LMFDB - Embedded newform 5292.2.i.f.1549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(1549,5292)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5292, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("5292.1549");

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.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1549.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	5292.1549
Dual form			5292.2.i.f.2125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.119562 + 0.207087i) q^{5} +O(q^{10})$	$q+(0.119562 + 0.207087i) q^{5} +(-2.56238 + 4.43818i) q^{11} +(2.44282 - 4.23109i) q^{13} +(1.85185 + 3.20750i) q^{17} +(-1.83009 + 3.16982i) q^{19} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(1.73229 + 3.00041i) q^{29} -0.717370 q^{31} +(-2.30150 + 3.98632i) q^{37} +(2.80150 - 4.85235i) q^{41} +(-6.24433 - 10.8155i) q^{43} -4.33981 q^{47} +(-0.471410 - 0.816506i) q^{53} -1.22545 q^{55} -7.57893 q^{59} +5.50808 q^{61} +1.16827 q^{65} -0.660190 q^{67} -13.7414 q^{71} +(1.83009 + 3.16982i) q^{73} -6.22545 q^{79} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-3.74433 + 6.48536i) q^{89} -0.875237 q^{95} +(8.57442 + 14.8513i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5}+O(q^{10}) $ 6 * q + q^5	$ 6 q + q^{5} + 2 q^{11} - 3 q^{13} + 2 q^{17} - 3 q^{19} + 14 q^{23} + 6 q^{25} + q^{29} - 6 q^{31} + 3 q^{37} - 3 q^{43} - 42 q^{47} + 6 q^{53} + 12 q^{55} - 62 q^{59} + 12 q^{61} - 30 q^{65} + 12 q^{67} - 34 q^{71} + 3 q^{73} - 18 q^{79} + 20 q^{83} + 15 q^{85} + 12 q^{89} - 40 q^{95} + 9 q^{97}+O(q^{100}) $ 6 * q + q^5 + 2 * q^11 - 3 * q^13 + 2 * q^17 - 3 * q^19 + 14 * q^23 + 6 * q^25 + q^29 - 6 * q^31 + 3 * q^37 - 3 * q^43 - 42 * q^47 + 6 * q^53 + 12 * q^55 - 62 * q^59 + 12 * q^61 - 30 * q^65 + 12 * q^67 - 34 * q^71 + 3 * q^73 - 18 * q^79 + 20 * q^83 + 15 * q^85 + 12 * q^89 - 40 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	0.891521	−	0.452979i	$-0.149639\pi$
$5$	0.119562	+	0.207087i	0.0534696	+	0.0926120i	−0.838052	+	0.545591i	$0.816305\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.56238	+	4.43818i	−0.772587	+	1.33816i	0.163554	+	0.986534i	$0.447704\pi$
$11$	−2.56238	+	4.43818i	−0.772587	+	1.33816i	−0.936141	+	0.351626i	$0.885629\pi$
$12$		0			0
$13$	2.44282	−	4.23109i	0.677516	−	1.17349i	−0.298210	−	0.954500i	$-0.596390\pi$
$13$	2.44282	−	4.23109i	0.677516	−	1.17349i	0.975727	−	0.218993i	$-0.0702770\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.85185	+	3.20750i	0.449139	+	0.777932i	0.998330	−	0.0577649i	$-0.0183974\pi$
$17$	1.85185	+	3.20750i	0.449139	+	0.777932i	−0.549191	+	0.835697i	$0.685064\pi$
$18$		0			0
$19$	−1.83009	+	3.16982i	−0.419853	+	0.727206i	−0.995924	−	0.0901932i	$-0.971252\pi$
$19$	−1.83009	+	3.16982i	−0.419853	+	0.727206i	0.576072	+	0.817399i	$0.304585\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.71053	+	6.42683i	0.773700	+	1.34009i	0.935522	+	0.353267i	$0.114929\pi$
$23$	3.71053	+	6.42683i	0.773700	+	1.34009i	−0.161823	+	0.986820i	$0.551737\pi$
$24$		0			0
$25$	2.47141	−	4.28061i	0.494282	−	0.856122i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.73229	+	3.00041i	0.321678	+	0.557162i	0.980834	−	0.194844i	$-0.0624200\pi$
$29$	1.73229	+	3.00041i	0.321678	+	0.557162i	−0.659157	+	0.752006i	$0.729087\pi$
$30$		0			0
$31$	−0.717370			−0.128843			−0.0644217	−	0.997923i	$-0.520520\pi$
$31$	−0.717370			−0.128843			−0.0644217	+	0.997923i	$0.520520\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.30150	+	3.98632i	−0.378365	+	0.655348i	−0.990825	−	0.135154i	$-0.956847\pi$
$37$	−2.30150	+	3.98632i	−0.378365	+	0.655348i	0.612459	+	0.790502i	$0.290180\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	−0.559976	−	0.828509i	$-0.689190\pi$
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	0.997498	+	0.0706992i	$0.0225230\pi$
$42$		0			0
$43$	−6.24433	−	10.8155i	−0.952251	−	1.64935i	−0.740538	−	0.672015i	$-0.765429\pi$
$43$	−6.24433	−	10.8155i	−0.952251	−	1.64935i	−0.211713	−	0.977332i	$-0.567904\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.33981			−0.633026			−0.316513	−	0.948588i	$-0.602512\pi$
$47$	−4.33981			−0.633026			−0.316513	+	0.948588i	$0.602512\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.471410	−	0.816506i	−0.0647531	−	0.112156i	0.831831	−	0.555029i	$-0.187293\pi$
$53$	−0.471410	−	0.816506i	−0.0647531	−	0.112156i	−0.896584	+	0.442873i	$0.853959\pi$
$54$		0			0
$55$	−1.22545			−0.165240
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.57893			−0.986693			−0.493347	−	0.869833i	$-0.664227\pi$
$59$	−7.57893			−0.986693			−0.493347	+	0.869833i	$0.664227\pi$
$60$		0			0
$61$	5.50808			0.705237			0.352619	−	0.935767i	$-0.385291\pi$
$61$	5.50808			0.705237			0.352619	+	0.935767i	$0.385291\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.16827			0.144906
$66$		0			0
$67$	−0.660190			−0.0806550			−0.0403275	−	0.999187i	$-0.512840\pi$
$67$	−0.660190			−0.0806550			−0.0403275	+	0.999187i	$0.512840\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.7414			−1.63081			−0.815405	−	0.578891i	$-0.803486\pi$
$71$	−13.7414			−1.63081			−0.815405	+	0.578891i	$0.803486\pi$
$72$		0			0
$73$	1.83009	+	3.16982i	0.214196	+	0.370999i	0.953024	−	0.302896i	$-0.0979534\pi$
$73$	1.83009	+	3.16982i	0.214196	+	0.370999i	−0.738827	+	0.673895i	$0.764620\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.22545			−0.700418			−0.350209	−	0.936672i	$-0.613889\pi$
$79$	−6.22545			−0.700418			−0.350209	+	0.936672i	$0.613889\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.85185	+	8.40365i	0.532560	+	0.922420i	0.999277	+	0.0380138i	$0.0121031\pi$
