LMFDB - Embedded newform 5292.2.w.b.1097.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(521,5292)]

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, 1, 1]))

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

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

chi := DirichletCharacter("5292.521");

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.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$42.2568327497$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1097.2
Root			$1.68042 - 0.419752i$ of defining polynomial
Character	$\chi$	$=$	5292.1097
Dual form			5292.2.w.b.521.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.48494 - 2.57199i) q^{5} +O(q^{10})$	$q+(-1.48494 - 2.57199i) q^{5} +(4.09466 + 2.36406i) q^{11} +(3.54045 + 2.04408i) q^{13} +(-0.835278 - 1.44674i) q^{17} +(4.25377 + 2.45592i) q^{19} +(-4.25297 + 2.45545i) q^{23} +(-1.91009 + 3.30837i) q^{25} +(-0.238557 + 0.137731i) q^{29} -1.60327i q^{31} +(-1.69681 + 2.93896i) q^{37} +(-3.55632 + 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} -10.9977 q^{47} +(-0.707381 + 0.408407i) q^{53} -14.0419i q^{55} +2.74856 q^{59} +7.20310i q^{61} -12.1413i q^{65} +11.6103 q^{67} +10.4406i q^{71} +(-13.6493 + 7.88042i) q^{73} -12.3033 q^{79} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(4.60872 - 7.98254i) q^{89} -14.5875i q^{95} +(-7.00772 + 4.04591i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 6 q^{11} + 3 q^{13} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + q^{37} - 6 q^{41} - 2 q^{43} - 36 q^{47} - 30 q^{59} + 14 q^{67} + 2 q^{79} + 6 q^{85} + 21 q^{89} + 3 q^{97}+O(q^{100}) $ 16 * q + 6 * q^11 + 3 * q^13 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + q^37 - 6 * q^41 - 2 * q^43 - 36 * q^47 - 30 * q^59 + 14 * q^67 + 2 * q^79 + 6 * q^85 + 21 * q^89 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.48494	−	2.57199i	−0.664085	−	1.15023i	−0.979532	−	0.201286i	$-0.935488\pi$
$5$	−1.48494	−	2.57199i	−0.664085	−	1.15023i	0.315447	−	0.948943i	$-0.397845\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.09466	+	2.36406i	1.23459	+	0.712790i	0.967983	−	0.251016i	$-0.0807648\pi$
$11$	4.09466	+	2.36406i	1.23459	+	0.712790i	0.266605	+	0.963806i	$0.414098\pi$
$12$		0			0
$13$	3.54045	+	2.04408i	0.981945	+	0.566926i	0.902857	−	0.429942i	$-0.141466\pi$
$13$	3.54045	+	2.04408i	0.981945	+	0.566926i	0.0790880	+	0.996868i	$0.474799\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.835278	−	1.44674i	−0.202585	−	0.350887i	0.746776	−	0.665076i	$-0.231601\pi$
$17$	−0.835278	−	1.44674i	−0.202585	−	0.350887i	−0.949360	+	0.314189i	$0.898267\pi$
$18$		0			0
$19$	4.25377	+	2.45592i	0.975882	+	0.563426i	0.901024	−	0.433768i	$-0.142816\pi$
$19$	4.25377	+	2.45592i	0.975882	+	0.563426i	0.0748577	+	0.997194i	$0.476150\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.25297	+	2.45545i	−0.886805	+	0.511997i	−0.872896	−	0.487906i	$-0.837761\pi$
$23$	−4.25297	+	2.45545i	−0.886805	+	0.511997i	−0.0139086	+	0.999903i	$0.504427\pi$
$24$		0			0
$25$	−1.91009	+	3.30837i	−0.382018	+	0.661675i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.238557	+	0.137731i	−0.0442989	+	0.0255760i	−0.521986	−	0.852954i	$-0.674809\pi$
$29$	−0.238557	+	0.137731i	−0.0442989	+	0.0255760i	0.477687	+	0.878530i	$0.341475\pi$
$30$		0			0
$31$		−	1.60327i		−	0.287956i	−0.989581	−	0.143978i	$-0.954011\pi$
$31$		−	1.60327i		−	0.287956i	0.989581	−	0.143978i	$-0.0459895\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.69681	+	2.93896i	−0.278954	+	0.483162i	−0.971125	−	0.238571i	$-0.923321\pi$
$37$	−1.69681	+	2.93896i	−0.278954	+	0.483162i	0.692171	+	0.721733i	$0.256654\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.55632	+	6.15972i	−0.555404	+	0.961987i	0.442468	+	0.896784i	$0.354103\pi$
$41$	−3.55632	+	6.15972i	−0.555404	+	0.961987i	−0.997872	+	0.0652031i	$0.979230\pi$
$42$		0			0
$43$	5.22930	+	9.05742i	0.797461	+	1.38124i	0.921265	+	0.388936i	$0.127157\pi$
$43$	5.22930	+	9.05742i	0.797461	+	1.38124i	−0.123804	+	0.992307i	$0.539509\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.9977			−1.60418			−0.802090	−	0.597203i	$-0.796279\pi$
$47$	−10.9977			−1.60418			−0.802090	+	0.597203i	$0.796279\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.707381	+	0.408407i	−0.0971663	+	0.0560990i	−0.547796	−	0.836612i	$-0.684533\pi$
$53$	−0.707381	+	0.408407i	−0.0971663	+	0.0560990i	0.450629	+	0.892711i	$0.351200\pi$
$54$		0			0
$55$		−	14.0419i		−	1.89341i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.74856			0.357832			0.178916	−	0.983864i	$-0.442741\pi$
$59$	2.74856			0.357832			0.178916	+	0.983864i	$0.442741\pi$
$60$		0			0
$61$			7.20310i			0.922262i	0.887332	+	0.461131i	$0.152556\pi$
$61$			7.20310i			0.922262i	−0.887332	+	0.461131i	$0.847444\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	12.1413i		−	1.50595i
$66$		0			0
$67$	11.6103			1.41842			0.709210	−	0.704998i	$-0.249052\pi$
$67$	11.6103			1.41842			0.709210	+	0.704998i	$0.249052\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.4406i			1.23907i	0.784968	+	0.619537i	$0.212680\pi$
$71$			10.4406i			1.23907i	−0.784968	+	0.619537i	$0.787320\pi$
$72$		0			0
$73$	−13.6493	+	7.88042i	−1.59753	+	0.922334i	−0.605567	+	0.795794i	$0.707054\pi$
$73$	−13.6493	+	7.88042i	−1.59753	+	0.922334i	−0.991962	+	0.126539i	$0.959613\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−12.3033			−1.38422			−0.692112	−	0.721790i	$-0.743320\pi$
$79$	−12.3033			−1.38422			−0.692112	+	0.721790i	$0.743320\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	0.554515	−	0.832174i	$-0.312904\pi$
