0348522	−	0.0201219i	−0.517325	+	0.855789i	$0.673072\pi$
$500$	5.97514	+	9.44975i	0.267216	+	0.422606i
$501$		0			0
$502$	−0.695075	+	2.59405i	−0.0310227	+	0.115778i
$503$	4.02834	+	4.02834i	0.179615	+	0.179615i	0.791188	−	0.611573i	$-0.209463\pi$
$503$	4.02834	+	4.02834i	0.179615	+	0.179615i	−0.611573	+	0.791188i	$0.709463\pi$
$504$		0			0
$505$	21.7980	+	17.7980i	0.969996	+	0.791999i
$506$	0.550510	−	0.317837i	0.0244732	−	0.0141296i
$507$		0			0
$508$	0.686765	+	2.56304i	0.0304702	+	0.113717i
$509$	−4.22659	+	7.32066i	−0.187340	+	0.324483i	−0.944363	−	0.328906i	$-0.893320\pi$
$509$	−4.22659	+	7.32066i	−0.187340	+	0.324483i	0.757022	+	0.653389i	$0.226653\pi$
$510$		0			0
$511$	22.2474	+	38.5337i	0.984169	+	1.70463i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			18.0454i			0.795949i
$515$	−17.7016	+	12.7520i	−0.780025	+	0.561920i
$516$		0			0
$517$	5.52613	−	1.48072i	0.243039	−	0.0651221i
$518$	−18.6892	+	5.00775i	−0.821156	+	0.220028i
$519$		0			0
$520$	7.64564	+	1.24264i	0.335284	+	0.0544934i
$521$			29.4449i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$521$			29.4449i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$522$		0			0
$523$	4.22474	−	4.22474i	0.184735	−	0.184735i	−0.608680	−	0.793416i	$-0.708301\pi$
$523$	4.22474	−	4.22474i	0.184735	−	0.184735i	0.793416	+	0.608680i	$0.208301\pi$
$524$	1.80348	+	3.12372i	0.0787855	+	0.136461i
$525$		0			0
$526$	−8.34847	+	14.4600i	−0.364011	+	0.630485i
$527$	0.0522921	+	0.195157i	0.00227788	+	0.00850116i
$528$		0			0
$529$	−19.0526	+	11.0000i	−0.828372	+	0.478261i
$530$	7.56388	−	9.26382i	0.328554	−	0.402395i
$531$		0			0
$532$	20.7980	+	20.7980i	0.901706	+	0.901706i
$533$	6.62471	−	24.7238i	0.286948	−	1.07090i
$534$		0			0
$535$	−39.2467	−	17.6641i	−1.69678	−	0.763686i
$536$	5.72474	+	3.30518i	0.247271	+	0.142762i
$537$		0			0
$538$	−14.5813	−	3.90704i	−0.628643	−	0.168444i
$539$	−8.77101			−0.377794
$540$		0			0
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$	27.0898	+	7.25869i	1.16361	+	0.311787i
$543$		0			0
$544$	0.389270	+	0.224745i	0.0166898	+	0.00963586i
$545$	−11.8161	+	4.48106i	−0.506144	+	0.191948i
$546$		0			0
$547$	−1.05279	+	3.92907i	−0.0450140	+	0.167995i	−0.984774	−	0.173841i	$-0.944382\pi$
$547$	−1.05279	+	3.92907i	−0.0450140	+	0.167995i	0.939760	+	0.341836i	$0.111049\pi$
$548$	−15.4135	−	15.4135i	−0.658431	−	0.658431i
$549$		0			0
$550$	−1.75255	+	2.65153i	−0.0747290	+	0.113062i
$551$	1.77526	−	1.02494i	0.0756284	−	0.0436641i
$552$		0			0
$553$	−2.89123	−	10.7902i	−0.122947	−	0.458846i
$554$	−14.0707	+	24.3712i	−0.597807	+	1.03543i
$555$		0			0
$556$	−1.55051	−	2.68556i	−0.0657563	−	0.113893i
$557$	−7.88171	+	7.88171i	−0.333959	+	0.333959i	−0.854088	−	0.520129i	$-0.825884\pi$
$557$	−7.88171	+	7.88171i	−0.333959	+	0.333959i	0.520129	+	0.854088i	$0.325884\pi$
$558$		0			0
$559$			12.0000i			0.507546i
$560$	−5.96058	−	8.27414i	−0.251880	−	0.349646i
$561$		0			0
$562$	16.5613	−	4.43759i	0.698597	−	0.187188i
$563$	−18.9819	+	5.08619i	−0.799993	+	0.214357i	−0.635581	−	0.772034i	$-0.719239\pi$
$563$	−18.9819	+	5.08619i	−0.799993	+	0.214357i	−0.164412	+	0.986392i	$0.552573\pi$
$564$		0			0
$565$	−7.57797	−	10.5193i	−0.318808	−	0.442551i
$566$			24.2166i			1.01790i
$567$		0			0
$568$	−4.44949	+	4.44949i	−0.186696	+	0.186696i
$569$	−9.58166	−	16.5959i	−0.401684	−	0.695737i	0.592245	−	0.805758i	$-0.298242\pi$
$569$	−9.58166	−	16.5959i	−0.401684	−	0.695737i	−0.993929	+	0.110021i	$0.964908\pi$
$570$		0			0
$571$	−18.4495	+	31.9555i	−0.772087	+	1.33729i	0.164330	+	0.986405i	$0.447454\pi$
$571$	−18.4495	+	31.9555i	−0.772087	+	1.33729i	−0.936417	+	0.350889i	$0.885880\pi$
$572$	0.569930	+	2.12701i	0.0238300	+	0.0889347i
$573$		0			0