$83$	4.85185	+	8.40365i	0.532560	+	0.922420i	−0.466718	+	0.884406i	$0.654564\pi$
$84$		0			0
$85$	−0.442820	+	0.766987i	−0.0480306	+	0.0831914i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.74433	+	6.48536i	−0.396898	+	0.687447i	−0.993341	−	0.115208i	$-0.963247\pi$
$89$	−3.74433	+	6.48536i	−0.396898	+	0.687447i	0.596444	+	0.802655i	$0.296580\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.875237			−0.0897974
$96$		0			0
$97$	8.57442	+	14.8513i	0.870600	+	1.50792i	0.861377	+	0.507967i	$0.169603\pi$
$97$	8.57442	+	14.8513i	0.870600	+	1.50792i	0.00922376	+	0.999957i	$0.497064\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.59097	−	6.21975i	0.357315	−	0.618888i	−0.630196	−	0.776436i	$-0.717026\pi$
$101$	3.59097	−	6.21975i	0.357315	−	0.618888i	0.987511	+	0.157548i	$0.0503589\pi$
$102$		0			0
$103$	6.41423	+	11.1098i	0.632013	+	1.09468i	0.987140	+	0.159860i	$0.0511044\pi$
$103$	6.41423	+	11.1098i	0.632013	+	1.09468i	−0.355127	+	0.934818i	$0.615562\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.78263	−	6.55171i	0.365681	−	0.633377i	−0.623204	−	0.782059i	$-0.714170\pi$
$107$	3.78263	−	6.55171i	0.365681	−	0.633377i	0.988885	+	0.148681i	$0.0475029\pi$
$108$		0			0
$109$	3.49028	+	6.04535i	0.334309	+	0.579040i	0.983352	−	0.181712i	$-0.0581639\pi$
$109$	3.49028	+	6.04535i	0.334309	+	0.579040i	−0.649043	+	0.760752i	$0.724831\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.78495	+	16.9480i	−0.920491	+	1.59434i	−0.121834	+	0.992550i	$0.538878\pi$
$113$	−9.78495	+	16.9480i	−0.920491	+	1.59434i	−0.798657	+	0.601787i	$0.794456\pi$
$114$		0			0
$115$	−0.887275	+	1.53681i	−0.0827388	+	0.143308i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−7.63160	−	13.2183i	−0.693782	−	1.20167i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.37756			0.212655
$126$		0			0
$127$	−16.8090			−1.49156			−0.745780	−	0.666192i	$-0.767923\pi$
$127$	−16.8090			−1.49156			−0.745780	+	0.666192i	$0.767923\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	0.952971	−	0.303061i	$-0.0980085\pi$
$131$	2.44966	+	4.24293i	0.214027	+	0.370706i	−0.738944	+	0.673767i	$0.764675\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.72257	−	4.71563i	0.232605	−	0.402884i	−0.725969	−	0.687727i	$-0.758608\pi$
$137$	2.72257	−	4.71563i	0.232605	−	0.402884i	0.958574	+	0.284844i	$0.0919417\pi$
$138$		0			0
$139$	−2.83009	+	4.90187i	−0.240046	+	0.415771i	−0.960727	−	0.277495i	$-0.910496\pi$
$139$	−2.83009	+	4.90187i	−0.240046	+	0.415771i	0.720681	+	0.693266i	$0.243829\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.5189	+	21.6833i	1.04688	+	1.81325i
$144$		0			0
$145$	−0.414230	+	0.717468i	−0.0343999	+	0.0595824i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.14132	+	1.97682i	0.0935002	+	0.161947i	0.908982	−	0.416836i	$-0.136861\pi$
$149$	1.14132	+	1.97682i	0.0935002	+	0.161947i	−0.815481	+	0.578783i	$0.803528\pi$
$150$		0			0
$151$	−5.63160	+	9.75422i	−0.458293	+	0.793787i	−0.998871	−	0.0475071i	$-0.984872\pi$
$151$	−5.63160	+	9.75422i	−0.458293	+	0.793787i	0.540578	+	0.841294i	$0.318206\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0857699	−	0.148558i	−0.00688921	−	0.0119325i
$156$		0			0
$157$	5.54583			0.442605			0.221303	−	0.975205i	$-0.428969\pi$
$157$	5.54583			0.442605			0.221303	+	0.975205i	$0.428969\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−3.33009	+	5.76789i	−0.260833	+	0.451776i	−0.966464	−	0.256804i	$-0.917331\pi$
$163$	−3.33009	+	5.76789i	−0.260833	+	0.451776i	0.705630	+	0.708580i	$0.250664\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.20370	−	3.81691i	0.170527	−	0.295362i	−0.768077	−	0.640357i	$-0.778786\pi$
$167$	2.20370	−	3.81691i	0.170527	−	0.295362i	0.938604	+	0.344996i	$0.112120\pi$
$168$		0			0
$169$	−5.43474	−	9.41325i	−0.418057	−	0.724096i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−25.3308			−1.92586			−0.962932	−	0.269745i	$-0.913061\pi$
$173$	−25.3308			−1.92586			−0.962932	+	0.269745i	$0.913061\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.77292	+	8.26693i	0.356744	+	0.617899i	0.987415	−	0.158151i	$-0.0505534\pi$
$179$	4.77292	+	8.26693i	0.356744	+	0.617899i	−0.630670	+	0.776051i	$0.717220\pi$
$180$		0			0
$181$	12.3743			0.919774			0.459887	−	0.887978i	$-0.347890\pi$
$181$	12.3743			0.919774			0.459887	+	0.887978i	$0.347890\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.10069			−0.0809241
$186$		0			0
$187$	−18.9806			−1.38800
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.1683			−0.952823			−0.476411	−	0.879223i	$-0.658063\pi$
$191$	−13.1683			−0.952823			−0.476411	+	0.879223i	$0.658063\pi$
$192$		0			0
$193$	11.1488			0.802511			0.401256	−	0.915966i	$-0.368574\pi$
$193$	11.1488			0.802511			0.401256	+	0.915966i	$0.368574\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.144194			0.0102734			0.00513669	−	0.999987i	$-0.498365\pi$
$197$	0.144194			0.0102734			0.00513669	+	0.999987i	$0.498365\pi$
$198$		0			0
$199$	9.73461	+	16.8608i	0.690068	+	1.19523i	0.971815	+	0.235744i	$0.0757528\pi$
$199$	9.73461	+	16.8608i	0.690068	+	1.19523i	−0.281747	+	0.959489i	$0.590914\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.33981			0.0935764
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.37880	−	16.2446i	−0.648745	−	1.12366i
$210$		0			0
$211$	1.61436	−	2.79615i	0.111137	−	0.192495i	−0.805092	−	0.593150i	$-0.797884\pi$
$211$	1.61436	−	2.79615i	0.111137	−	0.192495i	0.916229	+	0.400655i	$0.131217\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.49316	−	2.58623i	0.101833	−	0.176380i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	18.0949			1.21720
