LMFDB - Embedded newform 5292.2.j.h.1765.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5292,2,Mod(1765,5292)] 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, 2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5292.1765"); 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.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1765.3
Root			$1.13119 - 1.31165i$ of defining polynomial
Character	$\chi$	$=$	5292.1765
Dual form			5292.2.j.h.3529.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.764702 + 1.32450i) q^{5} +(0.417818 + 0.723682i) q^{11} +(1.81222 - 3.13886i) q^{13} +0.602113 q^{17} -1.69377 q^{19} +(-3.07202 + 5.32090i) q^{23} +(1.33046 + 2.30443i) q^{25} +(-4.99671 - 8.65455i) q^{29} +(1.65421 - 2.86517i) q^{31} -8.79691 q^{37} +(-3.51718 + 6.09194i) q^{41} +(0.846884 + 1.46685i) q^{43} +(4.23200 + 7.33004i) q^{47} -7.99232 q^{53} -1.27803 q^{55} +(0.0652138 - 0.112954i) q^{59} +(2.38343 + 4.12822i) q^{61} +(2.77162 + 4.80059i) q^{65} +(1.12166 - 1.94278i) q^{67} +9.39130 q^{71} +4.50909 q^{73} +(-7.87120 - 13.6333i) q^{79} +(3.16210 + 5.47692i) q^{83} +(-0.460438 + 0.797501i) q^{85} -1.06236 q^{89} +(1.29523 - 2.24340i) q^{95} +(-7.76364 - 13.4470i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} - 2 q^{11} + 2 q^{13} + 4 q^{17} - 14 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} - q^{31} - 20 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 30 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65}+ \cdots - 18 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 - 2 * q^11 + 2 * q^13 + 4 * q^17 - 14 * q^19 - 11 * q^23 - 9 * q^25 - q^29 - q^31 - 20 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 30 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 - 42 * q^73 - 10 * q^79 + 25 * q^83 + 8 * q^85 - 12 * q^89 + 28 * q^95 - 18 * q^97

Character values

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

$n$	$785$	$1081$	$2647$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.764702	+	1.32450i	−0.341985	+	0.592336i	−0.984801	−	0.173685i	$-0.944433\pi$
$5$	−0.764702	+	1.32450i	−0.341985	+	0.592336i	0.642816	+	0.766021i	$0.277766\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.417818	+	0.723682i	0.125977	+	0.218198i	0.922114	−	0.386917i	$-0.126460\pi$
$11$	0.417818	+	0.723682i	0.125977	+	0.218198i	−0.796137	+	0.605116i	$0.793127\pi$
$12$		0			0
$13$	1.81222	−	3.13886i	0.502620	−	0.870563i	−0.497375	−	0.867535i	$-0.665703\pi$
$13$	1.81222	−	3.13886i	0.502620	−	0.870563i	0.999995	−	0.00302796i	$-0.000963830\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.602113			0.146034			0.0730170	−	0.997331i	$-0.476737\pi$
$17$	0.602113			0.146034			0.0730170	+	0.997331i	$0.476737\pi$
$18$		0			0
$19$	−1.69377			−0.388577			−0.194289	−	0.980944i	$-0.562240\pi$
$19$	−1.69377			−0.388577			−0.194289	+	0.980944i	$0.562240\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.07202	+	5.32090i	−0.640561	+	1.10948i	0.344746	+	0.938696i	$0.387965\pi$
$23$	−3.07202	+	5.32090i	−0.640561	+	1.10948i	−0.985308	+	0.170789i	$0.945368\pi$
$24$		0			0
$25$	1.33046	+	2.30443i	0.266092	+	0.460885i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.99671	−	8.65455i	−0.927865	−	1.60711i	−0.786888	−	0.617096i	$-0.788309\pi$
$29$	−4.99671	−	8.65455i	−0.927865	−	1.60711i	−0.140977	−	0.990013i	$-0.545024\pi$
$30$		0			0
$31$	1.65421	−	2.86517i	0.297104	−	0.514599i	−0.678368	−	0.734722i	$-0.737312\pi$
$31$	1.65421	−	2.86517i	0.297104	−	0.514599i	0.975472	+	0.220123i	$0.0706458\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−8.79691			−1.44620			−0.723102	−	0.690741i	$-0.757284\pi$
$37$	−8.79691			−1.44620			−0.723102	+	0.690741i	$0.757284\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.51718	+	6.09194i	−0.549291	+	0.951401i	0.449032	+	0.893516i	$0.351769\pi$
$41$	−3.51718	+	6.09194i	−0.549291	+	0.951401i	−0.998323	+	0.0578850i	$0.981564\pi$
$42$		0			0
$43$	0.846884	+	1.46685i	0.129149	+	0.223692i	0.923347	−	0.383967i	$-0.125442\pi$
$43$	0.846884	+	1.46685i	0.129149	+	0.223692i	−0.794198	+	0.607659i	$0.792109\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.23200	+	7.33004i	0.617301	+	1.06920i	0.989976	+	0.141235i	$0.0451073\pi$
$47$	4.23200	+	7.33004i	0.617301	+	1.06920i	−0.372675	+	0.927962i	$0.621559\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.99232			−1.09783			−0.548915	−	0.835878i	$-0.684959\pi$
$53$	−7.99232			−1.09783			−0.548915	+	0.835878i	$0.684959\pi$
$54$		0			0
$55$	−1.27803			−0.172329
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.0652138	−	0.112954i	0.00849011	−	0.0147053i	−0.861749	−	0.507335i	$-0.830631\pi$
$59$	0.0652138	−	0.112954i	0.00849011	−	0.0147053i	0.870239	+	0.492629i	$0.163964\pi$
$60$		0			0
$61$	2.38343	+	4.12822i	0.305166	+	0.528564i	0.977298	−	0.211868i	$-0.0679546\pi$
$61$	2.38343	+	4.12822i	0.305166	+	0.528564i	−0.672132	+	0.740431i	$0.734621\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.77162	+	4.80059i	0.343777	+	0.595440i
$66$		0			0
$67$	1.12166	−	1.94278i	0.137033	−	0.237348i	−0.789339	−	0.613957i	$-0.789577\pi$
$67$	1.12166	−	1.94278i	0.137033	−	0.237348i	0.926372	+	0.376609i	$0.122910\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.39130			1.11454			0.557271	−	0.830331i	$-0.311848\pi$
$71$	9.39130			1.11454			0.557271	+	0.830331i	$0.311848\pi$
$72$		0			0
$73$	4.50909			0.527749			0.263874	−	0.964557i	$-0.415000\pi$
$73$	4.50909			0.527749			0.263874	+	0.964557i	$0.415000\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−7.87120	−	13.6333i	−0.885580	−	1.53387i	−0.845048	−	0.534691i	$-0.820428\pi$
