LMFDB - Embedded newform 2736.2.s.ba.1873.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(577,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("2736.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.s (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.1
Root			$0.643668 - 1.11487i$ of defining polynomial
Character	$\chi$	$=$	2736.1873
Dual form			2736.2.s.ba.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95872 + 3.39260i) q^{5} -2.04306 q^{7} +O(q^{10})$	$q+(-1.95872 + 3.39260i) q^{5} -2.04306 q^{7} -1.91744 q^{11} +(2.13010 + 3.68945i) q^{13} +(-3.04306 + 5.27073i) q^{17} +(-4.33039 - 0.497680i) q^{19} +(3.42711 + 5.93592i) q^{23} +(-5.17316 - 8.96018i) q^{25} +(-1.34277 - 2.32574i) q^{29} +1.46839 q^{31} +(4.00178 - 6.93128i) q^{35} +3.93677 q^{37} +(-1.70029 + 2.94499i) q^{41} +(3.77725 - 6.54239i) q^{43} +(-4.96050 - 8.59183i) q^{47} -2.82591 q^{49} +(4.91922 + 8.52033i) q^{53} +(3.75572 - 6.50510i) q^{55} +(1.61595 - 2.79891i) q^{59} +(-4.70477 - 8.14891i) q^{61} -16.6891 q^{65} +(5.28173 + 9.14823i) q^{67} +(-2.21715 + 3.84021i) q^{71} +(-6.33488 + 10.9723i) q^{73} +3.91744 q^{77} +(6.52601 - 11.3034i) q^{79} +4.43429 q^{83} +(-11.9210 - 20.6478i) q^{85} +(-3.47016 - 6.01050i) q^{89} +(-4.35192 - 7.53775i) q^{91} +(10.1705 - 13.7165i) q^{95} +(2.58704 - 4.48089i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 + 4 * q^7	$ 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) $ 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.95872	+	3.39260i	−0.875966	+	1.51722i	−0.0202354	+	0.999795i	$0.506442\pi$
$5$	−1.95872	+	3.39260i	−0.875966	+	1.51722i	−0.855730	+	0.517422i	$0.826892\pi$
$6$		0			0
$7$	−2.04306			−0.772204			−0.386102	−	0.922456i	$-0.626179\pi$
$7$	−2.04306			−0.772204			−0.386102	+	0.922456i	$0.626179\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.91744			−0.578129			−0.289065	−	0.957310i	$-0.593344\pi$
$11$	−1.91744			−0.578129			−0.289065	+	0.957310i	$0.593344\pi$
$12$		0			0
$13$	2.13010	+	3.68945i	0.590784	+	1.02327i	0.994127	+	0.108219i	$0.0345148\pi$
$13$	2.13010	+	3.68945i	0.590784	+	1.02327i	−0.403343	+	0.915049i	$0.632152\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.04306	+	5.27073i	−0.738050	+	1.27834i	0.215322	+	0.976543i	$0.430920\pi$
$17$	−3.04306	+	5.27073i	−0.738050	+	1.27834i	−0.953372	+	0.301797i	$0.902413\pi$
$18$		0			0
$19$	−4.33039	−	0.497680i	−0.993461	−	0.114176i
$19$	−4.33039	−	0.497680i	−0.993461	−	0.114176i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.42711	+	5.93592i	0.714601	+	1.23773i	0.963113	+	0.269096i	$0.0867250\pi$
$23$	3.42711	+	5.93592i	0.714601	+	1.23773i	−0.248512	+	0.968629i	$0.579942\pi$
$24$		0			0
$25$	−5.17316	−	8.96018i	−1.03463	−	1.79204i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.34277	−	2.32574i	−0.249345	−	0.431879i	0.713999	−	0.700147i	$-0.246882\pi$
$29$	−1.34277	−	2.32574i	−0.249345	−	0.431879i	−0.963344	+	0.268268i	$0.913549\pi$
$30$		0			0
$31$	1.46839			0.263730			0.131865	−	0.991268i	$-0.457903\pi$
$31$	1.46839			0.263730			0.131865	+	0.991268i	$0.457903\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.00178	−	6.93128i	0.676424	−	1.17160i
$36$		0			0
$37$	3.93677			0.647202			0.323601	−	0.946194i	$-0.395107\pi$
$37$	3.93677			0.647202			0.323601	+	0.946194i	$0.395107\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.70029	+	2.94499i	−0.265541	+	0.459930i	−0.967705	−	0.252085i	$-0.918884\pi$
$41$	−1.70029	+	2.94499i	−0.265541	+	0.459930i	0.702164	+	0.712015i	$0.252217\pi$
$42$		0			0
$43$	3.77725	−	6.54239i	0.576026	−	0.997705i	−0.419904	−	0.907569i	$-0.637936\pi$
$43$	3.77725	−	6.54239i	0.576026	−	0.997705i	0.995929	−	0.0901369i	$-0.0287304\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.96050	−	8.59183i	−0.723563	−	1.25325i	−0.959563	−	0.281494i	$-0.909170\pi$
$47$	−4.96050	−	8.59183i	−0.723563	−	1.25325i	0.236000	−	0.971753i	$-0.424163\pi$
$48$		0			0
$49$	−2.82591			−0.403702
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.91922	+	8.52033i	0.675706	+	1.17036i	0.976262	+	0.216593i	$0.0694945\pi$
$53$	4.91922	+	8.52033i	0.675706	+	1.17036i	−0.300556	+	0.953764i	$0.597172\pi$
$54$		0			0
$55$	3.75572	−	6.50510i	0.506422	−	0.877148i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.61595	−	2.79891i	0.210379	−	0.364387i	−0.741454	−	0.671004i	$-0.765864\pi$
$59$	1.61595	−	2.79891i	0.210379	−	0.364387i	0.951833	+	0.306616i	$0.0991968\pi$
$60$		0			0
$61$	−4.70477	−	8.14891i	−0.602385	−	1.04336i	−0.992459	−	0.122577i	$-0.960884\pi$
$61$	−4.70477	−	8.14891i	−0.602385	−	1.04336i	0.390074	−	0.920783i	$-0.372449\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−16.6891			−2.07003
$66$		0			0
$67$	5.28173	+	9.14823i	0.645266	+	1.11763i	0.984240	+	0.176838i	$0.0565870\pi$
$67$	5.28173	+	9.14823i	0.645266	+	1.11763i	−0.338973	+	0.940796i	$0.610080\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.21715	+	3.84021i	−0.263127	+	0.455749i	−0.967071	−	0.254506i	$-0.918087\pi$
$71$	−2.21715	+	3.84021i	−0.263127	+	0.455749i	0.703944	+	0.710255i	$0.251420\pi$
$72$		0			0
$73$	−6.33488	+	10.9723i	−0.741441	+	1.28421i	0.210398	+	0.977616i	$0.432524\pi$
$73$	−6.33488	+	10.9723i	−0.741441	+	1.28421i	−0.951839	+	0.306598i	$0.900809\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.91744			0.446434
$78$		0			0
$79$	6.52601	−	11.3034i	0.734234	−	1.27173i	−0.220825	−	0.975313i	$-0.570875\pi$
$79$	6.52601	−	11.3034i	0.734234	−	1.27173i	0.955059	−	0.296417i	$-0.0957917\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.43429			0.486727			0.243363	−	0.969935i	$-0.421749\pi$
$83$	4.43429			0.486727			0.243363	+	0.969935i	$0.421749\pi$
$84$		0			0
