LMFDB - Embedded newform 5292.2.x.b.4409.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5292,2,Mod(881,5292)]

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, 5, 3]))

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

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

chi := DirichletCharacter("5292.881");

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.x (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			4409.6
Root			$-1.61108 - 0.635951i$ of defining polynomial
Character	$\chi$	$=$	5292.4409
Dual form			5292.2.x.b.881.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09150 + 1.89054i) q^{5} +O(q^{10})$	$q+(1.09150 + 1.89054i) q^{5} +(-1.26889 - 0.732592i) q^{11} +(-2.92752 + 1.69021i) q^{13} -2.64271 q^{17} -7.94221i q^{19} +(-3.47245 + 2.00482i) q^{23} +(0.117249 - 0.203081i) q^{25} +(6.71261 + 3.87553i) q^{29} +(-0.612252 + 0.353484i) q^{31} -2.83477 q^{37} +(3.74173 + 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} +(6.27538 - 10.8693i) q^{47} -2.79062i q^{53} -3.19850i q^{55} +(-6.71650 - 11.6333i) q^{59} +(-6.75061 - 3.89747i) q^{61} +(-6.39079 - 3.68972i) q^{65} +(-2.92029 - 5.05809i) q^{67} -11.6854i q^{71} -4.57174i q^{73} +(-4.69189 + 8.12659i) q^{79} +(1.70847 - 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} -9.23875 q^{89} +(15.0150 - 8.66894i) q^{95} +(-6.38394 - 3.68577i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 6 q^{11} + 3 q^{13} - 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} - 6 q^{31} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 42 q^{89} + 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q - 6 * q^11 + 3 * q^13 - 18 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^29 - 6 * q^31 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 42 * q^89 + 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.09150	+	1.89054i	0.488134	+	0.845473i	0.999907	−	0.0136476i	$-0.00434429\pi$
$5$	1.09150	+	1.89054i	0.488134	+	0.845473i	−0.511773	+	0.859121i	$0.671011\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.26889	−	0.732592i	−0.382584	−	0.220885i	0.296358	−	0.955077i	$-0.404228\pi$
$11$	−1.26889	−	0.732592i	−0.382584	−	0.220885i	−0.678942	+	0.734192i	$0.737561\pi$
$12$		0			0
$13$	−2.92752	+	1.69021i	−0.811948	+	0.468779i	−0.847632	−	0.530585i	$-0.821972\pi$
$13$	−2.92752	+	1.69021i	−0.811948	+	0.468779i	0.0356837	+	0.999363i	$0.488639\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.64271			−0.640952			−0.320476	−	0.947257i	$-0.603843\pi$
$17$	−2.64271			−0.640952			−0.320476	+	0.947257i	$0.603843\pi$
$18$		0			0
$19$		−	7.94221i		−	1.82207i	−0.412331	−	0.911034i	$-0.635285\pi$
$19$		−	7.94221i		−	1.82207i	0.412331	−	0.911034i	$-0.364715\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.47245	+	2.00482i	−0.724056	+	0.418034i	−0.816244	−	0.577708i	$-0.803947\pi$
$23$	−3.47245	+	2.00482i	−0.724056	+	0.418034i	0.0921879	+	0.995742i	$0.470614\pi$
$24$		0			0
$25$	0.117249	−	0.203081i	0.0234498	−	0.0406163i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.71261	+	3.87553i	1.24650	+	0.719667i	0.970410	−	0.241464i	$-0.0776276\pi$
$29$	6.71261	+	3.87553i	1.24650	+	0.719667i	0.276091	+	0.961132i	$0.410961\pi$
$30$		0			0
$31$	−0.612252	+	0.353484i	−0.109964	+	0.0634876i	−0.553973	−	0.832534i	$-0.686889\pi$
$31$	−0.612252	+	0.353484i	−0.109964	+	0.0634876i	0.444009	+	0.896022i	$0.353556\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.83477			−0.466033			−0.233016	−	0.972473i	$-0.574860\pi$
$37$	−2.83477			−0.466033			−0.233016	+	0.972473i	$0.574860\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.74173	+	6.48086i	0.584360	+	1.01214i	0.994955	+	0.100323i	$0.0319876\pi$
$41$	3.74173	+	6.48086i	0.584360	+	1.01214i	−0.410595	+	0.911818i	$0.634679\pi$
$42$		0			0
$43$	−1.27112	+	2.20164i	−0.193844	+	0.335748i	−0.946521	−	0.322642i	$-0.895429\pi$
$43$	−1.27112	+	2.20164i	−0.193844	+	0.335748i	0.752677	+	0.658390i	$0.228762\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.27538	−	10.8693i	0.915358	−	1.58545i	0.108983	−	0.994044i	$-0.465241\pi$
$47$	6.27538	−	10.8693i	0.915358	−	1.58545i	0.806376	−	0.591403i	$-0.201426\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.79062i		−	0.383321i	−0.981461	−	0.191661i	$-0.938613\pi$
$53$		−	2.79062i		−	0.383321i	0.981461	−	0.191661i	$-0.0613873\pi$
$54$		0			0
$55$		−	3.19850i		−	0.431286i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.71650	−	11.6333i	−0.874414	−	1.51453i	−0.857385	−	0.514675i	$-0.827913\pi$
$59$	−6.71650	−	11.6333i	−0.874414	−	1.51453i	−0.0170287	−	0.999855i	$-0.505421\pi$
$60$		0			0
$61$	−6.75061	−	3.89747i	−0.864327	−	0.499020i	0.00113176	−	0.999999i	$-0.499640\pi$
$61$	−6.75061	−	3.89747i	−0.864327	−	0.499020i	−0.865459	+	0.500980i	$0.832973\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.39079	−	3.68972i	−0.792680	−	0.457654i
$66$		0			0
$67$	−2.92029	−	5.05809i	−0.356770	−	0.617945i	0.630649	−	0.776068i	$-0.282789\pi$
$67$	−2.92029	−	5.05809i	−0.356770	−	0.617945i	−0.987419	+	0.158124i	$0.949455\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.6854i		−	1.38680i	−0.720554	−	0.693398i	$-0.756113\pi$
$71$		−	11.6854i		−	1.38680i	0.720554	−	0.693398i	$-0.243887\pi$
$72$		0			0
$73$		−	4.57174i		−	0.535082i	−0.963547	−	0.267541i	$-0.913789\pi$
$73$		−	4.57174i		−	0.535082i	0.963547	−	0.267541i	$-0.0862110\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.69189	+	8.12659i	−0.527879	+	0.914312i	0.471593	+	0.881816i	$0.343679\pi$
$79$	−4.69189	+	8.12659i	−0.527879	+	0.914312i	−0.999472	+	0.0324963i	$0.989654\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.70847	−	2.95917i	0.187529	−	0.324811i	−0.756896	−	0.653535i	$-0.773285\pi$
