LMFDB - Embedded newform 2736.2.bm.m.559.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(559,2736)]

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([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2736.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.31726512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 10x^{4} + 3x^{3} + 84x^{2} - 27x + 9 $ x^6 - x^5 + 10x^4 + 3x^3 + 84x^2 - 27x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.1
Root			$-1.35887 + 2.35363i$ of defining polynomial
Character	$\chi$	$=$	2736.559
Dual form			2736.2.bm.m.1855.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.85887 + 3.21966i) q^{5} -2.36936i q^{7} +O(q^{10})$	$q+(-1.85887 + 3.21966i) q^{5} -2.36936i q^{7} +4.10141i q^{11} +(3.00000 - 1.73205i) q^{13} +(3.91080 - 6.77370i) q^{17} +(4.35887 + 0.0157306i) q^{19} +(-2.05193 + 1.18468i) q^{23} +(-4.41080 - 7.63973i) q^{25} +(-2.57661 + 1.48761i) q^{29} -1.33162 q^{31} +(7.62854 + 4.40434i) q^{35} -2.97521i q^{37} +(-2.07918 - 1.20041i) q^{41} +(3.00000 + 1.73205i) q^{43} +(5.05193 - 2.91673i) q^{47} +1.38612 q^{49} +(6.00000 - 3.46410i) q^{53} +(-13.2052 - 7.62400i) q^{55} +(-2.44807 + 4.24018i) q^{59} +(-0.141129 - 0.244443i) q^{61} +12.8786i q^{65} +(3.26967 + 5.66323i) q^{67} +(-3.00000 + 5.19615i) q^{71} +(-0.306942 + 0.531638i) q^{73} +9.71774 q^{77} +(-5.71774 + 9.90342i) q^{79} -0.0314612i q^{83} +(14.5393 + 25.1829i) q^{85} +(14.7324 - 8.50575i) q^{89} +(-4.10386 - 7.10809i) q^{91} +(-8.15322 + 14.0048i) q^{95} +(12.6532 + 7.30534i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5}+O(q^{10}) $ 6 * q - 2 * q^5	$ 6 q - 2 q^{5} + 18 q^{13} + 2 q^{17} + 17 q^{19} - 5 q^{25} + 12 q^{29} + 4 q^{31} + 6 q^{35} - 3 q^{41} + 18 q^{43} + 18 q^{47} + 2 q^{49} + 36 q^{53} - 12 q^{55} - 27 q^{59} - 10 q^{61} - 11 q^{67} - 18 q^{71} - 5 q^{73} + 40 q^{77} - 16 q^{79} + 26 q^{85} + 24 q^{89} + 6 q^{95} + 21 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 + 18 * q^13 + 2 * q^17 + 17 * q^19 - 5 * q^25 + 12 * q^29 + 4 * q^31 + 6 * q^35 - 3 * q^41 + 18 * q^43 + 18 * q^47 + 2 * q^49 + 36 * q^53 - 12 * q^55 - 27 * q^59 - 10 * q^61 - 11 * q^67 - 18 * q^71 - 5 * q^73 + 40 * q^77 - 16 * q^79 + 26 * q^85 + 24 * q^89 + 6 * q^95 + 21 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

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
$5$	−1.85887	+	3.21966i	−0.831312	+	1.43987i	0.0656858	+	0.997840i	$0.479076\pi$
$5$	−1.85887	+	3.21966i	−0.831312	+	1.43987i	−0.896998	+	0.442035i	$0.854257\pi$
$6$		0			0
$7$		−	2.36936i		−	0.895535i	−0.894150	−	0.447768i	$-0.852219\pi$
$7$		−	2.36936i		−	0.895535i	0.894150	−	0.447768i	$-0.147781\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$			4.10141i			1.23662i	0.785933	+	0.618311i	$0.212183\pi$
$11$			4.10141i			1.23662i	−0.785933	+	0.618311i	$0.787817\pi$
$12$		0			0
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	−0.0225039	−	0.999747i	$-0.507164\pi$
$13$	3.00000	−	1.73205i	0.832050	−	0.480384i	0.854554	+	0.519362i	$0.173830\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.91080	−	6.77370i	0.948508	−	1.64286i	0.199938	−	0.979808i	$-0.435926\pi$
$17$	3.91080	−	6.77370i	0.948508	−	1.64286i	0.748570	−	0.663056i	$-0.230741\pi$
$18$		0			0
$19$	4.35887	+	0.0157306i	0.999993	+	0.00360885i
$19$	4.35887	+	0.0157306i	0.999993	+	0.00360885i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.05193	+	1.18468i	−0.427857	+	0.247023i	−0.698433	−	0.715675i	$-0.746119\pi$
$23$	−2.05193	+	1.18468i	−0.427857	+	0.247023i	0.270576	+	0.962699i	$0.412786\pi$
$24$		0			0
$25$	−4.41080	−	7.63973i	−0.882160	−	1.52795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.57661	+	1.48761i	−0.478465	+	0.276242i	−0.719776	−	0.694206i	$-0.755756\pi$
$29$	−2.57661	+	1.48761i	−0.478465	+	0.276242i	0.241312	+	0.970448i	$0.422422\pi$
$30$		0			0
$31$	−1.33162			−0.239167			−0.119583	−	0.992824i	$-0.538156\pi$
$31$	−1.33162			−0.239167			−0.119583	+	0.992824i	$0.538156\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.62854	+	4.40434i	1.28946	+	0.744469i
$36$		0			0
$37$		−	2.97521i		−	0.489122i	−0.969634	−	0.244561i	$-0.921356\pi$
$37$		−	2.97521i		−	0.489122i	0.969634	−	0.244561i	$-0.0786439\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.07918	−	1.20041i	−0.324713	−	0.187473i	0.328779	−	0.944407i	$-0.393363\pi$
$41$	−2.07918	−	1.20041i	−0.324713	−	0.187473i	−0.653491	+	0.756934i	$0.726696\pi$
$42$		0			0
$43$	3.00000	+	1.73205i	0.457496	+	0.264135i	0.710991	−	0.703201i	$-0.248247\pi$
$43$	3.00000	+	1.73205i	0.457496	+	0.264135i	−0.253495	+	0.967337i	$0.581580\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.05193	−	2.91673i	0.736900	−	0.425449i	−0.0840414	−	0.996462i	$-0.526783\pi$
$47$	5.05193	−	2.91673i	0.736900	−	0.425449i	0.820941	+	0.571013i	$0.193449\pi$
$48$		0			0
$49$	1.38612			0.198017
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000	−	3.46410i	0.824163	−	0.475831i	−0.0276867	−	0.999617i	$-0.508814\pi$
$53$	6.00000	−	3.46410i	0.824163	−	0.475831i	0.851850	+	0.523786i	$0.175481\pi$
$54$		0			0
$55$	−13.2052	−	7.62400i	−1.78058	−	1.02802i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.44807	+	4.24018i	−0.318712	+	0.552025i	−0.980220	−	0.197913i	$-0.936584\pi$
$59$	−2.44807	+	4.24018i	−0.318712	+	0.552025i	0.661508	+	0.749938i	$0.269917\pi$
$60$		0			0
$61$	−0.141129	−	0.244443i	−0.0180698	−	0.0312978i	0.856849	−	0.515567i	$-0.172419\pi$
$61$	−0.141129	−	0.244443i	−0.0180698	−	0.0312978i	−0.874919	+	0.484269i	$0.839085\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			12.8786i			1.59740i
$66$		0			0
$67$	3.26967	+	5.66323i	0.399454	+	0.691874i	0.993659	−	0.112440i	$-0.0358665\pi$
$67$	3.26967	+	5.66323i	0.399454	+	0.691874i	−0.594205	+	0.804314i	$0.702533\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	−0.306942	+	0.531638i	−0.0359248	+	0.0622236i	−0.883429	−	0.468565i	$-0.844771\pi$
