LMFDB - Embedded newform 2592.2.s.j.863.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, 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("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.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:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 49x^{12} - 12x^{10} - 600x^{8} + 108x^{6} + 4057x^{4} + 18252x^{2} + 28561 $ x^16 - 12x^14 + 49x^12 - 12x^10 - 600x^8 + 108x^6 + 4057x^4 + 18252*x^2 + 28561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			863.5
Root			$0.850627 + 1.24273i$ of defining polynomial
Character	$\chi$	$=$	2592.863
Dual form			2592.2.s.j.1727.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12743 + 0.650924i) q^{5} +(-3.04406 + 1.75749i) q^{7} +O(q^{10})$	$q+(1.12743 + 0.650924i) q^{5} +(-3.04406 + 1.75749i) q^{7} +(0.909743 + 1.57572i) q^{11} +(2.62351 - 4.54406i) q^{13} -3.03908i q^{17} +3.05816i q^{19} +(2.61100 - 4.52238i) q^{23} +(-1.65260 - 2.86238i) q^{25} +(3.24875 - 1.87567i) q^{29} +(3.77159 + 2.17753i) q^{31} -4.57596 q^{35} +1.48502 q^{37} +(-7.32285 - 4.22785i) q^{41} +(5.57996 - 3.22159i) q^{43} +(6.34917 + 10.9971i) q^{47} +(2.67753 - 4.63762i) q^{49} +11.2841i q^{53} +2.36869i q^{55} +(0.342963 - 0.594030i) q^{59} +(2.07996 + 3.60259i) q^{61} +(5.91567 - 3.41542i) q^{65} +(10.9650 + 6.33063i) q^{67} +2.50541 q^{71} +12.3052 q^{73} +(-5.53862 - 3.19773i) q^{77} +(1.80836 - 1.04406i) q^{79} +(-8.58356 - 14.8672i) q^{83} +(1.97821 - 3.42636i) q^{85} +12.5300i q^{89} +18.4432i q^{91} +(-1.99063 + 3.44788i) q^{95} +(4.39561 + 7.61342i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7}+O(q^{10}) $ 16 * q + 12 * q^7	$ 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$5$	1.12743	+	0.650924i	0.504203	+	0.291102i	0.730448	−	0.682969i	$-0.239311\pi$
$5$	1.12743	+	0.650924i	0.504203	+	0.291102i	−0.226244	+	0.974071i	$0.572645\pi$
$6$		0			0
$7$	−3.04406	+	1.75749i	−1.15055	+	0.664268i	−0.949020	−	0.315215i	$-0.897923\pi$
$7$	−3.04406	+	1.75749i	−1.15055	+	0.664268i	−0.201526	+	0.979483i	$0.564590\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.909743	+	1.57572i	0.274298	+	0.475098i	0.969958	−	0.243274i	$-0.0782213\pi$
$11$	0.909743	+	1.57572i	0.274298	+	0.475098i	−0.695660	+	0.718371i	$0.744888\pi$
$12$		0			0
$13$	2.62351	−	4.54406i	0.727632	−	1.26030i	−0.230250	−	0.973132i	$-0.573954\pi$
$13$	2.62351	−	4.54406i	0.727632	−	1.26030i	0.957882	−	0.287164i	$-0.0927124\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	3.03908i		−	0.737084i	−0.929611	−	0.368542i	$-0.879857\pi$
$17$		−	3.03908i		−	0.737084i	0.929611	−	0.368542i	$-0.120143\pi$
$18$		0			0
$19$			3.05816i			0.701591i	0.936452	+	0.350796i	$0.114089\pi$
$19$			3.05816i			0.701591i	−0.936452	+	0.350796i	$0.885911\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.61100	−	4.52238i	0.544431	−	0.942981i	−0.454212	−	0.890894i	$-0.650079\pi$
$23$	2.61100	−	4.52238i	0.544431	−	0.942981i	0.998643	−	0.0520877i	$-0.0165875\pi$
$24$		0			0
$25$	−1.65260	−	2.86238i	−0.330519	−	0.572476i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.24875	−	1.87567i	0.603278	−	0.348303i	−0.167052	−	0.985948i	$-0.553425\pi$
$29$	3.24875	−	1.87567i	0.603278	−	0.348303i	0.770330	+	0.637645i	$0.220091\pi$
$30$		0			0
$31$	3.77159	+	2.17753i	0.677398	+	0.391096i	0.798874	−	0.601498i	$-0.205429\pi$
$31$	3.77159	+	2.17753i	0.677398	+	0.391096i	−0.121476	+	0.992594i	$0.538763\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.57596			−0.773479
$36$		0			0
$37$	1.48502			0.244136			0.122068	−	0.992522i	$-0.461047\pi$
$37$	1.48502			0.244136			0.122068	+	0.992522i	$0.461047\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.32285	−	4.22785i	−1.14364	−	0.660279i	−0.196308	−	0.980542i	$-0.562895\pi$
$41$	−7.32285	−	4.22785i	−1.14364	−	0.660279i	−0.947328	+	0.320264i	$0.896229\pi$
$42$		0			0
$43$	5.57996	−	3.22159i	0.850936	−	0.491288i	−0.0100309	−	0.999950i	$-0.503193\pi$
$43$	5.57996	−	3.22159i	0.850936	−	0.491288i	0.860966	+	0.508662i	$0.169860\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.34917	+	10.9971i	0.926121	+	1.60409i	0.789748	+	0.613431i	$0.210211\pi$
$47$	6.34917	+	10.9971i	0.926121	+	1.60409i	0.136373	+	0.990658i	$0.456455\pi$
$48$		0			0
$49$	2.67753	−	4.63762i	0.382504	−	0.662517i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			11.2841i			1.54999i	0.631965	+	0.774997i	$0.282248\pi$
$53$			11.2841i			1.54999i	−0.631965	+	0.774997i	$0.717752\pi$
$54$		0			0
$55$			2.36869i			0.319395i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.342963	−	0.594030i	0.0446500	−	0.0773361i	−0.842837	−	0.538169i	$-0.819116\pi$
$59$	0.342963	−	0.594030i	0.0446500	−	0.0773361i	0.887487	+	0.460833i	$0.152449\pi$
$60$		0			0
$61$	2.07996	+	3.60259i	0.266311	+	0.461265i	0.967906	−	0.251311i	$-0.0808618\pi$
$61$	2.07996	+	3.60259i	0.266311	+	0.461265i	−0.701595	+	0.712576i	$0.747528\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.91567	−	3.41542i	0.733749	−	0.423630i
$66$		0			0
$67$	10.9650	+	6.33063i	1.33958	+	0.773410i	0.986746	−	0.162275i	$-0.0518830\pi$
$67$	10.9650	+	6.33063i	1.33958	+	0.773410i	0.352839	+	0.935684i	$0.385216\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.50541			0.297338			0.148669	−	0.988887i	$-0.452501\pi$
$71$	2.50541			0.297338			0.148669	+	0.988887i	$0.452501\pi$
$72$		0			0
$73$	12.3052			1.44021			0.720107	−	0.693863i	$-0.244093\pi$
$73$	12.3052			1.44021			0.720107	+	0.693863i	$0.244093\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.53862	−	3.19773i	−0.631185	−	0.364415i
$78$		0			0
$79$	1.80836	−	1.04406i	0.203457	−	0.117466i	−0.394810	−	0.918763i	$-0.629190\pi$
$79$	1.80836	−	1.04406i	0.203457	−	0.117466i	0.598267	+	0.801297i	$0.295856\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.58356	−	14.8672i	−0.942169	−	1.63188i	−0.761323	−	0.648372i	$-0.775450\pi$
