LMFDB - Embedded newform 3024.2.df.e.1601.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(17,3024)] 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([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.17"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.5
Character	$\chi$	$=$	3024.1601
Dual form			3024.2.df.e.17.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59337 q^{5} +(2.61256 + 0.417759i) q^{7} +3.54299i q^{11} +(2.74094 - 1.58248i) q^{13} +(0.487640 + 0.844616i) q^{17} +(-2.11191 - 1.21931i) q^{19} -3.37675i q^{23} +1.72555 q^{25} +(-0.267645 - 0.154525i) q^{29} +(4.35965 + 2.51705i) q^{31} +(-6.77533 - 1.08340i) q^{35} +(-3.47324 + 6.01583i) q^{37} +(6.08175 + 10.5339i) q^{41} +(5.47630 - 9.48523i) q^{43} +(-1.43344 - 2.48279i) q^{47} +(6.65096 + 2.18284i) q^{49} +(-7.81416 + 4.51151i) q^{53} -9.18828i q^{55} +(-0.219727 + 0.380579i) q^{59} +(3.41242 - 1.97016i) q^{61} +(-7.10826 + 4.10396i) q^{65} +(1.82561 - 3.16204i) q^{67} -5.25055i q^{71} +(-14.0773 + 8.12752i) q^{73} +(-1.48012 + 9.25629i) q^{77} +(3.49659 + 6.05628i) q^{79} +(-7.23851 + 12.5375i) q^{83} +(-1.26463 - 2.19040i) q^{85} +(-2.31101 + 4.00279i) q^{89} +(7.82197 - 2.98928i) q^{91} +(5.47697 + 3.16213i) q^{95} +(12.4805 + 7.20560i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	−2.59337			−1.15979			−0.579894	−	0.814692i	$-0.696906\pi$
$5$	−2.59337			−1.15979			−0.579894	+	0.814692i	$0.696906\pi$
$6$		0			0
$7$	2.61256	+	0.417759i	0.987455	+	0.157898i
$7$	2.61256	+	0.417759i	0.987455	+	0.157898i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			3.54299i			1.06825i	0.845405	+	0.534126i	$0.179359\pi$
$11$			3.54299i			1.06825i	−0.845405	+	0.534126i	$0.820641\pi$
$12$		0			0
$13$	2.74094	−	1.58248i	0.760200	−	0.438902i	−0.0691677	−	0.997605i	$-0.522034\pi$
$13$	2.74094	−	1.58248i	0.760200	−	0.438902i	0.829367	+	0.558703i	$0.188701\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.487640	+	0.844616i	0.118270	+	0.204850i	0.919082	−	0.394066i	$-0.128932\pi$
$17$	0.487640	+	0.844616i	0.118270	+	0.204850i	−0.800812	+	0.598916i	$0.795599\pi$
$18$		0			0
$19$	−2.11191	−	1.21931i	−0.484506	−	0.279730i	0.237786	−	0.971318i	$-0.423578\pi$
$19$	−2.11191	−	1.21931i	−0.484506	−	0.279730i	−0.722293	+	0.691588i	$0.756912\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	3.37675i		−	0.704102i	−0.935981	−	0.352051i	$-0.885484\pi$
$23$		−	3.37675i		−	0.704102i	0.935981	−	0.352051i	$-0.114516\pi$
$24$		0			0
$25$	1.72555			0.345110
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.267645	−	0.154525i	−0.0497004	−	0.0286946i	0.474944	−	0.880016i	$-0.342468\pi$
$29$	−0.267645	−	0.154525i	−0.0497004	−	0.0286946i	−0.524644	+	0.851322i	$0.675802\pi$
$30$		0			0
$31$	4.35965	+	2.51705i	0.783017	+	0.452075i	0.837498	−	0.546440i	$-0.184017\pi$
$31$	4.35965	+	2.51705i	0.783017	+	0.452075i	−0.0544814	+	0.998515i	$0.517351\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.77533	−	1.08340i	−1.14524	−	0.183128i
$36$		0			0
$37$	−3.47324	+	6.01583i	−0.570997	+	0.988996i	0.425467	+	0.904974i	$0.360110\pi$
$37$	−3.47324	+	6.01583i	−0.570997	+	0.988996i	−0.996464	+	0.0840218i	$0.973223\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.08175	+	10.5339i	0.949810	+	1.64512i	0.745822	+	0.666146i	$0.232057\pi$
$41$	6.08175	+	10.5339i	0.949810	+	1.64512i	0.203988	+	0.978973i	$0.434610\pi$
$42$		0			0
$43$	5.47630	−	9.48523i	0.835128	−	1.44648i	−0.0587983	−	0.998270i	$-0.518727\pi$
$43$	5.47630	−	9.48523i	0.835128	−	1.44648i	0.893926	−	0.448214i	$-0.147940\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.43344	−	2.48279i	−0.209089	−	0.362152i	0.742339	−	0.670024i	$-0.233716\pi$
$47$	−1.43344	−	2.48279i	−0.209089	−	0.362152i	−0.951428	+	0.307872i	$0.900383\pi$
$48$		0			0
$49$	6.65096	+	2.18284i	0.950136	+	0.311834i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.81416	+	4.51151i	−1.07336	+	0.619703i	−0.929097	−	0.369836i	$-0.879414\pi$
$53$	−7.81416	+	4.51151i	−1.07336	+	0.619703i	−0.144261	+	0.989540i	$0.546080\pi$
$54$		0			0
$55$		−	9.18828i		−	1.23895i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.219727	+	0.380579i	−0.0286061	+	0.0495471i	−0.879974	−	0.475022i	$-0.842440\pi$
$59$	−0.219727	+	0.380579i	−0.0286061	+	0.0495471i	0.851368	+	0.524569i	$0.175773\pi$
$60$		0			0
$61$	3.41242	−	1.97016i	0.436916	−	0.252254i	−0.265373	−	0.964146i	$-0.585495\pi$
$61$	3.41242	−	1.97016i	0.436916	−	0.252254i	0.702289	+	0.711892i	$0.252162\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.10826	+	4.10396i	−0.881671	+	0.509033i
$66$		0			0
$67$	1.82561	−	3.16204i	0.223033	−	0.386305i	−0.732694	−	0.680558i	$-0.761737\pi$
$67$	1.82561	−	3.16204i	0.223033	−	0.386305i	0.955728	+	0.294253i	$0.0950708\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	5.25055i		−	0.623126i	−0.950226	−	0.311563i	$-0.899148\pi$
$71$		−	5.25055i		−	0.623126i	0.950226	−	0.311563i	$-0.100852\pi$
$72$		0			0
$73$	−14.0773	+	8.12752i	−1.64762	+	0.951254i	−0.669607	+	0.742716i	$0.733537\pi$
$73$	−14.0773	+	8.12752i	−1.64762	+	0.951254i	−0.978014	+	0.208539i	$0.933129\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.48012	+	9.25629i	−0.168675	+	1.05485i
$78$		0			0
$79$	3.49659	+	6.05628i	0.393397	+	0.681384i	0.992895	−	0.118992i	$-0.0379663\pi$
$79$	3.49659	+	6.05628i	0.393397	+	0.681384i	−0.599498	+	0.800376i	$0.704633\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.23851	+	12.5375i	−0.794529	+	1.37616i	0.128609	+	0.991695i	$0.458949\pi$
$83$	−7.23851	+	12.5375i	−0.794529	+	1.37616i	−0.923138	+	0.384469i	$0.874384\pi$
$84$		0			0
$85$	−1.26463	−	2.19040i	−0.137168	−	0.237582i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.31101	+	4.00279i	−0.244967	+	0.424295i	−0.962122	−	0.272619i	$-0.912110\pi$
