LMFDB - Embedded newform 864.2.s.a.287.3

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			287.3
Character	$\chi$	$=$	864.287
Dual form			864.2.s.a.575.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.81740 - 1.04928i) q^{5} +(-0.143714 + 0.0829731i) q^{7} +O(q^{10})$	$q+(-1.81740 - 1.04928i) q^{5} +(-0.143714 + 0.0829731i) q^{7} +(-0.784910 - 1.35950i) q^{11} +(-1.93212 + 3.34652i) q^{13} -5.27221i q^{17} +8.05210i q^{19} +(-2.67564 + 4.63435i) q^{23} +(-0.298034 - 0.516211i) q^{25} +(-6.75334 + 3.89904i) q^{29} +(2.10800 + 1.21705i) q^{31} +0.348247 q^{35} -8.53566 q^{37} +(-2.47895 - 1.43122i) q^{41} +(3.42127 - 1.97527i) q^{43} +(3.68689 + 6.38588i) q^{47} +(-3.48623 + 6.03833i) q^{49} +2.40174i q^{53} +3.29435i q^{55} +(-5.49855 + 9.52376i) q^{59} +(-7.11998 - 12.3322i) q^{61} +(7.02286 - 4.05465i) q^{65} +(-1.45698 - 0.841190i) q^{67} -12.5669 q^{71} +10.4679 q^{73} +(0.225605 + 0.130253i) q^{77} +(6.31710 - 3.64718i) q^{79} +(-1.35365 - 2.34460i) q^{83} +(-5.53201 + 9.58172i) q^{85} -2.40174i q^{89} -0.641255i q^{91} +(8.44888 - 14.6339i) q^{95} +(0.903600 + 1.56508i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.81740	−	1.04928i	−0.812767	−	0.469251i	0.0351491	−	0.999382i	$-0.488809\pi$
$5$	−1.81740	−	1.04928i	−0.812767	−	0.469251i	−0.847916	+	0.530131i	$0.822143\pi$
$6$		0			0
$7$	−0.143714	+	0.0829731i	−0.0543187	+	0.0313609i	−0.526913	−	0.849919i	$-0.676651\pi$
$7$	−0.143714	+	0.0829731i	−0.0543187	+	0.0313609i	0.472595	+	0.881280i	$0.343317\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.784910	−	1.35950i	−0.236659	−	0.409906i	0.723094	−	0.690749i	$-0.242719\pi$
$11$	−0.784910	−	1.35950i	−0.236659	−	0.409906i	−0.959754	+	0.280843i	$0.909386\pi$
$12$		0			0
$13$	−1.93212	+	3.34652i	−0.535872	+	0.928158i	0.463248	+	0.886229i	$0.346684\pi$
$13$	−1.93212	+	3.34652i	−0.535872	+	0.928158i	−0.999121	+	0.0419297i	$0.986649\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	5.27221i		−	1.27870i	−0.768917	−	0.639349i	$-0.779204\pi$
$17$		−	5.27221i		−	1.27870i	0.768917	−	0.639349i	$-0.220796\pi$
$18$		0			0
$19$			8.05210i			1.84728i	0.383264	+	0.923639i	$0.374800\pi$
$19$			8.05210i			1.84728i	−0.383264	+	0.923639i	$0.625200\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.67564	+	4.63435i	−0.557910	+	0.966328i	0.439761	+	0.898115i	$0.355063\pi$
$23$	−2.67564	+	4.63435i	−0.557910	+	0.966328i	−0.997671	+	0.0682135i	$0.978270\pi$
$24$		0			0
$25$	−0.298034	−	0.516211i	−0.0596069	−	0.103242i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.75334	+	3.89904i	−1.25406	+	0.724034i	−0.971914	−	0.235336i	$-0.924381\pi$
$29$	−6.75334	+	3.89904i	−1.25406	+	0.724034i	−0.282150	+	0.959370i	$0.591048\pi$
$30$		0			0
$31$	2.10800	+	1.21705i	0.378608	+	0.218589i	0.677212	−	0.735788i	$-0.263188\pi$
$31$	2.10800	+	1.21705i	0.378608	+	0.218589i	−0.298604	+	0.954377i	$0.596521\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.348247			0.0588645
$36$		0			0
$37$	−8.53566			−1.40325			−0.701627	−	0.712544i	$-0.747543\pi$
$37$	−8.53566			−1.40325			−0.701627	+	0.712544i	$0.747543\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.47895	−	1.43122i	−0.387146	−	0.223519i	0.293777	−	0.955874i	$-0.405088\pi$
$41$	−2.47895	−	1.43122i	−0.387146	−	0.223519i	−0.680923	+	0.732355i	$0.738421\pi$
$42$		0			0
$43$	3.42127	−	1.97527i	0.521739	−	0.301226i	−0.215907	−	0.976414i	$-0.569271\pi$
$43$	3.42127	−	1.97527i	0.521739	−	0.301226i	0.737646	+	0.675188i	$0.235937\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.68689	+	6.38588i	0.537788	+	0.931477i	0.999023	+	0.0441985i	$0.0140734\pi$
$47$	3.68689	+	6.38588i	0.537788	+	0.931477i	−0.461234	+	0.887278i	$0.652593\pi$
$48$		0			0
$49$	−3.48623	+	6.03833i	−0.498033	+	0.862618i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			2.40174i			0.329904i	0.986302	+	0.164952i	$0.0527469\pi$
$53$			2.40174i			0.329904i	−0.986302	+	0.164952i	$0.947253\pi$
$54$		0			0
$55$			3.29435i			0.444211i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.49855	+	9.52376i	−0.715850	+	1.23989i	0.246781	+	0.969071i	$0.420627\pi$
$59$	−5.49855	+	9.52376i	−0.715850	+	1.23989i	−0.962631	+	0.270817i	$0.912706\pi$
$60$		0			0
$61$	−7.11998	−	12.3322i	−0.911620	−	1.57897i	−0.811776	−	0.583969i	$-0.801499\pi$
$61$	−7.11998	−	12.3322i	−0.911620	−	1.57897i	−0.0998446	−	0.995003i	$-0.531835\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.02286	−	4.05465i	0.871079	−	0.502917i
$66$		0			0
$67$	−1.45698	−	0.841190i	−0.177999	−	0.102768i	0.408353	−	0.912824i	$-0.366103\pi$
$67$	−1.45698	−	0.841190i	−0.177999	−	0.102768i	−0.586352	+	0.810056i	$0.699436\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−12.5669			−1.49142			−0.745709	−	0.666272i	$-0.767889\pi$
$71$	−12.5669			−1.49142			−0.745709	+	0.666272i	$0.767889\pi$
$72$		0			0
$73$	10.4679			1.22518			0.612590	−	0.790401i	$-0.290128\pi$
$73$	10.4679			1.22518			0.612590	+	0.790401i	$0.290128\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.225605	+	0.130253i	0.0257100	+	0.0148437i
$78$		0			0
$79$	6.31710	−	3.64718i	0.710729	−	0.410339i	−0.100602	−	0.994927i	$-0.532077\pi$
$79$	6.31710	−	3.64718i	0.710729	−	0.410339i	0.811331	+	0.584587i	$0.198744\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.35365	−	2.34460i	−0.148583	−	0.257353i	0.782121	−	0.623126i	$-0.214138\pi$
$83$	−1.35365	−	2.34460i	−0.148583	−	0.257353i	−0.930704	+	0.365774i	$0.880804\pi$
$84$		0			0
$85$	−5.53201	+	9.58172i	−0.600031	+	1.03928i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	2.40174i		−	0.254584i	−0.991865	−	0.127292i	$-0.959372\pi$
$89$		−	2.40174i		−	0.254584i	0.991865	−	0.127292i	$-0.0406285\pi$
$90$		0			0
$91$		−	0.641255i		−	0.0672217i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.44888	−	14.6339i	0.866837	−	1.50141i
