LMFDB - Embedded newform 1296.2.i.t.865.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1296,2,Mod(433,1296)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1296, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1296.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1296 = 2^{4} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1296.i (of order $3$, 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:	$10.3486121020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 648)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1296.865
Dual form			1296.2.i.t.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 3.23205i) q^{5} +(1.73205 - 3.00000i) q^{7} +O(q^{10})$	$q+(1.86603 + 3.23205i) q^{5} +(1.73205 - 3.00000i) q^{7} +(-1.00000 + 1.73205i) q^{11} +(1.23205 + 2.13397i) q^{13} -2.26795 q^{17} +7.46410 q^{19} +(2.46410 + 4.26795i) q^{23} +(-4.46410 + 7.73205i) q^{25} +(2.13397 - 3.69615i) q^{29} +(-5.46410 - 9.46410i) q^{31} +12.9282 q^{35} -0.464102 q^{37} +(3.46410 + 6.00000i) q^{41} +(-2.26795 + 3.92820i) q^{43} +(-3.46410 + 6.00000i) q^{47} +(-2.50000 - 4.33013i) q^{49} +10.9282 q^{53} -7.46410 q^{55} +(-4.00000 - 6.92820i) q^{59} +(-5.23205 + 9.06218i) q^{61} +(-4.59808 + 7.96410i) q^{65} +(-0.267949 - 0.464102i) q^{67} -2.00000 q^{71} +1.00000 q^{73} +(3.46410 + 6.00000i) q^{77} +(0.267949 - 0.464102i) q^{79} +(1.46410 - 2.53590i) q^{83} +(-4.23205 - 7.33013i) q^{85} +5.19615 q^{89} +8.53590 q^{91} +(13.9282 + 24.1244i) q^{95} +(5.92820 - 10.2679i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5}+O(q^{10}) $ 4 * q + 4 * q^5	$ 4 q + 4 q^{5} - 4 q^{11} - 2 q^{13} - 16 q^{17} + 16 q^{19} - 4 q^{23} - 4 q^{25} + 12 q^{29} - 8 q^{31} + 24 q^{35} + 12 q^{37} - 16 q^{43} - 10 q^{49} + 16 q^{53} - 16 q^{55} - 16 q^{59} - 14 q^{61} - 8 q^{65} - 8 q^{67} - 8 q^{71} + 4 q^{73} + 8 q^{79} - 8 q^{83} - 10 q^{85} + 48 q^{91} + 28 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 - 4 * q^11 - 2 * q^13 - 16 * q^17 + 16 * q^19 - 4 * q^23 - 4 * q^25 + 12 * q^29 - 8 * q^31 + 24 * q^35 + 12 * q^37 - 16 * q^43 - 10 * q^49 + 16 * q^53 - 16 * q^55 - 16 * q^59 - 14 * q^61 - 8 * q^65 - 8 * q^67 - 8 * q^71 + 4 * q^73 + 8 * q^79 - 8 * q^83 - 10 * q^85 + 48 * q^91 + 28 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.86603	+	3.23205i	0.834512	+	1.44542i	0.894427	+	0.447214i	$0.147584\pi$
$5$	1.86603	+	3.23205i	0.834512	+	1.44542i	−0.0599153	+	0.998203i	$0.519083\pi$
$6$		0			0
$7$	1.73205	−	3.00000i	0.654654	−	1.13389i	−0.327327	−	0.944911i	$-0.606148\pi$
$7$	1.73205	−	3.00000i	0.654654	−	1.13389i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		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
$17$	−2.26795			−0.550058			−0.275029	−	0.961436i	$-0.588688\pi$
$17$	−2.26795			−0.550058			−0.275029	+	0.961436i	$0.588688\pi$
$18$		0			0
$19$	7.46410			1.71238			0.856191	−	0.516659i	$-0.172825\pi$
$19$	7.46410			1.71238			0.856191	+	0.516659i	$0.172825\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.46410	+	4.26795i	0.513801	+	0.889929i	0.999872	+	0.0160097i	$0.00509626\pi$
$23$	2.46410	+	4.26795i	0.513801	+	0.889929i	−0.486071	+	0.873919i	$0.661570\pi$
$24$		0			0
$25$	−4.46410	+	7.73205i	−0.892820	+	1.54641i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.13397	−	3.69615i	0.396269	−	0.686358i	−0.596993	−	0.802246i	$-0.703638\pi$
$29$	2.13397	−	3.69615i	0.396269	−	0.686358i	0.993262	+	0.115888i	$0.0369714\pi$
$30$		0			0
$31$	−5.46410	−	9.46410i	−0.981382	−	1.69980i	−0.657027	−	0.753867i	$-0.728186\pi$
$31$	−5.46410	−	9.46410i	−0.981382	−	1.69980i	−0.324355	−	0.945935i	$-0.605147\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	12.9282			2.18527
$36$		0			0
$37$	−0.464102			−0.0762978			−0.0381489	−	0.999272i	$-0.512146\pi$
$37$	−0.464102			−0.0762978			−0.0381489	+	0.999272i	$0.512146\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.46410	+	6.00000i	0.541002	+	0.937043i	0.998847	+	0.0480106i	$0.0152881\pi$
$41$	3.46410	+	6.00000i	0.541002	+	0.937043i	−0.457845	+	0.889032i	$0.651379\pi$
$42$		0			0
$43$	−2.26795	+	3.92820i	−0.345859	+	0.599045i	−0.985509	−	0.169621i	$-0.945746\pi$
$43$	−2.26795	+	3.92820i	−0.345859	+	0.599045i	0.639650	+	0.768666i	$0.279079\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	0.494690	+	0.869069i	$0.335282\pi$
$47$	−3.46410	+	6.00000i	−0.505291	+	0.875190i	−0.999981	+	0.00612051i	$0.998052\pi$
$48$		0			0
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.9282			1.50110			0.750552	−	0.660811i	$-0.229788\pi$
$53$	10.9282			1.50110			0.750552	+	0.660811i	$0.229788\pi$
$54$		0			0
$55$	−7.46410			−1.00646
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	−5.23205	+	9.06218i	−0.669895	+	1.16029i	0.308038	+	0.951374i	$0.400328\pi$
$61$	−5.23205	+	9.06218i	−0.669895	+	1.16029i	−0.977933	+	0.208919i	$0.933006\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.59808	+	7.96410i	−0.570321	+	0.987825i
$66$		0			0
$67$	−0.267949	−	0.464102i	−0.0327352	−	0.0566990i	0.849194	−	0.528082i	$-0.177088\pi$
$67$	−0.267949	−	0.464102i	−0.0327352	−	0.0566990i	−0.881929	+	0.471383i	$0.843755\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.46410	+	6.00000i	0.394771	+	0.683763i
$78$		0			0
$79$	0.267949	−	0.464102i	0.0301466	−	0.0522155i	−0.850558	−	0.525880i	$-0.823736\pi$
$79$	0.267949	−	0.464102i	0.0301466	−	0.0522155i	0.880705	+	0.473665i	$0.157069\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.46410	−	2.53590i	0.160706	−	0.278351i	−0.774416	−	0.632677i	$-0.781956\pi$
$83$	1.46410	−	2.53590i	0.160706	−	0.278351i	0.935122	+	0.354326i	$0.115290\pi$
