LMFDB - Embedded newform 2592.2.s.a.1727.4

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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 864)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1727.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2592.1727
Dual form			2592.2.s.a.863.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.275255 + 0.158919i) q^{5} +(1.25529 + 0.724745i) q^{7} +O(q^{10})$	$q+(-0.275255 + 0.158919i) q^{5} +(1.25529 + 0.724745i) q^{7} +(-0.548188 + 0.949490i) q^{11} +(-1.44949 - 2.51059i) q^{13} +3.46410i q^{17} -4.89898i q^{19} +(1.41421 + 2.44949i) q^{23} +(-2.44949 + 4.24264i) q^{25} +(7.89898 + 4.56048i) q^{29} +(-6.45145 + 3.72474i) q^{31} -0.460702 q^{35} +4.89898 q^{37} +(8.44949 - 4.87832i) q^{41} +(5.97469 + 3.44949i) q^{43} +(-4.56048 + 7.89898i) q^{47} +(-2.44949 - 4.24264i) q^{49} -4.41761i q^{53} -0.348469i q^{55} +(4.56048 + 7.89898i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(0.797959 + 0.460702i) q^{65} +(4.41761 - 2.55051i) q^{67} -7.56388 q^{71} +1.89898 q^{73} +(-1.37628 + 0.794593i) q^{77} +(-1.73205 - 1.00000i) q^{79} +(-7.93709 + 13.7474i) q^{83} +(-0.550510 - 0.953512i) q^{85} +11.9494i q^{89} -4.20204i q^{91} +(0.778539 + 1.34847i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5}+O(q^{10}) $ 8 * q - 12 * q^5	$ 8 q - 12 q^{5} + 8 q^{13} + 24 q^{29} + 48 q^{41} - 16 q^{61} - 72 q^{65} - 24 q^{73} - 60 q^{77} - 24 q^{85} + 20 q^{97}+O(q^{100}) $ 8 * q - 12 * q^5 + 8 * q^13 + 24 * q^29 + 48 * q^41 - 16 * q^61 - 72 * q^65 - 24 * q^73 - 60 * q^77 - 24 * q^85 + 20 * 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
$5$	−0.275255	+	0.158919i	−0.123098	+	0.0710706i	−0.560285	−	0.828300i	$-0.689308\pi$
$5$	−0.275255	+	0.158919i	−0.123098	+	0.0710706i	0.437187	+	0.899371i	$0.355975\pi$
$6$		0			0
$7$	1.25529	+	0.724745i	0.474457	+	0.273928i	0.718104	−	0.695936i	$-0.245010\pi$
$7$	1.25529	+	0.724745i	0.474457	+	0.273928i	−0.243647	+	0.969864i	$0.578344\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.548188	+	0.949490i	−0.165285	+	0.286282i	−0.936756	−	0.349982i	$-0.886188\pi$
$11$	−0.548188	+	0.949490i	−0.165285	+	0.286282i	0.771471	+	0.636264i	$0.219521\pi$
$12$		0			0
$13$	−1.44949	−	2.51059i	−0.402016	−	0.696312i	0.591953	−	0.805972i	$-0.298357\pi$
$13$	−1.44949	−	2.51059i	−0.402016	−	0.696312i	−0.993969	+	0.109660i	$0.965024\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			3.46410i			0.840168i	0.907485	+	0.420084i	$0.137999\pi$
$17$			3.46410i			0.840168i	−0.907485	+	0.420084i	$0.862001\pi$
$18$		0			0
$19$		−	4.89898i		−	1.12390i	−0.827170	−	0.561951i	$-0.810051\pi$
$19$		−	4.89898i		−	1.12390i	0.827170	−	0.561951i	$-0.189949\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.41421	+	2.44949i	0.294884	+	0.510754i	0.974958	−	0.222390i	$-0.0713857\pi$
$23$	1.41421	+	2.44949i	0.294884	+	0.510754i	−0.680074	+	0.733144i	$0.738052\pi$
$24$		0			0
$25$	−2.44949	+	4.24264i	−0.489898	+	0.848528i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	7.89898	+	4.56048i	1.46680	+	0.846859i	0.999310	−	0.0371370i	$-0.0118238\pi$
$29$	7.89898	+	4.56048i	1.46680	+	0.846859i	0.467493	+	0.883997i	$0.345157\pi$
$30$		0			0
$31$	−6.45145	+	3.72474i	−1.15871	+	0.668984i	−0.950996	−	0.309205i	$-0.899937\pi$
$31$	−6.45145	+	3.72474i	−1.15871	+	0.668984i	−0.207719	+	0.978189i	$0.566604\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.460702			−0.0778728
$36$		0			0
$37$	4.89898			0.805387			0.402694	−	0.915335i	$-0.368074\pi$
$37$	4.89898			0.805387			0.402694	+	0.915335i	$0.368074\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.44949	−	4.87832i	1.31959	−	0.761865i	0.335926	−	0.941888i	$-0.390951\pi$
$41$	8.44949	−	4.87832i	1.31959	−	0.761865i	0.983662	+	0.180023i	$0.0576174\pi$
$42$		0			0
$43$	5.97469	+	3.44949i	0.911132	+	0.526042i	0.880795	−	0.473497i	$-0.157009\pi$
$43$	5.97469	+	3.44949i	0.911132	+	0.526042i	0.0303367	+	0.999540i	$0.490342\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.56048	+	7.89898i	−0.665214	+	1.15218i	0.314013	+	0.949419i	$0.398326\pi$
$47$	−4.56048	+	7.89898i	−0.665214	+	1.15218i	−0.979227	+	0.202766i	$0.935007\pi$
$48$		0			0
$49$	−2.44949	−	4.24264i	−0.349927	−	0.606092i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	4.41761i		−	0.606806i	−0.952862	−	0.303403i	$-0.901877\pi$
$53$		−	4.41761i		−	0.606806i	0.952862	−	0.303403i	$-0.0981228\pi$
$54$		0			0
$55$		−	0.348469i		−	0.0469876i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.56048	+	7.89898i	0.593724	+	1.02836i	0.993726	+	0.111845i	$0.0356761\pi$
$59$	4.56048	+	7.89898i	0.593724	+	1.02836i	−0.400002	+	0.916514i	$0.630991\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.797959	+	0.460702i	0.0989746	+	0.0571430i
$66$		0			0
$67$	4.41761	−	2.55051i	0.539697	−	0.311594i	−0.205259	−	0.978708i	$-0.565804\pi$
$67$	4.41761	−	2.55051i	0.539697	−	0.311594i	0.744956	+	0.667113i	$0.232470\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.56388			−0.897667			−0.448834	−	0.893615i	$-0.648160\pi$
$71$	−7.56388			−0.897667			−0.448834	+	0.893615i	$0.648160\pi$
$72$		0			0
$73$	1.89898			0.222259			0.111129	−	0.993806i	$-0.464553\pi$
$73$	1.89898			0.222259			0.111129	+	0.993806i	$0.464553\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.37628	+	0.794593i	−0.156841	+	0.0905523i
$78$		0			0
$79$	−1.73205	−	1.00000i	−0.194871	−	0.112509i	0.399390	−	0.916781i	$-0.369222\pi$
$79$	−1.73205	−	1.00000i	−0.194871	−	0.112509i	−0.594261	+	0.804272i	$0.702555\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.93709	+	13.7474i	−0.871209	+	1.50898i	−0.0104623	+	0.999945i	$0.503330\pi$
$83$	−7.93709	+	13.7474i	−0.871209	+	1.50898i	−0.860747	+	0.509033i	$0.830003\pi$
