LMFDB - Embedded newform 5292.2.x.b.4409.1

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			4409.1
Root			$-0.544978 - 1.64408i$ of defining polynomial
Character	$\chi$	$=$	5292.4409
Dual form			5292.2.x.b.881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95741 - 3.39033i) q^{5} +O(q^{10})$	$q+(-1.95741 - 3.39033i) q^{5} +(-3.19958 - 1.84728i) q^{11} +(-0.480242 + 0.277268i) q^{13} -5.83832 q^{17} -5.33973i q^{19} +(-1.96965 + 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(-3.53638 - 2.04173i) q^{29} +(7.00132 - 4.04222i) q^{31} -7.79699 q^{37} +(3.59234 + 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(1.41416 - 2.44940i) q^{47} -0.0479960i q^{53} +14.4635i q^{55} +(4.45656 + 7.71900i) q^{59} +(-6.03343 - 3.48340i) q^{61} +(1.88006 + 1.08545i) q^{65} +(-0.587402 - 1.01741i) q^{67} +6.71061i q^{71} -4.07253i q^{73} +(1.97374 - 3.41861i) q^{79} +(3.84674 - 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +5.42600 q^{89} +(-18.1035 + 10.4520i) q^{95} +(-13.9874 - 8.07563i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.95741	−	3.39033i	−0.875381	−	1.51620i	−0.856357	−	0.516385i	$-0.827278\pi$
$5$	−1.95741	−	3.39033i	−0.875381	−	1.51620i	−0.0190238	−	0.999819i	$-0.506056\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.19958	−	1.84728i	−0.964710	−	0.556976i	−0.0670908	−	0.997747i	$-0.521372\pi$
$11$	−3.19958	−	1.84728i	−0.964710	−	0.556976i	−0.897620	+	0.440771i	$0.854705\pi$
$12$		0			0
$13$	−0.480242	+	0.277268i	−0.133195	+	0.0769002i	−0.565117	−	0.825011i	$-0.691169\pi$
$13$	−0.480242	+	0.277268i	−0.133195	+	0.0769002i	0.431922	+	0.901911i	$0.357836\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.83832			−1.41600			−0.708000	−	0.706213i	$-0.750402\pi$
$17$	−5.83832			−1.41600			−0.708000	+	0.706213i	$0.750402\pi$
$18$		0			0
$19$		−	5.33973i		−	1.22502i	−0.790464	−	0.612509i	$-0.790160\pi$
$19$		−	5.33973i		−	1.22502i	0.790464	−	0.612509i	$-0.209840\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.96965	+	1.13718i	−0.410700	+	0.237118i	−0.691090	−	0.722768i	$-0.742869\pi$
$23$	−1.96965	+	1.13718i	−0.410700	+	0.237118i	0.280390	+	0.959886i	$0.409536\pi$
$24$		0			0
$25$	−5.16291	+	8.94242i	−1.03258	+	1.78848i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.53638	−	2.04173i	−0.656690	−	0.379140i	0.134325	−	0.990937i	$-0.457113\pi$
$29$	−3.53638	−	2.04173i	−0.656690	−	0.379140i	−0.791014	+	0.611797i	$0.790447\pi$
$30$		0			0
$31$	7.00132	−	4.04222i	1.25748	−	0.726004i	0.284892	−	0.958560i	$-0.408042\pi$
$31$	7.00132	−	4.04222i	1.25748	−	0.726004i	0.972583	+	0.232556i	$0.0747089\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.79699			−1.28182			−0.640909	−	0.767617i	$-0.721442\pi$
$37$	−7.79699			−1.28182			−0.640909	+	0.767617i	$0.721442\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.59234	+	6.22212i	0.561030	+	0.971732i	0.997407	+	0.0719684i	$0.0229281\pi$
$41$	3.59234	+	6.22212i	0.561030	+	0.971732i	−0.436377	+	0.899764i	$0.643739\pi$
$42$		0			0
$43$	−0.754009	+	1.30598i	−0.114985	+	0.199160i	−0.917774	−	0.397103i	$-0.870015\pi$
$43$	−0.754009	+	1.30598i	−0.114985	+	0.199160i	0.802789	+	0.596264i	$0.203349\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.41416	−	2.44940i	0.206277	−	0.357282i	−0.744262	−	0.667888i	$-0.767199\pi$
$47$	1.41416	−	2.44940i	0.206277	−	0.357282i	0.950539	+	0.310606i	$0.100532\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	0.0479960i		−	0.00659276i	−0.999995	−	0.00329638i	$-0.998951\pi$
$53$		−	0.0479960i		−	0.00659276i	0.999995	−	0.00329638i	$-0.00104927\pi$
$54$		0			0
$55$			14.4635i			1.95026i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.45656	+	7.71900i	0.580195	+	1.00493i	0.995456	+	0.0952251i	$0.0303571\pi$
$59$	4.45656	+	7.71900i	0.580195	+	1.00493i	−0.415261	+	0.909703i	$0.636310\pi$
$60$		0			0
$61$	−6.03343	−	3.48340i	−0.772501	−	0.446004i	0.0612648	−	0.998122i	$-0.480487\pi$
$61$	−6.03343	−	3.48340i	−0.772501	−	0.446004i	−0.833766	+	0.552118i	$0.813820\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.88006	+	1.08545i	0.233193	+	0.134634i
$66$		0			0
$67$	−0.587402	−	1.01741i	−0.0717626	−	0.124296i	0.827911	−	0.560859i	$-0.189529\pi$
$67$	−0.587402	−	1.01741i	−0.0717626	−	0.124296i	−0.899674	+	0.436563i	$0.856196\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			6.71061i			0.796403i	0.917298	+	0.398202i	$0.130366\pi$
$71$			6.71061i			0.796403i	−0.917298	+	0.398202i	$0.869634\pi$
$72$		0			0
$73$		−	4.07253i		−	0.476654i	−0.971185	−	0.238327i	$-0.923401\pi$
$73$		−	4.07253i		−	0.476654i	0.971185	−	0.238327i	$-0.0765990\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	1.97374	−	3.41861i	0.222063	−	0.384624i	−0.733371	−	0.679828i	$-0.762054\pi$
$79$	1.97374	−	3.41861i	0.222063	−	0.384624i	0.955434	+	0.295204i	$0.0953877\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.84674	−	6.66275i	0.422235	−	0.731332i	−0.573923	−	0.818909i	$-0.694579\pi$
$83$	3.84674	−	6.66275i	0.422235	−	0.731332i	0.996158	+	0.0875774i	$0.0279125\pi$
$84$		0			0
$85$	11.4280	+	19.7938i	1.23954	+	2.14694i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.42600			0.575155			0.287577	−	0.957757i	$-0.407150\pi$
$89$	5.42600			0.575155			0.287577	+	0.957757i	$0.407150\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−18.1035	+	10.4520i	−1.85738	+	1.07236i
$96$		0			0
$97$	−13.9874	−	8.07563i	−1.42021	−	0.819956i	−0.423890	−	0.905714i	$-0.639336\pi$