$574$	−29.1824	+	16.8485i	−1.21805	+	0.703242i
$575$	−2.75699	+	4.17121i	−0.114975	+	0.173951i
$576$		0			0
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$	−4.34763	+	16.2256i	−0.180838	+	0.674895i
$579$		0			0
$580$	−0.664525	+	0.252011i	−0.0275929	+	0.0104642i
$581$	21.5227	+	12.4261i	0.892912	+	0.515523i
$582$		0			0
$583$	3.28404	+	0.879955i	0.136011	+	0.0364440i
$584$	−9.75663			−0.403732
$585$		0			0
$586$	−22.0454			−0.910687
$587$	−12.6009	−	3.37640i	−0.520095	−	0.139359i	−0.0107843	−	0.999942i	$-0.503433\pi$
$587$	−12.6009	−	3.37640i	−0.520095	−	0.139359i	−0.509310	+	0.860583i	$0.670099\pi$
$588$		0			0
$589$	−2.51059	−	1.44949i	−0.103447	−	0.0597252i
$590$	18.3068	+	8.23953i	0.753681	+	0.339216i
$591$		0			0
$592$	1.09808	−	4.09808i	0.0451307	−	0.168430i
$593$	−7.24604	−	7.24604i	−0.297559	−	0.297559i	0.542498	−	0.840057i	$-0.317479\pi$
$593$	−7.24604	−	7.24604i	−0.297559	−	0.297559i	−0.840057	+	0.542498i	$0.817479\pi$
$594$		0			0
$595$	−2.89898	+	3.55051i	−0.118847	+	0.145557i
$596$	3.82577	−	2.20881i	0.156709	−	0.0904762i
$597$		0			0
$598$	0.896575	+	3.34607i	0.0366637	+	0.136831i
$599$	9.97093	−	17.2702i	0.407401	−	0.705639i	−0.587197	−	0.809444i	$-0.699768\pi$
$599$	9.97093	−	17.2702i	0.407401	−	0.705639i	0.994598	+	0.103805i	$0.0331018\pi$
$600$		0			0
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	0.806866	−	0.590735i	$-0.201162\pi$
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	−0.915024	+	0.403399i	$0.867829\pi$
$602$	11.1708	−	11.1708i	0.455290	−	0.455290i
$603$		0			0
$604$		−	17.5959i		−	0.715968i
$605$	23.3863	+	3.80096i	0.950789	+	0.154531i
$606$		0			0
$607$	−11.3732	+	3.04744i	−0.461624	+	0.123692i	−0.482133	−	0.876098i	$-0.660138\pi$
$607$	−11.3732	+	3.04744i	−0.461624	+	0.123692i	0.0205092	+	0.999790i	$0.493471\pi$
$608$	−6.22973	+	1.66925i	−0.252649	+	0.0676971i
$609$		0			0
$610$	0.998798	−	0.719521i	0.0404401	−	0.0291325i
$611$			31.1769i			1.26128i
$612$		0			0
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	−0.556369	−	0.830936i	$-0.687806\pi$
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	0.830936	+	0.556369i	$0.187806\pi$
$614$	−4.71940	−	8.17423i	−0.190459	−	0.329885i
$615$		0			0
$616$	1.44949	−	2.51059i	0.0584016	−	0.101155i
$617$	4.37378	+	16.3232i	0.176082	+	0.657146i	0.996365	+	0.0851882i	$0.0271491\pi$
$617$	4.37378	+	16.3232i	0.176082	+	0.657146i	−0.820283	+	0.571958i	$0.806184\pi$
$618$		0			0
$619$	−42.2121	+	24.3712i	−1.69665	+	0.979560i	−0.747748	+	0.663982i	$0.768865\pi$
$619$	−42.2121	+	24.3712i	−1.69665	+	0.979560i	−0.948900	+	0.315578i	$0.897802\pi$
$620$	0.778539	+	0.635674i	0.0312669	+	0.0255293i
$621$		0			0
$622$	−19.4495	−	19.4495i	−0.779853	−	0.779853i
$623$	−9.47172	+	35.3489i	−0.379476	+	1.41623i
$624$		0			0
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	−10.3485	−	5.97469i	−0.413608	−	0.238797i
$627$		0			0
$628$	14.1363	+	3.78780i	0.564099	+	0.151150i
$629$	−1.90702			−0.0760380
$630$		0			0
$631$	−3.10102			−0.123450			−0.0617248	−	0.998093i	$-0.519660\pi$
$631$	−3.10102			−0.123450			−0.0617248	+	0.998093i	$0.519660\pi$
$632$	2.36603	+	0.633975i	0.0941154	+	0.0252182i
$633$		0			0
$634$	9.43879	+	5.44949i	0.374862	+	0.216427i
$635$	2.43518	−	5.41055i	0.0966370	−	0.214711i
$636$		0			0
$637$	12.3709	−	46.1689i	0.490153	−	1.82928i
$638$	−0.142865	−	0.142865i	−0.00565606	−	0.00565606i
$639$		0			0
$640$	2.22474	−	0.224745i	0.0879408	−	0.00888382i
$641$	−16.7474	+	9.66914i	−0.661484	+	0.381908i	−0.792842	−	0.609427i	$-0.791400\pi$
$641$	−16.7474	+	9.66914i	−0.661484	+	0.381908i	0.131358	+	0.991335i	$0.458066\pi$
$642$		0			0
$643$	1.63694	+	6.10913i	0.0645545	+	0.240921i	0.990662	−	0.136338i	$-0.0435334\pi$