$222$		0			0
$223$	−10.3856	−	17.9885i	−0.695474	−	1.20460i	−0.970021	−	0.243022i	$-0.921861\pi$
$223$	−10.3856	−	17.9885i	−0.695474	−	1.20460i	0.274547	−	0.961574i	$-0.411472\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	−0.229446	−	0.973321i	$-0.573691\pi$
$227$	10.9714	−	19.0030i	0.728198	−	1.26128i	0.957644	−	0.287955i	$-0.0929752\pi$
$228$		0			0
$229$	−11.3856	−	19.7205i	−0.752384	−	1.30317i	−0.946664	−	0.322222i	$-0.895570\pi$
$229$	−11.3856	−	19.7205i	−0.752384	−	1.30317i	0.194280	−	0.980946i	$-0.437763\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.8908	+	22.3276i	−0.844507	+	1.46273i	0.0415414	+	0.999137i	$0.486773\pi$
$233$	−12.8908	+	22.3276i	−0.844507	+	1.46273i	−0.886049	+	0.463592i	$0.846560\pi$
$234$		0			0
$235$	−0.518875	−	0.898718i	−0.0338477	−	0.0586259i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.6488	+	23.6405i	−0.882870	+	1.52918i	−0.0347345	+	0.999397i	$0.511059\pi$
$239$	−13.6488	+	23.6405i	−0.882870	+	1.52918i	−0.848136	+	0.529779i	$0.822275\pi$
$240$		0			0
$241$	−5.01724	+	8.69011i	−0.323189	+	0.559779i	−0.981144	−	0.193277i	$-0.938088\pi$
$241$	−5.01724	+	8.69011i	−0.323189	+	0.559779i	0.657955	+	0.753057i	$0.271422\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.94119	+	15.4866i	0.568914	+	0.985388i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	28.3171			1.78736			0.893680	−	0.448705i	$-0.148115\pi$
$251$	28.3171			1.78736			0.893680	+	0.448705i	$0.148115\pi$
$252$		0			0
$253$	−38.0312			−2.39100
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.4315	+	24.9960i	0.900210	+	1.55921i	0.827221	+	0.561877i	$0.189921\pi$
$257$	14.4315	+	24.9960i	0.900210	+	1.55921i	0.0729899	+	0.997333i	$0.476746\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.604645	+	1.04728i	−0.0372840	+	0.0645778i	−0.884065	−	0.467363i	$-0.845204\pi$
$263$	−0.604645	+	1.04728i	−0.0372840	+	0.0645778i	0.846781	+	0.531941i	$0.178537\pi$
$264$		0			0
$265$	0.112725	−	0.195246i	0.00692465	−	0.0119938i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.50684	+	7.80607i	0.274787	+	0.475944i	0.970081	−	0.242780i	$-0.0780594\pi$
$269$	4.50684	+	7.80607i	0.274787	+	0.475944i	−0.695295	+	0.718725i	$0.744726\pi$
$270$		0			0
$271$	−8.80150	+	15.2447i	−0.534653	+	0.926047i	0.464527	+	0.885559i	$0.346224\pi$
$271$	−8.80150	+	15.2447i	−0.534653	+	0.926047i	−0.999180	+	0.0404876i	$0.987109\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	12.6654	+	21.9371i	0.763752	+	1.32286i
$276$		0			0
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	−0.887042	−	0.461689i	$-0.847244\pi$
$277$	−0.727085	+	1.25935i	−0.0436863	+	0.0756669i	0.843355	+	0.537356i	$0.180577\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.1482	−	17.5771i	−0.605388	−	1.04856i	−0.991990	−	0.126316i	$-0.959685\pi$
$281$	−10.1482	−	17.5771i	−0.605388	−	1.04856i	0.386602	−	0.922247i	$-0.373649\pi$
$282$		0			0
$283$	−4.60301			−0.273621			−0.136810	−	0.990597i	$-0.543685\pi$
$283$	−4.60301			−0.273621			−0.136810	+	0.990597i	$0.543685\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.64132	−	2.84284i	0.0965479	−	0.167226i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.53667	+	6.12569i	−0.206614	+	0.357867i	−0.950646	−	0.310278i	$-0.899578\pi$
$293$	−3.53667	+	6.12569i	−0.206614	+	0.357867i	0.744031	+	0.668145i	$0.232911\pi$
$294$		0			0
$295$	−0.906150	−	1.56950i	−0.0527581	−	0.0913797i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	36.2567			2.09678
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.658555	+	1.14065i	0.0377088	+	0.0653135i
$306$		0			0
$307$	15.7518			0.899006			0.449503	−	0.893279i	$-0.351601\pi$
$307$	15.7518			0.899006			0.449503	+	0.893279i	$0.351601\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.6238			1.11276			0.556382	−	0.830926i	$-0.312189\pi$
$311$	19.6238			1.11276			0.556382	+	0.830926i	$0.312189\pi$
$312$		0			0
$313$	−25.4854			−1.44052			−0.720259	−	0.693705i	$-0.755977\pi$
$313$	−25.4854			−1.44052			−0.720259	+	0.693705i	$0.755977\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.28263			−0.465199			−0.232599	−	0.972573i	$-0.574723\pi$
$317$	−8.28263			−0.465199			−0.232599	+	0.972573i	$0.574723\pi$
$318$		0			0
$319$	−17.7551			−0.994096
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−13.5562			−0.754289
$324$		0			0
$325$	−12.0744	−	20.9135i	−0.669768	−	1.16007i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−11.9806			−0.658512			−0.329256	−	0.944241i	$-0.606798\pi$
$331$	−11.9806			−0.658512			−0.329256	+	0.944241i	$0.606798\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.0789334	−	0.136717i	−0.00431259	−	0.00746963i
$336$		0			0
$337$	6.46006	−	11.1892i	0.351902	−	0.609512i	−0.634681	−	0.772774i	$-0.718868\pi$
$337$	6.46006	−	11.1892i	0.351902	−	0.609512i	0.986583	+	0.163262i	$0.0522017\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.83818	−	3.18381i	0.0995428	−	0.172413i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.1866			−0.868942			−0.434471	−	0.900686i	$-0.643065\pi$
$347$	−16.1866			−0.868942			−0.434471	+	0.900686i	$0.643065\pi$
$348$		0			0
$349$	9.05718	+	15.6875i	0.484820	+	0.839732i	0.999848	−	0.0174409i	$-0.00555188\pi$
$349$	9.05718	+	15.6875i	0.484820	+	0.839732i	−0.515028	+	0.857173i	$0.672219\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.84897	+	10.1307i	−0.311309	+	0.539203i	−0.978646	−	0.205553i	$-0.934101\pi$
$353$	−5.84897	+	10.1307i	−0.311309	+	0.539203i	0.667337	+	0.744756i	$0.267434\pi$
$354$		0			0