$83$	−8.58356	−	14.8672i	−0.942169	−	1.63188i	−0.180845	−	0.983512i	$-0.557883\pi$
$84$		0			0
$85$	1.97821	−	3.42636i	0.214567	−	0.371640i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			12.5300i			1.32818i	0.747652	+	0.664091i	$0.231181\pi$
$89$			12.5300i			1.32818i	−0.747652	+	0.664091i	$0.768819\pi$
$90$		0			0
$91$			18.4432i			1.93337i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.99063	+	3.44788i	−0.204235	+	0.353745i
$96$		0			0
$97$	4.39561	+	7.61342i	0.446307	+	0.773026i	0.998142	−	0.0609271i	$-0.0194057\pi$
$97$	4.39561	+	7.61342i	0.446307	+	0.773026i	−0.551836	+	0.833953i	$0.686072\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.65960	−	0.958173i	0.165137	−	0.0953418i	−0.415154	−	0.909751i	$-0.636272\pi$
$101$	1.65960	−	0.958173i	0.165137	−	0.0953418i	0.580291	+	0.814409i	$0.302939\pi$
$102$		0			0
$103$	15.4641	+	8.92820i	1.52372	+	0.879722i	0.999606	+	0.0280760i	$0.00893804\pi$
$103$	15.4641	+	8.92820i	1.52372	+	0.879722i	0.524117	+	0.851646i	$0.324395\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−18.8573			−1.82301			−0.911503	−	0.411293i	$-0.865077\pi$
$107$	−18.8573			−1.82301			−0.911503	+	0.411293i	$0.865077\pi$
$108$		0			0
$109$	17.1679			1.64439			0.822195	−	0.569206i	$-0.192749\pi$
$109$	17.1679			1.64439			0.822195	+	0.569206i	$0.192749\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.23251	+	1.28894i	0.210017	+	0.121253i	0.601319	−	0.799009i	$-0.294642\pi$
$113$	2.23251	+	1.28894i	0.210017	+	0.121253i	−0.391302	+	0.920262i	$0.627975\pi$
$114$		0			0
$115$	5.88745	−	3.39912i	0.549008	−	0.316970i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.34114	+	9.25113i	0.489622	+	0.848049i
$120$		0			0
$121$	3.84474	−	6.65928i	0.349521	−	0.605389i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	10.8121i		−	0.967063i
$126$		0			0
$127$			9.73306i			0.863669i	0.901953	+	0.431835i	$0.142134\pi$
$127$			9.73306i			0.863669i	−0.901953	+	0.431835i	$0.857866\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.00784	−	12.1379i	0.612278	−	1.06050i	−0.378577	−	0.925570i	$-0.623587\pi$
$131$	7.00784	−	12.1379i	0.612278	−	1.06050i	0.990856	−	0.134927i	$-0.0430801\pi$
$132$		0			0
$133$	−5.37469	−	9.30923i	−0.466045	−	0.807213i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.49837	−	1.44244i	0.213450	−	0.123236i	−0.389464	−	0.921042i	$-0.627340\pi$
$137$	2.49837	−	1.44244i	0.213450	−	0.123236i	0.602914	+	0.797806i	$0.294006\pi$
$138$		0			0
$139$	−7.08083	−	4.08812i	−0.600588	−	0.346750i	0.168685	−	0.985670i	$-0.446048\pi$
$139$	−7.08083	−	4.08812i	−0.600588	−	0.346750i	−0.769273	+	0.638920i	$0.779381\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.54689			0.798351
$144$		0			0
$145$	4.88367			0.405567
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.95967	−	4.01817i	−0.570159	−	0.329181i	0.187054	−	0.982350i	$-0.440106\pi$
$149$	−6.95967	−	4.01817i	−0.570159	−	0.329181i	−0.757213	+	0.653168i	$0.773439\pi$
$150$		0			0
$151$	−11.3850	+	6.57314i	−0.926499	+	0.534915i	−0.885703	−	0.464253i	$-0.846323\pi$
$151$	−11.3850	+	6.57314i	−0.926499	+	0.534915i	−0.0407967	+	0.999167i	$0.512990\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.83481	+	4.91004i	0.227698	+	0.394384i
$156$		0			0
$157$	0.861878	−	1.49282i	0.0687853	−	0.119140i	−0.829582	−	0.558386i	$-0.811421\pi$
$157$	0.861878	−	1.49282i	0.0687853	−	0.119140i	0.898367	+	0.439246i	$0.144754\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			18.3552i			1.44659i
$162$		0			0
$163$			6.13698i			0.480686i	0.970688	+	0.240343i	$0.0772598\pi$
$163$			6.13698i			0.480686i	−0.970688	+	0.240343i	$0.922740\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.1137	−	17.5174i	0.782619	−	1.35554i	−0.147791	−	0.989019i	$-0.547216\pi$
$167$	10.1137	−	17.5174i	0.782619	−	1.35554i	0.930411	−	0.366518i	$-0.119450\pi$
$168$		0			0
$169$	−7.26565	−	12.5845i	−0.558896	−	0.968036i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.24426	−	1.29572i	0.170628	−	0.0985119i	−0.412254	−	0.911069i	$-0.635258\pi$
$173$	2.24426	−	1.29572i	0.170628	−	0.0985119i	0.582882	+	0.812557i	$0.301925\pi$
$174$		0			0
$175$	10.0612	+	5.80884i	0.760555	+	0.439107i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−25.4493			−1.90217			−0.951086	−	0.308925i	$-0.900031\pi$
$179$	−25.4493			−1.90217			−0.951086	+	0.308925i	$0.900031\pi$
$180$		0			0
$181$	−0.811874			−0.0603461			−0.0301730	−	0.999545i	$-0.509606\pi$
$181$	−0.811874			−0.0603461			−0.0301730	+	0.999545i	$0.509606\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.67426	+	0.966637i	0.123094	+	0.0710686i
$186$		0			0
$187$	4.78874	−	2.76478i	0.350187	−	0.202181i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.72010	+	13.3716i	0.558607	+	0.967536i	0.997613	+	0.0690518i	$0.0219974\pi$
$191$	7.72010	+	13.3716i	0.558607	+	0.967536i	−0.439006	+	0.898484i	$0.644669\pi$
$192$		0			0
$193$	12.4000	−	21.4774i	0.892571	−	1.54598i	0.0557886	−	0.998443i	$-0.482233\pi$
$193$	12.4000	−	21.4774i	0.892571	−	1.54598i	0.836782	−	0.547536i	$-0.184434\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.99395i			0.427051i	0.976937	+	0.213526i	$0.0684947\pi$
$197$			5.99395i			0.427051i	−0.976937	+	0.213526i	$0.931505\pi$
$198$		0			0
$199$		−	18.7700i		−	1.33057i	−0.746589	−	0.665286i	$-0.768310\pi$
$199$		−	18.7700i		−	1.33057i	0.746589	−	0.665286i	$-0.231690\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.59293	+	11.4193i	−0.462733	+	0.801477i
$204$		0			0
$205$	−5.50401	−	9.53323i	−0.384417	−	0.665830i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.81881	+	2.78214i	−0.333324	+	0.192445i
$210$		0			0
$211$	−16.6575	−	9.61720i	−1.14675	−	0.662075i	−0.198656	−	0.980069i	$-0.563657\pi$
$211$	−16.6575	−	9.61720i	−1.14675	−	0.662075i	−0.948093	+	0.317994i	$0.896991\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.38804			0.572060
