LMFDB - Embedded newform 2592.2.s.c.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:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 864)
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.c.863.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.896575 + 0.517638i) q^{5} +(0.232051 + 0.133975i) q^{7} +O(q^{10})$	$q+(-0.896575 + 0.517638i) q^{5} +(0.232051 + 0.133975i) q^{7} +(1.93185 - 3.34607i) q^{11} +(1.23205 + 2.13397i) q^{13} -6.69213i q^{17} -1.73205i q^{19} +(2.96713 + 5.13922i) q^{23} +(-1.96410 + 3.40192i) q^{25} +(1.79315 + 1.03528i) q^{29} +(0.464102 - 0.267949i) q^{31} -0.277401 q^{35} -6.46410 q^{37} +(-1.79315 + 1.03528i) q^{41} +(-6.46410 - 3.73205i) q^{43} +(4.76028 - 8.24504i) q^{47} +(-3.46410 - 6.00000i) q^{49} -13.3843i q^{53} +4.00000i q^{55} +(3.72500 + 6.45189i) q^{59} +(4.69615 - 8.13397i) q^{61} +(-2.20925 - 1.27551i) q^{65} +(-8.42820 + 4.86603i) q^{67} +11.3137 q^{71} +9.92820 q^{73} +(0.896575 - 0.517638i) q^{77} +(13.1603 + 7.59808i) q^{79} +(3.86370 - 6.69213i) q^{83} +(3.46410 + 6.00000i) q^{85} -6.69213i q^{89} +0.660254i q^{91} +(0.896575 + 1.55291i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 24 q^{37} - 24 q^{43} - 4 q^{61} - 12 q^{67} + 24 q^{73} + 36 q^{79} - 28 q^{97}+O(q^{100}) $ 8 * q - 12 * q^7 - 4 * q^13 + 12 * q^25 - 24 * q^31 - 24 * q^37 - 24 * q^43 - 4 * q^61 - 12 * q^67 + 24 * q^73 + 36 * q^79 - 28 * 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
$5$	−0.896575	+	0.517638i	−0.400961	+	0.231495i	−0.686898	−	0.726753i	$-0.741028\pi$
$5$	−0.896575	+	0.517638i	−0.400961	+	0.231495i	0.285938	+	0.958248i	$0.407695\pi$
$6$		0			0
$7$	0.232051	+	0.133975i	0.0877070	+	0.0506376i	0.543212	−	0.839596i	$-0.317208\pi$
$7$	0.232051	+	0.133975i	0.0877070	+	0.0506376i	−0.455505	+	0.890233i	$0.650541\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.93185	−	3.34607i	0.582475	−	1.00888i	−0.412710	−	0.910863i	$-0.635418\pi$
$11$	1.93185	−	3.34607i	0.582475	−	1.00888i	0.995185	−	0.0980141i	$-0.0312490\pi$
$12$		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
$17$		−	6.69213i		−	1.62308i	−0.584297	−	0.811540i	$-0.698630\pi$
$17$		−	6.69213i		−	1.62308i	0.584297	−	0.811540i	$-0.301370\pi$
$18$		0			0
$19$		−	1.73205i		−	0.397360i	−0.980064	−	0.198680i	$-0.936335\pi$
$19$		−	1.73205i		−	0.397360i	0.980064	−	0.198680i	$-0.0636654\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.96713	+	5.13922i	0.618689	+	1.07160i	0.989725	+	0.142982i	$0.0456692\pi$
$23$	2.96713	+	5.13922i	0.618689	+	1.07160i	−0.371036	+	0.928618i	$0.620997\pi$
$24$		0			0
$25$	−1.96410	+	3.40192i	−0.392820	+	0.680385i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.79315	+	1.03528i	0.332980	+	0.192246i	0.657163	−	0.753748i	$-0.271756\pi$
$29$	1.79315	+	1.03528i	0.332980	+	0.192246i	−0.324184	+	0.945994i	$0.605090\pi$
$30$		0			0
$31$	0.464102	−	0.267949i	0.0833551	−	0.0481251i	−0.457743	−	0.889085i	$-0.651342\pi$
$31$	0.464102	−	0.267949i	0.0833551	−	0.0481251i	0.541098	+	0.840959i	$0.318009\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.277401			−0.0468894
$36$		0			0
$37$	−6.46410			−1.06269			−0.531346	−	0.847155i	$-0.678314\pi$
$37$	−6.46410			−1.06269			−0.531346	+	0.847155i	$0.678314\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.79315	+	1.03528i	−0.280043	+	0.161683i	−0.633443	−	0.773789i	$-0.718359\pi$
$41$	−1.79315	+	1.03528i	−0.280043	+	0.161683i	0.353400	+	0.935472i	$0.385026\pi$
$42$		0			0
$43$	−6.46410	−	3.73205i	−0.985766	−	0.569132i	−0.0817602	−	0.996652i	$-0.526054\pi$
$43$	−6.46410	−	3.73205i	−0.985766	−	0.569132i	−0.904006	+	0.427520i	$0.859387\pi$
$44$		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
$49$	−3.46410	−	6.00000i	−0.494872	−	0.857143i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	13.3843i		−	1.83847i	−0.393710	−	0.919235i	$-0.628808\pi$
$53$		−	13.3843i		−	1.83847i	0.393710	−	0.919235i	$-0.371192\pi$
$54$		0			0
$55$			4.00000i			0.539360i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.72500	+	6.45189i	0.484954	+	0.839965i	0.999851	−	0.0172873i	$-0.00550300\pi$
$59$	3.72500	+	6.45189i	0.484954	+	0.839965i	−0.514897	+	0.857252i	$0.672170\pi$
$60$		0			0
$61$	4.69615	−	8.13397i	0.601281	−	1.04145i	−0.391347	−	0.920243i	$-0.627991\pi$
$61$	4.69615	−	8.13397i	0.601281	−	1.04145i	0.992627	−	0.121205i	$-0.0386760\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.20925	−	1.27551i	−0.274024	−	0.158208i
$66$		0			0
$67$	−8.42820	+	4.86603i	−1.02967	+	0.594480i	−0.916890	−	0.399140i	$-0.869309\pi$
$67$	−8.42820	+	4.86603i	−1.02967	+	0.594480i	−0.112779	+	0.993620i	$0.535975\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	11.3137			1.34269			0.671345	−	0.741145i	$-0.265717\pi$
$71$	11.3137			1.34269			0.671345	+	0.741145i	$0.265717\pi$
$72$		0			0
$73$	9.92820			1.16201			0.581004	−	0.813901i	$-0.302660\pi$
$73$	9.92820			1.16201			0.581004	+	0.813901i	$0.302660\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.896575	−	0.517638i	0.102174	−	0.0589903i
$78$		0			0
$79$	13.1603	+	7.59808i	1.48064	+	0.854850i	0.999759	−	0.0219334i	$-0.00698218\pi$
$79$	13.1603	+	7.59808i	1.48064	+	0.854850i	0.480885	+	0.876784i	$0.340316\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.86370	−	6.69213i	0.424097	−	0.734557i	−0.572239	−	0.820087i	$-0.693925\pi$
$83$	3.86370	−	6.69213i	0.424097	−	0.734557i	0.996336	+	0.0855301i	$0.0272584\pi$
$84$		0			0
$85$	3.46410	+	6.00000i	0.375735	+	0.650791i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	6.69213i		−	0.709364i	−0.934987	−	0.354682i	$-0.884589\pi$
$89$		−	6.69213i		−	0.709364i	0.934987	−	0.354682i	$-0.115411\pi$
$90$		0			0
