LMFDB - Embedded newform 864.2.s.a.287.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(287,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("864.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.s (of order $6$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			287.7
Character	$\chi$	$=$	864.287
Dual form			864.2.s.a.575.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.398132 + 0.229862i) q^{5} +(-4.28309 + 2.47284i) q^{7} +O(q^{10})$	$q+(0.398132 + 0.229862i) q^{5} +(-4.28309 + 2.47284i) q^{7} +(-1.17474 - 2.03471i) q^{11} +(-0.0384586 + 0.0666122i) q^{13} -5.92857i q^{17} -3.59561i q^{19} +(2.41469 - 4.18237i) q^{23} +(-2.39433 - 4.14710i) q^{25} +(6.54954 - 3.78138i) q^{29} +(-0.663421 - 0.383026i) q^{31} -2.27365 q^{35} -5.47993 q^{37} +(0.986492 + 0.569551i) q^{41} +(-6.79101 + 3.92079i) q^{43} +(-3.01076 - 5.21479i) q^{47} +(8.72990 - 15.1206i) q^{49} +9.71390i q^{53} -1.08011i q^{55} +(-4.15776 + 7.20145i) q^{59} +(2.63407 + 4.56234i) q^{61} +(-0.0306232 + 0.0176803i) q^{65} +(1.84450 + 1.06492i) q^{67} -10.6650 q^{71} -7.51416 q^{73} +(10.0630 + 5.80990i) q^{77} +(2.52870 - 1.45994i) q^{79} +(-4.44322 - 7.69588i) q^{83} +(1.36275 - 2.36035i) q^{85} -9.71390i q^{89} -0.380408i q^{91} +(0.826493 - 1.43153i) q^{95} +(3.16305 + 5.47856i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) $ 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.398132	+	0.229862i	0.178050	+	0.102797i	0.586376	−	0.810039i	$-0.300554\pi$
$5$	0.398132	+	0.229862i	0.178050	+	0.102797i	−0.408326	+	0.912836i	$0.633887\pi$
$6$		0			0
$7$	−4.28309	+	2.47284i	−1.61886	+	0.934647i	−0.631638	+	0.775263i	$0.717617\pi$
$7$	−4.28309	+	2.47284i	−1.61886	+	0.934647i	−0.987217	+	0.159383i	$0.949049\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.17474	−	2.03471i	−0.354198	−	0.613489i	0.632782	−	0.774330i	$-0.281913\pi$
$11$	−1.17474	−	2.03471i	−0.354198	−	0.613489i	−0.986980	+	0.160841i	$0.948579\pi$
$12$		0			0
$13$	−0.0384586	+	0.0666122i	−0.0106665	+	0.0184749i	−0.871309	−	0.490734i	$-0.836729\pi$
$13$	−0.0384586	+	0.0666122i	−0.0106665	+	0.0184749i	0.860643	+	0.509209i	$0.170062\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	5.92857i		−	1.43789i	−0.695068	−	0.718944i	$-0.744626\pi$
$17$		−	5.92857i		−	1.43789i	0.695068	−	0.718944i	$-0.255374\pi$
$18$		0			0
$19$		−	3.59561i		−	0.824889i	−0.910983	−	0.412444i	$-0.864675\pi$
$19$		−	3.59561i		−	0.824889i	0.910983	−	0.412444i	$-0.135325\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.41469	−	4.18237i	0.503498	−	0.872084i	−0.496494	−	0.868040i	$-0.665379\pi$
$23$	2.41469	−	4.18237i	0.503498	−	0.872084i	0.999992	−	0.00404388i	$-0.00128721\pi$
$24$		0			0
$25$	−2.39433	−	4.14710i	−0.478865	−	0.829419i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.54954	−	3.78138i	1.21622	−	0.702184i	0.252112	−	0.967698i	$-0.418875\pi$
$29$	6.54954	−	3.78138i	1.21622	−	0.702184i	0.964107	+	0.265514i	$0.0855416\pi$
$30$		0			0
$31$	−0.663421	−	0.383026i	−0.119154	−	0.0687935i	0.439238	−	0.898370i	$-0.355248\pi$
$31$	−0.663421	−	0.383026i	−0.119154	−	0.0687935i	−0.558392	+	0.829577i	$0.688582\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.27365			−0.384317
$36$		0			0
$37$	−5.47993			−0.900894			−0.450447	−	0.892803i	$-0.648735\pi$
$37$	−5.47993			−0.900894			−0.450447	+	0.892803i	$0.648735\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.986492	+	0.569551i	0.154064	+	0.0889490i	0.575050	−	0.818118i	$-0.304983\pi$
$41$	0.986492	+	0.569551i	0.154064	+	0.0889490i	−0.420986	+	0.907067i	$0.638316\pi$
$42$		0			0
$43$	−6.79101	+	3.92079i	−1.03562	+	0.597915i	−0.918590	−	0.395213i	$-0.870671\pi$
$43$	−6.79101	+	3.92079i	−1.03562	+	0.597915i	−0.117030	+	0.993128i	$0.537337\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.01076	−	5.21479i	−0.439165	−	0.760656i	0.558461	−	0.829531i	$-0.311392\pi$
$47$	−3.01076	−	5.21479i	−0.439165	−	0.760656i	−0.997625	+	0.0688755i	$0.978059\pi$
$48$		0			0
$49$	8.72990	−	15.1206i	1.24713	−	2.16009i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			9.71390i			1.33431i	0.744920	+	0.667154i	$0.232488\pi$
$53$			9.71390i			1.33431i	−0.744920	+	0.667154i	$0.767512\pi$
$54$		0			0
$55$		−	1.08011i		−	0.145642i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.15776	+	7.20145i	−0.541294	+	0.937548i	0.457536	+	0.889191i	$0.348732\pi$
$59$	−4.15776	+	7.20145i	−0.541294	+	0.937548i	−0.998830	+	0.0483574i	$0.984601\pi$
$60$		0			0
$61$	2.63407	+	4.56234i	0.337258	+	0.584147i	0.983916	−	0.178633i	$-0.0571674\pi$
$61$	2.63407	+	4.56234i	0.337258	+	0.584147i	−0.646658	+	0.762780i	$0.723834\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0306232	+	0.0176803i	−0.00379834	+	0.00219297i
$66$		0			0
$67$	1.84450	+	1.06492i	0.225342	+	0.130101i	0.608421	−	0.793614i	$-0.291803\pi$
$67$	1.84450	+	1.06492i	0.225342	+	0.130101i	−0.383079	+	0.923715i	$0.625136\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−10.6650			−1.26570			−0.632851	−	0.774273i	$-0.718115\pi$
$71$	−10.6650			−1.26570			−0.632851	+	0.774273i	$0.718115\pi$
$72$		0			0
$73$	−7.51416			−0.879466			−0.439733	−	0.898129i	$-0.644927\pi$
$73$	−7.51416			−0.879466			−0.439733	+	0.898129i	$0.644927\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.0630	+	5.80990i	1.14679	+	0.662100i
$78$		0			0
$79$	2.52870	−	1.45994i	0.284501	−	0.164256i	−0.350959	−	0.936391i	$-0.614144\pi$
$79$	2.52870	−	1.45994i	0.284501	−	0.164256i	0.635459	+	0.772135i	$0.280811\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.44322	−	7.69588i	−0.487706	−	0.844732i	0.512194	−	0.858870i	$-0.328833\pi$
$83$	−4.44322	−	7.69588i	−0.487706	−	0.844732i	−0.999900	+	0.0141378i	$0.995500\pi$
$84$		0			0
$85$	1.36275	−	2.36035i	0.147811	−	0.256016i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	9.71390i		−	1.02967i	−0.857289	−	0.514836i	$-0.827853\pi$