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	−0.997941	+	0.0641368i	$0.979571\pi$
$84$		0			0
$85$	−2.48067	+	4.29665i	−0.269067	+	0.466037i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.60872	−	7.98254i	0.488523	−	0.846147i	−0.511390	−	0.859349i	$-0.670869\pi$
$89$	4.60872	−	7.98254i	0.488523	−	0.846147i	0.999913	+	0.0132019i	$0.00420240\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	14.5875i		−	1.49665i
$96$		0			0
$97$	−7.00772	+	4.04591i	−0.711527	+	0.410800i	−0.811626	−	0.584177i	$-0.801417\pi$
$97$	−7.00772	+	4.04591i	−0.711527	+	0.410800i	0.100099	+	0.994977i	$0.468084\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.65365	+	6.32831i	−0.363552	+	0.629690i	−0.988543	−	0.150942i	$-0.951769\pi$
$101$	−3.65365	+	6.32831i	−0.363552	+	0.629690i	0.624991	+	0.780632i	$0.285103\pi$
$102$		0			0
$103$	6.08409	−	3.51265i	0.599483	−	0.346112i	−0.169355	−	0.985555i	$-0.554168\pi$
$103$	6.08409	−	3.51265i	0.599483	−	0.346112i	0.768838	+	0.639443i	$0.220835\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.2618	+	7.07938i	1.18540	+	0.684389i	0.957257	−	0.289239i	$-0.0934022\pi$
$107$	12.2618	+	7.07938i	1.18540	+	0.684389i	0.228140	+	0.973628i	$0.426735\pi$
$108$		0			0
$109$	−2.82203	−	4.88789i	−0.270301	−	0.468175i	0.698638	−	0.715476i	$-0.253790\pi$
$109$	−2.82203	−	4.88789i	−0.270301	−	0.468175i	−0.968939	+	0.247300i	$0.920457\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.6411	−	6.72099i	−1.09510	−	0.632258i	−0.160172	−	0.987089i	$-0.551205\pi$
$113$	−11.6411	−	6.72099i	−1.09510	−	0.632258i	−0.934930	+	0.354831i	$0.884538\pi$
$114$		0			0
$115$	12.6308	+	7.29239i	1.17783	+	0.680019i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.67752	+	9.83375i	0.516138	+	0.893977i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.50392			−0.313400
$126$		0			0
$127$	−12.7730			−1.13342			−0.566712	−	0.823916i	$-0.691785\pi$
$127$	−12.7730			−1.13342			−0.566712	+	0.823916i	$0.691785\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.70890	+	11.6202i	0.586159	+	1.01526i	0.994730	+	0.102531i	$0.0326941\pi$
$131$	6.70890	+	11.6202i	0.586159	+	1.01526i	−0.408570	+	0.912727i	$0.633973\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.79449	+	4.50015i	0.665928	+	0.384474i	0.794532	−	0.607222i	$-0.207716\pi$
$137$	7.79449	+	4.50015i	0.665928	+	0.384474i	−0.128604	+	0.991696i	$0.541050\pi$
$138$		0			0
$139$	−1.54902	−	0.894326i	−0.131386	−	0.0758557i	0.432866	−	0.901458i	$-0.357502\pi$
$139$	−1.54902	−	0.894326i	−0.131386	−	0.0758557i	−0.564252	+	0.825602i	$0.690836\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.66464	+	16.7397i	0.808198	+	1.39984i
$144$		0			0
$145$	0.708485	+	0.409044i	0.0588365	+	0.0339693i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.1779	−	6.45358i	0.915732	−	0.528698i	0.0334609	−	0.999440i	$-0.489347\pi$
$149$	11.1779	−	6.45358i	0.915732	−	0.528698i	0.882271	+	0.470742i	$0.156014\pi$
$150$		0			0
$151$	6.48364	−	11.2300i	0.527631	−	0.913884i	−0.471850	−	0.881679i	$-0.656414\pi$
$151$	6.48364	−	11.2300i	0.527631	−	0.913884i	0.999481	−	0.0322054i	$-0.0102531\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.12360	+	2.38076i	−0.331216	+	0.191227i
$156$		0			0
$157$			17.1728i			1.37054i	0.728291	+	0.685268i	$0.240315\pi$
$157$			17.1728i			1.37054i	−0.728291	+	0.685268i	$0.759685\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.53107	−	4.38394i	0.198249	−	0.343377i	−0.749712	−	0.661764i	$-0.769808\pi$
$163$	2.53107	−	4.38394i	0.198249	−	0.343377i	0.947961	+	0.318387i	$0.103141\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	−0.998293	−	0.0584072i	$-0.981398\pi$
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	0.549729	+	0.835343i	$0.314731\pi$
$168$		0			0
$169$	1.85653	+	3.21561i	0.142810	+	0.247354i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.26691			0.476464			0.238232	−	0.971208i	$-0.423432\pi$
$173$	6.26691			0.476464			0.238232	+	0.971208i	$0.423432\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.7668	−	7.37089i	0.954233	−	0.550927i	0.0598395	−	0.998208i	$-0.480941\pi$
$179$	12.7668	−	7.37089i	0.954233	−	0.550927i	0.894393	+	0.447281i	$0.147608\pi$
$180$		0			0
$181$			0.0833642i			0.00619641i	0.999995	+	0.00309821i	$0.000986191\pi$
$181$			0.0833642i			0.00619641i	−0.999995	+	0.00309821i	$0.999014\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.0786			0.740996
$186$		0			0
$187$		−	7.89857i		−	0.577601i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			15.4351i			1.11684i	0.829558	+	0.558421i	$0.188593\pi$
$191$			15.4351i			1.11684i	−0.829558	+	0.558421i	$0.811407\pi$
$192$		0			0
$193$	21.5557			1.55162			0.775808	−	0.630969i	$-0.217343\pi$
$193$	21.5557			1.55162			0.775808	+	0.630969i	$0.217343\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			9.88306i			0.704139i	0.935974	+	0.352069i	$0.114522\pi$
$197$			9.88306i			0.704139i	−0.935974	+	0.352069i	$0.885478\pi$
$198$		0			0
$199$	9.14623	−	5.28058i	0.648359	−	0.374330i	−0.139468	−	0.990227i	$-0.544539\pi$
$199$	9.14623	−	5.28058i	0.648359	−	0.374330i	0.787827	+	0.615896i	$0.211206\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	21.1237			1.47534
$206$		0			0
$207$		0			0
$208$		0			0
$209$	11.6118	+	20.1123i	0.803208	+	1.39120i
$210$		0			0
$211$	6.08453	−	10.5387i	0.418876	−	0.725514i	−0.576951	−	0.816779i	$-0.695758\pi$
$211$	6.08453	−	10.5387i	0.418876	−	0.725514i	0.995827	+	0.0912645i	$0.0290909\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	15.5304	−	26.8994i	1.05916	−	1.83453i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	6.82950i		−	0.459402i
$222$		0			0
