LMFDB - Embedded newform 1872.2.t.m.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1872,2,Mod(289,1872)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1872.289"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1872, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,6,0,-4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1872.289
Dual form			1872.2.t.m.1153.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +(-3.50000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +4.00000 q^{25} +(4.50000 + 7.79423i) q^{29} -2.00000 q^{31} +(-6.00000 + 10.3923i) q^{35} +(3.50000 + 6.06218i) q^{37} +(1.50000 + 2.59808i) q^{41} +(-2.00000 + 3.46410i) q^{43} -6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} -9.00000 q^{53} +(-2.50000 + 4.33013i) q^{61} +(-10.5000 + 2.59808i) q^{65} +(1.00000 + 1.73205i) q^{67} +(3.00000 - 5.19615i) q^{71} -1.00000 q^{73} +4.00000 q^{79} +12.0000 q^{83} +(4.50000 - 7.79423i) q^{85} +(3.00000 + 5.19615i) q^{89} +(4.00000 - 13.8564i) q^{91} +(3.00000 - 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{5} - 4 q^{7} - 7 q^{13} + 3 q^{17} + 2 q^{19} + 6 q^{23} + 8 q^{25} + 9 q^{29} - 4 q^{31} - 12 q^{35} + 7 q^{37} + 3 q^{41} - 4 q^{43} - 12 q^{47} - 9 q^{49} - 18 q^{53} - 5 q^{61} - 21 q^{65}+ \cdots - 14 q^{97}+O(q^{100}) $ 2 * q + 6 * q^5 - 4 * q^7 - 7 * q^13 + 3 * q^17 + 2 * q^19 + 6 * q^23 + 8 * q^25 + 9 * q^29 - 4 * q^31 - 12 * q^35 + 7 * q^37 + 3 * q^41 - 4 * q^43 - 12 * q^47 - 9 * q^49 - 18 * q^53 - 5 * q^61 - 21 * q^65 + 2 * q^67 + 6 * q^71 - 2 * q^73 + 8 * q^79 + 24 * q^83 + 9 * q^85 + 6 * q^89 + 8 * q^91 + 6 * q^95 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.00000	+	10.3923i	−1.01419	+	1.75662i
$36$		0			0
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−10.5000	+	2.59808i	−1.30236	+	0.322252i
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	4.00000	−	13.8564i	0.419314	−	1.45255i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	0.253837	+	0.967247i	$0.418307\pi$
$97$	−7.00000	+	12.1244i	−0.710742	+	1.23104i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	−2.00000			−0.197066			−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000			−0.197066			−0.0985329	+	0.995134i	$0.531415\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$		0			0
$115$	9.00000	+	15.5885i	0.839254	+	1.45363i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	0.554281	−	0.832330i	$-0.312993\pi$
$127$	−5.00000	−	8.66025i	−0.443678	−	0.768473i	−0.997959	+	0.0638564i	$0.979660\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$		0			0
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	−0.344493	−	0.938789i	$-0.611949\pi$
$137$	7.50000	−	12.9904i	0.640768	−	1.10984i	0.985262	−	0.171054i	$-0.0547174\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	13.5000	+	23.3827i	1.12111	+	1.94183i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		0			0
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.00000			−0.481932
$156$		0			0
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−24.0000			−1.89146
$162$		0			0
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.785687	+	0.618624i	$0.212310\pi$
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.142901	+	0.989737i	$0.454357\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−8.00000	+	13.8564i	−0.604743	+	1.04745i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$		0			0
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.124521	−	0.992217i	$-0.460261\pi$
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.797025	−	0.603947i	$-0.206406\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−36.0000			−2.52670
