LMFDB - Embedded newform 3024.2.bh.b.1871.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1871,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1871"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,0,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1871.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.1871
Dual form			3024.2.bh.b.2447.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{5} +(0.500000 - 2.59808i) q^{7} +3.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.50000 - 0.866025i) q^{17} +(1.50000 + 0.866025i) q^{19} +3.00000 q^{23} +2.00000 q^{25} +(7.50000 + 4.33013i) q^{29} +(3.00000 + 1.73205i) q^{31} +(-4.50000 - 0.866025i) q^{35} +(-2.50000 + 4.33013i) q^{37} +(4.50000 - 2.59808i) q^{41} +(-10.5000 - 6.06218i) q^{43} +(-6.50000 - 2.59808i) q^{49} +(4.50000 - 2.59808i) q^{53} -5.19615i q^{55} +(6.00000 - 10.3923i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-1.50000 + 0.866025i) q^{65} +(-9.00000 - 5.19615i) q^{67} +(-3.50000 - 6.06218i) q^{73} +(1.50000 - 7.79423i) q^{77} +(-9.00000 + 5.19615i) q^{79} +(7.50000 - 12.9904i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(1.50000 + 0.866025i) q^{89} +(-2.50000 + 0.866025i) q^{91} +(1.50000 - 2.59808i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{7} + 6 q^{11} - q^{13} + 3 q^{17} + 3 q^{19} + 6 q^{23} + 4 q^{25} + 15 q^{29} + 6 q^{31} - 9 q^{35} - 5 q^{37} + 9 q^{41} - 21 q^{43} - 13 q^{49} + 9 q^{53} + 12 q^{59} + 10 q^{61} - 3 q^{65}+ \cdots + 5 q^{97}+O(q^{100}) $ 2 * q + q^7 + 6 * q^11 - q^13 + 3 * q^17 + 3 * q^19 + 6 * q^23 + 4 * q^25 + 15 * q^29 + 6 * q^31 - 9 * q^35 - 5 * q^37 + 9 * q^41 - 21 * q^43 - 13 * q^49 + 9 * q^53 + 12 * q^59 + 10 * q^61 - 3 * q^65 - 18 * q^67 - 7 * q^73 + 3 * q^77 - 18 * q^79 + 15 * q^83 - 3 * q^85 + 3 * q^89 - 5 * q^91 + 3 * q^95 + 5 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.00000			0.904534			0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000			0.904534			0.452267	+	0.891883i	$0.350615\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	−0.306944	−	0.951727i	$-0.599307\pi$
$17$	1.50000	−	0.866025i	0.363803	−	0.210042i	0.670748	+	0.741685i	$0.265973\pi$
$18$		0			0
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	0.662094	−	0.749421i	$-0.269668\pi$
$19$	1.50000	+	0.866025i	0.344124	+	0.198680i	−0.317970	+	0.948101i	$0.603001\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$		0			0
$25$	2.00000			0.400000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	7.50000	+	4.33013i	1.39272	+	0.804084i	0.993615	−	0.112823i	$-0.0359893\pi$
$29$	7.50000	+	4.33013i	1.39272	+	0.804084i	0.399100	+	0.916907i	$0.369323\pi$
$30$		0			0
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.50000	−	0.866025i	−0.760639	−	0.146385i
$36$		0			0
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	−0.994999	−	0.0998840i	$-0.968153\pi$
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	0.584002	+	0.811752i	$0.301486\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$		0			0
$43$	−10.5000	−	6.06218i	−1.60123	−	0.924473i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−10.5000	−	6.06218i	−1.60123	−	0.924473i	−0.609994	−	0.792406i	$-0.708828\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.50000	−	2.59808i	0.618123	−	0.356873i	−0.158015	−	0.987437i	$-0.550509\pi$
$53$	4.50000	−	2.59808i	0.618123	−	0.356873i	0.776138	+	0.630563i	$0.217176\pi$
$54$		0			0
$55$		−	5.19615i		−	0.700649i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.50000	+	0.866025i	−0.186052	+	0.107417i
$66$		0			0
$67$	−9.00000	−	5.19615i	−1.09952	−	0.634811i	−0.163429	−	0.986555i	$-0.552255\pi$
$67$	−9.00000	−	5.19615i	−1.09952	−	0.634811i	−0.936096	+	0.351744i	$0.885589\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	−9.00000	+	5.19615i	−1.01258	+	0.584613i	−0.911946	−	0.410311i	$-0.865420\pi$
$79$	−9.00000	+	5.19615i	−1.01258	+	0.584613i	−0.100633	+	0.994924i	$0.532087\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	−0.0800311	−	0.996792i	$-0.525502\pi$
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	0.903263	−	0.429087i	$-0.141165\pi$
$84$		0			0
$85$	−1.50000	−	2.59808i	−0.162698	−	0.281801i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	0.577389	−	0.816469i	$-0.304072\pi$
$89$	1.50000	+	0.866025i	0.159000	+	0.0917985i	−0.418389	+	0.908268i	$0.637405\pi$
$90$		0			0
$91$	−2.50000	+	0.866025i	−0.262071	+	0.0907841i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.50000	−	2.59808i	0.153897	−	0.266557i
$96$		0			0
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			15.5885i			1.55111i	0.631280	+	0.775555i	$0.282530\pi$
$101$			15.5885i			1.55111i	−0.631280	+	0.775555i	$0.717470\pi$
$102$		0			0
$103$		−	5.19615i		−	0.511992i	−0.966678	−	0.255996i	$-0.917597\pi$