$643$	1.63694	+	6.10913i	0.0645545	+	0.240921i	−0.926108	+	0.377259i	$0.876867\pi$
$644$	2.28024	−	3.94949i	0.0898540	−	0.155632i
$645$		0			0
$646$	1.44949	+	2.51059i	0.0570294	+	0.0987778i
$647$	23.5416	−	23.5416i	0.925516	−	0.925516i	−0.0718961	−	0.997412i	$-0.522905\pi$
$647$	23.5416	−	23.5416i	0.925516	−	0.925516i	0.997412	+	0.0718961i	$0.0229050\pi$
$648$		0			0
$649$			5.70714i			0.224025i
$650$	−11.4853	−	12.9649i	−0.450490	−	0.508525i
$651$		0			0
$652$	6.07812	−	1.62863i	0.238037	−	0.0637819i
$653$	−25.5482	+	6.84563i	−0.999780	+	0.267890i	−0.721353	−	0.692567i	$-0.756480\pi$
$653$	−25.5482	+	6.84563i	−0.999780	+	0.267890i	−0.278427	+	0.960457i	$0.589813\pi$
$654$		0			0
$655$	1.29389	−	7.96096i	0.0505564	−	0.311060i
$656$		−	7.38891i		−	0.288488i
$657$		0			0
$658$	29.0227	−	29.0227i	1.13142	−	1.13142i
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	0.954917	−	0.296872i	$-0.0959435\pi$
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	−0.734557	+	0.678546i	$0.762610\pi$
$660$		0			0
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	−0.853076	−	0.521786i	$-0.825266\pi$
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	0.878418	+	0.477893i	$0.158599\pi$
$662$	−0.116337	−	0.434174i	−0.00452155	−	0.0168746i
$663$		0			0
$664$	−4.71940	+	2.72474i	−0.183148	+	0.105741i
$665$	−6.61037	−	65.4359i	−0.256339	−	2.53749i
$666$		0			0
$667$	−0.224745	−	0.224745i	−0.00870216	−	0.00870216i
$668$	−2.27708	+	8.49818i	−0.0881028	+	0.328804i
$669$		0			0
$670$	−5.24131	−	13.8208i	−0.202490	−	0.533942i
$671$	0.303062	+	0.174973i	0.0116996	+	0.00675474i
$672$		0			0
$673$	22.4704	+	6.02093i	0.866171	+	0.232090i	0.664431	−	0.747349i	$-0.268674\pi$
$673$	22.4704	+	6.02093i	0.866171	+	0.232090i	0.201740	+	0.979439i	$0.435340\pi$
$674$	3.11416			0.119953
$675$		0			0
$676$	1.00000			0.0384615
$677$	44.0423	+	11.8011i	1.69268	+	0.453553i	0.971080	−	0.238755i	$-0.0767393\pi$
$677$	44.0423	+	11.8011i	1.69268	+	0.453553i	0.721602	+	0.692308i	$0.243406\pi$
$678$		0			0
$679$	−10.6066	−	6.12372i	−0.407044	−	0.235007i
$680$	−0.356397	−	0.939780i	−0.0136672	−	0.0360389i
$681$		0			0
$682$	−0.0739521	+	0.275993i	−0.00283177	+	0.0105683i
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	0.390431	−	0.920632i	$-0.372326\pi$
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	−0.920632	+	0.390431i	$0.872326\pi$
$684$		0			0
$685$	4.89898	+	48.4949i	0.187180	+	1.85289i
$686$	−26.8485	+	15.5010i	−1.02508	+	0.591830i
$687$		0			0
$688$	0.896575	+	3.34607i	0.0341816	+	0.127568i
$689$	−9.26382	+	16.0454i	−0.352923	+	0.611281i
$690$		0			0
$691$	10.4722	+	18.1384i	0.398381	+	0.690016i	0.993526	−	0.113602i	$-0.0362388\pi$
$691$	10.4722	+	18.1384i	0.398381	+	0.690016i	−0.595145	+	0.803618i	$0.702906\pi$
$692$	9.12096	−	9.12096i	0.346727	−	0.346727i
$693$		0			0
$694$		−	23.7980i		−	0.903358i
$695$	−1.11240	+	6.84428i	−0.0421956	+	0.259618i
$696$		0			0
$697$	−3.20807	+	0.859599i	−0.121514	+	0.0325596i
$698$	28.0557	−	7.51750i	1.06192	−	0.284542i
$699$		0			0
$700$	−1.37737	+	22.7608i	−0.0520597	+	0.860276i
$701$		−	21.1024i		−	0.797028i	−0.917162	−	0.398514i	$-0.869526\pi$
$701$		−	21.1024i		−	0.797028i	0.917162	−	0.398514i	$-0.130474\pi$
$702$		0			0
$703$	19.3485	−	19.3485i	0.729741	−	0.729741i
$704$	0.317837	+	0.550510i	0.0119789	+	0.0207481i
$705$		0			0
$706$	17.1464	−	29.6985i	0.645314	−	1.11772i
$707$	14.8546	+	55.4382i	0.558666	+	2.08497i
$708$		0			0
$709$	25.6790	−	14.8258i	0.964394	−	0.556793i	0.0668716	−	0.997762i	$-0.478698\pi$
$709$	25.6790	−	14.8258i	0.964394	−	0.556793i	0.897523	+	0.440968i	$0.145365\pi$
$710$	13.9993	−	1.41421i	0.525383	−	0.0530745i
$711$		0			0
$712$	−5.67423	−	5.67423i	−0.212651	−	0.212651i