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	0.898392	−	0.439194i	$-0.144736\pi$
$211$	1.00000	+	1.73205i	0.0688428	+	0.119239i	−0.829549	+	0.558433i	$0.811403\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.00000	+	10.3923i	−0.409197	+	0.708749i
$216$		0			0
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$		0			0
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.861435	+	0.507869i	$0.169566\pi$
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.00910984	+	0.999959i	$0.497100\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$		0			0
$237$		0			0
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−13.5000	−	23.3827i	−0.862483	−	1.49387i
$246$		0			0
$247$	−2.00000	+	6.92820i	−0.127257	+	0.440831i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.00000	−	5.19615i	0.189358	−	0.327978i	−0.755678	−	0.654943i	$-0.772693\pi$
$251$	3.00000	−	5.19615i	0.189358	−	0.327978i	0.945036	+	0.326965i	$0.106026\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	0.909010	−	0.416775i	$-0.136840\pi$
$257$	1.50000	+	2.59808i	0.0935674	+	0.162064i	−0.815442	+	0.578838i	$0.803506\pi$
$258$		0			0
$259$	−28.0000			−1.73984
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$	−27.0000			−1.65860
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.107031	−	0.994256i	$-0.465866\pi$
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.807535	−	0.589819i	$-0.200801\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	−0.425684	−	0.904872i	$-0.639967\pi$
$277$	9.50000	−	16.4545i	0.570800	−	0.988654i	0.996484	−	0.0837823i	$-0.0267000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.00000			−0.178965			−0.0894825	−	0.995988i	$-0.528521\pi$
$281$	−3.00000			−0.178965			−0.0894825	+	0.995988i	$0.528521\pi$
$282$		0			0
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	0.524057	−	0.851683i	$-0.324418\pi$
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	−0.999608	+	0.0280052i	$0.991084\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.0000			−0.708338
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	−0.704117	−	0.710084i	$-0.748657\pi$
$293$	4.50000	−	7.79423i	0.262893	−	0.455344i	0.967009	+	0.254741i	$0.0819901\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.0000	−	15.5885i	−0.867472	−	0.901504i
$300$		0			0
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.50000	+	12.9904i	−0.429449	+	0.743827i
$306$		0			0
$307$	−26.0000			−1.48390			−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000			−1.48390			−0.741949	+	0.670456i	$0.766098\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.00000			0.340229			0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000			0.340229			0.170114	+	0.985424i	$0.445586\pi$
$312$		0			0
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.0000			0.842484			0.421242	−	0.906948i	$-0.361594\pi$
$317$	15.0000			0.842484			0.421242	+	0.906948i	$0.361594\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.00000	−	5.19615i	−0.166924	−	0.289122i
$324$		0			0
$325$	−14.0000	+	3.46410i	−0.776580	+	0.192154i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.851957	−	0.523612i	$-0.175416\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.00000	+	5.19615i	0.163908	+	0.283896i
$336$		0			0
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.5000	+	23.3827i	0.718532	+	1.24453i	0.961581	+	0.274521i	$0.0885192\pi$
$353$	13.5000	+	23.3827i	0.718532	+	1.24453i	−0.243049	+	0.970014i	$0.578147\pi$
$354$		0			0
$355$	9.00000	−	15.5885i	0.477670	−	0.827349i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	36.0000			1.90001			0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000			1.90001			0.950004	+	0.312239i	$0.101079\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.00000			−0.157027