$103$		−	5.19615i		−	0.511992i	0.966678	−	0.255996i	$-0.0824034\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	0.999512	+	0.0312328i	$0.00994332\pi$
$109$	5.50000	+	9.52628i	0.526804	+	0.912452i	−0.472708	+	0.881219i	$0.656723\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.50000	+	4.33013i	−0.705541	+	0.407344i	−0.809408	−	0.587247i	$-0.800212\pi$
$113$	−7.50000	+	4.33013i	−0.705541	+	0.407344i	0.103867	+	0.994591i	$0.466878\pi$
$114$		0			0
$115$		−	5.19615i		−	0.484544i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.50000	−	4.33013i	−0.137505	−	0.396942i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$		−	3.46410i		−	0.307389i	−0.988118	−	0.153695i	$-0.950883\pi$
$127$		−	3.46410i		−	0.307389i	0.988118	−	0.153695i	$-0.0491172\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−15.0000			−1.31056			−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000			−1.31056			−0.655278	+	0.755388i	$0.727449\pi$
$132$		0			0
$133$	3.00000	−	3.46410i	0.260133	−	0.300376i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	1.73205i		−	0.147979i	−0.997259	−	0.0739895i	$-0.976427\pi$
$137$		−	1.73205i		−	0.147979i	0.997259	−	0.0739895i	$-0.0235731\pi$
$138$		0			0
$139$	−13.5000	+	7.79423i	−1.14506	+	0.661098i	−0.947677	−	0.319230i	$-0.896576\pi$
$139$	−13.5000	+	7.79423i	−1.14506	+	0.661098i	−0.197378	+	0.980328i	$0.563243\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$		0			0
$145$	7.50000	−	12.9904i	0.622841	−	1.07879i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	8.66025i		−	0.709476i	−0.934966	−	0.354738i	$-0.884570\pi$
$149$		−	8.66025i		−	0.709476i	0.934966	−	0.354738i	$-0.115430\pi$
$150$		0			0
$151$		−	19.0526i		−	1.55048i	−0.631670	−	0.775238i	$-0.717630\pi$
$151$		−	19.0526i		−	1.55048i	0.631670	−	0.775238i	$-0.282370\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.50000	−	7.79423i	0.118217	−	0.614271i
$162$		0			0
$163$	1.50000	+	0.866025i	0.117489	+	0.0678323i	0.557593	−	0.830115i	$-0.311725\pi$
$163$	1.50000	+	0.866025i	0.117489	+	0.0678323i	−0.440104	+	0.897947i	$0.645058\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	0.637713	−	0.770274i	$-0.279881\pi$
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	−0.985933	+	0.167139i	$0.946547\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−12.0000	+	6.92820i	−0.912343	+	0.526742i	−0.881184	−	0.472773i	$-0.843253\pi$
$173$	−12.0000	+	6.92820i	−0.912343	+	0.526742i	−0.0311588	+	0.999514i	$0.509920\pi$
$174$		0			0
$175$	1.00000	−	5.19615i	0.0755929	−	0.392792i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$		0			0
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.50000	+	4.33013i	0.551411	+	0.318357i
$186$		0			0
$187$	4.50000	−	2.59808i	0.329073	−	0.189990i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			27.7128i			1.97446i	0.159313	+	0.987228i	$0.449072\pi$
$197$			27.7128i			1.97446i	−0.159313	+	0.987228i	$0.550928\pi$
$198$		0			0
$199$	7.50000	−	4.33013i	0.531661	−	0.306955i	−0.210032	−	0.977695i	$-0.567357\pi$
$199$	7.50000	−	4.33013i	0.531661	−	0.306955i	0.741693	+	0.670740i	$0.234023\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.0000	−	17.3205i	1.05279	−	1.21566i
$204$		0			0
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.50000	+	2.59808i	0.311272	+	0.179713i
$210$		0			0
$211$	−19.5000	+	11.2583i	−1.34244	+	0.775055i	−0.987164	−	0.159708i	$-0.948945\pi$
$211$	−19.5000	+	11.2583i	−1.34244	+	0.775055i	−0.355271	+	0.934763i	$0.615611\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.5000	+	18.1865i	−0.716094	+	1.24031i
$216$		0			0
$217$	6.00000	−	6.92820i	0.407307	−	0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.50000	−	0.866025i	−0.100901	−	0.0582552i
$222$		0			0
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	0.643046	−	0.765828i	$-0.277671\pi$
$223$	4.50000	+	2.59808i	0.301342	+	0.173980i	−0.341703	+	0.939808i	$0.611004\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.00000			−0.597351			−0.298675	−	0.954355i	$-0.596545\pi$
$227$	−9.00000			−0.597351			−0.298675	+	0.954355i	$0.596545\pi$
$228$		0			0
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	19.5000	+	11.2583i	1.27749	+	0.737558i	0.976386	−	0.216034i	$-0.0693123\pi$
$233$	19.5000	+	11.2583i	1.27749	+	0.737558i	0.301102	+	0.953592i	$0.402646\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.5000	−	18.1865i	−0.679189	−	1.17639i	−0.975226	−	0.221213i	$-0.928999\pi$
$239$	−10.5000	−	18.1865i	−0.679189	−	1.17639i	0.296037	−	0.955176i	$-0.404335\pi$
$240$		0			0
$241$	−17.0000			−1.09507			−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−17.0000			−1.09507			−0.547533	+	0.836784i	$0.684433\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.50000	+	11.2583i	−0.287494	+	0.719268i
$246$		0			0
$247$		−	1.73205i		−	0.110208i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	12.1244i		−	0.756297i	−0.925745	−	0.378148i	$-0.876561\pi$