$83$	1.70847	−	2.95917i	0.187529	−	0.324811i	0.944426	+	0.328724i	$0.106619\pi$
$84$		0			0
$85$	−2.88452	−	4.99614i	−0.312871	−	0.541908i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.23875			−0.979306			−0.489653	−	0.871918i	$-0.662876\pi$
$89$	−9.23875			−0.979306			−0.489653	+	0.871918i	$0.662876\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.0150	−	8.66894i	1.54051	−	0.889414i
$96$		0			0
$97$	−6.38394	−	3.68577i	−0.648191	−	0.374233i	0.139572	−	0.990212i	$-0.455427\pi$
$97$	−6.38394	−	3.68577i	−0.648191	−	0.374233i	−0.787763	+	0.615979i	$0.788761\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.96357	−	6.86510i	0.394390	−	0.683103i	−0.598633	−	0.801023i	$-0.704289\pi$
$101$	3.96357	−	6.86510i	0.394390	−	0.683103i	0.993023	+	0.117920i	$0.0376226\pi$
$102$		0			0
$103$	−3.26825	+	1.88693i	−0.322031	+	0.185924i	−0.652297	−	0.757963i	$-0.726195\pi$
$103$	−3.26825	+	1.88693i	−0.322031	+	0.185924i	0.330267	+	0.943888i	$0.392861\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			7.94712i			0.768277i	0.923275	+	0.384138i	$0.125501\pi$
$107$			7.94712i			0.768277i	−0.923275	+	0.384138i	$0.874499\pi$
$108$		0			0
$109$	−1.01028			−0.0967677			−0.0483838	−	0.998829i	$-0.515407\pi$
$109$	−1.01028			−0.0967677			−0.0483838	+	0.998829i	$0.515407\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.5557	−	6.09431i	0.992992	−	0.573304i	0.0868250	−	0.996224i	$-0.472328\pi$
$113$	10.5557	−	6.09431i	0.992992	−	0.573304i	0.906167	+	0.422919i	$0.138995\pi$
$114$		0			0
$115$	−7.58037	−	4.37653i	−0.706873	−	0.408113i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.42662	−	7.66713i	−0.402420	−	0.697012i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.4269			1.02206
$126$		0			0
$127$	6.79350			0.602826			0.301413	−	0.953494i	$-0.402542\pi$
$127$	6.79350			0.602826			0.301413	+	0.953494i	$0.402542\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.86790	+	11.8956i	0.600051	+	1.03932i	0.992813	+	0.119679i	$0.0381865\pi$
$131$	6.86790	+	11.8956i	0.600051	+	1.03932i	−0.392761	+	0.919640i	$0.628480\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	17.4028	+	10.0475i	1.48682	+	0.858416i	0.999887	−	0.0150235i	$-0.00478229\pi$
$137$	17.4028	+	10.0475i	1.48682	+	0.858416i	0.486933	+	0.873439i	$0.338116\pi$
$138$		0			0
$139$	−8.51403	+	4.91558i	−0.722151	+	0.416934i	−0.815544	−	0.578695i	$-0.803562\pi$
$139$	−8.51403	+	4.91558i	−0.722151	+	0.416934i	0.0933930	+	0.995629i	$0.470229\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.95292			0.414184
$144$		0			0
$145$			16.9206i			1.40518i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	17.3512	−	10.0177i	1.42146	−	0.820682i	0.425038	−	0.905175i	$-0.360261\pi$
$149$	17.3512	−	10.0177i	1.42146	−	0.820682i	0.996424	+	0.0844939i	$0.0269274\pi$
$150$		0			0
$151$	11.1168	−	19.2549i	0.904675	−	1.56694i	0.0833218	−	0.996523i	$-0.473447\pi$
$151$	11.1168	−	19.2549i	0.904675	−	1.56694i	0.821353	−	0.570420i	$-0.193220\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.33655	−	0.771657i	−0.107354	−	0.0619810i
$156$		0			0
$157$	−6.95305	+	4.01435i	−0.554914	+	0.320380i	−0.751102	−	0.660187i	$-0.770477\pi$
$157$	−6.95305	+	4.01435i	−0.554914	+	0.320380i	0.196188	+	0.980566i	$0.437144\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	12.4521			0.975323			0.487661	−	0.873033i	$-0.337850\pi$
$163$	12.4521			0.975323			0.487661	+	0.873033i	$0.337850\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.85984	−	17.0777i	−0.762978	−	1.32152i	−0.941309	−	0.337546i	$-0.890403\pi$
$167$	−9.85984	−	17.0777i	−0.762978	−	1.32152i	0.178332	−	0.983970i	$-0.442930\pi$
$168$		0			0
$169$	−0.786412	+	1.36211i	−0.0604933	+	0.104777i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.913733	+	1.58263i	−0.0694699	+	0.120325i	−0.898668	−	0.438629i	$-0.855464\pi$
$173$	−0.913733	+	1.58263i	−0.0694699	+	0.120325i	0.829198	+	0.558955i	$0.188797\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$			13.9929i			1.04588i	0.852370	+	0.522939i	$0.175164\pi$
$179$			13.9929i			1.04588i	−0.852370	+	0.522939i	$0.824836\pi$
$180$		0			0
$181$		−	16.3594i		−	1.21599i	−0.793942	−	0.607994i	$-0.791975\pi$
$181$		−	16.3594i		−	1.21599i	0.793942	−	0.607994i	$-0.208025\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.09415	−	5.35923i	−0.227486	−	0.394018i
$186$		0			0
$187$	3.35330	+	1.93603i	0.245218	+	0.141577i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.8326	−	6.83153i	−0.856173	−	0.494312i	0.00655557	−	0.999979i	$-0.497913\pi$
$191$	−11.8326	−	6.83153i	−0.856173	−	0.494312i	−0.862729	+	0.505667i	$0.831247\pi$
$192$		0			0
$193$	2.18885	+	3.79119i	0.157557	+	0.272896i	0.933987	−	0.357307i	$-0.116305\pi$
$193$	2.18885	+	3.79119i	0.157557	+	0.272896i	−0.776430	+	0.630203i	$0.782972\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.00603i			0.0716767i	0.999358	+	0.0358384i	$0.0114101\pi$
$197$			1.00603i			0.0716767i	−0.999358	+	0.0358384i	$0.988590\pi$
$198$		0			0
$199$		−	6.55453i		−	0.464638i	−0.972640	−	0.232319i	$-0.925369\pi$
$199$		−	6.55453i		−	0.464638i	0.972640	−	0.232319i	$-0.0746313\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−8.16820	+	14.1477i	−0.570492	+	0.988121i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.81840	+	10.0778i	−0.402467	+	0.697094i
$210$		0			0
$211$	−9.11202	−	15.7825i	−0.627297	−	1.08651i	−0.988092	−	0.153866i	$-0.950828\pi$
$211$	−9.11202	−	15.7825i	−0.627297	−	1.08651i	0.360794	−	0.932645i	$-0.382506\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.54972			−0.378487
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.73660	−	4.46673i	0.520420	−	0.300464i