$85$	−11.9210	−	20.6478i	−1.29301	−	2.23956i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.47016	−	6.01050i	−0.367837	−	0.637112i	0.621390	−	0.783501i	$-0.286568\pi$
$89$	−3.47016	−	6.01050i	−0.367837	−	0.637112i	−0.989227	+	0.146389i	$0.953235\pi$
$90$		0			0
$91$	−4.35192	−	7.53775i	−0.456206	−	0.790171i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	10.1705	−	13.7165i	1.04347	−	1.40728i
$96$		0			0
$97$	2.58704	−	4.48089i	0.262675	−	0.454966i	−0.704277	−	0.709925i	$-0.748729\pi$
$97$	2.58704	−	4.48089i	0.262675	−	0.454966i	0.966952	+	0.254959i	$0.0820621\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.79182	+	8.29967i	0.476804	+	0.825848i	0.999647	−	0.0265808i	$-0.00846193\pi$
$101$	4.79182	+	8.29967i	0.476804	+	0.825848i	−0.522843	+	0.852429i	$0.675129\pi$
$102$		0			0
$103$	−17.7128			−1.74530			−0.872648	−	0.488351i	$-0.837599\pi$
$103$	−17.7128			−1.74530			−0.872648	+	0.488351i	$0.837599\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.8578			1.04966			0.524830	−	0.851207i	$-0.324129\pi$
$107$	10.8578			1.04966			0.524830	+	0.851207i	$0.324129\pi$
$108$		0			0
$109$	3.41296	−	5.91141i	0.326902	−	0.566211i	−0.654994	−	0.755634i	$-0.727329\pi$
$109$	3.41296	−	5.91141i	0.326902	−	0.566211i	0.981895	+	0.189424i	$0.0606620\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.16868			−0.580300			−0.290150	−	0.956981i	$-0.593705\pi$
$113$	−6.16868			−0.580300			−0.290150	+	0.956981i	$0.593705\pi$
$114$		0			0
$115$	−26.8510			−2.50386
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.21715	−	10.7684i	0.569925	−	0.987139i
$120$		0			0
$121$	−7.32343			−0.665766
$122$		0			0
$123$		0			0
$124$		0			0
$125$	20.9439			1.87328
$126$		0			0
$127$	−10.4095	−	18.0299i	−0.923698	−	1.59989i	−0.793642	−	0.608385i	$-0.791818\pi$
$127$	−10.4095	−	18.0299i	−0.923698	−	1.59989i	−0.130056	−	0.991507i	$-0.541516\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.61773	−	2.80199i	0.141342	−	0.244811i	−0.786660	−	0.617386i	$-0.788192\pi$
$131$	1.61773	−	2.80199i	0.141342	−	0.244811i	0.928002	+	0.372575i	$0.121525\pi$
$132$		0			0
$133$	8.84725	+	1.01679i	0.767154	+	0.0881669i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.405993	−	0.703200i	−0.0346863	−	0.0600785i	0.848161	−	0.529738i	$-0.177710\pi$
$137$	−0.405993	−	0.703200i	−0.0346863	−	0.0600785i	−0.882847	+	0.469660i	$0.844377\pi$
$138$		0			0
$139$	−1.77725	−	3.07829i	−0.150745	−	0.261097i	0.780757	−	0.624835i	$-0.214834\pi$
$139$	−1.77725	−	3.07829i	−0.150745	−	0.261097i	−0.931501	+	0.363738i	$0.881500\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.08434	−	7.07428i	−0.341550	−	0.591581i
$144$		0			0
$145$	10.5204			0.873672
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.3445	−	17.9173i	0.847458	−	1.46784i	−0.0360112	−	0.999351i	$-0.511465\pi$
$149$	10.3445	−	17.9173i	0.847458	−	1.46784i	0.883469	−	0.468489i	$-0.155201\pi$
$150$		0			0
$151$	17.0408			1.38676			0.693381	−	0.720571i	$-0.256120\pi$
$151$	17.0408			1.38676			0.693381	+	0.720571i	$0.256120\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.87616	+	4.98165i	−0.231019	+	0.400136i
$156$		0			0
$157$	9.62918	−	16.6782i	0.768492	−	1.33107i	−0.169889	−	0.985463i	$-0.554341\pi$
$157$	9.62918	−	16.6782i	0.768492	−	1.33107i	0.938381	−	0.345604i	$-0.112326\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.00178	−	12.1274i	−0.551817	−	0.955776i
$162$		0			0
$163$	1.32801			0.104018			0.0520088	−	0.998647i	$-0.483438\pi$
$163$	1.32801			0.104018			0.0520088	+	0.998647i	$0.483438\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.49033	+	11.2416i	0.502237	+	0.869900i	0.999997	+	0.00258498i	$0.000822827\pi$
$167$	6.49033	+	11.2416i	0.502237	+	0.869900i	−0.497760	+	0.867315i	$0.665844\pi$
$168$		0			0
$169$	−2.57467	+	4.45946i	−0.198052	+	0.343036i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.49211	−	4.31646i	0.189472	−	0.328174i	−0.755603	−	0.655030i	$-0.772656\pi$
$173$	2.49211	−	4.31646i	0.189472	−	0.328174i	0.945074	+	0.326856i	$0.105989\pi$
$174$		0			0
$175$	10.5691	+	18.3062i	0.798947	+	1.38382i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.6101			−1.24150			−0.620748	−	0.784010i	$-0.713171\pi$
$179$	−16.6101			−1.24150			−0.620748	+	0.784010i	$0.713171\pi$
$180$		0			0
$181$	3.52382	+	6.10343i	0.261923	+	0.453664i	0.966753	−	0.255712i	$-0.0823099\pi$
$181$	3.52382	+	6.10343i	0.261923	+	0.453664i	−0.704830	+	0.709377i	$0.748977\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.71103	+	13.3559i	−0.566926	+	0.981945i
$186$		0			0
$187$	5.83488	−	10.1063i	0.426688	−	0.739046i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.1687			−1.16992			−0.584962	−	0.811061i	$-0.698891\pi$
$191$	−16.1687			−1.16992			−0.584962	+	0.811061i	$0.698891\pi$
$192$		0			0
$193$	−8.32250	+	14.4150i	−0.599067	+	1.03761i	0.393892	+	0.919157i	$0.371128\pi$
$193$	−8.32250	+	14.4150i	−0.599067	+	1.03761i	−0.992959	+	0.118458i	$0.962205\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.23191			0.657746			0.328873	−	0.944374i	$-0.393331\pi$
$197$	9.23191			0.657746			0.328873	+	0.944374i	$0.393331\pi$
$198$		0			0
$199$	−6.82031	−	11.8131i	−0.483479	−	0.837410i	0.516341	−	0.856383i	$-0.327294\pi$
$199$	−6.82031	−	11.8131i	−0.483479	−	0.837410i	−0.999820	+	0.0189729i	$0.993960\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.74335	+	4.75162i	0.192545	+	0.333499i
$204$		0			0
$205$	−6.66079	−	11.5368i	−0.465210	−	0.805767i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.30326	+	0.954271i	0.574349	+	0.0660083i
$210$		0			0
$211$	−2.10068	+	3.63849i	−0.144617	+	0.250484i	−0.929230	−	0.369502i	$-0.879528\pi$
$211$	−2.10068	+	3.63849i	−0.144617	+	0.250484i	0.784613	+	0.619986i	$0.212862\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	14.7972	+	25.6294i	1.00916	+	1.74791i
