LMFDB - Embedded newform 5292.2.bm.a.2285.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5292,2,Mod(2285,5292)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5292, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5292.2285"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5292.bm (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,0,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$42.2568327497$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2285.4
Root			$1.08696 - 1.34852i$ of defining polynomial
Character	$\chi$	$=$	5292.2285
Dual form			5292.2.bm.a.4625.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0764245 q^{5} +5.38437i q^{11} +(4.60313 + 2.65762i) q^{13} +(-1.89092 + 3.27516i) q^{17} +(4.33939 - 2.50535i) q^{19} +2.33784i q^{23} -4.99416 q^{25} +(-8.84430 + 5.10626i) q^{29} +(-4.97636 + 2.87310i) q^{31} +(0.354486 + 0.613988i) q^{37} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(-1.46192 + 2.53213i) q^{47} +(-10.4835 - 6.05264i) q^{53} +0.411498i q^{55} +(-0.289951 - 0.502210i) q^{59} +(2.40641 + 1.38934i) q^{61} +(0.351792 + 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} -3.32103i q^{71} +(6.17326 + 3.56413i) q^{73} +(-0.469123 + 0.812544i) q^{79} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-1.51794 - 2.62915i) q^{89} +(0.331636 - 0.191470i) q^{95} +(-6.18183 + 3.56908i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) $ 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 21 * q^89 - 6 * q^95 - 3 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5292\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0764245			0.0341781			0.0170890	−	0.999854i	$-0.494560\pi$
$5$	0.0764245			0.0341781			0.0170890	+	0.999854i	$0.494560\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$			5.38437i			1.62345i	0.584040	+	0.811725i	$0.301471\pi$
$11$			5.38437i			1.62345i	−0.584040	+	0.811725i	$0.698529\pi$
$12$		0			0
$13$	4.60313	+	2.65762i	1.27668	+	0.737091i	0.976236	−	0.216709i	$-0.0695324\pi$
$13$	4.60313	+	2.65762i	1.27668	+	0.737091i	0.300442	+	0.953800i	$0.402866\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.89092	+	3.27516i	−0.458615	+	0.794344i	−0.998888	−	0.0471458i	$-0.984987\pi$
$17$	−1.89092	+	3.27516i	−0.458615	+	0.794344i	0.540273	+	0.841490i	$0.318321\pi$
$18$		0			0
$19$	4.33939	−	2.50535i	0.995525	−	0.574767i	0.0886040	−	0.996067i	$-0.471759\pi$
$19$	4.33939	−	2.50535i	0.995525	−	0.574767i	0.906921	+	0.421300i	$0.138426\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			2.33784i			0.487473i	0.969841	+	0.243737i	$0.0783732\pi$
$23$			2.33784i			0.487473i	−0.969841	+	0.243737i	$0.921627\pi$
$24$		0			0
$25$	−4.99416			−0.998832
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8.84430	+	5.10626i	−1.64235	+	0.948209i	−0.662349	+	0.749196i	$0.730440\pi$
$29$	−8.84430	+	5.10626i	−1.64235	+	0.948209i	−0.979997	+	0.199013i	$0.936226\pi$
$30$		0			0
$31$	−4.97636	+	2.87310i	−0.893780	+	0.516024i	−0.875177	−	0.483803i	$-0.839255\pi$
$31$	−4.97636	+	2.87310i	−0.893780	+	0.516024i	−0.0186031	+	0.999827i	$0.505922\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.354486	+	0.613988i	0.0582771	+	0.100939i	0.893692	−	0.448681i	$-0.148106\pi$
$37$	0.354486	+	0.613988i	0.0582771	+	0.100939i	−0.835415	+	0.549620i	$0.814773\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	−0.484610	−	0.874730i	$-0.661039\pi$
$41$	3.29910	−	5.71422i	0.515234	−	0.892411i	0.999844	−	0.0176805i	$-0.00562816\pi$
$42$		0			0
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	0.915474	−	0.402377i	$-0.131816\pi$
$43$	0.716520	+	1.24105i	0.109268	+	0.189258i	−0.806206	+	0.591635i	$0.798483\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.46192	+	2.53213i	−0.213244	+	0.369349i	−0.952728	−	0.303825i	$-0.901736\pi$
$47$	−1.46192	+	2.53213i	−0.213244	+	0.369349i	0.739484	+	0.673174i	$0.235069\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−10.4835	−	6.05264i	−1.44002	−	0.831394i	−0.442167	−	0.896933i	$-0.645790\pi$
$53$	−10.4835	−	6.05264i	−1.44002	−	0.831394i	−0.997850	+	0.0655390i	$0.979123\pi$
$54$		0			0
$55$			0.411498i			0.0554863i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.289951	−	0.502210i	−0.0377484	−	0.0653822i	0.846534	−	0.532335i	$-0.178685\pi$
$59$	−0.289951	−	0.502210i	−0.0377484	−	0.0653822i	−0.884282	+	0.466953i	$0.845352\pi$
$60$		0			0
$61$	2.40641	+	1.38934i	0.308109	+	0.177887i	0.646080	−	0.763270i	$-0.276407\pi$
$61$	2.40641	+	1.38934i	0.308109	+	0.177887i	−0.337971	+	0.941156i	$0.609741\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.351792	+	0.203107i	0.0436344	+	0.0251923i
$66$		0			0
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	0.658877	−	0.752251i	$-0.271032\pi$
$67$	−2.63593	−	4.56556i	−0.322030	−	0.557771i	−0.980907	+	0.194479i	$0.937698\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.32103i		−	0.394134i	−0.980390	−	0.197067i	$-0.936858\pi$
$71$		−	3.32103i		−	0.394134i	0.980390	−	0.197067i	$-0.0631416\pi$
$72$		0			0
$73$	6.17326	+	3.56413i	0.722525	+	0.417150i	0.815681	−	0.578502i	$-0.196362\pi$
$73$	6.17326	+	3.56413i	0.722525	+	0.417150i	−0.0931564	+	0.995651i	$0.529696\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	−0.891208	−	0.453594i	$-0.850142\pi$
$79$	−0.469123	+	0.812544i	−0.0527804	+	0.0914184i	0.838428	+	0.545012i	$0.183475\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	−0.963635	−	0.267221i	$-0.913895\pi$
$83$	−6.49790	−	11.2547i	−0.713238	−	1.23536i	0.250398	−	0.968143i	$-0.419439\pi$
$84$		0			0
