LMFDB - Embedded newform 756.2.t.e.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(269,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("756.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.03669039281$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$1.56052 + 0.900969i$ of defining polynomial
Character	$\chi$	$=$	756.269
Dual form			756.2.t.e.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56052 - 2.70291i) q^{5} +(2.37047 - 1.17511i) q^{7} +O(q^{10})$	$q+(-1.56052 - 2.70291i) q^{5} +(2.37047 - 1.17511i) q^{7} +(-3.23975 - 1.87047i) q^{11} -2.93067i q^{13} +(-2.71678 + 4.70560i) q^{17} +(-6.07338 + 3.50647i) q^{19} +(1.44182 - 0.832437i) q^{23} +(-2.37047 + 4.10577i) q^{25} -7.07069i q^{29} +(6.60872 + 3.81555i) q^{31} +(-6.87538 - 4.57338i) q^{35} +(-4.03534 - 6.98942i) q^{37} -9.60054 q^{41} -5.74094 q^{43} +(-1.56052 - 2.70291i) q^{47} +(4.23825 - 5.57111i) q^{49} +(3.11266 + 1.79709i) q^{53} +11.6756i q^{55} +(2.20220 - 3.81431i) q^{59} +(-2.57069 + 1.48419i) q^{61} +(-7.92132 + 4.57338i) q^{65} +(4.90850 - 8.50177i) q^{67} -7.33513i q^{71} +(2.46466 + 1.42297i) q^{73} +(-9.87772 - 0.626842i) q^{77} +(-2.57338 - 4.45722i) q^{79} +15.6052 q^{83} +16.9584 q^{85} +(-2.59808 - 4.50000i) q^{89} +(-3.44385 - 6.94706i) q^{91} +(18.9553 + 10.9438i) q^{95} +2.39723i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 18 q^{19} - 24 q^{37} - 12 q^{43} + 18 q^{61} + 54 q^{73} + 24 q^{79} - 12 q^{85} + 42 q^{91}+O(q^{100}) $ 12 * q - 18 * q^19 - 24 * q^37 - 12 * q^43 + 18 * q^61 + 54 * q^73 + 24 * q^79 - 12 * q^85 + 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.56052	−	2.70291i	−0.697887	−	1.20878i	−0.969198	−	0.246285i	$-0.920790\pi$
$5$	−1.56052	−	2.70291i	−0.697887	−	1.20878i	0.271310	−	0.962492i	$-0.412543\pi$
$6$		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
$11$	−3.23975	−	1.87047i	−0.976821	−	0.563968i	−0.0755120	−	0.997145i	$-0.524059\pi$
$11$	−3.23975	−	1.87047i	−0.976821	−	0.563968i	−0.901309	+	0.433177i	$0.857392\pi$
$12$		0			0
$13$		−	2.93067i		−	0.812821i	−0.913691	−	0.406410i	$-0.866780\pi$
$13$		−	2.93067i		−	0.812821i	0.913691	−	0.406410i	$-0.133220\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.71678	+	4.70560i	−0.658915	+	1.14127i	0.321982	+	0.946746i	$0.395651\pi$
$17$	−2.71678	+	4.70560i	−0.658915	+	1.14127i	−0.980897	+	0.194529i	$0.937682\pi$
$18$		0			0
$19$	−6.07338	+	3.50647i	−1.39333	+	0.804438i	−0.993682	−	0.112231i	$-0.964200\pi$
$19$	−6.07338	+	3.50647i	−1.39333	+	0.804438i	−0.399646	+	0.916670i	$0.630867\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.44182	−	0.832437i	0.300641	−	0.173575i	−0.342090	−	0.939667i	$-0.611135\pi$
$23$	1.44182	−	0.832437i	0.300641	−	0.173575i	0.642731	+	0.766092i	$0.277801\pi$
$24$		0			0
$25$	−2.37047	+	4.10577i	−0.474094	+	0.821155i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	7.07069i		−	1.31299i	−0.754329	−	0.656497i	$-0.772038\pi$
$29$		−	7.07069i		−	1.31299i	0.754329	−	0.656497i	$-0.227962\pi$
$30$		0			0
$31$	6.60872	+	3.81555i	1.18696	+	0.685292i	0.957615	−	0.288053i	$-0.0930078\pi$
$31$	6.60872	+	3.81555i	1.18696	+	0.685292i	0.229347	+	0.973345i	$0.426341\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.87538	−	4.57338i	−1.16215	−	0.773042i
$36$		0			0
$37$	−4.03534	−	6.98942i	−0.663406	−	1.14905i	−0.979715	−	0.200397i	$-0.935777\pi$
$37$	−4.03534	−	6.98942i	−0.663406	−	1.14905i	0.316308	−	0.948656i	$-0.397557\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−9.60054			−1.49935			−0.749677	−	0.661804i	$-0.769791\pi$
$41$	−9.60054			−1.49935			−0.749677	+	0.661804i	$0.769791\pi$
$42$		0			0
$43$	−5.74094			−0.875485			−0.437742	−	0.899100i	$-0.644222\pi$
$43$	−5.74094			−0.875485			−0.437742	+	0.899100i	$0.644222\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.56052	−	2.70291i	−0.227626	−	0.394259i	0.729478	−	0.684004i	$-0.239763\pi$
$47$	−1.56052	−	2.70291i	−0.227626	−	0.394259i	−0.957104	+	0.289745i	$0.906430\pi$
$48$		0			0
$49$	4.23825	−	5.57111i	0.605464	−	0.795872i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.11266	+	1.79709i	0.427556	+	0.246850i	0.698305	−	0.715800i	$-0.253938\pi$
$53$	3.11266	+	1.79709i	0.427556	+	0.246850i	−0.270749	+	0.962650i	$0.587271\pi$
$54$		0			0
$55$			11.6756i			1.57434i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.20220	−	3.81431i	0.286701	−	0.496581i	−0.686319	−	0.727301i	$-0.740775\pi$
$59$	2.20220	−	3.81431i	0.286701	−	0.496581i	0.973020	+	0.230719i	$0.0741079\pi$
$60$		0			0
$61$	−2.57069	+	1.48419i	−0.329143	+	0.190031i	−0.655460	−	0.755229i	$-0.727525\pi$
$61$	−2.57069	+	1.48419i	−0.329143	+	0.190031i	0.326318	+	0.945260i	$0.394192\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.92132	+	4.57338i	−0.982519	+	0.567257i
$66$		0			0
$67$	4.90850	−	8.50177i	0.599669	−	1.03866i	−0.393201	−	0.919453i	$-0.628632\pi$
$67$	4.90850	−	8.50177i	0.599669	−	1.03866i	0.992870	−	0.119204i	$-0.0380344\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.33513i		−	0.870519i	−0.900305	−	0.435260i	$-0.856657\pi$
$71$		−	7.33513i		−	0.870519i	0.900305	−	0.435260i	$-0.143343\pi$
$72$		0			0
$73$	2.46466	+	1.42297i	0.288466	+	0.166546i	0.637250	−	0.770657i	$-0.280072\pi$
$73$	2.46466	+	1.42297i	0.288466	+	0.166546i	−0.348784	+	0.937203i	$0.613405\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.87772	−	0.626842i	−1.12567	−	0.0714353i
$78$		0			0
$79$	−2.57338	−	4.45722i	−0.289527	−	0.501476i	0.684170	−	0.729323i	$-0.260165\pi$
$79$	−2.57338	−	4.45722i	−0.289527	−	0.501476i	−0.973697	+	0.227847i	$0.926831\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	15.6052			1.71290			0.856449	−	0.516232i	$-0.172666\pi$
$83$	15.6052			1.71290			0.856449	+	0.516232i	$0.172666\pi$
$84$		0			0
$85$	16.9584			1.83939