$257$		−	12.1244i		−	0.756297i	0.925745	−	0.378148i	$-0.123439\pi$
$258$		0			0
$259$	10.0000	+	8.66025i	0.621370	+	0.538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.00000			−0.184988			−0.0924940	−	0.995713i	$-0.529484\pi$
$263$	−3.00000			−0.184988			−0.0924940	+	0.995713i	$0.529484\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	16.5000	−	9.52628i	1.00602	−	0.580828i	0.0959980	−	0.995382i	$-0.469396\pi$
$269$	16.5000	−	9.52628i	1.00602	−	0.580828i	0.910025	+	0.414554i	$0.136062\pi$
$270$		0			0
$271$	16.5000	+	9.52628i	1.00230	+	0.578680i	0.908929	−	0.416951i	$-0.136901\pi$
$271$	16.5000	+	9.52628i	1.00230	+	0.578680i	0.0933746	+	0.995631i	$0.470235\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.00000			0.361814
$276$		0			0
$277$	13.0000			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.50000	−	0.866025i	−0.0894825	−	0.0516627i	0.454591	−	0.890700i	$-0.349785\pi$
$281$	−1.50000	−	0.866025i	−0.0894825	−	0.0516627i	−0.544074	+	0.839038i	$0.683119\pi$
$282$		0			0
$283$	3.00000	+	1.73205i	0.178331	+	0.102960i	0.586509	−	0.809943i	$-0.300502\pi$
$283$	3.00000	+	1.73205i	0.178331	+	0.102960i	−0.408177	+	0.912903i	$0.633835\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.50000	−	12.9904i	−0.265627	−	0.766798i
$288$		0			0
$289$	−7.00000	+	12.1244i	−0.411765	+	0.713197i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.5000	+	6.06218i	−0.613417	+	0.354156i	−0.774301	−	0.632817i	$-0.781899\pi$
$293$	−10.5000	+	6.06218i	−0.613417	+	0.354156i	0.160885	+	0.986973i	$0.448565\pi$
$294$		0			0
$295$	−18.0000	−	10.3923i	−1.04800	−	0.605063i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.50000	−	2.59808i	−0.0867472	−	0.150251i
$300$		0			0
$301$	−21.0000	+	24.2487i	−1.21042	+	1.39767i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.0000	−	8.66025i	0.858898	−	0.495885i
$306$		0			0
$307$		−	17.3205i		−	0.988534i	−0.869310	−	0.494267i	$-0.835437\pi$
$307$		−	17.3205i		−	0.988534i	0.869310	−	0.494267i	$-0.164563\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.0000	+	13.8564i	−1.34797	+	0.778253i	−0.987962	−	0.154694i	$-0.950561\pi$
$317$	−24.0000	+	13.8564i	−1.34797	+	0.778253i	−0.360012	+	0.932948i	$0.617227\pi$
$318$		0			0
$319$	22.5000	+	12.9904i	1.25976	+	0.727322i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.00000			0.166924
$324$		0			0
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−3.00000	+	1.73205i	−0.164895	+	0.0952021i	−0.580176	−	0.814491i	$-0.697016\pi$
$331$	−3.00000	+	1.73205i	−0.164895	+	0.0952021i	0.415282	+	0.909693i	$0.363683\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.00000	+	15.5885i	−0.491723	+	0.851688i
$336$		0			0
$337$	14.5000	+	25.1147i	0.789865	+	1.36809i	0.926049	+	0.377403i	$0.123183\pi$
$337$	14.5000	+	25.1147i	0.789865	+	1.36809i	−0.136184	+	0.990684i	$0.543484\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.00000	+	5.19615i	0.487377	+	0.281387i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	15.5000	−	26.8468i	0.829696	−	1.43708i	−0.0685808	−	0.997646i	$-0.521847\pi$
$349$	15.5000	−	26.8468i	0.829696	−	1.43708i	0.898277	−	0.439430i	$-0.144820\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	15.5885i		−	0.829690i	−0.909892	−	0.414845i	$-0.863836\pi$
$353$		−	15.5885i		−	0.829690i	0.909892	−	0.414845i	$-0.136164\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.5000	−	23.3827i	0.712503	−	1.23409i	−0.251412	−	0.967880i	$-0.580895\pi$
$359$	13.5000	−	23.3827i	0.712503	−	1.23409i	0.963915	−	0.266211i	$-0.0857717\pi$
$360$		0			0
$361$	−8.00000	−	13.8564i	−0.421053	−	0.729285i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.5000	+	6.06218i	−0.549595	+	0.317309i
$366$		0			0
$367$			22.5167i			1.17536i	0.809093	+	0.587680i	$0.199959\pi$
$367$			22.5167i			1.17536i	−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.50000	−	12.9904i	−0.233628	−	0.674427i
$372$		0			0
$373$	−7.00000			−0.362446			−0.181223	−	0.983442i	$-0.558006\pi$
$373$	−7.00000			−0.362446			−0.181223	+	0.983442i	$0.558006\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	8.66025i		−	0.446026i
$378$		0			0
$379$			10.3923i			0.533817i	0.963722	+	0.266908i	$0.0860021\pi$
$379$			10.3923i			0.533817i	−0.963722	+	0.266908i	$0.913998\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.00000			0.153293			0.0766464	−	0.997058i	$-0.475579\pi$
$383$	3.00000			0.153293			0.0766464	+	0.997058i	$0.475579\pi$
$384$		0			0
$385$	−13.5000	−	2.59808i	−0.688024	−	0.132410i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			36.3731i			1.84419i	0.386966	+	0.922094i	$0.373523\pi$
$389$			36.3731i			1.84419i	−0.386966	+	0.922094i	$0.626477\pi$
$390$		0			0