$222$		0			0
$223$	8.71705	+	5.03279i	0.583737	+	0.337021i	0.762617	−	0.646850i	$-0.223914\pi$
$223$	8.71705	+	5.03279i	0.583737	+	0.337021i	−0.178880	+	0.983871i	$0.557247\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.94372	−	17.2230i	0.659988	−	1.14313i	−0.320630	−	0.947204i	$-0.603895\pi$
$227$	9.94372	−	17.2230i	0.659988	−	1.14313i	0.980618	−	0.195928i	$-0.0627720\pi$
$228$		0			0
$229$	−15.3854	+	8.88275i	−1.01669	+	0.586988i	−0.913145	−	0.407636i	$-0.866353\pi$
$229$	−15.3854	+	8.88275i	−1.01669	+	0.586988i	−0.103549	+	0.994624i	$0.533020\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			16.0592i			1.05208i	0.850461	+	0.526038i	$0.176323\pi$
$233$			16.0592i			1.05208i	−0.850461	+	0.526038i	$0.823677\pi$
$234$		0			0
$235$	27.3983			1.78727
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.11117	−	4.10564i	0.459983	−	0.265572i	−0.252054	−	0.967713i	$-0.581106\pi$
$239$	7.11117	−	4.10564i	0.459983	−	0.265572i	0.712037	+	0.702142i	$0.247773\pi$
$240$		0			0
$241$	−24.6614	−	14.2382i	−1.58858	−	0.917166i	−0.993542	−	0.113468i	$-0.963804\pi$
$241$	−24.6614	−	14.2382i	−1.58858	−	0.917166i	−0.595037	−	0.803698i	$-0.702863\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	13.4240	+	23.2510i	0.854147	+	1.47943i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.656343			0.0414280			0.0207140	−	0.999785i	$-0.493406\pi$
$251$	0.656343			0.0414280			0.0207140	+	0.999785i	$0.493406\pi$
$252$		0			0
$253$	5.87486			0.369349
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.82042	−	6.61716i	−0.238311	−	0.412767i	0.721918	−	0.691978i	$-0.243261\pi$
$257$	−3.82042	−	6.61716i	−0.238311	−	0.412767i	−0.960230	+	0.279211i	$0.909927\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.73888	−	3.31334i	−0.353874	−	0.204310i	0.312516	−	0.949913i	$-0.398828\pi$
$263$	−5.73888	−	3.31334i	−0.353874	−	0.204310i	−0.666390	+	0.745603i	$0.732162\pi$
$264$		0			0
$265$	5.27577	−	3.04597i	0.324088	−	0.187112i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.76693			−0.534529			−0.267265	−	0.963623i	$-0.586120\pi$
$269$	−8.76693			−0.534529			−0.267265	+	0.963623i	$0.586120\pi$
$270$		0			0
$271$		−	16.4669i		−	1.00029i	−0.865941	−	0.500147i	$-0.833279\pi$
$271$		−	16.4669i		−	1.00029i	0.865941	−	0.500147i	$-0.166721\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.297551	+	0.171791i	−0.0179430	+	0.0103594i
$276$		0			0
$277$	8.88732	−	15.3933i	0.533987	−	0.924893i	−0.465225	−	0.885193i	$-0.654026\pi$
$277$	8.88732	−	15.3933i	0.533987	−	0.924893i	0.999212	−	0.0397001i	$-0.0126402\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	14.0252	+	8.09748i	0.836676	+	0.483055i	0.856133	−	0.516755i	$-0.172860\pi$
$281$	14.0252	+	8.09748i	0.836676	+	0.483055i	−0.0194568	+	0.999811i	$0.506194\pi$
$282$		0			0
$283$	−24.5717	+	14.1865i	−1.46063	+	0.843298i	−0.999041	−	0.0437937i	$-0.986056\pi$
$283$	−24.5717	+	14.1865i	−1.46063	+	0.843298i	−0.461594	+	0.887091i	$0.652722\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−10.0161			−0.589181
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.38260	−	7.59088i	−0.256034	−	0.443464i	0.709142	−	0.705066i	$-0.249083\pi$
$293$	−4.38260	−	7.59088i	−0.256034	−	0.443464i	−0.965176	+	0.261602i	$0.915749\pi$
$294$		0			0
$295$	14.6621	−	25.3956i	0.853663	−	1.47859i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.77711	−	11.7383i	0.391931	−	0.678844i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	17.0164i		−	0.974354i
$306$		0			0
$307$			12.8497i			0.733372i	0.930345	+	0.366686i	$0.119508\pi$
$307$			12.8497i			0.733372i	−0.930345	+	0.366686i	$0.880492\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.29671	+	5.71007i	0.186939	+	0.323789i	0.944228	−	0.329291i	$-0.106810\pi$
$311$	3.29671	+	5.71007i	0.186939	+	0.323789i	−0.757289	+	0.653080i	$0.773477\pi$
$312$		0			0
$313$	2.95711	+	1.70729i	0.167146	+	0.0965018i	0.581239	−	0.813733i	$-0.302568\pi$
$313$	2.95711	+	1.70729i	0.167146	+	0.0965018i	−0.414093	+	0.910234i	$0.635901\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−27.8003	−	16.0505i	−1.56142	−	0.901485i	−0.997114	−	0.0759182i	$-0.975811\pi$
$317$	−27.8003	−	16.0505i	−1.56142	−	0.901485i	−0.564304	−	0.825567i	$-0.690855\pi$
$318$		0			0
$319$	−5.67836	−	9.83521i	−0.317927	−	0.550666i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			20.9890i			1.16786i
$324$		0			0
$325$			0.792700i			0.0439711i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	14.4416	−	25.0137i	0.793784	−	1.37487i	−0.129824	−	0.991537i	$-0.541441\pi$
$331$	14.4416	−	25.0137i	0.793784	−	1.37487i	0.923608	−	0.383338i	$-0.125225\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	6.37501	−	11.0418i	0.348304	−	0.603280i
$336$		0			0
$337$	4.82568	+	8.35833i	0.262872	+	0.455307i	0.967004	−	0.254762i	$-0.0819971\pi$
$337$	4.82568	+	8.35833i	0.262872	+	0.455307i	−0.704132	+	0.710069i	$0.748664\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.03584			0.0560938
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.6758	−	6.16367i	0.573106	−	0.330883i	−0.185283	−	0.982685i	$-0.559320\pi$
$347$	10.6758	−	6.16367i	0.573106	−	0.330883i	0.758389	+	0.651802i	$0.225987\pi$
$348$		0			0
$349$	10.2211	+	5.90115i	0.547123	+	0.315881i	0.747961	−	0.663743i	$-0.231033\pi$
$349$	10.2211	+	5.90115i	0.547123	+	0.315881i	−0.200838	+	0.979624i	$0.564366\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.59855	−	11.4290i	0.351205	−	0.608305i	−0.635256	−	0.772302i	$-0.719105\pi$
$353$	6.59855	−	11.4290i	0.351205	−	0.608305i	0.986461	+	0.163997i	$0.0524386\pi$
$354$		0			0
$355$	22.0916	−	12.7546i	1.17250	−	0.676943i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			6.03311i			0.318416i	0.987245	+	0.159208i	$0.0508940\pi$