$85$	−0.144512	+	0.250303i	−0.0156746	+	0.0271491i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.51794	−	2.62915i	−0.160901	−	0.278689i	0.774291	−	0.632830i	$-0.218107\pi$
$89$	−1.51794	−	2.62915i	−0.160901	−	0.278689i	−0.935192	+	0.354141i	$0.884773\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.331636	−	0.191470i	0.0340251	−	0.0196444i
$96$		0			0
$97$	−6.18183	+	3.56908i	−0.627670	+	0.362385i	−0.779849	−	0.625967i	$-0.784704\pi$
$97$	−6.18183	+	3.56908i	−0.627670	+	0.362385i	0.152179	+	0.988353i	$0.451371\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.17257			0.813201			0.406600	−	0.913606i	$-0.366714\pi$
$101$	8.17257			0.813201			0.406600	+	0.913606i	$0.366714\pi$
$102$		0			0
$103$		−	7.46628i		−	0.735675i	−0.929890	−	0.367837i	$-0.880098\pi$
$103$		−	7.46628i		−	0.735675i	0.929890	−	0.367837i	$-0.119902\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.99991	+	2.30935i	−0.386686	+	0.223253i	−0.680723	−	0.732541i	$-0.738334\pi$
$107$	−3.99991	+	2.30935i	−0.386686	+	0.223253i	0.294037	+	0.955794i	$0.405001\pi$
$108$		0			0
$109$	5.22792	−	9.05503i	0.500744	−	0.867314i	−0.499256	−	0.866455i	$-0.666393\pi$
$109$	5.22792	−	9.05503i	0.500744	−	0.867314i	1.00000		0.000859385i	$-0.000273551\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	16.6379	+	9.60591i	1.56516	+	0.903648i	0.996720	+	0.0809270i	$0.0257881\pi$
$113$	16.6379	+	9.60591i	1.56516	+	0.903648i	0.568445	+	0.822721i	$0.307545\pi$
$114$		0			0
$115$			0.178668i			0.0166609i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−17.9915			−1.63559
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.763798			−0.0683162
$126$		0			0
$127$	1.26488			0.112240			0.0561198	−	0.998424i	$-0.482127\pi$
$127$	1.26488			0.112240			0.0561198	+	0.998424i	$0.482127\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−14.4879			−1.26581			−0.632906	−	0.774229i	$-0.718138\pi$
$131$	−14.4879			−1.26581			−0.632906	+	0.774229i	$0.718138\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	15.4053i		−	1.31616i	−0.752947	−	0.658081i	$-0.771368\pi$
$137$		−	15.4053i		−	1.31616i	0.752947	−	0.658081i	$-0.228632\pi$
$138$		0			0
$139$	0.374701	+	0.216333i	0.0317817	+	0.0183492i	0.515807	−	0.856705i	$-0.327492\pi$
$139$	0.374701	+	0.216333i	0.0317817	+	0.0183492i	−0.484025	+	0.875054i	$0.660826\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−14.3096	+	24.7850i	−1.19663	+	2.07262i
$144$		0			0
$145$	−0.675921	+	0.390243i	−0.0561322	+	0.0324079i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			4.67117i			0.382677i	0.981524	+	0.191338i	$0.0612828\pi$
$149$			4.67117i			0.382677i	−0.981524	+	0.191338i	$0.938717\pi$
$150$		0			0
$151$	−8.24552			−0.671011			−0.335506	−	0.942038i	$-0.608907\pi$
$151$	−8.24552			−0.671011			−0.335506	+	0.942038i	$0.608907\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.380316	+	0.219575i	−0.0305477	+	0.0176367i
$156$		0			0
$157$	−15.2334	+	8.79500i	−1.21576	+	0.701917i	−0.964007	−	0.265875i	$-0.914339\pi$
$157$	−15.2334	+	8.79500i	−1.21576	+	0.701917i	−0.251749	+	0.967793i	$0.581006\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.27097	−	9.12959i	−0.412854	−	0.715085i	0.582346	−	0.812941i	$-0.302135\pi$
$163$	−5.27097	−	9.12959i	−0.412854	−	0.715085i	−0.995201	+	0.0978563i	$0.968801\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	−0.987169	−	0.159679i	$-0.948954\pi$
$167$	−4.59146	+	7.95265i	−0.355298	+	0.615395i	0.631871	+	0.775074i	$0.282287\pi$
$168$		0			0
$169$	7.62587	+	13.2084i	0.586605	+	1.01603i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.22358	+	2.11931i	−0.0930274	+	0.161128i	−0.908784	−	0.417268i	$-0.862988\pi$
$173$	−1.22358	+	2.11931i	−0.0930274	+	0.161128i	0.815756	+	0.578396i	$0.196321\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.05509	−	2.91856i	−0.377835	−	0.218143i	0.299041	−	0.954240i	$-0.403333\pi$
$179$	−5.05509	−	2.91856i	−0.377835	−	0.218143i	−0.676876	+	0.736097i	$0.736667\pi$
$180$		0			0
$181$			16.0704i			1.19451i	0.802053	+	0.597253i	$0.203741\pi$
$181$			16.0704i			1.19451i	−0.802053	+	0.597253i	$0.796259\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.0270914	+	0.0469237i	0.00199180	+	0.00344990i
$186$		0			0
$187$	−17.6347	−	10.1814i	−1.28958	−	0.744537i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.90415	+	3.98611i	0.499567	+	0.288425i	0.728535	−	0.685009i	$-0.240202\pi$
$191$	6.90415	+	3.98611i	0.499567	+	0.288425i	−0.228968	+	0.973434i	$0.573535\pi$
$192$		0			0
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	0.852814	−	0.522214i	$-0.174894\pi$
$193$	−0.359027	−	0.621853i	−0.0258433	−	0.0447620i	−0.878658	+	0.477452i	$0.841560\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			13.5035i			0.962083i	0.876698	+	0.481042i	$0.159741\pi$
$197$			13.5035i			0.962083i	−0.876698	+	0.481042i	$0.840259\pi$
$198$		0			0
$199$	−21.2568	−	12.2726i	−1.50685	−	0.869983i	−0.999968	−	0.00796947i	$-0.997463\pi$
$199$	−21.2568	−	12.2726i	−1.50685	−	0.869983i	−0.506886	−	0.862013i	$-0.669203\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.252132	−	0.436706i	0.0176097	−	0.0305009i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	13.4897	+	23.3649i	0.933105	+	1.61618i
$210$		0			0
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	0.100778	+	0.994909i	$0.467867\pi$
$211$	−11.7838	+	20.4101i	−0.811227	+	1.40509i	−0.912005	+	0.410178i	$0.865467\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0547597	+	0.0948465i	0.00373458	+	0.00646848i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17.4083	+	10.0507i	−1.17101	+	0.676081i
$222$		0			0
$223$	6.47489	−	3.73828i	0.433590	−	0.250334i	−0.267285	−	0.963618i	$-0.586126\pi$