$366$		0			0
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	−0.996129	−	0.0879086i	$-0.971982\pi$
$367$	−11.0000	−	19.0526i	−0.574195	−	0.994535i	0.421933	−	0.906627i	$-0.361352\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.0000	−	31.1769i	0.934513	−	1.61862i
$372$		0			0
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	−0.761074	−	0.648665i	$-0.775328\pi$
$373$	3.50000	−	6.06218i	0.181223	−	0.313888i	0.942297	+	0.334777i	$0.108661\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−22.5000	−	23.3827i	−1.15881	−	1.20427i
$378$		0			0
$379$	−5.00000	−	8.66025i	−0.256833	−	0.444847i	0.708559	−	0.705652i	$-0.249346\pi$
$379$	−5.00000	−	8.66025i	−0.256833	−	0.444847i	−0.965392	+	0.260804i	$0.916012\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.119974	−	0.992777i	$-0.461719\pi$
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.799783	−	0.600289i	$-0.204948\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−21.0000			−1.06474			−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000			−1.06474			−0.532371	+	0.846511i	$0.678699\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.0000			0.603786
$396$		0			0
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	−0.712843	−	0.701324i	$-0.752593\pi$
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	0.963786	+	0.266678i	$0.0859261\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	−0.902703	−	0.430263i	$-0.858421\pi$
$401$	−16.5000	−	28.5788i	−0.823971	−	1.42716i	0.0787327	−	0.996896i	$-0.474913\pi$
$402$		0			0
$403$	7.00000	−	1.73205i	0.348695	−	0.0862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	36.0000			1.76717
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$		0			0
$421$	5.00000			0.243685			0.121843	−	0.992549i	$-0.461120\pi$
$421$	5.00000			0.243685			0.121843	+	0.992549i	$0.461120\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	−10.0000	−	17.3205i	−0.483934	−	0.838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$		0			0
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	−0.853761	−	0.520665i	$-0.825684\pi$
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	0.877790	+	0.479046i	$0.159017\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0000			0.574038
$438$		0			0
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	0.940963	+	0.338508i	$0.109922\pi$
$439$	16.0000	+	27.7128i	0.763638	+	1.32266i	−0.177325	+	0.984152i	$0.556744\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	12.0000			0.570137			0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000			0.570137			0.285069	+	0.958507i	$0.407984\pi$
$444$		0			0
$445$	9.00000	+	15.5885i	0.426641	+	0.738964i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	−0.257743	−	0.966213i	$-0.582979\pi$
$449$	15.0000	−	25.9808i	0.707894	−	1.22611i	0.965637	−	0.259895i	$-0.0836878\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.0000	−	41.5692i	0.562569	−	1.94880i
$456$		0			0
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	−0.999014	−	0.0443868i	$-0.985867\pi$
$457$	−11.5000	−	19.9186i	−0.537947	−	0.931752i	0.461067	−	0.887365i	$-0.347467\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.5000	+	33.7750i	−0.908206	+	1.57306i	−0.0916500	+	0.995791i	$0.529214\pi$
$461$	−19.5000	+	33.7750i	−0.908206	+	1.57306i	−0.816556	+	0.577267i	$0.804119\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$		0			0
$469$	−8.00000			−0.369406
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$		0			0