$216$		0			0
$217$	−15.3079			−1.03917
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−13.8097	−	7.97306i	−0.928944	−	0.536326i
$222$		0			0
$223$	−5.18435	+	2.99318i	−0.347170	+	0.200438i	−0.663438	−	0.748231i	$-0.730903\pi$
$223$	−5.18435	+	2.99318i	−0.347170	+	0.200438i	0.316268	+	0.948670i	$0.397570\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.83645	+	6.64493i	0.254634	+	0.441040i	0.964796	−	0.262999i	$-0.0847116\pi$
$227$	3.83645	+	6.64493i	0.254634	+	0.441040i	−0.710162	+	0.704039i	$0.751378\pi$
$228$		0			0
$229$	10.2662	−	17.7815i	0.678406	−	1.17503i	−0.297054	−	0.954861i	$-0.596004\pi$
$229$	10.2662	−	17.7815i	0.678406	−	1.17503i	0.975461	−	0.220174i	$-0.0706624\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	26.0981i		−	1.70974i	−0.518839	−	0.854872i	$-0.673636\pi$
$233$		−	26.0981i		−	1.70974i	0.518839	−	0.854872i	$-0.326364\pi$
$234$		0			0
$235$			16.5313i			1.07838i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.533143	+	0.923431i	−0.0344862	+	0.0597318i	−0.882753	−	0.469837i	$-0.844313\pi$
$239$	−0.533143	+	0.923431i	−0.0344862	+	0.0597318i	0.848267	+	0.529568i	$0.177646\pi$
$240$		0			0
$241$	5.50037	+	9.52692i	0.354310	+	0.613683i	0.987000	−	0.160723i	$-0.0513825\pi$
$241$	5.50037	+	9.52692i	0.354310	+	0.613683i	−0.632690	+	0.774405i	$0.718049\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.03747	−	3.48574i	0.385720	−	0.222696i
$246$		0			0
$247$	13.8965	+	8.02314i	0.884212	+	0.510500i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.66440			−0.546892			−0.273446	−	0.961887i	$-0.588163\pi$
$251$	−8.66440			−0.546892			−0.273446	+	0.961887i	$0.588163\pi$
$252$		0			0
$253$	9.50134			0.597344
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.7849	+	9.11340i	0.984633	+	0.568478i	0.903666	−	0.428239i	$-0.140866\pi$
$257$	15.7849	+	9.11340i	0.984633	+	0.568478i	0.0809674	+	0.996717i	$0.474199\pi$
$258$		0			0
$259$	−4.52050	+	2.60991i	−0.280890	+	0.162172i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.12717	+	1.95232i	0.0695045	+	0.120385i	0.898683	−	0.438598i	$-0.144525\pi$
$263$	1.12717	+	1.95232i	0.0695045	+	0.120385i	−0.829179	+	0.558983i	$0.811192\pi$
$264$		0			0
$265$	−7.34510	+	12.7221i	−0.451206	+	0.781512i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	4.70436i		−	0.286830i	−0.989663	−	0.143415i	$-0.954192\pi$
$269$		−	4.70436i		−	0.286830i	0.989663	−	0.143415i	$-0.0458083\pi$
$270$		0			0
$271$		−	6.89999i		−	0.419145i	−0.977793	−	0.209572i	$-0.932793\pi$
$271$		−	6.89999i		−	0.419145i	0.977793	−	0.209572i	$-0.0672072\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.00688	−	5.20806i	0.181321	−	0.314058i
$276$		0			0
$277$	11.9582	+	20.7121i	0.718496	+	1.24447i	0.961596	+	0.274470i	$0.0885025\pi$
$277$	11.9582	+	20.7121i	0.718496	+	1.24447i	−0.243100	+	0.970001i	$0.578164\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.9950	−	6.92533i	0.715563	−	0.413130i	−0.0975546	−	0.995230i	$-0.531102\pi$
$281$	11.9950	−	6.92533i	0.715563	−	0.413130i	0.813117	+	0.582100i	$0.197769\pi$
$282$		0			0
$283$	0.0881183	+	0.0508751i	0.00523809	+	0.00302421i	0.502617	−	0.864509i	$-0.332371\pi$
$283$	0.0881183	+	0.0508751i	0.00523809	+	0.00302421i	−0.497379	+	0.867534i	$0.665704\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	29.7216			1.75441
$288$		0			0
$289$	7.76402			0.456707
$290$		0			0
$291$		0			0
$292$		0			0
$293$	19.1537	+	11.0584i	1.11897	+	0.646040i	0.941139	−	0.338021i	$-0.109757\pi$
$293$	19.1537	+	11.0584i	1.11897	+	0.646040i	0.177835	+	0.984060i	$0.443091\pi$
$294$		0			0
$295$	0.773336	−	0.446486i	0.0450254	−	0.0259954i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−13.7000	−	23.7291i	−0.792290	−	1.37229i
$300$		0			0
$301$	−11.3238	+	19.6134i	−0.652694	+	1.13050i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			5.41558i			0.310095i
$306$		0			0
$307$			11.3850i			0.649777i	0.945752	+	0.324889i	$0.105327\pi$
$307$			11.3850i			0.649777i	−0.945752	+	0.324889i	$0.894673\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.9707	+	19.0019i	−0.622094	+	1.07750i	0.367001	+	0.930220i	$0.380384\pi$
$311$	−10.9707	+	19.0019i	−0.622094	+	1.07750i	−0.989095	+	0.147278i	$0.952949\pi$
$312$		0			0
$313$	4.24338	+	7.34975i	0.239850	+	0.415433i	0.960671	−	0.277689i	$-0.0895683\pi$
$313$	4.24338	+	7.34975i	0.239850	+	0.415433i	−0.720821	+	0.693121i	$0.756235\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.5060	+	8.95241i	−0.870906	+	0.502818i	−0.867649	−	0.497177i	$-0.834370\pi$
$317$	−15.5060	+	8.95241i	−0.870906	+	0.502818i	−0.00325648	+	0.999995i	$0.501037\pi$
$318$		0			0
$319$	5.91106	+	3.41275i	0.330956	+	0.191077i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	9.29400			0.517132
$324$		0			0
$325$	−17.3424			−0.961985
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−38.6545	−	22.3172i	−2.13109	−	1.23039i
$330$		0			0
$331$	1.80836	−	1.04406i	0.0993966	−	0.0573867i	−0.449478	−	0.893292i	$-0.648390\pi$
$331$	1.80836	−	1.04406i	0.0993966	−	0.0573867i	0.548874	+	0.835905i	$0.315057\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.24152	+	14.2747i	0.450282	+	0.779912i
$336$		0			0
$337$	−13.8315	+	23.9569i	−0.753450	+	1.30501i	0.192691	+	0.981259i	$0.438278\pi$
$337$	−13.8315	+	23.9569i	−0.753450	+	1.30501i	−0.946141	+	0.323754i	$0.895055\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			7.92397i			0.429107i
$342$		0			0
$343$		−	5.78192i		−	0.312194i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.44289	−	2.49915i	0.0774582	−	0.134162i	−0.824694	−	0.565579i	$-0.808653\pi$
$347$	1.44289	−	2.49915i	0.0774582	−	0.134162i	0.902153	+	0.431417i	$0.141986\pi$
$348$		0			0
$349$	−0.198452	−	0.343730i	−0.0106229	−	0.0183994i	0.860665	−	0.509172i	$-0.170048\pi$