$223$	6.47489	−	3.73828i	0.433590	−	0.250334i	0.700875	+	0.713284i	$0.252793\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.637402			0.0423058			0.0211529	−	0.999776i	$-0.493266\pi$
$227$	0.637402			0.0423058			0.0211529	+	0.999776i	$0.493266\pi$
$228$		0			0
$229$		−	1.82848i		−	0.120829i	−0.998173	−	0.0604146i	$-0.980758\pi$
$229$		−	1.82848i		−	0.120829i	0.998173	−	0.0604146i	$-0.0192423\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.4232	+	10.0593i	−1.14143	+	0.659007i	−0.946785	−	0.321866i	$-0.895690\pi$
$233$	−17.4232	+	10.0593i	−1.14143	+	0.659007i	−0.194649	+	0.980873i	$0.562357\pi$
$234$		0			0
$235$	−0.111727	+	0.193516i	−0.00728825	+	0.0126236i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.41455	+	1.39404i	0.156184	+	0.0901730i	0.576055	−	0.817411i	$-0.304591\pi$
$239$	2.41455	+	1.39404i	0.156184	+	0.0901730i	−0.419871	+	0.907584i	$0.637925\pi$
$240$		0			0
$241$			23.1291i			1.48988i	0.667134	+	0.744938i	$0.267521\pi$
$241$			23.1291i			1.48988i	−0.667134	+	0.744938i	$0.732479\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	26.6331			1.69462
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.6541			1.17743			0.588717	−	0.808339i	$-0.299633\pi$
$251$	18.6541			1.17743			0.588717	+	0.808339i	$0.299633\pi$
$252$		0			0
$253$	−12.5878			−0.791388
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.8737			0.678286			0.339143	−	0.940735i	$-0.389863\pi$
$257$	10.8737			0.678286			0.339143	+	0.940735i	$0.389863\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$			18.9970i			1.17141i	0.810525	+	0.585704i	$0.199182\pi$
$263$			18.9970i			1.17141i	−0.810525	+	0.585704i	$0.800818\pi$
$264$		0			0
$265$	−0.801194	−	0.462570i	−0.0492170	−	0.0284154i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.29788	+	7.44415i	−0.262046	+	0.453878i	−0.966786	−	0.255589i	$-0.917731\pi$
$269$	−4.29788	+	7.44415i	−0.262046	+	0.453878i	0.704739	+	0.709467i	$0.251064\pi$
$270$		0			0
$271$	−1.58706	+	0.916292i	−0.0964073	+	0.0556608i	−0.547429	−	0.836852i	$-0.684393\pi$
$271$	−1.58706	+	0.916292i	−0.0964073	+	0.0556608i	0.451021	+	0.892513i	$0.351060\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	26.8904i		−	1.62155i
$276$		0			0
$277$	15.8186			0.950449			0.475224	−	0.879865i	$-0.342367\pi$
$277$	15.8186			0.950449			0.475224	+	0.879865i	$0.342367\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.95916	−	5.74992i	0.594114	−	0.343012i	−0.172609	−	0.984990i	$-0.555220\pi$
$281$	9.95916	−	5.74992i	0.594114	−	0.343012i	0.766722	+	0.641979i	$0.221886\pi$
$282$		0			0
$283$	8.59806	−	4.96409i	0.511101	−	0.295085i	−0.222185	−	0.975005i	$-0.571319\pi$
$283$	8.59806	−	4.96409i	0.511101	−	0.295085i	0.733286	+	0.679920i	$0.237986\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.34887	+	2.33631i	0.0793454	+	0.137430i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	−0.495467	−	0.868627i	$-0.665003\pi$
$293$	8.63598	−	14.9580i	0.504520	−	0.873854i	0.999986	−	0.00522664i	$-0.00166370\pi$
$294$		0			0
$295$	−0.0221594	−	0.0383812i	−0.00129017	−	0.00223464i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.21308	+	10.7614i	−0.359312	+	0.622346i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.183908	+	0.106180i	0.0105306	+	0.00607982i
$306$		0			0
$307$		−	21.6425i		−	1.23520i	−0.786490	−	0.617602i	$-0.788104\pi$
$307$		−	21.6425i		−	1.23520i	0.786490	−	0.617602i	$-0.211896\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.1016	+	17.4964i	0.572808	+	0.992133i	0.996276	+	0.0862215i	$0.0274793\pi$
$311$	10.1016	+	17.4964i	0.572808	+	0.992133i	−0.423468	+	0.905911i	$0.639187\pi$
$312$		0			0
$313$	18.9146	+	10.9203i	1.06911	+	0.617254i	0.927939	−	0.372731i	$-0.121579\pi$
$313$	18.9146	+	10.9203i	1.06911	+	0.617254i	0.141175	+	0.989985i	$0.454912\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.5288	+	12.4297i	1.20918	+	0.698120i	0.962580	−	0.270997i	$-0.0873535\pi$
$317$	21.5288	+	12.4297i	1.20918	+	0.698120i	0.246599	+	0.969117i	$0.420687\pi$
$318$		0			0
$319$	−27.4940	−	47.6210i	−1.53937	−	2.66626i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			18.9496i			1.05439i
$324$		0			0
$325$	−22.9888	−	13.2726i	−1.27519	−	0.736230i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	−0.997960	−	0.0638459i	$-0.979663\pi$
$331$	−8.07219	+	13.9814i	−0.443688	+	0.768490i	0.554272	+	0.832336i	$0.312997\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.201449	−	0.348920i	−0.0110063	−	0.0190635i
$336$		0			0
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	−0.996488	−	0.0837408i	$-0.973313\pi$
$337$	−7.81522	+	13.5364i	−0.425722	+	0.737372i	0.570765	+	0.821113i	$0.306647\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.4698	−	26.7946i	−0.837739	−	1.45101i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−28.0445	+	16.1915i	−1.50551	+	0.869206i	−0.505529	+	0.862810i	$0.668703\pi$
$347$	−28.0445	+	16.1915i	−1.50551	+	0.869206i	−0.999980	+	0.00639573i	$0.997964\pi$
$348$		0			0
$349$	26.0421	−	15.0354i	1.39400	−	0.804827i	0.400246	−	0.916408i	$-0.368925\pi$
$349$	26.0421	−	15.0354i	1.39400	−	0.804827i	0.993755	+	0.111581i	$0.0355915\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.0121			0.905465			0.452733	−	0.891646i	$-0.350449\pi$
$353$	17.0121			0.905465			0.452733	+	0.891646i	$0.350449\pi$
$354$		0			0
$355$		−	0.253808i		−	0.0134707i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−25.2692	+	14.5892i	−1.33366	+	0.769987i	−0.985858	−	0.167583i	$-0.946404\pi$
$359$	−25.2692	+	14.5892i	−1.33366	+	0.769987i	−0.347798	+	0.937570i	$0.613070\pi$
$360$		0			0