$481$	−17.5000	−	18.1865i	−0.797931	−	0.829235i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.0000	+	36.3731i	−0.953561	+	1.65162i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.0000	+	20.7846i	0.541552	+	0.937996i	0.998815	+	0.0486647i	$0.0154966\pi$
$491$	12.0000	+	20.7846i	0.541552	+	0.937996i	−0.457263	+	0.889332i	$0.651170\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$		0			0
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	−0.968223	−	0.250090i	$-0.919540\pi$
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	0.700696	+	0.713460i	$0.252873\pi$
$504$		0			0
$505$	13.5000	+	23.3827i	0.600742	+	1.04052i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$		0			0
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.00000			−0.264392
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	9.00000			0.394297			0.197149	−	0.980374i	$-0.436832\pi$
$521$	9.00000			0.394297			0.197149	+	0.980374i	$0.436832\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.00000	+	5.19615i	−0.130682	+	0.226348i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.50000	−	7.79423i	−0.324861	−	0.337606i
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.0000			−0.816874			−0.408437	−	0.912787i	$-0.633926\pi$
$541$	−19.0000			−0.816874			−0.408437	+	0.912787i	$0.633926\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−30.0000			−1.28506
$546$		0			0
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.0000			0.766826
$552$		0			0
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	4.00000	−	13.8564i	0.169182	−	0.586064i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	0.184950	+	0.982748i	$0.440788\pi$
$563$	−18.0000	+	31.1769i	−0.758610	+	1.31395i	−0.943560	+	0.331202i	$0.892546\pi$
$564$		0			0
$565$	−13.5000	+	23.3827i	−0.567949	+	0.983717i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	−32.0000			−1.33916			−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000			−1.33916			−0.669579	+	0.742741i	$0.733526\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.0000	+	20.7846i	0.500435	+	0.866778i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.0000	+	41.5692i	−0.995688	+	1.72458i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.00000			0.369586			0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000			0.369586			0.184793	+	0.982777i	$0.440839\pi$
$594$		0			0
$595$	18.0000	+	31.1769i	0.737928	+	1.27813i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−30.0000			−1.22577			−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000			−1.22577			−0.612883	+	0.790173i	$0.709990\pi$
$600$		0			0
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	0.876043	−	0.482233i	$-0.160174\pi$
$601$	0.500000	+	0.866025i	0.0203954	+	0.0353259i	−0.855648	+	0.517559i	$0.826841\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.5000	−	28.5788i	0.670820	−	1.16190i
$606$		0			0
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	−0.998154	−	0.0607380i	$-0.980655\pi$
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	0.551678	+	0.834058i	$0.313988\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	21.0000	−	5.19615i	0.849569	−	0.210214i
$612$		0			0
$613$	9.50000	+	16.4545i	0.383701	+	0.664590i	0.991588	−	0.129433i	$-0.0413159\pi$
$613$	9.50000	+	16.4545i	0.383701	+	0.664590i	−0.607887	+	0.794024i	$0.707983\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	−0.455211	−	0.890384i	$-0.650436\pi$
$617$	13.5000	−	23.3827i	0.543490	−	0.941351i	0.998700	−	0.0509678i	$-0.0162306\pi$
$618$		0			0
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−24.0000			−0.961540
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	−14.0000	+	24.2487i	−0.557331	+	0.965326i	0.440387	+	0.897808i	$0.354841\pi$
