LMFDB - Embedded newform 2268.2.bm.i.593.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(593,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.593"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.5
Root			$-0.385418 + 0.222521i$ of defining polynomial
Character	$\chi$	$=$	2268.593
Dual form			2268.2.bm.i.1025.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.15983 q^{5} +(2.37047 + 1.17511i) q^{7} -1.33513i q^{11} +(2.03534 - 1.17511i) q^{13} +(3.60166 + 6.23825i) q^{17} +(1.03803 + 0.599308i) q^{19} -2.40581i q^{23} -0.335126 q^{25} +(-5.32324 - 3.07338i) q^{29} +(7.11141 + 4.10577i) q^{31} +(5.11982 + 2.53803i) q^{35} +(2.57338 - 4.45722i) q^{37} +(2.23617 + 3.87316i) q^{41} +(0.332437 - 0.575798i) q^{43} +(-1.07992 - 1.87047i) q^{47} +(4.23825 + 5.57111i) q^{49} +(-11.0340 + 6.37047i) q^{53} -2.88365i q^{55} +(4.83424 - 8.37316i) q^{59} +(-10.6468 + 6.14691i) q^{61} +(4.39600 - 2.53803i) q^{65} +(1.86778 - 3.23509i) q^{67} -11.4058i q^{71} +(9.07338 - 5.23852i) q^{73} +(1.56891 - 3.16487i) q^{77} +(4.53803 + 7.86010i) q^{79} +(-5.39958 + 9.35235i) q^{83} +(7.77897 + 13.4736i) q^{85} +(2.59808 - 4.50000i) q^{89} +(6.20560 - 0.393808i) q^{91} +(2.24198 + 1.29440i) q^{95} +(1.07069 + 0.618162i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} - 18 q^{61} + 54 q^{73} + 24 q^{79} + 6 q^{85} + 42 q^{91} - 36 q^{97}+O(q^{100}) $ 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 - 18 * q^61 + 54 * q^73 + 24 * q^79 + 6 * q^85 + 42 * q^91 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.15983			0.965906			0.482953	−	0.875646i	$-0.339564\pi$
$5$	2.15983			0.965906			0.482953	+	0.875646i	$0.339564\pi$
$6$		0			0
$7$	2.37047	+	1.17511i	0.895953	+	0.444148i
$7$	2.37047	+	1.17511i	0.895953	+	0.444148i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	1.33513i		−	0.402556i	−0.979534	−	0.201278i	$-0.935491\pi$
$11$		−	1.33513i		−	0.402556i	0.979534	−	0.201278i	$-0.0645094\pi$
$12$		0			0
$13$	2.03534	−	1.17511i	0.564503	−	0.325916i	−0.190448	−	0.981697i	$-0.560994\pi$
$13$	2.03534	−	1.17511i	0.564503	−	0.325916i	0.754951	+	0.655781i	$0.227661\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.60166	+	6.23825i	0.873530	+	1.51300i	0.858321	+	0.513114i	$0.171508\pi$
$17$	3.60166	+	6.23825i	0.873530	+	1.51300i	0.0152091	+	0.999884i	$0.495159\pi$
$18$		0			0
$19$	1.03803	+	0.599308i	0.238141	+	0.137491i	0.614322	−	0.789055i	$-0.289430\pi$
$19$	1.03803	+	0.599308i	0.238141	+	0.137491i	−0.376181	+	0.926546i	$0.622763\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	2.40581i		−	0.501647i	−0.968033	−	0.250823i	$-0.919299\pi$
$23$		−	2.40581i		−	0.501647i	0.968033	−	0.250823i	$-0.0807013\pi$
$24$		0			0
$25$	−0.335126			−0.0670251
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.32324	−	3.07338i	−0.988501	−	0.570712i	−0.0836755	−	0.996493i	$-0.526666\pi$
$29$	−5.32324	−	3.07338i	−0.988501	−	0.570712i	−0.904826	+	0.425781i	$0.859999\pi$
$30$		0			0
$31$	7.11141	+	4.10577i	1.27725	+	0.737419i	0.976341	−	0.216235i	$-0.0693778\pi$
$31$	7.11141	+	4.10577i	1.27725	+	0.737419i	0.300905	+	0.953654i	$0.402711\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.11982	+	2.53803i	0.865407	+	0.429006i
$36$		0			0
$37$	2.57338	−	4.45722i	0.423060	−	0.732762i	−0.573177	−	0.819432i	$-0.694289\pi$
$37$	2.57338	−	4.45722i	0.423060	−	0.732762i	0.996237	+	0.0866697i	$0.0276225\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.23617	+	3.87316i	0.349231	+	0.604886i	0.986113	−	0.166076i	$-0.0531096\pi$
$41$	2.23617	+	3.87316i	0.349231	+	0.604886i	−0.636882	+	0.770961i	$0.719776\pi$
$42$		0			0
$43$	0.332437	−	0.575798i	0.0506962	−	0.0878084i	−0.839564	−	0.543261i	$-0.817189\pi$
$43$	0.332437	−	0.575798i	0.0506962	−	0.0878084i	0.890260	+	0.455453i	$0.150523\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.07992	−	1.87047i	−0.157522	−	0.272836i	0.776453	−	0.630176i	$-0.217017\pi$
$47$	−1.07992	−	1.87047i	−0.157522	−	0.272836i	−0.933974	+	0.357340i	$0.883684\pi$
$48$		0			0
$49$	4.23825	+	5.57111i	0.605464	+	0.795872i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.0340	+	6.37047i	−1.51563	+	0.875051i	−0.515802	+	0.856708i	$0.672506\pi$
$53$	−11.0340	+	6.37047i	−1.51563	+	0.875051i	−0.999832	+	0.0183431i	$0.994161\pi$
$54$		0			0
$55$		−	2.88365i		−	0.388831i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.83424	−	8.37316i	0.629365	−	1.09009i	−0.358314	−	0.933601i	$-0.616648\pi$
$59$	4.83424	−	8.37316i	0.629365	−	1.09009i	0.987679	−	0.156491i	$-0.0500183\pi$
$60$		0			0
$61$	−10.6468	+	6.14691i	−1.36318	+	0.787031i	−0.990045	−	0.140748i	$-0.955049\pi$
$61$	−10.6468	+	6.14691i	−1.36318	+	0.787031i	−0.373131	+	0.927778i	$0.621716\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.39600	−	2.53803i	0.545257	−	0.314804i
$66$		0			0
$67$	1.86778	−	3.23509i	0.228186	−	0.395229i	−0.729085	−	0.684423i	$-0.760054\pi$
$67$	1.86778	−	3.23509i	0.228186	−	0.395229i	0.957270	+	0.289194i	$0.0933873\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.4058i		−	1.35362i	−0.736157	−	0.676810i	$-0.763362\pi$
$71$		−	11.4058i		−	1.35362i	0.736157	−	0.676810i	$-0.236638\pi$
$72$		0			0
$73$	9.07338	−	5.23852i	1.06196	−	0.613122i	0.135985	−	0.990711i	$-0.456580\pi$
$73$	9.07338	−	5.23852i	1.06196	−	0.613122i	0.925973	+	0.377589i	$0.123247\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.56891	−	3.16487i	0.178794	−	0.360671i
$78$		0			0
$79$	4.53803	+	7.86010i	0.510569	+	0.884331i	0.999925	+	0.0122468i	$0.00389836\pi$
$79$	4.53803	+	7.86010i	0.510569	+	0.884331i	−0.489356	+	0.872084i	$0.662768\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.39958	+	9.35235i	−0.592681	+	1.02655i	0.401189	+	0.915995i	$0.368597\pi$
$83$	−5.39958	+	9.35235i	−0.592681	+	1.02655i	−0.993870	+	0.110558i	$0.964736\pi$
$84$		0			0