$84$		0			0
$85$	−0.550510	−	0.953512i	−0.0597112	−	0.103423i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			11.9494i			1.26663i	0.773893	+	0.633316i	$0.218307\pi$
$89$			11.9494i			1.26663i	−0.773893	+	0.633316i	$0.781693\pi$
$90$		0			0
$91$		−	4.20204i		−	0.440494i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.778539	+	1.34847i	0.0798764	+	0.138350i
$96$		0			0
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	13.6237	+	7.86566i	1.35561	+	0.782663i	0.989029	−	0.147723i	$-0.0471944\pi$
$101$	13.6237	+	7.86566i	1.35561	+	0.782663i	0.366582	+	0.930386i	$0.380528\pi$
$102$		0			0
$103$	−8.66025	+	5.00000i	−0.853320	+	0.492665i	−0.861770	−	0.507300i	$-0.830644\pi$
$103$	−8.66025	+	5.00000i	−0.853320	+	0.492665i	0.00844953	+	0.999964i	$0.497310\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.66025			−0.837218			−0.418609	−	0.908166i	$-0.637482\pi$
$107$	−8.66025			−0.837218			−0.418609	+	0.908166i	$0.637482\pi$
$108$		0			0
$109$	−4.89898			−0.469237			−0.234619	−	0.972088i	$-0.575384\pi$
$109$	−4.89898			−0.469237			−0.234619	+	0.972088i	$0.575384\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.2474	−	7.07107i	1.15214	−	0.665190i	0.202735	−	0.979234i	$-0.435017\pi$
$113$	12.2474	−	7.07107i	1.15214	−	0.665190i	0.949409	+	0.314044i	$0.101684\pi$
$114$		0			0
$115$	−0.778539	−	0.449490i	−0.0725991	−	0.0419151i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.51059	+	4.34847i	−0.230145	+	0.398624i
$120$		0			0
$121$	4.89898	+	8.48528i	0.445362	+	0.771389i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	3.14626i		−	0.281410i
$126$		0			0
$127$			15.2474i			1.35299i	0.736446	+	0.676496i	$0.236502\pi$
$127$			15.2474i			1.35299i	−0.736446	+	0.676496i	$0.763498\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.50170	−	2.60102i	−0.131204	−	0.227252i	0.792937	−	0.609304i	$-0.208551\pi$
$131$	−1.50170	−	2.60102i	−0.131204	−	0.227252i	−0.924141	+	0.382052i	$0.875218\pi$
$132$		0			0
$133$	3.55051	−	6.14966i	0.307868	−	0.533244i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.24745	+	5.33902i	0.790063	+	0.456143i	0.839985	−	0.542610i	$-0.182564\pi$
$137$	9.24745	+	5.33902i	0.790063	+	0.456143i	−0.0499218	+	0.998753i	$0.515897\pi$
$138$		0			0
$139$	17.3205	−	10.0000i	1.46911	−	0.848189i	0.469706	−	0.882823i	$-0.344360\pi$
$139$	17.3205	−	10.0000i	1.46911	−	0.848189i	0.999400	+	0.0346338i	$0.0110265\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.17837			0.265789
$144$		0			0
$145$	−2.89898			−0.240747
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.27526	−	1.89097i	0.268319	−	0.154914i	−0.359804	−	0.933028i	$-0.617157\pi$
$149$	3.27526	−	1.89097i	0.268319	−	0.154914i	0.628124	+	0.778114i	$0.283823\pi$
$150$		0			0
$151$	−14.9367	−	8.62372i	−1.21553	−	0.701789i	−0.251574	−	0.967838i	$-0.580948\pi$
$151$	−14.9367	−	8.62372i	−1.21553	−	0.701789i	−0.963959	+	0.266049i	$0.914282\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.18386	−	2.05051i	0.0950901	−	0.164701i
$156$		0			0
$157$	6.89898	+	11.9494i	0.550599	+	0.953665i	0.998231	+	0.0594472i	$0.0189338\pi$
$157$	6.89898	+	11.9494i	0.550599	+	0.953665i	−0.447633	+	0.894217i	$0.647733\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			4.09978i			0.323108i
$162$		0			0
$163$		−	6.00000i		−	0.469956i	−0.972001	−	0.234978i	$-0.924498\pi$
$163$		−	6.00000i		−	0.469956i	0.972001	−	0.234978i	$-0.0755019\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.4887	+	19.8990i	0.889021	+	1.53983i	0.841035	+	0.540981i	$0.181947\pi$
$167$	11.4887	+	19.8990i	0.889021	+	1.53983i	0.0479862	+	0.998848i	$0.484720\pi$
$168$		0			0
$169$	2.29796	−	3.98018i	0.176766	−	0.306168i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.62372	+	2.66951i	0.351535	+	0.202959i	0.665361	−	0.746522i	$-0.268278\pi$
$173$	4.62372	+	2.66951i	0.351535	+	0.202959i	−0.313826	+	0.949481i	$0.601611\pi$
$174$		0			0
$175$	−6.14966	+	3.55051i	−0.464871	+	0.268393i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	8.66025			0.647298			0.323649	−	0.946177i	$-0.395090\pi$
$179$	8.66025			0.647298			0.323649	+	0.946177i	$0.395090\pi$
$180$		0			0
$181$	−9.79796			−0.728277			−0.364138	−	0.931345i	$-0.618636\pi$
$181$	−9.79796			−0.728277			−0.364138	+	0.931345i	$0.618636\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.34847	+	0.778539i	−0.0991414	+	0.0572393i
$186$		0			0
$187$	−3.28913	−	1.89898i	−0.240525	−	0.138867i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.80312	+	15.2474i	−0.636971	+	1.10327i	0.349123	+	0.937077i	$0.386480\pi$
$191$	−8.80312	+	15.2474i	−0.636971	+	1.10327i	−0.986094	+	0.166190i	$0.946854\pi$
$192$		0			0
$193$	−1.05051	−	1.81954i	−0.0756174	−	0.130973i	0.825737	−	0.564055i	$-0.190759\pi$
$193$	−1.05051	−	1.81954i	−0.0756174	−	0.130973i	−0.901355	+	0.433082i	$0.857426\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			12.2672i			0.874003i	0.899461	+	0.437002i	$0.143960\pi$
$197$			12.2672i			0.874003i	−0.899461	+	0.437002i	$0.856040\pi$
$198$		0			0
$199$			20.3485i			1.44246i	0.692693	+	0.721232i	$0.256424\pi$
$199$			20.3485i			1.44246i	−0.692693	+	0.721232i	$0.743576\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.61037	+	11.4495i	0.463957	+	0.803597i
$204$		0			0
$205$	−1.55051	+	2.68556i	−0.108292	+	0.187568i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.65153	+	2.68556i	0.321753	+	0.185764i
$210$		0			0
$211$	24.6773	−	14.2474i	1.69886	−	0.980835i	0.752007	−	0.659155i	$-0.229086\pi$
$211$	24.6773	−	14.2474i	1.69886	−	0.980835i	0.946848	−	0.321680i	$-0.104248\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.19275			−0.149544
$216$		0			0