$97$	−13.9874	−	8.07563i	−1.42021	−	0.819956i	−0.996316	+	0.0857571i	$0.972669\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.811750	−	1.40599i	0.0807722	−	0.139901i	−0.822810	−	0.568317i	$-0.807595\pi$
$101$	0.811750	−	1.40599i	0.0807722	−	0.139901i	0.903582	+	0.428416i	$0.140928\pi$
$102$		0			0
$103$	−0.342653	+	0.197831i	−0.0337626	+	0.0194929i	−0.516786	−	0.856114i	$-0.672872\pi$
$103$	−0.342653	+	0.197831i	−0.0337626	+	0.0194929i	0.483024	+	0.875607i	$0.339539\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.66700i			0.547850i	0.961751	+	0.273925i	$0.0883219\pi$
$107$			5.66700i			0.547850i	−0.961751	+	0.273925i	$0.911678\pi$
$108$		0			0
$109$	13.5133			1.29434			0.647171	−	0.762345i	$-0.275952\pi$
$109$	13.5133			1.29434			0.647171	+	0.762345i	$0.275952\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.13651	+	0.656162i	−0.106913	+	0.0617265i	−0.552503	−	0.833511i	$-0.686327\pi$
$113$	−1.13651	+	0.656162i	−0.106913	+	0.0617265i	0.445590	+	0.895237i	$0.352994\pi$
$114$		0			0
$115$	7.71082	+	4.45184i	0.719038	+	0.415137i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.32489	+	2.29477i	0.120444	+	0.208615i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	20.8496			1.86485
$126$		0			0
$127$	−17.3935			−1.54342			−0.771710	−	0.635975i	$-0.780598\pi$
$127$	−17.3935			−1.54342			−0.771710	+	0.635975i	$0.780598\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.45361	+	9.44593i	0.476484	+	0.825295i	0.999637	−	0.0269442i	$-0.00857764\pi$
$131$	5.45361	+	9.44593i	0.476484	+	0.825295i	−0.523153	+	0.852239i	$0.675244\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.62547	+	4.40257i	0.651488	+	0.376137i	0.789026	−	0.614360i	$-0.210586\pi$
$137$	7.62547	+	4.40257i	0.651488	+	0.376137i	−0.137538	+	0.990496i	$0.543919\pi$
$138$		0			0
$139$	14.2352	−	8.21869i	1.20741	−	0.697100i	0.245220	−	0.969468i	$-0.421140\pi$
$139$	14.2352	−	8.21869i	1.20741	−	0.697100i	0.962193	+	0.272367i	$0.0878066\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.04876			0.171326
$144$		0			0
$145$			15.9860i			1.32757i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.5814	−	7.26390i	1.03071	−	0.595082i	0.113523	−	0.993535i	$-0.463786\pi$
$149$	12.5814	−	7.26390i	1.03071	−	0.595082i	0.917188	+	0.398454i	$0.130453\pi$
$150$		0			0
$151$	−2.80307	+	4.85505i	−0.228110	+	0.395099i	−0.957248	−	0.289268i	$-0.906588\pi$
$151$	−2.80307	+	4.85505i	−0.228110	+	0.395099i	0.729138	+	0.684367i	$0.239921\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−27.4089	−	15.8246i	−2.20154	−	1.27106i
$156$		0			0
$157$	15.4411	−	8.91493i	1.23233	−	0.711489i	0.264819	−	0.964298i	$-0.414688\pi$
$157$	15.4411	−	8.91493i	1.23233	−	0.711489i	0.967516	+	0.252809i	$0.0813545\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	1.15399			0.0903874			0.0451937	−	0.998978i	$-0.485610\pi$
$163$	1.15399			0.0903874			0.0451937	+	0.998978i	$0.485610\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.95550	−	15.5114i	−0.692997	−	1.20031i	−0.970851	−	0.239683i	$-0.922957\pi$
$167$	−8.95550	−	15.5114i	−0.692997	−	1.20031i	0.277854	−	0.960623i	$-0.410377\pi$
$168$		0			0
$169$	−6.34625	+	10.9920i	−0.488173	+	0.845540i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.74814	+	6.49197i	−0.284966	+	0.493576i	−0.972601	−	0.232481i	$-0.925316\pi$
$173$	−3.74814	+	6.49197i	−0.284966	+	0.493576i	0.687635	+	0.726057i	$0.258649\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$			0.720974i			0.0538881i	0.999637	+	0.0269441i	$0.00857760\pi$
$179$			0.720974i			0.0538881i	−0.999637	+	0.0269441i	$0.991422\pi$
$180$		0			0
$181$		−	5.07121i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$181$		−	5.07121i		−	0.376940i	0.982079	−	0.188470i	$-0.0603529\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	15.2619	+	26.4344i	1.12208	+	1.94350i
$186$		0			0
$187$	18.6802	+	10.7850i	1.36603	+	0.788678i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.0005	−	6.35111i	−0.795965	−	0.459551i	0.0460934	−	0.998937i	$-0.485323\pi$
$191$	−11.0005	−	6.35111i	−0.795965	−	0.459551i	−0.842058	+	0.539387i	$0.818656\pi$
$192$		0			0
$193$	11.4076	+	19.7586i	0.821140	+	1.42226i	0.904834	+	0.425765i	$0.139995\pi$
$193$	11.4076	+	19.7586i	0.821140	+	1.42226i	−0.0836931	+	0.996492i	$0.526672\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			0.0311360i			0.00221835i	0.999999	+	0.00110918i	$0.000353062\pi$
$197$			0.0311360i			0.00221835i	−0.999999	+	0.00110918i	$0.999647\pi$
$198$		0			0
$199$			22.9952i			1.63008i	0.579402	+	0.815042i	$0.303286\pi$
$199$			22.9952i			1.63008i	−0.579402	+	0.815042i	$0.696714\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	14.0634	−	24.3585i	0.982229	−	1.70127i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.86397	+	17.0849i	−0.682305	+	1.18179i
$210$		0			0
$211$	8.55841	+	14.8236i	0.589185	+	1.02050i	0.994339	+	0.106250i	$0.0338845\pi$
$211$	8.55841	+	14.8236i	0.589185	+	1.02050i	−0.405154	+	0.914248i	$0.632782\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.90362			0.402623
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.80380	−	1.61878i	0.188604	−	0.108891i
$222$		0			0
$223$	−1.25230	−	0.723016i	−0.0838602	−	0.0484167i	0.457484	−	0.889218i	$-0.348751\pi$
$223$	−1.25230	−	0.723016i	−0.0838602	−	0.0484167i	−0.541344	+	0.840801i	$0.682084\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.23596	+	3.87280i	−0.148406	+	0.257047i	−0.930639	−	0.365940i	$-0.880748\pi$
$227$	−2.23596	+	3.87280i	−0.148406	+	0.257047i	0.782232	+	0.622987i	$0.214081\pi$
$228$		0			0