$85$	7.77897	+	13.4736i	0.843748	+	1.46141i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	−0.694839	−	0.719165i	$-0.744525\pi$
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	0.970235	+	0.242166i	$0.0778579\pi$
$90$		0			0
$91$	6.20560	−	0.393808i	0.650523	−	0.0412823i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.24198	+	1.29440i	0.230022	+	0.132803i
$96$		0			0
$97$	1.07069	+	0.618162i	0.108712	+	0.0627648i	0.553370	−	0.832935i	$-0.313342\pi$
$97$	1.07069	+	0.618162i	0.108712	+	0.0627648i	−0.444658	+	0.895700i	$0.646675\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.91281			−0.389339			−0.194670	−	0.980869i	$-0.562363\pi$
$101$	−3.91281			−0.389339			−0.194670	+	0.980869i	$0.562363\pi$
$102$		0			0
$103$			4.12928i			0.406870i	0.979088	+	0.203435i	$0.0652106\pi$
$103$			4.12928i			0.406870i	−0.979088	+	0.203435i	$0.934789\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.39823	−	1.96197i	−0.328519	−	0.189671i	0.326664	−	0.945140i	$-0.394075\pi$
$107$	−3.39823	−	1.96197i	−0.328519	−	0.189671i	−0.655183	+	0.755470i	$0.727409\pi$
$108$		0			0
$109$	−0.664874	−	1.15160i	−0.0636834	−	0.110303i	0.832426	−	0.554137i	$-0.186951\pi$
$109$	−0.664874	−	1.15160i	−0.0636834	−	0.110303i	−0.896109	+	0.443834i	$0.853618\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.2737	+	8.24094i	−1.34276	+	0.775242i	−0.987212	−	0.159416i	$-0.949039\pi$
$113$	−14.2737	+	8.24094i	−1.34276	+	0.775242i	−0.355548	+	0.934658i	$0.615706\pi$
$114$		0			0
$115$		−	5.19615i		−	0.484544i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.20701	+	19.0199i	0.110646	+	1.74355i
$120$		0			0
$121$	9.21744			0.837949
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.5230			−1.03065
$126$		0			0
$127$	14.8877			1.32107			0.660534	−	0.750796i	$-0.270330\pi$
$127$	14.8877			1.32107			0.660534	+	0.750796i	$0.270330\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−15.8426			−1.38418			−0.692089	−	0.721812i	$-0.743309\pi$
$131$	−15.8426			−1.38418			−0.692089	+	0.721812i	$0.743309\pi$
$132$		0			0
$133$	1.75637	+	2.64044i	0.152297	+	0.228955i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	22.8116i		−	1.94893i	−0.224542	−	0.974464i	$-0.572089\pi$
$137$		−	22.8116i		−	1.94893i	0.224542	−	0.974464i	$-0.427911\pi$
$138$		0			0
$139$	14.1821	−	8.18804i	1.20291	−	0.694500i	0.241709	−	0.970349i	$-0.422292\pi$
$139$	14.1821	−	8.18804i	1.20291	−	0.694500i	0.961201	+	0.275849i	$0.0889589\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.56891	−	2.71744i	−0.131199	−	0.227244i
$144$		0			0
$145$	−11.4973	−	6.63798i	−0.954800	−	0.551254i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			8.73556i			0.715645i	0.933790	+	0.357823i	$0.116481\pi$
$149$			8.73556i			0.715645i	−0.933790	+	0.357823i	$0.883519\pi$
$150$		0			0
$151$	7.14675			0.581594			0.290797	−	0.956785i	$-0.406079\pi$
$151$	7.14675			0.581594			0.290797	+	0.956785i	$0.406079\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.3594	+	8.86778i	1.23370	+	0.712277i
$156$		0			0
$157$	10.6060	+	6.12340i	0.846453	+	0.488700i	0.859453	−	0.511215i	$-0.170805\pi$
$157$	10.6060	+	6.12340i	0.846453	+	0.488700i	−0.0129992	+	0.999916i	$0.504138\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.82709	−	5.70291i	0.222806	−	0.449452i
$162$		0			0
$163$	−8.03803	+	13.9223i	−0.629587	+	1.09048i	0.358047	+	0.933703i	$0.383443\pi$
$163$	−8.03803	+	13.9223i	−0.629587	+	1.09048i	−0.987635	+	0.156774i	$0.949891\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.68515	+	9.84697i	0.439930	+	0.761981i	0.997684	−	0.0680253i	$-0.0216699\pi$
$167$	5.68515	+	9.84697i	0.439930	+	0.761981i	−0.557753	+	0.830007i	$0.688337\pi$
$168$		0			0
$169$	−3.73825	+	6.47484i	−0.287558	+	0.498065i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.35241	+	11.0027i	0.482964	+	0.836519i	0.999809	−	0.0195605i	$-0.00622671\pi$
$173$	6.35241	+	11.0027i	0.482964	+	0.836519i	−0.516844	+	0.856079i	$0.672893\pi$
$174$		0			0
$175$	−0.794405	−	0.393808i	−0.0600514	−	0.0297691i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	13.8862	−	8.01722i	1.03791	−	0.599235i	0.118666	−	0.992934i	$-0.462138\pi$
$179$	13.8862	−	8.01722i	1.03791	−	0.599235i	0.919239	+	0.393699i	$0.128805\pi$
$180$		0			0
$181$		−	14.0729i		−	1.04603i	−0.852324	−	0.523015i	$-0.824807\pi$
$181$		−	14.0729i		−	1.04603i	0.852324	−	0.523015i	$-0.175193\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.55806	−	9.62684i	0.408637	−	0.707780i
$186$		0			0
$187$	8.32885	−	4.80866i	0.609066	−	0.351644i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	22.7662	−	13.1441i	1.64730	−	0.951071i	0.669166	−	0.743113i	$-0.266652\pi$
$191$	22.7662	−	13.1441i	1.64730	−	0.951071i	0.978138	−	0.207958i	$-0.0666817\pi$
$192$		0			0
$193$	−1.53803	+	2.66395i	−0.110710	+	0.191755i	−0.916057	−	0.401049i	$-0.868646\pi$
$193$	−1.53803	+	2.66395i	−0.110710	+	0.191755i	0.805347	+	0.592804i	$0.201979\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	9.08144i		−	0.647026i	−0.946224	−	0.323513i	$-0.895136\pi$
$197$		−	9.08144i		−	0.647026i	0.946224	−	0.323513i	$-0.104864\pi$
$198$		0			0
$199$	19.6468	−	11.3431i	1.39272	−	0.804088i	0.399106	−	0.916905i	$-0.369321\pi$
$199$	19.6468	−	11.3431i	1.39272	−	0.804088i	0.993616	+	0.112817i	$0.0359874\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.00704	−	13.5407i	−0.632170	−	0.950372i
$204$		0			0
$205$	4.82975	+	8.36537i	0.337324	+	0.584263i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.800152	−	1.38590i	0.0553476	−	0.0958649i
$210$		0			0
$211$	−4.90850	−	8.50177i	−0.337915	−	0.585286i	0.646125	−	0.763231i	$-0.276388\pi$
$211$	−4.90850	−	8.50177i	−0.337915	−	0.585286i	−0.984040	+	0.177945i	$0.943055\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.718009	−	1.24363i	0.0489678	−	0.0848147i