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	0.694839	−	0.719165i	$-0.255475\pi$
$89$	−2.59808	−	4.50000i	−0.275396	−	0.476999i	−0.970235	+	0.242166i	$0.922142\pi$
$90$		0			0
$91$	−3.44385	−	6.94706i	−0.361013	−	0.728249i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	18.9553	+	10.9438i	1.94477	+	1.12281i
$96$		0			0
$97$			2.39723i			0.243402i	0.992567	+	0.121701i	$0.0388349\pi$
$97$			2.39723i			0.243402i	−0.992567	+	0.121701i	$0.961165\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.87772	+	17.1087i	−0.982870	+	1.70238i	−0.331828	+	0.943340i	$0.607665\pi$
$101$	−9.87772	+	17.1087i	−0.982870	+	1.70238i	−0.651043	+	0.759041i	$0.725668\pi$
$102$		0			0
$103$	10.6468	−	6.14691i	1.04906	−	0.605673i	0.126671	−	0.991945i	$-0.459571\pi$
$103$	10.6468	−	6.14691i	1.04906	−	0.605673i	0.922385	+	0.386272i	$0.126237\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.7155	−	9.07338i	1.51928	−	0.877156i	0.519537	−	0.854448i	$-0.326104\pi$
$107$	15.7155	−	9.07338i	1.51928	−	0.877156i	0.999742	−	0.0227086i	$-0.00722899\pi$
$108$		0			0
$109$	−5.74094	+	9.94360i	−0.549882	+	0.952424i	0.448400	+	0.893833i	$0.351994\pi$
$109$	−5.74094	+	9.94360i	−0.549882	+	0.952424i	−0.998282	+	0.0585909i	$0.981339\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			1.81163i			0.170423i	0.996363	+	0.0852117i	$0.0271567\pi$
$113$			1.81163i			0.170423i	−0.996363	+	0.0852117i	$0.972843\pi$
$114$		0			0
$115$	−4.50000	−	2.59808i	−0.419627	−	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.910461	+	14.3470i	−0.0834619	+	1.31518i
$120$		0			0
$121$	1.49731	+	2.59342i	0.136119	+	0.235765i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.808542			−0.0723182
$126$		0			0
$127$	−7.47650			−0.663432			−0.331716	−	0.943379i	$-0.607628\pi$
$127$	−7.47650			−0.663432			−0.331716	+	0.943379i	$0.607628\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.52532	+	6.10603i	0.308009	+	0.533486i	0.977927	−	0.208949i	$-0.0670041\pi$
$131$	3.52532	+	6.10603i	0.308009	+	0.533486i	−0.669918	+	0.742435i	$0.733671\pi$
$132$		0			0
$133$	−10.2763	+	15.4488i	−0.891067	+	1.33958i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	12.7048	+	7.33513i	1.08545	+	0.626682i	0.932360	−	0.361531i	$-0.117746\pi$
$137$	12.7048	+	7.33513i	1.08545	+	0.626682i	0.153085	+	0.988213i	$0.451079\pi$
$138$		0			0
$139$		−	1.69434i		−	0.143712i	−0.997415	−	0.0718562i	$-0.977108\pi$
$139$		−	1.69434i		−	0.143712i	0.997415	−	0.0718562i	$-0.0228923\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.48172	+	9.49462i	−0.458405	+	0.793980i
$144$		0			0
$145$	−19.1114	+	11.0340i	−1.58712	+	0.916322i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.8319	−	7.40850i	1.05123	−	0.606928i	0.128237	−	0.991744i	$-0.459068\pi$
$149$	12.8319	−	7.40850i	1.05123	−	0.606928i	0.922994	+	0.384815i	$0.125735\pi$
$150$		0			0
$151$	3.03534	−	5.25737i	0.247013	−	0.427839i	−0.715683	−	0.698425i	$-0.753884\pi$
$151$	3.03534	−	5.25737i	0.247013	−	0.427839i	0.962696	+	0.270587i	$0.0872177\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	23.8170i		−	1.91303i
$156$		0			0
$157$	−12.1141	−	6.99408i	−0.966810	−	0.558188i	−0.0685479	−	0.997648i	$-0.521837\pi$
$157$	−12.1141	−	6.99408i	−0.966810	−	0.558188i	−0.898262	+	0.439460i	$0.855170\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.43960	−	3.66756i	0.192267	−	0.289044i
$162$		0			0
$163$	−0.926624	−	1.60496i	−0.0725788	−	0.125710i	0.827452	−	0.561536i	$-0.189790\pi$
$163$	−0.926624	−	1.60496i	−0.0725788	−	0.125710i	−0.900031	+	0.435826i	$0.856456\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.54991			0.197318			0.0986588	−	0.995121i	$-0.468545\pi$
$167$	2.54991			0.197318			0.0986588	+	0.995121i	$0.468545\pi$
$168$		0			0
$169$	4.41119			0.339322
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.95640	−	3.38859i	−0.148743	−	0.257630i	0.782020	−	0.623253i	$-0.214189\pi$
$173$	−1.95640	−	3.38859i	−0.148743	−	0.257630i	−0.930763	+	0.365623i	$0.880856\pi$
$174$		0			0
$175$	−0.794405	+	12.5182i	−0.0600514	+	0.946284i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.9284	+	9.77359i	1.26529	+	0.730513i	0.974092	−	0.226152i	$-0.0726145\pi$
$179$	16.9284	+	9.77359i	1.26529	+	0.730513i	0.291193	+	0.956664i	$0.405948\pi$
$180$		0			0
$181$		−	18.1929i		−	1.35226i	−0.736780	−	0.676132i	$-0.763655\pi$
$181$		−	18.1929i		−	1.35226i	0.736780	−	0.676132i	$-0.236345\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.5945	+	21.8143i	−0.925966	+	1.60382i
$186$		0			0
$187$	17.6033	−	10.1633i	1.28728	−	0.743214i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	13.0609	−	7.54072i	0.945054	−	0.545627i	0.0535132	−	0.998567i	$-0.482958\pi$
$191$	13.0609	−	7.54072i	0.945054	−	0.545627i	0.891541	+	0.452940i	$0.149625\pi$
$192$		0			0
$193$	5.57338	−	9.65337i	0.401180	−	0.694865i	−0.592688	−	0.805432i	$-0.701933\pi$
$193$	5.57338	−	9.65337i	0.401180	−	0.694865i	0.993869	+	0.110567i	$0.0352667\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.3696i			1.45127i	0.688079	+	0.725636i	$0.258454\pi$
$197$			20.3696i			1.45127i	−0.688079	+	0.725636i	$0.741546\pi$
$198$		0			0
$199$	6.42931	+	3.71197i	0.455762	+	0.263134i	0.710261	−	0.703939i	$-0.248577\pi$
$199$	6.42931	+	3.71197i	0.455762	+	0.263134i	−0.254499	+	0.967073i	$0.581910\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.30881	−	16.7608i	−0.583164	−	1.17638i
$204$		0			0
$205$	14.9819	+	25.9494i	1.04638	+	1.81238i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	26.2349			1.81471
$210$		0			0
$211$	−13.5526			−0.932997			−0.466499	−	0.884522i	$-0.654485\pi$
$211$	−13.5526			−0.932997			−0.466499	+	0.884522i	$0.654485\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.95887	+	15.5172i	0.610990	+	1.05827i
$216$		0			0