$391$	4.50000	−	2.59808i	0.227575	−	0.131390i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.00000	+	15.5885i	0.452839	+	0.784340i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	32.9090i		−	1.64340i	−0.569924	−	0.821698i	$-0.693027\pi$
$401$		−	32.9090i		−	1.64340i	0.569924	−	0.821698i	$-0.306973\pi$
$402$		0			0
$403$		−	3.46410i		−	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.50000	+	12.9904i	−0.371761	+	0.643909i
$408$		0			0
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−24.0000	−	20.7846i	−1.18096	−	1.02274i
$414$		0			0
$415$	−22.5000	−	12.9904i	−1.10448	−	0.637673i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.5000	+	28.5788i	0.806078	+	1.39617i	0.915561	+	0.402179i	$0.131747\pi$
$419$	16.5000	+	28.5788i	0.806078	+	1.39617i	−0.109483	+	0.993989i	$0.534920\pi$
$420$		0			0
$421$	−18.5000	+	32.0429i	−0.901635	+	1.56168i	−0.0762630	+	0.997088i	$0.524299\pi$
$421$	−18.5000	+	32.0429i	−0.901635	+	1.56168i	−0.825372	+	0.564590i	$0.809034\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.00000	−	1.73205i	0.145521	−	0.0840168i
$426$		0			0
$427$	25.0000	−	8.66025i	1.20983	−	0.419099i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.5000	+	18.1865i	0.505767	+	0.876014i	0.999978	+	0.00667224i	$0.00212386\pi$
$431$	10.5000	+	18.1865i	0.505767	+	0.876014i	−0.494211	+	0.869342i	$0.664543\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.50000	+	2.59808i	0.215264	+	0.124283i
$438$		0			0
$439$	27.0000	−	15.5885i	1.28864	−	0.743996i	0.310228	−	0.950662i	$-0.399595\pi$
$439$	27.0000	−	15.5885i	1.28864	−	0.743996i	0.978412	+	0.206666i	$0.0662612\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	1.50000	−	2.59808i	0.0711068	−	0.123161i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			20.7846i			0.980886i	0.871473	+	0.490443i	$0.163165\pi$
$449$			20.7846i			0.980886i	−0.871473	+	0.490443i	$0.836835\pi$
$450$		0			0
$451$	13.5000	−	7.79423i	0.635690	−	0.367016i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.50000	+	4.33013i	0.0703211	+	0.202999i
$456$		0			0
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−4.50000	−	2.59808i	−0.209586	−	0.121004i	0.391533	−	0.920164i	$-0.371945\pi$
$461$	−4.50000	−	2.59808i	−0.209586	−	0.121004i	−0.601119	+	0.799160i	$0.705278\pi$
$462$		0			0
$463$	−16.5000	+	9.52628i	−0.766820	+	0.442724i	−0.831739	−	0.555167i	$-0.812654\pi$
$463$	−16.5000	+	9.52628i	−0.766820	+	0.442724i	0.0649190	+	0.997891i	$0.479321\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.5000	+	33.7750i	−0.902352	+	1.56292i	−0.0779201	+	0.996960i	$0.524828\pi$
$467$	−19.5000	+	33.7750i	−0.902352	+	1.56292i	−0.824432	+	0.565961i	$0.808505\pi$
$468$		0			0
$469$	−18.0000	+	20.7846i	−0.831163	+	0.959744i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−31.5000	−	18.1865i	−1.44837	−	0.836218i
$474$		0			0
$475$	3.00000	+	1.73205i	0.137649	+	0.0794719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−27.0000			−1.23366			−0.616831	−	0.787096i	$-0.711584\pi$
$479$	−27.0000			−1.23366			−0.616831	+	0.787096i	$0.711584\pi$
$480$		0			0
$481$	5.00000			0.227980
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.50000	−	4.33013i	−0.340557	−	0.196621i
$486$		0			0
$487$	−16.5000	+	9.52628i	−0.747686	+	0.431677i	−0.824857	−	0.565341i	$-0.808745\pi$
$487$	−16.5000	+	9.52628i	−0.747686	+	0.431677i	0.0771710	+	0.997018i	$0.475411\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	0.950365	+	0.311136i	$0.100710\pi$
$491$	16.5000	+	28.5788i	0.744635	+	1.28974i	−0.205731	+	0.978609i	$0.565957\pi$
$492$		0			0
$493$	15.0000			0.675566
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	29.4449i		−	1.31813i	−0.752085	−	0.659067i	$-0.770952\pi$
$499$		−	29.4449i		−	1.31813i	0.752085	−	0.659067i	$-0.229048\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	27.0000			1.20148
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	15.5885i		−	0.690946i	−0.938429	−	0.345473i	$-0.887718\pi$
$509$		−	15.5885i		−	0.690946i	0.938429	−	0.345473i	$-0.112282\pi$
$510$		0			0
$511$	−17.5000	+	6.06218i	−0.774154	+	0.268175i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.00000			−0.396587
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	31.5000	−	18.1865i	1.38004	−	0.796766i	0.387876	−	0.921711i	$-0.373209\pi$
$521$	31.5000	−	18.1865i	1.38004	−	0.796766i	0.992164	+	0.124945i	$0.0398754\pi$
$522$		0			0
$523$	−22.5000	−	12.9904i	−0.983856	−	0.568030i	−0.0804241	−	0.996761i	$-0.525627\pi$
$523$	−22.5000	−	12.9904i	−0.983856	−	0.568030i	−0.903432	+	0.428731i	$0.858961\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000			0.261364
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.50000	−	2.59808i	−0.194917	−	0.112535i
$534$		0			0
$535$	4.50000	+	2.59808i	0.194552	+	0.112325i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$		0			0
$541$	−12.5000	+	21.6506i	−0.537417	+	0.930834i	0.461625	+	0.887075i	$0.347267\pi$