$216$		0			0
$217$	12.0327	+	18.0893i	0.816830	+	1.22798i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.6612	+	8.46466i	0.986220	+	0.569394i
$222$		0			0
$223$	−6.10603	−	3.52532i	−0.408890	−	0.236073i	0.281423	−	0.959584i	$-0.409194\pi$
$223$	−6.10603	−	3.52532i	−0.408890	−	0.236073i	−0.690313	+	0.723511i	$0.742527\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.7554			−1.31122			−0.655608	−	0.755102i	$-0.727587\pi$
$227$	−19.7554			−1.31122			−0.655608	+	0.755102i	$0.727587\pi$
$228$		0			0
$229$		−	3.33235i		−	0.220208i	−0.993920	−	0.110104i	$-0.964882\pi$
$229$		−	3.33235i		−	0.220208i	0.993920	−	0.110104i	$-0.0351184\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.48172	+	3.16487i	0.359120	+	0.207338i	0.668695	−	0.743537i	$-0.266853\pi$
$233$	5.48172	+	3.16487i	0.359120	+	0.207338i	−0.309575	+	0.950875i	$0.600187\pi$
$234$		0			0
$235$	−2.33244	−	4.03990i	−0.152151	−	0.263534i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−24.1514	+	13.9438i	−1.56223	+	0.901952i	−0.565196	+	0.824957i	$0.691199\pi$
$239$	−24.1514	+	13.9438i	−1.56223	+	0.901952i	−0.997031	+	0.0769957i	$0.975467\pi$
$240$		0			0
$241$			8.99916i			0.579687i	0.957074	+	0.289844i	$0.0936033\pi$
$241$			8.99916i			0.579687i	−0.957074	+	0.289844i	$0.906397\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.15391	+	12.0327i	0.584822	+	0.768738i
$246$		0			0
$247$	2.81700			0.179242
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.5230			0.727324			0.363662	−	0.931531i	$-0.381526\pi$
$251$	11.5230			0.727324			0.363662	+	0.931531i	$0.381526\pi$
$252$		0			0
$253$	−3.21206			−0.201941
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.13783			0.195732			0.0978662	−	0.995200i	$-0.468798\pi$
$257$	3.13783			0.195732			0.0978662	+	0.995200i	$0.468798\pi$
$258$		0			0
$259$	11.3378	−	7.54171i	0.704497	−	0.468619i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	11.4058i		−	0.703313i	−0.936129	−	0.351656i	$-0.885619\pi$
$263$		−	11.4058i		−	0.703313i	0.936129	−	0.351656i	$-0.114381\pi$
$264$		0			0
$265$	−23.8315	+	13.7591i	−1.46396	+	0.845217i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.6721	+	18.4846i	0.650688	+	1.12702i	0.982956	+	0.183839i	$0.0588526\pi$
$269$	10.6721	+	18.4846i	0.650688	+	1.12702i	−0.332269	+	0.943185i	$0.607814\pi$
$270$		0			0
$271$	−15.5434	−	8.97399i	−0.944195	−	0.545131i	−0.0529220	−	0.998599i	$-0.516853\pi$
$271$	−15.5434	−	8.97399i	−0.944195	−	0.545131i	−0.891273	+	0.453467i	$0.850187\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			0.447435i			0.0269813i
$276$		0			0
$277$	−31.7700			−1.90887			−0.954437	−	0.298412i	$-0.903543\pi$
$277$	−31.7700			−1.90887			−0.954437	+	0.298412i	$0.903543\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.08127	−	1.77897i	−0.183813	−	0.106125i	0.405270	−	0.914197i	$-0.367178\pi$
$281$	−3.08127	−	1.77897i	−0.183813	−	0.106125i	−0.589083	+	0.808073i	$0.700511\pi$
$282$		0			0
$283$	−6.71475	−	3.87676i	−0.399151	−	0.230450i	0.286967	−	0.957941i	$-0.407353\pi$
$283$	−6.71475	−	3.87676i	−0.399151	−	0.230450i	−0.686117	+	0.727491i	$0.740686\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.749397	+	11.8089i	0.0442355	+	0.697060i
$288$		0			0
$289$	−17.4438	+	30.2136i	−1.02611	+	1.77727i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.52174	+	4.36778i	0.147322	+	0.255168i	0.930237	−	0.366960i	$-0.119601\pi$
$293$	2.52174	+	4.36778i	0.147322	+	0.255168i	−0.782915	+	0.622129i	$0.786268\pi$
$294$		0			0
$295$	10.4412	−	18.0846i	0.607908	−	1.05293i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.82709	−	4.89666i	−0.163495	−	0.283181i
$300$		0			0
$301$	1.46466	−	0.974263i	0.0844214	−	0.0561556i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−22.9952	+	13.2763i	−1.31670	+	0.760198i
$306$		0			0
$307$		−	15.0080i		−	0.856552i	−0.903648	−	0.428276i	$-0.859121\pi$
$307$		−	15.0080i		−	0.856552i	0.903648	−	0.428276i	$-0.140879\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.04348	−	8.73556i	0.285989	−	0.495348i	−0.686859	−	0.726791i	$-0.741011\pi$
$311$	5.04348	−	8.73556i	0.285989	−	0.495348i	0.972849	+	0.231442i	$0.0743444\pi$
$312$		0			0
$313$	−15.5761	+	8.99284i	−0.880411	+	0.508306i	−0.870794	−	0.491648i	$-0.836395\pi$
$313$	−15.5761	+	8.99284i	−0.880411	+	0.508306i	−0.00961724	+	0.999954i	$0.503061\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.09646	+	2.36509i	−0.230080	+	0.132837i	−0.610609	−	0.791932i	$-0.709075\pi$
$317$	−4.09646	+	2.36509i	−0.230080	+	0.132837i	0.380529	+	0.924769i	$0.375742\pi$
$318$		0			0
$319$	−4.10334	+	7.10720i	−0.229743	+	0.397927i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			8.63401i			0.480409i
$324$		0			0
$325$	−0.682096	+	0.393808i	−0.0378359	+	0.0218445i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.361908	−	5.70291i	−0.0199526	−	0.314411i
$330$		0			0
$331$	1.38859	+	2.40511i	0.0763239	+	0.132197i	0.901661	−	0.432443i	$-0.142348\pi$
$331$	1.38859	+	2.40511i	0.0763239	+	0.132197i	−0.825337	+	0.564640i	$0.809015\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.03409	−	6.98725i	0.220406	−	0.381754i
$336$		0			0
$337$	3.49731	+	6.05752i	0.190511	+	0.329974i	0.945420	−	0.325855i	$-0.105652\pi$
$337$	3.49731	+	6.05752i	0.190511	+	0.329974i	−0.754909	+	0.655830i	$0.772319\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.48172	−	9.49462i	0.296852	−	0.514163i
$342$		0			0
$343$	3.50000	+	18.1865i	0.188982	+	0.981981i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.5840	+	10.1521i	0.943959	+	0.544995i	0.891199	−	0.453612i	$-0.149865\pi$
$347$	17.5840	+	10.1521i	0.943959	+	0.544995i	0.0527597	+	0.998607i	$0.483198\pi$
$348$		0			0
$349$	−8.46466	−	4.88707i	−0.453103	−	0.261599i	0.256037	−	0.966667i	$-0.417583\pi$
