LMFDB - Embedded newform 2592.2.s.f.1727.2

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:	$0$
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			1727.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2592.1727
Dual form			2592.2.s.f.863.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.448288 + 0.258819i) q^{5} +(2.36603 + 1.36603i) q^{7} +O(q^{10})$	$q+(-0.448288 + 0.258819i) q^{5} +(2.36603 + 1.36603i) q^{7} +(-0.189469 + 0.328169i) q^{11} +(1.23205 + 2.13397i) q^{13} -3.34607i q^{17} +4.73205i q^{19} +(-0.707107 - 1.22474i) q^{23} +(-2.36603 + 4.09808i) q^{25} +(5.91567 + 3.41542i) q^{29} +(-0.464102 + 0.267949i) q^{31} -1.41421 q^{35} -4.26795 q^{37} +(-4.57081 + 2.63896i) q^{41} +(4.56218 + 2.63397i) q^{43} +(4.76028 - 8.24504i) q^{47} +(0.232051 + 0.401924i) q^{49} -2.44949i q^{53} -0.196152i q^{55} +(6.83083 + 11.8313i) q^{59} +(-4.59808 + 7.96410i) q^{61} +(-1.10463 - 0.637756i) q^{65} +(9.63397 - 5.56218i) q^{67} -16.1112 q^{71} -10.2679 q^{73} +(-0.896575 + 0.517638i) q^{77} +(12.6340 + 7.29423i) q^{79} +(-0.378937 + 0.656339i) q^{83} +(0.866025 + 1.50000i) q^{85} -2.20925i q^{89} +6.73205i q^{91} +(-1.22474 - 2.12132i) q^{95} +(-7.19615 + 12.4641i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.448288	+	0.258819i	−0.200480	+	0.115747i	−0.596880	−	0.802331i	$-0.703593\pi$
$5$	−0.448288	+	0.258819i	−0.200480	+	0.115747i	0.396399	+	0.918078i	$0.370260\pi$
$6$		0			0
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.875338	−	0.483512i	$-0.160639\pi$
$7$	2.36603	+	1.36603i	0.894274	+	0.516309i	0.0189356	+	0.999821i	$0.493972\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.189469	+	0.328169i	−0.0571270	+	0.0989468i	−0.893175	−	0.449710i	$-0.851527\pi$
$11$	−0.189469	+	0.328169i	−0.0571270	+	0.0989468i	0.836048	+	0.548657i	$0.184861\pi$
$12$		0			0
$13$	1.23205	+	2.13397i	0.341709	+	0.591858i	0.984750	−	0.173974i	$-0.0556608\pi$
$13$	1.23205	+	2.13397i	0.341709	+	0.591858i	−0.643041	+	0.765832i	$0.722327\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	3.34607i		−	0.811540i	−0.913975	−	0.405770i	$-0.867003\pi$
$17$		−	3.34607i		−	0.811540i	0.913975	−	0.405770i	$-0.132997\pi$
$18$		0			0
$19$			4.73205i			1.08561i	0.839860	+	0.542803i	$0.182637\pi$
$19$			4.73205i			1.08561i	−0.839860	+	0.542803i	$0.817363\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.707107	−	1.22474i	−0.147442	−	0.255377i	0.782839	−	0.622224i	$-0.213771\pi$
$23$	−0.707107	−	1.22474i	−0.147442	−	0.255377i	−0.930281	+	0.366847i	$0.880437\pi$
$24$		0			0
$25$	−2.36603	+	4.09808i	−0.473205	+	0.819615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.91567	+	3.41542i	1.09851	+	0.634227i	0.935830	−	0.352452i	$-0.114652\pi$
$29$	5.91567	+	3.41542i	1.09851	+	0.634227i	0.162683	+	0.986678i	$0.447985\pi$
$30$		0			0
$31$	−0.464102	+	0.267949i	−0.0833551	+	0.0481251i	−0.541098	−	0.840959i	$-0.681991\pi$
$31$	−0.464102	+	0.267949i	−0.0833551	+	0.0481251i	0.457743	+	0.889085i	$0.348658\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.41421			−0.239046
$36$		0			0
$37$	−4.26795			−0.701647			−0.350823	−	0.936442i	$-0.614098\pi$
$37$	−4.26795			−0.701647			−0.350823	+	0.936442i	$0.614098\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.57081	+	2.63896i	−0.713841	+	0.412136i	−0.812481	−	0.582987i	$-0.801884\pi$
$41$	−4.57081	+	2.63896i	−0.713841	+	0.412136i	0.0986409	+	0.995123i	$0.468550\pi$
$42$		0			0
$43$	4.56218	+	2.63397i	0.695726	+	0.401677i	0.805753	−	0.592251i	$-0.201761\pi$
$43$	4.56218	+	2.63397i	0.695726	+	0.401677i	−0.110028	+	0.993929i	$0.535094\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.76028	−	8.24504i	0.694358	−	1.20266i	−0.276039	−	0.961147i	$-0.589022\pi$
$47$	4.76028	−	8.24504i	0.694358	−	1.20266i	0.970397	−	0.241517i	$-0.0776449\pi$
$48$		0			0
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$		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
$55$		−	0.196152i		−	0.0264492i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.83083	+	11.8313i	0.889298	+	1.54031i	0.840706	+	0.541491i	$0.182140\pi$
$59$	6.83083	+	11.8313i	0.889298	+	1.54031i	0.0485922	+	0.998819i	$0.484527\pi$
$60$		0			0
$61$	−4.59808	+	7.96410i	−0.588723	+	1.01970i	0.405677	+	0.914017i	$0.367036\pi$
$61$	−4.59808	+	7.96410i	−0.588723	+	1.01970i	−0.994400	+	0.105682i	$0.966297\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.10463	−	0.637756i	−0.137012	−	0.0791039i
$66$		0			0
$67$	9.63397	−	5.56218i	1.17698	−	0.679528i	0.221664	−	0.975123i	$-0.428851\pi$
$67$	9.63397	−	5.56218i	1.17698	−	0.679528i	0.955313	+	0.295595i	$0.0955179\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−16.1112			−1.91204			−0.956021	−	0.293298i	$-0.905247\pi$
$71$	−16.1112			−1.91204			−0.956021	+	0.293298i	$0.905247\pi$
$72$		0			0
$73$	−10.2679			−1.20177			−0.600886	−	0.799335i	$-0.705186\pi$
$73$	−10.2679			−1.20177			−0.600886	+	0.799335i	$0.705186\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.896575	+	0.517638i	−0.102174	+	0.0589903i
$78$		0			0
$79$	12.6340	+	7.29423i	1.42143	+	0.820665i	0.996422	−	0.0845230i	$-0.0269367\pi$
$79$	12.6340	+	7.29423i	1.42143	+	0.820665i	0.425012	+	0.905188i	$0.360270\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.378937	+	0.656339i	−0.0415938	+	0.0720425i	−0.886073	−	0.463546i	$-0.846577\pi$
$83$	−0.378937	+	0.656339i	−0.0415938	+	0.0720425i	0.844479	+	0.535589i	$0.179910\pi$
$84$		0			0
$85$	0.866025	+	1.50000i	0.0939336	+	0.162698i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	2.20925i		−	0.234180i	−0.993121	−	0.117090i	$-0.962643\pi$