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−25.9281			−1.74411
$222$		0			0
$223$	−7.82927	+	13.5607i	−0.524287	+	0.908092i	0.475313	+	0.879817i	$0.342335\pi$
$223$	−7.82927	+	13.5607i	−0.524287	+	0.908092i	−0.999600	+	0.0282750i	$0.990999\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−28.1758			−1.87009			−0.935046	−	0.354525i	$-0.884642\pi$
$227$	−28.1758			−1.87009			−0.935046	+	0.354525i	$0.884642\pi$
$228$		0			0
$229$	7.23731			0.478255			0.239128	−	0.970988i	$-0.423139\pi$
$229$	7.23731			0.478255			0.239128	+	0.970988i	$0.423139\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.96405	−	15.5262i	0.587255	−	1.01715i	−0.407336	−	0.913279i	$-0.633542\pi$
$233$	8.96405	−	15.5262i	0.587255	−	1.01715i	0.994590	−	0.103876i	$-0.0331246\pi$
$234$		0			0
$235$	38.8649			2.53527
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.08256			−0.134710			−0.0673549	−	0.997729i	$-0.521456\pi$
$239$	−2.08256			−0.134710			−0.0673549	+	0.997729i	$0.521456\pi$
$240$		0			0
$241$	5.90955	+	10.2356i	0.380667	+	0.659335i	0.991158	−	0.132688i	$-0.0423609\pi$
$241$	5.90955	+	10.2356i	0.380667	+	0.659335i	−0.610490	+	0.792024i	$0.709028\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.53517	−	9.58719i	0.353629	−	0.612503i
$246$		0			0
$247$	−7.38802	−	17.0369i	−0.470088	−	1.08403i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.434292	−	0.752216i	−0.0274123	−	0.0474795i	0.851994	−	0.523552i	$-0.175393\pi$
$251$	−0.434292	−	0.752216i	−0.0274123	−	0.0474795i	−0.879406	+	0.476072i	$0.842060\pi$
$252$		0			0
$253$	−6.57126	−	11.3818i	−0.413132	−	0.715565i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.85243	+	10.1367i	0.365065	+	0.632311i	0.988787	−	0.149336i	$-0.0477135\pi$
$257$	5.85243	+	10.1367i	0.365065	+	0.632311i	−0.623722	+	0.781646i	$0.714380\pi$
$258$		0			0
$259$	−8.04306			−0.499771
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.7038	+	27.1999i	−0.968341	+	1.67722i	−0.267982	+	0.963424i	$0.586357\pi$
$263$	−15.7038	+	27.1999i	−0.968341	+	1.67722i	−0.700358	+	0.713791i	$0.746976\pi$
$264$		0			0
$265$	−38.5414			−2.36758
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.68731	+	13.3148i	−0.468704	+	0.811818i	−0.999360	−	0.0357685i	$-0.988612\pi$
$269$	−7.68731	+	13.3148i	−0.468704	+	0.811818i	0.530657	+	0.847587i	$0.321945\pi$
$270$		0			0
$271$	−9.94574	+	17.2265i	−0.604161	+	1.04644i	0.388023	+	0.921650i	$0.373158\pi$
$271$	−9.94574	+	17.2265i	−0.604161	+	1.04644i	−0.992184	+	0.124787i	$0.960175\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.91922	+	17.1806i	0.598151	+	1.03603i
$276$		0			0
$277$	4.19698			0.252172			0.126086	−	0.992019i	$-0.459758\pi$
$277$	4.19698			0.252172			0.126086	+	0.992019i	$0.459758\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.95872	−	13.7849i	−0.474777	−	0.822339i	0.524805	−	0.851222i	$-0.324138\pi$
$281$	−7.95872	−	13.7849i	−0.474777	−	0.822339i	−0.999583	+	0.0288837i	$0.990805\pi$
$282$		0			0
$283$	−3.76269	+	6.51716i	−0.223668	+	0.387405i	−0.955919	−	0.293630i	$-0.905137\pi$
$283$	−3.76269	+	6.51716i	−0.223668	+	0.387405i	0.732251	+	0.681035i	$0.238470\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.47380	−	6.01679i	0.205052	−	0.355160i
$288$		0			0
$289$	−10.0204	−	17.3559i	−0.589436	−	1.02093i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−21.7962			−1.27335			−0.636674	−	0.771133i	$-0.719690\pi$
$293$	−21.7962			−1.27335			−0.636674	+	0.771133i	$0.719690\pi$
$294$		0			0
$295$	6.33039	+	10.9646i	0.368570	+	0.638382i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−14.6002	+	25.2882i	−0.844350	+	1.46246i
$300$		0			0
$301$	−7.71715	+	13.3665i	−0.444809	+	0.770432i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	36.8613			2.11067
$306$		0			0
$307$	15.3394	−	26.5685i	0.875463	−	1.51635i	0.0191951	−	0.999816i	$-0.493890\pi$
$307$	15.3394	−	26.5685i	0.875463	−	1.51635i	0.856268	−	0.516531i	$-0.172777\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.0530439			−0.00300784			−0.00150392	−	0.999999i	$-0.500479\pi$
$311$	−0.0530439			−0.00300784			−0.00150392	+	0.999999i	$0.500479\pi$
$312$		0			0
$313$	4.07374	+	7.05593i	0.230262	+	0.398825i	0.957885	−	0.287152i	$-0.0927085\pi$
$313$	4.07374	+	7.05593i	0.230262	+	0.398825i	−0.727623	+	0.685977i	$0.759375\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.1126	+	22.7118i	0.736479	+	1.27562i	0.954071	+	0.299580i	$0.0968464\pi$
$317$	13.1126	+	22.7118i	0.736479	+	1.27562i	−0.217592	+	0.976040i	$0.569820\pi$
$318$		0			0
$319$	2.57467	+	4.45946i	0.144154	+	0.249682i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.8008	−	21.3099i	0.879179	−	1.18571i
$324$		0			0
$325$	22.0387	−	38.1722i	1.22249	−	2.11741i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.1346	+	17.5536i	0.558738	+	0.967762i
$330$		0			0
$331$	−0.359379			−0.0197533			−0.00987664	−	0.999951i	$-0.503144\pi$
$331$	−0.359379			−0.0197533			−0.00987664	+	0.999951i	$0.503144\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−41.3817			−2.26093
$336$		0			0
$337$	−14.3454	+	24.8470i	−0.781443	+	1.35350i	0.149657	+	0.988738i	$0.452183\pi$
$337$	−14.3454	+	24.8470i	−0.781443	+	1.35350i	−0.931101	+	0.364762i	$0.881150\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.81554			−0.152470
$342$		0			0
$343$	20.0749			1.08394
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.64781	+	13.2464i	−0.410556	+	0.711103i	−0.994951	−	0.100366i	$-0.967999\pi$
$347$	−7.64781	+	13.2464i	−0.410556	+	0.711103i	0.584395	+	0.811469i	$0.301332\pi$
$348$		0			0
$349$	−5.75772			−0.308204			−0.154102	−	0.988055i	$-0.549248\pi$
$349$	−5.75772			−0.308204			−0.154102	+	0.988055i	$0.549248\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.8950			−0.739558			−0.369779	−	0.929120i	$-0.620567\pi$