$217$	−10.7980			−0.733013
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.69694	−	5.02118i	0.585019	−	0.337761i
$222$		0			0
$223$	−0.174973	−	0.101021i	−0.0117170	−	0.00676483i	0.494130	−	0.869388i	$-0.335487\pi$
$223$	−0.174973	−	0.101021i	−0.0117170	−	0.00676483i	−0.505847	+	0.862623i	$0.668820\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.83183	+	10.1010i	−0.387072	+	0.670428i	−0.992054	−	0.125811i	$-0.959847\pi$
$227$	−5.83183	+	10.1010i	−0.387072	+	0.670428i	0.604982	+	0.796239i	$0.293180\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	13.2207i		−	0.866119i	−0.901365	−	0.433059i	$-0.857434\pi$
$233$		−	13.2207i		−	0.866119i	0.901365	−	0.433059i	$-0.142566\pi$
$234$		0			0
$235$		−	2.89898i		−	0.189109i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.5352	−	18.2474i	−0.681463	−	1.18033i	−0.974534	−	0.224239i	$-0.928011\pi$
$239$	−10.5352	−	18.2474i	−0.681463	−	1.18033i	0.293071	−	0.956091i	$-0.405323\pi$
$240$		0			0
$241$	9.89898	−	17.1455i	0.637649	−	1.10444i	−0.348298	−	0.937384i	$-0.613240\pi$
$241$	9.89898	−	17.1455i	0.637649	−	1.10444i	0.985947	−	0.167057i	$-0.0534264\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.34847	+	0.778539i	0.0861505	+	0.0497390i
$246$		0			0
$247$	−12.2993	+	7.10102i	−0.782588	+	0.451827i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.3205			−1.09326			−0.546630	−	0.837374i	$-0.684090\pi$
$251$	−17.3205			−1.09326			−0.546630	+	0.837374i	$0.684090\pi$
$252$		0			0
$253$	−3.10102			−0.194959
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.1010	+	5.83183i	−0.630084	+	0.363779i	−0.780785	−	0.624800i	$-0.785180\pi$
$257$	−10.1010	+	5.83183i	−0.630084	+	0.363779i	0.150700	+	0.988579i	$0.451847\pi$
$258$		0			0
$259$	6.14966	+	3.55051i	0.382122	+	0.220618i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	12.4422	−	21.5505i	0.767218	−	1.32886i	−0.171847	−	0.985124i	$-0.554974\pi$
$263$	12.4422	−	21.5505i	0.767218	−	1.32886i	0.939066	−	0.343738i	$-0.111693\pi$
$264$		0			0
$265$	0.702041	+	1.21597i	0.0431260	+	0.0746965i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			10.3923i			0.633630i	0.948487	+	0.316815i	$0.102613\pi$
$269$			10.3923i			0.633630i	−0.948487	+	0.316815i	$0.897387\pi$
$270$		0			0
$271$			12.5505i			0.762389i	0.924495	+	0.381195i	$0.124487\pi$
$271$			12.5505i			0.762389i	−0.924495	+	0.381195i	$0.875513\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.68556	−	4.65153i	−0.161946	−	0.280498i
$276$		0			0
$277$	6.89898	−	11.9494i	0.414520	−	0.717969i	−0.580858	−	0.814005i	$-0.697283\pi$
$277$	6.89898	−	11.9494i	0.414520	−	0.717969i	0.995378	+	0.0960358i	$0.0306163\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.797959	−	0.460702i	−0.0476022	−	0.0274832i	0.476010	−	0.879440i	$-0.342083\pi$
$281$	−0.797959	−	0.460702i	−0.0476022	−	0.0274832i	−0.523612	+	0.851957i	$0.675416\pi$
$282$		0			0
$283$	2.68556	−	1.55051i	0.159640	−	0.0921683i	−0.418052	−	0.908423i	$-0.637287\pi$
$283$	2.68556	−	1.55051i	0.159640	−	0.0921683i	0.577692	+	0.816255i	$0.303954\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.1421			0.834784
$288$		0			0
$289$	5.00000			0.294118
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.20204	−	3.00340i	0.303906	−	0.175460i	−0.340290	−	0.940321i	$-0.610525\pi$
$293$	5.20204	−	3.00340i	0.303906	−	0.175460i	0.644196	+	0.764860i	$0.277192\pi$
$294$		0			0
$295$	−2.51059	−	1.44949i	−0.146172	−	0.0843926i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.09978	−	7.10102i	0.237096	−	0.410663i
$300$		0			0
$301$	5.00000	+	8.66025i	0.288195	+	0.499169i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	1.27135i		−	0.0727972i
$306$		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
$311$	−2.04989	−	3.55051i	−0.116238	−	0.201331i	0.802036	−	0.597276i	$-0.203750\pi$
$311$	−2.04989	−	3.55051i	−0.116238	−	0.201331i	−0.918274	+	0.395945i	$0.870417\pi$
$312$		0			0
$313$	−14.7474	+	25.5433i	−0.833575	+	1.44379i	0.0616102	+	0.998100i	$0.480376\pi$
$313$	−14.7474	+	25.5433i	−0.833575	+	1.44379i	−0.895185	+	0.445694i	$0.852957\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−25.6237	−	14.7939i	−1.43917	−	0.830906i	−0.441380	−	0.897320i	$-0.645511\pi$
$317$	−25.6237	−	14.7939i	−1.43917	−	0.830906i	−0.997792	+	0.0664143i	$0.978844\pi$
$318$		0			0
$319$	−8.66025	+	5.00000i	−0.484881	+	0.279946i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	16.9706			0.944267
$324$		0			0
$325$	14.2020			0.787787
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.4495	+	6.61037i	−0.631231	+	0.364441i
$330$		0			0
$331$	0.603566	+	0.348469i	0.0331750	+	0.0191536i	0.516496	−	0.856290i	$-0.327236\pi$
$331$	0.603566	+	0.348469i	0.0331750	+	0.0191536i	−0.483321	+	0.875443i	$0.660570\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.810647	+	1.40408i	−0.0442904	+	0.0767132i
$336$		0			0
$337$	−2.10102	−	3.63907i	−0.114450	−	0.198233i	0.803110	−	0.595831i	$-0.203177\pi$
$337$	−2.10102	−	3.63907i	−0.114450	−	0.198233i	−0.917560	+	0.397598i	$0.869844\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	8.16744i		−	0.442292i
$342$		0			0
$343$		−	17.2474i		−	0.931275i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.74094	−	4.74745i	−0.147141	−	0.254856i	0.783028	−	0.621986i	$-0.213674\pi$
$347$	−2.74094	−	4.74745i	−0.147141	−	0.254856i	−0.930170	+	0.367130i	$0.880341\pi$
$348$		0			0
$349$	−12.4495	+	21.5631i	−0.666406	+	1.15425i	0.312496	+	0.949919i	$0.398835\pi$
$349$	−12.4495	+	21.5631i	−0.666406	+	1.15425i	−0.978902	+	0.204330i	$0.934498\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.2474	+	7.07107i	0.651866	+	0.376355i	0.789171	−	0.614174i	$-0.210511\pi$
