LMFDB - Embedded newform 2592.2.s.b.1727.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(863,2592)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("2592.863");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$1$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1727.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2592.1727
Dual form			2592.2.s.b.863.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67303 + 0.965926i) q^{5} +(-0.633975 - 0.366025i) q^{7} +O(q^{10})$	$q+(-1.67303 + 0.965926i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.63896 - 4.57081i) q^{11} +(-2.23205 - 3.86603i) q^{13} +0.896575i q^{17} +1.26795i q^{19} +(0.707107 + 1.22474i) q^{23} +(-0.633975 + 1.09808i) q^{25} +(4.69093 + 2.70831i) q^{29} +(-6.46410 + 3.73205i) q^{31} +1.41421 q^{35} -7.73205 q^{37} +(0.328169 - 0.189469i) q^{41} +(7.56218 + 4.36603i) q^{43} +(-2.31079 + 4.00240i) q^{47} +(-3.23205 - 5.59808i) q^{49} -2.44949i q^{53} +10.1962i q^{55} +(5.41662 + 9.38186i) q^{59} +(0.598076 - 1.03590i) q^{61} +(7.46859 + 4.31199i) q^{65} +(-11.3660 + 6.56218i) q^{67} -13.2827 q^{71} -13.7321 q^{73} +(-3.34607 + 1.93185i) q^{77} +(-14.3660 - 8.29423i) q^{79} +(5.27792 - 9.14162i) q^{83} +(-0.866025 - 1.50000i) q^{85} -14.9372i q^{89} +3.26795i q^{91} +(-1.22474 - 2.12132i) q^{95} +(3.19615 - 5.53590i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{7}+O(q^{10}) $ 8 * q - 12 * q^7	$ 8 q - 12 q^{7} - 4 q^{13} - 12 q^{25} - 24 q^{31} - 48 q^{37} + 12 q^{43} - 12 q^{49} - 16 q^{61} - 84 q^{67} - 96 q^{73} - 108 q^{79} - 16 q^{97}+O(q^{100}) $ 8 * q - 12 * q^7 - 4 * q^13 - 12 * q^25 - 24 * q^31 - 48 * q^37 + 12 * q^43 - 12 * q^49 - 16 * q^61 - 84 * q^67 - 96 * q^73 - 108 * q^79 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.67303	+	0.965926i	−0.748203	+	0.431975i	−0.825044	−	0.565068i	$-0.808850\pi$
$5$	−1.67303	+	0.965926i	−0.748203	+	0.431975i	0.0768413	+	0.997043i	$0.475517\pi$
$6$		0			0
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	0.375382	−	0.926870i	$-0.377511\pi$
$7$	−0.633975	−	0.366025i	−0.239620	−	0.138345i	−0.615002	+	0.788526i	$0.710845\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.63896	−	4.57081i	0.795676	−	1.37815i	−0.126733	−	0.991937i	$-0.540449\pi$
$11$	2.63896	−	4.57081i	0.795676	−	1.37815i	0.922409	−	0.386214i	$-0.126217\pi$
$12$		0			0
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	−0.989658	−	0.143449i	$-0.954181\pi$
$13$	−2.23205	−	3.86603i	−0.619060	−	1.07224i	0.370598	−	0.928793i	$-0.379153\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			0.896575i			0.217451i	0.994072	+	0.108726i	$0.0346770\pi$
$17$			0.896575i			0.217451i	−0.994072	+	0.108726i	$0.965323\pi$
$18$		0			0
$19$			1.26795i			0.290887i	0.989367	+	0.145444i	$0.0464610\pi$
$19$			1.26795i			0.290887i	−0.989367	+	0.145444i	$0.953539\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.707107	+	1.22474i	0.147442	+	0.255377i	0.930281	−	0.366847i	$-0.119563\pi$
$23$	0.707107	+	1.22474i	0.147442	+	0.255377i	−0.782839	+	0.622224i	$0.786229\pi$
$24$		0			0
$25$	−0.633975	+	1.09808i	−0.126795	+	0.219615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.69093	+	2.70831i	0.871084	+	0.502920i	0.867708	−	0.497074i	$-0.165592\pi$
$29$	4.69093	+	2.70831i	0.871084	+	0.502920i	0.00337538	+	0.999994i	$0.498926\pi$
$30$		0			0
$31$	−6.46410	+	3.73205i	−1.16099	+	0.670296i	−0.951540	−	0.307524i	$-0.900500\pi$
$31$	−6.46410	+	3.73205i	−1.16099	+	0.670296i	−0.209447	+	0.977820i	$0.567166\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.41421			0.239046
$36$		0			0
$37$	−7.73205			−1.27114			−0.635571	−	0.772043i	$-0.719235\pi$
$37$	−7.73205			−1.27114			−0.635571	+	0.772043i	$0.719235\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.328169	−	0.189469i	0.0512514	−	0.0295900i	−0.474155	−	0.880441i	$-0.657246\pi$
$41$	0.328169	−	0.189469i	0.0512514	−	0.0295900i	0.525407	+	0.850851i	$0.323913\pi$
$42$		0			0
$43$	7.56218	+	4.36603i	1.15322	+	0.665813i	0.949670	−	0.313252i	$-0.101418\pi$
$43$	7.56218	+	4.36603i	1.15322	+	0.665813i	0.203551	+	0.979064i	$0.434752\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.31079	+	4.00240i	−0.337063	+	0.583811i	−0.983879	−	0.178836i	$-0.942767\pi$
$47$	−2.31079	+	4.00240i	−0.337063	+	0.583811i	0.646816	+	0.762646i	$0.276100\pi$
$48$		0			0
$49$	−3.23205	−	5.59808i	−0.461722	−	0.799725i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.44949i		−	0.336463i	−0.985747	−	0.168232i	$-0.946194\pi$
$53$		−	2.44949i		−	0.336463i	0.985747	−	0.168232i	$-0.0538057\pi$
$54$		0			0
$55$			10.1962i			1.37485i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.41662	+	9.38186i	0.705184	+	1.22141i	0.966625	+	0.256194i	$0.0824687\pi$
$59$	5.41662	+	9.38186i	0.705184	+	1.22141i	−0.261442	+	0.965219i	$0.584198\pi$
$60$		0			0
$61$	0.598076	−	1.03590i	0.0765758	−	0.132633i	−0.825195	−	0.564848i	$-0.808935\pi$
$61$	0.598076	−	1.03590i	0.0765758	−	0.132633i	0.901770	+	0.432215i	$0.142268\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.46859	+	4.31199i	0.926364	+	0.534837i
$66$		0			0
$67$	−11.3660	+	6.56218i	−1.38858	+	0.801698i	−0.993155	−	0.116800i	$-0.962736\pi$
$67$	−11.3660	+	6.56218i	−1.38858	+	0.801698i	−0.395426	+	0.918498i	$0.629403\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.2827			−1.57637			−0.788185	−	0.615439i	$-0.788979\pi$
$71$	−13.2827			−1.57637			−0.788185	+	0.615439i	$0.788979\pi$
$72$		0			0
$73$	−13.7321			−1.60721			−0.803607	−	0.595160i	$-0.797089\pi$
$73$	−13.7321			−1.60721			−0.803607	+	0.595160i	$0.797089\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.34607	+	1.93185i	−0.381320	+	0.220155i
$78$		0			0
$79$	−14.3660	−	8.29423i	−1.61630	−	0.933174i	−0.987865	−	0.155315i	$-0.950361\pi$
