LMFDB - Embedded newform 3024.2.df.e.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	3024.17
Dual form			3024.2.df.e.1601.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22830 q^{5} +(-2.51733 - 0.814280i) q^{7} -2.12135i q^{11} +(-5.10339 - 2.94644i) q^{13} +(2.34020 - 4.05335i) q^{17} +(4.54550 - 2.62435i) q^{19} +4.36380i q^{23} -0.0346748 q^{25} +(2.25182 - 1.30009i) q^{29} +(-6.59237 + 3.80611i) q^{31} +(5.60937 + 1.81446i) q^{35} +(-1.80274 - 3.12244i) q^{37} +(-0.0395039 + 0.0684228i) q^{41} +(1.24922 + 2.16371i) q^{43} +(1.89837 - 3.28807i) q^{47} +(5.67390 + 4.09962i) q^{49} +(4.08014 + 2.35567i) q^{53} +4.72701i q^{55} +(6.59695 + 11.4262i) q^{59} +(-7.06624 - 4.07970i) q^{61} +(11.3719 + 6.56556i) q^{65} +(-2.37614 - 4.11559i) q^{67} +10.0325i q^{71} +(-12.6610 - 7.30986i) q^{73} +(-1.72737 + 5.34014i) q^{77} +(-7.27414 + 12.5992i) q^{79} +(6.41294 + 11.1075i) q^{83} +(-5.21468 + 9.03209i) q^{85} +(-2.73464 - 4.73654i) q^{89} +(10.4477 + 11.5728i) q^{91} +(-10.1287 + 5.84783i) q^{95} +(-12.9290 + 7.46454i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$5$	−2.22830			−0.996526			−0.498263	−	0.867026i	$-0.666029\pi$
$5$	−2.22830			−0.996526			−0.498263	+	0.867026i	$0.666029\pi$
$6$		0			0
$7$	−2.51733	−	0.814280i	−0.951461	−	0.307769i
$7$	−2.51733	−	0.814280i	−0.951461	−	0.307769i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	2.12135i		−	0.639612i	−0.947483	−	0.319806i	$-0.896382\pi$
$11$		−	2.12135i		−	0.639612i	0.947483	−	0.319806i	$-0.103618\pi$
$12$		0			0
$13$	−5.10339	−	2.94644i	−1.41542	−	0.817196i	−0.419533	−	0.907740i	$-0.637806\pi$
$13$	−5.10339	−	2.94644i	−1.41542	−	0.817196i	−0.995892	+	0.0905443i	$0.971139\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.34020	−	4.05335i	0.567583	−	0.983082i	−0.429222	−	0.903199i	$-0.641212\pi$
$17$	2.34020	−	4.05335i	0.567583	−	0.983082i	0.996804	−	0.0798828i	$-0.0254546\pi$
$18$		0			0
$19$	4.54550	−	2.62435i	1.04281	−	0.602066i	0.122181	−	0.992508i	$-0.461011\pi$
$19$	4.54550	−	2.62435i	1.04281	−	0.602066i	0.920628	+	0.390442i	$0.127678\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			4.36380i			0.909915i	0.890513	+	0.454958i	$0.150346\pi$
$23$			4.36380i			0.909915i	−0.890513	+	0.454958i	$0.849654\pi$
$24$		0			0
$25$	−0.0346748			−0.00693496
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.25182	−	1.30009i	0.418152	−	0.241420i	−0.276134	−	0.961119i	$-0.589053\pi$
$29$	2.25182	−	1.30009i	0.418152	−	0.241420i	0.694286	+	0.719699i	$0.255720\pi$
$30$		0			0
$31$	−6.59237	+	3.80611i	−1.18402	+	0.683597i	−0.956942	−	0.290278i	$-0.906252\pi$
$31$	−6.59237	+	3.80611i	−1.18402	+	0.683597i	−0.227083	+	0.973876i	$0.572919\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.60937	+	1.81446i	0.948156	+	0.306700i
$36$		0			0
$37$	−1.80274	−	3.12244i	−0.296369	−	0.513326i	0.678934	−	0.734200i	$-0.262442\pi$
$37$	−1.80274	−	3.12244i	−0.296369	−	0.513326i	−0.975302	+	0.220874i	$0.929109\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.0395039	+	0.0684228i	−0.00616948	+	0.0106858i	−0.869094	−	0.494648i	$-0.835297\pi$
$41$	−0.0395039	+	0.0684228i	−0.00616948	+	0.0106858i	0.862924	+	0.505333i	$0.168630\pi$
$42$		0			0
$43$	1.24922	+	2.16371i	0.190504	+	0.329962i	0.945417	−	0.325862i	$-0.105655\pi$
$43$	1.24922	+	2.16371i	0.190504	+	0.329962i	−0.754914	+	0.655824i	$0.772321\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.89837	−	3.28807i	0.276905	−	0.479614i	−0.693709	−	0.720256i	$-0.744024\pi$
$47$	1.89837	−	3.28807i	0.276905	−	0.479614i	0.970614	+	0.240642i	$0.0773578\pi$
$48$		0			0
$49$	5.67390	+	4.09962i	0.810557	+	0.585660i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.08014	+	2.35567i	0.560451	+	0.323576i	0.753326	−	0.657647i	$-0.228448\pi$
$53$	4.08014	+	2.35567i	0.560451	+	0.323576i	−0.192876	+	0.981223i	$0.561781\pi$
$54$		0			0
$55$			4.72701i			0.637390i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.59695	+	11.4262i	0.858849	+	1.48757i	0.873028	+	0.487671i	$0.162153\pi$
$59$	6.59695	+	11.4262i	0.858849	+	1.48757i	−0.0141784	+	0.999899i	$0.504513\pi$
$60$		0			0
$61$	−7.06624	−	4.07970i	−0.904740	−	0.522352i	−0.0260047	−	0.999662i	$-0.508278\pi$
$61$	−7.06624	−	4.07970i	−0.904740	−	0.522352i	−0.878735	+	0.477310i	$0.841612\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	11.3719	+	6.56556i	1.41051	+	0.814357i
$66$		0			0
$67$	−2.37614	−	4.11559i	−0.290292	−	0.502800i	0.683587	−	0.729869i	$-0.260419\pi$
$67$	−2.37614	−	4.11559i	−0.290292	−	0.502800i	−0.973879	+	0.227069i	$0.927086\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.0325i			1.19064i	0.803490	+	0.595318i	$0.202974\pi$
$71$			10.0325i			1.19064i	−0.803490	+	0.595318i	$0.797026\pi$
$72$		0			0
$73$	−12.6610	−	7.30986i	−1.48186	−	0.855554i	−0.482075	−	0.876130i	$-0.660117\pi$
$73$	−12.6610	−	7.30986i	−1.48186	−	0.855554i	−0.999788	+	0.0205755i	$0.993450\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.72737	+	5.34014i	−0.196853	+	0.608566i
$78$		0			0
$79$	−7.27414	+	12.5992i	−0.818405	+	1.41752i	0.0884516	+	0.996080i	$0.471808\pi$
$79$	−7.27414	+	12.5992i	−0.818405	+	1.41752i	−0.906857	+	0.421439i	$0.861525\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.41294	+	11.1075i	0.703911	+	1.21921i	0.967083	+	0.254461i	$0.0818982\pi$
$83$	6.41294	+	11.1075i	0.703911	+	1.21921i	−0.263172	+	0.964749i	$0.584769\pi$
$84$		0			0
$85$	−5.21468	+	9.03209i	−0.565611	+	0.979667i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.73464	−	4.73654i	−0.289871	−	0.502072i	0.683907	−	0.729569i	$-0.260279\pi$
$89$	−2.73464	−	4.73654i	−0.289871	−	0.502072i	−0.973779	+	0.227497i	$0.926946\pi$
$90$		0			0
$91$	10.4477	+	11.5728i	1.09521	+	1.21315i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.1287	+	5.84783i	−1.03919	+	0.599975i