$353$	12.2474	+	7.07107i	0.651866	+	0.376355i	−0.137305	+	0.990529i	$0.543844\pi$
$354$		0			0
$355$	2.08200	−	1.20204i	0.110501	−	0.0637977i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−34.2911			−1.80981			−0.904907	−	0.425610i	$-0.860060\pi$
$359$	−34.2911			−1.80981			−0.904907	+	0.425610i	$0.860060\pi$
$360$		0			0
$361$	−5.00000			−0.263158
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.522704	+	0.301783i	−0.0273596	+	0.0157961i
$366$		0			0
$367$	−7.40496	−	4.27526i	−0.386536	−	0.223167i	0.294122	−	0.955768i	$-0.404973\pi$
$367$	−7.40496	−	4.27526i	−0.386536	−	0.223167i	−0.680658	+	0.732601i	$0.738306\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.20164	−	5.54541i	0.166221	−	0.287903i
$372$		0			0
$373$	−17.2474	−	29.8735i	−0.893039	−	1.54679i	−0.836213	−	0.548405i	$-0.815235\pi$
$373$	−17.2474	−	29.8735i	−0.893039	−	1.54679i	−0.0568261	−	0.998384i	$-0.518098\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	26.4415i		−	1.36180i
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.87492	+	3.24745i	0.0958037	+	0.165937i	0.909944	−	0.414732i	$-0.136125\pi$
$383$	1.87492	+	3.24745i	0.0958037	+	0.165937i	−0.814140	+	0.580669i	$0.802791\pi$
$384$		0			0
$385$	0.252551	−	0.437432i	0.0128712	−	0.0222936i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−27.7702	−	16.0331i	−1.40800	−	0.812911i	−0.412807	−	0.910818i	$-0.635452\pi$
$389$	−27.7702	−	16.0331i	−1.40800	−	0.812911i	−0.995195	+	0.0979078i	$0.968785\pi$
$390$		0			0
$391$	−8.48528	+	4.89898i	−0.429119	+	0.247752i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.635674			0.0319843
$396$		0			0
$397$	8.69694			0.436487			0.218243	−	0.975894i	$-0.429967\pi$
$397$	8.69694			0.436487			0.218243	+	0.975894i	$0.429967\pi$
$398$		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
$403$	18.7026	+	10.7980i	0.931644	+	0.537885i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.68556	+	4.65153i	−0.133118	+	0.230568i
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			13.2207i			0.650550i
$414$		0			0
$415$		−	5.04541i		−	0.247669i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.0458	−	22.5959i	−0.637327	−	1.10388i	−0.986017	−	0.166645i	$-0.946707\pi$
$419$	−13.0458	−	22.5959i	−0.637327	−	1.10388i	0.348690	−	0.937238i	$-0.386627\pi$
$420$		0			0
$421$	14.8990	−	25.8058i	0.726132	−	1.25770i	−0.232375	−	0.972626i	$-0.574650\pi$
$421$	14.8990	−	25.8058i	0.726132	−	1.25770i	0.958506	−	0.285071i	$-0.0920171\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−14.6969	−	8.48528i	−0.712906	−	0.411597i
$426$		0			0
$427$	−5.02118	+	2.89898i	−0.242992	+	0.140291i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	27.3629			1.31802			0.659011	−	0.752133i	$-0.270975\pi$
$431$	27.3629			1.31802			0.659011	+	0.752133i	$0.270975\pi$
$432$		0			0
$433$	32.3939			1.55675			0.778375	−	0.627799i	$-0.216044\pi$
$433$	32.3939			1.55675			0.778375	+	0.627799i	$0.216044\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0000	−	6.92820i	0.574038	−	0.331421i
$438$		0			0
$439$	16.6688	+	9.62372i	0.795557	+	0.459315i	0.841915	−	0.539610i	$-0.181428\pi$
$439$	16.6688	+	9.62372i	0.795557	+	0.459315i	−0.0463579	+	0.998925i	$0.514761\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.3171	−	24.7980i	0.680226	−	1.17819i	−0.294685	−	0.955594i	$-0.595215\pi$
$443$	14.3171	−	24.7980i	0.680226	−	1.17819i	0.974912	−	0.222592i	$-0.0714518\pi$
$444$		0			0
$445$	−1.89898	−	3.28913i	−0.0900203	−	0.155920i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	22.3417i		−	1.05437i	−0.849751	−	0.527185i	$-0.823248\pi$
$449$		−	22.3417i		−	1.05437i	0.849751	−	0.527185i	$-0.176752\pi$
$450$		0			0
$451$			10.6969i			0.503699i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.667783	+	1.15663i	0.0313061	+	0.0542238i
$456$		0			0
$457$	−12.5000	+	21.6506i	−0.584725	+	1.01277i	0.410184	+	0.912003i	$0.365464\pi$
$457$	−12.5000	+	21.6506i	−0.584725	+	1.01277i	−0.994910	+	0.100771i	$0.967869\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.62372	−	0.937458i	−0.0756244	−	0.0436618i	0.461711	−	0.887030i	$-0.347236\pi$
$461$	−1.62372	−	0.937458i	−0.0756244	−	0.0436618i	−0.537335	+	0.843369i	$0.680569\pi$
$462$		0			0
$463$	−23.4220	+	13.5227i	−1.08851	+	0.628453i	−0.933180	−	0.359409i	$-0.882978\pi$
$463$	−23.4220	+	13.5227i	−1.08851	+	0.628453i	−0.155333	+	0.987862i	$0.549645\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.174973			0.00809677			0.00404838	−	0.999992i	$-0.498711\pi$
$467$	0.174973			0.00809677			0.00404838	+	0.999992i	$0.498711\pi$
$468$		0			0
$469$	7.39388			0.341418
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.55051	+	3.78194i	−0.301193	+	0.173894i
$474$		0			0
$475$	20.7846	+	12.0000i	0.953663	+	0.550598i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.0458	−	22.5959i	0.596076	−	1.03243i	−0.397318	−	0.917681i	$-0.630059\pi$
$479$	13.0458	−	22.5959i	0.596076	−	1.03243i	0.993394	−	0.114753i	$-0.0366076\pi$
$480$		0			0
$481$	−7.10102	−	12.2993i	−0.323779	−	0.560801i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			1.58919i			0.0721612i
$486$		0			0
$487$			3.79796i			0.172102i	0.996291	+	0.0860510i	$0.0274248\pi$
$487$			3.79796i			0.172102i	−0.996291	+	0.0860510i	$0.972575\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.15855	+	12.3990i	0.323061	+	0.559558i	0.981118	−	0.193410i	$-0.0619548\pi$
$491$	7.15855	+	12.3990i	0.323061	+	0.559558i	−0.658057	+	0.752968i	$0.728621\pi$
$492$		0			0
$493$	−15.7980	+	27.3629i	−0.711504	+	1.23236i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.49490	−	5.48188i	−0.425904	−	0.245896i
$498$		0			0
$499$	−12.9029	+	7.44949i	−0.577613	+	0.333485i	−0.760184	−	0.649708i	$-0.774891\pi$