$353$	−13.8950			−0.739558			−0.369779	+	0.929120i	$0.620567\pi$
$354$		0			0
$355$	−8.68553	−	15.0438i	−0.460980	−	0.798441i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.936774	−	1.62254i	0.0494410	−	0.0856344i	−0.840246	−	0.542206i	$-0.817589\pi$
$359$	0.936774	−	1.62254i	0.0494410	−	0.0856344i	0.889687	+	0.456571i	$0.150923\pi$
$360$		0			0
$361$	18.5046	+	4.31030i	0.973928	+	0.226858i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−24.8165	−	42.9834i	−1.29895	−	2.24985i
$366$		0			0
$367$	−0.526011	−	0.911078i	−0.0274576	−	0.0475579i	0.851970	−	0.523590i	$-0.175408\pi$
$367$	−0.526011	−	0.911078i	−0.0274576	−	0.0475579i	−0.879428	+	0.476033i	$0.842074\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.0502	−	17.4075i	−0.521783	−	0.903754i
$372$		0			0
$373$	33.6908			1.74444			0.872221	−	0.489111i	$-0.162679\pi$
$373$	33.6908			1.74444			0.872221	+	0.489111i	$0.162679\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.72046	−	9.90813i	0.294619	−	0.510295i
$378$		0			0
$379$	−35.1157			−1.80377			−0.901887	−	0.431972i	$-0.857818\pi$
$379$	−35.1157			−1.80377			−0.901887	+	0.431972i	$0.857818\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.75054	−	13.4243i	0.396034	−	0.685951i	−0.597199	−	0.802093i	$-0.703720\pi$
$383$	7.75054	−	13.4243i	0.396034	−	0.685951i	0.993233	+	0.116142i	$0.0370529\pi$
$384$		0			0
$385$	−7.67316	+	13.2903i	−0.391060	+	0.677337i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.28215	−	10.8810i	−0.318518	−	0.551689i	0.661661	−	0.749803i	$-0.269852\pi$
$389$	−6.28215	−	10.8810i	−0.318518	−	0.551689i	−0.980179	+	0.198114i	$0.936518\pi$
$390$		0			0
$391$	−41.7155			−2.10965
$392$		0			0
$393$		0			0
$394$		0			0
$395$	25.5652	+	44.2803i	1.28633	+	2.22798i
$396$		0			0
$397$	3.01924	−	5.22948i	0.151531	−	0.262460i	−0.780259	−	0.625456i	$-0.784913\pi$
$397$	3.01924	−	5.22948i	0.151531	−	0.262460i	0.931791	+	0.362996i	$0.118246\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.1557	−	17.5902i	0.507151	−	0.878412i	−0.492814	−	0.870134i	$-0.664032\pi$
$401$	10.1557	−	17.5902i	0.507151	−	0.878412i	0.999966	−	0.00827741i	$-0.00263481\pi$
$402$		0			0
$403$	3.12781	+	5.41753i	0.155808	+	0.269867i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.54852			−0.374166
$408$		0			0
$409$	17.0580	+	29.5453i	0.843462	+	1.46092i	0.886950	+	0.461865i	$0.152820\pi$
$409$	17.0580	+	29.5453i	0.843462	+	1.46092i	−0.0434881	+	0.999054i	$0.513847\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.30149	+	5.71834i	−0.162455	+	0.281381i
$414$		0			0
$415$	−8.68553	+	15.0438i	−0.426356	+	0.738470i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.326693			−0.0159600			−0.00797999	−	0.999968i	$-0.502540\pi$
$419$	−0.326693			−0.0159600			−0.00797999	+	0.999968i	$0.502540\pi$
$420$		0			0
$421$	−10.0195	+	17.3543i	−0.488320	+	0.845795i	−0.999910	−	0.0134352i	$-0.995723\pi$
$421$	−10.0195	+	17.3543i	−0.488320	+	0.845795i	0.511590	+	0.859230i	$0.329057\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	62.9689			3.05444
$426$		0			0
$427$	9.61213	+	16.6487i	0.465163	+	0.805687i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.2297	+	29.8427i	0.829924	+	1.43747i	0.898097	+	0.439797i	$0.144949\pi$
$431$	17.2297	+	29.8427i	0.829924	+	1.43747i	−0.0681736	+	0.997673i	$0.521717\pi$
$432$		0			0
$433$	−6.10993	−	10.5827i	−0.293625	−	0.508573i	0.681039	−	0.732247i	$-0.261528\pi$
$433$	−6.10993	−	10.5827i	−0.293625	−	0.508573i	−0.974664	+	0.223674i	$0.928195\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.8865	−	27.4105i	−0.568610	−	1.31122i
$438$		0			0
$439$	−5.93356	+	10.2772i	−0.283193	+	0.490505i	−0.972169	−	0.234279i	$-0.924727\pi$
$439$	−5.93356	+	10.2772i	−0.283193	+	0.490505i	0.688976	+	0.724784i	$0.258060\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.154752	+	0.268039i	0.00735250	+	0.0127349i	0.869678	−	0.493619i	$-0.164326\pi$
$443$	0.154752	+	0.268039i	0.00735250	+	0.0127349i	−0.862326	+	0.506354i	$0.830993\pi$
$444$		0			0
$445$	27.1883			1.28885
$446$		0			0
$447$		0			0
$448$		0			0
$449$	22.5275			1.06314			0.531570	−	0.847015i	$-0.321602\pi$
$449$	22.5275			1.06314			0.531570	+	0.847015i	$0.321602\pi$
$450$		0			0
$451$	3.26020	−	5.64684i	0.153517	−	0.265899i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	34.0968			1.59848
$456$		0			0
$457$	29.6679			1.38781			0.693903	−	0.720069i	$-0.255890\pi$
$457$	29.6679			1.38781			0.693903	+	0.720069i	$0.255890\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.2530	+	19.4908i	−0.524105	+	0.907777i	0.475501	+	0.879715i	$0.342267\pi$
$461$	−11.2530	+	19.4908i	−0.524105	+	0.907777i	−0.999606	+	0.0280618i	$0.991066\pi$
$462$		0			0
$463$	30.7041			1.42694			0.713471	−	0.700685i	$-0.247122\pi$
$463$	30.7041			1.42694			0.713471	+	0.700685i	$0.247122\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−38.0932			−1.76274			−0.881372	−	0.472423i	$-0.843380\pi$
$467$	−38.0932			−1.76274			−0.881372	+	0.472423i	$0.843380\pi$
$468$		0			0
$469$	−10.7909	−	18.6904i	−0.498277	−	0.863041i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.24265	+	12.5446i	−0.333017	+	0.576803i
$474$		0			0
$475$	17.9425	+	41.3757i	0.823259	+	1.89845i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.4755	−	21.6082i	−0.570020	−	0.987304i	−0.996563	−	0.0828364i	$-0.973602\pi$
$479$	−12.4755	−	21.6082i	−0.570020	−	0.987304i	0.426543	−	0.904467i	$-0.359731\pi$
$480$		0			0
$481$	8.38573	+	14.5245i	0.382356	+	0.662261i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.1346	+	17.5536i	0.460188	+	0.797069i
$486$		0			0
$487$	16.6747			0.755603			0.377802	−	0.925887i	$-0.376680\pi$