$361$	3.05356	−	5.28892i	0.160714	−	0.278364i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.471788	+	0.272387i	0.0246945	+	0.0142574i
$366$		0			0
$367$			18.1266i			0.946200i	0.881009	+	0.473100i	$0.156865\pi$
$367$			18.1266i			0.946200i	−0.881009	+	0.473100i	$0.843135\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−20.3646			−1.05444			−0.527219	−	0.849730i	$-0.676765\pi$
$373$	−20.3646			−1.05444			−0.527219	+	0.849730i	$0.676765\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−54.2820			−2.79566
$378$		0			0
$379$	−21.9961			−1.12986			−0.564931	−	0.825138i	$-0.691097\pi$
$379$	−21.9961			−1.12986			−0.564931	+	0.825138i	$0.691097\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	32.6253			1.66708			0.833538	−	0.552462i	$-0.186312\pi$
$383$	32.6253			1.66708			0.833538	+	0.552462i	$0.186312\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	15.7501i		−	0.798560i	−0.916829	−	0.399280i	$-0.869260\pi$
$389$		−	15.7501i		−	0.798560i	0.916829	−	0.399280i	$-0.130740\pi$
$390$		0			0
$391$	−7.65680	−	4.42066i	−0.387221	−	0.223562i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.0358524	+	0.0620983i	−0.00180393	+	0.00312450i
$396$		0			0
$397$	2.95864	−	1.70817i	0.148490	−	0.0857308i	−0.423914	−	0.905702i	$-0.639344\pi$
$397$	2.95864	−	1.70817i	0.148490	−	0.0857308i	0.572404	+	0.819972i	$0.306011\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			0.983052i			0.0490913i	0.999699	+	0.0245456i	$0.00781390\pi$
$401$			0.983052i			0.0490913i	−0.999699	+	0.0245456i	$0.992186\pi$
$402$		0			0
$403$	−30.5424			−1.52143
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.30594	+	1.90868i	−0.163869	+	0.0946099i
$408$		0			0
$409$	−25.0195	+	14.4450i	−1.23714	+	0.714260i	−0.968508	−	0.248984i	$-0.919903\pi$
$409$	−25.0195	+	14.4450i	−1.23714	+	0.714260i	−0.268627	+	0.963244i	$0.586570\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−0.496599	−	0.860135i	−0.0243771	−	0.0422223i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	−0.670509	−	0.741901i	$-0.733924\pi$
$419$	6.28926	−	10.8933i	0.307251	−	0.532174i	0.977760	+	0.209727i	$0.0672577\pi$
$420$		0			0
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	−0.986576	−	0.163300i	$-0.947786\pi$
$421$	−13.0232	−	22.5568i	−0.634710	−	1.09935i	0.351866	−	0.936050i	$-0.385547\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.44354	−	16.3567i	0.458079	−	0.793416i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6.28454	−	3.62838i	−0.302716	−	0.174773i	0.340947	−	0.940083i	$-0.389252\pi$
$431$	−6.28454	−	3.62838i	−0.302716	−	0.174773i	−0.643662	+	0.765310i	$0.722586\pi$
$432$		0			0
$433$		−	8.29113i		−	0.398446i	−0.979954	−	0.199223i	$-0.936158\pi$
$433$		−	8.29113i		−	0.398446i	0.979954	−	0.199223i	$-0.0638419\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.85710	+	10.1448i	0.280183	+	0.485292i
$438$		0			0
$439$	2.83357	+	1.63596i	0.135239	+	0.0780802i	0.566093	−	0.824341i	$-0.308454\pi$
$439$	2.83357	+	1.63596i	0.135239	+	0.0780802i	−0.430854	+	0.902422i	$0.641788\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.46737	−	1.42454i	−0.117228	−	0.0676817i	0.440239	−	0.897880i	$-0.354894\pi$
$443$	−2.46737	−	1.42454i	−0.117228	−	0.0676817i	−0.557468	+	0.830199i	$0.688227\pi$
$444$		0			0
$445$	−0.116008	−	0.200931i	−0.00549929	−	0.00952505i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	19.9802i		−	0.942925i	−0.881886	−	0.471463i	$-0.843726\pi$
$449$		−	19.9802i		−	0.942925i	0.881886	−	0.471463i	$-0.156274\pi$
$450$		0			0
$451$	30.7675	+	17.7636i	1.44878	+	0.836455i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	−0.996697	−	0.0812053i	$-0.974123\pi$
$457$	−9.15008	+	15.8484i	−0.428023	+	0.741357i	0.568675	+	0.822563i	$0.307456\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	0.952016	−	0.306049i	$-0.0990071\pi$
$461$	4.52954	+	7.84539i	0.210962	+	0.365396i	−0.741054	+	0.671445i	$0.765674\pi$
$462$		0			0
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	−0.497021	−	0.867739i	$-0.665573\pi$
$463$	10.8227	−	18.7455i	0.502974	−	0.871176i	0.999994	−	0.00343694i	$-0.00109401\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.7761	−	23.8610i	−0.637484	−	1.10415i	−0.985983	−	0.166845i	$-0.946642\pi$
$467$	−13.7761	−	23.8610i	−0.637484	−	1.10415i	0.348500	−	0.937309i	$-0.386691\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.68227	+	3.85801i	−0.307251	+	0.177392i
$474$		0			0
$475$	−21.6716	+	12.5121i	−0.994362	+	0.574095i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.94651			0.226012			0.113006	−	0.993594i	$-0.463952\pi$
$479$	4.94651			0.226012			0.113006	+	0.993594i	$0.463952\pi$
$480$		0			0
$481$			3.76835i			0.171822i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.472443	+	0.272765i	−0.0214525	+	0.0123856i
$486$		0			0
$487$	−4.78573	+	8.28913i	−0.216862	+	0.375616i	−0.953847	−	0.300293i	$-0.902916\pi$
$487$	−4.78573	+	8.28913i	−0.216862	+	0.375616i	0.736985	+	0.675909i	$0.236249\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	33.0010	+	19.0531i	1.48931	+	0.859855i	0.999925	−	0.0122119i	$-0.00388725\pi$
$491$	33.0010	+	19.0531i	1.48931	+	0.859855i	0.489387	+	0.872067i	$0.337221\pi$
$492$		0			0
$493$		−	38.6220i		−	1.73945i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−24.8384			−1.11192			−0.555960	−	0.831209i	$-0.687649\pi$
$499$	−24.8384			−1.11192			−0.555960	+	0.831209i	$0.687649\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.2820			1.21645			0.608223	−	0.793766i	$-0.291883\pi$
$503$	27.2820			1.21645			0.608223	+	0.793766i	$0.291883\pi$
$504$		0			0
$505$	0.624584			0.0277936