$79$	−14.3660	−	8.29423i	−1.61630	−	0.933174i	−0.628439	−	0.777859i	$-0.716306\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.27792	−	9.14162i	0.579327	−	1.00342i	−0.416230	−	0.909259i	$-0.636649\pi$
$83$	5.27792	−	9.14162i	0.579327	−	1.00342i	0.995557	−	0.0941638i	$-0.0300178\pi$
$84$		0			0
$85$	−0.866025	−	1.50000i	−0.0939336	−	0.162698i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	14.9372i		−	1.58334i	−0.610951	−	0.791669i	$-0.709213\pi$
$89$		−	14.9372i		−	1.58334i	0.610951	−	0.791669i	$-0.290787\pi$
$90$		0			0
$91$			3.26795i			0.342574i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.22474	−	2.12132i	−0.125656	−	0.217643i
$96$		0			0
$97$	3.19615	−	5.53590i	0.324520	−	0.562085i	−0.656895	−	0.753982i	$-0.728131\pi$
$97$	3.19615	−	5.53590i	0.324520	−	0.562085i	0.981415	+	0.191897i	$0.0614639\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.46739	−	3.15660i	−0.544025	−	0.314093i	0.202683	−	0.979244i	$-0.435034\pi$
$101$	−5.46739	−	3.15660i	−0.544025	−	0.314093i	−0.746709	+	0.665151i	$0.768367\pi$
$102$		0			0
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	−0.319531	−	0.947576i	$-0.603525\pi$
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	0.660859	+	0.750510i	$0.270192\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.79315			−0.173350			−0.0866752	−	0.996237i	$-0.527624\pi$
$107$	−1.79315			−0.173350			−0.0866752	+	0.996237i	$0.527624\pi$
$108$		0			0
$109$	3.92820			0.376254			0.188127	−	0.982145i	$-0.439758\pi$
$109$	3.92820			0.376254			0.188127	+	0.982145i	$0.439758\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−17.5068	+	10.1075i	−1.64690	+	0.950838i	−0.668605	+	0.743617i	$0.733108\pi$
$113$	−17.5068	+	10.1075i	−1.64690	+	0.950838i	−0.978294	+	0.207221i	$0.933558\pi$
$114$		0			0
$115$	−2.36603	−	1.36603i	−0.220633	−	0.127383i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.328169	−	0.568406i	0.0300832	−	0.0521057i
$120$		0			0
$121$	−8.42820	−	14.5981i	−0.766200	−	1.32710i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.1087i		−	1.08304i
$126$		0			0
$127$			21.1244i			1.87448i	0.348680	+	0.937242i	$0.386630\pi$
$127$			21.1244i			1.87448i	−0.348680	+	0.937242i	$0.613370\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.0507680	−	0.0879327i	−0.00443562	−	0.00768272i	0.863799	−	0.503836i	$-0.168079\pi$
$131$	−0.0507680	−	0.0879327i	−0.00443562	−	0.00768272i	−0.868235	+	0.496154i	$0.834745\pi$
$132$		0			0
$133$	0.464102	−	0.803848i	0.0402427	−	0.0697024i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.21046	−	2.43091i	−0.359723	−	0.207686i	0.309236	−	0.950985i	$-0.399927\pi$
$137$	−4.21046	−	2.43091i	−0.359723	−	0.207686i	−0.668959	+	0.743299i	$0.733260\pi$
$138$		0			0
$139$	−10.7321	+	6.19615i	−0.910281	+	0.525551i	−0.880521	−	0.474006i	$-0.842807\pi$
$139$	−10.7321	+	6.19615i	−0.910281	+	0.525551i	−0.0297592	+	0.999557i	$0.509474\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−23.5612			−1.97028
$144$		0			0
$145$	−10.4641			−0.868996
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.58510	+	0.915158i	−0.129856	+	0.0749727i	−0.563521	−	0.826102i	$-0.690554\pi$
$149$	−1.58510	+	0.915158i	−0.129856	+	0.0749727i	0.433665	+	0.901074i	$0.357220\pi$
$150$		0			0
$151$	0.928203	+	0.535898i	0.0755361	+	0.0436108i	0.537292	−	0.843396i	$-0.319447\pi$
$151$	0.928203	+	0.535898i	0.0755361	+	0.0436108i	−0.461756	+	0.887007i	$0.652781\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.20977	−	12.4877i	0.579103	−	1.00304i
$156$		0			0
$157$	−5.33013	−	9.23205i	−0.425390	−	0.736798i	0.571066	−	0.820904i	$-0.306530\pi$
$157$	−5.33013	−	9.23205i	−0.425390	−	0.736798i	−0.996457	+	0.0841060i	$0.973197\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	1.03528i		−	0.0815912i
$162$		0			0
$163$			1.60770i			0.125924i	0.998016	+	0.0629622i	$0.0200548\pi$
$163$			1.60770i			0.125924i	−0.998016	+	0.0629622i	$0.979945\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.32868	+	9.22955i	0.412346	+	0.714204i	0.995146	−	0.0984115i	$-0.0313761\pi$
$167$	5.32868	+	9.22955i	0.412346	+	0.714204i	−0.582800	+	0.812616i	$0.698043\pi$
$168$		0			0
$169$	−3.46410	+	6.00000i	−0.266469	+	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.58991	+	5.53674i	0.729107	+	0.420950i	0.818095	−	0.575082i	$-0.195030\pi$
$173$	9.58991	+	5.53674i	0.729107	+	0.420950i	−0.0889883	+	0.996033i	$0.528363\pi$
$174$		0			0
$175$	0.803848	−	0.464102i	0.0607652	−	0.0350828i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	21.8695			1.63461			0.817303	−	0.576208i	$-0.195468\pi$
$179$	21.8695			1.63461			0.817303	+	0.576208i	$0.195468\pi$
$180$		0			0
$181$	−23.3205			−1.73340			−0.866700	−	0.498830i	$-0.833763\pi$
$181$	−23.3205			−1.73340			−0.866700	+	0.498830i	$0.833763\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	12.9360	−	7.46859i	0.951072	−	0.549101i
$186$		0			0
$187$	4.09808	+	2.36603i	0.299681	+	0.173021i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.2277	+	17.7148i	−0.740048	+	1.28180i	0.212425	+	0.977177i	$0.431864\pi$
$191$	−10.2277	+	17.7148i	−0.740048	+	1.28180i	−0.952473	+	0.304623i	$0.901470\pi$
$192$		0			0
$193$	4.23205	+	7.33013i	0.304630	+	0.527634i	0.977179	−	0.212418i	$-0.0681340\pi$
$193$	4.23205	+	7.33013i	0.304630	+	0.527634i	−0.672549	+	0.740052i	$0.734801\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			9.76079i			0.695428i	0.937601	+	0.347714i	$0.113042\pi$
$197$			9.76079i			0.695428i	−0.937601	+	0.347714i	$0.886958\pi$
$198$		0			0
$199$			8.00000i			0.567105i	0.958957	+	0.283552i	$0.0915130\pi$
$199$			8.00000i			0.567105i	−0.958957	+	0.283552i	$0.908487\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.98262	−	3.43400i	−0.139153	−	0.241019i
$204$		0			0
$205$	−0.366025	+	0.633975i	−0.0255643	+	0.0442787i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	5.79555	+	3.34607i	0.400887	+	0.231452i