$487$	16.6747			0.755603			0.377802	+	0.925887i	$0.376680\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.6881	−	21.9764i	0.572604	−	0.991780i	−0.423693	−	0.905806i	$-0.639266\pi$
$491$	12.6881	−	21.9764i	0.572604	−	0.991780i	0.996297	−	0.0859741i	$-0.0274002\pi$
$492$		0			0
$493$	16.3445			0.736118
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.52976	−	7.84577i	0.203187	−	0.351931i
$498$		0			0
$499$	5.92421	−	10.2610i	0.265204	−	0.459347i	−0.702413	−	0.711770i	$-0.747894\pi$
$499$	5.92421	−	10.2610i	0.265204	−	0.459347i	0.967617	+	0.252423i	$0.0812274\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−11.0125	−	19.0742i	−0.491024	−	0.850478i	0.508923	−	0.860812i	$-0.330044\pi$
$503$	−11.0125	−	19.0742i	−0.491024	−	0.850478i	−0.999947	+	0.0103338i	$0.996711\pi$
$504$		0			0
$505$	−37.5433			−1.67065
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.16512	−	14.1424i	−0.361913	−	0.626851i	0.626363	−	0.779532i	$-0.284543\pi$
$509$	−8.16512	−	14.1424i	−0.361913	−	0.626851i	−0.988276	+	0.152680i	$0.951210\pi$
$510$		0			0
$511$	12.9425	−	22.4171i	0.572543	−	0.991674i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	34.6944	−	60.0925i	1.52882	−	2.64799i
$516$		0			0
$517$	9.51145	+	16.4743i	0.418313	+	0.724539i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−35.3180			−1.54731			−0.773655	−	0.633607i	$-0.781574\pi$
$521$	−35.3180			−1.54731			−0.773655	+	0.633607i	$0.781574\pi$
$522$		0			0
$523$	6.22971	+	10.7902i	0.272406	+	0.471821i	0.969477	−	0.245180i	$-0.0788472\pi$
$523$	6.22971	+	10.7902i	0.272406	+	0.471821i	−0.697071	+	0.717002i	$0.745514\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.46839	+	7.73947i	−0.194646	+	0.337137i
$528$		0			0
$529$	−11.9901	+	20.7675i	−0.521309	+	0.902934i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−14.4872			−0.627510
$534$		0			0
$535$	−21.2673	+	36.8361i	−0.919466	+	1.59256i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.41851			0.233392
$540$		0			0
$541$	11.6629	+	20.2007i	0.501427	+	0.868496i	0.999999	+	0.00164801i	$0.000524577\pi$
$541$	11.6629	+	20.2007i	0.501427	+	0.868496i	−0.498572	+	0.866848i	$0.666142\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.3700	+	23.1576i	0.572710	+	0.991962i
$546$		0			0
$547$	2.26581	+	3.92449i	0.0968789	+	0.167799i	0.910391	−	0.413749i	$-0.135781\pi$
$547$	2.26581	+	3.92449i	0.0968789	+	0.167799i	−0.813512	+	0.581548i	$0.802447\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.65723	+	10.7396i	0.198405	+	0.457524i
$552$		0			0
$553$	−13.3330	+	23.0935i	−0.566978	+	0.982034i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.05782	+	10.4924i	0.256678	+	0.444579i	0.965350	−	0.260959i	$-0.0840387\pi$
$557$	6.05782	+	10.4924i	0.256678	+	0.444579i	−0.708672	+	0.705538i	$0.750705\pi$
$558$		0			0
$559$	32.1837			1.36123
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.3553			−0.605003			−0.302502	−	0.953149i	$-0.597822\pi$
$563$	−14.3553			−0.605003			−0.302502	+	0.953149i	$0.597822\pi$
$564$		0			0
$565$	12.0827	−	20.9279i	0.508323	−	0.880442i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.69927			0.238926			0.119463	−	0.992839i	$-0.461883\pi$
$569$	5.69927			0.238926			0.119463	+	0.992839i	$0.461883\pi$
$570$		0			0
$571$	−3.20155			−0.133981			−0.0669904	−	0.997754i	$-0.521340\pi$
$571$	−3.20155			−0.133981			−0.0669904	+	0.997754i	$0.521340\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	35.4579	−	61.4150i	1.47870	−	2.56118i
$576$		0			0
$577$	18.4957			0.769985			0.384992	−	0.922920i	$-0.374204\pi$
$577$	18.4957			0.769985			0.384992	+	0.922920i	$0.374204\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9.05952			−0.375852
$582$		0			0
$583$	−9.43229	−	16.3372i	−0.390646	−	0.676618i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.7487	+	18.6173i	−0.443646	+	0.768417i	−0.997957	−	0.0638928i	$-0.979648\pi$
$587$	−10.7487	+	18.6173i	−0.443646	+	0.768417i	0.554311	+	0.832310i	$0.312982\pi$
$588$		0			0
$589$	−6.35869	−	0.730787i	−0.262005	−	0.0301116i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−23.2225	−	40.2225i	−0.953633	−	1.65174i	−0.737466	−	0.675384i	$-0.763978\pi$
$593$	−23.2225	−	40.2225i	−0.953633	−	1.65174i	−0.216167	−	0.976356i	$-0.569356\pi$
$594$		0			0
$595$	24.3553	+	42.1846i	0.998469	+	1.72940i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.23013	−	2.13064i	−0.0502617	−	0.0870557i	0.839800	−	0.542896i	$-0.182672\pi$
$599$	−1.23013	−	2.13064i	−0.0502617	−	0.0870557i	−0.890062	+	0.455840i	$0.849339\pi$
$600$		0			0
$601$	−43.4329			−1.77167			−0.885833	−	0.464004i	$-0.846412\pi$
$601$	−43.4329			−1.77167			−0.885833	+	0.464004i	$0.846412\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	14.3445	−	24.8455i	0.583189	−	1.01011i
$606$		0			0
$607$	14.2875			0.579911			0.289956	−	0.957040i	$-0.406359\pi$
$607$	14.2875			0.579911			0.289956	+	0.957040i	$0.406359\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	21.1327	−	36.6030i	0.854939	−	1.48080i
$612$		0			0
$613$	−5.03526	+	8.72133i	−0.203372	+	0.352251i	−0.949613	−	0.313425i	$-0.898524\pi$
$613$	−5.03526	+	8.72133i	−0.203372	+	0.352251i	0.746241	+	0.665676i	$0.231857\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.72579	+	4.72121i	0.109736	+	0.190069i	0.915663	−	0.401946i	$-0.131666\pi$
$617$	2.72579	+	4.72121i	0.109736	+	0.190069i	−0.805927	+	0.592015i	$0.798333\pi$
$618$		0			0
$619$	−1.48602			−0.0597282			−0.0298641	−	0.999554i	$-0.509507\pi$
$619$	−1.48602			−0.0597282			−0.0298641	+	0.999554i	$0.509507\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.08975	+	12.2798i	0.284045	+	0.491980i
$624$		0			0
$625$	−15.1574	+	26.2534i	−0.606295	+	1.05013i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−11.9798	+	20.7497i	−0.477667	+	0.827344i
$630$		0			0