$349$	−0.198452	−	0.343730i	−0.0106229	−	0.0183994i	−0.871288	+	0.490772i	$0.836715\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.01374	+	4.62673i	−0.426528	+	0.246256i	−0.697866	−	0.716228i	$-0.745867\pi$
$353$	−8.01374	+	4.62673i	−0.426528	+	0.246256i	0.271338	+	0.962484i	$0.412534\pi$
$354$		0			0
$355$	2.82469	+	1.63083i	0.149919	+	0.0865556i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	16.8248			0.887981			0.443990	−	0.896032i	$-0.353562\pi$
$359$	16.8248			0.887981			0.443990	+	0.896032i	$0.353562\pi$
$360$		0			0
$361$	9.64763			0.507770
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.8733	+	8.00974i	0.726161	+	0.419249i
$366$		0			0
$367$	−0.307492	+	0.177531i	−0.0160510	+	0.00926703i	−0.508004	−	0.861355i	$-0.669616\pi$
$367$	−0.307492	+	0.177531i	−0.0160510	+	0.00926703i	0.491953	+	0.870622i	$0.336283\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.8317	−	34.3495i	−1.02961	−	1.78334i
$372$		0			0
$373$	1.52227	−	2.63664i	0.0788200	−	0.136520i	−0.823921	−	0.566705i	$-0.808218\pi$
$373$	1.52227	−	2.63664i	0.0788200	−	0.136520i	0.902741	+	0.430184i	$0.141551\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	19.6834i		−	1.01375i
$378$		0			0
$379$		−	36.6330i		−	1.88171i	−0.338805	−	0.940857i	$-0.610023\pi$
$379$		−	36.6330i		−	1.88171i	0.338805	−	0.940857i	$-0.389977\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.48710	−	6.03984i	0.178183	−	0.308621i	−0.763075	−	0.646309i	$-0.776312\pi$
$383$	3.48710	−	6.03984i	0.178183	−	0.308621i	0.941258	+	0.337688i	$0.109645\pi$
$384$		0			0
$385$	−4.16295	−	7.21044i	−0.212164	−	0.367478i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	26.3080	−	15.1890i	1.33387	−	0.770110i	0.347980	−	0.937502i	$-0.386868\pi$
$389$	26.3080	−	15.1890i	1.33387	−	0.770110i	0.985891	+	0.167391i	$0.0535344\pi$
$390$		0			0
$391$	−13.7439	−	7.93502i	−0.695057	−	0.401291i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.71841			0.136778
$396$		0			0
$397$	−12.6167			−0.633215			−0.316608	−	0.948557i	$-0.602544\pi$
$397$	−12.6167			−0.633215			−0.316608	+	0.948557i	$0.602544\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.75768	+	5.63360i	0.487275	+	0.281328i	0.723443	−	0.690384i	$-0.242558\pi$
$401$	9.75768	+	5.63360i	0.487275	+	0.281328i	−0.236168	+	0.971712i	$0.575892\pi$
$402$		0			0
$403$	19.7897	−	11.4256i	0.985793	−	0.569148i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.35099	+	2.33998i	0.0669661	+	0.115989i
$408$		0			0
$409$	−9.25833	+	16.0359i	−0.457795	+	0.792924i	−0.998844	−	0.0480668i	$-0.984694\pi$
$409$	−9.25833	+	16.0359i	−0.457795	+	0.792924i	0.541049	+	0.840991i	$0.318027\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			2.41102i			0.118638i
$414$		0			0
$415$		−	22.3490i		−	1.09707i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.5448	+	19.9962i	−0.564002	+	0.976880i	0.433140	+	0.901327i	$0.357406\pi$
$419$	−11.5448	+	19.9962i	−0.564002	+	0.976880i	−0.997142	+	0.0755530i	$0.975928\pi$
$420$		0			0
$421$	5.59126	+	9.68435i	0.272501	+	0.471986i	0.969502	−	0.245085i	$-0.0788157\pi$
$421$	5.59126	+	9.68435i	0.272501	+	0.471986i	−0.697000	+	0.717071i	$0.745482\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.69899	+	5.02237i	−0.421963	+	0.243621i
$426$		0			0
$427$	−12.6630	−	7.31100i	−0.612807	−	0.353804i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.3110			−0.833843			−0.416921	−	0.908943i	$-0.636891\pi$
$431$	−17.3110			−0.833843			−0.416921	+	0.908943i	$0.636891\pi$
$432$		0			0
$433$	−22.7194			−1.09183			−0.545913	−	0.837842i	$-0.683817\pi$
$433$	−22.7194			−1.09183			−0.545913	+	0.837842i	$0.683817\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.8302	+	7.98486i	0.661587	+	0.381968i
$438$		0			0
$439$	12.5562	−	7.24933i	0.599275	−	0.345992i	−0.169481	−	0.985533i	$-0.554209\pi$
$439$	12.5562	−	7.24933i	0.599275	−	0.345992i	0.768756	+	0.639542i	$0.220876\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.26639	−	2.19346i	−0.0601682	−	0.104214i	0.834372	−	0.551201i	$-0.185830\pi$
$443$	−1.26639	−	2.19346i	−0.0601682	−	0.104214i	−0.894540	+	0.446987i	$0.852497\pi$
$444$		0			0
$445$	−8.15611	+	14.1268i	−0.386637	+	0.669674i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			15.4046i			0.726988i	0.931596	+	0.363494i	$0.118416\pi$
$449$			15.4046i			0.726988i	−0.931596	+	0.363494i	$0.881584\pi$
$450$		0			0
$451$		−	15.3850i		−	0.724452i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.0051	+	20.7935i	−0.562808	+	0.974812i
$456$		0			0
$457$	−9.05489	−	15.6835i	−0.423570	−	0.733644i	0.572716	−	0.819754i	$-0.305890\pi$
$457$	−9.05489	−	15.6835i	−0.423570	−	0.733644i	−0.996286	+	0.0861095i	$0.972557\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−24.4180	+	14.0978i	−1.13726	+	0.656598i	−0.945751	−	0.324893i	$-0.894672\pi$
$461$	−24.4180	+	14.0978i	−1.13726	+	0.656598i	−0.191510	+	0.981491i	$0.561338\pi$
$462$		0			0
$463$	−28.2610	−	16.3165i	−1.31340	−	0.758293i	−0.330744	−	0.943720i	$-0.607300\pi$
$463$	−28.2610	−	16.3165i	−1.31340	−	0.758293i	−0.982658	+	0.185427i	$0.940633\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−26.6595			−1.23366			−0.616828	−	0.787098i	$-0.711582\pi$
$467$	−26.6595			−1.23366			−0.616828	+	0.787098i	$0.711582\pi$
$468$		0			0
$469$	−44.5040			−2.05501
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10.1527	+	5.86164i	0.466820	+	0.269518i
$474$		0			0
$475$	8.75363	−	5.05391i	0.401644	−	0.231889i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.0251	−	20.8280i	−0.549439	−	0.951656i	−0.998313	−	0.0580609i	$-0.981508\pi$
$479$	−12.0251	−	20.8280i	−0.549439	−	0.951656i	0.448874	−	0.893595i	$-0.351825\pi$
$480$		0			0
$481$	3.89598	−	6.74803i	0.177641	−	0.307684i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			11.4448i			0.519683i
$486$		0			0