$229$	2.24072	−	1.29368i	0.148071	−	0.0854888i	−0.424134	−	0.905599i	$-0.639421\pi$
$229$	2.24072	−	1.29368i	0.148071	−	0.0854888i	0.572205	+	0.820111i	$0.306088\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	17.4078i		−	1.14042i	−0.821498	−	0.570211i	$-0.806862\pi$
$233$		−	17.4078i		−	1.14042i	0.821498	−	0.570211i	$-0.193138\pi$
$234$		0			0
$235$	−11.0724			−0.722284
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.23642	+	2.44590i	−0.274031	+	0.158212i	−0.630718	−	0.776012i	$-0.717240\pi$
$239$	−4.23642	+	2.44590i	−0.274031	+	0.158212i	0.356687	+	0.934224i	$0.383906\pi$
$240$		0			0
$241$	7.04282	+	4.06618i	0.453668	+	0.261925i	0.709378	−	0.704828i	$-0.248976\pi$
$241$	7.04282	+	4.06618i	0.453668	+	0.261925i	−0.255710	+	0.966754i	$0.582309\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.48053	+	2.56436i	0.0942041	+	0.163166i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.9341			−1.63694			−0.818472	−	0.574546i	$-0.805179\pi$
$251$	−25.9341			−1.63694			−0.818472	+	0.574546i	$0.805179\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.4115	+	26.6935i	0.961344	+	1.66510i	0.719131	+	0.694874i	$0.244540\pi$
$257$	15.4115	+	26.6935i	0.961344	+	1.66510i	0.242213	+	0.970223i	$0.422127\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.6625	−	9.04276i	−0.965792	−	0.557600i	−0.0678413	−	0.997696i	$-0.521611\pi$
$263$	−15.6625	−	9.04276i	−0.965792	−	0.557600i	−0.897951	+	0.440096i	$0.854944\pi$
$264$		0			0
$265$	−0.162723	+	0.0939479i	−0.00999597	+	0.00577117i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	21.6406			1.31945			0.659725	−	0.751507i	$-0.270673\pi$
$269$	21.6406			1.31945			0.659725	+	0.751507i	$0.270673\pi$
$270$		0			0
$271$			14.2551i			0.865937i	0.901409	+	0.432968i	$0.142534\pi$
$271$			14.2551i			0.865937i	−0.901409	+	0.432968i	$0.857466\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	33.0383	−	19.0747i	1.99229	−	1.15025i
$276$		0			0
$277$	−4.40164	+	7.62386i	−0.264469	+	0.458073i	−0.967424	−	0.253160i	$-0.918530\pi$
$277$	−4.40164	+	7.62386i	−0.264469	+	0.458073i	0.702956	+	0.711234i	$0.251863\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.6889	+	9.63537i	0.995579	+	0.574798i	0.906937	−	0.421266i	$-0.138414\pi$
$281$	16.6889	+	9.63537i	0.995579	+	0.574798i	0.0886417	+	0.996064i	$0.471747\pi$
$282$		0			0
$283$	8.32822	−	4.80830i	0.495061	−	0.285824i	−0.231611	−	0.972809i	$-0.574399\pi$
$283$	8.32822	−	4.80830i	0.495061	−	0.285824i	0.726672	+	0.686985i	$0.241066\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	17.0859			1.00506
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.22598	+	2.12346i	0.0716225	+	0.124054i	0.899613	−	0.436689i	$-0.143849\pi$
$293$	1.22598	+	2.12346i	0.0716225	+	0.124054i	−0.827990	+	0.560743i	$0.810516\pi$
$294$		0			0
$295$	17.4467	−	30.2185i	1.01578	−	1.75939i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.630605	−	1.09224i	0.0364688	−	0.0631658i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$			27.2738i			1.56169i
$306$		0			0
$307$		−	10.6839i		−	0.609760i	−0.952391	−	0.304880i	$-0.901384\pi$
$307$		−	10.6839i		−	0.609760i	0.952391	−	0.304880i	$-0.0986163\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.3833	+	17.9843i	0.588780	+	1.01980i	0.994393	+	0.105752i	$0.0337250\pi$
$311$	10.3833	+	17.9843i	0.588780	+	1.01980i	−0.405612	+	0.914045i	$0.632942\pi$
$312$		0			0
$313$	−3.40449	−	1.96558i	−0.192433	−	0.111101i	0.400688	−	0.916215i	$-0.368771\pi$
$313$	−3.40449	−	1.96558i	−0.192433	−	0.111101i	−0.593121	+	0.805113i	$0.702104\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.98369	+	1.14528i	0.111415	+	0.0643256i	0.554672	−	0.832069i	$-0.312844\pi$
$317$	1.98369	+	1.14528i	0.111415	+	0.0643256i	−0.443257	+	0.896395i	$0.646177\pi$
$318$		0			0
$319$	7.54330	+	13.0654i	0.422344	+	0.731521i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			31.1750i			1.73462i
$324$		0			0
$325$		−	5.72603i		−	0.317623i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.46788	+	6.00655i	−0.190612	+	0.330150i	−0.945453	−	0.325758i	$-0.894381\pi$
$331$	−3.46788	+	6.00655i	−0.190612	+	0.330150i	0.754841	+	0.655908i	$0.227714\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.29957	+	3.98298i	−0.125639	+	0.217613i
$336$		0			0
$337$	−9.59771	−	16.6237i	−0.522821	−	0.905552i	−0.999647	−	0.0265545i	$-0.991546\pi$
$337$	−9.59771	−	16.6237i	−0.522821	−	0.905552i	0.476827	−	0.878997i	$-0.341787\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−29.8684			−1.61747
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.35287	+	4.24518i	−0.394723	+	0.227893i	−0.684204	−	0.729290i	$-0.739850\pi$
$347$	−7.35287	+	4.24518i	−0.394723	+	0.227893i	0.289482	+	0.957184i	$0.406517\pi$
$348$		0			0
$349$	16.5478	+	9.55386i	0.885782	+	0.511407i	0.872560	−	0.488506i	$-0.162458\pi$
$349$	16.5478	+	9.55386i	0.885782	+	0.511407i	0.0132216	+	0.999913i	$0.495791\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.82951	−	11.8291i	0.363498	−	0.629597i	−0.625036	−	0.780596i	$-0.714916\pi$
$353$	6.82951	−	11.8291i	0.363498	−	0.629597i	0.988534	+	0.150999i	$0.0482490\pi$
$354$		0			0
$355$	22.7512	−	13.1354i	1.20751	−	0.697156i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			17.1945i			0.907490i	0.891132	+	0.453745i	$0.149912\pi$
$359$			17.1945i			0.907490i	−0.891132	+	0.453745i	$0.850088\pi$
$360$		0			0
$361$	−9.51270			−0.500668
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.8073	+	7.97162i	−0.722705	+	0.417254i
$366$		0			0
$367$	14.6001	+	8.42936i	0.762118	+	0.440009i	0.830056	−	0.557680i	$-0.188309\pi$