$499$	−12.9029	+	7.44949i	−0.577613	+	0.333485i	0.182571	+	0.983193i	$0.441558\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	31.1127			1.38725			0.693623	−	0.720338i	$-0.256013\pi$
$503$	31.1127			1.38725			0.693623	+	0.720338i	$0.256013\pi$
$504$		0			0
$505$	−5.00000			−0.222497
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−23.1186	+	13.3475i	−1.02471	+	0.591619i	−0.915466	−	0.402395i	$-0.868178\pi$
$509$	−23.1186	+	13.3475i	−1.02471	+	0.591619i	−0.109249	+	0.994014i	$0.534845\pi$
$510$		0			0
$511$	2.38378	+	1.37628i	0.105452	+	0.0608828i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.58919	−	2.75255i	0.0700279	−	0.121292i
$516$		0			0
$517$	−5.00000	−	8.66025i	−0.219900	−	0.380878i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			21.7060i			0.950958i	0.879727	+	0.475479i	$0.157725\pi$
$521$			21.7060i			0.950958i	−0.879727	+	0.475479i	$0.842275\pi$
$522$		0			0
$523$		−	27.3939i		−	1.19785i	−0.800805	−	0.598925i	$-0.795595\pi$
$523$		−	27.3939i		−	1.19785i	0.800805	−	0.598925i	$-0.204405\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.9029	−	22.3485i	−0.562059	−	0.973515i
$528$		0			0
$529$	7.50000	−	12.9904i	0.326087	−	0.564799i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−24.4949	−	14.1421i	−1.06099	−	0.612564i
$534$		0			0
$535$	2.38378	−	1.37628i	0.103060	−	0.0595016i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.37113			0.231351
$540$		0			0
$541$	−20.0000			−0.859867			−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000			−0.859867			−0.429934	+	0.902861i	$0.641463\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.34847	−	0.778539i	0.0577621	−	0.0333489i
$546$		0			0
$547$	−20.6096	−	11.8990i	−0.881204	−	0.508764i	−0.0101491	−	0.999948i	$-0.503231\pi$
$547$	−20.6096	−	11.8990i	−0.881204	−	0.508764i	−0.871055	+	0.491185i	$0.836564\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	22.3417	−	38.6969i	0.951788	−	1.64855i
$552$		0			0
$553$	−1.44949	−	2.51059i	−0.0616386	−	0.106761i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	12.5529i		−	0.531886i	−0.963989	−	0.265943i	$-0.914317\pi$
$557$		−	12.5529i		−	0.531886i	0.963989	−	0.265943i	$-0.0856832\pi$
$558$		0			0
$559$		−	20.0000i		−	0.845910i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.4012	−	19.7474i	−0.480503	−	0.832256i	0.519247	−	0.854624i	$-0.326213\pi$
$563$	−11.4012	−	19.7474i	−0.480503	−	0.832256i	−0.999750	+	0.0223687i	$0.992879\pi$
$564$		0			0
$565$	−2.24745	+	3.89270i	−0.0945509	+	0.163767i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.10102	+	4.09978i	0.297690	+	0.171872i	0.641405	−	0.767203i	$-0.278352\pi$
$569$	7.10102	+	4.09978i	0.297690	+	0.171872i	−0.343715	+	0.939074i	$0.611685\pi$
$570$		0			0
$571$	17.1455	−	9.89898i	0.717518	−	0.414259i	−0.0963203	−	0.995350i	$-0.530707\pi$
$571$	17.1455	−	9.89898i	0.717518	−	0.414259i	0.813839	+	0.581091i	$0.197374\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−13.8564			−0.577852
$576$		0			0
$577$	−3.79796			−0.158111			−0.0790556	−	0.996870i	$-0.525190\pi$
$577$	−3.79796			−0.158111			−0.0790556	+	0.996870i	$0.525190\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.9268	+	11.5047i	−0.826702	+	0.477297i
$582$		0			0
$583$	4.19448	+	2.42168i	0.173718	+	0.100296i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.5441	−	19.9949i	0.476474	−	0.825278i	−0.523162	−	0.852233i	$-0.675248\pi$
$587$	11.5441	−	19.9949i	0.476474	−	0.825278i	0.999637	+	0.0269553i	$0.00858119\pi$
$588$		0			0
$589$	18.2474	+	31.6055i	0.751873	+	1.30228i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	8.13534i		−	0.334078i	−0.985950	−	0.167039i	$-0.946579\pi$
$593$		−	8.13534i		−	0.334078i	0.985950	−	0.167039i	$-0.0534206\pi$
$594$		0			0
$595$		−	1.59592i		−	0.0654263i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.7600	−	22.1010i	−0.521361	−	0.903023i	−0.999691	−	0.0248434i	$-0.992091\pi$
$599$	−12.7600	−	22.1010i	−0.521361	−	0.903023i	0.478331	−	0.878180i	$-0.341242\pi$
$600$		0			0
$601$	−5.15153	+	8.92271i	−0.210135	+	0.363965i	−0.951757	−	0.306854i	$-0.900724\pi$
$601$	−5.15153	+	8.92271i	−0.210135	+	0.363965i	0.741621	+	0.670819i	$0.234057\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.69694	−	1.55708i	−0.109646	−	0.0633042i
$606$		0			0
$607$	20.6096	−	11.8990i	0.836519	−	0.482965i	−0.0195602	−	0.999809i	$-0.506227\pi$
$607$	20.6096	−	11.8990i	0.836519	−	0.482965i	0.856080	+	0.516844i	$0.172893\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	26.4415			1.06971
$612$		0			0
$613$	30.0000			1.21169			0.605844	−	0.795583i	$-0.292835\pi$
$613$	30.0000			1.21169			0.605844	+	0.795583i	$0.292835\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−24.2474	+	13.9993i	−0.976166	+	0.563589i	−0.901110	−	0.433590i	$-0.857247\pi$
$617$	−24.2474	+	13.9993i	−0.976166	+	0.563589i	−0.0750552	+	0.997179i	$0.523913\pi$
$618$		0			0
$619$	−18.7026	−	10.7980i	−0.751722	−	0.434007i	0.0745941	−	0.997214i	$-0.476234\pi$
$619$	−18.7026	−	10.7980i	−0.751722	−	0.434007i	−0.826316	+	0.563207i	$0.809567\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.66025	+	15.0000i	−0.346966	+	0.600962i
$624$		0			0
$625$	−11.7474	−	20.3472i	−0.469898	−	0.813887i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			16.9706i			0.676661i
$630$		0			0
$631$			45.7423i			1.82097i	0.413538	+	0.910487i	$0.364293\pi$
$631$			45.7423i			1.82097i	−0.413538	+	0.910487i	$0.635707\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.42310	−	4.19694i	−0.0961579	−	0.166550i
$636$		0			0
$637$	−7.10102	+	12.2993i	−0.281353	+	0.487317i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−42.2474	−	24.3916i	−1.66867	−	0.963409i	−0.968354	−	0.249580i	$-0.919707\pi$