$96$		0			0
$97$	−12.9290	+	7.46454i	−1.31274	+	0.757909i	−0.982549	−	0.186006i	$-0.940446\pi$
$97$	−12.9290	+	7.46454i	−1.31274	+	0.757909i	−0.330188	+	0.943915i	$0.607112\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.26604			0.324983			0.162492	−	0.986710i	$-0.448047\pi$
$101$	3.26604			0.324983			0.162492	+	0.986710i	$0.448047\pi$
$102$		0			0
$103$			4.76828i			0.469833i	0.972016	+	0.234916i	$0.0754817\pi$
$103$			4.76828i			0.469833i	−0.972016	+	0.234916i	$0.924518\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.39655	−	3.69305i	0.618378	−	0.357021i	−0.157859	−	0.987462i	$-0.550459\pi$
$107$	6.39655	−	3.69305i	0.618378	−	0.357021i	0.776237	+	0.630441i	$0.217126\pi$
$108$		0			0
$109$	−1.17349	+	2.03254i	−0.112400	+	0.194682i	−0.916737	−	0.399490i	$-0.869187\pi$
$109$	−1.17349	+	2.03254i	−0.112400	+	0.194682i	0.804338	+	0.594173i	$0.202520\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.8961	−	6.86824i	−1.11909	−	0.646109i	−0.177925	−	0.984044i	$-0.556938\pi$
$113$	−11.8961	−	6.86824i	−1.11909	−	0.646109i	−0.941170	+	0.337935i	$0.890272\pi$
$114$		0			0
$115$		−	9.72386i		−	0.906754i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−9.19163	+	8.29804i	−0.842595	+	0.760680i
$120$		0			0
$121$	6.49987			0.590897
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.2188			1.00344
$126$		0			0
$127$	5.97913			0.530562			0.265281	−	0.964171i	$-0.414535\pi$
$127$	5.97913			0.530562			0.265281	+	0.964171i	$0.414535\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−20.9585			−1.83115			−0.915576	−	0.402146i	$-0.868264\pi$
$131$	−20.9585			−1.83115			−0.915576	+	0.402146i	$0.868264\pi$
$132$		0			0
$133$	−13.5795	+	2.90503i	−1.17749	+	0.251898i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	3.46483i		−	0.296021i	−0.988986	−	0.148010i	$-0.952713\pi$
$137$		−	3.46483i		−	0.296021i	0.988986	−	0.148010i	$-0.0472869\pi$
$138$		0			0
$139$	0.379607	+	0.219166i	0.0321979	+	0.0185895i	0.516013	−	0.856581i	$-0.327416\pi$
$139$	0.379607	+	0.219166i	0.0321979	+	0.0185895i	−0.483815	+	0.875170i	$0.660749\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.25044	+	10.8261i	−0.522688	+	0.905322i
$144$		0			0
$145$	−5.01773	+	2.89699i	−0.416700	+	0.240582i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			17.5006i			1.43370i	0.697225	+	0.716852i	$0.254418\pi$
$149$			17.5006i			1.43370i	−0.697225	+	0.716852i	$0.745582\pi$
$150$		0			0
$151$	0.374840			0.0305040			0.0152520	−	0.999884i	$-0.495145\pi$
$151$	0.374840			0.0305040			0.0152520	+	0.999884i	$0.495145\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	14.6898	−	8.48115i	1.17991	−	0.681223i
$156$		0			0
$157$	17.6279	−	10.1775i	1.40686	−	0.812249i	0.411773	−	0.911286i	$-0.364910\pi$
$157$	17.6279	−	10.1775i	1.40686	−	0.812249i	0.995084	+	0.0990372i	$0.0315763\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.55336	−	10.9851i	0.280044	−	0.865749i
$162$		0			0
$163$	7.25400	+	12.5643i	0.568177	+	0.984112i	0.996746	+	0.0806027i	$0.0256845\pi$
$163$	7.25400	+	12.5643i	0.568177	+	0.984112i	−0.428569	+	0.903509i	$0.640982\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.62510	−	13.2071i	0.590048	−	1.02199i	−0.404177	−	0.914681i	$-0.632442\pi$
$167$	7.62510	−	13.2071i	0.590048	−	1.02199i	0.994225	−	0.107313i	$-0.0342246\pi$
$168$		0			0
$169$	10.8630	+	18.8153i	0.835619	+	1.44733i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.940679	+	1.62930i	−0.0715185	+	0.123874i	−0.899567	−	0.436783i	$-0.856118\pi$
$173$	−0.940679	+	1.62930i	−0.0715185	+	0.123874i	0.828048	+	0.560657i	$0.189451\pi$
$174$		0			0
$175$	0.0872878	+	0.0282350i	0.00659834	+	0.00213436i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.64064	−	4.98867i	−0.645831	−	0.372871i	0.141026	−	0.990006i	$-0.454960\pi$
$179$	−8.64064	−	4.98867i	−0.645831	−	0.372871i	−0.786857	+	0.617135i	$0.788293\pi$
$180$		0			0
$181$			11.2828i			0.838641i	0.907838	+	0.419320i	$0.137732\pi$
$181$			11.2828i			0.838641i	−0.907838	+	0.419320i	$0.862268\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.01705	+	6.95773i	0.295339	+	0.511543i
$186$		0			0
$187$	−8.59858	−	4.96439i	−0.628791	−	0.363032i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.1418	−	6.43270i	−0.806189	−	0.465454i	0.0394414	−	0.999222i	$-0.487442\pi$
$191$	−11.1418	−	6.43270i	−0.806189	−	0.465454i	−0.845631	+	0.533768i	$0.820775\pi$
$192$		0			0
$193$	6.01861	+	10.4245i	0.433229	+	0.750374i	0.997149	−	0.0754547i	$-0.0240408\pi$
$193$	6.01861	+	10.4245i	0.433229	+	0.750374i	−0.563920	+	0.825829i	$0.690708\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			27.7262i			1.97541i	0.156339	+	0.987703i	$0.450031\pi$
$197$			27.7262i			1.97541i	−0.156339	+	0.987703i	$0.549969\pi$
$198$		0			0
$199$	−0.382862	−	0.221045i	−0.0271404	−	0.0156695i	0.486368	−	0.873754i	$-0.338321\pi$
$199$	−0.382862	−	0.221045i	−0.0271404	−	0.0156695i	−0.513509	+	0.858084i	$0.671655\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.72721	+	1.43914i	−0.472157	+	0.101008i
$204$		0			0
$205$	0.0880266	−	0.152467i	0.00614805	−	0.0106487i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.56716	−	9.64260i	−0.385088	−	0.666993i
$210$		0			0
$211$	0.219300	−	0.379839i	0.0150972	−	0.0261492i	−0.858378	−	0.513018i	$-0.828528\pi$
$211$	0.219300	−	0.379839i	0.0150972	−	0.0261492i	0.873475	+	0.486868i	$0.161861\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.78363	−	4.82139i	−0.189842	−	0.328816i
$216$		0			0
$217$	19.6944	−	4.21319i	1.33694	−	0.286010i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−23.8859	+	13.7905i	−1.60674	+	0.927653i
$222$		0			0
$223$	17.6417	−	10.1854i	1.18137	−	0.682066i	0.225041	−	0.974349i	$-0.427748\pi$