$223$	−0.714485	+	0.412508i	−0.0478455	+	0.0276236i	−0.523732	−	0.851883i	$-0.675461\pi$
$223$	−0.714485	+	0.412508i	−0.0478455	+	0.0276236i	0.475886	+	0.879507i	$0.342127\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.166778	−	0.288869i	0.0110695	−	0.0191729i	−0.860438	−	0.509556i	$-0.829810\pi$
$227$	0.166778	−	0.288869i	0.0110695	−	0.0191729i	0.871507	+	0.490383i	$0.163143\pi$
$228$		0			0
$229$	−12.4893	+	7.21072i	−0.825319	+	0.476498i	−0.852247	−	0.523139i	$-0.824761\pi$
$229$	−12.4893	+	7.21072i	−0.825319	+	0.476498i	0.0269285	+	0.999637i	$0.491427\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.7953	+	7.38739i	0.838250	+	0.483964i	0.856669	−	0.515867i	$-0.172530\pi$
$233$	12.7953	+	7.38739i	0.838250	+	0.483964i	−0.0184192	+	0.999830i	$0.505863\pi$
$234$		0			0
$235$	16.3309	+	28.2860i	1.06531	+	1.84518i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	22.5339	+	13.0100i	1.45760	+	0.841545i	0.998893	−	0.0470423i	$-0.0149795\pi$
$239$	22.5339	+	13.0100i	1.45760	+	0.841545i	0.458707	+	0.888588i	$0.348313\pi$
$240$		0			0
$241$	−1.66295	−	0.960105i	−0.107120	−	0.0618458i	0.445483	−	0.895290i	$-0.353032\pi$
$241$	−1.66295	−	0.960105i	−0.107120	−	0.0618458i	−0.552603	+	0.833445i	$0.686365\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.0402	+	17.3901i	0.638841	+	1.10651i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.97663			0.629719			0.314860	−	0.949138i	$-0.398043\pi$
$251$	9.97663			0.629719			0.314860	+	0.949138i	$0.398043\pi$
$252$		0			0
$253$	−23.2193			−1.45978
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.50364	+	12.9967i	0.468064	+	0.810711i	0.999334	−	0.0364915i	$-0.0116182\pi$
$257$	7.50364	+	12.9967i	0.468064	+	0.810711i	−0.531270	+	0.847203i	$0.678285\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.11010	−	3.52767i	−0.376765	−	0.217525i	0.299645	−	0.954051i	$-0.403132\pi$
$263$	−6.11010	−	3.52767i	−0.376765	−	0.217525i	−0.676410	+	0.736525i	$0.736465\pi$
$264$		0			0
$265$	2.10084	+	1.21292i	0.129053	+	0.0745090i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.8898	+	25.7898i	0.907844	+	1.57243i	0.817053	+	0.576562i	$0.195606\pi$
$269$	14.8898	+	25.7898i	0.907844	+	1.57243i	0.0907911	+	0.995870i	$0.471060\pi$
$270$		0			0
$271$	2.41462	+	1.39408i	0.146677	+	0.0846843i	0.571543	−	0.820572i	$-0.306345\pi$
$271$	2.41462	+	1.39408i	0.146677	+	0.0846843i	−0.424865	+	0.905257i	$0.639679\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−15.6424	+	9.03112i	−0.943270	+	0.544597i
$276$		0			0
$277$	−6.79074	+	11.7619i	−0.408016	+	0.706705i	−0.994667	−	0.103135i	$-0.967113\pi$
$277$	−6.79074	+	11.7619i	−0.408016	+	0.706705i	0.586651	+	0.809840i	$0.300446\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.95777	−	2.28502i	0.236101	−	0.136313i	−0.377283	−	0.926098i	$-0.623141\pi$
$281$	3.95777	−	2.28502i	0.236101	−	0.136313i	0.613383	+	0.789785i	$0.289808\pi$
$282$		0			0
$283$			20.4019i			1.21277i	0.795173	+	0.606383i	$0.207380\pi$
$283$			20.4019i			1.21277i	−0.795173	+	0.606383i	$0.792620\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.10462	−	12.3056i	0.417919	−	0.723857i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.41037	−	11.1031i	0.374498	−	0.648649i	−0.615754	−	0.787939i	$-0.711148\pi$
$293$	6.41037	−	11.1031i	0.374498	−	0.648649i	0.990252	+	0.139289i	$0.0444818\pi$
$294$		0			0
$295$	−4.08144	−	7.06926i	−0.237631	−	0.411589i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−20.0766			−1.16106
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	18.5263	−	10.6962i	1.06081	−	0.612461i
$306$		0			0
$307$			1.93411i			0.110386i	0.998476	+	0.0551928i	$0.0175773\pi$
$307$			1.93411i			0.110386i	−0.998476	+	0.0551928i	$0.982423\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.08916			0.118465			0.0592326	−	0.998244i	$-0.481135\pi$
$311$	2.08916			0.118465			0.0592326	+	0.998244i	$0.481135\pi$
$312$		0			0
$313$		−	22.4088i		−	1.26662i	−0.773899	−	0.633309i	$-0.781696\pi$
$313$		−	22.4088i		−	1.26662i	0.773899	−	0.633309i	$-0.218304\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	3.48474i		−	0.195723i	−0.995200	−	0.0978614i	$-0.968800\pi$
$317$		−	3.48474i		−	0.195723i	0.995200	−	0.0978614i	$-0.0312002\pi$
$318$		0			0
$319$	−1.30241			−0.0729212
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	8.20549i		−	0.456565i
$324$		0			0
$325$	−13.5252	+	7.80876i	−0.750241	+	0.433152i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−4.57715			−0.251583			−0.125791	−	0.992057i	$-0.540147\pi$
$331$	−4.57715			−0.251583			−0.125791	+	0.992057i	$0.540147\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−17.2405	−	29.8615i	−0.941951	−	1.63151i
$336$		0			0
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	0.117793	+	0.993038i	$0.462418\pi$
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	−0.918893	+	0.394508i	$0.870915\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.79023	−	6.56486i	0.205252	−	0.355507i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	19.6582i		−	1.05531i	−0.849459	−	0.527654i	$-0.823072\pi$
$347$		−	19.6582i		−	1.05531i	0.849459	−	0.527654i	$-0.176928\pi$
$348$		0			0
$349$	8.47286	−	4.89181i	0.453542	−	0.261852i	−0.255783	−	0.966734i	$-0.582333\pi$
$349$	8.47286	−	4.89181i	0.453542	−	0.261852i	0.709325	+	0.704882i	$0.249000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.5322	−	21.7065i	0.667023	−	1.15532i	−0.311709	−	0.950178i	$-0.600901\pi$
$353$	12.5322	−	21.7065i	0.667023	−	1.15532i	0.978733	−	0.205141i	$-0.0657652\pi$
$354$		0			0
$355$	26.8532	−	15.5037i	1.42522	−	0.822850i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.09861	+	4.67574i	0.427428	+	0.246776i	0.698251	−	0.715853i	$-0.253962\pi$