$506$		0			0
$507$		0			0
$508$		0			0
$509$	41.7721			1.85152			0.925758	−	0.378117i	$-0.123428\pi$
$509$	41.7721			1.85152			0.925758	+	0.378117i	$0.123428\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	0.570607i		−	0.0251439i
$516$		0			0
$517$	−13.6339	−	7.87154i	−0.599619	−	0.346190i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.02629	+	3.50963i	−0.0887732	+	0.153760i	−0.906993	−	0.421146i	$-0.861628\pi$
$521$	−2.02629	+	3.50963i	−0.0887732	+	0.153760i	0.818220	+	0.574906i	$0.194961\pi$
$522$		0			0
$523$	−26.2429	+	15.1514i	−1.14752	+	0.662523i	−0.948282	−	0.317428i	$-0.897181\pi$
$523$	−26.2429	+	15.1514i	−1.14752	+	0.662523i	−0.199241	+	0.979951i	$0.563848\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	21.7312i		−	0.946625i
$528$		0			0
$529$	17.5345			0.762370
$530$		0			0
$531$		0			0
$532$		0			0
$533$	30.3724	−	17.5355i	1.31558	−	0.759548i
$534$		0			0
$535$	−0.305691	+	0.176491i	−0.0132162	+	0.00763037i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.82681	+	15.2885i	0.379494	+	0.657303i	0.990989	−	0.133946i	$-0.0427647\pi$
$541$	8.82681	+	15.2885i	0.379494	+	0.657303i	−0.611495	+	0.791249i	$0.709431\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.399541	−	0.692026i	0.0171145	−	0.0296431i
$546$		0			0
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	0.815571	−	0.578657i	$-0.196423\pi$
$547$	−2.18319	−	3.78140i	−0.0933466	−	0.161681i	−0.908917	+	0.416976i	$0.863090\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−25.5859	+	44.3161i	−1.09000	+	1.88793i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.7527	+	8.51750i	0.625094	+	0.360898i	0.778849	−	0.627211i	$-0.215804\pi$
$557$	14.7527	+	8.51750i	0.625094	+	0.360898i	−0.153756	+	0.988109i	$0.549137\pi$
$558$		0			0
$559$			7.61695i			0.322163i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.45992	−	11.1889i	−0.272253	−	0.471556i	0.697185	−	0.716891i	$-0.254436\pi$
$563$	−6.45992	−	11.1889i	−0.272253	−	0.471556i	−0.969438	+	0.245335i	$0.921102\pi$
$564$		0			0
$565$	1.27155	+	0.734127i	0.0534943	+	0.0308850i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.8280	+	10.8704i	0.789313	+	0.455710i	0.839720	−	0.543019i	$-0.182719\pi$
$569$	18.8280	+	10.8704i	0.789313	+	0.455710i	−0.0504079	+	0.998729i	$0.516052\pi$
$570$		0			0
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	0.967007	+	0.254748i	$0.0819925\pi$
$571$	16.8254	+	29.1425i	0.704122	+	1.21958i	−0.262885	+	0.964827i	$0.584674\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	11.6755i		−	0.486904i
$576$		0			0
$577$	−12.5598	−	7.25141i	−0.522871	−	0.301880i	0.215237	−	0.976562i	$-0.430948\pi$
$577$	−12.5598	−	7.25141i	−0.522871	−	0.301880i	−0.738109	+	0.674682i	$0.764281\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	32.5897	−	56.4469i	1.34973	−	2.33779i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	0.982179	+	0.187948i	$0.0601837\pi$
$587$	15.8417	+	27.4386i	0.653857	+	1.13251i	−0.328322	+	0.944566i	$0.606483\pi$
$588$		0			0
$589$	−14.3963	+	24.9350i	−0.593187	+	1.02743i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.54101	−	6.13320i	−0.145412	−	0.251860i	0.784115	−	0.620616i	$-0.213117\pi$
$593$	−3.54101	−	6.13320i	−0.145412	−	0.251860i	−0.929526	+	0.368755i	$0.879784\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.20178	−	3.00325i	0.212539	−	0.122709i	−0.389952	−	0.920835i	$-0.627508\pi$
$599$	5.20178	−	3.00325i	0.212539	−	0.122709i	0.602491	+	0.798126i	$0.294175\pi$
$600$		0			0
$601$	0.530083	−	0.306043i	0.0216225	−	0.0124838i	−0.489150	−	0.872200i	$-0.662693\pi$
$601$	0.530083	−	0.306043i	0.0216225	−	0.0124838i	0.510772	+	0.859716i	$0.329360\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.37499			−0.0559012
$606$		0			0
$607$			2.04959i			0.0831904i	0.999135	+	0.0415952i	$0.0132440\pi$
$607$			2.04959i			0.0831904i	−0.999135	+	0.0415952i	$0.986756\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−13.4588	+	7.77047i	−0.544487	+	0.314360i
$612$		0			0
$613$	−4.93166	+	8.54189i	−0.199188	+	0.345003i	−0.948265	−	0.317479i	$-0.897164\pi$
$613$	−4.93166	+	8.54189i	−0.199188	+	0.345003i	0.749077	+	0.662482i	$0.230497\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.2143	−	13.4028i	−0.934571	−	0.539575i	−0.0463170	−	0.998927i	$-0.514748\pi$
$617$	−23.2143	−	13.4028i	−0.934571	−	0.539575i	−0.888254	+	0.459352i	$0.848082\pi$
$618$		0			0
$619$		−	0.0696297i		−	0.00279865i	−0.999999	−	0.00139933i	$-0.999555\pi$
$619$		−	0.0696297i		−	0.00279865i	0.999999	−	0.00139933i	$-0.000445420\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.9124			0.996497
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.68121			−0.106907
$630$		0			0
$631$	11.8214			0.470603			0.235301	−	0.971922i	$-0.424392\pi$
$631$	11.8214			0.470603			0.235301	+	0.971922i	$0.424392\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.0966675			0.00383613
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	20.5159i		−	0.810330i	−0.914244	−	0.405165i	$-0.867214\pi$
$641$		−	20.5159i		−	0.810330i	0.914244	−	0.405165i	$-0.132786\pi$
$642$		0			0
$643$	15.6081	+	9.01132i	0.615522	+	0.355372i	0.775123	−	0.631810i	$-0.217688\pi$
$643$	15.6081	+	9.01132i	0.615522	+	0.355372i	−0.159602	+	0.987182i	$0.551021\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.11827	+	15.7933i	−0.358476	+	0.620899i	−0.987706	−	0.156320i	$-0.950037\pi$
$647$	−9.11827	+	15.7933i	−0.358476	+	0.620899i	0.629230	+	0.777219i	$0.283370\pi$
$648$		0			0
$649$	2.70409	−	1.56121i	0.106145	−	0.0612827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			9.00158i			0.352259i	0.984367	+	0.176129i	$0.0563577\pi$