$223$	17.6417	−	10.1854i	1.18137	−	0.682066i	0.956332	+	0.292284i	$0.0944151\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.50987			0.100214			0.0501068	−	0.998744i	$-0.484044\pi$
$227$	1.50987			0.100214			0.0501068	+	0.998744i	$0.484044\pi$
$228$		0			0
$229$		−	21.2348i		−	1.40323i	−0.712554	−	0.701617i	$-0.752462\pi$
$229$		−	21.2348i		−	1.40323i	0.712554	−	0.701617i	$-0.247538\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.85938	+	5.69231i	−0.645909	+	0.372916i	−0.786887	−	0.617097i	$-0.788309\pi$
$233$	−9.85938	+	5.69231i	−0.645909	+	0.372916i	0.140978	+	0.990013i	$0.454975\pi$
$234$		0			0
$235$	−4.23013	+	7.32681i	−0.275944	+	0.477948i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.1401	+	8.16380i	0.914648	+	0.528072i	0.881924	−	0.471392i	$-0.156248\pi$
$239$	14.1401	+	8.16380i	0.914648	+	0.528072i	0.0327241	+	0.999464i	$0.489582\pi$
$240$		0			0
$241$			23.9706i			1.54408i	0.635571	+	0.772042i	$0.280765\pi$
$241$			23.9706i			1.54408i	−0.635571	+	0.772042i	$0.719235\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.6431	−	9.13519i	−0.807741	−	0.583626i
$246$		0			0
$247$	−30.9299			−1.96802
$248$		0			0
$249$		0			0
$250$		0			0
$251$	25.9828			1.64002			0.820009	−	0.572351i	$-0.193969\pi$
$251$	25.9828			1.64002			0.820009	+	0.572351i	$0.193969\pi$
$252$		0			0
$253$	9.25715			0.581992
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.95957			0.122235			0.0611173	−	0.998131i	$-0.480534\pi$
$257$	1.95957			0.122235			0.0611173	+	0.998131i	$0.480534\pi$
$258$		0			0
$259$	1.99555	+	9.32814i	0.123998	+	0.579623i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			3.59945i			0.221952i	0.993823	+	0.110976i	$0.0353976\pi$
$263$			3.59945i			0.221952i	−0.993823	+	0.110976i	$0.964602\pi$
$264$		0			0
$265$	−9.09179	−	5.24915i	−0.558504	−	0.322453i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.06967	−	7.04888i	0.248132	−	0.429778i	−0.714875	−	0.699252i	$-0.753517\pi$
$269$	4.06967	−	7.04888i	0.248132	−	0.429778i	0.963008	+	0.269474i	$0.0868499\pi$
$270$		0			0
$271$	−16.3378	+	9.43265i	−0.992452	+	0.572992i	−0.906006	−	0.423264i	$-0.860884\pi$
$271$	−16.3378	+	9.43265i	−0.992452	+	0.572992i	−0.0864458	+	0.996257i	$0.527551\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			0.0735574i			0.00443568i
$276$		0			0
$277$	21.6679			1.30190			0.650950	−	0.759120i	$-0.274371\pi$
$277$	21.6679			1.30190			0.650950	+	0.759120i	$0.274371\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.6851	+	6.74642i	−0.697077	+	0.402457i	−0.806258	−	0.591564i	$-0.798511\pi$
$281$	−11.6851	+	6.74642i	−0.697077	+	0.402457i	0.109181	+	0.994022i	$0.465177\pi$
$282$		0			0
$283$	1.76025	−	1.01628i	0.104636	−	0.0604115i	−0.446769	−	0.894649i	$-0.647425\pi$
$283$	1.76025	−	1.01628i	0.104636	−	0.0604115i	0.551405	+	0.834238i	$0.314092\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.155160	−	0.140075i	0.00915879	−	0.00826839i
$288$		0			0
$289$	−2.45310	−	4.24890i	−0.144300	−	0.249935i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	15.8661	−	27.4809i	0.926908	−	1.60545i	0.138446	−	0.990370i	$-0.455789\pi$
$293$	15.8661	−	27.4809i	0.926908	−	1.60545i	0.788463	−	0.615083i	$-0.210877\pi$
$294$		0			0
$295$	−14.7000	−	25.4611i	−0.855866	−	1.48240i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.8577	−	22.2702i	0.743579	−	1.28792i
$300$		0			0
$301$	−1.38283	−	6.46397i	−0.0797048	−	0.372577i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.7457	+	9.09079i	0.901597	+	0.520537i
$306$		0			0
$307$			0.266045i			0.0151840i	0.999971	+	0.00759200i	$0.00241663\pi$
$307$			0.266045i			0.0151840i	−0.999971	+	0.00759200i	$0.997583\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.18123	+	3.77799i	0.123686	+	0.214230i	0.921219	−	0.389046i	$-0.127195\pi$
$311$	2.18123	+	3.77799i	0.123686	+	0.214230i	−0.797533	+	0.603276i	$0.793862\pi$
$312$		0			0
$313$	−13.3702	−	7.71929i	−0.755728	−	0.436320i	0.0720315	−	0.997402i	$-0.477052\pi$
$313$	−13.3702	−	7.71929i	−0.755728	−	0.436320i	−0.827760	+	0.561082i	$0.810385\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−18.8143	−	10.8624i	−1.05671	−	0.610094i	−0.132192	−	0.991224i	$-0.542202\pi$
$317$	−18.8143	−	10.8624i	−1.05671	−	0.610094i	−0.924521	+	0.381130i	$0.875535\pi$
$318$		0			0
$319$	−2.75794	−	4.77690i	−0.154415	−	0.267455i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	24.5660i		−	1.36689i
$324$		0			0
$325$	0.176959	+	0.102167i	0.00981591	+	0.00566722i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.45623	+	6.73135i	−0.411075	+	0.371111i
$330$		0			0
$331$	−7.57310	+	13.1170i	−0.416255	+	0.720975i	−0.995559	−	0.0941362i	$-0.969991\pi$
$331$	−7.57310	+	13.1170i	−0.416255	+	0.720975i	0.579304	+	0.815112i	$0.303324\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.29475	+	9.17078i	0.289283	+	0.501053i
$336$		0			0
$337$	3.75166	−	6.49807i	0.204366	−	0.353973i	−0.745564	−	0.666434i	$-0.767820\pi$
$337$	3.75166	−	6.49807i	0.204366	−	0.353973i	0.949931	+	0.312461i	$0.101153\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.07409	+	13.9847i	0.437237	+	0.757316i
$342$		0			0
$343$	−10.9448	−	14.9402i	−0.590965	−	0.806697i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.23981	−	2.44786i	0.227605	−	0.131408i	−0.381862	−	0.924219i	$-0.624717\pi$
$347$	4.23981	−	2.44786i	0.227605	−	0.131408i	0.609467	+	0.792812i	$0.291384\pi$
$348$		0			0
$349$	−2.64213	+	1.52543i	−0.141430	+	0.0816546i	−0.569045	−	0.822306i	$-0.692687\pi$
$349$	−2.64213	+	1.52543i	−0.141430	+	0.0816546i	0.427615	+	0.903961i	$0.359354\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.0378			0.906830			0.453415	−	0.891299i	$-0.350205\pi$
$353$	17.0378			0.906830			0.453415	+	0.891299i	$0.350205\pi$