$359$	8.09861	+	4.67574i	0.427428	+	0.246776i	−0.270822	+	0.962629i	$0.587296\pi$
$360$		0			0
$361$	2.56305	+	4.43933i	0.134897	+	0.233649i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	40.5367	+	23.4039i	2.12179	+	1.22502i
$366$		0			0
$367$	−18.9530	−	10.9425i	−0.989337	−	0.571194i	−0.0842608	−	0.996444i	$-0.526853\pi$
$367$	−18.9530	−	10.9425i	−0.989337	−	0.571194i	−0.905076	+	0.425250i	$0.860186\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.30822	−	3.99795i	−0.119515	−	0.207006i	0.800061	−	0.599919i	$-0.204801\pi$
$373$	−2.30822	−	3.99795i	−0.119515	−	0.207006i	−0.919576	+	0.392913i	$0.871467\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.12613			−0.0579988
$378$		0			0
$379$	−6.22396			−0.319703			−0.159852	−	0.987141i	$-0.551102\pi$
$379$	−6.22396			−0.319703			−0.159852	+	0.987141i	$0.551102\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.9989	−	19.0506i	−0.562015	−	0.973439i	−0.997321	−	0.0731560i	$-0.976693\pi$
$383$	−10.9989	−	19.0506i	−0.562015	−	0.973439i	0.435305	−	0.900283i	$-0.356640\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.51109	+	4.91388i	0.431529	+	0.249144i	0.699998	−	0.714145i	$-0.253184\pi$
$389$	8.51109	+	4.91388i	0.431529	+	0.249144i	−0.268469	+	0.963288i	$0.586518\pi$
$390$		0			0
$391$	7.10481	+	4.10197i	0.359306	+	0.207445i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	18.2696	+	31.6439i	0.919243	+	1.59218i
$396$		0			0
$397$	−4.55324	−	2.62881i	−0.228520	−	0.131936i	0.381369	−	0.924423i	$-0.375453\pi$
$397$	−4.55324	−	2.62881i	−0.228520	−	0.131936i	−0.609889	+	0.792487i	$0.708786\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.7847	+	8.53594i	−0.738312	+	0.426265i	−0.821455	−	0.570273i	$-0.806837\pi$
$401$	−14.7847	+	8.53594i	−0.738312	+	0.426265i	0.0831432	+	0.996538i	$0.473504\pi$
$402$		0			0
$403$	3.27722	−	5.67631i	0.163250	−	0.282757i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.8957	+	8.02270i	−0.688786	+	0.397671i
$408$		0			0
$409$			19.5703i			0.967690i	0.875154	+	0.483845i	$0.160760\pi$
$409$			19.5703i			0.967690i	−0.875154	+	0.483845i	$0.839240\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−11.9977	+	20.7807i	−0.588946	+	1.02008i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	−0.496445	−	0.868068i	$-0.665361\pi$
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	0.999992	−	0.00410056i	$-0.00130525\pi$
$420$		0			0
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	0.882688	−	0.469959i	$-0.155731\pi$
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	−0.848341	+	0.529451i	$0.822398\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.38182			0.309564
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.6666	+	6.73569i	−0.561959	+	0.324447i	−0.753931	−	0.656953i	$-0.771845\pi$
$431$	−11.6666	+	6.73569i	−0.561959	+	0.324447i	0.191973	+	0.981400i	$0.438512\pi$
$432$		0			0
$433$			12.9356i			0.621646i	0.950468	+	0.310823i	$0.100605\pi$
$433$			12.9356i			0.621646i	−0.950468	+	0.310823i	$0.899395\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−24.1215			−1.15389
$438$		0			0
$439$		−	10.1039i		−	0.482233i	−0.970496	−	0.241116i	$-0.922486\pi$
$439$		−	10.1039i		−	0.482233i	0.970496	−	0.241116i	$-0.0775135\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	29.0084i		−	1.37823i	−0.724652	−	0.689115i	$-0.757999\pi$
$443$		−	29.0084i		−	1.37823i	0.724652	−	0.689115i	$-0.242001\pi$
$444$		0			0
$445$	−27.3747			−1.29768
$446$		0			0
$447$		0			0
$448$		0			0
$449$			7.94881i			0.375127i	0.982252	+	0.187564i	$0.0600591\pi$
$449$			7.94881i			0.375127i	−0.982252	+	0.187564i	$0.939941\pi$
$450$		0			0
$451$	−29.1239	+	16.8147i	−1.37139	+	0.791772i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.9617			−0.653100			−0.326550	−	0.945180i	$-0.605886\pi$
$457$	−13.9617			−0.653100			−0.326550	+	0.945180i	$0.605886\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.4030	−	28.4108i	−0.763964	−	1.32322i	−0.940793	−	0.338983i	$-0.889917\pi$
$461$	−16.4030	−	28.4108i	−0.763964	−	1.32322i	0.176829	−	0.984242i	$-0.443416\pi$
$462$		0			0
$463$	−13.8812	+	24.0429i	−0.645112	+	1.11737i	0.339163	+	0.940727i	$0.389856\pi$
$463$	−13.8812	+	24.0429i	−0.645112	+	1.11737i	−0.984276	+	0.176640i	$0.943477\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.4311	+	19.7992i	−0.528966	+	0.916196i	0.470463	+	0.882420i	$0.344087\pi$
$467$	−11.4311	+	19.7992i	−0.528966	+	0.916196i	−0.999429	+	0.0337767i	$0.989247\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$			49.4494i			2.27369i
$474$		0			0
$475$	−16.2502	+	9.38204i	−0.745609	+	0.430478i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.21212	−	2.09946i	0.0553834	−	0.0959269i	−0.837004	−	0.547196i	$-0.815695\pi$
$479$	1.21212	−	2.09946i	0.0553834	−	0.0959269i	0.892388	+	0.451269i	$0.149029\pi$
$480$		0			0
$481$	−12.0149	+	6.93683i	−0.547834	+	0.316292i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.8121	+	12.0159i	0.945028	+	0.545612i
$486$		0			0
$487$	5.19651	+	9.00061i	0.235476	+	0.407857i	0.959411	−	0.282012i	$-0.0910017\pi$
$487$	5.19651	+	9.00061i	0.235476	+	0.407857i	−0.723935	+	0.689868i	$0.757668\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.93014	+	1.69172i	0.132235	+	0.0763462i	0.564658	−	0.825325i	$-0.309008\pi$
$491$	2.93014	+	1.69172i	0.132235	+	0.0763462i	−0.432423	+	0.901671i	$0.642341\pi$
$492$		0			0
$493$	0.398522	+	0.230087i	0.0179485	+	0.0103626i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−19.7801	−	34.2602i	−0.885481	−	1.53370i	−0.845162	−	0.534511i	$-0.820496\pi$