$641$	−42.2474	−	24.3916i	−1.66867	−	0.963409i	−0.700320	−	0.713829i	$-0.746959\pi$
$642$		0			0
$643$	−32.3840	+	18.6969i	−1.27710	+	0.737335i	−0.976315	−	0.216356i	$-0.930583\pi$
$643$	−32.3840	+	18.6969i	−1.27710	+	0.737335i	−0.300788	+	0.953691i	$0.597250\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.7846			−0.817127			−0.408564	−	0.912730i	$-0.633970\pi$
$647$	−20.7846			−0.817127			−0.408564	+	0.912730i	$0.633970\pi$
$648$		0			0
$649$	−10.0000			−0.392534
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.0732	−	9.27987i	0.628993	−	0.363150i	−0.151369	−	0.988477i	$-0.548368\pi$
$653$	16.0732	−	9.27987i	0.628993	−	0.363150i	0.780362	+	0.625328i	$0.215035\pi$
$654$		0			0
$655$	0.826701	+	0.477296i	0.0323019	+	0.0186495i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.9118	−	24.0959i	0.541926	−	0.938644i	−0.456867	−	0.889535i	$-0.651029\pi$
$659$	13.9118	−	24.0959i	0.541926	−	0.938644i	0.998793	−	0.0491088i	$-0.0156381\pi$
$660$		0			0
$661$	2.24745	+	3.89270i	0.0874156	+	0.151408i	0.906418	−	0.422382i	$-0.138806\pi$
$661$	2.24745	+	3.89270i	0.0874156	+	0.151408i	−0.819002	+	0.573790i	$0.805473\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			2.25697i			0.0875215i
$666$		0			0
$667$			25.7980i			0.998901i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.19275	−	3.79796i	−0.0846503	−	0.146619i
$672$		0			0
$673$	18.2980	−	31.6930i	0.705334	−	1.22168i	−0.261236	−	0.965275i	$-0.584130\pi$
$673$	18.2980	−	31.6930i	0.705334	−	1.22168i	0.966571	−	0.256400i	$-0.0825365\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.49490	+	5.48188i	0.364919	+	0.210686i	0.671236	−	0.741244i	$-0.265764\pi$
$677$	9.49490	+	5.48188i	0.364919	+	0.210686i	−0.306318	+	0.951929i	$0.599097\pi$
$678$		0			0
$679$	6.27647	−	3.62372i	0.240869	−	0.139066i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−10.3923			−0.397650			−0.198825	−	0.980035i	$-0.563713\pi$
$683$	−10.3923			−0.397650			−0.198825	+	0.980035i	$0.563713\pi$
$684$		0			0
$685$	−3.39388			−0.129673
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−11.0908	+	6.40329i	−0.422526	+	0.243946i
$690$		0			0
$691$	−3.46410	−	2.00000i	−0.131781	−	0.0760836i	0.432660	−	0.901557i	$-0.357575\pi$
$691$	−3.46410	−	2.00000i	−0.131781	−	0.0760836i	−0.564441	+	0.825473i	$0.690908\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.17837	+	5.50510i	−0.120563	+	0.208820i
$696$		0			0
$697$	16.8990	+	29.2699i	0.640094	+	1.10868i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	38.7087i		−	1.46201i	−0.682374	−	0.731003i	$-0.739052\pi$
$701$		−	38.7087i		−	1.46201i	0.682374	−	0.731003i	$-0.260948\pi$
$702$		0			0
$703$		−	24.0000i		−	0.905177i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.4012	+	19.7474i	0.428786	+	0.742679i
$708$		0			0
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	−0.196167	−	0.980571i	$-0.562849\pi$
$709$	20.0000	−	34.6410i	0.751116	−	1.30097i	0.947282	−	0.320400i	$-0.103817\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−18.2474	−	10.5352i	−0.683372	−	0.394545i
$714$		0			0
$715$	−0.874863	+	0.505103i	−0.0327180	+	0.0188898i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.92820			0.258378			0.129189	−	0.991620i	$-0.458763\pi$
$719$	6.92820			0.258378			0.129189	+	0.991620i	$0.458763\pi$
$720$		0			0
$721$	−14.4949			−0.539818
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−38.6969	+	22.3417i	−1.43717	+	0.829749i
$726$		0			0
$727$	6.27647	+	3.62372i	0.232782	+	0.134396i	0.611855	−	0.790970i	$-0.290424\pi$
$727$	6.27647	+	3.62372i	0.232782	+	0.134396i	−0.379073	+	0.925367i	$0.623757\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−11.9494	+	20.6969i	−0.441964	+	0.765504i
$732$		0			0
$733$	−2.24745	−	3.89270i	−0.0830114	−	0.143780i	0.821531	−	0.570164i	$-0.193120\pi$
$733$	−2.24745	−	3.89270i	−0.0830114	−	0.143780i	−0.904542	+	0.426384i	$0.859787\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			5.59264i			0.206007i
$738$		0			0
$739$			19.3939i			0.713415i	0.934216	+	0.356708i	$0.116101\pi$
$739$			19.3939i			0.713415i	−0.934216	+	0.356708i	$0.883899\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	15.7313	+	27.2474i	0.577126	+	0.999612i	0.995807	+	0.0914785i	$0.0291593\pi$
$743$	15.7313	+	27.2474i	0.577126	+	0.999612i	−0.418681	+	0.908133i	$0.637507\pi$
$744$		0			0
$745$	−0.601021	+	1.04100i	−0.0220197	+	0.0381392i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.8712	−	6.27647i	−0.397224	−	0.229337i
$750$		0			0
$751$	41.3461	−	23.8712i	1.50874	−	0.871071i	0.508792	−	0.860890i	$-0.330092\pi$
$751$	41.3461	−	23.8712i	1.50874	−	0.871071i	0.999948	−	0.0101819i	$-0.00324107\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.48188			0.199506
$756$		0			0
$757$	−39.3939			−1.43179			−0.715897	−	0.698205i	$-0.753982\pi$
$757$	−39.3939			−1.43179			−0.715897	+	0.698205i	$0.753982\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	45.7980	−	26.4415i	1.66017	−	0.958502i	0.687545	−	0.726142i	$-0.258688\pi$
$761$	45.7980	−	26.4415i	1.66017	−	0.958502i	0.972630	−	0.232361i	$-0.0746449\pi$
$762$		0			0
$763$	−6.14966	−	3.55051i	−0.222633	−	0.128537i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.2207	−	22.8990i	0.477373	−	0.826834i
$768$		0			0
$769$	−5.74745	−	9.95487i	−0.207258	−	0.358982i	0.743592	−	0.668634i	$-0.233121\pi$
$769$	−5.74745	−	9.95487i	−0.207258	−	0.358982i	−0.950850	+	0.309652i	$0.899787\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	34.2911i		−	1.23336i	−0.787212	−	0.616682i	$-0.788476\pi$
$773$		−	34.2911i		−	1.23336i	0.787212	−	0.616682i	$-0.211524\pi$
$774$		0			0