$359$			6.03311i			0.318416i	−0.987245	+	0.159208i	$0.949106\pi$
$360$		0			0
$361$	−44.0787			−2.31993
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.64304	−	4.99006i	0.452397	−	0.261192i
$366$		0			0
$367$	14.8755	+	8.58836i	0.776494	+	0.448309i	0.835186	−	0.549967i	$-0.185360\pi$
$367$	14.8755	+	8.58836i	0.776494	+	0.448309i	−0.0586924	+	0.998276i	$0.518693\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.35902	−	4.08595i	−0.122146	−	0.211562i	0.798468	−	0.602037i	$-0.205644\pi$
$373$	−2.35902	−	4.08595i	−0.122146	−	0.211562i	−0.920614	+	0.390475i	$0.872311\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.2017			−1.34946
$378$		0			0
$379$	9.34015			0.479771			0.239886	−	0.970801i	$-0.422890\pi$
$379$	9.34015			0.479771			0.239886	+	0.970801i	$0.422890\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.85036	+	4.93696i	0.145646	+	0.252267i	0.929614	−	0.368535i	$-0.120140\pi$
$383$	2.85036	+	4.93696i	0.145646	+	0.252267i	−0.783968	+	0.620802i	$0.786807\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.63671	+	3.83171i	0.336495	+	0.194275i	0.658721	−	0.752387i	$-0.271098\pi$
$389$	6.63671	+	3.83171i	0.336495	+	0.194275i	−0.322226	+	0.946663i	$0.604431\pi$
$390$		0			0
$391$	9.17668	−	5.29816i	0.464085	−	0.267939i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.4848			−1.03070
$396$		0			0
$397$			1.30262i			0.0653766i	0.999466	+	0.0326883i	$0.0104069\pi$
$397$			1.30262i			0.0653766i	−0.999466	+	0.0326883i	$0.989593\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.18778	+	4.72722i	−0.408878	+	0.236066i	−0.690308	−	0.723516i	$-0.742525\pi$
$401$	−8.18778	+	4.72722i	−0.408878	+	0.236066i	0.281429	+	0.959582i	$0.409191\pi$
$402$		0			0
$403$	1.19492	−	2.06966i	0.0595233	−	0.103097i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.59700	+	2.07673i	0.178296	+	0.102940i
$408$		0			0
$409$	16.5182	−	9.53678i	0.816771	−	0.471563i	−0.0325304	−	0.999471i	$-0.510357\pi$
$409$	16.5182	−	9.53678i	0.816771	−	0.471563i	0.849302	+	0.527908i	$0.177023\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	7.45921			0.366158
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.20003	−	7.27466i	−0.205185	−	0.355390i	0.745007	−	0.667057i	$-0.232446\pi$
$419$	−4.20003	−	7.27466i	−0.205185	−	0.355390i	−0.950192	+	0.311666i	$0.899113\pi$
$420$		0			0
$421$	19.7178	−	34.1522i	0.960985	−	1.66448i	0.240951	−	0.970537i	$-0.422541\pi$
$421$	19.7178	−	34.1522i	0.960985	−	1.66448i	0.720035	−	0.693938i	$-0.244126\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.309855	+	0.536685i	−0.0150302	+	0.0260331i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$			11.9327i			0.574777i	0.957814	+	0.287389i	$0.0927871\pi$
$431$			11.9327i			0.574777i	−0.957814	+	0.287389i	$0.907213\pi$
$432$		0			0
$433$			12.2121i			0.586875i	0.955978	+	0.293437i	$0.0947992\pi$
$433$			12.2121i			0.586875i	−0.955978	+	0.293437i	$0.905201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.9227	+	27.5789i	0.761686	+	1.31928i
$438$		0			0
$439$	−14.4639	−	8.35076i	−0.690326	−	0.398560i	0.113408	−	0.993548i	$-0.463823\pi$
$439$	−14.4639	−	8.35076i	−0.690326	−	0.398560i	−0.803734	+	0.594989i	$0.797157\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.2403	+	15.1499i	1.24672	+	0.719791i	0.970453	−	0.241291i	$-0.0775708\pi$
$443$	26.2403	+	15.1499i	1.24672	+	0.719791i	0.276262	+	0.961082i	$0.410904\pi$
$444$		0			0
$445$	−10.0841	−	17.4662i	−0.478033	−	0.827977i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			30.1253i			1.42170i	0.703343	+	0.710851i	$0.251690\pi$
$449$			30.1253i			1.42170i	−0.703343	+	0.710851i	$0.748310\pi$
$450$		0			0
$451$		−	10.9646i		−	0.516305i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−12.6159	+	21.8513i	−0.590146	+	1.02216i	0.404067	+	0.914730i	$0.367596\pi$
$457$	−12.6159	+	21.8513i	−0.590146	+	1.02216i	−0.994212	+	0.107433i	$0.965737\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.3174	+	21.3344i	−0.573680	+	0.993643i	0.422503	+	0.906361i	$0.361151\pi$
$461$	−12.3174	+	21.3344i	−0.573680	+	0.993643i	−0.996184	+	0.0872820i	$0.972182\pi$
$462$		0			0
$463$	−6.33215	−	10.9676i	−0.294280	−	0.509708i	0.680537	−	0.732713i	$-0.261746\pi$
$463$	−6.33215	−	10.9676i	−0.294280	−	0.509708i	−0.974817	+	0.223006i	$0.928413\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.9445			−0.969198			−0.484599	−	0.874736i	$-0.661034\pi$
$467$	−20.9445			−0.969198			−0.484599	+	0.874736i	$0.661034\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.22581	−	1.86242i	0.148323	−	0.0856344i
$474$		0			0
$475$	−1.61291	−	0.931217i	−0.0740056	−	0.0427271i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.8852	−	27.5141i	0.725816	−	1.25715i	−0.232822	−	0.972519i	$-0.574796\pi$
$479$	15.8852	−	27.5141i	0.725816	−	1.25715i	0.958637	−	0.284630i	$-0.0918707\pi$
$480$		0			0
$481$	8.29884	−	4.79134i	0.378394	−	0.218466i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	16.0921i		−	0.730705i
$486$		0			0
$487$	35.5642			1.61157			0.805784	−	0.592210i	$-0.201744\pi$
$487$	35.5642			1.61157			0.805784	+	0.592210i	$0.201744\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.75734	+	1.59195i	−0.124437	+	0.0718437i	−0.560926	−	0.827866i	$-0.689555\pi$
$491$	−2.75734	+	1.59195i	−0.124437	+	0.0718437i	0.436490	+	0.899709i	$0.356222\pi$
$492$		0			0
$493$	−17.7395	−	10.2419i	−0.798947	−	0.461272i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−16.0214	−	27.7498i	−0.717215	−	1.24225i	−0.962099	−	0.272700i	$-0.912083\pi$
$499$	−16.0214	−	27.7498i	−0.717215	−	1.24225i	0.244884	−	0.969552i	$-0.421250\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.6608			0.519930			0.259965	−	0.965618i	$-0.416289\pi$