$91$			0.660254i			0.0692134i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.896575	+	1.55291i	0.0919867	+	0.159326i
$96$		0			0
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	−0.987181	−	0.159602i	$-0.948979\pi$
$97$	−3.50000	+	6.06218i	−0.355371	+	0.615521i	0.631810	+	0.775123i	$0.282312\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−13.3843	−	7.72741i	−1.33178	−	0.768906i	−0.346211	−	0.938157i	$-0.612532\pi$
$101$	−13.3843	−	7.72741i	−1.33178	−	0.768906i	−0.985573	+	0.169251i	$0.945865\pi$
$102$		0			0
$103$	15.2321	−	8.79423i	1.50086	−	0.866521i	0.500859	−	0.865529i	$-0.333017\pi$
$103$	15.2321	−	8.79423i	1.50086	−	0.866521i	1.00000		0.000992235i	$-0.000315838\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.1774			1.46726			0.733628	−	0.679551i	$-0.237826\pi$
$107$	15.1774			1.46726			0.733628	+	0.679551i	$0.237826\pi$
$108$		0			0
$109$	−0.928203			−0.0889057			−0.0444529	−	0.999011i	$-0.514154\pi$
$109$	−0.928203			−0.0889057			−0.0444529	+	0.999011i	$0.514154\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.58871	−	4.38134i	0.713885	−	0.412162i	−0.0986126	−	0.995126i	$-0.531440\pi$
$113$	7.58871	−	4.38134i	0.713885	−	0.412162i	0.812498	+	0.582964i	$0.198107\pi$
$114$		0			0
$115$	−5.32051	−	3.07180i	−0.496140	−	0.286447i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.896575	−	1.55291i	0.0821889	−	0.142355i
$120$		0			0
$121$	−1.96410	−	3.40192i	−0.178555	−	0.309266i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	9.24316i		−	0.826733i
$126$		0			0
$127$		−	3.46410i		−	0.307389i	−0.988118	−	0.153695i	$-0.950883\pi$
$127$		−	3.46410i		−	0.307389i	0.988118	−	0.153695i	$-0.0491172\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.86370	−	6.69213i	−0.337573	−	0.584694i	0.646402	−	0.762997i	$-0.276273\pi$
$131$	−3.86370	−	6.69213i	−0.337573	−	0.584694i	−0.983976	+	0.178303i	$0.942939\pi$
$132$		0			0
$133$	0.232051	−	0.401924i	0.0201214	−	0.0348512i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.38186	−	5.41662i	−0.801546	−	0.462773i	0.0424654	−	0.999098i	$-0.486479\pi$
$137$	−9.38186	−	5.41662i	−0.801546	−	0.462773i	−0.844012	+	0.536325i	$0.819812\pi$
$138$		0			0
$139$	1.03590	−	0.598076i	0.0878638	−	0.0507282i	−0.455424	−	0.890274i	$-0.650512\pi$
$139$	1.03590	−	0.598076i	0.0878638	−	0.0507282i	0.543288	+	0.839546i	$0.317179\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.52056			0.796149
$144$		0			0
$145$	−2.14359			−0.178016
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.79796	−	5.65685i	0.802680	−	0.463428i	−0.0417274	−	0.999129i	$-0.513286\pi$
$149$	9.79796	−	5.65685i	0.802680	−	0.463428i	0.844407	+	0.535701i	$0.179953\pi$
$150$		0			0
$151$	7.16025	+	4.13397i	0.582693	+	0.336418i	0.762203	−	0.647338i	$-0.224118\pi$
$151$	7.16025	+	4.13397i	0.582693	+	0.336418i	−0.179510	+	0.983756i	$0.557451\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.277401	+	0.480473i	−0.0222814	+	0.0385925i
$156$		0			0
$157$	1.53590	+	2.66025i	0.122578	+	0.212311i	0.920784	−	0.390074i	$-0.127550\pi$
$157$	1.53590	+	2.66025i	0.122578	+	0.212311i	−0.798206	+	0.602385i	$0.794217\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.59008i			0.125316i
$162$		0			0
$163$		−	15.5885i		−	1.22098i	−0.792023	−	0.610491i	$-0.790972\pi$
$163$		−	15.5885i		−	1.22098i	0.792023	−	0.610491i	$-0.209028\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.17398	−	2.03339i	−0.0908451	−	0.157348i	0.817022	−	0.576607i	$-0.195623\pi$
$167$	−1.17398	−	2.03339i	−0.0908451	−	0.157348i	−0.907867	+	0.419258i	$0.862290\pi$
$168$		0			0
$169$	3.46410	−	6.00000i	0.266469	−	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.00481	−	4.62158i	−0.608594	−	0.351372i	0.163821	−	0.986490i	$-0.447618\pi$
$173$	−8.00481	−	4.62158i	−0.608594	−	0.351372i	−0.772415	+	0.635118i	$0.780951\pi$
$174$		0			0
$175$	−0.911543	+	0.526279i	−0.0689062	+	0.0397830i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	19.5959			1.46467			0.732334	−	0.680946i	$-0.238431\pi$
$179$	19.5959			1.46467			0.732334	+	0.680946i	$0.238431\pi$
$180$		0			0
$181$	−6.46410			−0.480473			−0.240236	−	0.970714i	$-0.577225\pi$
$181$	−6.46410			−0.480473			−0.240236	+	0.970714i	$0.577225\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.79555	−	3.34607i	0.426098	−	0.246008i
$186$		0			0
$187$	−22.3923	−	12.9282i	−1.63749	−	0.945404i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.83083	+	11.8313i	−0.494262	+	0.856086i	−0.999978	−	0.00661351i	$-0.997895\pi$
$191$	−6.83083	+	11.8313i	−0.494262	+	0.856086i	0.505717	+	0.862700i	$0.331228\pi$
$192$		0			0
$193$	−0.0358984	−	0.0621778i	−0.00258402	−	0.00447566i	0.864731	−	0.502236i	$-0.167489\pi$
$193$	−0.0358984	−	0.0621778i	−0.00258402	−	0.00447566i	−0.867315	+	0.497761i	$0.834156\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			14.4195i			1.02735i	0.857985	+	0.513675i	$0.171716\pi$
$197$			14.4195i			1.02735i	−0.857985	+	0.513675i	$0.828284\pi$
$198$		0			0
$199$			25.5885i			1.81392i	0.421219	+	0.906959i	$0.361602\pi$
$199$			25.5885i			1.81392i	−0.421219	+	0.906959i	$0.638398\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.277401	+	0.480473i	0.0194698	+	0.0337226i
$204$		0			0
$205$	1.07180	−	1.85641i	0.0748575	−	0.129657i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.79555	−	3.34607i	−0.400887	−	0.231452i
$210$		0			0
$211$	−18.8205	+	10.8660i	−1.29566	+	0.748048i	−0.979651	−	0.200709i	$-0.935675\pi$
$211$	−18.8205	+	10.8660i	−1.29566	+	0.748048i	−0.316006	+	0.948757i	$0.602342\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.72741			0.527005
$216$		0			0
$217$	0.143594			0.00974776
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.2808	−	8.24504i	0.960633	−	0.554622i
$222$		0			0