$487$			17.4449i			0.790505i	0.918573	+	0.395252i	$0.129343\pi$
$487$			17.4449i			0.790505i	−0.918573	+	0.395252i	$0.870657\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.65849	−	11.5328i	0.300494	−	0.520470i	−0.675754	−	0.737127i	$-0.736182\pi$
$491$	6.65849	−	11.5328i	0.300494	−	0.520470i	0.976248	+	0.216657i	$0.0695153\pi$
$492$		0			0
$493$	−5.70030	−	9.87321i	−0.256729	−	0.444667i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.62662	+	4.40323i	−0.342101	+	0.197512i
$498$		0			0
$499$	−28.9161	−	16.6947i	−1.29446	−	0.747358i	−0.315021	−	0.949085i	$-0.602012\pi$
$499$	−28.9161	−	16.6947i	−1.29446	−	0.747358i	−0.979442	+	0.201726i	$0.935345\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	24.2884			1.08297			0.541483	−	0.840712i	$-0.317863\pi$
$503$	24.2884			1.08297			0.541483	+	0.840712i	$0.317863\pi$
$504$		0			0
$505$	2.49479			0.111017
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.4147	−	11.7864i	−0.904867	−	0.522425i	−0.0260907	−	0.999660i	$-0.508306\pi$
$509$	−20.4147	−	11.7864i	−0.904867	−	0.522425i	−0.878776	+	0.477235i	$0.841639\pi$
$510$		0			0
$511$	−37.4577	+	21.6262i	−1.65703	+	0.956688i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.6232	+	20.1319i	0.512178	+	0.887118i
$516$		0			0
$517$	−11.5522	+	20.0090i	−0.508066	+	0.879996i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	32.5603i		−	1.42649i	−0.700913	−	0.713246i	$-0.747224\pi$
$521$		−	32.5603i		−	1.42649i	0.700913	−	0.713246i	$-0.252776\pi$
$522$		0			0
$523$			5.17449i			0.226265i	0.993580	+	0.113132i	$0.0360884\pi$
$523$			5.17449i			0.226265i	−0.993580	+	0.113132i	$0.963912\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.61768	−	11.4622i	0.288271	−	0.499300i
$528$		0			0
$529$	−2.13461	−	3.69726i	−0.0928092	−	0.160750i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−38.4232	+	22.1836i	−1.66429	+	0.960880i
$534$		0			0
$535$	−21.2604	−	12.2747i	−0.919166	−	0.530681i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.74346			0.419680
$540$		0			0
$541$	15.6620			0.673362			0.336681	−	0.941619i	$-0.390696\pi$
$541$	15.6620			0.673362			0.336681	+	0.941619i	$0.390696\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	19.3557	+	11.1750i	0.829107	+	0.478685i
$546$		0			0
$547$	−24.6207	+	14.2148i	−1.05271	+	0.607780i	−0.923406	−	0.383826i	$-0.874606\pi$
$547$	−24.6207	+	14.2148i	−1.05271	+	0.607780i	−0.129300	+	0.991606i	$0.541273\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.73610	+	9.93522i	0.244366	+	0.423255i
$552$		0			0
$553$	−3.66984	+	6.35636i	−0.156058	+	0.270300i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	45.9337i		−	1.94627i	−0.230225	−	0.973137i	$-0.573946\pi$
$557$		−	45.9337i		−	1.94627i	0.230225	−	0.973137i	$-0.426054\pi$
$558$		0			0
$559$		−	33.8075i		−	1.42991i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.8021	+	30.8341i	−0.750269	+	1.29950i	0.197423	+	0.980318i	$0.436743\pi$
$563$	−17.8021	+	30.8341i	−0.750269	+	1.29950i	−0.947692	+	0.319186i	$0.896591\pi$
$564$		0			0
$565$	1.67800	+	2.90639i	0.0705942	+	0.122273i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.9254	+	17.2774i	−1.25454	+	0.724307i	−0.972007	−	0.234952i	$-0.924507\pi$
$569$	−29.9254	+	17.2774i	−1.25454	+	0.724307i	−0.282530	+	0.959259i	$0.591174\pi$
$570$		0			0
$571$	2.51801	+	1.45378i	0.105376	+	0.0608386i	0.551762	−	0.834002i	$-0.313956\pi$
$571$	2.51801	+	1.45378i	0.105376	+	0.0608386i	−0.446386	+	0.894840i	$0.647289\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−17.2597			−0.719779
$576$		0			0
$577$	−28.1251			−1.17086			−0.585431	−	0.810722i	$-0.699075\pi$
$577$	−28.1251			−1.17086			−0.585431	+	0.810722i	$0.699075\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	52.2578	+	30.1710i	2.16802	+	1.25171i
$582$		0			0
$583$	−17.7806	+	10.2656i	−0.736398	+	0.425160i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−14.2541	−	24.6888i	−0.588330	−	1.01902i	−0.994451	−	0.105198i	$-0.966452\pi$
$587$	−14.2541	−	24.6888i	−0.588330	−	1.01902i	0.406121	−	0.913819i	$-0.366881\pi$
$588$		0			0
$589$	−6.65925	+	11.5342i	−0.274390	+	0.475257i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			8.02682i			0.329622i	0.986325	+	0.164811i	$0.0527014\pi$
$593$			8.02682i			0.329622i	−0.986325	+	0.164811i	$0.947299\pi$
$594$		0			0
$595$			13.9067i			0.570119i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.60351	−	14.9017i	0.351530	−	0.608868i	−0.634988	−	0.772522i	$-0.718995\pi$
$599$	8.60351	−	14.9017i	0.351530	−	0.608868i	0.986518	+	0.163654i	$0.0523282\pi$
$600$		0			0
$601$	1.72841	+	2.99369i	0.0705032	+	0.122115i	0.899122	−	0.437698i	$-0.144206\pi$
$601$	1.72841	+	2.99369i	0.0705032	+	0.122115i	−0.828619	+	0.559813i	$0.810873\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.66937	−	5.00526i	0.352460	−	0.203493i
$606$		0			0
$607$	−7.85723	−	4.53637i	−0.318915	−	0.184126i	0.331994	−	0.943282i	$-0.392279\pi$
$607$	−7.85723	−	4.53637i	−0.318915	−	0.184126i	−0.650909	+	0.759156i	$0.725612\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	66.6285			2.69550
$612$		0			0
$613$	13.1044			0.529283			0.264642	−	0.964347i	$-0.414746\pi$
$613$	13.1044			0.529283			0.264642	+	0.964347i	$0.414746\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.22471	−	1.86179i	−0.129822	−	0.0749528i	0.433682	−	0.901066i	$-0.357214\pi$
$617$	−3.22471	−	1.86179i	−0.129822	−	0.0749528i	−0.563505	+	0.826113i	$0.690547\pi$
$618$		0			0
$619$	9.93219	−	5.73435i	0.399208	−	0.230483i	−0.286934	−	0.957950i	$-0.592636\pi$
$619$	9.93219	−	5.73435i	0.399208	−	0.230483i	0.686142	+	0.727467i	$0.259303\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−22.0214	−	38.1422i	−0.882269	−	1.52814i
$624$		0			0
$625$	−1.22513	+	2.12199i	−0.0490052	+	0.0848794i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	4.51310i		−	0.179949i