$503$	11.6608			0.519930			0.259965	+	0.965618i	$0.416289\pi$
$504$		0			0
$505$	17.3050			0.770061
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.4427	−	23.2834i	−0.595836	−	1.03202i	−0.993428	−	0.114457i	$-0.963487\pi$
$509$	−13.4427	−	23.2834i	−0.595836	−	1.03202i	0.397592	−	0.917562i	$-0.369846\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.13461	−	4.11917i	−0.314388	−	0.181512i
$516$		0			0
$517$	−15.9255	+	9.19459i	−0.700402	+	0.404378i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−34.0771			−1.49294			−0.746471	−	0.665418i	$-0.768254\pi$
$521$	−34.0771			−1.49294			−0.746471	+	0.665418i	$0.768254\pi$
$522$		0			0
$523$		−	5.43867i		−	0.237816i	−0.992905	−	0.118908i	$-0.962061\pi$
$523$		−	5.43867i		−	0.237816i	0.992905	−	0.118908i	$-0.0379394\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.61801	−	0.934157i	0.0704815	−	0.0406925i
$528$		0			0
$529$	−3.46140	+	5.99532i	−0.150496	+	0.260666i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−21.9080	−	12.6486i	−0.948940	−	0.547871i
$534$		0			0
$535$	−15.0243	+	8.67429i	−0.649558	+	0.375022i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−23.6658			−1.01747			−0.508737	−	0.860922i	$-0.669887\pi$
$541$	−23.6658			−1.01747			−0.508737	+	0.860922i	$0.669887\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.10273	−	1.90998i	−0.0472356	−	0.0818145i
$546$		0			0
$547$	−12.0824	+	20.9273i	−0.516606	+	0.894788i	0.483208	+	0.875505i	$0.339471\pi$
$547$	−12.0824	+	20.9273i	−0.516606	+	0.894788i	−0.999814	+	0.0192822i	$0.993862\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	30.7803	−	53.3130i	1.31128	−	2.27121i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	8.50223i		−	0.360251i	−0.983644	−	0.180126i	$-0.942350\pi$
$557$		−	8.50223i		−	0.360251i	0.983644	−	0.180126i	$-0.0576504\pi$
$558$		0			0
$559$		−	8.59381i		−	0.363480i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.473776	−	0.820605i	−0.0199673	−	0.0345844i	0.855869	−	0.517192i	$-0.173023\pi$
$563$	−0.473776	−	0.820605i	−0.0199673	−	0.0345844i	−0.875836	+	0.482608i	$0.839690\pi$
$564$		0			0
$565$	23.0430	+	13.3039i	0.969427	+	0.559699i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.7859	−	9.11401i	−0.661781	−	0.382079i	0.131175	−	0.991359i	$-0.458125\pi$
$569$	−15.7859	−	9.11401i	−0.661781	−	0.382079i	−0.792955	+	0.609280i	$0.791458\pi$
$570$		0			0
$571$	6.12121	+	10.6023i	0.256165	+	0.443691i	0.965211	−	0.261471i	$-0.0842077\pi$
$571$	6.12121	+	10.6023i	0.256165	+	0.443691i	−0.709046	+	0.705162i	$0.750874\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.940253i			0.0392112i
$576$		0			0
$577$		−	11.8357i		−	0.492726i	−0.969178	−	0.246363i	$-0.920764\pi$
$577$		−	11.8357i		−	0.492726i	0.969178	−	0.246363i	$-0.0792355\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−2.04439	+	3.54098i	−0.0846699	+	0.146653i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.57681	−	6.19521i	0.147631	−	0.255704i	−0.782721	−	0.622373i	$-0.786169\pi$
$587$	3.57681	−	6.19521i	0.147631	−	0.255704i	0.930351	+	0.366669i	$0.119502\pi$
$588$		0			0
$589$	2.80745	+	4.86264i	0.115679	+	0.200362i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−26.9622			−1.10721			−0.553603	−	0.832781i	$-0.686748\pi$
$593$	−26.9622			−1.10721			−0.553603	+	0.832781i	$0.686748\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−30.5223	+	17.6221i	−1.24711	+	0.720018i	−0.970532	−	0.240974i	$-0.922533\pi$
$599$	−30.5223	+	17.6221i	−1.24711	+	0.720018i	−0.276576	+	0.960992i	$0.589200\pi$
$600$		0			0
$601$	−3.39266	−	1.95875i	−0.138389	−	0.0798991i	0.429207	−	0.903206i	$-0.358793\pi$
$601$	−3.39266	−	1.95875i	−0.138389	−	0.0798991i	−0.567596	+	0.823307i	$0.692126\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.66332	−	16.7374i	0.392870	−	0.680470i
$606$		0			0
$607$	−12.5377	+	7.23862i	−0.508888	+	0.293807i	−0.732376	−	0.680900i	$-0.761589\pi$
$607$	−12.5377	+	7.23862i	−0.508888	+	0.293807i	0.223488	+	0.974707i	$0.428256\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			42.4267i			1.71640i
$612$		0			0
$613$	13.0352			0.526488			0.263244	−	0.964729i	$-0.415208\pi$
$613$	13.0352			0.526488			0.263244	+	0.964729i	$0.415208\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.14491	−	1.81571i	0.126609	−	0.0730979i	−0.435358	−	0.900258i	$-0.643378\pi$
$617$	3.14491	−	1.81571i	0.126609	−	0.0730979i	0.561967	+	0.827160i	$0.310045\pi$
$618$		0			0
$619$	−14.2737	−	8.24091i	−0.573708	−	0.331230i	0.184921	−	0.982753i	$-0.440797\pi$
$619$	−14.2737	−	8.24091i	−0.573708	−	0.331230i	−0.758629	+	0.651523i	$0.774130\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	11.8863	+	20.5876i	0.475450	+	0.823504i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.49147			0.298704
$630$		0			0
$631$	−34.8383			−1.38689			−0.693446	−	0.720508i	$-0.743909\pi$
$631$	−34.8383			−1.38689			−0.693446	+	0.720508i	$0.743909\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.41512	+	12.8434i	0.294260	+	0.509673i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	7.25538	+	4.18889i	0.286570	+	0.165451i	0.636394	−	0.771364i	$-0.280425\pi$
$641$	7.25538	+	4.18889i	0.286570	+	0.165451i	−0.349824	+	0.936815i	$0.613759\pi$
$642$		0			0
$643$	18.0021	−	10.3935i	0.709934	−	0.409881i	−0.101103	−	0.994876i	$-0.532237\pi$
$643$	18.0021	−	10.3935i	0.709934	−	0.409881i	0.811037	+	0.584995i	$0.198904\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.49540			−0.373303			−0.186651	−	0.982426i	$-0.559763\pi$
$647$	−9.49540			−0.373303			−0.186651	+	0.982426i	$0.559763\pi$
$648$		0			0