$96$		0			0
$97$	0.903600	+	1.56508i	0.0917467	+	0.158910i	0.908246	−	0.418436i	$-0.137422\pi$
$97$	0.903600	+	1.56508i	0.0917467	+	0.158910i	−0.816499	+	0.577346i	$0.804088\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.08158	−	1.77915i	0.306628	−	0.177032i	−0.338788	−	0.940863i	$-0.610017\pi$
$101$	3.08158	−	1.77915i	0.306628	−	0.177032i	0.645417	+	0.763831i	$0.276684\pi$
$102$		0			0
$103$	−8.28138	−	4.78126i	−0.815989	−	0.471111i	0.0330425	−	0.999454i	$-0.489480\pi$
$103$	−8.28138	−	4.78126i	−0.815989	−	0.471111i	−0.849031	+	0.528343i	$0.822814\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.60313			0.541675			0.270838	−	0.962625i	$-0.412699\pi$
$107$	5.60313			0.541675			0.270838	+	0.962625i	$0.412699\pi$
$108$		0			0
$109$	7.56853			0.724934			0.362467	−	0.931997i	$-0.381935\pi$
$109$	7.56853			0.724934			0.362467	+	0.931997i	$0.381935\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.495124	−	0.285860i	−0.0465773	−	0.0268914i	0.476531	−	0.879158i	$-0.341894\pi$
$113$	−0.495124	−	0.285860i	−0.0465773	−	0.0268914i	−0.523108	+	0.852266i	$0.675228\pi$
$114$		0			0
$115$	9.72543	−	5.61498i	0.906901	−	0.523600i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.437452	+	0.757688i	0.0401011	+	0.0694572i
$120$		0			0
$121$	4.26783	−	7.39210i	0.387985	−	0.672009i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			11.7437i			1.05038i
$126$		0			0
$127$			14.0438i			1.24619i	0.782146	+	0.623095i	$0.214125\pi$
$127$			14.0438i			1.24619i	−0.782146	+	0.623095i	$0.785875\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.699837	−	1.21215i	0.0611450	−	0.105906i	−0.833832	−	0.552018i	$-0.813858\pi$
$131$	0.699837	−	1.21215i	0.0611450	−	0.105906i	0.894977	+	0.446111i	$0.147191\pi$
$132$		0			0
$133$	−0.668108	−	1.15720i	−0.0579323	−	0.100342i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.21477	−	0.701347i	0.103785	−	0.0599201i	−0.447209	−	0.894429i	$-0.647582\pi$
$137$	1.21477	−	0.701347i	0.103785	−	0.0599201i	0.550994	+	0.834509i	$0.314249\pi$
$138$		0			0
$139$	−18.6630	−	10.7751i	−1.58298	−	0.913933i	−0.994422	−	0.105477i	$-0.966363\pi$
$139$	−18.6630	−	10.7751i	−1.58298	−	0.913933i	−0.588557	−	0.808456i	$-0.700304\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.06615			0.507277
$144$		0			0
$145$	16.3647			1.35902
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.10263	−	2.94601i	−0.418024	−	0.241346i	0.276208	−	0.961098i	$-0.410922\pi$
$149$	−5.10263	−	2.94601i	−0.418024	−	0.241346i	−0.694232	+	0.719752i	$0.744256\pi$
$150$		0			0
$151$	−6.86723	+	3.96480i	−0.558847	+	0.322651i	−0.752683	−	0.658383i	$-0.771241\pi$
$151$	−6.86723	+	3.96480i	−0.558847	+	0.322651i	0.193835	+	0.981034i	$0.437907\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.55405	−	4.42375i	−0.205147	−	0.355324i
$156$		0			0
$157$	1.00382	−	1.73867i	0.0801138	−	0.138761i	−0.823185	−	0.567773i	$-0.807805\pi$
$157$	1.00382	−	1.73867i	0.0801138	−	0.138761i	0.903299	+	0.429012i	$0.141138\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	0.888025i		−	0.0699862i
$162$		0			0
$163$		−	2.06036i		−	0.161379i	−0.996739	−	0.0806897i	$-0.974288\pi$
$163$		−	2.06036i		−	0.161379i	0.996739	−	0.0806897i	$-0.0257123\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.45382	−	16.3745i	0.731559	−	1.26710i	−0.224658	−	0.974438i	$-0.572127\pi$
$167$	9.45382	−	16.3745i	0.731559	−	1.26710i	0.956217	−	0.292659i	$-0.0945401\pi$
$168$		0			0
$169$	−0.966142	−	1.67341i	−0.0743186	−	0.128724i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.29843	+	5.36845i	−0.706946	+	0.408156i	−0.809929	−	0.586528i	$-0.800495\pi$
$173$	−9.29843	+	5.36845i	−0.706946	+	0.408156i	0.102983	+	0.994683i	$0.467161\pi$
$174$		0			0
$175$	0.0856632	+	0.0494577i	0.00647553	+	0.00373865i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	22.7748			1.70227			0.851133	−	0.524950i	$-0.175916\pi$
$179$	22.7748			1.70227			0.851133	+	0.524950i	$0.175916\pi$
$180$		0			0
$181$	9.72780			0.723062			0.361531	−	0.932360i	$-0.382254\pi$
$181$	9.72780			0.723062			0.361531	+	0.932360i	$0.382254\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	15.5127	+	8.95628i	1.14052	+	0.658479i
$186$		0			0
$187$	−7.16759	+	4.13821i	−0.524146	+	0.302616i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.27410	−	2.20681i	−0.0921908	−	0.159679i	0.816242	−	0.577710i	$-0.196054\pi$
$191$	−1.27410	−	2.20681i	−0.0921908	−	0.159679i	−0.908433	+	0.418031i	$0.862720\pi$
$192$		0			0
$193$	−2.49967	+	4.32955i	−0.179930	+	0.311648i	−0.941856	−	0.336016i	$-0.890921\pi$
$193$	−2.49967	+	4.32955i	−0.179930	+	0.311648i	0.761926	+	0.647664i	$0.224254\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.65685i			0.403034i	0.979485	+	0.201517i	$0.0645872\pi$
$197$			5.65685i			0.403034i	−0.979485	+	0.201517i	$0.935413\pi$
$198$		0			0
$199$		−	14.4713i		−	1.02584i	−0.858436	−	0.512921i	$-0.828564\pi$
$199$		−	14.4713i		−	1.02584i	0.858436	−	0.512921i	$-0.171436\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.647031	−	1.12069i	0.0454127	−	0.0786571i
$204$		0			0
$205$	3.00349	+	5.20220i	0.209773	+	0.363338i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.9469	−	6.32017i	0.757210	−	0.437176i
$210$		0			0
$211$	12.7320	+	7.35080i	0.876505	+	0.506050i	0.869504	−	0.493925i	$-0.164438\pi$
$211$	12.7320	+	7.35080i	0.876505	+	0.506050i	0.00700041	+	0.999975i	$0.497772\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.29043			−0.565403
$216$		0			0
$217$	−0.403931			−0.0274206
$218$		0			0
$219$		0			0
$220$		0			0
$221$	17.6436	+	10.1865i	1.18683	+	0.685219i
$222$		0			0
$223$	15.6729	−	9.04876i	1.04954	−	0.605950i	0.127016	−	0.991901i	$-0.459460\pi$
$223$	15.6729	−	9.04876i	1.04954	−	0.605950i	0.922519	+	0.385951i	$0.126127\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.29529	−	10.9038i	−0.417833	−	0.723708i	0.577888	−	0.816116i	$-0.303877\pi$