$210$		0			0
$211$	−16.5622	+	9.56218i	−1.14019	+	0.658287i	−0.946477	−	0.322771i	$-0.895386\pi$
$211$	−16.5622	+	9.56218i	−1.14019	+	0.658287i	−0.193710	+	0.981059i	$0.562052\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−16.8690			−1.15046
$216$		0			0
$217$	5.46410			0.370927
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.46618	−	2.00120i	0.233161	−	0.134615i
$222$		0			0
$223$	14.9545	+	8.63397i	1.00143	+	0.578174i	0.908670	−	0.417515i	$-0.137099\pi$
$223$	14.9545	+	8.63397i	1.00143	+	0.578174i	0.0927563	+	0.995689i	$0.470432\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.67475	−	15.0251i	0.575763	−	0.997251i	−0.420195	−	0.907434i	$-0.638038\pi$
$227$	8.67475	−	15.0251i	0.575763	−	0.997251i	0.995958	−	0.0898175i	$-0.0286284\pi$
$228$		0			0
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	0.625076	−	0.780564i	$-0.285068\pi$
$229$	−5.50000	−	9.52628i	−0.363450	−	0.629514i	−0.988526	+	0.151050i	$0.951735\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			18.8009i			1.23169i	0.787869	+	0.615843i	$0.211185\pi$
$233$			18.8009i			1.23169i	−0.787869	+	0.615843i	$0.788815\pi$
$234$		0			0
$235$		−	8.92820i		−	0.582412i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.52056	+	16.4901i	0.615834	+	1.06666i	0.990238	+	0.139390i	$0.0445140\pi$
$239$	9.52056	+	16.4901i	0.615834	+	1.06666i	−0.374404	+	0.927266i	$0.622153\pi$
$240$		0			0
$241$	8.06218	−	13.9641i	0.519331	−	0.899507i	−0.480417	−	0.877040i	$-0.659515\pi$
$241$	8.06218	−	13.9641i	0.519331	−	0.899507i	0.999748	−	0.0224667i	$-0.00715197\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	10.8147	+	6.24384i	0.690923	+	0.398904i
$246$		0			0
$247$	4.90192	−	2.83013i	0.311902	−	0.180077i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	23.8386			1.50468			0.752338	−	0.658777i	$-0.228926\pi$
$251$	23.8386			1.50468			0.752338	+	0.658777i	$0.228926\pi$
$252$		0			0
$253$	7.46410			0.469264
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.688524	+	0.397520i	−0.0429490	+	0.0247966i	−0.521321	−	0.853361i	$-0.674560\pi$
$257$	−0.688524	+	0.397520i	−0.0429490	+	0.0247966i	0.478372	+	0.878157i	$0.341227\pi$
$258$		0			0
$259$	4.90192	+	2.83013i	0.304591	+	0.175856i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.72500	+	6.45189i	−0.229694	+	0.397841i	−0.957717	−	0.287711i	$-0.907106\pi$
$263$	−3.72500	+	6.45189i	−0.229694	+	0.397841i	0.728024	+	0.685552i	$0.240439\pi$
$264$		0			0
$265$	2.36603	+	4.09808i	0.145344	+	0.251743i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	22.7661i		−	1.38807i	−0.719939	−	0.694037i	$-0.755830\pi$
$269$		−	22.7661i		−	1.38807i	0.719939	−	0.694037i	$-0.244170\pi$
$270$		0			0
$271$		−	13.2679i		−	0.805971i	−0.915206	−	0.402985i	$-0.867973\pi$
$271$		−	13.2679i		−	0.805971i	0.915206	−	0.402985i	$-0.132027\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.34607	+	5.79555i	0.201775	+	0.349485i
$276$		0			0
$277$	−0.535898	+	0.928203i	−0.0321990	+	0.0557703i	−0.881676	−	0.471856i	$-0.843584\pi$
$277$	−0.535898	+	0.928203i	−0.0321990	+	0.0557703i	0.849477	+	0.527626i	$0.176918\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.91808	+	5.72620i	0.591663	+	0.341597i	0.765755	−	0.643133i	$-0.222366\pi$
$281$	9.91808	+	5.72620i	0.591663	+	0.341597i	−0.174092	+	0.984729i	$0.555699\pi$
$282$		0			0
$283$	−16.7321	+	9.66025i	−0.994617	+	0.574242i	−0.906651	−	0.421881i	$-0.861370\pi$
$283$	−16.7321	+	9.66025i	−0.994617	+	0.574242i	−0.0879660	+	0.996123i	$0.528037\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.277401			−0.0163745
$288$		0			0
$289$	16.1962			0.952715
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−20.6126	+	11.9007i	−1.20420	+	0.695246i	−0.961487	−	0.274852i	$-0.911371\pi$
$293$	−20.6126	+	11.9007i	−1.20420	+	0.695246i	−0.242715	+	0.970098i	$0.578038\pi$
$294$		0			0
$295$	−18.1244	−	10.4641i	−1.05524	−	0.609244i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.15660	−	5.46739i	0.182551	−	0.316187i
$300$		0			0
$301$	−3.19615	−	5.53590i	−0.184223	−	0.319084i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			2.31079i			0.132315i
$306$		0			0
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.1087	−	20.9730i	−0.686624	−	1.18927i	−0.972923	−	0.231128i	$-0.925759\pi$
$311$	−12.1087	−	20.9730i	−0.686624	−	1.18927i	0.286299	−	0.958140i	$-0.407575\pi$
$312$		0			0
$313$	−14.1603	+	24.5263i	−0.800385	+	1.38631i	0.118978	+	0.992897i	$0.462038\pi$
$313$	−14.1603	+	24.5263i	−0.800385	+	1.38631i	−0.919363	+	0.393410i	$0.871295\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.33178	−	3.65565i	−0.355628	−	0.205322i	0.311533	−	0.950235i	$-0.399157\pi$
$317$	−6.33178	−	3.65565i	−0.355628	−	0.205322i	−0.667161	+	0.744913i	$0.732491\pi$
$318$		0			0
$319$	24.7583	−	14.2942i	1.38620	−	0.800323i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.13681			−0.0632539
$324$		0			0
$325$	5.66025			0.313974
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.92996	−	1.69161i	0.161534	−	0.0932618i
$330$		0			0
$331$	−6.75833	−	3.90192i	−0.371471	−	0.214469i	0.302630	−	0.953108i	$-0.402135\pi$
$331$	−6.75833	−	3.90192i	−0.371471	−	0.214469i	−0.674101	+	0.738639i	$0.735469\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	12.6772	−	21.9575i	0.692627	−	1.19967i
$336$		0			0
$337$	2.46410	+	4.26795i	0.134228	+	0.232490i	0.925302	−	0.379230i	$-0.123811\pi$
$337$	2.46410	+	4.26795i	0.134228	+	0.232490i	−0.791074	+	0.611720i	$0.790478\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			39.3949i			2.13335i
$342$		0			0
$343$			9.85641i			0.532196i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.88160	−	11.9193i	−0.369424	−	0.639860i	0.620052	−	0.784561i	$-0.287112\pi$
$347$	−6.88160	−	11.9193i	−0.369424	−	0.639860i	−0.989476	+	0.144700i	$0.953778\pi$