$354$		0			0
$355$		−	22.3554i		−	1.18650i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.27682	+	1.31452i	−0.120166	+	0.0693778i	−0.558878	−	0.829250i	$-0.688768\pi$
$359$	−2.27682	+	1.31452i	−0.120166	+	0.0693778i	0.438712	+	0.898628i	$0.355435\pi$
$360$		0			0
$361$	4.27438	−	7.40344i	0.224967	−	0.389655i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	28.2126	+	16.2886i	1.47672	+	0.852583i
$366$		0			0
$367$		−	18.7565i		−	0.979080i	−0.871981	−	0.489540i	$-0.837165\pi$
$367$		−	18.7565i		−	0.979080i	0.871981	−	0.489540i	$-0.162835\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.35289	−	9.25238i	−0.433660	−	0.480360i
$372$		0			0
$373$	4.85959			0.251620			0.125810	−	0.992054i	$-0.459847\pi$
$373$	4.85959			0.251620			0.125810	+	0.992054i	$0.459847\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.3225			−0.789151
$378$		0			0
$379$	3.46902			0.178192			0.0890959	−	0.996023i	$-0.471602\pi$
$379$	3.46902			0.178192			0.0890959	+	0.996023i	$0.471602\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.6060			−0.950720			−0.475360	−	0.879791i	$-0.657682\pi$
$383$	−18.6060			−0.950720			−0.475360	+	0.879791i	$0.657682\pi$
$384$		0			0
$385$	3.84911	−	11.8994i	0.196169	−	0.606452i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			15.5437i			0.788098i	0.919090	+	0.394049i	$0.128926\pi$
$389$			15.5437i			0.788098i	−0.919090	+	0.394049i	$0.871074\pi$
$390$		0			0
$391$	17.6880	+	10.2122i	0.894521	+	0.516452i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	16.2090	−	28.0748i	0.815562	−	1.41260i
$396$		0			0
$397$	−13.0507	+	7.53483i	−0.654996	+	0.378162i	−0.790368	−	0.612633i	$-0.790111\pi$
$397$	−13.0507	+	7.53483i	−0.654996	+	0.378162i	0.135371	+	0.990795i	$0.456777\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			7.78803i			0.388916i	0.980911	+	0.194458i	$0.0622947\pi$
$401$			7.78803i			0.388916i	−0.980911	+	0.194458i	$0.937705\pi$
$402$		0			0
$403$	44.8579			2.23453
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.62379	+	3.82425i	−0.328329	+	0.189561i
$408$		0			0
$409$	−7.79314	+	4.49937i	−0.385346	+	0.222480i	−0.680142	−	0.733081i	$-0.738082\pi$
$409$	−7.79314	+	4.49937i	−0.385346	+	0.222480i	0.294796	+	0.955560i	$0.404748\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−7.30252	−	34.1354i	−0.359334	−	1.67969i
$414$		0			0
$415$	−14.2900	−	24.7509i	−0.701466	−	1.21498i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.70022	+	11.6051i	−0.327327	+	0.566947i	−0.981981	−	0.188982i	$-0.939481\pi$
$419$	−6.70022	+	11.6051i	−0.327327	+	0.566947i	0.654653	+	0.755929i	$0.272815\pi$
$420$		0			0
$421$	9.44700	+	16.3627i	0.460419	+	0.797469i	0.998982	−	0.0451166i	$-0.0143659\pi$
$421$	9.44700	+	16.3627i	0.460419	+	0.797469i	−0.538563	+	0.842585i	$0.681033\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.0811460	+	0.140549i	−0.00393616	+	0.00681763i
$426$		0			0
$427$	14.4660	+	16.0238i	0.700061	+	0.775448i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	25.4056	+	14.6679i	1.22375	+	0.706530i	0.965714	−	0.259607i	$-0.0835931\pi$
$431$	25.4056	+	14.6679i	1.22375	+	0.706530i	0.258031	+	0.966137i	$0.416926\pi$
$432$		0			0
$433$			9.41744i			0.452573i	0.974061	+	0.226287i	$0.0726586\pi$
$433$			9.41744i			0.452573i	−0.974061	+	0.226287i	$0.927341\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.4521	+	19.8356i	0.547829	+	0.948868i
$438$		0			0
$439$	−27.5379	−	15.8990i	−1.31431	−	0.758819i	−0.331505	−	0.943453i	$-0.607556\pi$
$439$	−27.5379	−	15.8990i	−1.31431	−	0.758819i	−0.982807	+	0.184635i	$0.940890\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−32.0685	−	18.5147i	−1.52362	−	0.879662i	−0.999609	−	0.0279490i	$-0.991102\pi$
$443$	−32.0685	−	18.5147i	−1.52362	−	0.879662i	−0.524009	−	0.851713i	$-0.675564\pi$
$444$		0			0
$445$	6.09360	+	10.5544i	0.288864	+	0.500328i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			19.3840i			0.914789i	0.889264	+	0.457394i	$0.151217\pi$
$449$			19.3840i			0.914789i	−0.889264	+	0.457394i	$0.848783\pi$
$450$		0			0
$451$	0.145149	+	0.0838017i	0.00683479	+	0.00394607i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−23.2806	−	25.7876i	−1.09141	−	1.20894i
$456$		0			0
$457$	−5.26746	+	9.12351i	−0.246401	+	0.426780i	−0.962525	−	0.271194i	$-0.912581\pi$
$457$	−5.26746	+	9.12351i	−0.246401	+	0.426780i	0.716123	+	0.697974i	$0.245915\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.09138	−	12.2826i	−0.330278	−	0.572059i	0.652288	−	0.757971i	$-0.273809\pi$
$461$	−7.09138	−	12.2826i	−0.330278	−	0.572059i	−0.982566	+	0.185912i	$0.940476\pi$
$462$		0			0
$463$	−5.05071	+	8.74808i	−0.234726	+	0.406558i	−0.959193	−	0.282752i	$-0.908753\pi$
$463$	−5.05071	+	8.74808i	−0.234726	+	0.406558i	0.724467	+	0.689310i	$0.242086\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.1047	+	19.2340i	0.513866	+	0.890042i	0.999871	+	0.0160858i	$0.00512048\pi$
$467$	11.1047	+	19.2340i	0.513866	+	0.890042i	−0.486005	+	0.873956i	$0.661546\pi$
$468$		0			0
$469$	2.63028	+	12.2951i	0.121455	+	0.567737i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.58998	−	2.65003i	0.211048	−	0.121848i
$474$		0			0
$475$	−0.157614	+	0.0909986i	−0.00723184	+	0.00417530i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.42550			−0.430662			−0.215331	−	0.976541i	$-0.569083\pi$
$479$	−9.42550			−0.430662			−0.215331	+	0.976541i	$0.569083\pi$
$480$		0			0
$481$			21.2467i			0.968765i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	28.8096	−	16.6332i	1.30818	−	0.755276i
$486$		0			0
$487$	−14.6113	+	25.3076i	−0.662103	+	1.14680i	0.317959	+	0.948104i	$0.397003\pi$
$487$	−14.6113	+	25.3076i	−0.662103	+	1.14680i	−0.980062	+	0.198692i	$0.936331\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.31308	+	3.64486i	0.284905	+	0.164490i	0.635642	−	0.771984i	$-0.280735\pi$