$713$	−0.116337	+	0.434174i	−0.00435684	+	0.0162599i
$714$		0			0
$715$	2.02090	−	4.49009i	0.0755772	−	0.167920i
$716$	9.24745	+	5.33902i	0.345593	+	0.199528i
$717$		0			0
$718$	3.20807	+	0.859599i	0.119724	+	0.0320800i
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	−21.8260	−	5.84825i	−0.812279	−	0.217649i
$723$		0			0
$724$	−13.3797	−	7.72474i	−0.497251	−	0.287088i
$725$	1.50739	+	0.503284i	0.0559830	+	0.0186915i
$726$		0			0
$727$	12.5068	−	46.6759i	0.463850	−	1.73111i	−0.196822	−	0.980439i	$-0.563062\pi$
$727$	12.5068	−	46.6759i	0.463850	−	1.73111i	0.660673	−	0.750674i	$-0.270271\pi$
$728$	11.1708	+	11.1708i	0.414019	+	0.414019i
$729$		0			0
$730$	16.8990	+	13.7980i	0.625459	+	0.510685i
$731$	1.34847	−	0.778539i	0.0498749	−	0.0287953i
$732$		0			0
$733$	8.83821	+	32.9846i	0.326447	+	1.21832i	0.912850	+	0.408296i	$0.133877\pi$
$733$	8.83821	+	32.9846i	0.326447	+	1.21832i	−0.586403	+	0.810019i	$0.699457\pi$
$734$	−2.04989	+	3.55051i	−0.0756627	+	0.131052i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	2.97129	−	2.97129i	0.109449	−	0.109449i
$738$		0			0
$739$			28.9444i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$739$			28.9444i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$740$	−7.69748	+	5.54516i	−0.282965	+	0.203844i
$741$		0			0
$742$	23.5605	−	6.31300i	0.864931	−	0.231758i
$743$	9.56168	−	2.56204i	0.350784	−	0.0939923i	−0.0791245	−	0.996865i	$-0.525212\pi$
$743$	9.56168	−	2.56204i	0.350784	−	0.0939923i	0.429909	+	0.902872i	$0.358546\pi$
$744$		0			0
$745$	−9.75014	−	1.58468i	−0.357218	−	0.0580583i
$746$		−	0.492810i		−	0.0180431i
$747$		0			0
$748$	0.202041	−	0.202041i	0.00738735	−	0.00738735i
$749$	−43.8888	−	76.0176i	−1.60366	−	2.77762i
$750$		0			0
$751$	−10.3485	+	17.9241i	−0.377621	+	0.654059i	−0.990716	−	0.135951i	$-0.956591\pi$
$751$	−10.3485	+	17.9241i	−0.377621	+	0.654059i	0.613095	+	0.790010i	$0.289924\pi$
$752$	2.32937	+	8.69333i	0.0849434	+	0.317013i
$753$		0			0
$754$	0.953512	−	0.550510i	0.0347248	−	0.0200484i
$755$	−24.8844	+	30.4770i	−0.905636	+	1.10917i
$756$		0			0
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	0.983292	−	0.182038i	$-0.0582693\pi$
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	−0.182038	+	0.983292i	$0.558269\pi$
$758$	5.52539	−	20.6210i	0.200691	−	0.748990i
$759$		0			0
$760$	13.1509	+	5.91894i	0.477033	+	0.214703i
$761$	5.60102	+	3.23375i	0.203037	+	0.117223i	0.598071	−	0.801443i	$-0.295934\pi$
$761$	5.60102	+	3.23375i	0.203037	+	0.117223i	−0.395034	+	0.918666i	$0.629267\pi$
$762$		0			0
$763$	−24.8955	−	6.67072i	−0.901276	−	0.241496i
$764$	17.4634			0.631803
$765$		0			0
$766$	8.20204			0.296352
$767$	−30.0413	−	8.04954i	−1.08473	−	0.290652i
$768$		0			0
$769$	8.39780	+	4.84847i	0.302832	+	0.174840i	0.643715	−	0.765266i	$-0.277392\pi$
$769$	8.39780	+	4.84847i	0.302832	+	0.174840i	−0.340882	+	0.940106i	$0.610726\pi$
$770$	−6.06110	+	2.29858i	−0.218427	+	0.0828351i
$771$		0			0
$772$	4.48288	−	16.7303i	0.161342	−	0.602138i
$773$	30.8270	+	30.8270i	1.10877	+	1.10877i	0.993313	+	0.115456i	$0.0368331\pi$
$773$	30.8270	+	30.8270i	1.10877	+	1.10877i	0.115456	+	0.993313i	$0.463167\pi$
$774$		0			0
$775$	−0.449490	−	2.20204i	−0.0161461	−	0.0790996i
$776$	2.32577	−	1.34278i	0.0834901	−	0.0482030i
$777$		0			0
$778$	9.52497	+	35.5477i	0.341487	+	1.27445i
$779$	23.8273	−	41.2702i	0.853703	−	1.47866i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	0.317837	−	0.317837i	0.0113658	−	0.0113658i
$783$		0			0
$784$		−	13.7980i		−	0.492784i
$785$	−19.1280	−	26.5524i	−0.682707	−	0.947695i
$786$		0			0
$787$	9.42418	−	2.52520i	0.335936	−	0.0900137i	−0.0869079	−	0.996216i	$-0.527699\pi$
$787$	9.42418	−	2.52520i	0.335936	−	0.0900137i	0.422844	+	0.906203i	$0.361032\pi$