$630$		0			0
$631$		−	10.1436i		−	0.403810i	−0.979405	−	0.201905i	$-0.935287\pi$
$631$		−	10.1436i		−	0.403810i	0.979405	−	0.201905i	$-0.0647132\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.33548	+	10.9734i	−0.251416	+	0.435465i
$636$		0			0
$637$	−14.0491	−	24.3337i	−0.556645	−	0.964137i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.96582	−	5.75377i	0.393626	−	0.227260i	−0.290104	−	0.956995i	$-0.593690\pi$
$641$	9.96582	−	5.75377i	0.393626	−	0.227260i	0.683730	+	0.729735i	$0.260357\pi$
$642$		0			0
$643$	−24.2487	−	14.0000i	−0.956276	−	0.552106i	−0.0612510	−	0.998122i	$-0.519509\pi$
$643$	−24.2487	−	14.0000i	−0.956276	−	0.552106i	−0.895025	+	0.446016i	$0.852842\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−27.5438			−1.08286			−0.541430	−	0.840746i	$-0.682117\pi$
$647$	−27.5438			−1.08286			−0.541430	+	0.840746i	$0.682117\pi$
$648$		0			0
$649$	1.24803			0.0489896
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−39.7991	−	22.9780i	−1.55746	−	0.899199i	−0.997499	−	0.0706779i	$-0.977484\pi$
$653$	−39.7991	−	22.9780i	−1.55746	−	0.899199i	−0.559958	−	0.828521i	$-0.689183\pi$
$654$		0			0
$655$	15.8018	−	9.12315i	0.617426	−	0.356471i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.6666	+	28.8674i	0.649238	+	1.12451i	0.983305	+	0.181964i	$0.0582453\pi$
$659$	16.6666	+	28.8674i	0.649238	+	1.12451i	−0.334067	+	0.942549i	$0.608421\pi$
$660$		0			0
$661$	5.85128	−	10.1347i	0.227588	−	0.394195i	−0.729504	−	0.683976i	$-0.760249\pi$
$661$	5.85128	−	10.1347i	0.227588	−	0.394195i	0.957093	+	0.289781i	$0.0935826\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	13.9941i		−	0.542666i
$666$		0			0
$667$		−	19.5895i		−	0.758507i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.78445	+	6.55487i	−0.146097	+	0.253048i
$672$		0			0
$673$	24.6626	+	42.7169i	0.950674	+	1.64661i	0.743972	+	0.668211i	$0.232940\pi$
$673$	24.6626	+	42.7169i	0.950674	+	1.64661i	0.206702	+	0.978404i	$0.433727\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.3611	+	8.29137i	−0.551941	+	0.318663i	−0.749904	−	0.661546i	$-0.769901\pi$
$677$	−14.3611	+	8.29137i	−0.551941	+	0.318663i	0.197964	+	0.980209i	$0.436567\pi$
$678$		0			0
$679$	−26.7610	−	15.4505i	−1.02699	−	0.592935i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.39972			0.283142			0.141571	−	0.989928i	$-0.454785\pi$
$683$	7.39972			0.283142			0.141571	+	0.989928i	$0.454785\pi$
$684$		0			0
$685$	3.75566			0.143496
$686$		0			0
$687$		0			0
$688$		0			0
$689$	51.2757	+	29.6040i	1.95345	+	1.12782i
$690$		0			0
$691$	10.6396	−	6.14277i	0.404749	−	0.233682i	−0.283782	−	0.958889i	$-0.591589\pi$
$691$	10.6396	−	6.14277i	0.404749	−	0.233682i	0.688531	+	0.725207i	$0.258256\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.32211	−	9.21816i	−0.201879	−	0.349665i
$696$		0			0
$697$	−12.8487	+	22.2547i	−0.486681	+	0.842956i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	23.5927i		−	0.891084i	−0.895261	−	0.445542i	$-0.853011\pi$
$701$		−	23.5927i		−	0.891084i	0.895261	−	0.445542i	$-0.146989\pi$
$702$		0			0
$703$			4.54145i			0.171284i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.36796	+	5.83347i	−0.126665	+	0.219390i
$708$		0			0
$709$	−1.73385	−	3.00311i	−0.0651160	−	0.112784i	0.831629	−	0.555331i	$-0.187408\pi$
$709$	−1.73385	−	3.00311i	−0.0651160	−	0.112784i	−0.896745	+	0.442547i	$0.854075\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	19.6952	−	11.3711i	0.737593	−	0.425849i
$714$		0			0
$715$	10.7635	+	6.21430i	0.402531	+	0.232402i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	24.7874			0.924413			0.462206	−	0.886772i	$-0.347058\pi$
$719$	24.7874			0.924413			0.462206	+	0.886772i	$0.347058\pi$
$720$		0			0
$721$	−62.7649			−2.33749
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.7378	−	6.19945i	−0.398790	−	0.230242i
$726$		0			0
$727$	9.19668	−	5.30971i	0.341086	−	0.196926i	−0.319666	−	0.947530i	$-0.603571\pi$
$727$	9.19668	−	5.30971i	0.341086	−	0.196926i	0.660752	+	0.750604i	$0.270237\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.79066	−	16.9579i	−0.362121	−	0.627211i
$732$		0			0
$733$	−8.40594	+	14.5595i	−0.310480	+	0.537768i	−0.978466	−	0.206406i	$-0.933823\pi$
$733$	−8.40594	+	14.5595i	−0.310480	+	0.537768i	0.667986	+	0.744174i	$0.267157\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			23.0370i			0.848578i
$738$		0			0
$739$		−	46.0507i		−	1.69400i	−0.531591	−	0.847001i	$-0.678406\pi$
$739$		−	46.0507i		−	1.69400i	0.531591	−	0.847001i	$-0.321594\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.2592	+	17.7694i	−0.376372	+	0.651895i	−0.990531	−	0.137287i	$-0.956162\pi$
$743$	−10.2592	+	17.7694i	−0.376372	+	0.651895i	0.614159	+	0.789182i	$0.289495\pi$
$744$		0			0
$745$	−5.23104	−	9.06044i	−0.191651	−	0.331949i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	57.4028	−	33.1415i	2.09745	−	1.21096i
$750$		0			0
$751$	32.0784	+	18.5205i	1.17056	+	0.675823i	0.953812	−	0.300405i	$-0.0971219\pi$
$751$	32.0784	+	18.5205i	1.17056	+	0.675823i	0.216747	+	0.976228i	$0.430455\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−17.1145			−0.622859
$756$		0			0
$757$	−16.2740			−0.591487			−0.295744	−	0.955267i	$-0.595567\pi$
$757$	−16.2740			−0.591487			−0.295744	+	0.955267i	$0.595567\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.8215	−	7.97984i	−0.501029	−	0.289269i	0.228110	−	0.973635i	$-0.426746\pi$
$761$	−13.8215	−	7.97984i	−0.501029	−	0.289269i	−0.729138	+	0.684366i	$0.760079\pi$
$762$		0			0
$763$	−52.2602	+	30.1725i	−1.89195	+	1.09232i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.79954	−	3.11689i	−0.0649775	−	0.112544i
$768$		0			0
$769$	2.01498	−	3.49004i	0.0726619	−	0.125854i	−0.827405	−	0.561605i	$-0.810184\pi$