$89$	−2.31101	+	4.00279i	−0.244967	+	0.424295i	0.717156	+	0.696913i	$0.245444\pi$
$90$		0			0
$91$	7.82197	−	2.98928i	0.819965	−	0.313362i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.47697	+	3.16213i	0.561925	+	0.324428i
$96$		0			0
$97$	12.4805	+	7.20560i	1.26720	+	0.731617i	0.974457	−	0.224574i	$-0.0720991\pi$
$97$	12.4805	+	7.20560i	1.26720	+	0.731617i	0.292742	+	0.956192i	$0.405432\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.62921			0.858638			0.429319	−	0.903153i	$-0.358754\pi$
$101$	8.62921			0.858638			0.429319	+	0.903153i	$0.358754\pi$
$102$		0			0
$103$			6.09732i			0.600787i	0.953815	+	0.300394i	$0.0971180\pi$
$103$			6.09732i			0.600787i	−0.953815	+	0.300394i	$0.902882\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.8841	−	8.01599i	−1.34223	−	0.774935i	−0.355093	−	0.934831i	$-0.615551\pi$
$107$	−13.8841	−	8.01599i	−1.34223	−	0.774935i	−0.987134	+	0.159896i	$0.948884\pi$
$108$		0			0
$109$	2.78659	+	4.82652i	0.266907	+	0.462297i	0.968062	−	0.250713i	$-0.0806649\pi$
$109$	2.78659	+	4.82652i	0.266907	+	0.462297i	−0.701154	+	0.713010i	$0.747332\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	14.2144	−	8.20669i	1.33718	−	0.772021i	0.350791	−	0.936454i	$-0.385913\pi$
$113$	14.2144	−	8.20669i	1.33718	−	0.772021i	0.986388	+	0.164433i	$0.0525794\pi$
$114$		0			0
$115$			8.75716i			0.816609i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.921142	+	2.41033i	0.0844410	+	0.220954i
$120$		0			0
$121$	−1.55280			−0.141163
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.49185			0.759534
$126$		0			0
$127$	18.0255			1.59951			0.799754	−	0.600328i	$-0.204963\pi$
$127$	18.0255			1.59951			0.799754	+	0.600328i	$0.204963\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10.4393			0.912090			0.456045	−	0.889957i	$-0.349266\pi$
$131$	10.4393			0.912090			0.456045	+	0.889957i	$0.349266\pi$
$132$		0			0
$133$	−5.00813	−	4.06780i	−0.434260	−	0.352723i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			3.84991i			0.328920i	0.986384	+	0.164460i	$0.0525882\pi$
$137$			3.84991i			0.328920i	−0.986384	+	0.164460i	$0.947412\pi$
$138$		0			0
$139$	−18.7634	+	10.8330i	−1.59149	+	0.918847i	−0.598437	+	0.801170i	$0.704211\pi$
$139$	−18.7634	+	10.8330i	−1.59149	+	0.918847i	−0.993052	+	0.117677i	$0.962455\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.60672	+	9.71113i	0.468858	+	0.812085i
$144$		0			0
$145$	0.694102	+	0.400740i	0.0576420	+	0.0332796i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			9.50289i			0.778507i	0.921131	+	0.389254i	$0.127267\pi$
$149$			9.50289i			0.778507i	−0.921131	+	0.389254i	$0.872733\pi$
$150$		0			0
$151$	21.3380			1.73646			0.868232	−	0.496159i	$-0.165257\pi$
$151$	21.3380			1.73646			0.868232	+	0.496159i	$0.165257\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−11.3062	−	6.52763i	−0.908134	−	0.524312i
$156$		0			0
$157$	2.10532	+	1.21551i	0.168023	+	0.0970082i	0.581653	−	0.813437i	$-0.302406\pi$
$157$	2.10532	+	1.21551i	0.168023	+	0.0970082i	−0.413630	+	0.910445i	$0.635739\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.41067	−	8.82197i	0.111176	−	0.695269i
$162$		0			0
$163$	−8.31072	+	14.3946i	−0.650946	+	1.12747i	0.331948	+	0.943298i	$0.392294\pi$
$163$	−8.31072	+	14.3946i	−0.650946	+	1.12747i	−0.982894	+	0.184174i	$0.941039\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.6037	+	18.3661i	0.820535	+	1.42121i	0.905284	+	0.424806i	$0.139658\pi$
$167$	10.6037	+	18.3661i	0.820535	+	1.42121i	−0.0847489	+	0.996402i	$0.527009\pi$
$168$		0			0
$169$	−1.49150	+	2.58336i	−0.114731	+	0.198720i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.09062	+	8.81722i	0.387033	+	0.670361i	0.992049	−	0.125853i	$-0.0401667\pi$
$173$	5.09062	+	8.81722i	0.387033	+	0.670361i	−0.605016	+	0.796213i	$0.706833\pi$
$174$		0			0
$175$	4.50810	+	0.720863i	0.340781	+	0.0544922i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.589482	+	0.340338i	−0.0440600	+	0.0254380i	−0.521868	−	0.853026i	$-0.674765\pi$
$179$	−0.589482	+	0.340338i	−0.0440600	+	0.0254380i	0.477808	+	0.878464i	$0.341431\pi$
$180$		0			0
$181$			19.1298i			1.42191i	0.703239	+	0.710954i	$0.251737\pi$
$181$			19.1298i			1.42191i	−0.703239	+	0.710954i	$0.748263\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	9.00738	−	15.6012i	0.662236	−	1.14703i
$186$		0			0
$187$	−2.99247	+	1.72770i	−0.218831	+	0.126342i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.3174	−	10.5756i	1.32540	−	0.765221i	0.340817	−	0.940130i	$-0.389296\pi$
$191$	18.3174	−	10.5756i	1.32540	−	0.765221i	0.984585	+	0.174909i	$0.0559631\pi$
$192$		0			0
$193$	−6.41421	+	11.1097i	−0.461705	+	0.799697i	−0.999046	−	0.0436683i	$-0.986096\pi$
$193$	−6.41421	+	11.1097i	−0.461705	+	0.799697i	0.537341	+	0.843365i	$0.319429\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			22.2854i			1.58777i	0.608069	+	0.793884i	$0.291944\pi$
$197$			22.2854i			1.58777i	−0.608069	+	0.793884i	$0.708056\pi$
$198$		0			0
$199$	−6.65637	+	3.84306i	−0.471858	+	0.272427i	−0.717017	−	0.697056i	$-0.754493\pi$
$199$	−6.65637	+	3.84306i	−0.471858	+	0.272427i	0.245159	+	0.969483i	$0.421160\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.634685	−	0.515517i	−0.0445461	−	0.0361822i
$204$		0			0
$205$	−15.7722	−	27.3183i	−1.10158	−	1.90799i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.32002	−	7.48250i	0.298822	−	0.517575i
$210$		0			0
$211$	−8.33679	−	14.4397i	−0.573928	−	0.994073i	−0.996157	−	0.0875838i	$-0.972085\pi$
$211$	−8.33679	−	14.4397i	−0.573928	−	0.994073i	0.422229	−	0.906489i	$-0.361248\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−14.2021	+	24.5987i	−0.968572	+	1.67762i
$216$		0			0
$217$	10.3383	+	8.39722i	0.701813	+	0.570041i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.67318	+	1.54336i	0.179818	+	0.103818i
$222$		0			0