$788$	9.46410	−	2.53590i	0.337145	−	0.0903376i
$789$		0			0
$790$	−3.20150	−	4.44414i	−0.113904	−	0.158115i
$791$		−	26.4415i		−	0.940150i
$792$		0			0
$793$	−1.34847	+	1.34847i	−0.0478855	+	0.0478855i
$794$	7.46034	+	12.9217i	0.264757	+	0.458573i
$795$		0			0
$796$	−4.22474	+	7.31747i	−0.149742	+	0.259361i
$797$	−10.3005	−	38.4419i	−0.364861	−	1.36168i	−0.867609	−	0.497248i	$-0.834344\pi$
$797$	−10.3005	−	38.4419i	−0.364861	−	1.36168i	0.502747	−	0.864433i	$-0.332323\pi$
$798$		0			0
$799$	3.50343	−	2.02270i	0.123942	−	0.0715581i
$800$	−4.17121	−	2.75699i	−0.147474	−	0.0974745i
$801$		0			0
$802$	−6.24745	−	6.24745i	−0.220605	−	0.220605i
$803$	−1.60521	+	5.99071i	−0.0566465	+	0.211408i
$804$		0			0
$805$	−9.53491	+	3.61597i	−0.336061	+	0.127446i
$806$	−1.34847	−	0.778539i	−0.0474978	−	0.0274229i
$807$		0			0
$808$	−12.1562	−	3.25725i	−0.427655	−	0.114590i
$809$	−19.4490			−0.683792			−0.341896	−	0.939738i	$-0.611069\pi$
$809$	−19.4490			−0.683792			−0.341896	+	0.939738i	$0.611069\pi$
$810$		0			0
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	−1.40010	−	0.375156i	−0.0491339	−	0.0131654i
$813$		0			0
$814$	−2.33562	−	1.34847i	−0.0818633	−	0.0472638i
$815$	−12.8308	−	5.77489i	−0.449444	−	0.202286i
$816$		0			0
$817$	−5.78245	+	21.5804i	−0.202302	+	0.755003i
$818$	20.4347	+	20.4347i	0.714481	+	0.714481i
$819$		0			0
$820$	−10.4495	+	12.7980i	−0.364912	+	0.446924i
$821$	−19.3207	+	11.1548i	−0.674296	+	0.389305i	−0.797702	−	0.603051i	$-0.793951\pi$
$821$	−19.3207	+	11.1548i	−0.674296	+	0.389305i	0.123407	+	0.992356i	$0.460618\pi$
$822$		0			0
$823$	0.867910	+	3.23908i	0.0302534	+	0.112907i	0.979401	−	0.201923i	$-0.0647191\pi$
$823$	0.867910	+	3.23908i	0.0302534	+	0.112907i	−0.949148	+	0.314830i	$0.898052\pi$
$824$	4.87832	−	8.44949i	0.169944	−	0.294352i
$825$		0			0
$826$	20.4722	+	35.4589i	0.712319	+	1.23377i
$827$	31.5662	−	31.5662i	1.09766	−	1.09766i	0.102980	−	0.994683i	$-0.467162\pi$
$827$	31.5662	−	31.5662i	1.09766	−	1.09766i	0.994683	−	0.102980i	$-0.0328379\pi$
$828$		0			0
$829$		−	10.5505i		−	0.366434i	−0.983072	−	0.183217i	$-0.941349\pi$
$829$		−	10.5505i		−	0.366434i	0.983072	−	0.183217i	$-0.0586512\pi$
$830$	12.0276	+	1.95484i	0.417484	+	0.0678534i
$831$		0			0
$832$	−3.34607	+	0.896575i	−0.116004	+	0.0310832i
$833$	−5.99071	+	1.60521i	−0.207566	+	0.0556171i
$834$		0			0
$835$	15.9623	−	11.4990i	0.552397	−	0.397939i
$836$			4.09978i			0.141794i
$837$		0			0
$838$	3.55051	−	3.55051i	0.122650	−	0.122650i
$839$	0.246405	+	0.426786i	0.00850684	+	0.0147343i	0.870247	−	0.492615i	$-0.163959\pi$
$839$	0.246405	+	0.426786i	0.00850684	+	0.0147343i	−0.861741	+	0.507349i	$0.830625\pi$
$840$		0			0
$841$	14.4495	−	25.0273i	0.498258	−	0.863009i
$842$	1.32024	+	4.92721i	0.0454985	+	0.169803i
$843$		0			0
$844$	−7.88171	+	4.55051i	−0.271300	+	0.156635i
$845$	−1.73205	−	1.41421i	−0.0595844	−	0.0486504i
$846$		0			0
$847$	34.1691	+	34.1691i	1.17407	+	1.17407i
$848$	−1.38429	+	5.16622i	−0.0475366	+	0.177409i
$849$		0			0
$850$	−0.711751	+	2.13177i	−0.0244129	+	0.0731191i
$851$	−3.67423	−	2.12132i	−0.125951	−	0.0727179i
$852$		0			0
$853$	2.39403	+	0.641478i	0.0819700	+	0.0219638i	0.299571	−	0.954074i	$-0.403156\pi$
$853$	2.39403	+	0.641478i	0.0819700	+	0.0219638i	−0.217601	+	0.976038i	$0.569823\pi$
$854$	2.51059			0.0859106
$855$		0			0
$856$	19.2474			0.657864
$857$	−15.2597	−	4.08881i	−0.521260	−	0.139671i	−0.0114106	−	0.999935i	$-0.503632\pi$
$857$	−15.2597	−	4.08881i	−0.521260	−	0.139671i	−0.509849	+	0.860264i	$0.670299\pi$
$858$		0			0
$859$	40.2658	+	23.2474i	1.37385	+	0.793193i	0.991410	−	0.130788i	$-0.0417506\pi$
$859$	40.2658	+	23.2474i	1.37385	+	0.793193i	0.382440	+	0.923980i	$0.375084\pi$