$89$		−	9.71390i		−	1.02967i	0.857289	−	0.514836i	$-0.172147\pi$
$90$		0			0
$91$		−	0.380408i		−	0.0398776i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.826493	−	1.43153i	0.0847964	−	0.146872i
$96$		0			0
$97$	3.16305	+	5.47856i	0.321159	+	0.556263i	0.980727	−	0.195381i	$-0.0625944\pi$
$97$	3.16305	+	5.47856i	0.321159	+	0.556263i	−0.659569	+	0.751644i	$0.729261\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.50085	+	2.59857i	−0.447851	+	0.258567i	−0.706922	−	0.707291i	$-0.749917\pi$
$101$	−4.50085	+	2.59857i	−0.447851	+	0.258567i	0.259071	+	0.965858i	$0.416584\pi$
$102$		0			0
$103$	2.41781	+	1.39593i	0.238234	+	0.137545i	0.614365	−	0.789022i	$-0.289412\pi$
$103$	2.41781	+	1.39593i	0.238234	+	0.137545i	−0.376131	+	0.926567i	$0.622746\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.5911			1.41057			0.705286	−	0.708923i	$-0.250819\pi$
$107$	14.5911			1.41057			0.705286	+	0.708923i	$0.250819\pi$
$108$		0			0
$109$	−12.6711			−1.21368			−0.606838	−	0.794826i	$-0.707562\pi$
$109$	−12.6711			−1.21368			−0.606838	+	0.794826i	$0.707562\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−16.5820	−	9.57360i	−1.55990	−	0.900608i	−0.997265	−	0.0739025i	$-0.976455\pi$
$113$	−16.5820	−	9.57360i	−1.55990	−	0.900608i	−0.562634	−	0.826706i	$-0.690212\pi$
$114$		0			0
$115$	1.92273	−	1.11009i	0.179296	−	0.103517i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.6604	+	25.3926i	1.34392	+	2.32773i
$120$		0			0
$121$	2.73996	−	4.74576i	0.249088	−	0.431432i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	4.50008i		−	0.402499i
$126$		0			0
$127$		−	11.2364i		−	0.997071i	−0.866869	−	0.498535i	$-0.833871\pi$
$127$		−	11.2364i		−	0.997071i	0.866869	−	0.498535i	$-0.166129\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.54434	−	13.0672i	0.659152	−	1.14168i	−0.321684	−	0.946847i	$-0.604249\pi$
$131$	7.54434	−	13.0672i	0.659152	−	1.14168i	0.980836	−	0.194837i	$-0.0624178\pi$
$132$		0			0
$133$	8.89137	+	15.4003i	0.770979	+	1.33538i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.11622	−	1.79915i	0.266237	−	0.153712i	−0.360939	−	0.932589i	$-0.617544\pi$
$137$	3.11622	−	1.79915i	0.266237	−	0.153712i	0.627176	+	0.778877i	$0.284211\pi$
$138$		0			0
$139$	6.13766	+	3.54358i	0.520590	+	0.300563i	0.737176	−	0.675701i	$-0.236159\pi$
$139$	6.13766	+	3.54358i	0.520590	+	0.300563i	−0.216586	+	0.976264i	$0.569492\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.180716			0.0151122
$144$		0			0
$145$	3.47678			0.288731
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.985645	−	0.569062i	−0.0807472	−	0.0466194i	0.459083	−	0.888393i	$-0.348178\pi$
$149$	−0.985645	−	0.569062i	−0.0807472	−	0.0466194i	−0.539830	+	0.841774i	$0.681511\pi$
$150$		0			0
$151$	−9.68181	+	5.58979i	−0.787894	+	0.454891i	−0.839221	−	0.543791i	$-0.816988\pi$
$151$	−9.68181	+	5.58979i	−0.787894	+	0.454891i	0.0513265	+	0.998682i	$0.483655\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.176086	−	0.304990i	−0.0141436	−	0.0244974i
$156$		0			0
$157$	−8.18986	+	14.1853i	−0.653622	+	1.13211i	0.328615	+	0.944464i	$0.393418\pi$
$157$	−8.18986	+	14.1853i	−0.653622	+	1.13211i	−0.982237	+	0.187643i	$0.939915\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			23.8846i			1.88237i
$162$		0			0
$163$		−	4.04520i		−	0.316845i	−0.987371	−	0.158422i	$-0.949359\pi$
$163$		−	4.04520i		−	0.316845i	0.987371	−	0.158422i	$-0.0506408\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.58072	+	2.73790i	−0.122320	+	0.211865i	−0.920682	−	0.390313i	$-0.872367\pi$
$167$	−1.58072	+	2.73790i	−0.122320	+	0.211865i	0.798362	+	0.602178i	$0.205700\pi$
$168$		0			0
$169$	6.49704	+	11.2532i	0.499772	+	0.865631i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.4056	+	10.0491i	−1.32333	+	0.764022i	−0.984258	−	0.176739i	$-0.943445\pi$
$173$	−17.4056	+	10.0491i	−1.32333	+	0.764022i	−0.339068	+	0.940762i	$0.610112\pi$
$174$		0			0
$175$	20.5102	+	11.8416i	1.55043	+	0.895140i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.1699			0.760135			0.380067	−	0.924959i	$-0.375901\pi$
$179$	10.1699			0.760135			0.380067	+	0.924959i	$0.375901\pi$
$180$		0			0
$181$	15.0572			1.11920			0.559598	−	0.828764i	$-0.310956\pi$
$181$	15.0572			1.11920			0.559598	+	0.828764i	$0.310956\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.18174	−	1.25963i	−0.160404	−	0.0926095i
$186$		0			0
$187$	−12.0629	+	6.96454i	−0.882129	+	0.509297i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.41193	−	2.44554i	−0.102164	−	0.176953i	0.810412	−	0.585860i	$-0.199243\pi$
$191$	−1.41193	−	2.44554i	−0.102164	−	0.176953i	−0.912576	+	0.408907i	$0.865910\pi$
$192$		0			0
$193$	−8.95170	+	15.5048i	−0.644357	+	1.11606i	0.340092	+	0.940392i	$0.389542\pi$
$193$	−8.95170	+	15.5048i	−0.644357	+	1.11606i	−0.984450	+	0.175668i	$0.943792\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$		−	6.78022i		−	0.480637i	−0.970694	−	0.240319i	$-0.922748\pi$
$199$		−	6.78022i		−	0.480637i	0.970694	−	0.240319i	$-0.0772519\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.7015	+	32.3919i	−1.31259	+	2.27347i
$204$		0			0
$205$	0.261836	+	0.453514i	0.0182874	+	0.0316748i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.31603	+	4.22391i	−0.506060	+	0.292174i
$210$		0			0
$211$	14.2250	+	8.21281i	0.979289	+	0.565393i	0.902055	−	0.431620i	$-0.142058\pi$
$211$	14.2250	+	8.21281i	0.979289	+	0.565393i	0.0772337	+	0.997013i	$0.475391\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.60496			−0.245856
$216$		0			0
$217$	3.78865			0.257191
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.394915	+	0.228004i	0.0265649	+	0.0153372i
$222$		0			0
$223$	13.5026	−	7.79574i	0.904202	−	0.522041i	0.0256409	−	0.999671i	$-0.491837\pi$