$541$	−12.5000	+	21.6506i	−0.537417	+	0.930834i	−0.999042	+	0.0437584i	$0.986067\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.5000	−	9.52628i	0.706782	−	0.408061i
$546$		0			0
$547$	19.5000	+	11.2583i	0.833760	+	0.481371i	0.855138	−	0.518400i	$-0.173472\pi$
$547$	19.5000	+	11.2583i	0.833760	+	0.481371i	−0.0213785	+	0.999771i	$0.506805\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.50000	+	12.9904i	0.319511	+	0.553409i
$552$		0			0
$553$	9.00000	+	25.9808i	0.382719	+	1.10481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.50000	+	4.33013i	−0.317785	+	0.183473i	−0.650405	−	0.759588i	$-0.725401\pi$
$557$	−7.50000	+	4.33013i	−0.317785	+	0.183473i	0.332620	+	0.943061i	$0.392067\pi$
$558$		0			0
$559$			12.1244i			0.512806i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	7.50000	+	12.9904i	0.315527	+	0.546509i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	24.0000	−	13.8564i	1.00613	−	0.580891i	0.0960754	−	0.995374i	$-0.469371\pi$
$569$	24.0000	−	13.8564i	1.00613	−	0.580891i	0.910057	+	0.414483i	$0.136038\pi$
$570$		0			0
$571$	15.0000	+	8.66025i	0.627730	+	0.362420i	0.779873	−	0.625938i	$-0.215284\pi$
$571$	15.0000	+	8.66025i	0.627730	+	0.362420i	−0.152142	+	0.988359i	$0.548617\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.00000			0.250217
$576$		0			0
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	0.520952	−	0.853586i	$-0.325577\pi$
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	−0.999703	+	0.0243645i	$0.992244\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−30.0000	−	25.9808i	−1.24461	−	1.07786i
$582$		0			0
$583$	13.5000	−	7.79423i	0.559113	−	0.322804i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	−0.943824	−	0.330449i	$-0.892800\pi$
$587$	−4.50000	+	7.79423i	−0.185735	+	0.321702i	0.758089	+	0.652151i	$0.226133\pi$
$588$		0			0
$589$	3.00000	+	5.19615i	0.123613	+	0.214104i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	37.5000	+	21.6506i	1.53994	+	0.889085i	0.998841	+	0.0481262i	$0.0153250\pi$
$593$	37.5000	+	21.6506i	1.53994	+	0.889085i	0.541099	+	0.840959i	$0.318008\pi$
$594$		0			0
$595$	−7.50000	+	2.59808i	−0.307470	+	0.106511i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.0000	+	41.5692i	−0.980613	+	1.69847i	−0.320607	+	0.947212i	$0.603887\pi$
$599$	−24.0000	+	41.5692i	−0.980613	+	1.69847i	−0.660006	+	0.751260i	$0.729446\pi$
$600$		0			0
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	0.249565	+	0.968358i	$0.419712\pi$
$601$	−17.5000	+	30.3109i	−0.713840	+	1.23641i	−0.963405	+	0.268049i	$0.913621\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$			3.46410i			0.140836i
$606$		0			0
$607$			1.73205i			0.0703018i	0.999382	+	0.0351509i	$0.0111912\pi$
$607$			1.73205i			0.0703018i	−0.999382	+	0.0351509i	$0.988809\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−8.50000	−	14.7224i	−0.343312	−	0.594633i	0.641734	−	0.766927i	$-0.278215\pi$
$613$	−8.50000	−	14.7224i	−0.343312	−	0.594633i	−0.985046	+	0.172294i	$0.944882\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−37.5000	+	21.6506i	−1.50969	+	0.871622i	−0.509757	+	0.860318i	$0.670265\pi$
$617$	−37.5000	+	21.6506i	−1.50969	+	0.871622i	−0.999936	+	0.0113033i	$0.996402\pi$
$618$		0			0
$619$			46.7654i			1.87966i	0.341644	+	0.939829i	$0.389016\pi$
$619$			46.7654i			1.87966i	−0.341644	+	0.939829i	$0.610984\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.00000	−	3.46410i	0.120192	−	0.138786i
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$		0			0
$628$		0			0
$629$			8.66025i			0.345307i
$630$		0			0
$631$		−	3.46410i		−	0.137904i	−0.997620	−	0.0689519i	$-0.978035\pi$
$631$		−	3.46410i		−	0.137904i	0.997620	−	0.0689519i	$-0.0219655\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.00000			−0.238103
$636$		0			0
$637$	1.00000	+	6.92820i	0.0396214	+	0.274505i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	1.73205i		−	0.0684119i	−0.999415	−	0.0342059i	$-0.989110\pi$
$641$		−	1.73205i		−	0.0684119i	0.999415	−	0.0342059i	$-0.0108902\pi$
$642$		0			0
$643$	10.5000	−	6.06218i	0.414080	−	0.239069i	−0.278462	−	0.960447i	$-0.589824\pi$
$643$	10.5000	−	6.06218i	0.414080	−	0.239069i	0.692541	+	0.721378i	$0.256491\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.5000	+	38.9711i	0.884566	+	1.53211i	0.846210	+	0.532850i	$0.178879\pi$
$647$	22.5000	+	38.9711i	0.884566	+	1.53211i	0.0383563	+	0.999264i	$0.487788\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	15.5885i		−	0.610023i	−0.952349	−	0.305012i	$-0.901340\pi$
$653$		−	15.5885i		−	0.610023i	0.952349	−	0.305012i	$-0.0986604\pi$
$654$		0			0
$655$			25.9808i			1.01515i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.5000	+	18.1865i	−0.409022	+	0.708447i	−0.994780	−	0.102039i	$-0.967463\pi$