$860$	3.17914	−	7.06350i	0.108408	−	0.240863i
$861$		0			0
$862$	4.02628	−	15.0263i	0.137136	−	0.511797i
$863$	−20.7132	−	20.7132i	−0.705085	−	0.705085i	0.260413	−	0.965497i	$-0.416141\pi$
$863$	−20.7132	−	20.7132i	−0.705085	−	0.705085i	−0.965497	+	0.260413i	$0.916141\pi$
$864$		0			0
$865$	−28.6969	+	2.89898i	−0.975725	+	0.0985683i
$866$	16.4722	−	9.51023i	0.559748	−	0.323171i
$867$		0			0
$868$	0.530550	+	1.98004i	0.0180080	+	0.0672069i
$869$	0.778539	−	1.34847i	0.0264101	−	0.0457437i
$870$		0			0
$871$	11.4495	+	19.8311i	0.387951	+	0.671951i
$872$	3.99624	−	3.99624i	0.135330	−	0.135330i
$873$		0			0
$874$			6.44949i			0.218157i
$875$	34.5742	−	37.4749i	1.16882	−	1.26688i
$876$		0			0
$877$	−41.3188	+	11.0713i	−1.39524	+	0.373852i	−0.876632	−	0.481162i	$-0.840215\pi$
$877$	−41.3188	+	11.0713i	−1.39524	+	0.373852i	−0.518604	+	0.855014i	$0.673548\pi$
$878$	28.7826	−	7.71228i	0.971366	−	0.260277i
$879$		0			0
$880$	0.228029	−	1.40300i	0.00768685	−	0.0472952i
$881$			54.8365i			1.84749i	0.383010	+	0.923744i	$0.374887\pi$
$881$			54.8365i			1.84749i	−0.383010	+	0.923744i	$0.625113\pi$
$882$		0			0
$883$	6.27015	−	6.27015i	0.211007	−	0.211007i	−0.593688	−	0.804695i	$-0.702329\pi$
$883$	6.27015	−	6.27015i	0.211007	−	0.211007i	0.804695	+	0.593688i	$0.202329\pi$
$884$	0.778539	+	1.34847i	0.0261851	+	0.0453539i
$885$		0			0
$886$	2.72474	−	4.71940i	0.0915396	−	0.158551i
$887$	2.12284	+	7.92256i	0.0712781	+	0.266014i	0.992364	−	0.123347i	$-0.0393627\pi$
$887$	2.12284	+	7.92256i	0.0712781	+	0.266014i	−0.921085	+	0.389360i	$0.872696\pi$
$888$		0			0
$889$	10.4798	−	6.05051i	0.351481	−	0.202928i
$890$	1.80348	+	17.8526i	0.0604529	+	0.598422i
$891$		0			0
$892$	−18.1237	−	18.1237i	−0.606827	−	0.606827i
$893$	−15.0233	+	56.0676i	−0.502734	+	1.87623i
$894$		0			0
$895$	−8.46654	−	22.3253i	−0.283005	−	0.746253i
$896$	3.94949	+	2.28024i	0.131943	+	0.0761774i
$897$		0			0
$898$	0.890008	+	0.238477i	0.0296999	+	0.00795807i
$899$	0.142865			0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$	−4.53689	−	1.21566i	−0.151062	−	0.0404770i
$903$		0			0
$904$	5.02118	+	2.89898i	0.167002	+	0.0964186i
$905$	12.2498	+	32.3013i	0.407197	+	1.07373i
$906$		0			0
$907$	−0.978838	+	3.65307i	−0.0325018	+	0.121298i	−0.980271	−	0.197659i	$-0.936666\pi$
$907$	−0.978838	+	3.65307i	−0.0325018	+	0.121298i	0.947769	+	0.318957i	$0.103333\pi$
$908$	−17.6062	−	17.6062i	−0.584284	−	0.584284i
$909$		0			0
$910$	−3.55051	−	35.1464i	−0.117698	−	1.16509i
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	−0.395114	−	0.918632i	$-0.629295\pi$
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	0.598002	+	0.801495i	$0.295962\pi$
$912$		0			0
$913$	0.896575	+	3.34607i	0.0296723	+	0.110739i
$914$	−7.31747	+	12.6742i	−0.242040	+	0.419226i
$915$		0			0
$916$	0.825765	+	1.43027i	0.0272841	+	0.0472574i
$917$	11.6315	−	11.6315i	0.384107	−	0.384107i
$918$		0			0
$919$			12.6515i			0.417335i	0.977987	+	0.208668i	$0.0669127\pi$
$919$			12.6515i			0.417335i	−0.977987	+	0.208668i	$0.933087\pi$
$920$	0.358719	−	2.20711i	0.0118266	−	0.0727662i
$921$		0			0
$922$	−31.9256	+	8.55444i	−1.05141	+	0.281726i
$923$	−21.0552	+	5.64173i	−0.693041	+	0.185700i
$924$		0			0
$925$	21.1745	+	1.28138i	0.696212	+	0.0421314i
$926$		−	12.2351i		−	0.402071i
$927$		0			0
$928$	0.224745	−	0.224745i	0.00737761	−	0.00737761i
$929$	21.1024	+	36.5505i	0.692349	+	1.19918i	0.971066	+	0.238810i	$0.0767574\pi$
$929$	21.1024	+	36.5505i	0.692349	+	1.19918i	−0.278717	+	0.960373i	$0.589909\pi$
$930$		0			0
$931$	44.4949	−	77.0674i	1.45826	−	2.52578i
$932$	−5.29272	−	19.7527i	−0.173369	−	0.647021i
$933$		0			0
$934$	3.46410	−	2.00000i	0.113349	−	0.0654420i
$935$	−0.635674	+	0.0642162i	−0.0207888	+	0.00210009i