$89$		−	2.20925i		−	0.234180i	0.993121	−	0.117090i	$-0.0373567\pi$
$90$		0			0
$91$			6.73205i			0.705711i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.22474	−	2.12132i	−0.125656	−	0.217643i
$96$		0			0
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	0.225944	+	0.974140i	$0.427454\pi$
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	−0.956602	+	0.291397i	$0.905880\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.01790	−	1.74238i	−0.300292	−	0.173374i	0.342282	−	0.939597i	$-0.388800\pi$
$101$	−3.01790	−	1.74238i	−0.300292	−	0.173374i	−0.642574	+	0.766224i	$0.722133\pi$
$102$		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
$107$	6.69213			0.646953			0.323476	−	0.946236i	$-0.395148\pi$
$107$	6.69213			0.646953			0.323476	+	0.946236i	$0.395148\pi$
$108$		0			0
$109$	−9.92820			−0.950949			−0.475475	−	0.879729i	$-0.657724\pi$
$109$	−9.92820			−0.950949			−0.475475	+	0.879729i	$0.657724\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.58510	+	0.915158i	−0.149114	+	0.0860908i	−0.572700	−	0.819765i	$-0.694104\pi$
$113$	−1.58510	+	0.915158i	−0.149114	+	0.0860908i	0.423587	+	0.905856i	$0.360771\pi$
$114$		0			0
$115$	0.633975	+	0.366025i	0.0591184	+	0.0341320i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.57081	−	7.91688i	0.419005	−	0.725739i
$120$		0			0
$121$	5.42820	+	9.40192i	0.493473	+	0.854720i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	5.03768i		−	0.450584i
$126$		0			0
$127$		−	3.12436i		−	0.277242i	−0.990346	−	0.138621i	$-0.955733\pi$
$127$		−	3.12436i		−	0.277242i	0.990346	−	0.138621i	$-0.0442669\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.84873	+	17.0585i	0.860487	+	1.49041i	0.871459	+	0.490468i	$0.163174\pi$
$131$	9.84873	+	17.0585i	0.860487	+	1.49041i	−0.0109720	+	0.999940i	$0.503493\pi$
$132$		0			0
$133$	−6.46410	+	11.1962i	−0.560509	+	0.970830i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	19.0597	+	11.0041i	1.62838	+	0.940146i	0.984577	+	0.174955i	$0.0559779\pi$
$137$	19.0597	+	11.0041i	1.62838	+	0.940146i	0.643803	+	0.765191i	$0.277355\pi$
$138$		0			0
$139$	7.26795	−	4.19615i	0.616459	−	0.355913i	−0.159030	−	0.987274i	$-0.550837\pi$
$139$	7.26795	−	4.19615i	0.616459	−	0.355913i	0.775489	+	0.631361i	$0.217503\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.933740			−0.0780833
$144$		0			0
$145$	−3.53590			−0.293640
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.5068	+	10.1075i	−1.43421	+	0.828042i	−0.997438	−	0.0715293i	$-0.977212\pi$
$149$	−17.5068	+	10.1075i	−1.43421	+	0.828042i	−0.436773	+	0.899572i	$0.643879\pi$
$150$		0			0
$151$	12.9282	+	7.46410i	1.05208	+	0.607420i	0.923232	−	0.384244i	$-0.125538\pi$
$151$	12.9282	+	7.46410i	1.05208	+	0.607420i	0.128851	+	0.991664i	$0.458871\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.138701	−	0.240237i	0.0111407	−	0.0192963i
$156$		0			0
$157$	3.33013	+	5.76795i	0.265773	+	0.460332i	0.967766	−	0.251852i	$-0.0810395\pi$
$157$	3.33013	+	5.76795i	0.265773	+	0.460332i	−0.701993	+	0.712184i	$0.747706\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	3.86370i		−	0.304502i
$162$		0			0
$163$			22.3923i			1.75390i	0.480581	+	0.876950i	$0.340426\pi$
$163$			22.3923i			1.75390i	−0.480581	+	0.876950i	$0.659574\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.2277	−	17.7148i	−0.791440	−	1.37082i	−0.925075	−	0.379784i	$-0.875998\pi$
$167$	−10.2277	−	17.7148i	−0.791440	−	1.37082i	0.133635	−	0.991031i	$-0.457335\pi$
$168$		0			0
$169$	3.46410	−	6.00000i	0.266469	−	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.01669	+	0.586988i	0.0772978	+	0.0446279i	0.538151	−	0.842849i	$-0.319123\pi$
$173$	1.01669	+	0.586988i	0.0772978	+	0.0446279i	−0.460853	+	0.887477i	$0.652456\pi$
$174$		0			0
$175$	−11.1962	+	6.46410i	−0.846350	+	0.488640i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.0716			−0.902272			−0.451136	−	0.892455i	$-0.648981\pi$
$179$	−12.0716			−0.902272			−0.451136	+	0.892455i	$0.648981\pi$
$180$		0			0
$181$	11.3205			0.841447			0.420723	−	0.907189i	$-0.361776\pi$
$181$	11.3205			0.841447			0.420723	+	0.907189i	$0.361776\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.91327	−	1.10463i	0.140666	−	0.0812138i
$186$		0			0
$187$	1.09808	+	0.633975i	0.0802993	+	0.0463608i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.32868	−	9.22955i	0.385570	−	0.667827i	−0.606278	−	0.795253i	$-0.707338\pi$
$191$	5.32868	−	9.22955i	0.385570	−	0.667827i	0.991848	+	0.127426i	$0.0406715\pi$
$192$		0			0
$193$	0.767949	+	1.33013i	0.0552782	+	0.0957446i	0.892340	−	0.451363i	$-0.149062\pi$
$193$	0.767949	+	1.33013i	0.0552782	+	0.0957446i	−0.837062	+	0.547108i	$0.815729\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	17.1093i		−	1.21898i	−0.792792	−	0.609492i	$-0.791373\pi$
$197$		−	17.1093i		−	1.21898i	0.792792	−	0.609492i	$-0.208627\pi$
$198$		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
$203$	9.33109	+	16.1619i	0.654914	+	1.13434i
$204$		0			0
$205$	1.36603	−	2.36603i	0.0954074	−	0.165250i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.55291	−	0.896575i	−0.107417	−	0.0620174i
$210$		0			0
$211$	4.43782	−	2.56218i	0.305512	−	0.176388i	−0.339404	−	0.940641i	$-0.610225\pi$
$211$	4.43782	−	2.56218i	0.305512	−	0.176388i	0.644917	+	0.764253i	$0.276892\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.72689			−0.185972
$216$		0			0
$217$	−1.46410			−0.0993897
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.14042	−	4.12252i	0.480317	−	0.277311i
$222$		0			0