$217$	20.1494	+	1.27869i	1.36783	+	0.0868029i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	13.7905	+	7.96197i	0.927652	+	0.535580i
$222$		0			0
$223$		−	8.79200i		−	0.588756i	−0.955689	−	0.294378i	$-0.904888\pi$
$223$		−	8.79200i		−	0.588756i	0.955689	−	0.294378i	$-0.0951125\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.35241	+	11.0027i	−0.421624	+	0.730274i	−0.996099	−	0.0882484i	$-0.971873\pi$
$227$	−6.35241	+	11.0027i	−0.421624	+	0.730274i	0.574475	+	0.818522i	$0.305206\pi$
$228$		0			0
$229$	24.2201	−	13.9835i	1.60051	−	0.924056i	0.609126	−	0.793073i	$-0.291520\pi$
$229$	24.2201	−	13.9835i	1.60051	−	0.924056i	0.991385	−	0.130982i	$-0.0418131\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.2737	+	8.24094i	−0.935103	+	0.539882i	−0.888422	−	0.459028i	$-0.848198\pi$
$233$	−14.2737	+	8.24094i	−0.935103	+	0.539882i	−0.0466810	+	0.998910i	$0.514864\pi$
$234$		0			0
$235$	−4.87047	+	8.43590i	−0.317714	+	0.550297i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	5.52350i		−	0.357285i	−0.983914	−	0.178643i	$-0.942829\pi$
$239$		−	5.52350i		−	0.357285i	0.983914	−	0.178643i	$-0.0571706\pi$
$240$		0			0
$241$	−18.6414	−	10.7626i	−1.20080	−	0.693280i	−0.240064	−	0.970757i	$-0.577168\pi$
$241$	−18.6414	−	10.7626i	−1.20080	−	0.693280i	−0.960732	+	0.277477i	$0.910502\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−21.6721	−	2.76175i	−1.38458	−	0.176442i
$246$		0			0
$247$	10.2763	+	17.7990i	0.653864	+	1.13253i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.808542			0.0510347			0.0255174	−	0.999674i	$-0.491877\pi$
$251$	0.808542			0.0510347			0.0255174	+	0.999674i	$0.491877\pi$
$252$		0			0
$253$	−6.22819			−0.391563
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.48172	−	9.49462i	−0.341941	−	0.592258i	0.642853	−	0.765990i	$-0.277751\pi$
$257$	−5.48172	−	9.49462i	−0.341941	−	0.592258i	−0.984793	+	0.173732i	$0.944417\pi$
$258$		0			0
$259$	−17.7790	−	11.8262i	−1.10473	−	0.734847i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.35241	+	3.66756i	0.391706	+	0.226152i	0.682899	−	0.730513i	$-0.260719\pi$
$263$	6.35241	+	3.66756i	0.391706	+	0.226152i	−0.291193	+	0.956664i	$0.594052\pi$
$264$		0			0
$265$		−	11.2176i		−	0.689093i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.28569	−	7.42303i	0.261303	−	0.452590i	−0.705285	−	0.708924i	$-0.749181\pi$
$269$	4.28569	−	7.42303i	0.261303	−	0.452590i	0.966588	+	0.256333i	$0.0825144\pi$
$270$		0			0
$271$	6.79619	−	3.92378i	0.412839	−	0.238353i	−0.279170	−	0.960242i	$-0.590059\pi$
$271$	6.79619	−	3.92378i	0.412839	−	0.238353i	0.692009	+	0.721889i	$0.256726\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.3594	−	8.86778i	0.926210	−	0.534747i
$276$		0			0
$277$	1.13491	−	1.96572i	0.0681900	−	0.118109i	−0.829915	−	0.557890i	$-0.811611\pi$
$277$	1.13491	−	1.96572i	0.0681900	−	0.118109i	0.898105	+	0.439782i	$0.144944\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	28.9584i		−	1.72751i	−0.503910	−	0.863756i	$-0.668106\pi$
$281$		−	28.9584i		−	1.72751i	0.503910	−	0.863756i	$-0.331894\pi$
$282$		0			0
$283$	2.11679	+	1.22213i	0.125830	+	0.0726479i	0.561594	−	0.827413i	$-0.310188\pi$
$283$	2.11679	+	1.22213i	0.125830	+	0.0726479i	−0.435764	+	0.900061i	$0.643522\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.7578	+	11.2817i	−1.34335	+	0.665935i
$288$		0			0
$289$	−6.26175	−	10.8457i	−0.368338	−	0.637980i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.55460			0.499765			0.249883	−	0.968276i	$-0.419608\pi$
$293$	8.55460			0.499765			0.249883	+	0.968276i	$0.419608\pi$
$294$		0			0
$295$	−13.7463			−0.800341
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.43960	−	4.22550i	−0.141086	−	0.244367i
$300$		0			0
$301$	−13.6087	+	6.74621i	−0.784394	+	0.388845i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.02324	+	4.63222i	0.459409	+	0.265240i
$306$		0			0
$307$			23.8000i			1.35834i	0.733982	+	0.679169i	$0.237660\pi$
$307$			23.8000i			1.35834i	−0.733982	+	0.679169i	$0.762340\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.55460	+	14.8170i	−0.485087	+	0.840195i	−0.999853	−	0.0171354i	$-0.994545\pi$
$311$	−8.55460	+	14.8170i	−0.485087	+	0.840195i	0.514766	+	0.857331i	$0.327879\pi$
$312$		0			0
$313$	1.35325	−	0.781298i	0.0764901	−	0.0441616i	−0.461267	−	0.887261i	$-0.652605\pi$
$313$	1.35325	−	0.781298i	0.0764901	−	0.0441616i	0.537757	+	0.843100i	$0.319272\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.5511	+	13.0199i	−1.26660	+	0.731271i	−0.974343	−	0.225069i	$-0.927739\pi$
$317$	−22.5511	+	13.0199i	−1.26660	+	0.731271i	−0.292256	+	0.956340i	$0.594406\pi$
$318$		0			0
$319$	−13.2255	+	22.9072i	−0.740486	+	1.28256i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	38.1051i		−	2.12023i
$324$		0			0
$325$	12.0327	+	6.94706i	0.667452	+	0.385353i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.87538	−	4.57338i	−0.379052	−	0.252138i
$330$		0			0
$331$	15.1087	+	26.1691i	0.830450	+	1.43838i	0.897682	+	0.440645i	$0.145250\pi$
$331$	15.1087	+	26.1691i	0.830450	+	1.43838i	−0.0672312	+	0.997737i	$0.521417\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−30.6393			−1.67401
$336$		0			0
$337$	−22.2228			−1.21055			−0.605277	−	0.796015i	$-0.706938\pi$
$337$	−22.2228			−1.21055			−0.605277	+	0.796015i	$0.706938\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.2737	−	24.7228i	−0.772966	−	1.33882i
$342$		0			0
$343$	3.50000	−	18.1865i	0.188982	−	0.981981i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−31.6853	−	18.2935i	−1.70095	−	0.982047i	−0.944796	−	0.327658i	$-0.893741\pi$
$347$	−31.6853	−	18.2935i	−1.70095	−	0.982047i	−0.756159	−	0.654388i	$-0.772926\pi$
$348$		0			0
$349$		−	9.19369i		−	0.492127i	−0.969254	−	0.246063i	$-0.920863\pi$
$349$		−	9.19369i		−	0.492127i	0.969254	−	0.246063i	$-0.0791372\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.277180	+	0.480090i	−0.0147528	+	0.0255526i	−0.873308	−	0.487169i	$-0.838029\pi$