$631$	8.28173	+	14.3444i	0.329691	+	0.571041i	0.982450	−	0.186524i	$-0.0597222\pi$
$631$	8.28173	+	14.3444i	0.329691	+	0.571041i	−0.652760	+	0.757565i	$0.726389\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	81.5575			3.23651
$636$		0			0
$637$	−6.01948	−	10.4260i	−0.238501	−	0.413095i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.598395	+	1.03645i	−0.0236352	+	0.0409373i	−0.877601	−	0.479392i	$-0.840857\pi$
$641$	−0.598395	+	1.03645i	−0.0236352	+	0.0409373i	0.853966	+	0.520329i	$0.174191\pi$
$642$		0			0
$643$	−5.91067	+	10.2376i	−0.233094	+	0.403731i	−0.958717	−	0.284362i	$-0.908218\pi$
$643$	−5.91067	+	10.2376i	−0.233094	+	0.403731i	0.725623	+	0.688092i	$0.241552\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−40.6540			−1.59827			−0.799136	−	0.601150i	$-0.794709\pi$
$647$	−40.6540			−1.59827			−0.799136	+	0.601150i	$0.794709\pi$
$648$		0			0
$649$	−3.09849	+	5.36674i	−0.121626	+	0.210663i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.4522			0.722091			0.361046	−	0.932548i	$-0.382420\pi$
$653$	18.4522			0.722091			0.361046	+	0.932548i	$0.382420\pi$
$654$		0			0
$655$	6.33736	+	10.9766i	0.247621	+	0.428892i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.9429	−	24.1499i	−0.543140	−	0.940746i	−0.998721	−	0.0505517i	$-0.983902\pi$
$659$	−13.9429	−	24.1499i	−0.543140	−	0.940746i	0.455582	−	0.890194i	$-0.349431\pi$
$660$		0			0
$661$	7.33736	+	12.7087i	0.285390	+	0.494310i	0.972704	−	0.232051i	$-0.0745435\pi$
$661$	7.33736	+	12.7087i	0.285390	+	0.494310i	−0.687314	+	0.726361i	$0.741210\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−20.7788	+	28.0236i	−0.805769	+	1.08671i
$666$		0			0
$667$	9.20361	−	15.9411i	0.356365	−	0.617242i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	9.02111	+	15.6250i	0.348256	+	0.603197i
$672$		0			0
$673$	−15.5272			−0.598531			−0.299265	−	0.954170i	$-0.596742\pi$
$673$	−15.5272			−0.598531			−0.299265	+	0.954170i	$0.596742\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.9734			0.421742			0.210871	−	0.977514i	$-0.432370\pi$
$677$	10.9734			0.421742			0.210871	+	0.977514i	$0.432370\pi$
$678$		0			0
$679$	−5.28548	+	9.15472i	−0.202838	+	0.351326i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−34.5032			−1.32023			−0.660115	−	0.751165i	$-0.729492\pi$
$683$	−34.5032			−1.32023			−0.660115	+	0.751165i	$0.729492\pi$
$684$		0			0
$685$	3.18090			0.121536
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−20.9569	+	36.2984i	−0.798393	+	1.38286i
$690$		0			0
$691$	−32.2359			−1.22631			−0.613157	−	0.789961i	$-0.710101\pi$
$691$	−32.2359			−1.22631			−0.613157	+	0.789961i	$0.710101\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	13.9245			0.528188
$696$		0			0
$697$	−10.3482	−	17.9236i	−0.391965	−	0.678903i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.4261	+	24.9867i	−0.544866	+	0.943735i	0.453750	+	0.891129i	$0.350086\pi$
$701$	−14.4261	+	24.9867i	−0.544866	+	0.943735i	−0.998615	+	0.0526059i	$0.983247\pi$
$702$		0			0
$703$	−17.0478	−	1.95925i	−0.642969	−	0.0738947i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−9.78996	−	16.9567i	−0.368189	−	0.637723i
$708$		0			0
$709$	15.5486	+	26.9310i	0.583940	+	1.01141i	0.995007	+	0.0998090i	$0.0318232\pi$
$709$	15.5486	+	26.9310i	0.583940	+	1.01141i	−0.411066	+	0.911606i	$0.634843\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.03232	+	8.71623i	0.188462	+	0.326425i
$714$		0			0
$715$	32.0003			1.19674
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7.78108	+	13.4772i	−0.290185	+	0.502615i	−0.973853	−	0.227178i	$-0.927050\pi$
$719$	−7.78108	+	13.4772i	−0.290185	+	0.502615i	0.683668	+	0.729793i	$0.260384\pi$
$720$		0			0
$721$	36.1883			1.34772
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.8927	+	24.0629i	−0.515962	+	0.893672i
$726$		0			0
$727$	−1.05762	+	1.83186i	−0.0392251	+	0.0679399i	−0.884971	−	0.465645i	$-0.845822\pi$
$727$	−1.05762	+	1.83186i	−0.0392251	+	0.0679399i	0.845746	+	0.533585i	$0.179156\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	22.9888	+	39.8178i	0.850271	+	1.47271i
$732$		0			0
$733$	−36.5909			−1.35152			−0.675759	−	0.737123i	$-0.736184\pi$
$733$	−36.5909			−1.35152			−0.675759	+	0.737123i	$0.736184\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.1274	−	17.5412i	−0.373047	−	0.646137i
$738$		0			0
$739$	−6.62533	+	11.4754i	−0.243717	+	0.422130i	−0.961770	−	0.273858i	$-0.911700\pi$
$739$	−6.62533	+	11.4754i	−0.243717	+	0.422130i	0.718053	+	0.695988i	$0.245033\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.63427	−	14.9550i	0.316761	−	0.548645i	−0.663050	−	0.748575i	$-0.730738\pi$
$743$	8.63427	−	14.9550i	0.316761	−	0.548645i	0.979810	+	0.199930i	$0.0640715\pi$
$744$		0			0
$745$	40.5241	+	70.1898i	1.48469	+	2.57156i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−22.1831			−0.810551
$750$		0			0
$751$	3.32703	+	5.76259i	0.121405	+	0.210280i	0.920322	−	0.391162i	$-0.127927\pi$
$751$	3.32703	+	5.76259i	0.121405	+	0.210280i	−0.798917	+	0.601441i	$0.794593\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.3782	+	57.8127i	−1.21476	+	2.10402i
$756$		0			0
$757$	22.7980	−	39.4873i	0.828607	−	1.43519i	−0.0705234	−	0.997510i	$-0.522467\pi$
$757$	22.7980	−	39.4873i	0.828607	−	1.43519i	0.899131	−	0.437680i	$-0.144200\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.47448			−0.162200			−0.0810998	−	0.996706i	$-0.525843\pi$
$761$	−4.47448			−0.162200			−0.0810998	+	0.996706i	$0.525843\pi$
$762$		0			0
$763$	−6.97287	+	12.0774i	−0.252435	+	0.437230i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.7686			0.497155
$768$		0			0
$769$	0.310132	+	0.537164i	0.0111836	+	0.0193706i	0.871563	−	0.490283i	$-0.163107\pi$