$79$	−7.87120	−	13.6333i	−0.885580	−	1.53387i	−0.0405317	−	0.999178i	$-0.512905\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.16210	+	5.47692i	0.347085	+	0.601170i	0.985730	−	0.168332i	$-0.0538380\pi$
$83$	3.16210	+	5.47692i	0.347085	+	0.601170i	−0.638645	+	0.769502i	$0.720505\pi$
$84$		0			0
$85$	−0.460438	+	0.797501i	−0.0499415	+	0.0865011i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.06236			−0.112610			−0.0563049	−	0.998414i	$-0.517932\pi$
$89$	−1.06236			−0.112610			−0.0563049	+	0.998414i	$0.517932\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.29523	−	2.24340i	0.132888	−	0.230168i
$96$		0			0
$97$	−7.76364	−	13.4470i	−0.788279	−	1.36534i	−0.927021	−	0.375010i	$-0.877639\pi$
$97$	−7.76364	−	13.4470i	−0.788279	−	1.36534i	0.138742	−	0.990329i	$-0.455694\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.75757	+	16.9006i	0.970914	+	1.68167i	0.692807	+	0.721123i	$0.256374\pi$
$101$	9.75757	+	16.9006i	0.970914	+	1.68167i	0.278107	+	0.960550i	$0.410293\pi$
$102$		0			0
$103$	0.911770	−	1.57923i	0.0898394	−	0.155606i	−0.817604	−	0.575781i	$-0.804698\pi$
$103$	0.911770	−	1.57923i	0.0898394	−	0.155606i	0.907443	+	0.420175i	$0.138031\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.5416			−1.01909			−0.509546	−	0.860444i	$-0.670187\pi$
$107$	−10.5416			−1.01909			−0.509546	+	0.860444i	$0.670187\pi$
$108$		0			0
$109$	−12.6088			−1.20771			−0.603854	−	0.797095i	$-0.706369\pi$
$109$	−12.6088			−1.20771			−0.603854	+	0.797095i	$0.706369\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.76452	+	13.4485i	−0.730424	+	1.26513i	0.226278	+	0.974063i	$0.427344\pi$
$113$	−7.76452	+	13.4485i	−0.730424	+	1.26513i	−0.956702	+	0.291069i	$0.905989\pi$
$114$		0			0
$115$	−4.69837	−	8.13781i	−0.438125	−	0.758855i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.15086	−	8.92154i	0.468260	−	0.811050i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.7166			−1.04797
$126$		0			0
$127$	−10.8966			−0.966919			−0.483460	−	0.875367i	$-0.660620\pi$
$127$	−10.8966			−0.966919			−0.483460	+	0.875367i	$0.660620\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.73088	−	16.8544i	0.850191	−	1.47257i	−0.0308446	−	0.999524i	$-0.509820\pi$
$131$	9.73088	−	16.8544i	0.850191	−	1.47257i	0.881036	−	0.473050i	$-0.156847\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.13833	+	10.6319i	0.524433	+	0.908344i	0.999595	+	0.0284461i	$0.00905590\pi$
$137$	6.13833	+	10.6319i	0.524433	+	0.908344i	−0.475163	+	0.879898i	$0.657611\pi$
$138$		0			0
$139$	−6.44692	+	11.1664i	−0.546821	+	0.947121i	0.451669	+	0.892185i	$0.350829\pi$
$139$	−6.44692	+	11.1664i	−0.546821	+	0.947121i	−0.998490	+	0.0549357i	$0.982505\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.02872			0.253274
$144$		0			0
$145$	15.2840			1.26926
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.03267	+	15.6451i	−0.739986	+	1.28169i	0.212516	+	0.977158i	$0.431834\pi$
$149$	−9.03267	+	15.6451i	−0.739986	+	1.28169i	−0.952501	+	0.304535i	$0.901499\pi$
$150$		0			0
$151$	−4.29891	−	7.44593i	−0.349840	−	0.605941i	0.636381	−	0.771375i	$-0.280431\pi$
$151$	−4.29891	−	7.44593i	−0.349840	−	0.605941i	−0.986221	+	0.165434i	$0.947097\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.52995	+	4.38200i	0.203210	+	0.351971i
$156$		0			0
$157$	−1.59683	+	2.76579i	−0.127441	+	0.220734i	−0.922684	−	0.385556i	$-0.874010\pi$
$157$	−1.59683	+	2.76579i	−0.127441	+	0.220734i	0.795244	+	0.606290i	$0.207343\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.09618			−0.320838			−0.160419	−	0.987049i	$-0.551284\pi$
$163$	−4.09618			−0.320838			−0.160419	+	0.987049i	$0.551284\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.24859	+	14.2870i	−0.638295	+	1.10556i	0.347512	+	0.937676i	$0.387027\pi$
$167$	−8.24859	+	14.2870i	−0.638295	+	1.10556i	−0.985807	+	0.167883i	$0.946307\pi$
$168$		0			0
$169$	−0.0682984	−	0.118296i	−0.00525372	−	0.00909971i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.41063	−	11.1035i	−0.487391	−	0.844186i	0.512504	−	0.858685i	$-0.328718\pi$
$173$	−6.41063	−	11.1035i	−0.487391	−	0.844186i	−0.999895	+	0.0144987i	$0.995385\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−23.7499			−1.77515			−0.887576	−	0.460661i	$-0.847612\pi$
$179$	−23.7499			−1.77515			−0.887576	+	0.460661i	$0.847612\pi$
$180$		0			0
$181$	−16.0244			−1.19108			−0.595542	−	0.803324i	$-0.703063\pi$
$181$	−16.0244			−1.19108			−0.595542	+	0.803324i	$0.703063\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.72702	−	11.6515i	0.494580	−	0.856638i
$186$		0			0
$187$	0.251574	+	0.435739i	0.0183969	+	0.0318644i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.40475	−	9.36130i	−0.391074	−	0.677360i	0.601517	−	0.798860i	$-0.294563\pi$
$191$	−5.40475	−	9.36130i	−0.391074	−	0.677360i	−0.992591	+	0.121500i	$0.961230\pi$
$192$		0			0
$193$	−0.375130	+	0.649745i	−0.0270025	+	0.0467696i	−0.879211	−	0.476433i	$-0.841930\pi$
$193$	−0.375130	+	0.649745i	−0.0270025	+	0.0467696i	0.852208	+	0.523203i	$0.175263\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.3186			−0.735169			−0.367584	−	0.929990i	$-0.619815\pi$
$197$	−10.3186			−0.735169			−0.367584	+	0.929990i	$0.619815\pi$
$198$		0			0
$199$	5.70859			0.404671			0.202336	−	0.979316i	$-0.435147\pi$
$199$	5.70859			0.404671			0.202336	+	0.979316i	$0.435147\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−5.37919	−	9.31704i	−0.375699	−	0.650730i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.707687	−	1.22575i	−0.0489517	−	0.0847869i
$210$		0			0
$211$	2.73050	−	4.72937i	0.187976	−	0.325583i	−0.756600	−	0.653878i	$-0.773141\pi$
$211$	2.73050	−	4.72937i	0.187976	−	0.325583i	0.944575	+	0.328295i	$0.106474\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.59046			−0.176668