$73$	−0.306942	+	0.531638i	−0.0359248	+	0.0622236i	0.847504	+	0.530789i	$0.178104\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.71774			1.10744
$78$		0			0
$79$	−5.71774	+	9.90342i	−0.643296	+	1.11422i	0.341396	+	0.939920i	$0.389100\pi$
$79$	−5.71774	+	9.90342i	−0.643296	+	1.11422i	−0.984692	+	0.174302i	$0.944233\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	0.0314612i		−	0.00345332i	−0.999999	−	0.00172666i	$-0.999450\pi$
$83$		−	0.0314612i		−	0.00345332i	0.999999	−	0.00172666i	$-0.000549613\pi$
$84$		0			0
$85$	14.5393	+	25.1829i	1.57701	+	2.73147i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	14.7324	−	8.50575i	1.56163	−	0.901608i	0.564539	−	0.825407i	$-0.309054\pi$
$89$	14.7324	−	8.50575i	1.56163	−	0.901608i	0.997092	−	0.0762015i	$-0.0242792\pi$
$90$		0			0
$91$	−4.10386	−	7.10809i	−0.430201	−	0.745130i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.15322	+	14.0048i	−0.836503	+	1.43687i
$96$		0			0
$97$	12.6532	+	7.30534i	1.28474	+	0.741745i	0.977711	−	0.209955i	$-0.0673318\pi$
$97$	12.6532	+	7.30534i	1.28474	+	0.741745i	0.307029	+	0.951700i	$0.400665\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.19049	+	8.99020i	0.516474	+	0.894558i	0.999817	+	0.0191276i	$0.00608889\pi$
$101$	5.19049	+	8.99020i	0.516474	+	0.894558i	−0.483344	+	0.875431i	$0.660578\pi$
$102$		0			0
$103$	13.6432			1.34430			0.672152	−	0.740413i	$-0.265370\pi$
$103$	13.6432			1.34430			0.672152	+	0.740413i	$0.265370\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.20772			0.793470			0.396735	−	0.917933i	$-0.370143\pi$
$107$	8.20772			0.793470			0.396735	+	0.917933i	$0.370143\pi$
$108$		0			0
$109$	11.1532	+	6.43932i	1.06829	+	0.616775i	0.927712	−	0.373296i	$-0.121772\pi$
$109$	11.1532	+	6.43932i	1.06829	+	0.616775i	0.140573	+	0.990070i	$0.455106\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	1.73205i		−	0.162938i	−0.996676	−	0.0814688i	$-0.974039\pi$
$113$		−	1.73205i		−	0.162938i	0.996676	−	0.0814688i	$-0.0259611\pi$
$114$		0			0
$115$		−	8.80868i		−	0.821414i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−16.0494	−	9.26611i	−1.47124	−	0.849422i
$120$		0			0
$121$	−5.82160			−0.529236
$122$		0			0
$123$		0			0
$124$		0			0
$125$	14.2077			1.27078
$126$		0			0
$127$	3.82160	+	6.61920i	0.339112	+	0.587359i	0.984266	−	0.176693i	$-0.0565401\pi$
$127$	3.82160	+	6.61920i	0.339112	+	0.587359i	−0.645154	+	0.764053i	$0.723207\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.18047	−	2.99095i	−0.452620	−	0.261320i	0.256316	−	0.966593i	$-0.417491\pi$
$131$	−5.18047	−	2.99095i	−0.452620	−	0.261320i	−0.708936	+	0.705273i	$0.750824\pi$
$132$		0			0
$133$	0.0372715	−	10.3277i	0.00323185	−	0.895529i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.21774	+	14.2335i	0.702089	+	1.21605i	0.967732	+	0.251982i	$0.0810825\pi$
$137$	8.21774	+	14.2335i	0.702089	+	1.21605i	−0.265643	+	0.964072i	$0.585584\pi$
$138$		0			0
$139$	−2.44807	+	1.41339i	−0.207643	+	0.119883i	−0.600215	−	0.799838i	$-0.704918\pi$
$139$	−2.44807	+	1.41339i	−0.207643	+	0.119883i	0.392573	+	0.919721i	$0.371585\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.10386	+	12.3042i	0.594054	+	1.02893i
$144$		0			0
$145$		−	11.0611i		−	0.918573i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.24499	−	3.88843i	0.183917	−	0.318553i	−0.759294	−	0.650747i	$-0.774456\pi$
$149$	2.24499	−	3.88843i	0.183917	−	0.318553i	0.943211	+	0.332195i	$0.107789\pi$
$150$		0			0
$151$	−23.1825			−1.88657			−0.943284	−	0.331987i	$-0.892281\pi$
$151$	−23.1825			−1.88657			−0.943284	+	0.331987i	$0.892281\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.47532	−	4.28738i	0.198822	−	0.344370i
$156$		0			0
$157$	1.38612	−	2.40082i	0.110624	−	0.191607i	−0.805398	−	0.592734i	$-0.798048\pi$
$157$	1.38612	−	2.40082i	0.110624	−	0.191607i	0.916022	+	0.401128i	$0.131382\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.80694	+	4.86177i	0.221218	+	0.383161i
$162$		0			0
$163$			22.6336i			1.77280i	0.462918	+	0.886401i	$0.346802\pi$
$163$			22.6336i			1.77280i	−0.462918	+	0.886401i	$0.653198\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.0494	−	17.4060i	−0.777643	−	1.34692i	−0.933297	−	0.359106i	$-0.883082\pi$
$167$	−10.0494	−	17.4060i	−0.777643	−	1.34692i	0.155654	−	0.987812i	$-0.450252\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−15.0000	−	8.66025i	−1.14043	−	0.658427i	−0.193892	−	0.981023i	$-0.562111\pi$
$173$	−15.0000	−	8.66025i	−1.14043	−	0.658427i	−0.946537	+	0.322596i	$0.895445\pi$
$174$		0			0
$175$	−18.1013	+	10.4508i	−1.36833	+	0.790005i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.9455			0.892849			0.446425	−	0.894821i	$-0.352697\pi$
$179$	11.9455			0.892849			0.446425	+	0.894821i	$0.352697\pi$
$180$		0			0
$181$	−12.7350	+	7.35253i	−0.946582	+	0.546510i	−0.892018	−	0.452001i	$-0.850710\pi$
$181$	−12.7350	+	7.35253i	−0.946582	+	0.546510i	−0.0545647	+	0.998510i	$0.517377\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	9.57918	+	5.53054i	0.704275	+	0.406613i
$186$		0			0
$187$	27.7818	+	16.0398i	2.03160	+	1.17295i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	2.54925i		−	0.184457i	−0.995738	−	0.0922287i	$-0.970601\pi$
$191$		−	2.54925i		−	0.184457i	0.995738	−	0.0922287i	$-0.0293991\pi$
$192$		0			0
$193$	−2.73240	−	1.57755i	−0.196682	−	0.113555i	0.398425	−	0.917201i	$-0.369557\pi$
$193$	−2.73240	−	1.57755i	−0.196682	−	0.113555i	−0.595107	+	0.803646i	$0.702890\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.92546			−0.422171			−0.211086	−	0.977468i	$-0.567700\pi$
$197$	−5.92546			−0.422171			−0.211086	+	0.977468i	$0.567700\pi$
$198$		0			0
$199$	22.3064	−	12.8786i	1.58126	−	0.912942i	0.586586	−	0.809887i	$-0.300471\pi$
$199$	22.3064	−	12.8786i	1.58126	−	0.912942i	0.994676	−	0.103055i	$-0.0328619\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.52468	+	6.10493i	0.247384	+	0.428482i