$223$	17.9545	+	10.3660i	1.20232	+	0.694160i	0.961071	−	0.276303i	$-0.0891092\pi$
$223$	17.9545	+	10.3660i	1.20232	+	0.694160i	0.241250	+	0.970463i	$0.422443\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.1242	+	19.2677i	−0.738342	+	1.27885i	0.214900	+	0.976636i	$0.431057\pi$
$227$	−11.1242	+	19.2677i	−0.738342	+	1.27885i	−0.953242	+	0.302209i	$0.902276\pi$
$228$		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
$233$			3.24453i			0.212556i	0.994336	+	0.106278i	$0.0338934\pi$
$233$			3.24453i			0.212556i	−0.994336	+	0.106278i	$0.966107\pi$
$234$		0			0
$235$			4.92820i			0.321481i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.62158	−	8.00481i	−0.298945	−	0.517788i	0.676950	−	0.736029i	$-0.263301\pi$
$239$	−4.62158	−	8.00481i	−0.298945	−	0.517788i	−0.975895	+	0.218241i	$0.929968\pi$
$240$		0			0
$241$	−4.06218	+	7.03590i	−0.261668	+	0.453222i	−0.966685	−	0.255968i	$-0.917606\pi$
$241$	−4.06218	+	7.03590i	−0.261668	+	0.453222i	0.705017	+	0.709190i	$0.250939\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.208051	−	0.120118i	−0.0132919	−	0.00767408i
$246$		0			0
$247$	−10.0981	+	5.83013i	−0.642525	+	0.370962i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	15.3533			0.969090			0.484545	−	0.874766i	$-0.338985\pi$
$251$	15.3533			0.969090			0.484545	+	0.874766i	$0.338985\pi$
$252$		0			0
$253$	0.535898			0.0336916
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.1607	+	8.17569i	−0.883321	+	0.509986i	−0.871752	−	0.489947i	$-0.837016\pi$
$257$	−14.1607	+	8.17569i	−0.883321	+	0.509986i	−0.0115693	+	0.999933i	$0.503683\pi$
$258$		0			0
$259$	−10.0981	−	5.83013i	−0.627464	−	0.362266i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.17449	−	10.6945i	0.380736	−	0.659453i	−0.610432	−	0.792069i	$-0.709004\pi$
$263$	6.17449	−	10.6945i	0.380736	−	0.659453i	0.991168	+	0.132615i	$0.0423375\pi$
$264$		0			0
$265$	0.633975	+	1.09808i	0.0389447	+	0.0674543i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			15.4176i			0.940031i	0.882658	+	0.470015i	$0.155752\pi$
$269$			15.4176i			0.940031i	−0.882658	+	0.470015i	$0.844248\pi$
$270$		0			0
$271$		−	16.7321i		−	1.01640i	−0.861239	−	0.508200i	$-0.830311\pi$
$271$		−	16.7321i		−	1.01640i	0.861239	−	0.508200i	$-0.169689\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.896575	−	1.55291i	−0.0540655	−	0.0936443i
$276$		0			0
$277$	−7.46410	+	12.9282i	−0.448474	+	0.776780i	−0.998287	−	0.0585076i	$-0.981366\pi$
$277$	−7.46410	+	12.9282i	−0.448474	+	0.776780i	0.549813	+	0.835288i	$0.314699\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.55412	−	2.05197i	−0.212021	−	0.122410i	0.390229	−	0.920718i	$-0.372396\pi$
$281$	−3.55412	−	2.05197i	−0.212021	−	0.122410i	−0.602250	+	0.798307i	$0.705729\pi$
$282$		0			0
$283$	13.2679	−	7.66025i	0.788698	−	0.455355i	−0.0508062	−	0.998709i	$-0.516179\pi$
$283$	13.2679	−	7.66025i	0.788698	−	0.455355i	0.839504	+	0.543354i	$0.182846\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.4195			−0.851158
$288$		0			0
$289$	5.80385			0.341403
$290$		0			0
$291$		0			0
$292$		0			0
$293$	10.0060	−	5.77697i	0.584557	−	0.337494i	−0.178385	−	0.983961i	$-0.557087\pi$
$293$	10.0060	−	5.77697i	0.584557	−	0.337494i	0.762942	+	0.646466i	$0.223754\pi$
$294$		0			0
$295$	−6.12436	−	3.53590i	−0.356574	−	0.205868i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.74238	−	3.01790i	0.100765	−	0.174529i
$300$		0			0
$301$	7.19615	+	12.4641i	0.414779	+	0.718419i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	4.76028i		−	0.272573i
$306$		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
$311$	−5.03768	−	8.72552i	−0.285661	−	0.494779i	0.687109	−	0.726555i	$-0.258880\pi$
$311$	−5.03768	−	8.72552i	−0.285661	−	0.494779i	−0.972769	+	0.231776i	$0.925546\pi$
$312$		0			0
$313$	3.16025	−	5.47372i	0.178628	−	0.309393i	−0.762783	−	0.646655i	$-0.776167\pi$
$313$	3.16025	−	5.47372i	0.178628	−	0.309393i	0.941411	+	0.337262i	$0.109501\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.9384	+	9.77938i	0.951354	+	0.549265i	0.893501	−	0.449061i	$-0.148241\pi$
$317$	16.9384	+	9.77938i	0.951354	+	0.549265i	0.0578527	+	0.998325i	$0.481575\pi$
$318$		0			0
$319$	−2.24167	+	1.29423i	−0.125509	+	0.0724629i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.8338			0.881013
$324$		0			0
$325$	−11.6603			−0.646795
$326$		0			0
$327$		0			0
$328$		0			0
$329$	22.5259	−	13.0053i	1.24189	−	0.717007i
$330$		0			0
$331$	−15.7583	−	9.09808i	−0.866156	−	0.500075i	−8.71764e−5	−	1.00000i	$-0.500028\pi$
$331$	−15.7583	−	9.09808i	−0.866156	−	0.500075i	−0.866069	+	0.499925i	$0.833361\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.87920	+	4.98691i	−0.157307	+	0.272464i
$336$		0			0
$337$	−4.46410	−	7.73205i	−0.243175	−	0.421192i	0.718442	−	0.695587i	$-0.244856\pi$
$337$	−4.46410	−	7.73205i	−0.243175	−	0.421192i	−0.961617	+	0.274395i	$0.911522\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	0.203072i		−	0.0109970i
$342$		0			0
$343$		−	17.8564i		−	0.964155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.43211	+	7.67664i	0.237928	+	0.412104i	0.960120	−	0.279590i	$-0.0901984\pi$
$347$	4.43211	+	7.67664i	0.237928	+	0.412104i	−0.722192	+	0.691693i	$0.756865\pi$
$348$		0			0
$349$	14.9282	−	25.8564i	0.799088	−	1.38406i	−0.121122	−	0.992638i	$-0.538649\pi$
$349$	14.9282	−	25.8564i	0.799088	−	1.38406i	0.920210	−	0.391424i	$-0.128017\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−26.6806	−	15.4040i	−1.42006	−	0.819875i	−0.423761	−	0.905774i	$-0.639290\pi$