$649$			19.6818i			0.772579i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.64747	+	3.83792i	−0.260136	+	0.150189i	−0.624396	−	0.781108i	$-0.714655\pi$
$653$	−6.64747	+	3.83792i	−0.260136	+	0.150189i	0.364261	+	0.931297i	$0.381322\pi$
$654$		0			0
$655$	−14.9927	+	25.9680i	−0.585811	+	1.01465i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−38.0493	−	21.9678i	−1.48219	−	0.855743i	−0.482395	−	0.875954i	$-0.660233\pi$
$659$	−38.0493	−	21.9678i	−1.48219	−	0.855743i	−0.999796	+	0.0202102i	$0.993566\pi$
$660$		0			0
$661$	22.1649	−	12.7969i	0.862115	−	0.497742i	−0.00260513	−	0.999997i	$-0.500829\pi$
$661$	22.1649	−	12.7969i	0.862115	−	0.497742i	0.864720	+	0.502254i	$0.167496\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−31.0789			−1.20338
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.71051	+	9.89089i	0.220452	+	0.381834i
$672$		0			0
$673$	−7.64671	+	13.2445i	−0.294759	+	0.510538i	−0.974929	−	0.222517i	$-0.928573\pi$
$673$	−7.64671	+	13.2445i	−0.294759	+	0.510538i	0.680170	+	0.733055i	$0.261906\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.6459	+	39.2238i	−0.870352	+	1.50749i	−0.00871898	+	0.999962i	$0.502775\pi$
$677$	−22.6459	+	39.2238i	−0.870352	+	1.50749i	−0.861633	+	0.507532i	$0.830558\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			27.8157i			1.06434i	0.846638	+	0.532169i	$0.178623\pi$
$683$			27.8157i			1.06434i	−0.846638	+	0.532169i	$0.821377\pi$
$684$		0			0
$685$			43.8674i			1.67609i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.71672	+	8.16961i	0.179693	+	0.311237i
$690$		0			0
$691$	−14.1115	−	8.14729i	−0.536828	−	0.309938i	0.206965	−	0.978348i	$-0.433641\pi$
$691$	−14.1115	−	8.14729i	−0.536828	−	0.309938i	−0.743792	+	0.668411i	$0.766975\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.5862	−	10.7307i	−0.705013	−	0.407040i
$696$		0			0
$697$	−9.88831	−	17.1271i	−0.374546	−	0.648733i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	0.393403i		−	0.0148586i	−0.999972	−	0.00742932i	$-0.997635\pi$
$701$		−	0.393403i		−	0.0148586i	0.999972	−	0.00742932i	$-0.00236485\pi$
$702$		0			0
$703$			22.5143i			0.849143i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	16.3183	−	28.2641i	0.612846	−	1.06148i	−0.377912	−	0.925841i	$-0.623358\pi$
$709$	16.3183	−	28.2641i	0.612846	−	1.06148i	0.990758	−	0.135639i	$-0.0433087\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.41734	−	2.45491i	0.0530799	−	0.0919372i
$714$		0			0
$715$	5.40612	+	9.36368i	0.202178	+	0.350182i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.213207			−0.00795130			−0.00397565	−	0.999992i	$-0.501265\pi$
$719$	−0.213207			−0.00795130			−0.00397565	+	0.999992i	$0.501265\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.57409	−	0.908804i	0.0584604	−	0.0337521i
$726$		0			0
$727$	−31.8208	−	18.3717i	−1.18017	−	0.681370i	−0.224114	−	0.974563i	$-0.571949\pi$
$727$	−31.8208	−	18.3717i	−1.18017	−	0.681370i	−0.956053	+	0.293193i	$0.905282\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.35920	−	5.81831i	0.124245	−	0.215198i
$732$		0			0
$733$	9.41829	−	5.43765i	0.347873	−	0.200844i	−0.315875	−	0.948801i	$-0.602298\pi$
$733$	9.41829	−	5.43765i	0.347873	−	0.200844i	0.663748	+	0.747956i	$0.268965\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			8.55753i			0.315221i
$738$		0			0
$739$	−13.8256			−0.508584			−0.254292	−	0.967127i	$-0.581842\pi$
$739$	−13.8256			−0.508584			−0.254292	+	0.967127i	$0.581842\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.8751	−	9.16552i	0.582403	−	0.336250i	−0.179685	−	0.983724i	$-0.557508\pi$
$743$	15.8751	−	9.16552i	0.582403	−	0.336250i	0.762088	+	0.647474i	$0.224175\pi$
$744$		0			0
$745$	37.8776	+	21.8687i	1.38773	+	0.801206i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	9.97084	+	17.2700i	0.363841	+	0.630191i	0.988589	−	0.150635i	$-0.0481318\pi$
$751$	9.97084	+	17.2700i	0.363841	+	0.630191i	−0.624748	+	0.780826i	$0.714798\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	48.5362			1.76641
$756$		0			0
$757$	−46.9292			−1.70567			−0.852836	−	0.522178i	$-0.825119\pi$
$757$	−46.9292			−1.70567			−0.852836	+	0.522178i	$0.825119\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.7769	+	46.3789i	0.970661	+	1.68123i	0.693568	+	0.720391i	$0.256038\pi$
$761$	26.7769	+	46.3789i	0.970661	+	1.68123i	0.277093	+	0.960843i	$0.410629\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	39.3254	+	22.7045i	1.41996	+	0.819813i
$768$		0			0
$769$	34.7306	−	20.0517i	1.25242	−	0.723085i	0.280830	−	0.959758i	$-0.409390\pi$
$769$	34.7306	−	20.0517i	1.25242	−	0.723085i	0.971589	+	0.236673i	$0.0760570\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.6475			0.562801			0.281401	−	0.959590i	$-0.409201\pi$
$773$	15.6475			0.562801			0.281401	+	0.959590i	$0.409201\pi$
$774$		0			0
$775$			0.165783i			0.00595509i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	51.4724	−	29.7176i	1.84419	−	1.06474i
$780$		0			0
$781$	−8.56060	+	14.8274i	−0.306322	+	0.530566i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.1785	−	8.76333i	−0.541745	−	0.312777i
$786$		0			0
$787$	39.9920	−	23.0894i	1.42556	−	0.823048i	0.428795	−	0.903402i	$-0.358938\pi$
$787$	39.9920	−	23.0894i	1.42556	−	0.823048i	0.996766	+	0.0803536i	$0.0256050\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	26.3501			0.935719
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.9388	−	29.3388i	−0.600002	−	1.03923i	−0.992820	−	0.119618i	$-0.961833\pi$
$797$	−16.9388	−	29.3388i	−0.600002	−	1.03923i	0.392818	−	0.919616i	$-0.371500\pi$
$798$		0			0
$799$	−16.5840	+	28.7244i	−0.586701	+	1.01620i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.34922	+	5.80102i	−0.118191	+	0.204714i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	39.0142i		−	1.37167i	−0.727758	−	0.685834i	$-0.759438\pi$