$227$	−6.29529	−	10.9038i	−0.417833	−	0.723708i	−0.995721	+	0.0924078i	$0.970544\pi$
$228$		0			0
$229$	6.19995	−	10.7386i	0.409704	−	0.709628i	−0.585152	−	0.810923i	$-0.698965\pi$
$229$	6.19995	−	10.7386i	0.409704	−	0.709628i	0.994856	+	0.101295i	$0.0322986\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			7.13560i			0.467469i	0.972300	+	0.233734i	$0.0750947\pi$
$233$			7.13560i			0.467469i	−0.972300	+	0.233734i	$0.924905\pi$
$234$		0			0
$235$		−	15.4743i		−	1.00943i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.273904	+	0.474416i	−0.0177174	+	0.0306874i	−0.874748	−	0.484578i	$-0.838973\pi$
$239$	−0.273904	+	0.474416i	−0.0177174	+	0.0306874i	0.857031	+	0.515265i	$0.172307\pi$
$240$		0			0
$241$	−9.28792	−	16.0872i	−0.598288	−	1.03626i	−0.993074	−	0.117491i	$-0.962515\pi$
$241$	−9.28792	−	16.0872i	−0.598288	−	1.03626i	0.394786	−	0.918773i	$-0.370819\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.6718	−	7.31605i	0.809569	−	0.467405i
$246$		0			0
$247$	−26.9465	−	15.5576i	−1.71457	−	0.989905i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−19.2012			−1.21197			−0.605985	−	0.795476i	$-0.707221\pi$
$251$	−19.2012			−1.21197			−0.605985	+	0.795476i	$0.707221\pi$
$252$		0			0
$253$	8.40056			0.528138
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.90205	−	2.25285i	−0.243403	−	0.140529i	0.373337	−	0.927696i	$-0.378214\pi$
$257$	−3.90205	−	2.25285i	−0.243403	−	0.140529i	−0.616740	+	0.787167i	$0.711547\pi$
$258$		0			0
$259$	1.22669	−	0.708231i	0.0762229	−	0.0440073i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.92767	+	17.1952i	0.612166	+	1.06030i	0.990875	+	0.134787i	$0.0430351\pi$
$263$	9.92767	+	17.1952i	0.612166	+	1.06030i	−0.378708	+	0.925516i	$0.623632\pi$
$264$		0			0
$265$	2.52009	−	4.36492i	0.154808	−	0.268135i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	31.3938i		−	1.91411i	−0.289901	−	0.957057i	$-0.593622\pi$
$269$		−	31.3938i		−	1.91411i	0.289901	−	0.957057i	$-0.406378\pi$
$270$		0			0
$271$			0.868217i			0.0527405i	0.999652	+	0.0263702i	$0.00839488\pi$
$271$			0.868217i			0.0527405i	−0.999652	+	0.0263702i	$0.991605\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.467861	+	0.810358i	−0.0282131	+	0.0488664i
$276$		0			0
$277$	2.25608	+	3.90765i	0.135555	+	0.234788i	0.925809	−	0.377991i	$-0.123385\pi$
$277$	2.25608	+	3.90765i	0.135555	+	0.234788i	−0.790254	+	0.612779i	$0.790052\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−24.6156	+	14.2118i	−1.46844	+	0.847805i	−0.999375	−	0.0353583i	$-0.988743\pi$
$281$	−24.6156	+	14.2118i	−1.46844	+	0.847805i	−0.469066	+	0.883163i	$0.655409\pi$
$282$		0			0
$283$	−3.92629	−	2.26684i	−0.233394	−	0.134750i	0.378743	−	0.925502i	$-0.376356\pi$
$283$	−3.92629	−	2.26684i	−0.233394	−	0.134750i	−0.612137	+	0.790752i	$0.709690\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.475011			0.0280390
$288$		0			0
$289$	−10.7962			−0.635069
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.2072	+	7.62516i	0.771570	+	0.445466i	0.833435	−	0.552618i	$-0.186371\pi$
$293$	13.2072	+	7.62516i	0.771570	+	0.445466i	−0.0618642	+	0.998085i	$0.519705\pi$
$294$		0			0
$295$	19.9861	−	11.5390i	1.16364	−	0.671827i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.3393	−	17.9082i	−0.597937	−	1.03566i
$300$		0			0
$301$	−0.327789	+	0.567747i	−0.0188934	+	0.0327244i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			29.8833i			1.71111i
$306$		0			0
$307$			6.85996i			0.391519i	0.980652	+	0.195759i	$0.0627171\pi$
$307$			6.85996i			0.391519i	−0.980652	+	0.195759i	$0.937283\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.1876	+	21.1096i	−0.691097	+	1.19702i	0.280381	+	0.959889i	$0.409539\pi$
$311$	−12.1876	+	21.1096i	−0.691097	+	1.19702i	−0.971479	+	0.237127i	$0.923794\pi$
$312$		0			0
$313$	3.96030	+	6.85944i	0.223849	+	0.387719i	0.955974	−	0.293453i	$-0.0948043\pi$
$313$	3.96030	+	6.85944i	0.223849	+	0.387719i	−0.732124	+	0.681171i	$0.761471\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.4030	−	10.0476i	0.977447	−	0.564329i	0.0759487	−	0.997112i	$-0.475801\pi$
$317$	17.4030	−	10.0476i	0.977447	−	0.564329i	0.901498	+	0.432782i	$0.142468\pi$
$318$		0			0
$319$	10.6015	+	6.12080i	0.593572	+	0.342699i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	42.4523			2.36211
$324$		0			0
$325$	2.30335			0.127767
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.05971	−	0.611826i	−0.0584239	−	0.0337310i
$330$		0			0
$331$	−11.2223	+	6.47921i	−0.616835	+	0.356130i	−0.775636	−	0.631181i	$-0.782571\pi$
$331$	−11.2223	+	6.47921i	−0.616835	+	0.356130i	0.158801	+	0.987311i	$0.449237\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.76528	+	3.05756i	0.0964477	+	0.167052i
$336$		0			0
$337$	−6.96429	+	12.0625i	−0.379369	+	0.657086i	−0.990971	−	0.134080i	$-0.957192\pi$
$337$	−6.96429	+	12.0625i	−0.379369	+	0.657086i	0.611602	+	0.791166i	$0.290526\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	3.82111i		−	0.206925i
$342$		0			0
$343$		−	2.31868i		−	0.125197i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.0232	+	29.4851i	−0.913854	+	1.58284i	−0.105284	+	0.994442i	$0.533575\pi$
$347$	−17.0232	+	29.4851i	−0.913854	+	1.58284i	−0.808570	+	0.588399i	$0.799758\pi$
$348$		0			0
$349$	−0.599892	−	1.03904i	−0.0321115	−	0.0556188i	0.849523	−	0.527552i	$-0.176890\pi$
$349$	−0.599892	−	1.03904i	−0.0321115	−	0.0556188i	−0.881635	+	0.471933i	$0.843557\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−19.6933	+	11.3699i	−1.04817	+	0.605159i	−0.922135	−	0.386867i	$-0.873557\pi$
$353$	−19.6933	+	11.3699i	−1.04817	+	0.605159i	−0.126031	+	0.992026i	$0.540224\pi$
$354$		0			0