$367$	14.6001	+	8.42936i	0.762118	+	0.440009i	−0.0679376	+	0.997690i	$0.521642\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.704288	+	1.21986i	0.0364667	+	0.0631621i	0.883683	−	0.468086i	$-0.155056\pi$
$373$	0.704288	+	1.21986i	0.0364667	+	0.0631621i	−0.847216	+	0.531248i	$0.821723\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.26442			0.116624
$378$		0			0
$379$	−0.598572			−0.0307466			−0.0153733	−	0.999882i	$-0.504894\pi$
$379$	−0.598572			−0.0307466			−0.0153733	+	0.999882i	$0.504894\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.26039	−	7.37921i	−0.217696	−	0.377060i	0.736407	−	0.676538i	$-0.236521\pi$
$383$	−4.26039	−	7.37921i	−0.217696	−	0.377060i	−0.954103	+	0.299478i	$0.903187\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−29.9624	−	17.2988i	−1.51915	−	0.877084i	−0.999746	−	0.0225587i	$-0.992819\pi$
$389$	−29.9624	−	17.2988i	−1.51915	−	0.877084i	−0.519409	−	0.854526i	$-0.673848\pi$
$390$		0			0
$391$	11.4994	−	6.63920i	0.581551	−	0.335759i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−15.4537			−0.777558
$396$		0			0
$397$		−	32.2821i		−	1.62019i	−0.586296	−	0.810097i	$-0.699414\pi$
$397$		−	32.2821i		−	1.62019i	0.586296	−	0.810097i	$-0.300586\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.3473	−	6.55139i	0.566659	−	0.327161i	−0.189155	−	0.981947i	$-0.560575\pi$
$401$	11.3473	−	6.55139i	0.566659	−	0.327161i	0.755814	+	0.654787i	$0.227242\pi$
$402$		0			0
$403$	−2.24155	+	3.88248i	−0.111660	+	0.193400i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	24.9471	+	14.4032i	1.23658	+	0.713941i
$408$		0			0
$409$	−32.3493	+	18.6769i	−1.59957	+	0.923513i	−0.608002	+	0.793936i	$0.708029\pi$
$409$	−32.3493	+	18.6769i	−1.59957	+	0.923513i	−0.991569	+	0.129577i	$0.958638\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−30.1186			−1.47846
$416$		0			0
$417$		0			0
$418$		0			0
$419$	14.1954	+	24.5871i	0.693490	+	1.20116i	0.970687	+	0.240346i	$0.0772610\pi$
$419$	14.1954	+	24.5871i	0.693490	+	1.20116i	−0.277198	+	0.960813i	$0.589406\pi$
$420$		0			0
$421$	−17.3359	+	30.0267i	−0.844901	+	1.46341i	0.0408054	+	0.999167i	$0.487008\pi$
$421$	−17.3359	+	30.0267i	−0.844901	+	1.46341i	−0.885707	+	0.464245i	$0.846326\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	30.1427	−	52.2087i	1.46214	−	2.53249i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$			15.2240i			0.733315i	0.930356	+	0.366657i	$0.119498\pi$
$431$			15.2240i			0.733315i	−0.930356	+	0.366657i	$0.880502\pi$
$432$		0			0
$433$			3.97041i			0.190806i	0.995439	+	0.0954028i	$0.0304139\pi$
$433$			3.97041i			0.190806i	−0.995439	+	0.0954028i	$0.969586\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.07222	+	10.5174i	0.290474	+	0.503115i
$438$		0			0
$439$	−8.21910	−	4.74530i	−0.392276	−	0.226481i	0.290870	−	0.956763i	$-0.406055\pi$
$439$	−8.21910	−	4.74530i	−0.392276	−	0.226481i	−0.683146	+	0.730282i	$0.739389\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−28.3955	−	16.3942i	−1.34911	−	0.778910i	−0.360989	−	0.932570i	$-0.617561\pi$
$443$	−28.3955	−	16.3942i	−1.34911	−	0.778910i	−0.988124	+	0.153660i	$0.950894\pi$
$444$		0			0
$445$	−10.6209	−	18.3960i	−0.503479	−	0.872052i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.658896i		−	0.0310952i	−0.999879	−	0.0155476i	$-0.995051\pi$
$449$		−	0.658896i		−	0.0310952i	0.999879	−	0.0155476i	$-0.00494916\pi$
$450$		0			0
$451$		−	26.5443i		−	1.24992i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−7.94514	+	13.7614i	−0.371658	+	0.643730i	−0.989821	−	0.142320i	$-0.954544\pi$
$457$	−7.94514	+	13.7614i	−0.371658	+	0.643730i	0.618163	+	0.786050i	$0.287877\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.81626	+	17.0023i	−0.457189	+	0.791874i	−0.998811	−	0.0487477i	$-0.984477\pi$
$461$	−9.81626	+	17.0023i	−0.457189	+	0.791874i	0.541622	+	0.840622i	$0.317810\pi$
$462$		0			0
$463$	0.600159	+	1.03951i	0.0278918	+	0.0483099i	0.879634	−	0.475651i	$-0.157787\pi$
$463$	0.600159	+	1.03951i	0.0278918	+	0.0483099i	−0.851743	+	0.523960i	$0.824454\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−38.5618			−1.78443			−0.892213	−	0.451614i	$-0.850848\pi$
$467$	−38.5618			−1.78443			−0.892213	+	0.451614i	$0.850848\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.82503	−	2.78573i	0.221855	−	0.128088i
$474$		0			0
$475$	47.7501	+	27.5685i	2.19093	+	1.26493i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.61289	+	6.25771i	−0.165077	+	0.285922i	−0.936683	−	0.350179i	$-0.886121\pi$
$479$	−3.61289	+	6.25771i	−0.165077	+	0.285922i	0.771606	+	0.636101i	$0.219454\pi$
$480$		0			0
$481$	3.74444	−	2.16185i	0.170732	−	0.0985720i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			63.2293i			2.87110i
$486$		0			0
$487$	−9.71539			−0.440247			−0.220123	−	0.975472i	$-0.570646\pi$
$487$	−9.71539			−0.440247			−0.220123	+	0.975472i	$0.570646\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.2480	+	9.95814i	−0.778392	+	0.449405i	−0.835860	−	0.548943i	$-0.815031\pi$
$491$	−17.2480	+	9.95814i	−0.778392	+	0.449405i	0.0574682	+	0.998347i	$0.481697\pi$
$492$		0			0
$493$	20.6465	+	11.9203i	0.929872	+	0.536862i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−17.1920	−	29.7774i	−0.769619	−	1.33302i	−0.937770	−	0.347258i	$-0.887113\pi$
$499$	−17.1920	−	29.7774i	−0.769619	−	1.33302i	0.168150	−	0.985761i	$-0.446221\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.22542			0.0546388			0.0273194	−	0.999627i	$-0.491303\pi$