$353$	−26.6806	−	15.4040i	−1.42006	−	0.819875i	−0.996304	+	0.0858996i	$0.972624\pi$
$354$		0			0
$355$	7.22243	−	4.16987i	0.383327	−	0.221314i
$356$		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
$361$	−3.39230			−0.178542
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.60300	−	2.65754i	0.240932	−	0.139102i
$366$		0			0
$367$	−16.8564	−	9.73205i	−0.879897	−	0.508009i	−0.00927272	−	0.999957i	$-0.502952\pi$
$367$	−16.8564	−	9.73205i	−0.879897	−	0.508009i	−0.870625	+	0.491948i	$0.836285\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.34607	−	5.79555i	0.173719	−	0.300890i
$372$		0			0
$373$	−8.12436	−	14.0718i	−0.420663	−	0.728610i	0.575341	−	0.817913i	$-0.304869\pi$
$373$	−8.12436	−	14.0718i	−0.420663	−	0.728610i	−0.996004	+	0.0893034i	$0.971536\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			16.8319i			0.866885i
$378$		0			0
$379$			6.39230i			0.328351i	0.986431	+	0.164175i	$0.0524963\pi$
$379$			6.39230i			0.328351i	−0.986431	+	0.164175i	$0.947504\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.4369	−	21.5414i	−0.635497	−	1.10071i	−0.986410	−	0.164305i	$-0.947462\pi$
$383$	−12.4369	−	21.5414i	−0.635497	−	1.10071i	0.350913	−	0.936408i	$-0.385871\pi$
$384$		0			0
$385$	0.267949	−	0.464102i	0.0136560	−	0.0236528i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−28.8898	−	16.6796i	−1.46477	−	0.845687i	−0.465547	−	0.885023i	$-0.654142\pi$
$389$	−28.8898	−	16.6796i	−1.46477	−	0.845687i	−0.999226	+	0.0393359i	$0.987476\pi$
$390$		0			0
$391$	−4.09808	+	2.36603i	−0.207249	+	0.119655i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.55154			−0.379959
$396$		0			0
$397$	−9.58846			−0.481231			−0.240615	−	0.970621i	$-0.577349\pi$
$397$	−9.58846			−0.481231			−0.240615	+	0.970621i	$0.577349\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.80984	+	1.62226i	−0.140317	+	0.0810120i	−0.568515	−	0.822673i	$-0.692482\pi$
$401$	−2.80984	+	1.62226i	−0.140317	+	0.0810120i	0.428198	+	0.903685i	$0.359149\pi$
$402$		0			0
$403$	−1.14359	−	0.660254i	−0.0569665	−	0.0328896i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.808643	−	1.40061i	0.0400829	−	0.0694257i
$408$		0			0
$409$	−12.5981	−	21.8205i	−0.622935	−	1.07895i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−12.5981	−	21.8205i	−0.622935	−	1.07895i	0.366002	−	0.930614i	$-0.380726\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			37.3244i			1.83661i
$414$		0			0
$415$		−	0.392305i		−	0.0192575i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.3514	+	28.3214i	0.798818	+	1.38359i	0.920387	+	0.391010i	$0.127874\pi$
$419$	16.3514	+	28.3214i	0.798818	+	1.38359i	−0.121569	+	0.992583i	$0.538793\pi$
$420$		0			0
$421$	9.42820	−	16.3301i	0.459503	−	0.795882i	−0.539432	−	0.842029i	$-0.681361\pi$
$421$	9.42820	−	16.3301i	0.459503	−	0.795882i	0.998935	+	0.0461474i	$0.0146944\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	13.7124	+	7.91688i	0.665151	+	0.384025i
$426$		0			0
$427$	−21.7583	+	12.5622i	−1.05296	+	0.607926i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.48528			0.408722			0.204361	−	0.978896i	$-0.434488\pi$
$431$	8.48528			0.408722			0.204361	+	0.978896i	$0.434488\pi$
$432$		0			0
$433$	28.1769			1.35410			0.677048	−	0.735939i	$-0.263259\pi$
$433$	28.1769			1.35410			0.677048	+	0.735939i	$0.263259\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.79555	−	3.34607i	0.277239	−	0.160064i
$438$		0			0
$439$	−0.464102	−	0.267949i	−0.0221504	−	0.0127885i	0.488884	−	0.872349i	$-0.337404\pi$
$439$	−0.464102	−	0.267949i	−0.0221504	−	0.0127885i	−0.511034	+	0.859560i	$0.670737\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.4219	+	31.9077i	−0.875253	+	1.51598i	−0.0187597	+	0.999824i	$0.505972\pi$
$443$	−18.4219	+	31.9077i	−0.875253	+	1.51598i	−0.856493	+	0.516158i	$0.827362\pi$
$444$		0			0
$445$	0.571797	+	0.990381i	0.0271058	+	0.0469486i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	27.9053i		−	1.31693i	−0.752610	−	0.658467i	$-0.771205\pi$
$449$		−	27.9053i		−	1.31693i	0.752610	−	0.658467i	$-0.228795\pi$
$450$		0			0
$451$		−	2.00000i		−	0.0941763i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.74238	−	3.01790i	−0.0816842	−	0.141481i
$456$		0			0
$457$	6.59808	−	11.4282i	0.308645	−	0.534589i	−0.669421	−	0.742883i	$-0.733458\pi$
$457$	6.59808	−	11.4282i	0.308645	−	0.534589i	0.978066	+	0.208294i	$0.0667912\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.1309	+	10.4679i	0.844442	+	0.487539i	0.858772	−	0.512359i	$-0.171228\pi$
$461$	18.1309	+	10.4679i	0.844442	+	0.487539i	−0.0143297	+	0.999897i	$0.504561\pi$
$462$		0			0
$463$	−2.07180	+	1.19615i	−0.0962846	+	0.0555899i	−0.547369	−	0.836891i	$-0.684371\pi$
$463$	−2.07180	+	1.19615i	−0.0962846	+	0.0555899i	0.451085	+	0.892481i	$0.351037\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	21.8695			1.01200			0.506001	−	0.862533i	$-0.331123\pi$
$467$	21.8695			1.01200			0.506001	+	0.862533i	$0.331123\pi$
$468$		0			0
$469$	30.3923			1.40339
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.72878	+	0.998111i	−0.0794894	+	0.0458932i
$474$		0			0
$475$	−19.3923	−	11.1962i	−0.889780	−	0.513715i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.50215	+	2.60179i	−0.0686348	+	0.118879i	−0.898301	−	0.439381i	$-0.855198\pi$
$479$	−1.50215	+	2.60179i	−0.0686348	+	0.118879i	0.829666	+	0.558260i	$0.188531\pi$
$480$		0			0
$481$	−5.25833	−	9.10770i	−0.239759	−	0.415275i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	7.45001i		−	0.338287i
$486$		0			0
$487$		−	23.0718i		−	1.04548i	−0.852491	−	0.522741i	$-0.824909\pi$