$355$	22.8391	+	13.1862i	1.21218	+	0.699850i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−21.5652			−1.13817			−0.569083	−	0.822280i	$-0.692702\pi$
$359$	−21.5652			−1.13817			−0.569083	+	0.822280i	$0.692702\pi$
$360$		0			0
$361$	−45.8363			−2.41244
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−19.0245	−	10.9838i	−0.995786	−	0.574917i
$366$		0			0
$367$	−28.0399	+	16.1889i	−1.46367	+	0.845051i	−0.999179	−	0.0405253i	$-0.987097\pi$
$367$	−28.0399	+	16.1889i	−1.46367	+	0.845051i	−0.464493	+	0.885577i	$0.653764\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.199280	−	0.345163i	−0.0103461	−	0.0179199i
$372$		0			0
$373$	5.19629	−	9.00024i	0.269054	−	0.466015i	−0.699564	−	0.714570i	$-0.746622\pi$
$373$	5.19629	−	9.00024i	0.269054	−	0.466015i	0.968618	+	0.248555i	$0.0799557\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	30.1336i		−	1.55196i
$378$		0			0
$379$			20.1762i			1.03638i	0.855265	+	0.518190i	$0.173394\pi$
$379$			20.1762i			1.03638i	−0.855265	+	0.518190i	$0.826606\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	11.8556	−	20.5344i	0.605791	−	1.04926i	−0.386135	−	0.922442i	$-0.626190\pi$
$383$	11.8556	−	20.5344i	0.605791	−	1.04926i	0.991926	−	0.126818i	$-0.0404765\pi$
$384$		0			0
$385$	−0.273343	−	0.473444i	−0.0139308	−	0.0241289i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.76371	+	1.01828i	−0.0894236	+	0.0516288i	−0.544045	−	0.839056i	$-0.683108\pi$
$389$	−1.76371	+	1.01828i	−0.0894236	+	0.0516288i	0.454621	+	0.890685i	$0.349775\pi$
$390$		0			0
$391$	24.4332	+	14.1065i	1.23564	+	0.713399i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−15.3076			−0.770209
$396$		0			0
$397$	1.74252			0.0874547			0.0437274	−	0.999044i	$-0.486077\pi$
$397$	1.74252			0.0874547			0.0437274	+	0.999044i	$0.486077\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−20.4143	−	11.7862i	−1.01944	−	0.588574i	−0.105498	−	0.994419i	$-0.533644\pi$
$401$	−20.4143	−	11.7862i	−1.01944	−	0.588574i	−0.913942	+	0.405846i	$0.866977\pi$
$402$		0			0
$403$	−8.14580	+	4.70298i	−0.405771	+	0.234272i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.69973	+	11.6043i	0.332093	+	0.575202i
$408$		0			0
$409$	−10.8999	+	18.8792i	−0.538965	+	0.933515i	0.459995	+	0.887922i	$0.347851\pi$
$409$	−10.8999	+	18.8792i	−0.538965	+	0.933515i	−0.998960	+	0.0455934i	$0.985482\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	1.82493i		−	0.0897988i
$414$		0			0
$415$			5.68143i			0.278891i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.5076	−	18.1997i	0.513329	−	0.889112i	−0.486552	−	0.873652i	$-0.661745\pi$
$419$	10.5076	−	18.1997i	0.513329	−	0.889112i	0.999880	−	0.0154599i	$-0.00492125\pi$
$420$		0			0
$421$	6.86839	+	11.8964i	0.334745	+	0.579795i	0.983436	−	0.181257i	$-0.0580166\pi$
$421$	6.86839	+	11.8964i	0.334745	+	0.579795i	−0.648691	+	0.761052i	$0.724683\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.72157	+	1.57130i	−0.132016	+	0.0762192i
$426$		0			0
$427$	2.04648	+	1.18153i	0.0990360	+	0.0571784i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.476344			0.0229447			0.0114723	−	0.999934i	$-0.496348\pi$
$431$	0.476344			0.0229447			0.0114723	+	0.999934i	$0.496348\pi$
$432$		0			0
$433$	−11.6601			−0.560348			−0.280174	−	0.959949i	$-0.590392\pi$
$433$	−11.6601			−0.560348			−0.280174	+	0.959949i	$0.590392\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−37.3162	−	21.5445i	−1.78508	−	1.03061i
$438$		0			0
$439$	−29.8138	+	17.2130i	−1.42294	+	0.821533i	−0.996549	−	0.0830082i	$-0.973547\pi$
$439$	−29.8138	+	17.2130i	−1.42294	+	0.821533i	−0.426387	+	0.904541i	$0.640214\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.84473	+	8.39132i	0.230180	+	0.398684i	0.957861	−	0.287232i	$-0.0927351\pi$
$443$	4.84473	+	8.39132i	0.230180	+	0.398684i	−0.727681	+	0.685916i	$0.759402\pi$
$444$		0			0
$445$	−2.52009	+	4.36492i	−0.119464	+	0.206917i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			17.9789i			0.848477i	0.905550	+	0.424239i	$0.139458\pi$
$449$			17.9789i			0.848477i	−0.905550	+	0.424239i	$0.860542\pi$
$450$		0			0
$451$			4.49352i			0.211591i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.672854	+	1.16542i	−0.0315439	+	0.0546356i
$456$		0			0
$457$	6.95237	+	12.0419i	0.325218	+	0.563295i	0.981557	−	0.191172i	$-0.0612289\pi$
$457$	6.95237	+	12.0419i	0.325218	+	0.563295i	−0.656338	+	0.754467i	$0.727896\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.80521	−	1.04224i	0.0840772	−	0.0485420i	−0.457372	−	0.889275i	$-0.651209\pi$
$461$	1.80521	−	1.04224i	0.0840772	−	0.0485420i	0.541449	+	0.840733i	$0.317876\pi$
$462$		0			0
$463$	31.0337	+	17.9173i	1.44226	+	0.832688i	0.998000	−	0.0632104i	$-0.0201339\pi$
$463$	31.0337	+	17.9173i	1.44226	+	0.832688i	0.444258	+	0.895899i	$0.353467\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.4185			−1.17623			−0.588114	−	0.808778i	$-0.700129\pi$
$467$	−25.4185			−1.17623			−0.588114	+	0.808778i	$0.700129\pi$
$468$		0			0
$469$	0.279185			0.0128915
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.37078	−	3.10082i	−0.246949	−	0.142576i
$474$		0			0
$475$	4.15658	−	2.39980i	0.190717	−	0.110110i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.4545	+	19.8398i	0.523370	+	0.906503i	0.999630	+	0.0271987i	$0.00865867\pi$
$479$	11.4545	+	19.8398i	0.523370	+	0.906503i	−0.476260	+	0.879304i	$0.658008\pi$
$480$		0			0
$481$	16.4919	−	28.5648i	0.751965	−	1.30244i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	3.79251i		−	0.172209i
$486$		0			0
$487$		−	15.6846i		−	0.710738i	−0.934726	−	0.355369i	$-0.884355\pi$
$487$		−	15.6846i		−	0.710738i	0.934726	−	0.355369i	$-0.115645\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.2976	+	21.3001i	−0.554982	+	0.961258i	0.442922	+	0.896560i	$0.353942\pi$
$491$	−12.2976	+	21.3001i	−0.554982	+	0.961258i	−0.997905	+	0.0646979i	$0.979392\pi$
$492$		0			0