$355$	−1.64295	−	2.84567i	−0.0871987	−	0.151033i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	17.8623	−	30.9383i	0.942734	−	1.63286i	0.182507	−	0.983205i	$-0.441579\pi$
$359$	17.8623	−	30.9383i	0.942734	−	1.63286i	0.760227	−	0.649658i	$-0.225088\pi$
$360$		0			0
$361$	2.80150	+	4.85235i	0.147448	+	0.255387i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.437618	+	0.757977i	−0.0229060	+	0.0396743i
$366$		0			0
$367$	−8.52696	+	14.7691i	−0.445103	+	0.770942i	−0.998059	−	0.0622687i	$-0.980166\pi$
$367$	−8.52696	+	14.7691i	−0.445103	+	0.770942i	0.552956	+	0.833210i	$0.313500\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	0.977584	+	0.210547i	$0.0675246\pi$
$373$	12.9617	+	22.4503i	0.671131	+	1.16243i	−0.306453	+	0.951886i	$0.599142\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	16.9267			0.871767
$378$		0			0
$379$	26.8446			1.37892			0.689458	−	0.724326i	$-0.257849\pi$
$379$	26.8446			1.37892			0.689458	+	0.724326i	$0.257849\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	0.986525	+	0.163610i	$0.0523137\pi$
$383$	12.4263	+	21.5229i	0.634953	+	1.09977i	−0.351573	+	0.936161i	$0.614353\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.12640	+	15.8074i	−0.462727	+	0.801466i	−0.999096	−	0.0425174i	$-0.986462\pi$
$389$	−9.12640	+	15.8074i	−0.462727	+	0.801466i	0.536369	+	0.843984i	$0.319796\pi$
$390$		0			0
$391$	−13.7427	+	23.8030i	−0.694998	+	1.20377i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.744325	−	1.28921i	−0.0374511	−	0.0648671i
$396$		0			0
$397$	−6.18715	+	10.7164i	−0.310524	+	0.537843i	−0.978476	−	0.206361i	$-0.933838\pi$
$397$	−6.18715	+	10.7164i	−0.310524	+	0.537843i	0.667952	+	0.744204i	$0.267171\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.48113	−	9.49359i	−0.273714	−	0.474087i	0.696096	−	0.717949i	$-0.254919\pi$
$401$	−5.48113	−	9.49359i	−0.273714	−	0.474087i	−0.969810	+	0.243862i	$0.921586\pi$
$402$		0			0
$403$	−1.75241	+	3.03526i	−0.0872935	+	0.151197i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.7947	−	20.4290i	−0.584640	−	1.01263i
$408$		0			0
$409$	−13.3204			−0.658650			−0.329325	−	0.944217i	$-0.606821\pi$
$409$	−13.3204			−0.658650			−0.329325	+	0.944217i	$0.606821\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.16019	+	2.00951i	−0.0569515	+	0.0986429i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.35705	−	4.08253i	0.115149	−	0.199445i	−0.802690	−	0.596396i	$-0.796599\pi$
$419$	2.35705	−	4.08253i	0.115149	−	0.199445i	0.917839	+	0.396952i	$0.129932\pi$
$420$		0			0
$421$	−9.65856	−	16.7291i	−0.470729	−	0.815327i	0.528710	−	0.848802i	$-0.322676\pi$
$421$	−9.65856	−	16.7291i	−0.470729	−	0.815327i	−0.999440	+	0.0334755i	$0.989342\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.3067			0.888006
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.1397	−	26.2227i	−0.729253	−	1.26310i	−0.957199	−	0.289429i	$-0.906535\pi$
$431$	−15.1397	−	26.2227i	−0.729253	−	1.26310i	0.227947	−	0.973674i	$-0.426799\pi$
$432$		0			0
$433$	34.2060			1.64384			0.821918	−	0.569606i	$-0.192904\pi$
$433$	34.2060			1.64384			0.821918	+	0.569606i	$0.192904\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−27.1625			−1.29936
$438$		0			0
$439$	−0.622440			−0.0297075			−0.0148537	−	0.999890i	$-0.504728\pi$
$439$	−0.622440			−0.0297075			−0.0148537	+	0.999890i	$0.504728\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.17867			0.246046			0.123023	−	0.992404i	$-0.460741\pi$
$443$	5.17867			0.246046			0.123023	+	0.992404i	$0.460741\pi$
$444$		0			0
$445$	−1.79071			−0.0848878
$446$		0			0
$447$		0			0
$448$		0			0
$449$	10.4977			0.495416			0.247708	−	0.968835i	$-0.420323\pi$
$449$	10.4977			0.495416			0.247708	+	0.968835i	$0.420323\pi$
$450$		0			0
$451$	14.3571	+	24.8671i	0.676047	+	1.17095i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−3.20929			−0.150124			−0.0750621	−	0.997179i	$-0.523916\pi$
$457$	−3.20929			−0.150124			−0.0750621	+	0.997179i	$0.523916\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.1150	−	31.3762i	−0.843702	−	1.46133i	−0.886744	−	0.462261i	$-0.847038\pi$
$461$	−18.1150	−	31.3762i	−0.843702	−	1.46133i	0.0430418	−	0.999073i	$-0.486295\pi$
$462$		0			0
$463$	−14.5253	+	25.1586i	−0.675049	+	1.16922i	0.301406	+	0.953496i	$0.402544\pi$
$463$	−14.5253	+	25.1586i	−0.675049	+	1.16922i	−0.976455	+	0.215723i	$0.930789\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−18.7466	+	32.4701i	−0.867491	+	1.50254i	−0.00293952	+	0.999996i	$0.500936\pi$
$467$	−18.7466	+	32.4701i	−0.867491	+	1.50254i	−0.864552	+	0.502544i	$0.832398\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	64.0014			2.94279
$474$		0			0
$475$	9.04583	+	15.6678i	0.415051	+	0.718890i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	−0.290661	−	0.956826i	$-0.593875\pi$
$479$	14.9549	−	25.9026i	0.683305	−	1.18352i	0.973966	−	0.226693i	$-0.0727914\pi$
$480$		0			0
$481$	11.2443	+	19.4757i	0.512697	+	0.888017i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.05034	+	3.55130i	−0.0931013	+	0.161256i
$486$		0			0
$487$	−10.6316	−	18.4145i	−0.481764	−	0.834439i	0.518017	−	0.855370i	$-0.326670\pi$
$487$	−10.6316	−	18.4145i	−0.481764	−	0.834439i	−0.999781	+	0.0209309i	$0.993337\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10.6985	+	18.5303i	−0.482816	+	0.836262i	−0.999805	−	0.0197296i	$-0.993719\pi$
$491$	−10.6985	+	18.5303i	−0.482816	+	0.836262i	0.516989	+	0.855992i	$0.327053\pi$
$492$		0			0
$493$	−6.41586	+	11.1126i	−0.288956	+	0.500487i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−7.28263	−	12.6139i	−0.326015	−	0.564675i	0.655702	−	0.755020i	$-0.272373\pi$