$223$	13.5026	−	7.79574i	0.904202	−	0.522041i	0.878561	+	0.477630i	$0.158504\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.25723	+	3.90964i	0.149818	+	0.259492i	0.931160	−	0.364611i	$-0.118798\pi$
$227$	2.25723	+	3.90964i	0.149818	+	0.259492i	−0.781342	+	0.624103i	$0.785465\pi$
$228$		0			0
$229$	2.77842	−	4.81237i	0.183603	−	0.318010i	−0.759502	−	0.650505i	$-0.774557\pi$
$229$	2.77842	−	4.81237i	0.183603	−	0.318010i	0.943105	+	0.332495i	$0.107890\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	1.32613i		−	0.0868780i	−0.999056	−	0.0434390i	$-0.986169\pi$
$233$		−	1.32613i		−	0.0868780i	0.999056	−	0.0434390i	$-0.0138314\pi$
$234$		0			0
$235$		−	2.76824i		−	0.180580i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.1286	−	21.0073i	0.784534	−	1.35885i	−0.144744	−	0.989469i	$-0.546236\pi$
$239$	12.1286	−	21.0073i	0.784534	−	1.35885i	0.929277	−	0.369383i	$-0.120431\pi$
$240$		0			0
$241$	−3.00711	−	5.20846i	−0.193705	−	0.335507i	0.752770	−	0.658283i	$-0.228717\pi$
$241$	−3.00711	−	5.20846i	−0.193705	−	0.335507i	−0.946475	+	0.322777i	$0.895384\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.95131	−	4.01334i	0.444103	−	0.256403i
$246$		0			0
$247$	0.239511	+	0.138282i	0.0152397	+	0.00879867i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.7656			0.805760			0.402880	−	0.915253i	$-0.368009\pi$
$251$	12.7656			0.805760			0.402880	+	0.915253i	$0.368009\pi$
$252$		0			0
$253$	−11.3466			−0.713352
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.4638	+	6.61864i	0.715094	+	0.412860i	0.812944	−	0.582342i	$-0.197863\pi$
$257$	11.4638	+	6.61864i	0.715094	+	0.412860i	−0.0978505	+	0.995201i	$0.531197\pi$
$258$		0			0
$259$	23.4710	−	13.5510i	1.45842	−	0.842018i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.76791	+	6.52622i	0.232340	+	0.402424i	0.958496	−	0.285105i	$-0.0920286\pi$
$263$	3.76791	+	6.52622i	0.232340	+	0.402424i	−0.726157	+	0.687529i	$0.758695\pi$
$264$		0			0
$265$	−2.23286	+	3.86742i	−0.137163	+	0.237574i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			6.40793i			0.390699i	0.980734	+	0.195349i	$0.0625840\pi$
$269$			6.40793i			0.390699i	−0.980734	+	0.195349i	$0.937416\pi$
$270$		0			0
$271$		−	5.53211i		−	0.336051i	−0.985783	−	0.168026i	$-0.946261\pi$
$271$		−	5.53211i		−	0.336051i	0.985783	−	0.168026i	$-0.0537392\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.62543	+	9.74353i	−0.339226	+	0.587557i
$276$		0			0
$277$	−10.1627	−	17.6023i	−0.610616	−	1.05762i	−0.991137	−	0.132846i	$-0.957588\pi$
$277$	−10.1627	−	17.6023i	−0.610616	−	1.05762i	0.380520	−	0.924773i	$-0.375745\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.20013	+	3.57965i	−0.369869	+	0.213544i	−0.673401	−	0.739277i	$-0.735167\pi$
$281$	−6.20013	+	3.57965i	−0.369869	+	0.213544i	0.303532	+	0.952821i	$0.401834\pi$
$282$		0			0
$283$	−10.4042	−	6.00686i	−0.618465	−	0.357071i	0.157806	−	0.987470i	$-0.449558\pi$
$283$	−10.4042	−	6.00686i	−0.618465	−	0.357071i	−0.776271	+	0.630399i	$0.782891\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.63364			−0.332543
$288$		0			0
$289$	−18.1479			−1.06752
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−20.6573	−	11.9265i	−1.20681	−	0.696752i	−0.244749	−	0.969586i	$-0.578706\pi$
$293$	−20.6573	−	11.9265i	−1.20681	−	0.696752i	−0.962061	+	0.272834i	$0.912039\pi$
$294$		0			0
$295$	−3.31067	+	1.91142i	−0.192755	+	0.111287i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.185731	+	0.321696i	0.0107411	+	0.0186042i
$300$		0			0
$301$	19.3910	−	33.5862i	1.11768	−	1.93588i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			2.42188i			0.138677i
$306$		0			0
$307$		−	13.1729i		−	0.751818i	−0.926657	−	0.375909i	$-0.877331\pi$
$307$		−	13.1729i		−	0.751818i	0.926657	−	0.375909i	$-0.122669\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.14825	+	1.98883i	−0.0651114	+	0.112776i	−0.896743	−	0.442551i	$-0.854074\pi$
$311$	−1.14825	+	1.98883i	−0.0651114	+	0.112776i	0.831632	+	0.555327i	$0.187407\pi$
$312$		0			0
$313$	4.36557	+	7.56139i	0.246757	+	0.427395i	0.962624	−	0.270841i	$-0.0873018\pi$
$313$	4.36557	+	7.56139i	0.246757	+	0.427395i	−0.715867	+	0.698236i	$0.753968\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.23728	+	2.44640i	−0.237990	+	0.137403i	−0.614252	−	0.789110i	$-0.710542\pi$
$317$	−4.23728	+	2.44640i	−0.237990	+	0.137403i	0.376263	+	0.926513i	$0.377209\pi$
$318$		0			0
$319$	−15.3880	−	8.88428i	−0.861564	−	0.497424i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−21.3168			−1.18610
$324$		0			0
$325$	0.368330			0.0204313
$326$		0			0
$327$		0			0
$328$		0			0
$329$	25.7907	+	14.8903i	1.42189	+	0.820927i
$330$		0			0
$331$	3.14019	−	1.81299i	0.172601	−	0.0996511i	−0.411211	−	0.911540i	$-0.634894\pi$
$331$	3.14019	−	1.81299i	0.172601	−	0.0996511i	0.583812	+	0.811889i	$0.301561\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.489571	+	0.847962i	0.0267481	+	0.0463291i
$336$		0			0
$337$	−4.75655	+	8.23858i	−0.259106	+	0.448784i	−0.966003	−	0.258532i	$-0.916761\pi$
$337$	−4.75655	+	8.23858i	−0.259106	+	0.448784i	0.706897	+	0.707317i	$0.250094\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			1.79983i			0.0974661i
$342$		0			0
$343$			51.7308i			2.79320i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.42602	−	4.20199i	0.130236	−	0.225575i	−0.793532	−	0.608529i	$-0.791760\pi$
$347$	2.42602	−	4.20199i	0.130236	−	0.225575i	0.923767	+	0.382954i	$0.125093\pi$
$348$		0			0
$349$	4.40121	+	7.62312i	0.235591	+	0.408056i	0.959444	−	0.281898i	$-0.0909640\pi$
$349$	4.40121	+	7.62312i	0.235591	+	0.408056i	−0.723853	+	0.689954i	$0.757631\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.5392	−	9.54894i	0.880295	−	0.508239i	0.00953954	−	0.999954i	$-0.496963\pi$
$353$	16.5392	−	9.54894i	0.880295	−	0.508239i	0.870756	+	0.491716i	$0.163630\pi$
$354$		0			0