$493$	20.5566	+	35.6050i	0.925821	+	1.60357i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.80604	−	1.04272i	0.0810118	−	0.0467722i
$498$		0			0
$499$	−5.96333	−	3.44293i	−0.266955	−	0.154127i	0.360548	−	0.932741i	$-0.382590\pi$
$499$	−5.96333	−	3.44293i	−0.266955	−	0.154127i	−0.627503	+	0.778614i	$0.715923\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17.6347			−0.786294			−0.393147	−	0.919476i	$-0.628614\pi$
$503$	−17.6347			−0.786294			−0.393147	+	0.919476i	$0.628614\pi$
$504$		0			0
$505$	−7.46729			−0.332290
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.1218	+	8.15320i	0.625936	+	0.361384i	0.779177	−	0.626805i	$-0.215638\pi$
$509$	14.1218	+	8.15320i	0.625936	+	0.361384i	−0.153240	+	0.988189i	$0.548971\pi$
$510$		0			0
$511$	−1.50439	+	0.868558i	−0.0665502	+	0.0384228i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	10.0337	+	17.3789i	0.442139	+	0.765807i
$516$		0			0
$517$	5.78776	−	10.0247i	0.254545	−	0.440885i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	9.44397i		−	0.413748i	−0.978368	−	0.206874i	$-0.933671\pi$
$521$		−	9.44397i		−	0.413748i	0.978368	−	0.206874i	$-0.0663290\pi$
$522$		0			0
$523$		−	22.5688i		−	0.986865i	−0.869784	−	0.493433i	$-0.835742\pi$
$523$		−	22.5688i		−	0.986865i	0.869784	−	0.493433i	$-0.164258\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.41656	−	11.1138i	0.279510	−	0.484125i
$528$		0			0
$529$	−2.81812	−	4.88113i	−0.122527	−	0.212223i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.57922	−	5.53056i	0.414922	−	0.239555i
$534$		0			0
$535$	−10.1831	−	5.87924i	−0.440256	−	0.254182i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.9455			0.471457
$540$		0			0
$541$	−32.0491			−1.37790			−0.688950	−	0.724809i	$-0.741928\pi$
$541$	−32.0491			−1.37790			−0.688950	+	0.724809i	$0.741928\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−13.7551	−	7.94149i	−0.589202	−	0.340176i
$546$		0			0
$547$	14.6339	−	8.44889i	0.625701	−	0.361249i	−0.153384	−	0.988167i	$-0.549017\pi$
$547$	14.6339	−	8.44889i	0.625701	−	0.361249i	0.779085	+	0.626918i	$0.215684\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−31.3955	−	54.3786i	−1.33749	−	2.31660i
$552$		0			0
$553$	−0.605235	+	1.04830i	−0.0257372	+	0.0445782i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	32.6034i		−	1.38145i	−0.723118	−	0.690725i	$-0.757292\pi$
$557$		−	32.6034i		−	1.38145i	0.723118	−	0.690725i	$-0.242708\pi$
$558$		0			0
$559$			15.2658i			0.645675i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.58426	+	13.1363i	−0.319639	+	0.553630i	−0.980413	−	0.196955i	$-0.936895\pi$
$563$	−7.58426	+	13.1363i	−0.319639	+	0.553630i	0.660774	+	0.750585i	$0.270228\pi$
$564$		0			0
$565$	0.599892	+	1.03904i	0.0252377	+	0.0437129i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.18052	−	2.41363i	0.175257	−	0.101184i	−0.409806	−	0.912173i	$-0.634403\pi$
$569$	4.18052	−	2.41363i	0.175257	−	0.101184i	0.585062	+	0.810988i	$0.301070\pi$
$570$		0			0
$571$	4.07311	+	2.35161i	0.170454	+	0.0984118i	0.582800	−	0.812616i	$-0.301957\pi$
$571$	4.07311	+	2.35161i	0.170454	+	0.0984118i	−0.412346	+	0.911027i	$0.635290\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.18973			0.133021
$576$		0			0
$577$	−19.5812			−0.815175			−0.407587	−	0.913166i	$-0.633630\pi$
$577$	−19.5812			−0.815175			−0.407587	+	0.913166i	$0.633630\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.389077	+	0.224634i	0.0161416	+	0.00931938i
$582$		0			0
$583$	3.26517	−	1.88515i	0.135230	−	0.0780749i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.83368	+	15.3004i	0.364605	+	0.631515i	0.988713	−	0.149824i	$-0.0478707\pi$
$587$	8.83368	+	15.3004i	0.364605	+	0.631515i	−0.624108	+	0.781338i	$0.714537\pi$
$588$		0			0
$589$	−9.79984	+	16.9738i	−0.403795	+	0.699394i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			14.1557i			0.581307i	0.956828	+	0.290653i	$0.0938727\pi$
$593$			14.1557i			0.581307i	−0.956828	+	0.290653i	$0.906127\pi$
$594$		0			0
$595$		−	1.83603i		−	0.0752700i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.3209	+	23.0726i	−0.544279	+	0.942719i	0.454373	+	0.890812i	$0.349863\pi$
$599$	−13.3209	+	23.0726i	−0.544279	+	0.942719i	−0.998652	+	0.0519076i	$0.983470\pi$
$600$		0			0
$601$	−12.2321	−	21.1866i	−0.498959	−	0.864221i	0.501041	−	0.865424i	$-0.332951\pi$
$601$	−12.2321	−	21.1866i	−0.498959	−	0.864221i	−0.999999	+	0.00120220i	$0.999617\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−15.5127	+	8.95628i	−0.630682	+	0.364124i
$606$		0			0
$607$	24.5942	+	14.1995i	0.998247	+	0.576338i	0.907729	−	0.419556i	$-0.137814\pi$
$607$	24.5942	+	14.1995i	0.998247	+	0.576338i	0.0905181	+	0.995895i	$0.471148\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−28.4940			−1.15274
$612$		0			0
$613$	−6.79923			−0.274618			−0.137309	−	0.990528i	$-0.543845\pi$
$613$	−6.79923			−0.274618			−0.137309	+	0.990528i	$0.543845\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	32.6817	+	18.8688i	1.31571	+	0.759628i	0.983036	−	0.183412i	$-0.0587143\pi$
$617$	32.6817	+	18.8688i	1.31571	+	0.759628i	0.332678	+	0.943040i	$0.392048\pi$
$618$		0			0
$619$	−7.89600	+	4.55876i	−0.317367	+	0.183232i	−0.650218	−	0.759747i	$-0.725323\pi$
$619$	−7.89600	+	4.55876i	−0.317367	+	0.183232i	0.332851	+	0.942979i	$0.391989\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.199280	+	0.345163i	0.00798397	+	0.0138286i
$624$		0			0
$625$	10.8322	−	18.7619i	0.433287	−	0.750475i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			45.0018i			1.79434i
$630$		0			0
$631$			9.05133i			0.360328i	0.983637	+	0.180164i	$0.0576628\pi$
$631$			9.05133i			0.360328i	−0.983637	+	0.180164i	$0.942337\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	14.7359	−	25.5233i	0.584776	−	1.01286i
$636$		0			0