$223$	20.3205	+	11.7321i	1.36076	+	0.785636i	0.989725	−	0.142982i	$-0.0456691\pi$
$223$	20.3205	+	11.7321i	1.36076	+	0.785636i	0.371037	+	0.928618i	$0.379002\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.07055	+	3.58630i	−0.137427	+	0.238031i	−0.926522	−	0.376240i	$-0.877217\pi$
$227$	−2.07055	+	3.58630i	−0.137427	+	0.238031i	0.789095	+	0.614272i	$0.210550\pi$
$228$		0			0
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	11.3137i		−	0.741186i	−0.928795	−	0.370593i	$-0.879155\pi$
$233$		−	11.3137i		−	0.741186i	0.928795	−	0.370593i	$-0.120845\pi$
$234$		0			0
$235$			9.85641i			0.642961i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.72741	−	13.3843i	−0.499844	−	0.865756i	0.500156	−	0.865936i	$-0.333276\pi$
$239$	−7.72741	−	13.3843i	−0.499844	−	0.865756i	−1.00000		0.000179684i	$0.999943\pi$
$240$		0			0
$241$	−2.96410	+	5.13397i	−0.190935	+	0.330708i	−0.945560	−	0.325447i	$-0.894485\pi$
$241$	−2.96410	+	5.13397i	−0.190935	+	0.330708i	0.754626	+	0.656156i	$0.227818\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.21166	+	3.58630i	0.396848	+	0.229120i
$246$		0			0
$247$	3.69615	−	2.13397i	0.235181	−	0.135782i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.58630			−0.226365			−0.113183	−	0.993574i	$-0.536105\pi$
$251$	−3.58630			−0.226365			−0.113183	+	0.993574i	$0.536105\pi$
$252$		0			0
$253$	22.9282			1.44148
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.79315	−	1.03528i	0.111854	−	0.0645788i	−0.443029	−	0.896507i	$-0.646096\pi$
$257$	1.79315	−	1.03528i	0.111854	−	0.0645788i	0.554883	+	0.831928i	$0.312763\pi$
$258$		0			0
$259$	−1.50000	−	0.866025i	−0.0932055	−	0.0538122i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.72741	−	13.3843i	0.476492	−	0.825309i	−0.523145	−	0.852244i	$-0.675241\pi$
$263$	7.72741	−	13.3843i	0.476492	−	0.825309i	0.999637	+	0.0269349i	$0.00857468\pi$
$264$		0			0
$265$	6.92820	+	12.0000i	0.425596	+	0.737154i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			3.10583i			0.189366i	0.995507	+	0.0946829i	$0.0301837\pi$
$269$			3.10583i			0.189366i	−0.995507	+	0.0946829i	$0.969816\pi$
$270$		0			0
$271$		−	13.0526i		−	0.792886i	−0.918059	−	0.396443i	$-0.870244\pi$
$271$		−	13.0526i		−	0.792886i	0.918059	−	0.396443i	$-0.129756\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.58871	+	13.1440i	0.457616	+	0.792614i
$276$		0			0
$277$	−10.4641	+	18.1244i	−0.628727	+	1.08899i	0.359081	+	0.933307i	$0.383090\pi$
$277$	−10.4641	+	18.1244i	−0.628727	+	1.08899i	−0.987807	+	0.155680i	$0.950243\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−15.1774	−	8.76268i	−0.905408	−	0.522738i	−0.0264575	−	0.999650i	$-0.508423\pi$
$281$	−15.1774	−	8.76268i	−0.905408	−	0.522738i	−0.878951	+	0.476912i	$0.841756\pi$
$282$		0			0
$283$	−0.464102	+	0.267949i	−0.0275880	+	0.0159279i	−0.513731	−	0.857952i	$-0.671737\pi$
$283$	−0.464102	+	0.267949i	−0.0275880	+	0.0159279i	0.486143	+	0.873880i	$0.338404\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.554803			−0.0327490
$288$		0			0
$289$	−27.7846			−1.63439
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−24.0788	+	13.9019i	−1.40670	+	0.812158i	−0.995068	−	0.0991934i	$-0.968374\pi$
$293$	−24.0788	+	13.9019i	−1.40670	+	0.812158i	−0.411630	+	0.911351i	$0.635040\pi$
$294$		0			0
$295$	−6.67949	−	3.85641i	−0.388895	−	0.224529i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.31130	+	12.6636i	−0.422824	+	0.732352i
$300$		0			0
$301$	−1.00000	−	1.73205i	−0.0576390	−	0.0998337i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			9.72363i			0.556773i
$306$		0			0
$307$		−	22.3923i		−	1.27800i	−0.769208	−	0.638998i	$-0.779349\pi$
$307$		−	22.3923i		−	1.27800i	0.769208	−	0.638998i	$-0.220651\pi$
$308$		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
$313$	9.96410	−	17.2583i	0.563204	−	0.975499i	−0.434010	−	0.900908i	$-0.642902\pi$
$313$	9.96410	−	17.2583i	0.563204	−	0.975499i	0.997214	−	0.0745904i	$-0.0237649\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.79315	+	1.03528i	0.100713	+	0.0581469i	0.549511	−	0.835487i	$-0.314814\pi$
$317$	1.79315	+	1.03528i	0.100713	+	0.0581469i	−0.448797	+	0.893634i	$0.648147\pi$
$318$		0			0
$319$	6.92820	−	4.00000i	0.387905	−	0.223957i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.5911			−0.644947
$324$		0			0
$325$	−9.67949			−0.536922
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.20925	−	1.27551i	0.121800	−	0.0703213i
$330$		0			0
$331$	−21.8205	−	12.5981i	−1.19936	−	0.692453i	−0.238950	−	0.971032i	$-0.576803\pi$
$331$	−21.8205	−	12.5981i	−1.19936	−	0.692453i	−0.960413	+	0.278579i	$0.910137\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.03768	−	8.72552i	0.275238	−	0.476726i
$336$		0			0
$337$	7.42820	+	12.8660i	0.404640	+	0.700857i	0.994280	−	0.106809i	$-0.0340635\pi$
$337$	7.42820	+	12.8660i	0.404640	+	0.700857i	−0.589639	+	0.807667i	$0.700730\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	2.07055i		−	0.112127i
$342$		0			0
$343$		−	3.73205i		−	0.201512i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.72741	−	13.3843i	−0.414829	−	0.718505i	0.580582	−	0.814202i	$-0.302825\pi$
$347$	−7.72741	−	13.3843i	−0.414829	−	0.718505i	−0.995410	+	0.0956973i	$0.969492\pi$
$348$		0			0
$349$	−5.16025	+	8.93782i	−0.276222	+	0.478431i	−0.970443	−	0.241332i	$-0.922416\pi$
$349$	−5.16025	+	8.93782i	−0.276222	+	0.478431i	0.694221	+	0.719762i	$0.255749\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	30.3548	+	17.5254i	1.61562	+	0.932781i	0.988034	+	0.154237i	$0.0492921\pi$
$353$	30.3548	+	17.5254i	1.61562	+	0.932781i	0.627590	+	0.778544i	$0.284041\pi$
$354$		0			0
$355$	−10.1436	+	5.85641i	−0.538366	+	0.310826i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−32.1480			−1.69671			−0.848353	−	0.529432i	$-0.822405\pi$