$204$		0			0
$205$	7.72984	−	4.46282i	0.539875	−	0.311697i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0645178	+	17.8775i	−0.00446279	+	1.23661i
$210$		0			0
$211$	9.24242	−	16.0083i	0.636275	−	1.10206i	−0.349969	−	0.936761i	$-0.613808\pi$
$211$	9.24242	−	16.0083i	0.636275	−	1.10206i	0.986244	−	0.165299i	$-0.0528588\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.1532	+	6.43932i	−0.760644	+	0.439158i
$216$		0			0
$217$			3.15510i			0.214182i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	27.0948i		−	1.82259i
$222$		0			0
$223$	−11.8735	+	20.5656i	−0.795110	+	1.37717i	0.127659	+	0.991818i	$0.459254\pi$
$223$	−11.8735	+	20.5656i	−0.795110	+	1.37717i	−0.922769	+	0.385353i	$0.874080\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.15322			−0.142914			−0.0714572	−	0.997444i	$-0.522765\pi$
$227$	−2.15322			−0.142914			−0.0714572	+	0.997444i	$0.522765\pi$
$228$		0			0
$229$	−5.43548			−0.359187			−0.179593	−	0.983741i	$-0.557478\pi$
$229$	−5.43548			−0.359187			−0.179593	+	0.983741i	$0.557478\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.74242	−	15.1423i	0.572735	−	0.992007i	−0.423548	−	0.905873i	$-0.639216\pi$
$233$	8.74242	−	15.1423i	0.572735	−	0.992007i	0.996284	−	0.0861330i	$-0.0274510\pi$
$234$		0			0
$235$			21.6873i			1.41472i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			21.0815i			1.36365i	0.731517	+	0.681823i	$0.238813\pi$
$239$			21.0815i			1.36365i	−0.731517	+	0.681823i	$0.761187\pi$
$240$		0			0
$241$	−6.07405	+	3.50685i	−0.391264	+	0.225896i	−0.682708	−	0.730692i	$-0.739198\pi$
$241$	−6.07405	+	3.50685i	−0.391264	+	0.225896i	0.291444	+	0.956588i	$0.405864\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.57661	+	4.46282i	−0.164614	+	0.285119i
$246$		0			0
$247$	13.1039	−	7.50259i	0.833779	−	0.477379i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.28433	+	5.36031i	−0.586022	+	0.338340i	−0.763523	−	0.645781i	$-0.776532\pi$
$251$	−9.28433	+	5.36031i	−0.586022	+	0.338340i	0.177501	+	0.984121i	$0.443199\pi$
$252$		0			0
$253$	−4.85887	−	8.41581i	−0.305475	−	0.529097i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	16.2324	−	9.37178i	1.01255	−	0.584596i	0.100612	−	0.994926i	$-0.467920\pi$
$257$	16.2324	−	9.37178i	1.01255	−	0.584596i	0.911937	+	0.410330i	$0.134587\pi$
$258$		0			0
$259$	−7.04937			−0.438026
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.94294	−	2.85381i	−0.304795	−	0.175973i	0.339800	−	0.940498i	$-0.389641\pi$
$263$	−4.94294	−	2.85381i	−0.304795	−	0.175973i	−0.644595	+	0.764524i	$0.722974\pi$
$264$		0			0
$265$			25.7573i			1.58226i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.4648	−	8.35125i	−0.881934	−	0.509185i	−0.0106386	−	0.999943i	$-0.503386\pi$
$269$	−14.4648	−	8.35125i	−0.881934	−	0.509185i	−0.871296	+	0.490758i	$0.836720\pi$
$270$		0			0
$271$	10.9974	+	6.34937i	0.668047	+	0.385697i	0.795336	−	0.606169i	$-0.207294\pi$
$271$	10.9974	+	6.34937i	0.668047	+	0.385697i	−0.127289	+	0.991866i	$0.540628\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	31.3337	−	18.0905i	1.88949	−	1.09090i
$276$		0			0
$277$	5.82673			0.350094			0.175047	−	0.984560i	$-0.443992\pi$
$277$	5.82673			0.350094			0.175047	+	0.984560i	$0.443992\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.76760	−	1.02053i	0.105446	−	0.0608794i	−0.446349	−	0.894859i	$-0.647276\pi$
$281$	1.76760	−	1.02053i	0.105446	−	0.0608794i	0.551796	+	0.833979i	$0.313943\pi$
$282$		0			0
$283$	−7.92339	−	4.57457i	−0.470997	−	0.271930i	0.245660	−	0.969356i	$-0.420995\pi$
$283$	−7.92339	−	4.57457i	−0.470997	−	0.271930i	−0.716657	+	0.697426i	$0.754329\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.84421	+	4.92632i	−0.167889	+	0.290792i
$288$		0			0
$289$	−22.0887	−	38.2588i	−1.29934	−	2.25052i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			11.2410i			0.656704i	0.944555	+	0.328352i	$0.106493\pi$
$293$			11.2410i			0.656704i	−0.944555	+	0.328352i	$0.893507\pi$
$294$		0			0
$295$	−9.10129	−	15.7639i	−0.529898	−	0.917810i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.10386	+	7.10809i	−0.237332	+	0.411071i
$300$		0			0
$301$	4.10386	−	7.10809i	0.236542	−	0.409704i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.04937			0.0600865
$306$		0			0
$307$	7.93805	−	13.7491i	0.453048	−	0.784702i	−0.545525	−	0.838094i	$-0.683670\pi$
$307$	7.93805	−	13.7491i	0.453048	−	0.784702i	0.998574	+	0.0533918i	$0.0170032\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			6.81124i			0.386230i	0.981176	+	0.193115i	$0.0618590\pi$
$311$			6.81124i			0.386230i	−0.981176	+	0.193115i	$0.938141\pi$
$312$		0			0
$313$	2.30694	+	3.99574i	0.130396	+	0.225853i	0.923829	−	0.382805i	$-0.125042\pi$
$313$	2.30694	+	3.99574i	0.130396	+	0.225853i	−0.793433	+	0.608657i	$0.791708\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.15835	−	0.668774i	0.0650594	−	0.0375621i	−0.467117	−	0.884195i	$-0.654707\pi$
$317$	1.15835	−	0.668774i	0.0650594	−	0.0375621i	0.532177	+	0.846633i	$0.321374\pi$
$318$		0			0
$319$	−6.10129	−	10.5678i	−0.341607	−	0.591681i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	17.1532	−	29.4642i	0.954431	−	1.63943i
$324$		0			0
$325$	−26.4648	−	15.2795i	−1.46800	−	0.847552i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.91080	−	11.9699i	−0.381005	−	0.659920i
$330$		0			0
$331$	−0.619010			−0.0340239			−0.0170119	−	0.999855i	$-0.505415\pi$
$331$	−0.619010			−0.0340239			−0.0170119	+	0.999855i	$0.505415\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−24.3116			−1.32828
$336$		0			0
$337$	5.65835	+	3.26685i	0.308230	+	0.177957i	0.646134	−	0.763224i	$-0.276385\pi$
$337$	5.65835	+	3.26685i	0.308230	+	0.177957i	−0.337904	+	0.941181i	$0.609718\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	5.46154i		−	0.295759i
$342$		0			0
$343$		−	19.8698i		−	1.07287i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.0661	+	11.0078i	1.02352	+	0.590930i	0.915122	−	0.403177i	$-0.132094\pi$