$769$	2.01498	−	3.49004i	0.0726619	−	0.125854i	0.900067	+	0.435751i	$0.143517\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			7.21587i			0.259537i	0.991544	+	0.129768i	$0.0414234\pi$
$773$			7.21587i			0.259537i	−0.991544	+	0.129768i	$0.958577\pi$
$774$		0			0
$775$		−	14.3943i		−	0.517059i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.9295	−	22.3945i	0.463246	−	0.802365i
$780$		0			0
$781$	2.27928	+	3.94783i	0.0815591	+	0.141264i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.94342	−	1.12203i	0.0693636	−	0.0400471i
$786$		0			0
$787$	40.7871	+	23.5484i	1.45390	+	0.839411i	0.998700	−	0.0509764i	$-0.0162333\pi$
$787$	40.7871	+	23.5484i	1.45390	+	0.839411i	0.455203	+	0.890388i	$0.349567\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.06119			−0.322179
$792$		0			0
$793$	21.8272			0.775106
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.6339	−	9.60360i	−0.589204	−	0.340177i	0.175579	−	0.984465i	$-0.443820\pi$
$797$	−16.6339	−	9.60360i	−0.589204	−	0.340177i	−0.764783	+	0.644289i	$0.777154\pi$
$798$		0			0
$799$	33.4210	−	19.2956i	1.18235	−	0.682629i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	11.1946	+	19.3895i	0.395048	+	0.684242i
$804$		0			0
$805$	−11.9478	+	20.6942i	−0.421106	+	0.729376i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			36.8312i			1.29492i	0.762101	+	0.647458i	$0.224168\pi$
$809$			36.8312i			1.29492i	−0.762101	+	0.647458i	$0.775832\pi$
$810$		0			0
$811$		−	37.2208i		−	1.30700i	−0.756927	−	0.653499i	$-0.773300\pi$
$811$		−	37.2208i		−	1.30700i	0.756927	−	0.653499i	$-0.226700\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.99471	+	6.91904i	−0.139929	+	0.242363i
$816$		0			0
$817$	9.85215	+	17.0644i	0.344683	+	0.597009i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.1153	+	6.99475i	−0.422825	+	0.244118i	−0.696285	−	0.717765i	$-0.745165\pi$
$821$	−12.1153	+	6.99475i	−0.422825	+	0.244118i	0.273460	+	0.961883i	$0.411832\pi$
$822$		0			0
$823$	−7.35479	−	4.24629i	−0.256372	−	0.148016i	0.366306	−	0.930494i	$-0.380622\pi$
$823$	−7.35479	−	4.24629i	−0.256372	−	0.148016i	−0.622678	+	0.782478i	$0.713956\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	51.1755			1.77955			0.889774	−	0.456402i	$-0.150862\pi$
$827$	51.1755			1.77955			0.889774	+	0.456402i	$0.150862\pi$
$828$		0			0
$829$	−37.9762			−1.31897			−0.659484	−	0.751718i	$-0.729225\pi$
$829$	−37.9762			−1.31897			−0.659484	+	0.751718i	$0.729225\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−14.0941	−	8.13722i	−0.488331	−	0.281938i
$834$		0			0
$835$	22.8050	−	13.1665i	0.789199	−	0.455644i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.89806	+	8.48370i	0.169100	+	0.292890i	0.938104	−	0.346355i	$-0.112581\pi$
$839$	4.89806	+	8.48370i	0.169100	+	0.292890i	−0.769004	+	0.639244i	$0.779247\pi$
$840$		0			0
$841$	−7.46373	+	12.9276i	−0.257370	+	0.445778i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	18.9175i		−	0.650783i
$846$		0			0
$847$			27.0283i			0.928704i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.87739	−	6.71584i	0.132915	−	0.230216i
$852$		0			0
$853$	25.3132	+	43.8438i	0.866708	+	1.50118i	0.865341	+	0.501183i	$0.167102\pi$
$853$	25.3132	+	43.8438i	0.866708	+	1.50118i	0.00136699	+	0.999999i	$0.499565\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.2332	+	11.6816i	−0.691153	+	0.399037i	−0.804044	−	0.594570i	$-0.797322\pi$
$857$	−20.2332	+	11.6816i	−0.691153	+	0.399037i	0.112891	+	0.993607i	$0.463989\pi$
$858$		0			0
$859$	9.01963	+	5.20748i	0.307746	+	0.177677i	0.645917	−	0.763407i	$-0.276475\pi$
$859$	9.01963	+	5.20748i	0.307746	+	0.177677i	−0.338172	+	0.941084i	$0.609808\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.7458			−0.535992			−0.267996	−	0.963420i	$-0.586361\pi$
$863$	−15.7458			−0.535992			−0.267996	+	0.963420i	$0.586361\pi$
$864$		0			0
$865$	3.37366			0.114708
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.29029	+	1.89965i	0.111616	+	0.0644412i
$870$		0			0
$871$	57.5335	−	33.2170i	1.94945	−	1.12551i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	19.0021	+	32.9127i	0.642389	+	1.11265i
$876$		0			0
$877$	−12.7306	+	22.0501i	−0.429883	+	0.744578i	−0.996862	−	0.0791532i	$-0.974778\pi$
$877$	−12.7306	+	22.0501i	−0.429883	+	0.744578i	0.566980	+	0.823732i	$0.308112\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	20.8884i		−	0.703747i	−0.936048	−	0.351873i	$-0.885545\pi$
$881$		−	20.8884i		−	0.703747i	0.936048	−	0.351873i	$-0.114455\pi$
$882$		0			0
$883$			15.3039i			0.515018i	0.966276	+	0.257509i	$0.0829017\pi$
$883$			15.3039i			0.515018i	−0.966276	+	0.257509i	$0.917098\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.6145	+	23.5809i	−0.457129	+	0.791771i	−0.998808	−	0.0488149i	$-0.984456\pi$
$887$	−13.6145	+	23.5809i	−0.457129	+	0.791771i	0.541679	+	0.840586i	$0.317789\pi$
$888$		0			0
$889$	−17.1057	−	29.6280i	−0.573708	−	0.993691i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−33.6309	+	19.4168i	−1.12541	+	0.649758i
$894$		0			0
$895$	−28.6924	−	16.5656i	−0.959082	−	0.553726i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	16.3373			0.544880
$900$		0			0
$901$	34.2933			1.14248
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.915333	−	0.528468i	−0.0304267	−	0.0175669i
$906$		0			0
$907$	−13.6492	+	7.88036i	−0.453214	+	0.261663i	−0.709187	−	0.705021i	$-0.750938\pi$
$907$	−13.6492	+	7.88036i	−0.453214	+	0.261663i	0.255973	+	0.966684i	$0.417604\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−13.6537	−	23.6489i	−0.452367	−	0.783523i	0.546166	−	0.837677i	$-0.316087\pi$
$911$	−13.6537	−	23.6489i	−0.452367	−	0.783523i	−0.998533	+	0.0541547i	$0.982754\pi$
$912$		0			0
$913$	15.6177	−	27.0506i	0.516870	−	0.895244i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			49.2648i			1.62687i
$918$		0			0
$919$			39.7723i			1.31197i	0.754775	+	0.655984i	$0.227746\pi$