$359$	−32.1480			−1.69671			−0.848353	+	0.529432i	$0.822405\pi$
$360$		0			0
$361$	16.0000			0.842105
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−8.90138	+	5.13922i	−0.465920	+	0.268999i
$366$		0			0
$367$	14.7679	+	8.52628i	0.770881	+	0.445068i	0.833189	−	0.552989i	$-0.186513\pi$
$367$	14.7679	+	8.52628i	0.770881	+	0.445068i	−0.0623080	+	0.998057i	$0.519846\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.79315	−	3.10583i	0.0930958	−	0.161247i
$372$		0			0
$373$	−6.62436	−	11.4737i	−0.342996	−	0.594087i	0.641991	−	0.766712i	$-0.278108\pi$
$373$	−6.62436	−	11.4737i	−0.342996	−	0.594087i	−0.984988	+	0.172625i	$0.944775\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.10205i			0.262769i
$378$		0			0
$379$			9.19615i			0.472375i	0.971708	+	0.236187i	$0.0758979\pi$
$379$			9.19615i			0.472375i	−0.971708	+	0.236187i	$0.924102\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.5254	+	30.3548i	0.895504	+	1.55106i	0.833179	+	0.553003i	$0.186518\pi$
$383$	17.5254	+	30.3548i	0.895504	+	1.55106i	0.0623252	+	0.998056i	$0.480148\pi$
$384$		0			0
$385$	−0.535898	+	0.928203i	−0.0273119	+	0.0473056i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12.4877	+	7.20977i	0.633151	+	0.365550i	0.781971	−	0.623314i	$-0.214214\pi$
$389$	12.4877	+	7.20977i	0.633151	+	0.365550i	−0.148821	+	0.988864i	$0.547548\pi$
$390$		0			0
$391$	34.3923	−	19.8564i	1.73929	−	1.00418i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−15.7322			−0.791574
$396$		0			0
$397$	26.7846			1.34428			0.672141	−	0.740424i	$-0.265375\pi$
$397$	26.7846			1.34428			0.672141	+	0.740424i	$0.265375\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−19.5959	+	11.3137i	−0.978573	+	0.564980i	−0.901839	−	0.432072i	$-0.857783\pi$
$401$	−19.5959	+	11.3137i	−0.978573	+	0.564980i	−0.0767343	+	0.997052i	$0.524449\pi$
$402$		0			0
$403$	1.14359	+	0.660254i	0.0569665	+	0.0328896i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−12.4877	+	21.6293i	−0.618992	+	1.07212i
$408$		0			0
$409$	6.50000	+	11.2583i	0.321404	+	0.556689i	0.980778	−	0.195127i	$-0.0625118\pi$
$409$	6.50000	+	11.2583i	0.321404	+	0.556689i	−0.659374	+	0.751815i	$0.729178\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			1.99622i			0.0982277i
$414$		0			0
$415$			8.00000i			0.392705i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.86611	+	13.6245i	0.384284	+	0.665600i	0.991670	−	0.128807i	$-0.0411148\pi$
$419$	7.86611	+	13.6245i	0.384284	+	0.665600i	−0.607385	+	0.794407i	$0.707782\pi$
$420$		0			0
$421$	−4.76795	+	8.25833i	−0.232376	+	0.402486i	−0.958507	−	0.285070i	$-0.907983\pi$
$421$	−4.76795	+	8.25833i	−0.232376	+	0.402486i	0.726131	+	0.687556i	$0.241317\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	22.7661	+	13.1440i	1.10432	+	0.637579i
$426$		0			0
$427$	2.17949	−	1.25833i	0.105473	−	0.0608949i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.37945			−0.259119			−0.129560	−	0.991572i	$-0.541356\pi$
$431$	−5.37945			−0.259119			−0.129560	+	0.991572i	$0.541356\pi$
$432$		0			0
$433$	−26.7846			−1.28719			−0.643593	−	0.765368i	$-0.722557\pi$
$433$	−26.7846			−1.28719			−0.643593	+	0.765368i	$0.722557\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.90138	−	5.13922i	0.425811	−	0.245842i
$438$		0			0
$439$	18.4641	+	10.6603i	0.881243	+	0.508786i	0.871068	−	0.491162i	$-0.163428\pi$
$439$	18.4641	+	10.6603i	0.881243	+	0.508786i	0.0101753	+	0.999948i	$0.496761\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	13.6617	−	23.6627i	0.649085	−	1.12425i	−0.334257	−	0.942482i	$-0.608485\pi$
$443$	13.6617	−	23.6627i	0.649085	−	1.12425i	0.983342	−	0.181766i	$-0.0581815\pi$
$444$		0			0
$445$	3.46410	+	6.00000i	0.164214	+	0.284427i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			12.9038i			0.608967i	0.952518	+	0.304484i	$0.0984839\pi$
$449$			12.9038i			0.608967i	−0.952518	+	0.304484i	$0.901516\pi$
$450$		0			0
$451$			8.00000i			0.376705i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.341773	−	0.591968i	−0.0160225	−	0.0277519i
$456$		0			0
$457$	17.3923	−	30.1244i	0.813578	−	1.40916i	−0.0967670	−	0.995307i	$-0.530850\pi$
$457$	17.3923	−	30.1244i	0.813578	−	1.40916i	0.910345	−	0.413851i	$-0.135817\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	22.2856	+	12.8666i	1.03795	+	0.599258i	0.919251	−	0.393672i	$-0.128796\pi$
$461$	22.2856	+	12.8666i	1.03795	+	0.599258i	0.118695	+	0.992931i	$0.462129\pi$
$462$		0			0
$463$	−27.0167	+	15.5981i	−1.25557	+	0.724904i	−0.972210	−	0.234109i	$-0.924783\pi$
$463$	−27.0167	+	15.5981i	−1.25557	+	0.724904i	−0.283360	+	0.959013i	$0.591449\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−38.3596			−1.77507			−0.887536	−	0.460738i	$-0.847585\pi$
$467$	−38.3596			−1.77507			−0.887536	+	0.460738i	$0.847585\pi$
$468$		0			0
$469$	−2.60770			−0.120412
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−24.9754	+	14.4195i	−1.14837	+	0.663011i
$474$		0			0
$475$	5.89230	+	3.40192i	0.270357	+	0.156091i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.45001	+	12.9038i	−0.340399	+	0.589589i	−0.984507	−	0.175346i	$-0.943896\pi$
$479$	−7.45001	+	12.9038i	−0.340399	+	0.589589i	0.644107	+	0.764935i	$0.277229\pi$
$480$		0			0
$481$	−7.96410	−	13.7942i	−0.363132	−	0.628963i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	7.24693i		−	0.329066i
$486$		0			0
$487$			23.4449i			1.06239i	0.847250	+	0.531194i	$0.178257\pi$
$487$			23.4449i			1.06239i	−0.847250	+	0.531194i	$0.821743\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.86611	−	13.6245i	−0.354992	−	0.614865i	0.632124	−	0.774867i	$-0.282183\pi$
$491$	−7.86611	−	13.6245i	−0.354992	−	0.614865i	−0.987117	+	0.160002i	$0.948850\pi$
$492$		0			0