$349$	−8.46466	−	4.88707i	−0.453103	−	0.261599i	−0.709140	+	0.705068i	$0.750916\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.8575			−0.684335			−0.342167	−	0.939639i	$-0.611161\pi$
$353$	−12.8575			−0.684335			−0.342167	+	0.939639i	$0.611161\pi$
$354$		0			0
$355$		−	24.6346i		−	1.30747i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.7447	−	9.66756i	−0.883752	−	0.510234i	−0.0118583	−	0.999930i	$-0.503775\pi$
$359$	−16.7447	−	9.66756i	−0.883752	−	0.510234i	−0.871894	+	0.489695i	$0.837108\pi$
$360$		0			0
$361$	−8.78166	−	15.2103i	−0.462193	−	0.800541i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	19.5970	−	11.3143i	1.02575	−	0.592218i
$366$		0			0
$367$		−	26.8908i		−	1.40369i	−0.712330	−	0.701845i	$-0.752360\pi$
$367$		−	26.8908i		−	1.40369i	0.712330	−	0.701845i	$-0.247640\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−33.6417	+	2.13491i	−1.74659	+	0.110839i
$372$		0			0
$373$	−38.4456			−1.99064			−0.995320	−	0.0966369i	$-0.969191\pi$
$373$	−38.4456			−1.99064			−0.995320	+	0.0966369i	$0.969191\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.4462			−0.744016
$378$		0			0
$379$	3.05993			0.157178			0.0785891	−	0.996907i	$-0.474958\pi$
$379$	3.05993			0.157178			0.0785891	+	0.996907i	$0.474958\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	13.6828			0.699159			0.349579	−	0.936907i	$-0.386324\pi$
$383$	13.6828			0.699159			0.349579	+	0.936907i	$0.386324\pi$
$384$		0			0
$385$	3.38859	−	6.83560i	0.172699	−	0.348374i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			0.887691i			0.0450077i	0.999747	+	0.0225039i	$0.00716380\pi$
$389$			0.887691i			0.0450077i	−0.999747	+	0.0225039i	$0.992836\pi$
$390$		0			0
$391$	15.0081	−	8.66491i	0.758990	−	0.438203i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.80139	+	16.9765i	0.493161	+	0.854180i
$396$		0			0
$397$	−29.6114	−	17.0962i	−1.48615	−	0.858031i	−0.486278	−	0.873804i	$-0.661646\pi$
$397$	−29.6114	−	17.0962i	−1.48615	−	0.858031i	−0.999876	+	0.0157726i	$0.994979\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	27.8877i		−	1.39264i	−0.717729	−	0.696322i	$-0.754818\pi$
$401$		−	27.8877i		−	1.39264i	0.717729	−	0.696322i	$-0.245182\pi$
$402$		0			0
$403$	19.2989			0.961346
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.95095	−	3.43578i	−0.294977	−	0.170305i
$408$		0			0
$409$	−11.6848	−	6.74621i	−0.577775	−	0.333579i	0.182473	−	0.983211i	$-0.441590\pi$
$409$	−11.6848	−	6.74621i	−0.577775	−	0.333579i	−0.760249	+	0.649632i	$0.774923\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	21.2988	−	14.1676i	1.04804	−	0.697140i
$414$		0			0
$415$	−11.6622	+	20.1995i	−0.572474	+	0.991554i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.9684	−	24.1939i	−0.682400	−	1.18195i	−0.974246	−	0.225486i	$-0.927603\pi$
$419$	−13.9684	−	24.1939i	−0.682400	−	1.18195i	0.291846	−	0.956465i	$-0.405730\pi$
$420$		0			0
$421$	−6.27359	+	10.8662i	−0.305756	+	0.529585i	−0.977429	−	0.211262i	$-0.932243\pi$
$421$	−6.27359	+	10.8662i	−0.305756	+	0.529585i	0.671673	+	0.740848i	$0.265576\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.20701	−	2.09060i	−0.0585484	−	0.101409i
$426$		0			0
$427$	−32.4611	+	2.05999i	−1.57090	+	0.0996897i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−14.9720	+	8.64406i	−0.721174	+	0.416370i	−0.815185	−	0.579201i	$-0.803365\pi$
$431$	−14.9720	+	8.64406i	−0.721174	+	0.416370i	0.0940108	+	0.995571i	$0.470031\pi$
$432$		0			0
$433$			27.1920i			1.30676i	0.757028	+	0.653382i	$0.226651\pi$
$433$			27.1920i			1.30676i	−0.757028	+	0.653382i	$0.773349\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.44182	−	2.49731i	0.0689718	−	0.119463i
$438$		0			0
$439$	−9.49462	+	5.48172i	−0.453154	+	0.261628i	−0.709161	−	0.705046i	$-0.750926\pi$
$439$	−9.49462	+	5.48172i	−0.453154	+	0.261628i	0.256008	+	0.966675i	$0.417593\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.9697	+	9.22013i	−0.758745	+	0.438062i	−0.828845	−	0.559478i	$-0.811001\pi$
$443$	−15.9697	+	9.22013i	−0.758745	+	0.438062i	0.0701001	+	0.997540i	$0.477668\pi$
$444$		0			0
$445$	5.61141	−	9.71924i	0.266006	−	0.460736i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	23.6179i		−	1.11460i	−0.830312	−	0.557298i	$-0.811838\pi$
$449$		−	23.6179i		−	1.11460i	0.830312	−	0.557298i	$-0.188162\pi$
$450$		0			0
$451$	5.17115	−	2.98557i	0.243500	−	0.140585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	13.4030	−	0.850560i	0.628344	−	0.0398748i
$456$		0			0
$457$	14.6141	+	25.3124i	0.683619	+	1.18406i	0.973869	+	0.227111i	$0.0729281\pi$
$457$	14.6141	+	25.3124i	0.683619	+	1.18406i	−0.290250	+	0.956951i	$0.593739\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.95998	+	5.12684i	−0.137860	+	0.238781i	−0.926686	−	0.375835i	$-0.877356\pi$
$461$	−2.95998	+	5.12684i	−0.137860	+	0.238781i	0.788826	+	0.614616i	$0.210689\pi$
$462$		0			0
$463$	−17.2174	−	29.8215i	−0.800162	−	1.38592i	−0.919509	−	0.393069i	$-0.871413\pi$
$463$	−17.2174	−	29.8215i	−0.800162	−	1.38592i	0.119347	−	0.992853i	$-0.461920\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.3114	+	33.4483i	−0.893625	+	1.54780i	−0.0581276	+	0.998309i	$0.518513\pi$
$467$	−19.3114	+	33.4483i	−0.893625	+	1.54780i	−0.835497	+	0.549495i	$0.814820\pi$
$468$		0			0
$469$	8.22909	−	5.47384i	0.379984	−	0.252759i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.768763	−	0.443845i	−0.0353478	−	0.0204080i
$474$		0			0
$475$	−0.347871	−	0.200844i	−0.0159614	−	0.00921533i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.03632			0.138733			0.0693665	−	0.997591i	$-0.477902\pi$
$479$	3.03632			0.138733			0.0693665	+	0.997591i	$0.477902\pi$
$480$		0			0
$481$		−	12.0960i		−	0.551528i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.31251	+	1.33513i	0.105005	+	0.0606249i
$486$		0			0
$487$	13.3850	+	23.1835i	0.606532	+	1.05054i	0.991807	+	0.127743i	$0.0407733\pi$