$659$	−10.5000	+	18.1865i	−0.409022	+	0.708447i	0.585758	+	0.810486i	$0.300797\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.00000	−	5.19615i	−0.232670	−	0.201498i
$666$		0			0
$667$	22.5000	+	12.9904i	0.871203	+	0.502990i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$		0			0
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$677$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$678$		0			0
$679$	−10.0000	−	8.66025i	−0.383765	−	0.332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	−0.987275	−	0.159022i	$-0.949166\pi$
$683$	−16.5000	−	28.5788i	−0.631355	−	1.09354i	0.355920	−	0.934516i	$-0.384168\pi$
$684$		0			0
$685$	−3.00000			−0.114624
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.50000	−	2.59808i	−0.171436	−	0.0989788i
$690$		0			0
$691$	−15.0000	+	8.66025i	−0.570627	+	0.329452i	−0.757400	−	0.652952i	$-0.773531\pi$
$691$	−15.0000	+	8.66025i	−0.570627	+	0.329452i	0.186773	+	0.982403i	$0.440197\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	13.5000	+	23.3827i	0.512084	+	0.886956i
$696$		0			0
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			13.8564i			0.523349i	0.965156	+	0.261675i	$0.0842747\pi$
$701$			13.8564i			0.523349i	−0.965156	+	0.261675i	$0.915725\pi$
$702$		0			0
$703$	−7.50000	+	4.33013i	−0.282868	+	0.163314i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	40.5000	+	7.79423i	1.52316	+	0.293132i
$708$		0			0
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	0.756730	−	0.653727i	$-0.226796\pi$
$709$	−5.00000	−	8.66025i	−0.187779	−	0.325243i	−0.944509	+	0.328484i	$0.893462\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.00000	+	5.19615i	0.337053	+	0.194597i
$714$		0			0
$715$	−4.50000	+	2.59808i	−0.168290	+	0.0971625i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	−0.496527	−	0.868021i	$-0.665392\pi$
$719$	13.5000	−	23.3827i	0.503465	−	0.872027i	0.999992	−	0.00400572i	$-0.00127506\pi$
$720$		0			0
$721$	−13.5000	−	2.59808i	−0.502766	−	0.0967574i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	15.0000	+	8.66025i	0.557086	+	0.321634i
$726$		0			0
$727$	28.5000	+	16.4545i	1.05701	+	0.610263i	0.924603	−	0.380933i	$-0.124397\pi$
$727$	28.5000	+	16.4545i	1.05701	+	0.610263i	0.132404	+	0.991196i	$0.457730\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−21.0000			−0.776713
$732$		0			0
$733$	−11.0000			−0.406294			−0.203147	−	0.979148i	$-0.565117\pi$
$733$	−11.0000			−0.406294			−0.203147	+	0.979148i	$0.565117\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−27.0000	−	15.5885i	−0.994558	−	0.574208i
$738$		0			0
$739$	10.5000	−	6.06218i	0.386249	−	0.223001i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	10.5000	−	6.06218i	0.386249	−	0.223001i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	0.606590	−	0.795015i	$-0.292537\pi$
$743$	−10.5000	−	18.1865i	−0.385208	−	0.667199i	−0.991798	+	0.127815i	$0.959204\pi$
$744$		0			0
$745$	−15.0000			−0.549557
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.00000	+	5.19615i	0.219235	+	0.189863i
$750$		0			0
$751$		−	12.1244i		−	0.442424i	−0.975226	−	0.221212i	$-0.928999\pi$
$751$		−	12.1244i		−	0.442424i	0.975226	−	0.221212i	$-0.0710013\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.0000			−1.20099
$756$		0			0
$757$	46.0000			1.67190			0.835949	−	0.548807i	$-0.184918\pi$
$757$	46.0000			1.67190			0.835949	+	0.548807i	$0.184918\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			29.4449i			1.06738i	0.845682	+	0.533688i	$0.179194\pi$
$761$			29.4449i			1.06738i	−0.845682	+	0.533688i	$0.820806\pi$
$762$		0			0
$763$	27.5000	−	9.52628i	0.995567	−	0.344874i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.0000			−0.433295
$768$		0			0
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	0.580696	−	0.814120i	$-0.302780\pi$
$769$	−11.5000	−	19.9186i	−0.414701	−	0.718283i	−0.995397	+	0.0958377i	$0.969447\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	28.5000	−	16.4545i	1.02507	−	0.591827i	0.109504	−	0.993986i	$-0.465074\pi$
$773$	28.5000	−	16.4545i	1.02507	−	0.591827i	0.915570	+	0.402160i	$0.131740\pi$
$774$		0			0
$775$	6.00000	+	3.46410i	0.215526	+	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.00000			0.322458
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.0000	−	8.66025i	−0.535373	−	0.309098i
$786$		0			0
$787$	39.0000	+	22.5167i	1.39020	+	0.802632i	0.993337	−	0.115246i	$-0.0367655\pi$
$787$	39.0000	+	22.5167i	1.39020	+	0.802632i	0.396863	+	0.917878i	$0.370099\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.50000	+	21.6506i	0.266669	+	0.769808i
$792$		0			0
$793$	5.00000	−	8.66025i	0.177555	−	0.307535i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.5000	+	9.52628i	−0.584460	+	0.337438i	−0.762904	−	0.646512i	$-0.776227\pi$
$797$	−16.5000	+	9.52628i	−0.584460	+	0.337438i	0.178444	+	0.983950i	$0.442894\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−10.5000	−	18.1865i	−0.370537	−	0.641789i