$631$	−14.0000	+	24.2487i	−0.557331	+	0.965326i	−0.997718	+	0.0675178i	$0.978492\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.0000	−	25.9808i	−0.595257	−	1.03102i
$636$		0			0
$637$	22.5000	+	23.3827i	0.891482	+	0.926456i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	−0.679039	−	0.734103i	$-0.737603\pi$
$641$	7.50000	−	12.9904i	0.296232	−	0.513089i	0.975271	+	0.221013i	$0.0709364\pi$
$642$		0			0
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	−0.979541	−	0.201243i	$-0.935502\pi$
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	0.664052	+	0.747686i	$0.268835\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	0.801010	−	0.598651i	$-0.204296\pi$
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	−0.918952	+	0.394369i	$0.870963\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	−0.904345	−	0.426801i	$-0.859640\pi$
$653$	−21.0000	−	36.3731i	−0.821794	−	1.42339i	0.0825519	−	0.996587i	$-0.473693\pi$
$654$		0			0
$655$	18.0000			0.703318
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	0.926030	−	0.377450i	$-0.123199\pi$
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	−0.789896	+	0.613241i	$0.789865\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.0000	+	20.7846i	0.465340	+	0.805993i
$666$		0			0
$667$	−27.0000	+	46.7654i	−1.04544	+	1.81076i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	6.50000	+	11.2583i	0.250557	+	0.433977i	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	6.50000	+	11.2583i	0.250557	+	0.433977i	−0.713123	+	0.701039i	$0.752720\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$	−28.0000	−	48.4974i	−1.07454	−	1.86116i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	3.00000	−	5.19615i	0.114792	−	0.198825i	−0.802905	−	0.596107i	$-0.796713\pi$
$683$	3.00000	−	5.19615i	0.114792	−	0.198825i	0.917697	+	0.397282i	$0.130047\pi$
$684$		0			0
$685$	22.5000	−	38.9711i	0.859681	−	1.48901i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	31.5000	−	7.79423i	1.20005	−	0.296936i
$690$		0			0
$691$	−20.0000	−	34.6410i	−0.760836	−	1.31781i	−0.942420	−	0.334431i	$-0.891456\pi$
$691$	−20.0000	−	34.6410i	−0.760836	−	1.31781i	0.181584	−	0.983375i	$-0.441877\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.0000	+	41.5692i	−0.910372	+	1.57681i
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	14.0000			0.528020
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−36.0000			−1.35392
$708$		0			0
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	15.5000	−	26.8468i	0.582115	−	1.00825i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.00000	−	10.3923i	−0.224702	−	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	−0.955947	−	0.293538i	$-0.905167\pi$
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	0.732185	+	0.681106i	$0.238501\pi$
$720$		0			0
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$	29.0000			1.07114			0.535570	−	0.844491i	$-0.320097\pi$
$733$	29.0000			1.07114			0.535570	+	0.844491i	$0.320097\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	0.989230	−	0.146369i	$-0.0467586\pi$
$739$	10.0000	+	17.3205i	0.367856	+	0.637145i	−0.621374	+	0.783514i	$0.713425\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$		0			0
$745$	13.5000	−	23.3827i	0.494602	−	0.856675i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	30.0000			1.09181
$756$		0			0
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	−0.971652	−	0.236414i	$-0.924028\pi$
$757$	−19.0000	−	32.9090i	−0.690567	−	1.19610i	0.281086	−	0.959683i	$-0.409305\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		0			0
$763$	20.0000	−	34.6410i	0.724049	−	1.25409i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$		0			0