$809$		−	39.0142i		−	1.37167i	0.727758	−	0.685834i	$-0.240562\pi$
$810$		0			0
$811$		−	7.73397i		−	0.271577i	−0.990738	−	0.135788i	$-0.956643\pi$
$811$		−	7.73397i		−	0.271577i	0.990738	−	0.135788i	$-0.0433567\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.5915	+	23.5411i	0.476088	+	0.824609i
$816$		0			0
$817$	17.4859	+	10.0955i	0.611755	+	0.353197i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.443638	−	0.256134i	−0.0154831	−	0.00893915i	0.492238	−	0.870460i	$-0.336179\pi$
$821$	−0.443638	−	0.256134i	−0.0154831	−	0.00893915i	−0.507722	+	0.861521i	$0.669512\pi$
$822$		0			0
$823$	24.1753	+	41.8728i	0.842698	+	1.45960i	0.887606	+	0.460604i	$0.152367\pi$
$823$	24.1753	+	41.8728i	0.842698	+	1.45960i	−0.0449080	+	0.998991i	$0.514299\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	17.3086i		−	0.601879i	−0.953643	−	0.300940i	$-0.902700\pi$
$827$		−	17.3086i		−	0.601879i	0.953643	−	0.300940i	$-0.0973003\pi$
$828$		0			0
$829$			38.1288i			1.32427i	0.749385	+	0.662134i	$0.230349\pi$
$829$			38.1288i			1.32427i	−0.749385	+	0.662134i	$0.769651\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	21.5241	−	37.2808i	0.744871	−	1.29015i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−15.2026	+	26.3317i	−0.524852	+	0.909071i	0.474729	+	0.880132i	$0.342546\pi$
$839$	−15.2026	+	26.3317i	−0.524852	+	0.909071i	−0.999581	+	0.0289389i	$0.990787\pi$
$840$		0			0
$841$	15.5394	+	26.9151i	0.535842	+	0.928106i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.43348			−0.118115
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.84358	−	5.68319i	0.337434	−	0.194817i
$852$		0			0
$853$	−27.7143	−	16.0008i	−0.948919	−	0.547858i	−0.0561738	−	0.998421i	$-0.517890\pi$
$853$	−27.7143	−	16.0008i	−0.948919	−	0.547858i	−0.892745	+	0.450563i	$0.851223\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.5774	+	39.1053i	−0.771230	+	1.33581i	0.165659	+	0.986183i	$0.447025\pi$
$857$	−22.5774	+	39.1053i	−0.771230	+	1.33581i	−0.936889	+	0.349627i	$0.886308\pi$
$858$		0			0
$859$	−15.7911	+	9.11701i	−0.538786	+	0.311068i	−0.744587	−	0.667526i	$-0.767353\pi$
$859$	−15.7911	+	9.11701i	−0.538786	+	0.311068i	0.205801	+	0.978594i	$0.434020\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			7.64373i			0.260195i	0.991501	+	0.130098i	$0.0415291\pi$
$863$			7.64373i			0.260195i	−0.991501	+	0.130098i	$0.958471\pi$
$864$		0			0
$865$	−3.98937			−0.135643
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.9069	−	6.87448i	0.403915	−	0.233201i
$870$		0			0
$871$	17.0984	+	9.87179i	0.579358	+	0.334493i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.01581	−	13.8838i	−0.270675	−	0.468822i	0.698360	−	0.715747i	$-0.253913\pi$
$877$	−8.01581	−	13.8838i	−0.270675	−	0.468822i	−0.969035	+	0.246924i	$0.920580\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	24.7532			0.833958			0.416979	−	0.908916i	$-0.363089\pi$
$881$	24.7532			0.833958			0.416979	+	0.908916i	$0.363089\pi$
$882$		0			0
$883$	−11.6958			−0.393595			−0.196798	−	0.980444i	$-0.563054\pi$
$883$	−11.6958			−0.393595			−0.196798	+	0.980444i	$0.563054\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.5429	+	47.7058i	0.924801	+	1.60180i	0.791880	+	0.610676i	$0.209102\pi$
$887$	27.5429	+	47.7058i	0.924801	+	1.60180i	0.132921	+	0.991127i	$0.457564\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−86.3261	−	49.8404i	−2.88879	−	1.66785i
$894$		0			0
$895$	−26.4541	+	15.2733i	−0.884262	+	0.510529i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.47975			−0.182760
$900$		0			0
$901$			7.37481i			0.245691i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	30.9281	−	17.8563i	1.02808	−	0.593565i
$906$		0			0
$907$	12.9383	−	22.4098i	0.429610	−	0.744107i	−0.567228	−	0.823560i	$-0.691984\pi$
$907$	12.9383	−	22.4098i	0.429610	−	0.744107i	0.996839	+	0.0794540i	$0.0253177\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.86306	+	2.23034i	0.127989	+	0.0738944i	0.562627	−	0.826711i	$-0.309791\pi$
$911$	3.86306	+	2.23034i	0.127989	+	0.0738944i	−0.434639	+	0.900605i	$0.643124\pi$
$912$		0			0
$913$	−4.33572	+	2.50323i	−0.143491	+	0.0828448i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	42.4704			1.40097			0.700485	−	0.713667i	$-0.252967\pi$
$919$	42.4704			1.40097			0.700485	+	0.713667i	$0.252967\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	19.7507	+	34.2091i	0.650101	+	1.12601i
$924$		0			0
$925$	−0.332373	+	0.575688i	−0.0109284	+	0.0189285i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.72508	−	13.3802i	0.253452	−	0.438991i	−0.711022	−	0.703170i	$-0.751767\pi$
$929$	7.72508	−	13.3802i	0.253452	−	0.438991i	0.964474	+	0.264178i	$0.0851008\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$			8.45272i			0.276433i
$936$		0			0
$937$		−	46.1410i		−	1.50736i	−0.657241	−	0.753680i	$-0.728277\pi$
$937$		−	46.1410i		−	1.50736i	0.657241	−	0.753680i	$-0.271723\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.5052	+	35.5161i	0.668451	+	1.15779i	0.978337	+	0.207017i	$0.0663756\pi$
$941$	20.5052	+	35.5161i	0.668451	+	1.15779i	−0.309886	+	0.950774i	$0.600291\pi$
$942$		0			0
$943$	−25.9859	−	15.0030i	−0.846218	−	0.488564i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.50657	−	4.91127i	−0.276426	−	0.159595i	0.355378	−	0.934723i	$-0.384352\pi$
$947$	−8.50657	−	4.91127i	−0.276426	−	0.159595i	−0.631804	+	0.775128i	$0.717685\pi$
$948$		0			0
$949$	7.72718	+	13.3839i	0.250835	+	0.434459i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	17.0826i		−	0.553359i	−0.960962	−	0.276679i	$-0.910766\pi$