$936$		0			0
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	0.654637	−	0.755943i	$-0.272821\pi$
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	−0.755943	+	0.654637i	$0.772821\pi$
$938$	7.80247	−	29.1192i	0.254760	−	0.950776i
$939$		0			0
$940$	8.25964	−	18.3515i	0.269400	−	0.598561i
$941$	−27.5227	−	15.8902i	−0.897215	−	0.518007i	−0.0209191	−	0.999781i	$-0.506659\pi$
$941$	−27.5227	−	15.8902i	−0.897215	−	0.518007i	−0.876295	+	0.481774i	$0.839993\pi$
$942$		0			0
$943$	−7.13713	−	1.91239i	−0.232417	−	0.0622760i
$944$	−8.97809			−0.292212
$945$		0			0
$946$	2.20204			0.0715945
$947$	−2.94164	−	0.788210i	−0.0955904	−	0.0256134i	0.210707	−	0.977549i	$-0.432423\pi$
$947$	−2.94164	−	0.788210i	−0.0955904	−	0.0256134i	−0.306297	+	0.951936i	$0.599090\pi$
$948$		0			0
$949$	−29.2699	−	16.8990i	−0.950141	−	0.548564i
$950$	−14.4074	−	28.8501i	−0.467436	−	0.936020i
$951$		0			0
$952$	0.530550	−	1.98004i	0.0171952	−	0.0641735i
$953$	−5.79972	−	5.79972i	−0.187871	−	0.187871i	0.606904	−	0.794775i	$-0.292411\pi$
$953$	−5.79972	−	5.79972i	−0.187871	−	0.187871i	−0.794775	+	0.606904i	$0.792411\pi$
$954$		0			0
$955$	−30.2474	−	24.6969i	−0.978784	−	0.799174i
$956$	−14.6969	+	8.48528i	−0.475333	+	0.274434i
$957$		0			0
$958$	−1.83013	−	6.83013i	−0.0591287	−	0.220671i
$959$	−49.7046	+	86.0908i	−1.60504	+	2.78002i
$960$		0			0
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$	10.3923	−	10.3923i	0.335061	−	0.335061i
$963$		0			0
$964$		−	19.0000i		−	0.611949i
$965$	−31.4248	+	22.6380i	−1.01160	+	0.728744i
$966$		0			0
$967$	38.6937	−	10.3679i	1.24431	−	0.333411i	0.424172	−	0.905582i	$-0.360565\pi$
$967$	38.6937	−	10.3679i	1.24431	−	0.333411i	0.820134	+	0.572171i	$0.193899\pi$
$968$	−10.2349	+	2.74243i	−0.328961	+	0.0881449i
$969$		0			0
$970$	−5.92732	−	0.963364i	−0.190315	−	0.0309317i
$971$		−	21.4989i		−	0.689934i	−0.938615	−	0.344967i	$-0.887890\pi$
$971$		−	21.4989i		−	0.689934i	0.938615	−	0.344967i	$-0.112110\pi$
$972$		0			0
$973$	−10.0000	+	10.0000i	−0.320585	+	0.320585i
$974$	−8.48528	−	14.6969i	−0.271886	−	0.470920i
$975$		0			0
$976$	−0.275255	+	0.476756i	−0.00881070	+	0.0152606i
$977$	−1.68100	−	6.27359i	−0.0537801	−	0.200710i	0.933808	−	0.357773i	$-0.116464\pi$
$977$	−1.68100	−	6.27359i	−0.0537801	−	0.200710i	−0.987589	+	0.157063i	$0.949797\pi$
$978$		0			0
$979$	−4.41761	+	2.55051i	−0.141188	+	0.0815147i
$980$	−19.5133	+	23.8988i	−0.623328	+	0.763418i
$981$		0			0
$982$	19.7980	+	19.7980i	0.631778	+	0.631778i
$983$	7.04041	−	26.2752i	0.224554	−	0.838047i	−0.758029	−	0.652221i	$-0.773837\pi$
$983$	7.04041	−	26.2752i	0.224554	−	0.838047i	0.982583	−	0.185826i	$-0.0594961\pi$
$984$		0			0
$985$	−19.9786	−	8.99196i	−0.636571	−	0.286508i
$986$	−0.123724	−	0.0714323i	−0.00394019	−	0.00227487i
$987$		0			0
$988$	−21.5804	−	5.78245i	−0.686564	−	0.183964i
$989$	3.46410			0.110152
$990$		0			0
$991$	16.7423			0.531838			0.265919	−	0.963995i	$-0.414325\pi$
$991$	16.7423			0.531838			0.265919	+	0.963995i	$0.414325\pi$
$992$	−0.434174	−	0.116337i	−0.0137850	−	0.00369369i
$993$		0			0
$994$	24.8523	+	14.3485i	0.788266	+	0.455106i
$995$	17.6659	−	6.69954i	0.560048	−	0.212390i
$996$		0			0
$997$	−1.73955	+	6.49211i	−0.0550922	+	0.205607i	−0.987986	−	0.154545i	$-0.950609\pi$
$997$	−1.73955	+	6.49211i	−0.0550922	+	0.205607i	0.932893	+	0.360153i	$0.117275\pi$
$998$	−0.635674	−	0.635674i	−0.0201219	−	0.0201219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.m.a.17.2		8
3.2	odd	2		90.2.l.a.77.1	yes	8
5.2	odd	4		1350.2.q.g.1043.1		8
5.3	odd	4	inner	270.2.m.a.233.2		8
5.4	even	2		1350.2.q.g.557.1		8
9.2	odd	6	inner	270.2.m.a.197.2		8
9.4	even	3		810.2.f.b.647.2		8
9.5	odd	6		810.2.f.b.647.3		8
9.7	even	3		90.2.l.a.47.1	yes	8