$804$		0			0
$805$	−13.5000	−	2.59808i	−0.475812	−	0.0915702i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	25.5000	−	14.7224i	0.896532	−	0.517613i	0.0204587	−	0.999791i	$-0.493487\pi$
$809$	25.5000	−	14.7224i	0.896532	−	0.517613i	0.876074	+	0.482178i	$0.160154\pi$
$810$		0			0
$811$		−	10.3923i		−	0.364923i	−0.983213	−	0.182462i	$-0.941593\pi$
$811$		−	10.3923i		−	0.364923i	0.983213	−	0.182462i	$-0.0584065\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.50000	−	2.59808i	0.0525427	−	0.0910066i
$816$		0			0
$817$	−10.5000	−	18.1865i	−0.367348	−	0.636266i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.0000	+	24.2487i	−1.46581	+	0.846286i	−0.999270	−	0.0382140i	$-0.987833\pi$
$821$	−42.0000	+	24.2487i	−1.46581	+	0.846286i	−0.466541	+	0.884500i	$0.654500\pi$
$822$		0			0
$823$	3.00000	+	1.73205i	0.104573	+	0.0603755i	0.551375	−	0.834258i	$-0.314104\pi$
$823$	3.00000	+	1.73205i	0.104573	+	0.0603755i	−0.446801	+	0.894633i	$0.647437\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−0.500000	−	0.866025i	−0.0173657	−	0.0300783i	0.857212	−	0.514964i	$-0.172195\pi$
$829$	−0.500000	−	0.866025i	−0.0173657	−	0.0300783i	−0.874578	+	0.484885i	$0.838861\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.0000	+	1.73205i	−0.415775	+	0.0600120i
$834$		0			0
$835$	−13.5000	+	7.79423i	−0.467187	+	0.269730i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	16.5000	−	28.5788i	0.569643	−	0.986651i	−0.426958	−	0.904272i	$-0.640415\pi$
$839$	16.5000	−	28.5788i	0.569643	−	0.986651i	0.996601	−	0.0823795i	$-0.0262520\pi$
$840$		0			0
$841$	23.0000	+	39.8372i	0.793103	+	1.37370i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.0000	−	10.3923i	−0.619219	−	0.357506i
$846$		0			0
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.50000	+	12.9904i	−0.257097	+	0.445305i
$852$		0			0
$853$	−20.5000	+	35.5070i	−0.701907	+	1.21574i	0.265890	+	0.964003i	$0.414334\pi$
$853$	−20.5000	+	35.5070i	−0.701907	+	1.21574i	−0.967796	+	0.251734i	$0.918999\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	22.5167i		−	0.769154i	−0.923093	−	0.384577i	$-0.874347\pi$
$857$		−	22.5167i		−	0.769154i	0.923093	−	0.384577i	$-0.125653\pi$
$858$		0			0
$859$			19.0526i			0.650065i	0.945703	+	0.325032i	$0.105375\pi$
$859$			19.0526i			0.650065i	−0.945703	+	0.325032i	$0.894625\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	25.5000	−	44.1673i	0.868030	−	1.50347i	0.00402340	−	0.999992i	$-0.498719\pi$
$863$	25.5000	−	44.1673i	0.868030	−	1.50347i	0.864007	−	0.503480i	$-0.167947\pi$
$864$		0			0
$865$	12.0000	+	20.7846i	0.408012	+	0.706698i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−27.0000	+	15.5885i	−0.915912	+	0.528802i
$870$		0			0
$871$			10.3923i			0.352130i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−31.5000	−	6.06218i	−1.06489	−	0.204939i
$876$		0			0
$877$	−31.0000			−1.04680			−0.523398	−	0.852088i	$-0.675336\pi$
$877$	−31.0000			−1.04680			−0.523398	+	0.852088i	$0.675336\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	20.7846i		−	0.700251i	−0.936703	−	0.350126i	$-0.886139\pi$
$881$		−	20.7846i		−	0.700251i	0.936703	−	0.350126i	$-0.113861\pi$
$882$		0			0
$883$			38.1051i			1.28234i	0.767399	+	0.641170i	$0.221551\pi$
$883$			38.1051i			1.28234i	−0.767399	+	0.641170i	$0.778449\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.00000			0.100730			0.0503651	−	0.998731i	$-0.483962\pi$
$887$	3.00000			0.100730			0.0503651	+	0.998731i	$0.483962\pi$
$888$		0			0
$889$	−9.00000	−	1.73205i	−0.301850	−	0.0580911i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	22.5000	−	12.9904i	0.752092	−	0.434221i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$		0			0
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	17.3205i		−	0.575753i
$906$		0			0
$907$		−	15.5885i		−	0.517606i	−0.965930	−	0.258803i	$-0.916672\pi$
$907$		−	15.5885i		−	0.517606i	0.965930	−	0.258803i	$-0.0833281\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	4.50000	−	7.79423i	0.149092	−	0.258234i	−0.781800	−	0.623529i	$-0.785698\pi$
$911$	4.50000	−	7.79423i	0.149092	−	0.258234i	0.930892	+	0.365295i	$0.119032\pi$
$912$		0			0
$913$	22.5000	−	38.9711i	0.744641	−	1.28976i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.50000	+	38.9711i	−0.247672	+	1.28694i
$918$		0			0
$919$	28.5000	+	16.4545i	0.940128	+	0.542783i	0.890001	−	0.455960i	$-0.150704\pi$
$919$	28.5000	+	16.4545i	0.940128	+	0.542783i	0.0501277	+	0.998743i	$0.484037\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−5.00000	+	8.66025i	−0.164399	+	0.284747i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−30.0000	+	17.3205i	−0.984268	+	0.568267i	−0.903556	−	0.428470i	$-0.859053\pi$
$929$	−30.0000	+	17.3205i	−0.984268	+	0.568267i	−0.0807121	+	0.996737i	$0.525719\pi$