$775$	−8.00000			−0.287368
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000			0.214972
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−21.0000			−0.749522
$786$		0			0
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	−0.298521	−	0.954403i	$-0.596493\pi$
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	0.975798	−	0.218675i	$-0.0701734\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−18.0000	−	31.1769i	−0.640006	−	1.10852i
$792$		0			0
$793$	5.00000	−	17.3205i	0.177555	−	0.615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	−0.980237	−	0.197826i	$-0.936612\pi$
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	0.661441	+	0.749997i	$0.269945\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−72.0000			−2.53767
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	0.967219	−	0.253946i	$-0.0817284\pi$
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	−0.703533	+	0.710663i	$0.748395\pi$
$810$		0			0
$811$	10.0000			0.351147			0.175574	−	0.984466i	$-0.443822\pi$
$811$	10.0000			0.351147			0.175574	+	0.984466i	$0.443822\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.0000	−	20.7846i	0.420342	−	0.728053i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	0.665144	−	0.746715i	$-0.268370\pi$
$821$	−9.00000	−	15.5885i	−0.314102	−	0.544041i	−0.979246	+	0.202674i	$0.935037\pi$
$822$		0			0
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	0.982501	−	0.186256i	$-0.0596352\pi$
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	−0.652553	+	0.757743i	$0.726302\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−27.0000			−0.935495
$834$		0			0
$835$	36.0000	+	62.3538i	1.24583	+	2.15784i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	0.233973	+	0.972243i	$0.424827\pi$
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	−0.958974	+	0.283495i	$0.908506\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	34.5000	−	18.1865i	1.18684	−	0.625636i
$846$		0			0
$847$	22.0000	+	38.1051i	0.755929	+	1.30931i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−21.0000	+	36.3731i	−0.719871	+	1.24685i
$852$		0			0
$853$	5.00000			0.171197			0.0855984	−	0.996330i	$-0.472720\pi$
$853$	5.00000			0.171197			0.0855984	+	0.996330i	$0.472720\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$		0			0
$859$	−2.00000			−0.0682391			−0.0341196	−	0.999418i	$-0.510863\pi$
$859$	−2.00000			−0.0682391			−0.0341196	+	0.999418i	$0.510863\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$		0			0
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−5.00000	−	5.19615i	−0.169419	−	0.176065i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.00000	−	10.3923i	0.202837	−	0.351324i
$876$		0			0
$877$	−2.50000	+	4.33013i	−0.0844190	+	0.146218i	−0.905143	−	0.425106i	$-0.860237\pi$
$877$	−2.50000	+	4.33013i	−0.0844190	+	0.146218i	0.820724	+	0.571324i	$0.193570\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	0.872772	+	0.488127i	$0.162320\pi$
$881$	25.5000	+	44.1673i	0.859117	+	1.48803i	−0.0136556	+	0.999907i	$0.504347\pi$
$882$		0			0
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	0.747539	−	0.664218i	$-0.231235\pi$
$887$	−6.00000	−	10.3923i	−0.201460	−	0.348939i	−0.948999	+	0.315279i	$0.897902\pi$
$888$		0			0
$889$	40.0000			1.34156
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$	−36.0000	−	62.3538i	−1.20335	−	2.08426i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.00000	−	15.5885i	−0.300167	−	0.519904i
$900$		0			0
$901$	−13.5000	+	23.3827i	−0.449750	+	0.778990i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.0000			−0.698064
$906$		0			0