$487$		−	23.0718i		−	1.04548i	0.852491	−	0.522741i	$-0.175091\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−16.9198	−	29.3059i	−0.763580	−	1.32256i	−0.940994	−	0.338423i	$-0.890107\pi$
$491$	−16.9198	−	29.3059i	−0.763580	−	1.32256i	0.177415	−	0.984136i	$-0.443227\pi$
$492$		0			0
$493$	11.4282	−	19.7942i	0.514700	−	0.891487i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−38.1194	−	22.0082i	−1.70989	−	0.987205i
$498$		0			0
$499$	−19.4378	+	11.2224i	−0.870156	+	0.502385i	−0.867400	−	0.497611i	$-0.834211\pi$
$499$	−19.4378	+	11.2224i	−0.870156	+	0.502385i	−0.00275621	+	0.999996i	$0.500877\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.9743			0.667673			0.333836	−	0.942631i	$-0.391657\pi$
$503$	14.9743			0.667673			0.333836	+	0.942631i	$0.391657\pi$
$504$		0			0
$505$	1.80385			0.0802702
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.29719	+	1.32628i	−0.101821	+	0.0587864i	−0.550046	−	0.835135i	$-0.685390\pi$
$509$	−2.29719	+	1.32628i	−0.101821	+	0.0587864i	0.448225	+	0.893921i	$0.352056\pi$
$510$		0			0
$511$	−24.2942	−	14.0263i	−1.07471	−	0.620486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.03528	+	1.79315i	−0.0456197	+	0.0790157i
$516$		0			0
$517$	1.80385	+	3.12436i	0.0793331	+	0.137409i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			29.9759i			1.31327i	0.754210	+	0.656634i	$0.228020\pi$
$521$			29.9759i			1.31327i	−0.754210	+	0.656634i	$0.771980\pi$
$522$		0			0
$523$		−	5.80385i		−	0.253785i	−0.991917	−	0.126892i	$-0.959500\pi$
$523$		−	5.80385i		−	0.253785i	0.991917	−	0.126892i	$-0.0405003\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.896575	+	1.55291i	0.0390554	+	0.0676460i
$528$		0			0
$529$	10.5000	−	18.1865i	0.456522	−	0.790719i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−11.2629	−	6.50266i	−0.487852	−	0.281662i
$534$		0			0
$535$	−3.00000	+	1.73205i	−0.129701	+	0.0748831i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−0.175865			−0.00757506
$540$		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
$545$	4.45069	−	2.56961i	0.190647	−	0.110070i
$546$		0			0
$547$	−28.8564	−	16.6603i	−1.23381	−	0.712341i	−0.265989	−	0.963976i	$-0.585698\pi$
$547$	−28.8564	−	16.6603i	−1.23381	−	0.712341i	−0.967822	+	0.251635i	$0.919032\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−16.1619	+	27.9933i	−0.688521	+	1.19255i
$552$		0			0
$553$	19.9282	+	34.5167i	0.847433	+	1.46780i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	19.1798i		−	0.812675i	−0.913723	−	0.406337i	$-0.866806\pi$
$557$		−	19.1798i		−	0.812675i	0.913723	−	0.406337i	$-0.133194\pi$
$558$		0			0
$559$			12.9808i			0.549028i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.6646	−	39.2562i	−0.955198	−	1.65445i	−0.733914	−	0.679243i	$-0.762308\pi$
$563$	−22.6646	−	39.2562i	−0.955198	−	1.65445i	−0.221284	−	0.975209i	$-0.571025\pi$
$564$		0			0
$565$	0.473721	−	0.820508i	0.0199296	−	0.0345190i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	29.4261	+	16.9891i	1.23360	+	0.712222i	0.967779	−	0.251799i	$-0.0810223\pi$
$569$	29.4261	+	16.9891i	1.23360	+	0.712222i	0.265825	+	0.964021i	$0.414356\pi$
$570$		0			0
$571$	10.5167	−	6.07180i	0.440109	−	0.254097i	−0.263535	−	0.964650i	$-0.584888\pi$
$571$	10.5167	−	6.07180i	0.440109	−	0.254097i	0.703644	+	0.710553i	$0.251555\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.69213			0.279081
$576$		0			0
$577$	11.5359			0.480246			0.240123	−	0.970743i	$-0.422812\pi$
$577$	11.5359			0.480246			0.240123	+	0.970743i	$0.422812\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.79315	+	1.03528i	−0.0743924	+	0.0429505i
$582$		0			0
$583$	0.803848	+	0.464102i	0.0332920	+	0.0192211i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.50266	+	11.2629i	−0.268394	+	0.464871i	−0.968447	−	0.249219i	$-0.919826\pi$
$587$	−6.50266	+	11.2629i	−0.268394	+	0.464871i	0.700054	+	0.714090i	$0.253159\pi$
$588$		0			0
$589$	−1.26795	−	2.19615i	−0.0522449	−	0.0904909i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			25.3915i			1.04270i	0.853342	+	0.521351i	$0.174572\pi$
$593$			25.3915i			1.04270i	−0.853342	+	0.521351i	$0.825428\pi$
$594$		0			0
$595$			4.73205i			0.193995i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.138701	+	0.240237i	0.00566716	+	0.00981580i	0.868845	−	0.495084i	$-0.164863\pi$
$599$	0.138701	+	0.240237i	0.00566716	+	0.00981580i	−0.863178	+	0.504900i	$0.831529\pi$
$600$		0			0
$601$	18.8923	−	32.7224i	0.770633	−	1.33478i	−0.166583	−	0.986027i	$-0.553273\pi$
$601$	18.8923	−	32.7224i	0.770633	−	1.33478i	0.937216	−	0.348748i	$-0.113393\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.86679	−	2.80984i	−0.197863	−	0.114236i
$606$		0			0
$607$	−2.83013	+	1.63397i	−0.114871	+	0.0663210i	−0.556335	−	0.830958i	$-0.687793\pi$
$607$	−2.83013	+	1.63397i	−0.114871	+	0.0663210i	0.441464	+	0.897279i	$0.354459\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	23.4596			0.949075
$612$		0			0
$613$	34.3923			1.38909			0.694546	−	0.719448i	$-0.255605\pi$
$613$	34.3923			1.38909			0.694546	+	0.719448i	$0.255605\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.81225	−	3.93305i	0.274251	−	0.158339i	−0.356567	−	0.934270i	$-0.616053\pi$
$617$	6.81225	−	3.93305i	0.274251	−	0.158339i	0.630818	+	0.775931i	$0.282720\pi$
$618$		0			0
$619$	7.73205	+	4.46410i	0.310777	+	0.179427i	0.647274	−	0.762257i	$-0.275909\pi$
$619$	7.73205	+	4.46410i	0.310777	+	0.179427i	−0.336497	+	0.941685i	$0.609242\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.01790	−	5.22715i	0.120909	−	0.209421i
$624$		0			0