$499$	−7.28263	−	12.6139i	−0.326015	−	0.564675i	−0.981717	+	0.190345i	$0.939039\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−2.92339			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$503$	−2.92339			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$504$		0			0
$505$	1.71737			0.0764220
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.62025	−	16.6628i	−0.426410	−	0.738564i	0.570141	−	0.821547i	$-0.306889\pi$
$509$	−9.62025	−	16.6628i	−0.426410	−	0.738564i	−0.996551	+	0.0829830i	$0.973555\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.53379	+	2.65661i	−0.0675869	+	0.117064i
$516$		0			0
$517$	11.1202	−	19.2608i	0.489068	−	0.847091i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.8743	+	24.0310i	0.607844	+	1.05282i	0.991595	+	0.129380i	$0.0412986\pi$
$521$	13.8743	+	24.0310i	0.607844	+	1.05282i	−0.383751	+	0.923436i	$0.625368\pi$
$522$		0			0
$523$	1.36840	−	2.37014i	0.0598360	−	0.103639i	−0.834556	−	0.550924i	$-0.814276\pi$
$523$	1.36840	−	2.37014i	0.0598360	−	0.103639i	0.894392	+	0.447285i	$0.147609\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.32846	−	2.30096i	−0.0578686	−	0.100231i
$528$		0			0
$529$	−16.0361	+	27.7754i	−0.697222	+	1.20762i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.6871	−	23.7068i	−0.592856	−	1.02686i
$534$		0			0
$535$	1.80903			0.0782112
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5.98865	−	10.3726i	0.257472	−	0.445955i	−0.708092	−	0.706120i	$-0.750444\pi$
$541$	5.98865	−	10.3726i	0.257472	−	0.445955i	0.965564	+	0.260165i	$0.0837771\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.834608	+	1.44558i	−0.0357507	+	0.0619220i
$546$		0			0
$547$	10.7346	+	18.5929i	0.458979	+	0.794975i	0.998907	−	0.0467363i	$-0.0148821\pi$
$547$	10.7346	+	18.5929i	0.458979	+	0.794975i	−0.539928	+	0.841711i	$0.681549\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.6810			−0.540229
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.9246	−	27.5823i	−0.674748	−	1.16870i	−0.976542	−	0.215325i	$-0.930919\pi$
$557$	−15.9246	−	27.5823i	−0.674748	−	1.16870i	0.301794	−	0.953373i	$-0.402415\pi$
$558$		0			0
$559$	−61.0150			−2.58066
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−35.5483			−1.49818			−0.749091	−	0.662467i	$-0.769510\pi$
$563$	−35.5483			−1.49818			−0.749091	+	0.662467i	$0.769510\pi$
$564$		0			0
$565$	−4.67962			−0.196873
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.7486			−0.911748			−0.455874	−	0.890044i	$-0.650673\pi$
$569$	−21.7486			−0.911748			−0.455874	+	0.890044i	$0.650673\pi$
$570$		0			0
$571$	−9.59974			−0.401737			−0.200868	−	0.979618i	$-0.564376\pi$
$571$	−9.59974			−0.401737			−0.200868	+	0.979618i	$0.564376\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	36.6810			1.52970
$576$		0			0
$577$	−6.50916	−	11.2742i	−0.270980	−	0.469351i	0.698133	−	0.715968i	$-0.254014\pi$
$577$	−6.50916	−	11.2742i	−0.270980	−	0.469351i	−0.969113	+	0.246617i	$0.920681\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.83173			0.200110
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.64364	+	14.9712i	0.356761	+	0.617928i	0.987418	−	0.158134i	$-0.0505477\pi$
$587$	8.64364	+	14.9712i	0.356761	+	0.617928i	−0.630657	+	0.776062i	$0.717214\pi$
$588$		0			0
$589$	1.31285	−	2.27393i	0.0540952	−	0.0936957i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.20765	−	10.7520i	0.254918	−	0.441531i	−0.709955	−	0.704247i	$-0.751285\pi$
$593$	6.20765	−	10.7520i	0.254918	−	0.441531i	0.964873	+	0.262716i	$0.0846182\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.88564			0.322199			0.161099	−	0.986938i	$-0.448496\pi$
$599$	7.88564			0.322199			0.161099	+	0.986938i	$0.448496\pi$
$600$		0			0
$601$	−11.1413	−	19.2973i	−0.454464	−	0.787154i	0.544193	−	0.838960i	$-0.316836\pi$
$601$	−11.1413	−	19.2973i	−0.454464	−	0.787154i	−0.998657	+	0.0518055i	$0.983502\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.82489	−	3.16081i	0.0741925	−	0.128505i
$606$		0			0
$607$	−11.0458	−	19.1319i	−0.448336	−	0.776541i	0.549942	−	0.835203i	$-0.314650\pi$
$607$	−11.0458	−	19.1319i	−0.448336	−	0.776541i	−0.998278	+	0.0586617i	$0.981317\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.6014	+	18.3621i	−0.428886	+	0.742852i
$612$		0			0
$613$	14.7632	+	25.5706i	0.596280	+	1.03279i	0.993365	+	0.115005i	$0.0366885\pi$
$613$	14.7632	+	25.5706i	0.596280	+	1.03279i	−0.397085	+	0.917782i	$0.629978\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.01655	+	8.68892i	−0.201959	+	0.349803i	−0.949159	−	0.314796i	$-0.898064\pi$
$617$	−5.01655	+	8.68892i	−0.201959	+	0.349803i	0.747201	+	0.664598i	$0.231397\pi$
$618$		0			0
$619$	19.1283	−	33.1312i	0.768833	−	1.33166i	−0.169364	−	0.985554i	$-0.554171\pi$
$619$	19.1283	−	33.1312i	0.768833	−	1.33166i	0.938196	−	0.346103i	$-0.112495\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.0728	−	20.9107i	−0.482911	−	0.836427i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−17.0482			−0.679754
$630$		0			0
$631$	−23.0377			−0.917118			−0.458559	−	0.888664i	$-0.651634\pi$
$631$	−23.0377			−0.917118			−0.458559	+	0.888664i	$0.651634\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.00972	−	3.48093i	−0.0797531	−	0.138136i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.68646	+	15.0454i	−0.343094	+	0.594257i	−0.985006	−	0.172522i	$-0.944808\pi$
$641$	−8.68646	+	15.0454i	−0.343094	+	0.594257i	0.641911	+	0.766779i	$0.278142\pi$
$642$		0			0
$643$	9.47949	−	16.4190i	0.373835	−	0.647501i	−0.616317	−	0.787498i	$-0.711376\pi$