$487$	13.3850	+	23.1835i	0.606532	+	1.05054i	−0.385275	+	0.922802i	$0.625893\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.49023	−	5.47919i	0.428288	−	0.247272i	−0.270329	−	0.962768i	$-0.587132\pi$
$491$	9.49023	−	5.47919i	0.428288	−	0.247272i	0.698617	+	0.715496i	$0.253799\pi$
$492$		0			0
$493$		−	44.2770i		−	1.99413i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.4030	−	27.0371i	0.601209	−	1.21278i
$498$		0			0
$499$	−30.0998			−1.34745			−0.673725	−	0.738982i	$-0.735307\pi$
$499$	−30.0998			−1.34745			−0.673725	+	0.738982i	$0.735307\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.0941			−0.539250			−0.269625	−	0.962965i	$-0.586900\pi$
$503$	−12.0941			−0.539250			−0.269625	+	0.962965i	$0.586900\pi$
$504$		0			0
$505$	−8.45101			−0.376065
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−25.0531			−1.11046			−0.555230	−	0.831697i	$-0.687370\pi$
$509$	−25.0531			−1.11046			−0.555230	+	0.831697i	$0.687370\pi$
$510$		0			0
$511$	27.6640	−	1.75556i	1.22378	−	0.0776614i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			8.91856i			0.392999i
$516$		0			0
$517$	−2.49731	+	1.44182i	−0.109832	+	0.0634113i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.35956	+	14.4792i	0.366239	+	0.634345i	0.988974	−	0.148088i	$-0.0473119\pi$
$521$	8.35956	+	14.4792i	0.366239	+	0.634345i	−0.622735	+	0.782433i	$0.713979\pi$
$522$		0			0
$523$	−22.5327	−	13.0092i	−0.985284	−	0.568854i	−0.0814229	−	0.996680i	$-0.525946\pi$
$523$	−22.5327	−	13.0092i	−0.985284	−	0.568854i	−0.903861	+	0.427826i	$0.859280\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			59.1503i			2.57663i
$528$		0			0
$529$	17.2121			0.748351
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.10274	+	5.25547i	0.394284	+	0.227640i
$534$		0			0
$535$	−7.33960	−	4.23752i	−0.317319	−	0.183204i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.43813	−	5.65860i	0.320383	−	0.243733i
$540$		0			0
$541$	−15.4973	+	26.8421i	−0.666281	+	1.15403i	0.312655	+	0.949867i	$0.398782\pi$
$541$	−15.4973	+	26.8421i	−0.666281	+	1.15403i	−0.978936	+	0.204167i	$0.934552\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.43602	−	2.48725i	−0.0615122	−	0.106542i
$546$		0			0
$547$	18.1848	−	31.4970i	0.777525	−	1.34671i	−0.155839	−	0.987782i	$-0.549808\pi$
$547$	18.1848	−	31.4970i	0.777525	−	1.34671i	0.933364	−	0.358931i	$-0.116859\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.68380	−	6.38053i	−0.156935	−	0.271820i
$552$		0			0
$553$	1.52081	+	23.9648i	0.0646715	+	1.01909i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.6697	+	10.7790i	−0.791062	+	0.456720i	−0.840336	−	0.542066i	$-0.817642\pi$
$557$	−18.6697	+	10.7790i	−0.791062	+	0.456720i	0.0492745	+	0.998785i	$0.484309\pi$
$558$		0			0
$559$		−	1.56260i		−	0.0660908i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.356101	−	0.616785i	0.0150079	−	0.0259944i	−0.858424	−	0.512941i	$-0.828556\pi$
$563$	0.356101	−	0.616785i	0.0150079	−	0.0259944i	0.873432	+	0.486946i	$0.161889\pi$
$564$		0			0
$565$	−30.8288	+	17.7990i	−1.29698	+	0.748811i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.7742	+	17.1902i	−1.24820	+	0.720649i	−0.970750	−	0.240091i	$-0.922823\pi$
$569$	−29.7742	+	17.1902i	−1.24820	+	0.720649i	−0.277450	+	0.960740i	$0.589489\pi$
$570$		0			0
$571$	12.7201	−	22.0319i	0.532321	−	0.922007i	−0.466967	−	0.884275i	$-0.654653\pi$
$571$	12.7201	−	22.0319i	0.532321	−	0.922007i	0.999288	−	0.0377320i	$-0.0120133\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.806250i			0.0336229i
$576$		0			0
$577$	7.45928	−	4.30662i	0.310534	−	0.179287i	−0.336631	−	0.941636i	$-0.609288\pi$
$577$	7.45928	−	4.30662i	0.310534	−	0.179287i	0.647165	+	0.762350i	$0.275954\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−23.7895	+	15.8244i	−0.986956	+	0.656506i
$582$		0			0
$583$	8.50538	+	14.7317i	0.352257	+	0.610127i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.8426	−	27.4403i	0.653896	−	1.13258i	−0.328274	−	0.944583i	$-0.606467\pi$
$587$	15.8426	−	27.4403i	0.653896	−	1.13258i	0.982169	−	0.187998i	$-0.0601998\pi$
$588$		0			0
$589$	4.92125	+	8.52385i	0.202776	+	0.351219i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	24.1456	−	41.8215i	0.991543	−	1.71740i	0.383378	−	0.923592i	$-0.374761\pi$
$593$	24.1456	−	41.8215i	0.991543	−	1.71740i	0.608165	−	0.793811i	$-0.291906\pi$
$594$		0			0
$595$	2.60693	+	41.0798i	0.106874	+	1.68411i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−25.6952	−	14.8351i	−1.04988	−	0.606147i	−0.127262	−	0.991869i	$-0.540619\pi$
$599$	−25.6952	−	14.8351i	−1.04988	−	0.606147i	−0.922615	+	0.385722i	$0.873952\pi$
$600$		0			0
$601$	−35.5570	−	20.5289i	−1.45040	−	0.837390i	−0.451898	−	0.892070i	$-0.649253\pi$
$601$	−35.5570	−	20.5289i	−1.45040	−	0.837390i	−0.998504	+	0.0546796i	$0.982586\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.9081			0.809380
$606$		0			0
$607$		−	22.8649i		−	0.928057i	−0.885820	−	0.464028i	$-0.846404\pi$
$607$		−	22.8649i		−	0.928057i	0.885820	−	0.464028i	$-0.153596\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.39600	−	2.53803i	−0.177843	−	0.102678i
$612$		0			0
$613$	−12.7029	−	22.0021i	−0.513066	−	0.888656i	−0.999885	−	0.0151531i	$-0.995176\pi$
$613$	−12.7029	−	22.0021i	−0.513066	−	0.888656i	0.486820	−	0.873503i	$-0.338157\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.9590	−	7.48188i	0.521709	−	0.301209i	−0.215924	−	0.976410i	$-0.569276\pi$
$617$	12.9590	−	7.48188i	0.521709	−	0.301209i	0.737634	+	0.675201i	$0.235943\pi$
$618$		0			0
$619$		−	16.9472i		−	0.681166i	−0.940214	−	0.340583i	$-0.889376\pi$
$619$		−	16.9472i		−	0.681166i	0.940214	−	0.340583i	$-0.110624\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.4466	−	7.61410i	0.458600	−	0.305052i
$624$		0			0
$625$	−23.2121			−0.928483
$626$		0			0