$625$	−10.5263	−	18.2321i	−0.421051	−	0.729282i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			14.2808i			0.569414i
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.808643	+	1.40061i	0.0320900	+	0.0555815i
$636$		0			0
$637$	−0.571797	+	0.990381i	−0.0226554	+	0.0392403i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.94666	−	2.27860i	−0.155884	−	0.0899994i	0.420029	−	0.907511i	$-0.362020\pi$
$641$	−3.94666	−	2.27860i	−0.155884	−	0.0899994i	−0.575913	+	0.817511i	$0.695353\pi$
$642$		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
$647$	42.1218			1.65598			0.827989	−	0.560744i	$-0.189485\pi$
$647$	42.1218			1.65598			0.827989	+	0.560744i	$0.189485\pi$
$648$		0			0
$649$	−5.17691			−0.203212
$650$		0			0
$651$		0			0
$652$		0			0
$653$	39.3441	−	22.7153i	1.53966	−	0.888920i	0.540797	−	0.841153i	$-0.318123\pi$
$653$	39.3441	−	22.7153i	1.53966	−	0.888920i	0.998859	−	0.0477670i	$-0.0152105\pi$
$654$		0			0
$655$	−8.83013	−	5.09808i	−0.345022	−	0.199198i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.81294	−	6.60420i	0.148531	−	0.257263i	−0.782154	−	0.623085i	$-0.785879\pi$
$659$	3.81294	−	6.60420i	0.148531	−	0.257263i	0.930685	+	0.365822i	$0.119212\pi$
$660$		0			0
$661$	−18.2583	−	31.6244i	−0.710167	−	1.23004i	−0.964794	−	0.263006i	$-0.915286\pi$
$661$	−18.2583	−	31.6244i	−0.710167	−	1.23004i	0.254628	−	0.967039i	$-0.418047\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	6.69213i		−	0.259510i
$666$		0			0
$667$		−	9.66025i		−	0.374047i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.74238	−	3.01790i	−0.0672639	−	0.116505i
$672$		0			0
$673$	2.16025	−	3.74167i	0.0832717	−	0.144231i	−0.821382	−	0.570379i	$-0.806796\pi$
$673$	2.16025	−	3.74167i	0.0832717	−	0.144231i	0.904653	+	0.426148i	$0.140130\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.5119	−	22.2349i	−1.48013	−	0.854556i	−0.480387	−	0.877057i	$-0.659504\pi$
$677$	−38.5119	−	22.2349i	−1.48013	−	0.854556i	−0.999747	+	0.0225009i	$0.992837\pi$
$678$		0			0
$679$	−34.0526	+	19.6603i	−1.30682	+	0.754491i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.0764			−0.768202			−0.384101	−	0.923291i	$-0.625489\pi$
$683$	−20.0764			−0.768202			−0.384101	+	0.923291i	$0.625489\pi$
$684$		0			0
$685$	−11.3923			−0.435278
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.22715	−	3.01790i	0.199139	−	0.114973i
$690$		0			0
$691$	24.7583	+	14.2942i	0.941851	+	0.543778i	0.890540	−	0.454905i	$-0.150327\pi$
$691$	24.7583	+	14.2942i	0.941851	+	0.543778i	0.0513111	+	0.998683i	$0.483660\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.17209	+	3.76217i	−0.0823920	+	0.142707i
$696$		0			0
$697$	8.83013	+	15.2942i	0.334465	+	0.579310i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			30.1146i			1.13741i	0.822541	+	0.568706i	$0.192556\pi$
$701$			30.1146i			1.13741i	−0.822541	+	0.568706i	$0.807444\pi$
$702$		0			0
$703$		−	20.1962i		−	0.761712i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.76028	−	8.24504i	−0.179029	−	0.310087i
$708$		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
$713$	0.656339	+	0.378937i	0.0245801	+	0.0141913i
$714$		0			0
$715$	0.418584	−	0.241670i	0.0156542	−	0.00903794i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−31.4916			−1.17444			−0.587220	−	0.809427i	$-0.699778\pi$
$719$	−31.4916			−1.17444			−0.587220	+	0.809427i	$0.699778\pi$
$720$		0			0
$721$	10.9282			0.406988
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−27.9933	+	16.1619i	−1.03964	+	0.600239i
$726$		0			0
$727$	−34.5622	−	19.9545i	−1.28184	−	0.740071i	−0.304656	−	0.952463i	$-0.598541\pi$
$727$	−34.5622	−	19.9545i	−1.28184	−	0.740071i	−0.977185	+	0.212392i	$0.931875\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.81345	−	15.2653i	0.325977	−	0.564609i
$732$		0			0
$733$	−2.33975	−	4.05256i	−0.0864205	−	0.149685i	0.819575	−	0.572972i	$-0.194210\pi$
$733$	−2.33975	−	4.05256i	−0.0864205	−	0.149685i	−0.905996	+	0.423287i	$0.860876\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			4.21543i			0.155278i
$738$		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
$743$	24.6980	+	42.7781i	0.906081	+	1.56938i	0.819460	+	0.573136i	$0.194273\pi$
$743$	24.6980	+	42.7781i	0.906081	+	1.56938i	0.0866206	+	0.996241i	$0.472393\pi$
$744$		0			0
$745$	5.23205	−	9.06218i	0.191688	−	0.332013i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	15.8338	+	9.14162i	0.578553	+	0.334028i
$750$		0			0
$751$	35.1506	−	20.2942i	1.28266	−	0.740547i	0.305330	−	0.952247i	$-0.401233\pi$
$751$	35.1506	−	20.2942i	1.28266	−	0.740547i	0.977335	+	0.211700i	$0.0678999\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.72741			−0.281229
$756$		0			0
$757$	16.7846			0.610047			0.305024	−	0.952345i	$-0.401336\pi$
$757$	16.7846			0.610047			0.305024	+	0.952345i	$0.401336\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	29.9945	−	17.3173i	1.08730	−	0.627752i	0.154443	−	0.988002i	$-0.450642\pi$
$761$	29.9945	−	17.3173i	1.08730	−	0.627752i	0.932856	+	0.360250i	$0.117308\pi$
$762$		0			0
$763$	−23.4904	−	13.5622i	−0.850409	−	0.490984i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.8319	+	29.1536i	−0.607763	+	1.05268i
$768$		0			0
$769$	−25.0167	−	43.3301i	−0.902124	−	1.56252i	−0.824732	−	0.565524i	$-0.808674\pi$
$769$	−25.0167	−	43.3301i	−0.902124	−	1.56252i	−0.0773917	−	0.997001i	$-0.524659\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	53.1209i		−	1.91063i	−0.295594	−	0.955314i	$-0.595517\pi$
$773$		−	53.1209i		−	1.91063i	0.295594	−	0.955314i	$-0.404483\pi$
$774$		0			0