$355$	−4.24608	−	2.45148i	−0.225359	−	0.130111i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.99319			−0.263531			−0.131765	−	0.991281i	$-0.542065\pi$
$359$	−4.99319			−0.263531			−0.131765	+	0.991281i	$0.542065\pi$
$360$		0			0
$361$	6.07161			0.319558
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.99163	−	1.72722i	−0.156589	−	0.0904067i
$366$		0			0
$367$	−5.30108	+	3.06058i	−0.276714	+	0.159761i	−0.631935	−	0.775021i	$-0.717739\pi$
$367$	−5.30108	+	3.06058i	−0.276714	+	0.159761i	0.355221	+	0.934782i	$0.384406\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−24.0210	−	41.6055i	−1.24711	−	2.16005i
$372$		0			0
$373$	−2.06426	+	3.57540i	−0.106883	+	0.185127i	−0.914506	−	0.404572i	$-0.867420\pi$
$373$	−2.06426	+	3.57540i	−0.106883	+	0.185127i	0.807623	+	0.589699i	$0.200754\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			0.581706i			0.0299594i
$378$		0			0
$379$			28.0527i			1.44097i	0.693470	+	0.720485i	$0.256081\pi$
$379$			28.0527i			1.44097i	−0.693470	+	0.720485i	$0.743919\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.13318	−	14.0871i	0.415586	−	0.719816i	−0.579904	−	0.814685i	$-0.696910\pi$
$383$	8.13318	−	14.0871i	0.415586	−	0.719816i	0.995490	+	0.0948689i	$0.0302432\pi$
$384$		0			0
$385$	2.67095	+	4.62622i	0.136124	+	0.235774i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	31.3063	−	18.0747i	1.58729	−	0.916424i	0.593542	−	0.804803i	$-0.297729\pi$
$389$	31.3063	−	18.0747i	1.58729	−	0.916424i	0.993751	−	0.111621i	$-0.0356042\pi$
$390$		0			0
$391$	−24.7955	−	14.3157i	−1.25396	−	0.723974i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.34234			0.0675405
$396$		0			0
$397$	32.9550			1.65396			0.826982	−	0.562229i	$-0.190056\pi$
$397$	32.9550			1.65396			0.826982	+	0.562229i	$0.190056\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.54505	+	3.77879i	0.326844	+	0.188704i	0.654439	−	0.756115i	$-0.272905\pi$
$401$	6.54505	+	3.77879i	0.326844	+	0.188704i	−0.327595	+	0.944818i	$0.606238\pi$
$402$		0			0
$403$	0.0510285	−	0.0294613i	0.00254191	−	0.00146757i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.43750	+	11.1501i	0.319095	+	0.552689i
$408$		0			0
$409$	−4.05684	+	7.02666i	−0.200598	+	0.347446i	−0.948721	−	0.316114i	$-0.897622\pi$
$409$	−4.05684	+	7.02666i	−0.200598	+	0.347446i	0.748123	+	0.663560i	$0.230955\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	41.1259i		−	2.02367i
$414$		0			0
$415$		−	4.08530i		−	0.200540i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.99038	−	10.3756i	0.292649	−	0.506883i	−0.681786	−	0.731552i	$-0.738797\pi$
$419$	5.99038	−	10.3756i	0.292649	−	0.506883i	0.974435	+	0.224668i	$0.0721299\pi$
$420$		0			0
$421$	−12.5646	−	21.7626i	−0.612363	−	1.06064i	−0.990841	−	0.135034i	$-0.956886\pi$
$421$	−12.5646	−	21.7626i	−0.612363	−	1.06064i	0.378478	−	0.925610i	$-0.376448\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−24.5863	+	14.1949i	−1.19261	+	0.688555i
$426$		0			0
$427$	−22.5639	−	13.0273i	−1.09194	−	0.630433i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−18.7211			−0.901763			−0.450881	−	0.892584i	$-0.648890\pi$
$431$	−18.7211			−0.901763			−0.450881	+	0.892584i	$0.648890\pi$
$432$		0			0
$433$	−2.06315			−0.0991487			−0.0495744	−	0.998770i	$-0.515786\pi$
$433$	−2.06315			−0.0991487			−0.0495744	+	0.998770i	$0.515786\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−15.0382	−	8.68228i	−0.719372	−	0.415330i
$438$		0			0
$439$	−22.4517	+	12.9625i	−1.07156	+	0.618665i	−0.928607	−	0.371065i	$-0.878993\pi$
$439$	−22.4517	+	12.9625i	−1.07156	+	0.618665i	−0.142952	+	0.989730i	$0.545660\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.25888	+	12.5727i	0.344880	+	0.597349i	0.985332	−	0.170649i	$-0.0545864\pi$
$443$	7.25888	+	12.5727i	0.344880	+	0.597349i	−0.640452	+	0.767998i	$0.721253\pi$
$444$		0			0
$445$	2.23286	−	3.86742i	0.105848	−	0.183333i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	14.4797i		−	0.683341i	−0.939820	−	0.341670i	$-0.889007\pi$
$449$		−	14.4797i		−	0.683341i	0.939820	−	0.341670i	$-0.110993\pi$
$450$		0			0
$451$		−	2.67630i		−	0.126022i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0874413	−	0.151453i	0.00409931	−	0.00710021i
$456$		0			0
$457$	−12.7269	−	22.0437i	−0.595341	−	1.03116i	−0.993499	−	0.113844i	$-0.963684\pi$
$457$	−12.7269	−	22.0437i	−0.595341	−	1.03116i	0.398158	−	0.917317i	$-0.369650\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.81422	−	1.04744i	0.0844966	−	0.0487841i	−0.457156	−	0.889386i	$-0.651132\pi$
$461$	1.81422	−	1.04744i	0.0844966	−	0.0487841i	0.541653	+	0.840602i	$0.317799\pi$
$462$		0			0
$463$	−4.82478	−	2.78559i	−0.224226	−	0.129457i	0.383679	−	0.923466i	$-0.374657\pi$
$463$	−4.82478	−	2.78559i	−0.224226	−	0.129457i	−0.607906	+	0.794009i	$0.707990\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	39.0574			1.80736			0.903680	−	0.428208i	$-0.140855\pi$
$467$	39.0574			1.80736			0.903680	+	0.428208i	$0.140855\pi$
$468$		0			0
$469$	−10.5336			−0.486395
$470$		0			0
$471$		0			0
$472$		0			0
$473$	15.9554	+	9.21184i	0.733629	+	0.423561i
$474$		0			0
$475$	−14.9113	+	8.60906i	−0.684179	+	0.395011i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.8390	−	27.4340i	−0.723703	−	1.25349i	−0.959506	−	0.281689i	$-0.909105\pi$
$479$	−15.8390	−	27.4340i	−0.723703	−	1.25349i	0.235803	−	0.971801i	$-0.424228\pi$
$480$		0			0
$481$	0.210750	−	0.365030i	0.00960938	−	0.0166439i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			2.90825i			0.132057i
$486$		0			0
$487$		−	33.3903i		−	1.51306i	−0.653961	−	0.756528i	$-0.726894\pi$
$487$		−	33.3903i		−	1.51306i	0.653961	−	0.756528i	$-0.273106\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.52060	−	16.4902i	0.429659	−	0.744190i	−0.567184	−	0.823591i	$-0.691967\pi$
$491$	9.52060	−	16.4902i	0.429659	−	0.744190i	0.996843	+	0.0794005i	$0.0253006\pi$
$492$		0			0