$84$		0			0
$85$	−4.23205	−	7.33013i	−0.459030	−	0.795064i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.19615			0.550791			0.275396	−	0.961331i	$-0.411191\pi$
$89$	5.19615			0.550791			0.275396	+	0.961331i	$0.411191\pi$
$90$		0			0
$91$	8.53590			0.894805
$92$		0			0
$93$		0			0
$94$		0			0
$95$	13.9282	+	24.1244i	1.42900	+	2.47511i
$96$		0			0
$97$	5.92820	−	10.2679i	0.601918	−	1.04255i	−0.390613	−	0.920555i	$-0.627737\pi$
$97$	5.92820	−	10.2679i	0.601918	−	1.04255i	0.992530	−	0.121997i	$-0.0389299\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	5.46410	+	9.46410i	0.538394	+	0.932526i	0.998991	+	0.0449162i	$0.0143021\pi$
$103$	5.46410	+	9.46410i	0.538394	+	0.932526i	−0.460597	+	0.887609i	$0.652365\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.07180			−0.490309			−0.245155	−	0.969484i	$-0.578839\pi$
$107$	−5.07180			−0.490309			−0.245155	+	0.969484i	$0.578839\pi$
$108$		0			0
$109$	4.46410			0.427583			0.213792	−	0.976879i	$-0.431419\pi$
$109$	4.46410			0.427583			0.213792	+	0.976879i	$0.431419\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.866025	−	1.50000i	−0.0814688	−	0.141108i	0.822412	−	0.568892i	$-0.192628\pi$
$113$	−0.866025	−	1.50000i	−0.0814688	−	0.141108i	−0.903881	+	0.427784i	$0.859294\pi$
$114$		0			0
$115$	−9.19615	+	15.9282i	−0.857546	+	1.48531i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.92820	+	6.80385i	−0.360098	+	0.623708i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−14.6603			−1.31125
$126$		0			0
$127$	−0.535898			−0.0475533			−0.0237766	−	0.999717i	$-0.507569\pi$
$127$	−0.535898			−0.0475533			−0.0237766	+	0.999717i	$0.507569\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.53590	+	6.12436i	0.308933	+	0.535087i	0.978129	−	0.207998i	$-0.0666948\pi$
$131$	3.53590	+	6.12436i	0.308933	+	0.535087i	−0.669196	+	0.743086i	$0.733361\pi$
$132$		0			0
$133$	12.9282	−	22.3923i	1.12102	−	1.94166i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.3301	−	17.8923i	0.882562	−	1.52864i	0.0340799	−	0.999419i	$-0.489150\pi$
$137$	10.3301	−	17.8923i	0.882562	−	1.52864i	0.848482	−	0.529224i	$-0.177517\pi$
$138$		0			0
$139$	−2.53590	−	4.39230i	−0.215092	−	0.372550i	0.738209	−	0.674572i	$-0.235672\pi$
$139$	−2.53590	−	4.39230i	−0.215092	−	0.372550i	−0.953301	+	0.302022i	$0.902339\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.92820			−0.412117
$144$		0			0
$145$	15.9282			1.32277
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.86603	−	13.6244i	−0.644410	−	1.11615i	−0.984437	−	0.175735i	$-0.943770\pi$
$149$	−7.86603	−	13.6244i	−0.644410	−	1.11615i	0.340028	−	0.940415i	$-0.389564\pi$
$150$		0			0
$151$	0.535898	−	0.928203i	0.0436108	−	0.0755361i	−0.843396	−	0.537292i	$-0.819447\pi$
$151$	0.535898	−	0.928203i	0.0436108	−	0.0755361i	0.887007	+	0.461756i	$0.152781\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.3923	−	35.3205i	1.63795	−	2.83701i
$156$		0			0
$157$	−2.69615	−	4.66987i	−0.215176	−	0.372696i	0.738151	−	0.674636i	$-0.235699\pi$
$157$	−2.69615	−	4.66987i	−0.215176	−	0.372696i	−0.953327	+	0.301939i	$0.902366\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.0718			1.34545
$162$		0			0
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$		0			0
$169$	3.46410	−	6.00000i	0.266469	−	0.461538i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.86603	+	6.69615i	−0.293928	+	0.509099i	−0.974735	−	0.223364i	$-0.928296\pi$
$173$	−3.86603	+	6.69615i	−0.293928	+	0.509099i	0.680807	+	0.732463i	$0.261629\pi$
$174$		0			0
$175$	15.4641	+	26.7846i	1.16898	+	2.02473i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.92820			−0.517838			−0.258919	−	0.965899i	$-0.583366\pi$
$179$	−6.92820			−0.517838			−0.258919	+	0.965899i	$0.583366\pi$
$180$		0			0
$181$	7.85641			0.583962			0.291981	−	0.956424i	$-0.405686\pi$
$181$	7.85641			0.583962			0.291981	+	0.956424i	$0.405686\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.866025	−	1.50000i	−0.0636715	−	0.110282i
$186$		0			0
$187$	2.26795	−	3.92820i	0.165849	−	0.287259i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.92820	+	17.1962i	−0.718380	+	1.24427i	0.243262	+	0.969961i	$0.421783\pi$
$191$	−9.92820	+	17.1962i	−0.718380	+	1.24427i	−0.961642	+	0.274309i	$0.911551\pi$
$192$		0			0
$193$	−8.96410	−	15.5263i	−0.645250	−	1.11761i	−0.984244	−	0.176817i	$-0.943420\pi$
$193$	−8.96410	−	15.5263i	−0.645250	−	1.11761i	0.338994	−	0.940789i	$-0.389914\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.66025			0.189535			0.0947676	−	0.995499i	$-0.469789\pi$
$197$	2.66025			0.189535			0.0947676	+	0.995499i	$0.469789\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.39230	−	12.8038i	−0.518838	−	0.898654i
$204$		0			0
$205$	−12.9282	+	22.3923i	−0.902945	+	1.56395i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.46410	+	12.9282i	−0.516303	+	0.894263i
$210$		0			0
$211$	−12.6603	−	21.9282i	−0.871568	−	1.50960i	−0.860374	−	0.509662i	$-0.829770\pi$
$211$	−12.6603	−	21.9282i	−0.871568	−	1.50960i	−0.0111934	−	0.999937i	$-0.503563\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−16.9282			−1.15449
$216$		0			0
$217$	−37.8564			−2.56986
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.79423	−	4.83975i	−0.187960	−	0.325557i
$222$		0			0
$223$	0.267949	−	0.464102i	0.0179432	−	0.0310785i	−0.856914	−	0.515459i	$-0.827622\pi$
$223$	0.267949	−	0.464102i	0.0179432	−	0.0310785i	0.874858	+	0.484380i	$0.160955\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.39230	−	12.8038i	0.490645	−	0.849821i	−0.509298	−	0.860591i	$-0.670095\pi$
$227$	7.39230	−	12.8038i	0.490645	−	0.849821i	0.999942	+	0.0107693i	$0.00342805\pi$