$348$		0			0
$349$	1.07180	−	1.85641i	0.0573720	−	0.0993712i	−0.835913	−	0.548862i	$-0.815061\pi$
$349$	1.07180	−	1.85641i	0.0573720	−	0.0993712i	0.893285	+	0.449491i	$0.148395\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−24.2311	−	13.9898i	−1.28969	−	0.744604i	−0.311092	−	0.950380i	$-0.600695\pi$
$353$	−24.2311	−	13.9898i	−1.28969	−	0.744604i	−0.978599	+	0.205776i	$0.934028\pi$
$354$		0			0
$355$	22.2224	−	12.8301i	1.17944	−	0.680952i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.44949			−0.129279			−0.0646396	−	0.997909i	$-0.520590\pi$
$359$	−2.44949			−0.129279			−0.0646396	+	0.997909i	$0.520590\pi$
$360$		0			0
$361$	17.3923			0.915384
$362$		0			0
$363$		0			0
$364$		0			0
$365$	22.9742	−	13.2641i	1.20252	−	0.694277i
$366$		0			0
$367$	−10.8564	−	6.26795i	−0.566700	−	0.327184i	0.189130	−	0.981952i	$-0.439433\pi$
$367$	−10.8564	−	6.26795i	−0.566700	−	0.327184i	−0.755830	+	0.654768i	$0.772766\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.896575	+	1.55291i	−0.0465479	+	0.0806233i
$372$		0			0
$373$	16.1244	+	27.9282i	0.834887	+	1.44607i	0.894122	+	0.447823i	$0.147801\pi$
$373$	16.1244	+	27.9282i	0.834887	+	1.44607i	−0.0592345	+	0.998244i	$0.518866\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	24.1803i		−	1.24535i
$378$		0			0
$379$		−	14.3923i		−	0.739283i	−0.929174	−	0.369642i	$-0.879480\pi$
$379$		−	14.3923i		−	0.739283i	0.929174	−	0.369642i	$-0.120520\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.60849	−	16.6424i	−0.490971	−	0.850387i	0.508975	−	0.860781i	$-0.330025\pi$
$383$	−9.60849	−	16.6424i	−0.490971	−	0.850387i	−0.999946	+	0.0103947i	$0.996691\pi$
$384$		0			0
$385$	3.73205	−	6.46410i	0.190203	−	0.329441i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.29392	−	5.36585i	−0.471221	−	0.272059i	0.245530	−	0.969389i	$-0.421038\pi$
$389$	−9.29392	−	5.36585i	−0.471221	−	0.272059i	−0.716751	+	0.697330i	$0.754371\pi$
$390$		0			0
$391$	−1.09808	+	0.633975i	−0.0555321	+	0.0320615i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	32.0464			1.61243
$396$		0			0
$397$	21.5885			1.08349			0.541747	−	0.840542i	$-0.317763\pi$
$397$	21.5885			1.08349			0.541747	+	0.840542i	$0.317763\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−16.2820	+	9.40044i	−0.813086	+	0.469436i	−0.848026	−	0.529954i	$-0.822209\pi$
$401$	−16.2820	+	9.40044i	−0.813086	+	0.469436i	0.0349403	+	0.999389i	$0.488876\pi$
$402$		0			0
$403$	28.8564	+	16.6603i	1.43744	+	0.829906i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−20.4046	+	35.3417i	−1.01142	+	1.75182i
$408$		0			0
$409$	−7.40192	−	12.8205i	−0.366002	−	0.633933i	0.622935	−	0.782274i	$-0.285940\pi$
$409$	−7.40192	−	12.8205i	−0.366002	−	0.633933i	−0.988936	+	0.148340i	$0.952607\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	7.93048i		−	0.390233i
$414$		0			0
$415$			20.3923i			1.00102i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.795040	+	1.37705i	0.0388402	+	0.0672732i	0.884792	−	0.465986i	$-0.154300\pi$
$419$	0.795040	+	1.37705i	0.0388402	+	0.0672732i	−0.845952	+	0.533259i	$0.820967\pi$
$420$		0			0
$421$	−4.42820	+	7.66987i	−0.215817	+	0.373807i	−0.953525	−	0.301313i	$-0.902575\pi$
$421$	−4.42820	+	7.66987i	−0.215817	+	0.373807i	0.737708	+	0.675120i	$0.235908\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.984508	−	0.568406i	−0.0477557	−	0.0275717i
$426$		0			0
$427$	−0.758330	+	0.437822i	−0.0366982	+	0.0211877i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.48528			−0.408722			−0.204361	−	0.978896i	$-0.565512\pi$
$431$	−8.48528			−0.408722			−0.204361	+	0.978896i	$0.565512\pi$
$432$		0			0
$433$	−34.1769			−1.64244			−0.821219	−	0.570613i	$-0.806706\pi$
$433$	−34.1769			−1.64244			−0.821219	+	0.570613i	$0.806706\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.55291	+	0.896575i	−0.0742860	+	0.0428890i
$438$		0			0
$439$	−6.46410	−	3.73205i	−0.308515	−	0.178121i	0.337747	−	0.941237i	$-0.390335\pi$
$439$	−6.46410	−	3.73205i	−0.308515	−	0.178121i	−0.646262	+	0.763116i	$0.723669\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.52245	+	14.7613i	−0.404914	+	0.701331i	−0.994311	−	0.106512i	$-0.966032\pi$
$443$	−8.52245	+	14.7613i	−0.404914	+	0.701331i	0.589398	+	0.807843i	$0.299365\pi$
$444$		0			0
$445$	14.4282	+	24.9904i	0.683962	+	1.18466i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			23.0064i			1.08574i	0.839818	+	0.542868i	$0.182662\pi$
$449$			23.0064i			1.08574i	−0.839818	+	0.542868i	$0.817338\pi$
$450$		0			0
$451$		−	2.00000i		−	0.0941763i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.15660	−	5.46739i	−0.147984	−	0.256315i
$456$		0			0
$457$	1.40192	−	2.42820i	0.0655792	−	0.113587i	−0.831372	−	0.555717i	$-0.812444\pi$
$457$	1.40192	−	2.42820i	0.0655792	−	0.113587i	0.896951	+	0.442130i	$0.145777\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.8589	−	17.8164i	−1.43724	−	0.829791i	−0.439583	−	0.898202i	$-0.644874\pi$
$461$	−30.8589	−	17.8164i	−1.43724	−	0.829791i	−0.997657	+	0.0684108i	$0.978207\pi$
$462$		0			0
$463$	15.9282	−	9.19615i	0.740246	−	0.427381i	−0.0819125	−	0.996640i	$-0.526103\pi$
$463$	15.9282	−	9.19615i	0.740246	−	0.427381i	0.822159	+	0.569258i	$0.192769\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.0716			−0.558606			−0.279303	−	0.960203i	$-0.590103\pi$
$467$	−12.0716			−0.558606			−0.279303	+	0.960203i	$0.590103\pi$
$468$		0			0
$469$	9.60770			0.443642
$470$		0			0
$471$		0			0
$472$		0			0
$473$	39.9125	−	23.0435i	1.83518	−	1.05954i
$474$		0			0
$475$	−1.39230	−	0.803848i	−0.0638833	−	0.0368831i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.6443	+	27.0967i	−0.714805	+	1.23808i	0.248229	+	0.968701i	$0.420151\pi$
$479$	−15.6443	+	27.0967i	−0.714805	+	1.23808i	−0.963035	+	0.269378i	$0.913182\pi$
$480$		0			0