$493$	−22.4182	−	38.8294i	−1.00966	−	1.74879i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	45.6791	−	26.3729i	2.04899	−	1.18298i
$498$		0			0
$499$	−18.8684	−	10.8937i	−0.844664	−	0.487667i	0.0141827	−	0.999899i	$-0.495485\pi$
$499$	−18.8684	−	10.8937i	−0.844664	−	0.487667i	−0.858847	+	0.512232i	$0.828819\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.6101			0.963547			0.481774	−	0.876296i	$-0.339993\pi$
$503$	21.6101			0.963547			0.481774	+	0.876296i	$0.339993\pi$
$504$		0			0
$505$	−2.38924			−0.106320
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−22.5799	−	13.0365i	−1.00084	−	0.577834i	−0.0923421	−	0.995727i	$-0.529435\pi$
$509$	−22.5799	−	13.0365i	−1.00084	−	0.577834i	−0.908496	+	0.417893i	$0.862769\pi$
$510$		0			0
$511$	32.1838	−	18.5813i	1.42373	−	0.821989i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.641740	+	1.11153i	0.0282784	+	0.0489797i
$516$		0			0
$517$	−7.07373	+	12.2521i	−0.311102	+	0.538845i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	0.184295i		−	0.00807410i	−0.999992	−	0.00403705i	$-0.998715\pi$
$521$		−	0.184295i		−	0.00807410i	0.999992	−	0.00403705i	$-0.00128504\pi$
$522$		0			0
$523$			28.9997i			1.26807i	0.773304	+	0.634035i	$0.218603\pi$
$523$			28.9997i			1.26807i	−0.773304	+	0.634035i	$0.781397\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.27080	+	3.93314i	−0.0989175	+	0.171330i
$528$		0			0
$529$	−0.161471	−	0.279677i	−0.00702050	−	0.0121599i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.0758781	+	0.0438083i	−0.00328665	+	0.00189755i
$534$		0			0
$535$	5.80918	+	3.35393i	0.251153	+	0.145003i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−41.0215			−1.76692
$540$		0			0
$541$	40.1108			1.72450			0.862249	−	0.506484i	$-0.169055\pi$
$541$	40.1108			1.72450			0.862249	+	0.506484i	$0.169055\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.04479	−	2.91261i	−0.216095	−	0.124763i
$546$		0			0
$547$	−17.7795	+	10.2650i	−0.760198	+	0.438901i	−0.829367	−	0.558704i	$-0.811299\pi$
$547$	−17.7795	+	10.2650i	−0.760198	+	0.438901i	0.0691687	+	0.997605i	$0.477965\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.5963	−	23.5496i	−0.579224	−	1.00325i
$552$		0			0
$553$	−7.22042	+	12.5061i	−0.307043	+	0.531815i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.23121i			0.0521682i	0.999660	+	0.0260841i	$0.00830378\pi$
$557$			1.23121i			0.0521682i	−0.999660	+	0.0260841i	$0.991696\pi$
$558$		0			0
$559$		−	0.603152i		−	0.0255106i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.8990	+	18.8776i	−0.459337	+	0.795595i	−0.998926	−	0.0463337i	$-0.985246\pi$
$563$	−10.8990	+	18.8776i	−0.459337	+	0.795595i	0.539589	+	0.841928i	$0.318580\pi$
$564$		0			0
$565$	−4.40121	−	7.62312i	−0.185160	−	0.320707i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.3575	+	8.28931i	−0.601898	+	0.347506i	−0.769788	−	0.638300i	$-0.779638\pi$
$569$	−14.3575	+	8.28931i	−0.601898	+	0.347506i	0.167890	+	0.985806i	$0.446305\pi$
$570$		0			0
$571$	−0.452356	−	0.261168i	−0.0189305	−	0.0109295i	0.490505	−	0.871438i	$-0.336812\pi$
$571$	−0.452356	−	0.261168i	−0.0189305	−	0.0109295i	−0.509435	+	0.860509i	$0.670146\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−23.1262			−0.964431
$576$		0			0
$577$	34.5966			1.44028			0.720139	−	0.693830i	$-0.244078\pi$
$577$	34.5966			1.44028			0.720139	+	0.693830i	$0.244078\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	38.0614	+	21.9747i	1.57905	+	0.911666i
$582$		0			0
$583$	19.7650	−	11.4113i	0.818583	−	0.472609i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.942362	+	1.63222i	0.0388955	+	0.0673689i	0.884818	−	0.465937i	$-0.154283\pi$
$587$	0.942362	+	1.63222i	0.0388955	+	0.0673689i	−0.845922	+	0.533306i	$0.820949\pi$
$588$		0			0
$589$	−1.37721	+	2.38540i	−0.0567470	+	0.0982887i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			26.7478i			1.09840i	0.835691	+	0.549199i	$0.185067\pi$
$593$			26.7478i			1.09840i	−0.835691	+	0.549199i	$0.814933\pi$
$594$		0			0
$595$			13.4795i			0.552605i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11.7506	+	20.3527i	−0.480118	+	0.831589i	−0.999740	−	0.0228075i	$-0.992740\pi$
$599$	−11.7506	+	20.3527i	−0.480118	+	0.831589i	0.519622	+	0.854396i	$0.326073\pi$
$600$		0			0
$601$	−8.49651	−	14.7164i	−0.346580	−	0.600294i	0.639060	−	0.769157i	$-0.279324\pi$
$601$	−8.49651	−	14.7164i	−0.346580	−	0.600294i	−0.985640	+	0.168863i	$0.945990\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.18174	−	1.25963i	0.0887002	−	0.0512111i
$606$		0			0
$607$	16.5877	+	9.57694i	0.673276	+	0.388716i	0.797317	−	0.603561i	$-0.206252\pi$
$607$	16.5877	+	9.57694i	0.673276	+	0.388716i	−0.124041	+	0.992277i	$0.539585\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.463158			0.0187374
$612$		0			0
$613$	−16.5441			−0.668211			−0.334106	−	0.942536i	$-0.608434\pi$
$613$	−16.5441			−0.668211			−0.334106	+	0.942536i	$0.608434\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−27.4744	−	15.8624i	−1.10608	−	0.638595i	−0.168268	−	0.985741i	$-0.553817\pi$
$617$	−27.4744	−	15.8624i	−1.10608	−	0.638595i	−0.937811	+	0.347146i	$0.887151\pi$
$618$		0			0
$619$	−8.46158	+	4.88529i	−0.340099	+	0.196356i	−0.660316	−	0.750988i	$-0.729578\pi$
$619$	−8.46158	+	4.88529i	−0.340099	+	0.196356i	0.320217	+	0.947344i	$0.396244\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	24.0210	+	41.6055i	0.962379	+	1.66689i
$624$		0			0
$625$	−10.9372	+	18.9439i	−0.437490	+	0.757754i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			32.4881i			1.29539i
$630$		0			0
$631$			23.9365i			0.952896i	0.879203	+	0.476448i	$0.158076\pi$
$631$			23.9365i			0.952896i	−0.879203	+	0.476448i	$0.841924\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.58282	−	4.47358i	0.102496	−	0.177529i
$636$		0			0