$953$		−	17.0826i		−	0.553359i	0.960962	−	0.276679i	$-0.0892340\pi$
$954$		0			0
$955$		−	29.8265i		−	0.965163i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.2501	+	26.4139i	−0.491939	+	0.852063i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.77826	+	8.27619i	−0.153818	+	0.266420i
$966$		0			0
$967$	21.3240	+	36.9343i	0.685735	+	1.18773i	0.973205	+	0.229938i	$0.0738523\pi$
$967$	21.3240	+	36.9343i	0.685735	+	1.18773i	−0.287471	+	0.957789i	$0.592814\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.5124			−0.754549			−0.377275	−	0.926101i	$-0.623139\pi$
$971$	−23.5124			−0.754549			−0.377275	+	0.926101i	$0.623139\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−30.1944	+	17.4327i	−0.966003	+	0.557722i	−0.898015	−	0.439964i	$-0.854991\pi$
$977$	−30.1944	+	17.4327i	−0.966003	+	0.557722i	−0.0679878	+	0.997686i	$0.521658\pi$
$978$		0			0
$979$	11.7229	+	6.76824i	0.374666	+	0.216314i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.1804	+	22.8292i	−0.420390	+	0.728137i	−0.995978	−	0.0896033i	$-0.971440\pi$
$983$	−13.1804	+	22.8292i	−0.420390	+	0.728137i	0.575587	+	0.817740i	$0.304773\pi$
$984$		0			0
$985$	−1.90194	+	1.09808i	−0.0606008	+	0.0349879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	10.1935i		−	0.324133i
$990$		0			0
$991$	−0.161043			−0.00511568			−0.00255784	−	0.999997i	$-0.500814\pi$
$991$	−0.161043			−0.00511568			−0.00255784	+	0.999997i	$0.500814\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.3916	−	7.15427i	0.392839	−	0.226806i
$996$		0			0
$997$	14.5820	+	8.41890i	0.461816	+	0.266629i	0.712807	−	0.701360i	$-0.247423\pi$
$997$	14.5820	+	8.41890i	0.461816	+	0.266629i	−0.250992	+	0.967989i	$0.580757\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5292.2.x.b.4409.6		16
3.2	odd	2		1764.2.x.b.1469.2		16
7.2	even	3		5292.2.w.b.521.6		16
7.3	odd	6		5292.2.bm.a.4625.6		16
7.4	even	3		756.2.bm.a.89.3		16
7.5	odd	6		756.2.w.a.521.3		16
7.6	odd	2		5292.2.x.a.4409.3		16
9.4	even	3		1764.2.x.a.293.7		16
9.5	odd	6		5292.2.x.a.881.3		16
21.2	odd	6		1764.2.w.b.1109.7		16
21.5	even	6		252.2.w.a.101.2	yes	16
21.11	odd	6		252.2.bm.a.173.4	yes	16
21.17	even	6		1764.2.bm.a.1685.5		16
21.20	even	2		1764.2.x.a.1469.7		16
28.11	odd	6		3024.2.df.d.1601.3		16
28.19	even	6		3024.2.ca.d.2033.3		16
63.4	even	3		252.2.w.a.5.2	✓	16
63.5	even	6		756.2.bm.a.17.3		16
63.11	odd	6		2268.2.t.a.2105.3		16
63.13	odd	6		1764.2.x.b.293.2		16
63.23	odd	6		5292.2.bm.a.2285.6		16
63.25	even	3		2268.2.t.b.2105.6		16
63.31	odd	6		1764.2.w.b.509.7		16
63.32	odd	6		756.2.w.a.341.3		16
63.40	odd	6		252.2.bm.a.185.4	yes	16
63.41	even	6	inner	5292.2.x.b.881.6		16
63.47	even	6		2268.2.t.b.1781.6		16
63.58	even	3		1764.2.bm.a.1697.5		16
63.59	even	6		5292.2.w.b.1097.6		16
63.61	odd	6		2268.2.t.a.1781.3		16
84.11	even	6		1008.2.df.d.929.5		16
84.47	odd	6		1008.2.ca.d.353.7		16
252.67	odd	6		1008.2.ca.d.257.7		16
252.95	even	6		3024.2.ca.d.2609.3		16
252.103	even	6		1008.2.df.d.689.5		16
252.131	odd	6		3024.2.df.d.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	63.4	even	3
252.2.w.a.101.2	yes	16	21.5	even	6
252.2.bm.a.173.4	yes	16	21.11	odd	6
252.2.bm.a.185.4	yes	16	63.40	odd	6
756.2.w.a.341.3		16	63.32	odd	6
756.2.w.a.521.3		16	7.5	odd	6
756.2.bm.a.17.3		16	63.5	even	6
756.2.bm.a.89.3		16	7.4	even	3
1008.2.ca.d.257.7		16	252.67	odd	6
1008.2.ca.d.353.7		16	84.47	odd	6
1008.2.df.d.689.5		16	252.103	even	6
1008.2.df.d.929.5		16	84.11	even	6
1764.2.w.b.509.7		16	63.31	odd	6
1764.2.w.b.1109.7		16	21.2	odd	6
1764.2.x.a.293.7		16	9.4	even	3
1764.2.x.a.1469.7		16	21.20	even	2
1764.2.x.b.293.2		16	63.13	odd	6
1764.2.x.b.1469.2		16	3.2	odd	2
1764.2.bm.a.1685.5		16	21.17	even	6
1764.2.bm.a.1697.5		16	63.58	even	3
2268.2.t.a.1781.3		16	63.61	odd	6
2268.2.t.a.2105.3		16	63.11	odd	6
2268.2.t.b.1781.6		16	63.47	even	6
2268.2.t.b.2105.6		16	63.25	even	3
3024.2.ca.d.2033.3		16	28.19	even	6
3024.2.ca.d.2609.3		16	252.95	even	6
3024.2.df.d.17.3		16	252.131	odd	6
3024.2.df.d.1601.3		16	28.11	odd	6
5292.2.w.b.521.6		16	7.2	even	3
5292.2.w.b.1097.6		16	63.59	even	6
5292.2.x.a.881.3		16	9.5	odd	6
5292.2.x.a.4409.3		16	7.6	odd	2
5292.2.x.b.881.6		16	63.41	even	6	inner
5292.2.x.b.4409.6		16	1.1	even	1	trivial
5292.2.bm.a.2285.6		16	63.23	odd	6
5292.2.bm.a.4625.6		16	7.3	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.x (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09150 + 1.89054i) q^{5} +O(q^{10})\)	\(q+(1.09150 + 1.89054i) q^{5} +(-1.26889 - 0.732592i) q^{11} +(-2.92752 + 1.69021i) q^{13} -2.64271 q^{17} -7.94221i q^{19} +(-3.47245 + 2.00482i) q^{23} +(0.117249 - 0.203081i) q^{25} +(6.71261 + 3.87553i) q^{29} +(-0.612252 + 0.353484i) q^{31} -2.83477 q^{37} +(3.74173 + 6.48086i) q^{41} +(-1.27112 + 2.20164i) q^{43} +(6.27538 - 10.8693i) q^{47} -2.79062i q^{53} -3.19850i q^{55} +(-6.71650 - 11.6333i) q^{59} +(-6.75061 - 3.89747i) q^{61} +(-6.39079 - 3.68972i) q^{65} +(-2.92029 - 5.05809i) q^{67} -11.6854i q^{71} -4.57174i q^{73} +(-4.69189 + 8.12659i) q^{79} +(1.70847 - 2.95917i) q^{83} +(-2.88452 - 4.99614i) q^{85} -9.23875 q^{89} +(15.0150 - 8.66894i) q^{95} +(-6.38394 - 3.68577i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 6 q^{11} + 3 q^{13} - 18 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{29} - 6 q^{31} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - q^{79} + 6 q^{85} - 42 q^{89} + 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q - 6 * q^11 + 3 * q^13 - 18 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^29 - 6 * q^31 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - q^79 + 6 * q^85 - 42 * q^89 + 6 * q^95 + 3 * q^97

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