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.09116	−	1.88995i	0.0733996	−	0.127132i
$222$		0			0
$223$	−9.00530	−	15.5976i	−0.603040	−	1.04450i	−0.992358	−	0.123392i	$-0.960623\pi$
$223$	−9.00530	−	15.5976i	−0.603040	−	1.04450i	0.389318	−	0.921103i	$-0.372711\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.08699	−	15.7391i	−0.603125	−	1.04464i	−0.992345	−	0.123498i	$-0.960589\pi$
$227$	−9.08699	−	15.7391i	−0.603125	−	1.04464i	0.389220	−	0.921145i	$-0.372745\pi$
$228$		0			0
$229$	7.71391	−	13.3609i	0.509750	−	0.882912i	−0.490186	−	0.871618i	$-0.663071\pi$
$229$	7.71391	−	13.3609i	0.509750	−	0.882912i	0.999936	−	0.0112949i	$-0.00359534\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.41783			−0.420446			−0.210223	−	0.977653i	$-0.567419\pi$
$233$	−6.41783			−0.420446			−0.210223	+	0.977653i	$0.567419\pi$
$234$		0			0
$235$	−12.9449			−0.844431
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.33317	−	4.04118i	0.150920	−	0.261402i	−0.780646	−	0.624974i	$-0.785110\pi$
$239$	2.33317	−	4.04118i	0.150920	−	0.261402i	0.931566	+	0.363572i	$0.118443\pi$
$240$		0			0
$241$	9.42858	+	16.3308i	0.607348	+	1.05196i	0.991676	+	0.128761i	$0.0411000\pi$
$241$	9.42858	+	16.3308i	0.607348	+	1.05196i	−0.384327	+	0.923197i	$0.625567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.06948	+	5.31650i	−0.195307	+	0.338281i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−15.7016			−0.991074			−0.495537	−	0.868587i	$-0.665029\pi$
$251$	−15.7016			−0.991074			−0.495537	+	0.868587i	$0.665029\pi$
$252$		0			0
$253$	−5.13419			−0.322784
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.60892	−	7.98289i	0.287497	−	0.497959i	−0.685715	−	0.727870i	$-0.740510\pi$
$257$	4.60892	−	7.98289i	0.287497	−	0.497959i	0.973212	+	0.229911i	$0.0738436\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.241311	+	0.417962i	0.0148799	+	0.0257727i	0.873369	−	0.487058i	$-0.161930\pi$
$263$	0.241311	+	0.417962i	0.0148799	+	0.0257727i	−0.858490	+	0.512831i	$0.828597\pi$
$264$		0			0
$265$	6.11174	−	10.5859i	0.375442	−	0.650284i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.88576			−0.480803			−0.240402	−	0.970674i	$-0.577279\pi$
$269$	−7.88576			−0.480803			−0.240402	+	0.970674i	$0.577279\pi$
$270$		0			0
$271$	−25.5893			−1.55444			−0.777220	−	0.629229i	$-0.783371\pi$
$271$	−25.5893			−1.55444			−0.777220	+	0.629229i	$0.783371\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.11178	+	1.92566i	−0.0670429	+	0.116122i
$276$		0			0
$277$	−4.18466	−	7.24804i	−0.251432	−	0.435492i	0.712489	−	0.701684i	$-0.247568\pi$
$277$	−4.18466	−	7.24804i	−0.251432	−	0.435492i	−0.963920	+	0.266191i	$0.914235\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.551848	+	0.955828i	0.0329205	+	0.0570199i	0.882016	−	0.471219i	$-0.156186\pi$
$281$	0.551848	+	0.955828i	0.0329205	+	0.0570199i	−0.849096	+	0.528239i	$0.822853\pi$
$282$		0			0
$283$	−1.45369	+	2.51786i	−0.0864128	+	0.149671i	−0.905992	−	0.423294i	$-0.860874\pi$
$283$	−1.45369	+	2.51786i	−0.0864128	+	0.149671i	0.819580	+	0.572965i	$0.194207\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−16.6375			−0.978674
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.4381	−	21.5434i	0.726642	−	1.25858i	−0.231653	−	0.972798i	$-0.574413\pi$
$293$	12.4381	−	21.5434i	0.726642	−	1.25858i	0.958295	−	0.285782i	$-0.0922532\pi$
$294$		0			0
$295$	0.0997383	+	0.172752i	0.00580699	+	0.0100580i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.1344	+	19.2853i	0.643918	+	1.11530i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.29045			−0.417450
$306$		0			0
$307$	−23.7968			−1.35816			−0.679078	−	0.734066i	$-0.737620\pi$
$307$	−23.7968			−1.35816			−0.679078	+	0.734066i	$0.737620\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.35677	−	16.2064i	0.530574	−	0.918981i	−0.468790	−	0.883310i	$-0.655310\pi$
$311$	9.35677	−	16.2064i	0.530574	−	0.918981i	0.999364	−	0.0356711i	$-0.0113569\pi$
$312$		0			0
$313$	9.65797	+	16.7281i	0.545901	+	0.945527i	0.998550	+	0.0538387i	$0.0171457\pi$
$313$	9.65797	+	16.7281i	0.545901	+	0.945527i	−0.452649	+	0.891689i	$0.649521\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.897542	−	1.55459i	−0.0504110	−	0.0873144i	0.839719	−	0.543021i	$-0.182720\pi$
$317$	−0.897542	−	1.55459i	−0.0504110	−	0.0873144i	−0.890130	+	0.455707i	$0.849386\pi$
$318$		0			0
$319$	4.17543	−	7.23205i	0.233779	−	0.404917i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.01984			−0.0567455
$324$		0			0
$325$	9.64436			0.534973
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.06833	+	12.2427i	0.388511	+	0.672920i	0.992249	−	0.124262i	$-0.0396563\pi$
$331$	7.06833	+	12.2427i	0.388511	+	0.672920i	−0.603739	+	0.797182i	$0.706323\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.71547	+	2.97129i	0.0937264	+	0.162339i
$336$		0			0
$337$	−2.94072	+	5.09348i	−0.160191	+	0.277459i	−0.934937	−	0.354813i	$-0.884544\pi$
$337$	−2.94072	+	5.09348i	−0.160191	+	0.277459i	0.774746	+	0.632273i	$0.217878\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.76463			0.149713
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.17593	+	5.50087i	−0.170493	+	0.295302i	−0.938592	−	0.345028i	$-0.887869\pi$
$347$	−3.17593	+	5.50087i	−0.170493	+	0.295302i	0.768099	+	0.640331i	$0.221203\pi$
$348$		0			0
$349$	10.4321	+	18.0689i	0.558416	+	0.967205i	0.997629	+	0.0688222i	$0.0219241\pi$
$349$	10.4321	+	18.0689i	0.558416	+	0.967205i	−0.439213	+	0.898383i	$0.644743\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.07115	−	1.85528i	−0.0570114	−	0.0987466i	0.836111	−	0.548560i	$-0.184824\pi$
$353$	−1.07115	−	1.85528i	−0.0570114	−	0.0987466i	−0.893123	+	0.449813i	$0.851490\pi$