$637$	0.671479	+	1.16304i	0.0266050	+	0.0460811i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.947835	+	0.547233i	−0.0374372	+	0.0216144i	−0.518602	−	0.855016i	$-0.673547\pi$
$641$	−0.947835	+	0.547233i	−0.0374372	+	0.0216144i	0.481165	+	0.876630i	$0.340214\pi$
$642$		0			0
$643$	30.4240	+	17.5653i	1.19981	+	0.692708i	0.960512	−	0.278239i	$-0.0897506\pi$
$643$	30.4240	+	17.5653i	1.19981	+	0.692708i	0.239294	+	0.970947i	$0.423084\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−37.2369			−1.46393			−0.731966	−	0.681341i	$-0.761397\pi$
$647$	−37.2369			−1.46393			−0.731966	+	0.681341i	$0.761397\pi$
$648$		0			0
$649$	19.5372			0.766901
$650$		0			0
$651$		0			0
$652$		0			0
$653$	35.6290	+	20.5704i	1.39427	+	0.804982i	0.993784	−	0.111322i	$-0.0355085\pi$
$653$	35.6290	+	20.5704i	1.39427	+	0.804982i	0.400484	+	0.916304i	$0.368842\pi$
$654$		0			0
$655$	6.00729	−	3.46831i	0.234724	−	0.135518i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.31389	−	16.1321i	−0.362818	−	0.628419i	0.625606	−	0.780139i	$-0.284852\pi$
$659$	−9.31389	−	16.1321i	−0.362818	−	0.628419i	−0.988423	+	0.151721i	$0.951519\pi$
$660$		0			0
$661$	−1.50846	+	2.61273i	−0.0586722	+	0.101623i	−0.893870	−	0.448327i	$-0.852020\pi$
$661$	−1.50846	+	2.61273i	−0.0586722	+	0.101623i	0.835197	+	0.549950i	$0.185353\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			8.17514i			0.317019i
$666$		0			0
$667$		−	36.5234i		−	1.41419i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.18869	−	10.7191i	0.238912	−	0.413808i
$672$		0			0
$673$	−14.1646	−	24.5337i	−0.546004	−	0.945706i	−0.998543	−	0.0539618i	$-0.982815\pi$
$673$	−14.1646	−	24.5337i	−0.546004	−	0.945706i	0.452539	−	0.891744i	$-0.350518\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.8629	+	12.6226i	−0.840260	+	0.485124i	−0.857353	−	0.514730i	$-0.827892\pi$
$677$	−21.8629	+	12.6226i	−0.840260	+	0.485124i	0.0170927	+	0.999854i	$0.494559\pi$
$678$		0			0
$679$	−27.0952	−	15.6434i	−1.03982	−	0.600340i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.12320			0.349089			0.174545	−	0.984649i	$-0.444155\pi$
$683$	9.12320			0.349089			0.174545	+	0.984649i	$0.444155\pi$
$684$		0			0
$685$	1.65423			0.0632047
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.647065	−	0.373583i	−0.0246512	−	0.0142324i
$690$		0			0
$691$	40.6272	−	23.4561i	1.54553	−	0.892313i	0.547058	−	0.837095i	$-0.315748\pi$
$691$	40.6272	−	23.4561i	1.54553	−	0.892313i	0.998474	−	0.0552184i	$-0.0175855\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.62907	+	2.82163i	0.0617941	+	0.107030i
$696$		0			0
$697$	3.37662	−	5.84848i	0.127899	−	0.221527i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	14.2915i		−	0.539783i	−0.962891	−	0.269892i	$-0.913012\pi$
$701$		−	14.2915i		−	0.539783i	0.962891	−	0.269892i	$-0.0869879\pi$
$702$		0			0
$703$			19.7037i			0.743138i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	12.8517	−	22.2598i	0.483337	−	0.837165i
$708$		0			0
$709$	20.4700	+	35.4551i	0.768768	+	1.33155i	0.938231	+	0.346009i	$0.112463\pi$
$709$	20.4700	+	35.4551i	0.768768	+	1.33155i	−0.169463	+	0.985537i	$0.554203\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.20391	+	1.84978i	−0.119988	+	0.0692748i
$714$		0			0
$715$	0.0719487	+	0.0415396i	0.00269073	+	0.00155349i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	51.0710			1.90463			0.952313	−	0.305123i	$-0.0986974\pi$
$719$	51.0710			1.90463			0.952313	+	0.305123i	$0.0986974\pi$
$720$		0			0
$721$	−13.8076			−0.514222
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−31.3635	−	18.1077i	−1.16481	−	0.672503i
$726$		0			0
$727$	23.0591	−	13.3132i	0.855213	−	0.493758i	−0.00719304	−	0.999974i	$-0.502290\pi$
$727$	23.0591	−	13.3132i	0.855213	−	0.493758i	0.862406	+	0.506216i	$0.168956\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.2447	+	40.2610i	0.859736	+	1.48911i
$732$		0			0
$733$	−21.7287	+	37.6352i	−0.802567	+	1.39009i	0.115354	+	0.993324i	$0.463200\pi$
$733$	−21.7287	+	37.6352i	−0.802567	+	1.39009i	−0.917921	+	0.396763i	$0.870134\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	5.00405i		−	0.184326i
$738$		0			0
$739$		−	2.24313i		−	0.0825150i	−0.999149	−	0.0412575i	$-0.986864\pi$
$739$		−	2.24313i		−	0.0825150i	0.999149	−	0.0412575i	$-0.0131364\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.4331	+	38.8553i	−0.822991	+	1.42546i	0.0804542	+	0.996758i	$0.474363\pi$
$743$	−22.4331	+	38.8553i	−0.822991	+	1.42546i	−0.903445	+	0.428704i	$0.858970\pi$
$744$		0			0
$745$	−0.261611	−	0.453124i	−0.00958470	−	0.0166012i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−62.4949	+	36.0814i	−2.28351	+	1.31839i
$750$		0			0
$751$	−24.6400	−	14.2259i	−0.899128	−	0.519112i	−0.0222105	−	0.999753i	$-0.507070\pi$
$751$	−24.6400	−	14.2259i	−0.899128	−	0.519112i	−0.876917	+	0.480642i	$0.840404\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.13952			−0.187046
$756$		0			0
$757$	−17.8913			−0.650269			−0.325135	−	0.945668i	$-0.605410\pi$
$757$	−17.8913			−0.650269			−0.325135	+	0.945668i	$0.605410\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.80178	+	2.77231i	0.174064	+	0.100496i	0.584501	−	0.811393i	$-0.301290\pi$
$761$	4.80178	+	2.77231i	0.174064	+	0.100496i	−0.410437	+	0.911889i	$0.634624\pi$
$762$		0			0
$763$	54.2716	−	31.3337i	1.96476	−	1.13436i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.319803	−	0.553915i	−0.0115474	−	0.0200007i
$768$		0			0
$769$	11.3305	−	19.6250i	0.408589	−	0.707696i	−0.586143	−	0.810207i	$-0.699354\pi$
$769$	11.3305	−	19.6250i	0.408589	−	0.707696i	0.994732	+	0.102511i	$0.0326878\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	20.9941i		−	0.755105i	−0.925988	−	0.377552i	$-0.876766\pi$
$773$		−	20.9941i		−	0.755105i	0.925988	−	0.377552i	$-0.123234\pi$
$774$		0			0
$775$			3.66836i			0.131771i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.04788	−	3.54704i	0.0733730	−	0.127086i
$780$		0			0