$223$	4.45390	+	2.57146i	0.298255	+	0.172198i	0.641659	−	0.766990i	$-0.278247\pi$
$223$	4.45390	+	2.57146i	0.298255	+	0.172198i	−0.343404	+	0.939188i	$0.611580\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.9854			0.795500			0.397750	−	0.917494i	$-0.369791\pi$
$227$	11.9854			0.795500			0.397750	+	0.917494i	$0.369791\pi$
$228$		0			0
$229$		−	2.60911i		−	0.172415i	−0.996277	−	0.0862074i	$-0.972525\pi$
$229$		−	2.60911i		−	0.172415i	0.996277	−	0.0862074i	$-0.0274748\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.13306	−	1.80887i	−0.205253	−	0.118503i	0.393850	−	0.919175i	$-0.371143\pi$
$233$	−3.13306	−	1.80887i	−0.205253	−	0.118503i	−0.599103	+	0.800672i	$0.704476\pi$
$234$		0			0
$235$	3.71743	+	6.43878i	0.242499	+	0.420020i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.8069	−	7.39409i	0.828412	−	0.478284i	−0.0248967	−	0.999690i	$-0.507926\pi$
$239$	12.8069	−	7.39409i	0.828412	−	0.478284i	0.853309	+	0.521406i	$0.174592\pi$
$240$		0			0
$241$			6.44196i			0.414963i	0.978239	+	0.207481i	$0.0665267\pi$
$241$			6.44196i			0.414963i	−0.978239	+	0.207481i	$0.933473\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.2484	−	5.66091i	−1.10196	−	0.361662i
$246$		0			0
$247$	−7.71817			−0.491095
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.21012			0.391979			0.195990	−	0.980606i	$-0.437208\pi$
$251$	6.21012			0.391979			0.195990	+	0.980606i	$0.437208\pi$
$252$		0			0
$253$	11.9638			0.752158
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−21.1767			−1.32096			−0.660482	−	0.750842i	$-0.729648\pi$
$257$	−21.1767			−1.32096			−0.660482	+	0.750842i	$0.729648\pi$
$258$		0			0
$259$	−11.5872	+	14.2657i	−0.719995	+	0.886430i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	17.1579i		−	1.05800i	−0.848621	−	0.529002i	$-0.822566\pi$
$263$		−	17.1579i		−	1.05800i	0.848621	−	0.529002i	$-0.177434\pi$
$264$		0			0
$265$	20.2650	−	11.7000i	1.24487	−	0.718725i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.8061	−	18.7166i	−0.658857	−	1.14117i	−0.980912	−	0.194453i	$-0.937707\pi$
$269$	−10.8061	−	18.7166i	−0.658857	−	1.14117i	0.322055	−	0.946721i	$-0.395627\pi$
$270$		0			0
$271$	−21.8475	−	12.6137i	−1.32714	−	0.766227i	−0.342287	−	0.939595i	$-0.611202\pi$
$271$	−21.8475	−	12.6137i	−1.32714	−	0.766227i	−0.984857	+	0.173368i	$0.944535\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			6.11361i			0.368665i
$276$		0			0
$277$	22.4512			1.34896			0.674482	−	0.738291i	$-0.264367\pi$
$277$	22.4512			1.34896			0.674482	+	0.738291i	$0.264367\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.3691	−	5.98662i	−0.618571	−	0.357132i	0.157742	−	0.987480i	$-0.449579\pi$
$281$	−10.3691	−	5.98662i	−0.618571	−	0.357132i	−0.776312	+	0.630349i	$0.782912\pi$
$282$		0			0
$283$	−18.8187	−	10.8650i	−1.11865	−	0.645855i	−0.177596	−	0.984103i	$-0.556832\pi$
$283$	−18.8187	−	10.8650i	−1.11865	−	0.645855i	−0.941057	+	0.338249i	$0.890165\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.4883	+	30.0612i	0.678134	+	1.77445i
$288$		0			0
$289$	8.02442	−	13.8987i	0.472024	−	0.817570i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.38110	+	9.32035i	0.314367	+	0.544500i	0.979303	−	0.202400i	$-0.0648743\pi$
$293$	5.38110	+	9.32035i	0.314367	+	0.544500i	−0.664935	+	0.746901i	$0.731541\pi$
$294$		0			0
$295$	0.569833	−	0.986980i	0.0331770	−	0.0574642i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.34365	−	9.25547i	−0.309031	−	0.535258i
$300$		0			0
$301$	18.2697	−	22.4930i	1.05305	−	1.29647i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.84966	+	5.10935i	−0.506730	+	0.292561i
$306$		0			0
$307$		−	4.22117i		−	0.240915i	−0.992719	−	0.120457i	$-0.961564\pi$
$307$		−	4.22117i		−	0.240915i	0.992719	−	0.120457i	$-0.0384361\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.09266	+	3.62459i	−0.118664	+	0.205532i	−0.919238	−	0.393702i	$-0.871194\pi$
$311$	−2.09266	+	3.62459i	−0.118664	+	0.205532i	0.800575	+	0.599233i	$0.204528\pi$
$312$		0			0
$313$	−19.0867	+	11.0197i	−1.07885	+	0.622872i	−0.930585	−	0.366076i	$-0.880701\pi$
$313$	−19.0867	+	11.0197i	−1.07885	+	0.622872i	−0.148261	+	0.988948i	$0.547368\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.41440	+	4.85806i	−0.472600	+	0.272856i	−0.717327	−	0.696736i	$-0.754635\pi$
$317$	−8.41440	+	4.85806i	−0.472600	+	0.272856i	0.244727	+	0.969592i	$0.421302\pi$
$318$		0			0
$319$	0.547481	−	0.948264i	0.0306530	−	0.0530926i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	2.37834i		−	0.132335i
$324$		0			0
$325$	4.72963	−	2.73065i	0.262353	−	0.151469i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.70774	−	7.08527i	−0.149283	−	0.390624i
$330$		0			0
$331$	13.8588	+	24.0042i	0.761749	+	1.31939i	0.941948	+	0.335758i	$0.108992\pi$
$331$	13.8588	+	24.0042i	0.761749	+	1.31939i	−0.180200	+	0.983630i	$0.557674\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.73447	+	8.20034i	−0.258672	+	0.448032i
$336$		0			0
$337$	6.29141	+	10.8970i	0.342715	+	0.593600i	0.984936	−	0.172920i	$-0.0553201\pi$
$337$	6.29141	+	10.8970i	0.342715	+	0.593600i	−0.642221	+	0.766520i	$0.721987\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.91788	+	15.4462i	−0.482930	+	0.836460i
$342$		0			0
$343$	16.4641	+	8.48130i	0.888979	+	0.457947i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.4819	−	8.36115i	−0.777431	−	0.448850i	0.0580881	−	0.998311i	$-0.481500\pi$
$347$	−14.4819	−	8.36115i	−0.777431	−	0.448850i	−0.835519	+	0.549462i	$0.814833\pi$
$348$		0			0
$349$	−13.9900	−	8.07714i	−0.748869	−	0.432359i	0.0764164	−	0.997076i	$-0.475652\pi$
$349$	−13.9900	−	8.07714i	−0.748869	−	0.432359i	−0.825285	+	0.564717i	$0.808985\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−15.6566			−0.833318			−0.416659	−	0.909063i	$-0.636799\pi$
$353$	−15.6566			−0.833318			−0.416659	+	0.909063i	$0.636799\pi$