$347$	19.0661	+	11.0078i	1.02352	+	0.590930i	0.108399	+	0.994107i	$0.465427\pi$
$348$		0			0
$349$	12.3064			0.658749			0.329374	−	0.944199i	$-0.393162\pi$
$349$	12.3064			0.658749			0.329374	+	0.944199i	$0.393162\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−9.77223			−0.520124			−0.260062	−	0.965592i	$-0.583743\pi$
$353$	−9.77223			−0.520124			−0.260062	+	0.965592i	$0.583743\pi$
$354$		0			0
$355$	−11.1532	−	19.3179i	−0.591952	−	1.02529i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.79485	−	2.76831i	−0.253062	−	0.146106i	0.368103	−	0.929785i	$-0.380007\pi$
$359$	−4.79485	−	2.76831i	−0.253062	−	0.146106i	−0.621166	+	0.783679i	$0.713341\pi$
$360$		0			0
$361$	18.9995	+	0.137135i	0.999974	+	0.00721765i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.14113	−	1.97649i	−0.0597294	−	0.103454i
$366$		0			0
$367$	13.4622	−	7.77242i	0.702723	−	0.405717i	−0.105638	−	0.994405i	$-0.533688\pi$
$367$	13.4622	−	7.77242i	0.702723	−	0.405717i	0.808361	+	0.588687i	$0.200355\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.20772	−	14.2162i	−0.426123	−	0.738067i
$372$		0			0
$373$		−	17.6803i		−	0.915450i	−0.889094	−	0.457725i	$-0.848664\pi$
$373$		−	17.6803i		−	0.915450i	0.889094	−	0.457725i	$-0.151336\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.15322	+	8.92564i	−0.265405	+	0.459694i
$378$		0			0
$379$	16.3861			0.841698			0.420849	−	0.907131i	$-0.361732\pi$
$379$	16.3861			0.841698			0.420849	+	0.907131i	$0.361732\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.05193	−	13.9464i	0.411434	−	0.712625i	−0.583612	−	0.812032i	$-0.698361\pi$
$383$	8.05193	−	13.9464i	0.411434	−	0.712625i	0.995047	+	0.0994071i	$0.0316946\pi$
$384$		0			0
$385$	−18.0640	+	31.2878i	−0.920628	+	1.59457i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.82160	+	8.35125i	0.244465	+	0.423425i	0.961981	−	0.273116i	$-0.0880544\pi$
$389$	4.82160	+	8.35125i	0.244465	+	0.423425i	−0.717516	+	0.696542i	$0.754721\pi$
$390$		0			0
$391$			18.5322i			0.937214i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−21.2571	−	36.8183i	−1.06956	−	1.85253i
$396$		0			0
$397$	6.80438	−	11.7855i	0.341502	−	0.591499i	−0.643210	−	0.765690i	$-0.722398\pi$
$397$	6.80438	−	11.7855i	0.341502	−	0.591499i	0.984712	+	0.174191i	$0.0557311\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.9648	+	10.9493i	0.947057	+	0.546783i	0.892165	−	0.451709i	$-0.149185\pi$
$401$	18.9648	+	10.9493i	0.947057	+	0.546783i	0.0548914	+	0.998492i	$0.482519\pi$
$402$		0			0
$403$	−3.99487	+	2.30644i	−0.198999	+	0.114892i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.2026			0.604860
$408$		0			0
$409$	21.3856	−	12.3470i	1.05745	−	0.610520i	0.132725	−	0.991153i	$-0.457627\pi$
$409$	21.3856	−	12.3470i	1.05745	−	0.610520i	0.924726	+	0.380633i	$0.124294\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.0465	+	5.80037i	0.494358	+	0.285418i
$414$		0			0
$415$	0.101294	+	0.0584824i	0.00497235	+	0.00287079i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			3.69803i			0.180661i	0.995912	+	0.0903303i	$0.0287923\pi$
$419$			3.69803i			0.180661i	−0.995912	+	0.0903303i	$0.971208\pi$
$420$		0			0
$421$	−21.5715	−	12.4543i	−1.05133	−	0.606986i	−0.128308	−	0.991734i	$-0.540955\pi$
$421$	−21.5715	−	12.4543i	−1.05133	−	0.606986i	−0.923021	+	0.384749i	$0.874288\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−68.9990			−3.34694
$426$		0			0
$427$	−0.579175	+	0.334387i	−0.0280283	+	0.0161821i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.2077	+	19.4123i	0.539857	+	0.935059i	0.998911	+	0.0466511i	$0.0148549\pi$
$431$	11.2077	+	19.4123i	0.539857	+	0.935059i	−0.459055	+	0.888408i	$0.651812\pi$
$432$		0			0
$433$	29.8805	−	17.2515i	1.43596	−	0.829055i	0.438399	−	0.898781i	$-0.355546\pi$
$433$	29.8805	−	17.2515i	1.43596	−	0.829055i	0.997566	+	0.0697258i	$0.0222124\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.96273	+	5.13160i	−0.428745	+	0.245478i
$438$		0			0
$439$	3.38355	−	5.86049i	0.161488	−	0.279706i	−0.773914	−	0.633290i	$-0.781704\pi$
$439$	3.38355	−	5.86049i	0.161488	−	0.279706i	0.935403	+	0.353584i	$0.115037\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	27.1753	−	15.6897i	1.29114	−	0.745440i	0.312283	−	0.949989i	$-0.398906\pi$
$443$	27.1753	−	15.6897i	1.29114	−	0.745440i	0.978856	+	0.204549i	$0.0655729\pi$
$444$		0			0
$445$			63.2444i			2.99807i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	10.4778i		−	0.494478i	−0.968954	−	0.247239i	$-0.920477\pi$
$449$		−	10.4778i		−	0.494478i	0.968954	−	0.247239i	$-0.0795233\pi$
$450$		0			0
$451$	4.92339	−	8.52756i	0.231833	−	0.401547i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	30.5142			1.43053
$456$		0			0
$457$	−4.46480			−0.208854			−0.104427	−	0.994533i	$-0.533301\pi$
$457$	−4.46480			−0.208854			−0.104427	+	0.994533i	$0.533301\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.97482	−	17.2769i	0.464574	−	0.804665i	−0.534608	−	0.845100i	$-0.679541\pi$
$461$	9.97482	−	17.2769i	0.464574	−	0.804665i	0.999182	+	0.0404345i	$0.0128742\pi$
$462$		0			0
$463$			42.1000i			1.95655i	0.207304	+	0.978276i	$0.433531\pi$
$463$			42.1000i			1.95655i	−0.207304	+	0.978276i	$0.566469\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			13.5159i			0.625443i	0.949845	+	0.312722i	$0.101241\pi$
$467$			13.5159i			0.625443i	−0.949845	+	0.312722i	$0.898759\pi$
$468$		0			0
$469$	13.4183	−	7.74704i	0.619598	−	0.357725i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.10386	+	12.3042i	−0.326636	+	0.565750i
$474$		0			0
$475$	−19.1059	−	33.3700i	−0.876640	−	1.53112i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.10386	+	2.36936i	−0.187510	+	0.108259i	−0.590816	−	0.806806i	$-0.701194\pi$
$479$	−4.10386	+	2.36936i	−0.187510	+	0.108259i	0.403306	+	0.915065i	$0.367861\pi$
$480$		0			0