$775$		−	2.53590i		−	0.0910922i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.4877	−	21.6293i	−0.447418	−	0.774950i
$780$		0			0
$781$	3.05256	−	5.28719i	0.109229	−	0.189190i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.98571	−	1.72380i	−0.106565	−	0.0615251i
$786$		0			0
$787$	−18.4186	+	10.6340i	−0.656552	+	0.379060i	−0.790962	−	0.611866i	$-0.790419\pi$
$787$	−18.4186	+	10.6340i	−0.656552	+	0.379060i	0.134410	+	0.990926i	$0.457086\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−5.00052			−0.177798
$792$		0			0
$793$	−22.6603			−0.804689
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.30079	+	4.79246i	−0.294029	+	0.169758i	−0.639757	−	0.768577i	$-0.720965\pi$
$797$	−8.30079	+	4.79246i	−0.294029	+	0.169758i	0.345728	+	0.938335i	$0.387632\pi$
$798$		0			0
$799$	−27.5885	−	15.9282i	−0.976009	−	0.563499i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.94545	−	3.36963i	0.0686536	−	0.118912i
$804$		0			0
$805$	1.00000	+	1.73205i	0.0352454	+	0.0610468i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			23.2466i			0.817307i	0.912690	+	0.408653i	$0.134001\pi$
$809$			23.2466i			0.817307i	−0.912690	+	0.408653i	$0.865999\pi$
$810$		0			0
$811$		−	22.6410i		−	0.795034i	−0.917595	−	0.397517i	$-0.869872\pi$
$811$		−	22.6410i		−	0.795034i	0.917595	−	0.397517i	$-0.130128\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.79555	−	10.0382i	−0.203009	−	0.351623i
$816$		0			0
$817$	−12.4641	+	21.5885i	−0.436064	+	0.755285i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−38.7435	−	22.3686i	−1.35216	−	0.780669i	−0.363607	−	0.931552i	$-0.618455\pi$
$821$	−38.7435	−	22.3686i	−1.35216	−	0.780669i	−0.988552	+	0.150883i	$0.951788\pi$
$822$		0			0
$823$	21.1244	−	12.1962i	0.736349	−	0.425131i	−0.0843915	−	0.996433i	$-0.526895\pi$
$823$	21.1244	−	12.1962i	0.736349	−	0.425131i	0.820740	+	0.571302i	$0.193561\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.5259			−0.783302			−0.391651	−	0.920114i	$-0.628096\pi$
$827$	−22.5259			−0.783302			−0.391651	+	0.920114i	$0.628096\pi$
$828$		0			0
$829$	−39.7128			−1.37928			−0.689642	−	0.724151i	$-0.742232\pi$
$829$	−39.7128			−1.37928			−0.689642	+	0.724151i	$0.742232\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.34486	−	0.776457i	0.0465967	−	0.0269026i
$834$		0			0
$835$	9.16987	+	5.29423i	0.317337	+	0.183214i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.3359	−	30.0267i	0.598502	−	1.03664i	−0.394541	−	0.918878i	$-0.629096\pi$
$839$	17.3359	−	30.0267i	0.598502	−	1.03664i	0.993042	−	0.117757i	$-0.0375703\pi$
$840$		0			0
$841$	8.83013	+	15.2942i	0.304487	+	0.527387i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			3.58630i			0.123373i
$846$		0			0
$847$			29.6603i			1.01914i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.01790	+	5.22715i	0.103452	+	0.179184i
$852$		0			0
$853$	−19.7846	+	34.2679i	−0.677412	+	1.17331i	0.298345	+	0.954458i	$0.403565\pi$
$853$	−19.7846	+	34.2679i	−0.677412	+	1.17331i	−0.975758	+	0.218854i	$0.929768\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.3023	+	13.4536i	0.795993	+	0.459567i	0.842068	−	0.539371i	$-0.181338\pi$
$857$	23.3023	+	13.4536i	0.795993	+	0.459567i	−0.0460753	+	0.998938i	$0.514671\pi$
$858$		0			0
$859$	−37.6410	+	21.7321i	−1.28429	+	0.741488i	−0.977631	−	0.210330i	$-0.932546\pi$
$859$	−37.6410	+	21.7321i	−1.28429	+	0.741488i	−0.306664	+	0.951818i	$0.599213\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.0502			1.02292			0.511461	−	0.859307i	$-0.329105\pi$
$863$	30.0502			1.02292			0.511461	+	0.859307i	$0.329105\pi$
$864$		0			0
$865$	−0.607695			−0.0206623
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.78749	+	2.76406i	−0.162404	+	0.0937642i
$870$		0			0
$871$	23.7391	+	13.7058i	0.804368	+	0.464402i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.88160	−	11.9193i	0.232641	−	0.402945i
$876$		0			0
$877$	10.0622	+	17.4282i	0.339776	+	0.588509i	0.984390	−	0.175999i	$-0.0563155\pi$
$877$	10.0622	+	17.4282i	0.339776	+	0.588509i	−0.644615	+	0.764508i	$0.722982\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	37.7033i		−	1.27026i	−0.772407	−	0.635128i	$-0.780947\pi$
$881$		−	37.7033i		−	1.27026i	0.772407	−	0.635128i	$-0.219053\pi$
$882$		0			0
$883$		−	35.3205i		−	1.18863i	−0.804232	−	0.594315i	$-0.797423\pi$
$883$		−	35.3205i		−	1.18863i	0.804232	−	0.594315i	$-0.202577\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.39872	+	4.15471i	0.0805412	+	0.139501i	0.903483	−	0.428625i	$-0.141002\pi$
$887$	2.39872	+	4.15471i	0.0805412	+	0.139501i	−0.822941	+	0.568126i	$0.807668\pi$
$888$		0			0
$889$	4.26795	−	7.39230i	0.143142	−	0.247930i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	39.0160	+	22.5259i	1.30562	+	0.753800i
$894$		0			0
$895$	5.41154	−	3.12436i	0.180888	−	0.104436i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.66063			−0.122089
$900$		0			0
$901$	−8.19615			−0.273053
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.07484	+	2.92996i	−0.168694	+	0.0973953i
$906$		0			0
$907$	16.8564	+	9.73205i	0.559708	+	0.323147i	0.753028	−	0.657988i	$-0.228592\pi$
$907$	16.8564	+	9.73205i	0.559708	+	0.323147i	−0.193320	+	0.981136i	$0.561926\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.6796	+	28.8898i	−0.552618	+	0.957163i	0.445466	+	0.895299i	$0.353038\pi$
$911$	−16.6796	+	28.8898i	−0.552618	+	0.957163i	−0.998085	+	0.0618644i	$0.980295\pi$
$912$		0			0
$913$	−0.143594	−	0.248711i	−0.00475225	−	0.00823114i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			53.8144i			1.77711i
$918$		0			0