$354$		0			0
$355$			13.6166i			0.722694i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.1396	+	11.0502i	1.01015	+	0.583209i	0.911235	−	0.411887i	$-0.135130\pi$
$359$	19.1396	+	11.0502i	1.01015	+	0.583209i	0.0989127	+	0.995096i	$0.468464\pi$
$360$		0			0
$361$	−6.52655	−	11.3043i	−0.343502	−	0.594964i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	36.5075	−	21.0776i	1.91089	−	1.10325i
$366$		0			0
$367$		−	13.1513i		−	0.686492i	−0.939246	−	0.343246i	$-0.888474\pi$
$367$		−	13.1513i		−	0.686492i	0.939246	−	0.343246i	$-0.111526\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−22.2997	+	8.52216i	−1.15774	+	0.442448i
$372$		0			0
$373$	−4.43829			−0.229806			−0.114903	−	0.993377i	$-0.536656\pi$
$373$	−4.43829			−0.229806			−0.114903	+	0.993377i	$0.536656\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.978132			−0.0503763
$378$		0			0
$379$	−14.8875			−0.764718			−0.382359	−	0.924014i	$-0.624888\pi$
$379$	−14.8875			−0.764718			−0.382359	+	0.924014i	$0.624888\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.63802			0.288089			0.144045	−	0.989571i	$-0.453989\pi$
$383$	5.63802			0.288089			0.144045	+	0.989571i	$0.453989\pi$
$384$		0			0
$385$	3.83848	−	24.0049i	0.195627	−	1.22341i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	38.5120i		−	1.95263i	−0.216346	−	0.976317i	$-0.569414\pi$
$389$		−	38.5120i		−	1.95263i	0.216346	−	0.976317i	$-0.430586\pi$
$390$		0			0
$391$	2.85206	−	1.64664i	0.144235	−	0.0832741i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.06795	−	15.7061i	−0.456258	−	0.790262i
$396$		0			0
$397$	2.50780	+	1.44788i	0.125863	+	0.0726669i	0.561609	−	0.827402i	$-0.310182\pi$
$397$	2.50780	+	1.44788i	0.125863	+	0.0726669i	−0.435747	+	0.900069i	$0.643516\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	25.7333i		−	1.28506i	−0.766261	−	0.642530i	$-0.777885\pi$
$401$		−	25.7333i		−	1.28506i	0.766261	−	0.642530i	$-0.222115\pi$
$402$		0			0
$403$	15.9327			0.793666
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.3140	−	12.3057i	−1.05650	−	0.609969i
$408$		0			0
$409$	−24.9914	−	14.4288i	−1.23574	−	0.713457i	−0.267522	−	0.963552i	$-0.586205\pi$
$409$	−24.9914	−	14.4288i	−1.23574	−	0.713457i	−0.968221	+	0.250095i	$0.919538\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.733041	+	0.902492i	−0.0360706	+	0.0444088i
$414$		0			0
$415$	18.7721	−	32.5142i	0.921486	−	1.59606i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.07870	+	10.5286i	0.296964	+	0.514357i	0.975440	−	0.220266i	$-0.0706925\pi$
$419$	6.07870	+	10.5286i	0.296964	+	0.514357i	−0.678476	+	0.734623i	$0.737359\pi$
$420$		0			0
$421$	−13.9914	+	24.2338i	−0.681898	+	1.18108i	0.292503	+	0.956265i	$0.405512\pi$
$421$	−13.9914	+	24.2338i	−0.681898	+	1.18108i	−0.974401	+	0.224817i	$0.927821\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.841446	+	1.45743i	0.0408161	+	0.0706956i
$426$		0			0
$427$	9.73822	−	3.72160i	0.471265	−	0.180101i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.9975	−	8.08147i	0.674236	−	0.389271i	−0.123444	−	0.992352i	$-0.539394\pi$
$431$	13.9975	−	8.08147i	0.674236	−	0.389271i	0.797680	+	0.603081i	$0.206060\pi$
$432$		0			0
$433$		−	5.27197i		−	0.253355i	−0.991944	−	0.126677i	$-0.959569\pi$
$433$		−	5.27197i		−	0.253355i	0.991944	−	0.126677i	$-0.0404313\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.11732	+	7.13141i	−0.196958	+	0.341142i
$438$		0			0
$439$	−9.10263	+	5.25541i	−0.434445	+	0.250827i	−0.701238	−	0.712927i	$-0.747369\pi$
$439$	−9.10263	+	5.25541i	−0.434445	+	0.250827i	0.266794	+	0.963754i	$0.414036\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.15805	−	2.97800i	0.245066	−	0.141489i	−0.372437	−	0.928058i	$-0.621478\pi$
$443$	5.15805	−	2.97800i	0.245066	−	0.141489i	0.617503	+	0.786568i	$0.288144\pi$
$444$		0			0
$445$	5.99330	−	10.3807i	0.284109	−	0.492092i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			1.85897i			0.0877304i	0.999037	+	0.0438652i	$0.0139672\pi$
$449$			1.85897i			0.0877304i	−0.999037	+	0.0438652i	$0.986033\pi$
$450$		0			0
$451$	−37.3215	+	21.5476i	−1.75740	+	1.01464i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−20.2852	+	7.75230i	−0.950986	+	0.363433i
$456$		0			0
$457$	−14.8747	−	25.7637i	−0.695808	−	1.20517i	−0.969908	−	0.243473i	$-0.921713\pi$
$457$	−14.8747	−	25.7637i	−0.695808	−	1.20517i	0.274100	−	0.961701i	$-0.411620\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.9738	−	25.9353i	0.697398	−	1.20793i	−0.271968	−	0.962306i	$-0.587675\pi$
$461$	14.9738	−	25.9353i	0.697398	−	1.20793i	0.969366	−	0.245622i	$-0.0789921\pi$
$462$		0			0
$463$	−7.57406	−	13.1187i	−0.351997	−	0.609676i	0.634603	−	0.772839i	$-0.281164\pi$
$463$	−7.57406	−	13.1187i	−0.351997	−	0.609676i	−0.986599	+	0.163163i	$0.947830\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.85158	−	10.1352i	0.270779	−	0.469002i	−0.698283	−	0.715822i	$-0.746052\pi$
$467$	5.85158	−	10.1352i	0.270779	−	0.469002i	0.969061	+	0.246820i	$0.0793855\pi$
$468$		0			0
$469$	6.09048	−	7.49837i	0.281232	−	0.346243i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	33.6061	+	19.4025i	1.54521	+	0.892127i
$474$		0			0
$475$	−3.64421	−	2.10399i	−0.167208	−	0.0965375i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.1418			0.554771			0.277385	−	0.960759i	$-0.410532\pi$
$479$	12.1418			0.554771			0.277385	+	0.960759i	$0.410532\pi$
$480$		0			0
$481$			21.9854i			1.00245i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−32.3664	−	18.6868i	−1.46968	−	0.848522i
$486$		0			0
$487$	5.22070	+	9.04251i	0.236572	+	0.409755i	0.959728	−	0.280929i	$-0.0906426\pi$
$487$	5.22070	+	9.04251i	0.236572	+	0.409755i	−0.723156	+	0.690685i	$0.757309\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.9972	−	12.1227i	0.947589	−	0.547091i	0.0552576	−	0.998472i	$-0.482402\pi$