$493$	6.92820	−	12.0000i	0.312031	−	0.540453i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.62536	+	1.51575i	0.117763	+	0.0679907i
$498$		0			0
$499$	−10.8564	+	6.26795i	−0.485999	+	0.280592i	−0.722913	−	0.690939i	$-0.757197\pi$
$499$	−10.8564	+	6.26795i	−0.485999	+	0.280592i	0.236914	+	0.971531i	$0.423864\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−29.1165			−1.29824			−0.649120	−	0.760686i	$-0.724863\pi$
$503$	−29.1165			−1.29824			−0.649120	+	0.760686i	$0.724863\pi$
$504$		0			0
$505$	16.0000			0.711991
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.0740	+	9.28032i	−0.712467	+	0.411343i	−0.811974	−	0.583694i	$-0.801607\pi$
$509$	−16.0740	+	9.28032i	−0.712467	+	0.411343i	0.0995068	+	0.995037i	$0.468273\pi$
$510$		0			0
$511$	2.30385	+	1.33013i	0.101916	+	0.0588414i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.10446	+	15.7694i	−0.401190	+	0.694882i
$516$		0			0
$517$	−18.3923	−	31.8564i	−0.808893	−	1.40104i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			37.6018i			1.64736i	0.567053	+	0.823681i	$0.308084\pi$
$521$			37.6018i			1.64736i	−0.567053	+	0.823681i	$0.691916\pi$
$522$		0			0
$523$		−	10.8038i		−	0.472419i	−0.971702	−	0.236210i	$-0.924095\pi$
$523$		−	10.8038i		−	0.472419i	0.971702	−	0.236210i	$-0.0759052\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.79315	−	3.10583i	−0.0781109	−	0.135292i
$528$		0			0
$529$	−6.10770	+	10.5788i	−0.265552	+	0.459949i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−4.41851	−	2.55103i	−0.191387	−	0.110497i
$534$		0			0
$535$	−13.6077	+	7.85641i	−0.588312	+	0.339662i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.7685			−1.15300
$540$		0			0
$541$	14.6077			0.628034			0.314017	−	0.949417i	$-0.398325\pi$
$541$	14.6077			0.628034			0.314017	+	0.949417i	$0.398325\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.832204	−	0.480473i	0.0356477	−	0.0205812i
$546$		0			0
$547$	4.96410	+	2.86603i	0.212250	+	0.122542i	0.602356	−	0.798227i	$-0.294229\pi$
$547$	4.96410	+	2.86603i	0.212250	+	0.122542i	−0.390107	+	0.920770i	$0.627562\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.79315	−	3.10583i	0.0763908	−	0.132313i
$552$		0			0
$553$	2.03590	+	3.52628i	0.0865752	+	0.149953i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			10.2784i			0.435511i	0.976003	+	0.217756i	$0.0698736\pi$
$557$			10.2784i			0.435511i	−0.976003	+	0.217756i	$0.930126\pi$
$558$		0			0
$559$		−	18.3923i		−	0.777912i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.52056	−	16.4901i	−0.401244	−	0.694974i	0.592633	−	0.805473i	$-0.298089\pi$
$563$	−9.52056	−	16.4901i	−0.401244	−	0.694974i	−0.993876	+	0.110498i	$0.964755\pi$
$564$		0			0
$565$	−4.53590	+	7.85641i	−0.190827	+	0.330522i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	33.3963	+	19.2814i	1.40004	+	0.808316i	0.994397	−	0.105713i	$-0.0337125\pi$
$569$	33.3963	+	19.2814i	1.40004	+	0.808316i	0.405648	+	0.914029i	$0.367046\pi$
$570$		0			0
$571$	19.9641	−	11.5263i	0.835472	−	0.482360i	−0.0202508	−	0.999795i	$-0.506446\pi$
$571$	19.9641	−	11.5263i	0.835472	−	0.482360i	0.855722	+	0.517435i	$0.173113\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−23.3110			−0.972134
$576$		0			0
$577$	−26.0718			−1.08538			−0.542692	−	0.839932i	$-0.682595\pi$
$577$	−26.0718			−1.08538			−0.542692	+	0.839932i	$0.682595\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.79315	−	1.03528i	0.0743924	−	0.0429505i
$582$		0			0
$583$	−44.7846	−	25.8564i	−1.85479	−	1.07086i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.138701	+	0.240237i	−0.00572479	+	0.00991563i	−0.868874	−	0.495034i	$-0.835156\pi$
$587$	−0.138701	+	0.240237i	−0.00572479	+	0.00991563i	0.863149	+	0.504950i	$0.168489\pi$
$588$		0			0
$589$	−0.464102	−	0.803848i	−0.0191230	−	0.0331220i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	25.8076i		−	1.05979i	−0.848063	−	0.529895i	$-0.822231\pi$
$593$		−	25.8076i		−	1.05979i	0.848063	−	0.529895i	$-0.177769\pi$
$594$		0			0
$595$			1.85641i			0.0761052i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.93426	+	10.2784i	0.242467	+	0.419965i	0.961416	−	0.275097i	$-0.0887100\pi$
$599$	5.93426	+	10.2784i	0.242467	+	0.419965i	−0.718949	+	0.695062i	$0.755377\pi$
$600$		0			0
$601$	−3.39230	+	5.87564i	−0.138375	+	0.239673i	−0.926882	−	0.375354i	$-0.877521\pi$
$601$	−3.39230	+	5.87564i	−0.138375	+	0.239673i	0.788507	+	0.615026i	$0.210855\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.52193	+	2.03339i	0.143187	+	0.0826690i
$606$		0			0
$607$	9.23205	−	5.33013i	0.374717	−	0.216343i	−0.300800	−	0.953687i	$-0.597254\pi$
$607$	9.23205	−	5.33013i	0.374717	−	0.216343i	0.675517	+	0.737344i	$0.263920\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	23.4596			0.949075
$612$		0			0
$613$	−37.3923			−1.51026			−0.755130	−	0.655575i	$-0.772427\pi$
$613$	−37.3923			−1.51026			−0.755130	+	0.655575i	$0.772427\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−8.42091	+	4.86181i	−0.339013	+	0.195729i	−0.659836	−	0.751410i	$-0.729374\pi$
$617$	−8.42091	+	4.86181i	−0.339013	+	0.195729i	0.320822	+	0.947139i	$0.396041\pi$
$618$		0			0
$619$	0.571797	+	0.330127i	0.0229825	+	0.0132689i	0.511447	−	0.859315i	$-0.329110\pi$
$619$	0.571797	+	0.330127i	0.0229825	+	0.0132689i	−0.488465	+	0.872584i	$0.662443\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.896575	−	1.55291i	0.0359205	−	0.0622162i
$624$		0			0
$625$	−5.03590	−	8.72243i	−0.201436	−	0.348897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			43.2586i			1.72483i
$630$		0			0
$631$		−	19.9808i		−	0.795422i	−0.917511	−	0.397711i	$-0.869805\pi$
$631$		−	19.9808i		−	0.795422i	0.917511	−	0.397711i	$-0.130195\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.79315	+	3.10583i	0.0711590	+	0.123251i