$481$	17.2583	+	29.8923i	0.786912	+	1.36297i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			12.3490i			0.560739i
$486$		0			0
$487$		−	36.9282i		−	1.67338i	−0.547679	−	0.836688i	$-0.684489\pi$
$487$		−	36.9282i		−	1.67338i	0.547679	−	0.836688i	$-0.315511\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.12184	+	12.3354i	0.321404	+	0.556688i	0.980778	−	0.195127i	$-0.0625119\pi$
$491$	7.12184	+	12.3354i	0.321404	+	0.556688i	−0.659374	+	0.751815i	$0.729179\pi$
$492$		0			0
$493$	−2.42820	+	4.20577i	−0.109361	+	0.189418i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.42091	+	4.86181i	0.377729	+	0.218082i
$498$		0			0
$499$	31.5622	−	18.2224i	1.41292	−	0.815748i	0.417255	−	0.908790i	$-0.362992\pi$
$499$	31.5622	−	18.2224i	1.41292	−	0.815748i	0.995662	+	0.0930414i	$0.0296589\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	29.1165			1.29824			0.649120	−	0.760686i	$-0.275137\pi$
$503$	29.1165			1.29824			0.649120	+	0.760686i	$0.275137\pi$
$504$		0			0
$505$	12.1962			0.542722
$506$		0			0
$507$		0			0
$508$		0			0
$509$	31.9957	−	18.4727i	1.41818	−	0.818788i	0.422044	−	0.906575i	$-0.361313\pi$
$509$	31.9957	−	18.4727i	1.41818	−	0.818788i	0.996139	+	0.0877870i	$0.0279795\pi$
$510$		0			0
$511$	8.70577	+	5.02628i	0.385121	+	0.222350i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.86370	+	6.69213i	−0.170255	+	0.294891i
$516$		0			0
$517$	12.1962	+	21.1244i	0.536386	+	0.929048i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	15.2789i		−	0.669383i	−0.942328	−	0.334691i	$-0.891368\pi$
$521$		−	15.2789i		−	0.669383i	0.942328	−	0.334691i	$-0.108632\pi$
$522$		0			0
$523$		−	16.1962i		−	0.708208i	−0.935206	−	0.354104i	$-0.884786\pi$
$523$		−	16.1962i		−	0.708208i	0.935206	−	0.354104i	$-0.115214\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.34607	−	5.79555i	−0.145757	−	0.252458i
$528$		0			0
$529$	10.5000	−	18.1865i	0.456522	−	0.790719i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.46498	−	0.845807i	−0.0634554	−	0.0366360i
$534$		0			0
$535$	3.00000	−	1.73205i	0.129701	−	0.0748831i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−34.1170			−1.46952
$540$		0			0
$541$	7.00000			0.300954			0.150477	−	0.988614i	$-0.451919\pi$
$541$	7.00000			0.300954			0.150477	+	0.988614i	$0.451919\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.57201	+	3.79435i	−0.281514	+	0.162532i
$546$		0			0
$547$	1.14359	+	0.660254i	0.0488965	+	0.0282304i	0.524249	−	0.851565i	$-0.324346\pi$
$547$	1.14359	+	0.660254i	0.0488965	+	0.0282304i	−0.475352	+	0.879795i	$0.657679\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.43400	+	5.94786i	−0.146293	+	0.253387i
$552$		0			0
$553$	6.07180	+	10.5167i	0.258199	+	0.447214i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			2.03339i			0.0861574i	0.999072	+	0.0430787i	$0.0137166\pi$
$557$			2.03339i			0.0861574i	−0.999072	+	0.0430787i	$0.986283\pi$
$558$		0			0
$559$		−	38.9808i		−	1.64871i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.27981	−	7.41284i	−0.180372	−	0.312414i	0.761635	−	0.648006i	$-0.224397\pi$
$563$	−4.27981	−	7.41284i	−0.180372	−	0.312414i	−0.942007	+	0.335592i	$0.891064\pi$
$564$		0			0
$565$	19.5263	−	33.8205i	0.821477	−	1.42284i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.09154	−	3.51695i	−0.255371	−	0.147438i	0.366850	−	0.930280i	$-0.380436\pi$
$569$	−6.09154	−	3.51695i	−0.255371	−	0.147438i	−0.622221	+	0.782842i	$0.713769\pi$
$570$		0			0
$571$	34.5167	−	19.9282i	1.44448	−	0.833969i	0.446333	−	0.894867i	$-0.352730\pi$
$571$	34.5167	−	19.9282i	1.44448	−	0.833969i	0.998144	+	0.0608975i	$0.0193963\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.79315			−0.0747796
$576$		0			0
$577$	18.4641			0.768671			0.384335	−	0.923194i	$-0.374431\pi$
$577$	18.4641			0.768671			0.384335	+	0.923194i	$0.374431\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.69213	+	3.86370i	−0.277636	+	0.160293i
$582$		0			0
$583$	−11.1962	−	6.46410i	−0.463697	−	0.267716i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.845807	+	1.46498i	−0.0349102	+	0.0604663i	−0.882953	−	0.469462i	$-0.844448\pi$
$587$	−0.845807	+	1.46498i	−0.0349102	+	0.0604663i	0.848042	+	0.529928i	$0.177781\pi$
$588$		0			0
$589$	−4.73205	−	8.19615i	−0.194981	−	0.337717i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			21.1488i			0.868478i	0.900798	+	0.434239i	$0.142983\pi$
$593$			21.1488i			0.868478i	−0.900798	+	0.434239i	$0.857017\pi$
$594$		0			0
$595$			1.26795i			0.0519808i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.20977	+	12.4877i	0.294583	+	0.510233i	0.974888	−	0.222696i	$-0.0714859\pi$
$599$	7.20977	+	12.4877i	0.294583	+	0.510233i	−0.680305	+	0.732929i	$0.738153\pi$
$600$		0			0
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	−0.902036	−	0.431661i	$-0.857928\pi$
$601$	−1.89230	+	3.27757i	−0.0771887	+	0.133695i	0.824847	+	0.565356i	$0.191261\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	28.2013	+	16.2820i	1.14655	+	0.661959i
$606$		0			0
$607$	−5.83013	+	3.36603i	−0.236638	+	0.136623i	−0.613630	−	0.789593i	$-0.710291\pi$
$607$	−5.83013	+	3.36603i	−0.236638	+	0.136623i	0.376993	+	0.926216i	$0.376958\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	20.6312			0.834649
$612$		0			0
$613$	13.6077			0.549610			0.274805	−	0.961500i	$-0.411387\pi$
$613$	13.6077			0.549610			0.274805	+	0.961500i	$0.411387\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.03699	−	4.64016i	0.323557	−	0.186806i	−0.329420	−	0.944184i	$-0.606853\pi$
$617$	8.03699	−	4.64016i	0.323557	−	0.186806i	0.652977	+	0.757378i	$0.273520\pi$
$618$		0			0
$619$	−4.26795	−	2.46410i	−0.171543	−	0.0990406i	0.411770	−	0.911288i	$-0.364911\pi$
$619$	−4.26795	−	2.46410i	−0.171543	−	0.0990406i	−0.583313	+	0.812247i	$0.698244\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.46739	+	9.46979i	−0.219046	+	0.379399i