$491$	20.9972	−	12.1227i	0.947589	−	0.547091i	0.892331	+	0.451382i	$0.149069\pi$
$492$		0			0
$493$		−	0.301410i		−	0.0135748i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.19346	−	13.7174i	0.0983903	−	0.615309i
$498$		0			0
$499$	0.348239			0.0155893			0.00779466	−	0.999970i	$-0.497519\pi$
$499$	0.348239			0.0155893			0.00779466	+	0.999970i	$0.497519\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−32.3099			−1.44063			−0.720314	−	0.693648i	$-0.756002\pi$
$503$	−32.3099			−1.44063			−0.720314	+	0.693648i	$0.756002\pi$
$504$		0			0
$505$	−22.3787			−0.995839
$506$		0			0
$507$		0			0
$508$		0			0
$509$	13.7046			0.607448			0.303724	−	0.952760i	$-0.401770\pi$
$509$	13.7046			0.607448			0.303724	+	0.952760i	$0.401770\pi$
$510$		0			0
$511$	−40.1731	+	15.3527i	−1.77715	+	0.679165i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	15.8126i		−	0.696786i
$516$		0			0
$517$	8.79650	−	5.07866i	0.386870	−	0.223359i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.73516	+	15.1297i	0.382694	+	0.662846i	0.991446	−	0.130514i	$-0.0416629\pi$
$521$	8.73516	+	15.1297i	0.382694	+	0.662846i	−0.608752	+	0.793361i	$0.708330\pi$
$522$		0			0
$523$	23.3238	+	13.4660i	1.01988	+	0.588827i	0.914069	−	0.405559i	$-0.132923\pi$
$523$	23.3238	+	13.4660i	1.01988	+	0.588827i	0.105810	+	0.994386i	$0.466257\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			4.90965i			0.213868i
$528$		0			0
$529$	11.5975			0.504241
$530$		0			0
$531$		0			0
$532$		0			0
$533$	33.3394	+	19.2485i	1.44409	+	0.833746i
$534$		0			0
$535$	36.0066	+	20.7884i	1.55670	+	0.898761i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.73379	+	23.5643i	−0.333118	+	1.01499i
$540$		0			0
$541$	−7.43375	+	12.8756i	−0.319602	+	0.553567i	−0.980405	−	0.196993i	$-0.936882\pi$
$541$	−7.43375	+	12.8756i	−0.319602	+	0.553567i	0.660803	+	0.750559i	$0.270216\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.22666	−	12.5169i	−0.309556	−	0.536167i
$546$		0			0
$547$	4.17953	−	7.23915i	0.178704	−	0.309524i	−0.762733	−	0.646713i	$-0.776143\pi$
$547$	4.17953	−	7.23915i	0.178704	−	0.309524i	0.941437	+	0.337190i	$0.109476\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.376829	+	0.652687i	0.0160534	+	0.0278054i
$552$		0			0
$553$	6.60500	+	17.2831i	0.280873	+	0.734953i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.617917	−	0.356754i	0.0261820	−	0.0151162i	−0.486852	−	0.873485i	$-0.661855\pi$
$557$	0.617917	−	0.356754i	0.0261820	−	0.0151162i	0.513034	+	0.858368i	$0.328522\pi$
$558$		0			0
$559$		−	34.6646i		−	1.46616i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.5939	−	23.5452i	0.572912	−	0.992314i	−0.423352	−	0.905965i	$-0.639147\pi$
$563$	13.5939	−	23.5452i	0.572912	−	0.992314i	0.996265	−	0.0863485i	$-0.0275199\pi$
$564$		0			0
$565$	−36.8632	+	21.2830i	−1.55085	+	0.895381i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.51833	+	0.876606i	−0.0636515	+	0.0367492i	−0.531488	−	0.847066i	$-0.678367\pi$
$569$	−1.51833	+	0.876606i	−0.0636515	+	0.0367492i	0.467836	+	0.883815i	$0.345034\pi$
$570$		0			0
$571$	0.228817	−	0.396323i	0.00957570	−	0.0165856i	−0.861198	−	0.508270i	$-0.830285\pi$
$571$	0.228817	−	0.396323i	0.00957570	−	0.0165856i	0.870774	+	0.491684i	$0.163619\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	5.82675i		−	0.242992i
$576$		0			0
$577$	19.8800	−	11.4777i	0.827617	−	0.477825i	−0.0254193	−	0.999677i	$-0.508092\pi$
$577$	19.8800	−	11.4777i	0.827617	−	0.477825i	0.853036	+	0.521852i	$0.174759\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.1487	+	29.7309i	−1.00186	+	1.23345i
$582$		0			0
$583$	−15.9842	−	27.6855i	−0.662000	−	1.14662i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.81513	−	4.87594i	0.116193	−	0.201252i	−0.802063	−	0.597239i	$-0.796264\pi$
$587$	2.81513	−	4.87594i	0.116193	−	0.201252i	0.918256	+	0.395987i	$0.129598\pi$
$588$		0			0
$589$	−6.13814	−	10.6316i	−0.252918	−	0.438066i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.35121	+	2.34037i	−0.0554876	+	0.0961074i	−0.892435	−	0.451176i	$-0.851005\pi$
$593$	−1.35121	+	2.34037i	−0.0554876	+	0.0961074i	0.836947	+	0.547283i	$0.184338\pi$
$594$		0			0
$595$	−2.38886	−	6.25086i	−0.0979337	−	0.256260i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.3894	+	5.99831i	0.424498	+	0.245084i	0.697000	−	0.717071i	$-0.254518\pi$
$599$	10.3894	+	5.99831i	0.424498	+	0.245084i	−0.272502	+	0.962155i	$0.587851\pi$
$600$		0			0
$601$	26.7530	+	15.4459i	1.09128	+	0.630050i	0.933917	−	0.357491i	$-0.116368\pi$
$601$	26.7530	+	15.4459i	1.09128	+	0.630050i	0.157363	+	0.987541i	$0.449701\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.02697			0.163720
$606$		0			0
$607$		−	6.87463i		−	0.279033i	−0.990220	−	0.139516i	$-0.955445\pi$
$607$		−	6.87463i		−	0.279033i	0.990220	−	0.139516i	$-0.0445548\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.85794	−	4.53678i	−0.317898	−	0.183539i
$612$		0			0
$613$	−16.6455	−	28.8308i	−0.672304	−	1.16447i	−0.977249	−	0.212095i	$-0.931971\pi$
$613$	−16.6455	−	28.8308i	−0.672304	−	1.16447i	0.304945	−	0.952370i	$-0.401362\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−18.0757	+	10.4360i	−0.727702	+	0.420139i	−0.817581	−	0.575814i	$-0.804685\pi$
$617$	−18.0757	+	10.4360i	−0.727702	+	0.420139i	0.0898790	+	0.995953i	$0.471352\pi$
$618$		0			0
$619$		−	19.3846i		−	0.779133i	−0.920998	−	0.389567i	$-0.872625\pi$
$619$		−	19.3846i		−	0.779133i	0.920998	−	0.389567i	$-0.127375\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.70985	+	9.49208i	−0.308889	+	0.380292i
$624$		0			0
$625$	−30.6502			−1.22601
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.77476			−0.270127
$630$		0			0
$631$	27.3629			1.08930			0.544649	−	0.838664i	$-0.316663\pi$
$631$	27.3629			1.08930			0.544649	+	0.838664i	$0.316663\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−46.7468			−1.85509