$769$	0.310132	+	0.537164i	0.0111836	+	0.0193706i	−0.860379	+	0.509654i	$0.829773\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.0219	+	26.0186i	0.540299	+	0.935825i	0.998887	+	0.0471762i	$0.0150222\pi$
$773$	15.0219	+	26.0186i	0.540299	+	0.935825i	−0.458588	+	0.888649i	$0.651644\pi$
$774$		0			0
$775$	−7.59620	−	13.1570i	−0.272864	−	0.472614i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.82860	−	11.9068i	0.316317	−	0.426604i
$780$		0			0
$781$	4.25124	−	7.36336i	0.152121	−	0.263482i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	37.7217	+	65.3359i	1.34635	+	2.33194i
$786$		0			0
$787$	−41.7810			−1.48933			−0.744666	−	0.667437i	$-0.767391\pi$
$787$	−41.7810			−1.48933			−0.744666	+	0.667437i	$0.767391\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.6030			0.448110
$792$		0			0
$793$	20.0433	−	34.7160i	0.711758	−	1.23280i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−24.9231			−0.882823			−0.441411	−	0.897305i	$-0.645522\pi$
$797$	−24.9231			−0.882823			−0.441411	+	0.897305i	$0.645522\pi$
$798$		0			0
$799$	60.3803			2.13610
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.1467	−	21.0388i	0.428649	−	0.742442i
$804$		0			0
$805$	54.8581			1.93349
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−20.5993			−0.724232			−0.362116	−	0.932133i	$-0.617945\pi$
$809$	−20.5993			−0.724232			−0.362116	+	0.932133i	$0.617945\pi$
$810$		0			0
$811$	14.2831	+	24.7390i	0.501547	+	0.868705i	0.999998	+	0.00178759i	$0.000569009\pi$
$811$	14.2831	+	24.7390i	0.501547	+	0.868705i	−0.498451	+	0.866918i	$0.666098\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.60119	+	4.50540i	−0.0911158	+	0.157817i
$816$		0			0
$817$	−19.6130	+	26.4513i	−0.686172	+	0.925413i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.18475	+	8.98026i	0.180949	+	0.313413i	0.942204	−	0.335040i	$-0.108750\pi$
$821$	5.18475	+	8.98026i	0.180949	+	0.313413i	−0.761255	+	0.648453i	$0.775416\pi$
$822$		0			0
$823$	−17.9457	−	31.0829i	−0.625549	−	1.08348i	−0.988434	−	0.151649i	$-0.951542\pi$
$823$	−17.9457	−	31.0829i	−0.625549	−	1.08348i	0.362885	−	0.931834i	$-0.381792\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.5782	−	39.1066i	−0.785122	−	1.35987i	−0.928926	−	0.370265i	$-0.879267\pi$
$827$	−22.5782	−	39.1066i	−0.785122	−	1.35987i	0.143804	−	0.989606i	$-0.454066\pi$
$828$		0			0
$829$	30.6047			1.06294			0.531472	−	0.847076i	$-0.321639\pi$
$829$	30.6047			1.06294			0.531472	+	0.847076i	$0.321639\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	8.59942	−	14.8946i	0.297952	−	0.516068i
$834$		0			0
$835$	−50.8510			−1.75977
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−10.0089	+	17.3359i	−0.345545	+	0.598502i	−0.985453	−	0.169950i	$-0.945639\pi$
$839$	−10.0089	+	17.3359i	−0.345545	+	0.598502i	0.639907	+	0.768452i	$0.278973\pi$
$840$		0			0
$841$	10.8940	−	18.8689i	0.375654	−	0.650651i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.0861	−	17.4697i	−0.346973	−	0.600975i
$846$		0			0
$847$	14.9622			0.514107
$848$		0			0
$849$		0			0
$850$		0			0
$851$	13.4917	+	23.3684i	0.462491	+	0.801058i
$852$		0			0
$853$	4.71715	−	8.17034i	0.161512	−	0.279747i	−0.773899	−	0.633309i	$-0.781696\pi$
$853$	4.71715	−	8.17034i	0.161512	−	0.279747i	0.935411	+	0.353562i	$0.115030\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.330247	+	0.572005i	−0.0112810	+	0.0195393i	−0.871611	−	0.490199i	$-0.836924\pi$
$857$	−0.330247	+	0.572005i	−0.0112810	+	0.0195393i	0.860330	+	0.509738i	$0.170258\pi$
$858$		0			0
$859$	5.34992	+	9.26634i	0.182537	+	0.316163i	0.942744	−	0.333518i	$-0.108236\pi$
$859$	5.34992	+	9.26634i	0.182537	+	0.316163i	−0.760207	+	0.649681i	$0.774902\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−52.3471			−1.78192			−0.890958	−	0.454086i	$-0.849966\pi$
$863$	−52.3471			−1.78192			−0.890958	+	0.454086i	$0.849966\pi$
$864$		0			0
$865$	9.76269	+	16.9095i	0.331941	+	0.574939i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.5132	+	21.6735i	−0.424482	+	0.735224i
$870$		0			0
$871$	−22.5013	+	38.9733i	−0.762426	+	1.32056i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−42.7896			−1.44655
$876$		0			0
$877$	27.5362	−	47.6942i	0.929833	−	1.61052i	0.146234	−	0.989250i	$-0.453285\pi$
$877$	27.5362	−	47.6942i	0.929833	−	1.61052i	0.783598	−	0.621268i	$-0.213382\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−59.0183			−1.98838			−0.994188	−	0.107660i	$-0.965664\pi$
$881$	−59.0183			−1.98838			−0.994188	+	0.107660i	$0.965664\pi$
$882$		0			0
$883$	−14.8835	−	25.7790i	−0.500871	−	0.867534i	−0.999999	−	0.00100591i	$-0.999680\pi$
$883$	−14.8835	−	25.7790i	−0.500871	−	0.867534i	0.499129	−	0.866528i	$-0.333654\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.74074	−	6.47915i	−0.125602	−	0.217549i	0.796366	−	0.604815i	$-0.206753\pi$
$887$	−3.74074	−	6.47915i	−0.125602	−	0.217549i	−0.921968	+	0.387266i	$0.873419\pi$
$888$		0			0
$889$	21.2673	+	36.8361i	0.713283	+	1.23544i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.2049	+	39.6748i	0.575741	+	1.32767i
$894$		0			0
$895$	32.5345	−	56.3514i	1.08751	−	1.88362i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.97170	−	3.41509i	−0.0657599	−	0.113899i
$900$		0			0
$901$	−59.8778			−1.99482
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−27.6087			−0.917743
$906$		0			0
$907$	18.0071	−	31.1892i	0.597916	−	1.03562i	−0.395212	−	0.918590i	$-0.629329\pi$
$907$	18.0071	−	31.1892i	0.597916	−	1.03562i	0.993128	−	0.117031i	$-0.0373378\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	41.2605			1.36702			0.683511	−	0.729941i	$-0.260452\pi$
$911$	41.2605			1.36702			0.683511	+	0.729941i	$0.260452\pi$
$912$		0			0
$913$	−8.50248			−0.281391
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.30512	+	5.72463i	−0.109145	+	0.189044i