$636$		0			0
$637$	8.53590	−	14.7846i	0.338205	−	0.585788i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−36.5665	−	21.1117i	−1.44429	−	0.833861i	−0.446157	−	0.894955i	$-0.647208\pi$
$641$	−36.5665	−	21.1117i	−1.44429	−	0.833861i	−0.998132	+	0.0610939i	$0.980541\pi$
$642$		0			0
$643$	15.2487	−	8.80385i	0.601350	−	0.347190i	−0.168222	−	0.985749i	$-0.553803\pi$
$643$	15.2487	−	8.80385i	0.601350	−	0.347190i	0.769573	+	0.638559i	$0.220469\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.1822			0.911387			0.455694	−	0.890137i	$-0.349391\pi$
$647$	23.1822			0.911387			0.455694	+	0.890137i	$0.349391\pi$
$648$		0			0
$649$	28.7846			1.12989
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.96575	+	5.17638i	−0.350857	+	0.202567i	−0.665063	−	0.746788i	$-0.731595\pi$
$653$	−8.96575	+	5.17638i	−0.350857	+	0.202567i	0.314206	+	0.949355i	$0.398262\pi$
$654$		0			0
$655$	6.92820	+	4.00000i	0.270707	+	0.156293i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.2480	+	29.8744i	−0.671885	+	1.16374i	0.305484	+	0.952197i	$0.401182\pi$
$659$	−17.2480	+	29.8744i	−0.671885	+	1.16374i	−0.977369	+	0.211542i	$0.932151\pi$
$660$		0			0
$661$	21.6244	+	37.4545i	0.841090	+	1.45681i	0.888974	+	0.457958i	$0.151419\pi$
$661$	21.6244	+	37.4545i	0.841090	+	1.45681i	−0.0478841	+	0.998853i	$0.515248\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			0.480473i			0.0186320i
$666$		0			0
$667$			12.2872i			0.475762i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−18.1445	−	31.4273i	−0.700462	−	1.21324i
$672$		0			0
$673$	−10.4282	+	18.0622i	−0.401978	+	0.696246i	−0.993965	−	0.109702i	$-0.965010\pi$
$673$	−10.4282	+	18.0622i	−0.401978	+	0.696246i	0.591987	+	0.805948i	$0.298344\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.6993	+	10.7961i	0.718674	+	0.414927i	0.814264	−	0.580494i	$-0.197141\pi$
$677$	18.6993	+	10.7961i	0.718674	+	0.414927i	−0.0955904	+	0.995421i	$0.530474\pi$
$678$		0			0
$679$	−1.62436	+	0.937822i	−0.0623370	+	0.0359903i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−33.9411			−1.29872			−0.649361	−	0.760481i	$-0.724963\pi$
$683$	−33.9411			−1.29872			−0.649361	+	0.760481i	$0.724963\pi$
$684$		0			0
$685$	11.2154			0.428518
$686$		0			0
$687$		0			0
$688$		0			0
$689$	28.5617	−	16.4901i	1.08811	−	0.628222i
$690$		0			0
$691$	26.3205	+	15.1962i	1.00128	+	0.578089i	0.908627	−	0.417610i	$-0.137132\pi$
$691$	26.3205	+	15.1962i	1.00128	+	0.578089i	0.0926528	+	0.995698i	$0.470465\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.619174	+	1.07244i	−0.0234866	+	0.0406800i
$696$		0			0
$697$	6.92820	+	12.0000i	0.262424	+	0.454532i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			49.4703i			1.86847i	0.356663	+	0.934233i	$0.383914\pi$
$701$			49.4703i			1.86847i	−0.356663	+	0.934233i	$0.616086\pi$
$702$		0			0
$703$			11.1962i			0.422271i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.07055	−	3.58630i	−0.0778711	−	0.134877i
$708$		0			0
$709$	−6.08846	+	10.5455i	−0.228657	+	0.396045i	−0.957410	−	0.288731i	$-0.906767\pi$
$709$	−6.08846	+	10.5455i	−0.228657	+	0.396045i	0.728753	+	0.684776i	$0.240100\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.75410	+	1.59008i	0.103142	+	0.0595489i
$714$		0			0
$715$	−8.53590	+	4.92820i	−0.319225	+	0.184304i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.58630			0.133746			0.0668732	−	0.997761i	$-0.478698\pi$
$719$	3.58630			0.133746			0.0668732	+	0.997761i	$0.478698\pi$
$720$		0			0
$721$	4.71281			0.175514
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.04386	+	4.06678i	−0.261602	+	0.151036i
$726$		0			0
$727$	18.4641	+	10.6603i	0.684796	+	0.395367i	0.801659	−	0.597781i	$-0.203951\pi$
$727$	18.4641	+	10.6603i	0.684796	+	0.395367i	−0.116864	+	0.993148i	$0.537284\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−24.9754	+	43.2586i	−0.923747	+	1.59998i
$732$		0			0
$733$	16.4641	+	28.5167i	0.608115	+	1.05329i	0.991551	+	0.129719i	$0.0414076\pi$
$733$	16.4641	+	28.5167i	0.608115	+	1.05329i	−0.383435	+	0.923568i	$0.625259\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			37.6018i			1.38508i
$738$		0			0
$739$		−	14.3923i		−	0.529429i	−0.964327	−	0.264715i	$-0.914722\pi$
$739$		−	14.3923i		−	0.529429i	0.964327	−	0.264715i	$-0.0852778\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.7651	−	22.1098i	−0.468306	−	0.811129i	0.531038	−	0.847348i	$-0.321802\pi$
$743$	−12.7651	−	22.1098i	−0.468306	−	0.811129i	−0.999344	+	0.0362187i	$0.988469\pi$
$744$		0			0
$745$	−5.85641	+	10.1436i	−0.214562	+	0.371633i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.52193	+	2.03339i	0.128689	+	0.0742984i
$750$		0			0
$751$	−2.76795	+	1.59808i	−0.101004	+	0.0583146i	−0.549651	−	0.835394i	$-0.685239\pi$
$751$	−2.76795	+	1.59808i	−0.101004	+	0.0583146i	0.448647	+	0.893709i	$0.351906\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.55961			−0.311516
$756$		0			0
$757$	−5.39230			−0.195987			−0.0979933	−	0.995187i	$-0.531242\pi$
$757$	−5.39230			−0.195987			−0.0979933	+	0.995187i	$0.531242\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	37.9435	−	21.9067i	1.37545	−	0.794118i	0.383844	−	0.923398i	$-0.374600\pi$
$761$	37.9435	−	21.9067i	1.37545	−	0.794118i	0.991608	+	0.129281i	$0.0412668\pi$
$762$		0			0
$763$	−0.215390	−	0.124356i	−0.00779765	−	0.00450198i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.17878	+	15.8981i	−0.331427	+	0.574048i
$768$		0			0
$769$	−6.42820	−	11.1340i	−0.231807	−	0.401501i	0.726533	−	0.687132i	$-0.241130\pi$
$769$	−6.42820	−	11.1340i	−0.231807	−	0.401501i	−0.958340	+	0.285630i	$0.907797\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	20.5569i		−	0.739379i	−0.929155	−	0.369690i	$-0.879464\pi$