$491$	6.31308	+	3.64486i	0.284905	+	0.164490i	−0.350737	+	0.936474i	$0.614069\pi$
$492$		0			0
$493$		−	12.1699i		−	0.548104i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.16925	−	25.2550i	0.366441	−	1.13284i
$498$		0			0
$499$	−15.6199			−0.699243			−0.349622	−	0.936891i	$-0.613690\pi$
$499$	−15.6199			−0.699243			−0.349622	+	0.936891i	$0.613690\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.09425			−0.271729			−0.135865	−	0.990727i	$-0.543381\pi$
$503$	−6.09425			−0.271729			−0.135865	+	0.990727i	$0.543381\pi$
$504$		0			0
$505$	−7.27772			−0.323854
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−28.3599			−1.25703			−0.628515	−	0.777798i	$-0.716337\pi$
$509$	−28.3599			−1.25703			−0.628515	+	0.777798i	$0.716337\pi$
$510$		0			0
$511$	25.9198	+	28.7110i	1.14662	+	1.27010i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	10.6252i		−	0.468201i
$516$		0			0
$517$	−6.97515	−	4.02710i	−0.306767	−	0.177112i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.2896	+	33.4105i	−0.845091	+	1.46374i	0.0404517	+	0.999181i	$0.487120\pi$
$521$	−19.2896	+	33.4105i	−0.845091	+	1.46374i	−0.885542	+	0.464559i	$0.846213\pi$
$522$		0			0
$523$	24.1399	−	13.9372i	1.05556	−	0.609429i	0.131361	−	0.991335i	$-0.458065\pi$
$523$	24.1399	−	13.9372i	1.05556	−	0.609429i	0.924201	+	0.381905i	$0.124732\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			35.6283i			1.55199i
$528$		0			0
$529$	3.95726			0.172055
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.403208	−	0.232792i	0.0174649	−	0.0100833i
$534$		0			0
$535$	−14.2534	+	8.22923i	−0.616230	+	0.355781i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.69674	−	12.0363i	0.374595	−	0.518441i
$540$		0			0
$541$	−10.9182	−	18.9109i	−0.469410	−	0.813041i	0.529979	−	0.848011i	$-0.322200\pi$
$541$	−10.9182	−	18.9109i	−0.469410	−	0.813041i	−0.999388	+	0.0349697i	$0.988867\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.61489	−	4.52912i	0.112009	−	0.194006i
$546$		0			0
$547$	−12.5173	−	21.6806i	−0.535201	−	0.926995i	−0.999154	−	0.0411350i	$-0.986903\pi$
$547$	−12.5173	−	21.6806i	−0.535201	−	0.926995i	0.463953	−	0.885860i	$-0.346431\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.82376	−	11.8191i	0.290702	−	0.503511i
$552$		0			0
$553$	28.5707	−	25.7931i	1.21495	−	1.09683i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.1937	+	6.46267i	0.474291	+	0.273832i	0.718034	−	0.696008i	$-0.245042\pi$
$557$	11.1937	+	6.46267i	0.474291	+	0.273832i	−0.243743	+	0.969840i	$0.578375\pi$
$558$		0			0
$559$		−	14.7230i		−	0.622715i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.81056	−	13.5283i	−0.329176	−	0.570150i	0.653173	−	0.757209i	$-0.273438\pi$
$563$	−7.81056	−	13.5283i	−0.329176	−	0.570150i	−0.982349	+	0.187060i	$0.940104\pi$
$564$		0			0
$565$	26.5082	+	15.3045i	1.11521	+	0.643865i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	36.8986	+	21.3034i	1.54687	+	0.893087i	0.998378	+	0.0569323i	$0.0181319\pi$
$569$	36.8986	+	21.3034i	1.54687	+	0.893087i	0.548494	+	0.836155i	$0.315201\pi$
$570$		0			0
$571$	−9.89848	−	17.1447i	−0.414239	−	0.717482i	0.581110	−	0.813825i	$-0.302619\pi$
$571$	−9.89848	−	17.1447i	−0.414239	−	0.717482i	−0.995348	+	0.0963431i	$0.969285\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.151314i		−	0.00631022i
$576$		0			0
$577$	−40.6443	−	23.4660i	−1.69204	−	0.976902i	−0.952866	−	0.303391i	$-0.901881\pi$
$577$	−40.6443	−	23.4660i	−1.69204	−	0.976902i	−0.739178	−	0.673511i	$-0.764786\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.09883	−	33.1833i	−0.294509	−	1.37667i
$582$		0			0
$583$	4.99721	−	8.65542i	0.206963	−	0.358471i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.18063	+	3.77696i	0.0900041	+	0.155892i	0.907513	−	0.420025i	$-0.137979\pi$
$587$	2.18063	+	3.77696i	0.0900041	+	0.155892i	−0.817509	+	0.575917i	$0.804645\pi$
$588$		0			0
$589$	−19.9771	+	34.6013i	−0.823141	+	1.42572i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.31077	+	4.00236i	0.0948918	+	0.164357i	0.909563	−	0.415565i	$-0.136416\pi$
$593$	2.31077	+	4.00236i	0.0948918	+	0.164357i	−0.814672	+	0.579922i	$0.803083\pi$
$594$		0			0
$595$	20.4817	−	18.4905i	0.839668	−	0.758038i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.0986	−	12.7586i	0.902924	−	0.521304i	0.0247764	−	0.999693i	$-0.492113\pi$
$599$	22.0986	−	12.7586i	0.902924	−	0.521304i	0.878148	+	0.478389i	$0.158779\pi$
$600$		0			0
$601$	22.6824	−	13.0957i	0.925235	−	0.534185i	0.0399336	−	0.999202i	$-0.487285\pi$
$601$	22.6824	−	13.0957i	0.925235	−	0.534185i	0.885301	+	0.465018i	$0.153952\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.4837			−0.588845
$606$		0			0
$607$		−	5.87462i		−	0.238443i	−0.992868	−	0.119222i	$-0.961960\pi$
$607$		−	5.87462i		−	0.238443i	0.992868	−	0.119222i	$-0.0380399\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.3762	+	11.1869i	−0.783878	+	0.452572i
$612$		0			0
$613$	12.4511	−	21.5660i	0.502896	−	0.871041i	−0.497099	−	0.867694i	$-0.665601\pi$
$613$	12.4511	−	21.5660i	0.502896	−	0.871041i	0.999994	−	0.00334675i	$-0.00106531\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.1105	−	15.0749i	−1.05117	−	0.606894i	−0.128194	−	0.991749i	$-0.540918\pi$
$617$	−26.1105	−	15.0749i	−1.05117	−	0.606894i	−0.922977	+	0.384855i	$0.874251\pi$
$618$		0			0
$619$			34.1737i			1.37356i	0.726867	+	0.686779i	$0.240976\pi$
$619$			34.1737i			1.37356i	−0.726867	+	0.686779i	$0.759024\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.02712	+	14.1502i	0.121279	+	0.566915i
$624$		0			0
$625$	−24.8254			−0.993017
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−16.8751			−0.672855
$630$		0			0