$353$	−0.277180	+	0.480090i	−0.0147528	+	0.0255526i	0.858555	+	0.512722i	$0.171363\pi$
$354$		0			0
$355$	−19.8262	+	11.4466i	−1.05226	+	0.607524i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.3487	−	7.12953i	0.651740	−	0.376282i	−0.137383	−	0.990518i	$-0.543869\pi$
$359$	12.3487	−	7.12953i	0.651740	−	0.376282i	0.789123	+	0.614236i	$0.210536\pi$
$360$		0			0
$361$	15.0906	−	26.1377i	0.794242	−	1.37567i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	8.88231i		−	0.464922i
$366$		0			0
$367$	−12.0814	−	6.97522i	−0.630646	−	0.364104i	0.150356	−	0.988632i	$-0.451958\pi$
$367$	−12.0814	−	6.97522i	−0.630646	−	0.364104i	−0.781002	+	0.624528i	$0.785291\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.49023	+	0.602252i	0.492708	+	0.0312674i
$372$		0			0
$373$	−8.21744	−	14.2330i	−0.425483	−	0.736958i	0.570983	−	0.820962i	$-0.306562\pi$
$373$	−8.21744	−	14.2330i	−0.425483	−	0.736958i	−0.996465	+	0.0840042i	$0.973229\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−20.7218			−1.06723
$378$		0			0
$379$	34.5217			1.77326			0.886630	−	0.462479i	$-0.153040\pi$
$379$	34.5217			1.77326			0.886630	+	0.462479i	$0.153040\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.96480	−	3.40312i	−0.100396	−	0.173892i	0.811452	−	0.584420i	$-0.198678\pi$
$383$	−1.96480	−	3.40312i	−0.100396	−	0.173892i	−0.911848	+	0.410528i	$0.865344\pi$
$384$		0			0
$385$	13.7201	+	27.6768i	0.699242	+	1.41054i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	18.5992	+	10.7383i	0.943017	+	0.544451i	0.890905	−	0.454190i	$-0.150071\pi$
$389$	18.5992	+	10.7383i	0.943017	+	0.544451i	0.0521120	+	0.998641i	$0.483405\pi$
$390$		0			0
$391$			9.04618i			0.457485i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.03163	+	13.9112i	−0.404115	+	0.699948i
$396$		0			0
$397$	−15.8913	+	9.17483i	−0.797560	+	0.460472i	−0.842617	−	0.538513i	$-0.818986\pi$
$397$	−15.8913	+	9.17483i	−0.797560	+	0.460472i	0.0450569	+	0.998984i	$0.485653\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.78349	+	2.76175i	−0.238876	+	0.137915i	−0.614660	−	0.788792i	$-0.710707\pi$
$401$	−4.78349	+	2.76175i	−0.238876	+	0.137915i	0.375784	+	0.926707i	$0.377373\pi$
$402$		0			0
$403$	11.1821	−	19.3680i	0.557020	−	0.964787i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			30.1919i			1.49656i
$408$		0			0
$409$	−8.64406	−	4.99065i	−0.427421	−	0.246772i	0.270826	−	0.962628i	$-0.412703\pi$
$409$	−8.64406	−	4.99065i	−0.427421	−	0.246772i	−0.698248	+	0.715856i	$0.746037\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.738012	−	11.6295i	0.0363152	−	0.572252i
$414$		0			0
$415$	−24.3523	−	42.1795i	−1.19541	−	2.07051i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.2960			−0.502991			−0.251495	−	0.967858i	$-0.580922\pi$
$419$	−10.2960			−0.502991			−0.251495	+	0.967858i	$0.580922\pi$
$420$		0			0
$421$	10.4873			0.511118			0.255559	−	0.966794i	$-0.417741\pi$
$421$	10.4873			0.511118			0.255559	+	0.966794i	$0.417741\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.8801	−	22.3089i	−0.624775	−	1.08214i
$426$		0			0
$427$	−4.34966	+	6.53905i	−0.210495	+	0.316447i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	5.26668	+	3.04072i	0.253687	+	0.146466i	0.621451	−	0.783453i	$-0.286543\pi$
$431$	5.26668	+	3.04072i	0.253687	+	0.146466i	−0.367764	+	0.929919i	$0.619877\pi$
$432$		0			0
$433$			25.6452i			1.23243i	0.787579	+	0.616214i	$0.211334\pi$
$433$			25.6452i			1.23243i	−0.787579	+	0.616214i	$0.788666\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.83782	+	10.1114i	−0.279261	+	0.483694i
$438$		0			0
$439$	24.7228	−	14.2737i	1.17996	−	0.681248i	0.223951	−	0.974600i	$-0.428104\pi$
$439$	24.7228	−	14.2737i	1.17996	−	0.681248i	0.956004	+	0.293353i	$0.0947710\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	18.3702	−	10.6060i	0.872794	−	0.503908i	0.00451818	−	0.999990i	$-0.498562\pi$
$443$	18.3702	−	10.6060i	0.872794	−	0.503908i	0.868276	+	0.496082i	$0.165228\pi$
$444$		0			0
$445$	−8.10872	+	14.0447i	−0.384390	+	0.665783i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	22.5633i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$449$		−	22.5633i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$450$		0			0
$451$	31.1033	+	17.9575i	1.46460	+	0.845587i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.4030	+	20.1494i	−0.628344	+	0.944620i
$456$		0			0
$457$	−6.72013	−	11.6396i	−0.314354	−	0.544478i	0.664946	−	0.746892i	$-0.268455\pi$
$457$	−6.72013	−	11.6396i	−0.314354	−	0.544478i	−0.979300	+	0.202414i	$0.935121\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.9928			−0.931160			−0.465580	−	0.885006i	$-0.654154\pi$
$461$	−19.9928			−0.931160			−0.465580	+	0.885006i	$0.654154\pi$
$462$		0			0
$463$	10.0108			0.465239			0.232620	−	0.972568i	$-0.425270\pi$
$463$	10.0108			0.465239			0.232620	+	0.972568i	$0.425270\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.7699	−	29.0463i	−0.776018	−	1.34410i	−0.934221	−	0.356695i	$-0.883903\pi$
$467$	−16.7699	−	29.0463i	−0.776018	−	1.34410i	0.158203	−	0.987407i	$-0.449430\pi$
$468$		0			0
$469$	1.64496	−	25.9212i	0.0759574	−	1.19693i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.5992	+	10.7383i	0.855192	+	0.493745i
$474$		0			0
$475$		−	33.2479i		−	1.52552i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.15860	−	7.20291i	0.190011	−	0.329109i	−0.755242	−	0.655446i	$-0.772481\pi$
$479$	4.15860	−	7.20291i	0.190011	−	0.329109i	0.945254	+	0.326336i	$0.105814\pi$
$480$		0			0
$481$	−20.4837	+	11.8262i	−0.933975	+	0.539231i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.47950	−	3.74094i	0.294219	−	0.169867i
$486$		0			0
$487$	−1.36509	+	2.36441i	−0.0618583	+	0.107142i	−0.895296	−	0.445472i	$-0.853036\pi$