$775$		−	36.4949i		−	1.31094i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.8988	−	41.3939i	−0.856262	−	1.48309i
$780$		0			0
$781$	4.14643	−	7.18182i	0.148371	−	0.256986i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.79796	−	2.19275i	−0.135555	−	0.0782627i
$786$		0			0
$787$	30.4770	−	17.5959i	1.08639	−	0.627227i	0.153776	−	0.988106i	$-0.450857\pi$
$787$	30.4770	−	17.5959i	1.08639	−	0.627227i	0.932613	+	0.360879i	$0.117523\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	20.4989			0.728856
$792$		0			0
$793$	11.5959			0.411783
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.27526	−	3.62302i	0.222281	−	0.128334i	−0.384725	−	0.923031i	$-0.625704\pi$
$797$	6.27526	−	3.62302i	0.222281	−	0.128334i	0.607006	+	0.794697i	$0.292370\pi$
$798$		0			0
$799$	−27.3629	−	15.7980i	−0.968029	−	0.558892i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.04100	+	1.80306i	−0.0367360	+	0.0636287i
$804$		0			0
$805$	−0.651531	−	1.12848i	−0.0229634	−	0.0397738i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			11.9494i			0.420118i	0.977689	+	0.210059i	$0.0673656\pi$
$809$			11.9494i			0.420118i	−0.977689	+	0.210059i	$0.932634\pi$
$810$		0			0
$811$			24.4949i			0.860132i	0.902797	+	0.430066i	$0.141510\pi$
$811$			24.4949i			0.860132i	−0.902797	+	0.430066i	$0.858490\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.953512	+	1.65153i	0.0334001	+	0.0578506i
$816$		0			0
$817$	16.8990	−	29.2699i	0.591220	−	1.02402i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	19.8990	+	11.4887i	0.694479	+	0.400958i	0.805288	−	0.592884i	$-0.202011\pi$
$821$	19.8990	+	11.4887i	0.694479	+	0.400958i	−0.110809	+	0.993842i	$0.535344\pi$
$822$		0			0
$823$	25.6790	−	14.8258i	0.895113	−	0.516794i	0.0195015	−	0.999810i	$-0.493792\pi$
$823$	25.6790	−	14.8258i	0.895113	−	0.516794i	0.875611	+	0.483016i	$0.160459\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.6206			0.577955			0.288978	−	0.957336i	$-0.406685\pi$
$827$	16.6206			0.577955			0.288978	+	0.957336i	$0.406685\pi$
$828$		0			0
$829$	−37.5959			−1.30576			−0.652880	−	0.757461i	$-0.726439\pi$
$829$	−37.5959			−1.30576			−0.652880	+	0.757461i	$0.726439\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	14.6969	−	8.48528i	0.509219	−	0.293998i
$834$		0			0
$835$	−6.32464	−	3.65153i	−0.218873	−	0.126366i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.58919	−	2.75255i	0.0548648	−	0.0950286i	−0.837289	−	0.546761i	$-0.815861\pi$
$839$	1.58919	−	2.75255i	0.0548648	−	0.0950286i	0.892153	+	0.451733i	$0.149194\pi$
$840$		0			0
$841$	27.0959	+	46.9315i	0.934342	+	1.61833i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.46075i			0.0502515i
$846$		0			0
$847$			14.2020i			0.487988i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.92820	+	12.0000i	0.237496	+	0.411355i
$852$		0			0
$853$	−5.00000	+	8.66025i	−0.171197	+	0.296521i	−0.938839	−	0.344358i	$-0.888097\pi$
$853$	−5.00000	+	8.66025i	−0.171197	+	0.296521i	0.767642	+	0.640879i	$0.221430\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.1010	−	5.83183i	−0.345044	−	0.199211i	0.317456	−	0.948273i	$-0.397171\pi$
$857$	−10.1010	−	5.83183i	−0.345044	−	0.199211i	−0.662500	+	0.749062i	$0.730505\pi$
$858$		0			0
$859$	−34.2911	+	19.7980i	−1.17000	+	0.675498i	−0.953679	−	0.300826i	$-0.902738\pi$
$859$	−34.2911	+	19.7980i	−1.17000	+	0.675498i	−0.216317	+	0.976323i	$0.569404\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.92820			−0.235839			−0.117919	−	0.993023i	$-0.537622\pi$
$863$	−6.92820			−0.235839			−0.117919	+	0.993023i	$0.537622\pi$
$864$		0			0
$865$	−1.69694			−0.0576976
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.89898	−	1.09638i	0.0644185	−	0.0371920i
$870$		0			0
$871$	−12.8066	−	7.39388i	−0.433934	−	0.250532i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.28024	−	3.94949i	0.0770861	−	0.133517i
$876$		0			0
$877$	8.10102	+	14.0314i	0.273552	+	0.473806i	0.969769	−	0.244026i	$-0.0784681\pi$
$877$	8.10102	+	14.0314i	0.273552	+	0.473806i	−0.696217	+	0.717832i	$0.745135\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			7.27815i			0.245207i	0.992456	+	0.122604i	$0.0391244\pi$
$881$			7.27815i			0.245207i	−0.992456	+	0.122604i	$0.960876\pi$
$882$		0			0
$883$			52.8990i			1.78019i	0.455773	+	0.890096i	$0.349363\pi$
$883$			52.8990i			1.78019i	−0.455773	+	0.890096i	$0.650637\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.6595	−	39.2474i	−0.760832	−	1.31780i	−0.942422	−	0.334426i	$-0.891458\pi$
$887$	−22.6595	−	39.2474i	−0.760832	−	1.31780i	0.181590	−	0.983374i	$-0.441876\pi$
$888$		0			0
$889$	−11.0505	+	19.1400i	−0.370622	+	0.641937i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	38.6969	+	22.3417i	1.29494	+	0.747636i
$894$		0			0
$895$	−2.38378	+	1.37628i	−0.0796810	+	0.0460038i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−67.9465			−2.26614
$900$		0			0
$901$	15.3031			0.509819
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.69694	−	1.55708i	0.0896493	−	0.0517590i
$906$		0			0
$907$	−3.89270	−	2.24745i	−0.129255	−	0.0746253i	0.433978	−	0.900923i	$-0.357109\pi$
$907$	−3.89270	−	2.24745i	−0.129255	−	0.0746253i	−0.563233	+	0.826298i	$0.690443\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.460702	+	0.797959i	−0.0152637	+	0.0264376i	−0.873556	−	0.486723i	$-0.838192\pi$
$911$	−0.460702	+	0.797959i	−0.0152637	+	0.0264376i	0.858293	+	0.513161i	$0.171525\pi$
$912$		0			0
$913$	−8.70204	−	15.0724i	−0.287996	−	0.498823i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	4.35340i		−	0.143762i
$918$		0			0
$919$		−	2.75255i		−	0.0907983i	−0.998969	−	0.0453991i	$-0.985544\pi$
$919$		−	2.75255i		−	0.0907983i	0.998969	−	0.0453991i	$-0.0144560\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.9638	+	18.9898i	0.360877	+	0.625057i