$631$	−8.55990			−0.340764			−0.170382	−	0.985378i	$-0.554500\pi$
$631$	−8.55990			−0.340764			−0.170382	+	0.985378i	$0.554500\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−13.3233			−0.528719
$636$		0			0
$637$	−16.8768	−	37.6398i	−0.668683	−	1.49134i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	40.4996i		−	1.59964i	−0.600242	−	0.799818i	$-0.704929\pi$
$641$		−	40.4996i		−	1.59964i	0.600242	−	0.799818i	$-0.295071\pi$
$642$		0			0
$643$	31.8435	+	18.3849i	1.25579	+	0.725028i	0.972252	−	0.233935i	$-0.0751602\pi$
$643$	31.8435	+	18.3849i	1.25579	+	0.725028i	0.283533	+	0.958963i	$0.408493\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−23.5492	+	40.7884i	−0.925815	+	1.60356i	−0.135569	+	0.990768i	$0.543286\pi$
$647$	−23.5492	+	40.7884i	−0.925815	+	1.60356i	−0.790246	+	0.612790i	$0.790047\pi$
$648$		0			0
$649$	24.2391	−	13.9944i	0.951467	−	0.549330i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			2.50279i			0.0979416i	0.998800	+	0.0489708i	$0.0155941\pi$
$653$			2.50279i			0.0979416i	−0.998800	+	0.0489708i	$0.984406\pi$
$654$		0			0
$655$	46.7018			1.82479
$656$		0			0
$657$		0			0
$658$		0			0
$659$	36.2490	−	20.9284i	1.41206	−	0.815254i	0.416479	−	0.909146i	$-0.363264\pi$
$659$	36.2490	−	20.9284i	1.41206	−	0.815254i	0.995582	+	0.0938917i	$0.0299307\pi$
$660$		0			0
$661$	7.35519	−	4.24652i	0.286084	−	0.165170i	−0.350091	−	0.936716i	$-0.613849\pi$
$661$	7.35519	−	4.24652i	0.286084	−	0.165170i	0.636174	+	0.771545i	$0.280516\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	30.2592	−	6.47329i	1.17340	−	0.251023i
$666$		0			0
$667$	5.67333	+	9.82649i	0.219672	+	0.380483i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−8.65447	+	14.9900i	−0.334102	+	0.578682i
$672$		0			0
$673$	−16.9974	−	29.4403i	−0.655201	−	1.13484i	−0.981843	−	0.189694i	$-0.939251\pi$
$673$	−16.9974	−	29.4403i	−0.655201	−	1.13484i	0.326642	−	0.945148i	$-0.394083\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.5176	−	33.8054i	0.750121	−	1.29925i	−0.197643	−	0.980274i	$-0.563329\pi$
$677$	19.5176	−	33.8054i	0.750121	−	1.29925i	0.947764	−	0.318973i	$-0.103338\pi$
$678$		0			0
$679$	38.6247	−	8.26291i	1.48228	−	0.317101i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.91400	+	1.10505i	0.0732373	+	0.0422836i	0.536171	−	0.844109i	$-0.319870\pi$
$683$	1.91400	+	1.10505i	0.0732373	+	0.0422836i	−0.462934	+	0.886393i	$0.653203\pi$
$684$		0			0
$685$			7.72069i			0.294992i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−13.8817	−	24.0438i	−0.528851	−	0.915997i
$690$		0			0
$691$	−2.96039	−	1.70918i	−0.112619	−	0.0650203i	0.442633	−	0.896703i	$-0.354045\pi$
$691$	−2.96039	−	1.70918i	−0.112619	−	0.0650203i	−0.555251	+	0.831683i	$0.687378\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.845879	−	0.488369i	−0.0320860	−	0.0185249i
$696$		0			0
$697$	0.184894	+	0.320247i	0.00700338	+	0.0121302i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	37.5732i		−	1.41912i	−0.704645	−	0.709560i	$-0.748894\pi$
$701$		−	37.5732i		−	1.41912i	0.704645	−	0.709560i	$-0.251106\pi$
$702$		0			0
$703$	−16.3887	−	9.46203i	−0.618112	−	0.356867i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.22170	−	2.65947i	−0.309209	−	0.100020i
$708$		0			0
$709$	13.4390	−	23.2770i	0.504712	−	0.874187i	−0.495273	−	0.868738i	$-0.664932\pi$
$709$	13.4390	−	23.2770i	0.504712	−	0.874187i	0.999985	−	0.00544993i	$-0.00173477\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.6091	−	28.7678i	−0.622015	−	1.07736i
$714$		0			0
$715$	13.9279	−	24.1238i	0.520872	−	0.902177i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.41278	−	2.44701i	−0.0526879	−	0.0912580i	0.838479	−	0.544935i	$-0.183446\pi$
$719$	−1.41278	−	2.44701i	−0.0526879	−	0.0912580i	−0.891166	+	0.453676i	$0.850112\pi$
$720$		0			0
$721$	3.88272	−	12.0033i	0.144600	−	0.447028i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.0780813	+	0.0450803i	−0.00289987	+	0.00167424i
$726$		0			0
$727$	−0.622076	+	0.359156i	−0.0230715	+	0.0133203i	−0.511491	−	0.859288i	$-0.670907\pi$
$727$	−0.622076	+	0.359156i	−0.0230715	+	0.0133203i	0.488420	+	0.872609i	$0.337573\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	11.6937			0.432506
$732$		0			0
$733$		−	38.6236i		−	1.42659i	−0.700862	−	0.713297i	$-0.747201\pi$
$733$		−	38.6236i		−	1.42659i	0.700862	−	0.713297i	$-0.252799\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.73062	+	5.04063i	−0.321596	+	0.185674i
$738$		0			0
$739$	−11.9491	+	20.6965i	−0.439556	+	0.761334i	−0.997655	−	0.0684405i	$-0.978198\pi$
$739$	−11.9491	+	20.6965i	−0.439556	+	0.761334i	0.558099	+	0.829775i	$0.311531\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.5325	+	11.8544i	0.753264	+	0.434897i	0.826872	−	0.562390i	$-0.190118\pi$
$743$	20.5325	+	11.8544i	0.753264	+	0.434897i	−0.0736078	+	0.997287i	$0.523451\pi$
$744$		0			0
$745$		−	38.9966i		−	1.42872i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−19.1094	+	4.08804i	−0.698242	+	0.149374i
$750$		0			0
$751$	−13.7869			−0.503090			−0.251545	−	0.967846i	$-0.580939\pi$
$751$	−13.7869			−0.503090			−0.251545	+	0.967846i	$0.580939\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.835255			−0.0303981
$756$		0			0
$757$	−19.6447			−0.714000			−0.357000	−	0.934104i	$-0.616200\pi$
$757$	−19.6447			−0.714000			−0.357000	+	0.934104i	$0.616200\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−52.9464			−1.91931			−0.959653	−	0.281187i	$-0.909272\pi$
$761$	−52.9464			−1.91931			−0.959653	+	0.281187i	$0.909272\pi$
$762$		0			0
$763$	4.60912	−	4.16103i	0.166861	−	0.150639i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	77.7501i		−	2.80739i
$768$		0			0
$769$	17.6774	+	10.2060i	0.637462	+	0.368039i	0.783636	−	0.621220i	$-0.213363\pi$