$487$	−1.36509	+	2.36441i	−0.0618583	+	0.107142i	0.833438	+	0.552613i	$0.186369\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	10.4004i		−	0.469365i	−0.972072	−	0.234683i	$-0.924595\pi$
$491$		−	10.4004i		−	0.469365i	0.972072	−	0.234683i	$-0.0754051\pi$
$492$		0			0
$493$	33.2718	+	19.2095i	1.49849	+	0.865151i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.61955	−	17.3877i	−0.386640	−	0.779945i
$498$		0			0
$499$	5.37585	+	9.31124i	0.240656	+	0.416828i	0.960901	−	0.276891i	$-0.0893041\pi$
$499$	5.37585	+	9.31124i	0.240656	+	0.416828i	−0.720245	+	0.693719i	$0.755971\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	17.3466			0.773447			0.386723	−	0.922196i	$-0.373607\pi$
$503$	17.3466			0.773447			0.386723	+	0.922196i	$0.373607\pi$
$504$		0			0
$505$	61.6577			2.74373
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.689842	+	1.19484i	0.0305767	+	0.0529604i	0.880909	−	0.473286i	$-0.156932\pi$
$509$	0.689842	+	1.19484i	0.0305767	+	0.0529604i	−0.850332	+	0.526246i	$0.823599\pi$
$510$		0			0
$511$	7.51453	+	0.476874i	0.332423	+	0.0210956i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−33.2290	−	19.1848i	−1.46425	−	0.845383i
$516$		0			0
$517$			11.6756i			0.513494i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.19381	+	3.79978i	−0.0961123	+	0.166471i	−0.910072	−	0.414450i	$-0.863974\pi$
$521$	−2.19381	+	3.79978i	−0.0961123	+	0.166471i	0.813960	+	0.580921i	$0.197307\pi$
$522$		0			0
$523$	−30.6494	+	17.6955i	−1.34021	+	0.773769i	−0.986837	−	0.161715i	$-0.948297\pi$
$523$	−30.6494	+	17.6955i	−1.34021	+	0.773769i	−0.353369	+	0.935484i	$0.614964\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−35.9088	+	20.7320i	−1.56421	+	0.903099i
$528$		0			0
$529$	−10.1141	+	17.5181i	−0.439743	+	0.761658i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			28.1360i			1.21871i
$534$		0			0
$535$	−49.0490	−	28.3184i	−2.12057	−	1.22431i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−24.1514	+	10.1215i	−1.04028	+	0.435962i
$540$		0			0
$541$	−23.1114	−	40.0301i	−0.993637	−	1.72103i	−0.594359	−	0.804200i	$-0.702594\pi$
$541$	−23.1114	−	40.0301i	−0.993637	−	1.72103i	−0.399278	−	0.916830i	$-0.630739\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	35.8355			1.53502
$546$		0			0
$547$	4.28813			0.183347			0.0916735	−	0.995789i	$-0.470778\pi$
$547$	4.28813			0.183347			0.0916735	+	0.995789i	$0.470778\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	24.7931	+	42.9429i	1.05622	+	1.82943i
$552$		0			0
$553$	−11.3378	−	7.54171i	−0.482133	−	0.320706i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.49023	−	5.47919i	−0.402114	−	0.232161i	0.285282	−	0.958444i	$-0.407913\pi$
$557$	−9.49023	−	5.47919i	−0.402114	−	0.232161i	−0.687396	+	0.726283i	$0.741246\pi$
$558$		0			0
$559$			16.8248i			0.711612i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.3572	−	28.3315i	0.689375	−	1.19403i	−0.282666	−	0.959218i	$-0.591219\pi$
$563$	16.3572	−	28.3315i	0.689375	−	1.19403i	0.972040	−	0.234813i	$-0.0754479\pi$
$564$		0			0
$565$	4.89666	−	2.82709i	0.206004	−	0.118936i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	31.8124	−	18.3669i	1.33364	−	0.769980i	0.347788	−	0.937573i	$-0.386933\pi$
$569$	31.8124	−	18.3669i	1.33364	−	0.769980i	0.985856	+	0.167594i	$0.0535997\pi$
$570$		0			0
$571$	−7.10603	+	12.3080i	−0.297378	+	0.515074i	−0.975535	−	0.219843i	$-0.929446\pi$
$571$	−7.10603	+	12.3080i	−0.297378	+	0.515074i	0.678157	+	0.734917i	$0.262779\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			7.89307i			0.329164i
$576$		0			0
$577$	22.1848	+	12.8084i	0.923565	+	0.533220i	0.884771	−	0.466027i	$-0.154315\pi$
$577$	22.1848	+	12.8084i	0.923565	+	0.533220i	0.0387941	+	0.999247i	$0.487648\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	36.9917	−	18.3378i	1.53468	−	0.760781i
$582$		0			0
$583$	−6.72282	−	11.6443i	−0.278431	−	0.482256i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.1013			−0.582022			−0.291011	−	0.956720i	$-0.593992\pi$
$587$	−14.1013			−0.582022			−0.291011	+	0.956720i	$0.593992\pi$
$588$		0			0
$589$	−53.5163			−2.20510
$590$		0			0
$591$		0			0
$592$		0			0
$593$	18.9721	+	32.8606i	0.779090	+	1.34942i	0.932467	+	0.361255i	$0.117652\pi$
$593$	18.9721	+	32.8606i	0.779090	+	1.34942i	−0.153377	+	0.988168i	$0.549015\pi$
$594$		0			0
$595$	40.1993	−	19.9279i	1.64801	−	0.816964i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.9032	−	9.75906i	−0.690646	−	0.398744i	0.113208	−	0.993571i	$-0.463887\pi$
$599$	−16.9032	−	9.75906i	−0.690646	−	0.398744i	−0.803854	+	0.594827i	$0.797221\pi$
$600$		0			0
$601$			38.1555i			1.55639i	0.628020	+	0.778197i	$0.283865\pi$
$601$			38.1555i			1.55639i	−0.628020	+	0.778197i	$0.716135\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.67318	−	8.09419i	0.189992	−	0.329075i
$606$		0			0
$607$	−29.4756	+	17.0177i	−1.19638	+	0.690729i	−0.959746	−	0.280870i	$-0.909377\pi$
$607$	−29.4756	+	17.0177i	−1.19638	+	0.690729i	−0.236632	+	0.971599i	$0.576044\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.92132	+	4.57338i	−0.320462	+	0.185019i
$612$		0			0
$613$	−10.6676	+	18.4768i	−0.430859	+	0.746269i	−0.996947	−	0.0780750i	$-0.975123\pi$
$613$	−10.6676	+	18.4768i	−0.430859	+	0.746269i	0.566089	+	0.824344i	$0.308456\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	21.6233i		−	0.870519i	−0.900305	−	0.435260i	$-0.856657\pi$
$617$		−	21.6233i		−	0.870519i	0.900305	−	0.435260i	$-0.143343\pi$
$618$		0			0
$619$	−17.1902	−	9.92474i	−0.690931	−	0.398909i	0.113030	−	0.993592i	$-0.463944\pi$
$619$	−17.1902	−	9.92474i	−0.690931	−	0.398909i	−0.803961	+	0.594682i	$0.797278\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.4466	−	7.61410i	−0.458600	−	0.305052i
$624$		0			0
$625$	13.1141	+	22.7143i	0.524564	+	0.908571i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	43.8525			1.74851