$627$		0			0
$628$		0			0
$629$	37.0737			1.47822
$630$		0			0
$631$	−21.3534			−0.850067			−0.425033	−	0.905178i	$-0.639738\pi$
$631$	−21.3534			−0.850067			−0.425033	+	0.905178i	$0.639738\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	32.1549			1.27603
$636$		0			0
$637$	15.1729	+	6.35872i	0.601174	+	0.251942i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			44.8098i			1.76988i	0.465703	+	0.884941i	$0.345801\pi$
$641$			44.8098i			1.76988i	−0.465703	+	0.884941i	$0.654199\pi$
$642$		0			0
$643$	−16.3235	+	9.42436i	−0.643735	+	0.371660i	−0.786052	−	0.618161i	$-0.787878\pi$
$643$	−16.3235	+	9.42436i	−0.643735	+	0.371660i	0.142317	+	0.989821i	$0.454545\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.5404	−	33.8450i	−0.768213	−	1.33058i	−0.938531	−	0.345194i	$-0.887813\pi$
$647$	−19.5404	−	33.8450i	−0.768213	−	1.33058i	0.170319	−	0.985389i	$-0.445520\pi$
$648$		0			0
$649$	−11.1792	−	6.45432i	−0.438823	−	0.253354i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	11.8532i		−	0.463853i	−0.972733	−	0.231927i	$-0.925497\pi$
$653$		−	11.8532i		−	0.463853i	0.972733	−	0.231927i	$-0.0745030\pi$
$654$		0			0
$655$	−34.2174			−1.33699
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.8582	+	16.6613i	1.12416	+	0.649032i	0.942459	−	0.334323i	$-0.108508\pi$
$659$	28.8582	+	16.6613i	1.12416	+	0.649032i	0.181697	+	0.983355i	$0.441841\pi$
$660$		0			0
$661$	2.69285	+	1.55472i	0.104740	+	0.0604715i	0.551455	−	0.834205i	$-0.314073\pi$
$661$	2.69285	+	1.55472i	0.104740	+	0.0604715i	−0.446715	+	0.894676i	$0.647406\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.79347	+	5.70291i	0.147104	+	0.221149i
$666$		0			0
$667$	−7.39397	+	12.8067i	−0.286296	+	0.495879i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	8.20689	+	14.2148i	0.316823	+	0.548754i
$672$		0			0
$673$	−1.34050	+	2.32182i	−0.0516726	+	0.0894995i	−0.890705	−	0.454582i	$-0.849789\pi$
$673$	−1.34050	+	2.32182i	−0.0516726	+	0.0894995i	0.839032	+	0.544082i	$0.183122\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.2737	+	24.7228i	0.548584	+	0.950175i	0.998372	+	0.0570397i	$0.0181662\pi$
$677$	14.2737	+	24.7228i	0.548584	+	0.950175i	−0.449788	+	0.893135i	$0.648500\pi$
$678$		0			0
$679$	1.81163	+	2.72351i	0.0695238	+	0.104519i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	38.0377	−	21.9611i	1.45547	−	0.840317i	0.456688	−	0.889627i	$-0.349036\pi$
$683$	38.0377	−	21.9611i	1.45547	−	0.840317i	0.998784	+	0.0493101i	$0.0157022\pi$
$684$		0			0
$685$		−	49.2693i		−	1.88248i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.9720	+	25.9322i	−0.570386	+	0.987938i
$690$		0			0
$691$	−27.1060	+	15.6497i	−1.03116	+	0.595342i	−0.917317	−	0.398157i	$-0.869650\pi$
$691$	−27.1060	+	15.6497i	−1.03116	+	0.595342i	−0.113845	+	0.993499i	$0.536317\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	30.6309	−	17.6848i	1.16190	−	0.670822i
$696$		0			0
$697$	−16.1078	+	27.8996i	−0.610127	+	1.05677i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			23.2591i			0.878483i	0.898369	+	0.439241i	$0.144753\pi$
$701$			23.2591i			0.878483i	−0.898369	+	0.439241i	$0.855247\pi$
$702$		0			0
$703$	5.34249	−	3.08449i	0.201496	−	0.116334i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.27519	−	4.59797i	−0.348830	−	0.172924i
$708$		0			0
$709$	−10.2962	−	17.8335i	−0.386682	−	0.669752i	0.605319	−	0.795983i	$-0.293045\pi$
$709$	−10.2962	−	17.8335i	−0.386682	−	0.669752i	−0.992001	+	0.126231i	$0.959712\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.87772	−	17.1087i	0.369924	−	0.640727i
$714$		0			0
$715$	−3.38859	−	5.86921i	−0.126726	−	0.219496i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.76014	+	6.51275i	−0.140229	+	0.242884i	−0.927583	−	0.373617i	$-0.878117\pi$
$719$	−3.76014	+	6.51275i	−0.140229	+	0.242884i	0.787354	+	0.616502i	$0.211451\pi$
$720$		0			0
$721$	−4.85235	+	9.78834i	−0.180711	+	0.364537i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.78396	+	1.02997i	0.0662544	+	0.0382520i
$726$		0			0
$727$	28.8342	+	16.6474i	1.06940	+	0.617420i	0.928018	−	0.372535i	$-0.121511\pi$
$727$	28.8342	+	16.6474i	1.06940	+	0.617420i	0.141384	+	0.989955i	$0.454845\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.78930			0.177139
$732$		0			0
$733$		−	15.4567i		−	0.570907i	−0.958393	−	0.285453i	$-0.907856\pi$
$733$		−	15.4567i		−	0.570907i	0.958393	−	0.285453i	$-0.0921441\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.31925	−	2.49372i	−0.159102	−	0.0918574i
$738$		0			0
$739$	−3.10872	−	5.38446i	−0.114356	−	0.198071i	0.803166	−	0.595755i	$-0.203147\pi$
$739$	−3.10872	−	5.38446i	−0.114356	−	0.198071i	−0.917522	+	0.397685i	$0.869814\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.4175	+	6.01453i	−0.382180	+	0.220652i	−0.678766	−	0.734354i	$-0.737485\pi$
$743$	−10.4175	+	6.01453i	−0.382180	+	0.220652i	0.296586	+	0.955006i	$0.404152\pi$
$744$		0			0
$745$			18.8673i			0.691246i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.74987	−	8.64406i	−0.210096	−	0.315847i
$750$		0			0
$751$	−33.7754			−1.23248			−0.616241	−	0.787558i	$-0.711345\pi$
$751$	−33.7754			−1.23248			−0.616241	+	0.787558i	$0.711345\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.4358			0.561766
$756$		0			0
$757$	49.5870			1.80227			0.901135	−	0.433538i	$-0.142735\pi$
$757$	49.5870			1.80227			0.901135	+	0.433538i	$0.142735\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−39.9294			−1.44744			−0.723719	−	0.690095i	$-0.757569\pi$
$761$	−39.9294			−1.44744			−0.723719	+	0.690095i	$0.757569\pi$
$762$		0			0
$763$	−0.222816	−	3.51112i	−0.00806650	−	0.127111i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	22.7230i		−	0.820480i
$768$		0			0
$769$	13.3968	−	7.73467i	0.483103	−	0.278919i	−0.238606	−	0.971116i	$-0.576690\pi$