$653$			9.00158i			0.352259i	−0.984367	+	0.176129i	$0.943642\pi$
$654$		0			0
$655$	−1.10723			−0.0432630
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−30.4806	+	17.5980i	−1.18735	+	0.685519i	−0.957704	−	0.287754i	$-0.907091\pi$
$659$	−30.4806	+	17.5980i	−1.18735	+	0.685519i	−0.229650	+	0.973273i	$0.573758\pi$
$660$		0			0
$661$	10.8797	−	6.28141i	0.423172	−	0.244318i	−0.273262	−	0.961940i	$-0.588102\pi$
$661$	10.8797	−	6.28141i	0.423172	−	0.244318i	0.696433	+	0.717621i	$0.254769\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−11.9376	−	20.6765i	−0.462226	−	0.800599i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.48072	+	12.9570i	−0.288790	+	0.500199i
$672$		0			0
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.797960	+	0.602710i	$0.205913\pi$
$673$	23.8913	+	41.3810i	0.920942	+	1.59512i	0.122982	+	0.992409i	$0.460754\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−18.5235	+	32.0837i	−0.711918	+	1.23308i	0.252219	+	0.967670i	$0.418840\pi$
$677$	−18.5235	+	32.0837i	−0.711918	+	1.23308i	−0.964136	+	0.265407i	$0.914494\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	21.6844	+	12.5195i	0.829732	+	0.479046i	0.853761	−	0.520665i	$-0.174316\pi$
$683$	21.6844	+	12.5195i	0.829732	+	0.479046i	−0.0240289	+	0.999711i	$0.507649\pi$
$684$		0			0
$685$		−	1.17734i		−	0.0449839i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−32.1712	−	55.7222i	−1.22563	−	2.12285i
$690$		0			0
$691$	−40.2655	−	23.2473i	−1.53177	−	0.884370i	−0.999280	−	0.0379352i	$-0.987922\pi$
$691$	−40.2655	−	23.2473i	−1.53177	−	0.884370i	−0.532493	−	0.846434i	$-0.678745\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.0286363	+	0.0165332i	0.00108624	+	0.000627139i
$696$		0			0
$697$	12.4767	+	21.6102i	0.472587	+	0.818545i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			36.0041i			1.35986i	0.733279	+	0.679928i	$0.237989\pi$
$701$			36.0041i			1.35986i	−0.733279	+	0.679928i	$0.762011\pi$
$702$		0			0
$703$	3.07651	+	1.77622i	0.116033	+	0.0669915i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	0.395424	+	0.918499i	$0.370598\pi$
$709$	−15.9158	+	27.5670i	−0.597731	+	1.03530i	−0.993155	+	0.116802i	$0.962736\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.71685	−	11.6339i	−0.251548	−	0.435694i
$714$		0			0
$715$	−1.09360	+	1.89418i	−0.0408985	+	0.0708382i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.0271	−	34.6879i	−0.746883	−	1.29364i	−0.949310	−	0.314342i	$-0.898216\pi$
$719$	−20.0271	−	34.6879i	−0.746883	−	1.29364i	0.202427	−	0.979297i	$-0.435117\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	44.1699	−	25.5015i	1.64043	−	0.947101i
$726$		0			0
$727$	3.39242	−	1.95862i	0.125818	−	0.0726411i	−0.435770	−	0.900058i	$-0.643524\pi$
$727$	3.39242	−	1.95862i	0.125818	−	0.0726411i	0.561588	+	0.827417i	$0.310191\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.41952			−0.200448
$732$		0			0
$733$			23.5835i			0.871078i	0.900170	+	0.435539i	$0.143442\pi$
$733$			23.5835i			0.871078i	−0.900170	+	0.435539i	$0.856558\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.5827	−	14.1928i	0.905514	−	0.522798i
$738$		0			0
$739$	16.8641	−	29.2094i	0.620355	−	1.07449i	−0.369065	−	0.929404i	$-0.620322\pi$
$739$	16.8641	−	29.2094i	0.620355	−	1.07449i	0.989420	−	0.145083i	$-0.0463448\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−29.4003	−	16.9743i	−1.07859	−	0.622725i	−0.148076	−	0.988976i	$-0.547308\pi$
$743$	−29.4003	−	16.9743i	−1.07859	−	0.622725i	−0.930516	+	0.366251i	$0.880641\pi$
$744$		0			0
$745$			0.356991i			0.0130792i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	3.39663			0.123945			0.0619724	−	0.998078i	$-0.480261\pi$
$751$	3.39663			0.123945			0.0619724	+	0.998078i	$0.480261\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.630160			−0.0229339
$756$		0			0
$757$	29.1344			1.05891			0.529454	−	0.848339i	$-0.322397\pi$
$757$	29.1344			1.05891			0.529454	+	0.848339i	$0.322397\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.7258			0.606309			0.303154	−	0.952941i	$-0.401960\pi$
$761$	16.7258			0.606309			0.303154	+	0.952941i	$0.401960\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	3.08232i		−	0.111296i
$768$		0			0
$769$	24.0816	+	13.9035i	0.868404	+	0.501373i	0.866818	−	0.498625i	$-0.166162\pi$
$769$	24.0816	+	13.9035i	0.868404	+	0.501373i	0.00158643	+	0.999999i	$0.499495\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.42238	+	11.1239i	−0.230997	+	0.400098i	−0.958102	−	0.286428i	$-0.907532\pi$
$773$	−6.42238	+	11.1239i	−0.230997	+	0.400098i	0.727105	+	0.686526i	$0.240865\pi$
$774$		0			0
$775$	24.8527	−	14.3487i	0.892736	−	0.515421i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	33.0617i		−	1.18456i
$780$		0			0
$781$	17.8817			0.639856
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.16420	+	0.672153i	−0.0415522	+	0.0239902i
$786$		0			0
$787$	−6.55243	+	3.78305i	−0.233569	+	0.134851i	−0.612217	−	0.790689i	$-0.709722\pi$
$787$	−6.55243	+	3.78305i	−0.233569	+	0.134851i	0.378648	+	0.925541i	$0.376389\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	7.38467	+	12.7906i	0.262237	+	0.454208i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	−0.928579	−	0.371134i	$-0.878969\pi$
$797$	−4.03362	+	6.98643i	−0.142878	+	0.247472i	0.785701	+	0.618606i	$0.212302\pi$
$798$		0			0
$799$	−5.52875	−	9.57608i	−0.195593	−	0.338777i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.1906	+	33.2391i	−0.677222	+	1.17298i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0849492	+	0.0490454i	0.00298665	+	0.00172435i	0.501493	−	0.865162i	$-0.332784\pi$