$481$	−5.15322	−	8.92564i	−0.234967	−	0.406974i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−47.0414	+	27.1594i	−2.13604	+	1.23324i
$486$		0			0
$487$	−25.8458			−1.17118			−0.585592	−	0.810606i	$-0.699138\pi$
$487$	−25.8458			−1.17118			−0.585592	+	0.810606i	$0.699138\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−26.2622	−	15.1625i	−1.18520	−	0.684274i	−0.227986	−	0.973664i	$-0.573214\pi$
$491$	−26.2622	−	15.1625i	−1.18520	−	0.684274i	−0.957211	+	0.289391i	$0.906547\pi$
$492$		0			0
$493$			23.2709i			1.04807i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.3116	+	7.10809i	0.552250	+	0.318841i
$498$		0			0
$499$	−28.5908	−	16.5069i	−1.27990	−	0.738950i	−0.303069	−	0.952969i	$-0.598011\pi$
$499$	−28.5908	−	16.5069i	−1.27990	−	0.738950i	−0.976830	+	0.214019i	$0.931345\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.5219	+	15.8897i	−1.22714	+	0.708489i	−0.966430	−	0.256929i	$-0.917289\pi$
$503$	−27.5219	+	15.8897i	−1.22714	+	0.708489i	−0.260708	+	0.965418i	$0.583956\pi$
$504$		0			0
$505$	−38.5938			−1.71740
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.3116	+	8.84014i	−0.678674	+	0.391832i	−0.799355	−	0.600859i	$-0.794825\pi$
$509$	−15.3116	+	8.84014i	−0.678674	+	0.391832i	0.120682	+	0.992691i	$0.461492\pi$
$510$		0			0
$511$	1.25964	+	0.727256i	0.0557234	+	0.0321719i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.3609	+	43.9264i	−1.11754	+	1.93563i
$516$		0			0
$517$	11.9627	+	20.7201i	0.526120	+	0.911267i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	7.68248i		−	0.336576i	−0.985738	−	0.168288i	$-0.946176\pi$
$521$		−	7.68248i		−	0.336576i	0.985738	−	0.168288i	$-0.0538238\pi$
$522$		0			0
$523$	−12.5938	−	21.8132i	−0.550690	−	0.953823i	−0.998225	−	0.0595564i	$-0.981031\pi$
$523$	−12.5938	−	21.8132i	−0.550690	−	0.953823i	0.447535	−	0.894266i	$-0.352302\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.20772	+	9.02003i	−0.226852	+	0.392919i
$528$		0			0
$529$	−8.69306	+	15.0568i	−0.377959	+	0.654644i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.31670			−0.360236
$534$		0			0
$535$	−15.2571	+	26.4260i	−0.659621	+	1.14250i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			5.68504i			0.244872i
$540$		0			0
$541$	−11.3861	−	19.7213i	−0.489527	−	0.847886i	0.510400	−	0.859937i	$-0.329497\pi$
$541$	−11.3861	−	19.7213i	−0.489527	−	0.847886i	−0.999927	+	0.0120508i	$0.996164\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−41.4648	+	23.9397i	−1.77616	+	1.02546i
$546$		0			0
$547$	−19.9255	−	34.5119i	−0.851951	−	1.47562i	−0.879445	−	0.476000i	$-0.842086\pi$
$547$	−19.9255	−	34.5119i	−0.851951	−	1.47562i	0.0274940	−	0.999622i	$-0.491247\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−11.2545	+	6.44376i	−0.479459	+	0.274513i
$552$		0			0
$553$	23.4648	+	13.5474i	0.997825	+	0.576094i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.8710	+	25.7573i	0.630103	+	1.09137i	0.987530	+	0.157429i	$0.0503207\pi$
$557$	14.8710	+	25.7573i	0.630103	+	1.09137i	−0.357427	+	0.933941i	$0.616346\pi$
$558$		0			0
$559$	12.0000			0.507546
$560$		0			0
$561$		0			0
$562$		0			0
$563$	24.0545			1.01378			0.506888	−	0.862012i	$-0.330796\pi$
$563$	24.0545			1.01378			0.506888	+	0.862012i	$0.330796\pi$
$564$		0			0
$565$	5.57661	+	3.21966i	0.234610	+	0.135452i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	14.6962i		−	0.616096i	−0.951371	−	0.308048i	$-0.900324\pi$
$569$		−	14.6962i		−	0.616096i	0.951371	−	0.308048i	$-0.0996758\pi$
$570$		0			0
$571$			34.1174i			1.42777i	0.700264	+	0.713884i	$0.253066\pi$
$571$			34.1174i			1.42777i	−0.700264	+	0.713884i	$0.746934\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	18.1013	+	10.4508i	0.754876	+	0.435828i
$576$		0			0
$577$	−15.5645			−0.647959			−0.323980	−	0.946064i	$-0.605021\pi$
$577$	−15.5645			−0.647959			−0.323980	+	0.946064i	$0.605021\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.0745431			−0.00309257
$582$		0			0
$583$	14.2077	+	24.6085i	0.588423	+	1.01918i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.25708	+	3.61253i	0.258257	+	0.149105i	0.623539	−	0.781792i	$-0.285694\pi$
$587$	6.25708	+	3.61253i	0.258257	+	0.149105i	−0.365282	+	0.930897i	$0.619027\pi$
$588$		0			0
$589$	−5.80438	−	0.0209473i	−0.239165	−	0.000863117i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−21.8463	−	37.8389i	−0.897119	−	1.55386i	−0.831160	−	0.556034i	$-0.812322\pi$
$593$	−21.8463	−	37.8389i	−0.897119	−	1.55386i	−0.0659596	−	0.997822i	$-0.521011\pi$
$594$		0			0
$595$	59.6674	−	34.4490i	2.44612	−	1.41227i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−14.3090	−	24.7839i	−0.584650	−	1.01264i	−0.994919	−	0.100679i	$-0.967898\pi$
$599$	−14.3090	−	24.7839i	−0.584650	−	1.01264i	0.410269	−	0.911965i	$-0.365435\pi$
$600$		0			0
$601$			14.1307i			0.576402i	0.957570	+	0.288201i	$0.0930572\pi$
$601$			14.1307i			0.576402i	−0.957570	+	0.288201i	$0.906943\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.8216	−	18.7436i	0.439961	−	0.762034i
$606$		0			0
$607$	0.876091			0.0355595			0.0177797	−	0.999842i	$-0.494340\pi$
$607$	0.876091			0.0355595			0.0177797	+	0.999842i	$0.494340\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	10.1039	−	17.5004i	0.408758	−	0.707990i
$612$		0			0
$613$	1.33162	−	2.30644i	0.0537838	−	0.0931563i	−0.837880	−	0.545854i	$-0.816205\pi$
$613$	1.33162	−	2.30644i	0.0537838	−	0.0931563i	0.891664	+	0.452698i	$0.149538\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.0645178	+	0.111748i	0.00259739	+	0.00449881i	0.867321	−	0.497749i	$-0.165840\pi$
$617$	0.0645178	+	0.111748i	0.00259739	+	0.00449881i	−0.864724	+	0.502248i	$0.832507\pi$
$618$		0			0
$619$			32.1304i			1.29143i	0.763579	+	0.645715i	$0.223440\pi$
$619$			32.1304i			1.29143i	−0.763579	+	0.645715i	$0.776560\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.1532	−	34.9064i	−0.807422	−	1.39850i
$624$		0			0