$499$	−19.7801	−	34.2602i	−0.885481	−	1.53370i	−0.0403188	−	0.999187i	$-0.512837\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.5476			0.648645			0.324323	−	0.945947i	$-0.394864\pi$
$503$	14.5476			0.648645			0.324323	+	0.945947i	$0.394864\pi$
$504$		0			0
$505$	21.7018			0.965717
$506$		0			0
$507$		0			0
$508$		0			0
$509$	10.1958	+	17.6596i	0.451921	+	0.782750i	0.998505	−	0.0546542i	$-0.0174057\pi$
$509$	10.1958	+	17.6596i	0.451921	+	0.782750i	−0.546585	+	0.837404i	$0.684072\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−18.0690	−	10.4322i	−0.796216	−	0.459696i
$516$		0			0
$517$	−45.0319	−	25.9992i	−1.98050	−	1.14344i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.75122	−	13.4255i	−0.339587	−	0.588182i	0.644768	−	0.764379i	$-0.276954\pi$
$521$	−7.75122	−	13.4255i	−0.339587	−	0.588182i	−0.984355	+	0.176196i	$0.943621\pi$
$522$		0			0
$523$	−9.35989	−	5.40394i	−0.409280	−	0.236298i	0.281201	−	0.959649i	$-0.409267\pi$
$523$	−9.35989	−	5.40394i	−0.409280	−	0.236298i	−0.690480	+	0.723351i	$0.742601\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.31952	+	1.33918i	−0.101040	+	0.0583355i
$528$		0			0
$529$	0.558476	−	0.967309i	0.0242816	−	0.0420569i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−25.1819	+	14.5388i	−1.09075	+	0.629745i
$534$		0			0
$535$		−	42.0498i		−	1.81797i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−8.79357	+	15.2309i	−0.378065	+	0.654828i	−0.990781	−	0.135476i	$-0.956744\pi$
$541$	−8.79357	+	15.2309i	−0.378065	+	0.654828i	0.612716	+	0.790303i	$0.290077\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−8.38108	+	14.5165i	−0.359006	+	0.621817i
$546$		0			0
$547$	−5.72451	−	9.91513i	−0.244762	−	0.423940i	0.717303	−	0.696762i	$-0.245377\pi$
$547$	−5.72451	−	9.91513i	−0.244762	−	0.423940i	−0.962065	+	0.272821i	$0.912043\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.35302			−0.0576407
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	32.9159	−	19.0040i	1.39469	−	0.805226i	0.400863	−	0.916138i	$-0.368710\pi$
$557$	32.9159	−	19.0040i	1.39469	−	0.805226i	0.993830	+	0.110912i	$0.0353771\pi$
$558$		0			0
$559$			42.7565i			1.80841i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.7688			−0.748864			−0.374432	−	0.927254i	$-0.622162\pi$
$563$	−17.7688			−0.748864			−0.374432	+	0.927254i	$0.622162\pi$
$564$		0			0
$565$			39.9211i			1.67949i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	38.9601i		−	1.63329i	−0.577139	−	0.816646i	$-0.695831\pi$
$569$		−	38.9601i		−	1.63329i	0.577139	−	0.816646i	$-0.304169\pi$
$570$		0			0
$571$	16.9049			0.707448			0.353724	−	0.935350i	$-0.384915\pi$
$571$	16.9049			0.707448			0.353724	+	0.935350i	$0.384915\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	18.7605i		−	0.782368i
$576$		0			0
$577$	40.9329	−	23.6326i	1.70406	−	0.983840i	0.762506	−	0.646982i	$-0.223969\pi$
$577$	40.9329	−	23.6326i	1.70406	−	0.983840i	0.941555	−	0.336858i	$-0.109364\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−3.86199			−0.159947
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	0.999742	−	0.0227138i	$-0.00723065\pi$
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	−0.519542	+	0.854445i	$0.673897\pi$
$588$		0			0
$589$	3.93750	−	6.81995i	0.162242	−	0.281011i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.5962	+	32.2095i	−0.763654	+	1.32269i	0.177302	+	0.984157i	$0.443263\pi$
$593$	−18.5962	+	32.2095i	−0.763654	+	1.32269i	−0.940955	+	0.338530i	$0.890070\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	32.2844i		−	1.31910i	−0.751659	−	0.659552i	$-0.770746\pi$
$599$		−	32.2844i		−	1.31910i	0.751659	−	0.659552i	$-0.229254\pi$
$600$		0			0
$601$	14.7559	−	8.51933i	0.601906	−	0.347511i	−0.167885	−	0.985807i	$-0.553694\pi$
$601$	14.7559	−	8.51933i	0.601906	−	0.347511i	0.769791	+	0.638296i	$0.220360\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.8615	−	29.2051i	0.685519	−	1.18735i
$606$		0			0
$607$	−8.44393	+	4.87510i	−0.342728	+	0.197874i	−0.661478	−	0.749965i	$-0.730070\pi$
$607$	−8.44393	+	4.87510i	−0.342728	+	0.197874i	0.318749	+	0.947839i	$0.396737\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−38.9369	−	22.4802i	−1.57522	−	0.909452i
$612$		0			0
$613$	−6.86332	−	11.8876i	−0.277207	−	0.480136i	0.693483	−	0.720473i	$-0.256075\pi$
$613$	−6.86332	−	11.8876i	−0.277207	−	0.480136i	−0.970690	+	0.240337i	$0.922742\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.84301	+	1.64141i	0.114455	+	0.0660807i	0.556135	−	0.831092i	$-0.312284\pi$
$617$	2.84301	+	1.64141i	0.114455	+	0.0660807i	−0.441680	+	0.897173i	$0.645617\pi$
$618$		0			0
$619$	14.9907	+	8.65490i	0.602528	+	0.347870i	0.770036	−	0.638001i	$-0.220238\pi$
$619$	14.9907	+	8.65490i	0.602528	+	0.347870i	−0.167507	+	0.985871i	$0.553572\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.7536	+	25.5539i	0.590142	+	1.02216i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.66923			0.226047
$630$		0			0
$631$	−6.27821			−0.249932			−0.124966	−	0.992161i	$-0.539882\pi$
$631$	−6.27821			−0.249932			−0.124966	+	0.992161i	$0.539882\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	18.9672	+	32.8522i	0.752691	+	1.30370i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.9788	+	10.3801i	0.710120	+	0.409988i	0.811105	−	0.584900i	$-0.198866\pi$
$641$	17.9788	+	10.3801i	0.710120	+	0.409988i	−0.100986	+	0.994888i	$0.532200\pi$
$642$		0			0
$643$	17.2553	+	9.96236i	0.680483	+	0.392877i	0.800037	−	0.599950i	$-0.204813\pi$
$643$	17.2553	+	9.96236i	0.680483	+	0.392877i	−0.119554	+	0.992828i	$0.538146\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.7670	−	25.5772i	−0.580551	−	1.00554i	−0.995414	−	0.0956605i	$-0.969504\pi$