$354$		0			0
$355$	−7.18155	+	12.4388i	−0.381157	+	0.660183i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−21.2396			−1.12098			−0.560492	−	0.828160i	$-0.689388\pi$
$359$	−21.2396			−1.12098			−0.560492	+	0.828160i	$0.689388\pi$
$360$		0			0
$361$	−16.1311			−0.849008
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.44811	+	5.97230i	−0.180482	+	0.312605i
$366$		0			0
$367$	16.2053	+	28.0685i	0.845912	+	1.46516i	0.884827	+	0.465919i	$0.154276\pi$
$367$	16.2053	+	28.0685i	0.845912	+	1.46516i	−0.0389156	+	0.999243i	$0.512390\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−16.8101	+	29.1159i	−0.870393	+	1.50756i	−0.00880173	+	0.999961i	$0.502802\pi$
$373$	−16.8101	+	29.1159i	−0.870393	+	1.50756i	−0.861591	+	0.507603i	$0.830532\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−36.2206			−1.86545
$378$		0			0
$379$	28.2829			1.45279			0.726396	−	0.687276i	$-0.241194\pi$
$379$	28.2829			1.45279			0.726396	+	0.687276i	$0.241194\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.09473	+	8.82434i	−0.260329	+	0.450903i	−0.966329	−	0.257309i	$-0.917164\pi$
$383$	−5.09473	+	8.82434i	−0.260329	+	0.450903i	0.706001	+	0.708211i	$0.250498\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	5.22525	+	9.05040i	0.264931	+	0.458873i	0.967545	−	0.252697i	$-0.0813176\pi$
$389$	5.22525	+	9.05040i	0.264931	+	0.458873i	−0.702615	+	0.711570i	$0.747984\pi$
$390$		0			0
$391$	−1.84971	+	3.20379i	−0.0935437	+	0.162022i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	24.0765			1.21142
$396$		0			0
$397$	14.5007			0.727767			0.363884	−	0.931444i	$-0.381451\pi$
$397$	14.5007			0.727767			0.363884	+	0.931444i	$0.381451\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.7071	+	22.0094i	−0.634563	+	1.09909i	0.352045	+	0.935983i	$0.385486\pi$
$401$	−12.7071	+	22.0094i	−0.634563	+	1.09909i	−0.986608	+	0.163112i	$0.947847\pi$
$402$		0			0
$403$	−5.99558	−	10.3846i	−0.298661	−	0.517296i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.67551	−	6.36617i	−0.182188	−	0.315559i
$408$		0			0
$409$	−6.19535	+	10.7307i	−0.306340	+	0.530597i	−0.977559	−	0.210663i	$-0.932438\pi$
$409$	−6.19535	+	10.7307i	−0.306340	+	0.530597i	0.671219	+	0.741259i	$0.265771\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−9.67226			−0.474792
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.3596	−	26.6036i	0.750365	−	1.29967i	−0.197281	−	0.980347i	$-0.563211\pi$
$419$	15.3596	−	26.6036i	0.750365	−	1.29967i	0.947646	−	0.319323i	$-0.103455\pi$
$420$		0			0
$421$	−2.88912	−	5.00410i	−0.140807	−	0.243885i	0.786994	−	0.616961i	$-0.211636\pi$
$421$	−2.88912	−	5.00410i	−0.140807	−	0.243885i	−0.927801	+	0.373076i	$0.878303\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.801089	+	1.38753i	0.0388585	+	0.0673049i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.420556			−0.0202575			−0.0101287	−	0.999949i	$-0.503224\pi$
$431$	−0.420556			−0.0202575			−0.0101287	+	0.999949i	$0.503224\pi$
$432$		0			0
$433$	30.8208			1.48115			0.740576	−	0.671972i	$-0.234553\pi$
$433$	30.8208			1.48115			0.740576	+	0.671972i	$0.234553\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.20330	−	9.01237i	0.248907	−	0.431120i
$438$		0			0
$439$	−1.50590	−	2.60830i	−0.0718729	−	0.124488i	0.827849	−	0.560951i	$-0.189564\pi$
$439$	−1.50590	−	2.60830i	−0.0718729	−	0.124488i	−0.899722	+	0.436463i	$0.856231\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−9.22141	−	15.9719i	−0.438122	−	0.758850i	0.559422	−	0.828883i	$-0.311023\pi$
$443$	−9.22141	−	15.9719i	−0.438122	−	0.758850i	−0.997545	+	0.0700326i	$0.977690\pi$
$444$		0			0
$445$	0.812388	−	1.40710i	0.0385109	−	0.0667028i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.80998			0.321383			0.160691	−	0.987005i	$-0.448628\pi$
$449$	6.80998			0.321383			0.160691	+	0.987005i	$0.448628\pi$
$450$		0			0
$451$	−5.87817			−0.276792
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.18283	−	10.7090i	−0.289220	−	0.500944i	0.684403	−	0.729103i	$-0.260063\pi$
$457$	−6.18283	−	10.7090i	−0.289220	−	0.500944i	−0.973624	+	0.228159i	$0.926729\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.3651	+	28.3453i	0.762201	+	1.32017i	0.941714	+	0.336415i	$0.109214\pi$
$461$	16.3651	+	28.3453i	0.762201	+	1.32017i	−0.179513	+	0.983756i	$0.557452\pi$
$462$		0			0
$463$	9.61023	−	16.6454i	0.446625	−	0.773577i	−0.551539	−	0.834149i	$-0.685959\pi$
$463$	9.61023	−	16.6454i	0.446625	−	0.773577i	0.998164	+	0.0605719i	$0.0192924\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.01711			0.139615			0.0698075	−	0.997560i	$-0.477761\pi$
$467$	3.01711			0.139615			0.0698075	+	0.997560i	$0.477761\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.707687	+	1.22575i	−0.0325395	+	0.0563600i
$474$		0			0
$475$	−2.25349	−	3.90316i	−0.103397	−	0.179089i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.9486	−	22.4276i	−0.591635	−	1.02474i	−0.994012	−	0.109269i	$-0.965149\pi$
$479$	−12.9486	−	22.4276i	−0.591635	−	1.02474i	0.402377	−	0.915474i	$-0.368184\pi$
$480$		0			0
$481$	−15.9420	+	27.6123i	−0.726891	+	1.25901i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	23.7475			1.07832
$486$		0			0
$487$	41.7683			1.89270			0.946350	−	0.323143i	$-0.104739\pi$
$487$	41.7683			1.89270			0.946350	+	0.323143i	$0.104739\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.9879	−	24.2278i	0.631265	−	1.09338i	−0.356028	−	0.934475i	$-0.615869\pi$
$491$	13.9879	−	24.2278i	0.631265	−	1.09338i	0.987293	−	0.158908i	$-0.0507974\pi$
$492$		0			0
$493$	−3.00858	−	5.21102i	−0.135500	−	0.234693i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	12.4748	−	21.6070i	0.558450	−	0.967264i	−0.439176	−	0.898401i	$-0.644730\pi$