$809$	0.0849492	+	0.0490454i	0.00298665	+	0.00172435i	−0.498506	+	0.866886i	$0.666118\pi$
$810$		0			0
$811$			30.3085i			1.06428i	0.846658	+	0.532138i	$0.178611\pi$
$811$			30.3085i			1.06428i	−0.846658	+	0.532138i	$0.821389\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.402831	−	0.697724i	−0.0141106	−	0.0244402i
$816$		0			0
$817$	6.21853	+	3.59027i	0.217559	+	0.125608i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.5499	+	11.2871i	0.682295	+	0.393923i	0.800719	−	0.599040i	$-0.204451\pi$
$821$	19.5499	+	11.2871i	0.682295	+	0.393923i	−0.118424	+	0.992963i	$0.537784\pi$
$822$		0			0
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	0.996655	−	0.0817282i	$-0.0260439\pi$
$823$	12.2655	+	21.2445i	0.427549	+	0.740536i	−0.569106	+	0.822264i	$0.692711\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	40.3057i		−	1.40157i	−0.713375	−	0.700783i	$-0.752834\pi$
$827$		−	40.3057i		−	1.40157i	0.713375	−	0.700783i	$-0.247166\pi$
$828$		0			0
$829$	46.8081	+	27.0247i	1.62571	+	0.938605i	0.985353	+	0.170529i	$0.0545478\pi$
$829$	46.8081	+	27.0247i	1.62571	+	0.938605i	0.640359	+	0.768076i	$0.278786\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.350900	+	0.607777i	−0.0121434	+	0.0210330i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	0.585224	−	0.810872i	$-0.301007\pi$
$839$	−11.8650	−	20.5507i	−0.409624	−	0.709489i	−0.994847	+	0.101383i	$0.967673\pi$
$840$		0			0
$841$	37.6478	−	65.2079i	1.29820	−	2.24855i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.582803	+	1.00944i	0.0200490	+	0.0347259i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.43540	+	0.828731i	−0.0492050	+	0.0284085i
$852$		0			0
$853$	−48.0748	+	27.7560i	−1.64605	+	0.950347i	−0.667429	+	0.744673i	$0.732605\pi$
$853$	−48.0748	+	27.7560i	−1.64605	+	0.950347i	−0.978621	+	0.205674i	$0.934061\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	30.6097			1.04561			0.522803	−	0.852453i	$-0.324886\pi$
$857$	30.6097			1.04561			0.522803	+	0.852453i	$0.324886\pi$
$858$		0			0
$859$		−	42.1401i		−	1.43780i	−0.695113	−	0.718900i	$-0.744646\pi$
$859$		−	42.1401i		−	1.43780i	0.695113	−	0.718900i	$-0.255354\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−22.7782	+	13.1510i	−0.775379	+	0.447665i	−0.834790	−	0.550568i	$-0.814411\pi$
$863$	−22.7782	+	13.1510i	−0.775379	+	0.447665i	0.0594112	+	0.998234i	$0.481078\pi$
$864$		0			0
$865$	−0.0935118	+	0.161967i	−0.00317950	+	0.00550705i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.37504	−	2.52593i	−0.148413	−	0.0856863i
$870$		0			0
$871$		−	28.0211i		−	0.949460i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	35.7066			1.20573			0.602863	−	0.797845i	$-0.294027\pi$
$877$	35.7066			1.20573			0.602863	+	0.797845i	$0.294027\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−12.4482			−0.419392			−0.209696	−	0.977767i	$-0.567247\pi$
$881$	−12.4482			−0.419392			−0.209696	+	0.977767i	$0.567247\pi$
$882$		0			0
$883$	2.35637			0.0792982			0.0396491	−	0.999214i	$-0.487376\pi$
$883$	2.35637			0.0792982			0.0396491	+	0.999214i	$0.487376\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.4597			−1.12347			−0.561734	−	0.827318i	$-0.689866\pi$
$887$	−33.4597			−1.12347			−0.561734	+	0.827318i	$0.689866\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$			14.6505i			0.490261i
$894$		0			0
$895$	−0.386333	−	0.223049i	−0.0129137	−	0.00745572i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	29.3416	−	50.8212i	0.978597	−	1.69498i
$900$		0			0
$901$	39.6468	−	22.8901i	1.32083	−	0.762579i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			1.22817i			0.0408259i
$906$		0			0
$907$	−0.935925			−0.0310769			−0.0155384	−	0.999879i	$-0.504946\pi$
$907$	−0.935925			−0.0310769			−0.0155384	+	0.999879i	$0.504946\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−28.8739	+	16.6703i	−0.956634	+	0.552313i	−0.895136	−	0.445794i	$-0.852921\pi$
$911$	−28.8739	+	16.6703i	−0.956634	+	0.552313i	−0.0614988	+	0.998107i	$0.519588\pi$
$912$		0			0
$913$	60.5995	−	34.9871i	2.00555	−	1.15791i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.73484	−	3.00483i	−0.0572270	−	0.0991200i	0.835993	−	0.548741i	$-0.184893\pi$
$919$	−1.73484	−	3.00483i	−0.0572270	−	0.0991200i	−0.893220	+	0.449621i	$0.851559\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.82603	−	15.2871i	0.290512	−	0.503182i
$924$		0			0
$925$	−1.77036	−	3.06635i	−0.0582090	−	0.100821i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.57680	−	13.1234i	0.248587	−	0.430565i	−0.714547	−	0.699587i	$-0.753367\pi$
$929$	7.57680	−	13.1234i	0.248587	−	0.430565i	0.963134	+	0.269022i	$0.0867005\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.34772	−	0.778108i	−0.0440752	−	0.0254468i
$936$		0			0
$937$		−	33.6651i		−	1.09979i	−0.835233	−	0.549896i	$-0.814667\pi$
$937$		−	33.6651i		−	1.09979i	0.835233	−	0.549896i	$-0.185333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.8980	−	32.7323i	−0.616058	−	1.06704i	−0.990198	−	0.139671i	$-0.955395\pi$
$941$	−18.8980	−	32.7323i	−0.616058	−	1.06704i	0.374140	−	0.927372i	$-0.377938\pi$
$942$		0			0
$943$	13.3589	+	7.71277i	0.435026	+	0.251162i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.47426	−	5.46997i	−0.307872	−	0.177750i	0.338102	−	0.941110i	$-0.390215\pi$
$947$	−9.47426	−	5.46997i	−0.307872	−	0.177750i	−0.645974	+	0.763360i	$0.723548\pi$
$948$		0			0
$949$	18.9442	+	32.8123i	0.614955	+	1.06513i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	11.0914i		−	0.359284i	−0.983732	−	0.179642i	$-0.942506\pi$
$953$		−	11.0914i		−	0.359284i	0.983732	−	0.179642i	$-0.0574939\pi$