$781$	12.5286	+	21.7002i	0.448309	+	0.776494i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.52130	+	3.76507i	−0.232755	+	0.134381i
$786$		0			0
$787$	−11.4280	−	6.59793i	−0.407363	−	0.235191i	0.282293	−	0.959328i	$-0.408905\pi$
$787$	−11.4280	−	6.59793i	−0.407363	−	0.235191i	−0.689656	+	0.724137i	$0.742238\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	94.6960			3.36700
$792$		0			0
$793$	−0.405210			−0.0143894
$794$		0			0
$795$		0			0
$796$		0			0
$797$	43.2431	+	24.9664i	1.53175	+	0.884356i	0.999281	+	0.0379066i	$0.0120689\pi$
$797$	43.2431	+	24.9664i	1.53175	+	0.884356i	0.532469	+	0.846450i	$0.321264\pi$
$798$		0			0
$799$	−30.9162	+	17.8495i	−1.09374	+	0.631470i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.82719	+	15.2891i	0.311505	+	0.539542i
$804$		0			0
$805$	−5.49016	+	9.50923i	−0.193503	+	0.335156i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	38.4167i		−	1.35066i	−0.737516	−	0.675329i	$-0.764001\pi$
$809$		−	38.4167i		−	1.35066i	0.737516	−	0.675329i	$-0.235999\pi$
$810$		0			0
$811$			8.98092i			0.315363i	0.987490	+	0.157681i	$0.0504019\pi$
$811$			8.98092i			0.315363i	−0.987490	+	0.157681i	$0.949598\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.929838	−	1.61053i	0.0325708	−	0.0564143i
$816$		0			0
$817$	14.0976	+	24.4178i	0.493214	+	0.854271i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	48.8738	−	28.2173i	1.70571	−	0.984792i	0.765984	−	0.642859i	$-0.222252\pi$
$821$	48.8738	−	28.2173i	1.70571	−	0.984792i	0.939725	−	0.341932i	$-0.111081\pi$
$822$		0			0
$823$	35.6509	+	20.5831i	1.24271	+	0.717481i	0.969646	−	0.244514i	$-0.0786284\pi$
$823$	35.6509	+	20.5831i	1.24271	+	0.717481i	0.273068	+	0.961995i	$0.411962\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.24168			−0.217044			−0.108522	−	0.994094i	$-0.534612\pi$
$827$	−6.24168			−0.217044			−0.108522	+	0.994094i	$0.534612\pi$
$828$		0			0
$829$	−33.2083			−1.15337			−0.576686	−	0.816966i	$-0.695654\pi$
$829$	−33.2083			−1.15337			−0.576686	+	0.816966i	$0.695654\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−89.6437	−	51.7558i	−3.10597	−	1.79323i
$834$		0			0
$835$	−1.25868	+	0.726697i	−0.0435583	+	0.0251484i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.9352	−	20.6724i	−0.412049	−	0.713690i	0.583064	−	0.812426i	$-0.301854\pi$
$839$	−11.9352	−	20.6724i	−0.412049	−	0.713690i	−0.995114	+	0.0987356i	$0.968520\pi$
$840$		0			0
$841$	14.0976	−	24.4178i	0.486125	−	0.841994i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			5.97369i			0.205501i
$846$		0			0
$847$			27.1020i			0.931235i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.2323	+	22.9191i	−0.453599	+	0.785656i
$852$		0			0
$853$	19.5841	+	33.9206i	0.670545	+	1.16142i	0.977750	+	0.209775i	$0.0672731\pi$
$853$	19.5841	+	33.9206i	0.670545	+	1.16142i	−0.307205	+	0.951644i	$0.599394\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.87557	+	5.12431i	−0.303184	+	0.175043i	−0.643872	−	0.765133i	$-0.722673\pi$
$857$	−8.87557	+	5.12431i	−0.303184	+	0.175043i	0.340689	+	0.940176i	$0.389340\pi$
$858$		0			0
$859$	13.6163	+	7.86135i	0.464581	+	0.268226i	0.713968	−	0.700178i	$-0.246896\pi$
$859$	13.6163	+	7.86135i	0.464581	+	0.268226i	−0.249388	+	0.968404i	$0.580229\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−32.0370			−1.09055			−0.545276	−	0.838257i	$-0.683575\pi$
$863$	−32.0370			−1.09055			−0.545276	+	0.838257i	$0.683575\pi$
$864$		0			0
$865$	−9.23966			−0.314158
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.94113	−	3.43011i	−0.201539	−	0.116359i
$870$		0			0
$871$	−0.141874	+	0.0819110i	−0.00480722	+	0.00277545i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	11.1280	+	19.2742i	0.376194	+	0.651588i
$876$		0			0
$877$	−18.3684	+	31.8149i	−0.620255	+	1.07431i	0.369183	+	0.929357i	$0.379638\pi$
$877$	−18.3684	+	31.8149i	−0.620255	+	1.07431i	−0.989438	+	0.144957i	$0.953696\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			44.9995i			1.51607i	0.652213	+	0.758036i	$0.273841\pi$
$881$			44.9995i			1.51607i	−0.652213	+	0.758036i	$0.726159\pi$
$882$		0			0
$883$			28.0715i			0.944680i	0.881416	+	0.472340i	$0.156591\pi$
$883$			28.0715i			0.944680i	−0.881416	+	0.472340i	$0.843409\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.4625	−	23.3177i	0.452025	−	0.782930i	−0.546487	−	0.837468i	$-0.684035\pi$
$887$	13.4625	−	23.3177i	0.452025	−	0.782930i	0.998512	+	0.0545375i	$0.0173685\pi$
$888$		0			0
$889$	27.7859	+	48.1266i	0.931909	+	1.61411i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−18.7503	+	10.8255i	−0.627456	+	0.362262i
$894$		0			0
$895$	4.04897	+	2.33767i	0.135342	+	0.0781398i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.79347			−0.193223
$900$		0			0
$901$	57.5895			1.91859
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.99477	+	3.46108i	0.199273	+	0.115050i
$906$		0			0
$907$	5.49526	−	3.17269i	0.182467	−	0.105347i	−0.405984	−	0.913880i	$-0.633071\pi$
$907$	5.49526	−	3.17269i	0.182467	−	0.105347i	0.588451	+	0.808533i	$0.299738\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−11.6552	−	20.1874i	−0.386154	−	0.668838i	0.605775	−	0.795636i	$-0.292863\pi$
$911$	−11.6552	−	20.1874i	−0.386154	−	0.668838i	−0.991929	+	0.126798i	$0.959530\pi$
$912$		0			0
$913$	−10.4393	+	18.0813i	−0.345489	+	0.598405i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			74.6238i			2.46430i
$918$		0			0
$919$		−	16.2387i		−	0.535664i	−0.963466	−	0.267832i	$-0.913693\pi$
$919$		−	16.2387i		−	0.535664i	0.963466	−	0.267832i	$-0.0863072\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.410161	−	0.710419i	0.0135006	−	0.0233837i
$924$		0			0
$925$	13.1207	+	22.7258i	0.431407	+	0.747219i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.64731	+	2.10577i	−0.119664	+	0.0690882i	−0.558637	−	0.829412i	$-0.688676\pi$