$499$	12.4748	−	21.6070i	0.558450	−	0.967264i	0.997626	−	0.0688626i	$-0.0219370\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−34.1966			−1.52475			−0.762376	−	0.647135i	$-0.775967\pi$
$503$	−34.1966			−1.52475			−0.762376	+	0.647135i	$0.775967\pi$
$504$		0			0
$505$	−29.8465			−1.32815
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.84342	−	11.8532i	0.303329	−	0.525382i	−0.673559	−	0.739134i	$-0.735235\pi$
$509$	6.84342	−	11.8532i	0.303329	−	0.525382i	0.976888	+	0.213752i	$0.0685685\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.39447	+	2.41528i	0.0614475	+	0.106430i
$516$		0			0
$517$	−3.53641	+	6.12525i	−0.155531	+	0.269388i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−26.7496			−1.17192			−0.585960	−	0.810340i	$-0.699282\pi$
$521$	−26.7496			−1.17192			−0.585960	+	0.810340i	$0.699282\pi$
$522$		0			0
$523$	21.2262			0.928158			0.464079	−	0.885794i	$-0.346385\pi$
$523$	21.2262			0.928158			0.464079	+	0.885794i	$0.346385\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.996020	−	1.72516i	0.0433873	−	0.0751490i
$528$		0			0
$529$	−7.37466	−	12.7733i	−0.320637	−	0.555360i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.7478	+	22.0799i	0.552170	+	0.956386i
$534$		0			0
$535$	8.06116	−	13.9623i	0.348514	−	0.603644i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−20.2537			−0.870776			−0.435388	−	0.900243i	$-0.643389\pi$
$541$	−20.2537			−0.870776			−0.435388	+	0.900243i	$0.643389\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	9.64201	−	16.7005i	0.413019	−	0.715369i
$546$		0			0
$547$	−21.9668	−	38.0476i	−0.939233	−	1.62680i	−0.766906	−	0.641760i	$-0.778205\pi$
$547$	−21.9668	−	38.0476i	−0.939233	−	1.62680i	−0.172327	−	0.985040i	$-0.555129\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.46326	+	14.6588i	0.360547	+	0.624486i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.90965			−0.377514			−0.188757	−	0.982024i	$-0.560446\pi$
$557$	−8.90965			−0.377514			−0.188757	+	0.982024i	$0.560446\pi$
$558$		0			0
$559$	6.13897			0.259651
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−14.2096	+	24.6118i	−0.598865	+	1.03726i	0.394124	+	0.919057i	$0.371048\pi$
$563$	−14.2096	+	24.6118i	−0.598865	+	1.03726i	−0.992989	+	0.118207i	$0.962285\pi$
$564$		0			0
$565$	−11.8751	−	20.5683i	−0.499589	−	0.865313i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.28948	−	7.42959i	−0.179824	−	0.311465i	0.761996	−	0.647582i	$-0.224220\pi$
$569$	−4.28948	−	7.42959i	−0.179824	−	0.311465i	−0.941820	+	0.336117i	$0.890886\pi$
$570$		0			0
$571$	−9.68861	+	16.7812i	−0.405456	+	0.702270i	−0.994374	−	0.105922i	$-0.966221\pi$
$571$	−9.68861	+	16.7812i	−0.405456	+	0.702270i	0.588919	+	0.808192i	$0.299554\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.3488			−0.681793
$576$		0			0
$577$	−1.16888			−0.0486612			−0.0243306	−	0.999704i	$-0.507745\pi$
$577$	−1.16888			−0.0486612			−0.0243306	+	0.999704i	$0.507745\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.33934	−	5.78390i	−0.138301	−	0.239545i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.5863	+	26.9963i	0.643316	+	1.11426i	0.984688	+	0.174327i	$0.0557750\pi$
$587$	15.5863	+	26.9963i	0.643316	+	1.11426i	−0.341372	+	0.939928i	$0.610892\pi$
$588$		0			0
$589$	−2.80184	+	4.85293i	−0.115448	+	0.199962i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−30.3773			−1.24745			−0.623724	−	0.781645i	$-0.714381\pi$
$593$	−30.3773			−1.24745			−0.623724	+	0.781645i	$0.714381\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−3.65379	+	6.32855i	−0.149290	+	0.258577i	−0.930965	−	0.365108i	$-0.881032\pi$
$599$	−3.65379	+	6.32855i	−0.149290	+	0.258577i	0.781675	+	0.623685i	$0.214365\pi$
$600$		0			0
$601$	4.61461	+	7.99274i	0.188234	+	0.326031i	0.944661	−	0.328047i	$-0.106390\pi$
$601$	4.61461	+	7.99274i	0.188234	+	0.326031i	−0.756428	+	0.654077i	$0.773057\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.87774	+	13.6446i	0.320276	+	0.554734i
$606$		0			0
$607$	8.53370	−	14.7808i	0.346372	−	0.599934i	−0.639230	−	0.769016i	$-0.720747\pi$
$607$	8.53370	−	14.7808i	0.346372	−	0.599934i	0.985602	+	0.169082i	$0.0540801\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	30.6773			1.24107
$612$		0			0
$613$	0.786117			0.0317510			0.0158755	−	0.999874i	$-0.494946\pi$
$613$	0.786117			0.0317510			0.0158755	+	0.999874i	$0.494946\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.7960	+	41.2159i	−0.957991	+	1.65929i	−0.230621	+	0.973044i	$0.574076\pi$
$617$	−23.7960	+	41.2159i	−0.957991	+	1.65929i	−0.727370	+	0.686246i	$0.759257\pi$
$618$		0			0
$619$	−9.48717	−	16.4323i	−0.381321	−	0.660468i	0.609930	−	0.792455i	$-0.291198\pi$
$619$	−9.48717	−	16.4323i	−0.381321	−	0.660468i	−0.991251	+	0.131987i	$0.957864\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	2.30744	−	3.99660i	0.0922976	−	0.159864i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.29674			−0.211195
$630$		0			0
$631$	0.300343			0.0119565			0.00597823	−	0.999982i	$-0.498097\pi$
$631$	0.300343			0.0119565			0.00597823	+	0.999982i	$0.498097\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.33267	−	14.4326i	0.330672	−	0.572741i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	14.0548	+	24.3436i	0.555131	+	0.961514i	0.997893	+	0.0648756i	$0.0206651\pi$
$641$	14.0548	+	24.3436i	0.555131	+	0.961514i	−0.442763	+	0.896639i	$0.646002\pi$
$642$		0			0
$643$	−1.55289	+	2.68968i	−0.0612399	+	0.106071i	−0.895020	−	0.446026i	$-0.852839\pi$
$643$	−1.55289	+	2.68968i	−0.0612399	+	0.106071i	0.833780	+	0.552097i	$0.186172\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	46.7113			1.83641			0.918205	−	0.396105i	$-0.129638\pi$
$647$	46.7113			1.83641			0.918205	+	0.396105i	$0.129638\pi$