$503$	1.22542			0.0546388			0.0273194	+	0.999627i	$0.491303\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.05078	+	8.74820i	0.223872	+	0.387757i	0.955980	−	0.293431i	$-0.0947970\pi$
$509$	5.05078	+	8.74820i	0.223872	+	0.387757i	−0.732109	+	0.681188i	$0.761464\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.34143	+	0.774473i	0.0591103	+	0.0341274i
$516$		0			0
$517$	−9.04947	+	5.22471i	−0.397995	+	0.229783i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−21.0781			−0.923446			−0.461723	−	0.887024i	$-0.652769\pi$
$521$	−21.0781			−0.923446			−0.461723	+	0.887024i	$0.652769\pi$
$522$		0			0
$523$		−	19.7145i		−	0.862057i	−0.902338	−	0.431028i	$-0.858151\pi$
$523$		−	19.7145i		−	0.862057i	0.902338	−	0.431028i	$-0.141849\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−40.8760	+	23.5997i	−1.78058	+	1.02802i
$528$		0			0
$529$	−8.91366	+	15.4389i	−0.387550	+	0.671257i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.45039	−	1.99208i	−0.149453	−	0.0862866i
$534$		0			0
$535$	19.2130	−	11.0926i	0.830652	−	0.479577i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.44950			0.363272			0.181636	−	0.983366i	$-0.441861\pi$
$541$	8.44950			0.363272			0.181636	+	0.983366i	$0.441861\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−26.4511	−	45.8147i	−1.13304	−	1.96249i
$546$		0			0
$547$	−4.02889	+	6.97824i	−0.172263	+	0.298368i	−0.939211	−	0.343342i	$-0.888441\pi$
$547$	−4.02889	+	6.97824i	−0.172263	+	0.298368i	0.766948	+	0.641709i	$0.221774\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.9023	+	18.8833i	−0.464453	+	0.804456i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	21.0495i		−	0.891895i	−0.895059	−	0.445947i	$-0.852867\pi$
$557$		−	21.0495i		−	0.891895i	0.895059	−	0.445947i	$-0.147133\pi$
$558$		0			0
$559$		−	0.836249i		−	0.0353696i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−20.6410	−	35.7513i	−0.869916	−	1.50674i	−0.862082	−	0.506769i	$-0.830840\pi$
$563$	−20.6410	−	35.7513i	−0.869916	−	1.50674i	−0.00783378	−	0.999969i	$-0.502494\pi$
$564$		0			0
$565$	4.44922	+	2.56876i	0.187180	+	0.108068i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	31.2691	+	18.0532i	1.31087	+	0.756829i	0.982240	−	0.187630i	$-0.0600807\pi$
$569$	31.2691	+	18.0532i	1.31087	+	0.756829i	0.328627	+	0.944460i	$0.393414\pi$
$570$		0			0
$571$	9.62111	+	16.6642i	0.402631	+	0.697377i	0.994043	−	0.108993i	$-0.0347625\pi$
$571$	9.62111	+	16.6642i	0.402631	+	0.697377i	−0.591412	+	0.806370i	$0.701429\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	23.4846i		−	0.979375i
$576$		0			0
$577$		−	29.8031i		−	1.24072i	−0.784318	−	0.620359i	$-0.786987\pi$
$577$		−	29.8031i		−	1.24072i	0.784318	−	0.620359i	$-0.213013\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.0886621	+	0.153567i	−0.00367201	+	0.00636010i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.72218	−	8.17905i	0.194905	−	0.337586i	−0.751964	−	0.659204i	$-0.770893\pi$
$587$	4.72218	−	8.17905i	0.194905	−	0.337586i	0.946869	+	0.321618i	$0.104227\pi$
$588$		0			0
$589$	−21.5843	−	37.3852i	−0.889367	−	1.54043i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−24.8352			−1.01986			−0.509929	−	0.860216i	$-0.670328\pi$
$593$	−24.8352			−1.01986			−0.509929	+	0.860216i	$0.670328\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−10.3052	+	5.94974i	−0.421061	+	0.243100i	−0.695531	−	0.718496i	$-0.744831\pi$
$599$	−10.3052	+	5.94974i	−0.421061	+	0.243100i	0.274470	+	0.961596i	$0.411498\pi$
$600$		0			0
$601$	−22.1276	−	12.7754i	−0.902604	−	0.521118i	−0.0245596	−	0.999698i	$-0.507818\pi$
$601$	−22.1276	−	12.7754i	−0.902604	−	0.521118i	−0.878044	+	0.478580i	$0.841152\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.18669	−	8.98361i	0.210869	−	0.365236i
$606$		0			0
$607$	−19.5544	+	11.2897i	−0.793687	+	0.458235i	−0.841259	−	0.540632i	$-0.818185\pi$
$607$	−19.5544	+	11.2897i	−0.793687	+	0.458235i	0.0475718	+	0.998868i	$0.484852\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			1.56841i			0.0634510i
$612$		0			0
$613$	22.8588			0.923257			0.461628	−	0.887073i	$-0.347265\pi$
$613$	22.8588			0.923257			0.461628	+	0.887073i	$0.347265\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.78792	+	1.03226i	−0.0719791	+	0.0415572i	−0.535558	−	0.844499i	$-0.679899\pi$
$617$	−1.78792	+	1.03226i	−0.0719791	+	0.0415572i	0.463578	+	0.886056i	$0.346565\pi$
$618$		0			0
$619$	−28.2233	−	16.2947i	−1.13439	−	0.654940i	−0.189354	−	0.981909i	$-0.560639\pi$
$619$	−28.2233	−	16.2947i	−1.13439	−	0.654940i	−0.945035	+	0.326969i	$0.893973\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−14.9967	−	25.9751i	−0.599870	−	1.03901i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	45.5213			1.81505
$630$		0			0
$631$	38.4706			1.53149			0.765744	−	0.643145i	$-0.222371\pi$
$631$	38.4706			1.53149			0.765744	+	0.643145i	$0.222371\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	34.0461	+	58.9696i	1.35108	+	2.34014i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	41.3645	+	23.8818i	1.63380	+	0.943274i	0.982907	+	0.184104i	$0.0589384\pi$
$641$	41.3645	+	23.8818i	1.63380	+	0.943274i	0.650892	+	0.759170i	$0.274395\pi$
$642$		0			0
$643$	−29.2346	+	16.8786i	−1.15290	+	0.665626i	−0.949592	−	0.313489i	$-0.898502\pi$
$643$	−29.2346	+	16.8786i	−1.15290	+	0.665626i	−0.203306	+	0.979115i	$0.565169\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.07202			−0.0421453			−0.0210727	−	0.999778i	$-0.506708\pi$
$647$	−1.07202			−0.0421453			−0.0210727	+	0.999778i	$0.506708\pi$
$648$		0			0