$930$		0			0
$931$	−7.50000	−	9.52628i	−0.245803	−	0.312211i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.50000	−	7.79423i	−0.147166	−	0.254899i
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	48.0000	+	27.7128i	1.56476	+	0.903412i	0.996765	+	0.0803769i	$0.0256124\pi$
$941$	48.0000	+	27.7128i	1.56476	+	0.903412i	0.567991	+	0.823035i	$0.307721\pi$
$942$		0			0
$943$	13.5000	−	7.79423i	0.439620	−	0.253815i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			34.6410i			1.12213i	0.827771	+	0.561066i	$0.189609\pi$
$953$			34.6410i			1.12213i	−0.827771	+	0.561066i	$0.810391\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.50000	−	0.866025i	−0.145313	−	0.0279654i
$960$		0			0
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−15.0000	−	8.66025i	−0.482867	−	0.278783i
$966$		0			0
$967$	−4.50000	+	2.59808i	−0.144710	+	0.0835485i	−0.570607	−	0.821223i	$-0.693292\pi$
$967$	−4.50000	+	2.59808i	−0.144710	+	0.0835485i	0.425897	+	0.904772i	$0.359959\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$		0			0
$973$	13.5000	+	38.9711i	0.432790	+	1.24936i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.0000	−	10.3923i	−0.575871	−	0.332479i	0.183620	−	0.982997i	$-0.441218\pi$
$977$	−18.0000	−	10.3923i	−0.575871	−	0.332479i	−0.759491	+	0.650518i	$0.774552\pi$
$978$		0			0
$979$	4.50000	+	2.59808i	0.143821	+	0.0830349i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.00000			0.287055			0.143528	−	0.989646i	$-0.454155\pi$
$983$	9.00000			0.287055			0.143528	+	0.989646i	$0.454155\pi$
$984$		0			0
$985$	48.0000			1.52941
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−31.5000	−	18.1865i	−1.00164	−	0.578298i
$990$		0			0
$991$	13.5000	−	7.79423i	0.428842	−	0.247592i	−0.270011	−	0.962857i	$-0.587027\pi$
$991$	13.5000	−	7.79423i	0.428842	−	0.247592i	0.698853	+	0.715265i	$0.253694\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.50000	−	12.9904i	−0.237766	−	0.411823i
$996$		0			0
$997$	53.0000			1.67853			0.839263	−	0.543725i	$-0.182987\pi$
$997$	53.0000			1.67853			0.839263	+	0.543725i	$0.182987\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bh.b.1871.1		2
3.2	odd	2		1008.2.bh.a.191.1	yes	2
4.3	odd	2		3024.2.bh.a.1871.1		2
7.4	even	3		3024.2.cj.a.1439.1		2
9.4	even	3		1008.2.cj.b.527.1	yes	2
9.5	odd	6		3024.2.cj.b.2879.1		2
12.11	even	2		1008.2.bh.b.191.1	yes	2
21.11	odd	6		1008.2.cj.a.767.1	yes	2
28.11	odd	6		3024.2.cj.b.1439.1		2
36.23	even	6		3024.2.cj.a.2879.1		2
36.31	odd	6		1008.2.cj.a.527.1	yes	2
63.4	even	3		1008.2.bh.b.95.1	yes	2
63.32	odd	6		3024.2.bh.a.2447.1		2
84.11	even	6		1008.2.cj.b.767.1	yes	2
252.67	odd	6		1008.2.bh.a.95.1	✓	2
252.95	even	6	inner	3024.2.bh.b.2447.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bh.a.95.1	✓	2	252.67	odd	6
1008.2.bh.a.191.1	yes	2	3.2	odd	2
1008.2.bh.b.95.1	yes	2	63.4	even	3
1008.2.bh.b.191.1	yes	2	12.11	even	2
1008.2.cj.a.527.1	yes	2	36.31	odd	6
1008.2.cj.a.767.1	yes	2	21.11	odd	6
1008.2.cj.b.527.1	yes	2	9.4	even	3
1008.2.cj.b.767.1	yes	2	84.11	even	6
3024.2.bh.a.1871.1		2	4.3	odd	2
3024.2.bh.a.2447.1		2	63.32	odd	6
3024.2.bh.b.1871.1		2	1.1	even	1	trivial
3024.2.bh.b.2447.1		2	252.95	even	6	inner
3024.2.cj.a.1439.1		2	7.4	even	3
3024.2.cj.a.2879.1		2	36.23	even	6
3024.2.cj.b.1439.1		2	28.11	odd	6
3024.2.cj.b.2879.1		2	9.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{5} +(0.500000 - 2.59808i) q^{7} +3.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(1.50000 - 0.866025i) q^{17} +(1.50000 + 0.866025i) q^{19} +3.00000 q^{23} +2.00000 q^{25} +(7.50000 + 4.33013i) q^{29} +(3.00000 + 1.73205i) q^{31} +(-4.50000 - 0.866025i) q^{35} +(-2.50000 + 4.33013i) q^{37} +(4.50000 - 2.59808i) q^{41} +(-10.5000 - 6.06218i) q^{43} +(-6.50000 - 2.59808i) q^{49} +(4.50000 - 2.59808i) q^{53} -5.19615i q^{55} +(6.00000 - 10.3923i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-1.50000 + 0.866025i) q^{65} +(-9.00000 - 5.19615i) q^{67} +(-3.50000 - 6.06218i) q^{73} +(1.50000 - 7.79423i) q^{77} +(-9.00000 + 5.19615i) q^{79} +(7.50000 - 12.9904i) q^{83} +(-1.50000 - 2.59808i) q^{85} +(1.50000 + 0.866025i) q^{89} +(-2.50000 + 0.866025i) q^{91} +(1.50000 - 2.59808i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{7} + 6 q^{11} - q^{13} + 3 q^{17} + 3 q^{19} + 6 q^{23} + 4 q^{25} + 15 q^{29} + 6 q^{31} - 9 q^{35} - 5 q^{37} + 9 q^{41} - 21 q^{43} - 13 q^{49} + 9 q^{53} + 12 q^{59} + 10 q^{61} - 3 q^{65}+ \cdots + 5 q^{97}+O(q^{100}) \) 2 * q + q^7 + 6 * q^11 - q^13 + 3 * q^17 + 3 * q^19 + 6 * q^23 + 4 * q^25 + 15 * q^29 + 6 * q^31 - 9 * q^35 - 5 * q^37 + 9 * q^41 - 21 * q^43 - 13 * q^49 + 9 * q^53 + 12 * q^59 + 10 * q^61 - 3 * q^65 - 18 * q^67 - 7 * q^73 + 3 * q^77 - 18 * q^79 + 15 * q^83 - 3 * q^85 + 3 * q^89 - 5 * q^91 + 3 * q^95 + 5 * q^97

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