$648$		0			0
$649$	0.108990			0.00427823
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.998764	+	1.72991i	−0.0390847	+	0.0676966i	−0.884906	−	0.465770i	$-0.845778\pi$
$653$	−0.998764	+	1.72991i	−0.0390847	+	0.0676966i	0.845821	+	0.533466i	$0.179111\pi$
$654$		0			0
$655$	14.8825	+	25.7772i	0.581506	+	1.00720i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−8.37284	−	14.5022i	−0.326160	−	0.564925i	0.655587	−	0.755120i	$-0.272421\pi$
$659$	−8.37284	−	14.5022i	−0.326160	−	0.564925i	−0.981746	+	0.190195i	$0.939088\pi$
$660$		0			0
$661$	−6.28870	+	10.8924i	−0.244602	+	0.423664i	−0.962020	−	0.272980i	$-0.911991\pi$
$661$	−6.28870	+	10.8924i	−0.244602	+	0.423664i	0.717417	+	0.696644i	$0.245324\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	61.4000			2.37742
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.99168	+	3.44969i	−0.0768878	+	0.133174i
$672$		0			0
$673$	23.8175	+	41.2531i	0.918096	+	1.59019i	0.802304	+	0.596916i	$0.203607\pi$
$673$	23.8175	+	41.2531i	0.918096	+	1.59019i	0.115792	+	0.993273i	$0.463059\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.54664	−	7.87500i	−0.174741	−	0.302661i	0.765330	−	0.643638i	$-0.222576\pi$
$677$	−4.54664	−	7.87500i	−0.174741	−	0.302661i	−0.940072	+	0.340977i	$0.889242\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.83348			0.184948			0.0924741	−	0.995715i	$-0.470522\pi$
$683$	4.83348			0.184948			0.0924741	+	0.995715i	$0.470522\pi$
$684$		0			0
$685$	−18.7760			−0.717393
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.4839	+	25.0868i	−0.551791	+	0.955730i
$690$		0			0
$691$	5.39228	+	9.33969i	0.205132	+	0.355299i	0.950175	−	0.311718i	$-0.100904\pi$
$691$	5.39228	+	9.33969i	0.205132	+	0.355299i	−0.745043	+	0.667017i	$0.767571\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.85995	−	17.0779i	−0.374009	−	0.647803i
$696$		0			0
$697$	−2.11774	+	3.66804i	−0.0802152	+	0.138937i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	31.8393			1.20255			0.601276	−	0.799041i	$-0.294659\pi$
$701$	31.8393			1.20255			0.601276	+	0.799041i	$0.294659\pi$
$702$		0			0
$703$	14.8999			0.561962
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.6032	+	23.5614i	0.510879	+	0.884868i	0.999921	+	0.0126076i	$0.00401324\pi$
$709$	13.6032	+	23.5614i	0.510879	+	0.884868i	−0.489042	+	0.872260i	$0.662653\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	10.1635	+	17.6037i	0.380627	+	0.659265i
$714$		0			0
$715$	−2.31607	+	4.01154i	−0.0866160	+	0.150023i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−28.9098			−1.07815			−0.539076	−	0.842257i	$-0.681227\pi$
$719$	−28.9098			−1.07815			−0.539076	+	0.842257i	$0.681227\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	13.2958	−	23.0291i	0.493795	−	0.855278i
$726$		0			0
$727$	4.29978	+	7.44744i	0.159470	+	0.276210i	0.934678	−	0.355496i	$-0.115688\pi$
$727$	4.29978	+	7.44744i	0.159470	+	0.276210i	−0.775208	+	0.631706i	$0.782355\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.509920	+	0.883208i	0.0188601	+	0.0326666i
$732$		0			0
$733$	22.7753	−	39.4480i	0.841225	−	1.45705i	−0.0476340	−	0.998865i	$-0.515168\pi$
$733$	22.7753	−	39.4480i	0.841225	−	1.45705i	0.888859	−	0.458180i	$-0.151499\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.87460			0.0690519
$738$		0			0
$739$	−12.6898			−0.466803			−0.233401	−	0.972380i	$-0.574986\pi$
$739$	−12.6898			−0.466803			−0.233401	+	0.972380i	$0.574986\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.04492	−	8.73806i	0.185080	−	0.320568i	−0.758523	−	0.651646i	$-0.774079\pi$
$743$	5.04492	−	8.73806i	0.185080	−	0.320568i	0.943604	+	0.331078i	$0.107412\pi$
$744$		0			0
$745$	−13.8146	−	23.9276i	−0.506128	−	0.876640i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.50357	+	4.33631i	−0.0913565	+	0.158234i	−0.908082	−	0.418792i	$-0.862454\pi$
$751$	−2.50357	+	4.33631i	−0.0913565	+	0.158234i	0.816726	+	0.577026i	$0.195787\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.1495			0.478561
$756$		0			0
$757$	6.83620			0.248466			0.124233	−	0.992253i	$-0.460353\pi$
$757$	6.83620			0.248466			0.124233	+	0.992253i	$0.460353\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.4377	−	23.2747i	0.487115	−	0.843708i	−0.512775	−	0.858523i	$-0.671382\pi$
$761$	13.4377	−	23.2747i	0.487115	−	0.843708i	0.999890	+	0.0148147i	$0.00471582\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.236364	−	0.409394i	−0.00853460	−	0.0147824i
$768$		0			0
$769$	−2.00631	+	3.47503i	−0.0723493	+	0.125313i	−0.899931	−	0.436033i	$-0.856383\pi$
$769$	−2.00631	+	3.47503i	−0.0723493	+	0.125313i	0.827581	+	0.561346i	$0.189716\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−27.3723			−0.984512			−0.492256	−	0.870451i	$-0.663828\pi$
$773$	−27.3723			−0.984512			−0.492256	+	0.870451i	$0.663828\pi$
$774$		0			0
$775$	8.80343			0.316228
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.95729	−	10.3183i	0.213442	−	0.369693i
$780$		0			0
$781$	3.92385	+	6.79631i	0.140407	+	0.243191i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.44220	−	4.23001i	−0.0871658	−	0.150976i
$786$		0			0
$787$	6.43636	−	11.1481i	0.229432	−	0.397387i	−0.728208	−	0.685356i	$-0.759647\pi$
$787$	6.43636	−	11.1481i	0.229432	−	0.397387i	0.957640	+	0.287969i	$0.0929799\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	17.2772			0.613531
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.71139	−	15.0886i	0.308573	−	0.534465i	−0.669477	−	0.742833i	$-0.733482\pi$
$797$	8.71139	−	15.0886i	0.308573	−	0.534465i	0.978050	+	0.208368i	$0.0668152\pi$
$798$		0			0