$643$	9.47949	−	16.4190i	0.373835	−	0.647501i	0.990152	+	0.139997i	$0.0447094\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	9.50972	+	16.4713i	0.373865	+	0.647554i	0.990157	−	0.139964i	$-0.0446988\pi$
$647$	9.50972	+	16.4713i	0.373865	+	0.647554i	−0.616291	+	0.787518i	$0.711366\pi$
$648$		0			0
$649$	19.4201	−	33.6366i	0.762306	−	1.32035i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.59329	−	6.22377i	−0.140616	−	0.243555i	0.787112	−	0.616810i	$-0.211575\pi$
$653$	−3.59329	−	6.22377i	−0.140616	−	0.243555i	−0.927729	+	0.373255i	$0.878242\pi$
$654$		0			0
$655$	−0.585770	+	1.01458i	−0.0228879	+	0.0396430i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.7261	+	22.0423i	0.495740	+	0.858647i	0.999988	−	0.00491209i	$-0.00156357\pi$
$659$	12.7261	+	22.0423i	0.495740	+	0.858647i	−0.504248	+	0.863559i	$0.668230\pi$
$660$		0			0
$661$	8.28590			0.322284			0.161142	−	0.986931i	$-0.448482\pi$
$661$	8.28590			0.322284			0.161142	+	0.986931i	$0.448482\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.8554	+	22.2662i	−0.497764	+	0.862152i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−14.1138	+	24.4458i	−0.544857	+	0.943721i
$672$		0			0
$673$	5.91586	+	10.2466i	0.228040	+	0.394977i	0.957227	−	0.289338i	$-0.0934350\pi$
$673$	5.91586	+	10.2466i	0.228040	+	0.394977i	−0.729187	+	0.684314i	$0.760102\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.6063			−0.522932			−0.261466	−	0.965213i	$-0.584206\pi$
$677$	−13.6063			−0.522932			−0.261466	+	0.965213i	$0.584206\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.79071	+	3.10160i	0.0685196	+	0.118679i	0.898250	−	0.439485i	$-0.144839\pi$
$683$	1.79071	+	3.10160i	0.0685196	+	0.118679i	−0.829730	+	0.558165i	$0.811506\pi$
$684$		0			0
$685$	1.30206			0.0497492
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.60628			−0.175485
$690$		0			0
$691$	11.7174			0.445750			0.222875	−	0.974847i	$-0.428456\pi$
$691$	11.7174			0.445750			0.222875	+	0.974847i	$0.428456\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.35348			−0.0513405
$696$		0			0
$697$	20.7518			0.786032
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.5926			0.400077			0.200039	−	0.979788i	$-0.435893\pi$
$701$	10.5926			0.400077			0.200039	+	0.979788i	$0.435893\pi$
$702$		0			0
$703$	−8.42395	−	14.5907i	−0.317715	−	0.550299i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	38.2977			1.43830			0.719150	−	0.694855i	$-0.244532\pi$
$709$	38.2977			1.43830			0.719150	+	0.694855i	$0.244532\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.66182	−	4.61042i	−0.0996861	−	0.172661i
$714$		0			0
$715$	−2.99355	+	5.18499i	−0.111953	+	0.193908i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.8376	−	36.0918i	0.777112	−	1.34600i	−0.156488	−	0.987680i	$-0.550017\pi$
$719$	20.8376	−	36.0918i	0.777112	−	1.34600i	0.933600	−	0.358318i	$-0.116650\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	17.1248			0.635998
$726$		0			0
$727$	16.4126	+	28.4274i	0.608709	+	1.05432i	0.991453	+	0.130461i	$0.0416458\pi$
$727$	16.4126	+	28.4274i	0.608709	+	1.05432i	−0.382744	+	0.923854i	$0.625021\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	23.1271	−	40.0573i	0.855386	−	1.48157i
$732$		0			0
$733$	−4.64884	−	8.05203i	−0.171709	−	0.297408i	0.767309	−	0.641278i	$-0.221595\pi$
$733$	−4.64884	−	8.05203i	−0.171709	−	0.297408i	−0.939017	+	0.343870i	$0.888262\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.69166	−	2.93004i	0.0623130	−	0.107929i
$738$		0			0
$739$	−5.68878	−	9.85326i	−0.209265	−	0.362458i	0.742218	−	0.670158i	$-0.233774\pi$
$739$	−5.68878	−	9.85326i	−0.209265	−	0.362458i	−0.951483	+	0.307701i	$0.900441\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.16182	+	2.01234i	−0.0426232	+	0.0738256i	−0.886550	−	0.462633i	$-0.846905\pi$
$743$	−1.16182	+	2.01234i	−0.0426232	+	0.0738256i	0.843927	+	0.536458i	$0.180238\pi$
$744$		0			0
$745$	−0.272915	+	0.472703i	−0.00999883	+	0.0173185i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	5.56690	+	9.64215i	0.203139	+	0.351847i	0.949538	−	0.313652i	$-0.101552\pi$
$751$	5.56690	+	9.64215i	0.203139	+	0.351847i	−0.746399	+	0.665498i	$0.768219\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.69329			−0.0980190
$756$		0			0
$757$	52.1639			1.89593			0.947964	−	0.318376i	$-0.103138\pi$
$757$	52.1639			1.89593			0.947964	+	0.318376i	$0.103138\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.5127	−	40.7252i	−0.852336	−	1.47629i	−0.879095	−	0.476647i	$-0.841852\pi$
$761$	−23.5127	−	40.7252i	−0.852336	−	1.47629i	0.0267592	−	0.999642i	$-0.491481\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.5140	+	32.0671i	−0.668501	+	1.15788i
$768$		0			0
$769$	3.30314	−	5.72121i	0.119114	−	0.206312i	−0.800303	−	0.599596i	$-0.795328\pi$
$769$	3.30314	−	5.72121i	0.119114	−	0.206312i	0.919417	+	0.393284i	$0.128661\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.54351	+	16.5298i	0.343256	+	0.594537i	0.985035	−	0.172352i	$-0.0551368\pi$
$773$	9.54351	+	16.5298i	0.343256	+	0.594537i	−0.641779	+	0.766889i	$0.721803\pi$
$774$		0			0
$775$	−1.77292	+	3.07078i	−0.0636850	+	0.110306i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.2540	+	17.7605i	0.367389	+	0.636337i
$780$		0			0
$781$	35.2108	−	60.9869i	1.25994	−	2.18228i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.663069	+	1.14847i	0.0236659	+	0.0409906i
$786$		0			0
$787$	50.9007			1.81441			0.907207	−	0.420685i	$-0.138210\pi$
$787$	50.9007			1.81441			0.907207	+	0.420685i	$0.138210\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	13.4552	−	23.3052i	0.477810	−	0.827591i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.38727	−	7.59898i	0.155405	−	0.269170i	−0.777801	−	0.628510i	$-0.783665\pi$