$649$		−	32.9301i		−	1.29262i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	28.8503	−	16.6567i	1.12900	−	0.651828i	0.185317	−	0.982679i	$-0.440669\pi$
$653$	28.8503	−	16.6567i	1.12900	−	0.651828i	0.943683	+	0.330851i	$0.107336\pi$
$654$		0			0
$655$	21.3499	−	36.9791i	0.834210	−	1.44489i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.41890	+	4.86065i	0.327954	+	0.189344i	0.654932	−	0.755688i	$-0.272697\pi$
$659$	8.41890	+	4.86065i	0.327954	+	0.189344i	−0.326979	+	0.945032i	$0.606031\pi$
$660$		0			0
$661$	14.7856	−	8.53647i	0.575093	−	0.332030i	−0.184088	−	0.982910i	$-0.558933\pi$
$661$	14.7856	−	8.53647i	0.575093	−	0.332030i	0.759181	+	0.650880i	$0.225600\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.28724			0.359603
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.8696	+	22.2909i	0.496827	+	0.860529i
$672$		0			0
$673$	−18.3359	+	31.7588i	−0.706798	+	1.22421i	0.259240	+	0.965813i	$0.416528\pi$
$673$	−18.3359	+	31.7588i	−0.706798	+	1.22421i	−0.966039	+	0.258398i	$0.916805\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.1769	−	34.9474i	0.775461	−	1.34314i	−0.159073	−	0.987267i	$-0.550851\pi$
$677$	20.1769	−	34.9474i	0.775461	−	1.34314i	0.934535	−	0.355872i	$-0.115816\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$			9.51083i			0.363922i	0.983306	+	0.181961i	$0.0582444\pi$
$683$			9.51083i			0.363922i	−0.983306	+	0.181961i	$0.941756\pi$
$684$		0			0
$685$		−	34.4705i		−	1.31705i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.0133077	+	0.0230497i	0.000506985	+	0.000878123i
$690$		0			0
$691$	6.67519	+	3.85392i	0.253936	+	0.146610i	0.621565	−	0.783362i	$-0.286497\pi$
$691$	6.67519	+	3.85392i	0.253936	+	0.146610i	−0.367629	+	0.929972i	$0.619830\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−55.7282	−	32.1747i	−2.11389	−	1.22046i
$696$		0			0
$697$	−20.9732	−	36.3267i	−0.794418	−	1.37597i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	15.6388i		−	0.590671i	−0.955394	−	0.295336i	$-0.904569\pi$
$701$		−	15.6388i		−	0.590671i	0.955394	−	0.295336i	$-0.0954314\pi$
$702$		0			0
$703$			41.6338i			1.57025i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−6.72025	+	11.6398i	−0.252384	+	0.437142i	−0.964182	−	0.265242i	$-0.914548\pi$
$709$	−6.72025	+	11.6398i	−0.252384	+	0.437142i	0.711797	+	0.702385i	$0.247881\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.19343	+	15.9235i	−0.344297	+	0.596339i
$714$		0			0
$715$	−4.01027	−	6.94599i	−0.149976	−	0.259765i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−40.0619			−1.49405			−0.747027	−	0.664793i	$-0.768520\pi$
$719$	−40.0619			−1.49405			−0.747027	+	0.664793i	$0.768520\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	36.5161	−	21.0826i	1.35617	−	0.782986i
$726$		0			0
$727$	−43.2091	−	24.9468i	−1.60254	−	0.925225i	−0.990978	−	0.134027i	$-0.957209\pi$
$727$	−43.2091	−	24.9468i	−1.60254	−	0.925225i	−0.611560	−	0.791198i	$-0.709458\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.40214	−	7.62473i	0.162819	−	0.282011i
$732$		0			0
$733$	−9.91430	+	5.72402i	−0.366193	+	0.211422i	−0.671794	−	0.740738i	$-0.734476\pi$
$733$	−9.91430	+	5.72402i	−0.366193	+	0.211422i	0.305601	+	0.952160i	$0.401143\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			4.34038i			0.159880i
$738$		0			0
$739$	−8.92607			−0.328351			−0.164175	−	0.986431i	$-0.552496\pi$
$739$	−8.92607			−0.328351			−0.164175	+	0.986431i	$0.552496\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	45.8621	−	26.4785i	1.68252	−	0.971403i	0.722540	−	0.691329i	$-0.242974\pi$
$743$	45.8621	−	26.4785i	1.68252	−	0.971403i	0.959979	−	0.280074i	$-0.0903589\pi$
$744$		0			0
$745$	−49.2541	−	28.4369i	−1.80453	−	1.04185i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	13.2326	+	22.9195i	0.482865	+	0.836346i	0.999806	−	0.0196744i	$-0.00626295\pi$
$751$	13.2326	+	22.9195i	0.482865	+	0.836346i	−0.516942	+	0.856021i	$0.672930\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	21.9470			0.798733
$756$		0			0
$757$	8.46749			0.307756			0.153878	−	0.988090i	$-0.450824\pi$
$757$	8.46749			0.307756			0.153878	+	0.988090i	$0.450824\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.9968	−	46.7599i	−0.978635	−	1.69505i	−0.667377	−	0.744720i	$-0.732583\pi$
$761$	−26.9968	−	46.7599i	−0.978635	−	1.69505i	−0.311258	−	0.950325i	$-0.600750\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.28046	−	2.47132i	−0.154558	−	0.0892343i
$768$		0			0
$769$	−30.1912	+	17.4309i	−1.08872	+	0.628575i	−0.933236	−	0.359263i	$-0.883028\pi$
$769$	−30.1912	+	17.4309i	−1.08872	+	0.628575i	−0.155487	+	0.987838i	$0.549695\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.12749			0.0765207			0.0382603	−	0.999268i	$-0.487818\pi$
$773$	2.12749			0.0765207			0.0382603	+	0.999268i	$0.487818\pi$
$774$		0			0
$775$			83.4784i			2.99863i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	33.2244	−	19.1821i	1.19039	−	0.687272i
$780$		0			0
$781$	12.3964	−	21.4712i	0.443577	−	0.768298i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−60.4492	−	34.9004i	−2.15752	−	1.24565i
$786$		0			0
$787$	−24.5457	+	14.1715i	−0.874959	+	0.505158i	−0.868993	−	0.494824i	$-0.835232\pi$
$787$	−24.5457	+	14.1715i	−0.874959	+	0.505158i	−0.00596615	+	0.999982i	$0.501899\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	3.86334			0.137191
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.9123	−	32.7570i	−0.669907	−	1.16031i	−0.977930	−	0.208935i	$-0.933000\pi$
$797$	−18.9123	−	32.7570i	−0.669907	−	1.16031i	0.308022	−	0.951379i	$-0.400333\pi$