$637$	−13.4716	−	23.3335i	−0.533764	−	0.924507i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	27.1865	−	15.6961i	1.07380	−	0.619959i	0.144583	−	0.989493i	$-0.453816\pi$
$641$	27.1865	−	15.6961i	1.07380	−	0.619959i	0.929217	+	0.369533i	$0.120482\pi$
$642$		0			0
$643$	6.03917	+	3.48672i	0.238162	+	0.137503i	0.614332	−	0.789048i	$-0.289426\pi$
$643$	6.03917	+	3.48672i	0.238162	+	0.137503i	−0.376170	+	0.926551i	$0.622759\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	36.4189			1.43178			0.715888	−	0.698215i	$-0.246022\pi$
$647$	36.4189			1.43178			0.715888	+	0.698215i	$0.246022\pi$
$648$		0			0
$649$	17.2635			0.677650
$650$		0			0
$651$		0			0
$652$		0			0
$653$	27.9837	+	16.1564i	1.09509	+	0.632248i	0.934926	−	0.354843i	$-0.115466\pi$
$653$	27.9837	+	16.1564i	1.09509	+	0.632248i	0.160159	+	0.987091i	$0.448799\pi$
$654$		0			0
$655$	−2.54377	+	1.46865i	−0.0993933	+	0.0573847i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.52870	+	4.37984i	0.0985042	+	0.170614i	0.911066	−	0.412261i	$-0.135261\pi$
$659$	2.52870	+	4.37984i	0.0985042	+	0.170614i	−0.812562	+	0.582875i	$0.801928\pi$
$660$		0			0
$661$	6.31245	−	10.9335i	0.245526	−	0.425263i	−0.716753	−	0.697327i	$-0.754373\pi$
$661$	6.31245	−	10.9335i	0.245526	−	0.425263i	0.962279	+	0.272063i	$0.0877060\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			2.80412i			0.108739i
$666$		0			0
$667$		−	41.7298i		−	1.61578i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.1771	+	19.3593i	−0.431487	+	0.747357i
$672$		0			0
$673$	23.5547	+	40.7980i	0.907967	+	1.57265i	0.816884	+	0.576802i	$0.195700\pi$
$673$	23.5547	+	40.7980i	0.907967	+	1.57265i	0.0910837	+	0.995843i	$0.470967\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.1335	+	9.31465i	−0.620059	+	0.357991i	−0.776892	−	0.629634i	$-0.783205\pi$
$677$	−16.1335	+	9.31465i	−0.620059	+	0.357991i	0.156833	+	0.987625i	$0.449872\pi$
$678$		0			0
$679$	−0.259719	−	0.149949i	−0.00996712	−	0.00575452i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.4857			0.592544			0.296272	−	0.955104i	$-0.404257\pi$
$683$	15.4857			0.592544			0.296272	+	0.955104i	$0.404257\pi$
$684$		0			0
$685$	−2.94363			−0.112470
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.03747	−	4.64044i	−0.306203	−	0.176787i
$690$		0			0
$691$	−9.34942	+	5.39789i	−0.355669	+	0.205345i	−0.667179	−	0.744897i	$-0.732498\pi$
$691$	−9.34942	+	5.39789i	−0.355669	+	0.205345i	0.311510	+	0.950243i	$0.399165\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	22.6122	+	39.1654i	0.857728	+	1.48563i
$696$		0			0
$697$	−7.54569	+	13.0695i	−0.285813	+	0.495043i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	7.59493i		−	0.286857i	−0.989661	−	0.143428i	$-0.954187\pi$
$701$		−	7.59493i		−	0.286857i	0.989661	−	0.143428i	$-0.0458127\pi$
$702$		0			0
$703$		−	68.7300i		−	2.59220i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.295243	+	0.511376i	−0.0111038	+	0.0192323i
$708$		0			0
$709$	−11.5763	−	20.0508i	−0.434759	−	0.753024i	0.562517	−	0.826786i	$-0.309833\pi$
$709$	−11.5763	−	20.0508i	−0.434759	−	0.753024i	−0.997276	+	0.0737615i	$0.976500\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−11.2805	+	6.51280i	−0.422458	+	0.243906i
$714$		0			0
$715$	−11.0246	−	6.36507i	−0.412298	−	0.238040i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	7.49075			0.279358			0.139679	−	0.990197i	$-0.455393\pi$
$719$	7.49075			0.279358			0.139679	+	0.990197i	$0.455393\pi$
$720$		0			0
$721$	1.58686			0.0590979
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.02546	+	2.32410i	0.149502	+	0.0863148i
$726$		0			0
$727$	−28.2968	+	16.3372i	−1.04947	+	0.605911i	−0.922501	−	0.385995i	$-0.873858\pi$
$727$	−28.2968	+	16.3372i	−1.04947	+	0.605911i	−0.126969	+	0.991907i	$0.540525\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.4140	−	18.0376i	−0.385177	−	0.667146i
$732$		0			0
$733$	24.2248	−	41.9586i	0.894765	−	1.54978i	0.0606693	−	0.998158i	$-0.480676\pi$
$733$	24.2248	−	41.9586i	0.894765	−	1.54978i	0.834095	−	0.551620i	$-0.185990\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			2.64103i			0.0972838i
$738$		0			0
$739$			4.58382i			0.168619i	0.996440	+	0.0843094i	$0.0268684\pi$
$739$			4.58382i			0.168619i	−0.996440	+	0.0843094i	$0.973132\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18.5816	−	32.1842i	0.681691	−	1.18072i	−0.292773	−	0.956182i	$-0.594578\pi$
$743$	18.5816	−	32.1842i	0.681691	−	1.18072i	0.974464	−	0.224542i	$-0.0720886\pi$
$744$		0			0
$745$	6.18235	+	10.7082i	0.226504	+	0.392316i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.805247	+	0.464909i	−0.0294231	+	0.0169874i
$750$		0			0
$751$	−31.1292	−	17.9724i	−1.13592	−	0.655824i	−0.190503	−	0.981687i	$-0.561012\pi$
$751$	−31.1292	−	17.9724i	−1.13592	−	0.655824i	−0.945417	+	0.325863i	$0.894345\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.6407			0.605617
$756$		0			0
$757$	−4.99097			−0.181400			−0.0907000	−	0.995878i	$-0.528910\pi$
$757$	−4.99097			−0.181400			−0.0907000	+	0.995878i	$0.528910\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10.0903	+	5.82561i	0.365771	+	0.211178i	0.671609	−	0.740905i	$-0.265603\pi$
$761$	10.0903	+	5.82561i	0.365771	+	0.211178i	−0.305838	+	0.952084i	$0.598937\pi$
$762$		0			0
$763$	−1.08770	+	0.627985i	−0.0393774	+	0.0227346i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.2477	−	36.8020i	−0.767208	−	1.32884i
$768$		0			0
$769$	9.86238	−	17.0821i	0.355646	−	0.615998i	−0.631582	−	0.775309i	$-0.717594\pi$
$769$	9.86238	−	17.0821i	0.355646	−	0.615998i	0.987228	+	0.159312i	$0.0509274\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			39.5946i			1.42412i	0.702120	+	0.712059i	$0.252237\pi$
$773$			39.5946i			1.42412i	−0.702120	+	0.712059i	$0.747763\pi$
$774$		0			0
$775$		−	1.45090i		−	0.0521177i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	11.5243	−	19.9607i	0.412902	−	0.715167i