$630$		0			0
$631$	−26.3803			−1.05018			−0.525092	−	0.851045i	$-0.675969\pi$
$631$	−26.3803			−1.05018			−0.525092	+	0.851045i	$0.675969\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	11.6673	+	20.2083i	0.463001	+	0.801941i
$636$		0			0
$637$	−16.3271	−	12.4209i	−0.646902	−	0.492134i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	30.7441	+	17.7501i	1.21432	+	0.701087i	0.963697	−	0.266999i	$-0.0860320\pi$
$641$	30.7441	+	17.7501i	1.21432	+	0.701087i	0.250621	+	0.968085i	$0.419365\pi$
$642$		0			0
$643$			6.48881i			0.255894i	0.991781	+	0.127947i	$0.0408387\pi$
$643$			6.48881i			0.255894i	−0.991781	+	0.127947i	$0.959161\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.8076	+	37.7718i	−0.857343	+	1.48496i	0.0171104	+	0.999854i	$0.494553\pi$
$647$	−21.8076	+	37.7718i	−0.857343	+	1.48496i	−0.874454	+	0.485109i	$0.838780\pi$
$648$		0			0
$649$	−14.2691	+	8.23828i	−0.560112	+	0.323381i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.7119	+	12.5353i	−0.849650	+	0.490546i	−0.860533	−	0.509395i	$-0.829869\pi$
$653$	−21.7119	+	12.5353i	−0.849650	+	0.490546i	0.0108825	+	0.999941i	$0.496536\pi$
$654$		0			0
$655$	11.0027	−	19.0572i	0.429911	−	0.744627i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			13.4657i			0.524551i	0.964993	+	0.262276i	$0.0844729\pi$
$659$			13.4657i			0.524551i	−0.964993	+	0.262276i	$0.915527\pi$
$660$		0			0
$661$	40.4783	+	23.3702i	1.57442	+	0.908994i	0.995617	+	0.0935285i	$0.0298146\pi$
$661$	40.4783	+	23.3702i	1.57442	+	0.908994i	0.578806	+	0.815465i	$0.303519\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	57.7931	+	3.66756i	2.24112	+	0.142222i
$666$		0			0
$667$	−5.88590	−	10.1947i	−0.227903	−	0.394740i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.1045			0.428685
$672$		0			0
$673$	−37.9275			−1.46200			−0.730999	−	0.682378i	$-0.760946\pi$
$673$	−37.9275			−1.46200			−0.730999	+	0.682378i	$0.760946\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.56891	+	2.71744i	0.0602983	+	0.104440i	0.894599	−	0.446870i	$-0.147461\pi$
$677$	1.56891	+	2.71744i	0.0602983	+	0.104440i	−0.834300	+	0.551310i	$0.814128\pi$
$678$		0			0
$679$	2.81700	+	5.68257i	0.108107	+	0.218077i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.1449	+	7.01184i	0.464711	+	0.268301i	0.714023	−	0.700122i	$-0.246871\pi$
$683$	12.1449	+	7.01184i	0.464711	+	0.268301i	−0.249312	+	0.968423i	$0.580205\pi$
$684$		0			0
$685$		−	45.7866i		−	1.74941i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.26668	−	9.12216i	0.200645	−	0.347527i
$690$		0			0
$691$	28.6141	−	16.5204i	1.08853	−	0.628464i	0.155346	−	0.987860i	$-0.450351\pi$
$691$	28.6141	−	16.5204i	1.08853	−	0.628464i	0.933185	+	0.359396i	$0.117017\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.57965	+	2.64406i	−0.173716	+	0.100295i
$696$		0			0
$697$	26.0825	−	45.1763i	0.987946	−	1.71117i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			32.4058i			1.22395i	0.790877	+	0.611975i	$0.209625\pi$
$701$			32.4058i			1.22395i	−0.790877	+	0.611975i	$0.790375\pi$
$702$		0			0
$703$	49.0163	+	28.2996i	1.84869	+	1.06734i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.31028	+	52.1631i	−0.124496	+	1.96179i
$708$		0			0
$709$	23.7528	+	41.1410i	0.892055	+	1.54508i	0.837408	+	0.546578i	$0.184070\pi$
$709$	23.7528	+	41.1410i	0.892055	+	1.54508i	0.0546463	+	0.998506i	$0.482597\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.7048			0.475799
$714$		0			0
$715$	34.2174			1.27966
$716$		0			0
$717$		0			0
$718$		0			0
$719$	23.1139	+	40.0344i	0.862003	+	1.49303i	0.869993	+	0.493065i	$0.164123\pi$
$719$	23.1139	+	40.0344i	0.862003	+	1.49303i	−0.00798976	+	0.999968i	$0.502543\pi$
$720$		0			0
$721$	18.0145	−	27.0821i	0.670896	−	1.00859i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	29.0306	+	16.7608i	1.07817	+	0.622482i
$726$		0			0
$727$		−	14.2330i		−	0.527874i	−0.964540	−	0.263937i	$-0.914979\pi$
$727$		−	14.2330i		−	0.527874i	0.964540	−	0.263937i	$-0.0850210\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.5968	−	27.0145i	0.576870	−	0.999169i
$732$		0			0
$733$	34.7201	−	20.0457i	1.28242	−	0.740404i	0.305127	−	0.952312i	$-0.401301\pi$
$733$	34.7201	−	20.0457i	1.28242	−	0.740404i	0.977290	+	0.211908i	$0.0679676\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−31.8046	+	18.3624i	−1.17154	+	0.676388i
$738$		0			0
$739$	2.99731	−	5.19150i	0.110258	−	0.190972i	−0.805616	−	0.592438i	$-0.798166\pi$
$739$	2.99731	−	5.19150i	0.110258	−	0.190972i	0.915874	+	0.401465i	$0.131499\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			8.32437i			0.305392i	0.988273	+	0.152696i	$0.0487955\pi$
$743$			8.32437i			0.305392i	−0.988273	+	0.152696i	$0.951205\pi$
$744$		0			0
$745$	−40.0490	−	23.1223i	−1.46728	−	0.847135i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	26.5910	−	39.9756i	0.971616	−	1.46068i
$750$		0			0
$751$	−5.47650	−	9.48558i	−0.199840	−	0.346134i	0.748636	−	0.662981i	$-0.230709\pi$
$751$	−5.47650	−	9.48558i	−0.199840	−	0.346134i	−0.948477	+	0.316847i	$0.897376\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−18.9469			−0.689548
$756$		0			0
$757$	−3.28275			−0.119314			−0.0596568	−	0.998219i	$-0.519001\pi$
$757$	−3.28275			−0.119314			−0.0596568	+	0.998219i	$0.519001\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.4616	−	40.6367i	−0.850483	−	1.47308i	−0.880773	−	0.473538i	$-0.842977\pi$
$761$	−23.4616	−	40.6367i	−0.850483	−	1.47308i	0.0302909	−	0.999541i	$-0.490357\pi$
$762$		0			0
$763$	−1.92394	+	30.3172i	−0.0696511	+	1.09756i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−11.1785	−	6.45390i	−0.403632	−	0.233037i
$768$		0			0
$769$			4.52166i			0.163055i	0.996671	+	0.0815276i	$0.0259799\pi$