$769$	13.3968	−	7.73467i	0.483103	−	0.278919i	0.721709	+	0.692197i	$0.243357\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.3666	−	30.0798i	−0.624633	−	1.08190i	−0.988612	−	0.150489i	$-0.951915\pi$
$773$	−17.3666	−	30.0798i	−0.624633	−	1.08190i	0.363978	−	0.931407i	$-0.381418\pi$
$774$		0			0
$775$	−2.38321	−	1.37595i	−0.0856076	−	0.0494256i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			5.36062i			0.192064i
$780$		0			0
$781$	−15.2282			−0.544908
$782$		0			0
$783$		0			0
$784$		0			0
$785$	22.9072	+	13.2255i	0.817595	+	0.472039i
$786$		0			0
$787$	22.5814	+	13.0374i	0.804941	+	0.464733i	0.845196	−	0.534456i	$-0.179484\pi$
$787$	22.5814	+	13.0374i	0.804941	+	0.464733i	−0.0402547	+	0.999189i	$0.512817\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−43.5194	+	2.76175i	−1.54737	+	0.0981965i
$792$		0			0
$793$	−14.4465	+	25.0221i	−0.513011	+	0.888562i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.05064	−	12.2121i	−0.249746	−	0.432573i	0.713709	−	0.700442i	$-0.247014\pi$
$797$	−7.05064	−	12.2121i	−0.249746	−	0.432573i	−0.963455	+	0.267869i	$0.913681\pi$
$798$		0			0
$799$	7.77897	−	13.4736i	0.275200	−	0.476661i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.99408	−	12.1141i	−0.246816	−	0.427497i
$804$		0			0
$805$	6.10603	−	12.3173i	0.215209	−	0.434128i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	27.4791	−	15.8651i	0.966115	−	0.557787i	0.0680656	−	0.997681i	$-0.478317\pi$
$809$	27.4791	−	15.8651i	0.966115	−	0.557787i	0.898050	+	0.439894i	$0.144984\pi$
$810$		0			0
$811$		−	18.3590i		−	0.644671i	−0.946625	−	0.322336i	$-0.895532\pi$
$811$		−	18.3590i		−	0.644671i	0.946625	−	0.322336i	$-0.104468\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−17.3608	+	30.0698i	−0.608122	+	1.05330i
$816$		0			0
$817$	0.690161	−	0.398465i	0.0241457	−	0.0139405i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.8858	+	9.74900i	−0.589317	+	0.340243i	−0.764828	−	0.644235i	$-0.777176\pi$
$821$	−16.8858	+	9.74900i	−0.589317	+	0.340243i	0.175510	+	0.984478i	$0.443843\pi$
$822$		0			0
$823$	−0.317904	+	0.550626i	−0.0110814	+	0.0191936i	−0.871513	−	0.490372i	$-0.836861\pi$
$823$	−0.317904	+	0.550626i	−0.0110814	+	0.0191936i	0.860432	+	0.509566i	$0.170194\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			28.6939i			0.997786i	0.866664	+	0.498893i	$0.166260\pi$
$827$			28.6939i			0.997786i	−0.866664	+	0.498893i	$0.833740\pi$
$828$		0			0
$829$	29.5461	−	17.0584i	1.02618	−	0.592464i	0.110291	−	0.993899i	$-0.464822\pi$
$829$	29.5461	−	17.0584i	1.02618	−	0.592464i	0.915888	+	0.401435i	$0.131488\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−19.4892	+	46.5045i	−0.675262	+	1.61128i
$834$		0			0
$835$	12.2790	+	21.2678i	0.424931	+	0.736003i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.30523	+	12.6530i	−0.252205	+	0.436831i	−0.964132	−	0.265421i	$-0.914489\pi$
$839$	−7.30523	+	12.6530i	−0.252205	+	0.436831i	0.711928	+	0.702253i	$0.247822\pi$
$840$		0			0
$841$	4.39128	+	7.60592i	0.151423	+	0.262273i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.07399	+	13.9846i	−0.277754	+	0.481084i
$846$		0			0
$847$	21.8497	+	10.8315i	0.750763	+	0.372174i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.7232	−	6.19106i	−0.367588	−	0.212227i
$852$		0			0
$853$	−23.5380	−	13.5897i	−0.805927	−	0.465302i	0.0396125	−	0.999215i	$-0.487388\pi$
$853$	−23.5380	−	13.5897i	−0.805927	−	0.465302i	−0.845539	+	0.533913i	$0.820721\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.61785			0.0894241			0.0447121	−	0.999000i	$-0.485763\pi$
$857$	2.61785			0.0894241			0.0447121	+	0.999000i	$0.485763\pi$
$858$		0			0
$859$			45.0083i			1.53566i	0.640653	+	0.767831i	$0.278664\pi$
$859$			45.0083i			1.53566i	−0.640653	+	0.767831i	$0.721336\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.8475	+	14.9230i	0.879858	+	0.507986i	0.870611	−	0.491971i	$-0.163723\pi$
$863$	25.8475	+	14.9230i	0.879858	+	0.507986i	0.00924613	+	0.999957i	$0.497057\pi$
$864$		0			0
$865$	13.7201	+	23.7640i	0.466498	+	0.807999i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	10.4942	−	6.05884i	0.355992	−	0.205532i
$870$		0			0
$871$		−	8.77936i		−	0.297477i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−27.3149	−	13.5407i	−0.923411	−	0.457760i
$876$		0			0
$877$	40.7284			1.37530			0.687650	−	0.726042i	$-0.258642\pi$
$877$	40.7284			1.37530			0.687650	+	0.726042i	$0.258642\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.774980			−0.0261097			−0.0130549	−	0.999915i	$-0.504156\pi$
$881$	−0.774980			−0.0261097			−0.0130549	+	0.999915i	$0.504156\pi$
$882$		0			0
$883$	7.22819			0.243248			0.121624	−	0.992576i	$-0.461190\pi$
$883$	7.22819			0.243248			0.121624	+	0.992576i	$0.461190\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	53.9175			1.81037			0.905187	−	0.425015i	$-0.139731\pi$
$887$	53.9175			1.81037			0.905187	+	0.425015i	$0.139731\pi$
$888$		0			0
$889$	35.2908	+	17.4946i	1.18362	+	0.586751i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	2.58881i		−	0.0866312i
$894$		0			0
$895$	29.9919	−	17.3159i	1.00252	−	0.578805i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−25.2372	−	43.7121i	−0.841707	−	1.45788i
$900$		0			0
$901$	−79.4812	−	45.8885i	−2.64790	−	1.52877i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	30.3951i		−	1.01037i
$906$		0			0
$907$	34.2935			1.13870			0.569349	−	0.822096i	$-0.307195\pi$
$907$	34.2935			1.13870			0.569349	+	0.822096i	$0.307195\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.08127	+	1.77897i	0.102087	+	0.0589399i	0.550174	−	0.835050i	$-0.314561\pi$
$911$	3.08127	+	1.77897i	0.102087	+	0.0589399i	−0.448087	+	0.893990i	$0.647895\pi$
$912$		0			0
$913$	12.4866	+	7.20912i	0.413245	+	0.238587i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−37.5545	−	18.6168i	−1.24016	−	0.614780i
$918$		0			0