$624$		0			0
$625$	8.52628	+	14.7679i	0.341051	+	0.590718i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	6.93237i		−	0.276412i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−20.4046	−	35.3417i	−0.809730	−	1.40249i
$636$		0			0
$637$	−14.4282	+	24.9904i	−0.571666	+	0.990155i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−32.1158	−	18.5421i	−1.26850	−	0.732367i	−0.293794	−	0.955869i	$-0.594918\pi$
$641$	−32.1158	−	18.5421i	−1.26850	−	0.732367i	−0.974704	+	0.223502i	$0.928251\pi$
$642$		0			0
$643$	−3.46410	+	2.00000i	−0.136611	+	0.0788723i	−0.566748	−	0.823891i	$-0.691799\pi$
$643$	−3.46410	+	2.00000i	−0.136611	+	0.0788723i	0.430137	+	0.902764i	$0.358465\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.6660			0.655206			0.327603	−	0.944815i	$-0.393759\pi$
$647$	16.6660			0.655206			0.327603	+	0.944815i	$0.393759\pi$
$648$		0			0
$649$	57.1769			2.24439
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.64566	+	5.56892i	−0.377464	+	0.217929i	−0.676714	−	0.736246i	$-0.736597\pi$
$653$	−9.64566	+	5.56892i	−0.377464	+	0.217929i	0.299251	+	0.954175i	$0.403263\pi$
$654$		0			0
$655$	0.169873	+	0.0980762i	0.00663749	+	0.00383215i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.8840	−	18.8516i	0.423981	−	0.734356i	−0.572344	−	0.820014i	$-0.693966\pi$
$659$	10.8840	−	18.8516i	0.423981	−	0.734356i	0.996325	+	0.0856577i	$0.0272991\pi$
$660$		0			0
$661$	4.25833	+	7.37564i	0.165630	+	0.286879i	0.936879	−	0.349654i	$-0.113701\pi$
$661$	4.25833	+	7.37564i	0.165630	+	0.286879i	−0.771249	+	0.636534i	$0.780368\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			1.79315i			0.0695354i
$666$		0			0
$667$			7.66025i			0.296606i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.15660	−	5.46739i	−0.121859	−	0.211066i
$672$		0			0
$673$	−15.1603	+	26.2583i	−0.584385	+	1.01218i	0.410567	+	0.911830i	$0.365331\pi$
$673$	−15.1603	+	26.2583i	−0.584385	+	1.01218i	−0.994952	+	0.100354i	$0.968003\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−33.6130	−	19.4064i	−1.29185	−	0.745850i	−0.312869	−	0.949796i	$-0.601290\pi$
$677$	−33.6130	−	19.4064i	−1.29185	−	0.745850i	−0.978982	+	0.203946i	$0.934623\pi$
$678$		0			0
$679$	−4.05256	+	2.33975i	−0.155523	+	0.0897912i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	5.37945			0.205839			0.102920	−	0.994690i	$-0.467182\pi$
$683$	5.37945			0.205839			0.102920	+	0.994690i	$0.467182\pi$
$684$		0			0
$685$	9.39230			0.358862
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.46979	+	5.46739i	−0.360770	+	0.208291i
$690$		0			0
$691$	−2.24167	−	1.29423i	−0.0852771	−	0.0492348i	0.456755	−	0.889593i	$-0.349012\pi$
$691$	−2.24167	−	1.29423i	−0.0852771	−	0.0492348i	−0.542032	+	0.840358i	$0.682345\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.9700	−	20.7327i	0.454050	−	0.786437i
$696$		0			0
$697$	0.169873	+	0.294229i	0.00643440	+	0.0111447i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	8.06918i		−	0.304769i	−0.988321	−	0.152384i	$-0.951305\pi$
$701$		−	8.06918i		−	0.304769i	0.988321	−	0.152384i	$-0.0486952\pi$
$702$		0			0
$703$		−	9.80385i		−	0.369759i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.31079	+	4.00240i	0.0869062	+	0.150526i
$708$		0			0
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	−0.717769	−	0.696281i	$-0.754837\pi$
$709$	6.50000	−	11.2583i	0.244113	−	0.422815i	0.961882	+	0.273466i	$0.0881700\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.14162	−	5.27792i	−0.342356	−	0.197660i
$714$		0			0
$715$	39.4186	−	22.7583i	1.47417	−	0.851113i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	36.3906			1.35714			0.678570	−	0.734535i	$-0.262600\pi$
$719$	36.3906			1.35714			0.678570	+	0.734535i	$0.262600\pi$
$720$		0			0
$721$	−2.92820			−0.109052
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.94786	+	3.43400i	−0.220898	+	0.127535i
$726$		0			0
$727$	22.4378	+	12.9545i	0.832173	+	0.480455i	0.854596	−	0.519293i	$-0.173805\pi$
$727$	22.4378	+	12.9545i	0.832173	+	0.480455i	−0.0224233	+	0.999749i	$0.507138\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.91447	+	6.78006i	−0.144782	+	0.250770i
$732$		0			0
$733$	−19.6603	−	34.0526i	−0.726168	−	1.25776i	−0.958491	−	0.285121i	$-0.907966\pi$
$733$	−19.6603	−	34.0526i	−0.726168	−	1.25776i	0.232323	−	0.972639i	$-0.425367\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			69.2693i			2.55157i
$738$		0			0
$739$		−	32.0000i		−	1.17714i	−0.808447	−	0.588570i	$-0.799691\pi$
$739$		−	32.0000i		−	1.17714i	0.808447	−	0.588570i	$-0.200309\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.9000	−	25.8076i	−0.546628	−	0.946788i	−0.998502	−	0.0547064i	$-0.982578\pi$
$743$	−14.9000	−	25.8076i	−0.546628	−	0.946788i	0.451874	−	0.892082i	$-0.350756\pi$
$744$		0			0
$745$	1.76795	−	3.06218i	0.0647726	−	0.112190i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.13681	+	0.656339i	0.0415382	+	0.0239821i
$750$		0			0
$751$	8.15064	−	4.70577i	0.297421	−	0.171716i	−0.343863	−	0.939020i	$-0.611736\pi$
$751$	8.15064	−	4.70577i	0.297421	−	0.171716i	0.641284	+	0.767304i	$0.278402\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.07055			−0.0753551
$756$		0			0
$757$	−24.7846			−0.900812			−0.450406	−	0.892824i	$-0.648721\pi$
$757$	−24.7846			−0.900812			−0.450406	+	0.892824i	$0.648721\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.82534	−	1.05386i	0.0661684	−	0.0382023i	−0.466551	−	0.884494i	$-0.654504\pi$
$761$	1.82534	−	1.05386i	0.0661684	−	0.0382023i	0.532719	+	0.846292i	$0.321170\pi$
$762$		0			0
$763$	−2.49038	−	1.43782i	−0.0901578	−	0.0520527i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	24.1803	−	41.8816i	0.873101	−	1.51226i
$768$		0			0
$769$	20.0167	+	34.6699i	0.721819	+	1.25023i	0.960270	+	0.279073i	$0.0900271\pi$