$797$	4.38727	−	7.59898i	0.155405	−	0.269170i	0.933207	+	0.359341i	$0.116998\pi$
$798$		0			0
$799$	−8.03667	−	13.9199i	−0.284317	−	0.492451i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−18.7576			−0.661942
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.75692	−	8.23923i	−0.167244	−	0.289676i	0.770206	−	0.637796i	$-0.220154\pi$
$809$	−4.75692	−	8.23923i	−0.167244	−	0.289676i	−0.937450	+	0.348120i	$0.886820\pi$
$810$		0			0
$811$	−25.0118			−0.878282			−0.439141	−	0.898418i	$-0.644717\pi$
$811$	−25.0118			−0.878282			−0.439141	+	0.898418i	$0.644717\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.59261			−0.0557866
$816$		0			0
$817$	45.7108			1.59922
$818$		0			0
$819$		0			0
$820$		0			0
$821$	35.5940			1.24224			0.621119	−	0.783716i	$-0.286678\pi$
$821$	35.5940			1.24224			0.621119	+	0.783716i	$0.286678\pi$
$822$		0			0
$823$	16.0000			0.557725			0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000			0.557725			0.278862	+	0.960331i	$0.410043\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	25.4531			0.885090			0.442545	−	0.896746i	$-0.354076\pi$
$827$	25.4531			0.885090			0.442545	+	0.896746i	$0.354076\pi$
$828$		0			0
$829$	8.77292	+	15.1951i	0.304696	+	0.527749i	0.977194	−	0.212350i	$-0.0681118\pi$
$829$	8.77292	+	15.1951i	0.304696	+	0.527749i	−0.672498	+	0.740099i	$0.734778\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.05391			0.0364721
$836$		0			0
$837$		0			0
$838$		0			0
$839$	12.0562	+	20.8820i	0.416227	+	0.720927i	0.995556	−	0.0941668i	$-0.0300187\pi$
$839$	12.0562	+	20.8820i	0.416227	+	0.720927i	−0.579329	+	0.815094i	$0.696685\pi$
$840$		0			0
$841$	8.49837	−	14.7196i	0.293047	−	0.507572i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.29957	−	2.25093i	0.0447067	−	0.0774342i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−34.1592			−1.17096
$852$		0			0
$853$	−16.2616	−	28.1659i	−0.556785	−	0.964381i	−0.997762	−	0.0668621i	$-0.978701\pi$
$853$	−16.2616	−	28.1659i	−0.556785	−	0.964381i	0.440977	−	0.897518i	$-0.354632\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.299870	+	0.519390i	−0.0102434	+	0.0177420i	−0.871102	−	0.491103i	$-0.836594\pi$
$857$	−0.299870	+	0.519390i	−0.0102434	+	0.0177420i	0.860858	+	0.508845i	$0.169927\pi$
$858$		0			0
$859$	13.2174	+	22.8932i	0.450971	+	0.781104i	0.998447	−	0.0557171i	$-0.0177445\pi$
$859$	13.2174	+	22.8932i	0.450971	+	0.781104i	−0.547476	+	0.836822i	$0.684411\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.92270	−	17.1866i	0.337773	−	0.585039i	−0.646241	−	0.763134i	$-0.723660\pi$
$863$	9.92270	−	17.1866i	0.337773	−	0.585039i	0.984013	+	0.178094i	$0.0569932\pi$
$864$		0			0
$865$	−3.02859	−	5.24567i	−0.102975	−	0.178358i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	15.9520	−	27.6296i	0.541134	−	0.937271i
$870$		0			0
$871$	−1.61273	+	2.79332i	−0.0546451	+	0.0946481i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	0.639849	−	0.768501i	$-0.278997\pi$
$877$	−10.2352	−	17.7278i	−0.345617	−	0.598626i	−0.985466	+	0.169875i	$0.945664\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	31.1683			1.05009			0.525043	−	0.851076i	$-0.324049\pi$
$881$	31.1683			1.05009			0.525043	+	0.851076i	$0.324049\pi$
$882$		0			0
$883$	−2.64187			−0.0889060			−0.0444530	−	0.999011i	$-0.514154\pi$
$883$	−2.64187			−0.0889060			−0.0444530	+	0.999011i	$0.514154\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	0.603400	−	0.797439i	$-0.293812\pi$
$887$	−11.5825	−	20.0615i	−0.388902	−	0.673599i	−0.992302	+	0.123840i	$0.960479\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.94226	−	13.7564i	0.265778	−	0.460341i
$894$		0			0
$895$	−1.14132	+	1.97682i	−0.0381500	+	0.0660777i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.24269	−	2.15240i	−0.0414460	−	0.0717866i
$900$		0			0
$901$	1.74596	−	3.02409i	0.0581664	−	0.100747i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.47949	+	2.56255i	0.0491799	+	0.0851821i
$906$		0			0
$907$	25.0264	−	43.3470i	0.830988	−	1.43931i	−0.0662676	−	0.997802i	$-0.521109\pi$
$907$	25.0264	−	43.3470i	0.830988	−	1.43931i	0.897256	−	0.441511i	$-0.145558\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.42231	−	9.39172i	−0.179649	−	0.311161i	0.762111	−	0.647446i	$-0.224163\pi$
$911$	−5.42231	−	9.39172i	−0.179649	−	0.311161i	−0.941760	+	0.336285i	$0.890830\pi$
$912$		0			0
$913$	−49.7292			−1.64579
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−5.59549	+	9.69166i	−0.184578	+	0.319699i	−0.943434	−	0.331560i	$-0.892425\pi$
$919$	−5.59549	+	9.69166i	−0.184578	+	0.319699i	0.758856	+	0.651258i	$0.225759\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−33.5679	+	58.1413i	−1.10490	+	1.91374i
$924$		0			0
$925$	11.3759	+	19.7037i	0.374038	+	0.647853i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−41.2955			−1.35486			−0.677431	−	0.735586i	$-0.736907\pi$
$929$	−41.2955			−1.35486			−0.677431	+	0.735586i	$0.736907\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.26935	−	3.93063i	−0.0742156	−	0.128545i
$936$		0			0
$937$	−33.5620			−1.09642			−0.548211	−	0.836340i	$-0.684691\pi$
$937$	−33.5620			−1.09642			−0.548211	+	0.836340i	$0.684691\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−50.4224			−1.64372			−0.821862	−	0.569686i	$-0.807065\pi$
$941$	−50.4224			−1.64372			−0.821862	+	0.569686i	$0.807065\pi$
$942$		0			0
$943$	41.5803			1.35404
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−20.2424			−0.657789			−0.328895	−	0.944367i	$-0.606676\pi$
$947$	−20.2424			−0.657789			−0.328895	+	0.944367i	$0.606676\pi$