$799$	2.54815	+	4.41352i	0.0901469	+	0.156139i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.88398	+	3.26315i	0.0664842	+	0.115154i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.08195			−0.213830			−0.106915	−	0.994268i	$-0.534097\pi$
$809$	−6.08195			−0.213830			−0.106915	+	0.994268i	$0.534097\pi$
$810$		0			0
$811$	14.6219			0.513443			0.256722	−	0.966485i	$-0.417358\pi$
$811$	14.6219			0.513443			0.256722	+	0.966485i	$0.417358\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.13236	−	5.42540i	0.109722	−	0.190044i
$816$		0			0
$817$	−1.43443	−	2.48450i	−0.0501842	−	0.0869216i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.87162	−	8.43789i	−0.170021	−	0.294484i	0.768406	−	0.639962i	$-0.221050\pi$
$821$	−4.87162	−	8.43789i	−0.170021	−	0.294484i	−0.938427	+	0.345478i	$0.887717\pi$
$822$		0			0
$823$	−5.38983	+	9.33546i	−0.187878	+	0.325414i	−0.944542	−	0.328389i	$-0.893494\pi$
$823$	−5.38983	+	9.33546i	−0.187878	+	0.325414i	0.756665	+	0.653803i	$0.226827\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.0521			−0.453867			−0.226933	−	0.973910i	$-0.572870\pi$
$827$	−13.0521			−0.453867			−0.226933	+	0.973910i	$0.572870\pi$
$828$		0			0
$829$	−49.1095			−1.70564			−0.852822	−	0.522201i	$-0.825111\pi$
$829$	−49.1095			−1.70564			−0.852822	+	0.522201i	$0.825111\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−12.6154	−	21.8506i	−0.436575	−	0.756170i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.0830	+	20.9284i	0.417151	+	0.722527i	0.995652	−	0.0931549i	$-0.0296952\pi$
$839$	12.0830	+	20.9284i	0.417151	+	0.722527i	−0.578500	+	0.815682i	$0.696362\pi$
$840$		0			0
$841$	−35.4341	+	61.3737i	−1.22187	+	2.11633i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.208912			0.00718678
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	27.0243	−	46.8075i	0.926382	−	1.60454i
$852$		0			0
$853$	2.72681	+	4.72297i	0.0933641	+	0.161711i	0.908925	−	0.416960i	$-0.136905\pi$
$853$	2.72681	+	4.72297i	0.0933641	+	0.161711i	−0.815561	+	0.578672i	$0.803571\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.4194	+	28.4393i	0.560876	+	0.971466i	0.997420	+	0.0717835i	$0.0228691\pi$
$857$	16.4194	+	28.4393i	0.560876	+	0.971466i	−0.436544	+	0.899683i	$0.643798\pi$
$858$		0			0
$859$	−26.3299	+	45.6048i	−0.898365	+	1.55601i	−0.0687820	+	0.997632i	$0.521911\pi$
$859$	−26.3299	+	45.6048i	−0.898365	+	1.55601i	−0.829583	+	0.558383i	$0.811422\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	48.8189			1.66182			0.830908	−	0.556410i	$-0.187822\pi$
$863$	48.8189			1.66182			0.830908	+	0.556410i	$0.187822\pi$
$864$		0			0
$865$	19.6089			0.666722
$866$		0			0
$867$		0			0
$868$		0			0
$869$	6.57746	−	11.3925i	0.223125	−	0.386464i
$870$		0			0
$871$	−4.06540	−	7.04148i	−0.137751	−	0.238591i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.5373	−	21.7152i	0.423353	−	0.733269i	−0.572912	−	0.819617i	$-0.694186\pi$
$877$	12.5373	−	21.7152i	0.423353	−	0.733269i	0.996265	+	0.0863480i	$0.0275197\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	16.2437			0.547263			0.273632	−	0.961835i	$-0.411775\pi$
$881$	16.2437			0.547263			0.273632	+	0.961835i	$0.411775\pi$
$882$		0			0
$883$	29.7137			0.999945			0.499973	−	0.866041i	$-0.333343\pi$
$883$	29.7137			0.999945			0.499973	+	0.866041i	$0.333343\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.87353	+	13.6374i	−0.264367	+	0.457897i	−0.967398	−	0.253262i	$-0.918496\pi$
$887$	−7.87353	+	13.6374i	−0.264367	+	0.457897i	0.703030	+	0.711160i	$0.251830\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.16803	−	12.4154i	−0.239869	−	0.415465i
$894$		0			0
$895$	18.1616	−	31.4568i	0.607076	−	1.05149i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−33.0623			−1.10269
$900$		0			0
$901$	−4.81228			−0.160320
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.2539	−	21.2244i	0.407333	−	0.705522i
$906$		0			0
$907$	1.29001	+	2.23437i	0.0428342	+	0.0741910i	0.886648	−	0.462446i	$-0.153028\pi$
$907$	1.29001	+	2.23437i	0.0428342	+	0.0741910i	−0.843813	+	0.536637i	$0.819695\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.2170	−	40.2130i	−0.769214	−	1.33232i	−0.937990	−	0.346663i	$-0.887315\pi$
$911$	−23.2170	−	40.2130i	−0.769214	−	1.33232i	0.168776	−	0.985654i	$-0.446019\pi$
$912$		0			0
$913$	−2.64236	+	4.57671i	−0.0874495	+	0.151467i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	5.68774			0.187621			0.0938106	−	0.995590i	$-0.470095\pi$
$919$	5.68774			0.187621			0.0938106	+	0.995590i	$0.470095\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	17.0191	−	29.4780i	0.560191	−	0.970279i
$924$		0			0
$925$	−11.7040	−	20.2718i	−0.384824	−	0.666534i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.9803	+	41.5350i	0.786767	+	1.36272i	0.927938	+	0.372734i	$0.121580\pi$
$929$	23.9803	+	41.5350i	0.786767	+	1.36272i	−0.141172	+	0.989985i	$0.545087\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.769516			−0.0251659
$936$		0			0
$937$	−25.3542			−0.828285			−0.414142	−	0.910212i	$-0.635918\pi$
$937$	−25.3542			−0.828285			−0.414142	+	0.910212i	$0.635918\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.25651	−	2.17634i	0.0409611	−	0.0709468i	−0.844818	−	0.535054i	$-0.820291\pi$
$941$	1.25651	−	2.17634i	0.0409611	−	0.0709468i	0.885779	+	0.464107i	$0.153625\pi$
$942$		0			0
$943$	−21.6097	−	37.4292i	−0.703710	−	1.21886i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.26537	+	12.5840i	0.236093	+	0.408925i	0.959590	−	0.281403i	$-0.0907997\pi$
$947$	7.26537	+	12.5840i	0.236093	+	0.408925i	−0.723497	+	0.690328i	$0.757466\pi$
$948$		0			0
$949$	8.17147	−	14.1534i	0.265257	−	0.459439i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	36.5564			1.18418			0.592089	−	0.805873i	$-0.298303\pi$
$953$	36.5564			1.18418			0.592089	+	0.805873i	$0.298303\pi$