$924$		0			0
$925$	−12.0000	+	20.7846i	−0.394558	+	0.683394i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−13.1010	−	7.56388i	−0.429831	−	0.248163i	0.269444	−	0.963016i	$-0.413160\pi$
$929$	−13.1010	−	7.56388i	−0.429831	−	0.248163i	−0.699274	+	0.714853i	$0.746493\pi$
$930$		0			0
$931$	−20.7846	+	12.0000i	−0.681188	+	0.393284i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.20713			0.0394775
$936$		0			0
$937$	−15.0000			−0.490029			−0.245014	−	0.969519i	$-0.578793\pi$
$937$	−15.0000			−0.490029			−0.245014	+	0.969519i	$0.578793\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−35.9722	+	20.7686i	−1.17266	+	0.677036i	−0.954305	−	0.298834i	$-0.903402\pi$
$941$	−35.9722	+	20.7686i	−1.17266	+	0.677036i	−0.218355	+	0.975869i	$0.570069\pi$
$942$		0			0
$943$	23.8988	+	13.7980i	0.778251	+	0.449323i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.5441	+	19.9949i	−0.375132	+	0.649747i	−0.990347	−	0.138612i	$-0.955736\pi$
$947$	−11.5441	+	19.9949i	−0.375132	+	0.649747i	0.615215	+	0.788359i	$0.289069\pi$
$948$		0			0
$949$	−2.75255	−	4.76756i	−0.0893516	−	0.154762i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			10.7423i			0.347976i	0.984748	+	0.173988i	$0.0556653\pi$
$953$			10.7423i			0.347976i	−0.984748	+	0.173988i	$0.944335\pi$
$954$		0			0
$955$		−	5.59592i		−	0.181080i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.73885	+	13.4041i	0.249901	+	0.432840i
$960$		0			0
$961$	12.2474	−	21.2132i	0.395079	−	0.684297i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.578317	+	0.333891i	0.0186167	+	0.0107483i
$966$		0			0
$967$	42.6495	−	24.6237i	1.37152	−	0.791846i	0.380398	−	0.924823i	$-0.375787\pi$
$967$	42.6495	−	24.6237i	1.37152	−	0.791846i	0.991119	+	0.132977i	$0.0424538\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.3383			0.620595			0.310298	−	0.950639i	$-0.399571\pi$
$971$	19.3383			0.620595			0.310298	+	0.950639i	$0.399571\pi$
$972$		0			0
$973$	28.9898			0.929370
$974$		0			0
$975$		0			0
$976$		0			0
$977$	27.2474	−	15.7313i	0.871723	−	0.503290i	0.00380265	−	0.999993i	$-0.498790\pi$
$977$	27.2474	−	15.7313i	0.871723	−	0.503290i	0.867920	+	0.496703i	$0.165456\pi$
$978$		0			0
$979$	−11.3458	−	6.55051i	−0.362614	−	0.209355i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−26.2665	+	45.4949i	−0.837771	+	1.45106i	0.0539833	+	0.998542i	$0.482808\pi$
$983$	−26.2665	+	45.4949i	−0.837771	+	1.45106i	−0.891754	+	0.452520i	$0.850525\pi$
$984$		0			0
$985$	−1.94949	−	3.37662i	−0.0621159	−	0.107588i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			19.5133i			0.620486i
$990$		0			0
$991$		−	8.75255i		−	0.278034i	−0.990290	−	0.139017i	$-0.955606\pi$
$991$		−	8.75255i		−	0.278034i	0.990290	−	0.139017i	$-0.0443943\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.23375	−	5.60102i	−0.102517	−	0.177564i
$996$		0			0
$997$	30.3485	−	52.5651i	0.961146	−	1.66475i	0.241514	−	0.970397i	$-0.422356\pi$
$997$	30.3485	−	52.5651i	0.961146	−	1.66475i	0.719632	−	0.694356i	$-0.244311\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.s.a.1727.4		8
3.2	odd	2		2592.2.s.h.1727.2		8
4.3	odd	2	inner	2592.2.s.a.1727.3		8
9.2	odd	6		864.2.c.a.863.5	yes	8
9.4	even	3		2592.2.s.h.863.1		8
9.5	odd	6	inner	2592.2.s.a.863.3		8
9.7	even	3		864.2.c.a.863.3	✓	8
12.11	even	2		2592.2.s.h.1727.1		8
36.7	odd	6		864.2.c.a.863.4	yes	8
36.11	even	6		864.2.c.a.863.6	yes	8
36.23	even	6	inner	2592.2.s.a.863.4		8
36.31	odd	6		2592.2.s.h.863.2		8
72.11	even	6		1728.2.c.g.1727.4		8
72.29	odd	6		1728.2.c.g.1727.3		8
72.43	odd	6		1728.2.c.g.1727.6		8
72.61	even	6		1728.2.c.g.1727.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.c.a.863.3	✓	8	9.7	even	3
864.2.c.a.863.4	yes	8	36.7	odd	6
864.2.c.a.863.5	yes	8	9.2	odd	6
864.2.c.a.863.6	yes	8	36.11	even	6
1728.2.c.g.1727.3		8	72.29	odd	6
1728.2.c.g.1727.4		8	72.11	even	6
1728.2.c.g.1727.5		8	72.61	even	6
1728.2.c.g.1727.6		8	72.43	odd	6
2592.2.s.a.863.3		8	9.5	odd	6	inner
2592.2.s.a.863.4		8	36.23	even	6	inner
2592.2.s.a.1727.3		8	4.3	odd	2	inner
2592.2.s.a.1727.4		8	1.1	even	1	trivial
2592.2.s.h.863.1		8	9.4	even	3
2592.2.s.h.863.2		8	36.31	odd	6
2592.2.s.h.1727.1		8	12.11	even	2
2592.2.s.h.1727.2		8	3.2	odd	2

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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)

\(f(q)\)	\(=\)	\(q+(-0.275255 + 0.158919i) q^{5} +(1.25529 + 0.724745i) q^{7} +O(q^{10})\)	\(q+(-0.275255 + 0.158919i) q^{5} +(1.25529 + 0.724745i) q^{7} +(-0.548188 + 0.949490i) q^{11} +(-1.44949 - 2.51059i) q^{13} +3.46410i q^{17} -4.89898i q^{19} +(1.41421 + 2.44949i) q^{23} +(-2.44949 + 4.24264i) q^{25} +(7.89898 + 4.56048i) q^{29} +(-6.45145 + 3.72474i) q^{31} -0.460702 q^{35} +4.89898 q^{37} +(8.44949 - 4.87832i) q^{41} +(5.97469 + 3.44949i) q^{43} +(-4.56048 + 7.89898i) q^{47} +(-2.44949 - 4.24264i) q^{49} -4.41761i q^{53} -0.348469i q^{55} +(4.56048 + 7.89898i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(0.797959 + 0.460702i) q^{65} +(4.41761 - 2.55051i) q^{67} -7.56388 q^{71} +1.89898 q^{73} +(-1.37628 + 0.794593i) q^{77} +(-1.73205 - 1.00000i) q^{79} +(-7.93709 + 13.7474i) q^{83} +(-0.550510 - 0.953512i) q^{85} +11.9494i q^{89} -4.20204i q^{91} +(0.778539 + 1.34847i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5}+O(q^{10}) \) 8 * q - 12 * q^5	\( 8 q - 12 q^{5} + 8 q^{13} + 24 q^{29} + 48 q^{41} - 16 q^{61} - 72 q^{65} - 24 q^{73} - 60 q^{77} - 24 q^{85} + 20 q^{97}+O(q^{100}) \) 8 * q - 12 * q^5 + 8 * q^13 + 24 * q^29 + 48 * q^41 - 16 * q^61 - 72 * q^65 - 24 * q^73 - 60 * q^77 - 24 * q^85 + 20 * q^97

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