$636$		0			0
$637$	21.6842	−	4.54198i	0.859158	−	0.179960i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			34.7202i			1.37137i	0.727900	+	0.685683i	$0.240496\pi$
$641$			34.7202i			1.37137i	−0.727900	+	0.685683i	$0.759504\pi$
$642$		0			0
$643$	−3.52980	+	2.03793i	−0.139202	+	0.0803681i	−0.567983	−	0.823040i	$-0.692276\pi$
$643$	−3.52980	+	2.03793i	−0.139202	+	0.0803681i	0.428782	+	0.903408i	$0.358943\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.53976	−	11.3272i	−0.257105	−	0.445318i	0.708360	−	0.705851i	$-0.249435\pi$
$647$	−6.53976	−	11.3272i	−0.257105	−	0.445318i	−0.965465	+	0.260533i	$0.916102\pi$
$648$		0			0
$649$	−1.34839	−	0.778492i	−0.0529288	−	0.0305585i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	6.24179i		−	0.244260i	−0.992514	−	0.122130i	$-0.961027\pi$
$653$		−	6.24179i		−	0.244260i	0.992514	−	0.122130i	$-0.0389725\pi$
$654$		0			0
$655$	−27.0730			−1.05783
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.79139	+	1.03426i	0.0697827	+	0.0402891i	0.534485	−	0.845178i	$-0.320505\pi$
$659$	1.79139	+	1.03426i	0.0697827	+	0.0402891i	−0.464703	+	0.885467i	$0.653839\pi$
$660$		0			0
$661$	13.5306	+	7.81190i	0.526280	+	0.303848i	0.739500	−	0.673156i	$-0.235062\pi$
$661$	13.5306	+	7.81190i	0.526280	+	0.303848i	−0.213220	+	0.977004i	$0.568395\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.9879	+	10.5493i	0.503649	+	0.409085i
$666$		0			0
$667$	−0.521792	+	0.903771i	−0.0202039	+	0.0349941i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.98027	+	12.0902i	0.269470	+	0.466736i
$672$		0			0
$673$	−15.1108	+	26.1727i	−0.582478	+	1.00888i	0.412706	+	0.910864i	$0.364584\pi$
$673$	−15.1108	+	26.1727i	−0.582478	+	1.00888i	−0.995185	+	0.0980180i	$0.968750\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.3438	−	24.8442i	−0.551278	−	0.954841i	−0.998183	−	0.0602595i	$-0.980807\pi$
$677$	−14.3438	−	24.8442i	−0.551278	−	0.954841i	0.446905	−	0.894581i	$-0.352526\pi$
$678$		0			0
$679$	29.5958	+	24.0389i	1.13578	+	0.922528i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.48345	−	4.32057i	0.286346	−	0.165322i	−0.349947	−	0.936770i	$-0.613800\pi$
$683$	7.48345	−	4.32057i	0.286346	−	0.165322i	0.636293	+	0.771448i	$0.280467\pi$
$684$		0			0
$685$		−	9.98423i		−	0.381478i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−14.2788	+	24.7315i	−0.543978	+	0.942197i
$690$		0			0
$691$	−10.5993	+	6.11951i	−0.403216	+	0.232797i	−0.687871	−	0.725833i	$-0.741454\pi$
$691$	−10.5993	+	6.11951i	−0.403216	+	0.232797i	0.284655	+	0.958630i	$0.408121\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	48.6603	−	28.0940i	1.84579	−	1.06567i
$696$		0			0
$697$	−5.93140	+	10.2735i	−0.224668	+	0.389136i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			3.05683i			0.115455i	0.998332	+	0.0577274i	$0.0183854\pi$
$701$			3.05683i			0.115455i	−0.998332	+	0.0577274i	$0.981615\pi$
$702$		0			0
$703$	14.6704	−	8.46994i	0.553303	−	0.319450i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.5443	+	3.60493i	0.847867	+	0.135577i
$708$		0			0
$709$	6.04101	+	10.4633i	0.226875	+	0.392959i	0.956880	−	0.290482i	$-0.0938158\pi$
$709$	6.04101	+	10.4633i	0.226875	+	0.392959i	−0.730005	+	0.683441i	$0.760482\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.49945	−	14.7215i	0.318307	−	0.551324i
$714$		0			0
$715$	−14.5403	−	25.1845i	−0.543776	−	0.941847i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.27436	+	10.8675i	−0.233994	+	0.405290i	−0.958980	−	0.283474i	$-0.908513\pi$
$719$	−6.27436	+	10.8675i	−0.233994	+	0.405290i	0.724986	+	0.688764i	$0.241846\pi$
$720$		0			0
$721$	−2.54721	+	15.9296i	−0.0948630	+	0.593250i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.461835	−	0.266640i	−0.0171521	−	0.00990278i
$726$		0			0
$727$	−16.2736	−	9.39555i	−0.603553	−	0.348462i	0.166885	−	0.985976i	$-0.446629\pi$
$727$	−16.2736	−	9.39555i	−0.603553	−	0.348462i	−0.770438	+	0.637515i	$0.779962\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.6818			0.395082
$732$		0			0
$733$			35.4064i			1.30776i	0.756596	+	0.653882i	$0.226861\pi$
$733$			35.4064i			1.30776i	−0.756596	+	0.653882i	$0.773139\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.2031	+	6.46811i	0.412671	+	0.238256i
$738$		0			0
$739$	−11.1371	−	19.2900i	−0.409684	−	0.709593i	0.585170	−	0.810910i	$-0.301028\pi$
$739$	−11.1371	−	19.2900i	−0.409684	−	0.709593i	−0.994854	+	0.101317i	$0.967694\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.68932	+	5.01678i	−0.318780	+	0.184048i	−0.650849	−	0.759207i	$-0.725587\pi$
$743$	−8.68932	+	5.01678i	−0.318780	+	0.184048i	0.332069	+	0.943255i	$0.392253\pi$
$744$		0			0
$745$		−	24.6445i		−	0.902904i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−32.9243	−	26.7425i	−1.20303	−	0.977148i
$750$		0			0
$751$	−33.5541			−1.22441			−0.612203	−	0.790700i	$-0.709717\pi$
$751$	−33.5541			−1.22441			−0.612203	+	0.790700i	$0.709717\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−55.3373			−2.01393
$756$		0			0
$757$	0.0340541			0.00123772			0.000618859	−	1.00000i	$-0.499803\pi$
$757$	0.0340541			0.00123772			0.000618859		1.00000i	$0.499803\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−22.9691			−0.832631			−0.416315	−	0.909220i	$-0.636679\pi$
$761$	−22.9691			−0.832631			−0.416315	+	0.909220i	$0.636679\pi$
$762$		0			0
$763$	5.26383	+	13.7737i	0.190563	+	0.498642i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			1.39086i			0.0502210i
$768$		0			0
$769$	14.3775	−	8.30086i	0.518466	−	0.299337i	−0.217841	−	0.975984i	$-0.569901\pi$
$769$	14.3775	−	8.30086i	0.518466	−	0.299337i	0.736307	+	0.676648i	$0.236568\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.803138	+	1.39107i	0.0288868	+	0.0500335i	0.880107	−	0.474775i	$-0.157470\pi$