$798$		0			0
$799$	−8.25634	+	14.3004i	−0.292088	+	0.505912i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.52311	+	13.0304i	−0.265485	+	0.459833i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			45.3191i			1.59333i	0.604419	+	0.796667i	$0.293405\pi$
$809$			45.3191i			1.59333i	−0.604419	+	0.796667i	$0.706595\pi$
$810$		0			0
$811$		−	5.45145i		−	0.191426i	−0.995409	−	0.0957132i	$-0.969487\pi$
$811$		−	5.45145i		−	0.191426i	0.995409	−	0.0957132i	$-0.0305132\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.25883	−	3.91241i	−0.0791233	−	0.137046i
$816$		0			0
$817$	6.97359	+	4.02620i	0.243975	+	0.140859i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.7121	−	24.6598i	−1.49066	−	0.860634i	−0.490718	−	0.871318i	$-0.663266\pi$
$821$	−42.7121	−	24.6598i	−1.49066	−	0.860634i	−0.999943	+	0.0106847i	$0.996599\pi$
$822$		0			0
$823$	11.8496	+	20.5241i	0.413050	+	0.715424i	0.995222	−	0.0976419i	$-0.0311300\pi$
$823$	11.8496	+	20.5241i	0.413050	+	0.715424i	−0.582171	+	0.813066i	$0.697797\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			19.9706i			0.694445i	0.937783	+	0.347222i	$0.112875\pi$
$827$			19.9706i			0.694445i	−0.937783	+	0.347222i	$0.887125\pi$
$828$		0			0
$829$		−	15.4431i		−	0.536361i	−0.963369	−	0.268181i	$-0.913578\pi$
$829$		−	15.4431i		−	0.536361i	0.963369	−	0.268181i	$-0.0864224\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−35.0592	+	60.7242i	−1.21327	+	2.10145i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.53910	+	9.59401i	−0.191231	+	0.331222i	−0.945658	−	0.325162i	$-0.894581\pi$
$839$	−5.53910	+	9.59401i	−0.191231	+	0.331222i	0.754427	+	0.656383i	$0.227915\pi$
$840$		0			0
$841$	−6.16267	−	10.6741i	−0.212506	−	0.368071i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	49.6888			1.70935
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	15.3573	−	8.86656i	0.526442	−	0.303942i
$852$		0			0
$853$	42.1706	+	24.3472i	1.44389	+	0.833633i	0.998107	−	0.0615058i	$-0.0195903\pi$
$853$	42.1706	+	24.3472i	1.44389	+	0.833633i	0.445788	+	0.895139i	$0.352924\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.39130	−	14.5342i	0.286641	−	0.496477i	−0.686365	−	0.727258i	$-0.740795\pi$
$857$	8.39130	−	14.5342i	0.286641	−	0.496477i	0.973006	+	0.230780i	$0.0741279\pi$
$858$		0			0
$859$	−21.7682	+	12.5679i	−0.742722	+	0.428811i	−0.823058	−	0.567957i	$-0.807734\pi$
$859$	−21.7682	+	12.5679i	−0.742722	+	0.428811i	0.0803361	+	0.996768i	$0.474401\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	6.78244i		−	0.230877i	−0.993315	−	0.115438i	$-0.963173\pi$
$863$		−	6.78244i		−	0.230877i	0.993315	−	0.115438i	$-0.0368273\pi$
$864$		0			0
$865$	29.3466			0.997815
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.6303	+	7.29209i	−0.428452	+	0.247367i
$870$		0			0
$871$	0.564190	+	0.325735i	0.0191168	+	0.0110371i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	21.8630	+	37.8678i	0.738260	+	1.27870i	0.953278	+	0.302093i	$0.0976854\pi$
$877$	21.8630	+	37.8678i	0.738260	+	1.27870i	−0.215019	+	0.976610i	$0.568981\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.5307			−0.927531			−0.463766	−	0.885958i	$-0.653502\pi$
$881$	−27.5307			−0.927531			−0.463766	+	0.885958i	$0.653502\pi$
$882$		0			0
$883$	5.56040			0.187122			0.0935612	−	0.995614i	$-0.470175\pi$
$883$	5.56040			0.187122			0.0935612	+	0.995614i	$0.470175\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.3092	+	21.3202i	0.413303	+	0.715862i	0.995249	−	0.0973655i	$-0.0310416\pi$
$887$	12.3092	+	21.3202i	0.413303	+	0.715862i	−0.581945	+	0.813228i	$0.697708\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.0792	−	7.55125i	−0.437677	−	0.252693i
$894$		0			0
$895$	2.44434	−	1.41124i	0.0817054	−	0.0471726i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−33.0125			−1.10103
$900$		0			0
$901$			0.280216i			0.00933535i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.1931	+	9.92644i	−0.571518	+	0.329966i
$906$		0			0
$907$	5.04337	−	8.73537i	0.167462	−	0.290053i	−0.770065	−	0.637966i	$-0.779776\pi$
$907$	5.04337	−	8.73537i	0.167462	−	0.290053i	0.937527	+	0.347913i	$0.113109\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.5808	−	13.6144i	−0.781267	−	0.451065i	0.0556121	−	0.998452i	$-0.482289\pi$
$911$	−23.5808	−	13.6144i	−0.781267	−	0.451065i	−0.836879	+	0.547388i	$0.815622\pi$
$912$		0			0
$913$	−24.6159	+	14.2120i	−0.814668	+	0.470349i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	39.6986			1.30954			0.654769	−	0.755829i	$-0.272766\pi$
$919$	39.6986			1.30954			0.654769	+	0.755829i	$0.272766\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.86064	−	3.22272i	−0.0612436	−	0.106077i
$924$		0			0
$925$	40.2552	−	69.7240i	1.32358	−	2.29251i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.142283	−	0.246442i	0.00466816	−	0.00808550i	−0.863682	−	0.504037i	$-0.831847\pi$
$929$	0.142283	−	0.246442i	0.00466816	−	0.00808550i	0.868350	+	0.495952i	$0.165181\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	84.4427i		−	2.76157i
$936$		0			0
$937$			21.7298i			0.709881i	0.934889	+	0.354940i	$0.115499\pi$
$937$			21.7298i			0.709881i	−0.934889	+	0.354940i	$0.884501\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.64242	+	9.77295i	0.183938	+	0.318589i	0.943218	−	0.332174i	$-0.107782\pi$
$941$	5.64242	+	9.77295i	0.183938	+	0.318589i	−0.759280	+	0.650764i	$0.774449\pi$
$942$		0			0
$943$	−14.1513	−	8.17026i	−0.460830	−	0.266060i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.6701	+	11.3566i	0.639194	+	0.369039i	0.784304	−	0.620377i	$-0.213020\pi$