$228$		0			0
$229$	3.76795	+	6.52628i	0.248993	+	0.431269i	0.963247	−	0.268618i	$-0.0865670\pi$
$229$	3.76795	+	6.52628i	0.248993	+	0.431269i	−0.714254	+	0.699887i	$0.753234\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.73205			−0.637568			−0.318784	−	0.947827i	$-0.603274\pi$
$233$	−9.73205			−0.637568			−0.318784	+	0.947827i	$0.603274\pi$
$234$		0			0
$235$	−25.8564			−1.68669
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−5.46410	−	9.46410i	−0.353443	−	0.612182i	0.633407	−	0.773819i	$-0.281656\pi$
$239$	−5.46410	−	9.46410i	−0.353443	−	0.612182i	−0.986850	+	0.161637i	$0.948323\pi$
$240$		0			0
$241$	4.03590	−	6.99038i	0.259975	−	0.450290i	−0.706260	−	0.707953i	$-0.749619\pi$
$241$	4.03590	−	6.99038i	0.259975	−	0.450290i	0.966235	+	0.257663i	$0.0829523\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.33013	−	16.1603i	0.596080	−	1.03244i
$246$		0			0
$247$	9.19615	+	15.9282i	0.585137	+	1.01349i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	10.0000			0.631194			0.315597	−	0.948893i	$-0.397795\pi$
$251$	10.0000			0.631194			0.315597	+	0.948893i	$0.397795\pi$
$252$		0			0
$253$	−9.85641			−0.619667
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.5263	−	23.4282i	−0.843746	−	1.46141i	−0.886706	−	0.462334i	$-0.847012\pi$
$257$	−13.5263	−	23.4282i	−0.843746	−	1.46141i	0.0429595	−	0.999077i	$-0.486321\pi$
$258$		0			0
$259$	−0.803848	+	1.39230i	−0.0499487	+	0.0865136i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.3923	+	24.9282i	−0.887468	+	1.53714i	−0.0446084	+	0.999005i	$0.514204\pi$
$263$	−14.3923	+	24.9282i	−0.887468	+	1.53714i	−0.842859	+	0.538134i	$0.819129\pi$
$264$		0			0
$265$	20.3923	+	35.3205i	1.25269	+	2.16972i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.5167			−1.25092			−0.625461	−	0.780255i	$-0.715089\pi$
$269$	−20.5167			−1.25092			−0.625461	+	0.780255i	$0.715089\pi$
$270$		0			0
$271$	−16.5359			−1.00448			−0.502242	−	0.864727i	$-0.667491\pi$
$271$	−16.5359			−1.00448			−0.502242	+	0.864727i	$0.667491\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−8.92820	−	15.4641i	−0.538391	−	0.932520i
$276$		0			0
$277$	7.00000	−	12.1244i	0.420589	−	0.728482i	−0.575408	−	0.817867i	$-0.695157\pi$
$277$	7.00000	−	12.1244i	0.420589	−	0.728482i	0.995997	+	0.0893846i	$0.0284900\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.06218	−	3.57180i	0.123019	−	0.213076i	−0.797938	−	0.602740i	$-0.794076\pi$
$281$	2.06218	−	3.57180i	0.123019	−	0.213076i	0.920957	+	0.389664i	$0.127409\pi$
$282$		0			0
$283$	−8.92820	−	15.4641i	−0.530727	−	0.919245i	−0.999357	−	0.0358512i	$-0.988586\pi$
$283$	−8.92820	−	15.4641i	−0.530727	−	0.919245i	0.468631	−	0.883394i	$-0.344748\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	24.0000			1.41668
$288$		0			0
$289$	−11.8564			−0.697436
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.06218	−	5.30385i	−0.178894	−	0.309854i	0.762608	−	0.646861i	$-0.223919\pi$
$293$	−3.06218	−	5.30385i	−0.178894	−	0.309854i	−0.941502	+	0.337007i	$0.890585\pi$
$294$		0			0
$295$	14.9282	−	25.8564i	0.869154	−	1.50542i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.07180	+	10.5167i	−0.351141	+	0.608194i
$300$		0			0
$301$	7.85641	+	13.6077i	0.452836	+	0.784335i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−39.0526			−2.23614
$306$		0			0
$307$	18.9282			1.08029			0.540145	−	0.841572i	$-0.318369\pi$
$307$	18.9282			1.08029			0.540145	+	0.841572i	$0.318369\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	−11.8923	+	20.5981i	−0.672193	+	1.16427i	0.305088	+	0.952324i	$0.401314\pi$
$313$	−11.8923	+	20.5981i	−0.672193	+	1.16427i	−0.977281	+	0.211948i	$0.932019\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.86603	−	6.69615i	0.217138	−	0.376093i	−0.736794	−	0.676117i	$-0.763661\pi$
$317$	3.86603	−	6.69615i	0.217138	−	0.376093i	0.953932	+	0.300024i	$0.0969946\pi$
$318$		0			0
$319$	4.26795	+	7.39230i	0.238959	+	0.413890i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−16.9282			−0.941910
$324$		0			0
$325$	−22.0000			−1.22034
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	10.1244	−	17.5359i	0.556485	−	0.963860i	−0.441301	−	0.897359i	$-0.645483\pi$
$331$	10.1244	−	17.5359i	0.556485	−	0.963860i	0.997786	−	0.0665012i	$-0.0211836\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	−3.92820	−	6.80385i	−0.213983	−	0.370629i	0.738975	−	0.673733i	$-0.235310\pi$
$337$	−3.92820	−	6.80385i	−0.213983	−	0.370629i	−0.952957	+	0.303104i	$0.901977\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	21.8564			1.18359
$342$		0			0
$343$	6.92820			0.374088
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.4641	−	21.5885i	−0.669108	−	1.15893i	−0.978154	−	0.207882i	$-0.933343\pi$
$347$	−12.4641	−	21.5885i	−0.669108	−	1.15893i	0.309046	−	0.951047i	$-0.399990\pi$
$348$		0			0
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	−0.774493	−	0.632583i	$-0.781995\pi$
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	0.935079	+	0.354439i	$0.115328\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.07180	−	1.85641i	0.0570460	−	0.0988065i	−0.836092	−	0.548589i	$-0.815165\pi$
$353$	1.07180	−	1.85641i	0.0570460	−	0.0988065i	0.893138	+	0.449783i	$0.148499\pi$
$354$		0			0
$355$	−3.73205	−	6.46410i	−0.198077	−	0.343079i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.7846			−0.780302			−0.390151	−	0.920751i	$-0.627577\pi$
$359$	−14.7846			−0.780302			−0.390151	+	0.920751i	$0.627577\pi$
$360$		0			0
$361$	36.7128			1.93225
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.86603	+	3.23205i	0.0976722	+	0.169173i