$954$		0			0
$955$	0.527646	+	0.304637i	0.0170742	+	0.00985781i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	1.00942	−	1.74838i	0.0325621	−	0.0563992i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.0274384	−	0.0475248i	−0.000883275	−	0.00152988i
$966$		0			0
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	−0.335839	−	0.941920i	$-0.609020\pi$
$967$	20.1446	−	34.8915i	0.647807	−	1.12203i	0.983646	−	0.180115i	$-0.0576470\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.8458	+	41.3021i	0.765248	+	1.32545i	0.940115	+	0.340856i	$0.110717\pi$
$971$	23.8458	+	41.3021i	0.765248	+	1.32545i	−0.174867	+	0.984592i	$0.555950\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.4540	−	8.34504i	0.462426	−	0.266982i	−0.250638	−	0.968081i	$-0.580640\pi$
$977$	14.4540	−	8.34504i	0.462426	−	0.266982i	0.713064	+	0.701099i	$0.247307\pi$
$978$		0			0
$979$	14.1563	−	8.17314i	0.452437	−	0.261215i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	33.8509			1.07968			0.539838	−	0.841769i	$-0.318485\pi$
$983$	33.8509			1.07968			0.539838	+	0.841769i	$0.318485\pi$
$984$		0			0
$985$			1.03200i			0.0328821i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.90137	+	1.67511i	−0.0922583	+	0.0532653i
$990$		0			0
$991$	−4.09775	+	7.09751i	−0.130169	+	0.225460i	−0.923742	−	0.383016i	$-0.874885\pi$
$991$	−4.09775	+	7.09751i	−0.130169	+	0.225460i	0.793572	+	0.608476i	$0.208219\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.62454	−	0.937928i	−0.0515014	−	0.0297343i
$996$		0			0
$997$			21.6380i			0.685282i	0.939466	+	0.342641i	$0.111321\pi$
$997$			21.6380i			0.685282i	−0.939466	+	0.342641i	$0.888679\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.bm.a.2285.4		16
3.2	odd	2		1764.2.bm.a.1697.6		16
7.2	even	3		756.2.w.a.341.5		16
7.3	odd	6		5292.2.x.b.881.4		16
7.4	even	3		5292.2.x.a.881.5		16
7.5	odd	6		5292.2.w.b.1097.4		16
7.6	odd	2		756.2.bm.a.17.5		16
9.2	odd	6		5292.2.w.b.521.4		16
9.7	even	3		1764.2.w.b.1109.8		16
21.2	odd	6		252.2.w.a.5.1	✓	16
21.5	even	6		1764.2.w.b.509.8		16
21.11	odd	6		1764.2.x.a.293.5		16
21.17	even	6		1764.2.x.b.293.4		16
21.20	even	2		252.2.bm.a.185.3	yes	16
28.23	odd	6		3024.2.ca.d.2609.5		16
28.27	even	2		3024.2.df.d.17.5		16
63.2	odd	6		756.2.bm.a.89.5		16
63.11	odd	6		5292.2.x.b.4409.4		16
63.13	odd	6		2268.2.t.b.1781.4		16
63.16	even	3		252.2.bm.a.173.3	yes	16
63.20	even	6		756.2.w.a.521.5		16
63.23	odd	6		2268.2.t.b.2105.4		16
63.25	even	3		1764.2.x.b.1469.4		16
63.34	odd	6		252.2.w.a.101.1	yes	16
63.38	even	6		5292.2.x.a.4409.5		16
63.41	even	6		2268.2.t.a.1781.5		16
63.47	even	6	inner	5292.2.bm.a.4625.4		16
63.52	odd	6		1764.2.x.a.1469.5		16
63.58	even	3		2268.2.t.a.2105.5		16
63.61	odd	6		1764.2.bm.a.1685.6		16
84.23	even	6		1008.2.ca.d.257.8		16
84.83	odd	2		1008.2.df.d.689.6		16
252.79	odd	6		1008.2.df.d.929.6		16
252.83	odd	6		3024.2.ca.d.2033.5		16
252.191	even	6		3024.2.df.d.1601.5		16
252.223	even	6		1008.2.ca.d.353.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.1	✓	16	21.2	odd	6
252.2.w.a.101.1	yes	16	63.34	odd	6
252.2.bm.a.173.3	yes	16	63.16	even	3
252.2.bm.a.185.3	yes	16	21.20	even	2
756.2.w.a.341.5		16	7.2	even	3
756.2.w.a.521.5		16	63.20	even	6
756.2.bm.a.17.5		16	7.6	odd	2
756.2.bm.a.89.5		16	63.2	odd	6
1008.2.ca.d.257.8		16	84.23	even	6
1008.2.ca.d.353.8		16	252.223	even	6
1008.2.df.d.689.6		16	84.83	odd	2
1008.2.df.d.929.6		16	252.79	odd	6
1764.2.w.b.509.8		16	21.5	even	6
1764.2.w.b.1109.8		16	9.7	even	3
1764.2.x.a.293.5		16	21.11	odd	6
1764.2.x.a.1469.5		16	63.52	odd	6
1764.2.x.b.293.4		16	21.17	even	6
1764.2.x.b.1469.4		16	63.25	even	3
1764.2.bm.a.1685.6		16	63.61	odd	6
1764.2.bm.a.1697.6		16	3.2	odd	2
2268.2.t.a.1781.5		16	63.41	even	6
2268.2.t.a.2105.5		16	63.58	even	3
2268.2.t.b.1781.4		16	63.13	odd	6
2268.2.t.b.2105.4		16	63.23	odd	6
3024.2.ca.d.2033.5		16	252.83	odd	6
3024.2.ca.d.2609.5		16	28.23	odd	6
3024.2.df.d.17.5		16	28.27	even	2
3024.2.df.d.1601.5		16	252.191	even	6
5292.2.w.b.521.4		16	9.2	odd	6
5292.2.w.b.1097.4		16	7.5	odd	6
5292.2.x.a.881.5		16	7.4	even	3
5292.2.x.a.4409.5		16	63.38	even	6
5292.2.x.b.881.4		16	7.3	odd	6
5292.2.x.b.4409.4		16	63.11	odd	6
5292.2.bm.a.2285.4		16	1.1	even	1	trivial
5292.2.bm.a.4625.4		16	63.47	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5292.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.0764245 q^{5} +5.38437i q^{11} +(4.60313 + 2.65762i) q^{13} +(-1.89092 + 3.27516i) q^{17} +(4.33939 - 2.50535i) q^{19} +2.33784i q^{23} -4.99416 q^{25} +(-8.84430 + 5.10626i) q^{29} +(-4.97636 + 2.87310i) q^{31} +(0.354486 + 0.613988i) q^{37} +(3.29910 - 5.71422i) q^{41} +(0.716520 + 1.24105i) q^{43} +(-1.46192 + 2.53213i) q^{47} +(-10.4835 - 6.05264i) q^{53} +0.411498i q^{55} +(-0.289951 - 0.502210i) q^{59} +(2.40641 + 1.38934i) q^{61} +(0.351792 + 0.203107i) q^{65} +(-2.63593 - 4.56556i) q^{67} -3.32103i q^{71} +(6.17326 + 3.56413i) q^{73} +(-0.469123 + 0.812544i) q^{79} +(-6.49790 - 11.2547i) q^{83} +(-0.144512 + 0.250303i) q^{85} +(-1.51794 - 2.62915i) q^{89} +(0.331636 - 0.191470i) q^{95} +(-6.18183 + 3.56908i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{13} - 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + q^{37} + 6 q^{41} - 2 q^{43} - 18 q^{47} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 21 q^{89} - 6 q^{95} - 3 q^{97}+O(q^{100}) \) 16 * q - 3 * q^13 - 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + q^37 + 6 * q^41 - 2 * q^43 - 18 * q^47 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 21 * q^89 - 6 * q^95 - 3 * q^97

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