$769$	17.6774	+	10.2060i	0.637462	+	0.368039i	−0.146174	+	0.989259i	$0.546696\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.07789	+	1.86697i	−0.0387692	+	0.0671501i	−0.884759	−	0.466049i	$-0.845677\pi$
$773$	−1.07789	+	1.86697i	−0.0387692	+	0.0671501i	0.845990	+	0.533199i	$0.179010\pi$
$774$		0			0
$775$	0.228589	−	0.131976i	0.00821116	−	0.00474072i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			0.414688i			0.0148577i
$780$		0			0
$781$	21.2824			0.761544
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−39.2802	+	22.6784i	−1.40197	+	0.809428i
$786$		0			0
$787$	−18.0946	+	10.4469i	−0.645004	+	0.372393i	−0.786539	−	0.617540i	$-0.788129\pi$
$787$	−18.0946	+	10.4469i	−0.645004	+	0.372393i	0.141536	+	0.989933i	$0.454796\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.3538	+	26.9764i	0.865922	+	0.959170i
$792$		0			0
$793$	24.0412	+	41.6405i	0.853727	+	1.47870i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.9964	+	24.2424i	−0.495777	+	0.858710i	−0.999988	−	0.00486976i	$-0.998450\pi$
$797$	−13.9964	+	24.2424i	−0.495777	+	0.858710i	0.504211	+	0.863580i	$0.331783\pi$
$798$		0			0
$799$	−8.88513	−	15.3895i	−0.314333	−	0.544441i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.5068	+	26.8585i	−0.547222	+	0.947817i
$804$		0			0
$805$	−7.91794	+	24.4782i	−0.279071	+	0.862742i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	37.1345	+	21.4396i	1.30558	+	0.753777i	0.981355	−	0.192203i	$-0.0615633\pi$
$809$	37.1345	+	21.4396i	1.30558	+	0.753777i	0.324225	+	0.945980i	$0.394897\pi$
$810$		0			0
$811$		−	23.7421i		−	0.833699i	−0.908976	−	0.416849i	$-0.863134\pi$
$811$		−	23.7421i		−	0.833699i	0.908976	−	0.416849i	$-0.136866\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−16.1641	−	27.9970i	−0.566204	−	0.980693i
$816$		0			0
$817$	11.3566	+	6.55675i	0.397318	+	0.229392i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.37437	−	0.793495i	−0.0479660	−	0.0276932i	0.475825	−	0.879540i	$-0.342149\pi$
$821$	−1.37437	−	0.793495i	−0.0479660	−	0.0276932i	−0.523791	+	0.851847i	$0.675483\pi$
$822$		0			0
$823$	1.54101	+	2.66911i	0.0537164	+	0.0930395i	0.891633	−	0.452758i	$-0.149560\pi$
$823$	1.54101	+	2.66911i	0.0537164	+	0.0930395i	−0.837917	+	0.545798i	$0.816227\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			20.7448i			0.721369i	0.932688	+	0.360685i	$0.117457\pi$
$827$			20.7448i			0.721369i	−0.932688	+	0.360685i	$0.882543\pi$
$828$		0			0
$829$	−0.917576	−	0.529763i	−0.0318687	−	0.0183994i	0.483981	−	0.875079i	$-0.339190\pi$
$829$	−0.917576	−	0.529763i	−0.0318687	−	0.0183994i	−0.515850	+	0.856679i	$0.672524\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	29.8953	−	13.4043i	1.03581	−	0.464433i
$834$		0			0
$835$	−16.9910	+	29.4293i	−0.587999	+	1.01844i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.2137	−	33.2792i	−0.663332	−	1.14892i	−0.979735	−	0.200299i	$-0.935809\pi$
$839$	−19.2137	−	33.2792i	−0.663332	−	1.14892i	0.316403	−	0.948625i	$-0.397525\pi$
$840$		0			0
$841$	−11.1195	+	19.2596i	−0.383432	+	0.664124i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−24.2061	−	41.9262i	−0.832716	−	1.44231i
$846$		0			0
$847$	−16.3623	−	5.29271i	−0.562216	−	0.181860i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.6257	−	7.86680i	0.467083	−	0.269670i
$852$		0			0
$853$	−12.0659	+	6.96626i	−0.413129	+	0.238520i	−0.692133	−	0.721770i	$-0.743329\pi$
$853$	−12.0659	+	6.96626i	−0.413129	+	0.238520i	0.279004	+	0.960290i	$0.409996\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.9264			0.919788			0.459894	−	0.887974i	$-0.347887\pi$
$857$	26.9264			0.919788			0.459894	+	0.887974i	$0.347887\pi$
$858$		0			0
$859$		−	20.2001i		−	0.689217i	−0.938746	−	0.344609i	$-0.888012\pi$
$859$		−	20.2001i		−	0.689217i	0.938746	−	0.344609i	$-0.111988\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38.1427	+	22.0217i	−1.29839	+	0.749627i	−0.980126	−	0.198374i	$-0.936434\pi$
$863$	−38.1427	+	22.0217i	−1.29839	+	0.749627i	−0.318266	+	0.948001i	$0.603101\pi$
$864$		0			0
$865$	2.09612	−	3.63058i	0.0712701	−	0.123443i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	26.7273	+	15.4310i	0.906662	+	0.523461i
$870$		0			0
$871$			28.0046i			0.948900i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−28.2413	−	9.13522i	−0.954732	−	0.308827i
$876$		0			0
$877$	−54.0872			−1.82640			−0.913198	−	0.407517i	$-0.866395\pi$
$877$	−54.0872			−1.82640			−0.913198	+	0.407517i	$0.866395\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.82593			−0.229972			−0.114986	−	0.993367i	$-0.536682\pi$
$881$	−6.82593			−0.229972			−0.114986	+	0.993367i	$0.536682\pi$
$882$		0			0
$883$	9.87685			0.332382			0.166191	−	0.986094i	$-0.446853\pi$
$883$	9.87685			0.332382			0.166191	+	0.986094i	$0.446853\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	35.0825			1.17795			0.588977	−	0.808150i	$-0.299531\pi$
$887$	35.0825			1.17795			0.588977	+	0.808150i	$0.299531\pi$
$888$		0			0
$889$	−15.0514	−	4.86869i	−0.504809	−	0.163291i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	19.9279i		−	0.666861i
$894$		0			0
$895$	19.2539	+	11.1163i	0.643588	+	0.371576i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.89655	+	17.1413i	−0.330069	+	0.571695i
$900$		0			0
$901$	19.0967	−	11.0255i	0.636204	−	0.367313i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	25.1414i		−	0.835728i
$906$		0			0
$907$	−34.4463			−1.14377			−0.571885	−	0.820334i	$-0.693787\pi$
$907$	−34.4463			−1.14377			−0.571885	+	0.820334i	$0.693787\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−45.9046	+	26.5030i	−1.52089	+	0.878084i	−0.521190	+	0.853441i	$0.674512\pi$
$911$	−45.9046	+	26.5030i	−1.52089	+	0.878084i	−0.999696	+	0.0246430i	$0.992155\pi$
$912$		0			0