$366$		0			0
$367$	11.4641	−	19.8564i	0.598421	−	1.03650i	−0.394633	−	0.918839i	$-0.629128\pi$
$367$	11.4641	−	19.8564i	0.598421	−	1.03650i	0.993054	−	0.117657i	$-0.0375384\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	18.9282	−	32.7846i	0.982703	−	1.70209i
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.5167			0.541636
$378$		0			0
$379$	24.7846			1.27310			0.636550	−	0.771235i	$-0.280361\pi$
$379$	24.7846			1.27310			0.636550	+	0.771235i	$0.280361\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	0.539076	−	0.842257i	$-0.318774\pi$
$383$	−9.00000	−	15.5885i	−0.459879	−	0.796533i	−0.998954	+	0.0457244i	$0.985440\pi$
$384$		0			0
$385$	−12.9282	+	22.3923i	−0.658882	+	1.14122i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.4641	−	23.3205i	0.682657	−	1.18240i	−0.291510	−	0.956568i	$-0.594158\pi$
$389$	13.4641	−	23.3205i	0.682657	−	1.18240i	0.974167	−	0.225829i	$-0.0725090\pi$
$390$		0			0
$391$	−5.58846	−	9.67949i	−0.282620	−	0.489513i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.00000			0.100631
$396$		0			0
$397$	0.607695			0.0304993			0.0152497	−	0.999884i	$-0.495146\pi$
$397$	0.607695			0.0304993			0.0152497	+	0.999884i	$0.495146\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.59808	−	14.8923i	−0.429367	−	0.743686i	0.567450	−	0.823408i	$-0.307930\pi$
$401$	−8.59808	−	14.8923i	−0.429367	−	0.743686i	−0.996817	+	0.0797218i	$0.974597\pi$
$402$		0			0
$403$	13.4641	−	23.3205i	0.670695	−	1.16168i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.464102	−	0.803848i	0.0230047	−	0.0398452i
$408$		0			0
$409$	−7.96410	−	13.7942i	−0.393799	−	0.682081i	0.599148	−	0.800639i	$-0.295506\pi$
$409$	−7.96410	−	13.7942i	−0.393799	−	0.682081i	−0.992947	+	0.118558i	$0.962173\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−27.7128			−1.36366
$414$		0			0
$415$	10.9282			0.536444
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.9282	−	22.3923i	−0.631584	−	1.09394i	−0.987228	−	0.159314i	$-0.949072\pi$
$419$	−12.9282	−	22.3923i	−0.631584	−	1.09394i	0.355644	−	0.934622i	$-0.384262\pi$
$420$		0			0
$421$	−1.69615	+	2.93782i	−0.0826654	+	0.143181i	−0.904394	−	0.426698i	$-0.859677\pi$
$421$	−1.69615	+	2.93782i	−0.0826654	+	0.143181i	0.821729	+	0.569879i	$0.193010\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.1244	−	17.5359i	0.491103	−	0.850616i
$426$		0			0
$427$	18.1244	+	31.3923i	0.877099	+	1.51918i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−26.9282			−1.29709			−0.648543	−	0.761178i	$-0.724621\pi$
$431$	−26.9282			−1.29709			−0.648543	+	0.761178i	$0.724621\pi$
$432$		0			0
$433$	27.7846			1.33524			0.667622	−	0.744501i	$-0.267312\pi$
$433$	27.7846			1.33524			0.667622	+	0.744501i	$0.267312\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	18.3923	+	31.8564i	0.879823	+	1.52390i
$438$		0			0
$439$	−6.00000	+	10.3923i	−0.286364	+	0.495998i	−0.972939	−	0.231062i	$-0.925780\pi$
$439$	−6.00000	+	10.3923i	−0.286364	+	0.495998i	0.686575	+	0.727059i	$0.259113\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.535898	−	0.928203i	0.0254613	−	0.0441003i	−0.853014	−	0.521888i	$-0.825228\pi$
$443$	0.535898	−	0.928203i	0.0254613	−	0.0441003i	0.878475	+	0.477788i	$0.158561\pi$
$444$		0			0
$445$	9.69615	+	16.7942i	0.459642	+	0.796123i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.7846			−1.35843			−0.679215	−	0.733939i	$-0.737680\pi$
$449$	−28.7846			−1.35843			−0.679215	+	0.733939i	$0.737680\pi$
$450$		0			0
$451$	−13.8564			−0.652473
$452$		0			0
$453$		0			0
$454$		0			0
$455$	15.9282	+	27.5885i	0.746726	+	1.29337i
$456$		0			0
$457$	18.9641	−	32.8468i	0.887103	−	1.53651i	0.0438194	−	0.999039i	$-0.486047\pi$
$457$	18.9641	−	32.8468i	0.887103	−	1.53651i	0.843284	−	0.537468i	$-0.180619\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−12.3923	+	21.4641i	−0.577167	+	0.999683i	0.418635	+	0.908154i	$0.362509\pi$
$461$	−12.3923	+	21.4641i	−0.577167	+	0.999683i	−0.995802	+	0.0915284i	$0.970825\pi$
$462$		0			0
$463$	−20.0000	−	34.6410i	−0.929479	−	1.60990i	−0.784195	−	0.620515i	$-0.786924\pi$
$463$	−20.0000	−	34.6410i	−0.929479	−	1.60990i	−0.145284	−	0.989390i	$-0.546410\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	39.7128			1.83769			0.918845	−	0.394619i	$-0.129123\pi$
$467$	39.7128			1.83769			0.918845	+	0.394619i	$0.129123\pi$
$468$		0			0
$469$	−1.85641			−0.0857209
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.53590	−	7.85641i	−0.208561	−	0.361238i
$474$		0			0
$475$	−33.3205	+	57.7128i	−1.52885	+	2.64805i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.92820	+	10.2679i	−0.270867	+	0.469155i	−0.969084	−	0.246731i	$-0.920644\pi$
$479$	−5.92820	+	10.2679i	−0.270867	+	0.469155i	0.698217	+	0.715886i	$0.253977\pi$
$480$		0			0
$481$	−0.571797	−	0.990381i	−0.0260717	−	0.0451575i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	44.2487			2.00923
$486$		0			0
$487$	−34.9282			−1.58275			−0.791374	−	0.611332i	$-0.790634\pi$
$487$	−34.9282			−1.58275			−0.791374	+	0.611332i	$0.790634\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	21.9282	+	37.9808i	0.989606	+	1.71405i	0.619342	+	0.785121i	$0.287399\pi$
$491$	21.9282	+	37.9808i	0.989606	+	1.71405i	0.370264	+	0.928927i	$0.379267\pi$
$492$		0			0
$493$	−4.83975	+	8.38269i	−0.217971	+	0.377537i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.46410	+	6.00000i	−0.155386	+	0.269137i
$498$		0			0
$499$	12.1244	+	21.0000i	0.542761	+	0.940089i	0.998744	+	0.0501009i	$0.0159543\pi$
$499$	12.1244	+	21.0000i	0.542761	+	0.940089i	−0.455983	+	0.889988i	$0.650712\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	25.8564			1.15288			0.576440	−	0.817139i	$-0.304441\pi$