$769$	20.0167	+	34.6699i	0.721819	+	1.25023i	−0.238451	+	0.971155i	$0.576640\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			35.9745i			1.29391i	0.762527	+	0.646957i	$0.223959\pi$
$773$			35.9745i			1.29391i	−0.762527	+	0.646957i	$0.776041\pi$
$774$		0			0
$775$		−	9.46410i		−	0.339961i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.240237	+	0.416102i	0.00860737	+	0.0149084i
$780$		0			0
$781$	−35.0526	+	60.7128i	−1.25428	+	2.17248i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.8350	+	10.2970i	0.636557	+	0.367516i
$786$		0			0
$787$	−21.4186	+	12.3660i	−0.763490	+	0.440801i	−0.830547	−	0.556948i	$-0.811972\pi$
$787$	−21.4186	+	12.3660i	−0.763490	+	0.440801i	0.0670573	+	0.997749i	$0.478639\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	14.7985			0.526173
$792$		0			0
$793$	−5.33975			−0.189620
$794$		0			0
$795$		0			0
$796$		0			0
$797$	44.3632	−	25.6131i	1.57143	−	0.907264i	0.575432	−	0.817850i	$-0.304834\pi$
$797$	44.3632	−	25.6131i	1.57143	−	0.907264i	0.995995	−	0.0894138i	$-0.0284994\pi$
$798$		0			0
$799$	−3.58846	−	2.07180i	−0.126950	−	0.0732949i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−36.2383	+	62.7666i	−1.27882	+	2.21499i
$804$		0			0
$805$	1.00000	+	1.73205i	0.0352454	+	0.0610468i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	40.3930i		−	1.42014i	−0.704130	−	0.710071i	$-0.748663\pi$
$809$		−	40.3930i		−	1.42014i	0.704130	−	0.710071i	$-0.251337\pi$
$810$		0			0
$811$			46.6410i			1.63779i	0.573945	+	0.818894i	$0.305412\pi$
$811$			46.6410i			1.63779i	−0.573945	+	0.818894i	$0.694588\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.55291	−	2.68973i	−0.0543962	−	0.0942170i
$816$		0			0
$817$	−5.53590	+	9.58846i	−0.193677	+	0.335458i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	40.8649	+	23.5933i	1.42619	+	0.823413i	0.996818	−	0.0797126i	$-0.0254002\pi$
$821$	40.8649	+	23.5933i	1.42619	+	0.823413i	0.429376	+	0.903126i	$0.358734\pi$
$822$		0			0
$823$	3.12436	−	1.80385i	0.108908	−	0.0628782i	−0.444557	−	0.895751i	$-0.646639\pi$
$823$	3.12436	−	1.80385i	0.108908	−	0.0628782i	0.553465	+	0.832873i	$0.313305\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.92996			0.101885			0.0509424	−	0.998702i	$-0.483778\pi$
$827$	2.92996			0.101885			0.0509424	+	0.998702i	$0.483778\pi$
$828$		0			0
$829$	15.7128			0.545729			0.272864	−	0.962053i	$-0.412029\pi$
$829$	15.7128			0.545729			0.272864	+	0.962053i	$0.412029\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.01910	−	2.89778i	0.173901	−	0.100402i
$834$		0			0
$835$	−17.8301	−	10.2942i	−0.617037	−	0.356246i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	14.5075	−	25.1277i	0.500853	−	0.867504i	−0.499146	−	0.866518i	$-0.666353\pi$
$839$	14.5075	−	25.1277i	0.500853	−	0.867504i	1.00000		0.000985792i	$-0.000313787\pi$
$840$		0			0
$841$	0.169873	+	0.294229i	0.00585769	+	0.0101458i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	13.3843i		−	0.460433i
$846$		0			0
$847$			12.3397i			0.423999i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.46739	−	9.46979i	−0.187420	−	0.324620i
$852$		0			0
$853$	21.7846	−	37.7321i	0.745891	−	1.29192i	−0.203887	−	0.978995i	$-0.565357\pi$
$853$	21.7846	−	37.7321i	0.745891	−	1.29192i	0.949777	−	0.312926i	$-0.101309\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.0321856	+	0.0185824i	0.00109944	+	0.000634762i	0.500550	−	0.865708i	$-0.333131\pi$
$857$	0.0321856	+	0.0185824i	0.00109944	+	0.000634762i	−0.499450	+	0.866343i	$0.666465\pi$
$858$		0			0
$859$	−31.6410	+	18.2679i	−1.07958	+	0.623294i	−0.930782	−	0.365574i	$-0.880873\pi$
$859$	−31.6410	+	18.2679i	−1.07958	+	0.623294i	−0.148795	+	0.988868i	$0.547539\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	38.5355			1.31176			0.655882	−	0.754864i	$-0.272297\pi$
$863$	38.5355			1.31176			0.655882	+	0.754864i	$0.272297\pi$
$864$		0			0
$865$	−21.3923			−0.727360
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−75.8227	+	43.7762i	−2.57211	+	1.48501i
$870$		0			0
$871$	50.7391	+	29.2942i	1.71923	+	0.992597i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.43211	+	7.67664i	−0.149833	+	0.259518i
$876$		0			0
$877$	−2.06218	−	3.57180i	−0.0696348	−	0.120611i	0.829106	−	0.559092i	$-0.188850\pi$
$877$	−2.06218	−	3.57180i	−0.0696348	−	0.120611i	−0.898741	+	0.438481i	$0.855517\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			13.2084i			0.445002i	0.974932	+	0.222501i	$0.0714221\pi$
$881$			13.2084i			0.445002i	−0.974932	+	0.222501i	$0.928578\pi$
$882$		0			0
$883$		−	0.679492i		−	0.0228667i	−0.999935	−	0.0114334i	$-0.996361\pi$
$883$		−	0.679492i		−	0.0228667i	0.999935	−	0.0114334i	$-0.00363943\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.2982	+	21.3011i	0.412934	+	0.715222i	0.995209	−	0.0977695i	$-0.0311708\pi$
$887$	12.2982	+	21.3011i	0.412934	+	0.715222i	−0.582275	+	0.812992i	$0.697837\pi$
$888$		0			0
$889$	7.73205	−	13.3923i	0.259325	−	0.449163i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.07484	−	2.92996i	−0.169823	−	0.0980475i
$894$		0			0
$895$	−36.5885	+	21.1244i	−1.22302	+	0.706109i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−40.4302			−1.34842
$900$		0			0
$901$	2.19615			0.0731644
$902$		0			0
$903$		0			0
$904$		0			0
$905$	39.0160	−	22.5259i	1.29693	−	0.748786i
$906$		0			0
$907$	10.8564	+	6.26795i	0.360481	+	0.208124i	0.669292	−	0.743000i	$-0.266598\pi$
$907$	10.8564	+	6.26795i	0.360481	+	0.208124i	−0.308811	+	0.951124i	$0.599931\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−5.36585	+	9.29392i	−0.177779	+	0.307921i	−0.941119	−	0.338075i	$-0.890224\pi$
$911$	−5.36585	+	9.29392i	−0.177779	+	0.307921i	0.763341	+	0.645996i	$0.223558\pi$
$912$		0			0
$913$	−27.8564	−	48.2487i	−0.921912	−	1.59680i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			0.0743295i			0.00245458i
$918$		0			0