$929$	−3.64731	+	2.10577i	−0.119664	+	0.0690882i	0.438973	+	0.898500i	$0.355342\pi$
$930$		0			0
$931$	−54.3678	−	31.3893i	−1.78183	−	1.02874i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.40352			−0.209418
$936$		0			0
$937$	42.9154			1.40198			0.700992	−	0.713169i	$-0.252741\pi$
$937$	42.9154			1.40198			0.700992	+	0.713169i	$0.252741\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.89739	+	3.40486i	0.192249	+	0.110995i	0.593035	−	0.805177i	$-0.297929\pi$
$941$	5.89739	+	3.40486i	0.192249	+	0.110995i	−0.400786	+	0.916172i	$0.631263\pi$
$942$		0			0
$943$	4.76415	−	2.75058i	0.155142	−	0.0895713i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.8163	+	41.2511i	0.773927	+	1.34048i	0.935395	+	0.353603i	$0.115044\pi$
$947$	23.8163	+	41.2511i	0.773927	+	1.34048i	−0.161468	+	0.986878i	$0.551623\pi$
$948$		0			0
$949$	0.288984	−	0.500535i	0.00938081	−	0.0162480i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	56.0644i		−	1.81610i	−0.418859	−	0.908051i	$-0.637570\pi$
$953$		−	56.0644i		−	1.81610i	0.418859	−	0.908051i	$-0.362430\pi$
$954$		0			0
$955$		−	1.29820i		−	0.0420088i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−8.89804	+	15.4119i	−0.287333	+	0.497675i
$960$		0			0
$961$	−15.2066	−	26.3386i	−0.490535	−	0.849631i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.12792	+	4.11531i	−0.229456	+	0.132476i
$966$		0			0
$967$	6.10910	+	3.52709i	0.196455	+	0.113424i	0.595001	−	0.803725i	$-0.297152\pi$
$967$	6.10910	+	3.52709i	0.196455	+	0.113424i	−0.398546	+	0.917149i	$0.630485\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33.2137			−1.06588			−0.532939	−	0.846153i	$-0.678913\pi$
$971$	−33.2137			−1.06588			−0.532939	+	0.846153i	$0.678913\pi$
$972$		0			0
$973$	−35.0509			−1.12368
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.7166	+	6.76456i	0.374846	+	0.216418i	0.675574	−	0.737293i	$-0.263896\pi$
$977$	11.7166	+	6.76456i	0.374846	+	0.216418i	−0.300727	+	0.953710i	$0.597229\pi$
$978$		0			0
$979$	−19.7650	+	11.4113i	−0.631692	+	0.364708i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.59692	+	7.96210i	0.146619	+	0.253952i	0.929976	−	0.367621i	$-0.119828\pi$
$983$	4.59692	+	7.96210i	0.146619	+	0.253952i	−0.783357	+	0.621572i	$0.786494\pi$
$984$		0			0
$985$	1.30029	−	2.25218i	0.0414308	−	0.0717603i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			37.8700i			1.20420i
$990$		0			0
$991$		−	29.2577i		−	0.929402i	−0.885468	−	0.464701i	$-0.846162\pi$
$991$		−	29.2577i		−	0.929402i	0.885468	−	0.464701i	$-0.153838\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.55851	−	2.69943i	0.0494082	−	0.0855775i
$996$		0			0
$997$	−25.1497	−	43.5606i	−0.796500	−	1.37958i	−0.921883	−	0.387469i	$-0.873349\pi$
$997$	−25.1497	−	43.5606i	−0.796500	−	1.37958i	0.125383	−	0.992108i	$-0.459984\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.s.a.287.7		24
3.2	odd	2		288.2.s.a.95.3	✓	24
4.3	odd	2	inner	864.2.s.a.287.8		24
8.3	odd	2		1728.2.s.g.1151.5		24
8.5	even	2		1728.2.s.g.1151.6		24
9.2	odd	6	inner	864.2.s.a.575.8		24
9.4	even	3		2592.2.c.c.2591.9		24
9.5	odd	6		2592.2.c.c.2591.15		24
9.7	even	3		288.2.s.a.191.10	yes	24
12.11	even	2		288.2.s.a.95.10	yes	24
24.5	odd	2		576.2.s.g.383.10		24
24.11	even	2		576.2.s.g.383.3		24
36.7	odd	6		288.2.s.a.191.3	yes	24
36.11	even	6	inner	864.2.s.a.575.7		24
36.23	even	6		2592.2.c.c.2591.16		24
36.31	odd	6		2592.2.c.c.2591.10		24
72.5	odd	6		5184.2.c.m.5183.9		24
72.11	even	6		1728.2.s.g.575.6		24
72.13	even	6		5184.2.c.m.5183.15		24
72.29	odd	6		1728.2.s.g.575.5		24
72.43	odd	6		576.2.s.g.191.10		24
72.59	even	6		5184.2.c.m.5183.10		24
72.61	even	6		576.2.s.g.191.3		24
72.67	odd	6		5184.2.c.m.5183.16		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.3	✓	24	3.2	odd	2
288.2.s.a.95.10	yes	24	12.11	even	2
288.2.s.a.191.3	yes	24	36.7	odd	6
288.2.s.a.191.10	yes	24	9.7	even	3
576.2.s.g.191.3		24	72.61	even	6
576.2.s.g.191.10		24	72.43	odd	6
576.2.s.g.383.3		24	24.11	even	2
576.2.s.g.383.10		24	24.5	odd	2
864.2.s.a.287.7		24	1.1	even	1	trivial
864.2.s.a.287.8		24	4.3	odd	2	inner
864.2.s.a.575.7		24	36.11	even	6	inner
864.2.s.a.575.8		24	9.2	odd	6	inner
1728.2.s.g.575.5		24	72.29	odd	6
1728.2.s.g.575.6		24	72.11	even	6
1728.2.s.g.1151.5		24	8.3	odd	2
1728.2.s.g.1151.6		24	8.5	even	2
2592.2.c.c.2591.9		24	9.4	even	3
2592.2.c.c.2591.10		24	36.31	odd	6
2592.2.c.c.2591.15		24	9.5	odd	6
2592.2.c.c.2591.16		24	36.23	even	6
5184.2.c.m.5183.9		24	72.5	odd	6
5184.2.c.m.5183.10		24	72.59	even	6
5184.2.c.m.5183.15		24	72.13	even	6
5184.2.c.m.5183.16		24	72.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.398132 + 0.229862i) q^{5} +(-4.28309 + 2.47284i) q^{7} +O(q^{10})\)	\(q+(0.398132 + 0.229862i) q^{5} +(-4.28309 + 2.47284i) q^{7} +(-1.17474 - 2.03471i) q^{11} +(-0.0384586 + 0.0666122i) q^{13} -5.92857i q^{17} -3.59561i q^{19} +(2.41469 - 4.18237i) q^{23} +(-2.39433 - 4.14710i) q^{25} +(6.54954 - 3.78138i) q^{29} +(-0.663421 - 0.383026i) q^{31} -2.27365 q^{35} -5.47993 q^{37} +(0.986492 + 0.569551i) q^{41} +(-6.79101 + 3.92079i) q^{43} +(-3.01076 - 5.21479i) q^{47} +(8.72990 - 15.1206i) q^{49} +9.71390i q^{53} -1.08011i q^{55} +(-4.15776 + 7.20145i) q^{59} +(2.63407 + 4.56234i) q^{61} +(-0.0306232 + 0.0176803i) q^{65} +(1.84450 + 1.06492i) q^{67} -10.6650 q^{71} -7.51416 q^{73} +(10.0630 + 5.80990i) q^{77} +(2.52870 - 1.45994i) q^{79} +(-4.44322 - 7.69588i) q^{83} +(1.36275 - 2.36035i) q^{85} -9.71390i q^{89} -0.380408i q^{91} +(0.826493 - 1.43153i) q^{95} +(3.16305 + 5.47856i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 12 q^{25} - 24 q^{29} + 36 q^{41} + 12 q^{49} + 48 q^{65} + 24 q^{73} + 48 q^{77} + 12 q^{97}+O(q^{100}) \) 24 * q + 12 * q^25 - 24 * q^29 + 36 * q^41 + 12 * q^49 + 48 * q^65 + 24 * q^73 + 48 * q^77 + 12 * q^97

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