$503$	25.8564			1.15288			0.576440	+	0.817139i	$0.304441\pi$
$504$		0			0
$505$	−44.7846			−1.99289
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.3923	−	28.3923i	−0.726576	−	1.25847i	−0.958322	−	0.285690i	$-0.907777\pi$
$509$	−16.3923	−	28.3923i	−0.726576	−	1.25847i	0.231746	−	0.972776i	$-0.425556\pi$
$510$		0			0
$511$	1.73205	−	3.00000i	0.0766214	−	0.132712i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−20.3923	+	35.3205i	−0.898592	+	1.55641i
$516$		0			0
$517$	−6.92820	−	12.0000i	−0.304702	−	0.527759i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	28.7846			1.26108			0.630538	−	0.776158i	$-0.282834\pi$
$521$	28.7846			1.26108			0.630538	+	0.776158i	$0.282834\pi$
$522$		0			0
$523$	35.4641			1.55074			0.775368	−	0.631509i	$-0.217564\pi$
$523$	35.4641			1.55074			0.775368	+	0.631509i	$0.217564\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.3923	+	21.4641i	0.539817	+	0.934991i
$528$		0			0
$529$	−0.643594	+	1.11474i	−0.0279823	+	0.0484668i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.53590	+	14.7846i	−0.369731	+	0.640393i
$534$		0			0
$535$	−9.46410	−	16.3923i	−0.409169	−	0.708701i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.0000			0.430730
$540$		0			0
$541$	7.39230			0.317820			0.158910	−	0.987293i	$-0.449202\pi$
$541$	7.39230			0.317820			0.158910	+	0.987293i	$0.449202\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.33013	+	14.4282i	0.356823	+	0.618036i
$546$		0			0
$547$	−8.92820	+	15.4641i	−0.381742	+	0.661197i	−0.991311	−	0.131536i	$-0.958009\pi$
$547$	−8.92820	+	15.4641i	−0.381742	+	0.661197i	0.609569	+	0.792733i	$0.291343\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.9282	−	27.5885i	0.678564	−	1.17531i
$552$		0			0
$553$	−0.928203	−	1.60770i	−0.0394712	−	0.0683662i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.5885			0.575761			0.287881	−	0.957666i	$-0.407049\pi$
$557$	13.5885			0.575761			0.287881	+	0.957666i	$0.407049\pi$
$558$		0			0
$559$	−11.1769			−0.472733
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.535898	−	0.928203i	−0.0225854	−	0.0391191i	0.854512	−	0.519432i	$-0.173856\pi$
$563$	−0.535898	−	0.928203i	−0.0225854	−	0.0391191i	−0.877097	+	0.480313i	$0.840523\pi$
$564$		0			0
$565$	3.23205	−	5.59808i	0.135973	−	0.235513i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−21.7942	+	37.7487i	−0.913662	+	1.58251i	−0.104813	+	0.994492i	$0.533424\pi$
$569$	−21.7942	+	37.7487i	−0.913662	+	1.58251i	−0.808849	+	0.588016i	$0.799909\pi$
$570$		0			0
$571$	−6.92820	−	12.0000i	−0.289936	−	0.502184i	0.683858	−	0.729615i	$-0.260301\pi$
$571$	−6.92820	−	12.0000i	−0.289936	−	0.502184i	−0.973794	+	0.227431i	$0.926967\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−44.0000			−1.83493
$576$		0			0
$577$	−2.85641			−0.118914			−0.0594569	−	0.998231i	$-0.518937\pi$
$577$	−2.85641			−0.118914			−0.0594569	+	0.998231i	$0.518937\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.07180	−	8.78461i	−0.210414	−	0.364447i
$582$		0			0
$583$	−10.9282	+	18.9282i	−0.452600	+	0.783926i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.0000	+	22.5167i	−0.536567	+	0.929362i	0.462518	+	0.886610i	$0.346946\pi$
$587$	−13.0000	+	22.5167i	−0.536567	+	0.929362i	−0.999086	+	0.0427523i	$0.986387\pi$
$588$		0			0
$589$	−40.7846	−	70.6410i	−1.68050	−	2.91071i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.411543			0.0169000			0.00845002	−	0.999964i	$-0.497310\pi$
$593$	0.411543			0.0169000			0.00845002	+	0.999964i	$0.497310\pi$
$594$		0			0
$595$	−29.3205			−1.20202
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.46410	+	16.3923i	0.386693	+	0.669771i	0.992002	−	0.126219i	$-0.0402841\pi$
$599$	9.46410	+	16.3923i	0.386693	+	0.669771i	−0.605310	+	0.795990i	$0.706951\pi$
$600$		0			0
$601$	3.42820	−	5.93782i	0.139839	−	0.242209i	−0.787596	−	0.616192i	$-0.788675\pi$
$601$	3.42820	−	5.93782i	0.139839	−	0.242209i	0.927436	+	0.373983i	$0.122008\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.0622	+	22.6244i	−0.531053	+	0.919811i
$606$		0			0
$607$	19.5885	+	33.9282i	0.795071	+	1.37710i	0.922794	+	0.385293i	$0.125900\pi$
$607$	19.5885	+	33.9282i	0.795071	+	1.37710i	−0.127723	+	0.991810i	$0.540767\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−17.0718			−0.690651
$612$		0			0
$613$	3.85641			0.155759			0.0778794	−	0.996963i	$-0.475185\pi$
$613$	3.85641			0.155759			0.0778794	+	0.996963i	$0.475185\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.7224	+	25.5000i	0.592703	+	1.02659i	0.993867	+	0.110585i	$0.0352725\pi$
$617$	14.7224	+	25.5000i	0.592703	+	1.02659i	−0.401164	+	0.916006i	$0.631394\pi$
$618$		0			0
$619$	−2.39230	+	4.14359i	−0.0961549	+	0.166545i	−0.910090	−	0.414411i	$-0.863988\pi$
$619$	−2.39230	+	4.14359i	−0.0961549	+	0.166545i	0.813935	+	0.580956i	$0.197321\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.00000	−	15.5885i	0.360577	−	0.624538i
$624$		0			0
$625$	−5.03590	−	8.72243i	−0.201436	−	0.348897i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.05256			0.0419683
$630$		0			0
$631$	−12.7846			−0.508947			−0.254474	−	0.967080i	$-0.581902\pi$
$631$	−12.7846			−0.508947			−0.254474	+	0.967080i	$0.581902\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$		0			0
$637$	6.16025	−	10.6699i	0.244078	−	0.422756i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.9904	+	25.9641i	−0.592084	+	1.02552i	0.401867	+	0.915698i	$0.368361\pi$
$641$	−14.9904	+	25.9641i	−0.592084	+	1.02552i	−0.993951	+	0.109822i	$0.964972\pi$
$642$		0			0