$948$		0			0
$949$	17.8824			0.580486
$950$		0			0
$951$		0			0
$952$		0			0
$953$	29.3685			0.951340			0.475670	−	0.879624i	$-0.342206\pi$
$953$	29.3685			0.951340			0.475670	+	0.879624i	$0.342206\pi$
$954$		0			0
$955$	−1.57442	−	2.72698i	−0.0509470	−	0.0882429i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−30.4854			−0.983399
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.33297	+	2.30878i	0.0429099	+	0.0743222i
$966$		0			0
$967$	15.2157	−	26.3544i	0.489305	−	0.847501i	−0.510619	−	0.859807i	$-0.670584\pi$
$967$	15.2157	−	26.3544i	0.489305	−	0.847501i	0.999924	+	0.0123057i	$0.00391714\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.59329	−	6.22377i	0.115314	−	0.199730i	−0.802591	−	0.596530i	$-0.796546\pi$
$971$	3.59329	−	6.22377i	0.115314	−	0.199730i	0.917905	+	0.396799i	$0.129879\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−28.5426			−0.913157			−0.456579	−	0.889683i	$-0.650925\pi$
$977$	−28.5426			−0.913157			−0.456579	+	0.889683i	$0.650925\pi$
$978$		0			0
$979$	−19.1888	−	33.2359i	−0.613276	−	1.06223i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	−0.828659	−	0.559753i	$-0.810896\pi$
$983$	2.20821	−	3.82473i	0.0704310	−	0.121990i	0.899090	+	0.437763i	$0.144229\pi$
$984$		0			0
$985$	0.0172400	+	0.0298606i	0.000549313	+	0.000951438i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	46.3396	−	80.2625i	1.47351	−	2.55220i
$990$		0			0
$991$	2.90671	+	5.03456i	0.0923345	+	0.159928i	0.908493	−	0.417900i	$-0.137234\pi$
$991$	2.90671	+	5.03456i	0.0923345	+	0.159928i	−0.816159	+	0.577828i	$0.803900\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.32777	+	4.03182i	−0.0737953	+	0.127817i
$996$		0			0
$997$	26.3204	−	45.5882i	0.833575	−	1.44379i	−0.0616108	−	0.998100i	$-0.519624\pi$
$997$	26.3204	−	45.5882i	0.833575	−	1.44379i	0.895186	−	0.445694i	$-0.147043\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.i.f.1549.2		6
3.2	odd	2		1764.2.i.g.373.2		6
7.2	even	3		756.2.j.b.253.2		6
7.3	odd	6		5292.2.l.f.361.2		6
7.4	even	3		5292.2.l.e.361.2		6
7.5	odd	6		5292.2.j.d.1765.2		6
7.6	odd	2		5292.2.i.e.1549.2		6
9.2	odd	6		1764.2.l.e.961.3		6
9.7	even	3		5292.2.l.e.3313.2		6
21.2	odd	6		252.2.j.a.85.1	✓	6
21.5	even	6		1764.2.j.e.589.3		6
21.11	odd	6		1764.2.l.e.949.3		6
21.17	even	6		1764.2.l.f.949.1		6
21.20	even	2		1764.2.i.d.373.2		6
28.23	odd	6		3024.2.r.j.1009.2		6
63.2	odd	6		252.2.j.a.169.1	yes	6
63.11	odd	6		1764.2.i.g.1537.2		6
63.16	even	3		756.2.j.b.505.2		6
63.20	even	6		1764.2.l.f.961.1		6
63.23	odd	6		2268.2.a.i.1.2		3
63.25	even	3	inner	5292.2.i.f.2125.2		6
63.34	odd	6		5292.2.l.f.3313.2		6
63.38	even	6		1764.2.i.d.1537.2		6
63.47	even	6		1764.2.j.e.1177.3		6
63.52	odd	6		5292.2.i.e.2125.2		6
63.58	even	3		2268.2.a.h.1.2		3
63.61	odd	6		5292.2.j.d.3529.2		6
84.23	even	6		1008.2.r.j.337.3		6
252.23	even	6		9072.2.a.by.1.2		3
252.79	odd	6		3024.2.r.j.2017.2		6
252.191	even	6		1008.2.r.j.673.3		6
252.247	odd	6		9072.2.a.bv.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.a.85.1	✓	6	21.2	odd	6
252.2.j.a.169.1	yes	6	63.2	odd	6
756.2.j.b.253.2		6	7.2	even	3
756.2.j.b.505.2		6	63.16	even	3
1008.2.r.j.337.3		6	84.23	even	6
1008.2.r.j.673.3		6	252.191	even	6
1764.2.i.d.373.2		6	21.20	even	2
1764.2.i.d.1537.2		6	63.38	even	6
1764.2.i.g.373.2		6	3.2	odd	2
1764.2.i.g.1537.2		6	63.11	odd	6
1764.2.j.e.589.3		6	21.5	even	6
1764.2.j.e.1177.3		6	63.47	even	6
1764.2.l.e.949.3		6	21.11	odd	6
1764.2.l.e.961.3		6	9.2	odd	6
1764.2.l.f.949.1		6	21.17	even	6
1764.2.l.f.961.1		6	63.20	even	6
2268.2.a.h.1.2		3	63.58	even	3
2268.2.a.i.1.2		3	63.23	odd	6
3024.2.r.j.1009.2		6	28.23	odd	6
3024.2.r.j.2017.2		6	252.79	odd	6
5292.2.i.e.1549.2		6	7.6	odd	2
5292.2.i.e.2125.2		6	63.52	odd	6
5292.2.i.f.1549.2		6	1.1	even	1	trivial
5292.2.i.f.2125.2		6	63.25	even	3	inner
5292.2.j.d.1765.2		6	7.5	odd	6
5292.2.j.d.3529.2		6	63.61	odd	6
5292.2.l.e.361.2		6	7.4	even	3
5292.2.l.e.3313.2		6	9.7	even	3
5292.2.l.f.361.2		6	7.3	odd	6
5292.2.l.f.3313.2		6	63.34	odd	6
9072.2.a.bv.1.2		3	252.247	odd	6
9072.2.a.by.1.2		3	252.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.119562 + 0.207087i) q^{5} +O(q^{10})\)	\(q+(0.119562 + 0.207087i) q^{5} +(-2.56238 + 4.43818i) q^{11} +(2.44282 - 4.23109i) q^{13} +(1.85185 + 3.20750i) q^{17} +(-1.83009 + 3.16982i) q^{19} +(3.71053 + 6.42683i) q^{23} +(2.47141 - 4.28061i) q^{25} +(1.73229 + 3.00041i) q^{29} -0.717370 q^{31} +(-2.30150 + 3.98632i) q^{37} +(2.80150 - 4.85235i) q^{41} +(-6.24433 - 10.8155i) q^{43} -4.33981 q^{47} +(-0.471410 - 0.816506i) q^{53} -1.22545 q^{55} -7.57893 q^{59} +5.50808 q^{61} +1.16827 q^{65} -0.660190 q^{67} -13.7414 q^{71} +(1.83009 + 3.16982i) q^{73} -6.22545 q^{79} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-3.74433 + 6.48536i) q^{89} -0.875237 q^{95} +(8.57442 + 14.8513i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5}+O(q^{10}) \) 6 * q + q^5	\( 6 q + q^{5} + 2 q^{11} - 3 q^{13} + 2 q^{17} - 3 q^{19} + 14 q^{23} + 6 q^{25} + q^{29} - 6 q^{31} + 3 q^{37} - 3 q^{43} - 42 q^{47} + 6 q^{53} + 12 q^{55} - 62 q^{59} + 12 q^{61} - 30 q^{65} + 12 q^{67} - 34 q^{71} + 3 q^{73} - 18 q^{79} + 20 q^{83} + 15 q^{85} + 12 q^{89} - 40 q^{95} + 9 q^{97}+O(q^{100}) \) 6 * q + q^5 + 2 * q^11 - 3 * q^13 + 2 * q^17 - 3 * q^19 + 14 * q^23 + 6 * q^25 + q^29 - 6 * q^31 + 3 * q^37 - 3 * q^43 - 42 * q^47 + 6 * q^53 + 12 * q^55 - 62 * q^59 + 12 * q^61 - 30 * q^65 + 12 * q^67 - 34 * q^71 + 3 * q^73 - 18 * q^79 + 20 * q^83 + 15 * q^85 + 12 * q^89 - 40 * q^95 + 9 * q^97

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