$773$	0.803138	+	1.39107i	0.0288868	+	0.0500335i	−0.851221	+	0.524808i	$0.824137\pi$
$774$		0			0
$775$	7.52280	+	4.34329i	0.270227	+	0.156016i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	29.6623i		−	1.06276i
$780$		0			0
$781$	18.6027			0.665656
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.45988	−	3.15226i	−0.194871	−	0.112509i
$786$		0			0
$787$	13.7768	+	7.95401i	0.491088	+	0.283530i	0.725026	−	0.688722i	$-0.241828\pi$
$787$	13.7768	+	7.95401i	0.491088	+	0.283530i	−0.233938	+	0.972252i	$0.575161\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	40.5644	−	15.5023i	1.44231	−	0.551198i
$792$		0			0
$793$	6.23549	−	10.8002i	0.221429	−	0.383526i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.1844	+	17.6399i	0.360749	+	0.624836i	0.988084	−	0.153914i	$-0.0491878\pi$
$797$	10.1844	+	17.6399i	0.360749	+	0.624836i	−0.627335	+	0.778749i	$0.715854\pi$
$798$		0			0
$799$	1.39800	−	2.42141i	0.0494578	−	0.0856634i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−28.7957	−	49.8757i	−1.01618	−	1.76008i
$804$		0			0
$805$	−3.65838	+	22.8786i	−0.128941	+	0.806365i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	35.7396	−	20.6343i	1.25654	−	0.725462i	0.284137	−	0.958784i	$-0.408293\pi$
$809$	35.7396	−	20.6343i	1.25654	−	0.725462i	0.972400	+	0.233322i	$0.0749595\pi$
$810$		0			0
$811$		−	19.3660i		−	0.680032i	−0.940420	−	0.340016i	$-0.889568\pi$
$811$		−	19.3660i		−	0.680032i	0.940420	−	0.340016i	$-0.110432\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	21.5527	−	37.3305i	0.754960	−	1.30763i
$816$		0			0
$817$	−23.1309	+	13.3547i	−0.809249	+	0.467220i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	28.1405	−	16.2469i	0.982111	−	0.567022i	0.0792043	−	0.996858i	$-0.474762\pi$
$821$	28.1405	−	16.2469i	0.982111	−	0.567022i	0.902907	+	0.429836i	$0.141429\pi$
$822$		0			0
$823$	27.8957	−	48.3167i	0.972381	−	1.68421i	0.284063	−	0.958806i	$-0.408318\pi$
$823$	27.8957	−	48.3167i	0.972381	−	1.68421i	0.688319	−	0.725408i	$-0.258349\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	18.2989i		−	0.636314i	−0.948038	−	0.318157i	$-0.896936\pi$
$827$		−	18.2989i		−	0.636314i	0.948038	−	0.318157i	$-0.103064\pi$
$828$		0			0
$829$	12.6483	−	7.30247i	0.439292	−	0.253625i	−0.264005	−	0.964521i	$-0.585044\pi$
$829$	12.6483	−	7.30247i	0.439292	−	0.253625i	0.703297	+	0.710896i	$0.251710\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.39961	+	6.68195i	0.0484935	+	0.231516i
$834$		0			0
$835$	−27.4992	−	47.6299i	−0.951648	−	1.64830i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.7379	−	27.2588i	0.543332	−	0.941079i	−0.455378	−	0.890298i	$-0.650496\pi$
$839$	15.7379	−	27.2588i	0.543332	−	0.941079i	0.998710	−	0.0507803i	$-0.0161708\pi$
$840$		0			0
$841$	−14.4522	−	25.0320i	−0.498353	−	0.863173i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.86801	−	6.69959i	0.133064	−	0.230473i
$846$		0			0
$847$	−4.05677	−	0.648694i	−0.139392	−	0.0222894i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	20.3140	+	11.7283i	0.696354	+	0.402040i
$852$		0			0
$853$	−21.2554	−	12.2718i	−0.727771	−	0.420179i	0.0898353	−	0.995957i	$-0.471366\pi$
$853$	−21.2554	−	12.2718i	−0.727771	−	0.420179i	−0.817606	+	0.575778i	$0.804699\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.7302			0.400697			0.200348	−	0.979725i	$-0.435793\pi$
$857$	11.7302			0.400697			0.200348	+	0.979725i	$0.435793\pi$
$858$		0			0
$859$			34.1123i			1.16390i	0.813226	+	0.581948i	$0.197709\pi$
$859$			34.1123i			1.16390i	−0.813226	+	0.581948i	$0.802291\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−20.8863	−	12.0587i	−0.710978	−	0.410483i	0.100445	−	0.994943i	$-0.467973\pi$
$863$	−20.8863	−	12.0587i	−0.710978	−	0.410483i	−0.811423	+	0.584459i	$0.801307\pi$
$864$		0			0
$865$	−13.2018	−	22.8663i	−0.448876	−	0.777477i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−21.4573	+	12.3884i	−0.727890	+	0.420248i
$870$		0			0
$871$		−	11.5560i		−	0.391559i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	22.1855	+	3.54754i	0.750006	+	0.119929i
$876$		0			0
$877$	−51.7506			−1.74749			−0.873747	−	0.486381i	$-0.838317\pi$
$877$	−51.7506			−1.74749			−0.873747	+	0.486381i	$0.838317\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	30.3925			1.02395			0.511975	−	0.859000i	$-0.328914\pi$
$881$	30.3925			1.02395			0.511975	+	0.859000i	$0.328914\pi$
$882$		0			0
$883$	−35.4897			−1.19432			−0.597162	−	0.802121i	$-0.703705\pi$
$883$	−35.4897			−1.19432			−0.597162	+	0.802121i	$0.703705\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−46.5511			−1.56303			−0.781517	−	0.623884i	$-0.785554\pi$
$887$	−46.5511			−1.56303			−0.781517	+	0.623884i	$0.785554\pi$
$888$		0			0
$889$	47.0928	+	7.53033i	1.57944	+	0.252559i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			6.99125i			0.233953i
$894$		0			0
$895$	1.52874	−	0.882620i	0.0511003	−	0.0295027i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.777893	−	1.34735i	−0.0259442	−	0.0449366i
$900$		0			0
$901$	−7.62099	−	4.39998i	−0.253892	−	0.146585i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	49.6106i		−	1.64911i
$906$		0			0
$907$	14.6331			0.485883			0.242941	−	0.970041i	$-0.421888\pi$
$907$	14.6331			0.485883			0.242941	+	0.970041i	$0.421888\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.67661	−	3.85474i	−0.221206	−	0.127713i	0.385303	−	0.922790i	$-0.374097\pi$
$911$	−6.67661	−	3.85474i	−0.221206	−	0.127713i	−0.606508	+	0.795077i	$0.707430\pi$
$912$		0			0
$913$	−44.4201	−	25.6460i	−1.47009	−	0.848758i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	27.2734	+	4.36113i	0.900648	+	0.144017i
$918$		0			0
$919$	−13.4738	+	23.3373i	−0.444460	+	0.769827i	−0.998014	−	0.0629860i	$-0.979938\pi$