$643$	16.3923	+	28.3923i	0.646449	+	1.11968i	0.983965	+	0.178363i	$0.0570802\pi$
$643$	16.3923	+	28.3923i	0.646449	+	1.11968i	−0.337515	+	0.941320i	$0.609586\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	37.7128			1.48264			0.741322	−	0.671150i	$-0.234199\pi$
$647$	37.7128			1.48264			0.741322	+	0.671150i	$0.234199\pi$
$648$		0			0
$649$	16.0000			0.628055
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.39230	+	7.60770i	0.171884	+	0.297712i	0.939079	−	0.343703i	$-0.111681\pi$
$653$	4.39230	+	7.60770i	0.171884	+	0.297712i	−0.767194	+	0.641415i	$0.778348\pi$
$654$		0			0
$655$	−13.1962	+	22.8564i	−0.515616	+	0.893074i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.39230	+	2.41154i	−0.0542365	+	0.0939404i	−0.891869	−	0.452294i	$-0.850606\pi$
$659$	−1.39230	+	2.41154i	−0.0542365	+	0.0939404i	0.837632	+	0.546234i	$0.183939\pi$
$660$		0			0
$661$	15.1603	+	26.2583i	0.589666	+	1.02133i	0.994276	+	0.106842i	$0.0340738\pi$
$661$	15.1603	+	26.2583i	0.589666	+	1.02133i	−0.404611	+	0.914489i	$0.632593\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	96.4974			3.74201
$666$		0			0
$667$	21.0333			0.814413
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.4641	−	18.1244i	−0.403962	−	0.699683i
$672$		0			0
$673$	−12.9641	+	22.4545i	−0.499729	+	0.865557i	−1.00000		0.000312442i	$-0.999901\pi$
$673$	−12.9641	+	22.4545i	−0.499729	+	0.865557i	0.500271	+	0.865869i	$0.333234\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	15.3205	−	26.5359i	0.588815	−	1.01986i	−0.405573	−	0.914063i	$-0.632928\pi$
$677$	15.3205	−	26.5359i	0.588815	−	1.01986i	0.994388	−	0.105795i	$-0.0337387\pi$
$678$		0			0
$679$	−20.5359	−	35.5692i	−0.788095	−	1.36502i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.07180			0.0410112			0.0205056	−	0.999790i	$-0.493472\pi$
$683$	1.07180			0.0410112			0.0205056	+	0.999790i	$0.493472\pi$
$684$		0			0
$685$	77.1051			2.94604
$686$		0			0
$687$		0			0
$688$		0			0
$689$	13.4641	+	23.3205i	0.512941	+	0.888441i
$690$		0			0
$691$	−8.80385	+	15.2487i	−0.334914	+	0.580088i	−0.983468	−	0.181080i	$-0.942041\pi$
$691$	−8.80385	+	15.2487i	−0.334914	+	0.580088i	0.648554	+	0.761168i	$0.275374\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.46410	−	16.3923i	0.358994	−	0.621796i
$696$		0			0
$697$	−7.85641	−	13.6077i	−0.297583	−	0.515428i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−35.4449			−1.33873			−0.669367	−	0.742932i	$-0.733435\pi$
$701$	−35.4449			−1.33873			−0.669367	+	0.742932i	$0.733435\pi$
$702$		0			0
$703$	−3.46410			−0.130651
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.7846	+	36.0000i	0.781686	+	1.35392i
$708$		0			0
$709$	−11.1603	+	19.3301i	−0.419132	+	0.725958i	−0.995852	−	0.0909835i	$-0.970999\pi$
$709$	−11.1603	+	19.3301i	−0.419132	+	0.725958i	0.576720	+	0.816942i	$0.304332\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	26.9282	−	46.6410i	1.00847	−	1.74672i
$714$		0			0
$715$	−9.19615	−	15.9282i	−0.343917	−	0.595681i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	8.92820			0.332966			0.166483	−	0.986044i	$-0.446759\pi$
$719$	8.92820			0.332966			0.166483	+	0.986044i	$0.446759\pi$
$720$		0			0
$721$	37.8564			1.40985
$722$		0			0
$723$		0			0
$724$		0			0
$725$	19.0526	+	33.0000i	0.707594	+	1.22559i
$726$		0			0
$727$	−15.5885	+	27.0000i	−0.578144	+	1.00137i	0.417548	+	0.908655i	$0.362889\pi$
$727$	−15.5885	+	27.0000i	−0.578144	+	1.00137i	−0.995692	+	0.0927199i	$0.970444\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.14359	−	8.90897i	0.190243	−	0.329510i
$732$		0			0
$733$	−19.9282	−	34.5167i	−0.736065	−	1.27490i	−0.954255	−	0.298996i	$-0.903348\pi$
$733$	−19.9282	−	34.5167i	−0.736065	−	1.27490i	0.218190	−	0.975906i	$-0.429985\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.07180			0.0394801
$738$		0			0
$739$	28.0000			1.03000			0.514998	−	0.857191i	$-0.327793\pi$
$739$	28.0000			1.03000			0.514998	+	0.857191i	$0.327793\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.4641	+	19.8564i	0.420577	+	0.728461i	0.995996	−	0.0893979i	$-0.0284943\pi$
$743$	11.4641	+	19.8564i	0.420577	+	0.728461i	−0.575419	+	0.817859i	$0.695161\pi$
$744$		0			0
$745$	29.3564	−	50.8468i	1.07554	−	1.86288i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.78461	+	15.2154i	−0.320983	+	0.555958i
$750$		0			0
$751$	−8.66025	−	15.0000i	−0.316017	−	0.547358i	0.663636	−	0.748056i	$-0.269012\pi$
$751$	−8.66025	−	15.0000i	−0.316017	−	0.547358i	−0.979653	+	0.200698i	$0.935679\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.00000			0.145575
$756$		0			0
$757$	−35.8564			−1.30322			−0.651612	−	0.758553i	$-0.725907\pi$
$757$	−35.8564			−1.30322			−0.651612	+	0.758553i	$0.725907\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−24.5981	−	42.6051i	−0.891680	−	1.54443i	−0.837861	−	0.545884i	$-0.816194\pi$
$761$	−24.5981	−	42.6051i	−0.891680	−	1.54443i	−0.0538185	−	0.998551i	$-0.517139\pi$
$762$		0			0
$763$	7.73205	−	13.3923i	0.279919	−	0.484834i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.85641	−	17.0718i	0.355894	−	0.616427i
$768$		0			0
$769$	4.89230	+	8.47372i	0.176421	+	0.305570i	0.940652	−	0.339372i	$-0.110215\pi$
$769$	4.89230	+	8.47372i	0.176421	+	0.305570i	−0.764231	+	0.644942i	$0.776881\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−28.2679			−1.01673			−0.508364	−	0.861142i	$-0.669749\pi$
$773$	−28.2679			−1.01673			−0.508364	+	0.861142i	$0.669749\pi$
$774$		0			0
$775$	97.5692			3.50479
$776$		0			0
$777$		0			0
$778$		0			0
$779$	25.8564	+	44.7846i	0.926402	+	1.60458i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.0622	−	17.4282i	0.359135	−	0.622039i