$780$		0			0
$781$	9.86390	+	17.0848i	0.352958	+	0.611341i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.64870	+	2.10658i	−0.130228	+	0.0751870i
$786$		0			0
$787$	19.6360	+	11.3369i	0.699949	+	0.404116i	0.807329	−	0.590102i	$-0.200913\pi$
$787$	19.6360	+	11.3369i	0.699949	+	0.404116i	−0.107379	+	0.994218i	$0.534246\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.0948747			0.00337336
$792$		0			0
$793$	55.0265			1.95405
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.38454	+	0.799367i	0.0490431	+	0.0283150i	0.524321	−	0.851521i	$-0.324319\pi$
$797$	1.38454	+	0.799367i	0.0490431	+	0.0283150i	−0.475278	+	0.879836i	$0.657653\pi$
$798$		0			0
$799$	33.6677	−	19.4381i	1.19108	−	0.687669i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.21640	−	14.2312i	−0.289950	−	0.502209i
$804$		0			0
$805$	−0.931785	+	1.61390i	−0.0328411	+	0.0568825i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	50.2740i		−	1.76754i	−0.467922	−	0.883770i	$-0.654997\pi$
$809$		−	50.2740i		−	1.76754i	0.467922	−	0.883770i	$-0.345003\pi$
$810$		0			0
$811$			36.5884i			1.28479i	0.766372	+	0.642397i	$0.222060\pi$
$811$			36.5884i			1.28479i	−0.766372	+	0.642397i	$0.777940\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.16188	+	3.74449i	−0.0757275	+	0.131164i
$816$		0			0
$817$	15.9051	+	27.5484i	0.556448	+	0.963796i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	33.1310	−	19.1282i	1.15628	−	0.667579i	0.205871	−	0.978579i	$-0.433997\pi$
$821$	33.1310	−	19.1282i	1.15628	−	0.667579i	0.950410	+	0.311000i	$0.100664\pi$
$822$		0			0
$823$	0.874309	+	0.504783i	0.0304765	+	0.0175956i	0.515161	−	0.857094i	$-0.327732\pi$
$823$	0.874309	+	0.504783i	0.0304765	+	0.0175956i	−0.484684	+	0.874689i	$0.661066\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.17121			0.214594			0.107297	−	0.994227i	$-0.465780\pi$
$827$	6.17121			0.214594			0.107297	+	0.994227i	$0.465780\pi$
$828$		0			0
$829$	−10.6949			−0.371450			−0.185725	−	0.982602i	$-0.559463\pi$
$829$	−10.6949			−0.371450			−0.185725	+	0.982602i	$0.559463\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	31.8353	+	18.3801i	1.10303	+	0.636834i
$834$		0			0
$835$	−34.3628	+	19.8394i	−1.18917	+	0.686569i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−26.6888	−	46.2263i	−0.921399	−	1.59591i	−0.797252	−	0.603646i	$-0.793714\pi$
$839$	−26.6888	−	46.2263i	−0.921399	−	1.59591i	−0.124147	−	0.992264i	$-0.539619\pi$
$840$		0			0
$841$	15.9051	−	27.5484i	0.548451	−	0.949945i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			4.05500i			0.139496i
$846$		0			0
$847$			1.41646i			0.0486702i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	22.8384	−	39.5572i	0.782890	−	1.35600i
$852$		0			0
$853$	7.32038	+	12.6793i	0.250645	+	0.434130i	0.963704	−	0.266975i	$-0.0860240\pi$
$853$	7.32038	+	12.6793i	0.250645	+	0.434130i	−0.713059	+	0.701104i	$0.752691\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.8376	−	12.6080i	0.745959	−	0.430680i	−0.0782730	−	0.996932i	$-0.524941\pi$
$857$	21.8376	−	12.6080i	0.745959	−	0.430680i	0.824232	+	0.566252i	$0.191607\pi$
$858$		0			0
$859$	−3.77869	−	2.18163i	−0.128927	−	0.0744361i	0.434149	−	0.900841i	$-0.357049\pi$
$859$	−3.77869	−	2.18163i	−0.128927	−	0.0744361i	−0.563076	+	0.826405i	$0.690382\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	36.7626			1.25141			0.625706	−	0.780059i	$-0.284811\pi$
$863$	36.7626			1.25141			0.625706	+	0.780059i	$0.284811\pi$
$864$		0			0
$865$	22.5320			0.766110
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−9.91671	−	5.72541i	−0.336401	−	0.194221i
$870$		0			0
$871$	5.63012	−	3.25055i	0.190769	−	0.110141i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.974408	−	1.68772i	−0.0329410	−	0.0570555i
$876$		0			0
$877$	2.02843	−	3.51334i	0.0684951	−	0.118637i	−0.829744	−	0.558144i	$-0.811514\pi$
$877$	2.02843	−	3.51334i	0.0684951	−	0.118637i	0.898239	+	0.439507i	$0.144847\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	29.5979i		−	0.997179i	−0.866838	−	0.498589i	$-0.833852\pi$
$881$		−	29.5979i		−	0.997179i	0.866838	−	0.498589i	$-0.166148\pi$
$882$		0			0
$883$		−	42.1894i		−	1.41979i	−0.704309	−	0.709894i	$-0.748743\pi$
$883$		−	42.1894i		−	1.41979i	0.704309	−	0.709894i	$-0.251257\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.1442	+	26.2305i	−0.508491	+	0.880733i	0.491460	+	0.870900i	$0.336463\pi$
$887$	−15.1442	+	26.2305i	−0.508491	+	0.880733i	−0.999952	+	0.00983292i	$0.996870\pi$
$888$		0			0
$889$	−1.16526	−	2.01829i	−0.0390816	−	0.0676913i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−51.4198	+	29.6872i	−1.72070	+	0.993445i
$894$		0			0
$895$	−41.3909	−	23.8970i	−1.38355	−	0.798790i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.9814			−0.633065
$900$		0			0
$901$	12.6625			0.421848
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.6793	−	10.2072i	−0.587681	−	0.339298i
$906$		0			0
$907$	20.8861	−	12.0586i	0.693510	−	0.400398i	−0.111416	−	0.993774i	$-0.535538\pi$
$907$	20.8861	−	12.0586i	0.693510	−	0.400398i	0.804926	+	0.593376i	$0.202205\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	10.0067	+	17.3322i	0.331538	+	0.574241i	0.982814	−	0.184600i	$-0.0590991\pi$
$911$	10.0067	+	17.3322i	0.331538	+	0.574241i	−0.651276	+	0.758841i	$0.725766\pi$
$912$		0			0
$913$	−2.12499	+	3.68060i	−0.0703270	+	0.121810i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			0.232271i			0.00767025i
$918$		0			0
$919$		−	7.25070i		−	0.239178i	−0.992823	−	0.119589i	$-0.961842\pi$
$919$		−	7.25070i		−	0.239178i	0.992823	−	0.119589i	$-0.0381578\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	24.2807	−	42.0555i	0.799210	−	1.38427i
$924$		0			0