$919$		−	38.4449i		−	1.26818i	−0.773260	−	0.634090i	$-0.781375\pi$
$919$		−	38.4449i		−	1.26818i	0.773260	−	0.634090i	$-0.218625\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	29.6477	+	51.3514i	0.975866	+	1.69025i
$924$		0			0
$925$	4.90192	−	8.49038i	0.161174	−	0.279162i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	34.6532	+	20.0070i	1.13693	+	0.656410i	0.945670	−	0.325129i	$-0.105408\pi$
$929$	34.6532	+	20.0070i	1.13693	+	0.656410i	0.191265	+	0.981538i	$0.438741\pi$
$930$		0			0
$931$	7.09808	−	4.09808i	0.232630	−	0.134309i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.14162			−0.298963
$936$		0			0
$937$	7.39230			0.241496			0.120748	−	0.992683i	$-0.461471\pi$
$937$	7.39230			0.241496			0.120748	+	0.992683i	$0.461471\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	41.7379	−	24.0974i	1.36062	−	0.785552i	0.370910	−	0.928669i	$-0.379046\pi$
$941$	41.7379	−	24.0974i	1.36062	−	0.785552i	0.989706	+	0.143117i	$0.0457124\pi$
$942$		0			0
$943$	0.464102	+	0.267949i	0.0151132	+	0.00872563i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.9203	+	37.9671i	−0.712314	+	1.23376i	0.251672	+	0.967813i	$0.419020\pi$
$947$	−21.9203	+	37.9671i	−0.712314	+	1.23376i	−0.963986	+	0.265952i	$0.914314\pi$
$948$		0			0
$949$	30.6506	+	53.0885i	0.994962	+	1.72332i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	42.1862i		−	1.36654i	−0.730164	−	0.683272i	$-0.760556\pi$
$953$		−	42.1862i		−	1.36654i	0.730164	−	0.683272i	$-0.239444\pi$
$954$		0			0
$955$		−	39.5167i		−	1.27873i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.77955	+	3.08227i	0.0574646	+	0.0995316i
$960$		0			0
$961$	12.3564	−	21.4019i	0.398594	−	0.690385i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.1607	−	8.17569i	−0.455850	−	0.263185i
$966$		0			0
$967$	33.2032	−	19.1699i	1.06774	−	0.616462i	0.140179	−	0.990126i	$-0.455232\pi$
$967$	33.2032	−	19.1699i	1.06774	−	0.616462i	0.927564	+	0.373665i	$0.121899\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−50.0523			−1.60625			−0.803127	−	0.595808i	$-0.796832\pi$
$971$	−50.0523			−1.60625			−0.803127	+	0.595808i	$0.796832\pi$
$972$		0			0
$973$	9.07180			0.290828
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−37.3751	+	21.5785i	−1.19574	+	0.690359i	−0.959602	−	0.281362i	$-0.909214\pi$
$977$	−37.3751	+	21.5785i	−1.19574	+	0.690359i	−0.236134	+	0.971720i	$0.575881\pi$
$978$		0			0
$979$	−68.2750	−	39.4186i	−2.18208	−	1.25982i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	21.7308	−	37.6389i	0.693106	−	1.20050i	−0.277709	−	0.960665i	$-0.589575\pi$
$983$	21.7308	−	37.6389i	0.693106	−	1.20050i	0.970815	−	0.239830i	$-0.0770917\pi$
$984$		0			0
$985$	−9.42820	−	16.3301i	−0.300408	−	0.520321i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			12.3490i			0.392675i
$990$		0			0
$991$		−	26.4449i		−	0.840049i	−0.907513	−	0.420024i	$-0.862022\pi$
$991$		−	26.4449i		−	0.840049i	0.907513	−	0.420024i	$-0.137978\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.72741	−	13.3843i	−0.244975	−	0.424310i
$996$		0			0
$997$	1.59808	−	2.76795i	0.0506116	−	0.0876618i	−0.839610	−	0.543190i	$-0.817216\pi$
$997$	1.59808	−	2.76795i	0.0506116	−	0.0876618i	0.890221	+	0.455528i	$0.150550\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.b.1727.1		8
3.2	odd	2	inner	2592.2.s.b.1727.4		8
4.3	odd	2		2592.2.s.f.1727.1		8
9.2	odd	6		2592.2.c.a.2591.8	yes	8
9.4	even	3		2592.2.s.f.863.4		8
9.5	odd	6		2592.2.s.f.863.1		8
9.7	even	3		2592.2.c.a.2591.2	yes	8
12.11	even	2		2592.2.s.f.1727.4		8
36.7	odd	6		2592.2.c.a.2591.1	✓	8
36.11	even	6		2592.2.c.a.2591.7	yes	8
36.23	even	6	inner	2592.2.s.b.863.1		8
36.31	odd	6	inner	2592.2.s.b.863.4		8
72.11	even	6		5184.2.c.i.5183.1		8
72.29	odd	6		5184.2.c.i.5183.2		8
72.43	odd	6		5184.2.c.i.5183.7		8
72.61	even	6		5184.2.c.i.5183.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2592.2.c.a.2591.1	✓	8	36.7	odd	6
2592.2.c.a.2591.2	yes	8	9.7	even	3
2592.2.c.a.2591.7	yes	8	36.11	even	6
2592.2.c.a.2591.8	yes	8	9.2	odd	6
2592.2.s.b.863.1		8	36.23	even	6	inner
2592.2.s.b.863.4		8	36.31	odd	6	inner
2592.2.s.b.1727.1		8	1.1	even	1	trivial
2592.2.s.b.1727.4		8	3.2	odd	2	inner
2592.2.s.f.863.1		8	9.5	odd	6
2592.2.s.f.863.4		8	9.4	even	3
2592.2.s.f.1727.1		8	4.3	odd	2
2592.2.s.f.1727.4		8	12.11	even	2
5184.2.c.i.5183.1		8	72.11	even	6
5184.2.c.i.5183.2		8	72.29	odd	6
5184.2.c.i.5183.7		8	72.43	odd	6
5184.2.c.i.5183.8		8	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67303 + 0.965926i) q^{5} +(-0.633975 - 0.366025i) q^{7} +O(q^{10})\)	\(q+(-1.67303 + 0.965926i) q^{5} +(-0.633975 - 0.366025i) q^{7} +(2.63896 - 4.57081i) q^{11} +(-2.23205 - 3.86603i) q^{13} +0.896575i q^{17} +1.26795i q^{19} +(0.707107 + 1.22474i) q^{23} +(-0.633975 + 1.09808i) q^{25} +(4.69093 + 2.70831i) q^{29} +(-6.46410 + 3.73205i) q^{31} +1.41421 q^{35} -7.73205 q^{37} +(0.328169 - 0.189469i) q^{41} +(7.56218 + 4.36603i) q^{43} +(-2.31079 + 4.00240i) q^{47} +(-3.23205 - 5.59808i) q^{49} -2.44949i q^{53} +10.1962i q^{55} +(5.41662 + 9.38186i) q^{59} +(0.598076 - 1.03590i) q^{61} +(7.46859 + 4.31199i) q^{65} +(-11.3660 + 6.56218i) q^{67} -13.2827 q^{71} -13.7321 q^{73} +(-3.34607 + 1.93185i) q^{77} +(-14.3660 - 8.29423i) q^{79} +(5.27792 - 9.14162i) q^{83} +(-0.866025 - 1.50000i) q^{85} -14.9372i q^{89} +3.26795i q^{91} +(-1.22474 - 2.12132i) q^{95} +(3.19615 - 5.53590i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{7}+O(q^{10}) \) 8 * q - 12 * q^7	\( 8 q - 12 q^{7} - 4 q^{13} - 12 q^{25} - 24 q^{31} - 48 q^{37} + 12 q^{43} - 12 q^{49} - 16 q^{61} - 84 q^{67} - 96 q^{73} - 108 q^{79} - 16 q^{97}+O(q^{100}) \) 8 * q - 12 * q^7 - 4 * q^13 - 12 * q^25 - 24 * q^31 - 48 * q^37 + 12 * q^43 - 12 * q^49 - 16 * q^61 - 84 * q^67 - 96 * q^73 - 108 * q^79 - 16 * q^97

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