$913$	23.5630	−	13.6041i	0.779821	−	0.450230i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	52.7594	+	17.0661i	1.74227	+	0.563571i
$918$		0			0
$919$	−5.73193	−	9.92799i	−0.189079	−	0.327494i	0.755865	−	0.654728i	$-0.227217\pi$
$919$	−5.73193	−	9.92799i	−0.189079	−	0.327494i	−0.944943	+	0.327234i	$0.893884\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	29.5601	−	51.1996i	0.972983	−	1.68526i
$924$		0			0
$925$	0.0625096	+	0.108270i	0.00205530	+	0.00355989i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.3933	+	30.1261i	−0.570656	+	0.988405i	0.425843	+	0.904797i	$0.359978\pi$
$929$	−17.3933	+	30.1261i	−0.570656	+	0.988405i	−0.996499	+	0.0836078i	$0.973356\pi$
$930$		0			0
$931$	36.5495	+	3.74457i	1.19786	+	0.122723i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	19.1602	+	11.0622i	0.626606	+	0.361771i
$936$		0			0
$937$			18.5180i			0.604956i	0.953156	+	0.302478i	$0.0978139\pi$
$937$			18.5180i			0.604956i	−0.953156	+	0.302478i	$0.902186\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.89224	+	8.47360i	0.159482	+	0.276232i	0.934682	−	0.355485i	$-0.115684\pi$
$941$	4.89224	+	8.47360i	0.159482	+	0.276232i	−0.775200	+	0.631716i	$0.782351\pi$
$942$		0			0
$943$	−0.298583	−	0.172387i	−0.00972321	−	0.00561370i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	29.0554	+	16.7752i	0.944174	+	0.545119i	0.891266	−	0.453480i	$-0.149818\pi$
$947$	29.0554	+	16.7752i	0.944174	+	0.545119i	0.0529077	+	0.998599i	$0.483151\pi$
$948$		0			0
$949$	43.0762	+	74.6101i	1.39831	+	2.42195i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	10.8871i		−	0.352668i	−0.984330	−	0.176334i	$-0.943576\pi$
$953$		−	10.8871i		−	0.352668i	0.984330	−	0.176334i	$-0.0564239\pi$
$954$		0			0
$955$	24.8272	+	14.3340i	0.803389	+	0.463837i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.82134	+	8.72212i	−0.0911059	+	0.281652i
$960$		0			0
$961$	13.4729	−	23.3358i	0.434610	−	0.752766i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.4113	−	23.2290i	−0.431724	−	0.747768i
$966$		0			0
$967$	−26.3931	+	45.7142i	−0.848746	+	1.47007i	0.0335826	+	0.999436i	$0.489308\pi$
$967$	−26.3931	+	45.7142i	−0.848746	+	1.47007i	−0.882328	+	0.470635i	$0.844025\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.7931	−	27.3544i	−0.506824	−	0.877844i	−0.999969	−	0.00789735i	$-0.997486\pi$
$971$	−15.7931	−	27.3544i	−0.506824	−	0.877844i	0.493145	−	0.869947i	$-0.335847\pi$
$972$		0			0
$973$	−0.777134	−	0.860821i	−0.0249138	−	0.0275966i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	34.0048	−	19.6327i	1.08791	−	0.628106i	0.154891	−	0.987932i	$-0.450497\pi$
$977$	34.0048	−	19.6327i	1.08791	−	0.628106i	0.933019	+	0.359826i	$0.117164\pi$
$978$		0			0
$979$	−10.0479	+	5.80113i	−0.321131	+	0.185405i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−39.8341			−1.27051			−0.635255	−	0.772302i	$-0.719105\pi$
$983$	−39.8341			−1.27051			−0.635255	+	0.772302i	$0.719105\pi$
$984$		0			0
$985$		−	61.7822i		−	1.96855i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.44198	+	5.45133i	−0.300237	+	0.173342i
$990$		0			0
$991$	19.9472	−	34.5496i	0.633645	−	1.09750i	−0.353156	−	0.935565i	$-0.614891\pi$
$991$	19.9472	−	34.5496i	0.633645	−	1.09750i	0.986801	−	0.161940i	$-0.0517752\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.853132	+	0.492556i	0.0270461	+	0.0156151i
$996$		0			0
$997$			29.5700i			0.936492i	0.883598	+	0.468246i	$0.155114\pi$
$997$			29.5700i			0.936492i	−0.883598	+	0.468246i	$0.844886\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.17.6		48
3.2	odd	2		1008.2.df.e.689.3		48
4.3	odd	2		1512.2.cx.a.17.6		48
7.5	odd	6		3024.2.ca.e.2609.6		48
9.2	odd	6		3024.2.ca.e.2033.6		48
9.7	even	3		1008.2.ca.e.353.11		48
12.11	even	2		504.2.cx.a.185.22	yes	48
21.5	even	6		1008.2.ca.e.257.11		48
28.19	even	6		1512.2.bs.a.1097.6		48
36.7	odd	6		504.2.bs.a.353.14	yes	48
36.11	even	6		1512.2.bs.a.521.6		48
63.47	even	6	inner	3024.2.df.e.1601.6		48
63.61	odd	6		1008.2.df.e.929.3		48
84.47	odd	6		504.2.bs.a.257.14	✓	48
252.47	odd	6		1512.2.cx.a.89.6		48
252.187	even	6		504.2.cx.a.425.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.14	✓	48	84.47	odd	6
504.2.bs.a.353.14	yes	48	36.7	odd	6
504.2.cx.a.185.22	yes	48	12.11	even	2
504.2.cx.a.425.22	yes	48	252.187	even	6
1008.2.ca.e.257.11		48	21.5	even	6
1008.2.ca.e.353.11		48	9.7	even	3
1008.2.df.e.689.3		48	3.2	odd	2
1008.2.df.e.929.3		48	63.61	odd	6
1512.2.bs.a.521.6		48	36.11	even	6
1512.2.bs.a.1097.6		48	28.19	even	6
1512.2.cx.a.17.6		48	4.3	odd	2
1512.2.cx.a.89.6		48	252.47	odd	6
3024.2.ca.e.2033.6		48	9.2	odd	6
3024.2.ca.e.2609.6		48	7.5	odd	6
3024.2.df.e.17.6		48	1.1	even	1	trivial
3024.2.df.e.1601.6		48	63.47	even	6	inner

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.22830 q^{5} +(-2.51733 - 0.814280i) q^{7} -2.12135i q^{11} +(-5.10339 - 2.94644i) q^{13} +(2.34020 - 4.05335i) q^{17} +(4.54550 - 2.62435i) q^{19} +4.36380i q^{23} -0.0346748 q^{25} +(2.25182 - 1.30009i) q^{29} +(-6.59237 + 3.80611i) q^{31} +(5.60937 + 1.81446i) q^{35} +(-1.80274 - 3.12244i) q^{37} +(-0.0395039 + 0.0684228i) q^{41} +(1.24922 + 2.16371i) q^{43} +(1.89837 - 3.28807i) q^{47} +(5.67390 + 4.09962i) q^{49} +(4.08014 + 2.35567i) q^{53} +4.72701i q^{55} +(6.59695 + 11.4262i) q^{59} +(-7.06624 - 4.07970i) q^{61} +(11.3719 + 6.56556i) q^{65} +(-2.37614 - 4.11559i) q^{67} +10.0325i q^{71} +(-12.6610 - 7.30986i) q^{73} +(-1.72737 + 5.34014i) q^{77} +(-7.27414 + 12.5992i) q^{79} +(6.41294 + 11.1075i) q^{83} +(-5.21468 + 9.03209i) q^{85} +(-2.73464 - 4.73654i) q^{89} +(10.4477 + 11.5728i) q^{91} +(-10.1287 + 5.84783i) q^{95} +(-12.9290 + 7.46454i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

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