$918$		0			0
$919$	−57.0889			−1.88319			−0.941595	−	0.336747i	$-0.890673\pi$
$919$	−57.0889			−1.88319			−0.941595	+	0.336747i	$0.890673\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−18.8910			−0.621805
$924$		0			0
$925$	−20.3656	−	35.2742i	−0.669616	−	1.15981i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.19418	−	12.4607i	0.236033	−	0.408822i	−0.723539	−	0.690283i	$-0.757486\pi$
$929$	7.19418	−	12.4607i	0.236033	−	0.408822i	0.959572	+	0.281462i	$0.0908192\pi$
$930$		0			0
$931$	12.2373	+	1.40640i	0.401062	+	0.0460929i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	22.8578	+	39.5908i	0.747529	+	1.29476i
$936$		0			0
$937$	1.78836	+	3.09753i	0.0584231	+	0.101192i	0.893758	−	0.448550i	$-0.148059\pi$
$937$	1.78836	+	3.09753i	0.0584231	+	0.101192i	−0.835335	+	0.549742i	$0.814726\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.70842	−	9.88728i	−0.186089	−	0.322316i	0.757854	−	0.652424i	$-0.226248\pi$
$941$	−5.70842	−	9.88728i	−0.186089	−	0.322316i	−0.943943	+	0.330108i	$0.892915\pi$
$942$		0			0
$943$	−23.3083			−0.759023
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.7671	+	25.5773i	−0.479865	+	0.831151i	−0.999733	−	0.0230954i	$-0.992648\pi$
$947$	−14.7671	+	25.5773i	−0.479865	+	0.831151i	0.519868	+	0.854247i	$0.325981\pi$
$948$		0			0
$949$	−53.9757			−1.75213
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.7483	−	25.5448i	0.477744	−	0.827477i	−0.521930	−	0.852988i	$-0.674788\pi$
$953$	14.7483	−	25.5448i	0.477744	−	0.827477i	0.999675	+	0.0255109i	$0.00812125\pi$
$954$		0			0
$955$	31.6699	−	54.8539i	1.02481	−	1.77503i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.829467	+	1.43668i	0.0267849	+	0.0463928i
$960$		0			0
$961$	−28.8438			−0.930446
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−32.6029	−	56.4699i	−1.04952	−	1.81783i
$966$		0			0
$967$	−18.0446	+	31.2541i	−0.580274	+	1.00506i	0.415172	+	0.909743i	$0.363721\pi$
$967$	−18.0446	+	31.2541i	−0.580274	+	1.00506i	−0.995447	+	0.0953215i	$0.969612\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.68637	−	6.38497i	0.118301	−	0.204904i	−0.800793	−	0.598941i	$-0.795589\pi$
$971$	3.68637	−	6.38497i	0.118301	−	0.204904i	0.919095	+	0.394037i	$0.128922\pi$
$972$		0			0
$973$	3.63103	+	6.28913i	0.116405	+	0.201620i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−33.9705			−1.08681			−0.543406	−	0.839470i	$-0.682866\pi$
$977$	−33.9705			−1.08681			−0.543406	+	0.839470i	$0.682866\pi$
$978$		0			0
$979$	6.65383	+	11.5248i	0.212657	+	0.368333i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.0857	−	38.2535i	0.704423	−	1.22010i	−0.262476	−	0.964938i	$-0.584539\pi$
$983$	22.0857	−	38.2535i	0.704423	−	1.22010i	0.966899	−	0.255158i	$-0.0821275\pi$
$984$		0			0
$985$	−18.0827	+	31.3202i	−0.576163	+	0.997944i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	51.7802			1.64651
$990$		0			0
$991$	7.70048	−	13.3376i	0.244614	−	0.423684i	−0.717409	−	0.696652i	$-0.754672\pi$
$991$	7.70048	−	13.3376i	0.244614	−	0.423684i	0.962023	+	0.272968i	$0.0880054\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	53.4363			1.69404
$996$		0			0
$997$	−27.3218	−	47.3228i	−0.865291	−	1.49873i	−0.866758	−	0.498728i	$-0.833800\pi$
$997$	−27.3218	−	47.3228i	−0.865291	−	1.49873i	0.00146761	−	0.999999i	$-0.499533\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.s.ba.1873.1		8
3.2	odd	2		2736.2.s.bc.1873.4		8
4.3	odd	2		1368.2.s.l.505.1	✓	8
12.11	even	2		1368.2.s.m.505.4	yes	8
19.7	even	3	inner	2736.2.s.ba.577.1		8
57.26	odd	6		2736.2.s.bc.577.4		8
76.7	odd	6		1368.2.s.l.577.1	yes	8
228.83	even	6		1368.2.s.m.577.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.s.l.505.1	✓	8	4.3	odd	2
1368.2.s.l.577.1	yes	8	76.7	odd	6
1368.2.s.m.505.4	yes	8	12.11	even	2
1368.2.s.m.577.4	yes	8	228.83	even	6
2736.2.s.ba.577.1		8	19.7	even	3	inner
2736.2.s.ba.1873.1		8	1.1	even	1	trivial
2736.2.s.bc.577.4		8	57.26	odd	6
2736.2.s.bc.1873.4		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.s (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.95872 + 3.39260i) q^{5} -2.04306 q^{7} +O(q^{10})\)	\(q+(-1.95872 + 3.39260i) q^{5} -2.04306 q^{7} -1.91744 q^{11} +(2.13010 + 3.68945i) q^{13} +(-3.04306 + 5.27073i) q^{17} +(-4.33039 - 0.497680i) q^{19} +(3.42711 + 5.93592i) q^{23} +(-5.17316 - 8.96018i) q^{25} +(-1.34277 - 2.32574i) q^{29} +1.46839 q^{31} +(4.00178 - 6.93128i) q^{35} +3.93677 q^{37} +(-1.70029 + 2.94499i) q^{41} +(3.77725 - 6.54239i) q^{43} +(-4.96050 - 8.59183i) q^{47} -2.82591 q^{49} +(4.91922 + 8.52033i) q^{53} +(3.75572 - 6.50510i) q^{55} +(1.61595 - 2.79891i) q^{59} +(-4.70477 - 8.14891i) q^{61} -16.6891 q^{65} +(5.28173 + 9.14823i) q^{67} +(-2.21715 + 3.84021i) q^{71} +(-6.33488 + 10.9723i) q^{73} +3.91744 q^{77} +(6.52601 - 11.3034i) q^{79} +4.43429 q^{83} +(-11.9210 - 20.6478i) q^{85} +(-3.47016 - 6.01050i) q^{89} +(-4.35192 - 7.53775i) q^{91} +(10.1705 - 13.7165i) q^{95} +(2.58704 - 4.48089i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 + 4 * q^7	\( 8 q - 4 q^{5} + 4 q^{7} + 8 q^{11} - 4 q^{17} - 8 q^{19} + 8 q^{23} - 4 q^{25} + 4 q^{31} + 16 q^{37} - 4 q^{41} + 6 q^{43} + 4 q^{47} - 16 q^{49} - 16 q^{53} + 16 q^{55} + 12 q^{59} - 8 q^{61} - 48 q^{65} - 2 q^{67} - 4 q^{71} - 4 q^{73} + 8 q^{77} + 22 q^{79} + 8 q^{83} - 8 q^{85} + 12 q^{89} + 2 q^{91} + 32 q^{95} + 24 q^{97}+O(q^{100}) \) 8 * q - 4 * q^5 + 4 * q^7 + 8 * q^11 - 4 * q^17 - 8 * q^19 + 8 * q^23 - 4 * q^25 + 4 * q^31 + 16 * q^37 - 4 * q^41 + 6 * q^43 + 4 * q^47 - 16 * q^49 - 16 * q^53 + 16 * q^55 + 12 * q^59 - 8 * q^61 - 48 * q^65 - 2 * q^67 - 4 * q^71 - 4 * q^73 + 8 * q^77 + 22 * q^79 + 8 * q^83 - 8 * q^85 + 12 * q^89 + 2 * q^91 + 32 * q^95 + 24 * q^97

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