$769$			4.52166i			0.163055i	−0.996671	+	0.0815276i	$0.974020\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.8635	−	36.1367i	0.750409	−	1.29975i	−0.197216	−	0.980360i	$-0.563190\pi$
$773$	20.8635	−	36.1367i	0.750409	−	1.29975i	0.947625	−	0.319386i	$-0.103477\pi$
$774$		0			0
$775$	−31.3315	+	18.0893i	−1.12546	+	0.649786i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	58.3077	−	33.6640i	2.08909	−	1.20614i
$780$		0			0
$781$	−13.7201	+	23.7640i	−0.490945	+	0.850341i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			43.6577i			1.55821i
$786$		0			0
$787$	6.86957	+	3.96615i	0.244874	+	0.141378i	0.617415	−	0.786638i	$-0.288180\pi$
$787$	6.86957	+	3.96615i	0.244874	+	0.141378i	−0.372541	+	0.928016i	$0.621513\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.12885	+	4.29440i	0.0756933	+	0.152691i
$792$		0			0
$793$	4.34966	+	7.53383i	0.154461	+	0.267534i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.5840			−0.622857			−0.311429	−	0.950270i	$-0.600807\pi$
$797$	−17.5840			−0.622857			−0.311429	+	0.950270i	$0.600807\pi$
$798$		0			0
$799$	16.9584			0.599944
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.32324	−	9.22013i	−0.187853	−	0.325371i
$804$		0			0
$805$	−13.7201	−	0.870682i	−0.483571	−	0.0306875i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−45.9338	−	26.5199i	−1.61495	−	0.932390i	−0.988200	−	0.153168i	$-0.951052\pi$
$809$	−45.9338	−	26.5199i	−1.61495	−	0.932390i	−0.626747	−	0.779223i	$-0.715614\pi$
$810$		0			0
$811$		−	0.966384i		−	0.0339343i	−0.999856	−	0.0169672i	$-0.994599\pi$
$811$		−	0.966384i		−	0.0339343i	0.999856	−	0.0169672i	$-0.00540108\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.89204	+	5.00916i	−0.101304	+	0.175463i
$816$		0			0
$817$	34.8669	−	20.1304i	1.21984	−	0.704274i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	38.5209	−	22.2400i	1.34439	−	0.776183i	0.356940	−	0.934127i	$-0.383820\pi$
$821$	38.5209	−	22.2400i	1.34439	−	0.776183i	0.987448	+	0.157945i	$0.0504868\pi$
$822$		0			0
$823$	−13.0327	+	22.5732i	−0.454290	+	0.786853i	−0.998647	−	0.0520005i	$-0.983440\pi$
$823$	−13.0327	+	22.5732i	−0.454290	+	0.786853i	0.544357	+	0.838853i	$0.316774\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			13.4166i			0.466540i	0.972412	+	0.233270i	$0.0749426\pi$
$827$			13.4166i			0.466540i	−0.972412	+	0.233270i	$0.925057\pi$
$828$		0			0
$829$	−0.407601	−	0.235328i	−0.0141566	−	0.00817329i	0.492905	−	0.870083i	$-0.335935\pi$
$829$	−0.407601	−	0.235328i	−0.0141566	−	0.00817329i	−0.507062	+	0.861910i	$0.669268\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	14.7010	+	35.0789i	0.509359	+	1.21541i
$834$		0			0
$835$	−3.97919	−	6.89216i	−0.137706	−	0.238513i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−23.4309			−0.808923			−0.404461	−	0.914555i	$-0.632541\pi$
$839$	−23.4309			−0.808923			−0.404461	+	0.914555i	$0.632541\pi$
$840$		0			0
$841$	−20.9946			−0.723953
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.88377	−	11.9230i	−0.236809	−	0.410165i
$846$		0			0
$847$	6.59688	+	4.38812i	0.226671	+	0.150778i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−11.6365	−	6.71834i	−0.398894	−	0.230302i
$852$		0			0
$853$		−	18.9678i		−	0.649446i	−0.945809	−	0.324723i	$-0.894729\pi$
$853$		−	18.9678i		−	0.649446i	0.945809	−	0.324723i	$-0.105271\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.59820	+	11.4284i	−0.225390	+	0.390387i	−0.956436	−	0.291941i	$-0.905699\pi$
$857$	−6.59820	+	11.4284i	−0.225390	+	0.390387i	0.731046	+	0.682328i	$0.239032\pi$
$858$		0			0
$859$	7.78544	−	4.49493i	0.265636	−	0.153365i	−0.361267	−	0.932462i	$-0.617656\pi$
$859$	7.78544	−	4.49493i	0.265636	−	0.153365i	0.626903	+	0.779098i	$0.284322\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	12.0178	−	6.93847i	0.409090	−	0.236188i	−0.281309	−	0.959617i	$-0.590768\pi$
$863$	12.0178	−	6.93847i	0.409090	−	0.236188i	0.690399	+	0.723429i	$0.257435\pi$
$864$		0			0
$865$	−6.10603	+	10.5760i	−0.207611	+	0.359593i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			19.2537i			0.653137i
$870$		0			0
$871$	−24.9159	−	14.3852i	−0.844242	−	0.487423i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.91662	+	0.950123i	−0.0647937	+	0.0321200i
$876$		0			0
$877$	5.06531	+	8.77338i	0.171043	+	0.296256i	0.938785	−	0.344504i	$-0.111953\pi$
$877$	5.06531	+	8.77338i	0.171043	+	0.296256i	−0.767742	+	0.640760i	$0.778620\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.7189			1.03495			0.517473	−	0.855700i	$-0.326873\pi$
$881$	30.7189			1.03495			0.517473	+	0.855700i	$0.326873\pi$
$882$		0			0
$883$	−35.4403			−1.19266			−0.596330	−	0.802740i	$-0.703375\pi$
$883$	−35.4403			−1.19266			−0.596330	+	0.802740i	$0.703375\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	18.1384	+	31.4166i	0.609027	+	1.05487i	0.991401	+	0.130858i	$0.0417731\pi$
$887$	18.1384	+	31.4166i	0.609027	+	1.05487i	−0.382375	+	0.924007i	$0.624894\pi$
$888$		0			0
$889$	−17.7228	+	8.78568i	−0.594404	+	0.294662i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	18.9553	+	10.9438i	0.634315	+	0.366222i
$894$		0			0
$895$		−	61.0077i		−	2.03926i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	26.9785	−	46.7282i	0.899785	−	1.55847i
$900$		0			0
$901$	−16.9128	+	9.76460i	−0.563447	+	0.325306i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−49.1736	+	28.3904i	−1.63459	+	0.943728i
$906$		0			0
$907$	−3.92931	+	6.80577i	−0.130471	+	0.225982i	−0.923858	−	0.382735i	$-0.874982\pi$
$907$	−3.92931	+	6.80577i	−0.130471	+	0.225982i	0.793387	+	0.608717i	$0.208316\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			28.9584i			0.959434i	0.877423	+	0.479717i	$0.159261\pi$
$911$			28.9584i			0.959434i	−0.877423	+	0.479717i	$0.840739\pi$
$912$		0			0
$913$	−50.5570	−	29.1891i	−1.67319	−	0.966019i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.5319	+	10.3315i	0.512908	+	0.341177i