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	0.924762	−	0.380547i	$-0.124264\pi$
$907$	4.00000	+	6.92820i	0.132818	+	0.230047i	−0.791944	+	0.610594i	$0.790931\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.0000	+	20.7846i	−0.396275	+	0.686368i
$918$		0			0
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	−0.361447	−	0.932393i	$-0.617717\pi$
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	0.988199	−	0.153174i	$-0.0489495\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.00000	+	20.7846i	−0.197492	+	0.684134i
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	47.0000			1.53542			0.767712	−	0.640796i	$-0.221395\pi$
$937$	47.0000			1.53542			0.767712	+	0.640796i	$0.221395\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	30.0000			0.977972			0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000			0.977972			0.488986	+	0.872292i	$0.337367\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.00000	+	15.5885i	0.292461	+	0.506557i	0.974391	−	0.224860i	$-0.0721926\pi$
$947$	9.00000	+	15.5885i	0.292461	+	0.506557i	−0.681930	+	0.731417i	$0.738859\pi$
$948$		0			0
$949$	3.50000	−	0.866025i	0.113615	−	0.0281124i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$		0			0
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	30.0000	+	51.9615i	0.968751	+	1.67793i
$960$		0			0
$961$	−27.0000			−0.870968
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−16.5000	−	28.5788i	−0.531154	−	0.919985i
$966$		0			0
$967$	58.0000			1.86515			0.932577	−	0.360971i	$-0.117555\pi$
$967$	58.0000			1.86515			0.932577	+	0.360971i	$0.117555\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	−0.999771	−	0.0213768i	$-0.993195\pi$
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	0.518399	+	0.855139i	$0.326528\pi$
$972$		0			0
$973$	−32.0000	−	55.4256i	−1.02587	−	1.77686i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.5000	+	33.7750i	0.623860	+	1.08056i	0.988760	+	0.149511i	$0.0477699\pi$
$977$	19.5000	+	33.7750i	0.623860	+	1.08056i	−0.364900	+	0.931047i	$0.618897\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.00000			−0.191370			−0.0956851	−	0.995412i	$-0.530504\pi$
$983$	−6.00000			−0.191370			−0.0956851	+	0.995412i	$0.530504\pi$
$984$		0			0
$985$	9.00000	+	15.5885i	0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	0.881471	−	0.472237i	$-0.156554\pi$
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	−0.849705	+	0.527258i	$0.823220\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	39.0000	−	67.5500i	1.23638	−	2.14148i
$996$		0			0
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	−0.902895	−	0.429862i	$-0.858562\pi$
$997$	−2.50000	+	4.33013i	−0.0791758	+	0.137136i	0.823719	+	0.566999i	$0.191896\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.t.m.289.1		2
3.2	odd	2		208.2.i.a.81.1		2
4.3	odd	2		468.2.l.d.289.1		2
12.11	even	2		52.2.e.b.29.1	yes	2
13.9	even	3	inner	1872.2.t.m.1153.1		2
24.5	odd	2		832.2.i.i.705.1		2
24.11	even	2		832.2.i.c.705.1		2
39.2	even	12		2704.2.f.i.337.2		2
39.11	even	12		2704.2.f.i.337.1		2
39.23	odd	6		2704.2.a.m.1.1		1
39.29	odd	6		2704.2.a.l.1.1		1
39.35	odd	6		208.2.i.a.113.1		2
52.3	odd	6		6084.2.a.o.1.1		1
52.11	even	12		6084.2.b.k.4393.2		2
52.15	even	12		6084.2.b.k.4393.1		2
52.23	odd	6		6084.2.a.c.1.1		1
52.35	odd	6		468.2.l.d.217.1		2
60.23	odd	4		1300.2.bb.d.549.1		4
60.47	odd	4		1300.2.bb.d.549.2		4
60.59	even	2		1300.2.i.b.601.1		2
84.11	even	6		2548.2.i.g.1745.1		2
84.23	even	6		2548.2.l.b.1537.1		2
84.47	odd	6		2548.2.l.g.1537.1		2
84.59	odd	6		2548.2.i.b.1745.1		2
84.83	odd	2		2548.2.k.a.393.1		2
156.11	odd	12		676.2.d.a.337.1		2
156.23	even	6		676.2.a.b.1.1		1