$919$			39.7723i			1.31197i	−0.754775	+	0.655984i	$0.772254\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	6.57298	−	11.3847i	0.216352	−	0.374733i
$924$		0			0
$925$	−2.45414	−	4.25070i	−0.0806917	−	0.139762i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	30.1798	−	17.4243i	0.990168	−	0.571674i	0.0848436	−	0.996394i	$-0.472961\pi$
$929$	30.1798	−	17.4243i	0.990168	−	0.571674i	0.905325	+	0.424720i	$0.139628\pi$
$930$		0			0
$931$	14.1826	+	8.18833i	0.464816	+	0.268362i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.19864			0.235421
$936$		0			0
$937$	34.4177			1.12438			0.562188	−	0.827010i	$-0.309960\pi$
$937$	34.4177			1.12438			0.562188	+	0.827010i	$0.309960\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.05620	+	0.609795i	0.0344310	+	0.0198788i	0.517117	−	0.855915i	$-0.327005\pi$
$941$	1.05620	+	0.609795i	0.0344310	+	0.0198788i	−0.482686	+	0.875794i	$0.660339\pi$
$942$		0			0
$943$	−38.2399	+	22.0778i	−1.24526	+	0.718952i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.76244	−	9.98084i	−0.187254	−	0.324334i	0.757080	−	0.653323i	$-0.226625\pi$
$947$	−5.76244	−	9.98084i	−0.187254	−	0.324334i	−0.944334	+	0.328989i	$0.893292\pi$
$948$		0			0
$949$	32.2828	−	55.9155i	1.04795	−	1.81509i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	50.5559i		−	1.63767i	−0.574031	−	0.818834i	$-0.694621\pi$
$953$		−	50.5559i		−	1.63767i	0.574031	−	0.818834i	$-0.305379\pi$
$954$		0			0
$955$			20.1008i			0.650447i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−5.07013	+	8.78172i	−0.163723	+	0.283576i
$960$		0			0
$961$	−6.01672	−	10.4213i	−0.194088	−	0.336170i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	27.9603	−	16.1429i	0.900075	−	0.519658i
$966$		0			0
$967$	10.7945	+	6.23219i	0.347126	+	0.200414i	0.663419	−	0.748248i	$-0.269105\pi$
$967$	10.7945	+	6.23219i	0.347126	+	0.200414i	−0.316292	+	0.948662i	$0.602438\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.9467			−0.608029			−0.304015	−	0.952667i	$-0.598327\pi$
$971$	−18.9467			−0.608029			−0.304015	+	0.952667i	$0.598327\pi$
$972$		0			0
$973$	28.7393			0.921339
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.48974	−	2.59215i	−0.143640	−	0.0829304i	0.426458	−	0.904507i	$-0.359761\pi$
$977$	−4.48974	−	2.59215i	−0.143640	−	0.0829304i	−0.570097	+	0.821577i	$0.693095\pi$
$978$		0			0
$979$	−19.7439	+	11.3991i	−0.631016	+	0.364317i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−12.7710	−	22.1199i	−0.407330	−	0.705516i	0.587259	−	0.809399i	$-0.300207\pi$
$983$	−12.7710	−	22.1199i	−0.407330	−	0.705516i	−0.994590	+	0.103882i	$0.966873\pi$
$984$		0			0
$985$	−3.90161	+	6.75778i	−0.124316	+	0.215321i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	33.6462i		−	1.06989i
$990$		0			0
$991$			39.9173i			1.26801i	0.773327	+	0.634007i	$0.218591\pi$
$991$			39.9173i			1.26801i	−0.773327	+	0.634007i	$0.781409\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.2179	−	21.1620i	0.387332	−	0.670879i
$996$		0			0
$997$	2.17138	+	3.76094i	0.0687684	+	0.119110i	0.898359	−	0.439261i	$-0.144760\pi$
$997$	2.17138	+	3.76094i	0.0687684	+	0.119110i	−0.829591	+	0.558371i	$0.811426\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.j.863.5		16
3.2	odd	2	inner	2592.2.s.j.863.4		16
4.3	odd	2		2592.2.s.i.863.5		16
9.2	odd	6		2592.2.s.i.1727.5		16
9.4	even	3		2592.2.c.b.2591.7	✓	16
9.5	odd	6		2592.2.c.b.2591.9	yes	16
9.7	even	3		2592.2.s.i.1727.4		16
12.11	even	2		2592.2.s.i.863.4		16
36.7	odd	6	inner	2592.2.s.j.1727.4		16
36.11	even	6	inner	2592.2.s.j.1727.5		16
36.23	even	6		2592.2.c.b.2591.10	yes	16
36.31	odd	6		2592.2.c.b.2591.8	yes	16
72.5	odd	6		5184.2.c.l.5183.7		16
72.13	even	6		5184.2.c.l.5183.9		16
72.59	even	6		5184.2.c.l.5183.8		16
72.67	odd	6		5184.2.c.l.5183.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2592.2.c.b.2591.7	✓	16	9.4	even	3
2592.2.c.b.2591.8	yes	16	36.31	odd	6
2592.2.c.b.2591.9	yes	16	9.5	odd	6
2592.2.c.b.2591.10	yes	16	36.23	even	6
2592.2.s.i.863.4		16	12.11	even	2
2592.2.s.i.863.5		16	4.3	odd	2
2592.2.s.i.1727.4		16	9.7	even	3
2592.2.s.i.1727.5		16	9.2	odd	6
2592.2.s.j.863.4		16	3.2	odd	2	inner
2592.2.s.j.863.5		16	1.1	even	1	trivial
2592.2.s.j.1727.4		16	36.7	odd	6	inner
2592.2.s.j.1727.5		16	36.11	even	6	inner
5184.2.c.l.5183.7		16	72.5	odd	6
5184.2.c.l.5183.8		16	72.59	even	6
5184.2.c.l.5183.9		16	72.13	even	6
5184.2.c.l.5183.10		16	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:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12743 + 0.650924i) q^{5} +(-3.04406 + 1.75749i) q^{7} +O(q^{10})\)	\(q+(1.12743 + 0.650924i) q^{5} +(-3.04406 + 1.75749i) q^{7} +(0.909743 + 1.57572i) q^{11} +(2.62351 - 4.54406i) q^{13} -3.03908i q^{17} +3.05816i q^{19} +(2.61100 - 4.52238i) q^{23} +(-1.65260 - 2.86238i) q^{25} +(3.24875 - 1.87567i) q^{29} +(3.77159 + 2.17753i) q^{31} -4.57596 q^{35} +1.48502 q^{37} +(-7.32285 - 4.22785i) q^{41} +(5.57996 - 3.22159i) q^{43} +(6.34917 + 10.9971i) q^{47} +(2.67753 - 4.63762i) q^{49} +11.2841i q^{53} +2.36869i q^{55} +(0.342963 - 0.594030i) q^{59} +(2.07996 + 3.60259i) q^{61} +(5.91567 - 3.41542i) q^{65} +(10.9650 + 6.33063i) q^{67} +2.50541 q^{71} +12.3052 q^{73} +(-5.53862 - 3.19773i) q^{77} +(1.80836 - 1.04406i) q^{79} +(-8.58356 - 14.8672i) q^{83} +(1.97821 - 3.42636i) q^{85} +12.5300i q^{89} +18.4432i q^{91} +(-1.99063 + 3.44788i) q^{95} +(4.39561 + 7.61342i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7}+O(q^{10}) \) 16 * q + 12 * q^7	\( 16 q + 12 q^{7} + 4 q^{13} + 24 q^{25} + 72 q^{31} + 72 q^{37} + 84 q^{43} + 24 q^{49} + 28 q^{61} + 36 q^{67} + 96 q^{73} + 12 q^{79} + 12 q^{85} + 16 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 4 * q^13 + 24 * q^25 + 72 * q^31 + 72 * q^37 + 84 * q^43 + 24 * q^49 + 28 * q^61 + 36 * q^67 + 96 * q^73 + 12 * q^79 + 12 * q^85 + 16 * q^97

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