$647$	−14.7670	−	25.5772i	−0.580551	−	1.00554i	0.414863	−	0.909884i	$-0.363830\pi$
$648$		0			0
$649$	11.2544	+	6.49774i	0.441775	+	0.255059i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.7914	+	7.96249i	−0.539701	+	0.311596i	−0.744958	−	0.667112i	$-0.767530\pi$
$653$	−13.7914	+	7.96249i	−0.539701	+	0.311596i	0.205257	+	0.978708i	$0.434197\pi$
$654$		0			0
$655$	19.9246	−	34.5105i	0.778520	−	1.34844i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.80283	+	1.61822i	−0.109183	+	0.0630368i	−0.553597	−	0.832785i	$-0.686745\pi$
$659$	−2.80283	+	1.61822i	−0.109183	+	0.0630368i	0.444414	+	0.895821i	$0.353412\pi$
$660$		0			0
$661$			8.90498i			0.346364i	0.984890	+	0.173182i	$0.0554048\pi$
$661$			8.90498i			0.346364i	−0.984890	+	0.173182i	$0.944595\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.676383	−	1.17153i	0.0261896	−	0.0453618i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−17.0285	+	29.4943i	−0.657379	+	1.13861i
$672$		0			0
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	−0.999933	−	0.0116101i	$-0.996304\pi$
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	0.489912	−	0.871772i	$-0.337029\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.92848			0.343149			0.171575	−	0.985171i	$-0.445114\pi$
$677$	8.92848			0.343149			0.171575	+	0.985171i	$0.445114\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−32.7902	+	18.9314i	−1.25468	+	0.724390i	−0.972035	−	0.234834i	$-0.924545\pi$
$683$	−32.7902	+	18.9314i	−1.25468	+	0.724390i	−0.282645	+	0.959225i	$0.591212\pi$
$684$		0			0
$685$		−	26.7298i		−	1.02129i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.33927			−0.127216
$690$		0			0
$691$			5.70665i			0.217091i	0.994091	+	0.108546i	$0.0346194\pi$
$691$			5.70665i			0.217091i	−0.994091	+	0.108546i	$0.965381\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			5.31208i			0.201499i
$696$		0			0
$697$	11.8821			0.450065
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	8.19949i		−	0.309690i	−0.987939	−	0.154845i	$-0.950512\pi$
$701$		−	8.19949i		−	0.309690i	0.987939	−	0.154845i	$-0.0494879\pi$
$702$		0			0
$703$	−14.4357	+	8.33444i	−0.544452	+	0.314339i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.1515			0.756805			0.378402	−	0.925641i	$-0.376474\pi$
$709$	20.1515			0.756805			0.378402	+	0.925641i	$0.376474\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.93676	+	6.81866i	0.147433	+	0.255361i
$714$		0			0
$715$	28.7028	−	49.7147i	1.07342	−	1.85923i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	25.5996	−	44.3397i	0.954702	−	1.65359i	0.219654	−	0.975578i	$-0.429507\pi$
$719$	25.5996	−	44.3397i	0.954702	−	1.65359i	0.735048	−	0.678015i	$-0.237159\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	1.05231i		−	0.0390820i
$726$		0			0
$727$	−13.7848	+	7.95865i	−0.511249	+	0.295170i	−0.733347	−	0.679854i	$-0.762043\pi$
$727$	−13.7848	+	7.95865i	−0.511249	+	0.295170i	0.222098	+	0.975024i	$0.428710\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.73584	−	15.1309i	0.323107	−	0.559637i
$732$		0			0
$733$	−3.67216	+	2.12012i	−0.135634	+	0.0783086i	−0.566282	−	0.824212i	$-0.691619\pi$
$733$	−3.67216	+	2.12012i	−0.135634	+	0.0783086i	0.430647	+	0.902520i	$0.358285\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	47.5401	+	27.4473i	1.75116	+	1.01103i
$738$		0			0
$739$	−14.1835	−	24.5665i	−0.521747	−	0.903693i	−0.999680	−	0.0252966i	$-0.991947\pi$
$739$	−14.1835	−	24.5665i	−0.521747	−	0.903693i	0.477933	−	0.878397i	$-0.341386\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.8850	−	12.6353i	−0.802884	−	0.463545i	0.0415945	−	0.999135i	$-0.486756\pi$
$743$	−21.8850	−	12.6353i	−0.802884	−	0.463545i	−0.844479	+	0.535589i	$0.820090\pi$
$744$		0			0
$745$	−33.1971	−	19.1664i	−1.21625	−	0.702201i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−23.7730	−	41.1761i	−0.867490	−	1.50254i	−0.864554	−	0.502540i	$-0.832399\pi$
$751$	−23.7730	−	41.1761i	−0.867490	−	1.50254i	−0.00293597	−	0.999996i	$-0.500935\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−38.5113			−1.40157
$756$		0			0
$757$	37.3922			1.35904			0.679521	−	0.733656i	$-0.262188\pi$
$757$	37.3922			1.35904			0.679521	+	0.733656i	$0.262188\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.12142	−	7.13850i	−0.149401	−	0.258770i	0.781605	−	0.623774i	$-0.214401\pi$
$761$	−4.12142	−	7.13850i	−0.149401	−	0.258770i	−0.931006	+	0.365003i	$0.881068\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.73114	+	5.61827i	0.351371	+	0.202864i
$768$		0			0
$769$	20.2182	+	11.6730i	0.729086	+	0.420938i	0.818088	−	0.575094i	$-0.195034\pi$
$769$	20.2182	+	11.6730i	0.729086	+	0.420938i	−0.0890020	+	0.996031i	$0.528368\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.2201	+	29.8261i	0.619364	+	1.07277i	0.989602	+	0.143833i	$0.0459428\pi$
$773$	17.2201	+	29.8261i	0.619364	+	1.07277i	−0.370238	+	0.928937i	$0.620724\pi$
$774$		0			0
$775$	5.30422	+	3.06240i	0.190533	+	0.110004i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−30.2555	+	17.4680i	−1.08402	+	0.625857i
$780$		0			0
$781$	−24.6822	+	42.7508i	−0.883199	+	1.52975i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	44.1682	−	25.5005i	1.57643	−	0.910152i
$786$		0			0
$787$		−	8.31355i		−	0.296346i	−0.988961	−	0.148173i	$-0.952661\pi$
$787$		−	8.31355i		−	0.296346i	0.988961	−	0.148173i	$-0.0473393\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.7237	+	25.5022i	−0.522854	+	0.905610i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.426036	+	0.737916i	−0.0150910	+	0.0261383i	−0.873472	−	0.486874i	$-0.838137\pi$
$797$	−0.426036	+	0.737916i	−0.0150910	+	0.0261383i	0.858381	+	0.513012i	$0.171470\pi$