$947$	19.6701	+	11.3566i	0.639194	+	0.369039i	−0.145110	+	0.989416i	$0.546354\pi$
$948$		0			0
$949$	1.12918	+	1.95580i	0.0366548	+	0.0634880i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	16.5638i		−	0.536554i	−0.963342	−	0.268277i	$-0.913546\pi$
$953$		−	16.5638i		−	0.536554i	0.963342	−	0.268277i	$-0.0864543\pi$
$954$		0			0
$955$			49.7270i			1.60913i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	17.1790	−	29.7550i	0.554162	−	0.959837i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	44.6589	−	77.3515i	1.43762	−	2.49003i
$966$		0			0
$967$	8.38867	+	14.5296i	0.269762	+	0.467241i	0.968800	−	0.247843i	$-0.0797218\pi$
$967$	8.38867	+	14.5296i	0.269762	+	0.467241i	−0.699039	+	0.715084i	$0.746388\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	31.3640			1.00652			0.503259	−	0.864136i	$-0.332134\pi$
$971$	31.3640			1.00652			0.503259	+	0.864136i	$0.332134\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	49.0953	−	28.3452i	1.57070	−	0.906843i	0.574614	−	0.818424i	$-0.305152\pi$
$977$	49.0953	−	28.3452i	1.57070	−	0.906843i	0.996083	−	0.0884183i	$-0.0281812\pi$
$978$		0			0
$979$	−17.3609	−	10.0233i	−0.554858	−	0.320347i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.9204	−	34.5032i	0.635362	−	1.10048i	−0.351076	−	0.936347i	$-0.614184\pi$
$983$	19.9204	−	34.5032i	0.635362	−	1.10048i	0.986438	−	0.164133i	$-0.0524825\pi$
$984$		0			0
$985$	0.105562	−	0.0609460i	0.00336347	−	0.00194190i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	3.42977i		−	0.109060i
$990$		0			0
$991$	−62.5951			−1.98840			−0.994199	−	0.107558i	$-0.965697\pi$
$991$	−62.5951			−1.98840			−0.994199	+	0.107558i	$0.965697\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	77.9613	−	45.0110i	2.47154	−	1.42694i
$996$		0			0
$997$	39.0613	+	22.5520i	1.23708	+	0.714230i	0.968497	−	0.249025i	$-0.0801102\pi$
$997$	39.0613	+	22.5520i	1.23708	+	0.714230i	0.268586	+	0.963256i	$0.413444\pi$
$998$		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.4409.1		16
3.2	odd	2		1764.2.x.b.1469.6		16
7.2	even	3		5292.2.w.b.521.1		16
7.3	odd	6		5292.2.bm.a.4625.1		16
7.4	even	3		756.2.bm.a.89.8		16
7.5	odd	6		756.2.w.a.521.8		16
7.6	odd	2		5292.2.x.a.4409.8		16
9.4	even	3		1764.2.x.a.293.3		16
9.5	odd	6		5292.2.x.a.881.8		16
21.2	odd	6		1764.2.w.b.1109.1		16
21.5	even	6		252.2.w.a.101.8	yes	16
21.11	odd	6		252.2.bm.a.173.6	yes	16
21.17	even	6		1764.2.bm.a.1685.3		16
21.20	even	2		1764.2.x.a.1469.3		16
28.11	odd	6		3024.2.df.d.1601.8		16
28.19	even	6		3024.2.ca.d.2033.8		16
63.4	even	3		252.2.w.a.5.8	✓	16
63.5	even	6		756.2.bm.a.17.8		16
63.11	odd	6		2268.2.t.a.2105.8		16
63.13	odd	6		1764.2.x.b.293.6		16
63.23	odd	6		5292.2.bm.a.2285.1		16
63.25	even	3		2268.2.t.b.2105.1		16
63.31	odd	6		1764.2.w.b.509.1		16
63.32	odd	6		756.2.w.a.341.8		16
63.40	odd	6		252.2.bm.a.185.6	yes	16
63.41	even	6	inner	5292.2.x.b.881.1		16
63.47	even	6		2268.2.t.b.1781.1		16
63.58	even	3		1764.2.bm.a.1697.3		16
63.59	even	6		5292.2.w.b.1097.1		16
63.61	odd	6		2268.2.t.a.1781.8		16
84.11	even	6		1008.2.df.d.929.3		16
84.47	odd	6		1008.2.ca.d.353.1		16
252.67	odd	6		1008.2.ca.d.257.1		16
252.95	even	6		3024.2.ca.d.2609.8		16
252.103	even	6		1008.2.df.d.689.3		16
252.131	odd	6		3024.2.df.d.17.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	63.4	even	3
252.2.w.a.101.8	yes	16	21.5	even	6
252.2.bm.a.173.6	yes	16	21.11	odd	6
252.2.bm.a.185.6	yes	16	63.40	odd	6
756.2.w.a.341.8		16	63.32	odd	6
756.2.w.a.521.8		16	7.5	odd	6
756.2.bm.a.17.8		16	63.5	even	6
756.2.bm.a.89.8		16	7.4	even	3
1008.2.ca.d.257.1		16	252.67	odd	6
1008.2.ca.d.353.1		16	84.47	odd	6
1008.2.df.d.689.3		16	252.103	even	6
1008.2.df.d.929.3		16	84.11	even	6
1764.2.w.b.509.1		16	63.31	odd	6
1764.2.w.b.1109.1		16	21.2	odd	6
1764.2.x.a.293.3		16	9.4	even	3
1764.2.x.a.1469.3		16	21.20	even	2
1764.2.x.b.293.6		16	63.13	odd	6
1764.2.x.b.1469.6		16	3.2	odd	2
1764.2.bm.a.1685.3		16	21.17	even	6
1764.2.bm.a.1697.3		16	63.58	even	3
2268.2.t.a.1781.8		16	63.61	odd	6
2268.2.t.a.2105.8		16	63.11	odd	6
2268.2.t.b.1781.1		16	63.47	even	6
2268.2.t.b.2105.1		16	63.25	even	3
3024.2.ca.d.2033.8		16	28.19	even	6
3024.2.ca.d.2609.8		16	252.95	even	6
3024.2.df.d.17.8		16	252.131	odd	6
3024.2.df.d.1601.8		16	28.11	odd	6
5292.2.w.b.521.1		16	7.2	even	3
5292.2.w.b.1097.1		16	63.59	even	6
5292.2.x.a.881.8		16	9.5	odd	6
5292.2.x.a.4409.8		16	7.6	odd	2
5292.2.x.b.881.1		16	63.41	even	6	inner
5292.2.x.b.4409.1		16	1.1	even	1	trivial
5292.2.bm.a.2285.1		16	63.23	odd	6
5292.2.bm.a.4625.1		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)

\(f(q)\)	\(=\)	\(q+(-1.95741 - 3.39033i) q^{5} +O(q^{10})\)	\(q+(-1.95741 - 3.39033i) q^{5} +(-3.19958 - 1.84728i) q^{11} +(-0.480242 + 0.277268i) q^{13} -5.83832 q^{17} -5.33973i q^{19} +(-1.96965 + 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(-3.53638 - 2.04173i) q^{29} +(7.00132 - 4.04222i) q^{31} -7.79699 q^{37} +(3.59234 + 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(1.41416 - 2.44940i) q^{47} -0.0479960i q^{53} +14.4635i q^{55} +(4.45656 + 7.71900i) q^{59} +(-6.03343 - 3.48340i) q^{61} +(1.88006 + 1.08545i) q^{65} +(-0.587402 - 1.01741i) q^{67} +6.71061i q^{71} -4.07253i q^{73} +(1.97374 - 3.41861i) q^{79} +(3.84674 - 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +5.42600 q^{89} +(-18.1035 + 10.4520i) q^{95} +(-13.9874 - 8.07563i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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