$786$		0			0
$787$	9.73205	+	16.8564i	0.346910	+	0.600866i	0.985699	−	0.168516i	$-0.0538975\pi$
$787$	9.73205	+	16.8564i	0.346910	+	0.600866i	−0.638789	+	0.769382i	$0.720564\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.00000			−0.213335
$792$		0			0
$793$	−25.7846			−0.915638
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.74167	+	3.01666i	0.0616931	+	0.106856i	0.895222	−	0.445620i	$-0.147017\pi$
$797$	1.74167	+	3.01666i	0.0616931	+	0.106856i	−0.833529	+	0.552475i	$0.813683\pi$
$798$		0			0
$799$	7.85641	−	13.6077i	0.277940	−	0.481406i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$	31.8564	+	55.1769i	1.12279	+	1.94473i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−29.7321			−1.04532			−0.522662	−	0.852540i	$-0.675061\pi$
$809$	−29.7321			−1.04532			−0.522662	+	0.852540i	$0.675061\pi$
$810$		0			0
$811$	−33.5692			−1.17877			−0.589387	−	0.807851i	$-0.700631\pi$
$811$	−33.5692			−1.17877			−0.589387	+	0.807851i	$0.700631\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−16.9282	+	29.3205i	−0.592243	+	1.02579i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.66987	+	8.08846i	−0.162980	+	0.282289i	−0.935936	−	0.352170i	$-0.885444\pi$
$821$	−4.66987	+	8.08846i	−0.162980	+	0.282289i	0.772956	+	0.634459i	$0.218777\pi$
$822$		0			0
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	0.985997	−	0.166762i	$-0.0533313\pi$
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	−0.637419	+	0.770517i	$0.719998\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.8564			0.412288			0.206144	−	0.978522i	$-0.433909\pi$
$827$	11.8564			0.412288			0.206144	+	0.978522i	$0.433909\pi$
$828$		0			0
$829$	23.8564			0.828567			0.414284	−	0.910148i	$-0.364032\pi$
$829$	23.8564			0.828567			0.414284	+	0.910148i	$0.364032\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.66987	+	9.82051i	0.196449	+	0.340260i
$834$		0			0
$835$	33.5885	−	58.1769i	1.16238	−	2.01330i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.5359	+	19.9808i	−0.398263	+	0.689813i	−0.993512	−	0.113729i	$-0.963720\pi$
$839$	−11.5359	+	19.9808i	−0.398263	+	0.689813i	0.595248	+	0.803542i	$0.297054\pi$
$840$		0			0
$841$	5.39230	+	9.33975i	0.185942	+	0.322060i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	25.8564			0.889487
$846$		0			0
$847$	24.2487			0.833196
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.14359	−	1.98076i	−0.0392019	−	0.0678997i
$852$		0			0
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	−0.960621	−	0.277862i	$-0.910374\pi$
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	0.720946	+	0.692992i	$0.243708\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.7942	−	23.8923i	0.471202	−	0.816146i	−0.528255	−	0.849085i	$-0.677154\pi$
$857$	13.7942	−	23.8923i	0.471202	−	0.816146i	0.999457	+	0.0329399i	$0.0104870\pi$
$858$		0			0
$859$	−12.9282	−	22.3923i	−0.441105	−	0.764016i	0.556667	−	0.830736i	$-0.312080\pi$
$859$	−12.9282	−	22.3923i	−0.441105	−	0.764016i	−0.997772	+	0.0667201i	$0.978747\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.9282			1.12089			0.560445	−	0.828192i	$-0.310630\pi$
$863$	32.9282			1.12089			0.560445	+	0.828192i	$0.310630\pi$
$864$		0			0
$865$	−28.8564			−0.981147
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.535898	+	0.928203i	0.0181791	+	0.0314871i
$870$		0			0
$871$	0.660254	−	1.14359i	0.0223719	−	0.0387492i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−25.3923	+	43.9808i	−0.858417	+	1.48682i
$876$		0			0
$877$	−10.1603	−	17.5981i	−0.343087	−	0.594245i	0.641917	−	0.766774i	$-0.278139\pi$
$877$	−10.1603	−	17.5981i	−0.343087	−	0.594245i	−0.985004	+	0.172529i	$0.944806\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−50.6410			−1.70614			−0.853070	−	0.521797i	$-0.825262\pi$
$881$	−50.6410			−1.70614			−0.853070	+	0.521797i	$0.825262\pi$
$882$		0			0
$883$	−37.0718			−1.24757			−0.623783	−	0.781598i	$-0.714405\pi$
$883$	−37.0718			−1.24757			−0.623783	+	0.781598i	$0.714405\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.3205	−	38.6603i	−0.749449	−	1.29808i	−0.948087	−	0.318011i	$-0.896985\pi$
$887$	−22.3205	−	38.6603i	−0.749449	−	1.29808i	0.198638	−	0.980073i	$-0.436348\pi$
$888$		0			0
$889$	−0.928203	+	1.60770i	−0.0311309	+	0.0539204i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−25.8564	+	44.7846i	−0.865252	+	1.49866i
$894$		0			0
$895$	−12.9282	−	22.3923i	−0.432142	−	0.748492i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−46.6410			−1.55556
$900$		0			0
$901$	−24.7846			−0.825695
$902$		0			0
$903$		0			0
$904$		0			0
$905$	14.6603	+	25.3923i	0.487323	+	0.844069i
$906$		0			0
$907$	18.3923	−	31.8564i	0.610706	−	1.05777i	−0.380415	−	0.924816i	$-0.624219\pi$
$907$	18.3923	−	31.8564i	0.610706	−	1.05777i	0.991122	−	0.132959i	$-0.0424478\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.60770	+	4.51666i	−0.0863968	+	0.149644i	−0.905986	−	0.423309i	$-0.860869\pi$
$911$	−2.60770	+	4.51666i	−0.0863968	+	0.149644i	0.819589	+	0.572952i	$0.194202\pi$
$912$		0			0
$913$	2.92820	+	5.07180i	0.0969094	+	0.167852i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.4974			0.808976
$918$		0			0
$919$	27.1769			0.896484			0.448242	−	0.893912i	$-0.352050\pi$
$919$	27.1769			0.896484			0.448242	+	0.893912i	$0.352050\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.46410	−	4.26795i	−0.0811069	−	0.140481i
$924$		0			0
$925$	2.07180	−	3.58846i	0.0681203	−	0.117988i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.7942	+	30.8205i	−0.583810	+	1.01119i	0.411213	+	0.911539i	$0.365105\pi$