156.35	even	6		52.2.e.b.9.1	✓	2
156.47	odd	4		676.2.h.d.361.1		4
156.59	odd	12		676.2.h.d.485.1		4
156.71	odd	12		676.2.h.d.485.2		4
156.83	odd	4		676.2.h.d.361.2		4
156.95	even	6		676.2.e.d.529.1		2
156.107	even	6		676.2.a.a.1.1		1
156.119	odd	12		676.2.d.a.337.2		2
156.155	even	2		676.2.e.d.653.1		2
312.35	even	6		832.2.i.c.321.1		2
312.269	odd	6		832.2.i.i.321.1		2
780.347	odd	12		1300.2.bb.d.1049.1		4
780.503	odd	12		1300.2.bb.d.1049.2		4
780.659	even	6		1300.2.i.b.1101.1		2
1092.191	even	6		2548.2.i.g.165.1		2
1092.347	even	6		2548.2.l.b.373.1		2
1092.503	odd	6		2548.2.k.a.1569.1		2
1092.815	odd	6		2548.2.l.g.373.1		2
1092.971	odd	6		2548.2.i.b.165.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.2.e.b.9.1	✓	2	156.35	even	6
52.2.e.b.29.1	yes	2	12.11	even	2
208.2.i.a.81.1		2	3.2	odd	2
208.2.i.a.113.1		2	39.35	odd	6
468.2.l.d.217.1		2	52.35	odd	6
468.2.l.d.289.1		2	4.3	odd	2
676.2.a.a.1.1		1	156.107	even	6
676.2.a.b.1.1		1	156.23	even	6
676.2.d.a.337.1		2	156.11	odd	12
676.2.d.a.337.2		2	156.119	odd	12
676.2.e.d.529.1		2	156.95	even	6
676.2.e.d.653.1		2	156.155	even	2
676.2.h.d.361.1		4	156.47	odd	4
676.2.h.d.361.2		4	156.83	odd	4
676.2.h.d.485.1		4	156.59	odd	12
676.2.h.d.485.2		4	156.71	odd	12
832.2.i.c.321.1		2	312.35	even	6
832.2.i.c.705.1		2	24.11	even	2
832.2.i.i.321.1		2	312.269	odd	6
832.2.i.i.705.1		2	24.5	odd	2
1300.2.i.b.601.1		2	60.59	even	2
1300.2.i.b.1101.1		2	780.659	even	6
1300.2.bb.d.549.1		4	60.23	odd	4
1300.2.bb.d.549.2		4	60.47	odd	4
1300.2.bb.d.1049.1		4	780.347	odd	12
1300.2.bb.d.1049.2		4	780.503	odd	12
1872.2.t.m.289.1		2	1.1	even	1	trivial
1872.2.t.m.1153.1		2	13.9	even	3	inner
2548.2.i.b.165.1		2	1092.971	odd	6
2548.2.i.b.1745.1		2	84.59	odd	6
2548.2.i.g.165.1		2	1092.191	even	6
2548.2.i.g.1745.1		2	84.11	even	6
2548.2.k.a.393.1		2	84.83	odd	2
2548.2.k.a.1569.1		2	1092.503	odd	6
2548.2.l.b.373.1		2	1092.347	even	6
2548.2.l.b.1537.1		2	84.23	even	6
2548.2.l.g.373.1		2	1092.815	odd	6
2548.2.l.g.1537.1		2	84.47	odd	6
2704.2.a.l.1.1		1	39.29	odd	6
2704.2.a.m.1.1		1	39.23	odd	6
2704.2.f.i.337.1		2	39.11	even	12
2704.2.f.i.337.2		2	39.2	even	12
6084.2.a.c.1.1		1	52.23	odd	6
6084.2.a.o.1.1		1	52.3	odd	6
6084.2.b.k.4393.1		2	52.15	even	12
6084.2.b.k.4393.2		2	52.11	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.00000 q^{5} +(-2.00000 + 3.46410i) q^{7} +(-3.50000 + 0.866025i) q^{13} +(1.50000 - 2.59808i) q^{17} +(1.00000 - 1.73205i) q^{19} +(3.00000 + 5.19615i) q^{23} +4.00000 q^{25} +(4.50000 + 7.79423i) q^{29} -2.00000 q^{31} +(-6.00000 + 10.3923i) q^{35} +(3.50000 + 6.06218i) q^{37} +(1.50000 + 2.59808i) q^{41} +(-2.00000 + 3.46410i) q^{43} -6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} -9.00000 q^{53} +(-2.50000 + 4.33013i) q^{61} +(-10.5000 + 2.59808i) q^{65} +(1.00000 + 1.73205i) q^{67} +(3.00000 - 5.19615i) q^{71} -1.00000 q^{73} +4.00000 q^{79} +12.0000 q^{83} +(4.50000 - 7.79423i) q^{85} +(3.00000 + 5.19615i) q^{89} +(4.00000 - 13.8564i) q^{91} +(3.00000 - 5.19615i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{5} - 4 q^{7} - 7 q^{13} + 3 q^{17} + 2 q^{19} + 6 q^{23} + 8 q^{25} + 9 q^{29} - 4 q^{31} - 12 q^{35} + 7 q^{37} + 3 q^{41} - 4 q^{43} - 12 q^{47} - 9 q^{49} - 18 q^{53} - 5 q^{61} - 21 q^{65}+ \cdots - 14 q^{97}+O(q^{100}) \) 2 * q + 6 * q^5 - 4 * q^7 - 7 * q^13 + 3 * q^17 + 2 * q^19 + 6 * q^23 + 8 * q^25 + 9 * q^29 - 4 * q^31 - 12 * q^35 + 7 * q^37 + 3 * q^41 - 4 * q^43 - 12 * q^47 - 9 * q^49 - 18 * q^53 - 5 * q^61 - 21 * q^65 + 2 * q^67 + 6 * q^71 - 2 * q^73 + 8 * q^79 + 24 * q^83 + 9 * q^85 + 6 * q^89 + 8 * q^91 + 6 * q^95 - 14 * q^97

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