$625$	−4.35631	+	7.54535i	−0.174252	+	0.301814i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−20.1532	−	11.6355i	−0.803562	−	0.463937i
$630$		0			0
$631$	−7.05706	+	4.07439i	−0.280937	+	0.162199i	−0.633848	−	0.773458i	$-0.718525\pi$
$631$	−7.05706	+	4.07439i	−0.280937	+	0.162199i	0.352911	+	0.935657i	$0.385192\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−28.4154			−1.12763
$636$		0			0
$637$	4.15835	−	2.40082i	0.164760	−	0.0951241i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−24.6972	−	14.2589i	−0.975481	−	0.563194i	−0.0745779	−	0.997215i	$-0.523761\pi$
$641$	−24.6972	−	14.2589i	−0.975481	−	0.563194i	−0.900903	+	0.434021i	$0.857094\pi$
$642$		0			0
$643$	−23.2350	−	13.4147i	−0.916297	−	0.529025i	−0.0338455	−	0.999427i	$-0.510775\pi$
$643$	−23.2350	−	13.4147i	−0.916297	−	0.529025i	−0.882452	+	0.470402i	$0.844109\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			5.03558i			0.197969i	0.995089	+	0.0989845i	$0.0315594\pi$
$647$			5.03558i			0.197969i	−0.995089	+	0.0989845i	$0.968441\pi$
$648$		0			0
$649$	−17.3907	−	10.0406i	−0.682647	−	0.394126i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−25.1774			−0.985268			−0.492634	−	0.870237i	$-0.663966\pi$
$653$	−25.1774			−0.985268			−0.492634	+	0.870237i	$0.663966\pi$
$654$		0			0
$655$	19.2596	−	11.1196i	0.752537	−	0.434477i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.0987	+	24.4197i	0.549209	+	0.951257i	0.998329	+	0.0577859i	$0.0184041\pi$
$659$	14.0987	+	24.4197i	0.549209	+	0.951257i	−0.449120	+	0.893471i	$0.648263\pi$
$660$		0			0
$661$	33.1998	−	19.1679i	1.29132	−	0.745545i	0.312433	−	0.949940i	$-0.398856\pi$
$661$	33.1998	−	19.1679i	1.29132	−	0.745545i	0.978888	+	0.204395i	$0.0655228\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	33.1825	+	19.3179i	1.28676	+	0.749118i
$666$		0			0
$667$	3.52468	−	6.10493i	0.136476	−	0.236384i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.00256	−	0.578830i	0.0387035	−	0.0223455i
$672$		0			0
$673$		−	36.8183i		−	1.41924i	−0.704583	−	0.709621i	$-0.748866\pi$
$673$		−	36.8183i		−	1.41924i	0.704583	−	0.709621i	$-0.251134\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			9.24352i			0.355258i	0.984098	+	0.177629i	$0.0568426\pi$
$677$			9.24352i			0.355258i	−0.984098	+	0.177629i	$0.943157\pi$
$678$		0			0
$679$	17.3090	−	29.9801i	0.664259	−	1.15053i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.58457			0.290215			0.145108	−	0.989416i	$-0.453647\pi$
$683$	7.58457			0.290215			0.145108	+	0.989416i	$0.453647\pi$
$684$		0			0
$685$	−61.1029			−2.33462
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$		0			0
$691$			36.1496i			1.37519i	0.726092	+	0.687597i	$0.241334\pi$
$691$			36.1496i			1.37519i	−0.726092	+	0.687597i	$0.758666\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	10.5093i		−	0.398639i
$696$		0			0
$697$	−16.2625	+	9.38914i	−0.615985	+	0.355639i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.8044	−	18.7137i	0.408076	−	0.706808i	−0.586598	−	0.809878i	$-0.699533\pi$
$701$	10.8044	−	18.7137i	0.408076	−	0.706808i	0.994674	+	0.103070i	$0.0328666\pi$
$702$		0			0
$703$	0.0468020	−	12.9686i	0.00176517	−	0.489119i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	21.3011	−	12.2982i	0.801109	−	0.462520i
$708$		0			0
$709$	7.34885	+	12.7286i	0.275992	+	0.478032i	0.970385	−	0.241564i	$-0.0776604\pi$
$709$	7.34885	+	12.7286i	0.275992	+	0.478032i	−0.694393	+	0.719596i	$0.744327\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.73240	−	1.57755i	0.102329	−	0.0590798i
$714$		0			0
$715$	−52.8206			−1.97538
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.6674	+	11.9323i	0.770763	+	0.445000i	0.833147	−	0.553052i	$-0.186537\pi$
$719$	20.6674	+	11.9323i	0.770763	+	0.445000i	−0.0623834	+	0.998052i	$0.519870\pi$
$720$		0			0
$721$		−	32.3257i		−	1.20387i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	22.7298	+	13.1231i	0.844165	+	0.487379i
$726$		0			0
$727$	−19.8416	−	11.4556i	−0.735886	−	0.424864i	0.0846856	−	0.996408i	$-0.473011\pi$
$727$	−19.8416	−	11.4556i	−0.735886	−	0.424864i	−0.820572	+	0.571544i	$0.806345\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.4648	−	13.5474i	0.867877	−	0.501069i
$732$		0			0
$733$	−41.3106			−1.52584			−0.762921	−	0.646492i	$-0.776235\pi$
$733$	−41.3106			−1.52584			−0.762921	+	0.646492i	$0.776235\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−23.2273	+	13.4103i	−0.855588	+	0.493974i
$738$		0			0
$739$	19.6013	+	11.3168i	0.721045	+	0.416296i	0.815137	−	0.579268i	$-0.196661\pi$
$739$	19.6013	+	11.3168i	0.721045	+	0.416296i	−0.0940920	+	0.995564i	$0.529995\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.2545	−	29.8857i	0.633007	−	1.09640i	−0.353927	−	0.935273i	$-0.615154\pi$
$743$	17.2545	−	29.8857i	0.633007	−	1.09640i	0.986934	−	0.161127i	$-0.0515129\pi$
$744$		0			0
$745$	8.34628	+	14.4562i	0.305784	+	0.529634i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	19.4471i		−	0.710580i
$750$		0			0
$751$	9.28226	+	16.0773i	0.338714	+	0.586671i	0.984191	−	0.177109i	$-0.0566746\pi$
$751$	9.28226	+	16.0773i	0.338714	+	0.586671i	−0.645477	+	0.763780i	$0.723341\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	43.0933	−	74.6399i	1.56833	−	2.71642i
$756$		0			0
$757$	9.51003	−	16.4718i	0.345648	−	0.598679i	−0.639823	−	0.768522i	$-0.720993\pi$
$757$	9.51003	−	16.4718i	0.345648	−	0.598679i	0.985471	+	0.169842i	$0.0543259\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.6632			−0.567792			−0.283896	−	0.958855i	$-0.591627\pi$
$761$	−15.6632			−0.567792			−0.283896	+	0.958855i	$0.591627\pi$
$762$		0			0
$763$	15.2571	−	26.4260i	0.552343	−	0.956687i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			16.9607i			0.612417i
$768$		0			0
$769$	7.91080	+	13.7019i	0.285271	+	0.494103i	0.972675	−	0.232172i	$-0.0745832\pi$
$769$	7.91080	+	13.7019i	0.285271	+	0.494103i	−0.687404	+	0.726275i	$0.741250\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	38.1895	−	22.0487i	1.37358	−	0.793037i	0.382204	−	0.924078i	$-0.375165\pi$