$929$	−17.7942	+	30.8205i	−0.583810	+	1.01119i	−0.995023	+	0.0996488i	$0.968228\pi$
$930$		0			0
$931$	−18.6603	−	32.3205i	−0.611565	−	1.05926i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	16.9282			0.553611
$936$		0			0
$937$	32.5692			1.06399			0.531995	−	0.846747i	$-0.321443\pi$
$937$	32.5692			1.06399			0.531995	+	0.846747i	$0.321443\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.06218	+	5.30385i	0.0998241	+	0.172900i	0.911612	−	0.411052i	$-0.134839\pi$
$941$	3.06218	+	5.30385i	0.0998241	+	0.172900i	−0.811788	+	0.583953i	$0.801505\pi$
$942$		0			0
$943$	−17.0718	+	29.5692i	−0.555934	+	0.962906i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.464102	+	0.803848i	−0.0150813	+	0.0261215i	−0.873468	−	0.486882i	$-0.838134\pi$
$947$	−0.464102	+	0.803848i	−0.0150813	+	0.0261215i	0.858386	+	0.513004i	$0.171467\pi$
$948$		0			0
$949$	1.23205	+	2.13397i	0.0399941	+	0.0692717i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	37.9808			1.23032			0.615159	−	0.788403i	$-0.289092\pi$
$953$	37.9808			1.23032			0.615159	+	0.788403i	$0.289092\pi$
$954$		0			0
$955$	−74.1051			−2.39799
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−35.7846	−	61.9808i	−1.15555	−	2.00146i
$960$		0			0
$961$	−44.2128	+	76.5788i	−1.42622	+	2.47029i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	33.4545	−	57.9449i	1.07694	−	1.86531i
$966$		0			0
$967$	12.6603	+	21.9282i	0.407126	+	0.705163i	0.994566	−	0.104104i	$-0.0331975\pi$
$967$	12.6603	+	21.9282i	0.407126	+	0.705163i	−0.587440	+	0.809268i	$0.699864\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.9282			−0.414886			−0.207443	−	0.978247i	$-0.566514\pi$
$971$	−12.9282			−0.414886			−0.207443	+	0.978247i	$0.566514\pi$
$972$		0			0
$973$	−17.5692			−0.563243
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.4641	+	26.7846i	0.494740	+	0.856916i	0.999982	−	0.00606260i	$-0.00192980\pi$
$977$	15.4641	+	26.7846i	0.494740	+	0.856916i	−0.505241	+	0.862978i	$0.668596\pi$
$978$		0			0
$979$	−5.19615	+	9.00000i	−0.166070	+	0.287641i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	4.96410	+	8.59808i	0.158169	+	0.273957i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22.3538			−0.710810
$990$		0			0
$991$	−30.1051			−0.956321			−0.478160	−	0.878273i	$-0.658696\pi$
$991$	−30.1051			−0.956321			−0.478160	+	0.878273i	$0.658696\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.46410	−	12.9282i	−0.236628	−	0.409852i
$996$		0			0
$997$	−7.08846	+	12.2776i	−0.224494	+	0.388834i	−0.956167	−	0.292821i	$-0.905406\pi$
$997$	−7.08846	+	12.2776i	−0.224494	+	0.388834i	0.731674	+	0.681655i	$0.238739\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1296.2.i.t.865.2		4
3.2	odd	2		1296.2.i.r.865.1		4
4.3	odd	2		648.2.i.j.217.2		4
9.2	odd	6		1296.2.a.q.1.2		2
9.4	even	3	inner	1296.2.i.t.433.2		4
9.5	odd	6		1296.2.i.r.433.1		4
9.7	even	3		1296.2.a.m.1.1		2
12.11	even	2		648.2.i.i.217.1		4
36.7	odd	6		648.2.a.e.1.1	✓	2
36.11	even	6		648.2.a.h.1.2	yes	2
36.23	even	6		648.2.i.i.433.1		4
36.31	odd	6		648.2.i.j.433.2		4
72.11	even	6		5184.2.a.bg.1.1		2
72.29	odd	6		5184.2.a.bi.1.1		2
72.43	odd	6		5184.2.a.cb.1.2		2
72.61	even	6		5184.2.a.bz.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
648.2.a.e.1.1	✓	2	36.7	odd	6
648.2.a.h.1.2	yes	2	36.11	even	6
648.2.i.i.217.1		4	12.11	even	2
648.2.i.i.433.1		4	36.23	even	6
648.2.i.j.217.2		4	4.3	odd	2
648.2.i.j.433.2		4	36.31	odd	6
1296.2.a.m.1.1		2	9.7	even	3
1296.2.a.q.1.2		2	9.2	odd	6
1296.2.i.r.433.1		4	9.5	odd	6
1296.2.i.r.865.1		4	3.2	odd	2
1296.2.i.t.433.2		4	9.4	even	3	inner
1296.2.i.t.865.2		4	1.1	even	1	trivial
5184.2.a.bg.1.1		2	72.11	even	6
5184.2.a.bi.1.1		2	72.29	odd	6
5184.2.a.bz.1.2		2	72.61	even	6
5184.2.a.cb.1.2		2	72.43	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1296 = 2^{4} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1296.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.86603 + 3.23205i) q^{5} +(1.73205 - 3.00000i) q^{7} +O(q^{10})\)	\(q+(1.86603 + 3.23205i) q^{5} +(1.73205 - 3.00000i) q^{7} +(-1.00000 + 1.73205i) q^{11} +(1.23205 + 2.13397i) q^{13} -2.26795 q^{17} +7.46410 q^{19} +(2.46410 + 4.26795i) q^{23} +(-4.46410 + 7.73205i) q^{25} +(2.13397 - 3.69615i) q^{29} +(-5.46410 - 9.46410i) q^{31} +12.9282 q^{35} -0.464102 q^{37} +(3.46410 + 6.00000i) q^{41} +(-2.26795 + 3.92820i) q^{43} +(-3.46410 + 6.00000i) q^{47} +(-2.50000 - 4.33013i) q^{49} +10.9282 q^{53} -7.46410 q^{55} +(-4.00000 - 6.92820i) q^{59} +(-5.23205 + 9.06218i) q^{61} +(-4.59808 + 7.96410i) q^{65} +(-0.267949 - 0.464102i) q^{67} -2.00000 q^{71} +1.00000 q^{73} +(3.46410 + 6.00000i) q^{77} +(0.267949 - 0.464102i) q^{79} +(1.46410 - 2.53590i) q^{83} +(-4.23205 - 7.33013i) q^{85} +5.19615 q^{89} +8.53590 q^{91} +(13.9282 + 24.1244i) q^{95} +(5.92820 - 10.2679i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5}+O(q^{10}) \) 4 * q + 4 * q^5	\( 4 q + 4 q^{5} - 4 q^{11} - 2 q^{13} - 16 q^{17} + 16 q^{19} - 4 q^{23} - 4 q^{25} + 12 q^{29} - 8 q^{31} + 24 q^{35} + 12 q^{37} - 16 q^{43} - 10 q^{49} + 16 q^{53} - 16 q^{55} - 16 q^{59} - 14 q^{61} - 8 q^{65} - 8 q^{67} - 8 q^{71} + 4 q^{73} + 8 q^{79} - 8 q^{83} - 10 q^{85} + 48 q^{91} + 28 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 - 4 * q^11 - 2 * q^13 - 16 * q^17 + 16 * q^19 - 4 * q^23 - 4 * q^25 + 12 * q^29 - 8 * q^31 + 24 * q^35 + 12 * q^37 - 16 * q^43 - 10 * q^49 + 16 * q^53 - 16 * q^55 - 16 * q^59 - 14 * q^61 - 8 * q^65 - 8 * q^67 - 8 * q^71 + 4 * q^73 + 8 * q^79 - 8 * q^83 - 10 * q^85 + 48 * q^91 + 28 * q^95 - 4 * q^97

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