$919$	−13.4738	+	23.3373i	−0.444460	+	0.769827i	0.553555	+	0.832813i	$0.313271\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.30890	−	14.3914i	−0.273491	−	0.473700i
$924$		0			0
$925$	−5.99325	+	10.3806i	−0.197057	+	0.341312i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.8137	−	23.9261i	−0.453213	−	0.784989i	0.545370	−	0.838195i	$-0.316389\pi$
$929$	−13.8137	−	23.9261i	−0.453213	−	0.784989i	−0.998584	+	0.0532068i	$0.983056\pi$
$930$		0			0
$931$	−11.3847	−	12.7196i	−0.373118	−	0.416867i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.76057	−	4.48057i	0.253798	−	0.146530i
$936$		0			0
$937$		−	7.60743i		−	0.248524i	−0.992249	−	0.124262i	$-0.960344\pi$
$937$		−	7.60743i		−	0.248524i	0.992249	−	0.124262i	$-0.0396563\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.6498	−	35.7665i	0.673165	−	1.16596i	−0.303837	−	0.952724i	$-0.598268\pi$
$941$	20.6498	−	35.7665i	0.673165	−	1.16596i	0.977002	−	0.213231i	$-0.0683988\pi$
$942$		0			0
$943$	35.5704	−	20.5366i	1.15833	−	0.668763i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36.0318	+	20.8030i	−1.17088	+	0.676005i	−0.953886	−	0.300169i	$-0.902957\pi$
$947$	−36.0318	+	20.8030i	−1.17088	+	0.676005i	−0.216989	+	0.976174i	$0.569624\pi$
$948$		0			0
$949$	−25.7233	+	44.5541i	−0.835014	+	1.44629i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			47.2656i			1.53108i	0.643386	+	0.765542i	$0.277529\pi$
$953$			47.2656i			1.53108i	−0.643386	+	0.765542i	$0.722471\pi$
$954$		0			0
$955$	−47.5038	+	27.4263i	−1.53719	+	0.887494i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.60833	+	10.0581i	−0.0519358	+	0.324794i
$960$		0			0
$961$	−2.82894	−	4.89987i	−0.0912562	−	0.158060i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	16.6344	−	28.8116i	0.535480	−	0.927479i
$966$		0			0
$967$	2.60192	+	4.50665i	0.0836720	+	0.144924i	0.904825	−	0.425785i	$-0.140002\pi$
$967$	2.60192	+	4.50665i	0.0836720	+	0.144924i	−0.821153	+	0.570709i	$0.806669\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.67233	−	15.0209i	0.278308	−	0.482044i	−0.692656	−	0.721268i	$-0.743560\pi$
$971$	8.67233	−	15.0209i	0.278308	−	0.482044i	0.970964	+	0.239224i	$0.0768929\pi$
$972$		0			0
$973$	−53.5461	+	20.4634i	−1.71661	+	0.656027i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.3541	−	13.4835i	−0.747165	−	0.431376i	0.0775039	−	0.996992i	$-0.475305\pi$
$977$	−23.3541	−	13.4835i	−0.747165	−	0.431376i	−0.824668	+	0.565616i	$0.808638\pi$
$978$		0			0
$979$	−14.1818	−	8.18789i	−0.453254	−	0.261686i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.1129			−0.545817			−0.272909	−	0.962040i	$-0.587986\pi$
$983$	−17.1129			−0.545817			−0.272909	+	0.962040i	$0.587986\pi$
$984$		0			0
$985$		−	57.7942i		−	1.84148i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.0293	−	18.4921i	−1.01847	−	0.588015i
$990$		0			0
$991$	5.84386	+	10.1219i	0.185636	+	0.321531i	0.943791	−	0.330544i	$-0.107232\pi$
$991$	5.84386	+	10.1219i	0.185636	+	0.321531i	−0.758155	+	0.652075i	$0.773899\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	17.2624	−	9.96646i	0.547255	−	0.315958i
$996$		0			0
$997$			28.9017i			0.915325i	0.889126	+	0.457663i	$0.151313\pi$
$997$			28.9017i			0.915325i	−0.889126	+	0.457663i	$0.848687\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.e.1601.5		48
3.2	odd	2		1008.2.df.e.929.1		48
4.3	odd	2		1512.2.cx.a.89.5		48
7.3	odd	6		3024.2.ca.e.2033.5		48
9.4	even	3		1008.2.ca.e.257.9		48
9.5	odd	6		3024.2.ca.e.2609.5		48
12.11	even	2		504.2.cx.a.425.24	yes	48
21.17	even	6		1008.2.ca.e.353.9		48
28.3	even	6		1512.2.bs.a.521.5		48
36.23	even	6		1512.2.bs.a.1097.5		48
36.31	odd	6		504.2.bs.a.257.16	✓	48
63.31	odd	6		1008.2.df.e.689.1		48
63.59	even	6	inner	3024.2.df.e.17.5		48
84.59	odd	6		504.2.bs.a.353.16	yes	48
252.31	even	6		504.2.cx.a.185.24	yes	48
252.59	odd	6		1512.2.cx.a.17.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.16	✓	48	36.31	odd	6
504.2.bs.a.353.16	yes	48	84.59	odd	6
504.2.cx.a.185.24	yes	48	252.31	even	6
504.2.cx.a.425.24	yes	48	12.11	even	2
1008.2.ca.e.257.9		48	9.4	even	3
1008.2.ca.e.353.9		48	21.17	even	6
1008.2.df.e.689.1		48	63.31	odd	6
1008.2.df.e.929.1		48	3.2	odd	2
1512.2.bs.a.521.5		48	28.3	even	6
1512.2.bs.a.1097.5		48	36.23	even	6
1512.2.cx.a.17.5		48	252.59	odd	6
1512.2.cx.a.89.5		48	4.3	odd	2
3024.2.ca.e.2033.5		48	7.3	odd	6
3024.2.ca.e.2609.5		48	9.5	odd	6
3024.2.df.e.17.5		48	63.59	even	6	inner
3024.2.df.e.1601.5		48	1.1	even	1	trivial

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.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.59337 q^{5} +(2.61256 + 0.417759i) q^{7} +3.54299i q^{11} +(2.74094 - 1.58248i) q^{13} +(0.487640 + 0.844616i) q^{17} +(-2.11191 - 1.21931i) q^{19} -3.37675i q^{23} +1.72555 q^{25} +(-0.267645 - 0.154525i) q^{29} +(4.35965 + 2.51705i) q^{31} +(-6.77533 - 1.08340i) q^{35} +(-3.47324 + 6.01583i) q^{37} +(6.08175 + 10.5339i) q^{41} +(5.47630 - 9.48523i) q^{43} +(-1.43344 - 2.48279i) q^{47} +(6.65096 + 2.18284i) q^{49} +(-7.81416 + 4.51151i) q^{53} -9.18828i q^{55} +(-0.219727 + 0.380579i) q^{59} +(3.41242 - 1.97016i) q^{61} +(-7.10826 + 4.10396i) q^{65} +(1.82561 - 3.16204i) q^{67} -5.25055i q^{71} +(-14.0773 + 8.12752i) q^{73} +(-1.48012 + 9.25629i) q^{77} +(3.49659 + 6.05628i) q^{79} +(-7.23851 + 12.5375i) q^{83} +(-1.26463 - 2.19040i) q^{85} +(-2.31101 + 4.00279i) q^{89} +(7.82197 - 2.98928i) q^{91} +(5.47697 + 3.16213i) q^{95} +(12.4805 + 7.20560i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} - 18 q^{31} + 6 q^{41} + 6 q^{43} + 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} - 6 q^{79} + 18 q^{89} - 6 q^{91} - 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 - 18 * q^31 + 6 * q^41 + 6 * q^43 + 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 - 6 * q^79 + 18 * q^89 - 6 * q^91 - 54 * q^95

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