12.11	even	2		720.2.cu.a.257.1		8
15.2	even	4		450.2.p.a.293.2		8
15.8	even	4		90.2.l.a.23.1	✓	8
15.14	odd	2		450.2.p.a.257.2		8
36.7	odd	6		720.2.cu.a.497.1		8
45.2	even	12		1350.2.q.g.143.1		8
45.7	odd	12		450.2.p.a.443.2		8
45.13	odd	12		810.2.f.b.323.4		8
45.23	even	12		810.2.f.b.323.1		8
45.29	odd	6		1350.2.q.g.1007.1		8
45.34	even	6		450.2.p.a.407.2		8
45.38	even	12	inner	270.2.m.a.143.2		8
45.43	odd	12		90.2.l.a.83.1	yes	8
60.23	odd	4		720.2.cu.a.113.1		8
180.43	even	12		720.2.cu.a.353.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	15.8	even	4
90.2.l.a.47.1	yes	8	9.7	even	3
90.2.l.a.77.1	yes	8	3.2	odd	2
90.2.l.a.83.1	yes	8	45.43	odd	12
270.2.m.a.17.2		8	1.1	even	1	trivial
270.2.m.a.143.2		8	45.38	even	12	inner
270.2.m.a.197.2		8	9.2	odd	6	inner
270.2.m.a.233.2		8	5.3	odd	4	inner
450.2.p.a.257.2		8	15.14	odd	2
450.2.p.a.293.2		8	15.2	even	4
450.2.p.a.407.2		8	45.34	even	6
450.2.p.a.443.2		8	45.7	odd	12
720.2.cu.a.113.1		8	60.23	odd	4
720.2.cu.a.257.1		8	12.11	even	2
720.2.cu.a.353.1		8	180.43	even	12
720.2.cu.a.497.1		8	36.7	odd	6
810.2.f.b.323.1		8	45.23	even	12
810.2.f.b.323.4		8	45.13	odd	12
810.2.f.b.647.2		8	9.4	even	3
810.2.f.b.647.3		8	9.5	odd	6
1350.2.q.g.143.1		8	45.2	even	12
1350.2.q.g.557.1		8	5.4	even	2
1350.2.q.g.1007.1		8	45.29	odd	6
1350.2.q.g.1043.1		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(1.18034 - 4.40508i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.224745 - 2.22474i) q^{10} +(0.550510 - 0.317837i) q^{11} +(0.896575 + 3.34607i) q^{13} +(2.28024 - 3.94949i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.317837 - 0.317837i) q^{17} +6.44949i q^{19} +(0.358719 - 2.20711i) q^{20} +(0.614014 - 0.164525i) q^{22} +(0.965926 - 0.258819i) q^{23} +(-3.74264 + 3.31552i) q^{25} +3.46410i q^{26} +(3.22474 - 3.22474i) q^{28} +(-0.158919 - 0.275255i) q^{29} +(-0.224745 + 0.389270i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.389270 - 0.224745i) q^{34} +(-10.1459 + 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-1.66925 + 6.22973i) q^{38} +(0.917738 - 2.03906i) q^{40} +(-6.39898 - 3.69445i) q^{41} +(3.34607 + 0.896575i) q^{43} +0.635674 q^{44} +1.00000 q^{46} +(8.69333 + 2.32937i) q^{47} +(-11.9494 - 6.89898i) q^{49} +(-4.47323 + 2.23388i) q^{50} +(-0.896575 + 3.34607i) q^{52} +(3.78194 + 3.78194i) q^{53} +(-1.10102 - 0.898979i) q^{55} +(3.94949 - 2.28024i) q^{56} +(-0.0822623 - 0.307007i) q^{58} +(-4.48905 + 7.77526i) q^{59} +(0.275255 + 0.476756i) q^{61} +(-0.317837 + 0.317837i) q^{62} +1.00000i q^{64} +(6.28497 - 4.52761i) q^{65} +(6.38512 - 1.71089i) q^{67} +(0.434174 - 0.116337i) q^{68} +(-10.0655 - 1.63593i) q^{70} +6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(-3.22474 + 5.58542i) q^{76} +(-0.750311 - 2.80020i) q^{77} +(2.12132 - 1.22474i) q^{79} +(1.41421 - 1.73205i) q^{80} +(-5.22474 - 5.22474i) q^{82} +(-1.41043 + 5.26380i) q^{83} +(-0.916536 - 0.412514i) q^{85} +(3.00000 + 1.73205i) q^{86} +(0.614014 + 0.164525i) q^{88} -8.02458 q^{89} +15.7980 q^{91} +(0.965926 + 0.258819i) q^{92} +(7.79423 + 4.50000i) q^{94} +(13.4844 - 5.11376i) q^{95} +(0.695075 - 2.59405i) q^{97} +(-9.75663 - 9.75663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100}) \) 8 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 + 24 * q^11 + 4 * q^16 - 8 * q^22 + 4 * q^25 + 16 * q^28 + 8 * q^31 - 24 * q^37 - 12 * q^38 + 4 * q^40 - 12 * q^41 + 8 * q^46 - 24 * q^50 - 48 * q^55 + 12 * q^56 - 4 * q^58 + 12 * q^61 + 24 * q^65 + 4 * q^67 + 12 * q^68 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 24 * q^77 - 32 * q^82 - 12 * q^83 - 20 * q^85 + 24 * q^86 - 8 * q^88 + 48 * q^91 + 24 * q^95 + 12 * q^97

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