$798$		0			0
$799$	9.18614	+	15.9109i	0.324982	+	0.562886i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−74.5190			−2.62972
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−31.5580	+	18.2200i	−1.10952	+	0.640581i	−0.938705	−	0.344722i	$-0.887973\pi$
$809$	−31.5580	+	18.2200i	−1.10952	+	0.640581i	−0.170814	+	0.985303i	$0.554640\pi$
$810$		0			0
$811$		−	1.08986i		−	0.0382702i	−0.999817	−	0.0191351i	$-0.993909\pi$
$811$		−	1.08986i		−	0.0382702i	0.999817	−	0.0191351i	$-0.00609126\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−15.0339			−0.526616
$816$		0			0
$817$			51.3709i			1.79724i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	24.2196i		−	0.845270i	−0.906300	−	0.422635i	$-0.861105\pi$
$821$		−	24.2196i		−	0.845270i	0.906300	−	0.422635i	$-0.138895\pi$
$822$		0			0
$823$	5.71185			0.199102			0.0995512	−	0.995032i	$-0.468259\pi$
$823$	5.71185			0.199102			0.0995512	+	0.995032i	$0.468259\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	36.4579i		−	1.26777i	−0.773429	−	0.633883i	$-0.781460\pi$
$827$		−	36.4579i		−	1.26777i	0.773429	−	0.633883i	$-0.218540\pi$
$828$		0			0
$829$	0.498269	−	0.287676i	0.0173056	−	0.00999140i	−0.491322	−	0.870978i	$-0.663486\pi$
$829$	0.498269	−	0.287676i	0.0173056	−	0.00999140i	0.508628	+	0.860986i	$0.330153\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	34.4312			1.19154
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	0.900925	+	0.433974i	$0.142889\pi$
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	−0.0746300	+	0.997211i	$0.523778\pi$
$840$		0			0
$841$	−14.4621	+	25.0490i	−0.498692	+	0.863759i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.51368	−	9.54997i	0.189676	−	0.328529i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	16.6657i		−	0.571294i
$852$		0			0
$853$	40.5393	−	23.4054i	1.38804	−	0.801385i	0.394945	−	0.918705i	$-0.370764\pi$
$853$	40.5393	−	23.4054i	1.38804	−	0.801385i	0.993094	+	0.117320i	$0.0374303\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.78220	−	8.28302i	0.163357	−	0.282943i	−0.772714	−	0.634755i	$-0.781101\pi$
$857$	4.78220	−	8.28302i	0.163357	−	0.282943i	0.936071	+	0.351812i	$0.114434\pi$
$858$		0			0
$859$	4.68311	−	2.70379i	0.159786	−	0.0922523i	−0.417975	−	0.908459i	$-0.637260\pi$
$859$	4.68311	−	2.70379i	0.159786	−	0.0922523i	0.577761	+	0.816206i	$0.303927\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.5402	+	20.5191i	1.20980	+	0.698480i	0.962716	−	0.270514i	$-0.0871936\pi$
$863$	35.5402	+	20.5191i	1.20980	+	0.698480i	0.247086	+	0.968994i	$0.420527\pi$
$864$		0			0
$865$	−9.30598	−	16.1184i	−0.316413	−	0.548043i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−50.3777	−	29.0856i	−1.70895	−	0.986661i
$870$		0			0
$871$	41.1056	+	23.7323i	1.39281	+	0.804139i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.32509	+	12.6874i	0.247351	+	0.428424i	0.962790	−	0.270251i	$-0.0871067\pi$
$877$	7.32509	+	12.6874i	0.247351	+	0.428424i	−0.715439	+	0.698675i	$0.753773\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	44.8295			1.51034			0.755172	−	0.655527i	$-0.227553\pi$
$881$	44.8295			1.51034			0.755172	+	0.655527i	$0.227553\pi$
$882$		0			0
$883$	33.8527			1.13923			0.569617	−	0.821910i	$-0.307091\pi$
$883$	33.8527			1.13923			0.569617	+	0.821910i	$0.307091\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.3422	−	23.1093i	−0.447987	−	0.775936i	0.550268	−	0.834988i	$-0.314525\pi$
$887$	−13.3422	−	23.1093i	−0.447987	−	0.775936i	−0.998255	+	0.0590523i	$0.981192\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−46.7817	−	27.0094i	−1.56549	−	0.903837i
$894$		0			0
$895$	−37.9157	−	21.8907i	−1.26738	−	0.731724i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.220820	+	0.382472i	0.00736476	+	0.0127561i
$900$		0			0
$901$	1.18172	+	0.682266i	0.0393688	+	0.0227296i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.214412	−	0.123791i	0.00712729	−	0.00411494i
$906$		0			0
$907$	7.97211	−	13.8081i	0.264710	−	0.458490i	−0.702778	−	0.711409i	$-0.748057\pi$
$907$	7.97211	−	13.8081i	0.264710	−	0.458490i	0.967487	+	0.252919i	$0.0813906\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−40.9207	+	23.6256i	−1.35576	+	0.782750i	−0.989050	−	0.147584i	$-0.952850\pi$
$911$	−40.9207	+	23.6256i	−1.35576	+	0.782750i	−0.366713	+	0.930334i	$0.619517\pi$
$912$		0			0
$913$		−	38.2013i		−	1.26428i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	14.8163	−	25.6625i	0.488743	−	0.846528i	−0.511173	−	0.859478i	$-0.670789\pi$
$919$	14.8163	−	25.6625i	0.488743	−	0.846528i	0.999916	+	0.0129500i	$0.00412223\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−21.3415	+	36.9645i	−0.702463	+	1.21670i
$924$		0			0
$925$	−6.48212	−	11.2274i	−0.213131	−	0.369153i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	33.2372			1.09048			0.545238	−	0.838281i	$-0.316439\pi$
$929$	33.2372			1.09048			0.545238	+	0.838281i	$0.316439\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−20.3151	+	11.7289i	−0.664373	+	0.383576i
$936$		0			0
$937$		−	23.8190i		−	0.778134i	−0.921209	−	0.389067i	$-0.872797\pi$
$937$		−	23.8190i		−	0.778134i	0.921209	−	0.389067i	$-0.127203\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−54.2403			−1.76818			−0.884091	−	0.467315i	$-0.845221\pi$
$941$	−54.2403			−1.76818			−0.884091	+	0.467315i	$0.845221\pi$
$942$		0			0
$943$		−	34.9295i		−	1.13746i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			21.0648i			0.684515i	0.939606	+	0.342257i	$0.111191\pi$
$947$			21.0648i			0.684515i	−0.939606	+	0.342257i	$0.888809\pi$
$948$		0			0
$949$	−64.4329			−2.09158
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	4.50028i		−	0.145778i	−0.997340	−	0.0728892i	$-0.976778\pi$