$918$		0			0
$919$	17.1993	+	29.7901i	0.567353	+	0.982684i	0.996826	+	0.0796049i	$0.0253659\pi$
$919$	17.1993	+	29.7901i	0.567353	+	0.982684i	−0.429473	+	0.903080i	$0.641301\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21.4968			−0.707576
$924$		0			0
$925$	38.2626			1.25807
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.05052	+	5.28365i	0.100084	+	0.173351i	0.911719	−	0.410814i	$-0.134755\pi$
$929$	3.05052	+	5.28365i	0.100084	+	0.173351i	−0.811635	+	0.584165i	$0.801422\pi$
$930$		0			0
$931$	−6.20560	+	48.6967i	−0.203380	+	1.59597i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−54.9409	−	31.7201i	−1.79676	−	1.03736i
$936$		0			0
$937$			50.7128i			1.65671i	0.560201	+	0.828357i	$0.310724\pi$
$937$			50.7128i			1.65671i	−0.560201	+	0.828357i	$0.689276\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.5616	−	30.4177i	0.572493	−	0.991587i	−0.423816	−	0.905748i	$-0.639310\pi$
$941$	17.5616	−	30.4177i	0.572493	−	0.991587i	0.996309	−	0.0858389i	$-0.0273570\pi$
$942$		0			0
$943$	−13.8423	+	7.99185i	−0.450767	+	0.260250i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−34.2973	+	19.8016i	−1.11451	+	0.643465i	−0.939995	−	0.341189i	$-0.889170\pi$
$947$	−34.2973	+	19.8016i	−1.11451	+	0.643465i	−0.174519	+	0.984654i	$0.555837\pi$
$948$		0			0
$949$	4.17025	−	7.22309i	0.135372	−	0.234471i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			12.5942i			0.407966i	0.978974	+	0.203983i	$0.0653887\pi$
$953$			12.5942i			0.407966i	−0.978974	+	0.203983i	$0.934611\pi$
$954$		0			0
$955$	−40.7637	−	23.5349i	−1.31908	−	0.761573i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	38.7359	+	2.45819i	1.25085	+	0.0793790i
$960$		0			0
$961$	13.6168	+	23.5850i	0.439251	+	0.760805i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−34.7895			−1.11992
$966$		0			0
$967$	51.8407			1.66708			0.833542	−	0.552456i	$-0.186309\pi$
$967$	51.8407			1.66708			0.833542	+	0.552456i	$0.186309\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.918852	+	1.59150i	0.0294874	+	0.0510736i	0.880392	−	0.474246i	$-0.157279\pi$
$971$	0.918852	+	1.59150i	0.0294874	+	0.0510736i	−0.850905	+	0.525319i	$0.823946\pi$
$972$		0			0
$973$	−1.99103	−	4.01639i	−0.0638296	−	0.128760i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.2808	−	13.4412i	−0.744818	−	0.430021i	0.0790007	−	0.996875i	$-0.474827\pi$
$977$	−23.2808	−	13.4412i	−0.744818	−	0.430021i	−0.823818	+	0.566854i	$0.808160\pi$
$978$		0			0
$979$			19.4385i			0.621257i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	8.19850	−	14.2002i	0.261492	−	0.452917i	−0.705147	−	0.709061i	$-0.749119\pi$
$983$	8.19850	−	14.2002i	0.261492	−	0.452917i	0.966638	+	0.256145i	$0.0824523\pi$
$984$		0			0
$985$	55.0570	−	31.7872i	1.75426	−	1.01282i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.27742	+	4.77897i	−0.263207	+	0.151962i
$990$		0			0
$991$	1.17941	−	2.04279i	0.0374651	−	0.0648915i	−0.846685	−	0.532095i	$-0.821405\pi$
$991$	1.17941	−	2.04279i	0.0374651	−	0.0648915i	0.884150	+	0.467203i	$0.154738\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	23.1704i		−	0.734552i
$996$		0			0
$997$	−13.1114	−	7.56988i	−0.415242	−	0.239740i	0.277797	−	0.960640i	$-0.410396\pi$
$997$	−13.1114	−	7.56988i	−0.415242	−	0.239740i	−0.693040	+	0.720899i	$0.743729\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.t.e.269.1	✓	12
3.2	odd	2	inner	756.2.t.e.269.6	yes	12
7.3	odd	6		5292.2.f.e.2645.2		12
7.4	even	3		5292.2.f.e.2645.12		12
7.5	odd	6	inner	756.2.t.e.593.6	yes	12
9.2	odd	6		2268.2.bm.i.1025.1		12
9.4	even	3		2268.2.w.i.269.1		12
9.5	odd	6		2268.2.w.i.269.6		12
9.7	even	3		2268.2.bm.i.1025.6		12
21.5	even	6	inner	756.2.t.e.593.1	yes	12
21.11	odd	6		5292.2.f.e.2645.1		12
21.17	even	6		5292.2.f.e.2645.11		12
63.5	even	6		2268.2.bm.i.593.6		12
63.40	odd	6		2268.2.bm.i.593.1		12
63.47	even	6		2268.2.w.i.1349.1		12
63.61	odd	6		2268.2.w.i.1349.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.1	✓	12	1.1	even	1	trivial
756.2.t.e.269.6	yes	12	3.2	odd	2	inner
756.2.t.e.593.1	yes	12	21.5	even	6	inner
756.2.t.e.593.6	yes	12	7.5	odd	6	inner
2268.2.w.i.269.1		12	9.4	even	3
2268.2.w.i.269.6		12	9.5	odd	6
2268.2.w.i.1349.1		12	63.47	even	6
2268.2.w.i.1349.6		12	63.61	odd	6
2268.2.bm.i.593.1		12	63.40	odd	6
2268.2.bm.i.593.6		12	63.5	even	6
2268.2.bm.i.1025.1		12	9.2	odd	6
2268.2.bm.i.1025.6		12	9.7	even	3
5292.2.f.e.2645.1		12	21.11	odd	6
5292.2.f.e.2645.2		12	7.3	odd	6
5292.2.f.e.2645.11		12	21.17	even	6
5292.2.f.e.2645.12		12	7.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56052 - 2.70291i) q^{5} +(2.37047 - 1.17511i) q^{7} +O(q^{10})\)	\(q+(-1.56052 - 2.70291i) q^{5} +(2.37047 - 1.17511i) q^{7} +(-3.23975 - 1.87047i) q^{11} -2.93067i q^{13} +(-2.71678 + 4.70560i) q^{17} +(-6.07338 + 3.50647i) q^{19} +(1.44182 - 0.832437i) q^{23} +(-2.37047 + 4.10577i) q^{25} -7.07069i q^{29} +(6.60872 + 3.81555i) q^{31} +(-6.87538 - 4.57338i) q^{35} +(-4.03534 - 6.98942i) q^{37} -9.60054 q^{41} -5.74094 q^{43} +(-1.56052 - 2.70291i) q^{47} +(4.23825 - 5.57111i) q^{49} +(3.11266 + 1.79709i) q^{53} +11.6756i q^{55} +(2.20220 - 3.81431i) q^{59} +(-2.57069 + 1.48419i) q^{61} +(-7.92132 + 4.57338i) q^{65} +(4.90850 - 8.50177i) q^{67} -7.33513i q^{71} +(2.46466 + 1.42297i) q^{73} +(-9.87772 - 0.626842i) q^{77} +(-2.57338 - 4.45722i) q^{79} +15.6052 q^{83} +16.9584 q^{85} +(-2.59808 - 4.50000i) q^{89} +(-3.44385 - 6.94706i) q^{91} +(18.9553 + 10.9438i) q^{95} +2.39723i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 18 q^{19} - 24 q^{37} - 12 q^{43} + 18 q^{61} + 54 q^{73} + 24 q^{79} - 12 q^{85} + 42 q^{91}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 - 12 * q^43 + 18 * q^61 + 54 * q^73 + 24 * q^79 - 12 * q^85 + 42 * q^91

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