$919$	−20.3931	+	35.3218i	−0.672705	+	1.16516i	0.304429	+	0.952535i	$0.401534\pi$
$919$	−20.3931	+	35.3218i	−0.672705	+	1.16516i	−0.977134	+	0.212625i	$0.931799\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13.4030	−	23.2148i	−0.441167	−	0.764123i
$924$		0			0
$925$	−0.862404	+	1.49373i	−0.0283557	+	0.0491135i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	11.9356	+	20.6731i	0.391596	+	0.678263i	0.992660	−	0.120937i	$-0.0385899\pi$
$929$	11.9356	+	20.6731i	0.391596	+	0.678263i	−0.601065	+	0.799200i	$0.705257\pi$
$930$		0			0
$931$	1.06063	+	8.32301i	0.0347608	+	0.272776i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	17.9889	−	10.3859i	0.588300	−	0.339655i
$936$		0			0
$937$			48.4063i			1.58136i	0.612228	+	0.790682i	$0.290274\pi$
$937$			48.4063i			1.58136i	−0.612228	+	0.790682i	$0.709726\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.44676	−	7.70201i	0.144960	−	0.251078i	−0.784398	−	0.620258i	$-0.787028\pi$
$941$	4.44676	−	7.70201i	0.144960	−	0.251078i	0.929358	+	0.369180i	$0.120361\pi$
$942$		0			0
$943$	9.31809	−	5.37980i	0.303439	−	0.175191i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.7559	+	9.67403i	−0.544494	+	0.314364i	−0.746898	−	0.664938i	$-0.768458\pi$
$947$	−16.7559	+	9.67403i	−0.544494	+	0.314364i	0.202404	+	0.979302i	$0.435124\pi$
$948$		0			0
$949$	12.3116	−	21.3244i	0.399652	−	0.692218i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			21.7409i			0.704258i	0.935951	+	0.352129i	$0.114542\pi$
$953$			21.7409i			0.704258i	−0.935951	+	0.352129i	$0.885458\pi$
$954$		0			0
$955$	49.1711	−	28.3890i	1.59114	−	0.918645i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	26.8061	−	54.0743i	0.865614	−	1.74615i
$960$		0			0
$961$	18.2148	+	31.5489i	0.587573	+	1.01771i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.32189	+	5.75368i	−0.106935	+	0.185218i
$966$		0			0
$967$	6.09329	+	10.5539i	0.195947	+	0.339390i	0.947211	−	0.320612i	$-0.103889\pi$
$967$	6.09329	+	10.5539i	0.195947	+	0.339390i	−0.751264	+	0.660002i	$0.770555\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.67441	+	4.63222i	−0.0858260	+	0.148655i	−0.905743	−	0.423828i	$-0.860686\pi$
$971$	−2.67441	+	4.63222i	−0.0858260	+	0.148655i	0.819917	+	0.572483i	$0.194020\pi$
$972$		0			0
$973$	43.2400	−	2.74402i	1.38621	−	0.0879693i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.00851	+	2.31431i	0.128244	+	0.0740415i	0.562749	−	0.826628i	$-0.309744\pi$
$977$	4.00851	+	2.31431i	0.128244	+	0.0740415i	−0.434506	+	0.900669i	$0.643077\pi$
$978$		0			0
$979$	−6.00807	−	3.46876i	−0.192019	−	0.110862i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.06548			0.129669			0.0648344	−	0.997896i	$-0.479348\pi$
$983$	4.06548			0.129669			0.0648344	+	0.997896i	$0.479348\pi$
$984$		0			0
$985$		−	19.6144i		−	0.624966i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.38526	−	0.799782i	−0.0440488	−	0.0254316i
$990$		0			0
$991$	−25.7582	−	44.6144i	−0.818235	−	1.41722i	−0.906982	−	0.421170i	$-0.861619\pi$
$991$	−25.7582	−	44.6144i	−0.818235	−	1.41722i	0.0887467	−	0.996054i	$-0.471714\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	42.4337	−	24.4991i	1.34524	−	0.776674i
$996$		0			0
$997$		−	6.34775i		−	0.201035i	−0.994935	−	0.100518i	$-0.967950\pi$
$997$		−	6.34775i		−	0.201035i	0.994935	−	0.100518i	$-0.0320499\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.bm.i.593.5		12
3.2	odd	2	inner	2268.2.bm.i.593.2		12
7.3	odd	6		2268.2.w.i.269.5		12
9.2	odd	6		756.2.t.e.593.5	yes	12
9.4	even	3		2268.2.w.i.1349.2		12
9.5	odd	6		2268.2.w.i.1349.5		12
9.7	even	3		756.2.t.e.593.2	yes	12
21.17	even	6		2268.2.w.i.269.2		12
63.2	odd	6		5292.2.f.e.2645.4		12
63.16	even	3		5292.2.f.e.2645.9		12
63.31	odd	6	inner	2268.2.bm.i.1025.2		12
63.38	even	6		756.2.t.e.269.2	✓	12
63.47	even	6		5292.2.f.e.2645.10		12
63.52	odd	6		756.2.t.e.269.5	yes	12
63.59	even	6	inner	2268.2.bm.i.1025.5		12
63.61	odd	6		5292.2.f.e.2645.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.2	✓	12	63.38	even	6
756.2.t.e.269.5	yes	12	63.52	odd	6
756.2.t.e.593.2	yes	12	9.7	even	3
756.2.t.e.593.5	yes	12	9.2	odd	6
2268.2.w.i.269.2		12	21.17	even	6
2268.2.w.i.269.5		12	7.3	odd	6
2268.2.w.i.1349.2		12	9.4	even	3
2268.2.w.i.1349.5		12	9.5	odd	6
2268.2.bm.i.593.2		12	3.2	odd	2	inner
2268.2.bm.i.593.5		12	1.1	even	1	trivial
2268.2.bm.i.1025.2		12	63.31	odd	6	inner
2268.2.bm.i.1025.5		12	63.59	even	6	inner
5292.2.f.e.2645.3		12	63.61	odd	6
5292.2.f.e.2645.4		12	63.2	odd	6
5292.2.f.e.2645.9		12	63.16	even	3
5292.2.f.e.2645.10		12	63.47	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.15983 q^{5} +(2.37047 + 1.17511i) q^{7} -1.33513i q^{11} +(2.03534 - 1.17511i) q^{13} +(3.60166 + 6.23825i) q^{17} +(1.03803 + 0.599308i) q^{19} -2.40581i q^{23} -0.335126 q^{25} +(-5.32324 - 3.07338i) q^{29} +(7.11141 + 4.10577i) q^{31} +(5.11982 + 2.53803i) q^{35} +(2.57338 - 4.45722i) q^{37} +(2.23617 + 3.87316i) q^{41} +(0.332437 - 0.575798i) q^{43} +(-1.07992 - 1.87047i) q^{47} +(4.23825 + 5.57111i) q^{49} +(-11.0340 + 6.37047i) q^{53} -2.88365i q^{55} +(4.83424 - 8.37316i) q^{59} +(-10.6468 + 6.14691i) q^{61} +(4.39600 - 2.53803i) q^{65} +(1.86778 - 3.23509i) q^{67} -11.4058i q^{71} +(9.07338 - 5.23852i) q^{73} +(1.56891 - 3.16487i) q^{77} +(4.53803 + 7.86010i) q^{79} +(-5.39958 + 9.35235i) q^{83} +(7.77897 + 13.4736i) q^{85} +(2.59808 - 4.50000i) q^{89} +(6.20560 - 0.393808i) q^{91} +(2.24198 + 1.29440i) q^{95} +(1.07069 + 0.618162i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{19} - 24 q^{37} + 6 q^{43} - 18 q^{61} + 54 q^{73} + 24 q^{79} + 6 q^{85} + 42 q^{91} - 36 q^{97}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 + 6 * q^43 - 18 * q^61 + 54 * q^73 + 24 * q^79 + 6 * q^85 + 42 * q^91 - 36 * q^97

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