$954$		0			0
$955$	16.5321			0.534966
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	10.0272	+	17.3676i	0.323458	+	0.560246i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.573726	−	0.993722i	−0.0184689	−	0.0319890i
$966$		0			0
$967$	8.06111	−	13.9623i	0.259228	−	0.448996i	−0.706807	−	0.707406i	$-0.749865\pi$
$967$	8.06111	−	13.9623i	0.259228	−	0.448996i	0.966035	+	0.258410i	$0.0831986\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	17.2020			0.552038			0.276019	−	0.961152i	$-0.410985\pi$
$971$	17.2020			0.552038			0.276019	+	0.961152i	$0.410985\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.1225	−	34.8532i	0.643776	−	1.11505i	−0.340806	−	0.940133i	$-0.610700\pi$
$977$	20.1225	−	34.8532i	0.643776	−	1.11505i	0.984583	−	0.174920i	$-0.0559666\pi$
$978$		0			0
$979$	−0.443873	−	0.768810i	−0.0141862	−	0.0245713i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.2760	+	17.7985i	0.327753	+	0.567685i	0.982066	−	0.188539i	$-0.0603753\pi$
$983$	10.2760	+	17.7985i	0.327753	+	0.567685i	−0.654313	+	0.756224i	$0.727042\pi$
$984$		0			0
$985$	7.89065	−	13.6670i	0.251417	−	0.435467i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−10.4066			−0.330910
$990$		0			0
$991$	29.9744			0.952167			0.476083	−	0.879400i	$-0.342056\pi$
$991$	29.9744			0.952167			0.476083	+	0.879400i	$0.342056\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.36537	+	7.56105i	−0.138392	+	0.239701i
$996$		0			0
$997$	6.01944	+	10.4260i	0.190638	+	0.330194i	0.945462	−	0.325733i	$-0.105611\pi$
$997$	6.01944	+	10.4260i	0.190638	+	0.330194i	−0.754824	+	0.655927i	$0.772278\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.j.h.1765.3		14
3.2	odd	2		1764.2.j.g.589.1		14
7.2	even	3		756.2.l.b.361.5		14
7.3	odd	6		5292.2.i.i.1549.5		14
7.4	even	3		756.2.i.b.37.3		14
7.5	odd	6		5292.2.l.i.361.3		14
7.6	odd	2		5292.2.j.g.1765.5		14
9.2	odd	6		1764.2.j.g.1177.1		14
9.7	even	3	inner	5292.2.j.h.3529.3		14
21.2	odd	6		252.2.l.b.193.5	yes	14
21.5	even	6		1764.2.l.i.949.3		14
21.11	odd	6		252.2.i.b.121.4	yes	14
21.17	even	6		1764.2.i.i.373.4		14
21.20	even	2		1764.2.j.h.589.7		14
28.11	odd	6		3024.2.q.j.2305.3		14
28.23	odd	6		3024.2.t.j.1873.5		14
63.2	odd	6		252.2.i.b.25.4	✓	14
63.4	even	3		2268.2.k.f.1297.3		14
63.11	odd	6		252.2.l.b.205.5	yes	14
63.16	even	3		756.2.i.b.613.3		14
63.20	even	6		1764.2.j.h.1177.7		14
63.23	odd	6		2268.2.k.e.1621.5		14
63.25	even	3		756.2.l.b.289.5		14
63.32	odd	6		2268.2.k.e.1297.5		14
63.34	odd	6		5292.2.j.g.3529.5		14
63.38	even	6		1764.2.l.i.961.3		14
63.47	even	6		1764.2.i.i.1537.4		14
63.52	odd	6		5292.2.l.i.3313.3		14
63.58	even	3		2268.2.k.f.1621.3		14
63.61	odd	6		5292.2.i.i.2125.5		14
84.11	even	6		1008.2.q.j.625.4		14
84.23	even	6		1008.2.t.j.193.3		14
252.11	even	6		1008.2.t.j.961.3		14
252.79	odd	6		3024.2.q.j.2881.3		14
252.151	odd	6		3024.2.t.j.289.5		14
252.191	even	6		1008.2.q.j.529.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.4	✓	14	63.2	odd	6
252.2.i.b.121.4	yes	14	21.11	odd	6
252.2.l.b.193.5	yes	14	21.2	odd	6
252.2.l.b.205.5	yes	14	63.11	odd	6
756.2.i.b.37.3		14	7.4	even	3
756.2.i.b.613.3		14	63.16	even	3
756.2.l.b.289.5		14	63.25	even	3
756.2.l.b.361.5		14	7.2	even	3
1008.2.q.j.529.4		14	252.191	even	6
1008.2.q.j.625.4		14	84.11	even	6
1008.2.t.j.193.3		14	84.23	even	6
1008.2.t.j.961.3		14	252.11	even	6
1764.2.i.i.373.4		14	21.17	even	6
1764.2.i.i.1537.4		14	63.47	even	6
1764.2.j.g.589.1		14	3.2	odd	2
1764.2.j.g.1177.1		14	9.2	odd	6
1764.2.j.h.589.7		14	21.20	even	2
1764.2.j.h.1177.7		14	63.20	even	6
1764.2.l.i.949.3		14	21.5	even	6
1764.2.l.i.961.3		14	63.38	even	6
2268.2.k.e.1297.5		14	63.32	odd	6
2268.2.k.e.1621.5		14	63.23	odd	6
2268.2.k.f.1297.3		14	63.4	even	3
2268.2.k.f.1621.3		14	63.58	even	3
3024.2.q.j.2305.3		14	28.11	odd	6
3024.2.q.j.2881.3		14	252.79	odd	6
3024.2.t.j.289.5		14	252.151	odd	6
3024.2.t.j.1873.5		14	28.23	odd	6
5292.2.i.i.1549.5		14	7.3	odd	6
5292.2.i.i.2125.5		14	63.61	odd	6
5292.2.j.g.1765.5		14	7.6	odd	2
5292.2.j.g.3529.5		14	63.34	odd	6
5292.2.j.h.1765.3		14	1.1	even	1	trivial
5292.2.j.h.3529.3		14	9.7	even	3	inner
5292.2.l.i.361.3		14	7.5	odd	6
5292.2.l.i.3313.3		14	63.52	odd	6

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Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.764702 + 1.32450i) q^{5} +(0.417818 + 0.723682i) q^{11} +(1.81222 - 3.13886i) q^{13} +0.602113 q^{17} -1.69377 q^{19} +(-3.07202 + 5.32090i) q^{23} +(1.33046 + 2.30443i) q^{25} +(-4.99671 - 8.65455i) q^{29} +(1.65421 - 2.86517i) q^{31} -8.79691 q^{37} +(-3.51718 + 6.09194i) q^{41} +(0.846884 + 1.46685i) q^{43} +(4.23200 + 7.33004i) q^{47} -7.99232 q^{53} -1.27803 q^{55} +(0.0652138 - 0.112954i) q^{59} +(2.38343 + 4.12822i) q^{61} +(2.77162 + 4.80059i) q^{65} +(1.12166 - 1.94278i) q^{67} +9.39130 q^{71} +4.50909 q^{73} +(-7.87120 - 13.6333i) q^{79} +(3.16210 + 5.47692i) q^{83} +(-0.460438 + 0.797501i) q^{85} -1.06236 q^{89} +(1.29523 - 2.24340i) q^{95} +(-7.76364 - 13.4470i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} - 2 q^{11} + 2 q^{13} + 4 q^{17} - 14 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} - q^{31} - 20 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 30 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65}+ \cdots - 18 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 - 2 * q^11 + 2 * q^13 + 4 * q^17 - 14 * q^19 - 11 * q^23 - 9 * q^25 - q^29 - q^31 - 20 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 30 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 - 42 * q^73 - 10 * q^79 + 25 * q^83 + 8 * q^85 - 12 * q^89 + 28 * q^95 - 18 * q^97

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