$925$	2.54392	+	4.40620i	0.0836436	+	0.144875i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.6167	−	9.01628i	0.512366	−	0.295815i	−0.221440	−	0.975174i	$-0.571076\pi$
$929$	15.6167	−	9.01628i	0.512366	−	0.295815i	0.733806	+	0.679360i	$0.237742\pi$
$930$		0			0
$931$	−48.6212	−	28.0715i	−1.59350	−	0.920005i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	17.3685			0.568011
$936$		0			0
$937$	26.2806			0.858551			0.429276	−	0.903174i	$-0.358769\pi$
$937$	26.2806			0.858551			0.429276	+	0.903174i	$0.358769\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.6987	+	17.7239i	1.00075	+	0.577782i	0.908469	−	0.417951i	$-0.137252\pi$
$941$	30.6987	+	17.7239i	1.00075	+	0.577782i	0.0922782	+	0.995733i	$0.470585\pi$
$942$		0			0
$943$	13.2655	−	7.65886i	0.431986	−	0.249407i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.1432	−	17.5686i	−0.329610	−	0.570901i	0.652824	−	0.757509i	$-0.273584\pi$
$947$	−10.1432	−	17.5686i	−0.329610	−	0.570901i	−0.982434	+	0.186608i	$0.940251\pi$
$948$		0			0
$949$	−20.2253	+	35.0312i	−0.656541	+	1.13716i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			27.1172i			0.878411i	0.898387	+	0.439205i	$0.144740\pi$
$953$			27.1172i			0.878411i	−0.898387	+	0.439205i	$0.855260\pi$
$954$		0			0
$955$			5.34755i			0.173043i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.116386	+	0.201586i	−0.00375830	+	0.00650956i
$960$		0			0
$961$	−12.5376	−	21.7157i	−0.404437	−	0.700506i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.08581	−	5.24569i	0.292482	−	0.168865i
$966$		0			0
$967$	18.4921	+	10.6764i	0.594665	+	0.343330i	0.766940	−	0.641719i	$-0.221778\pi$
$967$	18.4921	+	10.6764i	0.594665	+	0.343330i	−0.172275	+	0.985049i	$0.555112\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−11.9224			−0.382608			−0.191304	−	0.981531i	$-0.561272\pi$
$971$	−11.9224			−0.382608			−0.191304	+	0.981531i	$0.561272\pi$
$972$		0			0
$973$	3.57618			0.114647
$974$		0			0
$975$		0			0
$976$		0			0
$977$	16.3300	+	9.42812i	0.522442	+	0.301632i	0.737933	−	0.674874i	$-0.235802\pi$
$977$	16.3300	+	9.42812i	0.522442	+	0.301632i	−0.215491	+	0.976506i	$0.569135\pi$
$978$		0			0
$979$	−3.26517	+	1.88515i	−0.104355	+	0.0602496i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.3810	+	42.2290i	0.777632	+	1.34690i	0.933303	+	0.359089i	$0.116912\pi$
$983$	24.3810	+	42.2290i	0.777632	+	1.34690i	−0.155672	+	0.987809i	$0.549754\pi$
$984$		0			0
$985$	5.93561	−	10.2808i	0.189124	−	0.327573i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			21.1405i			0.672228i
$990$		0			0
$991$			27.4703i			0.872622i	0.899796	+	0.436311i	$0.143715\pi$
$991$			27.4703i			0.872622i	−0.899796	+	0.436311i	$0.856285\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−15.1844	+	26.3001i	−0.481377	+	0.833770i
$996$		0			0
$997$	−22.0675	−	38.2220i	−0.698885	−	1.21050i	−0.968853	−	0.247635i	$-0.920347\pi$
$997$	−22.0675	−	38.2220i	−0.698885	−	1.21050i	0.269969	−	0.962869i	$-0.412987\pi$
$998$		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.287.3		24
3.2	odd	2		288.2.s.a.95.2	✓	24
4.3	odd	2	inner	864.2.s.a.287.4		24
8.3	odd	2		1728.2.s.g.1151.10		24
8.5	even	2		1728.2.s.g.1151.9		24
9.2	odd	6	inner	864.2.s.a.575.4		24
9.4	even	3		2592.2.c.c.2591.19		24
9.5	odd	6		2592.2.c.c.2591.5		24
9.7	even	3		288.2.s.a.191.11	yes	24
12.11	even	2		288.2.s.a.95.11	yes	24
24.5	odd	2		576.2.s.g.383.11		24
24.11	even	2		576.2.s.g.383.2		24
36.7	odd	6		288.2.s.a.191.2	yes	24
36.11	even	6	inner	864.2.s.a.575.3		24
36.23	even	6		2592.2.c.c.2591.6		24
36.31	odd	6		2592.2.c.c.2591.20		24
72.5	odd	6		5184.2.c.m.5183.19		24
72.11	even	6		1728.2.s.g.575.9		24
72.13	even	6		5184.2.c.m.5183.5		24
72.29	odd	6		1728.2.s.g.575.10		24
72.43	odd	6		576.2.s.g.191.11		24
72.59	even	6		5184.2.c.m.5183.20		24
72.61	even	6		576.2.s.g.191.2		24
72.67	odd	6		5184.2.c.m.5183.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.s.a.95.2	✓	24	3.2	odd	2
288.2.s.a.95.11	yes	24	12.11	even	2
288.2.s.a.191.2	yes	24	36.7	odd	6
288.2.s.a.191.11	yes	24	9.7	even	3
576.2.s.g.191.2		24	72.61	even	6
576.2.s.g.191.11		24	72.43	odd	6
576.2.s.g.383.2		24	24.11	even	2
576.2.s.g.383.11		24	24.5	odd	2
864.2.s.a.287.3		24	1.1	even	1	trivial
864.2.s.a.287.4		24	4.3	odd	2	inner
864.2.s.a.575.3		24	36.11	even	6	inner
864.2.s.a.575.4		24	9.2	odd	6	inner
1728.2.s.g.575.9		24	72.11	even	6
1728.2.s.g.575.10		24	72.29	odd	6
1728.2.s.g.1151.9		24	8.5	even	2
1728.2.s.g.1151.10		24	8.3	odd	2
2592.2.c.c.2591.5		24	9.5	odd	6
2592.2.c.c.2591.6		24	36.23	even	6
2592.2.c.c.2591.19		24	9.4	even	3
2592.2.c.c.2591.20		24	36.31	odd	6
5184.2.c.m.5183.5		24	72.13	even	6
5184.2.c.m.5183.6		24	72.67	odd	6
5184.2.c.m.5183.19		24	72.5	odd	6
5184.2.c.m.5183.20		24	72.59	even	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)

\(f(q)\)	\(=\)	\(q+(-1.81740 - 1.04928i) q^{5} +(-0.143714 + 0.0829731i) q^{7} +O(q^{10})\)	\(q+(-1.81740 - 1.04928i) q^{5} +(-0.143714 + 0.0829731i) q^{7} +(-0.784910 - 1.35950i) q^{11} +(-1.93212 + 3.34652i) q^{13} -5.27221i q^{17} +8.05210i q^{19} +(-2.67564 + 4.63435i) q^{23} +(-0.298034 - 0.516211i) q^{25} +(-6.75334 + 3.89904i) q^{29} +(2.10800 + 1.21705i) q^{31} +0.348247 q^{35} -8.53566 q^{37} +(-2.47895 - 1.43122i) q^{41} +(3.42127 - 1.97527i) q^{43} +(3.68689 + 6.38588i) q^{47} +(-3.48623 + 6.03833i) q^{49} +2.40174i q^{53} +3.29435i q^{55} +(-5.49855 + 9.52376i) q^{59} +(-7.11998 - 12.3322i) q^{61} +(7.02286 - 4.05465i) q^{65} +(-1.45698 - 0.841190i) q^{67} -12.5669 q^{71} +10.4679 q^{73} +(0.225605 + 0.130253i) q^{77} +(6.31710 - 3.64718i) q^{79} +(-1.35365 - 2.34460i) q^{83} +(-5.53201 + 9.58172i) q^{85} -2.40174i q^{89} -0.641255i q^{91} +(8.44888 - 14.6339i) q^{95} +(0.903600 + 1.56508i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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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