$919$			20.4449i			0.674414i	0.941431	+	0.337207i	$0.109482\pi$
$919$			20.4449i			0.674414i	−0.941431	+	0.337207i	$0.890518\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−19.8498	−	34.3808i	−0.653363	−	1.13166i
$924$		0			0
$925$	10.0981	−	17.4904i	0.332023	−	0.575080i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.5613	−	8.98434i	−0.510551	−	0.294767i	0.222509	−	0.974931i	$-0.428575\pi$
$929$	−15.5613	−	8.98434i	−0.510551	−	0.294767i	−0.733060	+	0.680164i	$0.761909\pi$
$930$		0			0
$931$	−1.90192	+	1.09808i	−0.0623330	+	0.0359880i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.656339			−0.0214646
$936$		0			0
$937$	−13.3923			−0.437508			−0.218754	−	0.975780i	$-0.570199\pi$
$937$	−13.3923			−0.437508			−0.218754	+	0.975780i	$0.570199\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	28.2657	−	16.3192i	0.921435	−	0.531991i	0.0373425	−	0.999303i	$-0.488111\pi$
$941$	28.2657	−	16.3192i	0.921435	−	0.531991i	0.884093	+	0.467312i	$0.154777\pi$
$942$		0			0
$943$	6.46410	+	3.73205i	0.210500	+	0.121532i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.9203	−	37.9671i	0.712314	−	1.23376i	−0.251672	−	0.967813i	$-0.580980\pi$
$947$	21.9203	−	37.9671i	0.712314	−	1.23376i	0.963986	−	0.265952i	$-0.0856863\pi$
$948$		0			0
$949$	−12.6506	−	21.9115i	−0.410657	−	0.711279i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			29.9387i			0.969810i	0.874567	+	0.484905i	$0.161146\pi$
$953$			29.9387i			0.969810i	−0.874567	+	0.484905i	$0.838854\pi$
$954$		0			0
$955$			5.51666i			0.178515i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	30.0638	+	52.0721i	0.970811	+	1.68149i
$960$		0			0
$961$	−15.3564	+	26.5981i	−0.495368	+	0.858002i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.688524	−	0.397520i	−0.0221644	−	0.0127966i
$966$		0			0
$967$	48.2032	−	27.8301i	1.55011	−	0.894957i	0.551978	−	0.833858i	$-0.313873\pi$
$967$	48.2032	−	27.8301i	1.55011	−	0.894957i	0.998132	−	0.0610982i	$-0.0194603\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	20.6584			0.662960			0.331480	−	0.943462i	$-0.392452\pi$
$971$	20.6584			0.662960			0.331480	+	0.943462i	$0.392452\pi$
$972$		0			0
$973$	22.9282			0.735044
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−17.7792	+	10.2648i	−0.568807	+	0.328401i	−0.756673	−	0.653794i	$-0.773176\pi$
$977$	−17.7792	+	10.2648i	−0.568807	+	0.328401i	0.187866	+	0.982195i	$0.439843\pi$
$978$		0			0
$979$	0.725009	+	0.418584i	0.0231714	+	0.0133780i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.2814	+	33.3963i	−0.614980	+	1.06518i	0.375408	+	0.926859i	$0.377502\pi$
$983$	−19.2814	+	33.3963i	−0.614980	+	1.06518i	−0.990388	+	0.138316i	$0.955831\pi$
$984$		0			0
$985$	4.42820	+	7.66987i	0.141094	+	0.244382i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	7.45001i		−	0.236896i
$990$		0			0
$991$			32.4449i			1.03065i	0.856996	+	0.515323i	$0.172328\pi$
$991$			32.4449i			1.03065i	−0.856996	+	0.515323i	$0.827672\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.07055	−	3.58630i	−0.0656409	−	0.113693i
$996$		0			0
$997$	−3.59808	+	6.23205i	−0.113952	+	0.197371i	−0.917360	−	0.398058i	$-0.869684\pi$
$997$	−3.59808	+	6.23205i	−0.113952	+	0.197371i	0.803408	+	0.595429i	$0.203018\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.f.1727.2		8
3.2	odd	2	inner	2592.2.s.f.1727.3		8
4.3	odd	2		2592.2.s.b.1727.2		8
9.2	odd	6		2592.2.c.a.2591.5	yes	8
9.4	even	3		2592.2.s.b.863.3		8
9.5	odd	6		2592.2.s.b.863.2		8
9.7	even	3		2592.2.c.a.2591.3	✓	8
12.11	even	2		2592.2.s.b.1727.3		8
36.7	odd	6		2592.2.c.a.2591.4	yes	8
36.11	even	6		2592.2.c.a.2591.6	yes	8
36.23	even	6	inner	2592.2.s.f.863.2		8
36.31	odd	6	inner	2592.2.s.f.863.3		8
72.11	even	6		5184.2.c.i.5183.4		8
72.29	odd	6		5184.2.c.i.5183.3		8
72.43	odd	6		5184.2.c.i.5183.6		8
72.61	even	6		5184.2.c.i.5183.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2592.2.c.a.2591.3	✓	8	9.7	even	3
2592.2.c.a.2591.4	yes	8	36.7	odd	6
2592.2.c.a.2591.5	yes	8	9.2	odd	6
2592.2.c.a.2591.6	yes	8	36.11	even	6
2592.2.s.b.863.2		8	9.5	odd	6
2592.2.s.b.863.3		8	9.4	even	3
2592.2.s.b.1727.2		8	4.3	odd	2
2592.2.s.b.1727.3		8	12.11	even	2
2592.2.s.f.863.2		8	36.23	even	6	inner
2592.2.s.f.863.3		8	36.31	odd	6	inner
2592.2.s.f.1727.2		8	1.1	even	1	trivial
2592.2.s.f.1727.3		8	3.2	odd	2	inner
5184.2.c.i.5183.3		8	72.29	odd	6
5184.2.c.i.5183.4		8	72.11	even	6
5184.2.c.i.5183.5		8	72.61	even	6
5184.2.c.i.5183.6		8	72.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.448288 + 0.258819i) q^{5} +(2.36603 + 1.36603i) q^{7} +O(q^{10})\)	\(q+(-0.448288 + 0.258819i) q^{5} +(2.36603 + 1.36603i) q^{7} +(-0.189469 + 0.328169i) q^{11} +(1.23205 + 2.13397i) q^{13} -3.34607i q^{17} +4.73205i q^{19} +(-0.707107 - 1.22474i) q^{23} +(-2.36603 + 4.09808i) q^{25} +(5.91567 + 3.41542i) q^{29} +(-0.464102 + 0.267949i) q^{31} -1.41421 q^{35} -4.26795 q^{37} +(-4.57081 + 2.63896i) q^{41} +(4.56218 + 2.63397i) q^{43} +(4.76028 - 8.24504i) q^{47} +(0.232051 + 0.401924i) q^{49} -2.44949i q^{53} -0.196152i q^{55} +(6.83083 + 11.8313i) q^{59} +(-4.59808 + 7.96410i) q^{61} +(-1.10463 - 0.637756i) q^{65} +(9.63397 - 5.56218i) q^{67} -16.1112 q^{71} -10.2679 q^{73} +(-0.896575 + 0.517638i) q^{77} +(12.6340 + 7.29423i) q^{79} +(-0.378937 + 0.656339i) q^{83} +(0.866025 + 1.50000i) q^{85} -2.20925i q^{89} +6.73205i q^{91} +(-1.22474 - 2.12132i) q^{95} +(-7.19615 + 12.4641i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{7}+O(q^{10}) \) 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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