$773$	38.1895	−	22.0487i	1.37358	−	0.793037i	0.991377	+	0.131041i	$0.0418318\pi$
$774$		0			0
$775$	5.87353	+	10.1732i	0.210983	+	0.365434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.04397	−	5.26515i	−0.324034	−	0.188644i
$780$		0			0
$781$	−21.3116	−	12.3042i	−0.762588	−	0.440280i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.15322	+	8.92564i	0.183926	+	0.318570i
$786$		0			0
$787$	2.60876			0.0929921			0.0464961	−	0.998918i	$-0.485195\pi$
$787$	2.60876			0.0929921			0.0464961	+	0.998918i	$0.485195\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.10386			−0.145916
$792$		0			0
$793$	−0.846777	−	0.488887i	−0.0300699	−	0.0173609i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			49.7059i			1.76067i	0.474351	+	0.880336i	$0.342683\pi$
$797$			49.7059i			1.76067i	−0.474351	+	0.880336i	$0.657317\pi$
$798$		0			0
$799$		−	45.6270i		−	1.61417i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.18047	−	1.25889i	−0.0769471	−	0.0444254i
$804$		0			0
$805$	−20.8710			−0.735605
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−51.1280			−1.79757			−0.898783	−	0.438393i	$-0.855548\pi$
$809$	−51.1280			−1.79757			−0.898783	+	0.438393i	$0.855548\pi$
$810$		0			0
$811$	−1.72287	−	2.98410i	−0.0604981	−	0.104786i	0.834190	−	0.551477i	$-0.185936\pi$
$811$	−1.72287	−	2.98410i	−0.0604981	−	0.104786i	−0.894688	+	0.446691i	$0.852602\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−72.8725	−	42.0730i	−2.55261	−	1.47375i
$816$		0			0
$817$	13.0494	+	7.59698i	0.456540	+	0.265785i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.59383	+	4.49265i	0.0905254	+	0.156795i	0.907732	−	0.419550i	$-0.137812\pi$
$821$	2.59383	+	4.49265i	0.0905254	+	0.156795i	−0.817207	+	0.576344i	$0.804479\pi$
$822$		0			0
$823$	−21.3661	+	12.3357i	−0.744774	+	0.429996i	−0.823803	−	0.566877i	$-0.808152\pi$
$823$	−21.3661	+	12.3357i	−0.744774	+	0.429996i	0.0790284	+	0.996872i	$0.474818\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.12598	−	8.87845i	−0.178248	−	0.308734i	0.763033	−	0.646360i	$-0.223709\pi$
$827$	−5.12598	−	8.87845i	−0.178248	−	0.308734i	−0.941280	+	0.337626i	$0.890376\pi$
$828$		0			0
$829$			43.7973i			1.52114i	0.649254	+	0.760572i	$0.275081\pi$
$829$			43.7973i			1.52114i	−0.649254	+	0.760572i	$0.724919\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.42082	−	9.38914i	0.187820	−	0.325315i
$834$		0			0
$835$	74.7219			2.58586
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.25964	+	12.5741i	−0.250631	+	0.434105i	−0.963700	−	0.266989i	$-0.913971\pi$
$839$	−7.25964	+	12.5741i	−0.250631	+	0.434105i	0.713069	+	0.701094i	$0.247305\pi$
$840$		0			0
$841$	−10.0740	+	17.4488i	−0.347381	+	0.601681i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.85887	−	3.21966i	−0.0639471	−	0.110760i
$846$		0			0
$847$			13.7935i			0.473950i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.52468	+	6.10493i	0.120825	+	0.209274i
$852$		0			0
$853$	11.3861	−	19.7213i	0.389853	−	0.675246i	−0.602576	−	0.798061i	$-0.705859\pi$
$853$	11.3861	−	19.7213i	0.389853	−	0.675246i	0.992429	+	0.122816i	$0.0391924\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.80645	−	1.62030i	−0.0958664	−	0.0553485i	0.451300	−	0.892372i	$-0.350960\pi$
$857$	−2.80645	−	1.62030i	−0.0958664	−	0.0553485i	−0.547167	+	0.837024i	$0.684294\pi$
$858$		0			0
$859$	15.4869	−	8.94138i	0.528407	−	0.305076i	−0.211961	−	0.977278i	$-0.567985\pi$
$859$	15.4869	−	8.94138i	0.528407	−	0.305076i	0.740367	+	0.672202i	$0.234652\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−27.9949			−0.952957			−0.476478	−	0.879186i	$-0.658087\pi$
$863$	−27.9949			−0.952957			−0.476478	+	0.879186i	$0.658087\pi$
$864$		0			0
$865$	55.7661	−	32.1966i	1.89610	−	1.09472i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−40.6180	−	23.4508i	−1.37787	−	0.795515i
$870$		0			0
$871$	19.6180	+	11.3265i	0.664731	+	0.383783i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		−	33.6632i		−	1.13803i
$876$		0			0
$877$	−37.1946	−	21.4743i	−1.25597	−	0.725137i	−0.283684	−	0.958918i	$-0.591557\pi$
$877$	−37.1946	−	21.4743i	−1.25597	−	0.725137i	−0.972289	+	0.233781i	$0.924890\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−10.9707			−0.369612			−0.184806	−	0.982775i	$-0.559166\pi$
$881$	−10.9707			−0.369612			−0.184806	+	0.982775i	$0.559166\pi$
$882$		0			0
$883$	25.2792	−	14.5950i	0.850713	−	0.491159i	−0.0101785	−	0.999948i	$-0.503240\pi$
$883$	25.2792	−	14.5950i	0.850713	−	0.491159i	0.860891	+	0.508789i	$0.169907\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.0494	−	22.6022i	−0.438155	−	0.758906i	0.559392	−	0.828903i	$-0.311034\pi$
$887$	−13.0494	−	22.6022i	−0.438155	−	0.758906i	−0.997547	+	0.0699966i	$0.977701\pi$
$888$		0			0
$889$	15.6833	−	9.05476i	0.526001	−	0.303687i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	22.0666	−	12.6342i	0.738430	−	0.422787i
$894$		0			0
$895$	−22.2052	+	38.4605i	−0.742236	+	1.28559i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.43108	−	1.98093i	0.114433	−	0.0660679i
$900$		0			0
$901$		−	54.1896i		−	1.80532i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	54.6696i		−	1.81728i
$906$		0			0
$907$	−10.8836	+	18.8509i	−0.361382	+	0.625933i	−0.988189	−	0.153242i	$-0.951028\pi$
$907$	−10.8836	+	18.8509i	−0.361382	+	0.625933i	0.626806	+	0.779175i	$0.284362\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	42.3116			1.40184			0.700922	−	0.713237i	$-0.252772\pi$
$911$	42.3116			1.40184			0.700922	+	0.713237i	$0.252772\pi$
$912$		0			0
$913$	0.129036			0.00427045
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.08664	+	12.2744i	−0.234021	+	0.405337i
$918$		0			0
$919$		−	28.3694i		−	0.935821i	−0.883776	−	0.467911i	$-0.845007\pi$
$919$		−	28.3694i		−	0.935821i	0.883776	−	0.467911i	$-0.154993\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			20.7846i			0.684134i