$773$		−	20.5569i		−	0.739379i	0.929155	−	0.369690i	$-0.120536\pi$
$774$		0			0
$775$			2.10512i			0.0756181i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.79315	+	3.10583i	0.0642463	+	0.111278i
$780$		0			0
$781$	21.8564	−	37.8564i	0.782084	−	1.35461i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.75410	−	1.59008i	−0.0982980	−	0.0567524i
$786$		0			0
$787$	26.2128	−	15.1340i	0.934386	−	0.539468i	0.0461899	−	0.998933i	$-0.485292\pi$
$787$	26.2128	−	15.1340i	0.934386	−	0.539468i	0.888196	+	0.459465i	$0.151959\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.34795			0.0834836
$792$		0			0
$793$	23.1436			0.821853
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.62536	+	1.51575i	−0.0929949	+	0.0536906i	−0.545776	−	0.837931i	$-0.683765\pi$
$797$	−2.62536	+	1.51575i	−0.0929949	+	0.0536906i	0.452781	+	0.891622i	$0.350432\pi$
$798$		0			0
$799$	−55.1769	−	31.8564i	−1.95202	−	1.12700i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	19.1798	−	33.2204i	0.676841	−	1.17232i
$804$		0			0
$805$	−0.823085	−	1.42563i	−0.0290100	−	0.0502467i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			19.5959i			0.688956i	0.938794	+	0.344478i	$0.111944\pi$
$809$			19.5959i			0.688956i	−0.938794	+	0.344478i	$0.888056\pi$
$810$		0			0
$811$			15.4641i			0.543018i	0.962436	+	0.271509i	$0.0875227\pi$
$811$			15.4641i			0.543018i	−0.962436	+	0.271509i	$0.912477\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.06918	+	13.9762i	0.282651	+	0.489566i
$816$		0			0
$817$	−6.46410	+	11.1962i	−0.226150	+	0.391704i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−18.6993	−	10.7961i	−0.652612	−	0.376785i	0.136845	−	0.990593i	$-0.456304\pi$
$821$	−18.6993	−	10.7961i	−0.652612	−	0.376785i	−0.789456	+	0.613807i	$0.789637\pi$
$822$		0			0
$823$	−34.6244	+	19.9904i	−1.20693	+	0.696821i	−0.962087	−	0.272742i	$-0.912069\pi$
$823$	−34.6244	+	19.9904i	−1.20693	+	0.696821i	−0.244842	+	0.969563i	$0.578736\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	54.3692			1.89060			0.945302	−	0.326196i	$-0.105767\pi$
$827$	54.3692			1.89060			0.945302	+	0.326196i	$0.105767\pi$
$828$		0			0
$829$	15.6795			0.544571			0.272286	−	0.962216i	$-0.412220\pi$
$829$	15.6795			0.544571			0.272286	+	0.962216i	$0.412220\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−40.1528	+	23.1822i	−1.39121	+	0.803216i
$834$		0			0
$835$	2.10512	+	1.21539i	0.0728506	+	0.0420603i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−26.4911	+	45.8840i	−0.914575	+	1.58409i	−0.107053	+	0.994253i	$0.534141\pi$
$839$	−26.4911	+	45.8840i	−0.914575	+	1.58409i	−0.807522	+	0.589837i	$0.799192\pi$
$840$		0			0
$841$	−12.3564	−	21.4019i	−0.426083	−	0.737997i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			7.17260i			0.246745i
$846$		0			0
$847$		−	1.05256i		−	0.0361664i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−19.1798	−	33.2204i	−0.657476	−	1.13878i
$852$		0			0
$853$	−13.3038	+	23.0429i	−0.455515	+	0.788975i	−0.998718	−	0.0506264i	$-0.983878\pi$
$853$	−13.3038	+	23.0429i	−0.455515	+	0.788975i	0.543203	+	0.839602i	$0.317212\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−32.9802	−	19.0411i	−1.12658	−	0.650432i	−0.183509	−	0.983018i	$-0.558745\pi$
$857$	−32.9802	−	19.0411i	−1.12658	−	0.650432i	−0.943073	+	0.332586i	$0.892079\pi$
$858$		0			0
$859$	−16.0359	+	9.25833i	−0.547138	+	0.315890i	−0.747967	−	0.663736i	$-0.768970\pi$
$859$	−16.0359	+	9.25833i	−0.547138	+	0.315890i	0.200829	+	0.979626i	$0.435636\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.6302			−0.361855			−0.180927	−	0.983496i	$-0.557910\pi$
$863$	−10.6302			−0.361855			−0.180927	+	0.983496i	$0.557910\pi$
$864$		0			0
$865$	9.56922			0.325363
$866$		0			0
$867$		0			0
$868$		0			0
$869$	50.8473	−	29.3567i	1.72488	−	0.995858i
$870$		0			0
$871$	−20.7679	−	11.9904i	−0.703695	−	0.406279i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.23835	−	2.14488i	0.0418638	−	0.0725102i
$876$		0			0
$877$	−12.6244	−	21.8660i	−0.426294	−	0.738363i	0.570246	−	0.821474i	$-0.306848\pi$
$877$	−12.6244	−	21.8660i	−0.426294	−	0.738363i	−0.996540	+	0.0831107i	$0.973514\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	12.9038i		−	0.434740i	−0.976089	−	0.217370i	$-0.930252\pi$
$881$		−	12.9038i		−	0.434740i	0.976089	−	0.217370i	$-0.0697478\pi$
$882$		0			0
$883$			24.1244i			0.811849i	0.913907	+	0.405925i	$0.133050\pi$
$883$			24.1244i			0.811849i	−0.913907	+	0.405925i	$0.866950\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.93426	−	10.2784i	−0.199253	−	0.345116i	0.749034	−	0.662532i	$-0.230518\pi$
$887$	−5.93426	−	10.2784i	−0.199253	−	0.345116i	−0.948286	+	0.317416i	$0.897185\pi$
$888$		0			0
$889$	0.464102	−	0.803848i	0.0155655	−	0.0269602i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−14.2808	−	8.24504i	−0.477890	−	0.275910i
$894$		0			0
$895$	−17.5692	+	10.1436i	−0.587274	+	0.339063i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.10961			0.0370074
$900$		0			0
$901$	−89.5692			−2.98398
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.79555	−	3.34607i	0.192651	−	0.111227i
$906$		0			0
$907$	47.2128	+	27.2583i	1.56768	+	0.905098i	0.996439	+	0.0843124i	$0.0268694\pi$
$907$	47.2128	+	27.2583i	1.56768	+	0.905098i	0.571236	+	0.820786i	$0.306464\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.277401	+	0.480473i	−0.00919072	+	0.0159188i	−0.870584	−	0.492019i	$-0.836259\pi$
$911$	−0.277401	+	0.480473i	−0.00919072	+	0.0159188i	0.861393	+	0.507938i	$0.169592\pi$
$912$		0			0
$913$	−14.9282	−	25.8564i	−0.494051	−	0.855722i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	2.07055i		−	0.0683757i
$918$		0			0
$919$		−	57.0333i		−	1.88136i	−0.339301	−	0.940678i	$-0.610191\pi$