$953$		−	4.50028i		−	0.145778i	0.997340	−	0.0728892i	$-0.0232219\pi$
$954$		0			0
$955$	39.6989	−	22.9201i	1.28462	−	0.741679i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	28.4295			0.917081
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−32.0090	−	55.4411i	−1.03040	−	1.78471i
$966$		0			0
$967$	−10.8811	+	18.8466i	−0.349912	+	0.606065i	−0.986233	−	0.165359i	$-0.947122\pi$
$967$	−10.8811	+	18.8466i	−0.349912	+	0.606065i	0.636322	+	0.771424i	$0.280455\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.5222	−	40.7416i	0.754862	−	1.30746i	−0.190581	−	0.981671i	$-0.561037\pi$
$971$	23.5222	−	40.7416i	0.754862	−	1.30746i	0.945443	−	0.325788i	$-0.105629\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$			25.1455i			0.804475i	0.915535	+	0.402237i	$0.131767\pi$
$977$			25.1455i			0.804475i	−0.915535	+	0.402237i	$0.868233\pi$
$978$		0			0
$979$	37.7423	−	21.7905i	1.20625	−	0.696429i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.1071	+	31.3624i	−0.577527	+	1.00031i	0.418235	+	0.908339i	$0.362649\pi$
$983$	−18.1071	+	31.3624i	−0.577527	+	1.00031i	−0.995762	+	0.0919674i	$0.970684\pi$
$984$		0			0
$985$	25.4191	−	14.6757i	0.809921	−	0.467608i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−44.4801	−	25.6806i	−1.41438	−	0.816595i
$990$		0			0
$991$	−9.32769	−	16.1560i	−0.296304	−	0.513213i	0.678984	−	0.734153i	$-0.262421\pi$
$991$	−9.32769	−	16.1560i	−0.296304	−	0.513213i	−0.975287	+	0.220940i	$0.929087\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.1632	−	15.6827i	−0.861131	−	0.497174i
$996$		0			0
$997$	15.1413	+	8.74181i	0.479528	+	0.276856i	0.720220	−	0.693746i	$-0.244041\pi$
$997$	15.1413	+	8.74181i	0.479528	+	0.276856i	−0.240691	+	0.970602i	$0.577374\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.w.b.1097.2		16
3.2	odd	2		1764.2.w.b.509.6		16
7.2	even	3		5292.2.x.b.881.2		16
7.3	odd	6		5292.2.bm.a.2285.2		16
7.4	even	3		756.2.bm.a.17.7		16
7.5	odd	6		5292.2.x.a.881.7		16
7.6	odd	2		756.2.w.a.341.7		16
9.2	odd	6		5292.2.bm.a.4625.2		16
9.7	even	3		1764.2.bm.a.1685.8		16
21.2	odd	6		1764.2.x.b.293.5		16
21.5	even	6		1764.2.x.a.293.4		16
21.11	odd	6		252.2.bm.a.185.1	yes	16
21.17	even	6		1764.2.bm.a.1697.8		16
21.20	even	2		252.2.w.a.5.3	✓	16
28.11	odd	6		3024.2.df.d.17.7		16
28.27	even	2		3024.2.ca.d.2609.7		16
63.2	odd	6		5292.2.x.a.4409.7		16
63.4	even	3		2268.2.t.b.1781.2		16
63.11	odd	6		756.2.w.a.521.7		16
63.13	odd	6		2268.2.t.a.2105.7		16
63.16	even	3		1764.2.x.a.1469.4		16
63.20	even	6		756.2.bm.a.89.7		16
63.25	even	3		252.2.w.a.101.3	yes	16
63.32	odd	6		2268.2.t.a.1781.7		16
63.34	odd	6		252.2.bm.a.173.1	yes	16
63.38	even	6	inner	5292.2.w.b.521.2		16
63.41	even	6		2268.2.t.b.2105.2		16
63.47	even	6		5292.2.x.b.4409.2		16
63.52	odd	6		1764.2.w.b.1109.6		16
63.61	odd	6		1764.2.x.b.1469.5		16
84.11	even	6		1008.2.df.d.689.8		16
84.83	odd	2		1008.2.ca.d.257.6		16
252.11	even	6		3024.2.ca.d.2033.7		16
252.83	odd	6		3024.2.df.d.1601.7		16
252.151	odd	6		1008.2.ca.d.353.6		16
252.223	even	6		1008.2.df.d.929.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	21.20	even	2
252.2.w.a.101.3	yes	16	63.25	even	3
252.2.bm.a.173.1	yes	16	63.34	odd	6
252.2.bm.a.185.1	yes	16	21.11	odd	6
756.2.w.a.341.7		16	7.6	odd	2
756.2.w.a.521.7		16	63.11	odd	6
756.2.bm.a.17.7		16	7.4	even	3
756.2.bm.a.89.7		16	63.20	even	6
1008.2.ca.d.257.6		16	84.83	odd	2
1008.2.ca.d.353.6		16	252.151	odd	6
1008.2.df.d.689.8		16	84.11	even	6
1008.2.df.d.929.8		16	252.223	even	6
1764.2.w.b.509.6		16	3.2	odd	2
1764.2.w.b.1109.6		16	63.52	odd	6
1764.2.x.a.293.4		16	21.5	even	6
1764.2.x.a.1469.4		16	63.16	even	3
1764.2.x.b.293.5		16	21.2	odd	6
1764.2.x.b.1469.5		16	63.61	odd	6
1764.2.bm.a.1685.8		16	9.7	even	3
1764.2.bm.a.1697.8		16	21.17	even	6
2268.2.t.a.1781.7		16	63.32	odd	6
2268.2.t.a.2105.7		16	63.13	odd	6
2268.2.t.b.1781.2		16	63.4	even	3
2268.2.t.b.2105.2		16	63.41	even	6
3024.2.ca.d.2033.7		16	252.11	even	6
3024.2.ca.d.2609.7		16	28.27	even	2
3024.2.df.d.17.7		16	28.11	odd	6
3024.2.df.d.1601.7		16	252.83	odd	6
5292.2.w.b.521.2		16	63.38	even	6	inner
5292.2.w.b.1097.2		16	1.1	even	1	trivial
5292.2.x.a.881.7		16	7.5	odd	6
5292.2.x.a.4409.7		16	63.2	odd	6
5292.2.x.b.881.2		16	7.2	even	3
5292.2.x.b.4409.2		16	63.47	even	6
5292.2.bm.a.2285.2		16	7.3	odd	6
5292.2.bm.a.4625.2		16	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.48494 - 2.57199i) q^{5} +O(q^{10})\)	\(q+(-1.48494 - 2.57199i) q^{5} +(4.09466 + 2.36406i) q^{11} +(3.54045 + 2.04408i) q^{13} +(-0.835278 - 1.44674i) q^{17} +(4.25377 + 2.45592i) q^{19} +(-4.25297 + 2.45545i) q^{23} +(-1.91009 + 3.30837i) q^{25} +(-0.238557 + 0.137731i) q^{29} -1.60327i q^{31} +(-1.69681 + 2.93896i) q^{37} +(-3.55632 + 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} -10.9977 q^{47} +(-0.707381 + 0.408407i) q^{53} -14.0419i q^{55} +2.74856 q^{59} +7.20310i q^{61} -12.1413i q^{65} +11.6103 q^{67} +10.4406i q^{71} +(-13.6493 + 7.88042i) q^{73} -12.3033 q^{79} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(4.60872 - 7.98254i) q^{89} -14.5875i q^{95} +(-7.00772 + 4.04591i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 6 q^{11} + 3 q^{13} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + q^{37} - 6 q^{41} - 2 q^{43} - 36 q^{47} - 30 q^{59} + 14 q^{67} + 2 q^{79} + 6 q^{85} + 21 q^{89} + 3 q^{97}+O(q^{100}) \) 16 * q + 6 * q^11 + 3 * q^13 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + q^37 - 6 * q^41 - 2 * q^43 - 36 * q^47 - 30 * q^59 + 14 * q^67 + 2 * q^79 + 6 * q^85 + 21 * q^89 + 3 * q^97

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