$924$		0			0
$925$	−22.7298	+	13.1231i	−0.747352	+	0.431484i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	22.4255	−	38.8420i	0.735755	−	1.27437i	−0.218636	−	0.975807i	$-0.570161\pi$
$929$	22.4255	−	38.8420i	0.735755	−	1.27437i	0.954391	−	0.298559i	$-0.0965060\pi$
$930$		0			0
$931$	6.04190	+	0.0218045i	0.198015	+	0.000714613i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−103.285	+	59.6319i	−3.37779	+	1.95017i
$936$		0			0
$937$	−10.3856	−	17.9884i	−0.339283	−	0.587656i	0.645015	−	0.764170i	$-0.276851\pi$
$937$	−10.3856	−	17.9884i	−0.339283	−	0.587656i	−0.984298	+	0.176514i	$0.943518\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.31157	−	1.91194i	0.107954	−	0.0623274i	−0.445051	−	0.895505i	$-0.646814\pi$
$941$	3.31157	−	1.91194i	0.107954	−	0.0623274i	0.553005	+	0.833178i	$0.313481\pi$
$942$		0			0
$943$	5.68843			0.185241
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.2571	−	17.4689i	−0.983223	−	0.567664i	−0.0799814	−	0.996796i	$-0.525486\pi$
$947$	−30.2571	−	17.4689i	−0.983223	−	0.567664i	−0.903242	+	0.429132i	$0.858819\pi$
$948$		0			0
$949$			2.12655i			0.0690309i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	10.2324	+	5.90768i	0.331460	+	0.191368i	0.656489	−	0.754336i	$-0.272041\pi$
$953$	10.2324	+	5.90768i	0.331460	+	0.191368i	−0.325029	+	0.945704i	$0.605374\pi$
$954$		0			0
$955$	8.20772	+	4.73873i	0.265595	+	0.153342i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	33.7244	−	19.4708i	1.08902	−	0.628745i
$960$		0			0
$961$	−29.2268			−0.942799
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.1584	−	5.86493i	0.327009	−	0.188799i
$966$		0			0
$967$	−25.2520	−	14.5792i	−0.812048	−	0.468836i	0.0356185	−	0.999365i	$-0.488660\pi$
$967$	−25.2520	−	14.5792i	−0.812048	−	0.468836i	−0.847667	+	0.530529i	$0.821993\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.49744	−	16.4500i	0.304787	−	0.527907i	−0.672427	−	0.740164i	$-0.734748\pi$
$971$	9.49744	−	16.4500i	0.304787	−	0.527907i	0.977214	+	0.212257i	$0.0680813\pi$
$972$		0			0
$973$	3.34885	+	5.80037i	0.107359	+	0.185951i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			26.1518i			0.836669i	0.908293	+	0.418335i	$0.137386\pi$
$977$			26.1518i			0.836669i	−0.908293	+	0.418335i	$0.862614\pi$
$978$		0			0
$979$	34.8856	+	60.4237i	1.11495	+	1.93115i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.3116	−	36.9127i	0.679734	−	1.17733i	−0.295327	−	0.955396i	$-0.595429\pi$
$983$	21.3116	−	36.9127i	0.679734	−	1.17733i	0.975061	−	0.221937i	$-0.0712380\pi$
$984$		0			0
$985$	11.0147	−	19.0779i	0.350956	−	0.607874i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.20772			−0.260990
$990$		0			0
$991$	8.46066	−	14.6543i	0.268762	−	0.465509i	−0.699781	−	0.714358i	$-0.746719\pi$
$991$	8.46066	−	14.6543i	0.268762	−	0.465509i	0.968542	+	0.248849i	$0.0800522\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			95.7588i			3.03576i
$996$		0			0
$997$	3.85374	+	6.67488i	0.122049	+	0.211396i	0.920576	−	0.390564i	$-0.127720\pi$
$997$	3.85374	+	6.67488i	0.122049	+	0.211396i	−0.798526	+	0.601960i	$0.794387\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.bm.m.559.1		6
3.2	odd	2		304.2.n.e.255.1	yes	6
4.3	odd	2		2736.2.bm.l.559.1		6
12.11	even	2		304.2.n.d.255.3	yes	6
19.12	odd	6		2736.2.bm.l.1855.1		6
24.5	odd	2		1216.2.n.d.255.3		6
24.11	even	2		1216.2.n.e.255.1		6
57.50	even	6		304.2.n.d.31.3	✓	6
76.31	even	6	inner	2736.2.bm.m.1855.1		6
228.107	odd	6		304.2.n.e.31.1	yes	6
456.107	odd	6		1216.2.n.d.639.3		6
456.221	even	6		1216.2.n.e.639.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.n.d.31.3	✓	6	57.50	even	6
304.2.n.d.255.3	yes	6	12.11	even	2
304.2.n.e.31.1	yes	6	228.107	odd	6
304.2.n.e.255.1	yes	6	3.2	odd	2
1216.2.n.d.255.3		6	24.5	odd	2
1216.2.n.d.639.3		6	456.107	odd	6
1216.2.n.e.255.1		6	24.11	even	2
1216.2.n.e.639.1		6	456.221	even	6
2736.2.bm.l.559.1		6	4.3	odd	2
2736.2.bm.l.1855.1		6	19.12	odd	6
2736.2.bm.m.559.1		6	1.1	even	1	trivial
2736.2.bm.m.1855.1		6	76.31	even	6	inner

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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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.85887 + 3.21966i) q^{5} -2.36936i q^{7} +O(q^{10})\)	\(q+(-1.85887 + 3.21966i) q^{5} -2.36936i q^{7} +4.10141i q^{11} +(3.00000 - 1.73205i) q^{13} +(3.91080 - 6.77370i) q^{17} +(4.35887 + 0.0157306i) q^{19} +(-2.05193 + 1.18468i) q^{23} +(-4.41080 - 7.63973i) q^{25} +(-2.57661 + 1.48761i) q^{29} -1.33162 q^{31} +(7.62854 + 4.40434i) q^{35} -2.97521i q^{37} +(-2.07918 - 1.20041i) q^{41} +(3.00000 + 1.73205i) q^{43} +(5.05193 - 2.91673i) q^{47} +1.38612 q^{49} +(6.00000 - 3.46410i) q^{53} +(-13.2052 - 7.62400i) q^{55} +(-2.44807 + 4.24018i) q^{59} +(-0.141129 - 0.244443i) q^{61} +12.8786i q^{65} +(3.26967 + 5.66323i) q^{67} +(-3.00000 + 5.19615i) q^{71} +(-0.306942 + 0.531638i) q^{73} +9.71774 q^{77} +(-5.71774 + 9.90342i) q^{79} -0.0314612i q^{83} +(14.5393 + 25.1829i) q^{85} +(14.7324 - 8.50575i) q^{89} +(-4.10386 - 7.10809i) q^{91} +(-8.15322 + 14.0048i) q^{95} +(12.6532 + 7.30534i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5}+O(q^{10}) \) 6 * q - 2 * q^5	\( 6 q - 2 q^{5} + 18 q^{13} + 2 q^{17} + 17 q^{19} - 5 q^{25} + 12 q^{29} + 4 q^{31} + 6 q^{35} - 3 q^{41} + 18 q^{43} + 18 q^{47} + 2 q^{49} + 36 q^{53} - 12 q^{55} - 27 q^{59} - 10 q^{61} - 11 q^{67} - 18 q^{71} - 5 q^{73} + 40 q^{77} - 16 q^{79} + 26 q^{85} + 24 q^{89} + 6 q^{95} + 21 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 + 18 * q^13 + 2 * q^17 + 17 * q^19 - 5 * q^25 + 12 * q^29 + 4 * q^31 + 6 * q^35 - 3 * q^41 + 18 * q^43 + 18 * q^47 + 2 * q^49 + 36 * q^53 - 12 * q^55 - 27 * q^59 - 10 * q^61 - 11 * q^67 - 18 * q^71 - 5 * q^73 + 40 * q^77 - 16 * q^79 + 26 * q^85 + 24 * q^89 + 6 * q^95 + 21 * q^97

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