$919$		−	57.0333i		−	1.88136i	0.339301	−	0.940678i	$-0.389809\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.9391	+	24.1432i	0.458810	+	0.794682i
$924$		0			0
$925$	12.6962	−	21.9904i	0.417447	−	0.723039i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	19.5959	+	11.3137i	0.642921	+	0.371191i	0.785739	−	0.618558i	$-0.212283\pi$
$929$	19.5959	+	11.3137i	0.642921	+	0.371191i	−0.142818	+	0.989749i	$0.545616\pi$
$930$		0			0
$931$	−10.3923	+	6.00000i	−0.340594	+	0.196642i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	26.7685			0.875424
$936$		0			0
$937$	6.21539			0.203048			0.101524	−	0.994833i	$-0.467628\pi$
$937$	6.21539			0.203048			0.101524	+	0.994833i	$0.467628\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.6651	−	15.9725i	0.901856	−	0.520687i	0.0240544	−	0.999711i	$-0.492343\pi$
$941$	27.6651	−	15.9725i	0.901856	−	0.520687i	0.877802	+	0.479024i	$0.159009\pi$
$942$		0			0
$943$	−10.6410	−	6.14359i	−0.346519	−	0.200063i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.138701	−	0.240237i	0.00450717	−	0.00780664i	−0.863763	−	0.503898i	$-0.831899\pi$
$947$	0.138701	−	0.240237i	0.00450717	−	0.00780664i	0.868270	+	0.496092i	$0.165232\pi$
$948$		0			0
$949$	12.2321	+	21.1865i	0.397069	+	0.687744i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			12.9038i			0.417995i	0.977916	+	0.208997i	$0.0670200\pi$
$953$			12.9038i			0.417995i	−0.977916	+	0.208997i	$0.932980\pi$
$954$		0			0
$955$		−	14.1436i		−	0.457676i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.45138	−	2.51386i	−0.0468674	−	0.0811768i
$960$		0			0
$961$	−15.3564	+	26.5981i	−0.495368	+	0.858002i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.0643712	+	0.0371647i	0.00207218	+	0.00119638i
$966$		0			0
$967$	10.1603	−	5.86603i	0.326732	−	0.188639i	−0.327657	−	0.944797i	$-0.606259\pi$
$967$	10.1603	−	5.86603i	0.326732	−	0.188639i	0.654389	+	0.756158i	$0.272926\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	46.6418			1.49681			0.748404	−	0.663243i	$-0.230820\pi$
$971$	46.6418			1.49681			0.748404	+	0.663243i	$0.230820\pi$
$972$		0			0
$973$	0.320508			0.0102750
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.00481	−	4.62158i	0.256096	−	0.147857i	−0.366456	−	0.930435i	$-0.619429\pi$
$977$	8.00481	−	4.62158i	0.256096	−	0.147857i	0.622553	+	0.782578i	$0.286096\pi$
$978$		0			0
$979$	−22.3923	−	12.9282i	−0.715661	−	0.413187i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.0082	−	38.1194i	0.701954	−	1.21582i	−0.265826	−	0.964021i	$-0.585645\pi$
$983$	22.0082	−	38.1194i	0.701954	−	1.21582i	0.967780	−	0.251799i	$-0.0810221\pi$
$984$		0			0
$985$	−7.46410	−	12.9282i	−0.237826	−	0.411927i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	44.2939i		−	1.40846i
$990$		0			0
$991$		−	7.48334i		−	0.237716i	−0.992911	−	0.118858i	$-0.962077\pi$
$991$		−	7.48334i		−	0.237716i	0.992911	−	0.118858i	$-0.0379233\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−13.2456	−	22.9420i	−0.419912	−	0.727310i
$996$		0			0
$997$	3.39230	−	5.87564i	0.107435	−	0.186084i	−0.807295	−	0.590148i	$-0.799069\pi$
$997$	3.39230	−	5.87564i	0.107435	−	0.186084i	0.914731	+	0.404064i	$0.132403\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.c.1727.2		8
3.2	odd	2	inner	2592.2.s.c.1727.3		8
4.3	odd	2		2592.2.s.g.1727.2		8
9.2	odd	6		864.2.c.b.863.5	yes	8
9.4	even	3		2592.2.s.g.863.3		8
9.5	odd	6		2592.2.s.g.863.2		8
9.7	even	3		864.2.c.b.863.3	✓	8
12.11	even	2		2592.2.s.g.1727.3		8
36.7	odd	6		864.2.c.b.863.4	yes	8
36.11	even	6		864.2.c.b.863.6	yes	8
36.23	even	6	inner	2592.2.s.c.863.2		8
36.31	odd	6	inner	2592.2.s.c.863.3		8
72.11	even	6		1728.2.c.f.1727.4		8
72.29	odd	6		1728.2.c.f.1727.3		8
72.43	odd	6		1728.2.c.f.1727.6		8
72.61	even	6		1728.2.c.f.1727.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.c.b.863.3	✓	8	9.7	even	3
864.2.c.b.863.4	yes	8	36.7	odd	6
864.2.c.b.863.5	yes	8	9.2	odd	6
864.2.c.b.863.6	yes	8	36.11	even	6
1728.2.c.f.1727.3		8	72.29	odd	6
1728.2.c.f.1727.4		8	72.11	even	6
1728.2.c.f.1727.5		8	72.61	even	6
1728.2.c.f.1727.6		8	72.43	odd	6
2592.2.s.c.863.2		8	36.23	even	6	inner
2592.2.s.c.863.3		8	36.31	odd	6	inner
2592.2.s.c.1727.2		8	1.1	even	1	trivial
2592.2.s.c.1727.3		8	3.2	odd	2	inner
2592.2.s.g.863.2		8	9.5	odd	6
2592.2.s.g.863.3		8	9.4	even	3
2592.2.s.g.1727.2		8	4.3	odd	2
2592.2.s.g.1727.3		8	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.896575 + 0.517638i) q^{5} +(0.232051 + 0.133975i) q^{7} +O(q^{10})\)	\(q+(-0.896575 + 0.517638i) q^{5} +(0.232051 + 0.133975i) q^{7} +(1.93185 - 3.34607i) q^{11} +(1.23205 + 2.13397i) q^{13} -6.69213i q^{17} -1.73205i q^{19} +(2.96713 + 5.13922i) q^{23} +(-1.96410 + 3.40192i) q^{25} +(1.79315 + 1.03528i) q^{29} +(0.464102 - 0.267949i) q^{31} -0.277401 q^{35} -6.46410 q^{37} +(-1.79315 + 1.03528i) q^{41} +(-6.46410 - 3.73205i) q^{43} +(4.76028 - 8.24504i) q^{47} +(-3.46410 - 6.00000i) q^{49} -13.3843i q^{53} +4.00000i q^{55} +(3.72500 + 6.45189i) q^{59} +(4.69615 - 8.13397i) q^{61} +(-2.20925 - 1.27551i) q^{65} +(-8.42820 + 4.86603i) q^{67} +11.3137 q^{71} +9.92820 q^{73} +(0.896575 - 0.517638i) q^{77} +(13.1603 + 7.59808i) q^{79} +(3.86370 - 6.69213i) q^{83} +(3.46410 + 6.00000i) q^{85} -6.69213i q^{89} +0.660254i q^{91} +(0.896575 + 1.55291i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{7}+O(q^{10}) \) 8 * q - 12 * q^7	\( 8 q - 12 q^{7} - 4 q^{13} + 12 q^{25} - 24 q^{31} - 24 q^{37} - 24 q^{43} - 4 q^{61} - 12 q^{67} + 24 q^{73} + 36 q^{79} - 28 q^{97}+O(q^{100}) \) 8 * q - 12 * q^7 - 4 * q^13 + 12 * q^25 - 24 * q^31 - 24 * q^37 - 24 * q^43 - 4 * q^61 - 12 * q^67 + 24 * q^73 + 36 * q^79 - 28 * q^97

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